i'll give brainliest plss help!!!Paul earns money each week for mowing his lawn. He earns a flat rate lawn and earns an extra $1.50 per hour for any additional yard work. This past week, he did 6 hours of additional work and earned a total of $24.a). This can be represented using a linear model. What would the x-variable be in the context of this problem? What would the y-variable be?b). Write the point-slope linear equation that can be used to determine amount of money Paul can earn during any given week.c). Rearrange your equation so it is in slope-intercept form. What does the “b” represent in the context of this problem?
Answers
ANSWERS
(a) x represents the number of hours and y represents Paul's earnings.
(b) y - 24 = 1.50(x - 6)
(c) y = 1.50x + 15; b represents the flat rate
EXPLANATION
(a) In linear models, the x-variable is usually the independent variable, while the y-variable is the dependent variable. In this problem, we know that Paul's earnings depend on how many hours of additional yard work he does. Hence, the x-variable represents the number of hours Paul does extra yard work and the y-variable represents his earnings.
(b) A linear equation in point-slope form is,
\(y-y_1=m(x-x_1)\)Where m is the slope and (x₁, y₁) is a point on the line.
In this case, we know that Paul earns an extra $1.50 per hour for additional yard work. If the additional yard work time in hours is represented by the x-variable, then the slope is 1.50.
Now, we need a point on the line. This is given in the problem, where it is said that when Paul worked 6 hours, he earned a total of $24. So the point is (6, 24),
\(y-24=1.50(x-6)\)Hence, the equation in point-slope form is y - 24 = 1.50(x - 6).
(c) The slope-intercept form of the equation of a line is,
\(y=mx+b\)We have to take the equation found in part (b) and rearrange it to find the equation in this form.
To do so, apply the distributive property to 1.50 on the right side of the equation,
\(\begin{gathered} y-24=1.50x-1.50\cdot6 \\ \\ y-24=1.50x-9 \end{gathered}\)And add 24 to both sides,
\(\begin{gathered} y-24+24=1.50x-9+24 \\ \\ y=1.50x+15 \end{gathered}\)The value of b is 15. Remember that b is the y-intercept, which is the value of the function when x = 0. This means that y = 15 when x = 0 and, therefore, 15 is the flat rate.
Hence, the equation in slope-intercept form is y = 1.50x + 15, and the y-intercept, b, represents the flat rate Paul earns without doing any extra work.
Related Questions
The cross-section of this prism is a square with side length 4 m. What is the surface area of the prism?
(photo attached below.)
Answers
The final answer for the surface area of the prism is 32 m^2 + 16h m^2.
To find the surface area of the prism, we need to calculate the area of each face and sum them up.
The prism has two identical square faces and four rectangular faces. The square face has a side length of 4 m. The area of one square face is given by:
Area of square face = side length^2 = 4^2 = 16 m^2
Since there are two square faces, the total area of the square faces is:
Total area of square faces = \(2 * 16 = 32 m^2\)
The rectangular faces have a length equal to the side length of the square face (4 m) and a width equal to the height of the prism. Let's assume the height of the prism is h. The area of one rectangular face is given by:
Area of rectangular face = length * width = \(4 * h = 4h m^2\)
Since there are four rectangular faces, the total area of the rectangular faces is:
Total area of rectangular faces = \(4 * 4h = 16h m^2\)
Therefore, the surface area of the prism is the sum of the areas of the square and rectangular faces:
Surface area of prism = Total area of square faces + Total area of rectangular faces
= \(32 m^2 + 16h m^2\)
= \(32 m^2 + 16h m^2\)
The answer for the surface area of the prism is 32 m^2 + 16h m^2.
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1 point
1. To win a prize, Jada must get a ball with an even number. Should she try
to win the prize using the tank of table tennis balls or the tank of golf balls?
A large fish tank is filled with table tennis balls with numbers written on them. Jada chooses 10
table tennis balls from the tank and writes down their numbers.
1
3
5
1
3.
2
4
1
5
3
A second tank is filled with golf balls with numbers written on them. Jada chooses 10 golf balls
from the tank and writes down their numbers.
1
4
5
2
6
2
2.
1
4
8
O Jada should use the tank of tennis balls.
O Jada should use the tank of golf balls.
1b. Explain your reasoning."
3 points
Your answer
Answers
Answer:
Jada should use the tank of golf balls
Step-by-step explanation:
Jada should choose the tank that has a higher probability of choosing a ball with even number from.
Tank of tennis balls has two even numbers out of the ten balls (2, 4)
Tank of golf balls has seven even numbers out of the ten balls.
Tank of golf balls would give Jada more chance to pick an even number to win the game
Therefore, Jada should use the tank of golf balls
Use the 68-95-99.7 rule to solve the problem.
For adults in the town of Bridgeport, systolic blood pressure is normally distributed with a mean of 137 mmHg and a standard deviation of 9 mmHg.
What percentage of adults in the town have a systolic blood pressure less than 128 mmHg?
Answers
32% of adults in the town of Bridgeport have a systolic blood pressure less than 128 mmHg based on standard deviation.
The empirical rule, commonly referred to as the 68-95-99.7 rule, is a helpful technique for estimating the proportion of a normally distributed population that falls inside a given range. Using this criterion, it may be estimated that 68% of the population is within one standard deviation of the mean, 95% is within two standard deviation, and 99.7% is within three standard deviations.
We may calculate the proportion of adults in the town of Bridgeport whose systolic blood pressure is less than 128 mmHg using this rule. Initially, we must use the following formula to determine the z-score for a 128 mmHg systolic blood pressure reading:
z = (x - μ) / σ
where x represents the systolic blood pressure reading, and,, and, respectively, represent the population mean and standard deviation. When we change the values, we obtain:
z = (128 - 137) / 9
z = -1
A systolic blood pressure reading of 128 mmHg is therefore one standard deviation below the mean. The empirical rule states that 68% of the population has a value between 128 + 9 = 137 and 128 - 9 = 119 mmHg, or within one standard deviation of the mean.
Calculating the proportion of adults who are outside the range of one standard deviation below the mean is necessary because we are interested in the proportion of individuals whose systolic blood pressure is less than 128 mmHg, which is outside of this range. In order to accomplish so, we deduct the proportion of adults within one standard deviation of 100% as follows:
100% - 68% = 32%
As a result, in the town of Bridgeport, 32% of individuals had systolic blood pressure that is less than 128 mmHg.
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Jacob bought 9 bags of balloons. Each bag has 25 balloons. He fills all the balloon and puts 5 balloons in each bunch. How many bunches can he make please help me
Answers
9 x 25 = 225
225 divided by 5= 45
So Jacob can make 45 bunches
Hopefully I’m right :)
The ordered pair (2, 10) is a point on a direct variation equation. Write the direct variation equation.
Answers
Answer:
Y=KX so its 10=K2
Step-by-step explanation:
Plug in the Number OR K=y/x
Mrs. Chang's class built a platform for use in a school play. What is the
volume of the platform?
PLEASE HELP!
Answers
Answer:
Total Platform = 128 ft^3
Step-by-step explanation:
Volume = Length * Width * Height
Left Volume: 2 ft * 4 ft * 3 ft = 24 ft^3
Mid Volume: 4 ft * 4 ft * 5 ft = 80 ft^3
Right Volume: 2 ft * 4 ft * 3 ft = 24 ft^3
Total Volume = 24 ft^3 + 80 ft^3 + 24 ft^3 = 128 ft^3
Answer:
v = \(108^{3}\)
Step-by-step explanation:
I'd start with breaking the platform into two parts, the long flat rectangle and then the bit on top. You'll have to add these together at the end!
_________________
So part one: the long piece
formula: v = lwh
dimensions: 12, 3, 2
plug in: v = 12 * 3 * 2
solve: v = 72^3
_________________
part two: smaller rectangle on top ::
formula: v = lwh
dimensions: 4, 3, 3
plug in: v = 4 * 3 * 3
solve:v = 36*3
__________________
now, we add for the total of the entire shape!
final answer: 72 + 36 = 108^3
Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Let the explanatory variable be the percent change in a stock market index in January. Let the response variable be the percent change in the stock market index for the entire year. You have a data set with 50 cases (where each case is a calendar year). Based on this data, you have the following statistics: mean of the x-variable: 2.75% standard devation of the x-variable: 4.48% mean of the y-variable: 8.17% standard devation of the y-variable: 22.31% correlation between the two variables: 0.655 Suppose that the mean change in January is 10.81%. What is the predicted value of the change in the stock market index for the year
Answers
Answer:
1.95
Step-by-step explanation:
Formula for slope is = γ Sy/Sx
γ = Correlation, Sy = S.D. of Y value, Sx= S.D. of X value
Sy = 8.17% = 0.0817
Sx = 2.75% = 0.0275
γ = 0.655
Slope = 0.655 *(0.0817/0.0275)
Slope = 1.94595
Slope = 1.94595
Slope = 1.95
Therefore, the slope of the regression line is 1.95
Lydia has drawn quadrilateral ABCD with diagonal AC . According to her measurements, m∠DAC=m∠BCA and m∠DCA=m∠BAC . Without taking additional measurements, Lydia claims △ABC≅△CDA according to the ASA triangle congruence criteria. Explain why Lydia is correct.
Answers
Answer:
Lydia is correct because the ASA criterion for triangle congruence states that if two triangles have two pairs of congruent angles and the common side of the angles in one triangle is congruent to the corresponding side in the other triangle, then the triangles are congruent which would prove her statement correct.
Step-by-step explanation:
A segment in the complex plane has a midpoint at -1 + 7i. If one endpoint of the segment is at 3 + 8i, what is the other endpoint?
Answers
The other endpoint
Answer: -5 , 6i
Answer: mark me brainliest please!!
1. -3+(-1)i
2. -7.5+2.5i
3. -5+6i
4. -7+1i
Step-by-step explanation:
edge
devide 255 in the ratio 3:7:7:10
Answers
Answer:5
Step-by-step explanation:
5098
Try to change the number back to standard form: 8.24 x 103
Answers
Answer:
= 8.24 × 10³
(scientific notation)
= 8.24e3
(scientific e notation)
= 8.24 × 103
(engineering notation)
(thousand; prefix kilo- (k))
= 8240
(real number)
How do you convert from scientific notation to standard form?
To change a number from scientific notation to standard form, move the decimal point to the left (if the exponent of ten is a negative number), or to the right (if the exponent is positive). You should move the point as many times as the exponent indicates.
At which x-value does the cosine function attain a maximum value?
x = 0
x = StartFraction pi Over 2 EndFraction
x = 1
x = StartFraction 3 pi Over 2 EndFraction
Answers
9514 1404 393
Answer:
x = 0
Step-by-step explanation:
It can help to keep a graph of the cosine function in mind. It starts off at its maximum value at x = 0.
Answer:
x = 0
Step-by-step explanation:
Which expression is equivalent to -6(-2/3+2x)
Answers
Answer:
4-12x
Step-by-step explanation:
-6*-2/3 = 4
-6 * 2x = -12x
In this case the answer is 4 - 12x
An exponential function f(x) = ab^x passes through the points (0, 6000) and (2, 2160). What are the values of a and b?
a = ___
b = ___
Answers
Answer:
a= 3
b.= 3
Step-by-step explanation:
F(x) = ab×
using the 2 given points to find a and b
(0,3)
3=ab⁰
a = 3
(2,27)
27 = 3b² = 9= b²
b = 3
f(x) = 3(3×)
please mark me as brainliest
1. BOWLING Brooke went bowling with her friends. She bowled 3 games, and
her average score for those games was 121. She had 117 her first game and
108 her second game. Write and solve an equation to find g, the score of
her third game.
pls show your work
Answers
Answer: x = 138
Step-by-step explanation:
\(108+117+x=3 * 121\\3 * 121 = 363\\Rearrange unknown terms to the left side of the equation\\x=(363-108)-117\\\\255-117=138\\x=138\)
In addition to putting books on the shelves, Mandy wants to put CD's on the shelves as well. If each shelf is 28 inches long and each CD is 1 3/ inch thick, how many CD's can she place on a shelf?
