8. A yard is closest in distance to a
a. kilometer.
b. centimeter.
C. meter.
d. millimeter.

The answer for given expressions is (f -g)(x) = -x² + 4x + 6.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

To find (f-g)(x), we need to subtract g(x) from f(x) and simplify the expression.

f(x) = 4x + 1

g(x) = x² - 5

(f - g)(x) = f(x) - g(x)

= (4x + 1) - (x² - 5)

= -x² + 4x + 6

Therefore, the answer for given expressions is (f -g)(x) = -x² + 4x + 6.

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y > 5  , x = y - 3 > 2Let's call the first number "x" and the second number "y". From the problem statement, we know that: x = y - 3  (because "one number is three less than a second number") 5x > 2y  (because "five times the first is more than times the second") We can use the first equation to substitute "y - 3" in for "x" in the second equation:

5(y - 3) > 2y

Distribute the 5:

5y - 15 > 2y

Subtract 2y from both sides:

3y - 15 > 0

Add 15 to both sides:

3y > 15

Divide both sides by 3:

y > 5

So we know that the second number is greater than 5. Let's try to find the first number now. We can use the equation we have for "x" and substitute it into the original equation that relates the two numbers:

5x > 2y

5(y - 3) > 2y

5y - 15 > 2y

Subtract 2y from both sides:

3y - 15 > 0

Add 15 to both sides:

3y > 15

Divide both sides by 3:

y > 5

So we have determined that y is greater than 5. Since x = y - 3, and both x and y are greater than 5, we know that x is greater than 2.

Therefore, we can conclude that the numbers are:

y > 5

x = y - 3 > 2

In summary, one number is three less than a second number, and five times the first is more than times the second. By setting up equations using x and y to represent the two unknown numbers, we can find that the numbers are: y > 5 and x = y - 3 > 2.

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Answer:

D

Step-by-step explanation:

when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.

f(x) = (x - 3)(x + 6)(x - 1)

we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :

-3 × +6 × -1 = +18

and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).

Answer:

bounce 1

Step-by-step explanation:

We need to do a rule of three, so we have that

So, the answer is he can travel in 2 hours 259.8 miles.

No, lecture notes collected during a bachelor degree study are not a type of date. Lecture notes are a collection of the notes taken by a student during the lectures in the course of their bachelor degree study.

They are not the same as dates, which are the specified days on which something happens or is planned to happen. Lecture notes are usually written in the form of summaries of a lecture, which are usually made up of the important points that the student has noted down during the lecture.

They may also include diagrams, equations, and other visual aids that the student has used to illustrate the material covered. Lecture notes are not the same as dates, as they are not related to any specified days. They are simply summaries of the lecture topics discussed by the professor in the course of the student’s bachelor degree study.

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Answer:

1.

31, 37, 43, 49, 55

2.

for nth number the value is 31+6(n-1)

3.

24th number, 169-31=138 and 138/6=23

Answer:

y = 3/2x

Step-by-step explanation:

it seems what they are asking for here is our slope.

To find this, we must figure out the change in  y over the change in x.

This can be viewed as:

Δy/Δx = slope

In this case, we can see that the line crosses at (4,6), and at (0,0)

Since our y changes by 6, and our x changes by 4, our slope is:

6/4 = slope

Or:

3/2 = slope

So your answer is 3/2x.

Hope this helps!

Answer:

x=3

Step-by-step explanation:

To solve for x, get x alone on one side of the equation.

First, add 3 to both sides.

3 = 1/3x^2

Multiply each side by 3

x^2 = 9

Take the square root of both sides

x = + or - 3

You want the positive solution, so x = 3

Answer:

△stu could be similar to △pqr IF They have 2 angles that are the same (congruent) also known as the AA theorem. Another way would be if the triangle have a 2 side that are congruent and an angle that is congruent that is between both sides (the rule is known as the SAS theorem)! The last rule would be if all the side are congruent OR if they equal the same thing. For example if you got a triangle with 3,4,5 as sides and another one that has 6,8,10 as sides. 3/6 = 4/8 = 5/10 so that would be the SSS rule

Hope you found that helpful!!!

Step-by-step explanation:

ΔSTU ~ ΔPQR if and only if \(\frac{ST}{PQ} = \frac{TU}{QR} = \frac{SU}{PR}\) and ∠S ≅∠P , ∠T≅∠Q and ∠U≅∠R.

" Two triangles are said to be similar if the ratio of the corresponding sides of one triangle to the other triangle are in proportion and corresponding angles are congruent."

According to the question,

ΔSTU is similar to  ΔPQR,

As per the definition of similar triangles we have,

Corresponding sides are in proportion.

ST ↔PQ

TU↔QR

SU↔PR

Therefore,

\(\frac{ST}{PQ} = \frac{TU}{QR} = \frac{SU}{PR}\)  are in proportion.

∠S↔∠P

∠T↔∠Q

∠U↔∠R

∠S ≅∠P ,

∠T≅∠Q

∠U≅∠R.

Hence, ΔSTU ~ ΔPQR if and only if \(\frac{ST}{PQ} = \frac{TU}{QR} = \frac{SU}{PR}\) and ∠S ≅∠P , ∠T≅∠Q and ∠U≅∠R.

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Answer:

A.30

Step-by-step explanation:

^ABC = 180⁰-60⁰=120⁰

=> 4x⁰=120⁰

=> x = 30⁰

The equivalent expression is: \(-x^5 y^3 + 6x^3 y^5\).

Let's simplify the given expression step by step using the given terms:
Expression:

\(3x^3 y^5 + 3x^5 y^3 - (4x^5 y^3 − 3x^3 y^5)\)
Distribute the negative sign outside the parentheses to the terms inside:
\(3x^3 y^5 + 3x^5 y^3 - 4x^5 y^3 + 3x^3 y^5\)
Combine like terms, which are terms that have the same variables raised to the same power:
\((3x^3 y^5 + 3x^3 y^5) + (3x^5 y^3 - 4x^5 y^3)\)
Add or subtract the coefficients of the like terms:
\(6x^3 y^5 - x^5 y^3\)
So, the simplified expression is:
\(6x^3 y^5 - x^5 y^3\)

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Answer:

y=32/3 or 10 2/3

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 2a^2-13b^2+12abc}\)

Step-by-step explanation:

\(=6a^2-4b^2+4abc-9b^2-4a^2+8abc\\\\Combine \ like \ terms\\\\=6a^2-4a^2-4b^2-9b^2+8abc+4abc\\\\=2a^2-13b^2+12abc\\\\\rule[225]{225}{2}\)

Answer:

Hello! The answer is: \(2a^2 - 13b^2 + 12abc\)

Step-by-step explanation:

\(6a^2 - 4b^2 + 4abc - 9b^2 - 4a^2 + 8abc\)

Rearrange to combine like terms:

\(6a^2 - 4a^2 - 4b^2 - 9b^2 + 4abc + 8abc\)

Combine like terms:

\(2a^2 - 13b^2 + 12abc\)

Therefore, there are 53,248 different super subs that can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from at Sandwich Station.

The super sub at Sandwich Station consists of 4 different toppings and 3 different condiments. The question is asking how many different super subs can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from.

To solve this problem, we can use the multiplication principle of counting. The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

Let's use the multiplication principle to solve this problem. There are four different toppings, and we can choose any of the eight toppings for each of the four spots.

Using the multiplication principle, there are

8 x 8 x 8 x 8 = 4096

ways to choose the toppings. Similarly, there are

6 x 6 x 6 = 216

ways to choose the condiments. Lastly, there are 6 different types of homemade bread to choose from. Using the multiplication principle again, there are

4096 x 216 x 6 = 53,248,

which means there are 53,248 ways to make the super subs.

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The ATI Capstone Comprehensive Assessment evaluation normally comprises of multiple-choice questions, with 90 to 130 possible answers. Certain versions may also include extra alternative questions kinds, such as fill-in-the-blank or select-all-that-apply

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The estimated current total cost for the installed and insulated tank is $12,065.73.

The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:

surface_area = 2 * pi * r * h + 2 * pi * r^2

where:

r is the radius of the cylinder

h is the height of the cylinder

In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:

surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586

The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:

surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293

The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:

cost = 6.806032934459293 * (40 + 95) = $1,165.73

The original cost of the tank was $10,900, so the total cost of the insulated tank is:

cost = 10900 + 1165.73 = $12,065.73

Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.

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Answer:

$16.08

Step-by-step explanation:

13.75+2.33=16.08

a. The probability that 1 or more nonconforming units are found is 0.2311.

b. The probability that exactly 3 units are nonconforming is 0.000058.

a. To solve the problem, you can use the complement rule. The complement rule states that the probability of an event occurring is 1 minus the probability of the event not occurring. So, in this case, the probability that no nonconforming units are found in a sample of 25 units is:

P(no nonconforming) = (0.99)²⁵ = 0.787.

Therefore, the probability that 1 or more nonconforming units are found is:

P(1 or more nonconforming) = 1 - P(no nonconforming) = 1 - 0.787 = 0.213.

Rounded to four decimal places, this is 0.2311.

b. To solve the problem, you can use the binomial probability formula:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k).

Here, n = 25 is the sample size, k = 3 is the number of nonconforming units, and p = 0.01 is the probability of a unit being nonconforming.

Using the formula, we get:

P(X=3) = (25 choose 3) * (0.01)³ * (0.99)²² = 2300 * 0.000001 * 0.5459 = 0.000058.

Rounded to six decimal places, this is 0.000058.

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Answer:

Step-by-step explanation:

sdfasdfffffffffff sdf sdf sdf sdf sdf sdf sdf

Answer:

Step-by-step explanation:

Anyas rate per hour = 40 ÷ 5 = 8

Lionel rate per hour = 14 ÷ 2 = 7

So the cheapest is Lionel

The required rate of the level of change of water in the swimming pool is 1 / 3 level per hour.

Given that,
The swimming pool is being filled with a hose.
The pool's water level rises 4 inches in hours.
To determine the rate per hour of the water level change.

Here,
Let 1 level of pool = 1 feet = 12 inches
The pool's water level rises 4 inches in hours. So, ti will rises 12 inches in 3 hours, which implies level change after 3 hours
Now the rate of level change of water = 1 / 3 level per hour

Thus, the required rate of the level of change of water in the swimming pool is 1 / 3 level per hour.

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The interest earned increases with higher principal amounts, higher interest rates, and longer time periods.

Principal (P) | Interest Rate (r) | Time Period (t) | Interest Earned (I)

$1,000 | 2% | 1 year | $20

$5,000 | 4% | 2 years | $400

$10,000 | 3.5% | 3 years | $1,050

$2,500 | 1.5% | 6 months | $18.75

$7,000 | 2.25% | 1.5 years | $236.25

To calculate the interest earned (I), we can use the simple interest formula: I = P * r * t.

For the first row, with a principal of $1,000, an interest rate of 2%, and a time period of 1 year, the interest earned is calculated as follows: I = $1,000 * 0.02 * 1 = $20.

For the second row, with a principal of $5,000, an interest rate of 4%, and a time period of 2 years, the interest earned is calculated as follows: I = $5,000 * 0.04 * 2 = $400.

For the third row, with a principal of $10,000, an interest rate of 3.5%, and a time period of 3 years, the interest earned is calculated as follows: I = $10,000 * 0.035 * 3 = $1,050.

For the fourth row, with a principal of $2,500, an interest rate of 1.5%, and a time period of 6 months (0.5 years), the interest earned is calculated as follows: I = $2,500 * 0.015 * 0.5 = $18.75.

For the fifth row, with a principal of $7,000, an interest rate of 2.25%, and a time period of 1.5 years, the interest earned is calculated as follows: I = $7,000 * 0.0225 * 1.5 = $236.25.

These calculations show the interest earned for different savings principals, interest rates, and time periods.

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Answer:

Simone is correct

Step-by-step explanation:

Given

Line 1:

\((x_1,y_1) = (-2, 7)\)

\((x_2,y_2) = (3, 0)\)

Line 2:

\((x_1,y_1) = (2, 1)\)

\((x_2,y_2) =(12, -13)\)

Required

Is Simone correct?

Slope (m) is calculated using:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

For Line 1

\(m = \frac{0 - 7}{3 - (-2)}\)

\(m = \frac{0 - 7}{3 +2}\)

\(m = \frac{-7}{5}\)

\(m = -\frac{7}{5}\)

For Line 2:

\(m = \frac{-13 - 1}{12 -2}\)

\(m = \frac{-14}{10}\)

Divide by 2/2

\(m = \frac{-14/2}{10/2}\)

\(m = \frac{-7}{5}\)

\(m = -\frac{7}{5}\)

By comparison, both lines have the same slope.

Hence, Simone is correct

Answer: have a good day

Step-by-step explanation:

because you deserve it

Answer:

add 6x to both sides (3x+3=-18)

subtract 3 from both sides (3x=-21)

divide by 3 on both sides (x=-7)

x=-7 is final answer

The complement of the given event, that all 100 engines are free of defects, is that at least one engine among the 100 shipped has a defect.

The complement of the given event, which is that all 100 engines shipped are free of defects, is the event that at least one engine among the 100 shipped has a defect. The complement represents the event that is the opposite of the given event. In this case, it is the event that at least one engine among the 100 has a defect, which could be described as the event of "failure" or "non-conformance". This is important in probability theory as it allows us to calculate the probability of the complement event and use it to determine the probability of the original event, among other applications.

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Complete question:

When 100 engines are shipped, all of them are free of defects. Select a written description the complement of the given event

A) At most one of the engines is defective.

B) All of the engines are defective.

C) At least one of the engines is defe

D) None of the engines are defective

Answer: 96

Step-by-step explanation:

This equation helps

X / 100 = is / of

32/100 = X / 300 (cross multiplication)

32 times 300, divided by 100

= 96

Answer:

96

Step-by-step explanation:

every percent is out of hundred so (32 * 300)/100 = 96

Step-by-step explanation:

it could travel 2/10 of a mile in one second because 1/10 ×2 =2/10

Answer:

1/5

Step-by-step explanation:

1/10*2=2/10=1/5