Evaluation
A family rents a truck to move from Buffalo to
Chicago. The rental has a base cost of $49.95,
plus, an additional
cost of $1.19 per mile driven.
The family also pays for gas,
which costs $3.89 per gallon.
The truck’s average gas mileage
is 18 miles per gallon.
The family decided to take a rest in Cleveland, what would be the distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85?

Answer: 780

Step-by-step explanation:

Two times 2 is 4

4 + 89 = 93

93 +765 = 858

858 - 78 = 780

Answer: A+B+C=π⇒A+B=π−C

Step-by-step explanation: I think not sure hope this helps :)

13+16 are the numbers that equals to 19.

The equal sign in the  mathematics describes by  equality between the values,. Of the  equations, or expressions are the  written on both sides. There symbol for equal to is two be the  small horizontal lines placed to parallelly. We place the to the  'equal to' sign is between two things that are to the same or equal.

As we know,

If two things are equal or if one thing is equal to the  another, they are the same or  in the size, number, standard, or values .

As per the question we have to find equal number of 19.

So 13+6 are the equal number that equals to 19.

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The required straight equation will be y = -0.5x + 27.5 passes through the points  (-5, 0) and (5, 2).

What are equations in a straight line?

A straight line's equation is given by y=mx+c, where c is the height at which the line intersects the y-axis (often referred to as the y-intercept) and m is the gradient.

According to the given graph,

We can see two points are (-5, 0) and (5, 2)

The linear equation will be: y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Here

x₁ = -5, y₁ = 0

x₂ = 5, y₂ = 2

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

Substitute values in the equation, we get

⇒ y - 0 = (2 - 0)/(8-4)(x-(-5))

⇒ y - 30 = (2)/(-4)(x + 5)

⇒ y - 30 = -1/2(x + 5)

⇒ y = (-1/2)x - 5/2 + 30

⇒ y = -0.5x + 27.5

Thus, the required equation will be y = -0.5x + 27.5 passes through the points  (-5, 0) and (5, 2).

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Write an equation for the graph shown in the form y=ax+b.

The slope of the line that contains the points: (-7, 8) and (12, 8) is 0

From the question, the points are given as

(-7, 8) and (12, 8)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) =  (-7, 8) and (12, 8)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) =  (-7, 8) and (12, 8)

Substitute the known values in the above equation

So, we have the following equation

Slope = (8 - 8)/(12 + 7)

Evaluate

Slope = 0

Hence, the slope of the line is 0

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The number in between 10 and 15 and having prime factors of 2 and 3 is 12.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

The integer between 10 and 15 are,

11,12,13,14

The prime factors of 2 and 3 will be given as,

[tex]2^{a} \times 3^{b}[/tex] where a and b can be positive.

Since, 12 = 2² × 3¹

Thus, 12 is the only number that is the prime factor of 2 and 3 both.

Hence "The number between 10 and 15 and having prime factors of 2 and 3 is 12".

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The required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,

Given that,
At a store, a shirt was marked down in price by $10.00. A pair of pants doubled in price. Following these changes, the price of every item in the store was cut in half.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
let y be the total cost for each different item
cost of the shirt = s - 10 and pair of pants = 2p
According to the question,
y = s - 10 / 2  and y = 2p / 2

Thus, the required new price of the shirts and pair of paints is given as y = [s - 10]/2 and y = [2p]/2 respectively,

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The transformations from the parent function are

From the question, we have the following parameters that can be used in our computation:

g(x) = -|x + 3| - 4

The above function is an absolute value function

Next, we plot the graph using a graphing calculator

See attachment for the graph

From the question, we have the following function that can be used in our computation:

f(x) = |x| --- the parent function of an absolute value function

g(x) = -|x + 3| - 4 -- the transformed function

First, we have the transformation to be:

From f(x) = |x| to f'(x) = |x + 3|

This means the function is translated left by 3 units

Next, we have:

From f'(x) = |x + 3| to f'(x) = -|x + 3|

This means the function is reflected across the x-axis

Lastly, we have:

From f'(x) = -|x + 3| to g(x) = -|x + 3| - 4

This means the function is translated down by 4 units

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Time ∝ 1/Speed

Time = k/Speed

k = Time x Speed

The time taken for the trip for the car moving at 30 mph is 12 hours.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 7 is an equation.

We have,

Time ∝ 1/Speed

This can be written as,

Time = k/Speed

k = Time x Speed

Now,

The trip takes 8 hours for a car moving at 45 mph.

This means,

k = 8 x 45

k = 360

Now,

The time taken at the speed of 30 mph.

Time = k / Speed

Time = 360/30

Time = 12 hours

Thus,

The time taken for the trip for the car moving at 30 mph is 12 hours.

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The length of the ladder is approximately 3 m. The correct option is the first option 3

From the question, we are to calculate the length of the ladder.

From the given information,

The ladder makes an angle 20° with the ground

and

The foot of the ladder is 3 m from the wall

This scenario gives a right triangle where the hypotenuse is the ladder and the adjacent is the distance of the foot of the ladder from the wall.

Let the length of the ladder be x

Thus,

Using SOH CAH TOA

We can write that

cos 20° = 3 / x

x = 3/(cos 20°)

x = 3.19

x ≈ 3 m
Hence, the length is approximately 3 m

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Answer:

the last one is obviously represent a linear of function

The sample mean is 5.0833 and the standard deviation is 3.476 and the confidence interval is (2.87, 7.29).

In the given question, a random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period).

Using these data to create a 95% confidence interval for the population mean days absent for sickness

2   5   3   7   10   0   6   8   5   11   3   1

a) We have to find the sample mean and the standard deviation (round to two decimal places).

The sample mean;

X = 2+5+3+7+10+0+6+8+5+11+3+1/12

X = 61/12

X = 5.0833

Now the standard deviation

SD = √[{x(1)-X)^2+(x(2)-X)^2…………….(x(12)-X)^2}/N]

After solving using that formula;

SD = 3.476

b) 95% confidence in interval for the population mean days absent for sickness.

Lower Bound = X - t(α/2)*s/√n

Upper Bound = X + t(α /2)*s/√n

where

α /2 = (1 - confidence level)/2 = 0.025

X = sample mean = 5.083333333

t(α/2) = critical t for the confidence interval = 2.20098516

s = sample standard deviation = 3.476108936

n = sample size = 12

df = n - 1 = 11

Thus,

Lower bound = 2.874719086

Upper bound = 7.291947581

Thus, the confidence interval is (2.87, 7.29).

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The right question is:

How healthy are the employees at direct marketing industry? A random sample of 12 employees was taken, and the number of days each was absent for sickness was recorded (for a 1-year period). Use these data to create a 95% confidence interval for the population mean days absent for sickness.

2   5   3   7   10   0   6   8   5   11   3   1

a) Find the sample mean and the standard deviation (round to two decimal places)

b) 95% confidence in interval for the population mean days absent for sickness.

The slopes of the lines are 2/3, 5, 5/6 and 1 respectively

The slope of a line is a measure of its steepness or incline. It is defined as the ratio of the vertical change (called the "rise") to the horizontal change (called the "run") between two points on the line.

The slope of a line can be expressed using the following formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

1.  P₁(0,2) and P₂(3,4):

Slope = (4-2)/(3-0) = 2/3

2.  P₁(1,2) and P₂(3, 7):

Slope = (7-2)/(3-2) = 5/1 = 5

3. P₁(-1,1) and P₂(5,6):

Slope = (6-1) / (5-(-1)) = 5/6

4. P₁(-1,-2) and P₂(10,11)

Slope = (11-(-1)) / (10-(-2)) = 12/12 = 1

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The first derivative of the implicit functions are listed below:

In this problem we have an implicit function of the form f(x, y) = 0, whose first derivative shall be found by implicit differentiation. Now we proceed to present the procedure. First, write the entire expression:

2 · x² + 8 · x · y + 6 · y² + 13 · y - 2 = 0

Second, use the derivative rules:

4 · x + 8 · y + 8 · x · y' + 12 · y · y' + 13 · y' = 0

4 · x + 8 · y + (8 · x + 12 · y + 13) · y' = 0

y' = - 4 · (x + 2 · y) / (8 · x + 12 · y + 13)

The same procedure is used in the next two implicit functions:

3 · x³ = 2 · y² - 9 · y

9 · x² = 4 · y · y' - 9 · y'

9 · x² = (4 · y - 9) · y'

y' = 9 · x² / (4 · y - 9)

3 · y² = 5 · x - (2 / 5) · x + 2

6 · y · y' = 5 - 2 / 5

6 · y · y' = 23 / 5

y' = 23 / (30 · y)

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Answer:

t ≈ 7.7

Step-by-step explanation:

                   r         ^nt

A = P ( 1 + ------- )

                  n

A = 3000

P = 1500

n = 12

r = 0.09

t = ?

