solve both for brainliest, 20 points, and thanks!

Where a 30° central angle in a circle is equivalent to π/6 radians, the complete sentence is given as: "the length of the arc intercepted by this central angle is 1/6 times the length of the circumference."

It is to be noted that a central angle is an angle formed by two radii of a circle with its vertex at the center of the circle.

In this case, the Central angle 30° = π/6 radians.

Thus, the length of the arc intercepted by this central angle is 1/6 times the length of the circumference.

This is a mathematical rule that applies to any circle's center angle. It asserts that the length of an arc intersected by a central angle is proportional to the measure of the central angle and that the proportionality constant is the circumference of the circle divided by 360 degrees (or 2 π radians).

Hence, if a central angle is measured in degrees (or ϴ radians), the length of the associated arc is (θ/360) times the circle's diameter (or (ϴ/2) times the circle's circumference).

Hence, it  is correct to state that: ""he length of the arc intercepted by this central angle is 1/6 times the length of the circumference."

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The measures on the isosceles triangles are given as follows:

9) <N = 42º. (option 3).

10) m < BCD = 130º. (option 4).

11) x = 28º. (option 2).

An isosceles triangle is a triangle that has two equal side lengths, hence it also has two equal angle measures.

For item 9, triangle LMO is isosceles, with two angles of 55º, hence the measure of angle M on triangle LMO is given as follows:

<M + 2 x 55 = 180

<M = 70º.

(sum of the internal angles of a triangle is of 180º).

On triangle NMO, the measure is given as follows:

<M = 180 - 70

<M = 110º.

(as it is external to the angle of triangle LMO).

Hence the measure of angle N is given as follows:

<N + 110 + 28 = 180

<N = 42º.

For item 10, the base angle is given as follows:

2x + 80 = 180

2x = 100

x = 50º.

Hence the exterior angle measure is given as follows:

m < BCD = 180 - 50

m < BCD = 130º.

(angle is supplementary with it's exterior).

For item 11, if AB = AC, the base angle is of (x + 20)º, hence the value of x is obtained as follows:

3x + 2(x + 20) = 180

5x + 40 = 180

5x = 140

x = 140/5

x = 28º.

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The value of p is 7 and the median number of liters is 18.

Simply put, the mean is the average of the values in the given set.

When a collection of data is supplied and ordered in order, the median is the middle value.

Given that the mean number of liters is:

The mean is represented as follows:

[tex]m = \frac{16(11) + 17(10) + 18(p) + 19(4) + 20(8)}{11+10+p+4+8} = 17.7[/tex]

[tex]m=\frac{582+18p}{33+p} = 17.7[/tex]

[tex]582 +18p = 17.7(33+p)[/tex]

[tex]582 +18p = 584.1 + 17.7p\\18p-17.7p = 584.1 - 582\\0.3p = 2.1\\p = 7[/tex]

The value of p is 7.

Now arrange the table in ascending order for the motorist.

The median represents the median value and hence the median is 18.

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The inequality which correctly represents the graph as required to be determined is; 5x - y ≥ 1.

It follows observation that the two point which can be used to evaluate the slope are; ( 2, 9 ) and ( -1, -6 ).

Hence, slope, m of the boundary line is;

m = ( 9 - (-6) ) / (2 - (-1) )

m = 15 / 3 = 5.

Hence, using the point slope equation; we have;

y - 9 = 5 ( x - 2 )

y = 5x - 1

On this note, the equation of the boundary line is; y = 5x - 1.

However, in the context of inequalities, since the region below the line is shaded and the boundary line is solid, it follows that the required inequality is;

y ≤ 5x - 1

Hence, by rearranging, we have that;

5x - 1 ≥ y

Therefore, the inequality which correctly repeat the graph is; 5x - y ≥ 1.

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The values of the lengths of x and y in the triangle are x = 5.06 and y = 6.33

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

This means that

x + y = 11.4

The theorem of angle bisector states that:

"The angle bisector of a triangle divides the opposite side into two parts proportional to the other two sides of the triangle"

This means that

a/b = x/y

In this case, we have

6.4/8 = x/y

So, we have

0.8 = x/y

Make x the subject

x = 0.8y

Substitute x = 0.8y in x + y = 11.4

0.8y + y = 11.4

Evaluate

1.8y = 11.4

Divide by 1.8

y = 6.33

Recall that

x = 0.8y

So, we have

x = 0.8 * 6.33

Evaluate

x = 5.06

Hence, the lengths are x = 5.06 and y = 6.33

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Answer:

Step-by-step explanation:

This would depend on how much ground beef you have. In order to determine how many batches of enchiladas you can make, you would divide the total amount of ground beef you have by the number of ounces needed per batch.

For example, if you have 24 ounces of ground beef, you could make 2 batches of enchiladas because 24 divided by 12 equals 2.

Answer:

C)  Portfolio 1, Portfolio 2, Portfolio 3

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Weighted Mean Formula}\\\\$ \overline{x}=\dfrac{\displaystyle\sum^{n}_{i=1}x_iw_i}{\displaystyle\sum^{n}_{i=1}w_i}$\\\\\\where:\\\phantom{ww} $\bullet$ $x_i$ is the data value\\\phantom{ww} $\bullet$ $w_i$ is the weight\\\end{minipage}}[/tex]

To calculate the weighted mean of the RoR for each portfolio:

Portfolio 1

[tex]\implies \overline{x}=\dfrac{1250 \cdot 0.039+575 \cdot 0.017 + 895 \cdot .0106 + 800 \cdot -0.032 + 1775 \cdot 0.081}{1250+575+895+800+1775}[/tex]

[tex]\implies \overline{x}=\dfrac{271.57}{5295}[/tex]

[tex]\implies \overline{x}=0.051288075...[/tex]

[tex]\implies \overline{x}=5.13\%\;\; \sf (2 \;d.p.)[/tex]

Portfolio 2

[tex]\implies \overline{x}=\dfrac{950\cdot 0.039+2025\cdot 0.017 + 1185\cdot .0106 + 445\cdot -0.032 + 625\cdot 0.081}{950+2025+1185+445+625}[/tex]

[tex]\implies \overline{x}=\dfrac{233.47}{5230}[/tex]

[tex]\implies \overline{x}=0.0446405353...[/tex]

[tex]\implies \overline{x}=4.46\%\;\; \sf (2 \;d.p.)[/tex]

Portfolio 3

[tex]\implies \overline{x}=\dfrac{900\cdot 0.039+2350\cdot 0.017 + 310\cdot .0106 + 1600\cdot -0.032 + 2780\cdot 0.081}{900+2350+310+1600+2780}[/tex]

[tex]\implies \overline{x}=\dfrac{281.89}{7940}[/tex]

[tex]\implies \overline{x}=0.0355025188...[/tex]

[tex]\implies \overline{x}=3.55\%\;\; \sf (2 \;d.p.)[/tex]

The RoR (rate of return) is the net gain (or loss) of an investment over a specified time period, expressed as a percentage of the investment's initial cost.

Therefore, based on the weighted means of the RoRs for each portfolio, the best to worst portfolios are:

(as Portfolio 1 has the highest RoR and Portfolio 3 has the lowest RoR).

For the given expressions option A and option C are true statements.

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal.

Given the expression as [tex]a^{\frac{1}{2} } = r[/tex]:

Powering the equations on both sides by n we have:

[tex]a= r^n[/tex]

Also, taking the nth root we have:

[tex]\sqrt[n]{a} = r[/tex]

Hence, for the given expressions option A and option C are true statements.

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Therefore , the solution of the given problem of speed comes out to be

40 km/h is the average speed of bicyclist.

We can determine how fast that anything is traveling by looking at it from a distance. The amount of distance an object can go in a given length of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most used units of speed are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).

Here,

Given : 1/2 hour

distance travelled by bicyclist = 20 kilometers.

Thus ,

Using distance / speed formula:

=> Speed  = distance/time

=> Speed = 20 / 1/2

=> Speed = 20 * 2

=> Speed  =40

So , 40 km/h is the average speed of bicyclist.

Therefore , the solution of the given problem of speed comes out to be

40 km/h is the average speed of bicyclist.

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In a triangle, the three sides are related by the sum of two angles being equal to 180 degrees. Knowing two angles and a side can be used to calculate the other two angles and sides.

a) B = 43.7degrees, A = 44.8degrees, c = 21.1m

b) B = 44.5degrees, A = 43.9degrees, c = 12.1m

c) B = 44.5degrees, A = 43.9degrees, c = 21.5m

d) B = 57.6degrees, A = 25.4degrees, c = 33.9m

a) B = 180-97-44.8 = 180-97-44.8 = 38.2

A = 180-97-43.7 = 38.3

c = 21.1

b) B = 180-103-43.9 = 33.1

A = 180-103-44.5 = 32.5

c = 12.1

c) B = 180-103-43.9 = 33.1

A = 180-103-44.5 = 32.5

c = 21.5

d) B = 180-103-25.4 = 51.6

A = 180-103-57.6 = 19.4

c = 33.9

In order to solve the triangle, you need to use the Law of Sines and the Law of Cosines. The Law of Sines states that the ratio of the sides to their opposite angles is constant, while the Law of Cosines states that the sum of the squares of the sides of a triangle equal the square of the hypotenuse. Using these two laws, you can calculate the angles and side lengths of the triangle.

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Answer:

x=5

Step-by-step explanation:

5x-4+3x=36

combine lke terms

5x+3x-4=36

8x-4=36

    +4. +4

8x=40

/8.  /8

x=5

hopes this helps

The median shows that about 7 out of every 20 students has a pet dog.

The median is a measure of central tendency that shows the middle value in a dataset when it is arranged in numerical order. It is often used to describe the middle value of a continuous variable or a set of observations.

When using a box plot, the median amount is the line inside the box plot. This line lands, on 7 which means that in a sample of 20 students, the median is 7 students.

This means that about 7 students out of every 20 students in the school has a pet dog.

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The question is:

How can the median of the samples help you make an inference about the population?

The median shows that about _____  out of every _____  students has a pet dog.

we will get -2 by Simplifying (1+√3)(1-√3)​

(a+b)(a-b)= a^2 - b^2

For each of the algebra formulas, the equations with variables, powers, and arithmetic operations, and on either side of the equals to sign are called algebraic expressions/variable expressions.

In the algebraic formula (a+b)(a-b)= a2- b2, the terms on either side of the equals sign are called algebraic expressions. by applying the above-mentioned formula.

So, we can use the formula for simplifying a given algebraic expression. Take a = 3 p and b = 4 q and substitute them in the a + b times a − b formula. Thus, we use the ( a + b) ( a − b) special binomial product rule in mathematics.

(1÷√3)(1-√3)​= 1^2-(√3)^2

1-3= -2

therefore, the answer is -2

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the complete question should be

Simplify: (1+√3)(1-√3)​

The estimated arrival time of the train in San Diego is 4:16 PM.

To find the arrival time, we must add the length of the trip to the starting time.

The trip is 4 hours and 26 minutes long, so we must add 4 hours, which is equivalent to 240 minutes, and 26 minutes to the starting time of 11:50 AM.

This results in a final time of 4:16 PM.

The equation in completing the square method is x= 3.15 or -3.15

Completing the square is a method of solving a quadratic equation where by the left hand side of the equation is made a perfect square.

The given equation is y=x^2+x-8

Using the completing the square method, take the constant to the RHS to get

x²+x=8

Then make the LHS a perfect square

x²+x+1/4 = 8+1/4

Factorize the RHS and simplify RHS to have

x²+5/4x +1/4=(32+1)/4

Factorize (x²+1/4c)² = 32/4

(x + 1/4)= ±√33/4

x+1/4 =±√8.25

x=--.025+2.9 or -0.25-2.9

x = 2.65 or -3.15

Thertefore, by completing the square x = x = 2.65 or -3.15

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The equation which represents the solution for x in terms of a as required is; Choice 4; 2a + 1.

As evident in the task content; the given equation is to be solved for the variable, x in terms of a;

( x - 1 ) / 2 - a / 4 = 3a / 4

( x - 1 ) / 2 = 3a / 4 + a / 4

(x - 1) / 2 = a

x - 1 = 2a

x = 2a + 1.

Ultimately, the answer choice which correctly expresses x in terms of a is; Choice 4; 2a + 1.

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[tex]~~~~~~~~~~~~ \textit{Amortized Loan Value} \\\\ pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]\implies pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left(\frac{n}{n+r}\right)^{nt}} \right][/tex]

[tex]~~~~~~ \begin{cases} P= \begin{array}{llll} \textit{original amount deposited}\\ \end{array}\dotfill & \begin{array}{llll} 48000 \end{array}\\ pymt=\textit{periodic payments}\\ r=rate\to 6.1\%\to \frac{6.1}{100}\dotfill &0.061\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &6 \end{cases}[/tex]

[tex]pymt=48000\left[ \cfrac{\frac{0.061}{12}}{1-\left(\frac{12}{12+0.061}\right)^{12 \cdot 6}} \right] \\\\\\ pymt=48000\left[ \cfrac{\frac{61}{12000}}{ ~~ \frac{18249137}{59666181} ~~ } \right] \implies {\Large \begin{array}{llll} pymt \approx 797.77 \end{array}}[/tex]

well, Linda is paying that much every month for 6 years or namely 72 months, so the total for those 72 months will simply be 72(797.77) ≈ 57439.44.

hmmmm what's the interest?  well, if we simply subtract the principal from the total amount Linda is paying that'll be 57439.44 - 48000 ≈ 9439.44.

By the converse of the corresponding angles theorem, [tex]\boxed{x=74}[/tex].

The likely mistake is the assumption that the two labeled angles are complementary.

Answer:

See below

Step-by-step explanation:

Because lines M and N are parallel, then T is the transversal, which means that 74° and X° are corresponding angles and have the same angle measure of 74°. The friend probably thought 74° and X° were complementary angles, but this is not the case.

a. There is a direct conversion fact you can use to go from gallons to fluid ounces.

b. The conversion factor is given as follows: 132.

c. The unit cancellation statement is given as follows: 1 gallon = 132 fluid ounces.

d. The number of fluid ounces in 2.5 gallons is of: 330 fluid ounces.

The conversion from gallons to fluid ounces is realized applying the proportions given in the table.

We have that:

Hence the conversion factor is of 132.

The number of fluid ounces in 2.5 gallons is calculated as follows:

132 x 2.5 = 330 fluid ounces.

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Answer: Two correct representations of the inequality -3(2x - 5) < 5(2 - x) are:

-6x + 15 < 10 - 5x

-6x + 15 < -5x + 10

Both of the above are correct because they are equivalent to the original inequality.

Note that in order to get the above representation, I first applied distributive property on both sides of the inequality and then combined like terms on both sides.

Step-by-step explanation:

The amount of zakat on gold and silver is Rs 10000 and Rs 5000 respectively.

As it is clear from the term per cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.

Given:

10 tola gold and 40 tola silver and the rate of gold is Rs 40,000 per tola and the rate of silver is Rs 5000 per tola.

Calculate the amount of gold and silver as shown below,

Amount of gold = 10 × 40000

Amount of gold = Rs 400000

Amount of silver = 40 × 5000

Amount of silver = Rs 200000

Calculate the amount of zakat on gold and silver as shown below,

Amount of zakat on gold = 2.5 × 400000 / 100  (zakat rate is 2.5%)

Amount of zakat on gold = 10000

Amount of zakat on silver = 2.5 / 100 × 200000

Amount of zakat on silver = 5000

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Answer:

D' (1,4)

Step-by-step explanation:

D(4,1)  When reflecting over y = x, switch the x and y values.

Answer: 336

Step-by-step explanation:

6 x 8 = 48 x 7 =336

the smallest possible perimeter of the rectangle is 22 cm and the largest possible perimeter of the rectangle is  26 cm.

The smallest possible perimeter of the rectangle is the perimeter when the length and width are both rounded down to the nearest whole number.

L =  6 cm

W = 5 cm

Perimeter = ( L + W ) * 2

Perimeter = ( 6+ 5 ) * 2

Perimeter = 22cm

The largest possible perimeter of the rectangle is the perimeter when the length and width are both rounded up to the nearest whole number.

L =  7 cm

W = 6cm

Perimeter = ( L + W ) * 2

Perimeter = ( 7+ 6 ) * 2

Perimeter = 26cm

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Answer:2/10

Step-by-step explanation:there are 2 sailor hats out of 10 hats meaning every 10 hats you pull you will get 2 sailor hats so this makes 2/10 correct

The given statement is true.

The two teams whose win/loss records are proportional will be team 1 and term 2.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The table below shows the number of all-time wins and losses for three basketball teams.

                   Wins          Losses

Team 1.      2,222           1,916

Team 2.      1,392           928

Team 3.     2,289          1,526

The ratio of the number of wins to losses for each team is calculated as,

For team 1, then we have

⇒ 2,222 / 1,916

⇒ 1.1597

For team 2, then we have

⇒ 1,392 / 928

⇒ 1.5

For team 3, then we have

⇒ 2,289 / 1,526

⇒ 1.5

The two teams whose win/loss records are proportional will be team 1 and term 2.

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Answer: 11,295,063

Step-by-step explanation:

You are requested to provide an estimate of the building's total window cleaning expense so that the board can make a decision.

Some window cleaners charge by the hour, though the majority bill by the square foot or the number of windows. For home work, professionals bill between $40 and $75 per hour.

Due of the increased safety dangers in high-rises, they usually charge $85 per hour. Many cleaners may charge by the pane if the house is medium-sized, anything from $2 to $7 for each one or more for larger windows. It's typical to charge an hourly rate in large homes when counting each window by itself would take too long or be impossible.

Window cleaning costs typically run between $40 and $75 per hour. If the house is medium-sized, many cleaners may charge per the pane; for larger windows, they may charge anywhere from $2 to $7 for each one or more.

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You are requested to provide an estimate of the building's total window cleaning expense so that the board can make a decision.

Some window cleaners charge by the hour, though the majority bill by the square foot or the number of windows. For home work, professionals bill between $40 and $75 per hour.

Due of the increased safety dangers in high-rises, they usually charge $85 per hour. Many cleaners may charge by the pane if the house is medium-sized, anything from $2 to $7 for each one or more for larger windows. It's typical to charge an hourly rate in large homes when counting each window by itself would take too long or be impossible.

Window cleaning costs typically run between $40 and $75 per hour. If the house is medium-sized, many cleaners may charge per the pane; for larger windows, they may charge anywhere from $2 to $7 for each one or more.

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