Bernard’s Bakery recently spent a total of $400 on new equipment and their average hourly operating costs are $5. Their average hourly receipts are $10. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal?

A trapezoid has an area of 60 and a height of 8. The longer base is 3 more than the shorter base. Thus, the length of the shorter base is: 3.75

The size of a region on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar sheet.

Let, the shorter base of trapezoid (a)= x

given that,

The longer base is 3 more than the shorter base.

so, longer base (b) = 3x

A trapezoid has an area of 60 and a height of 8.

Now as we know,

area of trapezoid = (a + b / 2) h

60 = {(x + 3x) / 2} × 8

or, 60 = (4x / 2) × 8

or, 60 = 16 x

or, x = 3.75

Thus, the length of the shorter base is: 3.75

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The answer will be f(x) = 5*. If f′(x)>0 on an open interval, then f is increasing on the interval and If f′(x)<0 on an open interval, then f is decreasing on the interval.

Hence, The answer will be f(x) = 5*. If f′(x)>0 on an open interval, then f is increasing on the interval and If f′(x)<0 on an open interval, then f is decreasing on the interval.

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Answer:

when v increases w tends to increase

Step-by-step explanation:

Answer:

No, they are not similar

Step-by-step explanation:

25/107 = 16/88

Cross multiply

25 * 88 = 107 * 16

2200 = 1712

No, they are not similar

Answer:

haikus are easy

But sometimes they don’t make sense

Refrigerator

Step-by-step explanation:

first 5 syllables

second is 7 syllables

third 5 syllables

Answer: the Equation is y-3=0.4(x-1) or y-5=0.4(x-6).

Step-by-step explanation: I hope this helps.

The correct statements are:

The triangle and trapezoid area formulas have 1/2.

The parallelogram and rectangle formulas are both the same.

In the trapezoid formula, the bases are added.

A triangle is a polygon with three sides and three vertices. A triangle's angles add up to 180 degrees.

Area of a triangle = 1/2 x base x height

A trapezium is a quadrilateral that is convex. A trapezium is made up of at least two parallel sides. Area of a trapezium = 1/2  x (sum of the lengths of the parallel sides) x height

A rectangle is a quadrilateral in two dimensions with four right angles. Area of a rectangle = length x width

A parallelogram is a quadrilateral with two parallel sides. The opposite sides equal in length

Area of a parallelogram = base x height

Hence, the correct statements are options (A), (B), and (D).

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The question seems to be incomplete the correct question would be:

A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is

considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that

apply.

A. The triangle and trapezoid area formulas have 1/2.

B. The parallelogram and rectangle formulas are both the same.

C. In the parallelogram formula, the bases are added.

D. In the trapezoid formula, the bases are added.

E. In the triangle formula, the sides are added, then multiplied by 1/2​

The value of the total area of the shaded region are,

⇒ 42 units²

We have to given that;

Sides of rectangle are,

AB = 9

BC = 6

Hence, The area of rectangle is,

⇒ 9 x 6

⇒ 54 units²

And, Area of triangle is,

A = 1/2 × 4 × 6

A = 12 units²

Thus, The value of the total area of the shaded region are,

⇒ 54 - 12

⇒ 42 units²

So, The value of the total area of the shaded region are,

⇒ 42 units²

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Check the picture below.

Make sure your calculator is in Degree mode.

Answer:

1=8 2=11/12

Step-by-step explanation:

At 32.2 rate is water pouring into a rectangular bathtub with base 23sq ft if the water level rises at a rate of 1.4ft/min

Volume: Every three-dimensional object occupies some space. This space is measured in terms of its volume. Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

at what rate is water pouring into a rectangular bathtub with base 23sq ft

lb=23

volume of rectangle, v=lbh

                                   v=23h

differentiate with respect to time

dv/dt=23 dh/dt.....equation(1)

the water level rises at a rate of 1.4ft/min

dh/dt=1.4ft/min

substitute in equation(1)

dv/dt=23(1.4)

dv/dt=32.2

At 32.2 rate is water pouring into a rectangular bathtub with base 23sq ft if the water level rises at a rate of 1.4ft/min

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Learning platforms that use algorithms to adjust the content that each student sees in order to maximize learning efficiency is called Adaptive learning

Adaptive learning platforms utilize algorithms to tailor the learning experience for individual students based on their needs, abilities, and learning progress.

By analyzing data and feedback, adaptive learning systems can dynamically adjust the content, pace, and difficulty level to optimize learning efficiency and personalize the educational journey for each student.

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The required competition mark is given as 60, as of the given condition.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
A competition mark is calculated by doubling the sum of the top and bottom four scores and then averaging them.
According to the question,
Competition mark = 2 [7 + 6 + 8 + 5] + [7 + 9] / 2
Competition mark = 52 + 8 = 60

Thus, the competition mark is  60.

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Answer:

Step-by-step explanation:

First take the square root of the first number 144, then take the square root of your variable x^3

your final answer should be 12x^(3/2)

The additional amount that Austin will have for his boat purchase after 2.5 years of depositing $5,000 at 3% simple interest is $375.

Simple interest is the interest system that computes interest only on the principal for each period.

The simple interest formula is Principal x Rate x Time.

The cost of the boat that Austin wants to purchase = $15,000

The initial deposit made by Austin in a savings account (principal) = $5,000

Simple interest rate = 3%

3% = 3 ÷ 100 = 0.03

Investment period = 2.5 years

Simple Interest (Additional money in the account) = $375 ($5,000 x 0.03 x 2.5)

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Answer:

1 hour and 5 minutes

Step-by-step explanation:

1 hour equals 60 minutes

60 plus 30 equals 90

90 plus 40 equals 130

130 divided by 2 is 65

65 is turned into 1 hour and 5 minutes

Hope this helps

Welcome to Brainly Community

Solving the equation for y, it is found that the amount that John spends on snacks is given by:

\(y = 8x + 15\)

---------------------------

The relation of these measures is given by the equation:

\(8x + 15 - y = 0\)

The amount spent on snacks is y, thus, we solve the equation for y.

\(8x + 15 - y = 0\)

\(- y = -8x - 15\)

\(y = 8x + 15\)

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The value of the principal investment is $2,789.95 (rounded to the nearest hundredths place).

what is  principal investment ?

Principal investment refers to the initial amount of money that is invested in a savings account, a loan, or any other financial instrument. In the context of compound interest, the principal investment is the amount of money that earns interest over time.

what is  interest ?

Interest is the cost of borrowing money, or the return on invested money. When you borrow money, you pay interest to the lender as a percentage of the amount borrowed. When you invest money, you earn interest on the principal amount as a percentage of the amount invested.

In the given question,

The given equation is:     A = P * (1 + 0.05/4)⁴*ⁿ

We are given that after 15 years, the amount in the account is $12,065.51. Therefore, we can substitute the given values in the equation and solve for P:

A = $12,065.51

t = 15 years

$12,065.51 = P * (1 + 0.05/4)⁴*⁴⁵

Simplifying the right-hand side of the equation:

$12,065.51 = P * 1.0509⁶

$12,065.51/1.0509⁶ = P

$12,065.51/4.3228 = P

P = $2,789.95 (rounded to the nearest hundredths place)

Therefore, the value of the principal investment is $2,789.95 (rounded to the nearest hundredths place).

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The profit-maximizing price and quantity for the monopolist are $350 and 150 units, respectively ,The expected return is greater than the initial investment And the producer surplus is $33,750, consumer surplus is $31,875, and firm profit is $37,500.

Ignoring the time value of money and discounting, the expected value of the lottery winnings each year is 2% × $1 million = $20,000, and this goes on for 10 years.

Thus, the expected value of the investment is 10 × $20,000 = $200,000.

Hence, the expected return is greater than the initial investment, and there is a condition under which the investment can be made.

The monopolist’s total cost can be represented as:

TC = 300 + 200Q + 3Q².

The demand function for the monopolist is given as:

Q = 500 - P,

which can be rearranged to derive the price function as:

P = 500 - Q.

From the total cost function, we can obtain the marginal cost (MC) as the derivative of TC with respect to Q, and it can be represented as follows:

MC = dTC/dQ = 200 + 6Q.

From the marginal cost, we can set the marginal revenue (MR) equal to MC to get the profit-maximising quantity as follows:

MR = dTR/dQ = P + Q(500 - P) = 500 - Q + 500Q - Q² = 1000Q - Q² - 500 = MC = 200 + 6Q.

Substituting P = 500 - Q in the above expression and rearranging yields the following:

Q = 150, and hence, P = $350.

Therefore, the profit-maximising price is $350, and the quantity is 150. We can verify that the solution is a maximum by computing the second-order condition, which is negative.

To calculate the producer surplus, we first need to obtain the area above the marginal cost and below the price.

Thus, we have:

PS = ∫ MC to QdQ

= ∫ (200 + 6Q) dQ from 0 to 150

= [200Q + 3Q²] from 0 to 150

= $33,750.

Similarly, the consumer surplus can be computed as the difference between the market value of the product and what the consumers paid for it. The area below the price line and above the demand curve yields the consumer surplus.

Thus, we have:

CS = ∫ P to QdQ

= ∫ (500 - Q) dQ from 0 to 150

= [(500 × Q) - (Q²/2)] from 0 to 150

= $31,875.

Finally, the firm profit can be obtained by multiplying the profit-maximizing quantity by the profit-maximizing price and subtracting the total cost.

Thus, we have:

Profit = TR - TC = Q × P - TC = (150 × $350) - (300 + 200 × 150 + 3 × 150²) = $37,500.

Hence, the producer surplus, consumer surplus, and firm profit are $33,750, $31,875, and $37,500, respectively.

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Answer:

Geometric

Ratio

10:1

Step-by-step explanation:

The sequence is geometric because the common connection between the numbers is divided by 10.

It is ratio, because the sequence is geometric

The ratio is 10:1, because the previous number is 10 times as large as the following number

Hope this helps

a. the general solution of differential equation is y = (C1 + C2x)e^(6x), where C1 and C2 are constants.

b. the specific solution is y = y_c + y_p = C1e^(4ix) + C2e^(-4ix) + (1/2)cos(x).

c. The order of the equation is 3 because the highest derivative involved is the third derivative.

d. the general solution is y = C1e^(-x)cos(3x) + C2e^(-x)sin(3x), where C1 and C2 are constants.

a) To solve the differential equation dx^2/d^2y - 12dx/dy + 36y = 0, we can use the operator D, where D = d/dx. Rewriting the equation in terms of the operator:

(D^2 - 12D + 36)y = 0.

Factoring out the common factor, we get:

(D - 6)^2 y = 0.

The auxiliary equation is (D - 6)^2 = 0, which has a repeated root of 6.

Therefore, the general solution is y = (C1 + C2x)e^(6x), where C1 and C2 are constants.

b) To find the specific solution to the nonhomogeneous differential equation 2dx^2/d^2y + 32y = 2cos(x), we can use the method of undetermined coefficients.

First, we find the complementary solution by solving the associated homogeneous equation 2dx^2/d^2y + 32y = 0. Using the auxiliary equation method, we assume a solution of the form y = e^(mx), where m is a constant.

The auxiliary equation is 2m^2 + 32 = 0, which yields m^2 = -16. The roots are imaginary, m1 = 4i and m2 = -4i.

Therefore, the complementary solution is y_c = C1e^(4ix) + C2e^(-4ix), where C1 and C2 are constants.

For the particular solution, we assume a solution of the form y_p = A cos(x) + B sin(x), where A and B are constants to be determined.

Taking the second derivative of y_p and substituting it into the differential equation, we find A = 1/2 and B = 0.

Therefore, the specific solution is y = y_c + y_p = C1e^(4ix) + C2e^(-4ix) + (1/2)cos(x).

c) The equation dx^3/d^3Z = 3Z(x) is a third-order linear homogeneous differential equation.

It is a linear differential equation because it is linear in terms of the unknown function Z(x) and its derivatives.

It is homogeneous because all terms in the equation involve the function Z(x) or its derivatives, with no non-zero constant term.

The order of the equation is 3 because the highest derivative involved is the third derivative.

d) To find the general solution to the homogeneous equation 2y'' + 4y' + 10y = 0, we can use the auxiliary equation method.

Assuming a solution of the form y = e^(mx), where m is a constant, we can substitute it into the equation:

2(m^2e^(mx) + 4me^(mx) + 10e^(mx)) = 0.

Dividing by e^(mx), we get the auxiliary equation: 2m^2 + 4m + 10 = 0.

Solving the quadratic equation, we find the roots to be m = (-2 ± √(-36)) / 4 = -1 ± i√9 = -1 ± 3i.

Therefore, the general solution is y = C1e^(-x)cos(3x) + C2e^(-x)sin(3x), where C1 and C2 are constants.

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Answer:

Step-by-step explanation:

Answer: c) 15

Step-by-step explanation:

3, 8, 13, 18, ... - the arithematic progression      an=73      n=?

Difference of an arithmetic progression:  d=a₂-a₁.

a₁=3    a₂=8

Hence,

d=8-3

d=5

                Nth element of an arithmetic progression

                                  \(\boxed {a_n=a_1+(n-1)*d}\)

\(73=3+(n-1)*5\\73=3+5n-5\\73=5n-2\\73+2-2=5n-2\\75=5n\\\)

Divide both sides of the equation by 5:

\(15=n\)

Answer:

259.5

Step-by-step explanation:

8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5

The equations of the lines are y = 3x - 5 and y = (1/2)x - 7

An equation is an expression that shows how numbers and variables are related to each other.

A linear function is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Two lines are parallel if they have the same slope

1) y = 3x + 6; (4, 7)

The parallel line would have a slope of 3 and pass through (4, 7), hence:

y - 7 = 3(x - 4)

y = 3x - 5

2) y = (1/2)x + 5; (4, -5)

The parallel line would have a slope of 1/2 and pass through (4, -5), hence:

y - (-5) = (1/2)(x - 4)

y = (1/2)x - 7

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The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer:

6 x 25 = 150-40=110

Step-by-step explanation:

It's right I promise you

Answer:

look for patterns also, Ann purchased 12 apples

Step-by-step explanation:

x apples

1/3 of x, (x - x/3) = (3x - x) /3 = 2x/3

Number of people who shared (2x/3) = 4 with each getting 2Total number shared = 4 * 2 = 8Fraction shared = total shared2x/3 = 8Multiply both sides by 3(2x/3) * 3 = 8 * 32x = 24x = 12

Therefore, 65% of all nurses have a starting salary, z = invNorm(0.35) ≈ -0.3853 and z = (41861.5 - 67694) / 10333 ≈ -2.49.

b) We need to find P(X ≥ 78371.8). To do this, we can standardize the value using the formula z = (x - μ) / σ, where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. Then we can look up the probability in a standard normal distribution table or use a calculator.

\(z = (78371.8 - 67694) / 10333 \approx 1.04\)

Using a standard normal distribution table or calculator, we find that P(Z ≥ 1.04) ≈ 0.1492. Therefore, the probability that a randomly selected nurse has a starting salary of 78371.8 dollars or more is about 0.1492.

c) We need to find P(X ≤ 91407.1). Again, we can standardize the value and look up the probability in a standard normal distribution table or use a calculator.

\(z = (91407.1 - 67694) / 10333 \approx 2.30\)

Using a standard normal distribution table or calculator, we find that P(Z ≤ 2.30) ≈ 0.9893. Therefore, the probability that a randomly selected nurse has a starting salary of 91407.1 dollars or less is about 0.9893.

d) We need to find P(78371.8 ≤ X ≤ 91407.1). We can standardize the values and use a standard normal distribution table or calculator to find the probability.

z1 = (78371.8 - 67694) / 10333 ≈ 1.04

z2 = (91407.1 - 67694) / 10333 ≈ 2.30

Using a standard normal distribution table or calculator, we find that P(1.04 ≤ Z ≤ 2.30) ≈ 0.4657. Therefore, the probability that a randomly selected nurse has a starting salary between 78371.8 and 91407.1 dollars is about 0.4657.

e) We need to find P(X ≤ 41861.5). Again, we can standardize the value and use a standard normal distribution table or calculator.

z = (41861.5 - 67694) / 10333 ≈ -2.49

Using a standard normal distribution table or calculator, we find that P(Z ≤ -2.49) ≈ 0.0062. Therefore, the probability that a randomly selected nurse has a starting salary that is at most 41861.5 dollars is about 0.0062.

f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse. This is because the probability of getting a starting salary at or below this value is very small, as we calculated in part (e).

g) We want to find the value x such that 65% of all nurses have a starting salary greater than x. This means we need to find the 35th percentile of the distribution, which we can do using a standard normal distribution table or calculator.

z = invNorm(0.35) ≈ -0.3853

Using the formula z = (x - μ) / σ, we can solve for x:

-0.3853 = (x - 67694) / 10333

x - 67694 = -0.3853 * 10333

x ≈ 63757.72

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The 3rd term of the sequence is 48

From the question, we have the following parameters that can be used in our computation:

an = 6x3 n-1

Rewrite properly

So, we have

a(n) = 6 * (3n - 1)

For the third term, we have n = 3

Substitute the known values in the above equation, so, we have the following representation

a(3) = 6 * (3 * 3 - 1)

Evaluate

a(3) = 48

Hence, the third term is 48

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Answer:

X = 28

Step-by-step explanation:

The angle is 90 degrees in total and one portion of the angle is 62 degrees

You subtract the 62 degrees from the 90-degree angle to figure out the other unknown portion of the angle

90 - 62 = 28