There are 80 pupils in a group. The only languages available for the group to study are Russian and Spanish. 50 pupils study Russian. 31 pupils study Spanish. 23 pupils study neither Russian nor Spanish. Find the probability to select a pupil that studies Spanish and Russian. Probability

The measures of the angles are (a) 180-C, and 180-A (b) 180 (c) 180 and supplementary.

You should understand that  cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle

For better understanding note the following

(a) m<A = 180 - m<C

m<C = 180 - m<A

(b)  m<A + m<C = 180 .......... (opposite angles are supplementary)

(c) m<A + m <C = 180 (Sum of opposite angles = 180⁰)

(d) <A and <C are supplementary angles

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The values of six trig functions are:

sinθ=− √5/5, cosθ=2√5/5, tanθ=-1/2, cot θ=−2, secθ=√5/2, cscθ=−√5

The relationship between the angles and sides of a triangle is given by these trig functions.

There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

The point's coordinates are:

x=2, y=−4

To calculate the functions we have to calculate the distance between the point and the origin:

r=√x²+y²=√2²+(−4)²=√16+4=√20

r=2√5

Now we can calculate the functions:

sinθ=y/r=−2/2√5=−√5/5

cosθ=x/r=4/2√5=2/√5=2√5/5

tanθ=y/x=−2/4=−1/2

cotθ=x/y=4/−2=−2

secθ=r/x=2√5/4=√5/2

cscθ=r/y=2/√5−2=−√5.

Hence, the values of trig functions are calculated.

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The probability of rolling an odd number on a fair six-sided die is P(odd) = (1/6) + (1/6) + (1/6) = 3/6 = 1/2. This is because there are three odd numbers (1, 3, and 5) out of the six possible outcomes, and they are each equally likely to occur.

The probability of rolling a number divisible by 3 on a fair six-sided die is P (divisible by 3) = (1/6) + (1/6) = 2/6 = 1/3. This is because there are two numbers (3 and 6) out of the six possible outcomes that are divisible by 3, and they are each equally likely to occur.

It's important to note that in both of these examples, we are assuming that the die is fair and unbiased, which means that each of the six possible outcomes has an equal chance of occurring. If the die is not fair, the probabilities of each outcome could be different.

Complete question:

More probability Aa Aa An event's probability measures the likelihood of its occurrence. The probability that an event X occurs is between 0 and 1, inclusive, and is denoted by P(X). If it is impossible for X to occur, then P(X) Rolling a standard six-sided die, the probability of rolling a 7 is zero, P(7)-0. If X is the set of all possible outcomes in the experiment, then X is certain to occur and P(X)1 In the die example, X could be that an integer is rolled, which must occur, and thus P(integer)-1 Otherwise, X is possible but uncertain, and 0<P(X) 1. In the die example, the probabilities of each of the six outcomes are equally likely (so long as the die is fairly balanced), so P(1)-P(2)-P(3)-P(4) = P(5)-P(6)- 1/3. If possible, you want to identify all the possible outcomes, called the If you are rolling a 1/6). fair die, your outcomes range from 1 to 6, with equal probability (P The probability of rolling an odd number is the probability of rolling a number divisible by 3 is

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92 Square inches is the area of the shaded region shown below

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given a rectangle, that has a length of 12 inches and 9-inch width

Since,

Area = length * width

Area of the given triangle = 12 * 9

Area of the given triangle = 108 square inch

There is also one square inside this rectangle of side 4 inch

Since the area of square = side * side

Thus in our case,

Area of square = 4 * 4 = 16 square inch

As we can see in the figure:

Area of shaded region  = complete area of rectangle - area of square

Area of shaded region  = 108 - 16

Area of shaded region  = 92 square inch

Therefore, The area of the shaded region is 92 Square inches.

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Complete question:

Answer:

400

Step-by-step explanation:

[tex]100 + 200 + 300 + 400 + 500 + 600 + 700 = 2800 [/tex]

There are 7 numbers ( No. of cakes in a month)

Therefore, we should divide it by sum of the cakes

[tex]2800 \div 7 = 400[/tex]

SO MEAN NUMBER IS 400//

To find the median of the data set, we first need to arrange the data in numerical order. We can do this by grouping the digits in the stem & leaf diagram according to the key:

8016

92 35 67

100 124 34

113

123 8

Then we will arrange them in order as: 8016 92 35 67 100 124 34 113 123 8

To find the median we have to identify the middle value of the data set, considering that we have 12 data points. The middle value is the 7th value in the set which is 100, therefore the median is 100.

Answer:

-31

Step-by-step explanation:

Let's put this into an equation:

[tex]4-5 *7[/tex]

Note that 5 less than 4 means I take 5 AWAY from 4, not 5-4.

Most people would go about this straight across, doing 4-5, -1, and then times 7 which would be -7.
BUT if there are no parentheses around 4-5, we do 5 times 7 first.

Why? In PEMDAS or order of operations, you multiply before subtracting.

That means I do 5 times 7 first. That is 35.

Now I subtract 4-35. That is -31.

To find the highest common factor (HCF) of two polynomials, we can use the Euclidean algorithm or the method of factoring the polynomials and comparing their common factors.

The first polynomial is x² - 2x - y² + 4y-3 and the second polynomial is x² + 2x - y² + 8y-15

x² - y² is common in both polynomials, let's factor it out.

x² - y² = (x-y)(x+y)

so the first polynomial can be written as (x-y)(x+y) - 2x + 4y - 3

and the second polynomial can be written as (x-y)(x+y) + 2x + 8y - 15

So the HCF of these two polynomials is (x-y)(x+y)

It is important to note that the HCF of polynomials is not unique, there can be more than one factorization.

The total length of paper needed to cover all the tables is equal to 10 tables multiplied by 104 inches per table, which is equal to 1040 inches.

According to the Pythagorean theorem, the hypotenuse's square length is equal to the sum of the squares of the two legs' lengths in a right triangle. The formula for this is a2 + b2 = c2, where a and b represent the lengths of the two legs, respectively, and c represents the length of the hypotenuse.

The theory used in this question is the Pythagorean theorem.

Number of tables:

Let's say there are 10 tables.

Length of each table plus 8 inches:

Each table is 8 feet long, which is equal to 96 inches. The extra 8 inches makes it 104 inches per table.

Total length of paper needed:

The total length of paper needed to cover all the tables is equal to 10 tables multiplied by 104 inches per table, which is equal to 1040 inches.

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Answer:

N103. 33

Step-by-step explanation:

let the cost of bottle of water be represented by B

Let the cost of wine be represented by W

3×W + 4×B =N450

3W+4B=450....(1)

one bottle of water(B)Costs N35

3W+ 4(N35)= N450

3W + 140=450

collect the.like terms

3W= 450-140

3W = 310

divide through by 3

W= N103.33

Answer:

[tex]\frac{17}{8}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{8} = (2*8)+1 =17= \frac{17}{8}[/tex]

Answer:

17/8

Step-by-step explanation:

I learned to save for the future and spend responsibly. In my adult life I will continue to save and be mindful of my spending habits. I will change my attitude towards money and become more frugal.

Saving money for the future requires discipline and dedication. One of the easiest ways to start saving is to create a budget and stick to it. Make sure to include a line item for savings in your budget and allocate a specific amount each month to save.

Additionally, set up automatic transfers from your checking account to your savings account to ensure money is put into savings each month. It's also important to find ways to minimize expenses. Cutting back on eating out, reducing your cell phone bill, and shopping for discounts are all great ways to save money.

Finally, look into investing your money in stocks, bonds, and other investments to help your savings grow. Saving money for the future takes time, but it is possible with the right strategies.

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If an open box is to be constructed from a square piece of sheet metal by removing a square of side 3 feet from each corner and turning up the edges. the dimensions of the sheet​ metal is 16 feet.

Let x represent the dimension of the sheet metal

So,

Volume =3×(x-2×3)×(x-2×3) = 300

Volume =3×(x-6)×(x-6) = 300

(x -6)² = 300/3 = 100

x-6 = √100 =10

x = 10 +6

x = 16 feet

Therefore the dimensions of the sheet​ metal is 16 feet

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Answer:

5 and 6

Step-by-step explanation:

sqrt of 32= 4sqrt2 = 5.656

Answer:  (-5, -7)

Multiply the y coordinate by -1. Keep the x coordinate the same. The point (-5,7) reflects over the x axis to land on (-5,-7)

The reason why we multiply by -1 is because [tex]\text{y} = \text{h}(\text{x})[/tex], so [tex]-\text{y} = -\text{h}(\text{x})[/tex]

Answer:

(-5,-7)

................

