A wheel with a 50 cm radius is rotating at a rate of 5 radians/sec. What is the linear speed of a point on its rim in meters per minute?

Answer:

122 Degrees

Step-by-step explanation:

Since we are given that angle 1 and 2 make a linear pair:

angle 1 + angle 2 = 180 degrees ----------------------------(1)

We have also been told that angle 2 is 6 more than twice the measure of angle 1

Which means: angle 2 = (2*angle1)  + 6 -------------------(2)

From putting the value of angle 2 in (1) from (2)

angle 1 + 2*angle 1 + 6 = 180

3*angle 1 = 174

angle 1 = 58 degrees -----------------------(3)

From (1) and (3):

angle 2 + 58 = 180

angle 2  = 122 degrees

Therefore, the measure of angle 2 is 122 degrees

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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Answer:

-------------------

3/5 part of 60 CD's were gifts.

That makes:

Answer:

It means \(\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}\) also converges.

Step-by-step explanation:

The actual Series is::

\(\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}\)

The method we are going to use is comparison method:

According to comparison method, we have:

\(\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n\)

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

\(=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}\)

\(\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}\)

Now:

\(\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}\)

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

\(\sum_{n=1}^{inf}\frac{1}{n^p}\)

if p>1 then series converges. In oue case we have:

\(\sum_{n=1}^{inf}b_n=\frac{1}{n^4}\)

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means \(\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}\) also converges.

Answer: 2^3 x 3 x 5^2

Step-by-step explanation:

All we have to do is divide 600

alright

Chopping off the two zeros:

6x100

Factoring 6:

2x3x100

Factoring 100:

2x3x10x10:

Factoring both 10s:

2x3x2x5x2x5

2^3 x 3 x 5^2

Therefore, we have factored 600 into 2^3 x 3 x 5^2

The data set which contains an outlier from the given answer choices is; Choice D; {16, 42, 45, 45, 46, 48}.

An outlier in a set of data values is a data value which differs significantly from other data points and hence, tends to affect the mean of such set of data values significantly.

On this note, choice D is the set of data values which contains an outlier.

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The equation of the line in fully simplified slope-intercept form is y = 1/2x + 4

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following points

(0, 4) and (-8, 0)

A linear equation is represented as

y = mx + c

Using the point (0, 4), we have

4 = 0 * m + c

So, we have

c = 4

Using the point (-8, 0), we have

0 = -8 * m + 4

So, we have

m = 1/2

So, we have

m = 1/2 and c = 4

Recall that we have

y = mx + c

This gives

y = 1/2x + 4

Hence, the equation is y = 1/2x + 4

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Answer:

6

Step-by-step explanation:

Because J is the midpoint of KL, it means that KJ ans JL are equal.

Think about it like this:

Hope this helps!

Step-by-step explanation:

the midpoint of a line splits the line into 2 equally long parts.

therefore, JI must be equally long to KJ.

x = 6

and with KJ = 6 and JI = 6, then KI = KJ + JI = 6+6 = 12

Answer:

(a) 191 had side effects

(b) 370 had nausea

(c) 86 had both anxiety and fatigue

Step-by-step explanation:

    See attached. We look at the Venn diagram to answer the different questions.

If you are color blind let me know and I will mark the attachment more clearly.

Answer:

2.6 hours

Step-by-step explanation:

75+85

160x/160= 416/160

=2.6

The required result if the given expression is \(11[\frac{t}{40}-2]\).

What is expression?

A finite combination of symbols that are well-formed in accordance with context-dependent principles constitutes an expression or mathematical expression.

Given the expression quantity three fourths times t minus 5 plus two fifths times t end quantity minus quantity five eighths times t plus 17 end quantity.

We write it in expression and we get

\(\frac{3}{4} \times t-5+\frac{2}{5} \times t-\frac{5}{8} \times t +17\)

Now

\(\frac{3}{4} \times t-5+\frac{2}{5} \times t-[\frac{5}{8} \times t +17]\\=\frac{3t}{4} +\frac{2t}{5} -\frac{5t}{8} -22\\=\frac{2t}{5}+\frac{6t-5t}{8}-22\\=\frac{2t}{5}+\frac{t}{8}-22\\=\frac{16t-5t}{40}-22\\=\frac{11t}{40}-22\\=11[\frac{t}{40}-2]\)

Therefore, the required result if the given expression is \(11[\frac{t}{40}-2]\).

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don't use the answer above this one, its wrong.

To construct a frequency histogram based on the given temperature data, we will use the temperature ranges as the x-axis and the number of days as the y-axis.

The temperature ranges and their corresponding frequencies are as follows:

30-39: 2 days

40-49: 26 days

50-59: 28 days

60-69: 8 days

70-79: 2 days

To create the histogram, we will represent each temperature range as a bar and the height of each bar will correspond to the frequency of days.

Using an appropriate scale, we can label the x-axis with the temperature ranges (30-39, 40-49, 50-59, 60-69, 70-79) and the y-axis with the frequency values.

Now, we can draw rectangles (bars) on the graph, with the base of each rectangle corresponding to the temperature range and the height representing the frequency of days. The height of each bar will be determined by the corresponding frequency value.

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Answer:

Step 1 of 2: Subtract.  

Subtract

(

negative 5 over 8  

−  

5

8

) − (

negative 4 over 3  

−  

4

3

) =  

17 over 24  

17

24

Step 1 of 2: Subtract, sub-step a: Subtract a negative.  

Subtract a negative

negative 5 over 8  

−  

5

8

− (

negative 4 over 3  

−  

4

3

) =  

negative 5 over 8  

−  

5

8

+  

4 over 3  

4

3

Subtracting a negative is the same as adding a positive.

Step 1 of 2: Subtract, sub-step b: Find common denominator.  

Find common denominator

negative 5 over 8  

−  

5

8

+  

4 over 3  

4

3

= −

( 5 × 3 ) over ( 8 × 3 )  

5 × 3  

8 × 3  

+  

( 4 × 8 ) over ( 3 × 8 )  

4 × 8  

3 × 8  

=  

negative 15 over 24  

−  

15

24

+  

32 over 24  

32

24

24 is the least common multiple of denominators 8 and 3. Use it to convert to equivalent fractions with this common denominator.

Step 1 of 2: Subtract, sub-step c: Add.  

Add

negative 15 over 24  

−  

15

24

+  

32 over 24  

32

24

=  

(  

negative 15  

−15 + 32 ) over 24  

negative 15  

−15 + 32  

24

=  

17 over 24  

17

24

Answer:

The answer would be 17/24

Step-by-step explanation:

1. Common denominator is going to be 24. 3(-5/8) - 8(-4/3)

2. Next multiply. -15/24 + 32/24

3. After addition you get 17/24 or 0.7

Answer:

n = 8

Step-by-step explanation:

The given sequence, 2, 6, 18, 54. . ., is a geometric sequence.

It has a common ratio of 3 => \( \frac{6}{2} = \frac{18}{6} = \frac{54}{18} = 3 \)

Thus, the sum of the first n terms of a geometric sequence is given as \(S_n = \frac{a_1(1 - r^n)}{1 - r}\)

Where,

\( a_1 \) = first term of the series = 2

r = common ratio = 3

\( S_n \) = sum of the first n terms = 6,560

Plug in the above values into the formula

\(6,560 = \frac{2(1 - 3^n)}{1 - 3}\)

\( 6,560 = \frac{2(1 - 3^n)}{-2} \)

\( 6,560 = \frac{1 - 3^n}{-1} \)

Multiply both sides by -1

\( -6,560 = 1 - 3^n \)

Subtract 1 from both sides

\( -6,560 - 1 = - 3^n \)

\( -6,561 = - 3^n \)

\( 6,561 = 3^n \)

Evaluate

\( 3^8 = 3^n \)

3 cancels 3

\( 8 = n \)

The value of n = 8

Answer:

30

Step-by-step explanation:

150/5 = 30

30+30+30+30+30 = 150

Ty's visibility if out the upper window of a building with an altitude of 1,602 feet is 49.

What is altitude?

The height of an object in relation to a planet's or a natural satellite's surface, like sea level or land. the degree to which a celestial body is elevated above the horizon.

Here, we have

Given

The formula V = 1.225 √a is used to estimate how far a person can see on a clear day, where V is the visibility in miles and A is the altitude in feet.

We have to find Ty's visibility out the upper window of a building with an altitude of 1,602 feet.

We know that

V = 1.225 √a

a = 1,602 feet.

V = 1.225 √1602

V = 49

Hence, Ty's visibility out the upper window of a building with an altitude of 1,602 feet is 49.

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The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

Below

Step-by-step explanation:

y=2x + 4

-7x + 6y=14       Sub in the value of y given in the first equation

-7x + 6 ( 2x+4) = 14

-7x + 12x + 24 = 14

5x = -10

x = -2              use this value in one of the equations to calculate y= 0

The Solution:

Given the pair of equations below:

We are asked to solve by the Elimination Method.

1. The variable that has an opposite pair is [variable y]

2. To solve for x, we shall add the corresponding terms in both equations together.

Dividing both sides by 5, we get

3. Substituting -2 for x in the first equation, to get the value of y.

Bringing the like terms to one side, we get

Dividing both sides by 5, we get

4. Writing the solution as an ordered pair, we have

Therefore, the correct answer is (-2 , -4)

If we use m compounded per year Bt will be to:

Where:

B0 = deposits = $45900

r = compound yearly interest rate = 1.5% = 0.015

t = years

m = 4

The first quarter's interest

We have following:

Then:

Answer: The interest in first quarter is $172.13

The first quarter's balance

The balance is Bt, therefore:

Answer: The balance after first quarter is $46,072.13

Answer:

The answer for the width of the building 5m

Step-by-step Explanation:

3cm=1m

15cm=x

cross multiply

x×3=15×1

3x=15

divide both sides by 3

3x/3=15/3x=5m

Check the pictures for the answer

Answer:

Increase by 10% of students that bought lunch.

Step-by-step explanation:

I think the percent change was by 10%. Because 10% of those students who packed lunched on Monday did not pack lunch on Tuesday, and assuming that they either buy or pack it that means that 10% more students bought lunch.

Answer:

B. They are not parallel because their slopes are not equal.

Step-by-step explanation:

Find the slope of the line that runs through points (6, 3) and (-1, 5):

\( slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-1 - 6} \)

\( slope (m) = \frac{2}{-7} = -\frac{2}{7} \)

Since the slope of the line that passes through points (6, 3) and (-1, 5) is not the same with line that has a slope of ¾, therefore, both lines cannot be parallel.

The answer is "B. They are not parallel because their slopes are not equal."

Answer:

Left tailed.

Step-by-step explanation:

A claim (alternative hypothesis) is set against the null hypothesis.

The claim (alternative hypothesis) of the  golf analyst is that the standard deviation of the​ 18-hole scores for a golfer is  less than 2.1 strokes

Ha: Sd< 2.1

The null hypothesis will be opposite of the alternate hypothesis

H0: sd ≥ 2.1

A test for which the entire rejection region is located in only one of the two tails - either left or right- is called one tailed test.

In the given example the acceptance region is located in the area greater or equal to 2.1 . The rejection region lies to the left and the acceptance region lies to the right.

As the rejection region lies to the left, it is a left tailed test.

Also if the alternative hypothesis contains equality less than it is left tailed.

Answer:

58 degrees

Step-by-step explanation:

find x first

8x+2 + 6x + 80 = 180
14x + 82 = 180
14x = 98

x = 7

then substitute it back into the angle measure of B

angle b = 8x + 2
8(7) + 2 = 58

Answer:

what is the determinant of human value

Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

Answer:

(1/4)³

Step-by-step explanation:

Hope it helps you

Answer:

\(\frac{1}{64}\)

Step-by-step explanation:

Negative exponents means you bring the base to the denominator, which becomes a fraction.

\(4^{-3} \\=\frac{1}{4^{3}}\)

The question wants us to write without an exponent.

The \(4^{3} = 4 * 4* 4=64\)

So, it becomes:

\(\frac{1}{64}\)