A line is perpendicular to y = −1/3x + 7
and intersects the point (4,2).
What is the equation of this
perpendicular line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x - X1)
Then write the equation in slope-intercept form.

Answer:

0.01 goes in the first box

0.10 goes in the second box

Therefore, the first equation is 0.01p + 0.10d = 1.50

===========================================================

Reason:

The last part mentions "A penny is 0.01" which means $0.01 or 1 cent. The 0.01 is the coefficient of the variable p.

1 penny = $0.01

p number of pennies = 0.01p dollars

A similar situation happens with the dimes.

The system of equations is:

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

Total amount invested = $110000

Using the fiollowing variable representations:

We have

a + b + c = 200000

Using the total interest earned of 7145, we have:

10.9% * a + 2.9% * b + 5% * c  = 11165

So, we have

0.109a + 0.029b + 0.05%c  = 11165

Country day invests $20000 more in bonds than in CDs.

So, we have

b = c + 20000

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The width of the mural (in feet) when it is finished is equal to 12.25 feet.

In Geometry, a scale factor is the ratio of two corresponding side lengths or diameter in two similar geometric figures which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

Scale factor = 2/5

For the width of the mural (in feet), we have:

2/5 = 4.9/x

x = (5 × 4.9)/2

x = 24.5/2

x = 12.25 feet.

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Based on a survey of 2718​ people, a research center concluded that​ 32% of Americans​ "always" make a special effort to sort and recycle​ glass, cans,​ plastic, or​ papers. Participation bias is there in this case.

The bias would have no effect on a reader's perception of the assertion because no group of persons is much more likely to respond to the poll than any other.

When comparisons are performed between groups of patients who differ in outcome determinants and the differences are connected to the result, participation bias emerges.

1. Participation bias is inherent in studies that involve participant enrollment.

2 Because selective participation might jeopardize study external validity, determining the magnitude of participation bias is critical for optimizing inference from these investigations.

Few community studies have looked into the impact of participation bias. Nonparticipants in one population-based study of myocardial infarction (MI) were older, had more comorbidity, and had a lower survival rate than participants.

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Angle of depression and elevation:The angle of depression refers to the angle above the hill.The ship is 349.8 feet away from the skyscraper's base horizontally.

You could calculate the angle of elevation, for instance, if you were standing on the ground and were looking up at a mountain's summit.

The angle between a line of sight's horizontal axis and its downward axis is known as the angle of depression.

The ship is 349.8 feet away from the skyscraper's base horizontally.

Angle of depression and elevation:The angle of depression refers to the angle above the hill.

given the aforementioned variables

The harbor is 824 feet tall.

Depression angle is 67 degrees.

SOH CAH TOA identification claims that:

Tan = opp/adj Tan = 824 Tan = 67

d = 824.8/tan67 d = 349.8 feet

Therefore, the vertical distance from the skyscraper's base to the ship is 349.8 feet.

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Answer:

Step-by-step explanation:

Answer:

20, 2.7, 7.4

Step-by-step explanation:

I completed the assingment and got it 100

Answer: i don't know sorry 99

Step-by-step explanation:

56+80

A) The measure of the central angle is  [tex]\frac{4}{3} \pi[/tex] .

B) The radius of the circle is 55.43 in.

A) We know,

The area of a sector is  [tex]\frac{n}{2\pi } \pi R^{2}[/tex]

where n = the degree of the central angle of the sector

          R = radius of the circle

Suppose, the measure of the central angle is x.

   [tex]\frac{x}{2\pi } .\pi .24^{2} = 384\pi[/tex]

⇒ [tex]\frac{x}{2\pi } = \frac{384\pi }{576\pi }[/tex]

⇒ [tex]x = \frac{384\pi }{576\pi } * 2\pi[/tex]

⇒ [tex]x = \frac{4}{3} \pi[/tex]

So, the measure of the central angle is  [tex]\frac{4}{3} \pi[/tex].

B) Suppose the radius of the circle is r in.

   [tex]\frac{\pi /4}{2\pi } .\pi .r^{2} =384\pi[/tex]

⇒[tex]\frac{1}{8} .\pi .r^{2} =384\pi[/tex]

⇒ [tex]r^{2} = 384\pi / \frac{1}{8} \pi[/tex]

⇒  [tex]r^{2} = 3072[/tex]

As r > 0

So, r = 55.43

Hence, The radius of the circle is 55.43 in.

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The point that lies on the function defined by the equation is (2, 7)

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

y = 2x + 3

The point in the ordered pair that lies on the graph of the equation is the solution set

Take for instance, we set x = 2

So, we have the following representation

y = 2 * 2 + 3

Evaluate the product and the sum

This gives

y = 7

When repesented as an ordered pair, we have

(2, 7)

Hence, the point is (2, 7)

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Applying combination, the number of playlist is: 75,435.

A combination is a way of selecting a certain number of items from a larger set, without regard to the order of the items.

The number of possible playlists would be the number of ways to select 7 songs out of 20 without regard to order, which is commonly known as a combination.

The formula for combination is nCr, where n is the total number of items and r is the number of items being chosen at a time. So in this case, the number of possible playlists would be 20C7.

This can also be written as 20!/(7!*13!)

The answer is 75,435

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The measures of angles BDA and BEA  is 90 degree and the fact that AD and AE are radii of circle A tell us about BD and BE must be a tangent to the circle.

The tangents to the circle are BD and BE.

∠BDA = 90

∠BEA = 90

Radii = AD and AE

A tangent's angle with a circle's radius is always measured as a 90-degree angle.

∠BDA = 90, and since AD is a radius, BD must be a tangent to the circle.

Similar, ∠BEA = 90 suggests that BE is a tangent to the circle and that AE is a radius.

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The complete question is:

What do the measures of angles BDA and BEA and the fact that AD and AE are radii of circle A tell us about BD and BE?

Answer: 6

Step-by-step explanation:

1. 16/1 × 3/8= 48/8

2. 48/8= 6

Answer:

Answer is in attached photo. (B)

Step-by-step explanation:

The solution is in the attached photo , do note the question might specify the method to use to solve the equations, just like this the question:

1) Substitution Method

2) Elimination Method

The measure of arc RT is: C. 204 degree.

arc ORT = 102° - 90°

arc = 12°

arc ROT = 180° - 2×12°

arc ROT = 180° -  24°

arc ROT = 156°

Hence:

Measure of arc RT

arc RT= 360° - 156°

arc RT = 204°

Therefore the correct option is C.

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Answer: ∠1= 75°, ∠2= 105°, ∠3=105°, ∠4=75°, ∠6=105°, ∠7= 105°, ∠8=75°

Step-by-step explanation:

∠1 is corresponding to angle 75° which make them equal.

∠2 is supplementary to ∠1 which means they add up to 180°. Since ∠1 is 75° you would subtract 75° from 180° to get 105°.

∠3 is vertical to ∠2 which makes them equal.

∠4 is vertical to ∠1 which makes them equal.

∠6 is corresponding to ∠2 which makes them equal.

∠7 is vertical to ∠6 which makes them equal.

∠8 is vertical to 75° which makes them equal.

The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.

432 hamburgers.

We can write an equation to represent the information given.

Hamburgers + Cheeseburgers = 491

Cheeseburgers = Hamburgers - 59

Substitute the second equation into the first equation:

Hamburgers + (Hamburgers - 59) = 491

Solve for 'Hamburgers':

2Hamburgers - 59 = 491

2Hamburgers = 550

Hamburgers = 275

Since the question asks for the number of hamburgers, the answer is 275 hamburgers.

The hamburger shop sold a total of 491 hamburgers and cheeseburgers on Friday. There were 59 fewer cheeseburgers sold than hamburgers, so the number of hamburgers sold on that day was 275.

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The roots of the parabola are given as follows:

x = -2 and x = -4.

The quadratic function for this problem is defined as follows:

y = x² + 6x + 8.

Completing the squares, the quadratic function can be factored as follows:

y = (x + 4)(x + 2).

As:

Then the roots are obtained as follows:

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The three points that lie on a line y = -2/5x with a slope -2/5 will be:

(0, 0)

(5, -2)

(10, -4)

Given slope = m = -2/5. We suppose the line passes through the origin, so b = 0

substituting m = -2/5 and b = 0 in the slope-intercept form

y = -2/5x + 0

y = -2/5x

Thus, the equation of line with the slope m = -2/5 and passes through the origin (0, 0) will be:

y = -2/5x

As the equation of line passes through (0, 0), thus the point (0, 0) lies on the line.

Putting x = 0 in the equation y = -2/5x

y = -2/5 × (0)

y = 0

Thus, (0, 0) is the point which also passes through the line

Putting x = 5 in the equation y = -2/5x

y = -2/5 × 5

y = -2

Thus, (5, -2) is the point which also passes through the line.

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Answer:

x = 6, length of the rectangle is 18cm, and width is 21cm

Step-by-step explanation:

To solve this problem, we can use the perimeter of a rectangle formula: P = 2l + 2w.

Here, l = 3x and w = 4x - 9, so the perimeter is P = 2(3x) + 2(4x - 9) = 52.

Solving for x, we get x = 6.

Therefore, the length of the rectangle is 3x = 18 cm, and the width is 4x - 9 = 21 cm.

she need 240 number of participant .

Graphing cell means to picture primary impacts and connections. The numbers in the secret elements address bunch implies in a 2 x 2 x 3 plan. The negligible means for factors An and B are likewise shown. The cell implies are plotted as line diagrams and as reference charts.

Now, According to the question:

We have Dr. Green is interested in conducting a 2 x 2 x 3 within-group factorial design.

There are 12 cells in factorial, and each cell 20 participant.

Then, number of participant = 20(12) = 240 participant.

Thus, she need 240 number of participant .

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Create a table with the place values for the first and second factors down the left and the top and bottom, respectively.

What is the box method?

Multiplication using the box method: Create a table with the place values of the first and second factors down the left and the top and bottom, respectively. Second step: multiply the place values and add the results to the table. Step 3: Add up all of the table's rows. Step 4: Add the sums of these rows.

Placing the first word in the first box and the last term in the last box is the first step in utilizing the box technique to factor a trinomial. Multiply the first and last boxes after that. Identify the first and last boxes' products, which together make up the middle word. Put these words in the remaining spaces.

Here's how you can use the box method to distribute and simplify the expression:

( -5x - 2 ) ( 5x + 4 )

⇒-5x -2

⇒5x 4

⇒-25x^2 -10x + 20x - 8

⇒-25x^2 + 10x - 8

So the simplified expression is:

-25x^2 + 10x - 8.

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We need to find how much water Ella needs to make the different concentrations of syrups. The solution will be for 1.5%, we need 32.83 lbs of water.

The percentage in the concentration tells us how much in the mixture is sugar.

So for example, in the 50% syrup, we have a 50% of sugar, meaning that half of it is sugar, and we have 0.5 lbs of sugar, so we need to add the same amount of water, 0.5 lbs of water.

For the 1.5% syrup, this will be:

= (0.5 - 0.5 × 0.015) / 0.015

= 32.83 lbs

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Complete question

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case.  1.5% syrup?

The no. of subsets with at least one odd number is ²⁰C₁₀ - 1

We have the sample set to be {1, 2, 3, 4, ... 20}

Now we need to make subsets of 10 from these 20 elements.

Hence, the number of possible subsets of 10 elements will be

²⁰C₁₀

Now, there are 10 odd elements in the given sample set.

Hence the number of sets that contain at least 1 odd element

= Total no. of possible sets - no. of possible sets with no odd no.

Now since there are only 10 even numbers, there can be only one such set possible.

Hence no. of the subsets with at least one odd number is

²⁰C₁₀ - 1

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The small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.

Similar triangles are triangles that have the same shape but can have different sizes. In this case, the shadow of the boy, the boy himself, and the light post form similar triangles.

Let h be the height of the light post, x be the distance between the boy and the light post, and s be the length of the shadow, we can use the following ratios -

(boy's height) / (boy's shadow) = (light post height) / (light post shadow)

i.e. (4 feet 6 inches) / (3 feet 4 inches) = (h) / (x)

Now, we can find the height of the light post by using the above equation and the given values of the boy's height and the shadow.

The small boy can measure the distance between him and the light post, and he can use this value in the above equation to determine the height of the light post. The equation is h/x = (4.5)/(3.33)

This is the ratio of the height of the light post and the distance between the boy and the light post, so h = (4.5 * x) / (3.33)

In this way, the small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.

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Th systems of Linear Inequalities are:

x>=-7,

y<6-2x/3,

y<=-1,

y>3/5x-5,

y<6+5x

Step1:

x>=-7,y<6-2x/3,y<=-1,y> 3/5x-5,y<6+5x: [x>=-7]

[y<6-2x/3]

[y<=-1]

[ y>3/5x-5]

[y<6+5x]

x>=-7

[tex]3y+2x < 6\sy < =-1\sy > \frac{3}{5}[/tex]

x-5\sy-5x<6

Separate y for 3y+2x6 as follows: y6-2x/3 3y+2x6

Step2:

shuffle twice to the right side

Divide both sides by 3 using the formula 3y/6/3-2x/3.

simplify

3y/3<6/32x/3

Simplify 3y/3 by dividing it by y.

3/3=1

simplify 6/3-2x/3: 6-2x/3

6/3-2x/3

Apply the formula a/c + b/c = a+-b/c = 6-2x/3 y 6-2x/3

Identify y for y-5x6: y6+5x y-5x6.

Y=6+5x move the right side by 5x.

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option D is correct- The length of quadrilateral of A’D’ is 6. When it is reflected ,the lengths don’t change.

image is attached below,

Quadrilateral

A quadrilateral is defined as a two-dimensional shape with four sides, four vertices, and four angles. There are two main types: concave and convex. There are also various subcategories of convex quadrilaterals, such as trapezoids, parallelograms, rectangles, rhombi, and squares.

Reflection

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.

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On dividing the expression [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)], the value obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression is given as - [(x²-9)/(x²+5x+4)]/[(x²-4x-5)/(x²-2x-15)]

Apply the fraction rule, (a/b)/(c/d) = a·d/b·c

= [(x²-9) × (x²-2x-15)]/[(x²-4x-5) × (x²+5x+4)]

= [(x²-9) × (x+3)]/[(x²-4x-5) × (x+1)]

Expand the expression -

= [(x²-9) × (x+3)]/(x³-3x²-9x-5)

= (x³+3x²-9x-27)/(x³-3x²-9x-5)

= 1 + [(6x²-22)/(x³-3x²-9x-5)]

Therefore, the expression obtained is 1 + [(6x²-22)/(x³-3x²-9x-5)].

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The MEAN best describes the monthly rents.

The best one is Mean : 898

Now, According to the question:

The monthly rents for five apartments advertised in a newspaper were $670, $670, $790, $1550, and $810.

We are required to use the mean, median and mode to explain which measure of central tendency best describes the monthly rent.

The mean, median and mode (as calculated) are the measures of central tendency for the data set given.

This measures which value is closest to the center such that it can conveniently represent every other data. Observe carefully that the least value is 670 while the highest is 1550.

Also, observe that the value which is "more central" to both extremes is the mean.

The median is closer to the lowest value and much farther from the highest value.

The mode is actually at the lowest end of the data set.

However, the mean is safely between both ends. Its farther away from the least value than the median which means its moving closer to the "center" unlike the other two measures.

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The given data is ordinal data.

This type of data is ordinal data, as the variables are collected on an ordered scale (the number of times per day the device is turned on and the number of inhalations per activation). Although the actual numerical values may not have equal distances, they can still be ordered and compared based on the magnitude of the numbers.

Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. These statistics are presented on an ordinal scale, one of the four measurement levels that S. S. Stevens described in 1946.

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The unit vector that has the same direction as the given vector is[tex]& (3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].

The given vector(v) is -3i+7j

The unit vector is found by dividing the vector by its magnitude

Unit vector of  [tex]$v=\frac{v}{\|v\|}$[/tex]

The formula of unit vector in the direction of a given vector is:

We have to find the magnitude first

So,

[tex]& \|v\|[/tex] =[tex]\sqrt{(3)^{2}+(-7)^{2} } =\sqrt{9+49} =\sqrt{58}[/tex]

[tex]& \|v\|=\sqrt{58}[/tex]

The unit vector is:

The i, j, and k are the unit vectors in the directions of the x-axis, y-axis, and z-axis respectively in a 3-dimensional plane. i.e.,

[tex]$$\begin{aligned}& =(1 / \sqrt{58})(3 \mathrm{i}-7 \mathrm{j}) \\& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}\end{aligned}$$[/tex]

Therefore, the unit vector is [tex]& =(3 / \sqrt{ } 58) \mathrm{i}-(7 / \sqrt{58}) \mathrm{j}[/tex].

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