A bag contains 10 green marbles and 4 yellow marbles. If two marbles are chosen at random, one at a time and without replacement, what is the probability of getting two green marbles?

Answer:

(x - 12)(x^2 - 2) or (x - 12)(x + sqrt(2) ) (x - sqrt(2))

Step-by-step explanation:

Step-by-step explanation:

[tex]\frac{2}{3} + \frac{2}{9} \\\\\frac{6+2}{9}\\\\\frac{8}{9}[/tex]

This is what i did to get the answer.

225/ 4.5 = 50 seconds to finish the slushy.

Answer:

Can I have the options? I cant check all that apply if i don't have options.

Step-by-step explanation:

Answer:

[tex]8.68,13.16[/tex]

Step-by-step explanation:

Hint- First we have to calculate the mean and standard deviation of the sample and then applying formula for confidence interval we can get the values.

Mean of the sample is,

[tex]\mu=\dfrac{\sum _{i=1}^{24}a_i}{24}=\dfrac{262}{24}=10.92[/tex]

Standard deviation of the sample is,

[tex]\sigma =\sqrt{\dfrac{\sum _{i=1}^{24}\left(x_i-10.92\right)^2}{24-1}}=5.6[/tex]

The confidence interval will be,

[tex]=\mu \pm Z\dfrac{\sigma}{\sqrt{n}}[/tex]

Here,

Z for 95% confidence interval is 1.96, and n is sample size which is 24.

Putting the values,

[tex]=10.92 \pm 1.96\cdot \dfrac{5.6}{\sqrt{24}}[/tex]

[tex]=10.92 \pm 2.24[/tex]

[tex]=8.68,13.16[/tex]

Confidence interval is used to express the degree of uncertainty associated with a sample.

95% confidence interval means that if we used the same sampling method to select different samples and calculate an interval, we would expect the true population parameter to fall within the interval for 95% of the time.

Final answer:

A 95 percent confidence interval is computed using the t-distribution and provides an estimated range where we can expect the population mean to lie. It reflects the level of certainty, but does not suggest that it contains 95 percent of the data.

Explanation:

To compute a 95 percent confidence interval for the number of hours students spent studying, we first need to calculate the mean and standard deviation of the given sample data. Then we can use the t-distribution because the sample size is small and we don't know the population standard deviation. The formula to calculate a confidence interval is: ± t× (s/√n), where t is the t-score associated with our confidence level and degrees of freedom (n-1), s is the sample standard deviation, and n is the sample size.

Confidence intervals provide a range of values that we are a certain percentage sure (95% in this case) contains the population mean. It is not correct to think that a 95% confidence interval contains 95% of the data. Instead, it means that if we were to take many samples and build a confidence interval from each of them, 95% of those intervals would contain the true population mean. Therefore, the confidence interval gives an interval estimate for where the population mean lies, not a precise value.

Answer:

Step-by-step explanation:

answer:heidi goes 0.12 miles a minute .

steps

average distance=time/miles

45/5.4

0.12

mark me as brainlest

Answer:

0.12 mile/minute

Step-by-step explanation:

Here you're being asked to find a unit rate.

Compute:

5.4 miles

--------------- = 0.12 mile/minute

45 min

This is the average distance covered in one minute.

Answer:

$.33 cents per roll

Step-by-step explanation:

a dozen rolls are 12 rolls

To find the unit prices, take the price and divide by the number of rolls.

$3.99/12

$.3325

But this is money so we round to the nearest cent

$.33 cents per roll

Answer:

Option A is correct.

1,017.36 square feet does the base of the building measure.

Step-by-step explanation:

Given: Diameter of the base (d) = 36 feet , Height of the building (h) = 57.2 feet and slant height of the building(l) = 60 feet.

We have to find the area of the base of the building.

Since, the building is in the form cone.

Area of the base(A) of the cone is given by:

[tex]A= \pi r^2[/tex] ......[1]; where r is the radius of the cone

Diameter(d) = 2r

36 = 2r

Divide both sides by 2 we get;

r = 18 feet.

Substitute the value of r = 18 feet and [tex]\pi = 3.14[/tex] in [1] we get;

Area of the base of the building = [tex]3.14 \times (18)^2 = 3.14 \times 324 = 1017.36[/tex] square feet.

Therefore, 1,017.36 square feet does the base of the building measure.

Answer:

A

Step-by-step explanation:

Answer:

105 parents said their kids were nice. 39 parents said their kids were naughty.  6 parents didn't answer.

Step-by-step explanation:

From the plot, we see that [tex]z_1=-4-3i[/tex]. Its conjugate would be [tex]\bar{z_1}=-4+3i[/tex], so that the product of the two is

[tex]z_1\bar{z_1}=(-4-3i)(-4+3i)=16-9i^2=16+9=25[/tex]

More generally, note that if [tex]z=x+yi[/tex], then

[tex]z\bar z=(x+yi)(x-yi)=x^2+y^2=|z|^2[/tex]

Answer:

The product of z1 and its conjugate is 25.

Step-by-step explanation:

In the given graph x-axis represents the real axis and y-axis represents the imaginary axis.

The end point of z1 are (0,0) and (-4,-3). So, the complex number z1 is defined as

[tex]z_1=x+iy=-4-3i[/tex]

The conjugate of z1 is

[tex]\overline {z_1}=x-iy=-4+3i[/tex]

The product of z1 and its conjugate is

[tex]z_1\overline {z_1}=(-4-3i)(-4+3i)[/tex]

[tex]z_1\overline {z_1}=-4(-4+3i)-3i(-4+3i)[/tex]

[tex]z_1\overline {z_1}=16-12i+12i-(3i)^2[/tex]

[tex]z_1\overline {z_1}=16-9(i)^2[/tex]

[tex]z_1\overline {z_1}=16-9(-1)[/tex]           [tex][\because i^2=-1][/tex]

[tex]z_1\overline {z_1}=16+9=25[/tex]

Therefore the product of z1 and its conjugate is 25.

Answer:

Step-by-step explanation:

you would use the distributive property, so the answer should be..... -377/1015, OR -13/35 BTW i'm not completely sure this is correct. Im not a calculator. But I think Im correct

Answer:

Number of cows is 23

Number of chickens is 46

Step-by-step explanation:

Let's assume

number of cows =x

we are given

Mr.Yan has almost as twice as many chickens and cows

so,

Number of chickens =2x

We know that

Number of legs in a cow =4

Number of legs in a chicken =2

now, we can set up equation

[tex]4\times x+2\times 2x=184[/tex]

[tex]4x+4x=184[/tex]

[tex]8x=184[/tex]

[tex]x=23[/tex]

So,

Number of cows =23

Number of chickens is

[tex]=2\times 23=46[/tex]

Answer:

To find the unit rate, you have reduce the fraction until you get 1 in the denominator.

Step-by-step explanation:

ex:  16/4 = 4/1 = 4 this is the unit rate.

unit means 1.

Answer:

m=0

Step-by-step explanation:

Zero power rule: a^0 = 1,   Anything raised to the zero power is 1  (a≠ 0).

So if m=0, as long as x does not equal zero   (x^8/yz^5)^m will equal one.

Answer:

1/10

Step-by-step explanation:

Assuming there are 3 red marbles:

3/10 × 3/9 = 9/90 = 1/10

There are 3 red, that is where the first numerator comes from and there are 10 marbles so that is where the denominator comes from. There are 3 yellows, hence the second numerator but as we have taken a marble out there are now only 9 marbles in total.

Answer:

1 : √3 : 2

Step-by-step explanation:

In the special right triangle, 30°-60°-90° triangle:-

Opposite side < Adjacent side < Hypotenuse.

1. The smallest side is opposite to angle 30°, also called opposite side.

2. Adjacent side is √3 times smallest side.

3. Hypotenuse is 2 times smallest side.

So the ratios of sides would be as follows:-

Opposite : Adjacent : Hypotenuse

1x : √3x : 2x

1 : √3 : 2

Answer:

12

Step-by-step explanation:

A parallelogram has 4 sides. Opposite sides of a parallelogram are parallel and congruent.

Since one side has length p, its opposite side also has length p.

Since one side has length 17 ft, its opposite side also has length 17 ft.

The lengths of the 4 sides are p, p, 17 ft, and 17 ft.

The perimeter is the sum of the lengths of the sides, and it is 58 ft.

p + p + 17 + 17 = 58

2p + 34 = 58

2p = 24

p = 12

I'll do the first one to get you started

So we have g(f(x)) which means that we start with g(x) and replace the 'x' with 'f(x)' to get g(f(x))

g(x) = ( x - 4 )/2

g(f(x)) = ( f(x) - 4)/2 .... replace every x with f(x)

g(f(x)) = (2x+4-4)/2 .... replace f(x) on the right side with 2x+4

g(f(x)) = (2x+0)/2

g(f(x)) = (2x)/2

g(f(x)) = 1x/1

g(f(x)) = 1x

g(f(x)) = x

Let me know if you need help with the other one.

Answer:

tax = $6.63

Step-by-step explanation:

We can find the tax by multiplying the original amount by the tax rate.

tax rate = 10 % = .1

tax = 66.30 * .10

     = 6.63

To solve this problem, we need to figure out how much tax Peter will be paying, given that the tax rate is 10% and his purchase costs $66.30.

To do this, we must first convert 10% into a decimal.  To do this, we must divide it by 100 (because it is a fraction out of a total of 100 percent), or simply move the decimal point two places to the left.  Therefore, 10% = 0.10.

To find the tax amount, we must multiply the sales tax rate (10% or 0.10) by the purchase cost ($66.30).  This gives us:

$66.30 * 0.10 = $6.63

Therefore, your answer is $6.63.

(A little tip: the method I used above can be used for any tax rates, but a trick for finding 10 percent of something is to move the decimal point of the cost one place to the left).

Hope this helps!

Answer: The correct answer is respiration.

Respiration can be defined as the biochemical process, by which cells obtain energy as ATP from oxygen and glucose, with release of carbon dioxide, water. This process is not at all involved in the synthesis of protein, as it produces energy for the cells of the body.

Answer:

The answer is a. 3x - y = -11

Step-by-step explanation:

Firstly, you must find the gradient. This is found using the following formula:

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

Make sure that the x2 and y2 values are in the same coordinate set:

Let's set (-3 , 2) as y1 and x1,

y1 = 2 and x1 = -3

That means that (-5 , 8) is y2 and x2,

y2 = 8 and x2 = -5

Plug the values in:

[tex]\frac{8 - 2}{-5 - - 3}[/tex]

Simplified:

[tex]\frac{6}{2}[/tex]

Or 3

So the gradient (or slope) is 3

Now, using the following equation of a line formula:

y - y1 = m(x - x1)

Where m is the gradient and y1 and x1 are two coordinates, we can plug these values in:

y1 = 2

x1 = -3

m = 3

y - 2 = 3(x - - 3)

The negative and the subtract makes it a positive:

y - 2 = 3(x + 3)

Now we can multiply the bracket out:

3 * x = 3x

3 * 3 = 9

So:

y - 2 = 3x + 9

The equation is usually in the form:

y = mx + c

So we need to move the -2 over to the other side making it a positive 2:

y = 3x + 9 + 2

y = 3x + 11

Which is the equation of the line.

The one option that this rearranges to is a) because if you move the y over to the 3x, and the + 11 over to the other side, making them both negatives, the result is:

3x - y = -11

So your answer is a.

Answer:

(1/4) / (2/3) = x / 1...1/4 book to 2/3 week = x books to 1 week

cross multiply because this is a proportion

2/3x = 1/4

x = 1/4 * 3/2

x = 3/8 per week

Answer

14 / 13 hope this helps

Step-by-step explanation:

Answer:

[tex]F(x)=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.[/tex]

Step-by-step explanation:

Consider the function [tex]F(x)=2x^2+13x+20.[/tex]

Rewrite it as follows:

[tex]F(x)=(2x^2+13x)+20=2\left(x^2+\dfrac{13}{2}x\right)+20=2\left(x^2+\dfrac{13}{2}x+\left(\dfrac{13}{4}\right)^2-\left(\dfrac{13}{4}\right)^2\right)+20=2\left(x^2+\dfrac{13}{2}x+\dfrac{169}{16}\right)-2\cdot \dfrac{169}{16}+20.[/tex]

Since

[tex]x^2+\dfrac{13}{2}x+\dfrac{169}{16}=\left(x+\dfrac{13}{4}\right)^2,[/tex]

you get

[tex]F(x)=2\left(x+\dfrac{13}{4}\right)^2+20-\dfrac{169}{8}=2\left(x+\dfrac{13}{4}\right)^2-\dfrac{9}{8}.[/tex]

Answer:

the correct answer is: f(x)=2(x+13/4)²+-9/8. i hope it help

Answer:

1) 16 adults

2) 2 adults at each table

3) 7

Step-by-step explanation: