What is the length of the midsegment of the trapezoid

Answer:

It is true that the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx

Step-by-step explanation:

Given function is a trignometric one

y = tanx

we have tanx has values 0 for all multiples of pi.

i.e. tan x =0 whenever [tex]x = 2n\pi[/tex] for all integers n.

Also tanx has a period of pi.

It is a discontinuous graph extending in one period from -pi/2 to pi/2.

Hence the mid point of each period is the x intercept.

It is true that the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx

Final answer:

The x-intercepts of the function y=tan(x) are at integer multiples of π. The concept of 'center points' for y=tan(x) is not well-defined due to the nature of the function having no central axis and being periodic.

Explanation:

The student is inquiring about the x-intercepts and center points of the function y=tan(x). The x-intercepts of the tangent function occur wherever y=0, which happens at values of x that are integer multiples of π, as the tangent function has a period of π.

On the other hand, the concept of center points is not well-defined for the tangent function since it does not have a central axis like an ellipse or a bounded pattern. The tangent function is periodic and continuous between its vertical asymptotes, which occur at odd multiples of π/2.

Answer:

A. 18%

Step-by-step explanation:

For independent events:

P(A and B) = P(A) × P(B)

P = 0.30 × 0.60

P = 0.18

There is an 18% probability that it will rain on both days and the game will be canceled.

Answer:

Angle

Step-by-step explanation:

In the image I added you can observe that the common endpoint is called a vertex, and the "turn" or aperture formed between the two straight lines (or arms) that converge in the vertex, is the angle and it can be measured on degrees.

I hope you find this information usefun and interesting! Good luck!

Final answer:

The amount of turn between two straight lines that have a common end point is referred to as an angle. This concept is central to the study of geometry and aids in measuring the difference in direction where two lines meet. Angles are typically measured in degrees as a part of spherical trigonometry and other geometric calculations.

Explanation:

The amount of turn between two straight lines that have a common end point is called an angle. An angle measures the difference in direction between two lines that extend from the same point. The concept of angle is found in the principles of geometry, where it is foundational to understanding shapes and their properties.

In more mathematical terms, the angle between two intersecting lines can also be seen as the distance between their poles when conceptualized on a sphere, a concept from advanced geometry and spherical trigonometry. The measurement of this angle is generally given in degrees, where a full circle is 360 degrees, and this system of measurement allows us to apply the angle measure to various geometric constructions and theorems, such as determining the sum of the angles of a triangle.

Answer:

[tex]\displaystyle 8\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\displaystyle \sqrt{3 \times 64} = 8\sqrt{3}[/tex]

I am joyous to assist you anytime.

Answer:

the answer is: [tex]8\sqrt{3}[/tex]

good luck

Answer: A No, the student should have added 3 + 4 to get the total number of sections, and used the fraction Three-sevenths instead of Three-fourths.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

210=1200*.035*5

Answer:

0.0414

Step-by-step explanation:

Each error is uniform between -0.5 and 0.5, so the mean error is 0, and the variance is (b-a)²/12 = (0.5-(-0.5))²/12 = 1/12

If we sum 50 numbers, the errors will sum with each other, and the resultant mean and variance will be summed, because the errors are independent. The mean of the sum of 50 number is 0*50 = 0, and the variance in 50/12.  

The central limit theorem states that the sum of identically distributed random variables has distribution approximately normal. In this case, if we call X the sum of the 50 random numbers, then X has distribution approximately N(μ = 0,σ = √(50/12)). If we divide X with its standard deviation √(50/12), we obtain (approximately) a standard normal random variable. Lets call Y = X/√(50/12). Y distribution is approximately N(0,1). Y is called the standarization of X.

The values of the cummulative distribution of the standard Normal random variable, denoted by Ф, are tabulated; you can find those values in the attached file. We want the error to be greater than 3. We will calculate the complementary event: the probability for the error to be between -3 and 3, and substract from 1 that result

P(-3 ≤ X ≤ 3) = P( -3/√(50/12) ≤ X/√(50/12) ≤ 3/√(50/12)) = P(-3/√(50/12) ≤ Y ≤ 3/√(50/12)) = Ф(3/√(50/12)) - Ф(-3/√(50/12))

Since the density function of a normal random variable centered at 0 is symmetric, then  Ф(-3/√(50/12)) = 1- Ф(3/√(50/12)), as a result

P(-3 ≤ X ≤ 3) = Ф(3/√(50/12)) - Ф(-3/√(50/12))  = 2 Ф(3/√(50/12)) - 1 = 2 * Ф(2.04) - 1 = 2*0.9793 - 1 = 0.9586

hence, the probability for the error to be greater thar 3 is 1-0.9586  = 0.0414

Answer: B) x = negative 1 plus-or-minus StartRoot 17 EndRoot

Step-by-step explanation:

The given equation is x squared + 2 x + 1 = 17. It is written as

x^2 + 2x + 1 = 17

It is a quadratic equation. The general form of a quadratic equation is ax^2 + bx + c

Rearranging the given equation, it becomes

x^2 + 2x + 1 - 17 = 0

x^2 + 2x - 16 = 0

We will apply the general formula for quadratic equation. It is expressed as

x = [-b ± √(b^2 - 4ac)]/2a

From the equation,

a = 1

b = 2

c = -16

x = [-2 ± √(2^2 - 4×1×-16)]/2×1

x = [-2 ± √(4 + 64)]/2

x = (-2 ± √68)/2

x = (-2 ± 2√17)/2

x = (-2 + 2√17)/2 or x = (-2 - 2√17)/2

x = -1 + √17 or x = -1 - √17

Answer:

B) x = negative 1 plus-or-minus StartRoot 17 EndRoot i hope this was help

Step-by-step explanation:

Answer:

1) f(x) + k

Step-by-step explanation:

1) that would result in a vertical shift  as the -3, would put parabola down 3

2) that would result in horizontal shift

3) That would change the original function

4) "kf" is not a function

Answer:

Step-by-step explanation:

Givens

[tex]f(x)=x^{2}[/tex]

[tex]k=-3[/tex]

A vertical shift of this function is represeted by the first choice: [tex]f(x)+k[/tex].

Remember, when add or subtract units to the whole function, or the dependent variable (vertical axis), we are actually shifting the function vertically. So, the first option is adding units to the dependent variable because [tex]f(x)=y[/tex].

Therefore, the right answer is 1) [tex]f(x)+k[/tex]

Answer:

Correct quotient =

[tex]\dfrac{8}{15}[/tex]

Step-by-step explanation:

We are given he following in the question:

[tex]\text{Clare's calculation:}\\\\\dfrac{4}{3}\div \dfrac{5}{2} = \dfrac{10}{3}\\\\\text{Clare's reason:}\\\\\dfrac{4}{3}\times 5 = \dfrac{20}{3}, \dfrac{20}{3} \div 2 = \dfrac{10}{3}[/tex]

Clare's, reason is incorrect.

The correct quotient can be calculated in the following manner:

[tex]\dfrac{4}{3}\div \dfrac{5}{2}\\\\= \dfrac{4}{3}\times \dfrac{2}{5} = \dfrac{8}{15}[/tex]

Clare simply multiplied the fraction with 5 and divided the product with 2 which is incorrect. We have to multiply the fraction with the reciprocal of divisor.

Answer:

The answer is 8/15

Step-by-step explanation:

4/3 divided by 5/2 is the same as 4/3 times 2/5

4/3 times 2/5= 8/15

8/15 is the answer

She is wrong because if you want to do it you have to multiply the fraction with 5 and then MULTIPLY it by 2 not divide it by 2.

Answer:

f(x) = x*3/4 + 42.5

Step-by-step explanation:

The original difference between the pair is 70 - 30 = 40

The new difference between the pair is 95 - 65 = 30

Since the differences are not the same, Mrs Bailey must first perform a (slope) multiplication by a factor of 30/40 or 3/4

Then 30 * 3/4 = 22.5

Then she can shift the scores up by 65 - 22.5 = 42.5 in order to get the range from 65 to 95

Therefore, f(x) = x*3/4 + 42.5. We can test that

f(30) = 30*3/4 + 42.5 = 65

f(70) = 70*3/4 + 42.5 = 95

Answer: 2nd and 3rd statement

Step-by-step explanation:

From the diagram, the 1st statement is wrong, the 2nd statement is correct

To know which of the rest of the statement is correct we have to find the value of MN

So we use the cosine rule to find the angle inside the triangle at point L

c2 = a2+b2-2abcosC

For our triangle

c= 12.8

b= 5.9+5.9=11.8

a= 3.7+3.7=7.4

C = ?

(12.8)2 = (7.4)2 + (11.8)2 - 2x11.8x7.4cosC

163.84 = 54.76+739.24 - 174.64cosC

163.84 = 194 - 174.64cosC

163.84-194 = -174.64cosC

-30.16 = -174.64cosC

-30.16/-174.64 =cosC

cosC = 0.1727

cos-1(0.1727) = 80.06

C = 80.06 degrees

So we use this value to find length MN with also cosine rule from the triangle NML

c2 = a2+b2-2abcosC

c = ?

a = 5.9

b = 3.7

C = 80.06

c2 = (5.9)2 + (3.7)2 - 2x5.9x3.7cosC

c2 = 34.81 + 13.69 - 43.66x0.1727

c2 = 48.5 - 7.54

c2 = 40.96

c = root(40.96)

c = 6.4

Which is half of KJ

So therefore, the third statement is correct

Answer:

b,c

Step-by-step explanation:

i did the test:)

Step-by-step explanation:

In the morning cat and dog walked 2 miles.

Total distance traveled in the morning = 2 x 2 = 4 miles

In the afternoon the dog walked 3 miles

Total distance traveled in the afternoon = 3 miles

We need to find how many miles did the cat and dog walk.

Total distance traveled by cat and dog = Total distance traveled in the morning + Total distance traveled in the afternoon

Total distance traveled by cat and dog = 4 + 3

Total distance traveled by cat and dog = 7 miles

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m = slope = (change in the value of y on the vertical axis) / (change in the value of x on the horizontal axis)

The equation of the given line is

9x+7y=4

7y = 4 - 9x = -9x + 4

y = -9x/7 + 4/7

Comparing with the slope intercept form, slope = -9/7

If the line passing through the given point is perpendicular to the given line, it means that its slope is the negative reciprocal of the slope of the given line.

Therefore, the slope of the line passing through (7,-4) is 7/9

To determine the intercept, we would substitute m = 7/9, x = 7 and y = - 4 into y = mx + c. It becomes

- 4 = 7/9×7 + c = 49/9 + c

c = - 4 - 49/9

c = - 85/9

The equation becomes

y = 7x/9 - 85/9

Answer:

A) the average value of Halloween spending of $52 in 2007 is claimed population mean and the value of Halloween spending $58 per household found out through survey done in 2008 is the sample mean

B) the average GPA 3.37 in 2001 is the claimed population mean and the average GPA through survey of 203 students is sample mean.

Step-by-step explanation:

'Claimed population mean' means the average value not taken through a survey of a sample size therefore in both options the average value is Claimed population mean

'Sample mean' is taken from a group of population therefore the value in both options taken through a survey of a sample population is Sample mean

A sample is a portion of a whole group. We use sample to predict data about the whole group(called population).

A) The sample mean is: average Halloween spending was $58 per household (survey in year 2008)

The population mean is: American households spent an average of about $52 in 2007

B) The sample mean is: average GPA of 3.59 (survey in 2012)

The population mean is: average GPA of students in 2001 at a private university was 3.37

Sample is a portion researchers or any interested person or community takes out from a big group(called population) so as to predict properties of that big group.

We work on sample because big groups are sometimes too big that we can't cover it all in normal time. There are some other reasons too because of which we work on samples instead of population.

Sample mean is the mean obtained in the sample taken.

Population mean is hypothesized mean of population(since we don't know real mean of population, that's why hypothesized).

Thus, for given condition, we have:

A) The sample mean is: average Halloween spending was $58 per household (survey in year 2008)

The population mean is: American households spent an average of about $52 in 2007

B) The sample mean is: average GPA of 3.59 (survey in 2012)

The population mean is: average GPA of students in 2001 at a private university was 3.37

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The largest sum of money that can be won under these condition is $90.

To start finding the maximum able to be drawn, they contest winner would draw 3 [tex]\times[/tex] $20 bills = $60.

Prior to drawing the 3rd $20 bill, the contest winner could draw 2 of the $5 bills and 2 of the $10 bills.

This added to the $20 bills they had drawn would give:

(2 [tex]\times[/tex] $5) = $10

(2 [tex]\times[/tex] $10) = $20

Add all the ability to win the contest.

$10 + $20 + $60 = $90

Thus, the largest sum of money that can be won under these condition is $90.

Answer:

  (x +5)²/4 +(y +8)²/36 = 1

Step-by-step explanation:

The equation of an ellipse with center (h, k) and semi-axes "a" and "b" (where "a" is in the x-direction and "b" is in the y-direction) can be written as ...

((x -h)/a)² +((y -k)/b)² = 1

Here, the center is at (h, k) = (-5, -8), and the semi-minor axis is a=2, while the semi-major axis is b=6.

The equation can be written as ...

  ((x +5)/2)² +((y +8)/6)² = 1

More conventionally, it is written ...

  (x +5)²/4 +(y +8)²/36 = 1

Answer:

The answer to your question is  [tex]\frac{(x + 5)^{2} }{4} + \frac{(y + 8)^{2} }{36} = 1[/tex]

Step-by-step explanation:

From the graph we know that the center = (-5, -8) and a= 6 and b = 2.

See the picture below

Here, we have a vertical ellipse so the equation is

                [tex]\frac{(x - h)^{2} }{b^{2} } + \frac{(y - k)^{2} }{a^{2} } = 1[/tex]

Substitution

                [tex]\frac{(x + 5)^{2} }{2^{2} } + \frac{(y + 8)^{2} }{6^{2} } = 1[/tex]

                [tex]\frac{(x + 5)^{2} }{4} + \frac{(y + 8)^{2} }{36} = 1[/tex]

Answer:

if r=4:

[tex]\displaystyle a_6=6144[/tex]

if r=1/4:

[tex]\displaystyle a_6=\frac{3}{32}[/tex]

Step-by-step explanation:

Geometric and Arithmetic Progressions

We define a geometric progression when each term [tex]a_n[/tex] is defined as the previous term [tex]a_{n-1}[/tex] times a constant called the common ratio. The iterative formula is

[tex]\displaystyle a_n=a_1.r^{n-1}[/tex]

In an arithmetic progression, each term is found by adding a constant called common difference, to the previous term

[tex]\displaystyle a_n=a_1+(n-1).r[/tex]

We are given the condition that the sum of the three first terms of a geometric progression is 126

[tex]\displaystyle a_1+a_2+a_3=126[/tex]

Using the iterative formula, we have

[tex]\displaystyle a_1+a_1.r+a_1.r^2=126[/tex]

Taking a common factor

[tex]\displaystyle a_1(1+r+r^2)=126....[eq\ 1][/tex]

We also know that if 14, 36, and 4 are added to each term, respectively, the new numbers form an arithmetic progression. It means they will have a common difference. The new numbers will be

[tex]\displaystyle a_1'=a_1+14[/tex]

[tex]\displaystyle a_2'=a_2+36[/tex]

[tex]\displaystyle a_3'=a_3+4[/tex]

The common difference between term 2 and term 1 is

[tex]\displaystyle a_2'-a_1'=a_2+36-a_1-14[/tex]

Using the iterative formula again

[tex]\displaystyle a_2'-a_1'=a_1.r-a_1+22[/tex]

The common difference between term 3 and term 2 is

[tex]\displaystyle a_3'-a_2'=a_3+4-a_2-36[/tex]

Using the iterative formula again

[tex]\displaystyle a_3'-a_1'=a.r^2-a.r-32[/tex]

Both common differences must be equal

[tex]\displaystyle a_1.r-a_1+22=a_1.r^2-a_1.r-32[/tex]

Rearranging

[tex]\displaystyle 2a_1r-a_1r^2-a_1=-54[/tex]

Solving for [tex]a_1[/tex]

[tex]\displaystyle a_1=\frac{54}{1-2r+r^2}......[eq\ 2][/tex]

Replacing in eq 1

[tex]\displaystyle \frac{54(1+r+r^2)}{1-2r+r^2}=127[/tex]

Dividing by 18 and cross-multiplying

[tex]\displaystyle 3+3r+3r^2=7-14r+7r^2[/tex]

Rearranging we have a second-degree equation

[tex]\displaystyle 4r^2-17r+4=0[/tex]

Factoring

[tex]\displaystyle (r-4)(4r-1)=0[/tex]

The solutions are

[tex]\displaystyle r=4\ ,\ r=\frac{1}{4}[/tex]

If r=4, and using eq 2

[tex]\displaystyle a_1=\frac{54}{1-8+16}=6[/tex]

Having [tex]a_1[/tex] and r, we compute [tex]a_6[/tex]

[tex]\displaystyle a_6=a_1.r^5=6.(4)^5[/tex]

[tex]\displaystyle a_6=6144[/tex]

If we use the other solution r=1/4

[tex]\displaystyle a_1=\frac{54}{1-\frac{1}{2}+\frac{1}{16}}=\frac{54}{\frac{9}{16}}[/tex]

[tex]\displaystyle a_1=96[/tex]

The sixth term is

[tex]\displaystyle a_6=96(\frac{1}{4})^5=\frac{96}{1024}[/tex]

[tex]\displaystyle a_6=\frac{3}{32}[/tex]

Both solutions are feasible

Final answer:

In this question, we explore geometric and arithmetic progressions to find the 6th term of a geometric progression given specific conditions.

Explanation:

Geometric Progression (GP): In a GP, the sum of the first three terms is 126. Let the first term be a and the common ratio be r. The sum of the first three terms can be represented as a + ar + ar^2 = 126.

Arithmetic Progression (AP): Adding 14, 36, and 4 to the terms of the GP forms an AP. The common difference of this AP is 36 - 14 = 22.

Finding the 6th Term: Using the formula for the nth term of a GP, the 6th term can be calculated as a * r^5.

Final answer:

The amount deducted weekly for Social Security taxes for Charles Stickley is $57.35.

Explanation:

The student's question is regarding the calculation of Social Security taxes based on a given gross weekly pay and applying the current tax rate.

Charles Stickley's weekly Social Security tax deduction can be calculated by multiplying his gross weekly pay by the Social Security tax rate of 6.2%.

Here's how to calculate it:

Therefore, the amount deducted weekly for Social Security taxes is $57.35.

Answer:

Option d - I and III.

Step-by-step explanation:

Given : If [tex]375y=x^2[/tex] and x and y are positive integers.

To find : Which of the following must be an integer?

Solution :

As we see all option there is a multiple of y.

So, we factoring the number 375

i.e. [tex]375=3\times 5\times 5\times 5[/tex]

[tex]375=15\times 5^2[/tex]

[tex]375=15\times 25[/tex]

In order for 375y to be a perfect square,

The prime factorization of y must contain at least one 3 and one 5.

or y must be a multiple of 15.

If y is a multiple of 15, then [tex]\frac{y}{15}[/tex] must be an integer.

and [tex]\frac{y^2}{25}[/tex] must be an integer.

Therefore, I and III will be correct i.e. option d.

Answer:the ratio of Julia’s frogs to Rimma’s frogs is 1.8 : 1

Step-by-step explanation:

Let x represent the total number of frogs that Rimma had.

Julia’s frogs are 2/5 of the amount of Rimma’s frogs. This means that the number of frogs that Julia had is

2/5 × x = 2x/5

If Rimma gives 1/2 of her frogs to Julia, the number of frogs that Julia gets from Rimma would be

1/2 × x = x/2 frogs. Total number of frogs that Julia would have becomes

2x/5 + x/2 = (4x + 5x)/10 = 9x/0

The number of frogs that Rimma has left would be 1/2 × x = x/2

The ratio of Julia’s frogs to Rimma’s frogs would be

(9x/10) / (x/2) = (9/5)/1

= 1.8 : 1

Answer: it took T.J. 48 months to pay the car loan.

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P = principal or amount loaned

R = interest rate

T = time in years.

I = interest

From the information given,

P = $5800

R = 6.5%

Over the course of the loan, he paid a total of $1508 in interest. Therefore,

I = $1508 Therefore,

1508 = (5800×6.5×T)/100

1508 = 377T

T = 1508/377 = 4 years

Assuming there are 12 months in a year, the number of months in 4 years would be 4×12 = 48 months

Answer:

A.) Multiply 46 by 5/9

Step-by-step explanation:

The formula to convert Fahrenheit degrees to Celsius degrees is as follows:

[tex]\\ C = \frac{5}{9}*(F-32) [/tex]

So, converting 78°F to °C, according this previous equation is:

[tex]\\ C = \frac{5}{9}*(78-32) [/tex] [Barbara subtracts 32 from 78]

[tex]\\ C = \frac{5}{9}*(46) [/tex]  [Barbara multiplies 46 by 5/9]

[tex]\\ C = \frac{5*46}{9} [/tex]

[tex]\\ C = \frac{230}{9} = 25.56 [/tex] or 25.56°C

Answer:

A) multiply 46 by 5/9

Step-by-step explanation:

Answer: basically just set them equal and solve

Step-by-step explanation: vertical angles are xongruent

Answer:

[tex] MAD= \frac{1}{14} 27.286 = 1.949 \approx 2.0[/tex]

Step-by-step explanation:

Previous concepts

The mean absolute deviation or MAD "is the average of the absolute deviations or the positive difference of the given data and that certain value (generally central values)". And is given by this formula:

[tex] MAD= \frac{1}{n} \sum_{i=1}^n |x_i -\bar X|[/tex]

Solution to the problem

Assuming the info from the picture. So then the data is this one:

66,69,70,70,71,72,72,72,73,73,74,75,75,75

So the first step is find the mean for the dataset with the following formula:

[tex] \bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And if we replace the values we got:

[tex]\bar X = \frac{66+69+70+70+71+72+72+72+73+73+74+75+75+75

}{14}=71.929[/tex]

And now we need to subtract for each value the mean like this:

Data      [tex] X_i -\bar X[/tex]

66               5.929

69               2.929

70               1.929

70               1.929

71                0.929

72               0.0714

72               0.0714

72               0.0714

73               1.0714

73               1.0714

74               2.0714

75               3.0714

75               3.0714

75               3.0714

Now we need to add the deviations and divide by the the number of data values and we got:

[tex] MAD= \frac{1}{14} 27.286 = 1.949 \approx 2.0[/tex]

Answer:

Tom required 23 months to save at least $2175.

Step-by-step explanation:

Given:

Money already Saved = $450

Money Needs to be saved  = $2,175

Each month saving = $75

We need to find the Number of months required to save at least $2,175

Solution:

Let the number of months be 'x'.

Now We can say Total Money which is already save plus Each month saving multiplied by number of months should be equal to Money Needs to be saved.

Framing in equation form we get;

[tex]450+75x=2175[/tex]

Solving the equation we get;

We will Subtract  both side by 450 we get;

[tex]450+75x-450=2175-450\\\\75x=1725[/tex]

Now By dividing 75 on both side we get;

[tex]\frac{75x}{75}= \frac{1725}{75}\\\\x= 23\ months[/tex]

Hence Tom required 23 months to save at least $2175.

Lizzie's answer is not right as two sides are not equal.

Step-by-step explanation:

Given equation is;

2+3x+3=3(x+3)+2x

Lizzy got;

x=2

We will put this value of x in Equation to determine if the sides are equal or not.

[tex]2+3(2)+3=3(2+3)+2(2)\\2+6+3=3(5)+4\\11=15+4\\11\neq 15[/tex]

Lizzie's answer is not right as two sides are not equal.

Keywords: linear equation, addition

Learn more about addition at:

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Answer:20.993

Step-by-step explanation:

The real price "r" is

100% and =29.99

The price after discount "d" is

100% - 30% = 70% and =?

So:

"r" is 100% =29.99

"d" is 70% =?

Do a cross multiplication so :

"d"= (29.99 * 70) / 100 = 20.993

The final price of the item is 20.993.

Frank Choi bought a rechargeable lantern that regularly sells for $29.99.

The markdown rate was 30% and there is no sales tax on the item.

The real price "r" is

100% =29.99

The markdown rate was 30%

29.99 * (30/100)

8.997

The price after discount

29.99 - 8.997 = 20.993.

Therefore, the final price of the item is 20.993.

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Answer:

At 20 miles both companies cost will be same.

Step-by-step explanation:

Let Number of miles be 'x'.

Given:

Quick movers charges $50 a day and $0.50 per mile .

So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.

framing in equation form we get;

Quick movers charges = [tex]50+0.5x[/tex]

Also Given:

ABC movers charges $45 a day and $0.75 per mile .

So we can say Total charge is equal to sum of per day charge plus number of miles multiplied by cost of per mile.

framing in equation form we get;

ABC movers charges = [tex]45+0.75x[/tex]

We need to find the number of miles at which both companies cost are are same.

Solving to find the same we get;

[tex]50+0.5x=45+0.75x[/tex]

Combining like terms we get;

[tex]0.75x-0.5x=50-45\\\\0.25x=5[/tex]

By Division property of equality we will divide both side by 0.25 we get;

[tex]\frac{0.25x}{0.25} =\frac{5}{0.25} \\\\x= 20 \ miles[/tex]

Hence at 20 miles both companies cost will be same.

Final answer:

By setting up an equation to equate the charges of Quick Movers and ABC Movers, it is determined that at 20 miles, the costs for both companies will be the same.

Explanation:

To find at how many miles the cost for both Quick Movers and ABC Movers is the same, we set up an equation where the cost of each company is equal. Quick Movers charges $50 a day plus $0.50 per mile, and ABC Movers charges $45 a day plus $0.75 per mile. Let's use m to represent the miles.

The equation based on the costs given will be:

50 + 0.50m = 45 + 0.75m

To solve the equation, we first bring all the m terms to one side and the constants to the other:

0.50m - 0.75m = 45 - 50

This simplifies to:

-0.25m = -5

Dividing both sides by -0.25, we find:

m = 20

Therefore, the cost for both companies is the same at 20 miles.

Answer:

Step-by-step explanation:

An exponential function is of the form

[tex]y=ab^x[/tex]

where a is the initial value and b is the growth/decay rate.  Our initial value is 64.  That's easy to plug in.  It goes in for a.  So the first choice is out.  Considering b now...

If the rate is decreasing at .5% per week, this means it still retains a rate of

100% - .5% = 99.5%

which is .995 in decimal form.

b is a rate of decay when it is greater than 0 but less than 1; b is a growth rate when it is greater than 1.   .995 is less than 1 so it is a rate of decay.  The exponential function is, in terms of t,

[tex]f(t) = 64(.995)^t[/tex]

Answer:

f(t) = 64 ⋅ 0.995t

Step-by-step explanation:

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