The simplification of the given expression is equal to 192524.3.
The expression is equal to,
√2 × √6 × √110 × √120 × √450 × √520
Simplify this expression by first simplifying the square roots under the radical signs,
√2 = √(2 × 1)
= √2 × √1
√6 = √(2 × 3)
= √2 × √3
√110 = √(2 × 5 × 11)
= √2 × √5 × √11
√120 = √(2 × 2 × 2 × 3 × 5)
= 2√2 × √3 × √5
√450 = √(2 × 3² × 5²)
= √2 × (3 × 5)²
= 15√2
√520 = √(2³ × 5 × 13)
= 2√2 ×√5 × √13
Substituting these simplifications back into the original expression, we have,
√2 × √6 × √110 × √120 × √450 × √520
= √2 × √2 × √3 × √2 × √5 × √11 × 2√2 × √3 × √5 × 15√2 × 2√2 ×√5 × √13
= 2⁵ × 3² × 5²√(5 × 11 × 13)
= 7200√715
= 192524.3
Therefore, the simplification value of √2 × √6 × √110 × √120 × √450 × √520 is equal to 192524.3.
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The above question is incomplete, the complete question is:
Simplify
√2 × √6 × √110 × √120 × √450 × √520
A movie theater charges 11$ for adults and 9$ for seniors. ( children pay the adult price) on a particular day when 294 people paid an admission, the total receipts were 3114. How many paid were adults? How many paid were seniors?
The number of adult that paid is 234 and the number of seniors that pad is 60.
How to find the number of seniors and adult?A movie theatre charges 11$ for adults and 9$ for seniors. On a particular day when 294 people paid an admission, the total receipts were 3114.
Therefore, let's find how many paid for adult and for seniors.
Let
x = number that paid for adult
y = number that paid for senior
Hence, the situation forms the following equation.
x + y = 294
11x + 9y = 3114
multiply equation(i) by 11
11x + 11y = 3234
11x + 9y = 3114
subtract the equation
2y = 120
y = 120 / 2
y = 60
Let's find x
x = 294 - 60
x = 234
Therefore,
number of adults that paid= 234
number of seniors that paid = 60
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PLSSS HELP ME SOLVE THIS DUE TOMORROW!!!
Each pair of polygons is similar. Find the value of x.
Answer:
7
Step-by-step explanation:
All of the numbers are going up by 4 so what times 4 gives 28
thats 7
Given:
p: Two linear functions have different coefficients of x.
q: The graphs of two functions intersect at exactly one point.
Which statement is logically equivalent to q-p?
If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one
point.
If two linear functions have the same coefficients of x, then the graphs of the two linear functions do not intersect
at exactly one point.
D
If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same
coefficients of x.
If the graphs of two functions intersect at exactly one point, then the two linear functions have the same
coefficients of x.
Complete the equation describing how x
and y are related.
X
-3
-2
-1
0
1
2
Y
24
16
8
0
-8
-16
y = [? ]x
Enter the answer that
belongs in [?].
A linear equation that describe how x and y are related include the following: A. y = -8x.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 24/-3 = 16/-2 = 8/-1 = -8/1 = -16/2
Constant of proportionality, k = -8.
Therefore, the required linear equation is given by;
y = kx
y = -8x
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A fair spinner has eight sides. They are labelled 1, 1, 3, 3, 4, 5, 5, 5. The diagram below shows a probability scale. 0 Which arrow shows the probability of a) scoring a 4? 5 5 5 1 4 3 1 3
A group of consumers were asked whether they prefermed Brand A or Brand B
Being male and preferring Brand A are independent, as:
P(male|Brand A) = P(male).
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
From the table, we are already given the relative frequencies, hence the probability of being male is given as follows:
0.5 + 0.15 = 0.65.
The conditional probability of being male, given that the person prefers brand A, is given as follows:
P(male|Brand A) = P(male and Brand A)/P(Brand A) = 0.5/0.8 = 0.625.
As the probabilities are equal, the events are independent.
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PLEASE HELP ASAP!!!
The length of ribbons found at a seamstress are listed.
2, 10, 10, 12, 12, 20
What is the appropriate measure of variability for the data shown, and what is its value?
The mean is the best measure of variability and equals 11.
The median is the best measure of variability and equals 11.5.
The range is the best measure of variability and equals 18.
The IQR is the best measure of variability and equals 2.
The appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.
The given data set is:
2, 10, 10, 12, 12, 20
To determine the appropriate measure of variability, we need to consider the spread or dispersion of the data. In this case, we can see that the range,
20 - 2 = 18.
A better measure of variability for this data set is the interquartile range (IQR), which is the range of the middle 50% of the data. To find the IQR, we first need to find the median of the data:
2, 10, 10, 12, 12, 20
The median is the middle value when the data set is arranged in order, which is 11. We can then divide the data set into two halves:
2, 10, 10 and 12, 12, 20
The lower half has a median of 10, and the upper half has a median of 12. The IQR is the difference between these medians:
IQR = 12 - 10 = 2
Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.
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Find the value of x
The value of x for the intersecting chords is derived to be 14 which makes option C correct.
What is the properties of intersecting chordsThe property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
x × 32 = 16 × 28
32x = 448
32x/32 = 144/32 {divide through by 32}
x = 14
Therefore, the value of x for the intersecting chords is derived to be 14
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A cake recipe calls for the following dry ingredients: 3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa. To the nearest cup, how much dry ingredients will be used?
The amount of dry ingredients used in the cake recipe is approximately 7 cups.
To find the total amount of dry ingredients used in the cake recipe, we need to add up the amounts of flour, sugar, and cocoa.
3 ½ cups of flour is equal to 3 cups plus 0.5 cups, or 3 cups and 8 ounces.
2 ⅔ cups of sugar is equal to 2 cups plus 0.67 cups, or 2 cups and 10.72 ounces.
1 ¾ cups of cocoa is equal to 1 cup plus 0.75 cups, or 1 cup and 12 ounces.
Adding these amounts together, we get:
3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces
To the nearest cup, this is equal to 7 cups.
Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.
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What is the sum of the rational expressions below?
2x-1
7x+x=2
X-2
OA. 9x²-5x+2
7x²-2
OB. 9x²-5x+2
7x²-14x
O C.
O D.
2x²-5x+2
7x²-14x
3x-1
8x-2
Answer:
C
Step-by-step explanation:
To find the sum of the rational expressions, we need to add the two expressions and simplify if possible:
(2x-1)/(7x+x+2) + (x-2)/(8x-2)
Simplifying the denominators, we get:
(2x-1)/(8x+2) + (x-2)/(8x-2)
Now, we need to find the LCD, which is (8x+2)(8x-2) = 64x²-4:
[(2x-1)(8x-2) + (x-2)(8x+2)] / (64x²-4)
Simplifying the numerator, we get:
[16x²-4x-16x+4+8x²-2x+16x-4] / (64x²-4)
Combining like terms, we get:
(24x²-2) / (64x²-4)
Factoring out a 2 from the numerator and denominator, we get:
2(12x²-1) / 2(32x²-2)
Simplifying further, we get:
(12x²-1) / (16x²-1)
Therefore, the sum of the rational expressions is:
12x²-1
-----------
16x²-1
So, the answer is option C.
PLEASE HELP
Ronald is painting wooden cylindrical columns before putting them in his yard. They are each 7 feet tall and have a diameter of 2 feet. There are 8 columns in all. How much paint will Ronald need to paint all the surfaces of the 8 Columns? Leave your answer in terms of π with proper units
Ronald will need 128π square feet to paint all the surfaces of the 8 Columns.
How calculate how much paint Ronald will need to paint all the surfaces of the 8 Columns?
The formula for the total surface area of a cylinder is given by:
A = 2πr(r + h)
Where r is the radius and h is the height
In this case, each wooden cylindrical columns is 7 feet tall and have a diameter of 2 feet. Thus:
r = 2/2 = 1 feet and h = 7 feet
Thus, the total surface area of each wooden cylindrical columns will be:
A = 2π * 1 * (1 + 7)
A = 2π * 1 * 8
A = 16π square feet
Then the total surface areas of all the 8 Columns will be:
A = 8 * 16π
A = 128π square feet
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A direct variation includes the points (2,18) and (n,9). Find n?
The value of the n is 1
In a direct variation, the relationship between two variables is of the form y = kx, where k is a constant of proportionality.
To find the constant of proportionality k in this problem, we can use the fact that the given points satisfy the equation for direct variation.
(2,18) is one of the given points, so we can substitute these values into the equation y = kx and solve for k:
18 = k(2)
k = 18/2
k = 9
Now that we have found the value of k, we can use it to find n when y = 9:
9 = 9n
n = 1
Therefore, the value of n is 1.
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The work unit which you supervise is responsible for processing fifteen reports per
month.
If your unit has four clerks and the best worker completes 40% of the reports himself,
how many reports would each of the other clerks have to complete if they all do an
equal number?
Each of the other three clerks have to complete 3 reports each.
The top employee finishes 40% of the reports, or: 0.40 x 15 = 6 reports.
Therefore, the other three clerks must finish the remaining 60% of the reports.
Total reports to be completed by the other clerks = 0.60 x 15 = 9 reports
We may distribute the remaining reports evenly among the other clerks since they all have an equal number of reports to complete:
Number of reports each of the other clerks have to complete = 9 reports ÷ 3 clerks = 3 reports
Therefore, each of the other three clerks have to complete 3 reports each.
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1. How many hours and minutes elapsed from 12:00 noon to 4:59 p.m.?
2. How many hours and minutes elapsed from 1:23 a.m. to 7:35 a.m.?
3. How many hours and minutes elapsed from 11:28 p.m. to 5:30 a.m.?
1) Total time elapsed = 4 hours 59 minutes.
2) Total time elapsed = 6 hours 12 minutes
3) Total time elapsed = 6 hours 2 minutes
1) Time difference from 12:00 noon to 4:00 p.m = 4 hours
Time difference from 4:00 p.m to 4:59 p.m. = 59 minutes
So, the total time elapsed = 4 hours 59 minutes.
2) The time difference from 1:23 a.m. to 2:00 a.m. = 37 minutes
The time difference from 2:00 a.m to 7:00 a.m. = 5 hours
The time difference from 7:00 a.m. to 7:35 a.m. = 35 minutes
Here, the minutes elasped = 37 + 35
= 72 minutes
= 1 hour 12 minutes
So, So, the total hours elapsed = 5 + 1
= 6 hours
Thus, the total time elapsed = 6 hours 12 minutes
3) Time difference from 11:28 p.m. to 12:00 midnight = 32 minutes
Time difference from 12:00 midnight to 5:30 a.m. = 5 hours 30 minutes
Here, the minutes elasped = 32 + 30
= 62 minutes
= 1 hour 2 minutes
So, the total time elapsed = 6 hours 2 minutes
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**I ONLY HAVE 6HOURS LEFT***
Which transformations can be used to carry ABCD onto itself? The point of rotation is (3, 2). Check all that apply.
A. Reflection across the line x = 3
B. Rotation of 180
C. Translation four units to the right
D. Dilation by a factor of 2
Answer:
it's b to to the angles rotation that is giving 180 each side of the square is 90 degrees now you add them up
A.
B.
4
x
+1
x+4
=−3
=−12
1) How can we get Equation
�
BB from Equation
�
AA?
4
x
+1
x+4
=−3
=−12
1) How can we get Equation
�
BB from Equation
�
AA?
The correct answers are given below:
D. Multiply/divide both sides by the same non-zero constant
A. Yes
How to solveTo achieve equity between Equation A and Equation B, one must:
A: 4x + 1(x+4) = -3B: -12x - 48 = -12Via combining 1 with the parenthesis of Equation A and conjoining common terms, one begins by distributing the 1 and fusing both sides together to form 5x + 4 = -3.
Afterward, multiplying both sides of the equation by -12 (the same non-zero constant), yields -60x - 48 = 36.
Ultimately, adding 72 to both equities presents the answer to furthering equations, -12x - 48 = -12.
