Match the trigonometric expressions to their solutions.
cos [140°- (50° +30°)]
√3
tan 240°
-√6-√2
cos 150°
1
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sin 255

The solution to the equation 1/3a = -15 is a = -45

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

1/3a = -15

Multiply 3 to both sides of the equation

so, we have the following representation

3 * 1/3a = -15 * 3

When the products are evalated, we have

a = -45

Hence, the solution to the equation is a = -45

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The total value of her liquid assets would be = $3,980. That is option B.

An asset is said to be a liquid asset because it can easily be converted into cash in a short period of time.

Examples of liquid assets include the following:

Therefore, the total value of liquid assets = $580+$3400 = $3980

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Answer: $561.63

Step-by-step explanation: To find the distance you subtract 500 by -61.63

You get the equation 500--61.63

The two negative signs cancel out to become a positive sign

So the new equation is 500+61.63

So the distance is $561.63

Answer:

$561.63

Step-by-step explanation:

To find out the distance between 500 and -61.63 it will be $500-$-61.63. So 500 - (-61.63) becomes 500 + 61.63 because 2 negatives in a row make a positive. So when you do 500+61.63, you'll get 561.63.

The surface area of given triangular prism = 24 ft².

For the given triangular prism

Base = 2 ft

height = 3 ft

side = 3ft

We know that,

Surface area of triangular prism

= side x base + 3x base x height

=  3 x 2  + 3x2x3

= 6 + 18

= 24 ft²

Thus,

Surface area = 24 ft²

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The given histogram is bimodal, which is the last option/ option E, as bimodal distribution means that the data set has two distinct peaks or modes. In a bimodal histogram, the bars are grouped in a way that shows two prominent peaks or modes in the data.

Each bar in the histogram represents a specific range of values, and the height of the bar indicates the frequency or count of data points falling within that range. In a bimodal histogram, there will be two relatively high bars that correspond to the two modes of the data. The bimodal histogram is useful for visualizing and analyzing data sets that exhibit two distinct groups or clusters. It provides a clear visual representation of the two modes and their frequencies, which can help in identifying patterns and understanding the underlying characteristics of the data.

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Answer:

∫(1 - 25x²) dx

Step-by-step explanation:

The probability that she selects the route of three specific capitals is 3/43

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

States = 43

Capitals = 3

The probability is then calculated as

P = Capitals/States

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

P = 3/43

Hence, the probability is 3/43

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No, the sides with lengths 7.5, 8.5, and 14.5 cannot form a triangle.

To form a triangle considering three lengths of sides, the sum of the lengths of any two sides must be greater than the length of the third side.

Checking the above condition

1. The sum of 7.5,8.5 is 16, which is greater than 14.5. So, the condition is satisfied.

2. The sum of 7.5, 14.5 is 22, which is greater than 8.5. So, the condition is satisfied.

3.  The sum of 8.5 and 14.5 is 23, which is less than 7.5. The condition is not satisfied.

Since the sum of the two shorter sides 8.5 and 14.5 is not greater than the longest side 7.5 these three sides with given lengths cannot form a triangle.

Therefore, the sides with lengths 7.5, 8.5, and 14.5 cannot form a triangle.

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The average speed of the car is 80 km per hour

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

Distance = 200 km

Time = 2 hours 30 minutes

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

Speed = Distance/Time

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

Speed = 200/2.5

Evaluate

Speed = 80 km per hour

Hence, the average speed of the car is 80 km per hour

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The equation of the line with a slope of 1/4 that passes through the point (3,0) is y = 1/4x - 3/4.

To find the equation of a line with a slope of 1/4 that passes through the point (3,0), we can use the point-slope form of the equation of a line.

The point-slope form of a line is:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Substituting the values into the formula, we have:

y - 0 = 1/4(x - 3)

Simplifying:

y = 1/4(x - 3)

Distributing 1/4 throughout the expression:

y = 1/4x - 3/4

Therefore, the equation of the line with a slope of 1/4 that passes through the point (3,0) is y = 1/4x - 3/4.

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The coordinate of vertices of DEF are;

D = ( -4, -3)

E = ( -7, 4)

F =( -7, -3)

Here, we have,

Reflection in the y-axis: The reflection of point (x, y) across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse  (x,y)→( -x,y) .

First, triangle ABC is reflected across the y axes.

So, we have:

(x,y)→( -x,y)

then, translated down 5 units.

so, transformation rule on ABC, we have:

(x,y)→( -x , y - 5)

so, the coordinate of vertices of DEF are;

D = ( - 4, 2 - 5) = ( -4, -3)

E = ( -7, 9 - 5) = ( -7, 4)

F = (-7 , 2 - 5) = ( -7, -3)

Hence, the coordinate of vertices of DEF are;

D = ( -4, -3)

E = ( -7, 4)

F =( -7, -3)

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Answer:

13cm

Step-by-step explanation:

The area of a trapezoid is given by the formula:

Area = ½*(b1+b2)*h

where:

In this problem, we are given that b1 = 6 cm, b2 = 15 cm, and Area = 136.5 square centimeters.

Plugging these values into the formula, we get:

136.5 = ½*(6 + 15)*h

Solving for h, we get:

136.5=10.5h

h = 136.5/10.5=13centimeters

Therefore, the height of the trapezoid is 13 centimeters.

The value of p² is approximately 0.999999528.

To find the value of oe (the standard error of estimate) and p² (the coefficient of determination), we can use the given population data set information.

The formula for the standard error of estimate (oe) is:

oe = √((Σy² - (Σy)² / N) / (N - 2))

Substituting the given values, we have:

oe = √((135675 - (1456)² / 250) / (250 - 2))

oe = √((135675 - 2124736 / 250) / 248)

oe = √(541.96)

oe ≈ 23.27

Therefore, the value of oe is approximately 23.27.

The coefficient of determination (p²) can be calculated using the formula:

p² = 1 - (Σxy - (Σx × Σy) / N) / ((Σx² - (Σx)² / N) × (Σy² - (Σy)² / N))

Substituting the given values:

p² = 1 - (85080 - (9880 × 1456) / 250) / ((485870 - (9880)² / 250) × (135675 - (1456)² / 250))

p² = 1 - (85080 - 14358080 / 250) / ((485870 - 968144 / 250) × (135675 - 2124736 / 250))

p² = 1 - (85080 - 57432.32) / (478352.56 × 123346.74)

p² = 1 - (27647.68) / (59022875580.02)

p² ≈ 0.999999528

Therefore, the value of p² is approximately 0.999999528.

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Answer:

-7/4

Step-by-step explanation:

we can see that every time the value of x increases by 4, the value of y decreases by 7.

let's pick two sets of coordinates (first two will be fine).

that is (-4, 6) and (0, -1)

Slope = (change in y values) / (change in x values)

= (-1 - 6) / (0 - -4)

= -7 / (0 + 4)

= -7/4.

so our slope (gradient) is -7/4

Answer: there is a total of 150 sixth graders

explanation :

0.8x = 120

120 / 0.8 = 150

6th graders at lunch =  150

This is not a question. Next time, please add a question so that others might be able to help you with it

Answer:

  150 m²

Step-by-step explanation:

You want the total area of a figure consisting of a 12 m wide rectangle 5 m high with a triangle above that bringing the total height to 20 m.

The area of the rectangle is the product of its length and width:

  A = LW

  A = (12 m)(5 m) = 60 m²

The area of the triangle is half the product of its base and height.

  A = 1/2bh

  A = 12/(12 m)(20 -5 m) = 90 m²

The area of the whole figure is the sum of the areas of its parts:

  total area = rectangle area + triangle area

  total area = 60 m² +90 m² = 150 m²

The area of the figure is 150 m².

__

Additional comment

Since you know a triangle's area is equivalent to the area of a rectangle that has half the height, the 15 m high triangle can be considered as a rectangle 7.5 m high. Adding that to the 5 m area of the rectangle already there gives the equivalent area as that of a rectangle 12 m wide and 5+7.5 = 12.5 m high: (12 m)(12.5 m) = 150 m².

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The x-intercept in the graph represent the height where the football was when the ball was kicked.

The x-intercept is the point where the graph of the line crosses the x-axis.

Therefore, the x-intercept the value of x when y equals to zero.

Therefore, let's find what the x-intercept of the graph represent in terms of the football.

The graph shows the height of the ball in metres after t second.

The y axis represent the height while the x-axis represent the time.

Hence, he x-intercept represents the height where the football was when the ball was kicked.

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The degrees of freedom for a sample size of 27 is 26, the alpha or significance level for a 98% confidence level is 0.02, and the t-critical value can be found using the t-table corresponding to a 98% confidence level and 26 degrees of freedom.

To find the degrees of freedom, alpha (significance level), and the t-critical value using the t-table, we need to consider the given information:

n = 27: This represents the sample size, which is 27 in this case.

CL = 98%: CL stands for the confidence level.

It indicates the level of confidence we want to have in our interval estimate.

In this case, the confidence level is 98%.

Degrees of Freedom (df): For a t-distribution, the degrees of freedom depend on the sample size.

Since we have a sample size of 27, the degrees of freedom would be n - 1.

Therefore, the degrees of freedom would be 27 - 1 = 26.

Alpha (α): Alpha, or the significance level, represents the probability of making a Type I error, which is rejecting a true null hypothesis.

The alpha level is determined by subtracting the confidence level from 1. In this case, the alpha level would be 1 - 0.98 = 0.02.

T-Critical Value: To find the t-critical value corresponding to a specific confidence level and degrees of freedom, we can consult the t-table. Since we have a confidence level of 98% and degrees of freedom of 26, we need to find the value that corresponds to the area of 0.01 (half of 1 - 0.98) in the t-distribution table.

The t-critical value would be the value from the table that matches these criteria.

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The correct options regarding the inequality are:

A. 1 hat, 1 scarf

D. 4 hats, 1 scarf

F. 2 hats, 1 scarf

Based on the time constraint, Phil can spend a maximum of 12 hours knitting, so we can set up the following inequality:

2h + 3s ≤ 12,

Phil can knit at most 6 hats per week, because 6 hats * 2 hours/hat = 12 hours.

Phil can knit at most 4 scarves per week, because 4 scarves * 3 hours/scarf = 12 hours.

Phil can use at most 900 yards of yarn, because he has 900 yards of yarn.

Phil can knit 1 hat and 1 scarf, because 1 hat * 150 yards/hat + 1 scarf * 400 yards/scarf = 550 yards < 900 yards.

Phil can knit 4 hats and 1 scarf, because 4 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 900 yards.

Phil can knit 2 hats and 1 scarf, because 2 hats * 150 yards/hat + 1 scarf * 400 yards/scarf = 700 yards < 900 yards.

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The preparation of the income statement of Buildex Company's adjusted trial balance is as follows:

Buildex Company

Services revenue           $70,500

Interest revenue                 5,700

Total revenue                $76,200

Expenses:

Depreciation expense   $4,700

Wages expense            52,000

Insurance expense         4,400

Supplies expense           2,700

Utilities expense              1,700

Total expenses          $65,500

Net income                 $10,700

The income statement is a financial statement that shows the financial performance of a business over a period.

In the income statement, the total expenses are deducted from the total revenue to compute the profit or loss.

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Use the following selected accounts and amounts with normal balances from Buildex Company's adjusted trial balance to prepare its income statement for the year ending December 31. Hint: Not all accounts need to be used.

Cash                        $10,400           Depreciation expense $4,700

Building                   185,000           Wages expense          52,000

Accounts payable      9,400           Insurance expense        4,400

Services revenue    70,500           Supplies expense          2,700

Interest revenue        5,700           Utilities expense             1,700

Answer:

Step-by-step explanation: you are sped that is the answer black n

The relative frequency that a randomly selected student's favorite exhibit was either dinosaurs, or planets is 0.7.

To find the relative frequency, we will divide the number of students who chose dinosaurs or planets by the total number of students surveyed.

The total number of students surveyed is 12 + 25 + 17 + 6 = 60.

The number of students who chose dinosaurs or planets is 25 + 17 = 42.

Therefore, the relative frequency will then be 42 / 60 = 0.7.

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Answer:

2

Step-by-step explanation:

Ujeli had 11 pencils and she kept 3 so 11-3 = 8

so that means that the remaining pencil were dived by 4 (8÷2) = 2

The two expressions that are less than 7/8 are 7/8 x 9/19 and 7/8 x 3/4.

To determine which expressions are less than 7/8, we can compare them individually to 7/8 and evaluate their values.

Let's consider each expression one by one:

7/8 x 9/19:

To compare this expression to 7/8, we multiply the fractions:

(7/8) x (9/19) = 63/152.

Since 63/152 is less than 7/8, this expression is less than 7/8.

7/8 x 3/4:

Multiplying the fractions:

(7/8) x (3/4) = 21/32.

Since 21/32 is less than 7/8, this expression is less than 7/8.

7/8 x 9/9:

The fraction 9/9 simplifies to 1, so the expression becomes:

(7/8) x 1 = 7/8.

Since 7/8 is equal to 7/8 (not less than), this expression is not less than 7/8.

7/8 x 4/3:

Multiplying the fractions:

(7/8) x (4/3) = 28/24.

We can simplify 28/24 to 7/6.

Since 7/6 is greater than 7/8, this expression is not less than 7/8.

Therefore, the two expressions that are less than 7/8 are 7/8 x 9/19 and 7/8 x 3/4.

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Answer:

x= -3

Step-by-step explanation:

x-3

-----------

x+3

This expression is undefined when the denominator is zero.

x+3 =0

x= -3

52.8 square inches of paper to cover the entire Pyramid.

The amount of paper needed to cover the entire pyramid, we need to determine the total surface area of the pyramid.

The pyramid consists of a square base and four triangular faces.

1. Base Surface Area:

The surface area of the square base can be calculated by finding the area of a square with sides measuring 4.4 inches. The formula for the area of a square is side length squared:

Base Surface Area = (4.4 in)² = 19.36 in²

2. Triangular Faces Surface Area:

Each triangular face of the pyramid has a base of 4.4 inches and a height of 3.8 inches. The formula for the area of a triangle is 1/2 times the base times the height:

Triangular Face Surface Area = 1/2 * (4.4 in) * (3.8 in) = 8.36 in²

Since the pyramid has four triangular faces, the total surface area of the triangular faces is:

Total Triangular Faces Surface Area = 4 * (8.36 in²) = 33.44 in²

3. Total Surface Area:

To calculate the total surface area of the pyramid, we add the base surface area to the total triangular faces surface area:

Total Surface Area = Base Surface Area + Total Triangular Faces Surface Area

                         = 19.36 in² + 33.44 in²

                         = 52.8 in²

Therefore, it would take approximately 52.8 square inches of paper to cover the entire pyramid.

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