Mr. Greene
purchased 6 movie
tickets for $57.30.
How much does
one movie ticket
cost?

The law of sine is the nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).

The value of the \(z\) is 3.2 (rounded to the nearest tenth). The option 2 is the correct option.

The law of sine is the nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).

It can be given as,

\(\dfrac{\sin A}{a} =\dfrac{\sin B}{b} =\dfrac{\sin C}{c}\)

Here \(A,B,C\) are the angle of the triangle and \(a,b,c\) are the sides of that triangle.

Given information-

The triangle for the given problem is attached below.

In the triangle the base of the triangle is 2.6 units long.

The sine law for the given triangle can be written as,

\(\dfrac{\sin X}{x} =\dfrac{\sin Y}{y} =\dfrac{\sin Z}{z}\)

As the value of \(y\) side is known and the value of \(z\) has to be find. Thus use

\(\dfrac{\sin Y}{y} =\dfrac{\sin Z}{z}\)

Put the values,

\(\dfrac{\sin 51}{2.6} =\dfrac{\sin 76}{z}\)

Solve it for the \(z\),

\(z=\dfrac{\sin 76\times 2.6}{\sin 51}\\z=3.2462\)

Hence the value of the \(z\) is 3.2 (rounded to the nearest tenth). The option 2 is the correct option.

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Area of square B is 729.

Now, According to the question:

A square is a two-dimensional figure with four sides. It is also known as a quadrilateral. The area of a square is defined as the total number of unit squares in the shape of a square. In other words, it is defined as the space occupied by the square.

"Information available from the question"

We have been given that the ratio of the side length of square a to the side length of square b is 4:9. The side length of square a is 12 yards.

First of all, we will find the side length of square b using proportions as:

\(\frac{a}{b} = \frac{4}{9}\)

\(\frac{12}{b}=\frac{4}{9}\)

Cross multiplying the equation:

4b = 108

b = 108/4

b = 27

We know that area of a square is \(side^2\)

=> b = 27

Area of square = \(27^2\)

Area of square = 729

Hence, Area of square B is 729.

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Answer:

Both 12/(-4) and - 12/4

Step-by-step explanation:

12/(-4) = - 3

- 12/4 = - 3

Answer:

B and C

Step-by-step explanation:

the correct answer is the family of the functions whose parent function is:

y = |x|

Which is the family of the absolute value functions.

Here we want to find a function family such that:

"The graph is made up of two straight lines, has an absolute maximum or absolute minimum, and has vertical symmetry"

This clearly describes the family of the absolute value functions, where we have two lines with opposite slopes (one is negative and the other is positive) that meet at the vertex, which is a maximum or a minimum depending on if the function opens upwards or downwards.

And if the vertex is (a, b), then all the absolute value functions have a symmetry around the vertical line y = b.

So we conclude that the correct answer is the family of the functions whose parent function is:

y = |x|

Which is the family of the absolute value functions.

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The correct answer is option (A). The answer is metes and bounds.

Given that,

Despite being antiquated, the most adaptable method of defining land, capable of characterizing even the most atypical of parcels, may be summed up as a very exact, compass-directed stroll around a parcel's boundaries.

To find : This approach is frequently known as ?

Metes and bounds are limits of  piece of a land that may be located on its natural features. Metes and bounds markers are frequently employed in a land's "legal description." Legal description, which is recorded with the land's deed, is the geographical description of a piece of land that pinpoints its exact location.

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Answer

Step-by-step Explanation

7 = 2x - 5

12 = 2x

6 = x

The movement from the first step to the second step involves adding 5 to both sides.

7 = 2x - 5

7 + 5 = 2x - 5 + 5

12 = 2x

Adding 5 to both sides, is what the addition property of equality means.

Then, the movement from the second step to the third step involves dividing both sides by 2.

39% of all customers prefer sport drinks and tea.

To get percentage of customers who prefer sport drinks and tea, we must get the intersection of the two groups.

Let's assume there are 100 customers in total.

From the survey, we know that 55% of customers preferred soft drinks, so 45% preferred sport drinks.

Of those who preferred sport drinks, 61% also preferred coffee over tea. So, out of the 45 customers who preferred sport drinks, 61% preferred coffee and the remaining 39% preferred tea.

The % of customers who prefer sport drinks and tea will be:

= (39/100) * 100

= 0.39 * 100

= 39%.

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Answer: A, {150,250}

Step-by-step explanation:

In 10 hours he can do 5x2 hours work.  or 5x$50 = $250 for 5 rooms

$150 is 3x $50 or 3x2 hours work.

He can work 6 hours and make $150

or he can work 10 hours and make $250

the range he can earn so that he makes at least $150 and no more than 10 hours is$150 to $250

($150,$250) in interval notation for working 6 to 10 hours (6,10)

The value of x in the series is 1.3

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

Infinite series

From the series, we have

Common ratio, r = x^2/x = x

First term, a = -1

The sum is then calculated as

Sum = a/(1 - r)

So, we have

-1/(1 - x) = 10/3

This gives

1/(x - 1) = 10/3

Take the inverse

x - 1 = 3/10

So, we have

x = 1 + 3/10

Evaluate

x = 1.3

Hence, the value of x is 1.3

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The measure of the third angle in the triangle is 152°.

It should be noted that a triangle has three sides and the sum of the total angles is 180°.

In this case, two of the angles in a triangle measure 20° and 8°. The third angle will be:

= 180° - (20° + 8°)

= 180° - 28°

= 152°

The angle is 152°.

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Answer:

1/2=(A+B)

area of triangle=1/2×base×height

At the zero point the curve can either cross the x-axis or just touch it. The root of the function is the number c with f(c) = 0.

If the graph intersects the x-axis and looks nearly linear at the intersection, it is a single root. Even multiplicity zero if the graph touches the x-axis and bounces off the axis.

Different graphs with different x-intercepts. The graph may intersect the x-axis at the intersection. Otherwise, the graph touches the x-axis and bounces.

For example, suppose you plot a function.

f (x) = (x + 1) (x - 2)²

See the figure above to see how the function behaves differently for different x intercepts.

x intercept at x = -1 is the solution of the equation

x + 1 = 0 , graph goes straight through the x intercept at x= −1 . We call it a single zero because zero corresponds to a single factor in the function.

x intercept at x = 2 is the iterative solution of the equation ( x - 2 )= 0

The graph touches the axis at the intercept and changes direction. The coefficients are quadratic (order 2), so, (x-2)²= (x - 2 )(x - 2)

coefficients are repeated and appears twice. The number of times a given factor appears in the factored form of a polynomial equation is called its multiplicity. Zero associated with this factor, the factor is (x-2), occurs twice, and has a multiplicity of 2 .

thus, the behaviour of graph shows that any point of f(x) which touch or intersect x-axis is call zero of f(x).

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Answer:

C= 100+25t

Step-by-step explanation:

The y-intercept of the function is 100 which represents the one-time joining fee.

that is the correct answer, hope it helped!

The y-intercept of the function is 100 which represents a one-time fee to join.

Given that,
Cameron is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. Let C represent the total cost of the gym membership over t months.
The graph of the function C = 100 +25m is given,

the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
C= 100+25t
Where C represents the total charge,
t represents the number of months as of 25 per month,
And 100 represents the one-time chargeable fee to join.

Thus, the y-intercept of the function is 100 which represents a one-time fee to join.

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Answer:

The solution of the given quadratic equation are,

\(y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}\).

What is quadratic equation?

Any equation in algebra that can be written in standard form as where x stands for an unknown value, where a, b, and c stand for known numbers, and where a ≠ 0 is true is known as a quadratic equation.

Consider, the given equation:

2y^2 + 11y + 10 = 0

Compare this equation with \(ay^2 + by + c = 0\)

⇒  a = 2,  b = 11, c = 10

Consider, the quadratic formula

\(y = \frac{-b+-\sqrt{xb^2-4ac} }{2a}\)

Plug the values of a, b, c in the quadratic formula.

⇒

\(y = \frac{-11+-\sqrt{11^2-4(2)(10)} }{2(2)} \\y = \frac{-11+-\sqrt{121-80} }{4}\\ y = \frac{-11+-\sqrt{41} }{4} \\y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}\)

Hence, the solution of the given quadratic equation are,

\(y = \frac{-11+\sqrt{41} }{4}, y = \frac{-11-\sqrt{41} }{4}\).

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The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

42

Step-by-step explanation:

Explanation in image

The required function after the trasformation of 3 units right and 1 unit up is given as g(x) = |x - 3| + 3.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given equation of function f(x) = |x| + 2

The above function is an aboslute function, so in order to translate the function right, the function after transformation will be as |x - 3|  + 2, we subtract 3 from x to translate in the horizontal x-axis.
Now,
Add + 1 to the function to translate it 1 unit up,
The function becomes,
g(x) = |x - 3| + 3

Thus, the required function after the trasformation of 3 units right and 1 unit up is given as g(x) = |x - 3| + 3.

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Answer

12/13

Step-by-step explanation:

1/2+1/3+1/4=?

6/12+4/12+3/12=?

13/12

Reciprocal is 12/13

12/13 is your answer.

Answer:

A

Step-by-step explanation:

\((10^{-2})^{4}\)

Apply the law of exponents.

\(10^{-2 \times 4}\)

\(=10^{-8}\)

Answer:

\( = {10}^{ - 8} \\ \)

Answer A is correct.

Step-by-step explanation:

\( {( {10}^{ - 2}) }^{4} \\ {10}^{ - 2 \times 4} \\ = {10}^{ - 8} \)

Answer: 24/m

Step-by-step explanation:

There are m members in the science club.

24 bumper stickers were purchased to be split amongst these m members.

The number of stickers that each member will get is:

= Number of stickers / Number of members

Number of stickers = 24

Number of members = m

The expression is therefore:

= 24/m

Answer:

Put one of the dots on (0, -3) and put the other one 3 below and 2 to the right of (0, -3)

Step-by-step explanation:

slope= -3/2

y intercept= (0,-3)

Based on the data, we have sufficient evidence to support the claim that the proportion of defects is greater on Monday and Friday compared to the other days of the week at the 0.05 level of significance.

To test the claim that the proportion of defects is the same each day of the week, we will use a two-sample proportion test.

Step 1: State the null and alternative hypotheses:

Null hypothesis: The proportion of defects is the same for each day of the week.

Alternative hypothesis: The proportion of defects is different on Monday and Friday compared to the other days of the week.

Step 2: Determine the significance level and the test statistic.

We are given a significance level of .05. Since we are comparing two proportions, we will use the Z-test statistic.

Step 3: Calculate the test statistic.

To calculate the test statistic, we need to calculate the proportion of defects for Monday and Friday, and the proportion of defects for the other days of the week.

For Monday and Friday:

p1 = (36 + 40) / (2 * 200) = 0.38

For the other days of the week:

p2 = (23 + 26 + 25) / (3 * 200) = 0.23

The pooled sample proportion is:

p = (36 + 40 + 23 + 26 + 25) / (5 * 200) = 0.27

The standard error is:

SE = sqrt(p*(1-p)*((1/100) + (1/100))) = 0.066

The test statistic is:

Z = (0.38 - 0.23) / 0.066 = 2.27

Step 4: Determine the p-value.

Using a Z-table, we find that the p-value for a Z-statistic of 2.27 is approximately 0.011.

Step 5: Make a decision.

Since the p-value (0.011) is less than the significance level of 0.05, we reject the null hypothesis. We have sufficient evidence to conclude that the proportion of defects is different on Monday and Friday compared to the other days of the week.

Step 6: State a conclusion.

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If the scale of drawing is 1 inches : 250 inche and the real horse height is 15 inche, then the height of the horse in drawing is 0.06 inches.

The ratio that describes the relationship between the true figure itself and model is called the scale. It serves as a representation of the real statistics in smaller units on maps. A scale of 1:5, for instance, indicates that 1 on the map is approximately the size of 5 in the actual world.

The scale of drawing the horse = 1 inch :

Therefore in scale

Horse height in drawing equals one inch

The  height of the horse = 250 inche

The original height of the horse = 15 inche

The height in the picture = x inches

To find the height the horse in the picture, we have to use proportion

1 inch : 250 inche = x inches : 15 inche

1 / 250 = x / 15

1 × 15= 250x

250x = 15

x = 15/250

x = 0.06 inches

Therefore, the height of the horse in drawing is 0.06 inches

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The standard form of the equation of the parallel line is x - 3y = 12

The equation is given as

x - 3y = -15

Make y the subject in the equation

So, we have

y = x/3 + 5

The point is also given as

point = (6, -2)

The equation of a line can be represented as

y = mx + c

Where

slope = m

By comparing the equations, we have:

m = 1/3

This means that the slope of x - 3y = -15 is 1/3

The slopes of parallel lines are equal

This means that the slope of the other line is 1/3

The equation of the parallel line is then calculated as

y = m(x - x₁) +y₁

Where

m = 1/3

(x₁, y₁) = (6, -2)

So, we have

y = 1/3(x - 6) - 2

Multiply through by 3

3y = x - 6 - 6

So, we have

3y = x - 12

Rewrite in standard form

x - 3y = 12

Hence, the parallel line has an equation of x - 3y = 12

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The total cost for the week can be calculated by adding the cost of producing the caramel apples (0.75n) to the fixed cost of the booth ($120), which gives us the function C(n) = 0.75n + 120.

C(n) = 0.75n + 120

A function is a rule that assigns a unique output value to each input value. A function can be thought of as a machine that takes in an input and produces an output based on a set of instructions. The input and output values can be numbers, but they can also be other types of data, such as text or images.

Functions are an important concept in mathematics and are used in a wide range of fields, including science, engineering, economics, and computer science. They are often used to model relationships between different variables and to make predictions based on data. There are many types of functions, including linear functions, quadratic functions, exponential functions, and trigonometric functions. Each type of function has its own unique properties and can be graphed to help visualize the relationship between the input and output values.

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Answer:

131.7 min so c

Step-by-step explanation:

Answer:

The answer that I got is not listed in the options but the closest to that is C) 113 mins

Step-by-step explanation:

btw I got 131.7

The width of each class interval from the given grouped frequency distribution table is 9.

In a frequency distribution, the numerical width of a class is referred to as the class interval. Data is organised into classes in a grouped frequency distribution. The class interval is determined by the difference between the upper and lower class limits.

The give class intervals are 20-29, 30-39, 40-49 and 50-59.

The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.

So, class width = Upper class - Lower class

29-20=9

39-30=9

Therefore, the width of each class interval is 9.

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As we know, The volume of the square prism is twice the volume of the cylinder

To determine the relationship between the volume of the square prism and that of the cylinder, we need to find both volumes.

The volume of the square prism is V = Ah where A is the cross-sectional area and h its height. Since A = 314 square units,

V = 314 × h = 314h

Also, the volume of the cylinder is V = A'h where A' is the cross-sectional area of the cylinder and h' its height. Since the A' = 50π square units,

V' = 50π × h' = 50πh'

The ratio of the volume of the square prism to that of the cylindrical prism is V/V' = 314h/50πh'

Since the height of the square prism equals that of the cylinder, h = h'.

So, V/V' = 314h/50πh .

V/V' = 314/50π

if we take π = 3.14,

V/V' = 314/(50 × 3.14)

V/V' = 100/50

V/V' = 2

So, V = 2V'

Thus, the volume of the square prism is twice the volume of the cylinder.

So, the answer is D.

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Answer:

D. The volume of the square prism is twice the volume of the cylinder.

Step-by-step explanation:

took the test, got it right, comment below if you would like a step by step explanation

The two statements that completes the above proof are:

ΔABC ~ ΔDEC - Side - Angle - Side Postulate

∠1≅∠2 - Corresponding angles.

The Side-Angle-Side (SAS) postulate states that if two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent.

Corresponding angles are equal because of the congruence of the triangles. Two angles are corresponding if they occupy the same relative position in two distinct intersecting lines, such that they are on the same side of the transversal and are in the same position in relation to the intersection. Corresponding angles are equal if the two intersecting lines are parallel.

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