Which criteria for triangle congruence allows you to immediately conclude that the triangles.

Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance.

The null hypothesis is accepted.

There is no significant difference between the attractiveness ratings given by the three groups of girls.

Surveyed two random samples of 390 men and 360 women who were tested.

first sample percentage,

p1 = 360 ÷ 390 = 0.9230

second sample percentage,

p2 = 47 ÷ 52 = 0.9030

There is no change, according to the null hypothesis the percentage of males who have positive tests is significantly from the percentage of women who have positive tests.

Different Hypotheses:

There is a discrepancy in the percentage of schoolgirls who heard about a male with stylish clothes, a great automobile, or a confident demeanor across the three groups that were randomly allocated.

Z = (p1 - p2) ÷ √(PQ((1 ÷ n1) + (1 ÷ n2)))

where

p = (n1p1 + n2p2) ÷ n1 + n2

p = 0.920

Z = (0.9230 - 0.9030) ÷ √(0.9230((1 ÷ 390) + (1 ÷ 52)))

Test statistic Z =  0.13008

Level of significance = 0.10

The critical value Z₀.₁₀ = 1.645

Test statistic Z=0.13008 < 1.645 at 0.1 level of significance

The null hypothesis is accepted.

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Speed the top of the ladder is sliding down = 1.6ft/sec  when it is 12 feet away from the wall

15-foot ladder is leaning against a wall.

the top of the ladder is sliding down the wall at a rate of 2 ft/sec.

how fast is the bottom of the ladder moving when it is 12 feet away

Using equivalent proportion

15 ft -------------------2ft/sec

12 ft-------------------X ft/sec

Hence X = (12 x 2) ÷ 15 =1.6 ft/sec

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For the given set G = {(-8, 7), (-9, 0), (3, 7)}, domain is {-8, -9, 3} and range is {7, 0, 7}.

Domain is the values of all inputs, In a function f(x), the set of all values of x is called domain

The given set is,

G = {( -8, 7 ), ( -9, 0 ), ( 3, 7 )}

Since, domain is the set of all values of x,

And range is the set of all values of y

In the given set,

Domain = {-8, -9, 3}

Range = {7, 0, 7}

The domain is {-8, -9, 3} and range is {7, 0, 7}.

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The correct option is, there is a main effect for Factor A but there is no interaction.

What is two factor anova?

The mean of a quantitative The mean of a quantitative variable is estimated using a two-way ANOVA in relation to the levels of two categorical variables.

Two-way analysis of variance is an extension of one-way analysis of variance in statistics that looks at the impact of two different categorical independent variables on a single continuous dependent variable.

The parallel lines indicates no interaction effect.

For the above problem option 'a' is correct.

There is a main effect for Factor A but there is no interaction

Hence, the correct option is, there is a main effect for Factor A but there is no interaction.

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Complete question:

A two-factor ANOVA is conducted and the data are plotted. The chart shows two parallel lines separated by a distance of 9 points. The lines represent Factor A and the x axis of the chart represents the levels of Factor B. How should you interpret these results?

Select one:

a. There is a main effect for Factor A but there is no interaction

b. There is a main effect for Factor A and there is also an interaction effect

c. There is a main effect for Factor B and there is an interaction effect

d. There is no interaction effect and no main effects

Answer:

A: 18/81

Step-by-step explanation:

A: 18/81 = 0.222222222.....

B: 11/88 = 0.125

C: 1/5 = 0.2

D 5/8 = 0.625

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A radioactive substance will have a decay of A ≈ 31.1936 mg after 32 hours.

Radioactive decay (additionally referred to as nuclear decay, radioactivity, radioactive disintegration, or nuclear disintegration) is the manner with the aid of using which an volatile atomic nucleus loses electricity with the aid of using radiation. A fabric containing volatile nuclei is taken into consideration radioactive.

Every atom seeks to be as strong as possible. In the case of radioactive decay, instability happens whilst there's an imbalance withinside the quantity of protons and neutrons withinside the atomic nucleus. Basically, there's an excessive amount of electricity withinside the nucleus to preserve all of the nucleons together.

Initial Radioactive substance, A₂ = 110 mg Remains substance, A = 55 mg time, t = 22 hours

Here, radioactive substance decay. exponentially.

[tex]a=a_{0}e^{at} \\\\55=110*e^{22k} \\\\\frac{55}{110} = e^{22k} \\\\ \\e^{22k} =\frac{1}{2}[/tex]

Taking lo both side, we get ln (1/2) = lne²²K

ln (1/2) = k*22

[tex]k=\frac{ln(1/2)}{22}[/tex]

K = -0.03150669

Substance remains after 32 hours,

t=32 hr

[tex]A=110*e^{( (-0.03150669))*32} \\A=110*e^{(-1.2602676)} \\\\[/tex]

A = 110x 0.283578131

A = 31.19359441

A ≈ 31.1936 mg

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Answer: x=12y+6/5

Let's solve for x.

y=5/12x − 1/2

Step 1: Flip the equation.

5/12x + −1/2 =y

Step 2: Add 1/2 to both sides.

5/12x + −1/2 + 1/2 = y + 1/2

5/12x = y + 1/2

Step 3: Divide both sides by 5/12.

5/12x 5/12 = y + 1/2/5/12

x=12y + 6/5

The trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

cos(-x) =cosx= 3/4

and tanx=

We need to find sin(-x)

tank is ratio of sinx and cosx

We know that tanx=sinx/cosx

√7/3=sinx/3/4

Apply cross multiplication

sinx=√7/3.3/4

sinx=√7/4

sin(-x)=-sinx=-√7/4

Hence, Trigonometric function sin(-x) is -√7/4 when cos(-x) = 3/4 and tanx= √7/3

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The mean of the stock's returns over the past 3 years minus the sample standard deviation of the stock's returns from the past 3 years is -6.54

What is the standard deviation?

A standard deviation is a measurement of the data's dispersion from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.

Standard deviation It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

Mean :

Mean = [10+3 + (-7) ] / 3 = 2

sample standard deviation :

subtract the mean from each data element.

10- 2 = 8

3-2 = 1

-7 - 2 = -9

Square those numbers.

8² = 64

1² = 1

(-9)² = 81

Add those

64+1+81 = 146

Divide by (number of elements -1 = 3 -1 = 2)

146/2 = 73

Take square root

8.54

So, the sample standard deviation  = 8.54

The mean of the stock's returns over the past 3 years minus the sample standard deviation of the stock's returns from the past 3 years

=  2 - 8.54

= -6.54

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Answer:  80%

Step-by-step explanation:

Answer:

[tex]\tt \left(3x+5\right)\left(x-1\right)-3[/tex]

Distribute:-

[tex]\tt 3x^2+2x-5-3[/tex]

[tex]\tt -5-3=-8[/tex]

[tex]\tt 3x^2+2x-8[/tex]

Hope this help you!

Answer:

1 3/4 * 3

we turn 1 3/4 to improper fraction:

7/4

so,

7/4 * 3 = 21/4 or 5 1/4

Step-by-step explanation:

Answer:

[tex]\begin{pmatrix}24&-40&-16\\ -64&8&-24\end{pmatrix}[/tex]

Step-by-step explanation:

Each element of the matrix is multiplied by -8

Total number of ways in which dinner can be assembled will be 120.

What is restaurant?

A restaurant is a place of business where customers can order and receive food and drinks. Meals are typically prepared and consumed on the premises, but many eateries also provide take-out and delivery options.

A commercial space where customers can buy food or drinks.

There are 4 different types of appetizers, so there are 4 ways to choose one of them, which comes out to 4C1 = 4.

Similarly, there are 3 ways to choose desserts and 5 ways to choose an entrees.

2 methods for selecting wines are also included.

As a result, there are

5 x 4 x 3 x 2 = 120 different ways to assemble dinner in total.

Hence, total number of ways in which dinner can be assembled will be 120.

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Answer:

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

8283’a

The time taken to travel upstream will be t = 5/(s - r) and the time taken to travel downstream will be equal to t = 10/(s + r).

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

Speed of boat in still water = s

Distance to travel upstream = 5 km and,

Distance to travel downstream = 10 km

Then, the time taken to travel upstream,

t = d/s

t = 5/(s - r)

And, the time is taken to travel downstream.

t = d/s

t = 10/(s + r)

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An exponential decay function is one that has a constant time of halving.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.

Here,

The function which has a constant halving time is in the following form,

A(t)=A₀(¹/²)^(t/h)

Where:  A₀ is the initial amount

             h   is the half life time or the halving time.

             t    is the time

             A(t) the amount that remains at time t

The previous function represents an Exponential decay function.

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The statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.

