The diagram shows a cuboid with a volume of 42 cm³. K ? cm Work out the missing length of the cuboid. 2 cm 3 cm​

The volume of the fish tank in the shape of a right circular cylinder with a radius of 3 in and a height of 10 in is 90π cubic inches.

Therefore the answer is 90π in³.

Recognize that the fish tank is in the shape of a right circular cylinder.

Remember that the formula for the volume of a cylinder is

V = πr^2h

where r is the radius and h is the height.

Plug in the given values for the radius (r = 3 inches) and the height (h = 10 inches) into the formula.

Perform the calculation:

πr^2h

= π(3^2)(10)

= π×9×10

= 90π cubic inches

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[tex]d-2=4.6[/tex]

Add 2 to both sides:

[tex]d-2+2=4.6+2[/tex]

[tex]\fbox{d = 6.6}[/tex]

The final answer after solving the given equation could be 14.

What is Linear Equation ?

Linear Equation can be defined as the equation in which the highest degree of the variable is one. Linear equations are generally three types , they are standard form , slope intercept form , point slope form and linear equation is also called as the equation of straight line.

Given,

Given equation,

2x + 6 = 3x -8

separating the value into a similar term:

2x-3x = -8 - 6

subtracting the equation:

-x = -14

remove negative sign:

x = 14

Therefore , the final answer could be 14.

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Answer:

120 cm.

Step-by-step explanation:

The perimeter of a rectangle is found by adding up the length of all four sides. In this case, the length is 36 cm and the breadth is 24 cm. Therefore, the perimeter of the rectangular table-top is

2 (length + breadth) = 2 (36 + 24) = 2 × 60 = 120 cm.

Answer:

[tex] \sf \: h(-3) = 13[/tex]

Step-by-step explanation:

Given information,

→ h(a) = a² + 4

The value of h(a) when a is -3,

→ h(a) = a² + 4

→ h(-3) = (-3)² + 4

→ h(-3) = 9 + 4

→ [ h(-3) = 13 ]

Hence, required answer is 13.

In word variation, we can write as;

⇒ In the equation, A = C + Kx, if K is a nonzero constant and C = 0, then you have the function A = Kx, which is called a direct variation.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The equation is,

⇒ A = C + Kx

Now, We know that;

The direct variation is of the form of y = kx.

Here, The equation is,

⇒ A = C + Kx

Hence, Its words variation is written as;

In the equation, A = C + Kx,

if K is a nonzero constant and C = 0, then you have the function A = Kx, which is called a direct variation.

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Answer: uhm...

Step-by-step explanation:

2...?

Based on the information given, the number of students from Florida will be; 9000 students.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

We are given that At Florida A&M University, the ratio of students from Florida to students not from Florida is about 3 : 1

The Total number of students = 12000

Fraction from Florida = 3/4

Fraction of students not from Florida = 1/4

Therefore, the students from Florida will be:

= 3/4 × 12000

= 9000

Hence, the number of students from Florida is 9000.

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Answer:

2,570 meters

Step-by-step explanation:

110% of what number is 2827

1.1x = 2827  Divide both sides by 1.1

[tex]\frac{1.1x}{1.1}[/tex] = [tex]\frac{2827}{1.1}[/tex]

x = 2570

The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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The amount of money more that Key Club still need to earn in order to have reached their target is  $ 382. 50

To find the amount of money needed  by Kay Club to get to their target, first, find the amount of money earned from the bake sale :

= 2 / 5 x Target amount

= 2 / 5 x 1, 700

= $ 680

Then, they did a good sale and earned 3 / 8 of the amount :

= 3 / 8 x 1, 700

= $ 637. 50

The amount of money that Key Club still needs is:

= Total amount - amount raised

= 1, 700 - 680 - 637. 50

= $ 382. 50

In conclusion. Key Club would still need to engage in other activities to be able to reach their goal of $ 1, 700 as they have to raise $ 382. 50.

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Answer:

5.5

Step-by-step explanation:

7*8=56

42-8=34

56-34=22

22/4=5.5

The Constraints of the inequality are

x ≤ 2y + 500

22500  < √ 35x + 50y

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The Company A (x) at most 500 more than twice then unit by B(y).

So, x ≤ 2y + 500

Now, the square of Company Profit will be equal to 35x + 50y

Then, the constraints will be

1. x ≤ 2y + 500

2. Company Profit² < 35x + 50y

Company Profit < √ 35x + 50y

22500  < √ 35x + 50y

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Answer:

0.0005

Step-by-step explanation:

this is a binomial experiment -- they are either cured or not, and the outcome is random

probability = n choose r * p^r * q^(n-r)

here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur

probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)

= 0.00049284342 rounding to 0.0005

Answer:

A

Step-by-step explanation:

each text message is .17 text messages are x the total bill is 28.45. the service charges are 24.20.

.17x + 24.50 = 28.45

The value of p is 12.322

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as: For x > 0 , a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here p=-log(2.1×10¹²)

                  p= - ( log(2.1) +12 log10)

                  p= -(0.322+12)

                  p=12.322

Hence, the value of p is 12.322

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Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

The properties of the rational exponents are given and a rational equation is of the form b = aˣ

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the rational exponent equation be A

Now , the properties of the exponent equations are

mᵃ×mᵇ = mᵃ⁺ᵇ

The powers of the exponents are added together

mᵃ / mᵇ = mᵃ⁻ᵇ

The powers of the exponents are subtracted together

( mᵃ )ᵇ = mᵃᵇ

The powers of the exponents are multiplied together

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

Any number raised to the power of 0 is 1

m⁻ᵃ = ( 1 / mᵃ )

Hence , the exponents are solved

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In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, equation and statistics.

In 7th grade math, students typically learn basic algebraic principles, including linear equations, variables, and functions. They also learn about ratios, proportions, and percents. Geometry is typically introduced, with topics such as angles, lines, triangles, and circles. Additionally, students may be taught more advanced topics such as graphing, probability, and statistics.In 7th grade math, students learn basic algebra, ratios and proportions, geometry, graphing, probability, and statistics.

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On solving the provided question, we can say that - the answer of the following sequence 1.9, 3x , 8x will be 13.78x

A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.

sequence 1.9, 3x , 8x

answer is = 13.78x

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No, I'm not agree with Noah. Because the equation 1. 20(d+5)=42 is a mathematical equation and can be false depending on the value of the variable d.

The equation 1. 20(d+5)=42 is a mathematical equation that contains a variable d. The equation states that when you multiply 20 with (d+5) the result should be 42.

The equation is true if there is a value of d that makes the equation true. For example, if d=1, then 20(1+5)=20(6)=120 which is not equal to 42, so this value of d does not make the equation true.

On the other hand, if d=-7, then 20(-7+5)=20(-2)= -40 which is equal to 42, so this value of d makes the equation true.

Therefore, the equation can be true or false depending on the value of the variable d. In general, without knowing the specific context or situation in which the equation is being used, it is impossible to determine if the equation accurately represents a situation or not.

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[tex]2xA^{3}[/tex]  is a polynomial as a result.  Constants, variables, and exponents can all be included in a polynomial, but variable division is never permitted.

In mathematics, a polynomial is an expression made up of variables (also known as indeterminates) and coefficients that exclusively uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation made up of variables, constants, and exponents that are mixed using mathematical operations including addition, subtraction, multiplication, and division (No division operation by a variable).

given

[tex]2xA^{3}[/tex]  is a polynomial as a result. Constants, variables, and exponents can all be included in a polynomial, but variable division is never permitted.

It is impossible to classify an expression as a polynomial if it contains a variable with exponents that are negative or fractional, divides by a variable, or is included inside a radical.

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The value of expression -x³+3x²+5x+1 is -1235 when x is 12

An expression is combination of variables, numbers and operators.

Given polynomial is -x³+3x²+5x+1

We need to find the value of the polynomial when x is 12.

To find this we just need replace x with 12

-(12)³+3(12)²+5(12)+1

Minus twelve cube plus three times of twelve square plus five times of twelve plus one

-1728+3(144)+5(12)+1

-1728+432+60+1

-1728+493

-1235

Hence, the value of expression -x³+3x²+5x+1 is -1235 when x is 12

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The option A "He should use the median because there is an outlier that affects the mean." is correct.

It is clear from the data that option E's house is much more expensive than those in the other options. A $9,00,000 price is therefore an outlier in this set of data.

In symmetrically distributed data, an inference is made using the mean. Due to the inclusion of an outlier, the data is not symmetrical. As a result, the mean won't accurately depict the data's centre. As a result, we shall refrain from drawing conclusions about the pricing of the residences using the mean.

Therefore, since the median is unaffected by outliers, we shall use it.

Therefore, since there is an outlier that influences the mean, we will utilise the median. The answer is (A).

Your sincere criticism is crucial for better outcomes.

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The factors of 2[tex]x^{2}[/tex] + 7x + 3 are ( x + 3) and (2x + 1)

Now, According to the question:

The given function is :

f(x) = [tex]2x^2+7x+3[/tex]

To find the factors of  [tex]2x^2+7x+3[/tex] we need to split the middle term, that is, 7x.

7x = 6x + x

Therefore, 2[tex]x^{2}[/tex] + 7x+ 3 can be written as 2[tex]x^{2}[/tex] + 6x + x + 3 .

On taking '2x' common from first two terms and +1 from next two terms we get

2x (x + 3) +1 (x + 3)

(x + 3) (2x + 1)

Thus, the factors of 2x2 + 7x + 3 are (x+3) and (2x+1)

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The complete question is this:

What are the factors of 2x^2+7x +3?

The perimeter of the rectangle, given the area and the segment from R ( 6, -16) to S (14, - 1 ) is 88 units

To find the perimeter, first find the distance between  R ( 6, -16) to S (14, - 1 ) which will allow you to find the length of one side. This distance can be found by the formula :
= √((x2 – x1)² + (y2 – y1)²)

= √((14 – 6)² + (-1 – (-16))²)

= 17 units

This means that one side of the rectangle measures 17 units so the other side would be:

Area = Length x Width

459 = 17 x Width

Width = 459 / 17

Width = 27 units

The perimeter of the rectangle is:

= Length + Width + Length + Width

= 17 + 27 + 17 + 27

= 88 units

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Answer:

v=πr²h

divide both sides by πh

v/πh=r²

r²=v/πh

square root both sides

r=√v/√πh

I hope this helps

6th terms of given geometric progression whose common ratio is 3/2 and first term is 4  is 243/8 using the farmula ar^(n-1).

What is a geometric sequence?

A mathematical sequence known as a geometric progression (GP) is one in which each following phrase is generated by multiplying each preceding term by a fixed integer, or "common ratio." This progression is sometimes referred to as a pattern-following geometric sequence of numbers. Learn development in mathematics here as well. Here, each phrase is multiplied by the common ratio to generate the subsequent term, which is a non-zero value. A geometric series with a common ratio of 2 is 2, 4, 8, 16, 32, 64, etc.

Geometric Progression takes the following general form: a, ar, ar^2, ar^3, ar^4,..., ar^(n-1).

a = First term where

The common Ratio is r.

nth term = ar^(n-1)

6th terms ar^(6-1) = ar^5.

given is that r =3/2. a = 4.

6th term = 4 * (3/2)^5

= 4 * 3^5/2^5

=4*243/4*8

=243/8.

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the answer to your question is 36