The probability that the student finishes the inquiry in less than 1.5 hours is 0.45.
Mean= 4/3 and standard deviation= √(11/90)
a) To find the probability that the student finishes the inquiry in less than 1.5 hours, we need to find the area under the probability density function (PDF) of f(x) between the lower limit of 1 and the upper limit of 1.5.
This is given by the definite integral of f(x) from 1 to 1.5:
∫f(x)dx from 1 to 1.5
= ∫(2/5(x + 1))dx from 1 to 1.5
= (2/5)∫(x + 1)dx from 1 to 1.5
= (2/5)[x^2/2 + x] from 1 to 1.5
= (2/5)[(1.5)^2/2 + 1.5 - (1)^2/2 - 1]
= (2/5)[2.25/2 + 1.5 - 1/2 - 1]
=(2/5)[2.25/2]
=0.45
b) To find the mean, we need to use the formula:
Mean = ∫x*f(x)dx from a to b
In this case:
Mean = ∫x*(2/5(x + 1))dx from 1 to 2
= (2/5)∫x(x + 1)dx from 1 to 2
= (2/5)[x^3/3 + x^2/2] from 1 to 2
=(2/5)[(2)^3/3 + (2)^2/2 - (1)^3/3 - (1)^2/2]
= (2/5)[8/3 + 4/2 - 1/3 - 1/2]
=(2/5)[7/3 + 3/2]
=(2/5)[(20)/6]
=4/3
=1.333
To find the standard deviation, we need to use the formula:
Standard deviation^2 =(∫(x-μ)^2*f(x)dx) from a to b
Where μ is the mean
In this case,
Standard Deviation ^2= ∫(x-μ)^2(2/5)(x+1) dx from 1 to 2
=(2/5)∫(x-μ)^2(x+1) dx from 1 to 2
Simplifying, we get,
(x-μ)^3*(3x+μ+4)/30 from 1 to 2
=[(2-μ)^3*(6+μ+4)-(1-μ)^3*(3+μ+4)]/30
=[(2-μ)^3*(10+μ)-(1-μ)^3*(7+μ)]/30
Substituting the value of μ,
=[(2-4/3)^3*(10+4/3)-(1-4/3)^3*(7+4/3)]/30
=11/90
Therefore, Standard Deviation= √(11/90)
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-57-31/x+3 what is x
Answer:
FACTOR
(−1)×2×3×5
2 or -150
Step-by-step explanation:
If someone walks along the outside of the garden from point A to point B, what percent of the garden's border would they have walked around? Round your answer to the nearest whole percent. Type the correct answer in the box. Use numerals instead of words. They would have walked around approximately % of the outside border of the garden.
The outside border of the garden would have walked around approximately 58%.
Without more information about the shape and dimensions of the garden, it's impossible to give an exact answer. However, if we assume that the garden is a rectangle, we can use the formula for the perimeter of a rectangle to estimate the percentage of the garden's border that would be walked around.
Let's say that the length of the garden is L and the width of the garden is W. The perimeter of the rectangle is then:
P = 2L + 2W
If the person walks from point A to point B along the outside of the garden, they are essentially walking along two sides of the rectangle. Let's call these sides S1 and S2. Depending on the location of A and B, S1 and S2 may be two adjacent sides, two opposite sides, or one side and one diagonal.
To estimate the percentage of the garden's border that the person would walk around, we can calculate the length of S1 and S2 and divide by the total perimeter of the rectangle:
Percentage walked = (S1 + S2) / P * 100%
Again, without more information about the shape and dimensions of the garden, we can't give an exact answer. However, if we assume that the person walks along two adjacent sides of the rectangle, the percentage of the garden's border that they would walk around would be:
Percentage walked = (2L + W) / (2L + 2W) * 100%
Simplifying this expression, we get:
Percentage walked = (2L + W) / (2(L + W)) * 100%
Assuming that L and W are measured in the same units (e.g. meters), we can simplify further:
Percentage walked = (2 + W/L) / (2 + 2W/L) * 100%
For example, if the length of the garden is 10 meters and the width of the garden is 5 meters, then the percentage of the garden's border that the person would walk around if they walked along two adjacent sides would be:
Percentage walked = (2 + 5/10) / (2 + 2*5/10) * 100%
= 7/12 * 100%
= 58.3%
So the outside border of the garden would have walked around approximately 58%.
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Find the area of the shape
The area of the given figure is 27.5 square centimeter which has a rectangle and triangles
The given figure has a rectangle and triangles
The area of rectangle is length times width
Area of rectangle =5×4
=20 square centimeter
Area of triangle =1/2×base×height
=1/2×2.5×3
=7.5/2
=3.75 square centimeter
As there are two triangle = 2(3.75)
=7.5 square centimeter
Total area = 7.5+ 20
=27.5 square centimeter
Hence, the area of the given figure is 27.5 square centimeter
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QUESTION 4 Refer to the map of South Africa below and answer the following questions. ATLANTIC OCEAN 4.1 4.2 W- 4.3 N S • Springbok Lamberts Bay Saldanha Baylo Cape Town • Upington Calvinia Beaufort Weste Stellenbosch- Agulhas Vryburg sna Pretoria Johannesborg o Kimberley Bloemfontein Colesburgo Polokwane o Graaf-Reinet ... Hogsback LESOTHO Sabie o Badplaas Port Elizabeth Bergville REast London Durban Port St Johns St. Lucia INDIAN OCEAN 1:15 000 000 What type of the scale is given in the diagram and interpret the given scale? Write down the general direction of Badplaas from Colesburg. Use the given scale and determine the actual straight line distance between East London and Bloemfontein. Show ALL calculations and give your answer in km. In which province is Stellenbosch on the map? What is the probability that this province will be randomly selected in South Africa? Write your answer correct to TWO decimal places. (3) (2) 3 05 (4) (3
The given text presents a map of South Africa with various locations marked. However, important information such as the scale of the map and the number of provinces is missing. Without the scale, we cannot accurately determine distances or calculate probabilities. Similarly, the absence of information regarding the provinces prevents us from calculating the probability of selecting a specific province. Therefore, based on the given text, we can only answer the first two questions, which involve the type of scale and the general direction between two locations.
1. The type of scale given in the diagram is a ratio scale, specifically a linear scale. It represents the relationship between map distance and actual distance in a straight line.
Interpretation of the given scale:
The scale on the map is not clearly visible in the provided text. However, it is typically written as a fraction or ratio, where the numerator represents the map distance and the denominator represents the corresponding actual distance on the ground. For example, a scale of 1:1,000,000 means that 1 unit on the map represents 1,000,000 units in the real world.
2. The general direction of Badplaas from Colesburg is to the northeast.
3. To determine the actual straight-line distance between East London and Bloemfontein, we would need the scale from the map. However, the scale is not provided in the given text, making it impossible to calculate the distance accurately.
4. Stellenbosch is located in the Western Cape province on the map.
5. To calculate the probability of randomly selecting the Western Cape province in South Africa, we would need the total number of provinces in South Africa and the number of provinces that belong to the Western Cape. However, this information is not provided in the given text, so it is not possible to calculate the probability.
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Your ability to borrow money at lower rates improves as
OA. you save more
OB. you earn more
OC. your debt ratio increases
OD. your credit score increases
Your ability to borrow money at lower rates improves as your credit score increases. Option D.
What is a credit score?Your ability to borrow money at lower rates improves as your credit score increases.
A higher credit score indicates to lenders that you have a strong credit history, responsible financial behavior, and a lower risk of defaulting on loans.
Lenders view borrowers with higher credit scores as more reliable and trustworthy, making them more likely to offer lower interest rates and better loan terms.
While saving more and earning more can indirectly contribute to improving your credit score by positively impacting your financial stability and ability to manage debt, they are not direct factors that lenders consider when determining interest rates.
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1.62,16.2,15/20 greatest to least
Answer
The order of the number from greatest to least is 1.62, 15/20, 16.2%
Step-by-step explanation
Given: 1.62 16.2% 15/20
To order these data in descending order (i.e. from highest to least), follow the steps below
1. Convert all numbers to decimals
1.62
16.2% = 16.2/100
16.2% = 0.162
15/20 = 0.75
So, the number are 1.62, 0.162, 0.75
2. Compare the three decimals and arrange in descending order
1.62 > 0.75 > 0.162
This means that 1.62 is greater than 0.75 and 0.75 is greater than 0.162
By substituting 16.2% for 0.162 and 15/20 for 0.75, the order of the number from greatest to least is
1.62, 15/20, 16.2%
What function is the inverse of the exponential function y = 4*?
OA
1
y=z.
OC y = log₂ 4
O B. y=(¹)²
O
D. y = log, z
The function that is the inverse of the exponential function y = 4ˣ is lnx/ln4
The inverse of a function f is denoted by [tex]f^{-1[/tex] and it exists only when f is both one-one and onto function. Note that [tex]f^{-1[/tex] is NOT the reciprocal of f. The composition of the function f and the reciprocal function [tex]f^{-1[/tex] gives the domain value of x.
(f o [tex]f^{-1[/tex] ) (x) = ( [tex]f^{-1[/tex] o f) (x) = x
For a function 'f' to be considered an inverse function, each element in the range y ∈ Y has been mapped from some element x ∈ X in the domain set, and such a relation is called a one-one relation or an injunction relation.
The standard exponential function is given as y = abˣ
Given the function,
y = 4ˣ
Replace y with x
[tex]x = 4^y[/tex]
Make y the subject of the formula,
[tex]lnx = ln4^y\\\\lnx = yln4[/tex]
Divide both sides by ln4
lnx/ln4 = y
Hence the function that is the inverse of the exponential function y = 4ˣ is lnx/ln4
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
Which term describes the distribution of this graph?
A. Uniform
B. Skewed Right
C. Normal
D. Skewed Left
(Reward, 50 Points.)
Help Me please!!!!!!!!!!!
The triangles are similar and
Yes , ΔPSQ ≅ ΔRST because ∠S ≅ ∠S and PS / RS = QS / TS . Thus the triangles are similar by the SAS theorem
Given data ,
Let the first triangle be ΔPSQ
Let the second triangle be ΔRST
Now , the corresponding sides are
PS / RS = QS / TS
where the corresponding sides of similar triangles are in the same ratio
And , the common angle to both the triangles is m∠S
So , ∠S ≅ ∠S and PS / RS = QS / TS
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , the triangles are similar
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3. It took an average of 20 days for a car dealership to sell a new car. Due to the current shortage in the new car market, you believe it is now quicker to sell a car. You take a sample of 30 recently sold cars and find that it took an average of 15 days to sell. You know the population standard deviation is 12 days and it is fairly stable. Test your hypotheses at the 5% significance level using the p-value approach. Follow the 4-step procedure and show your work.
Answer to the given Hypotheses is : The current shortage in the new car market has made it quicker to sell a car.
In this scenario, we have to determine if the current shortage in the new car market has affected the time it takes a car dealership to sell a new car. To answer this question, we will use the p-value approach.
First, we will determine the null and alternative hypotheses. The null hypothesis (H₀) is that the average time it takes to sell a car has not changed, while the alternative hypothesis (H₁) is that the current shortage in the new car market has made it quicker to sell a car.
H₀: μ = 20
H₁: μ < 20
Second, we will choose the appropriate test statistic and determine the level of significance. In this case, we will use a one-sample t-test, as the population standard deviation is known, and you will use a 5% level of significance (α = 0.05).
Third, we will calculate the test statistic and the p-value. The test statistic is calculated by dividing the difference between the sample mean and the hypothesized population mean by the standard error of the mean.
t = (x' - μ) / (σ / √n)
t = (15 - 20) / (12 / √30)
t = -2.89
Using a t-distribution table with 29 degrees of freedom, the p-value is 0.004.
Since the p-value is less than the level of significance, we reject the null hypothesis and conclude that the current shortage in the new car market has made it quicker to sell a car.
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Find the length of the three missing sides in the rhombus below.
y
Z
X
82
As all sides of a Rhombus are of equal length, the length of the missing sides are 82
Property of a RhombusThe property of a Rhombus required for answering this question is associated with the length of it's sides. A Rhombus has four sides with the length of all these sides being equal.
This means that with the length of one of it's sides being 82 , the length of the remaining 3 sides would be 82 as well.
The length of sides x = y = z = 82. Hence, x, y and z are 82
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The data set represents the number of miles Mary jogger each day for the past nine days.
Answer: 0
Step-by-step explanation: It is furthest away from the other numbers with a difference of at least 5. If plotted in a table it would visually be seen to be further away from the general trend.
What is the probability that either event will occur? 3 A 18 B 15 P(A or B) = P(A) + P(B) P(A or B) = [?] Enter as a decimal rounded to the nearest hundredth.
Answer:
the probability that either event will occur is 0.92
Step-by-step explanation:
the probability that either event will occur is 0.92
What is the probability that either event will occur?
From the question, we have the following parameters that can be used in our computation:
Event A = 18
Event B = 15
Other Events = 3
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 18 + 15 + 3
Evaluate
Total = 36
So, we have
P(A) = 18/36
P(B) = 15/36
For either events, we have
P(A or B) = 33/36 = 0.91666
Hence, the probability that either event will occur is 0.92 (rounded to nearest hundreth)
HELP ME PLS ASAP………….
Answer:
=
Step-by-step explanation:
0.67 is the same as 0.670
PLEASE HELP LOL
What is the value of x in this triangle?
Enter your answer in the box.
x =
The solution is: the value of x in this triangle is x = 83°.
Here, we have,
given that,
the angles of a triangle are:
44, 53 and x
now, we have to find the value of x in this triangle.
we know that,
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
so, we have,
44 + 53 + x = 180°
or, x= 83
Hence, The solution is: the value of x in this triangle is x = 83°.
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13. Find mzYZU.
(10x +9)
(6x-13)
34°
Right angle
Pls help ASAP
Given is a circle with center Z, we need to find the measure of the angle YZU,
We know that,
In a circle, the length of an arc and the length of the corresponding central angle are inextricably linked and equal.
Also,
The whole circle measures 360°.
So,
arc YU + arc UV + arc VX + arc YX = 360°.
10x+9 + 90° + 34° + 6x-13 = 360°
16x = 240°
x = 15
So, arc YU = 10(15) + 9
arc YU = 159°
Since arc YU = ∠ YZU
Therefore the measure of the angle YZU is 159°
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prove that: (cosec A- sec A) (cot A-tan A) = (cosec A + sec A) (sec A cosec A-2)
Answer: To prove the given identity:
(cosec A - sec A)(cot A - tan A) = (cosec A + sec A)(sec A cosec A - 2)
We will start by simplifying both sides of the equation.
Left-hand side (LHS):
(cosec A - sec A)(cot A - tan A)
Using trigonometric identities, we can rewrite cosec A, sec A, cot A, and tan A in terms of sin A and cos A:
cosec A = 1/sin Asec A = 1/cos Acot A = cos A / sin Atan A = sin A / cos A
Substituting these values into the LHS:
(cosec A - sec A)(cot A - tan A)
= (1/sin A - 1/cos A)(cos A / sin A - sin A / cos A)
= ((cos A - sin A) / (sin A * cos A)) * ((cos A^2 - sin A^2) / (sin A * cos A))
= (cos^2 A - sin^2 A) / (sin^2 A * cos^2 A) [Using the difference of squares identity: a^2 - b^2 = (a + b)(a - b)]
= ((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A)
Right-hand side (RHS):
(cosec A + sec A)(sec A cosec A - 2)
Again, using the same trigonometric identities:
(cosec A + sec A)(sec A cosec A - 2)= (1/sin A + 1/cos A)((1/cos A)(1/sin A) - 2)= ((cos A + sin A) / (sin A * cos A)) * (1 / (sin A * cos A) - 2)= (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)
Now, we need to show that the LHS is equal to the RHS:
((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A) = (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)
To prove this, we can cancel out the common factors in the numerator and denominator of the LHS:
(cos A - sin A) = 1 - 2sin^2 A * cos^2 A
Next, we'll simplify both sides individually:
1 - 2sin^2 A * cos^2 A= 1 - 2(sin A * cos A)^2= 1 - 2(sin A * cos A)(sin A * cos A)= 1 - 2sin A * cos A * sin A * cos A= 1 - 2sin^2 A * cos^2 A
Therefore, the LHS is equal to the RHS, and the given identity has been proven.
Please solve this question
Answer:2x-14
Step-by-step explanation:
�
=
# correct
X=# correctX, equals, start text, \#, space, c, o, r, r, e, c, t, end text
0
00
1
11
2
22
3
33
�
(
�
)
P(X)P, left parenthesis, X, right parenthesis
0.05
0.050, point, 05
0.20
0.200, point, 20
0.50
0.500, point, 50
0.25
0.250, point, 25
Mean:
�
�
=
1.95
μ
X
=1.95mu, start subscript, X, end subscript, equals, 1, point, 95
Standard deviation:
�
�
≈
0.8
σ
X
≈0.8sigma, start subscript, X, end subscript, approximately equals, 0, point, 8
Mr. Gupta decides to score the tests by giving
10
1010 points for each correct question. He also plans to give every student
5
55 additional bonus points. Let
�
YY represent a random student's score.
What are the mean and standard deviation of
�
YY?
�
�
=
Answer:
is every whole number a natural number
Which of the following is the equation of a line with a slope of -5/9
Answer:
Please help me important question in image
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Step-by-step explanation:
Please help me important question Please help me important question in image
in image
Please help me iPlease help me important question in image
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mportant question in image
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what are the answers to these questions
1) 4x=24
2) x3=11
3) 8=n÷3
4) 5x÷6=20
5) 3a=12
6) 5⋅z=35
7) 40=4y
8) 42=7k
9) 7x=105
10) 75=6⋅w
Answer:
X=6Step-by-step explanation:
X=6X=3.7n=24X=24a=4Z=7y=10k=6x=15w=12.5NO LINKS!!!! URGENT HELP PLEASE!!!!!
Solve ΔABC using the Law of Sines Part 1
3. A = 110°, a= 14, b= 9
4. B = 110°, c = 13, b = 21
Answer:
3) B = 37.2°, C = 32.8°, c = 8.1
4) A = 34.4°, C = 35.6°, a = 12.6
Step-by-step explanation:
To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Question 3Given values:
a = 14b = 9A = 110°Substitute the given values into the formula and solve for angle B:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]
[tex]\implies \dfrac{14}{\sin 110^{\circ}}=\dfrac{9}{\sin B}[/tex]
[tex]\implies 14\sin B=9\sin 110^{\circ}[/tex]
[tex]\implies \sin B=\dfrac{9\sin 110^{\circ}}{14}[/tex]
[tex]\implies B=\sin^{-1}\left(\dfrac{9\sin 110^{\circ}}{14}\right)[/tex]
[tex]\implies B=37.1632517...^{\circ}[/tex]
[tex]\implies B=37.2^{\circ}[/tex]
As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies C=180^{\circ}-A-B[/tex]
[tex]\implies C=180^{\circ}-110^{\circ}-37.1632517...^{\circ}[/tex]
[tex]\implies C=32.8367482...^{\circ}[/tex]
[tex]\implies C=32.8^{\circ}[/tex]
Finally, substitute the values of a, A, and C into the Law of Sines formula and solve for side c:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{14}{\sin 110^{\circ}}=\dfrac{c}{\sin 32.8367482...^{\circ}}[/tex]
[tex]\implies c=\dfrac{14\sin 32.8367482...^{\circ}}{\sin 110^{\circ}}[/tex]
[tex]\implies c=8.07866414...[/tex]
[tex]\implies c=8.1[/tex]
[tex]\hrulefill[/tex]
Question 4Given values:
b = 21c = 13B = 110°Substitute the given values into the formula and solve for angle C:
[tex]\implies \dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{21}{\sin 110^{\circ}}=\dfrac{13}{\sin C}[/tex]
[tex]\implies 21 \sin C=13\sin 110^{\circ}[/tex]
[tex]\implies \sin C=\dfrac{13\sin 110^{\circ}}{21}[/tex]
[tex]\implies C=\sin^{-1}\left(\dfrac{13\sin 110^{\circ}}{21}\right)[/tex]
[tex]\implies C=35.5712205...^{\circ}[/tex]
[tex]\implies C=35.6^{\circ}[/tex]
As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies A=180^{\circ}-B-C[/tex]
[tex]\implies A=180^{\circ}-110^{\circ}-35.5712205...^{\circ}[/tex]
[tex]\implies A=34.4287794...^{\circ}[/tex]
[tex]\implies A=34.4^{\circ}[/tex]
Finally, substitute the values of b, B, and A into the Law of Sines formula and solve for side a:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]
[tex]\implies \dfrac{a}{\sin 34.4287794...^{\circ}}=\dfrac{21}{\sin 110^{\circ}}[/tex]
[tex]\implies a=\dfrac{21\sin 34.4287794...^{\circ}}{\sin 110^{\circ}}[/tex]
[tex]\implies a=12.6349923...[/tex]
[tex]\implies a=12.6[/tex]
Given 1 || m ||
|| n, find the value of x.
(x-6)⁰
60⁰
1
m
n
The value of x in the lines is 126 degree
We are given that;
Three parallel line and one intersecting line
Angles= (x-6) and 60
Now,
By supplementary angles property
Angle 1 + Angle 2 = 180 degree
Substituting the values of angles
x-6 + 60 = 180
x + 54 = 180
x = 180-54
x = 126
Therefore by supplementary angles answer will be 126 degree.
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pls help marking as brainlist
Answer:
138ft^2
Step-by-step explanation:
9x2=18
10x12=120
18+120=138ft^2
Given PU-UR, and the radius of the circle is 55, find x and UT.
10. x.
11. UT.
Show work
Answer:
10. x = 4
11. UT = 44
Step-by-step explanation:
You want the value of x and the length of segment UT that bisects chord PR at point U into halves marked UP = (9x -3) and UR = (7x +5). The radius of circle T is 55 units.
10. ChordPoint U is the midpoint of chord PR, so ...
UP = UR
9x -3 = 7x +5
2x = 8 . . . . . . . . . add 3-7x
x = 4 . . . . . . . . divide by 2
11. UTSegments UP, UT and TP form a right triangle with one leg ...
UP = 9(4) -3 = 33
and hypotenuse 55.
We observe that the ratio of these measures being 33/55 indicates triangle PUT is a 3-4-5 right triangle, with scale factor 11. That means UT is 4·11 = 44 units.
UT = 44 units
__
Additional comment
Recognizing triangles made from Pythagorean triples, such as {3, 4,5}, {5, 12, 13}, {7, 24, 25}, or {8, 15, 17} can save a lot of work. If you don't recognize these, you can find the missing side length from ...
TP² = UP² +UT²
UT = √(TP² -UP²) = √(55² -33²) = √1936 = 44
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Elijah wraps a gift box in the shape of a right rectangular prism. The figure below shows a net for the gift box.How much wrapping paper did he use, in square meters?
The amount of wrapping paper which Elijah used is equal to 812 m².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a right rectangular prism, we have the following;
Surface area of a right rectangular prism = 2[3 × 10 + (10 × 12 × 2) + (13 × 12 × 2)]
Surface area of a right rectangular prism = 812 m².
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
sin 78° find the value
Answer:
Approx. 0.2079
Step-by-step explanation:
To find the value of sin 78°, we can use a scientific calculator or a trigonometric table. However, I can provide an approximate value using the trigonometric identity:
sin(90° - θ) = cos(θ)
In this case, we can use the identity sin(90° - 78°) = cos(78°). Since the cosine of 78° can be determined more easily, we can calculate that instead.
cos 78° ≈ 0.2079
Therefore, sin 78° is approximately equal to 0.2079.
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (negative 4) = 7
Negative 5 + x = negative 2
All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
We have to given that;
All expressions are,
2 + x = 5
x + 1 = 4
9 + x = 6
x + (-4) = 7
-5 + x = -2
Now, We can simplify all the expressions as;
⇒ 2 + x = 5
⇒ x = 5 - 2
⇒ x = 3
⇒ x + 1 = 4
⇒ x = 4 - 1
⇒ x = 3
⇒ 9 + x = 6
⇒ x = 6 - 9
⇒ x = - 3
⇒ x + (-4) = 7
⇒ x = 7 + 4
⇒ x = 11
⇒ -5 + x = -2
⇒x = - 2 + 5
⇒ x = 3
Thus, All the equations which are equivalents are,
⇒ 2 + x = 5
⇒ x + 1 = 4
⇒ Negative 5 + x = negative 2
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pls help, due today!
Answer:
A: Function 1
B: Function 4
C: Function 2
Explanation A:
In order to solve this problem, you will have to find the slope for each function.
1st Function: For the first function, you will need to find 2 points, let's use (0, -4) and (1, 1). Remember slope is rise over run, so you would count the spaces from the first point to the second, it rises (y-axis) 5 points and runs (x-axis) 1 point. Which would give you 5/1 = 5. Function 1's slope is 5.
2nd Function: Same equation, rise over run, or y over x, so we need to find the pattern on each side. For the x-values, we can see starting from the first point that they increase by one, -2 to -1 to 0, and for the whole x-values, so 1 will be our run, since it is the x-value. For the rise, or y-values, we can see a pattern of -1 starting from the top going towards the bottom. Now, we can rise over run, -1/1 = -1
3rd Function: Slope is -4, as the equation is y = mx + b, and m stands for slope.
4th Function: Says slope is 2.
Now that we know all the slopes, we can see that Function 1's slope is the greatest.
Explanation B:
For this problem, we will have to find the y-intercept for all the functions, this means where the x-value is 0, so that the y-value will be right on the y-axis.
Function 1: We can see that the function intercepts the y-axis at (0, -4), it's y-intercept being -4.
Function 2: Where the x-value is 0, we can find the y-intercept, which is (0, 1). Making the y-intercept 1.
Function 3: Following the y = mx + b format, the b is the y-intercept, so it is -2.
Function 4: Gives you the y-intercept as 5.
In the end, the only function with a y-intercept greater than 4 is Function 4.
Explanation C:
Since we already know the y-intercepts from the previous problem, we only need to see which one is closest to 0. In this case, it would be Function 2 with a y-intercept at -1, only 1 unit off of 0, making it the closest.