A sports ball has a diameter of 27 cm. Find the volume of the ball. cm.3 Round your answer to the nearest tenth if necessary

By making use of Set Theory, we calculate that a total of 38 students are enrolled in either physics or algebra.

Number of students taking algebra n(A)= 29

Number of students taking physics n(B)= 14

Number of students taking both subjects n(A∩B)= 5

So, the number of students taking either physics or algebra will be the union of sets i.e. n(A∪B)

The union of two sets is a set containing all elements that are in A or in B (possibly both).

As we know,

n(A∪B) = n(A) + n(B) - n(A∩B)

n(A∪B) = 29 + 14 - 5

n(A∪B) = 38

Therefore, A total of 38 students are enrolled in either physics or algebra.

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The size of angle x is 34.84°

What is right angled triangle ?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or formerly a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.

To find the value of x we will use the trigonometric formula

sin x = [tex]\frac{opposite}{hypotenuse}[/tex]

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex]

tan x = [tex]\frac{opposite}{adjacent}[/tex]

cosec x = [tex]\frac{1}{sin x}[/tex]

sec x = [tex]\frac{1}{cos x}[/tex]

cot x = [tex]\frac{1}{tan x}[/tex]

As we know the value

hypotenuse = 14cm

opposite side = 8cm

∴ sin x = [tex]\frac{8}{14}[/tex]

           = [tex]\frac{4}{7}[/tex]

       x  = 34.84°

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Answer:

angle x =34.8°

Step-by-step explanation:

sinX=opposite/hypotenuse this means  sin(θ) is the ratio of the opposite side to the hypotenuse

so, to solve this problem we have to find the value of sin X then we can get the value of X.

Let sin X = 8/14

               =0.571

SO, X =sin-1(0.571) =34.8°

Check the picture below.

yes of course it can surely be

Answer:

Yes, you can factor out common factors to write equivalent algebraic expressions.

[from edge's summary video script]

16.01 is the greatest number.

Numbers:

In everyday life, we use numbers. They are frequently known as numbers. We are unable to count things, dates, hours, money, etc. without numbers. These numerals are utilised for labelling and measurement purposes at various periods. The characteristics of numbers enable them to be used in arithmetic operations. Both verbal and quantitative representations are used to express these numbers.

Math teaches us about the various kinds of numbers there are. The types of numbers include natural and whole numbers, odd and even, rational and irrational, etc. In addition to this, the numbers are employed in numerous other contexts, including the creation of number series and arithmetic tables.

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Answer:

6i^2-12i

Step-by-step explanation:

3i×2i =6i^2

3i×4 =12i

[tex]\left \{ {{y=5x} \atop {y=4x+1}} \right.[/tex]

answer is option 2 : (1, 5) because:

when x = 1 , y should = 5:

[tex]\left \{ {{y=5x} \atop {y=4x+1}} \right.\\\\\left \{ {{y=5(1)} \atop {y=4(1)+1}} \right.\\\\\left \{ {{y=5} \atop {y=5}} \right.[/tex]

This is a question of Simple Interest. The simple interest is given by the formula:

That is:

Interest = Principal * Rate * Time

From the question, we have:

P = $10

R = 5% ---> 5/100 = 0.05

T = 2 years

Then, we have that the interest is (without units):

Therefore, the interest is $1.

However, Kayla will have in two years this interest plus the starting amount, that is:

$10 + $1 = $11.

Hence, Kayla will have $11 in two years in her savings account.

First, let's graph the complex number:

The trigonometric form will be given by:

The angle θ here is 225° (5π/4), the r-value will be

Now we have the trigonometric representation:

Therefore the correct answer is the letter D.

Using the properties of similar triangles and ratio and proportion we get the vale of x as 2.8 units.

In the given figure the triangle ΔKFG and ΔFJH

KG is parallel to JH

Hence ΔKFG is similar to ΔFJH

Now using the property of similarity and proportion we can say that:

FG/FH = KF/JF

putting the values in the above proportion we get:

7 /(7+x) = 5/ 7

or, 49 = 35 +5 x

or, 14 = 5x

or, x =14/5

or, x = 2.8

The majority of ratio and percentage explanations involve using fractions.

A proportion states that two variables are equal, whereas a ratio is a fraction that is written as a:b. The two ratios given are equal to one another, as demonstrated by the proportional equation.

Hence the value of x is 2.8 units.

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Step-by-step explanation:

When we multiply or divide both sides of an inequality by a negative number, what happens to the inequality symbol?

Answer:

The sign flips.

≤ becomes ≥

and ≥ becomes ≤

Answer:

Step-by-step explanation:

b/c we can fairly say,  that the parallelgram is also a rectangle of size 24 x 11, we can just solve that area

24*11= 264

We can see, this is a parallelogram.

The formula to calculate the area of a parallelogram is b x h, where b is base and h is height.

Given that base = 24 in, height = 11 in, we can calculate the area as : 24 x 11 = 264 in2.

Answer:

The answer is B

Explanation:

Associative properties for multiplication is stated as follows:

(a * b) * c =

Answer:

f(x)=x2 f ( x ) = x 2

Step-by-step explanation:

The mean of a data set can be greater than any of the data sets is True.

The average is basically a model of the dataset. The most frequently occurring value. However, the mean value is often not one of the actual values observed in the dataset. The median can be larger or smaller than the mean of the distribution. So the given statement is wrong.

The mean is affected by outliers that do not influence the mean. Therefore, when the average distribution of data is skewed to the left, the mean is often less than the median. When the distribution is skewed to the right, the mean is often greater than the median. No matter what value we add to the set, the mean, median, and mode will shift by that amount but the range and the IQR will remain the same. The same will be true if we subtract an amount from every data point in the set.

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Using substitution method of simultaneous linear equation the results are x = -1 and y = 3

What is simultaneous linear equation?

At first it is important to know about linear equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.

Here,

Substitution method of simultaneous linear equation is used

y = -2x + 1

-9x - 2y =3

Putting the value of y in the second equation

-9x - 2(-2x + 1) = 3

-9x +4x -2 = 3

-5x = 3 + 2

-5x = 5

[tex]x = -\frac{5}{5}\\x = -1[/tex]

Putting the value of x in the first equation,

[tex]y = -2 \times -1+1\\y = 3[/tex]

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Answer:

225

Step-by-step explanation:

From what I explained in the session before, the x value must be between 10 and 15, so only 2 options are viable, 14 and 12. Let's evaluate each of them

So, 12 is not the answer. Let's evaluate 14

So, x = 14 is the correct answer

Answer:

what's that bottom number???

Answer:

Answer: 54

Step-by-step explanation:

3x2=6 6x9=54

Step 1:

3x2=6

Step 2:

get the 6 from last step and multiply it by 9

6x9=54 √

The system of equations which are correct are mentioned below:

2 ) [tex]24/2^2= 50- 6^2 - 8[/tex]

and 4 ) 56÷8+3^2= 2⋅2^3

The solution of all the system of equations are given below;

1 ) [tex]8^2 - 5^2= 4^2 - 7[/tex]

LHS = 64 - 25 = 39

RHS = 16 - 7 = 9

Since LHS is not equal to RHS the given equation is not correct.

2) [tex]24/2^2= 50- 6^2 - 8[/tex]

LHS = 24 / 4 = 6

RHS = 50 - 36 - 8 = 6

Since LHS = RHS the above system of equation is correct.

3 ) [tex]39 - 3 X 6=6 X 10/4+4[/tex]

LHS = 39- 18 = 21

RHS = 60 / 8 = 7.5

Since LHS is not equal to RHS the given system of equations is wrong

4 ) 56÷8+3^2= 2⋅2^3

LHS = 12

RHS = 12

Since LHS = RHS the above system of equations is correct.

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Answer:

Step-by-step explanation:

This is decay, the rate of change is 49%

hope this helps!

The correct rate of change is B)49% decay.

What constant rate of change ?

