Which inequality statement describes the two numbers on a number line? "−13 and a number 18 units to the right of −13"
A) −13 < 5
B) −13 > 5
C) −13 > 18
D) −13 < 18

The expectation is -$9.6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.

Expected winning per ticket :

Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket

= 1 + 1.2 + 0.6 + 1 - 7

= 3.8-7

= -$3.2

Expected winning if 3 tickets are purchased :

3 × (-3.2) = -$9.6

Hence, the expectation is -$9.6

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The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)  is 2x+y = -2.

The line between these locations' slopes must equal the negative reciprocal of the bisector's slope. It must go through the segment midway.

The slope of the line through the given points :

m = (y2 -y1)/(x2 -x1) = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2

Then, The slope of the required bisector:   m = -1/(1/2) = -2

The midpoint of the given segment:

((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)

Then the point-slope form of the equation of the bisector:

y -y1 = m(x -x1)

y -2 = -2(x -(-2))

y = -2x -4 +2

y = -2x -2 . . . . . . . slope-intercept form equation

2x +y = -2 . . . . . . .standard form equation

Thus, The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5)  is 2x+y = -2.

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Answer:

25

Step-by-step explanation:

its needs to be under 90

Answer:

Explanation:

A triangle's three interior angles will add up to

180

∘

. Since it's a right angle, that means one angle is

90

∘

and the other is given as

15

∘

.

Therefore,

90

+

x

+

15

=

180

So

x

=

180

−

90

−

15

x

=

75

The acute angle is

75

∘

.

B = (2a + 11)/5 is an expression for b when expressed in terms of a.

What exactly are slopes and lines?

We are aware that lines might have several kinds of equations; the typical form is

The equation of a line in slope-intercept form is Ax + By + c = 0, and

y = mx + b.

m is the slope, and b is the y-intercept.

The y-intercept, or (0,b), is the point where the line crosses the y-axis when x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.

Given:

Coordinates of point Q = (2,3)

Coordinates of point R = (a,b)

The equation of the line is 5x + 2y = 9 ⇒ 2y = - 5x + 9

Therefore, y = (-5/2)x + 9/2.

We know slope m = (y2 - y1) / (x2 - x1)

∴ m = (b - 3)/(a - 2).

∴ (2/5) = (b - 3).(a - 2).

2(a - 2) = 5(b - 3).

2a - 4 = 5b - 15.

2a + 11 = 5b.

b = (2a + 11)/5.

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Answer:

(y-x=1.75)×2

2y-2x=3.5

2y-2x+4x-2y=3.5+4

2x. =7.5

X=3.75

y-x=1.75,

y. =1.75+3.75

y=5.5

Answer:

x=3

Step-by-step explanation:

Since the altitude of this triangle is at the midpoint of the base,

It is a isosceles triangle making MJ=MK

9x-18=3x

6x-18=0

6x=18

x=3

Answer: 624

Step-by-step explanation:

12 times 8 is 96 and 96 divided by 2 is 48 and 48 times 13 is 624

Answer:

hhhhhhhhhhhhhhhh hhhhhhhhhhh

Step-by-step explanation:

hhhhhhhhh hhhhhhhhh hhhhhhh hhhhhh

Answer:

yes

Step-by-step explanation:

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be 0 or 1 . In this case, The degree of f(x)=2x−3 f ( x ) = 2 x - 3 is 1 , which makes the function a linear function.

Answer:

-2, 4

-1, -2

0, 0

1, 2

2, 4

Step-by-step explanation:

X. Y

-2 = 4

-1 = 2

0 = 0

1 = -2

2 = -4

Answer:

It appears that the solution set of the inequality 5n + 1.5 ≥ 4 is the set of all real numbers greater than or equal to -0.3. This can be determined by looking at the graph and noting that the region to the right of the vertical line x = -0.3 is shaded, which indicates that all values of x in that region are included in the solution set.

To verify this, we can substitute -0.3 into the inequality in place of n to see if the inequality is satisfied:

5(-0.3) + 1.5 ≥ 4

This simplifies to:

-1.5 + 1.5 ≥ 4

Which further simplifies to:

0 ≥ 4

Since this is not true, -0.3 is not a solution of the inequality. However, all values of x that are greater than or equal to -0.3 are solutions, as indicated by the shaded region on the graph.

Step-by-step explanation:

Answer:

The distance of the boat from B is approximately 9.4 miles

Step-by-step explanation:

The location of light house B from A = 9 miles west

The distance of the boat from A = 4 miles

The bearing of the boat from A = NE65

We have;

4/(sin25) = 9/sin(B)

sin B = 9*sin(25)/4

B ≈ 71.969

a² = 4² + 9² - 2 × 4 × 9 × cos(180 - 25 - 71.969) ≈ 88.264

The distance of the boat from B, a ≈ √88.264 ≈ 9.4

Answer:

The cost for 1 pizza is $8.99

Step-by-step explanation:

We know

Natalia paid a total of 38.95 for 3 pizzas and a salad

A salad = $11.98

We first find the total cost of 3 pizzas by

38.95 - 11.98 = $26.97

$26.97 is the cost for 3 pizzas; to find the cost of 1 pizza, we take

26.97 divided by 3 = $8.99

So, the cost for 1 pizza is $8.99

Answer:

The cost of 1 pizza is $8.99.

Step-by-step explanation:

Let

[tex]t[/tex] = total price

[tex]p[/tex] = pizzas

[tex]s[/tex] = salads

Natalia bought 3 pizzas and 1 salad

[tex]38.95=3p+1s[/tex]

We are given the price of the salad.

[tex]38.95=3p+11.98[/tex]

Now we can find the cost of 1 pizza.

Lets solve for [tex]p[/tex].

Subtract 11.98 from both sides of the equation.

[tex]26.97=3p[/tex]

Divide both sides of the equation by 3.

[tex]p=\frac{26.97}{3}\\p=8.99[/tex]

Answer:

A

Step-by-step explanation:

Radius = 8

Volume = (pi)r^2(h)

Volume = (pi)8^2(7)

Answer:

Step-by-step explanation:

line given is x-y+1= 0

you can rewrite it in slope intercept y=mx+b where m is the slope, and b is the y-intercept where the line meets the y-axis

x-y+1 =0 subtract x and 1 from both sides of the equation

-y = -x-1 multiply both sides by -1

y = x+1 so the slope of this line is 1 and the y-intercept is 1

If you draw this line you can see that there are actually 2 lines that form 45° angles with y=x+1 and pass through (-1, 2), one is vertical x= -1 and one horizontal y =2

Answer:

a) 35/8

b) 7/3

c) 27/5

Step-by-step explanation:

Answer:

a) 35/8

b) 7/3

c) 27/5

Step-by-step explanation:

*to solve multiply the whole number by the denominater and add that total with the numerator, keep the denominater the same

a)

[tex]4 \frac{3}{8} [/tex]

[tex] \frac{32 + 3}{8} = \frac{35}{8} [/tex]

b)

[tex]2 \frac{1}{3} [/tex]

[tex] \frac{6 + 1}{3} = \frac{7}{3} [/tex]

c)

[tex]5 \frac{2}{5} [/tex]

[tex] \frac{25+ 2}{5} = \frac{27}{5} [/tex]

The number of nonzero letters that will see Ash and Bea's engraving prices being the same, is  25 letters

The formula for the cost to engrave with Ash, given that the number of letters engraved is x, would be :

= Flat fee + Cost per letter x Number of letters after 21 letters

= 1. 50 + 0. 08 x

The formula for the cost to engrave with Bea, given that the number of letters engraved is x, would be :

= Flat fee + Cost per letter x Number of letters after 15 letters

= 1. 60 + 0. 07 x

Equating these equations together will show the number of letters :

1. 50 + 0. 08 x = 1. 60 + 0. 07 x

0. 08 x - 0. 07 x =  1. 60 - 1. 50

0. 01 x = 1. 10

x = 0. 10 / 0. 01

x = 10 letters

Number of non zero number of letters would be 25 letters :
= 15 + 10

= 25 letters

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Answer:29,697

Step-by-step explanation: multiply 57x521 and you get 29,697

The value 8 is a numerical value that represents the quantity of eight. It is the natural number following seven and preceding 9. It is an even number and can be written as the sum of two squares: 8 = 3^2 + 2^2 = 4^2. In binary, it is 1000.

Eight is in the first position and has a place value of 8. Understanding the place value of digits in numbers aids in number comparison. It also aids in the composition of numbers in their enlarged form. For example, the extended version of the previous number, 13,548, is 10,000 + 3,000 + 500 + 40 + 8.

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Answer:

6 x 3 = 18, 18 x 2 = 36

9 x 3 = 27, 27 x 2 = 54

6 x 9 = 54, 54 x 2 = 108

Add all given areas:

108 + 54 + 36 = 198 cm^2 is your answer.

Answer:

198 is surface area

Step-by-step explanation:

length = 6

width = 9

height = 3

use the formula

2(wl+hl+hw )

2(54+ 18+ 27)

99x2 =  198

The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² = [tex](10 \sqrt{34})^2 \\[/tex]

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

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The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.

When two or more lines in a plane cross one another, they are referred to as intersecting lines. The common point shared by all intersecting lines is the point of intersection, which can be found on all of them.

The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Let speed of Car 1 = x mph

Speed of car 2 = (x + 10) mph

Hence,

OA = Distance travelled by car2 in 2 hours

⇒ OA = (x + 10) × 2 = 2x + 20

And, OB = Distance travelled by Car 1 in 2 hours

⇒ OB = x × 2 = 2 x

Now, In ΔOAB, OA² + OB² = AB²

substitute the values in the above equation

⇒  (2 x+20)² + (2 x)² =

⇒  4x² + 400 + 80x + 4x² = 3400

simplifying the equation

⇒ 8x² + 20x - 3000 = 0

⇒ x² + 10x - 375 = 0

⇒ x² + 25x - 15x - 375 = 0

simplifying the above equation, we get

⇒ x(x + 25) - 15(x + 25) = 0

⇒ (x + 25)(x - 15) = 0

⇒ x + 25 = 0, x - 15 = 0

⇒ x = -25, x = 15

Since speed can not be negative.

Hence, x = 15 mph

⇒ x + 10 = 15 + 10 = 25 mph.

Hence, speed of car moving towards south =15 mph.

And, speed of (as moving towards East = 25 mph.

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Answer:

AC ≈ 10.3

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{AC}{9.3}[/tex] ( multiply both sides by 9.3 )

9.3 × tan48° = AC , then

AC ≈ 10.3 ( to 3 sf )

Answer:

I think the third option

Step-by-step explanation:

Have a nice day! Hope this helps! Owa Owa!!!!

So x = 2.1 is the only possible value of x that makes the equation true.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The equation is given as follows:

-3x + 6.3 = 0

To find the value of x, we need to isolate x on one side of the equation. We can do this by adding 3x to both sides:

-3x + 3x + 6.3 = 0 + 3x

6.3 = 3x

Now we can divide both sides by 3:

x = 6.3/3

x = 2.1

So x = 2.1 is the only possible value of x that makes the equation true.

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Answer:

9(8d + 9)

Step-by-step explanation:

Since 72 and 81 are both divisible by 9, we can factor out a 9 from the expression:

72d + 81

9(8d + 9)

So, the factored expression is 9(8d + 9)

Answer:

between 49-55.

Answer:

117

Step-by-step explanation:

The figure is five sided, therefore the sum of the angles = (5-2)180

                                                                                             = 3*180

                                                                                             = 540

113 + 123+97+90(since its right angles)+y(unknown) = 540

423 + y = 540

y = 540 - 423

y = 117

Let the angle vertically opposite to y be z

y = z (vertically opposite angles)

z = 117

x = 117 (Corresponding angles are equal)

Hope u understand.

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if r(x) = x² and r(x) = 4, then the value of x = ± 2

Equal means same in all aspects, whereas equivalent means similar but not identical. For example, 2 is said to be equal to 2 but equivalent to 1 + 1.

For example y = x+5 and the same y = 2x+7

then we can say that x+5 Is also equal to 2x+7

2x+7 = x+5

then x = -2

similarly r(x) = x²

thesame r(x) = 4

this means that x² = 4

solving for x

we find the square root of both sides

√x² = √4

x= ±2

It is ± because square root value as two possible values of either both positive or both negative.

Therefore the value of x is ±2

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