In your math class, there are 8 boys and 11
girls. What is the ratio of boys to total
students?

Answer:

A

Step-by-step explanation:

Use the Pythagorean Theorem: a^2 + b^2 = c^2

The cable will be the hypotenuse, so c = 11.3 m

One leg is the distance of the anchor, so a = 4.2 m

(4.2)^2 + b^2 = (11.3)^2

17.64 + b^2 = 127.69

Subtract 17.64 from both sides

b^2 = 110.05

Square root both sides

b = ~10.5 m

The highest common factor is [tex]\boxed{y}[/tex].

Answer: [tex]x=-\frac{5}{4}[/tex] and [tex]x=-2[/tex]

Step-by-step explanation:

To factor an equation in the form of [tex]ax^2+bx+c[/tex] you need to find the value of [tex]ac[/tex]. So first solve for that

[tex](4)(10) = 40[/tex]

Now we need to find two numbers that add up to b and multiply together to make ac. In this case those numbers are 5 and 8 since 5+8=13 and (5)(8)=40

Now split 13x into 5x+8x and solve by grouping

[tex]4x^2+5x+8x+10\\(4x^2+5x)+(8x+10)[/tex]

Factor out the GCF in each quantity

[tex](4x^2+5x)+(8x+10)\\x(4x+5)+2(4x+5)[/tex]

Now group x+2 together

[tex](x+2)(4x+5)[/tex]

Finally, set each factor equal to 0 and solve for x

[tex]x+2=0\\x+2-2=0-2\\x=-2\\\\\\4x+5=0\\4x+5-5=0-5\\4x=-5\\\frac{4x}{4} =\frac{-5}{4} \\x=-\frac{5}{4}[/tex]

The number of minutes of the ride that are spent higher than 22 meters above the ground is; 2.64 minutes

We are given;

bottom of the Ferris Wheel is 4 meters off the ground.

Radius = diameter/2 = 24/2; r = 12 meters.

Thus, the center of the Ferris Wheel is 4 + 12 = 16 meters off the ground.

A horizontal line through the center of the Ferris Wheel is 16 meters off the ground, and therefore the lower half of the Ferris Wheel is always below 22meters.

The distance from the horizontal to 22 meters is 22 - 16 = 6 meters.

The angle between the horizontal and a radius to 22 meters is;

sin(θ) = 6/16

θ = sin⁻¹(6/16)

θ = 22.02°.

This angle height is on both sides of the Ferris Wheel and as such;

180° + (2 * 22.02) = 224.04° is always under 16 meters.

Thus, what is above 16 meters is 360° - 224.04° = 135.96°

Since it takes 7 minutes for 1 revolution, then the amount of time the Ferris Wheel is above 16 meters is;

(135.96/360) * 7 min ≈ 2.64 minutes

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Use the Pythagorean theorem.

The figure is given in the below diagram.

The steps of constructing a square inside a circle are as follows:

Start from the middle O of the provided circle.

Finding the center of a circle's approach can be used to create the center of the circle's center point is not known.

1. Draw a circle and label point A. This will turn into one of the square's vertices.

2. Create point C by drawing a diameter line from point A through the center and back out to the outside of the circle.

3. Set the width of the compass to a little bit more than the distance to O.

4. Sketch an arc above and under O.

5. Repeat by moving the compass to C.

6. To create the new points B and D, draw a line across the intersection of the arc pairs that is long enough to touch the circle at both the top and bottom.

This diameter is perpendicular to the first AC.

7. Draw a line connecting each pair of points A, B, C, and D.

Done. The circle is circled by the square ABCD.

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The probability that the number's units digit will be less than 5 is 0.5 that it is equal to 1/2.

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

There are 10 possible digits, 0, 1, 2, ... 9 that make up the 5-digit number made up of integral values.

There are 5 digits that are less than 5 which are 0, 1, 2, 3, and 4 so the probability will be found by taking only those nubers which have unit's place less than 5,

By probability formula , Probability= no. of favourable outcomes/total no. of outcomes

So probability will be found that will be equal to 5/10, or 1/2

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Answer:

x=1/3

Step-by-step explanation:

first multiply both bracket to together and then you get, 9x=3

x=1/3, then sub in to other equation and get the rest answer.

hope it helpful

Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions

Given the log function expressed as:

log(x-3) + logx=1

According to the law of logarithm, addition becomes product to have:

log x(x -3) = log₁₀10

x² - 3x = 10

x² - 3x -10 = 0
x² - 5x + 2x - 10 = 0
x(x-5) + 2(x-5) = 0
(x+2)(x-5)=0

x = -2 and 5

Of Janet’s two solutions, both x=5 and x=-2 are correct because both x=-2 and x=5 are extraneous solutions

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The value of the side c will be 5.56 cm and angle C is 32.49° and angle B is 42.51°.

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

a² + b² – 2ab cos C = c²

Given triangle ABC, A = 105°, a = 10 cm, b = 7 cm.

Then we have

7² + c² – (2 · 7 · c) cos 105° = 10²

c² + 3.62c – 51 = 0

On solving, we have

c = 5.56

Then the angle C will be

10² + 7² – 2 · 7 · 10 · cos C = 5.56²

                149 – 140 cos C = 30.91

                                 cos C = 0.8435

                                        C = 32.49°

We know that

       ∠A + ∠B + ∠C = 180°

105° + ∠B + 32.49° = 180°

                         ∠B = 42.51°

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Answer:

45 dollars for going over 2GB

Step-by-step explanation:

If he pays 25 dollars every month and he goes over 2 GB then he’ll have to pay 20 dollars extra since every GB over cost 10 dollars. The equation is 25+10+10 which equals 45.

An expression is a mixture of terms that are combined by using operations such as subtraction, addition, multiplication, and division. 

The amount when 2 GB is used over the limit in a month is $45.

An expression is a mixture of terms that are combined by using operations such as subtraction, addition, multiplication, and division. 

Example: 2x + 3x2  is an expression.

We have,

Cost of data plan with 2 GB = $25

Cost of one GB = $10

The equation that can be used to find the amount to pay when using x GB over the limit in a month:

= 25 + 10x

The amount when 2 GB is used over the limit in a month:

= 25 + 10 x 2

= 25 + 20

= $45

Thus,

The amount when 2 GB is used over the limit in a month is $45.

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Using the tangent theorem, the length of the radius is: B. 10 units.

According to the tangent theorem, since KL is tangent to the circle, therefore, angle JKL = 90°.

Since the triangle is a right triangle, apply the Pythagorean theorem:

(r+16)² = r² + 24²

r² + 32r + 256 = r² + 576

r² - r² + 32r + 256 = 576

32r + 256 = 576

32r = 576 - 256

32r = 320

r = 320/32

r = 10

The radius is: B. 10 units.

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Answer:

B. 10 Units

Step-by-step explanation:

The coefficient of the variable Q is 36 , Option A is the correct answer.

The complete question is

The coefficient of 2(3)(6)Q is _____. a.36 b.18 c.12

Coefficient is the constant term written in front of  variable in an expression.

The expression given in the question is

2(3)(6)Q

The coefficient is 2 * 3 * 6 = 36

Therefore , the coefficient of the variable Q is 36 , Option A is the correct answer.

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Answer:

155°

Step-by-step explanation:

z = 65° + y

y is a right angle

=> y = 90°

=> z = 65° + 90° = 155°

The value of (abscissa of P) -(abscissa of Q) is -1.

The given coordinates are P(4,6) and Q(5,-7).

We need to find (abscissa of P) -(abscissa of Q).

The horizontal coordinate of a point in a planar Cartesian coordinate system that is determined by measuring parallel to the x-axis is what abscissa stands for.

Now, (abscissa of P) -(abscissa of Q)=4-5=-1

Hence, the value of (abscissa of P) -(abscissa of Q) is -1.

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-5≥

so 8 x -5 = -40 - 16 = -56 and that's the smallest number you can get that will be greater than -64 hope this helps! :)

Answer:

x> -6

Step-by-step explanation:

Drag the -16 to -64. This will change the -16 to a positive 16. Add -64 and 16. The answer is -48. All that should be left is 8x>-48. Now we need to divide -48 and 8 so we can leave x. The answer should be -6 on one side, and x on the other side. x> -6

Answer:

c .26

Step-by-step explanation:

Male AND drama is 124  out of 479 total

124/479 = .26

Answer:

Step-by-step explanation:

-4(5x-3)+12

-20x+12+12

20x+24

my answer is 20x+24.

The simplified form of the given expression -4(5x-3)+12 would be 20x+24.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Given;

-4(5x-3)+12

Open the bracket

-20x+12+12

Solve the like terms;

20x+24

Hence, the simplified form of the given expression -4(5x-3)+12 would be 20x+24.

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g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.

First, a vertical shift of N units is written as:

g(x) = f(x) + N

A horizontal shift of N units is written as:

g(x) = f(x + N).

In this case, we have:

g(x) = f(x + 8) + 4

So g(x) is a shift of 8 units to the left and 4 units of f(x), then the correct statement is B.

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Answer:

length = 10 in, width = 6 in

Step-by-step explanation:

Let the width be x.

Then, length = (x+4)

Area = 60 in²

Area of a rectangle = width × length

60 = x × (x+4)

60 = x² + 4x

x² + 4x - 60 = 0

Splitting the middle term :-

x² + 10x - 6x - 60 = 0

x (x + 10) - 6 ( x + 10) =0

(x + 10) ( x - 6)

x = -10 (doesn't fulfill our requirement)

x = 6

So, width = 6 in

length = 6+4 = 10 in

Answer:

d

By the alternate interior angles theorem,

By the reflexive property, AB is congruent to itself.

Thus, the triangles will be congruent by ASA.

The coordinate of the point P will be (6/5, -7/5). Then the correct option is C.

The complete question is attached below.

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divide the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

Given the points X(-2, 5) and Y(2, -3).

Then the coordinates of the point P on directed line segment XY that partitions segment XY such that the ratio of XP to PY is 4:1.

(x₁, y₁) = (-2, 5)

(x₂, y₂) = (2, -3)

m = 4

n = 1

Then the point will be

x = [4 × 2 + 1 × (-2)] / (4 + 1)

x = 6 / 5

y = [4 × (-3) + 1 × 5] / (4 + 1)

y = -7 / 5

The coordinate of the point P will be (6/5, -7/5).

Then the correct option is C.

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Answer:

When 68.321 rounded to the nearest tenth the result is 68

Answer:

B

Step-by-step explanation:

Cube root of 27 is 3, which is in integer

Answer:

40 dollars

Step-by-step explanation:

Profit is what he earned minus his costs

Profit = 125 -85

Profit = 40

Answer:

52=x-15(being vertically opposite angle)

52+15=x

x=67

The way that the consistency of data is evaluated if more than one data collector is used is; Inter - rater reliability

When researching data about anything, it is pertinent to note that sometimes, we have to use more than one data collector just to get a more thorough result which only one person may not be able to generate.

Now, the way that consistency of data is evaluated when more than one data collector is used is via Inter-rater reliability. This is because Inter-rater reliability is the extent to which two or more raters or observers agree.

The benefit of Inter-rater reliability is that It addresses the issue of consistency of the implementation of a rating system. Inter-rater reliability can be evaluated by using a number of different statistics.

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The value of x is 8/5 or 1.6 when 343ˣ = 49⁴ ⁻ ˣ, using the laws of exponents.

Exponents are of the form aˣ, read as "a to the power of x", and signify the product of a multiplied by itself x number of times.

In the question, we are given that 343ˣ = 49⁴ ⁻ ˣ, and are asked to find the value of x.

We try to solve the exponential equation, using the laws of exponents in the following way:

343ˣ = 49⁴ ⁻ ˣ,

or, (7³)ˣ = (7²)⁽⁴ - ˣ⁾ {Since, 343 = 7³ and 49 = 7²}.

or, 7³ˣ = 7⁸ ⁻ ²ˣ {Using the law: [tex](x^{a})^{b} = x^{ab}[/tex]},

or, 3x = 8 - 2x {Using the law: [tex]x^a = x^b \Rightarrow a = b[/tex], when x ≠ 0}.

or, 3x + 2x = 8 - 2x + 2x {Adding 2x to both sides of the equation},

or, 5x = 8 {Simplifying}

or, 5x/5 = 8/5 {Dividing both sides by 5},

or, x = 8/5 or 1.6 {Simplifying}

Therefore, the value of x is 8/5 or 1.6 when 343ˣ = 49⁴ ⁻ ˣ, using the laws of exponents.

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