Answer:
B. 20 inches
Step-by-step explanation:
Remember that when dealing with ratios or unit rates you just have to do simple rules of three to calcuate what they are asking you, in this case you have that in the map for every 8 units in the length there will be 5 in the width, so how many will there be when the map is 32 inches in length?
[tex]\frac{8}{5}= \frac{32}{x}\\x=\frac{32*5}{8}\\ x=20[/tex]
So the width of a map with a length of 32 inches and a ratio of 8:5 will be 20 inches.
American cheese 0.45 to 4.26 what is the percent increase
Solve the equation for x, where x is a real number:
-4x^2 + 5x - 7 = 0
what value represents the horizontal translation from the graph of the parent function f(x)=x^2 to the graph of the function g(x)=(x+5)^2+3
Use spherical coordinates. let h be a solid hemisphere of radius 1 whose density at any point is proportional to its distance from the center of the base. (let k be the constant of proportionality.) (a) find the mass of h.
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.
Explanation: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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Suppose you rolled the 6-sided number cube 120 times, how many times would you expect to roll a 6? Explain.
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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You plant a tree that is 36 inches tall. After one year, the tree is 43 inches tall. Which expression describes the percent of increase in the tree's height?
Find the area of the following ellipse. a = 4.5 m; b = 5.5 m
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
If pluto's average distance is approximately 100 times mercury's average distance, how many units on the logarithmic scale is pluto from mercury?
A 16 ounce package of cereal cost $4.00? what is the unit cost
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:
Use the table to answer the question. House A $124,270 Annual appreciation 4% House B $114,270 Annual appreciation 5% In which of these years after it was purchased is the value of House A greater than the value of House B? Check all that apply. 7 8 9 10
A number, half of that number, and one fifth of that number are added. The result is 51. What is the original number?
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:
Find the least common multiple (LCM) of 2 and 5, which is 10.Multiply the entire equation by 10 to clear the fractions: 10x + 5x + 2x = 510.Combine like terms: 17x = 510.Divide both sides by 17 to solve for x: x = 510 / 17, which simplifies to x = 30.Therefore, the original number is 30.
A metal bar weighs 8.18 ounces. 96% of the bar is silver.How many ounces of silver are in the bar?
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].
24. Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.
how many number between 200 and 800 have the number 6?
A small school employs 5 teachers who make between $40,000 and $70,000 per year The newest teacher, Valerie, decides to teach part-time which decreases her salary from $40,000 to $20,000 per year. The rest of the salaries stay the same How will decreasing Valerie's salary affect the mean and median?
You can use the fact that median is affected only if the middle value(s) are changed if number of values are same.
The mean salary will become $4000 less than previous mean of salaries.The median will stay same as before.How are mean and median affected if a value is changed to some other value?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.
when you multiply 2/3 by a fraction less than one, how does the product compare to the factors. Explain.
please
hey can you please help me posted picture of question
Factor the monomial t^2-16t+48
Use the quadratic formula to solve, 2x^2=7x+6 Leave your answer in simplified radical form.
Please show all your work! (30 points)
A school typically sells 500 yearbooks each year for 50 dollars each. The economic calls does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. The revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook. Let x represent the number of $5 decrease in price. If the expression that represents the revenue is written in the form R(x)=(500+ax)(50-bx). Find the value of a and b
Final answer:
For the expression R(x)=(500+ax)(50-bx), a represents the increase in yearbooks sold for each $5 decrease in price and b represents the corresponding decrease in price per yearbook. The correct values for a and b are 100 and 5 respectively, resulting in the revenue expression R(x) = (500 + 100x)(50 - 5x).
Explanation:
The student's question revolves around the concept of revenue generation based on the number of items sold and the selling price per item.
When examining revenue, we understand it as the product of price per unit times the number of units sold. In the given example, a school is selling yearbooks with a base scenario of 500 yearbooks at $50 each. We are given that for every $5 decrease in price, the school can sell an additional 100 yearbooks. This can be formulated as:
R(x) = (500 + ax)(50 - bx)
Here x represents the number of $5 decreases from the original price. With each decrease, the number of books sold increases by 100, and the price decreases by $5.
Therefore, variable a must represent the increase in quantity sold for each $5 price decrease (a = 100), and variable b must represent the decrease in price per yearbook for each price decrease (b = 5).
Therefore, the values of a and b are 100 and 5, respectively.
The expression for the revenue becomes:
R(x) = (500 + 100x)(50 - 5x)
Explain why a counter with an upper limit of five(101) resets at six (110)
Density is mass divided by volume. Find the mass of a gold bar if the density is 19.32 g/cm3 and the volume is 50 cm3.
Answer:
d
Step-by-step explanation:
denisity * volume = mass
Evaluate C(7, 7).
A: 0
B: 1
C: 7
If you can, could you please explain how you got your answer. These problems honestly don't make any sense to me and I'm turning towards here as a last resort. Thanks in advance.
Answer:
Answer = 1
Step-by-step explanation:
What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of .
3x - y - 7 = 0
x - 3y + 7 = 0
x - 3y - 7 = 0
4(x-7)(x+6)=0
[tex]4(x - 7)(x + 6) = 0[/tex]
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
HELP ASAP PLEASE
Name the quadrant in which the point (x, y) lies.
x > 0 and y < 0
III
II
IV
I
Answer: quadrant 4
Step-by-step explanation:
if you laid one of each size bolt end to end, how long would the row of bolts be?
3/8 inch, 1/2 inch, 5/8 inch, 7/8 inch, 1 1/4 inches.
The length of row of bolt will be calculated by adding the size of all the bolts.
PLEASE HELP You have just applied, and have been approved for a $175,000 mortgage. The rate quoted to you by the lender is 5.5% for a 30 year fixed mortgage. Use the provided table to determine how much of your first month’s payment goes towards the principal.
a.
$191.92
c.
$187.32
b.
$190.23
d.
$184.88
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).
Explanation: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.
If you wanted to vertically stretch the graph of F(x) = |x| by five units, what would the equation of the new function, G(x), be?
A. G(x)=|x|-5
B. G(x)=|x+5|
C. G(x)=5|x|
D.G(x)=|5x|
mcr apex
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.
Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
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.