Question: Liliana has $3.80 in nickels and quarters in her purse. She has 22 more nickels than quarters. How many coins of each type does she have?
Solution:
Liliana has $3.80 in nickels and quarters in her purse.
She has 22 more nickels than quarters.
We first have to establish a system of equations. Since we have two unknown variables, we need to have two equations. The first equations;
let x = number of quarters
x+22 = number of nickels
The total worth of coins = $3.80
The value of a quarter is $0.25 and the value of a nickel is $0.05.
According to the problem:
\(0.25x+0.05(x+22)=3.80\)Applying the distributive property, we get:
\(0.25x+0.05x+1.1\text{ = 3.80}\)this is equivalent to:
\(0.25x\text{ +0.05x = 3.80}-1.1\)this is equivalent to:
\(0.3x=2.7\)Solving for x, we obtain:
\(x=\text{ }\frac{2.7}{0.3}=9\)Thus, we obtain that:
The number of quarters = x = 9
number of nickels = x+22 = 9+22 = 31
So t
Two books, A and B, are sold in three stores, X, Y and Z. The number of copies of book A sold in a month is 40, 20, and 60 from stores X, Y, and Z, respectively. The number of copies of book B sold is 10, 70, and 20 from X, Y, and Z, respectively. The profit from the sales of book A is $4, and the profit from the sales of book B is $1 for all the three stores. Which matrix represents the profit from the sales of book A for each store?
The matrix representing the profit from the sales of book A for each store is:
[ $4 ]
[ $4 ]
[ $4 ]
To represent the profit from the sales of book A for each store, we can use a matrix where the rows correspond to the stores (X, Y, Z) and the columns correspond to the book A.
The matrix representing the profit from the sales of book A for each store is as follows:
Store Book A
X $4
Y $4
Z $4
Therefore, the matrix representing the profit from the sales of book A for each store is:
[ $4 ]
[ $4 ]
[ $4 ]
Each element in the matrix represents the profit from the sales of book A in a specific store, which is $4 for all stores (X, Y, Z).
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4/5 + 1/3 simplified
Answer:
17/15
Step-by-step explanation:
I am playing a number game, there are 2 tiles for each number from 0 thru 9. One tile is chosen at random, can you list the possible outcomes ?
Answer:
If each tile has a number from 0 thru 9 then the possible outcomes for each tile are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
A colony of bacteria is growing exponentially according to the function below,where tis in hours. What will the approximate number of bacteria be after 8hours?
Answer:
Alternative D - 2407 bacteria
Step-by-step explanation:
The num
Lines m and p are perpendicular. If the slope of line m is -3, what is the slope of line p?
Answer: The slope of p is 1/3
Step-by-step explanation:
If the lines are perpendicular, this means they are opposite.
Thus, O is opposite P and since O = -3, P = 1/3
Question
The sum of the measures of the angles of a triangle is
180. The sum of the measures of the second and third angles is five
times the measure of the first angle. The third angle is 30 more than the second. Let T. y, and z represent the measures of
the first, second, and third angles, respectively. Find the measures of the three angles.
Provide your answer below:
Answer:
t = 30°y = 60°z = 90°Step-by-step explanation:
The given relations can be used to write three equations for the angle values.
Setupt + y + z = 180 . . . . . sum of all angle measures
y + z = 5t . . . . . . . . second and third total 5 times the first
y + 30 = z . . . . . . third angle is 30 more than the second.
__
SolutionUsing the third equation to substitute for z in the first two equations gives ...
t + y + (y +30) = 180 ⇒ t +2y +30 = 180
y + (y +30) = 5t ⇒ 2y +30 = 5t
Using the second of these equations to substitute for (2y+30) in the first, we have ...
t +5t = 180
t = 180/6 = 30 . . . . . . divide by the coefficient of t
Using this value in our equation for 5t gives ...
2y +30 = 5(30)
2y = 120
y = 60
Then the value of angle z is ...
y +30 = z = 60 +30
z = 90
The first, second, and third angles are 30°, 60°, and 90°, respectively.
What is the meaning of "each partition P of X defines an equivalence relation on X"?
The statement indicates that when a set X is partitioned, each partition forms an parity relation by grouping together rudiments that are considered original within each subset, thereby creating distinct and non-overlapping subsets within the original setX.
The statement" each partition P of X defines an parity relation on X" means that when a set X is divided into non-overlapping subsets or partitions, each partition creates an parity relation on the original set X.
An parity relation is a relation that satisfies three parcels reflexivity, harmony, and transitivity. In the environment of partitions, when a set X is divided into subsets, each partition forms an parity relation by grouping together rudiments that partake a common characteristic or property.
Within each partition, the rudiments are considered original or affiliated to each other, and they're distinct from rudiments in other partitions. The meaning of" each partition P of X" refers to every possible way of dividing the set X intonon-overlapping subsets.
It implies that different partitions may live grounded on different criteria or conditions for grouping rudiments.
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Determine the following ratio
Using relations in a right triangle, the secant of angle θ is given by:
D. 5/4.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Using the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:
h² = 9² + 12²
h = sqrt(9² + 12²)
h = 15.
The secant of an angle is 1 divided by the cosine, hence:
cos(θ) = 12/15 = 4/5.sec(θ) = 5/4.Which means that option D is correct.
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What is the volume of the container below? 2 rectangular prisms. A rectangular prism has a length of 14 inches, width of 6 inches, and height of 16 inches. A rectangular prism has a length of 10 inches, width of 6 inches, and height of 4 inches. 576 inches cubed 1,080 inches cubed 1,584 inches cubed 1,920 inches cubed
PLEASE ANSWER FAST ITS MY CUMULATIVE EXAM
Answer:
The volume of the container is 1584 inch³.
Step-by-step explanation:
The volume of a rectangular prism is:
\(\text{Volume}=\text{l}\times\text{w}\times\tect{h}\)
It is provided that the container is made up of two rectangular prisms.
The dimensions are as follows:
Prism 1: length of 14 inches, width of 6 inches, and height of 16 inches.Prism 2: length of 10 inches, width of 6 inches, and height of 4 inches.Compute the volume of the rectangular prism 1 as follows:
\(\text{V_{1}}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}\)\(\text{V}_{1}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}\)
\(=14\times 6\times 16\\=1344\)
Compute the volume of the rectangular prism 2 as follows:
\(\text{V_{1}}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}\)\(\text{V}_{2}=\text{l}_{2}\times\text{w}_{2}\times\text{h}_{2}\)
\(=10\times 6\times 4\\=240\)
Then the volume of the container will be:
\(\text{Volume of container}=\text{V}_{1}+\text{V}_{2}\)
\(=1344+240\\=1584\)
Thus, the volume of the container is 1584 inch³.
Answer:
Step-by-step explanation:
What is the volume of the container below?
2 rectangular prisms. A rectangular prism has a length of 14 inches, width of 6 inches, and height of 16 inches. A rectangular prism has a length of 10 inches, width of 6 inches, and height of 4 inches.
576 inches cubed
1,080 inches cubed
1,584 inches cubed
1,920 inches cubed
‼️‼️‼️‼️‼️‼️‼️Please tell me the area and attach work but please explain it to me
Answer:
You have to break it into two rectangles.
Step-by-step explanation:
Once you have it in two rectangles, I found the width of the smaller rectangle because I know the whole side is 16. I know the larger rectangle has a width of 13. I subtracted to find that extra little bit of space is 3. The formula for a rectangle is length x width. Now you just need to find the area of each rectangle and add them together.
Answer:
Step-by-step explanation:
so what I did is made the full rectangle then removed the blank.
21x16=336
Now the blank space
16x3=48
336-48=288
what would be the answers for these ????
Answer:
Step-by-step explanation: the y would be 50
27,813 students took the ACET this year. If only 2,836 students were admitted into the Ateneo among those students, what is the Ateneo’s acceptance rate? a. 7.5% b. 10.2% c. 13.4% d. 9.0%
If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.
How the rate is determined:The rate is the ratio of one value, expression, measurement, or quantity compared to another.
The rate represents the quotient of the numerator and the denominator.
The rate is expressed as a percentage by multiplication with 100.
The number of students who took the ACET this year = 27,813
The number of students who were admitted into the Ateneo = 2,836
The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)
= 10.2%
Thus, we can conclude that the acceptance rate or percentage is Option B.
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I need help asap!!!
Determine which pair of points has a negative slope.
a
(-10, -3), (-7, 6)
c. (7, 7), (-8, 1)
b. (5,2), (-9,-10)
d. (2,9), (-3,-1)
Answer:
We conclude that all the pairs of points have positive slopes.
Thus, there is NO pair of points that has a negative slope.
Step-by-step explanation:
a)
Determining the slope between (-10, -3), (-7, 6)
\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)
\(\left(x_1,\:y_1\right)=\left(-10,\:-3\right),\:\left(x_2,\:y_2\right)=\left(-7,\:6\right)\)
\(m=\frac{6-\left(-3\right)}{-7-\left(-10\right)}\)
\(m=3\)
b)
Determining the slope between (7, 7), (-8, 1)
\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)
\(m=\frac{1-7}{-8-7}\)
\(m=\frac{2}{5}\)
c)
Determining the slope between (5,2), (-9,-10)
\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)
\(m=\frac{-10-2}{-9-5}\)
\(m=\frac{6}{7}\)
d)
Determining the slope between (2,9), (-3,-1)
\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)
\(m=\frac{-1-9}{-3-2}\)
\(m=2\)
We conclude that all the pairs of points have positive slopes.
Thus, there is NO pair of points that has a negative slope.
nikooa buys a bouquet of 8 sunflowers for $18.
What is the cost of 1 sunflower?
Answer: The cost of one sunflower is $2.25
Step-by-step explanation:
To find the cost o 1 sunflower, divide each unit's value by 8. To get from 8 flowers to 1 you will divide 8 by 8. Now we have to divide the money by 8 as well.
18/8 = 2.25
This means the cost of one sunflower is $2.25
A jar contains 24 blue marbles, 16 red marbles, and 14 white marbles. Find the simplified ratio of total marbles to red marbles.
The simplified ratio of total marbles to red marbles is 27 to 8
How to determine the ratio of the marbles?In this question, we have the following parameters
Blue marbles = 24
Red marbles = 16
White marbles = 14
The above parameters mean that
Total marbles = sum of the individual marbles
Substitute the known values in the above equation, so, we have the following representation
Total marbles = 24 + 16 + 14
Evaluate
Total marbles = 54
The ratio is then represented as
Ratio = Total : Red
This gives
Ratio = 54 : 16
Simplify ratio
Ratio = 27 : 8
Hence, the simplified ratio is 27 : 8
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I need help with this
What is graph theory? Math
Any help please thank you I appreciate
Answer:
A)
Step-by-step explanation:
from 0 to 5, x was moved right 5 units on the first is + 5
then, -1 to -5. it went down 4 units so -4
How do u solve for h??
Answer:
(2a)/(B+b)=h
Step-by-step explanation:
multiply by the reciprocal of 1/2 to get 2 and then divide (B+b) to get h by itself
mark brainliest thankksss
20>5 + 2n - 9
Plz help me with this
Step-by-step explanation:
20>5+2n-9
20+9>5+2n
29-5>2n
n>12
hope it helps.
Let S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward. Find the flux of the vector field F = 1i + 1j + 3k across the surface S.
The vector field F = 1i + 1j + 3k has a flux of 2 across the surface S. We use Green's Theorem to determine the vector-flux field.
Explain the Green's Theorem?The simple formula for Green's theorem is the link between the total amount of microscopic circulation inside of curve C and the macroscopic circulation revolving around it.Green's Theorem in flux form for the specified vector-field:φ = ∫ F.n ds
φ = ∫∫ F. divG.dA
In which, G is equivalent to a part of given plane = 2x + 1y + z = 2.
And, F = 1i + 1j + 2k
Thus,
div G = div(2x + 1y + z = 2) = 2i + 4j + k
Flux = ∫(1i + 1j + 3k) (2x + 1y + z).dA
φ = ∫ (2 + 4 + 2).dA
φ = 8∫dA
A = 1/2 XY (on this given x-y plane)
2x+4y =2
For, x = 0, y = 1/2
y = 0, x = 1
1/2 (1*1/2) = 1/4
Thus, flux = 8*1/4 = 2
φ = 2.
There are several uses for Green's theorem. Solving two-dimensional flow integrals, whose assert that its sum of fluid outflows from just a volume equals the sum of outflows around an enclosed area, is one way to accomplish this.
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The complete question is-
Let S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward. Find the flux of the vector field F = 1i + 1j + 3k across the surface S. F = 1i + 1j + 3k across the surface s2x + 1y + z = 2 which lies in the first octant, oriented upward. Find the flux of the vector field.
what is the measure of the reference angle for a 102 degree angle? A. 78 degrees B. 68 degrees C. 57 degrees D. 12 degrees
Answer:
A. The reference angle measures 78 degrees
A total of 27 students are in your class. There are nine more males than females.
How many females are in your class?
find the sum for(2x−6)+4(x−3)
Answer:
6x - 18
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define expression
(2x - 6) + 4(x - 3)
Step 2: Simplify
Distribute 4: 2x - 6 + 4x - 12Combine like terms (x): 6x - 6 - 12Combine like terms (Z): 6x - 18If a perpetuity pays a cash flow (C) every time period, forever, how come it is not worth an
infinite amount of money right now? Explain.
21. In the voting for City Council Precinct 5, only of all eligible voters cast votes. What fraction of all eligible voters voted for Shelley? Morgan? Who received more votes?
All eligible voters voted for Shelley= 3/20 ,
All eligible voters voted for Morgan= 31/100, Morgan received most votes.
What is mean by multiplication?Multiplication is a mathematical operation that embodies the basic idea of numerous additions of the same number. The outcomes of multiplying two or more numbers are referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplication facilitates the process of adding the same number again.
Let's suppose Precinct 5 has 100 registered voters. There were 50 voters who participated in the election because only 50% of those who were eligible to vote actually did so.
3/10 of the votes were cast for Shelley, which translated as 3/10 x 50 or 15 votes.
With 5/8 of the vote, Morgan received 5/8 x 50 votes, or 31.25 votes. Therefore, we must round this figure down to 31 votes as we are dealing with whole voters.
We must divide the number of votes received by the total number of eligible voters in order to determine the percentage of all eligible voters who cast a ballot for Shelley: 100 eligible voters x 15 votes = 3/20.
Morgan won the most votes since she received more than Shelley.
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Carry out the following division.
Answer:
-6l²m
Step-by-step explanation:
v. -54l⁴m³n² / 9l²m²n²
= -6l²m
write the following mathematical expressions in simplest form 3.5 m + 2 (0.6 M - 5) + 4
Answer:hamburger
Hamburger
Step-by-step explanation:hamburger
Hamburger
PLEASE HELP! I'm lost. :(
In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean
µ = 520 and population standard deviation = 115.
What math SAT score is 1.5 standard deviations above the mean? Round answer to a whole number.
Answer:
A math SAT score of 693 is 1.5 standard deviations above the mean
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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 p-value, we get the probability that the value of the measure is greater than X.
Mean µ = 520 and population standard deviation = 115.
This means that \(\mu = 520, \sigma = 115\)
What math SAT score is 1.5 standard deviations above the mean?
This is X when \(Z = 1.5\). So
\(Z = \frac{X - \mu}{\sigma}\)
\(1.5 = \frac{X - 520}{115}\)
\(X - 520 = 1.5*115\)
\(X = 693\)
A math SAT score of 693 is 1.5 standard deviations above the mean