The segments shown below could form a triangle.

In order to find the total amount of miles Olivia rode in the two days, we just need to add the mixed numbers that represent the amount rode in each day.

So we have:

So Olivia rode 4 3/4 miles (that is, 4.75 miles) in the two days.

Answer:

a

Step-by-step explanation:

The given linear programming problem is to be solved using the simplex method. The problem is as follows:Maximize \(z = 5x1 + 8x2Subject to:x1 - 6x2 ≤ 354x1 - 2x2 ≤ 21x1 ≥ 0, x2 ≥ 0\)Explanation:We can solve the given linear programming problem using the simplex method, which involves the following steps:Step 1: Convert the given maximization problem to a minimization problem.

We can convert the given maximization problem to a minimization problem by multiplying each term of the objective function by -1. Thus, we get:\(Minimize -z = -5x1 - 8x2\)Step 2: Write the constraints in standard form.To write the constraints in standard form, we need to introduce slack variables. Thus, we get:

\(x1 - 6x2 + s1 = 354x1 - 2x2 + s2 = 21x1 ≥ 0, x2 ≥ 0, s1 ≥ 0, s2 ≥ 0\)

Step 3: Write the augmented matrix.We can write the augmented matrix as follows:

Step 4: Choose the pivot element.To choose the pivot element, we need to select the most negative element in the bottom row. Thus, the pivot element is -21.Step 5: Perform row operations.Divide the second row by -21 to make the pivot element equal to -1. Thus, we get:
Now, we can choose the next pivot element. The most negative element in the bottom row is -5. Thus, the pivot element is -5. Perform row operations to get:

Thus, the optimal solution is x1 = 0, x2 = 3, z = -24.The maximum value of the objective function is z = 24.

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A researcher wished to estimate the difference between the proportion of users of two shampoos who are satisfied with the product at a 90% confidence level,

the true difference between the proportion of users satisfied with shampoo A and shampoo B is estimated to be between -0.0262 and 0.0482.

To construct a 90% confidence interval for the true difference between the two population proportions, we can use the formula for the confidence interval for the difference between two proportions.

Let's denote the proportion of users satisfied with shampoo A as p1 and the proportion of users satisfied with shampoo B as p2.

The sample proportion for shampoo A, denoted as 1, is calculated by dividing the number of users satisfied in the sample of 400 (78) by the sample size (400):

1 = 78/400 = 0.195

The sample proportion for shampoo B, denoted as 2, is calculated by dividing the number of users satisfied in the sample of 500 (92) by the sample size (500):

2 = 92/500 = 0.184

Next, we calculate the standard error, which measures the variability of the difference between the two proportions:

SE = sqrt[(1 * (1 - 1) / n1) + (2 * (1 - 2) / n2)]

where n1 is the sample size for shampoo A (400) and n2 is the sample size for shampoo B (500).

SE = sqrt[(0.195 * (1 - 0.195) / 400) + (0.184 * (1 - 0.184) / 500)]

SE = sqrt[(0.152025 / 400) + (0.151856 / 500)]

SE ≈ 0.0226

Now, we can calculate the margin of error by multiplying the standard error by the critical value corresponding to a 90% confidence level. For a 90% confidence level, the critical value is approximately 1.645.

Margin of Error = 1.645 * 0.0226 ≈ 0.0372

Finally, we construct the confidence interval by subtracting and adding the margin of error from the difference in sample proportions:

Confidence Interval = (1 - 2) ± Margin of Error

Confidence Interval = (0.195 - 0.184) ± 0.0372

Confidence Interval = 0.011 ± 0.0372

Confidence Interval ≈ (-0.0262, 0.0482)

Therefore, at a 90% confidence level, the true difference between the proportion of users satisfied with shampoo A and shampoo B is estimated to be between -0.0262 and 0.0482.

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Answer:

C. $55.00

Step-by-step explanation:

10% of $50 is $5, then add it because it is a markup, $55.00

The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

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The estimated crop yield from the simulation is 443 (option b).

To estimate the crop yield from the given random numbers, we need to assign a specific meaning to each random number. Let's assume that each random number represents the crop yield for a particular year.

Given random numbers: 37, 23, 92, 01, 69, 50, 72, 12, 46, 81

To find the estimated crop yield, we sum up all the random numbers:

37 + 23 + 92 + 01 + 69 + 50 + 72 + 12 + 46 + 81 = 443

Therefore, the estimated crop yield from the simulation is 443. The correct option is b.

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Answer:

\(y=\frac{5}{4} x+1\)

Answer:

3/10. 0.3

Step-by-step explanation:

when you divide mixed numbers you should reciprocate them I mean take the reciprocal and that was 2 and over every number there is one so I took 1/2 hope you understand why I kept 1/2 I took its reciprocal hope you understand if I'm wrong tell me right away I'll try it out good luck.

Answer:

0.58 or 58%

Step-by-step explanation:

Answer:

49=5x+14

Step-by-step explanation:

The general solution of the damped spring-mass system with the given parameters is y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)]. By applying the initial conditions y(0) = 1 and y'(0) = 0, the specific solution can be obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t).

The equation for the damped spring-mass system can be expressed as my'' + cy' + ky = 0, where m is the mass, c is the damping coefficient, and k is the spring constant. In this case, m = 1 kg, c = 3 kg/s, and k = 2 kg/\(s^2\).

To find the general solution, we assume a solution of the form y(t) = e^(rt). By substituting this into the equation and solving for r, we get \(r^2\) + 3r + 2 = 0. Solving this quadratic equation gives us the roots r1 = -2 and r2 = -1.

The general solution is then given by y(t) = c1e^(-2t) + c2e^(-t). However, since we have a damped system, the general solution can be rewritten as y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)], where √7/2 = √(3/4).

By applying the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the coefficients c1 and c2. The specific solution is obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t). This satisfies the given initial value problem.

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Answer:

1) x = 6

2) x = 14

3) x = 4

4) x = 7

Step-by-step explanation:

1) x+5=11

x = 11-5

x =6

2) x-6=8

x = 8+6

x = 14

3) 3+x=7

x = 7-3

x = 4

4) 12=x+5

12-5 = x

7 = x

The probability 3 cars arrive in a second is  0.14037

Let X be a discrete random variable taking non-negative values. Then, X is said to follow the Poisson distribution if its probability mass function is given by:

P(X = x) = \(\frac{e^-^\lambda\lambda^x}{x!}\), x = 0, 1, 2, 3, 4....

where x = number of successes,

λ = mean or expected value of the variable.

This distribution is widely used to predict the likeliness of rare and independent events in a large population.

Now, We have to find the probability 3 cars arrive in a second.

Let X be a random variable denoting the number of cars arriving at a given intersection.

Now,

X is stated to follow a Poisson distribution with a mean rate of 4 per second, i.e. X∼P(λ = 5)

The probability that 3 cars arrive in a given second:

P(X = 3) = \(\frac{e^-^55^3}{3!}\) = 0.14037

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Answer:

-16

Step-by-step explanation:

Replace all t with -5:

w(t) = 3t - 1

w (-5) = 3(-5) - 1

w(-5) = -16

Answer:

-16

Step-by-step explanation:

The weight is less on the moon than on the Earth due to the force of gravity being less on the moon.

Weight can be defined as the force with which the center of the Earth, or even the center of a satellite planet such as Earth attracts a body towards its center. This is determined by:

This makes your weight to be less in the moon as the force of gravity there is also less.

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Answer:

224

Step-by-step explanation:

The correct statement regarding the probability of choosing a person at random who is a junior and plays video games, and whether these events are independent, is given as follows:

P(junior and video games) = 32%; The two events are not independent.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The outcomes in this problem are given as follows:

Hence the probability is of:

P(junior and video games) = 48/150 = 0.32 = 32%.

The separate probabilities are given as follows:

The multiplication of these probabilities is of:

0.66 x 0.4 = 0.264.

Which is different of 0.32, hence these events are not independent.

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Answer:

Carlos is 37 years old and Ella is 17.

Step-by-step explanation:

Let,

Carlos = c

Ella = e

If Carlos is 3 more than twice Ella's age, we get the equation:

2e + 3 = c (1)

Since the sum of their ages is 54, we get the equation:

c + e = 54 (2)

Now we have a system of equations.

Since equation number 1 already designated the value of c in terms of e, we can substitute it into the second equation.

(2e+3) + e = 54

Lets combine like terms and solve!

2e + e + 3 = 54

3e = 51

e = 17

Let's substitute e back into one of the equations to figure out the value of c. I'm going to use equation 1.

2e + 3 = c

2(17) + 3 = c

34 + 3 = c

37 = c

Let's substitute the values of c and e into the second equations to check our work! (We know c and e already fulfill the first equation as we substituted e into it to get c)

c + e = 54

37 + 17 = 54

54 = 54

Now that we've checked our work, we know our answer is correct! Carlos is 37 years old and Ella is 17.

The factor that most directly affects the amount of money borrowers must repay to lenders is d) the annual percentage rate.

This rate represents the cost of borrowing money and includes interest and other fees. The higher the APR, the more money borrowers will have to repay over time. The currency exchange rate, unemployment rate, and inflation rate can indirectly affect borrowing costs but are not as directly linked as the APR. The factor that most directly affects the amount of money borrowers must repay to lenders is d. the annual percentage rate (APR). The APR represents the total cost of borrowing, including interest and any additional fees, expressed as a percentage. A higher APR means a higher cost for borrowers, making it an essential factor to consider when repaying loans.

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Answer:

x=20

Step-by-step explanation:

35/14 is 2.5
Then 50/2.5 is 20
so x is 20

Answer:

Step-by-step explanation:

x/14 = 50/35

Or, 35x = 50*14

Or, 35x = 700

Or, x = 700/35

Or, x = 20

x = 20

Answer:

Step-by-step explanation:

Answer:

Did you get the answer to this. I am struggling on this as well.

Step-by-step explanation:

The equation that shows how the total number of science quizzes, y, depends on the number of months that have passed, x is y = 4x.

An equation is a mathematical statement that shows the relationship between two or more values.

In this case, Leon has already had 4 science quizzes this semester and expects to have 4 quizzes per month going forward.

We can use an equation to show how the total number of science quizzes, y, depends on the number of months that have passed, x.

The equation for this would be y = 4x, where x is the number of months that have passed and y is the total number of science quizzes.

This equation shows that for each month that passes, the total number of science quizzes increases by 4

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Answer:

200

Step-by-step explanation:

1cm=50m

1*4=50*4

4=200 miles

Answer:

DF≅YZ

angle R≅angle N

XW≅TH

angle M ≅angle C

new coordinate=(2,1)

new coordinate=(0,2)

Reflection:

new coordinate=(5,-6)

new coordinate=(1,4)

Last one is already done

Step-by-step explanation:

The value of m + n comes out to be 37

In order to get p(a), Let's consider the probabilities of the events that Alex and Dylan can choose from the set {a, a + 9}, so there are 8 other cards that they can not pick. This can be written as:

P(Alex chooses a) = 2/50 = 1/25 as there are two cards in {a, a + 9}.

P(Dylan chooses a+9) = 2/49 (since there are now 49 cards left)

Conditional Probability

What is conditional probability? It is defined as the probability of how likely an event is supposed to happen given the probabilities of events before that.

Conditional Probability Formula

For our case, A is "Alex and Dylan in the same team," and B is "Alex chooses a and Dylan chooses a+9". Hence, we can write the required probability P(A|B) as:

P(A|B) = P(A and B) / P(B)

where P(A and B) = the probability that Alex and Dylan end up in the same team and Alex chooses a and Dylan chooses a+9.

P(B) = the probability that Alex chooses a and Dylan chooses a+9.

P(B) = P(Alex chooses a) * P(Dylan chooses a+9) = (1/25) * (2/49) = 2/1225

Now, let's find the probability of (A and B) i.e. the probability that Alex and Dylan end up in the same team and Alex chooses a and Dylan chooses a+9.

P(A and B) = P(Alex and Dylan end up in the same team and Alex chooses a and Dylan chooses a+9)

P(A and B) = P(Alex and Dylan end up in the same team and Alex and Dylan pick two cards less than or equal to a + 9) + P(Alex and Dylan end up in the same team and Alex and Dylan pick two cards greater than or equal to a + 10)

For Alex and Dylan to end up on the same team, Blair and Corey must pick two cards greater than a + 9.

Hence, the probability of this happening is the probability of Blair and Corey choosing two cards from the set {a + 10, a + 11, . . ., 52}, and this can be written as:

P(Blair and Corey pick 2 cards from the set {a + 10, a + 11, . . ., 52}) = [(52 - a - 9) C 2] / [(52 - a) C 2] = [(43 - a) C 2] / [(43 + a) C 2]

Now we need to find the minimum value of p(a) for which p(a) > 1/2 can be written as m/n, where m and n are relatively prime positive integers. Let's solve this part of the question. We will equate the above equation with 1/2 and solve for a.

In other words, we need to solve the following equation:

2[(a - 1) C 2 / (52 - a) C 2] + 2[(43 - a) C 2 / (43 + a) C 2] = 1

Here, we can use the factorials method to find the combination:

\({(a-1)\choose2} = \frac{(a-1)!}{2!(a-1-2)!}\)

which simplifies to

\(\frac{(a-1)(a-2)}{2!}\)

\({(52-a)\choose2} = \frac{(52-a)!}{2!(50-a)!}\)

which simplifies to

\(\frac{(52-a)(51-a)}{2!}\)

\({(43-a)\choose2} = \frac{(43-a)!}{2!(41-a)!}\)

which simplifies to

\(\frac{(43-a)(42-a)}{2!}\)

We get the equation:

\((a-1)(a-2)(43-a)(42-a) + (52-a)(51-a)(a-1)(a-2) = \frac{1}{2}*(52-a)(51-a)(43-a)(42-a)\)

= \((a-1)(a-2)[(43-a)(42-a) + (52-a)(51-a)] = \frac{1}{2}*(52-a)(51-a)(43-a)(42-a)\)

= \((a-1)(a-2)(a^2 - 95a + 2230) = \frac{1}{2}(a-10)(a-9)(a-44)(a-43)\)

Now we can see that for the minimum value of p(a) for which p(a) > 1/2 can be written as m/n, where m and n are relatively prime positive integers, we will have the value of p(a) just greater than 1/2 as that will give the minimum value that satisfies the condition.

Hence, we need to find the smallest value of a that satisfies this equation.

Now we can solve for a using the above equation. If we solve this equation, we get a = 19 or a = 35. We can then compute p(a) for both values of a using the formula we derived above. For a = 19, we get p(a) = 14/23, and for a = 35, we get p(a) = 13/23.

Hence, the minimum value of p(a) for which p(a) > 1/2 can be written as m/n, where m and n are relatively prime positive integers, is 14 + 23 = 14+23 = 37.

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The probability of a household having more than 12 TVs is 0.7386.

(a) To find the probability of a household having 12 or 14 TVs, we need to find the probability of getting exactly 12 TVs and exactly 14 TVs and then add these probabilities together. The probability of getting exactly k successes in n trials with probability of success p is given by the binomial probability formula:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Using this formula, we have:

P(12 TVs) = (17 choose 12) * (0.8)^12 * (0.2)^5 = 0.0411

P(14 TVs) = (17 choose 14) * (0.8)^14 * (0.2)^3 = 0.176

Therefore, the probability of a household having 12 or 14 TVs is:

P(12 or 14 TVs) = P(12 TVs) + P(14 TVs) = 0.0411 + 0.176 = 0.2171

(b) To find the probability of a household having 12 or fewer TVs, we need to find the probability of getting 12 or fewer TVs. We can use the binomial probability formula to find the probabilities of getting 0, 1, 2, ..., 12 TVs and then add these probabilities together. Alternatively, we can use the cumulative distribution function (CDF) of the binomial distribution. The CDF gives the probability of getting k or fewer successes in n trials with probability of success p:

P(X ≤ k) = Σ P(X = i) from i = 0 to k

Using a binomial calculator or a statistical software, we can find that:

P(X ≤ 12) = 0.0604

Therefore, the probability of a household having 12 or fewer TVs is 0.0604.

(c) To find the probability of a household having 15 or more TVs, we need to find the probability of getting 15, 16, 17 TVs. Again, we can use the binomial probability formula or the CDF. Using a binomial calculator or a statistical software, we can find that:

P(X ≥ 15) = 0.0152

Therefore, the probability of a household having 15 or more TVs is 0.0152.

(d) To find the probability of a household having fewer than 14 TVs, we need to find the probability of getting 0, 1, 2, ..., 13 TVs. Using a binomial calculator or a statistical software, we can find that:

P(X < 14) = P(X ≤ 13) = 0.3152

Therefore, the probability of a household having fewer than 14 TVs is 0.3152.

(e) To find the probability of a household having more than 12 TVs, we need to find the probability of getting 13, 14, 15, 16, 17 TVs. Using a binomial calculator or a statistical software, we can find that:

P(X > 12) = P(X ≥ 13) = 0.7386

Therefore, the probability of a household having more than 12 TVs is 0.7386.

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the null hypothesis for the given t-test\(`[h, p, 0] = ttest(morningsections, eveningsection)`\)

In the t-test formula for hypothesis testing, the null hypothesis states that there is no difference between the two groups being tested. Therefore, for the given t-test below:

`[h, p, 0] = ttest(morningsections, eveningsection)`,

the null hypothesis is that there is no significant difference between the average bedtimes of students in morning sections versus evening sections.

To explain further, a t-test is a type of statistical test used to determine if there is a significant difference between the means of two groups. The formula for a t-test takes into account the sample size, means, and standard deviations of the two groups being tested. It then calculates a t-score, which is compared to a critical value in order to determine if the difference between the two groups is statistically significant.

In this case, the two groups being tested are morning sections and evening sections, and the variable being measured is the average bedtime of students in each group. The null hypothesis assumes that there is no significant difference between the two groups, meaning that the average bedtime of students in morning sections is not significantly different from the average bedtime of students in evening sections.

The alternative hypothesis, in this case, would be that there is a significant difference between the two groups, meaning that the average bedtime of students in morning sections is significantly different from the average bedtime of students in evening sections. This would be reflected in the t-score obtained from the t-test, which would be compared to the critical value to determine if the null hypothesis can be rejected or not.

In conclusion, the null hypothesis for the given t-test\(`[h, p, 0] = ttest(morningsections, eveningsection)`\) is that there is no significant difference between the average bedtimes of students in morning sections versus evening sections.

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Answer:

0.75 cm of rain per hour

Step-by-step explanation:

I know if the cm part made sense but okay

Answer:

0.75 cm of rain per hour

Step-by-step explanation:

i know its right-