Instructions:Select the correct answer from each drop-down menu. The range of all real numbers x such that 2x − 5 < 7 and 4x + 10 > 6 is . The range of all real numbers x such that 2x − 5 < 7 or 4x + 10 > 6 is

To find the mass of the solid hemisphere using spherical coordinates with density proportional to distance from center, integrate the density times the volume element over the hemisphere.

To find the mass of the solid hemisphere using spherical coordinates, we first need to understand that the density at any point is proportional to its distance from the center of the base. Let's denote the constant of proportionality as k. The mass can be found by integrating the product of density and volume over the entire hemisphere. The volume element in spherical coordinates is given by ρ² sinϕ dρ dϕ dθ, where ρ is the radial distance, ϕ is the polar angle, and θ is the azimuthal angle.

We can denote the density as ρ = kρ, where ρ is the radial distance from the center. The mass element dm is then given by dm = ρ² sinϕ dρ dϕ dθ = kρ³ sinϕ dρ dϕ dθ. To obtain the mass of the hemisphere, we need to integrate the mass element over the appropriate limits, which are ρ = 0 to 1, ϕ = 0 to π/2, and θ = 0 to 2π.

Performing the integration, we get the mass as M = ∫∫∫ kρ³ sinϕ dρ dϕ dθ = πk/6.

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Answer:

Expanded: 4x² - 4x - 168 = 0
Solutions: x = -6, 7

Explanation:
If you need to expand the expression:

First, distribute the 4 to the binomial directly to its right but multiply each term within the parentheses by 4.
4(x - 7) = 4(x) + 4(-7) = 4x - 28
The new equation is (4x - 28)(x + 6) = 0

Next, we use the FOIL method. This is an acronym that instructs which terms in each binomial are multiplied together. It stands for Firsts, Outsides, Insides, and Lasts.
Firsts: 4x(x) = 4x²
Outsides: 4x(6) = 24x
Insides: -28(x) = -28x
Lasts: -28(6) = -168

Put them into one equation and combine like terms.
4x² + 24x - 28x - 168 = 0
4x² - 4x - 168 = 0

If you need solutions to the expression:

First, divide both sides of the equation of the 4 that was previous factored out.
4(x - 7)(x + 6) = 0
[4(x - 7)(x + 6)] / 4 = 0 / 4
(x - 7)(x + 6) = 0

Now, set each binomial equal to 0 and solve for x using whatever operations are necessary.
x - 7 = 0                             x + 6 = 0
x - 7 + 7 = 0 + 7                 x + 6 - 6 = 0 - 6
x + 0 = 7                            x + 0 = - 6

x = 7                                  x = - 6

The solutions to the expression are x = -6, 7

To calculate the portion of the first month's payment that goes towards the principal, we need the monthly payment amount, which is calculated from the loan amount, interest rate, and term. From there, we subtract the first month's interest from the monthly payment. In the absence of adequate information or a mortgage calculator, we cannot provide the correct option from (a-d).

To determine how much of the first month's payment goes towards the principal of a $175,000 mortgage at a rate of 5.5% for a 30-year fixed mortgage, we need to calculate the monthly payment and then separate the interest from the principal.

The monthly payment M can be calculated using the formula:

M = P x (r(1+r)^n) / ((1+r)^n-1)

Where:

Next, we find the monthly interest portion by multiplying the principal by the monthly interest rate and subtract it from the monthly payment to find how much goes towards the principal.

Unfortunately, the information given does not provide a clear way to calculate the exact monthly payment or the portion applied to the principal without additional information or a financial calculator. In practice, you would use a formula or a mortgage calculator to find the total monthly payment, and then deduct the first month's interest to determine the amount applied to the principal. Without the correct formula or values, we can't determine the answer options (a-d) provided.

Answer:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

Step-by-step explanation:

A set of ordered pairs in the format [tex](x,y)[/tex] represents a function if for each value of x, there is only one value for y.

The first set of ordered pairs is:

{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}

There are two values of y for [tex]x = 1[/tex]. This means that this set of ordered pairs does not represent a function.

The second set of ordered pairs is:

{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}

For each value of x here, there is only one value of y. This means that this set of ordered pairs represents a function. This is the answer.

The third set of ordered pairs is:

{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}

There are two values of y for [tex]x = -2[/tex]. This means that this set of ordered pairs does not represent a function.

The fourth set of ordered pairs is:

{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}

There are two values of y for [tex]x = -3[/tex]. This means that this set of ordered pairs does not represent a function.

Final answer:

The original number is determined by setting up an algebraic equation based on the relationship given in the problem, solving for the variable, and using algebraic operations. The original number is found to be 30.

Explanation:

To find the original number when its half and fifth are added to it to get 51, we can set up an algebraic equation. Let's denote the original number as x. Half of that number would be x/2 and one fifth of that number would be x/5. The equation representing the given condition is:

x + x/2 + x/5 = 51

To solve this, we need a common denominator to combine the fractions:

Therefore, the original number is 30.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",

Given that a metal bar weighs 8.18 ounces and 96% of the bar is silver.

The amount of Silver in the bar is

[tex] A=\frac{96}{100}(8.18) =7.8528 [/tex].

The amount of Silver in the bar in ounces is [tex] 7.8528\;ounces [/tex].

Solution:

The Preimage function is , F(x)=|x|

Consider a point (a,b) on the function, F(x)=|x|. it means

b=|a|-----(1) satisfies the function.

Now the function F(x)=|x|  is vertically stretched by 5 units.It means

x=a , y= b+5

x=a, b=y-5

So, putting the value of a and b in equation (1).

y-5=|x|

y= |x| + 5 is vertical stretch of y= |x| by 5 units.

Answer:

Area of ellipse is ≈ 77.78 [tex]m^{2}[/tex]

Step-by-step explanation:

Given the dimension of ellipse

  a = 4.5 m

  b = 5.5 m

Now, Area of ellipse = [tex]\pi ab[/tex]

                                  = [tex]\frac{22}{7}\times 4.5\times 5.5[/tex]

                                  = [tex]\frac{5445}{70}[/tex]

                                  = 77.78 [tex]m^{2}[/tex]

Hence Area of ellipse will be 77.78 [tex]m^{2}[/tex]

The area of the ellipse is calculated using the formula A = ab, with the given semi-major axis of 4.5 m and semi-minor axis of 5.5 m, estimated to two significant figures as 78 m².

The area A of an ellipse with semi-major axis a and semi-minor axis b is given by the formula A = \ab. Given that a = 4.5 m and b = 5.5 m, we can calculate the area of the ellipse using a calculator. Keeping in mind that we should report our final answer to the same number of significant figures as the least precise measurement provided (which in this case is two significant figures), we have:

A = \(4.5 m)(5.5 m)

A = 3.1415927... × 24.75 m²

A = 77.66546225 m²

However, due to the significant figures rule our reported answer should be:

A = 78 m²

Answer:

Answer = 1

Step-by-step explanation:

Here, we need to find unit cost. Unit cost can be defined as a cost per unit of a product.

We are given that 16 ounce will cost $ 4.00.

That means -

Cost of 16 ounce of cereal package = $ 4.00

Cost of 1 ounce of cereal package -

(We will divide both sides by 16)

Cost of 16 ounce of cereal package ÷ 16 = $ 4.00 ÷ 16

Cost of 1 ounce of cereal package = $ 0.25.

Thus, the cost of 1 ounce of cereal package = $ 0.25.

Answer: 1 oz. Over 0.25 is your answer.

Step-by-step explanation:

Answer: quadrant 4

Step-by-step explanation:

Answer:

Option A. 1 over 5. 10 hours

Step-by-step explanation:

This question can be solved by the unitary method.

∵ Oil company fills [tex]\frac{1}{10}[/tex] of a tank in the time = [tex]\frac{1}{5}[/tex] hurs

∴ Full tank can be filled in the time = [tex]\frac{\frac{1}{5} }{\frac{1}{10} }[/tex] hours.

= [tex]\frac{1}{5}\times 10[/tex]

Therefore, the expression that can be used to determine the time that it will take to fill the tank completely will be Option A.

Using the equation for the margin of error, it is found that the 99% confidence interval will be wider than the 95% confidence interval for µ.

The margin of error of a confidence interval is given by an equation in the following format:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

In which:

In this problem, a 99% confidence interval will have a higher value of t than a 95% confidence interval, hence a higher margin of error, and thus will be wider.

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You can use the fact that median is affected only if the middle value(s) are changed if number of values are same.

The median is the middle value of the sorted(ordered in ascending or descending way)data values. If value changed is not the middle value (if number of observations are odd) or is not changing the average of two mid values (if number of observations are even), then the median won't change as it does't care about the value of the data unless its about the mid value of the sorted data or average of mid values.

The mean is affected by the data.

The mean of n values  is calculated as:

[tex]\overline{x} = \dfrac{x_1 + x_2 + ... + x_i + ... + x_n}{n}[/tex]

Suppose that x_i changed to y

Then we have then new mean as

[tex]\begin{aligned}\overline{x}_{new} &= \dfrac{x_1 + x_2 + ... + (x_i -x_i + y)+ ... + x_n}{n}\\&= \dfrac{x_1 + x_2 + ... + x_i+ ... + x_n}{n} + \dfrac{-x_i + y}{n}\\&= \overline{x} + \dfrac{y-x_i}{n}\\\end{aligned}[/tex]

For the given data, one value was changed from $40,000 to $20,000, thus, as $40,000 was lowest value of the data, thus median stays same as before,.

And for new mean, we have:

[tex]\overline{x}_{new} = \overline{x} + \dfrac{y-x_i}{n} = \overline{x} + \dfrac{-20000}{5}\\\\\overline{x}_{new} = \overline{x} -4000[/tex]

Thus, new mean salary will be $4000 less than the previous mean  salary.

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Decreasing Valerie's salary will lower the mean salary of the teachers. The effect on the median depends on the other salaries, but if Valerie's salary was the minimum, the median may remain unchanged.

Decreasing Valerie's salary from $40,000 to $20,000 will affect both the mean and median salaries of the teachers in the school. To determine the impact on the mean salary, we would subtract the amount of the decrease from the total salaries and then divide by the number of teachers. Originally, if we assume the other four teachers earn salaries between $40,000 and $70,000, the total salary pool would be the sum of all five teachers' salaries. With Valerie’s decrease, the new total would be $20,000 less. Dividing this new total by 5 would give us the new mean salary.

As for the impact on the median salary, this depends on where Valerie's original salary of $40,000 stood in relation to the other four salaries. Since she was making the minimum amount within the provided salary range, if all other teachers make more than $40,000, Valerie's reduced salary will not change the median, as the median is the middle value when all salaries are listed in order. However, if Valerie's salary was at the median, her reduced salary would lower the median if the next lowest salary is less than $40,000.

You would expect to roll a 6 approximately 20 times in 120 rolls. This is because, on average, in the long run, you would expect a specific outcome (in this case, rolling a 6) to occur with a frequency proportional to its probability (1/6) over a large number of trials (120 rolls).

When rolling a fair 6-sided number cube, each of the six faces has an equal probability of landing face up. The probability of rolling a 6 on a fair 6-sided number cube is 1/6.

To find out how many times you would expect to roll a 6 in 120 rolls, you can use the probability formula:

Expected number of successful outcomes = Probability of success * Total number of trials

Expected number of times to roll a 6 = (1/6) * 120

Expected number of times to roll a 6 = 20

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The length of row of bolt will be calculated by adding the size of all the bolts.