The ratio of boys to girls in a class is 3:4. There are 35 students in the class. How many students are girls?

Answer:

Step-by-step explanation:

-55/11

55/-11

The fraction is 23/27.

Let the numerator and denominator of the given fraction be x and y respectively.

According to the question,

Case 1 :-

Denominator of the fraction is 4 more than the numerator.

⇒ Numerator = Denominator - 4

⇒ x = y - 4 ...(1)

Case 2 :-

If 1 is added to numerator and 2 is subtracted from denominator fraction becomes 24/25

⇒ (Numerator + 1) / (Denominator + 2) = 4/5

⇒ (x + 1) / (y - 2) = 24/25

⇒ 25(x + 1) = 24(y - 2)

⇒ 25x + 25 = 24y - 48

⇒ 25x - 24y = -73 ...(2)

Substituting the value of x from (1) in (2), we have

⇒ 25(y - 4) - 24y = -73

⇒ 25y - 100 - 24y = -73

⇒ y = -73 + 100

y = 27

substitute the value of y in equation 1.

x = 27 - 4

x = 23

Now, At the beginning of our solution we took the numerator & denominator to be x & y respectively. So the fraction is:

⇒ x / y

⇒ 23/27

Hence the fraction is 23/27.

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Step-by-step explanation:

Hope it will help you a lot.

The experimental probability that Hilda pulled a red marble is 0.11752 or 11.752%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

For a class experiment, Hilda places different colored marbles in a bag. She pulls a marble at random from the bag, records its color, and then puts the marble back in the bag. She repeats this process 25 times.

The overall results are shown in the table.

Blue, Red, Yellow, Orange Frequency 6, 4, 8, 7 respectively.

P(red) will be 1/4 and P(not red) will be 3/4.

The number of trials (n) is 25.

Frequency of the red (r) = 4

Then the probability of getting red will be

\(\rm P(red) = \ ^nC_r( P(red) )^r*( P(not\ red))^{n-r}\\\\P(red) = \ ^{25}C_4 * (\dfrac{1}{4})^4 * (\dfrac{3}{4})^{25-4}\\\\P(red) = 0.11752\)

The experimental probability that Hilda pulled a red marble is 0.11752 or 11.752%.

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Answer:

here is ther anwser

Step-by-step explanation:

Each t-shirt costs $15, and each pair of gym shorts costs $16.

Let's call the cost of each t-shirt "x". Then the cost of each pair of gym shorts is x + $1.

We know that the total cost of the t-shirts is 5 * x, and the total cost of the gym shorts is 2 * (x + $1).

We also know that the total cost of all items is $107, so we can write an equation to represent this information:

5x + 2(x + $1) = $107

5x + 2x + 2 = $107

7x + 2 = $107

7x = $105

x = $15

So, each t-shirt costs $15, and each pair of gym shorts costs $15 + $1 = $16.

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The equation in slope-intercept form of the line that passes through the point is y = -2x+4 , Option B is the correct answer.

The equation of a straight line is given by the equation

y= mx+c

Where m is the slope and

c is the intercept on y axis.

The given data is

line passes through the point (3,-2) with slope -2.

m = -2

y = -2x + c

-2 = - 2 * 3 +c

-2 = -6 +c

c = +4

y = -2x+4

Therefore Option B is the correct answer.

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Answer:

Step-by-step explanation:

area =(4+4+4)/2×2+1/2×(4+4)×5.75

=12+23.00

=35 sq.cms.

Step-by-step explanation:

Area of triangle = \(\frac{1}{2}\)(b*h)

Area of rectangle = b*h

\(A(big-triangle) = \frac{1}{2} (5.75*4)\)

\(A(big-triangle) = \frac{1}{2}(23)\)

\(A(big-triangle) = 11.5\)

Since there are two big triangles, then we can multiply 11.5 by 2.

11.5 * 2 = 23

\(A(small-triangle) = \frac{1}{2}(2*2)\)

\(A(small-triangle) = \frac{1}{2} (4)\)

\(A(small-triangle) = 2\)

Since there are two small triangles, then we can multiply 2 by 2.

2 * 2 = 4

\(A(rectangle)= 4 * 2\)

\(A(rectangle) = 8\)

Now, we can add up all of the areas so we can find the total area of the entire shape.

23 + 4 + 8 = 35

So, the area of the entire shape is 35 square cm.

Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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2.426

Step-by-step explanation:

0 2. 4 2 6

6 1 4. 5 6 0

− 0

1 4

− 1 2

2 5

− 2 4

1 6

− 1 2

4 0

− 3 6

4

Answer as a fraction: \(\frac{75}{182}\)

Answer as a decimal: 2.42

Step-by-step explanation:

Hope it helps and have a great night! =D

~shining stars~

Answer:

Step-by-step explanation:

lim x -> +oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

+oo³ (-2 - 13/+oo + 8/+oo² + 52/oo³)

+oo(-2 + 0 + 0 + 0)

-oo

lim x -> -oo    -2x³ - 13x² + 8x + 52

x³ (-2 -13/x + 8/x² + 52/x³)

-oo³ (-2 - 13/-oo + 8/-oo² + 52/-oo³)

-oo(-2 + 0 + 0 + 0)

+oo

The post-split market capitalization of Walnut Creek Inc. is $12995089.

Given that, Walnut Creek Inc. is going to do a revers stock split with a 3:4 ratio. The current price per share is $234.75 and the current number of outstanding shares is 38,750,000.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, 3+4 = 7

Now, 1/7 × 38,750,000

= 5535714 .29 shares

So, capitalization is 5535714 × 234.75

= $12995089

Therefore, The post-split market capitalization of Walnut Creek Inc. is $12995089.

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Answer:

$1.28

Step-by-step explanation:

0.96 = 3 Oranges

0.96 ÷ 3 = 32 (32 cents for each orange)

0.96 + 0.32 = 1.28

Answer:

-4x3.5=-14

Step-by-step explanation:

divide -14 by -4 wich = 3.5

Answer

Step-by-step explanation:

i dont know but pls dont hate me no one anserd for 15 hours so i took some points

Thus, the rate at which the area of the triangle changes when the height is 18 cm and the base is 9 cm is -45 square centimeters per hour.

To find the rate at which the area of the triangle changes, we need to use the formula for the area of a triangle:

A = (1/2)bh, where A is the area, b is the base, and h is the height.

We are given that the base is shrinking at a rate of 7cm/hr and the height is increasing at a rate of 4cm/hr. This means that the rate of change of the base is -7cm/hr (negative because it is shrinking) and the rate of change of the height is 4cm/hr.

To find the rate at which the area is changing, we need to use the product rule of differentiation.

dA/dt = (1/2)(b dh/dt + h db/dt)

Substituting the given values for b, h, db/dt, and dh/dt, we get:

dA/dt = (1/2)(9*4 + 18*(-7))

dA/dt = (1/2)(36 - 126)

dA/dt = (1/2)(-90)

dA/dt = -45

Therefore, the rate at which the area of the triangle changes when the height is 18 cm and the base is 9 cm is -45 square centimeters per hour.

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The average rate of change is 4

Given:

h(x) = -x²+ 10x + 32

The interval is 3≤x≤11

To find:

The rate of change for the given interval

To find the above, we will apply the formula for rate of change:

Answer:

Step-by-step explanation:

f(g(x))

g(x) = 7x -4

f(7x - 4) = 2(7x - 4) + 15 = 14x - 8 + 15 = 14x + 7

The total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

In the given power system depicted in Figure 1, there are three units that are always running. Each unit has specific characteristics regarding their minimum power output (Pmin), maximum power output (Pmax), and incremental cost (Ci). Let's discuss the characteristics of each unit and calculate the total cost of power generation for a given load demand.

Unit 1:

Pmin = 200 MW

Pmax = 500 MW

Ci = $50/MWh

Unit 2:

Pmin = 150 MW

Pmax = 400 MW

Ci = $40/MWh

Unit 3:

Pmin = 100 MW

Pmax = 300 MW

Ci = $30/MWh

To calculate the total cost of power generation for a given load demand, we need to determine the optimal power output for each unit. We start by considering the units with the lowest incremental cost first.

Suppose the load demand is D MW. We allocate the load demand to the units as follows:

Step 1: Check if Unit 1 can meet the load demand within its power range. If yes, allocate the load demand to Unit 1 and calculate the cost:

Cost1 = Ci * P1, where P1 is the power output of Unit 1.

Step 2: If there is still remaining load demand, allocate it to Unit 2:

Cost2 = Ci * P2, where P2 is the power output of Unit 2.

Step 3: If there is still remaining load demand, allocate it to Unit 3:

Cost3 = Ci * P3, where P3 is the power output of Unit 3.

Finally, the total cost of power generation, Cost_total, is the sum of Cost1, Cost2, and Cost3:

Cost_total = Cost1 + Cost2 + Cost3

To find the optimal power output for each unit, we consider the load demand and compare it to the minimum and maximum power output limits for each unit. The power allocation is based on meeting the load demand while minimizing the overall cost of power generation.

In summary, given the characteristics of the three units in the power system (Pmin, Pmax, and Ci), the total cost of power generation for a specific load demand can be calculated by optimally allocating the load demand to each unit based on their power output limits. The allocation is done in a way that minimizes the overall cost while meeting the load demand.

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Answer:

0.6t - 4.3s -2.6

Step-by-step explanation:

Given the expression

(-3.5t - 4s + 4.5) + (-7.1 - 0.3s + 4.1t)

Collect the like terms

= -3.5t+4.1t-4s-0.3s+4.5-7.1

= 0.6t - 4.3s -2.6

Hence the required expression is 0.6t - 4.3s -2.6

The solution is found by slope of the graph and the solution is 2,200.

Let x the amount of money per hour and y the total amount of money.

Studio A:-

Rents for 100 dollars plus 50 dollars per hour.

\(y= 100 + 50x\)

So the slope is 50 and the y intercept is 100.

Studio B:-

rents for 50 dollars plus 75 dollars per hour.

\(y= 50 + 75x\)

So the slope is 75 and the y intercept is 50.

ThrTh solution is 2200 , see the gragraphph.

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Complete question:- You and your friends decide to rent some studio time to make a CD. Big Notes Studio rents for $100 plus $50 per hour. Great Sounds Studio rents for $50 plus $75 per hour. Solve the system by graphic method.

If the vector ℓ is within 3.85° of the z axis, then the smallest value that ℓ may have is 1.[1]

The possible values for the quantum number m are integers ranging from -ℓ to ℓ in steps of 1. Therefore, given ℓ, there are 2ℓ + 1 possible values for m.[2]

Since the question only asks for the smallest value that ℓ may have, we can't say for certain that 1 is the only possibility. However, based on the information given, 1 is the smallest possible value for ℓ in this scenario.

Therefore, the smallest value that ℓ may have if vector l is within 3.9° of the z axis is 1.

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Based on the data in two-way frequency table, "being in high school" and "gpa above 3.0" are not independent events.

The conditional probability is the happening of an event, when the probability of occurring of other event is given.

A two-way frequency table shows grades for students in college and students in high school.

Let H represent being in high school and G represent the GPA above 3.0. To be an independent event, they must be,

\(P(H|G)=P(H)\)

The conditional probability of event H, given that the G is occurred, can be calculated as,

\(P(H|G)=\dfrac{14}{40}\\P(H|G)=0.35\)

Total students below 3.0 GPA are 60 and the total number of student are 100. Thus, the probability of being in high school is

\(P(H)=\dfrac{60}{100}\\P(H)=0.6\)

Here, conditional probability \(P(H|G)\) is not equal to the probability of being in high school.

Hence, based on the data in two-way frequency table, "being in high school" and "gpa above 3.0" are not independent events.

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The common ratio (r) is 4, so our equation is \(a_6=5(4)^{5}a 6 ​ =5(4)5.\)Simplifying, we get \(a_6=6400a 6 ​ =6400.\) Therefore, the value of a_6 is 6400.

The sixth term of a geometric sequence with\(a_1=5a 1 ​ =5\) and \(a_n=4a_{n-1}a n ​ =4a n−1 ​ is a_6.\)To find the value of a_6, we can use the formula for the nth term of a geometric sequence: \(a_n=a_1r^{n-1}a n ​ =a 1 ​ rn−1.\)In this case, the common ratio (r) is 4, so our equation is \(a_6=5(4)^{5}a 6 ​ =5(4)5\). Simplifying, we get \(a_6=6400a 6 ​ =6400.\)Therefore, the value of a_6 is 6400.The question is asking us to find the value of a 6 ​ , given that the first element in the sequence is a 1 ​ = 5 and each subsequent element is 4 times the previous element. This can be expressed in a formula as a n ​ = 4a n-1 ​ .

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Answer:

-15

Step-by-step explanation:

I think

It would cost approximately 0.897 cents to run your laptop for 2.6 hours, assuming a cost of 15 cents per kWh.

To calculate the cost of running your laptop for 2.6 hours, we need to determine the energy consumed in kilowatt-hours (kWh) and then multiply it by the cost per kWh.

Power of the laptop (P) = 23 Watts

Time (t) = 2.6 hours

Cost per kWh (C) = 15 cents

First, let's convert the power from Watts to kilowatts:

P = 23 Watts = 23/1000 = 0.023 kilowatts

Next, we calculate the energy consumed in kilowatt-hours using the formula:

Energy (E) = P * t

Substituting the values:

E = 0.023 kilowatts * 2.6 hours = 0.0598 kilowatt-hours (kWh)

Finally, we calculate the cost using the formula:

Cost = E * C

Substituting the values:

Cost = 0.0598 kWh * 15 cents/kWh

Calculating this, we find:

Cost = 0.897 cents

Therefore, it would cost approximately 0.897 cents to run your laptop for 2.6 hours, assuming a cost of 15 cents per kWh.

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When switched on, your laptop recuires a power of 23 Watts. How many cents does it cost to run it for 2.6 hours, if a kWh costs you 15 cents?