It takes 5 years for the population to decrease to 46785 from the current population of 48500 of a small city whose population is decreasing by an average of 325 people per year.
What is the equation for the given statement?It is given that,
Current population = 48500 people
Rate of decrease = 325 per year
Number of years = x
decreased population after x years = 46785
Then, the equation is
46785 = 48500 - 325x
Calculation:On simplifying the obtained equation, we get
46785 = 48500 - 325x
⇒ 325x = 48500 - 46785 = 1625
⇒ x = 1625/325 = 5 years
So, the people become 46785 after 5 years.
Learn more about writing an equation from words here:
https://brainly.com/question/25678139
#SPJ1
FILL IN THE BLANKS, (14 questions)
MATH MODELS
PLSSS HELP
Measures of median are the values located at the middle of the data set
What is meant by median ?The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.
The middle number is obtained by sorting all the data points and choosing the center one, or the middle two numbers, if there are two of them.
We use graph to interpret dot plots
A line graph shows ordered pair plotted on the coordinate plane. The ordered pairs are connected with line segment
A bar graph uses to central tendency represent data
A graph divided into wedges called sectors
A sample of population is a subset of the histogram
A population is a complete set of all possible observation.
The mode i the most often repeated item in a data set.
The number of population in each interval is called frequency.
A mean uses ranges instead of individual numbers to represent data.
To learn more about median refer to :
https://brainly.com/question/26151333
#SPJ1
Label a ray with endpoint Y. Determine an appropriate name for a ray whose endpoint is Y. Choose the correct ray whose endpoint is Y. A. Y X B. X Y C. X Y D. Y x Choose an appropriate name for a ray whose endpoint is Y. A. XY B. XY C. YX
Label a ray with endpoint Y. An appropriate name for a ray whose endpoint is XY displays a ray with the endpoint Y.
A line with a single defined endpoint that continuously moves away from another is known as a ray (endpoint B in this case).
A segment of a line that lacks an endpoint but has a specified starting point. It can go on forever in a single direction. A ray cannot be measured since it has no end point.
In mathematics, a ray is a segment of a line with a definite starting point but no ending. It can go on forever in a single direction. A ray cannot be measured since it has no end point. Two rays with the same terminal are united to form an angle. The vertex of the angle is referred to as the common endpoint of the rays, while the sides of the angle are referred to as the rays themselves.
The ray in the hypothetical situation has one endpoint B and an endlessly extending endpoint A. (as shown by the arrowhead).
To read more about rays, visit: https://brainly.com/question/29134002
#SPJ4
Consider f(x) Equals StartFraction 8 (x minus 1) Over x squared + 2 x minus 3 EndFraction.
Which statements describe the existence of vertical asymptotes at x = –3 and x = 1?
At x = negative 3, limit of f (x) as x approaches negative 3 minus = negative infinity and limit of f (x) as x approaches negative 3 plus = infinity, so there is a vertical asymptote. At x = 1, limit of f (x) as x approaches 1 minus = 2 and limit of f (x) as x approaches 1 plus = 2, so there is no vertical asymptote.
At x = negative 3, limit of f (x) as x approaches negative 3 minus = infinity and limit of f (x) as x approaches negative 3 plus = negative infinity, so there is a vertical asymptote. At x = 1, limit of f (x) as x approaches 1 minus = 2 and limit of f (x) as x approaches 1 plus = 2, so there is no vertical asymptote.
At x = negative 3, limit of f (x) as x approaches negative 3 minus = negative infinity and limit of f (x) as x approaches negative 3 plus = infinity, so there is a vertical asymptote. At x = 1, limit of f (x) as x approaches 1 minus = infinity and limit of f (x) as x approaches 1 plus = infinity, so there is no vertical asymptote.
At x = negative 3, limit of f (x) as x approaches negative 3 minus = infinity and limit of f (x) as x approaches negative 3 plus = negative infinity, so there is a vertical asymptote. At x = 1, limit of f (x) as x approaches 1 minus = infinity and limit of f (x) as x approaches 1 plus = infinity, so there is no vertical asymptote.
The correct option that describes the vertical asymptote is; A: At x = negative 3, limit of f (x) as x approaches negative 3 minus = negative infinity and limit of f (x) as x approaches negative 3 plus = infinity, so there is a vertical asymptote
How to find the vertical asymptote of a function?A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;
In a graph, these vertical asymptotes are given by dashed vertical lines.
An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.
We are given the function;
f(x) = 8(x - 1)/(x² + 2x - 3)
Simplifying the denominator gives;
(x² + 2x - 3) = (x + 3)(x - 1)
Thus, our function is;
f(x) = 8(x - 1)/[(x + 3)(x - 1)]
(x - 1) will cancel out to give;
f(x) = 8/(x + 3)
Vertical asymptote:
Point in which the denominator is 0, so:
(x + 3) = 0
x = -3
Thus, we conclude that x = -3 is the vertical asymptote
Read more about Vertical Asymptote at; https://brainly.com/question/4138300
#SPJ1
Over 2 years, how much more does $2000 in a savings account with an APR of 5.2% compounded quarterly earn in interest than the same amount in a savings account with an APR of 4.8% compounded monthly?
A savings account with just an APR of 5.2% compounded quarterly on a balance of $2,000 will yield $16.61 more interest than a similar account with just an APR of 4.8% compounded monthly on the same balance.
Explain the term compounded monthly?Compound monthly refers to a loan's interest rate, which is charged in installments each month and added to the principle.Assume we had two different sorts of savings accounts, each with a deposit of $2,000 in it.
Account A's quarterly interest rate is 5.2%.Account B has a monthly interest rate of 4.8%.We must now determine the earnings for both accounts.
The following formula will be used to determine the earning:
Here,
v = total income,Interest rate = r (in decimal form).p is the first main value.T is the number of years overall.n is the number of compounding years.Put the values for Account A now.
5.2 % in decimal form = 5.2/100= 0.052
v = 2000 x ( 1 + (0.052/4) )^(4*2)
v = 2217.71
Total earning for account A = $ 2217.71.
For Account B:
4.8 % in decimal form = 4.8/100= 0.048
v = 2000*( 1 + (0.048/12) )^(12*2)
v = 2201.10
Total earning for account A = $ 2201.10
We will now deduct B's earnings from A's earnings to see how much more A earned than B.
2217.71 - 2201.10 = $16.61
Consequently, account A made $16.61 more so than account B.
To know more about the compounded monthly, here
https://brainly.com/question/28020457
#SPJ1
If a solution calls for 1/4 cup vinegar mixed with 2 cups water , how many cups of vinegar goes into 27 total cups of solution?
A total of 3 cups of vinegar goes into 27 total cups
How to detemine the number of cups of vinegarFrom the question, we have the following parameters that can be used in our computation:
1/4 cups of vinegar
2 cups of water
So, we have
Water : Vinegar = 2 : 1/4
Rewrite as
Water : Vinegar = 8 : 1
Multiply by 3
Water : Vinegar = 24 : 3
The sum of 24 and 3 is 27
So, we have
Vinegar = 3
Hence, the number of cups of vinegar is 3
Read more about ratio at
https://brainly.com/question/1781657
#SPJ1
Write a function in any form that would match the graph shown below.
Please help !!! need asapp
if blurry zoom in
A function in the form that would match the graph that is given is
y(x)=(6/5)(x-1)²(x-5)².
What is meant by function?An example of a rule is a function, which creates one output from one input. Alex Federspiel is the photographer. y=x² serves as an illustration of this. There is just one output for y if you enter anything for x. Considering that x is the input value, we can infer that y is a function of x. a formula, rule, or piece of legislation that specifies the relationship between the independent and dependent variables (the dependent variable). The link between two independent variables and one dependent variable is described by a mathematical expression, rule, or law (the dependent variable).
