(b) Work out an equation of the straight line that passes through (9, 2) and (3, 5)
[3 marks]

The probability that exactly 4 total launches will be performed until an unsuccessful launch occurs is approximately 0.0720 or 7.2%

The probability of exactly 4 total launches being performed until an unsuccessful launch occurs, we can use the geometric probability formula.

In this case, the probability of a successful launch (p) is 0.7 (since the probability of an unsuccessful launch is 0.3). We want to find the probability of 4 successful launches followed by an unsuccessful launch.

The probability of exactly 4 successful launches followed by an unsuccessful launch can be calculated as follows:

P(4 successful launches followed by an unsuccessful launch) = (p⁴) × (1-p)

P(4 successful launches followed by an unsuccessful launch) = (0.7⁴) × (1-0.7)

P(4 successful launches followed by an unsuccessful launch) = 0.7⁴ × 0.3

P(4 successful launches followed by an unsuccessful launch) = 0.2401 × 0.3

P(4 successful launches followed by an unsuccessful launch) ≈ 0.0720

Therefore, the probability that exactly 4 total launches will be performed until an unsuccessful launch occurs is approximately 0.0720 or 7.2%

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Answer:y=-5x-2

Step-by-step explanation:

Answer:

x=5 y= -7

Step-by-step explanation:

y= -3x +8

-(y= -5x -2)

=> y=-3x+8

-y=5x+2

=> 0=2x+10

=> x=5

=>y=-3(5)+8

=> y= -7

Answer:

3√95

Step-by-step explanation:

Easiest and quickest way to do this is to plug it into your calc. You should get 3√95 when you do so.

Answer:

The square root of 855 is a rational number if 855 is a perfect square. It is an irrational number if it is not a perfect square. Since 855 is not a perfect square, it is an irrational number. This means that the answer to "the square root of 855?" will have an infinite number of decimals. The decimals will not terminate and you cannot make it into an exact fraction.

√855 is an irrational number

Step-by-step explanation:

hope this helps :)

Answer:

C

Step-by-step explanation:

Both students are correct; the slope should be –1, passing through (4, 2) with a y-intercept of 6.

Answer: Its c

Step-by-step explanation:

Both students are correct.

The total square footage (area) of the apartment is 337 square feet.

It is given in the question that, In a small apartment:-

Dimensions of the bedroom = 10 ft by 10ft

Dimensions of the bathroom = 5 ft by 5 ft

Dimensions of the living room/kitchen = 14 ft by 18 ft

We have to find the total square footage (area) of the apartment.

We know that,

Area of square = \(side^2\)

Hence,

Area of the bedroom = 100 square feet

Area of the bathroom = 25 square feet

Area of the living room/ kitchen = 212 square feet

Hence,

Total square footage of the apartment = 100 + 25 + 212 = 337 square feet.

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Answer:

3 ways

Step-by-step explanation:

From the question:

Number of acres of the land = 100 acres

1 cow = 10 acres of land

1 sheep = 3 acres of land

To fully utilize the land, the number of ways to stock the ranch so that it includes at least one cow and at least one sheep is calculated as:

1) 1 cow and 30 sheep

1 cow × 10 acres + 30 sheep × 3 acres

10 + 90 = 100 acres

2) 4 cows and 20 sheep

4 cow × 10 acres + 20 sheep × 3 acres

40 + 60 = 100 acres

3) 7 cows and 10 sheep

7 cow × 10 acres + 10 sheep × 3 acres

70 + 30 = 100 acres

Therefore, to fully utilize the land, the number of ways to stock the ranch so that it includes at least one cow and at least one sheep is 3 ways

Chance is also referred to as probability and the probability that one is blue and one is red is 4/19

probability = Number of event/Total samples space

If there are 10 black socks,20 white socks,2 red socks, and 6 blue socks in a drawer, the total number of socks will be the sample space

Sample space = 10+20+2+6

Sample space = 38

Total number of blue and red socks is the event

Number of event one blue and one red = 8 blue socks

Chance that the socks is blue = n(E)/n(S)

Chance that the socks is one red and one blue  = 8/38

Chance that the socks is red and blue = 4/19

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A ratio in mathematics demonstrates how many times one number is present in another.

