This is because the given expression factors to (x+4)(x+4), which condenses to (x+4)^2.
To factor, think of two numbers that A) multiply to 16, and B) add to 8. Those values would be 4 and 4
4+4 = 8
4*4 = 16
So that's how we end up with (x+4)(x+4). You can use the FOIL rule to expand that out and get x^2+8x+16 again to help verify you have the correct factorization.
Question 6 of 10
The domain of a function f(x) is x = 0, and the range is ys -1. What are the
domain and range of its inverse function, '(x)?
Answer: y = 0 and x = -1
What is the order of rotational symmetry for the figure?
A. 3
B. 2
C. 4 or more
D. 1
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Answer:
C. 4 or more
Step-by-step explanation:
Rotating the figure in increments of 90° will give the same figure. There are 4 such rotations in a full turn. The order of rotational symmetry is 4.
The half-life of a radioactive substance is 20 years. If you start with some amount of this substance, what fraction will remain in 180 years?
Answer:
1/512
Step-by-step explanation:
Let staring fraction = x
Half-life = 20 years ; this is the time taken for an element to decrease to half of its original size
Hence,
After 20 years - - - > x/2
After 40 years - - - - > x/2 ÷ 2 = x/2 * 1/2 = x /4
After 60 years - - - - > x/4 ÷ 2 = x/4 * 1/2 = x/8
After 80 years - - - - -> x/8 ÷ 2 = x/8 * 1/2 = x / 16
After 100 years - - - > x/16 * 1/2 = x/32
After 120 years - - - - > x/32 * 1/2 = x/64
After 140 years - - - - -> x / 64 * 1/2 = x / 128
After 160 years - - - - - > x / 128 * 1/2 = x/256
After 180 years - - - - > x/256 * 1/2 = x / 512
Hence, the fraction after 180 years = 1/512
Please help explanation if possible
Answer:
18.84 feet. let me know if you have ay other questions.
Step-by-step explanation:
The way to find the formula for circumference is kinda complicated so it is best to ust memorize the formula, which is 2πr. or 2 times pi times the radius.
Your problem gives you the formula, but instead of 2 and r in it you have d, which is the diameter.
The diameter of the circle is 2 times the radius, so that's why it is replaced.
the radius is the distance from the center fo the circle to one edge, and the diameter is the distance through the circle passing through its center. so it's the center to one end plus the center to another end. or r+r which is also 2r.
So d = 2r, so in this problem d =6 feet.
So now the formula πd = 3.14*6 feet = 18.84 feet
Ms. Lowder has 2 children, one in first grade and one in fifth grade. Both children need paper for school. Paper costs $2.29 per pack. If the first grader needs 2 packs of paper and the fifth grader needs 6 packs of paper, how much money will Ms. Lowder spend on paper?
the answer is she spend $18.32
(5, 4)
11-5-2)
16.nat's the slope-intercept form of the equation of the line graphed in this figure?
O A. y = 5/3x + 1
O B.y=-3x + 1
O C. y = 3x + 1
O D.y = -5/3X - 1
Answer:
The answer is B. y=3/5x+1Factors and rewrite the expression 25x-15
Answer:
5(5x-3)
Step-by-step explanation:
The common factor in this expression is 5 so divide 5 to all the values
25/5=5
-15/5= -3
Put these values into parenthesis and leave the 5 on the left side and out of the parenthesis
5(5x-3)
Answer:
5(5x - 3)
Step-by-step explanation:
The greatest common factor here is 5. Divide each term by 5 and simplify.
25x/5 = 5x
15/5 = 3
Therefore, the answer is 5(5x - 3).
Find the local linear approximation L(x) of the function f(x) = 5−x^2 at x = 2.
Use this to estimate f(2.1).
Answer:
L(x)=-4x+9
L(2.1)=0.6
Step-by-step explanation:
It's asking us to find the tangent line to curve f(x) = 5−x^2 at x = 2.
Theb use this to estimate f(2.1).
To find slope of tangent line, we must differentiate and then plug in 2 for x.
f'(x)=0-2x by constant and power rule.
f'(x)=-2x
So the slope of the tangent line is -2(2)=-4.
A point on this tangent line shared by the curve is at x=2. We can find it's corresponding y-value using f(x)=5-x^2.
f(2)=5-(2)^2
f(2)=5-4
f(2)=1
So let's rephrase the question a little.
What's the equation for a line with slope -4 and goes through point (2,1).
Point-slope form y-y1=m(x-x1) where m is slope and (x1,y1) is a point on the line.
Plug in our information: y-1=-4(x-2).
Distribute: y-1=-4x+8
Add 1 on both sides: y=-4x+9
Let's call this equation L(x), an expression to approximate value for f near x=2.
L(x)=-4x+9
Now the appropriation at x=2.1:
L(2.1)=-4(2.1)+9
L(2.1)=-8.4+9
L(2.1)=0.6
If we did plug in 2.1 into given function we get 5-(2.1)^2=0.59 . This is pretty close to our approximation above.
Dad is twice as old as Junior. Gramps is twice as old as Dad. The sum of the three ages is 140. How old is Gramps?
Answer:
80
Step-by-step explanation:
We can start of with Junior's age. Then if dad is twice as old as Junior, then we add 2 parts and get 3 parts. Then Gramps is twice as old as Dad so we add 4 parts and get 7 parts. Now we divided 140 by 7. We get 20. This is Junior's age. By looking at that, we know Dad is 40, and Gramps is 80.
Gramps is 80 years old.
Hi! I'm happy to help!
We can say that Junior is x years old. This would mean that Dad is 2x years old, and Gramps is 4x years old. All together, their age is 7x. We can write an equation to solve.
7x=140
Divide both sides by 7 to find out x.
x=20
This means that Junior is 20 years old. Dad is double that, so he is 40 years old. And Gramps is double that so he is 80 years old.
To check our answer we can add all of them together.
20+40+80
140
This means that Gramps is 80 years old.
I hope this was helpful, keep learning! :D
five brothers of 4, 9, 11, 13 and 16 years respectively, receive an inheritance of 1,500,000, the will stipulated that that amount must be shared by the heirs so that, placed the shares in a bank, they would result in equal capitalized amounts, when each one reached 21, could raise his share. Knowing that the bank charges an interest rate of 9% per year, what is the amount of each share?
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Answer:
Youngest to oldest:
160,406.86246,805.83293,230.01348,386.58451,170.72Step-by-step explanation:
At 9% interest per year, the present value of 1 at age 20 is ...
p(a) = 1.09^(a-20)
Adding the present values for the different ages, we get a total of about 2.35528984846. Dividing the inheritance by that amount gives the multiplier for each of the present value numbers. The result is the list of shares shown above. At age 20, each brother will inherit about 636,864.29.
__
Additional comment
This is the sort of question that suggests the use of a graphing calculator or spreadsheet for doing the tedious number crunching.
(We assume the bank pays 9% per year, rather than charges 9% per year.)
accountancy
So i have to make trial balance and im kinda confused with 'interest'. So which side did it go to? Credit or debit? It didn't state the interest as received or expense/paid. someone told me to look at the bank but hey i need more explanation T^T
A popular beach erodes 4 inches per year on average.
An eroding beach.
A. How many years will it take for the coastline to erode one foot?
Answer:
3 years
Step-by-step explanation:
4 inches per year on average
1 foot = 12 inches
12 divided by 4 equals 3
therefore it is 3 years
HELPP plz don't send a file whats the answer and explanation plz if you can
Answer:
5/0 is not a rational number
Step-by-step explanation:
you cant divide by 0
Select the correct answers in the table.
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles in 2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile?
Give example to verify if the given statement is true or false
1) if two numbers are co-primes , at least one of them should be prime number.
Answer:
no
Step-by-step explanation:
if two numbers are co-prime that is not necessary that one of them must be a prime number
After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth
$213,022?
Provide your answer below:
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Answer:
19 years
Step-by-step explanation:
The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
Solving for t, we get ...
t = log(A/P)/(n·log(1 +r/n))
Using the given values, we find t to be ...
t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000
The investment will be worth $213,022 after 19 years.
Write each word phrase as an algebrale
expression for exercises 66-69
66) ten less than a number
67) the product of x andy
The algebraic expression for ten less than n
66) ten less than a number
Let the number be n
= n - 10
67) the product of x and y
= x × y or xy
68) The algebraic expression for ten less than n
= n - 10
Must click thanks and mark brainliest
The polygons in each pair are similar. Find the missing side length.
Let missing side be x
If both polygons are similar
[tex]\\ \sf\longmapsto \dfrac{3}{4}=\dfrac{18}{x}[/tex]
[tex]\\ \sf\longmapsto 3x=4(18)[/tex]
[tex]\\ \sf\longmapsto 3x=72[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{72}{3}[/tex]
[tex]\\ \sf\longmapsto x=24[/tex]
Last week, you spoke with 800 customers in 40 hours."
Employee: "That is an average of __________ customers every 30 minutes."
Answer:
10 customers
Step-by-step explanation:
Hi!
Each hour has 60 minutes, so two half hour (30 minute) blocks. Thus, 1 hour = 2 half hours, so 40 hours = 80 half hours.
800 customers in 80 half hours, divide that:
800 customers / 80 half hours = 10 customers / half hour
So, your answer is 10 customers every half hour, or 10 customers every 30 minutes.
Average is [tex]10[/tex] customers per hour
Average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Total number of customers [tex]=800[/tex]
Total number of hours [tex]=40[/tex]
[tex]=40\times 60[/tex]
[tex]=2400[/tex] minutes
Average (in every [tex]30[/tex] minutes) [tex]=[/tex] Total number of customers [tex]\div[/tex] Total number of hours
[tex]=\frac{800}{2400 \div 30}[/tex]
[tex]=10[/tex] customers per hour
For more information:
https://brainly.com/question/19622178?referrer=searchResults
The scatterplot shows the attendance at a pool for different daily high temperatures.
A graph titled pool attendance has temperature (degrees Fahrenheit) on the x-axis, and people (hundreds) on the y-axis. Points are at (72, 0.8), (75, 0.8), (77, 1.1), (82, 1.4), (87, 1.5), (90, 2.5), (92, 2.6), (95, 2.6), (96, 2.7). An orange point is at (86, 0.4).
Complete the statements based on the information provided.
The scatterplot including only the blue data points shows
✔ a strong positive
association. Including the orange data point at (86, 0.4) would
✔ weaken
the correlation and
✔ decrease
the value of r.
Answer:
✔ a strong positive
✔ weaken
✔ decrease
ED2021
Answer:
The scatterplot including only the blue data points shows
✔ a strong positive
association. Including the orange data point at (86, 0.4) would
✔ weaken
the correlation and
✔ decrease
the value of r.
Step-by-step explanation:
Algebra word problem plz help me
Step-by-step explanation:
here's the answer to your question
A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:________
a. H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6
b. H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6
c. H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6
d. H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
e. H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6
f. H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6
The test is:________
a. two-tailed
b. left-tailed
c. right-tailed
The test statistic is:_______ (to 3 decimals)
The p-value is:_______ (to 4 decimals)
Based on this we:________
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.
Null and alternative hypothesis:
Claim the the proportion is of 60%, thus, the null hypothesis is:
[tex]H_0: p = 0.6[/tex]
Test if the proportion is greater than 60%, thus, the alternative hypothesis is:
[tex]H_1: p > 0.6[/tex]
And the answer to the first question is given by option c.
Classification:
We are testing if the proportion is greater than a value, so it is a right-tailed test.
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.6 is tested at the null hypothesis:
This means that [tex]\mu = 0.6, \sigma = \sqrt{0.4*0.6}[/tex]
Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.
This means that [tex]n = 100, X = 0.69[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}[/tex]
[tex]z = 1.837[/tex]
The test statistic is z = 1.837.
p-value:
The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.
Looking at the z-table, z = 1.837 has a p-value of 0.9669.
1 - 0.9669 = 0.0331
The p-value is 0.0331.
