Given the function f(x) = 4^x - 1, explain and show how to find the average rate of change between x = 1 and x = 4.
Answer:
84
Step-by-step explanation:
f(1)=4^1 - 1 = 3
f(4) = 4^4 - 1 = 255
rate of change = [tex]\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
(255 - 3) / (4 - 1) = 252 / 3 = 84
ames has 268 cookies to put into bags. Each bag holds 8 cookies.
If James uses as many of the cookies as possible, how many bags can he make, and how many cookies are left over?
Enter your answers in the boxes.
Step-by-step explanation:
Total amount of cookies= 268
One bag can hold 8 cookies
268 / 8 = 33 (remainder 4)
He can make as many as 33 bags, and there are 4 cookies left over.
The product of two positive integer numbers is 40 and the sum of the same two numbers is 13.
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Answer:
5 and 8
Step-by-step explanation:
Factor pairs that make 40 are ...
40 = 1×40 = 2×20 = 4×10 = 5×8
The pair that has a sum of 13 is 5 and 8.
Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight-year life. What would be the present value of this loan if it carried a 10 percent interest rate?
Answer:
$919.98
Step-by-step explanation:
To solve using a financial calculator do
N=8
I/Y=10
PMT=85
FV=1000
CMPT PV get 919.98
To do by hand find the present value of the interst payments
85*(1-(1/1.1)^8)
which is 453.4687
Find the present value of the final ballon payment
1000*(1/1.1)^8
which is 466.507
take the sum
466.507+453.4678= 919.98
The City of Irvine upgraded a bicycle lane in a section of road to have a physical barrier between the cyclists as opposed to just a painted white line on the road. They now want to do a study to see if the bicycle lane upgrades have encouraged more people to utilize the bike lane. Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25. Test the hypothesis at the 0.05 significance level.
Answer:
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.
Step-by-step explanation:
Before the upgrade, on any given day, it was known that the section of road saw an average of 350 unique cyclists. Test if more people are using now.
At the null hypothesis, we test if the same number of people is still using, that is, the mean is 350. So
[tex]H_0: \mu = 350[/tex]
At the alternate hypothesis, we test if this mean increased, that is:
[tex]H_1: \mu > 350[/tex]
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.
350 is tested at the null hypothesis:
This means that [tex]\mu = 350[/tex]
After the upgrade, they took a random sample of 35 days in the year and counted the number of unique cyclists each day. The average was 405 cyclists with a standard deviation of 25.
This means that [tex]n = 35, X = 405, s = 25[/tex].
Test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{405 - 350}{\frac{25}{\sqrt{35}}}[/tex]
[tex]t = 13.02[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample mean above 405, which is a right-tailed test with t = 13.02 and 35 - 1 = 34 degrees of freedom.
Using a t-distribution calculator, this probability is of 0.
The p-value of the test is 0 < 0.05, which means that there is significant evidence to conclude that more people utilize the bike lane after the change.
A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1. If the distribution is approximately normal, find the probability that there will be fewer than 69 broken pretzels in a run.
Answer:
0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1.
This means that [tex]\mu = 73.5, \sigma = 5.1[/tex]
Find the probability that there will be fewer than 69 broken pretzels in a run.
This is the p-value of Z when X = 69.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{69 - 73.5}{5.1}[/tex]
[tex]Z = -0.88[/tex]
[tex]Z = -0.88[/tex] has a p-value of 0.1894
0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.
If f(x)=1−x^2 +x^3 , then f(−1)=
Answer:
f(-1) = -1
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 1 - x² + x³
f(-1) is x = -1 for the function f(x)
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-1) = 1 - (-1)² + (-1)³Exponents: f(-1) = 1 - 1 - 1Subtract: f(-1) = -1In a survey of 554 U.S. adults, it is found that 360 favor a ban on stem cell research. Set up the null and the alternative hypotheses to test whether there is sufficient evidence that over 61% favor a ban on stem cell research. If alpha is set to 3.0%, should the null hypothesis be rejected
Answer:
The null hypothesis will be rejected
Step-by-step explanation:
The null hypothesis is that people who favour ban on stem cell research is less than or equal to 0.61
The alternate hypothesis is that people who favour ban on stem cell research is greater than 0.61
Proportion of population = 0.61
Total events = 360
Sample size = 554
Sample proportion = 360/554 = 0.649
As per test statistics –
Z = (p-p0)/sqrt {(p0 (1-p0))/n} = (0.649 -0.61)/ {(0.61 (1-0.61))/554}
= 0.039/0.021
= 1.857
P (Z<1.857) = 1- P (Z<1.857) = 1-0.9664 = 0.0336
So alpha value is 0.064.
Thus, we will reject the null hypothesis
A local pizza shop has a membership program for frequent buyers. The membership costs $5 per month and members get a discounted price of $2 per slice of pizza. Aisha purchased a membership to this pizza shop. How much would Aisha have to pay the pizza shop if she bought 8 slices of pizza this month? What would be the monthly cost for
x slices of pizza?
Answer:
Aisha would pay 21 dollars for 8 slices.
Equation 2x(x=number of slices)+5
Step-by-step explanation:
Find five consecutive odd numbers where the sum of the first three numbers is 15 greater than the sum of the final two numbers.
Answer:
the consecutive numbers are: 23, 25, 27, 29, 31.
Step-by-step explanation:
23+25+27 is 75
29+31 is 60
75-60 is 15
Adam borrowed $16,780 at 12.5 percent for 10 years. What is his monthly payment?
A: $240.31
B: $245.83
C: $230.12
D: $229.81
ANSWER:
245.83
Step-by-step explanation:
16,780/100=167.8
167.8 x 1.465= 245.827
Using unitary method, Adam's monthly payment is 245.83 dollar.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Monthly payment with 12.5% interest rate for 10 years per 100 dollar is 1.465 dollar.
Monthly payment with 12.5% interest rate for 10 years per 1 dollar is 0.01465 dollar.
Monthly payment with 12.5% interest rate for 10 years per 16780 dollar is 1.465 * 16780 dollar = 245.83 dollar.
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Take a look at the photo and please right an explanation for your answer
The Ballantyne area has 200 people over the age of eighty-five living in it of these people, 56 of them have a dog, 24 of them have a cat, and 16 of them have both of a person
is chosen at random, find the probability that they have a cat, if it is known they have a dog.
a. 1/2
b.3/7
c.2/7
d.2/25
whats 7 times 8 divided by 2 i think the answer s 6 am i right or ring please tell me
Answer:
28Step-by-step explanation:
First,
7 times 8 = 7 × 8 = 56
Then,
The product divided by 2 = 56 ÷ 2 = 28
Hence,
The required answer is 28
i got yelled at for my grandma giving a coney dog at A and W and she got sick is there a way i can cut my dad out of his life
Answer:
this whole sentence confused me a lot
Step-by-step explanation:
yes there is, but it depends on how you want to do it
Answer:
I don't really get what you're implying can you please explain?
Step-by-step explanation:
haha this just really confused me :)
The sidewalk is 5 feet wide and the garden measures 20 feet across. Which measurement is closest to the area of the outer edge of the sidewalk?
A.
200 ft2
B.
400 ft2
C.
700 ft2
D.
1,000 ft2
Answer:
A (obviously)
Step-by-step explanation:
Info Given
Sidewalk is 5 ft. wideGarden is 20 ft. acrosssonya got 8 out of 10 questions right on a quiz.she got the same score on a quiz that had 20 questions. how many questions did sonya get right on the second quiz? how many questions did she get wrong on the second quiz?
MUST SHOW WORK
Answer:
Sonya got 16 questions correct.
Step-by-step explanation:
8/10=80%
80%×20=16
(To check)
16/20=80%
Jared has some birds and dogs in his backyard. He counts a total of 12 heads and 30 legs. How many birds and dogs are in Jared's garden?
Answer:
12, because both dogs and birds only have 12 heads
A pack of 4 chocolate bars costs £1.20
What is the price per unit?
what is it?
Answer:
0.30 you divided the total by the number of units which is 4
Answer:
£ 0.3
Step-by-step explanation:
Given that , a pack of 4 chocolates costs £1.20. We need to find cost of one chocolate .
We can simply use Unitary Method here ,as ,=> 4 chocolates costs £1.20 .
=> 1 chocolate will cost £1.20/4 = £ 0.3
Hence the cost of unit is £ 0.3hello if anyone would pls help
Answer:
x = 12
Step-by-step explanation:
It is a 90° angle which means that both of the angles need to add up to 90. 90-20 =70. 6×12 = 72.
6×9= 72
72-2 = 70
It adds up.
Hope this helps.
Which of the following ratios is not 2:5
A. 40:100
B. 10:20
C. 16:40
D. 6:15
Answer:
Step-by-step explanation:
Option B is the correct answer
10 : 20
In its simplest form
1 : 2
what is the estamate 1/4 of 16
Answer:
4
Step-by-step explanation:
1/4 of 16 is the same as 16 divided by 4. 16 divided by four is 4.
The high school is 3.6 inches from the middle school on a map. Each half inch on the map represents 0.4 mile. What is the actual distance between the two schools?
2.88 miles
4.5 miles
7.2 miles
9 miles
Answer:
2.88 miles
Step-by-step explanation:
because 3.6/.5 = 7.2
then 7.2 × .4 = 2.88
The sides of a square are all increased by 2 inches. The area of the NEW square is 49
inches squared. What is the length of a side of the original square?
A: 4.5 inches
B: 9 inches
C: 5 inches
D: 2 inches
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Answer:
C: 5 inches
Step-by-step explanation:
The length of the sides of the new square is the square root of the area:
s = √A = √49 = 7
The original square had sides 2 inches shorter, so they were ...
7 in -2 in = 5 in . . . . side length of original square
Plsss help. giving extra points if correct.
Degree and Radian Measures
Convert the given radian measure to a degree measure.
1.2 /pi (π)
a. -216°
b. 108°
c. 216°
d. -108°
Please select from the best choices provided
Answer:
C. 216°
Step-by-step explanation:
I calculated it logically
Consider point P(4, 2) and line l with equation −3x+4y=6 .
The equation of the line that passes through P and is parallel to l
Step-by-step explanation:
all working is above
hope that helps
part 1. Use side ratios to determine if the triangles in each pair of similar. If so complete the similarity statement. NO LINKS!!!
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Answer:
4) ΔEFG ~ ΔECD
6) Not Similar
Step-by-step explanation:
4) Shortest to longest sides are ...
EF : FG : GE = 14 : 16 : 20 = 7 : 8 : 10 (reduced)
EC : CD : DE = 7 : 8 : 10
The triangles have the same side length ratios, so are similar.
ΔEFT ~ ΔECD
__
6) Shortest to longest, the given sides have ratios ...
UT : TV = 71 : 84 (reduced)
GT : TH = 60 : 72 = 5 : 6 (reduced)
The side ratios are different, so the triangles are NOT SIMILAR.
Answer:
part 1. Use side ratios to determine if the triangles in each pair of similar. If so complete the similarity statement. NO LINKS!!!
Simplify.
4^3•4^-6
A. 1/4^3
B. 1/4^9
C. 1/4^18
D. 4^3
Answer:
A
Step-by-step explanation:
This can be rearranged as 4^3 * 1/(4^6)
or (4^3)/(4^6)
This can be changed to:
(4^3)/((4^3)*(4^3)
Which is equal to 1/(4^3)
or
4^(-3)
If f(x)= 1/x+2 and a>3, which of the following could be f(a)
A =1/2
B = 1/3
C = 1/4
D = 1/6
The equivalent value of the function is f ( a ) = ( 1/6 ) , when a > 3
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = 1 / ( x + 2 )
Now , the value of x > 3
So , the value of f ( x ) = f ( a )
And , when x > 3
f ( 4 ) = 1 / ( 4 + 2 )
f ( 4 ) = 1 / 6
Hence , the function is f ( 4 ) = 1 / 6
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