The student council at Newberg High School is making T-shirts to sell for a fundraiser, at a price of $12 apiece. The costs, meanwhile, are $7 per shirt, plus a setup fee of $65. Selling a certain number of shirts will allow the student council to cover their costs. How many shirts must be sold? What will the costs be?

The value of c so that cx-d=2x+4 has No Solution is c=2.

In the given question ,

we have

cx-d=2x+4       ....(i)

Given that d = 2 ,

We substitute the value of d=2 in equation (i)

On substituting we get

cx-2=2x+4

Simplifying further we get

cx=2x+4+2

cx=2x+6

cx-2x=6

x(c-2)=6

x=6/(c-2)

For x to have NO SOLUTION the denominator should be 0.

because when denominator becomes 0 the value becomes not defined , hence will have no solution.

Substituting the denominator = 0

we get c-2=0

c=2.

Therefore , the value of c so that cx-d=2x+4 has No Solution is c=2.

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Step-by-step explanation:

since g(f(x)) = x g (f (x) )= x, f - 1 (x) = 5x3 + 43 f - 1 (x) = 5 x 3 + 4 3

The inverse of the given function \(f(x) = 3(x-4)^{2} +5\) is \(f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4\).

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by \(f^{-1}\) or \(F^{-1}\).

According to the given equation.

We have a function.

\(f(x) = 3(x-4)^{2} +5\)

The above function can be written as

\(y = 3(x-4)^{2} +5\)

Write the above function for x.

\(\implies y -5 = 3(x-4)^{2}\)

\(\implies \frac{y-5}{3} = (x-4)^{2}\)

\(\implies \sqrt{\frac{y-5}{3} } =x-4\)

\(\implies \sqrt{\frac{y-5}{3} } +4=x\)

\(0r\ x = \sqrt{\frac{y-5}{3}}+4\)

Replace \(x\) by \(f^{-1}(x)\) and \(y\) by \(x\).

We get

\(f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4\)

Hence, the inverse of the given function \(f(x) = 3(x-4)^{2} +5\) is \(f^{-1} (x) = \sqrt{\frac{x-5}{3} } +4\).

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Answer:

x = 100, y = 80

Step-by-step explanation:

100° and x° are alternate interior angles and are congruent , so

x = 100

x° and y° are a linear pair and sum to 180° , that is

100 + y = 180 ( subtract 100 from both sides )

y = 80

Answer:

answer is simple

Step-by-step explanation:

you just need to find out solutions by your self

we conclude that the coordinates of U' are (-4, 5).

For any point (x, y), a reflection over the x-axis changes only the sign of the y-component, so after the reflection, we will get (x, -y).

In this case we start with U located at (-4, -5).

If we apply the reflection over the x-axis, then we will get:

(-4, - (-5))

If we apply the rule of signs, then:

(-4, - (-5)) = (-4, 5).

In this way, we conclude that the coordinates of U' are (-4, 5).

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The original number is -21/5 or -4.2 which is divided by 3 more than the number.

In mathematics, an equation is a statement or formula which shows two expressions having equal value and connected by an equal sign. The two expressions consist of variables and/or numbers.

Let the number be 'x' Two times the number = 2x3 more than the number = x + 3

According to the question,two times a number is divided by 3 more than the number is equal to 7 which means 2x / (x+3) = 7

By applying cross multiplication,2x = 7 × ( x+3)2x

= 7x + 7×32x

= 7x + 212x - 7x

= 21-5x = 21x = 21/ (-5)x

= -4.2

Hence the original number is -4.2

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A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is: \(3x^2-15x+12\)

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

For this case we have that the following function complies with the given conditions:

\(f(x)=3x^2-15x+12\)

To prove it, let's find the roots of the polynomial:

\(3x^2-15x+12=0\)

By doing common factor 3 we have:

\(3(x^2-5x+4)=0\)

Factoring the second degree polynomial we have:

\(3(x-1)(x-4)=0\)

Then, the solutions are:

Solution 1:

\(x-1=0 \ or \ x=1\)

Solution 2:

\(x-4=0\ \ or \ x=4\)

Hence A second degree polynomial function f (x) that has a lead coefficient of 3 and roots 4 and 1 is:\(3x^2-15x+12\)

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Answer:

f(x) = 3x² – 15x + 12

Step-by-step explanation:

I got it right on the unit test for edge

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.

When the distribution is normal, we use the z-score formula.

In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:

Z = (X – µ) / σ

The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

So, in this case, given that:

µ = 249, σ = 20

The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:

100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.

Now, put all the values into the formula:

Z = (X – µ) / σ

–0.253 = (X – 249) / 20

X – 249 = –0.253 * 20

X = 244

Hence, the candle burns for 244 minutes.

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The probability of winning a lottery game where the winning number is made up of three digits from 0 to 9 chosen at random and the numbers may repeat is 1/1000.

In the given problem, there are 10 digits from 0 to 9.If we are allowed to repeat the digits in the lottery number, then for each of the three digits, there are 10 possibilities.
Thus, the total number of possible lottery numbers = 10 × 10 × 10 = 1000.
Now, the player has only one winning number.
∴ The probability of winning the lottery = 1/1000\\

Thus, the probability of winning a lottery game where the winning number is made up of three digits from 0 to 9 chosen at random and the numbers may repeat is 1/1000.

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Answer:

X=2

Step-by-step explanation:

Answer: 5

Step-by-step explanation: A cube has all lengths equal.

Volume is 125 find the cube root

Pat left the office at 10:50 am.

What is the relation between speed, distance, and time?

The relation between speed, distance, and time would be

distance = speed x time

We know that Pat had a 12:30 pm appointment 72 miles from his office, arrived ten minutes late, and averaged 48 mph for the trip. So we can set up the equation as:

distance = speed x time

72 = 48 x time

To solve for time, we divide both sides of the equation by 48:

time = distance / speed

time = 72 / 48

time = 1.5 hours

Since Pat arrived 10 minutes late, we need to subtract that 10 minutes from the time it took him to get to the appointment

12:30pm - 00:10 = 12:20 pm

Now, we have to subtract the time it took Pat to get to the appointment from the time he left the office

12:20 pm - 1.5 hours = 10:50 am

So Pat left the office at 10:50 am.

Hence, Pat left the office at 10:50 am.

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If the fuselage of the Boeing 777 were made of steel instead of aluminum, the number of passengers it could carry would decrease.

Given that the fuselage of the Boeing 777 is a hollow aluminum cylinder, we can calculate its volume using the dimensions provided: length = 64.0 m, width = 6.2 m, and thickness = 2.5 mm. Using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height, we can determine the volume of the aluminum fuselage. Since the cylinder has no ends, the height is the same as the length of the fuselage. The radius can be calculated by dividing the width by 2. By substituting these values into the formula, we can find the volume of the aluminum fuselage. Once we have the volume, we can multiply it by the density of aluminum to find the mass of the aluminum fuselage. Dividing the mass by the average passenger mass of 79 kg will give us the approximate number of passengers the Boeing 777 could carry if its fuselage were made of steel. However, we need the specific maximum total mass or engine's lifting capacity to provide an exact answer.

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The given statement "Of the range, the interquartile range, and the variance, the interquartile range is least influenced by an outlying value in the data set." is False

Range: It is the difference between the minimum and maximum values of data. It is affected by the presence of outliers.

Interquartile range: It is the difference between the third quartile and the first quartile of data.

Variance:

Variance = \(\frac{\Sigma(x_{i} - \bar{x})^{2}}{n}\)

where xi are data points,  \(\bar{x}\) is the mean and n is the number of observations. It is a measure of the spread of the data. It is affected by the presence of outliers as they increase the variation in the data.

Hence, the given statement is false.

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Answer:

42/6

Each color blocks have 6 each, and they're 7 groups of them. Simple.

Function 1: f(x) = √x is a function from R to R with a range of non-negative real numbers (≥ 0).

Function 2: f(x) = 1/f(x^2 - 4) is not a function from R to R because it is not defined for x = -2 and x = 2.

Function 3: f(x) = √(x^2) is a function from R to R with a range of non-negative real numbers (≥ 0).

In order to determine which functions are from R to R and their ranges. We have three functions to consider:
1. f(x) = √x
This function is not from R to R because the square root of a negative number is not defined in real numbers. The domain is x ≥ 0, and the range is f(x) ≥ 0.
2. f(x) = 1/(x² - 4)
This function is also not from R to R because the denominator cannot be zero. The domain excludes x = -2 and x = 2. The range is f(x) > 0 for all x ≠ ±2.
3. f(x) = √(x²)
This function is from R to R because the square root of a squared number is always non-negative and defined for all real numbers. The domain is all real numbers (x ∈ R), and the range is f(x) ≥ 0.

f(x) = √x (Square root of x)

This function is a valid function from R to R. The domain is all real numbers (R), and the range is all non-negative real numbers (R+ or [0, +∞)) because the square root of a non-negative real number is always non-negative.

Range: [0, +∞)

f(x) = 1/f(x² - 4)

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Answer:

What is the most popular ice cream flavor this week ?

