In the trapezoid below, QR is parallel to NO. If NP = 9, QP = 7.2, NO = 8,
and PO 6, find the length of PR. Figures are not necessarily drawn to scale.
=
Answer: PR=
R
Q
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The values of x are 3 or 0. 3 and 0 will satisfy the equation |2x-3| +7 =10.

What is an absolute function?

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value. The parent function with an absolute value is defined as f(x)=| x |.

Given equation is

|2x-3| +7 =10

Subtract 7 from both sides:

|2x-3| +7 - 7 = 10 - 7

|2x-3| = 3

Applying absolute function:

Either, 2x-3 = 3         or, 2x-3 = -3

Add 3 on both sides:

2x = 6                         2x = 0

Divide both sides by 2:

x = 3      or     x = 0

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The requried, percentage of students who study less than 2.50 hours a day is approximately 25.14 percent.

A Z-score is stated as the fractional model of data point to the mean using standard deviations.

We need to convert 2.50 hours to a standard score (z-score) using the formula,

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation.

z = (2.50 - 3.00) / 0.75

z = -0.67

This means that 2.50 hours is 0.67 standard deviations below the mean.

We can use a standard normal distribution table or a calculator to find the percentage of the distribution that falls below this standard score. For example, using a standard normal distribution table, we can look up the area to the left of z = -0.67 and get:

P(z < -0.67) = 0.2514

So the correct answer is (a) 25.14 percent.

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Answer:

see explanation

Step-by-step explanation:

using the rules of radicals

• [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

• [tex]\sqrt{\frac{a}{b} }[/tex] ⇔ [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex]

(1)

[tex]\sqrt{108}[/tex]

= [tex]\sqrt{36(3)}[/tex]

= [tex]\sqrt{36}[/tex] × [tex]\sqrt{3}[/tex]

= 6[tex]\sqrt{3}[/tex]

(2)

[tex]\sqrt{14}[/tex] × [tex]\sqrt{35}[/tex]

= [tex]\sqrt{14(35)}[/tex]

= [tex]\sqrt{490}[/tex]

= [tex]\sqrt{49(10)}[/tex]

= [tex]\sqrt{49}[/tex] × [tex]\sqrt{10}[/tex]

= 7[tex]\sqrt{10}[/tex]

(3)

[tex]\sqrt{\frac{28}{64} }[/tex]

= [tex]\frac{28}{\sqrt{64} }[/tex]

= [tex]\frac{\sqrt{28} }{8}[/tex]

= [tex]\frac{\sqrt{4(7)} }{8}[/tex]

= [tex]\frac{\sqrt{4}(\sqrt{7}) }{8}[/tex]

= [tex]\frac{2\sqrt{7} }{8}[/tex]

= [tex]\frac{\sqrt{7} }{4}[/tex]

Answer:

Below

Step-by-step explanation:

.89      '9' is in the hundredths place and is greater than 8

Aircraft A has 496 seats and Aircraft B has 347 seats.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.

To find the number of seats for each aircraft, we can use the equation 643 = 496 + 147. From this equation, we can see that aircraft A has 496 seats and aircraft B has 147 seats.

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In summary, A, B, E are valid linear programming relationships, while C, D, F are not.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

A. -1A+2B less than or equal to 70: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

B. 2A -2B= 50: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

C. 1A-2B^2 less than or equal to 10: This relationship is not acceptable for a linear programming model because it contains a quadratic term, B^2. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

D. 3(square root of) A + 2B greater than or equal to 15: This relationship is not acceptable for a linear programming model because it contains a square root function. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

E. 1A+1B=6: This is a valid linear programming relationship, and it can be included in a linear programming model. The domain for A and B can be any non-negative real number.

F. 2A+5B+1AB less than or equal to 25: This relationship is not acceptable for a linear programming model because it contains a product of variables, AB. Linear programming models can only have linear relationships, i.e., relationships with variables raised to the first power.

Therefore, In summary, A, B, E are valid linear programming relationships, while C, D, F are not.

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Answer:

Using the ratio given, we know that for every 5 colored pencils, there are 2 markers in each box.

Therefore:

The first blank represents the number of colored pencils in the box. Since the ratio of colored pencils to markers is 5 to 2, we can calculate that there are 5 colored pencils for every 2 markers. This means that for each box, there are 5/7 of the total number of items are colored pencils. So the missing value in the first row is 25.

The second row indicates that there are 20 items in the box. We know that the first row (colored pencils) has 25 items, and since the total number of items in the box is 20, the missing value in the second row (markers) is 20 - 25/5 = 15.

The third row represents the total number of colored pencils and markers in each box. We know that there are 25 colored pencils and 15 markers in each box, so the total number of items in each box is 40.

Therefore, the completed table would be:

Number of Colored | 25 | 20 | 25 |

Pencils

Number of Markers | 6 | 15 | 6 |

Total Number of

Colored Pencils and | 31 | 35 | 40 |

Markers in the Box​

The Standard deviation of the given data is 989.615.

The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We have data as

$54,410, $51,991, $51,730, $51,300, $51,196, $51,190, $51,122, $51,115, $51,037 and $50,875.

Also we have

Count, N: 10

Sum, Σx: 515966

Mean, μ: 51596.6

Now, using the formula of Standard Deviation

= √1/ N[tex]\sum_{i=1}^n (x_i- \mu)[/tex]²

= (54410 - 51596.6)² + (51991 - 51596.6)² +(51730 - 51596.6)² + (51300 - 51596.6)²+ (51122- 51596.6)² + (51115- 51596.6)² + (51037- 51596.6)² + (50875 - 51596.6)² / 10

= √9793384.4 /10

= √979338.44

= 989.615

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Answer:

Step-by-step explanation:

The statement if Cathy does not love horses, she is not a gambler is valid.

Relative frequency is the ratio of the considered sub group's count to the total count. (so its frequency of the considered sub group relative to the total frequency).

We are given;

The two arguements

Now,

A). The argument is valid. This is an example of the disjunctive syllogism, which is a valid form of argument. If we have a disjunction "A or B", and we know that A is false, then we can conclude that B must be true. In this case, "she will go to school or she will get a job" is the disjunction, and "she will not get a job" tells us that "she will not get a job" is true. Therefore, we can conclude that "she will go to school" must be true.

B). The argument is invalid. This is an example of the fallacy of affirming the consequent. The conditional statement "if Cathy is a gambler, then she lives in Marine" tells us that if Cathy is a gambler, then she lives in Marine. However, it does not tell us anything about whether Cathy is a gambler or not. The fact that "Cathy lives in Marine and she loves horses" does not give us any information about whether Cathy is a gambler or not.

Therefore, by the given conditions answer "if Cathy does not love horses, she is not a gambler" will be valid

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Answer:

x = [tex]\frac{7}{12}[/tex]

Step-by-step explanation:

[tex]7-2(3-8x)=7-6-16x[/tex]

Add/subtract like terms

[tex]5(3-8x)=1-16x[/tex]

Distribute 5

[tex]15-40x=1-16x[/tex]

Simplify

[tex]-40x+15=-16x+1[/tex]

Add -16x to both sides

[tex]-24x+15=1[/tex]

Subtract 15 on both sides

[tex]-24x=-14[/tex]

Divide by -24

[tex]x=\frac{7}{12}[/tex]

Answer:

[tex]\frac{1}{8}[/tex] cup pretzels, [tex]\frac{3}{16}[/tex] cup nuts of your choice, [tex]\frac{1}{8}[/tex] cup raisins, [tex]\frac{1}{12}[/tex] cup chocolate chips (optional)

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

If we need to multiply the fractions in the recipe by [tex]\frac{1}{4}[/tex], we just need to multiply the denominator by 4.

[tex]\frac{2}{4}[/tex] cups pretzels becomes [tex]\frac{2}{16}[/tex] or [tex]\frac{1}{8}[/tex].

This is because the denominator (4) is multiplied by 4 to get 16. The numerator doesn't change.

[tex]\frac{3}{4}[/tex] cup nuts becomes [tex]\frac{3}{16}[/tex].

This is because the denominator (4) is multiplied by 4 to get 16. The numerator doesn't change.

[tex]\frac{1}{2}[/tex] cup raisins becomes [tex]\frac{1}{8}[/tex].

This is because the denominator (2) is multiplied by 4 to get 8. The numerator doesn't change.

[tex]\frac{1}{3}[/tex] cup chocolate chips becomes [tex]\frac{1}{12}[/tex].

This is because the denominator (3) is multiplied by 4 to get 12. The numerator doesn't change.

Now, the recipe looks like this:

[tex]\frac{1}{8}[/tex] cup pretzels

[tex]\frac{3}{16}[/tex] cup nuts of your choice

[tex]\frac{1}{8}[/tex] cup raisins

[tex]\frac{1}{12}[/tex] cup chocolate chips (optional)

The values to put in the box will be:

x

y

x.y

x^2

y^2

4

19

76

16

361

9

46

414

81

2116

7

30

210

49

900

6

31

186

36

961

5

23

115

25

529

5

28

140

25

784

4

21

84

16

441

8

42

336

64

1764

total

48

240

1561

312

7856

The sample size is the number of observations used for determining the estimations of a given population.

The size of the sample has been drawn from the population. Sampling is the process of selection of a subset of individuals from the population to estimate the characteristics of the whole population.

Inthi case, sample size n = 8 and the correlation coefficient is 0.9643.

The appropriate values are given above.

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Both Student A and Student B's representations of the expression 9/y³ⁿ are incorrect.

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a meaningful way. An expression can represent a value, a quantity, a function, or some other mathematical object. Expressions can be made up of one or more terms. A term is a group of numbers, symbols, and/or variables that are separated by a plus or minus sign. Expressions can also include mathematical operations, such as addition, subtraction, multiplication, and division, as well as exponents and parentheses. Expressions are used in various areas of mathematics, including algebra, calculus, and statistics, to represent mathematical relationships and to solve problems.

Here,

Student A represents the expression as the product of 9 and y times the product of 3 and t, which can be written as: 9 * y * 3 * t = 27yt.

This representation is incorrect because it does not include the exponent 3 in the denominator. The correct representation of the expression is: 9 / y^3t.

Student B represents the expression as the quotient of 9 and y times the sum of 3 and t, which can be written as: 9 / y * (3 + t) = (27 + 9t) / y.

This representation is also incorrect because it incorrectly combines the sum of 3 and t in the denominator. The correct representation of the expression is: 9 / y^3t.

To represent the expression correctly, we need to include the exponent 3 in the denominator, indicating that y is being raised to the power of 3, and include t as a separate factor in the denominator. Therefore, the correct representation of the expression is: 9 / (y^3 * t).

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Answer:

Student A says prodact of Tandy, but 9 is 9 y so it's quotient.

Step-by-step explanation:

Answer:

19. x = 60

20. x= 27

Step-by-step explanation:

19. Given 2 triangles are congruent

so BQ/BC = BR/BD

30/84 = x/168

84x = 30(168)

84x = 5040

x = 5040/84 = 60

20. Given 2 triangles are congruent

QS/QP = ST/PR

18/x = 10/15

10x = 18(15)

10x = 270

x = 270/10 = 27

Your statement is partially correct congruent .

Two triangles are similar if they have all three corresponding angles congruent or equal in measure, or if they have two corresponding angles congruent and the corresponding sides are in proportion (i.e., the ratio of the length of one side to the length of the corresponding side in the other triangle is constant). This is known as the Angle-Angle Similarity Theorem (AA Similarity), or the Angle-Side-Angle Similarity Theorem (ASA Similarity).

It is important to note that if only one pair of corresponding angles is congruent, the triangles are not necessarily similar. For example, two right triangles with one acute angle congruent are not necessarily similar, since the other acute angles are not congruent. Similarly, if two triangles have all three sides in proportion, they are not necessarily similar unless all three corresponding angles are also congruent.

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Answer:

To determine how much the tourist will receive while leaving Nepal, we need to know the total cost of the 5 Nepali caps including VAT, and then subtract any taxes or fees that the tourist may have paid when purchasing the caps.

Given that the tourist bought 5 Nepali caps at a cost of Rs 452 per piece including VAT, we can calculate the total cost of the caps as:

Total cost of 5 Nepali caps = 5 x Rs 452 = Rs 2260

Since the cost already includes VAT, we do not need to add any additional taxes or fees.

Therefore, if the tourist does not make any additional purchases or incur any other expenses while in Nepal, they will receive back Rs 2260 when leaving Nepal.

The age of Julia is 13 years.

Integers are whole numbers, including both positive and negative numbers, that do not have any fractions or decimals. In mathematics, integers are often used to represent real-world quantities such as age, time, and money.

In this problem, Julia is the oldest of three siblings whose ages are consecutive integers. We can represent this using the equation x + (x+1) + (x+2) = 42, where x is Julia's age.

To solve this equation, we can use the distributive property to expand the left side of the equation to 3x + 3 = 42.

We can then subtract 3 from both sides of the equation to get 3x = 39. Finally, we can divide both sides by 3 to get x = 13.

Therefore, Julia's age is 13.

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Complete Question:

Julia is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 42, find Julia's age.

If a homeowner would like to spread shredded bark (mulch) over her flowerbeds. it will cost $65.07 to cover all the flowerbeds with shredded bark.

To calculate the amount of mulch needed, we need to find the volume of each flowerbed and add them together. The recommended depth for the mulch is 4 inches, which is equal to 4/12 = 1/3 feet.

For the first flowerbed, the volume of mulch needed is:

24 ft x 3.1 ft x 1/3 ft = 24.8 cubic feet

For the second flowerbed, the volume of mulch needed is:

14 ft x 4.3 ft x 1/3 ft = 20.87 cubic feet

For the third flowerbed, the volume of mulch needed is:

30 ft x 1.5 ft x 1/3 ft = 15 cubic feet

The total volume of mulch needed to cover all three flowerbeds is:

24.8 cubic feet + 20.87 cubic feet + 15 cubic feet = 60.67 cubic feet

Since there are 27 cubic feet in a cubic yard, the total amount of mulch needed is:

60.67 cubic feet / 27 cubic feet per cubic yard = 2.25 cubic yards

At a cost of $27 per cubic yard, the total cost of the mulch is:

2.25 cubic yards x $27 per cubic yard = $60.75

Therefore, it will cost $60.75 to cover all of the flowerbeds with shredded bark.

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Answer:

90  berries

Step-by-step explanation:

There are total 15 students who take all three subjects.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We know that;

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C)- n(A ∩ C)+ n(A∩B ∩C)

Here, Total number of students in the school = 62

Hence, By using theorem;

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(B ∩ C)- n(A ∩ C)+ n(A∩B ∩C)

Here, Let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry

so putting values,

62 =  40 + 42 + 38 - 20 - 28 - 25 + n(A∩B ∩C)

62 + 73 - 120 = n(A∩B ∩C)

n(A∩B ∩C) = 15

Therefore, There are total 15 students who take all three subjects.

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Answer:320000

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's assume that the amount invested at 10% is x, and the amount invested at 5% is (60000 - x), since the total investment is $60,000.

The interest earned on the 10% investment after one year would be 0.10x, and the interest earned on the 5% investment after one year would be 0.05(60000 - x).

We are given that the interest earned by the two accounts is equal, so we can set up an equation:

0.10x = 0.05(60000 - x)

Simplifying this equation, we get:

0.10x = 3000 - 0.05x

Adding 0.05x to both sides, we get:

0.15x = 3000

Dividing both sides by 0.15, we get:

x = 20000

Therefore, the amount invested at 10% is $20,000, and the amount invested at 5% is ($60,000 - $20,000) = $40,000.

To check that the interest earned is equal for both investments, we can calculate:

Interest earned on 10% investment = 0.10($20,000) = $2,000

Interest earned on 5% investment = 0.05($40,000) = $2,000

As expected, the interest earned on both investments is equal.

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The Fibonacci numbers are defined by the following recursive formula: f0 = 1, f1 = 1, fn = fn−1 + fn−2 for n ≥ 2. Thus, each number in the sequence (after the first two) is the sum of the previous two numbers.

Answer:

Step-by-step explanation:

To find the equilibrium quantity and equilibrium price for the demand and supply functions, we need to find the point where the quantity demanded and the quantity supplied are equal. This point is known as the equilibrium point and is represented by the intersection of the demand and supply curves.

The demand function is given by p = -0.1q²-0.2q+9, and the supply function is given by p = 0.2q²+0.4q+1.8.

To find the equilibrium quantity, we need to set the quantity demanded equal to the quantity supplied:

-0.1q²-0.2q+9 = 0.2q²+0.4q+1.8

Simplifying and rearranging the terms, we get:

0.3q² + 0.6q - 7.2 = 0

Using the quadratic formula, we can solve for q:

q = (-0.6 ± √(0.6² - 4(0.3)(-7.2))) / (2(0.3))

q = (-0.6 ± √(0.6² + 8.64)) / 0.6

q = (-0.6 ± √9.36) / 0.6

q = (-0.6 ± 3.06) / 0.6

q = 4.6, -5.0

Since the quantity cannot be negative, the equilibrium quantity is q = 4.6.

To find the equilibrium price, we can substitute the equilibrium quantity into either the demand or supply function:

p = 0.2q²+0.4q+1.8

p = 0.2(4.6)²+0.4(4.6)+1.8

p = 7.82

Therefore, the equilibrium quantity is 4.6 units and the equilibrium price is $7.82.

Answer:

Rs 1098 can buy 45.75 apples (or approximately 45 apples, since we cannot buy a fractional part of an apple).

Step-by-step explanation:

We can use proportionality to solve this problem. Since the price of apples is directly proportional to the number of apples, we can set up a proportion:

2 apples / Rs 48 = x apples / Rs 1098

To solve for x, we can cross-multiply and simplify:

2 * Rs 1098 = 48 * x

Rs 2196 = 48x

x = Rs 2196 / 48

x = 45.75

Therefore, Rs 1098 can buy 45.75 apples (or approximately 45 apples, since we cannot buy a fractional part of an apple).

If rectangles S and T are similar then the area of rectangle T is 96 units².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

Since the rectangles S and T are similar, their corresponding sides are proportional.

Let the length of rectangle T be "x" units. Then -

width of S / width of T = length of S / length of T

Using the given values -

16/9.6 = (√160) / (√x)

Simplifying this equation it is obtained-

x = (9.6/16) × (√160)²

x = 10

Therefore, the length of rectangle T is 10 units.

The area of rectangle T is then -

Area of T = width of T × length of T

Area of T = 9.6 × 10

Area of T = 96 units²

Therefore, the area of rectangle T is 96 units².

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Answer:

x = 40° , y = 43° , z = 97°

Step-by-step explanation:

∠ DAC = y = ∠ ACB = 43°

• opposite angles in a parallelogram are congruent , then

z = ∠ D = 97°

the sum of the 3 angles in Δ ACD = 180° , that is

x + y + 97° = 180°

x + 43° + 97° = 180°

x + 140° = 180° ( subtract 140° from both sides )

x = 40°

then

x = 40° , y = 43° , z = 97°

Answer:

Step-by-step explanation:

125.

Answer:  22.50

Step-by-step explanation:

25 x 0.1

25 - 2.5

Answer:

The correct answer is 22.50