What is the value of x? Round to the nearest hundredth.

The average score of all the students in both classes is 84.

step1

The class with 20 students had an average score of 90 on a test. The total score will be:

= 20× 90=1800

A class with 10 students had an average score of 80 on the same test. The total score will be:

=10× 80

= 800

A class with 4 students had an average score of 70 on the same test. The total score will be:

=4×70

=280

step2

Total scores = 1800 + 800+ 280=2880

Number of students = 20 + 10+4=34

The average score will be:

= Total score / Total students

= 2880/ 34=84

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The average score of all the students in both classes is 84.

step1

The class with 20 students had an average score of 90 on a b. The total score will be:

= 20× 90=1800

A class with 10 students had an average score of 80 on the same test. The total score will be:

=10× 80

= 800

A class with 4 students had an average score of 70 on the same test. The total score will be:

=4×70

=280

step2

Total scores = 1800 + 800+ 280=2880

Number of students = 20 + 10+4=34

The average score will be:

= Total score / Total students

= 2880/ 34=84

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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:

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 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.

Answer:

$390

Step-by-step explanation:

780/2 = 390

One thing that is wrong with Sana's statement is that it is repetitive as negative three degrees Celsius is already below zero.

When temperature is measured in degrees Celsius then it means that there are temperatures above 0 degrees Celsius and those that are below it. Those temperatures above 0 degrees Celsius are positive temperatures and those below zero degrees Celsius are negative.

These negative temperatures are used for places that are very cold and the colder a place is, the lower the temperature will be below zero. This therefore means that saying a temperature is negative and saying it is below zero is the same thing.

This means that Sana was wrong to say, " temperature is negative three degrees below zero " as they could have either said that the temperature was 3 degrees below zero or negative 3 degrees Celsius.

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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 volume of the rectangular prism is 5 inches cube.

A rectangular prism is a three-dimensional shape or figure. Therefore, the volume of a rectangular prism can be represented as follows:

volume of a rectangular prism = lwh

where

Therefore,

l = 2 1 / 2 inches = 5  /2 inches

w = 1 inches

h = 2 inches

Hence,

volume of the rectangular prism = 5 / 2 × 1 × 2

volume of the rectangular prism = 10 / 2

volume of the rectangular prism = 5 inches cube

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Answer:It is 30 cubic inches.

Step-by-step explanation:

The value of x for which JKLM is a parallelogram is 21

It is important to note that the sum of angles in a parallelogram is 360 degrees.

From the information given, we have that;

This is represented as;

JKL + KLM + LMJ + MJK = 360

substitute the values

4x + 13 + 4x - 1 + 5x - 8 + 3x + 20 = 360

collect like terms

4x + 4x + 5x + 3x = 360 - 24

Add or subtract like terms

16x = 336

Divide both sides by the coefficient of x

x = 336/16

x = 21

Hence, the value is 21

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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:

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).

Answer:

43

133

Step-by-step explanation:

Complementary means that the two angles added together equal 90

90 - 47 = 43

Supplement means that the two angels added together equal 180

180 -47 = 133

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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The simplified inequality for this problem is given as follows:

0.65x - 0.35y + 0.65z ≥ 0.

Hence the value of A is of:

0.65.

The inequality for this problem is defined as follows:

(x + z)/(x + y + z) ≥ 0.35.

Cross multiplication would work in this case, as the right term is a constant, however if it was a rational expression it would not work.

Thus the first step is leaving the right side as 0, as follows:

(x + z)/(x + y + z) - 0.35 ≥ 0.

Then the least common factor is applied to the left side, as follows:

[x + z - 0.35(x + y + z)]/(x + y + z) ≥ 0.

Applying the distributive property and combining the like terms, we have that:

(0.65x - 0.35y + 0.65z)/(x + y + z) ≥ 0.

Now cross multiplication can be applied, hence the simplified inequality is:

0.65x - 0.35y + 0.65z ≥ 0.

The coefficient A has a value of 0.65, which is the term that multiplies x.

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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)​

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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Answer: 11,295,063

Step-by-step explanation:

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:

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 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.

Using the given function in variable 'x', substitute x=y and y =x to find the inverse, The answer is y=-3x/4 +1/2.

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. The most common symbol for a function is an arrow with the letter "f" written above it (f: X → Y), where "X" is the set of inputs and "Y" is the set of outputs. A function assigns a unique output to each input, and the inputs and outputs can be any mathematical objects, such as numbers, vectors, or polynomials.

To find the inverse of a function, you first need to make sure that the function is invertible, which means that it has a unique inverse. A function is invertible if and only if it is a bijection, that is, it is both a function (meaning that it assigns a unique output to each input) and a surjection (meaning that every element of the output set is the image of at least one element of the input set) and an injection (meaning that no two different inputs have the same output). Once you have verified that the function is invertible, you can find its inverse by "reversing" the input and output.

f(x) = -4/3x+2/3

replacing input and output,

x = -4/3y + 2/3

3x-2 = -4y

y = -3x/4 + 1/2

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The given statement is true.

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:

D' (1,4)

Step-by-step explanation:

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

The cost of 2 orders of fries and 4 drinks is $5.68 and the cost to get f orders of fries and d drinks is $0.92f+0.96d

When something is calculated on its one unit, then it is called its unit rate. for example: If 5 mangoes is of $50 then cost of 1 mango is 50/5 = 10 here $10 is unit rate for mangoes.

Given that, At the fast food restaurant, an order of fries costs $0.92 and a drink costs $0.96.

We have here unit rates of fries and drinks,

So, when 1 pack of fries costs $0.92, then cost of 2 pack of fries = 2×0.92 = $1.84

Similarly, when 1 drink costs $0.96, then the cost of 4 drinks = 4×0.96 = $3.84

Total cost = $5.68

Similarly, the cost to get f orders of fries = $0.92f

And, the cost of d drinks = $0.96d

Total cost =  $0.92f+0.96d

Hence, we get the answer as = a) $5.68 and b) $0.92f+0.96d

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Answer:

270 m^2

Step-by-step explanation:

formula for area of a triangle is base times height divided by 2

(30)x(18)÷2

30x9

270 m^2

hopes this helps

The statements a, c and d are true.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

From the figure we understood that h is the height and r is the radius.

The volume of the cone is 1/3πr²h

V= 1/3πr²h

When volume is 47 then we need to find the height

47= 1/3π(3)²h

47=3×3.14h

47=9.42h

h=4.92=5

So if the volume is 47cm³ then the height of the cone is 5cm approximately is true

Now let us find the statement 2 is true or not

V= 1/3π(3)²(10)

V=3×3.14×10

V=94.2 cm³

So the second statement is not true

The equation V= 1/3π(3)²h is the volume of the cone and h=3V/π(3)² an be used to find the height of the cone is true.

Hence, the statements a, c and d are true.

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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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