Use the distributive property to write equivalent expression 3(2 times +6)

Answer:

1 & 3, 2 & 4, 5 & 7, and 6 & 8 are vertically opposite angles

4 & 8, 3 & 7, 1 & 5, and 2 & 6 are corresponding angles

4 & 6 and 3 & 5 are alternate angles

1 & 2, 2 & 3, 3 & 4, 1 & 4, 5 & 6, 6 & 7, 7 & 8, and 5 & 8 are supplementary angles

Sum of squares of sample means about the grand mean is 6463.27 .

Firstly,

SS(error) = SS(total) - SS(treatments)

=8474.79-2011.52

=6463.27

Now,

df (treatments)=SS (treatments) / MS (treatments)

= 2011.52/287.36

= 7

Now,

df (error) = 18-7

=11

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Calculation table and question table is attached below .

Answer:

7.4secs

Step-by-step explanation:

If the path of a swim team member is modeled by the equation

h(t) = -0.875t²+5.25t+14

where t is time in seconds and h is the height above the surface of the water

If she need to finish in no later than 5feet above the surface, the expression will become:

-0.875t²+5.25t+14≤5

-0.875t²+5.25t+14-5≤0

-0.875t²+5.25t+9≤0

Rewriting using fraction

-7/8t²+21/9t+9≤0

To get the time that this happens we will need to factorize the resulting expression above;

On factorising

Find the roots of the equation using the formulas

t = 3+3√105/7

t = 3+ 3(10.25)/7

t = 3 + (30.75)/7

t = 3 + 4.393

t = 7.393

t = 7.4secs

Hence this happens at t = 7.4secs

Answer:

The time when the swim team member is 5 feet above the water surface is 7.4 seconds.

Step-by-step explanation:

You want to know when a member of the swim team finished his jump no later than 5 feet above the surface of the water to prepare for the splash, that is, when t is 5 feet above the surface of the water. Substituting h(t) for this value 5 in the equation you obtain:

5= -0.875*t²+5.25*t+14

A quadratic equation has the general form:

a*x² + b*x +c= 0

where a, b and c are known values ​​and a cannot be 0.

Taking the equation 5= -0.875*t²+5.25*t+14 to that form, you get:

 -0.875*t²+5.25*t+14-5=0

  -0.875*t²+5.25*t+9=0

The roots of a quadratic equation are the values ​​of the unknown that satisfy the equation. And solving a quadratic equation is finding the roots of the equation. For this you use the formula:

\(\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}\)

In this case, solving the equation is calculating the values ​​of t, that is, you find the time when the swim team member is 5 feet above the water surface.

Being a= -0.875, b=5.25 and c= 9, then

\(\frac{-5.25+-\sqrt{5.25^{2}-4*(-0.875)*9 } }{2*(-0.875)}\)

\(\frac{-5.25+-\sqrt{27.56+31.5 } }{-1.75}\)

\(\frac{-5.25+-\sqrt{59.06 } }{-1.75}\)

\(\frac{-5.25+-7.685}{-1.75}\)

Then:

\(t1=\frac{-5.25+7.685}{-1.75}\) and \(t2=\frac{-5.25-7.685}{-1.75}\)

Solving for t1:

\(t1=\frac{2.435}{-1.75}\)

t1= -1.39 ≅ -1.4

Solving for t2:

\(t2=\frac{-12.935}{-1.75}\)

t2= 7.39 ≅ 7.4

Since time cannot be negative, the time when the swim team member is 5 feet above the water surface is 7.4 seconds.

we can conclude that only about 2.28% of vehicles in Santa Clara are more than 6 years old, based on the given average age and standard deviation of the vehicle age distribution.

To answer this question, we can use the standard normal distribution table or a calculator to find the area under the standard normal distribution curve for the given probability. To do this, we need to standardize the variable of interest, which in this case is the age of the vehicle, into a standard normal variable with a mean of 0 and a standard deviation of 1. To standardize the variable of interest, we can use the formula

z = (x - mu) / sigma

where z is the standardized variable, x is the age of the vehicle, mu is the mean age of the vehicle (9 years), and sigma is the standard deviation of the vehicle age (18 months, or 1.5 years).

To find the percentage of vehicles that are more than 6 years old, we need to find the area under the standard normal distribution curve to the left of the standardized variable z = (6 - 9) / 1.5 = -2.

Using a standard normal distribution table or calculator, we can find that the area to the left of z = -2 is approximately 0.0228. This means that the percentage of vehicles that are more than 6 years old is approximately:

0.0228 * 100% = 2.28%

Therefore, we can conclude that only about 2.28% of vehicles in Santa Clara are more than 6 years old, based on the given average age and standard deviation of the vehicle age distribution.

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Answer: 4 square units

Step-by-step explanation:

To find the value of A in square units, substitute into the equation for s and solve.

Given the figure in the attached image.

The triangle JKL is a right-angled triangle.

Applying trigonometry;

Given;

Substituting the given values;

Cross multiply;

Recall that;

So, we have;

Therefore, the equ

Answer: \(\frac{\sqrt{3} }{2}\)

Step-by-step explanation:

Answer:

V = 3,367.6 cm³

Step-by-step explanation:

Diameter of sphere (D) = 18.6 cm

radius (r) = ½(18.6) = 9.3

π = 3.14

Formula for volume of a sphere = ⁴/3πr³

Plug in the values

V = ⁴/3 × 3.14 × 9.3³

V = ⁴/3 × 3.14 × 804.357

V = (4*3.14*804.357)/3

V = 3,367.57463

V = 3,367.6 cm³ (nearest tenth)

a = 5

b = 4

c= 0

Therefore, the equation for graph C is Y = a ^b + c

Y = 5 ^4 + 0

A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Graphs are a popular tool for graphically illuminating data relationships. A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.

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The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given phrase,

y is greater than or equal to two-thirds times x plus 1 ⇒ y ≥ (2/3)x + 1

y is less than negative one-fourth times x plus 2 ⇒ y < (-1/4)x + 2

Substitute, point (−6, −3)

-3 ≥ (2/3)(-6) + 1

-3 ≥ -3  

Substitute in second inequality,

-3 < (-1/4)(-6) + 2

-3 < 7/2

Hence "The inequalities are y ≥ (2/3)x + 1 and y < (-1/4)x + 2 and (−6, −3) satisfied the inequality".

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Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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Answer:

Hindi KO po Alam yan

Step-by-step explanation:

pagaralan mo nang mabuti

Answer:

6 plus 6 or 10 plus 2

Step-by-step explanation:

pretty

that adds up to 12

Answer:

8% increase.

Step-by-step explanation:

38880 - 36000 = 2800. 2800/36000 = 0.7777... x 100% = 8%

Answer:

first of all find increase in number

38880-36000

=2880

now divide 2880 by the first value i.e. 36000 and do multiply by 100%

=2880/36000*100%

=288000/36000

=8%

Step-by-step explanation:

Answer:

Step-by-step explanation:

The vertices of the square with diagonals contained in the lines y = x and y = -x + 6 are (3, 3), (3, -3), (-3, 3), and (-3, -3).

To find the vertices of a square with diagonals contained in the lines y = x and y = -x + 6, we can follow these steps:

Step 1: Understand the problem
In this problem, we are given two lines, y = x and y = -x + 6, and we need to find the vertices of a square with diagonals that lie on these lines.

Step 2: Understand the properties of a square
A square is a quadrilateral with four equal sides and four right angles. The diagonals of a square are also equal in length and intersect at right angles at the center of the square.

Step 3: Find the intersection point of the lines
To find the intersection point of the lines y = x and y = -x + 6, we can set the two equations equal to each other:
x = -x + 6
2x = 6
x = 3

Substituting this value of x into either equation, we find the y-coordinate of the intersection point:
y = 3

So the intersection point is (3, 3).

Step 4: Find the other vertices of the square
Since a square has four equal sides, we can find the other vertices by reflecting the intersection point across the x-axis and y-axis.

Reflecting the intersection point (3, 3) across the x-axis gives us the point (3, -3).

Reflecting the intersection point (3, 3) across the y-axis gives us the point (-3, 3).

Finally, reflecting the intersection point (3, 3) across both the x-axis and y-axis gives us the point (-3, -3).

So the vertices of the square are (3, 3), (3, -3), (-3, 3), and (-3, -3).

Step 5: Justify the reasoning
We have found the vertices of the square by first finding the intersection point of the given lines. Then, by reflecting this point across the x-axis and y-axis, we obtained the other three vertices. These vertices form a square because all the sides are equal in length, and the diagonals intersect at right angles.

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The pulse rates that are within 1 standard deviation of the mean represent approximately 68% of the total to the nearest 0.1 percent.

When working with a set of pulse rates that are normally distributed, we can use the Empirical Rule to determine the pulse rates that are within 1 standard deviation of the mean. According to the Empirical Rule, approximately 68% of the data falls within 1 standard deviation of the mean.

To find the pulse rates that are within 1 standard deviation of the mean, we need to first find the mean and standard deviation of the pulse rates. After we have these values, we can determine the range of pulse rates that fall within one standard deviation of the mean.

To calculate the percentage of the total that represents those rates, we can use the formula: Percentage = (Number of data points within 1 standard deviation / Total number of data points) x 100.

For example, let's say the mean pulse rate is 72 beats per minute and the standard deviation is 8 beats per minute. Using the Empirical Rule, we know that approximately 68% of the pulse rates fall within one standard deviation of the mean. This means that the pulse rates that fall within one standard deviation of the mean are between 64 and 80 beats per minute.

To find the percentage of the total that represents those rates, we need to count the number of data points within that range. If we assume that we have 1000 data points, then the number of data points within the range of 64 to 80 beats per minute is approximately 680. Therefore, the percentage of the total that represents those rates is:

Percentage = (680/1000) x 100

Percentage = 68%

Therefore, the pulse rates that are within 1 standard deviation of the mean represent approximately 68% of the total to the nearest 0.1 percent.

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By answering the given question, we may state that Therefore, the equivalent inequality is: x < 2

A relationship between two terms or values which is not equal is known as an inequality in mathematics. Inequality follows imbalances, therefore. In mathematics, an inequality makes a link among two quantities that are not equal. Egality and inequality are different. Use the not similar symbol most frequently when two components are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two parts until only the variables are left, one can solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left & right.

inequality using basic algebraic operations:

5(2x-6)+6(3-x)<2x+4

10x-30+18-6x < 2x+4

4x - 8 < 0

4x < 8

x < 2

Therefore, the equivalent inequality is:

x < 2

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Answer:

19

Step-by-step explanation:

115+10P=305

305-115=190

190/10=19

Answer:

x = 8

Step-by-step explanation:

x + 5 = 2x - 3

-x      = -x        subtract x from both sides.

   5 = 1x - 3

   +3 =      +3        add 3 to both sides.

8 = 1x

x = 8

Let X denote the amount of time a book on two-hour reserve is actually checked out, and suppose the cdf is the following. For \(0 ≤ x ≤ 2, F(1) = (1^3/12) = 0.0833.So, P(X ≤ 1) = 0.0833.\) Hence, the correct option is (a) P(X ≤ 1).

Given that X denotes the amount of time a book on two-hour reserve is actually checked out, and the cdf is the following:

\(cdf: 0 , x<0f(x) = ((x^2)/4) , 0 <= x <= 21 , 2<= x\)

To use the cdf to obtain the following.P(X ≤ 1)

So, the probability distribution function is the derivative of the cumulative distribution function.

∴ f(x) = d/dx(F(x))

Also, from the cdf, we know that:

\(f(x) = 0 when x < 0.f(x) = ((x^2)/4) when 0 ≤ x ≤ 2.\)

f(x) = 1 when x ≥ 2.

Using the above conditions, we have to calculate the following:

(a) P(X ≤ 1)

Here, P(X ≤ 1) = F(1).

When\(0 ≤ x ≤ 2, F(x) = ∫[0,x] f(t)dt=∫[0,x] (t^2/4)dt=[t^3/12]0x=(x^3/12)\)

Thus, for\(0 ≤ x ≤ 2, F(x) = (x^3/12).\)

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Answer:180

Step-by-step explanation: i am in collge

The false statement is: C. The sampling distribution of the sample mean is exactly normal if the observations are normally distributed.

Statement A is true. According to the central limit theorem, the sampling distribution of any statistic, including the sample mean, tends to become approximately normal as the sample size increases, regardless of the underlying distribution of the population.

Statement B is true. The standard deviation of the sample mean, also known as the standard error, decreases as the sample size increases. This decrease in standard deviation indicates that the sample mean becomes a more precise estimator of the population mean.

Statement C is false. The sampling distribution of the sample mean follows an approximately normal distribution for large sample sizes, even if the individual observations are not normally distributed. The central limit theorem ensures the approximate normality of the sample mean's distribution through the law of large numbers and the convergence of the sampling distribution to a normal distribution shape.

Therefore, the false statement is C, as the sampling distribution of the sample mean is not exactly normal even if the observations are normally distributed.

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Answer:

$409,600

Step-by-step explanation:

since it's the power of three you multiple 8,000×8,000×8,000 then you divide it by 5

To use polar coordinates, we need to first express the equations of the surfaces in polar coordinates.

In polar coordinates, we have x = r cosθ and y = r sinθ. Therefore, the equation x^2 + y^2 = 1 becomes r^2 = 1.

To find the volume of the solid, we can integrate over the region in the xy-plane bounded by the circle r=1. For each point (r,θ) in this region, the corresponding point in 3D space has coordinates (r cosθ, r sinθ, r^2+3)

Thus, the volume of the solid can be expressed as the double integral:

V = ∬R (r^2+3) r dr dθ

where R is the region in the xy-plane bounded by the circle r=1.

We can evaluate this integral using the limits of integration 0 to 2π for θ, and 0 to 1 for r:

V = ∫₀^¹ ∫₀^(2π) (r^3 + 3r) dθ dr

= ∫₀^¹ [(r^3/3 + 3rθ)]₀^(2π) dr

= ∫₀^¹ (2πr^3/3 + 6πr) dr

= 2π[(1/12) + (1/2)]

= 2π(5/12)

= (5/6)π

Therefore, the volume of the solid is (5/6)π.

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Answer:

43 4445 itmean near divide by 5

Answer:

10. y degree = 102 degree

11. x degree = 103 degree

Step-by-step explanation:

The formula to calculate the sum of the interior range of polygons is (n-2) * 180.

With n being the number of sides.

From that sum, you can then deduce the angles of y or x, by substracting the other angles.

10. n = 4 => ( 4 - 2 ) * 180 = 2 * 180 = 360 degree

y = 360 - 120 - 85 - 53 = 102 degree

11. n = 5 => (5 - 2) * 180 = 3 * 180 = 540 degree

x = 540 - 117 - 100 - 105 - 115 = 103 degree

From the word EPIPHANY, we can see that:

E,I,H,A,N,Y are unique and P repeats twice. Then we would have a permutation with repetition. Let's state some data to solve this problem:

n=8 (number of letters)

Repetitions of the letter E: 2

Then:

Therefore, we can make 20160 arrangements using the letters EPIPHANY

Using the graph of the function concept, the numeric value at x = 2 is f(-2) = 0.

To find the numeric value of a function at x = a, we look at the value of y(vertical axis) where x = a has a closed interval.

Researching the problem on the internet, looking at it's graph, it is found that when x = -2, there is a closed interval at y = 0, hence f(-2) = 0.

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Answer:

Step-by-step explanation: