Every new computer costs $702.37 from a local store. The nearby school has a policy that every 3 children must have at least 1 computer. If each class has 24 children, how much money should the school spend on computers if there is 17 classes?

Answer:

A

The  test statistics is  [tex]t = -1.7[/tex]

B

The  Null and  Alternative hypothesis are

      [tex]H_o : \mu = 47.2[/tex]   and  [tex]H_a : \mu \ne 47.2[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 47.2 miles/gallon(MPG)[/tex]

    The sample size is  [tex]n = 250 \ van[/tex]

     The  sample mean is  [tex]\= x = 47.0[/tex]

      The sample  standard deviation is  [tex]\sigma = 1.9[/tex]

      The level of significance is  [tex]\alpha = 0.02[/tex]

Given that the value which the manufacturer gave the automobile is  47.2 and  it is believed that this is not correct, then  

The  Null Hypothesis is  

        [tex]H_o : \mu = 47.2[/tex]

The alternative Hypothesis  is  

        [tex]H_a : \mu \ne 47.2[/tex]

The test statistics can be mathematically evaluated as  

        [tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

        [tex]t = \frac{\= 47- 47.2}{\frac{1.9 }{\sqrt{250} } }[/tex]

       [tex]t = -1.7[/tex]

Answer:

[tex] z =\frac{26-25}{\frac{3}{\sqrt{50}}}= 2.357[/tex]

And we can find the probability using the normal distribution table and we got:

[tex] P(z<2.357) =0.9908[/tex]

Step-by-step explanation:

Let X the random variable of interest and we can find the parameters:

[tex] \mu =25, \sigma= 3[/tex]

And for this case we select a sample size n =50. And since the sample size is higher than 30 we can use the central limit theorem and the distribution for the sample mean would be given by:

[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]

We want to find the following probability:

[tex] P(\bar X <26)[/tex]

And we can use the z score formula given by:

[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And replacing we got:

[tex] z =\frac{26-25}{\frac{3}{\sqrt{50}}}= 2.357[/tex]

And we can find the probability using the normal distribution table and we got:

[tex] P(z<2.357) =0.9908[/tex]

Answer:

0.02

Step-by-step explanation:

If n is 50, 1/n is equivalent to 1/50. 1/50 as a decimal is 0.02.

Answer:

198.5

Step-by-step explanation:

() = 200 - 1.5

() = 198.5

im not sure if this is what you are asking, but i hope it helps

Answer:

S=p(200-1.5)  

Answer:

  8 : 1

Step-by-step explanation:

The graph shows a point at the location corresponding to 8 cups of raspberry juice and 1 cup of lemon-lime soda. So the ratio is ...

  raspberry juice : lemon-lime soda = 8 : 1

Answer:

D

Step-by-step explanation:

raspberry : lemon lime soda::8:1

Answer:

The value will decrease.

Step-by-step explanation:

The 55th term of the 7, 10, 13, 16, ... arithmetic sequence is a(55) = 169.

This is an arithmetic sequence since there is a common difference between each term. In this case , adding 3 to the previous term in the sequence gives the next term.

a(n) = a(1) + d( n- 1)

d = 3

This is the formula of an arithmetic sequence.

an = a(1) + d( n- 1)

Substitute in the values of

a(1) = 7 and

d = 3

a(n) = 7 + 3 ( n- 1)

Simplify each term.

a(n) = 7 + 3n- 3

Subtract 3 from 7.

a(n) =  3n + 4

The nth term = 3n + 4. The formula for the nth term of an arithmetic progression is a(n) = dn + a(1) - d. Therefore in your sequence, the difference d = 3, and the first term a(1) = 7.

Substitute in the value of n to find the nth term.

a(55) = 3 (55) + 4

Multiply 3 by 55 .

a(55) = 165 + 4

Add 165 and 4.

a(55) = 169

Thus , The 55th term in the arithmetic progression of 7, 10, 13, 16,... is a(55) = 169.

To learn more about Aritmetic sequence

https://brainly.com/question/6561461

#SPJ1

Answer:

Option D

Step-by-step explanation:

It forms a linear pair (Angles on a straight line) with one of the interior angles of the triangle.

Answer:

D

Step-by-step explanation:

A linear pair of angles is when two angles add up to 180 degrees on a line.

Interior angles and exterior angles form a linear pair.

Answer:

The price of one reusable bottle is $8.12

Step-by-steetp explanation:

Ms stone wanted to purchase two reusable bottles but discovered she had only ⅝of the Mone and that ⅝ is equal to $ 10.15.

So the cost of what she wants to purchase will be called x.

Mathematically

⅝ * x = 10.15

X = (10.15*8)/5

X = 81.2/5

X= 16.24

The price of the two bottles is $16.24

So the price if one bottle will be calculated as follows.

