lee and maya are collecting leaves for an art project. lee collects 24-100 of the total leaves needed. maya collects 4-10 of the total leaves needed. What fraction of the total number leaves did they collect altogether

Answer:

In first quadrant, [tex]\tan B=\frac{8}{15}[/tex]

In second quadrant, [tex]\tan B=\frac{-8}{15}[/tex]

Step-by-step explanation:

Given: [tex]\sin B=\frac{8}{17}[/tex]

To find: [tex]\tan B[/tex]

Solution:

Trigonometry explains the relationship between the sides and the angles of the triangle.

Here,

[tex]\sin B=\frac{8}{17}[/tex]

So, B can be in first or second quadrant as sine is positive both first and second quadrants.

Cosine and tangent are positive in first quadrant but negative in second quadrant.

In first quadrant:

[tex]\cos B=\sqrt{1-\sin ^2B}=\sqrt{1-\left ( \frac{8}{17} \right )^2}=\sqrt{1-\frac{64}{289}}=\sqrt{\frac{225}{289}}=\frac{15}{17}[/tex]

So, [tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{15}{17}}=\frac{8}{15}[/tex]

In second quadrant:

[tex]\cos B=-\sqrt{1-\sin ^2B}=-\sqrt{1-\left ( \frac{8}{17} \right )^2}=-\sqrt{1-\frac{64}{289}}=-\sqrt{\frac{225}{289}}=\frac{-15}{17}[/tex]

[tex]\tan B=\frac{\sin B}{\cos B}=\frac{\frac{8}{17}}{\frac{-15}{17}}=\frac{-8}{15}[/tex]

Answer:

[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]

On this case n =6 and x =6 we got:

[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]

Step-by-step explanation:

The utility for the combination formula is in order to find the number of ways to order a set of elements

For this case we want to find the following expression:

[tex] 6C6[/tex]

And the general formula for combination is given by:

[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]

On this case n =6 and x =6 we got:

[tex] 6C6 = \frac{6!}{6! (6-6)!} = \frac{6!}{6! 0!}= \frac{6!}{6!}=1[/tex]

Find the total minutes:

15 + 30 + 25 + 35 = 105 minutes

This is equal to 1 hour and 45 minutes

Subtract 1 hour and 45 minutes from 9:30

She woke up at 7:45 am

Answer:

[tex]\frac{-1}{(\sqrt{8}+\sqrt{9} )}[/tex]

Answer:

the water here is wet.

Step-by-step explanation:

Answer:

llolololol

Step-by-step explanation:

Answer:80 grams

Step-by-step explanation:

Answer:

The mean and standard deviation of the combined distribution is 16 and 7.192 respectively.

Step-by-step explanation:

We have given that a distribution consists of three components with frequencies 200, 250, and 300 having means 25, 10, and 15 and standard deviations 3, 4, and 5 respectively.

And we have to find the mean and standard deviation of the combined distribution.

Firstly let us represent some symbols;

[tex]n_1[/tex] = 200           [tex]\bar X_1[/tex] = 25                 [tex]\sigma_1[/tex] = 3

[tex]n_2[/tex] = 250            [tex]\bar X_2[/tex] = 10                  [tex]\sigma_2[/tex] = 4

[tex]n_3[/tex] = 300            [tex]\bar X_3[/tex] = 15                  [tex]\sigma_3[/tex] = 5  

Here, [tex]\bar X_1, \bar X_2 , \bar X_3[/tex] represent the means and [tex]\sigma_1,\sigma_2,\sigma_3[/tex] represent the standard deviations.

Now, as we know that Mean of the combined distribution is given by;

                         [tex]\bar X = \frac{n_1 \times \bar X_1+n_2 \times \bar X_2+n_3 \times \bar X_3}{n_1+n_2+n_3}[/tex]

Putting the above values in the formula we get;

                         [tex]\bar X = \frac{200 \times 25+250 \times 10+300 \times 15}{200+250+300}[/tex]

                         [tex]\bar X = \frac{5000+2500 +4500}{750}[/tex]

                         [tex]\bar X = \frac{12000}{750}[/tex]  =  16

Similarly, the formula for combined standard deviation is given by;

       [tex]\sigma = \sqrt{\frac{n_1\sigma_1^{2} + n_1(\bar X_1-\bar X)^{2}+n_2\sigma_2^{2} + n_2(\bar X_2-\bar X)^{2}+n_3\sigma_3^{2} + n_3(\bar X_3-\bar X)^{2} }{n_1+n_2+n_3} }[/tex]

       [tex]\sigma = \sqrt{\frac{(200 \times 3^{2}) + 200 \times (25-16)^{2}+(250 \times 4^{2}) + 250 \times (10-16)^{2}+(300 \times 5^{2}) + 300 \times (15-16)^{2} }{200+250+300} }[/tex]

       [tex]\sigma = \sqrt{\frac{1800 + (200 \times 81)+4000 + (250 \times 36)+7500 +( 300 \times 1) }{750} }[/tex]        

       [tex]\sigma = \sqrt{\frac{1800 + 16200+4000 + 9000+7500 +300 }{750} }[/tex]  

       [tex]\sigma = \sqrt{\frac{38800 }{750} }[/tex]  =  7.192

Hence, the mean and standard deviation of the combined distribution is 16 and 7.192 respectively.

Answer:

a. $52.20

b. [tex]z=11x+0.09y[/tex]

Step-by-step explanation:

[tex]z=7x+0.11y[/tex]

a.

x = 4

y = 220

[tex]z=(7*4)+(0.11*220)\\z=28+24.2\\z=52.2[/tex]

It costs $52.20 under those conditions.

b.

[tex]z=11x+0.09y[/tex]

If z is still how much it costs in total

If x is how many days rented

If y is how many miles driven

Answer:

Step-by-step explanation:

At the Northside assembly plant, 30% of the workers were classied as minority, while at the Southside assembly plant, 60% of the workers were classied as minority. When Northside and Southside were closed, all workers transferred to the new Eastside plant to make up its entire work force. If 40% of the 3750 employees at Eastside are minority, then how many employees did Northside and Southside have originally?

Step-by-step explanation:

we have diameter and volume

and volume function is : v=(3.14)(r^2)h

so : h = 196/112

Answer:

His overal final score is 81.2. His letter grade is a B.

Step-by-step explanation:

Weighed average:

The sum of all values multiplied by it's weight. The weight is a proportion(a value between 0 and 1).

So.

Score of 72 on the midterm, which counts 5%.

Score of 83 on the project score, which counts 25%.

Score of 91 on homework assignments, which counts 35%.

Score of 74 on the final exam, which counts 35%.

His grade is:

G = 72*0.05 + 83*0.25 + 91*0.35 + 74*0.35 = 82.1.

His overal final score is 81.2.

At least 80 but less than 90 is a​ B

So his letter grade is a B.

Answer:

A = 55.15

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adjacent/ hypotenuse

cos A = 4/7

Take the inverse cos of each side

cos^-1 cos A = cos^-1 (4/7)

A = 55.15009542

To the nearest hundredth

A = 55.15

Answer:

a. 15

b. based on the result of part a, 15 standard deviation above the mean.

c. 2.5

d.  Earl's height is unusual

Step-by-step explanation:

We have that "x" would be the height of Earl = 196, the mean m = equals 181 and the standard deviation (sd) = 6, now:

a. the positive difference between the mean and Earl's height:

D = x - m

D = 196 - 181 = 15

b. based on the result of part a, 15 standard deviation above the mean.

c. The z value is given by:

z = x - m / sd

replacing:

z = (196 - 181) / 6

z = 2.5

d. the z-score is unusual since the value of z is 2.5 which is a value greater than than 2 standard deviations above the mean, which means that Earl's height is unusual

Answer:

(a)See attached

(b)[tex]\text{Average Weight =}\dfrac{1}{4}$ lb[/tex]

Step-by-step explanation:

The weights of the bag are given below:

[tex]1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/4 lb, 1/8lb, 1/2 lb \\1/8 lb, 1/4 lb, 1/8 lb, 1/2 lb, 1/8 lb, 1/8 lb, 1/4 lb, 1/2 lb.[/tex]

When sorted, we have:

[tex]1/8 lb, 1/8 lb, 1/8lb, 1/8 lb, 1/8 lb, 1/8 lb, 1/8 lb, 1/8 lb\\ 1/4 lb,1/4 lb, 1/4 lb, 1/4 lb\\ 1/2 lb, 1/2 lb, 1/2 lb,1/2 lb,[/tex]

Part A

See attached for the Line plot

Part B

Average Weight of the bags

[tex]=\dfrac{(8X\dfrac{1}{8})+ (4X\dfrac{1}{4})+(4X\dfrac{1}{2})}{16} \\=\dfrac{1+1+2}{16}\\=\dfrac{4}{16}\\$Average Weight =\dfrac{1}{4}$ lb[/tex]

Answer:

Surface Area: 1,200 units²

Lateral Area: 624 units²

Volume: 960 units³

Step-by-step explanation:

Surface Area is the area of all the faces of the object.

Lateral Area is the area of all the faces of the object NOT INCLUDING the base.

Volume is how much the object can hold.

Using the formula [tex]\frac{1}{2} *b*h[/tex] the area of ONE of the lateral faces of the pyramid is

0.5×24×13=

12×13=

156 units²

156 un² × 4 lateral faces =

624 un²

The lateral surface area is 624 units²

Since the lateral surface area + base is the total surface area:

The base is 24² or 576 units²

624 un²+576 un²=

1,200 units² is the total surface area.

Volume formula for a pyramid is [tex]\frac{1}{3} *b*h[/tex]

We know the base is 576 units².

We don't know the height yet.

We can use the Pythagorean Theorem to find the height of our pyramid.

a²+b²=c²

Half of 24 is 12

12²+b²=13²

144+b²=169

Subtract 144 from both sides.

b²=25

Square root both sides.

b=[tex]\sqrt{25}[/tex]

b=5

The height of our pyramid is 5.

[tex]\frac{1}{3} *576*5=\\\\192*5=\\\\960[/tex]

Our volume for the pyramid is 960 units³

Hope you understand more!

Answer:

B then C

Step-by-step explanation:

First screenshot:

Shape B because the net has a square base.

Second screenshot:

It is C

C does not make a cube

Step-by-step explanation:

5x - 2y

5(-2) - 2(-2)

-10 + 4

= - 6

Answer:

r = 3cm

Step-by-step explanation:

Use the formula for the surface area of a cylinder and solve to obtain r=3cm

Hence radius of base is 3 cm of right circular cylinder.

The cylinder is known as a right circular cylinder when the axis (one of the rectangle's sides) is perpendicular to the radius ((r)). The base and top of the right circular cylinder are both round and parallel to one another. The general formula for the total surface area of a cylinder is T. S. A. =[tex]2\pi rh+2\pi r^{2} .[/tex]

Given total surface area of right circular cylinder =84[tex]\pi cm^{2}[/tex]

Using formula for right circular cyinder =.[tex]2\pi rh+2\pi r^{2} .[/tex]=84

and height=11 cm

[tex]2\pi r11+2\pi r^{2} =84.\pi[/tex]

⇒[tex]11r+ r^{2} =84/2[/tex]

⇒[tex]11r+ r^{2} =42[/tex]

⇒[tex]r^{2} +11r-42=0[/tex]

⇒r = [tex]\frac{-11+-\sqrt{11^{2}-4(1)42 } }{2}[/tex]

⇒r=[tex]\frac{-11+-17}{2}[/tex]

⇒r=3,-1

Hence radius of base is 3 cm as value can't be negative .

Learn more about surface area of cylinder https://brainly.com/question/12763699

#SPJ2

Answer:

Step-by-step explanation:

To factor the expression we need to look for a value that is unique to both terms in the expression.

Given the expression

[tex]24g - 36h[/tex]

The available factors common to both terms are 2,3,4,6,8,12. but since we are expected to factor the expression completely we will use the greatest common factor (gcf) to find the solution

The greatest but common factor is 12, hence we have

[tex]=12(2g- 3h)[/tex]

Note: This is the correct table format.

Flour type                   z                      Mean                            StDev

No DBS                       00                      552                                 18

5% DBS                       00                      525                                 23

15% DBS                     00                      485                                  24

Answer:

5. ANOVA for several means

Step-by-step explanation:

In this question, three different means of the data are compared. ANOVA is used for comparing between two or more means to test for differences. It extends the z and t test that are only used for comparing two means.

Since three means are compared, the inference procedure to be used is ANOVA.

Step-by-step explanation:

The distance traveled varies directly with the time spent in motion. If d is distance and t is time taken. Then,

[tex]d\propto t[/tex]

or

[tex]d=kt[/tex]

k is the constant of variation

If d = 150 miles and t = 4 hours

[tex]k=\dfrac{d}{t}\\\\k=\dfrac{150}{4}\\\\k=37.5\ mph[/tex]

Answer:

a) 19,600 fishes were originally put in the pond.

b) Population of fishes after 10 years = 3,863

Population of fishes after 20 years = 1,733

Population of fishes after 30 years = 1,403

Step-by-step explanation:

The population follows a logistic model

P(t) = d (1 + ke⁻ᶜᵗ)

For a fish pond,

d = 1400, k = 13, c = 0.2

Inserting the values of these constants

P(t) = 1400 (1 + 13 e⁻⁰•²ᵗ)

a) How many fish were originally put in the pond?

At the start of the whole thing, t = 0

P(t=0) = 1400 (1 + 13 e⁰) = 1400 × 14 = 19,600

Hence, 19,600 fishes were originally put in the pond.

b) Find the population after 10, 20, and 30 years.

P(t) = 1400 (1 + 13 e⁻⁰•²ᵗ)

At t = 10, 0.2t = 0.2 × 10 = 2

P(t=10) = 1400 (1 + 13e⁻²) = 1400 (1 + 1.759) = 3,863.1 = 3,863

At t = 20, 0.2t = 0.2 × 20 = 4

P(t=20) = 1400 (1 + 13e⁻⁴) = 1400 (1 + 0.238) = 1,733.3 = 1,733

At t = 30, 0.2t = 0.2 × 30 = 6

P(t = 30) = 1400 (1 + 13e⁻⁶) = 1400 (1 + 0.00248) = 1,403.47 = 1,403

Hope this Helps!!

Answer:

x=0, y=8

slack is zero

surplus is 4

Step-by-step explanation:

See graph for optimal region

if x=0, y=8

15(0)+20(8)= 160

if x= 0, y=4

15(0) + 20(4)= 80

if x=10/3 , y=8/3

15(10/3) + 20(8/3)= 310/3

Slack

8(0)+ 5(8) ≤ 40

40≤40

slack is zero

0.4(0) + 8   ≥ 4

8  ≥ 4

Answer:

A.2 x minus y = negative 6 and 3 x minus y = negative 5

Step-by-step explanation:

A ) 2x-y=-6, and 3x-y=-5

Consider the provided information.

First convert the statement into mathematical representation.Consider the smaller number is x and the larger number is y.

y, is equal to twice the sum of a smaller number and 3.    

This information can be written as: y=2(x+3)

The larger number is also equal to 5 more than 3 times the smaller number.

This information can be written as: y=5+3x

Answer:

A ) 2x-y=-6, and 3x-y=-5

Step-by-step explanation:

Answer:

f[g(x)]= 7x + 27

Step-by-step explanation:

g(x) = x + 2,

f(x) = 7x + 13,

f[g(x)] means you substitute the value of g(x) into the variable of f(x);

Which is 7( x+2) + 13 = 7x +14 +13

= 7x + 27

Answer:

Step-by-step explanation:

They closed the 200 mile distance in 2.5 hours, so the sum of their speeds was ...

  (200 mi)/(2.5 h) = 80 mi/h

If s is the speed of the slower one, then ...

  s + (s+20) = 80

  2s = 60

  s = 30

The slower wander's speed was 30 mph; the faster one's was 50 mph.

Answer: 290 degrees

Step-by-step explanation:

subtract the minor arc's measure from 360 to get the major arc's measure

Answer: X = -5

Step-by-step explanation:

1) Multiply both sides by 6, which is 4x - 3 = 2 + 5x

2) Move the terms, 4x - 5x = 2 + 3

3) Combine like terms, -x = 5

4) Multiply both sides by -1, x = -5

Answer:

0.3891 = 38.91% probability that only one is a second

Step-by-step explanation:

For each globet, there are only two possible outcoes. Either they have cosmetic flaws, or they do not. The probability of a goblet having a cosmetic flaw is independent of other globets. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

17% of its goblets have cosmetic flaws and must be classified as "seconds."

This means that [tex]p = 0.17[/tex]

Among seven randomly selected goblets, how likely is it that only one is a second

This is P(X = 1) when n = 7. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{7,1}.(0.17)^{1}.(0.83)^{6} = 0.3891[/tex]

0.3891 = 38.91% probability that only one is a second

Answer:

The team ordered 7 black T-shirts.

The team ordered 14 red T-shirts.

Step-by-step explanation:

The team ordered 140 T-shirts.

How many black T-shirts did the baseball team order?

Of those, 5% are black.

0.05*140 = 7

The team ordered 7 black T-shirts.

How many red T-shirts?

Of those, 10% are red.

0.1*140 = 14

The team ordered 14 red T-shirts.