The following are the ages (years) of 5 people in a room: 25, 18, 17, 13, 24 A person enters the room. The mean age of the 6 people is now 22. What is the age of the person who entered the room?

Answer:

Student A says this estimate is reasonable because… Get ... Student A says this estimate is reasonable because the product is negative and about half of 1.5. Student B says you could find the product using a calculator as follows: "Divide −18 by 35, multiply the quotient by 1.43, then round the product

Step-by-step explanation:

calculations with a calculator or computer we need a way of checking that the answers it ... introduce students to this way of thinking and give them practice at estimating simple ... Do they always get the right answer no matter what? Invent a story illustrating a calculator error that you may have made or use the following.

Answer:

Step-by-step explanation:

Think about a right triangle with legs AB and AC. Then you have ...

  AB² +AC² = BC² = 10² = 100

If AB and AC are shorter than that, the sum of their squares will be less than 100. When the legs of a right triangle are shortened, the angle between them must increase in order for them to continue to form a triangle.

The triangle with AB² +AC² < 100 is an obtuse triangle.

__

Conversely, if AB and AC are lengthened so the sum of their squares is greater than 100, the angle between them will have to decrease for them to form a triangle.

The triangle with AB² +AC² > 100 is an acute triangle.

Answer:

A prism is a three-dimensional shape with the same cross-section all the way through.

Step-by-step explanation: Im not sure if i got the second right

A prism is a three-dimensional shape with the same cross-section all the way through.

A prism is a type of three-dimensional (3D) shape with flat sides. It has two ends that are the same shape and size (and look like a 2D shape).It has the same cross-section all along the shape from end to end; that means if you cut through it you would see the same 2D shape as on either end.

A prism has a solid shape consisting of two identical ends (such as triangle, square, rectangle, etc.), flat faces or surfaces and uniform cross-section across its length. The cross-section looks like a triangle hence called triangular prism. The shape of the prism does not have any curve.

To learn more about prism, refer

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Answer:

120

Step-by-step explanation:

Answer:

A. 40 degree+ 90 degree = x

The sum of the angles = 130 degree

Step-by-step explanation:

[tex]Given:\:\:\angle RSV = 40\degree,\:\:\angle VST = 90\degree\\\because \angle RSV + \angle VST = \angle RST\\\therefore 40\degree + 90\degree = x[/tex]

x = 130 degree

Answer:

  A.  A horizontal shift to the right 7.5 units

Step-by-step explanation:

Replacing x with x-7.5 shifts the graph 7.5 units to the right.

__

In general, g(x) = f(x-h)+k will shift h units right and k units up. In this problem there is no vertical shift.

Answer:

[tex]V = \frac{4}{3} \pi r^{2}[/tex] - is the formula for the volume of a circle.

Step-by-step explanation:

Step 1:

   - Insert your values:

       -  [tex]V = \frac{4}{3} \pi 4^{2}[/tex]

Step 2:

   - Simplify using order of operations:

       - Exponents First:

            - [tex]V = \frac{4}{3} \pi 64[/tex]

       - Division Second:

           - [tex]V = 1.333 \pi 64[/tex]

       - Multiplication Last:

           - [tex]V = 268.01555[/tex]

       - And Simplified:

           - V = 268 (approx.)

Hope this helps! Good luck!

Answer:

I think it's 462. I'm sry if I'm wrong.

Answer:

40 cm.

Step-by-step explanation:

So what I tried to do in this case is compare 96  to 64. I subtracted those two numbers which is 32. So since thats the difference between those two shapes, I did the same thing with 72 and I subtracted it but 32, which led me to 40.

Hope this helped :)

Answer:

u=48

Step-by-step explanation:

In similar triangles, corresponding sides have the same ratio.

64/96=u/72

Step 1: Cross-multiply

(64)*(72)=u*(96)

4608=96u

Step 2: Flip the equation.

96u=4608

Step 3: Divide both sides by 96.

96u /96=4608 /96

u=48

Answer:

H0: μ = 8.3 hours

Ha: μ > 8.3 hours

We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:

D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.

Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified

Step-by-step explanation:

For this case we want to determine if mean running time has increased as a result of the new change so then the system of hypothesis are given by:

Note: we assume that the value to check in order to be consistent with the options is 8.3

H0: μ = 8.3 hours

Ha: μ > 8.3 hours

We need to remember that a type of error II if the error associated when we NO reject the null hypothesis when actually the alternative hypothesis is true. And is also known as false negative. The best answer for this case would be:

D. The manufacturer will decide the mean battery life is 8.3 hours when in fact it is greater than 8.3 hours.

Since we are FAILING to reject the null hypothesis when the true mean is actually higher than the value specified

Answer:

290 m

Step-by-step explanation:

3*6*5=90

5*5*8= 200

200+90=290

Answer:

Step-by-step explanation:espinal hola defryet iSight x0 do hulp

Answer:

(x-1)^2= -0.5

Step-by-step explanation:

I DID THE USA TEST PREP AND THIS ANSWER WAS CORRECT

The general form for the equation of a line is:

[tex]y = mx + c[/tex]

Where:

m is the gradient of the line

c is the y intercept of the line  (y - intercept is where the graph crosses the y-axis)

So if you had the following equation:

[tex]y = 3x + 2[/tex]

Then:

m = 3

c = 2

So gradient = 3, and y intercept = 2

---------------------------------------------------

Rearranging

So first rearrange both of the equations in the form y = mx + c :

[tex]3x + 2y = -1[/tex]   becomes  [tex]y = -\frac{3}{2} x-\frac{1}{2}[/tex]      [tex](where: \ m = -\frac{3}{2} \ and, \ c = -\frac{1}{2} )[/tex]

and:

[tex]2x+7y=2[/tex]  becomes  [tex]y=-\frac{2}{7}x +\frac{2}{7}[/tex]     [tex](where: \ m = -\frac{2}{7} \ and, \ c = \frac{2}{7})[/tex]

---------------------------------------------

The question tells us that the equation of the line we are looking for has the same y-intercept as:

[tex]2x+7y=2[/tex]

So the line we are trying to work out will also have a y intercept of   [tex]\frac{2}{7}[/tex]

(refer to rearranging)

----------------------------

The question also tells us that the line is perpendicular to  [tex]3x + 2y = -1[/tex]

Perpendicular gradient = negative reciprocal of the gradient of the line it is perpendicular to.

So the gradient of the new line will be the  negative reciprocal of the gradient of  [tex]3x + 2y = -1[/tex]

Gradient of  [tex]3x + 2y = -1[/tex]  is: [tex]-\frac{3}{2}[/tex]

(refer to rearranging)

Gradient of new line: = negative reciprocal of  [tex]-\frac{3}{2}[/tex] , which is  [tex]\frac{2}{3}[/tex]

(just flip fraction and change the sign)

------------------------------------

So for the new line: [tex]m = \frac{2}{3} \ and, \ c = \frac{2}{7}[/tex]

So just substitute in the values for m and c into: y = mx + c

[tex]y = mx + c\\y = \frac{2}{3} x + \frac{2}{7}[/tex]

-----------------------------

Answer:

So equation of the new line is:

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

------------

Any questions, just ask.

Answer:

16%

percentage is calculated by 100

A. 2500 × 1/100 = 25%

B. 4100 x 1/100 = 41%

41% - 25%

16%

therefore bridge A is 16% shorter than bridge B

Answer:

$71

Step-by-step explanation:

Since x denotes the number of miles and we know that the car rode 100 miles, this means that x=100, and when we plug this in, we get C(x) = 0.5* 100 + 21 = 50 + 21 = $71. Hope this helps!

Answer:

C(100) = 71

Step-by-step explanation:

C(x) = .5x+21

Let x= 100

C(100) = .5(100)+21

         = 50+21

        = 71

Answer:

(3, -10)

Step-by-step explanation:

let A(x,y) and B(x1,y1)=(1,4)

by midpoint formula i.e. (x+x1)/2 ; (y+y1)/2

as midpoint is centre so,

(2, -3) = (x+1)/2 ; (y+4)/2

2=(x+1)/2  and -3=(y+4)/2

4-1=x    and   -6-4=y

x=3       and    y=-10

therefore A(x,y)=A(3,-10)

Answer:

32.4

Step-by-step explanation:

Answer:

32.4

Step-by-step explanation:

Product means the answer of a multiplication problem. So 75 x 0.45 = 32.4.

[tex]75 \times 0.45 = 32.4[/tex]

Hope this helped :)

Answer:

66

Step-by-step explanation:

So the volume of a cone is [tex]\pi r^2*\frac{h}{3}[/tex]

r = 3

h = 7

[tex]9\pi *\frac{7}{3} = 21\pi[/tex]

[tex]\frac{22}{7} *21=66[/tex]

Answer:

a) 252 square feet

Surface area of triangular prism = 252 square feet

Step-by-step explanation:

Explanation:-

Given diagram  Base = 3 feet

Height of the triangular = 4 feet

The slant height of triangular prism 'l' =20 feet

The hypotenuse of the triangle 'c' = 5 feet

 prism base area 'p' = h+b+c =  = 4 +3+5 =12

Surface area of triangular prism

                          = [tex]2 (\frac{1}{2} )bh +lA[/tex]

                           = b h + p l

                           = 3 ×4 + 12×20

                          = 252 square feet

Final answer:-

Surface area of triangular prism = 252 square feet

Answer:

252

Step-by-step explanation:

Answer:

2.82% probability that all of the sprinklers will operate correctly in a fire

Step-by-step explanation:

For each sprinkler, there are only two possible outcomes. Either they will operate correctly, or they will not. The probability of a sprinkler operating correctly is independent of other sprinklers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The researchers estimate the probability of a sprinkler to activate correctly to be 0.7.

This means that [tex]p = 0.7[/tex]

10 sprinklers.

This means that [tex]n = 10[/tex]

What is the probability that all of the sprinklers will operate correctly in a fire?

This is P(X = 10).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{10,10}.(0.7)^{10}.(0.3)^{0} = 0.0282[/tex]

2.82% probability that all of the sprinklers will operate correctly in a fire

The probability that all sprinklers will operate correctly in a fire is 0.028

The given parameters are:

p = 0.7 ---- the probability that a sprinkler to activate correctly

n = 10 --- the number of sprinklers

The probability that all sprinklers activate correctly is calculated as:

[tex]P(10) = p^n[/tex]

So, we have:

[tex]P(10) = 0.7^{10[/tex]

Evaluate

[tex]P(10) = 0.028[/tex]

Hence, the probability that all sprinklers will operate correctly in a fire is 0.028

Read more about probability at:

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sry my mistake wrong quesrion

Part A is correct; good job.

The universe is even numbers between 1 and 25, that's 2 thru 24. Count; there are twelve of them.

There's only one of them in the intersection of A and B, namely 8.

So the probability is one in twelve.

Answer: 1/12

Answer:

5/12

Step-by-step explanation:

The probability of rolling an odd number is 3/6, which is 1/2

The probability of rolling a factor of 12 is 5/6 (1,2,3,4,6)

1/2 x 5/6 = 5/12

Answer: Hot Dog $1.50 Drinks $2.00

Step-by-step explanation:

Answer:

17, 23

Step-by-step explanation:

First, to find the radius, we need to find the distance between the center of the circle, (-7, -1), and the point that the circle passes through, (8, 7). Plugging these coordinates into the distance formula we do [tex]\sqrt{(-7-8)^2+(-1-7)^2}[/tex] which gives us 17. Therefore, the radius of the circle is 17 units.

Next to find the y-coordinate of the point (-15, ), we need to write out the equation of the circle and then plug in the point. The equation of the circle would be [tex](x+7)^{2} +(y-8)^{2}=289[/tex]. Now we can plug in -15 for x and solve for y. So now we have [tex](-15+7)^{2} +(y-8)^{2}=289[/tex].

Simplifying the equation we have [tex](8)^{2} +(y-8)^{2}=289[/tex]. Subract [tex]8^{2}[/tex] from 289 and now the equation is [tex](y-8)^{2}=225[/tex]. Square root both sides to get [tex]y-8=15[/tex]. We solve for y to get 23. Therefore, the point is (-15, 23).

Answer:

Well, the answer would be 17,23 Also i had the same question as you so i already know the answer

Answer:

[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]

So then after 8 years we will have in the account 3283.153

And in order to find the interest we can do the following operation:

[tex] I = 3283.153 -1986 = 1297.153[/tex]

Step-by-step explanation:

For this case we can use the formula for the future value using compound interest given by:

[tex] A = P (1+ \frac{r}{n})^{nt}[/tex]

Where P= 1986 the initial amount invested. r = 0.063 represent the interest rate. n=12 represent the number of times that the rate is compounded in a year. And t =8 years . Replacing the info we got:

[tex] A = 1986(1+ \frac{0.063}{12})^{12*8} =3283.153[/tex]

So then after 8 years we will have in the account 3283.153

And in order to find the interest we can do the following operation:

[tex] I = 3283.153 -1986 = 1297.153[/tex]

We have been given that at a customer service call center for a large company, the number of calls received per hour is normally distributed with a mean of 150 calls and a standard deviation of 5 calls. We are asked to find the probability that during a given hour of the day there will be between 146 calls and 163 calls.

First of all, we will use z-score formula to find z-score corresponding to 146 and 163.

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

[tex]z=\frac{146-150}{5}[/tex]

[tex]z=\frac{-4}{5}[/tex]

[tex]z=-0.8[/tex]

[tex]z=\frac{163-150}{5}[/tex]

[tex]z=\frac{13}{5}[/tex]

[tex]z=2.6[/tex]

Our next step is to find percentage of data scores falls between both z-scores.

[tex]P(-0.8<z<2.6)=P(z<2.6)-P(z<-0.8)[/tex]

Using normal distribution table, we will get:

[tex]P(-0.8<z<2.6)=0.99534-0.21186[/tex]

[tex]P(-0.8<z<2.6)=0.78348[/tex]

Let us convert our answer into percentage.

[tex]0.78348\times 100\%=78.348\%[/tex]

Upon rounding our answer to nearest thousandths, we will get:

[tex]78.348\%\approx 78.35\%[/tex]

Therefore, the probability that during a given hour of the day there will be between 146 calls and 163 calls is approximately [tex]78.35\%[/tex].

Answer:

0.624

Step-by-step explanation:

DeltaMath

Answer:

16

Step-by-step explanation:

3x² + 4y² where x = 2, y = 1, and z = -3

Here we just need to plug in the given values to their respective variables

Answer:

0 if the original expression is : 3x^2 + 4yz

Step-by-step explanation:

3x^2 + 4yz ; I guess this is the original expression.

When x=2, y = 1 z =-3

3x^2 + 4yz = 3(2)^2 + 4 × (1)×(-3)

= 3×4 + 4 × (-3) = 12 - 12 = 0