what is the equation of the line that passes through the point (4,0) and has a slope of 5/4?

Using the t-distribution, it is found that since the test statistic is more than the critical value for the right-tailed test, it can be conclude that the isolated compound gives more counts than those from background, and hence, we can be 95% confident that the compound is indeed radioactive.

At the null hypothesis, it is tested if isolated compounds do not give more counts than those from background, that is:

[tex]H_0: \mu_1 - \mu_2 \leq 0[/tex]

At the alternative hypothesis, it is tested if the give more counts, that is:

[tex]H_1: \mu_1 - \mu_2 > 0[/tex]

Using a calculator, the mean and the standard deviation for each sample are given by:

[tex]\mu_1 = 33.2, s_1 = 6.058[/tex]

[tex]\mu_2 = 24.25, s_2 = 4.35[/tex]

Considering the sample sizes of 5 and 4, respectively, the standard errors are given by:

[tex]s_1 = \frac{6.058}{\sqrt{5}} = 2.71[/tex]

[tex]s_2 = \frac{4.35}{\sqrt{4}} = 2.175[/tex]

For the distribution of differences, the mean and standard error are given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 33.2 - 24.25 = 8.95[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.71^2 + 2.175^2} = 3.4749[/tex]

The standard error was found from the standard deviation for each sample, hence, the t-distribution is used.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{8.95 - 0}{3.4749}[/tex]

[tex]t = 2.58[/tex]

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with 5 + 4 - 2 = 7 df and a 0.05 significance level is of [tex]t^{\ast} = 1.895[/tex]

Since the test statistic is more than the critical value for the right-tailed test, it can be conclude that the isolated compound gives more counts than those from background, and hence, we can be 95% confident that the compound is indeed radioactive.

A similar problem is given at brainly.com/question/24826023

Explanation :

________________________________

Given:

(2+√3)+(4-√3)

To Find:

Evaluate the expression

Solution:

⇨Step 1:

Remove the parentheses

(2+√3)+(4-√3)

When there is + or no sign in front of an expression in parentheses, the expression remains the same

= 2 + √3+ 4-√3

⇨Step 2:

Cancel the opposite terms √3 and -√3

"Two numbers are opposites if they have the same absolute value but different signs"

= 2 + 4

⇨Step 3:

Add the numbers

= 6

Hence (2+√3)+(4-√3) = 6.

Answer:

616cm³

Step-by-step explanation:

you just need to multiply those numbers

7 x 8 x 11= 616

[tex]\text{Perimeter of the triangle,}\\\\ 2s = 7 + 8 +11 =26}\\\\\\\implies s = \dfrac{26}2 = 13\\\\\\\text{Apply Heron's formula to find the area of the triangle,}\\\\A = \sqrt{s(s-8)(s-7)(s-11)}\\\\\implies A = \sqrt{13(13-8)(13-7)(13-11)}\\\\\implies A = \sqrt{780} \\\\\implies A = 27.93~~ \text{cm}^2[/tex]

Answer:

300/75

Step-by-step explanation:

Cost of the Car = $15,000

a) Rate of interest received on savings(r) = 2%

Amount in savings account(p) =$3000

Time period(t) = 5 years    

simple intrest.

Interest received on savings account = $300

b) Rate of interest on loan = 0.5%

IF P= 15000

intrest.

Difference between the interest = $75

c) Taking loan of the whole amount that is of $15,000 is more reasonable because though the interest is more but Troy will receive interest($300) from his savings account as well. But if he withdraws $3000 from savings and takes the loan for the rest of the amount, he would have no earnings.

Answer:

P = -3, each line in the negative direction is 1 number

so you would have -1, -2, -3 , -4, etc.

P is on the -3 line.

See attached picture.

Step-by-step explanation:

Answer:

this might help

Step-by-step explanation:

this might be kinda similar

Chickens and rabbits

In the yard were chickens and rabbits. Together they had 18 heads and 56 legs. How many chickens and how many rabbits were in the yard?

Correct answer:

chickens:  8

rabbits:  10

Step-by-step explanation:

a+b=18

2a+4b=56

a=8

b=10

a+b = 18

2•a+4•b=56

a+b = 18

2a+4b = 56

a = 8

b = 10

Check the picture below.

Answer:

-2/15

this should work

Step-by-step explanation:

Answer:

13/15

Step-by-step explanation:

1 1/5 - 1/3 =

= 1 + 1/5 - 1/3

= 5/5 + 1/5 - 1/3

= 6/5 - 1/3

= 18/15 - 5/15

= 13/15

Given that f(x) = ax – 5 and f(4) = 15, then the value of a is 5

The given function is:

f(x)  =  ax  -  5

If f(4)  =  15, then x = 4

Substitute x = 4 into f(x) = ax - 5

f(4)  =  a(4)  -  5

15   =  4a   -  5

Solve for a by adding 5 to both sides

15  +  5  =  4a  -  5  +  5

20    =  4a

Divide both sides by 4

4a/4   =  20/4

a    =  5

Given that f(x) = ax – 5 and f(4) = 15, then the value of a is 5

Learn more on linear functions here: https://brainly.com/question/15602982

Answer:

200% increase

Step-by-step explanation:

Answer:

262

Step-by-step explanation:

4x4x4x4+6

256+6

262

Answer:

Yes, it is a function

Step-by-step explanation:

Each x value in the domain has its own output, and it does not have more than 1

Answer:

36   and -1/8

Step-by-step explanation:

x^2 = 3^2 = 9 * 4 = 36

y^-3 = (-2)^-3 = -1/8

Answer:

-4.5.

Step-by-step explanation:

4x^2 y^-3

= 4x^2 / y^3

When x = 3 and y = -2

it is 4(3)^2 / (-2)^3

= 36 / -8

= -4.5.

Answer: the answer is 7.5

Step-by-step explanation:

Based on the information, the best research question that Juan should choose will be "How does playing a team sport affect a child's development?"

A research question simply means a question that a researcher wants to answer. It should be noted that choosing a research question is an important element in research.

From the complete question, it should be noted that since Juan is writing a paper about children who play team sports, and he has different research questions, he should choose the one that conveys the research appropriately.

In this case, the best option will be  "How does playing a team sport affect a child's development?"

Learn more about research questions on:

https://brainly.com/question/25257437

Answer:

4,-1

Step-by-step explanation:

Please like!♥

The cost function is an illustration of a linear function

The equation of the cost function is C(x) = 35 + 0.5x

The given parameters are:

[tex]Rentals = 35[/tex] -- the cost of renting a cooler

[tex]Rate = 0.5[/tex] --- the rate per bottle

Assume the number of bottles in a cooler is x.

The cost function for the bottles in a cooler would be:

[tex]C(x) = Rentals + Rate \times x[/tex]

So, we have:

[tex]C(x) = 35 + 0.5\times x[/tex]

Evaluate the products

[tex]C(x) = 35 + 0.5x[/tex]

Hence, the equation is [tex]C(x) = 35 + 0.5x[/tex]

Read more about linear functions at:

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Answer:

Step-by-step explanation:

imagine you chop off a right triangle from the left side

now you have a rectangle and a right triangle

the rectangle

height 5

width 12

5 x 12 = 60

triangle

height 5

width 3

3 x 5 = 15

15 / 2 = 7.5

60 + 7.5 = 67.5 m^2

Answer: 67.5 m^2

Step-by-step explanation:

To find out the area of the yard, we split the shape up into a triangle and rectangle. The area of the triangle is,

A = 1 × b × h/2 = 1 × 3 × 5/2 = 7.5 m^2.

And the area of the rectangle is,

A = 12 × 5 = 60 m^2.

We then add the area of the triangle and the area of the rectangle.

A = 7.5 + 60 =67.5 m^2

Rounded to one decimal place, the area of the yard is 67.5 square meters.

Answer:

i think BC = 8.5

Step-by-step explanation:

19-(2+6.5+2)

19-10.5

8.5

There are 2 blue marbles out of 6 total marbles.

6-2 = 4 marbles are not blue.

Probability of not being blue = 4/6 which reduces to 2/3

Answer: 2/3

Answer:

the number 0 Originally called finding the vertical asymptote.

Answer:

C

Step-by-step explanation:

Slope is rise over run. Pick two points and then count the rise and run. The rise in this case is one and the run is 2 and one over 2 is 1/2

[tex]Hiya![/tex]

Sokka is here to help!

[tex]C.[/tex]

Because, All you need to do is.. Find the slope of proportional graph, by y and x, Which the line is [tex]\frac{4}{2}[/tex].

[tex]And, \frac{4}{2} =\frac{1}{2} .[/tex]

Hopefully, this helps you!!

[tex]Sokka[/tex]

Answer:

[tex]x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}[/tex] and [tex]y=-1,\frac{1}{2}[/tex]

The ordered pair solutions are [tex](-\sqrt{\frac{7}{4}},0.5)[/tex], [tex](\sqrt{\frac{7}{4}},0.5)[/tex], [tex](-1,-1)[/tex], and [tex](1,-1)[/tex].

Step-by-step explanation:

I'm assuming the system is [tex]\left \{ {x^2+y^2=2} \atop {y=2x^2-3}} \right.[/tex]:

[tex]x^2+y^2=2[/tex]

[tex]x^2+(2x^2-3)^2=2[/tex]

[tex]x^2+(4x^4-12x^2+9)=2[/tex]

[tex]x^2+4x^4-12x^2+9=2[/tex]

[tex]4x^4-11x^2+9=2[/tex]

[tex]4x^4-11x^2+7=0[/tex]

[tex]x^4-11x^2+28=0[/tex]

[tex](x^2-7)(x^2-4)=0[/tex]

[tex](4x^2-7)(x^2-1)=0[/tex]

[tex]4x^2-7=0[/tex]

[tex]4x^2=7[/tex]

[tex]x^2=\frac{7}{4}[/tex]

[tex]x=\pm\sqrt{\frac{7}{4}}[/tex]

[tex]x^2-1=0[/tex]

[tex]x^2=1[/tex]

[tex]x=\pm1[/tex]

[tex]y=2x^2-3[/tex]

[tex]y=2(\pm\sqrt{\frac{7}{4}})^2-3[/tex]

[tex]y=2({\frac{7}{4}})-3[/tex]

[tex]y=\frac{7}{2}-3[/tex]

[tex]y=\frac{1}{2}[/tex]

[tex]y=2x^2-3[/tex]

[tex]y=2(\pm1)^2-3[/tex]

[tex]y=2(1)-3[/tex]

[tex]y=2-3[/tex]

[tex]y=-1[/tex]

Therefore, [tex]x=-1,1,-\sqrt{\frac{7}{4} },\sqrt{\frac{7}{4}}[/tex] and [tex]y=-1,\frac{1}{2}[/tex]

The ordered pair solutions are [tex](-\sqrt{\frac{7}{4}},0.5)[/tex], [tex](\sqrt{\frac{7}{4}},0.5)[/tex], [tex](-1,-1)[/tex], and [tex](1,-1)[/tex].

I'll do the first two parts to get you started.

=====================================================

Part (i)

We can show that the operation [tex]\nabla[/tex] is not commutative by picking two random and different real numbers for a,b. In other words, I'm using a counter-example.

Let's say we go for a = 1 and b = 2

[tex]a \nabla b = \frac{3a+b}{5} - 1\\\\1 \nabla 2 = \frac{3*1+2}{5} - 1\\\\1 \nabla 2 = \frac{5}{5} - 1\\\\1 \nabla 2 = 1 - 1\\\\1 \nabla 2 = 0\\\\[/tex]

Now let's swap the values. We'll try a = 2 and b = 1

[tex]a \nabla b = \frac{3a+b}{5} - 1\\\\2 \nabla 1 = \frac{3*2+1}{5} - 1\\\\2 \nabla 1 = \frac{7}{5} - 1\\\\2 \nabla 1 = 1.4 - 1\\\\2 \nabla 1 = 0.4\\\\[/tex]

We can see that [tex]1 \nabla 2[/tex] and [tex]2 \nabla 1[/tex] are not the same value. In general, [tex]a \nabla b \ne b \nabla a[/tex] Therefore, the operation [tex]\nabla[/tex] is not commutative.

The only time [tex]a \nabla b = b \nabla a\\\\[/tex] is true is when [tex]a = b[/tex], since,

[tex]\frac{3a+b}{5}-1 = \frac{3b+a}{5}-1\\\\\frac{3a+a}{5}-1 = \frac{3a+a}{5}-1\\\\\frac{4a}{5}-1 = \frac{4a}{5}-1\\\\[/tex]

It's when [tex]a \ne b[/tex] is where the operation becomes noncommutative.

Another way to arrive at the [tex]a = b[/tex] condition is to solve the original equation for either 'a' or b.

=====================================================

Part (ii)

Using the previous part as inspiration, we'll do a counter-example to show that the operation is not associative. Pick 3 random values for a,b,c. Here are the values I'll pick.

Then,

[tex]d = b \nabla c = \frac{3b+c}{5}-1 = \frac{3*2+3}{5}-1 = 0.8\\\\a \nabla (b \nabla c) = a \nabla d = \frac{3a+d}{5}-1 = \frac{3*1+0.8}{5}-1 = -0.24\\[/tex]

Next, we can say:

[tex]d = a \nabla b = \frac{3a+b}{5}-1 = \frac{3*1+2}{5}-1 = 0\\\\(a \nabla b) \nabla c = d \ \nabla c = \frac{3d+c}{5}-1 = \frac{3*0+3}{5}-1 = -0.4[/tex]

Let's compare the two outputs:

[tex]a \nabla (b \nabla c) = -0.24\\\\(a \nabla b) \nabla c = -0.4[/tex]

They don't match up, so [tex]a \nabla (b \nabla c) \ne (a \nabla b) \nabla c[/tex] when (a,b,c) = (1,2,3).

In general, the operation is not associative in R.

Answer:

15+20=35+15 And then add an additional plus 15 for each hour

Step-by-step explanation:

Answer:

the answer you're looking for is D. when you move to the left the -4 becomes -6 and when you move up 2 becomes 4.

Answer:

2=-12.2/(-6.1

-2=16/(-8)

-3= -2 2/5/4/5

3= 3 3/7 / 1 1/7

Step-by-step explanation:

nCx⋅px⋅(1−p)n−x

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The vertices of the feasible region of the constraints is (0,2.5)

The constraints are given as:

x + 3y ≤ 6

4x + 6y ≥ 9

x ≥ 0,  y ≥ 0

Express the inequalities as equations

x + 3y = 6

4x + 6y = 9

Make x the subject in x + 3y = 6

x = 6 - 3y

Substitute x = 6 - 3y in 4x + 6y = 9

4(6 - 3y) + 6y = 9

Expand

24 - 12y + 6y = 9

Evaluate the like terms

-6y = -15

Divide by 6

y = 2.5

Substitute y = 2.5 in x = 6 - 3y

x = 6 - 3 * 2.5

Evaluate

x = -1.5

So, we have:

(x,y) = (-1.5, 2.5)

Recall that: x ≥ 0,  y ≥ 0

This means that the feasible region must have positive coordinates or zero

So, we set x = 0

(x,y) = (0, 2.5)

Hence, the vertices of the feasible region of the constraints is (0,2.5)

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