In ΔIJK, k = 7.2 cm, ∠J=55° and ∠K=67°. Find the length of i, to the nearest 10th of a centimeter.

Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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Answer:

35 pieces

(the leftover bits could be cobbled together to make one more, but that's probably just trying too hard. I wouldn't count it.)

Step-by-step explanation:

You can do this with everything in inches or with everything in feet.

The length of the cut ribbon is 15 inches. This is 1.25 feet (bc 15/12 = 1.25). The total length of the roll is 9 feet, which is 108 inches.

Either:

9 ÷ 1.25

OR 108÷15

Both of these calculations give the answer 7.2

This means that the seamstress can cut 7 pieces from the roll. There will be a little bit leftover but not enough to cut an 8th piece.

There are 5 rolls of ribbon to begin with. If 7 pieces can be cut from one roll, the multiply by 5 to find what can be cut from all 5 rolls.

7 × 5 = 35

The seamstress can cut 35 15-inches pieces of ribbon from her stash of 5 rolls.

Answer:

Step-by-step explanation:

when 13 bought we find these inequalities

x + 12y < 7  no

2x + 11y < 7.5 no

3x + 10y < 8 no

4x + 9y < 8.5 no

5x + 8y >  9  yes

When 14 bought we find these inequalities

x + 13y < 7.5 no

2x + 12y < 8 no

3x + 11y < 8.5 no

4x + 10y > 9 yes  

We want to find and solve a system of inequalities to determine some possible solutions to Arianna's situation.

The possible solution is:

x = 2

y = 12

And the graph can be seen at the end.

Now let's see how to solve this.

First, we need to write the system of inequalities, the information given is:

Now we can define the variables:

Then we must have:

x + y ≥ 13   (this means that she buys at least 13 fruits)

x*$1 + y*$0.50 ≤ $9  (this means that she can't spend more than $9)

Now we just need to graph these two lines, we can rewrite them as:

y ≥ 13 - x

y ≤ $9.00/$0.50 - x*$1/$0.50 = 18 - x*2

Then we just need to graph the two lines, and shade the region above the first one, and the region below the second one, the graph can be seen below:

Any point inside the double shaded region in the first quadrant is a possible solution. (we restrict only to the first quadrant because we can not use negative values for x nor for y).

Then a possible solution that we could choose is:

x = 2

y = 12

This means that she buys 2 peaches and 12 mangos.

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Answer:

y+4=3(x+2)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(8-(-4))/(2-(-2))

m=(8+4)/(2+2)

m=12/4

m=3

y-y1=m(x-x1)

y-(-4)=3(x-(-2))

y+4=3(x+2)

0.08

Convert the unit

\(Convert\ the\ unit\ for\ 7983centimeters:\\ 0.07983\)

Round the number

\(Round\ 0.07983\ to\ the\ required\ place\\ 0.08\)

I hope this helps you

:)

By the conversion of the 7983 centimeters to kilometers then 0.08

One kilometer is equal to 1000 centimeters. So, to convert one kilometer into a meter we have to divide by 1000.

We need to Convert the unit 7983 centimeters to a kilometer.

1 km = 1000 cm

Convert the unit to 7983 centimeters:

0.07983

Round the number

Therefore, Round 0.07983 to the required place 0.08 to the nearest hundredth.

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Answer:

y = -2x + 13

Need to know:

y = mx + b

Slope formula: y₂ - y₁/x₂ - x₁

Step-by-step explanation:

First, we have to find the slope of the equation.

To find this we use this equation: y₂ - y₁/x₂ - x₁

x₁ = 2

x₂ = 5

y₁ = 9

y₂ = 3

(3 - 9)/(5 - 3) = -6/3 = -2

The slope of of the equation is -2

y = -2x + b

Plug in one of the given coordinates. We'll use (5, 3)

3 = -2(5) + b

3 = -10 + b

Add 10 to both sides

3 = -10 + b

+ 10  + 10

b = 13

y = -2x + 13

The number of buses are 3 they took if each van holds 6 students and each bus holds 20 students.

What are the number of buses?

Let's use V and B to represent the number of vans and buses, respectively.

We know that:

V + B = 5 (since there were 5 vehicles in total)

6V + 20B = 72 (since there were 72 students in total)

We can use the first equation to solve for V in terms of B:

V = 5 - B

Then we can substitute this expression for V into the second equation:

6(5 - B) + 20B = 72

30 - 6B + 20B = 72

14B = 42

B = 3

Therefore, the class took 3 buses.

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Complete question is: A class of 72 students went on a field trip. They took 5 vehicles, some vans and some buses. the number of buses are 3, they took if each van holds 6 students and each bus holds 20 students.

Answer:

Step-by-step explanation:

The inequality that represents Jenny's situation is:

600 - 20w > 300

To solve for w, we can start by subtracting 600 from both sides of the inequality:

-20w > 300 - 600

-20w > -300

Next, we can divide both sides by -20, remembering to reverse the direction of the inequality because we are dividing by a negative number:

w < (-300) / (-20)

w < 15

Therefore, the number of weeks that Jenny can continue to withdraw $20 from her account is less than 15. Since Jenny cannot withdraw a fractional number of weeks, the largest whole number of weeks that satisfies the inequality is 14.

Therefore, Jenny can continue to withdraw $20 from her account for 14 weeks while still keeping more than $300 in her account for college.

Answer:

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

Given:

To find the arc measure (θ) in radians, we can use the formula:

Now, plug in the given values:

To solve for θ, divide both sides by 4:

Simplify the expression:

So, the arc measure (θ) is 2π/3 radians

The volume of the frustum of right circular cone =  7730 cube

The volume of the frustum of the right circular cone:

The formula for the Volume of Frustum of Cone (V)=\(\frac{1}{3} \pi H (R^2+r^2+Rr )\)

where,

         H = Height of frustum

         R = Radius of lower base

         r = Radius of top base

According to given question,

      Height of frustum(H) = 30 units

       Radius of lower base(R) = 21 units

        Radius of top base (r) = 11 units

Substituting all the given values in the formula of volume of the frustum of the cone we will get,

    The volume of a frustum of a right circular cone(V)   =\(\frac{1}{3} \pi H (R^2+r^2+Rr )\)

                                                                            \(=\frac{1}{3}*30(21^2+11^2+21*11)\\\\=10*(441+121+211)\\=10*(773)\\=7730 unit^3\)  

The volume of the frustum of the right circular cone =  271.22

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Answer:

not a function

Step-by-step explanation:

you're x or in this case, your domain, is not to repeat itself. however, there are 2 of a number (-2)

The probability that it has a mass of more than 120 g is 13/40.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Given,

frequency = 5   9   13   7   6

sum of frequency = 40

P(120<m<=180) = 13/40

P(180<m<=240) = 7/40

P(240<m<=300) = 6/40

Probability that it has a mass of more than 120 g = [P(120<m<=180) + P(180<m<=240) + P(240<m<=300) ]

⇒ 13/40 + 7/40 + 6/40

= 26/40

= 13/20

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Answer:

the probability is 2/9 x 4/9

probability is 8/81

Step-by-step explanation:

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

The calculated value of the probability of B is (c) 0.25

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

P(A or B) = 0.3

P(A and B) = 0.2

P(A/B) =0.8

First, we have

P(A/B) = P(A and B)/P(B)

Substitute the known values in the above equation, so, we have the following representation

0.2/P(B) = 0.8

So, we have

P(B) = 0.2/0.8

Evaluate

P(B) = 0.25

Hence, the probability of B is 0.25

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We have the line:

We have to find a perpendicular line that passes through point (-5,4).

As the original line is an horizontal line (slope = 0), a perpendicular line will be a line that is vertical (undefined slope) with an equation x = k, where k is a constant.

Then, as x = k defines the line that pass through all the points with coordinates (k,y), if it has to pass through (-5,4), then k = -5.

If k = -5, the line is x = -5.

We can picture this in a graph as:

Answer: the equation is x = -5.

The complete two-column proof that shows that ∠DBC ≅ ∠DCB using the definition of isosceles triangle is given in the image attached below.

Two sides directly opposite the two base angles of an isosceles triangle are congruent, so also are the two base angles congruent.

From the given diagram, we are told that:

AB ≅ AC and ∠BAD ≅ ∠CAD

Also, AD ≅ DA based on the reflexive property.

Thus, it implies that,

ΔBAD ≅ ΔCAD based on the SAS congruence theorem, because they have two pairs of congruent sides and one pair of congruent included angles.

Thus, since both triangles are congruent, therefore, DB = DC by CPCTC theorem.

Therefore, by the definition of isosceles triangle, ∠DBC ≅ ∠DCB.

Thus, the complete two-column proof that shows that ∠DBC ≅ ∠DCB using the definition of isosceles triangle is given in the image attached below.

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The number factor of a variable term is called the numerical coefficient.

Algebraic expression are made of terms . Terms might be a signed numbers, a variable, or a constant multiplied by a variable or variables.

Examples of an algebraic expression is as follows:

When a constant is multiplied by a variable or variables , that constant is called the coefficient.

In our example the variable is x . The number factor of the variable term x is called the numerical coefficient .

Therefore, the numerical coefficient in our case is 4.

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Answer:

a.) 0.115

b.) 0.087

Step-by-step explanation:

Given,

P(A) = 20% = 0.20

P(B) = 30% = 0.30

P(C) = 50% = 0.50

Let M - major repairing during first year

P(M/A ) = 0.05

P(M/B) = 0.10

P(M/C) = 0.15

a.)

P(M) = P(M∩A) + P(M∩B) + P(M∩C)

       = P(M/A).P(A) + P(M/B).P(B) + P(M/C).P(C)

      = (0.05)(0.20) + (0.30)(0.10) + (0.15)(0.50)

     = 0.01 + 0.03 + 0.075

     = 0.115

⇒P(M) = 0.115

b.)

P(A/M) = P(A∩M)/ P(M) = P(M/A).P(A)/P(M)

                                     = (0.05)(0.20) / 0.115

                                     = 0.01 / 0.115 = 0.087

⇒P(A/M) = 0.087

Answer:

$\(45\)

Step-by-step explanation:

\(30\)% \(\mathrm{of}\) $\(150\)

\(=\frac{30}{100}\times 150\\\)

\(=\) $\(45\)

1/\(a^{6}\) is the required number.

Numbers, symbols and operators (such as and times) grouped together that show the value of something.

Given an expression (a³)^-2

(a³)^-2 = \(a^{-6}\) = 1/\(a^{6}\)

Hence, 1/\(a^{6}\) is the value of the expression (a³)^-2

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The domain and the range of the piecewise function in this problem are given as follows:

The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:

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The product of 5 × 5ab × 5, a, b is 125ab5 when written in its most Simple form

The expression 5 × 5ab × 5, a, b is equal to 125ab5. The reasoning is that when we multiply 5 by 5ab, we get 25ab, which we then multiply by 5 to get 125ab. Since a, b are variables, the product 125ab5 is the product of 5 × 5ab × 5, a, b, when written in its most simple form.

The expression 5 × 5ab × 5, a, b is an algebraic expression, which consists of numbers, variables, and operators. Variables are usually represented by letters or other symbols, while operators such as +, -, ×, ÷, ^ are used to indicate mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. In algebra, expressions can be simplified by combining like terms, expanding brackets, and applying other rules of arithmetic.

The most simple form of an expression is the one that cannot be further simplified.In the given expression, 5 × 5ab × 5, a, b, we can see that the number 5 appears three times, so we can simplify the expression by multiplying the numbers together.

Similarly, we can multiply the variables a and b together to get the term ab. Finally, we write the result as 125ab5, which is the product of 5 × 5ab × 5, a, b, in its most simple form.

Therefore, the product of 5 × 5ab × 5, a, b is 125ab5 when written in its most simple form.

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Answer:

i think its 3 im not sure

Step-by-step explanation:

Answer:

x = -1

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30/30

→ [ x = -1 ]

Hence, the value of x is -1.

Using the unitary method, we found out that the cost of 6.5 ounces of a medium soft serve is $3.64.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. This method allows us to calculate both the value of many units from the value of one unit and the value of one unit from the value of many units. In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or fewer quantities are then determined. This method is known as the unitary method for this reason.

Given,

The cost of an ounce of medium soft serve = $0.56

The amount of soft serve in a medium size  = 6.5 ounces

We are asked to find the cost of the total amount of soft serve in a medium size.

This can be done using the unitary method.

If 1 ounce = $0.56

Then for 6.5 ounces, the cost is = 6.5 * 0.56 = $3.64

Therefore using the unitary method, we found out that the cost of 6.5 ounces of a medium soft serve is $3.64.

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Answer:

Each person would get 1 1/2 pounds worth of cookies

Step-by-step explanation:

4 1/2 pounds of cookies divided equally among 3 people

4 1/2 pounds divided by 3 people = 1 1/2 pounds of cookies

Each person gets 1 1/2 pounds of cookies

After answering the given query, we can state that  The Wilcoxon rank- unitary method sum test, the Mann-Whitney U test, and the Kruskal-Wallis test are a few nonparametric test examples.

The unit method is a strategy for handling issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply stated, the unit method is used to extract a unique unit number from a multiple that is given. For example, 40 pens would cost 400 rupees, which is equal to the expense of one pen. This procedure might follow a conventional procedure. a distinct nation. anything with a distinct character. Its adjoint and inverse are identical in terms of mathematics, algebra, linear algebra, mathematical analysis, or mathematics of matrices or operators.

A statistical hypothesis test known as a parametric test makes assertions about the underlying probability distribution of the data being examined. The data is supposed to be taken from a normal distribution or another well-known probability distribution, and these assumptions frequently include approximations about the data's mean and variation. ANOVA, linear regression, and t-tests are a few examples of parametric tests.

A nonparametric test, on the other hand, is a statistical hypothesis test that does not rely on any presumptions regarding the underlying Nonparametric tests do not need the data to be normally distributed or to have a particular form because they are built on rank-order statistics. The Wilcoxon rank-sum test, the Mann-Whitney U test, and the Kruskal-Wallis test are a few nonparametric test examples.

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Answer:

Hello!!

When simplifying the expression

\(17-{2+2[-1(7-10)]2}\)

The correct answer would be

\(3\)

Hope this helps!!