True or false: in the expression 6^8 there are 8 factors of 6

Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.

To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.

Let's denote the length of the actual tank as "x".

According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.

So, we can set up the following proportion:

1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)

Cross-multiplying and solving for x, we get:

x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm

The actual tank is 1620 cm long.

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Answer:

1570f³t

Step-by-step explanation:

V=πr²h

V=3.14×10²×5

V=3.14×100×5

V=314×5

V=1570

Answer:

The correct answer is true.

Answer:

65 x 160  / 100 = 104

Step-by-step explanation:

Answer:

x>1 (the first one)

Step-by-step explanation:

The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985

Probability is what has the potential to happen. This area of math examines how random events happen. A value between 0 and 1 is used to express it. In order to anticipate the possibility of events, probability has been introduced to mathematics. The degree of likelihood that something will happen can be used to define probability. This fundamental theory of probability, which is also applied to the probability distribution, can be used to estimate the likelihood of the results of a random experiment. We must first determine the total number of alternatives in order to determine the likelihood that a specific event will occur.

Given that : He or she did not have the disease. The individual actually had the disease No positive 9 , negative 133 Yes Positive 140 ,Negative 18 .

                      Yes              No

Positive :          140            9

negative :         18              133

P = \(\frac{Someone get positive }{he not had the disease}\)

= \(\frac{140}{142}\)

=0.985

The probability of getting someone who tested positive, given that he or she did not have the disease is 0.985

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The domain of a function is all the possible input values for which the function is defined.

Function is a block of code that performs a specific task. It is a reusable piece of code that can be called from other parts of the code, reducing the amount of code that needs to be written and making the code easier to read and maintain. Functions can take in parameters and return values, allowing for increased flexibility and reusability. Functions can also be used to break up large programs into smaller, more manageable pieces.

In this case, the reasonable domain for the function f(x) = 4x³-50x²+150x would be all real numbers. This is because the function is a polynomial, which is continuous, meaning that it is defined for all real numbers.

The input of the function is a width, and the output is a volume. Therefore, the domain of the function should include all reasonable widths that could produce a volume. This means that the domain should include all positive real numbers, as any negative value would produce a negative volume, which is not reasonable. Thus, the reasonable domain for the function f(x) = 4x³-50x²+150x is all positive real numbers.

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The biconditional statement for the given conditional statement would be:

2x = 18 if and only if x = 9.

The given conditional statement "If 2x = 18, then x = 9" can be represented symbolically as p → q, where p represents the statement "2x = 18" and q represents the statement "x = 9".

To form the biconditional statement, we need to determine if the converse of the conditional statement is also true. The converse of the original statement is "If x = 9, then 2x = 18". Let's evaluate the converse statement.

If x = 9, then substituting this value into the equation 2x = 18 gives us 2(9) = 18, which is indeed true. Therefore, the converse of the original statement is true.

Based on this, we can write the biconditional statement:

2x = 18 if and only if x = 9.

The biconditional statement implies that if 2x is equal to 18, then x must be equal to 9, and conversely, if x is equal to 9, then 2x is equal to 18. The biconditional statement asserts the equivalence between the two statements, indicating that they always hold true together.

In summary, the biconditional statement is a concise way of expressing that 2x = 18 if and only if x = 9, capturing the mutual implication between the two statements.

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I believe it will be y=3x−12 if I'm not mistaken?

Answer: 12+r=54

Step-by-step explanation:

r=Rhonda's height

12+r=54

Answer:

12+ r = 54

Step-by-step explanation:

If 54 is the sum, we put it at the end of the equations. Sum means 'the answer to an addition equation' so it must be add ( + )

If we use r to represent Rhonda's height then we have the equation of:

12+ r = 54

NOT PART OF THE QUESTION BUT IF NEEDED:

To figure out Rhonda's height, do 54 - 12= r

The measure of angle VUT is ∠VUT = 70°.

What are angles in a linear pair?

When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.

In the given figure, ∠RVU and ∠UVT are in linear pair, so by using the property of angles in a linear pair, we can write

                ∠RVU + ∠UVT = 180°

                  120° + ∠UVT = 180°

                         ∠UVT = 60°

Now as we know the sum of all angles of a triangle is equal to 180°,

               ∠UVT + ∠VTU + ∠VUT = 180°.

                   60° + 50° + ∠VUT =180°

                       110° + ∠VUT = 180°

                        ∠VUT = 180° - 110°

                        ∠VUT = 70°

Hence, the measure of angle VUT is ∠VUT = 70°.

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The given trinomial is:

It is required to choose the first step in the process of factoring the trinomial.

Recall that the first step in the process of factoring all trinomials is to list all the factors of the whole number in the constant term.

Hence, the first step for the given trinomial is to list all the factors of 40.

Option C is the answer.

Answer:

just sayin x=4

Step-by-step explanation:

Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

Answer:

28 and 30

Step-by-step explanation:

'x' = 1st consecutive #

'x+2' = 2nd consecutive #

x + x+2 = 58

2x + 2 = 58

2x = 56

x = 28

x+2 = 30

Answer:

B

Step-by-step explanation:

We are given the following relationship:

To solve for "x", we multiply both sides by 6, like this.

