car travels 22 miles for every gallon of gasoline used. The table below represents this relationship.

Gas Mileage
Distance Traveled
(miles)
Gasoline Used
(gallons)
22
1
44
2
x
3
88
4

The function f'(x) is decreasing on the interval (-√5, 0) and (0, √5)

A function is a mathematical equation that shows the relationship between two variables.

Givenj the function f'(x) = x⁵ - 5x³, to find the points at which the function is increasing, we find its critical points by equating it to zero.

So, f'(x) = x⁵ - 5x³

x⁵ - 5x³ = 0

x³(x² - 5) = 0

⇒ x³ = 0 and x² - 5 = 0

⇒ x = 0 and x² = 5

⇒ x = 0 and x = ±√5

To determine the points at which f'(x) is decreasing, we differentiate f'(x) with respect to x and substitute the values of x into it.

So, we have

f'(x) = x⁵ - 5x³

df'(x)/dx = d(x⁵ - 5x³)/dx

f"(x) = 5x⁴ - 15x²

So, f'(x) is decreasing when f"(x) > 0.

So, substituting x = 0 into the equation, we have that

f"(x) = 5x⁴ - 15x²

f"(x) = 0⁴ - 15(0)²

= 0 - 0

= 0

Since f"(x) = 0. This is a point of inflection

Substituting x = √5 into the equation, we have that

f"(x) = 5x⁴ - 15x²

f"(x) = 5(√5)⁴ - 15(√5)²

= 5 (25) - 15 (5)

= 125 - 75

= 50

Since f"(x) = 50 > 0, f'(x) is decreasing

Substituting x = -√5 into the equation, we have that

f"(x) = 5x⁴ - 15x²

f"(x) = 5(-√5)⁴ - 15(-√5)²

= 5 (25) - 15 (5)

= 125 - 75

= 50

Since f"(x) = 50 > 0, f'(x) is decreasing

So, f'(x) is decreasing on the interval (-√5, 0) and (0, √5)

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The graph that represents a function is:

The graph shows a parabola open to the top and touching the base at

(0, 0).

The graph shows a parabola open to the left and touching the base at

(0, 0).

Options B and D is the correct answer.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A function can have many-to-one but not one-to-many.

A

The graph shows a circle intercepting the x-axis at 5 and -5 and the y-axis also at 5 and -5.

This means,

If the center of the circle is (h, k).

The coordinates of the circle are:

(5, k), (-5, k), (h, 5), and (h, -5)

(h, 5) and (h, -5) indicate one-to-many.

This is not a function.

B.

The graph shows a parabola open to the top and touching the base at

(0, 0).

The equation of the parabola is y = x².

For x = 1, y = 1

For x= -1, y = 1

This indicates many-to-one only.

This is a function.

C.

The graph shows an s-shaped curved line starting from (10, 2) and taking the curve at points (0, 1), (-1, 0), (0, -1), and (0, -3) and ending at (-10, -4).

The points (0, 1), (0, -1), and (0, -3) indicate one-to-many.

This is not a function.

D

The graph shows a parabola open to the left and touching the base at

(0, 0).

The equation of the parabola is y² = 4px.

This equation is a function.

Thus,

The graph that represents a function is a parabola open to the top and a parabola open to the left.

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Answer: There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9). ✅

PLEASEEEE GIVE BRANLIEST

Step-by-step explanation:

There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9). One statement that could be true for g is:

g(x) = 2x + 8

This function has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45. It also satisfies the values of g(0) = -2 and g(-9) = 6.

It's important to note that this is only one possible function that satisfies the given information and there are many other functions that could also work such as:

g(x) = 3x -2

g(x) = -2x +10

g(x) = x+5

So the statement that could be true for g is that "There are multiple ways that a function, g, could satisfy the given domain, range, and values of g(0) and g(-9)."

*Keep in mind you didn't specify a specifc statement to verify false or true*

The meaning of the situation involving the camp director and the sack lunches, is D. The number of lunches left over after packing the boxes.

The remainder in this instance, shows the number of lunches that the camp director will not be able to fit in boxes and so will be left over after the boxes have been packed.

There are 85 sack lunches and yet only 3 lunches can go into a single box. The number of boxes would be:

= 85 / 10

= 10 boxes remainder 5 lunches

10 boxes will be filled with lunch sacks and 5 lunches will be leftover.

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The full question is:

The camp director is putting 85 sack lunches in boxes for a picnic. She can fit 8 lunches in each box. She does the division problem shown to find out how many boxes she will need. 85 divided 8 = 10 remainder 5

What is the meaning of the remainder in this situation?

A. The number of extra boxes needed.

B. The number of extra lunches needed.

C. The number of boxes left over after packing the lunches.

D. The number of lunches left over after packing the boxes.

To the nearest whole percent, the percentage Yvette paid over the price of the sandwiches is 27%.

The percentage represents a proportion of a whole value.

The percentage is determined as the quotient of the difference (increase or decrease) and the initial value, multiplied by 100.

The purchase price of restaurant sandwiches = $22

Sales tax = 8.5%

= $1.87 ($22 x 8.5%)

Additional tip for delivery = 18%

= $3.96 ($22 x 18%)

Total bill = $27.83 ($22 + $1.87 + $3.96)

Difference between the total bill and the purchase price = $5.83 ($27.83 - $22)

Percent difference = 26.5% ($5.83/$22 x 100)

= 27%

Thus, Yvette paid 27% above the price of the sandwiches in form of sales tax and tips.

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Answer: Paula spent $2 for each song.

Step-by-step explanation: For this question, we have to find the unit rate that Paula paid per song. As we're already given the amount of songs downloaded and the total cost, all that we really have to do is divide!

Because we want to know the amount of money spent on one song, we divide the amount of money spent by the amount of songs purchased. This gives us 32/16 = 2.

Paula spent $2 (don't forget the units!) for each song. This is out unit rate. Hope this helps!

The value of x is 10 the answer being ten is because the smaller triangle is half the size of the bigger one.

What is a formula for a triangle?

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On solving the provided question we can say that the total interest he pay in 5 year is = $17500.

The amount that the lender charges the borrower over and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money. The basic interest formula is as follows: Interest is equal to P, R, and T. P is the principal sum (the beginning balance). Interest rate, R (usually per year, expressed as a decimal). T = Number of intervals of time (generally one-year time periods).

Money required to borrow new car is $35,000.

and Rick pay 10% interest per year

so, interest he pay in one year = $35000 x 10% = $3500

total interest he pay in 5 year is = $17500

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The sum of the exterior angles for a parallelogram is 360°.

Exterior angles are angles that are formed outside two lines when they intersect. They are located outside the two lines, on the outside of the shape. They can be found by adding the two interior angles together, whose measurements are always equal to 180 degrees. Exterior angles are also supplementary angles, meaning that the sum of their measurements is always equal to 360 degrees.

This is because the four angles on the outside of the parallelogram are all right angles, and the sum of four right angles is 360°.

Similarly, the sum of the exterior angles for a hexagon is also 360°.

This is because the six angles on the outside of the hexagon are all 120° angles, and the sum of six 120° angles is 360°.

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For a combined energy of 15 students in a week, a truck will drive for 914.24 meters subjective to the number of students.

To find the meters a truck will drive when the energy of a class is combined in one week;

1 day per person = 32 kilometers

One week = 7 days

Assuming a math class with 15 students for 7 days = (15 students x 7 days)

= 1/(15 x 7) x 32

= 1/35 x 32 = 0.02857 x 32 = 0.91424 kilometers

Changing 0.91424 kilometers to meter = 0.91424 x 1000 = 914.24 meters. It will take 15 students 914.24 meters truck drive in one week.

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Answer:

Step-by-step explanation:

To find the percentage of men who are over 70.5 inches tall, we need to use the standard normal distribution table, which gives the proportion of observations that fall within a given range of standard deviation from the mean.

We first need to standardize the height of 70.5 inches by subtracting the mean (68 inches) and dividing by the standard deviation (2.5 inches) to get (70.5 - 68) / 2.5 = 0.8

This tells us that 70.5 inches is 0.8 standard deviations above the mean.

We can then look up the proportion of observations that fall within this range in the standard normal distribution table, which is approximately 0.1587 or 15.87%. So, the answer is (1-0.1587) = 84.13 or 84.13%.

So the answer is 84.13%

Answer:

Step-by-step explanation:

The inverse of the statement "If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent" is "If two triangles are not congruent, then the two sides and the included angle of a triangle are not congruent to two sides and the included angle of another triangle."

The graph of the function f(x, y) = [tex]x^2[/tex] is a three-dimensional parabolic surface that opens upwards.

It is symmetric around the x-axis. This means that the shape of the surface is the same on both the positive and negative x-values. It is also a concave-up function, which means the graph is curved upwards.

Its vertex is located at the origin (0,0) and the equation of the parabola is y =[tex]x^2[/tex]. This means that the x-values of the graph can be any real number, while the y-values will always be non-negative as the square of any real number is always non-negative.

As x-values increase or decrease, the y-values will also increase, resulting in a smooth and continuous surface. Overall, the graph represents the upward parabolic shape of x squared.

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Answer:

the having of the record is that

Probability of defect per blade = 1/500 = 0.002

Poisson distribution :

Pₓ (k) = (x ^k)/k × e⁻ˣ

Where k = The number of defective blades in a packet.

For a packet of 10 blades the mean number of defect x = 0.002 × 10 = 0.02

1.) When k = 0

Pₓ(0) = (0.02⁰ / 0!) × e - 0.02 = 0.980199

The approximate number of packets containing blades with no defective is :

10000 × 0.980199 = 9802

2.) When k = 1

Pₓ(1) = (0.02 / 1!) × e-0.02 = 0.019604

Approximate number containing one defective is :

10000 × 0.019604 = 196

3.) When k = 2

Pₓ(2) = (0.02² / 2!) × e - 0.02 = 0.000196

Approximate number containing 2 defective :

0.000196 × 10000 = 1.9 = 2

4.) When k = 3

Pₓ(3) = (0.02³ / 3!) × e-0.02 = 0.000013

Approximate number containing 3 defective is :

0.000013 × 10000 = 0.13 = 0

Answer:

no defective blades in a consignment of 1,00,000 packets is 99837.

Step-by-step explanation:

we first need to find the mean number of packets containing no defective blades. This mean is equal to the total number of packets (1,00,000) multiplied by the probability of a packet containing no defective blades.

The probability of a blade being defective is given as 0.002 (or 2/1000) or 2/100 or 1/50 or 2%.

Since a packet contains 10 blades. So the probability of a packet containing no defective blades is (1 - 0.002)^10 = 0.999936 or (1-0.02)^10 = 0.99837

So the mean number of packets containing no defective blades is (1,00,000 * 0.99837) = 99837

Answer:young boy

Step-by-step explanation:

Answer: 7-4

Step-by-step explanation:

So basically multiply (-1) to -7 and 4

-7(-1)=7 4(-1)=-4

then, 7-4

Answer:

b=2a+

Step-by-step explanation:

a=1/2(b-c)

a=1/2b-1/2c

a + 1/2c=1/2b

2/1(a+1/2c)=(1/2b)2/

2a+c=

b=2a+

Answer:

A

Step-by-step explanation:

6x² + 7x - 5

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 6 × - 5 = - 30 and sum = + 7

the factors are - 3 and + 10

use these factors to split the x- term

6x² - 3x + 10x - 5 ( factor the first/second and third/fourth terms )

= 3x(2x - 1) + 5(2x - 1) ← factor out (2x - 1) from each term

= (2x - 1)(3x + 5) ← in factored form

with 3x + 5 being a factor

Estimated total is equal to (500 + 300) = 800.

In mathematics, place value refers to the relative importance of each digit in a number.

These locations begin at the unit's location (ones place).

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located.

The value of a digit depends on its position in the number, which might result in a number having two comparable digits with distinct values.

