It should be noted that the correct matching of the expressions illustrated will be:
a. (2^3)(2^2) = 32
b. 2^(-2) x 2^(-3) = 1/32
C. (2^3) x (2^-3) = 1
d. (2^2)^3 = 64
e. 2^2/2^3 = 1/2
f. 2^3/2^2 = 2
How to illustrate the information?It should be noted that (2^3)(2^2) will be:
= 2³ × 2²
= 8 × 4
= 32
b. 2^(-2) x 2^(-3) will be illustrated as:
= 1/4 × 1/8
= 1/32
C. (2^3) x (2^-3)
= 8 × 1/8
= 1
d. (2^2)^3
= 4³
= 64
e. 2^2/2^3
= 4 / 8
= 1/2
f. 2^3/2^2
= 2³ / 2²
= 8 / 4
= 2
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-2(x-5)+10=-3(x+2)+x
Answer:-26
Step-by-step explanation:
-2+10+10=-3(x+2)+x=-26 np
Given g(x)=-4x-4g(x)=−4x−4, find g(-2)g(−2)
Evaluate (a - 4b)2 + 2a if a = 15 and b = 3.
Answer:
9
Step-by-step explanation:
(a-b)^2=a^2-2ab+b^2
(15-12)^2=9
Answer: 96
Step-by-step explanation:
Plug in a and b. so, (15-4(3))2+2(15). so (15-12)2+30. (3)32. Answer is 96.
How do I factor 5X = 3(X+6)
Answer:
Step-by-step explanation: 5x=3(x+6)
5x=3x+18
5x-2x=18
3x=18
x=18/3
x=6
Question 7
1 pt:
By January 2014, the US population had grown to 317.3 million
and the US Federal Debt was a reported $17.3 trillion. Calculate
the beginning-2014 Federal Debt per capita.
Express your answer rounded correctly to the nearest dollar.
Remember, do not include units with your answer!
In January 2014, the debt per capita was: = $54,522.53.
What is debt per capita?Net debt per capita is simply the total debt of a country or even other jurisdiction divided by the residents residing there. Net debt per capita can provide insight into how leveraged a government is.
How much debt is considered normal?The average American has $92,727 in consumer debt, according to 2020 Experian research. Consumer debt encompasses a wide range of personal credit accounts, including credit cards, auto loans, mortgage, and personal loans, including school loans.
According to the given data:Population = 317.3 million.
US Federal Debt was a reported = $17.3 trillion.
Federal Debt per capita. = ?
We know that:
by adding short-term and long-term debt, deducting cash and some other liquid assets, then dividing by population.
The debt per capita in Jan 2014 was:
=1.73 x 1013 / 3.173 x 108
= $54,522.53.
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Colton bought some strings of beads. The number of strings was 10 more than the number of beads on each string. There were 119 beads in all. How many strings of beads did Colton buy?
Answer: 17 strings
Step-by-step explanation:
let the number of strings be a
let the number of beads on each string be b
a − b = 10 (first equation)
a × b = 119 (second equation)
From the first equation:
a = 10 + b
substitute first equation into second equation
b × (10 + b) = 119
10b + b² − 119 = 0
b = 7 or b = -17 reject -17
a − 7 = 10
a = 17
The difference between the square of c and the total of c and 14
The given statement written as a mathematical expression is c² - c + 14
Writing an expressionFrom the question, we are to write the given statement as a mathematical expression
The given statement is
"The difference between the square of c and the total of c and 14"
The square of c is
c²
and
The total of c and 14 is
c + 14
Thus,
The statement becomes
c² - c + 14
Hence, the given statement written as a mathematical expression is c² - c + 14
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420 ÷ d = 30; d= 15
[tex]420 \div d = 30 \: d = 15[/tex]
The required answer for the given equation is d = 1/2, ±√14.
What is division?The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.
Now the given equation is,
420 ÷ d = 30d = 15
Now if,
30d = 15
Then divide both the side by 30 we get,
30d/30 = 15/30
Solving we get,
d = 1/2
this is the required value of d
Now if,
420 ÷ d = 30d
So simplifying it we get,
420/d = 30d
multiplying both the side by d we get,
d*420/d = 30d*d
Solving we get,
30d^2 = 420
Dividing both the side by 30 we get,
30d^2/30 = 420/30
Solving we get,
d^2 = 14
Taking square root both the side we get,
√d^2 = √14
Solving we get,
d = ±√14
this is the required value of d.
Thus, the required answer for the given equation is d = 1/2, ±√14.
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9. The graph represents the path of a football kicked by a player, where x is the horizontal
distance (in yards) and y is the height (in yards). The player kicks the ball a second time
so that it travels the same horizontal distance, but reaches a maximum height that is 6
yards greater than the maximum height of the first kick. Write a function that models
the path of the second kick.
y=-0.02(x - 30)2 + 18
The function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to write a function that models the path of the second kick?The function that models the path of the first kick is given as
y = -0.02(x - 0.30)^2 + 18
A quadratic function is represented as
y = a(x - h)^2 + k
Where
Vertex = (h, k)
In this case, the interpretation of the vertex is
Vertex = (Horizontal distance, Maximum height)
Using the above as a guide, we have
Vertex = (30, 18)
This means that
Horizontal distance = 30
Maximum height = 18
For the second ball, we have
Same horizontal distanceMaximum height is 6 yards greater than the maximum height of the first kickThis means that
Horizontal distance = 30
Maximum height = 18 + 6
Evaluate
Horizontal distance = 30
Maximum height = 24
So, the function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24
Hence, the function that models the path of the second kick is y = -0.02(x - 0.30)^2 + 24
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evaluate -4 - 5+4+(-5)
Zodwa, the operations manager of a large production plant would like to estimate the mean
amount of time a worker takes to assemble a new electronic component. Assume that the standard
deviation of this assembly time is 3.6 minutes.
3.1.1. After observing 120 workers assembling similar devices, Zodwa noticed that their
average time was 16.2 minutes. Construct a 92% confidence interval for the mean
assembly time. (9)
The confidence interval for the mean assembly time is [15.625, 16.775].
The mean (x) time of the workers to assemble similar devices is 16.2 minutes.The standard deviation (σ) of this assembly time is 3.6 minutes.The sample size (n) for observation is 120 workers.It is given that the confidence level is 92%.At α = 0.08, the critical value (z) is 1.751.The confidence interval for the mean assembly time is [x ± z(σ/√n)].The confidence interval for the mean assembly time is [16.2 ± 1.751(3.6/√120)].The confidence interval for the mean assembly time is [16.2 ± 1.751(3.6/10.954)].The confidence interval for the mean assembly time is [16.2 ± 1.751(0.329)].The confidence interval for the mean assembly time is [16.2 ± 0.575].The confidence interval for the mean assembly time is [15.625, 16.775].To learn more about standard deviation, visit :
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i know how to do a and c, but how do i do b)?
Explanation:
Start at -1 on the x axis number line. Then move vertically until reaching the function curve. You should arrive at (-1,2). This tells us that g(-1) = 2. In other words, the input x = -1 leads to the output y = 2.
Follow similar steps to find that g(1) = -2
Therefore, g(-1)+g(1) = 2 + (-2) = 0
Mrs. Thomas needs
to set up 5 rows of 3
marsh mellows. She
has 12 marsh C EX
mellows. Does she
have enough marsh
mellows?
A. No, she needs 20 marsh mellows
B. No, she needs 15 marsh mellows
C. Yes, she needs 10 marsh mellows
D. Yes, she needs 8 marsh mellows
Please help what is 8.9 divided
by 0.4
Answer:
8.9 ÷ 0.4 = 22.25
so the answer is 22.25
hope this helps
Answer:
22.25 is your answer
Step-by-st
-48.54 divided by -6
Answer:
-48.54 ÷ -6 = 8.09
so the answer is 8.09
hope this helps
At a basketball game, 54% of people attending were supporting the home team, while 46% were supporting the visiting team. If 1566 people attending the game supported the home team, what was the total number of people attending the game? HELPP FASTT
What is the slope of the line that contains these points?
Answer: Slope=5/3
Step-by-step explanation:
my teacher said
How much money do you save by purchasing the vanilla cupcakes in a dozen Pak versus buying 12 individual cupcakes? $11.53 for dozen pack and twelve individual cupcakes is $2.15
Answer:
You save $ 14.27
Step-by-step explanation:
12 dozen = 11.53
2.15 x 12 = 25.80
25.80 - 11.53 = 14.27
The sum of two consecutive even integers is 46. Find the integers.
Answer:
22, 24
Step-by-step explanation:
Hello!
Consecutive integers are integers that come after each other. We want to find two consecutive even integers that when added give us 46.
Let the first consecutive even integer be x. Since even integers come every 2 integers (even, odd, even), the second even integer should be x + 2.
Solve for xx + x + 2 = 462x + 2 = 462x = 44x = 22That means x + 2 should be 24.
The two numbers are 22 and 24.
The sidewalk around a lake is 9/10 mile long. You walk 3 laps Around the lake in the morning and 2 laps in the evening. Your friend walks the same total distance as you on a 1 1/2 mile track. How many laps does your friend walks?
The total laps your friend runs is 3.
How many laps does your friend run?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.
A proper fraction is a fraction where the numerator is less than the denominator. A mixed fraction is a fraction that is made up of a whole number and a proper fraction.
The first step is to determine the total miles you run
Total miles run = length of the side walk x total number of laps
9/10 x (3 + 2)
9/10 x 5 = 45 / 10 = 4.5 miles
The second step is to determine the total number of laps she runs:
4.5 miles / 1 1/2 miles
4.5 / 1.5 = 3 laps
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Can someone please help me :(?
Simplify and combine like
terms:
-2 x+14-20-8x
Answer:
-10x-6
Step-by-step explanation:
and simplify and add
Select all the expressions that have 23 as a product.
2125×5063
78×925
130×23
325×712
2027×2730
The expression that have 23 as a product is 130×23
How to select all the expressions that have 23 as a product?For an expression to have 23 as a product, the expression must be a multiple of 23
This is indicated by
x/23 => Integer
So, we have:
2125×5063/23 = 4677..... (false)
78×925/23 = 3136.9....(false)
130×23/23 = 130 --- true
325×712/23 = 10060.... (false)
2027×2730/23 = 240596.. (false)
Hence, the expression that have 23 as a product is 130×23
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Need to find the value of x
What is the justification for each step in the solution of the equation?
23x−13=2(x+2)
23x−13=2(x+2) Given
2x−1=6(x+2)
2x−1=6x+12
2x=6x+13
−4x=13
x=−134
The justification for each step in the solution of the equation are as follows:
2/3x − 1/3 = 2(x + 2) -- GivenBy the multiplication property of an equation: 2x − 1 = 6(x + 2)By the distributive property of an equation: 2x − 1 = 6x + 12Collect and evaluate the like terms: 2x = 6x + 13By the subtraction property of an equation: −4x = 13By the division property of an equation: x =−13/4How to determine the justification for each step in the solution of the equation?The equation is given as
23x − 13 = 2(x + 2)
Based on the solutions, we can rewrite the given equation as follows
So, we have
2/3x − 1/3 = 2(x + 2)
So, the justification for each step in the solution of the equation are as follows:
2/3x − 1/3 = 2(x + 2) -- Given
By the multiplication property of an equation, we have
2x − 1 = 6(x + 2)
By the distributive property of an equation, we have
2x − 1 = 6x + 12
Next, we collect and evaluate the like terms
2x = 6x + 13
By the subtraction property of an equation, we have
−4x = 13
By the division property of an equation, we have
x =−13/4
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A company spends $20 million dollars for an office building. Over what period should
the cost be written off?
Answer:The cost should be 300,000 dollars
Step-by-step explanation:
The area of a right triangle is 5 in 2. If the length of a leg is x, write the function h(x) that describes the length of the hypotenuse.
The length of the hypotenuse is given by the function h(x) = √[x² + (10/x)²]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The area of the right triangle is 5 in², the length of the leg is x, hence:
Area = (1/2) * base * height
5 = (1/2) * x * height
height = 10/x
hypotenuse = √[(leg)² + (height)²]
h(x) = √[x² + (10/x)²]
The length of the hypotenuse is given by the function h(x) = √[x² + (10/x)²]
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Susan gives five dollars to Joe if Susan started with $18 how much money does she have left
Tyler Tooling Company uses a job order cost system with overhead applied to products on the basis of machine hours. For the upcoming year, the company estimated its total manufacturing overhead cost at $420,000 and total machine hours at 60,000. During the first month of operations, the company worked on three jobs and recorded the following actual direct materials cost, direct labor cost, and machine hours for each job:
Job 101 Job 102 Job 103 Total
Direct materials used $ 19,200 $ 14,400 $ 9,600 $ 43,200
Direct labor $ 28,800 $ 11,200 $ 9,600 $ 49,600
Machine hours 1,000 4,000 2,000 7,000
Job 101 was completed and sold for $60,000.
Job 102 was completed but not sold.
Job 103 is still in process.
Actual overhead costs recorded during the first month of operations totaled $45,000.
Required:
Prepare a journal entry showing the transfer of Job 102 into Finished Goods Inventory upon its completion.
Prepare the journal entries to recognize the sales revenue and cost of goods sold for Job 101.
Prepare the journal entry to transfer the balance of the Manufacturing Overhead account to Cost of Goods Sold
1. The journal entry to show the transfer of Job 102 into Finished Goods Inventory after its completion is as follows:
Journal Entry:Debit Finished Goods $53,600
Credit Work in Process: Job 102 $53,600
2. The journal entries to recognize the sales revenue and cost of goods sold for Job 202 are as follows:
Journal Entries:Debit Cash/Accounts Receivable $60,000
Credit Sales Revenue $60,000
Debit Cost of goods sold $55,000
Credit Finished Goods Inventory $55,000
3. The journal entry to transfer the balance of the Manufacturing Overhead account to the Cost of Goods Sold account is as follows:
Journal Entry:Debit Manufacturing Overhead $4,000
Credit Cost of Goods Sold $4,000
Data and Calculations:Estimated total manufacturing overhead = $420,000
Estimated total machine hours = 60,000 hours
Predetermined overhead rate = $7 ($420,000/60,000)
Job 101 Job 102 Job 103 Total
Direct materials used $ 19,200 $ 14,400 $ 9,600 $ 43,200
Direct labor $ 28,800 $ 11,200 $ 9,600 $ 49,600
Applied overhead $7,000 $28,000 $14,000 $49,000
Total costs $55,000 $53,600 $33,200 $141,800
Machine hours 1,000 hours 4,000 hours 2,000 hours 7,000 hrs
Status of Jobs Sold Finished WIP
Sales revenue (Job 101) = $60,000
Manufacturing Overhead Account:Actual overhead costs for the first month = $45,000
Applied overhead for the first month = $49,000 ($7 x 7,000)
Overapplied overhead = $4,000 ($49,000 - $45,000)
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Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $30 per person, find the greatest number of people that they may invite and still stay within their budget
Solve for x then give the measure of the bolded angle.
Answer:
73 - Explanation and Check below
Step-by-step explanation:
11x - 4 = 9x + 10
1. Get variable (x) on one side.
11x - 4 = 9x + 10
- 9x - 9x
2x - 4 = 10
2. Solve 2 step equation - add 4 on both sides of equation.
2x - 4 = 10
+ 4 + 4
3. Divide 2 on both sides of equation.
2x = 14
---- ----
2 2
x = 7
Check:
11 (7) - 4 = 9(7) + 10
77 - 4 = 63 + 10
73 = 73 True statement.
Explanation:
If a transversal intersects two parallel lines, the corresponding angles will be always equal.
So in the problem, the two given equations are equal to each other.
The answer for the two angles with equations is 73.
Also, the angles vertical to the two equations are also 73 because vertical angles are congruent (equal).
Hope this helps :)
