Answers
Answer:
Dian has $250 originally.
Step-by-step explanation:
Let the total money Dian has originally = $S
Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,
Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]
Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]
= [tex]\frac{\text{5S-2S}}{5}[/tex]
= [tex]\frac{3S}{5}[/tex]
Since Dian has $150 left then the equation will be,
[tex]\frac{3S}{5}=150[/tex]
S = [tex]\frac{150\times 5}{3}[/tex]
S = $250
Therefore, Dian has $250 originally.
Related Questions
What linear function defines the following Arithmetic Sequence?
-8, -4, 0, 4, 8, ...
A : an = -8 + 4(n - 1)
B : an= 8 + 4(n - 1)
C : an = -8 - 4(n - 1)
D : an = 8 - 4(n - 1)
Answers
Explanation:
a = -8
d = +4
an = a + ( n - 1 ) d
= -8 + ( n - 1 ) 4
So;
= -8 + 4 ( n - 1 )
The linear equation defines the arithmetic sequence is an = -8 + 4(n - 1). The correct option is A.
What is an arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that, the sequence is -8, -4, 0, 4, 8, ...
a = -8
d = +4
The expression for the nth term will be written as,
an = a + ( n - 1 ) d
= -8 + ( n - 1 ) 4
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Solve the equation for the indicated variable. C=680x/h^2 for x
Answers
Answer:
C h^2 / 680 = x
Step-by-step explanation:
C=680x/h^2
Multiply each side by h^2
C h^2=680x/h^2 * h^2
C h^2=680x
Divide each side by 680
C h^2 / 680=680x/680
C h^2 / 680 = x
That gives you Ch^2= 680x
Second step: divide both sides by 680
That gives you (ch^2)/680=x
Simplify: x= (ch^2)/680
That is the simplest form
The rate of earnings is 6% and the cash to be received in four years is $20,000. The present value amount, using the following partial table of present value of $1 at compound interest, is
Answers
Answer:
$15,842
Step-by-step explanation:
We use the Present value formula
Present Value = Future value/(1 + r)ⁿ
r = 6% = 0.06
n = 4 years
Future value = $20,000
Present value = 20,000/(1 + 0.06)⁴
= $15841.873265
≈ $15,842
Which Graph represents the solution to the compound inequality 4x +8< -16 or 4x + 8 > 4
Answers
Answer:
option 3
Step-by-step explanation:
4x+8<-16
x<-6
4x+8_>-16
x_>-1
(it's more and equal .so the circle has to be shaded and move to the right of -1)
Answer:C
Step-by-step explanation:
Suppose that Vera wants to test the hypothesis that women make less money than men doing the same job. According to the Bureau of Labor Statistics (BLS), the median weekly earnings for men in the professional and related occupation sector in 2015 was $1343. Vera collected median weekly earnings data for women in 2015 from a random subset of 18 positions in the professional and related occupation sector. The following is the sample data. $1811, $728, $1234, $966, $953, $1031, $990, $633, $796, $1325, $1448, $1125, $1144, $1082, $1145, $1256, $1415, $1170 Vera assumes that the women's median weekly earnings data is normally distributed, so she decides to perform a t-test at a significance level of α = 0.05 to test the null hypothesis, H0:µ=1343H0:μ=1343 against the alternative hypothesis, H1:µ<1343H1:μ<1343 , where µμ is the population mean. If the requirements for performing a t-test have not been met, only answer the final question. Otherwise, answer all five of the following questions. First, compute the mean, x⎯⎯⎯x¯ , of Vera's sample. Report your answer with two decimals of precision.
Answers
Answer:
There is sufficient evidence to conclude that women make less money than men doing the same job.
Step-by-step explanation:
The hypothesis for the test can be explained as follows:
H₀: Women does not make less money than men doing the same job, i.e. [tex]\mu\geq \$1343[/tex].
Hₐ: Women make less money than men doing the same job, i.e. [tex]\mu<\$1343[/tex].
From the provided data compute the sample mean and standard deviation:
[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92[/tex]
Compute the test statistic as follows:
[tex]t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143[/tex]
The test statistic value is -3.143.
Compute the p-value as follows:
[tex]p-value=P(t_{n-1}<-3.143)=P(t_{17}<-3.143)=0.003[/tex]
*Use a t-table.
The p-value of the test is 0.003.
The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.
Conclusion:
There is sufficient evidence to conclude that women make less money than men doing the same job.
and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answers
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
Evaluate f(x) when x= 9
f(x) = {6x² +2 if 6
112 if 9
No solution
O 110
O 12
56
Answers
Answer:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
Step-by-step explanation:
For this problem we have the following function given:
[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]
[tex] f(x) = 12 , 9 \leq x <13[/tex]
And we want to evaluate f(x=9)
And for this case the answer would be:
[tex] f(9)= 12[/tex]
Best answer:
O 12
A data set is summarized in the frequency table below. Using the table, determine the number of values less than or equal to 6.
Answers
Answer:
18
Step-by-step explanation:
Given the above table of the data set, the number of values less than or equal to 6 would be the sum of the frequencies of all values that is equal to or less than 6.
From the table above, we would add up the frequencies of the values of 6 and below, which is:
2 + 3 + 6 + 4 + 3 = 18
Answer = 18
The number of values less than or equal to 6 is 18
Calculation of the number of values:Here the number of values should be less than or equivalent to 6 represent the sum of the frequencies i.e. equal or less than 6
So, here the number of values should be
= 2 + 3 + 6 + 4 + 3
= 18
Hence, we can conclude that The number of values less than or equal to 6 is 18
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The lowest temperature ever
recorded on earth was -89°C
in Antarctica. The average
temperature on Mars is about
-55°C. Which is warmer?
Write an inequality to support
your answer
Answers
Answer:
Mars
Step-by-step explanation:
America
During a camping trip, a group went one -third of the total distance by boat, 10km by foot and One – sixth of it by riding horses. Find the total distance of the trip.
Answers
Explanation:
Let d be the total distance
d = (1/3)d + 10 + (1/6)d
(6/6)d = (2/6)d + 60/6 + (1/6)d
6d = 2d + 60 + d
6d = 3d + 60
3d = 60
d = 60/3 = 20
hellllllllppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answers
Answer:
see below.
Step-by-step explanation:
1st row has four small boxes
2nd row has three big boxes
big box 1 has no items ragged in it.
big box 2 has small box 1 and also small box 1 dragged into it.
big box 3 has small box 3 and small box 4 dragged into it.
Drag each tile to the correct box. Order the expressions from least value to greatest value . -3 3/10 - ( -7/20 ), 5/-1.6, 5 6/15 + ( -2 4/5 ), -4.5 x -2.3
Answers
Answer:
B A C D
Step-by-step explanation:
Your calculator can tell you the values of these expressions. In the order given, they are ...
-3 3/10 -(-7/20) = -2.955/-1.6 = -3.1255 6/15 +(-2 4/5) = 2.6-4.5×-2.3 = 10.35We hope you have no trouble recognizing that swapping the first two expressions will put them all in increasing order.
-3 3/10 -(-7/20) = -2.95
5/-1.6 = -3.125
5 6/15 +(-2 4/5) = 2.6
-4.5×-2.3 = 10.35
Find the next two !!!
Answers
It's adding 3 and subtracting 2 every time.
This means the next two terms would be +3 and -2 since the last one was -2.
The next term = 4+3=7
The next next term = 7-2=5
Answer:
Answer : 7 , 5Please see the attached picture.
Hope it helps...
Best regards!!
Find the measure of the indicated angle to the nearest degree.
PLEASE HELP ASAP
Answers
A. 26
B. 42
C. 64
D. 48
Answers
Answer:
The answer is option C
Step-by-step explanation:
To find the indicated angle we use sine
sin ∅ = opposite / hypotenuse
From the question
The opposite is 37
The hypotenuse is 41
So we have
sin ? = 37/41
? = sin-¹ 37/41
? = 64.4805
? = 64° to the nearest degreeHope this helps you
Answer:
C.) 64
Step-by-step explanation:
I got it correct on founders edtell
A packet of candles and box of matches cost #420. The candles cost 20 times as much as the matches
Answers
Answer:
candles = $400
matches = $20
Step-by-step explanation:
Let cost of candles = $c
Let cost of matches = $m
c = 20 m (20 times m)
c + m = 420
20m + m = 420
21 m = 420
m = 20
c = 20 (20) = 400
The triangles are similar. Write a similarity statement for the triangles.
Answers
Answer:
Option (2)
Step-by-step explanation:
In the two triangles ΔWVZ and ΔYXZ,
If the sides WV and XY are parallel and the segments WY and VX are the transverse.
∠X ≅ ∠V [Alternate angles]
∠W ≅ ∠Y [Alternate angles]
Therefore, ΔWVZ ~ ΔYXZ [By AA postulate of the similarity]
Option (2) will be the answer.
I NEED HELP ASAP!!!!!!! Find 2 numbers that multiply to make -24 and add to make -10
Answers
Answer:
Step-by-step explanation:
-8*3= -24+14=-10
Answer:
-12 and 2.
Step-by-step explanation:
-12*2= -24,
-12+2=-10
A triangle has side lengths of 13, 9, and 5. Is the triangle a right triangle? Explain.
Use complete sentences in your explanation.
Hint: Pythagorean Theorem: a^2+ b^2 = c^2
Answers
Answer:
see below
Step-by-step explanation:
Using the Pythagorean Theorem:
a^2+ b^2 = c^2
5^2+ 9^2 = 13^2
25+81 = 169
106 = 169
This is not true so it is not a right triangle
Answer:
[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]
Step-by-step explanation:
Apply Pythagorean theorem to check if the triangle is a right triangle.
[tex]a^2+ b^2 = c^2[/tex]
[tex]5^2+ 9^2 = 13^2[/tex]
[tex]25+81=169[/tex]
[tex]106=109[/tex]
False statement.
The triangle is not a right triangle.
Currently Shawn pays $550 per month to rent his apartment. Next year his rent will increase by 13.5% from what he currently pays . a) find the amount that shawn's rent will increase . b) what will be shawn's new monthly rent?. c) If you divide your answer from (b) by shawn's original rent of $550, what is the decimal result? do you see any connection to part (a)?
Answers
a) Simply do 0.135(13.5%)*550 to get that his rent increases by $74.25.
b) Simply do 550+74.25 to get that his new rent is $624.25.
c) 624.25/550 = 1.135, or 100%+13.5%, the amount his rent increased.
Hope it helps <3
Answer:
A. $74.25
B. $624.25
C. 1.135, and this is a connection to part a because it's what we multiplied 550 by to get our new rent.
Step-by-step explanation:
If Shawn pays $550 per month for rent, and he has a 13.5% increase, we can multiply 550 by [tex]1+\frac{13.5}{100}[/tex] to get our new number.
[tex]1+0.135=1.135[/tex]
[tex]550\cdot1.135=624.25[/tex]
This is the new monthly rent, part B. To find Part A, let's subtract 550 from thi number.
[tex]624.25-550=74.25[/tex]
Now, for part C, let's divide 624.25 by 550.
[tex]624.25\div550 = 1.135[/tex]
If you notice, 1.135 is the same number we multiplied 550 by to get our new cost, and as a percent, 1.135 is 113.5%.
Hope this helped!
what is the constant of proportionality for 4y=16
Answers
Answer:
Step-by-step explanation:
y=4x
find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2
Answers
Answer: A) N'=(-2, 2) M'=(-1, 0) L'=(-5, -2)
Step-by-step explanation:
N = (-2, -4) M = (-3, -2) L = (1, 0)
Reflection over y = -1
N' = (-2, 2) M' = (-3, 0) L' = (1, -2)
Reflection over x = -2
N'' = (-2, 2) M'' = (-1, 0) L'' = (-5, -2)
Find the dimensions of a rectangle with area 512 m2 whose perimeter is as small as possible. (If both values are the same number, enter it into both blanks.)
Answers
Answer:
√512 by √512Step-by-step explanation:
Length the length and breadth of the rectangle be x and y.
Area of the rectangle A = Length * breadth
Perimeter P = 2(Length + Breadth)
A = xy and P = 2(x+y)
If the area of the rectangle is 512m², then 512 = xy
x = 512/y
Substituting x = 512/y into the formula for calculating the perimeter;
P = 2(512/y + y)
P = 1024/y + 2y
To get the value of y, we will set dP/dy to zero and solve.
dP/dy = -1024y⁻² + 2
-1024y⁻² + 2 = 0
-1024y⁻² = -2
512y⁻² = 1
y⁻² = 1/512
1/y² = 1/512
y² = 512
y = √512 m
On testing for minimum, we must know that the perimeter is at the minimum when y = √512
From xy = 512
x(√512) = 512
x = 512/√512
On rationalizing, x = 512/√512 * √512 /√512
x = 512√512 /512
x = √512 m
Hence, the dimensions of a rectangle is √512 m by √512 m
Jackson's robot moved 5 meters in 2 seconds How far did he move in 30 sec? (please explain and use fractions)
Answers
75 meters
Step-by-step explanation:
5 x 30/2
= 5 x 15
= 75 meters
Which inequality is equivalent to this one y-8_<-2
Answers
Answer:
[tex]\boxed{y\leq 6}[/tex]
Step-by-step explanation:
[tex]y-8 \leq -2[/tex]
Adding 2 to both sides
[tex]y \leq -2+8[/tex]
[tex]y \leq 6[/tex]
The function A(b) relates the area of a trapezoid with a given height of 10 and
one base length of 7 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
A(b) = 10.57?
Which equation below represents the inverse function B(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
O A. B(a) = -7
B. B(a) = 9, -5
Answers
Answer:
[tex]B(a)=\frac{a}{5} -7[/tex]
Step-by-step explanation:
The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.
y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),
y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )
Now switch the positions of y and b -
b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,
[tex]y+7=\frac{a}{5}[/tex],
[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]
Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7
Question 16 (5 points)
Given the recursive formula shown, what are the first 4 terms of the sequence?
Answers
Answer:
i think its b
???
Step-by-step explanation:
im sorry if im wrong im not very confident on my answer :(
Answer:
D
Step-by-step explanation:
Most logical looking if you look at the formula, the last number has to be smaller than the one before, so.
The graph shows how the length of time a boat is rented is related to the
rental cost. What is the rate of change shown in the graph?
Boat Rental
AY
440
400
380
320
Cost (dollars)
240
200
100
120
80
40
0
Time (hours)
A. $40/hour
B. $80/hour
C. 80 hours/dollar
D. 40 hours/dollar
Answers
A slope is also known as the gradient of a line is a number. The correct option is B.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The rate of change shown in the graph is the slope of the given line.
Now, to know the slope of the line consider any two points on the line, such as (0,0) and (5,400).
Therefore, the slope of the line can be written as,
Slope, m = ($400 - $0)/(5-0) hour
= $400/5 hour
= $80/hour
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Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Answers
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
What property do rectangles and parallelograms always share?
Answers
Hope this helps!!!!!
find the area under (sin x) bounded by x= 0 and x = 2π and x-axis
Answers
You probably want the unsigned area, which means you don't compute the integral
[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]
but rather, the integral of the absolute value,
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]
[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]