Answers
The missing length is 18
Using Pythagorean rule
Hyp^2 = Opp^2 + adj^2
Opp^2 = hyp^2 - adj^2
Opp^2 = 30^2 - 24^2
Opp^2 = 900 - 576
Opp^2 = 324
Opp = sqrt ( 324 )
Opp = 18
Related Questions
You open a money market account with $7500 at 5% compound quarterly. After two years, $1500 is withdrawn from the account to buy a new computer. A year later, $2000 is put in the account. What will be the ending balance if the money is kept in the account for another three years?
Answers
Answer:
$10,596.81
Step-by-step explanation:
The balance on an account earning 5% interest compounded quarterly can be found using the formula ...
A = P(1 +0.05/4)^(4t)
where P is the principal invested and t is the number of years.
__
Here, we are investing $7500.00. After 2 years, the account balance will be ...
A = $7500(1 +0.05/4)^(4·2) = $8283.65
After the $1500 withdrawal, the new balance will be ...
$8583.65 -1500.00 = $6783.65
__
This is the amount earning interest for the next year, after which time the balance will be ...
A = $6783.65·(1.0125)^(4·1) = $7129.24
When $2000 is added to the account, the principal earning interest for the last 3 years is ...
$7129.24 +2000.00 = $9129.24
__
The final balance after 3 more years is then ...
A = $9129.24·(1.0125)^(4·3) = $10,596.81
_____
These calculations are conveniently carried out by a spreadsheet, as in the attached. Since the account changes are all done at the end of the year, we don't have to keep track of the quarterly balances. The formula used to calculate the ending balance each year is shown.
In a small private school, 16 students are randomly selected from eighteen available students. What is the probability that they are the four youngest students?
Answers
Answer:
1/72
Step-by-step explanation:
16 * 18 = 288
4/288 = 1/72
Roger has 120 peanuts. He saves 48 for himself. He divides the rest equally among 8 friends. He wants to find how many peanuts each friend gets.
Which equations should he use? Select all that apply.
A.
72
÷
8
=
m
B.
120
+
48
=
p
C.
168
÷
8
=
n
D.
120
÷
8
=
l
E.
120
−
48
=
p
Answers
Answer:
A and E MARK BRAINLIEST!
Step-by-step explanation:
Well lets look into this question carefully ,
You should first subtract 120- 48= 72
Then 72/ 8 = 9 so we can check all that apply equations we used
A and E
If told that |A|=48 what are the possible values for X.
Please help!
Answers
If the value of |A| is 48 the possible values for x in the matrix is 4 or -2.
How to use determinant to find a value in a matrix?The determinant of the matrix A is as follows:
|A| = 48
Therefore,
48 = (3x × 2x) - (4x × 3)
48 = 6x² - 12x
6x² - 12x - 48 = 0
3x² - 6x - 24 = 0
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2 -4(x + 2) = 0
(x - 4)(x +2) = 0
Therefore,
x = 4 or -2
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What is the five-number summary of this data set?
{425, 255, 267, 507, 307, 435, 253, 250, 433}
What is the five-number summary of this data set?
{425, 255, 267, 507, 307, 435, 253, 250, 433}
Drag the numbers into the boxes to correctly complete the five-number summary.
Answers
Answer:
min250 max507 Q1=307 Q2=255 Q3=435
Step-by-step explanation:
The five-number summary of this data set is {250, 255, 307, 435, 507}
How to find the mean of a data set?
Mean is the ratio of the sum of the values of the data set to the total number of values available in the data set.
Thus, we get;
[tex]\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}[/tex]
We are given that;
The data set= {425, 255, 267, 507, 307, 435, 253, 250, 433}
Now,
The five-number summary of a data set consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum12.
To find the five-number summary of this data set, follow these steps:
Put the numbers in ascending order: {250, 253, 255, 267, 307, 425, 433, 435, 507}
Find the minimum: The smallest number is 250
Find the maximum: The largest number is 507
Find the median: The middle number is 307
Find Q1: The median of the lower half of the data is 255
Find Q3: The median of the upper half of the data is 435
Therefore, by the mean the answer will be {250, 255, 307, 435, 507}
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#SPJ3
Sarita deposits $1000 in an account paying 3.4% annual interest compounded continuously.
A. What is the balance in Sarita's account after 5 years?
Answers
Considering continuous compounding, it is found that the balance of her account after 5 years is of $1,185.3.
What is the equation for continuous compounding?It is given by:
[tex]A(t) = Pe^{kt}[/tex]
In which:
P is the principal.k is the interest rate.t is the time, in years.In this problem, the parameters are given as follows: P = 1000, r = 0.034, t = 5, hence:
[tex]A(5) = 1000e^{0.034(5)} = 1185.3[/tex]
The balance of her account after 5 years is of $1,185.3.
More can be learned about continuous compounding at https://brainly.com/question/15965736
A crate of a apples that usually cost 40$ is on sale for 20$ off. what is the sale price for the crate of apples?
Answers
Step-by-step explanation:
We are trying to find $40 on sale for 20$ off.
40*20/100
40*0.2
You save=$8
40-8
Final Price=$32
A total of 30000 tickets were sold for a concert of this amont 1/4 were sold for $1500 each 1/3 at $ 1000 each and the rest at $750 each .how many were sold at $750
Answers
Answer:
12,600
Step-by-step explanation:
1/3 = 4/12
1/4 = 3/12
Together they equal 7/12
The different is 5/12
5/12 = .416666 =.42
.42 x 30,000 = 12,600
A bag of chocolates is labeled to contain 0.384 pounds of chocolates. The actual weight of the chocolates is 0.3798 pounds. Are the chocolates heavier or lighter than the weight stated on the label?
Answers
Based on the information given the chocolates stated on the label is 0.0042-ounce lighter.
Weight:
Using this formula
Chocolate weight=Current weight-Actual weight
Where:
Current weight=0.384
Actual weight=0.3798
Let plug in the formula
Chocolate weight=0.384-0.3798
Chocolate weight=0.0042 ounce
In conclusion, the chocolates stated on the label are 0.0042-ounce lighter.
A 25-year, $1,000 par value bond has an 8.5% annual coupon. The bond currently sells for $875. If the yield to maturity remains at its current rate, what will the price be 5 years from now?
Answers
Given the current yield to maturity of the bond, the price of the bond five years for now is $883.10.
What is the price of the bond five years from now?The first step is to determine the yield to maturity of the bond. The yield to maturity is the return on the bond if the bond is held to matuity.
Yield to matuity can be determined using a financial calculator:
Cash flow in year 0 = -875
Cash flow each year from year 1 to 25 = 85
Cash flow in year 25 = $1000
Yield to matuity = 9.86%
Future price of the bond: (coupon x future price factor) + [FV / (1 + YTM)^n)]
Future price factor = [1 - (1/YTM)^n] / YTM
= [1 - 1/0.0986^20] 0.0986 = 8.595555
[85 x 8.595555 ] + 152.478323 = $883.10
To learn more about yield to maturity, please check: https://brainly.com/question/26484024
Question
Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−1/3+4
Answers
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
perpendicular to the line described by : y = -1/3 x +4
So : product for two slopes = -1 means : m×-1/3=-1
m = 3
now : y = 3 x+b
but this line :
through the point (4,3) : 3 =3(4)+b....... b=-9
conclusion :
the equation is : y =3x -9
125% of what number is 80?
Oa 36
Oь 40
Os 64
Od 72
Answers
Answer:
d. 72
Step-by-step explanation:
Answer :D
64
Step-by-step explanation:
We have, 125% x x = 80
or [tex]\frac{125}{100}[/tex] x x = 80
Multiplying both sides by 100 and dividing both sides by 125,
we have x = 80 x [tex]\frac{100}{125}[/tex]
x = 64
(or just divide 80 x 100 ÷ 125)
Hope this helps - Answered by Lilo
Find the average of this set of numbers.2, 5, 6, 14, 83
A) 22
B) 20
C) 19
D) none of the above
Answers
the answer is D i added then subtracted
Christy bought a 9- foot piece of lumber trim bookshelf. Altogether, she needs 100 inches of lumber. Did Christy buy enough lumber? Show your work and explain.
Answers
Answer:
Yes.
Step-by-step explanation:
because 9 feet converted to inches equals 108 inches, we know this because we can convert feet to inches via multiplication. To do this, simply multiply the given number (9) by 12 to get your answer.
logariths, please help
Answers
Answer:
{ - 2 , 8 }
Step-by-step explanation:
[tex]log_{4}[/tex] ( x² - 6x ) = 2
4² = ( x² - 6x )
x² - 6x - 16 = 0
- 6 = - 8 + 2
- 16 = - 8 * 2
( x - 8 )( x + 2 ) = 0 ⇒ [tex]x_{1}[/tex] = - 2 , [tex]x_{2}[/tex] = 8
{ - 2 , 8 }
Factor the equation k^2 + 25
Answers
Answer:
k^2+25
Step-by-step explanation:
Factor k^2+25
=k^2+25
Doesn't factor
one way to test if a graph is a function or not is by doing a?
Answers
One way to test if a graph is a function or not is by doing a vertical line test.
The vertical line test is tested by testing if any vertical line is drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function, if there isn't any such line, the graph is a function.
Hope that helps!
Answer:
Vertical line test. (literally what it say)
Step-by-step explanation:
Given a graph, use the vertical line test to determine if the graph represents a function. Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
Therefore you would have x value being the same for several points.
PLEASE HELP
Use the function f(x) to answer the questions.
f(x) = −16x2 + 22x + 3
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Answers
First graph
y=-16x^2+22x+3(Graph attached)#A
Use quadratic formula
[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm\sqrt{484+192}}{-32}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm\sqrt{676}}{-32}]/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-22\pm 26}{-32}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-1}{8}\:or\:\dfrac{3}{2}[/tex]
[tex]\\ \rm\rightarrowtail x=-0.125\:or\:1.5[/tex]
#B
Vertex will be maximum
Coordinates are
(0.688,10.563)#C
We have to find x intercepts (Part A)Then vertex(Part B)Then we can graph it[tex]\sf f(x) = -16x^2 + 22x + 3[/tex]
Part A
To find x-intercepts, the f(x) will be 0
[tex]\sf \hookrightarrow -16x^2 + 22x + 3=0[/tex]
[tex]\sf \hookrightarrow -16x^2 + 24x -2x+ 3=0[/tex]
[tex]\sf \hookrightarrow -8x(2x-3)-1(2x- 3)=0[/tex]
[tex]\sf \hookrightarrow (-8x-1)(2x+ 3)=0[/tex]
[tex]\sf \hookrightarrow -8x-1=0 , \ 2x+ 3=0[/tex]
[tex]\sf \hookrightarrow x=-0.125 , \ x=1.5[/tex]
find y-intercept:
to find y-intercept, x will be 0
[tex]\sf f(x) = -16(0)^2 + 22(0) + 3[/tex]
[tex]\sf f(x) = 3[/tex]
Part B
To find vertex use the formula: x = -b/2(a)
[tex]\sf \rightarrow x = \dfrac{-22}{2(-16)}[/tex]
[tex]\sf \rightarrow x = 0.6875[/tex]
find y coordinates:
[tex]\sf f(x) = -16(0.6875)^2 + 22(0.6875) + 3[/tex]
[tex]\sf f(x) =10.5625[/tex]
coordinates of vertex: (0.6875, 10.5625)
[tex]\bold{\mathrm{If}\:a < 0,\:\mathrm{then\:the\:vertex\:is\:a\:maximum\:value}}[/tex][tex]\bold{\mathrm{If}\:a > 0,\:\mathrm{then\:the\:vertex\:is\:a\:minimum\:value}}[/tex]As its positive and greater than 0, the vertex will be Maximum.
part C
To draw the graph, simplify point the vertex on the graph. Then point both the x-intercepts. Also the y-intercept and draw the curve with free hand.
Graph attached:
what is 1.5 +1.5 in a fraction
Answers
Therefore, 1.5 as a fraction is written 3/2.
Answer:
3/1
Step-by-step explanation:
1.5+1.5
calcular los dos primeros términos
3
escribe el número entero como una fracción
3/1
2. A student wanted to find the height h of a statue of a pineapple
in Nambour, Australia. She measured the pineapple's shadow
and her own shadow. The student's height is 5 feet 4 inches.
What is the height of the pineapple?
Answers
Using proportions, it is found that the height of the pineapple is of 280 inches = 23 ft 4 in.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, considering that a feet has 12 inches, the measures in inches, and applying the similarity of triangles, the proportions are as follows:
[tex]\frac{h}{64} = \frac{105}{24}[/tex]
Applying cross multiplication:
24h = 64 x 105
h = 64 x 105/24
h = 280
The height of the pineapple is of 280 inches = 23 ft 4 in.
More can be learned about proportions at https://brainly.com/question/24372153
solve picture question
Answers
Answer:
As it ایس the correct answer is 45
78
7.90
Answer:
Its me Viktor Kozhanov may I have brainliest pleaseI also answered all you questions so give brainliest to those as well
Step-by-step explanation:
Each of two computers can process bills at 160/min a newer model can process bills at 200/min after the first two computers have worked 1.5 min they are joined by the third computer how long will it take fromthe time the first two computers are turned on to process 1780
Answers
HELP ME OUT PLS!!!!!!!
The model represents an equation. What value of x makes the equation true?
A) 15/4
B) 15/8
C) -15/4
D) -15/8
Answers
Answer:
B
Step-by-step explanation:
-6x + 6 = 2x - 9
-6x + 15 = 2x
15 = 8x
x = 15/8
What is the division expression that is the same as 1/5 x 1/4?
A. 1/5÷4
B. 1/5÷5
C. 1/5÷3
D. 1/5÷2
Answers
[tex]=================================[/tex]
Option A is correct & here's why.
When dividing fractions, we take the first fraction and multiply it times the reciprocal of the second fraction (the second fraction flopped over)
So if we have 1/4, then its reciprocal is 4/1, or just 4.
Hence, Option A (1/5÷4) is correct.
[tex]==============================[/tex]
Notes:Hope everything is clear & let me know if you have any questions!Enjoy your day!Always remember: Knowledge is Power! :-)Answered by:~DiamonD~
PLEASE HURRY AND HELP ME WITH THIS !! ILL GIVE BRAINLIEST
Answers
Answer:
C. Reflection, translation
Step-by-step explanation:
If we compare Figure A to Figure B, you might notice that they mirror each other. This means that Figure A was reflected. Now, if we take a look at Figure B and Figure C, you should see that both figures are the exact same shape, size, and facing the same direction. The only thing that changed was the location. So, this means that Figure B was translated.
I hope this helps! Have a lovely day!! :)
Triangle B is reflected over the y axis which mirrors Triangle A, and Triangle C is translated over the x axis.
Mathematics pls help 4 questions will give brain to best answer
What is the mean for the data set, to the nearest whole number?
Answers
Answer:
[1] 8
[2] 10
[3] 8.5
[4] 8
Step-by-step explanation:
[1] What is the mode of the data set?
5,8,8,8,8,9,9,9,10,10
Answer = 8
Explanation: Mode = Appears Most
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[2] How many people were in the sample?
Answer = 10
Explanation:
Each x = 1 person
Hence, it a total of 10 "x" (10 People)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[3] What is the median of the data set?
5,8,8,8,8,9,9,9,10,10
Answer = 8.5
Explanation:
Median = Middle
5,8,8,8,8,9,9,9,10,10
5,8,8,8,8,9,9,9,10,10
8 + 9 = 17/2 = 8.5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[4] What is the mean for the data set, to the nearest whole number?
Answer = 8
Explanation:
Mean = Add up all data values to get the sum and Count the number of values in your data set. Divide the sum by the count
5 + 8 + 8 +8 + 8 + 9 + 9 + 9 + 10 + 10 = 84/10=8.4
8.4 Round = 8
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~Lenvy
Angle α is drawn on the unit circle in standard position. The terminal side of angle α intersects the unit circle at point (-0.292, 0.956). What is the approximate decimal value of tan(α)?
Answers
Using the unit circle, it is found that the approximate decimal value of tan(α) is given by -3.274.
What is the unit circle?For an angle [tex]\alpha[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\alpha}, \sin{\alpha})[/tex].
In this problem, we have point (-0.292, 0.956), hence [tex]\cos{\alpha} = -0.292, \sin{\alpha} = 0.956[/tex].
Applying the definition of the tangent, we have that:
[tex]\tan{\alpha} = \frac{\sin{\alpha}}{\cos{\alpha}} = \frac{0.956}{-0.292} = -3.274[/tex].
Hence the second option is correct.
More can be learned about the unit circle at https://brainly.com/question/16852127
The answer: -3.274.
Hope you got it right! :)
PLSSS HELP WHOEVER DOES THE CORRECT WILL GET BRAINLIEST
Ray is x years old. His brother Ron is y years older than Ray.
How old was Ray 3 years ago?
Answers
Answer: x-3
Step-by-step explanation:
It’s a variable
*Pls help me*
Yasmine is trying to find an outfit for the first day of school. She has to choose from 3 pairs of skirts: one black, one pink and one orange. She also has five blouses: one with flowers, one with polka-dots, one gray, one white and one with words saying I love New York! How many possible outfits can she choose from? *Hint-create a probability table.
Answers
Answer:
15 outfits
Step-by-step explanation:
Given
3 skirtsone blackone pinkone orange5 blousesone w/ flowersone w/ polka dotsone grayone whiteone w/ "I love New York!"Probability : No. of outfits
There are 3 elements in set A (skirts) and 5 elements in set B (blouses)Therefore possible outfits = A x B = 15 outfitsP.S. Sorry I couldn't create the probability table.
George wanted to measure the angle of a water slide at the lake. He used a sheet of folded paper that formed a 20° angle. He measured and found that three of the folded paper angles would fit in the angle made by the slide and the ground.
Which of the following was the angle of the water slide?
Answers
The angle of the water slide is 60 degrees.
The equation that models his work is 3 × 20 = 60 degrees.
How to find the sum of angles of a figure/object?
He wants to measure the angle of a water slide at the lake.
He used a sheet of folded paper that formed 20 degrees to measure the angle of the the water slide at the lake.
He noticed three folded paper angle fits in the angle made by the slide and the ground.
Since each angle is equals to 20 degrees, and the three fits into the angle made by the slide and the ground, the angle of the water slide is as follows:
20 × 3 = 60 degrees
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