In an experiment, the control variable is rand the response variable is s.
Which variable is not manipulated, but measured, and represents the data
being recorded?

A. Both r and s
B. s
C. Neither r nor s
D. r

f(x) = a(x-4)(x-2)

f(x) = b(x+6)(x-3)

f(x) = c(x-4)^2(x-2)where c is any non-zero constant. This equation also represents a parabola that opens upward and has x-intercepts at x=4 and x=2.

For the first equation, we know that the graph has two x-intercepts at x=4 and x=2. This means that the function will equal zero at those two values of x. One way to write this equation is:

f(x) = a(x-4)(x-2)

where a is any non-zero constant. This equation represents a parabola that opens upward and has x-intercepts at x=4 and x=2.

For the second equation, we know that the graph has two x-intercepts at x=-6 and x=3. This means that the function will equal zero at those two values of x. One way to write this equation is:

f(x) = b(x+6)(x-3)

where b is any non-zero constant. This equation represents a parabola that opens downward and has x-intercepts at x=-6 and x=3.

Yes, I do think there is more than one function that fits the condition in #1. For example, we could also write:

f(x) = c(x-4)^2(x-2)

where c is any non-zero constant. This equation also represents a parabola that opens upward and has x-intercepts at x=4 and x=2.

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Answer:

x

Explanation:

Let cost of leash = y

14.26 - y = x

Hope this helps and have a great day :)

And please mark me brainliest if you can :)

Answer: the answer is b

Step-by-step explanation:

Answer: D

Step-by-step explanation:

y =mx+c

Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

The relation 2 represents a function.

In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.

To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.

The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.

If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.

We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.

Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.

Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.

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The determinants for the given system of equations are D = 22, Dx = 34, and Dy = 0. These determinants will be used in Cramer's Rule to find the solution to the system.

1. To solve the system of equations using Cramer's Rule, we need to find the determinants D, Dx, and Dy. Clearing the fractions, the coefficients of the equations become 6x + y = 9 and 2x + 4y = 3. The determinant D is calculated as the determinant of the coefficient matrix, which is 2. The determinant Dx is obtained by replacing the coefficients of x with the constants in the first equation, resulting in 3. The determinant Dy is obtained by replacing the coefficients of y with the constants in the first equation, resulting in -3.

2. To solve the system of equations using Cramer's Rule, we start by writing the given system of equations with cleared fractions:

Equation 1: 3/2 x + 1/4 y = 3/4  ->  6x + y = 9

Equation 2: 1/6 x + 1/3 y = 1/4  ->  2x + 4y = 3

3. Now, we can calculate the determinants D, Dx, and Dy using the coefficient matrix:

D = |6 1| = 6 * 4 - 1 * 2 = 24 - 2 = 22

4. Next, we calculate the determinant Dx by replacing the coefficients of x in the coefficient matrix with the constants from the first equation:

Dx = |9 1| = 9 * 4 - 1 * 2 = 36 - 2 = 34

5. Similarly, we calculate the determinant Dy by replacing the coefficients of y in the coefficient matrix with the constants from the first equation:

Dy = |6 9| = 6 * 3 - 9 * 2 = 18 - 18 = 0

6. In summary, the determinants for the given system of equations are D = 22, Dx = 34, and Dy = 0. These determinants will be used in Cramer's Rule to find the solution to the system.

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Answer:

i dont understand

Step-by-step explanation:

Answer:

4 : 59

Step-by-step explanation:

Close. But good try

So what is "ratio?"

Well seems like you got 15/59 i think you meant 15:59 right? ratio has a : in it.

But, you see there is only 4 pizzas with pepperoni in it so actually it should be

4 : 59

Good attempt anyways Trying is always better than nothing.

Answer: No, they are not collinear.

Answer:

ok so first they drove 55 for 3 hours so

55*3=165

and then they drove 45 for 2 hours

45*2=90

165+90=255

so in total they drove 255 miles

Hope This Helps!!!

The solution is : 255 miles total miles did the Ramos family drive.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

here, we have,

given that,

The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. After lunch, they drove at a constant rate of 45 miles per hour for 2 hours.

we get,

Journey before lunch:

Speed = 55 mph

Time = 3 hrs

distance = 55*3 = 165 miles.

Journey after lunch:

Speed = 45 mph

Time = 2 hrs

distance = 45 * 2 = 90 miles

Total miles driven

= distance traveled before lunch + distance traveled after lunch

= 165 miles + 90 miles

= 255 miles

Therefore, the Ramos family drove 255 miles in total.

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The z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.

The determination of the z-coordinate of the mass center of the homogeneous paraboloid of revolution requires a long answer.

Firstly, we need to define the mass density of the paraboloid. Since it is a homogeneous object, its mass density is constant throughout its volume.

Let us denote this density as ρ.

Next, we need to find the volume of the paraboloid.

The volume of a paraboloid of revolution with a height h and a base radius r is given by V = (π/2) * r^2 * h/3.

In this case, the height of the paraboloid is 4 units and the radius of the base is 2 units. Thus, the volume of the paraboloid is:
V = (π/2) * (2)^2 * 4/3 = (8π/3) units^3

Now, we can find the mass of the paraboloid by multiplying its volume by its density:
M = ρ * V = ρ * (8π/3) units^3

The next step is to find the x and y coordinates of the mass center of the paraboloid.

We can do this by using double integrals:
x = (1/M) * ∬(paraboloid) x * ρ * dV
y = (1/M) * ∬(paraboloid) y * ρ * dV

Since the paraboloid is symmetric about the z-axis, we know that its mass center will lie on this axis, and thus, its x and y coordinates will be zero.

Finally, we need to find the z-coordinate of the mass center. We can do this by using the same double integral, but this time we integrate over the z-axis:
z = (1/M) * ∬(paraboloid) z * ρ * dV

To set up the double integral, we can use cylindrical coordinates, with ρ ranging from 0 to 2 and θ ranging from 0 to 2π.

The z-coordinate of any point on the paraboloid is given by z = (1/16) * (x^2 + y^2), so we can substitute this into the double integral:
z = (1/M) * ∫(0 to 2π) ∫(0 to 2) ∫(0 to (1/16)*(ρ^2)) ρ * z * ρ * ρ * dρ dθ dz

After evaluating this integral, we get:
z = (3/5) * h = (12/5) units

Therefore, the z-coordinate of the mass center of the homogeneous paraboloid of revolution shown is (12/5) units.

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Answer:

When writing your own two-column proof, keep these things in mind:

Number each step.

Start with the given information.

Statements with the same reason can be combined into one step. ...

Draw a picture and mark it with the given information.

You must have a reason for EVERY statement.

Step-by-step explanation:

We conclude that the assumed bijection f cannot be continuous on [0,1].

To prove that a bijection function f: [0,1] → (0,1) is not continuous, we can utilize the concept of the Intermediate Value Theorem (IVT).

Assume f is continuous on [0,1]. Since f is a bijection, it must be either strictly increasing or strictly decreasing. Without loss of generality, let's assume it is strictly increasing.

Consider the point f(0) ∈ (0,1). According to the IVT, for any y in the interval (0,1), there exists x in [0,1] such that f(x) = y. However, this contradicts the definition of f as a bijection.

To elaborate, if f is continuous, it would map the entire interval [0,1] to the interval (0,1) without any missing values. But since f(0) ∈ (0,1), there would be no value in the interval [0,1] that maps to 0, violating the surjectivity property of a bijection.

Therefore, we conclude that the assumed bijection f cannot be continuous on [0,1].

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The Greatest Common Factor of 32 and 48 is 16.

The longest necklace she can make is of 16 inches length.

Answer:

Long solution

Step-by-step explanation:

(a) Let the height of the cone be h cm. The volume of the hemisphere is given by (1/2)(4/3)πr³ = (2/3)πr³. The volume of the solid is the sum of the volumes of the hemisphere and the cone, which is (2/3)πr³ + (1/3)πr²h. Since the volume of the hemisphere is one third of the volume of the solid, we have:

(2/3)πr³ = (1/3)πr²h

Simplifying, we get:

2r = h

Therefore, h is expressed in terms of r as h = 2r.

(b) The slant height of the cone can be found using the Pythagorean theorem. Let l be the slant height, then we have:

l² = r² + h²

Substituting h = 2r, we get:

l² = r² + (2r)² = 5r²

Taking the square root of both sides, we get:

l = r√5

Since k is an integer, we can write:

l = Vk cm, where k is an integer

Comparing the two expressions, we get:

Vk = r√5

Therefore, the value of k is k = ⌊r√5⌋, where ⌊x⌋ denotes the largest integer less than or equal to x.

(c) The total surface area of the solid is the sum of the curved surface area of the cone, the curved surface area of the hemisphere, and the area of the circular base of the cone. We have:

Curved surface area of the cone = πr l = πr(r√5) = πr²√5

Curved surface area of the hemisphere = 2πr²

Area of the circular base of the cone = πr²

Therefore, the total surface area of the solid, in cm², is given by:

πr²√5 + 2πr² + πr² = (πr²)(√5 + 3)

Answer:

measure of angle XZY = 52 degrees

Step-by-step explanation:

The sum of measure of angles of a circle is 360 degrees.

therefore, m(arc XY) = 360 - (110 + 146)

m(arc XY) = 360 - 256

= 104 degrees

angle XZY is an inscribed angle.

By the inscribed angle theorem, the measure of an inscribed angle is half the measure of the intercepted arc.

So, m( angle XZY) = 1/2 * 104

= 52 degrees.

Answer:

y=-x+2

Step-by-step explanation:

y+x-x=2+x

y=-x+2

Answer: 2nd, 4th, and 5th options

Step-by-step explanation:

The x-intercept is where the graph meets the x axis line and is also known as being the roots/zeros of an expression. hope this helps

The standard deviation for the given sample data is 2.83.

To calculate the standard deviation, we first need to calculate the mean of the sample data:

Next, we calculate the deviation of each data point from the mean:

Then, we square each deviation:

Next, we calculate the sum of squared deviations:

To calculate the variance, we divide the sum of squared deviations by the sample size minus one:

Finally, we calculate the standard deviation by taking the square root of the variance:

Therefore, the standard deviation for the given sample data is 2.83. This tells us how spread out the data points are from the mean, with most data points being within 2.83 units of the mean.

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The sentence "64% of women in the sample are the principal investor in their household" serves as an example of descriptive statistics.

This sentence provides a summary of the survey's data and a descriptive statistic (percentage) that characterizes the sample's characteristics.

According to the survey's findings, "there is a correlation between American women and being the principal investor in their household." The sample data are used to draw this conclusion about the population. Despite the fact that the sample is not representative of all American women, the findings indicate that a sizable number of the women in the sample are the principal investors in their households.

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The statement 'For a random sample of size 15 from a normal population with known variance, the test statistic with the null hypothesis of H0: µ = µ0 is (X - µ0)/(σ/√n) when X is the sample mean' is true as in this case Z-test can be used.

For a random sample of size 15 from a normal population with known variance, the test statistic with the null hypothesis of H0: µ = µ0 is indeed (X - µ0)/(σ/√n) when X is the sample mean. This is because when the population variance is known, we use the Z-test to determine if the null hypothesis should be accepted or rejected. The Z-test statistic formula is given by Z = (X - µ0)/(σ/√n), where X is the sample mean, µ0 is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.

Note: The question is incomplete. The complete question probably is: True or False: For a random sample of size 15 from a normal population with known variance, the test statistic with the null hypothesis of H0: µ = µ0 is (X - µ0/(σ/√n) when X is the sample mean.

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The correct conclusion is that males prefer chocolate ice cream more than vanilla ice cream.

Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.

This conclusion can be drawn from the data in the table, which shows that there were more males who chose chocolate ice cream than vanilla, and more females who chose vanilla than chocolate.

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To verify the inequality without evaluating the integrals, we can use the properties of integrals.

First, we know that the integral of a positive function gives the area under the curve. Therefore, the integral of √(1-x^2) from -1 to 1 gives the area of a semicircle with radius 1. This area is equal to π/2, which is approximately 1.57.
Next, we can use the fact that the integral of a function over an interval is less than or equal to the product of the length of the interval and the maximum value of the function on that interval. Since the function √(1-x^2) is decreasing on the interval [-1,1], its maximum value is at x=-1, which is √2/2.
Using this property, we have:
∫1 -1 √(1-x^2) dx ≤ (1-(-1)) * √2/2 = √2
Finally, we can use a similar argument to show that the integral is greater than or equal to 2. Therefore, we have:
2 ≤ ∫1 -1 √(1-x^2) dx ≤ √2
To verify the inequality 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2 using properties of integrals, let's first establish that the integrand is non-negative on the interval [-1, 1]. Since 0 ≤ x^2 ≤ 1, we have 0 ≤ 1 - x^2 ≤ 1, so √(1 - x^2) is non-negative.
Now, consider the areas of two squares: one with side length 2 and the other with side length √2. The area of the first square is 2² = 4, and the area of the second square is (√2)² = 2. Since the integrand lies between 0 and 1, the area under the curve is less than the area of the first square but more than half of it (as it resembles half of the first square).
Therefore, 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2, as the area under the curve is between half of the first square's area and the second square's area.

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The derivative of y = x²(x) is dy/dx = 3x².

To find the derivative of y = x²(x), we can use the product rule. The product rule states that if we have a function of the form f(x) = g(x)h(x), then its derivative is given by f'(x) = g'(x)h(x) + g(x)h'(x).

Let's apply the product rule to find dy/dx:

y = x²(x)

Using the product rule, we have:

dy/dx = (d/dx)[x²(x)] = (d/dx)[x²] * x + x² * (d/dx)[x]

Taking the derivatives, we have:

dy/dx = (2x) * x + x² * 1

Simplifying further:

dy/dx = 2x² + x²

Combining like terms:

dy/dx = 3x²

Therefore, the derivative of y = x²(x) is dy/dx = 3x².

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The 95% "confidence-interval" for "mean-weight" of all bags of potatoes is (20.53614, 21.36386) pounds.

To find 95% "confidence-interval" for mean-weight of all bags of potatoes, we use formula : CI = x' ± t × (s/√(n)),

where CI = confidence interval, x' = sample mean, t = critical-value from the t-distribution based on desired confidence-level and degrees of freedom,

s = sample standard-deviation, and n = sample-size,

we substitute the values,

Sample mean (x') = (20.9 + 21.4 + 20.7 + 21.2)/4 = 20.95 pounds

Sample standard deviation (s) = √(((20.9 - 20.95)² + (21.4 - 20.95)² + (20.7 - 20.95)² + (21.2 - 20.95)²) / 3) ≈ 0.26 pounds

Sample size (n) = 4

Degrees-of-freedom (df) = n - 1 = 4 - 1 = 3,

The "critical-value" (t) for 95% "confidence-interval" and df = 3, is approximately 3.182,

CI = 20.95 ± 3.182 × (0.26/√(4))

= 20.95 ± 3.182 × (0.26/2)

= 20.95 ± 3.182 × 0.13

= 20.95 ± 0.41386

= (20.53614, 21.36386)

Therefore, the required confidence-interval is (20.53614, 21.36386).

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The given question is incomplete, the complete question is

The weights of four randomly and independently selected bags of potatoes labeled 20.0 pounds were found to be 20.9, 21.4, 20.7, and 21.2 pounds. Assume normality.

Find the 95% confidence-interval for the mean weight of all bags of potatoes.

Solution: x=2 ✅

\(\searrow\)

⚜Detailed explanation: ⚜

In this problem we need to solve for x, the unknown.

First, note that the terms 2x and 5x have an x in them, so why not add them and make life easier?

\(---\mapsto\boldsymbol{2x+5x=14}\\\\---\mapsto\boldsymbol{7x=14}\)

We're getting closer! Now we know that if we multiply 7 times the unknown, we'll get 14. So let's divide both sides by 7! Then we will have the value of the unknown.

\(---\mapsto\boldsymbol{x=2}\) is what we obtain upon dividing

Superb, it's ez as winking!

_________________________________________

Voila! There's our solution!

Hope I helped! Best wishes!

Reach far. Aim high. Dream big.

____________________________________________

Answer:

The answer would be C. An obtuse equilateral triangle :)

Answer:

60 minutes, 1 hour

Step-by-step explanation:

5 minutes for 1/3 of a mile, means 15 minutes per mile

15 x 4 = 60 minutes

If four students measure their heights to be 130 cm, 130, cm, 138 cm, and 176 cm, then the average(mean) height of these students is 143.5cm.

To find the average (mean) height, follow these steps:

Hence, the average (mean) height of these students is 143.5 cm.

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Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6