Paul came in with a discovery about subtracting integers. Rather than subtracting, Paul says all he has to do I add the opposite of the second number, Create a subtraction problem with integer tiles and check out Paul's claim. Is paul right?

The zeros of f(x)= x²-9 is +3 and -3

The zeros of f(x) = x²-16 is +4 and -4

An asymptote is a line that the graph of a function approaches as either x or y go to positive or negative infinity. There are three types of asymptotes: vertical, horizontal and oblique. Vertical Asymptotes.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0.

Therefore when f(x) =0

x²-9 = 0

x² = 9

x =√9

x = ±3

therefore the zeros of x²-9 is ±3

The vertical asymptote is 0 and horizontal asymptote is infinity.

x²-16 = 0

x² = 16

x = √16

x = ±4

the vertical asymptote is 0 and horizontal asymptote is infinity.

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Answer:

option A is the correct answer.

Answer: The inverse of the function y = 2^x^2 - 4 is not a function because it is not a one-to-one function.

Step-by-step explanation:

The inverse of a function is a reflection of the original function over the line y = x. To find the inverse of the function y = 2^x^2 - 4, we need to switch the variables x and y and then solve for x.

y = 2^x^2 - 4

x^2 = log2(y + 4)

x = sqrt(log2(y + 4))

However, this expression is not the inverse of the original function because it is not a one-to-one function, meaning that the same output can have multiple inputs. For example, log2(10) = 3 and log2(14) = 3.5, so sqrt(log2(10)) = sqrt(3) = sqrt(log2(14)) = sqrt(3.5). This means that for y = 10, x can be either sqrt(3) or sqrt(3.5), which is not allowed in a function.

Therefore, the inverse of the function y = 2^x^2 - 4 is not a function.

Answer:480

Step-by-step explanation

Answer:

he inequality to determine the years in which more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher is:

0.48t + 18 > 40

Subtracting 18 from both sides:

0.48t > 22

Dividing both sides by 0.48:

t > 45.83

So, for years t greater than 45.83, more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher.

Step-by-step explanation:

Answer:

102.4 square feet

Step-by-step explanation:

1. divide 32 by 5 to find how much square feet one bag of mulch covers

2. multiply that number (6.4) by 16 to find how many square feet 16 bags of mulch would cover

Answer:102.4 ft

Step-by-step explanation: do the math 32/5 = 6.4 6.4x16=102.4 ft

A total of 77 new flowers can be planted on the flower bed.

New flowers has to be planted in a circular flower bed that has a diameter of 14 ft.

Each one of the flower requires to square feet of the space.

The radius of the flower bed will be 7 feet.

The area of the flower bed can be calculated by using the formula,

A = πr²

Where r is the radius.

Put in the value of radius to find the area of the flower bed,

A = 3.14 x 7 x 7

A = 153.86 ft²

Now, let us say that N number of floors can be planted,

So,

N)(2) = 153.82

N = 76.93

So we can say that about 77 flowers can be planted on the flower bed.

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Answer: Y would be 4

If you look at the graph and find 7 on the x axis where the inputs are, you can see that if you go up, the only output for 7 is 4.

Answer:

Step-by-step explanation:

Part A
First find the measure of angle C which is 52° due to it being next to angle D

Next add 52 to angle B to get 142

Subtract 142 from 180 to get 38°

Angle A is 38°

Part B

The fourth option is correct

By determining the value of x when y = 0, (x, 0), and the value of y when x = 0, respectively, the x-intercept and y-intercept are determined (0, y).

A two-variable equation with a line-shaped graph is referred to as a linear equation. A collection of coordinate plane points that are all the solutions to the linear equation make up the graph. If all of the variables have true numerical values, the equation can be graphed by first drawing a sufficient number of points to identify a pattern, then connecting those points to include all of the points.

A linear equation is represented in standard form as

Ax+By=C,A,B≠0

The equation for y must first be solved before you may graph a linear equation in its usual form.

The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y).

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Answer:

[tex]\huge\boxed{\sf S=\frac{20}{6} \pi \ mm}[/tex]

Step-by-step explanation:

Radius = r = 10 mm

Degree = θ = 60°

Arc length = S = ?

[tex]\displaystyle S=\frac{\theta}{360} \times 2 \pi r[/tex]

Insert the values in formula.

[tex]\displaystyle S = \frac{60}{360} \times 2 \pi (10)\\\\S=\frac{1}{6} \times 20 \pi\\\\S=\frac{20}{6} \pi \ mm\\\\\rule[225]{225}{2}[/tex]

Factors other than independent variables which may act on the dependent variable , when these factors vary systematically with independent variable they are known as confounds variables or extraneous variable.

Therefore, factors which vary systematically with the given independent variable is called  confounds variables or extraneous variable.

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Answer:

  height = 2/5h

Step-by-step explanation:

You want the height of a frustum if the volume of the frustum is 98/125 times the volume of the original cone, which was of height h.

Let h' represent the height of the part of the cone that is removed to leave the frustum. Then its volume (v') is ...

  v' = (volume of large cone)(1 - 98/125) = v·(27/125)

The scale factor between h' and h is ...

  (h'/h)³ = v'/v = 27/125

  h'/h = ∛(27/125) = 3/5

The height of the frustum in terms of the height of the original cone is ...

  frustum height = (height of large cone) - (height of small cone)

  frustum height = h - (3/5)h

  frustum height = 2/5h

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The following statements best explains the steps to solve the pair of equations graphically is Option D.

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

The first equation is:

y = -x +1

so the slope is -1, and the y-intercept is +1.

The second equation is:

 y = 2x +4

so the slope is 2, and the y-intercept is 4.

The slopes and intercepts are properly described in the last selection.

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The complete question:

A pair of linear equations is shown below:

y = -x + 1

y = 2x + 4

Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)

On a graph, plot the line y = -x + 1, which has y-intercept = -1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of

Intersection of the two lines as the solution.

On a graph, plot the line y = -x + 1, which has y-intercept - 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of

intersection of the two lines as the solution.

On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = -2 and slope = 2, and write the coordinates of the point

of intersection of the two lines as the solution.

On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of

intersection of the two lines as the solution.

Answer: look it up frfr

Step-by-step explanation:

The rounding off the value 0.1347 to the nearest tenth is 0.1

What is rounding off?

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done.

The act of rounding off is merely an estimation. Rounding off is the process of estimating an actual number to a close number.

Given, 0.1347 round to the nearest tenth

While rounding to the nearest tenth, the value after the digit has been noticed.

In the number 0.1347, rounding to the nearest tenth, digit 3 should play a role to round the digit 1 which is in the tenth position. 3 is not equal to 5 and less than 5.

So, 0.1347 becomes 0.1

Hence, the required answer is 0.1

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The number of millions of bacteria when the temperature is 38°C is 7, 600, 000 bacteria

Proportion can simply be defined as a mathematical comparison of numbers.

The different types of proportion in mathematics are;

From the information given, we have that;

When the temperature was 35 degree Celsius, the number was 7 million

Then, we have the representation given as;

35°C = 7, 000, 000

Then 38°C = x

cross multiply, we get;

x = 7, 000, 000 × 38/35

divide the values

x = 7, 600, 000 bacteria

Hence, the value is 7, 600, 000 bacteria

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Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

The formula for Percent Decrease is: Decreased Value = (Original Value – New Value)/Original Value.

The computation of our Percent Decrease:

= (64 - 21)/61 * 100

= 70.49%

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The constant of proportionality (r) in the equation y = rx represents the rate of change of y with respect to x, indicating the factor by which x and y are related.

The constant of proportionality (r) in the equation y = rx is simply the coefficient in front of the x term. In this case, r is the constant of proportionality, and it represents the rate at which y changes as x changes. In other words, it gives the relationship between x and y, such that y is directly proportional to x with a constant of proportionality of r.

So, in the equation y = rx, the value of r is the constant of proportionality.

In a direct proportion, if x increases, then y also increases, and if x decreases, then y decreases as well. The constant of proportionality (r) gives us the factor by which x and y are related.

For example, if y is equal to twice x (y = 2x), then the constant of proportionality (r) is 2. If x increases by 1 unit, y increases by 2 units, and if x decreases by 1 unit, y decreases by 2 units. The constant of proportionality in this case is 2.

In the equation y = rx, the variable x represents the input and y represents the output. The constant of proportionality (r) tells us how much y changes for a unit change in x. It can be thought of as the ratio of the change in y to the change in x. The constant of proportionality can also be expressed as the slope of a line that represents the relationship between x and y.

In summary, the constant of proportionality (r) in the equation y = rx gives us the factor by which x and y are related and represents the rate of change of y with respect to x.

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The point of symmetry on f⁻¹(x) is (4, 6) which is false.

The domain of f(x) is (-∞, 4) which is false.

The graphs of f(x) and f(x) are reflections across the x-axis which is also false.

The range of f⁻¹(x) is (- ∞, ∞) which is true.

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The function is given below.

f(x) = 5(x - 6)³ + 4

The inverse function of the function f(x) is given as,

x = 5(y - 6)³ + 4

y = ∛[(x - 4) / 5] + 6

f⁻¹(x) = ∛[(x - 4) / 5] + 6

The graph of the function and inverse function is given below.

The point of symmetry on f⁻¹(x) is (4, 6) which is false.

The domain of f(x) is (-∞, 4) which is false.

The graphs of f(x) and f(x) are reflections across the x-axis which is also false.

The range of f⁻¹(x) is (- ∞, ∞) which is true.

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The Roth IRA will provide Ethan with the most future benefit, with the IRA valued at $195,902.08 and the Roth at $211,633.75. The difference in the future value of the two accounts is $15,731.67.

A purchase made with the intention of creating income or capital growth is known as an investment. An asset's value increasing over time is referred to as appreciation. When a person invests in a thing, they do not intend to utilise it as a source of immediate consumption, but rather as a tool for future economic growth.

The Roth IRA will provide Ethan with the most future benefit. The IRA will be valued $195,902.08 after 30 years, while the Roth IRA will be worth $211,633.75. As a result, the Roth IRA is valued $15,731.67 more than the IRA.

To determine the IRA's future value, use the formula FV = P(1+r)n, where P is the monthly payment, r is the interest rate, and n is the number of periods (in this case, 30 years). With our data in, we get: FV = 416.66(1+0.025)30 = $195,902.08.

We may apply the same approach to compute the future value of the Roth IRA, but with a $5,000 yearly payout. With our values in, we get: FV = 5000(1+0.025)30 = $211,633.75.

The difference in the future value of the two accounts is $15,731.67, which is the amount that the Roth IRA will be worth more than the IRA.

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Answer:

A large container is a better deal because for a large container the amount of jam per dollar is greater thank that in the three smaller containers.

Step-by-step explanation:

What is the volume of a cylinder?

The volume of a cylinder is given by -

V[c] = πr²h

Given is Terrel who has to buy either one large jar or three small jars of jam. A small jar has a diameter of 6 cm, a height of 7 cm, and costs $4. A large jar has a diameter of 8 cm, a height of 16 cm, and costs $12.

For one large container, its volume will be -

V[L] = πr²h = 22/7 x 4 x 4 x 16 = 804.56 cm³

Amount of jam per dollar = V[1] = 804.56 / 12 = 67.04 cm³

For three small containers, the total volume will be -

V[S] = πr²h = {22/7 x 3 x 3 x 7} x 3 = 594 cm³

Amount of jam per dollar = V[2] = 594 / 12 = 49.5 cm³

It can be seen that for a large container the amount of jam per dollar is greater than that in the three small container. Hence, a big container would be a better deal for Terrell.

Therefore, a large container is a better deal because  for a large container the amount of jam per dollar is greater than that in the three small container.

Answer:

Step-by-step explanation:

buy one large jar has which has a diameter of 8 cm, and a height of 16 cm.

The value of x, y and z in the trapezoid are solved to be

x = 6.3

y = 6.7

z = 5

This is a term used in geometry to mean that the respective sides of the polygons are proportional and the corresponding angles of the polygon are congruent

Hence assuming the corresponding angles of the polygon are congruent then the side should be in proportions

Examining the figure the constant of proportionality from the quadrilateral  is

10 / 24 = 0.417

hence we solve for the dimensions as follows

x = 16 * 0.417 = 6.3

y = 16 * 0.417 = 6.67

z = 12 * 0.417 = 5

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The mean waiting time for 40 patients is 44.10 minutes. The median waiting time is 43.5 minutes. The mode waiting time is 42 minutes.

The mean waiting time for these 40 patients is calculated by adding up all the waiting times and dividing by the number of patients, which gives:

(mean) = (46+49+40+44+45+45+38+51+45+42+46+41+41+48+42+49+49+40+43+42+41+43+42+41+55+43+42+40+42+40+49+43+44+45+61+37+49+40+42+43+43+42+41+41+55+43+42+40+42+40+49+43+44+45+61+37+43+40+37+39)/40 = 44.10

Therefore, the mean waiting time is 44.10 minutes.

To find the median waiting time, we first need to order the waiting times from lowest to highest:

37, 37, 38, 39, 40, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 43, 43, 44, 44, 45, 45, 45, 46, 46, 48, 49, 49, 49, 49, 51, 55, 55, 61, 61

We can see that there are 40 waiting times in this sample, which is an even number. The median is the average of the two middle values, which are 43 and 44. Therefore, the median waiting time is:

(median) = (43+44)/2 = 43.5

The median waiting time is 43.5 minutes.

The mode is the most common value in the data set. In this case, we can see that the waiting time of 42 minutes appears most frequently in the data set, occurring 6 times. Therefore, the mode waiting time is:

(mode) = 42

The mode waiting time is 42 minutes.

The first quartile (Q1) is the value below which 25% of the waiting times fall, and the third quartile (Q3) is the value below which 75% of the waiting times fall. To find these values, we first need to order the waiting times from lowest to highest (as we did in part b):

37, 37, 38, 39, 40, 40, 40, 40, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 43, 43, 44, 44, 45, 45, 45, 46, 46, 48, 49, 49, 49, 49, 51, 55, 55, 61, 61

There are 40 waiting times in the data set, so to find the first quartile, we need to find the value below which 25% of the waiting times fall. This means we need to find the waiting time that is at the 25th percentile. We can do this by finding the index of the waiting time that is at the 25th percentile:

25th percentile = (25/100) * 40 = 10

This means that the waiting time at the 10th index in the ordered list is the value at the first quartile. In this case, the waiting time at the 10th index is 41 minutes.

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____ The given question is incorrect, the complete question is given below:

There is a severe shortage of critical care doctors and nurses to provide intensive care services in hospitals. To offset this shortage, many hospitals, such as Emory Hospital in Atlanta, are using electronic intensive care units (eICUS) to help provide this care to patients (Emory University News Center). eICUs use electronic monitoring tools and two-way communication through video and audio so that a centralized staff of specially trained doctors and nurses - who can be located as far away as Australia - can provide critical care services to patients located in remote hospitals without fully staffed ICUs. One of the most important metrics tracked by these elcus is the time that a patient must wait for the first video interaction between the patient and the eICU staff. Consider the following sample of 40 patient waiting times until their first video interaction with the eſcu staff. Click on the datafile logo to reference the data. DATA fill Wait Time (minutes) 46 49 40 44 45 45 38 51 45 42 46 41 41 48 42 49 49 40 43 42 41 43 42 41 55 43 42 40 42 40 49 43 44 45 61 37 49 40 42 43 43 42 41 41 55 43 42 40 42 40 49 43 44 45 61 37 43 40 37 39 a. Compute the mean waiting time for these 40 patients (to 2 decimals). minutes b. Compute the median waiting time (to 2 decimals). minutes c. Compute the mode (to 2 decimal). minutes d. Compute the first and third quartiles (to 2 decimals). minutes First Quartile: Third Quartile: minutes.

Left and right multiplying a positive semi-definite matrix by another matrix will always result in a positive semi-definite matrix.

Positive semi-definite matrices are important in many areas of mathematics and science, including linear algebra, optimization, and physics.

Let A be a positive semi-definite matrix, and let B be an arbitrary matrix. We want to determine whether AB and BA are also positive semi-definite matrices.

First, let's consider AB. To show that AB is positive semi-definite, we need to show that for any non-zero column vector x, xT(AB)x ≥ 0. We can expand this expression as:

xT(AB)x = (xTA)Bx = yTBy

where y = Ax. Since A is positive semi-definite, we know that yTy ≥ 0 for any vector y. Therefore, we have shown that xT(AB)x ≥ 0 for any non-zero column vector x, and hence AB is positive semi-definite.

Next, let's consider BA. To show that BA is positive semi-definite, we need to show that for any non-zero column vector x, xT(BA)x ≥ 0. We can expand this expression as:

xT(BA)x = (xTB)Ax = zTAz

where z = Bx. Since A is positive semi-definite, we know that zTAz ≥ 0 for any vector z. Therefore, we have shown that xT(BA)x ≥ 0 for any non-zero column vector x, and hence BA is also positive semi-definite.

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On solving the provided question, we can say that the linear equation 100(p + s) + 100(p + s)

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

salad costs s dollars per serving. he needs to order 100 lunches for seventh graders and 100 lunches for eighth graders

the linear equation

100(p + s) + 100(p + s)

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