Algebra 1
> U.15 Solve a system of equations using any method: word problems GDQ
Tutor
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks
Victor and Susan each want to run for president of their school's student body council. In
order to do so, they must collect a certain number of signatures and get a nomination. So far,
Victor has 23 signatures, and Susan has 19. Victor is collecting signatures at an average rate
of 9 per day, whereas Susan is averaging 11 signatures every day. Assuming that their rate of
collection stays the same, eventually the two will have collected the same number of
signatures. How long will that take? How many signatures will they both have?
In
days, Victor and Susan will each have collected
signatures.
Submit
O
к

Standard deviation is a measurement of a collection of values' variance or dispersion. The standard deviation of the data set is 2.474.

Step 1: Find the mean

Step 2: Find each score’s deviation from the mean

Step 3: Square each deviation from the mean

Step 4: Find the sum of squares

Step 5: Apply the formula

[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}[/tex]

The data set that is given to us is {1, 4, 2, 2, 8, 7, 3}, now use the steps to calculate the standard deviation.

Step 1: Find the mean

The mean of the given data set can be written as,

[tex]Mean, \mu=\dfrac{1+4+2+2+8+7+3}{7} = 3.857[/tex]

Step 2: Find each score’s deviation from the mean

1 - 3.857 = -2.857

4 - 3.857 = 0.143

2 - 3.857= -1.857

2 - 3.857= -1.857

8 - 3.857 = 4.143

7 - 3.857 = 3.143

3 - 3.857 = -0.857

Step 3: Square each deviation from the mean

-2.857² = 8.162

0.143² = 0.02

-1.857² = 3.447

-1.857² = 3.447

4.143² = 17.165

3.143² = 9.877

-0.857²= 0.735

Step 4: Find the sum of squares

8.162+0.20+3.447+3.447+17.165+9.877+0.735 = 42.857

Step 5: Apply the formula

[tex]SD = \sqrt{\dfrac{\sum(x_i-\bar{x})^2}{n}}\\\\SD = \sqrt{\dfrac{42.857}{7}} \\\\SD= 2.474[/tex]

Hence, the standard deviation of the data set is 2.474.

Learn more about Standard Deviation:

https://brainly.com/question/12402189

Answer:

[tex]12.6 + b = 15.7[/tex]

[tex]b = 3.1[/tex]

Step-by-step explanation:

Given

[tex]Perimeter: 2a + b = 15.7[/tex]

[tex]a = 6.3[/tex]

Required

Which equation models b

Substitute 6.3 for a

[tex]2a + b = 15.7[/tex] becomes

[tex]2 * 6.3 + b = 15.7[/tex]

[tex]12.6 + b = 15.7[/tex]

Solve for b

[tex]b = 15.7 - 12.6[/tex]

[tex]b = 3.1[/tex]

Answer:

12.6 + b = 15.7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:-0.125 or 1/8

Step-by-step explanation: :)

Answer:

-1/8

Step-by-step explanation:

1/2 times -1/4 = -1/8

Answer:

B

Step-by-step explanation:

3/8 is equal to 0.375, also known as 37.5%.

The experimental probability (as a percent) that she will hit the ball next is 37.5%. Hence, option B is the right choice.

The experimental probability of an event occurring is the number of times it happened during the experiment as a ratio to the number of times the experiment was run.

In the question, we are given that Sarah hit the ball 3 times out of the 8 times.

We are asked to find the experimental probability (as a percent) that she will hit the ball next.

As we know, the experimental probability of an event occurring is the number of times it happened during the experiment as a ratio to the number of times the experiment was run.

∴ The experimental probability = The number of times Sarah hit the ball/The number of times she experimented = 3/8

or, The experimental probability = (3/8)*100 % = (3*25)/2 % = 75/2 % = 37.5%.

∴ The experimental probability (as a percent) that she will hit the ball next is 37.5%. Hence, option B is the right choice.

Learn more about the experimental probability at

https://brainly.com/question/8652467

#SPJ2

Answer:

1∶ 4

explanation

Answer:

C) (0, 2)

Step-by-step explanation:

The y-intercept is the y value when x = 0.

Another way to reword that is when the graph crosses the y-axis.

We see from the graph that it crosses the y-axis at 2. Therefore, our y-intercept is (0, 2).

Answer:

y = 7.2

Step-by-step explanation:

Given that y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 10 when x = 25, then

10 = 25k ( divide both sides by 25 )

[tex]\frac{10}{25}[/tex] = 0.4 = k

y = 0.4x ← equation of variation

When x = 18, then

y = 0.4 × 18 = 7.2

Answer:

1/3

Step-by-step explanation:

5/6 - 1/2

note that you could also write 1/2 as 3/6 since when divided you get half once again .

5/6- 3/6 = (5-3)/6= 2/6 = 1/3

Answer:

The answer is

[tex] \huge \frac{1}{3} [/tex]

Step-by-step explanation:

[tex] \frac{5}{6} - \frac{1}{2} \\ [/tex]

To solve this first find the common denominator

From the question the common denominator is 6

So we have

[tex] \frac{5}{6} - \frac{1}{2} = \frac{5 - 3}{6} = \frac{2}{6} = \frac{1}{3} \\ [/tex]

We have the final answer as

[tex] \frac{1}{3} \\ [/tex]

Hope this helps you

Answer:

102(vertically opposite angle)

Answer:

18[tex]\pi[/tex] yd.³ or 56.54867 yd.³

Step-by-step explanation:

The volume of a cylinder can be written as: height × base, where the base of the cylinder is [tex]\pi[/tex]r².

Since the radius (r) is half the diameter, it should be 1.5 or 3/2 yd.

r = 1.5

So, the area of the base of the cylinder is 1.5²([tex]\pi[/tex]), which is equal to 2.25[tex]\pi[/tex].

Now multiply that by the height, 8 yd.

2.25[tex]\pi[/tex] × 8 = 18[tex]\pi[/tex]

The area of the cylinder is 18[tex]\pi[/tex] or 56.54867

Answer:

56.55 yd.³ OR 56.52 yd.³

Step-by-step explanation:

The formula for the volume of a cylinder is; V=πr^2h

To find the volume let's put in the values they gave us.

Now: V=π times 1.5^2 times 8

(If you don't know what pi or π is its the area of a unit circle. So the area of a circle with diameter 2 or radius 1)

Continuing the volume would be 3.141592.. * 2.25 * 8 ( '*' indicates multiplication) Now the answer after you multiply would be approx. 56.54867 which rounded would be 56.55

V=πr^2h so 3.14*2.25*8 which would be 56.52 yd.³ (if this is the way you need it ignore ANY other answers)

Answer:

14,579.76

Step-by-step explanation:

New value =

16,855.21 - Percentage decrease =

16,855.21 - (13.5% × 16,855.21) =

16,855.21 - 13.5% × 16,855.21 =

(1 - 13.5%) × 16,855.21 =

(100% - 13.5%) × 16,855.21 =

86.5% × 16,855.21 =

86.5 ÷ 100 × 16,855.21 =

86.5 × 16,855.21 ÷ 100 =

1,457,975.665 ÷ 100 =

14,579.75665 ≈

14,579.76

Total amount saved in 1st case :

[tex]S_1=400+20t_1[/tex]

Total amount saved in 2nd case :

[tex]S_2=100+40t_2[/tex]

( Here [tex]t_1 \ and\ t_2[/tex] are number of months )

Let, after x months the amount saved in both cases is same.

So,

[tex]S_2=S_1\\\\100+40x=400+20x\\\\20x = 300\\\\x = 15\ months[/tex]

Amount saved :

[tex]S_1=400+20(15) =\$ 700[/tex]

[tex]S_2=100+40( 15)= \$700[/tex]

Hence, this is the required solution.

Dividing 6x^2 + 26x^2 + 23x + 5 by 3x + 1 using the long division involves the use of groups or parts

The result when 6x^2 + 26x^2 + 23x + 5 is divided by 3x + 1 is 2x^2 + 8x + 5 with no remainder

The dividend is given as:

6x^2 + 26x^2 + 23x + 5

And the divisor is 3x + 1

Divide 6x^3 by 3x:

Result = 2x^2

Multiply 2x^2 by 3x + 1

=> 6x^3 + 2x^2

Subtract 6x^3 + 2x^2 from 6x^3 + 26x^2 + 23x + 5

=>  24x^2 + 23x + 5

Divide 24x^2 by 3x:

Result = 8x

Multiply 8x by 3x + 1

=> 24x^2 + 8x

Subtract 24x^2 + 8x from 24x^2 + 23x + 5

=> 15x + 5

Divide 15x by 3x:

Result = 5

Multiply 5 by 3x + 1

=> 15x + 5

Subtract 15x + 5 from 15x + 5

=> 0

Write out the sum of the results

Result = 2x^2 + 8x + 5

Hence, the result when 6x^2 + 26x^2 + 23x + 5 is divided by 3x + 1 is 2x^2 + 8x + 5 with no remainder

See attachment for the long division process

Read more about long division at:

https://brainly.com/question/25289437

Answer:

12

Step-by-step explanation:

Answer:

Hello bakugo here!

Step-by-step explanation:

I don't see anything, is there supposed to be anything here? if not

Thank you extra for FREE points! :D

Answer: y = 10

Step-by-step explanation: Hi there!

To get started, first, we have to subtract 2y from 9y on the left side.

7y + 8 = 4y + 38

Then subtract 4y on both sides.

3y + 8 = 38

Then subtract 8 on both sides

3y = 30

Finally divide by 3 on both sides.

y = 10

The answer is y = 10.

Answer: y=10

Step-by-step explanation:

9y-2y+8=4y+38

[tex]\mathrm{Add\:similar\:elements:}\:9y-2y=7y[/tex]

7y+8=4y+38

[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]

7y+8-8=4y+38-8

[tex]\mathrm{Simplify}[/tex]

7y=4y+30

[tex]\mathrm{Subtract\:}4y\mathrm{\:from\:both\:sides}[/tex]

7y-4y=4y+30-4y

[tex]\mathrm{Simplify}[/tex]

3y=30

[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]

[tex]\frac{3y}{3}=\frac{30}{3}[/tex]

Simplify

y=10

Answer:

I think its the one on the bottom right

Step-by-step explanation:

Answer:

bottom right is the answer i think

Answer:

The answer is D : 4.

Step-by-step explanation:

=2x-3>11-5x

=2x-3+5x>11

=7x-3>11

=7x>11+3

=7x>14

=7x/7>14/7

=x>2

By simplifying the problem, you can see that "x" must be greater than 2. Therefore, eliminating all other possible answers that are shown, but 4.

I answered the same questions with the same exact wording and explanation so please don't report any answers that are the same as this one, they are all mine and written by me.

Answer:

Step-by-step explanation:

Vertices of the quadrilateral are (-4, 1), (-3, 2), (-1, 2) and (-2, 1).

If the given quadrilateral is dilated by ta scale factor of 1.5 about the origin.

Rule for the dilation,

(x, y) → (kx, ky) [k = scale factor]

New vertices of the quadrilateral after the transformation will be,

(-4, 1) → (1.5×4, 1.5×1)

        → (-6, 1.5)

(-3, 2) → (-4.5, 3)

(-1, 2) → (-1.5, 3)

(-2, 1) → (-3, 1.5)

Now the new points are rotated by 90° clockwise about the origin,

Rule for the rotation of the points,

(x, y) → (y, -x)

So the new vertices will be,

(-6, 1.5) → (1.5, 6)

(-4.5, 3) → (3, 4.5)

(-1.5, 3) → (3, 1.5)

(-3, 1.5) → (1.5, 3)

We can plot these points on the graph to form a new (image) quadrilateral.

Answer:

1) To determine how much the change of $9,000 to $10,395, we must subtract 9,000 from 10,395;

10,395 - 9,000 = $1,395 is the change in price (an increase).

Formula to find percentage of change;

Change in price/original amount x 100% (100/100)

Replace those values:

1,935 (change in price/increase)       100

_____                      x                        _____ = %0.215

9,000(original amount)                      100

Answer:

It $29.75

Step-by-step explanation:

Answer:

Orignal Price: $35

Discount Price: $29.75

Step-by-step explanation:

The original price is $35 since it says 15% off of $35. To get the discount price you would use the equation 35-15%, which would give you $29.75. Your new price is $29.75.

Hope this is what you were looking for. :D

Answer:

Number of trucks = 28

Number of cars = 14

Number of SUVs = 46

Total number of vehicles = 88

Step-by-step explanation:

Let T = the number of trucks, C = the number of cars, and S = the number of SUVs washed.

We are told :

They washed twice as many cars as trucks.

Hence: T = 2C

They washed a total of 28 trucks and cars and SUVs

Number of trucks = 28

Number of Cars =

T= 2 C

C = T/2

C = 28/2

C = 14

The number of trucks washed was 2 fewer than half the total number of cars and SUVs washed.

T = 1/2(C + S) - 2

T = 28

C = 14

Hence:

28 = 1/2(14 + S) - 2

28 = 1/2(14) + 1/2(S) - 2

28 = 7 - 2 +S/2

28 - 7 + 2 = S/2

30 - 7 = S/2

23 = S/2

S = 23 × 2

S = 46

Hence, number of SUVs = 46

Total number of vehicles = 28 + 14 + 46

= 88

Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity.

a) The volume of the box ([tex]V[/tex]), in cubic centimeters, is equal to the area of the base ([tex]A[/tex]), in square centimeters, multiplied by the height of the box ([tex]h[/tex]), in centimeters. The area of the surface is the product of the width ([tex]w[/tex]) and length (l), both in centimeters:

[tex]V = w\cdot l\cdot h[/tex]  

[tex]V = (36-2\cdot x)^{2}\cdot x[/tex]   (1)

The volume of the container is [tex]V = (36-2\cdot x)\cdot x[/tex] cubic centimeters. [tex]\blacksquare[/tex]

b) We need to apply first derivative analysis and second derivative analysis to determine the dimensions of the maximum squares to be cut:

[tex]-4\cdot (36-2\cdot x)\cdot x+(36-2\cdot x)^{2} = 0[/tex]

[tex]-4\cdot x + 36-2\cdot x = 0[/tex]

[tex]6\cdot x = 36[/tex]

[tex]x = 6[/tex]

[tex]V'' (x) = -4\cdot [(-2)\cdot x+(36-2\cdot x)]-4\cdot (36-2\cdot x)\cdot x + (36-2\cdot x)^{2}[/tex]

[tex]V''(x) = 8\cdot x-4\cdot (36-2\cdot x)-4\cdot (36\cdot x-2\cdot x^{2})+(36-2\cdot x)^{2}[/tex]

[tex]V'' (6) = -48[/tex]

Since [tex]V''(6) < 0[/tex], the critical value of [tex]x[/tex] leads to a maximum.

Four squares with size of 6 centimeters should be cut to produce the container of greatest capacity. [tex]\blacksquare[/tex]

To learn more on optimization, we kindly invite to check this verified question: https://brainly.com/question/5425085

Answer:

The volume of the circle is 21

Step-by-step explanation:

The volume of rectangular is 60

Answer:

h = 2.5 cm

Step-by-step explanation:

the volume (V) of a prism is calculated as

V = Al ( A is the area of triangular base and l the length )

A = [tex]\frac{1}{2}[/tex] bh = [tex]\frac{1}{2}[/tex] × 4 × h = 2h and l = 7

given V = 35 , then

2h × 7 = 35

14h = 35 ( divide both sides by 14 )

h = 2.5 cm

Answer:

Step-by-step explanation:

2x-2+2=12+2

= 2x+0=14

= 2x=14

= X=14÷2

= X=7

Thank you ☺️☺️☺️☺️

Answer and explanation:

The two events of choosing jolly ranchers from each bag, first and second are independent events so the probability of first event AND second event will be multiplied

First bag has 4 red 2 green and one blue

Second bag has 4 red and 2 orange

what is the probability that he would choose a purple jolly rancher from the first bag and a red jolly rancher from the second

Probability = number of favourable outcomes /total number of favourable outcomes

The first bag does not have a purple jolly rancher and so probability is zero

the second bag's probability of choosing a red jolly rancher =4/6

probability of choosing a purple jolly rancher from first bag and red jolly rancher from second bag

=0*4/6=0

Answer=0

Answer:

  (c)  $31.75

Step-by-step explanation:

First of all, you need to use some number sense to estimate an answer.

If the $900 loan had no interest, 1/3 of it would be paid off in each of the 3 years, or about $300 each year. You will be making 12 monthly payments each year, so the amount of principal being paid with each payment is $300/12 = $25. Any answer much above this amount will not make sense, so you can immediately reject all choices except $31.75.

__

The simple interest on the loan is ...

  I = Prt = $900×0.09×3 = $243

That, too, is divided among the 36 payments, so adds ...

  $243/36 = $6.75 to each of the $25 payments we calculated above.

The monthly payment is ...

  $25 +6.75 = $31.75