The real-world problem involving a related set of two equations is given below:
Problem: Cost of attending a concert is made up of base price and variable price per ticket. You are planning to attend a concert with your friends and want to know the number of tickets to purchase for lowest overall cost.
What are the two equations?The related set of two equations are:
Equation 1: The total cost (C) of attending the concert is given by:
The equation C = B + P x N,
where:
B = the base price
P = the price per ticket,
N = the number of tickets purchased.
Equation 2: The maximum budget (M) a person have for attending the concert is:
The equation M = B + P*X
where:
X = the maximum number of tickets a person can afford.
So by using the values of B, P, and M, you can be able to find the optimal value of N that minimizes the cost C while staying within your own budget M. so, you can now determine ticket amount to minimize costs and stay within budget.
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A variable that can only take on specific numeric values is called a _____. Group of answer choices categorical variable discrete random variable continuous random variable categorical variable
A variable that can only take on specific numeric values is called A discrete random variable.
According to the statement
A variable which is used to select a specific numeric value and we have to find a those variable
A discrete random variable is one which may take on only a countable number of distinct values.
So, A variable that can only take on specific numeric values is called A discrete random variable.
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3. Jorge earns a 9% commission on all of his sales. He had sales of
$89,400 for the month. Harris works for a different company, and also
sold $89,400 for the month but made $447 more than Jorge. What is
Harris' commission rate?
The commission rate exists at $8,493 with a rate of 9.5%.
How to estimate the commission rate?
Jorge earns 9% from all his sales, so his commission exists
89400 × 0.09 = $8046
Harris made $447 more than that, so his commission exists
8046 + 447 = $8493
To estimate his commission rate, we can utilize the subsequent equation
89400 × rate percentage = 8493
Rate percentage = 8493 / 89400
Rate percentage = 0.095
Rate percentage = 9.5%
So Harris' commission exists at $8,493 with a rate of 9.5%.
Therefore, the commission rate exists at $8,493 with a rate of 9.5%.
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A forest ranger wants to estimate the probability of catching a bass in a lake when using a special type of bait. Describe a process the ranger could use to estimate the probability of catching a bass in the lake.
The probability of catching a bass in the lake is given by:
Probability = probability 1 × probability 2
How to calculate the probability of catching a bass?Since the forest ranger caught a fish from his prior fishing experience, we can infer that he has a probability of catching a bass in a lake:
Probability 1 = Number of fish caught/Number of tries
By using a special type of bait, he should calculate the probability of catching a fish as follows:
Probability 2 = Number of fish caught/Number of tries
Therefore, the probability of catching a bass in the lake is given by:
Probability = probability 1 × probability 2
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Identify the range of values for y.
The figure shows a triangle. The first side of the triangle goes from the lower left corner to the upper right corner. The second side of the triangle goes from the lower right corner to the upper left corner. An angle between these sides is an obtuse angle. The third side of the triangle goes from the lower left corner to the lower right corner. A line connects a vertex of the obtuse angle with a point on the third side. This line divides the third side into left and right segments. An angle between this line and the second side measures 60 degrees. An angle between this line and the left segment of the third side measures 105 degrees. The second side of the triangle is congruent to the left segment of the third side. The right segment of the third side has a length of 5 times y plus 8 units. The first side of the triangle has a length of 4 times y plus 15 units.
The range of values of y is -1.6 < y < 7
How to determine the range?The complete question is added as an attachment
From the attached image, we have the following sides
4y + 15 and 5y + 8
Both sides must be greater than 0.
So, we have:
4y + 15 > 0 and 5y + 8 > 0
Rewrite as:
4y > -15 and 5y > - 8
Solve for y
y > -3.75 and y > -1.6
If y is less than -1.6, the side 5y + 8 would be negative.
So, we make use of the inequality y > -1.6 as one of the range
Also, 4y + 15 is greater than 5y + 8.
So, we have:
4y + 15 > 5y + 8
Evaluate the like terms
-y > -7
Divide by -1
y < 7
So, we have:
y > -1.6 and y < 7
Combine both inequalities
-1.6 < y < 7
Hence, the range of values of y is -1.6 < y < 7
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Towards neural Earth system modelling by integrating artificial intelligence in Earth system science
Answer:
This has nothing to do with math
Step-by-step explanation:
I don't know what this even means
For the following distribution: x p(x) 0 01.30 1 0.346 2 0.346 3 0.154 4 0.026 what is the mean of the distribution?
The mean of the distribution given is 0.569.
Given some distribution like under:
x p(x)
0 0.650
1 0.216
2 0.087
3 0.026
4 0.014
5 0.009
We have to find the mean of the distribution.
Mean is the sum of numbers divided by the numbers which are taken into consideration. It is also known as average.
Mean=sum/n
To find the mean of distribution we have to find sum of x*p(x)
∑xp(x)=0*0.650+1*0.216+2*0.0087+3*0.026+4*0.014+5*0.009
=0+0.216+0.174+0.078+0.056+0.045
=0.569
Hence the mean of the distribution given in the question is 0.569.
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Distribution in the given question is wrong and the right question is as the right distribution is as under:
x p(x)
0 0.650
1 0.216
2 0.087
3 0.026
4 0.014
5 0.009
Help me in this question please dont put wrong answers!
Step-by-step explanation:
Has greater balance = Heba
Has more debt = Nour
Read the "note" thing on there it says banks use Negative balances meaning the negative sign ( minus sign) to represent an account with debt which means an account that is owning money e.g -$11, -$15 etc.And they use positive balances meaning the positive sign to represent account that contains valuee.g $2, $7 etc( You might wonder why I didn't put a positive sign on it, the reason is because it's already a positive number so no need to add a positive sign (+) to it) ( BUT they can still add a positive sign to it but it isn't necessary )If you see any number or amount without a negative sign (-) then that number or amount is positive e.g 1, 2,3,4,5,6,11,14,17,20,100,8, $3, $15, $23 and so on..
Hope this helps.Good luck ✅.
Using the number line:
Heba has the greater account balance
Nour has the most debt.
What is a Number Line?A number line shows where a number lies according to the order. Values greater than 0 and are on the right side are greater than values and vice versa.
Given their balances, $29.17 is greater than -$11.99. Therefore, Heba has the greater account balance using the number line.
Since - indicates debt, Nour has the most debt.
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All the students in a science class complete a 15-point extra-credit assignment to raise their test scores the new test score is 15 points more than the original score let x = original score let y = new score ehich equation represents this situation?
The equation that represents the situation is,
y = x + 15
Given Information
It is given that the students complete a 15-point extra-credit assignment in order to raise their test scores.
The new test score is 15 more than the old test score.
We have to find an equation for this situation. A mathematical equation is a formula that uses the equals sign to connect two expressions in order to express their equality.
Forming Equation
Original Score = x
New Score = y ................... (1)
Thus, after the test, the score is raised by 15 points.
⇒ New score = x + 15 .................... (2)
The following equation can be deduced from (1) and (2)
y = x + 15
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A rectangle with a length of x - 4 and a width of 8 has a perimeter of 34. what is the value of x?
Answer:
13
Step-by-step explanation:
2(x-4+8)=34
x-4+8=17
x+4=17
x=13
Josie has 16 coins. Each of her coins is either a quarter or a dime. If she has 6 more dimes than quarters, and the total value is $2.35, how many quarters does Josie have?
Josie has a total of 5 quarters.
How to find the number of quarters using equation?Josie has 16 coins. Each of her coins is either a quarter or a dime.
Let
x = number of quarters
y = number of dime
she has 6 more dimes than quarters.
Therefore,
y = 6 + x
x + y = 16
-x + y = 6
2y = 22
y = 11
11 = 6 + x
x = 11 - 6
x = 5
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What are the solutions of the system of equations y = –(x + 2)2 + 1 and y = 2x + 5?
(–4, –3) and (–2, 1)
(–4, –3) and (2, 1)
(–4, 5) and (2, 1)
(–4, 5) and (–2, 1)
Answer:
(–4, 5) and (–2, 1)
Step-by-step explanation:
Answer: A: (-4,-3) (-2,1)
Step-by-step explanation:
I got this correct on the test. Using the substitution method give brainliest
Using algebra, prove that 0.136 (3,6 recurring) is equal in value to 1/33.
Answer:
0.1363636... = 3/22
Step-by-step explanation:
Let x = 0.1363636...
100x = 13.6363636...
(-) x = 0.1363636...
------------------------------------------
99x = 13.5
x = 13.5/99
x = 135/990
x = 27/198
x = 9/66
x = 3/22
0.1363636... = 3/22
0.1363636... is not equal to 1/33.
1/33 = 0.030303...
Green’s Sport Shop offers its salespeople an annual salary of $10,000 plus a 6% commission on all sales above $20,000. Every employee receives a Christmas bonus of $500. What are Mr. Cahn’s total earnings in a year in which his sales amounted to $160,000?
(A) $18,900
(B) $18,400
(C) $19,600
(D) $20,100
The total earnings for the year is $18,900.
What is the total earnings?The total earnings is a sum of the annual salary, commission and Christmas bonus.
Commission = 6% x (160,000 - 20,000) =
6% x $140,000
0.06 x 140,000 = $8,400
Total earnings = $8,400 + 10,000 + $500 = $18,900
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The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees work more than 40 hours per week because management demands longer hours or offers large monetary incentives. A random sample of 26 white-collar employees worked on average 42.08 hours per week. Is there any evidence that the true mean number of hours worked per week by white-collar employees is greater than 40? Assume that the population standard deviation is 3.39 hours. Please use the exact value (from R) for all critical values. c) Is there any evidence to suggest the true mean number of hours worked per week by white-collar workers is greater than 40? Perform the hypothesis test at a 0.5% significance level. (0.5 pts.) Calculate the test statistic. 3.13 You are correct. Your receipt no. is 152-5185 Previous Tries (0.5 pts.) Calculate the p-value. Please write your answer in scientific notation using an E for the exponent and including at least 3 decimal places. For example, 1.234 x 10-5 would be written as 1.234E-5. 8.782x10-4 (0.5 pts.) d) Calculate the appropriate 99.5% bound that is consistent with what you did in parts b) and c).
The necessary assumptions are to get the sample for random sampling and ensure they are normal.
a. The required assumptions to form hypothesis are:Sample has to be drawn from random sampling.Sample has to be approximately normalThe samples have to be independentb. The standard deviation is known hence we have to make use of the z distribution.
c. test statistic42.08 - 40 / (3.39 /√26)
= 2.08 / 0.6648
= 3.129
≈3.13
p value
p(Z > 3.13)
= 0.0008770
8.7e-4
d. Z critical value = 2.81
42.08 +- 2.81 * 3.39/√26
= 42.08 +- 2.81*0.6648
= 42.08 - 1.868, 42.08 + 1.868
= 40.212 ,43.948
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The median for the samples from the school math contest are:
The median of Sample 1 from Grades 9 and 10 is 79.
The median of Sample 2 from Grades 11 and 12 is 86.
What conclusions can you derive from the random samples?
The students performed equally between all the grades.
The students in grades 11 and 12 scored higher than the students in grades 9 and 10.
The students in grades 11 and 12 are likely to do well in college.
The students in grades 9 and 10 were not allowed enough time in the school math contest.
The sample size was too small to derive a valid conclusion
A conclusion which can be derived from these random samples is that: B. the students in grades 11 and 12 scored higher than the students in grades 9 and 10.
What is a median?A median can be defined as the middle number (center) of a sorted data set, which is when the data set is arranged in from the greatest to least or the least to greatest.
In Mathematics, the median of a data set is generally considered to be a better measure of center than the mean when there's an outlier in the data set.
Based on the information provided for these samples, we can logically conclude that the students in grades 11 and 12 scored higher than the students in grades 9 and 10 because a median score of 86 is greater than a median score of 79.
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An arc of length 8 in. is intersected by a central angle in a circle with a radius of 3 in. What is the measure of the angle
Answer: [tex]\theta=\frac{8}{3} \text{ radians}[/tex]
Step-by-step explanation:
[tex]8=3\theta\\\\\theta=\frac{8}{3} \text{ radians}[/tex]
Which equation describes this graph?
A. y=−2x
B. y=−2x−3
C. y=−2x+3
D. y=−3x−3
Answer:
D
Step-by-step explanation:
if you look the point on the y axis is -3 which is your starting point
in y=mx+b m is the slope
Which equation could represent the graph shown below?
F(x) = ^3√x + 2 (sqrt just over the x)
F(x) = ^3√x - 2 (sqrt just over the x)
F(x) = ^3√x + 2 (the sqrt is over the whole equation)
F(x) = ^3√x - 2 ( the sqrt is over the whole equation)
I DONT KNOW HOW TO PUT A PICTURE OF THE GRAPH!!
The equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]
How to determine the graph equation?The graph is added as an attachment
The form of the graph is
[tex]f(x) = a\sqrt{x + b[/tex]
The graph passes through the points (2, 0) and (6, -2).
So, we have:
[tex]0 = a\sqrt{2 + b[/tex] and [tex]-2 = a\sqrt{6 + b[/tex]
Solve for b in [tex]0 = a\sqrt{2 + b[/tex]
Divide both sides by a
[tex]0 = \sqrt{2 + b[/tex]
Square both sides
0 = 2 + b
Subtract 2 from both sides
b = -2
Substitute b = -2 in [tex]-2 = a\sqrt{6 + b[/tex]
[tex]-2 = a\sqrt{6 -2[/tex]
[tex]-2 = a\sqrt{4[/tex]
Evaluate the square root
-2 = 2a
Divide by 2
a = -1
Substitute b = -2 and a = -1 in [tex]f(x) = a\sqrt{x + b[/tex]
[tex]f(x) = -\sqrt{x -2[/tex]
Hence, the equation of the graph is [tex]f(x) = -\sqrt{x -2[/tex]
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Please help
!!!!!!!!!!!!!!
Answer: Option (2)
Step-by-step explanation:
[tex]DE=\sqrt{(-a-b-0)^2 + (c-2c)^2}=\sqrt{(a+b)^2 + c^2}[/tex]
15-point question. Pls help
Answer:
3/8
Step-by-step explanation:
There are 8 equal slices so each slice is 1/8th of the whole pizza
1/8+1/8=2/8 he ate right away
2/8+1/8 for what he ate before going to sleep
2/8+1/8=3/8
Question 12 of 20
Subtract.
(2x²+5)-(4x-3)
OA. 2x²-4x+2
OB. -2x² +8
OC. 2x2²-4x+8
OD. -2x²+2
Answer:
C
Step-by-step explanation:
Distribute the negative, (2x^2 + 5) + (-4x+3)
Add like terms, 2x^2 - 4x +(5+3)
2x^2-4x+8
please help me with this
Answer:
x = -9, y = 8
or,
(-9, 8)
Explanation:
Equation 1: 2x + 3y = 6
Equation 2: 4x - y = -44
To solve by substitution, make y subject for equation 2.
4x - y = -44
-y = -44 - 4x
y = 4x + 44
Substitute this y value into equation 1.
2x + 3(4x + 44) = 6
2x + 12x + 132 = 6
14x = 6 - 132
14x = -126
x = -9
Now, find y value:
y = 4x + 44
y = 4(-9) + 44
y = 8
To check for solution, insert x and y value in either equations.
2x + 3y = 6
insert values
2(-9) + 3(8) = 6
6 = 6
Hence, the solution is correct as both sides equal.
Therefore x = -9 and y = 8.
Step-by-step explanation:Substitution method
Equation (1) ——— 2x + 3y = 6
Equation (2) ——— 4x - y = -44
When using substitution method , make x the subject of equation (1).
2x + 3y = 6
2x = 6 - 3y
x = 3 - 3y/2
Substitute the value of x in equation (2) to find y.
4(3 - 3y/2) - y = -44
12 - 6y - y = -44
Subtract 12 from both sides.
12 - 12 - 7y = -44 - 12
-7y = -56
y = 8
Substitute the value of y in equation (1) to find x.
2x + 3y = 6
2x + 3(8) = 6
2x +24 = 6
Subtract 24 from both sides.
2x + 24 - 24= 6 - 24
2x = -18
x = -9
Therefore x = -9 and y = 8.
To check out the solution.
Equation (1) 2x + 3y = 6 , x = -9 , find y.
Substitute the value of x
2(-9) + 3y = 6
-18 + 3y = 6
Add 18 to both sides.
-18 + 18 + 3y = 6 + 18
3y = 24
y = 8
Substitute the value of y in equation (1) .
2x +3(8) = 6
2x + 24 = 6
Subtract 24 from both sides.
2x + 24 - 24 = 6 -24
2x = -18
x = -9
As you can see when you substitute the value of x and y in the equation(1) , you get the same value of x and y ,which is -9 and 8 respectively. So the solution is correct.
Instructions: Find the measure of the indicated angle to the nearest degree.
The measure of the indicated angle to the nearest degree is 47°.
What is the measure of the angle?Given the data in the question;
Adjacent = 36Hypotenuse = 53Angle θ = ?From trigonometric ratio, Cosθ = Adjacent / Hypotenuse
Cosθ = 36/53
θ = cos⁻¹( 36/53 )
θ = 47°
Therefore, the measure of the indicated angle to the nearest degree is 47°.
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f(x) = (two-fifths) Superscript x
g(x) = (two-fifths) Superscript x – 3
Which statement about f(x) and its translation, g(x), is true?
The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > –3}.
The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}.
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
The asymptote of g(x) is the asymptote of f(x) shifted three units up.
Answer: The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
Answer:
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
Step-by-step explanation:
bc I said so
The perimeter of the figure to the right, made up of identical squares, is equal to 56 cm. What is the area of the figure?
The area of the square will be 196cm².
How to calculate the area?It should be noted that the perimeter of a square is the addition of all its sides. Therefore, the length of the side will be:
= 56/4
= 14
Therefore, the area of the figure will be:
= 14²
= 14 × 14
= 196cm²
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Here is a list of numbers: 8.2, 0.4, 7.7, 2.8, 4.8, 6.1, 6.1 ,10 ,8.2 ,3 state the median.
Answer: 6.1
Step-by-step explanation:
The Drury Lane Theater has 10 seats in the first row and 38 rows in all. Each successive row contains one additional seat. How many seats are in the theater?
Answer:
Step-by-step explanation:
Given : 10 seat in first row, and the seat will increase 1 by 1 as we go above.... (as we go to the next row) - total rows - 38
Solve ; 38 rows, 10 seat in first row, 1 seat increases each row....
Extra seats - 37,
So,
37 x 10 = 370
TOTAL SEATS = 370
Answer:
1083 seats
Step-by-step explanation:
The number of seats is an arithmetic series with first term 10 and common difference 1. We want to find the sum of 38 terms of the series.
SetupThe sum of n terms of an arithmetic series with first term a1 and common difference d is given by the formula ...
Sn = (2a1 +d(n -1))(n/2)
The sum of the series of interest is ...
S38 = (2(10) +1(38 -1))(38/2)
Total seatsThe total number of seats in the theater can be found by evaluating the expression for S38:
S38 = (20 +37)(19) = 57×19 = 1083
There are 1083 seats in the theater.
If BE−→− bisects ∠ABD and m∠ABD = 66°, find m∠ABE.
Answer:
∠ABE = 33°
Step-by-step explanation:
Angle bisector:Angle bisector is a straight line that divides the angle into two congruent (equal) angles.
So, BE bisects the ∠ABD into two equal angles.
⇒∠ABE will be half of ∠ABD
∠ABD = ∠ABE + ∠BED
66° = ∠ABE + ∠ABE
66 = 2∠ABE
∠ABE = 66/2
∠ABE = 33°
Alice and Bob both go to a party which starts at $5:00$. Each of them arrives at a random time between $5:00$ and $6:00$. What is the probability that the number of minutes Alice is late for the party plus the number of minutes Bob is late for the party is less than $45$
The probability comes out to be 9/32.
Deducing Arrival Time Possibility
All the possible arrival times by Alice and Bob, in minutes after 5 PM, is constrained by the values of given values of x and y,
x = 0, y = 0, x = 60, y = 60.
Here, let the values of x represent how many minutes after 5 PM Alice arrives at the party.
Let the y values represent the time in minutes that Bob arrives at the party after 5 PM.
Calculating the Required Probability
The times that concern us, however, are obtained by the following probability function,
x + y ≤ 45.
And x = 0, y = 0, and x + y ≤ 45 define the constraints of this probability function. Thus the perimeter of such a graph will be given as,
(45² / 2) = 1012.5 square units
Since the total area of the various arrival times is 60 x 60, or 3600 square units, the probability that Alice and Bob will arrive together after 5 o'clock in the evening in less than 45 minutes is therefore = 1012.5 / 3600 = 9/32
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if roni and allie work together to mow the field, what part of the field would roni mow?
Based on the Roni using a lawn mower and Allie pushing one, Roni would be able to mow 0.71 of the field.
How much of the field would Roni mow?Assume that the part of the field that Roni would mow is x.
The relevant equation would be:
x/30 + x/75 = 1
5x/150 + 2x/150 = 1
7x / 150 = 1
x = 21.43
In 30 minutes, Roni would have mowed:
= 21.43 / 30
= 0.71
Full question is:
Roni and Allie are mowing the grass at the soccer field. Roni has a riding lawn mower and can mow the field in 30 minutes. Allie is pushing a lawn mower and can mow the field in 75 minutes.
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