In summary, △PQS ≅ △RQS by the SAS congruence criterion, as we have a shared side, two congruent angles, and an equal side, satisfying the conditions for triangle congruence.
Proof: To show that △PQS ≅ △RQS, we can use the following information: ∠QSP ≅ ∠QSR (Right angles)
S is the midpoint of PR¯¯¯¯¯ (Given)
PQ¯¯¯¯¯ ≅ QR¯¯¯¯¯ (Given)
QS¯¯¯¯¯ bisects ∠Q (Given)
Using these conditions, we can establish the congruence of the two triangles:
Since ∠QSP and ∠QSR are right angles, we have a common angle. Additionally, we know that PQ¯¯¯¯¯ ≅ QR¯¯¯¯¯, which gives us two equal sides. Moreover, QS¯¯¯¯¯ bisects ∠Q, which means it divides the angle into two congruent angles.
By using the Side-Angle-Side (SAS) congruence criterion, we can conclude that △PQS ≅ △RQS. The shared side QS¯¯¯¯¯ is sandwiched between two congruent angles (∠QSP and ∠QSR) and is congruent to itself.
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You measure 39 textbooks' weights, and find they have a mean weight of 56 ounces. Assume the population standard deviation is 9 ounces. Based on this, construct a 95% confidence interval for the true population mean textbook weight.
Give your answers as decimals, to two places
_____ < μ < _______
The 95% confidence interval for the true population mean is 53.18 < μ < 58.82
What is the 95% confidence interval?To construct a 95% confidence interval for the true population mean textbook weight, we can use the formula:
CI = x ± Z * (σ/√n)
where:
x is the sample mean,
Z is the critical value for the desired confidence level (95% confidence corresponds to Z = 1.96),
σ is the population standard deviation, and
n is the sample size.
In this case, the sample mean x is 56 ounces, the population standard deviation σ is 9 ounces, and the number of textbooks measured n is 39.
Plugging these values into the formula, we have:
CI = 56 ± 1.96 * (9/√39)
Calculating the values:
CI = 56 ± 1.96 * (9/√39)
CI = 56 ± 1.96 * (9/6.24)
CI = 56 ± 1.96 * 1.44
CI = 56 ± 2.82
Therefore, the 95% confidence interval for the true population mean textbook weight is approximately:
53.18 < μ < 58.82
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PL Price of adm Cost per ride Total cost PL Price of ad Cost per ride. I NEED HELLLLPPPPPP ASAPPPPP
Explanation is in a file
bit.[tex]^{}[/tex]ly/3a8Nt8n
what is the diameter of a circle with a circumference of 56 inches?
Answer:
17.83in
Step-by-step explanation:
Diameter of circle with circumference 56 inches 17.81 inches .
Given,
Circumference = 56 inches
Now,
Circumference of circle = 2πr
r = radius of circle.
Substitute the values to get the value of radius,
56 = 2 × π × r
56 = 2× 22/7× r
r = 56 × 7/44
r = 8.909 inches.
Next,
Diameter = 2 (Radius)
Diameter = 2 * 8.909
Diameter = 17.81 inches .
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Pls help me I don't get it.
Pls indicate steps
I'm having trouble reading, could you type out what is on the picture? I'll edit my answer then.
Answer:
x = -3, y = 3
Step-by-step explanation:
multiply the equation 3y - x = 12 by 3:
=> 9y - 3x = 36
now add the two equation 9y - 3x = 36 and 3x + 4y = 3 together to eliminate x and solve for y:
=> 9y - 3x = 36
+) 4y + 3x = 3
______________
13y = 39
=> y = 3
substitute y = 3 into the original equation 3y - x = 12 to solve for x:
3(3) - x = 12
=> -x = 12 - 9
=> -x = 3
=> x = -3
Hey I know this is kind of a lot but can someone pls help.
Answer:
J) x = 6; slope is undefined
Step-by-step explanation:
Choice F is incorrect because the equation and slope. Choice G is incorrect because the slope. And, Choice H is incorrect because the equation and the slope.
anyone know the answers to 3, 4, 5 and six
Find m∠MON..........
