The kinetic energy possessed by the skydiver is 14, 062. 5 Joules
What is kinetic energy?Kinetic energy of an object is defined as the energy possessed by an object due to its motion.
It is also described as the work that is required to accelerate a body of mass from rest to its given velocity.
The formula for calculating kinetic energy is expressed as;
Kinetic energy = 1/2 mv²
Where;
m is the mass of the objectv is the velocity of the objectNow, substitute the values
Kinetic energy = 1/2 (45)(25)²
Find the square
Kinetic energy = 1/2 (45)(625)
Find the product
Kinetic energy = 1/2(28125)
Find the quotient
Kinetic energy = 14, 062. 5 Joules
Hence, the value is 14, 062. 5 Joules
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mr.ocampo invested 150,000 at 10% compounded annually. he plans to get this amount for 6 years for his son's college education, how much will he get?
The most appropriate choice for compound interest will be given by -
Mr Ocampo recieves 265734.15
What is compound interest?
If the interest on a certain principal increases over a period of time at a certain rate exponentially rather than linearly, then the interest is called compound interest.
If P is the principal, r is the rate and n is the time in years,
Amount (A) = [tex]P(1 +\frac{r}{100})^n[/tex]
Principal invested by Mr. Ocampo = 150000
Rate = 10%
Time = 6 years
Amount recieved by Mr.Ocampo = [tex]150000(1+\frac{10}{100})^6[/tex]
[tex]150000(1 + \frac{1}{10})^6\\150000(\frac{10+1}{10})^6\\150000(\frac{11}{10})^6[/tex]
265734.15
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You borrow $90,000 for college at an APR of 6.25%. You plan to elect 25-year repayment. How much more must you repay in total if your loan is unsubsidized, as opposed to being subsidized?
Answer:
Step-by-step explanation:
If x = 3, y = 6, then cos e equal to:
The cosine of an angle theta in a right triangle is given by its adjacent side divided by the hypotenuse:
[tex]\cos \theta=\frac{x}{r}[/tex]We don't know the value of r but with x, y and the Pythagorean Theorem we can find it:
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2}=\sqrt[]{3^2+6^2}=\sqrt[]{9+36}=\sqrt[]{45} \\ r=6.71 \end{gathered}[/tex]Then the cosine we are looking for is:
[tex]\cos \theta=\frac{x}{r}=\frac{3}{6.71}=0.45[/tex]Then the correct option is the second one since:
[tex]\frac{\sqrt[]{5}}{5}=0.45[/tex]The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately Normal with mean μ = 300 and standard deviation σ = 35. (a) Choose one 12th-grader at random. What is the probability that his or her score is higher than 300? Higher than 335? Explain and show your work. (b) Now choose an SRS of four 12th-graders and calculate their mean score x. If you did this many times, what would be the mean and standard deviation of all the x-values? Explain and show your work. (c) What is the probability that the mean score for your SRS is higher than 300? Higher than 335? Explain and show your work.
a) To find the probability that the score is higher than 300 you have to find the Z-score for 300, by using the formula:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{300-300}{35}=\frac{0}{35}=0 \end{gathered}[/tex]The probability of x>300 P(z>0)=1-P(z<=0)
Using the Standard Normal Cumulative Probability Table, P(z<=0)=0.5
Then,
[tex]P(Z>0)=1-0.5=0.5[/tex]Now, you can do the same to find the probability that the score is higher than 335, let' see:
[tex]Z=\frac{335-300}{35}=\frac{35}{35}=1[/tex]The probability of x>335 is P(Z>1), then
[tex]P(Z>1)=1-P(Z\leq1)=1-0.8413=0.1587[/tex]These results mean that it is a 50% of probability that the score of the student chosen is greater than 300, and a 15.87% of probability that the score is greater than 335.
b) SRS=4, their mean score will be the same as the mean of the population = 300, the standard deviation of the sample is the standard deviation of the population divided by √n (n is the size of the sample=4).
[tex]\mu=300\text{ and }\sigma=\frac{35}{\sqrt[]{4}}=17.5[/tex]c) The probability that the mean score for the SRS is higher than 300 is:
[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{300-300}{17.5}=\frac{0}{17.5}=0 \end{gathered}[/tex][tex]P(Z>0)=1-P(Z\leq0)=1-0.5=0.5[/tex]The probability that the mean score for the SRS is higher than 335 is:
[tex]Z=\frac{335-300}{17.5}=2[/tex][tex]P(Z>2)=1-P(Z\leq2)=1-0.9772=0.0228[/tex]These results mean that it is a 50% of probability that the mean score of the SRS is greater than 300, and a 2.28% of probability that the mean score is greater than 335.
What is the negation of "Everybody loves somebody sometime"
Answer:
Everybody hates somebody sometimes.
Or Not everybody loves somebody sometime
Step-by-step explanation:
Consider the equation 2 (ax+ 3) = 4x- 3 (4x+ 8). For what value of a is there no solution to the equation?
The equation given is,
[tex]2(ax+3)=4x-3(4x+8)[/tex]Solving for a
Expand the terms
[tex]\begin{gathered} 2\times ax+2\times+3=4x-3\times4x-3\times+8 \\ 2ax+6=4x-12x-24 \\ 2ax+6=-8x-24 \end{gathered}[/tex]Comparing the two sides of the equation
[tex]2ax=-8x[/tex]Divide both sides by 2x
[tex]\begin{gathered} \frac{2ax}{2x}=-\frac{8x}{2x} \\ a=-4 \end{gathered}[/tex]Hence, the value of a for which there is no solution to the equation is
[tex]a=-4[/tex]write the ratio that represents the number of cars to total numbers of vehicles.A) 3/2B) 2/3C) 1/2D) 2/1
This is a simple question to be solved.
First we need to know the number of vehicles (there are 6 vehicles), and second we need to know the number of cars (there are 4 cars). So the relation between the number of cars and vehicles is ----> 4/6
But we can simplify this relation as follows and represent it in a simple way:
So the final answer is the letter B) 2/3
Suppose it took 19 riders a total of 11 days and 21 hours to ride from New Jersey to Virginia. If they all rode the same number of hours, how many hours did each rider ride?
Answer:
15 hours
Step-by-step explanation:
24 hours= 1 day
11 times 24 = 264
264 + 21 =285
285 dived by 19 = 15
each rider rode 15 hours
riya won a LCD TV in amall raffle draw , the tv screen measures 16 inches in height and 12 inches in width. find the hypotenuse of the TV
So far, Benny has run 3/2 miles, but that is only 2/5 of his total running distance. What is his total running
distance?
Step-by-step explanation:
this is 2/5 of his total.
that means we have to divide it by 2 (that delivers 1/5) and multiply by 5 (that delivers 5/5 or 1 = the whole).
in short : multiply by 5/2
3/2 × 5/2 = 15/4 miles = 3 3/4 miles
Graph the line y 3 on the axes shown below. Type of line: Choose one
We need to graph the line:
[tex]y=3[/tex]Notice that there is no restriction on the values of x. So, all the points with y-coordinate 3 belong to that line.
When we graph that line, we obtain:
Thus, this line is a horizontal line (parallel to the x-axis).
* I didn’t mean to choose 1 * I really need help because I don’t know how to solve this …
Okay, here we have this;
Considering the provided graph, we are going to calculate the requested height, so we obtain the following:
So to calculate the height of the trapezoid, we will replace in the area formula with the given information, so we have:
A=(b1+b2)h/2
10 ft²=(7ft+3ft)h/2
10 ft²*2=(10 ft)h
20 ft²=(10 ft)h
h=20 ft²/10 ft
h=2 ft
Finally we obtain that the height of the ramp is 2ft, then the correct answer is the second option.
angela spends $95 to buy 7 cakes for the office party. she cuts each cake into quarters, then cuts each quarter into 3 pieces. if kevin eats 5 pieces of cake during the party, how much did engela spend on just kevins share of the cake
If Angela spent $95 to buy 7 cakes for her office party, and she then cut each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces, then Angela had spent $5.65 on just the share of the cake that Kevin had.
As per the question statement, Angela spends $95 to buy 7 cakes for her office party, and she then cuts each cake into quarters and each quarter into further 3 pieces, of which Kevin ate 5 pieces.
We are required to calculate the amount Angela had spent on just the share of the cake that Kevin had.
To solve this question, first let us calculate the total number of pieces, did Angela cut all the 7 pieces of the cake into.
Considering one piece, that it was first cut into a quarter and then each quarter into further 3 pieces, one single piece out of original 7 pieces was cut into a total of [(4 * 3) = 12] pieces.
Therefore, all the 7 original pieces were altogether cut into a total of
[(7 * 12) = 84] pieces.
Now, since Angela spent $95 to buy the original 7 pieces,
Or, Angela actually spent $95 to buy 84 pieces of cake,
Then, 1 piece of the 84 costs $(95/84) = $1.13.
Now, since Kevin ate 5 such pieces of the 84, those 5 pieces cost
$(1.13 * 5) = $5.65.
Therefore, Angela had spent $5.65 on just the share of the cake that Kevin had.
Quarter: In Mathematics, when one whole of anything is divided into 4 equal parts, every part is known as a quarter.To learn more about Quarters, click on the link below.
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Write the relation as a set of ordered pairs.
A relation. An arrow goes from negative 2 to 4, 0 to 6, 2 to 8.
a.
ordered pairs: {(4, –2), (0, 6), (2, 8)}
b.
ordered pairs: {(–2, 4), (0, 6), (2, 8)}
c.
ordered pairs: {(4, –2), (0, 6), (8, 2)}
d.
ordered pairs: {(–2, 4), (6, 0), (8, 2)}
Its not c.
The set of coordinate pairs that represents the relation is the one in option b.
{(–2, 4), (0, 6), (2, 8)}
How to write the relation as a set?
A relation maps elements "x" into elements "y", such that the notation used is:
An arrow that goes from x to y.A ordered pair fo the form (x, y)Here we know that:
An arrow goes from negative 2 to 4, 0 to 6, 2 to 8.
Then we have the coordinate pairs:
(-2, 4)
(0, 6)
(2, 8)
Then the correct option is B: {(–2, 4), (0, 6), (2, 8)}
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Answer:
b
Step-by-step explanation:
in July Leia sold 32 fruit bars what was her profit
write the place value of 8 in 15.0008
Help , stuck on this one .
Answer:
D. -87 + 33i
Step-by-step explanation:
(7 + 5i)(-6 + 9i)
7(-6 + 9i) + 5i(-6 + 9i)
-42 + 63i + -30i + 45i²
-42 + 33i + 45(-1)
-42 + 33i - 45
-87 + 33i
I hope this helps!
What is twelve hundredths as a fraction
ANSWER
[tex]\frac{12}{100}[/tex]EXPLANATION
Now, imagine you are to divide something into 100 equal sections;
the 12th section of those sections is the twelve hundredths.
To represent this as a fraction we have 12/100.
Hence, the twelve hundredths as a fraction is 12/100.
PLEASE HELP!!
A fair die is rolled 4 times. What is the probability of having no 1 and no 3 among the rolls? Round your answer to three decimal places.
Answer:
66.667%
Step-by-step explanation:
In a fair die, there are 6 possible rolls. Out of the 6, 1 number is chosen each time. Since orde does not matter in this problem, we will be applying combination, so this would be written as 6C1 x 4. In order to exclude 3 and 4, from 6, the choices must be narrowed down to 4. Written out as an equation, this would be 4C1 x 4. To get the percentage, simply divide the two equations.
(4C1 x 4)/(6C1 x 4) = 0.66667 = 66.667%
hope it will be helpful
Solve 4|x + 7| = 24.
O A. x= -13 and x = -1
OB. x = 13 and x = -1
O C. x= 13 and x = -13
OD. x= -13 and x = 1
Owen, Caden, and Luke played basketball. Owen scored 26 more points than Caden, who scored 68 points. Luke scored half of the total of Owen and Caden's score. How many points did Luke score?
Please give an explanation! Whoever answers first and correctly gets brainlist!!
Answer:
81
Step-by-step explanation:
68+26=94+68=162/2=81
A client is ordered 30 mg of Lovenox by subcutaneous injection.150 mg in 1 ml of liquid for SQ Injection available. How many ml will you administer?
For this question we just need to use a simple rule of three as follows:
As we can see above, the rule of three solves the question "if we have 150mg for 1ml so how much do we have for 30 mg". So the final answer is 0.2 ml.
Eric received a $35.50 gift card for a photo center. He used it to buy prints that cost 6 cents each. The remaining balance, B (in dollars), on the card after buying x prints is given by the following function.
B (x) = 35.50 - 0.06x
What is the remaining balance on the card if Eric bought 40 prints?
Answer:
B(x) = 40.00 - 0.08x
Step-by-step explanation:
5 1 point The following table shows the relationship between the federal taxes owed and the adjusted gross income. Adjusted Gross income Federal tax 16,500 2,475 19,500 2,925 24,000 3,600 Find the tax rate and calculate the amount of federal taxes owed for 31,000. Type your answer... Prbvious
The answer is very simple
The federal tax rate is the relation between federal tax and the adjusted grooss income
[tex]\text{federal tax rate = }\frac{2475}{16500}=0.15[/tex]and the federal tax for 31000 is
[tex]\text{federal tax = 31000}\cdot0.15=4650[/tex]That is the solution.
A bag contains 6 red marbles and 7 white marbles. Two marbles are drawn in succession without replacement. Find the probabilities of the following events:
1. The first marble drawn is red and the second is white.
2. Both marbles drawn are red.
Using it's concept, the probabilities are given as follows:
1. Red then white: 7/26.
2. Both red: 5/26.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
For item 1, we have that:
For the first marble, the probability of it being red is of 6/13, as of the 13 marbles, 6 are red.Supposing that the first marble is red, the probability of the second being white is of 7/12, as of the 12 remaining marbles, 7 are white.Hence the probability is:
6/13 x 7/12 = 7/26.
For item 2, we have that:
For the first marble, the probability of it being red is of 6/13, as of the 13 marbles, 6 are red.Supposing that the first marble is red, the probability of the second being red is of 5/12, as of the 12 remaining marbles, 5 are red.Hence the probability is:
6/13 x 5/12 = 5/26.
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If Sally has 5 apples, 4 oranges, 3 bananas, 2 grapes, and a plum, how many people does it take to screw in a lightbulb?
Some responses are incorrect. They overlooked the fact that we must eventually add up the cost of one banana.
1 Apple = 7
5 + 7 Equals 12 grapes in a bunch.
After substituting the preceding variables, we arrive to the result that 1 banana equals 2 (7 = 1 + 3 bananas). 21 is incorrect
The second equation has 12 grapes, therefore after solving it, we obtain 1 grape = 1.
However, the final equation has 11 grapes, so we end up with (7+11+2)=20.
Eric, counting the grapes was difficult
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complete question:
If Sally has 5 apples, 4 oranges, 3 bananas, 2 grapes, and a plum, how many people does it take to screw in a lightbulb?
4% of a number is what fraction of that number?
First, let's remember how we calculate a percentage:
If we call the number "x", 4% is calculated by dividing x by 100 and then multiplying by 4:
[tex]\frac{x}{100}\times4[/tex]This can also be represented as follows:
[tex]\frac{4}{100}\times x[/tex]Thus, 4% of a number is 4/100 of that number. We can still simplify this result as follows:
[tex]\frac{4}{100}=\frac{1}{25}[/tex]We divide 4 by 4 and get 1, and also divide 100 by 4 and get 25.
Answer: 4% of a number is 1/25 of that number.
Jeriel is going to invest $640 and leave it in an account for 5 years. Assuming the
interest is compounded annually, what interest rate, to the nearest tenth of a percent,
would be required in order for Jeriel to end up with $760?
Using the compounding formula we can conclude that approximately a 3% of interest rate would be required in order for Jerial to end up with $760.
What is a compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit. It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it so that interest is earned the following period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.So, the principal amount is $640 and the obtained amount is $760.
Compounded annually for 5 years.Then the interest rate will be:
3.497%Rounding off to the nearest tenths: 3%(Refer to the image attached below for calculation)
Therefore, using the compounding formula we can conclude that approximately a 3% of interest rate would be required in order for Jerial to end up with $760.
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helpppp plsssssssss
..........................................
Answer:
D. An infinite number of real solutions
Step-by-step explanation:
3(2x + 1) = 2(3x + 5) - 7
6x + 3 = 6x + 10 - 7
6x + 3 = 6x + 3
I hope this helps!
the cost of 12 hot dogs and 8 fry portions is £52. The cost of 8 hot dogs and 12 fry portions is £48. What is the total cost of a hot dog and a portion of fries?
Answer:
Hot dogs cost £3 and fry's cost £2.
Total cost £5.
Step-by-step explanation:
Let a hot dog cost £x and a portion of fry's cost £y.
Then:
12x + 8y = 52
8x + 12y = 48
Simplifying these 2 equations we get:
3x + 2y = 13 ---------- (A)
2x + 3y = 12...............(B)
multiply the first equation by 2 and the second by 3:
6x + 4y = 26
6x + 9y = 36
Subtracting:
0 - 5y = -10
y = -10/-5 = 2.
Now, substituting in equation (A):
3x + 2(2) = 13
3x = 9
x = 3.