Solve the inequality: c² < − 3c + 70

1. Let y represent the amount of money earned, and x the number of cars they wash. Then

y = 5x

Why? Each car wash costs $5. So no car washes means no earnings; 1 car wash earns $5; 2 washes earn $10; 3 washes earn $15, and so on, so that x car washes generate $5x.

2. No matter how many cars they end up washing, they will have spent $75 to set up the operation, so you subtract 75 from the equation is part (1).

3. Taking into account the setup cost of $75, the profit they make is given by

y = 5x - 75

4. When x = 0, meaning no cars get washed, the profit is -$75, meaning the team loses $75.

5. Set the profit function equal to 0 and solve for x :

5x - 75 = 0

5x = 75

x = 75/5

x = 15

So the team has to wash at least 15 cars to break even.

Answer:

The setup cost is $75. To account for the setup cost, you need to subtract 75 from the right side of the equation obtained in part A.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

\( \frac{1}{2} - \frac{1}{3} \\ \\ = \frac{1}{6} \times 24 \\ = 4\)

Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Answer:

c on edge

Step-by-step explanation:

fr

Answer:

(B) Stretch z by a factor of 3 and rotate π/6 radians counterclockwise.

Step-by-step explanation:

edge:2022 Happy new year!

Answer:

0

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

factor the numerator and denominator and cancel the common factors!

Hope this helped!! <3

Answer:

87.5%

Step-by-step explanation:

These wholes together include 7/8 parts that are shaded. This as a percentage is 87.5%.

Hope this helps you out!! Have a great day ^^

To find the probability of two events without replacement, we can use the general multiplication rule, which states that:

P(A and B) = P(A) * P(B|A)

where P(A and B) is the probability of both events occurring, P(A) is the probability of the first event occurring, and P(B|A) is the probability of the second event occurring given that the first event has occurred.

In this case, we want to find the probability that both members are seniors. Let A be the event that the first member is a senior, and B be the event that the second member is a senior. Then:

P(A) = 12/22

since there are 12 seniors out of 22 members.

P(B|A) = 11/21

since there are 11 seniors left out of 21 members after choosing one senior.

P(A and B) = P(A) * P(B|A)

= (12/22) * (11/21)

= 132/462

= 0.2857

Rounding to two decimal places, the probability is **0.29**.

The equation given in slope-intercept form does not represent the graph because the y-intercept of the graph is equal to 4 while the y-intercept of the equation is equal to 5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided regarding the equations and graphs, the y-intercept are as follows:

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Answer:

\((2c+a+3b)(2c-a-3b)\)

Step-by-step explanation:

Given expression:  \(4c^2-a^2-6ab-9b^2\)

Factor \(-a^2-6ab-9b^2\)

\(\implies -(a^2+6ab+9b^2)\)

\(\implies -(a+3b)(a+3b)\)

\(\implies -(a+3b)^2\)

Factor \(4c^2\)

\(\implies(2c)(2c)\)

\(\implies (2c)^2\)

Therefore,

\((2c)^2-(a+3b)^2\)

Difference of Two Squares: \(x^2-y^2=(x+y)(x-y)\)

\(x^2=(2c)^2\implies x=2c\)

\(y^2=(a+3b)^2 \implies y=a+3b\)

Therefore,

\(\implies (2c + a + 3b)(2c - (a + 3b))\)

\(\implies (2c+a+3b)(2c-a-3b)\)

Answer:

(2c - a + 3b)(2c + a + 3b)

Step-by-step explanation:

4c² - a² - 6ab - 9b²

= 4c² - (a² + 6ab + 9b²) ← the terms in the parenthesiis are a perfect square )

= 4c² - (a + 3b)² ← this is a difference of squares which factors in general as

a² - b² = (a - b)(a + b) , then

= (2c)² - (a + 3b)²

= (2c - (a + 3b) )(2c + (a + 3b) )

= (2c - a - 3b)(2c + a + 3b)

Answer:

2x+2=58

2x=58-2=56

divide both sides by 2

x=28

The percentage change will be 25%.

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

Using these estimates, we can calculate the per cent decrease in the time spent driving as follows:

The initial time spent driving was 0.5 hours.

The final time spent driving was 0.375 hours.

The decrease in time spent driving was 0.5 - 0.375 = 0.125 hours.

The per cent decrease in time spent driving is,

P = (0.125/0.5) x  100%

P  = 25%.

Therefore, we can estimate that the per cent decrease in the time Jack spent driving his car is 25%.

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The roots of the given polynomial using the rational zero theorem are;  2, -4 and 6.

We are given the polynomial;

y = x³ - 4x² - 20x + 48

Since all coefficients are integers, we can apply the rational zeros theorem.

The trailing coefficient (the coefficient of the constant term) is 48

Find its factors (with the plus sign and the minus sign): ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

These are the possible values for p.

The leading coefficient (the coefficient of the term with the highest degree) is 1.

These are the possible rational roots:

±1, ±2, ±3, ±4, ±6, ±8, ±12, ±16, ±24, ±48.

Checking the possible roots: if a is a root of the polynomial P(x), the remainder from the division of P(x) by x - a should equal 0 (according to the remainder theorem, this means that P(a)=0

Plugging in those values, the only ones that yield P(a) = 0 are; 2, -4 and 6.

Thus, these are the roots of the given polynomial.

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"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.

It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.

In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.

The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.

Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.

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It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX

Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:

Diagonal WY bisects angles ZWX and ZYX because:

all corresponding parts of both triangles are congruent. (Option A).

If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.

Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.

If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).

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Answer:

0.79 ; 0.753

Step-by-step explanation:

Given that:

Students who have spent at least five hours studying GMAT review guides have a probability of 0.85 of scoring above 400 :

≥ 5 hours review = 0.85

Students who do not spend at least five hours reviewing have a probability of 0.65 of scoring above 400

< 5 hours = 0.65

70% (0.7) of business students spend atleast 5 hours review time

A.) probability of scoring above 400

(Proportion who spend atleast 5 hours review time * 0.85) + (Proportion who do not spend atleast 5 hours * 0.65)

Proportion who do not spend atleast 5 hours = (1 - proportion who spend atleast 5 hours) = 1 - 0.7 = 0.3

Hence,

P(scoring above 400) = (0.7 * 0.85) + (0.3 * 0.65) = 0.595 + 0.195

= 0.79

B.) probability that given a student scored above 400, he/she spent at least five hours reviewing for the test.

P(spent ≥5 hours review | score above 400) :

P(spent ≥5 hours review) / P(score > 400)

(0.7 * 0.85) / 0.79

0.595 / 0.79

= 0.753

Answer:

Step-by-step explanation:

Q1

The angle of rotation is twice the angle of intersection:

Q2

Dilation by a scale factor of 2 resulted in:

The endpoints of the original segment are:

Correct choice is B

The quadratic function graphed is defined as follows:

y = x² - 10x + 9.

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

From the graph, the roots are given as follows:

x = 1 and x = 9.

Hence the function as a product of it's linear factors is defined as follows:

y = a(x - 1)(x - 9)

y = a(x² - 10x + 9).

When x = 5, y = -16, hence the leading coefficient a is obtained as follows:

-16 = a(5² - 10(5) + 9)

-16a = -16

a = 1.

Thus the function is:

y = x² - 10x + 9.

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Answer:

\(2^{6}\)

Step-by-step explanation:

\(2^3 \div 2^{-3}\)

\(2^{3-(-3)}\)

\(2^{3+3}\)

\(2^{6}\)

In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.

In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.

To find the value of x in the given proportions, let's solve them one by one:

(5x + 1) : 3 = (2x + 2) : 7

To solve this proportion, we can cross-multiply:

7(5x + 1) = 3(2x + 2)

35x + 7 = 6x + 6

Subtracting 6x from both sides and subtracting 7 from both sides:

35x - 6x = 6 - 7

29x = -1

Dividing both sides by 29:

x = -1/29

Therefore, the value of x in the first proportion is -1/29.

(6x) : (4x) = 7

To solve this proportion, we can simplify the left side:

6x / 4x = 7

Dividing both sides by 2x:

3/2 = 7

This equation is not true, as 3/2 is not equal to 7.

Therefore, there is no value of x that satisfies the second proportion.

In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.

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Answer:

what's the table? but you solve it multiply however long she practiced on Wednesday by 0.66

Answer:

5/9

Step-by-step explanation:

i sacrificed a mistake on khanacademy just for this.

U DONT NEED IT

so

u

cannot

say

that

i

didnt

give

the

right

answer

n00bs

Answer:

12000

Step-by-step explanation:

15000 times 8% is 1200 for ten years making it 12000

Answer:

A: 5% High risk; 15% medium risk; 80% low risk.

Step-by-step explanation:

Option A will be the most appropriate because it follows the risk pyramid pattern that guides investors.

Now, in the risk pyramid, the low risk investment should be the biggest and should contain a large part of your assets since it will be low in risk and have good foreseeable returns. The medium risk investment should be the next biggest as it allows stable returns while capital appreciates. While the high risk return investment should be the lowest as it should consist of money you can lose and wouldn't really affect you.

Answer:

25,

8:5

4:3

Step-by-step explanation:

you have to model it as a system of equations.

first, we know there are a total of 65 children, boys and girls. so

\(65 = b + g\)

we also know there are 15 more boys than girls so

\(b = g + 15\)

now, we can plug the second equation into the first to get

\(65 = (g+15)+g\)

so

\(2g = 50, g = 25\)

if g = 25, b must = 40, because it is g+15.

the ratio will be 40 boys to 25 girls. 40:25 or 8:5 if you simplify.

if there are 5 more girls, g = 25+5 = 30, so the ratio is 40:30 or 4:3.

Answer:

A) 25

B) 40 : 25

C) 40 : 30

Step-by-step explanation:

I'm not positive on this but I think it might be right

Answer:

?=2 (ik i answered but i kinda want the points)

Step-by-step explanation:

first look at the problems ? x (3+5) = 6 +10

so ? x 8 = 16 so dvide 16 by 8 and you'll end up with a solid 2

the length of the rope is approximately 11.9 feet.

What is right angle triangle?

The term "right-angled triangle" refers to any triangle with an internal angle that is either a right angle or 90 degrees in value. The right triangle or the 90-degree triangle are other names for this triangle because of this. Right triangles have "opposite" and "adjacent" sides, which refer to the sides that are across from and next to respective angles, respectively. When a right triangle is formed, the hypotenuse is its longest side.

We can consider the flagpole, the ground, and the rope as forming a right triangle. The angle between the flagpole and the rope is 90 degrees, and the angle between the rope and the ground is 35 degrees. Therefore, the angle between the flagpole and the ground is 90 - 35 = 55 degrees.

Let's call the length of the rope "r". We can use the trigonometric function tangent to find r:

tan(35°) = opposite/adjacent = r/20

Multiplying both sides by 20, we get:

r = 20 tan(35°)

Using a calculator, we get:

r ≈ 11.9 feet

Therefore, the length of the rope is approximately 11.9 feet.

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Answer:

Step-by-step explanation:

a cuboid has length 18.5 cm, width 9.4 cm a height 6.2 cm. Work out the area of the cuboid​

assuming you are looking for thr surface area

Surface Area of a Cuboid ·

TSA = 2 (lw + wh + hl)

2*( 18.5 * 9.4 + 9.4 * 6.2 + 6.2 * 18.5) =         (remember PEMDAS)

2 * 346.88 =

693.76 cm²

The standard deviation of the restaurant profits in 2021 is given by $71181.

Restaurant profit for outcome 'move to A' = $ 260000

Restaurant profit for outcome 'move to B' = $ 120000

Restaurant profit for outcome 'stay in C' = $ 100000

The mean of restaurant profits = $(260000 + 120000 + 100000)/3 =$ 160000.

Standard deviation of the restaurant profits in 2021 is given by

= $ √({(260000 - 160000)² + (120000 - 160000)² + (100000 - 160000)²}/3)

= $ √(((100000)² + (40000)² + (60000)²)/3)

= $ √(15200000000/3)

= $ √5066666667

= $ 71181 (rounded to the nearest dollar)

Hence standard deviation of the restaurant profits in 2021 is given by $71181.

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The question is incomplete. The complete question will be -

For x = 4.1:

Slope of PQ =5.1

For x = 4.01:

Slope of PQ =6.01

For x = 3.9:

Slope of PQ =15.1

For x = 3.99:

Slope of PQ =105.99

From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.

To find the slope of the secant line PQ, we need to first find the coordinates of point Q in terms of x:

Q = (x, x² + x + 8)

Then, the slope of the secant line PQ is given by:

(yQ - yP) / (xQ - xP)

where yP = 28 and xP = 4, and yQ and xQ depend on the value of x.

For x = 4.1:

Q = (4.1, 4.1² + 4.1 + 8) = (4.1, 28.51)

Slope of PQ = (28.51 - 28) / (4.1 - 4)

= 0.51 / 0.1

= 5.1

For x = 4.01:

Q = (4.01, 4.01² + 4.01 + 8) = (4.01, 28.0601)

Slope of PQ = (28.0601 - 28) / (4.01 - 4)

= 0.0601 / 0.01

= 6.01

For x = 3.9:

Q = (3.9, 3.9² + 3.9 + 8) = (3.9, 26.49)

Slope of PQ = (26.49 - 28) / (3.9 - 4)

= -1.51 / -0.1

= 15.1

For x = 3.99:

Q = (3.99, 3.99² + 3.99 + 8) = (3.99, 26.9401)

Slope of PQ = (26.9401 - 28) / (3.99 - 4)

= -1.0599 / -0.01

= 105.99

As x approaches 4 from both sides, the x-coordinate of Q approaches 4, and the slope of PQ approaches the slope of the tangent line to the curve at P(4,28). From the results above, we can guess that the slope of the tangent line to the curve at P is approximately 6.

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