Answer:
855+135=990
90x11=990
10x11=110
25x11=275
110+275=385 990+110=1100
385+1100=1485
1485/11=135
the math books was $11 each so all to gether it is $275.
the english books was $65 each so all to gether it is 715.
275+715=990
Step-by-step explanation:
The required price of a Mathematics book is $27 and the price of an English book is $18.
What is the equation model?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Let's assume that the price of a Mathematics book is x dollars and the price of an English book is y dollars. Then we can form two equations based on the given information:
Equation 1: 25x + 10y = 855
This equation represents the total amount earned by selling 25 Mathematics books and 10 English books for $855.
Equation 2: 10x + 40y = 990
This equation represents the total amount that would have been earned by selling 10 Mathematics books and 40 English books for $135 more than the original total.
To solve for x and y, we can use elimination or substitution. Let's use elimination:
Multiplying Equation 1 by 4, we get:
100x + 40y = 3420
Now, we can subtract Equation 2 from this equation to eliminate y:
90x = 2430
x = 27
Substituting x = 27 into Equation 1, we can solve for y:
25(27) + 10y = 855
675 + 10y = 855
10y = 180
y = 18
Therefore, the price of a Mathematics book is $27 and the price of an English book is $18.
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A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalent. The class has suggested four different methods. Which describes the correct method? Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Answer:
Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
Step-by-step explanation:
its B
Option (D) both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent is the correct answer.
What is a word problem?
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The expressions are [tex]4x-x+5 , 8-3x-3[/tex]
If the expressions are equivalent then,
⇒ [tex]4x-x+5 = 8-3x-3[/tex]
⇒ [tex]3x+5=-3x+5[/tex]
In both the sides the x has different values.
So, Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Hence we can conclude that option (D) both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent is the correct answer.
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I need help with these questions
9514 1404 393
Answer:
17. 25 mile per gallon
18. Eduardo did should have divided by -4.
Step-by-step explanation:
17. The least mileage will be had when the most gas is used to go a given distance. For the given distance, the most gas that could have been used (without adding any) is 18 gallons. Then the least mileage is ...
(450 mi)/(18 gal) = 25 mi/gal
__
18. The appropriate method for solving this inequality is ...
-4x/(-4) < 120/(-4) . . . . divide both sides by -4 (and reverse the > symbol)
x < -30
The step Eduardo took of adding 4 will give ...
-4x +4 > 124 . . . . . puts him one step farther away from a solution
Eduardo chose an operation to perform that did not get him closer to a solution.
a certain number plus two is five find the number
x=3
Step-by-step explanation:
x+2=5
x=5-2
x=3
The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are
Answer:
The answer is "[tex]H_0:\mu \geq 50.1\ \ and \ \ H_0: \mu \geq 50.1[/tex]"
Step-by-step explanation:
An initial random selection of mail-order physicians representing firm A worked an average of 50.1 hours per week. My goal is to reject the Null Hypothesis since it is employed to make no difference. In this case,[tex]H_0 =\mu \geq50.1[/tex]
Medical insurance changes are attributed to reducing the average workweek. New medical coverage is claimed to be have reduced your average workday after the government change. [tex]H_1: \mu <50.1[/tex]
What is the solution to this system of equations?
a - b + c = -6
b - c = 5
2a - 2c = 4
A) 2
B) -1
C) -3
D) 1
(-1;2;-3)
а, b, c
~~~~~~
P is inversely proportional DY. IF P=1.2=when y=100, calculate
a the value of p when y=4
b the value of y when p=3
Answer:
a. P = 30
b. Y = 40
Step-by-step explanation:
Given the following data;
P = 1.2
Y = 100
First of all, we would have to determine the constant of proportionality;
P = k/Y (inverse proportion or relationship)
1.2 = k/100
k = 1.2 * 100
k = 120
a. To find the value of p when y = 4;
P = k/Y
P = 120/4
P = 30
b. To find the value of y when p = 3;
P = k/Y
Y = k/P
Y = 120/3
Y = 40
muscle max gym charges a $30 fee to join plus $2 each day that you go workout. Capital cross-fit charges $10 to join and $4 each day you use the gym. After how many days of workouts would the two gyms have cost you the same amount of money?
Set up equations for each gym.
multiply daily cost by number of days(x) and add the fee:
Muscle max: 2x + 30
Capital: 4x + 10
Now set them
Equal to each other and solve for x:
2x + 30 = 4x + 10
Subtract 2x from both sides :
30 = 2x + 10
Subtract 10 from both sides :
20 = 2x
Divide both sides by 2:
X = 10
It will take 10 days
Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] $ y = e^{{\color{red}5}\sqrt{x}} $
Answer:
The answer is "[tex]\frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]".
Step-by-step explanation:
Given:
[tex]y = e^{{\color{\red}5}\sqrt{x}}[/tex]
let
[tex]\to t= 5\sqrt{x}\\\\\frac{dt}{dx}= 5 \frac{1}{2\sqrt{x}}\\\\\frac{dt}{dx}= \frac{5}{2\sqrt{x}}\\\\[/tex]
and
[tex]\to y=e^t\\\\\to \frac{dy}{dt}=e^t\\[/tex]
[tex]\to \frac{dy}{dt}=e^{5\sqrt{x} }\\[/tex]
So,
[tex]\to \frac{dy}{dx}= \frac{dy}{dt} \times \frac{dt}{dx}[/tex]
[tex]=e^{5\sqrt{x} }\times \frac{5}{2\sqrt{x}}\\\\= \frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]
OR
[tex]\to g(x) = 5\sqrt{x} \\\\\to f(x) = e^{(x)}\\\\[/tex]
Derivate:
[tex]\to f''g' = \frac{e^{(5\sqrt{x})}5}{(2\sqrt{x})}[/tex]
-2y^2 - (y^2 + y) answer please
Answer:
The answer is −3y^2−y.
Steps:
Distribute the Negative Sign:
=−2y2+−1(y2+y)
=−2y2+−1y2+−1y
=−2y2+−y2+−y
Combine Like Terms:
=−2y2+−y2+−y
=(−2y2+−y2)+(−y)
=−3y2+−y
Answer:
-3y^2 - y
Step-by-step explanation:
-2y^2 - (y^2 + y)
Find the opposite of y^2 + y, so distribute the negative sign to the values inside the parentheses to get:
−2y^2 −y^2 − y
Then combine like terms to get:
-3y^2 - y
i need help on this PLS
I REALLY HOPE THIS HELPS! I’m sorry if this was wrong but I really believe it’s true.
Answer:
The value of P is $6.75.
Step-by-step explanation:
In the diagram to the left, we see 6 apples, and are labeled that the price is $4.50.
If the prices are proportional, that may mean that each apple has the same price. To find the price of apples in the diagram to the right, divide the total price by 6:
4.50/6 = 0.75
So the price per apple is 0.75.
As seen on the diagram, P represents the total price of 9 apples.
Multiply the price per apple by 9:
0.75 x 9 = 6.75
So the value of P is $6.75
Which of the following has the least value?
30% of 50
O 50% of 30
30% of 30
50% of 50
Answer:
30% of 30 has the least value out of all answer choices.
Step-by-step explanation:
Solve for the values of the given percentages of each number:
30% of 50:
Divide 50 by 100 to get 1%
50/100 = 0.5
Multiply 1% (0.5) by 50:
0.5 x 50 = 15
So 30% of 50 = 15
50 % of 30:
50% of a number means half of it since 50% is half of 100% so:
30/2 = 15
So 50% of 30 = 15
30% of 30:
Divide 30 by 100 to get 1%:
30/100 = 0.3
Multiply 1% (0.3) by 30:
0.3 x 30 = 9
So 30% of 30 = 9
50% of 50
50% of a number means half of it since 50% is half of 100% so:
50/2 = 25
So 50% of 50 = 25
Let’s arrange all of the values from greatest to least (left to right) to determine the most least value:
25, 15, 15, 9
9 is the most least, it is the value equal to the answer choice “30% of 30”
HOPE THIS HELPED!
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x – 9y = -72
the slope-intercept form of the given equation is y = x/3 + 8.
What is the slope?The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. The coordinate plane describes the slope of the line.
The slope-intercept form of a line is Y = m*X +C.
Given an equation 3x-9y = -72, which we will try to make in the slope-intercept form by using simplification.
3x-9y = -72
9y = 3x + 72
y = 1/3 * x + 8
Therefore y = x/3 + 8 is the slope-intercept form of the given equation. where its slope is 1/3.
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A number increased by a% and decreased by 80% is 400. What is the number?
Answer:
[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]
updated response , given that you confirmed the question....
if the percent is the variable a% then ....
[tex]x*(\frac{a+100}{100}) = 2000[/tex]
[tex]x = \frac{2000 }{(\frac{a+100}{100})}[/tex]
I think that there is missing information here ....
you can make any number work here the result of the number being increased by the percent has to be 2000...
so if if the number is 1000 then the percent would be 100%
if you make the number 1500 then the percent would be 33 1/3 %
Step-by-step explanation:
The number is [tex]\frac{2000}{(1+\frac{a}{100})}[/tex]
What will be the new number when the original number is increased by a% and decreased by 80%?Let us assume that the number be x.
When the number x is increased by a% the new number will be,
[tex]x(1+\frac{a}{100})[/tex]
Now, this number is decreased by 80%. So, the new number will be,
[tex]x(1+\frac{a}{100})*(1-\frac{80}{100} )\\=x(1+\frac{a}{100})*(1-0.8 )\\=x(1+\frac{a}{100})*0.20[/tex]
By the given condition,
When x increased by a% and decreased by 80% it becomes 400
Therefore, we can write
[tex]x(1+\frac{a}{100})*0.20=400[/tex]
[tex]x(1+\frac{a}{100})=\frac{400}{0.20}[/tex]
[tex]x(1+\frac{a}{100})=2000[/tex]
[tex]x=\frac{2000}{(1+\frac{a}{100})}[/tex]
So, the number will be [tex]\frac{2000}{(1+\frac{a}{100})}[/tex].
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6. Find the missing side. Round to the nearest tenth.
Answer:
31.9617 rounded to 32
Step-by-step explanation:
set up is sin24=13/x
A student found the solution below for the given inequality.Which of the following explains whether the student is correct?The student is completely correct because the student correctly wrote and solved the compound inequality.The student is partially correct because only one part of the compound inequality is written correctly.The student is partially correct because the student should have written the statements using “or” instead of “and.”The student is completely incorrect because there is “ no solution “ to this inequality.
Answer:
The student is completely incorrect because there is no solution to this inequality.
Answer:
D on edge
Step-by-step explanation:
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answer:
3.2 hours
Step-by-step explanation:
12 workers * 4 hours = 48 worker hours
15 workers * x hours = 48 worker hours
48 /15 =3.2 hours
Answer:
3 hours and 12 minutes.
Step-by-step explanation:
12 Workers complete a job in 4 hours
1 worker complete a job 12 × 4 = 48
15 workers complete a job = 48/15 = 3³/¹⁵ = 3¹/⁵
= 3 hours + 1/5 × 60 minutes = 3 hours 12 minutes.
5√48-4√27-2√108+√147
Answer:
[tex]3\sqrt{3}[/tex]
Step-by-step explanation:
Complete the Similarity statement below only if the triangles are similar.
Which table represents a linear function?
Answer:
C
Step-by-step explanation:
C is the only function that have a consistent decrease while A is a trigonometric function, B is a non linear function, D is an exponential function
What is the shape of the cross section?
Answer:
Step-by-step explanation:
Triangular cross-section.
Answer:
it is a triangle cross-section
hope this answer helps you
Plz make me a brainlist
Becky Anderson must pay a lump sum of $6000 in 5 yr. If only $5000 is available to deposit right now, what annual interest rate is necessary for the money to increase to $6000 in 5 yr?
Hello!
Out equation is: [tex]A=P(1+\frac{r}{n} )^t^n[/tex]
A= 6000
P=5000
N=1
T=5
R= What we are trying to find
This means we will have [tex]6000=5000(1+r)^5[/tex]
Divide both sides by 5000:
[tex]\frac{6000}{5000} = (1+r)^5[/tex]
Move the power to the other side by rooting both sides:
[tex]\frac{6000}{5000} ^1^/^5 = 1+r[/tex]
Subtract 1 from both sides:
[tex]\frac{6000}{5000} ^1^/^5 -1 = r[/tex]
Now we just need to calculate: R = 0.03713728...
I don't know how many decimal places you can have, but I will round to 2. This will give you an Interest Rate of 3.71%.
I hope this helps! :)
A box of tickets has an average of 420; the SD is 84. If we draw at random (with replacement) 50 times and compute the average of the draws, the expected value of the average of the draws equals 420 and the standard error of the average of the draws equals ____. (Enter correct to two decimal places.)
Answer:
Average of the draws equals 420
Standard Error = 11.88
Step-by-step explanation:
Given
[tex]\mu = 420[/tex]
[tex]\sigma = 84[/tex]
[tex]n =50[/tex]
Solving (a): The average of the draws
This implies that we calculate the sample mean
This is calculated as:
[tex]\bar x = \mu[/tex] --- Sample Mean = Population Mean
So, we have:
[tex]\bar x = 420[/tex]
Solving (b): The standard error
This is calculated as:
[tex]SE=\frac{\sigma}{\sqrt n}[/tex]
So, we have:
[tex]SE=\frac{84}{\sqrt {50}}[/tex]
Using the calculator, we have:
[tex]SE=11.88[/tex]
There are 11 students on a committee. To decide which 4 of these students will attend a conference, 4 names are chosen at random by pulling names one at a time from a hat. What is the probability that Sarah, Jamal, Kate, and Mai are chosen in any order
Answer:
0.003 = 0.3% probability that Sarah, Jamal, Kate, and Mai are chosen in any order.
Step-by-step explanation:
The students are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
11 students means that [tex]N = 11[/tex]
4 are Sarah, Jamal, Kate, and Mai, so [tex]k = 4[/tex]
4 are chosen, which means that [tex]n = 4[/tex]
What is the probability that Sarah, Jamal, Kate, and Mai are chosen in any order?
This is P(X = 4). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 4) = h(4,11,4,4) = \frac{C_{4,4}*C_{7,0}}{C_{11,4}} = 0.003[/tex]
0.003 = 0.3% probability that Sarah, Jamal, Kate, and Mai are chosen in any order.
Find the slope of the line that goes through the
(2,6) and (-1, -6)
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:Mark Brainliest please
Answer is 4.86 which is rounded to 5
Step-by-step explanation:
Cos 40 degree = VW/7
0.694 =VW/7
0.694 * 7 =VW
4.858 =VW
VW=4.86 is the answer
A certain bell rings every 60 minutes. Another Bell rings every 90 minutes. Both bells begin ringing at midnight (12:00 a.m). How many more times will both bells ring by 1 p.m
Answer in picture
….
An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an estimate at the 95% level of confidence. For a sample of 582 third graders, the mean words per minute read was 24.1. Assume a population standard deviation of 3.7. Construct the confidence interval for the mean number of words a third grader can read per minute.
Answer:
The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{3.7}{\sqrt{582}} = 0.3[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 24.1 - 0.3 = 23.8
The upper end of the interval is the sample mean added to M. So it is 24.1 + 0.3 = 24.4.
The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).
If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting 2 queens and 2 kings.
The probability is ___.
(Round to six decimal places as needed.)
Answer:
1.083
Step-by-step explanation:
Exact form: 13/12
Decimal form: 1.083 (put a line above the 3)
Mixed number form: 1 1/12
Pauline mixed 0.32 liter of syrup with 12 times as much water to make orange squash.She split 1.28 liter of orange squash.Then she poured the remaining orange squash equally into 4 bottles.How much orange squash were there in each bottle.Give your answer in Liters.
Answer:
0.72 litres
Step-by-step explanation:
Litres of syrup = 0.32 litres
Litres of water = 12 times the amount of syrup = 12 * 0.32 = 3.84 litres
Litres of orange squash = litres of syrup + litres of water
Litres of orange squash = (0.32 + 3.84) = 4.16 litres
Amount of orange squash litres split = 1.28 litres
Amount of orange squash left = (4.16 - 1.28) = 2.88 litres
Splitting the amount of squash left equally into 4 :
2.88 litres / 4 = 0.72 litres
HELP WILL GIVE BRAINLYIST
Answer:
The parent cubic function has been vertically stretched by a factor of 4.
Equation:G(x)= 4[tex]\sqrt[3]{x}[/tex]
Answer: Option B
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