The graph represents the amount of money Sal earns for babysitting.
Graph where the x- axis gives time in hours and runs from zero to three and beyond. The y- axis gives earnings in dollars and runs from zero to twenty four and beyond. A straight line intersects the axes at (0, 0). Its coordinates are (5, 4), (1, 8), (1.5, 12), (2, 16), and (2.5, 20)
Part A
What does the ordered pair (2.5, 20) represent in the situation?
A. $2.50 for 20 hours
B. $1 for 0.125 hours
C. $0.125 for 1 hour
D. $20 for 2.5 hours
Part B
Does the graph represent a proportional relationship? Explain.
A.
Yes. The line passes through the origin.
B.
Yes. The line has a variable rate of change.
C.
No. The slope is not constant.
D.
No. The line has a y-intercept greater than 0.
Part C
What is the linear equation represented by the graph?
A. y = 20x + 2.5
B. y = 2.5x + 20
C. y = 8x
D. y = 0.125x
Answers
Answer: d, a, and c
Step-by-step explanation:
Part(A)
The ordered pair (2.5, 20) represents $2.50 for 20 hours. the correct option is A.
Part(B),
Yes. the line passes through the origin. The correct option is A.
Part(C),
The linear equation represented by the graph is y = 8x. The correct option is C.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that coordinates are (0.5, 4), (1, 8), (1.5, 12), (2, 16), and (2.5, 20).
Part(A),
The ordered pair (2.5,20) represents that the earning is $20 for the work of 2.5 hours.
Part(B),
The slope of the line will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 8 - 4 ) / ( 1 - 0.5 )
Slope = 4 / 0.5
Slope = 40 / 5
Slope = 8 hours
The y-intercept is calculated as,
y = mx + c
16 = ( 2 x 8 ) + c
c = 16 - 16
c = 0
Hence, the line passes through the origin.
Part(C),
The equation of the line will be written as,
y = mx + c
y = 8x + 0
y = 8x
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Related Questions
can someone help me its due soon
Answers
Answer: 10
Step-by-step explanation:
Triangles have 3 sides. So each side is either equivalent or one side is short while the other two are equivalent.
Melani cai type a 600 word essay in
just 8 mini tes. How long will it take
her to type a 2,100 word essay?
Answers
Answer: It will take Johny 28 minutes to type a 2,100 word essay.
Step-by-step explanation:
600 words per 8 minutes. (6 * 3.5 = 21) 8 times 3.5 equals 28 minutes.
Work Shown:
(600 words)/(8 minutes) = (2100 words)/(x minutes)
600/8 = 2100/x
75 = 2100/x
75x = 2100
x = 2100/75
x = 28
PLEASE HELP!!
triangle abc is reflected about the line y=-x to give triangle a’b’c’ with vertices A’(-1, 1) B(-2, -1), C(-1, 0). what are the vertices of triangle abc
Answers
Answer:
-7,-6,-3.these are the vertices
Find the average value of the function over the given interval. (Round your answer to three decimal places.)
f(x) = 6e^x, [−3, 3]
=
Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.) x=
Answers
The only value of x in the interval [-3, 3] for which the function equals its average value is approximately x = 2.984.
What is integration?
Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.
To find the average value of the function f(x) = 6e^x over the interval [-3, 3], we need to evaluate the definite integral of f(x) over that interval and divide the result by the length of the interval:
Average value = (1/(3-(-3))) * ∫[−3, 3] 6e^x dx
= (1/6) * [\(6e^x\)] from -3 to 3
= (1/6) * (\(6e^3\) - \(6e^{(-3)}\))
≈ 118.936
Therefore, the average value of the function over the given interval is approximately 118.936.
To find all values of x in the interval [-3, 3] for which the function equals its average value, we need to solve the equation f(x) = 118.936, which means:
\(6e^x\) = 118.936
Dividing both sides by 6, we get:
\(e^x\) = 19.823666...
Taking the natural logarithm of both sides, we get:
x = ln(19.823666...)
≈ 2.984
Therefore, the only value of x in the interval [-3, 3] for which the function equals its average value is approximately x = 2.984.
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Trigonometric functions
Answers
9514 1404 393
Answer:
β ≈ 39.9°
θ ≈ 50.1°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to remind you of the relationships between the sides of a right triangle and the trig functions of the acute angles.
For angle β, we know the opposite side and the hypotenuse, so the relevant relation is ...
Sin = Opposite/Hypotenuse
sin(β) = 61/95
The inverse function is used to find the angle when the sine is known.
β = arcsin(61/95) ≈ 39.9°
Of course, the angle θ is the complement of this:
θ = 90° -39.9° = 50.1°
Answer:
Step-by-step explanation:
sin β = 61/95 = 0.642105
β = 39.95 degrees.
O = 90 - 39.95
= 50.05 degrees
cos O = 61/95.
Note that cos (90-β) = sin β.
10x + 6y - 5x idk how to do this
Answers
5x+6y is the answer i jope this helps you
Which ratio is equivalent to 12/2
Answers
Answer:
36/6
Step-by-step explanation:
12 x 3= 36.
2 x 3= 6.
Answer:
C. \(\frac{36}{6}\)
Step-by-step explanation:
In AXYZ, the angle measures are in the ratio 2:4:6. What are the measures of the angles?
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given that the measures of the Angles of the triangle ΔXYZ are in the ratio 2:4:6.
As the angles are in the proportion 2:4:6. Thus, the measure of the angles will have the same scale factor x.Also, the sum of the measure of angles in a triangle is 180°.
so
2x + 4x + 6x = 180
Add similar elements: 2x + 4x + 6x = 12x
12x = 180
Divide both sides by 12
12x/12 = 180/12
Simplify
x = 15
Therefore, the measure of the angles of a triangle will be:
2x = 2(15) = 30
4x = 4(15) = 60
6x = 6(15) = 90
Verification:
30 + 60 + 90 = 180
180 = 180
Tina made 4.5 liters of chicken soup. How can she convert this number to find out how many mililiters of soup she made?
Answers
1000 mililiters are equivalent to 1 liter, then Tina has to multiply 4.5 by 1,000 to convert liters to mililiters
help! I'll give brainliest!!!
Answers
Answer: V = 378 i think
Step-by-step explanation:
Round the number to the place of the underlined digit. 4.327
Answers
Answer:
Tenths -- 4.3
Hundredths -- 4.33
Thousandths -- 4.327
Ones -- 4
Step-by-step explanation:
t i) let [a; b] be a non-degenerate closed interval in r, and let f : [a; b] ! r be twice di§erentiable with f(a) < 0, f(b) > 0, f 0 (x) c > 0, and 0 f 00(x) m for all x 2 (a;
Answers
A. By the given conditions, the function f has a root in the interval [a, b].
B. The given conditions provide information about the function f and its derivatives.
Let's analyze the conditions step by step:
1. f(a) < 0 and f(b) > 0: This implies that function f takes negative values at the left endpoint a and positive values at the right endpoint b.
In other words, the function changes the sign between a and b.
2. f'(x) > 0 for all x in (a, b): This condition states that the derivative of f, denoted as f'(x), is always positive in the open interval (a, b).
This indicates that the function is increasing within this interval.
3. f''(x) > 0 for all x in (a, b): This condition states that the second derivative of f, denoted as f''(x), is always positive in the open interval (a, b).
This indicates that the function is concave up within this interval.
By combining these conditions, we can conclude that the function f is continuous, increasing, and concave up within the interval (a, b).
Since f(a) < 0 and f(b) > 0, and the function changes sign between a and b, by the Intermediate Value Theorem, there exists at least one root of the function f in the interval [a, b].
Therefore, the main answer is that the function f has a root in the interval [a, b].
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Elisa withdrew $26 at a time from her bank account and withdrew a total of $208. Frances
withdrew $49 at a time from his bank account and withdrew a total of $245. Who made the
greater number of withdrawals?
And how many withdrawals did each person make?
(Please help me!)
Answers
Answer:Elisa made the greater number of withdrawals
Step-by-step explanation:
208 divided by 26 is 8
245 divided by 49 is 5
Answer:
5
Step-by-step explanation:
divid lol
Somebody pls help me
Answers
Hello.
Put your finger on 4, which is under B, and keep doing jumps over digits to the left until you hit the dot that A is on. It takes 13 jumps to get there from B
Which are the better statistics to use to compare the team scores? Team A's scores H 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 Team B's scores 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 100 O A. Median and standard deviation O B. Mean and standard deviation O C. Mean and IQR O D. Median and IQR
Answers
Answer: median and IQR
Step-by-step explanation:
one is skewed
The better statistics to compare the team scores are median and IQR.
Option D is the correct answer.
We have,
From the box plot,
We can easily find the value of the median and Interquartile range.
Now,
Team A:
Median = 68
First quartile = 65
Third quartile = 80
IQR = 80 - 65 = 15
Team B:
Median = 79
First quartile = 68
Third quartile = 90
IQR = 90 - 68 = 22
Thus,
The better statistics to compare the team scores are median and IQR.
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(Chapter 12) If u * v = 0 and u X v = 0, then u or v = 0
Answers
Therefore, in either partial derivatives, we have u = 0 or v = 0.
The given information implies that two vectors u and v satisfy:
u * v = 0, where * denotes the dot product between vectors.
u X v = 0, where X denotes the cross product between vectors.
From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.
From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:
|u X v| = |u| * |v| * sin(θ)
= 0
Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).
In the case where u and v are parallel, we have:
u * v = |u| * |v| * cos(θ)
= |u|²
= 0
This implies that |u| = 0, which means that u = 0.
In the case where u and v are anti-parallel, we have:
u * v = |u| * |v| * cos(θ)
= -|u|²
= 0
This again implies that |u| = 0, which means that u = 0.
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Is W = 2 a solution to the inequality below?
8 < W
yes
no
Pls help
Answers
Answer: no
Step-by-step explanation: 8 is not less than 2
what does a z-score tell us about an individual observation in a data set? it is the number of standard deviations an observation is away from the mean. the midpoint of the sorted sample data set the sum of all data values divided by the number of data items. the average. the most frequently occurring data value in the set. none of the above
Answers
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.
A z-score is the value of an observation expressed in standard deviation units. The sign of the score indicates whether it is above (positive) or below (negative) the mean, and the value quantifies how many standard deviations the score is from the mean.
The purpose of z-scores is to identify and describe the exact location of each score in a distribution & to standardize an entire distribution to understand & compare scores from different tests.
Z-scores or Z-statistics represent a statistical technique of measuring the deviation of data from the mean. There are different formula used for Z-score or Z-statistics depending upon what is measured. Z-statistics is generally used with Z-test which is a hypothesis testing statistical technique.
Therefore,
A z-score tell us about an individual observation in a data set is, the number of standard deviations an observation is away from the mean.
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e. In a survey, it was found that the ratio of people who like tea and coffee is 9:8. If 25% liked tea and coffee both, 80 liked none of these and 20% liked tea only, find the total number of people participated in the survey.
Answers
Given 14 – 2(x + 8) = 5x – (3x – 34), prove x = -9 what are the steps to be able to prove x=-9
Answers
Answer: x = -9
steps
Simplifying
14 + -2(x + 8) = 5x + -1(3x + -34)
Reorder the terms:
14 + -2(8 + x) = 5x + -1(3x + -34)
14 + (8 * -2 + x * -2) = 5x + -1(3x + -34)
14 + (-16 + -2x) = 5x + -1(3x + -34)
Combine like terms: 14 + -16 = -2
-2 + -2x = 5x + -1(3x + -34)
Reorder the terms:
-2 + -2x = 5x + -1(-34 + 3x)
-2 + -2x = 5x + (-34 * -1 + 3x * -1)
-2 + -2x = 5x + (34 + -3x)
Reorder the terms:
-2 + -2x = 34 + 5x + -3x
Combine like terms: 5x + -3x = 2x
-2 + -2x = 34 + 2x
Solving
-2 + -2x = 34 + 2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x' to each side of the equation.
-2 + -2x + -2x = 34 + 2x + -2x
Combine like terms: -2x + -2x = -4x
-2 + -4x = 34 + 2x + -2x
Combine like terms: 2x + -2x = 0
-2 + -4x = 34 + 0
-2 + -4x = 34
Add '2' to each side of the equation.
-2 + 2 + -4x = 34 + 2
Combine like terms: -2 + 2 = 0
0 + -4x = 34 + 2
-4x = 34 + 2
Combine like terms: 34 + 2 = 36
-4x = 36
Divide each side by '-4'.
x = -9
7. Consider the equation x/3+ 7 = 13.
Part A: Write an equivalent equation using the multiplication property of
equality.
Part B: What properties will you use next to solve the equations?
Answers
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
i know it
What is the vertex of g(x) = 3x2 − 12x + 7?
Answers
\(\mathbf{Task.} ~ \mathrm{What~is~the~vertex~of}~ g(x) = 3x^{2} - 12x + 7?\)
\(\mathrm{Function~of~the~form} ~ f(x) = ax^{2} + bx + c, ~ a \neq 0, ~ \mathrm{is~ called~a~quadratic~function.}\\\mathrm{The~top} ~ (x_{0}; \ y_{0}) ~ \mathrm{of~this~function~can~be~found~by~the~formulas \colon}\)
\(x_{0} = \dfrac{-b}{2a};\)
\(y_{0} = ax_{0}^{2} + bx_{0} + c ~ \mathrm{or} ~ y_{0} = -\dfrac{b^{2} - 4ac}{4a}.\)
\(\mathrm{So,~for~the~function} ~ g(x) = 3x^{2} - 12x + 7 ~ \mathrm{we~have \colon}\)
\(x_{0} = \dfrac{-(-12)}{2 \cdot 3} = \dfrac{12}{6} = 2;\)
\(y_{0} = 3 \cdot 2^{2} - 12 \cdot 2 + 7 = -5.\)
\(Answer \colon (2; \ -5) \ \blacktriangle\)
Answer:
C
Step-by-step explanation:
Henry wants to estimate the cost of filling his water tank. First, he needs to find the volume of the water tank in order to fill it. What is the volume of the water tank?
Answers
Answer:
60 ft³
Step-by-step explanation:
2 x 3 x 4 = 24
3 x 3 x (6-2) = 36
24 + 36 = 60
hope this helps :)
Jack and Jill each opened accounts that earn 5% interest compounded annually. Jack deposited $2500 and Jill deposited $3000. No additional money was deposited or withdrawn. At the end of 6 years, what will be the combined balance of these two accounts? (Round to the nearest cent)
Answers
Answer:
3,850
Step-by-step explanation:
have a good day!!
I purchased 3.4 pounds of apples for $7.29. What is the cost per pound? I need the answer fast.
Answers
Answer:
The answer is $2.14 per pound of apples.
Step-by-step explanation:
7.29/3.4= roughly 2.14.
Answer:
is 24.786
Step-by-step explanation:
multiply the numbers and that's how you get your answer and I use my calculator so I know the answer is 24.786
8)
Which inequality statement describes the two numbers: - 22 and a number 47 units to the right of -22?
A)
-22 > 47
B)
-22 < 47
C)
-22 > 25
D)
-22 < 25
Answers
Answer:
D) -22 < 25
Step-by-step explanation:
If the number is 47 units to the right, then the number will be larger than -22, because negative values get larger the closer they are to zero.
47 units right from -22 is the same as: -22 + 47, which equals 25.
So, we can conclude that -22 < 25 is the inequality.
hope this helps!
of the 254 counties in texas, how many have child care programs that state they provide nighttime care for children?
Answers
By following these steps, you should be able to find the number of counties in Texas with childcare programs offering nighttime care for children.
To answer your question about how many of the 254 counties in Texas have child care programs that state they provide nighttime care for children, we would need to access current data on child care programs in Texas. Unfortunately, I do not have that specific data at the moment. However, I can guide you on how to find this information.
Begin by visiting the Texas Health and Human Services website (https://hhs.texas.gov) as they are responsible for overseeing child care licensing in the state. Look for information on licensed child care facilities that provide nighttime care.
Utilize websites such as Child Care Aware (https://www.childcareaware.org) or Child Care Finder (https://childcarefinder.com), where you can search for child care programs in Texas by county, and filter your search to include only programs offering nighttime care.
You may also want to check with local county websites or contact the County Clerk's office for information on child care programs within their jurisdiction, specifically those offering nighttime care.
Compile the data gathered from the above sources to determine how many of the 254 Texas counties have child care programs providing nighttime care for children.
By following these steps, you should be able to find the number of counties in Texas with child care programs offering nighttime care for children.
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what will the remainder over the divisor?
Answers
Question 2
5 pts
1. It was 8 degrees at nightfall. The temperature dropped 10 degrees by
midnight. What was the temperature at midnight?
[Select]
2. A diver is 25 feet below sea level. After he swims up 15 feet toward the
surface, what is his elevation?
[ Select ]
Answers
Answer:
1. -2 degrees
2. 10 feet below sea level
Step-by-step explanation:
Simplify.
8w^10 x 6w^5
Answers
when multiplying values with exponents, you add the exponents instead of multiplying them