A bag contains cars numbered from 1 to 14. Find the Probability of:
a) selecting a prime number or multiple of 4
b) selecting a multiple of 2 or 3
c) selecting 3 or 4
d) selecting 8 or a number less than 8

3x+2+x+8=180; 4x+10=180; 4x=170; x= 170/4= 42.5

Angle on top is x+8=42.5+8=50.8

Angle on the bottom is 3x+2=3•42.5+2= 129.5

The value of x is 42.5.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Straight lines that are always the same distance apart from one another are called parallel lines.

No matter how far apart they are in any direction, parallel lines will never intersect.

Given:

From figure (x+8) and(3x+ 2) are angles on same side of transversal.

So, (x+ 8) + (3x+ 2)= 180

4x+ 10 = 180

4x = 180- 10

4x= 170

x= 170/4

x= 42.5

Hence, the value of x is 42.5.

Learn more about parallel line here:

https://brainly.com/question/16701300

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Answer:

  24 cm²

Step-by-step explanation:

We assume that is a circumscribing quadrilateral, rather than one that is circumscribed. It is also called a "tangential quadrilateral" and its area is ...

  K = sr

where s is the semi-perimeter, the sum of opposite sides, and r is the radius of the incircle.

  K = (12 cm)(2 cm) = 24 cm²

_____

A quadrilateral can only be tangential if pairs of opposite sides add to the same length. Hence the given sum is the semiperimeter.

In this sequence, the first term is [tex]a_1[/tex] and every successive term is determined by

[tex]a_n=a_{n-1}+d[/tex]

where [tex]d[/tex] is the common difference between terms. We have

[tex]a_{11}=a_{10}+d=a_{9}+2d=\cdots=a_5+6d[/tex]

so that

[tex]41=11+6d\implies6d=30\implies d=5[/tex]

Then

[tex]a_5=a_4+5=a_3+2\cdot5=\cdots=a_1+4\cdot5[/tex]

[tex]\implies11=a_1+20\implies a_1=-9[/tex]

Answer:

The first term is -13.

Step-by-step explanation:

The general rule of an arithmetic sequence is the following:

[tex]a_{n+1} = a_{n} + d[/tex]

In which d is the common diference between each term.

This is the case going from one term to the next. However, when, as in this problem, we have the fifth and the tenth term, this formula can be expanded, as the following way:

[tex]a_{n + m} = a_{n} + m*d[/tex]

So

[tex]a_{10} = a_{5} + 5*d[/tex]

[tex]41 = 11 + 5d[/tex]

[tex]5d = 30[/tex]

[tex]d = 6[/tex]

The common diference is 6.

To find the first term, we do:

[tex]a_{5} = a_{1} + 4*d[/tex]

[tex]11 = a_{1} + 4*6[/tex]

[tex]a_{1} = -13[/tex]

The first term is -13.

Answer:

$95.48 was his commission

Step-by-step explanation:

First we need to find what the retail cost of the chest is.  If it's marked up 150%, we use 763.84 + 1.5(763.84) which gives us a retail price of $1909.60.  If Ben makes 5% on the sale as his commission, then we take 5% of 1909.60 which, in algebraic terms, looks like this:  .05(1909.60) which is $95.48

3wx^2

The third choice is the answer.

Answer :C

Answer:

3wx^2

Step-by-step explanation:

Answer:

  (3)  y = 12

Step-by-step explanation:

The circle is centered at (x, y) = (-5, 2) and has a radius of 10. Hence the most positive y-value is y = 12.

___

Complete the squares of x-terms and of y-terms.

  (x^2 +10x) + (y^2 -4x) = 71

  (x^2 +10x +25) + (y^2 -4x +4) = 71 + 25 + 4

  (x +5)^2 +(y -2)^2 = 10^2 . . . . . . . a circle centered at (-5, 2) with radius 10.

Answer:

[tex]4\frac{17}{24}[/tex] feet

Step-by-step explanation:

Total length of the board = [tex]7\frac{1}{3}=\frac{22}{3}[/tex] feet

Length of board that is removed from the larger board = [tex]2\frac{5}{8}=\frac{21}{8}[/tex]

When a smaller board is removed, the length of the remaining board can be calculated using subtraction as:

Remaining Length of board = Total Length - Length of smaller board

= [tex]\frac{22}{3}-\frac{21}{8}\\\\\text{Taking LCM, which is 24}\\\\ =\frac{8(22)-3(21)}{24}\\\\ =\frac{113}{24}\\\\ =4\frac{17}{24}[/tex]

This means [tex]4\frac{17}{24}[/tex] feet of board remains after removing the smaller board from it.

The answer is:

The area of the rectangle is equal to [tex]12units^{2}[/tex]

To find the area of the rectangle shown on the coordinate plan, first, we need to calculate the distance between the points that conforms two of the sides of the rectable (base and height).

We can use any of the four vertex points shown on the coordinate plane, so, we will use the points:

1 - (-4,1)

2 - (-1,-2)

3 - (-3,-4)

Then, calculating the length of the sides, we have:

Base:

[tex]Base=distance(FirstPoint,SecondPoint)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]

[tex]Base=\sqrt{(-1-(-4))^{2}+(-2-1)^{2}}\\\\Base=\sqrt{(3)^{2}+(-3)^{2}}\\\\Base=\sqrt{(9+9)}=\sqrt{18}units[/tex]

Height:

[tex]Height=distance(SecondPoint,ThirdPoint)=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}[/tex]

[tex]Height=\sqrt{(-3-(-1))^{2}+(-4-(-2))^{2}[/tex]

[tex]Height=\sqrt{(-2)^{2}+(-2)^{2}[/tex]

[tex]Height=\sqrt{4+4}[/tex]

[tex]Height=\sqrt{8}units[/tex]

Therefore, calculating the are of the rectangle, we have:

[tex]Area=base*height\\\\Area=\sqrt{18unis}*\sqrt{units}=\sqrt{144}=12units^{2}[/tex]

Hence, the area of the rectangle is equal to [tex]12units^{2}[/tex]

Have a nice day!

Aswer:

The area of the rectangle is 12 sq. units

step-by-step explanation:

From the question :

we first find the length and width of the rectangle using the distance formula.

For the length we use the points

(-1,-2) and (-4,1)

[tex]l = \sqrt{( {x - x_1)}^{2} + ( {y - y_1)}^{2} } [/tex]

[tex]l = \sqrt{( { - 1 - ( - 4))}^{2} +{(-2 - 1)}^{2} } [/tex]

[tex]l = \sqrt{{3}^{2} +{( - 3)}^{2}}[/tex]

[tex]l = \sqrt{9 + 9} [/tex]

[tex]l = \sqrt{18} = 3\sqrt{2} \: units[/tex]

For the width, let us take the points (-6,-1) and (-4,1)

[tex]w = \sqrt{ {( - 6 - ( - 4))}^{2} + {(-1 - 1) }^{2} }[/tex]

[tex]w = \sqrt{ {2}^{2} + {( - 2)}^{2} }[/tex]

[tex]w = \sqrt{4+4}[/tex]

[tex]w = \sqrt{8 } = 2 \sqrt{2} \: units[/tex]

The area of the rectangle

[tex] = l \times w[/tex]

[tex]A = 3 \sqrt{2} \times 2\sqrt{2} [/tex]

[tex]A = 3 \times 2 \times 2[/tex]

[tex]A =12 \: sq.units[/tex]

Answer:

  a) area of sidewalk: 346.5 ft²

  b) 278 bags

Step-by-step explanation:

The formula for the area of a circle is ...

  A = π·r² . . . . . where A is the area and r is the radius of the circle. (The radius is half the diameter.)

There are a couple of ways to find the area of a "washer" (a circle with a hole in the middle). One is to subtract the area of the hole from the area of the larger circle. Another way is to find the circumference of the circle whose radius is the average of the inner and outer radii, and multiply that by the width of the washer (the difference of the outer and inner radii).

For the latter purpose, the formula for the circumference of a circle is ...

  C = π·d . . . . . or, since the diameter is twice the radius, ...

  C = 2π·r

___

a) Here, the diameter of the circle that is the center of the walkway is ...

  28 ft + 3.5 ft = 31.5 ft

So, the circumference of that circle is ...

  C = π·d = (22/7)·(31.5 ft) = 99 ft

Then the area of the walkway is ...

  (99 ft)·(3.5 ft) = 346.5 ft²

__

b) 0.8 bags of concrete are required for each square foot, so we can find the number of bags by multiplying 0.8 times the number of square feet:

  bags = 0.8 × 346.5 = 277.2

If only whole bags are available, then 278 bags of concrete will be the minimum number needed.

_____

Comment on the two methods of doing this calculation

If r1 and r2 are the inner and outer radii of the circles, then the area of the washer is π(r2² -r1²).

The centerline diameter will be (2r2 +2r1)/2 = r1 +r2, and the width of the washer will be (r2 -r1). Then the washer area will be π·(r1 +r2)·(r2 -r1). This latter expression can be "simplified" to π(r2² -r1²), a formula for the washer area that is identical to the one above.

Answer:

  $2880

Step-by-step explanation:

I = Prt

= $3600·8%·10 = 0.80·$3600 = $2880

The simple interest on $3600 over a 10-year period is $2880.

Answer:

Step-by-step explanation:

I think the first part of that is asking for the equation for the line of symmetry, although I do not have access to your drop down menu to know for sure!  The axis of symmetry is the equation that splits the parabola into 2 parts that are mirror images of each other.  In this type of parabola, it will be an "x = " equation.  The line that splits the parabola in half is the line x = -2.  The function is increasing where the y values are going up.  This happens in the interval  (-∞, -2].

The function is decreasing where the y values are going down.  This happens in the interval [-2, ∞)

Answer:

C) 5000(0.987783)^t

Step-by-step explanation:

The monthly interest rate is the APR divided by 12, so is 22%/12 ≈ 0.018333.

Each month, the previous balance (B) has interest charges added to it, so the new balance is ...

balance with interest charges = B + (22%)/12×B = 1.018333×B

The minimum payment is 3% of this amount, so the new balance for the next month is ...

balance after payment = (1.018333B)(1 - 0.03) = 0.987783B

Since the balance is multiplied by 0.987783 each month, after t payments, the balance starting with 5000 will be ...

5000×0.987783^t . . . . . . . . . matches choice C

Answer:

The perimeter of one of the trapezoids is equal to [tex](16+8\sqrt{2})\ in[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The perimeter of a square is

[tex]P=4b[/tex]

where

b is the length side of the square

step 1

Find the length side of the smaller square

[tex]16=4b[/tex]

[tex]b=16/4=4\ in[/tex]

step 2

Find the length side of the large square

[tex]48=4b[/tex]

[tex]b=48/4=12\ in[/tex]

step 3

Find the height of one trapezoid

The height is equal to

[tex]h=(12-4)/2=4\ in[/tex]

step 4

Remember that in this problem, one trapezoid is equal to one square plus two isosceles right triangles.

Find the hypotenuse of one isosceles right triangle

Applying Pythagoras Theorem

[tex]c^{2}=4^{2} +4^{2} \\ \\c=4\sqrt{2}\ in[/tex]

step 5

Find the perimeter of one of the trapezoid

The perimeter is equal to

[tex]P=(4\sqrt{2} +4+4\sqrt{2}+12)\\ \\P=(16+8\sqrt{2})\ in[/tex]

Answer:

27.3 Inches

Step-by-step explanation:

Answer:

  28. [A] x² -2x +1 r -16

  29. [D] -x² -2x -5 -12/(x-2)

Step-by-step explanation:

In both cases, the answers can be chosen on the basis of the value of the remainder. That value can be found by evaluating the numerator expression at the value of x that makes the denominator zero.

___

28. The root of the denominator is x=-2. The value of the numerator there is ...

  (5(-2)³ -6 -15(-2) = -40 -6 +30 = -16 . . . . points to answer choice [A]

__

29. The root of the denominator is x=2. The value of the numerator there is ...

  -(2)³ -2 -2 = -8 -2 -2 = -12 . . . . points to answer choice [D]

Answer:

  Bagel

                                       plain                          

Tuna Eggs Chicken salad Cream cheese butter

                                      Poppy

Tuna Eggs Chicken salad Cream cheese butter

                                      Wheat

Tuna Eggs Chicken salad Cream cheese butter

3b

There are 15 combinations because tuna, eggs, chicken salad, cream cheese, and butter = 5

there are 3 different types of bagels plain poppy and wheat. with this information you can tell that the 5 combinations x 3 bagel types equal 15 total

Answer:

  0.5 cm

Step-by-step explanation:

You are given angles B and C and side b, so you can put those values into the given equation:

  sin(105°)/(2 cm) = sin(15°)/c

Multiply this equation by c·(2 cm)/sin(105°) and you get ...

  c = (2 cm)·sin(15°)/sin(105°) ≈ 0.535898 cm

  c ≈ 0.5 cm

_____

Comment on the given equation

When using the Law of Sines to find side lengths, I prefer to write the proportion in a form with the side length of interest in the numerator:

  b/sin(B) = c/sin(C)

or

  c/b = sin(C)/sin(B)

Using either of these forms, it is one step to find the value of c: Multiply the equation by the inverse of the coefficient of c.

  c = b·sin(C)/sin(B)

Answer:

1/4 ft

Step-by-step explanation:

The area is given by the product of length and width. Since the width of the rectangle was not changed, the new length L satisfies the equation ...

(1/6 ft)·L = 11/72 ft²

Multiplying by 6/ft tells us the new length:

L = (6/ft)·11/72 ft² = 11/12 ft

The original length is 2/3 ft shorter so is ...

L -2/3 ft = 11/12 ft -8/12 ft = 3/12 ft

L = 1/4 ft

Answer:

Step-by-step explanation:

Pick any point that is clearly on the line. (g, c) = (12, 40) is the end point, so will do nicely. The value of r (the constant of proportionality) is the slope of the line, which is the ratio of the y-value of the point to the x-value (or c to g, in this case).

  r = c/g = 40/12 = 10/3  . . . . . . the exact value of the constant r

Then your equation is ...

  c = 10/3g . . . . . . put the value of r where r is in the equation you are given

Answer:

f(x) ^-1 = 1/5 x

Step-by-step explanation:

f(x) = 5x

y =5x

To find the inverse, exchange x and y and solve for y

x =5y

Divide each side by 5

1/5x = 5y/5

1/5 x = y

1/5 x = f(x) ^-1

f(x) ^-1 = 1/5 x

ANSWER

B. [tex](x,y)\to (0.5x,0.5y)[/tex]

EXPLANATION

From the diagram, MN=6 units.

and M'N'=3 units.

The quadrilateral KLMN was dilated to obtain K'L'M'N'

We can observe that,

[tex] |M'N'| = 0.5|MN| [/tex]

This means that the scale factor of the dilation is 0.5.

The mapping for the dilation is :

[tex](x,y)\to (0.5x,0.5y)[/tex]

The correct answer is B.

It’s A the region one

Answer:

A). when the region is divided into a greater number of rectangles.

Step-by-step explanation:

This forms the basics of integration.

Integration can be use to calculate areas under the curve. To find the area under the curve we try to approximate the area under the curve by using rectangles. When we increased the number of rectangles of equal width of the rectangles, a better approximation of the area is obtained. We then find the area of each infinitesimally small rectangle and then integrate by taking two limits, the upper limit and the lower limit.

Answer:

C. n + n + 1 = 37; n = 18; n + 1 = 19

Step-by-step explanation:

If we let n represent the smaller integer, then the larger one is n+1. Their sum is 37, so you have ...

n + (n+1) = 37

When you subtract 1 and collect terms, you have ...

2n = 36

Dividing by 2 gives you ...

n = 18

Then the larger integer is ...

n+1 = 19

The matching choice is C.

Answer:

[tex]f(x)=\left\{ \begin{array}{rcl}\dfrac{8}{3}x+4&\text{for}&x\le3\\\\-3(x-3)^2+12&\text{for}&x>3\end{array} \right.[/tex]

Step-by-step explanation:

The line to the left of x=3 goes up from 4 to 12 as x goes from 0 to 3. Thus, the slope of it is ...

slope = (12 -4)/(3 -0) = 8/3

It intersects the y-axis at y=4, so its equation is ...

y = (8/3)x +4

__

For x > 3, we observe that the curve falls 3 units (from 12 to 9) as x goes from 3 to 4, then falls 9 units (from 9 to 0) as x goes from 4 to 5. The slope of the curved portion at x=3 looks like it might be zero, suggesting a polynomial function instead of an exponential function.

We note that the change in the value of y=x^2 as x goes from 0 to 1 is 1, then as x goes from 1 to 2, it is 4-1 = 3 — 3 times the change in the first interval. This suggests a quadratic function that has been scaled by a vertical factor of -3, and had its vertex moved to (3, 12). Such a function is described by ...

y = -3(x -3)² +12

Then the graph is modeled by a piecewise function, defined as a line for x < 3, and as a quadratic curve for x > 3. Since the function is continuous at x=3, we can put "or equal to" signs on either or both of these boundaries. We choose to write it as ...

f(x) = (8/3)x +4, x ≤ 3; -3(x -3)² +12, x > 3.

____

The graph of our function is attached. It substantially matches the given graph.

Answer:

C. 1.4x + 1.8y = 79.8

x + y = 53

Step-by-step explanation:

The problem statement gives rise to two equations, one for the amount of money made, and one for the number of items sold. If x and y represent the numbers of items, and if 53 items were sold, then one of the equations will be ...

x + y = 53

This is sufficient to let you choose the correct answer.

___

Since "x" items were sold for $1.40 and "y" items were sold for $1.80, the sales revenue will be the sum of products of price and quantity:

1.40x +1.80y = 79.80

This confirms the choice of answer.

Answer:

0

Step-by-step explanation:

f(x) = -3x^2 + 6x

Let x=2

f(2) = -3*(2)^2 + 6(2)

       =-3(4) +12

      = -12+12

     =0

Answer:

Step-by-step explanation:

The easiest way for me to answer your question is just to do it. If we agree, all well and good. If we don't, then you have the way I did it.

A = (4.75*x + 125)/10000

A = (4.75*10000 + 125) / 10000

A = (47500 + 125) / 10000

A = 47625/10000

A = 4.76

So it looks like we both think it is A.

The question is deceptive because the 125 is really quite small compared to 47500.

Answer:

A. $4.76

Step-by-step explanation:

This case is fairly typical of average cost problems. There is some fixed cost that is amortized over the number of T-shirts produced, and there is some variable cost associated with each item.

Here, if you divide out the equation, you get ...

A = 4.75 + 125/x

Then for x=10,000, the value of A is ...

A = 4.75 +125/10,000 = 4.75 +0.0125 ≈ 4.76

_____

Once you see that the fixed cost of $125 is divided by 10,000, you can look for an answer choice that is very slightly higher than $4.75.

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point

We have the equation:

[tex]y-5=-\dfrac{2}{3}(x+9)\\\\y-5=-\dfrac{2}{3}(x-(-9))[/tex]

Therefore we have

the slope m = -2/3

and the point (-9, 5)

A slope

[tex]m=\dfrac{rise}{run}[/tex]

rise = -2

run = 3

From the point (-9, 5) ⇒ 2 units down and 3 units to the right.

Answer:

x = 61

Step-by-step explanation:

Supplementary angles add to 180°, so we have ...

(2x) + (x -3) = 180

3x = 183 . . . . . . . . . add 3

x = 61 . . . . . . . . . . . divide by 3

The value of x is 61.

_____

The angles are m∠P = 122°, m∠Q = 58°. Their sum is 180°.

Answer:

60

Step-by-step explanation:

<H + <T = 180

2x+ 60 + x + 30 = 180

3x + 90 = 180

3x = 90

 x = 30

<T = x + 30 = 30 + 30 = 60

Answer

<T = 60

Answer:

Step-by-step explanation:

In the attached spreadsheet, I elected to model each shot of each game. The model only covers 50 games, so cannot give the desired probability with much accuracy.

The cell that models the outcome of a shot has the formula ...

  =IF(RAND()<=0.3;1;0)

The RAND() function in this NeoOffice spreadsheet program returns a number uniformly distributed between 0 and 1. We have elected to make numbers of 0.30 or less correspond to shots that are made. (On average, 30% of shots are made.) Each line of 20 shots models one game.

Column B adds the "Shot Successful" numbers to determine the total number of successful shots in that game. Cell B53 finds the total number of games with at least 7 shots made, and divides that number by 50 to find the probability of making 7 or more shots in a game.

I suspect one would need to model several thousand games to determine the probability with any confidence. (The probability based on the binomial distribution is about 0.392. A few different simulations (recalculating the spreadsheet) have given results ranging from 0.24 to 0.62.)