what is 1 1/3 x 1 3/4

The two-column proof that proves that ΔRSV ≅ ΔTSV by the SSS congruence theorem is explained below.

A Two-Column Proof is a method of providing a logical step-by-step demonstration of a mathematical statement or theorem using a column for statements and a column for corresponding justifications or reasons.

Tus, we have the two-column proof as explained below:

Statement                            Reason                                        

1. RS ≅ TS, V is the             1. Given

midpoint of RT.                            

2. RV ≅ TV                          2. Def. of midpoint

3. SV ≅ SV                          3. Reflexive property of congruency.

4. ΔRSV ≅ ΔTSV                 4. SSS

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Answer:

-33

Step-by-step explanation:

With the brackets in an equations, it just means you are going to be solving within there first before moving on.

For any equations such as this, you'll want to follow PEMDAS.

Parenthesis (x)
Exponents \(x^{2}\)
Multiplication x * y
Division x/y or x÷y or \(\frac{x}{y}\)
Addition x+y
Subtraction x-y

To start, we're just going to take the bracket equations 2+4 x 2 + (10 - 5)

\(2+4*2+5/5\)

Moving down PEMDAS we have no exponents, but multipication and division, whichever comes first in the equation.

4*2 = 8

5/5 = 1

2+8+1 = 11

-3[11] = (You use multiplication here) -33

-39

Step-by-step explanation:

\({ \blue{ \sf{ - 3{[2 + 4 \times 2 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[6 \times 2 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + (5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + 1]}}}}\)

\( { \blue{ \sf{ - 3[13]}}}\)

\({ \red{ \sf{ - 39}}}\)

Answer:

3355

Step-by-step explanation:

55 x 61 = 3355

12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

8 inches long. into how many pieces can the sausage be cut if each piece is to be two-thirds of an inch.

Divide 8 by 2/3

8÷ 2/3

8× 3/2

12

12 pieces can the sausage be cut if each piece is to be two-thirds of an inch.

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Answer:

( x + 2 )² + ( y - 6 )² = 49

Step-by-step explanation:

→ Write the form of an equation of a circle

( x - a )² + ( y - b )² = r²

→ Substitute in the centre remembering to switch the signs

( x + 2 )² + ( y - 6 )² = r²

→ Substitute in radius

( x + 2 )² + ( y - 6 )² = 49

The approximate number of students with Scores between 68 and 83 is 98.Answer: a. 98

The five-number summary for scores on a statistics exam is: 35, 68, 77, 83 and 97. In all, 196 students took this exam About how many students had scores between 68 and 83?

The five-number summary consists of the minimum value, the first quartile, the median, the third quartile, and the maximum value.

The interquartile range is the difference between the third and first quartiles. Interquartile range (IQR) = Q3 – Q1, where Q3 is the third quartile and Q1 is the first quartile. The 5-number summary for scores on a statistics exam is given below:

Minimum value = 35

First quartile Q1 = 68

Median = 77

Third quartile Q3 = 83

Maximum value = 97

The interval 68–83 is the range between Q1 and Q3.

Thus, it is the interquartile range.

The interquartile range is calculated as follows:IQR = Q3 – Q1 = 83 – 68 = 15

The interquartile range of the scores between 68 and 83 is 15. Therefore, the number of students with scores between 68 and 83 is roughly half of the total number of students. 196/2 = 98.

Thus, the approximate number of students with scores between 68 and 83 is 98.Answer: a. 98

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the sum of the measures of the interior angles of each convex polygon.

18-gon is 2880 degrees.

To find the sum of the measures of the interior angles of a convex polygon, we can use the formula:

Sum = (n - 2) * 180 degrees

where n is the number of sides (or vertices) of the polygon.

For an 18-gon, the number of sides (n) is 18. Substituting this value into the formula, we get:

Sum = (18 - 2) * 180 degrees = 16 * 180 degrees = 2880 degrees

Therefore, the sum of the measures of the interior angles of an 18-gon is 2880 degrees.

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Answer:

x=7

Step-by-step explanation:

The two triangles are congruent so the equation is

9x-15=7x-1

9x-7x=15-1

2x=14

x=7

Answer:

x=7

Step-by-step explanation:

9x-15=7x-1

To prove that τ and σ are multiplicative, we need to show that if m and n are relatively prime, then τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n).

To prove τ(mn) = τ(m)τ(n), we can start by considering the prime factorization of m and n. Let's say m = p₁^a₁ * p₂^a₂ * ... * pₖ^aₖ and n = q₁^b₁ * q₂^b₂ * ... * qₙ^bₙ, where p₁, p₂, ..., pₖ and q₁, q₂, ..., qₙ are distinct prime numbers. Since m and n are relatively prime, none of their prime factors overlap.

Now, the divisors of mn are the numbers of the form p₁^x₁ * p₂^x₂ * ... * pₖ^xₖ * q₁^y₁ * q₂^y₂ * ... * qₙ^yₙ, where 0 ≤ xᵢ ≤ aᵢ and 0 ≤ yⱼ ≤ bⱼ. Thus, the number of divisors of mn, τ(mn), can be calculated by multiplying the number of divisors of m, τ(m), with the number of divisors of n, τ(n). Hence, τ(mn) = τ(m)τ(n).

To prove σ(mn) = σ(m)σ(n), we can again use the prime factorization of m and n. Similar to the previous proof, the sum of divisors of mn, σ(mn), can be calculated by multiplying the sum of divisors of m, σ(m), with the sum of divisors of n, σ(n). Hence, σ(mn) = σ(m)σ(n).

Therefore, we have proved that τ and σ are multiplicative when m and n are relatively prime.

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We have shown that both τ and σ are multiplicative functions, satisfying the properties τ(mn) = τ(m)τ(n) and σ(mn) = σ(m)σ(n) for relatively prime numbers m and n.

To prove that τ (the number of positive divisors) and σ (the sum of positive divisors) are multiplicative functions, we need to show that for any two relatively prime numbers, m and n, the following properties hold:

1. τ(mn) = τ(m)τ(n)

2. σ(mn) = σ(m)σ(n)

Let's start with property 1:

1. τ(mn) = τ(m)τ(n)

If m and n are relatively prime, it means that they do not share any prime factors. Therefore, the divisors of mn are formed by taking a divisor of m and a divisor of n. Each divisor of mn can be uniquely expressed as the product of a divisor of m and a divisor of n.

Since the number of divisors of mn is equal to the product of the number of divisors of m and the number of divisors of n, we can conclude that τ(mn) = τ(m)τ(n).

Now let's move on to property 2:

2. σ(mn) = σ(m)σ(n)

Similar to property 1, we can express the sum of divisors of mn as the sum of products, where each product is formed by taking a divisor of m and a divisor of n. Again, since m and n are relatively prime, their divisors are distinct.

Using the distributive property, we can expand the sum of products as the sum of two separate terms: one involving the divisors of m and another involving the divisors of n. The sum of divisors of mn is therefore equal to the product of the sum of divisors of m and the sum of divisors of n.

Hence, we can conclude that σ(mn) = σ(m)σ(n).

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Answer:

7 (7y - 2)

Step-by-step explanation:

49y - 14

Factor out 7.

7 (7y - 2)

Hope it helps. =)

The chef should use approximately 80 milliliters of the first brand (5% vinegar) and (240 - 80) = 160 milliliters of the second brand (11% vinegar) to make 240 milliliters of dressing that is 9% vinegar.

Let's assume the chef uses x milliliters of the first brand (5% vinegar) and (240 - x) milliliters of the second brand (11% vinegar).

To find the amounts of each brand needed, we can set up an equation based on the vinegar content:

(0.05x + 0.11(240 - x)) / 240 = 0.09

Simplifying the equation:

0.05x + 0.11(240 - x) = 0.09 * 240

0.05x + 26.4 - 0.11x = 21.6

-0.06x = -4.8

x = -4.8 / -0.06

x ≈ 80

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112 gallons of white paint are needed to make the 140 gallons of pink paint.

We know that to make one gallon of pink paint, 4 parts must be white and 1 part must be red.

So, if we divide one gallon in 5 parts, we get five 1/5 gallons.

4 of these are white, then to make one gallon of pink paint we need 4/5 gallons of white paint.

Now, if we want 140 gallons of pink paint, then we need 140 times the above amount of white paint, which is:

140*(4/5) gal = 112 gal

112 gallons of white paint are needed to make the 140 gallons of pink paint.

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The length of the fence needed to enclose the garden is 27.792 meters.

Given that one side of the garden has a length of 10 meters. Assuming the points at each finish of this side are 44º and 58°.To find, The length of the wall expected to encase the gardenSolution: The triangle is shown below;Let Stomach muscle = 10 meters. BC x BD meters ADC = 44º;

Using the Sine rule, $frac10sin 78 = $fracxsin 44$ $Rightarrow x = $frac10sin 44$ $Rightarrow x = 7.154 meters in a triangle ADC. ABD = 58o. ACD = (180 - (44+58)) = 78o. Using the Sine rule, $frac10sin 58 = $fracxsin 78$; $Rightarrow x = $frac10sin 78$; $Rightarrow x = 10.638$ meters in the triangle ABD. The required fence length to enclose the garden is 27.792 meters, or 10 times 7.154 times 10.638. As a result, the fence that is required to enclose the garden must be 27.792 meters long.

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If the wax cost $1.38 a square foot, the cost of wax to cover the area of the floor is $1,569.75.

The correct option is B.

The total area of the floor is calculated from the shape of the floor.

The floor is made up of a trapezoid and a rectangle.

The area of a trapezoid can be calculated as:

A = (a + b)/2 * h

where

a and b are the lengths of the bases and h is the height.

The trapezoid has a height of 15 feet and bases of 35 feet and (20 - 20) or 10 feet. So its area is:

A = (35 + 10)/2 * 15

A = 337.5 square feet

The rectangle has a base of 20 feet and a height of 40 feet. So its area is:

A =20 * 40

A = 800 square feet

The total area of the figure is the sum of the areas of the trapezoid and triangle:

A = 337.5 + 800

A = 1137.5 square feet

Finally, to find the cost of the wax, we multiply the area by the cost per square foot:

Cost = 1137.5 * $1.38

Cost  = $1569.75

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Answer:

Step-by-step explanation:

Initial value of house is $478000

Change in value is 8% greater:

We need 8% of Value

\(\\ \sf\longmapsto 8\%\:of\;478000\)

\(\\ \sf\longmapsto 0.08(478000)\)

\(\\ \sf\longmapsto 38240\$\)

Current value:-

\(\\ \sf\longmapsto 478000+38240=516240\)

In a binomial experiment, there are only two possible outcomes for each of the n trials. True statement.

These outcomes are typically labeled as "success" and "failure," and they are mutually exclusive (meaning that only one outcome can occur per trial) and collectively exhaustive (meaning that one of the two outcomes must occur per trial).

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The union of two sets is to avoid counting the same elements twice.

The mathematical logic subfield of set theory investigates sets, which can be loosely defined as collections of objects. Although any object can be combined into a set, set theory, as a mathematical discipline, focuses primarily on those that are relevant to mathematics as a whole.

Given union of set

(A ∪ B),

The set of all objects that are members of either A or B, or both, is the union of the sets A ∪ B.

let us take example,

A = { 1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

(A ∪ B) = { 1, 2, 3, 4} ∪  {3, 4, 5, 6, 7}

we can simply write all of A and B's elements in a single set to avoid duplicates to find A U B.

(A ∪ B) = {1, 2, 3, 4, 5, 6, 7}

Hence the  union of two sets is a set that contains all the elements of both set and avoid duplicates.

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Answer:

=> (xy)⁵z³

Step-by-step explanation:

hope it's helpful ..

Answer:

x=-4, y=-1

Step-by-step explanation:

Given the following system of equations, solve the system using elimination.

\(\left \{ {{-2x-y=9} \atop {2x-9y=1}} \right.\)

(1) - Add the equations together

\(\left\begin{array}{ccc}&-2x-y=9\\+&2x-9y=1\end{array}\right\\\\\Longrightarrow -10y=10\\\\\therefore \boxed{y=-1}\)

Notice how the x term was eliminated, hence the name for this method is "elimination."

(2) - Take the value we just found for y and plug it into either of the two equations and solve for x

\(2x-9y=1\\\\\Longrightarrow 2x-9(-1)=1\\\\\Longrightarrow 2x+9=1\\\\\Longrightarrow 2x=-8\\\\\therefore \boxed{x=-4}\)

(3) - Thus, the system is solved. When x=-4, y=-1.

Nathan's salary is $48 and Will's salary which three times of Nathan's salary is $144.

What is salary?

An employment contract may include a salary clause as a type of recurring payment from an employer to an employee. In contrast, piece wages are paid separately for each job, hour, or other unit rather than on a regular schedule. Salary can also be seen from the perspective of operating a corporation as the expense of obtaining and keeping employees to carry out operations; this is known as a personnel expense or salary expense. Payroll accounts are used in accounting to record salaries.

It is given in the question that Will's salary is three times Nathan's salary.

So, lets assume that Nathan's salary is X it implies that Will's salary will be 3 times X = 3X

Together they earn $ 192.

So,

X + 3X = 192

4X = 192

X = 192/4

X = 48

Therefore, Nathan's Salary is $48

Since, Will's salary is 3 times of Nathan's salary,

So,

Will's salary = 3 (48) = 144

Therefore, Will's Salary is $144

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Answer:

5. 8

6. 18

Step-by-step explanation:

5.

a(a^2 + a - 1) + 7 =

= a^3 + a^2 - a + 7

For a = -1,

= (-1)^3 + (-1)^2 - (-1) + 7

= -1 + 1 + 1 + 7

= 8

6.

2ab(a + b) - 3ab(a - b) =

= 2a^2b + 2ab^2 - 3a^2b + 3ab^2

= -a^2b + 5ab^2

For a = 1 and b = 2,

= -(1)^2(2) + 5(1)(2)^2

= -1(2) + 5(4)

= - 2 + 20

= 18

Answer:

Step-by-step explanation:

a(a^2 + a -1) +7

a^3+a^2-a+7

f(-1)=(-1)^3+(-1)^2-(-1)+7

f(-1)=-1+1+1+7

f(-1)=0+1+7

f(-1)=8

2ab(a+b)-3ab(a-b)

2a^2*b+2ab^2-3a^2*b+3ab^2

−a^2*b+5ab^2

when a=1 and b=2

−a^2*b+5ab^2

−(1)^2*2+5*1*2^2

-1*2+5*1*4

-2+5*4

-2+20

18

The probability that the average grade in a statistics course is more than 74, given a sample of 52, is approximately 0.1446 or 14.46%.

To calculate the probability that the average grade is more than 74, we need to standardize the distribution using the z-score and then find the corresponding probability using the standard normal distribution table (Appendix B.1).

First, we calculate the z-score using the formula:

z = (x - μ) / (σ / √n)

Where:

x = desired average grade (74)

μ = population mean (71)

σ = population standard deviation (8.5)

n = sample size (52)

Plugging in the values, we get:

z = (74 - 71) / (8.5 / √52)

Now, let's calculate the z-score:

z = 1.0607

Next, we find the probability corresponding to this z-score using the standard normal distribution table or a calculator. The probability of obtaining a z-score of 1.0607 or more can be determined as:

P(z > 1.0607)

Looking up the z-value in the standard normal distribution table, we find that the probability is approximately 0.1446.

Therefore, the probability that the average grade is more than 74 is approximately 0.1446 or 14.46%.

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Answer: -2 and 0

Step-by-step explanation:

Answer:

The answer above is correct ( -2 & 0)

The answer to the next part is

- D. 1.27

- E. 4.73

Step-by-step explanation:

I got this correct on Egd. 2021

(Also, the question above should be written as "x4 − 4x3 = 6x2 − 12x

From least to greatest, what are the integral roots of the equation?" it is 4x cubed, not squared)

Answer:

The last one

Step-by-step explanation:

Step-by-step explanation:

A. Variables:

Let's denote:

S as the amount of money Kyrie has saved (in dollars)

t as the number of months that have passed since he started saving

B. Equation:

Since Kyrie starts with $5,000 and saves $650 each month, we can write the equation for his savings after t months as follows:

S = 5000 + 650t

C. After 15 months:

To find out how much Kyrie has saved after 15 months, we just need to substitute t = 15 into the equation we derived in part (B):

S = 5000 + 650(15) = 14,750

Therefore, Kyrie has saved $14,750 after 15 months.

The factorite Olympic sports survey had a sample size of around 753 people, based on a reported margin of error of 3.5%.

To determine the number of people surveyed in the factorite Olympic sports survey with a reported margin of error of 3.5%, we need to use a statistical formula. The formula is:

n = [(Z-score)² * p * (1-p)] / (margin of error)²

Where: ²
- n = sample size
- Z-score = value obtained from a standard normal distribution table for the desired confidence level (let's say 95%, which corresponds to a Z-score of 1.96)
- p = proportion of the population estimated to have the characteristic of interest (let's assume 0.5 for simplicity, which gives the maximum sample size)
- margin of error = 0.035 (given in the question)

Plugging in these values, we get:

n = [(1.96)* 0.5 * (1-0.5)] / (0.035)²
n = 752.84

Therefore, the sample size of the factorite Olympic sports survey was approximately 753 people.



The number of people surveyed in the factoring Olympic sports survey can be calculated using a statistical formula that takes into account the margin of error, confidence level, and estimated proportion of the population with the characteristic of interest. Assuming a 3.5% margin of error and a 95% confidence level, the sample size is approximately 753 people. This means that the results of the survey can be generalized to the population within a certain margin of error and confidence level.



In conclusion, the factorite Olympic sports survey had a sample size of around 753 people, based on a reported margin of error of 3.5%. This sample size is sufficient to provide reliable results with a 95% confidence level and within a certain margin of error. The statistical formula used to determine the sample size takes into account important factors that affect the accuracy and representativeness of the survey results.

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Answer:  resultant

Step-by-step explanation: