Evaluate the following Integrals ∫sin

Answer:

the cheapest for the 3 shirts you can get is 43.83 (Baja Coast)

Step-by-step explanation:

For the three shirts at Pogo it costs $44.97. However, at the Baja Coast it costs $43.83. So the least amount you pay is $43.87.

Answer:

[tex]0.4\%[/tex]

Step-by-step explanation:

Given: 60% of the boys play baseball and 24% of the boys play baseball and football in Seaton Park School

To find: percentage of those that play baseball also play football

Solution:

Let B denotes boys who play baseball and F denotes boys who play football.

[tex]P(B)=60\%[/tex]

[tex]P(F\cap B)=24\%[/tex]

Percentage of those that play baseball also play football = [tex]P\left ( F|B \right )=\frac{P(F\cap B)}{P(B)}=\frac{24}{60}=\frac{2}{5}=0.4\%[/tex]

Answer:

Parallelogram (A)

Question:

Sides KM and FH in the triangles below will be placed together to form a quadrilateral.

Triangle M L K. Side M L has a length of 15 and side L K has a length of 35. Angle L is 110 degrees. Triangle F G H. Side F G has a length of 35 and side G H has a length of 15. Angle G is 110 degrees.

Which best describes the quadrilateral that will be formed?

parallelogram

rectangle

rhombus

trapezoid

Step-by-step explanation:

Given:

∆MLK:

Side ML = 15

Side LK = 35

Angle L = 110°

∆ FGH:

Side FG = 35

Side GH = 15

Angle G = 110°

Side MK and FH placed together to form a quadrilateral.

A quadrilateral is a polygon which has 4 sides.

See attachment for diagram

From the diagram and information given:

LK is parallel to FG

ML is parallel to GH

MK = FH

∠L = ∠G (opposite angles are congruent)

Since two pairs of opposite sides are parallel and opposite angles are congruent, it is a paralellogram.

A parallelogram is a quadrilateral which has pairs of opposite sides are parallel and equal.

Answer: Option  A

(A) parallelogram

Step-by-step explanation:

Answer:

a) Calculate the current price of the corporate bond? (4 marks)

b) Calculate the current price of the ordinary share if the average return of the shares in the same industry is 9%? (3 marks)

c) Calculate the current price of the preferred share if the average return of the shares in the same industry is 10% (3 marks)

Step-by-step explanation:

total debt = $3,500,000 par value 10$ coupon with a YTM of 12%

YTM = [coupon + (F - P)/n] / [(F + P)/2]

0.12 = [100 + (1,000 - P)/20] / [(1,000 + P)/2]

0.12(500 + 0.5P) = 100 + 50 - 0.05P

60 + 0.06P = 150 - 0.05P

0.11P = 90

P = 90/0.11 = $818.18

total debt = $818.18 x 3,500

stock price:

Div₀ = $8.50

Div₁ = $8.50 x 104% = $8.84

g = 4%

rrr = 9%

using the perpetuity growth model:

stock price = $8.84 / (9% - 4%) = $8.84 / 5% = $176.80

preferred stock:

Div = $12

rrr = 10%

using the perpetuity formula:

preferred stock = $12 / 10% = $120

Given that we have 47 kids and each kid needs 10 marbles, find out how many bags of 24 marbles will we need.

First, we will multiply 47 by 10 to get the amount of marbles needed.

47 x 10 = 470

So, that means we need 470 marbles in total.

Then, we divide 470 by 24 to see how many bags of 24 marbles 470 marbles is.

470 / 24 = 19.5833

Since, we can't have 19.5833 bags, we have to check what it would be if we only used 19.

19 x 24 = 456

470 - 456 = 14

Since, 18 is the closest number of bags but it has less than 470 it would not be correct.

Therefore, the best answer would be B. 25 since it is better to have extra marbles but not a very wide margin.

Answer:

$1946

Step-by-step explanation:

Eric’s average income for the first 4 months of the year is $1,450.25

Therefore, his total earning in the first four months

= 4 X $1,450.25

=$5,801

Let the average income for the remaining 8 months= x

Then:

[tex]\text{Eric's Yearly Average Income}=\dfrac{5801+8x}{12} \\1,780.75=\dfrac{5801+8x}{12} \\$Cross multiply\\12*1,780.75=5801+8x\\21369=5801+8x\\8x=21369-5801\\8x=15568\\Divide both sides by 8\\x=\$1946[/tex]

Therefore, to get an average income for the year of $1,780.75, Eric must earn an average income of $1946 for the remaining 8 months.

Answer:

Loading/unloading hourly rate: $70

Packing/unpacking hourly rate: $55

Step-by-step explanation:

We can write this as a system of linear equations.

We define L as the loading/unloading hourly rate, and P as the packing/unpacking hourly rate.

"One quote was for a weekday move which is  for 8 hours of loading/unloading and 6 hours of packing/unpacking for $890":

[tex]8L+6P=890[/tex]

"The other quote was for a  weekend move which is for 5 hours of loading/unloading and 3 hours of packing/unpacking for $515":

[tex]5L+3P=515[/tex]

If we express L in function of P in the first equation, and then replace this value in the second equation, we have:

[tex]8L+6P=890\\\\8L=890-6P\\\\L=\dfrac{890-6P}{8}[/tex]

[tex]5L+3P=515\\\\5\cdot \dfrac{890-6P}{8}+3P=515\\\\556.25-3.75P+3P=515\\\\-0.75P=515-556.25=-41.25\\\\P=41.25/0.75=55[/tex]

Then, L is:

[tex]L=\dfrac{890-6P}{8}=\dfrac{890-6(55)}{8}=\dfrac{890-330}{8}=\dfrac{560}{8}=70[/tex]

Answer:

There is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.

Step-by-step explanation:

Here we have our null hypothesis as H₀: σ² = s²

Our alternative hypothesis is then Hₐ: σ² ≠ s²

We therefore have a two tailed test

To test the hypothesis of difference in standard deviation which is the Chi squared test given as follows

[tex]\chi ^{2} = \dfrac{\left (n-1 \right )s^{2}}{\sigma ^{2}}[/tex]

Where:

n = Size of sample

s² = Variance of sample = 950²

σ² = Variance of population = 650²

Degrees of freedom = n - 1 = 71 - 1 = 70

α = Significance level = 0.1

Therefore, we use 1 - 0.1 = 0.9

From the Chi-square table, we have the critical value as

1 - α/2 = 51.739,  

α/2 = 90.531

Plugging the values in the above Chi squared test equation, we have;

[tex]\chi ^{2} = \dfrac{\left (23-1 \right )950^{2}}{650 ^{2}} = 49.994[/tex]

Therefore, since the test value within the critical region, we do not reject the null hypothesis, hence there is sufficient statistical evidence to prove that the standard deviation of the technology-related workers and the standard deviation of the non-technology workers are equal.

Answer:

  [tex]p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)[/tex]

Step-by-step explanation:

  [tex]p(x)=32x^5y-2xy^5=2xy(16x^4-y^4)=2xy(4x^2-y^2)(4x^2+y^2)\\\\\boxed{p(x)=2xy(2x-y)(2x+y)(4x^2+y^2)}[/tex]

__

The factoring of the difference of squares is applicable:

  a^2 -b^2 = (a -b)(a +b)

Answer:

10 units

Explanation:

Create a right triangle, determine the a and b side lengths of the triangle by looking at the graph. (See image)

Then use the Pythagorean theorem to find c.

a² + b² = c²

(8)² + (6)² = c²

64 + 36 = c²

100 = c²

Square root both sides to get c.

[tex]\sqrt{100}[/tex] = c

10 = c

Answer:

Step-by-step explanation:

Twenty-five percent of thirty dollars is $7.50

(30 x 25)/100 = $7.50

Thirty percent of twenty-five dollars is $7.50

(25 x 30)/100 = $7.50

Therefore he is right

I hope this helps

Answer:

£77.6 per day

Step-by-step explanation:

388/5 = 77.6

Answer:

£77.60

Step-by-step explanation:

388/5=77.6

but remember that this is money so add the 0.

Answer:

Area of the StarKist label around the can in terms of π = 12π cm²

Step-by-step explanation:

Given;

the volume of a can of StarKist tuna, V = 18 π cm³

height of the can of StarKist tuna, h =  2 cm

To determine the area of the StarKist label that wraps around the entire can and does not overlap, we assume the can to have a shape of a cylinder.

