a line goes through the point (2,4) and has a slope of 3/2. Which of the following points is also on the line? Circle all that apply

Romeo is 171.5 feet away from Juliet when she saw her at an angle of depression of 5 degrees.

We know a right-angled triangle has three sides they are -: Hypotenuse,

Opposite and Adjacent.

We can remember SOH CAH TOA which is,

sin = opposite/hypotenuse, cos = adjecen/hypotenuse and

tan = opposite/adjacent.

Given, Juliet is standing atop a 15-­‐foot balcony when she spots Romeo at an angle of depression of 5°.

Here height is 15 feet and by interior alternate angles theorem angles is 5°

we have to determine the length of the adjacent side or base.

tan5° = 15/base.

base = 15/0.087.

base = 171.5 feet.

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The circumference of a circle is equal to the total length of its boundary. The length of label is 143 / 7 cm. the correct answer is option D.

A circle is a geometrical shape having all of its points equidistant from a fixed point known as the center.

The angle subtended by a circle is 360°.

Given that,

the radius of the circle r = 3 + 1 / 4

                                        = 13 / 4 cm

The length of label is equivalent to the circumference of circle having r =  13 / 4 cm.

The circumference is given as,

C = 2π × r

=> C = 2 × 22 / 7 × 13 / 4

=> C = ( 11 × 13 ) / 7

=> C = 143 / 7.

Hence, the length of the label is given as 143 / 7 cm.

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Answer:

d

Step-by-step explanation:

because i said so

The volume of the original pyramid is, 250/3 cubic inches, and the volume of the reduced size pyramid is, 80/3 cubic inches.

What is the pyramid?

A pyramid is a structure that has triangular exterior surfaces that converge to a single step at the summit, giving it roughly a pyramidal shape in the geometric sense. Any polygonal form, including triangular and quadrilateral, can serve as the base of a pyramid. A pyramid has at least three outside triangle surfaces as a result.

Let, the pyramid has a square base of lengths 5 inches  and the height is 10 inches.

Since,

Volume of pyramid = (l x b x h)/3

where,

l is the base length,

b is the base width and

h is the height.

Here, l = b = 5, h = 10

So,

V = (5 x 5 x 10)/3 = 250/3 cubic inches.

Now, to save costs in production, the lengths of the sides of the base are each reduced by one inch while the pyramid's height remains the same.

So, l = b = 4, h = 10

Therefore,

V = (l x b x h)/3 = (4 x 4 x 10)/ 3 = 80/3 cubic inches.

Hence, the volume of original pyramid is, 250/3 cubic inches and the volume of reduced pyramid is, 80/3 cubic inches.

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The correct option is, Mickey should have added –4 and 2 when combining the coefficients of the x terms.

Given,

The expression;  2x² - 4x - 9 - x² + 2x + 3

We have to simplify the expression;

To group and arrange an expression in such a way that it is easier to understand and solve is to simplify the expression.

We first group and find like terms and then add and cancel out

2x²-x²- 4x+2x - 9+ 3

=x²-2x-6

Mickey did not add the coefficients -4 and +2 for x terms in the expression, instead it looked like he added 4+2 as the coefficients

Therefore the correct option is

Mickey should have added –4 and 2 when combining the coefficients of the x terms.

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Using the probability, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

In the given question,

If you choose two cards out of a deck of cards, then we have to find the chances one is a red face card and the other is a black non-face card.

As we know that in a deck having 52 cards. In which 26 are red and 26 are black.

We have to choose a red face card.

As we know that in a deck have 12 face cards. In which 6 red face cards and 6 black face cards.

So the chance of getting red face card is

P(R)=Total number of red face cards/Total number of cards

P(R)=6/52

We have to choose a black non-face card.

We know that in a deck have 6 black face cards and total black cards are 26. So the non face cards are 20.

So the chance of getting black non-face card is

P(B)=Total number of black non-face cards/Total number of cards

P(B)=20/52

Now the chances of getting one is a red face card and the other is a black non-face card is

P(R or B)=P(R)+P(B)

P(R or B)=6/52+20/52

P(R or B)=(6+20)/52

P(R or B)=26/52

P(R or B)=1/2

Hence, if you choose two cards out of a deck of cards, then the chances one is a red face card and the other is a black non-face card is 1/2.

