Answer:
Step-by-step explanation:
5x^2 - 125 factors into 5 (x^2 - 25)
x^2 - 25 factors into (x + 5)(x - 5)
So the answer to this part is 5(x + 5)(x - 5)
x^2 - 10x + 25 factors into
(x - 5)(x - 5)
So the HCF is (x - 5)
If you read 84 pages in 156. At this rate how long will it take you to read 21 pages?
Answer:
39
Step-by-step explanation:
you can set a proportion
84/156 = 21/x
when u solve for x u get 39
CAN SOMEBODY SOLVE THE PROBLEM IVE BEEN STUCK ON IT I WILL GIVE BRAINIEST
The diameter of a cylinder is 3 yd. The height is 12 yd.Find the volume of the cylinder.
Answer:
84.78cube.yd
Step-by-step explanation:
Volume of cylinder= πr^2h
3.14 × 1.5 × 1.5 × 1284.78 cube.yd40 points answer ASAP
A manager is assessing the correlation between the number of employees in a plant and the number of products produced monthly. The table shows the data:
Number of employees
(x) 0 10 20 30 40 50 60 70 80
Number of products
(y) 120 200 280 360 440 520 600 680 760
Part A: Is there any correlation between the number of employees in the plant and the number of products produced monthly? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate? (3 points)
Answer: See below
Step-by-step explanation:
a) There is a correlation between the number of employees in the plant and the number of products produced yearly. Specifically, a positive correlation exists because, as we can see on the table, as the number of employees increases, the number of products also increases. And the rate of increase is constant.
b) Let the function be: y = mx + b
When x = 0; y = 120
So:
120 = 0 + c
c = 120
Now the slope:
[tex]\text { Slope }=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{200-120}{10-0}=\frac{80}{10}=8[/tex]
Therefore, the equation that best fits the data is y = 8x + 120
c) The slope in the function represents the constant rate of change, meaning that as the number of employees increases by 1, the number of products produced monthly increases by 20. While the y-intercept of the plot, which is 120, indicates the constant number of products, that is to say, when there are no employees, there are still 120 products.
40 + x + 25= 180
like i either get decimals for this or something that doesn’t at ALL equal 180, so confused.
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \:40 + x + 25 = 180[/tex]
[tex]\qquad \sf \dashrightarrow \:x + 65 = 180[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 180 - 65[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 115[/tex]
I hope you understood the procedure, please let me know if you have any doubts
In the following figure, the square ABCD is inscribed in the circle centered at point P. What is the area of the circle?
Answer:
[tex]A_{Circle} \approx 39.24\: units^2[/tex]
Step-by-step explanation:
Square ABCD is inscribed in a circle with center P such that BC = 5 units.
BD will be diagonal of the square as well as diameter of the circle.
[tex]BD = BC\times\sqrt 2[/tex]
[tex]\implies BD = 5\sqrt 2[/tex]
-> Diameter of the circle [tex](d) = 5\sqrt 2[/tex]
-> Radius of the circle [tex](r) = 2.5\sqrt 2=3.535\: units[/tex]
[tex]A_{Circle} =\pi(r)^2[/tex]
[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]
[tex]\implies A_{Circle} =3.14(3.535)^2[/tex]
[tex]\implies A_{Circle} =39.2381465[/tex]
[tex]\implies A_{Circle} \approx 39.24\: units^2[/tex]
[tex]solve \: the \: following \: problems \: below[/tex]
please answer it correctly I need It now
please none sense report
Answer:
1. Find the circumference, then multiply that by 120 turns.
Formula for circumference;
C = 2πr
But, we need to find the radius which is 1/2(half) of the diameter, so,
D/2 = R
D = Diameter
R = Radius
20/2 = 10 is the radius.
Plug in values now:-
C = 2(3.14) x 10
C = 6.28 x 10
C = 62.8 is the circumference, now we multiply this by 120 to get the total amount of centimetres it'll go.
62.8(120)
= 7,536 cm it'll go.
2. Find the circumference, then multiply that by 750 turns/revolutions.
C = 2πr
Find radius,
D/2 = R
50/2 = 25 is the radius.
Plug in values now:-
C = 2(3.14) x 25
C = 6.28 x 25
C = 157 cm it'll go.
3. Same thing, find circumference then compare values.
Given that radius is 10,
Use the formula for circumference;
C = 2πr
Replace values:-
C = 2(3.14) x 10
C = 6.28 x 10
C = 62.8 cm is the circumference of the first circle.
Now the second circle, (use same formula)
C = 2πr
Find radius,
D/2 = R
10/2 = 5 is the radius.
Replace values:-
C = 2(3.14) x 5
C = 6.28 x 5
C = 31.4 cm is the circumference for the second circle.
Now subtract the second circle's circumference from the first:
62.8 - 31.4
= 31.4, 31.4 cm is how much greater the second circle is than the first.
4 - 5. Find circumference, (using circumference formula)
C = 2πr
Find radius,
D/2 = R
760/2 = 380
Replace values:-
C = 2(3.14) x 380
C = 6.28 x 380
C = 2,386.4 km is the distance he'll travel.
If he wants to travel around it with 2,000 km, he'll need to travel at least once.
Consider the following initial-value problem. Y'' − 5y' = 8e4t − 4e−t, y(0) = 1, y'(0) = −1 find ℒ{f(t)}, for f(t) = 8e4t − 4e−t. (write your answer as a function of s. )
The Laplace transform of the non-homogeneous second order differential equation is [tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex].
How to determine the Laplace transform of a non-homogeneous second order differential equationA Laplace transform is a frequency-based algebraic substitution method used to determine the solutions of differential equations in a quick and efficient manner.
In this question we shall use the following Laplace transforms:
[tex]\mathcal {L} \{f(t) + g(t)\} = \mathcal {L} \{f(t)\} + \mathcal {L}\{g(t)\}[/tex] (1)
[tex]\mathcal {L} \{\alpha\cdot f(t)\} = \alpha\cdot \mathcal {L} \{f(t)\}[/tex] (2)
[tex]\mathcal{L} \left\{y^{(n)} \right\} = s^{n}\cdot \matcal {L}\{f(t)\}-s^{n-1}\cdot y(0) -...-y^{(n)}(0)[/tex] (3)
[tex]\mathcal {L} \{e^{-a\cdot t}\} = \frac{1}{s+a}[/tex] (4)
Now we proceed to derive an expression fo the Laplace transform of the solution of the differential equation:
[tex]y'' -5\cdot y' = 8\cdot e^{4\cdot t}-4\cdot e^{-t}[/tex]
[tex]s^{2}\cdot \mathcal {L}\{f(t)\}-5\cdot y(0) - y'(0) - 5\cdot s \cdot \mathcal {L} \{f(t)\} +5\cdot y(0) = \frac{8}{s-4}-\frac{4}{s+1}[/tex]
[tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex]
The Laplace transform of the non-homogeneous second order differential equation is [tex]\mathcal {L} \{f(t)\} = \frac{4\cdot (s+6)}{s\cdot (s-4)\cdot (s+1)\cdot (s-5)} +\frac{1}{s} -\frac{1}{s\cdot (s-5)}[/tex]. [tex]\blacksquare[/tex]
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The Laplace transform Y'' − 5y' = 8e4t − 4e−t when y(0) = 1, y'(0) = −1 for f(t) = 8e4t − 4e−t would be [tex]\frac{4(s+6)}{s.(s-4)(s+1).(s-5)} + \frac{1}{s} - \frac{1}{s.(s-5)}[/tex].
What is Laplace transform?A Laplace transform is a frequency-based algebraic substitution method used to determine the solutions of differential equations quickly and efficiently.
The Laplace transform
L[ f(t) + g(t) ] = Lf(t) + Lg(t)
Also,
L [[tex]y^{n}[/tex]] = [tex]s^{n} . L[ f(t) ] - s^{n-1} .y(0) .....y^{n}(0)[/tex]
We have
Y'' − 5y' = 8 . e^4t − 4 . e−t
[tex]s^{2} . L[ f(t) ] - 5. y(0)- y'(0) .....y^{n}(0)[/tex]
y(0) = 1, y'(0) = −1
for f(t) = 8e4t − 4e−t.
= [tex]\frac{8}{s-4} - \frac{4}{s+1}[/tex]
L [f(t)] = [tex]\frac{4(s+6)}{s.(s-4)(s+1).(s-5)} + \frac{1}{s} - \frac{1}{s.(s-5)}[/tex]
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Which of the following correctly measures the length (in cm) of the green box shown in the image below?
0.920 cm
0.92cm
0.9cm
Answer:
0.92 cm
Step-by-step explanation:
Do not pick 0.920 as it is the same as 0.92 but 0.92 is always the preferable option
The accurate measurement for the length of the green box is indeed 0.92 cm.
To measure the length of the green box accurately, we must carefully analyze the given image. By comparing the green box to the provided scale, we can deduce the correct measurement.
Upon examination, the green box appears to span almost the entirety of the "0.1 cm" scale division and extends slightly beyond it. Given that the box reaches around 9 divisions on the scale, it is reasonable to deduce that its length is 0.92 cm. This is because it's covering 9 divisions of 0.1 cm each, and considering the small extension.
Hence, the accurate measurement for the length of the green box is indeed 0.92 cm. This value takes into account its coverage of 0.9 cm (9 divisions) and a slight extension, aligning with the provided options.
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2x-10=12 what is the value of x+4
Answer:
15
Step-by-step explanation:
if 2x-10=12 then
2x=22 so
X=11
X+4= 15
Answer:
15
Step-by-step explanation:
1. we find what x is by finding out the first equation:
2x - 10 = 12
Add 10 to both sides (it cancels out on the first side)
-10 + 10 = 0 (cancels out)
12 + 10 = 22
2x = 22
Now we divide both sides by 2 to get x alone
22 divided by 2 = 11
X = 11
2. Now we can solve the equation x + 4:
Just fill in x, which as we solved, is 11
x + 4 = 11 + 4 = 15
Therefore, the value of x + 4 is 15.
please answer fast this answer with image
Answer:
3/2
use a calculator to try it on your own
do the 1/4 - 4/9 (4/2/3-11/12) first
then times 9/17
then plus 1/1/8
at last divide by 9/16
Find the 51st term of the arithmetic sequence 29,9, -11, ...
Answer:
Step-by-step explanation:
29-9=20
9-(-11)=20
50×-20=-1000
-1000+29=-971
Jasmyn and Samantha go to the mall to go shopping. Jasmyn buys a new t-shirt that is $24.99 and Samantha buys a new pair of pants that are $48.99. If sales tax is 6%, how much will they have to pay total for the t-shirt and pants including tax?
The total cost of both items is $ ____
Answer:
78.42
Step-by-step explanation:
[tex]1.06(24.99 + 48.99)[/tex]
[tex]1.06 \times 73.98 = 78.42[/tex]
pleaseeee check picture its about finding area of triangle.
Answer:
13.75 is your answer
Step-by-step explanation:
find area of whole triangle 5.5*7*1/2=19.25
Find area of blank spot 5.5*2*1/2=5.5
Subtract 19.25-5.5=13.75
Find the area of the figure below. You may assume all sides are perpendicular.
Multiple answer choice
23
19
27
17
Answer:
I think the answers is 27, just add all of those squares.
If in a certain year, 400 000 high school seniors took a test in the NSAT and 240 000 scored above the cut-off score, what is the cut-off score for that year?
Answer:
160 000
Step-by-step explanation:
400 000 - 240 000 = 160 000
Can y’all please solve this
Real Numbers: Mastery Test
Answer:
exuse me but i dont see the questions
Step-by-step explanation:
Solve the system using linear combination.
41
S 5x + 3y
Зх бу
9
We want to eliminate the variable y. What number should we multiply times the first
equation, so that when we add the two equations, we can eliminate the variable y?
Answer:
Delta does not have a relative extreme in the equation, so it is variable y It can not be true
Step-by-step explanation:
[tex]s = 5x + 3y[/tex]
There is an answer
The rest of the equation that has no substituted delta is not true, so the prime variables have relative extremes.
Pls help dont need an explanation just an answer
Answer:
[tex]\boxed{\text{Slope = 5}}[/tex]
[tex]\boxed{\text{y-intercept = 1}}[/tex]
Step-by-step explanation:
To find the slope of the line, we must pick any two points on the line. Using those two points, we will calculate the Rise and the Run. Then, we will use the slope formula (Rise/Run) to find the slope. The y-intercept is the intersection of the point on the y-axis.
[tex]\text{My chosen points: (0,1) and (1,6)}[/tex]
[tex]\text{Rise = 5; Run = 1}[/tex]
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
[tex]\text{Slope}= \dfrac{\text{Rise}}{\text{Run}}[/tex]
➡ [tex]\bold{Slope = \frac{5}{1} = \underline{5}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Rise = 5; Run = 1}][/tex]
[tex]\underline{........................................................................................................................}[/tex]
[tex]\text{Intersection on y-axis:} \ (0,1)[/tex]
➡ [tex]\text{y-intercept} \rightarrow (0,\bold{ 1}) \rightarrow \bold{\underline{{1}}}}[/tex]
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
A real estate agent is working for a developer who claims that the average commute time to downtown is 20 minutes with a standard deviation of 7 minutes. Stephon is an independent real estate agent and wants to check the times for his client. He took a random sample of 15 commute times and found an average of 26 minutes. He did hypothesis testing using a significance level of 5%. Which conclusion could he make? The z-statistic is 0. 22, so the null hypothesis should not be rejected. The z-statistic is 1. 69, so the null hypothesis should not be rejected. The z-statistic is 3. 32, so the null hypothesis should be rejected. The z-statistic is 3. 67, so the null hypothesis should be rejected.
We conclude that z-score = 0.0005 which is less than 5%.
To calculate the z-statistic,
We must first calculate the standard error.
What is the formula for standard error?
Standard error is standard deviation divided by the square root of the population.
[tex]standard error=\frac{standard deviation }{\sqrt{population} }[/tex]
In this case, it is equal to 1.81.
The z-score is defined the distance from the sample to the population mean in units of standard error.
z = (26 – 20)/1.81 = 3.31
Therefore we conclude that z-score = 0.0005 which is less than 5%.
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The cheer squad is ordering small towels to throw into the stands at the next pep rally. The printing company has quoted the following prices. Which function defined below represents the cost, C, in dollars for an order of x towels?.
The function D represents the cost is $175 for of x towels.
For the first 20 towels, the equation is simply 5x.
The 5 is the cost per towel ($5) times the number of towels sold up to and including 20 towels.
What is the meaning of maximum cost of 20 towels?
Replace x by 20 in given expression we get the maximum cost
So the maximum cost of those 20 towels is $5 (20)=$100.
Looking at towels 21 and greater, the price drops to $3 each. Putting this in a formula,
Therefore we get,
3(x-20)+100
Which is $3 for the cost per towel, (x-20) since it starts with towel number 21, and +100 for the cost of the first 20 towels.
Let's try it for 45 towels using the formula
3 (45-20)+ 100
=3(25) + 100
=75+ 100
= $175
The function D represents the cost is $175 for of x towels.
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Answer:
d
Step-by-step explanation:
edge 2022
A triangle has angles of 124°, 28°, and 28°. Will these angles create a triangle?
Answer:
yes it will
Step-by-step explanation:
28+28=56
124+56=180
a triangle consists of angles that add up to 180 degrees
If you borrowed $2000 from your friend to buy a triathlon bike with a simple interest loan of 7%
annual interest rate for 6 months. How much money will you need to pay them back after the 6
months?
The amount of money that you will need to pay them back after the 6 months is $2,070.
Given the following data:
Interest rate = 7% = 0.07.
Simple interest = $2000.
Time = 6 months.
Conversion:
12 months = 1 year.
6 months = 0.5 year.
How to calculate simple interest.Mathematically, simple interest is given by this formula:
[tex]I=PRT[/tex]
Where:
S.I is the simple interest.P is the principal or starting amount.R is the interest rate.T is the time measured in years.Substituting the given parameters into the formula, we have;
[tex]I=2000 \times 0.07 \times 0.5[/tex]
I = $70.
Amount to be paid;
[tex]A=I+P\\\\\A=70+2000[/tex]
A = $2,070.
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Roman Civilization began in 509 B.C. and ended in 476 A.D. How long did Roman Civilization last?
Answer:
Add 509 and 476; The Roman Era lasted for a total of 985 years from 509 B.C to 476 A.D.
Step-by-step explanation:
Hi can u please help me with this and also an explanation thank u
Question 1: Area of the base
The base is a triangle⇒ Area of a Triangle --> [tex]\frac{1}{2}*(base)*(height)[/tex]
⇒ Area = [tex]\frac{1}{2} * 6 * 8 = 3 * 8 =[/tex] 24 square kilometers
Question 2: Height of Pyramid
Height of pyramid ⇒ distance from the tip of the figure to its base⇒ Height = 12 km
Question 3: Volume of a pyramidFormula for Volume of a pyramid ⇒ 1/3 * (base area) * (height)
⇒ [tex]\frac{1}{3} *24 * 12 = 8 * 12[/tex] = 96 cubic kilometers
Hope that helps!
Type the correct answer in the box. round your answer to the nearest tenth. events m and n are independent events. in this scenario, if p(m) = 0.46 and p(m and n) = 0.138, then p(n) = .
The probability helps us to know the chances of an event occurring. The probability of event n occurring is 0.3.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
We know that for two independent events the probability of the two events occurring simultaneously is written as,
[tex]P(A \cap B) = P(A)\cdot P(B)[/tex]
Now, as we know the probability of event m occurring also we know the probability of both events occurring simultaneously, therefore, the probability of event n occurring can be written as,
[tex]P(A \cap B) = P(A)\cdot P(B)\\\\P(m \cap n) = P(m)\cdot P(n)\\\\0.138 = 0.46 \times P(n)\\\\P(n) = 0.3[/tex]
Hence, the probability of event n occurring is 0.3.
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Your coach bought 12 hamburgers and 6 large fries for your team for
dinner. Each hamburger cost $1.75. He spend $30. Write and solve
an equation to determine the cost c of a large fry.
Answer:
$1.5
Step-by-step explanation:
12 x 1.75 + 6c = 30
21 + 6c = 30
6c = 30 - 21
6c = 9
c = 9/6
c = 1.5
Answer:
do face reveal
Step-by-step explanation:
we don't talk about bruno
The total cost of a pizza and 3 drinks is $19. The price of the pizza is $10 and each drink is the same price, d. What is the prive of the one drink?
Answer:
each of the drinks are $3
Step-by-step explanation:
10 d d d /19 d=3
hope it help
Answer:
$3
Step-by-step explanation:
pizza-p
drink-d
p+3d=19
p=$10
10+3 (d)=19
3 (d)=19-10
3 (d)=9
d=9÷3
d=$3
There are 250 wolves in a national park. the wolf population is increasing at a rate of 16% per year. write an exponential model to represent the situation. use the model from problem 1 to determine how long it will take the wolf population in the national park to reach 1000. round the answer to the nearest hundredth.
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill[/tex]
[tex]A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}[/tex]
What are the domain and range of g of x equals the square root of the quantity x plus 4?
D: [4, ∞) and R: [0, ∞)
D: (–4, ∞) and R: (–∞, 0)
D: [–4, ∞) and R: [0, ∞)
D: (4, ∞) and R: (–∞, 0)
Using it's concept, it is found that the domain and range of the function are given by:
D: [–4, ∞) and R: [0, ∞)
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In this problem, the function is:
[tex]g(x) = \sqrt{x + 4}[/tex]
The square root function does not exist for negative values, hence the domain is represented by:
[tex]x + 4 \geq 0 \rightarrow x \geq -4[/tex]
The range of the square root function is [tex]x \geq 0[/tex], which remains the same as there are no vertical translations.
Hence the correct option is given by:
D: [–4, ∞) and R: [0, ∞)
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Answer: C) D: [–4, ∞) and R: [0, ∞)
Step-by-step explanation: