The solo plans Debra offers her clients are plan A and plan B. Each client can only do one plan .
According to the question the plan only ran on wednesday and thursday.
Wednesday = plan A has 5 client and plan B has 3 clients.
Thursday = plan A has 7 client and plan B has 9 clients.
On wednesday she trained her client for 6 hours.
On thursday she trained her client for 12 hours.
let
x = hour of plan A workout for each client
y = hour of plan B workout for each client
[tex]\begin{gathered} 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}\mathrm{}(i) \\ 7x\text{ + 9y = 12}\ldots\ldots\ldots\text{.(2)} \\ 3y\text{ = 6 - 5x} \\ y\text{ = }\frac{6}{3}\text{ - }\frac{5}{3}x \\ y\text{ = 2 - }\frac{5}{3}x \\ 7x\text{ + 9(2 - }\frac{5}{3}x\text{) = 12} \\ 7x\text{ + 18 - }\frac{45}{3}x\text{ = 12} \\ 7x\text{ + 18 - }15x\text{ = 12} \\ -8x\text{ = 12 - 18} \\ -8x\text{ = - 6} \\ x\text{ = }\frac{6}{8} \\ x\text{ = }\frac{3}{4} \\ 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}(i) \\ 5(\frac{3}{4})\text{ + 3y = 6} \\ \frac{15}{4}\text{ + 3y = 6} \\ 3y\text{ = 6 - }\frac{15}{4} \\ 3y\text{ = }\frac{24-15}{4} \\ 3y\text{ = }\frac{9}{4} \\ y\text{ = }\frac{9}{4}\text{ }\times\text{ }\frac{1}{3} \\ y\text{ = }\frac{9}{12} \\ y\text{ = }\frac{3}{4} \end{gathered}[/tex]on wednesday plan A lasted for 5 * 3/4 = 15/4 hrs and plan B lasted for 3 * 3/4 = 9/4 hrs
On thursday plan A lasted for 7* 3/4 = 21/4 hrs and plan B lasted for 9 * 3/4 = 27/4 hrs
Each of the work out lasted for 3/4 hrs = 0.75 hrs
The data for the production of number of components at an industry for three weeks are given below. Make a stem-and-leaf plot68, 91, 42, 85, 13, 96, 15, 46, 95, 46, 64, 18, 44, 83, 69
In a stem and leaf plot, the first digit is always the stem, while the other digits are the leaves.
For the data represented:
The stem = the first digit
The leaf = the second digit
In the plot:
13, 15, and 18 will be grouped together because they have the same stem (1)
42, 44, 46, 46 are grouped together because they have the same stem (4)
64, 68, 69 are grouped together because they have the same stem (6)
83, 85 are grouped together because they have the same stem (8)
91, 95 and 96 are grouped together because they have the same stem (9)
The stem-and-leaf plot is shown below:
Alleen's bi-weekly gross pay is $829.70. She sees that $174.25 was deducted for taxes. What percent of Alleen's bi-weekly gross pay has been withheld for tax? Round to the nearest whole percent. (1 point)
O 21%
20%
2%
O 1%
In 1990, there were 1330 registered alpacas in the United States. By summer of 2000, there were 29,856. What was the percent of increase in registered alpacas?
answer - 214% increase
explanation
formula = big number - small number ÷ original number
29856 - 1330 = 28,526 ÷ 1330 = 21.45
21.45 to percent = 214% then if rounded to nearest
The side of a square lot is (5×-3) meters. How many meters of fencing materials are needed to enclose the square lot?
The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
As per the given,
Side of square = 5x - 3
The fencing around the square will cover the complete perimeter of the square.
Since the perimeter of the square = 4 × side
Therefore,
Length of fencing = 4 × (5x - 3)
Length of fencing = 20x - 12
Hence "The length of the fencing will be the perimeter of the given square with side (5x - 3) thus (20x - 12) meters will be the fencing length".
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If $19,000.00 is invested in an account for 30 years. Find the value of the investment at the end of 30 years if the interestis:(a) 7% simple interest:(b) 7% compounded monthly:
Hello there. To answer this question, we need to remember some properties in simple and coumpound interests investments.
For simple interest, the balance will be equal to P(1 + rt), in which P is the amount invested, r is the interest rate in years and t is the time (can be either years of months).
For compound interest, the balance will be equal to P(1 + r)^t.
So, using the values P = $19,000.00 and the time is equal to 30 years, we have for:
a) 7% simple interest
It means that r = 7% and then we can use the first formula
19000(1 + 0.07*30)
We converted the rate to decimals above
Multiplying the values, we have:
19000(1 + 2.1)
19000*3.1
$58.900
b) 7% compounded monthly
First, we need to convert the time from years to months, multiplying by 12
30*12 = 360 months
Using the second formula, we have:
19000(1 + 0.07)^(360)
Sum the values into parenthesis
19000*1.07^(360)
Miguel Valdez sells appliances. He is paid an 8% commission on the first $5,000 worth of sales, 10% on the next $5,500, and 15% on all sales over $10,500. What is his commission on $14,910 worth of sales?
Total Sales = 14910
8% on 5000
10% on 5500
15% on
14910 - 10500 = 4410
So,
15% on 4410 [this is the excess of 10,500]
Converting percentages to decimal:
8% = 8/100 = 0.08
10% = 10/100 = 0.1
15% = 15/100 = 0.15
Total Commission
[tex]0.08(5000)+0.1(5500)+0.15(4410)=1611.5[/tex]$1611.50What is the midpoint of the x-intercepts off(x) = (x – 4)(x + 4)?(0,0)(0,4)(–4,0)(2,0)
Given:
[tex]f(x)=(x-4)(x+4)[/tex]Required:
To find midpoint of intercepts.
Explanation:
We know that when y=0,x=4,-4
therefore x- intercept of the function are (4,0) and (-4,0)
We know that the midpoint of this intercept is at equidistance from both the graph, therefore the points from which graph is equidistance is at origin (0,0)
Required answer:
Hence the midpoint of the x- intercepts of f(x) will be at (0,0) or at the origin of the graph so option 1 is correct.
Which choice is equivalent to the expression below?V-81A. 91B. AiC.D. -29E. -9SUBMIT
Given the expression:
[tex]\sqrt[]{-81}[/tex]As we know, there is no square root for the negative numbers
But, using the complex numbers:
[tex]i=\sqrt[]{-1}[/tex]So, the given expression can be written as:
[tex]\sqrt[]{-81}=\sqrt[]{-1}\cdot\sqrt[]{81}=i\cdot9=9i[/tex]So, the answer will be option A) 9i
Find the perimeter of the square.
Width = 4x
Length = 36 – 5x
Answer:
The perimeter of the square is 64 units===========================
GivenA square with dimensions:
Width = 4x,Length = 36 - 5x.To findThe perimeterSolutionSquare has all sides equal:
width = length4x = 36 - 5x4x + 5x = 369x = 36x = 4Each side is:
4*4 = 16 unitsPerimeter:
P = 4*16 = 64 unitsThe perimeter of the square is found as 64 units.
What is defined as the perimeter of the square?The perimeter of such a square is indeed the total length of all of its sides. As a result, we can calculate the perimeter of the a square besides adding its four sides.A square's sides are all equal. As a result, the perimeter of such a square is determined by multiplying the side of a square by four.For the given question,
The dimension of the square are given as;
Width = 4xLength = 36 – 5xFor square, as all sides are equal.
Then,
Width = Length
Put the values.
4x = 36 – 5x
9x = 36
x = 4
Put in dimensions.
Width = 4×4 = 16 unitsLength = 36 – 5×4 = 16 units.The perimeter of square is;
Perimeter = 4 × side
Perimeter = 4 × 16
Perimeter = 64 units.
Thus, the perimeter of the square is found as 64 units.
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Ben, Claire and Devon are training for a triathalon. Today, they are practicing their swimming by swimming one mile. Ben swam 0.77 of the mile before stopping. Claire swam 3/5 of the mile and Devon swam 82% of the mile before stopping. Who swam the farthest distance? Who swam the shortest distance?
Given:
Ben, Claire, and Devon are swimming one mile.
Ben swam 0.77 of the mile before stopping.
So, the distance Ben swam = 0.77 x 1 = 0.77 mile
Claire swam 3/5 of the mile.
So, the distance Claire swam = 3/5 x 1 = 3/5 = 0.6 miles
Devon swam 82% of the mile before stopping.
So, the distance Devon swam = 82% of 1 mile = 0.82 x 1 = 0.82 miles
Arrange the distances in order from the largest to the least:
0.82, 0.77, 0.6
So, the answer will be:
The farthest distance is for Devon = 0.82 miles
The shortest distance is for Claire = 0.6 miles
find the perimeter of a garden that measures 6 feet by 3/4 foot?
The perimeter of a garden that measures 6 feet by 3/4 foot is 13.50 feet.
What is the perimeter?The perimeter of a rectangle is calculated thus:
Perimeter = 2(Length + Width)
From the information, we want to find the perimeter of a garden that measures 6 feet by 3/4 foot.
This will be illustrated thus:
Perimeter = 2(Length + Width)
Perimeter = 2(6 + 3/4)
Perimeter = 2(6 + 0.75)
Perimeter = 2(6.75)
Perimeter = 13.50
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Through (1,-2) parallel to y=-2x+5
Answer:
Step-by-step explanation:The line parallel to y = -2x + 5 that passes through the point(1,1)
Has the same slope, m but a different y intercept (0,b)
So lets start by using the given point (1, 1) and the slope intercept form of the line to calculate b
y = mx + b
m = -2
1 = -2(1) + b
1 = -2 + b
Add 2 to both sides of the equation to solve for b
1 + 2 = b
3 = b
The line is
y = -2x + 3
Is my answer correct help please
Answer:
No, the correct answer is C.
Step-by-step explanation:
Five less than a number m = m - 5. and not 5 - m, so false.
A rectangular room is 1.5 times as long as it is wide, and its perimeter is 26 meters. Find the dimension of the room.The length is :The width is :
The rectangular room is 1.5times as long as it is wide and its perimeter is 26m. Let "x" represent the room's width, then the length of the room can be expressed as "1.5x"
The perimeter of a rectangle is equal to the sum of twice the width and twice the length following the formula:
[tex]P=2w+2l[/tex]We know that:
P=26m
w=x
l=1.5x
Then, replace the measurements on the formula:
[tex]\begin{gathered} 26=2x+2\cdot1.5x \\ 26=2x+3x \end{gathered}[/tex]From this expression, you can calculate x, first, add the like terms:
[tex]26=5x[/tex]Second, divide both sides by 5 to determine the value of x:
[tex]\begin{gathered} \frac{26}{5}=\frac{5x}{5} \\ 5.2=x \end{gathered}[/tex]The width is x= 5.2m
The length is 1.5x= 1.5*5.2= 7.8m
Using trigonometry functions find the value missing in the diagram round to the nearest whole number
Given a right angle triangle
As shown:
Given ∠58
the opposite side to the angle = 22
The adjacent side to the angle = x
So,
[tex]\begin{gathered} \tan 58=\frac{\text{opposite}}{\text{adjacent}} \\ \\ \tan 58=\frac{22}{x} \end{gathered}[/tex]solve for x:
[tex]x=\frac{22}{\tan 58}\approx13.747[/tex]round to the nearest whole number
So, the answer will be x = 14
For the line that passes through Y(3,0), parallel to DJ with D(-3,1) and J(3,3), complete the following: Find the slope. Write an equation in point-slope form. Graph the line.Slope:Point-slope form:
I am going to graph the situation on an external graphing utility and show you the answer, it will take a
minute, stay with me.
[tex]m\text{ = }\frac{rise\text{ }}{\text{run}}=\frac{change\text{ in y}}{\text{change in x}}=\frac{3}{1}=3[/tex][tex]y\text{ = mx+b}\rightarrow\text{ b =-1}[/tex]So the equation of the line is.
[tex]y\text{ =3x -1}[/tex][tex]y\text{ -1 = m(3-0)}[/tex]5+10+15+...+100 write the series using summation notation
The Solution.
To determine that the series is an arithmetic progression,
[tex]\begin{gathered} T_{2_{}}-T_1=T_3-T_2=d \\ \text{Where d = common difference} \end{gathered}[/tex][tex]d=10-5=15-10=5[/tex]The sum of n terms of an arithmetic progression is given as
[tex]\begin{gathered} S_n=\frac{n}{2}(a+l) \\ \text{Where S}_n=\sum ^{\square}_{\square} \\ n=n\text{ umber of terms}=\text{?} \\ a=\text{first term=5} \\ l=\text{last term=100} \end{gathered}[/tex]But we need to first find the number of terms (n), by using the formula below:
[tex]\begin{gathered} l=a+(n-1)d \\ \text{Where a = 5, l=100, d = 5 and n =?} \end{gathered}[/tex]Substituting the values, we get
[tex]\begin{gathered} 100=5+(n-1)5 \\ 100=5+5n-5 \\ 100=5n \\ \text{Dviding both sides by 5, we get} \\ n=\frac{100}{5}=20 \end{gathered}[/tex]Substituting into the formula for finding the sum of terms of the series, we get
[tex]\begin{gathered} S_{20}=\frac{20}{2}(5+100) \\ \text{ } \\ \text{ = 10(105) = 1050} \end{gathered}[/tex]Therefore, the correct answer is 1050.
Translate to an algebraic expression.10 more than dThe translation is
10 more than d is the same as d plus 10, so the algebraic expression is:
d + 10
Answer: d + 10
A bag of marbles contains 6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble. What is the
probability of reaching into the bag and selecting a yellow marble?
73.
13
16
26
Answer:
2/13
Step-by-step explanation:
Out of a total 13 marbles , 2 are yellow 2 out of 13 = 2/13
Answer:
2/13
Step-by-step explanation:
6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble = 13 marbles
P( yellow) = number yellow / total
= 2/13
in the graph below line k,y = -x makes a 45 degree angle with the X and Y axes complete the following
The point with a coordinate of (2,5) will be translated into y=-x line.
The transformation for y=-x would be:
1. x'= -y
2. y'= -x
For x=2 and y=5 would be:
x'= -y
x'= -5
y'= -x
y'= -2
The translated coordinate would be: (-5, -2)
Find the equation of the line passing through the points (3,-2) and (3, 4).The answer is x = 3. I'm just wondering how my textbook got to this solution.My work:y-y1=m(x-x1). m=y2-y1 / x2-x1. y=mx+bm=4--2 / 3-3 = 6/0 = 0. m=0.y--2=0(x-3) = y=0-2 y=-2 <<<
Given two points. we can find the equation of a line passing through the points
The formula to be used is:
[tex]\frac{y_2-y_1}{x_2-x_!}=\frac{y-y_1}{x-x_!}[/tex]where
[tex]x_1=3,y_!=-2,x_2=3,y_2=4[/tex][tex]\frac{4-(-2)}{3-3}=\frac{y-(-2)}{x-3}[/tex]=>
[tex]\frac{6}{0}=\frac{y+2}{x-3}[/tex]The next step is to cross multiply
[tex]6(x-3)=0(y+2)[/tex]=>
[tex]6(x-3)=0[/tex]Divide both sides by 6 and make x the subject
x=3
x- sq root 6 is a factor of x^4-36 true or false
We want to know if (x-sqroot(6)) is a factor of (x^4 - 36)
That's mean:
[tex](x^4-36)=(x-\sqrt[]{6})\text{ P(x)}[/tex]Where P(X) is a polinomial.
In this case, if x = sqroot(6) the polinomail (x^4 - 36) must be zero, that's mean sqroot(6) is a root (or a zero) of (x^4-36).
So, if we evaluate (x^4 - 36) in x=sqroot(6):
[tex](\sqrt[]{6})^4-36=6^2-36=0[/tex]So, the answer is true.
Fill In the proportion No explanation just need answer got disconnected from last tutor
Explanation
Since the given shapes are similar, which implies that they are proportional,
Therefore; we will have
Answer:
[tex]\frac{AB}{EF}=\frac{BC}{FG}[/tex]Use the given rounded values, the properties of logsand your knowledge of logarithmic functions to find thevalue of each log expression. Show your work.
We want to find the value for
[tex]\log _425[/tex]To do that, first let's rewrite this expression as
[tex]\log _425=\log _45^2[/tex]Using the following property
[tex]\log _ab^c=c\log _ab[/tex]We can rewrite our expression as
[tex]\log _45^2=2\log _45[/tex]Using the given value on the text, we get our answer
[tex]\log _425=2\log _45=2\cdot1.2=2.4[/tex]Hello! I need some guidance please. Having trouble with which graph is correct
Given:
[tex]y\ge3x+3[/tex]Required:
to show which graph is correct for the inequality.
Explanation:
Given graph is correct for the equation.
Required answer:
The given graph is correct.
A company has been forced to reduce its number of employees. Today the company has 29% fewer employees than it did a year ago. If there are currently355 employees, how many employees did the company have a year agoemployees?
to solve this, question, we would have to convert the percentage to fractions or decimals.
Let x represent the numbers of employees the had a year ago
[tex]\begin{gathered} \frac{29}{100}\times x=355 \\ 0.29x=355 \\ \text{divide both sides by the coefficient of x} \\ \frac{0.29x}{0.29}=\frac{355}{0.29} \\ x=1224.127 \\ x\approx1224 \end{gathered}[/tex]a year ago, the company had 1224 empolyees
jeslie ann has a 48 month installment loan of 82.91. the amount she borrowed was 3600
Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome of credit.
Step 1
Loan Amount(p)= 3600
Number of Payments per year(n)= 12
Time in Years (t)=4
Installment Payment (m)=83.81
Total amount paid in 48 installments= 4022.88
Amount Paid - Amount Financed = 4022.88 - 3500 = 522.88 in finance charges.
To determine the annual percentage rate. Prior to multiplying the result by 100, divide the finance charge by the total amount funded. The finance charge per $100 of the financed amount is the end outcome.
Finance Charge/ Amount financed × 100= 522.88/ 3600× 100= 14.5
To use Table , look for 48 in the far left-hand column under the heading Number of Payments. Then move across to the right until you find the value closest to 14.5. In this case, 14.5 is in the table. The value 7 is at the top of this column. The yearly percentage rate is therefore around 7. Monthly payments are 83.81. After 12 payments have been made, 30 payments remain. Therefore, P = 83.81 and n = 30. Use the APR table to calculate V . In the Number of Payments column, find the number of remaining payments, 30, and then look to the right until you reach the column headed by 7%, the APR. intersect at 9.30. Thus, V = 9.30.
:[tex]u=nPV/100+V\\u=30*83.81*9.30/100+9.30=213[/tex]
Total due amount = Total remaining payment including interest- saving on interest + 12th monthly payment= 2514.3- 213.934+ 83.81= 2384.17
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Which of the following equations could you solve by first adding six and then dividing by negative three?
3x - 6 = -9
6 - 3x = -9
-3x - 6 = -9
x/-3 + 6 = -9
Answer:
-3x-6=-9
Step-by-step explanation:
[tex]-3x-6=-9[/tex]
[tex]+6[/tex] [tex]+6[/tex]
[tex]-3x = -3[/tex]
[tex]-3x/-3 = -3/-3[/tex]
[tex]x=1[/tex]
PLEASE HELP: Which of the following are identities? Check all that apply. A. (sin x + cos x)^2 = 1 + sin 2x B. sin 3x - sinx/ cos3x + cosx = tan xC. sin 6x = 2 sin3x cos3x D. sin 3x/sin x cos x = 4 cos x - sec x
All the options are correct
Explanations:A quick and smart way is to substitute a value for x in each of the options and verify if the right hand side equals the left hand side
Let x = 30
A) (sin x + cos x)² = 1 + sin 2x
(sin 30 + cos 30)² = 1.866
1 + sin 2(30) = 1.866
Therefore (sin x + cos x)² = 1 + sin 2x
B)
[tex]\begin{gathered} \frac{\sin3x-\sin x}{\cos3x+\cos x}=\tan x \\ \frac{\sin3(30)-\sin30}{\cos3(30)+\cos30}=0.577 \\ \tan \text{ 30 = 0.577} \end{gathered}[/tex]Therefore:
[tex]\frac{\sin3x-\sin x}{\cos3x+\cos x}=\tan x[/tex]C) sin 6x = 2 sin3x cos3x
sin 6(30) = 0
2 sin3(30) cos3(30) = 0
Therefore sin 6x = 2 sin3x cos3x
This can also be justified by sin2A = 2sinAcosA
D.
[tex]\frac{\sin3x}{\sin x\cos x}=\text{ 4}\cos x-\sec x[/tex][tex]\begin{gathered} \frac{\sin 3(30)}{\sin 30\cos 30}=\text{ 2.31} \\ 4\cos 30-\sec 30=\text{ }2.31 \end{gathered}[/tex]Options A to D are correct
A principal of $3100 is invested at 5.5% interest, compounded annually. How much will the investment be worth after 9 years? Round your answer to the nearest dollar.
Given:
[tex]\begin{gathered} \text{Principal(P)}=\text{ \$3100 } \\ r=5.5\text{ \%} \\ n=9 \end{gathered}[/tex][tex]Final\text{ amount=P(1+}\frac{r}{100})^n[/tex][tex]\begin{gathered} Final\text{ amount after 9 years=}3100(1+\frac{5.5}{100})^9 \\ =3100(1.6191) \\ =\text{ \$50}19.21 \end{gathered}[/tex]Therefore, the investment be worth after 9 years is $5019.21