Thus, the resolution rest in choice D- multiply/divide both sides by the same non-zero constant.
By producing Equation B from Equation A through analogous methods on either side of the equation, it is confirmed that the two compilations are equivalent and manifest exact solutions. Therefore, the proper selection for this query is Yes- Choice A.
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A. B. 4 x +1 x+4 =−3 =−12 1) How can we get Equation BBB from Equation AAA? Choose 1 answer: Choose 1 answer: (Choice A) A Rewrite one side (or both) using the distributive property (Choice B) B Rewrite one side (or both) by combining like terms (Choice C) C Multiply/divide only one side by a non-zero constant (Choice D) D Multiply/divide both sides by the same non-zero constant 2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution? Choose 1 answer: Choose 1 answer: (Choice A) A Yes (Choice B) B No
Julio has a number cube that has 6 sides and each side is labeled 1 through 6. He is interested in whether or not the
number cube is a fair cube. Julio performs a simulation which generates 40 trials of 8 rolls of the number cube. He then
graphs the data on a dot plot.
Note: A fair number cube has equally likely outcomes.
Which statement explains how the number cube is fair?
O The data should be skewed left about a central value.
O The data should be skewed right about a central value.
O The data should be symmetric about a central value.
O The data should be randomly distributed.
The statement explains how the number cube is fair is The data should be symmetric about a central value.
How to get the right statementJulio's simulation results, when graphed on a dot plot, often demonstrate an example of symmetric distribution where every number occurs with roughly the same frequency.
While perfect symmetry may not be witnessed in this particular simulated experiment, which consists of 40 trials that incorporate 8 rolls each, granted its limited range, the data will commonly point to fairness in its results for a fair number cube.
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A family of mice is collecting pieces of food that fall on the floor in a restaurant. If the mice collect 24 pieces of food every day for 4 days, we want to estimate the number of pieces of food they have collected. Which of the following is the closest estimate to 24?
The estimate the number of pieces of food collected by mice is 96 and closest estimate to 24 is given by option b. 20.
Number of pieces of food collected by mice every day = 24 pieces
Total number of days mice collects the food = 4 days
To estimate the total number of pieces of food collected,
Now, multiply the number of pieces collected each day by the number of days,
Total number of pieces
= 24 pieces/day × 4 days
= 96 pieces
To estimate the answer closest to 24, we can round 24 to the nearest tens.
The nearest tens to 24 is 20.
Therefore, the estimate of collection of food pieces in 4 days by mice is equal to 96 and the closest estimate to 24 is option b. 20.
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The above question is incomplete , the complete question is:
A family of mice is collecting pieces of food that fall on the floor in a restaurant. If the mice collect 24 pieces of food every day for 4 days, we want to estimate the number of pieces of food they have collected. Which of the following is the closest estimate to 24?
a. 10
b. 20
c. 30
d. 40
Try These questions out and I’ll give you brainliest
The expressions are simplified to;
1. 72n² + 63n
2. 18t - 18t²
3. -18b² - 18b
4. -56r - 21r²
5. -6m + 9m²
What are algebraic expressions?Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.
These algebraic expressions are also made up of mathematical or arithmetic operations.
These operations are;
BracketParenthesesAdditionMultiplicationDivisionSubtractionFrom the information given, we have;
1. -9n (-8n -7)
expand the bracket
72n² + 63n
2. -2t(-9 + 9t)
expand the bracket
18t - 18t²
3. -3b(6b + 6)
expand the bracket
-18b² - 18b
4. -7r(8 + 3r)
expand the bracket
-56r - 21r²
5. 3m(-2 + 3m)
expand the bracket
-6m + 9m²
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Solve for x.
12x² -2=14
Answer:
�
=
1.154701
Step-by-step explanation:
12x sqaured - 2 = 14
so first add 2 to make it 16 in the other side.
