A number is chosen at random from 1 to 50. Find
the probability of selecting multiples of 10.
Step by step.

Answer:

Step-by-step explanation:

The answer is b

120.01 grams

Answer and Step-by-step explanation: Spherical coordinate describes a location of a point in space: one distance (ρ) and two angles (Ф,θ).To transform cartesian coordinates into spherical coordinates:

[tex]\rho = \sqrt{x^{2}+y^{2}+z^{2}}[/tex]

[tex]\phi = cos^{-1}\frac{z}{\rho}[/tex]

For angle θ:

Calculating:

a) (4,2,-4)

[tex]\rho = \sqrt{4^{2}+2^{2}+(-4)^{2}}[/tex] = 6

[tex]\phi = cos^{-1}(\frac{-4}{6})[/tex]

[tex]\phi = cos^{-1}(\frac{-2}{3})[/tex]

For θ, choose 1st option:

[tex]\theta = tan^{-1}(\frac{2}{4})[/tex]

[tex]\theta = tan^{-1}(\frac{1}{2})[/tex]

b) (0,8,15)

[tex]\rho = \sqrt{0^{2}+8^{2}+(15)^{2}}[/tex] = 17

[tex]\phi = cos^{-1}(\frac{15}{17})[/tex]

[tex]\theta = tan^{-1}\frac{y}{x}[/tex]

The angle θ gives a tangent that doesn't exist. Analysing table of sine, cosine and tangent: θ = [tex]\frac{\pi}{2}[/tex]

c) (√2,1,1)

[tex]\rho = \sqrt{(\sqrt{2} )^{2}+1^{2}+1^{2}}[/tex] = 2

[tex]\phi = cos^{-1}(\frac{1}{2})[/tex]

[tex]\phi[/tex] = [tex]\frac{\pi}{3}[/tex]

[tex]\theta = tan^{-1}\frac{1}{\sqrt{2} }[/tex]

d) (−2√3,−2,3)

[tex]\rho = \sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}+3^{2}}[/tex] = 5

[tex]\phi = cos^{-1}(\frac{3}{5})[/tex]

Since x < 0, use 2nd option:

[tex]\theta = \pi + tan^{-1}\frac{1}{\sqrt{3} }[/tex]

[tex]\theta = \pi + \frac{\pi}{6}[/tex]

[tex]\theta = \frac{7\pi}{6}[/tex]

Cilindrical coordinate describes a 3 dimension space: 2 distances (r and z) and 1 angle (θ). To express cartesian coordinates into cilindrical:

[tex]r=\sqrt{x^{2}+y^{2}}[/tex]

Angle θ is the same as spherical coordinate;

z = z

Calculating:

a) (4,2,-4)

[tex]r=\sqrt{4^{2}+2^{2}}[/tex] = [tex]\sqrt{20}[/tex]

[tex]\theta = tan^{-1}\frac{1}{2}[/tex]

z = -4

b) (0, 8, 15)

[tex]r=\sqrt{0^{2}+8^{2}}[/tex] = 8

[tex]\theta = \frac{\pi}{2}[/tex]

z = 15

c) (√2,1,1)

[tex]r=\sqrt{(\sqrt{2} )^{2}+1^{2}}[/tex] = [tex]\sqrt{3}[/tex]

[tex]\theta = \frac{\pi}{3}[/tex]

z = 1

d) (−2√3,−2,3)

[tex]r=\sqrt{(-2\sqrt{3} )^{2}+(-2)^{2}}[/tex] = 4

[tex]\theta = \frac{7\pi}{6}[/tex]

z = 3

Answer:

[tex]y+6=-\frac{1}{2} (x-3)[/tex]

Step-by-step explanation:

Since point-slope form is  [tex]y-y1=m(x-x1)[/tex], you have to plug in the values given to you to create the equation. The "y1" is the "y" coordinate given to us, while the x1 is the x coordinate given to us. So, you have to plug in the x and y coordinates, 3 and -6, into the equation. Since two negatives cancel out to be a positive, y--6= y+6. The "m" stands for the slope, so -1/2 is inserted into the equation, giving us  [tex]y+6=-\frac{1}{2} (x-3)[/tex].

Complete  Question

The complete question is shown on the first uploaded image

Answer:

Based on the result of his test , Thomas should fail to reject null hypothesis at a significance level of  0.01. Thomas sufficient evidence  to conclude that  the proportion of  households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.

Step-by-step explanation:

From the question we see that the p-value is greater than the level of significance (0.01 )so we fail to reject the null hypothesis.

This means that Thomas has  sufficient evidence to conclude that the proportion of households without children in the set of all future samples reached by phone is not equal to the proportion of households without children in the population of all households.

The shape has 11 sides.

Using the angle formula for polygons:

The sum of all the interior angles is:

11-2 x 180 = 9 x 180 = 1,620 degrees.

For one angle divide the total by number of sides:

1620 / 11 = 147.27 which rounds to 147.2

The answer is D.

Answer:

There are no values of  x  that make the equation true.

No solution

Step-by-step

hope it help

Hi

2-9x = -6x+5-3x

-9x+6x+3x = 5-2

  0x = 3

as  0 ≠ 3 , there is no answer possible to your equation.

Answer:

Below.

Step-by-step explanation:

As both the right sides of the 2 equations are equal to y, by the transitive law of equality 3x + 1 = -2x + 3.

W then solve this equation for x then substitute this value of x  in the first equation ( y = 3x + 1) to find the value of y.  

Answer:

45 mins

Step-by-step explanation:

Answer:

8 (19) or  8 (18 +1)

Step-by-step explanation:

Distributive property means to distribute.

HCF of 144 and 8.

=> 8 is the HCF of 144 and 8

8 (18 + 1)

=> 8 (19)

Answer:

Step-by-step explanation:

Given the log function [tex](y-1)log_{10}(4) = log_{10} 16\\ \\[/tex] to get the value of y, the following steps must be carried out;

[tex](y-1)log_{10}(4) = log_{10} 16\\\\(y-1)log_{10}(2^2) = log_{10} 2^4\\\\ (y-1)2log_{10}(2) = 4log_{10} 2\\ \\DIvide\ both\ sides\ by \ log_{10}2\\\\\frac{2(y-1)log_{10}2 }{log_{10}2} = \frac{4log_{10}2}{log_{10}2} \\\\2(y-1) = 4\\\\[/tex]

Open the bracket

[tex]2y-2(1) = 4\\\\2y -2 = 4\\\\add \ 2 \ to \ both \ sides\\\\2y-2+2 = 4+2\\\\2y = 6\\\\Divide \ both \ sides\ by \ 2\\\\2y/2 = 6/2\\\\y = 3[/tex]

Hence the value of y is 3

Answer:

[tex]\huge \boxed{6x^2 }[/tex]

Step-by-step explanation:

6 times a number squared.

Let the number be [tex]x[/tex].

6 is multiplied to [tex]x[/tex] squared.

[tex]6 \times x^2[/tex]

Answer:

1308.33

Step-by-step explanation:

In the pic

Answer:

The correlation of X and Y is 1.006

Step-by-step explanation:

Given

X: 2, 3, 5, 6

Y: 1, 2, 4, 5

n = 4

Required

Determine the correlation of x and y

Start by calculating the mean of x and y

For x

[tex]M_x = \frac{\sum x}{n}[/tex]

[tex]M_x = \frac{2 + 3+5+6}{4}[/tex]

[tex]M_x = \frac{16}{4}[/tex]

[tex]M_x = 4[/tex]

For y

[tex]M_y = \frac{\sum y}{n}[/tex]

[tex]M_y = \frac{1+2+4+5}{4}[/tex]

[tex]M_y = \frac{12}{4}[/tex]

[tex]M_y = 3[/tex]

Next, we determine the standard deviation of both

[tex]S = \sqrt{\frac{\sum (x - Mean)^2}{n - 1}}[/tex]

For x

[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{n -1}}[/tex]

[tex]S_x = \sqrt{\frac{(2-4)^2 + (3-4)^2 + (5-4)^2 + (6-4)^2}{4 - 1}}[/tex]

[tex]S_x = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]

[tex]S_x = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]

[tex]S_x = \sqrt{\frac{10}{3}}[/tex]

[tex]S_x = \sqrt{3.33}[/tex]

[tex]S_x = 1.82[/tex]

For y

[tex]S_y = \sqrt{\frac{\sum (y_i - My)^2}{n - 1}}[/tex]

[tex]S_y = \sqrt{\frac{(1-3)^2 + (2-3)^2 + (4-3)^2 + (5-3)^2}{4 - 1}}[/tex]

[tex]S_y = \sqrt{\frac{-2^2 + (-1^2) + 1^2 + 2^2}{3}}[/tex]

[tex]S_y = \sqrt{\frac{4 + 1 + 1 + 4}{3}}[/tex]

[tex]S_y = \sqrt{\frac{10}{3}}[/tex]

[tex]S_y = \sqrt{3.33}[/tex]

[tex]S_y = 1.82[/tex]

Find the N pairs as [tex](x-M_x)*(y-M_y)[/tex]

[tex](2 - 4)(1 - 3) = (-2)(-2) = 4[/tex]

[tex](3 - 4)(2 - 3) = (-1)(-1) = 1[/tex]

[tex](5 - 4)(4 - 3) = (1)(1) = 1[/tex]

[tex](6-4)(5-3) = (2)(2) = 4[/tex]

Add up these results;

[tex]N = 4 + 1 + 1 + 4[/tex]

[tex]N = 10[/tex]

Next; Evaluate the following

[tex]\frac{N}{S_x * S_y} * \frac{1}{n-1}[/tex]

[tex]\frac{10}{1.82* 1.82} * \frac{1}{4-1}[/tex]

[tex]\frac{10}{3.3124} * \frac{1}{3}[/tex]

[tex]\frac{10}{9.9372}[/tex]

[tex]1.006[/tex]

Hence, The correlation of X and Y is 1.006

Answer:

The distribution is  Poisson distribution

Step-by-step explanation:

From the question we are told that

   An expected number of fish was caught per hour is  1.5

The distribution that best characterize the number of fish you catch in one hour of fishing is the Poisson distribution

   This because generally the  Poisson distribution is a distribution that shows the number of times a given event will occur within a defined period of time

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

Explanation:

When we reflect any point (x,y) over the line y = x, the x and y coordinates swap. So for instance, we have K = (5, -9) turn into K ' = (-9, 5).

Consider a point like (1,2). We can move it down 1 unit to have it land on the line y = x, then we can move it one unit to the right to move it to (2,1). These two translations effectively move the original point to its reflected location. The distance from (1,2) to y = x, is the same as the distance from (2,1) to y = x. Furthermore, the line connecting (1,2) to (2,1) is perpendicular to y = x.

Answer:

The angle measures are 53.5° and 36.5°.

Step-by-step explanation:

We can create a systems of equations, assuming x and y are the angle measures.

Since the two angles are complementary, their angle measures will add up to 90.

x + y = 90

x - y = 17

We can now use the process of elimination, and end up with:

2x = 107

Dividing both sides by two gets us

x = 53.5

Substituting this value into an equation will get us y

53.5 + y = 90

y = 36.5

Hope this helped!

Answer:

d = 5

Step-by-step explanation:

Distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

d = sqrt[(1-4)^2+(-1-3)^2]

d = 5

Answer:

5

Step-by-step explanation:

distance =  square root of (1-4)^2 + (-1-3)^2

=> distance = square root of -3^2 +  (-4)^2

=> distance = square root of 9 + 16

=> distance = square root of 25

=> distance = 5

Answer:

[tex](\frac{4}{3},-\frac{10}{3})[/tex]

Step-by-step explanation:

If the extreme ends of a line segment AC are A[tex](x_1,y_1)[/tex] and C[tex](x_2,y_2)[/tex].

If a point B(x, y) divides the segment in the ratio of m : n

Then the coordinates of the point B are,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

If the ends of AC are A(-2, 5) and C(2, -5) and a point B divides it in the ratio of m : n = 5 : 1

Therefore, coordinates of this point will be,

x = [tex]\frac{5\times (2)+1(-2)}{5+1}[/tex]

  = [tex]\frac{10-2}{5+1}[/tex]

  = [tex]\frac{8}{6}[/tex]

  = [tex]\frac{4}{3}[/tex]

y = [tex]\frac{5\times (-5)+1(5)}{5+1}[/tex]

  = [tex]\frac{-25+5}{6}[/tex]

  = [tex]-\frac{20}{6}[/tex]

  = [tex]-\frac{10}{3}[/tex]

Therefore, coordinates of the point B are [tex](\frac{4}{3},-\frac{10}{3})[/tex].

Answer:

B

Step-by-step explanation:

Sin 45 = y/(11√6)

1/√2 = y/(11√6)

y= (11√6)/√2

y= 11√3

tan 60 = x/y

√3 = x/y

x = y√3

= (11√3)√3

= 11(3)

= 33

b. No, the requirements are not met because the sample has fewer than 10 failures, which violates the condition for approximating a normal distribution.

Step-by-step explanation:

from the question,  the number of successes is equal to 30

and it is more than the number of failures

for us to conduct this test such as the z test the data we are using should be a random sample from the population that we are interested in. the population should be at least as big as the sample by 10 times. first of all We need to check if the mean of the sample is normally distributed.

if 26 are successes out of a sample of 30, then failures would be 4. therefore option b is correct.

Answer:

a) P(x<40) = 0.90824

Therefore, the percent of the women watch TV less than 40 hours per week is 0.90824 × 100 = 90.8240%

b)P(x>25) = 1 - P(z = -0.78) = 0.7823

Therefore, percent of the men watch TV more than 25 hours per week?is 0.7823 × 100 = 78.230%

c)The number of hours that the one percent of WOMEN who watch the most TV per week watch is for 44.485hours

While, for the MEN, the number of hours that the one percent of men who watch the most TV per week watch is for 40.883 hours

Step-by-step explanation:

To solve this question, we would be using z score formula:

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

a. What percent of the women watch TV less than 40 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

z = (x-μ)/σ,

where x is the raw score = 40 hours

μ is the population mean = 34 hours

σ is the population standard deviation = 4.5

z = (40 - 34)/4.5

z = 1.33333

Approximately to 2 decimal places = z score = 1.33

Using the normal distribution z score table

Probabilty value from Z-Table:

P(z = 1.33) = P(x<40) = 0.90824

Therefore, the percent of the women watch TV less than 40 hours per week is 0.90824 × 100 = 90.8240%

b. What percent of the men watch TV more than 25 hours per week? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.)

z = (x-μ)/σ,

where x is the raw score = 25 hours

μ is the population mean = 29 hours

σ is the population standard deviation = 5.1

z = (25 - 29)/5.1

z = -0.78431

Approximately to 2 decimal places

z score = -0.78

Using the z score normal distribution table:

Probability value from Z-Table:

P(z = -0.78) = P(x<Z) = 0.2177

P(x>25) = 1 - P(z = -0.78) = 0.7823

Therefore, percent of the men watch TV more than 25 hours per week?is 0.7823 × 100 = 78.230%

c. How many hours of TV do the one percent of women who watch the most TV per week watch? Find the comparable value for the men. (Round your answers to 3 decimal places.)

First, we find what the z score is.

We were asked in the question to find how many hours 1% of the women watch TV the most.

We have to find the confidence interval

100 - 1% = 99%

The z score for the confidence interval of 99% or 0.99(in decimal form) = 2.33

z score = 2.33

Since we know the z score now, we proceed to find x = raw score.

z = (x-μ)/σ,

where x is the raw score = unknown

μ is the population mean = 34 hours

σ is the population standard deviation = 4.5

2.33= (x - 34)/4.5

Cross Multiply

2.33 × 4.5 = x - 34

10.485 = x - 34

x = 10.485 + 34

x = 44.485 hours.

Therefore, the number of hours that the one percent of women who watch the most TV per week watch is for 44.485hours

In the question, we were also asked to find the comparable value for men.

Hence, for one percent of the men.

We determine what the z score is.

We were asked in the question to find how many hours 1% of the men watch TV the most.

We have to find the confidence interval

100 - 1% = 99%

The z score for the confidence interval of 99% or 0.99(in decimal form) = 2.33

We already have our z score as 2.33

z = (x-μ)/σ,

where x is the raw score = unknown

μ is the population mean = 29 hours

σ is the population standard deviation = 5.1

2.33= (x - 29)/5.1

Cross Multiply

2.33 × 5.1 = x - 29

11.883 = x - 29

x = 11.883 + 29

x = 40.883 hours.

Therefore, the number of hours that the one percent of men who watch the most TV per week watch is for 40.883 hours

Answer:

depth 5 8.3 ft, length 5 24.9 ft, width 5 16.8 ft

Answer/Step-by-step explanation:

[tex] (4 + 5) + 2 = 4 + (5 + 2) [/tex] => any combination of numbers were formed or grouped when adding. The associative property of addition was applied.

[tex] 2(2x + 4) = 4x + 8 [/tex] => the sum of two terms (addend) are multiplied by by a number separately (I.e., a(b + c) = a(b) + a(c) = ab + ac). The property applied is distributive property.

[tex] (7x * x) * 3 = 7 * (x * 3) [/tex] => the numbers were grouped in any combination to arrive at same result when multiplying. Associative property of multiplication was applied.

[tex] (8 * x * 2) = (x * 8 * 2) [/tex] => the numbers where ordered in any manner to arrive at same result when multiplying. Cummutative property of multiplication was applied.

[tex] (7 + 3) + 1 = (1 + (7 + 3) [/tex] => the order in which the nnumbers in the were arranged doesn't matter, as same result is arrive at. This is Cummutative property of addition.

Answer:

(-2,-2); minimum

Step-by-step explanation:

From the graph, the vertex is (-2, -2) and since there are no y values that go less than the y value of the vertex, it is a minimum.

Answer:

  b.  $11,820

Step-by-step explanation:

The 'rule of 72' tells you the doubling time of this account is about ...

  (72 years)/(4.25) = 16.9 years

So, in 18 years, the amount will be slightly more than double the present value. That is, the present value is slightly less than half the future amount.

  $25,000/2 = $12,500

The closest answer choice is ...

  $11,820

__

The present value of that future amount is ...

  PV = FV×(1 +r)^-t = $25,000×1.0425^-18 ≈ $11,818.73

The present value is about $11,820.

Answer:

B

Step-by-step explanation:

Answer:

Solution : Option D

Step-by-step explanation:

The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )

x = - 3cos(t) ⇒ x / - 3 = cos(t)

y = 4sin(t) ⇒ y / 4 = sin(t)

Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )

( x / - 3 )² = cos²(t)

+ ( y / 4 )² = sin²(t)

_____________

x² / 9 + y² / 16 = 1

Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.

Answer:

Note that orthogonal to the plane means perpendicular to the plane.

Step-by-step explanation:

-1x+3y-3z=1 can also be written as -1x+3y-3z=0

The direction vector of the plane -1x+3y-3z-1=0 is (-1,3,-3).

Let us find a point on this  line for which the vector from this point to (0,0,5) is perpendicular to the given line. The point is x-0,y-0 and z-0 respectively

Therefore, the vector equation is given as:

-1(x-0) + 3(y-0) + -3(z-5) = 0

-x + 3y + (-3z+15) = 0

-x + 3y -3z + 15 = 0

Multiply through by - to get a positive x coordinate to give

x - 3y + 3z - 15 = 0

Answer:

The answer is 36

Step-by-step explanation:

Let the number be x

7 less than the quotient of a number and 3 is written as

The result is 5

So we have

Move - 7 to the right side of the equation

That's

Multiply both sides by 3 to make x stand alone

We have

We have the final answer as

Hope this helps you

Answer:

166.9 miles or 166 miles

Step-by-step explanation:

We can form an equation like this:

19.95 + .18x = 50

In this equation, "x" is the number of miles.

=> 19.95 - 19.95 +.18x = 50 -19.95

=> .18x = 30.05

=> .18x/.18 = 30.05/.18

=> x = 166.9

Ashton can drive 166.9 miles.

**Note: We cannot round the answer to 167, as she would not have enough money to drive the extra 0.1 mile.

Answer:

[tex] {(x - 3)}^{2} + {(y + 5)}^{2} = {5}^{2} [/tex]

Step-by-step explanation:

First find the radius

Which is the distance between the 2 points.

Radius =5

The answer in the standad form is above.

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

The standard equation of a circle is given as:

(x - a)² + (y - b)² = r²

where (a, b) is the center of the circle and r is the radius of the circle.

Given the center as (3, -5) hence the radius of the circle is the distance between (3, -5) and (-1, -8). Hence:

[tex]Radius=\sqrt{(-8-(-5))^2+(-1-3)^2} \\\\Radius=5\ units\\[/tex]

hence:

(x - 3)² + (y - (-5))² = 5²

(x - 3)² + (y + 5)² = 25

The equation of the circle in Standard Form is (x - 3)² + (y + 5)² = 25

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