what is the measurement of the unknown angle?​

we can simply do that by multiplying each by the other's denominator.

[tex]\cfrac{19}{21}\hspace{9em}\cfrac{8}{9} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{19}{21}\cdot \cfrac{9}{9}\implies \boxed{\cfrac{171}{189}}\hspace{9em}\cfrac{8}{9}\cdot \cfrac{21}{21}\implies \boxed{\cfrac{168}{189}}[/tex]

A set of information displaying string lengths in inches. The values in the data are as follows: 6, 5, 8, 4, 9, 7, 5, 7, 4, 8, 7, 6. This data set's mean is 6.

To find the mean of the data set, we need to add up all the values and then divide by the total number of values.

Adding up all the values:

[tex]6 + 5 + 8 + 4 + 9 + 7 + 5 + 7 + 4 + 8 + 7 + 6 = 76[/tex]

There are 12 values in the data set, so we divide the sum by 12:

76/12 = 6.33 (rounded to two decimal places)

Therefore, the mean of the data set is 6.33.

Therefore the correct answer is thus 6.

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The hyperbola's standard equation is thus:[tex]((x - 5)^2) / 4 - ((y + 2)^2) / 1 = 1[/tex]as by the distance down the conjugate axis.

Variables, numbers, and mathematical operations like addition, subtraction, multiplication, and division are frequently included. Equations are used in many disciplines, including physics, engineering, economics, and finance, to describe connections between quantities and to solve problems. For instance, the formula "2x + 5 = 11" states that the number 11 is equal to the sum of the two variables x and 5. We can determine that x equals 3 by finding a solution for x. On the basis of mathematical relationships, equations enable us to locate unknown values and create predictions.

given

The hyperbola shown above has a center at and a horizontal transverse axis (5, -2). Its vertices are at (3, -2) and (8, -2), while its foci are at (2, -2) and (8, -2). (7, -2).

The typical equation for a hyperbola with a center at (h, k) and a horizontal transverse axis is:

((x - h)2) / a2 - ((y - k)2) / b2) equals one.

where an is the distance along the transverse axis from the center to a vertex, and b is the distance along the conjugate axis from the center to a point on the hyperbola.

In this instance, an equals 2, since the distance along the transverse axis between the center and a vertex is 2.

B = 1 because the distance down the conjugate axis from the hyperbola's center to any point is 1.

The hyperbola's standard equation is thus:[tex]((x - 5)^2) / 4 - ((y + 2)^2) / 1 = 1[/tex]as by the distance down the conjugate axis.

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If person is standing at the end of a pier 12 ft above the water, then the velocity of the boat when it is 16 ft from the pier is 7.5 ft/min.

The distance between the person and the water (y) = 12 ft,

The distance between the boat and the pier is (x) = 16 ft,

So, p = √(12² + 16²) = 20 ft,

From the triangle given below,

⇒ x² + y² = p²,

taking "derivative" with respect to "x",

We get,

⇒ 2x(dx/dt) + 2y(dy/dt) = 2p(dp/dt);

⇒ dy/dt = 0 ..because height is constant,

The water is pulling on a rope at speed of (dp/dt) = 6 ft/min,

⇒ 2x(dx/dt) = 2p(dp/dt),

⇒ 2×16×(dx/dt) = 2×20×6,

⇒ dx/dt = 7.5 ft/min.

Therefore, the velocity of the boat is 7.5ft/min.

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The given question is incomplete, the complete question is

A person is standing at the end of a pier 12 ft above the water and is pulling on a rope attached to a rowboat at the waterline at a rate of 6 ft per minute. What is the velocity of the boat when it is 16 ft from the pier?

The graph below is a graph of a function in the form of f(x) = eˣ,

where ‘e’ is the mathematical constant known as Euler's number and is approximately equal to 2.718.

An exponential function has an output that increases rapidly with increasing inputs.

This function is an exponential function, which means that the output increases at an exponential rate as the input increases.

The graph shows that the output, which is represented by the y-axis, increases rapidly as the input, which is represented by the x-axis, increases.

This is a characteristic of an exponential function, which is why this graph is a representation of the function f(x) = eˣ.

The other three functions, f(x) = e.x, f(x) = log x and f(x) = ln x, do not represent the graph as they are not exponential functions.

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The three extra squares that should be shaded to have a pattern with 4 lines of symmetry and a rotational symmetry of order 4 are E, H, N.

It is required for the new shape to have four lines of symmetry, which means that if the new shape is divided we can obtain four identical lines; moreover, it should have a rotational symmetry of order 4, which means that if we rotate the shape it will coincide with the original shape four times. Based on this, the squares that should be shaded are E, H, N.

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Therefore, the solution set for the system is the point (1.8, 5.2).

A graph is a collection of points, called vertices (or nodes), and a set of connecting lines, called edges, that connect pairs of vertices. Graphs are often used to represent relationships between objects, such as roads between cities, social connections between people, or links between web pages.

Graphs can be classified based on their properties, such as whether they are directed or undirected, whether they have loops (edges that connect a vertex to itself), or whether they are connected (all vertices can be reached from any other vertex).

by the question.

To solve this system of equations graphically, we need to plot the lines represented by each equation on a coordinate plane and find their intersection point (if it exists).

First, let's rearrange the first equation to solve for y:

[tex]y = (2/3)x + 4[/tex]

Now, we can plot this line by finding two points on it. For example, when x = 0, y = 4, and when x = 3, y = 6. We can then connect these points with a straight line.

[tex]y < 4x[/tex]. This is an inequality, so we'll shade the region below the line y = 4x. To plot the line itself, we can again find two points on it. When x = 0, y = 0, and when x = 1, y = 4. Connecting these points.

we need to shade the region below this line, since y is less than 4x. This region includes all points on the coordinate plane that satisfy y < 4x. We can shade it by drawing a dotted line along the line y = 4x and shading the region below.

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The measure of angle x in the right triangle is 33.6 degrees.

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

The triangle PQR is a right angle triangle. Therefore, let's find the angle x using trigonometric ratios as follows:

cos x = adjacent / hypotenuse

where

adjacent =  15 cm

hypotenuse = 18 cm

Therefore,

cos x = 15 / 18

x = cos⁻¹ 0.83333333333

x = 33.5607646704

Therefore,

x = 33.6 degrees

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A hemisphere with a 7.1-inch radius has a volume of 2478.8 cubic inches.

To calculate a hemisphere's volume, use the following formula:

V = (2/3) × π × r³

where r is the radius of the hemisphere, and π (pi) is a mathematical constant approximately equal to 3.14159.

Substituting the given value of the radius, r = 7.1 inches, into the formula, we get:

V = (2/3) × π × 7.1³

V ≈ 2.094 × π × 7.1³ (rounded to three decimal places)

V ≈ 2.094 × 3.141 × 357.911

V ≈ 2478.796 cubic inches

Therefore, the volume of the hemisphere with a radius of 7.1 inches is approximately 2478.796 cubic inches. Rounded to the nearest tenth of a cubic inch, the volume is 2478.8 cubic inches.

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The probability of getting two heads and one tail in any order is 3/8.

What is probability ?

Probability is a measure of the likelihood 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. For example, the probability of flipping a coin and it landing heads up is 0.5, because there are two equally likely outcomes (heads or tails) and one of them is heads.

Probabilities can also be expressed as percentages or fractions. For instance, a probability of 0.25 can be expressed as a percentage of 25%, or as a fraction of 1/4.

According to the question:
The sample space for flipping three coins is:
HHH

HHT

HTH

THH

HTT

THT

TTH

TTT

where H represents heads and T represents tails.

Out of these eight outcomes, there are three outcomes in which two heads and one tail come up in any order: HHT, HTH, and THH. Therefore, the probability of getting two heads and one tail in any order is 3/8, or 0.375, which can also be written as a fraction.

To see why this is the case, you can also use a tree diagram to represent the sample space:
     H              T

   /   \          /   \

  H     T        H     T

 / \   / \      / \   / \

H   T H   T    H   T H   T

Each branch represents the outcome of one coin flip, and the branches lead to the possible outcomes of flipping three coins. The outcomes with two heads and one tail are HHT, HTH, and THH, which occur in three out of the eight possible outcomes, as previously stated. Therefore, the probability of getting two heads and one tail in any order is 3/8.


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The requried radius of the cylinder is 4 inches.

We are given the volume of the cylinder as 48π cubic inches and the height as 3 inches. So we can use the formula V = πr²h to solve for the radius.

48π = πr²(3)

16 = r²

r = ±4

Since the radius of a cylinder cannot be negative, we take the positive value of r, which is 4.

Therefore, the radius of the cylinder is 4 inches.

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Answer:

112 square meters

Step-by-step explanation:

The base is 14 meters, and the height is 8 meters. So the area is 14 × 8 = 112 square meters.

Answer:

2/3

Step-by-step explanation:

1) find the gcf of 16 and 24.

Method 1: By Listing Factors

List the factors of each number.

Factors of 16 : 1, 2, 4, 8, 16

Factors of 24 : 1, 2, 3, 4, 6, 8, 12, 24

Find the largest number that is shared by all rows above. This is the GCF.

GCF = 8

Method 2: By Prime Factors

List the prime factors of each number.

Prime Factors of 16 : 2, 2, 2, 2

Prime Factors of 24 : 2, 2, 2, 3

Find the intersection of these primes.

2,2,2

Multiply these numbers: 2x2x2=8. this is the gcf.

gcf = 8

2) Divide both the numerator and the denominator by the GCF.

16/8 / 24/8

3)simplify

2/3

option (C) is the box plot that best represents the given data set.

Based on the given data set, the box plot that best represents the data is (C). Here are the reasons:

The median of the data set is 30, and this is represented by the line inside the box in all four options.

The box in option (C) ranges from 22.5 to 33.5, which includes the interquartile range (IQR) of the data set, which is from 16 to 37. This means that 50% of the data falls within this range, and the box in option (C) represents this well.

The whiskers in option (C) extend to the minimum and maximum values in the data set, which are 9 and 39 respectively. This means that none of the data points fall outside the whiskers.

The range of the number line in option (C) (7 to 46) and the tick marks (every one unit) also match the range and increments of the given data set.

Therefore, option (C) is the box plot that best represents the given data set.    

Here is the visual representation of option (C):

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Answer:

To fine mean (average) you add up all the numbers and divide it by the amount of numbers. there are 8 scores

Step-by-step explanation:

55+60+65+70+75+80+85+90

=580

580/8=72.5

the mean is 72.5

Francesca salary in the first year is $169684.14

Let us assume that P be the first salary of Francesca.

The salary increases by 2% every year.

Let A be the amount she earns after n years at a rate of r.

Using the formula for the compound interest is:

A = P (1 + r)ⁿ

Here, A = $187345

n = 5 years

R = 2%

So, r = 0.02

We need to find the value of P

substituting these values in above equation we get,

187345 = P (1.02)⁵

187345 = 1.10408 × P

P = $169684.14

Therefore,her salary in the first year is $169684.14

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The complete question is:

Each year, Francesca earns a salary that is 2 percent higher than her previous year's salary. In her first 5 years at this job, she earned a total of $187,345. What was Francesca's salary in her 1st year at this job?

The correct table is:

A 2-column table with 4 rows. Column 1 is labeled cups with entries 1, 2, 4, 8. Column 2 is labeled tablespoons with entries 16, 32, 64, 128 which is option first.

This is because we know that there are 16 tablespoons in one cup. So, if we multiply the number of cups by 16, we get the corresponding number of tablespoons forming a geometric sequence. For example, 2 cups is equal to 2 x 16 = 32 tablespoons. This relationship is correctly shown in the first table where each entry in the second column is obtained by multiplying the corresponding entry in the first column by 16.

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The correct table that relates the number of cups to the number of tablespoons is:

A 2-column table with 4 rows.

- Column 1 is labeled cups with entries 1, 2, 4, 8.

- Column 2 is labeled tablespoons with entries 16, 32, 64, 128.

In this table, the first row tells us that there is 1 cup which is equivalent to 16 tablespoons. The second row shows that 2 cups is equal to 32 tablespoons. The third row indicates that 4 cups is equal to 64 tablespoons. And finally, the fourth row states that 8 cups is equal to 128 tablespoons.

This table follows the relationship where for every 1 cup, there are 16 tablespoons. So, to find the number of tablespoons for a given number of cups, you can use this table as a reference.

For example, if you have 3 cups, you can find the number of tablespoons by looking at the table. Since there is no row for 3 cups in the given table, you can approximate it by knowing that 2 cups is equal to 32 tablespoons, and 4 cups is equal to 64 tablespoons. Therefore, 3 cups would be somewhere between 32 and 64 tablespoons.

From the following option given, the correct option is option (3) - detect assignable cause variations versus normal random variations in the process.

The objective of statistical process control (SPC) is to monitor and control a process to ensure that it operates within its specifications and meets the desired quality level. One of the main goals of SPC is to distinguish between normal random variation in the process and variation that is caused by assignable or special causes.

By identifying and eliminating the assignable causes of variation, the process can be improved and the quality of the output can be maintained or improved over time. Therefore, the primary objective of SPC is to detect assignable cause variations versus normal random variations in the process.

Options 1, 2, and 4 are related to quality control and monitoring, but they do not capture the essence of what SPC is trying to achieve. SPC is focused on monitoring and improving the process, rather than simply accepting or rejecting batches of raw materials or finished goods or identifying variable versus attribute measures.

Therefore, the correct option is '3' - detect assignable cause variations versus normal random variations in the process.

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Answer: Based on the graph, I believe that the answer is a. x = -1/4, y = -1/2

Step-by-step explanation:

the cost of hiring Nicole for any number of hours "h" will be $15 plus $5 multiplied by the number of hours you hire her for.

To find the cost of hiring Nicole for any number of hours, you need to know the hourly rate and add it to the initial fee.

According to the problem, Nicole charges an initial fee of $15 and $5 per hour. So if you hire Nicole for "h" hours, the cost will be:

Cost = Initial fee + Hourly rate x Number of hours

Cost = $15 + $5 x h

Therefore, the cost of hiring Nicole for any number of hours "h" will be $15 plus $5 multiplied by the number of hours you hire her for.

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Step-by-step explanation:

I answered this on the other question

The center is (1,-4)

The new center is

(-4,-6)

The equation of the center is

[tex](x + 4) {}^{2} + (y + 6) {}^{2} = 16[/tex]

Answer:

1and 2/3

Step-by-step explanation:

using the factorization method

the product of the equation is positive 6(3×2)

then we find the factors of 6 which give us the product 6 and the sum of-5

the factors are-3 and -2

we then substitute negative 5 with these factors

it then be 3x^2-3x-2x+2=0

then we group factorise

we will have 3x(x-1)-2(x-1)=0

we find the common factors of the 2 groups

we will then have (x-1)(3x-2)=0

then we equate the both brackets to 0

(x-1)=0 and(3x-2)=0

for the first bracket add 1 both sidesand the second add 2 both sides and divide by 3

The value of x from the triangle using the triangle proportionality theorem is 8.4

Given that we have the triangle

Using the triangle proportionality theorem, we have the following equivalent ratio

3.5 : 5 = x : 12

When this ratio is represented as a fraction, we have

3.5/5 = x/12

So, we have

x = 12 * 3.5/5

Evaluate the products

This gives

x = 8.4

Hence. the solution for x is 8.4

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The answer of the given question based on the right angle triangle is , the height of the light pole to the nearest tenth of a foot is 9.3 feet.

A right-angled triangle, also known as a right triangle, is a triangle that has one angle equal to 90 degrees. The side opposite right angle is called hypotenuse, and other two sides is called legs. The leg opposite to a particular acute angle is known as the opposite side, and the leg adjacent to it is known as the adjacent side.

The Pythagorean theorem is a fundamental theorem that applies to all right-angled triangles. It states that square of hypotenuse of right-angled triangle is equal to sum of squares of its two legs

To determine the height of the light pole, we can use similar triangles.

Let's call height of light pole be  "x". Then we have:

(height of stop sign) / (length of stop sign's shadow) = (height of light pole)/(length of light pole's shadow)

Substituting the given values, we have:

8/12 = x/14

Simplifying this equation, we get:

x = (8/12) * 14 = 9.33 feet

Therefore, the height of the light pole to the nearest tenth of a foot is 9.3 feet.

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The value of t according to the given conditions equals 4.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

The t-value can be calculated by dividing the mean difference by the standard error of the mean difference.

The formula for calculating t is:

t = (mean difference) / (standard deviation / sqrt(n))

Given that the mean difference equals 1.2, the standard deviation of the difference equals 1.5, and n equals 25.

Therefore the t-value can be calculated as follows:

t = (1.2) / (1.5 / sqrt(25)) = (1.2) / (1.5 / 5)= (1.2) / (0.3)= 4

Therefore, t equals 4.

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Answer:

4y = x + 7.

Step-by-step explanation:

The slope of a line perpendicular to a line of slope m = -1/m

So the slope of the required line = -1/ (-4) = 1/4.

y - y1 = m(x - x1)

y - 2 = 1/4(x - 1)

y = 1/4(x - 1) + 2

y =  1/4x - 1/4 + 2

y = 1/4x + 7/4

4y = x + 7

Step-by-step explanation:

Arrange each of the equations into y = mx+ b to compare....m is the slope and b is the y -axis intercept

- 8x - y = 3     ======>    y = -8x -3

8x + y = - 3    ======>    y = - 8x -3

These are equations of the SAME LINE with   slope = -8    intercept = -3

Answer:

The equations have the same slopes and the same y-intercepts.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Rearrange both equations so that they are in slope-intercept form.

[tex]\underline{\sf Equation\;1}\\\\\begin{aligned}-8x-y&=3\\-8x-y+8x&=8x+3\\-y&=8x+3\\y&=-8x-3\end{aligned}[/tex]

[tex]\underline{\sf Equation\;2}\\\\\begin{aligned}8x+y&=-3\\8x+y-8x&=-8x-3\\y&=-8x-3\end{aligned}[/tex]

Therefore, the equations have the same slopes and the same y-intercepts.

For the first student with a score of 1910, the z-score is: 1.34 ,For the second student with a score of 1220, the z-score is: 0.81 , For the third student with a score of 2160, the z-score is:2.14 , For the fourth student with a score of 1370, the z-score is: -0.34 and , out of the four students, only the one with the test score of 2160 is considered an unusual score based on the z-score.

To find the z-score for a given data point, we use the formula:

z = (x - μ) / σ

where x is the data point, μ is the mean, and σ is the standard deviation.

For the first student with a score of 1910, the z-score is:

z = (1910 - 1479) / 317 = 1.34

For the second student with a score of 1220, the z-score is:

z = (1220 - 1479) / 317 = -0.81

For the third student with a score of 2160, the z-score is:

z = (2160 - 1479) / 317 = 2.14

For the fourth student with a score of 1370, the z-score is:

z = (1370 - 1479) / 317 = -0.34

Now, we need to determine whether any of these z-scores are unusual. One way to do this is to use the rule of thumb for normal distributions, which states that about 68% of the data falls within one standard deviation of the mean, about 95% of the data falls within two standard deviations of the mean, and about 99.7% of the data falls within three standard deviations of the mean.

Using this rule, we can say that a z-score greater than 2 or less than -2 is unusual, since it corresponds to data that falls more than two standard deviations from the mean.

From the z-scores we calculated, only the third student with a z-score of 2.14 falls outside of this range and can be considered an unusual score.

Therefore, out of the four students, only the one with the test score of 2160 is considered an unusual score based on the z-score.

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