What Are The Properties Of The Angles And Sides Of A Triangle? How Do You Use These Properties To Solve (2024)

8/3 or 2 2/3 cups of milk are needed for 16 servings.

What is the unitary method?

The unitary method is a technique for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.

Given that 3/4 cups of milk needs to make 4 1/2 servings

Converting mixed fraction into improper fraction:

or, 3/4 cups of milk needs to make 9/2 servings.

To make 9/2 servings, needs 3/4 cups of milk

Applying unitary method:

To make 1 servings, needs (3/4)/(9/2) cups of milk.

To make 16 servings, needs [(3/4) × 16]/(9/2) cups of milk.

Simplify the numerical expression:

[(3/4) × 16]/(9/2)

= [3 × 4]/(9/2)

= [3 × 4 × 2] /9

= 8/3

Convert improper fraction into mixed fraction:

=(6 + 2)/3

= 6/3 + 2/3

= 2 2/3

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Answer:

a ≈ 3.009075116

Step-by-step explanation:

cos(α) = adj/hyp

cos(53°) = a/5

a = 5 * cos(53°)

a ≈ 3.009075116

Answer:

1st one

Step-by-step explanation:

So 2|x|<4 = |x|<2, and since absolute values are always positive, I believe it is the 1st one.(Sorry if its not right I'm not very good in this area.)

Answer:

J

Step-by-step explanation:

shifts to the right by 1

The best prediction of the bird population in the year 2014 is 3132.

Explain the term population decline?The population mean could be determined by dividing the number of values with in given data/population by the sum of any and all values in the data/population.A decrease in the number of people in a population is known as a population drop in humans (sometimes referred to as underpopulation, population reduction, or population collapse).

The given data is-

2009 : 3,500 populationRate of decline ; 2.2% per year. 100% - 2.2% = 97.8%

Difference of the years;

2014 - 2009 = 5 years

Decline = 3,500 * (0.978)^5

Decline = 3,500 * 0.89473

Decline = 3131.57

Thus, the population of the birds in 2014 will be 3,131.57 ≈ 3,132.

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The choice that correctly names angles 2 and 3 is called the: D. vertical angles.

What is the Definition of Vertical Angles?

Two angles are named vertical angles if both angles form a pair of angles that share the same vertex both not the same side, and they are on the opposite sides of two straight lines that intersect each other.

Given the image above, it shows that angle 2 and angle 3 form a pair that shares the same vertex when two straight lines intersect, and both angles are non-adjacent angles, that is they do not share any common side with each other.

Therefore, according to the definition given above, the angles 2 and 3 can be correctly named as: D. vertical angles.

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Expenses are $12.50 less than the budget of 100$ given to Jackie Pope.

How to calculate Expenses?

Tabulate the expenses of all the things. Calculate the sum of all expenses to get Expenses.

Now for the given question:

Given:

Expenses of travelling of Jackie pope are

It costed $30.00 for Gas/Oil for car;

It costed $5.00 for Parking of car.

It costed $7.00 for Tolls on road.

It costed $45.50 for commuting.

Now total expenses is sum of all the above four expenses:

Expenses=30+5+7+45.5=$87.50.

Now budget=$100.

So, Remaining amount= Budget-Expenses;

Remaining amount= 100-87.5=$12.50;

Remaining amount from the budget is $12.50

Expenses are $12.50 less than the budget of 100$ given to Jackie Pope.

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Answer: 176.79

Step-by-step explanation:

15 (165) / 14

15 times 165 = 2475

2475 / 14 = 176.785

Round up to 176.79

176.9

15x165=2,475

2,475 divided by 14 is 176.79

Answer: b=2/5

Step-by-step explanation:

Step 1: Cross-multiply.

2b−1/2 = b−1/6

(2b−1)*(6)=(b−1)*(2)

12b−6=2b−2

Step 2: Subtract 2b from both sides.

12b−6−2b=2b−2−2b

10b−6=−2

Step 3: Add 6 to both sides.

10b−6+6=−2+6

10b=4

Step 4: Divide both sides by 10.

10b/10 = 4/10

b = 2/5

Answer: Exact Form: s = 5/4

Decimal Form: s = 1.25

Mixed Number Form: s = 1 1/4

Answer: Using the triangle theorem, the angle (64 + x)° and 110° are alternate angles, therefore the angle marked, x is 46°

Step-by-step explanation: Alternate angles are equals :

(64 + x)° = 110°

We can solve for x thus ;

x + 64 = 110

x + 64 - 64 = 110 - 64

x = 46°

Hence, the value of x in the triangle is 46°

If we are rolling a six-sided dice, where. a = get a roll that is even, then the value of [tex]$P\left(A^c\right)^$[/tex] will be 1/2

Option (c) is the correct choice.

As we know,

A dice has 6 faces on which 6 different numbers (1,2,3,4,5 and 6) are printed on each of the six faces of the dice.

