The volume of a cone is given by
[tex]V\text{ = }\frac{1}{3}\pi\text{ r}^2\text{ h }[/tex]Diameter = 34 in
radius = 34/2 = 17 in
Height = 17in
[tex]\begin{gathered} V\text{ = }\frac{1}{3}\text{ x 3.14 x 17 x 17 x17} \\ V\text{ =5142.27 inches} \end{gathered}[/tex]4. (02.05 MC)
Which statement is true if the quantity demanded of a good decreases by 10% while consumer incomes increase by 2 %? (5 points)
O The income elasticity of demand is -20, and the good is inferior.
The income elasticity of demand is -5, and the good is inferior.
The income elasticity of demand is 0.2, and the good is normal.
The income elasticity of demand is 5, and the good is inferior.
The income elasticity of demand is 20, and the good is normal.
Based on the decrease in the quantity demanded and the increase in income, the true statement is The income elasticity of demand is -5, and the good is inferior.
How to find the income elasticity?The income elasticity of a good can be found by the formula:
= Change in quantity demanded / Change in income
= -10% / 2%
= - 5
When the income elasticity of demand for a good is negative, it means that it is an inferior good. This is because people only buy them because its what they can afford but if income rises, people stop buying them.
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19. What fraction of the distance from M to V is MD?
Answer:the point is located on MV
Step-by-step explanation:
The Coordinates of D (0,-3/4)
Estimate by rounding each number to the nearest ten. Then find the difference.32.76 - 22.168An estimation of the difference isThe exact difference is
ANSWER
EXPLANATION
First let us find the actual difference:
32.76 -
The measure of <1 is greater than 97° and at most 115°. Graph the possible values of x.
Step-by-step explanation:
it help with work
Question 1-4
Rectangle ABCD is dilated into rectangle AB'C'D', as shown.
B'
B
A
3
6
C
2
D
C'
D'
What is the scale factor of dilation? Enter the answer as a whole number or a simplified fraction in the box. Use "/" for the fraction bar.
Draw a model to show a 26-pack of candy bars divided equally among 7 people. Howmany candy bars will each person have?
The diagram would be:
To find how many candy bars each person will get we divide 26 by 7:
[tex]\frac{26}{7}=3\frac{5}{7}[/tex]Therefore each person will get 3 5/7 of candy bar (appoximately 3.71 candy bars)
A C, С B, AC = 10 BC = 15 What is the length of AB? Round your answer to the nearest tenth, if necessary. Figure is not drawn to scale
You have a right triangle and the length of the legs, use Pythaorean theorem to find the length of the hypotenuse (AB)
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ \\ AB=\sqrt[]{AC^2+BC^2} \\ AB=\sqrt[]{10^2+15^2} \\ AB=\sqrt[]{100+225} \\ AB=\sqrt[]{325} \\ AB=18 \end{gathered}[/tex]Then, the length of AB is 18In a bag of Jolly Ranchers, the ratio of blue to red is 3 to 4. If I have a TOTAL of 56 Jolly Ranchers, how many of them are blue?
Answer:
24
Step-by-step explanation:
If ratio of blue to red is 3:4 or in fraction terms 3/4 then the ratio of blue to all Jolly ranchers = 3/(3+4) = 3/7
Since there are a total of 56, the number of blue ones = 56 x 3/7 = 24
Answer:
24
Step-by-step explanation:
Based on the given conditions, formulate: 56 x 3 divided by (3 + 4)
Calculate the product or quotient: 168/3+4
Calculate the sum or difference:168/7
Cross out the common factor:24
get the result:24
Answer: 24
The cheerleading team has won ¾ of their competitions. If the team competes in 16 competitions, how many did they win?
The statements below represent some possible deposits and withdrawals from Rachel's bank account Match each statement with the total amount that Rachel's account would change. -47.50 -22.50 22.50 She deposits $35 to her account. Then spends $12.50 from her account on lunch. She withdraws $35 from her account. Then spends $12.50 from her account on lunch. She spends $35 from her account on clothes. Then she deposits $12.50 to her account 17 Pause Previous
ok, If she did not initially have anything on the account, this is the process
[tex]\begin{gathered} +35 \\ -12.5 \\ -35 \\ -12.50 \\ -35 \\ +12.50 \\ -------- \\ -47.50 \end{gathered}[/tex]his bank account is at -47.50 dollars
What is the distance between three and 11 on the number line
We need to calculate the distance between 3 and 11 on the number line:
[tex]11-3[/tex]That is, from 0 we go 11 units forward and 3 units backward, like this:
Answer: 8
Answer:
8
Step-by-step explanation:
box with a square base and open top must have a volume of 171500c * m ^ 3 . We wish to find the imensions of the box that minimize the amount of material used.
