I need help evaluating this equation?

Answer:

a.36

b.8.5

c.2.5

d.6

e.9

f.8

Step-by-step explanation:

(f o g)(x)

= f(x - 3)

= 2(x - 3) + 1 = 2x - 5.

Hence (f o g)(-2) = 2(-2) - 5 = -4 - 5 = -9.

Answer:

-1/2 > x

Step-by-step explanation:

−2x − 4 > 8 x −6 x −2

Combine like terms

-2x -4 > 2x -2

Add 2x to each side

−2x+2x − 4 > 2x+2x −2

-4 > 4x-2

Add 2 to each side

-4 +2 > 4x -2 +2

-2 >4x

Divide each side by 4

-2/4 > 4x/4

-1/2 > x

Since the y-intercept of the line is (0,1) and the line passes through the point (2,4) which is also satisfied by the equation of the line, the given equation represents the graph of the line.

The slope-intercept form of a line is y = mx +c where m is the slope of the line and c is the y-intercept.

The given equation of the line is y = (3/2)x + 1.

To find the y-intercept of the line, substitute x = 0 into the given equation,

y = (3/2)(0) + 1

y = 1

Note that the y-intercept of the graph of the line is also 1.

The graph of the line passes through points (2,4).

To verify whether the equation satisfies the coordinates of (2,4) or not, substitute the coordinates of the point into the given equation:

4 = (3/2)(2) + 1

4 =4

The equation is true.

Hence, it can be said that the given equation represents the graph of the line.

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Answer:

Solution: g > 9

Interval Notation: (9 , ∞)

Step-by-step explanation:

-3 * (6-2g) > 4g

-18 + 6g > 4g

6g - 4g > 18

2g > 18

g > 9

The equations where b = 11 are A, B, C, D, and E. All of these equations are true when b = 11.

To point an equation on a graph, first, determine the equation and its variables. Then, plot the points of the equation on the graph by substituting the variable values and plotting the corresponding points. To find the equation’s slope, calculate the rise and run of two points on the graph. The slope is used to draw a line of best fit. Finally, draw a line that intersects the points of the equation and the line of best fit. This will be the equation’s graph.

Choice A states that 2b = 2112, b, equals, 211, which means that 2 times 11 is equal to 21. Choice B states that b + 18 = 7b, plus, 18, equals, 7, which means that 11 plus 18 is equal to 7. Choice C states that 77 = 7b77, equals, 7, b, which means that 77 divided by 7 is equal to 11. Choice D states that 9 = b − 29, equals, b, minus, 2, which means that 11 minus 2 is equal to 9. Finally, Choice E states that 11 = 33 ÷ b11, equals, 33, divided by, b, which means that 33 divided by 11 is equal to 11. Therefore, all of these equations are true when b = 11.

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Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

The money loaned at 9% annual interest was 1500 and the money loaned at 11% annual interest was 19000.

Let the amount of money loaned at 9% be x

the amount of money loaned at 11% be y

According to the question,

Total money loaned = 20,500

Thus the equation formed is,

x + y = 20,500 ------ (i)

Simple interest is calculated by

I = P * r * t

where I is the simple interest

r is the rate of interest

t is the time

Thus, the interest on x = 0.09x

the interest on y = 0.11y

Total interest gained = 2,225

Thus the equation formed is,

0.09x + 0.11y = 2225 -------(ii)

Multiply (i) by 0.09

0.09x + 0.09y = 1845

Subtract the above from (ii)

0.02y = 380

y = 19000

x = 1500

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Answer:

Step-by-step explanation:

5x + 10 + 10x + 5 = 180

15x + 15 = 180

15x = 165

x = 11

The point which could represent the player catching the ball is: C. (4, 25).

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

By critically observing the graph (see attachment) which models the given data, we can reasonably infer and logically deduce that the point (4, 45) where the "Distance from Goal" on the y-axis intersect with the "Time after Throw" on the x-axis represents the player catching the ball.

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Answer: 4, 25

Step-by-step explanation:

Answer:

By opting for the second option, Alice would save $ 15,740.00  in total mortgage cost

Step-by-step explanation:

In order to determine the better of the two options available, we need to determine the total cost under each option as follows:

Option 1:

cost of house=$625,000

loan amount=$625,000-(20%*$625,000)=$500,000

loan amount=monthly payment*(1-(1+r)^-n/r

monthly payment is the unknown

r=monthly interest rate=4%/12=0.33333333%

n=number of monthly payments in 30 years=30*12=360

500,000=monthly payment*(1-(1+0.33333333% )^-360/0.33333333%

500,000=monthly payment*(1-0.301795869 )/0.003333333

500,000=monthly payment*0.698204131 /0.003333333

monthly payment=500,000*0.003333333 /0.698204131

monthly payment=$ 2,387.08  

total monthly payments=$ 2,387.08*360=$859,348.80

Option 2:

upfront fee=$10,000

loan amount=monthly payment*(1-(1+r)^-n/r

monthly payment is the unknown

r=monthly interest rate=3.75%/12=0.3125%

n=number of monthly payments in 30 years=30*12=360

500,000=monthly payment*(1-(1+0.3125%  )^-360/0.3125%

500,000=monthly payment*(1-0.325222459  )/0.003125

500,000=monthly payment*0.674777541  /0.003125  

monthly payment=500,000*0.003125  /0.674777541=$2,315.58  

Total cost=total monthly payments+upfromt fee

total cost=($2,315.58 *360)+$10,000=$843,608.80  

savings by opting for the second option=$859,348.80-$843,608.80  

The fraction of their money remains for other expenses each month is 5/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

Williams spend 1/3 of their total monthly income for rent and 1/4 for food.

The fraction of their money remains for other expenses each month,

= 1 - 1/3 - 1/4

= 5/12

Therefore, 5/12 is the remaining money.

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Answer:

56 degrees

Step-by-step explanation:

Here, I think you just accidentally put the value for the angle ZWX, which would be ZWP+PWX(56+56).

You actually already wrote it on the paper, so nothing wrong with your math here, just a thinking error :)

start by bringing all b's to one side of the equation and all constants to the other

simplify both sides, remembering that 1 can be written as 3/3

since the fractions have the same denominator, we mantain the denominator and add the numerator together

multiply both sides by 3

divide both sides by 5

The joint relative frequency is calculated by dividing the frequency of a specific subset (in this case, the number of adults who prefer watermelon) by the total number of data points.

Here, the specific subset is adults who prefer watermelon, which is 111. The total number of data points is the sum of all children and adults, regardless of fruit preference, which is 445.

So, to find the joint relative frequency of being an adult who prefers watermelon, you would divide 111 by 445.

Hence, the correct answer is:

C. Divide 111 by 445.

A confidence interval that will capture the true population mean with 95% confidence. The value is ( 23.6459    , 24.8293 ) .

What is population mean?

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment. A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

Data: 18

for given data

\($$\begin{aligned}\bar{X} & =\frac{\sum X i}{n} \\& =2448 / 101 \\& =24.2376\end{aligned}$$\)

as population variance is unknown so we used sample variance

\($$\begin{aligned}S^2 & =\frac{1}{n-1}\left(\sum X i^2-n \times \bar{X}^2\right) \\S^2 & =\frac{1}{100}\left(60232-101 \times 24.2376^2\right) \\& =8.9830\end{aligned}$$\)

Now

\(\frac{\bar{X}-\mu}{S / \sqrt{n}} \sim t_{n-1}$$\)

hence 95 % of population mean is

As n=101 which is large so critical value is 1.98397

\($$\begin{aligned}& =\left(\bar{X}-\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}, \bar{X}+\sqrt{\frac{S}{n}} \times t_{(n-1, \alpha / 2)}\right) \\& =\left(24.2376-\sqrt{\frac{8.9830}{101}} \times 1.98397,24.2376+\sqrt{\frac{8.9830}{101}} \times 1.98397\right) \\& =(23.6459,24.8293)\end{aligned}$$\)

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The time spent higher than 26 meters above the ground is 0.42 minutes. Answer: 0.42

A Ferris wheel is 30 meters in diameter and boarded from a platform that is 4 meters above the ground.

The six o'clock position on the Ferris wheel is level with the loading platform.

The wheel completes 1 full revolution in 2 minutes.

We have to find how many minutes of the ride are spent higher than 26 meters above the ground.

So, let's start with some given data,Consider the height of a person at the six o'clock position = 4 meters

So, the height of a person at the highest point = 4 + 15 = 19 meters (since the diameter is 30 meters, the radius will be 15 meters)

Also, the height of a person at the lowest point = 4 - 15 = -11 meters

Therefore, the Ferris wheel completes one cycle from the lowest point to the highest point and back to the lowest point.

So, the total distance travelled will be = 19 + 11 = 30 meters.

Also, we are given that the wheel completes 1 full revolution in 2 minutes.

We need to calculate the time spent higher than 26 meters above the ground.

So, the angle between the 6 o'clock position and 2 o'clock position will be equal to the angle between the 6 o'clock position and the highest point.

This angle can be calculated as follows:

Angle = Distance travelled by the Ferris wheel / Circumference of the Ferris wheel * 360 degrees

Angle = 30 / (pi * 30) * 360 degrees

Angle = 360 degrees / pi

= 114.59 degrees

So, the total angle between the 6 o'clock position and the highest point is 114.59 degrees.

Now, we need to find out how much time is spent at an angle greater than 114.59 degrees.

This can be calculated as follows:

Time = (Angle greater than 114.59 degrees / Total angle of the Ferris wheel) * Total time taken

Time = (180 - 114.59) / 360 * 2 minutes

Time = 0.42 minutes

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Answer:

Already rounded to the nearest thousandth.

