How many permutations do I have it I select 4 things from a total of 9 with replacement? (9P4)​

Answer:

w = -4

Step-by-step explanation:

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The resultant of the two vectors or the sum of the two vector is equal to the diagonal of parallelogram.

Parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.

For the given vector a, and vector, the resultant of the two vector is calculated as;

-----------> a  and --------------->b = a + b

The diagram represents the addition of the two vectors, a and b;

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Answer:

1 quarter, 2 dimes, 1 nickel, and 3 pennies can be used to make 82 cents.

Step-by-step explanation:

One possible set of 7 coins that make 82 cents is:

1 quarter (25 cents)

2 dimes (10 cents each)

1 nickel (5 cents)

3 pennies (1 cent each)

Adding up the values of these coins:

25 + 10 + 10 + 5 + 1 + 1 + 1 = 82

Therefore, a set of 1 quarter, 2 dimes, 1 nickel, and 3 pennies can be used to make 82 cents.

Answer:No, X=-3, yly =-4,0,4

Step-by-step explanation:

Answer:

68

Step-by-step explanation:

the median is the term in the middle (53) the upper quartile is the median of the terms above the median. Since there are an even number of terms, you need to average them (58+78)/2

Answer:

The probability of guessing the first genre correctly is 1/10. After guessing the first genre, the probability of guessing the second genre correctly is 1/9. Similarly, the probability of guessing the third genre correctly is 1/8. Therefore, the probability of guessing the top 3 genres correctly and in the correct order is:

1/10 * 1/9 * 1/8 = 1/720

So the exact probability is 1/720, which is already reduced to its simplest form.

Answer:

The answer is 50% or 1/2

Step-by-step explanation:

There are four outcomes on that chart: 1,2,3,3

There are two threes which means 2/4=.5 or 1/2

Answer:

1/2 chance of landing on a 3.

Step-by-step explanation:

Out of the 4 sections on the spinner, 2 of them have the number 3. This means that there is a 2/4 chance that the spinner lands on a three. This fraction can be simplified into 1/2.

Answer:proving that EFGH is a square: points E,F,G,H

separate the sides of the square ABCD into two lines. if AE=BF=CG=DH then

AH=DG=EB=FC and it shows that if we connect the points E,F,G,H to each other with line we will have a square

HAE~EBF~FCG

The IQR of the data set is 4.

First, let's arrange the data set in order from smallest to largest:

1, 2, 3, 5, 6, 6, 6, 7, 9

Next, let's find the median (Q2) of the data set. Since there are an odd number of values in the data set, the median is the middle value:

Q2 = 6

Now, let's find the median (Q1) of the lower half of the data set. This includes the values from the minimum (1) up to (but not including) the median (6). There are four values in this lower half, so the median is the average of the two middle values:

Q1 = (2 + 3) / 2 = 2.5

Finally, let's find the median (Q3) of the upper half of the data set. This includes the values from the median (6) up to (and including) the maximum (9). There are also four values in this upper half, so the median is the average of the two middle values:

Q3 = (7 + 6) / 2 = 6.5

Now that we have Q1, Q2, and Q3, we can calculate the IQR as:

IQR = Q3 - Q1

IQR = 6.5 - 2.5

IQR = 4

Therefore, the IQR of the given data set is 5.5.

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Beth could not join the club because the highest age which is allowed here is only 55 years

We know that;

A statistical expression obtained from a list of data that refers an abnormal gap from other values.

And, The statistical rules that instruct us to divides the data or observation values into four parts.

After analyzing the stem leaf diagram, we noticed the youngest age allowed to join the club is 10 years and the club allow highest 55 years old to join.

the plot also defines that the number of members is declined with the age. There is only person in the club who is 55 years. There are few members with the age over 40 years.

hence, Beth did not join the club because her age was above the highest age that allowed in this club.

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Log₁₆(256b) in terms of the logarithm of b, which is the factor that was multiplied by 256 inside the logarithm is  2 + log₁₆(b)

We can use the product rule of logarithms, which states that the logarithm of a product is equal to the sum of the logarithms of the factors.

Therefore, we can write

log₁₆(256b) = log₁₆(256) + log₁₆(b)

We can simplify log₁₆(256) as follows:

log₁₆(256) = log₁₆(16^2) = 2

Therefore, we have:

log₁₆(256b) = log₁₆(256) + log₁₆(b)

= 2 + log₁₆(b)

So, we have rewritten log₁₆(256b) in terms of the logarithm of b, which is the factor that was multiplied by 256 inside the logarithm.

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The missing length is 11.0818 unit.

We have,

Angle = 52 degree

H = 18

Using Trigonometry

cos 52 = B/H

cos 52 = x / 18

0.615661 = x  /18

x = 11.0818 unit

Thus, the missing length is 11.0818 unit.

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The function of g(x) is 3 ([tex]2^x[/tex]) + 3.

We have,

f(x) = 3 ([tex]2^x[/tex]) -3

Now, the function f(x) have shifted by -3 unit to move 6 unit up.

This means that we have the shifting of

= -3 + 6

= +3 unit

Also, g(x) crosses the y-axis at about 5 or 6 when x=0.

Then, the function of g(x) is

= 3 ([tex]2^x[/tex]) + 3

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Answer:

The correlation coefficient of a data set can be significantly altered by removing an influential point from the data set.

Step-by-step explanation:

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The angle measures for the triangles are given as follows:

Similar triangles are triangles that share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle Z is given as follows:

m < Z + 20 + 105 = 180

m < Z + 125 = 180

m < Z = 55º.

Hence the measures are given as follows:

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The electricity cost for the Val's AC to run for a summer month of 30 days is $84.

Given that,

Val's whole-house central air conditioner uses 4,000 watts when running.

Val runs the AC 7 hours per summer day.

Electricity costs (10 cents)/(1 kilowatt-hour).

Total electricity used for the whole house = 4000 watts = 4 kilowatts

Number of hours that the AC runs = 7 hours

Cost of electricity = (10 cents)/(1 kilowatt-hour).

Cost of electricity for 4 kilowatts for 1 hour = 10 × 4 = 40 cents

Cost of electricity for 4 kilowatts for 7 hours = 40 × 7 = 280 cents

                                                                                       = $2.80

Cost of electricity for a summer month of 30 days = $2.80 × 30

                                                                                   = $84

Hence the total cost for the electricity is $84.

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Answer: A

Step-by-step explanation: -87

namely, what is "t" when f(t) = 2000

[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{f(t)}{2000}=500e^{0.195t}\implies \cfrac{2000}{500}=e^{0.195t}\implies 4=e^{0.195t} \\\\\\ \log_e(4)=\log_e\left( e^{0.195t}\right)\implies \log_e(4)=0.195t\implies \ln(4)=0.195t \\\\\\ \cfrac{\ln(4)}{0.195}=t\implies 7.11\approx t[/tex]

The probability that the sum of the numbers is even is,

⇒ P = 0.47

Since, We know that;

To have this kind of event you can have the following events, where

(d₁ ,d₂),  d1 is the number that appears uppermost on die 1 and d2 is the number that appears uppermost on dice 2:

(1, 1), (1, 3) , (1, 5), (2, 2), (2, 4) (2, 6) (3, 1) (3, 3) (4, 2) (4, 4) (4, 6), (5, 1) (5, 3), (5, 5) (6, 2) (6, 4) (6, 6)

And,  the total number of events is 36 since every dice have 6 numbers.

The probability is:

P(Event)=P(sum is even)/Total number of events

P = 17/36

P = 0.47

Thus, The probability that the sum of the numbers is even is,

⇒ P = 0.47

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The values of the arc length and angles are:

HE = 62

HD = 118

DG = 62

EG = 118

∠DEG + ∠HGE = 62

We have,

The central angle is equal to the intercepted arc length.

So,

62° = HE

And,

∠A = HD

∠A + 62 = 180

∠A = 180 - 62

∠A = 118

HD = 118

And,

DG = ∠M (say)

∠A + 118 = 180

∠M = 180 - 118

∠M = 62

DG = 62

And,

∠A is opposite to ∠N (say)

So,

∠A = ∠N = 118

∠A = EG

EG = 118

And,

From the definition of the exterior angle.

∠DEG + ∠HGE = 62 ______(1)

Also,

The sum of the three angles in AEG = 180

∠EAG + ∠DEG + ∠HGE = 180

∠EAG = 180 - 62 = 118

So,

∠DEG + ∠HGE = 180 - 118

∠DEG + ∠HGE = 62 _______(2)

Thus,

HE = 62

HD = 118

DG = 62

EG = 118

∠DEG + ∠HGE = 62

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The intervals for which each function is decreasing are f(x) = [0, ∝) and g(x) = (-∝, ∝)

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

From the graph of the functions, we can see that

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The meaning of the absolute value of -5.5 is given as follows:

The temperature decreases 5.5 degrees.

The absolute value of a number is the number without the signal, for example:

|-2| = |2| = 2.

The number in this problem is given as follows:

-5.5.

Hence:

Hence the second option is the correct option in the context of this problem.

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Answer:

Rs 2150.81.

Step-by-step explanation:

The interest rate for the first two years is 6% per annum, which is halved for each six-month period. Therefore, the interest for the first two years would be (6950*(1+(0.03))^8) - 6950 = Rs 1373.53.

For the third year, the interest rate is 9% per annum, which is also halved for each six-month period. Therefore, the interest for the third year would be (6950*(1+0.045))^2 - 6950 = Rs 777.28.

Hence, the total compound interest for three years would be Rs 2150.81.

The rate of interest with the given amount and compound interest is 5 percent.

Given that,

After 1 year: compound interest = $30 and total amount=$630.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Here, principal = 630-30=600

630=600(1+r/100)¹

630/600 = 1+r/100

1.05=1+r/100

1.05-1=r/100

0.05=r/100

r=5%

Therefore, the rate of interest with the given amount and compound interest is 5 percent.

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The requreid Mona's phone call was 13 minutes long.

Let's let the variable "m" represent the length of the phone call in minutes.

We know that Mona pays $1.00 for the first call of the day plus $0.15 per minute of the call. So the total cost of the call can be represented by the expression:

$1.00 + $0.15m

We also know that Mona paid $2.95 for her first call today. So we can set the expression for the total cost of the call equal to $2.95:

$1.00 + $0.15m = $2.95

To solve for the length of the call in minutes, we can first subtract $1.00 from both sides of the equation:

$0.15m = $1.95

Then we can divide both sides by $0.15:

m = 13

Therefore, Mona's phone call was 13 minutes long.

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Answer:

To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)

P = monthly deposit

r = annual interest rate (which is 9%)

n = number of times interest is compounded per year (which is 12 for monthly compounding)

t = number of years until retirement (which is 65 - 28 = 37)

Substituting the given values, we get:

1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)

Simplifying and solving for P, we get:

P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)

P ≈ $524.79

Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.

Step-by-step explanation:

The simplified expression for the difference in the areas of Circle A and Circle B is = 12π/(x+2)²

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is [tex]A = \pi r^2[/tex], where r is the radius of the circle. The unit of area is the square unit, for example, [tex]m^2, cm^2, in^2[/tex], etc.

We know that :

The formula of circle's circumference is = 2πr

We have :

Circle A has a circumference of [tex]\frac{8\pi }{x+2}[/tex] units

and Circle B has a circumference [tex]\frac{4\pi }{x+2}[/tex]

Now, First we calculate the area of circle A is:

8π/x+2 = 2πr

r = 8π/x+2 × 1/2π

r = 4/x+2

Area = πr² = (4/x+2)²π

Now, for circle B

4π/x+2 = 2πr

r = 4π/x+2 × 1/2π

r = 2/2x+2

Area =( 2/2x+2)²π

Simplified expression for the difference in the areas of Circle A and Circle B are:

(4/x+2)²π - ( 2/x+2)²π

= π/(x+2)²( 4²-2²)

= π/(x+2)²(16-4)

= 12π/(x+2)²

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The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:

Axis of symmetry, Xmax = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = -2x² - 4x + 12, we have:

Axis of symmetry, Xmax = -(-4)/2(-2)

Axis of symmetry, Xmax = 4/-4 = -1.

For the vertex of f(x) = -2x² - 4x + 12, we have:

f(-1) = -2(-1)² - 4(-1) + 12 = 14.

For the given quadratic function f(x) = x²-4x+3, we have:

Axis of symmetry, Xmax = -(-4)/2(1)

Axis of symmetry, Xmax = 4/2 = 2.

For the vertex of f(x) = x²-4x+3, we have:

f(2) = (2)²-4(2) +3 = -1.

Therefore, 2 is greater than -1.

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Answer:

Since the triangles are similar, their corresponding sides are in proportion. The ratio of sides AB to DE is 9:13.5, which simplifies to 2:3. Therefore, the ratio of their areas is the square of the ratio of their sides, which is 4:9.

If the area of triangle ABC is 34 cm, then the area of triangle DEF is:

Area of DEF = (Area of ABC) x (DE^2/AB^2) = 34 x (13.5^2/9^2) = 34 x 1.5^2 = 34 x 2.25 = 76.5 cm^2

Therefore, the area of triangle DEF is 76.5 cm^2.

Step-by-step explanation: