Answer:
Step-by-step explanation:
The question is incomplete. The complete question is:
Eagle Outfitters is a chain of stores specializing in outdoor apparel and camping gear. It is considering a promotion that involves mailing discount coupons to all its credit card customers. This promotion will be considered a success if more than 10% of those receiving the coupons use them. Before going national with the promotion, coupons were sent to a sample of 100 credit card customers. Out of the 100 customers, 13 customers said that they used the discount coupons to make a purchase at a Eagle Outfitters store. Use a 0.05 level of significance. (a) Develop the null and alternative hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national. (b) Compute the sample proportion. (c) Compute the test statistic. (d) Compute the critical value. (e) Based on the critical value, do we reject H0 or do we not reject H0? (f) Based on the result of the hypothesis test, should Eagle Outfitter go national with the promotion?
Solution:
a) We would set up the hypothesis test.
For the null hypothesis,
H0: p ≥ 0.1
For the alternative hypothesis,
Ha: p < 0.1
This is a left tailed test
Considering the population proportion, probability of success, p = 0.1
q = probability of failure = 1 - p
q = 1 - 0.1 = 0.9
b) Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 13
n = number of samples = 100
p = 13/100 = 0.13
c) We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.13 - 0.1)/√(0.1 × 0.9)/100 = 1
The calculated test statistic is 1 for the right tail and - 1 for the left tail.
d) Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.51/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
e) In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Since - 1 > - 1.96 and 1 < 1.96, we would fail to reject the null hypothesis.
Therefore, based on the result of the hypothesis test, the Eagle Outfitter should go national with the promotion
Consider the function y=f(x)=3x. The values of f(1/2) and f(1/4), rounded to the nearest hundredth, are_______ and__________ , respectively.
Answer:
f(1/2)=1.5
f(1/4)=0.75
Business Week conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume that the mean annual salary for male and female graduates 10 years after graduation is $168,000 and $117,000, respectively. Assume the standard deviation for the male graduates is $40,000 and for the female graduates it is $25,000. 1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why? 2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
Answer:
1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean
2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?
The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.
So
Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.
2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?
We have that:
[tex]\mu = 168000, \sigma = 40000, n = 100, s = \frac{40000}{\sqrt{100}} = 4000[/tex]
This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{164000 - 168000}{4000}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean
Simplify the following expression and then write down the coefficient of x²: x² + x² + x² + x²
Answer:
The expression is 4x² and coefficient is 4.
Step-by-step explanation:
All have the same variables, x², so you add up together :
[tex] 1{x}^{2} + 1{x}^{2} + 1{x}^{2} + 1{x}^{2} [/tex]
[tex] = 4 {x}^{2} [/tex]
What is the formula to find the area of a triangle
Answer:
A= 1/2bh
Step-by-step explanation:
(how its supposed to be said: Area= one half base times height)
:)
Answer:
(1) As a simple definition, a triangle is a two-dimensional figure that has 3 sides (and 3 angles as well).
(2) A triangle as shown in attached picture has the area that is typical calculated by the multiplication of half of base and height.
A = (1/2) x Base x Height
Base can be a particular side of triangle
Height is the perpendicular line segment between the opposite vertex of selected base and that base.
Hope this helps!
:)
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $400. If they offer a 2 year extended warranty for $27, what is the company's expected value of each warranty sold?
Answer:
The expected value of each warranty sold is $23.8.
Step-by-step explanation:
0.8% probability of the product failling.
If the product fails, the company will lose 400 - 27 = $373. So a net value of -373.
100 - 0.8 = 99.2% probability of the product not failling.
If the product does not fail, the company gains $27.
What is the company's expected value of each warranty sold?
We multiply each outcome by its probability.
0.008*(-373) + 0.992*27 = 23.8
The expected value of each warranty sold is $23.8.
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
Step-by-step explanation:
let s note a and b
x = ap+b
we can write two equations
(1) 300=3a+b
(2) 450=1.5a+b
multiply by 2 the (2) we got
900 =3a+2b
minus (1) it gives
900 - 300 = 3a+2b-3a-b = b
so b = 600
and from (1) it gives 3a = 300-600 = -300
so a = -100
then
x=-100p+600
thanks
Identify the domain of a radical function with an odd index.
Answer:When n is an odd number, [tex]\sqrt[n]{a}[/tex] is a real number for all values of a. Then, the domain is the real domain.
Which graph has the parent function 1/x?
Answer:
The graph of parent function [tex]f(x)=\frac{1}{x}[/tex] is a hyperbola.
Step-by-step explanation:
A rational function is described as the fraction of polynomials, where the denominator has degree of at least 1 .
Or it can be said that there must be a variable in the denominator.
The general form of a rational function is:
[tex]\text{Rational Function}= f(x)=\frac{p(x)}{q(x)}[/tex]
In this case the parent function provided is: [tex]f(x)=\frac{1}{x}[/tex].
The function is rational.
The graph of parent function [tex]f(x)=\frac{1}{x}[/tex] is a hyperbola.
The graph is attached below.
In the diagram below, AB is parallel to CD. What is the value of x?
А. 150
В. 60
С. 120
D. 30
Answer:
x=150 because these are supplementary angles
4. The average annual income of 100 randomly chosen residents of Santa Cruz is $30,755 with a standard deviation of $20,450. a) What is the standard deviation of the annual income? b) Test the hypothesis that the average annual income is $32,000 against the alternative that it is less than $32,000 at the 10% level. c) Test the hypothesis that the average annual income is equal to $33,000 against the alternative that it is not at the 5% level. d) What is the 95% confidence interval of the average annual income?
Answer:
a) The standard deviation of the annual income σₓ = 2045
b)
The calculated value Z = 0.608 < 1.645 at 10 % level of significance
Null hypothesis is accepted
The average annual income is greater than $32,000
c)
The calculated value Z = 1.0977 < 1.96 at 5 % level of significance
Null hypothesis is accepted
The average annual income is equal to $33,000
d)
95% of confidence intervals of the Average annual income
(26 ,746.8 ,34, 763.2)
Step-by-step explanation:
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation = $20,450
a)
The standard deviation of the annual income σₓ = [tex]\frac{S.D}{\sqrt{n} }[/tex]
= [tex]\frac{20,450}{\sqrt{100} }= 2045[/tex]
b)
Given mean of the Population μ = $32,000
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation ( σ)= $20,450
Null Hypothesis:- H₀: μ > $32,000
Alternative Hypothesis:H₁: μ < $32,000
Level of significance α = 0.10
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{30755-32000 }{\frac{20450}{\sqrt{100} } }[/tex]
Z= |-0.608| = 0.608
The calculated value Z = 0.608 < 1.645 at 10 % level of significance
Null hypothesis is accepted
The average annual income is greater than $32,000
c)
Given mean of the Population μ = $33,000
Given size of the sample 'n' =100
mean of the sample x⁻ = $30,755
The Standard deviation ( σ)= $20,450
Null Hypothesis:- H₀: μ = $33,000
Alternative Hypothesis:H₁: μ ≠ $33,000
Level of significance α = 0.05
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{30755-33000 }{\frac{20450}{\sqrt{100} } }[/tex]
Z = -1.0977
|Z|= |-1.0977| = 1.0977
The 95% of z -value = 1.96
The calculated value Z = 1.0977 < 1.96 at 5 % level of significance
Null hypothesis is accepted
The average annual income is equal to $33,000
d)
95% of confidence intervals is determined by
[tex](x^{-} - 1.96 \frac{S.D}{\sqrt{n} } , x^{-} + 1.96 \frac{S.D}{\sqrt{n} })[/tex]
[tex](30755 - 1.96 \frac{20450}{\sqrt{100} } , 30755 +1.96 \frac{20450}{\sqrt{100} })[/tex]
( 30 755 - 4008.2 , 30 755 +4008.2)
95% of confidence intervals of the Average annual income
(26 ,746.8 ,34, 763.2)
help pls take your time..
Answer:
As [tex]{x \to \infty}, \,\,{f(x) \to -\infty[/tex] and as [tex]{x \to -\infty}, \,\,{f(x) \to \infty[/tex]
Step-by-step explanation:
Please look at the plotted points in the attached image. There we see that as x grows toward infinity (to the right), the values for f(x) seem to become more negative (so f(x) seems to go towards minus infinity).
As we move towards the left with values of x (x going towards negative infinity, f(x) seems to become more and more positive (grow toward infinity)
Plastic knives are sold in packs of 15 for 32p. Plastic forks are sold in packs of 12 for 43p. Sam wants to buy the same number of forks as knives. What is the least amount of money Sam will be able to spend?
Step-by-step explanation:
Find the lowest common multiple of 15 and 12.
Which is 60.
15×4=60 so 32x4=£1.28
12x5=60 so 43x5=£2.15
2.15+1.28= £3.43
In a large population, 64% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal to 4 places.
Answer:
0.9940
Step-by-step explanation:
P(at least 1) = 1 − P(zero)
P(at least 1) = 1 − (1 − 0.64)⁵
P(at least 1) = 1 − (0.36)⁵
P(at least 1) = 0.9940
The probability that at least one of them has been vaccinated is 0.9939.
What is binomial distribution?
The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure. It helps to check the probability of getting “x” successes in “n” independent trials of a binomial experiment.
For the given situation,
Number of people vaccinated = 64% = 0.64
The formula of binomial distribution is
[tex]P(x:n,p) = nC_{x} p^x (1-p)^{n-x}[/tex]
Here x is the number of successes, x ≤ 1
n is the number of trials, n = 5
p is the probability of a success on a single trial, p = 0.64 and
where, [tex]nC_{x}=\frac{n!}{x!(n-x)!}[/tex]
The probability is [tex]P(X \leq 1)=1-P(X=0)[/tex]
[tex]P(X=0)= 5C_{0} (0.64)^{0} (1-0.64)^{5-0}[/tex]
⇒ [tex]P(X=0)= 1(1) (0.36)^{5}[/tex]
⇒ [tex]P(X=0)= 0.0060[/tex]
Thus, [tex]P(X \leq 1)=1-P(X=0)\\[/tex]
⇒ [tex]P(X \leq 1)=1-0.0060[/tex]
⇒ [tex]P(X \leq 1)=0.9939[/tex]
Hence we can conclude that the probability that at least one of them has been vaccinated is 0.9939.
Learn more about binomial distribution here
https://brainly.com/question/27939234
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Kristen wants to buy a Persian cat. She takes out a loan for $500 for one year. The bank charges
her an annual simple interest rate of 8%.
a. How much will she have to pay back at the end of the 1 year?
b. How much interest does she have to pay?
Answer:
a. How much will she have to pay back at the end of the 1 year?
Answer: $540
b. How much interest does she have to pay?
Answer: $40
Step-by-step explanation:
Simple interest for any amount p is given by
SI = p*r*t/100
where r is the annual rate rate of interest
t is the time
____________________________________________
Given
p= $500 (loan taken)
r = 8%
t = 1 year
SI = 500*8*1/100 = 40
Thus, $40 is the interest charged in a year.
Total money paid at the end of one year = loan taken + interest charged
= $500 + $40
= $540
a. How much will she have to pay back at the end of the 1 year?
Answer: $540
b. How much interest does she have to pay?
Answer: $40
How do you solve this?
Answer:
.75 teaspoons per ounce
Step-by-step explanation:
Take the number of teaspoons and divide by the number of ounces
10.5 / 14
.75 teaspoons per ounce
We have a bag containing 4 yellow, 5 green and 6 orange candies. We draw two candies without replacement.
Find the probability of getting both candies green
Answer:
9.52% probability of getting both candies green
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the candies are selected is not important. They are also selected without replacement. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Find the probability of getting both candies green
Desired outcomes:
2 green, from a set of 5. So
[tex]D = C_{5,2} = \frac{5!}{2!3!} = 10[/tex]
Total outcomes:
2 from a set of 4+5+6 = 15. So
[tex]T = C_{15,2} = \frac{15!}{2!13!} = 105[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{10}{105} = 0.0952[/tex]
9.52% probability of getting both candies green
3. Match each staternent with an expression that could be used to find the price
p+ 0.3p
0.7p
e. 85% more than the original time
f 15% less time than the original
g. 85% time decrease
h, 15% time increase
17p
p-07p
I
4. Ronnie increased the amount of money in his piggy bank by 25%. Which expres
find the amount of money in his bank? Let "m" represent the original
Answer:
3a) 30% more than original price
b) 70% of the original price
c) 17times the original price
d) 70% less than original price
e) t + 0.85t
f) t - 0.15t
g) t - 0.85t
h) t + 0.15t
4. The expression that can be used to find the amount of money in his bank = m + 0.25m
Question:
3. Match each statement with an expression that could be used to find the price.
'The expressions for a to d were not stated in the question'.
a) p+ 0.3p
b) 0.7p
c) 17p
d) p-07p
'From e to h, we were not told what to determine'.
Write the expression in terms of time
e. 85% more than the original time
f. 15% less time than the original
g. 85% time decrease
h. 15% time increase
4. Ronnie increased the amount of money in his piggy bank by 25%. Which expression can be used to find the amount of money in his bank? Let "m" represent the original.
Step-by-step explanation:
let original price = p
a) p+ 0.3p = p + 30% of p
30% more than original price
b) 0.7p = 70% of p
= 70% of the original price
c) 17p = 17 × p
= 17times of the original price
d) p-0.7p = p - 70% of p
= 70% less than original price
Let original time = t
e) 85% more than the original time = t + 85%of t
= t + 0.85t
f) 15% less time than the original time = t - 15% of t
= t - 0.15t
g) 85% time decrease = t - 85% of t
= t - 0.85t
h) 15% time increase = t + 15% of t
= t + 0.15t
4. Since "m" represent the original amount in Hus piggy bank
An increase of 25% = original amount + 25% of original amount
= m + 25% of m
'Of' means multiplication
= m + 0.25 ×m
= m + 0.25m
= 1.25m
The expression that can be used to find the amount of money in his bank = m + 0.25m
The graph shows the relationship between the number of hours that Michelle has been driving and the distance that she has left to travel to get to her destination. A graph on a coordinate plane titled Distance Remaining Over Time. The x-axis is labeled time (in hours), numbered 1 to 8, and the y-axis is labeled miles to destination, numbered 50 to 400. A straight line with a negative slope starts at point (0, 350) and ends at point (7, 0). Which statement is true? It took Michelle 6 hours to complete the trip. For each hour that Michelle drove, she traveled an additional 50 miles. In the first 6 hours, Michelle had traveled a total of 50 miles. In the first 3 hours, Michelle had traveled a total of 200 miles.
Answer:
For each hour that Michelle drove, she traveled an additional 50 miles.
Step-by-step explanation:
The point (0, 350) tells you Michelle's trip is 350 miles long. The point (7, 0) tells you she completed it in 7 hours. The point (6, 50) on the graph tells you she has 50 miles remaining of the original 350 after 6 hours.
True: for each hour Michelle drove, she traveled an additional 50 miles.
Answer:
B. For each hour that Michelle drove, she traveled an additional 50 miles.
Step-by-step explanation:
What’s the correct answer for this?
Answer:
C
Step-by-step explanation:
Measure of Arc FED = 51+79
= 130°
Since the measures of arcs and angles are the same
Hence
<FED = 130°
Suppose that the operations manager of a nose mask packaging delivery service is
contemplating the purchase of a new fleet of trucks. When
packages are efficiently stored in the trucks in preparation for delivery, two major constraints
have to be considered. The weight in pounds and volume in cubic feet for each item. Now
suppose that in a sample of 200 packages the average weight is 26.0 pounds with a standard
deviation of 3.9 pounds. In addition suppose that the average volume for each of these
packages is 8.8 cubic feet with standard deviation of 2.2 cubic feet. How can we compare the
variation of the weight and volume?
Answer:
Coefficient of variation (weight) = 15%
Coefficient of variation (volume) = 25%
Step-by-step explanation:
Let's begin by listing out the given information:
Population = 200, Average weight = 26 lb,
standard deviation (weight) = 3.9 lb,
Average volume = 8.8 ft³,
standard deviation (volume) = 2.2 ft³
Based on the data given, the manager will have to make a deduction by comparing the relative scatter of both variables due to the different units of measuring weight (pounds) and volume (cubic feet).
To compare the variation of the weight and volume, we use the coefficient of variation given by the formula:
Coefficient of Variation = (Standard deviation ÷ Mean) * 100%
⇒ [tex]C_{v}[/tex] = (σ ÷ μ) * 100%
For weight
σ = 3.9 lb, μ = 26 lb
[tex]C_{v}[/tex] (weight) = (3.9 ÷ 26.0) * 100% = 15%
[tex]C_{v}[/tex] (weight) = 15%
For volume
σ = 2.2 ft³, μ = 8.8 ft³
[tex]C_{v}[/tex] (volume) = (2.2 ÷ 8.8) * 100% = 25%
[tex]C_{v}[/tex] (volume) = 25%
∴ the relative variation of the volume of the package is greater than that of the weight of the package
What is 2/3 divided 1/6 ?
Answer: 4
Step-by-step explanation:
in order to divide one fraction by another, you must multiply by the reciprocal(the reverse of a certain fraction). the reciprocal of 1/6 is 6/1. so:
[tex]\frac{2}{3} / \frac{1}{6}[/tex] = multiply by the reciprocal of 1/6
[tex]\frac{2}{3} * \frac{6}{1}[/tex] = cross out
[tex]\frac{2}{1} * \frac{2}{1}[/tex] = multiply
[tex]\frac{4}{1}[/tex] = simplify
4
Answer:
4
Step-by-step explanation:
(2/3)/(1/6)
Eleminate the denominator by multiplying numerator and denominator with whatever is the reciprocal of the denominator. In this case the denominator is 1/6 so the reciprocal is 6/1 or "just" 6.
So, multiply numerator and denominator by 6. The next three (bold) steps, have been written down for explanatory purposes only, and normally are not nessasary.
(2/3)*6 / (1/6)*6
(2/3)*6 / (6/6)
(2/3)*6 / 1
(2/3)*6
12/3
4
Which of the following rational numbers is greater than 5/17 but less than 6/17.
Answer:
[tex]\frac{51}{170},\ \frac{52}{170},\frac{53}{170},...................\ \frac{59}{170}[/tex]
Step-by-step explanation:
As mention in the question number is
[tex]\frac{5}{17}\ < \frac{6}{17} \\multiply\ both\ side\ by\ 10\ in\ numerator\ and\ denominator\ we\ get \\\frac{50}{170} <\frac{60 }{170}\\[/tex]
Therefore the number is :
[tex]\frac{51}{170},\ \frac{52}{170},\frac{53}{170},...................\ \frac{59}{170}[/tex]
Select and place the symbol that will make the statement true |-a| |a|
Answer:
|-a|=|a|
Step-by-step explanation:
The lines beside the a's mean that you are trying to find the absolute value of what's inside. The absolute value of something is the distance it is from 0. You can't have a negative distance so anything inside of absolute value line are positive.
Therefor this is how we can solve this.
|-a| __ |a|
a __ a
a=a
What’s the correct answer for this question?
