Matthew drew a scale drawing of a summer camp. The sand volleyball court, which is 18 meters long in real life, is 27 millimeters long in the drawing. What is the scale of the drawing?

The measures of the internal angles of the triangle are given as follows:

A triangle is composed by three internal angles, and the sum of it's measures is of 180º.

In the context of this problem, the measures are given as follows:

Considering that the sum is of 180º, we can build an equation to solve for x as follows:

3x + 10 + 6x + 2x + 5 = 180

11x + 15 = 180

11x = 165

x = 165/11

x = 15

Hence the measures of the angles are given as follows:

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The measure of the angles are;

It is important to note that the sum of angles in a triangle is supplementary.

Also, supplementary angles are defined as pair of angles that sum up to 180 degrees.

Two angles are termed supplementary when they add up to give 180 degrees.

Since, we have that the sum of the interior angles of a triangle are supplementary, then,

Angle A + Angle B + Angle C = 180 degrees

Given the values as;

Now, put or substitute the values into the formula

3x + 10 + 6x + 2x + 5 = 180

collect like terms

3x + 6x + 2x = 180 - 15

Add or subtract like terms

11x = 165

Make 'x' the subject by dividing both sides by the coefficient of x, we have;

11x/11 = 165/11

Find the quotient

x = 15

But we have to find the angles by substituting the value of x

m∠ A = 3x + 10 = 3(15) + 10 = 55 degrees

m∠ B = 6x = 6(15) = 90 degrees

m∠ C = 2x + 5 = 2(15) + 5 = 35 degrees

Hence, the angles are 55 degrees,  90 degrees and 35 degrees respectively.

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We have the relation:

y = 4x + 3

Since the slope (4) and the y-intercept (3) were already found, we need now to graph this line.

In order to do so, we can find two points belonging to this line and then draw a line that passes through those points.

The first point can be (0, 3), since we know that the y-intercept is 3, i.e., y = 3 for x = 0.

Now, to find a second point we can choose a value for x, let's say x = 1, and use it in the equation of the line to find the corresponding value of y:

y = 4x + 3 , x = 1

y = 4 * 1 + 3

y = 4 + 3

y = 7

So, (1, 7) is another point we can use.

Now, we can select the second button on the toolbox to draw a line through the points (0, 3) and (1, 7):

The measure of the angles for the given parallel lines are-

For the given question;

The set of parallel lines are given;

Thus,

∠1 + 80 = 180 (linear pair)

∠1 = 100°

Now, two set of parallel line form a parallelogram.

Thus, in parallelogram opposite angles are equal.

∠1 = °∠3 = 100°

So, ∠3 = 100°

And, ∠2 = 80° (opposite angle of 80)

Thus, the measure of the angles are calculated.

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Answer:14 becuase

Step-by-step explanation:so your dad left you because he $H!T hates you and he want to divorces your mom and he told me to say $H!T you to you

Using the PEMDAS ( In order to know the order of the operations)

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

Accordint to this, we need to divide first, and then we need to add the resultant number, so:

Answer:

10

From a total of 8 books, she has a choice of 2 in 28 different ways.

When things are of diverse kinds, the term "permutation" is used to describe the various arrangements that could be made. Combination, meanwhile, is the quantity of smaller groups or sets that can be created from the components of a bigger set.

The member must select 2 books from a group of 8 books in the scenario that is provided. It is not important what sequence you select your books in. If a member chooses books A and B or books B and A, for instance, she is choosing the same books from the list of available titles (A,B,C,D,E,F,G, and H). By extension, this is a problem of combinations since the order of the selections is irrelevant in this situation.

Eight books, two at a time, must be combined to produce

The general formula of combination is :

[tex]nC_{r} = \frac{n!}{r!(n-r)!}[/tex]

Using the values of n=8 and r=2, we get:

[tex]8C_{2}[/tex] = [tex]\frac{8!}{2!(8-2)!}[/tex]

=28

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Answer:

7.36 g/cm3

Step-by-step explanation:

Density = mass ÷ volume

Mass in grams = 9200g

Volume in cm3 = 1250cm3

9200 ÷ 7850 = 7.36

7.36 is already in 2 d.p.

Using the hypergeometric distribution, the probabilities are given as follows:

a) All 13 hearts: [tex]1.57 \times 10^{-12}[/tex]

b) 13 cards of the same suit: [tex]6.30 \times 10^{-12}[/tex]

c) Seven spades and six clubs: [tex]5.4 \times 10^{-9}[/tex]

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The general parameters in this problem are given as follows:

In item i, there are 13 hearts in a standard deck, hence k = 13 and the probability is P(X = 13), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 13) = h(13,52,13,13) = \frac{C_{13,13}C_{39,0}}{C_{52,13}} = 1.57 \times 10^{-12}[/tex]

For item ii, we consider the same context of item i, just now we can consider any of the four types of cards, hence:

[tex]p = 4 \times 1.57 \times 10^{-12} = 6.30 \times 10^{-12}[/tex]

For item iii, we want:

Hence the probability is given as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 7) = h(7,52,13,13) = \frac{C_{13,7}C_{13,6}}{C_{52,13}} = 5.4 \times 10^{-9}[/tex]

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[tex]x^2=16\\\sqrt{x^2}=\sqrt{16}\\x=\lm+/-4[/tex]

x = 4, x = -4

La maxima velocidad lineal de la masa con la que se puede girar la masa es igual a 40 newtons.

En este problema tenemos el caso de una masa (m), en kilogramos, conectada a una cuerda y que experimenta un movimiento circular uniforme, en donde la partícula describe un movimiento a velocidad lineal constante (v), en metros por segundo, debido a una aceleración radial que está en la forma de tensión (T), en newtons, a través de la cuerda. En consecuencia, la velocidad máxima permitida es determinada a partir de las leyes de Newton:

T = m · (v² / R)

Donde:

Si sabemos que m = 2 kg, R = 5 m y T = 40 N, entonces la maxima velocidad lineal permitida es:

40 N = (2 kg) · v² / (5 m)

v = 10 m / s

La maxima velocidad lineal permitida es igual a 10 metros por segundo.

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An infinite set is infinite from start to end, but both sides can have continuity, unlike a finite set, which has both start and end elements. The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values. It returns a Boolean value for each vector element.

Hence, The finite() function in R Language is used to determine whether or not the elements of a vector are Finite values.

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The graph of the linear function t(m) = -0.2m + 6 is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

In this problem, the function is defined by:

t(m) = -0.2m + 6.

Hence:

To graph the function, we have to consider the constraint that the time cannot be negative, hence the domain is:

t ≥ 0.

Thus, the graph is given by the image at the end of the answer.

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The rate of change is      [tex]\frac{1}{2\sqrt{x} }[/tex]

The link between one quantity changing in respect to another is given by the rate of change formula.can be used to calculate the rate of change from y coordinates to x coordinates (x2 - x1 ). The rate of change m for a linear function is written as y=mx+b in the slope-intercept form for a line, whereas the rate of change for a function is written as (f(b)-f(a))/b-a. It is said that the rate at which one quantity changes in relation to another is known as the rate of change function. The amount of change in one item is simply divided by the comparable amount of change in another when calculating the rate of change.

Given that : The function f (x)=[tex]\sqrt{x}[/tex]

f (x)=[tex]\sqrt{x}[/tex]

[tex]f^{'} x = \frac{1}{2\sqrt{x} }[/tex]

The rate of change is      [tex]\frac{1}{2\sqrt{x} }[/tex]

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Solution:

Given that a livestock company reports that the mean weight of a group of young steers is 1123 pounds with a standard deviation of 84 pounds, this implies that

A) Percentage of steers that weigh over 1300 pounds.

Step 1: Evaluate the z score value.

The z score value is expressed as

In this case, x equals 1300.

Thus, the z score value is evaluated as

Step 2: Evaluate the probability that the steer would weigh over 1300 pounds.

Using the normal distribution table, we have

thus,

The percentage of young steers that weigh over 1300 pounds is thus evaluated as

B) Percentage of steers that have weights under 1050 pounds.

Step 1: Evaluate the z score value.

Thus, we have

Step 2: Evaluate the probability that the steer would have weights under 1050 pounds.

Using the normal distribution table, we have

thus,

Thus, the percentage of young steers that would have weight under 1050 pounds is evaluated as

C) Percentage of young steers that weigh between 1000 and 1200 pounds.

Step 1: Evaluate the z score value.

Step 2: Evaluate the probability that the steer would weigh between 1000 and 1200 pounds.

Using the normal distribution table, we have

thus, we have

15, 0, -8, -9

Negatives go backwards

we can use the formula

where F is the force, m the mass and a the acceleration

now, replacing

then solve for m

the mass is 19.05Kg

When Janet has $50 in a savings account that earns 10% annually, the interest is $15.

It should be noted that the interest is the extra amount that's given for keeping money for a specified period of time. Interest is the payment of a sum over and above the original amount owed by a lender or deposit-taking financial institution to a depositor or lender, at a set rate.

The formula for calculating interest is given as:

Interest = PRT / 100

where P = Principal. = $50

R = rate = 10%

T = Time = 3

Interest = PRT / 100

Interest = (50 × 10 × 3) / 100.

Interest = 1500 / 100

Interest = $15

The interest is $15.

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First:

1 divided 1/10:

1 divided 1/10= 10.

2. 4 divided 1/10:

Using the same procedure:

4 divided 1/10= 40.

Using the ruler:

this implies counting each millimeter contained in 1 centimeter, when it is 1 centimeter, there are ten centimeters, and when it is 4 cm there are 40 mm.

Answer:

1 divided 1/10= 10

4 divided 1/10= 40

A statement of order that shows the relation of the in-town speed limit to the highway speed limit is that the in-town speed limit is less than or equal to 30 and the highway speed limit is less than or equal to 60.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

In Mathematics, these four rules are generally used to write an inequality:

Now, we would apply the aforementioned inequality rules to write the solution to the compound inequality shown in the graph above:

30 ≤ x ≤ 60.

In conclusion, x represent the speed limit for in-town and highway.

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Step 1:

Draw the rectangle with the given dimensions

Step 2:

Next, apply the Pythagoras theorem

Opposite = 12

Adjacent = 18

Hypotenuse = L the side facing right angle

Step 3:

Final answer

The length of the diagonal is 21.6

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

function G(x)

Step 02:

discrete finite function:

range:

we must analyze the function to find the solution.

range:

{ 3 , 5 , 8 }

The answer is:

range:

{ 3 , 5 , 8 }

1) Alternate interior angles

2) Corresponding angles

3) Alternate exterior angles

4) Same-side interior angles

5) Vertical angles (angles opposite of each other)

Answer:

Josie can by 4 dish sets.

Step-by-step explanation:

Josie’s best friend is getting married and she wants to buy her something from her online wedding registry. She wants to buy some sets of dishes (d) that cost $35 each. Because she’s buying online, she must pay a shipping fee of $10. Josie wants to spend $150 or less. How many sets of dishes can Josie buy?

can be represented by equation:

35d + 10 = 150

subtract 10 from both sides:

35d + 10 - 10 = 150 - 10

35d = 140

divide both sides by 35:

35d/35 = 140/35

d = 4

Josie can by 4 dish sets.

check:

35(4) + 10 = 150

[tex] {x}^{2} - x - 1 = x + 2 \\ {x }^{2} - x - 1 - x - 2 = 0 \\ {x}^{2} - x - x - 1 - 2 = 0 \\ {x}^{2} - 2x - 3 = 0 \\ (x - 3)(x + 1) = 0 \\ x - 3 = 0 \\ \\ or \\ x + 1 = 0 \\ \\ x = 3 \\ \\ or \\ \\ x = - 1[/tex]

WHEN x=3

[tex]y = 3 + 2 \\ y = 5[/tex]

When x=-1

[tex]y = - 1 + 2 \\ y = 1[/tex]

NOW WE HAVE A PAIR OF SOLUTIONS AS

Answer: The answer is -4.37u-11

Step-by-step explanation: Just do math.

Number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.

As given in the question,

Let number of weeks be represented by a variable x.

Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.

Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.

For Jacob and Diego to tie in the race, their volunteer hours should be equal. Translating this into a linear algebraic equation,

6x = 5x+50

=> 6x-5x = 50

=> x = 50

Therefore, number of weeks required before Jacob and Diego will be tied in the race to complete community service hours for scouting is equal to 50 weeks.

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The expected value for the number of times Danny goes swimming during a week is 0.65.

Given that:-

Percentage of time Danny went swimming twice a week = 15 %

Percentage of time Danny went swimming once a week = 35 %

Percentage of time Danny doesn't go swimming at all in a given week = 50%

The expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.

Hence, based on the data given in the question, we can write,

Expected value n how many times Danny will go to swimming in a week = 15 %*2 + 35 % * 1 + 50 % *0 = 0.3 + 0.35 + 0 = 0.65

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