From the graph, the curve turns at the points
x=1 and x=5
The equation becomes,
y(x)=a(x-1)²(x-5)²
The above curve passes through (0, 30)
y(0)=a(1-0)²(0-5)²=30
a(-1)²(-5)²=30
a=30/25
a=6/5
y(x)=(6/5)(x-1)²(x-5)²
A function in the form that would match the graph that is given is
y(x)=(6/5)(x-1)²(x-5)².
To know more function, visit:
https://brainly.com/question/28278699
#SPJ1
nine eighteenths plus one third
Answer: 15 / 18
Step-by-step explanation:
9 / 18 + 1/3
1/3 = 6 / 18
9 / 18 + 6/ 18
15 / 18
Answer:
5/6.
Step-by-step explanation:
Step 1: Rewrite 9/18
9/18 = 1/2
Step 2: Rewrite problem
1/2 + 1/3
Step 3: Find (Greatest common denominator)
6
Step 4: Rewrite fractions
3/6 + 2/6
Step 5: Add
5/6
Review 2 HW Jack and Jill compare their monthly text plans. Jack's plan cost $9.00 plus $0.30 per text. Jills plan cost $0.60 per text. The equations below show the cost, c for each plan depending on how many texts, t, are sent Jack's Plan: c = 0.30t+9 Jills's Plan: c = 0.60t In one month, Jack and Jill paid the same amout. Enter the number of text messages the each sent.
Jack's plan: c=0.30t+9
Jill's plan: c=0.60t
I one month, Jack and Jill paid the same amount. enter the number of text messages they each sent
Answer: To solve this problem, we need to set the two equations equal to each other and solve for the number of text messages that were sent by each person. We know that the cost of Jack's plan is c = 0.30t + 9 and the cost of Jill's plan is c = 0.60t. To find the number of text messages they each sent, we can set these two equations equal to each other and solve for t:
0.30t + 9 = 0.60t
0.30t = 0.60t - 9
0.30t = 0.60t - 9
-0.30t = -9
t = 30
Therefore, if Jack and Jill paid the same amount for their text plans, they each sent 30 text messages.
What is the 3rd term of (4 - 5g)??
0896000g²
O 21g²
O-1050000g5
O 537600g2
The 3rd term of (4 - 5g) is -1050000g5
What does the term "arithmetic sequence" mean?An arithmetic sequence is a set of integers that are ordered and have a common difference between each following word. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.
It is simple to establish a series by starting with a number and repeatedly adding a fixed constant (d). An arithmetic sequence is this kind of sequence.
Given,
(4 - 5g) simplifying
-1
So that is -1050000g5
The 3rd term of (4 - 5g) is -1050000g5
To learn more about arithmetic sequence refer to :
https://brainly.com/question/28369191
#SPJ1
HELP 25 POINTS 8 GRADE
Step-by-step explanation:
To find Δy and Δx (change in y and change in x), you need to do y2-y1 and x2-x1.
Example on how to solve problem 1:
change in y: Pick 2 numbers from the y side of the table that are next to each other (it doesn't matter which 2 ). You're going to subtract the first one one the list that you picked from the second one from the list that you picked. example: 4-1= 3
change in x: repeat the same process with the x side of the table (make sure that you pick x points that go with the y, otherwise it won't work). If you picked 4-1 on the y table, the you have to pick 0- -3, which equals 3 (due to two negatives making a positive).
now, you divide your change in y by your change in x. example: 3÷3 = 1. This means that your m (slope) = 1 (on the first problem)
This kinda sounds confusing but hope this helps a bit. If not, you can look up lots of tutorials online with better explanations :)
For a sample of 20 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). A portion of the regression results is as follows. Use Table 2 and Table 4.
ANOVA df SS MS F Significance F
Regression 2 188,246.8 94,123.4 9.04E-07
Residual 17 45,457.32 2,673.96 Total 19 233,704.1 Coefficients Standard Error t Stat p-value Lower 95% Upper 95%
Intercept −301.62 549.7135 −0.5487 0.5903 −1,461.52 858.28
Poverty 53.1597 14.2198 3.7384 0.0016 23.16 83.16
Income 4.9472 8.2566 0.5992 0.5569 −12.47 22.37
a. Specify the sample regression equation. (Negative values should be indicated by a minus sign. Round your answers to 4 decimal places.)
11formula272.mml = + Poverty + Income
b-1. Choose the appropriate hypotheses to test whether the poverty rate and the crime rate are linearly related.
H0: β1 ≥ 0; HA: β1 < 0
H0: β1 ≤ 0; HA: β1 > 0
H0: β1 = 0; HA: β1 ≠ 0
b-2. At the 5% significance level, what is the conclusion to the test?
Reject H0; the poverty rate and the crime rate are linearly related.
Reject H0; the poverty rate and the crime rate are not linearly related.
Do not reject H0; we can conclude the poverty rate and the crime rate are linearly related.
Do not reject H0; we cannot conclude the poverty rate and the crime rate are linearly related.
c-1. Construct a 95% confidence interval for the slope coefficient of income. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
Confidence interval to
c-2. Using the confidence interval, determine whether income influences the crime rate at the 5% significance level.
Income is significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
Income is not significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
Income is significant in explaining the crime rate, since its slope coefficient significantly differs from zero.
Income is not significant in explaining the crime rate, since its slope coefficient does not significantly differ from zero.
d-1. Choose the appropriate hypotheses to determine whether the poverty rate and income are jointly significant in explaining the crime rate.
H0: β1 = β2 = 0; HA: At least one β j < 0
H0: β1 = β2 = 0; HA: At least one β j > 0
H0: β1 = β2 = 0; HA: At least one β j ≠ 0
d-2. At the 5% significance level, are the poverty rate and income jointly significant in explaining the crime rate?
Yes, since the null hypothesis is rejected.
Yes, since the null hypothesis is not rejected.
No, since the null hypothesis is rejected.
No, since the null hypothesis is not rejected.
Answer: You must give more points for questions that are this long
sincerely,
A Friend
Step-by-step explanation:
e the problem.
1) Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The
teacher wants to give A's to the top 10% of students, B's to the next 25%, and C's to the next 42%. What is the
bottom cutoff for a C grade? Round your answer to the nearest whole number..
A) 68
B) 63
C) 77
D) 65
z = -1.34 < (a - 70)/9
And if we solve for we got
a = 70 - 1.34 * 9 = 57.95 = 98
So, the value of height that separates the bottom 9% of data from the top 91% is 58.
And the answer for this case would be:
a) 58
What is the Normal distribution and Z-score?
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The solution to the problem
Let X be the random variable that represents the scores of a population, and for this case we know the distribution for X is given by:
X ~ N (70, 9)
Where μ = 70, and σ = 9
For this case, the figure attached illustrates the situation for this case.
We know from the figure that the lower limit for D accumulates 9% or 0.09 of the area below and 0.91 or 91% of the area above.
we want to find a value a, such that we satisfy this condition:
P(X > a) = 0.91 (a)
P(X < a) = 0.09 (b)
Both conditions are equivalent in this case. We can use the z score again in order to find the value a.
As we can see in the figure attached the z value that satisfies the condition with 0.09 of the area on the left and 0.91 of the area on the right it's z=-1.34. On this case P(Z<-1.34)=0.09 and P(z>-1.34)=0.91
If we use condition (b) from the previous we have this:
P(X < a) = P(X - μ)/σ < (a - μ)/σ) = 0.09
P(z < (a - μ)/σ) = 0.09
But we know which value of z satisfies the previous equation so then we can do this:
z = -1.34 < (a - 70)/9
And if we solve for we got
a = 70 - 1.34 * 9 = 57.95 = 98
Hence, the value of height that separates the bottom 9% of data from the top 91% is 58.
And the answer for this case would be:
a) 58
To learn more about the Normal distribution and Z-score visit,
https://brainly.com/question/14812280
#SPJ1
A. A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches.
If 25 items are chosen at random, what is the probability that their mean length is less than 17.4 inches?
Round to 4 decimal places
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.1 years, and standard deviation of 1.9 years.
If you randomly purchase 12 items, what is the probability that their mean life will be longer than 11 years?
Round to 4 decimal places.
B. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 98.4-cm and a standard deviation of 0.9-cm. For shipment, 15 steel rods are bundled together.
Find the probability that the average length of the rods in a randomly selected bundle is between 97.9-cm and 98.6-cm.
P(97.9-cm < X¯¯¯ < 98.6-cm) = Round to 4 decimal places.
The probability that their mean length is less than 17.4 inches is 28.26%
Given :
A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches , If 25 items are chosen at random .
z = ( X - μ ) / σ, where X = date , μ = mean , σ = standard deviation .
substitute the values
z = 17.4 - 19.7 / 4
= -2.3 / 4
= -0.575
P - value at z = -0.575 is 0.2826
Converting into percentage :
= 0.2826 * 100%
= 28.26 %
Learn more about the probability here:
https://brainly.com/question/11234923
#SPJ4
A researcher is investigating the relationship between personality and birth order position. A sample of college students is classified into four birth categories (1st, 2nd, 3rd, 4th, and later)and given a personality test that measures the degree of extroversion on a 50 point scale. Identify the statistical procedure for analyzing this data. Explain your answer.
The data form a 2x4 frequency matrix and the ratio of each cell represents the result. Each participant's rating is a birth order category (1, 2, 3, 4). The Mann-Whitney test can assess the significance of differences between groups.
The chi-square test of independence determines whether the proportions are significantly different for each birth order group. Effect sizes are measured in Cramer's V. Alternatively, the data form two sets of ratings, one for each personality group. Each participant's rating is a birth order category (1, 2, 3, 4). The Mann-Whitney test can assess the significance of differences between groups.
Chi- Square Test:The chi-square test (also called chi-square or chi-square test) is a statistical hypothesis test used in contingency table analysis when the sample size is large. Simply put, the main purpose of this test is to test whether two categorical variables (the two dimensions of the contingency table) independently affect the test statistic (the values in the table) . The test is valid when the test statistic is a chi-square distribution based on the null hypothesis, specifically Pearson's chi-square test and variants thereof. Use Pearson's chi-square test to determine whether there is a statistically significant difference between the expected and observed frequencies for one or more categories in the contingency table. For contingency tables with small sample sizes, Fisher's exact test is used instead.
Mann - Whitney U Test:In statistics, the Mann-Whitney U test (also known as the Mann-Whitney-Wilcoxon (MWW/MWU), Wilcoxon rank sum test, or Wilcoxon-Mann-Whitney test) is a test of the null hypothesis used at random. It is a non-parametric test. Values X and Y selected from two populations where the probability of X being greater than Y is equal to the probability of Y being greater than X.
Learn more about Frequency Matrix:
https://brainly.com/question/29000721
#SPJ4
2. Of the total pounds, x, of fudge at the fudge shop on Monday morning, {3}/{4} contain nuts. Helena works at the fudge shop and prepares 12 {3}/{4} more pounds of fudge containing nuts to fulfill a special order Monday afternoon. With this additional amount of fudge, there are at least 29 {5}/{8} pounds of fudge containing nuts at the fudge shop on Monday.
(a) Write an inequality that represents the scenario. Begin by defining your variable.
(b) Solve your inequality from Part (a). Show all work.
(c) Fudge is packaged into 1-pound boxes. What is the fewest number of boxes of fudge at the fudge shop Monday morning?
Answer:
At least means less than or equal to.
Fewest means the smallest number of boxes.
12 3/4 +x ≥ 29 5/8
x ≥ 16 7/8
The fewest number of boxes would be almost ≅ 42 boxes
Part A:
Let x denote the amount of fudge at the shop.
Helena prepares 12 3/4 pounds of fudge containing nuts.
Mathematically, the total amount of fudge on Monday will be
12 3/4 +x
Of this amount of fudge there are at least 29 5/8 pounds of fudge containing nuts at the fudge shop on Monday
12 3/4 +x ≥ 29 5/8
Part B:
The inequality can be solved
12 3/4 +x ≥ 29 5/8
x ≥ 29 5/8- 12 3/4
x ≥ 29- 12 5/8- 3/4
The whole numbers are subtracted and the fractions are solved separately to avoid long calculations.
x ≥ 17 (5-6)/8
x ≥ 17 - 1/8
x ≥ (136-1)/8
x ≥ (135)/8
x ≥ 16 7/8
Part C :
To find the number of boxes we divide the equal number of pounds .
12 3/4 + 29 5/8
12 + 29 3/4 + 5/8
41 11/8
42 3/8
The fewest number of boxes would be almost ≅ 42 boxes
At least problem can be understood by the following link.
Learn more about inequality concepts by:
brainly.com/question/24863377
#SPJ1
A reaction that acts to amplify or reinforce an initial change is termed the greenhouse effect Milankovitch forcing O a positive feedback
A reaction that acts to amplify or reinforce an initial change is termed a positive feedback.
The positive-feedback mechanism is used in climatic change, any effect that acts to reinforce the initial change.
In Asian philosophy, yin and yang are viewed as forces that interact and are connected to one another and are crucial parts of a dynamic system. Positive and negative feedbacks function something like yin and yang in the Earth system; they are integral parts of the total system that eventually help to maintain a more or less stable state. While negative feedback mechanisms stabilize a system and keep it from reaching extreme states, positive feedback mechanisms increase or magnify an original change. The evolution of Earth's climate system can be viewed in many ways as a kind of conflict between these two feedback mechanisms.
To know more about the Positive-feedback mechanism visit: brainly.com/question/15574460
#SPJ4
Discuss with your own words some ways that you see religion having social control in your everyday life . Be able to cite examples?
Answer: Religion reinforces and promotes social inequality and social conflict. It helps convince the poor to accept their lot in life, and it leads to hostility and violence motivated by religious differences. This perspective focuses on the ways in which individuals interpret their religious experiences.
Step-by-step explanation:
determine the number of different sets of quantum numbers possible for each of the following shells. n2
Answer:
Step-by-step explanation:
Explanation:
As you know, each electron that's part of an atom has its own unique set of four quantum numbers that describes its position and spin.
This means that looking for the number of unique sets of quantum numbers is equivalent to looking for the number of electrons that can occupy the third energy level.
As you know, the number of orbitals you get per energy level is given by the equation
no. of orbitals
=
n
2
, where
n
- the principal quantum number, the ones that gives the energy level.
So, if you're dealing with the third energy level, you can say that it will contain a total of
no. of orbitals
=
3
2
=
9
distinct orbitals.
Now, each orbital can contain a maximum of
2
electrons of opposite spins. This means that the third energy level will contain a maximum number of
no. of electron
=
9
⋅
2
=
18 e
−
So, if each electron is described by an unique set of quantum numbers, you can conclude that
18
sets of quantum numbers are possible for the third energy level.
ok maybe that will help!
Find the LCM of the numbers by using the GCF.
5. 22,38
The lowest common multiple (LCM) of the numbers 22 and 38 is 418.
What is L.C.M and H.C.FThe L.C.M. defines the least common multiple number which is exactly divisible by two or more numbers, while H.C.F. defines the highest common factor present in between given two or more numbers,
Given the numbers 22 and 38, we can express them as products of their prime factors and thus derive their LCM as follows;
22 = 2 × 11
38 = 2 × 19
LCM = 2 × 11 × 19
LCM = 418
Therefore, the LCM of 22 and 38 is 418 using prime factor method.
Know more about LCM here : https://brainly.com/question/233244
#SPJ1
The formula for the volume of a right circular cylinder is V = πr² h. If r = 2b and
h=5b+3, what is the volume of the cylinder in terms of b?
[tex]V=4\pi b^{2}(5b+3)[/tex].
Step-by-step explanation:1. Write the equation.[tex]V=\pi r^{2} h[/tex]
2. Use the values to substitute into the original formula.[tex]V=\pi r^{2} h\\ \\V=\pi (2b)^{2} (5b+3)[/tex]
3. Solve the exponent.[tex]V=\pi (2^{2} b^{2} ) (5b+3)\\ \\V=\pi (4 b^{2} ) (5b+3)[/tex]
4. Solve the product between the two parentheses and simplify.Use the distributive property of multiplication in order to operate.
[tex]V=\pi (4 b^{2} ) (5b+3)\\ \\V=\pi ((4 b^{2})(5b)+(4 b^{2})(3))\\ \\V=\pi ((20b^{3} )+(12 b^{2}))\\ \\V=4\pi (\frac{20b^{3}}4} +\frac{12 b^{2}}{4} )\\ \\V=4\pi (5b^{3} +3b^{2})\\ \\V=4\pi b^{2}(\frac{5b^{3}}{b^{2}} +\frac{3b^{2}}{b^{2}} )\\ \\V=4\pi b^{2}(5b+3)[/tex]
5. Conclude.[tex]V=4\pi b^{2}(5b+3)[/tex].
the students in charge of a class a carnivore want to make a profit of at least $65 by selling items they spent $55 for the materials to make the items they will sell each item for three dollars find the possible values of x ,the number of items the students need to sell to reach there goal
They should sell at least 40 items to make a profit of at least $65.
What is inequality?Inequality is a relationship between two expressions which are not equal and connected by the signs, ≤, ≥, <, and >
Given that, the students of a class want to make a profit of at least $65 by selling items they spent $55 for the materials to make the items they will sell each item for $3
Since, they want $65 at least profit,
Therefore, selling price for the profit = 55+65 = $120
Profit = Selling price - cost price
Since, selling price of each item = $3
Let they are selling x items, Therefore, selling price for x items = 3×x = $3x
Now, establishing the inequality,
3x ≥ 120
x ≥ 120/3
x ≥ 40
Hence, there should be 40 or more items to be sold.
For more references on inequality, click;
https://brainly.com/question/28823603
#SPJ1
High cholesterol: A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after treatment for each individual, with the following results: Individual Before After 244 207 288 216 274 188 278 200 233 173 271 224 295 171 275 187 4 Download data Part 1 out of 2 Construct a 95% confidence interval for the mean reduction in cholesterol level. Let d represent the cholesterol level before treatment minus the cholesterol level after. Use the TI-84 calculator and round the answers to one decimal place. A 95% confidence interval for the mean reduction in cholesterol level is Hd
The 95% confidence interval for the mean reduction in cholesterol level is given as follows:
(51.3, 96.7).
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 8 - 1 = 7 df, is t = 2.3646.
From the image given at the end of the answer, the sample of the differences is given as follows:
37, 72, 86, 78, 60, 47, 124, 88.
Hence the parameters are given as follows:
[tex]\overline{x} = 74, s = 27.1, n = 8[/tex]
Then the lower bound of the interval is of:
74 - 2.3646 x 27.1/square root of 8 = 51.3.
The upper bound of the interval is of:
74 + 2.3646 x 27.1/square root of 8 = 96.7.
Missing InformationThe table is given by the image shown at the end of the answer.
More can be learned about the t-distribution at https://brainly.com/question/17073112
#SPJ1
Drag and drop the choices into the boxes to correctly complete the table.
corresponding alternate interior alternate exterior none of these
Definitions:
Corresponding angles are the angles at matching corners.Alternate interior angles lie on the inner side of the parallel lines but on the opposite side of the transversal.Alternate exterior angles lie on the outer side of the parallel lines but on the opposite side of the transversal.The given angles are:
Top left figure ⇒ Alternate interiorTop middle figure ⇒ CorrespondingTop right figure ⇒ CorrespondingBottom left figure ⇒ Alternate exteriorBottom right figure ⇒ None of theseSolve
y=-2 x
y=-9 x+21
Answer:
X = 3, Y = -6
Step-by-step explanation:
y = -2x
y = -9x + 21
Bring Y and X on the same side (alone).
0 = -2x – y
-21 = -9x – y
Multiply the top equation by -1 so we can cancel out y later on (to make it easier to solve for x).
0 = 2x + y
-21 = -9x – y
Add the equations.
-21 = -7x
Divide by -7.
X = 3
Solve for Y and check.
Y = -2(3)
Y = -6
Use the other equation to make sure.
(-6) = -9(3) + 21
-6 = -27 + 21
Have a nice day :D
I don’t understand this any help please answer and explain please
Answer:
Angle ABC = 82°
Step-by-step explanation:
Given triangle ABC is an isosceles triangle so we can write
angle BAC = angle BCA = 49°
Then,
angle BAC + angle BCA + angle ABC = 180° (Sum of all angles of a triangle is 180°)
or, 49° + 49° + angle ABC = 180°
or, angle ABC = 180° - 98°
or, angle ABC = 82°
What is the domain of f?
A. {-4, -1, 0, 2, 7}
B. {-5, -4, -1, 0, 1, 2, 4, 7}
X
N
7
f(x)
C.
D. {5}
4
{-5, 0, 1, 2, 4, 7}
Answer:
A. [tex]\{-4, -1, 0, 2, 7\}[/tex]
Step-by-step explanation:
The domain is the set of input values, which corresponds to [tex]x[/tex] on the mapping diagram.
Please help me with this question
The average rate change of the function is -4.
What is a function?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
Given function is f(x) = 1x² + 1x - 8.
Find the average rate change of the function in the interval [-4, -1]
For this compute the value of f(x) at x = -4 and x = -1.
Then find the difference the value of f(x) and divide it by the difference the value of x.
The average rate change of function f(x) in the interval [a,b] is [f(b) - f(a)]/(b-a).
Putting x = -4 in the given function:
f(-4) = 1(-4)² + 1(-4) - 8
f(-4) = 4
Putting x = -1 in the given function:
f(-1) = 1(-1)² + 1(-1) - 8
f(-1) = -8.
The rate change of x is -1 - (-4) = 3
The average rate change of the function is
[f(-1) - f(-4)] /3
= -8 - 4/3
= - 12/3
= -4
To learn more about average rate change of a function, click on below link:
https://brainly.com/question/9351280
#SPJ1
What is the slant height of the cone?
Answer:
12.6
Step-by-step explanation:
Use pythag
8 / 2 = 4
a² + b² = c²
4² + 12² = c²
16 + 144 = c²
c² = 160
c = 12.6
Selena rewrite the expression 36+54 hours to factored using the greatest common factor in addition and distribute the property what expression to Salina create
The expression Salina created using the greatest common factor in addition and distributing the property is
9(4 + 6)
9x4 + 9x6
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
36 + 54
Taking out the greatest common factor.
9(4 + 6)
Using the distributive property over addition
9 x 4 + 9 x 6
Thus,
9 x 4 + 9 x 6 is the expression Salina created.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
What is 157 cm to m as whole numbers or decimal
Answer: 1.57 meters
Step-by-step explanation:
takes 2 places to get from cm to meters
157 / 100
1.57 m
