Answer:
We can start by simplifying the numerator of the expression:
csc^2x - 1 = (1/sin^2x) - 1 = (1 - sin^2x) / sin^2x = cos^2x / sin^2x = cos^2x csc^2x
Now we can substitute this into the original expression:
csc^2x-1/1+sin x = (cos^2x csc^2x) / (1 + sin x)
We can then simplify this further by using the identity 1 + sin x = (sin^2x + cos^2x) / sin x:
(cos^2x csc^2x) / (1 + sin x) = (cos^2x csc^2x) / [(sin^2x + cos^2x) / sin x]
= cos^2x csc^2x sin x / (sin^2x + cos^2x)
= cos^2x csc^2x sin x / 1
= cos^2x csc^2x sin x
This expression can be simplified using the identity cos^2x = 1 - sin^2x:
cos^2x csc^2x sin x = (1 - sin^2x) csc^2x sin x = (1/sin^2x - 1) sin x = csc^2x - sin x
Therefore, the simplified expression is csc^2x - sin x. Answer: none of the given options.
(please could you kindly mark my answer as brainliest)
18. En una tienda tienen la siguiente promoción por 1 día:
Gabriel necesita comprar un pantalón y una polera, pero al revisar estos en la tienda también miró calcetines y zapatillas. Escogió los siguientes productos:
Él piensa que si compra más productos aparte de la polera y el pantalón, podría pagar menos que si lleva solo la polera y el pantalón que necesita
According to the information, Gabriel should buy only the products he needs to spend less money.
How to calculate the option in which Gabriel would pay less?To calculate the option in which Gabriel would pay less, we must take into account the options that he has, first of all he has the option of buying only what he needs (pants and shirt). Second, he has the option to buy all the products to get a bigger discount.
If he buys only the pants and the shirt, he will have a 20% discount:
$10,000 + $20,000 = $30,000$30,000 / 100 = $300$300 * 20% = $6,000$30,000 - $6,000 = $24,000If you buy all four products you will have a 40% discount:
$10,000 + $20,000 + $30,000 + $1,000 = $61,000$61,000 / 100 = $610$610 * 40% = $24,400$61,000 - $24,400 = $36,600Based on the information, we can infer that if Gabriel buys all four products, he will get a greater discount of $24,400. However, if you do not want to spend so much money, it is better to only buy the two products you need because you will spend less money.
Note: This question is incomplete. Here is the complete information:
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Here is the question in English:
18. In a store they have the following promotion for 1 day:
Gabriel needs to buy pants and a shirt, but when checking these in the store he also looked at socks and sneakers. He chose the following products:
He thinks that if he buys more products besides the shirt and pants, he could pay less than if he only takes the shirt and pants he needs.
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Cara's new car holds 13.5 gallons of gas. If gas costs $2.98 per gallon, how much would it cost her to fill the gas tank from empty?
Thus, the total cost of gas for fill the tank of car tank is $40.23.
Explain about unitary method?Finding the sum of the values of one unit and then multiplying its amount by the sum of the values of one unit to get the value of even more or fewer units is the unitary method's formula. In this illustration, the "unit" represents the quantity of books, and the "value" is their purchase price.
When we visit the market to purchase any item, we inquire about the item's pricing from the shopkeeper. The term for this is unit price.
For the stated question:
Capacity of car = 13.5 gallons of gas.
Gas cost = $2.98 per gallon
So, cost to fill the tank:
Total cost = gas costs per gallon * Capacity of car
Total cost = $2.98 * 13.5
Total cost = $40.23
Thus, the total cost of gas for fill the tank of car tank is $40.23.
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Given that a=14 and b=25, work out the height of the triangle
The height of the triangle is 1.12 units (rounded to two decimal places).
The height of a triangle is the perpendicular distance from the base of the triangle to the opposite vertex. In other words, it is the length of the line segment that is perpendicular to the base and passes through the opposite vertex.
