Answer:
The total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.
Step-by-step explanation:
Key points:
Discount is subtracted from the regular price of an item.Sales tax is added to the regular price of an item.It is provided that the customers receive a 10% discount if they are members and all customers must pay 7% in sales tax.
Two functions are provided are:
f (x) = 0.90x ; the price of an item after the 10% member discount
g (x) = 1.07x ; the total amount customers pay for a purchase after sales tax is applied.
Compute the total amount a member pays for an item with a regular price of x dollars as follows:
T (x) = Discount × Sales Tax
= 0.90 × 1.07 × x
= 0.963x.
Thus, the total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.
In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 s
370 calories by drinking 2 servings of juice and 1 serving of milk. Marian
of milk and 1 soda. Using matrices to solve, how many calories are in
Answer:
B. 110
Step-by-step explanation:
In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?
A. 90
B. 110
C. 130
D. 180
Answer:
Let x represent the amount of calories in 1 servings of juice, y represent the amount of calories in 1 servings of milk and z represent the amount of calories in 1 servings of Soda.
Joe consumption can be represented by:
x + 2y + z = 530 (1)
Darius consumption can be represented by:
2x + y = 370 (2)
Marian consumption can be represented by:
3y + z = 510 (3)
The equations can be represented in matrix form as:
[tex]\left[\begin{array}{ccc}1&2&1\\2&1&0\\0&3&1\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}530\\370\\510\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&2&1\\2&1&0\\0&3&1\end{array}\right] ^{-1}\left[\begin{array}{c}530\\370\\510\end{array}\right] \\\\\\[/tex]
[tex]\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0.33&0.33&-0.33\\-0.67&0.33&0.67\\2&-1&-1\end{array}\right]\left[\begin{array}{c}530\\370\\510\end{array}\right]\\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right]=\left[\begin{array}{c}130\\110\\180\end{array}\right][/tex]
The amount of calories in one serving of milk is 110 calories
350 - 15x = 200 - 10x
Sam’s Jet Ski rental charges $350 to rent a jetski plus $15 per hour. Brian’s Jet Ski rental charges $200 to rent a jetski plus $10 per hour
Steven has an account with $350 in it and he withdrawals $15 per day. Jessica has an account with $200 and withdrawals $10 per day.
Water tank A has 350 gallons of water and is losing 10 gallons per minute. Water tank B has 200 gallons of water and is losing 15 gallons per minute
Tree A has a height of 350 centimeters and is growing at a rate of 15 cm per day. Tree B has a height of 200 centimeters and is growing at a rate of 10 centimeters per day
Answer
Steven has an account with $350 in it and he withdrawals $15 per day. Jessica has an account with $200 and withdrawals $10 per day.
Find f'(-2) if f(x) = x^4/5 - 7x.
f'(-2) = ?
(Simplify your answer. Type an integer or a fraction.)
Answer:
15.74
Step-by-step explanation:
[tex] {x}^{ \frac{4}{5} } - 7x[/tex]
Substitute - 2 for x.
[tex] { (- 2)}^{ \frac{4}{5} } - 7( - 2)[/tex]
[tex] \sqrt[ 5]{ { (- 2) }^{4} } - 7( - 2)[/tex]
[tex]1.74 + 14[/tex]
[tex]15.74[/tex]
(I rounded to the nearest hundredth).
each friend received 5/4 of a pound of berries, how many friends are sharing berries?
Answer:
2
Step-by-step explanation:
If 5 friends are sharing the berries, how many pounds of berries does each friend receive? Is the answer to 3/4 divided by 2/5 greater than or less than 1.
Which table of values does not represent a linear function
Answer: B.
I think that it is probably too late but it is table (B.)
Step-by-step explanation:
It is a proportional relationship becuase In table B. The y section goes up by .5 each time
Answer:
C does not represent a linear function.
Step-by-step explanation:
C is the only one that has a different rate of change. If you find the rate of change between the top two, the bottom two's rate of change will be different. For a function to be linear, it has to have a constant rate of change. C does not, therefore, C is the answer.
