The amount withheld in FICA Tax for Sol Berenson's weekly earnings is given as follows:
$749.7.
How much will be withheld by the FICA Tax?To calculate the amount withheld by Berenson's employer in FICA tax, we apply the proportion of the FICA tax to his total earnings.
Researching on a web search, the FICA tax rate is given as follows:
15.3% = 0.153.
As the FICA tax is a combination of the Medicare tax with the Social Security tax.
Sol Berenson's gross weekly earnings are given as follows:
$4,900.
(as stated in the problem).
The amount withheld is 15.3% of that, which is found applying the proportion, which is the multiplication of 0.153 by 4900 as follows:
Amount Withheld = 0.153 x 4900 = $749.7.
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Question
Taylor is competing in a 30 kilometers race. She has already run 12.35 kilometers through a park and swam 3.75 kilometers. She will bike the rest of the way.
How far does Taylor need to bike to finish the race?
Responses
8.6 km
13.9 km
16.1 km
17.65 km
Answer: She needs to ride 13.9 more kilometers on her bike to finish the race.
Step-by-step explanation:
==> 30 = 3.75 + 12.35 + x
Take 16.1 from both sides:
==> 30 = 16.1 + x
==> 30 = 13.9km
Answer:
Step-by-step explanation:
The answer would be 13.9, if you add 12.35 to 3.75 you get 16.1, then 16.1 added to 13.9 equals 30
please help me with this
The correct matching regarding the linear functions are given as follows:
i. A set of points where the coordinates of each point has a sum of 2: Line n.
ii. A set of points where the y-coordinate of each point is 10 less than the x-coordinate: Line m.
b - i) Two numbers with a sum of 2: A and C.
b - ii) Two numbers where the y-coordinate is 10 less than the x-coordinate: D and E.
b - iii) Two numbers with a sum of 2 and where the y-coordinate is 10 less than the x-coordinate: B.
How to match the options?The set of points where the coordinates of each point has a sum of 2 is defined by the following linear function
x + y = 2.
In slope-intercept form, it is of:
y = 2 - x.
Which is the decreasing line n, with an intercept of 2.
A set of points where the y-coordinate of each point is 10 less than the x-coordinate is defined by the following linear function
y = x - 10.
Which is the increasing line m, which an intercept of m.
The coordinates of each point are given as follows:
A(-2,4).B(6,-4).C(12,-10).D(2,-8).E(13,3).These points are then used to match the sentences in item b.
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To assemble a piece of furniture, a wood peg must be inserted into a predrilled hole. Suppose that the diameter of a randomly selected peg is a random variable with mean 0.25 inch and standard deviation 0.006 inch and that the diameter of a randomly selected hole is a random variable with mean 0.253 and standard deviation 0.002. Let x1= peg diameter, and let x2= denote hole diameter.Why would the random variable , defined as y=x2-x1 , be of interest to the furniture manufacturer?What is the mean value of the random variable y?Assuming that x1 and x2 are independent, what is the standard deviation of y?Is it reasonable to think that x1 and x2 are independent? Explain.Based on your answers to Parts (b) and (c), do you think that finding a peg that is too big to fit in the predrilled hole would be a relatively common or a relatively rare occurrence? Explain.
(a) Using y the manufacture can find the required diameter of the hole.
(b) The mean of the random variable y is 0.003.
(c) The standard deviation of the y is 0.0063.
(d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.
(e) We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.
Given that x1 be the peg diameter with mean 0.25 in. and standard deviation 0.0006 in.and x2 be the hole diameter with mean 0.253in. and deviation 0.002 in.
a) y=x2-x1 denote the difference between hole and peg diameter
if y<0 , the peg won’t go inside the hole and
if y>0 ,the peg be loose to the hole
So using y the manufacture can find the required diameter of the hole.
b)Now, we have to find the mean of the random variable y
μ(y) = μ(x2) - μ(x1)
μ(y) = 0.253-0.25
μ(y) = 0.003
c) Now we have to find the standard deviation of the y
σ(y) = √{var(x1)+ var(x2)}(x1 and x2 are independent)
σ(y) = √0.000036+0.000004
σ(y) = √0.00004
σ(y) = 0.0063
d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.
e) With a standard deviation larger than the mean , it would be fairly likely to observe a negative value of y, so it would be a relatively common occurrence to find a peg that was too big to fit in the predrilled hole. We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.
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2(x - 6) + 2 = 4x - 4
Answer:
x = - 3
Step-by-step explanation:
2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify
2x - 12 + 2 = 4x - 4
2x - 10 = 4x - 4 ( subtract 4x from both sides )
- 2x - 10 = 4x - 4 ( add 10 to both sides )
- 2x = 6 ( divide both sides by - 2 )
x = - 3
Answer:
SOLUTION
2(X-6)+2=4X-4
open the blanket by multiplication
2x-12+2=4x-4
2x-10=4x-4
collect like term
2x+4x=-4+10
6x=6
divide both side by 6
x=1
The window measures 32 inches wide 48 inches tall to put lights around the window how many inches will I need
Answer: 160 inches
Step-by-step explanation:
To put lights around the window, you will need a total of 32 + 48 + 32 + 48 = <<32+48+32+48=160>>160 inches of lights. You will need this much light to go completely around the window.
Daniel ran 5 kilometers less then Abhasra last week. Daniel ran 16 kilometers. how many kilometers did Abhasra run?
Can someone please solve this its on computer and im only good on paper
By graphing, the solution to the system, y = 5x + 2 and y = x - 2 is: A. (-1, -3)
How to Solve a System of Equations by Graphing?The solution to a system of equations is the coordinates of an ordered pair that will make both of the equations to be true. This coordinates is determined by graphing.
To do this, plot both lines on a coordinate plane, then determine the coordinates of the point of intersection of both lines.
Given the system of equations,
y = 5x + 2
y = x - 2
The graph that shows both equations are attached below where the red line is y = 5x + 2, and y = x - 2 is the blue line.
The point of intersection is at (-1, -3). Therefore, the solution is:
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You are given the statement: Vertical angles are equal in measure.
A. Rewrite the statement as an if-then statement.
B. Write the converse of the implication.
The if-then statement is:
If angles are vertical angles then their measure is equal.
and converse of the implication is:
If the measure of angles is equal then they are vertical angles.
What is the Converse Statement?
That sort of reversal is called a converse. Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry, the conditional statement is referred to as p → q. The Converse is referred to as q → p.
We have given the statement:
Vertical angles are equal in measure.
A). Rewrite the statement as an if-then statement.
If angles are vertical angles then their measure is equal.
B). Write the converse of the implication
If the measure of angles is equal then they are vertical angles.
Hence, the if-then statement is:
If angles are vertical angles then their measure is equal.
and converse of the implication is:
If the measure of angles is equal then they are vertical angles.
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for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is
For an independent-measures t test, the option that describes the estimated standard error of the difference in sample means is D. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.
What is a T test?A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment actually affects the population of interest or whether two groups differ from one another.
The Independent Samples t Test compares the means of two separate groups to see if there is statistical support that the population mean values are statistically significantly different. A parametric test is called the Independent Samples t Test. For instance, you could determine whether first-year graduate salaries varied by gender using an independent t-test.
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Complete question
for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is
a. a weighted average of the two sample
b. the difference between the standard deviationa
c. The variance
d. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.
an application is using a two-dimensional list defined as follows: write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. write nested loops that get an integer value from the user for each element in the list, example: values
Complete Question :
An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.
Sum of rows : [ 6, 60, 600, 6000 ]
Sum of columns : [ 1111, 2222, 3333]
Sum of all elements : 6666
The nested loops are :
Enter a number at row 0, and column 0 : 1
Enter a number at row 0, and column 1 : 2
Enter a number at row 0, and column 2 : 3
Enter a number at row 1, and column 0 : 10
Enter a number at row 1, and column 1 : 20
Enter a number at row 1, and column 2 : 30
Enter a number at row 2, and column 0 : 100
Enter a number at row 2, and column 1 : 200
Enter a number at row 2, and column 2: 300
Enter a number at row 3, and column 0 : 1000
Enter a number at row 3, and column 1 : 2000
Enter a number at row 3, and column 2 : 3000
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a line passes through the point (-6,3) and has a slope of 3/2
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
Given
A line passes through the point (-6,3)
and has a slope of 3/2
Slope intercept form
y = mx + b
Equation,
y - 3 = 3/2(x - (-6))
y - 3 = 3/2(x+6)
2y - 6 = 3x + 18
2y = 3x + 24
y = 3/2x + 12
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
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HELP ASAP
3. If the aspect ratio of a tire is 50%, width 10 inches, and the rim diameter is 19 inches, what is the tire diameter?
a. 59in b. 35.8in
d. 49in
4. The standard print paper is 11" by 8.5 in. What is the aspect ratio of a standard print paper?
a. 11:8
c. 8.5
c. 29 in
b. 22:17
d. 11
3) The tire diameter using the aspect ratio is; 29 inches
4) The aspect ratio of a standard print paper is; 22:17
How to solve aspect ratio problems?The aspect ratio is defined as the relationship between the width and height.
Now, in this case, the aspect ratio must be in whole numbers and not decimals and as such we can solve as follows;
3) We are told that the aspect ratio of a tire is 50%.
Thus, the aspect ratio is; 50/100 = 1/2 or 1:2.
Now, we are told that width 10 inches, and the rim diameter is 19 inches, then it means that the tire diameter = 10/2 + 19 + 10/2 = 29 inches
4) The standard print paper is 11" by 8.5. This can also be written as;
11 by 17/2 or 11 * 2 : 17
= 22:17
This then gives us the aspect ratio.
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A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x) .
a. The blue line represents g(x) = 250,000csc(π30x).
b. g(5) = 25,000 km. This is the distance of the comet from Earth after 5 days.
c. The minimum distance between the comet and Earth is 250,000 km, which occurs when x = 0. This corresponds to the constant csc(π30x).
d. The equation has a vertical asymptote at x = 30/π.
Write the solution to following questions:a. Graph the value of x on the range [0,35].b. Analyze g(5) and explain the results.c. What is the shortest path the comet must take to reach Earth? When does this take place? What equation constant does this match up to?d. Find any vertical asymptotes and explain their significance.a. Graph g(x):
To graph g(x), we can plot several points on the interval [0,35] and then connect them to form a graph of the function. For example, we can plot the points (0,250,000), (5,50,000), (10,25,000), (15,16,667), (20,12,500), (25,10,000), (30,8,333) and (35,7,143). Connecting these points will give us a graph of the function g(x).
b. Evaluate g(5):
The value of g(5) can be found by plugging in x = 5 into the equation: g(5) = 250,000 csc(π30*5) = 50,000 km. This means that after 5 days, the comet will be 50,000 km away from Earth.
c. Minimum distance between the comet and Earth:
The minimum distance between the comet and Earth can be found by taking the derivative of the equation and setting it to 0.
d. Vertical Asymptotes:
The vertical asymptotes of g(x) occur at x = 0 and x = 30. This means that the comet approaches an infinitely large distance from Earth at x = 0 and x = 30.
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Find the degree to the nearest point
The degree to turn before walking 673 paces is 59 degrees
How to determine the degree to walk?From the question, we have the following parameters that can be used in our computation:
Lengths = 989 paces, 673 paces and 861 paces
These paces can be represented as
x = 989
y = 673
z = 861
The measure of the required angle (angle Z) i.e. the degree to walk can be calculated using the following cosine rule
z² = x² + y² - 2xy * cos(Z)
Substitute the known values in the above equation, so, we have the following representation
861² = 989² + 673² - 2 * 989 * 673 * cos(Z)
Evaluate the exponents, the products and the summation
So, we have the following representation
741321 = 1431050 - 1331194 * cos(Z)
Evaluate the like terms
- 1331194 * cos(Z) = -689729
Divide both sides by - 1331194
cos(Z) = 0.51812808651
Take the arc-cos of both sides
Z = 58.7
Approximate
Z= 59 degrees
Hence, the measure of the angle is 59 degrees
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Graph the rational function Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X ?
The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.
Graph is attached.
As given in the question,
Given function is :
f(x) =6 /(- 2x +1)
f(x) = y
Degree of the numerator is zero
Degree of the denominator is 1.
Degree of denominator is greater than the degree of numerator.
Function represent the horizontal asymptotes for y =0
To get the vertical asymptotes equate denominator equals to zero
(- 2x +1) = 0
⇒2x = 1
⇒x = 1/2
Vertical asymptotes is given by x =1/2.
Graph is attached.
Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.
The above question is incomplete, the complete question is:
Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.
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Through C construct a parallel to AB.
Through A construct a parallel to BC.
Through B construct a parallel to AC.
Extend these lines to form a new triangle.
What relationship exists between the
two triangles?
A
C
B
Answer:
new triangle is similar to and 2 times the size of the original
Step-by-step explanation:
You want to construct a new triangle with the sides of the existing one being midsegments of the new one. Then you want to know the relationship between the triangles.
ConstructionThe attachment shows the described construction.
RelationshipThe sides of the original triangle are midsegments of the new triangle, so the new triangle is ...
scaled up by a factor of 2 (has 4 times the area)similar to the originalrotated 180° about the common centroid of the two trianglesActuarial math
A 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, is bought to yield 8% convertible semiannually. Find the price. Verify that all four formulas produce the same answer.
The price of a 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, bought to yield 8% convertible semiannually, is its present value of $115.87.
What is the price of a bond?The price of a bond is its present value.
The present value can be computed by setting the following parameters:
Number of periods = 20Effective interest rate = 8%Periodic interest payment = $5 ($100 x 10% x 6/12)Future value = $105.This can be done using an online finance calculator with the results as follows:
N (# of periods) = 20 semiannual periods (10 years x 2)
I/Y (Interest per year) = 8%
PMT (Periodic Payment) = $5 ($100 x 10% x 1/2)
FV (Future Value) = $105
Results:
Present Value (PV) = $115.87
Sum of all periodic payments = $100 ($5 x 20)
Total Interest = $89.13
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Question Completion:Answer: 115.87 (If you don't get this answer then the solution is incorrect.)
Go step by step to reduce the radical.
Answer:
[tex] \sqrt{176} [/tex]
[tex] \sqrt{16 + 11} [/tex]
[tex]4 \sqrt{11} [/tex]
Step-by-step explanation:
The answer is
[tex]4 \sqrt{11} [/tex]
We
need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11 . Thus, the square root of 176 in the lowest radical form is 4 √11.
i hope this helped
A wooden box is in the shape of a regular pentagonal prism. The sides, top, and bottom of the box are 1 centimeter thick. Approximate the volume of wood used to construct the box. Round your answer to the nearest tenth.
The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.
What is a pentagonal prism?A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.
The expression for the volume of a regular pentagon is given as V = 5/2 × abh
Where h is the height and a and b are the length of the sides.
Now, the value of a, b and h as per the question is given as,
a = b = h = 1.
Then, the volume can be calculated as,
V = 5/2 × 1 ×1 × 1
= 2.5
Hence, the volume of the regular pentagonal prism is given as 2.5 cm³.
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Consider the following measurements of the heat-producing capacity of the coal produced by two mines (in millions of calories per ton): Mine 1: 8260 8130 8350 8070 8340 Mine 2: 7950 7890 7900 8140 7920 7840 Can it be concluded that the two population variances are equal?
F0.05 (4,5)=5.19>f according to the F-distribution table. Following that, P(F>1.442)>P(F>f0.05 (94.5))=0.05. This leads us to conclude that the sample has a higher than 5% chance of producing such data under the premise that σx=σy.
We cannot conclude that the variances of the two populations are not equal based on the standards of a 95% confidence interval.
Step 1 : the mines' 1 and 2 standard deviations should be calculated. [tex]n_{x}[/tex] =5&[tex]n_{y}[/tex]=6.
To determine the sample means, use the formulas
x bar = 8260 + 8130 + 8350 + 8070 + 8340/ [tex]n_{x}[/tex]
x bar = 41150/ 5
x bar = 8230 and y bar = 7950 + 7890 + 7900 + 8140 + 7920 + 7840/ [tex]n_{y}[/tex]
y bar = 47640/6
y bar = 7940.
step 2: Now, [tex]s_{x}[/tex]provides the standard deviations.
[tex]s_{x}^{2}[/tex] =1/4i=1∑^5i=1(xi−x)^2
=1/ 4 ⋅63000
=15750
for [tex]s^{2}_{y}[/tex]
[tex]s^{2}_{y}[/tex]^2=1/5∑i=1^6(yi−y)^2
=1/5⋅54600
=10920
If we assume that the variances of the two populations are equal—
that is, σx=σy and
[tex]s_{x}^{2}[/tex] and[tex]s^{2}_{y}[/tex] are the variances of independent random samples with sizes of [tex]n_{x}[/tex]=5 and[tex]n_{y}[/tex] =6 drawn from normal populations—then we can say that the random variable exists.
The formula F is
=[tex]s_{x}^{2}[/tex]/ [tex]s^{2}_{y}[/tex]has an F distribution with
v1=nx- 1
=5- 1
=4 and
v2=ny-1
=6- 1
=5
The observed samples' f-value is f=[tex]s_{x}^{2}[/tex] / [tex]s^{2}_{y}[/tex]
=15750/10920
=1.442.
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Which property justifies the statement below? X(y+5)=xy+5x
Knowledge Check
Find x
x=
Answer:
x is 44 Hope that helps.
Find the value of each of these quantities a) P(6,3) c) P(8,1) e) P(8,8) b) P(6,5) d) P(8,5) f) P(10,9)
The values for the given data set is as follows 120 , 720 , 8 ,40320 , 6720 ,3628800 respectively.
The formula to calculate the permutation is , P = n! / ( n - r )!. Using this formula we get the result as,
P(6,3) = 6! / (6−3)!
= 6! / 3!
= 120
P(8,1) = 8! / (8 - 1)!
= 8! / 7!
= 8
P(6,5) = 6! / (6-5)!
6! / 1!
720
Similarly ,
P(8,8)= 40320
P(8,5) = 6720
P(10,9) = 3628800
A permutation is a specific arrangement of items. Set members or elements are arranged in a sequence or linear order here.
For example, the permutation of set A=1,6 is 2, as in 1,6,1.
There are no alternative ways to arrange the items in set A, as you can see.
In permutation, the elements must be organised in a specific sequence, whereas in combination, the order of the elements is irrelevant. Read also: Permutation And Combination
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find two polynomials whose difference is 2x^2 + x + 4
The two polynomials whose difference is 2x^2 + x + 4 are
6x² + 3x + 5 and 4x² + 2x + 1.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The difference between the two polynomials is 2x² + x + 4.
The two polynomials are:
6x² + 3x + 5 _____(1)
4x² + 2x + 1 ______(2)
The difference between (1) and (2)
6x² + 3x + 5 - 4x² - 2x - 1
2x² + x + 4
Thus,
The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.
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Waves that make up light have peaks and valleys just like the ocean. What are the scientific terms for peaks and valleys?
highs and lows
crests and troughs
ebbs and flows
protos and parallax
The scientific terms for peaks and valleys is B. Crests and troughs.
What are crests?The greatest amount of upward displacement within a cycle occurs at a wave's crest point. A surface wave's crest is a region where the medium's displacement is greatest. The minimum or lowest point in a cycle, a trough is the opposite of a crest.
The crest and trough of a wave, respectively, are its highest and lowest surface portions. The wave height is the vertical distance between the crest and trough. The wavelength is the horizontal separation between two adjacent crests or troughs.
The crest is the highest point on the wave. The trough is the area that is the lowest. The wave length, also known as the wavelength, is the separation between two successive crests (or troughs), while the wave height is the overall vertical change in height between the crest and the trough.
Therefore, based on the information given, the correct option is B.
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Sandra has 5.2 pounds of trail mix that she is splitting
2)
equally into bowls of 0.65 pounds. How many bowls does Sandra need?
Sandra needs 8 bowls to divide the trail mix equally.
To determine the number of bowls Sandra needs, we need to divide the total weight of the trail mix by the weight of each bowl.
First, we need to convert the weight of the trail mix from pounds to ounces. There are 16 ounces in a pound, so 5.2 pounds is equal to 5.2 x 16 = 83.2 ounces.
Next, we need to convert the weight of each bowl from pounds to ounces. There are 16 ounces in a pound, so 0.65 pounds is equal to 0.65 x 16 = 10.4 ounces.
Now that we have both weights in the same units, we can divide the total weight of the trail mix by the weight of each bowl to find the number of bowls needed.
⇒ 83.2 ounces / 10.4 ounces per bowl
Apply the division operation,
⇒ 8 bowls.
Therefore, she needs 8 bowls to divide the trail mix equally.
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Keisha and David each found the same value for cos0, as shown below, given sin0=-8/17. Keisha's Solution
tan²8+1 = sec²e
sin² e
cos² e
=+1=
17
cos² e
(-) + Co
+1=
1
cos² e
cos² e
+ cos²9=1
64
cos 9-1-
-- 289
15
cose=17
David's Solution
sin²+ cos² = 1
cos²8-1-(-17)
Со
cos = ±
225
289
15
cose=¹17 whose procedure is correct?
The procedure is correct is 1 + tan²(theta) = sec²(theta)
What is Fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
And
cos²(theta) = 1 - sin²(theta)
Are both valid identities
Keisha and the David.
As per the question Kisha and the David found the same value of the cosine theta as given by the Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).
Thus the answer is both procedures are correct.
As they both wanted to find the solutions to the numerical problems they made two different methods.
Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).
Hence both options are the same and true.
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Age of Senators The average age of senators in the 108" Congress was 57.5 years. If the standard deviation was 11.5 years, find the -scores corresponding to the oldest and youngest senators of age 87 and 44. Round scores to two decimal places. find the z-score corresponding to the oldest senator of age 85 is
The z-scores correspond to the oldest and youngest senators of ages 87 and 44 are 2.57 and -1.17. The z-score corresponding to the oldest senator of age 85 is 2.39.
A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. The formula to calculate this score [tex]z=\frac{x-\mu}{\sigma}[/tex]. Where z is the z-score, x is the observed value, μ is the sample mean, and σ is the sample standard deviation.
Given μ = 57.5 and σ = 11.5.
When x = 87, the z-score value is,
[tex]\begin{aligned}z&=\frac{87-57.5}{11.5}\\&=2.57\end{aligned}[/tex]
When x = 44, the z-score value is,
[tex]\begin{aligned}z&=\frac{44-57.5}{11.5}\\&=-1.17\end{aligned}[/tex]
When x = 85, the z-score value is,
[tex]\begin{aligned}z&=\frac{85-57.5}{11.5}\\&=2.39\end{aligned}[/tex]
The required answers are 2.57, -1.17, and 2.39.
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A company has computed a seasonal index for its quarterly sales. Which of the following statements is not correct?
Multiple Choice
The sum of the four quarterly seasonal index numbers is 4.
The index for any quarter must be between 0 and 2.
The average index is 1.
An index of 0.75 for quarter-one sales indicates that sales were 25 percent lower than average sales.
An index of 1.10 indicates sales 10% above the norm.
The option b "The index for any quarter must be between 0 and 2" is correct.
In the given question, we have to find the incorrect statement about a company has computed a seasonal index for its quarterly sales.
For its quarterly sales, the corporation has created a seasonal indicator.
Consequently, it is correct that the four quarterly seasonal index figures add up to 4.
True, the average index is 1.
In this situation, an index of 0.75 for the first quarter's sales implies that they were 25% below average, while an index of 1.10 shows that they were 10% over average.
Hence, the incorrect statement of the option b "The index for any quarter must be between 0 and 2" is correct.
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Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by f(t) = 160e0.03tin thousands of dollars per year. Find the total income from the machines over the first 5 years. (Round your answer to the nearest thousand dollars.)$______
The total income from the machines over the first 5 years is $185.89
How to determine the total income from the machines over the first 5 yearsFrom the question, we have the following parameters that can be used in our computation:
f(t) = 160e0.03t
Where
t = Number of yearsf(t) = thousands of dollars per yearRewrite the function properly
so, we have the following representation
f(t) = 160e⁰.⁰³ⁿ
The above function is an exponential function
So: In the first 5 years, we have the value of t to be 5
This is represented as follows
t = 5
Substitute the known values in the above equation, so, we have the following representation
f(5) = 160e⁰.⁰³ ˣ ⁵
Evaluate the product of the exponents
f(5) = 160e⁰.¹⁵
The products above give
f(5) = 185.89
Hence, the total income is $185.89
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