what is the slope of the line containing the points (-3,7) and (3,3)

Answer: 30 years

Step-by-step explanation:

From the question, we are told that the mean age of 10 women in an office is 30 years old. This means that the total ages of the women in the office will be:

= 10 × 30 years

= 300 years

Also, the mean age of 10 men in an office is 29 years old. This means that the total ages of the men in the office will be:

= 10 × 29 years

= 290 years

Since there are 10 men and 10 women in the office, the number of people in the office is: 10 + 10 = 20 people. Also, the total ages will be: 300 + 290 = 590 years.

The mean age (nearest year) of all the people in the office will then be:

= 590/20

= 29.5 years

= 30 years approximately

The correct answer is  c. 2 [tex]\frac{1}{2}[/tex] hours

Explanation:

The graphic shows the relationship between the distance Erin covers by running and the time this requires. Additionally, to know the specific time that takes for Erin to run a specific distance or vice versa it is necessary to observe at which point the two variables intersect in the line of the graph.

According to this, Erin runs 25 miles (y-axis) in 2.5 hours (x-axis), which you can know because in the line shown by the graph the distance 25 miles that is in the middle of 20 and 30 miles intersects with 2.5 hours or the middle between 2 and 3. Additionally, this number can be expressed as 2 and a half hours, 2.5 or even 2 [tex]\frac{1}{2}[/tex] hours because the fraction represents half. This makes option C the answer.

Answer:

Step-by-step explanation:

A square has equal sides. Let x represent the length of each side of the square carpet. The diagram representing the room and the carpet is shown in the attached photo. Therefore, the length of the room would be (x + 2)m while the width of the room would be (x + 1)m

Since the area of the room is 56m², it means that

(x + 2)(x + 1) = 56

x² + x + 2x + 2 = 56

x² + 3x + 2 - 56 = 0

x² + 3x - 54 = 0

x² + 9x - 6x - 54 = 0

x(x + 9) - 6(x + 9) = 0

x - 6 = 0 or x + 9 = 0

x = 6 or x = - 9

Since the dimension of the carpet cannot be negative, then x = 6

The dimension of the carpet is 6m × 6m

Answer:

[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]

Step-by-step explanation:

[tex]$\left(\frac{1}{2}x+3y \right)^4=\left(\frac{x}{2}+3y \right)^4\\$[/tex]

Binomial Expansion Formula:

[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex], also [tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]

We have to solve [tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\sum_{k=0}^{4} \binom{4}{k} \left(3 y\right)^{4-k} \left(\frac{x}{2}\right)^k$[/tex]

Now we should calculate for [tex]k=0, k=1, k=2, k=3 \text{ and } k =4;[/tex]

First, for [tex]k=0[/tex]

[tex]$\binom{4}{0} \left(3 y\right)^{4-0} \left(\frac{x}{2}\right)^{0}=\frac{4!}{(4-0)! 0!}\left(3 y\right)^{4} \left(\frac{x}{2}\right)^{0}=\frac{4!}{4!}(81y^4)\cdot 1 =81 y^{4}$[/tex]

It is the same procedure for the other:

For [tex]k=1[/tex]

[tex]$\binom{4}{1} \left(3 y\right)^{4-1} \left(\frac{x}{2}\right)^{1}=54 x y^{3}$[/tex]

For [tex]k=2[/tex]

[tex]$\binom{4}{2} \left(3 y\right)^{4-2} \left(\frac{x}{2}\right)^{2}=\frac{27}{2} x^{2} y^{2}$[/tex]

For [tex]k=3[/tex]

[tex]$\binom{4}{3} \left(3 y\right)^{4-3} \left(\frac{x}{2}\right)^{3}=\frac{3}{2} x^{3} y$[/tex]

For [tex]k=4[/tex]

[tex]$\binom{4}{4} \left(3 y\right)^{4-4} \left(\frac{x}{2}\right)^{4}=\frac{x^{4}}{16}$[/tex]

You can perform the calculations, I will not type everything.

The answer is the sum of elements calculated.

