Answers
Answer: x^2 (x+1) (4x-9)
Step-by-step explanation:
We can test the equation above x^2 (x+1) (4x-9) to see if it is true or not by rewriting it
x^2 ( 4x^2 -9x +4x -9)
x^2 (4x^2 - 5x -9)
4x^4 - 5x^3 - 9x^2
So x^2 (x+1) (4x-9) is the correct answer for this equation!
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Related Questions
how many four-digit numbers greater than $2999$ can be formed such that the product of the middle two digits exceeds $5$?
Answers
A total of 4970 four-digit numbers that are greater than 2999 can be created so that the middle two digits' product is greater than 5.
Combinations are mathematical operations that count the number of possible combinations for a set of elements when the order of the selection is irrelevant. One can choose the components of combinations in any order. Here, we have to find four-digit number combinations.
The digit in the thousands place should be greater than 2 so that the four-digit number be will greater than 2999. So the possible numbers are 3, 4, 5, 6, 7, 8, and 9. Therefore, this occurs in 7 ways.
The digit in the one's place can be any number from 0 to 9. Therefore, this occurs in 10 ways.
For the middle two digits, the combinations are given by,
If the hundreds digit is 1 then, the tens digit can be 6, 7, 8, and 9. This occurs in 4 ways.
If the hundreds digit is 2 and the tens digit can be from 3 to 9. This occurs in 7 ways.
If the hundreds digit is 3 and the tens digit can be from 2 to 9. This occurs in 8 ways.
If the hundreds digit is 4 and the tens digit can be from 2 to 9. This occurs in 8 ways.
If the hundreds digit is 5 and the tens digit can be from 2 to 9. This occurs in 8 ways.
If the hundreds digit is 6 and the tens digit can be from 1 to 9. This occurs in 9 ways.
If the hundreds digit is 7 and the tens digit can be from 1 to 9. This occurs in 9 ways.
If the hundreds digit is 8 and the tens digit can be from 1 to 9. This occurs in 9 ways.
If the hundreds digit is 9 and the tens digit can be from 1 to 9. This occurs in 9 ways.
The total ways for the middle two digits are 4+7+8+8+8+9+9+9+9=71 ways.
Therefore, the total number of four-digit numbers greater than 2999 is 7×10×71=4970.
The answer is 4970.
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During an electronic store's Sale Days, the regular price of CD Players is discounted $10. There is a state sales tax of 5%, and the $10 discount is applied before the sales tax is calculated.
A. Write an expression that shows the regular price r of a CD Player minus the $10 discount.
B. Write a rule for the function p(r) that expresses the final price p of a CD Player with the discount applied and sales tax included
C. How much would you pay during Sale Days for a CD Player regularly priced at $29.50?
Answers
Answer:
A) r - 10
B) p(r) = 1.05(r - 10)
C) $20.48 (nearest cent)
Step-by-step explanation:
Part AIf r is the regular price of a CD player, then an expression for the regular price minus the $10 discount is:
r - 10Part BIf a state tax of 5% is applied to a sale, then the cost of the item will be 105% of its regular price. 105% expressed as a decimal is 1.05.
Therefore, we need to multiply the expression from part A by 1.05 to find the final price of the CD player:
p(r) = 1.05(r - 10)Part CTo calculate how much would you pay during Sale Days for a CD Player regularly priced at $29.50, substitute r = 29.5 into the function from part B:
⇒ p(r) = 1.05(29.50 - 10)
⇒ p(r) = 1.05(19.50)
⇒ p(r) = 20.475
Therefore, you would pay $20.48 (rounded to the nearest cent) for a CD Player during Sale Days.
if the car has traveled 61.5 miles in 2 hours,how far will the car have traveled in 5 hours?
Answers
Answer:
in five hours you will travel 153.75 miles
Hello!
What does this problem want:
==> how far will the car have traveled in 5 hours
What we must find ==> how many miles does the car travel in an hour
[tex]\text{Rate}=\frac{61.5 \text{ miles}}{2 \text{ hours}} =30.75\text{ miles per hour}[/tex]
Therefore: the car will travel in 5 hours
5 * 30.75 = 153.75 miles
Hope that helps!
the graph shows a proportional relationship which equation maches the graph A. y=6x B. y= 1/2x C. y= 2x D. y=x
Answers
Answer:
A. y=6x
Step-by-step explanation:
A. y=6x that's all I know
Answer: A. y=6x
Step-by-step explanation:
linear regression analysis calculated a slope of -0.017 and a y intercept of 39.11. what would be the predicated depression score if the mhpg level was 1100?
Answers
As per the linear regression analysis, the predicated depression score if the MHPG level was 1100 is 20.41
Linear regression analysis:
In math , linear regression analysis means a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line.
Given,
linear regression analysis calculated a slope of -0.017 and a y intercept of 39.11.
Here we need to predict the depression score if the mhpg level was 1100.
We know the that standard form of the line of equation for straight line is written as,
y = mx + c
where m refers the slope and c refer the y intercept.
Then the line of the equation of this linear regression analysis is written as,
=> y = -0.017x + 39.11
In this equation x refers the MHPG level.
So, the value of x is 1100, then the predicated depression score is calculated as,
=> y = -0.017(1100) + 39.11
=> y = -18.7 + 39.11
=> y = 20.41
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chien visits the park every 5 days and goes to the library every 6 days if chien does both of these today how many days will pass before chien gets to do both on the same day again
Answers
Answer:
30
Step-by-step explanation:
For this problem she goes to the park every 5 days so, 5,10,15,20,25,30 and so on and she goes to the library every 6 days so, 6,12,18,24,30,36 and so on. 30 is the GCF of both so that is the answer
What does negative 4 over 7 > −2 indicate about the positions of negative 4 over 7 and −2 on the number line? (4 points) a is located on the right of −2, and −2 is located on the right of 0 b is located on the left of −2, and −2 is located on the right of 0 c is located to the right of −2 d is located on the left of −2
Answers
Answer: Negative 4 over 7 is located to the right of -2
In the number line, the numbers are written in ascending order or from left to right in increasing order,
That is if a < b, where a and b are any real number
⇒ b is located on the right side of an in the number line,
Here, given expression,
negative 4 over 7 > −2
That is,
⇒ Negative 4 over 7 is located to the right of -2
Step-by-step explanation:
A multiple regression model is to be constructed to predict the heart rate in beats per minute (bpm) of a person based upon their age, weight and height. Data has been collected on 30 randomly selected individuals: Heart Rate (bpm) Age (yrs) Weight (lb) Height (in) 77 54 178 63 69 39 138 58 108 57 227 68 88 48 154 64 59 58 154 57 84 59 180 73 62 30 232 71 119 54 242 65 65 38 169 61 62 27 182 66 56 34 208 58 60 31 243 62 81 42 213 74 108 56 205 69 56 56 124 71 89 59 213 65 68 28 209 72 57 23 188 62 107 55 212 59 95 50 221 61 55 48 154 60 110 49 196 61 110 33 250 64 62 29 109 63 90 33 201 74 73 51 121 70 88 55 159 63 59 49 103 66 69 36 214 68 57 34 102 65 a)Find the multiple regression equation using all three explanatory variables. Assume that x1 is age, x2 is weight and x3 is height. Give your answers to 3 decimal places. y^ = + age + weight + height b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis is or is not rejected? c)The explanatory variable that is most correlated with heart rate is: age weight height d)The explanatory variable that is least correlated with heart rate is: age weight height e)The value of R2 for this model, to 3 decimal places, is equal to f)The value of s for this model, to 3 decimal places, is equal to g)Construct a new multiple regression model by removing the variable height. Give your answers to 3 decimal places. The new regression model equation is: y^ = + age + weight h)In the new model compared to the previous one, the value of R2 (to 3 decimal places) is: increased decreased unchanged i)In the new model compared to the previous one, the value of s (to 3 decimal places) is: increased decreased unchanged
Answers
If the model's p-value is less than 0.05, we rule out the null hypothesis and declare it to be significant.
Using the R software.
R codes : d=read.table('data.csv',header=T,sep=',')
head(d)
attach(d)
fit=lm(Heart.Rate~Age+Weight+Height)
summary(fit)
fit2=lm(Heart.Rate~Age+Weight)
summary(fit2)
R outputs:
> d=read.table('data.csv',header=T,sep=',')
> head(d)
Heart Rate Age Weight Height
1 85 60 201 67
2 102 48 263 59
3 67 58 167 69
4 58 58 109 60
5 75 40 135 62
6 70 27 144 64
> attach(d)
> fit= lm(Heart.Rate~Age+Weight+Height)
> summary(fit)
Call:
lm(formula = Heart.Rate ~ Age + Weight + Height)
Residuals:
Min 1Q Median 3Q Max
-21.1662 -7.9919 0.3377 10.3521 25.4165
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.86211 36.23799 -0.079 0.9377
Age 0.45993 0.21595 2.130 0.0428 *
Weight 0.12192 0.04841 2.519 0.0183 *
Height 0.59428 0.50119 1.186 0.2464
Significant codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.15 on 26 degrees of freedom
Multiple R-squared: 0.2841, Adjusted R-squared: 0.2015
F-statistic: 3.439 on 3 and 26 DF, p-value: 0.03137
> fit2=lm(Heart.Rate~Age+Weight)
> summary(fit2)
Call:
lm(formula = Heart.Rate ~ Age + Weight)
Residuals:
Min 1Q Median 3Q Max
-26.126 -9.851 1.049 10.328 22.284
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 36.63974 14.36802 2.550 0.0168 *
Age 0.45122 0.21744 2.075 0.0476 *
Weight 0.12065 0.04876 2.474 0.0199 *
Significant codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 13.25 on 27 degrees of freedom
Multiple R-squared: 0.2454, Adjusted R-squared: 0.1895
F-statistic: 4.39 on 2 and 27 DF, p-value: 0.02235
a) Multiple linear regression equation :
y hat = -2.862 + 0.460 X1 + 0.122 x2 + 0.594 x3
b) F = 3.439 on 3 and 26 DF,
p-value: 0.03137
We reject the null hypothesis and determine that the model is significant because the p-value is less than 0.05.
c) Heart rate is highly linked with the variable whose p-value is less than that variable. Heart rate and fluctuating weight are strongly connected in this instance.
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On September 12, Jody Jansen went to Sunshine Bank to borrow $2,300 at 9% interest Jody plans to repay the loan on January 27. Assume the loan is on ordinary interest: (Use Days in a year table) a. What interest will Jody owe on January 27? (Do not round intermediate calculations. Round your answer to the nearest cent:) Interest 866.00 2 decimal places required. b. What is the total amount Jody must repay at maturity? (Do not round intermediate calculations Round your answer to the nearest cent:) Maturity value 3,166.00 2 decimal places required.
Answers
Jody will be forced to repay a total of $2,377.69 when the loan matures.
Ordinary interest, commonly referred to as simple interest, is computed by dividing the annual marginal rate by the 365 days that make up a year. It does not take compounding into account.
The number of days can be calculated as follows:
19(Sep), 31(Oct), 30(Nov), and 31(Dec) add up to 111 days in year 1.
Second-year days: 26 (Jan)
137 days in total
Rate = 0.09 Principal = $2,300
time = 137 ÷ 365
Interest = 2300 × 0.09 × (137 ÷ 365) = $77.69
Amount due at maturity is $2,300 plus $77.69, for a total of $2,377.69.
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To determine how American college students feel about commuting, 100 students at a private university were randomly chosen by selecting 50 men and 50 women to participate. They were asked how far they commute each day (in minutes) to campus.
The results of this survey are unreliable primarily because of
voluntary response bias
sampling bias
the absence of a control group
response bias
None of the above
Answers
The key reason why this investigation's findings are erroneous is sampling bias. In statistics, sampling bias refers to a bias during which a sample is constructed in a way that makes some members of the intended population less likely than others to be included.
A private university's 100 students, 50 men, and 50 women were randomly chosen to participate in a study on how American college students felt about commuting. They were questioned about their daily commuting distance (in minutes) to college. The key reason why this investigation's findings are erroneous is sampling bias.
When certain individuals of a population are consistently more likely to be chosen in a sample than others, this is known as sampling bias. In the medical sciences, it is also known as ascertainment bias. Because sampling bias jeopardizes external validity, particularly population validity, it restricts the generalizability of findings.
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if we wanted to compare the averages of each set of scores, what type of statistical test would you run and why?
Answers
A parametric test would be more suitable because it provides a more appropriate answer.
the term of a sequence is given. write the first four terms of the sequence. express the terms in simplified form when applicable.
Answers
The first four terms of the given sequence A(n)=4n^3+2 is 6, 34, 110, 258.
In the given question, the nth term of a sequence is given.
We have to write the first four terms of the sequence and we also have to express the terms in simplified form when applicable.
The given sequence is:
A(n)=4n^3+2
We find the four terms of the given sequence by putting n=1,2,3,4 in the given sequence.
Now putting n=1 in the given sequence
A(1)=4(1)^3+2
A(1)=4*1+2
A(1)=4+2
A(1)=6
Now putting n=2 in the given sequence
A(2)=4(2)^3+2
A(2)=4*8+2
A(2)=32+2
A(2)=34
Now putting n=1 in the given sequence
A(3)=4(3)^3+2
A(3)=4*27+2
A(3)=108+2
A(3)=110
Now putting n=1 in the given sequence
A(4)=4(4)^3+2
A(4)=4*64+2
A(4)=256+2
A(4)=258
Now the first four terms of the given sequence is 6, 34, 110, 258.
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The right question is:
The nth term of a sequence is given. Write the first four terms of the sequence. Express the terms in simplified form when applicable.
A(n)=4n^3+2
3 1/2 4. 2/5= ?
Please help me answer it please (you get 35 points
)
Answers
The Resulting values are
1. By adding
3 1/2 + 4 2/5= 79/10
2. Subtraction
3 1/2 - 4 2/5 = -9/10
3. By Multiplying
3 1/2 x 4 2/5 = 154/ 10
4. By Dividing
3 1/2 ÷ 4 2/5 = 35/44
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
3 1/2 4. 2/5
So, by adding
= 3 1/2 + 4 2/5
= 7/2 + 22/5
= 79/10
So, by Subtraction
= 3 1/2 - 4 2/5
= 7/2 - 22/5
= -9/10
So, by Multiplying
= 3 1/2 x 4 2/5
= 7/2 x 22/5
= 154/ 10
So, by Dividing
= 3 1/2 ÷ 4 2/5
= 7/2 ÷ 22/5
= 7/2 x 5/22
= 35/44
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Consider the exponential function f(x) = one-fifth(15x). What is the value of the growth factor of the function?one-fifthone-third515.
Answers
The value of the growth factor of the function is found as 15.
Explain the term exponential function?The formula for an exponential function is f (x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be greater than 0.A exponential function is one where the exponent contains the input, x.
Typically, an exponential function's equation looks like this:
y = abˣ
where,
The initial value, or a, is a number.The growth factor is an integer with the value b.In this issue
There are;
f(x) = 1/5.(15ˣ)
where,
1/5 -------> is the starting point.
15 --------> the growth factor.
Thus, the value of the growth factor of the function is found as 15.
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Answer:
D) 15 is the answer
Step-by-step explanation:
Jeffrey ate x ounces of M&M's. Priya ate 1/3 less than that. Which diagram matches that situation?
Answers
Jeffrey ate x ounces of M&M's. Priya ate 1/3 less than that. Which diagram matches that situation?
Option C
subtract $a-4$ from $4a 16$ and simplify your answer. the variable $a$ should appear only once in your answer.
Answers
The answer is (3a + 20) and also here variable ' a ' appears only once.
A linear expression is an algebraic expression in which each term is a constant or a variable raised to the first power. To put it another way, none of the exponents can be greater than 1.
[tex]x^2[/tex] is a variable raised to the second power, whereas x is a variable raised to the first power.
A linear expression is 2x - y + 3.
A constant is represented by the number, example 5.
Given,
expression (a - 4) and (4a + 16)
subtracting (a - 4) from (4a + 16), results in
= (4a + 16) - (a - 4)
= 4a + 16 - a + 4
=3a+20
Thus, the answer is (3a + 20), and variable 'a' appears only once.
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W varies jointly as x and y and inversely as the square of z. If w = 280 when x = 30, y = 12, and z = 3, find w when x = 20, y = 10 and z = 2. 117 350 69.
Answers
Using the inversely proportional method, we know that w=350.
What do we mean by inversely proportional?If two quantities are inversely related, one will increase while the other will decrease.
Building a wall would be an example of an inverse proportion in action.
The time it takes to construct a wall decreases as more people work on it.
So, the following is an expression for the joint variation of W with x, y, and z:
W = kxy / z²
Where k is the variational constant.
When the variables are given the initial set of values:
280 = k(30)(12) / 3²
K in the equation has a value of 7.
By adding the values of the subsequent:
w = (7)(20)(10) / 2² = 350
Therefore, using the inversely proportional method, we know that w=350.
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Answer:
350
Step-by-step explanation:
odyssey
If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
10,000n(x/100)
The reasoning is from the following:The formula for simple rate of interest is F = P(1+rt) whereF = future valueP = present valuer = ratet = time
Answers
If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)
What do you understand by the term simple interest?Simple interest is a quick and straightforward technique to compute interest on money. In the simple interest method, interest always applies to the initial principle amount, with the same rate of interest for each time cycle. When we put our money in a bank, we receive x percent simple annual interest on it. Banks charge many kinds of interest, one of which is simple interest. Now, before delving further into the idea of simple interest, let's first define what a loan is.
A loan is an amount borrowed by a person from a bank or other financial institution to meet their requirements. Home loans, auto loans, student loans, and consumer lending were just few examples of loans.
How to solve?
F = P(1+rt), where Future value is F, Present value is P, Rate is R, Time is t
F = 10,000(1+xn)
F = 10,000(xn)
F = 10,000(n * x/100)
F = 10,000n(x/100)
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If k is the midpoint of jl, jk=8x 11 and kl=14x-1, find jl
Answers
The value of the line segment jl is found as the 27 units.
Explain the term midpoint of the line segment?The center of a line segment is known as the midpoint. It represents the centroid of a segment and of its ends, and it is equally distant from both of them.The midpoint is really a point that lies on a line connecting two other locations and sits in the middle of it. The midpoint is the point on the middle position that is equally distant first from two points if a lines is drawn connecting the two points.For the given question.
jk = 8x + 11
kl = 14x - 1
K is the mid point of the line segment JL.
Thus,
jk = kl
Put the values-
8x + 11 = 14x - 1
14x - 8x = 11 + 1
6x = 12
x = 2
Thus, jl = 8x + 11
jl = 8(2) + 11
jl = 27
Thus, the value of the line segment jl is found as the 27 units.
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8(-2)^3 + (5) x 4^1
can you explain this is steps?
Answers
Answer: I did my best
Step-by-step explanation:
8(−2)3+5x41
Simplifies to:
5x4−64
=5x4−64
cassie pulled the boat onto the ice and adjusted its sails. once she got started she would be able to steer, change direction and control her speed with a few twists of the ropes. giving the boat a mighty heave across the ice, cassie jumped in.
Answers
Wind Energy is the kind of energy will Cassie uses to power the boat cassie jumped in.
What is wind energy?
The method of producing electricity using air or wind currents that naturally occur in the earth's atmosphere is known as wind energy (or wind power). Electricity is produced by modern wind turbines that harness the kinetic energy of the wind. Wind passing across the turbine's blades is the initial step.
What is the major problem with wind energy?
Wind energy has the potential to have negative environmental effects, including the possibility of reducing, fragmenting, or deteriorating habitat for wildlife, fish, and plants, as with all energy supply choices. Furthermore, flying animals like birds and bats may be harmed by turbine blades in operation.
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a kayack guide took two hours to paddle 20 miles downstream with the current and four hours to paddle 16 miles upstream against the current. find the speed of the current and the average paddling speed
Answers
The speed of current and average speed of paddling is 3 and 7 respectively.
Let p represents paddling speed of kayack guide and c represents speed of current.
If paddling downstream, the total speed is p + c because you’re paddling with the current. Similarly, if paddling upstream, the total speed is p - c because you would be paddling against the current.
Since paddling downstream took 2 hours so distance covered 2*(p + c)
which is equal to 20 miles.
2*(p + c) =20.
p + c = 10. -----i
Paddling upstream took 4 hours so distance covered 4*(p-c).
which is equal to 16 miles.
4*(p-c) = 16.
p - c = 4. -------ii
adding both equation c will be cancelled. 2*p=14 p =7.
put value of p in equation i.
7 + c = 10 ,c = 3.
So the speed of current and average speed of paddling is 3 and 7 respectively.
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The number of miles a motorcycle, x, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. With one gallon of gasoline in the motorcycle, find the probability that mike can travel more than 50 miles without refueling. Round your answer to four decimal places.
Answers
The probability of bike can travel more than 50 miles without refueling is 0.1151, according to the question.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
According to data in the given question,
We have the given information:
Mean = 44
deviation = 5
Let X be the random variable that represents the population's average number of motorcycle kilometers; in this instance, we know the distribution for X is provided by:
X ~ N(44.5)
Where μ=44 and σ=5,
We are interested on this probability,
P(X>50)
We can also apply the z score formula from:
z=x-μ/σ
Using this formula, we obtained:
P(X>50) = P(X-μ/σ > 50-μ/σ) = P(Z > 50-44/5) = P(z > 1.2)
Using the normal standard distribution and the complement rule, we can determine this probability, giving us:
P (z > 1.2) = 1 - P(z > 1.2) = 1 - 0.8849 = 0.1151
Therefore, the probability is 0.1151.
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Kobe is twice as old as Lebron. The sum of their ages is 48. How old are each of them?
Answers
Answer:
37 is LeBron 41 years old is kobe
Suppose the original quantity is and the new quantity is . Estimate the percent change. Is this an example of a percent increase or a percent decrease?
Answers
There is percent decrease is 12%.
What is Percent decrease?The difference between starting and ending values is the percentage decrease. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decrease.
Given:
original quantity is 100
new quantity is 88
So, change in quantity = 100-88= 12
and, percent decrease = 12 / 100 x 100 = 12%
Hence, there is percent decrease is 12%.
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How to show you work on 48 inches to Convert it to feet?
Answers
Answer:
Step-by-step explanation
How many feet in a centimeter. One centimeter is equal to 0.0328084 feet: 1cm = 1cm / 30.48cm/ft = 0.0328084ft.
How many centimeters in a foot. One foot is equal to 30.48 centimeters: 1ft = 30.48×1ft = 30.48cm.
How to convert 10cm to feet. Divide 10 centimeters by 30.48 to get feet:
Answer: 4 feet
Step-by-step explanation: 12 inches = 1 foot
48in/12 = 4
please help me with this. Ahhh sooon
Answers
Answer:
9x + 16
Step-by-step explanation:
When you are finding the perimeter of each shape, you are essentially combining all of the shape's side measurements together.
In this case, you are given a triangle, which has 3 sides. Add the 3 side's measurements together to obtain the perimeter of the given triangle.
P (Perimeter of triangle) = (3x + 10) + (3x) + (3x + 6)
Combine like terms. Like terms are terms that have the same variables:
P = (3x + 3x + 3x) + (10 + 6)
P = (9x) + (16)
P = 9x + 16
9x + 16 is your answer.
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A track and field team was calculating their long jump scores. The long jump teamates add up their scores to determine the best team. The current winning team has a combined score of 25.6 m. Alaina's teamates jumped the following jumps: 5.46m,4.84, 4.92 and 5.98m. What score would Alaina have to get to tie the Winning teams score? Show your work.
Answers
The score that Alaina will have to get to tie the Winning teams score is 4.4.
How to calculate the score?Given that the long jump teamates add up their scores to determine the best team. The current winning team has a combined score of 25.6 m.
Also, Alaina's teamates jumped the following jumps: 5.46m,4.84, 4.92 and 5.98m.
Therefore, Alaina's score to beat the other team will be:
= 25.6 - (5.46m + 4.84 + 4.92 + 5.98m)
= 25.6 - 21.2
= 4.4
Therefore, she must get 4.4 to tie.
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Phil takes out a bank loan of $150 000 to buy a house, at an annual interest rate of 3.5%. The interest is calculated at the end of each year and added to the amount outstanding. Find the amount Phil would owe the bank after 20 years. Give your answer to the nearest dollar.
Answers
Phil's final debt after 20 years will be around $320,679.
How is debt calculated?To purchase a home, Phil borrowed $150,000 from a bank at a 3.5% annual interest rate.
The annual compounding of interest causes the amount of interest for each year to rise in proportion to the debt. Phil will be required to pay the initial sum plus interest after the first year, which comes to
$150,000 + 3.5% of $150,000 = $155,250.
Since interest is charged on the new amount owed for the second year, Phil will owe
$155,250 + 3.5% of $155,250, which
= $160,551.75.
For the next 20 years, this procedure is repeated, with the amount owed rising yearly by the sum of the year before plus interest. Phil's debt after 20 years will be around $320,679.
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in a study of a disease in which all cases that developed were ascertained, if the relative risk for the association between a factor and the disease is equal to or less than 1.0, then:
Answers
For the given statement , correct answer is option e: there is either no association or a negative association between the factor and the disease.
Reason with explanation:
Relative risk is a ratio which help us to compares the risk of a health between two groups. When the value of relative risk is 1, it represents the risk among the two groups is same. When the value of relative risk is > 1, it represents the risk is increased for the exposed group. And when relative risk < 1, it represents exposure protect against the disease. Hence for the given statement , a value of relative risk is equal or less than represents there is no association or negative association between a factor or a disease.The complete question is:
In a study of a disease in which all cases that developed were ascertained, if the relative risk for the association between a factor and the disease is equal to or less than 1.0, then:
a. There is no association between the factor and the disease
b. The factor protects against development of the disease
c. Either matching or randomization has been unsuccessful
d. The comparison group used was unsuitable, and a valid comparison is not possible
e. There is either no association or a negative association between the factor and the disease
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