what is the domain and range of this function. ​

Answer:

this equation has 1 answer

Step-by-step explanation:

x = 2

Answer:

I think its 144!!!!!!!!!!!!!!!!!!

Answer:

Diagram 2  (Bottom diagram)

Step-by-step explanation:

The ratio is twice as many (2)

2:1

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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The total cost of the items purchased at each store is $68, $52, and $72 respectively.

The total bill at each store can be found by using matrix multiplication. We will create a matrix of the costs of each item, and then multiply it by a matrix of the amounts of each item purchased. The resulting matrix will give us the total cost of the items purchased.

Let x be the matrix of costs per item:

x = [[5, 2.5, 2, 3],

    [4, 2.75, 1.5, 2],

    [6, 3, 1.75, 3.5]]

Let y be the matrix of amounts of items purchased:

y = [[6, 3, 2, 5]]

We can then find the total cost at each store by multiplying x and y together:

xy = [[68, 36.75, 29, 45.5],

     [52, 28.25, 21, 30],

     [72, 40, 33.5, 52.5]]

Interpreting the solution with context to the application, we can see that the total cost of the items purchased at each store is $68, $52, and $72 respectively.

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Answer:

The 95% confidence interval for the true difference between the mean times on this course for teams of Siberian Huskies and teams of other breeds of sled dogs is (-0.8276, 0.2276).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.  

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Siberian Huskies:

Sample of 47, mean of 5.2 minutes, standard deviation of 1.4. So

\(\mu_1 = 5.2\)

\(s_1 = \frac{1.4}{\sqrt{47}} = 0.2042\)

Others:

Sample of 39, mean of 5.5 minutes, standard deviation of 1.1. So

\(\mu_2 = 5.5\)

\(s_2 = \frac{1.1}{\sqrt{39}} = 0.1761\)

Distribution of the difference:

\(\mu = \mu_1 - \mu_2 = 5.2 - 5.5 = -0.3\)

\(s = \sqrt{s_1^2+s_2^2} = \sqrt{0.2042^2+0.1761^2} = 0.2692\)

Confidence interval:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = zs\)

In which s is the standard error. So

\(M = 1.96(0.2692) = 0.5276\)

The lower end of the interval is the sample mean subtracted by M. So it is -0.3 - 0.5276 = -0.8276.

The upper end of the interval is the sample mean added to M. So it is -0.3 + 0.5276 = 0.2276

The 95% confidence interval for the true difference between the mean times on this course for teams of Siberian Huskies and teams of other breeds of sled dogs is (-0.8276, 0.2276).

Answer:

rectangle that measures 22cm x

25cm

A rectangle that measures 22cm x 25cm is more square.

The area of a rectangle is defined as the product of the length and width.

The area of a rectangle = L × W

To determine which rectangle is more square, we need to compare their aspect ratios, which is the ratio of the length to the width of the rectangle. A rectangle is considered to be more square when its aspect ratio is closer to 1.

In the first rectangle, the aspect ratio is 35cm/39cm = 0.897. In the second rectangle, the aspect ratio is 22cm/25cm = 0.88. Since the aspect ratio of the second rectangle is closer to 1, it is considered to be more square.

It's worth mentioning that a square is a special type of rectangle where all four sides are equal in length. So, if we compare the rectangles with a square, the rectangle that measures 22cm x 25cm is less square than a square with a side length of 22cm or 25cm.

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Answer:

x/16 + 10

Step-by-step explanation:

10+(x÷16)

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times 16/16.

10 x 16 / 16 + x/16

Since 10 x 16 / 16 and x/16 have the same denominator, add them by adding their numerators.

10 x 16 + x / 16

Do the multiplications in 10×16+x.

160 + x / 16 = x/16 + 10

The next three numbers here would be 0, 10, 1011, 1031, 102113, 10311213, 10411223, 1031221314, 1041222314.

The term number sequence is used to refer to the list of numbers that have the relationship of having a linked rule. The number that follows in the sequence has to be worked out from the previous numbers in that particular sequence. You have to follow the particular rule to be able to work out the number that has to follow in the sequence.

For example we have these numbers 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 etc. We would have to understand the pattern of numbers that are in the sequence. We can see that there is a difference of 3 between the number that succeeds the previous one in the sequence.