15 basketballs

3:1:4= 8

40/8= 5

3*5=15

1*5=5

4*5=20

15:5:20

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Answer:

14 in

Step-by-step explanation:

area cylinder= area of base × height of cylinder

area of cylinder = (pi × radius²) × H

(sub in values )

196×pi = (pi x r²) × 1

(196×pi)/1 = pi × r²

(196×pi)/pi = r²

(pics cancel each other )

then, square root 196= r

14 in = radius

Recall that by definition, the limit of a function

when x approches n is k if as x approches n, f(x) approches k.

As x approaches 2, the values of f(x) approach 7.

The population standard deviation by the square root of the sample size.

According to the central limit theorem, when multiple samples are taken from a population, the mean of the sample means will converge to the population mean.

In this case, if we repeatedly roll a standard die and calculate the mean of each sample, the mean of these sample means will approach 3.5, which is the population mean of the die.

The standard error of the mean is a measure of the variability of the sample means around the population mean. It can be calculated by dividing the population standard deviation by the square root of the sample size.

Since the sample size is not provided, we cannot determine the exact value of the standard error of the mean in this scenario.

In summary, the mean of the sample means will approach 3.5 (the population mean), while the standard error of the mean depends on the sample size and is not specified in this context.

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The expected activity time for the given statement is = 5.33

The average amount of time required for an activity when it is repeatedly performed is known as the expected time. The weighted average of the three estimated times, i.e., the optimistic time, the most probable time, and the pessimistic time, is used in project management analysis to determine the expected time of activity.

A network model called the Program Evaluation and Review Technique (PERT) allows for randomness in the timing of activity completion. PERT was created in the late 1950s again for a massively labor-intensive Polaris project for the US Navy. It might shorten a lot of time and cost needed to finish a project.

optimistic = 2

most likely = 5

pessimistic = 10.

We will use the following formula to calculate the anticipated time for each activity in order to solve this problem:

Expected Time = (Optimistic Time + (4 x Most likely) + Pessimistic Time) / 6

Putting the values into formula:

= (2 + (4 x 5) + 10)/ 6

= (2 + 20 + 10) / 6

= 5.33

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Answer:

Congressman Smith will defeat Challenger Jones

Step-by-step explanation:

Since the poll has a +/- 3% margin of error, the minimum and maximum possible percentages for each candidate are:

(44% - 3%) ≤ Jones ≤ (44% + 3%)

41% ≤ Jones ≤ 47%

(54% - 3%) ≤ Smith ≤ (54% + 3%)

51% ≤ Smith ≤ 57%

This means that, even in the worst possible scenario for Congressman Smith, he would still beat Jones with 51% against 47% of the votes. The pollster can safely predict that Congressman Smith will defeat Challenger Jones .

We can use the properties of the normal distribution to calculate the probability that the total volume shipped is more than 100,000 ft3.

Assuming that the xis are independent with each one having a normal distribution, the total volume shipped can be modeled as the sum of these individual normal distributions. Since the sum of independent normal distributions is also a normal distribution, we can use the properties of the normal distribution to calculate the probability that the total volume shipped is more than 100,000 ft3.

To do this, we need to find the mean and variance of the sum of the xis. The mean of the sum is simply the sum of the means of the individual distributions, while the variance of the sum is the sum of the variances of the individual distributions.

Once we have the mean and variance of the sum, we can standardize the distribution and use a normal probability table or calculator to find the probability that the total volume shipped is more than 100,000 ft3.

