The average life of individual is 70 years. With a standard deviation of 5.5 years. Assume that the lives of these individuals is normally distributed. a. Find the probability that a mean life of a random sample of 5 such turtles falls between 60 and 80 years. b. Find the mean data value that separates the top 10% from the rest of the means computed from a random sample of size 5.

Answer:

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Step-by-step explanation:

Given equation is:

[tex]15sin^2 x+11cosx-17=0[/tex]

To find:

Values of [tex]x[/tex] in the range [tex]0^\circ\leq x\leq180^\circ[/tex].

Solution:

First of all, let us recall one identity of square of sine and square of cosine.

Sum of square of sine of an angle and square of cosine of the same angle is equal to 1.

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

So

Putting [tex]sin^2x=1-cos^2x[/tex] in the given equation.

[tex]15(1-cos^2x)+11cosx-17=0\\\Rightarrow 15-15cos^2x+11cosx-17=0\\\Rightarrow -15cos^2x+11cosx-2=0\\\Rightarrow 15cos^2x-11cosx+2=0\\\Rightarrow 15cos^2x-5cosx-6cosx+2=0\\\Rightarrow 5cosx(3cosx-1)-2(3cosx-1)=0\\\Rightarrow (5cosx-2)(3cosx-1)=0\\\Rightarrow cosx=\dfrac{2}{5}, \dfrac{1}{3}[/tex]

So, in the range [tex]0^\circ\leq x\leq180^\circ[/tex]

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Answer:

a = -8

Step-by-step explanation:

-5/2 a + 5 = 25

Subtract 5 from each side

-5/2 a + 5-5 = 25-5

-5/2 a = 20

Multiply each side by -2/5

-2/5 *-5/2 a = 20*-2/5

a = -8

Answer:

Step-by-step explanation:

A line from the center of the circle to bisect  a chord is perpendicular to the chord.

Therefore, OA⊥ AS

Join O & R

OR is radius of the circle

ΔOAR is right angled triangle.

Use Pythagorean theorem to find OR

OR² = OA² + RA²

       = 3² + 4²

       = 9 +16

OR² = 25

OR = √25

OR = 5 cm

OP  is radius. Therefore, OP = OR = 5 cm

PA = OP + OA

     = 5 + 3

PA = 8 cm

Answer:

90°

Step-by-step explanation:

As given in the figure:

[tex]AC \perp CE\\

\therefore m\angle ACE = 90\degree \\ [/tex]

Answer:

162.5 Cedis

Step-by-step explanation:

Cost Price= 125

Profit % = 30%

Selling price=?

Selling price= Cost price+ profit

Profit = ?

[tex]profit \% = \frac{profit}{cost \: price} \times 100[/tex]

[tex]30 \% = \frac{x}{125} \times 100[/tex]

[tex]30 \% = \frac{100x}{125} \\ 30 \times 125 = 100x[/tex]

[tex]3750 = 100x \\ \frac{3750}{100} = \frac{100x}{100} \\ x = 37.5[/tex]

Profit = 37.5 gh Cedis

Selling price= 125+37.5

Selling price= 162.5 gh Cedis

The selling price of a bag is 162.5Cedis.

It is required to find the selling price.

The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product.

Given that :

Let the profit be x.

Cost Price= 125

Profit % = 30%

profit%=profit/cp*100

30=profit/125*100

3750=100x

x=37.5

profit=37.5

Selling price= Cost price+ profit

Selling price=125+37.5

Selling price=162.5ghcedis

So, the selling price of a bag is 162.5Cedis.

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Answer:

The correct option is;

C. Marginal frequency

Step-by-step explanation:

The objective of comparison of two distributions is to check the significant difference from each other

The general measures used to compare the difference between distributions are the measures of centers such as the mean, the measures of spread such as the standard deviation and the shape of the compared distribution curves

Marginal frequencies are the values found in the total row and total column portion of a two way frequency distribution table

The marginal frequency is used to calculate the marginal relative frequency

The values of the marginal frequency, which is a sum, does not characterize the details of a distribution to a large extent.

Answer:

C. Marginal frequency

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

V = Lwh

the volume (given) = 24 ft^3

the height (given) = 18" = 1.5'

24 = L*w*1.5

divide both sides by 1.5

16 = Lw

You need to find the number of feet in each side of the base

since the box has a square base

L = W

AND, found above, L*w = 16

so 4*4= 16

Answer - 4

Answer:

see below

Step-by-step explanation:

6 - (3x+10) + 4(2 - x) =15

Distribute

6 - 3x -10 +8 -4x = 15

Combine like terms

4 -7x = 15

Subtract 4 from each side

4 -7x-4 =15-4

-7x =11

Divide each side by -7

-7x/-7 = 11/-7

x = -11/7

Answer:

24

Step-by-step explanation:

What you have here is a permutation, seeing as each element can only be used once.

We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter

However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.

Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.

Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.

Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter

The way to calculate how many permutations we have without repetition is using factorials

N!

Where N is the number of elements you have.

In this case, it would be 4!

4! is 4 * 3 * 2 * 1

Which equals 24

If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on

Answer:

4 pints

Step-by-step explanation:

30 quarts ÷ 15 kids = 2 quarts per kid

there are 2 pints in a quart so..

2 quarts per kid x 2 pints per quarter = 4 pints

Answer: "B. [tex]12p^6q^5[/tex]

Step-by-step explanation:

The given monomial : [tex]6a^2b^8c[/tex]

Degree of this monomial = Sum of powers of variables=2+8+1= 11

Let's check all the options

A   [tex]18t^8[/tex]

Degree = 8

B [tex]12p^6q^5[/tex]

Degree = 6+5 =11

C [tex]9a^5b^3c^2[/tex]

Degree = 5+3+2=10

D [tex]6w^4x^2y^3z^3[/tex]

Degree =4+2+3+3=12

We can see that only option B has degree 11.

So, the monomial has the same degree as [tex]6a^2b^8c[/tex] is "B. [tex]12p^6q^5[/tex] "

1) 3 is the Coefficient.

2) 10 is the constant.

3) 10.8 is the ans.

Answer:

3 times the percent for the balance to be $221

Step-by-step explanation:

/////////////nvm///////////

Answer:

u^18

Step-by-step explanation:

(u^3)^6

=

u^(3*6)

=

u^18

Hope this helps!

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▹ Answer

30 miles

▹ Step-by-Step Explanation

Multiply mph by hours:

15 mph * 2 hrs = 30 miles

Hope this helps!

CloutAnswers ❁

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Answer:

The center of the circle is

Step-by-step explanation:

Equation of a circle is given by

where r is the radius

(h, k) is the center of the circle

The center of a circle is given by

( - h , - k)

From the question equation of the circle is

( x + 4)² + ( y - 2)² = 16

Comparing with the general equation above

( h , k) = ( 4 , - 2)

The center of the circle is

( - h , - k) = ( - 4 , -(-2))

We have the final answer as

Hope this helps you

Answer:

A) 0.875, 87.5%

B) 0.12, 12%

C) 1.6, 160%

Step-by-step explanation:

Answer:

A) 0.875, 87.5%

B) 0.001, 0.1%

C) 1.6, 160%

Step-by-step explanation:

I honestly just used a calculator, but it could also be solved using the butterfly technique. For percentages just move the decimal to the left two places.

Answer:

4

Step-by-step explanation:

i dont really know how to explain i used an algebra calculator

Answer:

x = 2

Step-by-step explanation:

6x-1=11

Add 1 to each side

6x-1+1=11+1

6x = 12

Divide by 6

6x/6 = 12/6

x = 2

Answer:

Step-by-step explanation:

[tex]6x-1=11 \\\\Collect \: like \:terms\\\\6x = 11+1\\\\Simplify\\\\6x =12\\\\Divide\:both\:sides\:by\:6\\\\\frac{6x}{6} = \frac{12}{6}\\ x = 2[/tex]

Answer:

f₁(x) = -3x + 2

f₂(x) = x - 4

f₃(x) = x + 8

f₄(x) = -2x - 6

f₅(x) = -3x

Step-by-step explanation:

1). Since function f₁ (blue line) passes through a point (0, 2) and (-2, 8)

Let the equation of the blue line is,

y = mx + b

Since slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{8-2}{-2-0}[/tex]

m = -3

Y-intercept 'b' = 2

Therefore, equation of the line will be,

y = -3x + 2

Linear function representing the line will be,

f₁(x) = -3x + 2

2). Let the equation of the red line passing through (0, -4) and (2, -2) is,

y = mx + b

Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m = [tex]\frac{-4+2}{0-2}[/tex]

m = 1

y-intercept 'b' = -4

Therefore, the linear function will be,

f₂(x) = x - 4

3). Let the equation of the green line passing through (-6, 2) and (-2, 6) is,

y = mx + b

Slope of the line 'm' = [tex]\frac{6-2}{-2+6}[/tex]

m = 1

y-intercept 'b' = 8

Therefore, linear function will be,

f₃(x) = x + 8

4). Let the equation of the yellow line passing through (-6, 6) and (-4, 2) is,

y = mx + b

Slope of the line = [tex]\frac{6-2}{-6+4}[/tex]

m = -2

y-intercept of the line 'b' = -6

Therefore, function representing the line will be,

f₄(x) = -2x - 6

5). Let the equation of the pink line is passing through (0, 0) and (-2, 6) is,

y = mx + b

Since the line is passing through origin, y-intercept 'b' = 0

Slope of the line = [tex]\frac{6-0}{-2-0}[/tex]

m = -3

Therefore, equation of the linear function will be,

f₅(x) = -3x

Answer:

Step-by-step explanation:

m<MON = 8x - 13°

m<LOM = 7x - 17°

To find : m <MON

First, we have to find the value of x :

Create an equation

[tex] \mathrm{8x - 13 + 7x - 17 = 180}[/tex] ( sum of angle in straight line )

Collect like terms

[tex] \mathrm{15x - 13 - 17 = 180}[/tex]

Calculate

[tex] \mathrm{15x - 30 = 180}[/tex]

Move constant to R.H.S and change its sign

[tex] \mathrm{15x = 180 + 30}[/tex]

Calculate the sum

[tex] \mathrm{15x = 210}[/tex]

Divide both sides of the equation by 15

[tex] \mathrm{ \frac{15x}{15} = \frac{210}{15} }[/tex]

Calculate

[tex] \mathrm{x = 14}[/tex]

Now, let's find the value of m<MON

[tex] \mathrm{8x - 13}[/tex]

Plug the value of x

[tex] \mathrm{ = 8 \times 14 - 13}[/tex]

Calculate the product

[tex] \mathrm{ = 112 - 13}[/tex]

Calculate the difference

[tex] \mathrm{ = 99}[/tex] °

Hope I helped!

Best regards!

Answer:

48

Step-by-step explanation:

because i say so

Answer:

12.198

Step-by-step explanation:

the thousandth is the third digit after the decimal point, so you round the next number after it, which is 5. so you round it up, ends with 12.198

We get 12.198 after rounding it to the nearest thousandth.

The rounding off decimal places is similar to the basic round-off. We check the previous number. If it is greater than or equal to 5, we increase the value up to which we are rounding by 1, or else keep it the same when the previous digit is less than 5.

The order of digits for decimal places is opposite to the normal number system.

In the number system we have units place, then tens place, then hundreds place, then thousands place, and like that.

In the decimal number system, we start from the highest and go on decreasing.

The first decimal place is the tenth place.

The second decimal place is the hundredth place.

The third decimal place is the thousandth place.

And so on.

In the question, we are asked to round 12.1975 to the nearest thousandth.

As discussed above, the nearest thousandth means rounding off up to the third decimal place.

So we round off 12.1975 up to the third decimal place, that is, we round off up to 7.

The next digit is 5, so we increase 7 by 1 to 8.

Thus, we get 12.198 after rounding it to the nearest thousandth.

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Answer:

Jake ran 10 1/6 miles in total

Step-by-step explanation:

4 1/4 + 2 2/3 - (4 1/4-1).

                  v

6 11/12 + 3 1/4

          v

6 11/12 + 3 3/12 = 10 1/6

Jake ran 10 1/6 miles in total (Mon, Tues, Wed).

Answer:

61/6 or 10.1666666667

Step-by-step explanation:

Monday = 4  1/4

Tuesday = 2  2/3

Wednesday = Monday - 1

=> Monday = 17/4 miles

=> Tuesday = 8/3 miles

=> Wednesday = 17/4 - 4/4 = 13/4 miles.

=> (17/4 + 13/4) + 8/3

=> 30/4 + 8/3

=> Take the LCM of the denominators.

=> LCM = 12

=> 90/12 + 32/12

=> 122/12

SImplify 122/12

=> 61/6 or 10.1666666667

Answer:

a.) For the Junior Varsity Team, mean would be the appropriate measure of center since the data is symmetric or well-proportioned while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.

b.) For the Varsity Team, the median would be the appropriate measure of the center since the data is skewed left and not evenly distributed so median could be used since it does not account for outliers while we use IQR or interquartile range in measuring the spread of data since IQR does not account for the data that is skewed.

For the Junior Varsity Team, the mean would be the appropriate measure of the center since the data is symmetric or well-proportioned .

Median represents the middle value of the given data when arranged in a particular order.

Since the data for the Junior Varsity Team is symmetric or well-proportioned, the mean would be the best way to determine the center, and standard deviation, which also measures the center and how far the values deviate from the mean, should be used to determine the spread.

The median could be utilized for the Varsity Team since the data is not evenly distributed and skewed to the left, and it does not take into account outliers.

We can use the interquartile range (IQR) to quantify the spread of the data because IQR does not take into account the skewed data.

Therefore, the varsity squad competes in intercollegiate or international competitions on behalf of the high school or institution while we should use standard deviation for getting the measure of spread since it also measures the center and how far the values are from the mean.

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Answer:

[tex]\Large \boxed{\mathrm{Option \ 2}}[/tex]

Step-by-step explanation:

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

The square root property requires a quantity squared by itself on one side of the equation. The only quantity squared is x, so divide both sides by 2 before applying the square root property.

The x variable should be isolated on one side of the equation. The x variable is squared so before performing the square root property where we take the square root of both sides, we divide both sides by 2, then take the square root of both sides.

Dividing both sides by 2.

[tex]\displaystyle \frac{2x^2 }{2} =\frac{16}{2}[/tex]

[tex]x^2 =8[/tex]

Taking the square root of both sides.

[tex]\sqrt{x^2 } =\pm \sqrt{8}[/tex]

[tex]x=\pm 2\sqrt{2}[/tex]

Answer:

Option 2

Step-by-step explanation:

2x² = 16

Since x is completely squared and and 2 isn't , so we need to divide both sides by 2. As to find x , we need to "isolate" x first so that is why we need to get rid of 2 with the x². We'll divide both sides by 2 in order to get rid of 2.

Dividing both sides by 2

=> x² = 8

Now , that is the x is isolated so we'll take square root on both sides

=> x = ±2√2

Answer:

4 I guess

Step-by-step explanation:

Because

3-1=2

2^2=2*2=4

Answer:

12 meters x 12 meters

Step-by-step explanation:

√144 = 12

Answer:

0.35, 0.359, 1

Step-by-step explanation:

0.359 = 359 thousandths

0.35 = 0.350 = 350 thousandths

1 = 1.000 = 1000 thousandths

Since 350 < 359 < 1000, then from least to greatest you get

0.35, 0.359, 1

Answer:

the mixed form is 28 [tex]19/100[/tex]

the improper form is ( 28 x 100) = 19 / 100

2819 / 00