If there are 736 students in a school, prove that at least three students have a birthday on the same day of the year.

Answer:

[tex] x^2 +(y-3)^2 = 25[/tex]

And we want to find the coordinate axes so then we can do the following:

If x=0 we have:

[tex] 0^2 +(y-3)^2 = 25[/tex]

[tex] (y-3)^2= 25[/tex]

[tex] y-3= \pm 5[/tex]

[tex] y_1 = 5+3=8[/tex]

[tex] y_2 = -5+3=-2[/tex]

Now of y =0 we have:

[tex] x^2 +9 = 25[/tex]

[tex] x^2 = 16[/tex]

[tex] x= \pm 4[/tex]

And then the coordinate axes are:

(4,0) (-4,0), (0,8), (0,-2)

Step-by-step explanation:

For this cae we have the following functon given:

[tex] x^2 +(y-3)^2 = 25[/tex]

And we want to find the coordinate axes so then we can do the following:

If x=0 we have:

[tex] 0^2 +(y-3)^2 = 25[/tex]

[tex] (y-3)^2= 25[/tex]

[tex] y-3= \pm 5[/tex]

[tex] y_1 = 5+3=8[/tex]

[tex] y_2 = -5+3=-2[/tex]

Now of y =0 we have:

[tex] x^2 +9 = 25[/tex]

[tex] x^2 = 16[/tex]

[tex] x= \pm 4[/tex]

And then the coordinate axes are:

(4,0) (-4,0), (0,8), (0,-2)

−π2≤sin−1x≤π2  

3π2≤5≤2π

−π2≤5−2π≤0≤π2

sin(5–2π)=sin5

Thus, sin−1(sin5)=5−2π

Answer:

The improper fraction 8/5 can be changed to the mixed number 1 3/5 by dividing the numerator (8) by the denominator (5). This gives a quotient of 1 and a remainder of 3.

Step-by-step explanation:

Answer:

x=10.

Step-by-step explanation:

Answer:

(a) $180

(b) 25%

Step-by-step explanation:

(a) $126 = 30% of x; x is the total

so from this, you get an equation: 126 = 0.3x

solve the equation: x = 180; so the amount before

discount is $180

(b) You know the price of discount for the rice cooker is

180-126 which is $54

Then you subtract 54 from 64 to get the discount amount for the toaster

10/40 is 1/4 or 25%

Answer:

a

The sample size is  [tex]n = 219.2[/tex]

b

The  sample size is  [tex]n = 537.5[/tex]

Step-by-step explanation:

From the question we are told  that

    The standard deviation is  [tex]\sigma = 45 \minutes[/tex]

    The  Margin of  Error is  [tex]E = \pm 5 \ minutes[/tex]

Generally the margin of  error is mathematically represented as

         [tex]E = z * \frac{\sigma }{\sqrt{n} }[/tex]

Where  n is the sample  size

    So

             [tex]n = [\frac{z * \sigma }{E} ]^2[/tex]

Now  at  90%  confidence level the z value for the z-table is  

        z =  1.645

So

       [tex]n = [\frac{1.645 * 45 }{5} ]^2[/tex]

       [tex]n = 219.2[/tex]

The z-value at 99%  confidence level is  

        [tex]z = 2.576[/tex]

This is obtained from the z-table  

   So the sample size is  

         [tex]n = [\frac{2.576 * 45 }{5} ]^2[/tex]

        [tex]n = 537.5[/tex]

For the 90% confidence interval, the sample size is 219.2 and for the 99% confidence interval, the sample size is 537.5 and this can be determined by using the formula of margin of error.

Given :

The formula of the margin of error can be used in order to determine the sample size is needed if the executive wants to be 90% confident of being correct to within 5 minutes.

[tex]\rm ME = z\times \dfrac{\sigma}{\sqrt{n} }[/tex]

For the 90% confidence interval, the value of z is 1.645.

Now, substitute the values of all the known terms in the above formula.

[tex]\rm n=\left(\dfrac{z\times \sigma}{ME}\right)^2[/tex]   --- (1)

[tex]\rm n=\left(\dfrac{1.645\times 45}{5}\right)^2[/tex]

n = 219.2

Now, for 99% confidence interval, the value of z is 2.576.

Again, substitute the values of all the known terms in the expression (1).

[tex]\rm n=\left(\dfrac{2.576\times 45}{5}\right)^2[/tex]

n = 537.5

For more information, refer to the link given below:

https://brainly.com/question/6979326

From the odd-degree terms, take out one copy and rewrite the series as

[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x+5x^3+\cdots[/tex]

[tex]1+6x+x^2+6x^3+\cdots=(1+x+x^2+x^3+\cdots)+5x(1+x^2+\cdots)[/tex]

Then if |x| < 1, we can condense this to

[tex]\displaystyle\sum_{n=0}^\infty x^n+5x\sum_{n=0}^\infty x^{2n}=\frac1{1-x}+\frac{5x}{1-x^2}=\frac{1+6x}{1-x^2}[/tex]

Since the series we invoked here converge on -1 < x < 1, so does this one.

The explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

The function definition is given as:

[tex]f(x) = 1 + 6x + x^2 + 6x^3 + x^4 + ...[/tex]

Expand the terms of the expression

[tex]f(x) = 1 + 5x + x + x^2 + 5x^3 + x^3 + x^4 + ...[/tex]

Split

[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x + 5x^3 + .. ...[/tex]

Factor out 5x

[tex]f(x) = (1 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Express 1 as x^0

[tex]f(x) = (x^0 + x + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Express x as x^1

[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(1 + x^2) + .. ...[/tex]

Also, we have:

[tex]f(x) = (x^0 + x^1 + x^2 +x^3 + .....) + 5x(x^0 + x^2) + .. ...[/tex]

Rewrite the series using the summation symbol

[tex]f(x) = \sum\limits^{\infty}_{n=0}x^n+ 5x\sum\limits^{\infty}_{n=0}x^{2n}[/tex]

The sum to infinity of a geometric progression is:

[tex]S_{\infty} = \frac{a}{1- r}[/tex]

Where:

a represents the first term, and r represents the common ratio

Using the above formula, we have:

[tex]\sum\limits^{\infty}_{n=0}x^n = \frac{1}{1 - x}[/tex]

[tex]5x\sum\limits^{\infty}_{n=0}x^{2n} = 5x * \frac{1}{1 - x^2} = \frac{5x}{1-x^2}[/tex]

So, we have:

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

Take the LCM

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

Evaluate the like terms

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

Hence, the explicit formula of the function f(x) is [tex]f(x) = \frac{1 + x + 5x}{1-x^2}[/tex]

Read more about geometric series at:

https://brainly.com/question/12563588

Answer:

A  B  C

Step-by-step explanation:

Answer:

abc or 123

Step-by-step explanation:

Answer:

14.24%

Step-by-step explanation:

We have found that the yield to call (YTC) formula is:

YTC = [C + (F-P) / N] / [(F + P) / 2]

Where:

C = Periodic coupon amount = 95

P = Current Price = 980

F = Redemption amount = 1150

N = time left to redemption = 3

We replace:

YTC = [95 + (1150-980) / 3] / [(1150 + 980) / 2]

YTC = 0.1424

In other words, the yield to call (YTC) is equal to 14.24%

Answer:

D.$80

Step-by-step explanation:

$5.26 x 15.5= $81.53

The closest amount to $81.53 is D.$80

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

Explanation:

Whenever the angle theta is between 0 and 90, the reference angle is exactly that value.

It's only when you get to other quadrants is when things get a bit tricky. Right now we're in quadrant 1, often written as Q1.

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

Extra info:

Answer:

60 degrees

Step-by-step explanation:

In Quadrant 1, the reference angle is the same as theta.

So,

Reference Angle = 60 degrees

Answer:

0.76 or 19/25

Step-by-step explanation:

Convert 4/10 so that it has a common denominator with 36/100.

4/10 x 10/10 = 40/100

Now that the denominator is the same, just add the top values.

40/100 + 36/100 = 76/100

We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.

Answer:

Step-by-step explanation:

[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]

[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]

[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]

Answer:

1. 24

2. 6

3. No

Step-by-step explanation:

The formula for cyclic alkene is [tex]C^{n} H^{2n}[/tex], so if it has 12 carbon atoms, it will have double the amount of hydrogen atoms, therefore, 24 hydrogen atoms.

The same works in reverse. If we have 12 hydrogen atoms in this, then there will be half the amount of carbon atoms, therefore 6.

Since the relationship between Carbon and Hydrogen here is double and half, odd numbers can't be divided by 2 and end up with a whole number, so an odd number of hydrogen atoms is not possible.

Hope this helped!

Answer:

Mean: 46

Median: 43

Mode: 43

Step-by-step explanation:

I hope this helped. I am sorry if you get this wrong.

Answer:

Step-by-step explanation:

4 = y - 4

Group the constants at the left side of the equation

That's

4 + 4 = y

Add the constants

Hope this helps you

Answer:

y=8

Step-by-step explanation:

To solve this equation, we need to find out what y is.

4= y-4

Therefore, we must get y by itself on one side of the equation.

4 is being subtracted from y. The inverse of subtraction is addition. Add 4 to both sides of the equation.

4+4=y-4+4

4+4=y

8=y

y=8

Let's check our solution. Plug 8 back in for y.

4= y-4

4= 8-4

4=4

The equation above is true, so we know our answer is correct.

Answer:

C. Supplementary

Step-by-step explanation:

Angle a and angle b are on the line CZA.

We can assume that line CZA is a straight line, which is equal to 180 degrees.

Since angle a and b are on the straight line together, they must add to 180 degrees. Therefore, they are supplementary angles.

So, choice C. Supplementary angles is correct.

Answer:

The large of a sample size is required is 6,592

Step-by-step explanation:

In order to calculate large of a sample size is required we would have to calculate the following formula:

large of a sample size is required=(Z∝I2/E)∧2* P(1-P)

According to the given data we have the following:

E= margin of error= 1%=0.01

95% confident that your esimate is within 1% of the true population proportion, therefore, level of significance=∝=1-0.95=0.05

Z value for the 95% confident is 1.960, therefore, Z∝I2=1.960

Therefore, large of a sample size is required=(1.960/0.01)∧2* (0.22)(1-0.22)

large of a sample size is required=6,592

The large of a sample size is required is 6,592

Answer:

3

Step-by-step explanation:

let's call X the length of the bedroom, Y the wide of the bedroom, A the length of the living room and B the wide of the living room

A living room is two times as long as the bedroom, so:

A = 2X

A living room is one and one-half times as wide as a bedroom, so:

B = 1.5Y

The amount of carpet needed for the living room is A*B and the amount of carpet needed by the bedroom is X*Y

So, AB in terms of XY is:

A*B = (2X)*(1.5Y) = 3(X*Y)

It means that the amount of c arpet needed for the living room is 3 times greater than the amount of carpet needed for the  bedroom.

Answer:

1/10

Step-by-step explanation:

1/2= 5/10 - make it an equivalent fraction with the same denominator as the other fraction.

3/5= 6/10

5/10-6/10- subtract

=1/10

Answer:

x = 8.9 units

Step-by-step explanation:

We will use the theorem of intersecting tangent and secant segments.

"If secant and tangent are drawn to a circle from an external point, the product of lengths of the secant and its external segment will equal the square of the length of tangent."

8(8 + 2) = x²

x² = 80

x = √80

x = 8.944

x ≈ 8.9 units

Therefore, length of the tangent = 8.9 units

Answer:

Step-by-step explanation:

y=4x

Answer:

it is a two tailed test

The p - value for z=1.92  is 0.9726

Using a significance level of α=0.10, We fail to reject H0. The calculated z value lies out side the Zα value.

Step-by-step explanation:

For p≠0.767

Taking  null hypothesis as p≠0.767 and alternate hypothesis as p =0.767

H0 :p≠0.767  Ha :p≠0.767  it is a two tailed test

The p - value for z=1.92  is 0.9726 from the table.

Using a significance level of α=0.10

z value for 0.10 for two tailed test is ± 1.645

Z >zα

1.92> ± 1.645

Using a significance level of α=0.10, We fail to reject H0. The calculated z value lies out side the Zα value.

Answer:

The vertices are (7,6), (-7,6), (-7,-7) and (7,-7).

Step-by-step explanation:

The vertices are the coordinates of each corner of the square.

In this drawing, we have one vertex in each quadrant.

The vertex in the first quadrant has a x-coordinate of 7 and a y-coordinate of 6, so let's call this vertex A = (7,6).

The vertex in the second quadrant has a x-coordinate of -7 and a y-coordinate of 6, so let's call this vertex B = (-7,6).

The vertex in the third quadrant has a x-coordinate of -7 and a y-coordinate of -7, so let's call this vertex C = (-7,-7).

The vertex in the fourth quadrant has a x-coordinate of 7 and a y-coordinate of -7, so let's call this vertex D = (7,-7).

So the vertices are (7,6), (-7,6), (-7,-7) and (7,-7).

Answer:

See the attachment for sketch

Thr region is unbounded

DNE

Step-by-step explanation:

y≤ -2x + 10

The inequality is a straight line and region marked by the inequality. It has no boundaries. The boundaries extend to infinity. So the region is unbounded. Unbounded region has no corner points.

Step-by-step explanation:

f(x)=2x²+3x+9

g(x) = - 3x + 10

In order to find (f⋅g)(1) first find (f⋅g)(x)

To find (f⋅g)(x) substitute g(x) into f(x) , that's for every x in f (x) replace it by g (x)

We have

(f⋅g)(x) = 2( - 3x + 10)² + 3(- 3x + 10) + 9

Expand

(f⋅g)(x) = 2( 9x² - 60x + 100) - 9x + 30 + 9

= 18x² - 120x + 200 - 9x + 30 + 9

Group like terms

(f⋅g)(x) = 18x² - 120x - 9x + 200 + 30 + 9

(f⋅g)(x) = 18x² - 129x + 239

To find (f⋅g)(1) substitute 1 into (f⋅g)(x)

That's

(f⋅g)(1) = 18(1)² - 129(1) + 239

= 18 - 129 + 239

We have the final answer as

Hope this helps you

Answer:

3.375

Step-by-step explanation:

Answer:

3.375

Step-by-step explanation:

Had it on Khan

Answer:

$28,500

Step-by-step explanation:

$6,000 + 5% of $450,000 =

= $6,000 + 0.05 * $450,000

= $6,000 + $22,500

= $28,500

Answer:

a = 8

b = -8

Step-by-step explanation:

You have the following function:

[tex]f(x)\\\\=at+b;\ \ t<2\\\\2t^2-1;\ \ 2\leq t[/tex]

A function is differentiable at a point c, if the derivative of the function in such a point exists. That is, f'(c) exists.

In this case, you need that the function is differentiable for t=2, then, you have:

[tex]f'(t)=a;\ \ \ \ t<2 \\\\f'(t)=4t;\ \ \ 2\leq t[/tex]

If the derivative exists for t=2, it is necessary that the previous derivatives are equal:

[tex]f'(2)=a=4(2)\\\\a=8[/tex]

Furthermore it is necessary that for t=2, both parts of the function are equal:

[tex]8(2)+b=2(2)^2-1\\\\16+b=8-1\\\\b=-8[/tex]

Then, a  = 8, b = -8

Answer:

14.16 miles further.

Step-by-step explanation:

Campbell to Summerfield

9.52mi + 4.62 mi + 10.08 mi = 24.24 mi

Princeton to summerfield

is 10.08 mi

Therefore difference is 24.24mi - 10.08mi = 14.16 mi

Hope this helps.

Answer:

One hour ten minutes

Step-by-step explanation:

departing trains can empty it in 40 minutes.

entering travelers can fill a station in 30 minutes.

Time it will take travellers to fill the train

= Time for departing train + time for filling a station

= 40 minutes+ 30 minutes

= 70 minutes

= One hour ten minutes