Answer:
the average is
add 22 8 times and add 13 4 times
8×22=176
4×13=52
52+176=228
The average price you paid for each movie will be $19.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean.
It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
You bought 8 DVDs for $22 each and 4 DVDs for $13 each.
Then the total number of the DVDs will be
Total DVDs = 8 + 4 = 12
The total amount of dollars spent will be
Total amount = 22 x 8 + 13 x 4
Total amount = $228
Then the average price you paid for each movie will be
Average = $228 / 12
Average = $19
The average price you paid for each movie will be $19.
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Write the number shown in standard notation. 1.02 x 10 First Correct answer gets Brainliest
Answer:
1.02×10¹ = 10.2
Step-by-step explanation:
We have given a number in scientific notation as follows 1.02×10¹
We need to convert it into standard notation.
1 is in ones place, 0 is in tenths place and 2 is in hundredths place.
[tex]1.02\times 10^1=\dfrac{102}{100}\times 10\\\\=\dfrac{102}{10}\\\\=10.2[/tex]
So, the standard notation of 1.02×10¹ is 10.2
A rectangular tank that is 2048 ft cubed with a square base and open top is to be constructed of sheet steel of a given thickness. Find the dimensions of the tank with minimum weight.
Answer:
The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft
Step-by-step explanation:
We were given the volume of the tank as, 2048 cubic feet.
Form minimum weight, the surface area must be minimum.
Let the height be h and the lengths be x
the volume will be: V=x²h then substitute the value of volume, we have
2048=hx²
hence
h=2048/x²
Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.
The surface area of the box described is
A=x²+4xh
Then substitute h into the Area equation we have
A= x² + 4x(2048/x²)
A= x² + 8192/x
We want to minimize
A
dA/dx = -8192/x² + 2 x= 0 for max or min
when dA/dx=0
dA/dx= 2x-8192/x²=0
2x=8192/x²
Hence
2x³=8192
x³=4096
x=₃√(4096)
X=16ft
Then h=2048/x²
h=2048/16²
h=8ft
The box should have base 16ft by 16ft and height 8ft
Hence the dimensions are 16 ft by 16 ft by 8 ft
The valve was tested on 210 engines and the mean pressure was 5.0 pounds/square inch (psi). Assume the population standard deviation is 0.9. The engineer designed the valve such that it would produce a mean pressure of 4.9 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
1.6101529
Step-by-step explanation:
Given the following :
Number of samples (n) = 210
Sample mean (x) = 5
Population standard deviation = 0.9
Population mean (m) = 4.9
Since the standard deviation of the population is known, we can use the z statistic
Z = (x - m) / standard error
Standard error = sd / √n
Standard error = 0.9 / √210
Standard error = 0.9 / 14.491376
Standard error= 0.0621059
Z statistic = (5 - 4.9) / 0.0621059
Z statistic = 0.1 / 0.0621059
Z statistic = 1.6101529
Data for price and thickness of soap is entered into a statistics software package and results in a regression equation of ŷ = 0.4 + 0.2x.
What is the correct interpretation of the slope if the price is the response variable and the thickness is an explanatory variable?
A. The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.
B. The price of the soap decreases by $0.40, on average, when the thickness increases by 1 cm.
C. The price of the soap increases by $0.40, on average, when the thickness increases by 1 cm.
D. The price of the soap decreases by $0.20, on average, when the thickness increases by 1 cm.
Answer: A. The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm
Step-by-step explanation:
Given the following :
Regression equation : ŷ = 0.4 + 0.2x
Price is the response variable (ŷ)
Thickness is the explanatory variable (x)
Relating the equation given to the regression model:
ŷ = c + mx
Here c = intercept ; y = response variable ;x = explanatory variable and m = slope or gradient.
Hence, mx = 0.2x
Where m = 0.2
The slope means :
Change in y / change in x
Changes in the response variable with respect to change in the explanatory variable.
The slope is positive meaning an increase in the thickness will result in a corresponding increase in price.
With a 0.2 gradient value, that means there is an $0.2 average increase in price of soap as the thickness increases by 1 cm.
Answer:
The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.
Step-by-step explanation:
Your forecasted income statement shows sales of $1,362,000, cost of goods sold at $830,000, depreciation expense of $310,000, and a forecasted free cash flow of $470,200. What are your forecasted earnings? What is your tax rate?
Answer:
Forecasted earning = $160,200
Tax rate = 27.84%
Step-by-step explanation:
The calculation of forecasted earning and tax rate is shown below:-
Earnings before income and taxes = Sales - Cost of goods sold - Depreciation Expense
= $1,362,000 - $830,000 - $310,000
= $222,000
So,
Forecasted Free cash flow = Net Income + Depreciation
$470,200 = Net Income + $310,000
Net Income = $470,200 - $310,000
= $160,200
Now, the Tax rate is
Net Income = EBIT × (1 - Tax Rate)
$160,200 = $222,000 × (1 - Tax rate)
(1 - Tax rate) = $160,200 ÷ $222,000
(1 - Tax rate) = 0.721622
Tax rate = 27.84%
Are these ratios equivalent 4:5 and 16:20 yes or no
Answer:
yes
Step-by-step explanation:
this is correct because if you multipy them both by 4 you get those answers .
4 x 4 = 16
5 x 4 = 20
The ratios 4:5 and 16:20 are equivalent to each other. Yes, the ratios are equal to 4: 5.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The equivalent is the expression that is in different forms but is equal to the same value.
The two ratios are given below.
4:5 and 16:20
Convert the ratios into their simplified form. Then the ratios are given as,
4:5 and 16:20
4:5 and 4:5
The ratios 4:5 and 16:20 are equivalent to each other. Yes, the ratios are equal to 4: 5.
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A 20-person fraternity is making their weekend plans around 5 different parties in IV. Each brother will attend exactly one of the parties. Fraternity rules state that the fraternity must have a representative at each party. Assume that only the number of brothers that show up at a party is important, i.e. the brothers are indistinguishable. (a) How many different arrangements of plans are possible
Answer:
3876
Step-by-step explanation:
Given the following :
Fraternity members = 20
They are to attend 5 different parties in groups of 4
Meaning a group = 4 persons
Atleast one brother will attend exactly one of the parties. (the brothers are indistinguishable).
Then, exactly one brother at a party (20 - 1) = 19, since they are indistinguishable.
Group members are in 4's
19C4
From: nCr = n! /(n-r)! r!
19C4 = 19! / (19 - 4)! 4!
= 19! / 15! 4!
= (19 * 18 * 17 * 16) / (4 * 3 * 2)
= 93024 / 24
= 3876
A rectangular box has a length of 9 inches, width of 5 inches, and hight of 1 foot. Find the volume of the box in cubic inches.
Answer:
[tex]45^{3}[/tex] inches
Step-by-step explanation:
To calculate the volume of a rectangular prism(or in this case, the rectangular box), you need to multiply the length, width and height together.
length x width x height
9 x 5 x 1
= [tex]45^{3}[/tex] inches
What number should be placed in the box to help complete the division calculation? long division setup showing an incomplete calculation. 12 is in the divisor, 8587 is in the dividend, and 7 hundreds and 1 tens is written in the quotient. 8400 is subtracted from 8587 to give 187. An unknown value represented by a box is being subtracted from 187.
Answer:
120
Step-by-step explanation:
Your description is a little different from below picture, but the logic is the same. The 1 in the tens position represents 10x12 = 120, hence 120 should be subtracted and leaves you with 67 to continue.
Answer:
187
Step-by-step explanation:
12 in not the divisor of 8587 in the dividend with 7 hundreds and 1 tens. 8400 you subtracted from 8587 to give 187.
The profit that a business made during a year is $536,897,000. If the business divides the profit evenly for each share, estimate how much each share made if there are 10,995,000 shares.
Assignment
Modeling Real-World Problems with Composite Functions
A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which
represents the situation, where x is the original cost of the item(s)?
Of(x) = 0.35x represents the discount price and g(x) = 0.07x represents the price after taxes. The total price would
be (fog)(x) = 0.35(0.07x) = 0.0245x.
Of(x) = 0.65x represents the discount price and g(x) = 0.07x represents the price after taxes. The total price would
be (fºg)(x) = 0.65(0.07x) = 0.0455x
f(x) = 1.07x represents the price after taxes and g(x) = 0.65x represents the discount price. The total price would
be (fºg)(x) = 1.07(0.65x)= 0.6955x.
Of(x) = 1.07x represents the price after taxes and g(x) = 0.35x represents the discount price. The total price would
be (fºg)(x) = 0.35(1.07x)=0.3745x.
Answer:
Total Price = 1.07(0.65x)= 0.6955x.
Step-by-step explanation:
The discount percentage is, d% = 35%.
The sales tax percentage is, s% = 7%.
The variable x represent the original cost of the item(s).
The discount is subtracted from the original amount.
So, the discounted amount will be, 0.65x.
And the sales tax is added to the original amount.
So, the value of tax plus price will be, 1.07x.
Then the final price of the item(s) will be:
Total Price = 1.07(0.65x)= 0.6955x.
Answer:
It's C for those on edgenuity
Step-by-step explanation:
The following data shows marks obtained by students in a mathematics test; 6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,68 a. construct a frequency distribution table data using a discrete values 0, 1, 2,............. 10 b. State the modal score of the distribution c. if a student is chosen at random, what is the probability that a student scored more than 5 means d. Using assumed mean of 6, calculate the arithmetic mean score of the distribution
Data
6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,8
Answer:
(a) shown in the attachment
(b) 0.54
(c) 5.32
Step-by-step explanation:(a) The frequency distribution table has been added to this response.
The table contains four columns:
First column (x): The discrete values of the marks
Second column (f): The corresponding frequency of the marks
Third column (d) : The difference between each mark(x) and the assumed mean(A). i.e d = x - A (Where A = 6 from the question)
Fourth column (fd): The product of the first column and the third column. i.e f * d
(b) From the table, it can be deduced that the modal score is 6
This is because the score 6 has the highest number of frequency which is 6
(c) If a student is selected at random, the probability P(>5), that the student scored more than 5 is given as follows;
P( >5 ) = [The sum of frequencies of marks greater than 5] / [Total frequency]
P( >5 ) = [6 + 4 + 2 + 3 + 1] / [28]
P( >5 ) = 15 / 28 = 0.54
Therefore, the probability that the student scored more than 5 is 0.54
(d) To get the arithmetic mean, M, from the assumed mean A = 6, we use the following relation;
M = A + [∑fd / N] -----------(*)
Where
N = total frequency = 28
A = 6
∑fd = sum of the items on the fourth column = -19
Substitute these values into equation (*)
M = 6 + [-19 / 28]
M = 149 / 28
M = 5.32
Therefore, the arithmetic mean is 5.32
Let f(x) = 1/x+2 and g (x) = 1/x-3. Find (f/g) (x). Assume all appropriate restrictions to the domain. help!!!!
Answer:
x ≠ -2 or 3
Step-by-step explanation:
No denominator can be zero, so ...
x +2 ≠ 0
x ≠ -2
__
x -3 ≠ 0
x ≠ 3
__
g(x) ≠ 0 . . . . . true for all x; no restriction needed for this
__
The appropriate restrictions are x ∉ { -2, 3 }.
Sam missed a question on his Algebra Test. He wrote his work down. Where is his error in solving 3x + 2 = 14?
Answer:
10/3
Step-by-step explanation:
Step 1: Subtract 4 from both sides.
3
x
+
4
−
4
=
14
−
4
3
x
=
10
Step 2: Divide both sides by 3.
3
x
3
=
10
3
2(3w+9z) simplify it please .
Answer:
6w + 18z
Step-by-step explanation:
distribute the 2
2 x 3w = 6w
2 x 9z = 18 z
6w + 18z
Answer:
6w+18z
Step-by-step explanation:
A researcher found a study relating the distance a driver can see, y, to the age of the driver, x. When researchers looked at the association of x and y, they found that the coefficient of determination was r = 0.542 Select two conclusions that the researcher can make from this data.
a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
b.) The correlation coefficient, r, is -0.736.
c.) About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see.
d.) About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
e.) The correlation coefficient, r, is -0.458.
f.) The correlation coefficient, r, is -0.271.
Answer: a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
b.) The correlation coefficient, r, is -0.736.
Step-by-step explanation:
The coefficient of determination is denoted [tex]R^2 \ or \ r^2[/tex] which gives the percent of the variance in the dependent variable that is predictable from the independent variable.
Given, [tex]r^2= 0.542[/tex]
That means 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.
Also, [tex]r=\sqrt{0.542}\approx\pm0.736[/tex] , where r determines the correlation coefficient.
As driver;s age increases the distance he can see decreases, so there is a negative correlation between them.
So r= -736.
Hence, The correlation coefficient, r, is -0.736.
So, the correct options are a.) and b.)
to find the distance between a point x and an inaccessible point z, a line segment xy is constructed. measurements show that xy=966 m, angle xyz=38°24', and angle yzx=94°6'. find the distance between x and z to the nearest meter.
Answer:
[tex]\approx \bold{602\ m}[/tex]
Step-by-step explanation:
Given the following dimensions:
XY=966 m
[tex]\angle XYZ[/tex] = 38°24', and
[tex]\angle YZX[/tex] = 94°6'
To find:
Distance between points X and Z.
Solution:
Let us plot the given values.
We can clearly see that it forms a triangle when we join the points X to Y, Y to Z and Z to X.
The [tex]\triangle XYZ[/tex] has following dimensions:
XY=966 m
[tex]\angle XYZ[/tex] = 38°24', and
[tex]\angle YZX[/tex] = 94°6'
in which we have to find the side XZ.
Kindly refer to the image attached.
Let us use the Sine rule here:
As per Sine Rule:
[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]
Where
a is the side opposite to [tex]\angle A[/tex]
b is the side opposite to [tex]\angle B[/tex]
c is the side opposite to [tex]\angle C[/tex]
[tex]\dfrac{XZ}{sin\angle Y} = \dfrac{XY}{sin\angle Z}\\\Rightarrow \dfrac{966}{sin94^\circ6'} = \dfrac{XZ}{sin38^\circ24'}\\\Rightarrow XZ=\dfrac{966}{sin94^\circ6'} \times sin38^\circ24'\\\Rightarrow XZ=\dfrac{966}{0.997} \times 0.621\\\Rightarrow XZ=601.69 \m \approx \bold{602\ m}[/tex]
5. ACT scores for a group of six students from a local high school is 21, 22, 23, 25, 26, 33. What is the range for this distribution of scores?
Answer:
12
Step-by-step explanation:
The formula for RANGE of a given set if data = Maximum value - Minimum value.
In the above question, we are given a group of ACT scores
21, 22, 23, 25, 26, 33.
Maximum value = 33
Minimum value = 21
Range = 33 - 21
= 12
Therefore, the range for this distribution of scores is 12
Help Please!!!!! What is the absolute value of ∣∣2 1/3 ∣∣? Use this number line to determine the absolute value. Enter your answer in the box as a mixed number in simplest form.
Answer:
2 1/3
Step-by-step explanation:
i know because i did the test in k 12
An absolute value of |x| {modulus of x} is the value of a real number x. The absolute value of ||2 1/3|| is 2 1/3.
What is Absolute Value?An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.
The absolute value of ||2 1/3|| is,
||2 1/3||
= |2 1/3|
= 2 1/3
Hence, The absolute value of ||2 1/3|| is 2 1/3.
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48% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 300 found that 45% of the readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim?
Answer:
There is no sufficient evidence to support the executive claim
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.48[/tex]
The sample proportion is [tex]\r p = 0.45[/tex]
The sample size is [tex]n = 300[/tex]
The level of significance is [tex]\alpha = 0.02[/tex]
The null hypothesis is [tex]H_o : p= 0.48[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.48[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1 - p )}{n} } }[/tex]
=> [tex]t = \frac{0.45 - 0.48 }{ \sqrt{ \frac{0.48 (1 - 0.48 )}{300} } }[/tex]
=> [tex]t = -1.04[/tex]
The p-value is mathematically represented as
[tex]p-value = 2P(z > |-1.04|)[/tex]
Form the z-table
[tex]P(z > |-1.04|) = 0.15[/tex]
=> [tex]p-value = 2 * 0.15[/tex]
=> [tex]p-value = 0.3[/tex]
Given that [tex]p-value > \alpha[/tex] we fail to reject the null hypothesis
Hence we can conclude that there is no sufficient evidence to support the executive claim
2y + 18 y + 39 Find y
Answer:
Step-by-step explanation: 2y+18 = y+39
y=21
Answer:
y = 21
Step-by-step explanation:
In the figure , 2y + 18 and y + 39 are opposite interior angles . We know that opposite interior angles are equal , so
2y + 18 = y + 39
=> 2y - y = 39 - 18
=> y = 21
Which figure shows △MNP reflected over the y-axis to form △M`N`P`?
Answer:
The answer is in the picture below
Step-by-step explanation:
Hope this helps!
Figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.
What is the reflection of an image?The reflection operator geometrically repositions image elements, or pixel values, in such a way that they are reflected about a user-specified image axis or image point and placed in a new position in a matching output image.
In the given image option fourth is showing the correct reflection of the triangle △MNP over the y-axis to the form △M`N`P'.
It is observed that every point of the triangle MNP is at the same distance from the y-axis as every point of the triangle M'N'P'.
Therefore, figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.
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Simplify: (x-3) (x-3)
Answer:
x^2 -6x +6
Step-by-step explanation:
Square of a difference (can be found in IM2)
Formula: a^2 -2ab +b^2
x= a; 3= b
(x -3)(x -3)
Plug in to formula.
x^2 -2(x)(3) +3^2
Simplify.
x^2 -6x +6
Answer:
[tex](x - 3)^{2}[/tex]
1 meter is equivalent to how many feet
Write -5 less than p as an expression
Answer:
the answer is -5 -p
Step-by-step explanation:
the reason why this is, because negative 5 is less than (-) the variable p.
**WILL GIVE BRAINLIEST** Absolute Value Question. PLEASE HELP QUICK.
Cross multiply the numbers in the matrix:
1 *2 + 5*x = -13
Simplify:
2 + 5x = -13
Subtract 2 from both sides:
5x = -15
Divide both sides by 5
X = -15/5
X = -3
Because it’s absolute value it needs to be positive so x = 3
If the computed minimum sample size n needed for a particular margin of error is not a whole number, round the value of n (up or down) to the next (smaller or larger) whole number.
a) down; smaller
b) down; larger
c) up; larger
d) up; smaller
Answer:
The correct option is c.
Step-by-step explanation:
The margin of error is the range of values lower than and more than the sample statistic in a confidence interval. It is the number of percentage point by which the sample result will differ from the population result.
The general formula to margin of error is:
[tex]MOE=CV\times\frac{SD}{\sqrt{n}}[/tex]
Here,
CV = critical value
SD = standard deviation
n = sample size
Now, if the computed minimum sample size needed for a particular margin of error is not a whole number, then round the value of n up to the next larger whole number.
Thus, the correct option is c.
The number of foxes in a national forest had grown by 1160 in the past year If the number of foxes at the beginning of the year was 5800 by what percent did it increase
Answer:
5800-1160=4640
1160×100÷4640=25
=25%
Find the value of x that makes AFGH~AJKL.
(Lesson 11.3) (1 point)
X+3.5
20
Answer: The answer is: " x = 2.833333333333...." .
___________________________
or: write as: " 2 [tex]\frac{5}{6}[/tex] " .
___________________________
Step-by-step explanation:
___________________________
Set up a ratio:
Note: Segment FH = (x + 35)
Segment JL = 20 ;
Segment FH ~ Segment JL ;
___________________________
Note: Segment GH = (x - 4) ;
Segment KL = 5 ;
Segment GH ~ Segment KL .
___________________________
So, ( x + 3.5) : 20 :: (x-4) : 5 ;
Write this ratio in fraction format:
___________________________
→ [tex]\frac{(x+3.5) }{20 } = \frac{(x-4) }{5}[/tex] ;
Now; "cross-factor multiply" :
→ [tex]\frac{a}{b} = \frac{c}{d }[/tex] ; → [tex]ad = bc[/tex] ; { [tex]{ a\neq0 ; b\neq0 ; c\neq0 ; d\neq0[/tex] .}.
___________________________
So:
5(x + 3.5) = 20(x - 4) ;
___________________________
→ To simplify, start by divide each side of the equation by "5" ;
___________________________
→ {5(x + 3.5) } / 5 = { 20(x - 4) } / 5 ;
to get:
→ (x + 3.5) = 4(x - 4) ;
___________________________
Now, on the right-hand side of the equation;
let us expand the expression;
___________________________
We have the expression: " 4(x - 4) " ;
To expand:
Note the "distributive property of multiplication:
→ a(b + c) = ab + ac ;
Likewise:
→ 4(x - 4) = 4x - 16 ;
___________________________
Now, we can rewrite our equation:
___________________________
→ " x + 3.5 = 4x - 15 " ;
Now, we can subtract "x" from each side of the question;
& add "15" to each side of the equation; as folllows:
___________________________
→ x + 3.5 = 4x - 15 ;
- x + 15 = - x +15
___________________________
to get: 8.5 = 3x ;
↔ 3x = 8.5 ;
Now, divide each side of the equation by "3" ;
to isolate "x" on one side of the equation;
& to solve for "x" ; as follows:
→ 3x / 3 = 8.5 / 3 ;
to get: x = 8.5 /3
= 2.83333333333 ;
or; write as: " 2 [tex]\frac{5}{6}[/tex] ."
___________________________
Hope this is helpful to you! Best wishes!
___________________________
Hayley is 5feet 5 inches tall. What is tis i metres to the nearest centimetre
Answer:
It might be 168 centimetres
Step-by-step explanation: