Answer:
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Step-by-step explanation:
Volume=576π cubic centimeters
Radius=8 cm
h=?
Her work:
Volume of a cyclinder=πr^2h
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h=9π cm
Correct workings:
Step 1:
576π= π8^2h
Step 2:
576π = 64πh
Step 3:
576π / 64π = 64πh / 64π
Step 4:
h= 9 centimeters
Her error is in step 4
C. In step 4, the (pie) should have canceled, making the correct answer 9 cm.
Answer:
the error was made in step 4, should have also been cancelled making the correct answer as 9 cm.
Step-by-step explanation:
which property is represented by 5+8(-8)=-8+5?
indentity, associative, commutative, distributive
Answer:
The Commutative property is represented by 5 + (-8) = -8 + 5.
Step-by-step explanation:
We are the following the following expression below;
5 + (-8) = -8 + 5
Identity property;This property says that is any number is added to 0, then the result is the number itself, i.e.;
2 + 0 = 2 or (-7) + 0 = -7.
Associative property;Suppose there are three numbers; a, b and c.
So, this property hold the condition that; a + (b + c) = (a + b) + c
If we add the second and third numbers and then add the first number to it or if we add the first and second numbers and then add the third number to it, the result will be the same.
Commutative property;Suppose there are two numbers 6 and 8.
This property states that if we add 6 + 8 or 8 + 6, both are equal, i,e;
6 + 8 = 8 + 6
14 = 14.
Distributive property;This property states the following condition;
a [tex]\times[/tex] (b + c) = (a [tex]\times[/tex] b) + (a [tex]\times[/tex] c)
So, 5 + (-8) = -8 + 5 is represented by the commutative property.
Express the alternative hypothesis in symbolic form
An automobile technician claims that the mean amount of time (in hours) per domestic car repair is more than that of foreign cars. Assume that two samples are independent. Let the domestic car repair times be the first population and the foreign car repair times be the second population.
A. H: mu1< mu2
B. H1: mu1 = mu2
C. H: mu1>mu2
D. H: mu not= mu2
Answer:
A. H: mu1< mu2
Step-by-step explanation:
Given that :
Mean amount of time per domestic cars = mu1
Mean amount of time per foreign cars = mu2
Automobile technicians claim :
The mean amount of time (in hours) per domestic car repair is more than that of foreign cars. This will be the Null hypothesis.
Null hypothesis : mu1 > mu2
The alternative hypothesis will negate the Null hypothesis and will hence be the opposite. This can this be expressed as :
Alternative hypothesis : mu1 < mu2
find the perimeter of the garden that has the side length of 4.3m, 8.7m and 10m
The temperature at the point (x, y, z) in a substance with conductivity K = 4.5 is u(x, y, z) = 5y2 + 5z2. Find the rate of heat flow inward across the cylindrical surface y2 + z2 = 7, 0 ≤ x ≤ 2.
Answer:
The rate of the heat flow = 1260 π
Step-by-step explanation:
From the information given :
k = 4.5
u(x,y,z) = 5y² + 5z²
Surface cylinder:
y² +z² = 5, 0 ≤ x ≤ 2
[tex]\mathtt{\overline F = \bigtriangledown u = -k(0,10y, 10z )}[/tex]
[tex]\mathtt{\overline F = -4.5(0,10y, 10z )}[/tex]
[tex]\mathtt{\overline F = (0,-45y, -45z ) \ --- (1)}[/tex]
Now parameterizing the surface by :
x = u , y = [tex]\mathtt{\sqrt{7} \ cos \ t}[/tex] , z = [tex]\mathtt{\sqrt{7} \ sin \ t}[/tex]
0 ≤ x ≤ 2 , 0 ≤ t ≤ 2π
[tex]\mathtt{{ \left. \begin{array}{1} \overline{r_y} = (1,0,0) } \\ \\ \overline{r_t} = (0, \ - \sqrt{7}\ sin \ t, \sqrt{7} \ cos \ t) \end{array} \right\} = r_u \times r_t}[/tex]
[tex]\mathtt{\overline r_u \times \overline r_t = ( -0, - \sqrt{7} \ cos \ t , - \sqrt{7} \ sin \ t) --- (2)}[/tex]
Taking integral of both equations; we have:
[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} (0, -45y, -45 z) (0, - \sqrt{7} \ cos \ t, - \sqrt{7} \ sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} ( 45\sqrt{7} \ y\ cos \ t+ 45 \sqrt{7} \ z \ sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= 45\sqrt{7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (( \sqrt{7} \ cos \ t)cos \ t + (\sqrt{7} \ \ sin \ t) sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= 45\times {7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (1) \ dtdu}[/tex]
= 315 × (2) × (2π)
= 1260 π
Help plzdont get this
Answer:
$3.
