If you are running a fuel economy study. the unit rate for miles per gallon for each car is 22.8 miles and 23.04 miles and the fastest car is Red car.
How to find the unit rate?Units rate = Distance /Time
Blue car
Unit rate = 28 1/2 miles ÷ 1 1/4 gallons of gasoline
Unit rate = 28.5miles ÷ 1.25 gallons of gasoline
Unit rate = 22.8 miles
Red car
Unit rate = 28 4/5 miles ÷ 4/5 gallons of gasoline
Unit rate = 28.8miles ÷ 0.8 gallons of gasoline
Unit rate = 23.04 miles (Fastest)
Therefore the unit rate for each car is 22.8 miles and 23.04 miles and the fastest car is Red car.
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Jason bought 10 of the 30 raffle tickets for a drawing. Assuming that he chooses the winning ticket each time, what is the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize, the ticket is thrown away?
The needed probability that Jason will take home all three awards is 2.96%.
Jason purchased 10 of the 30 tickets for the raffle, which was a drawing.
If a raffle ticket wins a prize and is then discarded, we must calculate the likelihood that Jason will win all three of the prizes.
Let A stand for the scenario in which Jason wins all 3 prizes, and let S stand for the sample area for the experiment in which 3 tickets are drawn at random from 30 raffle tickets.
Since a lottery ticket is discarded after winning a prize,
[tex]n(S) = ^{30} P_{3} = \frac{30!}{(30-3)!} =\frac{30!}{27!} = 24360\\\\n(A) = ^{10} P_{3} = \frac{10!}{(10-3)!} =\frac{10!}{7!} = 720\\[/tex]
Therefore, the probability of event A is given by
P(A) = [tex]\frac{n(A)}{n(S)} = \frac{720}{24360} =0.029955 = 2.96[/tex]%
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Jason can wax the family car in 30minutes, while his brother Kevin can wax the car in 120minutes. How long would it take Jason and Kevin to wax the car together?
____ minutes
This is a proportions math problem.
Using ratios and proportions, the time it takes for both of them to wash both cars is 24 minutes
ProportionsProportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a:b or a/b. Multiply and dividing each term of a ratio by the same number (non-zero), doesn’t affect the ratio.
When two or more such ratios are equal, they are said to be in proportion.
The time it takes for Jason to wax the car in 1 minute = 1/30 minutes
The time it takes for Kevin to wax the car in 1 minute = 1/120
The time it takes for both of them to do it will be in 1 minute = 1/30 + 1/120 = 1/24.
The time it takes for both of them to wax the car = 24 minutes
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Option 2: Summarizing Data with a Measure of Center
A high school basketball player is creating a scout summary of their sophomore season. Here are the points scored during their 12 game season listed out. 29, 24, 32, 20, 0, 22, 28, 29 33, 34, 30, and 27. What measure of center would give the player the best picture of their points scored per game average? Explain how data can be skewed or how measures of center (mean, median, or mode) can be used in favor or against different scenarios in this essay. This is a essay please help!
Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.
What is mean, median and mode?
The sum of the numbers is added, and the result is divided by the total number of numbers in the list to determine the arithmetic mean. An average usually refers to anything like this. In a list with values ranging from smallest to largest, the median is the middle value. On the list, the mode appears the most frequently.
As given, a high school basketball player is creating a scout summary of their sophomore season.
The points are, 29, 24, 32, 20, 0, 22, 28, 29 33, 34, 30, and 27.
Arrange these numbers in ascending order,
0, 20, 22, 24, 27, 28, 29, 29, 30, 32, 33, 34.
So,
Mean = (0 + 20 + 22 + 24 + 27 + 28 + 29 + 29 + 30 + 32 + 33 + 34) / 12
Mean = 308 / 12
Mean = 28
Median = 29
Mode = 29 (2 times repeating)
Because it is more robust, or unaffected by the specific numerical values of those outliers, the median is typically a better indicator of the center when there are extreme values or outliers.
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In the general multiple regression equation, which of the following variables represents the Y-intercept? Select one: O a. b1 O b. X1 c. d. a
Answer:
it is a since using the pythagoras theorium the brainly bahahaha
For rectangles with the same area, the length varies inversely to the width. Henry is trying to decide how to plan the dimensions of his new rectangular swimming pool. He is planning on his pool being 200 square feet. One option would be to have a length of 20 ft and a width of 10ft. Write an equation to model this scenario.
PLEASE HELP WILLMARK BRAINLIEST
A: 10=a/20
B: 20=a/10
C: 10=20/a
D: 20= 10/a
Answer:
It would be c.................
One positive number is 5 more than twice another. If their product is 738, find the numbers.
Answer:
the numbers are 53 and 24.
Step-by-step explanation:
let x be the positive number (x>0) and y the other number
one positive number is 5 more than twice another number x = 5 + 2y
their product is 1272
x*y = 1272
plug x = 5 + 2y into the last equation (5 + 2y)y = 1272 by solving we find y= 24 x = 5 + 2*24
x = 53
the numbers are 53 and 24.
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Scarlett and Kamila are throwing a pizza party. They invited 436 students from school. Each pizza was cut into 6 pieces. How many pizza should they order?
Answer:
73 pizzas
Step-by-step explanation:
Scarlett and Kamila are throwing a pizza party. They invited 436 students from school. Each pizza was cut into 6 pieces. How many pizza should they order?
pizzas are cut into 6 slices so:
436/6 = 72.66 pizzas
Because you cannot order a partial pizza round up to:
73 pizzas
need some help please
The values are given below,
Left Hand Limit i.e. [tex]\lim_{x \to 1^-} f(x)[/tex] = 3 ,
Right Hand Limit i.e. [tex]\lim_{x \to 1^+} f(x)[/tex] = 1 ,
Function value at x = 1 [tex]f(1)[/tex] = 1 ,
Left Hand Derivative [tex]\lim_{x \to 1^-} f'(x)[/tex] = -6 and
Right Hand Derivative [tex]\lim_{x \to 1^+} f'(x)[/tex] = -6.
So, the function f(x) is neither continuous nor differentiable at x = 1.
Given, a piecewise function
3㏑(3 - 2x) + 3 for x < 1
f(x) =
-3x² + 4 for x ≥ 1
Now, for [tex]\lim_{x \to 1^-} f(x)[/tex] we will consider the function 3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.
[tex]\lim_{x \to 1}[/tex] 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3
= 3 ㏑(1) + 3
= 0 + 3
= 3
Now, for [tex]\lim_{x \to 1^+} f(x)[/tex] we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.
[tex]\lim_{x \to 1}[/tex] -3x² + 4 = -3(1)² + 4
= -3 + 4
= 1
Now, for [tex]f(1)[/tex] we will consider the function -3x² + 4,
[tex]f(1)[/tex] = -3(1)² + 4
= -3 + 4
= 1
Now, for [tex]\lim_{x \to 1^-} f'(x)[/tex] we will consider the derivative of the function
3㏑(3 - 2x) + 3,
[tex]\lim_{x \to 1}[/tex] -6/(3 - 2x) = -6/(3 - 2(1))
= -6
Now, for [tex]\lim_{x \to 1^+} f'(x)[/tex] we will consider the derivative of the function
-3x² + 4,
[tex]\lim_{x \to 1}[/tex] -6x = -6(1)
= -6
So, the function f(x) is neither continuous nor differentiable at x = 1.
Hence, [tex]\lim_{x \to 1^-} f(x)[/tex] = 3 , [tex]\lim_{x \to 1^+} f(x)[/tex] = 1 , [tex]f(1)[/tex] = 1 , [tex]\lim_{x \to 1^-} f'(x)[/tex] = -6 and [tex]\lim_{x \to 1^+} f'(x)[/tex] = -6
The function is neither continuous nor differentiable at x = 1.
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Each element in the domain of a function corresponds to______
element in the range.
Each element in the domain of a function corresponds to exactly one
element in the range.
What is an element ?
A pure substance made entirely of one species of atoms, or a chemical element, is a species of atoms with a specific number of protons in their nuclei. Chemical elements, in contrast to chemical compounds, cannot be converted through any chemical reaction into simpler substances.
The items in a set are its elements. A property that all the objects share may serve to define a set. Consider the set E, which consists of all positive even integers. E is equivalent to 2, 4, 6, 8, or 10 dots. E={2,4,6,8,10…}.
A function is a relation in which each element of the domain corresponds to exactly one element of the range.
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a divided by 4 is equal to For a= 7
Answer:
no no lose me das las respuestas
Use the graph below to answer the following question: graph of parabola going through 0, 4, 2, negative 4, and 4, 4 What is the average rate of change from x = 0 to x = 4? Group of answer choices 0 1 4 8
The rate of change of the parabola on the interval [0, 4] is 0.
How to get the average rate of change?For any function f(x), we define the rate of change on an interval [a, b] as:
R = (f(b) - f(a))/(b - a)
Here we want to get the rate of change on the interval [0, 4], and we know that the graph has the points:
(0, 4), (2, -4), (4, 4)
Then:
f(0) = 4
f(4) = 4
Replacing that in the rate of change formula we get:
R = ( f(4) - f(0))/(4 - 0)
R = (4 - 4)/4 = 0
The rate of change on that interval is 0.
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i need help asap with this question
Answer: B
Step-by-step explanation:
The width = 23/4
The length = 2 × the width = 2 × 23/4 = 23/2
The perimeter of the rectangle = 2 ( length + width)
= 2 (23/2 + 23/4 )
= 2 ( 69/4)
= 69/2
= 34 .1/2
Solve the equation without using a calculator
[tex]\bf\log_x\big(2+\sqrt{3} \big)=log_{\big(x+6\big)}\big(1+2\sqrt{3} \big).[/tex]
Answer:
[tex]x=7+4\sqrt{3}[/tex]=====================
Given[tex]log_x(2+\sqrt{3})=log_{x+6}(1+2\sqrt{3})[/tex]Solve it in below steps[tex]2log_x(2+\sqrt{3})=2log_{x+6}(1+2\sqrt{3)}[/tex][tex]log_x(2+\sqrt{3})^2=log_{x+6}(1+2\sqrt{3})^2[/tex][tex]log_x(7+4\sqrt{3})=log_{x+6}(13+4\sqrt{3})[/tex][tex]log_x(7+4\sqrt{3})=log_{x+6}(7+4\sqrt{3}+6)[/tex]Let 7 + 4√3 = t, then[tex]log_xt = log_{x+6}(t+6)[/tex][tex]logt/logx=log(t+6)/log(x+6)[/tex][tex]logx/log(x+6)=logt/log(t+6)[/tex][tex]log_{x+6}x=log_{t+6}t[/tex][tex]x = t[/tex]The value of x is[tex]x=7+4\sqrt{3}[/tex]27. Given: BC || AD, Prove: AB = CD
In this congruent of the triangle its proven that AB = CD.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
Given BC || AD
Both triangles are congruent.
We know the distance between parallel lines always remains the same. So As it is given that BC || AD, AB, and CD both are just distances og the parallel lines
So we can say that both are equal AB = CD
Hence the side AB = CD, in this given figure,
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Which of the following is an equation of a line that is parallel to y = 6x - 2 and has a y-intercept of (0, 3)
A-y = 3x + 6
B-y = 6x - 3
C-y = 3x - 6
D-y = 6x + 3
The equation of a line which is parallel to the given line; y = 6x - 2 as required in the task content is; Choice D-y = 6x + 3.
Equation of parallel lines.It follows from the task content that the equation of a line which is parallel to the given equation; y = 6x - 2 is to be determined.
First, by comparison the given equation with the slope-intercept model of a linear equation; y = mx + c. where m is slope and c is y-intercept.
Slope, m = 6.
Hence, since parallel lines are lines which have equal slopes.
The slope of the required line is therefore; 6 and it's y-intercept (0, 3) has a y-coordinate of; 3.
The required equation of the line is therefore; y = 6x + 3.
The correct answer choice among the answer choices is; Choice D; y = 6x + 3.
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AR 14 What value of x makes this equation true?
12x-15=6-3x. F 7./3. G. 3/7. H5/7. J. 7/5
Answer: 7/5
Step-by-step explanation:
[tex]12x-15=6-3x\\\\15x-15=6\\\\15x=21\\\\\boxed{x=21/15 \ or\ 7/5}[/tex]
2. Раскройте скобки.
a) (6 + a) * 7;
6) 5 (10-x)
Answer:
a) 7a + 42 b) -5x + 50Step-by-step explanation:
a) (6 + a) × 7 = ?
→ (6 + a) × 7
→ (6 × 7) + (a × 7)
→ 42 + 7a
→ 7a + 42
The answer is 7a + 42.
b) 5(10 - x) = ?
→ 5(10 - x)
→ (5 × 10) - (5 × x)
→ 50 - 5x
→ -5x + 50
The answer is -5x + 50.
You deposit $2100 in an account earning 3.6% interest compounded monthly. How much will you have in the account in 7 years?
The compound interest after 7 years is $2701.
What is compound interest?
The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.
When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:
A = P (1 + r/12)[tex].^{n/12}[/tex]
A = 2100(1+3.6/12)[tex].^{7/12}[/tex]
A=2701
Hence the compound interest after 7 years will be $2701.
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I need help on question 5
4. In triangle ΔABC, AB≅BC An altitude is drawn from B to AC and intersects always true?
1) ∠ABD≅∠CBD
2) ∠BDA≅∠BDC
3) AD≅BD
4) AD≅DC
5. In ΔEFG, IF is a median, GE=3 x+5 and I E=x+6. Find x.
Answer:
4. 1), 2), 4) are true
5. x = 7
Step-by-step explanation:
In question 4.
1), 2), and 4) are true
Triangles ABD and CBD are congruent by AAS. Then by CPCTC, 1) and 4) are true. 2) is true by definition of altitude and all right angles are congruent.
5.
Your drawing is good.
Since IF is a median, then IE = IG = (1/2)GE
IE = (1/2)GE
x + 6 = (1/2)(3x + 5)
2x + 12 = 3x + 5
-x = -7
x = 7
Your cross country team ran at a pace of 6 mph for 90 minutes. How far did your team run?
Answer:
9 miles
Step-by-step explanation:
90 min = 1hr and 30 min
6(miles)*1(hr) = 6
6(miles)*0.5(hr) = 3
[ remember we multiply by 0.5 because half of 1 hour is 30 min. ]
Answer: 9 miles
Step-by-step explanation:
convert 90 minutes into hours: 90 mins/60 mins in an hour = 1.5 hours
find how far the team ran: 6mph * 1.5 hours = 9 miles
answer: the team ran 9 miles in 90 minutes
How can a polynomial expression be factored completely?
Answer:
Step-by-step explanation:
To factor the GCF out of a polynomial, we do the following:
Find the GCF of all the terms in the polynomial. Express each term as a product of the GCF and another factor. Use the distributive property to factor out the GCF.
hope it helps!
Find all values of m for which the equation has two real solutions.
3x² + 7x - (m + 1) = 0
Answer:
m > - 5 1/12----------------------
Given is the quadratic equation.
A quadratic equation has two real solutions if the discriminant is positive.
Set inequality and solve for m:D = b² - 4ac, where a = 3, b = 7, c = - (m + 1)D = 7² + 4*3*(m + 1) 7² + 4*3*(m + 1) > 049 + 12m + 12 > 012m + 61 > 012m > - 61m > - 61/12 m > - 5 1/12
3. A grocer has 60kg of potatoes. In one day, he sells 50% of the
potatoes. What mass of potatoes does he sell?
Answer: 30kg
Step-by-step explanation:
100% = 60kg
50% = 100% /2
60kg(100%)/2 = 30kg(50%)
Answer:
Step-by-step explanation:
Proportion:
60 kg - 100%
X kg - 50%
X = 60·50% / 100% = 30 kg
What mixed number is represented on the number line shown here?
Answer:
The mixed number is 1 and 2/5. If it is split into 5 parts.
Step-by-step explanation:
No explanation sorry!
Answer:
Step-by-step explanation:
We already know how to represent whole numbers on the number line. Let us consider the image shown, here, the digits 0 and 1 are represented on the number line.
Representation of 0 and 1 on The Number Line
If we divide the number line into two equal parts, as shown in the figure below, what value does that mid-point hold? Half of what the graduation between 0 and 1 holds.
So, the point represents (1-0)/2 = ½
Fraction - Representation Of Fraction On The Number Line
Thus we saw, to represent a fraction on the number line, we need to divide the line segment between two whole numbers into n equal parts where n represents the denominator of the fraction. For example, if we have to represent the fraction 1/5 on the number line, hence, we need to divide the line segment between 0 and 1 into five equal parts, where the first point as shown in the figure represents the fraction 1/5, the second represents 2/5 and so on.
Fraction Representation
We must note that, 0/5 = 0 here and 5/5 = 1.
Here you have seen the representation of proper fraction on the number line. To represent improper fractions, you first convert them into mixed fractions. The same procedure, as shown above, is used with the whole number as the starting point.
a teacher gives out 12 boxes of crayons for students to use for an art project. each student is given 1/4 of a box of crayons. how many students are given crayons
Answer:
The answer is 48
Step-by-step explanation:
First you have to get the number or crayons ehich is 12 then you can multiply it by the denominator in 1/4 so 12x4=48
Find the distance between the points (2,3) and (5,-2)
The distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.
