Which ordered pairs are on the line with equation 3x-y=2.

a) (0, -2) b) (-3, 4) c) (1, -5)

For this case we must find the solution of the following quadratic equation:

[tex]x ^ 2 + 5x + 7 = 0[/tex]

Where:

[tex]a = 1\\b = 5\\c = 7[/tex]

Then, the solution is given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Substituting the values:

[tex]x = \frac {-5 \pm \sqrt {5 ^ 2-4 (1) (7)}} {2 (1)}\\x = \frac {-5 \pm \sqrt {25-28}} {2}\\x = \frac {-5 \pm \sqrt {-3}} {2}[/tex]

By definition we have:[tex]i ^ 2 = -1[/tex]

[tex]x = \frac {-5 \pm \sqrt {3i ^ 2}} {2}\\x = \frac {-5 \pm i \sqrt {3}} {2}[/tex]

Thus, we have two complex roots.

Answer:

The equation has no real roots.

If you go by division is is eight to nine.

Final answer:

The ratio of threatened species of animals to threatened species of plants in the United States in 2001, expressed in simplest form, is 8:9 or 8/9 after dividing both numbers by their greatest common divisor, which is 16.

Explanation:

The question asks for the ratio of threatened species of animals to threatened species of plants in the United States in 2001, expressed as a fraction in simplest form. To find the ratio, we divide the number of threatened animal species by the number of threatened plant species. The given numbers are 128 threatened animal species and 144 threatened plant species.

To simplify the ratio 128:144, we divide both numbers by their greatest common divisor (GCD). The GCD of 128 and 144 is 16. Thus, dividing both sides of the ratio by 16, we obtain:

128 ÷ 16 = 8

144 ÷ 16 = 9

The simplified form of the ratio is 8:9, or written as a fraction 8/9.

Answer:

c. Stdev

Step-by-step explanation:

Excel stdev function is not appropriate to construct confidence interval estimate, because the estimation of the proportion of defective items that are produced by a certain machine has binomial distribution.

stdev fuction is used for calculating standard deviations where sample has more than two different values. (multinomial)

Norm.s.inv function calculates inverse of the standard normal cumulative distribution, and countif counts the number of cells that meet a criterion. Both functions are used to construct confidence interval estimate

Answer:

t≅13.33h

Step-by-step explanation:

Adam (A) works at constant rate of 50tiles/h

Briana (B) works at constant rate of 55tiles/h, this means that A=50 tiles per hour and B=55 tiles per hour, then A+B = 105tiles/h together, but the floor consists of 1400tiles, so if 105 tiles are installed in one hour, then 1400 tiles in how long they will be installed?

t = 1400tiles*h/105tiles≅ 13.33 h

The degrees of freedom (df) value for a chi-square test for independence is calculated using the formula: df = (number of columns - 1) x (number of rows - 1).

The degrees of freedom (df) value for a chi-square test for independence when both variables are classified into two categories can be calculated using the formula:

df = (number of columns - 1) x (number of rows - 1)

For example, if we have a contingency table with 2 columns and 2 rows, the df value would be:

df = (2 - 1) x (2 - 1) = 1 x 1 = 1

Answer:

  7 1/2 minutes

Step-by-step explanation:

When the time with both faucets is a submultiple of the time with one faucet, you can use this sort of reasoning to figure the missing time.

Filling the tub in 5 minutes is equivalent to having 3 faucets open, each of which can fill the tub in 15 minutes. Since we know the cold water faucet can fill the tub in 15 minutes, the hot water faucet is equivalent to two open 15-minute faucets. That is, it can fill the tub in 15/2 = 7 1/2 minutes.

_____

Perhaps a more conventional way to approach the problem is to consider "tubs per minute." The cold faucet runs at 1/15 tubs per minute, and the two faucets together run at 1/5 tub per minute. Then the hot runs at ...

  (1/5) - (1/15) = (3 -1)/15 = 2/15 . . . tubs per minute

So it will fill 2 tubs in 15 minutes, or 1 tub in 7 1/2 minutes.

Answer:

Step-by-step explanation:

At 4 P.M., the total snowfall is 4 centimeters

Snowfall at 4 P.M = 4 cm

At 7 P.M., the total snow fall is 11 centimeters.

Snowfall at 7 P.M = 11 cm

Duration  = 7 - 4 = 3 hours

Snowfall = 11 - 4 = 7 cm

[tex]\texttt{Mean hourly snowfall = }\frac{\texttt{Snowfall}}{\texttt{Duration}}=\frac{7}{3}cm/hr[/tex]

Mean hourly snowfall = [tex]\frac{7}{3}[/tex] cm/hr

The total number of elements in the union of the four sets is 195.

To find the total number of elements in the union of four sets, we need to subtract the number of elements shared by each pair of sets and the number of elements shared by each three of the sets. Here's the step-by-step calculation:

The total number of elements in the union of the four sets is 400 - 300 + 100 - 5 = 195 elements.

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The number of elements in the union of the four sets is 195.

To determine how many elements are in the union of four sets, we will use the principle of inclusion-exclusion. Let's denote the four sets as A, B, C, and D. According to the problem:

Each set has 100 elements:

|A| = |B| = |C| = |D| = 100

Each pair of sets shares 50 elements:

|A ∩ B| = |A ∩ C| = |A ∩ D| = |B ∩ C| = |B ∩ D| = |C ∩ D| = 50

Each three of the sets share 25 elements:

|A ∩ B ∩ C| = |A ∩ B ∩ D| = |A ∩ C ∩ D| = |B ∩ C ∩ D| = 25

All four sets share 5 elements: |A ∩ B ∩ C ∩ D| = 5

Using the principle of inclusion-exclusion for four sets, we have:

|A ∪ B ∪ C ∪ D| = |A| + |B| + |C| + |D| - (|A ∩ B| + |A ∩ C| + |A ∩ D| + |B ∩ C| + |B ∩ D| + |C ∩ D|) + (|A ∩ B ∩ C| + |A ∩ B ∩ D| + |A ∩ C ∩ D| + |B ∩ C ∩ D|) - |A ∩ B ∩ C ∩ D|

Substituting the given values:

|A ∪ B ∪ C ∪ D| = 100 + 100 + 100 + 100 - (50 + 50 + 50 + 50 + 50 + 50) + (25 + 25 + 25 + 25) -5

Combining these, we get:

|A ∪ B ∪ C ∪ D| = 400 - 300 + 100 - 5 = 195

So, the number of elements in the union of the four sets is 195.

Answer:

11.57 units east, 13.79 units upwards

11.57i + 13.79j

Step-by-step explanation:

V = 18 units at an angle of 50° to the positive x-axis

In component Form, this is how each component is calculated

a = 18cos50° = 11.57 units east

b = 18sin50° = 13.79 units upwards

check if your answer is correct

[tex]\sqrt{11.57^{2} +13.79^{2} } = 18.0[/tex]

In vector component form ai + bj = 11.57i + 13.79j

Answer:

There are 672 seeds in 14 kg of apples

Step-by-step explanation:

2 kg of apples = 1 dozen

1 dozen = 12 apples

So, 2 kg of apples =12 apples

1 kg of apples = [tex]\frac{12}{2} apples[/tex]

1 kg of apples = [tex]6 apples[/tex]

14 kg of apples =[tex]6 \times 14=84 apples [/tex]

Each apples has 8 seeds

So, 84 apples has seeds = [tex]8 \times 84= 672 seeds[/tex]

Hence there are 672 seeds in 14 kg of apples

Apple seeds are in 14 kg of apples is mathematically given as

672 seeds

Question Parameters:

2 kg of apples is 1 dozen and that each apple has 8 seeds. How many apple seeds are in 14 kg of apples

Generally the equation for the   is mathematically given as

2 kg of apples = 1 dozen

1 dozen = 12 apples

Hence

1 kg of apples = 12/2

1 kg of apples = 6

14 kg of apples = 6*14

84 apples has seeds = 8*84

84 apples has seeds = 672

There are 672 seeds in 14 kg of apples

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Answer:

External stakeholder.

