Two cars leave town at the same time going in the same direction. One travels 55 miles per hour and the other travels 48 miles per hour. And how many hours will they be 49 miles apart? ​

AC is not equal to CE based on the angle bisector theorem. The answer is: C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

According to the angle bisector theorem, when a line segment divides an angle of a triangle, the line segment also divides the opposite side but does so in such a way that the two segments are proportional to the other two sides of the triangle. However, the two segments are not congruent to each other.

In the diagram given below that shows the suspect, the police officer, and the 26th Street toward Cherry Street, the angle bisector divides the side opposite to the angle divided into AC and CE. Thus, their length cannot be ascertain to be congruent to each other, however, based on the angle bisector theorem, we can only prove that their length is proportional to the other two sides of the triangle.

Therefore, we can conclude as saying:

C. NO, you cannot use the angle bisector theorem to determine that AC = CE.

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The required two column proof is explained below.

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Expressing the trig ratio as a function of 50°, we have sin310° = sin(360 - 50)°

From the question, we have the following trigonometry function that can be used in our computation:

sin310°

The above expression is a sine function of 310 degrees

By mathematical expression, we have

360 - 50 = 310 degrees

This means that we can replace 310 degrees with (360 - 50) degrees in sin310°

So; in terms of 50 degrees, we have

sin310° = sin(360 - 50)°

Hence, the expression sin310° in terms of 50 degrees is sin(360 - 50)°

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Answer:

Width = 14ft     Length = 20ft

Step-by-step explanation:

Area (A) of rug (having rectangular shape) = L× W          A = \(280ft^{2}\)

but Length is 6ft more than width, this means L = (6 + W)ft

∴ 280 = (6+W)×W

    280 = 6W + \(W^{2}\)

solving the equation as a quadratic equation;  \(W^{2} + 6W - 280 = 0\)

(W - 14) (W + 20) = 0

W = 14 or W = -20                 but W ≠ negative

∴ Width (W) = 14ft

Length = 6 + 14

            = 20ft

Answer:

she would be spening over a thousand dollars

Step-by-step explanation:

Asnwer:

10,920$

Step-by-step explanation:

So if 3.00$ is for one pack and she wants 7 packs then it would be 21$.

But if we also multiply it by 52 weeks then that would be 1,092$.

Then if she's buying that for 10 years then we multiply 10 x 1,092$ which would equal 10,920$

(I'm not completely sure if I did the math right but I'm 90% sure I did because that's what the question is asking.)

The probability of both coins landing on heads when two coins are tossed is 1/4, or 0.25, or 25%.

When two coins are tossed, there are four possible outcomes: both coins can land on heads (HH), both coins can land on tails (TT), the first coin can land on heads and the second coin on tails (HT), or the first coin can land on tails and the second coin on heads (TH).

Since we are interested in the probability of both coins landing on heads, we need to determine the number of favorable outcomes (HH) out of the total number of possible outcomes.

Out of the four possible outcomes, only one outcome is favorable (HH). Therefore, the probability of both coins landing on heads is 1 out of 4.

In fraction form, this can be written as 1/4. The probability can also be expressed as a decimal, which is 0.25, or as a percentage, which is 25%.

It's important to note that in this case, we assume that the coins are fair and unbiased, meaning that the probability of landing on heads is equal to the probability of landing on tails, which is 1/2 or 0.5 for each coin individually.

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Answer:

Probability that student will be a girl = 17 / 28

Step-by-step explanation:

Given:

Total number of student = 28 student

Number of boys in the class = 11

Find:

Probability that student will be a girl = ?

Computation:

⇒ Number of girls in class = Total number of student - Number of boys in the class

⇒ Number of girls in class = 28 - 11

⇒ Number of girls in class = 17

⇒ Probability that student will be a girl = Number of girls in class / Total number of student

⇒ Probability that student will be a girl = 17 / 28

Answer:

1st question :55%

2nd ":122.22%

3rd ":81.82%

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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150°

Because it is not acute it cant be 30°

Answer:

1/ 1000 ;

X : _____ 0 ___________ 390

P(x) : ___ 999/1000 ___ 1/ 1000 ;

0.39 ;

D ;

-$61

Step-by-step explanation:

1.)

Probability of winning with a single bet:

Winning numbers in lottery = 1

Lottery size = 1000

P(winning per bet) = 1/ 1000

2.)

X : _____ 0 ___________ 390

P(x) : ___ 999/1000 ___ 1/ 1000

3.)

Σx*p(x)

(0 * 999/1000) + (390 * 1/1000)

0 + 390 / 1000

= 0.39

4)

Expected winning :

Loss = - 1 * 999/1000 ; win = 390 * 1/1000

- 0.999 + 0.39 = - 0.609 = - $0.61

Hence, on average, for every $1 bet, I lose $0.61 on average

E.)

Expected winning for playing 100 times ;

Loss per play:

Expected winning * 100

-$0.61 * 100 = -$61

Loss of - $61 on average

The solution to the function expression, (f - g)(x) is: D. 2x³ + 6x² - 8x + 1.

To evaluate or subtract functions that has polynomials, all we simply need to do is to pair like terms together and combine them.

Given the following:

f(x) = 2x³ + 6x² – 5x – 3 and g(x) = 3x – 4

Therefore:

(f - g)(x) = f(x) - g(x)

Substitute

(2x³ + 6x² – 5x – 3) – (3x – 4)

2x³ + 6x² - 5x - 3 - 3x + 4

Combine like terms

2x³ + 6x² - 5x - 3x - 3 + 4

2x³ + 6x² - 8x + 1

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Complete Question:

f(x) = 2x³ + 6x² – 5x – 3

g(x) = 3x – 4

Find (f - g)(x).

O A. (f - g)(x) = 2x³ + 6x² – 2x – 7

O B. (f - g)(x) = 2x³ + 6x² – 2x + 1

O c. (f - g)(x) = 2x³ + 6x² – 8x – 7

O D. (f - g)(x) = 2x³ + 6x² – 8x + 1

Answer:

Step-by-step explanation:

The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:

Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ​

where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35​=−0.75

This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35​=0.5

This means that 36 psi is 0.5 standard deviations above the mean.

Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.

Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649

This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.

Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%

The correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

We know that there are 40 students at summer camp who are divided into two groups for either swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking. The outcome frequency for swimming is 16 and for hiking is 24.
To compare the probabilities, we need to first understand the difference between theoretical probability and experimental probability. Theoretical probability is the expected probability of an event occurring based on mathematical calculations and assumptions, whereas experimental probability is the actual observed probability of an event occurring based on data from experiments or observations.
Option 1 states that the theoretical probability of swimming is one half, but the experimental probability is 24 over 40. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is false.
Option 2 states that the theoretical probability of swimming is one half, but the experimental probability is 16 over 40. This statement is correct because the theoretical probability of swimming is 50%, which is equal to one half, and the experimental probability of swimming is also 40%, which is equal to 16 over 40. Therefore, this option is true.
Option 3 states that the theoretical probability of swimming is 16 over 24, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 16 over 24, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
Option 4 states that the theoretical probability of swimming is 24 over 40, but the experimental probability is one half. This statement is incorrect because the theoretical probability of swimming is actually 50%, which is not equal to 24 over 40, and the experimental probability of swimming is also 40%, which is not equal to one half. Therefore, this option is false.
In conclusion, the correct statement is that the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 16 over 40.

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Answer: 7% at 6 years would best fit their payment option. They would then be paying $238.69 monthly and which is under $250, I hope this helps!

|-2.65| can be found between numbers 2.6 and 2.7

Absolute value means to remove any negative sign in front of a number and to think of the number as positive.  This is what the vertical lines |  | surrounding -2.65 means.

Thus,   |-2.65| = 2.65

If we examine the options, then we can say 2.65 is between 2.6 and 2.7 i.e. 2.6, 2.65, 2.7

Therefore,  |-2.65| can be found between the numbers 2.6 and 2.7. So option D is the answer

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Answer:

The first equation can be multiplied by 3 and the second equation by 2.

Step-by-step explanation:

We are given the following system of equations:

\(\boxed{\left \{ {{2x+3y=25} \atop {-3x+4y=22}} \right.}\)

To eliminate a variable in the equation, they must cancel out. For instance, if x = 1, in order to cancel out the numbers, you must add -1.

To multiply an equation, you must apply the constant that you are multiplying by to all constants and coefficients of the equation. For example, to multiply 2x + 4y = 8 by 3, you must multiply 2x by 3, 4y by 3, and 8 by 3.

Therefore, using this information, you can attempt each answer set and test the possibilities.

Answer Choice A

If you multiply the first equation by -3, you will get -6x - 9y = -75. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding -6 + -6 gives you -12, so these do not cancel out.

Answer Choice B

If you multiply the first equation by -4, you will get -8x - 12y = -100. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding -8 + -6 gives you -14, so these do not cancel out.

Answer Choice C

If you multiply the first equation by 3, you will get 6x + 9y = 75. If you multiply the second equation by 2, you will get -6x + 8y = 44. Adding 6 + -6 gives you 0, so these do cancel out.

Answer Choice D

If you multiply the first equation by 4, you will get 8x + 12y = 100. If you multiply the second equation by -3, you will get 9x - 12y = -66. Adding 8 + -9 gives you -1, so these do not cancel out.

The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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The median of the data is 71 and after replacement the median is 85.

The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three different metrics are employed in mathematics. The terms are median, mode, and mean. The term "measures of central tendency" refers to these three metrics. The mean of the provided data provides the average value. A median identifies the midpoint of the provided data. The given data's repeated value is determined by mode.

To find the median arrange the data in ascending order.

43, 47, 57, 61, 71, 88, 92, 99, 108

The number of observations are odd thus,

median = n + 1 /2 = (9 + 1) / 2 = 5th term.

median = 71

When we replace 57 with 85 we have:

43, 47, 61, 71, 85, 88, 92, 99, 108

The number of observations is odd thus,

median = n + 1 /2 = (9 + 1) / 2 = 5th term.

median = 85

Hence, the median of the data is 71 and after replacement the median is 85.

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Answer:

x=0.7

Step-by-step explanation:

Answer:

\(\sqrt[9]{x^{7} }\)

Step-by-step explanation:

Hope this helps

Answer:

n = -24/7

Step-by-step explanation:

3 -7n = 27

-7n = 24         Subtract 3 from both sides

n = -24/7        Divided by -7 both sides

So, the answer is n = -24/7

Answer:

Below

Step-by-step explanation:

Subtract 3 from both sides of the equation THEN divide both sides of the equation by  - 7

Answer: g(-2)=-2

Step-by-step explanation:

g(x)=-x-4

g(-2)=-(-2)-4

g(-2)=2-4

g(-2)=-2

Answer:

Explanation shown below

Step-by-step explanation:

In the study of statistics – INDIVIDUALS are objects that are described by a set of data.  

VARIABLE is said to be an important element of any statistical data. It is a characteristic of a unit that is being observed which may rightly assume many set of values. Numerical values can be assigned to them.  

CATEGORICAL VARIABLE – are usually referred to as qualitative data, which can be put into different categories based on their characteristics. Under this, we have the Nominal Variable – eg. Gender - Male, Female. They the set of variables that have two or more categories with no ordering. The Ordinal Variable – has two or more categories with clear ordering.

NUMERICAL VARIABLE include interval variable and ratio variable. In these types of variables, measurement have numerical meaning.    

DATA SET is a collection of data, permanently stored which relate to a particular subject. The test scores of each student in a particular class is an example of data set

The amount of tax the customer who purchased 88.00 on clothing will pay is 4.4

Amount of sales tax = 5% × 88.00

= 0.05 × 88

= 4.4

Therefore, the amount of tax the customer who purchased 88.00 on clothing will pay is 4.4

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Answer: i think c

Step-by-step explanation:

The weight of 12 large eggs in kilograms is 0.558 kg.

A calculation known as a weighted average accounts for the varying levels of significance of the numbers in a data collection. Each number in the data collection is multiplied by a predetermined weight before the final calculation is made when calculating a weighted average.

To convert the weight of 12 large eggs from grams to kilograms, we need to do the following:

Determine the total weight of the 12 large eggs in grams:

46.5 grams/egg x 12 eggs = 558 grams

Convert the total weight in grams to kilograms by dividing by 1000:

558 grams / 1000 = 0.558 kilograms

Therefore, the weight of 12 large eggs in kilograms is 0.558 kg.

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The probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001

In a series of 36 trials, if the subject is guessing randomly, then the probability of correctly guessing odd or even is 1/2.

Let X be the number of correct guesses in a series of 36 trials. X follows a binomial distribution with parameters n = 36 and p = 1/2.

The probability of guessing more than 20 correct is:

P(X > 20) = 1 - P(X ≤ 20)

Using a binomial distribution table, we can find that P(X ≤ 20) = 0.9999 (rounded to four decimal places).

Therefore: P(X > 20) = 1 - 0.9999 = 0.0001

So the probability that a subject would guess more than 20 correct in a series of 36 trials is 0.0001 (rounded to four decimal places).

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Answer:

Its 1

Step-by-step explanation:

just do the steps