Let X be a continuous random variable with the pdf given by f(x)= ax2 for 0 < x ≤ 3. Determine the value of constant 'a' correct to 2 decimal places.

Answer:7

Step-by-step explanation:

What it is asking you is what multiplied by it self gets you to 49. the answer would be 7 because 7*7=49

The base of the original triangle is 12 centimetres.

A triangle is a polygon with three sides. The perimeter of a triangle is 58 cm. The triangle is isosceles.

An isosceles triangle is a triangle with 2 sides equal to each other and two angles equal to each other.

Therefore, let's find the base of the original triangle when the base were lengthened by 4 cm and each leg were shortened by 7 cm,

Hence,

let

x = length of legs

y = length of the base

Therefore,

2x + y = 58

Hence,

y + 4 = x - 7

x - y = 11

2x + y = 58

x - y = 11

3x = 69

x = 69 / 3

x = 23

-y  = 11 - 23

-y = -12

y = 12

Therefore,

base of the original triangle = 12 cm

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Hello!

What does this problem want:

What we need to find: rate of bagels made per hour

    [tex]\text{Rate}=\frac{\text{Total number of bagels}}{\text{Number of hours}} =\frac{640}{4} =160 \text{ bagels per hour}[/tex]

Thus

                 8 * 160 = 1280 bagels

                6 * 160 = 960 bagels

Hope that helps!

Answer:172 cm²

Step-by-step explanation:

when we use the formula, and we can  solve out is like 172.05 and round to tenth and will have the answer

Formula is 1/2 × p × a  

Answer:

Irrational

Step-by-step explanation:

A rational number can be expressed as p/q where p and q are integers

3.04 is rational since it can be expressed as 304/100

√20 is not rational. √20 = √(4·5) = √4·√5 = 2√5
While 2 is a rational number, √5 is irrational since 5 is a prime number and square roots of primes are not rational

An irrational number multiplied by a rational number is irrational so √20 is irrational

An irrational number added to a rational number results in an irrational number.

So 3.04 + √20  is irrational

The correct values are;

⇒ a - d = - 2

⇒ c - a = 7

⇒ b - c = - 8

⇒ d - c = - 5

What is Number line?

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

The number line is shown in figure.

The values are,

a = - 3

b = - 4

c = 4

d = - 1

Now,

All the values are find as;

⇒ a - d = - 3 - (- 1)

           = - 3 + 1

           = - 2

⇒ c - a = 4 - (-3)

           = 4 + 3

           = 7

⇒ b - c = - 4 - 4

           = - 8

⇒ d - c = - 1 - 4

           = - 5

Thus, The correct values are;

⇒ a - d = - 2

⇒ c - a = 7

⇒ b - c = - 8

⇒ d - c = - 5

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Answer: 5 days.

Step-by-step explanation: To solve this problem, we first need to convert 1 7/10 bags of tortillas to a decimal number. We can do this by dividing the numerator of the fraction (7) by the denominator (10) and adding the result to the whole number (1) to get 1 + 7/10 = 1.7 bags of tortillas.

Next, we can divide the number of bags of tortillas that Garrett's burrito stand uses per day (1.7 bags) into the total number of bags of tortillas that are available (8.5 bags) to find out how many days the tortillas will last: 8.5 bags / 1.7 bags/day = 5 days

Therefore, the 8 1/2 bags of tortillas will last for 5 days.

The inequality that represents the situation given will be  

7x + 13y ≤ 91.

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

The inequality that represents the situation given will be  7x + 13y ≤ 91.

From the information given, Crawford is ordering pizzas and breadsticks for a school pizza party and has a budget of $91, but no more and an order of breadsticks costs $7 while a pepperoni pizza costs $13.

Therefore, the inequality that represents the situation given will be  

7x + 13y ≤ 91.

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Answer:

Step-by-step explanation:

443

Answer:

Volume = 282.6 ft.²

Step-by-step explanation:

Volume: V = πr²h

Step 1: The answer needs to be in cubic feet, so convert all units to feet

    1. 3 ft./12 in. = 0.25 ft.

Step 2: Subtract 0.5 ft from 6.5 ft to find the actual diameter of the pipe that the water will be passing through

    2. 6.5 ft. - 0.5 ft. = 6 ft.

Step 3: Plug 3 ft. (radius), 3.14 for π, and 5 ft for h

    3. V = (3.14)(3 ft.)²(5 ft.)

Step 4: Solve for the V (volume)

    4. V = (3.14)(9 ft.)(5 ft.) → V = (28.26)(5) → V = (28.26)(5) → V = 141.3 ft.²

Step 5: Divide 141.3 by 2, since we want half the capacity

    5. 141.3 ft.²/2 = 70.65 ft.²

Step 6: Multiply 70.65 by 4 since we want the total volume of water passing through four pipes

    6. 70.65 ft.² ∙ 4 = 282.6 ft.²

Answer: D

Step-by-step explanation:

The parent function abs(x) is a V, similar to graph B.

When it is multiplied by a negative number then it reflects across the Y axis, and if the number is greater than 1, then the graph is horizontally compressed (like you're squishing the sides together, closer to each other).  If the number is less than 1, either decimals or a fraction, then it is stretched (like you are pulling the sides away from each other and they are getting wider).  

In this case you are multiplying abs(x) by 4, which is greater than 1 so it is compressed by a factor of 4, and then multiplying it by a negative, which reflects it across the y axis.

Step-by-step explanation:

Here you are the answer.

Answer:

see instructions

Step-by-step explanation:

1. (x + 2) = 0  gives us x = -2 = x coordinate of vertex; and

  the -1 at the end gives us the y coordinate.

  Move the vertex of the parabola to the point (-2,-1)

2. The -4 in front of the (x+2)² gives the direction and stretch of the parabola. FROM the Vertex, position the other point Down 4 and Right 1 (at (1,-5)).

There are 45 defective cars if 1,500 cars are tested.

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities.

Given that;

During a test, 3 out of 100 cars selected at random were found to be defective.

Now,

Since, During a test, 3 out of 100 cars selected at random were found to be defective.

Let number of defective cars if 1,500 cars are tested = x

So, By definition of ratio, we get;

⇒ 3 / 100 = x / 1,500

Solve for x as;

⇒ 3 × 1500 / 100 = x

⇒ 3 × 15 = x

⇒ x = 45

Thus,  There are 45 defective cars if 1,500 cars are tested.

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X + 7 is not a factor of [tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +2x -8 because it gives a remainder when x + 7 divides it.

The remainder is the portion of the dividend that cannot be fairly divided by the divisor. After dividing whole numbers to find the quotient, the part that is left is called the remainder.

to know if x + 7 is a factor, x = -7 when substituted should give 0 as a remainder otherwise it is not a factor.

By substituting x = -7 we have

[tex](-7)^{3}[/tex] [tex]-3(-7)^{2}[/tex] +2(-7) - 8 = -343 -147 -14 - 8  which is -512

Therefore x + 7 is not a factor of the function.

In conclusion x + 7 is not a factor of [tex]x^{3}[/tex] -3[tex]x^{2}[/tex] +2x -8

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Answer:

What he said!

Step-by-step explanation:

Answer:

42-48 pound" number.

Step-by-step explanation:

The number 3,675,000,000 represents 3,675,100,608 rounded off to the nearest million.

When we round off large numbers, we consider the digit to the right of the number occupying the place value for which we are rounding off to. If the digit to the right is 4 or less, we round down (we leave the number we are rounding to), but if the digit is 5 or higher, we round up (we increase the digit we are rounding by 1). and thus round to the indicated place value.

From the question, we have the large number;

3,675,100,608

the digit 5 indicates the place value (million)

and the digit 1 is to the right and will be rounded down.

Therefore, the number 3,675,000,000 represents 3,675,100,608, rounded to the nearest million.

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Answer:

-4

Step-by-step explanation:

3x+15+2=5

3x=-15-2+5

3x=-12

x=-12/3

x=-4

Answer:

x=-4

Step-by-step explanation:

Given:

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

To find:

The value of x.

Explanation:

It is given that,

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

That implies,

[tex]3(x+5)+2=5\\3x+15+2=5\\3x+17=5\\3x=5-17\\3x=-12\\x=-\frac{12}{3} \\x=-4[/tex]

Hence, the value of x is -4.

The formula for the volume of a cone is given by the following equation:

V = 1/3 * π * r2 * h

where V is the volume of the cone, r is the radius of the cone, and h is the height of the cone.

In this case, we are given that the radius of the cone is 2.5 units and the volume of the cone is 19 cubic units. We can use this information to complete the expression that represents the height of the cone as follows:

V = 1/3 * π * r2 * h

19 cubic units = 1/3 * π * 2.5 units2 * h

19 cubic units = 1/3 * π * 6.25 units2 * h

19 cubic units = 1/3 * 19.63 units2 * h

19 cubic units = 6.54 units2 * h

h = 19 cubic units / 6.54 units2

h = 2.9 cubic units / 6.54 units

Therefore, the expression that represents the height of the cone is 2.9 cubic units / 6.54 units.

The only solution the system of the equation has is x = -1/3.

The number of solutions is one.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The system of equations:

y = -3x - 1

y = x² - 3x + 4

The solutions of the equation.

y = 0

So,

-3x - 1 = 0

-3x = 1

x = -1/3

x² - 3x + 4 = 0

It is in the form of ax² + bx + c = 0

a = 1, b = -3, and c = 4

Now,

x = -b ± √(b² - 4ac) / 4a

x = 3 ± √(9 - 16) / 4

x = 3 ±√-7 / 4

x = 3 ±i√7 / 4

This is a complex root.

So,

These are not real solutions.

Thus,

The only solution the system of the equation has is x = -1/3.

The number of solutions is one.

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Answer:

Step-by-step explanation:

Given the values in the table, you want to know if they represent a linear or exponential relation, along with the common difference or ratio, as applicable.

The first attachment shows the differences and ratios between successive table values. Neither the differences nor the ratios are constant. The wide variation in ratios and the relatively smaller variation in differences suggests the table is best modeled by a linear function.

Changes when the function is linear are additive. That is, the function values have a common difference.

The average difference between table values is (949.92 -229.44)/3 = 240.16. A linear regression analysis gives a slope of 240.12 as the "best fit" to the table values.

You can see from the first attachment that the differences are not constant, so there isn't really a common difference. The difference is approximately 240.12.

__

Additional comment

The second attachment shows linear and an exponential regression applied to this data. The residuals are much smaller for the linear approximation.

The slope of the line (common difference) is estimated at 240.12 using the regression formula. This makes the mean square residuals a minimum. As we show above, this slope is different (slightly lower) than the slope of the line through the first and last data points.

Answer:

y - 9 = 7(x - 1)

Step-by-step explanation:

The given equation is in Point Slope Form:  y - y₁ = m(x - x₁)

m is the slope, and parallel lines have the same slope (7)

x₁ and y₁ are the coordinates of a point on the line

The gas for the Trip cost is $8.39

The amount of gas motorcycle needed is 12 Liter of gas.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Jackson’s motorcycle gets 28 kilometers per liter.

He drives 336 kilometers and gas is $1.43 per liter.

The amount of gas motorcycle needed

= 336/28

= 12 Liter of gas

and, The gas for the Trip cost = 12/1.43

                                                  = $8.39

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Answer:

Step-by-step explanation:

6(6p-9)-10p-6(6p-9)-10p

36p-54-10p-36p+54-10p

36p-36p-54+54-10p= -10p

Answer:

21

Step-by-step explanation:

PEMDAS : Parenthesis, Exponent, Multiplication/Division, Addition/Subtraction.

First, we want to deal with the parenthesis within the parenthesis.

(4.6/2) = 2.3

Rewrite it into the equation.

[3 * 2.3] + 14.1 = ?

Now, do the work in the parenthesis again.

[6.9] + 14.1 = ?

There isn't anymore parenthesis, exponents, or multiplication/division, so we move onto addition now and add both terms.

6.9 + 14.1 = 21

? = 21

The answer is 21.

Answer:

3.06 meters

Step-by-step explanation:

The first thing you want to do, since we are working with different units here, is find out how many centimeters make a meter... and so on.

1cm = 0.01m

1mm = 0.001m

123cm = 1.23m (Dressing table)

410mm = 0.41m (Cupboard door)

Now all we need to do is subtract.

We can add the two numbers together or (If you prefer) subtract separately.

1.23 + 0.41 = 1.64

Now subtract that number from the measurement of the wall:

4.7 - 1.64 = 3.06

The amount of space left is 3.06m.

The function of reflect x-axis is g(x) =  -(1/2)*x - 8, according to the question.

What do you mean by function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given question,

First, let's define a reflection over the x-axis.

If we have a point (x, y) and we reflect it over the x-axis, our new point will be (x, -y).

Now, when we have a function

f(x) = y, the points can be written as:

(x, y = f(x) ) = (x, f(x))

Then, after the reflection over the x-axis, we have:

(x, y = g(x)) = (x, -f(x))

So now we have g(x) = -f(x)

and we know that f(x) = (1/2)*x + 8

then our new function is g(x) =  y = -f(x) = -( (1/2)*x + 8) = -(1/2)*x - 8.

g(x) =  -(1/2)*x - 8.

Therefore, the required answer is g(x) =  -(1/2)*x - 8.

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The graph of the equation is shown below

The x-intercept is -2

The y-intercept is undefined

From the question, we are to solve the equation by graphing and determine the x- and y-intercepts

The given equation is

3x + 1 = -5

To determine the x-intercepts, we will solve the equation

3x + 1 =-5

3x = -5 - 1

3x = -6

Divide both sides by 3

x = -2

Since, y is not defined in the equation, the y-intercept is undefined

The graph of the equation is shown below.

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