mathematicians divide the world of numbers into at least seven subsets. list seven subsets and define each

Answer:

Step-by-step explanation:

Using a standard normal table, we can find the area under the curve between -2.11 and -0.85.

P(-2.11 < z < -0.85) = P(z < -0.85) - P(z < -2.11)

Using the table, we find:

P(z < -0.85) = 0.1977

P(z < -2.11) = 0.0174

Therefore,

P(-2.11 < z < -0.85) = 0.1977 - 0.0174 = 0.1803

So the probability that a standard normal random variable falls between -2.11 and -0.85 is 0.1803.

Answer:

888.4 mL.

Step-by-step explanation:

To solve this problem, we can use the following formula:

Amount of drug (in mg) = concentration (in mg/mL) × volume (in mL)

We are given the concentration of the drug as 5.315 mg per 3.743 mL. To find the volume of the drug needed to give 4.719 g, we need to rearrange the formula to solve for volume:

Volume (in mL) = amount of drug (in mg) ÷ concentration (in mg/mL)

First, we need to convert 4.719 g to mg by multiplying by 1000:

4.719 g × 1000 mg/g = 4719 mg

Now we can substitute the given concentration and the calculated amount of drug into the formula and solve for volume:

Volume (in mL) = 4719 mg ÷ 5.315 mg/mL

Volume (in mL) ≈ 888.5 mL

Therefore, approximately 888.5 mL of the drug are needed to give 4.719 g. Rounded to 1 decimal, the answer is 888.4 mL.

The value of the probability is 0.3125 and this is proved by the calulations below

The probability of getting exactly 3 heads in 5 coin tosses can be calculated by multiplying the probability of one specific combination of 3 heads and 2 tails by the number of possible combinations.

The probability of one specific combination, for example HHTTT, is (1/2)^5 = 1/32, because each toss has a 1/2 chance of being a head or a tail.

There are 5C3 = 10 possible combinations of 3 heads and 2 tails in 5 tosses.

For example: HHTTT, HTHTT, HTTHT, HTHHT, TTHHH, etc.

Therefore, the probability of getting exactly 3 heads is:

Probability = 10 * (1/32)

Probability = 10/32

Probability = 0.3125.

Hence, the value of the probability is 0.3125.

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Roberto needs 4 square yards of fabric to make his costume.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. For instance, the fraction 7/3 is incorrect since 7 is bigger than 3. Mixed numbers, which combine a whole number and a correct fraction, can be created from improper fractions.

Given that, piece of fabric that is 2 2/3 yards long and 1 1/2 yard wide.

Convert the length from a mixed number to an improper fraction:

2 2/3 = (2 x 3 + 2)/3 = 8/3

1 1/2 = 3/2

The area of the rectangle is:

Area = Length x Width

Substituting the values we have:

Area = (8/3) x (3/2) = 4

Hence, Roberto needs 4 square yards of fabric to make his costume.

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(a) 12 cm 40° : Area of shaded segments = 301.44 sq. cm.

(b) 58° 16 cm ​: Area of shaded segments = 777.04 sq. cm.

Two radii that meet at the center to form a sector define a circle. The sector is the portion of the circle created by these two radii. Knowing a circle's central angle calculation and radius measurement are both crucial for solving circle-related difficulties.

Area of sector of circle = Ф/360 * πr²

π = 3.14

r  is the radius

Ф is the angle subtended.

(a) 12 cm 40°

Area of shaded segments = 40/60 * 3.14* 12²

Area of shaded segments = 40/60 * 452.16

Area of shaded segments = 301.44 sq. cm.

(b) 58° 16 cm ​

Area of shaded segments = 58/60 * 3.14* 16²

Area of shaded segments = 58/60 * 803.84

Area of shaded segments = 777.04 sq. cm.

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The diagram for the question is attached.

Answer: A matrix A of dimension n x n is called invertible if and only if there exists another matrix B of the same dimension, such that AB = BA = I, where I is the identity matrix of the same order.

Step-by-step explanation:

hope it helped! <3

The measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have a given a right angle triangle in the picture

It is required to find the measure of angle A

Applying cos ratio to find the measure of the angle A:

cosA = 9/14

cosA = 0.642

A = 49.99 ≈ 50 degree

Thus, the measure of the angle A is 49.99 degrees or 50 degrees if the length of AB = 14 and AC = 9.

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Answer:

19782m

Step-by-step explanation:

1  revolution = circumference

circumference = π * diameter

π = 3.1416

Then

circumference = 3.1416 * 63

= 197.92m

1 revolution = 197.82m

100 revolutions = 100*197.82m

= 19782m

Answer:

19.8 km

Step-by-step explanation:

To find:-

Answer:-

We are here given that,

We can first find the circumference of the wheel using the formula,

[tex]:\implies \sf C = 2\pi r \\[/tex]

Here radius will be 63/2 as radius is half of diameter. So on substituting the respective values, we have;

[tex]:\implies \sf C = 2\times \dfrac{22}{7}\times \dfrac{63}{2} \ m \\[/tex]

[tex]:\implies \sf C = 198\ m \\[/tex]

Now in one revolution , the cycle will cover a distance of 198m . So in 100 revolutions it will cover,

[tex]:\implies \sf Distance= 198(100)m\\[/tex]

[tex]:\implies \sf Distance = 19800 m \\[/tex]

[tex]:\implies \sf Distance = 19.8 \ km\\[/tex]

Hence the bicycle would cover 19.8 km in 100 revolutions.

Answer:

No diagram provided here

Answer:

C) ∠1 ≅ ∠7

Step-by-step explanation:

If ∠1 = ∠3, then ∠3 = ∠7, behind there is written ∠1 = ∠3, so it's A) ∠1 = ∠7.

Answer: D) Angle R is 65 degrees

Step-by-step explanation:

In the given figure, we have a right-angled triangle PQR.

Using the property of angles in a triangle, we know that the sum of angles in a triangle is 180 degrees. Therefore,

∠QRP + ∠QPR + ∠PRQ = 180 degrees

Since ∠PRQ is a right angle (90 degrees), we have:

∠QRP + ∠QPR = 90 degrees

Now, we are given that ∠QPR is 25 degrees. Substituting this in the above equation, we get:

∠QRP + 25 = 90 degrees

Solving for ∠QRP, we get:

∠QRP = 90 - 25 = 65 degrees

Therefore, the measure of angle R is 65 degrees, which is option (D).

Answer:

Answer is D

Step-by-step explanation:

SPiDerMom is so hot bTw

Parameterizing a surface over a rectangle Parameterizing the surface z = x²+2y² over the rectangular region R defined by -3 ≤ x ≤ 3, −1 ≤ y ≤ 1 are falls under the range of R.

Let's start by expressing x and y as functions of u and v. Since x varies between -3 and 3 over R, we can use the following parameterization for x:

x = u

where u varies between -3 and 3. Similarly, since y varies between -1 and 1 over R, we can use the following parameterization for y:

y = v

where v varies between -1 and 1.

Next, we can use these parameterizations for x and y to express z as a function of u and v. Substituting x = u and y = v into the equation z = x² + 2y², we get:

z = u² + 2v²

So, the parameterization of the surface z = x² + 2y² over the rectangular region R is given by:

x = u, y = v, z = u² + 2v²

where -3 ≤ u ≤ 3 and -1 ≤ v ≤ 1.

The parameterization allows us to study various properties of the surface z = x² + 2y² over the rectangular region R.

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Complete Question:

Parameterizing a surface over a rectangle Parameterizing the surface z = x²+2y² over the rectangular region R defined by -3 ≤ x ≤ 3, −1 ≤ y ≤ 1.

f(x) = (x+4)^2(x-3) has polynomial function with the following zeros: double zero at -4 simple zero at 3.

If a polynomial has a double zero at -4, it means that it can be factored as (x+4)^2.

If it also has a simple zero at 3, then the factorization must include (x-3).

Therefore, the polynomial function with these zeros is :-

f(x) = (x+4)^2(x-3)

This polynomial has a double zero at -4, because $(x+4)^2$ has a zero of order 2 at -4, and a simple zero at 3, because $(x-3)$ has a zero of order 1 at 3.

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Answer:

A

Step-by-step explanation:

∠ o and ∠ z are alternate exterior angles and are congruent, that is

∠ z = ∠ o = 125°

The number of hours it will take the same dog to run 26 1/10 miles is 7.2 hours

7 1/4 miles in 2 hours

26 1/10 miles in x hours

Equate miles ratio hours

7 ¼ miles : 2 hours = 26 ⅒ miles : x hours

7.25 / 2 = 26.10 / x

cross product

7.25 × x = 26.10 × 2

7.25x = 52.20

divide both sides by 7.25

x = 52.20 / 7.25

x = 7.2 hours

Ultimately, it will take 7.2 hours for the dog to run 26⅒ miles.

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Answer:

Answer: B. Symmetric.

Explanation:

In a symmetric distribution, the data is evenly distributed around the mean or median, creating a mirror image on both sides of the center. In this histogram, the median and mean are very close together at 55 and the bars on both sides of the center are roughly equal in height, indicating a fairly even distribution. Therefore, the histogram is symmetric.

Answer:

Step-by-step explanation:

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.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

That is what Slope is.

Answer:

Step-by-step explanation:

Slope :( 1,1)

You start on the y-axis point which is (0,1) as you can see it is going up so I used the “up left” strategy. You go up 1 to the left 1 since the line intersects at point (1,2)

The displacement of the block at any time t is then x= 0.05cos5tm. (option b).

Now, when the block is released, it starts oscillating back and forth about its equilibrium position due to the force exerted by the spring. This motion is described by the equation of motion for a simple harmonic oscillator:

x = Acos(ωt + φ)

The angular frequency ω of the oscillation is given by:

ω = √(k/m)

where k is the spring constant and m is the mass of the block.

Substituting the given values of k and m, we get:

ω = √(50/2) = 5 rad/s

The phase angle φ depends on the initial conditions of the system, i.e., the initial displacement and velocity of the block. Since the block is initially at rest, its initial velocity is zero and the phase angle is zero as well.

Therefore, the equation of motion for the displacement of the block is:

x = 0.05cos(5t)

Hence, option B, x = 0.05cos(5t), is the correct answer.

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The result of the formula  [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is  [tex]-29/2[/tex]  .

When [tex]y = 3[/tex] is used, the value of the expression [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex]  has a value of  [tex]-29/2[/tex] .

To analyse an algebraic expression is to determine its value when a certain number is used in lieu of the variable. To evaluate the expression, we first replace the variable with the given number, then we use the order of operations to simplify the expression.

If  [tex]y = 3[/tex] , we can insert it into the expression & simplify as follows to evaluate   [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for  [tex]y = 3[/tex]  .

[tex]12 - 3(3)^2 + (√4) / (2(3) - 2)[/tex] (y = 3 replacement)

[tex]12 - 27 + 2 / 4\s-15 + 1/2\s-29/2[/tex]

Therefore, The result of the formula  [tex]12 - 3y2 + (v=4) / (2y - 2)[/tex] for y = 3 is  [tex]-29/2[/tex]  .

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The given statement 'to calculate the average of the numeric values in a list  the first step is to get the sum of all the given values ' is a true.

Average of the numeric values in a list,

First step is to get the sum of values in the list.

It is not the total number of values.

Once we have the sum, we can divide it by the number of values to get the average.

Here is an example,

Suppose we have a list of numeric values are as follow,

[2, 4, 6, 8, 10].

To calculate the average of these values, we first find their sum,

2 + 4 + 6 + 8 + 10 = 30

Next,

divide the sum by the number of values in the list

Number of values = 5

30 / 5 = 6

This implies,

The average of the values in the list is 6.

Therefore, to get the average first step is to get the total of all values is true statement.

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In response to the stated question, we may state that The equivalent trigonometry expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.

The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.

tan(A + B) = (tan A + tan B)/(1 - tan A tan B)

Set A = 90 degrees and B = b degrees:

tan(90 + b) = (tan 90 + tan b)/(1 - tan 90 tan b)

tan(90 + b) = (undefined + tan b)/(1 - undefined tan b)

tan(90 + b) = -cot b

7/tan b + 7tan b

= 7/(tan b) + 7(tan(90 + b) - 1)

= 7/(tan b) + 7(-cot b - 1)

= (7 - 7tan b cot b)/sin b

The equivalent expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.

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Therefore , the solution of the given problem of unitary method comes out to be  the attraction sold 943 child tickets and 736 adult tickets on that particular day.

It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.

Here,

Assume the attraction sold x tickets for adults and y tickets for kids.

Based on the supplied data, we can construct the following two equations:

=>  x + y = 1679 (equation 1, representing the total number of tickets sold)

=>  35x + 20y = 44620 (equation 2, representing the total revenue generated)

Using the elimination technique, we can find the values of x and y.

When we divide equation 1 by 20, we obtain:

=>  20x + 20y = 33580 (equation 3)

Equation 3 is obtained by subtracting equation 2 to yield:

=>  15x = 11040

=>  x = 736

When we enter x = 736 into equation 1, we obtain:

=>  736 + y = 1679

=> y = 943

As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.

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Toward the end of a game of Scrabble, you hold the letters D, O, G, and Q. You can choose 3 of these 4 letters and arrange them in order in 24 different ways.

To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we need to find the number of permutations that can be made from the letters D, O, G, and Q when we choose 3 of these 4 letters.

The formula for finding the number of permutations is:

n! / (n-r)!

where n is the total number of objects and r is the number of objects we choose.

Using this formula, we can calculate the number of permutations as follows:

4! / (4-3)!

= 4! / 1!

= 4 x 3 x 2 x 1 / 1

= 24

Therefore, we can arrange the chosen 3 letters in 24 different ways.

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For the equations 2xy - y^2 = 1 and xy + x + y = x^2y^2 using implicit differentiation the value Dxy is given by Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3  respectively.

Equation 2xy - y^2 = 1,

Differentiate both sides of the equation with respect to x,

Treating y as function of x and then differentiate again with respect to x.

Using implicit differentiation,

First, differentiate both sides with respect to x,

2y + 2xy' - 2yy' = 0

Next, solve for y',

⇒2xy' - 2yy' = -2y

⇒y' (2x - 2y) = -2y

⇒y' = -y/(x - y)

Now, differentiate again with respect to x,

y''(x - y) - y'(2x - 2y) = y/(x - y)^2

Substitute the expression we obtained for y' in terms of y and x,

y''(x - y) - (-y/(x - y))(2x - 2y) = y/(x - y)^2

Simplify and solve for y'',

y''(x - y) + (2xy - 3y^2)/(x - y)^2 = 1/(x - y)^2

The expression for Dxy is,

Dxy = (1 - 2xy + 3y^2)/(x - y)^3

For the equation xy + x + y = x^2y^2,

Differentiate both sides of the equation with respect to x,

Using implicit differentiation,

First, differentiate both sides with respect to x,

⇒y + xy' + 1 + y' = 2xyy'

Solve for y',

⇒xy' - 2xyy' + y' = -y - 1

⇒y' (x - 2xy + 1) = -y - 1

⇒y' = -(y + 1)/(x - 2xy + 1)

Now, differentiate again with respect to x,

y''(x - 2xy + 1) - y'(2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2

Substitute the expression we obtained for y' in terms of y and x,

y''(x - 2xy + 1) - (-y - 1)/(x - 2xy + 1)^2 (2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2

Simplify and solve for y''

y''(x - 2xy + 1) - (2y^2 - 2xy - 2y)/(x - 2xy + 1)^2 = (y + 1)/(x - 2xy + 1)^2

The expression for Dxy is,

Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3

Therefore , the value of Dxy using implicit differentiation for two different functions is equal to

Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3

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Answer:b

Step-by-step explanation:

The amount of water that was in the cooler before it started leaking was 6 gallons.

Integration is a mathematical process that involves finding the integral of a function. It is the reverse operation of differentiation, which involves finding the derivative of a function. The integral of a function is a measure of the area under the curve of the function, between two given limits of integration.

The graph shows the rate at which water leaks from the cooler as a function of time, which means that the y-axis represents the rate of leakage in gallons per minute (gal/min), and the x-axis represents the time in minutes.

Since we know that the cooler emptied in 2 minutes, we can integrate the leakage rate over the time interval [0, 2] to find the total amount of water that leaked out:

Total amount of water leaked = ∫[0,2] leakage rate(t) dt

The leakage rate is given by the graph, which consists of a straight line connecting two points: (0,6) and (2,0). We can express this line as a linear equation in slope-intercept form:

leakage rate(t) = mt + b

where m is the slope of the line and b is the y-intercept. To find the slope, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (0,6) and (x2, y2) = (2,0). Plugging in the values, we get:

m = (0 - 6) / (2 - 0) = -3

So the equation of the line is:

leakage rate(t) = -3t + 6

Now we can integrate this equation over the time interval [0, 2] to get the total amount of water leaked:

Total amount of water leaked = ∫[0,2] (-3t + 6) dt

= [-3t²/2 + 6t] from 0 to 2

= (-3(2)²/2 + 6(2)) - (-3(0)²/2 + 6(0))

= (6 - 0) - (0 - 0)

= 6 gallons

Therefore, the amount of water that was in the cooler before it started leaking was 6 gallons.

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The complete question is :

The cost to rent one shed of the rectangular prism shaped shed is $2772.

The size of a section on a surface is determined by its area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent sides. It also goes by the name cuboid. Six faces, each with a rectangle form and twelve edges, make up a rectangular prism. It is referred to as a prism because of the extent of its cross-section.

Volume of prism= BH

where B= area of base and H= height

B= 11*7 = 77 feet²

H= 12 feet

Volume= 77*12=924 cubic feet

Cost =$3 per cubic foot

Total cost= 3*924= $2772

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The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.

Two lines intersect at a location, creating an angle.

An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.

Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.

In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.

An angle has two primary components: the arms and the vertex. T

he two rays' shared vertex serves as their common terminal.

Hence, The measure of the arc intercepted by the angle and the vertical angles make up the angle subtended at the center. As a result, XYZ has a value of 35°.

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