Decision:
The p-value of the test is 0.0331 > 0.01, and thus:
a. Fail to reject the null hypothesis
For another example of a problem of a test of hypothesis, you can take a look at:
https://brainly.com/question/24166849
factorize : ( p- q ) cube
Answer:
[tex]( {p - q}^{3} ) \\ = {p}^{2} - 3 {p}^{2} q + 3p {q}^{2} - {q}^{3} [/tex]
What is the simplified form of square root 400 x to the power 100
Step-by-step explanation:
[tex]thank \: you[/tex]
Answer:
20x⁵⁰
Step-by-step explanation:
With the equation √400x¹⁰⁰
we need to take the square root away separately
√400 = √20*20 = 20
Then with x¹⁰⁰
√x¹⁰⁰ = √x⁵⁰*x⁵⁰ = x⁵⁰
So √400x¹⁰⁰ = 20x⁵⁰
hope this helps
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
FH ≈ 6.0
Step-by-step explanation:
Using the sine ratio in the right triangle
sin49° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FH}{FG}[/tex] = [tex]\frac{FH}{8}[/tex] ( multiply both sides by 8 )
8 × sin49° = FH , then
FH ≈ 6.0 ( to the nearest tenth )
Answer:
6
Step-by-step explanation:
sin = opposite/hypotenuse
opposite = sin * hypotenuse
sin (49) = 0,75471
opposite = 0,75471 * 8 = 6,037677 = 6
Find the greatest rational number r such that the ratios 8/15 ÷ r and 18/35 ÷ r are whole numbers?
The answer is "[tex]\bold{\frac{2}{105}}[/tex]", and the further calculation can be defined as follows:
When the "r" is the greatest common divisor for the two fractions.
So, we will use Euclid's algorithm:
[tex]\to \bold{(\frac{8}{15}) -(\frac{188}{35})}\\\\\to \bold{(\frac{8}{15} -\frac{188}{35})}\\\\\to \bold{(\frac{56-54}{105})}\\\\\to \bold{(\frac{2}{105})}\\\\[/tex]
this is [tex]\bold{(\frac{8}{15}) \ \ mod \ \ (\frac{18}{35})}[/tex]
we can conclude that the GCD for [tex]\bold{\frac{54}{105}}[/tex], when divided by [tex]\bold{\frac{2}{105}}[/tex], will be the remainder is 0. Rational numbers go from [tex]\bold{\frac{2}{105}}[/tex] with the latter being the highest.
So, the final answer is "[tex]\bold{\frac{2}{105}}[/tex]".
Learn more:
greatest rational number:brainly.com/question/16660879
Needddd annnsssweeerrr
Answer:
90in2
Step-by-step explanation:
3x5x6=90
Answer:
C.90
Step-by-step explanation:
first multiply 3 and 5 which is 15 then times it with 6 which equals 90
Starting with a fresh bar of soap, you weigh the bar each day after you take a shower. Then you find the regression line for predicting weight from number of days elapsed. The slope of this line will be:__________.
Answer:
The slope will be negative
Step-by-step explanation:
The slope of the regression line tells us about the relationship or behavior of the dependent and independent variables. In the scenario above, where the weight is being compared with the number of days elapsed. What is expected of the weight and quantity of a bar soap each time it is used for a shower is that it will decrease in weight. Therefore, as the number of days increases, and hence, number of showers rise, the weight of soap will decrease. Hence, we'll obtain a negative slope, one in which the increase in a variable leads to decrease in the other.
Where r is the radius of the cylinder and h is the height of the cylinder.
Find the surface area when r is 7 inches and h is 9 inches.
Sa of cylinder= 2(pi)rh + 2(pi)r squared
Answer:
703.7 in²
Step-by-step explanation:
SA = 2πrh+2πr²
= 2×π×7×9+2×π×7²
= 224π
= 703.7 in² (rounded to the nearest tenth)
Answer:
224π
in²
Step-by-step explanation:
Please help me with this on the picture
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Answer:
(-5, 4)
Step-by-step explanation:
The inside corner moves from (2, -2) to (-3, 2). That is 5 is subtracted from the x-coordinate, and 4 is added to the y-coordinate. (x, y) ⇒ (x -5, y +4)
The translation vector can be written horizontally as (-5, 4), or vertically as ...
[tex]\displaystyle\binom{-5}{4}[/tex]
