1. Use a calculator to approximate the given value to four decimal places.
sin 52 degrees=____
2. Use the calculator to approximate the given value to four decimal places.
cod 18 degrees=____

1.- The sum of the internal angles in a triangle equals 180°.

8x + 5x + 6x = 180°

19x = 180

x = 180/19

x = 180/19

2.- Calculate angle ABC

ABC = 8x

ABC = 8(180/19)

ABC = 1440 / 19

ABC = 75.8°

Answer:

The extra fee was 1.31

It brought her total up to 44.96

Hi there!

fee:1.31

1.Multiply percent term by 0.01:

\(3\)·\(0.01=0.03\)

2.Multiply cost by 0.03:

\(43.65\)·\(0.03= 1.3095\)

3.Round into nearest hundred:

\(1.3095=1.31\)

Therefore, the cost of the fee would be 1.31$.

As we have proved that the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.

Let's start by defining what a linear function is. A linear function is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope represents the rate of change of the line, and the y-intercept represents the value of y when x is equal to zero. To create a linear function, we need two points on the line.

Now, let's create another linear function using points B and C:

slope (m) = (y₂ - y₁) / (x₂ - x₁) = (6 - 4) / (5 - 3) = 1

y-intercept (b) = y - mx = 4 - 1 * 3 = 1

Therefore, the linear function that passes through points B and C is also y = x + 1. We can check if point A lies on this line by substituting its x and y values into the equation:

2 = 1 + 1

This is true, so point A lies on the line created by points B and C. Therefore, we have also proved that the line created works exclusively with these three points.

In conclusion, we have created two linear functions using three points and proved that they work exclusively with those three points.

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Answer:

3is the scale factor and it is similar

Step-by-step explanation:

The distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector.

To find the distance between the point P(2, 6, -4) and the line defined by the parametric equations r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩, we can use the formula for the distance between a point and a line in three-dimensional space.

The formula for the distance between a point and a line is given by:

d = ||PQ||/||v||

where PQ is the vector connecting the point P to any point Q on the line, v is the direction vector of the line, and || || represents the magnitude of a vector.

Let's first find the direction vector of the line. By examining the parametric equations, we can see that the direction vector of the line is v = ⟨1, 4, -2⟩.

Now, we need to find the vector PQ connecting the point P(2, 6, -4) to any point Q on the line. We can represent PQ as the difference between the coordinates of P and Q:

PQ = ⟨2 - 1, 6 - 3t, -4 - 1, 4t, -4 - 3, -2t⟩ = ⟨1, 6 - 3t, -5, 4t, -7, -2t⟩

Next, we calculate the magnitude of PQ:

||PQ|| = √(1^2 + (6 - 3t)^2 + (-5)^2 + (4t)^2 + (-7)^2 + (-2t)^2)

= √(1 + 36 - 36t + 9t^2 + 25 + 16t^2 + 49 + 4t^2)

= √(29t^2 - 36t + 111)

Finally, we calculate the magnitude of the direction vector v:

||v|| = √(1^2 + 4^2 + (-2)^2) = √(1 + 16 + 4) = √21

Now we can substitute these values into the formula for the distance:

d = ||PQ||/||v|| = (√(29t^2 - 36t + 111))/√21

To find the minimum distance between the point P and the line, we need to minimize the function d with respect to t. We can accomplish this by finding the critical points of the function and determining the value of t that gives the minimum distance.

Taking the derivative of d with respect to t and setting it equal to zero, we have:

d' = (29t - 18)/(√21(√(29t^2 - 36t + 111))) = 0

Solving for t, we get:

29t - 18 = 0

29t = 18

t = 18/29

By substituting this value of t into the formula for d, we can find the minimum distance between the point P and the line.

d = (√(29(18/29)^2 - 36(18/29) + 111))/√21

Simplifying this expression will give us the final value of the distance.

In summary, the distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector

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When we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

To subtract 3 from 22, we can perform the subtraction operation as follows:

22

3

19

We align the numbers vertically and subtract each corresponding place value from right to left. In this case, subtracting 3 from 2 requires borrowing or regrouping. However, since 2 is greater than 3, we can directly subtract 3 from 2 and write the difference, which is 1, in the one's place.

Therefore, the simplified answer is 19.

The subtraction process involves taking away or removing a certain quantity from another. In this case, we subtracted 3 from 22, resulting in a difference of 19. The process of simplifying the answer is simply expressing the result in its most concise and reduced form.

By subtracting 3 from 22, we removed 3 units from the original value of 22, leaving us with 19. This can be visualized as taking away three objects from a group of 22 objects, resulting in a remaining count of 19.

In summary, when we subtract 3 from 22, the simplified answer is 19. The subtraction operation involves removing or deducting one value from another, resulting in the difference between the two quantities.

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Answer:

0.5 minutes

Step-by-step explanation:

Since we are provided the equation and the current height of the candle (which would be 25 inches) we can simply replace this current height with the variable h and then solve the rest of the equation to find out the value of m when the height of the candle is at 25 inches.

h = 32−14m

25 = 32−14m ... subtract both sides by 32

-7 = -14m ... divide both sides by -14

0.5 = m

Finally, we can see that after 0.5 minutes the candle would have melted down to 25 inches.

Answer:

twenty is 4 more than students

20 = 4 + students

20= 4 + 1/2 m

hence

2nd and 4th option is correct

Answer:

3:5

The ratio of pens:pencils is 3:5.

Step-by-step explanation:

Answer:

2.53

Step-by-step explanation:

divison

Interior angles: the angle formed inside a polygon .

Exterior angles: the angles formed between sides of polygon and extended adjacent side.

Answer:

256 in²

Step-by-step explanation:

Multiply length by width or 16 times 16 to get 256, squared of from two planes

Answer:

The length of the rectangle is 17 yards and the width of the rectangle is 14 yards.

Explanation:

To find the perimeter of the rectangle, you had to add twice the length of the rectangle to twice the width of the rectangle since the shape of a rectangle is made up of two legs (each representing the rectangle's length) and two legs (each representing the rectangle's width.

The perimeter can be mathematically seen as p = 2l+2w, where p is the amount corresponding to the perimeter of the rectangle, l is the amount representing the length of the rectangle, and w is the quantity reflecting the width of the rectangle. This equation can be modified using the equation l = w+3, since it is given that the length is 3 yards longer than the width.

Therefore, the p = 2l+2w equation can be modified to solve for w using the given conditions and the equation defining l.

p = 2l+2w  

p = 2(w+3)+2w               [Substituting l = w+3]

p = 2w+6+2w

p = 4w+6

p-6 = 4w+6-6

p-6 = 4w

(p-6)/4 = 4w/4

w = (p-6)/4

w = (62-6)/4                  

w = 56/4

w = 14

Now the length of the rectangle can be determined using the equation l = w+3.

l = 14+3 = 17

Hope this helps Also Plz mark brainliest:)

Answer:

P

Step-by-step explanation:

Answer:

P is the independant variable.

Step-by-step explanation:

Since B is dependent on P, being B=P6, P is the independent variable.

The approximate proportion of lightbulb replacement requests numbering between 37 and 47 can be determined using the empirical rule. The proportion is approximately 0.3413.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% of the data falls within two standard deviations of the mean.

- Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean is 37 and the standard deviation is 10. To find the proportion of lightbulb replacement requests between 37 and 47, we can use the empirical rule:

Proportion = P(37 ≤ X ≤ 47) ≈ P(mean - 1 standard deviation ≤ X ≤ mean + 1 standard deviation)

Proportion ≈ P(37 ≤ X ≤ 47) ≈ P(27 ≤ X ≤ 47)

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Therefore, the proportion of requests between 27 and 47 is approximately 68%.

However, we need to find the proportion between 37 and 47, so we subtract the proportion of requests below 37. Since the distribution is symmetric, this proportion is the same as the proportion above 47.

Proportion = 68% - (100% - 68%)

Proportion ≈ 0.68 - 0.32

Proportion ≈ 0.36

Rounding the proportion to four decimal places, we get approximately 0.3413.

The approximate proportion of lightbulb replacement requests numbering between 37 and 47, based on the empirical rule, is 0.3413. This means that around 34.13% of the daily requests fall within this range.

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Answer: I believe that the answer would be "In an isosceles triangle, two of the angles are congruent."

Step-by-step explanation:

Answer:

In an isosceles triangle, two of the angles are congruent.

hope this helps :)

Answer:

1.6

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (1, 4 ) and (x₂, y₂ ) = (3, - 4 )

m = \(\frac{-4-4}{3-1}\) = \(\frac{-8}{2}\) = - 4 , then

y = - 4x + c ← is the partial equation

to find substitute either of the 2 points into the partial equation

using (1, 4 ) , then

4 = - 4 + c ⇒ c = 4 + 4 = 8

y = - 4x + 8 ← equation of line

Answer:

A

Step-by-step explanation:

Substitute in the equation remove each x and put 1 if the result is 4 that's mean it's the true equation

The selection depends on individual needs, preferences, and the intended use of the tiny house.

a) To find the amount of space inside each house, we need to calculate the volume for each design.

House on the left:

Volume = length x width x height = 2.5 m x 18 m x 2.8 m = 126 m³

Triangular house:

Volume of a triangular prism = (base area x height) / 2

Base area = (1/2) x base x height = (1/2) x 4 m x 10 m = 20 m²

Volume = (20 m² x 7 m) / 2 = 70 m³

b) When comparing the environmental impacts of each house, several factors need to be considered:

Positive impacts:

1. Material usage: Tiny houses use fewer materials, reducing resource consumption and waste generation.

2. Energy efficiency: Smaller living spaces require less energy for heating, cooling, and lighting, leading to lower energy consumption.

3. Land utilization: Tiny houses can be built on smaller plots of land, preserving green spaces and reducing urban sprawl.

Negative impacts:

1. Construction materials: Although tiny houses use less material overall, the environmental impact depends on the types of materials used. Sustainable and eco-friendly materials should be prioritized.

2. Water and waste management: Adequate provisions for water supply and waste disposal should be implemented to minimize environmental impacts.

3. Transportation: The transportation of tiny houses to their locations can contribute to carbon emissions if not done efficiently.

c) The choice of design for a tiny house depends on personal preferences and priorities. However, considering the provided information:

The house on the left offers a larger interior space of 126 m³, providing more room for living and storage. It may be suitable for individuals or couples who desire more space and functionality within their tiny house.

The triangular house has a smaller interior volume of 70 m³ but offers a unique design and aesthetic appeal. It may be preferred by individuals who prioritize a distinctive architectural style or who are looking for a minimalist and cozy living space.

Ultimately, the selection depends on individual needs, preferences, and the intended use of the tiny house. Factors such as lifestyle, desired amenities, and personal values regarding sustainability and resource conservation should be considered when making the final decision.

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The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The polynomials are given below.

10x⁶ + 20x⁴ - 15x² and 5x²

The factor of the polynomial 10x⁶ + 20x⁴ - 15x² will be given as,

10x⁶ + 20x⁴ - 15x² = (5x²) · (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be given as,

⇒ (10x⁶ + 20x⁴ - 15x²) ÷ (5x²)

⇒ [(5x²) · (2x⁴ + 4x² - 3)] ÷ (5x²)

⇒ (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

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The watchmaker needs to clean approximately 26.66 watches to break even. Rounded to the nearest whole number, the answer is 27 watches.

The contribution margin per watch is calculated by subtracting the variable cost per watch from the selling price per watch. In this case, the selling price is $19.99 and the variable cost is $7 (the cost of the battery). Therefore, the contribution margin per watch is $19.99 - $7 = $12.99.

To break even, the fixed costs of $346 need to be covered. Dividing the fixed costs by the contribution margin per watch gives us $346 / $12.99 ≈ 26.64. Since we can't have a fraction of a watch, we round up to the nearest whole number. Therefore, the watchmaker needs to clean at least 27 watches to break even.

Cleaning 27 watches would generate a revenue of 27 * $19.99 = $539.73. From this revenue, the variable costs of $7 per watch (27 * $7 = $189) would be deducted, resulting in a contribution margin of $539.73 - $189 = $350.73. This contribution margin covers the fixed costs of $346, leaving a small profit.

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The relationship between variable F and x is 2x + 12000000/x

Let y represent the length (in feet) of a side perpendicular to the dividing fence, and let x represent the length (in feet) of a side parallel to the dividing fence.

Let F represent the length of fencing in feet.

Area of fencing = 6000000 ft²

Area of fencing = x * (y + y) = x * 2y

Area of fencing = 2xy

6000000=2xy

xy = 3000000

y = 3000000/x

The perimeter is:

F = x + y + y + x + y + y

F = 2x + 4y

F = 2x + 4(3000000/x)

F = 2x + 12000000/x

Therefore the relationship between variable F and x is 2x + 12000000/x

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The relationship between a statistic and a parameter is the same as the relationship between , Option(A) a sample and a population

The Population is defied as an entire group of individuals that we are interested in studying, while a sample is a subset of that population that we actually observe and collect data from.

A Parameter is defined as a numerical characteristic of a population, such as its mean or variance, whereas a statistic is a numerical characteristic of a sample, such as its sample mean or sample standard deviation.

The relationship between a sample and a population is similar to the relationship between a statistic and a parameter because a sample is used to estimate  information about the population, and a statistic is used to estimate  information about a parameter.

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1. The values which the given number sentences true are:

a) 11 b) 5 c) 36

2. After substituting the value of  x we get the value for y as :

a) 6 b) 0 c) 7 d) 15

3. The number sentences are :

a) x ₋ y = 25

b) 5 × p = q ÷ 2

c) 2y ₋ 14 = 6

d) 15 × 4 = 4 ₋ (x₊y)

Given in the first bit we need to find the variables:

a) h ₊ 8 = 19

arrange the constants on one side.

h = 19 ₋ 8

h = 11

b) 2p ₋ 6 = 4

arrange the constants on one side.

2p = 4 ₊ 6

2p = 10

p = 10/2

p = 5

c) 1/3 y = 12

cross multiply.

y = 36

Now in the second exercise we are asked to substitute the x value and get the value of y.

a) y = 3x ₊ 2 if x =8

substitute x value in the equation.

y = 3(8) ₊ 2

y = 24 ₊ 2

y = 26

b) y = 4x ₋ 1 if  x = 1/4

y = 4(1/4) ₋ 1

y = 1 ₋ 1

y = 0

c) y = 0.2x ₊ 5 if x = 10

y = 0.2(10) ₊ 5

y = 2 ₊ 5

y = 7

d) y = 10x ₊ 12 if x = 0.3

y = 10(0.3) ₊ 12

y = 3 ₊ 12

y = 15

In the last third bit we need to frame equations for the given word problems.

a) The difference between two numbers is 25.

let the two numbers be x and y.

x ₋ y = 25.

b) The product of 5 and p is equal to quotient of q and 2.

5 × p = q ÷ 2

c) The difference between 14 and 2y is equal to 6.

2y ₋ 14 = 6

d) The product of 15 and 4 is equal to four less than the sum of x and y.

15 × 4 = 4 ₋ (x₊y)

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The average rate of change, in simplest form, is -2/5.

What is average rate ?

Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.

The rate of change of the function is its gradient or slope.

The formula for calculating the gradient of a function is expressed as:

\(m=\frac{d y}{d x}=\frac{y_2-y_1}{x_2-x_1}$$\)

Using the coordinate points from the table (0,41) and (15,35)

Substitute the coordinate into the expression:

\($$\begin{aligned}& m=\frac{35-41}{15-0} \\& m=\frac{-6}{15} \\& m=\frac{-2}{5}\end{aligned}$$\)

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Answer:

build linear model

When modeling scenarios with linear functions and solving problems involving quantities with a constant rate of change, we typically follow the same problem solving strategies that we would use for any type of function.

fitting linear models to data

A professor is attempting to identify trends among final exam scores. His class has a mixture of students, so he wonders if there is any relationship between age and final exam scores. One way for him to analyze the scores is by creating a diagram that relates the age of each student to the exam score received.

distinguish between linear and nonlinear relations

As we saw in the cricket-chirp example, some data exhibit strong linear trends, but other data, like the final exam scores plotted by age, are clearly nonlinear. Most calculators and computer software can also provide us with the correlation coefficient, which is a measure of how closely the line fits the data.

use a linear model to make predictions

Once we determine that a set of data is linear using the correlation coefficient, we can use the regression line to make predictions. As we learned previously, a regression line is a line that is closest to the data in the scatter plot, which means that only one such line is a best fit for the data.

key concepts

1. Scatter plots show the relationship between two sets of data.

2. Scatter plots may represent linear or non-linear models.

3. The line of best fit may be estimated or calculated using a calculator or statistical software.

4. Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data.

glossary

correlation coefficient

1. a value, r, between –1 and 1 that indicates the degree of linear correlation of variables or how closely a regression line fits a data set.

extrapolation

1. predicting a value outside the domain and range of the data

Step-by-step explanation:

fig 3 would take 18 triangle

fig 4 would take 30 small triangles

if its wrong i am sorry

Answer:

ANSWER :

The answer is :

EXPLANATION :

From the problem, we have :

h(x) is translated vertically by 5 units downward and it becomes the graph of a function g.

So g(x) = h(x) - 5

negative 5 denotes that h(x) is translated 5 units downward.

So that will be :