12x sqaured =16 then divide the sqaured and get 4 on the other side
so 12x = 4 then the answer is 4/12 or 1/3
Answer:
Step-by-step explanation:
12x²-2=14 add 2 to both sides
12x²=16 divide both sides by 12
x² = 16/12 reduce by dividing top and bottom by 4
x²=4/3 take square root of both sides to cancel square
when you take sq root you also get ±
x=±[tex]\sqrt{\frac{4}{3} }[/tex] you can take square root of 4
= ± [tex]\frac{2}{\sqrt{3} }[/tex] you can never leave root on bottom so multiply by
root on top and bottom to simplify
= ± [tex]\frac{2}{\sqrt{3} } \frac{\sqrt{3} }{\sqrt{3} }[/tex]
= ± [tex]\frac{2\sqrt{3} }{3}[/tex]
i really need help!!!!!
there are like 5 questions.
Answer:
3
Step-by-step explanation:
The answer is three because u need to simply the fractions
Marcus jogged 1 2/5 miles on Saturday and 9/10 miles on Sunday. Rounding the
fractions to the nearest 1/2, approximately how many miles did he jog over the
weekend? Express your answer as an improper fraction.
Marcus jogged approximately 2 1/2 miles over the weekend.
How to find the how many miles did he jog over the weekendWe need to discover a common denominator to add the miles run on Saturday and Sunday. Because 10 is the least common multiple of 5 and 2,
we may convert the fractions to have a denominator of 10:
1 2/5 = 1 + 4/5 = 5/5 + 4/5 = 9/5
9/10 = 0.9 = 9/10
Now we can add the two distances:
9/5 + 9/10 = 18/10 + 9/10 = 27/10
Rounding 27/10 to the nearest 1/2 gives:
27/10 ≈ 2 1/2
Therefore, Marcus jogged approximately 2 1/2 miles over the weekend.
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Please answer fast!!
What are the x-intercepts for the graph y = cos x, where
0≤x≤ 2n?
The x-intercepts for the function y = cos x, where 0≤x≤ 2n are
x = π/2, x = 3π/2, and x = 2π
We have,
The cosine function has an x-intercept whenever it crosses the x-axis, which happens at every multiple of π/2 radians (or 90 degrees).
So the x-intercepts for the graph y = cos x, where 0 ≤ x ≤ 2π are at
x = π/2, x = 3π/2, and x = 2π
(corresponding to 90 degrees, 270 degrees, and 360 degrees).
Now,
If we take 2n to be a multiple of 2π (i.e., 2n = k2π for some integer k), then the x-intercepts for the graph y = cos x,
where 0 ≤ x ≤ 2n, will be at x = kπ/2 for k = 0, 1, 2, ..., 4n-1.
The x-intercepts for the graph y = cos x, where 0≤x≤ 2n are
x = π/2, x = 3π/2, and x = 2π
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Water is pumped out of the conical tank with vertex down and radius 8 ft and height 20 ft. If the volume is decreasing at a rate of 4 ft^3sec :
how fast is the depth of the water decreasing when the water is 9 ft deep? (Note: Don't approximate the answer and state its exact value in terms of π.)
It took approximately 151 seconds to decrease 9 ft water in conical tank.
The volume of a conical tank with vertex down and radius 8 ft and height 20 ft is V = (1/3)πr²h
When the water is 9 ft deep
= (1/3) ×3.14×(8)²×(9)
= 602.88 ft³
We know that the rate of change of volume is 4 ft³/sec. So, the rate of change of depth can be calculated as follows:
Rate of change of depth (dh/dt) = Volume of tank/4 ft³ per sec
= 602.88/4
= 150.72 sec
Therefore, it took approximately 151 seconds to decrease 9 ft water in conical tank.
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Graph the feasible region and find the values of x and y that give the maximum possible value of g=8x+12y subject to the following constraints:
The solution is:
(a) A (20, 60), B = (0, 0) and C = (80, 0).
(b) The values of x and y that maximize the objective function are
(20, 60).
(c) From graph we can see that (20, 60) is the maximum value of the objective function on the feasible region.
We have,
The set of all possible points of an optimization problem that satisfy the problem's constraints—which may include inequalities, equalities, and integer constraints—is referred to in mathematics as a feasible region, feasible set, search space, or solution space.
Given,
x ≥0, y ≥ 0
x + y ≤ 80
y ≤ 3x
Objective function: z = 250x + 300y
(a) For the given constraints the feasible region is attached below.
The feasible region is ABC.
where, A (20, 60), B = (0, 0) and C = (80, 0).
(b) Now to find the values of x and y which maximize the objective function.
z = 250x + 300y
At A = (20, 60)
z = 250(20) + 300(60) = 5000 + 18000 = 23000
At B = (0, 0)
z = 250(0) + 300(0) = 0
At C(80, 0)
z = 250(80) + 300(0) = 2000 + 0 = 2000
Therefore, the values of x and y that maximize the objective function are (20, 60).
(c) From graph we can see that (20, 60) is the maximum value of the objective function on the feasible region.
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Which expression represents twice the sum of a number and six
Answer:
2(x + 6)
Step-by-step explanation:
If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:
2(x + 6)
Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)
Write the following equation in polar form.
y=3
r=3sinθ
r=1/3sinθ
r=3cscθ
r=1/3cscθ
r=3cosθ
r=1/3cosθ
Answer:r=3cscθ
Step-by-step explanation:The equation y = 3 represents a horizontal line at a distance of 3 units above the x-axis in the Cartesian coordinate system. To convert this equation into polar form, we can use the fact that x = rcos(theta) and y = rsin(theta) in polar coordinates.
Since y = 3 for all values of x, we can say that r*sin(theta) = 3. Solving for r, we get:
r = 3/sin(theta)
This equation represents a family of circles with center at the origin and radius 3/sin(theta), for all values of theta except for multiples of pi. We can simplify this equation by using the identity sin(theta) = 1/csc(theta), giving us:
r = 3csc(theta)
Ted works for 160 hours in a given month, and his wage rate is $10 per hour. What amount will show as Ted's contribution to Social Security?
OA. $1,500.80
OB. $9.92
O C. $99.20.
OD. $150.08
Assuming the Social Security contribution rate is 6.2% of the wage, Ted's contribution to Social Security can be calculated as follows:
Ted's total wage for the month = 160 hours * $10/hour = $1600
Social Security contribution = 6.2% * $1600 = $99.20
Therefore, the answer is option C. $99.20.
Talia tutors and wants to save money. Talia currently has $60 and plans to save an additional $35 per month. Which graph represents the number of months it will take Talia to save at least $200? 4 number lines labeled A, B, C, and D. Line A: At 3, there is a closed circle. To the right of 3, the number line is shaded with an arrow pointing to the right. Line B: At 4, there is a closed circle. To the right of 4, the number line is shaded with an arrow pointing to the right. Line C: At 5, there is a closed circle. To the left of 5, the number line is shaded with an arrow pointing to the left. Line D: At 7, there is a closed circle. To the left of 7, the number line is shaded with an arrow pointing to the left.
The graph which represents the number of months it will take Talia to save at least $200 is Line B.
Given that,
Talia tutors and wants to save money.
Talia currently has $60 and plans to save an additional $35 per month.
Current amount = $60
Additional amount each month = $35
Let n be the number of months taken to at least save $200.
60 + 35n ≥ 200
35n ≥ 140
n ≥ 4
So the graph will be a number line which has a closed circle on 4 and pointing to the right, because number of months should be either equal to or greater than 4.
Hence the correct option is B.
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Select the correct answer.
In the given diagram, line segment BD
bisects angle ABC
. Segment BD
is extended to E, where line segment EC
is parallel to line segment AB
. Write a two-column proof to show that AB/AD = BC/DC
.
The missing statement and the reason in the two-column proof:
EC = BC; property iof isosceles triangles
The corret answer is an option (A)
A two-column proof to show that AB/AD = BC/DC is:
Statement Reason
∠1 ≅ ∠2 given
∠1 ≅ ∠5 alternate interior angles theorem
∠3 ≅ ∠4 vertical angles theorem
ΔABD is similar to ΔCED AA similarity
AB/AD = EC/DC property of similar triangles
∠2 ≅ ∠5 substitution property of congruency
EC = BC property iof isosceles triangles
AB/AD = BC/DC substitution property of equality
Therefore, the correct answer is an option (A)
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