step 1
Find out the equation of the volume of the box
[tex]\begin{gathered} V=x^2h \\ V=171,500\text{ cm}^3 \\ 171,500=x^2h \\ h=\frac{171,500}{x^2} \end{gathered}[/tex]step 2
Find out the expression for the surface area
The surface area is given by the expression
[tex]A=x^2+4xh[/tex]substitute the value of h
[tex]\begin{gathered} A=x^2+4x\frac{171,500}{x^2} \\ simplify \\ A(x)=x^2+\frac{686,000}{x} \\ \\ A(x)=\frac{x^3+686,000}{x} \end{gathered}[/tex]step 3
Find out the derivative A'(x)
[tex]A^{\prime}(x)=2x-\frac{686,000}{x^2}[/tex]step 4
Equate the derivative to zero
[tex]\begin{gathered} 2x-\frac{686,000}{x^2}=0 \\ 2x=\frac{686,000}{x^2} \\ \\ 2x^3=686,000 \\ x^3=343,000 \\ x=70 \end{gathered}[/tex]A'(x)=0 when x=70step 5
Find out the second derivative A''(x)
[tex]A^{\prime}^{\prime}(x)=2+\frac{1,372,000}{x^3}[/tex]Evaluate the second derivative for x=70
[tex]\begin{gathered} A^{\prime}^{\prime}(x)=2+\frac{1,372,000}{(70)^3} \\ A^{\prime}^{\prime}(x)\text{ is positive} \\ that\text{ means} \\ The\text{ value of A\lparen x\rparen i}s\text{ a maximum for x=70 cm} \end{gathered}[/tex]Ruben purchases a violin that is on sale for a total price of$1,250, which includes tax and all other fees. He makes aninitial payment of $300 in cash and puts the remainder on hisnew credit card. He makes no other purchases on the card andpays off the credit card balance with 9 monthly payments of$150. What is the difference between the total amount Rubenpays for the violin, including the initial payment and the creditcard payments, and the sale price of the violin?
Given:
Actual price of a violin is $1,250
Credit card monthly payment as $150.
Initial payment is $300.
[tex]\text{Total money paid by Ruben for violin=300+(150}\times9)[/tex][tex]\text{Total money paid by Ruben for violin=300+}1350[/tex][tex]\text{Total money paid by Ruben for violin= \$1650}[/tex]The difference between the total amount Ruben pays for the violin, including the initial payment and the credit card payments, and the sale price of the violin:
[tex]\text{Diffference amount=1650-1250}[/tex][tex]\text{Diffference amount= \$400}[/tex]Difference amount is $400.
A candy company has decided to sell candy in a new package that is shaped like a triangular prism in order to calculate the volume of the package, the area of the base must be determined.If the base of the package is equilateral triangle with sides 10 centimeters (cm) long, what is the area of the base?
Using the formula for the area of the equilateral triangle, we have:
[tex]\begin{gathered} A=\frac{\sqrt[]{3}}{4}a^2 \\ A=\frac{\sqrt[]{3}}{4}(10)^2cm^2\text{ (Replacing)} \\ A=\frac{\sqrt[]{3}}{4}(100)^{}cm^2\text{ (Raising 10 to the power of 2)} \\ A=25\sqrt[]{3}\text{ }cm^2\text{(Dividing 100 by 4}) \\ A=43.3\text{ }cm^2\text{ (Multiplying 25 by }\sqrt[]{3}) \\ \text{The answer is 43.3 cm}^2 \end{gathered}[/tex]pls answer!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: -49
Step-by-step explanation: 7 x 7 = 49, but since it has the (-) symbol it will be -49.
Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ less than 128.
The probability that the IQ is less than 128 is 0.91924
How to determine the probability?The given parameters about the distribution are
Mean value of the set of data, μ = 100Standard deviation value of the set of data σ = 20IQ value, x = 128The z-score of the data value is calculated as
z = (x - μ)/σ
Substitute the given parameters in the above equation
z = (128 - 100)/20
Evaluate
z = 1.4
The probability that the IQ is less than 128 is then calculated as:
P(x < 128) = P(z < 1.4)
From the z table of probabilities, we have;
P(x < 128) = 0.91924
Hence, the probability is 0.91924
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x
Answer:
Step-by-step explanation:
Enter the equation of the circle with the given center and radlus. Center: (0,5); radius: 8 The equation of the circle is
The equation of the circle with the given data is given as,
where,
[tex]centeris(x_1,y_1\text{) and radius is r}[/tex][tex]\begin{gathered} (x-x_1)^2+(y-y_1)^2=r^2 \\ (x-0)^2+(y-5)^2=8^2 \\ x^2+(y-5)^2=64 \end{gathered}[/tex]Is y = 2x² a linear or nonlinear function? Please explain.
A linear function has the form:
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept, bot constants.
As we see, the exponent of variable x is 1 for a linear function.
So, since the exponent in the given function y = 2x² is 2, this function is a nonlinear function.
In fact, it is a quadratic function.
Multiply. Stars and restrictions on the variable. Simplify the rational expression.
