$ 2772 is paid in state income tax
Solution:
Given that, Tina lives in a state that charges her 4.5% state income tax on her federal taxable income
Federal taxable income = $61,600
To find: Amount paid by Tina in state income tax
Tax rate = 4.5 %
Which means, 4.5 % of $61,600 is paid as tax
[tex]Tax\ Rate = 4.5 \% \text{ of } 61600[/tex]
Here, "of" means multiplication or product
[tex]Tax\ Rate = 4.5 \% \times 61600\\\\Tax\ Rate = \frac{4.5}{100} \times 61600\\\\Tax\ Rate = 0.045 \times 61600\\\\Tax\ Rate = 2772[/tex]
Thus $ 2772 is paid in state income tax
4.5% of 61,600
0.045(61,600) = 2772
How did i get the decimal in 16.2 by dividing by 48.6 and 3
how to simplify (2√5)²
(2√5 )²
= 2√5 × 2√5
= 4×5
= 20
All tickets for a concert are the same price the tickets agency as a fixed fee to every order a person to order six tickets paid 135 another person who orders three tickets paid 75 right in equation relating to the total cost to the number of tickets purchased in slope intercept form
x will represent the number of tickets.
y will represent the fixed fee given by the ticket agency
6x + y = 135
3x + y = 75
To solve, we can use the process of elimination by multiplying the second equation by -2 so that 6y will cancel:
-6x - 2y = -150
+6y + y = 135
Now we simplify by adding/subtracting:
-y = -15 or y = 15
Plug the value of y into any of the two equations and solve for x. I will use the second equation:
3x + 15 = 75
3x = 60
x = 20
To set this up in slope intercept form (y = mx + b), we need to identify what m and b are.
m is x because it is not a fixed number, and b is y because it is a fixed number (price of “fixed” fee). This brings us to y = 20x + 15
4 times the quotient of 3 and 4
Answer:
3
Step-by-step explanation:
You would start by dividing
3 by 4. Then multiply 3/4 and 4. The 4s would cancel out leaving you with 3. 3/ 4×4=3
hope this helps
Final answer:
To answer the student's question, first find the quotient of 3 and 4, which is ¾, and then multiply that result by 4 to get the final answer of 3.
Explanation:
The student is asking for the result of multiplying 4 with the quotient of 3 and 4. To solve this, first calculate the quotient of 3 and 4, which is ¾. Then, multiply this result by 4.
Step 1: Quotient of 3 and 4 = 3 ÷ 4 = ¾
Step 2: Multiply the quotient by 4 = ¾ × 4
When you calculate step 2, you get:
¾ × 4 = (3 × 4) / 4 = 3
So, 4 times the quotient of 3 and 4 is 3.
For all values of X, Which expression is equivalent to 2x+5-x+3x+x-2
Answer:
=5x+3
Step-by-step explanation:
Hope this helps!
Answer:
annnnnnn
Step-by-step explanation:
u r wronggggggggggggggggggggggggggg
Why does it take 3 copies of 1/6 to show the amount as 1 copy of 1/2
3 copies of 1/6 makes it 1 copy 1/2 because 3 times of 1/6 is 3/6 which is 1/2
Step-by-step explanation:
3 times 1/6 = 3/6
which is 1/2.
Hence it takes 3 copies of 1/6 to show the amount as 1 copy of 1/2
Alternatively,
1/6+1/6+1/6= 1/2
3/6=1/2
1/2=1/2
fill in the blanks 1 1/2 is ____ % of 7 1/2 ; 7 1/2 is ____ % of 1 1/2
Answer:
20; 500
Step-by-step explanation:
1.5 is what percent of 7.5. 7.5 is 5 times 1.5, so 1.5 is 1/5 of 7.5. 1/5=20%. Inversely, 7.5 is 5 times 1.5, 5=500%.
[tex]1 \frac{1}{2} \text{ is } \underline{20\%} \text{ of } 7 \frac{1}{2}[/tex]; [tex]7 \frac{1}{2} \text{ is } \underline{500\%} \text{ of } 1 \frac{1}{2}[/tex]
First, convert the mixed numbers to improper fractions:[tex]1 \frac{1}{2}[/tex] becomes [tex]\frac{3}{2}[/tex].
[tex]7 \frac{1}{2}[/tex] becomes [tex]\frac{15}{2}[/tex].
To determine the percentage, we use the percentage formula:[tex]\text{Percentage} = \frac{\text{part}}{\text{whiole}} \times 100\%[/tex]
Determine what percentage of [tex]1 \frac{1}{2}[/tex] is [tex]7 \frac{1}{2}[/tex]:[tex]\frac{\frac{3}{2}} {\frac{15}{2}} \times 100\% = \frac{3}{15}\times 100\% = \frac{1}{5}\times 100\% = 20\%.[/tex]
Thus,
[tex]1 \frac{1}{2} \text{ is } \underline{20\%} \text{ of } 7 \frac{1}{2}.[/tex]
For the second part, determine what percentage [tex]7\frac{1}{2}[/tex] is of [tex]1 \frac{1}{2}[/tex]:[tex]\frac{\frac{15}{2}} {\frac{3}{2}} \times 100\% = \frac{15}{3}\times 100\% = 5\times 100\% = 500\%.[/tex]
Thus,
[tex]7 \frac{1}{2} \text{ is } \underline{500\%} \text{ of } 1 \frac{1}{2}.[/tex]
Complete question:
fill in the blanks:
[tex]1 \frac{1}{2}[/tex] is ____ % of [tex]7 \frac{1}{2}.[/tex] ; [tex]7 \frac{1}{2}[/tex] is ____ % of [tex]1 \frac{1}{2}.[/tex]
A dress that is regularly priced $80 is on sale for 30% off. What is the sale price of the dress?
Answer:
$56?
Step-by-step explanation:
I think you get 100%-30%=70%.
70%=0.70
0.70*$80= $56
What is the diameter of a hemisphere with a volume of 60570
The diameter of hemisphere is 61.4 units
Solution:
Given that, volume of hemisphere is 60570 cubic units
To find: Diameter of hemisphere
The formula for volume of hemisphere is given as:
[tex]V = \frac{2}{3} \pi r^3[/tex]
Where, "r" is the radius of hemisphere
Substituting the values we get,
[tex]60570 = \frac{2}{3} \times 3.14 \times r^3\\\\60570 = 2.093 \times r^3\\\\r^3 = \frac{60570}{2.093}\\\\r^3 = 28939.32\\\\\text{Take cube root on both sides }\\\\r = \sqrt[3]{28939.32} \\\\r = 30.7017248 \approx 30.7[/tex]
We know diameter is twice of radius
[tex]Diameter = 2 \times radius\\\\Diameter = 2 \times 30.7\\\\Diameter = 61.4[/tex]
Thus diameter of hemisphere is 61.4 units
The diameter of the hemisphere is [tex]\( 60.2 \, \text{cm} \)[/tex].
To find the diameter of a hemisphere with a volume of [tex]\( 60,570 \, \text{cm}^3 \)[/tex], we can follow these steps:
Step 1: Write a hemisphere's volume formula.
A hemisphere's volume (V) is determined by:
[tex]\[ V = \frac{2}{3} \pi r^3 \][/tex]
where ( r ) is the radius.
Step 2: Set up the equation with the given volume
Given [tex]\( V = 60,570 \, \text{cm}^3 \)[/tex], we substitute into the formula:
[tex]\[ 60,570 = \frac{2}{3} \pi r^3 \][/tex]
Step 3: Find the value of [tex]\( r^3 \)[/tex]
First, isolate [tex]\( r^3 \)[/tex]:
[tex]\[ r^3 = \frac{60,570 \times 3}{2 \pi} \][/tex]
Step 4: Calculate the value inside the equation
[tex]\[ r^3 = \frac{181,710}{2 \pi} \approx \frac{181,710}{6.2832} \approx 28,931.89 \][/tex]
Step 5: Solve for ( r )
Take the cube root of both sides to find ( r ):
[tex]\[ r = \sqrt[3]{28,931.89} \approx 30.1 \][/tex]
Step 6: Calculate the diameter
Two times the radius is the diameter (D):
[tex]\[ D = 2r \approx 2 \times 30.1 = 60.2 \][/tex]
Thus, the diameter of the hemisphere is [tex]\( 60.2 \, \text{cm} \)[/tex].
Complete Question:
What is the diameter of a hemisphere with a volume of 60570 [tex]cm^{3}[/tex] , to the nearest tenth of a centimeter?
Are you cyclist travels at a rate of 1.8 km/min. how far will the cycle is travel in 48 minutes
Answer:
86.4 km
Step-by-step explanation:
Since the cyclist travels 1.8km in a minute, he will travel 48 times that in 48 minutes:
[tex]48*1.8 = 86.4[/tex]
A mother is five times as old as her daughter. In 6 years, the mother will be three times as old as her daughter. How old is each now?
Answer: daughter = 6 years
mother = 30 years
Step-by-step explanation:
Let the daughter's age be x and the mother's age be y , then from the first statement
y = 5x .......................... equation 1
In 6 years time , the mother will be y + 6 and the daughter will be x + 6 ,from the second statement , we have
y + 6 = 3 ( x + 6 )
y + 6 = 3x + 18 ..................................... equation 2
substituting equation 1 into equation 2 , we have
5x + 6 = 3x + 18
5x - 3x = 18 - 6
2x = 12
x = 6
Therefore , the daughter's age is 6 years ,then the mother's age will be 6x5 = 30 years
What is the value of the expression below? (Four-fifths + three-fifths) + 3.5 times 5
Answer:
21
Step-by-step explanation:
Answer:
18 and 9/10
Step-by-step explanation:
if you add 4/5+3/5=7/5 or 1.4. 3.5*5=17.5, then you add them together to get 18.9 or in the fraction version= 18 and 9/10
Find an equivalent fraction for the decimal number. In your final answer, include all of your work.
___
0.802
Simplify 13x + 2y - 10x -7y
Answer:
3x-5y
Step-by-step explanation:
Combine like terms
To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. The simplified expression is 3x - 5y.
Explanation:To simplify the expression 13x + 2y - 10x - 7y, combine the like terms together. Start by combining the x terms and then combine the y terms.
13x - 10x = 3x
2y - 7y = -5y
Therefore, the simplified expression is "3x - 5y."
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Simplify (3a 2) 3.
.
Answer: [tex]27a^6[/tex]
Step-by-step explanation:
The question is not clear. So, assuming that the expression you need to simplify is this one:
[tex](3a^2)^3[/tex]
You need to remember a property called "Power of a power property". This property states the following:
[tex](b^m)^n=b^{(m*n)}=b^{(mn)}[/tex]
Therefore, you need to apply the Power of a power property explained before, in order to simplify the expression provided in the exercise, multiplying the exponents inside the parentheses by the exponent outside of the parentheses. Then:
[tex](3a^2)^3=3^{(1*3)}a^{(2*3)}=3^3a^6[/tex]
Now, you must remember that:
[tex]3^3=3*3*3=27[/tex]
Finally, you get:
[tex]=27 a^6[/tex]
The area of the following rectangle is 24 square units.
Write an equation that can be used to find the value of n.
Solve the equation to find the value of n. In your answer, show all of your work.
Answer:
Step-by-step explanation:
Area of rectangle A = L × W
Length L = n - 3
Width = 2
Area = 24square unit
:- 24 = (n - 3)2
24 = 2n - 6 ...... This the equation
24 + 6 = 2n
30 = 2n
n = 30/2
n = 15
The radius of a sphere is 6 units.Which expression represents the volume of the sphere, in cubic units?
Answer:
V=(4/3)πr^3
Step-by-step explanation:
This is the equation to find the volume of a sphere
V=(4/3)πr^3
than plug in 6 for x, and solve
The volume of a sphere with a radius of 6 units is represented by the expression [tex]\frac{4}{3}[/tex] πr³, which calculates to V = [tex]\frac{4}{3}[/tex] π(6)³, cubic units. If two such spheres combine, the volume doubles, and the new radius is the cube root of the new volume.
The expression that represents the volume of a sphere with a given radius in cubic units is given by the formula V = [tex]\frac{4}{3}[/tex] πr³. For a sphere with a radius of 6 units, you can substitute the value of the radius into this formula to calculate the volume.
The calculated volume V would be V = [tex]\frac{4}{3}[/tex] π(6)³, which simplifies to V = [tex]\frac{4}{3}[/tex] π(216), or V = 288π cubic units. Therefore, the volume of the sphere is 288 times π cubic units.
What is a quarter til 1:00
Answer:
12:45
Step-by-step explanation:
quik maths
Answer:12:45
Step-by-step explanation:
Edin has £300 in his savings account.his bank offers him 5% simple intrest rate ped annum for a period of 3 years.how much intrest will he make after 3 years
Answer:
$45
Step-by-step explanation:
We are given the following information;
Money invested (Principal) is $300Rate of interest is 5% per annumTime the money is invested is 3 yearsWe need to determine the amount of interest the money will earn after three years.
Simple interest is calculated by the formula;Simple interest =(PRT) ÷ 100, Where P is the principal amount, R is the rate of interest and T is the time.Therefore, in this case;
Simple interest = ($300 × 5 × 3) ÷ 100
= $45
Thus, the money invested earned a simple interest of $45
Using the formula for simple interest, we find out that Edin will earn £45 as interest on his savings of £300 over a period of 3 years at a simple interest rate of 5% per annum.
Explanation:The subject of this question is simple interest. The formula for simple interest is: Principal * Rate * Time. Let's plug in the given values into the formula. Here, the principal amount is £300, the rate of interest is 5% per annum (or 0.05 in decimal form), and the time is 3 years. So, the calculation will be: £300 * 0.05 * 3.
After performing the calculation, we find that the interest Edin will earn after 3 years is £45.
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A factory makes sheets of metal that are 2/3 of an inch thick. If a worker at the factory makes a stack of 8 of the sheets, how many inches thick will the stack be?
Write your answer as a fraction or as a whole or mixed number.
The thickness of a stack of 8 sheets of metal, each 2/3 of an inch thick, is 5 1/3 inches.
To determine the thickness of a stack of 8 sheets of metal that are each 2/3 of an inch thick, we simply multiply the thickness of one sheet by the number of sheets in the stack:
(2/3 inch/sheet) x 8 sheets = (2/3) x 8
Now, we simplify the expression by multiplying 2 by 8 which equals 16, and then we keep the same denominator:
16/3 inches
This fraction can also be converted to a mixed number:
5 1/3 inches
So, the stack will be 5 1/3 inches thick.
A Line passes through the point (-1,-2) and is perpendicular to the line with the equation y= -x - 1 what’s the equation of the line
Answer:
y = x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x - 1 ← is in slope- intercept form
with slope m = - 1
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1, thus
y = x + c ← is the partial equation of the perpendicular line
To find c substitute (- 1, - 2) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = x - 1 ← equation of perpendicular line
What is the value of h?
O h= 1.5
Oh=9
0 h = 10
0 h = 13.5
Answer:
The answer is 9 on edgggggggggggg
Step-by-step explanation:
Based on the information given, the value of h is 9.
Firstly, it should be noted that the sum of the angles that are on a straight line is 180°.
In this case, we'll have to equate both values that are given and this will be:
3h + 18° + 15h = 180°
Collect like terms
3h + 15h = 180° - 18°
18h = 162°
Divide both sides by 18
18h/18 = 162°/18
h = 9
Therefore, the value of h will be 9
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Which number(s) below belong to the solution set of the inequality? Check all
that apply.
X+9=26
A. 234
B. 3
C. 17
D. 35
E. 52
F. 26
A person is standing 50 ft from a statue. The person looks up at an angle of elevation of 8° when staring at the top of the statue. Then the person looks down at an angle of 14° when staring at the base of the statue. How tall is the statue to the nearest tenth of a foot?
Answer:
The statue is 22.24 ft tall.Step-by-step explanation:
The given question says that, the man is standing 50 ft away from the statue.
Looking at the top of the statue, the angle of elevation is 8°.
Hence, where the man is standing, from that horizontal plane, the distance of the top of the statue is [tex]50 tan 8°[/tex].
Similarly, looking down towards the base, the angle is 14°.
Hence, the height from the base of the statue to the horizontal plane, where the man is standing is [tex]50 tan 14°[/tex].
The total height of the statue is [tex]50 tan 8° + 50 tan 14° = 50( tan 8° + tan 14°)[/tex] = 22.24475804 ≅22.24 ft.
At a party, 4 identical tables are placed side by side as shown. The dimensions of one table are given.
2.5x - 3 and x
Which expressions represent the perimeter of the rectangle formed by all the tables together? Choose all that apply.
10x - 12 + x + 10x - 12 + x
8(2.5x - 3) + 5x
2(10x - 12) + 2x
4(2.5x - 3) + x
2(11x - 12)
*There is more than one answer. Please look at the image and please tell me is I’m correct in the ones I chose*
Answer:
The answer is the first choice: 10x - 12 + x + 10x - 12 + x
Step-by-step explanation:
Let the length of a table 2.5x - 3 and let the width of the table be x.
Four tables with identical dimensions are placed together.
So we can say that width of the new table formed by placing the four tables side to side will be the same as the width of one table, that is x.
And the two sides of the new table which will represent the width will be the width of one table at one end and the width of the table at the other end, that is x + x.length
Now as we saw before there are are two widths which are part of the perimeter there are also two lengths which are part of the perimeter.
The perimeter of a table is given by (2 × length) + (2 × width).
Now one length of the new table will be equal to (4 × length of one table) = 4 × (2.5 x - 3) = 10x -12
Therefore perimeter of the new table is given from the formula of the perimeter = Length + width + Length + width
= 10x - 12 + x + 10x -12 + x
250 surveyed. 15 do not like pizza. 66% like pizza and burritos. 30% do not like burritos. Fill in the two way frequency table to show the results of the survey.
Answer:
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&165&10&175\\\text{Do not like burritos}&70&5&75\\ \text{Total}&235&15&250\end{array}[/tex]
Step-by-step explanation:
250 people are surveyed. 15 of them do not like pizza, then
250 - 15 = 235 like pizza.
30% do not like burritos. 30% of 250 is
[tex]250\cdot 0.3=75[/tex] people which do not like burritos and 250 - 75 = 175 people like burritos.
Then the incomplete two way frequency table is
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&&&175\\\text{Do not like burritos}&&&75\\ \text{Total}&235&15&250\end{array}[/tex]
66% like pizza and burritos. Then
[tex]250\cdot 0.66=165[/tex] people like pizza and burritos.
Hence,
[tex]235-165=70[/tex] people like pizza and do not like burritos
[tex]175-165=10[/tex] people like burritos and do not like pizza
[tex]250-165-70-10=5[/tex] people do not like pizza and do not like burritos
Hence the complete two way frequency table is
[tex]\begin{array}{cccc}&\text{Like pizza}&\text{Do not like pizza}&\text{Total}\\ \\\text{Like burritos}&165&10&175\\\text{Do not like burritos}&70&5&75\\ \text{Total}&235&15&250\end{array}[/tex]
Two weeks in a row, the golf course hosts a group of golfers. The second week had 10 more golfers than the first week. Use the dot plots to choose the true statement.
A. The range for Week 1 equals the range for Week 2.
B. The range for Week 1 is greater than the range for Week 2.
C. The median for Week 1 is less than the median for Week 2.
D. The mean for Week 1 is greater than the mean for Week 2.
Answer:
The true statement is: A. The range for Week 1 equals the range for Week 2.
Step-by-step explanation:
Let's recall that the range of a data set is the difference between the largest number and the smallest number.
As we can confirm in the plot for week 1, the range is:
Range for week 1 = Largest number - smallest number
Range for week 1 = 89 - 62 = 27
In the same way, we can confirm in the plot for week 2 that the range is:
Range for week 2 = Largest number - smallest number
Range for week 2 = 89 - 62 = 27
Ranges for week 1 and 2 are equal, thus,
The true statement is: A. The range for Week 1 equals the range for Week 2.
The physician tells a woman who usually drinks 5 cups of coffee daily to cut down on her coffee consumption by 75%. If this woman is compliant with the physician's instruction, how many ounces of coffee is she allowed daily?
Answer:
Step-by-step explanation:
5 cups per day.....1 cup = 8oz.....so 5 cups = (5 * 8) = 40 oz
cut down by 75%....means ur only drinking 25%
25% of 40 oz =
0.25(40) = 10 oz per day <===
A home owner is building a square patio and will cover the patio with square tiles. Each tile has an area of 256 square inches and costs $3.45 each. The home owner has \$500 to spend on tiles. Calculate how many tiles the home owner can buy. Find the side length
(in feet) of the largest patio the home owner can build.
Answer:
The homeowner can buy 144 tiles maximum.
Side length = 16 feet.
Step-by-step explanation:
The cost of each tile is $3.45.
So, at $500, the homeowner can buy [tex]\frac{500}{3.45} = 144.92[/tex] ≈ 144 number of tiles. {As the number of tiles can not be a fraction.}
Since each tile is a square with area 256 square inches, so the homeowner can arrange the tiles in 12 by 12 arrangements.
Each tile has side length = √256 = 16 inches.
So, the side length of the largest patio is (16 × 12) inches = 16 feet. (Since, 1 foot = 12 inches). (Answer)
A paper hat is folded into the shape of a kite, as shown.
A kite is shown. The left and right angles are right angles. The sides above the right angles are (3 x + 5) inches and (5 x + 1) inches. The sides below the right angle are (2 x + 1) inches and 5 inches.
What total length of ribbon is needed to line the two long sides of the hat?
Answer:
D is correct
Step-by-step explanation:
The total length of ribbon needed to line the two long sides of the hat is 22 inches.
Given that, the sides above the right angles are (3x + 5) inches and (5x + 1) inches. The sides below the right angle are (2x + 1) inches and 5 inches.
What are the properties of kites?A kite is a quadrilateral that has 2 pairs of equal adjacent sides. The angles where the adjacent pairs of sides meet are equal.
Now, (3x + 5)=(5x + 1)
⇒x=2
2x+1=5
⇒x=2
Thus, (3x + 5)=11 inches
Now, 11+11=22 inches
Therefore, the required answer is 22 inches.
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