The volume of the sphere = (4.0 / 3.0) π r^3.

What is the volume of the sphere?

The quantity of space occupied within a sphere is referred to as its volume. Every point on the surface of the sphere is equally spaced from its center, making it a three-dimensional round solid object. The fixed point and fixed distance are referred to as the sphere's center and radius, respectively.

Here, we have

The volume program in Python, where comments are used to explain each line is as follows

#This initializes pi to 3.142

pi= 3.142

#This gets input for the radius

sphere_radius = float(input("Radius: "))

#This calculates the sphere volume

sphere_volume = (4.0 / 3.0) * sphere_radius**3

#This prints the sphere volume

print(sphere_volume)
Hence, the volume of the sphere = (4.0 / 3.0) π r^3.

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Answer:  1⅗

Step-by-step explanation:  We can write 8 divided by 5 as 8/5.

As 8/5 is an improper fraction, when we divide 8 by 5, we get 1 as quotient and 3 as remainder.

To convert an improper fraction into a mixed fraction, we take quotient 1 as a whole part and in the fractional part remainder 1 as the numerator, and divisor 5 as the denominator.

The GCF of 5 and 1 is 1. So, divide both the numerator and denominator by the GCF to simplify and convert it to a mixed fraction.

Thus, 8 divided by 5 as a fraction in simplest form is 1⅗.

The function that describes the height of the ball as a function of time t (in seconds) can be represented as:

h(t) = -16t^2 + 64t + 40

Where h(t) is the height of the ball in feet above the ground, t is the time in seconds, and the -16t^2 represents the acceleration due to gravity. The 64t represents the initial velocity of the ball, and 40 is the initial height of the ball above the ground.

Check the picture below.

Expressing the binomial coefficients in terms of factorials and simplifying algebraically. we have proved that  

[tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]

The binomial coefficient [tex]\left(\begin{array}{l}n \\ k\end{array}\right)[/tex] is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols [tex]_nC_k[/tex] and [tex]\left(\begin{array}{l}n \\ k\end{array}\right)[/tex] are used to denote a binomial coefficient, and are sometimes read as "n choose k."

[tex]$$In general, $\left(\begin{array}{l}n \\ r\end{array}\right) \neq\left(\begin{array}{c}n \\ r-1\end{array}\right)$To solve (a), simply expand LHS.$$\left(\begin{array}{l}n \\r\end{array}\right)=\frac{n !}{r ! \cdot(n-r) !}=\frac{n !}{r \cdot(r-1) ! \cdot(n-r) !}$$Multiply numerator and denominator by $(n-r+1)$, then,$$\left(\begin{array}{l}n \\r\end{array}\right)=\frac{n-r+1}{r} \cdot \frac{n !}{(r-1) ! \cdot(n-r+1) !}=\frac{n-r+1}{r} \cdot\left(\begin{array}{c}n \\r-1\end{array}\right)$$[/tex]

Thus, Expressing the binomial coefficients in terms of factorials and simplifying algebraically. we have proved that  

[tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]

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Full question:

Expressing the binomial coefficients in terms of factorials and simplifying algebraically, show that:

(a) [tex]$\left(\begin{array}{l}n \\ r\end{array}\right) = \dfrac{n-r+1}{r} \cdot \left(\begin{array}{c}n \\ r-1\end{array}\right)[/tex]

Answer:

vendor sold 90 sodas and 45 hot dogs

Step-by-step explanation:

Let x = number of sodas sold

Let y = number of hot dogs sold

We have x = 2y (1)
( The number of sodas sold was two times the number of hot dogs sold)

We also have x + y = 135 (2)

( sold a combined total of 135 sodas and hot dogs.)

Substituting x = 2y we get

2y + y = 135

3y = 135

y = 135/3

y = 45

Therefore x = 135 - 45

x = 90

Therefore vendor sold 90 sodas and 45 hot dogs

Answer: 41,000

Step-by-step explanation:

If the hundreds column 5 or more than it rounds up if it is lower it rounds down

Answer:

No!

Step-by-step explanation:

(1 5/2)

is a mixed fraction so you will change it to proper fraction.

the solution is

=7/2 or 3.5

You will multiple two by one and add by five given 7/2.

Answer:

----------------------------

Given expression:

Simplify it in steps below:

Answer:

[tex] \sf \: 98h - 56k [/tex]

Step-by-step explanation:

Given expression,

→ 9(7h - 4k) + 10k - 5(6k - 7h)

Let's simplify the expression,

→ 9(7h - 4k) + 10k - 5(6k - 7h)

→ 63h - 36k + 10k - 30k + 35h

→ (63h + 35h) + (-36k + 10k - 30k)

→ (98h) + (-56k)

→ 98h - 56k

Hence, answer is 98h - 56k.

Least-cost planning methodology (LCPM), sometimes known as "least-cost planning" (LCP), is a relatively new strategy used by economists to make logical decisions about investments in transportation and other urban infrastructure projects.

The complete question is,

What is a project's least cost?          

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1. The antiderivative would be x.

2. The antiderivative would be sec(θ)tan(θ)−5e^(θ^3).

3. The antiderivative would be 1+2x.

What is the antiderivative of the function?

An antiderivative of a function is a function whose derivative is equal to the original function. It is also known as an indefinite integral of a function with respect to its variable. The process of finding an antiderivative is called integration.

1. The most general antiderivative of the function f(x)=x is F(x) = (1/2)x^2 + C, where C is the constant of the antiderivative. To check this, we can differentiate F(x) using the power rule for derivatives and see if we get back f(x) = x: d/dx [(1/2)x^2 + C] = d/dx (1/2)x^2 + d/dx C = x

2. The most general antiderivative of the function r(θ)=sec(θ)tan(θ)−5e^(θ^3) is R(θ)=∫sec(θ)tan(θ)−5e^(θ^3) dθ = -ln(cos(θ))+5e^(θ^3)/3+C, where C is the constant of the antiderivative. To check this, we can differentiate R(θ) using the rules of integration by substitution, and see if we get back r(θ) = sec(θ)tan(θ)−5e^(θ^3): d/dθ [-ln(cos(θ))+5e^(θ^3)/3+C] = sec(θ)tan(θ)−5e^(θ^3)

3. The most general antiderivative of the function f(x)=1+2x is F(x) = x+x^2 + C, where C is the constant of the antiderivative. To check this, we can differentiate F(x) using the power rule for derivatives and see if we get back f(x) = 1+2x: d/dx (x+x^2 + C) = d/dx x+d/dx x^2 + d/dx C = 1+2x

Hence,

1. The antiderivative would be x.

2. The antiderivative would be sec(θ)tan(θ)−5e^(θ^3).

3. The antiderivative would be 1+2x.

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Answer:

$18.85

Step-by-step explanation:

1. 127*18 = 2286 pages.

2. 2286/500 = 4.6 (approx.)

3. You need to buy 5 reams of paper 500 pages each.

     It will cost 5*$3.77 = $18.85

Answer:

12 inches

Step-by-step explanation:

3 inches / (1 / 4) = 12 inches

Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum property and therefore ΔJFH ≅ ΔJGH with AAA congruency.

Two triangles are congruent if they have the same shape and size. Congruent triangles have all corresponding angles and sides congruent, meaning they are equal in measure.

A triangle can be shown to be congruent to another triangle by using one or more of the following criteria:

SSS (Side-Side-Side) Congruence: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

SAS (Side-Angle-Side) Congruence: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

ASA (Angle-Side-Angle) Congruence: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

HL (Hypotenuse-Leg) Congruence: If the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

Richard is incorrect, As if two angles are same then the 3rd angle must be same too using angle sum of property and therefore ΔJFH ≅ ΔJGH

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The distance between two points on a line segment .

Learn how to use the distance formula to calculate the distance between two points, which is an application of the Pythagorean theorem. To calculate the distance between any two points, we may rewrite the Pythagorean theorem as d=((x 2-x 1)2+(y 2-y 1)2). Sal Khan and the CK-12 Foundation created it.

A line segment is delimited by two separate points on a line in geometry. A line segment is a section of a line that links two locations. A line has no endpoints and stretches in both directions indefinitely, but a line segment has two defined or definite endpoints.

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Answer:

-1 ≤ y ≤ 6

[-1, 6]

Step-by-step explanation:

The y coordinates of all points on the graph are from -1 to 6, so the range is:

-1 ≤ y ≤ 6

[-1, 6]