Using place value diagrams, we can check that the digits are positioned correctly.

The right place for each digit in a number is shown on a place value chart. In order to precisely determine the positional values or worth of the various digits in a number, we must first write the.

According to our question -

to the next hundreds of 458 = 500, the estimated value

to the nearest hundreds of 324, the estimated value is 300.

Estimated total is equal to (500 + 300) = 800.

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Answer:

The answer is option c.

Please could you give me brainliest

If 30+6t=11t then the value of  t is: 6

This is a simple algebraic equation. To solve for t, we can start by isolating t on one side of the equation.

The equation is 30 + 6t = 11t

First we can subtract 11t from both sides:

30 + 6t - 11t = 11t - 11t

This gives:

30 - 5t = 0

Next, we can add 5t to both sides:

30 - 5t + 5t = 0 + 5t

This gives:

30 = 5t

Finally, we can divide both sides by 5:

30 / 5 = 5t / 5

This gives:

t = 6

So, t is equal to 6.

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For upcoming trip. Tim should hire company A

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.

Given,

Distance to cover = 250 miles

For company A

By the graph line passes through

(200, 200) , (0,150)

equation of the line,

y-150 = [(200-150)/(200-0)](x-0)

y-150 = [50/200] x

y = x/4 + 150

y = 0.25 x + 150

No. of miles = 250

y = 0.25×250 + 150

y = 62.5 + 150

y = $212.5

Price for company B

y' = 0.75x + 50

where x is number of miles

for 250 miles price of company B

y' = 0.75 × 250 + 50

y' = 187.5 + 50

y' = $237.5

∵ y < y'

∴Price of trip with company A is less than company B

Hence, Tim should hire Company A for upcoming trip.

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Answer:

b = 10

Step-by-step explanation:

[tex]y=(x-h)^2+k\\y=(x-(-5))^2+9\\y=(x+5)^2+9\\y=x^2+10x+25+9\\y=x^2+10x+34[/tex]

Answer:

$6

Step-by-step explanation:

50% x 2 = 100%

3 x 2 = $6

The number of groups of 5/3 are in 1 would be equal to 3/5

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

Division of fraction

Given that groups of 5/3 are in 1

= 1 ÷ 5/3

Then Multiply by the reciprocal of 5/3

The reciprocal of 5/3 is 3/5

1 ÷ 5/3

= 1 × 3/5

= 3/5

Therefore, the number of groups of 5/3 are in 1 is; 3/5

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a. The function, (f + g)(x), is evaluated as: (f + g)(x) = 5x + 11

b. The function (f + g)(5) = 36

c. (f + g)(5) = 36 means in 5 months, the total number of animals adopted at the two shelters is 36.

We can evaluate functions just as we solve normal algebraic equations when we plug in the given value of a variable.

Given the following:

f(x) = 4x + 9 [number of animals at one shelter]

g(x) = x + 2 [number of animals at another shelter

Part A: Find (f + g)(x)

(f + g)(x) = f(x) + g(x) = 4x + 9 + x + 2

Combine like terms:

(f + g)(x) = 5x + 11

Part B: Find (f + g)(5)

Substitute the x = 5 into the function (f + g)(x)

(f + g)(5) = 5(5) + 11

(f + g)(5) = 25 + 11

(f + g)(5) = 36

Part C: It means in 5 months, the total number of animals adopted at the two shelters is 36.

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The dy for the given values of x and dx. x = 2 and dx = 0.2 dy is 0.16

The given function f(x) = ln(1 + x2) dy

In differentiation, we have a formula where f(x) is calculated:

d/dx ln=1/u.du/dx

Apply this formula for the given function:

f(x) = ln(1 + x2) dy

f'(x)= 1/x²+1*2x dx

f'(x)=2x/x²+1 dx

To calculate the dy for the given values of x and dx. x = 2 and dx = 0.2 dy

substitute these values into f'(x) we get:

f'(x)=2x/x²+1 dx

f'(x)=2(2)/2²+1 (0.2)

f'(x)=4/5(0.2)

f'(x)=0.16

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