Explain why the two triangles below are similar by writing the appropriate similarity theorem. Then find x. Round your answer to the nearest tenth. (example answer ---> SSS,9.2 ---> no spaces)
Answers
Answer:
SSS Theorem
[tex]x = 35.7[/tex]
Step-by-step explanation:
Given
The attached triangle
Solving (a) The similarity theorem
The given sides of the triangle are similar.
In other words, they are similar by sides.
Hence, the theorem is: SSS
Solving (b): Find x
To find x, we make use of the following equivalent ratios.
[tex]\frac{14}{25} = \frac{14+6}{x}[/tex]
This gives:
[tex]\frac{14}{25} = \frac{20}{x}[/tex]
Cross multiply
[tex]14 * x = 20 * 25[/tex]
[tex]14 * x = 500[/tex]
Solve for x
[tex]x = \frac{500}{14}[/tex]
[tex]x = 35.7[/tex] -- approximated
Related Questions
A certain brand of candies have a mean weight of 0.8616g and a standard deviation of 0.0518 based on the sample of a package containing 447 candies. The package label stated that the net weight is 381.8g If every package has 447 candies the mean weight of the candies must exceed 381.8/447=0.8542 for the net contents to weight at least 381.8g.
a) If 1 candy is reandomly selected, find the probability that it weights more than 0.8542g.
The probability is ________.
(round to four decimal places as needed)
b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.
the probability that a sample of 447 candies will have a mean of 0.8542g or greater is __________.
(round to four decimal places as needed)
c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Answers
Answer:
a) The probability is 0.5557 = 55.57%.
b) The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.
c) Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean weight of 0.8616g and a standard deviation of 0.0518
This means that [tex]\mu = 0.8616, \sigma = 0.0518[/tex]
a) If 1 candy is reandomly selected, find the probability that it weights more than 0.8542g.
This is 1 subtracted by the pvalue of Z when X = 0.8542. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.8542 - 0.8616}{0.0518}[/tex]
[tex]Z = -0.14[/tex]
[tex]Z = -0.14[/tex] has a pvalue of 0.4443
1 - 0.4443 = 0.5557
The probability is 0.5557 = 55.57%.
b) If 447 candies are reandomly selected find the probability that their mean weight is at least 0.8542 g.
Sample of 447 means that [tex]n = 447, s = \frac{0.0518}{\sqrt{447}} = 0.00245[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8542 - 0.8616}{0.0245}[/tex]
[tex]Z = -3.02[/tex]
[tex]Z = -3.02[/tex] has a pvalue of 0.0013
1 - 0.0013 = 0.9987
The probability that a sample of 447 candies will have a mean of 0.8542g or greater is 0.9987 = 99.87%.
c) Given these results does it seem that the candy company is providing consumers with the amount claimed on the label?
Yes, because there is a very large probability, of 99.87%, that the amount will be at least the one claimed on the label.
The original price of a mirror was priced at $15 but was on sale. The amount of the discount is $3. What percent is the discount of the mirror?
Answers
Answer:
20%
Step-by-step explanation:
You do 3 divided by 15 which is 0.2, or 20 percent.
The angle between the lines xy=0 is
(a) 00
(b) 60°
(c) 90°
(d) 120°
Answers
Answer:
(c) 90°
Step-by-step explanation:
Given
[tex]xy = 0[/tex]
Required
The angle between the line
First, solve for x and y
[tex]xy = 0[/tex]
[tex]x = 0[/tex] or [tex]y=0[/tex]
This means that: y axis and x axis
The angle between the two axes is 90 degrees
Hence: (c) is correct
Find the area (in square centimeters) of a regular pentagon
Answers
Answer:
Given
apothegm [a]=3.2cm
since Pentagon has 5 equal side
perimeter [P]=5×4.6=23cm
now
Area of regular pentagon
A=1/2 aP=1/2×3.2×23=36.8cm²
Order the angles in each triangle from smallest to largest
Answers
Answer:
<E, <F, <G
Step-by-step explanation:
4. Below are histograms displaying the values taken by three sample statistics in
several hundred samples from the same population. Each histogram has the
same scale and the true value of the population parameter is marked by an
arrow on each histogram. Which statistic is the best estimator of the parameter?
Answers
Answer:
(B) Statistic B because A and B are unbiased but B has lower variability.
Step-by-step explanation:
The correct answer is (B). The best statistic is unbiased, with the lowest variability.
A probability calculator is required on this problem; answer to six decimal places. Suppose we will flip a fair coin 100 times. Using a calculator, find the probability of getting between 42 and 58 heads (inclusive) in two ways: By a Normal approximation: 0.910869 Exactly: 0.920609 How far off is the Normal approximation
Answers
Answer:
0.910870.911374 0.000504Step-by-step explanation:
Number of toss ( n ) = 100
probability of a head in 1 toss ( p ) = 0.5
Hence : np = 100 * 0.5 = 50 > 5, also n( 1-p) = 50 > 5
mean value ( μ ) = np = 50
std = √ n(p)(1-p) = √100(0.5)(0.5) = 5
Using Normal approximation
P( 42 ≤ x ≤ 58 ) = P ( 42-0.5 ≤ x ≤ 58 + 0.5 )
= P( (41.5 - 50) / 5 < Z < (58.5 - 50) / 5 )
= P ( -1.7 < Z < 1.7 )
= 0.91087
Using Calculator to get the exact value
P( 42 ≤ x ≤ 58 ) = 0.911374
How far off is the Normal distribution (Absolute value of error )= | 0.911374 - 0.91087 | = 0.000504
Triangles ABC and XYZ are shown below. A student knows that AX and 2cm 22. The student claims that AABC is similar to AXYZ
Determine whether each statement below can be used as part of a justification for the claim that ABC is similar to AXYZ Select Yes or No for each statement.
Yes No
AC
A dilation of AABC by scale factor k =
through center results in A4'B'C where A'C = XZ
Triangle A'B'C, which results from a dilation of ABC such that A'c = XZ, is congruent to AXY2 by Angie-Side-Angle (ASA) O
There exists a sequence of rigid transformations and dilations that carries A4BC to AXYZ, so it follows that AABC is similar to AXYZ OO
Answers
sorry i couldn't answer tho
What’s the answer please help me no links at all if you do I will report
Answers
Answer: 78
Step-by-step explanation:
in the diagram, AB=18. find AC and BC
Answers
Answer:
b
Step-by-step explanation:
In a 30-60-90 right triangle, the hypotenuse is twice the length of the short leg.
The hypotenuse is AB and is 18.
The short leg is BC and is 9.
The only choice with BC = 9 is b.
Answer: b
What is 140% of 60
Pls help I need help pls pls pls pls pls pls
Answers
Answer:
84
Step-by-step explanation:
To calculate how much 140% of 60 does we need to multiply 60 with 140 then divide it by 100
60 x 140 ÷ 100 = 84
what are 2 challenges that Will Smith faced
Answers
Answer:
Will Smiths wife cheated on him!
Step-by-step explanation:
You are standing on the ground (height of 0) and kick a ball across the park with an initial velocity of 64 feet per second. Using the vertical motion model, calculate each of the following: Don't forget units
a. What is the highest height the ball reaches?
b. When will the ball be at the highest height?
c. How long is the ball in the air?
I need this question to be answered it's 30 points and please no links just leave the answer
Answers
Can someone help me pls
Answers
I think the answer is B) Find m (arc DC)
Add 7 by g then divide 10 by the result write an expression
Answers
Answer:
7 = 1 = 21
Step-by-step explanation:
Answer:
10 / (7 + g)
Step-by-step explanation:
the initial deposit into an account?
a. compound interest
b. simple interest
c. interest rate
d. principal
Answers
Answer:
B
Step-by-step explanation:
Simple interest is based on the principal amount of a loan or deposit.
As part of a holf-marathon route, Charlie
ron 4.1 miles east then 9 miles south. How
for is he from his starting points
Answers
Answer:
He is 9.9 miles far from his starting point.
Kym used the integer tiles to find the sum of (–3)+6.The line showed that the answer is negative 3.Which of the following does Kym need to do to get the correct answer
Answers
Answer:I need points
Step-by-step explanation:
adsfnsafasfj;ljfdksfas;lfkjdf;lksdfjsdlksfajf
Answer:
remove the zero pairs
so B
Step-by-step explanation:
What is the answer to this?
Answers
9514 1404 393
Answer:
$125 per car
Step-by-step explanation:
The problem statement tells you Jazmin's pay goes up by $125 for each car she sells. That rate of change is $125 per car.
Consider the equation below.
Determine which equation has the same solutions as the given equation.
Answers
Answer:
A) (x - 5)² = 36
Step-by-step explanation:
x² - 10x - 11 = 0
A) CORRECT
(x - 5)² = 36
x² - 10x + 25 = 36
x² - 10x + 25 - 36 = 0
x² - 10x - 11 = 0
Josie baked a cake and ate .6 of it. Express this decimal as a percent and as a fraction.
Answers
Step-by-step explanation:
Hi,
To write this answer as a percent, simply divide it by 10.
6/10 is the same thing as 60%.
As a fraction, it's 6/10.
As a percent it's 60%
I hope this helps :)
The volume of a pool should be measured using which of the following units?
cubic yards
cubic feet
square feet
gallons
Answers
Answer:
Square feet
Step-by-step explanation:
Hope this helped
The radius of a chord and a tangent line are_ at the point of tangency
Answers
Answer:
fine
cause of it's fine point of tangency
At a local college, an admissions officer wants to survey the incoming class of 500 first-year students concerning their preference of major. The officer randomly selects 100 of them to complete the survey, and finds that 45 are planning to major in liberal arts. The admissions officer uses the data to construct a 95% confidence interval for the proportion of first-year students who are planning on majoring in liberal arts. Are the conditions for inference met? Yes, the conditions for inference are met. No, the 10% condition is not met. No, the randomness condition is not met. No, the Large Counts Condition is not met.
Answers
Answer:
No, the 10% condition is not met.
Step-by-step explanation:
got it right on edge
Answer:
c
Step-by-step explanation:
Brainliest for correct answer
Answers
Answer:
I got 678.58401 but i think it is C. 648n cubic units
Step-by-step explanation:
The mean breaking strength of a ceramic insulator must be at least 10 psi. The process by which this insulator is manufactured must show equivalence to this standard. If the process can manufacture insulators with a mean breaking strength of at least 9.5 psi, it will be considered equivalent to the standard. A random sample of 50 insulators is available, and the sample mean and standard deviation of breaking strength are 9.32 psi and 0.21 psi, respectively. a. State the appropriate hypotheses that must be tested to demonstrate equivalence.
Answers
Answer:
H0: u ≥ 9.5
Ha: u < 9.5
Step-by-step explanation:
The null hypothesis and the alternate hypothesis are reverse of each other.
The claim is either set as the null or alternate hypothesis
The null hypothesis is : H0: u ≥ 9.5 the mean breaking strength of a ceramic insulator is at least 9.5 which is considered equivalent to the standard.
The alternate hypothesis is: Ha: u < 9.5 the mean breaking strength of a ceramic insulator is less than 9.5 which is not considered equivalent to the standard.
7 over 6 divided by 4
Answers
Answer:
0.29
Step-by-step explanation:
I used a calculator
What is the volume of a sphere with the diameter = 10 cm and the height = 200 cm
Answers
the answer is 4,188.8 cubic centimeters
2b + 8 =? I don't know this one either
Answers
Hope this helped
The trapezoid below is formed from two triangles and a rectangle. What is the area of the trapezoid?
9 cm
3 cm
6 cm
3 cm
A 81 cm 2
B 108 cm 2
C 67.5 cm 2
D 54 cm 2
Answers
Answer:
A. 81 cm^2
Step-by-step explanation:
9*6 = 54
9*3 = 27
54+27 = 81