Test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not affected by the course. Assume all requirements are met. Use the critical value method of testing hypotheses.
Before 74 83 75 88 84 63 93 84 91 77
After 73 77 70 77 74 67 95 83 84 75
A. State the null hypothesis (H_0) and the alternate (H_1).
B. What is the test statistic and the critical value(s.
C. Find the confidence interval values.
D. Interpret the information and state what can you say about the claim?

Answer:

28.26

hop thats better the the first anser

Answer:

The median is 43

Step-by-step explanation:

I dont know why your answers dont have any of them,cause with the numbers

3425, 24, 50, 18. 46. 43, 36.32

that makes your median is 43

Answer: 1.3

Step-by-step explanation: Ok, let's make a number line...

0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6

From the number line, the only number that fits is 1.3

I hope this helps!

Answer:

1.3

Step-by-step explanation:

Hope this helps have a wonderful day

Answer:

The number is 36.

Step-by-step explanation:

Given that 1/3 of a number is 12. So let's make this number into any variable, I will choose x which means that 1/3 of x is equals to 12. Next we have to write an expression :

[tex] \frac{1}{3} \times x = 12[/tex]

In order to solve x, you have to multiply 3 to both sides :

[tex] \frac{1}{3} \times x \times 3 = 12 \times 6[/tex]

[tex]x = 36[/tex]

To find out what number 12 is one-third of, we can set up an equation. Let's assume the unknown number is represented by "x".

According to the given statement, we can write the equation as: 12 = (1/3)x To solve for x, we need to isolate it on one side of the equation.

We can do this by multiplying both sides of the equation by 3, canceling out the fraction: 3 * 12 = (1/3)x * 3 36 = x Therefore, 12 is one-third of 36. In other words, if we take one-third of 36, it will equal 12.

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Answer:

3 option is correct according to me

Answer:

Second option is the correct answer

[tex](x-2)^{2} =79[/tex]

Step-by-step explanation:

[tex]x^{2} -4x -75=0\\(x^{2} -4x+ 4)-4 -75=0\\(x-2)^{2}-79=0\\(x-2)^{2} =79\implies (x-h)^{2} =p[/tex]

Answer:

The value of x is 0.624.

Property used: Symmetric property of equality

Step-by-step explanation:

The expression to be solved is:

[tex]f (x) = 2.5\cdot (6.25x+0.5)-11[/tex]

Compute the solution as follows:

[tex]f (x) = 2.5\cdot (6.25x+0.5)-11[/tex]

       [tex]=(2.5\times 6.25\ x)+(2.5\times 0.5)-11[/tex]

∵ Distributive property (a (b + c) = ab + ac)

       [tex]=15.625x+1.25-11\\=15.625x-9.75[/tex]

Substitute equation equal to 0 to compute the value of x as follows:

[tex]0=15.625x-9.75\\\\15.625x=9.75\\\\[/tex]

∵ Symmetric property of equality if a = b then b = a

[tex]x=\frac{9.75}{15.625}\\\\x=0.624[/tex]

Thus, the value of x is 0.624.

Answer:

lol

Step-by-step explanation:

1.)  2.5(6.25x + 0.5) = 11

​2.)  15.625x + 1.25 = 11  

3.)  15.625x = 9.75

​4.)  x = 0.624

Reason

1.)  Given

2.)  Distributive Property  

3.)  Subtraction Property of Equality

4.)  ​Division Property of Equality

Answer: 40,000

Step-by-step explanation:

Rounding 39,918.23 to the nearest thousands is 40,000.

The given decimal number is 39,918.23.

We need to round the given decimal to the nearest thousand.

We follow the given steps to round numbers to the nearest whole number:

Step 1- We look at the number we want to round.

Step 2- As we are rounding our number to the nearest whole, we mark the digit in the one’s place.

Step 3- Now we look at the ‘tenths’ place (the digit to the right of the decimal point).

Step 4- (i) If the digit in the tenths column is 0, 1, 2, 3 or 4, we will round down the number from one place to the nearest whole number.

(ii) If the digit in the tenths column is 5, 6, 7, 8 or 9, we will round up the number at the one’s place to the nearest whole number.

Step 5- Remove all the digits after the decimal point. The left-out number is the desired answer.

Now, in the given decimal, the number in the thousand places is 9, which is greater than 5, and then the number becomes 40,000.

Therefore, rounding 39,918.23 to the nearest thousands is 40,000.

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Answer:

Denote the principal amount: P

In 25 years, a bond with a 4.75% annual interest rate earned $2,375 as interest.

=> P x (1 + 4.75/100)^25 - P = 2375

=> P x 3.19 - P = 2375

=> P x 2.19 = 2375

=> P = 2375/2.19 = 1084.48$

Hope this helps!

:)

Answer:$2000

Step-by-step explanation:

Answer:

2 triangles

Step-by-step explanation:

2 triangles are said to be congruent when all the corresponding sides of the angle and the interior angles are congruent . The two triangle are said to be the mirror image of each other.

Step-by-step explanation:

Now she has 6 watermelons.

Answer:

6 watermelons

Step-by-step explanation:

8-2=6 watermelons

Answer:

(0,2)

Step-by-step explanation:

2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB

Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0

Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2

The point is (0,2)

Answer:

$2.55 per kilogram bag of sugar.

Step-by-step explanation:

To calculate the cost of only 1 bag of sugar, you would take what you know - 2 kilograms costs $5.09 - and use that to determine your answer.

Since you know how much 2 bags costs, and you need to know the cost of 1, you would divide the cost of 2 bags of sugar by 2. (5.09 ÷ 2)

That equals 2.545, but since the problem is asking you to round to the nearest cent, you would end up with -------> $2.55

Hope this helps!

stay safe

Answer:

The quotient is [tex]10x+16[/tex]

The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]

Step-by-step explanation:

(See my image for my work)

Once the problem is set up, we need to figure out how to make [tex]x^3[/tex] become [tex]10x^4[/tex]. To do this, we must multiply it by [tex]10x[/tex].

This becomes the first number at the top of our work.

Now, we need to create the second row. To do this, we need to multiply all of the terms on the left by [tex]10x[/tex] and then multiply it by a negative.

Once that is done, we need to subtract these two rows.

After we subtract, we are left with [tex]16x^3-20x^2+26x-10[/tex]

Now we can do the same thing. This time, the number that we must multiply by is 16, so that is the next term on top

Next, we multiply the terms on the left by 16 and then subtract them from the previous expression

This leaves us with [tex]34x^2+10x+22[/tex].

As this has a smaller power than the left-hand side, this is our remainder, which we need to divide by the left hand side.

Our quotient is the number that we have found on the top.

This gives us the answer of

The quotient is [tex]10x+16[/tex]

The remainder is [tex]\frac{34x^2+10x+22}{x^3-3x^2+x-2}[/tex]

(Sorry. This process is hard to do in this form, so I had to write it by hand.)

Answer:

the quotient is 10x + 16

the remainder is 28x² + 10x + 22

Answer:

r = 3

Step-by-step explanation:

q = k / [tex]r^{2}[/tex]

k = q[tex]r^{2}[/tex] = 1.2 x 3 x 3 = 10.8

q = 10.8/[tex]r^{2}[/tex]

1.2 = 10.8/[tex]r^{2}[/tex]

r = [tex]\sqrt{10.8 /1.2}[/tex] = 3

As q is inversely proportional to r square the value of r is 1.66 when q is equal to 1.2

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant 'k' and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

Given, q is inversely proportional to r square which is,

q ∝ 1/r².

q = k/r².

q = 30 when r = 3, From this we'll have the value of the constant of proportionality(k).

30 = k/9.

k = 30/9.

k = 10/3.

Now, q = 1.2 and k = 10/3.

Therefore,

1.2 = (10/3)/r².

r² = (10/3)×(1/1.2).

r² = 10/3.6.

r² = 2.77.

r = 1.66

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Answer:

  137.26 m^3

Step-by-step explanation:

Put the numbers into the formula and do the arithmetic.

  v = (1/6)(√3.14)(60 m^2)^(3/2) = 137.26 m^3

Answer:

Height of second tower = 17.32m

Step-by-step explanation:

I have attached a diagram depicting the question.

From the diagram, The first tower is depicted by side AEB and the second tower CD.

While d is the distance that separates the two towers and it's given as 15m.

Now, since the angle of depression of the second tower’s base is 60°, then for triangle BAC. Angle C = 60°.

Thus; using trigonometric ratios;

tan 60° = AB/AC.

This gives; AB = d*tan 60°

Similarly, for the triangle BED, BE = d*tan 30°

Since, AE = CD, thus ;

CD = AB − BE

CD = d (tan 60° − tan 30°)

CD = 15(1.7321 − 0.5774)

CD = 15 × 1.1547

CD ≈ 17.32 m.

So, height of second tower = 17.32 m

Answer:

scalene

Step-by-step explanation:

We know it isn't a right triangle because it doesn't satisfy the Pythagorean Theorem (9² + 16² ≠ 17²). Because the lengths of the sides are all different, it can't be an equilateral (all equal sides) or an isosceles (2 equal sides) either. Therefore, it is a scalene triangle (all 3 sides different). Hope this helps!

Answer:

a. It is in standard form because the exponents are in order from highest to lowest.

Complete question:

a. It is in standard form because the exponents are in order from highest to lowest.

b. It is in standard form because the coefficients are in order from highest to lowest.

c. It is not in standard form because the constant should be the first term.

d. It is not in standard form because it can be further simplified.

Step-by-step explanation:

-24x^7-12x^2-9x+6

A polynomial is in standard form when the exponents are in order from highest to lowest. In the given expression , the exponent is in order x^7 and then x^2 and then x and constant.

Standard form does not depends on the coefficient of each each.

The given polynomial is in standard form because the exponent are in order from highest to lowest.

Answer:

A

Step-by-step explanation:

Answer:

[tex]\dfrac{90}{341}[/tex]

Step-by-step explanation:

3rd grade:

Number of girls = 16

Number of boys = 15

Total number of students = 31

4th grade:

Number of girls = 15

Number of boys = 18

Total number of students = 33

Formula for probability of an event E can be observed as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Probability of picking a boy from 3rd grade, [tex]P_{1} = \dfrac{15}{31} ..... (1)[/tex]

Probability of picking a boy from 4th grade, [tex]P_{2} = \dfrac{18}{33} ..... (2)[/tex]

These are two independent events of picking a boy from 3rd grade and 4th grade.

So, probability the captain chooses 2 boys in the first pick can be found by multiplying (1) and (2) above.

[tex]P = P_{1} \times P_{2}\\\Rightarrow \dfrac{15}{31} \times \dfrac{18}{33}\\\Rightarrow \dfrac{90}{341}[/tex]

Answer:

a

Step-by-step explanation:

Answer:

A on edge trust

Step-by-step explanation:

The first three term of the sequence are,

⇒ 1/2 , 1/4, 1/8

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The recursive function is,

⇒ [tex]A_{n} = \frac{1}{2} a_{n - 1}[/tex]

And, We have;

⇒ a₁ = 1

Now, The recursive function is,

⇒ [tex]A_{n} = \frac{1}{2} a_{n - 1}[/tex]

Put n = 2;

⇒ [tex]A_{2} = \frac{1}{2} a_{2 - 1}[/tex]

⇒ [tex]A_{2} = \frac{1}{2} a_{1}[/tex]

⇒ [tex]A_{2} = \frac{1}{2}\ * 1[/tex]

⇒ [tex]A_{2} = \frac{1}{2}[/tex]

Put n = 3;

⇒ [tex]A_{3} = \frac{1}{2} a_{3 - 1}[/tex]

⇒ [tex]A_{3} = \frac{1}{2} a_{2}[/tex]

⇒ [tex]A_{3} = \frac{1}{2}\ * \frac{1}{2}[/tex]

⇒ [tex]A_{3} = \frac{1}{4}[/tex]

Put n = 4;

⇒ [tex]A_{4} = \frac{1}{2} a_{4 - 1}\\[/tex]

⇒ [tex]A_{4} = \frac{1}{2} a_{3}[/tex]

⇒ [tex]A_{4} = \frac{1}{2}\ * \frac{1}{4}[/tex]

⇒ [tex]A_{4} = \frac{1}{8}[/tex]

Thus, The first three term of the sequence are,

⇒ 1/2 , 1/4, 1/8

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Answer:

1) No, there is  not  enough evidence to support the claim that the vaccine was effective (P-value=0.104) .

The null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

being the subindex 1 for the experimental group and subindex 2 for the control group.

2) Test statistic z=-1.26

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the vaccine was effective.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2< 0[/tex]

The significance level is 0.01.

The sample 1 (experimental group), of size n1=100000 has a proportion of p1=0.0002.

[tex]p_1=X_1/n_1=21/100000=0.0002[/tex]

The sample 2 (control group), of size n2=100000 has a proportion of p2=0.0003.

[tex]p_2=X_2/n_2=30/100000=0.0003[/tex]

The difference between proportions is (p1-p2)=-0.0001.

[tex]p_d=p_1-p_2=0.0002-0.0003=-0.0001[/tex]

The pooled proportion, needed to calculate the standard error, is:

[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{21+30}{100000+100000}=\dfrac{51}{200000}=0.00026[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.00026*0.99974}{100000}+\dfrac{0.00026*0.99974}{100000}}\\\\\\s_{p1-p2}=\sqrt{0+0.0000000025}=\sqrt{0.0000000051}=0.000071[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.00009-0}{0.000071}=\dfrac{-0.00009}{0.000071}=-1.26[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as (using a z-table):

[tex]P-value=P(z<-1.26)=0.104[/tex]

As the P-value (0.104) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is  not  enough evidence to support the claim that the vaccine was effective.

Answer:

9x^2 - 12x + 6 =0

work is pictured and shown

Answer:

3000 gallons of gasoline and 2000 gallons of kerosene

Step-by-step explanation:

The first thing is that 16 ¢ and 15 ¢ are 16 and 15 cents, therefore we can express it as $ 0.16 and $ 0.15 respectively.

Now, we can solve by means of a 2x2 system of equations, we have to:

"x" is the number of gallons of gasoline

"y" be the number of gallons of kerosene

x + y = 5000 => x = 5000 - y

0.16 * x + 0.15 * y = 780

replacing

0.16 * (5000 - y) + 0.15 * y = 780

800 - 0.16 * y + 0.15 * y = 780

-0.01 * y = 780 - 800

y = -20 / -0.01

y = 2000

Therefore x:

x = 5000 - 2000

x = 3000

which means 3000 gallons of gasoline and 2000 gallons of kerosene

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The centre coordinates would be the opposite value of what is in the brackets

For example, the x value in the brackets is -3, the centre coordinate x value would be positive 3

The same would apply to the y value

The radius would be the square root of 36

Thus, your answer would be option A

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Answer:

336 is the answer

Step-by-step explanation:

hope this helps

Answer:

a

Step-by-step explanation:

A percentage is a way to describe a part of a whole. The correct matrix is C.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the table shows Amy's, Jenny's, and Meg's sales for the month of February. They get a 5% commission on their sales. Therefore, the commission on each product category and for each person can be calculated as shown below.

Commission on book sales for Amy, a₁₁ = 120 × 0.05 = 6

Commission on book sales for Jenny, a₁₂= 250× 0.05 = 12.5

Commission on book sales for Meg, a₁₃ = 215 × 0.05 = 10.75

Commission on Games sales for Amy, a₂₁ = 155 × 0.05 = 7.75

Commission on Games sales for Jenny, a₂₂= 106 × 0.05 = 5.3

Commission on Games sales for Meg, a₂₃ = 175 × 0.05 = 8.75

Commission on Tables sales for Amy, a₃₁ = 350 × 0.05 = 17.5

Commission on Tables sales for Jenny, a₃₂= 400 × 0.05 = 20

Commission on Tables sales for Meg, a₃₃ = 290 × 0.05 = 14.5

Now, the matrix can be made as shown below,

[tex]\left[\begin{array}{ccc}6&12.5&10.75\\7.75&5.3&8.75\\17.5&20&14.5\end{array}\right][/tex]

Hence, the correct matrix is C.

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Step-by-step explanation:

One way

x3 + 11x2 - 3x - 33

x2(x + 11) - 3(x + 11)

(x + 11) (x2 - 3) are the factors

Answer:

[tex]=8x^6y^6z^7[/tex]

Step-by-step explanation:

[tex](4x^3*y^2*z^4)(2x^3*y^4*z^3)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\\:a^c=a^{b+c}\\=4y^2z^4\cdot \:2x^{3+3}y^4z^3\\\mathrm{Add\:the\:numbers:}\:3+3=6\\=4y^2z^4\cdot \:2x^6y^4z^3\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\y^2y^4=\:y^{2+4}\\=4z^4\cdot \:2x^6y^{2+4}z^3[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\z^4z^3=\:z^{4+3}\\=4\cdot \:2x^6y^6z^{4+3}\\\mathrm{Add\:the\:numbers:}\:4+3=7\\=4\cdot \:2x^6y^6z^7\\\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2=8\\=8x^6y^6z^7[/tex]

Answer:

  independent

Step-by-step explanation:

Dependent equations graph as the same line. These lines are not the same, so the equations are independent.

___

However, the lines are parallel, so the equations are also inconsistent. There is no solution to this system of equations.

Answer:

0.864p

Step-by-step explanation:

A discount of 20% is (1 - .2) = .8

8% tax is 1.08

.8 * 1.08 = 0.864

That means the new price is 0.864p