Select the correct option.
In a game, bonus points are awarded based on the number of the level that is cleared. The bonus points are calculated by a function
that is 15 times the cube root of the level cleared and rounded to the closest integer value.
Which of the following options represents the bonus points scored as the levels advance?

Answer: A).  A Blue, then a Red.

     = 4/8 * 1/7

     = 1/14

B). A Red, then a White.

     = 1/7 * 3/8

     = 3/56

C). A Blue, then a Blue, then another Blue.

   = 4/8 * 3/7 * 2/6

   = 1/14

Step-by-step explanation:

had to complete the question first.

Find the following probabilities of Derek drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn.

(a) A Blue, then a Red =  

(b) A Red, then a White =  

(c) A Blue, then a Blue, then a Blue =  

given data:

blue marble = 4

white marble = 3

red marble = 1

total marble = 8

solution:

probability of drawing

A).  A Blue, then a Red.

     = 4/8 * 1/7

     = 1/14

B). A Red, then a White.

     = 1/7 * 3/8

     = 3/56

C). A Blue, then a Blue, then another Blue.

   = 4/8 * 3/7 * 2/6

   = 1/14

Answer:

6.64 ft²

Step-by-step explanation:

Given the above triangle with 2 sides of lengths 3.2 ft and 4.7 ft respectively, and angle 62° in between, the following formula can be used to calculate the area: ½*a*b*sin(θ).

Thus, a and b are the 2 given sides and θ is the included angle in between both sides.

Therefore,

Area = ½*3.2*4.7*sin(62)

Area = ½*15.04*0.88295

Area = ½*13.279568

Area = 6.639784

Area = 6.64 ft² (to the nearest hundredth)

Answer: 6

Step-by-step explanation:

If we call each team, A, B, C and D, each team has to play each other team once. Let's call each pairing between 2 teams the 2 teams' letters next to each other, e.g. AB is A playing against B. A has to play against B, C and D so we have AB, AC and AD. So we have 3 so far.

We have already counted that B is playing A but we haven't counted B playing C and D yet so we also have BC and BD. So we have 5 in total

Lastly, C needs to play D, we have already counted C playing B and C playing A so we have CD left. In total that gives 6.

Now we have already included D playing every other team so we don't include any other pairings.

In total, now every team has played every other team giving a total of 6.

(another way of solving this is doing "3!2 but if you haven't learnt factorials yet stick to the first method.

Answer:

6 games.

Step-by-step explanation:

The answer is the number of combinations of 2 from 4

= 4*3 / 2*1

= 6.

Answer:

The height of the right circular cylinder is 14/√3 and its radius is 7√6/3.

Step-by-step explanation:

Check the attachment for the diagram.

The volume of a right circular cylinder =  πr²h

r is the radius of the cylinder

h is the height of the cylinder

V = πr²h... 1

From the diagram, we can use Pythagoras theorem on the right angled triangle to get r². From the triangle P² = r²+(h/2)²

P is the radius of the sphere.

P = 7

7² = r²+(h/2)²

r² = 49-(h/2)²... 2

Substituting equation 2 into 1:

V = π(49-(h/2)²)h

V = π(49h-h³/4)...3

To get the height h of the cylinder, we need to differentiate the volume of the cylinder with respect to h and equate to zero. i.e dV/dh = 0 since it's the maximum volume.

dV/dh = π(49-3h²/4)

0 = π(49-3h²/4)

Dividing both sides by π

0/π = π(49-3h²/4)/π

49-3h²/4 = 0

49 = 3h²/4

3h² = 49×4

3h² = 196

h² = 196/3

h = √196/√3

h = 14/√3

To get the radius of the cylinder, we will substitute h = 14/√3 into equation 2

r² = 49-(h/2)²

r² = 49-{(14/√3)/2}²

r² = 49-{14/2√3}²

r² = 49-(7/√3)²

r² = 49 - 49/3

r² = (147-49)/3

r² = 98/3

r = √98/√3

r = √49× √2/√3

r = 7√2/√3

r = 7√2/√3 × √3/√3

r = 7√6/3

The height of the right circular cylinders is 14/√3 and its radius is 7√6/3.

Answer:

9 and 18

Step-by-step explanation:

2x and x are the numbers

1/x-1/2x=1/18

2/2x-1/2x=1/18

1/2x=1/18

2x=18X=9,

2x=18

The two integers are 9 and 18

Step-by-step explanation:

1/a = 1/b + 1/c

Multiply both sides by a.

1 = a/b + a/c

Multiply both sides by b.

b = a + ab/c

Multiply both sides by c.

bc = ac + ab

Subtract ab from both sides.

bc − ab = ac

Factor b.

b (c − a) = ac

Divide both sides by c − a.

b = ac / (c − a)

Answer:

see below

Step-by-step explanation:

1/a = 1/b+1/c

Multiply each side of the equation by a

a( 1/a) =a( 1/b+1/c)

1 = a/b + a/c

Then multiply each side of the equation by b

b*1 =b( a/b + a/c)

b = a + ab/c

Then multiply each side of the equation by c

cb = c( a+ ab/c)

bc = ac + ab

We have gotten rid of the fractions

Now we can solve for a

Factor out a on the right side

bc = a( c+b)

Then divide by c+b on each side

bc / ( c+b) = a ( c+b) / ( c+b)

bc / ( c+b) = a

Now we can solve for b

bc = ac + ab

Subtract  ab from each side

bc -ab = ac + ab-ab

bc -ab = ac

Factor out b on the left side side

b( c-a) = ac

Then divide by c-a on each side

b( c-a) / ( c-a) = ac / ( c-a)

b  = ac/ ( c-a)

We can factor out -1

b = -ac/( a-c)

Answer:

Yes

Step-by-step explanation:

Well the integer (-1, -1) means x = -1 and y = -1

So we can plug this into the equation

-1 = 3(-1) + 2

-1 = -3 + 2

-1 = -1

So yes (-1, -1) is a solution.

Answer:

[tex]1.49S + 4.39B \leq 20[/tex]

Step-by-step explanation:

The options are not given; However, the question can be solved without the list of options

Given

Let S represent packs of Streamers

Let B represent packs of  Balloons

Required

Represent this with an inequality

From the question, we understand that;

[tex]1S\ =\ \$1.49\ and\ \ 1B\ = \ \$4.39[/tex]

Also, it's stated that Aracely can't spend more than $20;

This mean that the maximum Aracely can spend is $20 and it can be represented with the inequality sign [tex]\leq 20[/tex]

Bringing them together;

[tex]1.49S + 4.39B \leq 20[/tex]

Answer:

19*25= 475

Step-by-step explanation:

You can either use a calculator or use the standard operation

Answer:

9/49 or 0.184

Answer:

9/49

Step-by-step explanation:

(6/7)² × (1/2)²

Distribute the square to the fractions.

6²/7² × 1²/2²

36/49 × 1/4

Multiply.

36/196

Simplify.

9/49

Answer:

Step-by-step explanation:

The surface area of a cone is:

● Sa = Pi*r^2 +Pi*r*l

r is the radius and l is the slant heigth

The diameter of this cone is 12 inches so the radius is 6 (12/2=6).

●Sa = Pi*36 +Pi*6*10

●Sa = 301.59 in^2

Answer:

pi (6) * 10+ pi ( 6)^2

Step-by-step explanation:

The surface area of a cone is given by

SA =  pi rl +pi r^2  where r is the radius and l is the slant height

We know the diameter is 12 so the radius is 12/2 = 6

SA =  pi (6) * 10+ pi ( 6)^2

Answer:

The mean is defining the average length(2.5in) of the 100 measured screws.

Step-by-step explanation:

The mean is usually calculated in order to determine the average of a set of values.

Answer:

0, 22, 44, 66

Step-by-step explanation:

Given the equation for the model, [tex] d = 11t [/tex] , you can complete the table above by simply plugging in each value of "t" has given in the table to solve for "d".

*When t (seconds) = 0, distance (feet) would be:

[tex] d = 11(0) [/tex]

[tex] d = 0 [/tex]

*When t (seconds) = 2, distance (feet) would be:

[tex] d = 11(2) [/tex]

[tex] d = 22 [/tex]

*When t (seconds) = 4, distance (feet) would be:

[tex] d = 11(4) [/tex]

[tex] d = 44 [/tex]

*When t (seconds) = 6, distance (feet) would be:

[tex] d = 11(6) [/tex]

[tex] d = 66 [/tex]

Answer:

The answer is d

Step-by-step explanation:

h(3.2) represents the height of the rock 3.2 seconds after it is propelled.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given a function,

h(t) = -16t² + 28t + 500

Here t represents the time after it is propelled.

h(t) represents the height of the rock t seconds after it is propelled.

So, h(3.2) represents the height of the rock 3.2 seconds after it is propelled.

Hence the correct option is D.

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Answer:

[tex]\boxed{\frac{x^2 }{8} }[/tex]

Step-by-step explanation:

The quotient is the result from division.

Let x be that number.

Division between x² and 8.

[tex]\frac{x^2 }{8}[/tex]

The algebraic expression representing the quotient of a number squared and eight is x²/8.

An algebraic expression is a combination of terms formed using mathematical operators (+, -, *, /). The terms are made by the combination of variables and constants.

In the question, we are asked to write an algebraic expression that represents the quotient of a number squared and eight.

We know that an algebraic expression constitutes both variables and constants.

We assume the number in the expression to be x.

The number squared is then represented by x².

The quotient of the number squared and eight can be represented as x²/8.

Therefore, the algebraic expression representing the quotient of a number squared and eight is x²/8.

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Answer:

3 pairs

Step-by-step explanation:

Top and Bottom

Front and Back

Side and Side.

Cereal Boxes have 6 sides

Answer:

1). x = 2

2). x = -10

3). x = [tex]-\frac{2}{5}[/tex]

4). x = 10

Step-by-step explanation:

1). x - 6 = -4

  (x - 6) + 6 = -4 + 6 [By adding 6 to both the sides of the equation]

  x = 2

2). x + 3 = -7

  (x + 3) - 3 = -7 - 3 [By subtracting 3 to both the sides of the equation]

  x = -10

3). 5x = -2

   [tex]\frac{5x}{5}=\frac{-2}{5}[/tex] [By dividing with 5 from both the sides of the equation]

   x =  [tex]-\frac{2}{5}[/tex]

4). 0.5x = 5

   [tex]\frac{0.5x}{0.5}=\frac{5}{0.5}[/tex] [By dividing with 0.5 from both the sides of the equation]

   x = 10

Answer:

15 feet

Step-by-step explanation:

We have 2 similar right triangles with legs height and length of shadows.

height of men : length of shadows of the man = height of tree : length of shadows of the tree

5 : 8 = x : 24

8x = 5* 24

x = 5*24/8 = 15 (feet)

Answer:

15ft

Step-by-step explanation:

5 ft  is to 8 ft

A ft is to  24 ft

A = 24*5/8

A = 15ft

15ft

[tex] v = \sqrt{4900} + \sqrt{8100} = 70 + 90 = 160[/tex]

Answer: D. 160

Answer:

B. edge 2021

B. is correct for the next one too.

Step-by-step explanation:

B. is the correct answer for the first one
B. is also the correct answer for the second one

Answer:

what do you need help with its not really clear

Answer

1. 48 2. 308

Step-by-step explanation:

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The given line passes through the points (-4, -3) and (4, 1).

What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (-4, 3)?

a) y - 3 = -2(x + 4)

b) y - 3= - (x + 4)

c) y - 3 = (x + 4)

d) y - 3 = 2(x + 4)

Answer:

The equation of the line that is perpendicular to the given line and passes through the point (-4, 3) is

a) y - 3 = -2(x +4)

Step-by-step explanation:

First of all, we will find the slope of the given line.

We are given that the line passes through the points (-4, -3) and (4, 1)

[tex](x_1, y_1) = (-4,-3) \\\\(x_2, y_2) = (4,1) \\\\[/tex]

The slope of the equation is given by

[tex]$ m_1 = \frac{y_2 - y_1 }{x_2 - x_1} $[/tex]

[tex]m_1 = \frac{1 -(-3) }{4 -(-4)} \\\\m_1 = \frac{1 + 3 }{4 + 4} \\\\m_1 = \frac{4 }{8} \\\\m_1 = \frac{1 }{2} \\\\[/tex]

Recall that the slopes of two perpendicular lines are negative reciprocals of each other.

[tex]$ m_2 = - \frac{1}{m_1} $[/tex]

So the slope of the other line is

[tex]m_2 = - 2[/tex]

Now we can find the equation of the line that is perpendicular to the given line and passes through the point (-4, 3)

The point-slope form is given by,

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

Substitute the value of slope and the given point

[tex]y - 3 = -2(x -(-4) \\\\y - 3 = -2(x +4)[/tex]

Therefore, the correct option is (a)

y - 3 = -2(x + 4)

The equation of the line in point-slope form is y - 3 = -2(x + 4)

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the y intercept.

The line passes through the point (-4, -3) and (4, 1). Hence:

Slope = (1 - (-3)) / (4 - (-4)) = 1/2

The slope of the line perpendicular to this line is -2 (-2 *  1/2 = -1).

The line passes through (-4, 3), hence:

y - 3 = -2(x - (-4))

y - 3 = -2(x + 4)

The equation of the line in point-slope form is y - 3 = -2(x + 4)

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Answer:

0.95988 (Accuracy of the test )

Step-by-step explanation:

To determine the accuracy of this test we have to list out the given values

Prevalence rate of the disease = 0.3% = 0.003

sensitivity rate of the disease = 92% = 0.92

specificity rate for the test = 96% = 0.96

The accuracy of the test can be found using this equation

Accuracy = sensitivity * prevalence + specificity ( 1 - prevalence )

                = 0.92 * 0.003 + 0.96 ( 1 - 0.003 )

                = 0.00276 + 0.95712

                = 0.95988

Answer:

0

Step-by-step explanation:

An integer is colloquially defined as a number that can be written without a fractional component.

-3/4 ---- It is a fraction itself, so it is a fractional component

0 ---- Has no fractional component

2.3 Pi ---- Pi is irrational and is a decimal, so is 2.3. Most of this is a fractional component already.

The only one we can't eliminate using just the definition is 0.

Hope that helps, tell me if you need a further explanation

From the given numbers the number that is an integer is 0. The correct option is B.

An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.

Given the following numbers -(3/4), 0, 2.3, and π. Therefore, from the given numbers the number that is an integer is 0.

Hence, From the given numbers the number that is an integer is 0.

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Answer:

The volume of sphere is 267.95 units³.

Step-by-step explanation:

Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :

[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]

[tex]let \: r = 4[/tex]

[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]

[tex]v = \frac{4}{3} \times \pi \times 64[/tex]

[tex]v = \frac{256}{3} \times 3.14[/tex]

[tex]v = 267.95 \: {units}^{ 3} [/tex]

Answer:

Reject the null hypothesis

Step-by-step explanation:

The claim is H0:p=0.35 Ha:p>0.35

At a significance level of 0.05, if the p value observed is less than 0.05, then we reject the null hypothesis, but if the p value observed is greater than the null hypothesis, then we fail to reject the null hypothesis.

In this case study: the p value is 0.03 which is less than the significance level, this we will reject the null hypothesis and conclude that there is enough statistical evidence to prove that the proportion of snoring events compared to other events during a sleep study is more than 35%.

Answer:

shadow cow

Step-by-step explanation:

In new estimate cost of labor and material is 35,700 and 12,300 respectively.

Reduction Factor means the percentage obtained by dividing the Net Worth Shortfall Amount by the Required Net Worth Amount.

According to the question

A contractor originally estimated the total cost of a job including labor and materials at $ 57,000.

let  Labor cost = l

     Material cost = m

Now ,

l + m = 57000 ----------(1)

A new estimate of $ 48,000 is made, reducing the labor cost by 15% and the material cost by 18%.

i.e,

[tex]\frac{(100-15)}{100} l + \frac{(100-18)}{100} m = 48000[/tex]

[tex]\frac{(85)}{100} l + \frac{(82)}{100} m = 48000[/tex]

0.85l + 0.82m = 48000  --------------------------------(2)

multiplying equation (1) from 0.85

0.85l + 0.85m = 48450   -------------------------------(3)

subtracting equation (1) and (3)

0.85l + 0.85m = 48450

-0.85l -0.82m = -48000

0.03m=450

m = 15000 (old cost )

new cost of m is = 0.82 * 15000 =12,300

putting value of m in equation (1)

l + m = 57000

l + 15000 = 57000

l = 42000   (old cost)

new cost of l is = 0.85l  = 0.85*42000

new cost of l is =  35,700

Hence, The new cost of labor is 35,700 and new cost of material is 12,300 .

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Answer:

see below

Step-by-step explanation:

Addition and subtraction are both closed under polynomials.

That means that when we add and subtract polynomials, we will end up with a polynomial

f(x) + g(x) will =  always be a polynomial when we start with polynomials

f(x) - g(x) will =  always be a polynomial when we start with polynomials

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients.

[tex]f(x)[/tex] and [tex]g(x)[/tex] are polynomial functions.

Adding polynomials and subtracting polynomials is essentially combining like terms of polynomial expressions.

[tex]f(x)+g(x)[/tex] is always a polynomial

[tex]f(x)-g(x)[/tex] is always a polynomial

If you add, subtract or multiply any two polynomials then the result will be always a polynomial.