Answer:
1,680
Step-by-step explanation:
8 positions with basically 8 choices.
that is 8! arrangements.
but 2 is there 2 times.
8 is there 2 times.
5 is there 3 times.
only 3 is a single digit.
so, we need to eliminate every arrangement, where the 2s trade places, where the 5s trade places, and where the 8s trade places, because they are the same numbers.
that means we have to divide the 8! by 2!, then again by 2!, and again by 3!.
8! / (2! × 2! × 3!) = 8! / 24 = 1,680
Find the changes in each four month period
Month and Year Prices in Dollars per Gallon Absolute Change Relative Change
Apr-20 1.841 n/a n/a
Aug-20 2.183
Dec-20 2.195
Apr-21 2.858
Aug-21 3.158
Dec-21 3.307
Apr-22 4.109
b. How would you describe the change in the gas prices? Explain your answer.
c. Use the inflation calculator to find the costs of gas in April 2020 in 2022 dollars. Here is the
link to the calculator from the U.S. Bureau of Labor Statistics:
https://www.bls.gov/data/inflation_calculator.htm
d. How does the inflation-adjusted cost of gas in April 2020 compare to the April 2022 as an
absolute and relative change?
e. What can be attributed to the two most drastic rises in gasoline prices? Explain in a sentence
or two.
a. The changes in each four-month period are as follows:
Month and Prices Absolute Relative
Year in Dollars Change Change
Apr-20 1.841 n/a n/a
Aug-20 2.183 $0.342 18.58%
Dec-20 2.195 0.012 0.55%
Apr-21 2.858 0.663 30.21%
Aug-21 3.158 0.300 10.50%
Dec-21 3.307 0.149 4.72%
Apr-22 4.109 0.802 24.25%
b. The change in gas prices has been relatively unstable.
c. Using the inflation calculator, the costs of gas in April 2020 in 2022 dollars terms should be $2.08.
d. The inflation-adjusted cost of gas in April 2020 when compared to April 2022 as absolute and relative changes are as follows:
Absolute change = $2.268 ($4.109 - $1.841)
Relative change = 123.2% ($2.268/$1.841 x 100)
e. The two most drastic rises in gasoline prices in April 2021 and April 2022 can be attributed to spikes in demand relative to supply.
What causes gasoline prices to rise?Gasoline prices rise when there is an increased demand relative to supply.
Increasing prices in gasoline prices can also be attributed to cuts in production and supply by the oil cartel.
What is the difference between Absolute and Relative Changes?An absolute change is a dollar change from one period to another.
A relative change is an absolute change expressed in percentages.
The calculations of absolute change and relative change are demonstrated below.
Data and Calculations:Month and Prices Absolute Relative
Year in Dollars Change Change
Apr-20 1.841 n/a n/a
Aug-20 2.183 $0.342 18.58% ($0.342/$1.841 x 100)
Dec-20 2.195 0.012 0.55% ($0.12/$2.183 x 100)
Apr-21 2.858 0.663 30.21% ($0.663/$2.195 x 100)
Aug-21 3.158 0.300 10.50% ($0.3/$2.858 x 100)
Dec-21 3.307 0.149 4.72% ($0.149/$3.158 x 100)
Apr-22 4.109 0.802 24.25% ($0.802/$3.307 x 100)
Absolute Change for Aug-20 = $0.342 ($2.183 - $1.841)
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Solve the system of equations below using a matrix equation.
2x + y = - 7
x − y = 4
Select one:
a.
( 1, 5 )
b.
( - 1, - 5 )
c.
( - 1, -2 )
d.
( 0, - 7 )
Answer: B. (-1, -5)
Step-by-step explanation:
Given equations
2x + y = -7
x - y = 4
Concept
[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
[tex]A*A^{-1}=A^{-1}*A=I~(Which~is~basically~1)[/tex]
Convert into matrix
[tex]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]
Calculate the inverse of the matrix
[tex]A=\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right][/tex]
[tex]A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
[tex]A^{-1}=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right][/tex]
Solve by multiplying the inverse of the matrix
[tex]A*A^{-1}=A^{-1}*A=I[/tex]
[tex]-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}2&1\\1&-1\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3} \left[\begin{array}{ccc}-1&-1\\-1&2\\\end{array}\right]\left[\begin{array}{ccc}-7\\4\\\end{array}\right][/tex]
[tex]1*\left[\begin{array}{ccc}x\\y\\\end{array}\right]=-\frac{1}{3}\left[\begin{array}{ccc}3\\15\\\end{array}\right][/tex]
Simplify by multiplication
[tex]\left[\begin{array}{ccc}x\\y\\\end{array}\right]=\left[\begin{array}{ccc}-1\\-5\\\end{array}\right][/tex]
Therefore, the answer is [tex]\Large\boxed{(-1,~-5)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The rat population in a major metropolitan city is given by the formula
n
(
t
)
=
24
e
0.015
t
where
t
is measured in years since 2004 and
n
(
t
)
is measured in millions.
What was the rat population in 2004 ?
rats
What does the model predict the rat population was in the year 2012 ?
rats
The rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.
How to determine the populationGiven the function of the population to be;
n (t) = 24 e^0. 015t
Where;
t is measured in years since 2004n(t) is measured in millionsIn 2004, t = 1
Substitute into the formula;
n(1) = 24 e^0. 015t
n(1) = 24 e^(0.015 × 1)
n(1) = 24 e^0. 015
n(1) = 24. 8 millions
In year 2012, t = 8
n(8) = 24 e^(0. 015 × 8)
n(8) = 24e^0. 12
n(8) = 31. 6 millions
Thus, the rat population is 2004 and 2012 are 24. 8 millions and 31. 6 millions respectively.
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what is 23,995 rounded to the nearest ten
Answer: 24,000
Step-by-step explanation:
us
Find a formula for the nth term in this
arithmetic sequence:
a₁ = 7, a2 = 4, a3 = 1, a4 = -2, ...
an = [? ]n +
The formula for the nth term of the arithmetic sequence is [-3]n+10
What is the nth term of an arithmetic sequence?
⇒ The general form of the nth term of an arithmetic sequence is
an = a1 + (n - 1)d
Where,
a1 - first term
n - number of terms in the sequence
d - the common difference
Calculation:
It is given that the given sequence is an arithmetic sequence.
First term a1 = 7
Second term a2 = 4
Common difference d = 4-7
⇒ d=3
From the general formula,
an = a1 + (n - 1)d
On substituting,
an = 7+ (n-1)(-3)
an = 7-3n+3
an = -3n+10
⇒ Thus the general formula for the nth term of the arithmetic sequence is -3n+10
an= [-3]n+10
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Function: y=x2+5x−7
Vertex: ( , )
Solutions: ( , ) and ( , )
Answer:
vertex : (-5/2, -53/4)
solutions: (-(5-sqrt53)/2, 0) (-(5+sqrt53)/2, 0)
Step-by-step explanation:
1.The vertex of the function is (-5/2, -53/4).
2.We have two solutions:
x = (-5 + √53) / 2 ≈ 0.73
x = (-5 - √53) / 2 ≈ -5.73
To find the vertex and solutions of the function y = x^2 + 5x - 7, we can use the formula for the vertex and the quadratic formula for finding solutions.
1. Vertex:
The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula:
x = -b / (2a)
y = f(x) = ax^2 + bx + c
Given: a = 1, b = 5, c = -7
x = -5 / (2 * 1) = -5 / 2
Now, substitute the value of x into the equation to find y:
y = (-5/2)^2 + 5 * (-5/2) - 7
y = 25/4 - 25/2 - 7
y = 25/4 - 50/4 - 7
y = (25 - 50 - 28) / 4
y = -53 / 4
So, the vertex of the function is (-5/2, -53/4).
2. Solutions (or roots or x-intercepts):
To find the solutions (x-intercepts) of the function, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Given: a = 1, b = 5, c = -7
x = (-5 ± √(5^2 - 4 * 1 * -7)) / 2 * 1
x = (-5 ± √(25 + 28)) / 2
x = (-5 ± √53) / 2
Now, we have two solutions:
x = (-5 + √53) / 2 ≈ 0.73
x = (-5 - √53) / 2 ≈ -5.73
So, the solutions of the function are approximately x ≈ 0.73 and x ≈ -5.73.
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A bagel factory produced 300 bags of bagels. There were 7 bagels in each bag. How many
bagels did the factory produce?
bagels
The length of a rectangle is 3 m longer than its width.
If the perimeter of the rectangle is 34 m, find its area.
Step-by-step explanation:
With this question ,
The length of the rectangle is 3m longer than it's width=3 +w
then the width =w
therefore perimeter= 2L +2w
34= 2(3+w) +2w
34= 6+2w +2w
34-6 = 4w
28=4w
7= w
Area= Length x breadth
Area = (7+3) x7
Area= 10 x7
Area= 70cm square
value of 10 in A/B
value of letter
The value of the expression (a - b)² from the given equations is; 16
How to solve simultaneous equations?
We are given the two equations as;
a + b = 10 -----(eq 1)
ab = 21 ------(eq 2)
From eq 1, square both sides;
(a + b)² = 10²
a² + 2ab + b² = 100
a² + b² = 100 - 2ab
We are given ab = 21. Thus;
a² + b² = 100 - 2(21)
a² + b² = 58
Now, we know that (a - b)² = a² - 2ab + b²
Thus;
(a - b)² = 58 - 2(21)
(a - b)² = 16
Complete question is;
If a + b = 10 and ab = 21, then the value of (a - b)² is?
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How many 4-digit numbers can be created using
the digits 1, 3, 5, 7, and 9 without repeating any
digits within that 4-digit number?
Answer:
120 four digit numbers can be created from the gives.
Step-by-step explanation:
Solution
You are given 5 digits in the givens.
1 3 5 7 9
Therefore
5 * 4 * 3 * 2 is the answer to your question. 4 and 3 and 2 determine that none of the digits can be repeated. That equals 120.
Find the volume of a grain storage building that has
a cylinder bottom that is 20 meters in diameter and
10 meters in height. It has a cone-shaped top as a
roof that has the same diameter as the bottom and a
height of 6 meters. Find the volume of the building
in cubic meters if it was full of grain from the
bottom to the top of the roof. All measures noted in
the diagram below are in meters. Use = 3.14 in
your calculations. Enter only the number.
m
10 m
The solution is
10 m
The volume of the grain storage building is 3770. 4 m³
How to determine the volume
From the given question, it can be deduced that the grain storage is a combination of a cylinder and a cone
The volume of the grain storage = volume of the cone + the volume of the cone
The formula for finding the volume of a cylinder is given as;
Volume of cylinder = πr²h
But we know that radius is the diameter divided by 2
radius = 20/2
radius = 10 meters
height = 10 meters
Substitute the values in the formula
Volume of cylinder = 3. 142 × 10 × 10 × 10
Volume = 3. 142 × 1000
Volume = 3142 m³
The formula for finding the volume of a cone is given as;
Volume of cone = [tex]\pi r^2\frac{h}{3}[/tex]
If the cone has the same diameter, then the radius is 10 meters and the height is 6 meters
Substitute the values into the formula
Volume of the cone = 3. 142 × 10 × 10 × 6/ 3
Volume = 3. 142 × 100 × 2
Volume = 628. 4 m³
The volume of the grain storage building = 3142 + 628. 4
The volume of the grain storage building = 3770. 4 m³
Thus, the volume of the grain storage building is 3770. 4 m³
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Answer:
3770. 4 m³
Step-by-step explanation:
i took the test
In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 27% with a margin of error of 1.9% . Describe the conclusion about p using an absolute value inequality.
The conclusion for p, from the confidence interval, using an absolute value inequality is:
[tex]|p - 0.27| \leq 0.019[/tex]
What is a confidence interval?A confidence interval is given by the estimate plus minus the margin of error. As an inequality, we have that the absolute value of the difference between the proportion and the estimate is of at most the margin of error, that is:
[tex]|p - E| \leq M[/tex]
For this problem, the estimate and the margin of error are:
E = 0.27, M = 0.019.
Hence the inequality is:
[tex]|p - 0.27| \leq 0.019[/tex]
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2. Us i ng the filled table above,
a) calculate just one PED.
b) Is the demand elastic or inelastic?
c) Based on your answer to c) what price change would you recommend to increase TR?
The price elasticity of demand of the pen will be -0.2.
How to compute the elasticity?The demand and supply schedule will be:
Price Qd. Qs
$10. 250. 100
$20. 200. 90
$30. 180. 80
The price elasticity of demand from $1 to $2 will be:
= Percentage change in quantity demanded/percentage change in price
Percentage change in quantity demanded will be:
= (200 - 250)/250 × 100
= -20%
Percentage change in price will be:
= (20 - 10)/10 × 100
= 100%
Therefore, the elasticity of demand will be:
= -20/100
= - 0.2
The value gotten illustrates an inelastic demand.
In order to increase the total revenue, the price can be reduced as it will lead to more sales.
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Complete question:
Choose any product or service. Create the demand and supply schedule.
Calculate just one PED.
Is the demand elastic or inelastic?
What price change would you recommend to increase TR?
