Answer:
x^6-9 = x^-3 = 1/x^2
Step-by-step explanation:
Hi! I'm happy to help!
To solve this, we need to simplify this expression as much as possible. We see that in the exponent, we have the expression 6-9, which we can substitute for -3.
[tex]x^{6-9}[/tex]
[tex]x^{-3}[/tex]
To further simplify, we need to find out what [tex]x^{-3}[/tex] is. Whenever using a negative exponent, follow this equation.
[tex]x^{-y}[/tex]=[tex]\frac{1}{x^{y} }[/tex]
Using this, we can turn [tex]x^{-3}[/tex], into [tex]\frac{1}{x^{3}}[/tex]. Since we do no know what x is, we cannot simplify any further.
To sum it up, [tex]\frac{1}{x^{3}}[/tex] is an equivalent expression for [tex]x^{6-9}[/tex].
I hope this was helpful, keep learning! :D
A fire truck parks 30 feet
away from a building. The
fire truck extends its ladder
45 feet to the very top of
the building. How tall is the
building?
Answer:
34 ft. tall
Step-by-step explanation:
Your first step should to draw a diagram. When you do that, your diagram should look like a right triangle, the leg, or the distance from the firetruck to the building, (we'll call this a) should be 30ft. and the hypotenuse, or the ladder (we'll call this c), should be 45ft.
Now we have a visual so it'll be easier.
We know that this problem is a right triangle and we know that to solve for a missing side of a right triangle you use pythagorean theorem: a^2+b^2=c^2
We know one leg 'a' and the hyp. 'c' and we just need to find 'b' the other leg (aka the building):
Plug in numbers and simplify:
30^2+b^2=45^2
900+b^2=2025
b^2=1125
≈33.54 OR 34 ft. tall
Answer:
about 33.5 feet tall
Step-by-step explanation:
use pythagorean's theorem:
a^2+b^2=c^2
plug in values:
30^2 + b^2 = 45^2
(we know the ladder extends diagonally so 45 is the hypotenuse meaning we plug it in for c)
rearrange the equation:
b^2= 45^2 - 30^2
b^2= 2025 - 900
b^2 = 1125
b= [tex]\sqrt{1125} \\[/tex]
b= 33.5
See the attachment to answer the question
What is the prime factorization of 72?
22 × 32
22 × 33
23 × 32
23 × 33
Answer: its C
Step-by-step explanation:
Answer:
Its C on Edge 2021
Step-by-step explanation:
HELLPPP Mariah is shopping at the mall for a sweatshirt. She finds a sweatshirt that is marked down 55% off the original price of the sweatshirt is $78.25. What is the sale price of the sweatshirt?
Answer:
Her Original PRICE WAS $117.375
Step-by-step explanation:
If the sale price is 55% of the original price of the sweatshirt, the sale price is $78.25.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Given that, Mariah is shopping at the mall for a sweatshirt. She finds a sweatshirt that is marked down 55% off the original price of the sweatshirt is $78.25.
The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.
The sale price of the sweatshirt is,
sale price = 55% of the current price
sale price =(55/100)× $78.25
sale price = $43.03
Thus, if the sale price is 55% of the original price of the sweatshirt, the sale price is $78.25.
Learn more about the percentage here:
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Lines that appear tangent are tangent. What is the value of x?
Answer:
x = 68°
Step-by-step explanation:
4+4x8 100 points for whoever gets it right
Answer:
36
Step-by-step explanation:
4+4x8
Remember PEMDAS: We have to multiply first.
4+(4x8)
4x8 = 32. Now we add.
4+32 = 36
Answer:
The answer is 36
Step-by-step explanation:
4 X 8 = 32 +4 = 36
Derek has a cylindrical water bottle with a diameter of 4 centimeters and a height of 15 centimeters. If he filled the water 3/4 full of water, how much water is in the water bottle?
Answer:
141 3/8
Step-by-step explanation:
First find the volume by multiplying pi, the radius squared, and the height. Pi is 3.14. The radius is half the diameter, so it would be 2. 2^2 is 4. The height is 15. 3.14*4*15=188.5 Then multiply 3/4 and 188.5 to get your answer. 141.375 or 141 3/8.
MAY SOMEBODY HELP ME THANKS!
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 706.50 square feet? Use 3.14 for pi.
IM MARKING BRAINLIEST!!
Answer:
15 feet of water spread
Step-by-step explanation:
Area of the circular pattern is 706.50 sq. feet
Area = A = π r^2 = (3.14)* r^2
706.50 = (3.14)* r^2
r^2 = 706.50 / 3.14
r^2 = 706.50 / 3.14
r = root (225)
r = 15 feet
Answer:
15 feet
Step-by-step explanation:
The area of a circle is pi*r^2, and we're using 3.14 as pi, so we get: area= 3.14 r^2
We plug 706.50 into the equation and get:
706.50 = 3.14 r^2
Divide both sides by 3.14:
225 = r^2
Square root both sides:
15 = r
A survey in one middle school showed that 3 out of 5 students
enjoy biking on the weekends. Predict how many of the 485
students in the school would say they enjoy biking on the
weekends.
To predict how many out of 485 students enjoy biking on the weekends, set up a proportion and solve for the missing value.
Three out of five students enjoy biking on the weekends, so to predict how many out of 485 students would say they enjoy biking, we can set up a proportion.
3 students out of 5 enjoy biking
Set up a proportion: 3/5 = x/485
Cross-multiply to find x: 5x = 3 × 485
Solve for x: x = (3 × 485) / 5
x = 291 students would be predicted to enjoy biking on the weekends.
Here are the weights, in pounds, of a sample of 13 adult female golden retriever dogs: 59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4. what are the degrees of freedom, and what's the critical value of t needed to construct a 95% confidence interval for the population mean weight of adult female golden retrievers? answer:
Answer:
95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].
Step-by-step explanation:
We are given that the weights, in pounds, of a sample of 13 adult female golden retriever dogs :
59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4.
Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean weight = [tex]\frac{\sum X }{n}[/tex] = 54.9 pounds
s = sample standard deviation = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex] = 3.12 pounds
n = sample of female = 13
[tex]\mu[/tex] = population mean weight
Here for constructing 95% confidence interval we have used One-sample t test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.179 < [tex]t_1_2[/tex] < 2.179) = 0.95 {As the critical value of t at 12 degree
of freedom are -2.179 & 2.179 with P = 2.5%}
P(-2.179 < [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.179) = 0.95
P( [tex]-2.179 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X -\mu}[/tex] < [tex]2.179 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.179 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X +2.179 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [tex]\bar X \pm 2.179 \times {\frac{s}{\sqrt{n} } }[/tex]
= [ [tex]54.9 - 2.179 \times {\frac{3.12}{\sqrt{13} } }[/tex] , [tex]54.9 +2.179 \times {\frac{3.12}{\sqrt{13} } }[/tex] ]
= [53.01 pounds , 56.78 pounds]
Therefore, 95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].
7/8 subtracted by 2/7
Find common denominators.
7/8 = 49/56
2/7 = 16/56
Subtract.
49/56 - 16/56 = 33/56
The fraction cannot be simplified any further.
Best of Luck!
Lester's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 80 espressos in all, 80% of which were single-shot. How many single-shot espressos did the cafe sell?
Answer:
64 single-shot espressos
Step-by-step explanation:
Let's say that the cafe sold x single-shot espressos. The total number of espressos sold was 80, and 80% of that total 80 were single-shot. So, we have the equation:
x = 80% * 80
Remember that % just means "out of 100". So, 80% = 80/100:
x = (80/100) * 80 = 6400/100 = 64 single-shot espressos
Hope this helps!
Answer:
64
Step-by-step explanation:
80% of 80 were single-shots
80/100 × 80
64
Write an exponential equation to represent the situation and answer the question.
a. If the cost of a loaf of bread is now $2.75 and is increasing at 5% per year, what will it cost 10 years from now?
b. The population of Flood River City is now 42,000. Experts predict the population will decrease 25% each year for the next five years. What will be the population in five years?
c. A share of Orange stock that was worth $25 in 2000 was worth $60 in 2010. What is the multiplier and percent increase?
Answer:
a. $4.48¢
b. 9,967 people
ci. Multiplier: F = 25 × (1.09)^t
cii. Percent increase = 9.15%
Step-by-step explanation:
a. The equation we are going to use to calculate the future cost of bread in 5 years:
P = F/(1+r)^t
Where P is current cost, F = future cost(what we are required to calculate), r = percentage increase per year, t = time (years).
Where P = 2.75
r = 5/100 or 0.05
t = 10
F = ?
Substituting appropriately, we have:
2.75/1 = F/(1+0.05)^10
We then cross multiply
F = 2.75 × (1+0.05)^10
F = 2.75 × (1.05)^10
F = 2.75 × 1.62889
F = $4.48¢
Therefore, the bread will cost $4.48 in 10 years.
b. Here population is 42,000 people now. There's predicted 25% decrease in population every year for the next 5years. We are to calculate the expected population in 5 years. The equation that can be used to calculate the expected population:
P = F/(1 - r)^t
F = future population
P = present population
r = percentage of decrement
t = period.
Here P = 42,000
r = 25/100 = 0.25
t = 5
F = ?
Substituting accordingly:
42000 = F/(1 - 0.25)^5
Cross multiply
F = 42000 × [(1 - 0.25)^5]
F = 42000 × 0.2373
F = 9,967
The population in the next 5 years will decrease to 9,967 people.
c. Share of orange stock = $25 in the year 2000
The same share = $60 in 2010, we are required to determine the multiplier and percent increase.
Since the future value = $60, the present value = $25, the time = 2010 - 2000 = 10 years. Then we can use the formula:-
F = P × (1 + r)^t
60 = 25 × (1 + r)^10
(1 + r)^10 = 60/25
(1 + r)^10 = 2.4
1 + r = 10√2.4
1 + r = 1.0915
r = 1.0915 - 1
r = 0.0915
r = 9.15%
Therefore the multiplier is:
F = 25 × (1.09)^t
The percent increase = 9.15%
a. The cost of bread in 10 years will be approximately $4.48. b. Flood River City's population will drop to around 9,965 in 5 years. c. The Orange stock had a 2.4 multiplier, corresponding to a 140% increase over 10 years.
Let's address each part of the question with appropriate exponential equations:
a. Cost of a loaf of bread in 10 years:
We use the exponential growth formula:
Future Value = Present Value × (1 + growth rate)^number of years.
Here, the Present Value (P) is $2.75, the growth rate (r) is 5% or 0.05, and the number of years (n) is 10.
Future Value = 2.75 × (1 + 0.05)¹⁰
= 2.75 × (1.05)¹⁰
≈ 2.75 × 1.6289
≈ $4.48
So, in 10 years, the cost of the bread will be approximately $4.48.
b. Population of Flood River City in 5 years:
We use the exponential decay formula:
Future Value = Present Value × (1 - decay rate)^number of years.
Here, the Present Value (P) is 42,000, the decay rate (r) is 25% or 0.25, and the number of years (n) is 5.
Future Value = 42,000 × (1 - 0.25)⁵
= 42,000 × (0.75)⁵
≈ 42,000 × 0.2373
≈ 9,965
So, in 5 years, the population will be approximately 9,965.
c. Stock value multiplier and percent increase:
The stock value increased from $25 to $60 over 10 years. First, find the multiplier (M):
Multiplier (M) = Final Value / Initial Value
= 60 / 25 = 2.4
Next, calculate the percent increase:
Percent Increase = (Multiplier - 1) × 100
Percent Increase = (2.4 - 1) × 100 = 1.4 × 100 = 140%
So, the multiplier is 2.4 and the percent increase is 140%.
Dena is going to construct a paper box. She will make the box x inches wide. The height of the box is 3 inches greater than the width, and the box is twice as deep as it is high. The volume of the box is 6464 in33. Which equation correctly describes the volume of the box?
