Trinity drives 3 miles then walks another 930 yd. How many feet does she
travel in total?

A relation that assigns to each element x from a set of inputs, or domain, exactly one element y in a set of outputs, or range, is called a  function.

This is further explained below.

Generally, A mathematical function from set X to set Y gives each element of X a unique value in Y. The set X is known as the function's domain and the set Y is its codomain. The original function was a simplification of the relationship between two variables.

In conclusion, A relation is said to be a function if it assigns precisely one element y from a set of outputs to each and every one of the domain's inputs.

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$15,000 were invested at 7% and $1,000 were invested at 15%.

Let the amount invested by Dilbert at 7% be x and the amount invested at 15 % be y. A total amount of $16,000 was invested.

x + y = 16,000    (1)

After one year, the total interest was $1,200.

0.07x + 0.15y = 1,200     (2)

We will solve the first equation for y and substitute its value in the second equation.

y = 16,000 - x

Multiply the second equation by 100 to remove the decimals,

7x + 15y = 1,20,000

7x + 15 (16,000 - x) = 1,20,000

7x + 2,40,000 - 15x = 1,20,000

-8x = = 1,20,000 - 2,40,000

-8x = -1,20,000

x = 15,000

y = 16,000 - x

y = 16,000 - 15,000

y = 1,000

Therefore, $15,000 were invested at 7% and $1,000 were invested at 15%.

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The given expression is as follows:[infinity] ncnxn − 1 n=1 − [infinity] 7cnxn n=0.

We need to rewrite the given expression using a single power series whose general term involves xk. For that, we will rewrite the given series as follows:

[infinity] ncnxn − 1 n=1 − [infinity] 7cnxn n=0

= [infinity] [ncnxn − 1 − 7cnxn]n=0

= [infinity] [cn (n + 1)xnn − 7cnxn]n=0

= [infinity] [cnxnn + cnxn] − [infinity] [7cnxn]n=0n=0

= [infinity] cnxnn + [infinity] cnxn − [infinity] 7cnxn n=0 n=0

= [infinity] cnxnn + [infinity] (cn − 7cn)xnn= [infinity] cnxnn + [infinity] −6cnxnn= [infinity] (cn − 6cn)xnn= [infinity] (1 − 6)cnxnn= [infinity] −5cnxnn.

Thus, we can rewrite the given expression as a single power series whose general term involves xk as: ∑(-5cn)xn

where ∑ is from n = 0 to infinity.

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The answers are:

The first blank is: 8

The second blank is: -3

The last blank is: -7

Hope this helps!

Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

The contractor would have to work for 20 hours on the site to earn $555 total pay

What is total cost function?

Total cost function is the sum of the fixed charge, which is fixed cost to the person paying the contractor when the contractor visits the site and charge per hour multiplied by the number of hours spent working

TC=a+bX

TC=total cost=$555

a=fixed charged=$55

b=charge per hour=variable element of contractor's pay=$25

X=number of hours spent working=unknown

$555=$55+$25X

$555-$55=$25X

$500=$25*X

X=$500/$25

X=20

The contractor needs to work for 20 hours in order to earn a total pay of $555

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Answer:

900 ft

Step-by-step explanation:

first you plug in the x for -5 because it said "5 minutes before"

second you do the math

y = -20(-5) + 800

y= -00+ 800

y = 900

Answer:

E=20, F=50, G=110

Step-by-step explanation:

E=2/18*180=20

F=5/18*180=50

G=180-20-50

  =110

The slope is -2 and which means that each page that is printed uses two millilitres of toner. Therefore, option C is the correct answer.

Given that, the number of millilitres of toner in a printer, y, depends on the number of pages of paper printed (in hundreds), x. The equation that can be used to model the situation is y = -2x + 60.

We need to find what is the slope and what it represents in the context of the problem.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

When we compare the equation y = -2x + 60 with the slope intercept form y=mx+b, we get slope(m) as -2.

The slope is -2 and which means that each page that is printed uses two millilitres of toner.

Therefore, option C is the correct answer.

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Answer:

The answer is D.) A random sample may represent the population.

Step-by-step explanation:

Collecting samples from anyone at random increases the chances of representing the overall people because that's where they're getting it from. But there is still a chance it will not represent everyone or the general population.

Answer:B) A random sample may represent the population is your best answer.

Step-by-step explanation:

this is what i got for this one. have a good day everyone. :)

Answer:

he would have to use all of it and then $16 more to make both plans cost the same. I think he should go with US Cellular

Step-by-step explanation:

just because

The correct statement regarding the variation of the two measures is given as follows:

C. Yes, they vary directly. When one quantity increases, the other quantity also increases.

For this problem, we have that when the number of correct answers on the test increases, the score also does, hence the two quantities vary directly, and option c is the correct option for this problem.

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Answer:

The value of x is 5.8

Step-by-step explanation:

Here. we want to find the value of x

To do this, we need the appropriate trigonometric identity

As we can see 10 is the opposite as it faces the side given

x is the adjacent

The trigonometric identity relating opposite and adjacent is tan . Tan is the ratio of the opposite to the adjacent

Thus, mathematically;

Tan 60 = 10/x

x = 10/tan 60

x = 5.8

Answer:

see explanation

Step-by-step explanation:

8

If you take the square root of 52 and then divide by two you get about 3.6. You take i and multiply it by that and you get 4. Then divide 40 by 2 to get 20. Then you subtract the inverse of the mulltiagion thereom to get 4.

4+4=8

Answer:

$32

Step-by-step explanation:

0.8*40

the area of her entire bedroom is 176 feet².

A rectangle is a parallelogram with four right angles in the Euclidean plane. It can also be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equivalent. A square is a rectangle with four equal edges.

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Area of first rectangle = length * breadth= 10*8=80 feet²

Area of second rectangle = length * breadth= 12*8 = 96 feet²

Total area of bedroom= 80+96= 176 feet²

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The quadratic equation x² + 8x + 6 written in the form (x + a)² + b, is:

(x + 4)² -  10. where a and b are constant.

Consider the given equation;

x² + 8x + 6  .......equation 1

Let,

8x = 2ax

x will get cancelled,

a = 4

a² = 16

Add and subtract 16 from equation 1.

x² + 8x + 6 + 16 - 16

Rearranging.

x² + 8x + 16 + 6 - 16

This can be written as;

(x + 4)² - 10

The result expression is in the form of (x + a)² + b, in which a and b are the constant whose values are 4 and -10 respectively.

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Answer:

domain and the range

Step-by-step explanation:

Answer:

the value of x is 2^9/4 then 2^3x-4=2^11/4

The derivative of k(x) is:

k'(x) = (-5/4) x^(1/4) e^[-1/4x^(5/4) + 5/3x^(-5/2)] - (25/6) x^(-7/2) e^[-1/4x^(5/4) + 5/3x^(-5/2)]

To find the derivative of k(x) with respect to x, we need to use the chain rule and product rule of differentiation.

Let's first simplify the expression inside the exponential function using the laws of exponents.

k(x) = e^[-1/4x^(5/4) + 5/3x^(-5/2)]

= e^[-(1/4)x^(5/4)] * e^[5/3x^(-5/2)]

Now, we can find the derivative of k(x) as follows:

k'(x) = [-5/4 * x^(1/4) * e^(-1/4x^(5/4))] * e^[5/3x^(-5/2)]

+ e^[-1/4x^(5/4)] * [-5/2 * 5/3 * x^(-7/2) * e^(5/3x^(-5/2))]

= (-5/4) x^(1/4) e^(-1/4x^(5/4)) e^(5/3x^(-5/2)) - (25/6) x^(-7/2) e^(-1/4x^(5/4)) e^(5/3x^(-5/2))

  = (-5/4) x^(1/4) e^(-1/4x^(5/4) + 5/3x^(-5/2)) - (25/6) x^(-7/2) e^(-1/4x^(5/4) + 5/3x^(-5/2))

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The z score on his first quiz was 1.29 and the z score on his second quiz was 1.73.

Alvin feels he did better on the second quiz than the first because he received a higher z score. A z score is a measure of how many standard deviations an individual score is from the mean. The higher the z score, the more standard deviations away from the mean the individual score is.

In this case, Alvin's score of 15 on his second quiz was 1.73 standard deviations away from the mean of 12.2, which is higher than his score of 16 on his first quiz which was 1.29 standard deviations away from the mean of 14.3.

This indicates that Alvin's second quiz score was further away from the mean than his first quiz score, which is why he feels he did better on the second quiz than the first.

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Answer:

Step-by-step explanation:

Average speed is total distance divided by total time.

