Examine the power 5^3

Answer:

E

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let the diagonal ( hypotenuse ) be d , then

d² = 5² + 5² = 25 + 25 = 50 ( take square root of both sides )

d = \(\sqrt{50}\) = \(\sqrt{25(2)}\) = \(\sqrt{25}\) × \(\sqrt{2}\) = 5\(\sqrt{2}\) → E

The  probability is 102.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Moderate Success     0.3 102.0 120 208.0

Failure                        0.4 102.0 10.0 100

Now, the probability

E(x) = \(\sum^3_i\)= \(S_iP_i\)

      = 102 x 0.3 + 102 x 0.3 + 102 x 0.4

      = 30.6 + 30.6 + 40.8

      = 102

Hence, the probability is 102.

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Answer:

y = \(-\frac{4}{3}\)x + 6

Step-by-step explanation:

y = mx + b

m: slope

b: y-intercept

y-intercept point on the graph is (0, 6) because it's the point that's on the y-axis.

Therefore, y-intercept is 6.

Slope: \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Point A: (0, 6)

Point B: (4, -2)

Slope (m) = \(\frac{-2 - 6}{4 - -2}\)

\(m = \frac{-2 - 6}{4 +2}\)

\(m = \frac{-8}{6}\)

\(m = -\frac{4}{3}\)

y = \(-\frac{4}{3}\)x + 6

Hope this helped! <3

Answer:

is this answer correct?

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Step-by-step explanation:

hope you liked it!

Given that the average salary in a city is $46,500, and the standard deviation is $18,400.
The question is to find if the average is different for single people. Let's see the explanation below.

Average salary: It is the sum of all the salaries divided by the number of salaries.

Standard Deviation: It is the measure of the dispersion of data from its mean value. A low standard deviation indicates that the data is clustered around the mean, while a high standard deviation indicates that the data is widely scattered from the mean value.To find if the average is different for single people or not, more information or context is required. Without more information or context, it is not possible to determine whether the average salary is different for single people or not.

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No information is given to determine whether the average salary is different for single people in the city. Thus, it cannot be concluded that the average salary is different for single people.

Explanation:

Mean and standard deviation are two common measures of central tendency used to characterize data. The mean is the sum of all the values divided by the total number of values, while the standard deviation is the square root of the average squared deviation from the mean.

In the given scenario, the average salary in the city is $46,500, and the standard deviation is $18,400, so we can use these two values to calculate the central tendency of the dataset.

However, no information is given to determine whether the average salary is different for single people in the city. Thus, it cannot be concluded that the average salary is different for single people.

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A- When one variable increases the other variable decreases. :)

Answer:

x = 2.4

Step-by-step explanation:

16^(4x - 3) = 8 ^ (2x + 4)

16 = 2^4

8 = 2^3

2 ^ 4*(4x - 3) = 2^3(2x + 4)

Since the bases are the same, you can equate the powers

4(4x - 3) + 3*(2x + 4)           Remove the brackets.

16x - 12 = 6x + 12                 Subtract 6x from both sides

16x - 6x - 12 = 12                Combine the terms on the left

10x - 12 = 12                        Add 12 to both sides

10x = 24                              Divide by 10

x = 2.4

There are 120 ways in which 5  riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways \(^nN_r = \frac{n!}{(n-r)!}\),

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways \(^nN_r = \frac{n!}{(n-r)!}\),

Now,

Substituting values,

We get,

\(^5N_5 = \frac{5!}{(5-5)!}\)

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5  riders and 5 horses can be arranged.

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Answer:

C. 16

Step-by-step explanation:

y^2-z^2

(-5)^2-(-3)^2

25-9

16

Answer:

Step-by-step explanation:

y = - 5

y^2 = (-5)^2

y^2 = 25

z = - 3

z^2 = (-3)^2

z^2 = 9

y^2 - z^2 = 25 - 9 = 16

Answer:

C - 768cm for Plato

Step-by-step explanation:

Answer:

6. 12cm

7. 11.2 cm

8. 92 degrees

9. 53 degrees

10. 37.5 cm

11. $ 693.12

Step-by-step explanation:

For questions 6-9 the triangle is congurent which means both their angles will be equal.

For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5

So for Q. 6 we can multiply side PQ by 1.5.

For Q.7 divide CA by 1.5.

For Q. 10 we can do cross multiplication:

5/4 = x/30

= 150= 4x

= 37.5=x

For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)

So the shorter side is 30.4 cm.

Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.

Then to figure out the money we multiply again and we get $693.12.

Answer:

a = 3 , b = - 2

Step-by-step explanation:

5a + b = 17 → (1)

3a + 2b = 5 → (2)

multiplying (1) by 2 and adding to (2) will eliminate b

10a + 2b = 34 → (3)

add (2) and (3) term by term to eliminate b

13a + 0 = 39

13a = 39 ( divide both sides by 13 )

a = 3

substitute a = 3 into either of the 2 equations and solve for b

substituting into (1)

5(3) + b = 17

15 - b = 17 ( subtract 15 from both sides )

- b = 2 ( multiply both sides by - 1 )

b = - 2

then solution is a = 3 , b = - 2

Here, we want to select an equation that is perpendicular to the given equation

We start by writing the given equation in the general form

The general form is;

where m is the slope and b represents the y-intercept

We can rewrite the given equation so that we have;

The slope here is 4; so the equation we are going to have as its perpendicular will be an equation in which its slope multiplied by the slope of the given equation will be -1

So we are looking for an equation with the slope as -1/4

From the options, the equation that fits this description is;

Answer:

73.2 cm³

Step-by-step explanation:

The volume of the cylinder without the prism is V" = volume of cylinder, V' - volume of rectangular prism, V

Volume of cylinder = πr²h where r = radius of cylinder = 2 cm and h = height of cylinder = 6 cm.

So, V = πr²h

= π(2 cm)²(6 cm)

= π × 4 cm² × 6 cm

= 24π cm³

= 75.4 cm³

V = volume of rectangular prism = Area of 0.6 cm square × height = L²h where L = 0.6 cm and h = height of rectangular prism = 6 cm.

So, V = L²h = (0.6 cm)² × 6 cm = 2.16 cm³

volume of the cylinder without the prism is V" = V' - V

= 75.4 cm³ - 2.16 cm³

= 73.24 cm³

≅  73.2 cm³

Answer:

Not an answer

Step-by-step explanation:

Using proportions, it is found that you will need to save $54.89 more each month in order to reach your goal.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The amount you will need is:

75 x 17 = $1,275.

After 10 months you have only saved $524, hence the amount you will have to save is:

1275 - 524 = 751.

In 7 months, hence the monthly amount is:

751/7 = $107.29.

The difference is:

107.29 - (524/10) = $54.89.

You will need to save $54.89 more each month in order to reach your goal.

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Answer:

The expression represents the price you paid per gallon is:

Step-by-step explanation:

To identify the expression is right, I'll show you with an example: suppose that you paid $56 buying 7 gallons of gas, now you can replace those values in the expression I gave you:

And you can check this value by multiplying the price paid by the gallon and the number of gallons, which you obtain the number of dollars you spent:

The direction of the greatest increase in heat from the point (2, 5) is in the direction of the vector (-21, -20).

To find the direction of the greatest increase in heat from point (2, 5), we need to find the gradient vector of the temperature function T(x,y) at that point, and then determine the direction in which the gradient vector points.

The gradient vector of T(x,y) is given by:

∇T(x,y) = (∂T/∂x)i + (∂T/∂y)j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the partial derivatives of T(x,y) with respect to x and y, we get:

∂T/∂x = (x² - y²)/(x² + y²)²

∂T/∂y = -2xy/(x² + y²)²

Substituting x = 2 and y = 5, we get:

∂T/∂x = (4 - 25)/(29)² = -21/1681

∂T/∂y = -20/1681

Therefore, the gradient vector of T(x,y) at the point (2, 5) is:

∇T(2,5) = (-21/1681)i - (20/1681)j

The direction of the greatest increase in heat from points (2, 5) is in the direction of the gradient vector. We can normalize the gradient vector to get the unit vector in this direction:

u = (∇T(2,5))/|∇T(2,5)|

where |∇T(2,5)| is the magnitude of the gradient vector, given by:

|∇T(2,5)| = √((-21/1681)² + (-20/1681)²) = sqrt(841)/1681 = 1/41

Thus, the unit vector in the direction of greatest increase in heat from the point (2, 5) is:

u = (-21/1681i - 20/1681j)/(1/41) = -21i - 20j

Therefore, the direction of the greatest increase in heat from points (2, 5) is in the direction of the vector (-21, -20).

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When a cylinder is sliced in such a way that the plane passes through the cylinder in a slanted direction without going through either base, the resulting cross section is an elliptical shape.

To visualize this, imagine a cylinder with circular bases. When a plane intersects the cylinder in a slanted direction, it cuts through the curved surface of the cylinder, creating an elliptical cross section.

The exact shape and size of the elliptical cross section will depend on the angle at which the plane intersects the cylinder and the specific orientation of the cylinder. The major axis of the resulting ellipse will be parallel to the slanted direction of the plane, while the minor axis will be perpendicular to it.

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Answer:

la4

Step-by-step explanation:

(5)8

Given:

The base of the prism is a right triangle with legs 1 m and 2 m.

The height of the prism is 17 m.

To find:

The volume of the given prism.

Solution:

The area of a triangle is:

\(Area=\dfrac{1}{2}\times base\times height\)

So, the area of base of the prism is:

\(Area=\dfrac{1}{2}\times 1\times 2\)

\(Area=1\)

Now, the volume of the prism is:

\(V=Bh\)

Where, B is the base area and h is the height of the prism.

Substituting \(B=1,h=17\), we get

\(V=(1)(17)\)

\(V=17\)

The volume of the prism is 17 cubic m. Therefore, the correct option is (d).

The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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We can see that 7 is the total that is most likely to result, since it has the highest number of possible ways to roll it (6).


1) To find the probability of rolling a 10, we need to determine how many ways we can roll a 10 and then divide that by the total number of possible outcomes.

To roll a 10, we can get a 4 on one dice and a 6 on the other, or a 5 on one dice and a 5 on the other. So there are 2 ways to roll a 10.

The total number of possible outcomes is 6 x 6 = 36, since each dice has 6 possible outcomes.

Therefore, the probability of rolling a 10 is 2/36, which can be simplified to 1/18.

To find the probability of rolling higher than 10, we need to determine how many ways we can roll a total of 11, 12, or 13, and then divide that by the total number of possible outcomes.

To roll an 11, we can get a 5 on one dice and a 6 on the other, or a 6 on one dice and a 5 on the other. To roll a 12, we can get a 6 on both dice. To roll a 13, we can get a 6 on one dice and a 6 on the other.

So there are 4 ways to roll higher than 10.

Therefore, the probability of rolling higher than 10 is 4/36, which can be simplified to 1/9.

2) To find the probability of rolling an odd number, we need to determine how many ways we can roll an odd number and then divide that by the total number of possible outcomes.

To roll an odd number, we can get a 1, 3, or 5 on one dice and any number on the other dice, or we can get a 2, 4, or 6 on one dice and a 1, 3, or 5 on the other dice.

So there are 18 ways to roll an odd number.

Therefore, the probability of rolling an odd number is 18/36, which can be simplified to 1/2.

3) To find the total that is most likely to result, we need to determine which total has the most possible ways to roll it.

We can create a table to show how many ways we can roll each total:

Total | Number of Ways

2 | 1

3 | 2

4 | 3

5 | 4

6 | 5

7 | 6

8 | 5

9 | 4

10 | 3

11 | 2

12 | 1

From the table, we can see that 7 is the total that is most likely to result, since it has the highest number of possible ways to roll it (6).

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Answer: 30.0 feet

Step-by-step explanation:

Answer:

30.0 ft

Step-by-step explanation:

Answer: The answer would be B which is 4

Step-by-step explanation:

I took the quiz and got it right.

Answer:

It's 576 if you mean 64 times 9!

Step-by-step explanation:

Answer:

The LCM of 88 and 90 is 3960.

Answer:

By the Euclidean algorithm, \(\gcd(88, 90) = \gcd(88, 2) = \gcd(0, 2) = 2\). Therefore, \(\text{lcm}(88,90) = \frac{88 \cdot 90}{\gcd(88, 90)} = \frac{88 \cdot 90}{2} = \boxed{3960}.\)

The values of x in both figures are 45 and 34, respectively.

Start by calculating the angle CAB using:

CAB + ABC + BCA = 180 --- angles in a triangle

The triangle is an isosceles triangle.

So, we have:

CAB + ABC + CAB = 180

Evaluate

2CAB + 25 + 75 = 180

This gives

CAB = 40

Calculate angle BEA using:

BEA + CAB + ABE = 180 --- angles in a triangle

This gives

BEA + 40 + 25 = 180

Evaluate

BEA = 115

Vertical angles are equal.

So, we have:

CED = BEA = 115

Calculate angle EDC using:

EDC + CED + DCE = 180 --- angles in a triangle

This gives

EDC + 115 + 30 = 180

Evaluate

EDC = 35

Opposite angles of quadrilaterals add up to 180.

So, we have:

x + EDC + ABC = 180

This gives

x + 35 + 25 + 75 = 180

Evaluate

x = 45

Hence, the value of x is 45

Start by calculating the angle DEC using:

DEC + CDE + EED = 180 --- angles in a triangle

This gives

DEC + 18 + 30 = 180

Evaluate

DEC  = 132

Vertical angles are equal.

So, we have:

AEB = DEC = 112

Calculate angle EAB using:

EAB + AEB + ABE = 180 --- angles in a triangle

This gives

EAB + 112 + 42  = 180

Evaluate

EAB  = 26

Triangle ABC is an isosceles triangle.

So, we have:

BCE = EAB  = 26

Calculate angle CBE using:

CBE + BCE + CEB = 180 --- angles in a triangle

Where CEB = 180 - DEC --- angle on a straight line

So, we have:

CBE + BCE + 180 - DEC = 180

This gives

CBE + 26 + 180 - 112 = 180

Evaluate

CBE  = 86

Opposite angles of quadrilaterals add up to 180.

So, we have:

x + EDC + ABC = 180

This gives

x + 18 + 42 + 86 = 180

Evaluate

x = 34

Hence, the value of x is 34

Note that the figures are labeled to ease explanation (see attachment)

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The general solution of the given differential equation, sec^2(x) * (dy/dx)^2 = 0, is y = C, where C is a constant.

To solve the differential equation, we can rewrite it as (dy/dx)^2 = 0 / sec^2(x). Since sec^2(x) is never equal to zero, we can divide both sides of the equation by sec^2(x) without losing any solutions.

(dy/dx)^2 = 0 / sec^2(x)

(dy/dx)^2 = 0

Taking the square root of both sides, we have:

dy/dx = 0

Integrating both sides with respect to x, we obtain:

∫ dy = ∫ 0 dx

y = C

where C is the constant of integration.

Therefore, the general solution of the given differential equation is y = C, where C is any constant. This means that the solution is a horizontal line with a constant value of y.

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The data measured on ordinal scale exhibits all the properties of data measured on nominal scale.

A nominal scale  can be described as the scale of measurement  which is been assign events or objects with respect to a discrete categories.

However in relation with nominal scale, Ordinal scale  serves as the  2nd level of measurement  which help to give the reports of  ranking as well as  ordering of the data  however the  degree of variation  is not usually considered, hence data measured on ordinal scale exhibits all the properties of data measured on nominal scale.

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