Simplifying:

Therefore, the value of "x" is 9.

Let's solve your equation step-by-step.

4+5(x−3) =2 (x−3)
5x−11=2x−6 (Simplify both sides of the equation)

Answer: 5/3

1) Since we have a cylinder, then we can write out the formula to find the volume as the product of its circular base times its height, simply put:

Remember that the area of a circle is pi times r²

2) So now let's plug into that the given values:

Hence, the volume of that Cylinder is 37.5 in³

The distance that would be covered after t seconds = 1.5t meters

The speed of the race=distance/time =1.5m/s

The time given = t seconds

The distance (d) = ?

From the formula of speed = distance/time, make distance the subject of formula,

distance (d) = speed×time

= 1.5×t

= 1.5t meters

Therefore, the distance covered is 1.5t meters after t seconds.

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The cosine of the angle opposite the side of length 5.64 meters is 0.4536.

In a triangle, the cosine of the angle opposite a side is given by the formula:

cos(angle) = (a^2 + b^2 - c^2)/(2ab) where a, b, and c are the lengths of the sides of the triangle and angle is the angle opposite the side of length c. Given the side lengths of the triangle as 3.18 meters, 7.82 meters and 5.64 meters, the side opposite angle we want to find is 5.64 meters.

so we can use the above formula and substitute the values,

cos(angle) = (3.18^2 + 7.82^2 - 5.64^2)/(23.187.82) = 0.4536

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Answer:

43°

Step-by-step explanation:

7x+1+9x-7=90

16x-6=90

16x=96

x=6

the minor arc AD = 7x+1 =7(6)+1

= 42+1=43°

measure of AD

Thus, the cost of steel for making  500 solid steel part for a wind turbine is found as: Total Price = $1170.04 .

Atmospheric gases move according to their densities as one material rises above another. It affects what floats and what starts to sink in a body of water. A estimate of how compressed matter is is what density means. How much "stuff" is crammed into an area, to put it simply.

It is a calculable and manipulable formula in mathematics. Density is used to discuss population in various fields, such as the social sciences.

Density = mass / volume

mass = density * volume.

density of steel =  7.95 g/cm³

volume of steel = 1,015 cm³

Unit rate =  $0.29 per kilogram

mass = 7.95 * 1,015 g

mass = 8069.25 g

mass of 500 parts = 500* 8069.25

mass of 500 parts = 4034625 grams

mass of 500 parts = 4034625/1000 = 4034.625 kg

Total Price = mass of 500 parts *Unit rate

Total Price = 4034.625 * 0.29

Total Price = $1170.04

Thus, the cost of steel for making  500 solid steel part for a wind turbine is found as: Total Price = $1170.04 .

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Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

It is better to buy the 16-ounce drink and it is 0.01 cent cheaper

Step-by-step explanation:

We have to find out how much each sports drinks cost per ounce.

0.96 ÷ 12 = 0.08 per ounce

1.12 ÷ 16 = 0.07 per ounce

It is better to buy the 16-ounce drink and it is 0.01 cent cheaper

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

2916 ft³

Volume helps describe the amount of space that a shape takes up.

Volume of a Sphere

Volume describes the 3-dimensional size of a shape. Since volume is a 3-D measurement, the units should be cubed; this explains why the answer is given in feet cubed. In order to find the volume, we need to use the radius. The radius of a sphere is the distance from the center to the outside. In this case, we are told that the radius is 9 ft.

Volume Formula

Every regular shape has its own volume formula. For a sphere, the formula is:

So, to find the volume, all we need to do is plug in the radius. For this sphere, r = 9.

When using 3 for pi, the volume of the sphere is 2916 ft³.

1. Proportional relationship is also called a direct variation of y with x. The equation that describes such variation is:

y = kx

Where k is a constant of proportionality.

One common example of a direct variation is:

The pound of candies cost $0.45. Write the equation for the cost of x pounds of candies.

The equation for the problem is y = 0.45x

The graph of this function is a line that passes through the origin.

2. Inverse variation. The equation for this function is:

yx = k

Where k is the constant of inverse proportionality.

An example could be: One worker builds a house (alone) in 60 days. Write the equation of the time needed to build the house for x workers at the same pace.

The equation is:

yx = 60

The graph of this equation is one branch of a hyperbola. See the figure below:

3. Neither inverse nor direct variation. Any other form of the equation cannot be classified as inverse or direct variation. We could use, for example:

y = mx + b

A real situation can be stated as follows: A gym charges $40 as a fixed fee and $25 per month. The equation for the cost of the gym as a function of the number of months (x) is:

y = 25x + 40

The graph of this equation is a line that does not pass through the origin, so it's not a direct variation.

Answer:

-10

Step-by-step explanation:

Let the number be x

x - 40 = 5x

⇒ -40 = 5x - x

⇒ 4x = -40

⇒ x = -40/4

⇒ x = -10

Answer:

-10

Step-by-step explanation:

Let the number be x

x - 40 = 5x

4x = -40

x = -10

Answer:

3log(z)/2−2log(x)−5log(y)

Step-by-step explanation: