What is the solution to the system of equations?
5x – 4y = 6
-5x + 4y = -10
O (4,4)
0 (-2,-5)
O infinitely many solutions
O no solution

Answer:

7.5

Step-by-step explanation:

Answer:

m∠Q = 61°

m∠S = 61°

m∠R = 58°

Step-by-step explanation:

Since we have an isosceles triangle, we know that ∠Q and ∠S are congruent.

Step 1: Definition of isosceles triangle

2x + 41 = 3x + 31

41 = x + 31

x = 10

Step 2: Find m∠Q

m∠Q = 2(10) + 41

m∠Q = 20 + 41

m∠Q = 61°

Step 3: Find m∠S

Since m∠Q = m∠S,

m∠S = 61°

Step 4: Find m∠R (Definition of a triangle)

Sum of angles in a triangle adds up to 180°

m∠R = 180 - (61 + 61)

m∠R = 180 - 122

m∠R = 58°

Answer:

The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]

The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]

Step-by-step explanation:

The summary of the given statistics is:

Population Mean = 26,500

Sample Mean = 30,150

Standard deviation = 10560

sample size = 24

The objective is to state the null hypothesis and the alternate hypothesis.

An hypothesis is a claim with  insufficient information which tends to be challenged into  further testing and experimentation in order to determine if such claim is significant or not.

The null hypothesis is a default hypothesis where there is no statistical significance between the two variables in the hypothesis.

The alternative hypothesis is the research hypothesis that the  researcher is trying to prove.

The null hypothesis [tex]\mathtt{H_0 : \mu = 26500}[/tex]

The alternative hypothesis [tex]\mathtt{H_1 : \mu \neq 26500}[/tex]

The test statistic can be  computed as follows:

[tex]z = \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{30150 - 26500}{\dfrac{10560}{\sqrt{24}}}[/tex]

[tex]z = \dfrac{3650}{\dfrac{10560}{4.8989}}[/tex]

[tex]z = \dfrac{3650 \times 4.8989 }{{10560}}[/tex]

z = 1.6933

Answer:

(x=6) is less than 18 which would give you the cost of the current plan

Step-by-step explanation:

If you take six, first you must multiply 4.50 by 6, ($27) then add it, to $94, giving you $121. Now we have to find which phone will give us the same cost, for this I choose 18. if you do 18 x 4.50, you get $81, and if you add this to 94, it gives you 175.

y = a(x  + 1.5)^2 - 12.5

y intercept is (0,-8) so:-

-8 = a(0+1.5)^2 - 12.5

-8 = 2.25a - 12.5

a =  4.5/ 2.25 = 2

so we have  

y  = 2 ( x +1.5)^2 - 12.5

solving for x  when y = 0:-

(x + 1.5)^2 = 12.5/2 = 6.25

taking sqrt's  x + 1.5  = +/- 2.5

x =  -4,   1

so the x intercepts are (-4,0) and (1,0)

Answer:

y = –1∕4(x – 8)^2 – 1

Step-by-step explanation:

I took the exam and  got  it  right.

Answer:

14x+4

Step-by-step explanation:

17x-3x=14x

Answer:

1) a) [tex]x = \frac{3}{2}\cdot a[/tex], b) [tex]x = 5-3\cdot a[/tex], c) [tex]x = -a[/tex], d) [tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]x = -\frac{3}{4}[/tex], b) [tex]x = -5[/tex], c) [tex]x = 3[/tex]

Step-by-step explanation:

1) a) [tex]5\cdot x - a = x + 5\cdot a[/tex]

[tex]5\cdot x - x = 5\cdot a + a[/tex]

[tex]4\cdot x = 6\cdot a[/tex]

[tex]x = \frac{3}{2}\cdot a[/tex]

b) [tex]4\cdot x + 3\cdot a = 3\cdot x + 5[/tex]

[tex]4\cdot x - 3\cdot x = 5 - 3\cdot a[/tex]

[tex]x = 5-3\cdot a[/tex]

c) [tex]2\cdot (3\cdot x - a) - 4\cdot (x-a) = 3\cdot (x+a)[/tex]

[tex]6\cdot x -2\cdot a -4\cdot x +4\cdot a = 3\cdot x +3\cdot a[/tex]

[tex]6\cdot x -4\cdot x -3\cdot x = 3\cdot a -4\cdot a +2\cdot a[/tex]

[tex]-x = a[/tex]

[tex]x = -a[/tex]

d) [tex]\frac{2\cdot x}{5} - \frac{x-2\cdot a}{3} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x-5\cdot (x-2\cdot a)}{15} = \frac{a}{2}[/tex]

[tex]\frac{6\cdot x - 5\cdot x+10\cdot a}{15} = \frac{a}{2}[/tex]

[tex]2\cdot (x+10\cdot a) = 15 \cdot a[/tex]

[tex]2\cdot x = 5\cdot a[/tex]

[tex]x = \frac{5}{2}\cdot a[/tex]

2) a) [tex]\frac{3}{x} + \frac{5}{x+2} = 0[/tex]

[tex]\frac{3\cdot (x+2)+5\cdot x}{x\cdot (x+2)} = 0[/tex]

[tex]3\cdot (x+2) + 5\cdot x = 0[/tex]

[tex]3\cdot x +6 +5\cdot x = 0[/tex]

[tex]8\cdot x = - 6[/tex]

[tex]x = -\frac{3}{4}[/tex]

b) [tex]\frac{7}{x-2} = \frac{5}{x}[/tex]

[tex]7\cdot x = 5\cdot (x-2)[/tex]

[tex]7\cdot x = 5\cdot x -10[/tex]

[tex]2\cdot x = -10[/tex]

[tex]x = -5[/tex]

c) [tex]\frac{2}{x-3}-\frac{4\cdot x}{x^{2}-9} = \frac{7}{x+3}[/tex]

[tex]\frac{2}{x-3} - \frac{4\cdot x}{(x+3)\cdot (x-3)} = \frac{7}{x+3}[/tex]

[tex]\frac{1}{x-3}\cdot \left(2-\frac{4\cdot x}{x+3} \right) = \frac{7}{x+3}[/tex]

[tex]\frac{x+3}{x-3}\cdot \left[\frac{2\cdot (x+3)-4\cdot x}{x+3} \right] = 7[/tex]

[tex]\frac{2\cdot (x+3)-4\cdot x}{x-3} = 7[/tex]

[tex]2\cdot (x+3) -4\cdot x = 7\cdot (x-3)[/tex]

[tex]2\cdot x + 6 - 4\cdot x = 7\cdot x -21[/tex]

[tex]2\cdot x - 4\cdot x -7\cdot x = -21-6[/tex]

[tex]-9\cdot x = -27[/tex]

[tex]x = 3[/tex]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

    [tex]P(3) = 0.154[/tex]

b

    [tex]P(4) = 0.026[/tex]

c

   [tex]P( X \ge 3 ) = 0.18[/tex]

d

   option C is correct

Step-by-step explanation:

From the question we are told that

      The probability of success is  p =  0.4

      The sample size is n=  4

 This adults believe follow a binomial distribution is because there are only two outcome one is an adult  believes in  reincarnation and the second an adult does not believe in reincarnation

  The probability of  failure is mathematically evaluated as

              [tex]q = 1 - p[/tex]

substituting values

             [tex]q = 1 - 0.4[/tex]

             [tex]q = 0.6[/tex]

Considering a  

The  probability that exactly 3 of the selected adults believe in reincarnation is mathematically represented as

       [tex]P(3) = \left n} \atop {}} \right. C_ 3 * p^3 * q^{n-3}[/tex]

substituting values

     [tex]P(3) = \left 4} \atop {}} \right. C_ 3 * (0.40)^3 * (0.60)^{4-3}[/tex]

Here [tex]\left 4} \atop {}} \right.C_3[/tex] means  4  combination 3 . i have calculated this using a calculator and the value is  

           [tex]\left 4} \atop {}} \right.C_3 = 4[/tex]

So

         [tex]P(3) = 4* (0.4)^3 * (0.6)[/tex]

          [tex]P(3) = 0.154[/tex]

Considering b

The probability that all of the selected adults believe in reincarnation is mathematically represented as

        [tex]P(n) = \left n} \atop {}} \right. C_ n * p^n * q^{n-n}[/tex]

substituting values

         [tex]P(4) = \left 4} \atop {}} \right. C_ 4 * (0.40)^4 * (0.60)^{4-4}[/tex]

Here [tex]\left 4} \atop {}} \right.C_3[/tex] means  4  combination  . i have calculated this using a calculator and the value is  [tex]\left 4} \atop {}} \right.C_4 = 1[/tex]

so

          [tex]P(4) = 1* (0.4)^4 * 1[/tex]

=>       [tex]P(4) = 0.026[/tex]

Considering c

the probability that at least 3 of the selected adults believe in reincarnation is mathematically represented as

     [tex]P( X \ge 3 ) = P(3 ) + P(n )[/tex]

substituting values

    [tex]P( X \ge 3 ) = 0.154 + 0.026[/tex]

     [tex]P( X \ge 3 ) = 0.18[/tex]

From the calculation the probability that all the 4 randomly selected persons believe in reincarnation is  [tex]p(4) = 0.026 < 0.05[/tex]

But the the probability of 3 out of the 4 randomly selected person believing in reincarnation is [tex]P(3) = 0.154 \ which \ is \ > 0.05[/tex]

Hence 3 is not a  significantly high number of adults who believe in reincarnation because the probability that 3 or more of the selected adults believe in reincarnation is greater than 0.05.

Answer:

See below.

Step-by-step explanation:

1 gal = 4 qt

With a full gallon oil tank, you can fill 4 1-qt bottles.

The problem does not mention the number of quarts that go in a case, so there is not enough information to answer the question.

Also, is the full tank really only 1 gallon, or is there a number missing there too?

Step-by-step explanation:

To find the value of y when z = 14 we must first find the relationship between them

The statement

y varies directly as z is written as

y = kz

where k is the constant of proportionality

when y = 180

z = 10

180 = 10k

Divide both sides by 10

k = 18

The formula for the variation is

y = 18z

When z = 14

y = 18(14)

Hope this helps you

Answer:

2+4+6+8

Step-by-step explanation:

We have the sum of 2n  where n runs from 1 to 4

n=1  2(1) = 2

n=2  2(2) = 4

n=3  2(3) = 6

n=4  2(4) = 8

The sum is add

2+4+6+8

Answer:

1) For every copy she sells, her pay increases by $110

2) Her total pay is 2300

Step-by-step explanation:

1) X is the number of copies she sells. In the equation 110X+ 2300 = Y, X will determine how many times 110 is multiplied. So, for every increase by one in X, Y will also go up by 110

eg.

110(50) + 2300 = 7800   -- if she sells 50 copies

110(51) + 2300 = 7910  -- if she sells 51 copies,

2) If she doesn't sell any copies, the equation becomes 110 * 0 + 2300. Anything multiplied by 0 equals 0, so the equation equals 0 + 2300 = 2300 = Y

Therefore, if she doesn't sell any copies, she will get a pay of $2300  

Graphed using the given range equation. The shaded area is the possible range, extending to infinity, infinity from 0, -1.

Now, it look like there is some information missing in the answer. The whole problem should look like this:

Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?

Answer:

She sold 24 copies of the cd each day.

Step-by-step explanation:

In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:

x= Number of copies sold.

So we can start setting our equation up. So we take the first part of the problem:

"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."

This can be translated as:

40-x

where this expression represents the number of copies left on the shelf by the end of monday.

"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."

so we represent it like this:

(40-x)+(40-x)

"In other words, she doubled the number that was left in the display."

so the previous expression can be simplified like this:

2(40-x)

"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."

so the expression now turns to:

2(40-x)-x   this is the number of copies left by the end of tuesday.

"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."

this translates to:

3[2(40-x)-x]

This is the number of copies on the shelf by the begining of Wednesday.

"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."

this piece of information lets us finish writting our equation:

3[2(40-x)-x] -x = 0

since there were no copies left on the shelf, then the equation is equal to zero.

So now we proceed and solve the equation for x:

3[2(40-x)-x] -x = 0

We simplify it from the inside to the outside.

3[80-2x-x]-x=0

3[80-3x]-x = 0

we now distribute the 3 so we get:

240-9x-x=0

we combine like terms so we get:

240-10x=0

we move the 240 to the other side of the equation so we get:

-10x=-240

and divide both sides into -10 so we get:

x=24

so she sold 24 copies each day.

4) 2x-2y+3 > 0

although it is spelt "26" on the choices

Answer:

A)

2. H0: Pe = Pw

H1: Pe [tex]\neq[/tex] Pw

B) Test statistics 1.96

Step-by-step explanation:

Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. In the given scenario the test is to identify whether there is any difference in annual goals between western division and eastern division. The  null hypothesis will be the Goals of western are equal to eastern division and alternative hypothesis will be Goals of western are not equal to eastern division.

Answer:

3x^4+(x^3)y-8x^2y^2+9xy^3-13y^4

Step-by-step explanation:

3x^4+(nothing)=3x^4

x^3y+(nothing)=x^3y

-10x^2y^2=2x^2y^2=-8x^2y^2

9xy^3+(nothing)=0

-4y^4-9y^4=-13y^4

Add it all up and write the terms by descending order of exponent value, and u get my answer.

Complete Question

The  complete question is shown on the first uploaded image

Answer:

  The correct option is C

Step-by-step explanation:

From the question we are told that

      The  number of purple  kernel is  [tex]n_k = 3593[/tex]

        The number of  yellow kernel is  [tex]n_y = 1102[/tex]

Generally the ration of the purple to the yellow kernels is mathematically evaluated as

              [tex]r = \frac{n_k}{n_y}[/tex]

substituting values

              [tex]r = \frac{3593}{1102}[/tex]

              [tex]r = 3.3[/tex]      

              [tex]r \approx 3[/tex]

Therefore the ratio is  

               [tex]1 \ Yellow : 3 \ Purple[/tex]

Answer:

Hey there!

We can use the midpoint formula to find that the midpoint is (-1, -9).

Let me know if this helps :)

The midpoint of the segment between the points (8,−10) and (−10,−8) will be (−1, −9). Then the correct option is A.

What is the midpoint of line segment AB?

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The midpoint of the segment between the points (8,−10) and (−10,−8)

x = (8 – 10) / 2

x = –1

y = (– 10 – 8) / 2

y = –9

Then the correct option is A.

More about the midpoint of line segment AB link is given below.

https://brainly.com/question/17410964

#SPJ5

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

Answer:

y = (9/4)x - 9

Step-by-step explanation:

The x-intercept is (4, 0) and the y-intercept is (0, -9).

As we move from (0, -9) to (4, 0), x (the 'run' increases by 4 and y (the 'rise' increases by 9.  Thus, the slope of the line connecting these two points is m = rise/run = 9/4, from which we can write the desired equation in the form y = mx + b:

y = (9/4)x - 9

Complete Question

The complete question is shown on the first uploaded image

Answer:

the null hypothesis is  [tex]H_o : \mu = 122[/tex]

the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]

The test statistics is  [tex]t = - 1.761[/tex]

The p-value is  [tex]p = P(Z < t ) = 0.039119[/tex]

so

    [tex]p \ge 0.01[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 122[/tex]

     The sample size is  n=  38

    The sample mean is  [tex]\= x = 116 \ feet[/tex]

     The standard deviation is [tex]\sigma = 21[/tex]

Generally the null hypothesis is  [tex]H_o : \mu = 122[/tex]

                the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]

Generally the test statistics is mathematically evaluated as

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

substituting values

         [tex]t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }[/tex]

         [tex]t = - 1.761[/tex]

The p-value is mathematically represented as

      [tex]p = P(Z < t )[/tex]

From the z- table  

     [tex]p = P(Z < t ) = 0.039119[/tex]

So  

     [tex]p \ge 0.01[/tex]

Answer:

220m

Step-by-step explanation:

l=85m

b=25m

perimeter=2(l+b)

2(85+25)

2(110)

=220m

perimeter is 220m

Answer:

Step-by-step explanation:

The distance around the field means the perimeter of the field

Since the field is rectangular

Perimeter of a rectangle = 2l + 2w

where l is the length

w is the width

From the question

l = 85m

w = 25m

Perimeter = 2(85) + 2(25)

Perimeter = 170 + 50

The final answer is

Perimeter = 220m

Hope this helps you

Answer:

92.9997<[tex]\mu[/tex]<99.5203

Step-by-step explanation:

Using the formula for calculating the confidence interval expressed as:

CI = xbar ± Z * S/√n where;

xbar is the sample mean

Z is the z-score at 90% confidence interval

S is the sample standard deviation

n is the sample size

Given parameters

xbar = 96.52

Z at 90% CI = 1.645

S = 10.70.

n = 25

Required

90% confidence interval for the population mean using the sample data.

Substituting the given parameters into the formula, we will have;

CI = 96.52 ± (1.645 * 10.70/√25)

CI = 96.52 ± (1.645 * 10.70/5)

CI = 96.52 ± (1.645 * 2.14)

CI = 96.52 ± (3.5203)

CI = (96.52-3.5203, 96.52+3.5203)

CI = (92.9997, 99.5203)

Hence a 90% confidence interval for the population mean using this sample data is 92.9997<[tex]\mu[/tex]<99.5203

Answer: 30 i think 10x3=30

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

We need to find the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex]

We know that,

[tex]\Sigma n^2=\dfrac{n(n+1)(2n+1)}{6}[/tex]

Here, n = 3

So,

[tex]\Sigma n^2=\dfrac{3(3+1)(2(3)+1)}{6}\\\\\Sigma n^2=14[/tex]

So,

[tex]\Sigma_{x=0}^3\ 2x^2=2\times 14\\\\=28[/tex]

So, the value of [tex]\Sigma_{x=0}^3\ 2x^2[/tex] is 28. Hence, the correct option is (d).

Answer:

154.2

Step-by-step explanation:

To find the average of the bowlers scores, you have to find the mean by adding the values and dividing by the number of values.

To find the bowlers average add the scores and divide by the number of games.

143+156+172+133+167/5=154.2 is the average score for the bowler.

Answer:

v(m) = 8 + 48m+ 180m² +216m³

Step-by-step explanation:

Let's first of all represent the edge of the the cube as a function of minutes.

Initially the egde= 2feet

As times elapsed , it increases at the rate of 6 feet per min, that is, for every minute ,there is a 6 feet increase.

Let the the egde be x

X = 2 + 6(m)

Where m represent the minutes elapsed.

So we Al know that the volume of an edge = edge³

but egde = x

V(m) = x³

but x= 2+6(m)

V(m) = (2+6m)³

v(m) = 8 + 48m+ 180m² +216m³

The volume of cube as function of m is,   [tex]V(m)=72m[/tex]

Let us consider that edge of cube is a feet.

Since,   The edge is increasing at the rate of 6 feet per minute.

                      [tex]\frac{da}{dt}=6feet/min.[/tex]

Volume of cube , V = [tex]a^{3}[/tex]

            [tex]\frac{dV}{dt} =3a^{2} \frac{da}{dt}[/tex]

Substituting the value of  da/dt in above equation.

We get,     [tex]\frac{dV}{dt}=3a^{2}*(6) =18a^{2} \\\\dV=18a^{2}dt[/tex]

Integrating on both side.

          [tex]V=18a^{2}t[/tex]

Since, number of minutes elapsed is m.

Substitute , t = m and a = 2 feet in above equation.

We get,     [tex]V=18(2)^{2}*m=72m[/tex]

Thus, the volume of cube as function of m is,   [tex]V(m)=72m[/tex]

Learn more:

https://brainly.com/question/14002029

Answer:

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Step-by-step explanation:

An augmented matrix is the coefficients of the variables and then the solution in rows

Rewriting the equations

2x -7y +6x = 7

x +3y -4z = 5

x +6y -15z = -6

The matrix is

2 -7  6   7

1 3    -4  5

1 6  -15  -6

Answer:

First option

Step-by-step explanation:

Common ratio is greater than 1