Answer:
6
Step-by-step explanation:
We have y ∝ x which is another way of saying y varies directly with x
We can rewrite the direct proportion relation y ∝ x as y = k.x where k is a constant - the constant of proportionality
So y = kx or x = y/k
using y and x values know, we can solve for k and then solve for any x given y
We have
y = 37.4 = k (17)
Therefore k = (37.4/17) = 2.2
To find x given y = 13.2, use the second equation
x = y/k = 13.2 / 2.2 = 6
SOME ONE PLEASE ANSWER ASAP NEED EXPLAIN FULL STEPS
Answer:
[tex]{ \tt{( \frac{ - 4}{9} \times \frac{63}{28}) - ( \frac{33}{66} \times \frac{ - 51}{17} ) + ( \frac{5}{8} \times \frac{4}{10)} }} \\ \\ = { \tt{( \frac{ - 4}{28} \times \frac{63}{9}) - ( \frac{1}{2} \times \frac{ - 3}{1} ) + ( \frac{5}{10} \times \frac{4}{8} )}} \\ \\ { \tt{ = ( - 1) - ( - \frac{3}{2} ) + ( \frac{1}{4}) }} \\ \\ = { \tt{ \frac{3}{4} }}[/tex]
Answer:
[tex]\sf \dfrac{3}{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]\implies \sf \left(\dfrac{-4}{9} \times \dfrac{63}{28}\right)-\left(\dfrac{33}{66} \times \dfrac{-51}{17}\right)+\left(\dfrac{5}{8} \times \dfrac{4}{10}\right)[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{a \times b}{c \times d}:[/tex]
[tex]\implies \sf \left(\dfrac{-4\times63}{9\times28} \right)-\left(\dfrac{33 \times -51}{66 \times 17}\right)+\left(\dfrac{5\times4}{8\times10} \right)[/tex]
Multiply the numbers:
[tex]\implies \sf \left(\dfrac{-252}{252} \right)-\left(\dfrac{-1683}{1122}\right)+\left(\dfrac{20}{80} \right)[/tex]
Reduce the fractions:
[tex]\implies \sf -1-\left(\dfrac{-3}{2}\right)+\left(\dfrac{1}{4} \right)[/tex]
[tex]\textsf{Apply rule}\quad \:a-\left(-b\right)=a+b:[/tex]
[tex]\implies \sf -1+\dfrac{3}{2}+\dfrac{1}{4}[/tex]
Adjust the fractions based on the LCM of 4:
[tex]\implies \sf \dfrac{-4}{4}+\dfrac{6}{4}+\dfrac{1}{4}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c}:[/tex]
[tex]\implies \sf\dfrac{-4+6+1}{4}[/tex]
Add the numbers in the numerator:
[tex]\implies \sf \dfrac{3}{4}[/tex]
5. What is the monthly periodic rate on a loan with an APR of 19.5%? Provide answer in thre
decimal places.
Answer:
Step-by-step explanation:
0.195/12 = 0.0163 = 1.63%
Hence, the monthly periodic rate is [tex]1.63[/tex]%.
What is the periodic rate?
A periodic interest rate is a rate that can be charged on a loan, or realized on an investment over a specific period of time.
Lenders typically quote interest rates on an annual basis, but the interest compounds more frequently than annually in most cases.
Here given that,
Loan with an APR of [tex]19.5[/tex]%
So, [tex]19.5[/tex]% is
[tex]\frac{19.5}{100}=0.195[/tex]
Annual periodic rate means [tex]12[/tex] months.
then,
[tex]{0.195}{12}=0.0163\\[/tex]
[tex]=1.63[/tex]%
Hence, the monthly periodic rate is [tex]1.63[/tex]%.
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Mr. McDahl has planned a day of independent work for his English students when they next have a substitute teacher. One-third of the students choose to work on an essay. One-half of the remaining students choose to read. The remaining 5 students work on vocabulary. How many students are present in the class on that day?
The total number of student present in the class is 15.
How to express the number of student in the class?One-third of the students choose to work on an essay.
Let
x = the total number of student in the class
Therefore,
student that takes essay = 1 / 3 x
One-half of the remaining students choose to read.
Therefore, the expression is as follows
student that choose to read = 1 / 2(x - 1 / 3 x) = 1 / 2( 3x - x/ 3) = 1 / 2(2 / 3 x) = 2 / 6 x = 1 / 3x
The remaining 5 students work on vocabulary. Therefore, the expression is as follows:
Student that works on vocabulary = x - 1 / 3 x - 1 / 3 x
5 = x - 1 / 3 x - 1 / 3 x
5 = 3x- x - x / 3
5 = x / 3
x = 15
Therefore,
the student present in the class = 1 / 3 (15) + 1 / 3(15) + 5
the student present in the class = 5 + 5 + 5
the student present in the class = 15
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A researcher is studying the growth of bacteria.
He starts with 320 of the bacteria. It grows
continuously at a rate of 4% per hour. How
many bacteria will there be in 17 hours?
(Round to the nearest integer if necessary)
136000 many bacteria will there be in 17 hours at a rate of 4 percentage per hour.
What is an example of a percentage?
Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.given ,
rate = 4%
bacteria starts growing = 320
rate = 4%
4% = 320
1 = [tex]\frac{320 * 100}{4} = 8000[/tex]
bacteria will there be in 17 hours = 17 × 8000
= 136000
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Suppose that a certain college class contains 51 students. Of these, 23 are freshmen, 30 are mathematics majors, and 7 are neither. A student is selected at random from the class.
(a) What is the probability that the student is both a freshman and a mathematics major?
(b) Given that the student selected is a freshman, what is the probability that he is also a mathematics major
Considering the definition of probability and its properties:
the probability that the student is both a freshman and a mathematics major is 3/17. given that the student selected is a freshman, what is the probability that he is also a mathematics major is 3/10.Definition of ProbabitityProbability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
The probability of any event A is defined as the ratio between the number of favorable cases (number of cases in which event A may or may not occur) and the total number of possible cases. This is called Laplace's Law.
P(A)= number of favorable cases÷ number of total cases
Union of eventsThe union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.
Complementary eventA complementary event, also called an opposite event, is made up of the inverse of the results of another event.
The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:
P(A´)= 1- P(A)
Conditional probabilityThe conditional probability P(A|B) is the probability that an event A occurs, knowing that another event B also occurs. That is, it is the probability that event A occurs if event B has occurred. It is defined as:
P(A|B) = P(A∩B)÷ P(B)
Probability that the student is both a freshman and a mathematics majorIn first place, let's define the following events:
F: The event that the student is a freshman.M: The event that the student is a mathematics major.You know:
A certain college class contains 51 students. 23 students are freshmen. → P(F)= 23÷51 → P(F)= 23/5130 students are mathematics majors. → P(M)= 30÷51 → P(M)= 30/517 students are neither a freshman or a mathematics mayor → P [(F∪M)']= 7÷51= 7/51The probability that a student is a freshman or a mathematics mayor is:
P [(F∪M)']= 1- P(F∪M)
7/51= 1 - P(F∪M)
7/51 - 1= -P(F∪M)
-44/51= -P(F∪M)
44/51= P(F∪M)
So, the probability that the student is both a freshman and a mathematics major is calculated as:
P(F∪M)= P(F) + P(M) -P(F∩M)
44/51= 23/51 + 30/51 - P(F∩M)
44/51- 23/51 - 30/51= - P(F∩M)
-3/17= - P(F∩M)
3/17= P(F∩M)
Finally, the probability that the student is both a freshman and a mathematics major is 3/17.
Probability that a student is a mathematics major being a freshmanThe probability that a student is a mathematics major, knowing that he is also a freshman, is calculated as:
P(M|F) = P(M∩F)÷ P(M)
So:
P(M|F) = 3/17÷ 30/51
P(M|F) = 3/10
Finally, given that the student selected is a freshman, what is the probability that he is also a mathematics major is 3/10.
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Formulate 600lbs of a 13% cp ration using alfalfa hay (18%cp) and clover 4%cp)
The amount of Alfalfa hay is 385.71 lbs
The amount of Clover is 572.45 lbs.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
We have,
Alfalfa hay = 18 % CP
Clover = 4% CP.
The total amount of ration is 600 lbs of a 13% CP.
Let x pounds of alfalfa hay have been used.
The amount of clover will be 600 - x lbs.
The CP amount in 600 lbs mixture will be equal to the sum of CP amounts in x lbs alfalfa and (600 - x) lbs clover.
13% of 600 = 18% of x + 4% of (600 - x)
We need to find x.
13/100 x 600 = 18/100 x (x) + 4/100 x (600 -x)
78 = 18x / 100 + 24 - 4x/100
78 - 24 = 18x/100 - 4x/100
54 = 14x / 100
14x = 54 x 100
x = 5400/14
x = 385.71 lbs
Thus,
The amount of Alfalfa hay= 385.71 lbs
The amount of Clover = 600 - 385.71 = 572.45 lbs.
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∠A and \angle B∠B are supplementary angles. If m\angle A=(2x-4)^{\circ}∠A=(2x−4) ∘ and m\angle B=(4x-14)^{\circ}∠B=(4x−14) ∘ , then find the measure of \angle A∠A.
The measure of angle A is 62 degrees
Supplementary anglesSupplementary angles are angles that sunset up to 180 degrees. For instance, if A+B = 180, then A and B are supplementary
The sum of supplementary angles is 180 degrees such that;
<A + <B = 180
Given the following parameters
<A = 2x-4
<B = 4x-14
Substitute
2x-4 +4x-14 = 180
6x - 18 = 180
6x = 198
x = 198/6
x = 33
<A = 2x - 4
<A = 2(330 - 4
<A = 62 degrees
Hence the measure of angle A is 62 degrees
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240 % of a number is 68000, what is that number
Answer:
28333.33
Step-by-step explanation:
68000/240% = 28333.33333333333
= 28333.33
Writing proportional equations from tables
Sarah bought snacks for her team's practice. She bought a bag of chips for $1.56 and a 20-pack of juice bottles. The total cost before tax was $33.96. Write and solve an equation which can be used to determine jj, how much each bottle of juice cost.
Cost of a bottle of juice is $ 1.62
Equation for determining the cost of juice is 1.56 + 20x = 33.96
Given,
The cost of a bag of chips = $ 1.56
Number of juice bottles bought by Sarah = 20 pack
Total cost before tax = $ 33.96
Cost of one bottle of juice = x
We have to find x:
Then the equation will be:
1.56 + 20x = 33.96
Add -1.56 to both sides:
1.56 + 20x - 1.56 = 33.96 - 1.56
We get,
20x = 32.4
Now find x,
x = 32.4 / 20
Then,
x = 1.62
That is, the equation for finding the cost of a bottle of juice is 1.56 + 20x = 33.96.
The cost of one bottle of juice is $1,62
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A circle is centered at the origin and has a radius of 4 units. Which points on the circle have a y -coordinate of 3?
Answer:The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)
Step-by-step explanation:
The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)
The equation of a circle usually takes the form;
(x-a)² + (y-b)² = r²
where a and b are x- and y- coordinates of the center of the circle.
In this scenario, the center is at the origin (0,0).
In essence, the points on the circle which have an x-coordinate of 1 can be evaluated as follows;
(1-0)² + (y - 0)² = 4²
1 + y² = 16.
y² = 15
y = ±√15.
The points on the circle which have an x-coordinate of 1 are:. (1,+√15) and (1,-√15)
A coffee company wants a new flavor of Cajun coffee. How many pounds of coffee worth $10 a pound should be added to 30 pounds of coffee worth $4 a pound to get a mixture worth $6 a pound? To get a mixture worth $6 a pound, pounds of coffee should be added. (Type an integer, proper fraction, or mixed number.) what is this answer please need help
The weight of coffee worth $10 to be added to mixture to worth $6 a pound is 15 pounds the mixture will be 15 pounds
Let the weight of coffee worth $10 to be added to mixture be x pounds
The weight of coffee worth $4 to be added to mixture is 30 pounds
We want a mixture that worth $6 a pound
The weight of mixture of coffee worth $ 6 is the sum of $10 coffee and $4 coffee
= x + 30
From the above equation we can form a linear equation
X 10 + 30 ×4 = (x+ 30) 6
10x + 120= 6x +180
10x-6x= 180 -120
4x = 60
X= 15
Hence, the weight of coffee worth $10 to be added to mixture to worth $6 a pound is 15 pounds
what's a linear equation ?
A linear equation only has one or variables. No variable in a linear equation is raised to a strength greater than 1 or used because the denominator of a fraction. while you discover pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all the factors lie at the same line
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[estimate] 245.7+5.8=?
Answer:
estimate 245.7+5.8
251.5
Evaluate 5x, for x = 9
Answer:
Step-by-step explanation:
5(9) = 45
At a baseball game, 56% of people attending were supporting the home team, while 44% were supporting the visiting team. If the total number of people attending the game was 3000, how many people attending were supporters of the home team?
Answer: 1680
Step-by-step explanation:The answer is 1680 because 56 percent of 3000 is 1680 people and 44 percent of 3000 is 1320 people
Travis orders a new streaming system. He must pay $26 to join the service
then pays $6 per month. Write a numerical expression to represent Travis'
cost for 6 months of the stream service.
Unit 1 geometry basics
Homework 5 angle relationships
Answer:
Where is the question?
what value of x makes 6e^4x = 14 true?
For the given equation 6e^4x = 14, the value of x is [tex]x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]
How to Find x's Value?Getting x alone on one side of the equation and everything else on the other side will be the first step towards solving for x. The golden rule of algebra states that everything done to one side of an equation must also be done to the other.
Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.
For the given equation,
6e^4x = 14
[tex]x = ln \frac{3^{3/4} * \sqrt[4]{7} }{3}\\ \\x = ln\frac{3^{3/4} * \sqrt[4]{7} }{3}[/tex]
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please help will give more points in a separate question if all correct i will give 200 points
Answer:
true for the first one and also true for the other one.
# Simplify the following using the law of indices :
[tex]2a \times 3a {}^{2} [/tex]
Simplifying the given value using the law of indices is 6[tex]a^{3}[/tex]
2a * 3[tex]a^{2}[/tex]
=6[tex]a^{3}[/tex]
Index laws are the rules for simplifying expressions involving powers of the same base number.
Here are the essential steps to follow to simplify an algebraic expression:
Remove parentheses by multiplying factors.
Use exponent rules to get rid of parentheses in terms with exponents.
Combine like terms by adding coefficients.
Combine the constants.
Here's differently to explain it: The is used to refer to a specific or particular member of a group. for instance , "I just saw the foremost popular movie of the year." There are many movies, but just one particular movie is the most popular.
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R= S If m R =3x +5 an m S =5x-25 solve for x and find m R
The values of x and m∠R are 15 and 50 respectively.
How to determine the valuesFrom the information given, we have the following parameters;
R = Sm ∠ R = 3x + 5m ∠ S = 5x - 25Now, let's equate the angles
m ∠ R = m ∠ S
3x + 5 = 5x - 25
collect like terms
3x - 5x = -25 - 5
subtract like terms
-2x = - 20
Make 'x' the subject
x = -30/ -2
x = 15
But m ∠ R = 3x + 5 = 3(15) + 5 = 45 + 5 = 50
Thus, the values of x and m∠R are 15 and 50 respectively.
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If m = 8 and n = 4, all of the following represent the same value except
Correct answer is D. For the numerical equation, If m = 8 and n = 4, all of the following represent the same value except mn.
What is a numerical equation?Numbers and their operations are used to represent a numerical equation. Statements can also be used to create mathematical expressions.
On calculating, the following values,
If m = 8 and n = 4;
For 1/2m, the value will be -
1/2 × 8 = 4 .......(1)
For n/1 the value will be -
4/1 = 4 .......(2)
For m-n the value will be -
8 - 4 = 4 .......(3)
For mn, the value will be -
8 × 4 = 32 ......(4)
From (1), (2), (3), (4) it can be seen that the value is same instead for mn.
Complete question -
If m = 8 and n = 4, all of the following represent the same value except _____.
1/2 m
n/1
m-n
mn
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The diameter of a circular rug is 7 m. Find the area it will cover.
The area covered by circular rug of diameter 7 is 38.5 m².
What is the area of a circle?Circle is locus of points equidistant from a center point. This distance from center to the boundary of circle is radius.
If r is the radius of a circle , then its Area = π(r²)
Given that a circular rug has diameter = 7 m
Then, Let radius of circular rug be r ,r = diameter /2
r = 7/2 m
Area = π(7/2)² = (22/7)*(7/2)² m² = 38.5 m²
Therefore , Area of the circular rug is 38.5 m²
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Find the value of x.
Answer:
250°Step-by-step explanation:
360° - the know angles
360 - 20 - 70 - 20 = 250°
Step-by-step explanation:
Well this is a full circle, and in a full circle, theres 360 degrees.
So if we add up 20, 70 and 20 degrees, it comes to a total of 110 degrees.
If we subtract 110 d from 360 d, we get 250 degrees. Therefore,
X = 250 degrees
Hope this helped
Which of the following represents an INEFFICIENT point of production?
a. Point A
b. Point B
c. Point D
d. None
e. Point C
The point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
In this question we have been given a graph of Skateboards vs. Bikes.
We need to find the point that represents an INEFFICIENT point of production.
Inefficient production means the economy can be producing more goods without using any additional resources.
In given production possibility curve, an INEFFICIENT point of production is point A.
Therefore, the point that represents an INEFFICIENT point of production is point A.
The correct answer is an option (a)
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3y is greater than or equal to 9
[tex]3y \geqslant 9 \\ y \geqslant \frac{9}{3} \\ y \geqslant 3[/tex]
Answer: y > 3
Step-by-step explanation: 3y > 9
3y/3 > 9/3
y > 3
For f(x) = 2 - x and g(x)= 3x +x+5, find the following functions.
a. (fog)(x); b. (gof)(x); c. (fog)(2); d. (gof)(2)
a. (fog)(x)=-3x²-x-3
(Simplify your answer.)
b. (gof)(x) = 3x² - 13x+19
(Simplify your answer.)
c. (fog)(2)= -17
d. (gof)(2)= ?
The answers are below.
a) (fog)(x) = f(g(x)) = 2 - ( 3x² +x+5) = -3x² - x - 3
b) (gof)(x) = g(f(x)) = 3*(2 - x)² + (2 - x) +5 = 3x² - 13x + 19
a) (fog)(2) = -3x² - x - 3 = -3*4 - 2 - 3 = -12 - 2 - 3 = -17
b) (gof)(2) = 3x² - 13x + 19 = 3*4 - 13*2 + 19 = 12 - 26 + 19 = 5
How to find the following functions?Just replace evaluate the function g(x)= 3x² +x+5 insode of the function f(x) = 2 - xfor the first one.
a) (fog)(x) = f(g(x)) = 2 - ( 3x² +x+5) = -3x² - x - 3
b) (gof)(x) = g(f(x)) = 3*(2 - x)² + (2 - x) +5 = 3x² - 13x + 19
ok, now that you have these two values, just evaluate the equations in x = 2 to get the rest.
a) (fog)(2) = -3x² - x - 3 = -3*4 - 2 - 3 = -12 - 2 - 3 = -17
b) (gof)(2) = 3x² - 13x + 19 = 3*4 - 13*2 + 19 = 12 - 26 + 19 = 5
These are the outcomes when we evaluate the compositions in x = 2.
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HELP 65 POINTSS!! Answer BOTH parts of the question by drawing on the following coordinate plane. For each of the transformations, use the ORIGINAL pre-image to make the new image.
(a) Draw the image of ∆PQR after a rotation of 90° clockwise about the origin. Label the image ∆P'Q'R'.
(b) Draw the image of ∆PQR after a reflection across the y-axis. Label the image ∆P''Q''R''.
Using translation concepts, the transformed triangles are given in the graph at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis, or rotations of a degree measure around the origin.
For this problem, the coordinates of triangle PQR are given as follows:
P(-1,-1), Q(-3,-2), R(-3,-4).
The rule for a 90º clockwise rotation around the origin is given by:
(x,y) -> (y,-x).
Hence the coordinates of triangle P'Q'R' are given by:
P': (-1,-1) -> (-1,1).Q': (-3, -2) -> (-2, 3).R' : (-3, -4) -> (-4, 3).The rule for a reflection over the y-axis is:
(x,y) -> (-x,y).
Hence the coordinates of triangle P''Q''R'' are given by:
P'': (-1,-1) -> (1,-1).Q'': (-3, -2) -> (3, -2).R'' : (-3, -4) -> (3, -4).Both triangles are given in the graph at the end of the answer.
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A deck of cards contains RED cards numbered 1,2,3,4 and BLUE cards numbered 1,2,3,4,5. Let R be the event of drawing a red card, B the event of drawing a blue card, E the event of drawing an even numbered card, and O the event of drawing an odd card.
Drawing the Blue 4 is an example of which of the following events? Select all correct answers.
Answer: what is question here?
Step-by-step explanation:
Where are answers?
the bookstore sold 8 books for 66$ at that rate how much would one book be.