Given,
The expression is:
[tex]\frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}[/tex]Required:
The simplified rational expression.
Simplifying the expression,
[tex]\begin{gathered} \frac{x^2+2x-8}{x^2+4x-12}\times\frac{5x+30}{x+5}=\frac{x^2+4x-2x-8}{x^2+6x-2x-12}\times\frac{5x+30}{x+5} \\ =\frac{x(x+4)-2(x+4)}{x(x+6)-2(x+6)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)(x-2)}{(x+6)(x-2)}\times\frac{5(x+6)}{x+5} \\ =\frac{(x+4)}{1}\times\frac{5}{x+5} \\ =\frac{5(x+4)}{x+5} \\ =\frac{5x+20}{x+5} \end{gathered}[/tex]Hence, the simplified rational expression is (5x+20)/(x+5).
The restriction of the expression is:
[tex]x\ne-5,\text{ 2,-6}[/tex]
if one face of a cubr has a area of 6.75 square inches, what is the surface of the entire cube.
The surface area of the entire cube is 40.5 square inches
Here, we want to get the surface area of a cube given the measure of the area of one of the faces
Looking at the net of a cube, we can identify six identical and equal-dimension faces
So to get the total surface area of the cube, we have to multiply the surface area of one of the faces by 6
Mathematically, that would be;
[tex]6.75\text{ }\times\text{ 6 = 40.5}[/tex]A student argued that a pizza cut into 12 pieces was more than a pizza cut into 6 pieces. How would you respond?
Answer:
i say a pizza with six has more for less people but twelve is for more people so equally they are both a lot.
Step-by-step explanation:
On Tuesday d dollars worth of merchandise was sold. On Wednesday the amount of merchandise sold was $150 less than twice the amount of merchandise sold on Tuesday
Answer:
2d-150
Explanation:
The worth of Merchandise sold on Tuesday = d dollars.
On Wednesday the amount of merchandise sold was $150 less than twice the amount of merchandise sold on Tuesday .
• Twice the amount of merchandise sold on Tuesday = 2d
,• 150 less than 2d = 2d-150.
An expression for the amount of merchandise sold on Wednesday is:
[tex]2d-150[/tex]The third option is correct.
is this relation a function ? yes or noif no , identify two ordered pairs as proof.
A relation is said to be a function when each input value is related to only one output.
It can also be said that a function is a relation that has only output for any unique input.
In a function, each x-value is related to only one output.
From the relation given here, we have a straight-line graph. Here, each x-value is related to only one y-value.
Since each x-value is related to only one y-value, this relation is a function.
ANSWER:
Yes, this relation is function.
Marbel surveyed 55 people to find out their favorite types of music the results shown in the bar graph
To find the correct option, we need to find, first, the rate of the population that chose each type of music. Then, when we sum the rates of the types in the correct answer, it should result in 40%.
The rate of population for each type of music is given by the number of peaple that chose this type, divided by the total amount of people (55):
Country: 15/55
Jazz: 12/55
Opera: 10/55
Roch: 18/55
In the first option, we have:
Country and Opera
There is one number that is neither crossed out nor circled. Why is it treated differently?
r is the character which is not treated
you get charged $12.50 for each movie you buy on amazon prime.Somehow you accidentally spent $87.50 on movies last month. How many movies did you buy
You buy seven movies from Amazon Prime which is determined by the division operation.
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.
For example 4/2 = 2
A movie ticket costs $12.50 which is given in the question
Last month, $87.50 was spent on Amazon Prime.
Your total movie expenditure is
⇒ 87.50/12.50
Apply the division operation to get
⇒ 7.
As a result, you buy seven movies from Amazon Prime.
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Please help me with this problem Let f(x)=25x2−2. The function g(x) is a vertical stretch of f(x) by a factor of 2. What is the equation of g(x)? Enter your answer in the box. g(x) =
Solution
Given the function below
[tex]f(x)=\frac{2}{5}x^2-2[/tex]The function g(x) is a vertical stretch of f(x) by a factor of 2, i.e
[tex]\begin{gathered} g(x)=2(\frac{2}{5}x^2-2) \\ g(x)=\frac{4}{5}x^2-4 \end{gathered}[/tex]Hence, the equation of g(x) is
[tex]g(x)=\frac{4}{5}x^2-4[/tex]Pls help with this problem
Answer:
[tex] \frac{5}{24} [/tex]
Step-by-step explanation:
5/24 * 3 = 15/24 that can be reduced to 5/8
Answer: 5/24
Step-by-step explanation:
5/8 devided by 3
3 turns into 1/3
5/8 X 1/3 =5/24
76 cm57 cmWhat is the length of the hypotenuse?C=centimeters
Using pythagoras Theory which is:
(Hypotenuse)^2 = (opposite)^2 + (Adjacent)^2
C^2 = 76^2 + 57^2
C^2 = 7776 + 3249
C^2 = 11025
C = SQUAREROOT(11025)
C = 105cm