2 bottles=$ 16.24

One bottle= $16.24/2

One bottle= $8.12

The price of one reusable bottle is $8.12

Answer:

given,

AB= 17

AC= 8

angle BCA =90°

as it is a Right angled triangle ,

taking reference angle BAC

we get,h=AB=17

b=AC=8

p=BC=?

now by the Pythagoras theorem we get,

p=

[tex] \sqrt{h { }^{2} - b {}^{2} } [/tex]

so,p=

[tex] \sqrt{17 {}^{2} - 8 {}^{2} } [/tex]

[tex] = \sqrt{225} [/tex]

=15 is the answer....

hope its wht u r searching for....

Answer:

  x + y + z = 14

Step-by-step explanation:

If the points are designated A, B, C, then ...

  AB × AC = (7, -7, 0) × (7, 0, -7) = (49, 49, 49).

That is, a vector perpendicular to the plane is (1, 1, 1), so the equation of the plane can be ...

  (1, 1, 1)·(x, y, z) = (1, 1, 1)·A

  x + y + z = 14

Answer:

(a) remainder is -40

(b) The remaining zeroes are (x+3) and (x-3)

Step-by-step explanation:

p(x) = x^4 - 2x^3 -7x^2 + 18x – 18

(a) Remainder of P(x) / (x+1) can be found using the remainder theorem, namely

let x + 1 = 0 => x = -1

remainder

= P(-1)

= (-1)^4 - 2(-1)^3 -7(-1)^2 + 18(-1) – 18

= 1 +2 -7-18-18

= -40

remainder is -40

(b)

If one zero is 1-i, then the conjugate 1+i is another zero.

in other words,

(x-1+i) and (x-1-i) are both factors.

whose product = (x^2-2x+2)

Divide p(x) by (x^2-2x+2) gives

p(x) by (x^2-2x+2)

= (x^4 - 2x^3 -7x^2 + 18x – 18) / (x^2-2x+2)

= x^2 -9

= (x+3) * (x-3)

The remaining zeroes are (x+3) and (x-3)

Answer:

(f - g)(x) = -x - 14

Step-by-step explanation:

Step 1: Plug in equations

4x - 8 - (5x + 6)

Step 2; Distribute negative

4x - 8 - 5x - 6

Step 3: Combine like terms

-x - 14

Answer:

-x-14

Step-by-step explanation:

Hope this helps

Answer:

True

Step-by-step explanation:

Coefficient of realism called alpha which is a decimal number between 0 and 1. This number provides the optimistic view. The number 1 - [tex]\alpha[/tex] is amount of emphasis that is placed in pessimistic outcome. If the coefficient of realism alpha is 1 then criterion of realism will yield same result as maxi max criterion.

Answer:

Hey there! Your answer would be:  [tex]3x^2+4=x[/tex]

The quadratic formula is (-b±√(b²-4ac))/(2a), and helps us find roots to a quadratic equation.

All quadratic equations can be written in the [tex]ax^2+bx+c[/tex] form, and a, b, and c, are numbers we need for the quadratic equation.

Our given quadratic equation is 1±√(-1)²-4(3)(4)/2(3)

We can see that b is -1, as -b is positive 1.

That gives us  [tex]ax^2+-1x+c[/tex], which can be simplified to [tex]ax^2-x+c[/tex].

We can see that a is 3, because 2a=6, so a has to be 3.

That gives us [tex]3x^2-x+c[/tex]

Finally, we see that 4 is equal to b, clearly shown in the numerator of this fraction.

Which gives us a final answer of [tex]3x^2-x+4[/tex], or [tex]3x^2+4=x[/tex]

Answer:

D

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

This can be written as 5r:9g. Add 5 and 9 to get the total of 14. You can write a ratio of 9 green: (out of) 14 total = x green: (out of) 70 total. Multiply 9 and 14 by 7 to get 45:70. Therefore, if there are 70 hairbands, 45 are green.

Answer:

4

Step-by-step explanation:

(segment piece) x (segment piece) =   (segment piece) x (segment piece)

JN* NK = LN * NM

3x = 2*6

3x = 12

Divide by 3

3x/3 =12/3

x =4

Answer:

31ft

Step-by-step explanation:

6 ft  + 2.5 ft + 12 ft  + 2.5 ft  + 8 ft  = 31ft

I assumed the slash in the space between 2.5ft and 12ft was an error, so I ignored it in the solution to this problem.

Besides that, perimeter is found by adding all sides of the shape or figure together, and the sum of that is the perimeter.

The basic formula for perimeter is:

base + height + base + height.

I do not think you square perimeter as you do area (e.g. 31ft^2).

Answer:

173.20 ft

Step-by-step explanation:

[tex] \tan \: 30 \degree = \frac{length \: of \: tunnel}{depth \: of \: tunnel} \\ \\ \frac{1}{ \sqrt{3} } = \frac{length \: of \: tunnel}{300} \\ \\ length \: of \: tunnel \\ \\ = \frac{300}{ \sqrt{3} } \\ \\ = \frac{300 \sqrt{3} }{3} \\ \\ = 100 \sqrt{3} \\ \\ = 100 \times 1.7320 \\ \\ = 173.20 \: ft[/tex]

Answer:Ratio

Step-by-step explanation:

The ratio data because length has a true zero, and ratios of lengths are meaningful.

