The probability that more than 7 of the invoices will be paid within ten working days is 0.8281
This is a binomial distribution problem where:
n = 10 (sample size)
p = 0.5 (probability of success, i.e., an invoice being paid within ten working days)
We need to find the probability of getting more than 7 invoices paid within ten working days, i.e., P(X > 7), where X is the number of invoices paid within ten working days.
Using the binomial probability formula, we get:
[tex]P(X > 7) = 1 - P(X ≤ 7)[/tex]
=[tex]1 - ∑(i=0 to 7) [nCi * p^i * (1-p)^{(n-i)][/tex]
where nCi is the number of ways to choose i items from n items, given by [tex]nCi = n! / (i! * (n-i)!).[/tex]
Calculating the above expression, we get:
[tex]P(X > 7) = 1 - [10C0 * 0.5^0 * 0.5^10 + 10C1 * 0.5^1 * 0.5^9 + ... + 10C7 * 0.5^7 * 0.5^3][/tex]
[tex]= 1 - 0.1719[/tex]
[tex]= 0.8281[/tex]
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what is the sales tax rate on an $8.50 purchase if the sales-tax rate is 6[tex]\frac{x}{y} 1/2[/tex]%
The sales tax rate is 6%
what is the sales tax rate on an $8.50 purchase if the sales-tax rate is 6x/y1/2%?If the sales-tax rate is 6%, the tax paid on an $8.50 purchase would be:
Tax = 0.06 x $8.50
Tax = $0.51
Therefore, the total cost of the purchase including sales tax would be:
Total cost = $8.50 + $0.51
Total cost = $9.01
The sales tax rate is 6%.
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Using the graph, determine the coordinates of the vertex of the parabola.
Answer:
Vertex = (-3, -4)
Step-by-step explanation:
The given graph is a parabola that opens upwards.
The vertex of a parabola that opens upwards is its lowest point (minimum value).
From inspection of the given graph, the lowest point is (-3, -4).
Therefore, the vertex of the parabola is (-3, -4).
justin developed the below hypothesis. h1: younger adults (18-28 years old) spend more time on social media than the middle-aged (29-65 years old) group and older adults (older than 65 years old). what statistical test should he use to test his hypothesis?
To verify if older adults and middles ages people spend less time on social media, Justin can use the Analysis of variance (ANOVA) test.
ANOVA is used to compare means across two or more groups. Justin can use this test on the different category of younger adults, middle-aged and older adult. This test is done when there is statistically significant difference between the group of samples.
Justin can utilize post-hoc tests (such as Tukey's HSD and Bonferroni) to identify whether particular groups are statistically different from one another if an ANOVA shows a significant difference.
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an oil prospector will drill a succession of holes in a given area to find a productive well. the probability that he is successful on a given trial is .2. a what is the probability that the third hole drilled is the first to yield a productive well? b if the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?
a) The probability that the third hole drilled is the first to yield a productive well is given by the following sequence of events: the first two holes must be unproductive, followed by a productive third hole. The probability of each of these events happening is:
- Probability of an unproductive hole: 0.8
- Probability of two unproductive holes in a row: 0.8
it is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. an experienced travel agent believes this is wrong. of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. we want to test the travel agent's theory with a hypothesis test. if you used a significance level of 0.05, what is your decision?
Based on the given information, we can set up the following hypotheses for the hypothesis test:
Null Hypothesis (H0): The actual proportion of people taking the cruise within 1 year is equal to the believed proportion of 5%.
Alternative Hypothesis (H1): The actual proportion of people taking the cruise within 1 year is not equal to the believed proportion of 5%.
Let p be the proportion of people taking the cruise within 1 year. We can use the sample proportion, denoted as p-hat, which is calculated as the ratio of the number of people who took the cruise within 1 year (3 in this case) to the total number of people who requested the brochures (100 in this case).
Given that the significance level is 0.05, we can use a z-test to compare the sample proportion with the believed proportion of 5%. The z-test statistic is calculated as:
z = (p-hat - p) / sqrt(p * (1 - p) / n)
where n is the sample size, which is 100 in this case.
Now we can calculate the z-test statistic and compare it with the critical value for a two-tailed test at a significance level of 0.05. If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis; otherwise, we would fail to reject the null hypothesis.
Since the sample proportion p-hat is 3/100 = 0.03, and the believed proportion p is 0.05, we can substitute these values into the z-test formula:
z = (0.03 - 0.05) / sqrt(0.05 * (1 - 0.05) / 100)
Calculating the above expression, we get the value of z. We can then compare this value with the critical value for a two-tailed test at a significance level of 0.05 from a standard normal distribution table or using a statistical calculator.
If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis and conclude that the actual proportion of people taking the cruise within 1 year is different from the believed proportion of 5%. If the calculated z-test statistic falls within the critical value, we would fail to reject the null hypothesis and not conclude that the actual proportion is different from the believed proportion.
Without the actual values of the calculated z-test statistic and the critical value, we cannot provide a specific decision for this hypothesis test. Please note that hypothesis testing requires careful consideration of the sample size, significance level, and other relevant factors, and should be conducted with caution and in consultation with a qualified statistician or expert in statistical analysis.
A survey found that the ratio of students who play intruments to those who do not was 7/20 of the students do not play an instrument 440 surveyd how many students surveyd play an instument
The number of students surveyed who plays an instrument is 114 students.
The ratio of students who play instruments to those who do not is 7/20, which means that out of every 7+20=27 students, 7 of them play an instrument and 20 of them do not.
If we know that 440 students were surveyed, we can set up a proportion to find the number of students who play an instrument:
7/27 = x/440
To solve for x, we can cross-multiply:
7 * 440 = 27 * x
3080 = 27x
x = 114.07
Since we can't have a fraction of a student, we should round up to the nearest whole number, which means that approximately 114 students surveyed play an instrument.
Therefore, the required answer is 114.
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what are the first four terms if a1=2 and an= an-1 +3?
The first four terms of the sequence are a₁ = 2, a₂ = 5, a₃ = 8, a₄ = 11.
What is arithmetic progression?The difference between every two successive terms in a sequence is the same; this is known as an arithmetic progression (AP). A good example of an arithmetic progression (AP) is the series 2, 6, 10, 14,..., which follows a pattern in which each number is created by adding 4 to the previous term.
The given sequence is defined as a₁=2 and aₙ= aₙ₋₁ + 3 for n > 1.
To find the first four terms of the sequence, we can use the recursive formula repeatedly:
a₁ = 2 (given)
a₂ = a₁ + 3 = 2 + 3 = 5
a₃ = a₂ + 3 = 5 + 3 = 8
a₄ = a₃ + 3 = 8 + 3 = 11
Therefore, the first four terms of the sequence are a₁ = 2, a₂ = 5, a₃ = 8, a₄ = 11.
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does the calculated percent fat from the experimental data in question 2 agree with the percent fat calculated from the label in question 3? why or why not? group of answer choices yes, they are the same. the two values differ by less than 1%. no, they are different. the two values differ by more than 1%.
If the experimental value is 10.1% and the label value is 10%, then the relative difference is 1%, which is equal to 1%. Therefore, you can say that they agree.
To determine if the calculated per cent fat from the experimental data in question 2 agrees with the per cent fat calculated from the label in question 3, follow these steps:
1. Calculate the per cent fat from the experimental data in question 2.
2. Calculate the per cent fat from the label in question 3.
3. Compare the two values.
If the two values are the same or differ by less than 1%, then the answer is yes, they agree. If the two values differ by more than 1%, then the answer is no, they do not agree.
Without the specific data from questions 2 and 3, I cannot provide a definite answer. However, you can use the steps provided above to determine if the calculated per cent fat from the experimental data agrees with the per cent fat calculated from the label.
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a simple random sample of 100 8th graders at a large suburban middle school indicated that 86% of them are involved with some type of after school activity. find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity. a) (0.699, 0.941) b) (0.829, 0.834) c) (0.779, 0.941) d) (0.679, 0.891) e) (0.779, 0.741) f) none of the above
For a random sample of 100 students related to aftee school activity. The 98% confidence interval that estimates the proportion of students who are involved in an after school activity is equals to (0.779, 0.941). So, option (c) is right one.
Confidence intervals represents the variation around a statistical estimate. A confidence interval is a range of interval of estimates for an unknown parameter.
[tex]CI = \hat p ± z_ \frac{ \alpha}{2}\sqrt{\frac{ ( 1 - \hat p)\hat p}{n}}[/tex]
where [tex]\hat p[/tex]-->sample proportion
n --> sample size
We have a simple random sample of 8ᵗʰ graders at a large suburban middle school. Sample size, n = 100
Sample proportion for students who involved with some type of school activity, [tex]\hat p[/tex] = 86% = 0.86
We have to calculate the 98% confidence interval that estimates the proportion of students sample.
Level of significance, α = 98%
= 0.98
Using the normal distribution table, value of z-score for 98% of confidence interval is 2.326 . Now, plug all known values in following confidence interval formula,
[tex]CI = \hat p ± z_ \frac{ \alpha}{2}\sqrt{\frac{ ( 1 - \hat p)\hat p}{n}}[/tex]
[tex]= 0.86 ± (2.326) \sqrt{\frac{ ( 1 - 0.86)0.86}{100}}[/tex]
[tex]= 0.86 ± (2.326) \sqrt{\frac{ ( 0.14)0.86}{100}}[/tex]
[tex]= 0.86 ± 0.081 [/tex]
[tex]= (0.86 - 0.081 , 0.86 + 0.081) [/tex]
= (0.779, 0.941)
Hence, required value is (0.779, 0.941).
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Find the distance, d, of AB.
The distance between A and B is approximately 8.06 units.
In order to find the distance, d, of AB, we need to use the distance formula. The distance formula gives us the distance between two points in a coordinate plane. It is given as:$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where (x1, y1) and (x2, y2) are the coordinates of the two points in question.
In this case, A and B are the two points for which we need to find the distance. Let's assume that the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2).
Then the distance formula becomes:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
$$d = \sqrt{((8 + 4) - 2)^2 + ((5 - 1) - 3)^2}$$
$$d = \sqrt{(10 - 2)^2 + (4 - 3)^2}$$
$$d = \sqrt{(8)^2 + (1)^2}$$
$$d = \sqrt{64 + 1}$$
$$d \approx \sqrt{65}$$
$$d \approx 8.06$$
Therefore, the distance between A and B is approximately 8.06 units.
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At a candy store, gummy bears are $5.25 per pound and jelly beans are $3.90 per pound. David has 1 3/4 pounds of jelly beans in his basket. Write and solve an inequality to determine the maximum number of pounds of gummy bears David can buy if he has $15 to spend. (Weights are measured to the nearest hundredth of a pound.)
If David already has 7/4 pounds of jelly beans, then 1.55 pounds of gummy bears can he buy.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
To determine the remaining amount of money available left to buy gummy bears, we have to find the amount of money already spent on jelly beans.
Amount of money spent on jelly beans;
= 7/4 × 3.90
= 6.825
Amount of money left for gummy bears ;
= 15-6.825
= 8.175
Thus, Pounds of gummy bears bought = 8.175 ÷ 5.25
= 1.55 pounds
Hence, If David already has 7/4 pounds of jelly beans, then 1.55 pounds of gummy bears can he buy.
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21st term: 3,8,13,18 What is the indicated term
The 21st term of the sequence 3, 8, 13, 18, .. is 103
To find the indicated term in the sequence, we first need to identify the pattern followed by the sequence. It appears that each term is obtained by adding 5 to the previous term. So, we can write the general formula for the nth term of the arithmetic sequence as
a(n) = a(1) + (n-1)d
where a(1) is the first term of the sequence, d is the common difference, and n is the term number.
In this case, we have:
a(1) = 3 (the first term)
d = 5 (the common difference)
To find the 21st term, we substitute n = 21 in the formula:
a(21) = a(1) + (21-1)d
a(21) = 3 + 20(5)
a(21) = 103
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At a grocery store a four pack of yogurt cost $3.95 how much does each container of yogurt cost explain?
Answer: ~$0.99 (0.9875)
Just divide 3.95 by 4
A rock of radioactive material has 500 atoms in it. The number of atoms decreases at a rate of 11% a day. Write an exponential function that models this situation. f(x) type your answer... (1 choose your answer... choose your answer... ✓)^x
Answer:
[tex]f(x) = 500( {.89}^{x} )[/tex]
Charlie made the following table to record the height of each person in his family.
If Cheyenne and Hannah lay end to end, how far will they reach?
A. 9
B. 9, 1/2
C. 10
D. 8
Walking tours at a park begin every 25 minutes and bus tours begin every 45 minutes. Both tours start at 8:00 a.m. when the park opens. When is the next time the tours will start at the same time?
The next time the walking and bus tours will start at the same time is 11:45 a.m.
What is the lcm?
The LCM is multiple which is useful if fractions need to be expressed in the same name, when the other number is multiple, LCM will have the larger number:
To find out when the walking and bus tours will start at the same time, we need to find the least common multiple (LCM) of 25 and 45, which is the smallest time interval that is a multiple of both 25 minutes and 45 minutes.
The prime factorization of 25 is 5 * 5, and the prime factorization of 45 is 3 * 3 * 5. To find the LCM, we take the highest power of each prime factor that appears in either factorization, so:
LCM = 3 * 3 * 5 * 5 = 225
Therefore, the walking and bus tours will start at the same time every 225 minutes, or 3 hours and 45 minutes. To find the next time they will start at the same time, we need to add 225 minutes to the starting time of 8:00 a.m.
8:00 a.m. + 3 hours and 45 minutes = 11:45 a.m.
Hence, the next time the walking and bus tours will start at the same time is 11:45 a.m.
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The lengths of two sides of a triangle are 5.2 inches and 3.1 inches. Which lengths, in inches, could be the length of the third side?
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
Triangle Inequality Theorem:In a triangle, the length of any side must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides.
We can apply this rule to find the possible lengths of the third side of the triangle, given that the lengths of the two sides are 5.2 inches and 3.1 inches.
Here we have
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches
Let's denote the length of the third side as x. Then, we have:
3.1 + 5.2 > x > 5.2 - 3.1
8.3 > x > 2.1
Therefore, the length of the third side x must be greater than 2.1 inches and less than 8.3 inches.
We can write this as an inequality:
2.1 < x < 8.3
Therefore,
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
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suppose that 30% of new yorkers own a dog, 25% of new yorkers own a cat and 15% of new yorkers own a cat given they own a dog. a new yorker is chosen at random and reported to own a cat. what is the probability they also own a dog?
The probability that a New Yorker who possesses a cat also owns a dog is 0.103. if a new yorker is chosen at random.
New Yorkers own a dog (D) = 30%
New Yorkers own a cat (C) = 25%
New Yorkers own a cat and dog = 15%
This problem can be calculated using Bayes' theorem, which notes that the possibility of an event A given event B is equal to the possibility of event B given A times the probability of A, divided by the probability of event B.
P(D) = 0.30
P(C) = 0.25
P(C|D) = 0.15
Using Bayes' theorem:
P(D|C) = P(C|D) * P(D) / P(C)
P(C) = [tex]P(C|D) * P(D) + P(C|not D) * P(not D)[/tex]
P(C) = [tex]P(C|D) * P(D) + P(C) * P(not D)[/tex]
P(C) =[tex]P(C|D) * P(D) / (1 - P(D) * P(C|not D))[/tex]
Now we can substitute these values into the Bayes' theorem formula:
P(D|C) = P(C|D) * P(D) / P(C)
P(D|C) = [tex]0.15 * 0.3 / (P(C|D) * P(D) + P(C) * P(not D))[/tex]
P(D|C) = [tex]0.15 * 0.3 / (0.15 * 0.3 + P(C) * 0.7)[/tex]
P(C) = [tex]0.15 * 0.3 / (1 - 0.3 * 0.25)[/tex]
P(C) = 0.16
P(D|C) = [tex]0.15 * 0.3 / (0.15 * 0.3 + 0.16 * 0.7)[/tex]
P(D|C) = 0.103
Therefore, we can conclude that the probability that a New Yorker who owns a cat also owns a dog is 0.103.
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Any help? Please. Whoever answer it first gets brainliest!
Answer:
[tex]c + 15 > 24[/tex]
[tex]c > 9[/tex]
The additional amount will be more than $9.
2. Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his school, 1 mile from his house. The function d gives the distance d(t), in miles, of Tyler from his house t minutes after 7:00 a.m. a. Explain what d(5) = 0.25 means in this context. b. On snowy days, Tyler's school has a 2 hour delayed start time (120 minutes). The function is gives Tyler's distance s(t), in miles, from home t minutes after 7:00 a.m. with a 120 minute delayed start time. If d(5) = 0.25, then what is the corresponding point on the function s? c. Write an expression for s in terms of d. A new function, n, is defined as n(t) = d(t +60) explain what this means in terms of Tyler's distance from school.
Answer: a. In this context, d(5) = 0.25 means that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. This is because the function d(t) gives the distance of Tyler from his house t minutes after 7:00 a.m.
b. If d(5) = 0.25, then we know that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. If there is a 120-minute delayed start time, then Tyler will walk for 20 + 120 = 140 minutes to reach his school. We want to find the corresponding point on the function s, which gives Tyler's distance from home t minutes after 7:00 a.m. with a 120-minute delayed start time. Since Tyler walks the same distance regardless of the delayed start time, we can use the same function for s as we did for d. Therefore, s(145) = 1.25, since Tyler is 1 mile away from his house after walking for 140 minutes and then an additional 5 minutes to account for the delayed start time.
c. Since Tyler walks the same distance regardless of the delayed start time, we can express s(t) in terms of d(t) by adding 120 minutes to the time t. Therefore, s(t) = d(t + 120).
d. The function n(t) = d(t + 60) gives Tyler's distance from his house t minutes after 8:00 a.m. This is because adding 60 minutes to t corresponds to adding one hour to the time, which means that Tyler leaves his house at 8:00 a.m. instead of 7:00 a.m. Therefore, n(t) gives Tyler's distance from school one hour after he leaves his house.
Step-by-step explanation:
find the smallest which 108 must be multiplied to get a perfect square
Answer:
The answer is 3
Step-by-step explanation:
x×108=y
x×2²×3³=y
3×108=324
Susan's cell phone plan includes unlimited texting. The amount she pays for texting each
month can be described by the function y = 20, where y is the number of dollars spent on
texting as a function of x, the number of texts.
What is true about the function?
It is linear because the rate of change is zero.
It is linear because the rate of change is increasing.
It is nonlinear because the rate of change is zero.
It is nonlinear because the rate of change is
increasing.
Find the measures of angle a and B. Round to the
nearest degree.
The measure of angle A and B is 29° and 61° respectively
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
The opposite is 6 and the adjascent = 11
Therefore tan (tetha) = 11/6 = 1.833
tetha = tan^-1( 1.833)
= 61°( nearest degree)
The sum of angle in a triangle is 180°
therefore,
angle A = 180-( 61+90)
= 180-151
= 29°
therefore the measure of angle A and B is 29° and 61° respectively.
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Find the measure of Angle A and round the answer to the nearest tenth.
(Show work if you can, thank you).
68.5 is the measure of Angle A and round the answer to the nearest tenth.
What is Trigonometry?Trigonometry is the area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangential (tan), cotangent (cot), secant (sec), & cosecant (csc) are their names, respectively.
Here we have to use the tan ratio to find the answer.
tanθ = base/perpendicular
Given: perpendicular = 19, base = 22
tan θ = 19/22
θ = tan^-1 (19/22)
tan θ = 1.2
so the angle θ is
68.5 degree
Answer: B) 68.5 degrees
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Answer:
The measure of angle A is 40.8° to the nearest tenth.
Step-by-step explanation:
The given triangle ABC is a right triangle.
We want to find the measure of angle A, and have been given the length of the sides opposite and adjacent to angle A.
The tangent ratio of an angle in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side of that angle.
Therefore, we can use the tangent trigonometric ratio to find the measure of angle A.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
Given values:
θ = angle A = xO = side BC = 19A = side AC = 22Substitute the given values into the ratio and solve for x:
[tex]\implies \tan(x)=\dfrac{19}{22}[/tex]
[tex]\implies x=\tan^{-1}\left(\dfrac{19}{22}\right)[/tex]
[tex]\implies x=40.8150838...^{\circ}[/tex]
[tex]\implies x=40.8^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the measure of angle A is 40.8° to the nearest tenth.
If anyone is reading this, rn i would be so flipping happy if u got this for me ive been waiting for so long and got nothing please answer correctly please
Answer: The answer is A.
Step-by-step explanation: Because I am smart don't underestimate me.
Answer:
C
Step-by-step explanation: (look at attachment)
3x + 4 = -2x -2
By looking at the y-intercepts, you automatically know the answer is C.
The y-intercept of the pink line is 4 because of 3x + 4.
The y-intercept of the blue line is -2, because of -2x - 2.
If f(x) = 5x - 6, which of these is the inverse of f(x)?
A. f^-¹(x) = x/5 +6
B. f^-¹(x) = x/5 -6
C. f^-¹(x) = x+6/5
D. F^-¹(x) = x-6/5
To find the inverse of a function, we need to swap the positions of x and y and then solve for y. In other words, we replace f(x) with y and then solve for x.
So, let's start by swapping x and y in the function f(x) = 5x - 6:x = 5y - 6
Next, we'll solve this equation for y:
x + 6 = 5y
y = (x + 6)/5
Therefore, the inverse of f(x) is f^-1(x) = (x + 6)/5, which is option C.The scale factor of the larger of two similar triangular prisms is 6. The surface area of the smaller prism is 36 ft2. Identify the surface area, rounded to the nearest tenth, of the larger prism
The surface area, rounded to the nearest tenth, of the larger prism is 1296 square feet.
If the scale factor of the larger prism to the smaller prism is 6, then the corresponding ratio of their surface areas is 6² or 36:1.
Scale factor is the ratio of the lengths of corresponding sides of two similar figures. It is used to determine how much larger or smaller one figure is compared to another, and it is often expressed as a fraction or a decimal.
We know that the surface area of the smaller prism is 36 ft², so we can set up the equation
x = 36 × 36
where x is the surface area of the larger prism.
Simplifying the equation
x = 1296 square feet
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Number 7. I don’t understand, what’s the fraction? How do you get fraction and the + a number.
Answer:
A
Step-by-step explanation:
Equation of a line is: y = mx + b where m = slope b = y axis intercept
To find the slope between any two of the given points :
say 18, 100 and 27, 85
m = slope = (y1-y2) / (x1-x2) = (85-100) / ( 27-18) = -15/12 = -5/3
so now you have
y = - 5/3 x + b we still need to find the value of b
use any point to calculate b
say 15, 106
106 = - 5/3 (15) + b
b = ~ 131
the equation is then y = - 5/3 x + 131 closest to answer 'A'
given: weight a: 140 pounds at 17 inches aft of datum weight b: 120 pounds at 110 inches aft of datum weight c: 85 pounds at 210 inches aft of datum based on this information, the cg would be located how far aft of datum?
The center of gravity is located 96.7 inches aft of the datum.
To determine the location of the center of gravity (CG) of the system, we need to calculate the moment of each weight about the datum, and then divide the sum of the moments by the total weight of the system.
The moment of each weight is equal to its weight multiplied by its distance from the datum. In this case:
Moment of weight a = 140 pounds x 17 inches = 2,380 inch-pounds
Moment of weight b = 120 pounds x 110 inches = 13,200 inch-pounds
Moment of weight c = 85 pounds x 210 inches = 17,850 inch-pounds
The total weight of the system is:
Total weight = weight a + weight b + weight c = 140 + 120 + 85 = 345 pounds
Therefore, the location of the CG can be calculated as follows:
CG location = (Moment of weight a + Moment of weight b + Moment of weight c) / Total weight
CG location = (2,380 + 13,200 + 17,850) / 345
CG location = 33,430 / 345
CG location = 96.7 inches aft of datum
As a result, the center of gravity is 96.7 inches aft of the datum.
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Three machines are used to produce nails. The table displays the total number of nails produced by the 3 machines
over different lengths of time.
Nail Production with 3 Machines
Time (minutes)
Number of Nails
(thousands)
15
16
45
48
55
593
ON
If each machine produces nails at the same rate, how many nails can 1 machine produce in 1 hour?
nails
One machine can produce 600,000 nails in one hour.
Finding the total number of nails produced by the three machines in a minute and dividing that number by three to obtain the number of nails produced by a single machine in a minute are the first two steps in the solution to this problem.
The number of nails produced by a single machine in an hour can then be calculated by multiplying that number by 60.
Now, we add up the total number of nails produced during :
(15 + 16 + 45 + 48 + 55 + 59 + 3) / 7 = 30
To find the number of nails produced by one machine in one hour, we multiply by 60: 10,000 x 60 = 600,000
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