We can use the formula for the area of a triangle:
Area = (1/2) * base * height
And since we know the values of the base (b) and the area (a), we can rearrange the formula to solve for the height (h):
h = (2a) / b
Plugging in the values of a and b:
h = (2 * 14) / 25
h = 28 / 25
Therefore, the height of the triangle is 1.12 units (rounded to two decimal places).
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Use Pythagoras' theorem to work out the length of AD in this triangular prism. Give your answer in centimetres (cm) to 1 d. P
The length of AD in the triangular prism is 9.8 cm.
The length of AD in the triangular prism can be found using Pythagoras' theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The base of the prism is a right triangle, so:
AD² = AE² + ED²
AD² = 4² + 9²
AD² = √97
AD = √97
AD = 9.8 cm (rounded to 1 decimal)
Therefore, the length of AD in the triangular prism is 9.8 cm.
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Complete Question:
Use Pythagoras' theorem to work out the length of AD in this triangular prism. Give your answer in centimeters (cm) to 1 decimal point.
PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited and depends on a single gene that codes for a taste receptor on the tongue. Interestingly, although the PTC molecule is not found in nature, the ability to taste it correlates strongly with the ability to taste other naturally occurring bitter substances, many of which are toxins. About 75 % of Italians can taste PTC. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC. (a) Starting with the 75 % estimate for Italians, how large a sample must you collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence? (Enter your answer as a whole number.) n = (b) Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC. (Enter your answer as a whole number.) n =
(a) Starting with the 75% estimate for Italians, the sample you must collect in order to estimate the proportion of PTC tasters within ± 0.1 with 90 % confidence is n = 51.
(b) The sample size required if you made no assumptions about the value of the proportion who could taste PTC is n = 68.
(a) To estimate the sample size needed to find the proportion of PTC tasters within ± 0.1 with 90% confidence, we will use the formula for sample size estimation in proportion problems:
n = (Z² * p * (1-p)) / E²
Where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.645 for 90% confidence), p is the proportion of PTC tasters (0.75), and E is the margin of error (0.1).
n = (1.645² * 0.75 * (1-0.75)) / 0.1²
n = (2.706 * 0.75 * 0.25) / 0.01
n ≈ 50.74
Since we need a whole number, we round up to the nearest whole number:
n = 51
(b) If no assumptions were made about the proportion of PTC tasters, we would use the worst-case scenario, which is p = 0.5 (maximum variance):
n = (1.645² * 0.5 * (1-0.5)) / 0.1²
n = (2.706 * 0.5 * 0.5) / 0.01
n ≈ 67.65
Again, rounding up to the nearest whole number:
n = 68
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Find a tangent vector of unit length at the point with the given value of the parameter t.r(t) = 2 sin(t)i + 3cos(t)jt= pi/6Please express answer in terms of i + j
A tangent vector of unit length at the point with the given value of the parameter t. r(t) = 2 sin(t)i + 3cos(t)j , t= π/6 is r'(t) = √3 i +3/2 j.
Differentiation:
Differentiation is the rate of change of one quantity relative to another. Velocity is calculated as the rate of change of distance over time. The speed at each instant is different from the calculated average. Speed, like grade, is nothing more than the instantaneous rate of change in distance over a period of time.
The ratio of a small change in one quantity to a small change in another quantity as a function of the first quantity is called differentiation.
An important concept in calculus focuses on the differentiation of functions. The maximum or minimum of a function, the speed and acceleration of a moving object, and the tangent to a curve are all determined by differentiation. If y = f(x) is differentiable, then the differential is expressed by f'(x) or dy/dx.
According to the Question:
Given that:
r(t) = 2sin(t)i + 3 cos(t)j,
and, t =π/6
Now,
Differentiating with respect to t, we get:
r'(t) = [tex]2\frac{d}{dt}sin(t) + 3 \frac{d}{dt} cos(t)[/tex]
⇒ r'(t) = 2cos(t) + 3 sin(t)
Putting t = π/6, we get:
r'(t) = 2cos(π/6) + 3 sin(π/6)
⇒ r'(t) = 2×√3/2 + 3× 1/2
⇒ r'(t) = √3 + 3/2
Writing the equation in the vector form:
r'(t) = √3 i +3/2 j
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The equation y=ax describes the graph of a line. If the value is negative, The Line: A. Is vertical.
B.is horizontal.
C.goes up and to the right.
D.goes down and to the right.
Graph the line with slope 3 passing through the point (1,-5),
Can somebody help me
Answer:
Step-by-step explanation:
To graph the line with slope 3 passing through the point (1,-5), we can use the point-slope form of the equation of a line, which is:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line.
Substituting the given values, we get:
y - (-5) = 3(x - 1)
Simplifying the equation, we get:
y + 5 = 3x - 3
Subtracting 5 from both sides, we get:
y = 3x - 8
Now we have the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Comparing this equation to the one we just found, we can see that the slope is 3 and the y-intercept is -8.
To graph the line, we can plot the y-intercept at (0,-8) and then use the slope to find other points on the line. Since the slope is 3, we can go up 3 units and to the right 1 unit to find another point on the line. We can repeat this process to find more points on the line, and then connect them to graph the line.
triangle ABD is right angled at B. On AD, there is a point C for which AC=CD and AB=BC. find angle DAB
The measure of the angle DAB for the right angled triangle ABD is found as 45°.
Explain about the angle sum property of the right angled triangle?A right-angled triangle has two acute angles that add up to 90°. The smallest angle is the one that is opposite the smallest side, and the greatest angle is the one that is against the largest side.
In a triangle, the two angles that face the two equivalent sides are also equal. There can only be one right angle and one obtuse angle in a triangle.
For the question-
Triangle ABC is right angled at B.
D point makes: AC = CD
And , AB = BC
Since ∠ABD = 90, given C is mid point.
Then, It is altitude on AD and it bisects the angle ABD into 2 equal halves as: ∠ABC = ∠CBD = 45.
Now, For triangle ABC
∠ABC = 45
∠BCA = 90
Then,
∠BAC + ∠ABC + ∠BCA = 180
∠BAC + 45 + 90 = 180
∠BAC = 180 - 135
∠BAC = 45°
Thus, the measure of the angle DAB for the right angled triangle ABD is found as 45°.
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The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 7 cm and the width is 5 cm, how fast is the area of the rectangle increasing (in cm²/s)?
Answer:
Step-by-step explanation: In the problem, they tell us that
dL / dt = 7 cm/s (the rate at which the length is changing) and
dw / dt = 8 cm/s (the rate at which the width is changing)
Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm
The equation for the area of a rectangle is:
A = L·w, so will need the product rule when taking the derivative.
dA/dt = L (dw/dt) + w (dL/dt)
Now just plug in all of the given numbers:
dA/dt = (7)(7) + (5)(8) = 49+40 = 89 cm²/s
Find a basis for the space of 2x2 lower triangular matrices:
A basis for the space of 2x2 lower triangular matrices is [tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex].
Lower triangular matrices resemble the following:
[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right][/tex]
We can write it like this:
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right][/tex]
This demonstrates the set's
[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]
covers the set of lower triangular matrices with dimensions 2x2. Moreover, these are linearly independent, so attempting to
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
leads to
[tex]\left[\begin{array}{ccc}a&0\\b&c\end{array}\right] =\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
which results in a = b = c = 0 right away. As there is no other way to
[tex]a\left[\begin{array}{ccc}1&0\\0&0\end{array}\right]+b\left[\begin{array}{ccc}0&0\\1&0\end{array}\right]+c\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]=\left[\begin{array}{ccc}0&0\\0&0\end{array}\right][/tex]
, these matrices are linearly independent if a = b = c = 0.
Since
[tex]\left(\left[\begin{array}{ccc}1&0\\0&0\end{array}\right],\left[\begin{array}{ccc}0&0\\1&0\end{array}\right],\left[\begin{array}{ccc}0&0\\0&1\end{array}\right]\right)[/tex]
they serve as a foundation by spanning the collection of 2x2 lower triangular matrices and being linearly independent.
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As a town gets smaller, the population of its high school decreases by 7% each year. The senior class has 320 students now. In how many years will it have about 100 students? Write
an equation. Then solve the equation without graphing.
Write an equation to represent this situation. Let n be the number of years before the class will have 100 students.
(Type an equation using n as the vanable. Use integers or decimals for any numbers in the equation)
Help again please
Therefore, in about 15 years and 2 months, the senior class will have about 100 students.
What is equation?An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.
Given by the question.
Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).
Then, we can write the following equation to represent the situation:
P[tex](1-r)^{n}[/tex] = 100
We know that the current population of the senior class is 320, so we can substitute these values into the equation:
320[tex](1-0.07)^{n}[/tex] = 100
Simplifying the equation, we get:
[tex]0.93^{n}[/tex] = 0.3125
Taking the natural logarithm of both sides, we get:
n ln (0.93) = ln (0.3125)
Dividing both sides by ln (0.93), we get:
n = ln (0.3125) / ln (0.93)
Using a calculator, we find that n is approximately equal to 15.21 years.
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1. The line segment AB has endpoints A(-5, 3) and B(-1,-5). Find the point that partitions the line segment in
a ratio of 1:3
Answer:
To find the point that partitions the line segment AB in a ratio of 1:3, we can use the following formula:
P = (3B + 1A) / 4
where P is the point that partitions the line segment in a ratio of 1:3, A and B are the endpoints of the line segment, and the coefficients 3 and 1 represent the ratio of the segment we are dividing.
Substituting the values, we get:
P = (3*(-1, -5) + 1*(-5, 3)) / 4
P = (-3, -7)
Therefore, the point that partitions the line segment AB in a ratio of 1:3 is (-3, -7).
Step-by-step explanation:
The interest rate of an auto
loan is 4%. Express this
number as a decimal.
Answer: 0.04
Step-by-step explanation:
In order to get 4% as a decimal, you must divide 4 by 100.
4/100 = 0.04
Thus, the answer to your question is 0.04
- La decisión más difícil que tuve que tomar durante el proceso fue……………………………………………………… Fue difícil porque……………………………………………………………………………………………………………………………. 2. - Si pudiera mejorar algo de mi emprendimiento, mejoraría…………………………………………………………………… 3. - Lo aprendido en esta experiencia lo podré aplicar también en……………………………………………………………
1. The most difficult decision I had to make during the process was whether or not to pursue a higher degree. It was difficult because I had to weigh the financial and time commitment.
2. If I could improve something about my business, it would improve the customer service and communication.
3. What I learned in this experience I can also apply in many other areas of my life such as problem solving, communication, and time management.
1. Throughout the process, choosing whether or not to go for a graduate degree was the hardest choice I had to make. It was challenging since I had to compare the costs and time required to finish the degree against any potential advantages it might have for my job. Ultimately, I decided to pursue a higher degree since I felt that the benefits of doing so would outweigh the costs.
2. I would invest in better tools for customer support, implement a customer feedback system, and create more opportunities for customers to share their feedback and ideas. I would also invest in better training for customer service staff to ensure they are equipped with the necessary skills to handle customer inquiries and complaints effectively.
3. These skills can be used in my work life, personal relationships, and even my studies. By learning how to better manage my time and communicate effectively, I can become more productive and efficient in any task I take on. Additionally, problem solving is a skill that is applicable to many aspects of life, such as finding creative solutions to difficult issues or troubleshooting technical problems.
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The complete question is:
1. The most difficult decision I had to make during the process was …………… It was difficult because ……………. .
2. If I could improve something about my business, it would improve …… .
3. What I learned in this experience I can also apply in …………….
5+T(6-3); T=4 what’s the answer in a hurry
Answer:
17
Step-by-step explanation:
5+T(6-3); T=4
Use order of operations. Parenthesis, multiplying, then add last.
