Which point lies on the line with point-slope equation y - 3 = 4(x + 7)?

A.
(7, 3)

B.
(7, -3)

C.
(-7, -3)

D.
(-7, 3)

[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^{7-4}2^4\\T_5=\dfrac{7!}{4!3!}\cdot x^3\cdot16\\T_5=16\cdot \dfrac{5\cdot6\cdot7}{2\cdot3}\cdot x^3\\\\T_5=560x^3[/tex]

Answer:

[tex]\large \boxed{560x^3}[/tex]

Step-by-step explanation:

[tex](x+2)^7[/tex]

Expand brackets.

[tex](x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)[/tex]

[tex](x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)[/tex]

[tex](x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)[/tex]

[tex]x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128[/tex]

The fifth term is 560x³.

Answer:

The present value is  [tex]PV = \$ 396,987[/tex]

Step-by-step explanation:

From the question we are told that

   The  interest payment per year is  [tex]C = \$ 85[/tex]

    The principal payment is  [tex]P = \$ 1000[/tex]

     The  duration is  n =  8   years

      The  interest rate is  [tex]r = 10\% = 0.10[/tex]

The present value is  mathematically represented as

      [tex]PV = [ \frac{C}{r} * [1 - \frac{1 }{ (1 +r)^n} ] + \frac{P}{(1 + r)^n} ][/tex]

substituting values

      [tex]PV = [ \frac{85}{0.10} * [1 - \frac{1 }{ (1 +0.10)^8} ] + \frac{1000}{(1 + 0.10)^ 8} ][/tex]

      [tex]PV = \$ 396,987[/tex]

Answer:

A) one-sample t-test

B) two sample t-test

C) two sample t-test

Step-by-step explanation: The one - sample t-test is used to determine the existence of a statistical difference between a sample mean and a given population mean. The one sample t test is only capable of making comparison between a singular sample mean and an established value. Such is the case in (A) where the aim is to determine if a group of night workers sleep for 8 hours.

The other two cases however, involves making comparison between the sample means of two different groups, this requires the use of a two independent sample t-test

For a one-sample t test:

(Sample mean - population mean) / standard error.

Sample mean = s

Population mean = p

Sample size = n

For a two sample t-test :

[(s2 - s1) - (p2 - p1)] ÷ √[(sd1^2/n1) + (sd2^2/n2)]

Answer:

D.

Step-by-step explanation:

In direct variations, we would have:

[tex]q=kr[/tex]

Where k is some constant.

Since this is indirect variation, instead of that, we would have:

[tex]q=\frac{k}{r}[/tex]

To determine the equation, find k by putting in the values for q and r:

[tex]10=\frac{k}{2.5}\\k=2.5(10)=25[/tex]

Now plug this back into the variation:

[tex]q=\frac{25}{r}[/tex]

The answer is D.

Answer:

If the null hypothesis is true in a chi-square test, discrepancies between observed and expected frequencies will tend to be small enough to qualify as a common outcome.

Step-by-step explanation:

Here in this question, we want to state what will happen if the null hypothesis is true in a chi-square test.

If the null hypothesis is true in a chi-square test, discrepancies between observed and expected frequencies will tend to be small enough to qualify as a common outcome.

This is because at a higher level of discrepancies, there will be a strong evidence against the null. This means that it will be rare to find discrepancies if null was true.

In the question however, since the null is true, the discrepancies we will be expecting will thus be small and common.

Answer:

x = 2/3 or x = -2/5

Step-by-step explanation:

15x^2 - 4x - 4 = ?

factor the left side of the expression and set factors equal to zero:

(3x-2)(5x+2)=0

3x - 2 =0 or 5x + 2 =0

3x =2 or 5x = -2

x = 2/3 or x = -2/5

Answer:

Even set = {HTT, THT, TTH, TTT}

Step-by-step explanation:

We are given that three coins are tossed; the result is at most one head.

And we have to find the sets of elements that are included in the sample space.

Firstly, as we know that when three coins are tossed, the total number of cases formed is 8.

Let Head on the coin be represented by 'H' and the Tail on the coin be represented by 'T'.

So, the sample space so formed is;

S = {HHH, HTH, HHT, THH, THT, TTH, HTT, TTT}

Now, our event is at most one head. So, the sample space for the favorable event is given by;

Even set = {HTT, THT, TTH, TTT}

In this, three cases are of head occurring only once and one case is of head not appearing in three tosses of a coin.

Step-by-step explanation:

To solve for x, we set up our equation like this:

7x - 7 = 4x + 14

Next, we subtract 4x from the right side to cancel it out and then subtract 4x from the left side.

7x (-4x) - 7 = 4x (-4x) + 14

3x - 7 = 14

Then, we add 7 on both sides (to cancel the -7 out and place it on the right)

3x - 7 (+7) = 14 + 7

3x = 21

Finally, we divide both sides by 3 to isolate our variable, x.

3x ÷ 3 = x

21 ÷ 3 = 7

Our final answer: x = 7

Triangle PQR=TSR

PROVED

Answer:

Image provided is correct, thank you!

Answer:

7.15 miles

Step-by-step explanation:

4/5 of a mile is equivalent to .8 miles.

32.95

-25.8

7.15

Answer:

Step-by-step explanation:

39.95 - 25.80 = 7.15 miles

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The 90% confidence interval is  [tex][108.165 ,112.895][/tex]

The  95%  confidence interval is [tex][107.7123 ,113.3477][/tex]

The  correct option is  D

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  48

     The sample  mean is  [tex]\= x = \$ 110.53[/tex]

    The standard deviation is  [tex]\sigma = \$ 9.96[/tex]

Considering first question

  Given that the confidence level is  90% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 90)\%[/tex]

           [tex]\alpha = 0.10[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = ZZ_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.645 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.365[/tex]

The  90% confidence interval is  

       [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]110.53 - 2.365 < \mu < 110.53 + 2.365[/tex]

=>    [tex]108.165 < \mu < 112.895[/tex]

Considering second question

  Given that the confidence level is  95% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 95)\%[/tex]

           [tex]\alpha = 0.05[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = Z_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.96 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.8177[/tex]

The  95% confidence interval is  

       [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]110.53 - 2.8177 < \mu < 110.53 + 2.8177[/tex]

=>    [tex]107.7123 < \mu < 113.3477[/tex]

Answer:

D. The zeros are the hot dog prices that give $0.00 profit (no profit).

Step-by-step explanation:

Given the function  y=-2(x-3)² + 4

The zeros of the function are the points at which the graph of the function crosses the x axis if plotted. y is the daily profit (in hundreds of dollars) and x is the price of the hot dog. To find the zeros, we substitute x = 0 and solve.

Therefore:  y=2(x-3)² + 4

0 = 2(x-3)² + 4

-2(x² - 6x + 9) + 4 = 0

-2x² + 12x - 18 + 4 = 0

2x² - 12x + 18 - 4 = 0

2x² - 12x + 14 = 0

2(x² - 6x + 7) = 0

x² - 6x + 7 = 0

Solving the quadratic equation gives:

x = 3 + √2 and x = 3 - √2

This means that the graph crosses x at 3 + √2 and 3 - √2.

The zeros of the function are 3 + √2 and 3 - √2. The zeros of the function is the point where y = 0, that is the point that the hot dog prices that give $0.00 profit (no profit).

Answer:

0.4

Step-by-step explanation:

we are required to find the probability that the ring is within 12 meters from nthe car.

we start by defining a random variable x to be the distance from the car. the car is the starting point.

x follows a normal distribution (0,30)

[tex]f(x)=\frac{1}{30}[/tex]

[tex]0<x<30[/tex]

probabilty of x ≤ 12

= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]

a = 12

b = 0

[tex]\frac{1}{30} *(12-0)[/tex]

[tex]\frac{12}{30} = 0.4[/tex]

therefore 0.4 is the probability that the ring is within 12 feet of your car.

Answer:

w ≥ -18

Step-by-step explanation:

Answer:

w is greater than or equal to-18

Answer:

Step-by-step explanation:

Answer:

C. 1/4

Step-by-step explanation:

Parallel lines always have the same slope.

Answer:

  C.  1/4

Step-by-step explanation:

Parallel lines have the same slope. If line b is parallel to line a, and line a has slope 1/4, then line b has slope 1/4.

Answer:

The 95% CI is   [tex]2.108 < \mu < 2.892[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean [tex]\mu = 2.5[/tex]

    The standard deviation is  [tex]\sigma = 0.8[/tex]

Given that the confidence level is  95% then the level of confidence is mathematically evaluated as

          [tex]\alpha = 100 - 95[/tex]

   =>  [tex]\alpha = 5\%[/tex]

  =>    [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is  [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

          [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

here we would assume that the sample size is  n =  16 since the person that posted the question did not include the sample size

  So    

               [tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]

               [tex]E = 0.392[/tex]

The  95% CI is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

              [tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]

substituting values

              [tex]2.108 < \mu < 2.892[/tex]

Answer:

Option (1)

Step-by-step explanation:

Given question is incomplete; find the picture of the graph in the attachment.

Parent function f(x) = [tex]\frac{1}{2^x}[/tex]

When function 'f' is translated by 4 units up which is evident form the graph, the translated function obtained is,

g(x) = f(x) + 4

g(x) = [tex]\frac{1}{2^x}+4[/tex]

Therefore, Option (1). [Translation of 4 units up] is defined by the graph attached.

Answer:

Option (1)

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Janet - 12 = Cody

60 - 12 = Cody

60 - 12 = 48

Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Answer: A. The sampling follows a normal distribution.

              B. Between 25.14 and 30.86

              C. About 95% will contain the true mean and about 5% won't

Step-by-step explanation: A. The sampling is normally distributed because:

B. For a 95% confidence interval: α/2 = 0.025

Since n = 210, use z-score = 1.96

To calculate the interval:

mean ± [tex]z.\frac{s}{\sqrt{n} }[/tex]

Replacing for the values given:

28 ± [tex]1.96.\frac{21}{\sqrt{210} }[/tex]

28 ± [tex]1.96*1.45[/tex]

28 ± 2.84

lower limit: 28 - 2.84 = 25.14

upper limit: 28 + 2.84 = 30.86

Confidence Interval is between 25.14 and 30.86.

C. Confidence Interval at a certain percentage is an interval of values that contains the true mean with a percentage of confidence. In the case of number of times per day students text, 95% of the interval will contain the true mean, while 5% will not contain it.

Answer:

The correct answer will be option b

Step-by-step explanation:

We know that x = rcos( θ ), and y = rsin( θ ), so let's rewrite this polar equation.

r = 4( x / r ) + 2( y / r ),

r = 4x / r + 2y / r,

r = 4x + 2y / r,

r / 1 = 4x + 2y / r ( Cross - Multiply )

4x + 2y = r²

We also know that r² = x² + y², so let's substitute.

x² + y² = 4x + 2y,

x² - 4x - 2y + y² = 0,

Circle Equation : ( x - 2 )² + ( y - 1 )² = ( √5 )²,

Solution : ( x - 2 )² + ( y - 1 )² = 5

Answer:

111 ft²

Step-by-step explanation:

wall: 10 x 12 = 120

window: 3 x 3 = 9

wall - window = area to wallpaper

120 - 9 = 111

111 ft²

Answer:

111 sq ft

Step-by-step explanation:

wall: 10 x 12 = 120

window: 3 x 3 = 9

wall - window = area to wallpaper

120 - 9 = 111

111 ft²

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

The determinant of the coefficient matrix is ...

  [tex]D=\left|\begin{array}{ccc}2&5&3\\4&-1&-4\\-5&-2&6\end{array}\right|\\\\=2(-1)(6)+5(-4)(-5)+3(4)(-2)-2(-4)(-2)-5(4)(6)-3(-1)(-5)\\\\=-12+100-24-16-120-15=\boxed{-87}[/tex]

The other determinants are found in similar fashion after substituting the constants on the right for each of the above matrix columns, in turn.

Those determinants are ...

  [tex]D_x=\left|\begin{array}{ccc}21&5&3\\-13&-1&-4\\0&-2&6\end{array}\right|=174[/tex]

  [tex]D_y=\left|\begin{array}{ccc}2&21&3\\4&-13&-4\\-5&0&6\end{array}\right|=-435[/tex]

  [tex]D_z=\left|\begin{array}{ccc}2&5&21\\4&-1&-13\\-5&-2&0\end{array}\right|=0[/tex]

The solutions are ...

  x = 174/-87 = -2

  y = -435/-87 = 5

  z = 0

That is, (x, y, z) = (-2, 5, 0).

Answer:

13.85

Step-by-step explanation:

U use the pythagorean theorem

So 2^2 + x^2 = 14^2

Simplify the equation: 4+x^2=196

--> x^2=192

--> x=13.85

-Hope this helps :)

9514 1404 393

Answer:

  c.  8√3

Step-by-step explanation:

The Pythagorean theorem applies.

  14² = s² + 2²

  s = √(14² -2²) = √192 = 8√3

The length of the remaining side is 8√3.

Answer:

Step-by-step explanation:

We could start by listing multiples of 4 and looking for patterns. Do  

you know what a multiple of a number is?  It's that number multiplied  

by another number. So the first multiple of 4 is 4x1, the second  

multiple of 4 is 4x2=8, the third multiple of 4 is 4x3=12, etc.  

Let's make a table of multiples of 4 from 1 to 100, with columns A-E  

across the top and rows 1-5 down the left-hand side:

    A      B      C      D      E

1    4      8     12     16     20

2   24     28     32     36     40

3   44     48     52     56     60

4   64     68     72     76     80

5   84     88     92     96    100

Now let's look at these multiples, remembering that there will be nine  

more tables like this one from 101-1000.

Let's look for 6,7,8,9, and 0 in the columns first. Aha! We can erase  

all of columns B, D, and E because there's a 6 or an 8 or a 0 in each  

number in those columns.  Now we're left with just:

    A      C  

1    4     12  

2   24     32  

3   44     52  

4   64     72  

5   84     92  

Now let's look at the rows. Wow! We can eliminate rows 4 and 5 because  

they have 6, 7, 8, or 9, leaving:

    A      C  

1    4     12  

2   24     32  

3   44     52  

Just 6 numbers left!

So if from 1-100 there are 6 multiples of four that do not contain any  

of the digits 6, 7, 8, 9, or 0, how many multiples of four like this  

are there from 1-1000?

Answer:

$188.91

Step-by-step explanation:

$999*.09=$89.91

$89.91+$99=$188.91

Answer:

the like terms are:

3x+8x+x+y+8

12x+y+8

Answer:

The like terms are

3x, 8x, x

Step-by-step explanation:

3x+8x+y+x+8

The like terms are

3x, 8x, x

They are the terms that are in terms of the first power of x

Answer:

316.08 inches

Step-by-step explanation:

There are 3 feet in a yard, and there is 12 inches in 1 foot, so there are 36 inches in one yard. If there is 8 7/9 yards it is the same at 8.78 yards, and  8.78 x 36 = 316.08 inches. Therefore 8 7/9 yards = 316.08 inches.