An equilateral triangle and an isosceles triangle share a common side. What is the measure of ∠ ​ABC?

The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is approximately 0.00000000024 or 0.000000002%.

The probability of four Kings being all next to each other in a well shuffled deck of 52 cards is:

(1/51) * (1/50) * (1/49) * (1/48)

= 0.000000000077 or 0.00000077%

The probability of four Queens being all next to each other in a well shuffled deck of 52 cards is:

(1/51) * (1/50) * (1/49) * (1/48)

= 0.000000000077 or 0.00000077%

The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is:

0.000000000077 * 0.000000000077

= 0.00000000024 or 0.000000002%

The probability of four Kings and four Queens being all next to each other in a well shuffled deck of 52 cards is very small, approximately 0.00000000024 or 0.000000002%. This is because there are many other combinations of cards that can occur in a shuffled deck.

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Answer: A. [tex]4[/tex]

Step-by-step explanation:

Since the points have the same [tex]y[/tex]-coordinate, take the absolute value of the difference of the [tex]x[/tex]-coordinates. Doing so yields [tex]|-4-0|=4[/tex].

The equation of a line passing through (10,10) that is perpendicular to the line with equation 5x + 8y = -9 is y - 10 = (8/5)(x - 10) or y = (8/5)x - 6.

Get the slope of the line 5x + 8y = -9 by rewriting it in slope-intercept form. Subtract 5x from both sides and divide by 8.

y = (-5/8)x - (9/8)

The slope of this line is -5/8. The negative reciprocal of -5/8 is 8/5. Therefore, the slope of the line that is perpendicular to 5x + 8y = -9 is 8/5.

Using point-slope form, determine the equation of the line.

y - y₁ = m(x - x₁)

y - 10 = (8/5)(x - 10)

or using the slope-intercept form,

y = mx + b

y = (8/5)x + b

10 = (8/5)10 + b

b = -6

y = (8/5)x - 6

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Answer:

The y-intercept is 450, and it represents how much money he has in his account when he starts out with 0 essays proofread

Step-by-step explanation:

Looking at the standard slope-intercept equation, we see:

y = mx + b

Where b is the y-intercept. In our equation, our b is replaced by 450:

y = 15x + 450

So, the y-intercept is 450, and it represents how much money he has in his account when he starts out with 0 essays proofread.

Hope this helped!

We select every fifth invoice in a file is systematic sampling.

'What is systemic sampling?'

Systematic sampling is a probability sampling technique where researchers choose individuals from the population at predetermined intervals (or k).

This method will provide you with a representative sample that can be utilized to make inferences about your community of interest if the population order is random or random-looking (for example, alphabetical).

Simple random sampling has numerous advantages over systematic sampling in terms of randomization, but systematic sampling is a little bit simpler to carry out. Similar to basic random sampling, systematic sampling can be used using a list of every member of the population. Contrary to simple random sampling, however, you can also utilize this strategy if you don't have access to a list of your population in advance.

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Check the picture below.

(8, 3) is the point that is two-thirds segment of the way from point $r$ to point $s$, we can use the following method:

initially to get the difference between the x-coordinates of points $r$ and $s$, and multiply the values  by 2/3. let us consider that value as  $dx$.

and to get the difference between the y-coordinates of points $r$ and $s$, and multiply it by 2/3. let us assume the value as  $dy$. then add $dx$ to the x-coordinate of point $r$ and $dy$ to the y-coordinate of point $r$.on doing certain operations we get as:

hence the  coordinates of the point at two-thirds of the way from $r$ to $s$ is $(x,y)$ can be established as

x = -6 + (15 - (-6))(2/3) = -6 + 21(2/3) = -6 + 14 = 8

y = 19 + (-5 - 19)(2/3) = 19 - 24(2/3) = 19 - 16 = 3

therefore  the point two-thirds of the distance from point $r$ to point $s$ is (8, 3).

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Pat left the office at 10:50 am.

What is the relation between speed, distance, and time?

The relation between speed, distance, and time would be

distance = speed x time

We know that Pat had a 12:30 pm appointment 72 miles from his office, arrived ten minutes late, and averaged 48 mph for the trip. So we can set up the equation as:

distance = speed x time

72 = 48 x time

To solve for time, we divide both sides of the equation by 48:

time = distance / speed

time = 72 / 48

time = 1.5 hours

Since Pat arrived 10 minutes late, we need to subtract that 10 minutes from the time it took him to get to the appointment

12:30pm - 00:10 = 12:20 pm

Now, we have to subtract the time it took Pat to get to the appointment from the time he left the office

12:20 pm - 1.5 hours = 10:50 am

So Pat left the office at 10:50 am.

