Juan has 5 ​ties, 5 ​shirts, and 3 pairs of pants. How many different outfits can he wear if he chooses one​ tie, one​ shirt, and one pair of pants for each​ outfit?

Our standard linear slope equation is:

mx + b = y

We're told our slope is 1/2, so that's our m value.

When x = 0 our value is 5. If you need this visualized, then:

1/2 * 0 +b = 5

0 + b = 5

b = 5

So our equation looks like:

x/2 + 5 = y

Answer:

24 inches

Step-by-step explanation:

We assume that with a linear relationship between two variables, for any fixed value of x, the observed residuals follows a normal distribution.

This assumption is based on the Central Limit Theorem, which states that when the sample size is large enough, the distribution of sample means will be approximately normal, regardless of the shape of the underlying population distribution.

In the case of a linear relationship between two variables, we can assume that the residuals (the difference between the observed y values and the predicted values based on the linear regression model) follow a normal distribution with mean 0 and constant variance. This assumption is important because it allows us to use statistical methods that rely on normality, such as hypothesis testing and confidence intervals.

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Answer:

11 / 9

Step-by-step explanation:

Let number = x

(x * 9) + 4 = 15

9x + 4 = 15

9x = 15 - 4

9x = 11

x = 11 / 9

Hence, the number is 11 /9

Answer: 14 inches

Step-by-step explanation:

Given the following :

James wants to cut a floor tile in the shape of a trapezium with the following dimension :

Top base = 12 inches

Bottom base = 16 inches

To obtain the medan, we take the average of the two bases :

(top base + bottom base) / 2

(12 inches + 16 inches) / 2

28 inches / 2

= 14 inches.

Answer:

15/13 OR 1.154

Step-by-step explanation:

2 1/2=5/2

2 1/6=13/6

5/2 / 13/6

=5/2 x 6/13

=30/26

=15/13

=1.15384615385

≈ 1.154

Answer:

46

Step-by-step explanation:

Answer:

V = 96 pi m^3

Step-by-step explanation:

V = (1/3) pi(r^2)h

Radius = 1/2(Diameter)

R = 1/2(12)

R = 6

Input.  

V = (1/3) pi(6^2)8

Solve.

V = (1/3) pi(36)8

V = (1/3) 904.32

V = 301.44

V = 301.44/pi

V = 96 pi m^3

Answer:

The correct answer is option (C) 96π m³.

Step-by-step explanation:

As per given question we have provided that :

Here's the required formula to find the volume of cone :

\({\longrightarrow{\pmb{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}}}\)

Substituting all the given values in the formula to find the volume of cone :

\({\implies{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{r}^{2}h}}}\)

\({\implies{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{(6)}^{2}8}}}\)

\({\implies{\sf{V_{(Cone)} = \dfrac{1}{3}\pi{(6 \times 6)}8}}}\)

\({\implies{\sf{V_{(Cone)} = \dfrac{1}{3}\pi \times {(36)} \times 8}}}\)

\({\implies{\sf{V_{(Cone)} = \dfrac{1}{3} \times \pi \times 36 \times 8}}}\)

\({\implies{\sf{V_{(Cone)} = \dfrac{1}{\cancel{3}} \times \pi \times \cancel{36} \times 8}}}\)

\({\implies{\sf{V_{(Cone)} = \pi \times 12 \times 8}}}\)

\({\implies{\sf{V_{(Cone)} = \pi \times 96}}}\)

\({\implies{\sf{V_{(Cone)} =96\pi}}}\)

\(\star{\underline{\boxed{\sf{\red{V_{(Cone)} =96\pi \: {m}^{3}}}}}}\)

Hence, the volume of cone is 96π m³.

\(\rule{300}{2.5}\)

The density of metal is 7022.2 kg/m^3 and the metal is not gold. We were cheated.

In the given question, we purchase a rectangular piece of metal that has dimensions 5.0 x 15.0 x 30.0 mm and mass 0.0158 kg.

The seller tells you that the metal is gold.

We have to find the density of piece.

Then Given ,

Mass = 0.0158 kg

Volume = 5.0 mm * 15.0 mm * 30.0 mm

Density = mass / volume

Putting the values

Density = 1.58 * 10^(-2) kg/(5.0*10^{-3}*15.0*10^{-3}*30.0*10^{-3}) m^3

Density = 7022.2 kg/m^3

The density of metal is 7022.2 kg/m^3 and the metal is not gold. We were cheated.

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Answer:

Somewhat illegible but looks like the equation should be:

S = u t + 1/2 a t^2

100 = 20 + 1/2 * a * 4    where t = 2

a* 4 = 160

a = 40

Answer:

D

Step-by-step explanation:

Answer:

a) 80in peri, 320 in²

b) 19.426 peri, 26.139

9514 1404 393

Answer:

  b.  2692 ft

Step-by-step explanation:

The relation of interest between the sides of the right triangle is ...

  Tan = Opposite/Adjacent

Using the given numbers, that is ...

  tan(32°) = (building height)/(4300 ft)

Multiplying by 4300 ft, we get ...

  building height = (4300 ft)·tan(32°) ≈ 2686.9 ft

This is the height above the observer's eyes, so the height of the building above the ground is ...

  2687 +5 = 2692 . . . . feet

The building is 2692 feet tall.

The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.

A continuous probability distribution for a real-valued random variable is called a normal distribution or a Gaussian distribution.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it properly depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.

the mean of the data = 9.12 oz

The SD = 0.05 oz

The probability of the bag to be less than 9.07 oz

x = 9.07

z = x - mean / SD = 9.07 - 9.12/0.05 = - 1

for z = -ve

Ф(z) = 1 - Ф(-z) = 1 - Ф(1) = 1 - 0.8413 = 0.1587

The probability that a bag of chip is lower than 9.07 oz of weight is 0.1587.

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Answer:

X = 35/8

Y = -5

The single transformation that maps a onto triangle b is a rotation of 180 degrees across the common vertex of triangles a and b

From the figure, we have the following highlights

The above highlights mean that the single transformation that maps a onto triangle b is a rotation of 180 degrees across the common vertex of triangles a and b

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Answer:

x=50 degrees

Step-by-step explanation:

I'm not sure but hope this helps and have a  wonderful day!!!!

Answer:

x = 48

Step-by-step explanation:

2x + 10 + x + 26 = 180

3x + 36 = 180

3x = 180 - 36

3x = 144

x = 48

From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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on a necklace two-thirds of the bees are blue of the blue beads 1/4 or oval shaped what fraction of the necklace is made up of blue ovals ​

we have that

2/3 ------> blue

1/4(2/3)=2/12-1/6

answer is 1/6

The value of m in the proportion is given as follows m = 3.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The proportion is defined as follows:

3/4 = (1/4)m.

As the values have a proportional relationship, the value of m can be obtained applying cross multiplication, as follows:

3/4 = (1/4)m

cross multiplication;

3/4 x 4 = m

m = 3

Hence m =3 is the value that satisfies the proportion in this problem.

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The  probability of event A is P(A) = 1/4 or 0.25.

The formula to find P(A) for a series of simple events is:

P(A) = (number of outcomes that satisfy the event A) / (total number of possible outcomes)

For example, if you are tossing a coin and selecting a number at the same time, and event A is defined as getting a head and an even number, then:

- The number of outcomes that satisfy event A is 1 (getting a head and an even number, i.e., H2)
- The total number of possible outcomes is 4 (H1, H2, T1, T2)
- Therefore, the probability of event A is P(A) = 1/4 or 0.25.

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Answer:

Yes

no

no

yes

Step-by-step explanation:

I hope it's serving

:v

The volume of the given set using integration in cylindrical coordinates is 12π.

Main part: The given set U can be visualized as a cylinder of radius 1 and height 5, that is truncated by removing a smaller cylinder of the same height and radius 1/2. We will use cylindrical coordinates (ρ,θ,z) to describe points in space. The volume of the set U is given by the integral:

∫∫∫_U〖dV=∫_0^(2π)∫_0^1∫_0^(5-r)ρdzdρdθ

Solution: We can see that z varies from 0 to 5 - x - y. In cylindrical coordinates, x = ρ cos θ and y = ρ sin θ. Therefore, z = 5 - ρ cos θ - ρ sin θ. Since ρ goes from 0 to 1, we have:

∫_0^(2π)∫_0^1∫_0^(5-r)ρdzdρdθ = ∫_0^(2π)∫_0^1∫_0^((5-ρcosθ-ρsinθ))ρdzdρdθ

= ∫_0^(2π)∫_0^1[5ρ - ρ²/2 - ρ² cos θ/2 - ρ² sin θ/2] dρ dθ

= ∫_0^(2π)[5/2 - 1/2 cos θ - 1/2 sin θ] dθ

= 2π [5/2 - 1/2 cos θ - 1/2 sin θ] from 0 to 2π

= π (5 - cos θ - sin θ) from 0 to 2π

= π (5 - (-1) - 0 - (-1) - 0)

= 12 π

Therefore, the volume of the set U is 12 π.

Conclusion: Thus, the volume of the given set using integration in cylindrical coordinates is 12π.

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Answer:

The two polynomials are:

(x + 1) and (x² + x)

Step-by-step explanation:

A polynomial is simply an expression which consists of variables & coefficients involving only the operations of addition, subtraction, multiplication, and non - negative integer exponents of variables.

Now, 1 and x are both polynomials. Thus; 1/x is already a quotient of a polynomial.

Now, to get two polynomial expressions whose quotient, when simplified, is 1/x, we will just multiply the numerator and denominator by the same polynomial to get more quotients.

So,

Let's multiply both numerator and denominator by (x + 1) to get;

(x + 1)/(x(x + 1))

This gives; (x + 1)/(x² + x)

Now, 1 and x are both polynomials but the expression "1/x" is not a polynomial but a quotient and thus polynomials are not closed under division.

The approximate measure of angle JGH is 70.5°.

According to this question, we have a right triangle in which lengths of its hypotenuse (GH), in centimeters, and one leg (JH) are known and we must determine the measure of an angle (∠JGH), in degrees. A representation of this triangle is included in the image attached below.

By trigonometry we have the following expression for the required angle:

cos∠GJH = HJ/GH               .......(1)

Given, HJ = 2, GH = 6

cos∠GJH = 2/6

     ∠GJH = \(cos^{-1}\frac{2}{6}\)

                ≈ 70.529

The approximate measure of angle JGH is 70.5°.

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The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Answer:

1.05263

explanation:

8 divided by 7.6

\(\hookrightarrow \dfrac{8}{7.6}\)

multiply both by 10

\(\hookrightarrow \dfrac{80}{76}\)

final answer

\(\hookrightarrow 1.05263\)

According to the Intermediate Value Theorem, if a function f(x) is continuous on a closed interval [a, b], and if f(a) and f(b) have opposite signs, then there exists at least one value c in the interval (a, b) such that f(c) = 0. According to the Intermediate Value Theorem, the interval in which the equation cos(x) = 2^(x-6) must have a solution is (0, π/2).

Let's apply this theorem to the function f(x) = cos(x) - 2^(x-6).
First, we need to find two values a and b such that f(a) and f(b) have opposite signs. Let's start with a = 0 and b = π/2.
f(0) = cos(0) - 2^(0-6) = 1 - 1/64 > 0
f(π/2) = cos(π/2) - 2^(π/2-6) = 0 - 1/4 < 0
Since f(a) and f(b) have opposite signs, there exists at least one value c in the interval (0, π/2) such that f(c) = 0. Therefore, the equation cos(x) = 2^(x-6) has at least one solution in the interval (0, π/2).
To summarize, according to the Intermediate Value Theorem, the interval in which the equation cos(x) = 2^(x-6) must have a solution is (0, π/2).

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Answer:

800m

Step-by-step explanation:

If 100cm is equivalent to a meter (1 Meter). 8 Meters would be equivalent to 8 Meters multiplied by 100cm and divided by a meter (1 Meter)