Jamie swims 1/2 of the length of the swimming pool every 1/4 of a minute

Two numbers are in the ratio 4: 7. If their L.C.M. is 168,The numbers would be 56 and 98.

The smallest positive integer that is divisible by both a and b is known as the least common multiple (lcm) in mathematics and number theory. It can also be referred to as the lowest common multiple (lcm), or the smallest common multiple of two numbers (a and b).

The given ratio is 4:7, which can be written as 4/7.

To find the individual numbers, we can use the formula:

Number1 = LCM × Ratio1/ (Ratio1 + Ratio2)

Number2 = LCM × Ratio2/ (Ratio1 + Ratio2)

Therefore,

Number1 = 168 × 4/ (4 + 7) = 56

Number2 = 168 × 7/ (4 + 7) = 98

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The closure property states that any operation performed on the numbers of a set will be closed under that very state.

This means that in any mathematical operation like multiplication, addition, subtraction, or division when performed on two or more numbers of a particular set, the result will belong to that very set.

For example, addition is closed under whole numbers. This means tat the sum of any 2 whole numbers will always be a whole number.

For example, the sum of whole numbers 10 and 20 is 0, a whole number.

Another case is that of subtraction, which is closed under integers.

For example- the difference between integers 30 and 40 is -10, which is an integer.

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Yes the distributive property can be used to rewrite the equation 2 x (7- 4) to appear in the form

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

In other words, an equation of the type A (B + C) can be solved as

= A (B + C)

= AB + AC

in accordance with the distributive property.

As it relates to the problem, 2 x (7- 4)

A = 2

B = 7

C = 4

2 x (7- 4)

= 2 * 7 - 2 * 4

The distributive property is also applicable to subtraction as used in the problem,

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The required chances to win the game is more than 50% no matter what two are.

The  probability is the proportion of the likelihood of an occasion to occur. It estimates the conviction of the occasion. The recipe for likelihood is given by; P(E) = Number of Ideal Results/Number of all out results.

Allow the two numbers to be an and b, with a<b. Look at an acknowledgment of X (free of your decision of an or b) with the worth of the main number you see. Assuming that X is greater, switch, in any case keep the number.

The likelihood of winning can be registered as follows:

In the event that you pick a (with 12 possibility), you win assuming you switch, ie if X>a. This has prob. P(X>a).

Comparably assuming you pick b (with 12 possibility), you win on the off chance that you don't switch, ie if X≤b. This has prob. P(X≤b).

So the general likelihood of winning is 1/2+1/2P(a<X≤b), which is marginally bigger than 1/2 in view of our presumptions on X.

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Answer:

Step-by-step explanation:

2.) 143 7/23

3.) 291 46/48

4.) 220

5.) 56

6.) 1292 63/4

Answer: The domain is constrained by the number of days in January, [1,31]. The range is constrained by how far she can run each day.

Step-by-step explanation:

The dimension of a rectangle is 15m and 15m.

Here we have to find the area of a rectangle as large as possible.

Data given:

Perimeter = 60m

The formula for the perimeter of the rectangle:

perimeter = 2(length + breadth)

60 = 2( l + b)

l + b = 30

We have to find the largest area, so when we will take the length and

breadth same then we get the largest area.

So length = breadth

2 length = 30

length = 15m

length = breadth = 15m

Therefore the dimensions are 15m and 15m.

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Answer:

The slope of the line passing through the points (-3,3) and (5,9) is 3/4

3/2 is the second one

1 ) y = - 1 / 3 x + 2

2 ) y = 0x - 7

To find the slope of the line you can use the equation.

m = y2 - y1 / x2 -x1 = tan(Ф)

Answer:

1 ) y = - 1 / 3 x + 2

2 ) y = 0x - 7

Step-by-step explanation:

To find the slope of the line you can use the equation...

m = y2 - y1 / x2 -x1 = tan(Ф)

Hope this helps! :)

Answer:

We know P(x<$180,000)=.25 and P(x>$320,000)=.25

Using the formula for normal distributions, we can find the mean and standard deviation (z = (x-mean)/SD) using the given info. Then you'll have two equations with two unknowns.

Finally when finding part a, make sure to do a continuity correction [P(x<$200,000) = P(x≤$200,000.5) = ?]

Step-by-step explanation:

Answer:

y=-3x+5

Step-by-step explanation:

As the new line is perpendicular to the original line, the gradient of the new line (m) will be -1 ÷ gradient of original line = -1 ÷ 1/3 =3

The area of the shaded sector of the circle will be 12π units².

Area of a sector of a circle = θ/360 × πr², where r is the radius of the circle and θ is the central angle.

In circle Q, QR = 6 and m∠RQS = 120°.

As per the given question given data:

θ = 120°

r = QR = 6

Substitute the values in the formula to get:

Area of sector of a circle = 120/360 × π(6)²

Area of sector of a circle = 1/3 × π(36)

Area of a sector of a circle = 12π units²

Thus, the area of the shaded sector of the circle is 12π units².

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The question seems to be incomplete the correct question would be:

In circle Q, QR = 6 and m∠RQS = 120°. Find the area of the shaded sector.

Express your answer as a fraction times pi.

The perimeter of the given right-angle triangle is 40 cm.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

We also know that the perimeter of a triangle is the sum of the lengths of all the sides.

First, we need to figure out the length of the base of the right-angle triangle.

Assuming the base to be 'x'.

∴ 17² = 15² + x².

x² = 17² - 15².

x² = 64.

x = ± 8.

So, The base of the triangle is 8 cm.

∴ The perimeter of the triangle is (17 + 15 + 8) = 40 cm.

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The probability that more than a minute foes by without a hit is  0.0498.

Let X denote the waiting time in minutes until the next hit.

From the question, we have

The probability density function of exponential distribution is,

f(x)=λe^(-λ*)        λ>0

Probability =

P(X>1) =∫_1^∞  3e^(-3x) dx

=3(e^(-3z)/(-3))_1^∞

=e^(-3)

=0.0498

Probability = 0.0498

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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If one flock is flying at a rate of 25 miles per hour and the other flock is flying at a rate of 37 miles per hour then both the flocks will meet each other after 3.39 hours.

Given, two flocks of birds are 210 miles apart and heading directly toward each other. one flock is flying at a rate of 25 miles per hour.

In comparison, the other flock is flying at a rate of 37 miles per hour.

We have to find in how much time will the two flocks meet.

Let, both take t hours to meet,

now, according to the question

first flock will travel the distance, 25t

and similarly second flock will travel the distance, 37t

so, 25t + 37t = 210

62t = 210

t = 3.39

So, both the flocks will meet each other after 3.39 hours.

Hence, if one flock is flying at a rate of 25 miles per hour and the other flock is flying at a rate of 37 miles per hour then both the flocks will meet each other after 3.39 hours.

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Answer:      .48

Step-by-step explanation:

Answer:

Option B is correct

The numerical values of the circumference and area are equal.

Step-by-step explanation:

Circumference(C) and Area (A)of the circle is given by:

             ....[1]

          ......[2]

where, r is the radius of the circle.

As per the statement:

A circle has a diameter of 4 inches.

We know:

Diameter = 2 (radius(r))

then;

4 = 2r

Divide both sides by 2 we have;

r = 2 inches

Substitute these in [1] and [2] we have;

Therefore, the numerical values of the circumference and area are equal i.e 12.56

The volume of the right circular cone is 122.94754 in³.

The axis of a right circular cone is the line joining the vertex and the base's center.

In other words, a right angle is formed at the place where the apex of the cone and the center of the circular base meet.

Following is the correct circular cone volume formula:

V=1/3hπr²

Diameter = 8.5 in

Radius = 8.5/2 = 4.25 in

Now calculate the volume as follows:

V = 1/3hπr²

V = 1/3(6.5)π(4.25)²

V = 122.94754 in³

Therefore, the volume of the right circular cone is 122.94754 in³.

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A square Class 1 is a type of four-sided polygon. It is a regular polygon, meaning that all of its sides have the same length and all of its angles are equal.

There are only right angles in a square. Having the opposing sides parallel defines a square as a quadrilateral. Only one dimension, the side length, may be used to describe a square. Each angle is 90° in length and has an equal number of sides. To help you comprehend the topic better, let's talk more about square angles and work through a few instances. A square Class 1 is a type of four-sided polygon. It is a regular polygon, meaning that all of its sides have equal length and all of its angles are equal. The sides of a square Class 1 are all of the same length, and the angles between them are all 90 degrees. This type of polygon is also known as a regular square.

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The difference between the predicted regression value and the actual value is called the residual.

Let's assume a simpler model: Y= β₀+ β₁X + E. For linear regression, let ε∼N(0,σ2). The most important thing here is that ϵ is a normal random variable. This makes Y a normal random variable with mean β0+β1X and variance σ₂.

Regression Analysis:

Regression analysis is a set of statistical techniques used to estimate the relationship between a dependent variable and one or more independent variables. It can be used to assess the strength of relationships between variables and model future relationships between variables.

Assumptions:

One of the main assumptions of regression analysis is that residuals with mean equal to 0 are normally distributed. Residuals must be both positive and negative. If this condition is not met (residuals are only positive or negative, i.e. the model is either consistently Regardless, it means that it has not been properly selected for prediction.

Poor predictions are due to (i) the regression model should contain non-linear terms rather than only linear terms, (ii) multicollinearity of the independent variables, and (iii) missing important predictor variables (features). Poor understanding of the problem and data, (iv) non-constant data variance, or (v) extrapolation (prediction) far beyond the range of the independent variables used to estimate the parameters of the model.

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a) The value of x=0 will be a solution for both the inequalities .

b) One equality is false and only one in correct when value of x = 4

What is inequalities?

a) x =0

i) -2.x < 10

-2(0) < 10

0 < 10

ii) -6 < -2x

-6 < -2(0)

-6 < 0

The value of x will be a solution for both the inequalities .

b) x = 4

i) -2.x < 10

-2(4) < 10

-8< 10

ii) -6 < -2x

-6 < -2(4)

-6 < -8

Hence, one inequality is false and only one in correct when the value of x =4.

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Answer:

greater than

Step-by-step explanation:

4/9+1/4

16/36+9/36

25/36

25/36>18/36

We can use the distributive property to find an expression equivalent to 15(x+2) as 15x + 30.

The given equation is 15(x+2).

The distributive property can be used on the component outside of the brackets, that is 15.

Therefore, we would multiply 15 by each term inside the rounded brackets.

It becomes, 15 times x = 15x and 15 times 2 = 30

That is, 15*(x+2) = 15* x +15* 2 = 15x + 30

Hence, the equation 15(x+2) becomes 15x + 30.

By using the distributive property, expression equivalent to 15(x+2) is 15x + 30

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Answer:

C. 7

Step-by-step explanation:

Draw out the triangle if you want.

You’ll notice you’ll have a hypotenuse and one other side.

Use Pythagoras’ theorem: a^2 + b^2 = c^2
c = the hypotenuse

24^2 + b^2 = 25^2

solve for b:

576 + b^2 = 625

b^2 = 625 - 576

b^2 = 49

b = 7

2 hours will pass before they meet.

"Information available from the question"

In the question:

Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.

Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.

Now, According to the question:

Total distance = 20mi

Aaron starts riding a bike at a rate of  = 3mi/h

Zhang rides his bike toward Aaron along the same road at  = 2mi/h

Let y be the number of hours for them to meet.

The expression is given as

3y + 2y = 20

solving for y, we have

5y = 20

y = 20/5

y = 4hrs

Therefore, 2 hours will pass before they meet.

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Answer: 145.3

Step-by-step explanation:

the solution for the given expression 11.5x + 10.9y  is 145.3

What is an Equations?

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) symbol. It demonstrates how the expressions written on the left and right sides are equivalent. Equations can be solved to find the value of a variable that represents an unknown quantity. If there is no "equal to" symbol in a statement, it is not an equation. It will be viewed as a phrase.

11.5x + 10.9y

Here x = 6 and y = 7

11.5*6 + 10.9*7 = 145.3

Hence, the solution the given expression is 145.3

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Answer:

2,241

Step-by-step explanation:

7470 x 0.3

Answer:

[tex]-\frac{6}{x^{2} } -6x-2[/tex]

Step-by-step explanation:

[tex]x^{-2}[/tex]  is equivalent  [tex]\frac{1}{x^{2} }[/tex]

Then, that is multiplied by the coefficient of -6

Thus [tex]-6x^{-2}[/tex] becomes [tex]-\frac{6}{x^{2} }[/tex]

Answer:

1/3 x -3

Step-by-step explanation:

The value of the expression 7 to the power of negative 2 is 1/49.

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]7^{-2}[/tex]

The value of this expression.

= 1/7²

= 1/49

Thus,

The value [tex]7^{-2}[/tex] is 1/49.

Option B is the correct answer.

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