The following data was obtained from 32 people aged 25-29 who were asked how many hours of TV they watched per week.

4,2,8,9,4,5,10,11,7,8,3,4,10,3,8,5,1,7,0,4,3,2,2,1,1,0,2,3,5,2,1,1.

Group the data in intervals and record the frequency of each interval as well as the cumulative frequency and relative frequency. Make a table showing this information.
Graph the data using frequency histogram.
Graph the data using a cumulative frequency chart.

Answer:

0.52 = 52% probability that an email is detected as spam.

Step-by-step explanation:

Probability that an email is detected as spam:

99% of 50%(are spam).

5% of 100 - 50 = 50%(false positives, that is, e-mails that are not spam but are detected as spams).

What is the probability that an email is detected as spam?

[tex]p = 0.99*0.5 + 0.05*0.5 = 0.52[/tex]

0.52 = 52% probability that an email is detected as spam.

Answer:

8 suits

Step-by-step explanation:

Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then

30 ÷ 3.75 = 8

Then 8 suits can be made from 30 m of cloth

Answer:

"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".

Step-by-step explanation:

Let be the following system of linear equations:

[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)

[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)

[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)

1) We eliminate [tex]y[/tex] by adding (1) and (2):

[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]

[tex]6\cdot x +2\cdot z = 24[/tex] (4)

2) We eliminate [tex]y[/tex] by adding (1) and (3):

[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]

[tex]9\cdot x -4\cdot z = 36[/tex] (5)

Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".

Step-by-step explanation:

You can simply plot these points on a graph and see where the line goes. It go

Answer:

if x=0 then they have same value

1 and 2 options are out

for x=-1

g(-1)=1

h(-1)=-1

3 is true

4th

FALSE

for all values except 0, g(x)>h(x)

correct ones are

g(x) > h(x) for x = -1.

For positive values of x, g(x) > h(x).

For negative values of x, g(x) > h(x).

Step-by-step explanation:

Answer:

Area swept by the blade = 448[tex]in^{2}[/tex]

Step-by-step explanation:

The arc the wiper wipes is for 135 degrees angle.

So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.

Then subtract the area of sector with 14 inches  from area of sector with radius as 24 inches.

So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]

Simplify it,

                                                  =216[tex]\pi[/tex]

Now, let's find area of sector with radius 14 inches

Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]

Simplify it

                                          =73.5[tex]\pi[/tex]

So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]

Simplify it and use pi as 3.14.....

Area of swept =678.584 - 230.907

                               =447.6769

Round to nearest whole number

So, area swept by the blade = 448[tex]in^{2}[/tex]

I believe this is your question:

A.) find an angle between 0 degrees and 360 degrees that is coterminal with 570 degrees.

Answer:

210 degrees

Explanation:

Coterminal angles begin on the same initial side and end or terminate on the same side as an angle. Example 45 degrees and 405 degrees are coterminal angles because they both begin and end on the same side.

To find an angle between 0 and 360 that is coterminal with 570 degrees, w simply subtract 360 degrees from 570, hence:

570-360=210 degrees

570 degrees is coterminal with 210 degrees

Answer:

(a) Temperature: Numerical

(b) Traffic congestion: Categorical

Step-by-step explanation:

Required

Determine the variable type

(a) Temperature

Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.

Hence, the variable is numerical

(b) Traffic congestion

From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....

Hence, the variable is categorical

Answer:

2nd Graph

Step-by-step explanation:

Bases off the graphs, you gave me, I assume your the equation is

[tex]f(x) = - 4(2) {}^{x} [/tex]

The parent equation of this function is

[tex]f(x) = b {}^{x} [/tex]

Let say x=0

Using the rules of exponets, the y value must be 1 so a critical point is

(0,1)

The function is multiplied by -4.

This means the function is stretched in the y direction by 4 and reflected over the x axis. So our new point will be

(0,-4).

The base 2 the function will get compressed by 1/2.

The best graph that represents this is the second graph

Answer:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

Step-by-step explanation:

Given

[tex]f(x,y) = \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Required

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex]

[tex]\lim_{(x,y) \to (0,0)} f(x,y)[/tex] becomes

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}[/tex]

Multiply by 1

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2}\cdot 1[/tex]

Express 1 as

[tex]\frac{y^2}{y^2} = 1[/tex]

So, the expression becomes:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} \cdot \frac{y^2}{y^2}[/tex]

Rewrite as:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} \cdot \frac{\sin^2y}{y^2}[/tex]

In limits:

[tex]\lim_{(x,y) \to (0,0)} \frac{\sin^2y}{y^2} \to 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2} *1[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 y^2}{x^2+2y^2}[/tex]

Convert to polar coordinates; such that:

[tex]x = r\cos\theta;\ \ y = r\sin\theta;[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{(r\cos\theta)^2 (r\sin\theta;)^2}{(r\cos\theta)^2+2(r\sin\theta;)^2}[/tex]

Expand

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2\cos^2\theta+2r^2\sin^2\theta}[/tex]

Factor out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^4\cos^2\theta\sin^2\theta}{r^2(\cos^2\theta+2\sin^2\theta)}[/tex]

Cancel out [tex]r^2[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+2\sin^2\theta}[/tex]

Express [tex]2\sin^2 \theta[/tex] as [tex]\sin^2\theta+\sin^2\theta[/tex]

So:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{\cos^2\theta+\sin^2\theta+\sin^2\theta}[/tex]

In trigonometry:

[tex]\cos^2\theta + \sin^2\theta = 1[/tex]

So, we have:

[tex]\lim_{(x,y) \to (0,0)} \frac{r^2\cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

Evaluate the limits by substituting 0 for r

[tex]\frac{0^2 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0 \cdot \cos^2\theta\sin^2\theta}{1+\sin^2\theta}[/tex]

[tex]\frac{0}{1+\sin^2\theta}[/tex]

Since the denominator is non-zero; Then, the expression becomes 0 i.e.

[tex]\frac{0}{1+\sin^2\theta} = 0[/tex]

So,

[tex]\lim_{(x,y) \to (0,0)} \frac{x^2 \sin^2y}{x^2+2y^2} = 0[/tex]

If the slope of the line y = mx − 4 is  less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement

The slope of a line defines the steepness of such a line. It is the ratio of the rise to the run of a line.

The general formula for calculating an equation of a line is expressed as:

[tex]y = mx + b[/tex] where:

m is the slope of the line

Given the equation of the line, [tex]y=x-4[/tex] the slope of the line will be derived through comparison as shown:

[tex]mx=1x\\[/tex]

Divide through by x

[tex]\dfrac{mx}{x} = \dfrac{1x}{x}\\ m=1[/tex]

Hence the slope of the line y = x - 1 is 1.

According to the question, since we are told that the  slope of the line

y = mx − 4 is  less than the slope of the line y = x − 4, this shows that m will be any values less than 1 i.e. m < 1. This gives a true statement

Learn more about the slope of a line here: https://brainly.com/question/16949303

Answer:

Step-by-step explanation:

Answer:

0.015

Step-by-step explanation:

1.5% = means 1.5 per 100 or simply 1.5/100.if you divide 1.5 by 100 you will get 0.015

Answer:

Table B

Step-by-step explanation:

correct on edge :)

Given that exp(2x) is a solution, we assume another solution of the form

y(x) = v(x) exp(2x) = v exp(2x)

with derivatives

y' = v' exp(2x) + 2v exp(2x)

y'' = v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)

Substitute these into the equation:

(2x + 5) (v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)) - 4 (x + 3) (v' exp(2x) + 2v exp(2x)) + 4v exp(2x) = 0

Each term contains a factor of exp(2x) that can be divided out:

(2x + 5) (v'' + 4v' + 4v) - 4 (x + 3) (v' + 2v) + 4v = 0

Expanding and simplifying eliminates the v term:

(2x + 5) v'' + (4x + 8) v' = 0

Substitute w(x) = v'(x) to reduce the order of the equation, and you're left with a linear ODE:

(2x + 5) w' + (4x + 8) w = 0

w' + (4x + 8)/(2x + 5) w = 0

I'll use the integrating factor method. The IF is

µ(x) = exp( ∫ (4x + 8)/(2x + 5) dx ) = exp(2x - log|2x + 5|) = exp(2x)/(2x + 5)

Multiply through the ODE in w by µ :

µw' + µ (4x + 8)/(2x + 5) w = 0

The left side is the derivative of a product:

[µw]' = 0

Integrate both sides:

∫ [µw]' dx = ∫ 0 dx

µw = C

Replace w with v', then integrate to solve for v :

exp(2x)/(2x + 5) v' = C

v' = C (2x + 5) exp(-2x)

∫ v' dx = ∫ C (2x + 5) exp(-2x) dx

v = C₁ (x + 3) exp(-2x) + C₂

Replace v with y exp(-2x) and solve for y :

y exp(-2x) = C₁ (x + 3) exp(-2x) + C₂

y = C₁ (x + 3) + C₂ exp(2x)

It follows that the second fundamental solution is y = x + 3. (The exp(2x) here is already accounted for as the first solution.)

Answer:

Cardinality of the power set of the given set = [tex]2^6=64[/tex]

Step-by-step explanation:

Power set is the set of all the possible subsets that can be formed from the given set including the null set and the set itself.

Example set:

{1,2,3}

All the possible subsets of this set:

{}; {1}; {2}; {3}; {1,2,3}; {1,2}; {1,3}; {2,3}

The power set of the above set is written as:

P({ {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} })

Since the no. of elements in the above power set in this example is 8 therefore its cardinality is 8.

Cardinality of the power set of a given set is expressed by a formula: [tex]2^n[/tex]

where n is the cardinality (no. of elements) of the given set whose power set is to be formed for determining cardinality of the power set.

Hence in the given case, we have  n = 6.

Answer:b

Step-by-step explanation:

Ive done this

Answer:

[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]

Step-by-step explanation:

Multiplication,

[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]

Answer:

No unless x is being used to define only elements of an integer set.

Step-by-step explanation:

No, not in general unless x is defined as a integer or a subset of the integers like the naturals, whole numbers....

Usually 6<=x<=10 means all real numbers between 6 and 10, inclusive. This means example that 6.6 or 2pi are in this set with infinitely other numbers that I can't name.

{6,7,8,9,10} just means the set containing the numbers 6,7,8,9,10 and that's only those 5 numbers.

Answer:

90

Step-by-step explanation:

=> x + y = 12

=> x² + y² + 2xy = 144

=> x² + y² + 2 * 27 = 144

=> x² + y² = 144 - 54

=> x² + y² = 90

Answer:

30

Step-by-step explanation:

The given is right triangle with angle measure 90-60 and 30 degrees as we can see on the image.

Answer:

.33x = 105.60

$371

Step-by-step explanation:

Answer:

63.44

Step-by-step explanation:

its 63.44697 but you round so its 63.44

Answer:

Peter is a-8 in 9 years, (a-8)+ 9+ a+ 9= 76

Answer:

P = 25

A = 33

Step-by-step explanation:

P + 8 = A

P + 9 + A + 9 = 76

P + A = 58

~~~~~~~~~~~~~~

P = 58 - A

P = 58 - P - 8

2 P = 50

P = 25

A = 33

Answer:

[tex]Sales = 86.749[/tex]

Step-by-step explanation:

Given

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

[tex]Competitors = 4[/tex]

[tex]Population = 12000[/tex]

See comment for complete question

Required

The sales

We have:

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

Substitute values for competitors and population

[tex]Sales = 0.845*4 + 5.79*12 + 13.889[/tex]

[tex]Sales = 3.38 + 69.48 + 13.889[/tex]

[tex]Sales = 86.749[/tex]

Answer:

Step-by-step explanation:

50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.

Answer:

y = 2x

Step-by-step explanation:

Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,

[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]

Answer:

12,500

Step-by-step explanation:

P = R-E

b.e.p : P=0

R=E

140x = 1000000 + 60 x

80x = 1000000

x=12,500

Answer:

∠ BCA = 90°

Step-by-step explanation:

∠ BCA is an angle in the semicircle and equals 90°