A cycling race is 17 miles long. The cyclists will begin at point S and ride a number of laps around a neighborhood block. After the last lap, the cyclists will sprint 2.0 miles to the finish line. A rectangle with a width of 0.75 miles and height of 0.5 miles. The 2 mile finish comes out of one corner. Using the equation w (1.5 + 1) + 2 = 17, the race's organizer determined the cyclists will need to ride 9 laps before the sprint to the finish. Which explains the error? The equation should be 0.75 w + 0.5 w + 2 = 17, and the cyclists will need to ride 12 laps before the sprint to the finish. The equation should be 2 (0.75 w + 0.5) + 2 = 17, and the cyclists will need to ride 21 laps before the sprint to the finish. The solution should be 6, and the cyclists will need to ride 6 laps before the sprint to the finish. The solution should be 8, and the cyclists will need to ride 8 laps before the sprint to the finish.

Step-by-step explanation:

[tex]\dfrac{w}{3}<1\qquad\text{multiply both sides by 3}\\\\3\!\!\!\!\diagup\cdot\dfrac{w}{3\!\!\!\!\diagup}<3\cdot1\\\\w<3\\===========================\\3w+5>11\qquad\text{subtract 5 from both sides}\\\\3w+5-5>11-5\\\\3w>6\qquad\text{divide both sides by 3}\\\\\dfrac{3w}{3}>\dfrac{6}{3}\\\\w>2\\\\[/tex]

[tex]\text{If is}\ \bold{OR},\ \text{then}:\\\\w<3\ or\ w>2\Rightarrow w\in\mathbb{R}\ /\text{any real number/}\\\\\text{If there is a mistake, and it should be}\ \bold{AND},\ \text{then}:\\\\w<3\ and\ w>2\Rightarrow 2<w<3\to w\in(2;\ 3)[/tex]

Answer:

80 and 20

Step-by-step explanation:

80+80+20=180

Answer:

The graph shaded outside the parabola and the curve is solid.

Step-by-step explanation:

The given inequality is  

[tex]y+4x\leq x^2+2[/tex]

It can be rewritten as

[tex]y\leq x^2-4x+2[/tex]

The sign of inequality is [tex]\leq[/tex], so the curve is a solid line.

The related equation of line is

[tex]y=x^2-4x+2[/tex]

Table of values is

x          0          2          4

y          2         -2          2

Plot these points and draw a U-shaped curve.

Check the equality for (0,0).

[tex]0\leq (0)^2-4(0)+2[/tex]

[tex]0\leq 2[/tex]

This statement is true. So, (0,0) lies in the shaded portion.

So, shade the graph outside the parabola.

Answer:

Step-by-step explanation:

A rational number are numbers that can be expressed as as fraction. They can be expressed as a ratio of two integers. An irrational is quite the opposite.  An irrational number cannot be expressed as a ratio of two integers.

Taking square root of two as an example;

√2 cannot be expressed as a ratio of two integers because the result will always be a decimal. If expressed as √2/1, it is still not a rational number because of the square root of 2 at the numerator. Square root of 2 is not an integer even though 1 is an integer.

Mark is wrong because √2 is irrational and it is irrational because it cannot be expressed as a ratio of two integers not due to the fact that he can write it as a fraction.

Answer:

12

Step-by-step explanation:

The proper divisors of 12 are

1 2 3 4 6

Add those together you get 16

Answer:

[tex]y\ =\ \left|\frac{1}{2}x-2.5\right|+3[/tex]

Step-by-step explanation:

Look at the image below ↓

Answer:

Check below the graph.

Step-by-step explanation:

Hi, for this function, check the graph below:

1) Note that in this function the value outside the brackets points how high the graph will be traced.

2) The value within the brackets, points since it's a negative expression how far to the right the graph will be traced.

Answer:

11

Step-by-step explanation:

6.7 / .6

Multiply top and bottom by 10

67/6

66/6 = 11 so this is close to 11

Answer:

8: 1721 m

9: 1173 m

Step-by-step explanation:

8:

[tex]d = v_{i} t + \frac{1}{2}at^{2}[/tex]

because initial velocity is 0:

[tex]d = \frac{1}{2} at^{2} = \frac{1}{2}(3.2m/s^2)(32.8 s)^2 = 1721.344 m[/tex]

9:

[tex]v_f^2 = v_i^2 + 2ad[/tex]

because velocity initial is 0:

[tex]v_f^2 = 2ad[/tex]