Answers
There are 9 CD's can she place on a shelf.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Each shelf is 28 inches long and each CD is 1 3/ inch thick.
Now,
Since, Each shelf is 28 inches long and each CD is 1 3/ inch thick.
Hence, The number of CD's = 28 x 1/3
= 9.33
= 9
Thus, There are 9 CD's can she place on a shelf.
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Fill in the blanks.
1. The slopes of perpendicular lines are ______.
2. Parallel lines have the _____ slope.
3. The shortest distance from any point to a line is a ______.
Answers
1. The slopes of perpendicular lines are a negative reciprocal
2. Parallel lines have the same slope.
3. The shortest distance from any point to a line is a straight line
What is the slope perpendicular lines?The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.
if two lines of slope m and m' are perpendicular their slopes is written as
m = -1/m'
What is the slope parallel lines?Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.
if two lines of slope m and m' are perpendicular their slopes is written as
m = m'
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3. Sandra earns P62,954 per month. Determine the following Percentage Amount of Deduction Whld Tax 24% SSS 1.4% Philhealth 1.1% SSS 1.4% Pag-ibig 0.2% Total Deduction Net Pay
Answers
Sandra's total deductions are $16,808.71, and her net pay is $46,145.29.
Given that Sandra earns $ 62,954 per month, to determine the percentage of deductions the following calculations must be performed:
Withhold Tax 24% 62,954 x 0.24 = 15,108.96 SSS 1.4% 62,954 x 0.014 = 881.35 Philhealth 1.1% 62.954 x 0.011 = 692.49 Pag-ibig 0.2% 62.954 x 0.002 = 125.90 Total Deduction = 15,108.96 + 881.35 + 692.49 + 125.90 = 16,808.71 Net Pay = 62,954 - 16,808.71 = 46,145.29
Therefore, Sandra's total deductions are $16,808.71, and her net pay is $46,145.29.
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Solve each proportion 3 = 72 – 7
Answers
x=168
2. 64=20m
m=3.2
1. 3/7 = 72/x
By cross multiplication we get :
➟ 3x = 72 × 7
➟ x = 72 × 7/3
➟ x = 24 × 7
➟ x = 168
2. m/8 = 8/20
By cross multiplication we get :
➟ 20m = 8 × 8
➟ 20m = 64
➟ m = 64/20
➟ m = 16/5
Which equation choice could represent the graph show below?
Answers
Answer:
A
Step-by-step explanation:
Hopefully this helps
the sum of 22 and n is equal to 45.13
Answers
Answer:
23.13
Step-by-step explanation:
According to the property , which choice is equivalent to the quotient below?3577 35 A.5B.C.D.-5E.25
Answers
Answer:
Option A is the right answer mate...
A company offers free shipping on orders that weigh less than 5000grams. Use the facts to find how much this is in kilograms
Answers
Answer:
5 Kilograms
Step-by-step explanation:
So here's how. 1000 grams = 1 kilogram since 1000 grams = 1 kilogram 5000 grams = 5 kilograms.
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What is the answer?? 3(b-5)<-2b
Answers
Answer:
b < 3
Step-by-step explanation:
3 ( b - 5 ) < - 2b
3 ( b ) - 3 ( 5 ) < - 2b
3b - 15 < - 2b
3b + 2b < 15
5b < 15
b < 15/5
b < 3
3(b-5)<-2b
3b<-2b+5
Add the 2b over.
5b<5
Divide by 5.
b<1
Check by plugging in.
