Answer:
The answer is 0.3.
How do you solve this? r^2+32=12r
Answer:
r = {-8, -4}
Step-by-step explanation:
Simplifying
r2 = -32 + -12r
Solving
r2 = -32 + -12r
Solving for variable 'r'.
Reorder the terms:
32 + 12r + r2 = -32 + -12r + 32 + 12r
Reorder the terms:
32 + 12r + r2 = -32 + 32 + -12r + 12r
Combine like terms: -32 + 32 = 0
32 + 12r + r2 = 0 + -12r + 12r
32 + 12r + r2 = -12r + 12r
Combine like terms: -12r + 12r = 0
32 + 12r + r2 = 0
Factor a trinomial.
(8 + r)(4 + r) = 0
Subproblem 1
Set the factor '(8 + r)' equal to zero and attempt to solve:
Simplifying
8 + r = 0
Solving
8 + r = 0
Move all terms containing r to the left, all other terms to the right.
Add '-8' to each side of the equation.
8 + -8 + r = 0 + -8
Combine like terms: 8 + -8 = 0
0 + r = 0 + -8
r = 0 + -8
Combine like terms: 0 + -8 = -8
r = -8
Simplifying
r = -8
Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve:
Simplifying
4 + r = 0
Solving
4 + r = 0
Move all terms containing r to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + r = 0 + -4
Combine like terms: 4 + -4 = 0
0 + r = 0 + -4
r = 0 + -4
Combine like terms: 0 + -4 = -4
r = -4
Simplifying
r = -4
Solution
r = {-8, -4}
For the function y=3x, what is the output when the input is -4?
Answer:
x is the input, y is the output
Step-by-step explanation:
Answer:
I believe the answer is -12.
Step-by-step explanation:
If the input if the x value, then y would be equal to -12.
Diet cola was on sale last week, it cost $10 for every 4 pack. How much do 2 packs of diet cola cost
Answer:
Step-by-step explanation: Your answer to this question is 5$. Reason is because for 4 packs is 10$. You are trying to figure out how much it will be for 2 packs. The only thing you have to do is divide 10$ by 2 which should give you 5. Hope this helps!!!!
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if the formula for the perimeter of a rectangle is p=2l+2w, what is the formula for w in terms of p and l
Answer:
(p-2l)/2 = w
Step-by-step explanation:
p=2l+2w
We want to solve for w.
The first step is to subtract 2l from each side
p-2l=2l-2l+2w
p-2l=2w
Then we will divide each side by 2 to isolate w
(p-2l)/2 = 2w/2
(p-2l)/2 = w
need help turning this improper fraction into mixed number, it's super easy.
Answer:
2 3/4
Step-by-step explanation:
22/8 = 2 6/8 = 2 3/4
Hope that helps and feel free to ask me more questions :)Brainliest??
Common denominator for 9/15 and 4/9
Answer:
45 and 36
Step-by-step explanation:
The common denominator for the two proper fractions is 45
What are proper fractions?A proper fraction is a fraction which has its numerator value less than the denominator. For example, ⅔, 6/7, 8/9, etc. are proper fractions.
Given here: The proper fractions 9/15 and 4/9
now LCM(9,15) = 45
Thus, 9×3/45=27/45 , 4×5/45=20/45
Hence, The common denominator for the two proper fractions is 45
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The wall in the family room is exactly 12 feet long. Your couch is 10 feet and 6 inches long. Once the couch is placed, how much room is left for your end table?
Answer:
1 foot 6 inches
Step-by-step explanation:
That would be the difference between 12 feet and 10 feet 6 inches.
Answer:
the answer is 18 inches (:
Step-by-step explanation:
Alana earnerd money doing chores. Her grandmother agreed to add $4.00 to the amount Alana earned and then give her half of that sum. Alana's grandmother gave her gave her $4.25. Write and solve an equation to find the amount of Alana's donation
Answer:
Hence amount of Alana's donation is $4.5.
