3 × 10² miles can you drive, if your car gets 25.00 miles per gallon and you have 12.00 gallons of gas.
What is distance?Distance is the sum of an object's movements, regardless of direction. Distance may be defined as the amount of space an item has covered, regardless of its beginning or finishing position.
Given that,
car gets 25.00 miles per gallon.
In 1 gallon car covers 25 miles distance.
In 12 gallon the car will cover = 25 × 12 miles distance
= 300 miles distance.
Thus, distance covered in 12 gallons = 300 miles.
= 3 × 10² miles.
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Let f be a differentiable function with f(1) = 2, f'(1) = 3, f(-4)= -3, and
f'(-4)= 4. Let the function g(x) = f(2x - 6). Write the equation of the line
tangent to the graph of g at the point where x = 1.
The equation of the line tangent to the graph of g at the point where x = 1 y + 10x + 44 =0.
What is line tangent?
A line that touches a curve at one point is said to be tangent. A point of tangency is the location where a curve and a line intersect. Y = mx + b is the slope-intercept formula for a line, where m is the line's slope. The straight line that "just touches" the curve at a particular location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.
Given g(x)=f(2x)
Differentiate it on both side with respect to x.
[tex]\begin{aligned}& \frac{d g(x)}{d x}=2 * \frac{d f(2 x)}{d x} \\& \frac{d g(-1)}{d x}=2 * \frac{d f(-8)}{d x}=-5^* 2=-10\end{aligned}[/tex]
Slope =-10
Here x coordinate = -4
g(-4)=f(-8)=-4 = y coordinate
Thus point of tangency on function g is (-4,-4)
Thus equation of tangent is
y + 4= -10(x+4)
y + 10x + 44 =0
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Answer:
y = 8x -11
Step-by-step explanation:
You want the equation of the line tangent to g(x) = f(2x-6) at x=1, where f is a differentiable function with f(1) = 2, f(-4) = -3, f'(1) = 3, f'(-4) = 4.
Tangent lineThe equation of the tangent line at x=1 can be written ...
y = g'(1)(x -1) +g(1)
The necessary function values are ...
g(1) = f(2·1 -6) = f(-4) = -3
and
g'(x) = f'(2x -6)·(2x -6)' = 2f'(2x -6)
g'(1) = 2f'(2·1 -6) = 2f'(-4) = 8
Then the equation of the line is ...
y = 8(x -1) +(-3) = 8x -8 -3
y = 8x -11 . . . . . . tangent to g(x) at x=1
__
Additional comment
The minimum polynomial function f(x) that can have the desired values and derivatives is a cubic. The attached graph shows g(x) and the tangent at x=1 using that cubic for f(x).
There are 95 green balls and 90 red balls in a box. How many balls must be chosen to
be certain we have the following?
Three of each color?
To be certain of attaining the required result , 5 green balls must be selected.
We are informed that a box contains 90 red balls and 95 green balls.
To ensure that we have the items below, we must find the balls.
One red and one green
Consequently, take away the box's 90 red and 95 green balls.
95-90 = 5
Consequently, 5 green balls must be picked.
The unitary method , in its most basic form, is used to calculate the value of a single unit from a specified multiple. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.
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On a hike, Oscar's elevation change after 12 minutes was -84 feet. Assuming his elevation was changing at a constant rate, what integer represents his elevation change per minute?
2/3 x=27
PLEASE HELPPPP ASAPPP
Answer:
81/2 is answer.......2/3× 81/ 2 = 27
Answer:
x=40.5
Step-by-step explanation:
2/3x=27
x3. x3
2x=81
/2 /2
x=40.5
hopes this helps please mark brainliest
What is the slope of a line parallel to the line whose equation is
8x-6y=-24
The slope of a line parallel to the line 8x - 6y = -24 is 4/3.
What is slope of a line parallel to the line whose equation is given?The slope-intercept formula is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the line.
8x - 6y = -24
First, rewrite in slope-intercept form.
8x - 6y = -24
Solve for y
8x + 24 = 6y
6y = 8x + 24
y = (8/6)x + 24/6
y = (4/3) + 4
Now, from the slope-intercept form;
y = mx + b
Where m is the slope
Slope of the line y = (4/3) + 4 will be
m = 4/3
All line parallel to the line y = (4/3) + 4 must have the same slope.
Hence, the slope of a parallel line to the line y = (4/3) + 4 will be;
m_parallel = 4/3
Therefore, the slope of the parallel line is 4/3.
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Using Graphs to compare two quantities.
In order to make a pecific hade of green paint a paint mixe 1/2 of a gallon of blue paint with 4/5 of a gallon of yellow piant how many gallon of each color ate needed to make 26 total gallon of thi color
To make 26 gallons of the shade of green paint, 13 gallons of blue paint is needed.To make 26 gallons of the shade of green paint, 20.8 gallons of yellow paint is needed.
What is meant by multiplication?Finding the product of two or more integers is done mathematically through the action of multiplication. It entails adding a number, known as the , known as the multiplier. For instance, adding three to itself four times produces the result of multiplying three by four, which is twelve. In other ways, repeated addition may be expressed using the abbreviation "multiplication." It is frequently used to calculate the overall worth of a set of paint, such as the cost of numerous products in a shopping cart. Finding the area of a rectangle or the volume of a cube are two more more difficult mathematical procedures that employ it.
How to solve?
To make 26 gallons of the shade of green paint, 1/2 * 26 = 13 gallons of blue paint is needed.
To make 26 gallons of the shade of green paint, 4/5 * 26 = 20.8 gallons of yellow paint is needed.
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Alexandra grew 9 flowers with 3 seed packets. How many seed packets does Alexandra need to have a total of 18 flowers in her garden? Solve using unit rates.
Answer:
The answer is 6, I am going to give you a explanation just in case you need one.
Step-by-step explanation:
We are going to refer seed packets as SP just to make it more simple. And flowers F this is just to make it easier on ourselves.
Ok since we know that in order to plant 9 F we need 3 SP.
If we do the equation correctly we should get
3 SP × ? = 9
In order to do this there is two ways I am going with the easier one we just have to add 3 to 3 until we get 9 ok so 3 + 3 = 6 so lets add more 3's 6 + 3 = 9 great so this means 3 + 3 + 3 = 9. Now if you noticed he had three three's which means our equation now is
3 SP × 3 = 9
Now that we are done with the first part it should just get easier from here.
We know that each SP has 3 F to grow and each SP has 9 F to grow we just have to do 9 + 9 which gives us 18.
Therefore the answer is 2 SP needed to plant 18 flowers.
Hope this helped :)
Morgan ha 6 pack of eraer. Each pack of eraer ha x eraer in it. After Avery give her 3 more eraer, he ha a total of 27 eraer. A. Model the ituation with an equation. B. Find a olution to your equation from part (a)
c. Interpret the olution in the context of the problem
The equation that represents the model is 6x + 3 = 27, the solution of the equation is x = 4
Total number of pack of eraser = 6
Number of eraser in one pack = x
Number of erasers in 6 pack = 6x
Add 3 more erasers
Total number of erasers = 6x + 3
Total number of erasers = 27
Then the equation that represents the model will be
6x + 3 = 27
Solve the equation
6x = 27 - 3
Subtract the numbers
6x = 24
x = 24/6
Divide the numbers
x = 4
Therefore, the equation is 6x + 3 = 27, and the solution of the equation x = 4
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What is the value of Y?
(Please help me with this question.)
Answer:
x = 8
y = 36
Step-by-step explanation:
The triangle shown in the image is an isosceles triangle.
We can find the value of x using the above mentioned information:
∠B = ∠A
5x = 40 divide both sides by 5
x = 8
The sum of interior angles in a triangle is equal to 180°.
Since ∠B and ∠C are both 40°:
40 + 40 + 3y - 8 = 180 add/subtract like terms
72 + 3y = 180 subtract 73 from both sides
3y = 108 divide both sides by 3
y = 36
Which equation represents a vertical line? *
A. y =2x
B. x = 2
C. y = 3
D. y = -x
Answer:
x = 2
Step-by-step explanation:
X is the vertical edge
x=2
Answer: x = 2
Step-by-step explanation:
The slope of a vertical line is undefined, so the equation of a vertical line is x = a
In this problem, the only choice that represents a vertical line is x = 2 (where a = 2)
The point (6,9) is shown on the graph. Write an equation that represent this situation, where Y represent the amount of water, in cups, and X represents the number of lemons
The equation that represents the situation will be y = 1.5x.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
From the graph, the y-intercept of the line is zero. Then the equation is given as,
y = mx
The line is passing through (6, 9), then we have
9 = 6m
m = 9 / 6
m = 1.5
Then the equation that represents the situation will be y = 1.5x.
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The length of a rectangle is twice its width. How many times as long as the width of the rectangle is the perimeter of the rectangle?
Answer:
perimeter is 6 times as long as the width
Step-by-step explanation:
let width be w then length l = 2w
perimeter (P) of a rectangle is calculated as
P = 2(l + w )
= 2(2w + w)
= 2(3w)
= 6w
Perimeter is 6 times as long as the width
The width of the rectangle is (1/6) times long as the perimeter of the rectangle.
What is the area of a rectangle?The area of a rectangle is given by -
A{R} = Length x Breadth
A{R} = L x B
Given is the length of a rectangle is twice its width.
Assume the width of the rectangle be [x] units. Then, the length will be [2x] units. For the width of the rectangle to be as long as the perimeter of the rectangle -
{P} = 2{L + B} = 2{x + 2x} = 6x
Now -
{w} = x
So, we can write that -
{P} = 6{w}
{w} = {1/6}{P}
Therefore, the width of the rectangle is (1/6) times long as the perimeter of the rectangle.
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Which situation below represents a 30% decrease?
from 50 to 35 OR from 30 to 27
Answer: 50-35
Step-by-step explanation:
Because if you calculate it, 50x70% or 50x0.7 is 35. I multiply bt 70% not 30% because you are trying to find the amount after the 30% decrease, meaning it is 70% of the orginal value.
Answer:
50 to 35
Step-by-step explanation:
[tex]\frac{30}{27} =\frac{100}{y}[/tex]
30y = 2700
y = 90
27 is 90% of 30.
[tex]\frac{50}{35}=\frac{100}{y}[/tex]
50y = 3500
y = 70
35 is 70% of 50.
100 Points , MAX. Please help I dont have a lot of time, assignment goes due tonight.
I will give brainliest.
Answer:pt 1). Oliver is correct
pt 2). The volumes are the same
yw
The number of vhs movie rentals has declined since the year 2000 due to the popularity of dvds, as the following table shows. The exponential regression equation was found to be where x represents the number of years since 2000. Use the regression equation to predict the number of vhs movies in 2011. Year 2000 2001 2002 2003 2004 2005 2006 vhs rentals (in millions) 10. 5 8. 1 6. 4 5. 2 4. 5 3. 8 3. 1 a. 1. 13 c. 0. 929 b. 1. 37 d. 3. 7 please select the best answer from the choices provided a b c d.
In 2011 we can predict there will be only 1.13 million VHS movie rentals.
What is regression equation?
A regression equation is utilized in details to figure out what relationship, if any, exists between sets of information. For instance, assuming that you measure a kid's level consistently you could find that they develop around 3 inches a year. That pattern (growing three inches a year) can be displayed with a regression equation.
According to question:
The remarkable relapse condition is the dramatic capability that best fits the arrangement of information and it is given in the structure:
y = a · bˣ
where:
a = beginning worth of the model
b = remarkable develop or rot
x = time elapsed all along
For our situation,
y = 9.92 · (0.8208)ˣ
where:
a = 9.92
b = 0.8208
Since 0 < b < 1 we have an outstanding rot, affirming that the quantity of VHS is diminishing with time.
We can then utilize this condition to gather the quantity of VHS motion pictures in 2011.
As something first, compute how long all along (2000) would pass:
x = 2011 - 2000 = 11
Presently, substitute this worth in the situation:
y = 9.92 · (0.8208)¹¹
= 1.13
Thus, number of vhs movies in 2011 is 1.13 million.
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Which expression is represented by this model?
Responses
The correct option is 1/8 for the given expression.
What is fraction?
In Maths, a fraction is employed to represent the portion/part of the full issue. It represents the equal elements of the full. A fraction has 2 elements, particularly dividend and divisor. the quantity on the top is named the numerator, and therefore the range on the bottom is named the denominator.
Main body:
firstly , the model shows that it is divided into 4 parts
so the fraction becomes 1/4
as one part of 1/4 is divided into half so we can say
half of quarter which can be represented as
1/4*1/2 = 1/8
Hence the correct option is 1/8
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reteaching 5-4 proportions (PLEASE HELP)
The Answers are shown below:
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
1. 3 x 20= 60
10 x 6 =60
Yes, it is proportion.
2. 12 x 4 =48
24 x 2= 48
Yes, it is proportion.
3. 8 x 8= 64
5 x 16 = 80
No, it is not proportion.
4. 7/5, 21/15 is proportion
5. 16/3, 5/1 is not proportion
6. 12/9, 4/3 is proportion
7. 4/24, 2/6 is not proportion
8. 15/5, 6/2 is proportion
9. 9/3, 27/9 is proportion
10. 25/35, 5/7
or, 5/7, 5/7
The ratio is in proportion.
11. 15/3, 10/2
or, 3/1, 5/1
The ratio not in proportion.
12. 9/3, 12/4
or, 3/1, 3/1
The ratio is in proportion.
13. 2/5, 6/15
or, 2/5, 2/5
The ratio is in proportion.
14. 3.6/200, 1.8/100
The ratio is in proportion.
15. 6/12, 4/8
or, 1/2, 1/2
The ratio is in proportion.
16. 16/ 12 , 96/24
or, 4/3, 4/1
The ratio not in proportion.
17. 3/7, 2/5
The ratio not in proportion.
18. 2/22, 1/11
or, 1/ 11, 1/11
The ratio not in proportion.
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help with math 7 12345678910
1) 18 Quarts of Sparkling water needs to be mixed with 9 quarts grape juice.
2) 15/2 Quarts of grape juice is required for 15/4 quarts of sparkling water.
3) The Quantity of grape juice and sparkling water in 100 quarts of punch are 33 1/3 quarts and 66 2/3 quarts respectively.
Step-by-step explanation:Learn more about the answer to your question here at:
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I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
In a rhombu, ide a equal 160 cm and angle alpha equal 60 degree. Calculate the ize of the diagonal
5√3 is of the diagonal of rhombus .
What is a rhombus, exactly?
A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal.
A rhombus's diagonals are right angles to one another, and all of its sides are equal in length. The term "rhombus" can also refer to a diamond or rhombus.
Since all the sides are equal, the altitude is
10 sin60° = 5√3
To see this, draw the rhombus ABCD and drop an altitude from D to AB.
Now you have a right triangle with hypotenuse=10 and base angle=60°
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the periodic interest rate for a loan with an annual interest rate of 15.98% compounded weekly is 0.3073%, rounded to four decimal places.
a. True
b. False
yes, the periodic interest rate for a loan with an annual interest rate of 15.98% compounded weekly is 0.3073%
How do you calculate periodic interest rate?The yearly interest rate is divided by the quantity of compounding periods to produce the periodic interest rate. Interest can be earned on or added to interest more frequently when there are more compounding periods.
What is a periodic monthly rate?The interest rate that is levied on a periodic basis, such as monthly or quarterly, is known as the periodic rate. A credit card with an annual percentage rate of 18% has a periodic rate of 1.5 percent per month. The periodic rate is calculated by multiplying it by the number of periods in a year.
according to the formula :
periodic interest rate is annual interest rate divided by the number of times per year interest compounds so,
we have;
Annual interest rate = 15.98%
no.of week in a year= 52
so ;
periodic interest rate=15.98%/52
=0.3073%,
so the given statement is true.
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what is 8x8 divided by 4
Answer:
16 is the answer
Step-by-step explanation:
hope this helps
Answer:
16
Step-by-step explanation:
8 x 8 = 64
divide
64 divided by 4 = 16
during his college basketball season, jeff made 646 baskets out of 1360 attempts. what was his shooting percentage? round to the nearest whole percent.
Answer: I think its 10%
Step-by-step explanation: I hope that helps
Are the lines C and D parallel? (The figure may not be drawn to scale). Giving brainliest for whoever answers correctly
1. Yes
2.no
3. Can’t be determined
If there are 170 cal in a 12 oz can of Mountain how many calories are in a 2 oz can
Answer: 28.3 calories
Step-by-step explanation:
From 12 oz down to 2 oz, we divided by 6
So take 170 divided by 6 = 28.33 cal; ground up will be 28.3 cal
RATIO AND PROPORTION
EXERCISE 12.1
1. There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number of boys?
(b) What is the ratio of number of girls to the total number of students in the class?
The ratio of aving and expene of Sheryl i 2 : 3. If Sheryl ave $4000, find her income. (Income mean total earning)
She makes $10,000 a year.
What is ratio?An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. An equation with two ratios set equal to one another is called a proportion.
Sheryl's savings to spending ratio is 2:3, and she has $4,000 available.
Let her earnings be X.
She rescued 2*X/5 = $4000
X = 5*$4000/2
X= 10,000
Consequently, she earns 10,000.
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Rachel has a $10,000, three-year loan with an APR of 7.25%.
a. What is the monthly payment?
b. What is the total amount of the monthly payments?
c. What is the finance charge
Simple interest analysis reveals that
a) The installment was $321.53 per month.
b) The total amount of the payments is $11,575.
c) Interest was paid of $1,575.
How to find the Calculation?After t years, the amount of simple interest is calculated using:
A(t) = p(1 + rt)
that where:
The initial deposit is known as the primary, or P.
The interest rate in decimal form is r.
In this issue:
Hence, a $10,000 loan.
APR of 5.25%, which equals 3 years, therefore
Item c:
The result is A(3), so:
A(t) = P( 1 + rt)
A(3) = 10000[ 1 + 0.0525(3)]
A(3) = 11575
The total amount of the monthly installments is $11,575.
Item d:
I = A(3) - P = 11575 - 10000 = 1575
When interest is calculated, the principal is removed, so:
Interest was paid of $1,575.
Item b:
36 payments were made over a period of 3 years, or 3 x 12 months.
Item a:
11575/3 = 321.53
The amount due each month was $321.53.
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A theater has 41 rows of seats. If there are 22 seats in the 1st row, 26 in the 2nd row, 30 in the 3rd row . How many seats are there in total? Show and explain all work.
PLEASE HELP!
A survey was conducted of 371 teenagers. Thirty-five percent of the teenagers said they occasionally smoked cigarettes.
A. Find the margin of error for this survey
B. Write a statement about the percentage of teenagers who occasionally smoke cigarettes
a. The margin of error for this survey is of: 4.85%.
b. The 95% confidence interval for the percentage of teenagers who occasionally smoke cigarettes is of:
(30.15%, 39.85%).
How to obtain the confidence interval?Confidence intervals for proportions are obtained using the z-distribution.
The bounds of the interval are given as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size and the estimate in this problem are given as follows:
[tex]n = 371, \pi = 0.35[/tex]
The margin of error is given as follows:
[tex]M = 1.96\sqrt{\frac{0.35(0.65)}{371}} = 0.0485[/tex]
As a percentage, it is of 4.85%.
Then the bounds of the interval are given by the estimate plus/minus the margin of error, hence:
Lower bound: 35 - 4.85 = 30.15%.Upper bound: 35 + 4.85 = 39.85%.More can be learned about the z-distribution at https://brainly.com/question/25890103
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