Hope this helps! Please vote me as Brainliest. Let me know if you need more of an explanation. Remember, cheating is never the answer. Try your best before you seek answers. Good luck with whatever you are doing! Have an amazing day!
The quotient of q and 14 is less than 28
Answer:
q<392
Step-by-step explanation:
First, we turn words into an inequality. Then, we solve for q.
[tex]\frac{q}{14} <28\\q<28*14\\q<392[/tex]
It is also a good idea to check our answer, to make sure it is reasonable and we did not make a careless mistake.
[tex]3<392\\\frac{3}{14} <28[/tex]
The value satisfies the equation, so this should be correct.
Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric paintings and drawings on walls and ceilings of a cave in Lascaux, France. Use the information in Example 3 of Section 3.1 to determine the appropriate age of a piece of burned wood, if it was found that 88% of the C-14 found in living trees of the same type had decayed. (Round your answer to the nearest hundred years.) years
Answer:
The age of the wood is [tex] t = 17527.5 \ years [/tex]
Step-by-step explanation:
From the question we are told that 88% of of the C-14 found in living trees of the same type had decayed , this means that the proportion of C-14 that is remaining is mathematically evaluated as
[tex] 1 - 0.88 = 0.12[/tex]
Hence
[tex] N = 0.12N_o[/tex]
Here N represents the remaining C-14 while [tex]N_o[/tex] is the original amount of C-14
Generally the half life of C-14 is [tex]h = 5730 \ years[/tex]
Generally from the formula of radioactive decay
[tex]N = N_o * 2^{-\frac{t}{h} }[/tex]
=> [tex]0.12N_o = N_o * 2^{-\frac{t}{5730} }[/tex]
=> [tex]0.12 = 2^{-\frac{t}{5730} }[/tex]
taking the natural log of both sides
=> [tex] ln [0.12] = ln[ 2^{-\frac{t}{5730} }][/tex]
=> [tex] ln [0.12] = -\frac{t}{5730}ln(2) [/tex]
=> [tex] t = 17527.5 \ years [/tex]
The appropriate age of burned wood will be "17527.5 years".
Radioactive decayAccording to the question,
The proportion of C-14 = 1 - 0.88
= 0.12
then,
N = 0.12 N₀
Now,
The half-life of C-14 will be:
h = 5730 years
By using Radioactive decay formula, we get
→ N = N₀ × [tex](2)^{-\frac{t}{h} }[/tex]
By substituting the values,
0.12N₀ = N₀ × [tex](2)^{-\frac{t}{5730} }[/tex]
0.12 = [tex]2^{-\frac{t}{5730} }[/tex]
By taking "log" both sides,
ln[0.12] = ln[[tex]2^{-\frac{t}{5730} }[/tex]]
ln[0.12] = -[tex]\frac{t}{5730 \ ln(2)}[/tex]
hence,
The age will be:
t = 17527.5 years
Thus the above response is correct.
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Candice is preparing for her final exam in Statistics. She knows she needs an 65 out of 100 to earn an A overall in the course. Her instructor provided the following information to the students. On the final, 200 students have taken it with a mean score of 57 and a standard deviation of 6. Assume the distribution of scores is bell-shaped. Calculate to see if a score of 65 is within one standard deviation of the mean.
Answer:
a. 72
b. 816
c. 570
d. 30
Step-by-step explanation:
Given the graph is a bell - shaped curve. So, we understand that this is a normal distribution and that the bell - shaped curve is a symmetric curve.
Please refer the figure for a better understanding.
a. In a normal distribution, Mean = Median = Mode
Therefore, Median = Mean = 72
b. We have to know that 68% of the values are within the first standard deviation of the mean.
i.e., 68% values are between Mean Standard Deviation (SD).
Scores between 63 and 81 :
Note that 72 - 9 = 63 and
72 + 9 = 81
This implies scores between 63 and 81 constitute 68% of the values, 34% each, since the curve is symmetric.
Now, Scores between 63 and 81 =
= 68 X 12 = 816.
That means 816 students have scored between 63 and 81.
c. We have to know that 95% of the values lie between second Standard Deviation of the mean.
i.e., 95% values are between Mean 2(SD).
Note that 90 = 72 + 2(9) = 72 + 18
Also, 54 = 63 - 18.
Scores between 54 and 90 totally constitute 95% of the values. So, Scores between 72 and 90 should amount to of the values.
Therefore, Scores between 72 and 90 =
= 570.
That is a total of 570 students scored between 72 and 90.
d. We have to know that 5 % of the values lie on the thirst standard Deviation of the mean.
In this case, 5 % of the values lie between below 54 and above 90.
Since, we are asked to find scores below 54. It should be 2.5% of the values.
So, Scores below 54 =
= 2.5 X 12 = 30.
That is, 30 students have scored below 54.
Step-by-step explanation:
It is found that score of 62 is not within one standard deviation of the mean.
What is z - score?The Z-score measures how many standard deviations the measure is from the mean. If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have [tex]X \sim N(\mu, \sigma)[/tex]then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
In a set with mean and standard deviation, the z- score of a measure X is given by:
[tex]Z = \dfrac{X - \mu}{\sigma},[/tex]
Z-score, we look at the z-score table and find the p-value associated with this z-score.
Given that Mean score of 54 and a standard deviation of 6.
This means to see if a score of 62 is within one standard deviation of the mean.
Is Z between -1 and 1 when X = 62.
[tex]Z = \dfrac{X - \mu}{\sigma},\\Z = \dfrac{62 - 54}{6},[/tex]
Z = 1.33
Therefore, It is found that score of 62 is not within one standard deviation of the mean.
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The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 1100 voters in the town and found that 54% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than 50%. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
The p-value is [tex]p-value = 0.0039854[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 1100
The population proportion is p = 0.50
The sample proportion is [tex]\^ p = 0.54[/tex]
The null hypothesis is [tex]H_o : p = 0.50[/tex]
The alternative hypothesis is [tex]H_a : p > 0.50[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^ p - p }{ \sqrt{\frac{ p(1 - p)}{n} } }[/tex]
=> [tex]z = \frac{ 0.54 - 0.54 }{ \sqrt{\frac{ 0.50 (1 - 0.50)}{1100} } }[/tex]
=> [tex]z = 2.6533[/tex]
Generally from the z-table the probability of 2.6533 for a right tailed test is
[tex]p-value = 0.0039854[/tex]
2. How many coefficients are in the expression 3,2 – 18y + 2y??
Answer:
2
Step-by-step explanation:
A coefficient is a number that is usually place before a variable to multiply it with.
Given expression:
3.2 - 18y + 2y
The variable in this problem is y;
So, the coefficients are:
-18 and +2
We have two coefficients.
Expand the following expression 3(4−5x)
Answer:
12-15x
Step-by-step explanation:
3 × 4=12
3 × -5x=-15x
12 - 15x
The distribution of speeds on a particular highway has a mean of 60 mph with a standard deviation of 10 mph. The distribution of speeds is NOT known to be bell-shaped. Use the scenario to answer the next 3 questions.
At least what percentage of cars is traveling between 40 and 80 mph?
At least what percentage of cars is traveling between 20 and 100 mph?
If a sample of 40 cars is selected at random, estimate the number of cars that are traveling between 40 and 80 mph.
Answer:
a) At least what percentage of cars is traveling between 40 and 80 mph?
75%
b) At least what percentage of cars is traveling between 20 and 100 mph?
93.75%
c) If a sample of 40 cars is selected at random, estimate the number of cars that are traveling between 40 and 80 mph.
30 cars.
Step-by-step explanation:
We apply Chebyshev's Theorem
This states that:
1) At least 3/4 (75%) of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
2) At least 8/9 (88.89%) of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
3) At least 15/16 (93.75%) of data falls within 4 standard deviations from the mean - between μ - 4σ and μ + 4σ.
From the question, we have:
Mean of 60 mph
Standard deviation of 10 mph.
a) At least what percentage of cars is traveling between 40 and 80 mph?
Applying:
Applying the first rule: At least 3/4 (75%) of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
μ – 2σ
60 - 2(10)
60 - 20
= 40 mph
μ + 2σ.
60 + 2(10)
60 + 20
= 80 mph
Hence, at least 75% of cars is traveling between 40 and 80 mph.
b) At least what percentage of cars is traveling between 20 and 100 mph?
At least 15/6 (93.75%) of data falls within 4 standard deviations from the mean - between μ – 4σ and μ + 4σ.
μ – 4σ
60 - 4(10)
60 - 40
= 20 mph
μ + 4σ.
60 + 4(10)
60 + 40
= 100 mph
Hence, at least 93.75% of cars is traveling between 40 and 80 mph.
c) If a sample of 40 cars is selected at random, estimate the number of cars that are traveling between 40 and 80 mph.
Since we know from question a) that
at least 75% of cars is traveling between 40 and 80 mph.
Given a sample of 40 cars:
75% of 40 cars
= 75/100 × 40
= 30 cars.
The number of cars that are traveling between 40 and 80 mph is 30 cars.
To visit the top of the Empire State building , a ticket in 1999 cost four dollars , in 2019 the same ticket cost $32 ,what was the percentage change in the cost of the ticket ?
Answer:
700%
Step-by-step explanation:
The formula to find the percentage is found below =
[tex]\frac{changeinvalue}{absolutevalueoftheoriginalvalue} * 100[/tex]
So to find the change in value, we must subtract 32 from 4, which gets us -28.
We know the og value already, 4 dollars.
So do the division
[tex]\frac{-28}{4} =-7[/tex]
Now the multiplcation,
-7 * 100
-700
700%
josh has $300 in his savings account. his account earns 2% interest each month
Answer:
$6 dollars i guess
Step-by-step explanation:
Communities A, B and C are faced with water problem. The distance between communities A and B is 5km and that of A and C is 7km, the angle between the path AB and AC is 45 degrees. If a well a well is to dug for the communities, indicate by way of sketching exact place to dig the well
Answer:
3.5 km between communities AC
Step-by-step explanation:
The idea is to find a common position for all the communities to locate the well
Kindly find attached a rough sketch of the problem for your reference.
Given that
AB=5km
AC=7km
From the diagram we can see that for all three communities to travel equal distance to the common well, the well has to be situated at 3.5km between communities AC.
Also, from the diagram the location of well is the intersection between the diagonals of the rectangular shape.
what is the slope of the line that contains these points x=12,13,14,15 y=-4,2,8,14
Answer:
6
Step-by-step explanation:
Fid the difference in the y-coordinates of any two points. This is the rise.
Then find the difference in the corresponding x-coordinates of the same points. This is the run.
slope = rise/run
Let's use x = 12, x = 15, and y = -4, y = 14.
rise = -4 - 14 = -18
run = 12 - 15 = -3
slope = rise/run = -18/(-3) = 6
Answer: slope = 6
4(7 + 8m)=8(-1 + 4m)
Answer:
There is no solution
Step-by-step explanation:
Let's use distributive property to solve this equation.
4(7+8m) = 8(-1+4m)
28+32m = -8+32m
-32m -32m
28= -8
There is no solution
Hope this helps!
Does anyone stan Twice??
Answer:
This is literally me.
Step-by-step explanation:
A large bag of cashews weighs 9 1/4 pounds. One serving is 1/5 pound. How many servings are in the bag.
Answer as a mixed number = 46 & 1/4
Answer as a decimal = 46.25
===============================================
Work Shown:
9 & 1/4 = 9 + 1/4 = 9 + 0.25 = 9.25
1/5 = 0.2
A bag of cashews weighs 9.25 pounds and one serving is 0.2 pounds.
Let x be the number of servings
1 serving = 0.2 pounds
x servings = 0.2x pounds after multiplying both sides by x
0.2x pounds represents the total bag's weight so,
0.2x = 9.25
x = 9.25/0.2
x = 46.25 answer in decimal form
x = 46 + 0.25
x = 46 + 1/4
x = 46 & 1/4 answer in mixed number form
This means we have 46 full servings plus an additional 1/4 of a serving.
Ronald has a 10% solution of the fertilizer Super Grow. How much pure Super Grow should he add to the mixture to get 36 oz of a 12.5% concentration?
Answer:
1 oz
Step-by-step explanation:
Given that:
% solution of super grow fertilizer = 10%
To obtain mixture of 36oz of a 12.5% concentration
Let oz of pure supergrowth to be added = s
(Initial % * (36 - s) + s) / 36 = target concentration
(10% * (36 - s) + s) / 36 = 12.5%
(0.1(36 - s) + s) / 36 = 0.125
Cross multiply:
0.1(36 - s) + s =. 0.125 * 36
3.6 - 0.1s + s = 4.5
3.6 + 0.9s = 4.5
0.9s = 4.5 - 3.6
0.9s = 0.9
s =. 0.9/0.9
s = 1
Hence, 1 oz of pure supergrowth should be added to the 10% solution to get 36 oz of a 12.5% concentration.
what are the partial products of 9 x 813
Answer:
813
* 9. 9*800= 7200
9*10. =90
7200
90. 9*3. =27
27
7317
The partial product is 7317.
What is partial product?The partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place. (So, the 2 in 23 would actually be 20.)
Given:
9 x 813
Now, breaking the number according to their place value.
So, 813
=(800 + 10 +3)
Then the partial product will be written as
=9 * (800 + 10 +3)
=9* 800+ 9*10 + 9*3
=7200 + 90 + 27
= 7317
Hence, the partial product is 7317.
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There are 8 fluid ounces in one cup.
Write this as a unit rate.
Hint: use per, every, or each.
Answer:
8
Step-by-step explanation:
How many groups of 5 are 35?
I need answer stat!
Answer:
Step-by-step explanation:
7
Answer:
There are 7 groups of 5 in 35.
2.) You need a carpet installed in your living room. You reach out to 2 different companies
for installation pricing. Lowes charges $ 2 a square foot and $60 to bring the
materials. Home Depot Charges $1.50 a square foot and $ 80 to bring the materials.
If your living room is 100 square feet, which company would you use?
Answer:
Home Depot
Step-by-step explanation:
Home Depot Has better charges because you have to multiply the question to see which one is lower.
Point E is located at -1p on the number line, Point F is located at 9 on the number line.
What is the distance between Point E and Point F on the number line? Enter the answer in the box. PLS HELP MEEEE
Answer:
-1 p will be a ok answer please with
The weights of baby tortoises are approximately Normal with a mean of 25.6 ounces and a standard deviation of 2.3 ounces. What proportion of baby tortoises weigh between 25 and 30 ounces?
592344435555544433234555
Which of the following is not equal to the rational number 7/4
Answer:
2
Step-by-step explanation:
What is 9,200 equal in hundreds
The capacity of a dump truck is listed by the manufacturer as 10 yd3 . A construction site requires the removal of of dirt, and the contractor has four identical trucks. How many trips will each need to make
Question:
The capacity of a dump truck is listed by the manufacturer as 10 yd^3. A construction site requires the removal of 200 m^3 of dirt, and the contractor has three identical trucks. How many trips will each need to make?
Answer:
7 trips
Step-by-step explanation:
Given
[tex]Capacity = 10yd^3[/tex]
[tex]Dirts = 200m^3[/tex]
[tex]Trucks = 4[/tex]
Required
Determine the number of trips of each truck
Divide the volume of dirts by 4 to get the portion of each truck
[tex]Each\ Truck = \frac{200m^3}{4}[/tex]
[tex]Each\ Truck = 50m^3[/tex]
Divide the portion of each truck by capacity of each truck to get the number of trip
[tex]Trip = \frac{50m^3}{10yd^3}[/tex]
Convert m^3 to yd^3
[tex]Trip = \frac{50 * 1.30795yd^3}{10yd^3}[/tex]
[tex]Trip = \frac{65.3975yd^3}{10yd^3}[/tex]
[tex]Trip = \frac{65.3975}{10}[/tex]
[tex]Trip = 6.53975[/tex]
Approximate:
[tex]Trip = 7[/tex]
The figure is composed of a rectangular prism and a triangular prism. Find the volume of the figure.
14 in.
32 in.
14 in.
9 in.
The volume of the figure is
in?
Answer:
either 4032 or 56448
Step-by-step explanation:
you have to multiply length times height times width.
