Answer:
60
Step-by-step explanation:
there are three sides to a triangle so 20x3 is 60 which is the perimeter
Pls help!! URGENT!!
What is RU? Use the figure below.
Answer: 20 ( Choice A )
Step-by-step explanation: You can prove that triangle RTS and triangle RTU are the same using the Side-Angle-Side method, so ultimately, side RS should equal RU. Therefore, 8x = 6x + 5.
x should equal 2.5. The question is asking you how long side RU is, simply plug in 2.5 and you get 20.
Now, write an expression using the two terms from parts C and D to represent the net change to Quiana’s loan as a result of her payments.
Part D's answer: -5
Part C's answer: -$247.43
info: Quiana took out a loan to pay for a new car. Initially, she owed the lender $15,234.68. She has repaid $247.43 of the loan each month for the past 5 months. What is the net change to the loan from Quiana’s perspective over the past 5 months?
Complete the steps below to help Quiana calculate the loan amount that she’s repaid to the lender.
From Quiana's perspective, the net change in the loan during the last 5 months is $1237.15.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign.
Here,
15234.68-247.43*5=13997.53
Net change
= Initial loan amount - current balance
= $15,234.68 - $13,997.53
= $1237.15
The net change to the loan from Quiana’s perspective over the past 5 months is $1237.15.
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suppose you are offered one slice from a round pizza, that is, a sector of a circle, and the slice must have a perimeter of 32 inches. what diameter pizza will produce the largest slice?
On solving the provided question, we can say that D, diameter pizza will produce the largest slice is 16
what is diameter?Any straight line segment with an endpoint on the circle and that travels through its center is considered a circle's diameter in geometry. The longest chord of a circle is another way to describe it.
Let r be the radius and be the angle of a circle.
According with the graph, the area of the sector is given by
A = 1/2r^2∅
The arc length of a circle with radius r and angle∅ is r∅
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
2r + r∅ = 32 in
r∅ = 32 - 2r
∅ = 32- 2r / r
Now,
A = 1/2r^2[32- 2r / r]
A = 16r - r^2
A' = 16 - 2r 16 -2r = 0
r = 8
A" = -2
so, D, diameter pizza will produce the largest slice is 16
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What is the best approximation of the solution to the system to the nearest integer values X minus Y equals negative 65X plus 3Y equals 24
The best approximation of the solution to the system to the nearest integer values X minus Y equals negative 65X plus 3Y equals 24 are x = 43 and y = 22
How to determine the solutionFrom the information given, we have the expressions;
X minus Y equals negative 65X plus 3Y equals 24This is represented as;
x - y = -65
x + 3y = 24
Make 'x' the subject from equation 1
x = -65 + y
Now, substitute the expression into equation (2), we get;
-65 + y + 3y = 24
collect the like terms
4y = 24 + 65
Add the like terms
4y = 89
Divide the values by the coefficient of y
y = 89/4 = 22
Substitute the value in eqation3
x = -65 + 22
Add the values
x = 43
Hence, the values are 43 and 22
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A 7x1 board is completely covered by mx1 tiles without overlap; each tile may cover any number of consecutive squares, and each tile lies completely on the board. Each tile is either red, blue, or green. Let N be the number of tilings of the 7x1 board in which all three colors are used at least once. For example, a 1x1 red tile followed by a 2x1 green tile, a 1x1 green tile, a 2x1 blue tile, and a 1x1 green tile is a valid tiling. Note that if the 2x1 blue tile is replaced by two 1x1 blue tiles, this results in a different tiling. Find the remainder when N is divided by 1000.
The remainder when N is divided by 1000 is 106.
What is the Principle of Inclusion-Exclusion?The Principle of Inclusion-Exclusion, often known as PIE, offers a method/formula for organizing information about the size of each set, the number of elements in the union of a given set of sets, and the size of all potential set intersections.
From the question,
First, we think about all the possible divisions of the 7×1 board. Since we require at least one tile of each color, we exclude the cases of just one or two pieces.
Three pieces = 5+1+1 , 4+2+1 , 4+1+2 etc (6C2) = 15 ways
Four pieces = 6C3 = 20
Five pieces = 6C4 = 15
Six pieces = 6C5 = 6
Seven pieces =6C6 = 1
Now, we apply the Principle of Inclusion-Exclusion to consider how many ways to color them:
Three pieces : 3³ - 3 × 2³ + 3 = 6
Four pieces: 3⁴ - 3 × 2⁴ + 3 = 36
Five pieces : 3⁵ - 3 × 2⁵ + 3 = 150
Six pieces : 3⁶ - 3 × 2⁶ + 3 = 540
Seven pieces : 3⁷ - 3 × 2⁷ + 3 = 1806
Adding them together, we get
15×6 + 20×36 + 15×150 + 6×540 + 1×1806 = 8106
Hence, the remainder when it is divided by 1000 is 106.
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Answer:
106
Step-by-step explanation:
it takes 3 people 12 hours to paint a room. How long would it take 1 person to paint the same room?
Answer:
36 hours
Step-by-step explanation:
3 x 12 = 36
Answer:
36 hours
Step-by-step explanation:
if it took 3 people to paint a room in 12 hours, we have,
3 people = 12 hours
divide by 3. multiply by 3
1 person = 36 hours.
the radius of a sphere is decreasing at a constant rate of 6 feet per second. at the instant when the volume of the sphere is 163163 cubic feet, what is the rate of change of the volume? the volume of a sphere can be found with the equation v
865.96 is the rate of change of the volume. This can be solved using the concept of rate of change of the volume.
What is volume of sphere?The volume of a sphere is the maximum volume of air that may be contained within it. Volume of sphere = 4/3 πr³ is the formula for computing the volume of a sphere of radius "r."
As we know,
volume (V) = 4/3 πr³
Given that,
volume of the sphere is 163 cubic feet
the radius of a sphere is decreasing at a constant rate of 6 feet per second (dr/dt) = 6
So, 163 = 4/3 × 22/7 r³
or, r³ = (3423/88)
or, r = [tex][\frac{3423}{88}]^{1/3}[/tex]
again, dv/dt = 4/3 × π × 3 r² × dr/dt
or, dv/dt = 4 × π × r² × dr/dt
or, dv/dt = 4 × 22/7 ×[tex][\frac{3423}{88}]^{2/3}[/tex] × 6
or, dv/dt = 75.43 × [tex][\frac{3423}{88}]^{2/3}[/tex]
or, dv/dt = 865.96
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Between what two consecutive integers does the square root of 12 lie
The two consecutive integers that the square root of 12 lies between are 3 and 4.
How to find the integers ?Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." All whole numbers and negative numbers are considered integers. This means that if we combine negative numbers with whole numbers, a collection of integers results.
An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion. This therefore means that integers can only be whole numbers and consecutive integers follow each other. For instance, 1, 2, and 3 are consecutive integers.
To find the two consecutive integers that the square root of 12 lies between, find the square root of 12 :
= √ 12
= 3.46
This means that the lower integer would be 3 and the consecutive integer following would be 4.
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If A(2, 3) and B(-4, -6), find AB. Round to the nearest tenth.
the length of a rectangle is increasing at a constant rate of 3 cm/s, and its width is increasing at a constant rate of 0.5 cm/s. at the time the length is 5 cm and the width is 1.2 cm, how fast is the area of the rectangle increasing?
The area of a rectangle is increasing at a constant rate of 3.5 cm²/s when the length is increasing at a constant rate of 3 cm/s and the width is increasing at a constant rate of 0.5 cm/s.
The area of a rectangle is calculated as length multiplied by width (A = L x W). At the given time, the length is 5 cm and the width is 1.2 cm, so the area is 6 cm². When the length is increasing at a constant rate of 3 cm/s, and the width is increasing at a constant rate of 0.5 cm/s, then the area is increasing at a rate of 3.5 cm²/s. This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5). This is the rate of increase of the area and is expressed as 3.5 cm²/s This can be calculated by multiplying the constant rate of increase of the length and width together (3 x 0.5 = 1.5).
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Sarah invested £16 000 in a unit trust five years ago. The value of the unit trust has increased by 6% per annum for each of the last 3 years. Before this, the price had decreased by 4% per annum. Calculate the current price of the unit trust. Give your answer to the nearest whole number of pounds.
Answer:
17562 pounds
Step-by-step explanation:
16000*96%=15360. 15360*96%=14745.6. 14745.6*106%=15630.336. 15630.336*106%=16568.1562. 16568.1562*106%=17562.2456. 17562.2456 approximately equals 17562 pounds.
prove by the sum of arithmetic induction that the sum of the first n terms of a n arithmetic sequence
The sum of the first n terms of an arithmetic sequence can be proven using the principle of induction. We assume the formula holds for n = k, and then show it holds for n = k+1, thus showing it holds for all values of n.
The sum of the first n terms of an arithmetic sequence can be determined using the formula S_n = (n/2)(a_1 + a_n), where a_1 is the first term and a_n is the nth term.
We can prove this formula using the principle of induction.
Base Case: Let n = 1. Then S_1 = (1/2)(a_1 + a_1), which simplifies to S_1 = a_1. This is the same result we would get if we added the first term of the sequence.
Inductive Step: Assume that the formula holds for n = k.
Then S_k = (k/2)(a_1 + a_k).
Now consider n = k+1.
S_k+1 = (k+1/2)(a_1 + a_k+1)
= (k/2)(a_1 + a_k) + (1/2)(a_1 + a_k+1)
= S_k + (1/2)(a_k+1 - a_1)
= S_k + (1/2)(a_k+1 - a_k) + (1/2)(a_k - a_1)
= S_k + (1/2)(a_k+1 - a_k) + [S_k - (k/2)(a_1 + a_k)]
= (k+1/2)(a_1 + a_k+1)
= S_k+1
Therefore, we have shown that if the formula holds for n = k, then it also holds for n = k+1. By the principle of induction, the formula holds for all n.
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more workers what sample size would be required to reduce the standard deviation of the sampling distribution to one-third the value you found in exercise 36(b)? justify your answer.
On solving the provided question, we can say that the sample size would have to be multiple by 4 = 4048
what is sample size?The number of observations utilized to calculate estimates for a given population is referred to as the sample size. From the population, a sample size was chosen. The term "sample size" describes the number of subjects or observations that make up a study. n is typically used to represent this number. The sample size influences two statistical characteristics: 1) The precision of our estimates; 2) The ability of research to produce inferences. The results of random tests are the samples. When sampling a random variable, a particular value is chosen from a range of potential values. A sample is this specific value. The random variable's probability distribution determines the possible values and their probabilities.
the sample size would have to be multiple by 4
n = 1012
n X 4
= 1012 X 4
= 4048
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T/F. In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is 16.
As per the concept of probability that it takes three rolls until the player rolls doubles is 0.11574 and this can be determined by using the given data.
In math the term probability of an event is defined as nothing but a number between 0 and 1 where zero shows the impossibility and one shows the certainty.
Here we have given that a certain board game, here the player rolls two fair six-sided dice until the player rolls doubles.
And here we know that the probability of rolling doubles with one roll of two fair six-sided dice is 1/6.
Here first we need to determine the probability of rolls to obtain doubles in each roll.
That can be calculated as ,
=> 1 - 1/6 = 5/6
Then the fails in the second roll is calculated as,
=> 1 - 1/6 = 5/6
Then the third roll the player rolls doubles that is calculated as,
=> 1/6
So, the probability of requiring 3 rolls until getting doubles will be calculated as
=> 5/6 x 5/6 x 1/6
=> 25/216
When we simplify this one then we get,
=> 0.115
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Two APs have same common difference. If the first term is -1 and that of the other is -8. then the difference between their 4th term is?
Answer:
7
Step-by-step explanation:
Let the common difference of the two APs be" D"
Let 1st term of 1st AP be A₁ i.e = -1
And the first term of the second AP b₁ i.e = -8
We know that the nth term of an AP is;
an = a+(n-1)d
4th term of first AP,
a₁ + (4-1)d = − 1 + 3d. --Eqn. 1
And 4th term of the second AP,
b₁ + (4-1) d=-8+ 3d -- Eqn 2
Now, the difference between their 4th terms is i.e.
= (- 1+ 3d ) - (-8 + 3d )
= -1 + 3d + 8 - 3d = 7
So, the answer is 7.
The value of a ring ($1000) increases exponentially so that it has a value of $3,000 after 5 years. Find the rate.
Answer: [tex]\sqrt[5]{3}-1[/tex]
Step-by-step explanation:
Let the annual rate of increase be [tex]r[/tex].
[tex]3000=1000(1+r)^5\\\\3=(1+r)^5\\\\\sqrt[5]{3}=1+r\\\\r=\sqrt[5]{3}-1[/tex]
why is the answer here (-∞, 6)
why 6
Answer:
Step-by-step explanation:
Basically, because till x = 6, f(6) was less than 0.
They are asking the value of f(x), not x.
Thanks
Paul usually makes the 100 km journey to visit his family. The trip involves three separate stages:
a) A stage of 20 km that is travelled on small roads at a constant speed of 30 km/h.
b) A stage of 50 km that is travelled on the highway at a constant speed of 100 km/h.
c) A stage of 30 km that is travelled on standard roads at a constant speed of 40 km/h.
The length of the section of roadworks was 121 km.
What is the concept of time and distance?
Time is directly proportional to distance. It means that speed remains constant, if we have two vehicles moving two distances for two different time duration then the time is directly proportional to the distance. Speed is directly proportional to distance.
1) Total time = 1 hr 55 minutes
2) Distance = 121 km
To calculate Matthew's journey we have to use the formula of :
Time = distance /speed
Are doing the calculations for each Stage, like this:
Stage A, we know that:
Distance: 20 km
speed: 30 km/h
Time = 20/30
T = 2/3h
Time = 40 minutes
Stage B, we know that:
Distance: 50 km
speed: 100 km/h
Time = 50/100
T = 0.5 h
Time = 30 minutes
Stage C, we know that:
Distance: 30 km
speed: 40 km/h
Time = 30/40
T = 3/4 h
Time = 45 minutes
1) So using all the values calculated above, let's calculate the total value of the trip that will take place by:
Total = (40 + 30 + 45)minutes
Total = 115 minutes
Total = 1 hour 55 minutes
2) For the second part of this question we want to calculate the total distance of travel hours so:
Speed: 60 km/h
Time: 6 minutes + x
x =1 hr 55 minute + 6 minutes 2 hr 1 minute
Time = 2.01666667
Distance = speed * time
Distance = 60 * 2.01666667
Distance = 121 km
hence, the length of the section of roadworks was 121 km.
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The US has a population of approximately 330 million people. Given that 0. 35 of the population have blue eyes, calculate the number of people in the US who do not have blue eyes.
The number of people in the US who do not have blue eyes is 214.5 million.
The given question has been solved using Probability. It is given that the number of people in the US is 330 million
for the time being, we let P=330 which represents the population of the US
also, it is given that the number of people having blue eyes is 0.35 times the Population
So, Pb= 0.35 × P
here, Pb represents the number of people having blue eyes
So the number of people that do not have blue eyes must be the number of people having blue eyes subtracted from those having blue eyes
i.e, Pnb=P-Pb
=P-(P × 0.35)
=P(1-0.35)
=330 (0.65 )
=214.5
Thereby, the number of people that do not have blue eyes is 214.5 million.
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What is a point that divides a line segment into 2 equal parts called?
Answer: Midpoint
Step-by-step explanation:
Becky has 14 pints of pudding. How many cups of pudding does she have?
Answer:
28 cups
Step-by-step explanation:
[tex]\frac{2}{1}[/tex] = [tex]\frac{x}{14}[/tex]
1 x 14 = 14, so 2 x 14 = 28
Ages Numbers of students 15-18 2 19-22 7 23-26 5 27-30 5 31-34 6 35-38 3 Based on the frequency distribution above, find the relative frequency for the class with lower class limit 27 Relative Frequency =%Give your answer as a percent, rounded to one decimal place
Relative frequency for the class with lower class limit 27 is 20.0%.
To find the relative frequency for the class with lower class limit 27, we must first find the total frequency of the data set. The total frequency is 28 (2+7+5+5+6+3=28). Since the class with lower class limit 27 has a frequency of 5, we can calculate the relative frequency of this class by dividing the frequency of the class by the total frequency.
Formula:
Relative Frequency = (Number of Students in the Class)/(Total Number of Students in the Group) x 100
Relative Frequency = (5)/(28) x 100
Relative Frequency = 0.1786 x 100
Relative Frequency = 17.86%
Rounded to one decimal place, Relative Frequency = 20.0%.
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if the radius of a circle is 12 ft what is the area in terms of π
Step-by-step explanation:
The area of a circle is radius²· π
12x12=144
So the answer is 144π.
Answer:
37.71428571425567788
what are the four conditions necessary for x to have a binomial distribution? mark all that apply.
Characteristic of binomial distribution Mean should be n *p n is the number of trials p is the successful outcome of the process
a set number of trials, such as three rolls of the dice or five flips of the coin.Each trial can either be successful or unsuccessful. Note that the example with the die seems to have six possible outcomes. We must take into account options like "get a 6" (success) or "not obtain a 6." (failure).The likelihood of success must be constant (equal for every try). P(6) = 1/6 for each roll of the die in the example.The trials are separate. The likelihood of success in future trials is unaffected by the outcome of the first.Know more about binomial at:
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Write an abolute value inequality comparing the ditance of the tour guide and the diver to eal level. Who i cloer to ea level? Explain how you know. Sea level = -18 ft
Tour guide = 5 ft
One diver = -11 ft
The diver is closer to sea level since their distance to sea level (7 ft) is less than the distance of the tour guide to sea level (23 ft).
As we know,
|Tour guide - sea level| < |One diver - sea level|
The distance between the tour guide and sea level is 5 - (-18) = 23 feet.
The distance between one diver and sea level is -11 - (-18) = 7 feet.
Since the absolute value of the difference between the tour guide and the sea level is greater than the absolute value of the difference between one diver and the sea level, we can conclude that the diver is closer to the sea level.
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Can anyone help me with the answer. Sorry if it’s hard to see , please just zoom in
Answer:
NOLO
Step-by-step explanation:
3x + 3y = 3
\y=-1/x+2
y=-2
y = 0
y = 3
y = 1
Answer: [tex]y=3[/tex]
Step-by-step explanation:
The intersection point of the graphs is the solution. So, you need to find the [tex]y[/tex]-coordinate of the intersection point.
Write the slope-intercept form of the equation of each line.
7) y - 9 =2/3 (x + 6)
8) y + 4 = 8(x - 2)
Answer:
7) y = [tex]\frac{2}{3}[/tex]x + 13
8) y = 8x - 20
Step-by-step explanation:
Question 7
y - 9 = [tex]\frac{2}{3}[/tex](x + 6)
Step 1: Distribute [tex]\frac{2}{3}[/tex] to (x + 6); y - 9 = [tex]\frac{2}{3}[/tex]x + 4
Step 2: Add 9 to both sides; y = [tex]\frac{2}{3}[/tex]x + 13
Question 8
y + 4 = 8(x - 2)
Step 1: Distribute 8 to (x - 2); y + 4 = 8x - 16
Step 2: Subtract 4 from both sides; y = 8x - 20
Can somebody help me
Answer:
Look, I don't know how to tell the answers by looking at the squares but I can tell you how to do it.
a) Subtract the number on the left with the number on the top, pretty simple, i am sure u can do that.
b) After you have done that, count how many negative scores you got and divide that by 9.
c)Finally, count all the numbers more than 3 again and divide it by 9.
Note: 9 here is the total number of outcomes.
Thanks
f(n)=n+3
g(n)=2n-4
Find (fog)(-3)
Answer:
-7
Step-by-step explanation:
(fog)(-3) = f(g(-3)) = f (2(- 3) - 4) = f(-10) = -10 + 3 = -7
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