14.4 A Book and a Cake A book costs $45. Sales tax on the book is 7%. Write two different expressions that represent the final cost of the book in dollars. Pne of the expressions should use only a single multiplication and no other operations.
A cake that costs $32 is on sale for 15% off and there are no taxes. Explain why the expression (0.85).32 represents the final price of the cake in dollars
(0.85). 32 represents the final price of the cake in dollars because...​

It would be the first option>>"negative slope"

Answer:

Step-by-step explanation:

A positive slope goes from lower left to upper right.

A negative slope goes from lower right to upper left.

So neither of those two are correct.

slope = (y2 - y1) / (x2 - x1)

y2 = y1 = -2

Therefore the slope = 0

Answer:

425 monkeys

Step-by-step explanation:

Subtract the number of birds from the number of monkeys to find the difference between the two.

The equation of the line with a slope of zero that goes through (2, -5) is y = -5.

If a line has a slope of zero, it means that the line is horizontal. A horizontal line has the same y-coordinate for all points along the line.

Since the line passes through the point (2, -5), the equation of the line can be written as y = -5, where y is the dependent variable and -5 is the constant value.

Therefore, the equation of the line with a slope of zero that goes through (2, -5) is y = -5.

A line with a slope of zero is a horizontal line, which means it has a constant y-coordinate for all points along the line. In this case, since the line passes through the point (2, -5), the y-coordinate remains -5 for all x-values.

The general equation of a horizontal line can be written as y = c, where c is a constant. Since the line passes through the point (2, -5), we can substitute the values of x = 2 and y = -5 into the equation to determine the specific constant.

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It would be less expensive to join Gym A for b. Less than 12 months.

The total cost C for Gym A can be represented by the equation,

C = 50 + 79n

where n represents the number of months of membership.

The total cost C for Gym B can be represented by the equation,

C = 250 + 63n

where n represents the number of months of membership.

To find the conditions under which joining Gym A would be less expensive, we need to set up an inequality. Since we want to compare the costs for the two gyms, we will set the inequality of Gym A's cost less than Gym B's cost. This can be written as

50 + 79n < 250 + 63n

This can be simplified and solved:

16n < 200

n < 12.5

Therefore, if Delilah is planning to be a member of a gym for less than 12 months, then joining Gym A will be less expensive. If she is planning to be a member for more than 12 months, then joining Gym B will be less expensive. Hence, the answer is option b. Less than 12 months.

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Answer:

f(x)=x^2

Step-by-step explanation:

if you wanted have a function where both of the robot's arms are in the air the function could be x to the power of any even number such f(x)=x^2, f(x)=x^4, f(x)=x^6, or even f(x)=x^10. And you could still do the same transformations with these equations.

Answer:

0.74

Step-by-step explanation:

Answer:

I think it's the first one if not put the last

PLS PUT ME BRIANIEST

Step-by-step explanation:

The sales tax rate for a specific type of wood-frame door priced at $1480 is 25%, or $370.

Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. For instance, if you answered 75 questions correctly out of 100 on a test (75/100), you would have received a 75%. A percentage is a relative value that represents one hundredth of a quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice the given quantity. A percentage is a fraction of a whole expressed as a number between 0 and 100.

Here,

Sale tax=$370

Price of door=$1480

Sales tax percent=370/1480*100

=25%

The rate of sales tax for a particular type of wood-frame door is priced at $1480 is 25% that is $370.

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Answer:

x = 5

y = 3

Step-by-step explanation:

x + 4y = 17

2x + 5y = 25

We multiply the first equation by -2

-2x - 8y = -34

2x + 5y = 25

-3y = -9

y = 3

Now we put 3 in for y and solve for x

x + 4(3) = 17

x + 12 = 17

x = 5

Let's Check the answer

5 + 4(3) = 17

5 + 12 = 17

17 = 17

So, x = 17 and y = 3 is the correct answer.

Degree of freedom for chi-square test for 10 categories will be 9.

What is chi- square test?

A test that evaluates how well a model matches real observed data is that the chi-square (χ²) statistic. A chi-square statistic can only be calculated with data that's random, unprocessed, mutually exclusive, obtained from independent variables, and drawn from a large enough sample.

The Formula for Chi-Square Is

χ(c)=²∑(Oₐ-Eₐ)₂/Eₐ²

where:

c=Degrees of freedom

O=Observed value(s)

E=Expected value(s)

​

Main Body:

Degree of freedom = total categories -1

so no. of categories= 10

Degree of freedom = 10 - 1

Hence degree of freedom = 9

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Answer:

57 1/10

(14× 3/4)+(4× 1/2)+(8× 1/2)+(10× 2/5)+(10× 2/5)+(12× 4/5)= 571/10 or 57× 1/10

Answer: 3 people had 4 credit cards.

Step-by-step explanation:

The question does not ask about the e-mail accounts, so you can ignore that. Then look for which line is for 4 cards and see how many dots are on the line, and there's your answer.

Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.

To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:

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

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:

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

P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.

P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.

P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.

To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.

The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.

Therefore, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= (2/3) * (6/13) + (5/9) * (7/13)

= 89/117

Now we can plug in all the values into Bayes' theorem to find P(A|B):

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

= (2/3) * (6/13) / (89/117)

= 52/89

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.

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Answer:

A. Opposite angles of a rhombus are congruent.

Step-by-step explanation:

Answer:

2) 4 and 2/5

4) 6 and 3/8

6) 4 and 5/12

8) 2 and 1/3

10) 24 and 2/3

12) 7 and 5/6

14) 33/5

16) 102/11

18) 81/5

20) 163/7

22) 1295/6

24) 1329/16

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

30 feet

Step-by-step explanation:

A ratio of 4:3 means that if one part can be represented by x, the original height is equal to 4 * x and the mural height is equal to 3 * x. This is because the ratio of original : mural is 4 : 3, so if one part = x, we have 4 * x : 3 * x. Therefore,

original mast height = 40 feet

4 * x = original mast height = 40 feet

divide both sides by 4 to get x

x = 10 feet

3 * x = mural mast height = 3 * 10 feet = 30 feet

none of the provided options (a, b, c, d) appear to be accurate or close to the minimum space required.

To determine the minimum space required for a male restroom design with the given plumbing requirements, we need to consider the minimum space required for water closets and lavatories.

The minimum space required for water closets is typically around 30-36 inches per unit, and for lavatories, it is around 24-30 inches per unit.

Since the design requires a minimum of 12 water closets and 13 lavatories, we can estimate the minimum space required as follows:

Minimum space required for water closets = 12 water closets * 30 inches = 360 inches

Minimum space required for lavatories = 13 lavatories * 24 inches = 312 inches

Adding these two values together, we get a total minimum space requirement of 672 inches.

Among the given options, the closest value to 672 inches is option d) 249. However, this value seems significantly lower than the expected minimum space requirement.

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Answer: x < √3 - x

Step-by-step explanation:

-x^2+x-3<0

= x^2+x < 3

= x^2 < 3 - x

= x < √3 - x

Answer:

16 girls

Step-by-step explanation:

boys : girls : total

5          4        5+4 = 9

take the total number of people and divide by 9

36/9 = 4

Each number should be multiplied by 4

boys : girls : total

5*4        4*4     9*4

20          16        36

There are 16 girls

Answer:

x² - x - 2 = 0

Step-by-step explanation:

plotting the graph of x and y,we have that the root of the equation is -1 or 2

x = -1 or 2

the eqn therefore is;

x² - (sum of the root)x + (product of the root) =. 0

x² - (-1+2)x + (-1*2) = 0

x² - x - 2 = 0

Applying the Factor Theorem, it is found that the quadratic function is:

\(p(x) = x^2 - x - 2\)

------------------------

The Factor Theorem states that if a polynomial \(p(x)\) has roots \(x_1, x_2, ..., x_n\), it is described by the following equation:

\(p(x) = a(x - x_1)(x - x_2)...(x - x_n)\)

In which a is the leading coefficient.

\(p(x) = a(x - (-1))(x - 2)\)

\(p(x) = a(x + 1)(x - 2)\)

\(p(x) = a(x^2 - x - 2)\)

When x = 0, p(x) = -2, and we use this to find a.

\(p(x) = a(x^2 - x - 2)\)

\(-2 = a(0^2 - 0 - 2)\)

\(2a = 2\)

\(a = \frac{2}{2}\)

\(a = 1\)

Thus, the quadratic function is:

\(p(x) = x^2 - x - 2\)

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Answer:

x = 3

Step-by-step explanation:

Is x an exponent?

\( y = 3^x \)

\( 27 = 3^x \)

\( 3^3 = 3^x \)

\( x = 3 \)

The mean of the sampling distribution of the sample mean is 1550, and the standard deviation is 30.

The mean and standard deviation for the sampling distribution of the sample mean can be calculated using the following formulas:

mean of sampling distribution = population mean = 1550

standard deviation of sampling distribution = population standard deviation / sqrt(sample size)

= 180 / sqrt(36)

= 30

Therefore, the mean of the sampling distribution of the sample mean is 1550, and the standard deviation is 30.

It is important to note that the central limit theorem applies in this scenario, which allows us to assume that the distribution of the sample mean is approximately normal, even if the underlying population is not normally distributed. This is because the sample size (36) is relatively large and the sampling distribution of the mean will become increasingly normal as the sample size increases.

Using this information, the theatre owner can estimate the range of likely values for the average number of attendees for weeknight shows in the current year, assuming that the population mean and standard deviation have remained the same as in the past 20 years. She can also use this information to make inferences about the population mean based on her sample mean and standard deviation.

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The area bounded by the curve x = t - 1/t, y = t + 1/t, and line y = 2.5 can be found by integrating the difference between the x-coordinates of the curve and the line with respect to t, from t = 0.5 to t = 2.

We know that y = 2.5 intersects the curve at t = 0.5 and t = 2, giving us two separate regions to consider. For t = 0.5, x = 0.5, and for t = 2, x = 2. We can calculate the integral to find the area as follows: ∫[0.5, 2] (2.5 - (t + 1/t)) - (2.5 - (t - 1/t)) dt. The resulting area is approximately 3.265, with a word count of 100 words.
To find the area bounded by the curve x = t - 1/t, y = t + 1/t, and the line y = 2.5, we need to integrate the curve with respect to x between the intersection points you found, (1.5, 2.5) and (-1.5, 2.5). Since x = t - 1/t, we can rewrite t as t = x + 1/x. Substitute this into the equation for y: y = (x + 1/x) + 1/(x + 1/x). Simplify to y = x + 1/x + 1/(2x). Now, integrate this function with respect to x from -1.5 to 1.5.
Area = ∫[-1.5 to 1.5] (x + 1/x + 1/(2x)) dx. Calculate the integral and find the area of the region bounded by the curve and the line y = 2.5.

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Depreciation expense is  $20,121  in equation .

What is Depreciation expense?

Additional to retained earnings                =  5,900

Add : dividends paid                                  =  2,040

Net income                                                 = $7940

Tax                                                              =  22%

Before tax income 97940 -/( 1 - 0.22)       =  $10179.48

Add : Interest expense                              =   $4600

operating income                                      =                            $14,779.48      

Sales                                                            =  $66,000    

Less : costs                                                = $31,100

Gross profit                                                  =                             $34,900

Depreciation expense                                =                              $20,121

(34,900 - 14,779.48)

Depreciation expense is    $20,121 .

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To pay off a loan of $49,000 at an annual interest rate of 9% compounded monthly, with monthly payments of $400, it will take approximately 12.9 years.

To determine the time it takes to pay off the loan, we can use the formula for the number of periods (n) in the compound interest formula. In this case, the loan amount is $49,000, the monthly payment is $400, and the monthly interest rate is 9% divided by 12 (0.09/12 = 0.0075). We can use the following formula:

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

where r is the monthly interest rate, P is the monthly payment, and A is the loan amount.

Plugging in the values, we have:

\(n = -log(1 - (0.0075 * 49000) / 400) / log(1 + 0.0075)\)

Calculating this expression, we find that n is approximately 12.9 years. Therefore, it will take approximately 12.9 years to pay off the loan with monthly payments of $400, rounded to one decimal place.

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Answer:

-3

Step-by-step explanation:

1. Choose two coordinates on the line and count up and over to get the slope. For example, let's use coordinates (0,4) and (1,1).

Remember, slope is equal to rise/run. However, since the line is drawn in a downward diagonal direction, the slope is negative.

Start from (1,1) and count up and then left until you get to (0,4).

Count up 3 and left 1

Rise/run = -3/1.

2. Reduce it down to 3.

Slope is -3

Answer:

a+b=-34

Step-by-step explanation:

a and b represent the two unknown numbers, which we know to sum to -34

A scalene triangle is a triangle with three different side lengths and three different angle measurements.

All of the sides of the triangle known as the Scalene Triangle are of various lengths. It indicates that all three angles and all three sides of a scalene triangle are of different sizes. According to sides, there are three different kinds of triangles.

We'll go over its definition, formulas for its area and perimeter, and its characteristics. The sides and angles of the triangles are used to define them. A triangle is represented as a three-sided polygon in geometry and is a closed, two-dimensional plane object having three sides and three angles. There are three edges and three vertices on it.

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Given statement solution is :- It takes 5.625 minutes for the front of the train to enter the tunnel. Since it takes the same amount of time for the back of the train to exit the tunnel, the answer is also 5.625 minutes.

To solve this problem, we need to convert the train's speed from minutes per hour to miles per minute.

Given:

Train's speed = 45 minutes per hour

Length of the train = 1/8 mile

Length of the tunnel = 1 mile

First, let's convert the train's speed from minutes per hour to miles per minute:

Speed = 1 hour / 45 minutes = 1/45 hours per minute

Since the train is traveling at a constant speed, we can assume it takes the same amount of time to travel the entire length of the tunnel. Therefore, the time it takes for the back of the train to exit the tunnel will be the same as the time it takes for the front of the train to enter the tunnel.

Let's calculate the time it takes for the front of the train to enter the tunnel:

Distance = Speed × Time

1/8 mile = (1/45) miles per minute × Time

Solving for Time:

Time = (1/8) / (1/45)

Time = (1/8) × (45/1)

Time = 45/8

Time = 5.625 minutes

Therefore, it takes 5.625 minutes for the front of the train to enter the tunnel. Since it takes the same amount of time for the back of the train to exit the tunnel, the answer is also 5.625 minutes.

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