In a school, the number of girls is 70 more than boys. the total number of students is 1280. find the number of girls and boys simple equations

Answer:

im not too sure about that sorry!

Step-by-step explanation:

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It takes 15 seconds for the first cyclist to overtake the second cyclist.

First, identify the two phases of the first cyclist's motion.

Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.

Phase 2: The cyclist travels at a constant speed of 8 m/s.

Find the equations of the two straight-line sections of the graph.

The equations of the two straight-line sections of the graph are as follows:

Phase 1:

s = [tex]2t^2[/tex]

Phase 2:

s = 8t

where s is the distance traveled by the cyclist and t is the time

Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist

The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.

Let t be the time it takes the first cyclist to overtake the second cyclist.

The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).

Setting these two expressions equal to each other, we get:

8t = 8(t - 5)

Solving for t, we get:

t = 15

Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist

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Answer:

y = 25°

Step-by-step explanation:

115° and x are a linear pair and sum to 180° , so

x + 115° = 180° ( subtract 115° from both sides )

x = 65°

the sum of the 3 angles in the triangle = 180° , then

x + x + 2y = 180°

65° + 65° + 2y = 180°

130° + 2y = 180° ( subtract 150° from both sides )

2y = 50° ( divide both sides by 2 )

y = 25°

An equation is formed of two equal expressions. The estimated solution of the two system of equations is at (5/2,4/3). Thus, the correct option is D.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the system of equation is the point at which the two lines will intersect as shown below. Therefore, the solution will be,

Solution = (5/2, 4/3)

Hence, the estimated solution of the two system of equations is at (5/2,4/3). Thus, the correct option is D.

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The answer for the following question is

1. m= 10  

2. y- intercept = 300

3. y = 10x + 300

A regression line is a graphic representation of the regression equation expressing the hypothesized relationship between an outcome or dependent variable and one or more predictors or independent variables

1.slope= rise/ run

m= 10  

2. y- intercept = 300

3. Now, the regression line:

y = 10x + 300

At, x = 1

y = 10(1) + 300

y = 310 calories

and  x = 14

y = 10(14) + 300

y = 440

We know the actual value is 330.

Hence, the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.

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The probability that you lose all five times will be 0.59.

From the information given, the chances of winning are 0.1. Therefore, the chance of losing will be:

= 1 - 0.1 = 0.9

Therefore, the probability that you lose all five times will be:

= 0.9 × 0.9 × 0.9 × 0.9 × 0.9

= 0.59

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Answer: 50%

Step-by-step explanation:  50%

Step-by-step explanation:

x = 2. 2(x) = 2(2). 2x= 4. Multiplication Property of Equality (if you have two equals sides and then multiply them by the same quantity both sides will remain equal)

5=3a therefore 3a = 5. Symmetric Property if a=b then b=a

T = 4 => 5T = 20 (Multiplication Property of Equality) => 5T + 7 = 27 (Addition Property of Equality. basically if two sides are equal and you add the same quantity they will remain equal)

Last one is transitive property which states. if a=b and b=c then a=c so in this case a would be 9, b would be 4x and c would be m

Answer:

No, she is not correct. Because this is a proportional relationship.

Step-by-step explanation:

Proportional relationships are relationships having equal ratios.

here, Mandy's conclusion is incorrect because the relationship is proportional, and it has a uniform ratio of 5.

column 1               column 2           column 2/column1

   'x'                            'y'          

    1                             5                               5

    2                            10                              5

    5                            25                             5

    10                           50                             5

As we clearly see that ratio of column 2 and column 1 is same for every row, therefore we can conclude that the given relation in the relation is proportional.

Thus,  the given relation is proportional.