Hence, Pat left the office at 10:50 am.

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Answer:

let the 2 unknown numbers be 'x' and 'y'

given: x+y=15 - equation 1

5x-3y=19 - equation 2

from equation 1 :

x = 15 -y

substitute this in equation 2

5(15-y) -3y = 19

75 - 5y - 3y = 19

75-8y=19

8y=56

y=7(substitute value of y in equation 1)

x+7=15

x=8

hence the two numbers are 8 and 7

Answer:

x = 8

y = 7

Step-by-step explanation:

let's assume the first number as x, and the second number as y

Now, according to the question,

x + y = 15

Moving on to the next statement,

five times the first number = 5x

three times the second number = 3y

Thus,

5x  - 3y = 19

Now that we have two equations, we can either write 'x' in 'y' terms, or y in 'x' terms.

For example, from the first equation:

x + y = 15

y = 15 - x

Now, let's put this value of y into the second equation, i.e.

5x - 3(15 - x) = 19

5x - 45 +3x = 19

8x = 19 + 45

x = 64/8

x = 8

Now, let's put this value of x into the first equation, i.e.

x + y = 15

8 + y = 15

y = 7

In conclusion, the two numbers, x and y, are 8 and 7 respectively

Yes, a function can have 3 roots. This means that the function has 3 values of x where the y value is equal to 0. A polynomial of degree 3 or higher can have 3 roots.

Yes, a function can have 3 roots. A root of a function is a value of x for which the y value of the function is 0. This means that when a function has 3 roots, it has 3 values of x for which the y value of the function is 0. To have 3 roots, the function must be a polynomial of degree 3 or higher. A polynomial of degree 3 is usually written in the form ax^3 + bx^2 + cx + d = 0. This equation can be solved using the quadratic formula to find the 3 roots, which will be the 3 values of x for which the y value of the function is 0. The roots of the polynomial can also be found graphically by plotting the polynomial and finding where it intersects with the x-axis. This will be the 3 roots of the function.

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The ordered set pairs (-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11),

is not a function. Because one x value corresponds to two different y values.

Given a set of ordered pairs (-2, 2), (-1, 2), (3, -1), (3, 1), (4, 11),

Function is special relations that pair each member of set A (domain) with exactly one member of set B (codomain).

Discuss the options provided.

a. yes, because there are two x values that are the same that is 3. Then the statement is false, the value of x cannot be the same.

b yes, because every x value corresponds to exactly one y-value. Then the statement is false.

c. no, because two of the y-values are the same. Then the statement is false.

d. no, because one xvalue corresponds to two different y-values. Then the statement is true.

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The solution of u in the equation where u is a real number is -10.

In the number system, real numbers are only the fusion of rational and irrational numbers. These numbers can generally be used for all arithmetic operations and can also be expressed on a number line. Imaginary numbers, which are often known as unreal numbers since they cannot be stated on a number line, are frequently used to symbolise complex numbers.

Given that u is a real number and the value of [tex]u^3 = -1000[/tex].

Take cube root on both sides of the equation:

[tex]\sqrt[3]{u^3} = \sqrt[3]{-1000} \\\\u = \sqrt[3]{(-10)(-10)(-10)} \\\\u = -10[/tex]

Hence, the value of u is -10.

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According to the separable differential equation, the family of implicit solution is  1/2 (x² - y²)

The term separable differential equation is defined as in which the variables can be separated from each other are called separable differential equations.

As per the definition the general form to write separable differential equations is dy/dx = f(x) g(y), where the variables x and y can be separated from each other.

Here we have given that (dy/dx) = (x/y)

When we cross multiply the terms, then we get,

=> y dy = x dx

When we differentiate the terms, then we get the following,

=> ∫y dy = ∫x dx

The solution of this integral can be written as,

=> y²/2 + C = x²/2 + C

When we simplify this one then we get the resulting expression as,

=> x²/2 - y²/2 = 0

=> 1/2 (x² - y²)

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Answer:

other leg ≈ 7.5 cm

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x represent the other leg , then

x² + 13² = 15²

x² + 169 = 225 ( subtract 169 from both sides )

x² = 56 ( take square root of both sides )

x = [tex]\sqrt{56}[/tex] ≈ 7.5 cm ( to the nearest tenth )

1) The function f(x) is defined as follows: B. F(x) = -(x + 2)²(x - 2).

2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.

4) The approximate solution to the system of equations is given as follows: A. (-3.43, 6.30).

The function f(x) is defined according to the Factor Theorem, with the product of the linear factors of the function, which are dependent on the roots of the functions.

The zeros of the function, along with their multiplicity, are given as follows:

Hence the function is defined as follows:

F(x) = a(x + 2)²(x - 2).

The y-intercept is positive, meaning that:

-8a > 0.

Thus the leading coefficient a is negative, and the correct option is given by option B.

A cubic function, in which the coefficients a and d are positive, is represented as follows:

A. F(x) = ax³ + bx² + cx + d.

The solution to the system of equations is found through graphing, and is the point of intersection of the two functions.

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The fixed equation in the given question is y=x-4

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A simple equation is a mathematical formula that, on both sides of the "equal to" sign, expresses the connection between two expressions. Equations in this category include a variable, which is often expressed as x or y. Simple equations frequently need to be rearranged in order to be solved.

In the given equation

To fix the equation such that the line coincides with the star

the equation should be

y=x-4

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At a constant speed of 45 miles per hour it will take 0.71 hours for Darla to run her errands and get back home.

What is constant speed?

An object is considered to be moving at a constant speed when it covers the same distance in the same amount of time. When moving at a constant pace, an object covers a certain distance in a fixed amount of time.

Darla drives at a constant speed of 45 miles per hour.

She drives for y miles and it takes her x hours.

The number of miles Darla can drive in x hours is y = 45x.

Darla drives to the market, 14 miles from her house.

Then she drives to the post office, 3 miles from the market.

Then she drives back to her house, 15 miles from the post office.

Calculate Darla's total distance travelled -

14 + 3 + 15 = 32 miles

Now, substituting the value of y with 32 -

32 = 45x

x = 32/45

x = 0.71

Therefore, the time taken by Darla is 0.71 hours.

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Answer:

Step-by-step explanation:

2(x + 3)=5x + 6 - 3x true or never true?

2(x + 3)=5x + 6 - 3x

2x + 6 = 2x + 6

2x - 2x = 6 - 6

0 = 0

The value of x in the similar triangles is 40.

Those triangles that looks the same but different in sizes.

And in the similar triangle,

the corresponding sides in proportion to each other and corresponding angles are equal to each other.

Given:

Triangles are similar.

That means,

the corresponding sides are in the proportion to each other.

That means,

(x + 8)/x = 12/10

10x + 80 = 12x

2x = 80

x = 40

Therefore, the value of x is 40.

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Answer:

it is not an option for the rest of your life with a new one of the year old girl who is the best friend and I have a great day to be a great day to be a great day to be a great 6

Step-by-step explanation:

or false hope I can I get to be a great day to be

To solve the differential equation y" + y = csc(x) using variation of parameters, we first need to find a particular solution.

Since the non-homogeneous term is csc(x), we can try a particular solution of the form yp = u(x) csc(x), where u(x) is a function to be determined.

Substituting yp into the differential equation:

u''(x)csc(x) + u(x)csc(x) = csc(x)

To find u(x), we can multiply both sides by csc(x) and integrate with respect to x:

∫u''(x)csc(x) dx + ∫u(x)csc^2(x) dx = ∫csc(x) dx

Integrating the first term by parts:

u'(x) = ∫csc(x) dx = ln|cot(x/2)| + C1

Integrating the second term by parts:

u(x) = -∫csc(x)cot(x) dx = -ln|sin(x)| + C2

So, the particular solution for yp is:

yp = u(x)csc(x) = -ln|sin(x)|csc(x) + C1csc(x) + C2

Now we need to find the general solution y = yc + yp

where yc is the general solution for the complementary homogeneous equation y" + y = 0

yc = C1cos(x) + C2sin(x)

Now we can use the method of variation of parameters to find the general solution for the non-homogeneous equation

By this method, we need to find two functions v1(x) and v2(x) such that W(yc, yp) = v1(x)cos(x) + v2(x)sin(x)

W(yc, yp) = (yc * yp') - (yp * yc')

W(yc, yp) = (C1cos(x) + C2sin(x)) * (-cot(x)csc(x) + C1) - (-ln|sin(x)|csc(x) + C1csc(x) + C2) * (-sin(x)cos(x) + cos(x)sin(x))

W(yc, yp) = -C1cot(x)csc(x) + C1^2 + C2csc(x)

As W(yc, yp) is not identically zero, we can proceed to find v1(x) and v2(x)

v1'(x) = -cot(x)csc(x) + C1

v2'(x) = csc(x)

Integrating both sides by parts:

v1(x) = ln|cot(x/2)| - cot(x) + C3

v2(x) = -cot(x) + C4

The general solution for the non-homogeneous equation y" + y = csc(x) is:

y = yc + yp = (C1cos(x) + C2sin(x)) + (sin(x)ln|sin(x)|

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It takes Mika about 1 1/8 minutes to read per page.

Now, According to the question:

Let's know:

What is Simplification?

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Mika read a 405-page book in 6 hours.

We convert pages per hours (405/6.) to pages per minute [60 minutes per hour]:

[tex]\frac{405}{6}[/tex] × [tex]\frac{1}{60}[/tex]

To simplify the above expression:

= 1.125

So, it takes Mika about 1 1/8 minutes to read per page.

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The measure of the angle ∠CFE is 330°.

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc.

Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

The angle ∠CFE is calculated as:-

∠CFE = 360 - ∠CEF

∠CFE = 360 - 30

∠CFE = 330

Hence, the angle ∠CFE is 330°.

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This question is based on the concept of sequence. Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.

This question is based on the concept of sequence. Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.

Given:

Sequence is 55, 44, 33, 22, ...

We need to find the next two terms in the sequence.

According to the question,

Now, calculating the common difference of arithmetic sequence.

d1 = 44  - 55 = -11

d2 = 33 - 44 = -11

Hence, the common difference d is -11.

Now, calculating the next two terms of given sequence.

We know that,

a5 = 55+ (4) * (-11)

a5=55-44

a5  = 11

a6 = 55+(5)*(-11)

a6 = 55- 55

a6 = 00

This question is based on the concept of sequence. Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.

Therefore, the next two terms of sequence is 55, 44, 33, 22, 11, 00.

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The solutions for the equation are b = 0, 3.

What is the cubic equation?

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. Polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.

To find the solution for the equation 5/3b³ - 2b² - 5, we can factor it or use the quadratic formula.

One way to factor it is to note that it is a cubic equation in terms of b, and can be written as:

5/3b³ - 2b² - 5 = (5/3b³ - 2b²) - 5 = (5/3b³ - 2b²- 5b) + (5b)

= (5/3b)(b² - 3b) + 5

So, b=0 is one solution, but we can also factor the remaining quadratic equation (b² - 3b) = 0,

b=0 and b=3 are the solutions for the equation.

Hence, the solutions for the equation are b = 0, 3.

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Answer: he use 4 pepperoni more than sausage every times he put 10 meat on the pizza

Step-by-step explanation: both are on 10 so you don't need to change it so 7-3=4 and it's on ten which mean that every times he put 3 sausage, he have to put 7 pepperoni

The required ways can 3 club members be chosen as president, vice president, and treasurer are 56.

When the order doesn't matter, the combination is a choice between all of the objects in the set or just a portion of them. As a result, the combination formula is provided by; n, and the number of combinations of n objects taken r at a time.

Total number of eligible members for these positions = 8

To choose three members,

C(8, 3)

(8×7×6)/(3×2)

336/6

= 56 ways.

Thus,the required number of ways are 56.

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Answer:

16 peices

Step-by-step explanation:

52/3.25 = 16

Answer:

0.75 is less than 1, so the portrait will be smaller than the actual head.

Step-by-step explanation:

The art teacher has said that the portrait will be 0.75 times as tall as the actual head.

0.75 is less than 1, so the portrait will be smaller than the actual head.

A ratio of 0.75 means that the portrait will be 3/4 the size of the actual head. So, if the actual head is 8 inches tall, the portrait will be 6 inches tall (8*0.75 = 6). Therefore, the portrait will be smaller than the actual head.

By the Pythagorean theorem, [tex]y=\sqrt{6^2-3^2}=3\sqrt{3}[/tex].

By the geometric mean theorem, [tex]y^2=3x \implies x=9[/tex].