In this problem, you are asked to compute for the value of y when x = 21. The function shows how the value of y changes with the given value of x.
Y = 2/3x + 20
Y = 2/3 (21) + 20
Y = 14 + 20
Y = 34
Answer:
5
Step-by-step explanation:
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You are standing 40 feet away from a building that is 115 feet tall. What is the angle from the ground to the top of the building to the nearest degree?
Two numbers are in the ratio of 2 to 3. If the smaller number is 18, the larger number is _____. 21 27 36 54
Answer: If two numbers are in a ratio of 2 to 3, this means that two times one number is equal to 3 times the other, or:
2*X = 3*Y, where X and Y are any numbers, and X is the bigger one and Y is the smaller one.
If Y=18, then:
2*X = 3*18 = 54
X=54/2 = 27
So the answer is 27.
Find the derivative of f(x) = |x2 – 1| at the point (1, 0).
How to solve
187=1/2*17(6+X)
The value of y varies directly with x, and y = 12 when x = 16.
Find y when x = 6.
A. 8
B.12
C.2/9
D.9/2
Final answer:
Given that the value of y varies directly with x, and y = 12 when x = 16, we find that y when x = 6 is 9/2, corresponding to option D.
Explanation:
The question asks to find the value of y when x = 6, given that the value of y varies directly with x, and y = 12 when x = 16. This is a problem of direct variation, where the relationship between the variables can be represented by the equation y = kx, where k is the constant of variation.
To find k, we use the given values: y = 12 when x = 16. Substituting these into the equation gives 12 = k(16), leading to k = 12/16 or k = 3/4. Then, to find y when x = 6, we substitute x = 6 into the direct variation equation with our found k value: y = (3/4)(6), simplifying to y = 9/2.
Therefore, the value of y when x = 6 is 9/2, which matches option D.
Choose the correct discount or markup. If an item has a retail price retail price = $995 and a discount of 15%, how much is the discount? It is $ options a. 149.25 b. 139.25 c. 144.50
Final answer:
The discount amount on an item with a retail price of $995 and a 15% discount is $149.25 that is option a is correct answer.
Explanation:
Discount Amount Calculation:
Calculate the discount amount by multiplying the retail price by the discount percentage.
Discount = $995 x 0.15 = $149.25.
The correct answer is $149.25 (option a).
A key difference between calculating the sample mean and the population mean is that:
a.we use and n instead of µ and n.
b.we divide the sum of the observations by n - 1 instead of n.
c.the sample observations are ranked and the middle value is selected as the population mean.
d.there are no differences.
Final answer:
The key difference between calculating the sample mean and the population mean is that when calculating the sample mean, we use x and n instead of µ and n. Additionally, we divide the sum of the observations by n - 1 instead of n. Correct Option -B
Explanation:
The key difference between calculating the sample mean and the population mean is that when calculating the sample mean, we use x and n instead of µ and n. Additionally, we divide the sum of the observations by n - 1 instead of n.
The reason for dividing by n - 1 in the sample mean calculation is that it provides a better estimate of the population variance. Dividing by n - 1 instead of n accounts for the fact that the sample mean is an estimate of the population mean based on a limited set of data.
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What is the value of x in the figure below? In this diagram, ΔABD ~ ΔCAD
Value of x for the similar triangles ΔABD ~ ΔCAD is equals to [tex]\frac{25}{4}[/tex].
What are similar triangles?" Similar triangles are defined as the triangles with same shape but different in their size, corresponding sides of similar triangles are always in proportion."
According to the question,
As per the diagram,
ΔABD and ΔCAD are similar triangles.
AB = 10 units
BD = x units
BC = 16 units
CD = BC - BD
= 16 - x
ΔABD is a right angle triangle.
Therefore,
Using Pythagoras theorem,
[tex]AD ^{2} = 10^{2} -x^{2}[/tex]
ΔABD corresponding ΔCAD as per the given diagram.
From the definition of similar triangles corresponding sides are in proportion.
[tex]\frac{AD}{CD} =\frac{BD}{AD}[/tex]
⇒[tex]AD^{2} =(BD )(CD)[/tex]
Substitute the value of AD, BD and CD we get,
[tex]10^{2} -x^{2} = (x) (16-x)[/tex]
⇒[tex]100 -x^{2} =16x-x^{2}[/tex]
⇒[tex]100 = 16x[/tex]
⇒[tex]x= \frac{100}{16}[/tex]
⇒[tex]x=\frac{25}{4}[/tex]
Hence, Option(F) is the correct answer.
