what the measure of ​

The equation of the line of best fit is: y = (-2/3)x + 26/3

To estimate the line of best fit using two points on the line, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.

Given the two points (7, 4) and (10, 2), we can calculate the slope (m) using the formula:

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

Substituting the coordinates of the points:

m = (2 - 4) / (10 - 7)

m = -2 / 3

Now that we have the slope, we can substitute it into the equation and solve for the y-intercept (b). Let's use the coordinates of one of the points, such as (7, 4):

4 = (-2/3)(7) + b

4 = -14/3 + b

To find the value of b, we can rearrange the equation:

b = 4 + 14/3

b = 12/3 + 14/3

b = 26/3

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The value of x is 58.51 degree.

We have,

Perpendicular= 8

Base = 4.9

Using trigonometry

tan x = Perpendicular/ Base

tan x = 8/4.9

tan x= 1.63265306122449

x = 58.51253064

Thus, the value of x is 58.51 degree.

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The equivalent expression in the form [tex]x^2 + rx + sx + 6[/tex] is:

[tex]x^2 + 2x + 3x + 6[/tex], which can be further factored as (x + 2)(x + 3).

To rewrite the expression [tex]x^2 + 5x + 6[/tex] in the form [tex]x^2 + rx + sx + 6[/tex], we need to find values for r and s such that the coefficients of the x terms match.

Given expression: [tex]x^2 + 5x + 6[/tex]

To factorize this expression, we need to find two numbers that multiply to give 6 and add up to 5. The numbers that satisfy these conditions are 2 and 3.

Now, let's rewrite the expression using these values:

[tex]x^2 + 2x + 3x + 6[/tex]

By grouping the terms, we can rewrite it as:

[tex](x^2 + 2x) + (3x + 6)[/tex]

Factoring out the common terms in each group:

x(x + 2) + 3(x + 2)

Now, notice that (x + 2) appears as a common factor in both terms. We can further simplify the expression:

(x + 2)(x + 3)

Thus, the equivalent expression in the form [tex]x^2 + rx + sx + 6[/tex] is:

[tex]x^2 + 2x + 3x + 6[/tex], which can be further factored as (x + 2)(x + 3).

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We can see here that the total weight of candy in a 5/6 pound bag site is 377 grams.

Weight is a measure of the force exerted by gravity on an object. It is the measure of how heavy an object is. Weight is typically expressed in units such as pounds or kilograms. The weight of an object can vary depending on the gravitational force acting on it.

There are 16 ounces in a pound.

Thus, a 5/6 pound bag of candy weighs

5/6 × 16 = 13.3 ounces.

If you want to know the weight in grams, 13.3 ounces is equal to 377 grams.

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The values are; Option C. x = 18; y = 6√10

Using the tangent identity, we have;

tan θ = opposite/adjacent

tan θ = 2/6

θ = 18. 4

Then

Angle CDB = 90 - 18. 4 = 71. 5 degrees

Using tangent identity, we have;

tan 71.5 = x/6

cross multiply the values

x = 18

Then, we have using Pythagorean theorem ;

y²= 18² + 6²

y = 360

y = 6√10

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The correct answer is,

⇒ as a trapezoid, a rectangle, and two squares

We have to given that,

The composite figure is shown in image.

Now, By given figure,

The figure is make by,

⇒ a trapezoid,

⇒  a rectangle,

⇒ two squares.

Where, Trapezoid is shown in upper side.

And, Rectangle is shown in middle.

And, Two small Squares are shown below.

Thus, The correct answer is,

⇒ as a trapezoid, a rectangle, and two squares

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Answer:

The cement that is needed to build the monument will be 7 m³. Thus, the correct option is B.

What is the volume?

The volume of the rectangular prism is calculated as,

V = LWH

V = 4 m x 0.5 m x 4 m

V = 8 m³

The volume of the triangular prism is calculated as,

V = (BHL) / 2

V = (2 m x 1 m x 0.5 m) / 2

V = 0.5 m³

Since there are two triangular prisms, the total volume of both triangular prisms is:

⇒ 2 x 0.5 m³

= 1 m³

The total amount of cement is calculated as,

⇒ (Volume of rectangular prism - Total volume of both triangular prisms)

⇒ (8m³ - 1m³)

⇒ 7 m³

Thus, the correct option is B.

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The value of angle m/EFG is 54°.

We are given that;

Arc GH=96

ARC HE=108

Now,

If a polygon is four sided (a quadrilateral), the sum of its angles is 360°

To find m/EFG, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, we can use the length of EF as the opposite side and the length of FG as the adjacent side.

So, we have:

tan(m/EFG) = EF / FG

We are given that EF = 4.6 and FG = 3.

Substituting these values into the equation above, we get:

tan(m/EFG) = 4.6 / 3

we can find that:

m/EFG = tan^-1(4.6 / 3) ≈ 54°

Therefore, by the given quadrilateral the answer will be 54°.

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The best measure of center for the given data is the median and the median is 17.

We have,

The best measure of center for the given data is the median because it represents the middle value when the data is arranged in ascending order.

In this case, the data is:

10, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

To find the median, we look for the middle value.

Since there are 13 numbers in total, the middle value is the 7th number, which is 17.

Therefore, the median is 17.

The mean, on the other hand, may not be the best measure of center in this case because it can be affected by extreme values.

Since we don't have information about the distribution of the data or the presence of outliers, the median is a more robust measure that gives a better representation of the central tendency of the data.

Thus,

The best measure of center for the given data is the median and the median is 17.

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Answer:

option A

2/11

Step-by-step explanation:

odds in favor of an event are calculated as,

number of favorable outcomes : number of unfavorable outcomes

here the favorable outcomes is either a jack or a 10

(8 cards from a deck of 52 playing cards)

all the rest of the cards are unfavorable outcomes

(44 remaining cards of the deck)

thus,

odds in favor = 8 : 44

= 2 : 11

if you were traveling at 30 mph and were distracted for just one second, you would travel approximately 44.7 feet blindly.

Here we have to calculate,

How many feet you would travel in one second at 30 mph.

In order to find this

Convert mph (miles per hour) to fps (feet per second)

Since we are looking for the distance in feet.

⇒ 1 mph = 1.47 fps

So,

⇒ 30 mph = 44.7 fps

Now that we know how fast you are traveling in feet per second,

Calculate how far you would travel in one second if you were distracted for just one second.

⇒ 44.7 feet per second x 1 second

⇒ 44.7 feet

Hence,

you would travel approximately 44.7 feet .

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Answer:

The answer is 126ft³

Step-by-step explanation:

V=1/3LWH

V=1/3×9×6×7

V=3×6×7

V=126ft³

Answer:

The answer are

B and C

Step-by-step explanation:

r=d/2=12/2=6

r=16/2=8

Circumference=2pir

C=2×6pi

C=12pi

C=2pir

C=2×8pi

C=16pi

Answer:

2002.7 (1 d.p.).

The value of the exports reached $8.8 billion during the year 2002.

Step-by-step explanation:

The function modelling the approximate value of China's exports of automobiles and parts (in billions of dollars) is:

[tex]f(x)=1.8208e^{0.3387x}[/tex]

where x = 0 corresponds to 1998.

To find the year when the exports reach $8.8 billion, substitute f(x) = 8.8 into the given equation, solve for x, then add this value to 1998.

[tex]\begin{aligned}1.8208e^{0.3387x}&=8.8\\\\e^{0.3387x}&=\dfrac{8.8}{1.8208}\\\\\ln e^{0.3387x}&=\ln \left(\dfrac{8.8}{1.8208}\right)\\\\0.3387x&=\ln \left(\dfrac{8.8}{1.8208}\right)\\\\x&=\dfrac{\ln \left(\dfrac{8.8}{1.8208}\right)}{0.3387}\\\\x&=4.65153751...\end{aligned}[/tex]

Add the found value of x to the year 1998:

[tex]\implies 1998+4.65153751...=2002.65153...[/tex]

Therefore, the the value of the exports reached $8.8 billion during the year 2002.

As the answer requires the year with at least one decimal place, the final answer is 2002.7 (1 d.p.).

Based on the formula of Venn Diagram, the number of customers at the supermarket who purchased both shirts and pants is 26.

A Venn Diagram is a pictorial representation of data such that the relationships between two or more data sets are highlighlighted for similarities and differences.

A Venn Diagram may use overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items.

The total number of customers at a supermarket = 118

The number of customers who purchased shirts, n(A) = 45

The number of customers who purchased pants, n(B) = 59

The number of customers who purchased neither shirts nor pants = 40

Let the number of customers who purchased both shirts and pants = n(A ∩ B)

n(A ∪ B) = n(A) + n(B) - n(A ∩ B)

n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78

Substituting values:

78 = 45 + 59 - n(A ∩ B)

Solving for n(A ∩ B), we get:

n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26

Thus, we can conclude that 26 customers purchased both shirts and pants, using the formula of Venn Diagram.

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Answer: -1/3

Step-by-step explanation: To solve the equation -18t - 6 = 0, we need to isolate the variable t on one side of the equation.

First, we add 6 to both sides of the equation to get:

-18t = 6

Then, we divide both sides by -18 to get:

t = -6/18

Simplifying -6/18 by dividing both the numerator and denominator by 6, we get:

t = -1/3

Therefore, the solution to the equation -18t - 6 = 0 is t = -1/3.

The difference between the slopes of two function is,

⇒ 2

We have to given that,

Mary compared to slope of the function y = 5x + 6 ​to the slope of the table.

Now, We have;

Function is,

y = 5x + 6

Hence, Slope = 5

And, For equation for table,

Let two points on table are (1, 3) and (2, 6).

Hence, Slope of table is,

m = (6 - 3) / (2 - 1)

m = 3/1

m = 3

Thus, The difference between the slopes of two function is,

⇒ 5 - 3

⇒ 2

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As per the given details, the starting height of the ball is 5 units from the ground.

Setting h(t) = 0:

-16t² + 112t + 5 = 0

The solutions are t = 0.125 and t = 7.

The vertex of the parabola given by h(t) = -16t² + 112t + 5 can be found using the formula t = -b / (2a).

In this case, a = -16 and b = 112.

t = -112 / (2 * -16)

t = -112 / -32

t = 3.5

h(3.5) = -16(3.5)² + 112(3.5) + 5

h(3.5) = -196 + 392 + 5

h(3.5) = 201

So, the maximum height of the ball is 201 units.

The time when the maximum height occurs is t = 3.5 seconds.

Thus, plotting points using various t values and figuring out the appropriate values of h(t) will allow us to graph the function.

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Answer:

Step-by-step explanation:

The text is a statistics problem that asks to find the probability of a certain range of values in a normal distribution. A normal distribution is a bell-shaped curve that shows how data values are spread around the mean. The mean is the average of all the data values, and the standard deviation is a measure of how much the data values vary from the mean. To solve this problem, we can use the following steps:

Convert the given range of values to standard scores or z-scores. A z-score tells us how many standard deviations a value is away from the mean. To find the z-score, we use the formula: z=σx−μ​

where x is the value, μ is the mean, and σ is the standard deviation. For example, to find the z-score for 33.5 psi, we plug in the values: z=233.5−35​=−0.75

This means that 33.5 psi is 0.75 standard deviations below the mean. Similarly, to find the z-score for 36 psi, we plug in the values: z=236−35​=0.5

This means that 36 psi is 0.5 standard deviations above the mean.

Use a z-table to find the area under the curve for each z-score. A z-table is a table that shows the probability of getting a z-score less than or equal to a given value. For example, to find the area under the curve for -0.75, we look up the row for -0.7 and the column for 0.05 in the z-table and get 0.2266. This means that there is a 22.66% chance of getting a z-score less than or equal to -0.75. Similarly, to find the area under the curve for 0.5, we look up the row for 0.5 and the column for 0 in the z-table and get 0.6915. This means that there is a 69.15% chance of getting a z-score less than or equal to 0.5.

Subtract the smaller area from the larger area to find the area between the two z-scores. This area represents the probability of getting a value between 33.5 and 36 psi in the normal distribution. For example, to find the area between -0.75 and 0.5, we subtract: 0.6915−0.2266=0.4649

This means that there is a 46.49% chance of getting a value between 33.5 and 36 psi in the normal distribution.

Multiply the area by 100 to convert it to a percentage and write it with the appropriate units: The percentage of tires that are inflated to a pressure between 33.5 and 36 psi is 0.4649×100=46.49%

The company can maximize profit by producing 25 units of each good A and good B.

The company can maximize profit by choosing the levels of production x and y that satisfy the following conditions:

Marginal revenue for good A = Marginal cost for good A

Marginal revenue for good B = Marginal cost for good B

To put it differently, the organization must manufacture products A and B until the extra income gained from producing an additional unit of each product is the same as the extra expenses involved in creating that unit.

The marginal revenue for good A is given by p = 100 − x, and the marginal revenue for good B is given by q = 100 − y.

The marginal cost for good A is given by 2x + y, and the marginal cost for good B is given by 2y + x.

Substituting these expressions into the above conditions, we get the following system of equations:

100 − x = 2x + y

100 − y = 2y + x

Solving this system of equations, we get x = 25 and y = 25.

Therefore, the company can maximize profit by producing 25 units of each good A and good B.

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The probability that Julie will be a captain, given that she makes the team, is 1/10.

To find the probability that Julie will be captain given that she makes the team, we need to consider the number of possible outcomes where Julie is a captain, and divide it by the total number of outcomes where she makes the team.

Given that there are 40 students trying out for the soccer team and 16 of them will make the team, the probability of Julie making the team is 16/40, which can be simplified to 2/5.

Out of the 16 students who make the team, we know that 4 of them will be captains.

Therefore, the probability of Julie being a captain among those who make the team is 4/16, which can be simplified to 1/4.

To calculate the probability that Julie will be a captain given that she makes the team, we multiply the probability of making the team (2/5) by the probability of being a captain among those who make the team (1/4):

(2/5) [tex]\times[/tex] (1/4) = 2/20 = 1/10.

So, the probability that Julie will be a captain, given that she makes the team, is 1/10.

This means that out of all the students who make the team, there is a 1 in 10 chance that Julie will be selected as a captain.

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The volume of the biggest candle given the volume of the smallest candle would be = 90.75cm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder =πr²h

π = 3.14

r = radius

Volume of the smallest candle = 3.14 x 5 x 1.7² = 45.37 cm³

But the scale factor = 2

Volume of the largest candle = 45.37 cm³ x 2 = 90.75cm³

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Complete question:

Mrs. Lopez made decorative candles in different

sizes for sale at her church. All of the candles are in

cylindrical jars. The size of the largest candle was bigger

than the smallest candle by a scale factor of two. If the

height and radius of the smallest candle are 5 cm and

1.7 cm, respectively, calculate the volume of the biggest

candle. Use 3.14 for T. Round to the nearest hundredth.

The solutions to the systems of equations graphically are (-2, 3) and (3, 8)

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

f(x) = x + 5

g(x) = x² - 1

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (-2, 3) and (3, 8)

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The measurements of the angles are 15 degrees, 45 degrees and 120 degrees.

We are given that;

The statement of triangle

Now,

Let x be the smallest angle, then the largest angle is 8x and the middle angle is 3x. Using the triangle angle sum theorem, we can write an equation:

x + 8x + 3x = 180

Simplifying, we get:

12x = 180

Dividing by 12, we get:

x = 15

This means that the smallest angle is 15 degrees. To find the other angles, we can multiply x by 8 and 3:

8x = 8 * 15 = 120 3x = 3 * 15 = 45

Therefore, by the angle the answer will be 15 degrees, 45 degrees and 120 degrees.

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The complete question is;

A triangle has angle measures that are related as follows: -the largest angle is eight times the smallest angle -the middle angle is triple the smallest angle find the measurements of the angles.

The calculated volume of the solid figure is 421.08 cubic feet

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

Base area = 38.28 square feet

Height = 11 feet

Using the above as a guide, we have the following:

Volume = Base area * Height

substitute the known values in the above equation, so, we have the following representation

Volume = 38.28  * 11

Evaluate

Volume = 421.08

Hence, the volume of the solid figure is 421.08 cubic feet

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The yearly interest rate of Karl's account is 0.02, which is equivalent to 2% (since 0.02 multiplied by 100 gives the percentage value).

The function f(x) = 1,000 * 1.02^t represents the amount in Karl's savings account over t years. The number 1.02 is the growth factor, which is equal to (1 + r), where r is the yearly interest rate.

To find the yearly interest rate, we need to solve the equation:

1.02 = 1 + r

Subtracting 1 from both sides of the equation:

0.02 = r

Therefore, the yearly interest rate of Karl's account is 0.02, which is equivalent to 2% (since 0.02 multiplied by 100 gives the percentage value).

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1. The Value if x= 41.21 and y= 43.85

2. The value of x is 21.71

1. Using Trigonometry

tan 20 = 15/x

x= 41.2121

and, sin 20 = 15/y

y= 43.857

2. Using Pythagoras theorem

H² = P² + B²

So, 24²= x² + y²

45² = (51-y)² + x²

Solving the above equation we get

576 = x² + y²

2025 = 2601 + y² - 102y + x²

Now, 2025 = 2601 - 102y + 576

-102y = -1152

y= 11.2941

So, x = 21.71

3. The measure of <2 = 180 - 72

= 108

This is because angles on same side if transversal is are supplementary.

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Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

[tex]\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}[/tex]

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

[tex]\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}[/tex]

[tex]\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4[/tex]

[tex]\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}[/tex]

[tex]\textsf{Step 4:} \quad y+2=-4x+24[/tex]

[tex]\textsf{Step 5:} \quad y+2-2=-4x+24-2[/tex]

[tex]\textsf{Step 6:} \quad y=-4x+22[/tex]

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

Answer:

The answer is 7.1cm to 1d.p

Step-by-step explanation:

Area of square =L²

25=L²

√L²=√25

L=5cm

hyp²=opp²+adj²

x²=5²+5²

x²=25+25

x²=50

√x²=√50

x=7.1cm to 1d.p

The function that describes the table of values is y = 4x + 7

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

The table of values

From the table, we can see that

As x increases by 1

The y values increase by 4

So, we have

m = Slope = 4/1 = 4

The equation is calculated as

y = mx + c

So, we have

y = 4x + c

Using the other points, we have

c = 7

This gives

y = 4x + 7

Hence, the function that describes the table of values is y = 4x + 7

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