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Let's take this problem step by step:

To find the ordered pair of the system:

⇒ must set both equations equal to each other

    ⇒ must solve for 'x'

Let's solve:

 [tex]x^2-2x+3=-2x+28\\x^2-2x+3+2x-28=0\\x^2-25=0\\(x-5)(x+5)=0[/tex]

Let's find the x-values:

 [tex](x-5)=0\\x=5\\\\(x+5)=0\\x=-5[/tex]

Let's find f(x)'s value for each of the 'x':

[tex]x=5\\f(5)=-2(5)+28=18\\\\x=-5\\f(-5)=-2(-5)+28=38[/tex]

Answer: (5, 18), (-5,38)

Hope that helps!

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The intervals of the function in which it is increasing, decreasing and constant are given as follows:

a) Increasing: [tex]x \in \left[-4.5, 2\right][/tex].

b) Decreasing: [tex]x \in \left[4,6\right][/tex].

c) Constant: [tex]x \in \left[2,4\right][/tex].

A function is increasing when the graph of the function is pointing upwards, hence this function is increasing on the interval [tex]x \in \left[-4.5, 2\right][/tex].

A function is increasing when the graph of the function is pointing downwards, hence this function is decreasing on the interval [tex]x \in \left[4, 6\right][/tex].

A function is constant when it is graph is a line without inclination, hence this function is constant n the interval [tex]x \in \left[2, 4\right][/tex].

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Answer:

  31

Step-by-step explanation:

We can solve the given equation for 'b', then find the integer values of 'a' that make 'b' a positive integer. There are 3 such values. One of these minimizes the objective function.

__

  ab +5b = 373 +6a . . . . . . isolate b terms by adding 6a

  b = (6a +373)/(a +5) . . . . . divide by the coefficient of b

  b = 6 +343/(a +5) . . . . . . . find quotient and remainder

The value of 'b' will only be an integer when (a+5) is a factor of 343. The divisors of 343 = 7³ are {1, 7, 49, 343}. so these are the possible values of a+5. Since a > 0, we must eliminate a+5=1. That leaves ...

  a = {7, 49, 343} -5 = {2, 44, 338}.

Possible values of b are ...

  b = 6 +343/{7, 49, 343} = 6 +{49, 7, 1} = {55, 13, 7}

Then possible (a, b) pairs are ...

  (a, b) = {(2, 55), (44, 13), (338, 7)}

The values of the objective function for these pairs are ...

  |a -b| = |2 -55| = 53

 |a -b| = |44 -13| = 31 . . . . . the minimum value of the objective function

  |a -b| = |338 -7| = 331

The "sample" with "mean absolute deviation" indicate about a sample mean absolute deviation is being used as an estimator of the mean absolute deviation of a​ population

Generally,  The MAD measures the average dispersion around the mean of a given data collection.

[tex]1/n \sum_i-1^{n} |x_i -m(X)|[/tex]

In conclusion, for the corresponding same to mean

the sample  mean absolute deviation

7,7  ↔         0

7,21  ↔         7

7,22         ↔    7.5

21,7        ↔          7

21,21 ↔     0

21,22 ↔    0.5

22,7   ↔     7.5

Therefore

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Answer:

Step-by-step explanation:

Here we will show you step-by-step how to get the solution to: "What is 5/14 rounded to the nearest whole number?"

First, we convert the fraction to a decimal number by dividing the numerator by the denominator:

5 / 14 = 0.3

Then, we round to the nearest whole number using the following rules:

If the number to the right of the decimal point is .5 or higher, then add 1 to the left of the decimal point.

If the number to the right of the decimal point is less than .5, then leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.

.4 is less than .5. Thus, we leave the number to the left of the decimal point as is and remove the digit to the right of the decimal point.

5/14 rounded to the nearest whole number is therefore:

0

The statements which are true from the given table are:

The function that best represents the data is f(x) = 24,512(0.755)x.

The function decreases indefinitely.

It is reasonable to interpolate the value of the car at 4.5 years.

Depreciation refers to the accounting method where the value of a tangible asset reduces over a period of time.

The value of the car is shown with the purchase with entries that shows its value over time,

The function that best represents the data is f(x) = 24,512(0.755)x and that this function decreases indefinitely.

The statements which are true from the given table are:

The function that best represents the data is f(x) = 24,512(0.755)x.

The function decreases indefinitely.

It is reasonable to interpolate the value of the car at 4.5 years.

The complete question is

"The value of a car decreases as shown in the table below.

A 2-column table with 6 rows.

The first column is labeled years after purchase with entries 0, 1, 2, 3, 4, 5.

The second column is labeled value (dollar sign) with entries 25,000; 18,000; 14,000; 10,500; 8,000; 6,000.

Which statements are true? Check all that apply.

The function that best represents the data is f(x) = 24,512(0.755)x.

The function that best represents the data is f(x) = 554x2 – 5,439x + 24,600.

The function decreases indefinitely.

It is reasonable to interpolate to the value of the car at 4.5 years.

It is reasonable to extrapolate to 40 years"

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Part (c)

[tex]\text{LHS}=\csc^{2} x-2\csc x\cot x+\cot^{2} x\\\\=(\csc x-\cot x)^{2}\\\\=\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x} \right)^{2}\\\\=\left(\frac{1-\cos x}{\sin x})^{2}\\\\=\tan^{2} \left(\frac{x}{2} \right)\\\\=\text{RHS}[/tex]

Part (d)

[tex]\text{LHS}=[\cos x \cos y][\tan x+\tan y]\\\\=[\cos x\cos y]\left[\frac{\sin x}{\cos x}+\frac{\sin y}{\cos y} \right]\\\\=\sin x \cos y+\sin y \cos x\\\\=\sin(x+y)\\\\=\text{RHS}[/tex]

Answer:

Area = 168 cm²

Step-by-step explanation:

**Please note that there is an error in the drawing of the given parallelogram.  In order for the parallelogram to have the given shape, the diagonal AC is actually 22.5 cm in length, whereas diagonal DB is 15 cm in length (see attached diagram). Therefore, I shall be using the attached diagram for my calculations.  However, please note that due of the properties of a parallelogram, the final answer will be the same, regardless of which diagonal is used.**

To calculate the area of a parallelogram, we would usually multiply the base by the perpendicular height.  As the perpendicular height is unknown in the given parallelogram, use the following formula:

[tex]\textsf{Area of parallelogram} = ab \sin (x)[/tex]

where:

As the diagonal of the parallelogram is given, use the cosine rule to calculate the measure of the included angle ∠DCB.

Cosine Rule (for finding angles)

  [tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

where:

From inspection of the given diagram:

Substitute the given values into the cosine rule formula and solve for ∠ABC:

[tex]\implies \sf \cos(DCB)=\dfrac{13^2+14^2-15^2}{2(13)(14)}[/tex]

[tex]\implies \sf \cos(DCB)=\dfrac{140}{364}[/tex]

[tex]\implies \sf \cos(DCB)=\dfrac{5}{13}[/tex]

[tex]\implies \sf \angle DCB=67.38013505...^{\circ}[/tex]

Substitute the found angle and the length of the parallel sides into the area formula:

[tex]\begin{aligned}\textsf{Area of parallelogram} & = ab \sin (x)\\\\\implies \textsf{Area} & = \sf (13)(14) \sin (DCB)\\& = \sf (13)(14) \left(\dfrac{12}{13}\right)\\& = \sf 168\:\:cm^2\end{aligned}[/tex]

Therefore, the area of the given parallelogram is 168 cm².

The correct statements are options C and option D.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.

The inequality is -3(2x - 5) < 5(2 - x)

At first, simplify each side

-3(2x - 5) = -3(2x) + -3(-5)

Remember (-)(-) = (+)

-3(2x - 5) = - 6x + 15

5(2 - x) = 5(2) + 5(-x)

Remember (+)(-) = (-)

5(2 - x) = 10 - 5x

- 6x + 15 < 10 - 5x

Subtract 15 from both sides

- 6x < -5 - 5x

Add 5x to both sides

- x < - 5

Remember the coefficient of x is negative, then when you divide both sides by it you must reverse the sign of inequality

The coefficient of x is -1

Divide both sides by -1

x > 5

Therefore the correct statements are options C and option D.

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The option that best describes the graphed function is: D. inverse variation; k = 4

Given two variables x and y has an inverse variation, the equation that models the relationship of the inverse variation is: y = k/x, where k = xy.

This means that as x increases, y decreases. This is the same for the graph given. So, it is an inverse variation.

When x = 2, y = 2. Therefore:

k = (2)(2)

k = 4

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The scale factor from A to B is 5/3 and the value of r is 33/5

From the figure, we have the following corresponding sides

A : B = 5 : 3

Express as fraction

B/A = 3/5

This means that, the scale factor from A to B is 5/3

From the figure, we have the following corresponding sides

A : B = 11 : r

Express as fraction

B/A = r/11

Recall that:

B/A = 3/5

So, we have:

3/5 = r/11

Multiply by 11

r = 33/5

Hence, the value of r is 33/5

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Answer: Coordinates: (1,3) length RS: 3 length RT: 2 ST: 3.6

Step-by-step explanation:

a^2+b^2=c^2

3^2+2^2=c^2

9+4=c^2

13=c^2

3.6=c

Answer:

2

Step-by-step explanation:

An arithmetic progression with first term a and common difference d has the following first 6 terms:

a, a + d, a + 2d, a + 3d, a + 4d, a + 5d

We are given a = 1 and a + 5d = 11.

1 + 5d = 11

5d = 10

d = 2

Answer: The common difference is 2.

Answer:

12

Step-by-step explanation:

1 hour = 60 minutes

2 people paint a fence in 1 hour = 60 minutes

10 people are 5 times 2 people, so they need 5 times less time than 2 people.

10 people paint a fence in 60/5 minutes

10 people paint a fence in 12 minutes.

Answer:

length = 20 cm

width = 3 cm

Step-by-step explanation:

Answer:

6) B

7) D

Step-by-step explanation:

6)

The surface area of a cylinder is 2 * pi * r * (r + h)

SA = 2 * 3.14 * 3.6 * (3.6 + 8.5) = 2 * 3.14 * 3.6 * 12.1 = 273.6 cm^2

7)

The volume of a cylinder is pi * r^2 * h

V = 3.14 * (3.6)^2 * 8.5 = 345.9 cm^3

Answer:

6. surface area= 2πrh

where r=radius of the base

h=height of the cylinder

π=pie

π=22/7, r=3.6, h=8.5

2×22/7×3.6×8.5= 192.3cm²

square root of 192.3 is 13.9, the one whose square root is closest to that of 192.3 in the options is 178 whose square root is 13.3. A

7. volume=product of the height and its base area

volume=πr²h

22/7×3.6²×8.5 = 346.2. D

Answer:

150 yd

Step-by-step explanation:

the angle bisector divides the opposite sides into segments that are proportional to the other 2 sides .

let x be the distance from the oak tree to the hole, then

[tex]\frac{225}{x}[/tex] = [tex]\frac{375}{250}[/tex] ( cross- multiply )

375x = 56250 ( divide both sides by 375 )

x = 150 yd

By the fact that the sum of internal angles in a triangle and the law of the cosines, the possible lengths of the side EF are represented by 16 ≤ EF ≤ 900.

In this question we have a triangle with two known lengths and there many possible solutions for the length of the segment EF. By geometry we know that the sum of the internal angles in a triangle equals 180° and by the law of cosines we have the following expression for the missing length:

EF² = 17² + 13² - 2 · (13) · (17) · cos D

EF² = 458 - 442 · cos D, 0 ≤ θ ≤ 180°

As the cosine is a function bounded between - 1 and 1, then the possible lengths of the side EF are:

16 ≤ EF ≤ 900

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