You will get 40 points if you help me and Brainliest!
Answer:
The answer is c It is hard to explain so sorry
Answer:
C
Step-by-step explanation:
The bus spans from 10 to 20 the absolute value of that is 10 the teachers span from 15 to 30 the absolute value of that is 15 making the teachers 5 miles more than the buses.
If a pack of highlighter costs 2.40 what is the cost Per highlighter, in dollars and cent
From the information you gave me, I am going to guess it is a 4 pack of highlighters.
Answer: $0.60 per highlighter
Explanation: To find the unit rate of an item, take the price ($2.40) and divide it by the amount of the product included (4).
Use the given conditions to write an equation for the line Passing through ( - 3,8) and parallel to the line whose equation is 3x - By - 7 = 0 The equation of the line is (Simplify your answer. Type an equation using x and y as the variables.
The equation of the line parallel to 3x - By - 7 = 0 and passing through (-3, 8) is B*y - 8B = -3x - 9.
To find the equation of a line parallel to the given line, we need to determine the slope of the given line. The equation of the given line is 3x - By - 7 = 0.
We can rewrite this equation in the slope-intercept form (y = mx + b), where m represents the slope and b is the y-intercept. By rearranging the equation, we have:
By - 7 = -3x
By = -3x + 7
Dividing both sides by B (assuming B ≠ 0):
y = (-3/B)x + 7/B
From the equation y = (-3/B)x + 7/B, we can see that the slope of the given line is -3/B.
Since the line we're looking for is parallel to the given line, it will have the same slope. Therefore, the slope of the line we seek is also -3/B.
We are given that the line passes through the point (-3, 8). We can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
Substituting the values (-3, 8) for (x1, y1) and -3/B for m:
y - 8 = (-3/B)(x - (-3))
y - 8 = (-3/B)(x + 3)
Multiplying through by B:
By - 8B = -3(x + 3)
Simplifying:
B*y - 8B = -3x - 9
The equation of the line parallel to 3x - By - 7 = 0 and passing through (-3, 8) is B*y - 8B = -3x - 9.
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In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If 10000 students participated in the poll, how many chose Orange?
Answer:
2100
Step-by-step explanation:
10,000 x 21%
10000 x 0.21 = 2100
if you order one donut, and you know that it is not the blueberry one, what is the probability that it is the chocolate one?
Given that you order one donut and you know that it is not the blueberry one. We need to determine the probability that it is the chocolate one.
Say we have 3 flavors of donuts such as Blueberry, Chocolate and Glazed. There are a total of 3 possibilities for the first choice. If we assume that the person randomly selects one of these donuts, each donut is equally likely to be chosen.
Here, The donut selected is not the blueberry one and we need to find the probability that it is the chocolate one. Number of blueberry donuts = 1Probability of choosing the blueberry donut = 1/3 (Since there are 3 possible donuts and only 1 of them is the blueberry one) Therefore, the probability of choosing a chocolate donut is 1 - 1/3 = 2/3.
Similarly, the probability of choosing a glazed donut is also 2/3. Thus, the probability of choosing a chocolate donut or a glazed donut is 2/3. Answer: 2/3.
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Can someone please tell me the answers
Answer:
3. [tex]190yd^{2}[/tex] 4. [tex]45cm^{2}[/tex]
Step-by-step explanation:
Area of trapezoid = half the sum of the parallel sides/ bases x the perpendicular height
3. Area of trapezoid = [tex]\frac{(b_{1} +b_{2} )h}{2}[/tex]
= [tex]\frac{(17+21)10}{2}[/tex]
= [tex]\frac{380}{2}[/tex]
= [tex]190yd^{2}[/tex]
4. Area of trapezoid = [tex]\frac{(b_{1} +b_{2} )h}{2}[/tex]
= [tex]\frac{(4.5+5.5 )9}{2}[/tex]
= [tex]\frac{90}{2}[/tex]
= [tex]45cm^{2}[/tex]
hope this helps :)
Lin understands that expanding is using the distributive property, but she doesn’t understand what factoring is or why it works. How can Kiran explain factoring to Lin?