7433654.000

Using the normal distribution, it is found that 0.4068 of crocodiles live between 17.5 and 20.5 years.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The mean and the standard deviation are given as follows:

\(\mu = 18, \sigma = 2.6\)

The proportion of crocodiles live between 17.5 and 20.5 years is the p-value of Z when X = 20.5 subtracted by the p-value of Z when X = 17.5, hence:

X = 20.5:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{20.5 - 18}{2.6}\)

Z = 0.96

Z = 0.96 has a p-value of 0.8315.

X = 17.5:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{17.5 - 18}{2.6}\)

Z = -0.19

Z = -0.19 has a p-value of 0.4247.

0.8315 - 0.4247 = 0.4068

0.4068 of crocodiles live between 17.5 and 20.5 years.

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there are 1,008 different computer systems possible, given the constraints provided.

what is constraints?

Constraints are limitations or conditions that must be satisfied in order to solve a problem or make a decision. In other words, constraints are rules or restrictions that define the boundaries within which a solution or decision must be made.

In the given question,

To determine the number of different computer systems possible, we need to multiply the number of choices for each component. This is based on the multiplication principle of counting, which states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things together.

So, for this problem, we have:

8 different choices for computers

7 different choices for monitors

9 different choices for printers

2 different choices for scanners

Using the multiplication principle, the total number of different computer systems possible is:

8 x 7 x 9 x 2 = 1,008

Therefore, there are 1,008 different computer systems possible, given the constraints provided.

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Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Answer:

\(cos\theta=\frac{3}{5}\)

Step-by-step explanation:

Since \(sin\theta=0.8\) is the same as \(sin\theta=\frac{4}{5}\) and \(sin\theta=\frac{opposite}{hypotenuse}\), then we know that the side opposite to the angle \(\theta\) is 4 units and the hypotenuse is 5 units.

Because \(cos\theta=\frac{adjacent}{hypotenuse}\), then we have to find the adjacent side to the angle \(\theta\) using the Pythagorean Theorem:

\(a^2+b^2=c^2\\\\(adjacent)^2+(opposite)^2=(hypotenuse)^2\\\\(adjacent)^2+4^2=5^2\\\\(adjacent)^2+16=25\\\\(adjacent)^2=9\\\\adjacent=3\)

Therefore, since the adjacent side is 3 units, then \(cos\theta=\frac{3}{5}\)

More than once a week: 0.11

Once a week: 0.51

Every other week: 0.26

Every three weeks: 0.05

Less often than every three weeks: 0.07

To make a relative frequency distribution, follow these steps:

Count the number of occurrences of each category in the data. In this case, 11% of the 251 participants responded "more than once a week", so the number of occurrences for this category is 0.11 * 251 = 27.61 (rounded to 28). Similarly, 51% of the participants responded "once a week", so the number of occurrences for this category is 0.51 * 251 = 127.51 (rounded to 128). And so on for the other categories.

Divide the number of occurrences for each category by the total number of participants. In this case, the total number of participants is 251, so the relative frequency for "more than once a week" is 28 / 251 = 0.11. The relative frequency for "once a week" is 128 / 251 = 0.51. And so on for the other categories.

And that's it! These are the relative frequencies for each category in the data.

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Answer:

Hello! answer: x = 15

Step-by-step explanation:

Here is a visual i created of what the complementary angle would look like!

Step-by-step explanation:

D(.10) + Q(.25) = 4

I think

Answer:

D(.10) + Q(.25) = 4

Step-by-step explanation:

Step-by-step explanation:

f(x) = 3x² - 2x + 8 , x = 3

f(3) = 3.3² - 2.3 + 8

= 27 - 6 + 8

= 29

Answer: A. $15.5

B. 1:10 pm

Step-by-step explanation:

A. We will use the formula,

y = kx

where,

y = cost of turkey = $21.36

x = weight of turkey = 24.1lb

k = constant of proportionality

Therefore,

21.36 = 24.1k

k = 21.36/24.1

k = 0.8863

A 17.5 lb turkey would then cost:

= 17.5 × 0.8863

= $15.5

B. A stuffing recipe takes 40 min to bake. A sweet potato pie recipe takes twice as long as the stuffing recipe. If a sweet potato pie goes in the oven at 11:50 am, what time will the sweet potato pie be done baking?

Since the sweet potato pie recipe takes twice as long as the stuffing recipe. This means it'll take:

= 2 × 40minutes

= 80 minutes

= 1 hour 20 minutes

When the sweet potato pie goes in the oven at 11:50 am, the time that it will take the sweet potato pie to be done baking will then be:

= 11.50 am + 1 hour 20 minutes

= 01:10 pm

Answer:

..........

Step-by-step explanation:

needs points out of them srry

Answer:

B)

Step-by-step explanation:

They are intersected to make a same side interior angle.

Answer:

A) alternate interior angles are always congruent.