The relation between time, speed, and distance is ...

  time = distance/speed

The time to travel 5 mi at 35 mi/h is ...

  time = (5 mi)/(35 mi/h) = 1/7 h

30 seconds is (30 s)/(3600 s/h) = 1/120 h, so the total time for this trip is ...

  1/7 +1/120 = (120 +7)/840 = 127/840 hours

At 80 mph, the distance traveled in 1/120 hour is ...

  distance = speed × time = (80 mi/h)(120 h) = 2/3 mi

So, the total distance traveled is ...

  (5 mi) +(2/3 mi) = 17/3 mi

The average speed is then ...

  speed = distance/time

  speed = (17/3 mi)/(127/840 h) = 17·840/(3·127) mi/h = 37 61/127 mi/h

The average speed is about 37.48 miles per hour.

_____

Additional comment

In order for the average speed to be 55.56 mph, the time spent at 80 mph would need to be about 7 minutes 12.6 seconds, for a distance at 80 mph of about 9.61 mi.

The Marginal Rate of Substitution (MRS) for the given function is equal to -2/sqrt(x). To find the Marginal Rate of Substitution (MRS), we need to take the derivative of the given function with respect to x.

Given: y = 24 - 4(sqrt(x))

Step 1: Differentiate the function y with respect to x.

dy/dx = d/dx(24 - 4(sqrt(x)))

Step 2: Differentiate each term separately using the power rule and chain rule.

dy/dx = 0 - 4(1/2)(x^(-1/2))(1)

Step 3: Simplify the derivative.

dy/dx = -2(x^(-1/2))

Step 4: Rewrite the derivative in terms of MRS.

MRS = dy/dx = -2/sqrt(x)

Therefore, the Marginal Rate of Substitution (MRS) for the given function y = 24 - 4(sqrt(x)) is -2/sqrt(x).

The negative sign indicates that the MRS is inversely related to x, which means as x increases, the MRS decreases. The value of MRS represents the rate at which a consumer is willing to substitute y (the dependent variable) for an incremental change in x (the independent variable). In this case, as x increases, the consumer is willing to substitute less y for the additional units of x.

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Answer:

144cm²

Step-by-step explanation:

The surface area of a shape = area of all the sides added together

area of bottom side (square) = 6 x 6 = 36

area of triangles = \(\frac{1}{2}\) x 6 x 9 = 27

27 x 4 =108

108 + 36 = 144

Answer:

\(A_{total} = 144\ cm^2\)

Step-by-step explanation:

Step 1:  Determine the area of the bottom square

\(A = l * w\)

\(A = 6\ cm * 6\ cm\)

\(A = 36\ cm^2\)

Step 2:  Determine the area of the triangle

\(A= \frac{h *b}{2}\)

\(A=\frac{9\ cm * (6\ cm/2)}{2}\)

\(A=\frac{9\ cm * 3\ cm}{2}\)

\(A=13.5\ cm^2\)

Since we have two of these right triangles on each side we come out to having 8 of these triangles total since we have 4 sides.  We multiply 8 by our area from one triangle.

\(A=13.5\ cm^2*8\)

\(A = 108\ cm^2\)

Step 3:  Determine the surface area

\(A_{total} = 36\ cm^2 + 108\ cm^2\)

\(A_{total} = 144\ cm^2\)

Answer:  \(A_{total} = 144\ cm^2\)

Answer:

f(5) = -5

Step-by-step explanation:

To find the value of f(5), find the value of y when x = 5.

To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line.

Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.

Therefore, the value of f(5) is -5.

See attachment.

Answer:

Step-by-step explanation:

Given the graph of the function f(x).

In order to find the value of f for any value of x on the graph, find the point x on the x-axis, then add a vertical line from this point to the graph. The y-coordinate of the intersection is the value of the function at given x-coordinate.

We are asked to find the value of f(5).

This is f(5) = - 5 as per above explanation.

See the attached for better understanding.

Answer:

personal values

Step-by-step explanation:

values = principals. that being said, you won't live your life following your friends or spouses principles, instead you'd live your life by your own principles.

Answer:

The answer is D

Step-by-step explanation:

When the exponent is negative then you go in to decimals

Answer:

since its a negative number you need to to go to the decimals> therefore the answer would be (D)

To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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Answer:

x = 45°

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

since the whole angle is a right angle, we know its worth 90 degrees. since the line separates the 90 into two, with one part being 45, we can take 45 away from 90, and get our answer. 90-45=45. so the value of x=45