[tex]d = \frac{v_f^2}{2a} = \frac{(88m/s)^2}{2(3.3 m/s^2)} = 1173.3333 m[/tex]

Answer:

do it youself

Step-by-step explanation:

Answer:

4/3

12

44/30

Step-by-step explanation:

2/5:3/10

=2/5*10/3

=20/15

=4/3

1/2:1/4:1/6

=1/2*4/1*6/1

=4/2*6/1

=24/2

=12

2⅕:1¼:1⅕

11/5:5/4:6/5

=11/5*4/5*5/6

=44/25*5/6

=220/150

=44/30

Hope this helps ;) ❤❤❤

Answer:

x = -6

Step-by-step explanation:

First write the equation.

4x + -3 = 5x + 3

The isolate x in the equation. Add -4x to both sides.

4x + -3 + -4x = 5x + 3 + -4x

-3 = x + 3

Then add -3 to both sides.

-3 + -3 = x + 3 + -3

-6 = x

Now you have the value of x = -6.

Cheers.

Answer:

Step-by-step explanation:

          +3             +3

          -5x       -5x

            ÷(-1)     ÷(-1)    

Answer:

Step-by-step explanation:

8j^3-10j^2-7-6j^3+10j^2+j-12

2j^3+j-12

Answer:

b

Step-by-step explanation:

The answer is b because we are looking for opposites

The opposite of +x is -x

While the opposite of -3 is +3

with this, we can switch them around.

this gives us the inverse of 3-x

Answer:

x = -5

Step-by-step explanation:

-7(x + 2) = 21​

Divide each side by -7

-7/-7(x + 2) = 21​/-7

x+2 = -3

Subtract 2 from each side

x+2-2 = -3-2

x = -5

Answer:

x = -5

Step-by-step explanation:

distribute: -7x-14 = 21

add 14 to both sides

divide by -7

x = -5

Answer:

8+n^2

Step-by-step explanation:

Answer:

f(n+1)=(f[n]-1)^2, where f(1)=8

Step-by-step explanation:

"it appears your explanation includes a link" so you don't get an explanation

Answer: There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500

Step-by-step explanation:

given that;

n = 14

mean Ж = 19,850

standard deviation S = 1,084

degree of freedom df = n - 1 = ( 14 -1 ) = 13

H₀ : ц ≥ 20,500

H₁ : ц < 20,500

Now the test statistics

t = (Ж - ц) / ( s/√n)

t = ( 19850 - 20500) / ( 1084/√14)

t = -2.244

we know that our degree of freedom df = 13

from the table, the area under the t-distribution of the left of (t=-2.244) and for (df=13) is 0.0215

so P = 0.0215

significance ∝ = 0.05

we can confidently say that since our p value is less than the significance level, we reject the null hypothesis ( H₀ : ц ≥ 20,500 )

There is sufficient evidence to reject the dealer's claim that the mean price is at least $20,500

Answer:

$3 discount

Step-by-step explanation:

If Fredo originally had the markdown as $0 (meaning no change), then he arrived at the store, seeing the markdown was $2, the current markdown is $2.

Now that he has an extra $1 off, he gets 2+1 = $3 off the bread.

Hope this helped!

Answer:y = 2/3

Step-by-step explanation:

2x + y = 10

x - y = 4

-----------------add

3x = 14

x = 14/3

x - y = 4

14/3 - y = 4

-y = 4 - 14/3

-y = 12/3 - 14/3

-y = -2/3

y = 2/3 <==

Answer:

2x + y = 10

x - y = 4

-----------------add

3x = 14

x = 14/3

x - y = 4

14/3 - y = 4

-y = 4 - 14/3

-y = 12/3 - 14/3

-y = -2/3

y = 2/3 <==

Step-by-step explanation:

Answer:

clay sphere gives more clay for less money

Step-by-step explanation:

Volume of cone=1/3πr^2h

=1/3*3.14*(9^2)*12

=1/3*3.14*81*12

=3,052.08/3

=1017.36 inches^3

Volume of a cyclinder=πr^2h

=3.14*(9^2)*12

=3.14*81*12

=3,052.08 inches^3

Volume of a sphere=4/3πr^3

=4/3*3.14*(9^3)

=4/3*3.14*(9^3)

=4/3*3.14*729

=9,156.24 / 3

=3,052.08 inches^3

Clay cone=$12

Clay cyclinder=$30

Clay sphere=$28

Which is the best to buy

Comparing volume

Volume of sphere=3,052.08 inches^3

Volume of cyclinder=3,052.08 inches^3

Volume of cone=1017.36 inches^3

Sphere and cyclinder both have the same volume which is 3 times more than volume of a cone

Clay sphere cost $28 which is cheaper than clay cyclinder at the same volume.

Therefore, clay sphere gives more clay for less money

Answer:

The answer is no.

Step-by-step explanation:

The questions does no specify how many people are watching the movies each week.

Hoped this helped you out a bit! :)

Answer:

The data that we have is:

f(x) = x + 5

g(x) = x^2 + 1

p(x) = g(x) + f(x) = (x^2 + 1) + (x + 5) = x^2 + x + 6.

q(x) = g(x) - f(x) =  (x^2 + 1) - (x + 5) = x^2 - x - 4

We want to find  p(x)*q(x)

well, we can replace:

p(x)*g(x) = (g(x) + f(x))*(g(x) - f(x))

Now, you can recall the relationship:

a^2 - b^2 = (a + b)*(a - b)

then we have that:

(g(x) + f(x))*(g(x) - f(x)) = g(x)^2 - f(x)^2

now we can replace g(x) and f(x) by the expressions that we know:

g(x)^2 - f(x)^2 = (x^2 + 1)^2 - (x + 5)^2

now we can simplify this:

(x^2 + 1)^2 - (x + 5)^2 = (x^4 + 2*1*x + 1^2) - (x^2 + 2*5*x +5^2)

= x^4 + 2*x + 1 - x^2 - 10x - 25

= x^4 - x^2 - 8*x - 24

p(x)*q(x) = x^4 - x^2 - 8*x - 24

Answer:

x^4+x^2-10x-24

Step-by-step explanation:

Logan Chivery owns her own car. Her June monthly interest was $300. The rate is 8.5 percent. Logan's principal balance at the beginning of June is: (Use 360 days-do not round the denominator.)

A. $42,353.14

B. $42,335.14

C. $2,335.14

Answer: A. $42,353.14

Step-by-step explanation:

When taking a loan, we have to pay interest. The Simple Interest Formula is:

Simple Interest (I) = Principal (P) × Interest Rate (r)

Principal (P) is the borrowed amount.

Interest Rate (r) is the percent of the principal to be paid.

Time (t) is the length of time that money is borrowed.

If Logan Chivery has the monthly interest of $300  at a rate of 8.5% per year, first, we have to convert the year rate to the month of June rate.

30 days = 8.5÷360÷30 = 0.7083333333 interest rate

Then, find the Principal by using the formula

Simple Interest (I) = Principal (P) × Interest Rate (r)

4,2352.94×0.7083333333÷100=299.99

Answer:

[tex]C(x) = 540x + 72120[/tex]

Step-by-step explanation:

Given

Cost = $78,600 when Printing Press = 12

Cost = $82,380 when Printing Press = 19

Required

Determine the linear equation

From the given parameters; Cost is a function of Printing Press

Represent Cost by C and Printing press by x;

This implies that C = f(x)

The given parameters can then be modeled as; [tex](x, C)[/tex]

[tex](x_1, C_1) = (12,78600)[/tex]

[tex](x_2, C_2) = (19,82380)[/tex]

The first step is to calculate the slope, m;

[tex]m = \frac{C_1 - C_2}{x_1 - x_2}[/tex]

[tex]m = \frac{78600 - 82380}{12 - 19}[/tex]

[tex]m = \frac{-3780}{-7}[/tex]

[tex]m = 540[/tex]

The linear equation can then be calculated using slope formula

[tex]m = \frac{C- C_2}{x - x_2}[/tex]

Substitute 540 for m and [tex](x_2, C_2) = (19,82380)[/tex]

[tex]540 = \frac{C- 82380}{x - 19}[/tex]

Multiply both sides by x - 19

[tex]540 * (x-19)= \frac{C- 82380}{x - 19} * (x-19)[/tex]

[tex]540 * (x-19)= C- 82380[/tex]

Open bracket

[tex]540x - 10260 = C - 82380[/tex]

Add 82380 to both sides

[tex]540x - 10260 + 82380= C - 82380 + 82380[/tex]

[tex]540x - 10260 + 82380= C[/tex]

[tex]540x + 72120= C[/tex]

[tex]C = 540x + 72120[/tex]

Hence;

[tex]C(x) = 540x + 72120[/tex]

Answer:

[tex]10\sqrt{2[/tex]y²

Step-by-step explanation:

So I am not sure if the root is only on 200, but if it is not, please comment, and I will add to it.

Answer:

The mean number of the children is 1.2

Step-by-step explanation:

Given

Children: 0, 1, 2, 1, 2

Required

Determine the Mean number

The mean of a set is calculated as follows;

[tex]Mean = \frac{\sum x}{n}[/tex]

Where x is the given set and n is the number of sets

In this case, n = 5 children

Hence;

[tex]Mean = \frac{0 + 1 + 2 + 1 + 2}{5}[/tex]

[tex]Mean = \frac{6}{5}[/tex]

[tex]Mean = 1.2[/tex]

Hence, the mean number of the children is 1.2

Answer:

1. It has 5 sides.

2. It has 6 walls.

3. Octagon

4. a. Pentagon (The figure has 5 sides.) b. Triangle (The figure has 3 sides.) c. Hexagon (The figure has 6 sides.) d. Hexagon (The figure has 6 sides.)

5. a. 6 cm + 6 cm + 6 cm + 6 cm = 24 cm, or 4 × 6 cm = 24 cm, b. 7 in. + 7 in. + 7 in. = 21 in., or 3 × 7, in. = 21 in., c. 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. = 28 ft., or 7 × 4 ft. = 28 ft., d. 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. = 81 in., or 9 × 9 in. = 81 in.

6. a. 4 ft. + 3 ft. + 3 ft. + 2 ft. + 4 ft. + 5 ft. = 21 ft. b. 8 in. + 8 in. + 8 in. + 8 in. + 3 in. + 3 in. + 3 in. + 3in. = 44 in. c. 3 cm + 3 cm + 3 cm + 2 cm + 2 cm = 13 cm

7. Shelly has enough lights to decorate four windows.

8. a. 8 ft, b. 4 m, c. 24 ft, d. 7 cm

Step-by-step explanation:

PennFoster

Answer:

It has 5 sides.

It has 6 walls.

Octagon

a. Pentagon (The figure has 5 sides.)

b. Triangle (The figure has 3 sides.)

c. Hexagon (The figure has 6 sides.)

d. Hexagon (The figure has 6 sides.)

a. 6 cm + 6 cm + 6 cm + 6 cm = 24 cm, or 4 × 6 cm = 24 cm

b. 7 in. + 7 in. + 7 in. = 21 in., or 3 × 7 in. = 21 in.

c. 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. + 4 ft. = 28 ft., or 7 × 4 ft. = 28 ft.

d. 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. + 9 in. = 81 in., or 9 × 9 in. = 81 in.

a. 4 ft. + 3 ft. + 3 ft. + 2 ft. + 4 ft. + 5 ft. = 21 ft.

b. 8 in. + 8 in. + 8 in. + 8 in. + 3 in. + 3 in. + 3 in. + 3in. = 44 in.

c. 3 cm + 3 cm + 3 cm + 2 cm + 2 cm = 13 cm

Let w stand for the number of windows Shelly can decorate. Each window is a square with sides measuring 5 feet. The perimeter of one window is 4 × 5 feet. Divide the total length of the light strings by the perimeter of one window.

80 ft. ÷ (4 × 5ft.) = w

80ft. ÷ 20ft. = w

4 = w

Answer: Shelly has enough lights to decorate four windows.

Step-by-step explanation:

PENN

Answer:

The common difference is -5/4

T(n) = T(0)  - 5n/4,

where T(0) can be any number. d = -5/4

Assuming T(0) = 0, then first term

T(1) = 0 -5/4 = -5/4

Step-by-step explanation:

T(n) = T(0) + n*d

Let

S1 = T(x) + T(x+1) + T(x+2) + T(x+3) = 4*T(0) + (x + x+1 + x+2 + x+3)d = 240

S2 = T(x+4) + T(x+5) + T(x+6) + T(x+7) = 4*T(0) + (x+5 + x+6 + x+7 + x+8)d = 220

S2 - S1

= 4*T(0) + (x+5 + x+6 + x+7 + x+8)d - (4*T(0) + (x+1 + x+2 + x+3 + x+4)d)

= (5+6+7+8 - 1 -2-3-4)d

= 4(4)d

= 16d

Since S2=220,  S1 = 240

220-240 = 16d

d = -20/16 = -5/4

Since T(0) has not been defined, it could be any number.

Answer:

area=17.5

Step-by-step explanation:

area=1/2(base*height)

area=1/2(3*7)

are=17.5