Answer:
68.29% probability that between 20 and 30 of these shoppers only review one page when searching online
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using 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.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 100, p = 0.28[/tex]
So
[tex]\mu = E(X) = np = 100*0.28 = 28[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.28*0.72} = 4.49[/tex]
What is the probability that between 20 and 30 of these shoppers only review one page when searching online?
Using continuity correction, this is [tex]P(20 - 0.5 \leq X \leq 30 + 0.5) = P(19.5 \leq X \leq 30.5)[/tex], which is the pvalue of Z when X = 30.5 subtracted by the pvalue of Z when X = 19.5.
X = 30.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30.5 - 28}{4.49}[/tex]
[tex]Z = 0.56[/tex]
[tex]Z = 0.56[/tex] has a pvalue of 0.7123.
X = 19.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19.5 - 28}{4.49}[/tex]
[tex]Z = -1.89[/tex]
[tex]Z = -1.89[/tex] has a pvalue of 0.0294
0.7123 - 0.0294 = 0.6829
68.29% probability that between 20 and 30 of these shoppers only review one page when searching online
if you work make 15 an hour for 8 hour shift how much is that
Answer:
120
Step-by-step explanation:
15*8=120
Explain how to find the relationship between two quantities, x and y, in a table. How can you use the relationship to calculate the missing values in the table?
Explanation:
In general, for arbitrary (x, y) pairs, the problem is called an "interpolation" problem. There are a variety of methods of creating interpolation polynomials, or using other functions (not polynomials) to fit a function to a set of points. Much has been written on this subject. We suspect this general case is not what you're interested in.
__
For the usual sorts of tables we see in algebra problems, the relationships are usually polynomial of low degree (linear, quadratic, cubic), or exponential. There may be scale factors and/or translation involved relative to some parent function. Often, the values of x are evenly spaced, which makes the problem simpler.
Polynomial relations
If the x-values are evenly-spaced. then you can determine the nature of the relationship (of those listed in the previous paragraph) by looking at the differences of y-values.
"First differences" are the differences of y-values corresponding to adjacent sequential x-values. For x = 1, 2, 3, 4 and corresponding y = 3, 6, 11, 18 the "first differences" would be 6-3=3, 11-6=5, and 18-11=7. These first differences are not constant. If they were, they would indicate the relation is linear and could be described by a polynomial of first degree.
"Second differences" are the differences of the first differences. In our example, they are 5-3=2 and 7-5=2. These second differences are constant, indicating the relation can be described by a second-degree polynomial, a quadratic.
In general, if the the N-th differences are constant, the relation can be described by a polynomial of N-th degree.
You can always find the polynomial by using the given values to find its coefficients. In our example, we know the polynomial is a quadratic, so we can write it as ...
y = ax^2 +bx +c
and we can fill in values of x and y to get three equations in a, b, c:
3 = a(1^2) +b(1) +c
6 = a(2^2) +b(2) +c
11 = a(3^2) +b(3) +c
These can be solved by any of the usual methods to find (a, b, c) = (1, 0, 2), so the relation is ...
y = x^2 +2
__
Exponential relations
If the first differences have a common ratio, that is an indication the relation is exponential. Again, you can write a general form equation for the relation, then fill in x- and y-values to find the specific coefficients. A form that may work for this is ...
y = a·b^x +c
"c" will represent the horizontal asymptote of the function. Then the initial value (for x=0) will be a+c. If the y-values have a common ratio, then c=0.
__
Finding missing table values
Once you have found the relation, you use it to find missing table values (or any other values of interest). You do this by filling in the information that you know, then solve for the values you don't know.
Using the above example, if we want to find the y-value that corresponds to x=6, we can put 6 where x is:
y = x^2 +2
y = 6^2 +2 = 36 +2 = 38 . . . . (6, 38) is the (x, y) pair
If we want to find the x-value that corresponds to y=27, we can put 27 where y is:
27 = x^2 +2
25 = x^2 . . . . subtract 2
5 = x . . . . . . . take the square root*
_____
* In this example, x = -5 also corresponds to y = 27. In this example, our table uses positive values for x. In other cases, the domain of the relation may include negative values of x. You need to evaluate how the table is constructed to see if that suggests one solution or the other. In this example problem, we have the table ...
(x, y) = (1, 3), (2, 6), (3, 11), (4, 18), (__, 27), (6, __)
so it seems likely that the first blank (x) will be between 4 and 6, and the second blank (y) will be more than 27.
Here is your answer | To determine the relationship between quantities, you must determine what to do to the x-values to make them into y-values. The correct operation must turn every x-value into the corresponding y- value in the table. Once you know the relationship, you can use the same operation on all of the x-values that have unknown y-values.
In an experiment to study the effect of temperature (x) on the yield of a chemical reaction (y), 30 experimental runs were conducted. The level of temperature was carefully controlled at each of five levels, coded as x = -2, -1, 0, 1, 2. Two catalysts were used. For each catalyst three runs were taken at each level of temperature, and the yield was measured. The model y = beta_0 + beta_1x + beta_2x^2 + beta_3z + epsilon, epsilon ~ N(0, sigma^2) was considered, where z = 0 for catalyst 1 and z = 1 for catalyst 2. a. Carefully interpret the parameter beta_3 in this model. b. The model was fit to the data and the output is summarized below. The residual sum of squares is 25.05, and Is there any evidence of a difference in the two catalysts? Find a 95% confidence interval for beta_2. c. We also know that (X'X)^-1 = [0.114 0 -0.023 -0.067 0 0.017 0 0 -0.023 0 0.012 0 -0.067 0 0 0.133] i. Explain why ^beta_1and ^beta_3 are independent random variables. ii. Find a 95% confidence interval for the expected yield when the standard temperature (x = 0) and catalyst 2 are used. iii. Find a 95% prediction interval for the yield of a new experiment run under standard temperature (x = 0) and with catalyst 2.
Answer:
=5
Step-by-step explanation:
Given that an experimenter is studying the effects of temperture, pressure, and type of catalyst on yield from a certain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.
a) Experimental runs possible if use of single temperature, pressure and catalyst is there = no of temperatures x no of pressures x no of catalysts
= b) Here pressure and temperature have no choice as lowest is selected.
no of methods = no of catalysts x 1 x1
= 5
9(5r-2) and 14r-7 yes or no to tell if this expression is equivalent or not
Answer:
No instead of doing multiplication u did division
Step-by-step explanation:
This equation is called distributive property where u multiply the answer from the outside by the inside number
what is 9 1/2 x 1/4? i just need it for a math question on study island.
Answer:
[tex]2 \frac{3}{8} [/tex]
Step-by-step explanation:
[tex]9 \frac{1}{2} \times \frac{1}{4} \\ \frac{19}{2} \times \frac{1}{4} \\ = \frac{19}{8} \\ = 2 \frac{3}{8} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Answer:
2 3/8
Hope this helps :)
Please help !!! Ill give you brainliest!!!
Answer:
72
Step-by-step explanation:
s=9
t=8
therefore , st
9×8
= 72
Answer:
st
Putting the value of s and t in above equation
=> 9 × 8
=> 72
A recipe uses cup of brown sugar to make 18 cookies. How many cups of brown sugar are needed to make 45 cookies? ASAP
Answer:
2.5
Step-by-step explanation:
it takes 1 cup to make 18 cookies so you divide 45 by 18 to get your answer
Overeating for just four weeks can increase fat mass and weight over two years later, a Swedish study shows.Researchers recruited 18 healthy and normal-weight people with an average age of 26. For a four-week period, participants increased calorie intake by (mostly by eating fast food) and limited daily activity to a maximum of 5000 steps per day (considered sedentary). Not surprisingly, weight and body fat of the participants went up significantly during the study and then decreased after the study ended. Participants are believed to have returned to the diet and lifestyle they had before the experiment. However, two and a half years after the experiment, the mean weight gain for participants was 6.8 lbs with a standard error of 1.2 lbs. A control group that did not binge had no change in weight.
Required:
a. Give a 95% confidence interval for parameter.
b. Give the margin of error.
Answer:
a) [tex] 6.8 -2.110*1.2 =4.268[/tex]
[tex] 6.8 +2.110*1.2 =9.332[/tex]
b) [tex] ME = t_{\alpha/2} SE= 2.110*1.2= 2.532[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] \bar X= 6.8[/tex] represent the sample mean
[tex] Se= 1.2[/tex] represent the standard error
[tex] n =18[/tex] the sample size
Part a
For this case the confidence interval for the mean is given by:
[tex] \bar X \pm t_{\alpha/2} SE[/tex]
The degrees of freedom are given by:
[tex] df =n-1=18-1=17[/tex]
And the critical value for a confidence interval of 95% is given by:
[tex] t_{\alpha/2}=2.110[/tex]
And the confidence interval would be:
[tex] 6.8 -2.110*1.2 =4.268[/tex]
[tex] 6.8 +2.110*1.2 =9.332[/tex]
Part b
The margin of error is given by:
[tex] ME = t_{\alpha/2} SE= 2.110*1.2= 2.532[/tex]
The product of a number and 18 is -378. what does that mean or what's the equation
Answer:
Hope this helps you to solve it
a bucket that holds 5 1/4 gallons of water is being used to fill a tub that can hold 34 1/8 gallons. How many buckets will be needed to fill the tub?
The answer is 6 1/2 buckets.
What is did was turn the fractions into decimals to make it easier.
So the ratio is 5.25 gallons per bucket. I divided 34 1/8 by 5 1/4 in decimal form (34.125/5.25) and got 6.5
So therefore, the answer is 6 1/2 buckets of water is needed ti fill up the tub.
Twenty percent of what number is equal to five percent of 680
Answer:
170
Step-by-step explanation:
5/100 ×680
=34
20%=34what about 100%=?
(100×34)÷20
170
Twenty percent of 170 is equal to five percent of 680.
What is percentage?The term ‘per cent’ means ‘out of a hundred’. In mathematics, percentages are used like fractions and decimals, as ways to describe parts of a whole. When you are using percentages, the whole is considered to be made up of a hundred equal parts. The symbol % is used to show that a number is a percentage.
Let the number be x
According to question:
20% of x = 5% of 680
[tex]\frac{20}{100}[/tex] x = [tex]\frac{5}{100}[/tex] × 680
20 x = 5 × 680
x = 170
Hence, Twenty percent of 170 is equal to five percent of 680.
Learn more about percentage:
https://brainly.com/question/13450942
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A rancher has a roll of fencing to enclose a rectangular area. The table shows how the area that the rancher can enclose with the fencing depends on the width of the rectangle. Which quadratic equation gives the area A of the rectangle in square feet given its width in w feet? ✔ A(w) = -w² + 100w The rancher decides to make the width of the rectangle 40 ft. What is the area of the rectangle? PLEASE HURRY
Answer:
A(w) = -w^2 + 100w
Step-by-step explanation:
just took the assignment
Finding the numeric value of the function, it is found that the area of the rectangle is of 2400 square feet.
---------------------------
The area of a rectangle of width w is given by:
[tex]A(w) = -w^2 + 100w[/tex]
In this question, we have a width of 40 ft, thus [tex]w = 40[/tex], and the area is of:
[tex]A(40) = -40^2 + 100(40) = -1600 + 4000 = 2400[/tex]
The area is of 2400 square feet.
A similar problem is given at https://brainly.com/question/24231879
Of the 200 students surveyed at the local high school, 126 say that they prefer earlier start times for school. What is the mean of the sampling distribution of the proportion of the students who prefer later start times for school
Answer:
The mean of sampling distribution of the proportion of the students who prefer later start times for school
μₓ = p = 0.63
Step-by-step explanation:
Explanation:-
Given sample size 'n' =200
given data Of the 200 students surveyed at the local high school, 126 say that they prefer earlier start times for school
sample proportion
[tex]p = \frac{x}{n} = \frac{126}{200} = 0.63[/tex]
The mean of sampling distribution of the proportion of the students who prefer later start times for school
μₓ = p = 0.63
Standard deviation of the proportion
[tex]S.D = \sqrt{\frac{p(1-p)}{n} } = \sqrt{\frac{0.63(1-0.63)}{200} } = 0.034[/tex]
Nathan spins 2 different spinners at the same time. There are a total of 10 possible
outcomes. Which pair of spinners did Nathan spin?
A
B
A
B
1
2
E
2
E
5
3
D
4
A
B
2
A
B
E
c
COM
3
D
с
Answer:
Since the spinners have been spun simultaneously, every side on each of the spinner carries equal probability of landing. In order for there to be only 10 possible outcomes, no more no less, the spinners cannot be identical. One of the spinner in two sided while the other spinner must then be a five sided spinner. Choosing this particular pair of spinners gives Nathan 10 possibilities of combinations.
Hope that answers the question, have a great day!
Answer:
The spinners he spins are the ones that together add up to ten numbers.
Step-by-step explanation:
Some contact lens wearers report problems with dryness in their eyes. A study was conducted to evaluate the effectiveness of a new eye-drop solution to relieve dryness for contact lens wearers. Twenty-five volunteers who wore contact lenses agreed to use the new solution for one month. At the end of the month, 36 percent of the volunteers reported that the new solution was effective in relieving dryness. The company that produced the new eye-drop solution concluded that using the new solution is more effective in relieving dryness than using no solution. Which of the following best explains why the study does not support such a conclusion.
(A) The sample size was too small.
(B) The study had no control group.
(C) The participants were volunteers.
(D) The participants self-reported the frequency with which they used the new solution.
(E) The participants self-reported the effectiveness of the new solution.
The preceding help understand why the study doesn't really support such a conclusion: the sample size was too small.
The assumption is approximate [tex]\hat{P}[/tex] by a normal distribution will be:
[tex]np \geq 10[/tex][tex]n (1-p) \geq 10[/tex][tex]n = 25[/tex]→ [tex]np = 25\times 0.36[/tex]
[tex]=9[/tex]
→ [tex]n (1-p) = 25\times (1-0.36)[/tex]
[tex]= 25\times 0.64[/tex]
[tex]= 16[/tex]
The above assumption is not satisfied. Thus the above answer i.e., "option A" is the appropriate one.
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Please answer this correctly
Answer:
volume = 75 cubic yards
Step-by-step explanation:
Base is 3×5 or 15 yd²
110-15-15=b×3×2+b×5×2
80=6b+10b
80=16b
Divide both sides by 16
b=5
The height of the rectangular prism is 5 yards
Now the volume is l×w×h
3×5×5=
75 yd³ or 75 cubic yards
Answer:
Volume = 75 yards³
Step-by-step explanation:
Surface Area = 110 yards²
But
Surface area = 2(wl+lb+bw) --(1)
Where w is the width , l is length and b is height
L = 5 yards, w = 3 yards
Putting in (1)
110 = 2{(3)(5)+(5)b+3b}
110 = 2(15+5b+3b)
110 = 2(15+8b)
110 = 30+16b
16b = 110-30
16b = 80
Dividing both sides by 18
b = 5
Now
Volume of rectangular prism = wlb
Where w is width, l is length and b is height
= (5)(3)(5)
= 75 yards³
29 POINTS AND BRAINLIEST !!! Jim likes to rock climb in his spare time. Recently, he climbed down from the top of a cliff to the bottom. At the top, where Jim started, he was 2500 ft above the ground. He moved down the cliff at a speed of 20 ft/min.
a) Write an equation to represent the height h, in feet, that Jim was above the ground after t minutes.
b) Make a table of values for Jim's height above the ground for values of t from 0 to 4.
c) What was Jim's height above the ground after 40 minutes?
d) How many minutes did it take to reach the ground?
Answer:
Step-by-step explanation:
A) y = -20x + 2500
The above equation is written in slope intercept form - y=mx+b - the y int. is 2500, while the rate of change, aka the slope, is -20 feet per minute.
B) (0,2500) (1,2480) (2,2460) (3,2440) (4,2420)
For this question just plug in the x values 0 to 4 into the equation above. For example -20(0) +2500 = 2500
C) 1700 feet above the ground
Plug the number 40 into the equation above. -20(40) + 2500 = 1700
D) 125 minutes
The y-int. represents the time it takes him to reach the ground, this means you can set the equation equal to zero and solve to find the answer.
0 = -20x + 2500
subtract 2500 from both sides
-2500 = -20x
divide -20 from both sides
125 = x
Answer:50m
Step-by-step explanation: the highest
f(x)=log2(x-3) find the domain of x
A construction company finally completed a major project that paid $1,786,000. This company uses contract workers instead of employees. The money is to be divided in the ratio 4:2:3:3 among the company, The plumber, the electrician and the auxiliary workers. Calculate how much each of them receives.
Answer:
The company receives $595,333.333.
The plumber receives $297,666.667.
Each the electrician and the auxiliary workers receive $446,500.
Step-by-step explanation:
The total amount is $1,786,000.
Company:
The company receives [tex]\frac{4}{4 + 2 + 3 + 3} = \frac{4}{12} = \frac{1}{3}[/tex] of the total amount. So
[tex]\frac{1*1786000}{3} = 595333.333[/tex]
The company receives $595,333.333.
Plumber:
[tex]\frac{2}{4 + 2 + 3 + 3} = \frac{2}{12} = \frac{1}{6}[/tex] of the total amount. So
[tex]\frac{1*1786000}{6} = 297666.667[/tex]
The plumber receives $297,666.667.
Electrician and the auxiliary workers:
Each receives [tex]\frac{3}{4 + 2 + 3 + 3} = \frac{3}{12} = \frac{1}{4}[/tex] of the total amount. So
[tex]\frac{1*1786000}{4} = 446500[/tex]
Each the electrician and the auxiliary workers receive $446,500.
It is known that 25% of inhabitants of a community favour a political party A.
A random sample of 20 inhabitants was selected from the community and each person was asked he/she will vote for party A in an impending election. This follows a Binomial distribution, what is the probability that:
(i) exactly two persons will vote for party A?
(ii) at least three persons will vote for party A?
(iii) fewer than two persons will vote for party A?
Answer:
i) [tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
ii) [tex]P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317[/tex]
[tex]P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211[/tex]
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
And replacing we got:
[tex] P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883[/tex]
iii) [tex]P(X <2)= 0.00317+ 0.0211= 0.02427[/tex]
Step-by-step explanation:
Let X the random variable of interest "number of inhabitants of a community favour a political party', on this case we now that:
[tex]X \sim Binom(n=20, p=0.25)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
Part i
We want this probability:
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
Part ii
We want this probability:
[tex]P(X\geq 3)[/tex]
And we can use the complement rule and we have:
[tex]P(X\geq 3) = 1-P(X<3)= 1-P(X \leq 2) =1- [P(X=0) +P(X=1) +P(X=2)][/tex]
And if we find the individual probabilites we got:
[tex]P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317[/tex]
[tex]P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211[/tex]
[tex]P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669[/tex]
And replacing we got:
[tex] P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883[/tex]
Part iii
We want this probability:
[tex] P(X <2)= P(X=0) +P(X=1)[/tex]
And replacing we got:
[tex]P(X <2)= 0.00317+ 0.0211= 0.02427[/tex]
once again i need help with my 8th grade hw [tex]-9\leq 7-8x[/tex] ... thnx
Step-by-step explanation:
-9 ≤ 7 − 8x
8x ≤ 16
x ≤ 2
On a coordinate plane, 4 lines are shown. Line L M goes through (negative 5, negative 3) and (0, 3). Line N O goes through (negative 6, negative 5) and (0, 0). Line J K goes through (negative 6, 1) and (0, negative 4). Line P Q goes through (negative 5, 4) and (0, negative 2). Which line is perpendicular to a line that has a slope of Negative five-sixths? line JK line LM line NO line PQ
Answer:
no pq
Step-by-step explanation:
Answer:
Line LM
Step-by-step explanation:
Got it right on Edge2020
The average marks of candidates in an aptituste test
was 128.5with a standard deviation of 8.2
Three scores extracted from the test are
148,102, 152, what is the average of the
extracted scores that are extreme values
fouthers (out the coutlier)
Answer:
102
Step-by-step explanation:
We must calculate the value of z for each value and then compare each one and thus manage to see what is an outlier, we know that z is equal to:
z = (x - m) / sd
where x is the value to evaluate, m the mean and sd the standard deviation. Now we have to:
For x = 148:
z = (148 - 128.5) /8.2
z = 2.37
For x = 102:
z = (102 - 128.5) /8.2
z = -3.23
For x = 152:
z = (152 - 128.5) /8.2
z = 2.86
The value of this is generally between -3.09 and 3.09, so when x is 102, it goes out of range of the value of z, which means that this is the outlier.
what number is to be multiplied with 1/3 to get 1/21
Answer:
1/7
Step-by-step explanation:
Since we do not know the number let us use the alphabet A to represent the unknown number
A × 1/3= 1/21
A/3= 1/21
Cross multiply both sides
A×21= 3×1
21A= 3
Divide both sides by the coefficient of A which is 21
21A/21=3/21
A=1/7
Hence the unknown number is 1/7
Answer:
The number to multiply with 1/3 to get 1/21 is 1/7.
Step-by-step explanation:
The question wants us to find the number you can multiply with 1/3 to get 1/21. The number is unknown but when you multiply that unknown number by 1/3 your answer should be 1/21.
Let
the number to be multiplied with = a
Therefore,
1/3 × a = 1/21
a/3 = 1/21
cross multiply
21a = 3
divide both sides by 21
a = 3/21
a = 1/7
The number to multiply with 1/3 to get 1/21 is 1/7.
A ball is thrown straight up from a cliff. The function f(x) = –4.9t2 + 17t + 19 describes the height of the ball, in meters, as a function of time, t, in seconds. What is the maximum height of the ball? At what time is that height reached? Round your answers to 1 decimal place.
Maximum height:
__ meters
Time:
__ seconds
Answer:
Maximum height: 33.7 meters
Time: 1.7 seconds
Step-by-step explanation:
Suppose we have a quadratic equation in the following format:
[tex]f(t) = at^{2} + bt + c[/tex]
In a is negative, the maximum point of the function happens at the time of
[tex]t_{v} = -\frac{b}{2a}[/tex]
And it's value is: [tex]f(t_{v})[/tex]
In this question:
[tex]f(t) = -4.9t^{2} + 17t + 19[/tex]
So [tex]a = -4.9, b = 17, c = 19[/tex]
The time of the maximum height is:
[tex]t_{v} = -\frac{b}{2a} = -\frac{17}{2*(-4.9)} = 1.7[/tex]
The maximum height is:
[tex]f(1.7) = -4.9*(1.7)^{2} + 17*1.7 + 19 = 33.7[/tex]
The function f(x) = –StartRoot x EndRoot is represented by the graph. What is the range of the given function? {y | all real numbers} {y | y ≤ 0} {y | y ≥ 0}
Answer:
{y | y ≤ 0}
Step-by-step explanation:
The vertical extent of the graph is all values of y less than or equal to zero:
{y | y ≤ 0}
Answer: {y | y ≤ 0}
Step-by-step explanation: It is the correct answer <3 have an amazing day.
Eric’s average income for the first 4 months of the year is $1,450.25, what must be his
average income for the remaining 8 months so that his average income for the year is
$1,780.75?
Answer:
Average income of Eric for the remaining 8 months = [tex]\$1946[/tex]
Step-by-step explanation:
Given: Average income of Eric for the first 4 months of the year is equal to $1,450.25
To find: average income for the remaining 8 months so that his average income for the year is $1,780.75
Solution:
Average income = Total income for the year/Total number of months
Average income of Eric for the first 4 months = $1,450.25
So,
Total income of Eric for the first 4 months = 1,450.25 × 4 = 5801
Let x denotes total income of Eric for the remaining 8 months
Total income for the year = 5801 + x
Therefore,
Average income for the year = [tex]\frac{5801+x}{12}[/tex]
Also, average income for the year is $1,780.75
[tex]1780.75=\frac{5801+x}{12}\\1780.75\times 12=5801+x\\21369=5801+x\\21369-5801=x\\15568=x[/tex]
Total income of Eric for the remaining 8 months = $15568
Average income of Eric for the remaining 8 months = [tex]\frac{15568}{8}=\$1946[/tex]
Which phrase best describe the translation from the graphy y=(x+2)² to the graph of y=x²+3
Answer:
2 units right
3 units up
Step-by-step explanation:
the graph y=(x+2)² is the parent function y=x^2 translated 2 units left
the graph y=x²+3 is the parent function y=x^2 translated 3 units up
so, the translation from y=(x+2)² to y=x²+3 is:
2 units right (to get to zero)
3 units up
(you can change the order if you want, it doesn't really matter here)
Leah ran the track 8 times. She ran a total of 2,000 meters. How many meters equals 1 lap?
Answer:
250m
Step-by-step explanation:
2000m/ 8laps = 250m
The publishers of a business magazine are running sales promotions for the weekly magazine. The number of prospective customers a sales representative sees per day varies 1 to 40. If the sales representative is able to her 20% of the prospective customers to subscribe, the maximum expected number of subscriptions per week is .if the sales representative earns $3 per subscription in addition to daily wages, the minimum expected value of the extra income per week is .
Answer:
the maximum expected number of subscriptions per week is
34 subscriptionsthe minimum expected value of the extra income per week is
$94.20Step-by-step explanation:
number of sales visits per day 1 - 40
success rate in closing sales 20%
total visits per week:
week 1 = 20 + 22 + 27 + 17 + 31 + 12 + 39 = 168week 2 = 26 + 13 + 30 + 18 + 24 + 14 + 32 = 157week 3 = 21 + 12 + 22 + 37 + 30 + 23 + 18 = 163week 4 = 15 + 33 + 10 + 28 + 34 + 24 + 22 = 166week 5 = 11 + 33 + 21 + 32 + 26 + 19 + 22 = 164week 6 = 19 + 27 + 20 + 18 + 31 + 14 + 37 = 166week 7 = 29 + 22 + 27 + 30 + 16 + 9 + 36 = 159week 8 = 8 + 28 + 19 + 28 + 25 + 36 + 26 = 170estimated sales per week:
week 1 = 168 x 20% = 33.6week 2 = 157 x 20% = 31.4week 3 = 163 x 20% = 32.6week 4 = 166 x 20% = 33.2week 5 = 164 x 20% = 32.8week 6 = 166 x 20% = 33..2week 7 = 159 x 20% = 31.8week 8 = 170 x 20% = 34extra income per week:
week 1 = 33.6 x $3 = $100.80week 2 = 31.4 x $3 = $94.20week 3 = 32.6 x $3 = $97.80week 4 = 33.2 x $3 = $99.60week 5 = 32.8 x $3 = $98.40week 6 = 33.2 x $3 = $99.60week 7 = 31.8 x $3 = $95.40week 8 = 34 x $3 = $102Answer: subscriptions per week: 34
Extra income per week: $94.20
Step-by-step explanation: I got this right on Edmentum