Step-by-step explanation:
All you have to do is 9/3 = 3.
An online retailer is offering a 30% savings on your total order. You decide to purchase a pair of pants for $82, two shirts for $53 each, and a pair of shoes for $120. A sales tax of 8.25% will be added to your order. What is the final price including all discounts and taxes for the clothing? Round your answer to the nearest cent
Answer:
$233.39
Step-by-step explanation:
Pants = $82, 2 Shirts = $53 * 2, Shoes = $120
Add all these values up to find the total cost of your order excluding tax.
82 + 53(2) + 120 = 308
Next find the price w/ tax. Multiply 308 by 8.25%, or 0.0825.
308 * 0.0825 = 25.41
Now you add the tax to the total value.
308 + 25.41 = 333.41
The total value including tax is $333.41. The online retailer is offering a 30% savings (discount), so multiply the total price including tax by 30% (0.30).
333.41 * 0.30 = 100.023
Now you subtract the discount from the total price.
333.41 - 100.023 = 233.38700
The question say the answer rounded to the nearest cent or hundredths, so your final answer is 233.39.
The final price of the clothing including all discounts and taxes is $233.39.
Was it evaluated correct?
explain your reasoning
Answer:
Yes
Step-by-step explanation:
Yes. They did exponents and grouping symbols first, then multiplication and division left to right. Addition came before multiplication and division because it was inside a grouping symbol.
The quadratic $10x^2+100x+1000$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?
Answer:
765
Step-by-step explanation:
Hello, please consider the following.
[tex]10x^2+100x+1000=10(x^2+10x+100)\\\\=10((x+5)^2-25+100)\\\\=10(x+5)^2+750[/tex]
So, a = 10, b = 5, c = 750 and the sum is 765.
Thank you
You please help me with this problem I’ll give you brainless
Answer:
C
Step-by-step explanation:
-27 -(-38)
when you subtract a negative it turns into addition
-27+38
Answer:
c) -27 +38
Step-by-step explanation:
the reason is because when a number is in parentheses, especially if they are negatives, they become the opposite which in this case is + so -(-38) can be the same as saying -1 × -38 and since they are both negatives, the sign becomes positive and it's just 38 while the 27 isn't affected because there's nothing in front of it I hope I helped.
janice published a novel. Last month the book sold 1364 copies, earning Janice a total of $1579.16. This month the book sold 1347 copies. How much should Janice expect to receive in royalties this month?
[tex]\$1562.52[/tex]
Unitary MethodThe unitary method is a methodology for solving problems that involves first determining the value of a single unit and then multiplying that value by the required value. The unitary method is used to calculate the value of a single unit from a given multiple.
Number of books sold last month [tex]=1364[/tex]
Total amount earned [tex]=\$1579.16[/tex]
So,
Price of each book [tex]=\frac{1579.16}{1364}[/tex]
[tex]=\$1.16[/tex]
Number of books sold this month [tex]=1347[/tex]
Total amount earned [tex]=1.16\times 1347[/tex]
[tex]=\boldsymbol{\$1562.52}[/tex]
Find out more information about unitary method here:
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Determine the domain and range of the following function. Record your answers in set notation. The domain is {x∈R| x≠−5}, and the range is {y∈R| y≠−2}. The domain is {x∈R| x≠−2}, and the range is {y∈R| y≠−5}. The domain is all real numbers, and the range is all real numbers as well. The domain is {x∈R| x≠−3}, and the range is {y∈R| y≠−5}.
Answer:
Option (2)
Step-by-step explanation:
Domain of a function is represented by the set of x-values (Input values) and Range of the function is represented by the set of y-values (Output values)
From the graph attached,
Given function is,
[tex]f(x)=\frac{x^2-x-6}{x+2}[/tex]
Domain of this function will be {x ∈ R | x ≠ -2}
[Since, point x = -2 doesn't lie on the given graph]
Range of the function will be {y ∈ R | y ≠ -5}
Therefore, Option (2) will be the correct option.
Answer:
the correct answer is A
Step-by-step explanation:
just did it on edg
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of. ... by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. ... How many square inches of wrapping paper were left over?
Answer:
380 square inches
Step-by-step explanation:
Step 1
We find the Surface Area of the Rectangular Prism
The Rectangular Prism has the dimensions of Length × Width × Height = 8 inches by 9 inches by 10 inches
Surface Area of a Rectangular Prism = 2(WL+ HL + HW)
Where W = Width = 9 inches
L = Length = 8 inches
H = Height = 10 inches
Surface Area of the Rectangular Prism = 2(9 × 8 + 10 × 8 + 9 × 10)
= 2(72 + 80 + 90)
= 2(242)
= 484 square inches.
Step 2
Find the area of the Rectangular shaped wrapping paper
The wrapping paper has dimensions :
2 feet by 3 feet
We have to convert to inches first
1 foot = 12 inches
2 feet = 2 × 12 inches = 24 inches
3 feet = 3 × 12 inches = 36 inches
Area of the Rectangular shaped wrapping paper = Length × Width
= 24 inches × 36 inches
= 864 square inches
Step 3
We calculate the amount of square inches of wrapping paper left.
The Amount left over = Area of Rectangular wrapping paper - Area of Rectangular prism
= 864 square inches - 484 square inches
= 380 square inches.
Therefore, the square inches of wrapping paper left over is 380 square inches.
HELP ME PLEASE
(The problem is in the picture)
Answer:
Hey there!
In this expression, 5k and -6 are terms, not factors.
In this expression, 5 and k are factors, so the last option is correct.
Let me know if this helps :)
Answer:
5 and k are factors.
Step-by-step explanation:
A factor would be a value or variable which is multiplied by something else. It is 'a part' of the product.
In [tex]5k-6[/tex], 5 and k are being multiplied by each other. This would mean that 5 and k are factors.
Option E should be the correct answer.
If 2(x+7)+x=20 what does x equal?
Start by distributing the 2 through both terms inside the parentheses.
This gives us 2x + 14 + x = 20.
Now subtract 14 from both sides to get 2x + x = 6.
Now combine like terms on the left to get 3x = 6.
Now, dividing both sides by 3, we find that x = 2.
What is the decision regarding the differences between the observed and expected frequencies if the critical value of the chi-square is 9.488 and the computed chi-square value is 6.079 g
Answer:
Accept the null hypothesis if it is two tailed test.
Step-by-step explanation:
The null hypotheses can only be accepted if it is a two tailed test and calculated chi square must be less than the critical value of chi square.
Then the difference between the the observed and expected frequencies will be zero.
where
H0 : σ²-σ²= 0 Ha: σ²-σ²≠0
For this the critical region would be greater than the calculated value of chi square. If so we will accept the null hypothesis and reject the alternative hypothesis.
FUNNY ONE ANSWER ! !!!!!!!!!
Answer: trapezoid
Step-by-step explanation: A trapezoid is a quadrilateral
with exactly one pair of parallel sides.
Also, quadrilaterals are two-dimensional shapes.
So it's impossible that's its 3-d.
Answer:
A. trapezoid
Step-by-step explanation:
Daniel is starting his own sewing business. Daniel has calculated that he needs to earn $360 per week to support his family. If he knows he will only be able to work 30 hours per week, what is the minimum amount of dollars per hour will he need to charge his customers?
Answer:
$12 the hour
Step-by-step explanation: $360 divided by 30 is 12, meaning he will need to make a minimum of 12 an hour to support his family.
Answer:
12
Step-by-step explanation:
cos2A is equivalent to: A. sin2A−cos2A B. sin2A+cos2A C. cos2A−sin2A D. cosA−sinA
Answer:
C. [tex]cos^2A -sin^2A[/tex]
Step-by-step explanation:
Given:
[tex]cos2A[/tex]
To find:
The given expression is equivalent to:
A. [tex]sin^2A-cos^2A[/tex]
B. [tex]sin^2A+cos^2A[/tex]
C. [tex]cos^2A -sin^2A[/tex]
D. [tex]cosA-sinA[/tex]
Solution/Proof:
First of all, let us have a look at the compound angle formula for [tex]cos(X+Y)[/tex].
Compound angle means in which there is sum of two angles given.
In the above we are having X+Y i.e. sum of two angles X and Y. So it is compound angle.
The compound angle formula for cosine is given as:
[tex]\bold{cos(X+Y)=cosXcosY-sinXsinY}[/tex]
Here, let us put X = Y = A
[tex]cos(A+A)=cosAcosA-sinAsinA\\\Rightarrow \bold{cos(2A)=cos^2A-sin^2A}[/tex]
So, cos2A is equivalent to [tex]cos^2A -sin^2A[/tex].
Correct answer is:
Option C. [tex]cos^2A -sin^2A[/tex]
Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°. (2+4) 3 (x + 4) =
Answer: 45 45 90
Step-by-step explanation:
Determine the measure of the central angle for a regular
7-sided polygon, round answers to one decimal place.
Select one:
a. 25.7°
b. 51.4°
c. 61.4°
d. 62.2°
Answer:
B
Step-by-step explanation:
If the figure is regular, then everyone of the central angles are equal. They add up to 360 degrees.
x + x + x + x + x + x + x = 360 Combine
7x = 360 Divide by 7
x = 360/7
x = 51.43
Multiply.
(y- 4z) (4y - 7)
Simplify your answer
Answer:
4y²-7y+16yz+28z
Step-by-step explanation:
4y²-7y+16yz+28z
A bag contains 4 red marbles, 6 blue marbles, and 7 green marbles. What is the probability of choosing a blue marble when one marble is drawn?
Answer:
Probabilty of selecting a blue marble if one marble is drawn
= 0.3529
Step-by-step explanation:
A bag contains 4 red marbles, 6 blue marbles, and 7 green marble.
Total number of marbles
=4 red+ 6 blue+7 green
= 17 marbles in total
Probabilty of selecting a blue marble if one marble is drawn
= Number of blue marble/total number of marble
Probabilty of selecting a blue marble if one marble is drawn
= 6/17
Probabilty of selecting a blue marble if one marble is drawn
= 0.3529
The volume of a sphere is 36ft. What is the radius
Answer:
r≈2.05
Step-by-step explanation:
Answer:3
Step-by-step explanation:
The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car Age (years) Selling Price ($000)
1 9 11.1
2 5 9.5
3 13 4.4
4 17 4.4
5 7 8.0 6
6 12.0 7
7 10.6
8 14 8.1
9 12 8.1
10 17 4.8
11 4 12.5
12 4 10.7
a. Determine the regression equation. Use the rounded slope value to compute the y-intercept. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
a = ___
b = ___
b. Estimate the selling price (in dollars) of a 7-year-old car. (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
$____
c. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
For each additional year, the car decreases $ ___ in value.
(Scroll Down for Answer!)
Answer:
b= - 1.26317
a = 17.237
b. The selling price (in dollars) of a 7-year-old car
y = 8394.81 dollars
C. For each additional year, the car decreases $ ___ in value.
1263.17 $ decreases per year
Step-by-step explanation:
Let y be the selling price in thousands and x be the age in years
Car Age Selling Price
(years) ($000) XY X²
X Y
1 9 11.1 99.9 81
2 5 9.5 47.5 25
3 13 4.4 57.2 169
4 17 4.4 74.8 289
5 7 8.06 56.42 49
6 1 2.07 2.07 1
7 1 0.6 0.6 1
8 14 8.1 113.4 196
9 12 8.1 97.2 144
10 17 4.8 81.6 289
11 4 12.5 50 16
12 4 10.7 42.8 16
∑ 97 84.33 723.49 1276
The estimated regression line of Y on X is
Y= a +bX
and the two normal equations are
∑ y= na + b∑X
∑XY= a∑X + b∑X²
Now
X`= ∑X/n = 97/12= 8.083
b= n∑XY - (∑X)(∑Y)/ n∑ X²- (∑X)²
b= 723.49 - (97)(84.33)/ 12(1276) - (97)²
b= -7456.52/ 5903
b= - 1.26317
a= Y`- b X`
a= 7.0275 - (-- 1.26317)8.083
a = 17.237
Y = 17.237 - 1.26317 X
y= - 1.26317 X + 17.237
b. The selling price (in dollars) of a 7-year-old car
y = - 1.26317 (7) + 17.237
y= 8.39481
y = 8394.81 dollars
C. For each additional year, the car decreases $ ___ in value.
1.26317 *1000= 1263.17 $ decreases per year
What is the ratio 18 to 27 written as a fraction and lowest terms
Step-by-step explanation:
18:27
=18/27
=2/3 or 2:3
Debbie needs to fill juice cups for her little brother's birthday party. There are 20 juice cups and each juice cup holds 10 fluid ounces. The juice comes in 1-gallon bottles. How many 1-gallon bottles of juice will Debbie need to purchase?
Answer:
Debbie would need to purchase 2 1-gallon bottles of juice.
Step-by-step explanation:
So we have 20 cups and each cup holds 10 fluid ounces. 20 times 10 equals 200 fluid ounces. We need to see how many fluid ounces are in 1 gallon. There are 128 fluid ounces in 1 gallon. 200 divided by 128 equals to 1.56 gallons. Debbie needs more than 1 gallon. Since we have a decimal and 1 is on the left of the decimal, Debbie would need to purchase 2 1-gallon bottles of juice.
Pleaase help with both questions ! PLease explain if you can!
Answer:
See below for answers to both questions.
Step-by-step explanation:
Question 13)
We know that the perimeter is the sum of all of the side lengths of the square, and we know that a square has 4 sides that are all the same length. This lets us set up the following equation:
4(10x + 6) = 74
To solve this equation, we should first distribute the 4 through the parentheses using the distributive property.
40x + 24 = 74
Next, we should subtract 24 from both sides of the equation.
40x = 50
Finally, we should divide both sides by 40.
x = 50/40 = 1.25
Therefore, the answer to question 13 is x = 1.25.
Question 14)
If we know the rectangle and triangle have the same perimeter, we can set up the following equation:
2(4x-1) + 2(x-1) = (4x + 1) + (3x + 5) + (x + 1)
We should begin by simplifying the left side of the equation using the distributive property, as we did above.
8x - 2 + 2x -2 = 4x + 1 + 3x + 5 + x + 1
Next, we can combine like terms on both sides of the equation. This means adding together the constant terms (numbers) and also combining the variable terms (x's). This is modeled below:
(8x + 2x) + (-2 + -2) = (4x + 3x + x) + (1 + 5 + 1)
10x - 4 = 8x + 7
Next, we should subtract 8x from both sides.
10x - 8x - 4 = 8x - 8x + 7
2x - 4 = 7
Next, we should add 4 to both sides.
2x - 4 + 4 = 7 +4
2x = 11
Finally, we should divide both sides by 2.
x = 11/2 = 5.5
The question asks us to find the perimeter, so we can use the perimeter of the rectangle:
10x - 4 = 10(5.5) - 4 = 51
Therefore, the answer is 51 units.
Hope this helps!
Statistical Quality Control Stat class
1) For a single-sampling plan for attributes, what do the following symbols represent?
a. N
b. n
c. c
d. d
2) For a double-sampling plan for attributes, what do the following symbols represent?
a. n1
b. n2
c. c1
d. c2
e. d1
f. d2
Answer:
Step-by-step explanation:
In a single - sampling plan, when a decision on acceptance / rejection of the lot is made on the basis of only one sample, Then , the acceptance plan is said to be a single sampling plan. The single sampling plan is known as the most common and easiest sampling plan
The following symbol representation can be written as follows:
a. N → Lot size from which the sample is drawn
b. n → sample size
c. c → acceptance number
d. d → number of defectives in the sample
For example:
if we take a randomized sample of size 'n' from the Lot size.
The next step will be to inspect all items in the sample to find the defectives 'd'
The decision rule is that:
If the number of defectives is less than or equal to acceptance number, then answer is YES i.e d ≤ c, Then , we accept the Lot
If the number of defectives is not less than or equal to acceptance number, then the answer is NO . Then , we reject the Lot.
So if we reject, we either do 100% inspection or return the lot to the supplier.
In a double sampling plan , the decision on acceptance/rejection of the Lot is based on two samples.
The following symbol representation can be written as follows:
a. n1 → number of size of sample 1
b. n2 → number of size of sample 2
c. c1 → acceptance number for sample 1
d. c2 → acceptance number for sample 2
e. d1 → number of defectives in sample 1
f. d2 → number of defectives in sample 2
.If you dye 1/3 of it blue, ¼ pink and 2/5 black, how much of your original hair colour is left?
Answer:
You have 1/60 of the original hair color left
Step-by-step explanation:
Add up the fractions
1/3 + 1/4 + 2/5
Get a common denominator of 60
1/3 * 20/20 + 1/4 * 15/15 + 2/5 * 12/12
20/60 + 15/60 + 24/60
59/60
The total is 1 or 60/60
60/60 - 59/60
1/60
You have 1/60 of the original hair color left
A bowl holds the pieces of fruit shown below. The image shows 8 apples and 7 oranges. If Jasmine correctly writes the fraction of fruit that are apples, which of the following would be the numerator of the fraction?
Answer:
8+7=15 therefore 8
5
Step-by-step explanation:
The numerator from the fraction of apple fruits to total fruits is 8
How to find fraction of apples to total fruits?
Number of apples = 8Number of oranges = 7Total fruits = apples + oranges
= 8 + 7
= 15
Fraction of apple fruits to total fruits = Number of apples / Total fruits
= 8/15
Therefore, the numerator from the fraction of apple fruits to total fruits is 8
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