[5-TI] 4. The layout of Joe's yard is shown below. Joe must spread out topsoil to a depth
of 15 inches over the entire yard. One truckload of topsoil costs $67.89 and
contains 10 cubic yards of topsoil. How much will the topsoil cost to complete
this job?
75 feet
64 feet
36 feet
53 feet
19 feet
22 feet

Answer:

x = 101°

Step-by-step explanation:

180-147 = 32

180-47-33 = 101

also this is not college math what

The given sphere has a diameter d=7 cm.

The surface area of a sphere is given by the formula:

Where r is the radius, it is half the diameter. So r=3.5 cm.

By replacing this value, we can find the surface area:

The surface area of the sphere is 49pi square centimeters.

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Using the binomial distribution, it is found that there is a:

a) 0.9298 = 92.98% probability that at least 8 of them passed.

b) 0.0001 = 0.01% probability that fewer than 5 passed.

For each student, there are only two possible outcomes, either they passed, or they did not pass. The probability of a student passing is independent of any other student, hence, the binomial distribution is used to solve this question.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

In this problem:

Item a:

The probability is:

\(P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)\)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 8) = C_{10,8}.(0.9)^{8}.(0.1)^{2} = 0.1937\)

\(P(X = 9) = C_{10,9}.(0.9)^{9}.(0.1)^{1} = 0.3874\)

\(P(X = 10) = C_{10,10}.(0.9)^{10}.(0.1)^{0} = 0.3487\)

Then:

\(P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1937 + 0.3874 + 0.3487 = 0.9298\)

0.9298 = 92.98% probability that at least 8 of them passed.

Item b:

The probability is:

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)\)

Using the binomial formula, as in item a, to find each probability, then adding them, it is found that:

\(P(X < 5) = 0.0001\)

Hence:

0.0001 = 0.01% probability that fewer than 5 passed.

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The years where the spending will be more than $89 billion are: after 2009, i.e., 5 years after 2004, as found by basic algebra.

Numbers, variables, constants, expressions, equations, linear equations, and quadratic equations are all part of the basics of algebra. Additionally, the algebraic expressions contain the basic arithmetic operations of addition, subtraction, multiplication, and division.

Given: y = 14.4x + 17,

where: x = number of years after 2004

y = amount spent by businesses

To find: number of years where spending

$89 billion.

Finding:

We are given: y = 89, for which, we have to find the x, i.e., the number of years.

By basic algebra, substituting the value of y and solving for x:

89 = 14.4x + 17

72 = 14.4x

x = 5

Hence, The years where the spending will be more than $89 billion are: after 2009, i.e., 5 years after 2004, as found by basic algebra.

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To find the value of N, we need the future value of the retirement fund. If you provide the desired future value, I can calculate the exact value of N.

To find the value of N, we need to calculate the number of monthly deposits Sam made for his retirement fund over 20 years.

Sam deposited $1000 every month for 20 years, which is a total of 20 x 12 = 240 deposits. Each deposit has a compounded interest rate of 5% per year, compounded monthly.

The formula to calculate the future value of a series of monthly deposits is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value of the investment,

P is the monthly deposit amount,

r is the monthly interest rate, and

n is the number of deposits.

In this case, P = $1000, r = 5% / 12 = 0.05 / 12 = 0.00417 (monthly interest rate), and FV is the value of the retirement fund after 20 years.

By rearranging the formula, we can solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Plugging in the values, we get:

n = log((FV * 0.00417) / (1000 * 0.00417 + FV)) / log(1 + 0.00417)

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To solve this question we will use the following diagram:

The area of the big rectangle minus the area of the small rectangle is:

Since the frame has a uniform width, then:

Solving the above equation for x we get:

Then:

but 11 is not a solution with real meaning, therefore x=4.

Answer: The width is 4 in.

Answer:

Step-by-step explanation:

Given sides of rectangle:

Its perimeter is:

Answer:

\(\textsf{Perimeter}= 8x^2+12y\)

Step-by-step explanation:

A rectangle has 2 pairs of parallel, congruent sides.

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, the perimeter of a rectangle is twice the sum of its length and width.

