Answer:
Angle A = 78
Step-by-step explanation:
Start with the equation 8x+20=180 and solve for x which equals x=20. You then substitute for x with the equation for angle A. A=3(20)+18 which makes angle A = 78
The measure of ∠A is 78 degrees.
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles.
Which means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
∠A and ∠B are supplementary angles. If ∠A=(3x+18) and ∠B=(5x+2)
then find the measure of ∠A.
Now Start with the equation
8x+20 = 180
solve for x which equals x=20.
then substitute for x with the equation for angle A.
A=3(20)+18
angle A = 78
Hence, the measure of ∠A is 78 degrees.
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What is the mean of: 9.6, 2, 4.1, 8, 5.9, 2, 3.7, 6, 7.6?
Answer:
5.43333 recurring
Step-by-step explanation:
Mean is the average of a set of numbers. That is, the sum of the digits in the set, divided by the number of the digits.
In the question above, we have 9 digits. So we find the sum of the digits divided by 9.
(9.6+2+4.1+8+5.9+2+3.7+6+7.6)/9
48.9/9
5.4333recurring
there are 6 girls in a music class. this represents 3/7 of the entire class. solve 3/7s=6 to find the number of students,s, in the class.
The number of students in the class is [tex]s=14[/tex]
Explanation:
It is given that there are 6 girls in a music class.
This represents [tex]\frac{3}{7}[/tex] of the entire class.
To determine the number of students in the class, we need to solve the equation [tex]\frac{3}{7}s=6[/tex]
Let us solve the expression for s.
Multiplying both sides of the equation by [tex]\frac{7}{3}[/tex], we have,
[tex](\frac{7}{3} )\frac{3}{7}s=6(\frac{7}{3} )[/tex]
Simplifying the expression, we have,
[tex]s=\frac{42}{3}[/tex]
Dividing by 3, we have,
[tex]s=14[/tex]
Thus, the number of students in the class are 14.
what is the difference between the points (-3,4) and (5,4)
Answer:
That 1st one will be in the negatine seconw one will de positive
which of these rational numbers are also an integer?
a.2/4
b.0.24
c.4/2
d.2.4
Answer:
D.2.4
Step-by-step explanation:
Because it's a fraction and can be written in fraction as 240/100
Answer:
answer is C
Step-by-step explanation:
4/2 : rational
4/2 = 2 : integer
and When you simplify 4/2 you get 2, 2 is an integer.
If point E is translated 2 units right and 4 units up, what are the coordinates of E'?
Answer:
6
Step-by-step explanation:
Answer:
Answer is (2,6) B.
Step-by-step explanation:
Justin and TJ are servers at a local restaurant. The table below shows the tips they earned.
Which student has a higher median tip for the week and by how much?
Answer:
1. For the median (as per the question posted): the median of Justin's earnings is more than the median of TJ's earnings
Difference = $3
2. For the mean (as per the requirement in the image): the mean of TJ's earnings is more than the mean of Justin's earnings
Difference = $4
Explanation:
The complete question is shown in the attached image
1. The median:
It is defined as the value found in the middle of a set of arranged data/numbersIf the set has odd number of data, then the median is simply the middle valueIf the set has even number of data, then the median is the average of the two middle valuesTo get the median, we need to first arrange the given dataa. For Justin:
He earned the following: $32, $45, $50, $33 and $50
Arranging the data: $32, $33, $45, $50 and $50
The middle value is: $45
The median is: $45
b. For TJ:
He earned the following: $58, $48, $40, $42 and $42
Arranging the data: $40, $42, $42, $48 and $58
The middle value is: $42
The median is: $42
c. Comparing the medians:
From the above, we can conclude that the median of Justin's earnings is more than the median of TJ's earnings
Difference = $45 - $42 = $3
2. The mean:
It is defined as the average value of a set of dataIt is calculated by summing the values in the set and then dividing this sum by the number of vales in the seta. For Justin:
He earned the following: $32, $45, $50, $33 and $50
Summing the data: $32 + $33 + $45 + $50 + $50 = 210
Number of values in the data= 5
The mean is: [tex]\frac{210}{5}=42[/tex]
b. For TJ:
He earned the following: $58, $48, $40, $42 and $42
Summing the data: $40 + $42 + $42 + $48 + $58 = $230
Number of values in the data: 5
The mean is: [tex]\frac{230}{5} = 46[/tex]
c. Comparing the values:
From the above, we can conclude that the mean of TJ's earnings is more than the mean of Justin's earnings
Difference = 46 - 42 = $4
Hope this helps :)
How many solutions does the system of equations have?
The system has infinitely many solutions.
The system has no solution.
The system has exactly one solution.
Answer:
This system has infinitely many solutions because they right on top of each other.
If the lines were perpendicular, then there would be exactly one solution.
If the lines were parallel, there would be no solutions.
Erwin had 2 5/12 gallons of lemonade. He spilled 11/12 gallon of lemonade. How much lemonade dose he have left? Write in simplest form
Answer:
Erwin have 1 [tex]\frac{1}{2}[/tex] gallons of lemonade left
Step-by-step explanation:
Erwin had 2 5/12 gallons of lemonade. He spilled 11/12 gallon of lemonade. How much lemonade dose he have left? Write in simplest form
All we need to do is to subtract 11/12 from 2 5/12. But to do this, we will convert 2 5/12 to improper fraction
converting 2 5/12 to improper fraction yields : 29/12
Lemonade have left = Total lemonade - lemonade spilled
= 29/12 - 11/12
= 18/12
Lemonade have left =18/12
But we can reduce 18/12 to its lowest term
18÷6/ 12÷6 = 3/2
Lemonade have left = 3/2
We can change to 3/2 to a mixed number to give us 1 [tex]\frac{1}{2}[/tex]
Therefore Erwin have 1 [tex]\frac{1}{2}[/tex] gallons of lemonade left
Answer:
(3/2) or (1 1/2) gallons of lemonade
Step-by-step explanation:
Erwin had 2 5/12 gallons of lemonade at his disposal which also translate to 29/12 gallons.
If he spills 11/12 gallon of the lemonade,then the quantity left with him will be (29/12) - (11/12) = 18/12(change to proper fraction): 3/2 or 1 1/2 gallons of lemonade
Which equation, in point-slope form, passes through (-2, 4) and has a slope of 3?
a. y - 4= 3(x - 2)
b. y - 4= 3(x + 2)
c. y + 4 = 3(x - 2)
d. y + 4 = 3(x + 2)
Answer:
B
Step-by-step explanation:
The formula is Y-Y1= M(X-X1)
So y-4=3(x+2)
You buy a car for $8000 that depreciates (loses value) at a rate of 11% a year. How much is the care
worth after 5 years?
Answer:
$3600
Step-by-step explanation:
Cost of the car = $8000
The car loses value at 11% each year .
That’s
11% /100% x $8000
0.11 x 8000
$880
11% decrease each year means that the cost of the car is reduced by $880 per year.
Therefore,
Worth of the car in 5 years
= $8000 - ($880 x 5)
= $8000 - $4400
= $3600
The car will be worth $3600 in five years
A company plans to ship 2,000 packages of chocolate. The company randomly selects 100 packages and finds that five packages have an incorrect weight.
Based on this data, how many packages out of the 2,000 should be predicted to have an incorrect weight?
Answer:
100
Step-by-step explanation:
1. 100 divided by 5 = 20
2. 20 x 100 = 2000
3. Final Answer = 100
A company plans to ship 2,000 packages of chocolate, the number of packages is X=100. This is further explained below.
How many packages out of the 2,000 should be predicted to have an incorrect weight?Generally, the number of packages is given as
X=(No Packages* incorrect weight)/ random selections
Therefore
X=2000*5/100
X=100
In conclusion, the number of packages predicted to have an incorrect weight is
X=100
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Help me with this pls!!! You need to fill in the blanks with the words given above 99 Points!
A simulation is a mathematical model used to represent a situation.
A simulation can be a program or a physical test to "simulate" a situation to predict the outcomes.When we combine two or more simple events we have a compound event
"Compound" means to combine, like a compound word would be a combination of two wordsA Tree Diagram is a diagram that shows all the possible outcomes of an event
In a tree diagram, each possible outcome "branches" off the main stem, making the final diagram look like a tree with many separating branches.All the possible outcomes or results is called the sample space
The outcomes are each different samples, and a sample space is a space that collects each of these samplesWhen an event is not affected by a previous outcome we have an independent event
This event is "independent", not affected by other factors, making it an independent eventLet me know if you need any clarifications, thanks!
~ Padoru
If two fractions are between 0 and 1 can their sum be more than 1 ? Explain your thought process.
Answer:
YES
Step-by-step explanation:
If both the fractions are greater than .5, then yes.
Ex. 3/4 and 4/5
Yes if two fractions are between 0 and 1 can their sum be more than 1. Examples are 3 / 4 and 4 / 5.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
If two fractions are between 0 and 1 can their sum be more than 1If both the fractions are greater than .5, then yes. examples are 3/4 and 4/5.
Sum = 3 / 4 + 4 / 5
Sum = 31 / 20
We can see that the sum is greater than one.
Therefore if two fractions are between 0 and 1 can their sum be more than 1. Examples are 3 / 4 and 4 / 5.
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Convert: 100 kilograms to pounds.
22.05
220.5
O 2205
22,050
Answer:
220.5
Step-by-step explanation:
:3
Answer:
220.5 lb
Step-by-step explanation:
1 kg = 2.20462262185 lb
100 kg = 100×2.20462262185 lb
100 kg = 220.462 lb
100 kg = 220.5 lb
A cube has an edge length of 8 meters. What is its volume, in cubic meters?
Answer:
[tex]512\ m^{3}[/tex]
Step-by-step explanation:
Volume of any cube equals a product of all the edge lengths. Since there are 3 edges:
[tex]V = a^{3} = 8^{3} = 512\ m^{3}[/tex]
The required area of the cube with an edge length of 8 meters is 512 cubic meters.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
here,
A cube has an edge length of 8 meters.
The volume of the cube = a³
The volume of the cube = 8³ = 512 cubic meters
Thus, the required area of the cube with an edge length of 8 meters is 512 cubic meters.
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Addyson's goal is to spend less than $415 on a trip. So far, she has spent $25 on gas for her car. She will spend $100 each day on other expenses. Addyson's trip must last fewer than how many days?
Answer:
4 days
Step-by-step explanation:
$25 on gas
$415-$25=$390 she still can spend $390
390/100=3.9 days
that means she can go for 3.9 days
so she must go for less than 4 days
Jim worked for three different employers. They each paid him $15 000. How much income tax should he have paid?
Jim's income tax liability for the $45,000 he earned from his three employers would be $9,500.
To calculate Jim's income tax, we first need to find his total income. Since he worked for three different employers, his total income would be the sum of his earnings from each employer, which is $15,000 * 3 = $45,000.
Next, we need to know the tax rates that apply to Jim's income. Income tax rates are usually progressive, meaning different portions of income are taxed at different rates.
Using the hypothetical tax rates mentioned above, we can calculate Jim's income tax liability:
First $10,000 at 10%: $10,000 * 0.10 = $1,000
Next $20,000 at 20%: $20,000 * 0.20 = $4,000
Remaining $15,000 at 30%: $15,000 * 0.30 = $4,500
Now, summing up the tax amounts from each tax bracket: $1,000 + $4,000 + $4,500 = $9,500.
Therefore, Jim's income tax liability should have been $9,500.
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Final answer:
Jim earned a total of $45,000 from three employers. Using a simplified marginal tax rate example, his total income tax comes to approximately $7,106.25. This calculation method demonstrates how the marginal tax rate system works in a basic form.
Explanation:
To determine how much income tax Jim should have paid on his earnings from three different employers, where each paid him $15,000, we first need to calculate his total income. Jim's total income is $15,000 from each job, multiplied by 3, because he worked for three different employers, resulting in a total income of $45,000.
Assuming a simple tax rate example (for illustrative purposes), let's use the marginal tax rates provided in the reference:
Income from $0 to $9,075 is taxed at 10%
Income from $9,075 to $36,900 is taxed at 15%
Income from $36,900 and beyond is taxed at 25%
Since Jim earns $45,000, here is how his taxes would be calculated:
The first $9,075 is taxed at 10%, amounting to $907.50.
The next $27,825 ($36,900 - $9,075) is taxed at 15%, amounting to $4,173.75
The remaining $8,100 ($45,000 - $36,900) is taxed at 25%, amounting to $2,025.
Add up these amounts to get the total tax:
$907.50 + $4,173.75 + $2,025 = $7,106.25
Therefore, applying this simplified tax calculation, Jim should have paid a total of roughly $7,106.25 in income tax on his total earnings of $45,000 from three different employers.
What is 9 to the power of zero simplified
Does anyone have any useful tips for the ACT? They would be much appreciated!
great someone deleted all my answers again
What number does x stand for 18*x=54
A. 3
B.1
C. 91
D. 85
Answer:
3
Step-by-step explanation:
18*x=54 (divide both sides by 18)
x = 54 ÷ 18
x = 3
Hello!
The answer to your problem is A) 3
Move all terms to the left
[tex]18x-(54)=0[/tex]
Move all terms containing x to the left, all other terms to the right
[tex]18x=54[/tex]
[tex]x=54/18[/tex]
Get your answer
[tex]x=3[/tex]
Hope This Helps!
PLEASE I NEED HELP!!!
A. The perimeter of quadrilaterals are same when x=2.
B. The area of quadrilaterals are same when x=4.6
Step-by-step explanation:
A. Perimeter of the quadrilaterals must be equal.
Perimeter of square is 4a.where, a = 6Perimeter of rectangle is 2(l+b).where, l = 2 and b = (3x+4)Perimeter of square = Perimeter of rectangle
4(6) = 2(2+3x+4)
⇒ 24 = 2(3x+6)
⇒ 24 = 6x + 12
⇒ 6x = 12
⇒ x = 12/6
x = 2
For x=2, the perimeters of both the quadrilaterals are same.
B. Area of the quadrilaterals must be equal.
Area of square is a².where, a = 6.Area of rectangle is l[tex]\times[/tex]b.where, l = 2 and b = (3x+4)Area of square = Area of rectangle
(6)² = 2(3x+4)
36 = 6x+8
6x = 28
x = 28/6
x = 4.6
For x=4.6, the area of both the quadrilaterals are same.
Grace earns $7 for each car she washes. She always saves $22 of her weekly earnings. This week, she wants to have at least $63 in spending money. How many cars must she wash? Enter and solve an inequality to represent this situation. Enter your value as a simplified mixed number, if necessary.
Answer:
12 1/7 cars
Step-by-step explanation:
Let the number of cars she'd wash to earn $63 in spending money be A.
Given she saves $22 of her weekly earnings and wants to have at least $63 for spending money.
That means she’d have to make $63 + $22 = $85
The expression is thus
$85 = A x $7
Where A is the number of cars and $7 is the amount she earns for washing one car and $85 is the total amount she has to make .
Therefore,
85 = A x 7
Divide both sides by 7
85/7 = A x 7/7
12 1/7 = A
A = 12 1/7 cars
She must wash 12 1/7 cars to have at least $63 spending money and also have her weekly Savings of $22
Patrick spins both spinners below. What is the probability the hw spins green on both spinners?
Answer:
4/12 or 2/6 or 1/3
Step-by-step explanation:
On a sunny day around noon , a tree casts a shadow that is 12 feet long . At the same time , a person who is 6 feet tall standing beside the tree casts a shadow that is 2 feet long . How tall is the tree?
Answer:
36 ft. tall
Step-by-step explanation:
We can easily solve this problem with a simple proportion:
12 feet / height = 2 feet / 6 feet
6 * 12 = 2h
72 = 2h
h = 36 ft.
It's found that the tree is 36 feet tall.
To find the height of the tree using the lengths of the shadows and the person's height, we can use a proportion based on similar triangles. Since the sun's rays hit both the tree and the person at the same angle, the ratio of the height of the tree to the length of its shadow is the same as the ratio of the person's height to the length of their shadow.
Let's let 'h' represent the height of the tree. We can set up the proportion as follows:
Person's height / Person's shadow length = Tree's height / Tree's shadow length
6 feet / 2 feet = h / 12 feet
Now we solve for 'h' by cross-multiplying:
6 feet * 12 feet = 2 feet * h
72 feet2 = 2 feet * h
Divide both sides by 2 feet to get:
h = 36 feet
Therefore, the tree is 36 feet tall.
Find the height of the lamppost to the nearest inch.
Collection: Private
DRAG DROP VALUES
109 in.
108 in.
110 in.
107 in.
Height of the lamppost =
Solution:
We have to find the height of lamppost
From the figure in question,
Given is a right angled triangle
Where,
base = 40 inches
height = ?
By definition of tan,
[tex]tan\ 70 = \frac{opposite}{base}\\\\tan\ 70 = \frac{height}{40}\\\\height = tan\ 70 \times 40\\\\height = 2.7474 \times 40\\\\height = 109.89 \approx 110[/tex]
Thus height of lamp post to nearest inch is 110 inches
90 in terms of pi please help
Answer:
90 degrees pi/2 radians
I think so but i dont know
Step-by-step explanation:
A pound of chocolate cost 8 dollars. Ivanna buys p pounds. Write an equation to represent the total cost c that Ivanna pays.
2x−5 = 3 (1−x)+22?
is x=6?
Answer:
x=6
Step-by-step explanation:
You are correct. x does equal 6
Answer:
Yes
x = 6
Step-by-step explanation:
Given
2x - 5 = 3(1 - x) + 22
First distribute 3 into (1 - x)
We have
2x - 5 = 3 x 1 -3 x X + 22
2x - 5 = 3 - 3x + 22
The expression can be rearranged as
2x - 5 = 3 + 22 - 3x
2x - 5 = 25 - 3x
Add 3x to both sides
3x + 2x - 5 = 25 - 3x + 3x
5x - 5 = 25
Add five to both sides
5x - 5 + 5 = 25 + 5
5x = 30
Divide both sides by 5
5x/5 = 30/5
x = 6
Multiply.
38⋅45
Express your answer in simplest form.
A. 3/10
B. 7/40
C. 7/13
D. 12/13
: The You Move It Company (YMI) advertises that the cost to rent a moving truck for one day is $40 plus $1.99 for each mile the truck is driven. The Drive and Move Company (DM) advertises that the cost to rent a moving truck for one day is $60 plus $1.79 for each mile the truck is driven. Alex wants to rent a single truck to use on both Saturday and Sunday on a weekend. Part A For what driving distance does it not matter from which company Alex rents the truck? miles. If Alex only plans of driving 150 miles over the weekend, which company should he use? Part B Give a mathematical explanation as to how you arrived at your answer.
Part A: For 100 miles, the cost will be same for both companies.
Part B: Alex should use Drive and Move company as it will cost him less money.
Step-by-step explanation:
Given,
Starting amount of YMI= $40
Per mile charges = $1.99
Let,
x be the number of miles.
y be the total charges.
y = 1.99x+40 Eqn 1
Starting amount of DM = $60
Per mile charges = $1.79
y=1.79x+60 Eqn 2
Part A:
For same charges;
Eqn 1 = Eqn 2
[tex]1.99x+40=1.79x+60\\1.99x-1.79x=60-40\\0.20x=20[/tex]
Dividing both sides by 0.20
[tex]\frac{0.20x}{0.20}=\frac{20}{0.20}\\x=100[/tex]
For 100 miles, the cost will be same for both companies.
Part B:
Total miles = x = 150
Putting x=150 in Eqn 1
y=1.99(150)+40
y=298.5+40
y=$338.50
Putting x=150 in Eqn 2
y=1.79(150)+60
y=268.5+60
y=$328.50
Alex should use Drive and Move company as it will cost him less money.