Answers
Rounding to the nearest cm², the area of the shaded region is 32 cm².
Describe Area of triangle?The area of a triangle is the measure of the region enclosed by the three sides of a triangle. It is measured in square units. The formula to find the area of a triangle is given as:
Area = 1/2 x base x height
where "base" is the length of the side of the triangle that is perpendicular to the height and "height" is the distance between the base and the opposite vertex.
The base and height can be any two sides of the triangle as long as the height is perpendicular to the base. If the base and height are not known, they can be found using the Pythagorean theorem or other trigonometric functions.
We can find the area of the shaded region by subtracting the area of triangle ABD from the area of rhombus ABCD.
To find the area of triangle ABD, we need to first find the length of BD. Since angle BAD is 70 degrees and ABCD is a rhombus, we know that angle BCD is also 70 degrees. Therefore, angle BXD is 70 degrees / 2 = 35 degrees.
Using trigonometry, we can find BD:
tan(35) = BD/9
BD = 9 tan(35)
BD ≈ 5.458 cm
To find the area of triangle ABD, we use the formula:
Area of triangle = (base x height) / 2
The base of triangle ABD is BD, which we just found, and the height is the perpendicular distance from A to BD. We can find this distance using trigonometry and the fact that angle BAC is 20 degrees:
tan(20) = height/9
height = 9 tan(20)
height ≈ 3.170 cm
Therefore, the area of triangle ABD is:
Area of triangle ABD = (BD x height) / 2
Area of triangle ABD = (5.458 x 3.170) / 2
Area of triangle ABD ≈ 8.661 cm²
The area of rhombus ABCD is:
Area of rhombus ABCD = (diagonal 1 x diagonal 2) / 2
Area of rhombus ABCD = (9 x 9) / 2
Area of rhombus ABCD = 40.5 cm²
Therefore, the area of the shaded region is:
Area of shaded region = Area of rhombus ABCD - Area of triangle ABD
Area of shaded region = 40.5 - 8.661
Area of shaded region ≈ 31.839 cm²
Rounding to the nearest cm², the area of the shaded region is 32 cm².
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Related Questions
could someone help out?
Answers
Answer:
27.18
Step-by-step explanation:
Firstly, you must label the triangle.
r- opposite
13.85- adjacent
We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.
tan (63) = r/13.85
Then, times 13.85 on both sides so we only have our unknown on one side.
(x13.85) tan(63)= r/13.85 (x13.85)
r= tan (63) x 13.85
r=27.18
:)
Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
A figure consists of two curves labeled Upper A and Upper B. Curve Upper A is shorter and more spread out than curve Upper B, and curve Upper B is farther to the right than curve Upper A.
Select all that apply:
1. A has the larger mean.
2. B has the larger mean.
3. The means of A and B are equal.
4. A has the larger standard deviation.
5. B has the larger standard deviation.
6. The standard deviations of A and B are equal
Answers
The true statements regarding the plot of normal distributions A and B are B has the larger mean, and B has the larger standard deviation; options 2 and 3.
What is a plot of normal distribution?A plot of a normal distribution is a bell-shaped curve that represents the probability distribution of a continuous random variable that follows a normal distribution.
The plot shows the frequency of occurrence of values of the variable, with the most common values near the mean and the less common values near the tails of the distribution.
The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean determines the location of the center of the distribution, while the standard deviation determines the spread or width of the distribution.
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Q2 NEED HELP PLEASE HELP
Answers
Answer:
The skydiver has an initial height of 3600.
Step-by-step explanation:
3600 is the y-intercept in the form y=mx+b
In the point (0,3600) .Time is the x-axis and Height is the y-axis.
Replacing,
3600= m(0)+b
b=3600
Taking another point: (2, 3536)
We apply the formula to obtain the slope.
m= (y2-y1) / (x2-x1)
m= (3536 - 3600) / (2-0)
m= -64 / 2
m= -32
Joining all the terms:
y=-32x+3600
Find the radius of the sphere with the given volume
V=4500 mm^3
Answers
Answer:
10.24
Step-by-step explanation:
i used an online calculator
What is the y-intercept of y = 2/3 x + 2? Responses A (3, 2)(3, 2) B (2, 3)(2, 3) C (-3, 0)(-3, 0) D (0, 2)
Answers
Answer:
Y intercept is (0,2) Answer D.
Step-by-step explanation:
I included a graph for equation y=2/3 x + 2.
BRAINLY AND 20 POINTS IF ANSWERED!!!!!! roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds
[ ] meters per second
Answers
1.4m/s is the rate that Roberto is walking. We know the formula for calculating the time i.e. t= d/r.
The term "distance" refers to how far we move. The rate is a measurement of our trip speed. Time is measured by how far we travel. The distance an object will travel over time and at a specific average rate is the subject of rate problems.
Given,
Distance = D
D= 1.4t
Rate= ?
Substituting the given values in the formula t= d/r
where,
t= time in seconds
d= distance
r= rate
We get,
t= 1.4t/r
t/1.4t= 1/r
t gets cancelled
so we have,
1/1.4= 1/r
r= 1.4m/s
Therefore, 1.4m/s is the rate at which Roberto is walking.
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The complete question is as follows:
Roberto is walking. The distance, D, in meters, he walks can be found using the equation D=1. 4t, where t is time in seconds.
What is the rate that Roberto's walking in meters per second?
find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 7xy. (note: start your answer with y
Answers
The equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 7xy. by starting with y equation will be y = 7xy + 1.
An explanation of this equation will be this is the equation of a curve that passes through the point (0,1) and has a slope of 7xy at (x,y).
To find this equation, we use the point-slope formula, which states that for any point (x1, y1) and a slope m, the equation of the line through the point with that slope is given by y - y1 = m(x - x1).
Substituting in the given values, we get y - 1 = 7xy(x - 0).
Simplifying the equation, we have y = 7xy + 1.
Equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is y = 7xy + 1.
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The cost of 2 jackets and 3 dresses is £46. The cost of 2 jackets and 4 dresses is £54. How much does 1 dress cost?
Answers
Answer:
£11
Step-by-step explanation:
Let cost of jackets : x, DRESSES: y.
ATP,
2x+3y = 46 ...(1)
2x + 4y = 54 ...(2)
From 1, we get x = (46-3y)/2
By Substitution in (2), we get:
2(46-3y)/2 +4y = 54
=> 46-3y+4y= 54
=> x = 8
Thus, 1 dress cost: 46-3*8/2 = 46-24/2 =22/2 = £11
kayode bought 50 oranges for 60k. if he sells them in groups of five,for how much should he sell in order to make 50% profit
Answers
Answer:
Cost price of 5 orange=(60/50)*5=6k
Now to get 50% profit
Selling price of group of 5 orange
=6*1.5=9k.
What is the area of the triangle?
Answers
Answer:
b×h ÷2 esa es la fórmula para el área
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
we see that the baseline is 4 units long.
and the height from the top vertex down to that baseline is 5 units.
so, the area is
4 × 5 / 2 = 20/2 = 10 units²
A) A resistor has a resistance 1.5 ohm and a voltage 6.00 V across it. What is the current in the resistor? What power does it dissipate? Show your work.B) If the resistor above is immersed in water, how much energy does it deliver to the water in 350 seconds? Express answer in joules and in calories. Show your work.
Answers
A) Current (I)= 4A and power dissipated is 24W
B) The energy delivers to the water in 350 sec is 2009.57 cal.
We have, Resistance of the resistor, R = 1.5 ohm
The voltage across the resistor, V = 6.00 V
Let the current in the resistor be 'I'
By using Ohms' Law
I = V/R ⇒ 6.00 V / 1.5 ohm ⇒ 4 A
Therefore, the current in the resistor is 4 A.
The power dissipated by the resistor,
P = I²R ⇒ (4 A)² × 1.5 ohm ⇒ 24 W
Therefore, the power dissipated by the resistor is 24 W.
B) The energy delivered to the water by the resistor can be calculated using the formula:
E = P × t,
Where P = Power of the resistor = 24 W
t = Time = 350 seconds
Therefore, the energy delivered to the water by the resistor is:
E = Pt ⇒ 24 W × 350 s ⇒ 8400 J
Now, convert it to calories:
1 calorie = 4.18 J
Therefore, Energy in calories = Energy in joules / 4.18
⇒ 8400 J / 4.18
⇒ 2009.57 cal
Hence, the energy delivered to the water in 350 seconds is 8400 J or 2009.57 cal.
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The circle graph describes the distribution of preferred music from a sample of 400 randomly selected middle school students.
a circle graph titled preferred music, with five sections labeled rock 13 percent, hip hop 25 percent, pop 35 percent, classical 13 percent, and jazz 14 percent
Which of the following conclusions can we draw from the circle graph?
