Answer:
Therefore, Peter is 21 years old.
Step-by-step explanation:
[tex]\bf{ x+11=\dfrac{(x-13)^2}{2} \ \Longrightarrow \ 2x+22=x^2-26x+169 }[/tex]
[tex]\bf{ 0=x^2-28x+147=(x-21)(x+7) }[/tex]
Find (a) arc length and (b) Area of a sector.
Answer:
a) 29.45 cm (2 dp)
b) 220.89 cm² (2 dp)
Step-by-step explanation:
Formula
[tex]\textsf{Arc length}=r \theta[/tex]
[tex]\textsf{Area of a sector}=\dfrac{1}{2}r^2 \theta[/tex]
[tex]\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in radians)}[/tex]
Calculation
Given:
[tex]\theta=\dfrac{5 \pi}{8}[/tex] r = 15 cm[tex]\begin{aligned}\implies \textsf{Arc length} & =r \theta\\& = 15\left(\dfrac{5 \pi}{8}\right)\\& = \dfrac{75}{8} \pi \\& = 29.45\: \sf cm\:(2\:dp)\end{aligned}[/tex]
[tex]\begin{aligned} \implies \textsf{Area of a sector}& =\dfrac{1}{2}r^2 \theta\\\\ & = \dfrac{1}{2}(15^2) \left(\dfrac{5 \pi}{8}\right)\\\\& = \dfrac{225}{2}\left(\dfrac{5 \pi}{8}\right)\\\\ & = \dfrac{1125}{16} \pi \\\\& = 220.89 \: \sf cm^2\:(2\:dp)\end{aligned}[/tex]
SOmeone please help me with this math puzzle
Answer:
1) (I) 1/4, 2) (B) 11/20, 3) (G) 3/20, 4) (C) 4/5
Step-by-step explanation:
Probability is Desired Outcome/All Possible Outcomes. For the first problem, we want apples, which is 25. Altogether though, there are 100 options. So, we get 25/100 or 1/4. For the second, oranges and grapes together (because either would be a desired outcome) are 55. So, we have 55/100, or 11/20. For the third, apples and oranges, the max can be 15, because that's how many total oranges (the lesser of the two) and you can't have anything other than that. So, we get 15/100 or 3/20. Finally, we're looking for everything but bananas, which is 100-20, or 80. For that, we get 80/100 or 4/5.
Hope this helped!
Answer:
Question 1: The Students favorite fruit is an apple is 1/4
Question 2: 3/20
Question 3: 2/5
Question 4: 4/5
Step-by-step explanation:
* All of the fruits equal up to 100, so 25 percent of 100 is 1/4 or 0.25
* Do 100/55. It should give you 5.8181818181818181818181818181818 which would be at least 3/20 because it is closer to 1.
* 25+15=40. 2/5=0.4 which is 40% of 100.
Does anybody know this? Find the circumference of a circle if the diameter is 8 meters do not round your answer use 3.14 for pi
Answer:
The circumference of the circle is 25.12 meters
Step-by-step explanation:
By definition, the circumference of a circle is the perimeter or the length around the circle.
To find the circumference of a circle, all we need to do is multiply the radius by pi and 2. Giving us the equation :
C = 2 * pi * r
We are also given that the diameter of the circle is 8 meters. With this, we can cut it in half to get the radius. 8 / 2 = 4
Now, we plug in our values:
2 * 3.14 * 4
When we evaluate this, we get the answer to be : 25.12
The circumference of the circle is 25.12 meters
Extra references for the definitions of radius and circumference.
The radius is the length from the center of the circle, to the outside (perimeter aka circumference point) of it. The diameter is the length across one end of the circle, to the other end, crossing through the center point.
Kindly help me solve this questions
a) 3/X+2-2=1/1/2
b) 3(4-7x)/5-0.7=x-6/2
Answer:
a) x=6
b) x= 498/463
hope this helps!!
Marcia has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate. the table below shows the information about the two credit cards marcia currently uses. card a card b amount $1,389.47 $1,065.32 apr 16% 12% monthly payment $39.38 $28.05 after 4 years, approximately how much will marcia have saved in interest by consolidating the two balances? a. $1,890.24 b. $133.92 c. $543.84 d. $1,346.40 please select the best answer from the choices provided. a b c d
The amount save by Marcia in interest by consolidating the two balances is $133.92.
What is the total payment for APR of 16%?
The total monthly payment for APR of 16% is calculated as follows;
Total monthly payments for 16% =$39.38x48 = $1890.24
What is the total payment for APR of 12%?Total monthly payments for 12% APR = $36.59*48 = $1756.32
Amount saved by MarciaA = $1890.24 - $1756.32
A = $133.92
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HELLPP!
Change 17/34 into a percent. Show your work.
Answer:
50%
Step-by-step explanation:
[tex] \frac{17}{34} = \frac{1}{2} = 50\%[/tex]
Colin's family started driving to Grandma´s house at 8:00 am. The family arrived at 11:30. How long did it take to drive to Grandma´s house? use the number line to solve the problem. (pls help)
Answer:
3 hrs 30 min
Step-by-step explanation:
calculate the magnitude of the angle ABC from the breeze data
Answer:
∠ ABC = 67°
Step-by-step explanation:
the angle between a tangent and a chord is equal to the angle in the opposite segment, that is
∠ ABC = ∠EAC = 67°
Urgent Please Help!!!!
What percentage of scores lie in the shaded region? Use the empirical rule to find your answer.
Answer:
81.5%
Step-by-step explanation:
A city Science High School uses standardized IQ test to screen students for admission. It is known that the population standard deviation of these IQ scores is 15. The school principal claimed that the average IQ of the students in their school is 110. Miss Cruz, a researcher, wants to validate the claim. She selected a random sample of 50 students and administered the IQ test. She found that the mean IQ of the sample is 105. Perform a test of hypothesis at 0.05 level of significance.
Using the z-distribution, it is found that we reject the null hypothesis, which means that her claim is not validated.
What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 110, that is:
[tex]H_0: \mu = 110[/tex].
At the alternative hypotheses, it is tested if the mean is less than 110, that is:
[tex]H_1: \mu < 110[/tex].
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.In this problem, we have that the parameters are given as follows:
[tex]\overline{x} = 105, \mu = 110, \sigma = 15, n = 50[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{105 - 110}{\frac{15}{\sqrt{50}}}[/tex]
z = -2.36.
What is the decision?Using a z-distribution calculator, z = -2.36 has a p-value that is less than the standard significance level of 0.05, hence we reject the null hypothesis, which means that her claim is not validated.
More can be learned about the z-distribution at https://brainly.com/question/16313918
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Which graph below shows the solutions for the linear inequality y2-x+1?
Answer:
The answer will be 1 + y2 - xA car has an average speed of 45 miles per hour. how long will it take to travel 360 miles? which equation and decimal form are represented by the visual model?
Answer:
It would take 8 hours to drive 360 miles.
Step-by-step explanation:
360/45=8
D=R*T
Options :
(24 - n ) - 6
(25 - n) + 6
25 + 4x
25 - (6 + n)
Answer: 25 - (6 + n)
Explanation:The number 25 is decreased by and sum of number.
The numbers are 6 and n, Their Sum = (6 + n)
When 25 is decreased by this sum of numbers
25 - (6 + n)Answer:
25 - (6+n)
Step-by-step explanation:
Important terms:
Decreased means to go down which represents subtraction Sum means the total amount which represents additionLet "a number" = nFinding the answer
We want to find a word phrase that matches the expression, 25 decreased by the sum of 6 and a number.
Using the terms we just defined we know that the sum of 6 and a number would be 6 + n. ( as again sum = addition or total amount of )
25 is being decreased by the sum of 6 and n so in other words the sum of 6 + n is being subtracted by 25 which would result us in getting 25 - (6+n)
Why the "6+n" must be in parenthesis
The 6 + n must be in the parenthesis because the individual sum of those two numbers is being subtracted from 25.
A bag contains 5 blue marbles and 3 yellow marbles. You randomly select two marbles from the bag. What is the probability that both marbles are blue when you replace each marble before selecting the next marble? Write your answer as a decimal rounded to three decimal places.
Answer:
0.625
Step-by-step explanation:
5/8 because there are 5 blue marbles and there are 3 yellow marbles. If you add them it equals 8.
The probability is 5/8.
If you do 5 divided by 8 it gives you 0.625.
Honestly i don't know what you mean by "rounded to three decimal places."
Sorry if it's not really healpful.
CAN SOMEONE HELP ME PLEASE?
Answer:
values
x=17
AT = 49 units
OG = 21 units
your and friend got 20 frog and your friend caught 5 times more? how many did ur friend catch please explain
If you catch 3.33 frogs. Then the number of the frogs that were caught by your friend will be 16.67.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
You and your friend got 20 frogs and your friend caught 5 times more.
Let you catch x frogs. Then the number of the frogs that were caught by your friend will be 5x.
x + 5x = 20
6x = 20
x = 3.33
More about the linear system link is given below.
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Let you caught x and friend caught 5x
Now
x+5x=206x=20x=20/6x=3.335x=16.67
Divide 15/18 by 6 any answers??
Answer:
[tex] \frac{5}{36} [/tex]
Step-by-step explanation:
[tex] \frac{15}{18} \div 6 \\ = \frac{15}{18} \times \frac{1}{6} = \frac{5}{18\times 2} = \frac{5}{36} [/tex]
A bag contains 5 pictures of Paris and 7 pictures of London. Determine whether the events of selecting the picture of Paris and another picture of Paris with replacement are independent or dependent. Then identify the indicated probability.
The events of selecting the picture of Paris and another picture of Paris with replacement are independent events.
The probability of picking two Paris pictures is 25/144.
What is an independent event?Independents events are events whose occurrence do not depend on each other. They are random event.
The probability of picking two Paris pictures = (number of Paris pictures / total number of pictures) x (number of Paris pictures / total number of pictures)
5/12 x 5/12 = 25 / 144
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Some paint is made by mixing 2 cans of white paint for every 5 cans of red
paint. To make the same tint, how many cans of white paint would you need if
you used 13 cans of red paint? Explain how you solved the problem.
Non-Liner System of Equations:
I created two systems of equations (one being linear one being quadratic) and need to solve them algebraically with work shown.
pls help
f(x) = 3x + 5
f(x) 3x^2 + 5
Answer: x=1, x=0
Step-by-step explanation:
3/4 to decimal what the answer
Answer:
0.75
Step-by-step explanation:
4/4=1
3/4=0.75
2/4=1/2=0.5
1/4=0.25
scale drawings
the scale drawing car length
is 3.5 cm. if the scale is
1 cm:4.5 ft, what is the actual car
stion length?
length?
Answer:
13•5ft
Step-by-step explanation:
1cm = 4.5ft
3cm = x
cross multiply
x= 3×4•5
:- x = 13•5ft
A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 3200 seats. The students filled 2496 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
The percentage of the seats in the theater were filled by the 6th graders on the trip is 78%.
What is the percentage?Percentage is a measure of frequency that is expressed as the fraction of a number out of 100.
The percentage of the seats in the theater were filled by the 6th graders = (number of filled seats / total number of seats) x 100
(2496/3200) x 100 = 78%
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Marsha sold 78 boxes of cookies. 51 boxes
were chocolate mint cookies. Of the remainder
sold, 1/3 were peanut butter crunchies. How many
boxes of peanut butter crunchies did Marsha sell?
Answer: 9
Step-by-step explanation:
78 subtract 51 is 27. One third of 27 is 9.
How many graduates from university a had an income under 20,000
a song has 12 beat in 5 second . how many beats are in 30 seconds
A quadrilateral has diagonals which are perpendicular to one another. What is the most we can determine about what kind of quadrilateral this is?
Step-by-step explanation:
a rhombus.
all 4 sides are of equal length.
wat is 2+2? im doing this to give you an extra 2 points!
Answer:
oh oh....I know...it's 4....I'm I right
Answer:
4
Step-by-step explanation:
Thanks btw
Let's pretend the [] are boxes.
[] this is one box.
[] [] these are 2 boxes, which is 2
if you put 2 plus 2,
[] [] + [] []
count them, you get 4
Hooray!
If you dunno how to count, you just see each of the boxes, then count up
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and so on. when you stop seeing the boxes, stop counting - the number you're on is the answer to your + question!
What are “holes” in algebra 2?
Answer:
Step-by-step explanation:
A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero.
Prove: An odd number squared is an odd number. = (2n + 1)2
Answer:
[tex] {(2n + 1)}^{2} = 4 {n}^{2} + 4n + 1 = 2(2 {n}^{2} + 2n) + 1[/tex]