A bag contains 8 red marbles, 2 blue marbles and 5 green marbles. If two marbles are
drawn out of the bag, what is the probability, to the nearest 100oth, that both
marbles drawn will be green?

Answer:

A and B

Step-by-step explanation:

1 meter = 100 centimeters

6 meters = 600 centimeters

1 meter = 1000 millimeters

6 meters = 6000 millimeters

Answer:

2/5

Step-by-step explanation:

We can find the slope using two points

(0,0) and (5,2)

m = (y2-y1)/(x2-x1)

    = (2-0)/(5-0)

   = 2/5

The complete values of the table for time taken to sign the diploma are: Seconds | 30 | 90 | 150 | 210; Diplomas | 4 | 12 | 20 | 28.

Two ratios are said to be equal when a proportion is stated. Ratios, which can be written as a fraction or a colon, are used to compare two objects or values. For instance, a class might have a boy to girl ratio of 2:3 or 2/3. A percentage is an equation proving the equality of two ratios. The formula is a/b = c/d, where a, b, c, and d are all numerical values or variables. Numerous branches of mathematics, science, and daily life, including banking, engineering, and cookery, require proportions.

Given that, it takes the principal 30 seconds to sign 4 diplomas.

Setting the proportion we have:

30 seconds / 4 diplomas = x seconds / y diplomas

x = 7.5y

Substituting the values of x and y from the table we have:

For y = 12

x = 7.5(2) = 90

Similarly, for y = 20:

x = 7.5(20) = 150

For x = 210:

210 = 7.5y

y = 28

The complete values of the table for time taken to sign the diploma are: Seconds | 30 | 90 | 150 | 210; Diplomas | 4 | 12 | 20 | 28.

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The complete question is:

Answer: You didn't give answer choices but I think the answer would be (17, 73/3)

Answer:

-1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

-1/3

Answer:

Here are the steps

Step-by-step explanation:

708 divided by 9

9 goes into 7 zero times,

9 goes into 70 seven times (63)

so carry the seven

drop the 8

9 goes into 78 eight times

subtract 72

brings you a remainder of 6

So it is 78 remainder 6

(Would appreciate brainliest)

Step-by-step explanation:

We are trying to find $40 on sale for 20$ off.

40*20/100

40*0.2

You save=$8

40-8

Final Price=$32

Answer: 2a < 2b

Step-by-step explanation:

We are given a statement:

a < b and b < c, then 2a ____ 2b

We can use simple numbers that make the statement true.

Where,

a = 2

b = 3

c = 4

Now lets plug it in.

2 < 3 and 3 < 4, then 2(2) ____ 2(3)

and lets simplify:

2 < 3 and 3 < 4, then 4 ____ 6

We can see that 4 is less than 6,

so as a is less than b, 2a is less than 2b.

The only thing changing is the coefficient being multiplied by the variables a and b.

To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.

To model this relationship, we can use the inverse variation equation, which can be expressed as:

y = k/x

Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.

Let's examine the data given in the table to find the value of k:

Number of Photos (x) Cost per Photo (y)

10 10

25 4

50 2

100 1

We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):

2 = k/50

Solving for k:

k = 2 * 50 = 100

Now that we have the value of k, we can write the function that models the data:

y = 100/x

Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.

The rate of change = the slope of the function.

Slope = (5 - (-5)) / (2 - 0) = (5 + 5) / 2 = 10 / 2 = 5

Answer choice A is correct.

Answer:

In the first one you are missing (a +7) so it's going to be 9(a +7) or when you factor that out it will be 9a 63

In the other one you are missing the (a +5) so it's going to be 7a(a + 5) or when you factor it out it will be 7a2 + 35a

Step-by-step explanation:

a2+ 9a + 20 = (a + 4) (a + 5)

a2 + 11a+ 28 = ( a + 7) ( a + 4 )

Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

Answer:

https://www.omnicalculator.com/finance/compound-interest

Step-by-step explanation:

this is a link to a compound interest calculator and it helped me with similar problems hope it helps you

Answer:

54

Step-by-step explanation:

x-1=3

2xy=24

3+24=27

27·2=54

Answer:

54

Step-by-step explanation:

Answer:

Force      F = 60 ×10⁻⁵ N

Step-by-step explanation:

Given that mass of the given object (m)  = 30 grams

Given that the acceleration

                                 a = 2 m/s²

Force:-

The push or pull on an object with mass that causes it to change its velocity

Formula for force

The formula for force    F = m a

                                      F = 30 × 2

                                     F  = 60 gm/s²

                                   F = 60 ×10⁻⁵ N     (∵ 1 d y n = 1gm² = 10⁻⁵N

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

\(45^{3}\) inches

Step-by-step explanation:

To calculate the volume of a rectangular prism(or in this case, the rectangular box), you need to multiply the length, width and height together.

length x width x height

9 x 5 x 1

=  \(45^{3}\) inches

Answer: slope is 3, y-intercept is 2

Step-by-step explanation:

The slope of a line is the ratio at which the y value changes with respect to the x value. Since the entire line is straight, the slope at every single point along the line is the exact same. This means that we can find the slope at any point along the line and it'll represent the slope for the entire line.

When x = 0, the y = 2. Therefore we have the point, (0, 2). When x = 1, the y value is y = 5. Therefore, we have another point, (1, 5). The difference between the y values is:

\(5-2=3\)

The difference between the x values is:

\(1-0=1\)

Therefore, their ratio is:

\(3/1=3\)

The y-intercept is the y value at which the function intercepts the y-axis. That would be when y = 2

Answer: 20°

the measure of the third angle of the triangle is x ( 0 < x < 90)

because this is 3 angles in a triangle, we have:

120 + 40 + x = 180

⇔ x = 180 - 120 - 40

⇔ x = 20°

Step-by-step explanation:

If the dairy farmer wants to mix a 80% protein. The amount of pounds of each that he should use is 80% 280 pounds and 55% 1120 pounds.

Protein I 80% = x pounds

Protein II 55% = 1400 - x pounds

Mixture 60% = 1400

Hence,

80% x + 55% ( 1400 - x ) = 60% × 1400

80 x + 55 ( 1400 - x ) = 84000

80 x + 77000 - 55 x = 84000

Combine like terms

80 x - 55 x = 84000 - -77000

25 x = 7000

Divide both side by 25x

x= 7000/25

x =280 pounds ( Protein I)

Protein II

1400 - x pounds

1400 -280

=  1120 pounds

Therefore the farmer should use 280 pounds and 1120 pounds.

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Answer:

x = 1, x = -5

\(x/5 = 1/x+4\\Apply Fraction and Multiply : \\\\x(x+4)=5 x 1\\Simplify :\\x(x+4) = 5\\Solve.\)

I hope this is what you were looking for !

Answer:

-15

Step-by-step explanation:

Given:-

To find the correct inequality between the given datas.

So now we simplify. so we get,

So we get,

So the inequality is,

Answer:-3.5

Step-by-step explanation:

Answer:

(a) We conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism at 5% significance level.

(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child.

Step-by-step explanation:

We are given that Autism and Maternal Antidepressant Use A recent study 41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected control children without the disorder.

Of the children with autism, 20 of the mothers had used antidepressant drugs. Of the control children, 50 of the mothers had used the drugs.

Let \(p_1\) = proportion of mothers who had used drugs having Autism Spectrum Disorder in their children.

\(p_2\) = proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children.

(a) Null Hypothesis, \(H_0\) : \(p_1=p_2\)      {means that there is no significant association between prenatal exposure to antidepressant medicine and the risk of autism}

Alternate Hypothesis, \(H_A\) : \(p_1\neq p_2\)     {means that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism}

The test statistics that would be used here Two-sample z test for proportions;

                         T.S. =  \(\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }\)  ~ N(0,1)

where, \(\hat p_1\) = sample proportion of mothers who had used drugs having Autism Spectrum Disorder in their children = \(\frac{20}{298}\) = 0.067

\(\hat p_2\) = sample proportion of mothers who had used drugs not having Autism Spectrum Disorder in their children = \(\frac{50}{1507}\) = 0.033

\(n_1\) = sample of children with Autism Spectrum Disorder = 298

\(n_2\) = sample of children without Autism Spectrum Disorder = 1507

So, the test statistics  =  \(\frac{(0.067-0.033)-(0)}{\sqrt{\frac{0.067(1-0.067)}{298}+\frac{0.033(1-0.033)}{1507} } }\)

                                       =  2.281

The value of z test statistics is 2.281.

Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that there is a significant association between prenatal exposure to antidepressant medicine and the risk of autism.

(b) Yes, we can conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child because if we reconsider our hypothesis for one-tailed test in which the null hypothesis states that the prenatal exposure to antidepressant medicine does not increases the risk of autism in the child.

For this hypothesis also, our test statistics will be more than the critical value of z and due to which we reject our null hypothesis and conclude that prenatal exposure to antidepressant medicine increases the risk of autism.

1. Table 4 values shows a Linear function.

2. 6 seconds faster were the runner in Group 2 than runners in Group 1.

Linear function are those which are in the form of f(x) = x ( here the line is passing through the origin )

Also Linear function can be in the form of y = mx + c where 'm' is the slope of the given line and 'c' is constant.

1. In the table 4 we conclude that:

y = f(x)

f(2) = 4         -------- point is ( 2, 4)

f(4) = 6         -------- point is ( 4, 6)

f(6) = 8         -------- point is ( 6, 8)

f(8) = 10        -------- point is ( 8, 10)

for the points to be in a line their slope must be equal:

Slope of line from point (2, 4) and (4, 6):

Slope = ( y2 - y1 )/ (x2 - x1)

Slope = ( 6 - 4 )/(4-2)

Slope = 2/2 = 1

Similarly,

Slope of line from point (4, 6) and (6, 8):

Slope = ( 8- 6 )/(6-4)

Slope = 1

Same as for points (6, 8) and (8,10)

Slope = 1

here the slop of the all points are same, so they lie on a single line and forms a linear equation in form of y = mx + c.

Hence, Table 4 values shows a Linear function.

2.  Here we have given the data:

For group 1: 55 68 64 66 70

For group 2: 56 58 59 61 57

Average or Geometric mean :

Sum of all the observation / number of observation

Average for Group 1 = ( 55 + 68 +64 +66 + 70)/5

Average for Group 1 = 64.6

Average for Group 2 = (56 + 58 + 59 + 61 +  57)/5

Average for Group 2 = 58.2

Difference between the Average of group 1 and group 2: 6.4.

in whole number 6 seconds.

Hence,

6 seconds faster were the runner in Group 2 than the runners in Group 1.

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Answer:

No

Step-by-step explanation:

10 is not less than 6, so 10 < r when r=6 is not true.