A solid lies between planes perpendicular to the x-axis at x=0 and x=3. The cross-sections perpendicular to the axis on the interval 0≤x≤3 are squares whose diagonals run from the parabola y=−x‾‾√ to the parabola y=x‾‾√.Find the volume of the solid.

Answer:

Step-by-step explanWe can easily calculate for the height of the prism since all needed measurements are given. Volume of a rectangular prism is expressed by the equation:

V = lwh

where l is the length, w is the width and h is the height of the prism.

655 = 9 (5.2) hation:

h=14ft

Judy Clark will pay back $7,993.03 on January 20 for her loan of $7,800 at a 6.5% interest rate, with the interest being calculated for 140 days.

To calculate the amount Judy Clark will repay for a loan of $7,800 borrowed from Reel Bank at an ordinary interest rate of 6.5%, we need to determine the amount of interest accumulated by the loan from September 2 to January 20. This involves calculating the time period for the loan, applying the ordinary interest formula, and then adding the interest to the principal amount to find the total repayment amount.

We first calculate the number of days between September 2 and January 20. Without knowing the year of the loan, we can use an approximate count and consider a non-leap year for this example, which would be 140 days (30 days for September after the 2nd, 31 for October, 30 for November, 31 for December, and 18 for January).

Using the formula I = PRT, where P is the principal ($7,800), R is the annual interest rate (0.065), and T is the time in years (140/365), we can calculate the interest:

I = 7,800 × 0.065 × (140/365) = $193.03 (rounded to two decimal places).

To find the total repayment amount, we add the interest to the principal: $7,800 + $193.03 = $7,993.03.

Therefore, Judy Clark will pay back $7,993.03 on January 20.

Answer:

-2

Step-by-step explanation:

he wants to get -7 because -4 + -3 = -7

he has -5 currently, so to get to -7 I added -2 which is the amount he needs.

I hope this helps you :)

Stuart requires a score of atleast - 2 on his last hole in other to beat his best score.

Best score = - 4

Required score < Best score + (-2)

Required score < - 4 + (-2)

Current score = - 5

Therefore, the least score required to beat his best score is - 7

Therefore, the required score on last hole will be :

Therefore, a score of - 2 is required on last hole in other to beat his best score.

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Answer:

The answer to your question is: 387.5 times distance from earth to the sun than distance from the earth to the moon

Step-by-step explanation:

Data

distance from earth to the sun = 9.3 x 10⁷ miles

distance from the earth to the moon = 2.4 x 10⁵ miles

distance ES to EM

Then we need to divide

 distance from earth to the sun / distance from the earth to the moon

9.3 x 10⁷ miles / 2.4 x 10⁵ miles

= 387.5 times is greater.

The distance from Earth to the Sun is about 387.5 times greater than the distance from Earth to the Moon. This is calculated by dividing the distance from Earth to the Sun by the distance from Earth to the Moon.

To determine how many times greater the distance from Earth to the Sun is than the distance from Earth to the Moon, we need to divide the distance from Earth to the Sun by the distance from Earth to the Moon. So, we have 9.3 × 107 miles (distance to the Sun) divided by 2.4 × 105 miles (distance to the Moon).

When you perform this calculation, you get a value of approximately 387.5. Therefore, the distance from Earth to the Sun is about 387.5 times greater than the distance from Earth to the Moon.

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Explanation:

A "common denominator" is the least common multiple (LCM) of the denominators of the rational expressions involved. As such it can be found as the product of the unique factors of those denominators, each to its highest power.

For example, the common denominator for fractions with denominators of 20 and 25 will be 100. It can be found by considering the factors ...

  20 = 2² × 5

  25 = 5²

The unique factors here are 2 and 5, each with a highest power of 2. The product of these unique factors to their highest powers is ...

  2²·5² = 4·25 = 100.

___

Using this method of finding the LCM, it is essential that we know the factors of the numbers.

The LCM can also be found as the product of the numbers, divided by their greatest common factor (GCF). For this method, too, you need to know factors of the numbers involved--or, at least, the greatest common factor.

For the above example numbers, the GCF is 5, so their LCM is ...

  20·25/5 = 500/5 = 100

Factors can help you find a common denominator by revealing common multiples. By multiplying the denominators of the fractions together, you can often find a common multiple that can be used as a common denominator. Simplify the resulting fraction by canceling out any common factors.

Finding a common denominator involves identifying a common multiple of the denominators of the fractions you are working with. Factors can help you find a common denominator by revealing common multiples. By multiplying the denominators of the fractions together, you can often find a common multiple that can be used as a common denominator. It's important to simplify the resulting fraction by canceling out any common factors.

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Answer:

  b: elimination

Step-by-step explanation:

My vote is for elimination, though any of these methods (and some not listed) will get an answer quickly.

Subtracting the second equation from twice the first gives ...

  2(9x +8y) -(18x -15y) = 2(7) -(14)

  31y = 0 . . . simplify

  y = 0 . . . . . divide by 31 (or invoke the zero-product rule)

Then the value of x can be found from the first equation:

  9x = 7

  x = 7/9

__

I like this method because it tells you that y=0 in one step. (Graphing does the same.) For the numbers here, you can do it mentally. Once you recognize that the x-coefficients and the constants are related by the same factor, and that factor is different for the y-coefficients, it becomes apparent that elimination will immediately tell you that y=0.

Answer:

The C-intercept, 15, means that if Janelle drove 0 miles on a particular day it would cost her 15 dollars to rent the car for that day.

Step-by-step explanation:

The slope, 0.32, means that the cost for renting the car on a particular day increases by 0.32 of a dollar for each mile she drives on that day.

The slope of the equation C=0.32m+15 is 0.32. The slope represents the rate of change in the cost per day for each unit increase in the number of miles Janelle drives. In this case, for every additional mile Janelle drives, the cost of renting the car increases by 0.32 dollars.

Answer:

20 months

Step-by-step explanation:

Let the number of months be denoted by x.

Then, we shall form two equations to represent the total cost from each dealer. Thus,

2500 + 150x is the cost of the motorcycle from the first dealer.

3000 + 125x is the cost of the motorcycle from the second dealer.

If the costs from the dealers are equal, then

2500 + 150x =3000 +125x

150x- 125x = 3000-2500

        25x = 500

          x = 500/ 25

           x =20 months

Final answer:

When Mike increased the size of his truck tires from the original P215/60R16 to the larger P235/70R16 without recalibrating his speedometer, the actual speed he was going on the new tires when his speedometer showed 60 mph was approximately 54.2 mph.

Explanation:

When Mike increased the size of his truck tires without recalibrating his speedometer, his speedometer reading would be inaccurate. To determine how fast he is going on the new tires when his speedometer shows 60 mph, we can use the concept of tire revolutions per mile.

The original tire size, P215/60R16, has a diameter of approximately 25.7 inches, while the larger tire size, P235/70R16, has a diameter of approximately 29.0 inches. The new tires cover a greater distance in one revolution compared to the original tires.

To calculate the actual speed, we can use the equation:

Actual Speed = Speedometer Reading * (Original Tire Diameter / New Tire Diameter)

Substituting the given values:

60 mph * (25.7 inches / 29.0 inches)

By simplifying this calculation, the actual speed is approximately 54.2 mph. Therefore, the correct answer is A. 54.2 mph.

Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.

Calculate the difference in tire circumference:

Original circumference: 2 * π * radius = 2 * π * (215 mm / 25.4 mm/inch) * (60 + 30%) = 79.3 inches (assuming 30% aspect ratio)

New circumference: 2 * π * (235 mm / 25.4 mm/inch) * (70 + 30%) = 85.1 inches

Difference: 85.1 inches - 79.3 inches = 5.8 inches

Calculate the percentage increase in circumference:

(5.8 inches / 79.3 inches) * 100% = 7.3%

Apply the percentage increase to the speedometer reading:

Actual speed = Speedometer reading * (1 + % increase)

Actual speed = 60 mph * (1 + 7.3%) = 60 mph * 1.073

Actual speed ≈ 64.4 mph

Therefore, when the speedometer shows 60 mph, Mike is actually traveling approximately 64.4 mph. Hence the correct option is c.

Answer:

[tex]\dfrac{x}{4}[/tex]

C is correct.

Step-by-step explanation:

At a picnic,

Number of adults is 3 times as number of children.

Number of women is twice as number of men.

Total number of men, women and children at the picnic be x

Let number of children be c

Let number of men be m

Let number of women be w

# Number of women is twice as number of men, w = 2m

# Number of adults is 3 times as number of children, w + m = 3c

      2m + m = 3c     (∴  w=2m )

                c = m

Total number of men, women and children at the picnic be x

∵       c + m + w = x

     m + m + 2m = x

                    4m = x

Number of men, [tex]m=\dfrac{x}{4}[/tex]

Hence, The total number of men will be  [tex]\dfrac{x}{4}[/tex]

Answer:

y = 3x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line

m = [tex]\frac{2+4}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3

Note the line crosses the y- axis at (0, - 4) ⇒ c = - 4

y = 3x - 4 ← equation of line

Answer:

h(- 8) = - 8

Step-by-step explanation:

To evaluate h(- 8) substitute x = - 8 into h(x), that is

h(- 8) = [tex]\frac{(-8)^2+3(-8)}{4(-8)+27}[/tex]

        = [tex]\frac{64-24}{-32+27}[/tex]

       = [tex]\frac{40}{-5}[/tex] = - 8

Answer:

57/4

Step-by-step explanation:

Answer:

11 + 4 = 15

Rewrite the problem:

15-3/4= ?

15-3= 12

the divide it by 4:

12 / 4 = 3

ANSWER: 3

Step-by-step explanation:

Answer:

Part 1) m∠DBC=25°

Part 2) m∠DCB=65°

Part 3) m∠CDB=90°

Part 4) m∠ACD=25°

Part 5) m∠ADC=90°

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle DBC

we know that

The sum of the interior angles of a triangle must be equal to 180 degrees

In the right triangle ABC

m∠A+m∠B+m∠C=180° ----> equation A

we have

m∠A=65° ----> given problem

m∠C=90° ----> given problem

Substitute the given values in the equation A and solve for m∠B

65°+m∠B+90°=180°

m∠B+155°=180°

m∠B=180°-155°

m∠B=25°

Remember that the measure of Angle B is equal to say the measure of angle DBC

so

m∠B=m∠DBC

therefore

m∠DBC=25°

step 2

Find the measure of angle DCB and angle CDB

In the right triangle DBC

The sum of the interior angles of a triangle must be equal to 180 degrees

m∠DBC+m∠DCB+m∠CDB=180°

we have

m∠DBC=25°

m∠CDB=90° ----> is a right angle (CD is the height to AB)

substitute the values and solve for m∠DCB

25°+m∠DCB+90°=180°

m∠DCB+115°=180°

m∠DCB=180°-115°=65°

step 3

Find the measure of angle ACD

we know that

m∠ACD+m∠DCB=90° -----> by complementary angles

we have

m∠DCB=65°

substitute the value

m∠ACD+65°=90°

m∠ACD=90°-65°=25°

step 4

Find the measure of angle ADC

m∠ADC=90° ----> is a right angle (CD is the height to AB)

Explanation:

3. ∠2 and ∠3 are a linear pair → definition of a linear pair

4. ∠3 and ∠4 are a linear pair → definition of a linear pair

5. m∠2 +m∠3 = 180° → definition of a linear pair (or angle addition postulate)

6. m∠3 +m∠4 = 180° → definition of a linear pair (or angle addition postulate)

7. m∠2 +m∠3 = m∠3 +m∠4 → substitution property

8. m∠2 = m∠4 → subtraction property

9. ∠2 ≅ ∠4 → definition of congruent angles

_____

A pair of angles is a "linear pair" if they are adjacent and supplementary. ∠2 and ∠3 are adjacent and the non-common legs form a straight line. It isn't clear what your definition of linear pair is and what you need to do to claim that the angles sum to 180°. Above, we have assumed a definition of "linear pair" that includes the facts that → they sum to 180°; → non-adjacent sides form a straight line.

Answer:

The answer to your question is letter C

Step-by-step explanation:

A. [9-4x2) + (-4x2y) + 10x2y] + 2xy2  : in this polynomial the first term is not a like term, then this is incorrect.

B. 10x2y + 2xy2 + [(-4x2) + (-4x2y)]  : in this polynomial, the terms that are grouped, are not like terms, then is incorrect.

C. (-4x2) + 2xy2 + [10x2y + (-4x2y)]  ; This polynomial is the right answer because the like terms are grouped.

D. [10x2y + 2xy2 + (-4x2y)] + (-4x2): This polynomial is incorrect because one of the terms that are grouped is not a like term.

Answer:

Perimeter = 120 m

Step-by-step explanation:

Perimeter = (24+36)*2 = 120 m

Answer:

[tex] - \frac{2[1 - x]}{3} = g[f(x)] \\ \\ \frac{3x}{2 - x} = f[g(x)][/tex]

Step-by-step explanation:

They are not.

For the g[f(x)] function, you substitute ³/ₓ ₋ ₁ from the f(x) function in for x in the g(x) function to get this:

[tex] \frac{2}{ \frac{3}{x - 1}} [/tex]

Then, you bring x - 1 to the top while changing the expression to its conjugate [same expressions with opposite symbols]:

[tex] - \frac{2[1 - x]}{3}[/tex]

You could also do this [attaching another negative would make that positive].

For the f[g(x)] function, ²/ₓ from the g(x) function for x in the f(x) function to get this:

[tex] \frac{3}{ \frac{2}{x} - 1}[/tex]

Now, if you look closely, ²/ₓ is written as 2x⁻¹, and according to the Negative Exponential Rule, you bring the denominator to the numerator while ALTERING THE INTEGER SYMBOL FROM NEGATIVE TO POSITIVE:

[tex] \frac{3x}{2 - x} [/tex]

When this happens, x leaves the two and gets attached to the three, and 1 gets an x attached to it.

I am joyous to assist you anytime.

Answer:

4

Step-by-step explanation:

(16*1/2)*1/2

((16*1)/2)*1/2

(16/2)*1/2

8*1/2

8/2

4

or

16*1/2*1/2

16*(1/4)

16/4

4

Answer:

the answer will be d.PLATO users

Answer:$18.00

Step-by-step explanation:5×3=15

$3+$15=$18

Answer:

Step-by-step explanation:

To

Answer:

Step-by-step explanation:

z = a + bi

the complex conjugate is : Z = a-bi

so : Z-z =  (a-bi) - ( a + bi ) = a-bi -a -bi

Z-z = -2bi ...is a pure imaginary number (the statement is true)

The statement is true, Z-z is a pure imaginary number = -2bi.

What is conjugate complex?

A conjugate of a complex number is another complex number which has the same real part as the original complex number and the imaginary part has the same magnitude but opposite sign.

Here, given that, z = a+ib,

Let, Z be the complex conjugate of z, then, Z=a-ib

Now, Z-z = (a-ib)-(a+ib)

               =a-ib-a-ib

               =-i2b  (which is purely imaginary)

Hence, proved. The given statement is true.

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Answer:

Probability of winning on one try : 1.16060875e-8

Step-by-step explanation:

For the first first 4 numbers.

Probability is 1/46 for the first number. Since the numbers are different, and it doesnt matter the order, the second number has a probability now of 1/45, the third has a probability of 1/44 and the last one a probability of 1/43.

Since the probability is dependan of the results of hitting the other number the probability of the first for numbers is the multiple of the 4 probabilities.

So it is 1/46 * 1/45 * 1/44 * 1/43 = 1 / 3916440

And that number is then multiplied by the probabilty of hitting the last number. 1/22

So the final probability is :

1/86161680   = 1.16060875e-8

Answer:

The probability of winning the jackpot on one try is 2.78 * 10^-7

Step-by-step explanation:

There are 46 balls in total  (46-1)+1 = 46 . (b-a)+1 is the formula for number of elements between a and b included.

We need to find the number of combinations possible of 4 balls ( as order doesn't matter - 1234 is the sames as 2341) . So the number of possible combinations of 4 balls taken from 1 - 46  is given by

C= n!/(r!(n-r)!) where n is the number of possible balls = 46 and r the size of combination = 4 and ! is factorial ( ex 3! = 3*2*1) This gives for this case

C= n!/(r!(n-r)!) = 46!/(4!(46-4)!)= 163,185 combinations.

But as there is a fifth ball with (22-1)+1   = 22 posible options each combination must be multiplied by 22( for example 1234 22 is one but also 1234 10 is other)

163,185*22= 3,590,070  possibilities.

The probability of winning is 1 in  3,590,070  possibilities. or

p = 1/ 3,590,070= 2.78 * 10^-7

Answer:

Step-by-step explanation:

B is the answer

Answer:

Length = 128.3

Step-by-step explanation:

The 3 sides of a regular triangle are the same, the 2 sides that are in terms of x are equal:

5x + 40 = 8x - 13

40 + 13 = 8x - 5x

53 = 3x

17.7 = x

The length of a side = 5(17.7) + 40 = 128.3

Answer:

  see the attachment

Step-by-step explanation:

(8, -3) is added to each of the preimage coordinates to get the coordinates of the image. For example, ...

  X' = X + (8, -3) = (-2, 5) + (8, -3) = (-2+8, 5-3)

  X' = (6, 2)

Final answer:

Explanation of how to find the preimage and image of a triangle under a translation along specified vector.

Explanation:

Translation is a transformation that moves all points of a figure the same distance in the same direction. Given a translation along (8, -3), we can find the preimage and image of the triangle with the given vertices by shifting each point 8 units to the right and 3 units down.

Preimage: X'(-2+8, 5-3) = X(6, 2), Y'(-3+8, 2-3) = Y(5, -1), Z'(-6+8, 6-3) = Z(2, 3).

Image: Triangle XYZ under the translation along (8, -3) has vertices X'(6, 2), Y'(5, -1), Z'(2, 3).

In the equation, x represents the number of balloons. We say that 25 cents per balloon becomes 0.25x.

Jimmy also purchased a chocolate cake. This is the PLUS sign in the equation.

The total for everything purchased is $35.

Balloons x at 25 cents each = 0.25x plus a chocolate cake for $10 together equals $35.

Answer:

Step-by-step explanation:

Answer:

The probability that a particular death is due to an automobile accident is 2.72%

Step-by-step explanation:

The probability can be calculated as the percentage of each particular death.

The formula for this case is:

P(car accident) =  (Number of death due a car accident / Total of deaths) * 100

P(car accident) = (24/883)100 = 2.72%

Probabilities of each particular death:

Automobile accident = (24/883)100 = 2.72%

Cancer = (182/883)*100 = 20.61%

Heart disease = (333/883) * 100 = 37.71%

On solving the equation -(6x+7)+8=19, we get value of x = -3.

To solve the equation -(6x+7)+8=19, we will first simplify each side of the equation and then solve for x. Here's how to do it step-by-step:

Distribute the negative sign across the parenthesis: -6x - 7 + 8 = 19.

Combine like terms on the left side: -6x + 1 = 19.

Subtract 1 from both sides: -6x = 18.

Divide both sides by -6 to find the value of x: x = -3.