Given:

Therefore:

\(\begin{aligned}\sf Perimeter & = 2(\sf width + length)\\& = 2 \left((x+4y)+(4x^2-x+2y)\right)\\& = 2(x+4y+4x^2-x+2y)\\& = 2x+8y+8x^2-2x+4y\\& = 8x^2+2x-2x+8y+4y\\& = 8x^2+12y\end{aligned}\)

\(18*(7*(-3))=18*7+18*(-3)\\18*-21=126 - 54\\-378 \neq 72\)

LHS \(\neq\) RHS

Answer :

To verify an equation, we need to see if the LHS = RHS.

Equation \(\downarrow\)

\(18\times(7\times(-3))=18\times7+18\times(-3)\)

Let's solve the left hand side (LHS) first.

\(18\times(7\times(-3))\\= 18 \times (-21)\\=\underline{ -378}\)

Now, let's solve the right hand side (RHS).

\(18\times7+18\times(-3)\\= 126 - 54\\=\underline {72}\)

But,

\(\boxed{-378 \neq 72}\)

We can see that the LHS doesn't match or isn't equal to the RHS.

Hence, we can say that LHS \(\neq\) RHS & the  equation is NOT true.

\(\rule{150pt}{2pt}\)

Answer:

2z-4

Step-by-step explanation:

By using distributive property, 2/3 * 3z =  2z and 2/3 * -6 = -4

This means the answer is 2z-4

\(Answer: \large\boxed{2z-4}\)

Step-by-step explanation:

To solve:

\(\frac{2}{3} (3z-6)\)

We must use the distributive property and distribute 2/3 to the 3z and -6

...

\(\frac{2}{3} (3z-6)\)

\(=\frac{2}{3} (3z) + \frac{2}{3} (-6)\)

\(=\frac{6z}{3} + -\frac{12}{3}\)

\(=2z-4\)

Answer:

(3x+4)(x−8)

Step-by-step explanation:

Answer:4

Step-by-step explanation:

2 slices each ten people times them together 20 slices .4 pizzas*5slices=20

To distinguish between linear growth and exponential growth, you need to look at the equation of the function and the shape of the graph.

Linear functions have a constant rate of change, meaning that the slope of the line is always the same. The equation for a linear function is y = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line.

Exponential functions, on the other hand, have a variable rate of change, meaning that the slope of the line changes as the x-value increases. The equation for an exponential function is y = ab^x, where a and b are constants. The graph of an exponential function is a curve that increases or decreases rapidly.

If the graph is a straight line it is linear, if it is curved and increases or decreases rapidly then it is exponential, otherwise, it would be considered as other.

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The probability that a randomly selected student will like pizza but not chicken nuggets is (28n - 8)/(28n + 7), where 28n is the students who like pizza and 8 is students who like both pizza and chicken nuggets.

To find the probability that a randomly selected student will like pizza but not chicken nuggets.

Let P = the number of students who like pizza but not chicken nuggets

Then, P = the number of students who like pizza - the number of students who like both pizza and chicken nuggets

P = 28n - 8

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students)

We can find the total number of students who like either pizza or chicken nuggets by adding the number of students who like pizza and the number of students who like chicken nuggets, and then subtracting the number of students who like both:

Total number of students = 28n + 15 - 8 = 28n + 7

So, the probability that a randomly selected student will like pizza but not chicken nuggets is:

P(Pizza but not nuggets) = P/(Total number of students) = (28n - 8)/(28n + 7)

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Answer:

8^2+12x

Step-by-step explanation:

4x(2x+3)

=4x times 2x+4x times 3

=4 times 2xx+4 times 3x

Answer:

8x^2 +12x

Step-by-step explanation:

Step 1) Multiply each term in the parentheses by 4x

4xx2x+4xx3

Step 2) Calcuate the product

8x^2 +12x

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

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The allusion in this statement is "Sasquatch," referencing a legendary creature known for its large size and used humorously to imply the person's abnormally large shoe size.

The allusion in the given statement is "Sasquatch." Sasquatch, also known as Bigfoot, is a legendary creature often depicted as a large, hairy, and elusive humanoid. In this context, the reference to Sasquatch is used metaphorically to humorously imply that the person's shoe size is abnormally large.

The mention of Sasquatch adds a playful and exaggerated tone to the conversation about shopping for shoes. It serves as a lighthearted way for the dad to comment on the frequency of buying new shoes, suggesting that the person's feet grow rapidly or that they have a high shoe consumption rate.

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Answer:18

Step-by-step explanation:15 + 6 u add the 15 and the 6 for it to be 18

After four years, Arianna will have a total of $60 in her savings account.

What is Compound Interest ?

Compound interest is interest that is calculated not only on the initial principal amount, but also on the accumulated interest of previous periods. In other words, the interest earned is added to the principal amount and then the interest for the next period is calculated based on the new total amount, which includes both the principal and the previously earned interest.

For example, if you deposit $1,000 in a savings account with a 5% annual interest rate, and the interest is compounded annually, at the end of the first year, you would earn $50 in interest, and your balance would be $1,050. If you leave the money in the account and don't make any further deposits or withdrawals, in the second year, you would earn interest not only on the original $1,000, but also on the $50 in interest earned in the first year, which would be a total of $52.50 in interest. Your new balance at the end of the second year would be $1,102.50.

The power of compound interest lies in the fact that the interest earned in each period is added to the principal, so the amount of interest earned in each subsequent period increases, resulting in a larger and larger balance over time.

Since the interest is not compounded, the interest earned each year will be the same, and it can be calculated as:

Interest earned each year = Principal * Annual interest rate

So for Arianna, the interest earned each year will be:

Interest earned each year = $50 * 0.05 = $2.50

After one year, Arianna will have $50 + $2.50 = $52.50

After two years, she will have $52.50 + $2.50 = $55

After three years, she will have $55 + $2.50 = $57.50

After four years, she will have $57.50 + $2.50 = $60

Therefore, after four years, Arianna will have a total of $60 in her savings account.

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Answer and Step-by-step explanation:

A) For the model to be a probability distribution, it has to follow two conditions:

1) The probability of each value of the discrete random variable is between, and included, 0 and 1:

2) The sum of all probabilities is 1;

In the table shown, the probabilities are from 0 to 0.3 - between 0 and 1;

Adding the probabilities: 0 + 0.3 + 0.1 + 0.3 + 0.3 = 1

Therefore, this model is a valid probability distribution model.

B) They are discrete because each value correspond to a finite number of possible values.

C) Expected value is calculated by

\(E(X) = \Sigma xP(x)\)

\(E(X) = 0.0 + 1*0.3 + 2*0.1 + 3*0.3 + 4*0.3\)

E(X) = 2.6

D) P(X=3) = P(3), which means probability of 3:

P(X=3) = 0.3

E) P(X<4): probabilities of values of X that are less than 4:

P(X<4) = P(0) + P(1) + P(2) + P(3)

P(X<4) = 0 + 0.3 + 0.1 + 0.3

P(X<4) = 0.7

F) P(X>0) = P(1) + P(2) + P(3) + P(4)

P(X>0) = 0.3 + 0.1 + 0.3 + 0.3

P(X>0) = 1

G) P(X=5) = P(5)

There is no probability of P(5) because the model doesn't "cover" that number.

H) P(X=0) = P(0)

P(X=0) = 0

I) The total area of any density curve is 1 because it represents all the possible values a variable can assume.

The answers are given as- A) Model is a valid probability distribution model.

B ) The described random variable is discrete.

C ) Mean E(X) = 2.6

D)  P(X=3) = 0.3

E )  P(X < 4) = 2.6

F )  P(X > 0) = 1

G ) There is no probability of P(5)

H ) P(X = 0) = 0

I ) The total area of any density curve is 1

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

A) For the model to be a probability distribution, it has to follow two conditions:

In the table shown, the probabilities are from 0 to 0.3 - between 0 and 1;

Adding the probabilities: 0 + 0.3 + 0.1 + 0.3 + 0.3 = 1

Therefore, this model is a valid probability distribution model.

B) They are discrete because each value correspond to a finite number of possible values.

C) Expected value is calculated by

E(x) = ∑ P(x)

E ( x) = 0 + ( 1 x 0.3 ) + ( 2 x 0.1 ) + 3 ( 0.3 ) + 4 ( 0.3 )

E(X) = 2.6

D) P(X=3) = P(3), which means a probability of 3:

P(X=3) = 0.3

E) P(X<4): probabilities of values of X that are less than 4:

P(X<4) = P(0) + P(1) + P(2) + P(3)

P(X<4) = 0 + 0.3 + 0.1 + 0.3

P(X<4) = 0.7

F) P(X>0) = P(1) + P(2) + P(3) + P(4)

P(X>0) = 0.3 + 0.1 + 0.3 + 0.3

P(X>0) = 1

G) P(X=5) = P(5)

There is no probability of P(5) because the model doesn't "cover" that number.

H) P(X=0) = P(0)

P(X=0) = 0

I) The total area of any density curve is 1 because it represents all the possible values a variable can assume.

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Answer:

Opal saves more

Step-by-step explanation:

The required solution of the differential equation is given as y² = -4logx + 9.

The method of determining the derivative of an implicit function by differentiating each term separately, expressing the derivative of the dependent variable as a symbol, and solving the resulting expression for the symbol.

here,
Given the differential equation,
Y’+2/x*y=0
Y' = -2/xy
y (dy/dx) = -2/x
ydy = -2/xdx
y²/2 = -2logx + C

From the initial condition y(1)=3
9/2 = -2log1 + c

c = 9/2

Now,
y²/2 = -2logx + 9/2
y² = -4logx + 9

Thus, the required solution of the differential equation is given as y² = -4logx + 9.

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Hence the acute angle made by the given line is =33.6 degrees.

A straight line is a line with an infinite length and no curves. A straight line can also be drawn between any two places, but its endpoints must stretch into the infinite. When two places A (x1, y1) and B (x2, y2) are connected by the shortest path possible, and the line ends are stretched to infinity, a straight line is a result.

The given equation \(y=\frac{2}{3}x+2\),

We know that the standard equation is a straight line y=mx+b, where m is the slope called tanA and b is the y-intercept,

in our given case

\(m=\frac{2}{3}\\\\tanA=\frac{2}{3}\\\\A=33.6 \ degree\)

Hence the acute angle made by the given line is =33.6 degrees.

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Your analysis is correct. Here's a summary:

If it is sunny, then it is 80° Fahrenheit. (Original statement)

Converse: If it is 80° Fahrenheit, then it is sunny. (Valid)

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Valid)

If it is not sunny, then it is not 80° Fahrenheit. (Original statement)

Converse: If it is not 80° Fahrenheit, then it is not sunny. (Invalid)

Counterexample: A day that is not 80° Fahrenheit and not sunny (e.g., 70° and cloudy).

If it is 80° Fahrenheit, then it is sunny. (Original statement)

Converse: If it is sunny, then it is 80° Fahrenheit. (Invalid)

Counterexample: A day that is 80° Fahrenheit and cloudy.

In cases 1 and 2, the original statements and their converses are valid because the relationship between "sunny" and "80° Fahrenheit" holds in both directions. However, in cases 3 and 4, the converses are invalid because there are counterexamples where the second part of the statement (either "not 80° Fahrenheit" or "cloudy") does not necessarily imply the first part ("not sunny" or "80° Fahrenheit").

Chad has $70 before buying the Shirt and shoes using the equation formation

How do we form equations?

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

In the given question:

We have,

Cost of a shirt = $19

Let the cost of pair of shoes be $x.

According to the question:

A pair of shoes for $28 more than the shirt.

Forming the equation, we get:

x = $(28+19)

x = $ 47

So, The cost of a pair of shoes is $ 47.

Now, It is given that chad had $13 left over.

So, The total money that she had before buying the shirt and a pair of shoes will be:

{ Sum of the Price of the shirt and a pair of shoes} + $13

that is,

$47 + $19 + $13 = $70.

Hence, Money chad before buying the shirt and shoes is $70.

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Answer:

Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

The system of equations are parallel lines and they do not intersect. Thus, the system has no solution.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

No matter how far we extend a parallel line, it will never meet another parallel line.

Given that,

y=x-2

y=x-1

For x = 1:

y = x - 2 = 1 -2 = -1

y = x - 1 = 1 - 1 = 0

For x = 2:

y = 2- 2 = 0

y = 2 -1 = 1

Plot the graph using the points.

The two lines have the same slope hence they are parallel lines.

Since, the two lines are parallel the system has no solutions.

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