The first value here is given to be 0

Next we have the 1 0 = 10

The next that we have is 1 0 and 1 1 written as 1011

Next is 1 zero and three one = 1031

We continue to follow the pattern till we arrive at 1041222314. This is where the sequence would then have to stop.

Hence we have to conclude that the next numbers are 10411223, 1031221314, 1041222314.

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Answer:

C - No, the graph does not make a straight line.

Step-by-step explanation:

Just did on edg

There is no proportional relationship between the time and the amount of popcorn popped.

No, the graph does not make a straight line.

Option C is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

A graph has minutes on the x-axis and ounces of popcorn on the y-axis and goes through the following coordinates.

(0,0), (50, 12), and (110, 18)

This means,

For 0 minutes, 0 ounces of popcorn.

For 50 minutes, 12 ounces of popcorn.

For 110 minutes, 18 ounces of popcorn.

50 minutes = 12 ounces

Divide 50 on both sides.

1 minute = 12/50 ounces

1 minute = 0.24 ounces ____(1)

110 minutes = 18 ounces

Divide 110 on both sides.

1 minute = 18/110 ounces

1 minute = 0.16 ounces ____(2)

From (1) and (2) we see that there is no proportional relationship between the time and the amount of popcorn popped.

Thus,

There is no proportional relationship between the time and the amount of popcorn popped.

No, the graph does not make a straight line.

Option C is the correct answer.

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Answer: \((f \cdot g)(x) = x^4-11x^2+30.\)

Step-by-step explanation:

We want to find the value of \(f(g(x)).\) To do this, we plug in \(g(x)\) into the expression for \(f(x).\) This gives us:

\(f(g(x)) = (x^2-9)^2+7(x^2-9)+12 = x^4-18x^2+81+7x^2-63+12 = \boxed{x^4-11x^2+30}.\)

Answer:

5/12 (five-tweltfhs)

Step-by-step explanation:

4/6 - 3/12 = 5/12

4 x 2  = 8

-------   -----

6 x 2  = 12

8/12 - 3/12 = 5/12

Answer:

All the engine fan blades must be replaced

Step-by-step explanation:

From the question we are told that:

Sample size \(n=71\)

\(\sigma^2 = 0.18 mm2\)

Variance \(s^2=0.32\)

Level of significance \(\alpha =0.01\)

Generally the hypothesis is

The test hypothesis is

Null \(H_0:\sigma^2<=0.18\)  

Alternative \(Ha:\sigma^2>0.18\)

Generally the equation for Chi distribution  is mathematically given by

The test statistic is  

\(X^2 = \frac{(n-1)*s^2}{\sigma^2}\)  

\(X^2={70*0.32}{0.18}\)  

\(X^2= 124.4\)

Since

Critical Value

\(C_{\alpha, df}=C_{0.99 , 70}\)

\(C_{0.99 , 70} =100.4252\)

Hence, we Reject \(H_0\) ,Given that 124.4 is Greater than 100.4252

Therefore

All the engine fan blades must be replaced

The value of cos(45°) is √2/2. The correct answer choice is D. √2.

In the given diagram, the angle labeled as 45° is part of a right triangle. To find the value of cos(45°), we need to determine the ratio of the adjacent side to the hypotenuse.

Since the angle is 45°, we can assume that the triangle is an isosceles right triangle, meaning the two legs are congruent. Let's assume the length of one leg is x. Then, by the Pythagorean theorem, the length of the hypotenuse would be x√2.

Now, using the definition of cosine, which is adjacent/hypotenuse, we can substitute the values:

cos(45°) = x/(x√2) = 1/√2

Simplifying further, we rationalize the denominator:

cos(45°) = 1/√2 * √2/√2 = √2/2

Therefore, the value of cos(45°) is √2/2.

The correct answer choice is D. √2.

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Answer:

Yes 20

Step-by-step explanation:

3 add 2 is 5. The circle means times by. 5 times by 4 is 20

Answer:

You hav elearned order or perations yes, well first you would(in this equation) multiply 2 and 4together to get 8 then add 8 and 3 to get 11 the correct answer is b

Step-by-step explanation:

Answer:

Option A is correct

Step-by-step explanation:

Given: FH is the altitude to the hypotenuse EG

To find: length of FH

Solution:

According to Pythagoras theorem, square of hypotenuse is equal to sum of squares of other two sides.

In \(\Delta EHF\),

\(\angle EHF=90^{\circ}\)

So,

\(EF^2=EH^2+FH^2\)

Put EH = 6 units and EF = 7 units

\(7^2=6^2+FH^2\\49=36+FH^2\\49-36=FH^2\\13=FH^2\)

Option A is correct

Take square root on both sides

\(FH=\sqrt{13}=3.606\,\,units\)

Answer:

x = 6.24

Step-by-step explanation:

x =

Tan32° = OPP/ADJ

Tan32° = x/10

0.624 = x/10

cross-multiply

x = 6.24

Step-by-step explanation:

As a salesperson at Scrapbooks and Treasures, Alysse receives a monthly base pay plus commission on all that she sells. If she sells $400 worth of merchandise in one month, she is paid $292. If she sells $800 of merchandise in one month, she is paid $384.

Here is the salary function used to represent this situation in terms of the amount of merchandise sold:

s(x) = 0.23x + 200

Find Alysse's salary when she sells $2,200 worth of merchandise.

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

The location of point A''' after the three transformations would be (-4, 1).

To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.

When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.

So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).

When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).

When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).

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Answer:

4691.74

Step-by-step explanation:

A = P(1 + r/n)^nt

   = 2300(1 + .08/4)^(4 * 9)

   = 2300(1.02)³⁶

   = 2300 * 2.039887

   = 4691.74

Liz will not have saved $100,000 by age 30. As calculated using the compound interest formula, Liz will have a total of approximately $12,953.55 in her retirement account.

What is Compound Interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

To determine if Liz's goal is achievable, use the future value formula for a lump sum investment -

\(FV = PV \times (1 + r)^n\)

where:

FV = Future value of the investment

PV = Present value or initial investment

r = Annual interest rate

n = Number of years

Using the information given, plug in the values -

PV = $0 (since Liz is starting from scratch)

r = 8% per year, compounded annually

n = 10 years (since Liz wants to reach her goal by the time she's 30)

\(FV = 6,000 \times (1 + 0.08)^{10}\\FV = 6,000 \times (1.08)^{10}\)

FV = 6,000 × 2.158925

FV = 12,953.55

So after the first year of saving, Liz will have $6,000 × 1.08 = $6,480.

After 10 years of saving, she will have a total of $12,953.55 in her retirement account.

However, this falls short of her goal of $100,000. To reach her goal, Liz would need to save more per year, or invest in a higher yielding investment.

Therefore, the compound interest value is $12,953.55.

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When applying the some rule, we only combine two equal ratios at once. Consequently, we deal with pairs of sides and angles that have equivalent ratios.

When two ratios are equal, a percentage is formed; alternatively, two equal ratios can be said to produce a proportion. When we understand that two ratios are equal, you can write a proportion. The ratios of these two numbers are equal.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant. Two angles are said to be complimentary if their sum is 90 degrees. Alternatively put, two angles are said to be complimentary if they combine to make a right angle.

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Answer:

10 ? or 7.6 ?

(not 100% sure)

The resulting graph is a circle with center at (-3,-1) and radius 3.

The graph of the equation (x+3)²+(y+1)²=9

is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.

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Answer:

14 millimeters

Step-by-step explanation:

V=(4/3)πr³

1372π(1/3)=(4/3)πr³

1372=4r³        (cancel out the pi and multiply both sides by 3)

r³=343

r=7

Diameter is twice the radius = 2(7) = 14

The equation below that does not show equivalent expressions when y = 2, is  5y + 25  = 5 ( y + 4 ).

option C.

The equation below that does not show equivalent expressions when y = 2, is determined by solving for y in all the given equation.

y + 4y  = y ( 1 + 4 )

y + 4y = y + 4y

5y = 5y

y = y

y + y + y = 3y

3y = 3y

y = y

5y + 25  = 5 ( y + 4 )

5y + 25 = 5y + 20

5y + 5 = 5y

5 ( y + 1 ) = 5y

y + 1 = y

2 (y + 2 ) = 2y + 4

2y + 4 = 2y + 4

2y = 2y

y = y

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