Joni sold 376 tickets for the school play. Student tickets cost $4 and adult tickets cost $7. Joni's sales totaled $2080.

Answer:

\(x + 0.05x = 15\), solution is $14.29

Step-by-step explanation:

We can create an equation for this scenario to try and solve it.

Assuming the cost of the CD is x, it’s sale tax will be 0.05x (as that is 5% of x, 0.05.)

We can write the equation in two ways:

\(x + 0.05x = 15\) or \(1.05x = 15\).

Assuming we take the second one (easier to work with), we can divide both sides by 1.05. The equation simplifies to x = 14.289... which rounds to x = 14.29.

Therefore, the equation is \(x + 0.05x = 15\) and the solution is $14.29.

Hope this helped!

Answer:

x + 0.05x = 15; x = $14.29

Step-by-step explanation:

Based on the following given inequality; the symbol will be reversed when the variable is isolated

The condition for the symbol of an inequality to be reversed is;

if the variable is isolated and a negative number is used to divide.

The symbols of inequality are;

Greater than >

Less than <

Greater than or equal to ≥

Less than or equal to ≤

Equal to=

–10.5 < 3a

a < -10.5/3

a > -3.5

Yes

b6 ≤ 7

b ≤ 7/6

b ≤ 1.17

No

–4.5c > 9

c > 9/-4.5

c < -2

Yes

–215 ≤ –52d

d ≤ -215 / -52

d ≤ 4.14

No

Hence, the symbol will be reversed when the variable is isolated if the result of the division is negative.

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Answer:

3.5595feet

Step-by-step explanation:

Given the function f(x)=15(.75)^x which models the height of the ball in feet of each bounce, where x is the bounce number. The height after the 5th bounce will be gotten by substituting x = 5 into the function

f(x)=15(.75)^x

f(5)=15(.75)^5

f(5)=15(0.2373)

f(5)= 3.5595

Hence the height after the 5th bounce is 3.5595feet

Answer:the answer is 3.6 if you’re rounding to the nearest 10th of a foot

Step-by-step explanation:

.75 to the power of 5 times 15

The expression is divisible by both 7 and 19, it is divisible by 133.

To prove that if n is a positive integer, then 133 divides 11^n + 122^(n-1), we need to show that the expression is divisible by 133. Note that 133 = 7 * 19. Let's check for divisibility by both 7 and 19.

Using modular arithmetic, consider the expression mod 7 and mod 19:
11^n (mod 7) ≡ (-3)^n (mod 7) and 122^(n-1) (mod 7) ≡ (-2)^(n-1) (mod 7).
11^n + 122^(n-1) (mod 7) ≡ (-3)^n + (-2)^(n-1) (mod 7).

Since both terms are congruent to 1 (mod 7) for all n, the sum is divisible by 7.

Similarly, 11^n (mod 19) ≡ (-8)^n (mod 19) and 122^(n-1) (mod 19) ≡ 9^(n-1) (mod 19).
11^n + 122^(n-1) (mod 19) ≡ (-8)^n + 9^(n-1) (mod 19).

Both terms are congruent to 1 (mod 19) for all n, so the sum is divisible by 19.
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11ⁿ • 122ⁿ⁻¹ can be expressed as the product of 133 and another integer. Therefore, we have proven that if n is a positive integer, then 133 divides 11ⁿ • 122ⁿ⁻¹.

To prove that 133 divides 11ⁿ • 122ⁿ⁻¹, it should be shown that there exists an integer k such that 11ⁿ • 122ⁿ⁻¹ = 133k.

Let's start by factoring the expression 11ⁿ • 122ⁿ⁻¹:

11ⁿ • 122ⁿ⁻¹ = (11 • 122)n² - 1

Now, rewrite 11 • 122 as 133 + 11:

(133 + 11)n² - 1

Expanding the expression, we get:

133n² + 11n² - 1

Now, rewrite 133n² as (133n)(n):

(133n)(n) + 11n² - 1

This expression can be further simplified as:

133n² + 11n² - 1 = (133n² + 11n²) - 1 = 144n² - 1

Now, let's focus on 144n² - 1. Notice that 144 = 11 • 13 + 1:

144n² - 1 = (11 • 13 + 1)n² - 1 = 11 • 13n² + n² - 1

Rearranging the terms, we get:

11 • 13n² + n² - 1 = 11(13n²) + (n² - 1)

The expression n² - 1 can be factored as (n - 1)(n + 1):

11(13n²) + (n² - 1) = 11(13n²) + (n - 1)(n + 1)

Now, we have an expression of the form 11 • (something) + (n - 1)(n + 1). We can see that (n - 1)(n + 1) represents the product of two consecutive integers, which means one of them must be even.

Let's consider two cases:

1. If n is even, then n = 2k for some integer k. Substituting this into the expression, we get:

11(13(2k)²) + ((2k) - 1)((2k) + 1)

Simplifying further:

11(13(4k²)) + (4k² - 1) = 572k² + 4k² - 1 = 576k² - 1

Now, we have an expression of the form 576k² - 1, which can be factored as (24k)² - 1²:

576k² - 1 = (24k)² - 1²

This is a difference of squares, which can be further factored as (24k - 1)(24k + 1). Therefore, we have expressed the original expression as a product of 133 and another integer (24k - 1)(24k + 1), which shows that 133 divides 11ⁿ • 122ⁿ⁻¹ when n is even.

2. If n is odd, then n = 2k + 1 for some integer k. Substituting this into the expression, we get:

11(13(2k + 1)²) + ((2k + 1) - 1)((2k + 1) + 1)

Simplifying further:

11(13(4k² + 4k + 1)) + (4k² + 2k) = 572k² + 572k + 143 + 4k² + 2k

Combining like terms:

576k² + 574k + 143

Now, we need to show that 576k² + 574k + 143 is divisible by 133. Let's express 133 as 11 • 12 + 1:

576k² + 574k + 143 = 11 • 12 • k² + 11 • 12 • k + 143

Now, we can rewrite 11 • 12 as 132 + 11:

11 • 12 • k² + 11 • 12 • k + 143 = (132 + 11)k² + (132 + 11)k + 143

Expanding the expression, we get:

132k² + 11k + 132k + 11k + 143

Combining like terms:

132k² + 264k + 143

Now, notice that 132k² + 264k is divisible by 132:

132k² + 264k = 132(k² + 2k)

Therefore:

132k² + 264k + 143 = 132(k² + 2k) + 143

We can express 143 as 132 + 11:

132(k² + 2k) + 143 = 132(k² + 2k) + (132 + 11)

Expanding the expression:

132k² + 264k + 132 + 11

Combining like terms:

132k² + 264k + 143

We have arrived at the original expression, which means that 576k² + 574k + 143 is divisible by 133 when n is odd.

In both cases, we have shown that 11n • 122ⁿ⁻¹ can be expressed as the product of 133 and another integer. Therefore, we have proven that if n is a positive integer, then 133 divides 11ⁿ • 122ⁿ⁻¹.

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Answer: 13. 30

Step-by-step explanation:

13. Area = 18x * 10y = 180xy

Length = 6th

With ?

180xy = 6xy x width

180 x/6xy

Width = 30

14. 3^(9-5)= 3^4 = 81 the truck weighs 81 times as the driver

3^5

Answer:

original recipe

Step-by-step explanation:

Answer:

If a linear system has more than one solution, then the kernel of the coefficient matrix is a nonzero subspace, and the solution set is an affine subspace parallel to the kernel. So, (over an infinite field), the solution set must be infinite. The definition of a linear system is your key.

Answer:

Step-by-step explanation:

Sale price of the coat:

Total of three items:

Add tax to get the total:

P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer:

21cm2

Step-by-step explanation:

Area (A = BH)

B = 7cm

H = 3cm

Therefore we multiply Base(B) with height (H) to get the area.

Hence;

Area = (7 × 3) cm2

= 21cm2

The productivity of the truck in bank measure is most nearly 32.3 (option C).

To calculate the productivity of the truck in bank measure, we need to convert the loose density to bank density. Bank measure refers to the volume of material when it is compacted or in its natural state, while loose measure refers to the volume of material when it is loose or not compacted.

The formula to convert loose density to bank density is as follows:

Bank Density = Loose Density / (1 + Moisture Content)

Since the moisture content is not provided in the question, we assume it to be zero for simplicity. Therefore, the bank density is equal to the loose density.

Next, we need to calculate the truck's productivity in bank measure. The formula for productivity is:

Productivity = Truck Capacity / Cycle Time

However, the truck capacity and cycle time are not provided in the question. Therefore, we cannot directly calculate the productivity.

Given that we have the specifications of the truck's density, we can make an estimation based on industry standards. A common truck capacity for earth hauling is around 20 cubic yards. The cycle time can vary depending on factors such as loading and dumping time, travel distance, and road conditions. For estimation purposes, let's assume a cycle time of 30 minutes (0.5 hours).

Using these values, we can calculate the productivity as follows:

Productivity = Truck Capacity / Cycle Time

Productivity = 20 / 0.5

Productivity = 40 cubic yards per hour

However, the productivity is measured in bank measure (yd³/hr), so we need to adjust the result based on the bank density.

Adjusted Productivity = Productivity * (Loose Density / Bank Density)

Adjusted Productivity = 40 * (100 / 110)

Adjusted Productivity ≈ 32.3 cubic yards per hour (bank measure)

Therefore, the productivity of the truck in bank measure is most nearly 32.3 (option C).

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The circumcenter of the given triangle with vertices D(-3, 3), E(3, 2), F(1, -4) is (0, 1/2).

We need to find the circumcenter coordinates for the given triangle D(-3, 3), E(3, 2), F(1, -4).

We will use the following steps to find the coordinates of the circumcenter of the triangle given above.

Step 1: Find the midpoint of two sides of the triangle

The midpoint of DE is:

$\left( {\frac{{ - 3 + 3}}{2},\frac{{3 + 2}}{2}} \right) = \left( {0, \frac{5}{2}} \right)$

The midpoint of EF is: $\left( {\frac{{3 + 1}}{2},\frac{{2 - 4}}{2}} \right) = (2, - 1)$

The midpoint of DF is: $\left( {\frac{{ - 3 + 1}}{2},\frac{{3 - 4}}{2}} \right) = ( - 1, - \frac{1}{2})$

Step 2: Find the perpendicular bisectors of the sides.

The equation of the perpendicular bisector of DE is:

y - {5}{2} = -{1}{3}( {x - 0}

The equation of the perpendicular bisector of EF is:

y + 1 = {1}{2}( {x - 2}

The equation of the perpendicular bisector of DF is:

y + {1}{2} = - 3( {x + 1}

Step 3: Find the intersection point of the bisectors; that is, the circumcenter of the triangle.

The intersection point of the bisectors is (0, 1/2).

Therefore, the coordinates of the circumcenter of the triangle are (0, 1/2).

Answer: The circumcenter of the given triangle with vertices D(-3, 3), E(3, 2), F(1, -4) is (0, 1/2).

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This line has a slope of -1/3 and y-intercept of -1. Therefore, it passes through the points (0,-1) and (3,-2).

The system of linear equations consists of two equations:

y = (1/3)x + 1 (Equation 1)

x + 3y = -3 (Equation 2)

To determine the number of solutions, we need to find the intersection point of the two lines represented by these equations.

The first equation is in slope-intercept form, where the slope is 1/3 and the y-intercept is 1. Therefore, we know that the line passes through the point (0,1) and (3,2).

The second equation can be written in slope-intercept form as:

y = (-1/3)x - 1 (Equation 3)

This line has a slope of -1/3 and y-intercept of -1. Therefore, it passes through the points (0,-1) and (3,-2).

We can see from the graph that the two lines intersect at a single point, which appears to be (-3,0). This means that the system has a unique solution, and the answer is One solution at (-3,0).

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The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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Answer:

21.2

Step-by-step explanation:

it's basically asking you to solve the long side of a right angle triangle by giving you one side is 7 and the other is 20

so 7²+20² = 449

√449 = 21.2

The angle included by the sides line PN and line NM is < N

The term included angels refers to the angle formed when two lines meet. The angle as a result of the two lines meeting is the included angle, The angle is located at the meeting point of the two lines.

The following are deduced from the given figure

Line NN

Line NM

Line MP

Looking at the two lines in the question that is Line PN and line NM. The angle at the meeting point is < N and hence the included angle.

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Answer:

17.5hrs

Step-by-step explanation:

Set they worked for x hours,

10x+35=210

10x=175

x=17.5

Answer:

Step-by-step explanation:

According to the graph, the line goes down in both sections as the value of x increases. It means the function is always decreasing.

Correct answer choice is:

The best describes the function is,

''The function is never increasing.''

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

This graph shows a reciprocal parent function.

Since, We have;

According to the graph, the line goes down in both sections as the value of x increases.

It means the function is always decreasing.

Hence, Correct answer choice is:

C. The function is never increasing.

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The probability of getting a jack, a three, a club, or a diamond is approximately 0.65.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It quantifies the uncertainty associated with an outcome or event.

To determine the probability of getting a jack, a three, a club, or a diamond when one card is drawn from a standard 52-card playing deck, we need to calculate the probability of each event and sum them up.

Number of Jacks: There are 4 jacks in a deck (one jack for each suit).

Number of Threes: There are 4 threes in a deck (one three for each suit).

Number of Clubs: There are 13 clubs in a deck (one club for each rank).

Number of Diamonds: There are 13 diamonds in a deck (one diamond for each rank).

Total favorable outcomes = Number of Jacks + Number of Threes + Number of Clubs + Number of Diamonds

= 4 + 4 + 13 + 13

= 34

Total possible outcomes = Total number of cards in a deck = 52

Probability = Favorable outcomes / Total outcomes

= 34 / 52

≈ 0.6538

Rounding to the nearest hundredth, the probability of getting a jack, a three, a club, or a diamond is approximately 0.65.

Therefore, the correct answer is d. 0.65.

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Answer:

A

Step-by-step explanation:

14/15 is less than 7/5

Answer:

dang me too I'm like almost failing

The largest number common to both sequences is 67.

The arithmetic sequence with first term 1 has a common difference of 6 is given by:-

1,7,13,19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, and 97

The arithmetic sequence with first term 4 has a common difference of 7 is given by:-

4,11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, and 95.

I have written the sequence until 100 only.

Hence, the numbers common to both the arithmetic sequences are :-

25 and 67

Hence, the largest number common to both sequences is 67.

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Answer:

C, D, B.

Step-by-step explanation:

y=mx+b

look at what numbers are in the variable spots.

Answer:

Commutative and multiplicative identity

Step-by-step explanation:

mark brainlyist

Answer:

height of the waste is 20.0 inches.

Step-by-step explanation:

given data

volume = 5, 667.7cubic inches

radius = 9.5 inches

solution

we use here volume of a cylinder is express as

V = πr²h     .................1

put here value

5667.7 = (3.14) × (9.5²) × h

solve it we get

h = 20 inch

so height of the waste is 20.0 inches.

The weights that separate the top and bottom 8% are approximately 5.26 ounces and 5.12 ounces, respectively.

I need to find the weight that separates the top 8% and bottom 8% of the normal distribution.

Let X be the weight of the mechanical part. \(X ~ N(5.19, 0.05^2)\), H. X is normally distributed with mean μ = 5.19 ounces and standard deviation σ = 0.05 ounces.

You'll be able to utilize the z-score equation to standardize the conveyance and discover the z-scores comparing to the best 8% and foot 8% of the dispersion. 

For the top 8%:

z = invNorm(1-0.08) = 1.405

For the bottom 8%:

z = invNorm(0.08) = -1.405

where invNorm is the inverse normal distribution function.

You can use the Z-score formula to find the corresponding weights.

For the top 8%:

z = (x - μ) / σ

1.405 = (x - 5.19) / 0.05

x - 5.19 = 0.07025

x = 5.26025 ounces

For the bottom 8%:

z = (x - μ) / σ

-1.405 = (x - 5.19) / 0.05

x - 5.19 = -0.07025

x = 5.11975 ounces

Therefore, the weights that separate the top and bottom 8% are approximately 5.26 ounces and 5.12 ounces, respectively. Components with weights outside this range may be rejected.

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• For every increase in height, the temperature is -5

• The temperature on the surface is when y = 23

Given the equation:

Where y represent the temperature (in degrees Celsius), and x represent the height above the surface (in kilometers).

For x = 1, we have:

23 - 5(1) = y

y = 23 - 5 = 18

For x = 2, we have:

23 - 5(2) = y

y = 23 - 10 = 13

For x = 3, we have:

23 - 5(3) = y

y = 23 - 15 = 8

For every increase in height, the temperature is -5

The temperature on the surface is when x = 0

23 - 5(0) = y

y = 23

Age will be 40 years old.

R, in beats per minute, can be approximated by the formulas, where a represents the person's age.

where R= 143 - 0.65a for women.... (1)

and R= 165 - 0.75a for men,..... (2)

So by implementing these two equation we get a = 40

If the sum of ages is X and Y, and the ratio of their ages is p:q, then the age of Y can be calculated using the formula shown below: Y's age = Y's ratio/Sum of ratios x sum of ages The age dependency ratio is the ratio of dependents (people under the age of 15 or over the age of 64) to the working-age population (people between the ages of 15 and 64). The proportion of dependents per 100 working-age population is shown in the data.

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Answer: -k

Step-by-step explanation:

Answer:

It is the fourth one.

Step-by-step explanation: You use it to find it to see if it is a right triangle.

Step-by-step explanation:

Two lines that are perpendicular to each other has -1 as the product of thir gradient.

Since the gradient of the line y = 3 - x is -1, the gradient of the other line must be 1.

So y = x + c.

When x = 7, y = 1. 1 = 7 + c, c = -6.

Hence the equation of the line is y = x - 6.