Remy obtains a 30-year mortgage in the amount of $625,000 for a co-op. She secures a 7/1 ARM at an initial interest rate of 3%. Her initial monthly payment is $2,635.03. After 7 years, the interest rate on her loan changes to 4.925%. Calculate her new monthly payment in year 8 of the loan. (Round your answer to the nearest cent.)
The new monthly payment is $3,181.53
What is ARM?
ARM stands adjustable rate mortgage, which means that the interest rate applicable to the mortgage would change during the life of the mortgage, in this case, 7/1 ARM means that interest rate of 3% is applicable for the first 7 years and the rate would change in year 8 to another interest rate, which is 4.925% as hinted at in the question.
To determine the monthly payment in year 8 , we need to compute the outstanding balance at the end of year 7, which is the opening balance in year 8 using the present value formula of an ordinary annuity since monthly payments would occur at the end of each month
PV(balance at the end of year 7)=PMT*(1-(1+r)^-N/r
PMT=initial monthly payment=$2,635.03
r=initial monthly interest rate=3%/12=0.0025
N=number of monthly payments in the remaining 23 years(i.e 30-7)=23*12
N=number of monthly payments in the remaining 23 years(i.e 30-7)=276
PV=$2,635.03*(1-(1+0.0025)^-276/0.0025
PV=$2,635.03*(1-0.502008144755209)/0.0025
PV=$2,635.03*0.497991855244791/0.0025
PV=$ 524,889.39
With the balance at the end of year 7, we can now compute monthly payment in year 8 using the same formula as above where the unknown is the PMT, PV=$ 524,889.39 and r= 4.925%.
$524,889.39=PMT*(1-(1+4.925%/12)^-276/4.925%/12)
$524,889.39=PMT*(1-(1.00410416666666667
)^-276/0.00410416666666667
$524,889.39=PMT*(1-0.32289378683267300
)/0.00410416666666667
$524,889.39=PMT*164.98019407122700000
PMT=$524,889.39/164.98019407122700000
PMT=$3,181.53
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A company's sales equal $60,000 and cost of goods sold equals $20,000. Its beginning inventory was $1,600 and its ending inventory is $2,400. The company's inventory turnover ratio equals:
The company's inventory turnover ratio, based on the financial data, equals 10 times.
What is the inventory turnover ratio?The inventory turnover ratio measures the number of times the company sells and replaces its inventory over a given period.
The formula for calculating the Inventory Turnover Ratio is the Cost of Goods Sold divided by the Average Inventory.
The Average Inventory is the mean of the beginning and ending inventories.
Data and Calculations:Sales revenue = $60,000
Cost of goods sold = $20,000
Beginning inventory = $1,600
Ending inventory = $2,400
Average inventory = $2,000 ($1,600 + $2,400)/2
Inventory turnover ratio = 10x ($20,000/$2,000)
Thus, the company sells and replaces its inventory over a period of 10 times.
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Helppppppoooooooo me please
Answer:
0
Step-by-step explanation:
We are looking at the change in y over the change is x. The change is y is always 0 and 0 divided by anything will be zero.
The Smith family and the Stewart family each used their sprinklers last summer. The water output rate for the Smith family's sprinkler was 25L per hour. The water output rate for the Stewart family's sprinkler was 30L per hour. The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1750L. How long was each sprinkler used?
The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.
According to the statement
we have given that the Smith family's sprinkler was 25L per hour and
Stewart family's sprinkler was 30L per hour and The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1750L.
And we have to find the How long was each sprinkler used.
So, For this purpose,
The given statements in the equation form become:
Let Smith family's sprinkler be x
Let Stewart family's sprinkler be y then
The equation become
x + y = 65 -(1)
25x + 30y = 1750 -(2)
Here we use the elimination method.
So, Multiply (1) by 25 and (2) by 1 then
25x + 25y = 1625
25x + 30y = 1750
Now eliminate x from the equations then
-5y = -125
y = 25
then x value becomes
x + y = 65
x + 25 = 65
x = 40.
So, The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.
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Which of the following expressions would simplify to be the multiplicative identity?
023.32
023.23
021
0 20
NEXT QUESTION
ASK FOR HELP
need help I don't know the answer
Seb bikes at a constant rate of 20 kilometers per hour.
1. Write an equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate.
2. How far will Seb travel if he bikes at this rate for 2.5 point, 5 hours?
The equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t
1. Write an equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate.The given parameter is
constant rate of 20 kilometers per hour.
This means that
Rate = 20km per hour
When Seb bikes for t hours, the distance is
d = rate * t
This gives
d = 20t
Hence, the equation that represents the distance, in kilometers, Seb travels (d) based on how many hours he bikes (t) at this rate is d = 20t
How far will Seb travel if he bikes at this rate for 2.5 point, 5 hours?This means that
t = 5
So, we have:
d = 20 * 5
Evaluate
d = 100
Hence, Seb will travel 100 kilometers if he bikes at this rate for 5 hours
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Answer:
1. d=20t
2. 50
the measure of the angels of a quadrilateral are in ratio 2:4:5:7 find the measure of each of it's angles
Answer:
Step-by-step explanation:
If they all exist in proportion to one another (READ: ratio) then multiplying each of the angles by the same number (here, some unknown "x" value) will maintain the proportionality. Since all the angles of a quadrilateral have to add up to equal 360, then
2x + 4x + 5x + 7x = 360 and
18x = 360. Divide both sides by 18 to get that
x = 20. That means that
2x = 2(20) = 40 and
4x = 4(20) = 80 and
5x = 5(20) = 100 and
7x = 7(20) = 140. Adding all of those up:
40 + 80 + 100 + 140 = 360
Answer:
40,80,100,140
Step-by-step explanation:
Let the ratio 2:4:5:7 angles be 2x, 4x, 5x, 7x
Now
2x + 4x + 5x + 7x=360 degrees
18x = 360 degrees
x =360/18
x=20
2x=2 *20=40
4x=4 *20=80
5x=5 *20=100
7x=7* 20=140
HELPP PLSSS I NEED HELP!!!
Answer:
(3+3) x (3+1)
Step-by-step explanation:
free
We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.
Solution :» (1 + 3) × (3 + 3)
» (4) × (6)
» 24
Here's our answer..!!
Did you ever purchase a bag of M & M Peanut candies and wonder about the distribution of the colors ? A recent article reported that 30 percent of the candies are brown , 20 percent yellow , 20 percent red , 20 percent green , and 10 percent orange . A one - pound bag of M & M peanut candies was purchased at Wal - Mart here in Lubbock . A total of 188 candies were in the bag , with 67 brown , 22 yellow , 51 red , 24 green , and 24 orange .
Filling in the frequency table according to the colors observed and expected on the M & M Peanut candies is as follows:
Frequency Table:Color Brown Yellow Red Green Orange Total
Absolute FrequenciesObserved Frequency 67 22 51 24 24 188
Expected Frequency 56 38 38 38 18 188
Relative Frequencies:
Observed Frequency 36% 12% 27% 13% 13%
Expected Frequency 30% 20% 20% 20% 10%
What is a frequency table?A frequency table is a display of the number of occurrences of a particular value or characteristic.
A frequency table makes it easy to display and interpret a distribution of data.
The absolute frequencies shows the absolute values of the observed and expected frequencies, while the relative frequencies shows the percentage values of the observed and expected frequencies.
Data and Calculations:Color Brown Yellow Red Green Orange Total
Observed Frequency 67 22 51 24 24 188
Expected Frequency 30% 20% 20% 20% 10% 100%
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Question Completion:Fill in the following table on the frequency of the colors, indicating the absolute and relative frequencies of the distributions.
Which of the following is a proportion?
The option that is a proportion is: B. 4/6 = 2/3.
What is a Proportion?A proportion can be defined as an equation whereby two ratios are set equal to each other, in such a way that the ratio on one side equals the ratio on the other side of the equation when simplified.
First Option is not a proportion because:
5/7 ≠ 10/12 (10/12 can be simplified further as 5/6, which is not equal to 5/7).
Second option is a proportion because:
4/6 = 2/3
8/12 = 2/3
Thus, 4/6 = 8/12.
Third Option is not a proportion because:
14/21 = 2/3
9/12 = 3/4
Therefore, 14/21 ≠ 9/12.
Fourth Option is not a proportion because:
9/15 = 3/5
12/18 = 2/3
Therefore, 9/15 ≠ 12/18.
In conclusion, the option that is a proportion is: B. 4/6 = 2/3.
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Find the value of c.
answer choices
A. 26
B. 104
C. 52
D. 93.5
Answer:
option B is the answer of given question
Answer:
D. 93.5
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)
The lower arc is twice 52
c = 1/2( 104 +83)
c = 1/2 ( 187)
c =93.5
A baker has 4 3/4 pounds of cookie dough. He uses 1/16 pound of dough for each cookie. How many cookies can he make? Simplify the answer.
This shows that 76 cookies will be made with the total pounds of cookies
Ratio and proportionFractions are written as a ratio of two integers. Given the following parameters
Total pounds of cookies made = 4 3/4 pounds
Total pounds of cookies made = 19/4 pounds
If he uses 1/16 pound of dough for each cookie, the total amount of cookies made is given;
Number of cookies = 19/4 ÷ 1/16
Number of cookies = 19/4 * 16/1
Number of cookies = 19 * 4
Number of cookies = 76
This shows that 76 cookies will be made with the total pounds of cookies
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8. If one of the 1124 people is randomly selected, find the probability that the person is a man or heavy smoker. (a) 145 /281 (b) 617 /1124 (c) 1031 /1124 (d) 37 /1124
The probability that the person is a man or heavy smoker is 621 / 1124.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability that the respondent is a man or heavy smoker can be determined by adding the probability that the respondent is a man and the probability that the respondent is a heavy smoker together.
The probability that the person is a man or heavy smoker = (number of men / total number of respondents) + (number of heavy smokers / total number of respondents)
(531 / 1124) + (90 / 1124) = 621 / 1124
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the drawing plan for a new CrossFit studio shows a rectangle that is 19.5 inches by 15 inches, as shown below. The scale in the plan is 3in.:8ft. Find the length and width of the actual studio.
Answer:
Length = 52 ft
Width = 40 ft
Step-by-step explanation:
Given information:
length = 19.5 inwidth = 15 inscale = 3 in : 8 ftScale
[tex]\implies \sf 3 \: in : 8 \: ft[/tex]
[tex]\implies \sf 1 \: in : \dfrac{8}{3} \: ft[/tex]
To find the length and width of the studio in feet, multiply the length and width in inches by 8/3:
[tex]\sf Length = 19.5 \times \dfrac{8}{3}=52\:ft[/tex]
[tex]\sf Width = 15 \times \dfrac{8}{3}=40\:ft[/tex]
Therefore, the length of the actual studio is 52 ft and the width of the actual studio is 40 ft.
Scale is 3in:8ft
So
1in=8/3ftLength
19.5(8/3)ft52ftWidth
15(8/3)40ftFind mEHFˆ. PLEASE HELP ASAP
Answer:
30°
Step-by-step explanation:
[tex]\frac{195-(8x+17)}{2}=5x-10 \\ \\ 178-8x=10x-20 \\ \\ 198=18x \\ \\ x=11[/tex]
So, this means arc FH measures 105 degrees.
Since the circumference of a circle measures 360 degrees, arc EF measures 60 degrees.
By the inscribed angle theorem, angle EHF measures 30°.
Questions are in the picture
The closest point is (3.5, 1.9) and the distance is 1.96 units
How to determine the point and the distance?The coordinate is given as:
(4, 0)
The equation of the function is
y = √x
The distance between two points is calculated using
d = √(x2 - x1)^2 + (y2 - y1)^2
So, we have the following points
(x1, y1) = (4, 0) and (x2, y2) = (x, 0)
This gives
d = √(x - 4)^2 + (√x - 0)^2
Evaluate the difference
d = √(x - 4)^2 + (√x)^2
Evaluate the exponent
d = √x^2 - 8x + 16 + x
Evaluate the like terms
d = √x^2 - 7x + 16
Next, we differentiate using a graphing calculator
d' = (2x - 7)/[2√(x^2 - 7x + 16)]
Set to 0
(2x - 7)/[2√(x^2 - 7x + 16)] = 0
Cross multiply
2x - 7 = 0
Add 7 to both sides
2x = 7
Divide by 2
x = 3.5
So, we have:
Substitute x = 3.5 in y = √x
y = √3.5
Evaluate
y = 1.9
So, the point is (3.5, 1.9)
The distance is then calculated as:
d = √(x2 - x1)^2 + (y2 - y1)^2
This gives
d = √(3.5 - 4)^2 + (1.9 - 0)^2
Evaluate
d = 1.96
Hence, the closest point is (3.5, 1.9) and the distance is 1.96 units
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A box contains orange balls and green balls. The number of green balls is seven more than four times the number of orange balls. If there are 102 balls altogether, then how many green balls and how many orange balls are there in the box?
green balls = 83
orange balls = 19
Step-by-step explanation:
green balls = g
orange balls = r
g = 7 + 4r
g + r = 102
7 + 4r + r = 102
5r = 95
r = 19
g + 19 = 102
g = 83
