plz help me solve this. and any song requests

Answer:

B

Step-by-step explanation:

Answer:

its 7/3 . multiplicative inverse is just its opposite

Answer:

You have two variables, and only one condition. It means you have infinite solutions of the form \((t; t^2+5t-7)\). Technically correct, probably not what you want to know.

If you wanted to know if and where the RHS crosses the x axis, the points are the solution to

\(x^2+5x-7= 0 \rightarrow x=\frac12(-5\pm\sqrt{25+28})\\x_1= \frac12(\sqrt{53}-5); x_2=-\frac12(\sqrt{53}+5)\)

If you wanted the graph it's a parabola passing through the two points we just found, (0;-7), and with an axis of equation \(x=-\frac52\).

The null hypothesis for this test is that the mean weight of adult cats of the same breed is equal to 9.0 lb, while the alternative hypothesis is that it is different from 9.0 lb.

In statistical hypothesis testing, the null hypothesis is a statement that is assumed to be true unless there is sufficient evidence to reject it in favor of an alternative hypothesis. In this case, the null hypothesis is that the mean weight of adult cats of the same breed is equal to 9.0 lb, which is what we are trying to test. The alternative hypothesis, on the other hand, is that the mean weight of adult cats of the same breed is different from 9.0 lb, which could be either higher or lower. This is the hypothesis that we would accept if there is sufficient evidence to reject the null hypothesis.

To test these hypotheses, we would need to collect a sample of adult cats of the same breed, measure their weights, and calculate the sample mean. We could then use statistical methods to determine whether the sample mean is significantly different from the hypothesized value of 9.0 lb. If it is, we would reject the null hypothesis in favor of the alternative hypothesis.

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Therefore, the correct a priori reply from Spock would be that the probability of rolling the dice and observing 6 sixes is approximately \(1.6537 x 10^(-8), or 0.000000016537.\)

To calculate the probability, we need to consider the total number of possible outcomes and the number of favorable outcomes. Each die has six possible outcomes, ranging from 1 to 6. Since we have 6 dice, the total number of possible outcomes is \(6^6\)= 46656.

To obtain the number of favorable outcomes, we need to determine the number of ways to roll six sixes. Since there is only one possible outcome of rolling a six on each die, we have\(1^6\)= 1 favorable outcome.

The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes: 1 / 46656 ≈ 1.6537 x \(10^(-8).\)

Therefore, the correct a priori reply from Spock would be that the probability of rolling the dice and observing 6 sixes is approximately \(1.6537 x 10^(-8), or 0.000000016537.\)

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The probability that nadia randomly picks up a reference book and then without replacing it picks up a nonfiction book is 5/136.

Given:

17 total number books out of which 10 are fiction books,2 are reference books , 5 non fiction books.

Number of ways of picking reference book = \(2_C_1\)

Probability of picking a reference book = \(2_C_1/17_C_1\)

= 2/17

The total number of books left on the shelf is 16.

The number of ways in which a non fiction book can be picked after a reference book is already picked = \(5_C_1/16_C_1\)

= 5/16.

Total probability = 2/17*5/17

= 10/272

= 5/136.

Therefore The probability that nadia randomly picks up a reference book and then without replacing it picks up a nonfiction book is 5/136.

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4-1. The probability of drawing a king from the deck will not be affected by the output of the coin toss. The two events are independent of each other, meaning the outcome of one event does not affect the outcome of the other. Therefore, the probability of drawing a king from a deck of 52 cards remains 4/52 or 1/13 regardless of whether the coin landed heads or tails.

4-3. The sample space for two customers choosing from vanilla, chocolate, and strawberry ice cream flavors is:
{VV, VC, VS, CV, CC, CS, SV, SC, SS}
where the first letter represents the first customer's choice and the second letter represents the second customer's choice. V represents vanilla, C represents chocolate, and S represents strawberry.

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Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer:

1. 12 square kilometers

2.18 square inches

Step-by-step explanation:

To find the area of a square you multiply the base and the height. Then you divide it by 2. 8 times 3 divided by 2 is 12. 4 times 9 divided by 2 is 18. Hope this helps!

Answer:

5.25 inches after 5 wks

7 inches after 12 wks

Step-by-step explanation:

after 5 weeks:  y = .25(5) + 4 which is 5.25 inches

after 12 weeks:  y = .25(12) + 4 which is 7 inches

We need to know the percentage of companies in the sample that are likely to require higher employee contributions in order to calculate the confidence interval.

Based on the information provided, we can calculate the margin of error and confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in the upcoming year. First, we need to know the sample size and the percentage of companies in the sample that are likely to require higher employee contributions. Unfortunately, this information is not given in the question. Without this information, it is impossible to calculate the margin of error and confidence interval. We need to know the sample size to determine the standard error of the proportion, which is necessary for calculating the margin of error. Additionally, we need to know the percentage of companies in the sample that are likely to require higher employee contributions in order to calculate the confidence interval.