                             0.09        

3000 = 1500 ( 1 + ------- ) ^(12)(t)

                               12

                             0.09        

3000 = 1500 ( 1 + ------- ) ^(12)(t)

÷1500  ÷1500         12

              0.09        

2 =  ( 1 + ------- ) ^(12)(t)

               12

Change into logs and divide

  log 2

----------------------    =   12t

              0.09

log (1 + ----------)

               12

multiply both sides by (1/12)

                 log 2

(1/12) ----------------------    =   12t (1/12)

                    0.09

      log (1 + ----------)

                     12

7.7304805 = t

7.7 ≈ t

I hope this helps!

The simplified expression, when using the Quotient rule is b. 1 / 8⁴.

The Quotient Rule allows us to be able to carry out operations on quotients. The rule is such that when dividing quotients with the same base, you should subtract the quotients. For multiplication, you add the quotients.

8 ⁵ / 8 ⁹ will therefore be:

= 8 ⁵ ⁻ ⁹

= 8 ⁻⁴

8 ⁻⁴  is the equivalent of  1 / 8⁴ because when a number is taken to a negative power, then that number becomes a denominator to 1.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{50}~,~\stackrel{y_1}{45})\qquad (\stackrel{x_2}{70}~,~\stackrel{y_2}{61}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{61}-\stackrel{y1}{45}}}{\underset{run} {\underset{x_2}{70}-\underset{x_1}{50}}} \implies \cfrac{ 16 }{ 20 } \implies {\Large \begin{array}{llll} \cfrac{4 }{ 5 } \end{array}}[/tex]

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. the expression.343 ^ { 4 / 3 } is 7,625

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 = 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.The expression 343^ {4/3} can be broken down into 343 to the power of 4 divided by 3. Before we evaluate the expression, we must understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 can be calculated using the formula 343 x 343 x 343 x 343. This results in 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.

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The probability that a person selected at random will live on campus OR have a low intention of attending the Fair is 0.584.

The data of Intention of Attending the Fall Career Fair is given below:

                           High                Medium                 Low               TOTAL

On Campus         99                       102                     22                   223

Off Campus         78                        80                      43                   201

>20 mi. Away      18                         32                      26                    76

TOTAL                 195                      214                     91                     500

We have to find the probability that a person selected at random will live on campus OR have a low intention of attending the Fair.

Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = P(on campus) + P(low) - P(on campus and low)

Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 223/500 + 91/500 - 22/500

Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 292/500

Probability that a person selected at random will live on campus OR have a low intention of attending the Fair = 0.584

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The right question is:

The data shown below is for a sample of LSU students to evaluate their intention of attending the Fall 2023 Career Fair based on where they live.

                         Intention of Attending the Fall Career Fair

                           High                Medium                 Low               TOTAL

On Campus         99                       102                     22                   223

Off Campus         78                        80                      43                   201

>20 mi. Away      18                         32                      26                    76

TOTAL                 195                      214                     91                     500

What is the probability that a person selected at random will live on campus OR have a low intention of attending the Fair?

Step-by-step explanation:

you devide the upper half of a fraction with the part under it. for example

6x2+x+1

_______=6. that is asymptote

x2+2

when you multiply 6 and lower half of a fraction you get 6x2+12

if you substract that from 6x2+x+1 you get x-11

if you make x-11=0 the number that x represents is the point where the function crosses the asymptote

Answer:

P(A) =0.5 obviously since it didn't say like P(AC) or P(AD)

Given √24−x when x = 6 in simple radical form is 3*√2.

Simply put, simplifying a radical eliminates the need to find any further square roots, cube roots, fourth roots, etc.

Additionally, it entails eliminating any radicals from a fraction's denominator.

The square root of 2 or root 2 is represented using the square root symbol √ and written as √2 whose value is 1.414.

So, we have:

√24−x when x = 6
Thus we must now calculate the square root of 18.

The square root, if you're allowed to use a calculator, is 4.242.

If not, however, let's come as close as we can:

√(9 * 2)

Since 3 is the square root of 9:

3*√2

Therefore, given √24−x when x = 6 in simple radical form is 3*√2.

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Answer:

x = 50

Step-by-step explanation:

we have 110, so

180 - 110 = 70

sum of all angles is 180

60 + 70 + x = 180

x = 180 - 60 - 70

x = 50

Therefore, option (c)normality assumption is checked when looking at a  Q–Q plot in one-way ANOVA model.

In statistics, a Q–Q plot is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. A point on the plot corresponds to one of the quantiles of the second distribution plotted against the same quantile of the first distribution

Here,

normality assumption is checked when looking at a Q–Q plot in one-way ANOVA model.

Explanation: The core tenet of the assumption of normality states that the sample mean distribution (across independent variables) is normal. Technically speaking, the Assumption of Normality asserts that the mean's sampling distribution or the distribution of means among samples is normal.

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Answer:(29.85km/h)

Step-by-step explanation:

1000m=1km

200m=x  [x=(200m/1000m)x1km]

x=0.2km

3600second= 1 hour  

24 seconds =b   [b=(24s/3600s)x1 hour ]

b=0.0067(in 2 decimal place)

velocity in km/h will be

0.2km/0,0067secs

=29.85(in 2 decimal place)

Answer:

speed = 30 km/h

Step-by-step explanation:

We are told that a 200 metres race is run by an athlete in 24 seconds. The question then asks us to calculate the athlete's speed in km/h.

To do this, let's first convert the given data into the required units:

• Converting from metres to kilometres:
To convert from 200 metres to kilometres, we have to divide it by 1000:

200 m = 200 m ÷ 1000 m/km

           = 0.2 km

• Converting from seconds to hours:
To convert 24 seconds to hours, we have to divide it by 3600:

24 s = 24 s ÷ 3600 s/h

        = [tex]\frac{24}{3600}[/tex] h

Now that we have the data in the appropriate units, we can use the following formula to calculate speed:

[tex]\boxed{\mathrm{speed = \frac{distance}{time}}}[/tex]

⇒ speed = [tex]\mathrm{\frac{0.2 \ km}{24/3600 \ h}}[/tex]

⇒ speed = 30 km/h

Therefore, the speed of the athlete is 30 km/h.

Answer:

x = 40°

y = 35°

Step-by-step explanation:

Let us take two triangles ∆ABC and ∆ADE

We know that, in a triangle the sum of all angles is equal to 180°

So,

For the traingle ABC

Now,

m∠A + m∠B + m∠C = 180°

80° + 60° + x° = 180°

140° + x° = 180°

x° + 140° - 140° = 180° - 140°

x = 40°

For the triangle ADE

Now,

m∠A + m∠D + m∠E = 180°

80° + 65° + y° = 180°

145° + y° = 180°

y° + 145° - 145° = 180° - 145°

y = 35°

Thus, The value of x and y is 40° and 35° respectively

Answer:

a₂₅ = 157

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 13 and d = 6 , then

a₂₅ = 13 + (24 × 6) = 13 + 144 = 157

The value of ∠WXY = 20.

What is Exterior angle theorem?

The exterior angle theorem describes the connection between the two remote angles in a triangle and the external angle created by an extended side outside the triangle.

Given: Measure of angle YWX = (3x + 17) °

Measure of angle WXY = (3x + 2) °

Measure of angle XYZ = (10x − 5) °

Therefore, m∠XYZ = m∠YWX + m∠WXY (exterior angle theorem)

⇒ (10x − 5) ° = (3x + 17) ° + (3x + 2) °

Solve for x,

⇒ 10x - 5 = 3x + 17 + 3x + 2

⇒ 10x - 6x = 17 + 7

⇒ 4x = 24

⇒ x = 6

∴ ∠WXY = (3x + 2) = 18 + 2 = 20

Hence, value of ∠WXY = 20.

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Answer:

B) 4%

Step-by-step explanation:

The total is

.8 + 4 + .2 = 5

[tex]\frac{r}{t}[/tex] = [tex]\frac{.2}{5}[/tex] = 0.04 = 4%  To change a decimal to a percent multiply by 100%