Amelia is calculating the density of soccer balls in a bag. She knows the number of balls in the bag and the volume of the bag. Which of the following formulas can be used to calculate the density of balls in the bag?

Density = volume of bag over number of balls
Volume of shelf = density over number of balls
Density = number of balls over volume of bag
Number of books = density over volume of bag

Answer:

At the beginning, there were 2,678.26 grams of sugar in the container.

Step-by-step explanation:

Since Lisa used 880g of a container of sugar to bake a cake and 1/10 of the creaming sugar to make cookies, and she then had 3/7 of the container of sugar left, to determine how much sugar was in the container at first, the following calculation must be performed:

880 + 1 / 10X = 3 / 7X

880 + 0.1X = 0.4285X

880 = 0.4285X - 0.1X

880 = 0.3285X

880 / 0.3285 = X

2,678.26 = X

Therefore, at the beginning there were 2,678.26 grams of sugar in the container.

Answer:

Muhammad lives 8 km away from the school.

Hita lives 4 km away from the school.

Step-by-step explanation:

First of all, find a number that, when you double that number and add both numbers, you will get 12. That number is 4. So double 4 and get 8. Then add both to get 12.

Recall that for |x| < 1, we have

[tex]\displaystyle \frac1{1-x} = \sum_{n=0}^\infty x^n[/tex]

Differentiating both sides gives

[tex]\displaystyle \frac1{(1-x)^2} = \sum_{n=0}^\infty nx^{n-1} = \sum_{n=0}^\infty (n+1)x^n[/tex]

and multiplying both sides by 8 gives the series for f(x) :

[tex]f(x)=\displaystyle \frac8{(1-x)^2} = \boxed{8\sum_{n=0}^\infty (n+1)x^n}[/tex]

and this converges over the same interval, |x| < 1, so that the radius of convergence is 1.

Answer: 9

Step-by-step explanation:

[tex] \frac{3}{5} \times 16.1 = 9.66[/tex]

Hi!

8 - 24 = -(24 - 8) = -16

Answer:

-16

Step-by-step explanation:

8-24=-16

Answer:

[tex]P(x=3)=0.2269[/tex]

Mean=2.1

Standard deviation=1.21

Step-by-step explanation:

We are given that

n=7

Probability of success, p=0.3

q=1-p=1-0.3=0.7

We have to find the probability of 3 success for the binomial experiment  and find the mean and standard deviation.

Binomial distribution formula

[tex]P(X=x)=nC_xp^{x}q^{n-x}[/tex]

Using the formula

[tex]P(x=3)=7C_3(0.3)^3(0.7)^{7-3}[/tex]

[tex]P(x=3)=7C_3(0.3)^3(0.7)^{4}[/tex]

[tex]P(x=3)=\frac{7!}{3!4!}(0.3)^3(0.7)^{4}[/tex]

[tex]P(x=3)=\frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}(0.3)^{3}(0.7)^{4}[/tex]

Using the formula

[tex]nC_r=\frac{n!}{r!(n-r)!}[/tex]

[tex]P(x=3)=0.2269[/tex]

Now,

Mean, [tex]\mu=np=7\times 0.3=2.1[/tex]

Standard deviation, [tex]\sigma=\sqrt{np(1-p)}[/tex]

Standard deviation, [tex]\sigma=\sqrt{7\times 0.3\times 0.7}[/tex]

Standard deviation, [tex]\sigma=1.21[/tex]

Answer:

Step-by-step explanation:

The sides of a 30-60-90 triangle are in the ratio 1:√3:2

The side opposite the 30° angle is (12√6)÷2 = 6/√6.

The side opposite the 60° angle is √3×6/√6 = 6/√2 =3√2.

The sides of a 45-45-90 triangle are in the ratio 1:1:√2

The hypotenuse is 3√2, so the side opposite the 45° angle is 3.

x = 3

Answer:The correct answer is  They wanted to impede the sale of alcohol.

Step-by-step explanation:

They had beliefs that alcohol was against Christianity and that it ruins families and since it ruins families it should be prohibited. They eventually managed to win enough support and ban all alcohol which lasted for a few years before the prohibition ended.

Answer:

a. Set-builder form: {y | y is a natural number and 12 ≤ y ≤ 15}

Or

{y | y is a natural number and 11 < y < 16}

b. Rooster form: {3, 4, 5 ,6, ...}

Step-by-step explanation:

a. Rooster form: {12, 13, 14, 15}

All four numbers are natural numbers, therefore we would write this set of numbers in set builder form such that they will all have the same property. Thus:

Set-builder form: {y | y is a natural number and 12 ≤ y ≤ 15}

Or as

{y | y is a natural number and 11 < y < 16}

b. Set-builder form: {y | y is a natural number and y > 2}

Since natural numbers are positive integers, this tells us that all values of the set are not less than or equal to 2. Therefore, they are integers that range from 3 and above.

Thus:

Rooster form: {3, 4, 5 ,6, ...}

Answer:

y+10=2

y=-8

Step-by-step explanation:

y=2-10

y=-8

Answer:

15

Step-by-step explanation:

By order of operations, multiplication and division are done first, then the addition and subtraction. Remember, multiplication and division have the same precedence, as does addition and subtraction.

21*6 = 126

126/7 = 18

18 + 12 = 30

30 - 15 = 15

Answer:

15

Step-by-step explanation:

21 × 6 ÷ 7 + 12 - 15​

= 126 ÷ 7 + 12 - 15

= 18 + 12 - 15

= 30 - 15

= 15

Answer:

Step-by-step explanation:

Answer:

3/8 x 5/8= 15/64

Step-by-step explanation:

Answer:

so you need a khan academy account?

Answer:

The length of a side of a cubic die of volume equal to 343/4 is 4.41 inches.

Step-by-step explanation:

The volume of a cube is given by:

[tex] V = l^{3} [/tex]

Where:

l: is the length =?  

V: is the volume = 343/4 in³

By solving the above equation for "l" we have:

[tex] l = (V)^{1/3} = (343/4 in^{3})^{1/3} = 4.41 in [/tex]

Therefore, the length of a side of a cubic die of volume equal to 343/4 is 4.41 inches.

None of the options are correct for the given volume.

I hope it helps you!                                

Answer:

Step-by-step explanation:

g(5) = 2 > 0

:::::

g(x) = 0 for x = -2, 2, 4

:::::

g(x) < 0 for  -3 ≤ x < -2

Answer: 0.86 and -2800 (choice A)

Explanation:

Think of the given equation as y = 0.86x - 2800

Then compare it to y = mx + b

We see that m = 0.86 is the slope and b = -2800 is the y intercept.

Answer:

Slope: 0.86 , Y-intercept:-2800

Step-by-step explanation:

Linear equations go by the form of y=mx + c

where m is the gradient(slope of the graph) and c is the y-intercept

include the notation and just do the work on the page

i think the answer is 2.24

This question is incomplete, the complete question is;

The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

What proportion of the students scored at least 23 points on this test, rounded to five decimal places?

Answer:

proportion of the students that scored at least 23 points on this test is 0.30850

Step-by-step explanation:

Given the data in the question;

mean μ = 22

standard deviation σ = 2

since test closely followed a Normal Distribution

let

Z = x-μ / σ      { standard normal random variable ]

Now, proportion of the students that scored at least 23 points on this test.

