3
If a product costs $15,000 for the first unit and there is
a 15% discount starting on the second unit, a 30%
discount (from the original price) starting on the 4th
unit, what would be the cost for 7 units?

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 person is 16. 55ft from the boat

From the information given, we have that;

To determine the distance between the boat and the person, let's use the trigonometric identity, sine

sine θ = opposite side/hypotenuse side

Given that;

Substitute the value

sin 65 = 15/d

cross multiply

d = 15/sin 65

Find the value

d = 15/0.9063

divide the values

d = 16. 56 ft

Hence, the value is 16.56ft

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Using dimensional analysis we have converted 44 yards/sec = 90 miles/hour.

Dimensional analysis is the study of how dimensions and units of measurement affect the relationship between physical quantities.

Dimensional analysis is crucial because it maintains the consistency of the units, which facilitates accurate mathematical computation.

As we use conversion factors to obtain the same units, dimensional analysis is also known as the Factor Label Method or Unit Factor Method.

We know that 1 yards/sec = 2.04545 miles/hour

Here given that 44yds/s = ? miles/hour

Lets solve

1 yards/sec = 2.04545 miles/hour

44 yards/sec = 44 × 2.04545 miles/hour

44 yards/sec = 89.9998 miles/hour

44 yards/sec = 90 miles/hour

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The product of 6√8 and 3√24 in simplest radical form is 144√3

We can solve this problem by using the distributive property and simplifying the radicals.

6√8 * 3√24 = (6 * 3) * √(8 * 24)

Evaluate the products

6√8 * 3√24 = 18 * √(8 * 24)

Evaluate the products of radicals

6√8 * 3√24 = 18 * √(192)

Simplify the radical

6√8 * 3√24 = 18 * 4 * √12

So, we have

6√8 * 3√24 = 72√12

Now to simplify the radical, we can divide the radicand by the greatest perfect square that is a factor of it.

So, we have

72√12 =  72 * 2 * √3

= 144√3

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Answer:

Step-by-step explanation:

26.25 divided by three = 8.75

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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The value of the expression x² - 9x - 7 when x = 6 is -25.

Quadratic equations are second degree polynomial equations which are of the form ax² + bx + c = 0, where a, b and c are real numbers and x is the variable with the highest degree of 2.

Given the quadratic expression,

x² - 9x - 7

We have to find the value of the expression when x = 6.

Substitute x = 6, we get,

6² - (9 × 6) - 7 = 36 - 54 - 7

                       = -25

Hence the value of the given expression when the value of x = 6 is -25.

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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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The table that shows a proportional relationship between x and y is:

C. x 1 5 8 10 y 15 75 120 150

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of that constant.

If every pair of data values is related in the same way, by multiplying by a factor, then the relationship is proportional. A proportional relationship can be identified by looking at data, an equation, or a graph.

In this case, the constant based on the information will be:

= 15 / 1

= 15

Also when x is 5, y will be:

= 5 × 15.

= 75..

The correct option is C.

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Answer: The domain of a function is the set of all input values (x-values) for which the function produces a valid output value (y-value).

For the function y = 3^√x, the input value x can't be negative because the value under the square root should be non-negative and 3^√x is defined for all x in the domain of real numbers. This means that the domain of the function y = 3^√x is (-∞,∞).

Step-by-step explanation:

The domain of the function is  [0, ∞).

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the 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,

The function y = 3^√x has a base of 3, which means that the output of the function is always a positive number.

For the function to be defined, the input x must also be a positive number or zero, as the square root of a negative number is not a real number.

Therefore,

The domain of the function is all non-negative real numbers, or [0, ∞).

In interval notation, the domain can be written as [0, ∞).

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If 500m is split in the ratio of 1:4, then the first part would equal 125m and the second part would equal 375m.

The ratio is a comparison of two or more related values or amounts. It is expressed as a fraction or a decimal number, and is used to compare the relative size of two or more values. Ratios can be used to compare numbers, objects, people, or other elements in order to study their relative size or relationships.

If 500m is split in the ratio of 1:4, then the first part would equal 125m and the second part would equal 375m. This is because the ratio of 1:4 can be simplified to 1/5 and 1/5 of 500m is 125m. Therefore, the first part is 125m and the second part is 375m.

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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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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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The answer to the work shown is x = 8.

The law of indices are laws that has to be applied to expressions involving powers or fractions. These laws have individual application.

Considering the given question, we have;

16^(3x - 6) = 64^(x + 4)

It can be deduced that, the factors of;

16 = 4 x 4

   = 4^2

and

64 = 4 x 4 x 4

    = 4^3

So that;

4^2(3x - 6) = 4^3(x + 4)

Divide through by 4 to have;

2(3x - 6) = 3(x + 4)

6x - 12 = 3x + 12

collect like terms,

6x - 3x = 12 + 12

6x = 24

x = 24/6

  = 8

The answer to the work shown in the question is: x = 8

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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.

The equation of the cross-section of the reflector which is in the form of a parabola is y² = -10x

A parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.

Given that, The cross-section of the reflector in a flashlight is a parabola, the light bulb is located at the focus of the cross-section, 2.5 cm in front of the vertex.

We know that, the equation of the parabola turned to the left i.e. to the negative side of the coordinate system is:

y² = -2px  

where p is the parameter of the parabola

The relationship between the parameter and the focus is.

p = 2 f  

p = 2×2.5 = 5 cm  

Since, the equation of the parabola is:

y² = -2p

Therefore, put p = 5

y² = - 2×5x = -10x

y² = -10x

Hence, the equation is y² = -10x

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Answer: A: x=6

Step-by-step explanation: If we plug in 6 for X in the equation we get

33 - 6. 33 - 6 does equal 27.

Now to make sure X = 4 is not an answer, we plug that in too. 33 - 4.

33 - 4 = 29, so this is not the answer.

Answer:

A: x = 6 is a solution, but x = 4 is not.

Step-by-step explanation:

33-x=27

-33    -33

-x=-6

-x/   -x/

x=6

Therefore ,  solving the provided question, we can say that the, probability P( 24 period hour) = 5/24

The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number from 0 and 1, in which about 0 represents how likely the event should be to occur and 1 represents certainty. A probability is a quantitative illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100% or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrence in a whole set all equally likely options that lead to a specific occurrence.

Here,

=> E1 = stops at 5 clock

=>  E2 = start at 24 hours

=> P( 24 period hour) = 5/24

=> the, probability P( 24 period hour) = 5/24

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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 pints of punch that Jason served were 52 pints.

The number of pints that make up a gallon is 8 pints. So, in 8 gallons, we can expect that there will be 64 pints. Now, we are told that Jason served 1 pint container and now he has 12 points remaining, what we are to do is to subtract the remaining pints from the original pints that he had.

Since the original was 64 pints, removing 12 pints will amount to 52 pints. This means that 52 pints of punch were served in the 1-pint containers.

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DE and FG have the same slope, so both the sides are parallel. The opposite side of the quadrilateral are equal. Because, the opposite side of the quadrilateral are equal and parallel, DEFG is a parallelogram.

A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces.

DE and FG have the same slope, so both the sides are parallel.

Since, DE = FG, the opposite side of the quadrilateral are equal.

Because, the opposite side of the quadrilateral are equal and parallel, DEFG is a parallelogram.

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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!

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:

Step-by-step explanation:

77/100 or 0.77

a. The y-intercept of the graph is 35,000, which represents the original purchase price of the car. Therefore, the car was purchased for $35,000.

b. We can see from the graph that the car's value becomes 0 after 9 years. Therefore, the car totally depreciates after 9 years.

c. The equation of a straight line can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope of the graph is the rate of depreciation, which is -4000. The y-intercept is the original price of the car, 35000.

So the equation of the straight line depreciation graph is: y = -4000x + 35000

This equation represents the value of the car, where y is the value of the car (in dollars) x is the number of years since the car was purchased and -4000 is the rate of depreciation and 35000 is the original price of the car.

The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

You can find the standard mean error and then use that to find the confidence interval limits.

The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by

Lower limit = 0.0104

Upper limit = 0.0496

The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

To find the confidence interval for proportions

Let the sample size be n

Let the interested quantities in the sample be present x times

Let the confidence level be of p%.

Then the level of significance is given by

The standard mean error is calculated by:

Then the confidence interval limits can be found by

Using the above formula for finding the confidence interval

We have n = 500, x = 15 and

Finding the standard mean error:

From the z tables, we get z = 2.5758

Thus, the confidence interval is obtained by

Lower limit = 0.0104

Upper limit = 0.0496

Thus,

The 99% confidence interval for the proportion of all employees at the company who own an electric car is given by

Lower limit = 0.0104

Upper limit = 0.0496

Therefore, The confidence interval is (0.0104, 0.0496) (can include those endpoints too)

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Answer:

the having of the record is that

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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The value of the variable, x is 7

Algebraic expressions are defined as expressions that are composed of terms, coefficients, variables, constants and factors.

These mathematical operations are also made up of arithmetic operations. These operations includes;

From the information given, we have;

-5(2x+14)=-2(x+63)

expand the bracket

-10x -70 = -2x - 126

Now, collect like terms

-10x + 2x = -126 + 70

Add or subtract the terms

-8x = -56

Make 'x'' the subject

x = 7

Hence, the value is 7

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