Answer: The answer would be 4 biking outfits o=4
Step-by-step explanation:
First add all the money he spent excluding the outfits. The answer would be 315.72. Then subtract 600 and 315.72 = 284.28. Last multiply 71.07 by 4 which gets you 284.28. The EXACT amount he has left. Answer is he can be 4 new biking outfits within his budget. Hope I could help!
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 44 minutes of calls is $22.96, and the remaining credit after 68 minutes of calls is $19.12. What is the remaining credit after 81 minutes of calls?Calling Time In MinutesRemaining Credit In Dollars$
The remaining credit after 81 minutes of calls is $17.04.
Given that, the remaining credit after 44 minutes of calls is $22.96, and the remaining credit after 68 minutes of calls is $19.12.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Let x be the number of minutes and y be the number of dollars.
According to question, the ordered pair is
(44, 22.96) and (68, 19.12)
The point slope form is (y-y1)=m(x-x1)
Slope = (y2-y1)/(x2-x1)
= (19.12-22.96)/(68-44)
= -3.84/24
m= -0.16
Put m= -0.16 and (x1, y1)=(44, 22.96), we get
(y-22.96)=-0.16(x-44)
When x=81
y-22.96=-0.16(81-44)
⇒ y-22.96=-0.16×37
⇒ y-22.96=-0.16×37
⇒ y-22.96=-5.92
⇒ y=-5.92+22.96
⇒ y=17.04
Therefore, the remaining credit after 81 minutes of calls is $17.04.
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What is the sum of the 9th square number and the 5th cube number?
Answer:
Step-by-step explanation:
Is it a, b, or c, and if A what goes in the box
Answer is (a) The solution set is {x | (-∞,-7)∪(5,12)}.
Given equation,
[tex]\frac{(x-5)(x+7)}{x-12} < 0[/tex]
For values (-∞,-7)
equation stands true
For values (-7,5)
equation stands false
For values (5,12)
equation stands true
For values (12,∞)
equation stands false
Hence, x ∈ (-∞,-7)∪(5,12).
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how heavy a load (in pounds) is needed to pull apart pieces of douglas fir 4 inches long and 1.5 inches square? data from students doing a laboratory exercise are given.
With the help of binomial distribution we can conclude our answer.
What is binomial distribution?The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probability displaystyle q=1-pq=1-p). This distribution is used in probability theory and statistics. A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution. The popular binomial test of statistical significance is based on the binomial distribution. [1]A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.acc to our question-
The confidence interval can be found out using,
Confidence interval = Mean ± MOE = 30,800 ± 1,314.8079 = 29,485.192 , 32,114.8Hence, the confidence interval for the mean load required to pull the wood apart is (29,485.192 , 32,114.8).
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Write the point-slope form of the equation of the line through the given point with the given
slope.
3) through: (5, 1), slope
=
1
5
The point slope form of the equation is y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
What is equation of line ?
A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system. The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
Here the given point ,
=> [tex](x_1,y_1)=(5,1)[/tex]
Slope m = [tex]\frac{1}{5}[/tex]
Here using equation formula
=> [tex]y-y_1 = m ( x- x_1)[/tex]
=> y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
Hence the point slope form of the equation is y - 1 = [tex]\frac{1}{5}[/tex] ( x-5)
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b According to estimates, there are over 300 million people living in the Unite
States. How many Neyland Stadiums would it take to hold 300 million people
Answer:
it would take 3,000 neyland stadiums to take 300milion people is rounded i hope this helps
Step-by-step explanation:
ESSENTIAL
Chuck
Match up each scenario with the equation that models the word problem.
Skate rental charges an additional $3.
Jeff is 3 years less than Tony's age.
Marie buys balloons for a party that
are $3.00 each.
Intro
y=x+3
y=x-3
y = 3x
Done
En this is the answer
The following are the equations which matches the given word problems:
a. Skate rental charges an additional $3 :
y = x+3
b. Jeff is 3 years less than Tony's age:
y=x-3
c. Marie buys balloons for a party that are $3.00 each:
y = 3x
Given, we have the word problems:
a. Skate rental charges an additional $3 :
here, based on the fixed charge, additional charge is taken as $3.
let the total charge be represented as y and
x represent the fixed charge,
hence the equation we get is:
y = x+3
b. Jeff is 3 years less than Tony's age.
let y represent the age of Jeff
and x represent the age of Tony.
hence we frame the equation as:
y = x - 3
c. Marie buys balloons for a party that are $3.00 each:
let the cost of the balloon be represented as y
and x represent the number of balloons Marie wants to buy for $3 each.
hence the equation we frame is:
y = 3x
Hence we get the required equations.
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Graph this function:
y = |x − 3| + 1
Click to plot the vertex first.
Given function:
y = |x − 3| + 1
Table:
x y
1 3
2 2
3 1
4 2
5 3
Here the vertex is (3,1).
Graph is in the image uploaded.
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Determine the value of y for the inequality 2 times the quantity y plus one third end quantity is greater than two thirds. Y is greater than negative 1 over 36 y is less than negative 1 over 36 y > 0 y < 0
The solution to the inequality is y < -12 ( y less than negative 12).
Given inequality is;
y + 15 less-than 3
y+15<3
For solving the inequality, we will subtract 15 from both sides in order to find y.
Subtracting 15 from both sides of inequality
The solution to the inequality is y < -12 ( y less than negative 12).
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in which of the following african countries is the population growth rate above 2.5% and life expectancy at least 61 years old?
Answer: Ethiopia has a population growth rate above 2.5% and a life expectancy of 61 years old
What are the domain and range of the function f(x) = -
OD: {X E R | X + -2},R: {ye Rly +-8}
E
OD: (x = R X
4),R: {ye Rly -2}
OD: {x € R | x # 2},R: {y = R | y + 8)
x² - 4x-12?
X+2
OD:{X = R | x # -4},R: {y = R | y + 2}
The domain is { x ∈ R | x ≠ -2 }.
The range is { y ∈ R | x ≠ -8 }.
What are the domain and range of a function?
The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.
A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)
Find domain:
Set the denominator equal to zero and solve for x.
x+2=0
x=-2
This means, domain is set of all real numbers except x=2.
Set builder notation: { x ∈ R | x ≠ -2 }. R= real numbers
Find range:
Replace f(x) by y in the given equation and solve for x.
[tex]y=\frac{x^2-4x-12}{x+2}[/tex]
Write the factors of the numerator
[tex]y=\frac{(x+2)(x-6)}{x+2}[/tex]
common terms x+2 cancel out
y=x-6
x=y+6
substitute x=-2
-2=y+6
y= -8
This means range is the set of all real numbers except y= -8.
Set builder notation: { y ∈ R | y ≠ -8 }. R= real numbers
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There are 95 males and 125 females participating in a marathon. What
percent of the participants are female? Round your answer to the nearest
hundredth.
Answer: 55.56%
Step-by-step explanation:
To find the percentage, we need to do part over whole. Part being the females and the total marathon runners being the total. So that would be 95/95+125, then 95/225, then 55.555555 and repeating. Then we would round that to 55.56%.
Ruth has 36 vases of flowers. Some of the vases contain 3 daisies. The other vases contain 4 lilacs. There are 125 flowers in the vases in total. How many vases of each type of flower does Ruth have?
Answer:
13 vases of lilacs23 vases of daisiesStep-by-step explanation:
You want to know the number of vases of each type of flower if there are 36 vases containing 125 flowers, with 3 daisies or 4 lilacs in a vase.
SetupLet x and y represent daisy and lilac vases, respectively. The problem statement gives two relations:
x +y = 36 . . . . . total number of vases
3x +4y = 125 . . . total number of flowers
SolutionSubstituting for x, we have ...
x = 36 -y
3(36 -y) +4y = 125
108 +y = 125
y = 13
x = 36 -13 = 23
There are 23 vases of daisies and 13 vases of lilacs.
Use the information given to enter an equation in standard form.
Slope is 6, and (1, 8) is on the line.
Answer:
y=6x+2
Step-by-step explanation:
y=mx+c
8=6(1)+c
8=6+c
c=2
y=6x+2
Check the month and dollar value that represent a correct ordered pair. In April, Cathy's Clothmart had a profit of $3,000. In May, the profit was $4,000. In June, the profit was $5,000. April May June July $1,000 $2,000 $4,000 $6,000
The Cathy's Clothmart job had a profit comprises of pairings of the form (x,y), where the two integers are paired because of some relation.
In this instance, the relation is effectively "in month x it truly had a profit y" The ordered pairs are then, in a really significant sense, (April, 3000), (May, 4000), and (June, 5000). The ordered pairs can be written as follows if the month's number is used to identify them: (4,3000), (5,4000), They generally believed that both kinds of ordered pairings are generally correct.
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May, 4,000
The only correct pair is may and 4,000 because the other options don't have the proper profit to represent the corresponding months.
Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?
The graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).
The system of equation are
-3x + y = 3
-x + 2y = -4
Here we have to use the substitution method
-3x + y = 3
y = 3 + 3x
Substitute the value of y in the second equation
-x + 2(3 + 3x) = -4
-x + 6 + 6x = -4
-x + 6x = -4-6
5x = -10
x = -10/5
x = -2
Substitute the value of x in the first equation
-3x + y = 3
-3(-2) + y = 3
6 + y = 3
y = 3 - 6
y = -3
Hence, the graph represents the system of equations -3x + y = 3 and -x + 2y = -4 is option (b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).
The complete question is:
Which graph represents the system of equations –3x + y = 3 and –x + 2y = –4?
a) On a coordinate plane, 2 lines intersect at (3, 0).
b) On a coordinate plane, 2 lines intersect at (negative 2, negative 3).
c) On a coordinate plane, 2 lines intersect at (negative 1.5, 1).
d) On a coordinate plane, 2 lines intersect at (1.5, 2.5).
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Answer:
B
Step-by-step explanation:
both point intersect at ( -2, -3)
The first container has 3 gallons 3 quarts 1 pint of diesel fuel, the second container has 5 gallons 2 quarts of diesel fuel, and the third container has 6 gallons 1 quart 1 pint of diesel fuel. what is the total quantity of diesel fuel?
The total quantity of diesel fuel is 15.75 gallons.
The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.
1 quart = 0.25 gallon
For first container, 3 quarts = 0.25 × 3
3 quarts = 0.75 gallon
For second container, 2 quarts = 0.25 × 2
2 quarts = 0.5 gallon
For third container, it has 0.25 gallon
1 pint = 0.125 gallon
For first and third container, it has 0.125 gallon
So, amount of diesel fuel in first container = 3 + 0.75 + 0.125
Amount of diesel fuel in first container = 3.875 gallons
Amount of diesel in second container = 5 + 0.5
Amount of diesel in second container = 5.5 gallons
Amount of diesel in third container = 6 + 0.25 + 0.125
Amount of diesel in third container = 6.375 gallons
So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375
The total quantity of diesel fuel = 15.75 gallons
Hence, the total quantity is 15.75 gallons.
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Complete the equation so that it has no solution.
9(x – 4) – 5x =__x-30
For the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.
As given in the question,
Given equation is equal to :
9 ( x - 4) - 5x = _ x - 30
Simplify Left hand side of the given equation we get,
9 ( x - 4) -5x
= 9x - 36 - 5x
Collect the like terms we have,
9x - 5x - 36
= 4x - 36
Now compare left hand side and right hand side to get no solution of the equation,
4x -36 = _x -30
Blank should be filled by 4
Therefore, for the given equation 9(x-4) -5x = __x -30 has no solution when it is written as 9(x - 4) -5x = 4x -30.
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Find quotient of 1/3 divided by 5/6
Answer:
2/5
Step-by-step explanation:
flip 5/6 to become 6/5 then cross reduce then cross multiply
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The equations that are quadratic in form include:
A. x⁴ – 6x²– 27 = 0
D. 6x⁴ = -x² + 5
E. 8x⁴ + 2x² – 4x = 0
What is a quadratic equation?A quadratic equation simply refers to the equation which is in an algebraic equation that is of the second degree.
It should be noted that a quadratic equation is in the form of ax² + bx + c = 0.
In this situation, a and b are the coefficients while c is the constant in the equation.
Therefore, based in the information given, the correct options are A, D, abd E.
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Answer:
The equations that are quadratic in form include:
A. x⁴ – 6x²– 27 = 0
D. 6x⁴ = -x² + 5
E. 8x⁴ + 2x² – 4x = 0
Step-by-step explanation:
An emperor penguin dive down into the ocean at a contant rate. From the urface, he dive 1,760 feet in 8 minute. The number −1,760 repreent the location of the penguin in relation to the urface. What number repreent the location of the penguin in relation to the urface 2 minute after beginning hi dive?
The number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.
An emperor penguin dives down into the ocean at a constant rate. From the surface, he dives 1,760 feet in 8 minutes. The number 1,760 represents the location of the penguin in relation to the surface. We need to find out the number that represents the location of the penguin in relation to the surface two minutes after he begins his dive.
First, we will calculate the speed of the penguin. The speed is represented by the variable "s".
s = 1,760/8
s = 220 feet per minute
The location of the penguin after 2 minutes is calculated below.
d = 2×s
d = 2×220
d = 440
Hence, the number that represents the location of the penguin in relation to the surface 2 minutes after beginning his dive is 440.
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10 POINTS!
What is the equation of the line in standard form?
(-3,2) and (2,-1)
Answer: y = -.06x + 0.2
Step-by-step explanation: Find the slope by plugging in the given values to the slope formula to find that the slope is -0.6. Next, determine the y-intercept is b=y1−m⋅x1: b = 2 - (-0.6) ⋅ (-3) = 0.2 Finally, the equation of the line can be written in standard form y= -0.6x + 0.2.
A lines Y intercept is changed from -1 to 0 which way did it shift
By studying the change of the y-intercept, we can see that the shift is of one unit upwards.
In which way did the line shift?
We know that the original y-intercept of the line is y = -1, then the line is of the form:
y = a*x - 1
Where a is the slope.
Now we apply a vertical shift of N units, this is written as:
y = a*x - 1 + N
And we know that the new y-intercept is 0, so:
y = a*0 - 1 + N = 0
y = -1 + N = 0
-1 + N = 0
N = 1
The shift is of 1 unit up.
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How do you solve this? (-7 + i)(-3 + 6i).
After simplification, the solution of the expression (-7 + i)(-3 + 6i) is 15 - 45i.
In the given question we have to solve the given expression.
The given expression is (-7 + i)(-3 + 6i).
Using the distributive property to solve the given expression.
a(b+c)=ab+ac
Now simplifying the expression.
(-7 + i)(-3 + 6i) = -7(-3 + 6i) + i(-3 + 6i)
(-7 + i)(-3 + 6i) = (-7)*(-3) + (-7)*(6i) + (-3)i + (6i)i
(-7 + i)(-3 + 6i) = 21 - 42i - 3i + 6i^2
As we know that i^2 = -1. So
(-7 + i)(-3 + 6i) = 21 - 42i - 3i + 6(-1)
(-7 + i)(-3 + 6i) = 21 - 42i - 3i - 6
Simplifying
(-7 + i)(-3 + 6i) = 15 - 45i
Hence, the solution of the expression (-7 + i)(-3 + 6i) is 15 - 45i.
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These points are linear.
Find the slope.
x 56 7 8 9
y| 11 | 16 | 21 | 26 | 31
Hint: First calculate the change
between each y-value.
[?]
Slope =
The slope is m = 5.
What is slope?
The change in y coordinate relative to the change in x coordinate is referred to as a line's slope in mathematics. The symbols Δy and Δx stand for the net change in the y-coordinate and the net change in the x-coordinate, respectively. where "m" denotes a line's gradient. tanθ then represents the slope of a line.
We have to find the slope of the points given.
First to find the change between each y - value.
16 - 11 = 5
21 - 16 = 5
26 - 21 = 5
31 - 26 = 5
So the change between each y - value is 5.
Now, to find the slope of the points.
Since,
Slope = m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_1=\frac{16-11}{6-5}= \frac{5}{1} =5\\ m_2=\frac{21-16}{7-6}=\frac{5}{1} =5\\ m_3=\frac{26-21}{8-7}=\frac{5}{1}=5\\m_4=\frac{31-26}{9-8}=\frac{5}{1} =5[/tex]
Hence, the slope of the given points is 5.
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Answer:
The answer is 5
Step-by-step explanation:
Though there is also a bottom number, just put a 1 in the bottom number
-3(4x-7) please answer quickly!!
Finding the derivatives using The Chain Rule
a) The derivative of the composite function is F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x².
b) The standard form of the polynomial is F'(x) = (2 / 3) · x⁵ + 7 · x².
How to determine the derivative of a function by chain rule
Chain rule is a differentiation rule use to find the derivative of a composite function of the form f(u(x)), whose operation is defined below:
df / dx = (df / du) · (du / dx)
a) Let be f(x) = x² + 6 · x - 40 and g(x) = (1 / 3) · x³ + 7, such that F(x) = f(g(x)). Then, the resulting expression for the derivative of the function is obtained below:
F'(x) = [2 · g(x) + 6] · g'(x)
F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x²
b) Now we proceed to expand the polynomial in its standard form:
F'(x) = [(2 / 3) · x³ + 7] · x²
F'(x) = (2 / 3) · x⁵ + 7 · x²
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Please help meee!!!!!!
The required value of "b" is 7, where the equation is y = -3x + 7.
As per the given table, we take the two points (9, 1) and (3,7).
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -3, y₁ = 16
x₂ = 1, y₂ = 4
y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute the values in the above equation,
y - 16 = [(4 - 16)/(1 - (-3))](x - (-3))
y - 16 = (-12/4)(x+3)
y - 16 = -3(x+3)
y - 16 = -3x - 9
y = -3x - 9 + 16
y = -3x + 7 ....(i)
Compare the given equation y = mx + b with the above equation, and we get
b = 7
Therefore, the required value of "b" is 7.
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in a shipment of 54 vials, only 16 do not have hairline cracks. if you randomly select one vial from the shipment, what is the probability that it has a hairline crack?
The probability that it has a hairline crack is 19/27.
Given that;
In a shipment of 54 vials, only 16 do not have hairline cracks.
Let shipment of 54 Vials;
x(s) = 54
Let,' A ' be the event that selects 16
x(A) = 16
P(A) = x(A) / x(s)
= 16/54
But only 16 don't have hairline Crakes;
To solve a given case;
The probability that it has a hairline crack is:
P(A') = 1 - P(A)
= 1- 16/54
P(A') = 19/27
Hence, the probability that it has a hairline crack is 19/27.
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Can anyone write the equation of the graph?
The function of the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we have the graph that can be used in our computation:
Given that the graph is an absolute value graph
We start by calculating the vertex of the graph
In this case, the minimum point on the graph is located at the point (3, 5)
This means that
Vertex = (3, 5) i.e. (h, k) = (3, 5)
Recall that the general form of an absolute value function is f(x) = |x - h| + k
Substitute the known values in the above equation
So, we have the following equation
f(x) = |x - 3| + 5
On the graph, we have
(x, f(x)) = (2, 6)
So, we have
6 = a|2 - 3| + 5
This gives
a = 1
So, we have
f(x) = 1 * |x - 3| + 5
Evaluate
f(x) = |x - 3| + 5
Hence, the equation of the graph represented by the figure is f(x) = |x - 3| + 5
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