b) How many times would you expect the
spinner to land on a shaded section if it were
spun 40 times?

Answer:

\(\frac{1}{10000} = 0.0001\) probability of a correct guess on the first try.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Only one correct key, so \(D = 1\)

Total outcomes:

4 digits, each with 10 possible outcomes. So

\(T = 10^4 = 10000\)

What is the probability of a correct guess on the first try?

\(p = \frac{D}{T} = \frac{1}{10000} = 0.0001\)

\(\frac{1}{10000} = 0.0001\) probability of a correct guess on the first try.

∵ The form of the linear equation is y = m x + b, where

→ m is the slope of the line

→ b is the y-intercept

∵ The equation is

→ Compare it by the form of the equation above to find the values of m and b

∴ b = -4

∴ m = -3/8

∵ m is the slope

∴ The slope of the line is -3/8

If traveling with the current certain boat went 9 mph against the same boat it only went 1 mph the speed of the current  is 4km/h  and no current is 5km/h.

Let b represent  the speed of the boat

Let c represent  the speed of the current

Downstream:

b + c = 9

Upstream:

b - c = 1

Subtraction

2c = 9-1

2c = 8

Divide both side by 2c

c = 8/2

c = 4 km/h (current)

No current

b = 9 - 4

b = 5 km/h

Therefore the speed is 4km/h and no current is 5km/h.

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Miranda has $130 of discretionary income per month after all her needs are met with the list above. The answer is option D.

To calculate Miranda's discretionary income, we need to first add up her expenses:

$60 + $85 + $195 + $55 + $575 = $970

Next, we need to calculate her monthly income.

Since Miranda gets paid semi-monthly, we'll need to multiply her paycheck amount by 24 (the number of pay periods in a year) and divide by 12 (the number of months in a year):

$550 x 24 / 12 = $1,100

Now we can calculate her discretionary income by subtracting her expenses from her income:

$1,100 - $970 = $130

Therefore, Miranda has $130 of discretionary income per month after all her needs are met with the list above. The answer is option D.

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The statement that supports Cody's reasoning is given as follows:

b. 1/4÷3=1/12 and 1/4 × 1/3=1/12

To divide two fractions, you can use these two following steps:

Hence the division of the fraction 1/4 by the number 3 is given as follows:

(1/4)/3 = 1/4 x 1/3 = 1/12.

Which is the statement given by option B in this problem, and supports Cody's reasoning that dividing a unit fraction by a whole number is the same as multiplying the unit fraction by a unit fraction with the whole number as the denominator.

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Answer:

1. The chi-squared statistic = 10.36

The degrees of freedom = 17

The p-value for the test = 0.89

2. The range of the p-value from the Chi squared table = 0.75 < p-value < 0.90

Step-by-step explanation:

1. The Chi squared test is given as follows;

\(\chi ^{2} = \sum \dfrac{\left (Observed - Expected \right )^{2}}{Expected }\)

Therefore,

                              UTI   No UTI    %     Total

Cranberry juice       8           42      84     50

Lactobacillus          19          30       61     49

Control                    18          30      60    50

The chi-squared statistic is given as follows;

\(\chi ^{2} = \dfrac{\left (8- 18\right )^{2}}{18} + \dfrac{\left (42 - 30\right )^{2}}{30} = 10.36\)

The chi-squared statistic = 10.36

The degrees of freedom, df = 18 - 1 = 17 since the all of the expected count have a minimum value of 18

With the aid of the calculator we find the p value as p as follows;

\(p = 0.9 - \dfrac{10.36 - 10.085}{12.972 - 10.085} \times (0.9 - 0.75)\)

The p-value for the test = 0.89  

2. The range of the p-value from the Chi squared table is given as follows;

0.75 < p-value < 0.90.

The Probability distribution table is;

x P(x)

0 0.4167

1 0.5

2 0.0833

3 0

The speedometers are 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:

P(X = x) = h(x, N, n, k) = C_k,x * C_n - k, n - x)/(C_N,n)

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.

In this question:

7 + 2 = 9 speedometers, which means that N = 9

2 are not correctly calibrated, which means that k = 2

3 are chosen, which means that n =3

Complete the probability distribution table.

Probability of each outcome.

P(X = 0) = h(0, 9, 3, 2) = 0.4167

P(X = 1) = h(1, 9, 3, 2) = 0.5

P(X = 2) = h(0, 9, 3, 2) = 0.0833

P(X = 3) = h(0, 9, 3, 2) = 0

Probability distribution table:

x P(x)

0 0.4167

1 0.5

2 0.0833

3 0

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Answer:

C is 6 / 32 = 3 / 16.

Step-by-step explanation:

The total cost of the paving stones for building a circular patio with a diameter of 12 feet is C. $1,187.

The area of the circular patio using its diameter and pi (22/7) is determined with the formula below.

The unit cost per square foot is multiplied by the area to determine the total cost.

A = π (d/2)^2

The diameter of a circular patio = 12 feet

The area, A = π (d/2)^2

= 22/7(12/2)^2

= 113.14 ft²

The cost per square foot of paving stones = $10.50

The total cost = $1,187.97 ($10.50 x 113.14)

= $1,188

Thus, using the mathematical operation of multiplication, we can conclude that Mr. Aba's project will cost Option C.

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Answer:

+20

we need to consider rules of solving integers

if you + X + = +

- X - = + and + X - = -

Thus we solve it as -(-20)

= +20 or simply 20

Answer:

0.0207 = 2.07% approximate probability of finding at least 157 defects

Step-by-step explanation:

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\lambda\) is the mean in the given interval.

Normal Probability Distribution

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

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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.

n instances of a Poisson distribution can be approximated to a normal distribution, with \(\mu = n\lambda, \sigma = \sqrt{\lambda}\sqrt{n}\)

The average defect rate on a 2010 Volkswagen vehicle was reported to be 1.33 defects per vehicle.

This means that \(\lambda = 1.33\)

Suppose that we inspect 100 Volkswagen vehicles at random.

This means that \(n = 100\)

Mean and standard deviation:

\(\mu = n\lambda = 100*1.33 = 133\)

\(\sigma = \sqrt{\lambda}\sqrt{n} = \sqrt{1.33}\sqrt{100} = 11.53\)

What is the approximate probability of finding at least 157 defects?

Using continuity correction(Poisson is a discrete distribution, normal continuous), this is \(P(X \geq 157 - 0.5) = P(X \geq 156.5)\), which is 1 subtracted by the p-value of Z when X = 156.5. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{156.5 - 133}{11.53}\)

\(Z = 2.04\)

\(Z = 2.04\) has a p-value of 0.9793.

1 - 0.9793 = 0.0207

0.0207 = 2.07% approximate probability of finding at least 157 defects

The set of factors used to factor the given trinomial are -4 and -4. Therefore, option C is the correct answer.

The given trinomial is x²-8x+16.

Factors of 16           Sum of factors

-1 and -16               -1+(-16)=-17

-2 and -8                  -2+(-8)=-10

-4 and -4                  -4+(-4)=-8

The set of factors would used to factor the trinomial are -4 and -4.

Therefore, option C is the correct answer.

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It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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Solution

The final answer

Step-by-step explanation:

=2(20)+2(14)

=2⋅20+2(14)

=40+2(14)

=40+2⋅14

=40+28

=40+28

=68

Answer:

Step-by-step explanation:

P = 2L + 2W

P = 2(20) + 2(14)

P = 40 + 28

P = 68//

Answer:

i can answer that if v and g were representing integers. if not, then then this can`t be solved

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Answer:

a) y=f(x)-2

b) y=f(-x)

Answer:

you got that

Step-by-step explanation:

wet wet wet

Answer:

{ x : x > 2 }

Step-by-step explanation:

4x - 3 + 6x > 5x + 7 , that is

10x - 3 > 5x + 7 ( subtract 5x from both sides )

5x - 3 > 7 ( add 3 to both sides )

5x > 10 ( divide both sides by 5 )

x > 2

That's correct. The rate in the portion formula can be expressed as a decimal, fraction, or percentage, depending on the context and what is most convenient for the problem being solved.

How do you calculate ratio and proportion? Ans: The ratio formula is written as a: b a/b for any two numbers. Contrarily, the percentage formula is written as a:b::c:da:b::c:da:b=cd.

An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls) 1 out of 4 are boys, and 3/ 4 are girls.

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Answer:

37%

$4trillion

$12000

Step-by-step explanation:

Answer:

18-cup jug of water for $3.78

Step-by-step explanation:

3-gallon jug of water for $16.80

3 gallon = 48 cups

16.80 / 48 = $0.35 per cup

18-cup jug of water for $3.78

3.78 / 18 = $0.21 per cup

So, 18-cup jug of water for $3.78 is a better buy.

i) 4 more gallons of petrol will be needed to complete the journey.

ii) The cost of the petrol for the 420 km journey is GH¢55.00.

i) To determine the number of gallons of petrol needed to complete the journey, we can calculate the total distance that can be covered with the available petrol and then subtract it from the total distance of the journey.

Given that the car consumes 1 gallon of petrol for every 30 km, we can calculate the distance that can be covered with 10 gallons of petrol by multiplying 10 (gallons) by 30 (km/gallon):

Distance covered with 10 gallons = 10 * 30 = 300 km

To find the remaining distance that needs to be covered, we subtract the distance covered with the available petrol from the total distance of the journey:

Remaining distance = Total distance - Distance covered with available petrol

Remaining distance = 420 km - 300 km = 120 km

Since the car consumes 1 gallon of petrol for every 30 km, we can determine the additional gallons of petrol needed by dividing the remaining distance by 30:

Additional gallons needed = Remaining distance / 30 = 120 km / 30 km/gallon = 4 gallons

Therefore, the driver will need 4 more gallons of petrol to complete the journey.

ii) To calculate the cost of the petrol for the journey of 420 km, we need to multiply the total number of gallons used for the journey by the cost per gallon.

Given that a gallon of petrol costs GH¢5.50, and the total number of gallons used for the journey is 10 (given in the problem), we can calculate the cost using the formula:

Cost of petrol = Total gallons used * Cost per gallon

Cost of petrol = 10 gallons * GH¢5.50/gallon = GH¢55.00

Therefore, the cost of the petrol for the journey of 420 km is GH¢55.00.

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\(n+11=25\)

Subtract 11 from both sides:

\(n+11-11=25-11\)

\(\boxed{n=14}\)

a) The probability of no orders in 5 minutes is calculated to be 0.36788.

b) The probability of three or more orders in 5 minutes is calculated to be 0.08.

c) The length of the time interval such that the probability of no orders in a time interval of this length is 0.001 is calculated to be 34.5 min.

X is assumed to be the poisson's distribution where λ = 12 orders per hour.

a) At T = 1/12 hours which is 5 min, probability of no orders,

P (X = 0) = e^(-12/12) = 0.36788

b) At T = 1/12 hours which is 5 min, probability of three or more orders,

P (X ≥ 3) = 1 - P (X ≤ 2) = 1 - e⁻¹(1 + 1 + 1/2) = 0.08

c) Let us find the interval T for which:

P (X = 0) = 0.001

e^(-12T) = 0.001

Solving the equation for T we have,

T = -1/12 ln(0.001) = 0.5756 hours = 34.5 min

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Answer:

Step-by-step explanation:

!od

7x=96