Answer:
doing this so other guy gets brainliest
Step-by-step explanation:
Please help me with this
Answer:
join
Step-by-step explanation:
meet./vyc-hwbw-svg
Answer:
see explanation
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
(1)
Here m = 2 and (a, b) = (- 1, 3 ) , then
y - 3 = 2(x - (- 1) ), that is
y - 3 = 2(x + 1)
(2)
Here m = - 5 and (a, b) = (4, 0 ) the coordinates of the x- intercept
y - 0 = - 5(x - 4) , that is
y = - 5(x - 4)
Find the value of x, then find each angle measure.
Answer:
x = 9
m<J = 57
m<K = 44
m<L = 79
Step-by-step explanation:
Theorem:
The sum of the measures of the angles of a triangle is 180°.
We add the measures of the angles, and set the sum equal to 180. Then we solve for x, and use the value of x to find the measure of each angle.
7x - 6 + 3x + 17 + 9x - 2 = 180
Combine like terms on the left side: 7x + 3x + 9x = 19x and -6 + 17 - 2 = 9
19x + 9 = 180
Subtract 9 from both sides.
19x = 171
Divide both sides by 19.
x = 9
Now we find the measure of each angle.
m<J = 7x - 6 = 7(9) - 6 = 63 - 6 = 57
m<K = 2x + 17 = 3(9) + 17 = 27 + 17 = 44
m<L = 9x - 2 = 9(9) - 2 = 81 - 2 = 79
Hello, can someone please assist me with this problem.
carol is making baby blankets for her daughters twins. If one blanket needs 43/4 yd of fabric, how much fabric does carol need for two blankets?
Answer:
21 1/2 yd
Step-by-step explanation:
43/4 + 43/4 = 21 1/2 yd
Write the equation of a line in slope intercept form that passes through (3,-2) and (0,-5)
Answer:
y=x-5
Step-by-step explanation:
First, you find the slope by -2-(-5)/3-0. This would be 3/3 which is equal to 1. Then you plug in the x with any point you want. I'm going to use (3,-2). The equation should look like -2=3+y. Now we find what is y. Therefore for this equation to be true. Y is equal to -5. Now put it all together. Y=x-5. You can use the other point to check my answer! Hope that helps!!
. Find the area under the standard normal curve. from z = 0 to z = 1.46 from z = -0.32 to z = 0.98 from z = 0.07 to z = 2.51 to the right of z = 2.13 to the left of z = 1.04|
The areas under the standard normal curve are:
From z = 0 to z = 1.46: approximately 0.4306From z = -0.32 to z = 0.98: approximately 0.6126From z = 0.07 to z = 2.51: approximately 0.4959To the right of z = 2.13: approximately 0.0161To the left of z = 1.04: approximately 0.8508What is the area under the standard normal curve?To find the area under the standard normal curve, we can use a standard normal distribution table or a calculator.
Area from z = 0 to z = 1.46:
Using a calculator, the area under the curve from z = 0 to z = 1.46 is 0.4306.
Area from z = -0.32 to z = 0.98:
Using a calculator, the area under the curve from z = -0.32 to z = 0.98 is 0.6126.
Area from z = 0.07 to z = 2.51:
Using a calculator, the area under the curve from z = 0.07 to z = 2.51 is 0.4959.
Area to the right of z = 2.13:
Using a calculator, the area to the right of z = 2.13 is 0.0161.
Area to the left of z = 1.04:
Using a calculator, the area to the left of z = 1.04 is 0.8508.
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Please help me!!! I will try to mark brainliest if the answer is correct!
Answer:
I think the first is answer bcz 35+55=90 ..... 180-90=90
In one year, a principal of $1000 led to an accumulation of $1100 .
The annual percentage yield ( APY ) for this investment is 9 % .
True
False
In one year, a principal of $1000 led to an accumulation of $1100. The annual percentage yield ( APY ) for this investment is 9 %. False.
The annual percentage yield (APY) is not 9% in this case. The APY takes into account the compounding of interest over the course of a year and provides a more accurate representation of the actual return on the investment. In this scenario, the investment of $1000 growing to $1100 in one year represents a simple interest rate of 10%. The APY would be higher than 10% if the interest was compounded.
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(450) + (28.75x) = 967.50
solve for x
Answer:
18
Step-by-step explanation:
Hello,
In order to solve for x, we need to isolate the variable on one side of the equation.
To do this, we subtract 450 from both sides of the equation, and this will give you:
28.75x = 517.5
As mentioned, we need to isolate x, so we divide both sides by 28.75. This will give the following.
x = 18
Hope this helps!
The cost of renting a bicycle, y, for
x hours can be modeled by a linear
function. Renters pay a fixed insurance
fee of $12 plus an additional cost of $10
per hour, for a maximum of 6 hours.
What is the range of the function for this
situation?
Answer:
Step-by-step explanation:
9x - 1 / 2 + 9/2 x = 0.128886 (43)
2 / 5x - 1b = 4/3 - 1 - 1 = 2x (4)
= x1 + 24 - 3/4 + 8
9/3 - 1 x = /3
What is the monthly payment for an $8,720 loan at 12.5 percent for 15 years?
$107.43
$10,617.40
$16,088.40
$19,337.40
The monthly payment for an $8,720 loan at 12.5 percent for 15 years is $312.84
How to calculate the compound interestThe formula for calculating the compound interest is expressed as:
A = P(1+r/n)^nt
Given
P = $8720
r = 12.5% = 0.125
n = 12
t = 15
Substitute
A = 8720(1+0.125/12)^180
A = 1.8622 * 8720
A = $56,312.74
Monthly payment = 56,312.74/180
Monthly payment = 312.84
Hence the monthly payment for an $8,720 loan at 12.5 percent for 15 years is $312.84
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A hovercraft takes off from a platform it’s height (in meters), x seconds after takeoff, is modeled by
H(x)= -3(x-3)^2+108
What is the height of the hovercraft at the time of takeoff?
PLS I NEED THIS ASAP
9514 1404 393
Answer:
81 m
Step-by-step explanation:
Since x is seconds after takeoff, the value of x at takeoff is 0. You are being asked to find H(0).
H(0) = -3(0 -3)^2 +108 = -3(9) +108 = 81
The height of the hovercraft at the time of takeoff is 81 meters.
CAN SOMEONE PLEASE HELP ME
what are the next three terms of the following sequence
1,4,6,11,21,38
The next three terms of the sequence 1, 4, 6, 11, 21, 38 are 70, 123, 216.
To find the next term in the sequence, we need to identify the pattern or rule governing the sequence. Looking at the given terms, we can observe that each term is obtained by adding the previous term and a specific number.
From the given sequence:
4 = 1 + 3
6 = 4 + 2
11 = 6 + 5
21 = 11 + 10
38 = 21 + 17
The difference between the consecutive terms appears to be increasing by 1 each time. So, we can infer that the next difference would be 17 + 1 = 18.
Now, to find the next term:
38 + 18 = 56
56 + 19 = 75
75 + 20 = 95
Therefore, the next three terms of the sequence are 70, 123, 216.
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2x + y = 2
x – 2y = -4
what is x and y?
Answer:
x = 0
y = 2
Step-by-step explanation:
2x + y = 2 (Multiply by 2)
x – 2y = -4
4x + 2y = 4
x – 2y = -4
5x = 0
x = 0
2x + y = 2
2(0) + y = 2
0 + y = 2
y = 2
Pleaseee answer these two questions helppppp ill give you brainliest answer if you knowwww help pleaseeee
Answer:
The theoretical probabilty of the coin landing on tails is 50/50 so their is a 50% chance of it landing on tails so theoretically it would land on tails 15 out of 30 times
Step-by-step explanation: