Question 5What is the measure of the missing angle?

Triangle with two of its angles measuring 125 degrees and 42 degrees.

42°

125°

13°

3°

Answers

Answer 1

Answer: a triangles interior angles always add up to 180 degrees, so you add 125 and 42 and you get 167, then you do 180 minus 167 and you get 13

Answer 2

Answer: 125 hope this helps :) XOXO

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Use the given data to find the minimum sample size required to estimate a population proportion or percentage. Margin of error: seven percentage points, confidence level 95%, from a prior study,^p is estimated by the decimal equivalent of 42%n=_____ (round to the nearest integer.)

Answers

Answer: 191

Step-by-step explanation:

Formula to find the minimum sample size required to estimate a population proportion or percentage:

$n= \hat{p}(1-\hat{p})((z^*)/(E))^2$

, where $\hat{p}$ = proportion estimated by prior study.

E= Margin of error.

z* = Critical z-value.

Given : Confidence level = 95%

Critical value for 95% confidence = z*=1.96

$\hat{p}=\ 42\%=0.42$

E= 7%= 0.07

Then, $n= 0.42(1-0.42)((1.96)/(0.07))^2$

$n= 0.42(0.58)(28)^2$

$n= 0.2436(784)=190.9824approx191$

Hence, the minimum sample size required=191

Which expression is equivalent to 4^ 5x4^ -7÷4 ^-2?4^ -4

4^ 0

4^ 5÷4^9

(4^5)(4^-2)/4^-7

Answers

The equivalent value of the exponential equation is A = 4⁰ = 1

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = ( 4⁵ x 4⁻⁷ ) / ( 4⁻² )

Now , from the laws of exponents , we get

m⁻ᵃ = ( 1 / mᵃ )

So , A = ( 4⁵ x 4⁻⁷ ) x 4²

And , mᵃ×mᵇ = mᵃ⁺ᵇ

On further simplification , we get

A = 4⁵⁺²⁻⁷

A = 4⁰

A = 1

Hence , the exponential equation is solved

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Limit of x^2-81/x+9
As x goes toward -9

Answers

Hello,

Use the factoration

a^2 - b^2 = (a - b)(a + b)

Then,

x^2 - 81 = x^2 - 9^2

x^2 - 9^2 = ( x - 9).(x + 9)

Then,

Lim (x^2- 81) /(x+9)

= Lim (x -9)(x+9)/(x+9)

Simplity x + 9

Lim (x -9)

Now replace x = -9

Lim ( -9 -9)

Lim -18 = -18
_______________

The second method without using factorization would be to calculate the limit by the hospital rule.

Lim f(x)/g(x) = lim f(x)'/g(x)'

Where,

f(x)' and g(x)' are the derivates.

Let f(x) = x^2 -81

f(x)' = 2x + 0
f(x)' = 2x

Let g(x) = x +9

g(x)' = 1 + 0
g(x)' = 1

Then the Lim stay:

Lim (x^2 -81)/(x+9) = Lim 2x /1

Now replace x = -9

Lim 2×-9 = Lim -18

= -18

The productivity of workers at a shoe factory (in pairs of shoes per hour) can be modeled using the function p(h) = -2/7h + 5, where h is the number of hours. If a worker must create at least 3 pairs of shoes per hour for the company to be profitable, how long should the worker's shift be?

Answers

Answer:

no more than 7 hours

Step-by-step explanation:

You want p(h) ≥ 3, so ...

p(h) ≥ 3

-2/7h +5 ≥ 3

2 ≥ 2/7h . . . . . . add 2/7h -3

7 ≥ h . . . . . . . . . multiply by 7/2

The worker's shift should be 7 hours or less.

Final answer:

The equation is solved by equating it to 3 and solving for h (hours). It results in a maximum work shift of 7 hours to maintain an average productivity of at least 3 pairs of shoes per hour.

