a) The linear function is:
y = 2 + 0.25x.
b) The amount of snow on the ground after 4 hours will be of 3 inches.
c) The time that he has to complete the hike is of 16 hours, which is enough to finish the hike, as they don't take this long.
What is a linear function?The slope-intercept representation of a linear function is presented by the rule as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the unit rate of change of the output y by the input x.b is the y-intercept of the function, which is the numeric value of the output y when the input x assumes a value of zero.In this problem, the values of these coefficients are given as follows:
b = 2, which is the initial amount of snow on the ground.m = 0.25, which is the hourly rate of snow.Hence the equation is:
y = 2 + 0.25x.
After four hours, the amount of snow on the ground will be of:
y = 2 + 0.25(4) = 2 + 1 = 3 inches.
The time until the amount reaches 6 inches is of:
2 + 0.25x = 6
0.25x = 4
x/4 = 4
x = 16 hours.
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An bucket starts with 872 gallons of water and is emptying at a rate of 19 gallons per hour. If I know that the bucket has 8 gallons of water, how long has it been emptying?
Answer:
45.47368421 (round as much as you need)
Step-by-step explanation:
We can model the equation using G(h) = -19h + 872, where -19 is the rate at which the bucket is emptying and 872 is the amount of gallons the bucket starts with.
Since gallons is the output, we would have 8 = -19h + 872 and we simply need to solve for h
[tex](8 = -19h+872)-872\\\frac{(-864=-19h)}{-19} \\h=45.47368421[/tex]
0/1
At the carnival, there is a game with 600 ducks. If 75% of the ducks have stars on the
bottom, how many ducks have stars? Make sure to label your answer in ducks
Answer:
450 ducks
Step-by-step explanation:
75% can be rewritten as 75/100
75/100 of 600 can be rewritten as 75/100 * 600
Solve 75/100 = 0.75
0.75 * 600 = 450
ordered pairs solution for 7x+2y>-26
The ordered pairs that are solutions of the inequality are of the form:
(x, y > -3.5*x - 13)
Which ordered pairs are solutions of the inequality?
Here we have the inequality:
7x + 2y > -26
The solutions of this are the pairs (x, y) that, when replaced on the inequality, make it true.
If we isolate y on the inequality we get:
7x + 2y > -26
2y > - 26 - 7x
y > (-26 - 7x)/2
y > -3.5*x - 13
Then the ordered pairs are of the form:
(x, y > -3.5*x - 13)
For example, suppose that we fix the value of x in 0, then:
y > -3.5*0 - 13
y > -13
So the points of the form (0, y > -13) are solutions.
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Select all statements that are true about the graph of h (x) = –3 |x – 1| + 4.
A. Its vertex is at (–1, 4).
B. Its vertex is at (1, 4).
C. Its line of symmetry is x = –1.
D. Its line of symmetry is x = 1.
E. It crosses the y-axis at (0, 1).
F. It crosses the y-axis at (0, 4).
The statements that are true according to the equation h (x) = –3 |x – 1| + 4. are
B. Its vertex is at (1, 4)D. Its line of symmetry is x = 1E. It crosses the y-axis at (0, 1)How to find the functions as requiredThe graph of the described function is attached
The vertex is marked (1, 4) in the graph
The y intercept is marked (0, 1) in the graph
Also from the equation, the y intercept is solved by
h (x) = –3 |x – 1| + 4
plugging the value of x
h (x) = –3 |0 – 1| + 4
h (x) = –3 |– 1| + 4
removing the modulus sign
h (x) = –3 * 1 + 4
h (x) = –3 + 4
h (x) = 1
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Tiana is buying party favors for the guests at her 12th birthday party. Each party favor costs $2.39. If she buys 15 party favors, how much money does she spend?
Answer:
$35.85
Multiply 2.39 * 15
Which of these is a factor in this expression
The cost of 15 books is $33.75. Find the cost of 12 such books?
Answer:$27
Step-by-step explanation:
$33.75/15 = $2.25 per book
12 books x $2.25/book = $27
Write an equation for a line parallel to y=-4x+3 and passing through the point (4, -20)
The equation of the line is y = -4x -4.
We need to calculate the line which is parallel to y = -4x +3 and passes through the point (4, -20)
The given equation is y = -4x +3
Comparing this equation with the general equation of the line, y = mx +c, we get the slope of the equation is -4.
Now, When two lines are parallel to each other, their slopes are equal.
So, the slope of the required equation is -4.
Now, the equation of the line which passes through the points, [tex](x_{1} ,y_{1} )[/tex] and has slope m, is given by
[tex]y - y_{1} = m(x-x_{1} )[/tex]
Putting the values in the general equation, we get,
y - (-20) = -4(x - 4 )
y + 20 = -4x +16
y +4x = 16 -20 = -4
The equation of the line is y = -4x -4.
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(-9,-4); y=-3x+3
Write an equation for the line in slope-intercept form.
A right triangle has a leg length of square root of 6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle. 3 36 square root of 39 square root of 43
Answer:
√43
Step-by-step explanation:
Implement the Pythagorean formula to solve for sides of a right triangle: a^2 + b^2 = c^2, where "a" and "b" are the legs and "c" is the hypotenuse.
a = √6 and c = 49
√6^2 + b^2 = 49
6 + b^2 = 49
b^2 = 43
b = √43
Answer:
The square root of 43
Step-by-step explanation:
I did this in class the other day
Find the area of a rectangle with dimensions
11/12 in x 1/8 in.
The area of the rectangle is 11/96 in²
How to determine the area of the rectangle?In this question, we have the following parameters
Dimensions of rectangular area: 11/12 in x 1/8 in.
The area of a rectangle is the products of its dimensions
i.e. Area = products of dimensions
This implies that
Area = Length x Width
Substitute the known values in the above equation, so, we have the following representation
Area = 11/12 in x 1/8 in
Evaluate
Area = 11/96 in²
Hence, the rectangle area is 11/96 in²
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when potatoes are peeled do you lose more peel when you use big potatoes or small potatoes
Answer:
depends on how you peel it
Step-by-step explanation:
if you peel it with one quick peel, you will have only one
if you do it with 2, you will have 2 peels an so on
The amount of peels will be greater in the bigger potato as compared to the smaller potato.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given data in the question,
There are two potatoes, a small one and a bigger one.
If you peel the bigger one, because of the bigger surface area, you will get more peels as compared to the smaller potato because the surface are is small, and you will get less number of peels.
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Given a standard deck of playing cards, what is the probability of drawing each hand:
2 diamonds
1 diamond and 1 heart
Explain why the more likely outcome, above, is more likely
The probability of drawing 2 Diamonds is 1/17.
The probability of drawing 1 diamond and 1 heart is 13/204.
How to find probability for a deck of cards?
In total there are 52 cards in a deck.these 52 cards are divided in 4 suits each having 13 card values.The 4 suits are: Clubs, Spades, Diamonds and Hearts.13 card values are: 2-10, King, Queen, Jack and an AceKing, Queen and Jack are called Face cards.For finding probability of chosen cards to cases arise: 1. With replacement of the drawn card; 2. Without replacement of the drawn cardAccording to the given question:
Since there are 52 cards, the probability of getting a diamond in the first draw is 13/52.
After the first card is drawn, there are just 12 diamonds left.
So, the probability of drawing the diamond now is 12/51.
The total probability is the product of two probabilities
So, P = 13/52 x 12/51 = 1/4 x 4/17
P = 1/17 ≈ 0.058
So the probability of drawing 2 Diamonds is 1/17.
Similarly, we know probability of getting a diamond in first is 13/52.
Also the probability of drawing a heart from 51 cards is 13/51.
The total probability P = 13/52 x 13/51
P = 1/4 x 13/51
P = 13/204 ≈ 0.063
So the probability of drawing 1 diamond and 1 heart is 13/204.
More likely outcome is the one whose probability is closer to unity. Since 13/204 > 1/17 that is 0.063 > 0.058 therefore drawing a heart and a diamond is a more likely outcome.
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900 students attend Ridgewood Junior High School. 2% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
The number of students who brought lunch on Thursday is 18 students.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Number of students = 900
Number of students that brought lunch = 2% of 900
The number of students who brought lunch on Thursday.
= 2% of 900
= 2/100 x 900
2 x 9
= 18 students.
Thus,
The number of students who brought lunch on Thursday is 18 students.
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Susie is visiting Germany from the U.S. One day she stopped by a market and found a stall selling tomatoes for 1.74 euro per kilogram. If 1 euro was worth 1.09
dollars that day, how much did the tomatoes cost in dollars per pound?
