20% of all the children in a class are left-handed. 4 children are left handed. How many children are there in a class altogether? ​

Answer:

The equivalent expression to show another way to represent the new price is b - 0.86b = c .

Step-by-step explanation:

Given that the original price of the purchase is b and the coupon gives a 14% discount, the new price of the purchase is given by:

c = b - 0.14b

To write an equivalent expression, we can multiply both sides of the equation by 100% - 14% to simplify:

c * 100% = b * 100% - 0.14b * 100%

c * 100% = b * (100% - 14%)

c * 100% = b * 86%

c = b * 86%

So, another way to represent the new price of the purchase is c = b * 86%.

In light of the query we've got The circle's radius is equivalent to 3.832 units.

In geometry, the perimeter is the overall area of a shape's boundary. A shape's perimeter is computed by adding the lengths of all of its sides and edges. Linear measurements like cm, metres, inch, and feet are used to express its dimensions.

The answers to our problem is that area

A = (θ/360) * π * r^2

π = 3.14

Perimeter is 24 degree, The formula for circumference is:

C = 2 x πr

Now, we can calculate the radius using the circumference:

r = C / (2 x π)

Substituting the value of C from the equation above, we get:

r = (24 / (2 x π))

Therefore, the radius of the circle is approximately equal to 3.832 units.

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The new wage if the performance is Adequate is $23.1 per hour.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

If an employee's performance is adequate, then he will get a raise of 5%.

The employee wage is 22 per hour.

The performance is Adequate.

That means,

the wage is,

= 22 + 22x 0.05

= 23.1

Hence, $23.1 is the wage per hour.

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Answer: 18

Step-by-step explanation: Solve using algebra and angles given.

The amount that Reuben owe after 9 years, rounded to the nearest cent is $19,252.95..

The formula compound interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = $8,000( 1 + 0.1/2 )^( 2 × 9 )

A = $8,000( 1 + 0.05 )¹⁸

A = $8,000( 1.05 )¹⁸

A = $19,252.95

Therefore, the accrued amount is $19,252.95.

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The value of b/a is b/a = 91/3 {(1-b/a)²}.

Cubic equations are polynomials of degree 3. That means the maximum degree of the polynomial is three.

And the standard form of a cubic equation is;

f(x) = ax³ + bx² +cx +d, where a, b, c, and d are constant coefficients a ≠ 0.

Given:

A cubic equation,

a³ - b³ / (a-b)³ = 91 where a and b are real numbers a>b>0.

Simplifying,

(a-b)(a²+b²+ab)/(a-b)³ = 91

(a²+b²+ab)/(a-b)² = 91

(a²+b²+ab-3ab+3ab)/(a-b)³ = 91

3ab/(a-b)² = 91

b/a = 91/3 {(a - b)²/a²}

b/a = 91/3 {(a - b/a)²}

b/a = 91/3 {(1-b/a)²}

Hence, b/a = 91/3 {(1-b/a)²}.

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The number 56 when compared to 10 is the same as 28 compared to 5.

Option- C(56)

Let x be the number when compared to 10 is same as 28 compared to 5.

So, finding the value of x by comparing the ratios of the above stated values.

Therefore,

                    [tex]\frac{x}{10} = \frac{28}{5}[/tex]

So, Cross multiplying the above equation,

                      x × 5 = 28 × 10

                       5x = 280

                        x = [tex]\frac{280}{5}[/tex]

                        x = 56

So, 56 when compared to 10 bears the same ratio as 28 compared to 5.

Option number - C

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The first ship with an angle of depression 9° has a 2399.23m distance from the shore. And the first and second ship are on a 1944.19m distance apart.

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the height of the cliff and the distance of the ships from the shore, we shall derive a complementary angle considering their respective angles of depression as:

90° - 9° = 81° for the first ship

90° - 5° = 85° for the second ship

such that;

tan 81° = distance of the first ship from the shore/380m {opposite/adjacent}

distance of the first ship from the shore = 380m × cos 81°

distance of the first ship from the shore = 2399.23m

tan 85° = distance of the second ship from the shore/380m {opposite/adjacent}

distance of the second ship from the shore = 380m × cos 85°

distance of the second ship from the shore = 4343.42

the ships distance apart = 4343.42m - 2399.23m

the ships distance apart = 1944.19m

Therefore, first ship with an angle of depression 9° has a 2399.23m distance from the shore. And the first and second ship are on a 1944.19m distance apart.

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Answer:

b > –6 and b < 6

Step-by-step explanation:

The expression "|b| > 6" means that the absolute value of b is greater than 6. Therefore, b can either be greater than 6 or less than -6. So, the equivalent expression is b > –6 and b < 6.

The answer is:

A frequency distribution for a collection of data is shown in the accompanying table.

The intervals or ranges of the data are displayed in the left column of the table, and the frequency or number of observations within each interval is displayed in the right column.

For instance, the first row demonstrates that 3 observations fall within the range of 10 to 19, the second demonstrates that 5 observations fall within the range of 20 to 29, and so on.

We only combine the frequencies to determine the total number of observations:

Total observations are equal to 3 + 5 + 7 + 4 + 1 = 20.

By averaging the bottom and upper interval bounds, we can also determine each interval's midpoint. As an illustration, the first interval's midway (10-19) is as follows:

Midpoint: (14.5) (10 + 19) / 2

This may be done for each interval, and to display the midpoints, we can add a third column to the table.

The cumulative frequency, which is the overall frequency as we progress from the shortest interval to the longest interval, can then be calculated. The cumulative frequency can be displayed in the table by using a fourth column.

The finished table is shown here:

Interval Frequency Midpoint Cumulative Frequency

Oct-19 3 14.5 3

20-29 5 24.5 8

30-39 7 34.5 15

40-49 4 44.5 19

50-59 1 54.5 20

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Answer: The equation 63 = 9k is correct.

To solve for k, you can divide both sides of the equation by 9:

63/9 = 9k/9

k = 7

So, k = 7 is the solution to the equation 63 = 9k.

Step-by-step explanation:

The value of k in the equation 63= 9k is 7

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

The equation 63 = 9k is a type of linear equations with one variable.. The variable here is K

To find k;

63 = 9k

divide both sides by 9

63/9 = 9k/9

k = 7

therefore the value of k is 7

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As the single fraction, we can write the expression as -

k/x.

Given is the expression as follows -

{(kx + k²)/x²} × {x/(x + k)}

The given expression is -

{(kx + k²)/x²} × {x/(x + k)}

{k(x + k)/x²} × {x/(x + k)}

k/x

Therefore, as the single fraction, we can write the expression as -

k/x.

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We got that the probability that the hand contains 4 cards of the same suit and 1 of another suit = 0.042917

In the given question the hand contains 4 cards of the same suit, and 1 of another suit and we have to find the probability of this.

As we know that in standard card deck have 4 suits and 13 ranks in each suit and each deck have total 52 cards. If 13 ranks separated then 39 cards are left.

So the probability that the hand contains 4 cards of the same suit and 1 of another suit is

Probability =  [tex]\frac{|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|+|^{13}C_{4}\times^{39}C_{1}|}{^{52C_{5}}}[/tex]

Probability = [tex]\frac{|715 \times 39| + |715 \times 39|+|715 \times 39|+|715 \times 39|}{2,598,960}[/tex]

Probability = (27,885 + 27,885 + 27,885 + 27,885)/2,598,960

Probability = 111,540/2,598,960

Probability = 0.042917

we got that the probability that the hand contains 4 cards of the same suit and 1 of another suit = 0.042917

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The complete question is:

A 5-card hand is (randomly) drawn from a standard 52 card deck. What is the probability that the hand contains 4 cards of the same suit, and 1 of another suit?

Answer:

the answer is foot/hour

Step 1: Calculate the ratio.

The ratio is 77 out of 100.

Step 2: Convert the ratio to a percent.

To convert the ratio to a percent, divide the numerator by the denominator and multiply the result by 100.

Therefore, 77 out of 100 can be written as 77/100 x 100 = 77%.

The conversion process known as "ratio to percentage" aids in turning a ratio into a percentage. As is common knowledge, two quantities of the same unit are compared using the ratio. A percentage, on the other hand, is a particular kind of ratio where the value of the sum is always equal to 100. Let's go over the formula, the value of the ratio to percentage for some of the most commonly used numbers, and several solved examples in depth in this article.

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To find the missing  sides of the special right angle,

The ratio for 45°,45°and 90°,   1:1:√2,

and for 60°, 30°, 90°,   1:√3:2.

Special right triangles are right triangles with three defined interior angles and fixed side ratios. If one side is known in these right-angled triangles, we can find the value of the two missing sides. The 45°- 45°- 90° triangle and the 30°- 60°- 90° triangle are additional names for the two exceptional right triangles.

Given finding the  missing sides of the special right angle,

Only right triangles with other internal angles of 30° and 60° or 45°and 45°. are valid according to this criteria. Furthermore, it makes no difference whatever side's length you know in order for the rule to function.

for 45°,45°and 90°.

The 45°,45°,90° theorem states that triangles with these angles will have sides in a ratio 1:1:√2,

where the side opposite 45° equates to 1 in the ratio and the side opposite to 90° equates to √2. To find the missing side, just put the given value in the following ratio and find the value.

For 60°, 30°, 90°

Similar to this, according to the 30°, 60°, 90° theorem, triangles with these angles will have sides in the ratio 1:√3:2,

where the side opposite to 30° equates to 1 in the ratio, the side opposite to 60° equates to √3, and the side opposite to 90° equates to 2 in the ratio. Simply enter the given amount into the following ratio to determine the value to discover the missing side.

Hence the ratios are for 45°,45°and 90°,   1:1:√2,

and for 60°, 30°, 90°,   1:√3:2.

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Another way to write the division expression 34 divided by 8 is 34/8 or 4.25, where 4.25 is the result of the division.

What is a mathematical expression?

A mathematical expression consists of a statement, at least two variables or integers, and one or more arithmetic operations. It is possible to multiply, divide, add, or subtract values with this mathematical operation. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

Another way to write the division expression 34 divided by 8 is 34/8 or 4.25, where 4.25 is the result of the division.

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a) The measure of an interior angle is of 135º.

b) The polygon has 8 sides.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Hence the measure of the interior angle of a polygon with exterior angle of 45º is given as follows:

180 - 45 = 135º.

The sum of the interior angle measures of a polygon with n sides is given by the equation presented as follows:

S(n) = 180 x (n - 2).

For a regular polygon, all the angles have the same measure, hence:

S(n) = 135n.

Then the value of n, representing the number of sides of the polygon, is obtained as follows:

135n = 180(n - 2)

135n = 180n - 360

45n = 360

n = 360/45

n = 8 sides.

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Answer:

Step-by-step explanation:

Mr. Adams will fill 21 plates, and he will have 5 extra cookies.

To find the number of plates filled by Mr. Adams, we need to divide 730 cookies by 35 cookies per plate:

730 ÷ 35 = 21

So, Mr. Adams will fill 21 plates.

To find the number of extra cookies, we use the modulo operator to find the remainder after dividing 730 by 35:

730 % 35 = 5

So, Mr. Adams will have 5 extra cookies.

For the given equation, we can complete the statements below:

Ariel is correct. For any value of y, the statement -12 = 3 is always true.

The equation has no solutions.

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The first part of the question is as given below.

Ariel simplifies the equation 3y - 12 = 3(y+1) and says it has no solution.

We are asked to complete the statements based on the above information.

Simplifying the equation,

 3y - 12 = 3(y+1)

3y - 12 = 3y + 3

-12 = 3

Since the y term in the above equation is not present, the given equation has indeed no solution.

Also if we take any value of y, the final answer will always be -12 = 3.

Therefore we can complete the statements as below:

Ariel is correct. For any value of y, the statement -12 = 3 is always true.

The equation has no solutions.

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Answer: Ariel is correct. For any value of y the statement -12=3 is always false and it’s no solution

Step-by-step explanation:

So there are ten different combinations of two pupils out of five when there are five kids in my class and I want to choose two to treat to lunch.

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

Here,

To determine the number of ways to pick 2 students out of 5 to treat them to lunch, you can use the combination formula, which is given by nCr, where n is the number of items to choose from, r is the number of items to choose, and nCr is the number of combinations of n items taken r at a time. In this case, n = 5 and r = 2, so the number of ways to pick 2 students out of 5 is:

5C2 = 5! / (2! * (5 - 2)!) = 10

So, there are 10 possible combinations of 2 students out of 5 when there are 5 students in my class and I want to pick 2 to treat them to a lunch.

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Answer:

88

Step-by-step explanation:

We can set up the proportion 8/1 = x/11. By cross-multiplying, we get that x = 88.

Answer:

$89 for each payment

Step-by-step explanation:

3,204 / 36 = 89

Answer: Each payment is 89 dollars

Step-by-step explanation:

Divide 3,204 by 36 to get how much each payment will be.

The closest number to 320 that can be made using these cards is 327.5

From the question, we have the following parameters that can be used in our computation:

5 27

FIVE

7 3

TWO

SEVEN

THREE

DECIMAL POINT

To get this number, place the decimal point between the 7 and 5

We also make use of the card with "THREE" and add the number "TWO".

The resulting number is 327.5.

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The probability of the product of the two numbers being a multiple of 5 are 9/36.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

We can approach this problem by listing out all the combinations of two numbers from 1 to 6 and counting the number of combinations for which the product is a multiple of 5.

There are 6 x 6 = 36 possible combinations of two numbers from 1 to 6.

The combinations for which the product is a multiple of 5 are: (1, 5), (5, 1), (2, 5), (5, 2), (3, 5), (5, 3), (4, 5), (5, 4), and (5, 5).

So, there are 9 possible combinations for which the product is a multiple of 5.

The probability that the product of the two numbers is a multiple of 5 is 9/36. Expressing this as a common fraction, we have:

P(product is a multiple of 5) = 9/36 = 1/4

The probability that the product of the two numbers is a multiple of 5 is 9/36.

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a) The value of x is 20 cm

b) The area of cones that sought is 680π cm²

a) To find the length of x

Compare the ratio and height of the small cone with the large cone

4/x= 7/35

4.35=7x

x= 20 cm, x is the radius of the large cone

b) To calculate the area of the whole cone

The area you are looking for = (Area of the large cone - Area of the small cone) + area of the circle

The area sought = (π20.35 - π4.7) + 2π4

The area sought = 700π-28π+8π

Area sought = 680π cm²

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Answer:

728

Step-by-step explanation:

910/5 = 182 per week

4 weeks = 4*182 =728

Answer: 3,2

Step-by-step explanation: The degree represents the highest exponent in the function. In this case, there is a cubed term which has an exponent of 3. The leading coeffient represents the number before x that makes that highest exponent and in this case its 2.

We can quickly determine that the person has been moved by 10 miles by logical reasoning.

A mental process called logical reasoning seeks to reach a conclusion in a precise way.

By beginning with a set of premises and reasoning to a conclusion supported by these premises, it takes the shape of inferences or arguments.

Propositions, or true or false statements about the reality of a situation, are what the premises and the conclusion are.

They have a disagreement as a group.

In the sense that it seeks to develop correct arguments that any sane person would find persuasive, logical reasoning is norm-governed.

Logic is the primary academic field that studies logical reasoning.

So, using logical thinking, we can easily tell that the person is displaced by 10 miles.

(refer to the image attached below)

Therefore, we can quickly determine that the person has been moved by 10 miles by logical reasoning.

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