A belt runs a pulley of radius 8 inches at 60 revolutions per minute. a) Find the angular speed in radians per minute. b) Find the linear speed in inches per minute.

Answer:

Step-by-step explanation: See annex

The figures are in feet

Answer:

  yes

Step-by-step explanation:

The club can sell 100 more tickets before they reach their maximum. If they sell those at the "day-of" price, they will have additional revenue of ...

  100 × $15 = $1500

Then their total revenue would be ...

  300 × $10 + $1500 = $4500 . . . . more than enough to meet expenses.

_____

To make up the additional $500 they need, the drama club only needs to sell ...

  ceiling($500/$15) = 34 . . . tickets at the "day-of" price.

Answer:

c Flower/ Week

Step-by-step explanation:

think about it like this

hours          (flowers)

____.    x.  _______

Weeks     hours

Both of the hours cancel out similar to unit conversions in chemistry and you are left with flowers per week. since the value of flowers you get per hour you work, and x is dependant on the amount of hours you work in a week. These two functions work in conjuction to give flowers per week picked, this crossing off happens diagonally from left down to the right.

The units of measurement for the composite function s(W(h)) is Option(C) flowers/week.

Given that the function s(t) approximates how many flowers Matthew picks per hour.  

Unit of function s(t) is flowers/hours.

Also given that the function W(h) represents how many hours per week Matthew spends picking flowers.

Unit of W(h) = hours/week .

The composite function s(W(h)) will have unit -

= Flowers/hours * hours/week

= Flowers/week

The units of measurement for the composite function s(W(h)) is Option(C) flowers/week.

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Answer:

  18,062.5 square feet

Step-by-step explanation:

The largest area will be obtained when half the fence is used in each of the orthogonal directions. That is, the pen will have two parallel sides that total 425 feet, and 5 parallel sides and partitions that total 425 feet.

The long sides are 212.5 feet, and the short sides are 85 feet, so the overall area is ...

  (212.5 ft)(85 ft) = 18,062.5 ft²

__

Working Out

Suppose the long side is length x. Then the lengths of the 2 ends and 3 dividers are ...

  short side = (850 -2x)/5

Then the overall area is the product of long side and short side:

  A = x(850 -2x)/5 = (2/5)(x)(425 -x)

This equation is that of a parabola that opens downward. Its vertex (maximum) is at the value of x halfway between the zeros of 0 and 425. That is, area is a maximum when x=212.5.

That maximum area is ...

  A = (2/5)(212.5)(425 -212.5) = 18,062.5 . . . square feet

Answer: The difference is $16

Step-by-step explanation:

n will equal the amount of t-shirts bought

Website 1's Costs: c = 24n + 8

Website 2's cost: c = 22n + 12

Then, we substitute 10 for n

c = 24(10) + 8

c = 240 + 8

c = 248

c = 22(10) + 12

c = 220 + 12

c = 232

248 - 232 = 16

The difference between the total cost of the first website and that of the second based on the given function will be $16.

A certain kind of relationship called a function binds inputs to essentially one output.

A function can be regarded as a computer, which is helpful.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given,

On the first website,

Cost to buy 10 T-shirts.

C = 24(10) + 8

C = 240 + 8

C = $248

The second website

The total cost to buy 10 T-shirts

C = 22(10) + 12

C= 220 + 12

C= $232

The differnce $248 - $232 = $16

Hence "The difference between the total cost of the first website and that of the second based on the given function will be $16".

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The player will get 10 hits for 15 times strikes out.

The player will strike out 69 times for 46 hits.

Step-by-step explanation:

Given,

Ratio of strike out to hits = 3:2

Condition 1: If the player gets 15 strikes out;

Let,

x be the hits for 15 times strikes out.

Using proportion;

Strike out : hit :: strike out : hit

[tex]3:2::15:x[/tex]

Product of mean = Product of extreme

[tex]15*2=3*x\\3x=30[/tex]

Dividing both sides by 3;

[tex]\frac{3x}{3}=\frac{30}{3}\\x=10[/tex]

The player will get 10 hits for 15 times strikes out.