First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side of
the equation.
The cost of the tomatoes, in dollars per pound, using proportions, is of:
$0.86 per lb.
What is a proportion?A proportion represents a fraction relative to a total amount, which is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in whichever context of a problem.
In this problem, the costs is obtained as follows:
Cost: 1.74 euros per kilogram.Exchange ratio: 1 euro = 1.09 dollars.Hence the cost in dollars per kg of the tomatoes is obtained as follows:
1.74 x 1.09 = $1.8966 per kg.
The relationship between kg and pounds is given as follows:
1 kg = 2.20 lb.
Hence the cost is written as follows:
$1.8966 per 2.20 lb.
The cost per pound of the tomatoes is of:
1.8966/2.20 = $0.86 per lb.
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How do I simplify this expression
A fitted linear regression equation is y = 6-2x. If × - 3 and the corresponding observed value of y = 2, the residual at this observation is:
The value of the residual is 2.
We are given a fitted linear regression equation. The equation is given below.
ŷ = 6 - 2x
The x-value for the data points is 3, and the corresponding y-value is 2. We have to find the value of the residual.
We will substitute the given values in the equation of the regression line.
ŷ = 6 - 2x
ŷ = 6 - 2(3)
ŷ = 6 - 6
ŷ = 0
Thus, the predicted value of y in the given regression equation is 0. The actual value of y is 2. The residual is the difference between the actual and predicted values of y. Let the residual be denoted by the variable "r".
r = y - ŷ
r = 2 - 0
r = 2
Hence, the residual is 2.
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Given the polynomial equation: x^3-7x^2-x+7=0
1. Make a list of possible rational roots
2. Test the possible roots until you find one that produces a reminder of 0. Show your work.
3. Write the resulting quadratic function.
4. Factor or use the quadratic formula to find the final 2 roots.
Find the value of x ( please help die today!)
Answer:tell me the math soulation first
Step-by-step explanation:
The 23 members of the westview journalism club are trying to raise at least 2,100 to buy new publishing desgin software. The members have already raised 1180. How much should each student still raise, on average, to meet the goal?
PLEASEEEE
The amount that each student will have to raise on average in order to meet the goal would be $40
How to find the amount to raise?First, find the remaining amount that the members of the Westview Journalism Club are trying to raise:
= Amount to raise - Amount already raised
= 2, 100 - 1, 180
= $920
The amount that each student in the club will have to raise on average can be found as:
= Amount remaining to be raised / Number of students in the Westview Journalism Club
= 920 / 23
= $40
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Which set of side lengths will NOT create a triangle?
Responses
8, 9, 10
2, 5, 8
10, 15, 20
10, 14, 18
Step-by-step explanation:
8,9,10 would not create a Triangle
Learn at brainlyplease help!! will mark brainlyist!!
Answer:
1. 4√5
2. 3√5
3. √149
4. √58
Step-by-step explanation:
The Pythagorean theorem states "a^2 + b^2 = c^2", where "a" and "b" are the legs, while "c" is the hypotenuse.
Knowing this, we can substitute each variable with given values on the triangles
1. "4" and "8" are legs "a" and "b" and we need to find the hypotenuse "c"
4^2 + 8^2 = c^2
16 + 64 = c^2
80 = c^2
√80 = c
4√5 = c
2. "6" and "3" are legs "a" and "b" and we need to find the hypotenuse "c"
6^2 + 3^2= c^2
36 + 9 = c^2
45 = c^2
√45 = c
3√5 = c
3. "7" and "10" are legs "a" and "b" and we need to find the hypotenuse "c"
7^2 + 10^2 = c^2
49 + 100 = c^2
149 = c^2
√149 = c
4. "3" and "7" are legs "a" and "b" and we need to find hypotenuse "c"
3^2 + 7^2 = c^2
9 + 49 = c^2
58 = c^2
√58 = c
Which expression is equivalent to 9 + 4y + 5 + 22 + 8?
Answer: The answer is 11x+4y+13
(18−42+2)21÷4⋅12 what does it equal
2
32
64
128
The value of (18−42+2)21÷4⋅12 equal to -1386
Algebra is a branch of mathematics that assists in the representation of problems or situations through the use of mathematical expressions. In algebra, we use numbers with definite or fixed values such as 2, -1, 0.33, and so on. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression. 5 and 6 are fixed numbers, while x is a variable.
Given that
(18−42+2)21÷4⋅12
Now we have to simplify the equation
(20-42)21/ 4 x 12
(-22)21/ 4 x 12
= (-462/4) x 12
= - 115.5 x 12
= - 1386
Therefore the value of (18−42+2)21÷4⋅12 equals to -1386
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One group of children has 15 red blocks and 45 green blocks. Another group of children has 30 red blocks and 90 green blocks. Which proportion correctly describes the relative amounts of each color?
A, 15/45 = 30/90
B, 15/45
C, 1/3
D, 15/45 = 90/ 30
From the chart, estimate (roughly) the number of transistors per IC in 2016. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040?
Please explain
The estimates for the number of transistors per IC, using an exponential function, are given as follows:
2016: 16,777,216,000.2040: 6.87 x 10¹³.What is the format of an exponential function?An exponential function has the general format presented as follows:
[tex]y = ab^\frac{x}{n}[/tex]
In which the parameters of the function are listed as follows:
a is the initial value of the function.b is the rate of change of the function.n is the period relative to the rate of change.By Moore's Law, the number of transistors per IC doubles every two years, hence the values of parameters b and n are both two, that is:
b = 2, n = 2.
We take 1972 as the reference year, when the amount was of 4000 transistors per IC, hence the value of parameter a is given as follows:
a = 4000.
Thus the equation is:
[tex]A(t) = 4000(2)^{\frac{t}{2}}[/tex]
Giving the number of transistors per IC in t years after the reference year of 1972.
2016 was 44 years after 1972, hence the estimate for the amount of transistors by IC was of:
[tex]A(44) = 4000(2)^{\frac{44}{2}} = 16,777,216,000[/tex]
2040 will be 68 years after 1972, hence the estimate for the amount of transistors by IC is of:
[tex]A(68) = 4000(2)^{\frac{68}{2}} = 6.87 \times 10^{13}[/tex]
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The revenue for a business, as a function of units produced, x, is shown below by R(x). C(x) represents the cost of producing x units. Calculate the profit function and then determine how many units must be produced for the business to break even.
R(x) = 24x
C(x) = 17x + 161
By calculating profit function to break even, the company needs to produce 23 units.
What is meant by profit function?The amount received when a good or service is sold for a price is referred to as revenue. The cost of a product or service is the amount spent on its sale. Profit is defined as the difference between revenue and costs. A profit function is a relationship that shows the difference between the cost and revenue functions. The graph of a profit function can show the best combination of revenue and costs to produce the most profit. This is known as optimization.
Profit is defined as revenue less costs. This means that there is a profit function, P(x).
P(x) = R(x) - C(x)
Breaking even is the point at which revenue begins to exceed costs. It is thus the point at which P(x) = 0. Because these are all linear functions, you know that the business will be profitable after that point.
P(x) = 0
R(x) - C(x) = 0
R(x) = 24x
C(x) = 17x + 161
From the above equation,
R(x)=C(x)
24x=17x+161
7x=161
x=161/7
x=23
For the company to break even, 23 units must be produced.
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80 percent increased by 30 percent is what percent of 80
30% of 80% is 24% and the resulted percent will be 104% when 80% is increased by 30%.
What is fraction?A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. A fraction is a portion of a larger total. The number is stated in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator.
Here,
30% of 80%
=30*100(80*100)*100
=30*80/100
=24%
When 80% is increased by 30%, the resultant percent is 104% because 30% of 80% is equal to 24%.
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Which of the following choices is the y-intercept of the equation -3x - 2y = 10?
3
-3
5
-5
Tommy bounces a basketball 25 times in 45 seconds, At that rate, approximately how many
times will pat bounce the ball in 405 seconds?
Tommy will pat bounce the ball 225 times in 405 seconds which was found using the given data.
What is the unitary method's formula?The unitary method's formula is to identify the value of a single unit, then multiply that value by the number of units to obtain the required value. However, this approach is useful for determining the value of a unit from the value of a multiple, and hence the value of a multiple.Given: In 45 seconds, Tommy bounces a basketball 25 times.
Number of times he will pat bounce the ball in 405 seconds will be given as follows:
= (405 × 25)/45
=225
Therefore, Tommy will pat bounce the ball 225 times in 405 seconds which was found using the given data.
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