In general, the probability of the sum of independent normal distributions exceeding a certain value depends on the number of distributions being summed, their means and variances, and the level of significance chosen for the test. Therefore, we need to specify these parameters to calculate the desired probability.

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Answer:

400 pages in total

Step-by-step explanation:

60 = 15% (2)

120/3 = 30%/3

40= 10%(10)

400=100%

I'm bad at explaining

Answer:

3 to 4

Step-by-step explanation:

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 12 and 16 is 4

Divide both terms by the GCF, 4:

12 ÷ 4 = 3

16 ÷ 4 = 4

The ratio 12 : 16 can be reduced to lowest terms by dividing both terms by the GCF = 4 :

12 : 16 = 3 : 4

Therefore:

12 : 16 = 3 : 4

Answer:

the answer is -3

Step-by-step explanation:

0.7x - 1.4 = -3.5

add 1.4 to both sides of the equation

you're left with 0.7x = -2.1

then divide both sides by 0.7

you're left with your answer of -3

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Answer:

Elga is 32 years old.

Step-by-step explanation:

Let Alvin's age = A

Let Elga's age = E

Alvin is 10 years younger than Elga, so A = E - 10

The sum of their ages is 54, so A + E = 54

Replace the A in the second equation with E - 10, then solve for E.

A + E = 54 becomes (E - 10) + E = 54

Combine like terms

2E - 10 = 54

Add 10 to both sides

2E = 64

Divide both sides by 2

E = 32

The value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.

Any equation of the form \(\rm ax^2+bx+c=0\) where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\(\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}\)

It is given that:

The quadratic equation is:

y² = 144

As we know, the polynomial equation is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

Taking square root on both sides:

y = ±√144

y = ±12

Thus, the value of y is +12 or -12 or y = ±12 if the quadratic equation is y² = 144 option (A) y = ±12 is correct.

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Answer:

0.85x+2.75<=10

Step-by-step explanation:

x is the number of miles he drives

the +2.75 is the flat rate

the <=10 is it must cost no more than 10, it may cost less, or equal, but no more than 10

The minimum magnitude of force \($p_1$\) required to cause the block to move is approximately 0.55 times the weight of the block.

The minimum magnitude of force \($p_1$\) can be calculated using the formula \($p_1 = \mu N$\), where \($\mu$\) is the coefficient of static friction and \($N$\) is the normal force acting on the block. The normal force \($N$\) can be calculated as \($N = mg\cos\theta$\), where \($m$\) is the mass of the block, \($g$\) is the acceleration due to gravity, and \($\theta$\) is the angle of inclination.

The coefficient of static friction can be found using the formula \($\mu = \tan\phi$\), where \($\phi$\) is the angle of friction. For most surfaces, the angle of friction is related to the angle of inclination as $\phi = \arctan(\theta)$.

Substituting the given values, we get:

\($\phi = \arctan(30^o) \approx 0.54$\)

\($N = mg\cos(30^o) = \frac{\sqrt{3}}{2}mg$\)

\($\mu = \tan(0.54) \approx 0.63$\)

\($p_1 = \mu N = 0.63\times\frac{\sqrt{3}}{2}mg \approx 0.55mg$\)

Therefore, the minimum magnitude of force \($p_1$\) required to cause the block to move is approximately 0.55 times the weight of the block.

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Answer:

35

Step-by-step explanation:

each side is longer by 1 cm and every side has 2 corners so it would be 27+8=35

Answer:

Joe has the most money

Step-by-step explanation:

Mike has a balance of -250

Gammy has a balance of -145

Guy has a balance of +300

Joe has a balance of +350

Answer:

k=1

Step-by-step explanation:

\(3k + 8 = 11\\\)

Subtract 8 from both sides

\(3k = 3\)

Divide

\(\frac{3k}{3} = \frac{3}{3}\)

Simplify

\(k =1\)

Answer:

k=1

Step-by-step explanation:

Answer:

-6

Chang the - to -1 cause that’s what is means multiple and get -6