Describe the two possible outcomes of the​ test, using the context of the given situation. The governor claims that the percentage of adults over 21 who have graduated from high school is greater than 78​%,the national average.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

The area is changing at 15.75 square feet per second.

Step-by-step explanation:

The triangle between the wall, the ground, and the ladder has the following dimensions:

H: is the length of the ladder (hypotenuse) = 10 ft

B: is the distance between the wall and the ladder (base) = 6 ft

L: the length of the wall (height of the triangle) =?

dB/dt = is the variation of the base of the triangle = 9 ft/s        

First, we need to find the other side of the triangle:  

\(H^{2} = B^{2} + L^{2}\)

\( L = \sqrt{H^{2} - B^{2}} = \sqrt{(10)^{2} - B^{2}} = \sqrt{100 - B^{2}} \)

Now, the area (A) of the triangle is:            

\( A = \frac{BL}{2} \)  

Hence, the rate of change of the area is given by:

\( \frac{dA}{dt} = \frac{1}{2}[L*\frac{dB}{dt} + B\frac{dL}{dt}] \)      

\( \frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} + B\frac{d(\sqrt{100 - B^{2}})}{dt}] \)        

\(\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - B^{2}}*\frac{dB}{dt} - \frac{B^{2}}{(\sqrt{100 - B^{2}})}*\frac{dB}{dt}]\)  

\(\frac{dA}{dt} = \frac{1}{2}[\sqrt{100 - 6^{2}}*9 - \frac{6^{2}}{\sqrt{100 - 6^{2}}}*9]\)      

\(\frac{dA}{dt} = 15.75 ft^{2}/s\)  

Therefore, the area is changing at 15.75 square feet per second.

I hope it helps you!                                    

The rate of change (ROC) of the area with respect to (w.r.t.) time can be

found from the ROC of the area w.r.t. x and the ROC of x w.r.t. time.

Reasons:

The length pf the ladder = 10 feet

Rate at which the ladder is pulled from the wall, \(\displaystyle \frac{dx}{dt}\) = 9 feet per second

Required:

The rate at which the area of the triangle formed by the ladder, the wall

and the ground, is changing at the instant the ladder is 6 feet from the wall.

Solution:

The area the triangle, A = 0.5·x·y

Where;

x = The distance of the ladder from the wall

y = The height of the ladder on the wall

By Pythagoras's theorem, we have;

10² = x² + y²

Which gives;

y = √(10² - x²)

Therefore;

The area the triangle, A = 0.5 × x × √(10² - x²)

By chain rule, we have;

\(\displaystyle \frac{dA}{dt} = \mathbf{\frac{dA}{dx} \times \frac{dx}{dt}}\)

\(\displaystyle \frac{dA}{dx} = \frac{d\left(0.5 \cdot x \cdot \sqrt{10^2 - x^2} }{dx} = \mathbf{\frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100}}\)

\(\displaystyle \frac{dA}{dx} = \frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100}\)

Therefore;

\(\displaystyle \frac{dA}{dt} = \mathbf{\frac{\left(x^2 - 50\right) \cdot \sqrt{100-x^2} }{x^2-100} \times 9}\)

When the ladder is 6 feet from the wall, we have;

x = 6

\(\displaystyle \frac{dA}{dt} = \frac{\left(6^2 - 50\right) \cdot \sqrt{100-6^2} }{6^2-100} \times 9 = \mathbf{15.75}\)

At the time the ladder is 6 feet from the wall, the area is increasing at 15.75 ft.²/sec.

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Answer: 3x + 15

Step-by-step explanation:

In order to use the distributive property, you simply multiply the number on the outside by both the number inside the parenthesis

So, in this case, we would multiply 3 by X and 3 by 5

3 times x = 3x

3 times 5 =15

Your new equation is then made by adding these two together

3x+15

Answer 3x + 15

Answer:

50 degrees

Step-by-step explanation:

Angle ABE is the opposite of the angle given on two converging lines, making it the same degree :)

The sum Y = X1 + X2 + X3's mgf is 1 + 2X + 3X².

Given,

Y = X1 + X2 + X3.

\($\frac{d}{d X}\left(X^1+X^2+X^3\right)\)

Simplifying the above equation,

\($X^1+X^2+X^3: \quad X+X^2+X^3$\)

= \($\frac{d}{d X}\left(X+X^2+X^3\right)\)

=\($\frac{d}{d X}(X)+\frac{d}{d X}\left(X^2\right)+\frac{d}{d X}\left(X^3\right)\)

\($\frac{d}{d X}(X)=1\)

Simplifying,

\($\frac{d}{d X}\left(X^2\right)=2 X\)

\($\frac{d}{d X}\left(X^3\right)=3 X^2\)

Then we get,

= 1 + 2X + 3X²

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Answer:

D. 8x - 3

Step-by-step explanation:

Simply add all the sides up - 2x+3x+3x - 1+1+1 = 8x - 3

The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Answer:

Step-by-step explanation:

To prove that the sum of the first n even +ve integers is:

\(\mathsf{2+4+6+8+ . . . +2n = n^2+ n }\)

By using mathematical induction;

For n = 1, we get:

2n = 2 × 1 = 2

2 = 1² + 1 ----- (1)

∴ the outcome is true if n = 1

However, let assume that the result is also true for n = k

Now, \(\mathsf{2+4+6+8+. . .+2k = k^2 + k --- (2)}\)

\(\mathsf{2+4+6+8+. . .+2k+2(k+1)}\)

we can now say:

\(\mathsf{= (k^2 + k) + 2(k + 1)} \\ \\ \mathsf{= k^2 + k + 2k + 1}\)

\(\mathsf{= (k^2 + 2k + 1) + (k + 1)}\)

\(\mathsf{= (k + 1)^2 + (k + 1)}\)

∴

\(\mathsf{2 + 4 + 6 + 8 + . . . + 2k + 2(k + 1) = (k + 1)^2 + (k + 1)}\)

Thus, the result is true for n = m+1, hence we can posit that the result is also true for each value of n.

As such \(\mathsf{2+4+6+8+. . .+2n = n^2 + n }\)

a) Y=38.6594-5.4198x; b) 39.1% explained variation; c) Y=44.9379-5.9522x1-1.2758x2-2.0102x3; d) 49.9% explained variation; e) Y=45.2478-6.1081x1-0.9945x2-2.5692x3+0.9963x4; f) 53.1% .

a) The estimated regression equation for predicting fuel efficiency for highway driving is Y = 38.6594 - 5.4198x, where x represents the engine's displacement in liters.

b) The estimated regression equation explains 39.1% of the variation in the sample values of HwyMPG.

c) The estimated regression equation that includes the dummy variables ClassMidsize and ClassLarge is Y = 44.9379 - 5.9522x1 - 1.2758x2 - 2.0102x3, where x1 represents engine's displacement, x2 represents variable ClassMidsize, and x3 represents variable ClassLarge.

d) The estimated regression equation with the added dummy variables explains 49.9% of the variation in the sample values of HwyMPG.

e) The estimated regression equation that includes the dummy variable FuelPremium is Y = 45.2478 - 6.1081x1 - 0.9945x2 - 2.5692x3 + 0.9963x4, where x1 represents engine's displacement, x2 represents variable ClassMidsize, x3 represents variable ClassLarge, and x4 represents variable FuelPremium.

f) The estimated regression equation with all three dummy variables explains 53.1% of the variation in the sample values of HwyMPG.

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The probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.

What is the central limit theorem?

The central limit theorem, which states that the sample means of large samples (n > 30) from a population with any distribution approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

We can solve this problem by using the central limit theorem,

In this case, the sample size is n = 56, which is larger than 30, so we can assume that the sample means are normally distributed. The mean of the sample means is equal to the population mean, which is 55.5 inches, and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size:

standard deviation = 6 / √(56) = 0.801

To find the probability that the mean height of the sample will be greater than 53 inches, we can standardize the sample mean using the standard deviation calculated above:

z = (sample mean - population mean) / (standard deviation)

= (53 - 55.5) / 0.801

= -3.12

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is greater than -3.12:

P(Z > -3.12) = 0.9991 (rounded to four decimal places)

Therefore, the probability that the mean height of a random sample of 56 ten-year-old males will be greater than 53 inches is approximately 0.9991, or 99.91% when rounded to three decimal places.

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200.60 interest does andy’s account earn.

Let x be the amount of interest earned by Andy's account.

According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:

x = 200 + 0.3% of 200

Simplifying the right-hand side of the equation, we get:

x = 200 + 0.003 × 200

x = 200.60

Therefore, the answer is option 1: 200.60.

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For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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Answer:

A. 3x+12

Step-by-step explanation:

8x+3-5x+9

8x-5x=3x

3+9=12

then put them together

3x+12

answer= A

Answer:

its line fjfjfjjejjdjdj

As per the given condition, the required one dimensional object with no end point is a line.

"In geometry, a ray can be defined as a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.

On its way to infinity, a ray may pass through more than one point. When naming a ray, it is denoted by drawing a small ray on top of the name of the ray. "

"A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints."

"A line is a one-dimensional object, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. "

"A point is a primitive notion that models an exact location in the space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space."

Given, a one dimensional object with no endpoint.

Therefore, the require object is a line.

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11, - 6, -1, 4, 9, 14, 19, ... are mapped onto 4. ... A;-l = (-ltQn (mod N),. (A5.34) ... 131 2, 14, 34, 38, 42, 78, 90, 178, 778, 974(1000).

Step-by-step explanation:

the nearest .1/2 incp, we say the 'unit 131/2 incl. 1.4 a measUrement is-stated tp- be 546 inch, this UM= the

Answer:

  (A)  the addition property of equality and then the division property of equality

Step-by-step explanation:

To get from Step 1 to Step 2, we have added 5 to both sides of the equation:

  -3x -5 +5 = 13 +5

  -3x = 18

To get from Step 2 to Step 3, we have divided both sides of the equation by -3:

  -3x/-3 = 18/-3

  x = -6

These operations can be described as ...

  the addition property of equality and then the division property of equality

__

However, since addition and subtraction are the same thing, but with opposite numbers, and since multiplication and division are the same thing, but with reciprocal numbers, any of the answer choices is arguably correct.

  (add 5, divide by -3) = (add 5, multiply by -1/3) =

  (subtract -5, divide by -3) = (subtract -5, multiply by -1/3)

Answer:

A.) the addition property of equality and then the division property of equality

Step-by-step explanation:

Got It Right. Trust me

Step-by-step explanation:

We know from the problem that:

1 centimeter = 0.3937 inches

1 yard = 36 inches

I suggest that we convert the starting length of 2.4 meters to centimeters, and from there we could convert to inches, and then convert to yards.

\(\frac{2.4\ meters}{}|\frac{100\ centimeters}{1.0\ meters} |\frac{0.3937\ inches}{1.0\ centimeters} |\frac{1.0\ yards}{36\ inches}\)

\(=(2.4)(\frac{100}{1.0})(\frac{0.3937}{1.0})(\frac{1.0}{36})\)

\(=(\frac{(2.4)(100)(0.3937)}{36})yards\)

\(=2.62\ yards\)

Answer:

10P-25

Step-by-step explanation:

Answer: -25 is not greater than 10 :P

Answer:

Step-by-step explanation:

\(2xsin(2y)dx-(x^2+10) cosy dy =0\\\\\frac{2x}{x^2 + 10}dx= \frac{cosy}{sin(2y)}\)

Take integration both side (apply substitution for the left hand side, apply sin(2y) = 2 sin(y) cos(y) for the right hand side) you will have the condition.

Problem solved

Hey there!

If d = 3 then substitute where “d” is at, now let’s work out the equation!

5(9 + 3) – 6

• DISTRIBUTE:

5(9) + 5(3)

5(9) = 45

5(3) = 15

• NEW EQUATION:

45 + 15 – 6

45 + 15 = 60

60 – 6 = 54

Answer: 54 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

SIDE NOTE:

You could use PEMDAS to solve this as well.

Here’s what it means ⬇️

• Parentheses

• Exponent

• Multiplication

• Division

• Addition

• Subtraction

Answer:  No, we don't have a right triangle

==========================================================

Explanation:

If a triangle with sides a,b,c makes the equation a^2+b^2 = c^2 true, where c is the longest side, then this triangle is a right triangle. This is the converse of the pythagorean theorem.

Here we have a = 2, b = 5 and c = 7.

So...

a^2+b^2 = c^2

2^2+5^2 = 7^2

4+25 = 49

29 = 49

The last equation is false, so the first equation is false for those a,b,c values. Therefore, we do not have a right triangle.

------------

In contrast, consider the classic 3-4-5 right triangle

a = 3, b = 4 and c = 5 would make a^2+b^2 = c^2 true because 3^2+4^2 = 5^2 is a true equation (both sides lead to 25).

Answer:

Step-by-step explanation:

area of circle=π*r^2

=3.14*2.5^2

=3.14*6.25

=19.625

=19.63

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:

y- (0,2.5) x-(3.5,0)

Step-by-step explanation:

This is because the intercepts of a graph are the points at which a line intersects with a desired axis. So for the Y axis the inercept would be at 2.5 making the y intercept (0,2.5). The same concept is used on the X axis.

Answer:

4 ( 4 + 4 + 4 )

Step-by-step explanation:

Answer:

40%.

Step-by-step explanation:

There are 6 / 15 apples out of the bowl.

6/15 = 2/5 = 0.4

So, 40% of the fruit in the bowl are apples.

Hope this helps!

Answer:

line AB and line CD are parallel

line AB and line EF are perpendicular

Step-by-step explanation:

it is the third option