Volume of the can = πr²h

where;

r is radius of the can

h is height of the can

πr² x 2 = 18 π

2r² = 18

r² = 18/2

r² = 9

r = 3

Area around the can = curved surface area of the can (cylinder)

Curved surface area of the can = 2πr × h = 2πrh

Curved surface area of the can = 2πrh = 2π x 3 x 2 = 12π cm²

Area of the StarKist label around the can in terms of π = 12π cm²

Answer:

11*20!

Step-by-step explanation:

(20!+21!+22!)/44=

20!(1+21+21*22)/44=

20!(22+22*21)/44=

20!*22*22/44= 11*20!

The simplified expression of (20!+21!+22!)/44 is 20! * 11

The expression is given as:

(20!+21!+22!)/44

The factorial of a number n is:

n! = n * (n - 1)!

So, we start by expanding 22!

(20!+21!+22!)/44 = (20!+21!+22 * 21 * 20!)/44

Next, we expand 21!

(20!+21!+22!)/44 = (20!+21 * 20!+22 * 21 * 20!)/44

Factor out 20!

(20!+21!+22!)/44 = 20! * (1 + 21 + 22 * 21)/44

Evaluate the expression in the bracket

(20!+21!+22!)/44 = 20! * 484/44

Divide

(20!+21!+22!)/44 = 20! * 11

Hence, the simplified expression of (20!+21!+22!)/44 is 20! * 11

Read more about simplified expression at:

https://brainly.com/question/723406

#SPJ6

Answer:

I think +5 or 5

Answer:

there both 5

Step-by-step explanation: did the question on edg

Answer:

Step-by-step explanation:

[tex]T: x = \frac{56}{65}u - \frac{33}{65}v, \ \ y = \frac{33}{65}u + \frac{56}{65}v[/tex]

A)

[tex]\frac{d(x,y)}{d(u,v)} =\left|\begin{array}{ccc}x_u&x_v\\y_u&y_v\end{array}\right|[/tex]

[tex]=(\frac{56}{65} )^2+(\frac{33}{65} )^2\\\\=\frac{(56)^2+(33)^2}{(65)^2} \\\\=\frac{4225}{4225} \\\\=1[/tex]

B )

[tex]S:-65 \leq u \leq 65, -65 \leq v \leq 65[/tex]

[tex]T(65,65)=(x=\frac{56}{65} (65)-\frac{33}{65} (65),\ \ y =\frac{33}{65} (65)+\frac{56}{65} (65)\\\\=(23,89)[/tex]

[tex]T(-65,65)=(-56-33,\ \ -33+56)\\\\=(-89,23)[/tex]

[tex]T(-65,-65) = (-56+33,-33-56)\\\\=(-23,-89)[/tex]

[tex]T(65,-65)=(56+33, 33-56)\\\\=(89,-23)[/tex]

C)

[tex]\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}[/tex]

[tex]=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(x^2+y^2)(\frac{d(x,y)}{d(u,v)} du\ \ dv[/tex]

Now

[tex]x^2+y^2=(\frac{56}{65} u-\frac{33}{65} v)^2+(\frac{33}{65} u+\frac{56}{65} v)^2[/tex]

[tex][(\frac{56}{65} )^2+(\frac{33}{65}) ^2]u^2+[(\frac{33}{65} )^2+(\frac{56}{65}) ^2]v^2[/tex]

[tex]=\frac{(65)^2}{(65)^2} u^2+\frac{(65)^2}{(65)^2} v^2=u^2+v^2[/tex]

[tex]\int \!\! \int_{T(S)} \ x^2 + y^2 \ {dA}[/tex]

[tex]=\int\limits^{65}_{v=-65} \int\limits^{65}_{u=-65}(u^2+v^2) du\ \ dv[/tex]

[tex]=\int\limits^{65}_{-65}\int\limits^{65}_{-65}u^2du \ \ dv+\int\limits^{65}_{-65}\int\limits^{65}_{-65}v^2du \ \ dv[/tex]

By symmetry of the region

[tex]=4\int\limits^{65}_0 \int\limits^{65}_0u^2 du \ \ dv + u\int\limits^{65}_0 \int\limits^{65}_0v^2 du \ \ dv[/tex]

[tex]= 4(\frac{u^3}{3} )^{65}_{0}(v)_0^{65}+(\frac{v^3}{3} )^{65}_{0}(u)_0^{65}\\\\=4[\frac{(65)^4}{3} +\frac{(65)^4}{3} ][/tex]

[tex]=\frac{8}{3} (65)^4[/tex]

Answer:

  60°

Step-by-step explanation:

The value of y is half the measure of the arc the chord subtends:

  y = 120°/2

  y = 60°

Answer:

pounds

Step-by-step explanation:

pounds : ounces

   10      :      [tex]x[/tex]

    1        :     16

[tex]x=160[/tex]

The numerator would be pounds. [tex]\frac{10 pounds}{160 ounces}[/tex]

Answer:

12h < 60

Step-by-step explanation:

A rectangle, with height h and base length l, has the following area.

[tex]A = l*h[/tex]

In this question:

[tex]l = 12, A < 60[/tex]

So

[tex]A < 60[/tex]

[tex]l*h < 60[/tex]

[tex]12h < 60[/tex]

So the correct answer is:

12h < 60

Answer:

12h < 60

hope this helps, its right because i took the test and it shows

Answer:

0

Step-by-step explanation:

The 0, or the last digit is the insignificant digit because it serves no purpose.

Answer:

The last zero in the number is insignificant.

Step-by-step explanation:

The 0 at the extreme right indicates that the number is accurate to the fifth decimal place, that is, one in ten thousandths.

Answer:

Exterior and interior angles are supplementary, meaning they sum to 180 degrees. If the exterior and interior angles are x and 5x respectively, we can write x + 5x = 180, and solving for x we get x = 30°. This means that the answer to a) is 30° and the answer to b) is 30 * 5 = 150°.

For c), to find the number of sides we can do:

180 - 150 = 30

180 / 30 = 6 so the answer to c) is 6.

ABC and DEC are similar, since the line segments AB and DE are parallel.

This means corresponding sides of these triangles occur in a fixed ratio with one another.

In particular, this tells us

DE/AB = DC/AC

or

7/11 = 15/(15 + x)

Solve for x:

11/7 = (15 + x)/15

11/7 = 1 + x/15

4/7 = x/15

x = 60/7

Answer:

1) D. None of these.

2) False

3) C. No, Jane is too old to be considered a qualifying child and fails the support test of a qualifying relative.

Step-by-step explanation:

1) AGI deductions are subtracted from the gross income to calculate the taxable income. Not all the individual's earnings are subject to taxation, therefore some expenses are deducted to calculate the Adjusted Gross Income, the one that will be taxed.

All of the three options listed ( Standard deduction, Itemized deduction, and personal exemption) are AGI deductions.

2) False

The potential qualifying relative does not have to be family/biologically related with the taxpayer. The IRS condition states that he/she is either family related or have lived in the taxpayer's abode for a whole year to be a qualified relative of the taxpayer. So far any of the two conditions are met, it is fine.

C. For a student to be regarded as a qualifying relative of her parents, she must not be up to 24 years at the end of the year according to IRS. Jane is already 25, she is too old and fails the test as a qualifying relative.

Answer:

There are 200 4th grades and 360 third graders

Step-by-step explanation:

560/2=280-80=200 280+80=360

Answer:

Step-by-step explanation:

f(x) = -2(64) + 3 is not a function of x; it's a constant with the single value -125.

Ensure that you have copied down this problem correctly.

Answer: -2 multiply 64 add 3 equals -125

Step-by-step explanation:

-2 multiply 64 add 3

then multiply 2 and 64 which is 128

then add/subtract: -128 add 3 which is -125

Then final answer -2 multiply 64 add 3 equals -125

Answer:

13 goats and 23 cows

Step-by-step explanation:

Use x to solve :) it's a hint

Answer:

g=goats

c=cows

a=cars

g + c = 36

10 + g = a

Step-by-step explanation:

the number of cows and goats together are equal to 36, so for the first equation you can write g + c = 36.

For the second equation, the number of cars he has is equal to the number of goats he has plus 10, so you can express that as 10 + g = a. (I used a since I already used c for the cows)

I think this is what you need if you need 2 equations to represent how many cars he has.

I'm not entirely sure what its asking you can comment if you need more or something else.

Answer:

A. T > 2.539

Step-by-step explanation:

We have a hypothesis test of the mean, with unknown population standard deviation.

The hypothesis are:

[tex]H_0: \mu = 2.1 \\\\H_a: \mu > 2.1[/tex]

From the hypothesis we can see that the test is right-tailed, so the critical value of t should be a positive value.

The degrees of freedom can be calculated as:

[tex]df=n-1=20-1=19[/tex]

The significance level is 0.01, so the critical value tc should be the one that satisfies:

[tex]P(t>t_c)=0.01[/tex]

Looking up in a t-table, for 19 degrees of freedom, this critical value is tc=2.539.

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

A tangent to a circle forms a right angle with the radius

As it is a right angled triangle, we can use Pythagoras' theorem

a^2 + b^2 = c^2

Rearrange this for a side length:

a^2 = c^2 - b^2

Sub the values in:

a^2 = 6.5^2 - 6^2

a^2 = 6.25

Square root this for the answer

a = 2.5

Thus, your answer is option D

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Answer:

2.5 ft

Step-by-step explanation:

As radius is perpendicular to tangent ,

LT [tex]\perp[/tex]KT

By pythagoras theorem:

LT² = LK² - KT²

LT² = (6.5)² - 6²

LT² = 42.25 - 36

LT² = 6.25

LT = 2.5 ft

LT = radius = 2.5 ft

Here is  the correct computation of the question given.

Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place. Listed below are the systolic blood pressures (in mm Hg) for a sample of men aged 20-29 and for a sample of men aged 60-69.

Men aged 20-29:      117      122     129      118     131      123

Men aged 60-69:      130     153      141      125    164     139

Group of answer choices

a)

Men aged 20-29: 4.8%

Men aged 60-69: 10.6%

There is substantially more variation in blood pressures of the men aged 60-69.

b)

Men aged 20-29: 4.4%

Men aged 60-69: 8.3%

There is substantially more variation in blood pressures of the men aged 60-69.

c)

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

d)

Men aged 20-29: 7.6%

Men aged 60-69: 4.7%

There is more variation in blood pressures of the men aged 20-29.

Answer:

(c)

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.

Step-by-step explanation:

From the given question:

The coefficient of variation can be determined by the relation:

[tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]

We will need to determine the coefficient of variation both men age 20 - 29 and men age 60 -69

To start with;

The coefficient of men age 20 -29

Let's first find the mean and standard deviation before we can do that ;

SO .

Mean = [tex]\dfrac{\sum \limits^{n}_{i-1}x_i}{n}[/tex]

Mean = [tex]\frac{117+122+129+118+131+123}{6}[/tex]

Mean = [tex]\dfrac{740}{6}[/tex]

Mean = 123.33

Standard deviation  [tex]= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }[/tex]

Standard deviation =[tex]\sqrt{\dfrac{(117-123.33)^2+(122-123.33)^2+...+(123-123.33)^2}{(6-1)} }[/tex]

Standard deviation  = [tex]\sqrt{\dfrac{161.3334}{5}}[/tex]

Standard deviation = [tex]\sqrt{32.2667}[/tex]

Standard deviation = 5.68

The [tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]

[tex]coefficient \ of \ variation = \dfrac{5.68}{123.33}*100[/tex]

Coefficient of variation = 4.6% for men age 20 -29

For men age 60-69 now;

Mean = [tex]\dfrac{\sum \limits^{n}_{i-1}x_i}{n}[/tex]

Mean = [tex]\frac{ 130 + 153 + 141 + 125 + 164 + 139}{6}[/tex]

Mean = [tex]\dfrac{852}{6}[/tex]

Mean = 142

Standard deviation  [tex]= \sqrt{\dfrac{\sum (x_i- \bar x)^2}{(n-1)} }[/tex]

Standard deviation =[tex]\sqrt{\dfrac{(130-142)^2+(153-142)^2+...+(139-142)^2}{(6-1)} }[/tex]

Standard deviation  = [tex]\sqrt{\dfrac{1048}{5}}[/tex]

Standard deviation = [tex]\sqrt{209.6}[/tex]

Standard deviation = 14.48

The [tex]coefficient \ of \ variation = \dfrac{standard \ deviation}{mean}*100[/tex]

[tex]coefficient \ of \ variation = \dfrac{14.48}{142}*100[/tex]

Coefficient of variation = 10.2% for men age 60 - 69

Thus; Option C is correct.

Men aged 20-29: 4.6%

Men aged 60-69: 10.2 %

There is substantially more variation in blood pressures of the men aged 60-69.