Last winter Armand had StartFraction 5 Over 6 EndFraction of a row of stacked logs. At the end of the winter he had StartFraction 8 Over 15 EndFraction of the same row left. How much wood did he burn over the winter?

Answer:

P-value =0.062

At a signficance level of 0.05, there is not enough evidence to support the claim that the unemployment rate is less than 5%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the unemployment rate is less than 5%.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]

The significance level is 0.05.

The sample has a size n=1500.

The sample proportion is p=0.041.

[tex]p=X/n=61/1500=0.041[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.041-0.05+0.5/1500}{0.0056}=\dfrac{-0.0087}{0.0056}=-1.5401[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.5401)=0.062[/tex]

As the P-value (0.062) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the unemployment rate is less than 5%.

Answer:

∠[tex]2=131[/tex]°

Step-by-step explanation:

We know that ∠[tex]4[/tex] is ≅ ∠[tex]1[/tex].

This means that ∠ [tex]1=49[/tex]°

Therefore, [tex]49+49=98[/tex]°

We know that a trapezoid is [tex]360[/tex]°.

To find ∠[tex]2[/tex] ,which is congruent to ∠[tex]3\\[/tex], we will have to subtract [tex]360[/tex]° from [tex]98[/tex]°.

[tex]360-98=262[/tex]°.

Because ∠[tex]2[/tex]≅∠[tex]3[/tex], we will have to divide [tex]262[/tex] by [tex]2[/tex] to see their measurement.

So,

[tex]\frac{262}{2}=131[/tex].

Hence, ∠[tex]2=131[/tex]°.

I really hope this helps:D

-Jazz

Answer:

solution,

[tex] \frac{ac}{ef} = \frac{cb}{fd} \\ or \: \: \frac{12}{y} = \frac{15}{5} \\ or \: 15 \times y = 12 \times 5( \: cross \: multiplication) \\ or \: 15y = 60 \\ or \: y = \frac{60}{15} \\ y = 4[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

The value of y is 4

Step-by-step explanation:

What is similarity ?

In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given,

ΔACB~ΔEFD

The proportional sides are equal.

[tex]\frac{AC}{EF}=\frac{CB}{FD}=\frac{AB}{DE} \\\frac{12}{y}=\frac{15}{5} \\y=12*\frac{5}{15}\\\\ y=4[/tex]

To know more about similarity, similar here

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Answer: 1) 21-25

               2) III

               3) II

               4) 8

               5) 4

Step-by-step explanation:

Question 1: Which numbers are missing?

            The previous interval ends at 20 the following interval starts at 26.

            The missing interval is 21 - 25

Question 2: How many tally marks to draw?

           The frequency is given as 3, so draw three tally marks: III

Question 3: How many tally marks to draw?

           The frequency is given as 2, so draw two tally marks: II

Question 4: What is the frequency?

          There are eight tally marks so the frequency is 8.

Question 5: What is the frequency?

          There are four tally marks so the frequency is 4.

Answer:

4,300

Step-by-step explanation:

Lateral area of a squared Pyramid is given as ½ × Perimeter of base (P) × slant height of pyramid

Thus, we are given,

Side base length (s) = 43 yd

height (h) = 25 yd

Let's find the perimeter

Permimeter = 4(s) = 4(43) = 172 yd

Calculate the slant height using Pythagorean theorem.

Thus, l² = s²+h²

l² = 43²+25² = 1,849+625

l² = 2,474

l = √2,474

l ≈ 50 yd

=>Lateral area = ½ × 172 × 50

= 172 × 25

= 4,300 yd

Answer:

1. Compound Interest

2. Simple Interest

Step-by-step explanation:

Simple Interest multiplies the interest rate on the principal rate by the number of days.

Compound Interest multiplies the interest rate on the principal rate and existing rate by periods. 

Answer:

:)

Step-by-step explanation:

Answer: Area is 1840units²

Step-by-step explanation:

From the given information,

Firstly, area of a rectangle is given as

A = l × b ie, length multiply by the breadth.

One of the side of the rectangle is known , AD = 16 , now to calculate the other side, we need some calculations.Since FE = 23 and

FD = DE ,,therefore,

DE = 23/2.

From the information, DE = 1/10 of DC. We now find DC the required side for finding the area of the rectangle by simple equation. Since DE = 23/2 , the equation now looks like this to get DC

23/2 = DC/10. Now , solving this

2DC = 23 × 10

2DC = 230

DC = 230/2

= 115.

Now the area of the rectangle will be

A = 16 × 115

= 1840units²

Answer:

You did not post the options, but i will try to answer this in a general way.

Because we have two solutions, i know that we are talking about quadratic equations, of the form of:

0 = a*x^2 + b*x + c.

There are two easy ways to see if the solutions of this equation are real or not.

1) look at the graph, if the graph touches the x-axis, then we have real solutions (if the graph does not touch the x-axis, we have complex solutions).

2) look at the determinant.

The determinant of a quadratic equation is:

D = b^2 - 4*a*c.

if D > 0, we have two real solutions.

if D = 0, we have one real solution (or two real solutions that are equal)

if D < 0, we have two complex solutions.

Answer:

This was for 5 points. not 20 my dude. Also the first answer is correct.

Step-by-step explanation:

Answer:

y=-4/3x-3

Step-by-step explanation:

You look for the slope using the the slope formula (m=y2-y1/x2-x1)

You will end up with (m=1-5/3-6)

Simplify to end up with (-4/3) as your slope.

Then, pick a coordinate point. Your choices are (6,5) and (3,1). You will us it to plug into the equation.

I am picking (3,1) The y-value here is 1 and the x-value is 3.

Your equation to find b, or the y-intercept is going to be (1=-4/3(3)+b)

You will have to simplify.

1=-4/3(3)+b

You will multiply -4/3 and -3 and end up with 4 so it looks like...

1=4+b

You subtract 4 on both sides and then end up with....

-3=b

So, the final answer is: y=-4/3x-3

Answer:

12pi(8-pi), or

183.158 to third decimal place

Step-by-step explanation:

The geometry is indicated in the attached figure.

A. by integration

We will find the volume of the solid by the method of shells, i.e. we will integrate strips parallel to the axis of rotation to form many thin shells, then integrate to get the sum of all these shells.

For each shell, of thickness dy, we integrate strips of length located at y

L(x) = y(x)

and area

L(x)dy

Each strip is at a distance of (4-y) from

for which the volume of each shell equals

dV = 2*pi*(4-y)*L(x)dy = 2*pi*(4-y)*y(x) dy

The total volume of the solid can be obtained by integrating y from 0 to pi

integral( dV ) from 0 to pi

= integral (2*pi*(4-y)*y(x) dy) for y from 0 to pi

= 12*pi(-sin(y)+y*cos(y)-4*cos(y)) for y from 0 to pi

=12(8-pi)*pi

= 183.158

B. Using Pappus theorem

Pappus theorem simplifies the calculation of volume of revolution by multiplying the area of the rotating region by 2pi times the distance between the centroid and the rotation axis.

Here the area of the figure is A=2*6=12, (2 is the area under the sine curve from 0 to pi), or

A = integral (6sin(x))dx, x from 0 to pi

= 6 cos(x), x from 0 to pi

= 6(1- (-1))

= 12

Distance from centroid to axis of rotation = (4-pi/2)

Volume = 2*pi*A*(4-pi/2) = 2*pi*12*(4-pi/2)

= 12pi(8-pi)

=183.158    as before

Answer:

0.9 (9/10)

Step-by-step explanation:

(see picture)

Answer:

[tex] |w-0.3| \leq 0.0003[/tex]

And solving we got:

[tex] -0.0003 \leq w-0.3 \leq 0.0003[/tex]

[tex]0.3-0.0003 \leq w \leq 0.3+0.0003[/tex]

[tex] 0.2997 \leq w \leq 0.3003[/tex]

Step-by-step explanation:

For this case we can define the following notation:

[tex] W[/tex] represent the width

And we want a maximum error of 0.0003 so we can set up the following equation:

[tex] |w-0.3| \leq 0.0003[/tex]

And solving we got:

[tex] -0.0003 \leq w-0.3 \leq 0.0003[/tex]

[tex]0.3-0.0003 \leq w \leq 0.3+0.0003[/tex]

[tex] 0.2997 \leq w \leq 0.3003[/tex]

Answer:

D.y-4=f(x+3)

Step-by-step explanation:

The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

The equation of the translation image of the function is  y - 4 = f(x + 3).

which is the correct answer would be an option (D).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.

For example, If shift up by 1 unit,  add 1 to the function

If shift down by 4 units, subtract 4 from the function

To determine the graph of y (x) is translated as 3 units right and 4 units down.

The x-coordinate will increase by 3 if we move it to the right.

If we shift it downward, it will become negative and read as y - 4.

So y - 4 = f(x + 3)

Therefore, the equation of the translation image of the function is  y - 4 = f(x + 3).

Learn more about the graph here:

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Answer:

0 (zero)

Step-by-step explanation:

A horizontal line has zero slope.

The function is f(x)= 2x+1/x+3.

A work domain is a set of all possible inputs for a job. For example, the domain f (x) = x² is all real numbers, and the domain g (x) = 1 / x is all real numbers except x = 0. And we can define the special functions of its most limited domains.

The function domain f (x) is a set of all values ​​defined by the function, and the scope of the function is a set of all values ​​taken by f. (In grammar school, you probably call the domain a set of substitutes and a set of solutions.

Learn more about the function domain here:  brainly.com/question/24090845

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Answer:

B

Step-by-step explanation:

i got it right! :)

Answer:

Yes

Step-by-step explanation:

b is as in 1b so. . .

2 + 1 = 3

We can plug in b or as "b"

2b + b = 3b

So yes in whatever case 2b + b's value  will always equal 3b's value

Answer:

yes

Step-by-step explanation:

because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9

Answer:

B. y = 3x + 4

Step-by-step explanation:

Step 1: Find slope-intercept form of 1st equation

2y = 6x + 4

2y/2 = 6x/2 + 4/2

y = 3x + 2

A parallel line has the same slope but different y-intercept:

y = -3x + 3 (No, different slope)

y = 3x + 4 (Yes, same slope, different y-int)

y = x + 3 (No, different slope)

y = -2x - 3 (No, different slope)

y = 1/2x + 3 (No, different slope)

Answer:

30 ways

Step-by-step explanation:

Given the following :

Number of boys in school (n1) = 5

Number of girls in school (n2) = 3

Total number of team members to be selected = 4

Number of boys required in team(r1) = 2

Number of girls required in team(r2) = 2

How many different teams made up of two girls and two boys could be chosen?

= (2 boys from 5) * (2 girls from 3)

Using combination :

5C2 * 3C2

Recall :

nCr = n! ÷ (n-r)! r!

5C2 = 5! ÷ (5-2)! 2!

5C2 = 5! ÷ 3!2!

5C2 = (5*4) / 2 * 1 = 10ways

3C2 = 3! ÷ (3-2)! 2!

3C2 = 3! ÷ 1!2!

3C2 = (3) /  1 = 3ways

3C2 = 3/1 = 3ways

10 * 3 = 30 ways

Complete question is;

In a random sample of 370 cars driven at low altitudes, 43 of them exceeded a standard of 10 grams of particulate pollution per gallon of fuel consumed. In an independent random sample of 80 cars driven at high altitudes, 23 of them exceeded the standard. Can you conclude that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard at an level of significance? Group of answer choices

Answer:

Yes we can conclude that there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard (P-value = 0.00005).

Step-by-step explanation:

This is a hypothesis test for the difference between the proportions.

The claim is that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.

Then, the null and alternative hypothesis are:

H0 ; π1 - π2 = 0

H1 ; π1 - π2 < 0

The significance level would be established in 0.01.

The random sample 1 (low altitudes), of size n1 = 370 has a proportion of;

p1 = x1/n1

p1 = 43/370

p1 = 0.116

The random sample 2 (high altitudes), of size n2 = 80 has a proportion of;

p2 = x2/n2

p2 = 23/80

p2 = 0.288

The difference between proportions is pd = (p1-p2);

pd = p1 - p2 = 0.116 - 0.288

pd = -0.171

The pooled proportion, we need to calculate the standard error, is:

p = (x1 + x2)/(n1 + n2)

p = (43 + 23)/(370 + 80)

p = 66/450

p = 0.147

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

S_(p1-p2) = √[((p(1 - p)/n1) + ((p(1 - p)/n2)]

1 - p = 1 - 0.147 = 0.853

Thus;

S_(p1-p2) = √[((0.147 × 0.853)/370) + ((0.147 × 0.853)/80)]

S_(p1-p2) = 0.044

Now, we can use the formula for z-statistics as;

z = (pd - (π1 - π2))/S_(p1-p2)

z = (-0.171 - 0)/0.044

z = -3.89

Using z-distribution table, we have the p-value = 0.00005

Since the P-value of (0.00005) is smaller than the significance level (0.01), then the effect is significant.

We conclude that The null hypothesis is rejected.

Thus, there is enough evidence to support the claim that the proportion of high-altitude vehicles exceeding the standard is greater than the proportion of low-altitude vehicles exceeding the standard.

Answer:

(C)[tex]6t^2+5[/tex]

Step-by-step explanation:

Given the distance, d(t) of a particle moving in a straight line at any time t is:

[tex]d(t) = 2t^3 + 5t - 2, $ where t is given in seconds and d is measured in meters.[/tex]

To find an expression for the instantaneous velocity v(t) of the particle at any given point in time, we take the derivative of d(t).

[tex]v(t)=\dfrac{d}{dt}\\\\v(t) =\dfrac{d}{dt}(2t^3 + 5t - 2) =3(2)t^{3-1}+5t^{1-1}\\\\v(t)=6t^2+5[/tex]

The correct option is C.

Answer:

6t2+5

Step-by-step explanation:

Answer:

We start with the expression:

exp( (4/3)*ln(2) - 1)

Here we can use that:

exp(ln(x)) = x.

and e^(a + b) = e^a*e^b.

the first step here is:

e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)

So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.

now, we have that:

a*ln(x) = ln(x^a)

then we can write:

(4/3)*ln(2) = ln(2^(4/3))

and e^(ln(2^(4/3)) = 2^(4/3)

then we have:

e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e

now we can write this as:

∛(2^4)/e

here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.

so the expression actually is:

∛(16)/e

Answer:

1/2

Step-by-step explanation:

The non-even numbers are 1, 3, and 5 on the dice.

3 numbers out of 6.

3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

Total sides of 6-sided die = 6

Numbers not even = 3

Probability of not getting an even = 3/6

=> 1/2

Answer:

see below

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

  = 4/3 pi ( 7)^3

  = 1372/3 pi in^3

Using 3.14 for pi

V =1436.0266666 in^3

Using the pi button

1436.75504 in^3

Step-by-step explanation:

The difference between. Each numbers is 5 so, it's answer is 22 and 27

Answer:

  13.636

Step-by-step explanation:

The area can be found using Heron's formula:

  A = √(s(s-a)(s-b)(s-c))

where s=(a+b+c)/2.

For the given triangle, ...

  a=9, b=4, c=12, s=(9+4+12)/2 = 12.5

  A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636

The area of the triangle is about 13.636 square units.

Answer:

24 units\

Step-by-step explanation:

Answer:

B. No; the graph fails the vertical line test.

Step-by-step explanation:

If you hold a pencil up to the graph, the parabola would technically touch the pencil at more than one point. That means it failed the test, and therefore it is not a function.

hope this helped :)

Answer:

Step-by-step explanation:

When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.

__

If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":

  g(x) = (-2x +3)x -5

Then we have ...

  g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19

  g(0) = (-2(0) +3)(0) -5 = -5

  g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14

Answer:

5cm for  each side

Answer:

solution,

Surface area= 150 cm^2

Side of a cube(a)=?

Now,

[tex]surface \: area \: of \: cube = 6 {a}^{2} \\ or \: 150 = 6 {a}^{2} \\ or \: {a}^{2} = \frac{150}{6} \\ or \: {a}^{2} = 25 \\ or \: a = \sqrt{25} \\ or \: a = \sqrt{ {(5)}^{2} } \\ a = 5 \: cm[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

7b+21

Step-by-step explanation:

7(b+3)

Distribute

7*b + 7*3

7b+21