Answer:
68°
Step-by-step explanation:
Angle IJK is 112
Opposite angles of a quadrilateral inscribed in a circle add up to 180°
So
m<IHK = 180-112
m<IHK = 68°
Please help me with this question!!!
Answer:
3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))
Step-by-step explanation:
Using Euler's formula, this can be written as ...
x^2 = 9·e^(i5π/6)
Then the square roots are ...
x = (±√9)e^((i5π/6)/2) = ±3e^(i5π/12)
Of course, multiplying by -1 is the same as adding 180° to the angle.
The square roots are ...
3(cos(75°) +i·sin(75°)) and 3(cos(255°) +i·sin(255°))
8+8?
Pls help will mark you or whatever
Answer:
8+8=16
Step-by-step explanation:
Lets say you have 8 apples and your friend gives you 8 more apples. So, you count 9,10,11,12,13,14,15,16 which was 8 times.
Hope this helps.
A population of beetles are growing according to a linear growth model. The initial population (week 0) is
P0=6, and the population after 8 weeks is P8=86 Find an explicit formula for the beetle population after n weeks.
After how many weeks will the beetle population reach 236?
Answer:
The number of weeks it will take for the beetle population to reach 236 is 28.75.
Step-by-step explanation:
If a quantity starts at size P₀ and grows by d every time period, then the
quantity after n time periods can be determined using explicit form:
[tex]P_{n} = P_{0} + d \cdot n[/tex]
Here,
d = the common difference, i.e. the amount that the population changes each time n is increased by 1.
In this case it is provided that the original population of beetle was:
P₀ = 6; (week 0)
And the population after 8 weeks was,
P₈ = 86
Compute the value of d as follows:
[tex]P_{8} = P_{0} + d \cdot 8\\86=6+8d\\86-6=8d\\80=8d\\d=10[/tex]
Thus, the explicit formula for the beetle population after n weeks is:
[tex]P_{n}=P_{0}+8n[/tex]
Compute the number of weeks it will take for the beetle population to reach 236 as follows:
[tex]P_{n}=P_{0}+8n\\\\236=6+8n\\\\8n=236-6\\\\8n=230\\\\n=28.75[/tex]
Thus, the number of weeks it will take for the beetle population to reach 236 is 28.75.
Find the radius of a circle given that the area is three times its circumference
Answer:
Radius of the circle = 6 units
Step-by-step explanation:
Let the radius of the circle be r
According to the given condition:
Area of the circle = 3 times the circumference of the circle
[tex]\therefore \pi r^2 =3\times 2\pi r\\\therefore r^2 = \frac{3\times 2\pi r}{\pi}\\\therefore r^2 = 3\times 2r\\\therefore r = 6\: units\\[/tex]
The original price of a mountain bike was reduced by $125.
If p= the mountain bike's original price in dollars, which algebraic expression
represents the reduced price?
Answer:
p-125
Step-by-step explanation:
p represents the original price, which was reduced by 125. therefore, the reduced price is represented by the algebraic expression p-125
Answer: p - 125
Step-by-step explanation: Here, notice that the value that we don't know is the mountain bike's original price in dollars.
Since the original price of the mountain bike was reduced by $125,
we take away 125 from our variable, which is p.
So we have p - 125.
what is the answer to -9x = -27
Answer:
x = 3
Step-by-step explanation:
9x = 27
Divide both sides by 9,
x = 27/9 which on factorization of the numerator is written as
x = 9 x 3/9 = 3
Calculation 2: Exponent Or Index Method
9x = 27
Since 9 = 3² and 27 = 3³, the given equation takes the form
3² x = 3³
This gives
x = 3³ ÷ 3² = 3³¯² [using the formula a^m ÷ a^n = a^(m-n)]
= 3¹ = 3 (since the first power of a number is the number itself)
9 x 1 = 9
9 x 2 = 16
9 x 3 = 279 x 4 = 36
We stop here because we have already got the answer 27, the right-side of the equality, when 9 is multiplied by 3 . So,
x = 3
hope this helped!