Do kids usually prefer a cup or a cone?

What does a group of 4 typically spend on ice cream at this shop?

Step-by-step explanation:

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data. Statistics can be used to make better-informed business and investing decisions.

Knowing that information you can infer that if the Ice cream shop is trying to see how well their business is doing what ice cream flavors they don't need to get rid of or other things, these are questions they would typically ask.

Answer:

3

Step-by-step explanation:

Answer:

Look below in the Explanation.

Step-by-step explanation:

A. Greater than one

B.  Greater than One

C. Less than one

D. Greater than 1

E. Equal to one

The significance of the slope in regression can be determined by conducting a hypothesis test

The slope of the regression line in a regression analysis shows how  dependent variable changes as the independent variable increases by a unit. A hypothesis test on a slope coefficient, commonly referred to as the beta coefficient or the regression coefficient, can be used to ascertain the significance of the slope. The slope coefficient is compared to a null hypothesis value of zero in the hypothesis test.

The null hypothesis is rejected and it is determined that there is a significant association between the independent and dependent variables if the p-value for the slope coefficient is less than the significance threshold. Therefore, slope is not equal to zero and there is an association amongst changes in the independent variable and those in the dependent variable.

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The rate of change of radius is 2.832 mm per second, when the radius is 6 mm.

A height of cone = 15 mm

An initial radius of cone = 16 mm

The volume of the inverted cone is decreasing at a rate of 534 cubic mm per second, with the height being held constant.

The formula of Volume of cone;

V = 1/3 πr^2h

where, r =  radius of the cone and h = height of the cone

To determine the rate of change of the radius we differentiate the volume with respect to t.

dV/dt = 2/3 πrdr/dt h

Now putting the values

534 = 2/3 × 22/7 × 6 × dr/dt × 15

534 = 3,960/21 × dr/dt

Multiply by 21 on both side, we get

3960 dr/dt = 11,214

Divide by 3960 on both side, we get

dr/dt = 2.832

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A chart that compares three sets of values in a three-dimension chart is called surface.

A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.

A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.

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The  line at the coffee shop during rush hour is 15 people long.

Given:

- 5 people arrive at the coffee shop each minute.

- Each person has to wait for 3 minutes to be served.

Since 5 people arrive each minute,  the rate of people entering the line is 5 people/minute.

Now, Each person has to wait for 3 minutes to be served.

So, Average length of line = Rate of people entering * Time for a person to be served

Average length of line = 5 people/minute * 3 minutes

Average length of line = 15 people

Therefore, on average, the line at the coffee shop during rush hour is 15 people long.

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The solutions of the given equation in the interval [0, 2π) are: x = 0, x = π/2, x = π, x = 3π/2

solve the equation sin(2x)cos(x) = 0 in the interval [0, 2π).

First, we'll use the double-angle formula to simplify the equation. The double-angle formula for sine is:

sin(2x) = 2sin(x)cos(x)

Now, substitute this into the given equation:

2sin(x)cos(x)cos(x) = 0

This simplifies to:

2sin(x)cos^2(x) = 0

Now, we can solve the equation by setting each factor equal to zero:

1) sin(x) = 0
2) cos^2(x) = 0 or cos(x) = 0

For the first case (sin(x) = 0), the solutions within the interval [0, 2π) are:

x = 0, x = π

For the second case (cos(x) = 0), the solutions within the interval [0, 2π) are:

x = π/2, x = 3π/2

So, the solutions of the given equation in the interval [0, 2π) are:

x = 0, x = π/2, x = π, x = 3π/2

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Step-by-step explanation:

-7-13>-15x

-20>-15x

x>-20/-15

x>4/3

please give the domain.

or write on your own.!

Answer:

\(1 \frac{1}{3} < x \: \: \: or \: \: \: x > 1 \frac{1}{3} \\ \)

Step-by-step explanation:

\( - 7 > 13 - 15x \\ - 7 - 13 > - 15x \\ - 20 > - 15x \\ \frac{ - 20}{ - 15} < x \\ \frac{4}{3} < x \\ 1 \frac{1}{3} < x \\ \)

Answer:

PA = PB

Step-by-step explanation:

The radius OA = OB

so triangles OPA is congruent to OPB because OA = OB, OP is the same side, angle OPA = angle OPB = 90o

therefore PA = PB

At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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Answer:

756m²

Step-by-step explanation:

Answer:

\(12 - 3\)

Step-by-step explanation:

\(( - 12 + 3) \\ = 12 - 3 \\ =- 9\)