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The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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Answer:

x=23, y=13

Step-by-step explanation:

x+y=36

x-y=10

23+13=36

23-13=10

Answer:

cos0 = 1

sin30= 1/2

tan0 = 0

Answer:

\(a) cos0^o = 1\\b) sin30^o = \frac{1}{2} \\c) tan0^o =0\)

The length of HG after the dilation by the factor of 2 is 6.6.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

\(D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.\)

We are given that;

The points H(-3,-5) & G(2, 2)

Dilation = 2

Now

D^2= (2+3)^2 + (2+5)^2

D^2= 25+49

D^2= 74

D=8.6

After dilation =8.6-2

=6.6

Therefore, the distance by the given dilation will be 6.6

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middot u5(t)

To find the inverse Laplace transform of the given function F(s) = 5e^-5s/s^2 - 25,

you need to use the Laplace transform formula: L-1{F(s)} = middot u5(t).

The solution is therefore middot u5(t), which can be expressed in terms of t.

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If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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Answer:

9/12 and 10/12

Step-by-step explanation:

Lowest common denominator = Lowest common multiple for denominators only

Lowest common multiple of 4 and 6 is 12

3/4 × 3/3 = 9/12

5/6 × 2/2 = 10/12

So our final answer is

9/12 and 10/12

Hope this helped and have a good day

Answer:

75/100 and 100/120

Step-by-step explanation:

3 × 25 = 75 and 4 × 25 = 100. So 75/100. You can choose any numbers. If i choose 9 by example: 3 × 9 = 27 and 4 × 9 = 36. So 27/36 = 3/4.

The maximum height covered is 32m and the time taken to reach maximum height is 1.25 seconds

Rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then. rate of change = change in y / change in x. Rates of change can be positive or negative.

h(t) = -16\(t^{2}\) +40t + 7

at maximum height the rate of change of h(t) with respect to t is zero.

so \(\frac{dh(t)}{dt}\) = 0

but  \(\frac{dh(t)}{dt}\) =  -32t + 40

so,

-32t + 40 = 0

32t = 40

t = 40/32

t = 1.25

to find h(t), we substitute t = 1.25 into the equation above

h(t) = -16\((1.25)^{2}\) + 40(1.25) + 7

h(t) = 32m

In conclusion, the maximum height reached is 32m and the time taken to reach maximum height is 1.25 seconds

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You can buy 10 songs and 2 albums for your playlist with a budget of $15. Let's assume the cost of each song is $1 and the cost of each album is $5. With a total budget of $15, you can buy a maximum of 15 songs or 3 albums.

However, the playlist can only have a total of 12 items (albums and songs) combined. To maximize the number of items within the given budget and constraint, we need to find a combination that satisfies the equation: 10S + 5A = 15, where S represents the number of songs and A represents the number of albums.

By trying different values, we can see that if we buy 10 songs (10S = 10) and 2 albums (5A = 10), the total cost would be $15 (10 + 10 = 15).

Therefore, you can buy 10 songs and 2 albums for your playlist with a total budget of $15, staying within the limit of 12 items.

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The adjacent sides of rectangle form 90° to each other or are

perpendicular, while the opposite sides are parallel.

The error, is that the coefficient of x, in the four equations can only take on two values, such that if one of the values is m, the other will be \(-\dfrac{1}{m}\)

Reasons:

In a rectangle, the adjacent sides are perpendicular to each other, while

the opposite sides are parallel.

The slope of parallel lines are equal, and the slope, of a line perpendicular to another line with slope, m, is \(-\dfrac{1}{m}\), therefore the slopes of the parallel sides should be equal, which gives;

Therefore;

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a) The length of the base is 10 units and the height is 7 units. The area is 35 square units.

B) The length of the base is 10 units and the height is 6 units. The area is 30 square units.

C) The length of the base is 10 units and the height is 3 units. The area is 15 square units.

D) The length of the base is 4 units and the height is 11 units. The area is 22 square units.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The base and height are highlighted in each triangle.

A)

The length of the base is 10 units.

The length of height is 7 units.

The area of the triangle is 1/2 × 10 × 7 = 35 square units.

B)

The length of the base is 10 units.

The length of height is 6 units.

The area of the triangle is 1/2 × 10 × 6 = 30 square units.

C)

The length of the base is 10 units.

The length of height is 3 units.

The area of the triangle is 1/2 × 10 × 3 = 15 square units.

D)

The length of the base is 11 units.

The length of height is 4 units.

The area of the triangle is 1/2 × 11 × 4 = 22 square units.

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False. A rectangle is conventionally used in a process flowchart to represent a storage area or queue. Triangles are typically used in flowcharts to represent decision points, where a choice must be made between two or more alternatives.

Rectangles are used to represent activities or operations, while arrows connecting the shapes indicate the flow or direction of the process. The use of standardized shapes in flowcharts helps to make them easily understandable and accessible to a wide range of individuals, regardless of their background or experience with the specific process being depicted.

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The radius of the circle is s√3π, which is equal to 3√π. Hence, the answer is option (B).

To calculate the radius of the circle, we need to first calculate the perimeter of the equilateral triangle. The perimeter of an equilateral triangle is equal to 3 times the side length of the triangle. Thus, we can say that the perimeter of the equilateral triangle is 3s.

Now, we need to calculate the area of the circumscribed circle. The area of a circle is equal to π times the square of the radius. Thus, the area of the circumscribed circle is equal to πr2.

Therefore, we can say that 3s = πr2. Solving this equation for r, we get r = s√3π. Thus, the radius of the circle is s√3π, which is equal to 3√π. Hence, the answer is option (B).

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Answer:

I go for I and IV....................

Rounding this to the nearest cent, the balance after 10 years is $1349.86.
To find the balance after 10 years with continuous compounding, we can use the formula for continuous compound interest:

A = P * e^(rt)

Where:
A is the final amount or balance
P is the principal amount (initial deposit)
e is the mathematical constant approximately equal to 2.71828
r is the annual interest rate (in decimal form)
t is the time in years

In this case, the principal amount is $1000, the annual interest rate is 3% (or 0.03 in decimal form), and the time is 10 years.

Substituting these values into the formula, we have:

A = \($1000 * e^(0.03 * 10)\)

Using a calculator, we can evaluate \(e^(0.03 * 10)\) to be approximately 1.3498588076.

Therefore, the balance after 10 years is:

A = $1000 * 1.3498588076

Evaluating this expression, we find that the balance is approximately $1349.86.

Rounding this to the nearest cent, the balance after 10 years is $1349.86.

Note: Continuous compounding is a theoretical concept and not commonly used in practice. However, it allows us to calculate the maximum possible balance that can be achieved with compound interest.

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The total area covered by the track and the area within it is 13024 square meter and the total area of the track is 3714.56 square meter.

Given that, the running track in a stadium is 8 m wide and surrounds a rectangle measuring 100 m by 80 m, with semi-circular ends.

a) The distance around the inside edge of the track = Circumference of two semicircles + 2×length of Rectangle

Circumference of two semicircles = 2πr

= 2×3.14×40

= 251.2

The distance around the inside edge of the track = 251.2+100+100

= 451.2 meters

b) The distance covered by a runner who runs on the outside edge of the track = Circumference of two semicircles + 2×length of Rectangle

Circumference of two semicircles = 2×3.14×48

= 301.44 meters

The distance covered by a runner who runs on the outside edge of the track = 301.44 +108+108

= 517.44 meters

c) The total area covered by the track and the area within it = Area of a rectangle + Area of two semicircles

= 100×80+πr²

= 8000+3.14×40²

= 8000+5024

= 13024 square meter

d) The total area of the track​ = 108×88+3.14×48²- 13024

= 9504+7234.56 -13024

= 16738.56 -13024

= 3714.56 square meter

Therefore, the total area covered by the track and the area within it is 13024 square meter and the total area of the track is 3714.56 square meter.

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Answer:

We know that, if in a distribution one tail is longer than the other, the distribution is skewed.

Here in the given histogram, it has a long right tail which is in the positive direction on the x axis. So it is right skewed distribution. That is also known as positive skewed distribution.

Step-by-step explanation:

So here we have got the required answer. Option C is correct.

Answer:

150

Step-by-step explanation:

First, we can simplify 5³:

5³ = 5 × 5 × 5 = 125

Then, we can simplify 4²:

4² = 4 × 4 = 16

Next, we can simplify √81:

√81 = √(9 × 9) = 9

Finally, we can add these simplified values:

5³ + 4² + √81

= 125 + 16 + 9

= 150

_____

Note:

An exponent shows how many times its base (the big number next to it) should be multiplied by itself.

A square root gives the number that is multiplied by itself to get the number under the root sign.

The solutions for the given conditions are;

a)Twenty people are to be divided into two teams with ten players on each team, this can be done in 184756 ways.

(b)Thirty-five discrete math students are to be divided into seven discussion groups, each consisting of five students, this can be done in \(\frac{35!}{(5!)^7}\)

Here we are given two different cases where we can solve both cases using Combinations.

(a) Twenty people are to be divided into two teams with ten players on each team, this can be done in;

⇒ ²⁰ C ₁₀ * ¹⁰ C ₁₀

= \(\frac{20!}{10! *(20-10)!}\) * 1

= 184,756

(b) Thirty-five discrete math students are to be divided into seven discussion groups, each consisting of five students, this can be done in;

⇒ ³⁵ C ₅ * ³⁰ C ₅ * ²⁵ C ₅ * ²⁰ C ₅ * ¹⁵ C ₅ * ¹⁰ C ₅ * ⁵ C ₅

= \(\frac{35!}{5!(35-5)!}*\frac{30!}{5!(30-5)!}*\frac{25!}{5!(25-5)!}*\frac{20!}{5!(20-5)!}*\frac{15!}{5!(15-5)!}*\frac{10!}{5!(10-5)!}*1\)

= \(\frac{35!}{(5!)^7}\)

Hence;

(a)Twenty people are to be divided into two teams with ten players on each team, this can be done in 184756 ways.

(b)Thirty-five discrete math students are to be divided into seven discussion groups, each consisting of five students, this can be done in \(\frac{35!}{(5!)^7}\)

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