= 5 + 4(6 -3)
= 5 + 4(3)
= 5 + 12
= 17
mrs bosoga recieved a share of 15 boxes of nestle cremora from a stokvel during december 2022
The journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga would be as follows:
The Journal EntryDate Account Debit Credit
Dec 2022 Nestle Cremora ZAR 3,750
Dec 2022 Mrs. Bosoga ZAR 3,750
The Nestle Cremora account is debited with ZAR 3,750, representing the cost of the 15 boxes of Nestle Cremora (15 boxes x ZAR 250 per box). The Mrs. Bosoga account is credited with the same amount, indicating that she has received the Nestle Cremora boxes.
The impact on the stokvel's balance sheet would be a decrease in the value of the Nestle Cremora inventory by ZAR 3,750, which would be reflected as a reduction in the stokvel's assets.
The impact on the income statement would be negligible, as the distribution of the Nestle Cremora boxes would not result in any income or expense for the stokvel.
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Mrs. Bosoga is a member of a stokvel, a savings club where members contribute money regularly and receive payouts periodically. During December 2022, Mrs. Bosoga received a share of 15 boxes of Nestle Cremora from the stokvel. The market value of each box of Nestle Cremora at the time was ZAR 250. The stokvel keeps track of its transactions using a ledger. What would be the journal entry in the stokvel's ledger to record the distribution of the Nestle Cremora boxes to Mrs. Bosoga? Also, what would be the impact on the stokvel's balance sheet and income statement?
In this problem you will use variation of parameters to solve the nonhomogeneous equation y" – 4y' + 4y = -6e2t A. Write the characteristic equation for the associated homogeneous equation. (User for your variable.) B. Write the fundamental solutions for the associated homogeneous equation and their Wronskian. y2 = 41 = W(91, y2) = C. Compute the following integrals. ✓ W dt = 929 dt = и D. Write the general solution. (Use c1 and c2 for cy and c2). y= (Note: Your general solution will only be correct if it is a general solution to the differential equation.)
A. The characteristic equation for the associated homogeneous equation is:
r² - 4r + 4 = 0
B. The characteristic equation has a repeated root of 2, so the fundamental solutions for the associated homogeneous equation are:
[tex]y1(t) = e^(2t)[/tex]
[tex]y2(t) = te^(2t)[/tex]
The Wronskian of these solutions is:
[tex]W(y1, y2) = det([y1 y2; y1' y2']) = det([e^(2t) te^(2t); 2e^(2t) (2t+1)e^(2t)]) = 4e^(4t)[/tex]
So,[tex]W(y1, y2) = 4e^(4t)[/tex]
C. We need to compute the following integrals:
[tex]W(t)dt = ∫(2e^(2t))(te^(2t))dt = ∫(2t)e^(4t)dt = (1/4)te^(4t) - (1/8)e^(4t) + C1[/tex]
[tex]W(dt) = ∫(4e^(4t))dt = (1/4)e^(4t) + C2[/tex]
D. The general solution is:
[tex]y(t) = c1 y1(t) + c2 y2(t) + yp(t)[/tex]
To find a particular solution, we assume yp(t) takes the form:
[tex]yp(t) = A e^(2t)[/tex]
where A is a constant to be determined. We substitute this into the nonhomogeneous equation and solve for A:
[tex]y'' - 4y' + 4y = -6e^(2t)[/tex]
[tex](4A - 4A) e^(2t) = -6e^(2t)[/tex]
[tex]0 = -6e^(2t)[/tex]
This equation has no solution, so we need to modify our assumption for yp(t) by multiplying by t:
[tex]yp(t) = A t e^(2t)[/tex]
We substitute this into the nonhomogeneous equation and solve for A:
[tex]y'' - 4y' + 4y = -6e^(2t)[/tex]
[tex](8A - 8A + 4A) te^(2t) = -6e^(2t)[/tex]
[tex]4A = -6[/tex]
[tex]A = \frac{-3}{2}[/tex]
So, a particular solution is:
[tex]yp(t) = (-3/2) t e^(2t)[/tex]
Therefore, the general solution to the nonhomogeneous equation is:
[tex]y(t) = c1 e^(2t) + c2 t e^(2t) - (3/2) t e^(2t)[/tex]
or
[tex]y(t) = (c1 - (3/2) t) e^(2t) + c2 t e^(2t)[/tex]
where c1 and c2 are constants determined by initial conditions.
A non-homogeneous equation is a type of mathematical equation that involves both homogeneous and nonhomogeneous terms. In general, a homogeneous equation is one in which all the terms have the same degree, whereas a nonhomogeneous equation contains terms of different degrees.
In the context of linear algebra, a nonhomogeneous equation is typical of the form Ax = b, where A is a matrix, x is a vector, and b is a non-zero vector. The term "nonhomogeneous" refers to the fact that b is not the zero vector. In differential equations, a nonhomogeneous equation is one that includes a forcing function or input that is not equal to zero. The solution to such an equation can be found by adding the particular solution to the general solution of the corresponding homogeneous equation.
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A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre
The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).
The volume of any cylinder can be calculated using the formula,
V = πr²h
(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)
As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:
Volume of oil = (1/5) x Total Volume
Substituting the given values, we have:
Total Volume = π(80cm)²(200cm) = 4,031,240 cm³
Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³
Converting cm³ to litres, we have:
1 litre = 1000 cm³
Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres
Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:
(10a-6) + (7a+4) + (7a+4) + (10a-6)
Simplifying the expression:
= 34a - 4
Therefore, the perimeter of the quadrilateral is 34a - 4.
Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)a. 81stb. 19thc. 76thd. 24the. 10 th
The percentiles for the standard normal distribution
a. 0.93
b. -0.88
c. 0.67
d. -0.65
e. -1.28
To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.
The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.
Step 1: Write down the given percentiles as a decimal and round to two decimal places.
For example, for the 81st percentile, 0.81 will be used.
Step 2: Use the standard normal distribution table to find the corresponding z-score.
Step 3: Round off the obtained answer to two decimal places.
a) 81st percentile:
The area to the left of the z-score is 0.81.
The corresponding z-score is 0.93.
Hence, the 81st percentile for the standard normal distribution is 0.93.
b) 19th percentile:
The area to the left of the z-score is 0.19.
The corresponding z-score is -0.88.
Hence, the 19th percentile for the standard normal distribution is -0.88.
c) 76th percentile:
The area to the left of the z-score is 0.76.
The corresponding z-score is 0.67.
Hence, the 76th percentile for the standard normal distribution is 0.67.
d) 24th percentile:
The area to the left of the z-score is 0.24.
The corresponding z-score is -0.65.
Hence, the 24th percentile for the standard normal distribution is -0.65.
e) 10th percentile:
The area to the left of the z-score is 0.10.
The corresponding z-score is -1.28.
Hence, the 10th percentile for the standard normal distribution is -1.28.
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Please answer the both questions in the photos below ( will mark brainliest if available + 20p )
Answer:
x=0 & x=2
Step-by-step explanation:
To find when f(x)=g(x), then look for a value that is the same for both functions in the table. 0 occurs twice for the same x value. 0 also appear twice for the x value 2. This is when they are equal. The solution is x=0 and x=2
For some real number a and some positive integer n, the first few terms in the expansion of (1 + ax)^n are [1 - 20x + 150x^2 + cx^3 ]. find c?
Using binomial theorem we can expand the equation but We are not given the value of a or n, so we cannot determine c exactly.
What is the difference between real and integer?Integers are real numbers that only comprise positive and negative whole integers as well as natural numbers. Because of rational and irrational numbers, real numbers may include fractions, whereas integers cannot.
What's a real number?A real number is a quantity in mathematics that may be expressed as an infinite decimal expansion. Real numbers, as opposed to natural numbers such as 1, 2, 3,..., which are generated from counting, are used in measures of continually changing quantities such as size and time.
by applying the binomial theorem:
[tex](1 + ax)^n = C(n, 0) + C(n, 1)(ax) + C(n, 2)(ax)^2 + C(n, 3)(ax)^3 + ...[/tex]
where C(n, k) is the binomial coefficient, which equals[tex]n!/(k!(n-k)!).[/tex]
The first few terms of this expansion are:
[tex](1 + ax)^n = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Comparing with the given expression [1 - 20x + 150x^2 + cx^3], we have:
[tex]1 - 20x + 150x^2 + cx^3 = 1 + nax + n(n-1)(a^2/2)x^2 + n(n-1)(n-2)(a^3/6)x^3 + ...[/tex]
Equating coefficients of [tex]x^3[/tex] on both sides, we get:
[tex]c = n(n-1)(n-2)(a^3/6)[/tex]
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can someone complete Q2 with an explanation? (15 points)
Answer:
To find the average distance away from the mean, we need to first find the mean distance from the mean. To do this, we need to find the mean of the distances from the mean:
|32 - 33| = 1
|45 - 33| = 12
|23 - 33| = 10
|35 - 33| = 2
|30 - 33| = 3
Mean distance from the mean = (1 + 12 + 10 + 2 + 3) / 5 = 6. However, the question asks for the average distance away from the mean, so we need to take the absolute value of this result:
Average distance away from the mean = |6| = 6
Therefore, the answer is C) 5.6 feet.
To find the mean absolute deviation, we first need to find the deviations from the mean:
12.7 - 15.2 = -2.5
22 - 15.2 = 6.8
23.5 - 15.2 = 8.3
24 - 15.2 = 8.8
11 - 15.2 = -4.2
22 - 15.2 = 6.8
Next, we need to take the absolute value of each deviation:
|-2.5| = 2.5
|6.8| = 6.8
|8.3| = 8.3
|8.8| = 8.8
|-4.2| = 4.2
|6.8| = 6.8
The sum of these absolute deviations is:
2.5 + 6.8 + 8.3 + 8.8 + 4.2 + 6.8 = 37.4
To find the mean absolute deviation, we divide this sum by the number of data points:
Mean absolute deviation = 37.4 / 6 = 6.23
Therefore, the answer is not listed among the choices given.
Answer:
B. 33
Step-by-step explanation:
1) Find the mean
32+45+23+35+30/5
165/5
=33
Solve equation for x
216=6^4x+5
Answer: x=211/1296
Step-by-step explanation:
12. In the accompanying diagram, DE || BC, DB = 6,
and AE = 8. If EC is three times AD, find AD.
B
6
D
A
8
E
C
Answer:
AD=4
Step-by-step explanation:
please mark as brainliest
Could anyone help out with this?
The volume of the frustum is 970 cm².
What is frustum?
In geometry, a frustum is a three-dimensional solid that is created by cutting a larger solid, such as a cone or pyramid, with a plane parallel to its base, and then removing the smaller solid that lies above the plane. The resulting solid has two parallel bases of different sizes, and its sides are trapezoidal in shape.
We know that, volume of frustum is given by
V = (1/3) * h * (A + B + sqrt(A * B))
where V is the volume of the frustum, h is the height of the frustum, A is the area of the rectangular base, and B is the area of the rectangular top.
So, A = base × height = 8 × 16
= 128 cm²
Similarly, B = base × height = 3 × 6
= 18 cm²
and, given height of frustum = 15 cm
Now, putting all values into the formula:
So, V = (1/3)× h × (A + B + sqrt(A×B))
= 1/3 × 15 × ( 128+18 + √(128×18))
= 5 × ( 146 + 48 )
= 970 cm²
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Stay if the triangles in each pair or similar if so state, how do you know they are similar and complete the similarity statement
Here, QRS represents the proportion of longest triangle to middle-length sides. 26/36 = 13/18 QUT: 12/16 = ¾ ≠ 13/18
Why does a square differ from a triangle?Students should be taught that whereas a triangle can have many various side lengths and angles, a square must have all of its sides be the same length and all of its angles must be right angles.
Will three triangles form a square?Hence, a square cover must contain a minimum of 4 corner-power points. Nevertheless, each triangles may include one corners in its inside or twin vertex on edges (score of 1) for a not more than one point. Three triangles only cover a square with a maximum of three corner-power points.
[tex]QRS: 26/36 = 13/18[/tex]
[tex]QUT: 12/16 = 3/4 not equal 13/18[/tex]
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5) By AAA congruency rule, ΔVWU ≅ ΔMNU.
6) By SAS congruency rule, ΔCAB ≅ ΔUAV
What is congruency rule?If any twο sides and the angle included between the sides οf οne triangle are equivalent tο the cοrrespοnding twο sides and the angle between the sides οf the secοnd triangle, then the twο triangles are said tο be cοngruent by SAS rule.
5) ∠V ≅ ∠V = 36°
∠VUW ≅ ∠NUM
then according to angle sum property
∠VWU ≅ ∠MNU
Then,
ΔVWU ≅ ΔMNU
By AAA congruency rule, ΔVWU ≅ ΔMNU.
6) 77 ≅ 66 (common side)
42 ≅ 36 (common side)
∠CAB ≅ ∠UAV (common angle)
Then,
ΔCAB ≅ ΔUAV
By SAS congruency rule, ΔCAB ≅ ΔUAV
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Can someone please help me with this?
The value of the angle m<CED is 100 degrees
What are corresponding angles?Corresponding angles are simply described as those angles that are formed by same corners or corresponding corners with a transversal when two parallel lines are joined by any other line.
Also, corresponding angles are created when two parallel lines are intersected by a transversal.
The different types of corresponding angles are;
Those angles formed by parallel lines and transversals.Those angles formed by non-parallel lines and transversals.Note that corresponding angles are equal.
From the information given, we have that;
m < BHG = m<CED
If m< BHG = 100 degrees
Then, m< CED = 100 degrees
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HELP! I WILL MAKE U BRAINLIST! DUE BY 12:00 AM!
I have inserted what you need to do and just search Buzzfeed "Can TV Make Us Not Hate Ourselves?" and read it!
I often see myself represented in the media as a strong, independent woman who lives fearlessly and passionately. I'm a black woman, and I'm proud to be a part of the diverse range of people in our society.
What is passionately ?Passionately is an adjective that describes a person who is filled with intense emotion and enthusiasm. This can be expressed through action or behavior. When someone is passionate about something, they often feel an overwhelming urge to pursue it with great intensity. Being passionate about something is often associated with seeking to make a difference or make an impact on the world.
My representation in the media is not always positive, however. I've been depicted as being too opinionated, too outspoken, or too headstrong. I'm often seen as a stereotype, or as someone who doesn't fit into the roles that society has determined for me.
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I see myself represented in the media by characters who are strong, independent, and confident.
What is media?Media is the broad term used to describe any form of communication that can be used to disseminate information to a large group of people. Media includes traditional media such as newspapers, magazines, radio, and television, as well as more modern forms such as digital media, including websites, social media, and online streaming.
They may have had a difficult start, but they don't let it define them. They are determined to make something of themselves, regardless of the odds. They are resilient and are not afraid to stand up for what they believe in. Through these characters, I can relate to and identify with the struggles and successes of the journey.
My own writer's voice is often reflective and contemplative. I strive to be thoughtful and honest in my writing, and often use metaphors and imagery to make a point. For example, I might write, "Her journey was like a rollercoaster, with highs and lows along the way, but she kept her eyes on the horizon, never losing sight of her goals." Here, I am using an analogy to convey the idea of how a person's path might not always be easy, but they can remain focused on the end result.
The author of the essay used rhetorical questions to emphasize their points and express their opinion. I have also adopted this technique in my writing. For example, I might write, "Do we ever really know how our stories will unfold? Or what it takes to get there?" The use of rhetorical questions captures the reader's attention and sparks their imagination.
Overall, I feel that my writer's voice is distinct and I am confident in my use of literary devices. By incorporating the use of rhetorical questions and analogies, I am able to effectively convey my opinion and perspective in a unique way.
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