The given points are (2,3) and (5, -2)
The distance (D) between two points [tex](x_{1} ,y_{1} )[/tex] [tex](x_{2} ,y_{2} )[/tex] is
D = [tex]\sqrt{(x_{1} -x_{2} )^{2} +(y_{1} -y_{2} )^{2} }[/tex]
For evaluating the distance between the points (2,3) and (5, -2)
The distance (D) = [tex]\sqrt{(2 - 5)^{2} +(3 -(-2) )^{2} } = \sqrt{(-3)^{2} +5^{2} } = \sqrt{9+25} = \sqrt{34}[/tex]
Hence, the distance between points (2,3) and (5, -2) is [tex]\sqrt{34}[/tex] units.
Distance is a numerical or occasionally qualitative dimension of how a ways apart objects or points are.
In normal utilization, distance may additionally discuss with a bodily duration or an estimation primarily based on different standards.
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A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. The plant's height, H (in meters), after x months is given by the following.
The plant's height after x months is 11.25 + 15x.
How to calculate the plants height?From the information illustrated, the plant is already 11.25 meters tall, and it will grow 15 centimeters every month.
In this case, let the plant's height be H (in meters)
Let the number of months be x.
The plant height will be:
= 11.25 + (15 × x)
= 11.25 + 15x
This is the height.
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Complete question
A plant is already 11.25 meters tall, and it will grow 15 centimeters every month. When is the plant's height, H (in meters), after x months?
Use synthetic division to find the quotient if polynomial P(x) = x³ - 7 x + 6 is divided by x - 2
A) x²+2 x+3
B) x²-2 x-3
C) x²-2 x+3
D) x²+2 x-3
The polynomial function p(x) = x³ - 7x + 6 divided by x - 2 = x² + 2x - 3
Synthetic Division of PolynomialsSynthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor. One of the advantages of using this method over the traditional long method is that the synthetic division allows one to calculate without writing variables while performing the polynomial division, which also makes it an easier method in comparison to the long division.
We can represent the division of two polynomials in the form:
p(x)/q(x) = Q(x) + R/(q(x))
where,
p(x) is the dividendq(x) is the linear divisorQ(x) is quotientR is remainderThe polynomial function p(x) = x³ - 7x + 6 is divided by x - 2
x³ - 7x + 6 ÷ x - 2 = (x - 1)(x + 3)
x² + 3x - x - 3 = x² + 2x - 3
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13. Critique Reasoning In math class, you are checking how a friend balanced an equation. His work is at the right. What error did your friend make? Explain.
The error in balancing the equation is that the although the number terms on both sides of the equation are the same, the operation on the 1 on the left is an addition while the operation on the number 1 on the Right Hand Side of the equation is a subtraction
What is a balanced equation?A balanced equation is one in which the values or amounts on both sides of the equation are the same.
The unbalanced equation is presented as follows;
16 ÷ 8 = 16 ÷ 8 - 1
The form balanced equation in the question is; 16 ÷ 8 + 1 = 16 ÷ 8 - 1
The error is that in the balanced equation a 1 was added to the Left Side of the equation, while in the unbalanced equation, the difference between the left and right side of the equation is a subtraction of a 1 from the Right Hand Side of the equation.
The step to correctly balance the unbalanced equation involves the subtraction of a 1 from the Left Hand Side as follows;
16 ÷ 8 - 1 = 16 ÷ 8 - 1 (Balanced equation)The unbalanced equation 16 ÷ 8 = 16 ÷ 8 - 1 can be balanced by applying the addition (or subtraction) property of equality, which states that the when the same quantity is added (or subtracted) from two quantities that are initially equal, the resulting quantities that have a different amount following the addition (or subtraction) will remain equal.
The expression, 16 ÷ 8 and 16 ÷ 8 are the same.
Subtracting the same amount of 1 from both sides will result in two new expressions that are also equal in amount as follows;
16 ÷ 8 = 16 ÷ 8
16 ÷ 8 - 1 = 16 ÷ 8 - 1
The error is therefore in adding rather than subtracting a 1 from the Left Hand Side of the equation to balance the equations.
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-1.5x+3(-0.3x-1) simplify the linear expression
Answer: -2.4x-3
Step-by-step explanation:
