Answer:
David is 55 years old
Morgan is 23 years old
__________________________________________________________
Step-by-step explanation:
Let the age of David = x years
Let the age of Morgan = y years
We are Given:
The sum of David and Morgan's age is 78
7 years ago, David's age was 3 times Morgan's age
__________________________________________________________
Making the equations:
from the first statement, the sum of their ages is 78
So, we can write it as:
x + y = 78
from the second statement,7 years ago, David's age was 3 times Morgan's age
David's age 7 years ago = (x - 7)
Morgan's age 7 years ago = (y-7)
So, we can write the equation as:
(x - 7) = 3(y - 7)
which can be simplified to:
x = 3y - 14
__________________________________________________________
Solving the equations:
We have the 2 equations:
x + y = 78x = 3y - 14from the first equation, we can say that:
x = 78 - y
Using this value in the second equation:
x = 3y - 14
78 - y= 3y - 14 [since x = 78 - y]
78 + 14 = 4y
4y = 92
y = 23
Using this value in the first equation:
x + y = 78
x + 23 = 78 [since y = 23]
x = 55
__________________________________________________________
The Age of David and Morgan:
Since we assigned x to the age of David:
David is 55 years old
We assigned y to the age of Morgan. So,
Morgan is 23 years old
Find the missing side lengths leave your answerss as radicals
Answer:
a= 5[tex]\sqrt{2}[/tex]
b=5
I’m not very good at math, anyone can answe this plz and thanks
Answer:
B
Step-by-step explanation:
Answer:
If it is asking for the total of both then it should be 6 1/4
Step-by-step explanation:
I added 4 3/4 and 1 1/2
what is the image of (6,-6) after a dilation by a scale factor of 4 centered at the origin
9514 1404 393
Answer:
(24, -24)
Step-by-step explanation:
Dilation centered at the origin multiplies each coordinate by the dilation factor.
image = 4 × (6, -6)
image = (24, -24)
when
a
=
4
a
=
4
AND
B
=
6
B
=
6
what is the value of
7
a
+
b
2
÷
9
7
a
+
b
2
÷
9
Answer:
12
Step-by-step explanation: A - A = B and B - 8 = 12
HEEEEEEEEEEELLLLLLLPPPPP PLEASE );
Kingston deposited $90 in a savings account earning 6% interest, compounded annually. To the nearest cent, how much will he have in 2 years?
Answer: 101.12
Step-by-step explanation: This answer is rounded to the nearest cent. The other is not, and will count it wrong.
1. Jake makes $11.15 per hour and works for 28 hours. What is his
straight-time pay? (Financial 1.1)
SHOW YOUR WORK
Answer:
$312.2
Step-by-step explanation:
Given that:
Amount earned per hour = $11.15
Number of hours worked = 28 hours
Straight time pay is the total amount earned in a given pay period. Hence,
Starlight time pay earned during the period he worked will be :
Amount per Hour * number of hours
$11.15 * 28 = $312.2
Question 8 » Our galaxy, the Milky Way, has a diameter of about 1* 1021 meters. The largest galaxy known to man, the IC 1101, has a diameter of 5 * 1022 meters. The diameter of the IC 1101 is about how many times greater than the diameter of the Milky Way? Milky Way: 1x 1021 m IC 1101: 5 x 1022 m 5 50 5,000 500
Answer:
the Milky Way, has a diameter of about 1x10^21 meters. the largest galaxy known to man, the ic 1101, has a diameter of 5x10^22 meters.
Step-by-step explanation:
In each month, the proportion of ‘Prize’ bonds that win a prize is 1 in 11,000. There is a large number of prizes and all bonds are equally likely to win each prize.
(a) Show that, for a given month, the probability that a bondholder with
5000 bonds wins at least one prize, is 0.365, correct to 3 significant figures.
(b) For a given month, find the probability that, in a group of 10 bondholders
each holding 5000 bonds, four or more win at least one prize
Answer:
Step-by-step explanation:
Given that:
The proportion of price bonds that wins a prize is 1 in 111000
The probability of winning at least one prize = 1 - Probability of winning no prize at all.
Probability of winning at least one prize = [tex]1 - \bigg (\dfrac{10999}{11000} \bigg)^{5000}[/tex]
Probability of winning at least one prize = 1 - 0.9999090909⁵⁰⁰⁰
Probability of winning at least one prize = 1 - 0.635
Probability of winning at least one prize = 0.365
Since this question follows a binomial distribution with the probability of p = 0.365 and number of sample n = 10
Then; the probability of four or more will win at least one prize can be computed as follows:
[tex]= \sum \limits ^{10}_{x=4} \bigg( ^{10}_{x} \bigg)(0.365)^x (1- 0.365)^{10-x}[/tex]
[tex]= \bigg( ^{10}_{4} \bigg)(0.365)^4 (0.635)^{10-4}[/tex]
[tex]= \bigg( \dfrac{10!}{4!(10-4)!} \bigg)(0.365)^4 (0.635)^{6}[/tex]
[tex]= 0.244[/tex]
4) Adult tickets for the evening show at XD Theater are $11 and children's tickets are $Belf the theater seats 250 people, how many adult tickets must be sold for $2.300 of total sales? Answer: adult tickets
Omitted value: The price of children ticket was omitted in the question, so i used $8 to solve. You can input the correct value and solve the same way following the steps.
Answer: 100 adult tickets must be sold.
Step-by-step explanation:
step 1
let x represent Adults
AND y represent children
Since the theater seats 250 people we have that
x+y = 250..... equation 1
Also price for Adult ticket = $11
and price children ticket =$8
With total sales at $2,300, we have that
11x + 8y= 2300----- equation 2
Step 2
Making y subject in equation 1
' x+y = 250
y= 250-x
Putting y= 250- x in equation 2
11x + 8(250-x)= 2300
11x +2000-8x= 2300
11x -8x = 2300-2000
3x= 300
x 300/3
x= 100.
To find y
x+y = 250
100+y=250
y=250-100
y=150
Therefore 100 adult tickets and 150 children tickets must be sold to get a total sales of $2,300
Give the slope between the points
(-2,0) (-11,-4)
Answer:
Step-by-step explanation:
12,12
Answer:
The slope is 4/9
6 cm
8 cm
8 cm
12 cm
The perimeter of the polygon above is
Answer:
12 cm !!!
hope you mark me bainliest or your friend
Which of the following is equal to 5 1/3?
During a jump, a sky diver reaches terminal velocity. Which forces are in effect during a sky dive, and are they balanced or unbalanced when the jumper is at terminal velocity?(1 point)
Unbalanced. The force of gravity is stronger than the force of air resistance, which is why the sky diver is falling.
Balanced. The forces of gravity, air resistance, and speed are all in balance.
Balanced. The force of gravity is balanced with the force of air resistance.
Unbalanced. The force of air resistance is stronger than the force of gravity, which is why the sky diver is at terminal velocity.
Answer:
1.) Unbalanced
Step-by-step explanation:
have a great day
3{[3(9 – 2)] + [7(8 – 1)]}
Based on the position vs. time graph, which velocity vs. time graph would correspond to the data? A graph with horizontal axis time (seconds) and vertical axis position (meters). A line runs straight upward from 0 seconds 0 minutes.
Answer:
C or the graph with continuous acceleration (straight line)
Step-by-step explanation:
It's the right answer on edguinity
Answer:
c
Step-by-step explanation:
1/3 exponent 4??? pls help immediately
What is the missing number?
Question 4 options:
Answer:
i dont see it
Step-by-step explanation:
Stainless steels can be susceptible to stress corrosion cracking under certain conditions. A materials engineer is interested in determining the proportion of steel alloy failures that are due to stress corrosion cracking. In the absence of preliminary data, what is the minimum sample size required to ensure a 90% confidence interval for p to within 0.02
Using the z-distribution, as we are working with a proportion, the minimum sample size required to ensure a 90% confidence interval for p to within 0.02 is of 1692.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
No prior estimate, hence the proportion is [tex]\pi = 0.5[/tex].Margin of error of M = 0.02.90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].Then, solving for n:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.645\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.645(0.5)[/tex]
[tex]\sqrt{n} = \frac{1.645(0.5)}{0.02}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645(0.5)}{0.02}\right)^2[/tex]
[tex]n = 1691.3[/tex]
Rounding up, a sample size of 1692 is needed.
More can be learned about the z-distribution at https://brainly.com/question/25890103
what is 5x -5?
And Could you explain, im truly lost
its 5x5 but with a negative
Step-by-step explanation:
What is: 7x + 1.8 + 2.2 = 30
Step-by-step explanation pls! :)
Elizabeth gave 13% of the cost as a tip to the delivery person who delivered her car after service at a cost of $294. What will be the total cost with tip to the nearest cent?
Answer:
If an amount is included as a "Gratuity" or "Service Charge," tipping is not required. ... If the tip is included, the breakdown of the bill will read "gratuity" or "service charge," which means that a tip is already included.
Step-by-step explanation:
hope this helps!
What are the solutions to the equation 3x2 + 10x = 8
Answer:
(3x-2)(X+4)
X=2/3,-4
Step-by-step explanation:
3x^2 + 10x = 8
3x^2+12x-2x-8=0
3x(X+4)-2(X+4)=0
(3x-2)(X+4)=0
X=2/3,-4
So the solution is 2/3,-4
A 12 inch board is cut into three pieces so that the second piece is as long as the first piece and the third piece is 3 times as long as the first piece of x represents the first piece find the lengths
Step-by-step explanation:
well that seems like a you problem lol
PLEASE HELLPP MEEEEEEEEeeeeeeeeeeeeeeeeee
Answer:
D, 32
Step-by-step explanation:
First input all the numbers. Then do what’s inside the parenthesis first then multily by 12. lastly divide that number by 2.4
Answer:
32
Step-by-step explanation:
[tex]\frac{12(4+2.4)}{2.4}\\\frac{12(6.4)}{2.4} \\ \frac{76.8}{2.4}=32[/tex]
On a map, 4 inches represents 240 miles. What is the scale of the map?
Negative 3/5 ×17 5/8=
Answer:
-10.575
Step-by-step explanation:
Help me Please 20 POINTS
When two variables are in a proportional relationship, which of the following is true about
1 their values.
2 their sums are a constant
3 their differences are a constant
4 their products are a constant
5 their quotients are a constant
Answer:
(5)
for eg;
3/5 is proportional to 15/25
Answer:
I would say 1 or 4
Step-by-step explanation:
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
A rectangular room is
1.8
times as long as it is wide, and its perimeter is
27
meters. Find the dimension of the room.
We should fuigre it out by first doing 1.7x since we don't know the 2 different widths and lengths.
P= 2*length + 2*width(the distance around)
Question says...
2(1.7x)+2x = 28
3.4x+2x=28
5.4x=28
X= 28m divided by 5.4
x = 5.2m: the width The length is : 8.8m
At Pages Aplenty book store, the more books you buy, the more books you get! With the special deal, a customer gets 2 free books for every 7 purchased books. Larry purchased 21 books. How many free books did Larry get?
Answer:
6
Step-by-step explanation:A customer gets 2 free books for every 7 purchased books. Larry purchased 21 books, and you need to find how many free books he got. Write a proportion.
2 free books
7 purchased books
=
? free books
21 purchased books
Compare the denominators.
2 free books
7purchased books
=
? free books
21purchased books
To get from 7 to 21, multiply by 3. Multiply the numerator and denominator by 3 to find the number of free books Larry got.
2 free books3
7 purchased books3
=
6free books
21 purchased books
Larry got 6 free books.
Lerry will get 6 free books . Because she gets 2 free books for every 7 purchased books.
What exactly is simplification?Simplifying means making something easier to do or comprehend, as well as making something less difficult.
For every 7 books a consumer buys, they receive 2 free books. Larry bought 21 books.
If the larry bought 21 book.She get 6 book as;
On the purchased of 7 book then on 14 book and then on the 21 book.
The free books did Larry get is found as;
⇒2+2+2
⇒6
Hence Lerry will get 6 free books .
To learn more about the simplification, refer to:
https://brainly.com/question/23509407
#SPJ2
Let’s fix some n e {1,2,3,...}. A biased coin with probability of head p is tossed n times, and the number of heads, N1, is counted. The coin is then tossed Ni more times, and the number of heads, N2, is counted. Find the expected total number of heads, E[Ni + N2], generated by this process. The answer should depend on n and p only.
Answer:
The answer is "np(1+p)".
Step-by-step explanation:
[tex]N_1[/tex] = Number of n tossed heads
According to [tex]N_1[/tex], Y = amount of [tex]N_1[/tex] tossing heads
So, [tex]N_1[/tex]~ Bin(n, p) and [tex]N_2[/tex] | [tex]N_1[/tex] ~ Bin([tex]N_1[/tex], p)
[tex]E(N_1+N_2) & = E\Big[N_1+N_2\vert N_1\Big]\\ &[/tex]
[tex]= E(N_1)+E\Big[N_2\vert N_1\Big]\\\\ & = E(N_1) + E(N_1\,p)\\\\ & = np + np.p \\\\ =np+np^2\\\\ =np(1+p)[/tex]