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The angle of triangle ∠LMN = 60 degrees,

Right angle triangle MLN where at L it is a right angle ∠MLN=90  and the line LN of triangle MLN lies on the ray LO passes through LN it makes an exterior angle with MN it is given by 3x+15 degrees whereas angle M in the triangle MLN is given by ∠LMN = x+15 degrees.

By using the exterior angle relation that exterior angle =sum of two opposite internal angles,

Here, 3x+15=x+15+90,

We get x=45 degrees ,

So angle ∠LMN is x+15 which is 60,

Hence, The angle of triangle ∠LMN = 60 degrees.

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Answer:

y = [tex]\frac{5}{3}[/tex] x -9

Step-by-step explanation:

Put both equations in the slope intercept form

y =mx + b

5x - 3y = 7  Subtract 5x from both sides

-3y = -5x + 7  Divide both sides by -3

y = [tex]\frac{-5}{-3}[/tex] x + [tex]\frac{7}{-3}[/tex]  Cleaned up

y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{7}{3}[/tex]

4x -y = 9  Subtract 4x from both sides

-y = -4x + 9  Divide all the way through by -1

y = 4x - 9

To make a line parallel to the first equation, we need the same slope.  The slope of the first equation is [tex]\frac{5}{3}[/tex].  We are also told to have the same y intercept as the second equation which is -9

y = [tex]\frac{5}{3}[/tex] x  - 9

Answer: This looks like the periodic table, just find the variable and then you're good to go!

Step-by-step explanation:

Answer: I EXPLAINED IT TELL ME IF YOU NEED THE ANSWER!

Step-by-step explanation: You can find the final equation for the segment of a circle area: A segment = A sector - A isosceles triangle = (0.5 × r² × α) - (0.5 × r² × sin(α)) = 0.5 × r² × (α – sin(α)) Formula given radius and height. A segment = r² × Arcos((r-h)/r) - (r-h) × √ (2 × r × h - h²) where h is the height of a segment, also known as sagitta.

The probability that the next person will purchase no costume as a percent is 80%.

Number of visitors who purchase no costume = 349

Number of visitors who purchase exactly one costume = 71

Number of visitors who purchase more than one costume = 12

Total number of visitors = 349 + 71 + 12 = 432

Probability of an event P(E) = Number of favorable outcomes (visitors who purchase no costume)/Total number of outcomes

⇒ P(E) = 349/432

⇒ P(E) = 349/432

Percent form of P(E) = (349×100)/432 = 80%

Hence the probability in percent form that next person will purchase no costume is 80%.

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[tex]\cfrac{tan(\theta )}{sec(\theta )}\implies \cfrac{~~ \frac{sin(\theta ) }{cos(\theta ) } ~~}{\frac{1}{cos(\theta )}}\implies \cfrac{sin(\theta ) }{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} cos(\theta ) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1}\implies sin(\theta )[/tex]

Answer:

(-5,5)

Step-by-step explanation:

The numerical expression will be;

⇒ 5 × (67 + 86) = 765

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division

Given that;

The algebraic expression is,

''5 multiplied by the sum of 67 and 86''

Now,

Write the mathematical expression as;

''5 multiplied by the sum of 67 and 86''

⇒ 5 × (67 + 86)

⇒ 5 × 153

⇒ 765

Thus, The numerical expression will be;

⇒ 5 × (67 + 86) = 765

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The equation that show the relationship between the truck's weight in tons and the number of refrigerator in the truck x is y = 15 + 0.16x

The weight of the each refrigerator = 0.16 tons

The weight of truck when its empty = 15 tons

The weight of the truck = y

The number of refrigerators in the truck is x

Then the equation will be

y = 15 + 0.16x

Where y is the weight of the truck

x is the number of refrigerators

Hence, the equation that show the relationship between the truck's weight in tons and the number of refrigerator in the truck x is y = 15 + 0.16x

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Based on the provided data and the residual plot from the least squares method fit, the pattern of the residuals tells you about the linear model that the residual plot clearly contradicts the linearity of the data. (Option D).

The least square method refers to the process of determining the best-fitting curve or line of best fit for the data points by decreasing the sum of the squares of the offsets (residual part) of the points from the curve.  It is a mathematical regression analysis which is utilized to establish the best fit for processing data while providing a visual demonstration of the relation between the data points. The residual plot in the given situation indicated that the residual plot clearly contradicts the linearity of the data.

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Answer: (x/5)+x=y

Step-by-step explanation:

No, feeding both tanks the same amount of food is impossible.

Let's assume a pet store has two fish tanks and tank A contains Z number of smaller fish.

In tank A, she fed each fish one gram of food per day,

which equals Z*1, while

in tank B, she fed each fish two grams of food per day,

which is (2/3*Z)*2.

Let's now test the feasibility of feeding both tanks the same amount of food.

Z*1 = (2/3*Z) *2

Z = (2/3*Z) *2  

3Z = 2*Z*2

3Z = 4 Z Lia will not be able to feed both tanks with the same amount of food because it is not possible.

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Using the Uniform Distribution and the Z- distribution, it is found that 1591 specimens should be tested.

Uniform Distribution: It refers to a type of probability distribution in which all outcomes are equally likely.

Z- Distribution: The standard normal distribution, also known as z distribution, is a special normal distribution where the mean is 0 and standard deviation is 01.

For an uniform distribution of bounds a & b the standard deviation is given by:  α = √ (b-a)²÷12

here, α= standard deviation.

in this problem, a = 45 and b = 750, thus the estimate is:

α = √(750-45)² ÷ 12

  = √497025 ÷ 12

  = 203.5

the margin of error of a Z confidence interval is given by:

                  M = z (α ÷√n)

where, z is the critical value

            α is the population Standard deviation

             n is the sample size.

Now, finding the critical value which is z with a p - value of (1+∝ )÷2, where ∝ is confidence level.

here, ∝ = 0.95, thus z with a p-value of (1+0.95)÷ 2 = 0.96

∴ z= 0.96

standard deviation estimates is 203.5.

now, we want sample for a margin of error of 10, then,

               M= z( α ÷ √n)

         ⇒ 10 = 1.96 ( 203.5 ÷ √n)

         ⇒ 10√n = 1.96 (203.5)

         ⇒ √n = 0.196 (203.5)

         ⇒ (√n)² = [0.196(203.5)]²

         ⇒ n = 1590.89

Round up the value 1590.89 by:

1591 specimen should be tested

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Answer:

20 + 6L ≤ 60 :)

The equivalent expression for the exponential expression 4³ . 4⁻⁹ is either 4⁻⁶ or 1/4⁶

Exponential expression:

Exponential expression means a mathematical expression consisting of a constant raised to some power.

Given,

Here we have the expression 4³ . 4⁻⁹.

Now, we have to simplify this expression to find the equivalent expression.

According to the following exponent rule,

xᵃ . xᵇ = x⁽ᵃ⁺ᵇ⁾

Based on this rule, we have rewritten the expression as,

=> 4⁽³ ⁺ ⁽⁻⁹⁾⁾

Thus the resulting value of the expression is,

=> 4 ⁽³⁻⁹⁾

=> 4⁻⁶

By using the another exponent rule, we get the value as,

=> 1/4⁶

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Answer:

10.5

Step-by-step explanation:

each quart is half a pint so 21 divided by 2 is this 10.5

Answer:

------------------------

Translate

Solution

Option B is the closest one.

Answer:

b) n - 6 > 2 ; n > 8

Step-by-step explanation:

Given statement,

→ The result of 6 subtracted from a number n is at least 2.

Forming the inequation,

→ n - 6 > 2

Now the value of n will be,

→ n - 6 > 2

→ n > 2 + 6

→ [ n > 8 ]

Hence, the value of n is 8.

Required standard form for given circle is [tex](x-2)^{2}+(y+9)^{2}=4[/tex]

Standard form of circle is expressed as[tex](x-h)^{2}+(y-k)^2=r^{2}[/tex] ,where h,k are the coordinate of the center of circle and r is radius.

Center (h, k) = (2, -9)

radius = 2 units

Using standard form of equation,

[tex](x-h)^{2}+(y-k)^2=r^{2}[/tex]

Putting the given values,we get

[tex](x-2)^{2}+(y-(-9))^{2}=2^{2}[/tex]

⇒ [tex](x-2)^{2}+(y+9)^{2}=4[/tex]

Hence, the standard form of equation of circle is [tex](x-2)^{2}+(y+9)^{2}=4[/tex] .

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What is 30% of 40?

30% = 0.3

so:

0.3 * 40 = 12

_________________________

Lou's class has 12 students in it. 8 of the students ran a race last weekend. What percent ran the race?

8 out of 12 ran so:

8/12 = 2/3

2/3 = 0.6667

0.6667 as a percentage:

0.6667 * 100 = 66.667%

[if you need it rounded to two decimal places: 66.67%]

Answer:

The x value does not change between the two points, meaning that our line includes all possible points in which x=5.

x=5 is the slope.

Answer:

x = 5

Step-by-step explanation:

slope: undefined

So, x = 5

If in Last week, Colton sold 14 magazine subscriptions and 36 raffle tickets for a fundraiser. This week, he sold 18 magazine subscriptions and 26 raffle tickets. If Colton charged $10.25 for each magazine subscription and $0.50 for each raffle ticket, Then $359 money he earned for the fundraiser over these two weeks

Two or more expressions with an Equal sign is called as Equation

Given,

10.25 for each magazine subscription and $0.50 for each raffle ticket,

M=10.25 and T=0.50

Last week:

14 magazine subscriptions and 36 raffle tickets for a fundraiser.

14M+36T

Now substitute M and T values

14(10.25)+36(0.50)

143.5+18

161.5

Current week:

18 magazine subscriptions and 26 raffle tickets.

18M+26T

Now substitute M and T values

18(10.25)+26(0.50)

184.5+13

197.5

So total money he earned for two weeks is 161.5+197.5

$359

Hence $359 money did he earn for the fundraiser over these two weeks

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The distance at which the ladder slips down the wall is equal to 5cm.

As given in the question,

figure of the given situation attached.

Length of the ladder AD or BE = 3m

                                                  = 300cm

Distance between base of wall and ladder before slipping 'DC'= 60cm

Distance after slipping 'EC' = 80 cm

In ΔADC,

AC =√AD² -CD²

     = √ 300² - 60²

     = √86400

     = 293.9

     = 294 cm ( nearest cm)

BC = √ BE² - EC²

     = √300² -80²

    = √ 83600

    = 289.1

    = 289 cm ( nearest cm)

Distance AB = AC - BC

                     = 294 - 289

                     = 5cm

Therefore, distance between the ladder before and after slipping on the wall is 5cm.  

The complete question is :

At the start of the day , a decorator rested a 3m ladder against a vertical wall so that the foot of the ladder was 60cm away from the base of the wall. During the day, the ladder slipped down the wall, causing the foot of the ladder to move 80cm further away from the base of the wall. How far down the wall, in centimeters, did the ladder slip? Give your answer to the nearest 1cm.

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The total amount of wood that Harry will need for the project is [tex]19\frac{1}{3}[/tex] feet.

What is a mixed fraction?

A mixed fraction is one that has both its quotient and remainder represented.

Or, a mixed fraction is a fraction that is created by combining a whole number and a fraction.

Given, 4 pieces of wood that have a length of  [tex]2\frac{3}{4}[/tex]  feet

And, 5 pieces of wood that have a length of  [tex]1\frac{2}{3}[/tex] feet

So,

The total amount of wood = [tex]4*2\frac{3}{4} +5*1\frac{2}{3}[/tex]

                                            = [tex]4*\frac{11}{4} + 5*\frac{5}{3}[/tex]

                                            = [tex]11+ \frac{25}{3}[/tex]

                                            = [tex]\frac{(11*3)+25}{3} = \frac{33+25}{3} = \frac{58}{3} = 19\frac{1}{3}[/tex]

Hence, the total amount of wood is  [tex]19\frac{1}{3}[/tex] feet.

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Answer:

Radius is 7π cm.

Step-by-step explanation:

Formula we use,

→ 2πr = 14π

→ 2r = 14π

Now the value of radius is,

→ 2r = 14 π

→ r = (14/2)π

→ [ r = 7π cm ]

Hence, the radius is 7π cm.

Answer:Answer:

Radius is 7π cm.

Step-by-step explanation:

Formula we use,

→ 2πr = 14π

→ 2r = 14π

Now the value of radius is,

→ 2r = 14 π

→ r = (14/2)π

→ [ r = 7π cm ]

Hence, the radius is 7π cm.

Step-by-step explanation: