A pitcher contains 13 cups of iced tea. You drink 1. 75 cups of the tea each morning
and 1. 5 cups of the tea each evening. When will you run out of iced tea?
The duration of days after which the individual will run out of iced tea is 4 days, under the condition that a pitcher can hold 13 cups of iced tea. The individual drinks 1. 75 cups of the tea every morning and 1. 5 cups of the tea each evening.
So to solve this problem we have to relie on the basic principles of division
Total amount of tea consumed per day = 1.75 cups (morning) + 1.5 cups (evening)
= 3.25 cups
Total amount of tea in the pitcher = 13 cups
Number of days before running out of iced tea = 13 cups / 3.25 cups per day
= 4 days
Then, the duration of days until the iced tea runs out is 4 days.
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Correct the error in finding the area of sector XZY when the area of ⊙Z is 255 square feet.
n/360=115/225
n=162. 35
Round to the nearest tenth.
The area should equal ______ft2.
The error in the calculation is that n/360 should be equal to the central angle of the sector in degrees divided by 360. However, the given value of 115/225 is not the correct central angle. To find the correct central angle, we need to use the formula for the area of a sector:
Area of sector XZY = (central angle/360) x πr^2
We know that the area of circle ⊙Z is 255 square feet, so we can find the radius:
πr^2 = 255
r^2 = 81.11
r ≈ 9 feet
Now we can solve for the central angle:
Area of sector XZY = (central angle/360) x π(9)^2
Area of sector XZY = (central angle/360) x 81π
Area of sector XZY = (central angle/360) x 254.47
Since the area of sector XZY is not given, we cannot use the given equation n/360 = 115/225 to find the central angle. Instead, we need to use the formula above and solve for the central angle. Let A be the area of sector XZY:
A = (n/360) x 254.47
n/360 = A/254.47
n = 360A/254.47
Now we can substitute the given area of circle ⊙Z and solve for the area of sector XZY:
255 = (n/360) x πr^2
255 = (n/360) x π(81)
255 = (n/360) x 254.47
n = (360 x 255)/254.47
n ≈ 360.15
Note that n should be rounded to the nearest integer since it represents the central angle in degrees. Therefore, the central angle is approximately 360 degrees. Now we can use this value to find the area of sector XZY:
Area of sector XZY = (360/360) x π(9)^2
Area of sector XZY = 81π
Area of sector XZY ≈ 254.47 ft^2
Therefore, the area of sector XZY should be approximately 254.47 square feet.
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10% of a competition’s contestants like dogs. 60% of them like rabbits. 90% of them like cats. Liking each of these animals is independent. That means, for example, that whether or not you like dogs does not affect whether you like cats. If we choose a random contestant:
a. What is the probability of this contestant
liking cats and dogs, but not rabbits?
b. What is the most likely outcome of this contestant’s preferences? As in, which animals does s/he like, and which does s/he not like?
To find the probability of a contestant liking cats and dogs but not rabbits, we can use the formula for calculating the probability of independent events. That is, P(A and B and not C) = P(A) * P(B) * P(not C).
So in this case, P(cats and dogs and not rabbits) = 0.1 * 0.9 * 0.4 = 0.036. Therefore, the probability of a contestant liking cats and dogs but not rabbits is 0.036 or 3.6%.
As for the most likely outcome of this contestant's preferences, we can see that 90% of the contestants like cats, so it's very likely that this contestant likes cats. However, only 10% of the contestants like dogs, so it's less likely that this contestant likes dogs.
And 60% of the contestants like rabbits, so it's even more likely that this contestant does not like rabbits. Therefore, the most likely outcome is that this contestant likes cats but does not like dogs or rabbits.
In conclusion, given the probabilities provided, we can calculate the probability of a contestant liking cats and dogs but not rabbits, and we can also determine the most likely outcome of this contestant's preferences. The independence of the events allows us to use simple probability calculations to make these determinations.
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Help is extremely appreciated! :)
Answer:
To find the weighted mean, we need to multiply each delivery value by its corresponding frequency, add the products, and divide by the total frequency.
(3 x 7) + (6 x 6) + (9 x 1) + (12 x 0) = 21 + 36 + 9 + 0 = 66
Total frequency = 7 + 6 + 1 + 0 = 14
Weighted mean = 66 / 14 = 4.7 (rounded to the nearest tenth)
Therefore, the weighted mean is 4.7
Find the t value that forms the boundary of the critical region in the right-hand tail for a one-tailded test with o=. 01 for each of the folling sample size n=10
The t critical value at 29 degrees of freedom and 0.01 level of significance is 2. 46
How to calculate the valueUsing Critical value calculator we calculate the values.
a) at n = 10
Therefore degrees of freedom is = n - 1= 9, So therefore at 9 degrees of freedom and 0.01 level of significance, t critical value is 2.82
b) at n= 20
Degrees of freedom is 19.
The t critical value at 19 degrees of freedom and 0.01 level of significance is 2.54
c) at n = 30
Degrees of freedom is 29.
So therefore t critical value at 29 degrees of freedom and 0.01 level of significance is 2. 46
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Frank solved the equation using the following steps. Is he correct? Explain.
1/5 t + 2 = 17 1/5 t + 2 - 2 = 17 1/5 y = 17. t = 85
Answer:
see below
Step-by-step explanation:
Here are the steps that Frank took:
1/5t+2=17
1/5t+2-2=17
1/5t=17
t=85
Frank is incorrect. He is incorrect because in step 2, he forgot to subtract both sides by 2, and only did this to the left side of the equal sign. He has to subtract 2 from both sides of the equal side to have the equation remain balanced. Frank should've gotten t=75.
Hope this helps! :)
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 1, 4, 16, ... sequence and the is equal to
the sequence 1, 4, 16, ... is a geometric sequence with a common ratio of 4.
what is geometric sequence ?
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number called the common ratio (r).
In the given question,
The sequence 1, 4, 16, ... is geometric.
To determine the common ratio, we divide any term by the previous term. For example:
The ratio between 4 and 1 is 4/1 = 4.
The ratio between 16 and 4 is 16/4 = 4.
Since the ratio is the same for any two consecutive terms, we can conclude that the common ratio is 4.
We can also verify this by using the general formula for a geometric sequence:
aₙ= a₁ * r⁽ⁿ⁻¹⁾
where aₙ is the nth term, a_1 is the first term, r is the common ratio, and n is the term number.
Using the given sequence, we have:
a₁ = 1 (the first term)
a₂ = 4 (the second term)
a₃ = 16 (the third term)
We can use these values to solve for the common ratio:
a₂ / a₁ = r
4 / 1 = r
r = 4
Therefore, the sequence 1, 4, 16, ... is a geometric sequence with a common ratio of 4.
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Let f(x) = x^2 - 5x. Round all answers to 2 decimal places.
Find the slope of the secant line joining (1, f(1) and (9, f(9)).
-3.8 is the slope of the secant line connecting (1, f(1)) and (9, f(9)).
To get the slope of the secant line, we must first compute the values of f(1) and f(9):
f(1)
= 1² - 5(1)
= -4
f(9)
= 9² - 5(9)
= 36 - 45
= -9
The formula for the slope of the secant line running between these two locations is:
slope = (y-change)/(x-change)
= (f(9)-f(1))/(9-1)
Substituting f(1) and f(9) values and simplifying yields slope ,
= (-9-(-4))/(9-1)
= -5/8
= -0.625
When we round this to two decimal places, we get:
slope = -0.63
The slope of the secant line connecting (1, f(1)) and (9, f(9)) is thus -0.63.
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I NEED INEQUALITY!!! WILL MARK BRAINLY + 50 POINTS IF GIVEN VALID ANSWER !!!!!!Your ice-cream cart can hold 550 frozen treats. Your friend Anna also has an ice-cream cart and sold frozen treats last summer. She has agreed to help you decide which frozen treats to sell.
Table 1 displays the cost to you, the selling price, and the profit of some frozen treats.
Choco bar cost you $0.75 ea, selling price $2.00, profit for each sale $1.25
Ice cream sandwich cost you $0.85 each, selling price $2.25, profit $1.40
Frozen fruit bar cost you $0.50 each, selling price $1.80, profit $1.30
Your budget is to spend no more than $450 on frozen treats.
Enter an INEQUALITY to represent the number of chocolate fudge bars, C, the number of ice-cream sandwiches, I, and the number of frozen fruit bars, F, that will cost you no more than $450.
Answer:
$450
Step-by-step explanation:
Let's use the variables C, I, and F to represent the number of chocolate fudge bars, ice cream sandwiches, and frozen fruit bars, respectively, that you will sell.
The cost of each chocolate fudge bar is $0.75, the cost of each ice cream sandwich is $0.85, and the cost of each frozen fruit bar is $0.50. Therefore, the total cost of the frozen treats that you buy will be:
Total cost = 0.75C + 0.85I + 0.50F
We want to make sure that this total cost is no more than $450. Therefore, we can write the following inequality:
0.75C + 0.85I + 0.50F ≤ 450
This inequality represents the number of chocolate fudge bars, C, the number of ice-cream sandwiches, I, and the number of frozen fruit bars, F, that will cost you no more than $450.
PLEASE HELPPPP!! 20pts Students in the Drama Club are purchasing accessories for a play. They shop at two different stores over the span of three days. The items purchased at Store A al cost the same amount. The tems pur
⢠Day 1: Students spent $30. They purchased 4 items from Store A and 7 items from Store B.
⢠Day 2: Students spent $22. They purchased 3 items from Store A and 5 items from Store B.
On Day 3 students will need to buy 10 items from Store A and 17 items from Store B. What is the amount of money the students will need on the third day?
Part A: Write a system of equations to model the situations
The students will need $74 on the third day.
Let x be the cost of one item at Store A and y be the cost of one item at Store B. Then the system of equations to model the situation is:
4x + 7y = 30
3x + 5y = 22
To find the cost on Day 3, we need to solve for x and y, and then use those values to calculate:
10x + 17y = ?
Part B: Solve the system of equations to find x and y
To solve the system of equations, we can use elimination or substitution. Here, we'll use substitution.
From the first equation, we can solve for x:
4x + 7y = 30
4x = 30 - 7y
x = (30 - 7y)/4
Substitute this expression for x into the second equation:
3x + 5y = 22
3((30 - 7y)/4) + 5y = 22
(90 - 21y)/4 + 5y = 22
90 - 21y + 20y = 88
-y = -2
y = 2
Now that we know y = 2, we can substitute this value back into either equation to find x:
4x + 7y = 30
4x + 7(2) = 30
4x + 14 = 30
4x = 16
x = 4
So x = 4 and y = 2.
Part C: Calculate the amount of money needed on Day 3
Finally, we can use these values to calculate the amount of money needed on Day 3:
10x + 17y = 10(4) + 17(2) = 40 + 34 = 74
Therefore, the students will need $74 on the third day.
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What is the probability that a randomly chosen contestant had a brown beard and is only in the beard competition
The probability that a randomly chosen contestant has a brown beard and is only in the beard competition is 0.402. The correct answer is option (D) 0.402.
What is the probability about?Let B denote the event that a contestant has a brown beard, and M denote the event that a contestant is only in the beard competition. We are given:
P(B) = 0.406
P(M) = 0.509
P(B U M) = 0.513
We want to find P(B ∩ M), the probability that a contestant has a brown beard and is only in the beard competition. We can use the formula:
P(B U M) = P(B) + P(M) - P(B ∩ M)
Rearranging and substituting the given values, we get:
P(B ∩ M) = P(B) + P(M) - P(B U M)
= 0.406 + 0.509 - 0.513
= 0.402
Therefore, the probability that a randomly chosen contestant has a brown beard and is only in the beard competition is 0.402.
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See full text below
POSSIBLE POINTS: 1
Trevor was the lucky journalist assigned to cover the Best Beard Competition. He recorded the contestants' beard colors in his notepad. Trevor also noted the contestants were signed up for the mustache competition later in the day.
The probability that a contestant has a brown beard is 0.406, the probability that a contestant is only in the beard competition is 0.509, and the probability that a contestant has a brown beard or is only in the beard competition is 0.513.
What is the probability that a randomly chosen contestant has a brown beard and is only in the beard competition?
0.915
0.582
0.004
0.402
O 0.103
O 0.441
what percentage of 2 hours is 48 minutes
Answer:
40%
Step-by-step explanation:
[tex] \frac{48}{120} \times 100 = 40[/tex]
Answer:
40%
Step-by-step explanation:
To find out what percentage of 2 hours is 48 minutes, we need to first convert both values to the same unit of time, such as minutes.
2 hours is equal to 120 minutes (2 x 60).
So, the fraction of 2 hours that is represented by 48 minutes is:
48/120
Simplifying this fraction by dividing both the numerator and denominator by 12, we get:
4/10
Multiplying the numerator and denominator by 10 to convert this fraction into a percentage, we get:
40%
Therefore, 48 minutes is 40% of 2 hours.
A national organization sets out to investigate the change in prevalence of HIV since the last census in 2010. A total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be HIV positive. Assume that the data from the census indicated that the prevalence of HIV in the particular population was 7. 5%. A) Write out the null and alternative hypotheses for a formal test of significance. B) Interpret your results at 95% confidence
A) The null hypothesis (H0) is that there has been no change in the prevalence of HIV since the last census. The alternative hypothesis (Ha) is that there has been a change in the prevalence of HIV since the last census
B) At a 95% confidence level, the critical value for a two-tailed test is ±1.96.
A) The null hypothesis (H0) is that there has been no change in the prevalence of HIV since the last census, i.e., the current prevalence of HIV is still 7.5%. The alternative hypothesis (Ha) is that there has been a change in the prevalence of HIV since the last census, i.e., the current prevalence of HIV is different from 7.5%.
B) To test the hypothesis, we can use a z-test for proportions. The test statistic can be calculated as:
z = (p - p0) / [tex]\sqrt{(p0(1-p0)/n)}[/tex]
where p is the sample proportion of HIV positive cases, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size.
In this case, p = 468 / 4706 = 0.099, p0 = 0.075, and n = 4706. Plugging these values into the formula, we get:
z = (0.099 - 0.075) / [tex]\sqrt{0.075(1-0.075)/4706}[/tex] = 8.80
At a 95% confidence level, the critical value for a two-tailed test is ±1.96. Since the calculated z-value (8.80) is much larger than the critical value, we can reject the null hypothesis and conclude that there is strong evidence to suggest that the prevalence of HIV has changed since the last census. In other words, the prevalence of HIV is different from 7.5%.
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What is the finance charge on a credit card account if the balance is $660. 30 with an
APR of 6. 2%?
The finance charge on a credit card account with a balance of $660.30 and an APR of 6.2% is $3.41.
To calculate the finance charge on a credit card account with a balance of $660.30 and an APR of 6.2%. Here's a step-by-step explanation:
1. Convert the APR (Annual Percentage Rate) to a decimal by dividing it by 100: 6.2 / 100 = 0.062
2. Divide the APR decimal by 12 to find the monthly interest rate: 0.062 / 12 = 0.005167
3. Multiply the credit card balance by the monthly interest rate: $660.30 * 0.005167 = $3.41
The finance charge on a credit card account with a balance of $660.30 and an Annual Percentage Rate (APR) of 6.2% is determined to be $3.41. This finance charge represents the cost of borrowing on the credit card and is calculated based on the outstanding balance and the interest rate.
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In the figure, is tangent to the circle at point U. Use the figure to answer the question.
Hint: See Lesson 3. 09: Tangents to Circles 2 > Learn > A Closer Look: Describe Secant and Tangent Segment Relationships > Slide 4 of 8. 4 points.
Suppose RS=8 in. And ST=4 in. Find the length of to the nearest tenth. Show your work.
1 point for the formula, 1 point for showing your steps, 1 point for the correct answer, and 1 point for correct units.
If you do not have an answer please dont comment
The length of UT, to the nearest tenth, is approximately 10.5 inches.
How long is segment UT?
To find the length of UV, we can use the tangent-secant theorem, which states that the square of the length of the tangent segment (UV) is equal to the product of the lengths of the secant segments (RS and ST).
First, we need to find the length of RS + ST:
RS + ST = 8 in + 4 in = 12 in
Next, we can use the formula for the tangent-secant theorem:
[tex]UV^2 = RS * ST[/tex]
[tex]UV^2 = 8 in * 4 in[/tex]
[tex]UV^2 = 32 in^[/tex]
To find the length of UV, we take the square root of both sides:
[tex]UV = √32 in[/tex]
Calculating the square root, we get:
UV ≈ 5.7 in (rounded to the nearest tenth)
Therefore, the length of UV is approximately 5.7 inches.
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It is claimed that 75% of puppies are house-trained by the time they are 6 months old. To investigate this claim, a random sample of 50 puppies is selected. It is discovered that 42 are house-trained by the time they are 6 months old. A trainer would like to know if the data provide convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. The standardized test statistic is z = 1. 47 and the P-value is 0. 708. What conclusion should be made using the Alpha = 0. 05 significance level?
Because the P-value is greater than Alpha = 0. 05, there is convincing evidence that 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is not convincing evidence that 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old.
Because the P-value is greater than Alpha = 0. 05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old
The conclusion should be made using the Alpha = 0. 05 significance level is because the P-value is greater than Alpha = 0.05, there is not convincing evidence that greater than 75% of puppies are house-trained by the time they are 6 months old. The correct answer is B.
The given null hypothesis is that 75% of puppies are house-trained by the time they are 6 months old. The alternative hypothesis is that greater than 75% of puppies are house-trained by the time they are 6 months old.
The test statistic is a z-score, which is calculated by subtracting the hypothesized proportion (0.75) from the sample proportion (42/50 = 0.84), dividing by the standard error of the sample proportion, and then standardizing with respect to the standard normal distribution. The resulting z-score is 1.47.
The P-value is the probability of observing a test statistic as extreme or more extreme than the calculated z-score, assuming the null hypothesis is true. A P-value of 0.708 means that there is a 70.8% chance of observing a sample proportion as extreme or more extreme than 0.84, assuming that 75% of puppies are house-trained by the time they are 6 months old.
Since the P-value is greater than the significance level (alpha) of 0.05, we fail to reject the null hypothesis. In other words, there is not convincing evidence to suggest that greater than 75% of puppies are house-trained by the time they are 6 months old.
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A game has a spinner with 15 equal sectors labeled 1 through 15. what is p(multiple of 3 or multiple of 7)? 215 13 25 715
Answer: D. 7/15 or
Step-by-step explanation:
You have 15 possible outcomes
Probability= possibilities/outcomes
Possible numbers that are multiples of 3 are: 3, 6, 9, 12, 15. There are 5 possibilities.
P(multiple of 3) = 5/15
Possible numbers that are multiples of 7 are: 7, 14, . There are 2 possibilities.
P(7) = 2/15
Because of the or you add th e probabilities
P(multiple of 3 or multiple of 7) = 5/15 +2/15 =7/15
D
Find the area of the composite figure to the nearest hundredth.
55 mm
32. 5 mm
12. 5 mm
12. 5 mm
The area of the composite figure is approximately 2447.43 square millimeters to the nearest hundredth.
To find the area of the composite figure, we need to divide it into simpler shapes and then find their areas separately. The composite figure is made up of a rectangle and two semicircles.
First, let's find the area of the rectangle. The length of the rectangle is 55 mm and the width is 32.5 mm, so the area of the rectangle is:
[tex]$$A_{rect} = length \times width = 55 \text{ mm} \times 32.5 \text{ mm} = 1787.5 \text{ mm}^2$$[/tex]
Next, let's find the area of each semicircle. The diameter of each semicircle is equal to the width of the rectangle, which is 32.5 mm. Therefore, the radius of each semicircle is:
[tex]$$r =[/tex] [tex]\frac{32.5 \text{ mm}}{2} = 16.25 \text{ mm}$$[/tex]
The formula for the area of a semicircle is:
[tex]$$A_{semicircle} = \frac{1}{2} \pi r^2$$[/tex]
So, the area of each semicircle is:
[tex]$$A_{semicircle} = \frac{1}{2} \pi (16.25 \text{ mm})^2 \approx 329.97 \text{ mm}^2$$[/tex]
To find the total area of the composite figure, we add the area of the rectangle to the area of the two semicircles.
[tex]$$A_{total} = A_{rect} + 2 \times A_{semicircle} \approx 2447.43 \text{ mm}^2$$[/tex]
Therefore, the area of the composite figure is approximately 2447.43 square millimeters to the nearest hundredth.
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Given l||m||n, find the value of x
Answer:
x = 13
Step-by-step explanation:
We Know
(5x - 6) + (8x + 17) must equal 180°
Find the value of x.
Let's solve
5x - 6 + 8x + 17 = 180
13x + 11 = 180
13x = 169
x = 13
So, the value of x is 13.
Once Farid spends 15 minutes on a single level in his favorite video game, he loses a life. He has already spent 10 minutes on the level he's playing now.
Let x represent how many more minutes Farid can play on that level without losing a life. Which inequality describes the problem?
A. 10 + x > 15
B. 10 + x < 15
Solve the inequality. Then, complete the sentence to describe the solution.
Farid can play less than _______ more minutes on that level without losing a life
The correct inequality to describe the problem is A. 10 + x > 15, which means that the total time Farid spends on the level (10 + x) must be greater than 15 minutes in order for him to lose a life.
To solve the inequality, we can start by isolating x on one side of the inequality:
10 + x > 15
Subtracting 10 from both sides, we get:
x > 5
This means that Farid can play for up to 5 more minutes on the level without losing a life, since spending a total of 10 + 5 = 15 minutes on the level would cause him to lose a life.
Therefore, the solution to the inequality is "Farid can play less than 5 more minutes on that level without losing a life."
Overall, the correct option is A. 10 + x > 15.
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Find f(a) if y = f(a) satisfies
dy/dx = 24yx³
and the y-intercept of the curve y = f(2) is 5. f(x) = ...
The solution to the differential equation is f(a) = 1/√(12a⁴/125 - 769/5000).
How to find the derivative of given equation?To find f(a), we need to solve the differential equation:
dy/dx = 24yx³
Separating variables, we get:
dy/y³ = 24x³ dx
Integrating both sides, we get:
-1/(2y²) = 6x⁴ + C
where C is the constant of integration.
To find the value of C, we use the fact that the y-intercept of the curve y = f(2) is 5. This means that when x = 2, y = 5. Substituting these values into the equation above, we get:
-1/(2(5)²) = 6(2)⁴ + C
Simplifying and solving for C, we get:
C = -1/(2(5)²) - 6(2)⁴
C = -769/125
So the solution to the differential equation is:
-1/(2y²) = 6x⁴ - 769/125
Solving for y, we get:
y = 1/√(12x⁴/125 - 769/5000)
Therefore, f(a) = 1/√(12a⁴/125 - 769/5000).
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1. If RZ = 2x + 5 and TW = 5x - 20, find the value of 'x'. (just write the number no
text) *
The value of the x is 8.33 under the given condition that RZ is given as 2x + 5 and TW is given as 5x - 20.
From the given question and illustrative diagram we can clearly see that
RZ = 2x + 5
TW = 5x - 20
Now, we have to find the value of 'x' if RZ = 2x + 5 and TW = 5x - 20.
Then, from the given rectangle figure, we can say that RZ is equal to TW.
Hence equating both the equation we can evaluate that the value of x and the equation can be expressed in the forms of
RZ = TW
2x + 5 = 5x - 20
20 + 5 = 5x - 2x
25 = 3x
x = 25/3
x = 8.33
Then, the value of the x is 8.33.
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Pls help me out with this!
Answer: C
Step-by-step explanation:
Since from your original g(x) went to f(x) which is up 6
add 6 to g(x)
g(x)= f(x) +6
The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 1995, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1282.
The nearest year, we can estimate that the number of new cases would reach 1282 in the year 2017.
Find the linear regression equation and estimate the year when the number of new cases would reach 1282 for a county in New York state, given the accompanying table.
To find the linear regression equation, we need to use the formula:
y = a + bx
where y is the number of new cases, x is the number of years since 1995, a is the y-intercept and b is the slope of the line.
Using the given data, we can find the values of a and b using the formulas:
b = (nΣxy - ΣxΣy) / (nΣ[tex]x^2[/tex] - (Σx)[tex]^2)[/tex]
a = (Σy - bΣx) / n
where n is the number of data points, Σxy is the sum of the products of x and y, Σx is the sum of x, Σy is the sum of y, and Σ[tex]x^2[/tex] is the sum of squares of x.
Using these formulas and the given data, we get:
n = 9
Σx = 36
Σy = 7386
Σx^2 = 162
Σxy = 3330
b = (93330 - 367386) / (9*162 - 36^2) ≈ -75.44
a = (7386 - (-75.44)*36) / 9 ≈ 2612.67
Therefore, the linear regression equation is:
y ≈ 2612.67 - 75.44x
To estimate the year in which the number of new cases would reach 1282, we can substitute y = 1282 into the equation and solve for x:
1282 ≈ 2612.67 - 75.44x
75.44x ≈ 2612.67 - 1282
x ≈ 22.36
This means that the number of new cases would reach 1282 approximately 22.36 years after 1995. Adding this to 1995 gives us an estimate of the calendar year:
1995 + 22.36 ≈ 2017.36
Rounding to the nearest year, we can estimate that the number of new cases would reach 1282 in the year 2017.
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Type the correct answer in the box.
use numerals instead of words.
the initial population of the town was estimated to be 12,500 in 2005. the population has increased by about 5.4% per year since 2005.
formulate the equation that gives the population, a(x), of the town xyears since 2005. if necessary, round your answer to the nearest
thousandth.
a(x)=__(__)^x
wrong answers will be reported!!
The correct equation that gives the population, a(x), of the town x years since 2005 is:
a(x) = 12,500 * (1 + 0.054)ˣ
How to formulate the population equation for the town?The given problem states that the population of the town has been increasing by about 5.4% per year since 2005. To formulate the equation for the population, we need to use the initial population of 12,500 in 2005 and apply the growth rate of 5.4% per year.
The general formula for exponential growth is:
a(x) = a(0) * (1 + r)ˣ
Where:
a(x) is the population at a given time x years since the initial time,
a(0) is the initial population (12,500 in this case),
r is the growth rate (5.4% or 0.054 as a decimal),
x is the number of years since the initial time (2005 in this case).
Plugging in the values, we get:
a(x) = 12,500 * (1 + 0.054)ˣ
This equation calculates the population of the town x years since 2005.
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Cuánto interés ganará lesli si presta l 5000 a pagar en 3años? al:5%simple anual. 10%simple anual. 5%compuesto anual
The interest gained by Lesli is if she lends $5000 for 3 years at 5% simple interest annually is $750, 10% simple interest annually is $1500, and on 5% compound interest annually is $790
The simple interest is calculated by
I = P * r * t
where P is the principal
r is the rate of interest
t is the time
I is the simple interest
The compound interest is calculated by:
I = P[tex](1 +r)^t[/tex] - P
where I is the compound interest
P is the principal
r is the rate of interest
t is the time
According to the question,
P = $5000
t = 3 years
1. r = 5% simple interest
I = 5000 * 3 * 0.05
= $750
2. r = 10% simple interest
I = 5000 * 3 * 0.10
= $1500
3. r = 5% compounded annually
I = 5000 [tex](1+0.05)^3[/tex] - 5000
= 5000 * 1.158 - 5000
= $790
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The question is in Spanish, and the question in English is:
How much interest will Lesli earn if she lends 15,000 to be paid in 3 years? at: 5% annual simple. 10% simple annual. 5% compounded annually
Choose all the expressions that are equal to 45×67 4 5 × 6 7. A. 2435 24 35 B. 4×75×6 4 × 7 5 × 6 C. 4×56×7 4 × 5 6 × 7 D. 6×54×7 6 × 5 4 × 7 E. 6×45×7 6 × 4 5 × 7
None of the given expressions (A, B, C, D, E) are equal to 45 x 67.
How to find which expressions are equal to multiplication?To find which expressions are equal to 45 x 67, we simply need to simplify each of the expressions given.
Starting with option A, 24 x 35, this is not equal to 45 x 67.Moving on to option B, we have 4 x 75 x 6. Simplifying this, we get 1,800, which is not equal to 45 x 67.Option C is 4 x 56 x 7, which simplifies to 1,568, not equal to 45 x 67.Option D is 6 x 54 x 7, which simplifies to 2,268, not equal to 45 x 67.Finally, option E is 6 x 45 x 7, which simplifies to 1,890, also not equal to 45 x 67.Therefore, none of the expressions are equal to 45 x 67.
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Complete the description of a real-world situation that might involve three linear equations in three variables.
you are trying to find the ages of three people. you know the sum of all three ages, the sum of the first two ages and blank (the answer choices are twice the third or the third age squared), and the sum of the first and third ages and blank (the answer choices are twice the second or the square root of the second)
* just to be clear there are two blanks and two possible answer choices for each
A real-world situation that might involve three linear equations in three variables is trying to determine the ages of three siblings.
Let's call them A, B, and C. We know that the sum of all three ages is a certain value, let's say it's 60. We also know the sum of the first two ages is either twice the third age or the third age squared. For example, if the sum of the first two ages is twice the third age, we could write it as A + B = 2C.
Alternatively, if the sum of the first two ages is the third age squared, we could write it as A + B = C^2. Similarly, we know the sum of the first and third ages is either twice the second age or the square root of the second age. So, we could write it as A + C = 2B or A + C = sqrt(B).
We now have three linear equations in three variables that we can use to solve for the ages of the three siblings. By solving the system of equations, we can find out how old each sibling is.
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3. Suppose a simple random sample of 150 college students is drawn. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 95% confidence interval for the ents^ prime IQ score?
Answer: is approximately between 113.39 and 116.61
To calculate the 95% confidence interval for the students' average IQ score, we'll use the given information: sample size (n=150), sample mean (X=115), and sample standard deviation (s=10). We'll use the t-distribution since the population standard deviation is unknown.
First, we need to find the t-value for a 95% confidence interval with n-1 (149) degrees of freedom. Using a t-table or calculator, we find the t-value to be approximately 1.976.
Next, we'll calculate the standard error (SE) using the formula: SE = s/√n. In this case, SE = 10/√150 ≈ 0.816.
Now, we can find the margin of error (ME) using the formula: ME = t-value × SE. For this problem, ME = 1.976 × 0.816 ≈ 1.61.
Finally, to calculate the 95% confidence interval, we'll use the formula: X ± ME. Thus, the 95% confidence interval is 115 ± 1.61, which is approximately (113.39, 116.61).
So, the 95% confidence interval for the students' average IQ score is approximately between 113.39 and 116.61.
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In a restaurant 1/5 of the customers are vegetarian and 3/4 eat meat. The remainder of the customers are dairy intolerant. What fraction of the customers are dairy intolerant? Give your answer as a fraction in its lowest terms
1/20 of the customers are dairy intolerant.
We know that 1/5 of the customers are vegetarian, and 3/4 eat meat. Let's first find the total fraction of vegetarian and meat-eating customers:
1/5 (vegetarian) + 3/4 (meat)
To add these fractions, we need a common denominator. The least common denominator (LCD) for 5 and 4 is 20. So, we'll convert both fractions to have the same denominator:
(1/5)*(4/4) = 4/20 (vegetarian)
(3/4)*(5/5) = 15/20 (meat)
Now, let's add the fractions:
4/20 (vegetarian) + 15/20 (meat) = 19/20 (vegetarian and meat)
Now we know that 19/20 of the customers are either vegetarian or meat-eaters. The remainder must be dairy intolerant. To find this fraction, subtract the combined fraction from 1:
1 - 19/20 = 1/20
So, 1/20 of the customers are dairy intolerant.
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