Answer:
Approximately 66 feet
Step-by-step explanation:
Given d = 28 inFind the circumference:
C = πd = 3.14*28 = 87.92 inFind the distance covered by 9 turns:
9C = 9*87.92 = 791.28 inConvert inches to feet:
1 foot = 12 in791.28 in = 791.28/12 ft = 65.94 ft ≈ 66 ftParty trays which cost $14 to make not including labor are sold for $35 if two people work eight hour shifts making the tray at seven dollars per hour how many trays must be sold to cover the cost including the labor?
Approximately 5 number of trays must be sold to cover all costs including labor.
How to find the work proportion?The profit on each tray that was sold excluding labor cost is;
Profit = $35-$14
Profit = $21
Total labor cost for making party tray for a day is;
Total Labor Cost = Total labor hours * wages per hour * No. of labors
Total Labor cost = $7 * $8*2
Total Labor Cost = $112
Number of trays that must be sold to cover cost is;
Total labor cost/ Profit per tray
Number of trays = $112/$21
= 5.33
Approximately 5 trays must be sold to cover all costs including labor.
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f(x)=x+3
g(x) = 2x² - 4
Find (f. g)(x).
Answer:
[tex](f \cdot g)(x)[/tex] = [tex]2x^2 -1[/tex]
Step-by-step explanation:
[tex](f \cdot g)(x)[/tex], read as "f of g of x", means we have to use the function [tex]\bf g(x)[/tex] as input for the function [tex]\bf f(x)[/tex]. This means, we have to replace the [tex]x[/tex] in the definition of [tex]f(x)[/tex] with [tex]g(x)[/tex].
[tex]f(x)=x+3[/tex]
[tex]g(x) = 2x^2 - 4[/tex]
∴ [tex](f \cdot g)(x) = f(g(x))[/tex]
⇒ [tex]g(x) + 3[/tex]
⇒ [tex](2x^2 - 4) + 3[/tex]
⇒ [tex]2x^2 -1[/tex]
A manufacturer has a steady annual demand for 38016 cases of sugar. It costs $9 to store 1 for 1 year, $33 in set up cost to produce each batch, and $18 to produce each case. Find the number of cases per batch that should be produced to minimize cost.
Based on the setup costs, the steady annual demand, and the costs to store, the number of cases to produce to minimize cost is 528 units .
How many cases should be produced to minimize cost?This can be found by using the Economic Order Quantity.
= √ ( (2 x Setup costs x annual demand) / holding costs for the year)
Solving gives:
= √ ( ( 2 x 33 x 38,016) / 9)
= √278,784
= 528 units
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Given f (x) = x2 + 4x + 5, what is f of the quantity 2 plus h end quantity minus f of 2 all over h equal to?
h2 + 8h
2x + h + 4
8 + h
h + 4
By evaluating the quadratic function, we will see that the differential quotient is:
[tex]\frac{f(2 + h) - f(2)}{h} = 8 + h[/tex]
How to get (f(2 + h) - f(2))/h?Here we have the quadratic function:
[tex]f(x) = x^2 + 4x + 5[/tex]
Evaluating the quadratic equation we get:
[tex]\frac{f(2 + h) - f(2)}{h}[/tex]
So we need to replace the x-variable by "2 + h" and "2" respectively.
Replacing the function in the differential quotient:
[tex]\frac{(2 + h)^2 + 4*(2 + h) + 5 - (2)^2 - 4*2 - 5}{h} \\\\\frac{4 + 2*2h + h^2 + 8 + 4h - 4 - 8 }{h} \\\\\frac{ 2*2h + h^2 + 4h }{h} = \frac{8h + h^2}{h}[/tex]
If we simplify that last fraction, we get:
[tex]\frac{8h + h^2}{h} = 8 + h[/tex]
The third option is the correct one, the differential quotient is equal to 8 + 4.
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The graph of a line passes through the two points below
(2,-4);(-3,1)
Which of these can be used to determine the slope of the line
The expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)
What are slopes?The slope of a line is the gradient or the average rate of change of the line or a line equation
Note that linear equations are equations that have constant average rates of change, slope or gradient
How to determine the slopes?The two points are given as
(2,-4);(-3,1)
The slope of a line is calculated using
m = (y2 - y1)/(x2 - x1)
Substitute the coordinates of the points in the above equation
m = (1 + 4)/(-3 - 2)
Evaluate the numerator
m = 5/(-3 - 2)
Evaluate the denominator
m = 5/-5
Rewrite the quotient as
m = -5/5
Evaluate the quotient
m = -1
Hence, the expression that can be used to determine the slope of the line is (1 + 4)/(-3 - 2)
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what’s the equation for g(x)?
Answer:
Step-by-step explanation:
hello :
g(x) = (x+5)²
you can correct your mistake.
Oliver flipped a coin 10 times. The
outcomes are shown in the table below.
a) Work out the experimental probability of
the outcome being heads. Give your
answer as a decimal.
b) Using one of the options below, copy
and complete the sentence to explain how
Oliver could improve his experiment to get
a better estimate for the probability.
a)
Outcome Frequency
Heads
7
Tails
3
b) He could improve his experiment by
using a different coin
wearing a hat
flipping the coin outside
doing more coin flips
doing fewer coin flips
a) The probability of a head exists at 0.7.
b) He could improve his experiment by doing more coin flips.
What is probability?Probability signifies possibility. It exists a branch of mathematics that values the event of a random event. The value exists represented from zero to one.
Given: Coin flipped 10 times.
The Head comes T times and the tail comes 7 times.
To estimate the probability of head in the outcome.
The total number of outcomes is 10 and the head comes 7 times.
a) Probability(head) = 7/10 = 0.7
The probability of a head exists at 0.7.
b) He could improve his experiment by doing more coin flips
Therefore, the correct answer is option c) doing more coin flips.
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someone please help me find the value of x
Hello,
5x² = 90/2
5x² = 45
x² = 45/5
x² = 9
x = √9 or x = -√9
x = 3 or x = -3
There are 81 athletes who joined a parade. Four-ninths of them are basketball players. How many basketball players joined the parade?
Answer:
36
Step-by-step explanation:
81 x (4/9) =
36
1. Quadratics.
The path of the longest shot put by the Women's track team at Sun Devil U is modeled by h(x) = -0.017x² + 1.08x + 5.8, where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground. (Both x and h(x) are measured in feet.)
a. 4 points. Determine h(24). Round your answer to 2 decimal places. Then explain what your answer means in the context of the problem. ("In the context of the problem" means "in terms of the shot put's horizontal distance from the start and in terms of the height of the shot put above the ground.")
b. 4 points. Determine the numerical value of the vertical intercept and explain what this means in the context of the problem.
c. 4 points. Determine the numerical values of the vertex coordinates and explain what they mean in the context of the problem.
d. 4 points. How far from the start did the shot put strike the ground? Round your answer to 2 decimal places.
h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.
What is the value of h(24)?Given,
h(x) = -0.017x² + 1.08x + 5.8
Put h = 24,
h(24) = -0.017(24)² + 1.08(24) + 5.8
h(24) = -9.792 + 25.92 + 5.8
h(24) = 21.93
The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.
What is the value of the vertical intercept?Vertical intercept, x = 0
h(0) = -0.017(0)² + 1.08(0) + 5.8
h(0) = 5.8
The height of the shot put above the ground is 5.8 feet at the start.
What is the values of the vertex coordinates?vertex coordinates,
(h,k) = [(-b/2a),-(b²- 4ac)/4a]
(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]
(h,k) = [(1.08/0.034),(1.5608)/0.068)]
(h,k) = (31.76,22.95)
The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.
How far from the start did the shot put strike the ground?Put h(x) = 0,
-0.017x² + 1.08x + 5.8 = 0
Use quadratic formula for solving x,
x = (-b±√b²- 4ac)/2a
Here a = -0.017, b=1.08, c=5.8
x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)
x = [-1.08±√1.5608]/-0.034
x = [-1.08-1.2493]/-0.034 and x = [-1.08+1.2493]/-0.034
x = 68.509 and x = - 4.98
Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²
= √73.49²
= 73.49 feet
Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.
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The function f(x)=−4x+1 has a horizontal asymptote at?
The function has a horizontal asymptote at y = 1
How to determine the horizontal asymptote?The function is given as:
f(x) = -4/x + 1
Set the radicand to 0.
So, we have:
y = 0 + 1
Evaluate
y = 1
Hence, the function has a horizontal asymptote at y = 1
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Hence, write down the smallest integer value of x that satisfies 7(6+x) -x>0
Answer:
-6
Step-by-step explanation:
[tex]7(6+x)-x > 0[/tex]
[tex]42 + 7x-x > 0[/tex]
[tex]42+6x > 0[/tex]
[tex]6x > -42[/tex]
[tex]x > -7[/tex]
The smallest integer that satisfies the condition, [tex]x > -7[/tex], is -6.
what is the equation for -2(5x+8)
Answer:
Step-by-step explanation:
-10x-16
Answer:
distribute the -2 so your answer is -10x-16
Step-by-step explanation:
? Question
Warm-Up
Given: AB || CD
m/ZYB = 60°
Prove: m/DXW = 120°
A
W
Z
Y/60°
X
Select the correct answer from each drop-down menu.
Statements
AB || CD
m/ZYB
ZYXDand ZDXWform a linear pair.
K
B
=
60°
m/YXD
m/DXW = 120°
Reasons
given
given
definition of a linear pair
corresponding angles have equal measures
The missing Statement and reason for the transverse line angles is; m∠YXD = 60° and Supplementary angles sum up to 180°.
How to prove congruent angles?Statement 1; AB ║ CD
Reason 1; Given
Statement 2; m∠ZYB = 60°
Reason 2; Given
Statement 3; ∠YXD and ∠DXW form a linear pair
Reason 3; Definition of Linear Pair
Statement 4; m∠YXD = 60°
Reason 4; Corresponding angles have equal measure.
Statement 5; m∠DXW = 120°
Linear pairs usually sum up to 180° because they are supplementary angles. Thus;
m∠YXD = 180° - 60° = 120°
Reason 5; Supplementary angles sum up to 180°.
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Show the calculation to find the μ and σ of a binomial variable whose probability of success if 0.3 with a total number of attempts of 20.
Using the binomial distribution, we have that:
The mean is of [tex]\mu = 6[/tex].The standard deviation is of [tex]\sigma = 2.05[/tex].What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
[tex]\mu = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem, the parameters are:
n = 20, p = 0.3.
Hence:
[tex]\mu = np = 20 \times 0.3 = 6[/tex][tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20 \times 0.3 \times 0.7} = 2.05[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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the time between customer visits to the bank from midday to 1pm is evenly distributed over the period from 0 to 120 seconds. what is the standard deviation of the timeout?
Using the uniform distribution, the standard deviation of the timeout is of 34.64 seconds.
What is the uniform probability distribution?It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The standard deviation is:
[tex]S = \sqrt{\frac{(b - a)^2}{12}}[/tex].
For this problem, the bounds are:
a = 0, b = 120.
Hence the standard deviation is found as follows:
[tex]S = \sqrt{\frac{(120 - 0)^2}{12}} = 34.64[/tex].
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9. For Investment Plan A to C, solve for the future value at the end of the term based on the
information provided.
Investment Plan Principal
A
$7,500
B
$53,000
C
$19,000
Interest Rate
8% compounded quarterly
6% compounded monthly
5.75% compounded semi-annually
Term
3 years
4
years and 3 months
6 years and 6 months
The future value of Investment A is 9511.81
The future value of Investment B is 68,351.02
The future value of Investment C is29.067.07.
What are the future values?When an amount earns a compound interest, it means that both the amount invested and the interest rate already accrued increases in value at the next compounding date. For example, if interest is compounded quarterly, both the amount invested and the interest accrued increases every quarter.
The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsInvestment A = 7500 x [(1 + (0.08/4)]^(4 x 3) = 9511.81
Investment B = 53,000 x [(1 + (0.06/12)]^[(4 x 12) + 3) = 68,351.02
Investment C = 19,000 x [(1 + (0.0575/2)]^{6 x 2) + 6/2) = 29.067.07
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(07.06) There are currently 4 people signed up to play on a baseball team. The team must have at least 9 players.
Which of the following graphs includes the possible values for the number of people who still need to sign up for the team?
Number line with closed circle on 5 and shading to the left
Number line with closed circle on 5 and shading to the right.
Number line with open circle on 5 and shading to the left.
Number line with open circle on 5 and shading to the right.
A graph which includes the possible values for number of people who can still sign up for the team is: B. number line with closed circle on 5 and shading to the right.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains numerical values (positive and negative numbers) that are placed at equal intervals along its length.
Let the number of people who can still sign up for the team be represented by x. Thus, the inequality is given by:
x + 4 ≥ 9
x ≥ 9 - 4
x ≥ 5.
This ultimately implies that, there could be five (5) or more people that can still sign up for the team and a graph which includes these possible values is a number line with closed circle on five (5) and shading to the right because it can get larger.
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
a. central angle is ∠QPR
b. semicircle is QRS
c. major arc is arc QTS
d. m∠QPR = 130° [central angle theorem]
e. arc QTS = 180°
What is the Central Angle Theorem?The central angle theorem states that the measure of the intercepted arc will always be equal to the central angle.
a. A central angle is ∠QPR
b. A semicircle is QRS
c. A major arc is arc QTS
d. Measure of arc QR = m∠QPR = 130° [central angle theorem]
e. arc QTS = semicircle = 180°
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What are the domain and range of the function f of x equals the quantity of x squared minus 3 x minus 28, all over x plus 4?
domain is x is all real numbers where x does not equal 4 comma range is y is all real numbers where y does not equal 11
domain is x is all real numbers where x does not equal 7 comma range is y is all real numbers where y does not equal negative 4
domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11
domain is x is all real numbers where x does not equal negative 7 comma range is y is all real numbers where y does not equal 4
The domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11. Option C
What is the domain of a function?The domain of a function refers to the entire area for which the function returns a value. The function in this case is; f(x) = x^2 - 3x - 28/x + 4. The domain of the function will be real numbers except -4.
Hence, we can say that domain is x is all real numbers where x does not equal negative 4 comma range is y is all real numbers where y does not equal negative 11.
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Answer:
The answer is C.
Exponentiation is the raising of one number to the power of another. This operation is performed using two asterisks **. Let's use exponentiation to solve a known problem. You are offered a choice of either $1.000.000 or $0.01 (one penny) doubled every day for 30 days (the resulting amount is doubled every day). Task: Write a program to calculate the amount that will result from the doubling to understand which choice results in a larger amount. Hint: Let's see how exponentiation can be useful to perform the calculation. For example, if we want to calculate how much money we will have on the 5th day, we can use this expression: 0.01*(2**5) = 0.32 dollars (multiply the penny by 2 raised to the power of 5).
In math, Exponentiation refers to the operation of raising one quantity to the power of another. See the program running the exponentiation below.
What is the required code?The code is given below:
number_of_days = 30
amount_after_30days = 0.01 * (2 ** number_of_days)
# print the amount
print(amount_after_30days)
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What is the additive inverse of the number given below?
6
Answer:
-6 is the answer for instance 6=-6 or +(-6)
Amy made a circle graph of the U.S. population for 2000. This is the data that she used and the graph that she made.
The true statement is (b). No, because males and females should add up to 100% of the population.
How to determine the true statement?The complete question is added at the end of this solution.
From the complete question, we have the following percentages
Male = 26%Female = 27%When the above percentages are added, we have
Total = 26% + 27%
Evaluate the sum
Total = 53%
The above shows that the display of the circle graph is accurate.
This is so because the total percentage of the male and the female population must add up to 100%
Hence, the true statement is (b). No, because males and females should add up to 100% of the population.
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Complete question
Amy made a circle graph of the U.S. population for 2000. This is the data that she used and the graph that she made. U.S. Population (2000)
A circle graph titled U S Population (2000).
Males, 26 percent;
Females, 27 percent;
White, 39 percent;
Black, 6 percent;
Asian, 2 percent.
Males 138,053,563
Females 143,368,343
White 211,460,626
Black 34,658,190
Asian 10,242,998
Do you think this is an accurate display of the U.S. population? Why or why not?
a. Yes, because the percentages add up to 100%.
b. No, because males and females should add up to 100% of the population.
c. Yes, because the majority of the population is white.
d. No, because the percentage of males and females should be equal.
A dairy needs 336 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 336 gallons?
We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.
How to work with percentages?Let x = number of gallons of 3% milk
Thus;
336 - x = number of gallons of 7% milk
Therefore;
0.03x + 0.07(336 - x) = 0.06(336)
0.03x + 23.52 - 0.07x = 20.16
-0.04x = -3.36
x = 84 gallons
We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.
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The graph of a quartic function crosses the x-axis at -4 and -2 and touches it at 3. State the equation for the family.
The equation of the quartic function is f(x) = x⁴ - 18 · x² + 6 · x + 72.
How to find the possible equations for a quartic polynomial that passes through the x-axis at three points
Herein we must construct at least a polynomial that satisfies all conditions described in the statement. According to the fundamental theorem of algebra, quartic functions may have no real roots, two real roots or four real roots, which means that one of the roots must have a multiplicity of 2.
The root with a multiplicity of 2 is x = 3 and both x = - 4 and x = - 2 have only a multiplicity of 1, then we have the following expression by using the factor form of the definition of polynomials:
f(x) = (x - 3)² · (x + 4) · (x + 2)
Now we expand the expression to get the standard form:
f(x) = (x² - 6 · x + 9) · (x² + 6 · x + 8)
f(x) = x⁴ - 6 · x³ + 9 · x² + 6 · x³ - 36 · x² + 54 · x + 8 · x² - 48 · x + 72
f(x) = x⁴ - 18 · x² + 6 · x + 72
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(-11x+3)-2(-11/4x-5/2)= simplify it
Answer:
(+22x^2+16x+11)/(2x)
wwqrwqretertertreterterter
Answer:
answer: no spam please
oly questions
f(x)
X
(b)
Use the graph to determine the limit visually (if it exists). (If an answer does not exist, enter DNE.)
(a)
lim f(x)
X--1
-2
lim f(x)
x 0
Write a simpler function that agrees with the given function at all but one point.
q(x) =
a) Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.
b) The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].
How to determine whether a limit exists or not
According to theory of limits, a function f(x) exists for x = a if and only if [tex]\lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x)[/tex]. This criterion is commonly used to prove continuity of functions.
Rational functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following lateral limits:
[tex]\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty[/tex]
[tex]\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty[/tex]
Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.
In addition, we can simplify the function by algebra properties:
[tex]\frac{x}{x^{2}+ x} = \frac{x}{x\cdot (x + 1)} = \frac{1}{x + 1}[/tex]
[tex]g(x) = \frac{1}{x + 1}[/tex]
The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].
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The speed of the boat in still water is mph.
The speed of a river current is 3 mph. If a boat travels 30 miles downstream in the same time that it takes to travel 20 miles upstream, find the speed of the boat in still water.
Answer: the speed of the stream is 9mph
explain why the equation y=5x is a special case of the slope-intercept form. what are the slope a nd y intercept of the line represented in this equation
Answer:
It is proportional. When You graph it, it will go through the origin. The slope is 5. The y intercept is 0.
Step-by-step explanation:
When a linear function is proportional, the slope will be in the form of y/x.
So, say we put 2 in for x, then y would be 10. 2 is the x and 10 is the y. What is 10/2? 5 (the slope)
If we put in 6 for x, then y would be 30. 5 is the x and 30 would be the y. What is 30/5? 5 (the slope)
if we put in -3 for x, then y would be -15. -3 is the x and -15 would be the y. What is -15/-3? 5 (the slope).
We could not find the slope this way, if the line was not proportional.
For example, if the y intercept is not zero, like
y = 5x + 2. If I put 3 in for the x, then the y would be 17. Is 17/3 equal to 5? No, because the line is not proportional.