What is the solution of log (3x+2) = log2 (4x-6)?
08
0-6
08
9

Range is R={n^2: n is natural number} U {n(n+1) : n is natural number}

The expression ⌈y⌉⋅⌊y⌋ represents the product of the ceiling and floor functions of y.

To find the range of all possible values of y, we need to consider the possible values of the ceiling and floor functions individually.

1. Ceiling function (⌈y⌉): This function rounds y up to the nearest integer. Since y is greater than 0, the ceiling of y will always be greater than or equal to y.

2. Floor function (⌊y⌋): This function rounds y down to the nearest integer. Again, since y is greater than 0, the floor of y will always be less than or equal to y.

Now, let's consider the product of the ceiling and floor functions, ⌈y⌉⋅⌊y⌋.

The product ⌈y⌉⋅⌊y⌋ will always be greater than or equal to 0 since y > 0 and this can take only integral values.

Therefore, the range of all possible values of y such that ⌈y⌉⋅⌊y⌋ is the set R={n^2: n is natural number} U {n(n+1): n is natural number}

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Answer:

See below:

Step-by-step explanation:

As there doesn't appear to be a full question, I guess you want me to tell you the definition of complementary.

Complementary and Supplementary angles are when angles make up 90 degrees or 180 degrees respectively, the order being:

+ Supplementary Angles are angles that add up to 180 degrees

+ Complementary Angles are angles that add up to 90 degrees.

So in this context, it means that the sum of the degrees of angles 9 and 10 are equal to 90 degrees.

Cheers!

In this simulation, we will represent correct answers as "C" and incorrect answers as "I." The quiz will consist of five true-or-false questions. To find the experimental probability of getting at least three correct answers,

we will repeat the quiz multiple times and keep track of the number of times we obtain three or more correct answers. The experimental probability is then calculated by dividing the number of successful outcomes by the total number of trials.

Running the simulation for a large number of trials, let's say 10,000, we will randomly guess the answers for each question. For each trial, we count the number of correct answers. If the count is three or greater, we consider it a successful outcome.

After running the simulation with 10,000 trials, we record the number of successful outcomes and divide it by the total number of trials. This provides us with the experimental probability of getting at least three correct answers on the quiz when guessing randomly.

By calculating the experimental probability through simulation, we can estimate the likelihood of obtaining three or more correct answers on a five-question true-or-false quiz when guessing randomly.

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Answer:

Step-by-step explanation:

Point M being midpoint of AB means:

\(x_B-x_M=x_M-x_A\qquad\quad\ \wedge\qquad y_B-y_M=y_M-y_A\\\\x_B-(-3)=-3-(-8)\qquad\quad\wedge\quad\quad y_B-3=3-1\\\\x_B=-3+8-3\qquad\qquad\ \wedge\qquad\quad y_B=2+3\\\\x_B=2\qquad\qquad\ \wedge\qquad\qquad y_B=5\)

Answer: |t - 15| ≤ 30 ; -30 ≤ t - 15 ≤ 30

Step-by-step explanation:

To set up the equation, we have to find the center, and the tolerance, so that we can use formula "|x - c| ≤ t"

First, we can find the tolerance by adding both number, then dividing by 2 --> -15 + 45 = 30 --> 30/2 = 15, so we now know that the center is 15

Next, we can find the tolerance by finding the distance between the center and one of the number --> 15 - (-15) = 30, so we now know that the tolerance is 30

Now we can set up our equation,

center (c) = 15

tolerance (t) = 30

|t - 15| ≤ 30

Now that we have our equation, we can set up the inequality

|x - c| ≤ t = -t ≤ x - c ≤ t

so,

-30 ≤ t - 15 ≤ 30

Hope this helps!

(sorry it was so long)

Answer:

34.491

Step-by-step explanation:

Calculator :>

Answer:

34.491

Step-by-step explanation:

To define the event {A < 3}, where A is an exponential random variable with parameter λ = 0.35, we need to specify the range of values for which A is less than 3.

For an exponential random variable, the probability density function (PDF) is given by:

f(x) = λ * e^(-λx), for x ≥ 0

To find the probability of A being less than 3, we need to integrate the PDF from 0 to 3:

P(A < 3) = ∫[0 to 3] λ * e^(-λx) dx

Integrating the above expression gives us the cumulative distribution function (CDF):

F(x) = ∫[0 to x] λ * e^(-λt) dt = 1 - e^(-λx)

Substituting λ = 0.35 and x = 3 into the CDF equation:

F(3) = 1 - e^(-0.35 * 3)

Calculating the value:

F(3) ≈ 0.4866

Therefore, the event {A < 3} has a probability of approximately 0.4866.

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Julie will have $303 to spend after buying the chair

Julie has $237 to spend

She returns a calculator and gets a refund of $128

She then bought a chair of $62

Therefore the amount left to spend after buying the chair can be calculated as follows

(237 + 128) - 62

= 365 - 62

= 303

Hence Julie has $303 left to spend

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Answer:

1) x = 9

2) y = 16

3) y = -1

Step-by-step explanation:

Do PEMDAS in reverse.

For every equation, your goal is to seperate the variable (x,y, or whatever letter) by itself.

1) 2x-7 = 11

Add 7 to both sides.

2x = 18

Divide both sides by 2.

x = 9

2) \(\frac{3}{4}y = 12\)

Divide both sides by 3/4 (which turns into multiplying by 4/3).

Left side

\(\frac{3}{4}x * \frac{4}{3}\\\\\frac{3}{4}x * \frac{4}{3} = \frac{3*4}{4*3}x\\1x\\x\)

Right side

\(12*\frac{4}{3}\\\\\frac{12}{1} *\frac{4}{3}\\\\ \frac{12}{1} *\frac{4}{3} = \frac{12*4}{1*3}\\\\\frac{48}{3} \\16\)

3) 9(y+3) = 18

Remember do PEMDAS in reverse.

Divide both sides by 9.

y+3 = 2

Subtract both sides by 3.

y = -1

a. To calculate the solid angle subtended by the thunderstorm cloud, we can use the formula for the solid angle of a cone-like region given by: Solid Angle = ∫∫ sin(θ) dθ dφ.

In this case, the limits of integration are π/6 < θ < π/2 and 0 < φ < π/8. ∫∫ sin(θ) dθ dφ = ∫(π/8 to π/2) ∫(0 to π/8) sin(θ) dθ dφ. Evaluating this integral will give us the solid angle subtended by the thunderstorm cloud. b. To determine the percentage of the sky occupied by the thunderstorm cloud, we need to calculate the ratio of the solid angle subtended by the cloud to the total solid angle of a full sphere (4π steradians), and then multiply by 100. Percentage of Sky Occupied = (Solid Angle / 4π) * 100.

By substituting the value of the solid angle obtained in part (a) into this formula, we can determine the percentage of the sky occupied by the thunderstorm cloud. Please note that without specific numerical values for the limits of integration, it is not possible to provide a numerical answer in this case.

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Answer:

yeah sure, what you need?

Mullet ratio of 1.5 is 1.8

Given:

The mullet ratio is 1.5

Rm=\(\frac{party}{buisness}\)

Rm = 17/9

Rm=1.8

The ratio to their Mullet and several other higher-level extension questions.

Trimmed short in the front and sides, but left wild and long in the back. Mullet begins the experience with intuition, the lowest rung on the ladder of abstraction, asking students to decide using nothing more than their gut “which one is more Mullet-y” By the end, they’ve named variables and defined operations, entirely abstracting the context.

The pipe cleaner was inserted along the hair, and the students straightened it on their rulers to determine the size of the Party. The Business was often rather honest.

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Answer:

8. the x is always 0

9. (u can graph it, right?) the y is always 0

10. (2,0), (3,1), (4,2), (5,3)

Step-by-step explanation:

Step-by-step explanation:

8 no....the X is 0 .

9no.....after graphing the y is also O in the following

10no....(2,0)(3,1)(4,2)(5,3)

Answer:

B

Step-by-step explanation:

Edge 2021.

A) the probability of scoring 1 is 1/2

B) the probability of scoring a total of 6 is 3/64

The probability of scoring a total of 4 is 17/64

A probability of an occurrence is a number in science that shows how probable the event is to occur. It is represented as a number between 0 and 1, or as a percentage between 0% and 100% in percentage notation.

To compute for A)

Scoring 1 is denoted by P = 4/8 = 1/2

To compute for B)i

All = 8 x 8 = 64

Total of 6 = 3+3
P = 6/64

P = 3/32


To compute for B)ii

Total of 4 = 2 + 2 or 1 + 3 when measured out this given us

P = 17/64

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If a 10 percent cut in price causes a 15 percent increase in sales, then it is likely that the product has an elastic demand. This means that customers are highly responsive to changes in price and are willing to purchase more of the product when it is cheaper.

In this scenario, the decrease in revenue from the price cut may be offset by the increase in sales volume. However, it is important to consider the potential long-term effects on the product's brand value and profitability.

If a 10 percent cut in price causes a 15 percent increase in sales, then:

1. Calculate the new price after the 10 percent cut:
New price = Original price x (1 - 0.10)

2. Calculate the new quantity sold after the 15 percent increase in sales:
New quantity sold = Original quantity sold x (1 + 0.15)

In this scenario, the price elasticity of demand is greater than 1, indicating that the product has elastic demand. This means that a decrease in price will result in a proportionally larger increase in quantity demanded, leading to higher revenue for the seller.

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Answer:

B.

Step-by-step explanation:

First, it must be in descending order (i.e. largest to smallest). Thus, we can eliminate C and D since they go from smallest to largest.

Next, we need to find the degree of A and B. The degree of a polynomial is simply the highest exponent value of all the variables in a single term. If this is confusing, let's use A as an example.

In A, we have four terms: x^3y^3, xy^2, 5xy, and -4. This is a sixth degree polynomial. This is because for the first and largest term, x^3 and y^3, the total value of their exponents is 6. Because of this, A is not our answer.

For B, the biggest term is xy^2, and the degree is 1+2=3. Therefore, our answer is B since it is a third degree polynomial and it's in descending order.

Note that C is also a third-degree polynomial, but it's not written in descending order.

Answer:

The probability of getting a white or green gumball is 35.64%.

Step-by-step explanation:

1. calculate the total number of gumballs in the gumball machine

35 + 22 + 30 + 14 = 101 gumballs

2. calculate the number of white and green gumballs combined

22 + 14 = 36 w/g gumballs

3. divide the number of white and green gumballs combined by the total number of gumballs in the gumball machine

36 / 101 = 0.3564

Answer: the probability of getting a white or green gumball is 35.64% (0.3564).

Probability is the chance of occurring an event from the total possible outcomes.

The probability of getting a white or a green gumball is 57/101.

It is the chance of occurring an event from the total possible outcomes.

We have,

Green gumballs = 35

White gumballs = 22

Purple gumballs = 30

Blue gumballs = 14

Total gumballs = 35 + 22 + 30 + 14 = 101

The combination is given by:

= \(^nC_{r}\)

= n! / r! (n-r)!

The probability of choosing a white gumball:

= \(\frac{^{22}C_{1}}{^{101}C_{1} }\)

= 22 / 101

The probability of choosing a green gumball:

= \(\frac{^{35}C_{1}}{^{101}C_{1} }\)

= 35 / 101

The probability of getting a white or a green gumball:

= 22/101 + 35 / 101

= (22 +35) / 101

= 57 / 101

Thus the probability of getting a white or a green gumball is 57/101.

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Answer:

350m

Step-by-step explanation:

• Capacity= volume/1000

• but we know that the volume of the cylinder is

\(\pi {r}^{2}h\)

so substitute it I'm the volume space

• The substitute for

\(\pi \: as \: \frac{22}{7} \: and \: h \: as \: 1.4 \: and \: also \: capacity \: as \: 539\)

• 539 = ((22/7)× r²× 1.4)/1000

• when you simplify you get r as 350m

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Answer:

A

Step-by-step explanation:

So we have the equation:

\(-15=5a+12-2a+6\)

On the right combine like terms:

\(-15=5a-2a+12+6\\-15=3a+18\)

Subtract 18 from both sides. The right cancels:

\((-15)-18=(3a+18)-18\\-33=3a\)

Divide both sides by 3:

\((-33)/3=(3a)/3\\a=-11\)

The answer is A, -11.

Answer:

a = -11

Step-by-step explanation:

-15 = 5a +12- 2a + 6

Combine like terms

-15 = 3a +18

Subtract 18 from each side

-15-18 = 3a+18-18

-33 = 3a

Divide each side by 3

-33/3 = 3a/3

-11 =a

Answer:

x^3/4.

Step-by-step explanation:

√︎(x) • ∜︎(x)

= x^1/2 * x^1/4

= x^3/4.

The symmetric equations of the normal line to the given surface at point P(2,1,18) are (x - 10/2) = (y - 1/-1) = (z - 18/-5).

Given a surface equation z = 5x² - 2y² and a point P(2,1,18)

Symmetric equation of a normal line can be obtained using the following steps:

Step 1: Finding gradient vector

∇f = (5x, -4y, -1)

At point P(2,1,18) ∇f = (10, -4, -1)

Step 2: Evaluating the gradient vector at point P(2,1,18)(10, -4, -1) evaluated at P(2,1,18) = (20, -4, -1)

Step 3: Writing the equation of the normal line passing through P(2,1,18) with the gradient vector obtained from step 2.

Vector form: r(t) = P + tN

where P = (2,1,18) and N = (20, -4, -1)

Symmetric equation:

x - 2/20 = y - 1/-4 = z - 18/-1

Multiply each fraction by their LCD.

4x - 40 = -10y + 10 = z - 18

We can write this as:

(x - 10/2) = (y - 1/-1) = (z - 18/-5)

These are the symmetric equations of the normal line to the given surface at point P(2,1,18).

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Answer: 4

Step-by-step explanation: 8 times 1 is 8, and 8 divided by 2 is 4.

If the exact answer was 14.016.2163 kilograms each of them miss the exact answer by:

The guess made by Mary was closer

From the question given, the following data were obtained:

Charles guessed thirteen thousand, forty-one and six ten-thousandths kilograms

Mary guessed fourteen thousand, nine hundred ninety-one and twenty-three hundredths kilograms

Writing the guess in figures

Charles: 13 041 . 0006

Mary: 14 991 . 23

Finding how much they missed by subtraction

Charles

= 14,016.2163 -  13 041 . 0006

= 975.2157

Mary

= 14,016.2163 -  14 991 . 23

= 975.0137

Considering how much they missed Mary's guess was closer

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Average Speed is 23/32 laps per minute.

In the given statement is:

Carlos jogged 5 3/4 laps around the school track in 8 minutes.

What is Average speed?

Average Speed is calculated by dividing the total distance travelled by the time interval. For example, Someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph)

Now, According to the Question:

5 3/4laps = 23/4 laps

23/4 ÷8

=23/4 × 1/8

=23/32

So, 23/32 laps per minute

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Answer: g=5

Step-by-step explanation:

To determine the minimum sample size required when you want to be 90% confident that the sample mean is within one unit of the population mean, we can use the formula:

n = [Z*(σ/√n)]^2

where n is the sample size, Z is the Z-score corresponding to the confidence level (90% in this case), σ is the population standard deviation, and √n is the square root of the sample size.

Substituting the given values, we get:

n = [1.645*(12.2/√n)]^2

Simplifying this equation, we get:

n = 22.99

Since we can't have a fractional number of people in a sample, we round up the result to get:

n = 23

Therefore, a sample size of at least 23 is required to be 90% confident that the sample mean is within one unit of the population mean when σ=12.2 and assuming a normal distribution of the population.

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Answer:

They are all trapezoids.

Step-by-step explanation:

We have shown that every element in T also belongs to S∪T. Combining the above arguments, we can conclude that S∪T=T iff S⊆T.

To prove this statement, we need to show that every element in the left-hand side also belongs to the right-hand side and vice versa.

First, consider an element x in S∩(S∪T). This means that x belongs to both S and S∪T. Since S is a subset of S∪T, x must also belong to S. Therefore, we have shown that every element in S∩(S∪T) also belongs to S.

Next, consider an element y in S. Since S is a subset of S∪T, y also belongs to S∪T. Moreover, since y belongs to S, it also belongs to S∩(S∪T). Therefore, we have shown that every element in S belongs to S∩(S∪T).

Combining the above arguments, we can conclude that S∩(S∪T)=S.

Proof of S∪(S∩T)=S:

Similarly, to prove this statement, we need to show that every element in the left-hand side also belongs to the right-hand side and vice versa.

First, consider an element x in S∪(S∩T). There are two cases to consider: either x belongs to S or x belongs to S∩T.

If x belongs to S, then clearly it belongs to S as well. If x belongs to S∩T, then by definition, it belongs to both S and T. Since S is a subset of S∪T, x must also belong to S∪T. Therefore, we have shown that every element in S∪(S∩T) also belongs to S.

Next, consider an element y in S. Since S is a subset of S∪(S∩T), y also belongs to S∪(S∩T). Moreover, since y belongs to S, it also belongs to S∪(S∩T). Therefore, we have shown that every element in S belongs to S∪(S∩T).

Combining the above arguments, we can conclude that S∪(S∩T)=S.

Proof of S∪T=T iff S⊆T:

To prove this statement, we need to show two implications:

If S∪T = T, then S is a subset of T.

If S is a subset of T, then S∪T = T.

For the first implication, assume S∪T = T. We need to show that every element in S also belongs to T. Consider an arbitrary element x in S. Since x belongs to S∪T and S is a subset of S∪T, it follows that x belongs to T. Therefore, we have shown that every element in S also belongs to T, which means that S is a subset of T.

For the second implication, assume S is a subset of T. We need to show that every element in T also belongs to S∪T. Consider an arbitrary element y in T. Since S is a subset of T, y either belongs to S or not. If y belongs to S, then clearly it belongs to S∪T. Otherwise, if y does not belong to S, then y must belong to T\ S (the set of elements in T that are not in S). But since S∪T = T, it follows that y must also belong to S∪T. Therefore, we have shown that every element in T also belongs to S∪T.

Combining the above arguments, we can conclude that S∪T=T iff S⊆T.

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