Customers at two clothing stores were asked about their color preferences in shirts. The responses of the customers at each store are summarized in the table.
Based on the information in the table, which statement best describes the customers' preferences on shirt colors?

A. At both stores, more customers prefer white shirts than shirts in either of the other two colors.

B. At store 2, the same number of customers prefer blue and black shirts.

C. At both stores, fewer customers prefer blue shirts than shirts in either of the other two colors.

D. At store 1, more customers prefer either blue or black shirts than white shirts.

After solving the given expression, the value of x is 5.

What exactly are expressions?

An expression in mathematics is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that may be evaluated to generate a value. Expressions can be simple or complicated, with one or more variables involved.

Now,

To solve the equation 6x+14x+5=5(4x+1), we first need to simplify both sides of the equation using the distributive property of multiplication:

6x + 14x + 5 = 20x + 5

Now we can simplify further by subtracting 20x and 5 from both sides of the equation:

6x + 14x - 20x = 0 - 5

Simplifying again:

x = -5

Finally, we can solve for x by multiplying both sides by -1:

x = 5

Therefore, the solution to the equation 6x+14x+5=5(4x+1) is x=5.

Word problem:

A clothing store sells two types of shirts: T-shirts and polo shirts. The store makes a profit of $6 on each T-shirt sold and a profit of $14 on each polo shirt sold. Last week, the store sold a total of 5 shirts and made a total profit of $25. If x represents the number of T-shirts sold, write an equation to represent the situation.

Solution:

Let x be the number of T-shirts sold, then the number of polo shirts sold is 5 - x (since a total of 5 shirts were sold). The total profit from selling x T-shirts and (5-x) polo shirts can be calculated as:

Profit = (profit per T-shirt x number of T-shirts) + (profit per polo shirt x number of polo shirts)

Profit = (6x) + (14(5-x))

Profit = 6x + 70 - 14x

Profit = -8x + 70

Since the total profit is given as $25, we can write the equation:

-8x + 70 = 25

Simplifying:

-8x = -45

x = 5.625

Since we can't sell a fraction of a shirt, we need to round down to the nearest integer. Therefore, the store sold 5 T-shirts.

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by simplifying the expression, option d ,sec θ is the correct answer.

how can we solve this expression?

We can simplify the given expression as follows:

(tan θ - [tex]sec^2[/tex] θ) / tan θ

= (tan θ / tan θ) - ([tex]sec^2[/tex] θ / tan θ) ,

by diving it by tan θ

= 1 - (1/[tex]cos^2[/tex] θ)([tex]sin^2[/tex] θ / cos θ),

since sec = 1/cos and tan=sin/cos

placing the value in expression and solving it , we get

= 1 - ([tex]sin^2[/tex] θ / ([tex]cos^3[/tex] θ))

= [tex]cos^3[/tex] θ / [tex]cos^3[/tex] θ - [tex]sin^2[/tex] θ

= [tex]cos^3[/tex]θ / [tex]cos^2[/tex] θ (1 - [tex]tan^2[/tex] θ)

We can simplify the given expression as follows:

= cos θ ( [tex]cos^2[/tex]θ -  [tex]sin^2[/tex]θ) / ([tex]cos^2[/tex] θ)

= cos θ (cos θ / [tex]cos^2[/tex]θ)

= 1/cos θ is equal to sec θ

Therefore, the simplified expression is sec θ.

Hence, the answer is option (d) sec θ.

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Answer:Ken 3 3\4 pounds of apples

Step-by-step explanation:

The perimeter is 14 x 6 = 84 inches .The area is (1/4) x 14 x 6²x cot(π/14) = 153.94 square inches.

Perimeter is a measurement of the total length of the boundary of a two-dimensional shape, such as a polygon or a circle. It is the distance around the outside of a shape, and is usually measured in units such as centimeters, meters, or feet.

Area is a measurement of the amount of space enclosed by a two-dimensional shape, such as a polygon or a circle. It is usually measured in square units such as square centimeters, square meters, or square feet.

In the given question,

We can use the following formulas to find the measure of one interior angle, the perimeter, and the area of a regular polygon:

The measure of one interior angle of a regular polygon with n sides is given by:

(n-2) x 180 / n degrees.

The perimeter of a regular polygon with n sides and side length s is given by: P = n x s.

The area of a regular polygon with n sides and side length s is given by: A = (1/4) x n x s² x cot(π/n), where cot is the cotangent function.

Given that the polygon has 14 sides and one side is equal to 6 inches, we have:

The measure of one interior angle is (14-2) x 180 / 14 = 154.29 degrees (rounded to the nearest whole degree).

The perimeter is 14 x 6 = 84 inches (rounded to the nearest whole number).

The area is (1/4) x 14 x 6² x cot(π/14) = 153.94 square inches (rounded to the nearest hundredths place).

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Using the right cone formula we know that the surface area is 1281.77638m³ respectively.

An axis that is perpendicular to the base plane defines a right circular cone. By rotating a right triangle around one of its legs, we may create a right cone.

The right circular cone in the illustration has an axis that is perpendicular to the base and a circular base with a radius r.

So, the formula for the surface area of the right cone is as follows:

πr(r+√h²+r²)

We have the values: r = 13m and h = 13m

Now, insert values as follows:

= πr(r+√h²+r²)

= π13(r+√13²+13²)

= 1281.77638

Therefore, using the right cone formula we know that the surface area is 1281.77638m³ respectively.

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Answer:

2/3

Step-by-step explanation:

A six sided number cube :

Sample space = 1,2,3,4,5,6

Non composite numbers on a six sided number cube = 1,2,3,5

Probability of an event = required outcome / Total possible outcomes

Required outcome = number of non composite number = 4

Total possible outcomes = sample space = 6

P(not composite)= 4/6 = 2/3

Simultaneous equations are a set of equations that are solved together to determine the values of the variables that satisfy both equations.

1) 4x + 5y = 3 ---(1)

y - 3x = -7 ----(2)

Using the substitution method;

y = -7 + 3x ----(3)

Thus

4x + 5(-7 + 3x) = 3

4x -35 +15x = 3

19x - 35 = 3

19x = 3 + 35

x = 2

Then

4(2) + 5y = 3

8 + 5y = 5

y = 13/5

y = 2 3/5

2) 2x - 4y = 24 ----- x 3

  -3x + 2y = -48 ----- x 2

   6x - 12 y = 72 ---- (3)

  -6x + 4y = -96 ---- (4)

Add 3 and 4

         16y = -24

y = -24/16

Substitute y = -24/16 into (1)

2x - 4(-24/16) = 24

2x + 6 = 24

x = 15

3) -x + y = 13 --- 1

  3x - 4y = 46 ---- 2

y = 13 + x ---- 3

Substitute 3 into 2

3x - 4(13 + x) = 46

3x - 52 - 4x = 46

-x - 52 = 46

x = 98

Substitute x = 98 into (1)

-98 + y = 13

y = 13 + 98

y = 111

Let C be x and D be y

x + y = 180

x = 33 + 6y

x - 6y = 33

x = 180 - y

Substitute and obtain;

180 - y - 6y = 33

180 - 7y = 33

y = 33 - 180/-7

y = 21

Then

x + 21 = 180

x = 180 - 21

x = 159

Lastly

Let small = x , medium = y

x + y = 150

4x + 6y = 764

x = 150 - y

4(150 - y) + 6y = 764

600 - 4y + 6y = 764

600 + 2y = 764

2y = 764 - 600

y = 82

Then;

x + 82 = 150

x = 68

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The solutions to the simultaneous equations are:

1) x = 2 and y = -1

2) x = 18 and y = 3

3) y = -7 and x = 6

There are three main methods in solving simultaneous equations and they are:

1) Elimination Method

2) Substitution Method

3) Graphical Method

1) 4x + 5y = 3

y = 3x - 7

Substitute 3x - 7 for y in the first equation to get:

4x + 5(3x - 7) = 3

4x + 15x - 35 = 3

19x - 35 = 3

19x = 35 + 3

19x = 38

x = 38/19

x = 2

Thus:

y = 3(2) - 7

y = -1

2) 2x - 4y = 24

-3x + 2y = -48

Multiply eq 2 by 2 and eq 1 by 1 to get:

2x - 4y = 24    -----(3)

-6x + 4y = -96   -----(4)

Add eq 3 to eq 4 to get:

-4x = -72

x = 18

2(18) - 4y = 24

36 - 4y = 24

36 - 24 = 4y

4y = 12

y = 3

3) -x + y = -13

3x - 4y = 46

From eq 1, x = y + 13

Thus:

3(y + 13) - 4y = 46

3y + 39 - 4y = 46

39 - y = 46

y = 39 - 46

y = -7

x = -7 + 13

x = 6

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Answer: x=2 is the answer

Answer:

Step-by-step explanation

Rearrange terms

-16=(- 4)- 6 x

-16=-6x - 4

Add 4 to both sides

-16= - 6x - 4

-16 + 4=  -6x  - 4 + 4

Simplify the expression

-16+4=6x - 4+4

-12=6x

Divide both sides by the same factor

-12=6x

-12/-6= -6x/-6

so

x=2

Answer:

13.) y=(x-4)^(2)+3

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

3.15 can be read as  3 and 15 hundredths =   3   15/100  = 3  3/20

Answer:  63/20

Step-by-step explanation:

Answer: i think its A and B

Step-by-step explanation: 33 divided by 2 is 16.5

                                             50 divided by 3 is 16.6667

                                             72 divided by 4 is 18 so that would be to much

                                             89 divided by 5 is 17.8 which is also to much

Answer:

Measures of Central Tendancy

Mean: 429

Median: 344

Mode: 134,185,193,217,471,580,799,853

Range: 719

Step-by-step explanation:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is

[tex]\mu = \frac{{\sum}x}{N}[/tex]

The formula for the mean of a sample is

[tex]\bar{x} = \frac{{\sum}x}{n}[/tex]

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is:

[tex]\frac{3432}{8} = 429[/tex]

The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:

[tex]134, 185, 193, 217, 471, 580, 799, 853[/tex]

Since there is an even number of data values in this data set, there are two middle numbers. With 8 data values, the middle numbers are the data values at positions 4 and 5. These are 217 and 471. The median is the average of these numbers. We have

[tex]{\frac{ 217 + 471 }{2}}[/tex]

Therefore, the median is

[tex]344[/tex]

The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are

[tex]134,185,193,217,471,580,799,853[/tex]

Answer:

To solve 2^x = 32, we need to find the value of x that satisfies the equation.

We can rewrite 32 as a power of 2 by noting that 2^5 = 32. Therefore, we have:

2^x = 2^5

Since the bases of the powers are equal, we can equate the exponents:

x = 5

So the solution to 2^x = 32 is x = 5.

To rewrite this equation in a logarithmic form, we can use the definition of logarithms:

log(base 2)32 = x

Here, the logarithm with base 2 of 32 is equal to x.

Mark my answer as Brainliest!!

Answer: To solve the problem, we can use Bayes' theorem. Let D be the event that a device is defective, and let A be the event that the quality assurance check concludes that a device is defective.

We want to find P(A and not D) + P(not A and D), which represents the probability of an incorrect conclusion.

We know that P(D) = 1 - P(not D) = 1 - 0.84 = 0.16, and that P(A | not D) = 0.03 and P(A | D) = 0.97.

Using Bayes' theorem, we can compute:

P(not A | not D) = 1 - P(A | not D) = 1 - 0.03 = 0.97

P(not A | D) = 1 - P(A | D) = 1 - 0.97 = 0.03

Therefore,

P(A and not D) = P(not D) * P(A | not D) = 0.84 * 0.03 = 0.0252

P(not A and D) = P(D) * P(not A | D) = 0.16 * 0.03 = 0.0048

So the probability of an incorrect conclusion is:

P(A and not D) + P(not A and D) = 0.0252 + 0.0048 = 0.03

Therefore, the probability of an incorrect conclusion is 0.03, or 3% (rounded to the nearest tenth of a percent).

Why was this answer deleted prior?

Answer:

To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:

r = (a/2) * cot(π/n)

where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.

In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:

6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)

36 = 50 - 50cos(x)

cos(x) = (50 - 36)/50

cos(x) = 0.28

x = cos^-1(0.28) ≈ 73.7°

Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:

(5/2)^2 + h^2 = 5^2

25/4 + h^2 = 25

h^2 = 75/4

h = sqrt(75)/2 = (5/2)sqrt(3)

Now we can find the radius of the inscribed circle using the formula:

r = (a/2) * cot(π/n)

where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:

r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm

Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.

By circle , 15 is the length of x .

What is a circle, exactly?

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by each line that traverses the circle.

                                Moreover, every angle has rotational symmetry around the center. With no sides or edges, a circle is a figure with a round shape. A circle can be characterized in geometry as a closed shape, a two-dimensional shape, or a curved shape.

AE² = EC . CD

10² = 5 * x

100 = 5 * x

100/5 = x

 20 = x

ED = 20 - 5   = 15

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Answer:

The probability that a randomly selected subject tested negative or did not use marijuana is 0.589.

Step-by-step explanation:

a. The probability of rolling a number greater than 10 is 1/6.

b. The probability of rolling a number less than 5 is 1/3.

c. The expected number of times a 4, 6, or 9 will be rolled in 200 rolls is 50

a. The probability of rolling a number greater than 10 is equal to the number of faces with numbers greater than 10 (i.e., 11 and 12) divided by the total number of faces. Thus, P(number greater than 10) = 2/12 = 1/6.

b. The probability of rolling a number less than 5 is equal to the number of faces with numbers less than 5 (i.e., 1, 2, 3, and 4) divided by the total number of faces. Thus, P(number less than 5) = 4/12 = 1/3.

c. The probability of rolling a 4, 6, or 9 is equal to the number of faces with those numbers (i.e., 1 each) divided by the total number of faces. Thus, the probability of rolling a 4, 6, or 9 is 3/12 = 1/4.

Therefore, the expected number of times a 4, 6, or 9 will be rolled in 200 rolls is:

(expected number of times) = (probability of rolling a 4, 6, or 9) x (total number of rolls)

= (1/4) x (200)

= 50

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Answer:

6 weeks and 840 hours

Step-by-step explanation:

There are 168 hours in one week.

24 hrs/day * 7 days = 168 hours

1008 hours ÷ 24 hours(1 day) = 42 days ÷ 7 days in a week = 6 weeks

168 hours/week * 5 weeks = 840 hours

Answer:

To find the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces, and then add them together.

First, let's find the length of one side of the base of the pyramid:

Perimeter of the square base = 4 x side length

48 inches = 4 x side length

Side length = 12 inches

Now we can find the area of the base:

Area of the base = side length squared

Area of the base = 12 inches x 12 inches

Area of the base = 144 square inches

Next, we need to find the area of each triangular face. To do this, we need to find the length of the slant height of the pyramid. We can use the Pythagorean theorem to do this:

Slant height squared = height squared + (1/2 base length) squared

Slant height squared = 8 inches squared + (6 inches) squared

Slant height squared = 64 inches squared + 36 inches squared

Slant height = square root of (64 + 36) inches

Slant height = 10 inches

Now we can find the area of each triangular face:

Area of a triangular face = (1/2 base length) x slant height

Area of a triangular face = (1/2 x 12 inches) x 10 inches

Area of a triangular face = 60 square inches

Finally, we can add the area of the base and the area of the four triangular faces together to find the total surface area of the pyramid:

Total surface area = Area of the base + (4 x Area of a triangular face)

Total surface area = 144 square inches + (4 x 60 square inches)

Total surface area = 384 square inches

Therefore, the surface area of the pyramid is 384 square inches.

Part 1: a. A. The sample size needs to be greater than or equal to 30.

Part 2: The probability is approximately 0.0013.

Part 3: There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.

The number of individuals or items in a population that are selected for study.

A. The sample size needs to be greater than or equal to 30.

This is due to the Central Limit Theorem, which states that the sample size of a normal distribution must be 30 or more to produce reliable results.

If a sample size is less than 30, the results may be skewed and not accurately represent the true population mean and standard deviation.

B. The probability is approximately 0.0013.

This probability can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.

The z-score for a sample mean of 15 minutes =-3.3,

which translates to a probability of 0.0013 using the z-score table.

C. There is a 10% chance of being at or below a mean oil-change time of 14.9 minutes.

This can be calculated by using the z-score formula and plugging in the mean, standard deviation, and sample size.

The z-score for a 10% chance= -1.28,

which translates to a mean oil-change time of 14.9 minutes.

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The true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

In geometry, how an item is positioned in the space it occupies—such as a line, plane, or rigid body—is described in terms of its orientation, angular position, attitude, bearing, and direction.

It refers more particularly to the fictitious rotation required to shift an object from a reference placement to its present location.

To get to the current positioning, a rotation might not be sufficient.

It could be required to include a fictitious translation known as the object's location (or position, or linear position).

Together, the position and orientation completely explain where the object is situated in space.