Given,  three different groups of subjects memorized a list of nonsense syllables and were then tested for their memory of those syllables at different delays.

Group 1 was tested for memory after a delay of one hour.

Group 2 was tested after a delay of two hours.

Group 3 was tested after three hours.

we have to find the statistical test that is used to test whether length of delay affects memory.

So, the statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.

Hence, the statistical test that will test the above given scenario is an exponential function. Therefore, an exponential function can be helpful to test whether length of delay affects memory or not.

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We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.

Given that,

With respect to x, the value of y varies exponentially, and the 1-unit growth factor is 1.7.

We have to find which of the following best describes the significance of this growth factor.

We know that,

The required expression for y with respect to x is

y=(1.7)ˣ------>equation(1)

1.7=1- unit growth factor.

When ever x changes by 1.

x=x-1----->equation(2)

Putting equation (2) in (1)

y'=1.7ˣ⁺¹

y'=1.7ˣ×1.7----->equation(3)

Here [ y is new value after increase]

Taking ratio of (3) and (1)

y'/y= (1.7)ˣ×(1.7)/(1.7)ˣ

y'=(1.7)y

Therefore, We can say that whenever x changes by 1, the value of y becomes 1.7 times as large as its previous value.

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The sample results would be somewhat expected if the null hypothesis were true.

The correct option is (b).

Given,

In the question:

The complete question is this:

Select the most appropriate response.

What does it mean when sample results are not statistically significant?

The question is based on MCQ's

Now, According to the question:

What does it mean when sample results are not statistically significant?

It means  The sample results would be somewhat expected if the null hypothesis were true.

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the Degree of freedom is 9.

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with more variability.

We have given,

Sample size =n=10

Degree of freedom =n-1=10-1=9

Hence the Degree of freedom is 9

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golden rectangles are rectangles for which the ratio of the width w to the length l is equal to the ratio of l to l 1 w. The value of this golden ratio = 1/2 (1 + √5) = 1.618

Ratio:

Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion. We apply the concepts of ratio and proportion every day, for example, while dealing with money in business or when preparing any meal, etc. Students occasionally struggle to understand the difference between ratio and proportion.

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Answer: none of them

Step-by-step explanation:

they are not equal and dont look right i dont think im sorry if i get it wrong

Absolute increase in population will be 2050

And percentage increase will be 56.94 %

We have given population in 2005 is 3600

And population in 2011 is 5650

So absolute increase in population = 5650-3600 = 2050

We have to find the percentage increase in population

So relative percentage increase in population will be 2050/3600 *100 = 56.94  %

So population will increase by 60 %

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Answer:

Winning jump = 5.474

Her best jump = 4.76

Step-by-step explanation:

4.25×1.12=4.76

4.76×1.15=5.474

The statements 1,2,3 are false, true and true respectively.

Given that,

Based on the policyholder's age in years (x1) and the insured car's worth in dollars, IHI Insurance performed a multiple linear regression analysis to forecast the value of the number of yearly claims made by a policyholder for motor insurance (y) (X2). 500 policyholders were chosen at random for the analysis. The sample included people ranging in age from 16 to 70, and the cars ranged in price from $1,100 to $52,000. I = 13 + (-0.5)X1i + (0.1)X2i is the multiple linear regression equation that corresponds to IHI's study.

a) y^i = 13 + (-0.5)x1i + (0.1)x2i

Here X 1i = 26 , X zi = 20

y^i = 13 + (-0.5)x1i + (0.1)x2i

y^i = 13 + (-0.5)(26) + (0.1)(20)

y^i = 2 it doesnt make 28 so it is false.

b) As the coefficient of X 1i  is negative, it will decrease by 0.5

So, it is true.

c) As the coefficient of X 2i  is positive, it will increase by 0.1

So, it is true.

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Answer:

y = 2/3 x - 7

Step-by-step explanation:

y = mx + b

y = 2/3 x + b

-1 = 2/3 × 9 + b

-1 = 6 + b

b = -7

y = 2/3 x - 7

Answer:

y = 2x-17

Step-by-step explanation:

We have a point and a slope, we can write the equation in point slope form and then convert to slope intercept form

y-y1 = m(x-x1) where m is the slope and (x1,y1) is the point

y-1 = 2(x-9)

Distribute

y-1=2x-18

Add 1 to each side

y-1+1 = 2x-18+1

y = 2x-17

This is slope intercept form

Step-by-step explanation: