Answer:
3:1 (Girls:Boys)
6 divided by 2
The percent of Tom winning a game is 20%, he played 30 games. How mang games did he lose?
Answer:
He won 6 games and lost 24 games.
Approximate the area of the region bounded by the graph of f(t) = cos (t/2 - 3 pi /8) and the t - axis on [3 pi /8, 11 pi /8] with n = 4 subintervals. Use the midpoint of each subinterval to determine the height of each rectangle (see figure). The approximate area of the region is . (Round to two decimal places as needed.)
To approximate the area of the region bounded by the graph of f(t) = cos(t/2 - 3π/8) and the t-axis on the interval [3π/8, 11π/8] using 4 subintervals, we can use the midpoint rule.
The width of each subinterval is (11π/8 - 3π/8) / 4 = π/2.
We can calculate the height of each rectangle by evaluating the function at the midpoint of each subinterval.
The midpoints of the subintervals are:
t₁ = 3π/8 + π/4 = 5π/8
t₂ = 5π/8 + π/4 = 7π/8
t₃ = 7π/8 + π/4 = 9π/8
t₄ = 9π/8 + π/4 = 11π/8
Calculating the corresponding heights:
f(t₁) = cos(5π/16 - 3π/8)
f(t₂) = cos(7π/16 - 3π/8)
f(t₃) = cos(9π/16 - 3π/8)
f(t₄) = cos(11π/16 - 3π/8)
Now we can calculate the area of each rectangle by multiplying the width by the height.
Area of rectangle 1: (π/2) * f(t₁)
Area of rectangle 2: (π/2) * f(t₂)
Area of rectangle 3: (π/2) * f(t₃)
Area of rectangle 4: (π/2) * f(t₄)
Finally, we can approximate the total area by summing up the areas of all the rectangles:
Approximate area = Area of rectangle 1 + Area of rectangle 2 + Area of rectangle 3 + Area of rectangle 4
Please note that I cannot provide the exact numerical values as the calculation involves trigonometric functions and the specific values of π/8.
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Please help me. I don’t know
Step-by-step explanation:
Area of square = Length x Length =
[tex] {length}^{2} [/tex]
Given Area of square =
[tex]256 {ft}^{2} [/tex]
[tex] {length}^{2} = 256 \\ length = \sqrt{256} \\ = 16ft[/tex]
Tell whether the angles are complementary, supplementary, or neither.
Answer:
supplementary (add together to = 180°)
Step-by-step explanation:
Step-by-step explanation:
Supplementary angles add up to 180
complementary angles add up to 90
75+105=180
so the angles are supplementary
Hope that helps :)
Pls help ASAP. SHOW WORK
The new figure after the revolution is a cylinder of radius 5 and length 8
The volume is 200π
How to determin the new figure after the revolutionFrom the question, we have the following parameters that can be used in our computation:
The graph
The shape on the graph is a rectangle with
length = 5
width = 8
When revolved across the x-axis, we have the shape to be
A cylinder of radius 5 and length 8 (option a)
This is calculated as
V = πr²h
substitute the known values in the above equation, so, we have the following representation
V = π * 5² * 8
Evaluate
V = 200π
Hence, the volume is 200π
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let f(x) = x 4 and g(x) = x – 3. if g is a vertical translation of f, how many units and in what direction is f translated to form g?
The number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x) is -2 units. Since the value of d is negative, the direction of the translation is downwards. Thus, we can say that f(x) is translated 2 units downwards to form g(x).
f(x) = x⁴ and g(x) = x – 3, Since g is a vertical translation of f, we know that the graph of g(x) can be obtained by translating the graph of f(x) vertically up or down by some units, d. Thus, we can express g(x) as follows:g(x) = f(x) + d
Here, d represents the number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x). Now, f(x) = x⁴, which means that the graph of f(x) is a standard cubic graph that has not undergone any transformation. We can represent this graph by the equation y = x⁴.
When g(x) is a vertical translation of f(x), we can write g(x) = y + d where d is the number of units by which f(x) is translated vertically to obtain g(x). Thus, we can rewrite g(x) as:
g(x) = f(x) + d
Substituting the values of f(x) and g(x), we get: x – 3 = x⁴ + d
Rearranging the equation, we have:x⁴ = x – 3 – d
Now, the number of units by which the graph of f(x) is translated vertically to obtain the graph of g(x), we need the value of d. To do this, we can use the fact that the graphs of f(x) and g(x) intersect at some point. At this point, the value of f(x) is equal to the value of g(x). Thus, we can write x⁴ = x – 3 – d
Solving this equation, we get x⁴ = x – (3 + d), the value of d by comparing the coefficients of x on both sides of the equation. On the left-hand side of the equation, the coefficient of x is 0, while on the right-hand side of the equation, the coefficient of x is 1. Thus, we can write:
0 = 1 – (3 + d)
Simplifying this equation, we get: d = -2
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PLEASE HELP! WILL GIVE BRAINLIEST ANSWER!!
Distance run by each member of the Chicago Race Club.
In which interval is the median distance?
A. 0-5
B. 5-10
C. 10-15
D. 15-20
Answer:
I wanna say that it is 10-15
Step-by-step explanation:
Answer:
10-15
Step-by-step explanation:
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Work out the surface area of this cylinder. Give your answer in terms of π.
Please help.
Don’t comment a random link or I will report you!!
Answer:
2010.62cm²
Step-by-step explanation:
The equation for the surface area of cylinder is:
A = 2πrh + 2πr²
Hope it was helpful
Which expression is represented on the number line?
Answer:
b
Step-by-step explanation:
Let's assume you are conducting an experiment to determine the effect of a new drug on the incidence of epileptic seizures. You select 20 epileptics from the 150 epileptics being treated at a nearby hospital and administer the drug to them. You record the number of seizures in each of the 20 subjects for one month. The 20 subjects constitute _________.
Answer:
The 20 subjects constitutes the sample
Step-by-step explanation:
Given
[tex]Total = 150[/tex]
[tex]Selected = 20[/tex]
Required
What does 20 represent?
The 150 patients being treated is the population of the study. When a certain amount is selected from a population, the selected is referred to as a sample.
So, this means that, 20 represents sample of the study.
The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal with mean 8.1 ounces and standard deviation 0.1 ounces. Company managers do not want the weight of a chocolate bar to fall below 8 ounces, for fear that consumers will complain. (a) Find the probability that the weight of a randomly selected candy bar is less than 8 ounces Forty candy bars are selected at random and their mean weight is computed. (b) Calculate the mean and standard deviation of the sampling distribution of (c) Find the probability that the mean weight of the forty candy bars is less than 8 ounces. (d) Would your answers to (a), (b), or (c) be affected if the weights of chocolate bars produced by this machine were distinctly non-Normal? Explain.
a. the probability that the weight of a randomly selected candy bar is less than 8 ounces is approximately 0.1587 or 15.87%. b. the standard deviation of the sampling distribution is 0.1 / sqrt(40) ≈ 0.0159 ounces. c. the probability that the mean weight of the forty candy bars is less than 8 ounces is almost 0 or very close to 0.
(a) The probability that the weight of a randomly selected candy bar is less than 8 ounces can be found by calculating the cumulative probability using the Normal distribution. Given that the distribution of weights is Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces, we want to find P(X < 8), where X represents the weight of a candy bar.
Using the properties of the Normal distribution, we can standardize the variable X using the formula Z = (X - μ) / σ, where Z is the standard normal random variable, μ is the mean, and σ is the standard deviation.
For our case, we have Z = (8 - 8.1) / 0.1 = -1.
Using a standard normal distribution table or a calculator, we find that the cumulative probability for Z = -1 is approximately 0.1587. Therefore, the probability that the weight of a randomly selected candy bar is less than 8 ounces is approximately 0.1587 or 15.87%.
(b) The mean of the sampling distribution of the sample mean can be calculated as the same as the mean of the population, which is 8.1 ounces.
The standard deviation of the sampling distribution of the sample mean, also known as the standard error of the mean, can be calculated using the formula σ / sqrt(n), where σ is the standard deviation of the population and n is the sample size.
In our case, the standard deviation of the population is 0.1 ounces, and the sample size is 40 candy bars. Therefore, the standard deviation of the sampling distribution is 0.1 / sqrt(40) ≈ 0.0159 ounces.
(c) To find the probability that the mean weight of the forty candy bars is less than 8 ounces, we can again use the properties of the Normal distribution. Since the mean and standard deviation of the sampling distribution are known, we can standardize the variable using the formula Z = (X - μ) / (σ / sqrt(n)).
In this case, we have Z = (8 - 8.1) / (0.0159) ≈ -6.29.
Using a standard normal distribution table or a calculator, we find that the cumulative probability for Z = -6.29 is extremely close to 0. Therefore, the probability that the mean weight of the forty candy bars is less than 8 ounces is almost 0 or very close to 0.
(d) The answers to (a), (b), and (c) would not be affected if the weights of chocolate bars produced by this machine were distinctly non-Normal. This is because of the Central Limit Theorem, which states that regardless of the shape of the population distribution, as the sample size increases, the sampling distribution of the sample mean approaches a Normal distribution.
In our case, we have a sufficiently large sample size of 40, which allows us to rely on the Central Limit Theorem. As long as the sample size is large enough, the sampling distribution of the sample mean will still be approximately Normal, even if the population distribution is non-Normal.
Therefore, we can still use the Normal distribution to calculate probabilities and determine the mean and standard deviation of the sampling distribution, regardless of the population distribution being non-Normal.
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A Correlation Coefficient Of −0.8 Indicates Strong Indirect Relationship. TRUE/FALSE
The given statement “A correlation coefficient of −0.8 indicates strong indirect relationship” is true because it indicates a strong inverse or negative relationship between the variables.
What is the correlation coefficient?A correlation coefficient is a statistical measure of the degree to which variables are related to one another. It is a numerical value that ranges from -1 to 1 and represents the strength and direction of the relationship between two variables.
If the correlation coefficient is -1, the relationship is strong and negative (inverse). On the other hand, if the correlation coefficient is 1, the relationship is strong and positive (direct).
When the correlation coefficient is zero, it indicates no relationship between the variables. When the correlation coefficient is near zero, it indicates a weak relationship between the variables.
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You have an annual salary of $47,334. Your monthly expenses include a $1,115 mortgage payment, a $336 car lease payment, $112 in minimum credit card payments, and a $108 payment on your student loan. Calculate your DTI (debt-to-income) ratio as a PERCENTAGE (no % symbol needed).
Answer:
DTI ratio in percentage = 42.36
Step-by-step explanation:
Annual salary = $47334
This means that gross monthly pay = 47334/12 = $3944.5
Now,
Total monthly debt payments = 1115 + 336 + 112 + 108 = $1671
Debt to income ratio = (1671/3944.5) × 100% = 42.36%
Since we are told not to put the % symbol, then answer is 42.36
Assume that the differences are normally distributed. Complete parts (a) through (d) below.
Observations 1, 2, 3, 4, 5, 6, 7, 8
хi 45.4 45.5 45.5 42.9 45.2 47.4 51.4 43.1
Yi 46.5 46.6 49.7 47.5 48.1 50.3 52.2 45.5
(a) Determine di = Xi - Yi for each pair of data.
Observations 1 2 3 4 5 6 7 8
di = _______________
The differences di = Xi - Yi for each pair of data are:
-1.1, -1.1, -4.2, -4.6, -2.9, -2.9, -0.8, -2.4.
To determine the differences di = Xi - Yi for each pair of data, we subtract the corresponding values of Xi and Yi:
Observations: 1 2 3 4 5 6 7 8
Xi: 45.4 45.5 45.5 42.9 45.2 47.4 51.4 43.1
Yi: 46.5 46.6 49.7 47.5 48.1 50.3 52.2 45.5
di = Xi - Yi: -1.1 -1.1 -4.2 -4.6 -2.9 -2.9 -0.8 -2.4
Therefore, the differences di = Xi - Yi for each pair of data are:
-1.1, -1.1, -4.2, -4.6, -2.9, -2.9, -0.8, -2.4.
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The charge to ship a package from one town to another, C, is given below as a function of the weight of the object, w, in pounds.
C = $3.50 + $0.55w
If the shipping cost for Cathy's item was $7.02, what was its weight?
A. 6.4 pounds
B. 64 pounds
C. 16.4 pounds
D. 0.64 of a pound
Answer:
Option A
Step-by-step explanation:
The total shipping cost given was $7.02.
C = 7.02
Solve for 'w'.
[tex]C = $3.50 + $0.55w\\\\7.02=3.50+0.55w\\\\3.52=0.55w\\\\\boxed{6.4=w}[/tex]
Hope this helps.
Does someone mind helping me with this? I thought I had it but didnt. Thank you!
When x = 5, y = -1
When x = 6, y = 0
When x = 9, y = 1
When x = 14, y = 2
Jake writes this word expression.
the product of 9 and m
Enter an algebraic expression for the word expression.
The expression is m.
Then, evaluate the expression for m = 6.
Ben needs to replace two sides of his fence. One side is meters long, and the other is meters long. How much fence does Ben need to buy?
Answer:
696 39/100 meters
Step-by-step explanation:
Ben needs to replace two sides of his fence. One side is 367 9/100 meters long, and the other is 329 3/10 meters long. How much fence does Ben need to buy?
Side A = 367 9/100 meters
Side B = 329 3/10 meters
How much fence does Ben need to buy?
Total fence Ben needs to buy = Side A + side B
= 367 9/100 + 329 3/10
= 36709/100 + 3293/10
= (36709+32930) / 100
= 69639/100
= 696 39/100 meters
Ben needs to buy 696 39/100 meters
Find the value of x so that the ratios 8 : x and 12 : 18 are equivalent.
Answer:
12
Step-by-step explanation:
12:18=2:3 multiply by four to get 8 as the first term
8:12
8:x
so x is 12.
*this could be wrong so check my work
Answer:
x = 12
Explanation:
8 : x
12 : 18
to find the value of x, we need to convert 12 into 8. since they both have a common factor of 4, we can divide 12 by 3 to get 4, and then multiply it by 2 to get 8. in numerical terms, this is:
12 ÷ 3 = 4
4 × 2 = 8
now, we can do the same for 18.
18 ÷ 3 = 6
6 × 2 = 12
thus, 12 : 18 is equivalent to 8 : 12. x = 12.
Find the amount necessary to fund the given withdrawals.
Semiannual withdrawals of 270$ for 6 years, interest rate is 6.2% compounded semiannually
Answer:
the amount that necessary to fund is $2,671.61
Step-by-step explanation:
The computation of the amount is shown below;
Given that
PMT = $270
NPER = 6 × 2 = 12
RATE = 6.2% ÷ 2 = 3.1%
FV = $0
The formula is shown below:
=-PV(RATE;NPER;PMT;FV;TYPE)
After applying the above formula the present value is $2,671.61
hence, the amount that necessary to fund is $2,671.61
A bag contains 12 yellow tiles and 12 blue tiles. A student will choose one tile from the bag without looking. Which word(s) describe the probability of choosing a blue tile from the bag? likely O certain O impossible O equally likely
on a k12 quiz btw
Answer:
Equally Likely
Find the total lateral area of the following
cone. Leave your answer in terms of a.
4 cm
3 cm
LA = ? cm2
Answer:
15π cm²
Step-by-step explanation:
The total lateral area of a cone
= πr√h² + r²
= √h² + r² = l
h = Height = 4cm
r = radius = 3cm
Hence:
= π × 3 √4² + 3²
= 3π × √16 + 9
= 3π × √25
= 3π × 5
= 15π cm²
if the probability of winning $10 on a bet is 50% and the probability of winning nothing is 50%, what is the expected value of the bet?
The expected value of the bet is $5.
The expected value of the bet is calculated by multiplying each possible outcome by its corresponding probability and summing them up. In this case, there are two possible outcomes: winning $10 with a probability of 50% (0.5) and winning nothing with a probability of 50% (0.5).
To find the expected value, we multiply the value of each outcome by its probability:
Expected Value = ($10 * 0.5) + ($0 * 0.5) = $5 + $0 = $5.
Therefore, the expected value of the bet is $5. This means that, on average, for each bet placed, we can expect to win $5. It represents the long-term average outcome and is useful in assessing the overall value or profitability of the bet.
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Solve the inequality.
- 5x > 25
Answer and Step-by-step explanation:
Divide -5 from both sides of the inequality.
x < -5 is the answer.
Here's Why:
If you were to add 5x to both sides, it results in this:
0 > 25 + 5x
Now, we subtract 25 from both sides.
-25 > 5x
When we divide 5 from both sides, we see that it results in -5 > x, which is the same as x < -5.
#teamtrees #PAW (Plant And Water)
Given the line y = 3x + 5:
Write the equation of a line, in point-slope form, that is parallel to the original and passes through the point (7,1)
1. A random sample of 400 married couples was selected from a large population of married couples. There were 20 couples in which the wife was taller than her husband, and there were 380 couples in which the wife was shorter that her husband. Find a 95 percent confidence interval for the proportion of married couples in the population for which the wife is taller than her husband. Interpret your interval in the context of this question.
Answer:
[tex]CI = (0.028636,0.071364)[/tex]
I am 95% confident that the true proportion of couples where the wife is taller than her husband is captured in the interval (.028, .071)
Step-by-step explanation:
Given
[tex]n = 400[/tex]
[tex]x = 20[/tex] --- taller wife
[tex]y = 380[/tex] --- shorter wife
Required
Determine the 95% confidence interval of taller wives
First, calculate the proportion of taller wives
[tex]\hat p = \frac{x}{n}[/tex]
[tex]\hat p = \frac{20}{400}[/tex]
[tex]\hat p = 0.05[/tex]
The z value for 95% confidence interval is:
[tex]z = 1.96[/tex]
The confidence interval is calculated as:
[tex]CI = \hat p \± z \sqrt{\frac{\hat p (1 - \hat p)}{n}}[/tex]
[tex]CI = 0.05 \± 1.96* \sqrt{\frac{0.05 (1 - 0.05)}{400}}[/tex]
[tex]CI = 0.05 \± 1.96 * \sqrt{\frac{0.0475}{400}}[/tex]
[tex]CI = 0.05 \± 1.96 * \sqrt{0.00011875}[/tex]
[tex]CI = 0.05 \± 1.96 * 0.01090[/tex]
[tex]CI = 0.05 \± 0.021364[/tex]
This gives:
[tex]CI = (0.05 - 0.021364,0.05 + 0.021364)[/tex]
[tex]CI = (0.028636,0.071364)[/tex]
Using the Proportion to Find a Missing Measure
Try it
5
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Use the proportion to solve for the unknown base measure of the enlarged trapezoid.
2 .
1 Set up the proportion
3.25 6.5
2.Use cross products
2(6.5) = 3.25()
3. Simplify
13 = 3.25x
4 Divide both sides by 3.25
The missing base measure of the enlarged trapezoid is
cm
Answer:
4 cm
Step-by-step explanation:
match the lines l1 (blue), l2 ( red) and l3 (green) with the slopes by placing the letter of the slopes next to each set listed below:
I apologize, I cannot visually perceive or manipulate colors or lines directly. However, if you provide me with the equations of the lines or any additional information about their slopes, I would be more than happy to help you match the slopes with the corresponding lines.
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To match the lines (l1, l2, l3) with their corresponding slopes, we need to assign letters representing the slopes to each set.
Without specific information about the lines l1, l2, and l3, it is not possible to determine the exact slopes or their corresponding letters. In order to match the lines with their slopes, we would need additional details such as the equations of the lines or the coordinates of points on the lines.
The slope of a line represents the rate at which the line changes vertically (y-axis) with respect to the horizontal (x-axis). It is typically denoted by the letter "m" in mathematical notation.
To accurately match the lines l1, l2, and l3 with their respective slopes, we require more information about the lines themselves. Once the equations or coordinates are provided, we can calculate the slopes using the formula for slope, which is the change in y divided by the change in x.
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Pedro said, "On summer vacation, I spent 3 1/2 weeks with my uncle and two weeks more with my friend than with my uncle." How many weeks did he spend with his uncle and his friend? Use fraction strips or number lines to find the sum.
Answer:
Pedro spent 9 weeks with his uncle and his friend.
Step-by-step explanation:
First, you need to find the amount of weeks Pedro spent with his friend. The statement indicates that he spent two weeks more with his friend than with his uncle which means that you have to add the number of weeks he spent with his uncle plus 2, which you can show in a number line:
[tex]3\frac{1}{2}[/tex] 2
___________________
1 2 3 4 5 6 7 8 9 10
[tex]3\frac{1}{2}+2=5\frac{1}{2}[/tex]
Now, you can find the and answer by adding up the number of weeks he spent with his uncle plus the weeks he spent with his friend:
[tex]3\frac{1}{2}[/tex] [tex]5\frac{1}{2}[/tex]
__________________________________
1 2 3 4 5 6 7 8 9 10
[tex]3\frac{1}{2} + 5\frac{1}{2}=9[/tex]
According to this, the answer is that Pedro spent 9 weeks with his uncle and his friend.
Write an equation of the line that passes through the point (4, 14) and is parallel to the line whose equation is y=3x-7.
Answer:
y = 3x + 2
Step-by-step explanation:
If the line is parallel, then the slope remains the same.
To find the y-intercept, just plug the coordinates into the equation
y = 3x + b
14 = 3(4) + b
14 = 12 + b
2 = b
The equation is y = 3x + 2
Answer:
Slope intercept form
y=3x^2−19x+42
or
Point slope form
y−14=(3x−7)⋅(x−4)
Step-by-step explanation:
:)