Answer:
-8
Step-by-step explanation:
-4d=32
d=32/-4
d=-8
Given: AD is parallel to BC
Prove: DC = 6 units
Which step is missing?
To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.
Option C is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
AD is parallel to BC
From the figure and the given information,
We have,
∠DAC ≅ ∠BCA
AC ≅ AC∠DCA ≅∠BACThis means,
Angle-Side-Angle (ASA) Congruence
ΔDAC ≅ ΔBCA
Thus,
To prove DC = 6 units the missing step is ΔDAC ≅ ΔBCA by ASA.
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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.
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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Quick algebra 1 assignment for 50 points!
Experts and Geniuses please help asap, TYSM!
Oh by the way this is just a section of the real assignment, the assignment calls for you to make an app that people can play to learn inverse variation & direct variation and stuff.
Hope that helps solve this! :)
By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.
How to use inverse variation to represent a situation
Herein we should present a statement that represents a real life situation and solve that statement. Here is an example:
In accordance with the Coulomb's law, electric force is inversely proportional to the square of the distance between the two electrically charged particles. If you know that electric force is 20 N when the two particles are 10 cm apart, what is the electric force if the distance is doubled.
Based on the statement, we have the following relationship:
F ∝ 1/r²
Where:
F - Electric charge, in newtonsr - Distance between the two electrically charged particles, in centimeters.From such relation, we can determine the resulting force by the following equation:
F/20 = 10²/20²
F = 20 × 10²/20²
F = 5 N
By inverse variation, the electric force between the two particles is 5 newtons when they are 20 centimeters apart.
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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
The sales department has determined that the average purchase value for their catalog business is normally distributed with a mean of $30.44 and a standard deviation of $14.99. What is the purchase value at the 20th percentile
The purchase value at the 20th percentile is $17.85 for the distribution with a mean of $30.44 and a standard deviation of $14.99.
How to calculate Z-score to raw score X?The formula for the X is
X = μ + Z × σ
where,
Z- score, μ is the mean, and σ is the standard deviation
Calculation:It is given that,
μ = $30.44
σ = $14.99
x% is given as the 20th percentile
So, α = 0.20
then, the Z score from the normal distribution table is -0.84
On substituting,
X = μ + Z × σ
= 30.44 + (-0.84 × 14.99)
= 30.44 - 12.59
= 17.85
Therefore, the purchase value at the 20th percentile is $17.88.
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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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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°
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
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:
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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Direct materials $ 5.50 direct labor $ 3.00 variable manufacturing overhead $ 1.50 fixed manufacturing overhead $ 4.00 fixed selling expense $ 2.50 fixed administrative expense $ 2.00 sales commissions $ 1.00 variable administrative expense $ 0.50 13. if the selling price is $21.50 per unit, what is the contribution margin per unit? (do not round intermediate calculations. round your answer to 2 decimal places.)
The contribution margin per unit is $ 1.50
The contribution margin is the percentage of a product's sales revenue that isn't consumed by variable costs and goes toward paying the firm's fixed expenses.
One of the main components of break-even analysis is the idea of contribution margin.
Labor-intensive businesses with few fixed expenses tend to have low contribution margins, whereas capital-intensive, industrial businesses have more fixed costs and, thus, higher contribution margins.
According to the question,
Total expenses per unit = $(5.50+3.00+1.50+4.00+2.50+2.00+1.00+0.50)
= $ 20
Selling Price per unit = $ 21.50
Thus, contribution margin per unit = $ (21.50 - 20)
= $ 1.50
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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
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...
need answered asapp!!
Answer:b
Step-by-step explanation:goooooooo
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
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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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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Solve for x using
cross multiplication.
3x + 6
4
=
4x - 3
5
x = [?]
Enter
Answer:
x = 42
Step-by-step explanation:
Cross multiplying is done as follows:
the denominator of the second fraction is multiplied with the numerator of the first equation and denominator of the first fraction is multiplied with the numerator of the second equation
5(3x+6) = 4(4x-3) multiply inside the parenthesis
15x + 30 = 16x - 12 transfer like terms to same side of the equation
30 + 12 = 16x - 15x
42 = x
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
3x-6=15 what is the value of x?
Answer:
7
Step-by-step explanation:
frist simplfying
3x-6=15
addind six to both side
3x-6+6=15+6
3x=21 dividing by 3
x=7
Calculating Volume of a Composite Figure 2 rectangular pyramids are connected at their bases. The total height of the 2 figures if 10 units. The base edge lengths are 9 units and 1.5 units. The height of each pyramid is 5 units. Which statements about the composite figure are true? Check all that apply. The composite figure consists of two rectangular pyramids. The composite figure can be broken down into rectangular prisms. The volume of the composite figure is 1.5(9)(5) + 1.5(9)(5). The total volume is 45 units3. The total volume is 90 units3.
The answer which are true about the two rectangular pyramids are;
The composite figure consists of two rectangular pyramids.The composite figure can be broken down into rectangular prisms.The volume of the composite figure is 1.5(9)(5) + 1.5(9)(5).Which statements about the composite figure are true?It follows from the task content that the dimensions of the rectangular prisms are the same and are as given.
On this note, it follows that the volume of the composite figure is; 1.5(9)(5) + 1.5(9)(5) = 135units³.
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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
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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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.
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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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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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]
Note: Figure is not drawn to scale.
The object above is symmetrical through Z. If Y = 14 inches, Z = 14 inches, and H = 10 inches, what is the area of the object?
The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The area of kite = (product of diagonals)/2
Area of kite = (10 * 14) / 2 = 70 in²
The area of the object with a shape of kite having diagonals of 14 inches and 10 inches is 70 in².
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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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