rewrite the expression in the form x^nx n x, start superscript, n, end superscript. \sqrt{x^{^{\scriptsize\dfrac34}}x^{-1}}

A triangle is a three-edged polygon with three vertices. The length of the sides of the triangle is 5, 5, and 5√2.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.

Since the two angles are equal, therefore, the length of the two legs of the isosceles right triangle will be equal and will be less than the hypothenuse.

Hence, the length of the sides of the triangle is 5, 5, and 5√2.

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To find the half-life of a radioactive isotope, one needs to determine the time it takes for the mass of the sample to decay to half of its original value. In this case, the mass of the sample of bismuth-214 decays from 87.7 micrograms to 24.6 micrograms, which is less than half of its original value.

From First order reactions, ln[A]/[B] = kt

Putting the values from the question,

ln[87.7]/[24.6] = k(36.1)

1.271 = k(36.1)

k = 1.271/36.1

= 0.03521 min ⁻¹

t₀.₅ = 0.693/k

    =0.693/0.03521

    = 19.68 minutes.

∴ The half-life of bismuth-214 is 19.68 minutes.

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In the coordinate axis the point D is located at the position of (5,-2) .

In the given graph of the coordinate axis , we can see that the four points A,B,C and D are located

The coordinates of each point are :

A (-5,-2)

B (-2,5)

C (2,-5)

D (5,-2)

Therefore using the given abscissae and ordinate of the points the point that is located at (5,-2) is D.

A coordinate system in geometry is a way to use one or more integers, or coordinates, to determine the exact placement of points or other geometrical objects on a manifold, such Euclidean space.

The order of the coordinates is crucial, and they are frequently identified by their position in an ordered tuple or by a letter, such as "the x-coordinate." The coordinates are often real values in elementary mathematics, but they could also be complex numbers or parts of a more abstract system, such a commutative ring.

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Answer:

The expression "Keep body and soul together" is an idiom, a well-known phrase or collection of words that together mean something distinctly.

Around 1950, family sociologists described a standard marriage pattern at about age 20 for women and age a) 22 for men.

The standard marriage pattern today, based on the time a couple marries, is mid-to-late twenties.  Some marriages are contracted very late, with some in the forties.

Sociologists have pointed out that the current delay in marriages is caused by the higher priority placed on education and career by youths.

However, marriage patterns based on the type of arrangement include:

Traditionally, marriages have served two societal purposes:

Thus, around 1950, family sociologists described a standard marriage pattern at about age 20 for women and age  22 for men.

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Answer:

_______

Step-by-step explanation:

i cant read that sorry :|

Answer:  She needs to sell exactly 173 pies.

Step-by-step explanation: Don't ask me how, but I'll tell you this 1. it wasn't easy and 2. It took me FOREVER. So conclusion- be happy.

Answer:

If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.

45(45) = (2x + 75)(27)

2,025 = (2x + 75)(27)

2x + 75 = 75, so x = 0 and GH = 48

The ratio of Mary's share to Katherine's share to Alex's share is 5:4:1, which means Mary pays 5/10 of the bill, Katherine pays 4/10 of the bill, and Alex pays 1/10 of the bill.

To find the ratio, we can write their contribution as a fraction of the total parts and then solve the fractions then they'll have the same denominator.

So, Mary's share is 5/10, Katherine's share is 4/10, and Alex's share is 1/10.

To convert this as a ratio, we write 5:4:1, where each number represents the number of parts each person pays, and the colon separates each person's contribution.

Therefore, the ratio of Mary's share to Katherine's share to Alex's share is 5:4:1

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Answer:

2 cans

Step-by-step explanation:

1 can = $2

$4 divided by $2 is 2 cans

Compared with the graph of the parent function, an equation which shows only a vertical compression by a scale factor of 1/3 and a shift downward of 4 units is: A. y = 1/3∛x - 4.

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either vertically or horizontally enlarge or reduce (compress) a function representing their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (1/3x, 1/3y)

Where:

In this scenario, the only equation that is vertically compressed by a scale factor of 1/3 and translated (shifted) downward by 4 units is given by:

y = 1/3∛x - 4.

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Answer:

The first part is A

and second part is D

Step-by-step explanation:

100% on edge 2023

Step-by-step explanation:

The three types of Rigid Transformations are Reflection, Rotation, and Translation.

Congruent means equal in all lengths, size and shape.

Rigid transformations are always congruent (or equal) because they never change their form, size or shape. They will always be the same shape and size no matter when it is moved.

They can be congruent when the shape is not different from the original, same size, same length/width, same form.

Dilation is NOT part of a rigid transformation because it widens or decreases its size/shape.

Answer:

15/60

Step-by-step explanation:

10/40 is equivalent to 5/20, and you can multiply the top and bottom of this fraction by 3 to get 15/60

Answer

Step-by-step explanation  find the roots of the equation by solving for x

Answer:

240

Step-by-step explanation:

5.5 x 20 = 110

6.4  x 20 = 130

110 + 130 = 240

Answer:

240 centimeters squared

Answer: god please help the world

Step-by-step explanation: we are struggling

Answer: -6/7p+1/7

Step-by-step explanation: thank god I'm smart lol... I'm a big brain!!!

Answer: ur mom

Step-by-step explanation: is so pretty

A fixed point refers to a type of numerical representation where a certain number of digits are reserved for the integer part of the number, and a certain number of digits are reserved for the decimal part.

In this case, the fixed point needs to occupy a minimum of 8 digits, which means that there will be 6 digits reserved for the integer part of the number, and 2 digits reserved for the decimal part.

The number should also be left-aligned, which means that it will be aligned with the left side of the column or field where it is displayed. This ensures that all numbers are easily readable and comparable.

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Answer:

514,400 plants.

Step-by-step Explanation:

From the attached diagram given below which shows the coordinate grid, we can say the shape of the farm is that of a trapezium.

Number of plants to be planted by the farmer at 40,000 plants per acre = area of land in acres * 40,000.

Let's find the area of the land(trapezium):

Area of trapezium = ½(a+b)*h

From the coordinate grid, from point E to H on the y-axis, we have 900 units = 900 ft (Given that 1 unit = 1 foot).

Also, from F to G, we have 500 units = 500ft; and the height of the trapezium is represented by the number of units the trapezium covers on the x-axis = 800units = 800ft.

a = 900ft, b = 500ft, c= 800ft

==> Area of Land/trapezium = ½(a+b)*h

= ½(900+500)*800

= ½(1400)*800

= 700*800 = 560,000ft²

Given that 1acre = 43,560ft²

x acre = 560,000ft²

x = 560,000*1 /43,560

x = 12.86 acres

Therefore, number of plants to be planted = 12.86 acres * 40,000 plants = 514,400 plants.

We will use the first principle of differentiation, to prove the function.

y = f(x) with respect to its variable x. If this limit exists and is finite, then we say that: Wherever the limit exists is defined to be the derivative of f at x.

Given function cosec x

d(cscx)dx = d(1/sinx)dx

= limh→0 1/sin(x+h)-1/sinx / (x+h)-x

= limh→0 sinx - sin(x + h)/sinxsin(x + h) /h

= limh→0 sinx - sin(x + h) / h sinx sin(x + h)

= limh→0 -(sin(x + h) - sinx)/h sinx sin(x + h)

= limh→0 - (sin(x + h) - sinx)h × 1/limh→0 sinx sin(x + h)

= -cosx × 1/sin2x

= -cosx/sinx × 1/sinx

= -cotx cscx

Therefore, proved the derivative of cosec x to be -cot x cosec x using the first principle of differentiation.

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21 miles per hour is the speed of boat still in water and 9 miles per hour is the speed of current.

Downstream - A boat is said to be moving downstream if it is moving in the same direction as the stream.

Upstream - A boat is said to be moving upstream if it is moving downstream of the stream. The term "upstream speed" in this context refers to the boat's net speed.

13) Given that, a boat traveled 280 miles downstream and back.

Time taken by boat in downstream is 7 hours and in upstream is 14 hours.

Let the speed of a boat be x miles per hour and the speed of a current be y miles per hour.

So, the total speed in downstream is x+y miles per hour and the total speed in upstream is x-y miles per hour.

We know that, Distance = Speed × Time

Now, 280=(x+y)×7

⇒ x+y=40 ------(I)

Here, 280=(x-y)×14

⇒ x-y=20 ------(II)

Add equation (I) and (II), we get

x+y+x-y=40+20

⇒ 2x=60

⇒ x=30 miles per hour

So, x+y=40

⇒ y=10 miles per hour

14) Given that, a boat traveled 252 miles downstream and back.

Time taken by boat in downstream is 12 hours and in upstream is 84 hours.

Let the speed of a boat be p miles per hour and the speed of a current be q miles per hour.

So, the total speed in downstream is p+q miles per hour and the total speed in upstream is p-q miles per hour.

We know that, Distance = Speed × Time

Now, 252=(p+q)×12

⇒ x+y=21 ------(I)

Here, 252=(p-q)×84

⇒ p-q=3 ------(II)

Add equation (I) and (II), we get

p+q+p-q=21+3

⇒ 2p=24

⇒ p=12 miles per hour

So, p+q=21

⇒ q=9 miles per hour

Therefore, the speed of boat still in water is 21 miles per hour and the speed of current is 9 miles per hour.

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The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

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The area of the new square is 128 square feet larger than the area of the original square.

When the side lengths of a square are tripled, the new square will have side lengths of 12 feet (4 feet multiplied by 3). To find the area of the original square, we use the formula A = s^2, where A is the area and s is the side length. Thus, the area of the original square is 4^2 = 16 square feet.

Similarly, the area of the new square with side lengths of 12 feet is 12^2 = 144 square feet. To determine how much larger the area of the new square is than the area of the original square, we subtract the area of the original square from the area of the new square: 144 - 16 = 128 square feet.

Therefore, the area of the new square is 128 square feet larger than the area of the original square. This means that the new square is three times nine times six times larger in terms of area compared to the original square.

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There are 40 people on the team. Each van has 8 number of people, so 5 vans multiplied by 8 people each equals 40 people.

A sports team is divided equally into five vans. Each van has eight people in it. To determine the total number of people on the team, begin by counting the number of people in each van. Since each van has eight people, multiply 8 people by 5 vans to get the total number of people on the team. 8 x 5 = 40. Therefore, there are 40 people on the team. To check the answer, count the total number of people in the five vans. 8 people in each van multiplied by 5 vans equals 40 people. This confirms the answer that there are 40 people on the team.

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a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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The difference between the three variances, Var(x), Var(y), and Var(x + y), can be determined analytically in the context of the bus ridership example.

In the given context, let's consider two variables: x represents the ridership on line l2, and y represents the ridership on line l1. The statement mentions that intuitively, l1 and l2 are not independent, meaning they are related in some way.

To determine the difference between the variances, we need to calculate the variances of x, y, and the sum of x and y, which is x + y.

Var(x): This represents the variance of the ridership on line l2. It quantifies the spread or variability in the data points of x. To calculate Var(x) analytically, you can use the formula: Var(x) = E[(x - μx)^2], where E represents the expectation (mean) operator and μx represents the mean of x.

Var(y): This represents the variance of the ridership on line l1. Similar to Var(x), it quantifies the spread or variability in the data points of y. Var(y) can be calculated using the same formula as Var(x): Var(y) = E[(y - μy)^2], where μy represents the mean of y.

Var(x + y): This represents the variance of the sum of ridership on both lines l1 and l2. It measures the combined variability of the two variables. To calculate Var(x + y), you can use the formula: Var(x + y) = E[(x + y - μ(x + y))^2], where μ(x + y) represents the mean of the sum of x and y.

By analytically calculating the three variances, Var(x), Var(y), and Var(x + y), you can compare them to understand their differences and the relationship between the ridership on line l1 and line l2.

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The equation that could be used to solve for the time t in hours that she drove before her stop is 80t + 100(8/3 - t) = 250.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let t = time she drove before her stop

If the total trip time is 3 hours including the stop, which took 20 minutes, then the time she drove after the stop is 3 - t - 1/3 or 8/3 - t.

If altogether she drove a distance of 250 km, then the sum of the products of the rate of speed and time each drive is equal to 250.

(80 km/h)(t) + (100 km/h)(8/3 - t) = 250

Simplify the equation.

80t + 100(8/3 - t) = 250

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