On a snow day, Brooklyn created two snowmen in her backyard. Snowman A was built to a height of 60 inches and Snowman B was built to a height of 44 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 5 inches per hour and Snowman B's height decreased by 3 inches per hour. Let A(t)A(t) represent the height of Snowman A tt hours after sunrise and let B(t)B(t) represent the height of Snowman B tt hours after sunrise. Write the equation for each function and determine the number of hours after sunrise when both snowmen have an equal height.

Answer:

[tex]P(-1.94<X<-1.5)=P(\frac{-1.94-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.5-\mu}{\sigma})=P(\frac{-1.94-0}{1}<Z<\frac{-1.5-0}{1})=P(-1.94<z<-1.5)[/tex]

And we can find this probability with this difference:

[tex]P(-1.94<z<-1.5)=P(z<-1.5)-P(z<-1.94)=0.0668-0.026= 0.0408[/tex]

Step-by-step explanation:

Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(0,1)[/tex]  

Where [tex]\mu=0[/tex] and [tex]\sigma=1[/tex]

We are interested on this probability

[tex]P(-1.94<X<-1.5)[/tex]

And using the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

And using this formula we got:

[tex]P(-1.94<X<-1.5)=P(\frac{-1.94-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.5-\mu}{\sigma})=P(\frac{-1.94-0}{1}<Z<\frac{-1.5-0}{1})=P(-1.94<z<-1.5)[/tex]

And we can find this probability with this difference:

[tex]P(-1.94<z<-1.5)=P(z<-1.5)-P(z<-1.94)=0.0668-0.026= 0.0408[/tex]

Answer:

D

Step-by-step explanation:

Two lines are parallel if they have the same slope

those with same m,

It only appears in the last option where m= -5 for both lines, so option d

Answer:

  36 bottles

Step-by-step explanation:

Each spherical bottle will have a volume of ...

  V = (4/3)πr³ = (4/3)π(4.57³) = 399.8 . . . . cubic inches

Each box (12-pack?) will have a volume of ...

  V = LWH = (15 in)(5 in)(4.4 in) = 330 in³

This is a smaller volume than even one spherical bottle, so 36 bottles will have the larger volume.

Answer:

36% of the students are girls

Step-by-step explanation:

(Boys) 16/25 = 64%

(Girls) 9/25 = 36%

Answer:

36%

Step-by-step explanation:

you first do 25 minus 16 to find out how many girls are in the class which is 9

now u do 9/25 = ?/100 to find out the percent of girls

9 times 100 divided by 25 which gives u 36%

hope this helps

Answer:

C.)

Step-by-step explanation:

C.) Because it states the exact decimals rather than just stating about $2.36. Also, the other options were not specific. Hope this helps!  

A function assigns values. The graph of the equation y-1=2/3(x-3) is the second graph.

A function assigns the value of each element of one set to the other specific element of another set.

As the function is given to us that y-1=2/3(x-3), now substitute the value of x as 0 and y as 0 to get the intercept of the function. Therefore,

x-intercept

[tex]y-1=\dfrac23(x-3)\\0-1= \dfrac23x-\dfrac23(3)\\\\-1 = \dfrac23x - 2\\\\-1+2 = \dfrac23x\\\\x = \dfrac32[/tex]

y-intercept

[tex]y-1=\dfrac23(x-3)\\\\y-1=\dfrac23(0-3)\\\\y-1=\dfrac23(-3)\\\\y= -2+1\\\\y=-1[/tex]

Thus, we need to look for the graph which intersects the x-axis at 3/2 while the y-axis at -1. Therefore, as shown the below graph.

Hence, the graph of the equation y-1=2/3(x-3) is the second graph.

Learn more about Function:

https://brainly.com/question/5245372

Answer:

1 / 2,787,760,560

Step-by-step explanation:

The number of permutations is:

41 × 40 × 39 × 38 × 37 × 31 = 2,787,760,560

So the probability of winning the jackpot is 1 / 2,787,760,560.

Answer:

25pi

Step-by-step explanation:

If the circle has a diameter of 10, it has an radius of 5. The area of a circle is pi*r^2. If r=5, then it is 25pi.

Answer:

25π feet^2

Step-by-step explanation:

The area of a circle can be found using the following formula.

a=πr^2

We are given the diameter, but we need to find the radius. The radius is half of the diameter, or

r=d/2

We know the diameter is 10 feet. Therefore, we can substitute 10 in for d.

r=10/2

Divide 10 by 2

r=5

The radius is 5 feet.

Now we know the radius, and can substitute it into the area formula.

a=πr^2

r=5

a=π*5^2

Evaluate the exponent.

5^2 is equal to 5*5, which is 25.

a=π*25

a=25π

Add appropriate units. Area always uses units^2, and the units in this problem are feet.

a=25π feet^2

The area of the circle is 25π square feet

Answer:

What we know about the p-value for the test is that it will be less than 0.05

Step-by-step explanation:

The complete question is as follows;

Suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result (-4.977, -2.177). Suppose that we had a significance test with the following hypothesis:

H0: population mean weight loss = 0

Ha: population mean weight loss does not equal 0

What do we know about the p-value for the test?

solution;

Given the information in the question, we are concerned with saying what we know about the p-value for the test

To answer this question, we shall be looking at it from the angle of the confidence interval

The confidence interval given is 95%.

Now what does this indicate?

It indicates that 95% confidence interval contains only values which are less than 0.

What does this mean for the p-value?

This means that the p-value will be less than 0.05

Answer:

x=3

Step-by-step explanation:

15/5=3 now I gotta get 20 chatacters

Answer:

[tex]x=75[/tex]

Step-by-step explanation:

[tex]\frac{x}{5} =15[/tex]

[tex]x=15 \times 5[/tex]

[tex]x=75[/tex]

Answer:

D and F

Step-by-step explanation:

In the attached file

Answer:

  y = -2

Step-by-step explanation:

A horizontal line has an equation of the form ...

  y = constant

In order for the line to go through a point with a y-coordinate of -2, the constant must be -2.

  y = -2 . . . . horizontal line through (-5, -2)

Answer:

40% profit

Step by step Explanation:

Profit percentage

=( profit/cost price) * 100

0.2 = profit/cost

10+15+20+25+30= 100

Let's assume the cost price of the items is $1 each

Cost price total= $100

Profit made when buyer of 20 toffe didn't say was

0.2=profit/cost

0.2*100 =$20

If the$ 20 paid.

Total profit = $40

So percentage profit now

40/100 * 100 = 40%

The shopkeeper makes a loss of 40% and this can be determined by using the given data.

Given :

The following steps can be used in order to determine the profit or loss the shopkeeper makes:

Step 1 - The total number of toffees can be calculated as:

[tex]\rm Total \; Toffees = 10 +15 + 20+ 25+ 30\\\rm Total \; Toffees = 100\\[/tex]

Step 2 - Now, let the cost of 1 toffee be $1. So, the cost of 80 toffees is $80.

Step 3 - So, the value of 20% profit by selling 80 toffees be 'x'. So, the value of 'x' is:

[tex]x = \dfrac{20}{100}\times 80[/tex]

[tex]x = \$16[/tex]

Step 4 - Now, let the profit or loss be 'y'. So, the value of 'y' is:

[tex]y = \dfrac{20}{80}\times 16[/tex]

[tex]y = \$4[/tex]

Step 5 - So, the loss percentage is 40%.

Therefore, the correct option is C).

For more information, refer to the link given below:

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Answer:

2625*0.2= $525 in profit

Pls brainliest!!

Answer:The answer for the first one is log2(.25)=-2

The answer for the second one is 8^3=512

Step-by-step explanation:

Answer:

The answer is drawing the 6 of clubs or the 6 of spades because those are the only black 6's.

Answer:

20 ton

Step-by-step explanation:

We created a system of two separate equations to answer these questions.

"y" will be the total cost to transport the sugar

"x" will be the amount of sugar transported

Therefore, we have to:

y = 3995 + 225.50 * x

y = 6500 + 100.25 * x

We must establish these equations equal to each other because it asks how much of x is necessary to make the same amount of y, therefore:

3995 + 225.50 * x = 6500 + 100.25 * x

solved we have:

225.50 * x - 100.25 * x  = 6500 - 3995

125.25 * x = 2505

x = 2505 / 125.25

x = 20

which means that when the amount of sugar transported is 20 tons, the price is the same

Answer: Needs to be flat with opposite sides that are parallel and are the same in length

Answer:

-The arrows should be a length of 6

-The arrows should point in the negative direction

-The arrows should start at zero

Step-by-step explanation:

Hope this helps!

Answer:

B

D

E

Step-by-step explanation:

Answer:

1,300,000,000

Step-by-step explanation:

 78    300   000

 550  400   000

 648  700   000

1  277  400   000

To the nearest million

1,2 | 77 400 000            more than 4, so +1

1,300,000,000

Answer:

15/4

Step-by-step explanation:

3/4:1/5= 3/4*5= 15/4

Answer:

1. 9x-8y=9

2. -18x+16y= -18 ⇒ -9x+8y= -9 ⇒ 9x-8y=9

as we see both equations are same, it means the lines overlap and there is infinite number of solutions

Answer:

Step-by-step explanation:

We would assume that triangle ABC is a right angled triangle. This means that we can apply Pythagoras theorem in determining the unknown side length.

For the case of the minimum side length, we would assume that the unknown length, L is one of the shorter legs of the triangle. By applying Pythagoras theorem, it becomes

11² = 9² + L²

L² = 121 - 81 = 40

L = √40 = 6.32

For the case of the maximum side length, we would assume that the unknown length, L is one of the hypotenuse of the triangle. By applying Pythagoras theorem, it becomes

L² = 9² + 11²

L² = 81 + 121 = 202

L = √202 = 14.21

The minimum side length is 6.32 and the maximum side length is 14.21

Answer:

Step-by-step explanation:

a) Find the gradient

[tex]\nabla f(x,y) =f_x(x,y)\bold{i} +f_y (x,y)\bold{j}[/tex]

[tex]Also, sin(4x+3y)= sin(4x)cos(3y)+sin(3y)cos (4x)[/tex]

[tex]f_x(x,y) = 4cos(4x)cos(3y)-4sin(3y)sin(4x) = 4 cos(4x-3y)[/tex]

[tex]f_y(x,y) = -3sin(4x)sin(3y)+3cos(3y)cos(4x)=3cos(4x-3y)[/tex]

Hence

[tex]\nabla f(x,y) = 4cos(4x-3y)\bold{i}+3cos(4x-3y)\bold{j}[/tex]

b) At point (-6, 8) just replace the values in gradient to find it out. You can do it.

c) directional derivative in the direction u.

[tex]D_uf(x,y)=\nabla f(x,y). u[/tex]

I stuck with your 1 2 3 i -j . What does 1 2 3 mean? is it not 123 or 1 2/3 or else?

Answer:P(BBR) = 1/2 × 25/51 × 26/50 = 13/102 if cards are not replaced.

P(RBB) = 1/2 × 26/51 × 25/50 (simplified 1/2) = 13/102

P(BRB) = 1/2 × 26/51 ×25/50 (simplified 1/2) = 13/102

Step-by-step explanation: P(B) at first step is 26 cards out of a possible 52 therefore 26/52 (or simplified 1/2). We then have 25 black cards left out of a possible 51 therefore 25/51. The final card then has to be red to meet the criteria, we have 26 red cards still out of a possible 50 therefore 26/50.

This would be an example of binomial probability as at each step there are only 2 options R or B.

Answer:

6

Explanation:

According to secant-secant theorem,

(PB)(PA)=(PD)(PC)

(7)(12)=(PD)(14)

NOW

84/14 = PD

PD = 6

Answer:

a) [tex] t_{\alpha/2}=\pm 2.447[/tex]

b) [tex] t_{\alpha/2}=\pm 2.718[/tex]

c) [tex] t_{\alpha/2}=\pm 2.779[/tex]

d) [tex] t_{\alpha/2}=\pm 2.650[/tex]

Step-by-step explanation:

Part a

The degrees of freedom are given by:

[tex] df=n-1= 7-1=6[/tex]

The confidence is 95% or 0.95 the significance would be [tex]\alpha=0.05[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.447[/tex]

Part b

The degrees of freedom are given by:

[tex] df=n-1=12-1=11[/tex]

The confidence is 98% or 0.98 the significance would be [tex]\alpha=0.02[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.718[/tex]

Part c

The degrees of freedom are given by:

[tex] df=n-1=27-1=26[/tex]

The confidence is 99% or 0.99 the significance would be [tex]\alpha=0.01[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.779[/tex]

Part d

The degrees of freedom are given by:

[tex] df=n-1=14-1=13[/tex]

The confidence is 98% or 0.98 the significance would be [tex]\alpha=0.02[/tex] and the critical values would be:

[tex] t_{\alpha/2}=\pm 2.650[/tex]

A value of a test statistic defines the upper bounds of a confidence interval, statistical significance in a test statistic is known as the crucial value.

For part a )

n = 7

Calculating the degrees of freedom [tex]= df = n - 1 = 7 - 1 = 6[/tex]

At [tex]95\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 95\% = 1 - 0.95 = 0.05\\\\\frac{\alpha}{ 2} = \frac{0.05}{ 2} = 0.025\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.025,6} = 2.447\\\\[/tex]

The critical value = 2.447

For part b )

n =12

Calculating the degrees of freedom[tex]= df = n - 1 = 12 - 1 = 11[/tex]

At [tex]98\%[/tex] the confidence level , the t:

[tex]\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2}= \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.01,11} =2.718\\\\[/tex]

The critical value =2.718

For part c )

n = 27

Calculating the degrees of freedom [tex]= df = n - 1 = 27 - 1 = 26[/tex]

At [tex]99\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 99\% = 1 - 0.99 = 0.01\\\\\frac{\alpha}{ 2} = \frac{0.01}{ 2} = 0.005\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.005,26}=2.779\\\\[/tex]

The critical value =2.779

For part d )

n = 14

Calculating the degrees of freedom [tex]= df = n - 1 = 14 - 1 = 13[/tex]

At [tex]98\%[/tex] the confidence level, the t:

[tex]\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2} = \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}} \\\\df = t_{0.01,13} =2.650[/tex]

The critical value =2.650

Find out more about the critical value here:

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Answer:

C. V(x) = 2x^3 + 12x^2 + 22x + 12

Step-by-step explanation:

The volume of a fish tank is the multiplication of the area of the base by the height.

In this question:

Area of the base: [tex]B(x) = 2x^{2} + 6x + 4[/tex]

Height: [tex]H(x) = x + 3[/tex]

Volume:

[tex]V(x) = B(X)*H(x) = (2x^{2} + 6x + 4)(x + 3) = 2x^{3} + 6x^{2} + 4x + 6x^{2} + 18x + 12 = 2x^{3} + 12x^{2} + 22x + 12[/tex]

So the correct answer is:

C. V(x) = 2x^3 + 12x^2 + 22x + 12

Answer:

3

Step-by-step explanation:

x^2 + y^2 = 9

The equation of a circle is

(x-h)^2 + (y-k)^2 = r^2

( h,k) is the center and r is the radius

x^2 + y^2 = 3^2

The radius is 3