Condition 2: if the player gets 46 hits

Let,

y be the strikes out.

Using proportion,

Strike out : hit :: strike out : hit

[tex]3:2::y:46[/tex]

Product of mean = Product of extreme

[tex]2*y=46*3\\2y=138[/tex]

Dividing both sides by 2;

[tex]\frac{2y}{2}=\frac{138}{2}\\y=69[/tex]

The player will strike out 69 times for 46 hits.

Keywords: Ratio, proportion

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Answer:The player will get 10 hits for 15 times strikes out.

The player will strike out 69 times for 46 hits.

Step-by-step explanation:

Given,

Ratio of strike out to hits = 3:2

Condition 1: If the player gets 15 strikes out;

Let,

x be the hits for 15 times strikes out.

Using proportion;

Strike out : hit :: strike out : hit

Product of mean = Product of extreme

Dividing both sides by 3;

The player will get 10 hits for 15 times strikes out.

Condition 2: if the player gets 46 hits

Let,

y be the strikes out.

Using proportion,

Strike out : hit :: strike out : hit

Product of mean = Product of extreme

Dividing both sides by 2;

The player will strike out 69 times for 46 hits.

Keywords: Ratio, proportion

Step-by-step explanation:

If all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.

Given that  

Surface area of a triangular prism = 288 square unit  

Need to evaluate new surface area if all four measurement of triangular prism is double.

Relation between surface area and the four dimensions of the triangular prism is given by following formula

Surface Area of triangular prism = bh + 2ls + lb

Where h is height of the prism , b is length of base of the prim , l is length of the prism and s is side length of the prism.

Given that Area of triangular prism = 288 square unit

=> bh + 2ls +lb  = 288

Doubling the four dimensions means replace b by 2b, l by 2l , s by 2s and h by 2h in formula of Surface area of triangular prism.

[tex]\text { We get Surface area of new triangular prism }=2 b \times 2 h+2 \times 2 l \times 2 s+2 l \times 2 b[/tex]

[tex]\begin{array}{l}{=4 \times b h+4 \times 2 l s+4 \times l b} \\\\ {=4(b h+2 l s+l b)}\end{array}[/tex]

=> Surface area of new triangular prism = 4 (bh + 2ls +lb)  

=> Surface area of new triangular prism = 4 x 288 = 1152 square unit.

Hence we can conclude that if all four dimensions of triangular prism having surface area as 288 is doubled than new surface area will be four times than the initial prism that is 1152 square unit.  

Answer: C, the surface area increases by 4 times

Step-by-step explanation:

Answer:

Step-by-step explanation:

The area of a circle is expressed as

Area = πr^2

Where r = radius of the circle

π = constant = 3.14

The radius of a circle is increased from 8.00800 to 8.03803 m. This means that the original radius of the circle is 8.00800 and the new radius of the circle is 8.03803

Area of original circle =

3.14 × 8.00800^2 = 201.36212096

Area of new circle =

3.14 × 8.03803^2 = 202.87516852203

Increase in area = 202.87516852203 - 201.36212096

= 1.51304756203

Expressing the change as a percentage, it becomes

1.51304756203/201.36212096 ×100

Percentage change = 0.75 %

Answer:

  B.  1.14, -0.77

Step-by-step explanation:

As you know the quadratic formula gives you the solution to

  ax² + bx + c = 0

as ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Here, we have a=8, b=-3, c=-7, so the formula tells us the solution is ...

  [tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(8)(-7)}}{2(8)}=\dfrac{3\pm\sqrt{233}}{16}\\\\x\approx \{-0.7665,1.1415\} \qquad\text{matches choice B}[/tex]

Answer:

1.14, –0.77

Step-by-step explanation:

I got it right in grandpoint.

Answer:

Option D: 2 . cos(90 + x) = -2a

Step-by-step explanation:

Given that:

sin x = a --------- eq1

As we know that trignometry says:

cos(90 + x) = -sinx-------- eq2

In option two we are given that:

cos(90 + x) = -2a ---------- eq3

So by equating both sides of eq2 and eq3:

-2a = -2sinx

By cancelling -2 from both sides we get:

sinx = a

That is given in eq1

hence proved

i hope it will help you!

Answer:

Step-by-step explanation:

First we will subtract $2 from $3.2 since that is late fee to get $1.2.

Now we divide $1.2 by $0.15 to get number of cents hence 8 days.

The answer is Maria is 8 days too late to hand over the book.

Hope this helps.

The linear equation is 3.20 = 2.00 + 0.15*x. Hence, Maria's book was 8 days late.

To find out how many days Maria's book was late, we need to set up a linear equation using the given information.

The total late fee equation is given by:

Late Fee = 2.00 + 0.15*x

Where $2.00 is the base fee, and 0.15 dollars is the additional late fee per day. Since Maria's total fee was $3.20, we can set up the equation as follows:

3.20 = 2.00 + 0.15*x

Now, solve for x, which represents the number of days the book was late:

Subtract $2.00 from both sides:

3.20 - 2.00 = 0.15*x

Simplify the equation:

1.20 = 0.15*x

Divide both sides by 0.15 to isolate x:

x = 1.20 / 0.15

Calculate the result:

x = 8

So, Maria's book was 8 days late.

Answer:

0 additional miles

Step-by-step explanation:

Miguel travelled from his hotel to the beach by taxi. Total distance travelled by Miguel during the journey is 23 miles.

During the return journey, he travelled by a bus for 11 miles to an intermediate location.

From this point his friend picked him up and drove him towards the hotel for 12 miles.

So the total distance travelled by Miguel during the return journey = 11 + 12 = 23 miles

But this is the same distance as the onward journey. So at the end, Miguel is back at the hotel and there are 0 additional miles that he needs to cover.

Answer: 0 miles

Step-by-step explanation:

Miguel took a taxi to the beach 23 miles from his hotel. After his day at the beach, he took a bus back for 11 miles. This means at this point, his distance from his hotel is 23 - 11 = 12 miles. Then a friend pick him up and drove another 12 miles towards the hotel. This means that they covered the remaining 12 miles from the hotel. Therefore

Miguel needs to go 12 - 12 = 0 miles until he is back at his hotel.

Answer:

C(p)  = 4,96 (in thousands of dollars)

l = 2980 $  invest in labor

k = 2980 $ invest in equipment

Step-by-step explanation:

Information we have:

Monthly output   P = 450*l*k       ⇒  k = P/450*l

But the production need to be 4000

Then k = 4000/450*l

Cost of production = l * k     (in thousands of dollars)

C(l)  =  l  + 4000/450*l

Taking derivatives (both members of the equation)

C´(l) = 1 - 400 /45*l²          ⇒ C´(l) = 0          ⇒ 1 - 400/45l²  = 0

45*l² -  400  = 0              ⇒  l²  = 400/45

l = 2.98 (in thousands of dollars)

l = 2980 $ And

k = 400/45*l           ⇒  k 400/45*2.98

k = 2.98  (in thousands of dollars)

C(p) = l + k

C(p)  =  2980 + 2980  

C(p)  = 5960 $

Answer:

The number of bracelets with she start are 48.

Step-by-step explanation:

Given:

Julia was recently given 9 bracelets. She plans to give 1/3 of her bracelets. She will be left with 23.

Now, we need to find with how many did she start.

Let the bracelets with she start be [tex]x[/tex].

She plans to give [tex]\frac{1}{3}ofx[/tex] = [tex]\frac{x}{3}[/tex].

According to question:

[tex]x-9-\frac{x}{3}=23[/tex]

On solving the equation:

[tex]\frac{3x-27-x}{3} =23[/tex]

Multiplying both sides by 3 we get:

[tex]3x-27-x=69[/tex]

[tex]2x-27=69[/tex]

Adding both sides by 27 and then dividing by 2 we get:

[tex]x=48[/tex]

Therefore, the number of bracelets with she start are 48.

Answer:

  4x^2 -2x -1

Step-by-step explanation:

Synthetic division works well for dividing by a linear binomial. See the attached for the working and the interpretation of the result.

Answer:

[tex]24[/tex] [tex]\text{cm}[/tex]

Step-by-step explanation:

Given: The distance from the centroid of a triangle to its vertices are [tex]16\text{cm}[/tex], [tex]17\text{cm}[/tex], and [tex]18\text{cm}[/tex].

To Find: Length of shortest median.

Solution:

Consider the figure attached

A centroid is an intersection point of medians of a triangle.

Also,

A centroid divides a median in a ratio of 2:1.

Let G be the centroid, and vertices are A,B and C.

length of [tex]\text{AG}[/tex] [tex]=16\text{cm}[/tex]

length of [tex]\text{BG}[/tex] [tex]=17\text{cm}[/tex]

length of [tex]\text{CG}[/tex] [tex]=18\text{cm}[/tex]

as centrod divides median in ratio of [tex]2:1[/tex]

length of [tex]\text{AD}[/tex] [tex]=\frac{3}{2}\text{AG}[/tex]

                                              [tex]=\frac{3}{2}\times16[/tex]

                                              [tex]=24\text{cm}[/tex]

length of [tex]\text{BE}[/tex] [tex]=\frac{3}{2}\text{BG}[/tex]

                                              [tex]=\frac{3}{2}\times17[/tex]

                                              [tex]=\frac{51}{2}\text{cm}[/tex]

length of [tex]\text{CF}[/tex] [tex]=\frac{3}{2}\text{CG}[/tex]

                                              [tex]=\frac{3}{2}\times18[/tex]

                                              [tex]=27\text{cm}[/tex]

Hence the shortest median is [tex]\text{AD}[/tex] of length [tex]24\text{cm}[/tex]

Answer:

a) Alternative hypothesis should be one sided. Because Null and Alternative hypotheses are:

[tex]H_{0}[/tex]: μ=2.66 dyne-cm.

[tex]H_{a}[/tex]: μ<2.66 dyne-cm.

b) the hypothesis that mean adhesion is at least 2.66 dyne-cm is true

Step-by-step explanation:

Let μ be the mean adhesion in dyne-cm.

a)

Null and alternative hypotheses are:

[tex]H_{0}[/tex]: μ=2.66 dyne-cm.

[tex]H_{a}[/tex]: μ<2.66 dyne-cm.

b)

First we need to calculate test statistic and then the p-value of it.

test statistic of sample mean can be calculated as follows:

t=[tex]\frac{X-M}{\frac{s}{\sqrt{N} } }[/tex] where

Sample mean is the average of 2.69, 5.76, 2.67, 1.62 and 4.12 dyne-cm, that is [tex]\frac{2.69+5.76+2.67+1.62+4.12}{5}[/tex] ≈ 3.37

using the numbers we get

t=[tex]\frac{3.37-2.66}{\frac{0.7}{\sqrt{5} } }[/tex] ≈ 2.27

The p-value is ≈ 0.043. Taking significance level as 0.05, we can conlude that sample proportion is significantly higher than 2.66 dyne-cm.

Thus, according to the sample the hypothesis that mean adhesion is at least 2.66  dyne-cm is true

Answer:

yes

Step-by-step explanation:

For example, 8 and 2.

8 - 2 = 6.

6 is the difference

Answer:

Null Hypothesis: [tex]\sigma=0.2[/tex]

Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)

Step-by-step explanation:

s represent the sample standard deviation

[tex]\sigma[/tex] represent the population standard deviation (variable of interest)

[tex]\sigma_o =0.2[/tex] represent the value that we want to test

n represent the sample size

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Based on this the system of hypothesis should be:

Null Hypothesis: [tex]\sigma=0.2[/tex]

Alternative hypothesis: [tex]\sigma \neq 0.2[/tex] (Changes on the deviation)

In order to test these system of hypothesis we need to select a significance level [tex]\alpha[/tex], then we need to calculate an statistic given by this formula.

[tex]\chi^2 =\frac{(n-1)s^2}{\sigma^2_o}[/tex]

Then we need to calculate the degrees of freedom for the statistic on this case

[tex]df=n-1[/tex]

And after this we need to calculate the pvalue based on the significance, the alternative hypothesis and the statistic calculated.

If the [tex]p_v <\alpha[/tex] we reject the null hypothesis

If the [tex]p_v >\alpha[/tex] we FAIL reject the null hypothesis

Answer:

18 answers

Step-by-step explanation:

1) 30 of 60%

2)30*.6

3)18

check:

18/30=0.6

0.6=60%

Step-by-step explanation:

30=100%

? =60

=18 problems

Answer:

  y = (5/2)x

Step-by-step explanation:

The rise is 5 squares and the run is 2 squares between the two marked points. That means the slope is 5/2. The line starts at (0, 0), so the equation is ...

  y = (5/2)x

Answer:

I think that the answer is 24

Answer:

The number is 80. 25% of that number is = 20.

Step-by-step explanation:

Answer:

Amount each friend pays for the gift = $20

Step-by-step explanation:

Market price of a gift = $70

The store manager takes $10 off the market price.

Marked down amount = $10

New cost price = Marked price - Marked down amount [tex]=\$70-\$10=\$60[/tex]

The cost of the gift is divided among three friends.

This means that the cost of gift which is $60 is divided by three to get each one's contribution in the gift.

∴ Amount each friend pays for the gift [tex]=\frac{60}{3}=\$20[/tex]

Answer:

From the solution we come to know that every student in a party contain 10% chance of being chosen . And it is not SRS because student have been  grouped into over 21 and under 21

Step-by-step explanation:

This question asks about sampling methods in statistics to determine attitudes toward alcohol at a party.

This question is about sampling methods in statistics. The goal is to determine the attitudes toward alcohol of students at a party. To achieve this, the party attendees are divided into two groups: those over 21 and those under 21. Then, a random sample of 3 students over 21 and a random sample of 2 students under 21 are chosen to be interviewed. This method ensures that each student at the party has an equal chance of being interviewed and provides a representative sample of the party's attendees.

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Answer:  $10881.81 is invested at 6% and $1518.18 is invested at 5%.

Step-by-step explanation:

Since we have given that

Amount invested = $12400

Rate of interest for first part = 6%

Rate of interest for second part = 5%

Let the amount invested for 6% be 'x'.

Let the amount invested for 5% be 'y'

According to question, we get that

[tex]0.06x-0.05y=577\\\\x+y=12400\\\\\implies x=12400-y[/tex]

So, it becomes,

[tex]0.06(12400-y)-0.05y=577\\\\744-0.06y-0.05y=577\\\\-0.11y=577-744\\\\-0.11y=-167\\\\y=\dfrac{167}{0.11}\\\\y=1518.18[/tex]

x=12400-y=12400-1518.18=$10881.81

Hence, $10881.81 is invested at 6% and $1518.18 is invested at 5%.

Answer:

48

Step-by-step explanation:

the number of shirts are 3, number of pants 4, number of socks pairs 2 and 2 pairs of shoes.

first lets start with shirts and pants, number of unique combinations are,

(for each shirt there are 4 different pant combinations) = [tex](3)(4)[/tex]

=12

similiarly for each shirt pant pair there are 2 shoes and 2 socks pairs.

thus, total number of combinations are=

[tex](12)(2)(2)[/tex]

= 48

The statement that is NOT a requirement to conduct a goodness-of-fit test is (a) For each category, the observed frequency is at least 5

To conduct a goodness-of-fit test, only the expected frequency must be at least 5.

This means that it is false that the observed frequency is at least 5

Hence, the statement that is NOT a requirement to conduct a goodness-of-fit test is  (a)

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raising some base to the power of 1/2 is the same as square root

Answer:

Step-by-step explanation:

4 to the first power is 4

then divide by 2

Answer:

100 billion

Step-by-step explanation:

Some astronauts reveals that there are 100 billion galaxies in the universe.