Final answer:
The equation to describe the volume of the box, given its dimensions in terms of x, is 6464 = [tex]x(x + 3)^2[/tex](x + 3), where x represents the width of the box.
Explanation:
The question asks us to find an equation that represents the volume of a box where the width is x inches, height is x + 3 inches (since it's 3 inches greater than the width), and depth is 2(x + 3) inches because the box is twice as deep as it is high. The volume is given to be 6464 in3. The formula to calculate the volume of a rectangular box is volume = length × width × height.
In this scenario, the width is x, the height is x + 3, and the depth (or length) is 2(x + 3). So, the volume equation can be expressed as:
V = x × (x + 3) × 2(x + 3)
Since we know the volume is 6464 in3, we can set up the equation as:
6464 = [tex]x(x + 3)^2[/tex](x + 3)
y= arctan(-4x) when dy/dx at x = 3
Answer:
200\cdot25-84\cdot\frac{91}{12-65}\cdot\frac{8412}{1.000}-2000000\cdot46512
Step-by-step explanation:=−9.30227818×1010
Which of these is a correct expansion of (4x-2)(2x + 3)?
O A. 4x: 2x + 4x:3+ (-2): 2x + (-2): 3
O B. 4x. 27+ 4x• 3 + 2 + 2+ + 2-3
O c. 4x• 2x + (-2): 2x + 27.3+(-2) - 3
Answer:
C
Step-by-step explanation
You have to do the rainbow move which is basically multiplying
4x*2x, 4x*3, -2*2x, -2*3
which then simplified would equal to 8x^2+8x-6
What is the volume of the pyramid?
The formula for the volume of a pyramid is ...
length × width × height
_________________ = V
3
Factor out a GCF
[tex]3x^{2} +12x[/tex]
Answer:
3x(x+4)
Step-by-step explanation:
3x^2+12x
3x^2 = 3*x*x
12x = 2*2*3*x
We can factor out 3x
3x (x+2*2)
3x(x+4)
in his first year, a math teacher earned $32,000. Each successive year, he
earned a 5% raise. How much did he earn in his 20th year? What were his total
earnings over the 20-year period?
Explain steps by step
Answer:
Step-by-step explanation:
Each successive year, he
earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence(amount earned in the first year).
r represents the common ratio.
n represents the number of terms(years).
From the information given,
a = $32,000
r = 1 + 5/100 = 1.05
n = 20 years
The amount earned in his 20th year, T20 is
T20 = 32000 × 1.05^(20 - 1)
T20 = 32000 × 1.05^(19)
T20 = $80862.4
To determine the his total
earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as
Sn = (ar^n - 1)/(r - 1)
Therefore, the sum of the first 20 terms, S20 is
S20 = (32000 × 1.05^(20) - 1)/1.05 - 1
S20 = (32000 × 1.653)/0.05
S20 = $1057920
The math teacher's salary in the 20th year, with a 5% annual raise, is approximately $85,200. Over the 20-year period, the total earnings amount to about $1,068,753.
The calculation also includes finding the total earnings over the 20-year period.
The salary in the 20th year can be calculated using the formula for compound interest: A = P(1 + r)^n, where A is the amount (salary in this case), P is the principal amount (initial salary), r is the rate of increase (5% expressed as 0.05), and n is the number of years.
Using the formula: A = 32000(1 + 0.05)^19, since the first year salary is given and we calculate the increase starting from the second year,
the salary in the 20th year is approximately $85,200.
To calculate the total earnings over 20 years, we sum all annual salaries over the 20 years which involve a geometric series. The sum of a geometric series can be found using the formula S = P(1 - (1+r)^n) / (1 - (1+r)), where S is the total sum, P is the initial amount, r is the rate, and n is the number of terms.
So, total earnings over 20 years is approximately $1,068,753.
I need help fast!!!!!!!!!!!!!!!!!!!!!
Answer:
(30,784) and (58,0),(2,0)
Step-by-step explanation:
The vertex is (30,784)
The X-intercept is (58,0),(2,0)
The Y-intercept is (0,-116)
When a number is increased by 2.8%, the result is 56. What is the original number to
the nearest tenth?
Answer:
The original number was 54.5.
Step-by-step explanation:
If a number is increased by 2.8%, then it is 102.8% of it's original number.
In mathematics, "of" in virtually all cases means "multiplied by".
Therefore, we do the opposite:
1. Convert to a decimal.
102.8% = 1.028
2. Divide by the decimal.
[tex]56 \div 1.028 = 54.47[/tex]
3. Round it to the nearest tenth.
54.47 rounds to 54.5.
To find the original number when increased by 2.8%, we set up and solve an equation. The original number to the nearest tenth is approximately 54.4.
Explanation:To find the original number, we can set up the equation:
x + 0.028x = 56
Simplifying gives:
1.028x = 56
Dividing both sides by 1.028 gives:
x = 56 / 1.028 ≈ 54.41
So, the original number to the nearest tenth is approximately 54.4.
Learn more about Original Number :https://brainly.com/question/24082954
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1. What is the shape of the distribution below?
(a) The distribution is symmetrical
(b) The distribution is not symmetrical
Answer: A
Step-by-step explanation: Because you have a dot in the middle and it is very equal
Answer: the distribution is symmetrical.
Step-by-step explanation:
What is the ratio for relative frequency?
Relative frequency = StartFraction row total Over column total EndFraction
Relative frequency = StartFraction row total Over total count EndFraction
Relative frequency = StartFraction total count Over subtotal count EndFraction
Relative frequency = StartFraction subtotal count Over total count EndFraction
Answer:
Relative frequency= subtotal count - total count
Step-by-step explanation:
Answer:
D.Relative frequency= subtotal count / total count
Can someone please help with this?
Answer:
8 square units
Step-by-step explanation:
Draw vertical and horizontal lines, dividing the triangle into 9 equally sized smaller triangles. 4 of the smaller triangles are shaded, so the area of the square is 4/9 the area of the triangle.
A = 4/9 (½ (6)(6))
A = 8
what are the coordinates of point A if it is rotated 90 degrees counterclockwise about the origin?
Answer:-5
Step-by-step explanation:
HELP PLEASE!
Jackson runs around a track in the evening for exercise. How far does Jackson run each evening if he runs 3 times around the track shown in the diagram below? Round your answer to the nearest whole yard.
1042 I just took the test I can't remember if that is the right number but it is the largest number
which of the following statements about rotations are true? select all that apply
suppose a circle with center (1,-3) passes through point (1,-1). Which equation represents the circle ?
Answer:-4
Step-by-step explanation:
Answer:
The answer is C) (x − 1)^2 + (y + 3)^2 = 4
Step-by-step explanation:
The radius is the distance between the center and the point on the circle.
Center: (1, −3); Point: (1, −1)
Distance formula: d = square root of {(x2 - x1)^2 + (y2 - y1)^2}
r = square root of {(1 − 1)^2 + (−1 + 3)^2 }
r = square root of {0 + 4 } = 2
(x − h)^2 + (y − k)^2 = r2 ----> (x − 1)^2 + (y + 3)^2 = 4
Hope this isn't confusing and helps. I also know its right because I just did this on USA Testprep.
The middle schools baseball team the badgers won 20 games last year this year they won 22 games what is the percentage increase of games one from this year to last year
Answer:
The correct answer is 10%.
Step-by-step explanation:
The middle school's baseball team the badgers won 20 games last year.
This year they won 22 games.
Increase in the number of wins = 22 - 20 = 2.
We need to find the percentage increase of games as compared to the last year. That is given by dividing the increase in wins divided by the wins last year multiplied by 100.
Percentage increase as compared to the last years is given by [tex]\frac{2}{20}[/tex] × 100 = 10%
There is an increase of 10% in the number of wins in this year as compared to the last year.
The temperature on Sunday was -4 degrees Fahrenheit (ºF). The temperature on Monday was 9 degrees warmer than the temperature on Sunday. Was the temperature, in degrees Fahrenheit, positive or negative on Monday?
It would be 5 degrees Fahrenheit. It is a positive number.