A rectangular prism has a length of 3/4 cubic inch and a width of 1/2 inch. The volume is 21/32 cubic inch. Find the height of the prism. Write your answer as a mixed number in simplest form.

The missing nucleus in the nuclear decay reaction of Thorium-232 into Radium-228 is an alpha particle, or Helium-4.

The question pertains to a nuclear decay reaction where Thorium-232 decays into Radium-228 and a missing nucleus. The missing nucleus can be determined by subtracting the atomic mass and atomic number of the daughter nucleus (Radium-228 with atomic number 88) from the parent nucleus (Thorium-232 with atomic number 90). This yields an alpha particle (He), which has an atomic mass of 4 and atomic number of 2. Here's how it works:

232 90Th (parent nucleus) → 228 88Ra (daughter nucleus) + 4 2He (missing nucleus).

Thus, the missing nucleus is an alpha particle (Helium-4).

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The value of x is AB/3, which is equal to KD/3.

In the given scenario, we have two similar triangles, HKD and KFD. Since they are similar, their corresponding sides are proportional. In triangle HKD, the width KD is equal to x, and in triangle KFD, the base KF is equal to 3x (proportional to AB). Therefore, the value of x is AB/3, which is equal to KD/3.

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Answer: x=16

Step-by-step explanation:

In the processes of the dilation each number displayed in the first triangle is multiplied by four in order for the second figure to be created. Therefore you would also multiple 4 x 4 in order to get 16.

Answer:

  D.  7x -4

Step-by-step explanation:

You want the simplified form of the expression 2x-4+5x.

An expression is simplified by eliminating parentheses and combining like terms. Here, there are no parentheses, but there are like terms: 2x and 5x. Combining them gives ...

  2x -4 +5x

  = (2 +5)x -4

  = 7x -4 . . . . . . . . . matches choice D

The age of sister will be 97 years.

Using operands and a math operator to calculate a value is referred to as an "operation" in mathematics. The rules that apply to the given operands or numbers are predetermined by the math operator's symbol.

A collection of numbers and operations is an expression in mathematics. The following are the parts of a math expression that do a math operation.

Given David age = 6 years

his sister age = half of David age = 6/2 = 3

David is 3 years older than his sister

equation for ages of both David and his sister is

David age = Sister age + 3

when David is 100 years

sister age = David age - 3 = 100 - 3 = 97

Hence when David is 100 years old his sister will be 97 years.

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(x^2 + 16 + 8^2 = 18 + 8^2

The sum of the measures of the complementary, supplementary, and vertical angles for angle a of 33° is 237°.

The question asks for the sum of the measures of the complementary angle, supplementary angle, and vertical angle for angle a, given that angle a is 33°.

The complementary angle to angle a would be one that adds up to 90° with angle a. Since angle a is 33°, the complementary angle would be 90° - 33° = 57°.

The supplementary angle to angle a is one that adds up to 180° with angle a. The supplementary angle would thus be 180° - 33° = 147°.

The vertical angle to angle a shares the same measure as angle a, because vertical angles are equal. So, the vertical angle measure is 33°.

To find the total sum of these angles, you would add 57° + 147° + 33° = 237°.

Answer:- The total number of roots in the given polynomial function is 2.

Explanation:-

We know that corollary of Fundamental Theorem of Algebra tells that polynomial will have exactly as many roots(m) as its degree(m>0).

The given polynomial function [tex]g(x)=5x-12x^2+3[/tex] is a quadratic polynomial with degree 2.

Thus by corollary of Fundamental theorem of algebra

The total number of roots in the given polynomial function must be 2.

The required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The numbers on the number line increase as one moves from left to right and decrease on moving from right to left.

We have to determine the three decimals between 0.55 and 0.56

As per the attached number line,

Three decimals between 0.55 and 0.56 are :

⇒ 0.552, 0.553, and 0.554

Hence, the required three decimals between 0.55 and 0.56 are 0.552, 0.553, and 0.554 which are shown in the number line.

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Answer:

The correct option is all real numbers greater than or equal to -3.

Step-by-step explanation:

The concept of domain of a function refers to all the points in the x axis for which the function is defined. In the graph as you can see the function starts in x = -3 (includes that point) and growths towards positive values of x, to +∞. So its domain is [-3, ∞) or {R, x≥ -3} in other words "all real numbers greater than or equal to -3."

Answer: equation of a linear function in point-slope form

Step-by-step explanation:

Given : The equation of a linear function in point-slope form passing through point [tex](x_1,y_1)[/tex] is

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

The equation written by Harold correctly

[tex]y = 3(x - 7)[/tex]

It can be written as:[tex]y-0 = 3(x - 7)[/tex]

When we compare to the equation of a linear function in point-slope form, we get [tex]y_1=0,\ x_1=7[/tex]

Hence, the point used by Harold = [tex](x_1,y_1)=(7,0)[/tex]

If one inlet pipe can fill the pool in 12 hours and the drain can empty it in 20 hours, the combined rate of the two is 1/30 pools per hour. Therefore, it will take 30 hours to fill the pool with the drain open.

The question addresses a common concept in mathematics, which is rates and work problems. To determine the time it takes for the inlet pipe to fill the pool with the drain open, we first have to figure out the rates at which the pipe fills and the drain empties the pool.

If an inlet pipe can fill the pool in 12 hours, its rate of work is 1/12 pool per hour. Similarly, if the drain can empty the pool in 20 hours, then its rate is 1/20 pool per hour.

When both the inlet and drain are open, their combined rate will be the fill rate minus the drain rate, which is (1/12) - (1/20) = 1/30 pool per hour.

Therefore, at the combined rate, it will take 1 divided by 1/30 = 30 hours to fill the pool with the drain open.

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When both the inlet pipe and drain are open, it will take 30 hours to fill the pool, computed by dividing the total work done (1 pool) by the net rate (1/30 pool/hour).

In mathematics, problems such as these are usually solved by working with the concept of rates. In this scenario, we have two rates: the inlet pipe, and the drain. The rate of the inlet pipe is 1 pool per 12 hours, or 1/12 pool/hour. The rate of the drain is 1 pool per 20 hours, or 1/20 pool/hour. The net rate when both are open is thus (1/12 - 1/20) pool/hour, which simplifies to 1/30 pool/hour. To find out how long (t) it will take to fill the pool with both the inlet and drain open, we would use the fact that Rate x Time = Work Done. The Work Done in this case is 1 (equivalent to one pool), and the rate we’ve calculated as 1/30 pool/hour.

So, solving for time, we get:

t = Work Done / Rate = 1 pool / (1/30 pool/hour) = 30 hours.

So, it would take 30 hours to fill the pool with the inlet pipe and the drain open.

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Final answer:

The compound interest inequality for the investment account is 3500(1 + 0.08)^t < 6000. Solving this, we find that the account will have less than $6,000 for approximately 6 years.

Explanation:

To solve this problem, we will use the formula for compound interest which is [tex]A = P(1 + r)^t,[/tex] where:

We are trying to find the number of years, t, when the account will have less than $6,000, at an annual interest rate of 8%, i.e., r = 0.08.

The inequality will be:

[tex]3500(1 + 0.08)^t < 6000[/tex]

To solve for t, we first divide both sides by 3,500:

[tex](1 + 0.08)^t[/tex]< ≈ 1.7143

Now, take the natural logarithm of both sides:

[tex]ln((1 + 0.08)^t) < ln( 1.7143)[/tex]

t · ln(1.08) < ln(≈ 1.7143)

Divide both sides by ln(1.08) to isolate t and calculate:

t < ≈ ln(≈ 1.7143) / ln(1.08) < ≈ 6.6

Therefore, the investment account will have less than $6,000 for approximately 6 years.

Answer:

The approximate value of milos car 11 years after he purchased it is 3929.

Step-by-step explanation:

The given equation is

[tex]y=20646(0.86)^x[/tex]

Here, y is the estimates the value of a brand of car x years after it was purchased new.

We have to find the approximate value of milos car 11 years after he purchased it.

Substitute x=11 in the given equation.

[tex]y=20646(0.86)^{11}[/tex]

[tex]y=3929.33346204[/tex]

[tex]y\approx 3929[/tex]

Therefore the approximate value of milos car 11 years after he purchased it is 3929.