Just organizing:

[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]

Answer:  [tex]\bold{\dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4}[/tex]

Step-by-step explanation:

                     Binomial Tree

n=0                         1

n=1                      1      1

n=2                  1    2     1

n=3               1    3    3     1

n=4            1    4    6    4    1

Using the Binomial Theorem

[tex]\bigg(\dfrac{1}{2}x+3y\bigg)^4\\\\\\=1\bigg(\dfrac{1}{2}x\bigg)^4(3y)^0\quad \rightarrow \quad \dfrac{1}{16}x^4\\\\+4\bigg(\dfrac{1}{2}x\bigg)^3(3y)^1\quad \rightarrow \quad \dfrac{3}{2}x^3y\\\\+6\bigg(\dfrac{1}{2}x\bigg)^2(3y)^2\quad \rightarrow \quad \dfrac{27}{2}x^2y^2\\\\+4\bigg(\dfrac{1}{2}x\bigg)^1(3y)^3\quad \rightarrow \quad 54xy^3\\\\+1\bigg(\dfrac{1}{2}x\bigg)^0(3y)^4\quad \rightarrow \quad 81y^4[/tex]

______________________

[tex]= \dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4[/tex]

Answer:

Step-by-step explanation:divide both sides by the coefficient of x that is the number beside x and in inequality, when dividing with a negative sign the sign would change to its opposite sign.

-6<-2x

-6/-2>-2x/-2

3>x

X<3 this is the answer.

Answer:

4 times

Step-by-step explanation:

1 quart is equivalent to 32 fluid ounces.

If each eruption consumes 8 fluid ounces of vinegar. Assuming that the amount of vinegar required per eruption is constant, the number of times Tanvi can make her volcano erupt is:

[tex]n=\frac{32}{8}\\n=4\ times[/tex]

Tanvi can make her volcano erupt 4 times  with 1 quart of vinegar.

Answer:

Step-by-step explanation:

Sarah: School to mall = 21

           mall to library = 20

Total distance for Sarah = 20 + 21 = 41 miles.

Use the Pythagorean theorem to find the distance Bret traveled:

Distance = SQRT(21^2 + 20^2)

              = sqrt(441 + 400)

              = sqrt(841)

              = 29 miles

Total distance  = 41 + 29 = 70 miles

Answer is D. 70 miles.

Answer:

70

Step-by-step explanation:

i took the test

Answer:

A) 52.5 inches²

Step-by-step explanation:

The equation for the area of a trapezoid is a=1/2h(b1+b2). This basically means that you take the height of the trapezoid, multiply it by the top base plus the bottom base and divide that by 2. When you do this, you take 8.5 plus 6.5, which equals 15, and multiply that by 7 to get 105. After you get this, you divide it by 2 to get 52.5 inches².

Answer:

3/4 teaspoons of pepper

Step-by-step explanation:

1/4 teaspoons : 3 potatoes = x teaspoons : 9 potatoes

(1/4)/3 = x/9

3x = 9 * 1/4

x = 3 * 1/4

x = 3/4

Answer: 3/4 teaspoons of pepper

Answer:

B

step-by-step explanation:

1/4 over 3 p/9

Answer:

The answer is 13

Step-by-step explanation:

You'll say what will you multiply by itself to give you 169.

It will be 13 times itself and it will be =169.

Answer:

Las inecuaciones que pueden ayudar a calcular cuantos litros de pintura blanca se pueden tener como son [tex]\frac{4\cdot x + 7\cdot y}{500}> 5\,\frac{USD}{L}[/tex] y [tex]\frac{4\cdot x + 7\cdot y}{500}< 6\,\frac{USD}{L}[/tex].

Step-by-step explanation:

Esta situación puede ser descrita mediante una ecuación y una inecuación simultánea. La ecuación es de la capacidad del tanque, mientras que la inecuación es del coste unitario de la mezcla. Sean [tex]x[/tex] y [tex]y[/tex] las capacidades empleadas de pintura blanca y pintura azul en litros, entonces:

Capacidad del tanque (en litros)

[tex]x + y = 500\,L[/tex]

Coste unitario de la mezcla (en dólares por litro)

[tex]5\,\frac{USD}{L} < \frac{4\cdot x + 7\cdot y}{500} < 6\,\frac{USD}{L}[/tex]

Es decir:

[tex]\frac{4\cdot x + 7\cdot y}{500}> 5\,\frac{USD}{L}[/tex] y [tex]\frac{4\cdot x + 7\cdot y}{500}< 6\,\frac{USD}{L}[/tex]

Las inecuaciones que pueden ayudar a calcular cuantos litros de pintura blanca se pueden tener como son [tex]\frac{4\cdot x + 7\cdot y}{500}> 5\,\frac{USD}{L}[/tex] y [tex]\frac{4\cdot x + 7\cdot y}{500}< 6\,\frac{USD}{L}[/tex].

Answer:

I think it is either 85 or 51 because the question was not specific

Step-by-step explanation:

I am not entirely sure if you mean Jose changed jobs or added a new job on top but i will do both.

34/2=17

17+34=51

OR

51+34=85

Answer:

51 miles.

Step-by-step explanation:

That would be 34 * 1 1/2

= 34 * 3/2

= 17 * 3

= 51 miles.

Answer:

[tex]\begin{center}\begin{tabular}{ c c c }Hours(h) & Total Cost(C) \\ 1 & 15 \\ 2 & 20 \\ 3 & 25 \\ 4 & 30 \\ 5 & 35 \end{tabular}\end{center}[/tex]

Step-by-step explanation:

Given that:

Kevin charges $10 plus $5 per hours

C = 5h + 10

To find:

The table of values for hours worked from 1 to 5.

Solution:

First of all, let us put h = 1 in the given equation:

C = 5 \times 1 + 10

C = 5 + 10 = $15

Now, let us put h = 2 in the given equation:

C = 5 \times 2 + 10

C = 10 + 10 = $20

Now, let us put h = 3 in the given equation:

C = 5 \times 3 + 10

C = 15 + 10 = $25

Now, let us put h = 4 in the given equation:

C = 5 \times 4 + 10

C = 20 + 10 = $30

Now, let us put h = 5 in the given equation:

C = 5 \times 5 + 10

C = 25 + 10 = $35

So, the table becomes each row incrementing h by 1:

[tex]\begin{center}\begin{tabular}{ c c c }Hours(h) & Total Cost(C) \\ 1 & 15 \\ 2 & 20 \\ 3 & 25 \\ 4 & 30 \\ 5 & 35 \end{tabular}\end{center}[/tex]

Answer:

[tex]a = 3[/tex]

Step-by-step explanation:

[tex]3 {a}^{2} = 27 \\ \frac{3 {a}^{2} }{3} = \frac{27}{3} \\ {a}^{2} = 9 \\ a = \sqrt{9} \\ a = 3[/tex]

Answer: 9

Step-by-step explanation:

First divide both sides by 3

[tex]a^2=9[/tex]

Then root both sides([tex]\sqrt{a^2}=\sqrt{9}[/tex])

a = 9

Hope it helps <3

Edit: :o this is my 250th answer

Answer:13

Step-by-step explanation:

Answer:

a = -1/2

b = 2

Step-by-step explanation:

Step 1: Rewrite 1st equation

-b = -5 - 6a

b = 5 + 6a

Step 2: Substitution

4a - 3(5 + 6a) = -8

Step 3: Solve

4a - 15 - 18a = -8

-14a - 15 = -8

-14a = 7

a = -1/2

Step 4: Plug in a to find b

6(-1/2) - b = -5

-3 - b = -5

-b = -2

b = 2

Answer:

Equation: f(x) = -x² + 3

Step-by-step explanation:

If we want to find the roots/solve for x, we can either graph the problem or use quadratic formula to find when f(x) = 0:

To get the equation of the graph, our parent function is: f(x) = a(x - h)² + k, or f(x) = x². Since we are reflecting over the x-axis with a vertical stretch and vertically moving up to (0, 3), we are modifying a and k only.

Answer:

I think its A

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The graph would be a curve because of the exponent.

Answer:

P = 0.2517

Step-by-step explanation:

In this case we must calculate the probability of event, which would be the number of specific events (that is, at least one woman and the rest men, 4), then it would be to choose 1 of 6 women by 4 of 9 men divided by the number of total events, which would be to choose 5 (committee size) out of 15 (9 men + 6 women, total number of people)

P (at least one woman) = 6C1 * 9C4 / 15C5

we know that nCr = n! / (r! * (n-r)!)

replacing we have:

6C1 = 6! / (1! * (6-1)!) = 6

9C4 = 9! / (4! * (9-4)!) = 126

15C5 = 15! / (5! * (15-5)!) = 3003

Therefore it would be:

P (at least one woman) = 6 * 126/3003

P = 0.2517

That is, approximately 1 out of 4 women.

Answer:

it will take 0.056025 seconds to complete

Step-by-step explanation:

Here, we want to know the amount of time it will take. the computer to sort 15 items.

What to do here is simply substitute the value of 15 for x

Thus, we have

t = 0.007(15)^2 + 0.003(15)

t = 0.011025 + 0.045

t = 0.056025

answer: 1.62

step-by-step explanation: apx :)

A=4[tex]\pi -8[/tex]

that is your answer :-)

Answer:

[tex]A = 4\pi - 8[/tex]

Step-by-step explanation:

ody

Answer:

C).

Step-by-step explanation:

In A and B  they  are making generalisations . Their deductions are not valid.

Answer:

That is true, but there is no question being asked.

Answer:

900L per minute

Step-by-step explanation:

1- 70 - 20 = 50

2- in this 50 min the 45000L has been drawned

3- 45000L / 50 = 900L

.. ..

Answer:

X=1

Step-by-step explanation:

12x-14=-2

    +14 +14

12x=12

x=1

Answer:

x = 1

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS. PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

First, add 14 to both sides:

12x - 14 = -2

12x - 14 (+14) = -2 (+14)

12x = -2 + 14

12x = 12

Next, divide 12 from both sides:

(12x)/12 = (12)/12

x = 12/12

x = 1

x = 1 is your answer.

~

2.3%

divide the infected number by the deaths. Then move the decimal points to the left.

Answer:

2.3%

divide the infected number by the deaths. Then move the decimal points to the left.

Step-by-step explanation:

Answer:

V = 3534 cm^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

the radius is 7.5 and the height is 20

V = pi ( 7.5)^2 * 20

V =1125 pi cm^3

Using the pi button for pi

V =3534.291735 cm^3

Rounding to the nearest whole number

V = 3534 cm^3

Answer:

b)3534 cm^3

Step-by-step explanation:

To find the area of a cylinder, you first have to find the area of the base which is in the shape of a circle. The area of a circle is given by the equation πr^2. In this case r, the radius, is 7.5 cm. So plugging in 7.5 for r you get 7.5^2 × π. Plugging in 3.1415 for π you get ~176.671. Now all you do is multiply this by the height, 20cm, and get the answer of ~3534 cm^3.

Answer:

m = ½; b = 0

Please mark my answer as brainliest

the equation can be written y=mx+d.so

m=1/2 and d=3

In an arithmetic sequence, consecutive terms differ by a fixed number d :

[tex]a_8=a_7+d[/tex]

[tex]a_9=a_8+d=a_7+2d[/tex]

[tex]a_{10}=a_9+d=a_7+3d[/tex]

and so on up to

[tex]a_{19}=a_7+12d[/tex]

Solve for d :

[tex]140=32+12d\implies12d=108\implies d=9[/tex]

Work backwards to find the first term in the sequence, and hence the n-th term:

[tex]a_6=a_7-d[/tex]

[tex]a_5=a_6-d=a_7-2d[/tex]

and so on down to

[tex]a_1=a_7-6d[/tex]

So the first term is

[tex]a_1=32-6\cdot9=-22[/tex]

which means the n-th term is

[tex]a_n=a_1+(n-1)d=-22+9(n-1)=9n-31[/tex]

[tex]S_n[/tex] denotes the n-th partial sum of the sequence, i.e. the sum of the first n terms. We want to find the number of terms such that this sum is 511:

[tex]\displaystyle S_n=\sum_{i=1}^na_i=\sum_{i=1}^n(9i-31)=511[/tex]

Distribute the summation and recall the formulas,

[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]

[tex]\implies S_n=\displaystyle9\sum_{i=1}^ni-31\sum_{i=1}^n1[/tex]

[tex]\implies511=9\cdot\dfrac{n(n+1)}2-31n[/tex]

[tex]\implies1022=9n^2-53n[/tex]

[tex]\implies9n^2-53n-1022=0[/tex]

[tex]\implies(n-14)(9n+73)=0[/tex]

[tex]\implies n=14\text{ or }n=-\dfrac{73}9[/tex]

n must be a positive integer, so we the sum is obtained from the first n = 14 terms.

Answer:a

Step-by-step explanation: