Solve for X. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.

From the given triangle, the value of the given green box / unknown variable is 13. So, correct option is B.

To find the length of side AC, we can use the law of sines, which states that in any triangle ABC,

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides opposite the corresponding angles A, B, and C.

In this case, we know the length of side BC (b) is 15, and the measures of angles B and C are 50 and 35 degrees, respectively. Therefore, we can set up the following equation:

15/sin 50 = AC/sin 35

To solve for AC, we can multiply both sides by sin 35:

AC = (15/sin 50) * sin 35

Using a calculator, we can evaluate this expression to find that AC is approximately 13. Therefore, the answer is not one of the options given.

So, correct option is B.

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Answers:

The first answer is 10

Second answer 7.5

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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-Bayes' theorem is used to revise probabilities when one has new information.

-Bayes' theorem is used to revise probabilities when one has new information. It relates the conditional probabilities of two events, A and B, as follows:

[tex]P(\frac{A}{B})= P(\frac{B}{A}) \frac{P(A)}{P(B)}[/tex]

-where P(A|B) is the conditional probability of A given that B has occurred, [tex]P(\frac{B}{A})[/tex] is the conditional probability of B given that A has occurred, P(A) is the prior probability of A, and P(B) is the prior probability of B.

-Bayes' theorem allows us to update our knowledge about the probability of A after we have observed B. It is widely used in fields such as statistics, machine learning, and artificial intelligence.

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At the initial term, both patterns display identical values (0). From there on, succeeding terms in Pattern 1 encompass greater numbers than those of Pattern 2.

In this manner, as x-value (term figure) boosts, y-value (number in the framework) begin to amplify at a more rapid rate for the former sequence than for the latter.

The alliance between their analogous terms can be declared as a linear function where y-value for Pattern 1 is equivalent to that of Pattern 2, together with an extra 4 units. Simply put, the equation can be expressed as: y = x + 4.

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The expression 48s represents the cost of the scarves.

Given

Emiko makes Shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves.

Let s represent the price of the scarves.

The cost of each scarves is 48.

Therefore,

The cost of scarves = Number of scarves × cost of each scarves.

The cost of scarves = s × 48

The cost of scarves = 48s

Hence, the expression 48s represents the cost of the scarves.

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This means that the car needs to go at least 64 mph to overtake the bus in 5 hours, and it needs to cover the same distance as the bus did in those 3 hours, which is 120 miles.

To figure out the speed the car needs to go to overtake the bus in 5 hours, we first need to figure out how far the bus travels in those 5 hours.

Since the bus travels for 3 hours before the car starts, we can find the distance the bus travels in those 3 hours by using the formula:

distance = rate × time

where the rate is the speed of the bus, which is 40 mph, and the time is 3 hours.

So the distance the bus travels in those 3 hours is:

distance = 40 mph × 3 hours = 120 miles

Now, for the car to overtake the bus in 5 hours, it needs to cover the same distance the bus did in 3 hours plus some additional distance to get ahead of the bus. Let's call this additional distance "x".

So, the total distance the car needs to travel is:

total distance = 120 miles + x

Now we can set up an equation that relates the distances and speeds of the car and the bus:

distance covered by car = distance covered by bus + x

rate of car × time = rate of bus × time + x

where the rate of the bus is 40 mph, the time is 5 hours (since that's how long it takes for the car to overtake the bus), and the rate of the car is what we're trying to find.

Substituting the values we know:

rate of car × 5 hours = 40 mph × 8 hours + x

Simplifying:

rate of car = (40 mph × 8 hours + x) / 5 hours

We still need to find the value of "x". To do this, we can use the fact that the car overtakes the bus, which means that the distance covered by the car is greater than the distance covered by the bus:

distance covered by car > distance covered by bus

rate of car × time > rate of bus × time

rate of car × 5 hours > 40 mph × 8 hours

rate of car > 64 mph

So the car needs to go faster than 64 mph to overtake the bus in 5 hours.

To find the value of "x", we can substitute the rate of the car into the earlier equation:

rate of car × 5 hours = 40 mph × 8 hours + x

64 mph × 5 hours = 40 mph × 8 hours + x

320 miles = 320 miles + x

x = 0

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The median number of emails sent per day in the given survey is 23.

To find the median, we first need to arrange the data in order from smallest to largest

20 20 20 21 22 22 22 23 23 24 24 25 26 26 27 27 27 27 27 27

The median is the middle value in the ordered list. Since there are 20 observations, we can find the median as follows

The 10th observation is 24, which is the first value greater than or equal to the median.

The 9th observation is 23, which is the last value less than or equal to the median.

Therefore, the median number of E-mails sent per day is 23.

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Answer:

29.4

Step-by-step explanation:

the are of a parallelogram is =base ×height

height=sin 45×6

height=4.2

base is 7

7×4.2

The area of a desk pad eight yards wide and 4/5 yards long is given as follows:

A = 0.3 yd².

Considering a rectangle of length l and width w, we have that:

The dimensions for this problem are given as follows:

Hence the area is given as follows:

A = 0.375 x 0.8

A = 0.3 yd².

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The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. In this case, the radius of the circle is 8 units. You can use either 22/7 or 3.14 as an approximation for π.

Using 22/7 for π:

C = 2(22/7) * 8 = (44/7) * 8 = 352/7 ≈ 50.29 units

Using 3.14 for π:

C = 2 * 3.14 * 8 = 6.28 * 8 = 50.24 units

Both approximations yield similar results for the circumference of the circle: 50.29 units when using 22/7 and 50.24 units when using 3.14. You may choose either of these values, depending on the desired level of accuracy. Keep in mind that these are approximations, and the true value of the circumference would involve using the exact value of π.

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The algebraic expression that represents the situation should be x + 4.

The expression x + 4 represents the sum of a variable x and a constant 4. In algebra, x is often used to represent an unknown value or a variable quantity, while constants are fixed values that do not change. Adding the two together gives us the expression x + 4. It is important to note that there is no operation or value given after the last plus sign in the expression provided, so it is incomplete. We need to know what to add to x and 4 in order to have a complete expression.

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The solution is, : The probability that a girl will win free popcorn is 4/21.

Here, we have,

⇒This question is on probability

⇒Number of boys=3

⇒Number of girls=4

⇒P(S)= 4+3=7

Probability for a girl to win is= 4/7

We have 3 awards a free movie ticket, a collectible poster, or a free popcorn

P(S)= 3

Probability of being awarded a free popcorn = 1/3

The probability that a girl will win free popcorn =4/21

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complete question:

Three boys and four girls enter a contest at the local movie theater. A randomly chosen winner will be awarded a free movie ticket, a collectible poster, or free popcorn. What is the probability that a girl will win free popcorn?

Answer:

Parallelogram, quadrilateral, rectangle, square

Step-by-step explanation:

It is a quadrilateral because there are four sides to the shape. The sides are in two parallel pairs, as evidenced by the fact that the interior angles are all 90 degrees. The angles being 90 degrees in particular also makes the shape a rectangle. Lastly, because of the side measures we also know that the shape has to be a square, because a square has sides that are all the same.

The correct matching is given below.

600   ⇒ Amount charged to Ama's credit card

0       ⇒ Zero balance.

|600| ⇒ Difference between Ama's balance and zero balance.

The credit card balance for Ama is displayed on the number line in US dollars. A credit card's positive balance indicates how much has been charged to the card.

A number line is often shown horizontally and can be postponed in any direction.

The number 600 represents the amount charged to Ama's credit card

The number 0 represents the zero balance.

The number |600| represents the difference between Ama's balance and zero balance.

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[tex](x+a)^{2}[/tex] is the factored form of the expression.

The factored form of the expression [tex]x^{2}[/tex] + 2ax + [tex]a^{2}[/tex] is [tex](x+a)^{2}[/tex] .

We can see this by recognizing that this expression is a perfect square trinomial, which means it can be factored into the square of a binomial.

To find the binomial, we take the square root of the first and last terms, which gives us x and a respectively. Then, we double the product of these terms, which gives us 2ax. This is exactly the middle term of the original expression, so we can write:

[tex]x^{2}[/tex] + 2ax + [tex]a^{2}[/tex] is [tex](x+a)^{2}[/tex]

And that is the factored form of the expression.

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It will take (V₂ / V₁) number of figure D to fill the volume of figure E.

Since the volume of the figures is not given, let us assume that the volume of figure D is V₁ and that of figure E is V₂. Assume that it takes {x}, figure D to fill figure E. So, we can write the relation as -

V₁ {x} = V₂

{x} = (V₂ / V₁)

So, it will take (V₂ / V₁) number of figure D to fill the volume of figure E.

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Answer:

Okay, let's solve this using PEMDAS (Please Excuse My Dear Aunt Sally):

56-6x3+7

Perform operations inside parentheses: There are no parentheses.

Multiply: 6 x 3 = 18

Subtract: 56 - 18 = 38

Add: 38 + 7 = 45

So the final answer is: 45

In steps:

56-6x3+7

6 x 3 = 18 (multiply)

56 - 18 = 38 (subtract)

38 + 7 = 45 (add)

Step-by-step explanation:

The 95% confidence interval that the true mean income for parking meters in the resort community falls between $3.14 and $5.28 per day.

To find the 95% confidence interval for the true mean income of parking meters in the resort community, we can use a t-distribution since our sample size is small (n=10).
First, we need to find the sample mean and standard deviation. The sample mean is simply the average of the incomes:
x = 4.21
The sample standard deviation can be found using the formula:
s = √[ Σ(xi - x)² / (n-1) ]
Now that we have the sample mean and standard deviation, we can use a t-distribution to find the 95% confidence interval. We need to find the t-value with 9 degrees of freedom (n-1), since our sample size is 10.
Using a t-table or calculator, we can find that the t-value with 9 degrees of freedom and a 95% confidence level is approximately 2.262.
The formula for the confidence interval is:
CI = x ± (t-value x s / √n)
Plugging in the values:
CI =($3.14, $5.28)
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If sentence 6 states that ¬C is true, and sentence 7 presents a conditional statement with C as the antecedent and Q as the consequent, we can use modus ponens to infer that Q is false.

Modus ponens is a deductive reasoning rule that allows us to derive a conclusion from a conditional statement and its antecedent. Therefore, we can apply modus ponens to sentence 7 given that we know ¬C from sentence 6.
Since from sentence 6 we know ¬C, we can apply modus ponens to sentence 7. To do this, follow these steps:
1. Identify the premises: One premise is sentence 6, which states ¬C. The other premise should be a conditional statement, such as "If ¬C, then P" (replace P with the relevant proposition).
2. Apply modus ponens: Modus ponens is a rule of inference that allows us to deduce a conclusion from the given premises. If we have the premises "If ¬C, then P" and "¬C", we can conclude "P" using modus ponens.
3. State the conclusion: After applying modus ponens, we can conclude "P" based on the given premises, which include sentence 6 (¬C) and the conditional statement.

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Credit is an important part of modern financial systems, and it is used to make purchases, access loans, and invest in different projects. Creditworthiness is a key factor in determining whether an individual can obtain a loan or a credit card.

Matching Vocabularies with Examples:

1. Shows how well previous debt has been managed. - Credit report

2. Gives an approved line of credit with an agreed-upon interest rate. - Credit card

3. Helps lenders and others predict how likely you are to make your credit payments on time. - Credit score

4. Assessment of how likely a borrower will default or not make payments on his or her debt obligations. - Credit worthiness

Credit Report:

A credit report is a detailed record of an individual's credit history, including past loans, credit card balances, and payment history. It provides information on how well a person has managed their previous debt obligations and their current outstanding balances. It also shows whether the person has been involved in any legal proceedings related to their credit.

Credit Card:

A credit card is a financial product that allows an individual to borrow money up to a certain credit limit approved by the lender. It provides a convenient and quick method of making purchases, but it comes with interest charges and fees that must be repaid on time.

Credit Score:

A credit score is a numerical representation of a person's creditworthiness. It is calculated based on the individual's credit report, payment history, current debt, and other factors. A higher credit score indicates a lower risk of defaulting on a loan or credit card payment.

Creditworthiness:

Creditworthiness refers to a borrower's ability to repay their debts and their overall financial health. It is an assessment of how likely a borrower is to default on their debt obligations. Lenders use creditworthiness to determine whether to approve a loan or credit card application and at what interest rate.

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The Volume of the given composite shape is: 432 ft³

The formula for the volume of a triangular prism is:

Volume = base area * height

The volume of a cuboid is:

Volume = Length * Width * Height

Thus:

Volume of composite shape = (6 * 12 * 4) + (6 * 6 * 4)

= 432 ft³

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Whenever a sampled population is normally distributed or whenever the conditions of the central limit theorem are fulfilled.

The sample mean is a normally distributed random variable with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.
Whenever a sampled population is normally distributed or whenever the conditions of the central limit theorem are fulfilled, the sample mean is an unbiased estimator of the population mean. This means that the sample mean is a reliable and accurate representation of the true population mean under these conditions.

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Yes, an 11, 60, 61 triangle has a right angle. This is because the Pythagorean theorem applies to right triangles, stating that the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

In this case, we can apply the theorem and see that 11^2 + 60^2 = 3721 + 3600 = 7321. Taking the square root of 7321 gives us approximately 85.4, which is the length of the hypotenuse.

Now, if we compare the square of the hypotenuse (85.4^2 = 7291.16) to the sum of the squares of the legs (11^2 + 60^2 = 3721 + 3600 = 7321), we can see that they are not equal. Therefore, the 11, 60, 61 triangle is not a right triangle.

However, if we compare the square of the hypotenuse (61^2 = 3721) to the sum of the squares of the legs (11^2 + 60^2 = 3721), we can see that they are equal. Therefore, the 11, 60, 61 triangle is a right triangle.

In conclusion, the 11, 60, 61 triangle has a right angle because it satisfies the Pythagorean theorem, which applies only to right triangles.

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There is a 3.8% chance that this baseball team will win the World Series.

If the sports book at the highroller Casino put the odds of a certain baseball team to win the World Series at 1:25, it means that for every one time the team wins, they will lose 25 times.

To calculate the probability, we need to use the following formula:

[tex]Probability = \frac{ Number of times the event will occur }{Total number of possible outcomes}[/tex]

In this case, the number of times the team will win is 1, and the total number of possible outcomes is 1 + 25 = 26 (1 win + 25 losses).

Therefore, the probability of this baseball team winning the World Series is:

[tex]\frac{1}{26} = 0.038 or 3.8%[/tex]
So, based on the odds given by the sports book, there is a 3.8% chance that this baseball team will win the World Series.

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Answer:

The correct answer is: A 2-column table with 3 rows. Column 1 is labeled x with entries negative 5, 0, 3. Column 2 is labeled y with entries negative 18, negative 2, 10.

To create the table, you can plug in each value of x into the equation -2 + 4x = y, then simplify to find the corresponding value of y. Here are the steps:

When x = -5:

-2 + 4(-5) = y

-2 - 20 = y

y = -22

When x = 0:

-2 + 4(0) = y

-2 + 0 = y

y = -2

When x = 3:

-2 + 4(3) = y

-2 + 12 = y

y = 10

So the table has 3 rows, with x-values of -5, 0, and 3, and corresponding y-values of -22, -2, and 10.

The difference of the given expressions is 2(w+3).

The given expressions are (w+6) and (3w+12).

Subtract (w+6) from (3w+12), we get

3w+12-(w+6)

3w+12-w-6

By grouping like terms we get

(3w-w)+(12-6)

= 2w+6

= 2(w+3)

Therefore, the difference of the given expressions is 2(w+3).

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The given quadratic equation cannot be factored as real factors.

Given quadratic equation is,

4x² + 20x + 200 = 0

We have to factor the equation.

Dividing throughout by 4,

x² + 5x + 50 = 0

Using the factorization method,

There exists two numbers p and q such that (x + p) (x + q) = 0, where pq = 50 and p + q = 5.

There are no such numbers.

If the equation is x² + 5x - 50 = 0, it can be factorized as (x + 10)(x - 5).

Since the equation is x² + 5x + 50 = 0, this cannot be factorized.

Hence this cannot be factorized.

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If a and b are integers, the notation a | b denotes that a divides b, or in other words, that b is a multiple of a. The symbol "|" is read as "divides." For example, we write 2 | 6, which means that 2 divides 6 since 6 is a multiple of 2.

On the other hand, the notation a / b denotes the quotient of a divided by b, or in other words, the result of dividing a by b. The symbol "/" is read as "divided by." For example, we write 6 / 2 = 3, which means that the quotient of 6 divided by 2 is equal to 3.

It is important to note that the notation a | b and a / b are not equivalent. The former is a statement about the divisibility of two integers, while the latter is a numerical expression representing the result of dividing one integer by another.

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The price of the stereo system after the markup was $691.20.

The original price of the stereo system was $720.

During the sale, the price was reduced by 20%, which is equivalent to multiplying by (1 - 0.2) = 0.8.

The discounted price was:

720 × 0.8 = $576

After the sale, the discounted price was marked up by 20%

It is equivalent to multiplying by (1 + 0.2) = 1.2.

So the final price was 576 × 1.2

= $691.20

Therefore, the price of the stereo system after the markup was $691.20.

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