Answer:
[tex]A(t)=975(1.025)^t[/tex]
In 2025,the number of students at the villages high school=1159
Step-by-step explanation:
We are given that in 2018
Number of students at the villages high school=975
Increasing rate,r=2.5%=0.025
We have to write and use of exponential growth function to project the populating in 2025.
[tex]A_0=975,t=0[/tex]
According to question
Number of students at the villages high School is given by
[tex]A(t)=A_0(1+r)^t[/tex]
Substitute the values
[tex]A(t)=975(1+0.025)^t=975(1.025)^t[/tex]
t=7
Substitute the value
Then, the number of students at the villages high school in 2025
[tex]A(7)=975(1.025)^7=1158.96\approx 1159[/tex]
Answer:
1,159 students
Step-by-step explanation:
the exponential growth rate formula:
A = P ( 1 + r)ⁿ
A = amount after growth = ??P = current/original amount = 975 studentsr = yearly growth rate = 2.5% or 0.025n = number of years = 2025 - 2018 = 7Pop. 2025 = 975 (1 + 0.025)⁷
Pop. 2025 = 975 x 1.025⁷ = 1,158.97 ≈ 1,159 students
A jury pool has 15 men and 21 women, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of:_____
(a) all men
(b) all women
(c) 8 men and 4 women
(d) 6 men and 6 women
Give all answers accurate to four decimal places.
Answer:
(a) all men = 3.6351 * 10^ -7
(b) all women = 2.3483* 10^ -4
(c) 8 men and 4 women = 0.0308
(d) 6 men and 6 women= 0.2170
Step-by-step explanation:
A jury pool has 15 men and 21 women, from which 12 jurors will be selected.
Total = 36 people
Probability of
(a) all men
= 15C12/36C12
= 455/1251677700
= 3.6351 * 10^ -7
(b) all women
= 21C12/36C12
= 293930/1251677700
= 2.3483* 10^ -4
(c) 8 men and 4 women
=( 15C8 * 21C4)/36C12
= (6435*5985)/1251677700
= 38513475/1251677700
= 0.0308
(d) 6 men and 6 women
= (15C6 * 21C6)/(36C12)
= (5005*54264)/1251677700
= 271591320/1251677700
= 0.2170
8. Nate bought two large pizzas and one small pizza and paid $36. If the difference in cost between a large and small pizza is $5.25, how much does a small pizza cost?
Answer:
$8.5
Step-by-step explanation:
We need to propose a system of equations with the information provided to us.
two large pizzas and one small pizza cost $36:
[tex]2L+S=36[/tex]
where
[tex]L[/tex]: Large pizza
[tex]S:[/tex] Small pizza
and the difference in cost between a large and small pizza is $5.25:
[tex]L-S=5.25[/tex]
our system of equations is:
[tex]2L+S=36[/tex]
[tex]L-S=5.25[/tex]
We are asked for the price of small pizza, so we must manipulate the equations in such a way that adding or subtracting them removes the variable L and we are left with an equation for S.
Multiply the second equation of the system by -2
[tex](-2)(L-S=5.25)\\\\-2L+2S=-10.5[/tex]
and now we sum this with the first equation of the system:
[tex]-2L+2S=-10.5\\+(2L+S=36)\\-------------\\-2L+2L+2S+S=-10.5+36[/tex]
simplifying the result:
[tex]3S=25.5[/tex]
and solving for S (the price of a small pizza)
[tex]S=25.5/3\\S=8.5[/tex]
which is pattern 12,24,36,48
Answer:
multiples of 12
Step-by-step explanation: when looking at the GCF, the answer is 12
help asap giving branlist!!!
Answer:
option 2
Step-by-step explanation:
Because (0, 900) is a point on the line it means that it costs $900 to make the commercial. A slope of 110 means that they pay $110 every time it's aired so the answer is Option 2.
g Suppose the company operates mine #1 for x1 days and mine #2 for x2 days. Write a vector equation in terms of v1 and v2 whose solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver. Do not solve the equation.
Answer:
The vector equation in terms of v1 and v2 is x₁v₁ +x₂v₂ = [296 2454]
Step-by-step explanation:
Solution
The aim is to write down a vector equation in terms of v1 and v2, when solution gives the number of days each mine should operate in order to produce 296 tons of copper and 2454 kilograms of silver.
Thus,
Suppose that b = [ 296 2454] is the corresponding vector which is representing the total needed output.
Now,
If the company operates mine 1 for x1 days and mine #2 for x2 days
Then,
The total output becomes x₁v₁ +x₂v₂ which is the same output to b = [296 2454]
Hence, x₁ and x₂ should be satisfactory to the needed vector equation x₁v₁ +x₂v₂ = [296 2454]
So, the vector equation becomes x₁v₁ +x₂v₂ = [296 2454]
Please answer this correctly
Answer: 30
Step-by-step explanation:
Q1: 120
Q3: 150
To find the interquartile range, subtract Q1 from Q3, which is 150-120. Therefore, the interquartile range of the kitten's weight, is 30
Answer: 30 grams
Step-by-step explanation:
The interquartile range is the range within the boxed areaa. You subtract the minimum value from the maximum value.
150 - 120 = 30
What is the sum of 1/6 and 1/7
1/6 + 1/7 = 13/42
aka: 7/42 + 6/42
Answer:
13/42
Step-by-step explanation:
1/6 + 1/7
We need a common denominator of 42
1/6 *7/7 + 1/7 *6/6
7/42 + 6/42
13/42
From an urn containing 3 white and 2 black balls, two balls are drawn one after the other without replacement. What is the probability that the first ball drawn is white and the second black?
Answer:
There is a 3/5 chance of the first ball being white, and a 3/10 chance the second one is black.
Step-by-step explanation:
There are 5 balls, of which 3 are white, so you have a 3/5 chance of the first one being white. Then you have 2 white and 2 black balls. There is a 2/4 chance of picking a black ball. Multiply 3/5 and 2/4 to get 6/20, or 3/10 for choosing a white ball then a black ball.
which situation cannot be represented by this expression 13+8
A Ben gave 8 of his bagels to friends. Now he has 13 left. How many bagels did he start with?
B Jack bought 8 books. He will buy 13 more. How many books will he buy altogether?
C Zoe is reading an article with 13 pages. She has 8 pages left. How many pages has she read?
D Caleb swam for 13 minutes. Then he swam for 8 more minutes. For how many minutes did he swim?
D because Caleb had swam 8 more after swimming 13
Which of the lists of letters all have rotational symmetry?
a. C, H, N, X
b. N, O, S, Z
c. H, J, N, S
d. F, H, X, Z
Answer:
So C doesn't have symmetry so that rules out a
b does though
J doesn't work so that rules out c
F doesn't work so that rules out d
B is answer
Answer:
B. is the rotational symmetry
Step-by-step explanation:
lucy buys 3 liters of apple juice. How many millilitres of apple juice does she buy?
*please help*
Answer:
3000 milliliters
Step-by-step explanation:
1liter contains 1000militers
3liters contain (3*1000)militers
Answer:
3000 millilitres
Step-by-step explanation:
since 1 litre = 1000 millimetres
3 litres will be equal to 1000 x 3 = 3000 ml
A bottler of drinking water fills plastic bottles with a mean volume of 1,007 milliliters (mL) and standard deviation The fill volumes are normally distributed. What proportion of bottles have volumes less than 1,007 mL?
Answer:
0.5 = 50% of bottles have volumes less than 1,007 mL
Step-by-step explanation:
Problems of normally distributed samples are 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.
In this question, we have that:
[tex]\mu = 1007[/tex]
What proportion of bottles have volumes less than 1,007 mL?
This is the pvalue of Z when X = 1007. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1007 - 1007}{\sigma}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.5 = 50% of bottles have volumes less than 1,007 mL
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval.
x4 + x ? 7 = 0, (1, 2)
f(x) = x4 + x ? 7
is (FILL IN)
a) defined
b) continuous
c) negative
d) positive on the closed interval [1, 2],
f(1) = ?? FILL IN , and f(2) = ?? FILL IN
Since ?5 < FILL IN a)? b)? c)? d)0 < 11, there is a number c in (1, 2) such that
f(c) = FILL IN a)? b)? c)0 d)11 e)-5
by the Intermediate Value Theorem. Thus, there is a FILL IN a) limit b)root c) discontinuity of the equation
x4 + x ? 7 = 0
in the interval (1, 2).
Answer:
The correct option is d
[tex]f(1) = -5[/tex]
[tex]f(2) = 11[/tex]
The correct option is d
The correct option is c
the correct option is b
Step-by-step explanation:
The given equation is
[tex]f(x) = x^4 + x -7 =0[/tex]
The give interval is [tex](1,2)[/tex]
Now differentiating the equation
[tex]f'(x) = 4x^3 +7 > 0[/tex]
Therefore the equation is positive at the given interval
Now at x= 1
[tex]f(1) = (1)^4 + 1 -7 =-5[/tex]
Now at x= 2
[tex]f(2) = (2)^4 + 2 -7 =11[/tex]
Now at the interval (1,2)
[tex]f(1) < 0 < f(2)[/tex]
i.e
[tex]-5 < 0 < 11[/tex]
this tell us that there is a value z within 1,2 and
f(z) = 0
Which implies that there is a root within (1,2) according to the intermediate value theorem
It has been suggested that night shift-workers show more variability in their output levels than day workers. Below, you are given the results of two independent random samples.
Night Shift (N) Day Shift (D)
Sample Size 9 8
Sample Mean 520 540
Sample Variance 38 20
Required:
a. At 95% confident level, what is the critical value?
b. State the null and alternative hypotheses to be tested.
c. Compute the test statistic.
d. Determine the p-value.
Answer:
Null hypotheses = H₀ = σ₁² ≤ σ₂²
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic = 1.9
p-value = 0.206
Since the p-value is greater than α therefore, we cannot reject the null hypothesis.
So we can conclude that the night shift workers don't show more variability in their output levels than day workers.
Step-by-step explanation:
Let σ₁² denotes the variance of night shift-workers
Let σ₂² denotes the variance of day shift-workers
State the null and alternative hypotheses:
The null hypothesis assumes that the variance of night shift-workers is equal to or less than day-shift workers.
Null hypotheses = H₀ = σ₁² ≤ σ₂²
The alternate hypothesis assumes that the variance of night shift-workers is more than day-shift workers.
Alternative hypotheses = Ha = σ₁² > σ₂²
Test statistic:
The test statistic or also called F-value is calculated using
Test statistic = Larger sample variance/Smaller sample variance
The larger sample variance is σ₁² = 38
The smaller sample variance is σ₂² = 20
Test statistic = σ₁²/σ₂²
Test statistic = 38/20
Test statistic = 1.9
p-value:
The degree of freedom corresponding to night shift workers is given by
df₁ = n - 1
df₁ = 9 - 1
df₁ = 8
The degree of freedom corresponding to day shift workers is given by
df₂ = n - 1
df₂ = 8 - 1
df₂ = 7
We can find out the p-value using F-table or by using Excel.
Using Excel to find out the p-value,
p-value = FDIST(F-value, df₁, df₂)
p-value = FDIST(1.9, 8, 7)
p-value = 0.206
Conclusion:
p-value > α
0.206 > 0.05 ( α = 1 - 0.95 = 0.05)
Since the p-value is greater than α therefore, we cannot reject the null hypothesis corresponding to a confidence level of 95%
So we can conclude that the night shift workers don't show more variability in their output levels than day workers.
Inflation causes things to cost more, and for our money to buy less (hence your grandparents saying "In my day, you could buy a cup of coffee for a nickel"). Suppose inflation decreases the value of money by 4% each year. In other words, if you have $1 this year, next year it will only buy you $0.96 worth of stuff. How much will $100 buy you in 25 years?
Answer:
Step-by-step explanation:
[tex]100 (0.96)^{25} =[/tex] around 36.04
Solve seven square root three plus two square root nine and explain whether the answer is rational or irrational
Answer:
Step-by-step explanation:
5
What’s the correct answer for this question?
Answer:
C.
Step-by-step explanation:
Diameter = 11 inches.
Radius = D/2 = 5.5 inches
Volume = 4/3πr³
= 4/3(3.14)(5.5)³
= 696.6 in.³
Please answer this correctly
Answer:
# of broken crayons # of boces
1-5 1
6-10 4
11-15 5
16-20 3
21-25 1
Step-by-step explanation:
1-5: 4 (1 number)
6-10: 6, 6, 8, 9 (4 numbers)
11-15: 12, 13, 14, 14, 15 (5 numbers)
16-20: 17, 17, 19 (3 numbers)
21-25: 24 (1 number)
Answer:
Number of broken crayons Number of boxes
1-5 = 4
6-10 = 9
11-15 = 14
16-20 =19
21-25 =24
Step-by-step explanation:
To find the number of boxes compared to the number of broken crayons you have to find 5 consecutive (hence there being five boxes to fill in) numbers with a constant rate of change. Start with the largest number possible that you can pick and then find the second largest so 24 and 19 the rate of change is 5. Compared to 17 and 19 the rate of change is 2 so it doesn’t have the same rate of change but if you try 19-5 you get 14 which is an option if you subtract 14-5 you get 9 which is another option 9-5 is 4 the lowest number you could possibly pick and they all have a constant rate of change of 5 so the answer is correct.
help as quick as possible 18 points :)
Answer:
Step-by-step explanation:
1/10*5 is the answer i think...
b) A man purchased 5 dozen of eggs at Rs 5 each. 10 eggs were broken and he
sold the remaining at Rs 5.70 each. Find
(ii) Profit or loss percent.
(i) his total profit or loss.
Answer:
Dear User,
Answer to your query is provided below
(i) Total Loss = Rs.15
(ii) Loss percent = 5%
Step-by-step explanation:
Eggs purchased = 5x12 = 60
Total Cost = 60x5 = Rs 300
Eggs Broken = 10
Eggs Broken cost = 10x5= Rs. 50
Eggs sold = 60-10 = 50
Egg Sale cost = 50x5.70 = Rs 285
(i) Total Loss = C.p. - S.p. = 300 - 285 = 15
(ii) Loss Percent = (Loss/CP)x100 = (15/300)x100 = 5%
PLEASE ANSWER THIS!
In the diagram, PQRS, JQK and LRK are straight lines
Р
Question 1
Question 2
Question 3
J-
2yQ
Question 4
O
x
K
Question 5
Question 6
Question 7
Question 8
Question 9
M
33°
DO
R
L
2x/
Question 10
S
What is the size of the angle JKL?
Question 11
Question 12
Question 13
Question 14
A Question 15
Question 16
Question 17
Question 18
Question 19
37°
38°
36°
34°
35°
Answer:
38°
Step-by-step explanation:
The sum of angles that make a line is 180°; the sum of angles in a triangle is 180°. So, we have the following relations:
2x +y +A = 180
2y +x + B = 180
A +B +33 = 180
Adding the first two equations and subtracting the third, we get ...
(2x +y +A) +(2y +x +B) -(A +B +33) = 180 +180 -180
3x +3y -33 = 180
x + y - 11 = 60
x + y = 71
__
We know vertical angles are congruent, so in triangle QRK, we have ...
2y +2x +∠K = 180
∠K = 180 -2x -2y = 180 -2(x +y) = 180 -2(71)
∠JKL = 38°
Answer:
38 degrees
Step-by-step explanation:
Saved
250 mg
sing value in
50 mg
10 ml
X
Choice
I need help pleaseeee help meee
Answer:
x>-1
Step-by-step explanation:
Answer:
x > -1
Step-by-step explanation:
First we need to determine what sign this inequality uses:
A closed circle represents greater than or equal to (≥) or less than or equal to (≤)An open circle represent greater than (>) or less than (<)Here we have an open circle so we know our sign will either be > or <
Our point is on the -1, and the arrow points in the direction of the sign as long as the variable x is on the left side of the answer
So the arrow is point to the right, indicating our sign will also be "pointing" to the right (>)
The inequality of this graph reads: x > -1
WILL GIVE BRAINLIEST IF ANSWERED NOW
Write an equation of a line that passes through the point (3, 2) and is parallel to the line y = 3x +7
y = 3x -7
y = 1/3x+2
y= 1/3x-2
Answer:
y=3x-7
Step-by-step explanation:
lines are parallel hence gradient from the equation in question is the same as the gradient of the equation to be found.. comparing to y=mx+c, eq in question has grad 3... from the formula y-y1=m(x-x1) where (x1,y1) is equal to the point in question
Answer:
Make That Guy Brainliest Now ^^^^^ You can now that there are two answers!
Jan's All You Can Eat Restaurant charges $9.10 per customer to eat at the restaurant. Restaurant management finds that its expense per customer, based on how much the customer eats and the expense of labor, has a distribution that is skewed to the right with a mean of $8.10 and a standard deviation of $4.
A. If the 100 customers on a day have the characteristics of the random sample from their customer base, find the mean and standard error of the sampling distribution of the restaurant's sample mean expense per customer.
B. Find the probability that the restaurant makes a profit that day, with the sample mean expense being
less than $8.95.
Answer:
Step-by-step explanation:
From the given question;
Given that:
Jan's All You Can Eat Restaurant charges $9.10 per customer to eat at the restaurant.
Distribution is skewed and and has a mean of $8.10 and a standard deviation of $4.
A. If the 100 customers on a day have the characteristics of the random sample from their customer base, find the mean and standard error of the sampling distribution of the restaurant's sample mean expense per customer.
the mean by using the central limit theorem is 8.10
the standard error of the sampling distribution = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]
the standard error of the sampling distribution = [tex]\dfrac{4}{\sqrt{100}}[/tex]
= 4/10
= 0.4
B.
P(X > $8.95) = P (Z > 8.95 - 8.10/0.4)
P(X > $8.95) = P (Z > 2.1)
P(X > $8.95) = 1 - P (Z < 2.1)
P(X > $8.95) = 1 - 0.9821
P(X > $8.95) = 0.0179
if a-2= (2^2/3+2^1/3) find a^3-6a^2+12a-14
Answer:
Step-by-step explanation:
7. 1, for r = 0 - 1, for r = 1 Hence, determine alo. Using characteristic root ... find the solution of the recurrence relation y, + 9 y, 2 = 6y, 1, subjected to the ... Solve a, -5a, 1 + 6a, 2 = 0 , given initial conditions ao = 2 and a1 = 5. ... Solve the recurrence relation a, – 7a, 1 + 16a, 2 – 12a, 3 = 0 for n > 3 with ... 2"; 3. a = (2)” – n.
Answer:
2
Step-by-step explanation:
I solved in the picture
Hope this helps ^-^
Please answer this correctly
Answer:
Area of the figure = 169.5 yards²
Step-by-step explanation:
Area of Rectangle = Length × Width
Area of triangle = 1/2(base × height)
We'll divide the whole figure into parts so that we can find the area more easily!
Rectangle 1 (uppermost):
10 × 4 = 40 yards²
Square 1 (right below the rectangle 1):
7 × 7 = 49 yards²
Rectangle 2 (with square 1):
7 × 3 = 21 yards²
Triangle 1 (Below rectangle 2):
1/2(17 × 7) = 119/2 = 59.5 yards²
Now adding up all to get the area of the whole figure:
Area of the figure = 40 + 49 + 21 + 59.5
Area of the figure = 169.5 yards²
Use z scores to compare the given values. The tallest living man at one time had a height of 252 cm. The shortest living man at that time had a height of 79.2 cm. Heights of men at that time had a mean of 176.74 cm and a standard deviation of 8.06 cm. Which of these two men had the height that was moreâ extreme?
Answer:
The more extreme height was the case for the shortest living man at that time (12.1017 standard deviation units below the population's mean) compare with the tallest living man (at that time) that was 9.3374 standard deviation units above the population's mean.
Step-by-step explanation:
To answer this question, we need to use standardized values, and we can obtain them using the formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
x is the raw score we want to standardize.[tex] \\ \mu[/tex] is the population's mean.[tex] \\ \sigma[/tex] is the population standard deviation.A z-score "tells us" the distance from [tex] \\ \mu[/tex] in standard deviation units, and a positive value indicates that the raw score is above the mean and a negative that the raw score is below the mean.
In a normal distribution, the more extreme values are those with bigger z-scores, above and below the mean. We also need to remember that the normal distribution is symmetrical.
Heights of men at that time had:
[tex] \\ \mu = 176.74[/tex] cm.[tex] \\ \sigma = 8.06[/tex] cmLet us see the z-score for each case:
Case 1: The tallest living man at that time
The tallest man had a height of 252 cm.
Using [1], we have (without using units):
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{252 - 176.74}{8.06}[/tex]
[tex] \\ z = \frac{75.26}{8.06}[/tex]
[tex] \\ z = 9.3374[/tex]
That is, the tallest living man was 9.3374 standard deviation units above the population's mean.
Case 2: The shortest living man at that time
The shortest man had a height of 79.2 cm.
Following the same procedure as before, we have:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{79.2 - 176.74}{8.06}[/tex]
[tex] \\ z = \frac{-97.54}{8.06}[/tex]
[tex] \\ z = -12.1017[/tex]
That is, the shortest living man was 12.1017 standard deviation units below the population's mean (because of the negative value for the standardized value.)
The normal distribution is symmetrical (as we previously told). The height for the shortest man was at the other extreme of the normal distribution in [tex] \\ 12.1017 - 9.3374 = 2.7643[/tex] standard deviation units more than the tallest man.
Then, the more extreme height was the case for the shortest living man (12.1017 standard deviation units below the population's mean) compare with the tallest man that was 9.3374 standard deviation units above the population's mean.
The author purchased a slot machine (Bally Model 809) and tested it by playing it 1197 times. There are 10 different categories of outcomes, including no win, win jackpot, win with three bells, and so on. When testing the claim that the observed outcomes agree with the expected frequencies, the author obtained a test statistic of x^2 = 8.185 . Use α= 0.05 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as expected?
Answer:
No the slot machine doesn't appear to function as expected.
Step-by-step explanation:
From chi-squared table , for 9 degrees of freedom and alpha 0.05,
critical value is, 3.325.
Since observed value is greater than critical value we can say that actual outcomes do not agree with the expected frequencies. The slot machine doesn't appear to function as expected.
If you vertically stretch the exponential function f(x)=2x by a factor of 3, what is the equation of the new function
Answer:
g(X)=3(2^x)
Step-by-step explanation: