The earnings and deductions, are given as follows:
Gross pay: $720.Net pay: $498.07.Federal income tax: $82.45.Social security tax: $44.64.Medicare tax: $10.44.State tax: $21.60.Local tax: $10.80.Medical due: $35.Union due: $17.What are her earnings and deductions?First we find her gross earning, which is given by the hourly wage multiplied by the number of hours worked, hence:
Gross pay = 40 x 18 = $720.
Hence her yearly income is given by:
Yearly income = 52 x 720 = $37440.
Meaning that her federal tax rate is of $19.76 a week plus 12% of the excess over $197.60, then:
Federal tax = 19.76 + 0.12 x (720 - 197.60) = $82.45.
The social security tax rate is of 6.2% of her gross weekly earnings, hence it is given by:
Social Security = 0.062 x 720 = $44.64.
The medicare tax rate is of 1.45% for Lynn(employee), hence:
Medicare = 0.0145 x 720 = $10.44.
The state tax is 3% of her gross earnings, hence:
State tax = 0.03 x 720 = $21.60.
The local tax is 1.5% of her gross earnings, hence:
State tax = 0.015 x 720 = $10.80.
The medical and union dues are stated in the problem, hence the sum of all discounts is given by:
82.45 + 44.64 + 10.44 + 21.60 + 10.80 + 35 + 17 = $221.93.
The net pay is the gross pay subtracted by the discounts, hence:
Net pay = 720 - 221.93 = $498.07.
Missing informationThe value of an allowance is not stated, hence they are not considered for the calculations.
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Can someone please help with my homework?
NASA launches a rocket at t=0 seconds. Its height, in meters above sea level, as a function of time is given by h(t) = −4.9t^2 + 241t + 402 Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
1. The rocket splashes down after________seconds.
2. How high above sea level does the rocket get at its peak? The rocket peaks at_________ meters above sea level.
Considering the given quadratic function, it is found that:
1. The rocket splashes down after 50.8 seconds.
2. The rocket peaks at 3365.3 meters above sea level.
When does the rocket splashes down?The height of the rocket after t seconds is given according to the following rule:
h(t) = -4.9t² + 241t + 402.
Which is a quadratic equation with coefficients given by:
a = -4.9, b = 241, c = 402.
It splashes down when it hits the ground, that is, when h(t) = 0, hence:
-4.9t² + 241t + 402 = 0.
Then:
[tex]\Delta = 241^2 - 4(-4.9)(402) = 65960.2[/tex][tex]x_1 = \frac{-241 + \sqrt{65960.2}}{-9.8} = -1.62[/tex][tex]x_2 = \frac{-241 - \sqrt{65960.2}}{-9.8} = 50.8[/tex]Time is a positive measure, hence it splashes down after 50.8 seconds.
What is the maximum height?The height of the rocket is a concave down quadratic equation, hence the maximum height is the y-coordinate of the vertex, given as follows:
[tex]h_{MAX} = -\frac{\Delta}{4a}[/tex]
Both these parameters have been found in the previous item, hence:
[tex]h_{MAX} = -\frac{65960.2}{4(-4.9)} = 3365.3[/tex]
3365.3 meters.
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Please help I don’t get what did teacher even wants bro
Base of the rectangle is 9 inches.
What is Area of Rectangle ?
You may determine the area of any form by counting how many unit squares fit inside of it.
In this context, a square with a side of 1 unit is referred to as a unit square.
In other words, the area of the rectangle is equal to the number of unit squares inside its perimeter.
Area = base * height
Given,
Area = 108 in²
height = 12 inches
put these values in given formula,
108 = 12 * base
base = 108 / 12
= 9 inches
Therefore, Base of the rectangle is 9 inches.
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I need help with putting 64/128 fully simplified and to a decimal
Given:
[tex]\frac{64}{128}[/tex]To convert into decimal:
Explanation:
Let us write it as the factored form for each term.
[tex]undefined[/tex][tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{64}{128}}\\\\\mathsf{= \dfrac{64\div8}{128\div8}}\\\\\mathsf{= \dfrac{8}{16}}\\\\\mathsf{= \dfrac{8\div4}{16\div4}}\\\\\mathsf{= \dfrac{2}{4}}\\\\\mathsf{= \dfrac{2\div2}{4\div2}}\\\\\mathsf{= \dfrac{1}{2}}\\\\\\\huge\text{Therefore, the answer simplified is:}\\\huge\boxed{\mathsf{\dfrac{1}{2}}}\huge\checkmark[/tex]
[tex]\mathsf{\dfrac{1}{2}\rightarrow 1\div2 \rightarrow 0.5}\\\\\\\huge\text{Therefore your decimal form of }}\huge\boxed{\boxed{\rm{\dfrac{1}{2}}}}\huge\text{ is:}\\\\\huge\boxed{\mathsf{0.5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Find the common ratio and write out the first four terms of the geometric sequence (1.06)n−1 Common ratio is a1= a2= a3= a4=
Solution
Step 1
Write the nth term ex[pression and the common ratio formula.
[tex]\begin{gathered} T_n\text{ = \lparen1.06\rparen}^{n-1} \\ Common\text{ ratio = }\frac{2^{nd}term}{1^{st}term} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} T_1\text{ = \lparen1.06\rparen}^{1-1}\text{ = 1} \\ T_2\text{ = \lparen1.06\rparen}^{2-1}\text{ = 1.06} \\ T_3\text{ = \lparen1.06\rparen}^{3-1}\text{ = \lparen1.06\rparen}^2\text{ = 1.1236} \\ T_4\text{ = \lparen1.06\rparen}^{4-1}=\text{ \lparen1.06\rparen}^3\text{ = 1.191016} \end{gathered}[/tex]Step 3
[tex]Common\text{ ratio r = }\frac{1.06}{1}\text{ = 1.06}[/tex]Final answer
Determine whether each sample method is unbiased or biased. If the method is unbiased, use it to make a prediction. If the method is biased, explain why. 1. A cable company representative randomly calls 250 households to determine how many customers subscribe to the movie channels. Of the 250 households contacted, 22% do not subscribe to movie channels. If there are 5,240 customers, how many do not subscribe to movie channels.
The representative took a sample to estimate the proportion of customers that do not subscribe to movie channels.
He took a sample from the customer base and the sample proportion he gets is 22% (p = 0.22). This sample proportion is an unbiased estimator of the populations proportion, so we can use it to calculate how many customers do not subscribe to movie channels:
[tex]n=N\cdot p=5240\cdot0.22\approx1153[/tex]Answer: we can estimate that there are 1153 customers that do not subscribe to movie channels.
solve for x using the figure below. (view image)
The value of x in the figure is 3
How to find x from the figure?
Let us re -write the given values as fractions
[tex]\frac{5}{8} =\frac{x+3.25}{10} \\\\[/tex]
By applying cross multiplication method,
5(10) = 8(x+3.25)
50 =8x +26
8x = 50-26
8x = 24
x = 3
Similarly re- writing next set of vales as fractions,
[tex]\frac{2}{5} =\frac{2.5}{x+3.25} \\\\[/tex]
By applying cross multiplication method,
2(x+3.25) = 5(2.5)
2x+6.5 = 12.5
2x = 12.5 - 6.5
2x = 6
x = 3
What is cross multiplication of fractions?
To cross multiply two fractions, multiply the denominator of one by the numerator of the other, and then compare the results. The larger fraction is the one having the larger value.Virtually all fractions that are cross multiplied will have various denominators. It is a quick way to compare fractions by reducing them to a common denominator.To learn more about cross multiplying fractions, refer:
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Really need help solving thisIt’s trigonometry It’s from my ACT prep guide
We have the following configuration for this problem:
where y is the distance, in feet, Corey stepped back.
Then, we have:
[tex]\begin{gathered} \tan 68\degree=\frac{80}{x} \\ \\ x=\frac{80}{\tan 68\degree} \end{gathered}[/tex]And:
[tex]\begin{gathered} \tan 41\degree=\frac{80}{x+y} \\ \\ x+y=\frac{80}{\tan 41\degree} \\ \\ y=\frac{80}{\tan 41\degree}-x \end{gathered}[/tex]Now, using the first into the second equation, we obtain:
[tex]\begin{gathered} y=\frac{80}{\tan41\degree}-\frac{80}{\tan 68\degree} \\ \\ y=59.71 \end{gathered}[/tex]Therefore, Corey stepped back approximately 59.71 feet.
Statically question
Answer: We have to select the statistical questions out of the given options,
the statistical questions are any questions that involve the use of data, therefore following options are the statistical questions:
[tex]\begin{gathered} \text{ Following Options:} \\ \\ (1)\text{ \lparen2\rparen and }(4) \end{gathered}[/tex]Therefore (1) (2) and (4) use the data, they are the statistical questions.
|4x - 5| = 8A. x= 13/4 or x= -3/4B. x= 3/4 or x= -13/4C. x= 13/4 onlyD. no solutionE. infinitely many solutions
We will solve this problem thus:
[tex]\begin{gathered} \lvert4x-5\rvert=8 \\ \text{means} \\ 4x-5=+8\text{ or 4x-5= -8} \end{gathered}[/tex]Solving further we will have:
[tex]\begin{gathered} 4x=8+5\text{ or 4x=-8}+5 \\ 4x=13\text{ or 4x = -3} \\ x=\frac{13}{4}\text{ or x=}\frac{-3}{4} \\ \text{The correct answer is option A} \end{gathered}[/tex]Select all value of c for which f(x) = g(x)Please look gráficos.
Statement Problem: Select all values of x for which;
[tex]f(x)=g(x)[/tex]Solution:
The value of x for which the two functions are equal is the x-coordinate of their insections;
The coordinates of the intersections are;
[tex](0,-3)\text{ and }(4,5)[/tex]Thus, the values of x that is correct are;
[tex]x=0,x=4[/tex]Hence, CORRECT OPTIONS are;
[tex]A\text{ and D}[/tex]26. If 25% of a number p is 19, what is 15% of p?
Given:
25% of p is 19.
[tex]\begin{gathered} \frac{25}{100}\times p=19 \\ p=19\times\frac{100}{25} \\ p=19\times4 \\ p=76 \end{gathered}[/tex]The expression to calculate the 15% of p is,
[tex]\frac{15}{100}\times p[/tex]Substitute value of p=76 in the above expression.
[tex]\begin{gathered} \frac{15}{100}\times76=\frac{3}{20}\times76 \\ =\frac{228}{20} \\ =11.4 \end{gathered}[/tex]Thus, 15% of p is 11.4.
the sum of -5 and six times a number
Six times menas multiply by six:
a number = x
The sum of -5 and six times a number
-5 + 6x
pls help 9th grade geometry
Answer:
< 6 = 58°
< 8 = 58°
< 5 = 122°
<7 = 122°
Step-by-step explanation:
<6 = <8 because corresponding angles are equal
5y + 13 = 7y -5 Subtract 5 y from both sides
13 = 2y -5 Add 5 to both sides
18 = 2y
9 = y
Now that we know that y = 9, we plug it back into either equation
5y + 13
5(9) + 13
45 + 13
58
<5 is supplemental to <6 so 180 - 58 = 122
<8 is supplemental to < 7 so it is 122 also
A tree trunk may be considered a circular cylinder.
Suppose the diameter of the trunk increases 1 inch per
year and the height of the trunk increases 6 inches per
year. How fast is the volume of wood in the trunk
increasing when it is 100 inches high and 5 inches in
diameter?
The volume of the tree trunk increases 52.64% in one year.
Given,
The height of a tree trunk = 100 inches
The diameter of a tree trunk = 5 inches
Diameter increases 1 inch per year
Height increases 6 inches per year
We have to find the increase in its volume.
Consider the trunk as a circular cylinder.
Volume of circular cylinder = πr²h
Radius, r = 5/2
Height, h = 100
Initial Volume = πr²h
Volume = π × (5/2)² × 100 = π × 6.25 × 100 = 1963.50 cubic inches
After one year
Diameter = 6
Height = 106
Increased Volume = πr²h
Volume = π × (6/2)² × 100 = π × 9 × 106 = 2997.08 cubic inches
The rate of increase in volume = (Increased volume × 100) ÷ Initial volume
= (2997.08 × 100) ÷ 1963.50 = 152.64
That is,
The volume of the tree trunk increases 52.64% in one year.
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Here are the recorded temperatures at the different times on a winter evening
ANSWER
Tyler was right
EXPLANATION
To answer the question, we have to find the rate at which the temperature dropped between 4pm - 6pm and 6pm - 10pm
By 4pm, the temperature was 25°F and by 6pm, the temperature was 17°F.
The temperature difference is:
T = 17 - 25 = -8°F
There are 2 hours between 4 and 6 pm.
Now, we divide by the number of hours that elapsed:
[tex]\text{Rate = }\frac{-8}{2\text{ hours}}\text{ =}-4\degree F\text{ / hr}[/tex]By 6 pm the temperature was 17°F and by 10pm, the temperature was 8°F.
The temperature difference is:
T = 8 - 17 = -9°F
There are 4 hours between 6 and 10 pm.
Now, divide by the number of hours that elapsed:
[tex]\text{Rate = }\frac{-9}{4}\text{ = }-2.25\degree F\text{ / hr}[/tex]As we can see, the rate at which the temperature dropped between 4pm and 6 pm is more (since it became colder at a faster rate during that period)
Therefore, Tyler was right.
Elon has removed two dead batteries from a flashlight and inadvertently mingled them with the two good batteries he intended as replacements. The four batteries look identical. Elon now randomly selects two of the four batteries. What is the probability he selects the two good batteries? (Hint: sampling is without replacement here)
The probability of the required event is [tex]\frac{1}{2}[/tex]
Number of batteries removed by Elon = 2
And then he mixed these batteries with the other two batteries
Thus total number of batteries = 4
These 4 batteries as given is identical
Now since it is given in the question that there aren't any replacements thus it means that we don't have to apply the Baye's theorem. So we can simply write it as it is mentioned below.
Thus the probability of taking out two batteries which are good without any replacement :
Probability = [tex]\frac{number of outcomes }{total number of favorable outcomes}[/tex]
Given number of outcomes = 2
Total number of favorable outcomes = 4
Thus the probability of the given event is = [tex]\frac{2}{4}[/tex]
Thus P( E ) = [tex]\frac{1}{2}[/tex]
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In 4 1/2 hours Greg reads 9 3/4 chapters what is the unit rate in chapters per hour
2 1/6 is the answer
9 3/4 divided by 4 1/2 = 2 1/6
Abdul drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 8 hours. When Abdul drove home, there was no traffic and the trip only took 6 hours. If his average rate was 16 miles per hour faster on the trip home, how far away does Abdul live from the mountains? Please show work because it doesn’t make sense any other way!
Find the missing angle:
?=
134⁰
Answer: 46
Step-by-step explanation:
180 - 134 = 46
A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. The figure shows both designs.Which set of additional details are the minimum required to ensure the new design will have the same volume as the original design?A. The heights of both designs must be the same, and at least one cross-section taken at the same height on both designs must have the same area.B. The heights of both designs must be the same, the base areas of both designs must be the same, and each cross-section taken at the same height on both designs must have the same area.C. The heights of both designs must be the same, and the base areas of both designs must be the same.D. The heights of both designs must be proportional, the base areas of both designs must be proportional, and each cross-section taken at the same height on both designs must have the same radius.
1) In this problem, we need to keep in mind the formula for the volume of one cylinder:
[tex]V=\pi r²h[/tex]Or in other words, the base area (area of a circle) times the height.
2) Since the point here is not to lose capacity (volume) the new design must keep its base areas as well as their height, so examining the answers we can tell that the answer is:
[tex]C[/tex]
These are the minimum requirements
Help, please, it's urgent
∠10 and ∠16 are Alternate exterior angles, ∠4 and ∠12 are Consecutive exterior angles, ∠12 and ∠13 are Consecutive Interior angles and ∠3 and ∠9 are Alternate Interior angles.
1. If two lines which are in the same plane are intersected by another line at two different lines, eight angles are formed, and that another line is called the transversal.
In the provided figure,
In the angles,
∠10 and ∠16, q is the transversal and these are Alternate exterior angles.
∠4 and ∠12, n is the transversal and these are Consecutive exterior angles.
∠12 and ∠13, q is the transversal and these are Consecutive Interior angles.
∠3 and ∠9, n is the transversal and these are Alternate Interior angles.
2. Referring tot the cube ABCDHGFE,
a. All planes that are parallel to the plane DEH are CBF and FGC.
b. All segments that are parallel to AB are EF, HG and DC.
c. All segments that intersect GH are EH, HG, FG and CG.
d. All segments that are skew to CD are AB, EF and HG.
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[tex] \frac{5}{3}s = \frac{15}{3} + \frac{3}{2}s - \frac{1}{4} [/tex]i dont under stand it and other questions like it because I'm sorta slower than the rest of my class. We're doing Types of Solutions of Linear Equations.
The question we have to solve is:
[tex]\frac{5}{3}s=\frac{15}{3}+\frac{3}{2}s-\frac{1}{4}[/tex]To solve this equation, we take all the "s"'s to one side and numbers to the other and simplify:
[tex]\begin{gathered} \frac{5}{3}s=\frac{15}{3}+\frac{3}{2}s-\frac{1}{4} \\ \frac{5}{3}s-\frac{3}{2}s=\frac{15}{3}-\frac{1}{4} \\ \frac{5(2)-3(3)}{6}s=\frac{15(4)-1(3)}{12} \\ \frac{1}{6}s=\frac{57}{12} \\ s=\frac{\frac{57}{12}}{\frac{1}{6}} \end{gathered}[/tex]When we want to divide by a fraction, we mulitply by its reciprocal. So,
[tex]\begin{gathered} s=\frac{\frac{57}{12}}{\frac{1}{6}} \\ s=\frac{57}{12}\times\frac{6}{1} \\ s=\frac{57}{2} \end{gathered}[/tex]5. Among 100 students, 60 participated on playing games and 50 participated in music. How many students participated in both the activities? Also find how many students participated in music only?
Find X.
Circumscribed Angles
Answer:
x=20
Step-by-step explanation:
To find x you must first set up an equation. (3x+90+90+120=360) the reason why i did that is because the red boxes indicate that they are 90° angles. They add up to 360 is because the quadrilaterals add up to 360. after solving for x, you should get x = 20.
If a running back runs 28 yards in the first quarter, how many yards can you expect him to gain
throughout the game?
Answer:
112 yards
Step-by-step explanation:
quarter is 1/4 right¿
28 × 4 = 112
Find the circumference and area of the circle. Express answers in terms of and then round to the nearest tenth. Part 1. Find the circumference in terms of . C = _ cmPart 2. Find the circumference rounded to the nearest tenth.C = _ cmPart 3. Find the area in terms of A = _ cm2Part 4. Find the area rounded to the nearest tenth. A = _ cm3
Answer:
1. C = 8π cm
2. C = 25.1 cm
3. A = 16π cm²
4. A = 50.3 cm²
Explanation:
Part 1.
The circumference of a circle can be calculated as
[tex]C=2\pi r[/tex]Where r is the radius. So, replacing r = 4 cm, we get:
C = 2π(4 cm)
C = 8π cm
Part 2.
To round the circumference to the nearest tenth, we need to replace π = 3.14, so
C = 8(3.14) cm
C = 25.1 cm
Part 3.
The area of a circle can be calculated as
A = πr²
Replacing r = 4cm, we get:
A = π(4 cm)²
A = 16π cm²
Part 4.
To round to the nearest tenth, we need to replace π = 3.14, so
A = 16(3.14) cm²
A = 50.3 cm²
Therefore, the answers are
1. C = 8π cm
2. C = 25.1 cm
3. A = 16π cm²
4. A = 50.3 cm²
Match the order of the step to the steps to solve this equation2x/3 -6 =2 Column A 1. ___ What is the first step? 2. ___ What is the second step? 3. ___ What is the third step? 4. ___ What is the value of X? Column B a. Multiply both sides by 3 b. Divide both sides by 2 c. X=12 d. Add 6 to both sides Please help me with this.
The first step is to collect like terms:
This is done by adding 6 to both sides of the equation
1) add 6 to both sides (option D)
2x/3 -6+6 = 2+6
2x/3 = 8
The second step is to cross multiply OR
multiply both sides of the equation by 3
2x = 8(3)
2x = 24
2) Multiply both sides by 3 (option A)
The third step is to divide both sides by 2
2x/2 = 24/2
3) Divide both sides by 2 (option B)
x = 24/2
4) x = 12 (option C)
What is the volume of this triangular Pyramid photo attached
To find the volume of a triangular pyramid, the formula is:
[tex]V=\frac{1}{3}(Area\text{ }of\text{ }thebase)(height)[/tex]So we start by finding the area of the base, which is in the shape of a right triangle in this case.
The area of a right triangle is equal to 1/2 x base x height.
[tex]\begin{gathered} A=\frac{1}{2}bh \\ \\ A=\frac{1}{2}(5)(6) \\ \\ A=15\text{ square feet} \end{gathered}[/tex]We use this area to find the volume.
[tex]\begin{gathered} V=\frac{1}{3}Ah \\ \\ V=\frac{1}{3}(15)(6) \\ \\ V=30\text{ cubic feet} \end{gathered}[/tex]The volume of the triangular pyramid is 30 cubic feet.
Write the numbers in increasing order with a comma separating eachnumber: 1.99, -3.45, 2.01, -3.42, 0.99
To write the numbers in increasing order, we start from the most negative to the most positive:
[tex]-3.45,-3.42,0.99,1.99,2.01.[/tex]Answer
-3.45, -3.42, 0.99, 1.99, 2.01
(d) Find the domain of function R. Choose the correct domain below.
Answer:
d
Step-by-step explanation:
The number of years must be non-negative. This eliminates all of the options except for d.