P( x ≥ 23 ) = P( (x-μ / σ) ≥  ( 23-22 / 2 )

= P( Z ≥ 1/2 )

= P( Z ≥ 0.5 )

= 1 - P( Z < 0.5 )

Now, from z table

{ we have P( Z < 0.5 ) = 0.6915 }

= 1 - P( Z < 0.5 ) = 1 - 0.6915 = 0.30850

P( x ≥ 23 ) = 0.30850

Therefore, proportion of the students that scored at least 23 points on this test is 0.30850

Answer:

-2

-1

-2

Step-by-step explanation:

really ? this is a problem ? why ?

f(0) means the functional value for x = 0.

is x = 2 ? no.

so, automatically the other case applies, and f(0) = -2

f(2) means x=2

is x = 2 ? yes.

so that case applies, and f(2) = -1

f(5) means x=5

is x = 2 ? no.

so again, the case for x <> 2 applies, f(5) = -2

Answer:

15. 52

16. 6

17. 59

18. 11

Step-by-step explanation:

9514 1404 393

Answer:

  C.  837

Step-by-step explanation:

The remaining angle is ...

  C = 180° -A -B = 180°-62° -67° = 51°

The law of sines tells us that the length AC is ...

  AC/sin(B) = AB/sin(C)

  AC = AB·sin(B)/sin(C) = 40·sin(67°)/sin(51°)

Using the area formula given, we now have ...

  area = 1/2(AB)(AC)sin(A)

  = (1/2)(40)(40·sin(67°)sin(62°)/sin(51°) ≈ 836.7

The area of the triangle is about 837 square units.

Answer:

(a) 23000(1-15%)^t

(b) about 12006.14375

Step-by-step explanation:

(a) There's a formula for this problem y = A(d)^t where, A is the initial value you are given, d is the growth or decay rate and t is the time period. So, in this case, as the car cost is decreasing it is a decay problem and we can write the formula as such; y = A(1-R)^t

And with the values, we get the exponential model 23000(1-15%)^t

(b) From question (a) we already have the model and the time period given here is 4 years. So putting it in the formula we get,

23000(1-15%)^4

=23000(1-15/100)^4

=23000(0.85)^4

=23000x0.52200625

=12006.14375     (Ans)

Answer:

0.3898 = 38.98% probability that there will be 4 failures

Step-by-step explanation:

A sequence of Bernoulli trials forms the binomial probability distribution.

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.

Let the probability of success on a Bernoulli trial be 0.26.

This means that [tex]p = 0.26[/tex]

a. In five Bernoulli trials, what is the probability that there will be 4 failures?

Five trials means that [tex]n = 5[/tex]

4 failures, so 1 success, and we have to find P(X = 1).

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

[tex]P(X = 1) = C_{5,1}.(0.26)^{1}.(0.74)^{4} = 0.3898[/tex]

0.3898 = 38.98% probability that there will be 4 failures

9514 1404 393

Answer:

Step-by-step explanation:

Assuming the dimensions are integer numbers of feet, you're looking for factors of 580 that have a difference of 9.

 580 = 1×580 = 2×290 = 4×145 = 5×116 = 10×58 = 20×29

The last pair of factors differs by 9, so ...

  the length is 29 feet; the width is 20 feet.

Answer:

0.5665 = 56.65% probability of less than four twos.

Step-by-step explanation:

For each roll, there are only two possible outcomes. Either it is a two, or it is not a two. The probability of a roll ending up in a two is independent of any other roll, which means that the binomial probability distribution is used.

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.

A die is rolled 20 times

This means that [tex]n = 20[/tex]

One out of six sides is 2:

This means that [tex]p = \frac{1}{6} = 0.1667[/tex]

Probability of less than four twos:

This is:

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

So

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

[tex]P(X = 0) = C_{20,0}.(0.1667)^{0}.(0.8333)^{20} = 0.0261[/tex]

[tex]P(X = 1) = C_{20,1}.(0.1667)^{1}.(0.8333)^{19} = 0.1043[/tex]

[tex]P(X = 2) = C_{20,2}.(0.1667)^{2}.(0.8333)^{18} = 0.1982[/tex]

[tex]P(X = 3) = C_{20,3}.(0.1667)^{3}.(0.8333)^{17} = 0.2379[/tex]

So

[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0261 + 0.1043 + 0.1982 + 0.2379 = 0.5665[/tex]

0.5665 = 56.65% probability of less than four twos.