the average hourly wage in the u.s. in september 2017 was $22.19. since the economy seemed to have contracted in october it is expected the hourly wage in october 2017 decreased. the correct null hypothesis for this problem is

The equation will be written as (42/2) = 21.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the quotient of a number, 2, and 21 is 42. The equation of the quotient will be written as,

42 / 2 = 21

Here the value 42 when divided by 2 will give 21.

Therefore, the equation will be written as (42/2) = 21.

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Answer:

15πcm

Step-by-step explanation:

2πr = circumference

radius = 0.075m = 7.5cm

Circumference = 7.5X2π

15π cm

Answer:

\(2 {x}^{2} - 8\)

hope it's helpful ❤❤❤

THANK YOU.

Answer:

2x² - 8

Step-by-step explanation:

Given

(x - 2)(2x + 4)

Each term in the second factor is multiplied by each term in the first factor, that is

x(2x + 4) - 2(2x + 4) ← distribute both parenthesis

= 2x² + 4x - 4x - 8 ← collect like terms

= 2x² - 8

Answer: 8w is greater than or equal to 40 and the final answer is 8w is greater than or equal to 5

Step-by-step explanation:

The first step was to write an inequality. You take the number of weeks, w, and multiple it by 8 which is the number of toy cars he buys each weak to get to 40 or more. So the inequality is 8w is greater than or equal to 40. Now you divide both sides of the inequality by 8 which gives us the answer w is greater than or equal to 5.

The least amount of weeks it will take Trenton to have at least 40 cars in his collection is 5.

Answer:

Each pound of peaches costs $2.25

Then we can define:

x = number of pounds someone buys

y = cost for the x peaches.

So if you buy x pounds of peaches, you will pay x times $2.25

Then we have the relation:

y = x*$2.25

If Greta buys 22 pounds, then we have x = 22

y = 22*$2.25 = $49.50

The cost of buying 22 pounds of peaches is $49.50

Answer:

ASA and it can be proven that the triangles are congruent

Step-by-step explanation:

The probability that a randomly chosen specimen has an acceptable hardness is 0.7887. 

The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3.

The specimen is acceptable only if its hardness is between 67 and 75.

We need to find the probability that a randomly chosen specimen has an acceptable hardness.

Given that the Rockwell hardness of a particular alloy is normally distributed with mean μ = 70 and standard deviation σ = 3.

Let X be the Rockwell hardness of the alloy.

Then, X ~ N(70, 3)

We need to find the probability that a randomly chosen specimen has an acceptable hardness, i.e.,

P(67 < X < 75) = P((67-70)/3 < (X-70)/3 < (75-70)/3)P(-1 < Z < 5/3)

Using a standard normal table, we get

P(-1 < Z < 5/3) = Φ(5/3) - Φ(-1) = 0.9474 - 0.1587 = 0.7887

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Answer:

i) 104 °F

ii) 343 °K

Step-by-step explanation:

We have the relationship between temperature in degrees Fahrenheit(y) and degrees Kelvin(x) as:

\(y\:=\:\dfrac{9}{5}\left(x-273\right)+32\)

i) When temperature in Kelvin is 313°K, the equivalent temperature in °F is:
\(\begin{aligned}y &= \dfrac{9}{5}(313-273) + 32\\& = \dfrac{9}{5}(40) + 32\\&= 9 \cdot 8 + 32\\\\&= 72 + 32\\\\& = 104^\circ F\end{aligned}\\\)

So at 313°K, the equivalent temperature is 104°F

\(====================================\)

ii) We are given the temperature in degrees Fahrenheit and asked to find the temperature in degrees Kelvin

We have the equation for temperature conversion from °K to °F  as:
\(y\:=\:\dfrac{9}{5}\left(x-273\right)+32\)

Let's manipulate this equation so that x is given in terms of y

Here x = degrees Kelvin and y = degrees Fahrenheit

Given y = 158°F, just plug in this value into the equation for x giving
\(\begin{aligned}x &= \dfrac{5}{9}(158 - 32) + 273\\& = \dfrac{5}{9}(126) + 273\\&= 70 + 273\\&= 343\end{aligned}\)

Therefore temperature in °K for temperature 158°F = 342 °K

Outliers might be explained by factors such as tornadoes in largely rural states causing less property damage or crop damage not being counted as property damage.

Tornado damage from 1950 to 1999, I would need to have access to the data from Table 1.5. However, I can guide you on how to analyze the data and answer the questions.

a) To find the top and bottom five states for tornado damage:

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Answer:

A) Rational

Step-by-step explanation:

0.275 is a rational number.

Answer:

Rational

Real

Step-by-step explanation:

A rational number in which the decimal doesn't repeat forever.

A real number is any number that isn't imaginary.

The number 0.275 checks those two categories.

An integer is a number that is not a fraction.

A natural number is any positive number that is not a decimal.

The number 0.275 does not check these two categories.

Best of Luck!

Answer: it is b

Step-by-step explanation:

Answer:

measure of angle E is 45 degrees because if you look closely then it is a

45, 45, 90 triangle, and so e is 45 degrees

Measure of c = 360-45+79+134 = 102 degrees

Step-by-step explanation:

The measures are 1) ∠ C = 101°, 2) ∠ Q = 89°, 3) ∠ M = 97°, 4) ∠ W = 34°, 5) x = 4 and 6) x = 13

A trapezoid, also known as a trapezium, is a flat-closed shape having 4 straight sides, with one pair of parallel sides. The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs.

Given that, the quadrilateral in the figure is a trapezoid, we need to find the asked measures,

We know that, trapezoids are having one pair of opposite side parallel, therefore, adjacent angles are supplementary,

1) ∠ C + ∠ F = 180°

∠ C = 180°-79° = 101°

2) ∠ T + ∠ Q = 180°

∠ Q = 180°-91°

∠ Q = 89°

3) JKLM is an isosceles trapezoid, therefore, opposite angle are supplementary,

∠ M + ∠ K = 180°

∠ M = 180°-83°

∠ M = 97°

4) WXYZ is an isosceles trapezoid, therefore, opposite angle are supplementary,

∠ Y + ∠ W = 180°

∠ W = 180°-146°

∠ W = 34°

5) ∠ S + ∠ V = 180°

14x-15 + 139 = 180

14x = 180-124

x = 4

6) ∠ A + ∠ B = 180°

9x+2+5x-4 = 180

14x-2 = 180

14x = 182

x = 13

Hence, the measures are 1) ∠ C = 101°, 2) ∠ Q = 89°, 3) ∠ M = 97°, 4) ∠ W = 34°, 5) x = 4 and 6) x = 13

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Answer:

1/2(AC) = A'C'

Step-by-step explanation:

IF Triangle ABC is 100% then, A'B'C' be 50% which is 1/2(AC) = A'C'

Answer:

1/2(AC) = A'C' Is gonna be the answer

Step-by-step explanation:

hope it helped

Answer:

Ivan got £90 more than Tanya.

Step-by-step explanation:

Ivan and Tanya share the amount £150 in the ratio of 4 : 1

Amount received by Ivan = \(150\times \frac{4}{(4+1)}\)

                                          = \(150\times \frac{4}{5}\)

                                          = £120

Similarly, amount received by Tanya = \(150\times \frac{1}{(4+1)}\)

                                                             = £30

Difference in their amounts = 120 - 30

                                              = £90

Therefore, Ivan got £90 more than Tanya.                                                                                                        

Let's call x to an unknown even integer. The next (consecutive) even integer will be x + 2. For instance, if x = 6, then the next even integer will be 6 + 2 = 8.

In consequence, the sum of two consecutive even integers is:

x + (x + 2)

Answer:

A. Sample space = 6

B. 0.17

C. No

D. Yes

Step-by-step explanation:

A. The sample space of an experiment is the set of all possible outcomes of that experiment.

since there are three colours and 2 outcomes for a coin toss,

sample space = 3 * 2 = 6

B. Probability of picking a green first = 4/12 = 1/3

probability of a tail = 1/2

Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17

C. No.

Considering the two events;

A; green card is picked first

C ; a green or red card is picked

There is an intersection point for the two events.  Therefore, they are not mutually exclusive.

D. Yes.

Considering the two events;

A; green card is picked first

B ; a blue or red card is picked

There is no intersection point for the two events. Therefore, they are mutually exclusive.

The numbers π, √8 , and 3.5 in the correct order from greatest to least is√8, π, 3.5 . we have the correct order: √8, π, 3.5. The correct answer is B

To determine the order, we need to compare the magnitudes of the numbers.
First, we compare √8 and π. The square root of 8 (√8) is approximately 2.83, while the value of π is approximately 3.14. Therefore, √8 is smaller than π.

Next, we compare π and 3.5. We know that π is approximately 3.14, and 3.5 is greater numbers than π.

Finally, we compare √8 and 3.5. Since 3.5 is greater than √8, we have the correct order: √8, π, 3.5.

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Answer:

  80/81

Step-by-step explanation:

Mental multiplication of fractions is often easier if factors common to the numerator and denominator are cancelled.

Here the numerator value of 76 in the first fraction cancels the denominator value of 76 in the second fraction. The remaining numerator factor is 80; the remaining denominator factor is 81, which is mutually prime with 80.

The product is 80/81.

Answer:

The answer should be 15 cans GD and 25 cans CH

Step-by-step explanation:

Answer:

\($ \frac{\text{13}}{\text{85}} $\)

Step-by-step explanation:

Given :

ΔRST is a right angled triangle with right angle at ∠RTS.

RT = 13, SR = 85 and TS = 84

We are required to find the ratio that represents the sine of angle RST.

Therefore, using trigonometric ratios, we know that :

\($\sin \angle RST = \frac{\text{perpendicular}}{\text{hypothenuse}} $\)

\($\sin \angle RST = \frac{\text{RT}}{\text{RS}} $\)

\($\sin \angle RST = \frac{\text{13}}{\text{85}} $\)

Therefore, the ratio that represents the sine of of ∠S is   \($ \frac{\text{13}}{\text{85}} $\) .

According to the given information Every 10th product in the line is selected.

Systematic sampling is a probabilistic strategy that includes selecting people from the general population at predetermined intervals, such as each 15th people on a list of the population. If the community is set up in a random order, this can replicate the benefits of simple random sampling.

Biased sample sizes and subpar survey results are reduced by systematic sampling. If there is a low chance that data will be manipulated: Data validity may be compromised if researchers rearrange a data set. The best strategy for surveys when there is little likelihood of data manipulation is systematic sampling.

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Answer:

345 miles per hour = 300 knots per hour

Step-by-step explanation:

k being knots

300 times 1.15

1.15 miles per hour for every 1 knot per hour

Based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

To determine the amount of capital this year based on the given information, we can use the investment and depreciation rates.

Let's denote the amount of capital this year as K1.

According to the information provided:

People invest 55% of income, but we don't have any information about income. Therefore, we cannot determine the exact investment amount.

10% of capital depreciates. Based on this, the capital at the beginning of this year (K1) can be calculated as follows:

K1 = K - 0.1K

= 0.9K

Since we know that the capital last year was equal to 25, we substitute K = 25 into the equation above:

K1 = 0.9 * 25

= 22.5

Therefore, based on the given information, the amount of capital this year (K1) could be something less than 25 (option c).

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The vertical height of pyramid is 3.6 cm.

Given that,

The base area of the pyramid is 5 cm², or 25 cm²

The formula V = (1/3) base area height can be used to determine the volume of a pyramid,

Where the solid's total height equals the sum of the cuboid and pyramid heights. T.

Let's abbreviate the pyramid's vertical height "h"

The height of the cuboid would thus be,

=  (1000g - 104.17gh)/(200g) or (1000g - (8g (25 h)/3))/(8 (5)²).

Therefore,

V = (1/3) 25cm2 h + 5cm (1000g - 104.17gh)/(8g/cm³ * (5cm)²)

It represents the solid's overall volume.

Given that we are aware that the solid has a mass of 1 kg (1000 g),

Adjust density times volume to equal mass:

8g/cm³ * V = 1000g

When we solve for V,

⇒V = 125cm3.

Solve for h by adding V to the previous equation and getting the following result:

h = (3(125cm³ 8g/cm³ - 5cm 1000g)/(25cm² 8g/cm³)

which can be expressed as h = 3.6 cm.

As a result, the pyramid has a 3.6 cm vertical height.

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Answer:

1.05 (0.2x + 1/2y + 0.75z)

Step-by-step explanation:

Finding the cost of each item :

1 Sweatshirt

2 T-shirts

1 Pair of Pants

Now, the final cost (after applying sales tax) is :

It is reasonable to say that the puppies can predict the winning basketball teams for the NCAA tournament the majority of the time.

Based on the given information, we need to choose the correct null and alternative hypothesis that determines if it is reasonable to say that puppies can predict the winning basketball teams for the NCAA tournament the majority of the time.

Null Hypothesis (H0): It is not reasonable to say that the puppies can predict the winning teams of the NCAA tournament the majority of the time. Alternative Hypothesis (Ha): It is reasonable to say that the puppies can predict the winning teams of the NCAA tournament the majority of the time.

To determine whether it is reasonable to say that puppies can predict a win the majority of the time, we need to perform the hypothesis test using the given data. Here, p = 347/652 = 0.5317 = 53.17%, which is the proportion of correct predictions. The sample size is 652, which is greater than 30, so we can use a normal distribution for the hypothesis test.

Let’s assume a significance level of α = 0.05. Therefore, the critical z-value for a two-tailed test is:

zα/2 = ±1.96.Z = (p - P) / √ (P (1 - P) / n)

Where, p = proportion of correct predictions = 0.5317 (from given data)

P = proportion of correct predictions assumed under null hypothesis = 0.5 (no significant difference)

n = sample size = 652Z = (0.5317 - 0.5) / √ [(0.5 × 0.5) / 652]= 2.23 (approx)

The calculated value of z is 2.23 which is greater than the critical value 1.96 at a 5% level of significance. Thus, we can reject the null hypothesis.

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a) One-tailed hypothesis defines a direction of an effect (it indicates either a positive or negative effect), whereas a two-tailed hypothesis does not make any specific prediction.

In one-tailed tests, a researcher has a strong belief or expectation as to which direction the result will go and wants to test whether this expectation is correct or not. If a researcher has no specific prediction as to the direction of the outcome, a two-tailed test should be used instead.

A Type I error is committed when the null hypothesis is rejected even though it is correct. A Type II error, on the other hand, is committed when the null hypothesis is not rejected even though it is false. The power of a test is its ability to detect a true difference when one exists. The more powerful a test, the less likely it is to make a Type II error. The more significant a difference is, the more likely it is that a test will detect it.

As a result, one-tailed tests are usually more powerful than two-tailed tests because they have a narrower area of rejection. The calculation step for the given set of data would be as follows:

z = (X-μ)/σ  

z = (80-90)/σ;

z = -1.645. From the Z table, the area is 0.05 to the left of z, and hence 0.05 is equal to 1.645σ.

σ = 3.14.

Therefore, the standard deviation is 3.14.

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Answer:

Triangle C

Step-by-step explanation:

Triangle A: All sides have length 9 cm.

By SSS this is a unique triangle.

Triangle B: Two sides have length 10 cm, and the included angle measures 60°.

By SAS this is a unique triangle.

Triangle C: Two angles measure 50°.

This gives us at most SS Similarity, so we do not have a unique triangle. The triangle sides can be any length. This is not unique.

Triangle D: Base has length 8 cm, and base angles measure 45°. Which triangle is not a unique triangle?

This gives us ASA, so we have a unique triangle.

Answer: Triangle C

Answer:

It is Triangle C.