Answer:

(A)  (-19,-8)

Step-by-step explanation:

Given that the graph is an inverse variation.

The equation of variation is:

[tex]x=\dfrac{k}{y}[/tex]

Since point (-8, -19) is on the graph

[tex]-8=\dfrac{k}{-19}\\k=152[/tex]

Therefore, the equation connecting x and y is:

[tex]x=\dfrac{152}{y}[/tex]

[tex]\text{When y=-8},x=\dfrac{152}{-8}=-19\\\\\text{When y=19},x=\dfrac{152}{19}=8\\\\\text{When y=8},x=\dfrac{152}{8}=19\\\\\text{When y=-19},x=\dfrac{152}{-19}=-8[/tex]

Therefore, the point that is also on the graph is:

(A)  (-19,-8)

Answer:

Vertical Line

Step-by-step explanation:

A vertical line is x = [a number]

A horizontal line is y = [a number]

Answer:

vertical line

Step-by-step explanation:

A vertical line is of the form

x =

All the x values are the same and the y value changes

x = -4 is a vertical line

Answer: Volume = [tex]\frac{20\pi }{3}[/tex]

Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be

V = [tex]\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx[/tex]

For this case, the region generated by the conditions proposed above is shown in the attachment.

Because it is revolting around the y-axis, the formula will be:

[tex]V=\pi \int\limits^a_b {(R(y))^{2} - (r(y))^{2}} \, dy[/tex]

Since it is given points, first find the function for points (3,2) and (1,0):

m = [tex]\frac{2-0}{3-1}[/tex] = 1

[tex]y-y_{0} = m(x-x_{0})[/tex]

y - 0 = 1(x-1)

y = x - 1

As it is rotating around y:

x = y + 1

This is R(y).

r(y) = 1, the lower limit of the region.

The volume will be calculated as:

[tex]V = \pi \int\limits^2_0 {[(y+1)^{2} - 1^{2}]} \, dy[/tex]

[tex]V = \pi \int\limits^2_0 {y^{2}+2y+1 - 1} \, dy[/tex]

[tex]V=\pi \int\limits^2_0 {y^{2}+2y} \, dy[/tex]

[tex]V=\pi(\frac{y^{3}}{3}+y^{2} )[/tex]

[tex]V=\pi (\frac{2^{3}}{3}+2^{2} - 0)[/tex]

[tex]V=\frac{20\pi }{3}[/tex]

The volume of the region bounded by the points is [tex]\frac{20\pi }{3}[/tex].

Answer:

Lateral area of the pyramid = 120 square units

Step-by-step explanation:

In the figure attached,

A pyramid has been given with square base with edges of 12 units and perpendicular height as 8 units.

Lateral area of a pyramid = Area of the lateral sides

Area of one lateral side = [tex]\frac{1}{2}(\text{Base})(\text{Lateral height})[/tex]

                                       = [tex]\frac{1}{2}(\frac{b}{2})(\sqrt{(\frac{b}{2})^2+h^2})[/tex]  [Since l = [tex]\sqrt{r^{2}+h^{2}}[/tex]]

                                       = [tex]\frac{1}{2}(6)(\sqrt{6^2+8^2})[/tex]

                                       = [tex]3\sqrt{100}[/tex]

                                       = 30 units²

Now lateral area of the pyramid = 4 × 30 = 120 square units

Answer: 240 units^2

Step-by-step explanation:

LA= 1/2 Pl

P= perimeter of base

l= lateral height

l= 8^2 + (12/2)^2 = 10^2

P= 12 x 4 = 48

48 x 10 = 480

480/2 = 240

240 units^2

Answer:

Area = 40×20

=800Step-by-step explanation:

Answer:

C. 44 °

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

180 - 88 = 92

Angles in a triangle add up to 180 degrees.

y + y + 92 = 180

y + y = 88

2y = 88

y = 88/2

y = 44

Answer:

The answer is 46"

Step-by-step explanation:

A triangle is 180 degrees

so u already know one side

180"-88" is 92

then divide 92 by 2 which is 46

Answer: 46"

Answer: 50 miles

Step-by-step explanation:

75 miles in one and half hours.

That's 25 miles per half hour

So, in 1 hour, he will drive 50 miles

Answer:

B. 0.220

Step-by-step explanation:

The table is presented properly below:

[tex]\left|\begin{array}{c|cccc|c}$toppings&$Freshman&$Sophomore&$Junior&$Senior&$Total\\---&---&---&---&---&---\\$Cheese&11&15&24&28&78\\$Meat&23&28&15&11&77\\$Veggie&15&11&23&28&77\\---&---&---&---&---&---\\$Total&&&&&232\end{array}\right|[/tex]

Number of junior students who prefers veggies =23

Number of senior students who prefers veggies =28

Total =23+28=51

Therefore, the probability that a randomly selected student who is a junior or senior prefers veggie

=51/232

=0.220 (to the nearest thousandth)

The correct option is B.

Answer:

30 m^3

Step-by-step explanation:

Answer:

B. 20m3

Step-by-step explanation:

i dont know if its correct, hope it is tho