Answer:
the population of the city in the year 2035 is 126,226
Step-by-step explanation:
The population of a city is modeled by
[tex]P(t)= 78300(1.023 )^t[/tex]
P ( t ) represents the number of people and t is the number of years since 2014.
in the year 2014, the year t=0
we need to find the population in the year 2035
2035-2015= 21
so find population when t=21
[tex]P(t)= 78300(1.023 )^t[/tex]
[tex]P(21)= 78300(1.023 )^{21}=126226.36[/tex]
standard form of x^2 + 16x + 71
Answer:
It's (-8,7) I believe, I hope this helps!
Step-by-step explanation:
What is 20% as an whole number
Final answer:
20% does not directly convert into a whole number; it represents a fractional part of a whole. If you look at the percent as a part of some quantity, you calculate 20% of that quantity to find the represented part. However, 20% by itself is 0.20 in decimal form, not a whole number.
Explanation:
What is 20% as a whole number?
When talking about percentages, it's important to understand that a percent is a way of expressing a fractional amount as part of a whole divided into 100 parts. For example, 5% means 5 out of 100.
In the case of 20%, you are looking at 20 out of 100. As a whole number, however, percentages less than 100% do not directly convert since they represent a part of a whole, not the whole itself. 20% can be represented as 0.20 in decimal form, which still does not constitute a whole number. The closest concept related to whole numbers would be if you had some quantity that you wish to find 20% of; you would then calculate 20% of that number to find the part it represents. But the 20% by itself remains a fraction, not a whole number.
Which terms complete the factorization of x2+27x+162
represented by the model?
27, 9x, 18%
9, 9x, 18x
27, 9x, 27x
9, 9x, 27x
Answer:
B. 9, 9x, 18x
Step-by-step explanation:
The value in each box is the product of the row heading and column heading. You can find the missing column heading by dividing the box value (162) by the row heading (18).
The correct terms are 9, 9x, and 18x. Hence, option B is correct.
To factorize the quadratic expression x² + 27x + 162, we need to find two numbers that multiply to 162 (the constant term) and add up to 27 (the coefficient of x). These numbers are 9 and 18.
Identify the constant term (162) and the coefficient of the linear term (27).
Find two numbers that multiply to 162 and add to 27. These numbers are 9 and 18.
Rewrite the middle term using these numbers: x² + 9x + 18x + 162.
Factor by grouping: (x² + 9x) + (18x + 162).
Factor out the greatest common factor from each group: x(x + 9) + 18(x + 9).
Factor out the common binomial factor: (x + 9)(x + 18).
Therefore, the factorization of x² + 27x + 162 is (x + 9)(x + 18).
Based on this factorization, the correct terms from the choices provided are (B) 9, 9x, and 18x.
Michelle receives 32K per year as an assistant fast food manager. Her benefits include health insurance, paid holidays, retirement contributions, and a 2-week paid vacation each year. Because she wears a uniform, Michelle calculates that she saves $2,500 on clothing costs per year. She constructed this table to show the value of each benefit. What is her annual salary, including benefits?
Michelle's annual salary, including benefits, is $43,330.
Explanation:To calculate Michelle's annual salary, we need to add up her base salary and the value of her benefits. Based on the information given, her base salary is $32,000 per year. In addition, her benefits include health insurance, paid holidays, retirement contributions, and a 2-week paid vacation, as well as saving $2,500 on clothing costs. Let's calculate the value of these benefits:
Health insurance: This benefit is not given a specific value, so we will assume a typical cost of $5,000 per year. (Note: This is an assumption and may vary depending on the specific circumstances).Paid holidays: Assuming 10 paid holidays per year, at an average daily rate of $100, the value of this benefit is $1,000.Retirement contributions: Assuming a 5% contribution from Michelle's salary, the value of this benefit is $1,600.2-week paid vacation: Assuming Michelle's base salary is $32,000 per year, the value of a 2-week paid vacation is $1,230 (($32,000/52)*2).Savings on clothing costs: As given, Michelle saves $2,500 on clothing costs per year.Now let's add up the base salary and the value of the benefits:
Base salary: $32,000
Health insurance: $5,000
Paid holidays: $1,000
Retirement contributions: $1,600
2-week paid vacation: $1,230
Savings on clothing costs: $2,500
Total annual salary, including benefits: $43,330
What is the reason for each step in the solution of the equation? 18x-2x=4x. Match the reasons with each step in the equation
The correct answer is:
The equation simplifies to [tex]\(x = 0\)[/tex] after combining like terms and isolating [tex](x\), resulting in \(x\)[/tex] being zero.
the equation [tex]\(18x - 2x = 4x\)[/tex] step by step:
1. Original equation:
[tex]\[ 18x - 2x = 4x \][/tex]
2. Combine like terms on the left side:
[tex]\[ 16x = 4x \][/tex]
Explanation: We add or subtract coefficients of like terms. Here,[tex]\(18x - 2x\) simplifies to \(16x\).[/tex]
3. Subtract [tex]\(4x\)[/tex] from both sides:
[tex]\[ 16x - 4x = 0 \][/tex]
Explanation: We want to isolate [tex]\(x\)[/tex] on one side. Subtracting [tex]\(4x\)[/tex] from both sides ensures the equation remains balanced.
4. Simplify:
[tex]\[ 12x = 0 \][/tex]
Explanation: After subtracting, we simplify the expression [tex]\(16x - 4x\) to \(12x\).[/tex]
5. Divide both sides by [tex]\(12\)[/tex]:
[tex]\[ \frac{12x}{12} = \frac{0}{12} \] \[ x = 0 \][/tex]
Explanation: To solve for [tex]\(x\), we divide both sides by the coefficient of \(x\), which is \(12\).[/tex]
Therefore, the solution to the equation [tex]\(18x - 2x = 4x\) is \(x = 0\)[/tex]. This means [tex]\(x\)[/tex] is zero, satisfying the equation.
Dad bought $200,000 of term life insurance at the rate of $5.40 per thousand-dollar unit. How much is the annual premium?
Answer:
It is clear that the annual premium = $1080
Explanation:
Given:
As the total term amount for life insurance is given in the question which is $200,000
rate per $1000 unit = $5.40
Simple Calculation Procedure to get the annual premium:
First step:
Let’s assume $1000 is one unit and the mentioned rate per $1000 unit is $5.40. Now, all you need is to find total number of $1000 units in total term insurance amount ($200,000).
So,
divide $200,000 by $1000 to establish the total number of
1000 units in $200,000 = $200,000/$1000 = 200
Second step:
As 200 is found to be the total number of $1000 units in $200,000.
So, just multiply 200 with $5.40 to ultimately find the annual premium
i.e. $5.40 × 200 = $1080
Hence, it is clear that the annual premium = $1080
Keywords: life insurance, annual premium, premium term rate
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how can i solve thus problem help me
Answer:
Position from point A= 383.33 meters
Step-by-step explanation:
A concept to know is that the integral of velocity will give you the distance traveled.
[tex]d=\int\limits^{t_1}_{t_0}{v(t)} \, dt[/tex]
where the interval of integration are the starting time and ending time.
I let the starting time be t₀ = 0, and the ending time t₁=10 for the 10 seconds that it traveled.
I did the integration and got 383.33m traveled in 10 seconds.
So the answer is 383.33 meters.
Ignore the final answer in the image. I misread the question.
Which of the following shows the expression −3t2−2t(4s−9t)+7st in simplest form
Answer:
15t^2-ts
Step-by-step explanation:
-3t^2-2t(4s-9t)+7ts
-3t^2-8ts+18t^2+7ts
-3t^2+18t^2-8ts+7ts
15t^2-ts
The expression −3t^2−2t(4s−9t)+7st can be simplified to 15t^2-st.
Explanation:This expression is a quadratic equation in the form of −3t^2−2t(4s−9t)+7st. To simplify, we can start by distributing the -2t across the terms inside the parentheses:
−3t^2−8st+18t^2+7st
Combining like terms, we get:
15t^2-st
So, the expression −3t^2−2t(4s−9t)+7st in simplest form is 15t^2-st.
Let a = x2 + 4. Use a to find the solutions for the following equation:
(x2 + 4)2 + 32 = 12x2 + 48
Which of the following are solutions for x?
The solutions for x are -2, 0, 2
Solution:
Given that,
[tex]\text { Let } a = x^2 + 4[/tex]
Given equation is:
[tex](x^2 + 4)^2 + 32 = 12x^2 + 48[/tex]
[tex](x^2 + 4)^2 + 32 = 12(x^2 + 4)[/tex]
[tex]\text { Subtsitute } a = x^2 + 4 \text{ in above equation }[/tex]
[tex]a^2 + 32 = 12a\\\\a^2 -12a + 32 = 0[/tex]
[tex]\text{ Let us factorize the above equation }\\\\\text{ Splitting the middle term -12a as -4a - 8a we get, }[/tex]
[tex]a^2 -4a - 8a + 32 = 0[/tex]
Taking "a" as common term from first two terms and taking "-8" as common from last two terms
[tex]a(a-4)-8(a - 4) = 0[/tex]
[tex]\text{Taking (a - 4) as common term, }\\\\(a - 4)(a - 8) = 0[/tex]
[tex]\text{Equating to zero we get, }\\\\(a - 4) = 0 \text{ or } (a - 8) = 0\\\\a = 4 \text{ or } a = 8[/tex]
[tex]\text{Now substitute the value of a = 8 and a = 4 in: }\\\\a = x^2 + 4[/tex]
[tex]\text{ For a = 8: }\\\\a = x^2 + 4\\\\8 = x^2 + 4\\\\x^2 = 4\\\\x = \pm2\\\\x = +2 \text{ or } -2[/tex]
[tex]\text{For a = 4: }\\\\a = x^2 + 4\\\\4 = x^2 + 4\\\\x = 0[/tex]
[tex]\text{Thus solutions of } x \text{ are: }\\\\x = 0 \text{ or } x = 2 \text{ or } x = -2[/tex]
How can you express 5 1/3 + (-7 2/3) as the sum of its integer and fractional parts
Answer:
-7/3
Step-by-step explanation:
-7 2/3=-23/3
5 1/3=16/3
-----------------
16/3+(-23/3)
16/3-23/3
-7/3
Final answer:
To express 5 1/3 plus (-7 2/3), separate and add the integers to get -2, then add the fractions to find -1/3, resulting in the final expression -2 1/3.
Explanation:
To express the sum of 5 1/3 and (-7 2/3) as the sum of its integer and fractional parts, we need to perform the following steps:
First, separate the integers from the fractions: 5 + 1/3 and -7 + (-2/3).Now, add the integers: 5 + -7 = -2.Next, add the fractions: 1/3 + (-2/3). Recall that subtracting a negative is the same as adding a positive, so this becomes 1/3 - 2/3 = -1/3.Combine the integer and fractional results to get the final expression: -2 1/3.Our intuition about addition and subtraction of fractions can be helpful in visualizing the mixing of different pie pieces to form a whole, and understanding how changing the sign affects the direction of the operation.
The length of a rectangle is 6 yards longer than its width and
If the perimeter of the rectangle is 72 yards, find its length and width.
Let...
length=x+6
width=x
x+x+x+6+x+6=72
4x+12=72
4x=60
x=15
x+6=21
answer: length=21 and width=15
To solve for the length and width of the rectangle, we first need to understand the formulas and relationships involved:
- The perimeter (P) of a rectangle is the total distance around its boundary, which is calculated by adding together twice the length (L) and twice the width (W): `P = 2L + 2W`.
- We have two pieces of information to work with:
1. The length is 6 yards longer than the width, which we can express as `L = W + 6`.
2. The perimeter is 72 yards, so `P = 72`.
With these equations, we can set up our system to solve for the length and width:
1. Substitute the expression for L from the first piece of information into the perimeter formula:
`P = 2(W + 6) + 2W`
2. Plug in the value for the perimeter:
`72 = 2(W + 6) + 2W`
3. Distribute the 2 through the parentheses:
`72 = 2W + 12 + 2W`
4. Combine the W terms:
`72 = 4W + 12`
5. Isolate the W term by subtracting 12 from each side:
`72 - 12 = 4W`
`60 = 4W`
6. Divide by 4 to solve for W:
`W = 60 / 4`
`W = 15`
Now that we have the width, we can use the first equation to solve for the length:
`L = W + 6`
`L = 15 + 6`
`L = 21`
So, the width (W) is 15 yards and the length (L) is 21 yards.
A 14-gram serving of mayonnaise contains
11 grams of fat. What percent of the mayonnaise,
to the nearest tenth of a percent, is fat?
Answer:
Step-by-step explanation:
the answer is 78.6%
11/14*100=78.6
The total percentage of fat in mayonnaise 78.6 %
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total amount of mayonnaise be A = 14 grams
Let the total amount of fat be B = 11 garms
Now , the equation will be
The total percentage of fat in mayonnaise is =
( total amount of fat / total amount of mayonnaise ) x 100
The total percentage of fat in mayonnaise is = ( 11 / 14 ) x 100
= 0.7857 x 100
= 78.57 %
Now , on simplifying the equation we get
The total percentage of fat in mayonnaise 78.6 %
Hence , The total percentage of fat in mayonnaise 78.6 %
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What percent of time does marissa spend playing basketball ? Show or explain how you got your answer?
Walking 45percent
Jogging 15 percent
Swimming 10 percent
Bowling 10 percent
Answer:
20% of the time
Step-by-step explanation:
Marissa spends 20% of the time playing basketball. I figured this out my subtracting all of the other sports from 100% , (the whole), to get 20%.
Hope this helps :)
there are 2.54 centimeters in 1 inch. there are 100 centimeters in 1 meter. to the nearest inch, how many meters are in 511 inches
12.9794 meters or 13 meters (rounded)
You can find out this answer by looking at the 2 formulas given. Then set up a ratio and cross multiply to get your answer.
Hope this helped! (Please mark me brainliest!)
Answer:
12.9794 meters or 13 meters (rounded)
Step-by-step explanation:
You can find out this answer by looking at the 2 formulas given. Then set up a ratio and cross multiply to get your answer.
I need help please and thank you
Answer:
10 000
Step-by-step explanation:
For each choice of the first two digits you have 10 choices for the third digit. Thus you have 10x10x10 = 1000 choices for the first three digits. Finally you have 10 choices for the fourth digit and thus there are 10x10x10x10 = 10 000 possible 4 digit combinations from 0-9.
The value of x in the expression 2x+3=13 is
A. 8
B.5
C.4
D.3
Answer:
the anwer of youre question is B.5 .
Let $x=(0.\overline{6})(0.\overline{60})$. When $x$ is written out as a decimal, what is the sum of the first $15$ digits after the decimal point?
Answer:
32
Step-by-step explanation:
The sum of the first $15$ digits is 32.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Let $x = 0.666666.....
$x = = 6/9 = 2/3
And .606060..... = 60/99
⇒(2/3) (60/99)
⇒ (2/99)(60/3)
⇒(2/99)(20)
⇒ 40/99
⇒ .040404.........
So, the sum of the first 15 digits = 8(4) + 7(0) + 0 = 32
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a number machine uses a rule to charge input numbers into output numbers. this number machine charged 4 into 16, 5 into 20, and 6 into 24. what number will 7 be cgarged into?
Answer:
28
Step-by-step explanation:
The function that we have in this is f(x) = 4x. We can see this in 4 * 4 = 16, 5 * 4 = 20 and 6 * 4 = 24. Therefore, following the pattern, 7 * 4 = 28.
If tan 0=11/60, what is the value of cot 0?
Answer:
Step-by-step explanation:
tan 0 = 1/ cot 0
so, tan 0=11/60,
cot 0= 1/ (11/60)
cot 0= 60/ 11
Evaluate the expression of 9! - 4! (5!)
Answer:
360,000.
Step-by-step explanation:
9! - 4! (5!)
= 9*8*7*6*5*4*3*2*1 - 4*3*2*1 * 5*4*3*2*1
= 5*4*3*2*1 ( 9*8*7*6 - 4*3*2*1)
= 120( 3024 - 24)
= 120 * 3000
= 360,000
9 - 4(7x - 8x) = x - 3
Answer:
.2 or 1/5
Step-by-step explanation:
sorry for bad picture
Is -x+4y=-2 a direct variation?
Answer:
No
Step-by-step explanation:
Direct variation: two variables, one variable is a constant multiple of another variable
y = k x .... k constant
-x+4y=-2
4y = x - 2
y = 1/4 x -1/2 ..... y = k x + b y is not a simple multiple of x
20 points
The graphs of functions f and g are shown below.
a) Find all values of x for which f(x)=g(x).
b) Find all values of x for which f(x)
c) Find all values of x for which f(x)>g(x).
Answer:
a) x=-10,0,11
b) x<-10, 0<x<11
c) x>11, -10<x<0
Step-by-step explanation:
a) Find all the intersecting points of the two graphs.
b) Find all the x values when g(x) (the curving one) is higher than f(x). g(x) or f(x) is kind of like the y coordinate in these graphs. There for to find when f(x)<g(x), you have to find when g(x) is above f(x). Any part of g(x) above the intersecting points is your answer. So we can see that at -10, the curving line is above the straight one, f(x). There for that would be when x<-10, g(x)>f(x). Use these intersection points to figure out the rest.
c) Find all the x values of when the curving line, g(x) is below f(x), the straight line. Use the points where the two lines intersect t start off your answer. For example, we can see the curved line is below the straight one between -10 and 0. Therefore, f(x)>(g) when -10<x<0. x>11 is the only other moment when g(x), the curving line is also below f(x).
I also struggled with this question and I tried my best to explain.
Solve the equation.
9x + 33 = -30
Answer:
x=-7
Step-by-step explanation:
Subtract 33 from -30 (because subtraction is the opposite of addition.
that's leaves 9x=-63
you want to isolate the variable so divide -63 by 9 (since division is the opposite of multiplication)
x=-7
factory workers make $15 per hour and work 40 hours per week. how much should the Radcliff Company budget for salary each week if they have 250 workers?
Answer:
123,000
Step-by-step explanation: 40×15=600
For 1 worker
600×250=123,000
For all 250 workers
Jim went to a carnival with $25.00. He bought some food for $3.75. Jim wants to spend the rest of his money on tickets for rides, r, which cost $1.25 each. Which represents, r, the number of tickets Jim can purchase?
(A) r is < than equal to 17
(B) r is > greater than equal to 17
(C) r is < less than equal to 20
(D) r is > greater than equal to 20
Answer:
(A) [tex]r[/tex] is < than equal to 17
Step-by-step explanation:
Total amount Jim had for the carnival =$25.00
Amount spent on food = $3.75
Amount left with him = [tex]\$25.00-\$3.75=\$21.25[/tex]
Jim plans to sped rest on tickets for rides.
Cost of each ride ticket = $1.25
Given: [tex]r[/tex] represents the number of ride tickets bought.
Using unitary method
If 1 ride ticket cost = $1.25
Cost of [tex]r[/tex] ride tickets in dollars will be = [tex]1.25r[/tex]
Amount spent on rides must be less than or equal to the total amount left with Jim which is =$21.25.
So, we have:
⇒ [tex]1.25r\leq 21.25[/tex]
Dividing both sides by 1.25.
⇒ [tex]\frac{1.25r}{1.25}\leq \frac{21.25}{1.25}[/tex]
∴ [tex]r\leq 17[/tex]
Thus, the inequality representing te number of tickets Jim can purchase is given by:
[tex]r\leq 17[/tex]
Consider the following system of equations:
Equation 1: 3x + y = 5
Equation 2:5x – 4y = -3
What is the solution to this system?
(To answer this question, we need to know the value of y.)
O (1.8)
O (1,2)
O (1,1)
O (1.3)
Answer:
x=1, y=2. (1, 2).
Step-by-step explanation:
3x+y=5
5x-4y=-3
---------------
4(3x+y)=4(5)
5x-4y=-3
----------------------
12x+4y=20
5x-4y=-3
---------------
17x=17
x=17/17
x=1
3(1)+y=5
y=5-3
y=2
MP2 Reasoning Joel is 23 inches
shorter than Carlos Carlos is 12 inches
taller than Dan. If Dan is 587 inches ta
how many inches tall is Joel?
Answer: 576 inches
Step-by-step explanation:
Carlos’ height :587+12=599
Joel’s height: 599-23=576
:)
Answer:
Step-by-step explanation:
Height of Dan = 587 inches
Height of Carlos = 587 + 12 = 599 inches
Height of Joel = 599 - 23 = 576 inches
I need help please and thank you
Answer:
15
Step-by-step explanation:
n is the number of people and k the number of chairs
here n = 6 and k = 4
note n! = n(n - 1)(n - 2).... × 3 × 2 × 1, thus
[tex]\frac{6!}{4!(6 -4)!}[/tex]
= [tex]\frac{6(5)(4)(3)(2)(1)}{4!(2!)}[/tex]
= [tex]\frac{720}{4(3)(2)(1)2(1)}[/tex]
= [tex]\frac{720}{24(2)}[/tex]
= [tex]\frac{720}{48}[/tex]
= 15
Which shows a difference of squares? 10 y squared minus 4 x squared 16 y squared minus x squared 8 x squared minus 40 x + 25 64 x squared minus 48 x + 9
Answer:
16y² - x² shows a correct difference of squares.
Step-by-step explanation:
Following are the given options from which we have to chose which represents the difference of squares.
A) 10y² - 4x²
B) 16y² - x²
C) 8x² - 40x+25
D) 64x² - 48x+9
Difference of square is given by:
a² - b² = (a + b) (a - b)
If we analyze the expressions from the choices given in the question. We should figure out that option B) should be the right answer that shows a difference of squares. i.e. 16y² - x² shows a correct difference of squares. All other options do not represent the difference of perfect squares.
As in option A) 10y² - 4x²
10y² is not a complete square of any number. Hence, option A) is incorrect.
As in option C) 8x² - 40x+25
Neither of the terms in the expression as shown in option C can be a perfect square. Hence, option C) is incorrect.
As in option D) 64x² - 48x+9
The term 48x+9 in the expression as shown in option D can not be a perfect square. Hence, option D) is incorrect.
Lets take the expression 16y² - x² of option B) and solve it.
First simplify the terms separately to associate them as perfect squares as shown below:
⇒ 16y² = (4y)² Equation (1)
⇒ x² = (1x)² Equation (2)
Now, take the difference of Equation (1) and Equation (2).
⇒ 16y² - x²
⇒ (4y)² - (1x)² Equation (3)
So,
Equation (3 )shows a difference of squares. It can also be represented as factorizing the difference of two perfect squares such as (4y - x) (4y + x).
Which is
(4y - x) (4y + x) = 16y² - x²
= (4y)² - (1x)²
So, option B) i.e. 16y² - x² shows a correct difference of squares.
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Answer:
the correct answer would be
16y² - x²