Step-by-step explanation:
Amount of Alana's donation = x
Her grandmother agreed to add $4.00 to the amount Alana earned.
So new amount of money = (x+4)
She gives only half of the sum which is (x+4)/2.
She gave her $4.25 so both values must be equal.
[tex]\frac{\left(x+4\right)}{2}=4.25[/tex]
[tex]x+4=4.25*2[/tex]
[tex]x+4=8.5[/tex]
[tex]x=8.5-4[/tex]
[tex]x=4.5[/tex]
Hence amount of Alana's donation is $4.5.
Alana earned $4.50 from doing chores before her grandmother added an additional $4.00 and then gave her half of the total, which was $4.25.
The question relates to finding out how much money Alana earned by doing chores before her grandmother added $4.00 and then gave her half. In this scenario, we let x represent the amount of money that Alana earned from doing chores. According to the information provided, Alana's grandmother agreed to add $4.00 to Alana's earnings and then give her half of the total sum. This can be expressed as:
(x + 4.00) / 2 = 4.25
To solve for x, we first multiply both sides of the equation by 2 to get rid of the denominator:
x + 4.00 = 4.25 * 2
x + 4.00 = 8.50
Next, we subtract $4.00 from both sides of the equation to solve for x:
x = 8.50 - 4.00
x = 4.50
Therefore, the amount of money Alana earned from doing chores is $4.50.
if i clock out at 11:53 and i have 30 Minutes what time do i get in?
Answer:
you get in at 11:23
Step-by-step explanation:
53-30=30
so 11:23
Answer:
11:27
Step-by-step explanation:
0.524 as a percentage
Answer:
52.4%
Step-by-step explanation:
Simply multiply the value with 100 to find the percentage
thus 0.524× 100 = 52.4%
To convert the decimal 0.524 to a percentage, you multiply it by 100, which results in 52.4%.
Explanation:To convert 0.524 to a percentage, you multiply the number by 100. This is because when converting a decimal to a percentage, you are essentially calculating how many parts out of 100 it represents. Thus, converting the decimal 0.524 to a percentage involves the calculation:
0.524 × 100 = 52.4%.
So, the decimal 0.524 is equal to 52.4% when expressed as a percentage. This concept is useful in various contexts such as interpreting statistics, understanding the rise in cost of living, or when calculating a rate of growth or decline in a given scenario.
If x = 6 units and y = 15 units, then what is the volume of the square pyramid shown above?
Answer:
I need the picture of the pyramid to solve.
Step-by-step explanation:
what is the measure of a base angle of an isosceles triangle if its vertex angle measure 80
Knowing base angles theorem, we know that if the triangle is isosceles, then the bottom base angles and congruent. That means that, we must subtract 80 from 180 and then divide the number by 2, since we must find 1 base angle. This brings us to the answer, 50 degrees.
Hope this helps! <3
Women athletes at the a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 42 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 1% level of significance.
Answer:
The null and alternative hypotheses are:
[tex]H_{0}: p=0.67[/tex]
[tex]H_{a} : p <0.67[/tex]
Under the null hypothesis, the test statistic is:
[tex]z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]
Where:
[tex]\hat{p}= \frac{23}{42} = 0.5476[/tex]
[tex]\therefore z = \frac{ 0.5476 -0.67}{\sqrt{\frac{0.67(1-0.67)}{42} }}[/tex]
[tex]=\frac{-0.1224}{0.072555398}[/tex]
[tex]=-1.69[/tex]
Now, we have to find the left tailed z critical value at 0.01 significance level using the standard normal table. The z critical value at 0.01 significance level is:
[tex]z_{critical} = -2.33[/tex]
Conclusion: Since the test statistic does not fall in the critical region, therefore, we fail to reject the null hypothesis, and conclude that there is not sufficient evidence to say that the population proportion of women athletes who graduate from the university is now less than 67%.
Answer: No
Step-by-step explanation:By considering the given information , the null and the alternative hypotheses will be :-
[tex]H_0: p=0.67\\\\H_a: p<0.67[/tex]
Since the alternative hypotheses is left-tailed , so the test applied here is left-tailed.
Sample size : n= 42
The sample proportion of graduated : [tex]\hat{p}=\dfrac{23}{42}\approx0.55[/tex]
The test statistic for population proportion :-
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
i.e. [tex]z=\dfrac{0.55-0.67}{\sqrt{\dfrac{0.67(1-0.67)}{42}}}\approx-1.65[/tex]
The p-value : [tex]P(z<-1.645)=0.0494715[/tex]
Since the p-value is greater than the significance level, then we do not reject the null hypothesis.
Hence, it does not give enough evidence to indicate that the population proportion of women athletes who graduate from the university is now less than 67%.
Evaluate. Round your answer to the nearest hundredth (precalculus)
Answer:
-1.83
Step-by-step explanation:
To find sum of geometric series we use formula
[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex]
In the question , given i=1 so a= 11* -1/5 = -11/5
Here a= 11
r= -1/5, n=10
Plug in the values in the formula
[tex]S_10 = \frac{-11}{5}*\frac{(1-(\frac{-1}{5})^{10}}{1-(\frac{-1}{5})}[/tex]
S_10 = -1.83
The correct option is c.
To evaluate ∑(i=1 to 10) 11(-1/5)^i, we substitute each value of i into the formula and sum the results. Rounding the answer to the nearest hundredth gives -0.01.
Explanation:To evaluate the given expression, we need to substitute each value of i from 1 to 10 into the formula 11(-1/5)^i and then sum up the results:
i = 1: 11(-1/5)^1 = -11/5i = 2: 11(-1/5)^2 = 11/25i = 3: 11(-1/5)^3 = -11/125i = 4: 11(-1/5)^4 = 11/625i = 5: 11(-1/5)^5 = -11/3125i = 6: 11(-1/5)^6 = 11/15625i = 7: 11(-1/5)^7 = -11/78125i = 8: 11(-1/5)^8 = 11/390625i = 9: 11(-1/5)^9 = -11/1953125i = 10: 11(-1/5)^10 = 11/9765625Summing up all these values, we get:
-11/5 + 11/25 - 11/125 + 11/625 - 11/3125 + 11/15625 - 11/78125 + 11/390625 - 11/1953125 + 11/9765625 ≈ -0.00001
Therefore, the rounded answer to the nearest hundredth is C. -0.01.
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The complete question is here:
Evaluate \sum_{i=1}^{10} 11\left(-\frac{1}{5}\right)^i. Round your answer to the nearest hundredth.
A. 13.75
B. 9.17
C. -0.01
D. -1.83
School started at 8:05 a.m. and ended at 2:40 p.m. The work below shows Erica’s calculation of the length of the school day.
Erica made errors by failing to borrow 1 hour when subtracting the hours and misrepresenting the final duration of the school day as 5 hours and 25 minutes instead of the correct 6 hours and 45 minutes.
Erica's calculation:
7hr 65
8 hr 5 min -
2hr 40 min
---------------
5hr 25 minutes
1. **Subtraction of minutes:**
Erica correctly subtracted the minutes: 5 minutes - 40 minutes = 25 minutes.
2. **Subtraction of hours:**
Here's where the error lies. Erica attempted to subtract the hours directly without borrowing. Let's correct this step:
Borrow 1 hour from the 7 hours:
[tex]\[7 \text{ hours} - 1 \text{ hour} = 6 \text{ hours}\][/tex]
Now subtract the remaining hours:
[tex]\[6 \text{ hours} - 2 \text{ hours} = 4 \text{ hours}\][/tex]
So, the corrected calculation is:
6 hr 65
4 hr 25 min -
2hr 40 min
---------------
1hr 45 minutes
```
Therefore, the correct length of the school day is 6 hours and 45 minutes, not 5 hours and 25 minutes.
Complete correct question:
School started at 8:05 a.m. and ended at 2:40 p.m. The work below shows Erica’s calculation of the length of the school day.
7hr 65
8 hr 5 min -
2hr 40 min
---------------
5hr 25 minutes
Which two errors did Erica make?
The variables y and x have a proportional relationship, and y = 9 when x = 2.
What is the value of y when x = 3?
Answer: [tex]y=13.5[/tex]
Step-by-step explanation:
1. By definition, if [tex]y=9[/tex] when [tex]x=2[/tex], then:
[tex]\frac{y}{x}=\frac{9}{2}[/tex]
2. Keeping this on mind, to find the value of [tex]y[/tex] when [tex]x=3[/tex], you must apply the following proccedure:
[tex]\frac{y}{3}=\frac{9}{2}[/tex]
3. Now, you must solve for [tex]y[/tex], as following:
[tex]y=3(\frac{9}{2})\\y=\frac{27}{2}\\y=13.5[/tex]
4. Then, the result is:
[tex]y=13.5[/tex]
20 PTS!
Which situation is best modeled with a division expression?
finding the number of equal-sized parts into which a number can be split
finding the combined value of several different number
finding the distance between two numbers on a number line
finding the total value when several of the same number are grouped together
Answer:
finding the number of equal-sized parts into which a number can be split
Step-by-step explanation:
Let us split the number 80 into 10 equal parts.
80 = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8
= 8 + 8 + 8 +...to 10 times
= 8(10)
or [tex]\frac{80}{10} =8[/tex]
So, if N is any number and p is one of its equal part, then the number of parts into which N is split by p is [tex]\frac{N}{p}[/tex].
Hence, finding the number of equal-sized parts is best modeled with a division expression.
Answer:
Finding the number of equal-sized parts into which a number can be split
Step-by-step explanation:
The correct answer is - finding the number of equal-sized parts into which a number can be split.
Division is defined as the action of splitting something in equal parts.
So, here the first option states this definition.
Taking an example of: Lets divide 100 in 5 equal parts. So, this becomes
[tex]\frac{100}{5}=20[/tex]
This can be also written like : [tex]20+20+20+20+20=100[/tex]
So, division is where you split something equally.
If a,b,c,d are replaced by four different digits from 1 to 9, inclusive, then what's the largest possible value for a.bc + 0.d ?
Answer:
Step-by-step explanation:
I'm not sure but I would nominate 9 8 7 6 written this way.
9.86
0.7
10.56
Answer:
9.86 plus 0.7 is 10.56
Step
which of the following expressions are equivalent to 2/x^8-y^8? choose all that applyA.2/(x^4-y^4)*1/(x^4+y^4)B.2/(x^4)^2-(y^4)^2C.2/(x4-y^4)*1/(x^4-y^4)D.1/(x^4-y^4)*1/(x^4+y^4)
Answer: option a and b are correct :)
Step-by-step explanation:
which graph shows rotation?
Julie designs gardens for a living. For a year she kept track of the amount of time she spent designing the garden and whether or not the customer returned. She recorded the time and probability that a customer returned.
To have the greatest probability of a returning customer, what amount of time should Julie spend per customer?
TIME DESIGNING PROBABILITY OF RETURN
1-2 Hours 5/8
2-3 Hours 5/9
3-4 Hours 7/8
4-5 Hours 3/4
5-6 Hours 1/2
6-7 Hours 3/7
7-8 Hours 2/9
A. 1-2 Hours
B. 2-3 Hours
C. 3-4 Hours
D. 4-5 Hours
Answer:
To have the greatest probability of a returning customer, Julie should 3-4 Hours per customer
Step-by-step explanation:
==> To compare the Time Designing Probability of Return, we need to convert the Probabilities into Percentage form by multiplying them with 100.
1-2 Hour = (5÷8) × 100 = 62.5%
2-3 Hours = (5÷9) × 100 = 55.55%
3-4 Hours = (7÷8) × 100 = 87.5%
4-5 Hours = (3÷4) × 100 = 75%
5-6 Hours = (1÷2) × 100 = 50%
6-7 Hours = (3÷7) × 100 = 42.85%
7-8 Hours = (2÷9) × 100 = 22.22%
To have the greatest probability of a returning customer, Julie should 3-4 Hours per customer
Answer:C)3-4 hours
Step-by-step explanation:
Given the regular decagon (10-sided polygon), which statements are true?
Choose all that apply
A. The polygon has 90° rotational symmetry
B. The polygon has 36° rotational symmetry
C. The polygon has 144° rotational symmetry
D. The polygon has point symmetry
The regular decagon has 36° rotational symmetry and point symmetry because it can map onto itself by rotating 36° and when flipped 180° around its center.
Explanation:The subject of the question is a regular decagon, which is a 10-sided polygon.
To find out which statements are true regarding its symmetry, consider that rotational symmetry of a polygon is determined by the angle of rotation that maps the polygon back onto itself without altering its general outline.
For a regular decagon, the angle of rotation that achieves this is 360 degrees divided by the number of sides, which is 10 in this case.
Therefore, the correct angle of rotational symmetry is 360/10 = 36 degrees.
Thus, the correct answer from the provided options is:
B. The polygon has 36° rotational symmetryD. The polygon has point symmetryWhat is the additive inverse of the complex number –8 + 3i?
Additive inverse is what you add to a number to get zero.
So, by definition, the additive inverse of (-8 + 3i) would be (8 - 3i).
Jasmine borrowed $15,000 for 8 years and she paid $6,600 in interest. What was the interest rate for Jasmine's loan?
A) .055%
B) 6%
C) 3.25%
D) 5.5%
Answer:
D) 5.5%
Step-by-step explanation:
To find the interest rate, use the equation: I = prt
I = Interest = $6,600
p = principal = $15,000
r = rate = unknown
t = time = 8 years
Now plug the numbers into the equation.
6,600 = 15,000 * r * 8
6,600 = 120,000 * r
Now isolate the variable by dividing both sides of the equation by 120,000.
0.055 = r
Now change the rate to a percent by moving the decimal point 2 digits to the right.
5.5% = r OR r = 5.5%
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Help me please it due today.
The value of a stock increases 14 2/3 points twice in one week.the other 3 days the value decreases by 10 points,8 1/3 points and 12 2/3 points.By how many points did the value of the stock change that week? A 2/3 points. B 1/3 points C -1 1/3 points D -1 2/3 points
Answer:
D
Step-by-step explanation:
The number of points the stock changed in a week will be equal to -1 2/3. Hence, option D is correct.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the given information in the question,
Value of a stock increased 14 2/3 twice in one week.
Then, its value will be.
= 2 × 14 2/3
= 2 × 44/3
= 88/3
Then, the other 3 days it decreased by 10, 8 1/3, and 12 2/3 points.
So, the total decrease will be,
10 + 25/3 + 38/3
= (30 + 25 + 38)/3
= 93/3
So, the value of stock change will be,
88/3 - 93/3
= - 5/3 or,
In mixed fraction form, it can be written as -1 2/3.
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An author has 18 pages to send to a publisher. The author has only small envelopes and can't fit all the pages into a single envelope. It ends up taking 6 envelopes to hold all the pages. If each envelope has the same number of pages in it, how many pages are there in each envelope? A) 2 pages B) 3 pages C) 4 pages D) 5 pages
Which expression is equivalent to 36x^2-25
Answer
The answer is the fourth one or D.
Step-by-step explanation:
Answer:
THE ANSWER IS D
Step-by-step explanation:
I DID TEST GOT 100
which equation and ordered pair represent the correct vertex form and vertex for j(x) = x^2 - 12 x +7?
Answer:
see explanation
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Given the equation in standard form : ax² + bx + c : a ≠ 0
then the x-coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
j(x) = x² - 12x + 7 is in standard form
with a = 1, b = - 12 and c = 7, hence
[tex]x_{vertex}[/tex] = - [tex]\frac{-12}{2}[/tex] = 6
substitute x = 6 into j(x) for y- coordinate
y = 6² - 12(6) + 7 = 36 - 72 + 7 = - 29
vertex = (6, - 29 ) and
j(x) = (x - 6)² - 29 ← equation in vertex form
James and Terry open a savings account that has a 2.75% annual interest rate, compounded monthly. They despoit $400. Into the account each month. How much will be in the account after 20 years.
Answer:
$128,088.54
Step-by-step explanation:
Year Year Deposits Year Interest Total Deposits Total Interest Balance
1 $4,800.00 $72.10 $4,800.00 $72.10 $4,872.10
2 $4,800.00 $207.79 $9,600.00 $279.89 $9,879.89
3 $4,800.00 $347.25 $14,400.00 $627.15 $15,027.15
4 $4,800.00 $490.60 $19,200.00 $1,117.74 $20,317.74
5 $4,800.00 $637.94 $24,000.00 $1,755.68 $25,755.68
6 $4,800.00 $789.38 $28,800.00 $2,545.06 $31,345.06
7 $4,800.00 $945.04 $33,600.00 $3,490.11 $37,090.11
8 $4,800.00 $1,105.04 $38,400.00 $4,595.14 $42,995.14
9 $4,800.00 $1,269.49 $43,200.00 $5,864.63 $49,064.63
10 $4,800.00 $1,438.52 $48,000.00 $7,303.15 $55,303.15
11 $4,800.00 $1,612.26 $52,800.00 $8,915.41 $61,715.41
12 $4,800.00 $1,790.83 $57,600.00 $10,706.24 $68,306.24
13 $4,800.00 $1,974.38 $62,400.00 $12,680.62 $75,080.62
14 $4,800.00 $2,163.05 $67,200.00 $14,843.67 $82,043.67
15 $4,800.00 $2,356.96 $72,000.00 $17,200.63 $89,200.63
16 $4,800.00 $2,556.28 $76,800.00 $19,756.91 $96,556.91
17 $4,800.00 $2,761.14 $81,600.00 $22,518.05 $104,118.05
18 $4,800.00 $2,971.72 $86,400.00 $25,489.77 $111,889.77
19 $4,800.00 $3,188.15 $91,200.00 $28,677.92 $119,877.92
20 $4,800.00 $3,410.62 $96,000.00 $32,088.54 $128,088.54
Answer:
The account after 20 years is $73798.8.
Step-by-step explanation:
Given : James and Terry open a savings account that has a 2.75% annual interest rate, compounded monthly. They despoit $400. Into the account each month.
To find : How much will be in the account after 20 years ?
Solution :
Using monthly payment formula,
[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor is [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Substitute in the formula,
[tex]\text{Amount}=M\times \frac{1-(1+i)^{-n}}{i}[/tex]
Where, M=$400 amount deposited monthly
r= 2.75%=0.0275 is the interest rate
[tex]i=\frac{0.0275}{12} =0.00229[/tex]
t=20 years is the time
[tex]n=12\times 20=240[/tex]
Substitute the value,
[tex]\text{Amount}=400\times \frac{1-(1+0.00229)^{-240}}{0.00229}[/tex]
[tex]\text{Amount}=400\times \frac{1-0.5775}{0.00229}[/tex]
[tex]\text{Amount}=400\times 184.497[/tex]
[tex]\text{Amount}=73798.8[/tex]
Therefore, the account after 20 years is $73798.8.