Identify the pair numbers

Answer:

7 and 3 are two numbers that work

Step-by-step explanation:

7-3=4

7×3=21

Answer:

0.0076 = 0.76% probability that all five plants emerged from treated seeds

Step-by-step explanation:

The plants were chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

In this question:

6 + 6 = 12 seeds, which means that [tex]N = 12[/tex]

6 treated, which means that [tex]k = 6[/tex]

Five sprouted, which means that [tex]n = 5[/tex]

What is the probability that all five plants emerged from treated seeds?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,12,5,6) = \frac{C_{6,5}*C_{6,0}}{C_{12,5}} = 0.0076[/tex]

0.0076 = 0.76% probability that all five plants emerged from treated seeds

Answer:

7×(8/6)=9.33

Step-by-step explanation:

7 is whole number

8/6 is the fraction

8/6 is 1.333

so, 7×1.333=9.33

Answer:

Assuming a constant rate of travel that is the same as yesterday, 416 miles in 8 hours.

Step-by-step explanation:

We are assuming that the first day's rate will be used in the second. After that, it is a proportions question. We divide 312 by 6 to get 52 miles an hour. Then, we multiply 8 hours by 52 miles to get 416 miles 8 hours.

Answer:

237.9 yards

Step-by-step explanation:

90-23=67

cos 67⁰=x/610

x=610 cos 67

x= 610 x 0.39

x=237.9 yards

Answer:

The midpoint is (1,-13.5)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoints and divide by 2

(7+-5) /2 = 2/2 =1

To find the y coordinate of the midpoint, add the y coordinates of the endpoints and divide by 2

(-12+-15) /2 = -27/2 =-13.5

The midpoint is (1,-13.5)

Answer:

All the angles on the bottom line are 60. The angles on the top line from left to right is 130, 60, 60, 130.

Step-by-step explanation:

Answer:

the first page :

x =20

the second page :

x = 45

Step-by-step explanation:

first question

to find angle BOC subtract 110 from 180( because 180 degrees is a straight line)

angle BOC = 70 degrees

this means that the angle opposite to it is also 70 degrees ( DOA)

now to find x, add up 110, 70, 70, 90, x to get 360

110 + 70 + 70 + 90 + x = 360

x = 20

second question :

every thing adds up to 360 degrees.

90 + 5x + x = 360

6x = 270

x = 45

Answer:

[tex]B)[/tex]

[tex](-1,1)(-3,3)\\\frac{3-1}{-3+1} =-1\\1=1+b\\b=0\\y=-x[/tex]

OAmayOHopeO

Answer:

9^2 + 12^2 = x^2

81 + 144 = 225

225 ÷ 15 = 15

the answer for this question is 15

Step-by-step explanation:

Answer:

The two numbers are:

x = 500

y = 125

Step-by-step explanation:

We want to find two numbers x and y, such that:

x + 4*y = 1000

f(x, y) = x*y is maximum.

From the first equation, we can isolate one of the variables to get

x = 1000 - 4y

now we can replace it in f(x, y):

x*y = (1000 - 4*y)*y  = 1000*y - 4*y^2

So now we want to maximize the function:

f(y) =- 4*y^2 + 1000*y

where y must be an integer.

Notice that this is a quadratic equation with a negative leading coefficient (so the arms of the graph will open downwards), thus, the maximum will be at the vertex.

Remember that for a general quadratic equation:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/(2*a)

so, in the case of:

f(y) =- 4*y^2 + 1000*y

the y-value of the vertex will be:

y = -1000/(2*-4) = 1000/8 = 125

So we found the value of y.

now we can use the equation:

x = 1000 - 4*y

x = 1000 - 4*125 = 1000 - 500 = 500

x = 500

Then the two numbers are:

x =500

y = 125

Answer:

26 gallons

Step-by-step explanation:

Take the miles and divide by the gallons

455 miles / 17.5 gallons

26 miles per gallon

Answer:

x = 16

Step-by-step explanation:

7(x + 2) = 6(x + 5)

First, to start solving this problem, we have to distribute the "7" to the "x + 2" in the parenthesis and the "6" to the "x + 5" in the parenthesis.

7x + 14 = 6x + 30

Next, let's subtract "6x" from both sides of this equation!

x + 14 = 30

Now, we have to subtract "14" from both sides of the equation.

x = 16

Lastly! Let's make sure our "x=" equation is correct by inputting our value into the "x" values.

7(16 + 2) = 6(16 + 5)

7(18) = 6(21)

126 = 126

Since our equations equal each other we know that our x-value is correct!

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

wheres the picture?

Step-by-step explanation:

Answer:

-75/4

Step-by-step explanation:

75 x 100 = 7500

4 x 100 = 400

9514 1404 393

Explanation:

The attachment shows such a construction. Here are the steps.

1. Draw circle B with radius 3.5 cm

2. Mark a point X on the circle and draw circle X with the same radius. Mark the intersection points of circles B and X as points A and C.

3. Draw circles A and C with radii 5.2 cm. Mark the intersection point as point D so that X is on segment BD.

4. Finish by drawing kite ABCD.

Answer:

300

Step-by-step explanation:

9514 1404 393

Answer:

  3

Step-by-step explanation:

The length of A'B' is 3 units.

The length of AB is 1 unit.

The scale factor is A'B'/AB = 3/1 = 3.

Answer:

Reject H0

Step-by-step explanation:

Given :

H0: The frequencies are equal. H1: The frequencies are not equal

Category f0 A 10 B 30 C 30 D 10

Total f0 = (10 + 30 + 30 + 10) = 80

Expected frequency is the same for all categories :

Expected frequency = 1/4 * 80 = 20

χ² = Σ(observed - Expected)² / Expected

χ² = (10-20)^2 / 20 + (30-20)^2 /20 + (30-20)^2 / 20 + (10-20)^2 / 20

χ² = (5 + 5 + 5 + 5) = 20

Pvalue = 0.00017

Pvalue < α

Answer:

[tex]{ \tt{4 log_{4}(3100) }} \\ = { \tt{4 log_{4}(775 \times 4) }} \\ = { \tt{4 log_{4}(775) + 4 log_{4}(4) }} \\ = { \tt{4( (\frac{ log_{10}775 }{ log_{10}4 } ) +1)}} \\ = { \tt{4(4.8 + 1)}} \\ = { \tt{23.2}}[/tex]

Answer:

C. 6 nights in Washington, 4 nights in Atlanta, and 12 nights in Dallas

Step-by-step explanation:

Answer:

If this is asking for the set:

Z = {-3, -2, -1, 0, 1, 2, 3}

Step-by-step explanation:

Z is the set of all integers and it appears that you are being asked for the values in the set Z that are within the range:  -3 ≤x ≤ 3

Answer:

[tex]x<\frac{6}{5}[/tex]

Refer to picture for number line

Step-by-step explanation:

To solve this inequality, we want to isolate the variable. We can do this my getting like terms onto one side

[tex]6x-7<2-\frac{3x}{2}[/tex]       [add both sides by 7]

[tex]6x<9-\frac{3x}{2}[/tex]             [add both sides by 3x/2]

[tex]6x+\frac{3x}{2}<9[/tex]             [multiply both sides by 2]

[tex]12x+3x<18[/tex]          [add]

[tex]15x<18[/tex]                  [divide both sides by 15]

[tex]x<\frac{18}{15}[/tex]                     [simplify]

[tex]x<\frac{6}{5}[/tex]

Now that we have out inequality, we want to graph it. Since we know that [tex]x<\frac{6}{5}[/tex], that means we have an open circle. Since x is less than, the arrow would be pointing left.

Answer:

Volume is 167.6 yd³

Step-by-step explanation:

[tex]{ \boxed{ \bf{volume = \frac{1}{3}\pi {r}^{2} h}}} \\ { \sf{volume = \frac{1}{3} \times 3.14 \times {(4)}^{2} \times 10}} \\ \\ { \sf{volume = 167.6 \: {yd}^{3} }}[/tex]

Answer:

a) 0.06% probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years.

b) 90.15% probability that 285 or more companies outsourced some part of their manufacturing process in the past two or three years.

c) 0.23% probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years.

Step-by-step explanation:

For questions a and b, the normal approximation to the binomial is used, while for question c, the central limit theorem is used.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years.

This means that [tex]p = 0.54[/tex]

555 of these companies are contacted.

This means that [tex]n = 555[/tex]

Mean and standard deviation: Normal approximation to the binomial:

[tex]\mu = E(X) = np = 555*0.54 = 299.7[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{555*0.54*0.46} = 11.74[/tex]

a. What is the probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years?

Using continuity correction, this is [tex]P(X \geq 338 - 0.5) = P(X \geq 337.5)[/tex], which is 1 subtracted by the p-value of Z when X = 337.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{337.5 - 299.7}{11.74}[/tex]

[tex]Z = 3.22[/tex]

[tex]Z = 3.22[/tex] has a p-value of 0.9994.

1 - 0.9994 = 0.0006

0.0006*100% = 0.06%

0.06% probability that 338 or more companies outsourced some part of their manufacturing process in the past two or three years.

b. What is the probability that 285 or more companies outsourced some part of their manufacturing process in the past two or three years?

Using continuity correction, this is [tex]P(X \geq 285 - 0.5) = P(X \geq 284.5)[/tex], which is 1 subtracted by the p-value of Z when X = 284.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{284.5 - 299.7}{11.74}[/tex]

[tex]Z = -1.29[/tex]

[tex]Z = -1.29[/tex] has a p-value of 0.0985.

1 - 0.0985 = 0.9015

0.9015*100% = 90.15%

90.15% probability that 285 or more companies outsourced some part of their manufacturing process in the past two or three years.

c. What is the probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years?

Now we use the sampling distribution of the sample proportions, which have:

[tex]\mu = p = 0.54[/tex]

[tex]s = \sqrt{\frac{0.54*0.46}{555}} = 0.0212[/tex]

The probability is the p-value of Z when X = 0.48. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.48 - 0.54}{0.0212}[/tex]

[tex]Z = -2.84[/tex]

[tex]Z = -2.84[/tex] has a p-value of 0.0023.

0.0023*100% = 0.23%

0.23% probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two or three years.

Answer:

345 bags and would each have 2

Answer:

The first picture is the solution that I worked out and the second is the graph of the two solutions.

The graph of the solution of inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is as shown below.

"It is a mathematical statement of an order relationship (greater than, greater than or equal to, less than, or less than or equal to) between two numbers or algebraic expressions."

For given question,

We have been given a inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex]

We solve above inequality.

[tex]\Rightarrow -\frac{1}{3} (2x+1) < 3\\\\\Rightarrow \frac{1}{3} (2x+1) > -3\\\\\Rightarrow 2x+1 > -9\\\\\Rightarrow 2x > -10\\\\\Rightarrow x > -5[/tex]

so, the solution of the inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is all points on the X-axis which are greater than x = -5.

The graph of the solution of inequality [tex]-\frac{1}{3} (2x+1) < 3[/tex] is as shown below.

Learn more about the inequality here:

https://brainly.com/question/19003099

#SPJ2