Joanna saves $55 each month from her part-time job. She saves 1/5 of her earnings. Write and solve an equation determine Joanna’s earnings

Answer:

2,0?

Step-by-step explanation:

To do this, find your first derivative and then find where it is equal to zero. Because we are only concerned about the interval from -5 to 0, we only need to test points on that interval. (i really don't know hot to explain)

The formula for converting from km/h to mph is mph = km/h x 0.621371. To convert a speed of 35 km/h to mph, we must multiply 35 by 0.621371, which gives us a value of 21.765 mph.

The conversion from kilometers per hour (km/h) to miles per hour (mph) is a common conversion that is used when discussing speed limits or travel times. The formula for converting from km/h to mph is mph = km/h x 0.621371. To illustrate this, if you have a speed of 35 km/h, then you would multiply 35 by 0.621371 to get the speed in miles per hour, which is 21.765 mph.

To calculate a speed of 35 km/h to mph, we must first understand the relationship between the two measurements. The conversion factor between km/h and mph is 0.621371. This means that one kilometer per hour is equivalent to 0.621371 miles per hour.

Now, to convert 35 km/h to mph, we must multiply 35 by 0.621371. This gives us a value of 21.765 mph. We can then say that a speed of 35 km/h is equivalent to a speed of 21.765 mph.

To summarize, the formula for converting from km/h to mph is mph = km/h x 0.621371. To convert a speed of 35 km/h to mph, we must multiply 35 by 0.621371, which gives us a value of 21.765 mph. This means that a speed of 35 km/h is equivalent to a speed of 21.765 mph.

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A) Let the side length of the square base be x, and the height of the box be h. Then, the volume of the box is given by:

V = \(x^2\) * h = 8500

Solving for h, we get:

h = 8500 / \(x^2\)

The surface area of the box can be expressed as:

S = 2x^2 + 4xh

Substituting the value of h obtained above, we get:

S = \(2x^2\) + 4x(8500 / \(x^2\)) = 2\(x^2\)+ 34000 / x

Thus, the surface area of the box can be expressed as a function of x.

B) To graph the function, plot the surface area (S) on the y-axis and the side length of the square base (x) on the x-axis. Since x cannot be negative, the domain of the function is (0, infinity). As x gets very large or very small, the surface area approaches infinity, so we should only graph the function for values of x that make sense in the context of the problem.

C) The minimum amount of cardboard required to construct the box is equal to the surface area of the box. To find the minimum surface area, we need to find the minimum of the function S(x) obtained in part A.

D) To find the dimensions of the box that minimize the surface area, we need to find the value of x that minimizes the function S(x). We can do this by taking the derivative of S(x) with respect to x, setting it equal to zero, and solving for x. This gives us:

dS/dx = 4x - 34000/\(x^2\) = 0

Multiplying both sides by \(x^2\) and solving for x, we get:

x = (8500/2\()^(1/3)\) ≈ 18.3

Therefore, the dimensions of the box that minimize the surface area are a square base with side length of approximately 18.3 inches, and a height of:

h = 8500 / \(x^2\) ≈ 26.2 inches

E) UPS might be interested in designing a box that minimizes the surface area because it can reduce the amount of cardboard used in each box, resulting in cost savings and a reduced environmental impact. Additionally, minimizing the surface area of a box can make it more efficient to stack and transport, reducing shipping costs and making the overall process more sustainable.

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A) The Surface Area = \(X^2 + 34000/X\)

B) The y-axis and the side length X on the x-axis.

C) The minimum amount of cardboard required to construct the box is approximately 1649.39 square inches.

D) The dimensions of the box that minimize the surface area are X = 20.5 inches and Y = 16.87 inches.

E)  Smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

A) Express the surface area of the box as a function of X:

Let the side length of the square base be X and the height of the box be Y. Then, we know that the volume of the box is 8500 cubic inches, so:

\(X^{2Y} = 8500\)

To find the surface area of the box, we need to add up the area of each face. There are 5 faces in total (the bottom square and 4 identical rectangular sides), so:

Surface Area = \(X^2 + 4XY\)

We can substitute the value of Y from the equation for volume, giving:

Surface Area = \(X^2 + 4X(8500/X^2)\)

Surface Area = \(X^2 + 34000/X\)

B) Graph the function found in part a:

To graph this function, we can plot the surface area on the y-axis and the side length X on the x-axis. The graph will have a minimum value, which we can find using calculus or by using a graphing calculator.

C) What is the minimum amount of cardboard that can be used to construct the box:

The minimum amount of cardboard required to construct the box is the surface area of the box. To find this minimum value, we need to find the minimum point on the graph in part b. From the graph or by using calculus, we can see that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. Substituting this value into the equation for surface area, we get:

Surface Area = \(20.5^2 + 4(20.5)(8500/20.5^2)\)= 1649.39 square inches

D) What are the dimensions of the box that minimize the surface area:

From part c, we know that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. To find the height of the box, we can substitute this value of X into the equation for volume:

\(X^2Y = 8500\)

\((20.5)^2 Y = 8500\)

\(Y = 8500/(20.5)^2 = 16.87\) inches

E) Why might UPS be interested in designing a box that minimizes the surface area:

UPS and other parcel delivery services are always looking for ways to reduce their costs and increase efficiency. By designing a box that minimizes the surface area while still containing the same volume of goods, they can reduce the amount of cardboard used for each shipment. This would save them money on materials and shipping costs, while also reducing their environmental impact. Additionally, smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

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Looking at the sequence 2, 4, 6, 8, 10, ..., we can see that the first element is 2 and each subsequent element is 2 units more than the previous element.

Knowing that, we can write the equations:

Therefore the correct option is A.

Answer:

It should be 60 degrees

Step-by-step explanation:

Answer:

10 is the answer of q u estion

Answer:

C 60 inches

Step-by-step -

60 x 2 = 120, which is both lengths, and since he width is half the length, then 30 x 2 = 60. So 130 (length) + 60 (width) = 180. So 60 inches would be the maximum length for both sides.

Answer:

C

Step-by-step explanation:

I just took the unit test

Answer:

1.10 x 108.

Step-by-step explanation:

Answer:

Amy can purchase up to 14 lunches until her mother receives the notification. When she has the 15th lunch, the notification will be sent.

Step-by-step explanation:

The balance Amy has in her lunch account is a function of the number of lunches she has consumed.

The initial balance is $50 and it decreases by $3 for every lunch Amy has. Thus, the function that models the balance in her lunch account is:

\(B(x)=50-3x\)

Where x is the number of lunches.

Her mother receives a notification when the balance goes at $5 or lower, thus the condition that triggers the notification is:

\(B(x) \le 5\)

Or, equivalently:

\(50-3x\le 5\)

Subtracting 50:

\(-3x\le 5-50\)

\(-3x\le -45\)

Multiplying by -1 (and flipping the sign):

\(3x\ge 45\)

Solving:

\(x\ge45/3\)

\(x\ge 15\)

Amy can purchase up to 14 lunches until her mother receives the notification. When she has the 15th lunch, the notification will be sent.

The two mutually exclusive events where we have a spinner with 4 sections: 1, 2, 4, and 3, where sections 1 and 4 are shaded and the spinner is pointed at number 2 are: Selecting a shaded section (1 or 4)
and Selecting an unshaded section (2 or 3)

The term "mutually exclusive" refers to events that cannot occur at the same time.
To determine which events are mutually exclusive, we need to consider the possibilities:

1. Selecting a shaded section (1 or 4): This event is mutually exclusive with selecting an unshaded section (2 or 3). The two options cannot happen simultaneously.

2. Selecting an unshaded section (2 or 3): This event is mutually exclusive with selecting a shaded section (1 or 4). Again, these two options cannot occur at the same time.

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Answer:

1/5

Step-by-step explanation:

you go up one over 5

The shortest distance for her to swim to the other side of the lake would be = 116cm.

To cross over to the other side of the lake two similar triangle are being created.

The shortest distance that can be used to cross the lake is to determine the opposite sides of the new triangle.

Scale factor = Dimension of the new shape ÷ Dimension of the original shape

The adjacent of original triangle = 19cm

The adjacent of new shape = 76cm

The scale factor = 76/19 = 4

The opposite side of the new triangle = 4×29 = 116cm

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Each person (Tammy, John, Allison, and Henry) paid $11.25 for a movie ticket.

To determine the cost of each movie ticket, we will divide the total amount paid by the number of people who bought tickets.

Total amount paid: $45
Number of people: Tammy, John, Allison, and Henry (4 people)

Step 1: Divide the total amount paid by the number of people.
$45 ÷ 4 = $11.25

So, Allison and each of her friends paid $11.25 for a movie ticket.

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Answer:

true

Step-by-step explanation:

Answer:

false I'm pretty sure...

Answer:23.4$

Step-by-step explanation:

1.The equivalent algebraic expression becomes: y(x + 5) + 2(x + 5)

2.The common factor in the two terms is (x + 5). Both terms have (x + 5) as a factor.

3. The polynomial can be expressed as a product of two binomials: (x + 5)(y + 2)

Let's start by factoring out the common factors from each group:

From the first group (xy + 5y), we can factor out y, which gives us y(x + 5).

From the second group (2x + 10), we can factor out 2, which gives us 2(x + 5).

So, the equivalent algebraic expression becomes:

y(x + 5) + 2(x + 5)

The common factor in the two terms is (x + 5). Both terms have (x + 5) as a factor.

Now, using the distributive property, we can factor out (x + 5) from both terms:

y(x + 5) + 2(x + 5) = (x + 5)(y + 2)

The polynomial can be expressed as a product of two binomials: (x + 5)(y + 2).

In this factored form, we can see that we have two binomial expressions multiplied together. The first binomial (x + 5) represents the common factor, and the second binomial (y + 2) represents the remaining terms after factoring out the common factor.

Overall, the factoring process involved identifying the common factor, using the distributive property to factor it out, and expressing the polynomial as a product of two binomials. This factored form can be useful in further simplification, solving equations, or analyzing the polynomial's behavior

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Answer:

The answer is C (0.30) are NOT going to particulate

Step-by-step explanation:

We can find the answer by simply putting all of the results into order, which gives the following for the non-participants:

28: 6's

27: 7's

29: 8's

15: 9's

Now to find the answer, we must know the total amount of results, which I found to be 250. We also need to know the total amount of non-participants there are, which is 99. So if we take 99 and divide it by 250 (99/250); we get 0.396. Although this isn't the exact answer, it is the closest.

To further prove that this should be right, Yuri found 60% of students to participate, which leaves around 40% left to not participate. So this should be right.

Hope this helps! - SC

(Let me know if it's wrong so I can change my answer if needed).

According one-way ANOVA, the test is false.

In the given question,

When comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment, a​ one-way ANOVA is appropriate. It is also appropriate in this​ situation, however, to compare two means at a time using multiple independent two sample​ t-tests. We have to check whether this is true or​ false.

We firstly learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the means of two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given method it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations means within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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Answer:

AB/ PQ = BC/QR

Step-by-step explanation:

In similar triangles, ratio of corresponding sides are equal.

So, \(\frac{AB}{PQ}= \frac{BC}{QR}=\frac{AC}{PR}\)

Answer:

dang thats tough..

Step-by-step explanation:

idrk what an asvab is but it sounds horrible im

sorry that happened :(

The flow rate of 5 MGD is equivalent to 7.73615 cfs

To convert million gallons per day (MGD) to cubic feet per second (cfs), we need to use the conversion factor between the two units. The conversion factor is 1 MGD = 1.54723 cfs.

Therefore, to convert MGD to cfs, we can multiply the given value of MGD by the conversion factor. For example, if we have a flow rate of 5 MGD, we can convert it to cfs as follows:

5 MGD x 1.54723 cfs/MGD = 7.73615 cfs

So, the flow rate of 5 MGD is equivalent to 7.73615 cfs. Similarly, we can convert any given flow rate in MGD to cfs by using the same conversion factor.

It is important to note that these units are commonly used in the context of water supply and distribution systems, where flow rates are a crucial factor in the design and operation of such systems. Therefore, knowing how to convert between different flow rate units is essential for engineers and technicians working in this field.

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The possible definitions of f(x) and g(x), considering the composition of the functions, are given as follows:

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The functions for this problem are defined as follows:

As the composition of the functions is then given as follows:

\(h(x) = f(g(x)) = f(8x + 6) = \sqrt{8x + 6}\)

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The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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Answer:

Step-by-step explanation:

As we know all primes but 2 are odd numbers.

It means sum of any 3 primes not including 2 is odd.

Since we have sum of 202, one of our primes is 2.

Sum of the other two primes is 200.

In order to have maximum value of p*(200 - p) these two numbers must be closer to each other. So we are looking for two primes around 100.

We can test all primes less than 200:

The 3 primes with max product are:

The value is:

(a) To find the probability that no one enters the casino between 12:00 and 12:05, we can use the Poisson distribution, where λ = the expected number of arrivals during the given time interval. In this case, λ = (1/2) x 5 = 2.5 (since the rate is 1 person every 2 minutes, and the time interval is 5 minutes). Therefore, the probability of no one entering during this time is:

P(0 arrivals) = (e^(-2.5) x 2.5^0) / 0! ≈ 0.0821

(b) To find the probability that at least 4 people enter the casino during the 5-minute interval, we can again use the Poisson distribution. We want to find the probability of 4, 5, or more arrivals, so we can add up the probabilities of each of these events. Using λ = 2.5 again, we get:

P(4 arrivals or more) = P(X ≥ 4) = Σ(2.5^k x e^-2.5 / k!) from k=4 to infinity

Using a calculator or computer program, we can find that P(X ≥ 4) ≈ 0.0363.

(c) To find the probability that at least one person entered the casino in each of at least 3 of these 5 minutes, we can use the inclusion-exclusion principle. First, we find the probability that at least one person entered the casino during all 5 minutes:

P(5 arrivals) = (e^(-2.5) x 2.5^5) / 5! ≈ 0.0088

Next, we find the probability that at least one person entered during exactly

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Answer:

Answer: B

Step-by-step explanation: Function A starts at 0,2 and function B starts at 2,2

Step-by-step explanation:

It is required to find which option is correct with what is given in the question.

No, function A has initial value 0 and function B has initial value of 2. So, the functions do not have the same initial value.

In a Cartesian coordinate system each point on it is defined with respect to the two axes x and y.

The initial value of the given function A in the graph is

\(x=0\)

The initial value of the given function B in the table is

\(x=2\)

So, the correct option is

No, function A has initial value 0 and function B has initial value of 2. So, the functions do not have the same initial value.

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Answer:

66MPH

Step-by-step explanation:

First you would add up all three amounts of miles, so 177+188+163 to get 528. Then you would divide 528 by 8 to get the average MPH, which would be 66MPH.

Part A: The equation of least squares regression line is

ŷ = 0.4684X + 64.69888

Part B: The residual that we have here is - 1.382

Part C: Residual refers to the difference between the observed value and the predicted value

Sum of X = 102.5

Sum of Y = 695

Mean X = 10.25

Mean Y = 69.5

Sum of squares (SSX) = 33.625

Sum of products (SP) = 15.75

Regression Equation = ŷ = bX + a

b = SP/SSX = 15.75/33.63 = 0.4684

a = MY - bMX = 69.5 - (0.47*10.25) = 64.69888

ŷ = 0.4684X + 64.69888

Residual = observed - predicted

The observed = 68

The predicted = 0.4684 x 10 + 64.69888

= 4.684 + 64.69888

= 69.382

residual = 68 - 69.382

= -1.38

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