Help Select the expressions that are polynomials.

To calculate the total number of scores, we need to multiply the frequency of each score by its corresponding value of x and add up the results. The total number of scores for the distribution shown in the table is 18, option (c).

To calculate the total number of scores, we need to multiply the frequency of each score by its corresponding value of x and add up the results. For example, for x = 4, the frequency is 7, so there are 7 scores of 4. Similarly, for x = 3, there are 5 scores of 3, and so on.

Using this approach, we can calculate the total number of scores as follows:

Total number of scores = (4 x 7) + (3 x 5) + (2 x 4) + (1 x 2) = 28 + 15 + 8 + 2 = 53

However, this result counts each individual score, whereas we want to count the total number of students or items represented in the distribution. Therefore, we need to sum up the frequencies:

Total number of scores = 7 + 5 + 4 + 2 = 18

So, option (c) is the correct answer.

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Answer:

, two mathematicians, Andrew Sutherland of MIT and Andrew Booker of Bristol, have jointly proven that 42 is indeed the sum of three cubes. For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from

Answer:

294?

Step-by-step explanation:

The inverse of a biconditional statement is not equivalent to the original statement. The inverse statement may have a different meaning or convey a different condition.

The inverse of a biconditional statement involves negating both the "if" and the "only if" parts of the statement. In this case, the inverse of the biconditional statement would be:Inverse of Statement 1: A figure is not a polygon if and only if not all of its sides are line segments.

Now, let's analyze the relationship between Statement 2 and its inverse.

Statement 2: A figure is not a polygon if and only if not all of its sides are line segments.

Inverse of Statement 2: A figure is not a polygon if and only if all of its sides are line segments.

The inverse of Statement 2 is not equivalent to Statement 1. In fact, the inverse of Statement 2 is a different statement altogether. It states that a figure is not a polygon if and only if all of its sides are line segments. This means that if all of the sides of a figure are line segments, then it is not considered a polygon.

In contrast, Statement 1 states that a figure is a polygon if and only if all of its sides are line segments. It affirms the condition for a figure to be considered a polygon, stating that if all of its sides are line segments, then it is indeed a polygon.

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The smallest possible inside length of the cubical steel tank that can hold 275 liters of water is approximately 0.640 meters.

The side length of the cube is found by converting the volume of water from liters to cubic meters, as the unit of measurement for the side length is meters.

Given that the volume of water is 275 liters, we convert it to cubic meters by dividing it by 1000 (1 cubic meter = 1000 liters):

275 liters / 1000 = 0.275 cubic meters

Since a cube has equal side lengths, we find the side length by taking the cube root of the volume. In this case, we find the cube root of 0.275 cubic meters:

∛(0.275) ≈ 0.640

Rounded to the nearest 0.001 meters, the smallest possible inside length of the tank is approximately 0.640 meters.

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The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855

a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.

b) The population deviation divided by the square root of the sample size gives the standard deviation value.

standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073

c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by

1 - P (X < x)= P (X > x)

= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 is given by:

1 -P (X - 0.7) = P (X > 0.7)

= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)

= 1 - 0.91455 = 0.0855

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Answer:

Angela is 13 years old and Angela's aunt is 41 years old.

Step-by-step explanation:

With the information provided you know that Angela's aunt is two more than three times her age, which could be expressed as:

x=3y+2, where:

x is Angela's aunt age

y is Angela's age

Also, you know that the total of their ages is 54, which is:

x+y=54

Now, you can replace x=3y+2 in x+y=54 and solve for y:

3y+2+y=54

4y=54-2

4y=52

y=52/4

y=13

Finally, you can replace the value of y in x=3y+2 to find x:

x=3(13)+2

x=39+2

x=41

According to this, the answer is that Angela is 13 years old and Angela's aunt is 41 years old.

Answer:

21.9 m

Step-by-step explanation:

Take the amount for one dress and multiply by 6

3.65*6 =21.9 m

Answer:

21.9m

Step-by-step explanation:

3.65m*6=21.9m

that is how to solve it because one clothe is 3.65m so therfore six clothe will be 3.65*6=21.9m

1

(5(0)+1/2)2

(1/2)2

2/2

1

Answer:

c. 18 feet

Step-by-step explanation:

The area is 180ft². The height is 10ft.

Now, we need to divide 180ft² by 10ft.

180/10 = 18

ft²/ft = ft

The length of the wall is 18ft.

Answer:

The measure of the wall given is square ft., meaning you can divide it by either length or height to get the corresponding side.

We are given a height of 10 ft.

So 180 / 10 = 18ft

L = 18ft

Have a lovely day!

The statement predicts that 3/28 will be the answer.

In regard to quantitative measurements ranging from zero to one, the probability theory offers a way to estimate the possibility of occurrence of various occurrences coming from a random experiment. A certain occurrence has a probability of one while an impossible event has a probability of zero.

Probability is the study of random events in mathematics, and it can be classified into four main categories: logical, classic, empirical, and subjective.

According to what they meant:

the first chocolate toffee 3/8

Toffee chocolate number two: 2/7

So, 3/8 × 2/7 = 6/56 = 3/28

Thus, 3/28 is the correct response.

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For a balloon mortgage, the monthly payments are usually lower, but there is a final "balloon" payment due at the end of the term.

a. Property Taxes:

The assessed value of the building is $500,000, and the property tax rate is 2.415%. To calculate the property taxes, we multiply the assessed value by the tax rate:

Property taxes = Assessed value * Tax rate

Property taxes = $500,000 * 2.415% (convert percentage to decimal)

Property taxes = $500,000 * 0.02415

Property taxes = $12,075

Therefore, the property taxes on the assessed value of the building will be $12,075.

b. Monthly Mortgage Payment:

To calculate the monthly mortgage payment, we need to consider the loan amount, interest rate, and loan term. The down payment is 20%, so the loan amount will be 80% of the market value of the building:

Loan amount = Market value * (1 - Down payment percentage)

Loan amount = $457,350 * (1 - 20%) (convert percentage to decimal)

Loan amount = $457,350 * 0.8

Loan amount = $365,880

We can now use this loan amount, along with the mortgage interest rate and loan term, to calculate the monthly payment using the formula for a fixed-rate mortgage:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

The monthly interest rate is the annual interest rate divided by 12, and the total number of months is the loan term multiplied by 12.

Annual interest rate = 4.55% (convert percentage to decimal)

Monthly interest rate = 4.55% / 12

Loan term = 30 years

Total number of months = 30 * 12

Now, let's calculate the monthly payment:

Monthly payment = ($365,880 * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

c. Total Interest Paid:

To calculate the total interest paid over the life of the loan, we multiply the monthly payment by the total number of months and subtract the loan amount:

Total interest paid = (Monthly payment * Total number of months) - Loan amount

d. Closing Costs:

The closing costs can vary, but a common range is between 2% and 5% of the purchase price. To calculate the range for closing costs, we'll use these percentages:

Minimum closing costs = Purchase price * 2%

Maximum closing costs = Purchase price * 5%

e. Balloon Mortgage Payment:

For a balloon mortgage, the monthly payments are usually lower, but there is a final "balloon" payment due at the end of the term. To calculate the monthly payment for the balloon mortgage, we'll use the loan amount, interest rate, and loan term:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Total number of months))

Now, let's calculate the monthly payment for the balloon mortgage.

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To determine the number of cups of cereal in 10 servings, you need to perform a calculation and move the appropriate number to each box. If the result is a whole number, that number should be moved to the first box. Otherwise, a 0 should be moved to the first box.

To find the number of cups of cereal in 10 servings, you need to know the amount of cereal in each serving. Without that information, it is not possible to provide an exact answer. However, if we assume that each serving contains a certain number of cups, we can calculate the total cups for 10 servings.
For example, let's assume each serving contains 1 cup of cereal. In this case, the calculation would be: 1 cup/serving * 10 servings = 10 cups. Since this is a whole number, we would move 10 to the first box.
If we assume each serving contains a fraction of a cup, such as 0.5 cups, the calculation would be: 0.5 cup/serving * 10 servings = 5 cups. Since this is also assume  a  whole number, we would move 5 to the first box.
In the absence of specific information about the amount of cereal in each serving, we cannot provide an exact answer.

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Answer:

6 3/4 cups.

Step-by-step explanation:

Multiply 3/4 by 9.

Hope this helps!

1) If the couple must sit together, there are 240 ways that they can be seated.

2) If the couple must not be together, there are 720 ways that they can be seated.

1) If the couple must sit together, we can think of them as one unit. So, there are 5 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.

The couple can be arranged in two different ways within their unit. So, the total number of ways they can be seated is: 5! × 2 = 240.

2) If the couple must not sit together, we can think of them as separate units. So, there are 6 units to be seated around the table. We can choose any one of these units to be the starting point, and then arrange the other units clockwise around the table.

The couple cannot be seated next to each other, so there are 3 possible units where they cannot be seated next to each other. Once we have chosen one of these units for the starting point, there are 2 ways to arrange the couple within their unit. Therefore, the total number of ways they can be seated is: 5! × 2 × 3 = 720.

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Answer: $4.50

Step-by-step explanation:

48-21=27

27 divided by 6= 4.50

Therefore each case costs 4.50

Answer:

$4.50

Step-by-step explanation:

48 - 21

27

divide by 6

4.50

Answer:

Step-by-step explanation:

Job can be determines as:

We have:

Sum of the parts completed by both Rocco and Giulia gives the job, which is considered as a whole or 1:

or

Correct choice is B

gj,xDGIDYOry

oFYORYODYIYDOCYODYODYODOYYDSOYSITTIsst.isti.ti.s.sitsi.ttsliyd.i.odygis.x.ittxi.x,jgxfj,.jtxtis.x.tii.ts.kdttic.

Answer:

24 hours for the following conditions. (Round your answers to the nearest whole number.) (a) No antibiotic is

Answer:C

Step-by-step explanation:

180-(60+40)=80°

C=80°

20/sin80. =a/sin40

a=(20sin40)÷sin80

=13.1

Magnification of a convex mirror is 0.67 times for objects 3.8 m from the mirror .the focal length is negative, this means that the mirror is a diverging mirror (convex mirror). Therefore, the focal length of this mirror is 2.4 meters.

To find the focal length of a convex mirror, we can use the mirror formula:

1/f = 1/v + 1/u

where f is the focal length, v is the image distance, and u is the object distance.

In this case, we know that the magnification (M) of the mirror is 0.67, and the object distance (u) is 3.8 m. We also know that for a convex mirror, the image is always virtual and upright, so the image distance (v) is negative.

The magnification formula is:

M = -v/u

Substituting the values we have:

0.67 = -v/3.8

v = -2.546 m

Now we can use the mirror formula to find the focal length:

1/f = 1/-2.546 + 1/3.8

1/f = -0.416

f = -2.4 m

Since the focal length is negative, this means that the mirror is a diverging mirror (convex mirror). Therefore, the focal length of this mirror is 2.4 meters.

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

My reasonable answer would be that it was a translation and then dilation

Step-by-step explanation:

Option C is the most appropriate answer. When outliers are discovered in a data set, they should not always be automatically removed. Outliers should be investigated to understand their cause, and then a decision can be made whether to remove or adjust them based on their relevance and impact on the analysis.

Outliers can provide valuable information and insights into the data, such as data entry errors or extreme observations that represent rare events or special circumstances. Therefore, blindly removing outliers without understanding their cause can lead to loss of important information and biased analysis.Instead, it is important to investigate outliers to determine their cause. This may involve checking for data errors, verifying data sources, or considering contextual factors that could explain the extreme values. Once the cause of the outlier is determined, it can be assessed whether it should be removed from the data set based on its relevance to the analysis and the potential impact on the results.Regarding z-scores, option E is the correct answer. Z-scores allow for a unitless comparison of how many standard deviations an observation is from the mean. They take into account the relative size and variability of the data and provide a standard basis for comparison. Z-scores can also help in detecting possible outliers, as observations with z-scores that are significantly larger or smaller than the mean can indicate extreme values in the data.

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Answer:

D) 2x² + x - 10

Step-by-step explanation:

First, distribute the negative sign to all terms within the second parenthesis:

- (4x - x² + 6) = -4x + x² - 6

Next, combine like terms:

5x + x² - 4 - 4x + x² - 6

(x² + x²) + (5x - 4x) + (-4 - 6)

2x² + x - 10

2x² + x - 10 , or D) is your answer.

Answer:

2x^2+x-10 (the pink/red one)

Step-by-step explanation:

(5x+x^2-4)-(4x-x^2+6)

5x+x^2-4-4x+x^2-6

2x^2+x-10

The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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The required,
19. AB is tangent to circle C.
20. AB is not tangent.

In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.

Here,
Form figure 19.

Applying the Pythagorean theorem,
BS² = AS² + AB²

Substitute the value in the above expression.
12² = 7.2² + [2*4.8]²    [radius = diameter /2]

144  = 51.84+92.16
144 = 144

Thus, the required AB is tangent to circle C.

Similarly,
In figure 20 AB is not tangent because,
BC² ≠ AB² + AC²

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Answer:

The answer would be 13

Step-by-step explanation:

(6 x 7 - 22) - 7

(42 - 22) - 7

(20) - 7

13

The value of x is 10

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

The large triangle is divided into 2 similar triangles

The ratios of corresponding sides are equal

8/12 = x+4/2x+1

=> 8( 2x+1) = 12( x+4 )

=>  16x+8 = 12x+48

=> 16x-12x = 48-8

=> 4x = 40

=> x= 40/4 = 10

The value of x is 10

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After using the method of undetermined coefficients, the specific solution to the initial value problem is: y(t) = (-5 + 4t)e^(3t) + 8e^(5t)

To solve the given second-order linear homogeneous differential equation, we can use the method of undetermined coefficients. The characteristic equation for this equation is:

r^2 - 6r + 9 = 0

Solving the quadratic equation, we find that the characteristic roots are r = 3 (with multiplicity 2). This implies that the homogeneous solution to the differential equation is:

y_h(t) = (c1 + c2t)e^(3t)

Now, let's find the particular solution using the method of undetermined coefficients. Since the right-hand side of the equation is 32e^(5t), we assume a particular solution of the form:

y_p(t) = Ae^(5t)

Taking the derivatives:

y_p'(t) = 5Ae^(5t)

y_p''(t) = 25Ae^(5t)

Substituting these derivatives into the original differential equation:

25Ae^(5t) - 30Ae^(5t) + 9Ae^(5t) = 32e^(5t)

Simplifying:

4Ae^(5t) = 32e^(5t)

Dividing by e^(5t):

4A = 32

Solving for A:

A = 8

Therefore, the particular solution is:

y_p(t) = 8e^(5t)

The general solution is the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

    = (c1 + c2t)e^(3t) + 8e^(5t)

To find the specific solution that satisfies the initial conditions, we substitute y(0) = 3 and y'(0) = 7:

y(0) = (c1 + c2 * 0)e^(3 * 0) + 8e^(5 * 0) = c1 + 8 = 3

c1 = 3 - 8 = -5

y'(t) = 3e^(3t) + c2e^(3t) + 8 * 5e^(5t) = 7

3 + c2 + 40e^(5t) = 7

c2 + 40e^(5t) = 4

Since this equation should hold for all t, we can ignore the e^(5t) term since it grows exponentially. Therefore, we have:

c2 = 4

Thus, the specific solution to the initial value problem is:

y(t) = (-5 + 4t)e^(3t) + 8e^(5t)

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