Therefore, the true statements are:

(B) Both figures are congurent.

(C) The two figures have the same orientation but different positions.

(E) Corresponding angles and sides have the same measures.

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Answer:

2/5 of the cookie

Step-by-step explanation:

12 friends need to split 4 cookies

4 cookies needs to divided by 10 people

[tex]\frac{4cookies}{10 people}[/tex] = [tex]\frac{4}{10}[/tex]

simplify: [tex]\frac{4}{10} = \frac{2}{5}[/tex]

Answer:

(a) 22 inches

(b) 770 inches

(c) 26,950 inches

Step-by-step explanation:

(a) To find the perimeter of the drawing, we add up the lengths of all four sides:

Perimeter of drawing = 7 + 4 + 7 + 4 = 22 inches

(b) The length and width of the actual garden are 35 times larger than the dimensions in the drawing. This means that the actual length is 7 x 35 = 245 inches and the actual width is 4 x 35 = 140 inches. To find the perimeter of the actual garden, we add up the lengths of all four sides:

Perimeter of actual garden = 245 + 140 + 245 + 140 = 770 inches

(c) When the dimensions of the garden are multiplied by 35, the perimeter of the garden will also be multiplied by 35. This is because each side will increase by a factor of 35, so the total length of all four sides will increase by a factor of 35 as well. Therefore, the new perimeter will be:

New perimeter = 35 x Perimeter of actual garden = 35 x 770 = 26,950 inches

Answer:

Step-by-step explanation:

yes since they are both divisible by their denominators and equal the same thing

Answer:

yes, they are equivalent

Step-by-step explanation:

2/2 = (2/2)x(4/4) = 8/8 = 1

Answer:

Step-by-step explanation:

Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. It is used in various fields such as mathematics, statistics, science, and finance to make predictions and analyze data.

Here,

1. The z-score for a sample mean of $75 is calculated as:

z = (75 - 76) / (6 / √(40)) = -2.36

Using a z-table, the probability of a z-score less than -2.36 is 0.0099 (rounded to 4 decimal places).

2. The z-score for a sample mean of $75 is calculated as:

z1 = (75 - 76) / (6 / √(40))

= -2.36

The z-score for a sample mean of $77 is calculated as:

z2 = (77 - 76) / (6 / √(40))

= 0.79

Using a z-table, the probability of a z-score between -2.36 and 0.79 is 0.8669 (rounded to 4 decimal places).

3. The z-score for a sample mean of $77 is calculated as:

z1 = (77 - 76) / (6 / √(40))

= 0.79

The z-score for a sample mean of $78 is calculated as:

z2 = (78 - 76) / (6 / √(40))

= 1.57

Using a z-table, the probability of a z-score between 0.79 and 1.57 is 0.0823 (rounded to 4 decimal places).

4. The standard error of the mean (SEM) is calculated as:

SEM = standard deviation / sqrt(sample size)

SEM = 6 / √(40) = 0.9487

The z-score for a sampling error of $1.50 is calculated as:

z = 1.50 / 0.9487 = 1.58

Using a z-table, the probability of a z-score less than 1.58 is 0.9429 (rounded to 4 decimal places).

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1. Batman spent $99 this month after starting with $57 and ending with a balance of -$42.

2. The average change in Barbie's position each minute in the scuba diving is -7.3 meters.

3. The change in Ms. Blue's weight after one year of dieting and losing 4 pounds monthly is -48 pounds.

Initial balance in the bank account = $57

Final balance at month-end = $-42

The total amount spent = $99 ($57 + $42)

Thus, when $99 is taken away from $57, the balance is $-42.

Initial position = -2.1 m

Final position = -38.6 m

Change in position = -36.5 m (-38.6 - -2.1)

The number of minutes used to change position = 5 minutes

The average change per minute = -7.3 m (-36.5 ÷ 5)

The quantity of pounds lost per month = 4 pounds

The period of dieting = 1 year = 12 months

The total change in weight after one year of dieting = -48 pounds (-4 x 12)

Thus, these three problems are solved using mathematical operations.

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Answer:

p= -3-1/2

p= -7/2

Step-by-step explanation:

(you transpose the fraction /take the liketerms)

( you transpose your fraction will change the sign and become negative then -3-0.5or -3-1/2=-7/2.)then you substitute to the original equation 1/2+p=-3 check your answer .