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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{2}) \\\\\\ y-7=- \cfrac{ 1 }{ 2 }x+1\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 2 }x+8 \end{array}}[/tex]

Answer:

0.29

Step-by-step explanation:

Total number of students = 35

Number of students who got B = 10

Probability that a student earns grade B :

Probability = required outcome / Total possible outcomes

P(grade B) = 10 / 35 = 0.2875

= 0.29

Answer:

que?

Step-by-step explanation:

Answer:

54 boys

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

the ratio 3/2 means 1.5 so we divide 36 over 1.5 we get 24…

to make sure we 36/24= 3/2=2.5

Answer:

D is correct option 840 meters

Step-by-step explanation:

S=vt

S= (24)(35)

S= 840 meters

Answer:

Following are the responses to the given question:

Step-by-step explanation:

Please find the table in the attached file.

mean and standard deviation difference: [tex]\bar{d}=\frac{\Sigma d}{n} =\frac{-4-6-.......-4-4}{8}=-4.125 \\\\S_d=\sqrt{\frac{\Sigma (d-\bar{d})^2 }{n-1}}=\sqrt{\frac{(-4 + 4.125)^2 +.......+(-4 +4.125)^2 }{8-1}}= 1.246[/tex]

For point a:

hypotheses are:

[tex]H_0 : \mu_d \geq -3\\\\H_a : \mu_d < -3\\\\[/tex]

degree of freedom:

[tex]df=n-1=8-1=7[/tex]

 From t table, at[tex]\alpha = 0.05[/tex], reject null hypothesis if [tex]t <-1.895[/tex].

test statistic:  

[tex]t=\frac{\bar{d}-\mu_d }{\frac{s_d}{\sqrt{d}}}=\frac{ -4.125- (-3)}{\frac{1.246}{ \sqrt{8}}} =-2.55[/tex]

because the [tex]t=-2.553 <-1.895[/tex], removing the null assumption. Data promotes a food product manufacturer's assertion with a likelihood of Type 1 error of 0.05.

For point b:

From t table, at [tex]\alpha =0.01[/tex], removing the null hypothesis if [tex]t<-2.998[/tex].

because [tex]t=-2.553 >-2.908[/tex], fail to removing the null hypothesis.  

The data do not help the foodstuff producer's point with the likelihood of a .01-type mistake.

For point c:

Hypotheses are:

[tex]H_0: \mu_d \geq -5\\\\H_a: \mu_d < -5[/tex]

Degree of freedom:

[tex]df=n-1=8-1=7[/tex]

From t table, at [tex]\alpha =0.05[/tex], removing the null hypothesis if [tex]t <-1.895[/tex].

test statistic:  [tex]t=\frac{\bar{d}-\mu_d}{\frac{s_d}{\sqrt{n}}} =\frac{-4.125-(-5)}{\frac{1.246}{\sqrt{8}}}=1.986[/tex]

Since [tex]t-1.986 >-1.895[/tex], The null hypothesis fails to reject. The results do not support the packaged food producer's claim with a Type 1 error probability of 0,05.

From t table, at[tex]\alpha= 0.01[/tex], reject null hypothesis if[tex]t<-2.998[/tex].

Since [tex]t=1.986>-2.998[/tex] , fail to reject null hypothesis.  

Data do not support the claim of the producer of the dietary product with the probability of Type 1 error of .01.

Answer:

Given that we know the base of the parabola is at the origin, and that it is symetrical about the y-axis, we can simplify the equation to

y=ax2=14px2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=ax2=14px2y=ax2=14px2

which corresponds to the given equation a=14p" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=14pa=14p given above.

Since y=6" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">y=6y=6 when x=2" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">x=2x=2,

6=a(2)2=4a" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">6=a(2)2=4a6=a(2)2=4a

and

a=32" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">a=32a=32

Thus we have

32=14p12p=2p=16" role="presentation" style="display: table-cell !important; line-height: 0; text-indent: 0px; text-align: center; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 3.337em; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; width: 10000em; position: relative;">32=14p12p=2p=1632=14p12p=2p=16

So, the receiver should be placed 16" role="presentation" style="display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.66px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;">1616 of a foot, or 2 inches, above the base.

If James paid with a $20 bill, he would get $7.25 in change ($20 - $12.20 = $7.25).

Change is a natural part of life. It is the process of making or becoming different, and can happen in an instant or over a long period of time. Change may refer to a transformation in a person’s life, such as a career switch, a change in lifestyle, or growth in maturity. It can also refer to a shift in the environment, such as a change in the weather, a demographic shift, or a dramatic event.

The equation c + $8.45 = $12.20 can be rewritten as c = $12.20 - $8.45. Solving this equation yields c = $3.75. This means James bought a popcorn for $3.75.
If James paid with a $20 bill, he would get $7.25 in change ($20 - $12.20 = $7.25).

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Answer:

a= 5

b= 9

c= -7

d= 12

Step-by-step explanation:

Therefore , R(N) = 100 + 400 (N+1)(2N+1) + 800 x N2 N3 and area are the formulas for R(N) for the function f(x) = (5x)2 on [1, 5] and the function f(x) = (5x)2 in terms of N. R(N) = 767(approx) (approx).

Each x value in the domain has one but only one y value range, according to the rule of a function. Definition. If there is only one and only one value of x variable such that f(x) = y, then the function is one-to-one.

Here,

In the given question, we have to find a formula for R(N) for the function f(x) =(5x)^2 on [1, 5] in terms of N.

The given function is f(x)=(5x)^2 on [1, 5].

Ax = (5-1)/N

Ax = 4/N

X = 1+iAx

X = 1+i4/N

f(x) = 25X^2

f(x) = 25(1+i4/N)^2

f(x) = 25(1+i8/N+16/N^2 i^{2})

R(N) = 1ƒ(X) Ax

Now putting the value of f(x) and Ax

R(N)==1 [25 (1+ &i + 16i2)]

R(N) = 1001 (1 +Ni + 16i2)

N100 (1+i+12)N

100 (N += i +122)+16 N(N+1)(2N+1)(+1)(2N+1)

R(N)=100 (N + √2/ N(N+1) x 100

R(N) =2/6× N + 100 × 5 × N(N+1) + 100 x 2

[tex]\lim_{n \to \infty}[/tex] R(N) = 100 + 400 + 800/3

[tex]\lim_{n \to \infty}[/tex] R(N) = 766.67

[tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx)

Therefore , the solution of the given problem of function comes out to be [tex]\lim_{n \to \infty}[/tex] R(N) = 767(approx).

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Answer:

A. -9/2

Step-by-step explanation:

Rate of change of y in respect to x = change in y/change in x

Using two pairs of values, say (-6, 33) and (-2, 15),

Rate of change = (15 - 33)/(-2 - (-6))

Rate of Change = -18/4

Simplify

Rate of change = -9/2

Answer:

d

Step-by-step explanation:

so the first part is multiplication and the second part is division bc it's a fraction hope this helps <3

Answer: 58 i think

Step-by-step explanation: i guess you have to add sorry if it wrong

Answer:

y=mx+b format... 8th grade math class memories...ahhh

Step-by-step explanation:

Employee B-

one time bonus of 90 gets plugged into the b spot

13 an hour goes into the m space

415 total paid goes into the y spot

415=13(x)+90

subtract 90 from 415 and 90

325=13(x)

divide 325 by 13 and 13

25=(x)

Now plug x into the y=mx+b format with all your other numbers to check

y=13(25)+90

y=415!!

Hope this wasn't too confusing, good luck!

Answer:

Step-by-step explanation: reduce mean divide so 400 divided by 4 =28

Answer:

46

Step-by-step explanation:

No Alisa do not have enough fence.

The perimeter of an object is given by adding the side lengths of the object.

Given that Alisa needs 4.65 feet of fencing to complete the fence she is building. She has a piece of fencing that is 4 ft long.

We need to determine whether she have enough fencing or not,

Since we know that the fencing can be considered as perimeter of the building,

So, if she only has 4 ft long fence, she cannot cover a 4.65 ft long fence.

Hence Alisa do not have enough fence.

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Answer:

The volume is 384 cm^2.

Step-by-step explanation:

The equation for a pyramid is the base area times the height divided by 3, so [tex]a^2h/3[/tex]. In this case, we know the side length but we do not know the height. We can use the Pythagorean Theorem to get:

6^2 + b^2 = 10^2

36 + b^2 = 100

b^2 = 64

b = 8

Therefore, our height is 8. Plug this into the equation to get:

12^2 (8) / 3

144 (8) / 3

1152 / 3

384

The number of atoms that are there in 400 grams of hydrogen will be 2.408 × 10^26.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.

In this case, there are 6.02 × 10^23 atoms in 1 gram of hydrogen.

The number of atoms that are there in 400 grams of hydrogen will be:

= 6.02 × 10^23 × 400

= 2408 × 10^23

= 2.408 × 10^3 × 10^23

= 2.408 × 10^26

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Answer:

3*(5 + q) = 15 + 3*q

Step-by-step explanation:

The distributive property is:

A*(B + C) = A*B + A*C

We know that you buy 5 small pots and q packages of seeds for $3 each.

And we know that the equation that models the cost is:

3*(5 + q)

Now we can simply apply the distributive property to rewrite this expression as:

3*(5 + q) = 3*5 + 3*q = 15 + 3*q

So the equivalent expression is: 15 + 3*q

The value of the expression 8x² + 6x - 8 below when x=2 is 36.

The expression can be evaluated by following the steps below:

8x² + 6x - 8 in x = 2 means that the variable x will be replaced by the given number which is 2.

8*2² + 6*2 - 8

8*4 + 12 - 8

32 + 16 - 8 = 36

This therefore means that when x= 2 in 8x² + 6x - 8 , the value gotten will be 36.

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Therefore , (1, 3), (2, 5), (3, 7) (4, 9) and (1, 3), (2, 3), (3, 3) (4, 3) are the relations that represent a function.  

According to a function's rule, every x value in the domain has one and only one range of y values. Definition. A one-to-one function exists when there is just one and only one value of x such that f(x) = y.

Here,

The relationship is (1, 3), (2, 5), and (2, 7) (4, 9)

Given that 2 is repeated, the connection is not a function.

The relationship is (1, 3), (2, 5), and (3, 7) (4, 9)

Since there are no repeating numbers, the relation is a function.

The relationship stated is (1, 3), (1, 5), and (1, 7). (4, 9)

The relationship is not a 1 repeated function.

The relationships are (1, 3), (2, 3), and (3, 3). (4, 3)

Since there are no repeating numbers, the relation is a function.

The relationship stated is (1, 2), (2, 5), and (2, 1) (4, 5)

As 2 repeated, the relationship is not a function.

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Answer:

C)is an expression because it cannot be solved

Answer:

Step-by-step explanation:

3.14x (3)^2

28.3ft

Answer:

The area of the circle is 28.3 [tex]ft^2[/tex].

Step-by-step explanation:

The formula to find the area of a circle is [tex]\pi r^2[/tex], where [tex]r[/tex] represents the radius of the circle. In this case, the area would be [tex]3.14 * 3^2 = 3.14 * 9 = 28.26[/tex] ≈ 28.3 [tex]ft^2[/tex].

Answer:

x + 3x = 1172, where x is the cost of the coffee table and 3x equals the cost of the couch.  

4x = 1172  

x = 293  

thus, 3x = 293

293 x 3= 879

The couch is $879 and the coffee table is $293

The density in terms of  pounds per cubic foot is 101.2 pounds/ft³

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here; 6900 g for every 4.05 quarts thus expressing in terms of pounds per cubic foot we get = 15.22/0.15039

                                                  = 101.2

Hence, The density in terms of  pounds per cubic foot is 101.2 pounds/ft³

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