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6.
Evaluate cot 290º. Round your answer to the nearest hundredth.
–1.06
–0.36
2.92
–2.75,
The number of members f(x) in a local swimming club increased by 30% every year over a period of x years. The function below shows the relationship between f(x) and x:
f(x) = 10(1.3)x
Which of the following graphs best represents the function?
Graph of f of x equals 1.3 multiplied by 10 to the power of x
Graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing towards infinity
Graph of f of x equals 10 multiplied by 1.3 to the power of x
Graph of f of x equals 1.3 to the power of x
The graphs that best represents the function is:
Graph of f(x) equals 10 multiplied by 1.3 to the power of x.
Step-by-step explanation:The function that shows the relationship between f(x) and x: is:
[tex]f(x)=10\times (1.3)^x[/tex]
a)
Graph of f(x) equals 1.3 multiplied by 10 to the power of x.
This means that the expression is given by:
[tex]f(x)=1.3\times (10)^x[/tex]
Hence, option: a is incorrect since it is not equal to the given function f(x).
b)
Graph of exponential function going up from left to right in quadrant 1 through the point (0, 0) and continuing towards infinity.
In the given function f(x) when x=0 we have:
[tex]f(x)=10\times (1.3)^0\\\\\\f(x)=10\neq 0[/tex]
Hence, option: b is incorrect.
c)
Graph of f(x) equals 10 multiplied by 1.3 to the power of x.
This means that the function f(x) is given by:
[tex]f(x)=10\times (1.3)^x[/tex]
which is obviously true.
Hence, option: c is correct.
d)
Graph of (x) equals 1.3 to the power of x.
This means that the function f(x) is given by:
[tex]f(x)=(1.3)^x[/tex]
which does not m,atches the actual expression.
Hence, option: d is incorrect.
Time 6 years Interest rate 1.9% Principal- $850 What amount of simple interest will be earned? $16.15 O $96.90 $946.90 $9,690.00
Which value(s) of x would result in Set B being a function of the values in Set A? Select Function or Not a Function for each value of x. Are the following numbers a function or not a function
To determine if Set B is a function of the values in Set A, we need to ensure that each value of x in Set A has only one corresponding value in Set B:
-2: Function5: Function0: Not a Function1: Function-3: FunctionFor each value of x, we can determine if Set B is a function or not by checking if there is only one corresponding value in Set B.
For x = -2, there is only one corresponding value in Set B, so it is a function.
For x = 5, there is only one corresponding value in Set B, so it is a function.
For x = 0, there are multiple corresponding values in Set B, so it is not a function.
For x = 1, there is only one corresponding value in Set B, so it is a function.
For x = -3, there is only one corresponding value in Set B, so it is a function.
Therefore, Set B is a function of the values in Set A for all values of x except for x = 0.
a building in san francisco is shaped like a square pyramid it has a slant height og 856.1 feet and each side of its base is 145 feel long find the lateral area of the building
A. 11 cm^3
B. 14 cm^3
C. 15 cm^3
D. 25 cm^3
Jamie has 4 apples and 6 bananas. Each apple cost 0.75 and each banana cost 0.6” write an expression representing the total cost
A prism with a volume of 3125 ft³ is scaled down to a volume of 200 ft³.
What is the scale factor?
Enter your answer, as a decimal or a fraction in simplest form, in the box.
I think it's 2/5 or 0.4
Answer:
The scale factor is equal to [tex]0.4[/tex] or [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
we know that
If two figures are similar. then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z------> the scale factor
x------> the volume of the dilated prism
y------> the volume of the original prism
so
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]x=200\ ft^{3}[/tex]
[tex]y=3,125\ ft^{3}[/tex]
substitute
[tex]z^{3}=\frac{200}{3,125}[/tex]
[tex]z=\sqrt[3]{\frac{200}{3,125}}[/tex]
[tex]z=0.4[/tex] or [tex]z=\frac{2}{5}[/tex]
To solve a problem, we often _________ the given information into algebraic expressions and equations.
Example: The phrase "4 more than twice a number" becomes '2n + 4'.,
Answer:
Translate or transform
Step-by-step explanation:
Took the test (USA test prep)
What is 8.3x10^-9 in standard form?
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A circular pool is surrounded by a circular walkway. The radius of the pool is y − 4 and the radius of the full circle formed by the walkway is y + 4. Write a polynomial that represents the area of just the walkway itself, not including the space covered by the pool. (The area of a circle is given by A = πr ^2, where r represents the radius of the circle.)
The polynomial representing the area of the walkway is the difference between the area of the large circle (π(y + 4)²) and the small circle (π(y − 4)²).
Explanation:To find the polynomial that represents the area of the walkway surrounding a circular pool, we need to calculate the difference between the area of the larger circle (walkway plus pool) and the area of the smaller circle (just the pool).
The radius of the pool is y − 4, and the radius of the walkway plus the pool is y + 4. The area of a circle is given by A = πr².
First, calculate the area of the large circle:
Area of the large circle = π(y + 4)²
Then, calculate the area of the small circle:
Area of the small circle = π(y − 4)²
Finally, the polynomial for the area of the walkway is found by subtracting the area of the small circle from the area of the large circle:
Area of the walkway = π(y + 4)² − π(y − 4)²
The polynomial that represents the area of just the walkway (not including the pool) is π(8y + 32).
Explanation:To find the area of just the walkway, we need to subtract the area of the pool from the area of the full circle formed by the walkway. The area of the pool is given by A = πr ^2, where r is the radius of the pool (y - 4). The area of the full circle is given by A = πr ^2, where r is the radius of the walkway (y + 4). Therefore, the area of the walkway is (π(y + 4) ^2) - (π(y - 4) ^2). Simplifying this expression, we get the polynomial: π(8y + 32).
The slope of the line whose equation is x+2y=3 is
Jill had an AGI of $25,000. She had $2800 in medical expenses, paid $6000 in rent, and had to buy a new uniform for work, which was not reimbursed by her employer. Which expense(s) can she itemize on her tax return?
A.Nonreimbursed work expenses, mortgage interest, and medical expenses
B.Mortgage interest and medical expenses
C.Medical expenses and nonreimbursed work expenses.
D.Mortgage interest only
Answer:
C.Medical expenses and nonreimbursed work expenses.
Step-by-step explanation:
just did it on apex
Answer:
C
Step-by-step explanation:
Medical expenses and nonreimbursed work expenses.
evaluate the principal square root of 36 .
answer ??? help plz thank u :)),
A trinket factory can produce 3,000 trinkets per day. The warehouse has a capacity of 50,000 trinkets. Currently, there are 8,000 trinkets in the warehouse. Assume that no trinkets are going to be shipped out of the warehouse for a while. 1) Write an equation for the number of trinkets in the warehouse after days. 2) How many days will it take to fill the warehouse?
The equation for number of trinkets after x days is 8,000 + 3000 * x = y and the number of days required to fill the warehouse is 14.
What is an Equation?An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.
The trinket factory can produce 3,000 trinkets per day
Total Capacity of warehouse is 50,000 trinkets
The trinkets in the warehouse is 8,000
The equation for the number of trinkets in the warehouse after x days is
Let y represents the total number of trinkets after x days
8,000 + 3000 * x = y
The days required to completely fill the warehouse is
8,000 + 3,000 * x = 50,000
3,000* x = 42,000
x = 14
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find the second, fourth, and eleventh terms of the sequence described by each explicit formula A(n)=2+(n-1)(-2.5)
Find the length of a line segment with endpoints of -9 and 7.
I don't understand how to do this.
A.-16
B.-2
C.16
D.26,
I need both answers now!
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The ages of students in a school are normally distributed with a mean of 15 years and a standard deviation of 2 years. Approximately what percent of the students are between 14 and 18 years old?
24.17%
62.47%
30.85%
93.32%,
Which high school math course, algebra or geometry, is more closely related to engineering? justify your answer?
Final answer:
Both algebra and geometry are integral to engineering, with algebra being more directly related to the numerical problem-solving aspects, and geometry being crucial for spatial understanding and design. A well-rounded engineering education incorporates both, to prepare students for advanced mathematical concepts and engineering science courses.
Explanation:
Both algebra and geometry are closely related to engineering, but they serve different purposes within the field. Algebra is fundamental for problem-solving and numerical analysis in engineering. It allows for the creation of mathematical models that can describe physical processes, and is often used alongside computer programs to solve complex real-life problems. Geometry, on the other hand, is essential for a thorough understanding of spatial relationships and structures, which are critical in fields such as mechanical, civil, and architectural engineering.