Rhombus B, which has dimensions three times larger than Rhombus A, has an area that is nine times larger than the area of Rhombus A.
Explanation:This question is based on geometry and compares the areas of two rhombuses. Firstly, remember that the area of a rhombus is obtained by the formula A = base x height. For Rhombus A, with a base of 7 inches and area 35 square inches, this implies that its height is 5 inches (since 7 x 5 = 35). Therefore, the height of Rhombus B which is three times larger than that of Rhombus A would be 15 inches, and its base would be 21 inches (three times that of Rhombus A).
Now applying these values into the formula for the area of a rhombus, for rhombus B we get A = 21 x 15, which equals 315 square inches - this is the area of Rhombus B. Comparing this with the area of Rhombus A (35 square inches), we find that Rhombus B is 9 times larger than Rhombus A (because 315 divided by 35 equals 9).
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By increasing the base and height of Rhombus A by three times, the resulting area of Rhombus B is nine times the area of Rhombus A. The area of Rhombus A is 35 square inches and the area of Rhombus B is 315 square inches.
Explanation:The subject of this question is area of rhombuses. A key concept to remember is that the area of a rhombus is calculated by the formula: Area = base x height.
Rhombus A has base of 7 inches and an area of 35 square inches. This means the height h of Rhombus A is A/base = [tex]35/7 = 5[/tex] inches.
The base and height of Rhombus B are three times the base and height of rhombus A. So, Rhombus B has a base of [tex]7 * 3 = 21[/tex] inches and height of [tex]5 * 3 = 15[/tex] inches.
To find the area of Rhombus B, you apply the same formula, Substituting the values we get, B = base x height = [tex]21 * 15 = 315[/tex] square inches. Therefore, the area of Rhombus B is nine times the area of Rhombus A since 315/35 = 9.
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Suppose that 44% of all Americans approve of the job the President is doing. The most recent Gallup poll consisted of a random sample of 1,400 American adults.
a. What is the mean of the sampling distribution?
b. What is the standard deviation of the sampling distribution (don't forget to justify the use of the formula)?
c. Describe the normal approximation for this sampling distribution (don't forget to justify this) You can simply write as N (mean, standard deviation)
d. What is the probability that the Gallup poll will come up with a proportion within three percentage points of the true 44%
A technique used to rewrite a quadratic function in standard form to vertex form is
Answer:
completing the square.
Step-by-step explanation:
trust me
Ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. After recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. What does 0.45 represent in the equation? A) the lowest ticket price B) the number of miles traveled C) the expected change in the price of multiple tickets Eliminate D) the expected change in price of the ticket for each mile traveled
Find the derivative of f(x) = (1 + 5x2)(x − x2) in two ways. use the product rule. f '(x) = perform the multiplication first. f '(x) = do your answers agree? yes no
Answer:
The answers agree.
[tex]f^{\prime}(x) = - 20x^{3} + 15x^{2} - 2x + 1[/tex]
Step-by-step explanation:
The product rule is:
[tex]f(x) = g(x)h(x)[/tex]
[tex]f^{\prime}(x) = g^{\prime}(x)h(x) + g(x)h^{\prime}(x)[/tex]
In this problem, we have that:
[tex]f(x) = (1 + 5x^{2})(x - x^{2})[/tex]
So
[tex]g(x) = 1 + 5x^{2}[/tex]
[tex]g^{\prime}(x) = 10x[/tex]
[tex]h(x) = x - x^{2}[/tex]
[tex]h^{\prime}(x) = 1 - 2x[/tex].
[tex]f^{\prime}(x) = g^{\prime}(x)h(x) + g(x)h^{\prime}(x)[/tex]
[tex]f^{\prime}(x) = (10x)*(x - x^{2}) + (1 + 5x^{2})(1-2x)[/tex]
[tex]f^{\prime}(x) = 10x^{2} - 10x^{3} + 1 - 2x + 5x^{2} - 10x^{3}[/tex]
[tex]f^{\prime}(x) = - 20x^{3} + 15x^{2} - 2x + 1[/tex]
Multiplication first:
[tex]f(x) = (1 + 5x^{2})(x - x^{2})[/tex]
[tex]f(x) = x - x^{2} + 5x^{3} - 5x^{4}[/tex]
[tex]f(x) = -5x^{4} + 5x^{3} - x^{2} + x[/tex]
[tex]f^{\prime}(x) = -20x^{3} + 15x^{2} - 2x + 1[/tex]
Comparing the results, we can see that the derivatives obtained using the two methods are indeed the same. The answer is yes.
What's the function about?The derivative of f(x) = (1 + 5x2)(x − x2) can be found using the product rule and by performing the multiplication first.
Using the product rule:
The product rule states that the derivative of f(x)g(x) is f′(x)g(x)+f(x)g′(x).
In this case, f(x) = 1 + 5x2 and g(x) = x − x2. So the derivative of f(x)g(x) is:
f′(x)g(x)+f(x)g′(x)
=(10x+10x3)(x−x2)+(1+5x2)(2x−2x3)
=10x2−10x3+10x3−10x4+2x−2x3+1+10x2−10x3
=−10x4+12x2+2x
Performing the multiplication first:
We can first multiply out the expression (1 + 5x2)(x − x2) to get:
x2−5x4+x3−5x3+x−x2
=−5x4+12x2+x
Then, we can take the derivative of this expression to get the same derivative as we found using the product rule:
f′(x)=−10x4+12x2+2x
Therefore, the derivative of f(x) = (1 + 5x2)(x − x2) is -10x4+12x2+2x, regardless of whether we use the product rule or perform the multiplication first.