Explanation:

The question deals with a linear function that models the productivity rate of workers in a shoe factory. The function is p(h) = -2/7h + 5 which presents the productivity (p) in pairs of shoes per hour, depending on the hours worked (h). If the company requires a minimum productivity of 3 pairs of shoes per hour to stay profitable, we want to find the maximum value of h such that p(h) is equal to or greater than 3.

To solve, equate the function to 3, that is: 3 = -2/7h + 5. By simplifying, you obtain: -2/7h = 3 - 5 = -2. Then, divide both sides by -2/7, we get h = -2 / (-2/7) = 7 hours.

Therefore, for the company to stay profitable, the worker's shift should not exceed 7 hours.

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Joe solved this linear system correctly. 6x + 3y =6
y = -2x + 2
These are the last two steps of his work.
6x - 6x + 6 = 6
Which statement about this linear system must be true?

A: x must equal 6
B: y must equal 6
C: There is no solution
D: There are infinitely many solutions to this system

Answers

Since 6x-6x = 0, any number could be used as x to equal 0. The answer is D

Answer:

the answer will equal d

Step-by-step explanation:

In a recent survey it was found that Americans drink an average of 23.2 gallons of bottled water in a year. If the standard deviation is 2.7 gallons and the variable is normally distributed, find the probability that a randomly selected American drinks more than 25 gallons of bottled water in a year. What is the probability that the selected person drinks between 22 and 30 gallons

Answers

Answer:

a) 0.25249

b) 0.66575

Step-by-step explanation:

We solve this question using z score formula

= z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 23.2 gallons

σ is the population standard deviation = 2.7 gallons

a) Find the probability that a randomly selected American drinks more than 25 gallons of bottled water in a year.

For x = 25 gallons

z = 25 - 23.2/2.7

z = 0.66667

Probability value from Z-Table:

P(x<25) = 0.74751

P(x>25) = 1 - P(x<25)

1 - 0.74751

= 0.25249

The probability that a randomly selected American drinks more than 25 gallons of bottled water in a year is 0.25249

2) What is the probability that the selected person drinks between 22 and 30 gallons

For x = 22 gallons

z = 22 - 23.2/2.7

z = -0.44444

Probability value from Z-Table:

P(x = 22) = 0.32836

For x = 30 gallons

z = 30 - 23.2/2.7

z =2.51852

Probability value from Z-Table:

P(x = 30) = 0.99411

The probability that the selected person drinks between 22 and 30 gallons is

P(x = 30) - P(x = 22)

= 0.99411 - 0.32836

= 0.66575

Final answer:

The probability that a randomly selected American drinks more than 25 gallons of bottled water in a year is approximately 0.2514, while the probability that they will drink between 22 and 30 gallons is approximately 0.6643.

Explanation:

This is a statistics question about probability distribution, specifically, normal distribution. You need to find the z-scores and use the standard normal distribution table to find the probabilities.

The average or mean (μ) consumption is 23.2 gallons and standard deviation (σ) is 2.7 gallons.

First, we use the z-score formula: z = (X - μ) / σ

To find out the probability that a selected American drinks more than 25 gallons annually, we substitute X = 25, μ = 23.2 and σ = 2.7 into the z-score formula to get z = (25 - 23.2) / 2.7 ≈ 0.67. Z value of 0.67 corresponds to the probability of 0.7486 in standard normal distribution table, but this is the opposite of what we want. We need to subtract this probability from 1 to find the probability that a person drinks more than 25 gallons annually. So 1 - 0.7486 = 0.2514.

Second, to find the probability an individual drinks between 22 and 30 gallons, we calculate two z-scores: For X = 22, z = (22 - 23.2) / 2.7 ≈ -0.44 with corresponding probability 0.3300, and for X = 30, z = (30 - 23.2) / 2.7 ≈ 2.52 with corresponding probability 0.9943. We find the probability of someone drinking between these quantities by subtracting the smaller probability from the larger, 0.9943 - 0.3300 = 0.6643.