    A rate of change is constant when, at any given point along the function, the ratio of the output to the input remains constant. The slope is another name for the rate of change that is constant. A linear function's rate of change will be constant.

Here the given function is ,

=> h(x)=38(0.51)x.

For any exponential function in which the base is less than 1, it will be an exponential decay situation.

In this problem, the base is 0.51.

Then,The amount that the base is less than 1  ( i.e. 1 - base) . It represents the rate of change in decimal ,

=> 1-0.51 = 0.49

Converting into percentage => 0.49 *100 = 49%

Therefore the correct option is B) 49% decay.

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Answer: The family would buy the three pairs of shoes for $26.31 because you have to divide $52.62 in half since they bought half the amount of pairs of shoes that are given in the sale.

Answer:

$26.31

Step-by-step explanation:

3 × [tex]\frac{52.62}{6}[/tex]

3 × [tex]\frac{5262}{600}[/tex]

3 × [tex]\frac{877}{100}[/tex]

[tex]\frac{3 *877}{100}[/tex]

[tex]\frac{2631}{100}[/tex]

= 26.31

The statement represents the commutative property of Multiplication.

Commutative is derived from "commute," which means to move about or travel. The commutative property of multiplication states that the result is unaffected by the order in which the numbers are multiplied.

According to the commutative property, the result of addition or multiplication remains the same regardless of the sequence in which the numbers are added or multiplied. It should be noted that the commutative feature only applies to addition and multiplication, not to division or subtraction. As an illustration, the sum of 6 + 7 and 7 + 6 equals 13. Like 6 x 7 = 42, so does 7 x 6.

A statement is given as follows:

[tex]2\left(-\frac{3}{9}\right)=\left(-\frac{3}{9}\right) 2[/tex]

Observe that terms are exchanged on the left side and right side of the given equation.

It stands on the definition of the commutative property of Multiplication.

So, the statement represents the commutative property of Multiplication.

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Answer:

length:12m width: 6m

Step-by-step explanation:

w=l-6, lw=72. l*l-6=72, l^2-6l=72. l^2-6l-72=0, l=12 or -6, length cant be negative. L=12. W=L-6, w=6.

The equation of the line that passes through the points (5,2) and (1,4) is given by  [tex]y=-\frac{x}{2} +\frac{9}{2}[/tex].

Let the points  [tex](5,2) = (x_{1} , y_{1} )[/tex] and [tex](1,4) = (x_{2} , y_{2} ).[/tex]

The two-point form of the equation of a line is given by,

[tex]y-y_{1} =\frac{y_{2} -y_{1} }{x_{2}- x_{1} } (x-x_{1} )[/tex]

Substituting the values of [tex]x_{1} , x_{2}, y_{1}[/tex] and [tex]y_{2}[/tex] in the above equation, we get,

[tex]y-2=\frac{4-2 }{1-5 } (x-5 )\\\\ y-2 = \frac{2 }{-4 } (x-5 )\\\\ y-2=-\frac{1}{2} (x-5)\\ \\y-2=-\frac{x}{2} +\frac{5}{2} \\ \\y=-\frac{x}{2} +\frac{5}{2} +2\\ \\y=-\frac{x}{2} +\frac{9}{2}[/tex]

Thus the equation of the line is [tex]y=-\frac{x}{2} +\frac{9}{2}[/tex].

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Question:

The local furniture store pays $ 60 for a sofa and sells it with a 30% markup. What is the selling price of the sofa?.

Solution:

Let the following data:

Base price = $60

30% of base price = $60 x 0.3 = $18

Then:

Selling price = $60 + $18 = $78.

Then, we can conclude that the correct answer is:

The selling price of the sofa is $78.

The domain refers to all the values of x (inputs) for the function

The range refers to all the values of y (outputs) for the function

We have the domain & range thus:

Answer: D

Step-by-step explanation:

248 = 28x + 20y

x = 3y - 6

x = 28

y = 20

Solution:

Since the sample size is fixed;

And the probability of picking a girl is constant for each trial, the binomial distribution is appropriate;

Thus;

ANSWER: 0.32