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A table is going to be painted. How much less surface area of the table will be painted if the underside remains unpainted. The length is 22 in, the width is 20 in, and the height is 1 in
If the volume is 56 1/4 cubic feet and the length is 7 1/2ft and the width is 3 3/4ft what is the height?
This graph shows how much Marie earns babysitting compared with the number of hours she works select the correct statement about the graph
Answer:
Option D is the answer.
Step-by-step explanation:
This graph represents a linear function representing earnings of Marie at y axis and hours of working at x axis. To get the change in Marie's earnings for every 5 hours we will find the slope of the given line.
Slope of the line will define the rate of change in earning of Marie with respect to the time.
End points of the line at time t = 0 and t = 5 hours are (0, 0) and (5, 50).
Therefore slope = [tex]\frac{y-y'}{x-x'}=\frac{50-0}{5-0}=\frac{50}{5}=10[/tex]
So for each hour she works her earnings go up by $10.
Option D is the correct option.
You have been averaging 55 sales per day. Per our new policy, everyone needs to increase his or her sales per day by 10% in the next month. Rounding up, by next month you will need to be up to __________ sales.
The next month sales should be 1,815.
Given that,
You have been averaging 55 sales per day. increase his or her sales per day by 10% in the next monthBased on the above information, the calculation is as follows:
[tex]= 55 \times 1.10 \times 30 days[/tex]
= 1,815
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Final answer:
To meet the new policy of a 10% increase in sales, you would multiply your current average sales by the increase percentage and round up to the nearest whole number. Starting from 55 sales, a 10% increase results in an additional 5.5 sales, which when rounded up equals 6. Therefore, you need to achieve 61 sales per day.
Explanation:
If you have been averaging 55 sales per day and need to increase your sales by 10%, you will first need to calculate the increase. To calculate a 10% increase, you multiply your current average sales (55) by the percentage increase (10%), expressed as a decimal (0.10). The increase in sales can be found by the formula:
Increase = Current Sales × Percentage Increase
For your sales:
Increase = 55 × 0.10 = 5.5 sales
Since you need to round up, the increase will be 6 sales when considering whole units, as you cannot sell half a unit.
Therefore, the new target sales per day will be:
New Sales Target = Current Sales + Increase
New Sales Target = 55 + 6 = 61 sales
By next month, you will need to be up to 61 sales per day after rounding up.
If the radius of a cone is doubled and the height is tripled, what happens to the volume?
The elevation is 12,000 feet. the altimeter reading in an airplane is 17.00 in hg. this pressure is equal to
5u exponent 7 - 21u exponent 7
Simply
The height of an object from a distance
Bruce bought a map that cost $7.35 he used a $10 bill to pay for his map what is the change
What is the value of x in the equation –6 + x = –2?
8
4
–4
–8
solve the system using substitution method
3x+y=6
2x-4y=10
Find the area of the figure
A standard dartboard has a diameter of 18 in. What is its area to the nearest square inch?
Iris is building a model of the Washington Monument. Her model measures 15 in. tall and is 1.5 in. wide at the base. The actual width measurement at the base of the Washington Monument is about 55 ft. About how tall is the Washington Monument?
Answer: 550
Step-by-step explanation:Solve the proportion: 15 in./1.5 in. = h/55 ft. The value of h is 550 ft. The Washington Monument is about 550 ft tall.
write an expression that represents the difference between t and 8
what is the solution to the equation 3sqrt(5x-4)=3sqrt(7x+8)
Answer:
The answer is: 'no solution'
Step-by-step explanation:
The given equation is: [tex]3\sqrt{5x-4}=3\sqrt{7x+8}[/tex]
Dividing both sides of the equation by 3, we will get.....
[tex]\sqrt{5x-4}=\sqrt{7x+8}[/tex]
Taking square on both sides.....
[tex](\sqrt{5x-4})^2=(\sqrt{7x+8})^2\\ \\ 5x-4=7x+8\\ \\ 5x-7x=8+4\\ \\ -2x=12\\ \\ x=\frac{12}{-2}=-6[/tex]
Plugging this [tex]x=-6[/tex] back to the given equation......
[tex]3\sqrt{5(-6)-4}=3\sqrt{7(-6)+8}\\ \\ 3\sqrt{-34}=3\sqrt{-34}[/tex]
As we are getting a negative number inside the square root, so the equation becomes imaginary. Thus [tex]x=-6[/tex] is a restricted value.
Hence, there is 'no solution' for this equation.
The perimeter of the base of a regular quadrilateral prism is 60 cm, the area of a lateral face is 105 cm2. Find: the volume of the prism
hey can you please help me posted picture of question
What percent of the scores were between 71 and 96
dr. Trekcir has $875 to invest. he invests some of it in account#1 paying 8% annual interest and the rest of it in account#2 paying 4% annual interest. After 1 year total interest is $49.00. find hou much is invested in each account
Oil-rich countries in the middle east cover about 4% of earth’s total land area but possess about 48% of the world’s known oil reserves. what is the main reason for the high concentration of reserves in this part of the world?
The area of the parallelogram is 65 square miles. Find its base and height.
if an object is propelled upward from a height of s feet at an initial velocity of v feet per second h=-16t^2+96t+8 after how many seconds is the height 116 feet?
sq root of x +11 =15
N a class, 20% of the students are male and 80% female. among male students, 40% wears eyeglasses; among female students, 30% wear eye glasses. if we select a student from the class at random, what is the probability that the student wears eyeglasses
Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The figures are not drawn to scale
A. yes; 1:1:2
B. yes; 1:1:4
C. yes; 1:2:4
D. no