A single die is rolled twice. Find the probability of getting a 1 the first time and a 4 the second time.

Josiah and Chana travel at constant and different speeds.

Josiah's head start = 10 meters from the start

Josiah's speed = 2 m/s

Chana's speed = 3 m/s

Expressing the distance traveled as an equation, we have;

D = d + s × t

Where;

D = The distance covered

d = The distance from the starting line the runner starts

s = The speed of the runner

t = The time spent running

For Josiah, we have;

D = 10 + 2•t (line a)

For Chana, we have;

D = 0 + 3•t = 3•t (line b)

The above equations are straight line equations.

The point F is on line a, which shows Josiah distance after 25 seconds which is 60 meters. The corresponding point on line b, Chana's distance after 25 minutes is 75 meters.

Therefore;

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Answer:

Chana's and Josiah's distance from the starting line at the time when Chana catches up with Josiah

Step-by-step explanation:

I got it right on khan.

Answer:

Option A) [tex]\bf{ x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]

Step-by-step explanation:

we have

[tex]\sf{\dfrac{\sqrt[7]{x^{2}}}{\sqrt[5]{y^{3}}}}[/tex]

we know that

[tex]\sf{\sqrt[7]{x^{2}}=x^{\frac{2}{7}}}[/tex]

[tex]\sf{\sqrt[5]{y^{3}}=y^{\frac{3}{5}}}[/tex]

substitute in the expression

[tex]\sf{\dfrac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=x^{\frac{2}{7}}*y^{-\frac{3}{5}}}[/tex]

The percentage of a given number in another implies the fraction of the given number to that other number with respect to 100%. Thus the required expression is: [tex]\frac{m}{100}[/tex] x n

When a given number is written in percentage, it implies that the fraction of the number to the total number in relation to 100%. For example, to determine the percentage of a number r in s, -we have:

[tex]\frac{r}{s}[/tex] x 100%

Therefore in the given question, the required expression is;

m% = [tex]\frac{m}{100}[/tex]

So that;

m% of n can be expressed as;

[tex]\frac{m}{100}[/tex] x n

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Answer:

x = 6

Step-by-step explanation:

We want to find x,

[tex]\frac{3}{5} = \frac{x}{10}[/tex]

to get x alone, we multiple both side by 10

[tex]\frac{3}{5} * 10 = \frac{x}{10} *10[/tex]

[tex]\frac{30}{5} = x[/tex]

30 divided by 5 is 6

Check:

We can see that 5 x ____ = 10 where ____ is 2

5 x 2 = 10

so 3 x 2 = 6

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Answer:

7

Step-by-step explanation:

2 = 2

4 = 2²

6 = 2 * 3

8 = 2³

adding the exponents of 2, we get 1+2+1+3 = 7

The domain of A(r) will be (0, ∞), the inverse function to A(r) will be r = 2π[A(r)]² + 12πA(r), and the radius will be 3.07 inches.

A statement, principle, or policy that creates the link between two variables is known as a function.

A cylinder (round can) has a circular base and a circular top with vertical sides in between.

Let r be the radius of the top of the can and let h be the height.

The surface area of the cylinder (A) is given as

A=2πr² + 2πrh

Part A: Assume that the height of your cylinder is 6 inches.

Consider A as a function of r, so we can write that as

A(r) = 2πr² + 12πr

Then the domain of A(r) will be (0, ∞).

Part B: Continue to assume that the height of your cylinder is 6 inches.

Then the inverse function to A(r) will be

r = 2π[A(r)]² + 12πA(r)

Part C: If the surface area is 175 square inches.

Then the radius will be

                    175 = 2πr² + 12πr

r² + 6r – 27.866 = 0

                        r = 3.07, -9.07

Then the radius will be 3.07 inches.

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Answer:

{(3,-2), (4,-2),(5,-2), (6,-2)}  this relation is not a function.

Answer:

I think so, but maybe if the schools are different they change.

Answer: First step is to determine the total cost

Total cost at 2,800

=$0.80 ×2,800

=$2,240

Total cost at 5,600

=$0.75 × 5,600

=$4,200

Second step is to determine the Variable cost per unit

Variable cost per unit=$4,200-$2,240

Variable cost per unit=$1,960

Variable cost per unit=5,600-2,800

Variable cost per unit=2,800

Variable cost per unit=$1,960/2,800

Variable cost per unit=$0.70

Now let determine the average cost

Average cost=$0.70×4,800+[($0.80×2800)-(2,800 ×$0.70)]

Average cost=$3,360+($2,240-$1,960)

Average cost=$3,360+$280

Average cost=$3,640

Average cost =$3,640/4,800

Average cost=$0.76

In conclusion What will be the average cost to bake 4,800 is $0.76

Step-by-step explanation:

The work done in pushing the box is 64000 lb-ft²/s²

Since person pushing a 40 pound box up an incline that is 30 degrees above the horizontal and 100 feet long, the work done, W is

W = mgh where

So, W = mgh

W = mgLsinФ

So, substituting the values of the variables into the equation, we have

W = mgLsinФ

W = 40 lb × 32 ft/s² × 100 ftsin30°

W = 1280 lb-ft/s² × 100 ft × 0.5

W = 1280 lb-ft/s² × 50 ft

W = 64000 lb-ft²/s²

So, the work done in pushing the box is 64000 lb-ft²/s²

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Answer:2

Step-by-step explanation:

(2x+5)/3 = 3/2

Multiply both sides by 3:

2x + 5 = 9/2

Subtract 5 from both sides:

2x = 9/2 - 5 = 9/2 - 10/2 = 3/2

Divide both sides by :

x = 3/4

Answer:

-1/3

Step-by-step explanation:

A number x is multiplied by 2, then has 3 added to it, then is divided by x+5, and the answer is 3 halves.

Or, as an equation:

[tex] \frac{2x + 3}{x + 5} = \frac{3}{2} [/tex]

Let's cross multiply:

[tex]4(2x + 3) = 2(x + 5)[/tex]

Expand:

[tex]8x + 12 = 2x + 10[/tex]

Now solve:

[tex]6x + 12 = 10[/tex]

[tex]6x = -2[/tex]

[tex]x = \frac{-1}{3} [/tex]

So the answer is -1/3

The required probability is given by 0.012 for the director chooses 4 boy kittens and 3 girl kittens

A TV studio has brought in 6 boy kittens and 8 girl kittens for a cat food commercial.

Probability, can be define as the ratio of favorable events to the n number of total events

The director is going to choose 7 of these kittens at random to be in the commercial. the director chooses 4 boy kittens and 3 girl kittens.

Here, probability of to choose 7 of these kittens at random
= c(14,7)

probability to chooses 4 boy kittens and 3 girl kittens
= c(6,4) x c(8,3)

Required probability = [tex]\frac{c(6, 4) * c(8, 3)}{c(14, 7)}[/tex] = 0.012

Thus, The required  required probability is given by 0.012 for the director chooses 4 boy kittens and 3 girl kittens.

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Answer:

801.5625

Step-by-step explanation:

25.65×100/1.6×2=801.5625

The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.

Simple interest is a method of calculating the interest charge.

Simple interest can be calculated as the product of principal amount, rate and time peroid.

Simple Interest = (Principal × Rate × Time) / 100

The principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years.

Simple Interest = (Principal × Rate × Time) / 100

25.65 × 100/(1.6 × 2 )

= 801.5625

Therefore, the  principal on a savings account with 1.6% interest rate that has earned $25.65 over 2 years will be 801.56 dollars.

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It is false that the midpoint is in quadrant IV

The endpoints are given as:

S (1,4) and T (5,2

The midpoint is

(x, y) = 0.5 *(x1 + x2, y1 + y2)

So, we have:

(x, y) = 0.5 *(1 + 5, 4 + 2)

Evaluate the expression

(x, y) = (3, 3)

The point (3, 3) is located in the first quadrant

Hence, it is false that the midpoint is in quadrant IV

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Answer:

y > 2/3x + 3

Step-by-step explanation:

It is first option because > because shaded above the line and 2/3x is rise/run so 2/3.

+3 is because y-intercept is 3

The system of linear inequalities represented by the graph is the option;

y ≥  (1/3)·x + 3 and 3·x - y > 2

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

The system of linear inequalities are given by the in the question, that

describes the inequalities.

The points on the given graph are;

(3, 4), and (-3, 2)

The slope is; (2 - 4)÷((-3) - 3) = 1/3

The equation is;

y - 4 = (1/3)·(x - 3)

y = (1/3)·x - 1 + 4 = (1/3)·x + 3

Therefore;

The graph is y ≥  (1/3)·x + 3

Point on the second graph are;

(0, -2) and (2, 4)

The slope is; (4 - (-2)) ÷ (2 - 0) = 3

The equation is; y - (-2) = 3·(x - 0)

y = 3·x - 2

The inequality is; y < 3·x -2

Which gives;

2 < 3·x - y

Therefore;

3·x - y > 2

The correct option is the first option;

y ≥  (1/3)·x + 3 and 3·x - y > 2

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Answer:

[tex]-\frac{8\sqrt{2}+2}{15}.[/tex]

Step-by-step explanation:

1) sin(a+b)=sin(a)cos(b)+sin(b)cos(a);

2) if sin(a)=-0.4, then cos(a)=0.8; if cos(b)=1/3, then sin(b)=-√8/3;

3) finally, sin(a+b)=-0.4*1/3-√8/3*0.8=

[tex]=-\frac{8\sqrt{2}+2}{15}.[/tex]

Using proportions, her gross pay is given as follows:

d. $779.10.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Her gross pay is divided as follows:

Hence the total pay is:

33 x 14.70 + 2 x 10 x 14.70 = $779.10.

Which means that option d is correct.

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The equation of the line represented by the table in slope intercept form is; y = ²/₁₅x + 2

The formula for equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The y-intercept will occur when x = 0. Thus, from the table, it is clear hat the y-intercept will be c = 2.

Let us find the slope using the first two points;

m = (2 - 0)/(0 - (-15))

m = 2/15

Thus, the equation is;

y = ²/₁₅x + 2

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The object compresses the spring up to 0.8577m.

Potential Energy is the energy possessed by an object at rest.

The object is falling from the rest and it is assumed that the friction on the ramp is zero and the air resistance is also considered to be zero so only the gravitational force acts and the total potential energy gets converted to Kinetic Energy.

The total amount of potential energy at the top of the ramp is given by

Ep=mgh

Ep=3 * 9.81 *5

Ep=147.15 Joules

This is equal to kinetic energy.

From the formula for elastic potential energy

The distance up to which the spring is compressed is determined

The force constant = 400N/m

147.15 =(1/2)k(x²)

294.3=(400)(x²)

0.73575=x²

x=0.8577 m

So, the object compresses the spring up to 0.8577m.

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Using Pythagoras theorem, the top of the ladder will slide down the wall 1.64 ft

The ladder leaning against the wall forms a right-angled triangle of sides 8 ft and 6 ft.

The length of the ladder is y.

Using Pythagoras theorem:

[tex]y = \sqrt{8^{2} + 6^{2}} = 10 \:ft[/tex]

When the ladder is  pulled 1 foot away from the wall, the new height, h the ladder rises up the wall is given below:

[tex]h = \sqrt{10^{2} - 9^{2}} = 4.36 \:ft[/tex]

The top of the ladder will slide 6 - 4.36 ft = 1.64 ft

In conclusion, the length the ladder will slide down is obtained using Pythagoras theorem.

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Answer: 4, 2, 8

Step-by-step explanation:

4 + 2 + 8 = 14

14 = 14

2(4) + 4(2) + 5(8) = 56

8 + 8 + 40 = 56

56 =56

| 4(4) - 2 | = 14

|16-2| = 14

14 = 14

The probability that the hacker guesses the password in first go is

[tex]\dfrac{1}{5^5}[/tex]

While statistics examines the frequency of previous events, probability deals with estimating the possibility of future events.

The primary goal of the theoretical branch of mathematics known as the probability is the investigation of the consequences of mathematical concepts. At its core, statistics is a field of mathematics that seeks to explain observations in the actual world.

Both topics are significant, pertinent, and helpful. However, they are distinct, and appreciating this difference is essential to correctly assessing the applicability of mathematical evidence.

Since sample space has 5⁵ possibilities.
The event space has only one possibility which is to successfully hack the password perfectly.
Hence, the probability is

[tex]\dfrac{1}{5^5}[/tex]

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Answer:

A turning point is the highest or lowest point on a quadratic graph.

Step-by-step explanation:

A quadratic graph looks something like the graph below.

The equation of a quadratic graph would normally look like

+/- ax^2 + bx + c

An example might be -16x^2 + 5x + 4

Note the negative symbol in front of the 16. The negative means that the graph will be facing downwards, or that the turning point is the highest point. A positive graph will mean that the graph is facing upwards, or that the turning point is the lowest point.

Essentially, it is the location where a graph has its lowest or highest point and where the y-values (can include x-values in horizontal quadratics) "turn" to the direction they originated.

The Angle of rotation of the given regular pentagon after undergoing rotational transformation is; 72°

We are told that the image is a perfect pentagon that all its' sides are all equal with no uneven sides.

Now, A figure is said to have rotational symmetry if it looks exactly the same after rotating it some angle less than 360° which is a full rotation.

Now, a regular pentagon will have a rotational symmetry of order 5 because it will look the same after 5 turns.

Thus;

Angle of rotation = 360/5

Angle of rotation = 72°

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The form which should be used when you know the slope of a line and one of the points on the line is: d. point-slope form.

The point-slope form can be defined as an equation which is used when the slope of a line and one of the points on this line is known.

Mathematically, the point-slope form of a line is given by:

y - y₁ = m(x - x₁)

Where:

In conclusion, you should use the point-slope form when you know the slope of a line and one of the points on the line is given.

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Answer:

b

Step-by-step explanation:

(3x-5)/2 = 8

3x - 5 = 2 × 8

3x - 5 = 16

3x = 16 + 5

3x = 21

x = 21/3

x = 7

Answer:

Step-by-step explanation:

Equation

(3x - 5)/2 =  8                         Multiply both sides by 2

2*(3x - 5)/2 = 8 * 2                Combine

3x - 5 = 16                             The 2s on the left cancel. Add 5 to each side

3x - 5 + 5 = 16+5                    Combine

3x = 21                                    Divide both sides by 3

3x/3 = 21/3

x = 7

Answer: x = 7

The total amount of money which the Stewart family would have to pay into the annuity each quarter is $242.12.

Mathematically, annuity can be calculated by using this formula:

[tex]A = P[\frac{(1+\frac{r}{n} )^{nt} - 1)}{\frac{r}{n} }][/tex]

Given the following data:

Substituting the given parameters into the formula, we have;

[tex]13000 = P[\frac{(1+\frac{0.036}{4} )^{4 \times 11} - 1)}{\frac{0.036}{4} }]\\\\13000 = P[\frac{(1+0.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{(1.009 )^{44} - 1)}{0.009 }]\\\\13000 = P[\frac{1.48323960867 - 1}{0.009 }]\\\\13000 = P[\frac{0.48323960867 }{0.009 }]\\\\13000 = 53.6932898522P[/tex]

P = 13000/53.6932898522

P = $242.12.

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Complete Question:

The Stewart family wants to save money to travel the world. They plan to invest in an ordinary annuity that earns 3.6% interest, compounded quarterly. Payments will be made at the end of each quarter. How much money do they need to pay into the annuity each quarter for the annuity to have a total value of $13,000 after 11 years?

Answer:

m = 300w OR w = m/300

Step-by-step explanation:

They start with 10k, but that's immediately sold, so they're back at a flat 0. Every week they gain 1000 but lose 700 for a net profit of positive 300.

Therefore, the maximum capacity would be 300 multiplied by the number of weeks. If we know the maximum, then the answer would be m (maximum) divided by 300.

An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.

Herein we have an application of unit conversions between weight units, from kilograms to pounds. Unit conversions follow this direct proportional formula:

y = k · x

Where:

x - Weight in kilograms

y - Weight in pounds

k - Conversion ratio

If we know that x = 75 kg and k = 2.208 lb/kg, then the weight of the adult in pounds is:

y = (2.208 lb/kg) · (75 kg)

y = 165.6 lb

An adult with a weight of 75 kilograms have an equivalent weight of 165.60 pounds.

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