Here are five spinners with orange and white sectors. Each spinner is divided into equal sectors. A a) b) a) For one of the spinners, the probability of spinning orange is Which spinner is this? B A b) For two of the spinners, the probability of spinning orange is more than 40%. Which two spinners are these? ​

The slope of the line that passes through C(4, 5) and D(9, 5) is (B) Undefined . As The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

Point C (xC,  yC) = (4, 5)

Point D  (xD , yD)= (9, 5)

Slope

m = yD−yC / xD−xC

Slope

m=5-5/9-5=undefined (B)

In mathematics, the slope of a line is the change in y-coordinate with respect to the change in x-coordinate.

The net change in the y coordinate is denoted by Δy and the net change in the x coordinate is denoted by Δx.

Therefore, the change in y-coordinate for a change in x-coordinate is given by The slope of a straight line can also be expressed as follows.

In general, the slope of a line is a measure of its steepness and direction. The slope of the line between two points (x1,y1) and (x2,y2) can be easily determined by finding the difference in the coordinates of the points. The slope is usually represented by the letter 'm'.

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Answer:

54

Step-by-step explanation:

92 (how much his sister has) - 38 (how much he has) = 54 (how much more money his sister has then him)

Answer: His sister had 54 more dollars than him.

Step-by-step explanation: 92 (sister's amount) -38 (Bobby's amount) = 54 (total difference).

Answer:

B. xy(y - x) (y + x)

Step-by-step explanation:

Answer:

A quadratic function can only have one y-intercept.  The y-intercept is also called a zero of the function. The y-intercept is located at the point where the value of y is 0.

Step-by-step explanation:

Answer:

step by step

take v to divide

r=h/v

The mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

To find the mean number of movies the students saw, you need to calculate the average of the given data. Here are the reported numbers of movies seen by the 6 students: 14, 11, 15, 19, 12, 10.

To calculate the mean, you sum up all the reported numbers and divide by the total number of students. In this case, the total number of students is 6.

So, let's calculate the mean:

(14 + 11 + 15 + 19 + 12 + 10) / 6 = 81 / 6 = 13.5

Therefore, the mean number of movies that the students saw is 13.5 (rounded to the nearest tenth).

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Answer:

C. H0 : p = 0.8 H 1 : p ≠ 0.8

The test is:_____.

c. two-tailed

The test statistic is:______p ± z (base alpha by 2) \(\sqrt{\frac{pq}{n} }\)

The p-value is:_____. 0.09887

Based on this we:_____.

B. Reject the null hypothesis.

Step-by-step explanation:

We formulate null and alternative hypotheses as  proportion of people who own cats is significantly different than 80%.

H0 : p = 0.8 H 1 : p ≠ 0.8

The alternative hypothesis H1 is that the 80% of the  proportion is different and null hypothesis is , it is same.

For a two tailed test for significance level = 0.2 we have critical value  ± 1.28.

We have alpha equal to 0.2  for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28

The test statistic is

p ± z (base alpha by 2) \(\sqrt{\frac{pq}{n} }\)

Where p = 0.8 , q = 1-p= 1-0.8= 0.2

n= 200

Putting the values

0.8 ± 1.28 \(\sqrt{\frac{0.8*0.2}{200} }\)

0.8 ± 0.03620

0.8362, 0.7638

As the calculated value of z lies within the critical region  we reject the null hypothesis.

Answer:

1 ×48=48

2×24=48

3×16=48

4×12=48

6×8= 48

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

The numbers are compared with the inequality symbols as follows:

a. 3 > -3.

b. 12 < 24.

c. -12 > -24.

d. 5 = - (-5).

e. 7.2 > 7.

f. -7.2 < 7.

g. -1.5 = -3/2.

h. -4/5 > -5/4.

i. -3/5 = -6/10.

j. -2/3 < 1/3.

The inequality symbols used in this problem are defined as follows:

The observations to some items are given as follows:

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The differential equation dy/dt = y(3-y) smug all of the given conditions.

One possible autonomous differential equation with equilibrium solutions at y=0 and y=3, and with y' > 0 for 0 < y < 3 and y' < 0 for -∞ < y < 0 and 3 < y < ∞, is:

dy/dt = y(3-y)

We can see that y=0 and y=3 are equilibrium solutions by setting dy/dt = 0 and solving for y:

dy/dt = y(3-y) = 0

y = 0 or y = 3

To check the sign of y', we can use the derivative of y(3-y) with respect to y:  d/dy (y(3-y)) = 3 - 2y

For y < 0, we have y(3-y) < 0, so d/dy (y(3-y)) < 0, which says that y' < 0.

For 0 < y < 3, we have y(3-y) > 0, so d/dy (y(3-y)) > 0, which implies that y' > 0.

For y > 3, we have y(3-y) < 0, so d/dy (y(3-y)) < 0, which implies that y' < 0.

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Answer:

.75 i think

Step-by-step explanation:

The graph that represents the given piecewise function has a range of

R: (-∞, 0) ∪ (0,2] ∪ (4, ∞).

A piecewise function is a combination of subfunctions that are defined with different intervals in the domain.

The range of the piecewise function is the union of all the ranges of the subfunctions.

The given piecewise function is

g(x) = x², x < 0

      = 1/2 x, 0 < x ≤ 4

      = x, x > 4

The domain and range for the subfunctions in the given piecewise function are:

for g(x) = x²; Domain is {x < 0} and Range is (-∞, 0)

for g(x) = 1/2 x; Domain is {0 < x ≤ 4} and Range is (0, 2]

for g(x) = x; Domain is {x > 4} and Range is (4, ∞)

Then, the range of the given piecewise function is

Range: (-∞, 0) ∪ (0, 2] ∪ (4, ∞)

Thus, the graph shown in the question is the correct one.

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Answer: c, its da 3rd graph

Step-by-step explanation:

\(x=-2 \implies y=(1/3)^{-2}=3^{2}=9\\\\x=-1 \implies y=(1/3)^{-1}=3\\\\x=0 \implies y=(1/3)^0=1\\ \\ x=1 \implies y=1/3\\\\x=2 \implies y=(1/3)^2 =1/9\)

Using these points, the correct graph is shown in option C.

Answer: -2, 1, all real numbers, all real numbers

Step-by-step explanation:

g o f(n) is basically g(f(n))

Using the question as an example we can get that f(0) = 1 so

g(f(0)) = g(1) = -2

f(1) = 0 so g(f(1)) = g(0) = 1

The domain of f(x) is all real numbers and the range of g(x) is all real numbers

Answer:

1.15%

Step-by-step explanation:

It's asking  would not be a solution soo

(-10, -9) as you can see

You're welcome thank me later

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Total respondent : n(T) = 937

n(male) = 694

n(Female) = 243

n(multiple AFL) = 194

_______________AFL

Male ____694___169

Female __243___ 25

Total____ 937___194

1.) What is the probability that a randomly selected fan has attended multiple games?

n(Multiple AFL) / n(Total)

= 194 / 937

= 0.207

2.) Given that a randomly selected fan has attended multiple games, what is the probability of this person being male?

Male who attended multiple AFL / n(multiple AFL)

= 169 / 194

= 0.871

3- What is the probability of a randomly selected fan being male and having attended multiple games?

Number of males who have attended multiple games / n(Total)

= 169 / 937

= 0.180

4- Given that a randomly selected fan is male, what is the probability that this person has attended multiple games?

Number of males who have attended multiple AFL / n(male)

169 / 694

= 0.2435

5- What is the probability that a randomly selected fan is male or has attended multiple games?

[n(male) + n(multiple AFL)] / n(Total)

(694 + 194) / 937

= 888 / 937

= 0.9477

Answer:

How do you calculate revolving credit?

Image result for Alex opened a $5,000 line of revolving credit at the bank. What is his current available balance if he has already borrowed $2,250 and paid back $1,000 of that amount?

The formula for a revolving line of credit is the balance multiplied by the interest rate, multiplied by the number of days in a given month, all divided by 365 (to represent the number of days in a year).

Step-by-step explanation:

Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.

Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.

Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.

Assuming that the basketball follows a parabolic path, we can use the formula:

y = ax² + bx + c,

where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.

To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.

Therefore, the points on the trajectory of the basketball are:

(0, 1.5), (8.5/2, h), and (8.5, 0),

where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,

we get:

1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)

Simplifying equations (1) and (2),

we get:

c = 1.5...(4)b = -a(8.5)²/8.5...(5)

Substituting equation (4) in equation (3), we get:

h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5

Substituting the value of a from equation (5) in the above equation,

we get:

h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5

Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,

we can use the formula:

x = ut + 0.5at²,

where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.

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Answer:

P’(-1, 1), I’ (1, 2), G’(1,0)

Step-by-step explanation:

The expression represents the volume of the can is 2x³ + 35x² + 176x + 192.

Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. The measurement for volume is in cubic units, such m3.

Expression: (Math Operator, Number/Variable, Math Operator)

We have,

radius = (x + 8) and, height = (2x + 3)

So, Volume of can

= πr²h

= π(x+8)² (2x+3)

= π (x² + 16x + 64) (2x+3)

= π (2x³ + 3x² + 32x² + 48x + 128x + 192)

= π (2x³ + 35x² + 176x + 192)

So, the Expression for volume is 2x³ + 35x² + 176x + 192.

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Answer:

which subject ....

The probability of the event is calculated by taking the probability of the event occurring 0.53, or about 0.03125.

A coin being flipped five times is an example of a Bernoulli trial, which is a type of experiment where the outcome can be either success or failure. The probability of success (a heads) is equal to the probability of failure (a tails). So, for this experiment, the probability of a heads is 0.5 and the probability of a tails is 0.5.

The event of a coin being flipped five times can be expressed as a set in roster notation as {HHHHT, HHHTH, HHTHH, HTHHH, THHHH, HHHTT, HHTTH, HTHHT, THHHT, HTTHH, TTHHH, HHTTT, HTTHT, THHTT, TTHHT, TTTHH, HTTTT, THTTT, TTHTT, TTTHT, TTTTH, TTTTT}.

The probability of the event is calculated by taking the probability of the event occurring (in this case, 0.5 for a heads and 0.5 for a tails) and multiplying it by the number of trials (in this case, 5). This gives us a probability of 0.53, or about 0.03125.

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a) The probability that the computer will be fixed by either A or B is 58%.

b) The probability that it was fixed by B is 57.14%

Given data:

a)

To find the probability that the computer will be fixed by either A or B, we can use the principle of addition for probabilities.

The probability that A can fix the computer is 30% or 0.30, and the probability that B can fix the computer if A cannot is 40% or 0.40.

Therefore, the probability that either A or B can fix the computer is the sum of these probabilities:

P(A or B) = P(A) + P(B if A cannot) = 0.30 + (0.70 * 0.40) = 0.30 + 0.28 = 0.58

Therefore, there is a 58% probability that the computer will be fixed by either A or B.

b)

Let's denote event A as A fixing the computer and event B as B fixing the computer.

P(A) = 0.30 (probability A can fix the computer)

P(B|A') = 0.40 (probability B can fix the computer given that A cannot)

To find P(B|A), the probability that B fixes the computer given that it was fixed, use Bayes' theorem:

P(B|A) = (P(A|B) * P(B)) / P(A)

Since the computer is fixed, P(A) + P(A') = 1, so P(A) = 1 - P(A') = 1 - 0.30 = 0.70

P(B|A) = (P(A|B) * P(B)) / P(A)

P(B|A) = (1 * 0.40) / 0.70

P(B|A) = 0.40 / 0.70

P(B|A) ≈ 0.5714

Hence, if the computer is fixed, there is a 57.14% probability that it was fixed by B.

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Answer:

2.5 years

Step-by-step explanation:

Amount= $8036

Principal= $7000

Rate =5.6%

t= ?

n= 2

A= P(1 + r/n)^nt

8036= 7000(1 + 0.028)^2t

1.148= (1 + 0.028)^2t

log(1.148) = log (1 + 0.028)^2t

0.05994= 2t × 0.01199

t= 2.5 years

It will take t = 2.5 years for the account to grow to $8036.

Given that,

Total saving amount = $7000

Annual rate = 5.6% = 0.056

We have to determine,

Assuming that no withdrawals are made, how long will it take for the account to grow to $8036.

According to the question,

Amount = $8036

Principal = $7000

Rate = 0.056

n = 2

To find the value of time t calculation done in single unit,

\(A = P (1+ \frac{r}{n} )^{nt} \\\\8036 = 7000 (1+\frac{0.056}{2})^{2t} \\\\\frac{8036}{7000} = (1+0.028})^{2t} \\\\1.148 = (1+0.028)^{2t} \\\\\)

Taking log on both sides,

\(log(1.148) = log(1+0.028)^{2} \\\\0.0599 = 2t\times0.0119\\\\\frac{0.599}{0.022} = t\\\\t = 2.5 years\)

Hence, It will take t = 2.5 years for the account to grow to $8036.

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Answer:

947393

Step-by-step explanation:

The expression arcctg(tg(x)) simplifies to arcctg(tan(x)).

To simplify the expression arcctg(tg(x)), we can apply trigonometric identities and properties.

The function arcctg(x) is the inverse cotangent function, which is the angle whose cotangent is x. Similarly, tg(x) represents the tangent function.

First, let's simplify the expression inside the arcctg function, which is tg(x):

tg(x) = sin(x) / cos(x)

Now, we can substitute this value into the original expression:

arcctg(tg(x)) = arcctg(sin(x) / cos(x))

Using the property of inverse trigonometric functions, we can rewrite this as:

arcctg(sin(x) / cos(x)) = arcctg(1 / tan(x))

Now, we can simplify further using the identity:

1 / tan(x) = cot(x)

Therefore:

arcctg(1 / tan(x)) = arcctg(cot(x))

Using another identity, we know that the cotangent function is the reciprocal of the tangent function:

cot(x) = 1 / tan(x)

Therefore, we can simplify the expression to:

arcctg(cot(x)) = arcctg(1 / tan(x)) = arcctg(tan(x))

Finally, we arrive at the simplified expression:

arcctg(tg(x)) = arcctg(tan(x))

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Answer:

2

Step-by-step explanation:

g(x) = 2x - 6

g(4) = 2*4 - 6

g(4) = 2

f(x) = x - 2

f(3) = 3 - 2

f(3) = 1

Thus g (4) / f (3) = 2 / 1 = 2

The value of the function g (4) / f (3) is 2.

Function is a type of relation, or rule, that maps one input to specific single output.

We are given the function as;

f(x)=x-2 and g(x)=2x-6, then we need to find g(4)/f(3)

Therefore, g(x) = 2x - 6

g(4) = 2*4 - 6

g(4) = 2

Similalry,

f(x) = x - 2

f(3) = 3 - 2

f(3) = 1

Thus we have the value of function as

g (4) / f (3) = 2 / 1

g (4) / f (3) = 2

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