Now, considering an unbiased die the probability of any of the faces appearing in a single roll is 1/6.

So, we can write it as:

P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6

Now that number to be even is 2,4,6

And for each individual number, the probability will be 1/6

So, the value of P(A) =P(2) + P(4)+ P(6)

= 1/6 + 1/6 +1/6 =3/6

P(Ac) = 1 - P(A) = 1 - ( 3/6 ) = 1/2.

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The complete question may be:

Suppose that you are rolling a six sided dice.

Let A= get a roll that is even

What is [tex]$P\left(A^c\right)^$[/tex] ?

(a) 1 / 3

(b) 1 / 4

(c) 1 / 2

(d) 1 / 6

In this case, the amount of population of fruit flies doubled in 18 days, meaning the doubling time is 9.5 days.

The doubling time of a population is the amount of time it takes for a population to double in size. In this case, the population of fruit flies started at 182 individuals and grew to 340 in 18 days. To calculate the doubling time, we used the equation (182 x 2^(18/9.5)) = 340, where the 2^(18/9.5) is the exponentiation of the number of days divided by the doubling time. This equation can be rearranged to solve for the doubling time, yielding a result of 9.5 days. This means that the population of fruit flies doubled in size every 9.5 days, which is the doubling time of the population.

182 x 2^(18/9.5) = 340

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to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term then it is a true statement

we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.

So, For his purpose, we know that the

A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.

And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.

By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.

So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.

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The option that gives the number of solutions to the system of equations is given as follows:

A. One solution.

How to obtain the number of solutions in a system of equations?

For a system of linear equations, the system is composed by multiple lines, and the number of solutions is defined according to the features of the lines.

The possible numbers of solutions are given as follows:

Infinite solutions: the lines are equal, hence they intersect at all points.No solutions: the lines are parallel, meaning that they intersect only at infinity.One solution: the lines intersect at one point.

From the graph given in this problem, we have that the two lines intersect at one point, hence the system of equations has one solution and the correct option is given by option A.

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Answer:

To find the minimum number of lawns Jacob will need to mow, we can set up the following inequality:

12x + 150 >= 380

To solve this inequality, we need to get x by itself on one side of the inequality. We can do this by subtracting 150 from both sides of the inequality:

12x >= 230

Then, we can divide both sides of the inequality by 12 to get the value of x:

x >= 19.17

Since x represents the number of lawns Jacob needs to mow, it must be an integer. Therefore, the minimum number of lawns Jacob will need to mow is 20.

This means that Jacob needs to mow at least 20 lawns in order to earn enough money to buy the electronic tablet. If he mows more than 20 lawns, he will have more than enough money to buy the tablet.

Answer:

I believe that the answer is 2/5 because all of the other answers equal 10 (for b and c) or 20 (for a)

Step-by-step explanation:

π/32 is the area enclosed by the curve r= sin(8θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex]

where a and b is the boundary at which r=0

so after equation r=0

sin(8θ) =0

=> sin(8θ) =0

=> 8θ = 0,π

=> θ = 0, π/8

so a=0 , b= π/8

now

A = [tex]\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta[/tex] ------(i)

so [tex]r^2[/tex] = (sin(8θ))^2

=> [tex]sin^2[/tex] ( 8θ )

ans we know that

cos(2α) = 1 - 2[tex]sin^2[/tex] α

so [tex]r^2[/tex] = (1- cos(16θ) )/2

putting the value of r in the equation (i) we get :-

A = [tex]\int\limits^a_b {\frac{1}{4} *(1-cos(16\alpha ) } \, d\alpha[/tex]

=> 1/4* [tex]\int\limits^a_b {(1-cos(16\alpha ) } \, d\alpha[/tex]

here a=0 and b=π/8

after putting the value and solving the integral

A = π/32

so A is the area enclosed by r=sin(8θ) is π/32

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he provider ordered lactated ringers (lr) to infuse at 75 ml/hr for the next 24 hours. 18.0 liters of lr will infuse with rate of infusion.

First, we need to determine how many milliliters of LR will be infused over 24 hours. So, we need to multiply the rate of infusion (75 mL/hr) by the number of hours (24). This will give us the total number of milliliters that will be infused. In this case, it is 75 x 24 = 1800 mL. To determine the number of liters, we need to divide this by 1000 since there are 1000 mL in 1 L. Therefore, 1800 mL/1000 = 1.8 L. We can round this number up to the tenth (one decimal place), and the answer is 18.0 L.

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on solving the provided question, we can say that - 5/13 measure shown in the triangle are equivalent to sin [tex]\alpha[/tex] and cos [tex]\beta[/tex].

what are trigonometric functions?

Trigonometry uses the first six fundamental trigonometric functions. Trigonometric ratios are these functions. The six fundamental trigonometric functions are the sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function. A right-angled triangle's side ratio corresponds to the trigonometric functions and identities. In order to determine the sine, cosine, tangent, secant, and cotangent values, trigonometric formulae are applied to the perpendicular side, hypotenuse, and base of a right triangle.

as cos x = base/ hypotenuse

and, sin x = perpendicular/ hypotenuse

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By applying the fraction concept, it can be calculated that Mrs. Stewart sold 300 cakes.

How does the concept of fractions apply in real life?

In real life, the concept of a fraction is often used when we want to talk about a part of a whole, a part of something, a part of a group of people, etc.

In this case, it is stated that Mrs. Stewart made several pies, some of which were sold and given to food banks, and some were left over.

If we know that 1/4 of the unsold pies were given to the food bank, then the unsold pies that were not given to the food bank = 1 - 1/4 = 3/4 part.

Additionally, we also know that the number of unsold pies that were not given to the food bank (leftover pies) was 150.

If x is the number of unsold cakes, then the two statements above can be written in mathematical notation:

3/4 x = 150

x = 150 : 3/4

= 150 x 4/3

= 200 pies

If pies made are y, then pies not sold = pies made - pies sold

x = y - 3/5y

= 2/5y

if we put the value of x into this equation it becomes:

200 = 2/5y

y = 200 : 2/5

= 200 x 5/2

= 500 pies

Then the pies were sold = 3/5y

= 3/5 x 500

= 300 pies

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Answer:

b) (0.10p + 0.35f) + 0.0875 (0.10p+0.35P)

first is Jamir total cost + the sales tax of 0.0875 of the total cost

a. this is wrong because both is the sales tax only, theres no total cost include

c. wrong because its just also sales tax only

d. wrong because the total cost must only multiplied by the sales tax

PART B

12(0.10) + 8(0.35)

= 1.2 + 2.8

= $4 as the total cost

4(1.035)

= $4.14 as after tax bill

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The graph of x = 3et cos(t), y = 3et sin(t), 0 ≤ t ≤ π is shown below.

In this question we have been given two curves x = 3e^t cos(t), y = 3e^t sin(t), 0 ≤ t ≤ π

We need to graph the given curves.

First we find find few coordinates.

For t = 0,

x = 3e^0 cos(0)

x = 3 * 1 * 1

x = 3

and y = 3 * e^0 * sin(0)

y = 3 * 1 * 0

y = 0

For t = π,

x = 3 * e^π * cos(π)

x = 3 * 23.14 * (-1)

x = -69.42

and y = 3 * e^π * sin(π)

y = 3 * 23.14 * 0

y = 0

For x = π/2

x = 3 * e^π/2 * cos(π/2)

x = 3 * 4.81 * 0

x = 0

and y = 3 * e^π/2 * sin(π/2)

y = 3 * 4.81 * 1

y = 14.43

So, we have the coordinates (3, 0), (-69.42, 0) and (0, 14.43)

The graph of x = 3et cos(t), y = 3et sin(t) is as shown below.

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The price of the winter coats is going to be $17.325.

what is marked price?

The marked price or list price is the amount that appears on a product's label. This is the price that the product will be sold for. But this price might be discounted in some way, and the product's real selling price might be less than the advertised price.

given,

Marked Price of winter coats = $57.75 and discount = 70%

Discount = 70%

57.75 × 70/100

5.775 × 7

40.425

Selling Price = M.P - Discount

57.750 - 40.425

17.325

therefore ,

The price of the winter coats is going to be $17.325.

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Answer:

2 < x < 26

Step-by-step explanation:

The length of the side of a triangle must be less than the sum of the lengths of the other two sides of a triangle.
Therefore:

12+14>x

x<26

However, the following must also be true:

x+12>14 (The sum of x and 14 will always be greater than 12 because 14>12, so we don’t need to include that in the inequality)

So, x>2.
This means that the answer is 2<x<26

The solution to the equation eˣ + 1 = 2ˣ + 2 is x = 1.2

How to determine the solution to the equation

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

eˣ + 1 = 2ˣ + 2

Split to system of equations

This gives

y = eˣ + 1

y = 2ˣ + 2

Next, we plot the graph of the system of equations

In this case, the point of intersection of the equations represent the solution to the system

From the graph, the curves intersect at (1.2, 4.3)

This means that

x = 1.2 (approximated)

Hence, the solution is x = 1.2

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Option D is the correct answer. if the residuals from a fitted regression violate the assumption of hom*oscedasticity their variance is not constant.

hom*oscedasticity: It is an assumption of equal or similar variances in different groups are being compared. It is a condition in which the variance of the residual, or error term, in a regression model, is constant.

This is one of the most important assumptions of parametric statistical tests because they are sensitive to any dissimilarities. It is valid when X and Y are independent.

To deal with this First, we have attempted to transform your target using square root, log, reciprocal square root, or reciprocal transformations.

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The value that would complete the table to make the relationship between the two quantity proportional is 4.

what is quantity proportional?

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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