In a class of 42 students, the number of boys is 2/5 of the girls. Find the number of boys and girls in the class.

Answer: [tex]=\frac{2x}{x-3}[/tex]  

Step-by-step explanation:

 [tex]\frac{2x^{2} +10x}{x^{2} + 2x-15}[/tex]                        >Take out GCF(greatest common factor) on top

                                       >factor the bottom,  find 2 numbers that mulitply to

                                         "c" term, -15 and adds to the "b" term, +2

                                        >+5 and -3 mulitpy to -15 and add to +2

                                        > put +5 and -3 into factored form on bottom

[tex]=\frac{2x(x+5)}{(x-3)(x+5)}[/tex]                      >reduce the x+5 on top and bottom

[tex]=\frac{2x}{x-3}[/tex]                                >This is simplified

The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.

To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:

Nominal rate [tex]= (1 + r/m)^m - 1[/tex]

Where:

r = effective rate

m = number of compounding periods per year

In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.

Since compounding is done semi-annually, m would be 2.

Plugging in the values:

Nominal rate [tex]= (1 + 0.145/2)^2 - 1[/tex]  

Simplifying the expression inside the parentheses:

Nominal rate [tex]= (1 + 0.0725)^2 - 1[/tex]

Calculating the exponent:

Nominal rate [tex]= (1.0725)^2-1[/tex]

Performing the calculations:

Nominal rate = 1.14900625 - 1

Nominal rate = 0.14900625

Converting the nominal rate to a percentage:

Nominal rate = 14.900625%

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Answer:

5541.77 cm^2

Step-by-step explanation:

The correct interpretation of the slope and y-intercept of the equation y = mx + b in this context is:

A. The slope predicts a temperature increase of about 50° for every increase of 1 chirp per minute. The y-intercept shows that when the crickets are not chirping (x=0), the temperature is 0.

In other words, according to the given equation, for each additional chirp per minute, the temperature is expected to increase by approximately 50 degrees Fahrenheit. Additionally, when there are no chirps (x=0), the equation suggests that the temperature is 0 degrees Fahrenheit.

~~~Harsha~~~

Answer:

C

Step-by-step explanation:

I am pretty certain the math is incorrect on the other posted answer

The slope is   rise/run   means every degree produces 6 chirps more ....or conversely , 1/6 degree produces one more chirp.  

  when the temperature is 50 F there are ZERO chirps

Answer:

[tex]a_n=3n-16[/tex]

Step-by-step explanation:

[tex]a_n=a_1+(n-1)d\\\\a_8=a_1+(8-1)d\rightarrow 8=a_1+7d\\a_{20}=a_1+(20-1)d\rightarrow 44=a_1+19d[/tex]

[tex]-36=-12d\\3=d[/tex]

[tex]8=a_1+7(3)\\8=a_1+21\\-13=a_1[/tex]

[tex]a_n=-13+(n-1)(3)\\a_n=-13+3n-3\\a_n=3n-16[/tex]

The own price elasticity of good X is -0.60, so we can conclude that good X is price inelastic.

The own price elasticity of good X is calculated using the formula:

Given the demand function for good X: Qxd = 6 - 2Px + 5Py, we can calculate the initial quantity demanded at a price of $3 per unit:

Qxd1 = 6 - 2(3) + 5(2)

= 6 - 6 + 10

= 10

The new quantity demanded when the price changes to $2.90 per unit:

[tex]Qxd_2[/tex] = 6 - 2(2.90) + 5(2)

[tex]Qxd_2[/tex] = 6 - 5.80 + 10

[tex]Qxd_2[/tex] = 10.20

Now, we can calculate the percentage change in quantity demanded:

% Change in Quantity Demanded = (Qxd2 - Qxd1) / Qxd1 * 100

% Change in Quantity Demanded = (10.20 - 10) / 10 * 100

% Change in Quantity Demanded = 0.20 / 10 * 100

% Change in Quantity Demanded = 2%

Next, we calculate the percentage change in price:

% Change in Price = (New Price - Old Price) / Old Price * 100

% Change in Price = (2.90 - 3) / 3 * 100

% Change in Price = -0.10 / 3 * 100

% Change in Price = -3.33%

The own price elasticity will be:

Elasticity = (% Change in Quantity Demanded) / (% Change in Price)

Elasticity = 2% / -3.33%

Elasticity ≈ -0.60

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To prove ∠AOW = 45°

Given,

∠WOZ = 90°

∠ZOB = 45°

Now,

∠XOA +∠AOW = 90°............(1)

∠XOA = ∠ZOB ( Vertically opposite angle  )

∠XOA = 45°

Substitute in (1),

45° +  45° = 90°

Now,

∠WOX = ∠XOA +∠WOA

So,

∠WOA + ∠WOZ + ∠ZOB = 180°( Linear pair )

∠WOA + 90° + 45° = 180°

∠WOA = 45°

Hence proved.

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The value of angle x is determined as 40 degrees.

The value of angle y is determined as 180 degrees.

The value of the missing angles is calculated by applying intersecting chord theorem which states that the angle at tangent is half of the arc angle of the two intersecting chords.

The value of angle x is calculated as follows;

50 = ¹/₂ (140 - x ) (exterior angle of intersecting secants)

2(50) = 140 - x

100 = 140 - x

x = 140 - 100

x = 40

The value of angle y is calculated as follows;

The value of angle y is equal to the value of the remaining arc.

y = 360 - (40 + 140 ) ( sum of angles in a circle)

Simplify further as follows;

y = 360 - 180

y = 180⁰

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Hello!

4/7 = 44/77

6/11 = 42/77

42/77 < 43/77 < 44/77

the rationnal number between 4/7 and 6/11​ is 43/77

A. The hypothesis is stated in a correlational form.

B. It does not specify whether it uses a directional or non-directional test.

C. The level of measurement for these variables is not specified.

D. The higher the level of anxiety among Staff Nurses, the lower their performance.

a. The hypothesis "The performance of the Staff Nurses is affected by their level of anxiety." is stated in a correlational form.

b) The given hypothesis does not specify whether it uses a directional or non-directional test.

c) The variables in this hypothesis are "performance of the Staff Nurses" and "level of anxiety." The level of measurement for these variables is not specified.

d) To convert the non-directional hypothesis into a directional one, we would need to specify the direction of the relationship between the variables. For example: "The higher the level of anxiety among Staff Nurses, the lower their performance."

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Hello :)

P(A) = 1/2

P(B) = 5 or greater = 5,6 => 2/6 = 1/3

P(A and B) = 1/2 x 1/3 = 1x1/2x3 = 1/6 ≈ 0.17

the answer is 0.17

The calculated productivities are:

Labor Productivity: 10 units per labor hour.

Multifactor Productivity: 0.8 units per dollar.

Energy Productivity: 20 units per dollar.

To calculate the labor productivity, divide the units produced by the labor hours:

Labor Productivity = Units Produced / Labor Hours

Labor Productivity = 10,000 / 1,000 = 10 units per labor hour.

To calculate the multifactor productivity, divide the units produced by the sum of labor, material, and energy costs:

Multifactor Productivity = Units Produced / (Labor Cost + Material Cost + Energy Cost)

In this case, the labor cost is $10 per labor hour, so the labor cost is 1,000 labor hours * $10 = $10,000.

The material cost is $2,000, and the energy cost is $500.

Multifactor Productivity = 10,000 / ($10,000 + $2,000 + $500)

Multifactor Productivity = 10,000 / $12,500 = 0.8 units per dollar.

Finally, to calculate the energy productivity, divide the units produced by the energy cost:

Energy Productivity = Units Produced / Energy Cost

In this case, the units produced are 10,000, and the energy cost is $500.

Energy Productivity = 10,000 / $500 = 20 units per dollar.

Therefore, the calculated productivities are:

Labor Productivity: 10 units per labor hour.

Multifactor Productivity: 0.8 units per dollar.

Energy Productivity: 20 units per dollar.

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Hello!

Solutions = -3 and 1.5

Which is the standard equation for a circle centered at the origin with radius r be,

⇒   x² + y²  = r²

Hence option D is correct.

We have to find the standard equation of circle,

Given that,

Center of circle is at (0, 0)

And radius is r

Let a point (x, y) on the circle.

We know that,

The distance between the point (x, y) and origin is also known as radius of the circle,

Since we know that,

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Therefore distance between (0, 0) and (x, y),

⇒   √[ (x - 0)² + (y - 0)²] = r

Squaring both sides we get,

⇒   (x - 0)² + (y - 0)²  = r²

⇒   x² + y²  = r²

This  is the standard equation of circle.

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Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

Answer:

664 Square yards

Step-by-step explanation:

Surface area= 2lw+2lh+2hw

=2(17×6)+2(17×10)+2(10×6)

=2(102)+2(340)+2(120)

=204+340+120

=664 Square yards

A construction of the box-and-whisker plot representing the data set is shown below.

In Mathematics and Statistics, a box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the data (information) provided above, the five-number summary for the given data set include the following:

In conclusion, we can logically deduce that the maximum number is 100 while the minimum number is 35, and the median is equal to 88.

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Mr. Jones in Johannesburg is billed R9,767.12 and Ms. Brown in Cape Town is billed R680.24 for their respective properties.

From the provided information for Cape Town's sanitation tariffs:

0-4.2 kl: R16.03 per kl

Since 4.1 ke is equivalent to 4100 liters, which is less than 4.2 kl, we can use the tariff rate for the 0-4.2 kl range.

Cost for 4.1 ke of sanitation

= 4.1 ke x R16.03 per kl

= 4100 liters x R16.03 per kl

= R65.83

For Mr. Jones and Ms. Brown, who own properties with an area of 550 m² each and were billed for 22 kl of sanitation.

we need to determine the applicable tariff rate based on the property size and calculate the cost.

In Johannesburg, based on the provided information, the tariff rate for properties larger than 300 m² to 1,000 m² is R443.96.

Cost of sanitation for Mr. Jones in Johannesburg:

= 22 kl x R443.96 per kl

= R9,767.12

Cost of sanitation for Ms. Brown in Cape Town:

= 22 kl x R30.92 per kl = R680.24

Therefore, Mr. Jones in Johannesburg is billed R9,767.12 and Ms. Brown in Cape Town is billed R680.24 for their respective properties.

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Answer:

7.6

Step by step explanation

[tex]a^2+ab=a(a+b)\\ab+b^2=b(a+b)[/tex]

Therefore

[tex]\text{hcf}(a^2+ab,ab+b^2)=a+b[/tex]

Answer:

Let's denote the original cost of the season train ticket as "x".

According to the given information, a reduction of $33.10 corresponds to a 10% reduction in the original cost. We can set up the following equation to represent this:

10% of x = $33.10

To solve for x, we need to convert 10% to decimal form, which is 0.10. We can rewrite the equation as:

0.10 * x = $33.10

Simplifying the equation, we have:

0.10x = $33.10

To isolate x, we divide both sides of the equation by 0.10:

x = $33.10 / 0.10

x = $331.00

Therefore, the original cost of the season train ticket is $331.00.

Step-by-step explanation:

The length of segment TU for the intersecting chords is determined as 28.

The length of segment TU is calculated by applying intersecting chord theorem for two chords in a circle as shown below.

From the given diagram we will have the following equation;

UV (UV + TU) = WV (WV + XW)

We know that TU is 3 more than XW;

TU = XW + 3

So our new equation becomes;

26( ( 26 + XW + 3) = 27( 27 + XW)

26(29 + XW) = 27 (27 + XW)

Simplify further as follows;

754 + 26XW = 729 + 27XW

754 - 729 = XW

25 = XW

The length of segment TU is calculated as;

TU = 3 + 25

TU = 28

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The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

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If you want to find the base area of a rectangular prism, then all you need is length and width only.

[tex] \boxed{Volume = length \times width \times height} [/tex]

You don't need height. So, this is a must be easy.

[tex]\blue{\small{\mathfrak{That's \: it. \: Thanks \::)}}} [/tex]

Answer:

3

Step-by-step explanation:

To find the z-score for a data value of 155 in a normal distribution with a mean of 137 and a standard deviation of 6, you can use the formula:

z = (x - μ) / σ

where:

x is the data value,

μ is the mean, and

σ is the standard deviation.

Plugging in the values, we have:

z = (155 - 137) / 6

Calculating this expression:

z = 18 / 6 = 3

Answer:  4, 14

Step-by-step explanation:

Bring everything over to other side that is not in the absolute value:

3 |x - 9| + 5 = 20                  >Subtract 5 from both sides

3 |x - 9| = 15                         >Divide both sides by 3

|x - 9| = 5                              >Create a positive and negative version to

                                                 drop the absolute value

x - 9 = 5                        x - 9 = -5

x= 14                                    x = 4

Answer:

The optimal size of each production run is 180 pounds, and the total annual inventory cost is $832,825.

Step-by-step explanation:

To determine the optimal size and total annual inventory cost, we need to consider the production capacity, demand, setup costs, and carrying costs.

Given:

Production capacity per day = 250 pounds

Demand per day = 180 pounds

Setup cost = $125

Carrying cost per pound per year = $12

First, let's calculate the optimal production size. We want to produce enough cheese to meet the demand without exceeding the production capacity.

Optimal production size per day = Minimum(Production capacity, Demand)

Optimal production size per day = Minimum(250 pounds, 180 pounds) = 180 pounds

Next, let's calculate the total annual inventory cost. This cost includes both the setup cost and the carrying cost.

Total annual inventory cost = (Setup cost * Number of setups per year) + (Carrying cost per pound * Optimal production size * Number of days in a year)

Number of setups per year = Number of production runs per year

Number of production runs per year = Total days in a year / Days per production run

Assuming a year has 365 days and each production run takes one day:

Number of production runs per year = 365 days / 1 day = 365 runs

Total annual inventory cost = ($125 * 365) + ($12 * 180 pounds * 365)

Total annual inventory cost = $45,625 + $787,200

Total annual inventory cost = $832,825

[tex]|\Omega|=8\\|\text{odd}|=4\\\\P(\text{odd})=\dfrac{4}{8}=\dfrac{1}{2}[/tex]

Answer:

4/8

or, 1/2

Step-by-step explanation:

odd numbers (O) = (1,3,5,7) = 4

total numbers (T) = 8

P(odd) = n(O)/n(T)

           = 4/8