3(1-5)<-2(1)
3(-4)<-2
-12<-2
1 is a possibly solution to the inequality.
NO BULL SH*T REAAAAAAAL A F
You have $1000 to invest in an account and need to have $2000 in one year. What interest rate would you need to have in order to have this if the amount is compounded weekly? Round your answer to the nearest percent.
4%
2%
1%
3%
Answers
how can you find the area and perimeter?
Answers
After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape
What is equatiοn?An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.
The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:
1. Rectangle:
• Area: A = length x width
• Perimeter: P = 2(length + width)
2. Square:
• Area: A = side x side (οr A = side²)
• Perimeter: P = 4 x side
3. Circle:
• Area: A = π x radius²
• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)
4. Triangle:
• Area: A = (base x height) / 2
• Perimeter: P = side1 + side2 + side3
5. Trapezοid:
• Area: A = ((base1 + base2) x height) / 2
• Perimeter: P = side1 + side2 + side3 + side4
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What additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria?
Question 5 options:
A)
||
B)
≅
C)
≅
D)
∠F ≅ ∠H
Answers
The additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria is
EJ ≅ GJ. Option A
How to prove the statementWe need to know the properties of a parallelogram, we have;
Opposite sides are parallel.Opposite sides are congruent.Opposite angles are congruent.Same-Side interior angles (consecutive angles) are supplementary.We know that FJ ≅ JH, it's given by the marks, now if it were to happen that EJ ≅ GJ, that would mean that the diagonals on that quadrilateral are bisecting each other, and if that's so, then the quadrilateral it's indeed a parallelogram.
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The complete question:
What additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria?
A)
ej ≅ gj
B)
ej || gj
C)
fg || eh
D)
ef ≅ hg
Identify the value for C in the following equation that would make theconic section a hyperbola: 2x2 + y2 + 3x + 5y + 1 = 0
Answers
ANSWER:
C = -1
STEP-BY-STEP EXPLANATION:
We know that the general formula of hyperbola is the following
\(\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\)Which means that the sign must have y must be negative for it to be a hyperbola.
Therefore y must be equal to -1.
\(2x^2-1y^2+3x+5y+1=0\)Which event is considered neither likely nor unlikely?
A, Rolling a number greater than 1 on a six-sided number cube.
B, Rolling a 1 on a six-sided number cube.
C, Getting heads when flipping a coin.
D, Choosing an X,Y, or Z from a bag containing all the letters of the alphabet.
Answers
According to the information, the event C, getting heads when flipping a coin, is considered neither likely nor unlikely.
Which event is considered neither likely nor unlikely?In probability, an event is considered likely if its probability is high, and it is considered unlikely if its probability is low. An event is considered neither likely nor unlikely if its probability is close to 0.5 or 50%. In this case we have to consider the probability of each option to establish a conclusion. Here is the analysis:
A, rolling a number greater than 1 on a six-sided number cube, has a probability of 5/6, which is greater than 0.5, so it is considered likely.B, rolling a 1 on a six-sided number cube, has a probability of 1/6, which is less than 0.5, so it is considered unlikely.C, getting heads when flipping a coin, has a probability of 1/2, which is equal to 0.5, so it is considered neither likely nor unlikely.D, choosing an X, Y, or Z from a bag containing all the letters of the alphabet, would depend on the specific contents of the bag. If the bag contains an equal number of each letter of the alphabet, the probability would be 3/26, which is less than 0.5, so it would be considered unlikely.According to the above, the event C, getting heads when flipping a coin, is considered neither likely nor unlikely because its probability is exactly 0.5 or 50%.
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Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x)
Answers
| x | 2.5x - 10.5 | 64(0.5x) |
|-------|-----------------|--------------|
| 0 | -10.5 | 0 |
| 2 | 2 | 64 |
| 4 | 7 | 128 |
| 6 | 11 | 192 |
By substituting different values of x into the equation, we can see that there is no single value of x that satisfies the equation for both sides. Therefore, there is no solution to the given equation.