Step-by-step explanation:

Radio Plus is invested in this relationship because it generates most of its revenue from advertising Organic Food's products.

In this scenario, Radio Plus is Organic Food Inc.'s - external stakeholder.

External stakeholders are those individuals or companies that do not lie within a business itself, but these care about the business and are affected by the business's performance.

Answer:

C. Savings instrument that requires a desposit for a period of time during which there is a penalty for withdrawals.

Step-by-step explanation:

A Certificate of Deposit is a financial savings product offered by banks. A Certificate of Deposit, also known as a CD, can be obtained from a bank or a credit union.

CDs have a greater interest rate return than savings accounts due the conditions that savings from a CD cannot be withrawn for a fixed period of time. The higher the return the longer the period the savings cannot be withdrawn or the higher the intital investment.

CDs are insured by the Federal Deposit Insurance Corporation (FDIC) and if savings are not needed for a known period of time offer a better return than a savings account.

Answer:

C. Savings instrument that requires a desposit for a period of time during which there is a penalty for withdrawals.

Answer:

[tex]x^2 + x - 72 = 0[/tex]

Explanation:

We are given product of two consecutive odd integers is equal to 72.

Let one integer be x , then since these are consecutive and odd so the other integer will be equal to x + 1.  

Their product is equal to 72. So,

x * (x + 1) = 72

=> [tex]x^2 + x = 72[/tex]

=>  [tex]x^2 + x - 72 = 0[/tex] is the required quadratic equation.

Answer:

a. First derivative

Step-by-step explanation:

To determine the nature of the stationary points:

Either  Find  dy/dx or d2y/dx2

If the result is: positive—the point is a minimum one; negative—the point is a maximum one; zero—the point is a point of inflexion

or

Determine the sign of the gradient of the curve just before and just after the stationary points.

If the sign change for the gradient of the curve is: positive to negative—the point is a maximum one; negative to positive—the point is a minimum one; positive to positive or negative to negative— the point is a point of inflexion

A method for determining whether a critical point is a minimum, maximum, or neither using the slope of the curve is the First Derivative Test (Letter A).

Critical  points  represent the values of x for that f '(x) is zero or the derivative doesn't exist.  Therefore, they represent the only places where a function can have a local minimum, maximum or neither using the slope of the curve. See the rules for this method:

Read more about the First Derivative Test here:

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Answer:

  v = 5cos(73°)i +5sin(73°)j

Step-by-step explanation:

The components of the velocity vector are ...

  horizontal (i direction): 5·cos(73°)

  vertical (j direction): 5·sin(73°)

Then the velocity vector is the sum of these component vectors:

  v = 5cos(73°)i +5sin(73°)j

f(x) = 0.5x   -   money per ticket

g(x) = 8x   -   tickets per hour

We replace g(x) with its value (8x).

f(g(x)) = f(8x)

We replace the x in f(x) with 8x.

f(8x) = 0,5 × 8x

f(8x) = 4x

⇒ f(g(x)) = 4x

Correct answer:

a. f(g(x)) = 4x, which represents the money Aurora made in dollars per hour

Composing functions means to use the output of the inner function as the input for the outer function.

In this case, the inner function is g(x)=8x, which means that Aurora sells 8 tickets per hour.

So, if we give 8x (number of tickets sold) as input to the function f(x)=0.5x, we'll get

[tex]f(x)=0.5x \implies f(8x)=0.5(8x)=4x[/tex]

Since the function f tells us how much Aurora gains per ticket, f(g(x)) basically means:

Aurora gains 0.5 dollars per ticket, and she sells 8 ticket per hour, so she gains 4 dollars per hour.

Answer:

  160°

Step-by-step explanation:

The corresponding exterior angle is 180°-140° = 40°. When the polygon has 2n sides, that angle will be cut in half to 20°. The interior angle of that polygon will be 180°-20° = 160°.

_____

The exterior angles always sum to 360°. Since their sum is a constant, doubling the number of them will cut their measure in half.

To find the size of each interior angle in a regular polygon with 2n sides, when n sides gives 140° each, we use the interior angle formula (n-2) * 180 / n. First, we find n using 140 = (n-2) * 180 / n and substitute n into ((2*n) - 2) * 180 / (2*n) for the result.

The size of each interior angle in a regular polygon is calculated using the formula (n-2) * 180 / n, where n is the number of sides. Given that a polygon with n sides has an interior angle of 140°, we can use this formula to calculate the size of each interior angle in a regular polygon with 2*n sides. The calculation would be: ((2*n) - 2) * 180 / (2*n).

Therefore, to calculate the size of each interior angle in a regular polygon with 2*n sides - if n sides gives 140° each, we must first calculate n using 140 = (n-2) * 180 / n and then substitute n in ((2*n) - 2) * 180 / (2*n) to get the result.

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Answer:

a) [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]

b) [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]

c) [tex]t_{\alpha/2}=-2.11[/tex]

d) [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]

Step-by-step explanation:

Part a

On this case the confidence is 87% or 0.87 so the significance level is [tex]\alpha=1-0.87=0.13[/tex] and [tex]\alpha/2 =0.065[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.

We need values a,b on the normal standard distribution such that:

[tex]P(Z<a)=0.065[/tex] or [tex]P(Z>b)=0.065[/tex] and in order to find it we can use the following code in excel:

"NORM.INV(0.065,0,1)" or "NORM.INV(1-0.065,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.51[/tex] and [tex]z_{\alpha/2}=1.51[/tex]

Part b

On this case the confidence is 92% or 0.92 so the significance level is [tex]\alpha=1-0.92=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we can assume that is a bilateral test or a confidence interval so we will have two critical values.

First we need to calculate the degrees of freedom given by:

[tex]df=n-1=15-1=14[/tex]

We need values b,c on the t distribution with 14 degrees of freddom such that:

[tex]P(t_{(14)}<b)=0.04[/tex] or [tex]P(t_{(14)}>c)=0.04[/tex] and in order to find it we can use the following code in excel:

"T.INV(0.04,14)" or "T.INV(1-0.04,14)", and we see that the critical values [tex]t_{\alpha/2}=-1.89[/tex] and [tex]t_{\alpha/2}=1.89[/tex]

Part c

The significance level is [tex]\alpha=0.025[/tex] and is a left tailed test. On this case we know that is a left tailed test so then we have just one critical value.

First we need to calculate the degrees of freedom given by:

[tex]df=n-1=18-1=17[/tex]

We need a value c on the t distribution with 17 degrees of freddom such that:

[tex]P(t_{(17)}<c)=0.025[/tex], and in order to find it we can use the following code in excel:

"T.INV(0.025,17)", and we see that the critical values [tex]t_{\alpha/2}=-2.11[/tex]

Part d

The significance level is [tex]\alpha=0.08[/tex] and [tex]\alpha/2 =0.04[/tex]. On this case we know that w ehave a two tailed proportion test, so we will have two critical values.

We need values a,b on the normal standard distribution such that:

[tex]P(Z<a)=0.04[/tex] or [tex]P(Z>b)=0.04[/tex] and in order to find it we can use the following code in excel:

"NORM.INV(0.04,0,1)" or "NORM.INV(1-0.04,0,1)", and we see that the critical values [tex]z_{\alpha/2}=-1.75[/tex] and [tex]z_{\alpha/2}=1.75[/tex]

a. The critical value z????/2 for a level of confidence of 87% is approximately 1.475. b. The critical t-value t????/2 for a 92% confidence level and n = 15 is approximately 1.761. c. The critical value for a left-tailed test at α = 0.025 and n = 18 is approximately -2.101. d. The critical value for a two-tailed test of a population proportion with α = 0.08 is approximately 1.755.

a. To find the critical value z????/2 for a level of confidence of 87%, we need to find the z-score that leaves an area of 0.87 in the center. This means the area in each tail is (1 - 0.87) / 2 = 0.065. Using a z-table or calculator, the critical value is approximately 1.475.

b. For a 92% confidence level and a sample size of 15, we need to find the critical t-value t????/2. First, we determine the degrees of freedom, which is n - 1 = 15 - 1 = 14. Using a t-table or calculator, the critical t-value is approximately 1.761.

c. For a left-tailed test at the α = 0.025 level of significance and a sample size of 18, we need to find the critical value. Since the level of significance is α = 0.025, the area in the left tail is 0.025. Using a t-table or calculator, the critical value is approximately -2.101.

d. For a two-tailed test of a population proportion with α = 0.08, we need to find the critical value. Since we have a two-tailed test, we divide α by 2 to get 0.08 / 2 = 0.04. Using a z-table or calculator, the critical value is approximately 1.755.

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Answer:

a)1/4

b)1/2

Step-by-step explanation:

a) The selection is with replacement, then we already have 1 $ bill and in the hat again the four bills. What is the probability  of select 1$ bill ? well it is 1/4.

The point here is,  replacement condition make the second trial totally independent of the first one

b)Following the same reasoning now we have selected a 10 $ bill, and we have two possibles positive outcome a 10 $ and a 20 $ bill and a total of 4 outcomes th th probability is 1/2

The probabilities are:

a) 1/16

b) 1/8.

We assume that all the bills have the same probability of being randomly selected.

a) Then the probability of randomly selecting a $1 bill is equal to the number of $1 bills on the hat divided by the total number of bills.

There is one $1 bill on the hat, and 4 bills in total, so the probability is:

p = 1/4.

Then you return the $1 bill to the hat and want to draw it again, with the same probability as before.

q = 1/4.

The joint probability is the product of the individual probabilities, so we have:

P = p*q = (1/4)*(1/4) = 1/16.

b) There are 2 bills that have a larger value than $5, then the probability for the first draw is:

p = 2/4

For the second draw, we must get the $10 bill, and the probability of getting it is:

q = 1/4.

The joint probability is:

P = p*q = (2/4)*(1/4) = 1/8.

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Answer:

5 i)  Space occupied by 1 ball = 137.26 cubic centimeters

5 ii)  Space occupied by 6 tennis balls =  823.56 cubic centimeters

6 i)  19.2 centimeters

6 ii)  12.8 centimeters

6 iii) 6.4 centimeters

6 iv)  1572.86 cubic centimeters

7.  749.3 cubic centimeters

Step-by-step explanation:

5.

i)

A tennis ball is in a shape of a sphere. The space occupied by 1 tennis ball is the volume of a sphere. The formula is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where

V is the volume and r is the radius (half of diameter)

Given diameter is 6.4 , the radius would be:

r = 6.4/2 = 3.2

Now, we substitute and find the volume:

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (3.2)^3\\V=137.26[/tex]

Space occupied by 1 ball = 137.26 cubic centimeters

ii)

We found space occupied by 1 ball, so space occupied by 6 balls would be 6 times that. So that would be:

Space occupied by 6 tennis balls = 137.26 * 6 = 823.56 cubic centimeters

6.

i)

The length of the box would be 3 diameters lined up. Since the length comprises of 3 balls side by side, we can say that 6 diameters would make up the length of the box, so:

diameter = 6.4

3 diameters = 6.4 * 3 = 19.2 centimeters

ii)

Now, we want the width of the box. That is 2 tennis balls lined up (as seen in the picture). That would be 2 diameters. so:

diameter = 6.4

2 diameters = 6.4 * 2 = 12.8 centimeters

iii)

The height of the box would be the height of 1 balls (see pic). That would be just 1 diameter of the ball. Given:

Diameter = 6.4 cm

So,

Height = 6.4 cm

iv)

The box is a rectangular prism. Which has a capacity (volume) formula as:

Volume = length * width * height

In the first 3 parts of this problem, we found each. Let's multiply each out to find the capacity of the box.

Volume = 19.2 * 12.8 * 6.4 = 1572.86 cubic centimeters

7.

The amount of empty space in the box is the volume of the rectangular box MINUS the volume of all the 6 balls. We have already found:

Volume of Box = 1572.86

Volume of 6 balls = 823.56

Hence,

Empty Space = 1572.86 - 823.56 = 749.3 cubic centimeters

Answer:

[tex]cos^{-1} (\frac{8}{[tex]\sqrt{113}[/tex]} )[/tex]

Step-by-step explanation:

Given two vectors a and b,we are rquired to find the angle between them.

a=(8,7);b=(7,0).

Angle between two vectors can be found by dot product of them.

If a and b are two vectors then the dot product of them is given by|a||b|cos(α).

Where α is the angle between the vectors a and b.

Now [tex]|a|=\sqrt{113}\text{ } and\text{ } |b|=\sqrt{49}[/tex]. and [tex]a.b=8\ times 7+7\times 0[/tex] =56.

Now cosα=[tex]\frac{8}{\sqrt{113} }[/tex] so α= cosine inverse of that.

∴α=

[tex]cos^{-1} (\frac{8}{[tex]\sqrt{113}[/tex]} )[/tex]

Answer:

A local café serves tea, coffee, cookies, scones, and muffins. They recently gathered data about their customers who purchase both a drink and a snack. The given frequency table shows the results of the survey.

If approximately 24% of the customers surveyed have a scone with their tea and approximately 36% of the customers surveyed buy a muffin, complete the column and row headings for the given table.

Step-by-step explanation:

you have a list of conversion factors.Just use them to cancel the unwanted units:246.6ft * 12in/1ft * 6lenthi/39in * 7ganthi/345.6lenthii= (246.6*12*6*7)/(1*39*345.6) ganthii

[tex] \frac{d}{dx} {x}^{2} = 2x \\ x = 0 \\ 2 \times 0 = 0[/tex]

When the derivative equals zero, that point is either the maximum or minimum.

[tex] {x}^{2} \geqslant 0[/tex]

The smallest real value of x² is 0, which is at x = 0.

Hence, x² at x = 0 has both a local and global minimum.

Step-by-step explanation:

y = x²

Find the first derivative:

dy/dx = 2x

Find the critical values by setting dy/dx to 0:

0 = 2x

x = 0

Evaluating the first derivative before and after x=0, we see that dy/dx changes signs from negative to positive.

x < 0, dy/dx < 0

x > 0, dy/dx > 0

That means x=0 is a local minimum.

To find the global minimum, we need evaluate the function at x=0 and at the end points.

x = -∞, y = ∞

x = 0, y = 0

x = ∞, y = ∞

So x=0 is also the global minimum.

The options are not clear but we can describe exponential function as follows

Exponential  function are of the form

[tex]y = b^x \; where\; b >0 = Exponentially\; Growing\\b<0 \; Exponentially\; Decaying \\\\x = Exponent[/tex]

The exponential functions are curved upwards gradually (figure attached )

Figure  1 (graph attached ) Shows the graph of function

[tex]y = 2^x[/tex]

We can   conclude that exponential function is a monotonous function and

depending upon the value of b the exponential function is either continuously increasing or continuously decreasing

[tex]y = -3^x[/tex]

as shown by Figure 2 (figure attached )

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Answer:

It's D

Hopefully this helps someone :D

Answer: $4.30

Step-by-step explanation: if you take 6.09 and subtract 1.79 you will get $4.30

Answer:

230.

Step-by-step explanation:

You have a 50% chance to get heads or tails. So that's half of 490, which is 245. It says estimate, so that means a relative guess. 230 would be the closest.

Final answer:

To estimate the number of times a coin flipped 490 times lands on heads, one should expect approximately half of the flips to be heads, which is about 245. Thus, option B. 230 is the closest estimation.

Explanation:

The question deals with the probability of outcomes when flipping a coin multiple times. When you flip a coin, the probability of it landing on heads is 50 percent each time, irrespective of previous outcomes. Thus, if you flip a coin 490 times, a good estimate for the number of times it will land on heads is roughly half of 490, which is 245. Therefore, the best estimate from the given options would be B. 230, as it is the closest to 245.

Answer:

Step-by-step explanation:

A school has two computer labs and each lan has 30 computers. This means that the total number of computers is the sum of the number of computers in each lab

Total number of computers = 30+30 = 60

A total of six computers in the school or not working.

The expression that can be used to find the number of working computers in the school will be

Let the number of computers that are working be x

the number of computers that are working is total number of computers minus the number of computers that are not working be

The expression that can be used to find the number of working computers in the school will be

x = 60 - 6

x = 54

Answer:

a and b both are true.

Step-by-step explanation:

Given : A coin is tossed 10 times.

To find : True or false, and explain ?

Solution :

(a) The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex]

Coin has two face head and tail.

The probability of getting head is [tex]P(H)=\frac{1}{2}[/tex]

The probability of getting 10 heads in a row is

[tex]P=(P(H))^{10}[/tex]

[tex]P=(\frac{1}{2})^{10}[/tex]

[tex]P=\frac{1}{1024}[/tex]

The chance of getting 10 heads in a row is [tex]\frac{1}{1024}[/tex] is true.

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex].

The probability of getting 10 heads in a row is [tex]P_1=(\frac{1}{2})^{10}[/tex]

The probability of getting 9 tosses were heads is [tex]P_2=(\frac{1}{2})^{9}[/tex]

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is given by,

[tex]P=\frac{P_1}{P_2}[/tex]

[tex]P=\frac{(\frac{1}{2})^{10}}{(\frac{1}{2})^{9}}[/tex]

[tex]P=(\frac{1}{2})^{10-9}[/tex]

[tex]P=\frac{1}{2}[/tex]

Given that the first 9 tosses were heads, the chance of getting 10 heads in a row is [tex]\frac{1}{2}[/tex] is true.

(a) True: The chance of getting 10 heads in a row is [tex]\( \frac{1}{1024} \)[/tex].

(b) True: Given 9 heads, the chance of the 10th being heads remains [tex]\( \frac{1}{2} \).[/tex]

Step 1:

(a) The chance of getting 10 heads in a row:

The probability of getting heads on a single toss of a fair coin is [tex]\( \frac{1}{2} \).[/tex]

Since each toss is independent, the probability of getting 10 heads in a row is calculated by multiplying the individual probabilities:

[tex]\[ \left( \frac{1}{2} \right)^{10} = \frac{1}{1024} \][/tex]

Step 2:

(b) Given that the first 9 tosses were heads, the chance of getting 10 heads in a row:

Since each toss is independent, the probability of getting heads on the 10th toss is still  [tex]\( \frac{1}{2} \).[/tex]

So, the chance of getting 10 heads in a row given the first 9 were heads remains [tex]\( \frac{1}{2} \).[/tex]

Therefore, the calculations support the statements:

(a) The chance of getting 10 heads in a row is indeed [tex]\( \frac{1}{1024} \)[/tex].

(b) Given the first 9 tosses were heads, the chance of getting 10 heads in a row is still [tex]\( \frac{1}{2} \).[/tex]

Answer:

  • 80%

Step-by-step explanation:

Consult your course reference materials.

Advice found on the Internet varies from 70% to 90%, depending on a number of factors. 70% has been a guide historically, but more recent advice favors higher numbers, it seems.