Pop is the preferred music for 35 students.
Jazz is the preferred music for 56 students.
Together, Hip Hop, Rock, and Jazz are the preferred music for less than half the students.
Together, Hip Hop and Pop are the preferred music for 260 students.
Answers
The conclusion we can draw from the circle graph is (2) Jazz is the preferred music for 56 students.
Which of the conclusions can we draw from the circle graph?From the circle graph, we can draw the following conclusions:
Pop is the preferred music for 35% of the sample, which is equivalent to 0.35 x 400 = 140 students.
Therefore, conclusion (1) is incorrect.
Jazz is the preferred music for 14% of the sample, which is equivalent to 0.14 x 400 = 56 students.
Therefore, conclusion (2) is correct.
The combined percentage of Hip Hop, Rock, and Jazz is 13% + 25% + 14% = 52%, which is more than half of the sample.
Therefore, conclusion (3) is incorrect.
Hip Hop and Pop are the preferred music for 25% + 35% = 60% of the sample, which is equivalent to 0.6 x 400 = 240 students.
Therefore, conclusion (4) is incorrect.
Therefore, the only correct conclusion that can be drawn from the circle graph is that Jazz is the preferred music for 56 students.
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Measure the diameter of the tin mm and write down the real diameter in mm
Answers
Answer:
Step-by-step explanation:
calculate the value of expression 2x squared - 3x + 1 if x equals to -2
Answers
The value of expression is 15.
Define the term quadratic expression?A quadratic equation is a mathematical expression of the second degree, in which the highest power of the variable is 2. An expression is a mathematical phrase that combines numbers, variables, and mathematical operations to represent a value or a set of values.
It takes the form of ax² + bx + c = 0, where a, b, and c are coefficients, and x is the variable.
Given equation is;
⇒ 2x² - 3x + 1
If x = -2, then the solution of equation will be,
⇒ 2×(-2)² - 3×(-2) + 1
⇒ (2×4) + 6 + 1
⇒ 8 + 6 + 1
⇒ 15
Therefore, the value of expression 2x² - 3x + 1 if x = -2 is 15.
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stive efforts in
Eamples (finding slope in tables and graphs)
termine the slope of each linear equation. You may want to use the slope formula.
X O
1
2
3
y
S5
7
9
11
b)
566
X
-7
-6
-5
-4
y
10
7
4
1
c)
X
-2
0
2
4
y
I
3
5
can't
7
9
Answers
The slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
What is equation?An equation is an expression that states the equality of two things. It typically consists of an equal sign (=) and two expressions on either side of the equal sign that represent the same thing. Equations are used to describe relationships between different variables and can be used to solve mathematical problems. They can also be used to show the relationships between different quantities in physics and chemistry.
a)The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 6, and the run is 2, so the slope is 3.
b) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 3, and the run is -7, so the slope is -3/7.
c) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 4, and the run is 6, so the slope is 2/3.
Finding slope in tables and graphs is a common mathematical skill that is used to identify the rate of change of a linear equation. This is determined by finding the change in the dependent variable (the y-axis) divided by the change in the independent variable (the x-axis). This is what is referred to as the slope of the equation. To find the slope in tables and graphs, you must look at the differences between the points on the x-axis and y-axis, and divide the change in the y-axis by the change in the x-axis. This will give you the slope of the equation. Finding the slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
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A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. Refer to Exhibit 7-4. The point estimate of the mean content of all bottles is? a) 0.22 b) 4 c) 121 d) 0.02
Answers
The point estimate of the mean content of 121 bottles with the average content of 4 ounces and the standard deviation 0.22 ounces is 4. Option B is the correct answer.
A point estimate is a statistic used to predict the corresponding population parameter. In a sense, a point estimate is a guess about a parameter that uses data from a sample as the basis of the guess. Point estimates can be used to estimate population parameters such as the population mean or population standard deviation.
The point estimate is a single numerical value that represents a guess for a parameter. The sample mean and sample standard deviation are examples of point estimates for the population mean and population standard deviation. If a point estimate is a good guess, it should be fairly close to the true value of the parameter.
Thus, option B is the correct answer.
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Sunflower canola oil is a cooking oil sold in south african supermarkets a 750ml bottle cost R28 and a 2litre bottle cost R63 evaluate which option will be the most cost effective option
Answers
Therefore, the 2-liter bottle is the more cost-effective option as it has a lower cost per milliliter.
What are millimeters?Millimeters (mm) is a unit of length in the metric system. It is a subunit of a meter, with one meter being equal to 1000 millimeters. Millimeters are commonly used to measure small distances such as the thickness of paper, the width of a fingernail, or the diameter of a small object. The abbreviation for millimeters is "mm".
by the question.
To evaluate which option is the most cost-effective, we need to compare the cost per milliliter of each option.
Calculate the price per liter: To compare the cost of the two options, you'll need to calculate the price per liter of each. You can do this by dividing the price of the bottle by its volume in liters. For example, if the 2-liter bottle costs $4, the price per liter would be $2 ($4/2 liters). If the 750ml bottle costs $2.50, the price per liter would be $3.33 ($2.50/0.75 liters).
Compare the price per liter: Once you have the price per liter for each option, you can compare them. In this example, the 2-liter bottle is cheaper at $2 per liter compared to the $3.33 per liter for the 750ml bottle.
Consider the convenience: While the 2-liter bottle may be cheaper, you should also consider if it's more convenient for you. If you won't be able to use all the 2-liters before it goes bad, or if it's difficult to carry around, then multiple 750ml bottles may be a better option for you despite the higher cost per liter.
For the 750ml bottle:
[tex]Cost per milliliter = R28 /750ml[/tex]
[tex]Cost per milliliter = R0.0373/ml[/tex]
For the 2-liter bottle:
[tex]Cost per milliliter = R63 / 2000ml[/tex]
[tex]Cost per milliliter = R0.0315/ml[/tex]
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The equation y = 8x represents the
relationship between the amount of
time Shanay takes to weave thread
into fabric and the number of rows.
How long will it take Shanay to weave
72 rows of fabric at this constant rate?
Answers
X=9
It will take 9
13
Select the correct answer.
Solve the following equation for x.-
x²-36=0
Ο Α.
OB.
OC.
O D.
X = 1; x = -36
x= -1; x = 36
x = -6; x = 6
x=-18; x = 18
Answers
Answer:
C.
Step-by-step explanation:
x² - 36 = 0
x = 6
6² = 6 x 6 = 36
So..
36 - 36 = 0
As there are so many equations in mathematics, it is a very broad subject. These are a few illustrations of typical mathematical equations: [tex]x = -6; x = 6[/tex]. Thus, option C is correct.
What is the equation used in maths?To solve the equation [tex]x² - 36 = 0[/tex] , we can use the difference of squares formula:
A, B, and C are constants in the quadratic equation: ax2 + bx + c = 0. A quadratic function, often known as a function with the form f(x) = ax2 + bx + c, can be solved using this equation to get its roots.
[tex]a² - b² = (a + b)(a - b)[/tex]
In this case, a² = x² and b² = 36, so we can write:
[tex]x² - 36 = (x + 6)(x - 6)[/tex]
Setting this expression equal to 0 and solving for x, we get:
[tex](x + 6)(x - 6) = 0[/tex]
[tex]x + 6 = 0 or x - 6 = 0[/tex]
[tex]x = -6 or x = 6[/tex]
Therefore, the solutions to the equation [tex]x² - 36 = 0[/tex] are [tex]x = -6[/tex] and [tex]x = 6.[/tex]
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A cylindrical tin filled with oil has a diameter of 12cm and a height of 14cm. The oil is then poured in rectangular tin 16cm long and 11cm wide. What is the depth of the oil in the tin
Answers
The volume of cylindrical tin is 1584 [tex]cm^3[/tex]. The depth of the oil in the tin is 9cm.
[tex]V_1 =[/tex] VOLUME OF CYLINDRICAL TIN
[tex]= \pi r^2 h[/tex]
[tex]=\frac{22}{7}[/tex] x 6 x 6 x 14
= 44 x 36
= 1584 [tex]cm^3[/tex]
[tex]V_2 =[/tex] VOLUME OF RECTANGULAR TIN
= lbh = 1584
= (16)(11)(h) = 1584
= 176h =1584
= h = 1584 / 176
= h = 9 cm
A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.
To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.
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according to a census, 3.3% of all births in a country are twins. if there are 2,500 births in one month, calculate the probability that more than 90 births in one month would result in twins. use a ti-83, ti-83 plus, or ti-84 calculator to find the probability. round your answer to four decimal places. provide your answer below:
Answers
According to a census, 3.3% of all births in a country are twins. In a month, there are 2,500 births. The census reports that 3.3% of all births result in twins, and the probability of having more than 90 twins in a month is "0.4351."
We will solve this problem using the binomial distribution formula, which is as follows:P (X > 90) = 1 - P (X ≤ 90)where P represents the probability, X represents the number of twins born in a month, and X is a binomial random variable with a sample size of n = 2,500 and a probability of success (having twins) of p = 0.033. Using the TI-83 calculator, TI-83 Plus, or TI-84 calculator, the following steps can be followed:
Press the "2nd" button followed by the "VARS" button (DISTR) to access the distribution menu. Scroll down and select "binomcdf (" from the list of options (use the arrow keys to navigate). The binomcdf ( menu will appear on the screen. The first number in the parentheses is the number of trials, n, and the second number is the probability of success, p. We want to find the probability of having more than 90 twins, so we need to use the "compliment" option. Therefore, we will subtract the probability of having 90 twins or less from 1 (using the "1 -" key). Type in "binomcdf (2500,0.033,90)" and press the "ENTER" button on your calculator.
This will give you the probability of having 90 twins or fewer in a month. Subtract this value from 1 to obtain the probability of having more than 90 twins in a month, which is the answer to our question. P(X>90) = 1 - binomcdf (2500,0.033,90)P(X>90) = 1 - 0.5649P(X>90) = 0.4351Therefore, the probability of having more than 90 twins in a month is 0.4351.
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I need help with answer this question
Answers
Answer:
y = 2x/15 + 6
Step-by-step explanation:
3y/2 = x/5 + 9
3y = (x/5 + 9) (2) The 2 that was dividing goes on to multiply on the other side.
3y= 2x/5 + 18
y = (2x/5 + 18) / 3 The 3 that was multiplying goes on to divide on the other side.
y = 2x/15 + 6
16. Find the average rate of change of the function f(x)=x²+2x+1 over the interval [0,1/2]
Answers
As a result, f(x) changes at a rate of 1/2 on average over the range [0, 1/2].
what is function ?A function is a mathematical formula that relates every element in one set, known as the domain, to a single element in another set, known as the range. The most prevalent way to represent a function is as f(x), where f(x) stands for the output or dependent variable and "x" stands for the input or independent variable. There is a value of f(x) in the range for each value of x in the domain. Consider the function f(x) = 2x + 1 as an illustration. This function's range and scope possibilities are both limited to the real numbers.
given
We must determine the slope of the secant line that goes through the interval's endpoints in order to determine the average rate of change of a function over the interval. Since the range in this instance is [0, 1/2], we must determine the slope of the secant line that connects (0, f(0)) and (1/2, f(1/2)).
Let's first assess the function at the interval's endpoints:
f(0) = 0² + 2(0) + 1 = 1
f(1/2) = (1/2)² + 2(1/2) + 1
= 5/4
Next, we can calculate the slope of the secant line using the slope formula:
slope is equal to (f(1/2)-f(0)) / (1/2 - 0)
= ((5/4)-1) / (1/2)
= (1/4) / (1/2)
= 1/2.
As a result, f(x) changes at a rate of 1/2 on average over the range [0, 1/2].
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Solve this math problem below
Answers
the only option that satisfies both conditions is option B:[tex]y = 12 \sqrt{(x)} - 1[/tex]. Its range is all real numbers and its graph is decreasing from left to right.
What is quadratic equation?
A quadratic equation is a type of polynomial equation of degree two, meaning it contains one or more terms that involve x raised to the power of two (i.e., x^2).
To determine which of these functions has a range of all real numbers and a graph that is decreasing from left to right, we can examine the behavior of the functions as x approaches positive or negative infinity.
For option A, we see that the term (x+7) inside the square root will approach infinity as x approaches infinity, and since the term is subtracted from 3 and multiplied by -6, the y-values will approach negative infinity.
For option B, as x approaches infinity, the square root term will also approach infinity, and since it is being multiplied by 12 and subtracted by 1, the y-values will approach positive infinity.
For option C, as x approaches negative infinity, the term (x+1) inside the cube root will approach negative infinity, and since it is being multiplied by 3 and subtracted by 4, the y-values will approach negative infinity.
For option D, as x approaches negative infinity, the cube root term will approach negative infinity, and since it is being multiplied by -5 and added to 15, the y-values will approach positive infinity.
Therefore, the only option that satisfies both conditions is option B: y = [tex]12 \sqrt{(x)} - 1.[/tex] Its range is all real numbers and its graph is decreasing from left to right.
For the first question, we know that the given square root function has an endpoint at (-4, 19). Let's substitute these values into the function to solve for the unknown parameter 'a':
[tex]y = a\sqrt{(x-h)}+k[/tex]
[tex]19 = a \sqrt{(-4-h)}+k[/tex]
We also know that the square root function has a domain of all values of 'x' such that the expression inside the square root is non-negative. Therefore:
(x-h) >= 0
x >= h
Combining the two equations, we get:
[tex]19 = a\sqrt{(-4-h)}+k[/tex]
h <= x
Since we have only one equation with two unknowns ('a' and 'k'), we cannot solve for the exact values of 'h' and 'a'. However, we can eliminate some of the answer choices based on the domain condition:
For the second question, we need to find a function that has a range of all real numbers and a graph that is decreasing from left to right. Let's analyze each option:
Option A: y=-6√x+7+3 has a maximum value of 3 and a decreasing graph from left to right, but its range is limited to y <= 3, so it does not satisfy the range condition.
Option B: y = 12-1 has a constant value of 11, so its range is limited to y = 11, which does not satisfy the range condition.
Option C: y=3x+1-4 has a graph that is increasing from left to right, so it does not satisfy the decreasing graph condition.
Option D: y=-5 +15 has a constant value of 10, so its range is all real numbers, and its graph is decreasing from left to right (a horizontal line).
Therefore, the answer is Option D: y=-5 +15.
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W(–1, 4), X(4, 0), Y(–5, 1), and Z(0, –3) are vertices of quadrilateral WXZY. What is true of wx and yz?
Answers
The length of WX is greater than the length of YZ, and that the sides are neither parallel nor perpendicular.
Quadrilateral WXZY has four vertices: W(-1,4), X(4,0), Y(-5,1), and Z(0,-3). We are asked what is true about the sides WX and YZ.
To determine the length of WX, we can use the distance formula: d = √((x2-x1)² + (y2-y1)²). So, d(W,X) = √((4-(-1))² + (0-4)²) = √(5² + 4²) = √41. Similarly, d(X,Z) = √((0-4)² + (-3-0)²) = √16 + 9 = √25 = 5.
To determine the length of YZ, we can use the same formula: d(Y,Z) = √((-3-(-5))²+ (0-1)²) = √4 + 1 = √5.
Now, we need to compare the lengths of WX and YZ to determine what is true about them. √41 is greater than √5, so we know that WX is longer than YZ.
However, this does not tell us whether WX and YZ are parallel, perpendicular, or neither. To determine this, we need to examine the slopes of the sides.
The slope of WX is (0-4)/(4-(-1)) = -4/5. The slope of YZ is (0-(-3))/(-5-0) = 3/5. Since the slopes are not equal, we know that the sides are not parallel.
To determine if the sides are perpendicular, we can multiply their slopes. If the product is -1, then the sides are perpendicular. So, (-4/5) * (3/5) = -12/25, which is not equal to -1. Therefore, we can conclude that the sides WX and YZ are neither parallel nor perpendicular.
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Question 8 (4 points)
For a meat raffle, 100 tickets were sold.
The following were prizes:
number of winners
1
4
15
prize
grand prize - $1000 cash
$250 meat package
$50 meat package
What is the probability of winning the grand prize? 1/20
What is the expected value for someone buying a single ticket for $10.00 ? $
Answers
In a hat, you have index cards with the numbers 1 through 10 written on them. Find how many of the 10 possible numbers you can pick match the described event, then drag and drop each of the numbers into the correct box to order the events from least likely to happen (1) to most likely to happen (8) when you pick one card at random.A. You pick a number greater than 0.B. You pick an even number.C. You pick a number that is at least 2.D. You pick a number that is at most 0.E. You pick a number divisible by 3.F. You pick a number divisible by 5.G. You pick a prime number.H. You pick a number less than the greatest prime number among the numbers 1 through 10.
Answers
The order of events from least likely to most likely are as follows:
D. You pick a number that is at most 0A. You pick a number greater than 0C. You pick a number that is at least 2B. You pick an even numberE. You pick a number divisible by 3F. You pick a number divisible by 5G. You pick a prime numberH. You pick a number less than the greatest prime number among the numbers 1 through 10The reason for this order is because of the chances of each event occurring. Event D has the least chance of occurring because no numbers in the set have a value less than or equal to 0. Event A is the next least likely because only one number in the set is greater than 0, which is the number 1. Event C is the next least likely because only two numbers in the set are at least 2 (2 and 3). Event B is the next least likely, as there are only five even numbers in the set (2, 4, 6, 8, and 10). Events E, F, G, and H are the most likely to occur, because of the number of numbers that are divisible by 3, and 5, and are prime numbers.
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Sophie invested $92,000 in an account paying an interest rate of 6 1/8% compounded
continuously. Damian invested $92,000 in an account paying an interest rate of 6 5/8%
compounded monthly. After 14 years, how much more money would Damian have in
his account than Sophie, to the nearest dollar?
Answers
Answer:
Step-by-step explanation:
To solve this problem, we need to use the formula for compound interest:
A = P*e^(rt)
where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).
For Sophie's account, we have:
P = $92,000
r = 6 1/8% = 0.06125 (as a decimal)
t = 14 years
A = 92000*e^(0.06125*14)
A = $219,499.70 (rounded to the nearest cent)
For Damian's account, we have:
P = $92,000
r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)
t = 14*12 = 168 months
A = 92000*(1+0.005521)^168
A = $288,947.46 (rounded to the nearest cent)
Now we can subtract Sophie's final amount from Damian's final amount to find the difference:
Difference = $288,947.46 - $219,499.70
Difference = $69,447.76
Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.
How can you tell if a point is a solution to a two variable inequality?
Answers
One way to determine whether a point is a solution to a two-variable inequality is to substitute the values of the variables in the inequality and determine whether the inequality is true or false. If the inequality is true, the point is a solution, and if the inequality is false, the point is not a solution.
For example, consider the inequality 2x + 3y > 7. Let’s see if the point (1,2) is a solution. To do so, substitute x=1 and y=2 into the inequality:2(1) + 3(2) > 7 Simplify to get:2 + 6 > 7 This is true, so the point (1,2) is a solution to the inequality. Conversely, let’s see if the point (4,-1) is a solution. To do so, substitute x=4 and y=-1 into the inequality:2(4) + 3(-1) > 7 Simplify to get:8 - 3 > 7 This is false, so the point (4,-1) is not a solution to the inequality .There are some general rules that can be followed to help determine which side of a line is shaded in an inequality. If the inequality is greater than or less than, the line should be dashed, and the shading should be above or below the line, respectively. If the inequality is greater than or equal to or less than or equal to, the line should be solid, and the shading should be above or below the line, respectively.
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Assume that the firm for which you work faces a demand function given by:
P=20-2Q
and a total cost function:
TC=100-2Q^3-100Q+34Q^2
a) Find the profit maximizing level of output (Q)
b) What price should you charge for your product?
c) Based on your answers in the previous two questions, how much profit is this firm making at the profit maximizing level of output?
Answers
The profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.
a) Find the profit-maximizing level of output (Q)To determine the profit-maximizing level of output, we must calculate the marginal cost and marginal revenue of the firm.MC= dTC/dQ= -6Q^2-100+68Q=2(17Q^2-34Q-50)So, the marginal cost of the firm is MC= 2(17Q^2-34Q-50)To find the marginal revenue (MR) we must differentiate the revenue function with respect to Q.MR= dTR/dQ= P + Q(dP/dQ)= 20-4QHence, the marginal revenue is MR= 20-4QAt the point of maximum profit, marginal cost (MC) equals marginal revenue (MR).Therefore, 2(17Q^2-34Q-50)=20-4Q34Q^2-68Q-100=0Solving the above equation gives Q=1.91Therefore, the profit-maximizing output is 1.91 units.b) What price should you charge for your product?The price the firm should charge for its product is given by the demand function, P=20-2Q.Substituting Q=1.91 into the demand function,P= 20-2(1.91) = $16.18c) Based on your answers in the previous two questions, how much profit is this firm making at the profit-maximizing level of output?The total profit of the firm is given by the difference between the revenue and the total cost.TR= P x Q = 16.18 x 1.91 = $30.92TC= 100-2(1.91)^3-100(1.91)+34(1.91)^2 = $60.34Profit = TR- TC= $30.92-$60.34= -$29.42At the profit-maximizing output of 1.91, the firm is incurring a loss of $29.42.
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