17. In a spelling competition, school X had 12 more participants than school Y and 18 fewer participants than school Z. The ratio of the number of boys to the number of girls in school X, Y and Z were 1:2, 1:5 and 2: 1 respectively. There were 50 more girls than boys in total from the 3 schools. How many participants from the 3 school were there in all?​

Answer:

x > -4

Step-by-step explanation:

[tex]2x+3 \geq 7 \\ \\

2x \geq 4 \\ \\

x \geq 2[/tex]

[tex]2x+9>1 \\ \\ 2x>-8 \\ \\ x>-4[/tex]

So, the union of these solutions is x > -4.

Answer:

(A∩B)' = A'∪B'

Step-by-step explanation:

U is the universal set

A and B are two subsets of U

let A' be the complement subset of A

and  B' be the complement subset of B

U = {-10,-9,…,-1,0,1,…,9,10}

A = {-1,0,1}

B = {1,2,…,9,10}

Then

A∩B = {1}

Then

the complement of A∩B :

(A∩B)' = {-10,-9,…,-1,0,2,…,9,10}

(notice the absence of 1)

On the other hand,

A' = {-10,…,-2}∪{2,…,10}

B' = {-10,…,0}

Then

A'∪B' = {-10,-9,…,-1,0}∪{2,…,10}

         =  {-10,-9,…,-1,0,2,…,9,10}

Conclusion:

(A∩B)' = A'∪B'

I'll go for 40.

To find the value of y,

draw a line up from the x - axis at 1910,

all the way up to cross the blue line;

then, draw a horizontal line from the point where the recent line meets the blue one.

Now read of the value you get for y.

Hope this helps!

The expressions 14, 6 + 8, and (6 + 8) are equivalent because they are all equal to 1

14

6 + 8

= 14

(6 + 8)

= 14

The coefficient of (6 + 8) is 1, so, the expression remains the same.

Equivalent expressions refers to those expressions that work the same even though they look different.

The importance or significance of equivalent expression is that its makes expressions easier to work with and solve.

Therefore, the expressions 14, 6 + 8, and (6 + 8) are all equivalent to 14.

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The given height of this trapezoid is given to be 4.5m

We have to solve for this by making use of the height of a trapezoid. The height is given as

A = (1/2) h (b1 + b2)

The variables here are

h = height

b1 = lenght at base 1

b2 = length at base 2

If the trapezoid that we have is a isosceles triangle, then base 1 is going to be the same length as that of the first base

b1 = 4 ft is the area. Given that the height has to be at least 4.5feet, then this would ensure that the trapezoid would be able to hold the shed.

Hence the height would begiven as 4.5 ft

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Answer: 4.5

Step-by-step explanation:

The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).

A linear function is modeled by:

y = mx + b

In which:

The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:

g(x) = 5 + 2x.

The solution to the system of equations is found as follows:

f(x) = g(x)

2x² + x + 4 = 5 + 2x

2x² - x - 1 = 0

Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:

When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).

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Answer:

D. (1,7)

Step-by-step explanation:

I took the exam

Answer: C. - √2

Step-by-step explanation:

Given requirements from the question

Find the exact value of sec 135°

Convert into common trigonometric expression

sec = secant

secx = 1 / cosx

Therefore, sec 135° = 1 / (cos 135°)

Find the reference angle

135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.

Since 135° is in the second quadrant, its reference angle will be

                                         180° - 135° = 45°

However, we need to consider the positive and negative.

In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.

Therefore, when the value of cosine is in QII, it is negative.

The reference angle = - (1 / cos 45°)

Determine the final value

Given that the reference angle = - (1 / cos 45°)

cos 45° = 1 / √2

Therefore:

sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) = [tex]\boxed{-\sqrt{2} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

EVALUATE

false

Step-by-step explanation:

Complex number

(39+5=5a=9)

Helen is currently is 8 years old.

Endeavor to understand the question, analyze it and interpret it into equation.

Given that Helen's age is multiples of 4. Next year it'll be a multiple of 3. Helen's older brother is now 19.

This means Helen current age is multiple of 4 and next year it will be a multiple of 3. Also, Helen's age is less than 19

The two available numbers that fit this analysis and less than 19 are 8 and 9. 8 is multiple of 4. 8 + 1 = 9 which is multiple of 3

Therefore, Helen is 8 years old now

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Answer:

4

Step-by-step explanation:

10 - 6 = 4

Answer:

a = 3

Step-by-step explanation:

4(2a - 3) = -2(a - 9)

8a - 12 = -2a + 18

10a = 30

a = 3

Let's check if we got it correct by substituting 3 for a in the original equation.

4(2*3 - 3) = -2(3 - 9)

4(6 - 3) = -2(-6)

4(3) = 12

12 = 12

The general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]

For given question,

We have been given a differential equation y'' − y' − 12y = e^(4x)

We need to solve the given differential equation by undetermined coefficients.

We can write given differential equation as [tex](D^2-D-12)y=e^{4x}[/tex] where [tex]D=\frac{d}{dx}[/tex]

First solve the corresponding homogeneous differential equation:

y'' - y' - 12y = 0

The characteristic equation is:

m² - m - 12 =0

Let's find the roots of above quadratic equation by factorization.

⇒ m² - m - 12 = 0

⇒ (m - 4)(m + 3) = 0

⇒ m - 4 = 0   OR  m + 3 = 0

⇒ m = 4   OR   m = -3

Hence the complementary solution is,

[tex]y_c=C_1e^{4x}+C_2e^{-3x}[/tex]

Let the general solution of a second order homogeneous differential equation be [tex]y(x)=C_1(x)e^{4x}+C_2(x)e^{-3x}[/tex]

The unknown functions C1(x) and C2(x) can be determined from the system of two equations:

[tex]C'_1e^{4x}+C'_2e^{-3x}=0~~~~~~~............(1)\\\\C'_1(4e^{4x})+C'_2(-3e^{-3x})=e^{4x}~~~~~~~...................(2)[/tex]

from (1),

[tex]C'_2e^{-3x}=-C'_1e^{4x}[/tex]

Substitute this value in equation (2)

[tex]4C'_1e^{4x}+3C'_1e^{4x}=e^{4x}[/tex]

[tex]\Rightarrow C'_1=\frac{1}{7}[/tex]  and  [tex]C'_2=-\frac{1}{7}e^{7x}[/tex]

[tex]\Rightarrow C_1=\frac{1}{7} x+c_3[/tex]     and     [tex]C_2=\frac{1}{49}e^{7x}+c_2[/tex]

Therefore, the general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]

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From my analysis, the answer is likely to be D. I don't have a formula to prove it though.

Answer: 78 degrees.

Step-by-step explanation:

The other guy is wrong don't listen to him.

Here is the five-number summary:

Minimum: 9

Lower quartile:   11

Median: 24

Upper quartile:  34

Maximum: 45

Interquartile range: 23

The minimum number is the smallest number in the dataset. The  minimum number is 9. The maximum number is the largest number in the dataset. The maximum number is 45.

The first quartile, third quartile and the interquartile range are used to measure dispersion.

The first quartile : 1/4(n + 1)

1/4 x (12) = 3rd term = 11

The third quartile : 3/4 x (n + 1)

3/4 x (12) = 9th term = 34

Interquartile range = third quartile - first quartile

34 - 11 = 23

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

Median = 25

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The correct answers to the sample space illustrated will be:

S = {I, L, L, M, P, T, U, Y}.

S = {g, r, b, y, o}.

S = {W, X, Y, Z}.

Flipping a fair, two-sided coin.

Sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.

S = {Joy, Bob, Ben, Peter, John}

A paper bag has five colored marbles. The marbles are red, green, blue, yellow, and orange. The sample space when choosing one marble will be S = {g, r, b, y, o}.

A four-part spinner is spun once and the spinner with four parts labeled W, X, Y, and Z. The sample space for the experiment is S = {W, X, Y, Z}.

The event will have a sample space of S = {h, t} is the flipping a fair, two-sided coin.

The correct sample space for the gumballs in her bag will be sample space = lemon-lime, lemon-lime, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape.

My experiment with 5 or more possible outcomes will be that a teacher wants to randomly give one of his give students a pack of chocolate.

The sample space for the experiment will be based on their names. This will be S = (Joy, Bob, Ben, Peter, John).

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a) 1. The backpack weight sample mean is 6.375 pounds.

a) 2. The backpack weight sample mean is 6.375 pounds.

a) 3. The backpack weight sample mean is 6.625 pounds.

b) The range of the sample means is between 6.375 and 6.625, which approaches 0.250 pounds, plus or minus.

c) Since the students are using the sample means to estimate the mean backpack weight of their schoolmates, the true statements are A. and D.

The farther the range of the sample means is from O, the less confident they can be in their estimate.

A sample mean is a statistic computed from a sample of data or variables.

The sample mean represents the average value of the sample data.

The range describes the difference between the largest number and the smallest number.

Thus, based on the range of the sample means, the farther it is from 0, the less confident the students can be in their estimate.

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Answer:

8 pi yd.

Step-by-step explanation:

The circumference of a circle can be calculated as follows:

c = [tex]2 \cdot \pi \cdot r[/tex]

Where r is the radius of the circumference.

So in our case:

c = [tex]2 \cdot \pi \cdot 4yd = 8\cdot \pi[/tex] yd.

The circumference of the circle, in the attached image is approximately 25.1 yards.

To find the circumference of a circle, you can use the formula:

Circumference = 2 * π * radius

where π = 3.14159.

Given the radius of the circle is 4 yards, the circumference can be calculated as follows:

Circumference = 2 * 3.14159 * 4 yards ≈ 25.13272 yards

Now, rounding to the nearest tenth, the circumference of the circle is approximately 25.1 yards.

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Answer:

When dividing both sides by a negative.

Step-by-step explanation:

When dividing OR multiplying both sides by a negative, we need to flip the inequality signs.

The system of linear equations has at least one solution is consistent , whereas a system of linear equations that has no solution is inconsistent

What is a system of linear equations?

A collection of one or more linear equations involving the same variables is known as a system of linear equations (or linear system) in mathematics.

The subject of linear algebra, which is employed in most areas of contemporary mathematics, is based on the theory of linear systems. Numerical linear algebra includes computational strategies for obtaining the solutions, which are crucial to the fields of engineering, physics, chemistry, computer science, and economics. A helpful strategy when creating a mathematical model or computer simulation of a relatively complex system is to approximate a system of non-linear equations by a linear system (see linearization).

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Answer:

x = 1; y = a

Step-by-step explanation:

ax+y=2a

x+ay=1+a^2

-a²x-ay=-2a²

x+ay=1+a^2

(1 - a²)x = 1 - a²

x = (1 - a²)/(1 - a²)

x = 1

a + y = 2a

1 + ay = 1 + a²

a = y

x = 1; y = a

Answer:

Step-by-step explanation:

6*[4-(42-63)]=

6*[4-(-21)]=

6*[4+21]=

6*25=150.

6*[4-9÷3]=

6*[4-27]=

6*(-23)=-138.

6*[4-3]=

6*1=6.

Answer:

3

Step-by-step explanation:

f(x)-g(x)=3-cos(x)

when u limit it

u have

3-cos180

which is 3-0

3

Answer:

Step-by-step explanation:

Midpoint a point equidistant from the ends of a line or the extremities of a figure.

To find the midpoint of the line segment with endpoint, use the midpoint formula.

Midpoint formula:

[tex]\Rightarrow: \sf{\dfrac{x_2+x_1}{2}, \dfrac{y_2+y_1}{2} }}}[/tex]

y2=(-10)

y1=16

x2=6

x1=(-4)

Rewrite the problem down.

[tex]\sf{\left(\dfrac{6-4}{2},\:\dfrac{-10+16}{2}\right)}[/tex]

Solve.

6-4=2

2/2=1

-10+16=6

6/2=3

= (1,3)

Therefore, the correct answer is B (1,3).

I hope this helps, let me know if you have any questions.

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Answer: [tex]\Large\boxed{15~dimes~;~9~nickels}[/tex]

Step-by-step explanation:

Given information

Number of coins = 24 coins

Total amount = $1.95

Dime = 10 cents = $0.1

Nickel = 5 cents = $0.05

Set variables

Let d be the number of dimes

Let n be the number of nickels

Set a system of equation

1) d + n = 24

2) 0.1d + 0.05n = 1.95

Multiply 10 on both sides of 2) equation

0.1d · 10 + 0.05n · 10 = 1.95 · 10

d + 0.5n = 19.5

Current system

1) d + n = 24

2) d + 0.5n = 19.5

Subtract 2) equation from the 1) equation

(d + n) - (d + 0.5n) = (24) - (19.5)

Expand the parenthesis

d + n - d - 0.5n = 24 - 19.5

Combine like terms

d - d + n - 0.5n = 4.5

0.5n = 4.5

Divide 0.5 on both sides

0.5n / 0.5 = 4.5 / 0.5

[tex]\Large\boxed{n=9}[/tex]

Substitute the n value into one of the equations to find the d value

d + n = 24

d + (9) = 24

d = 24 - 9

[tex]\Large\boxed{d=15}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

90 degrees

Step-by-step explanation:

Same side interior angles, or consecutive angles, are supplementary (angle measures add up to 180 degrees). Since both angles have measures 3x degrees, the angles are congruent (same angle measure). In Geometry, when two angles are congruent and supplementary, the two angles are right angles (angles measuring 90 degrees). Therefore the angle measures of the two angles are 90 degrees and 90 degrees.

Or, to solve this algebraically, add 3x and 3x, let it equal to 180 degrees, solve for x, and find the angle measures by substituting x into the expression.

3x + 3x = 180

6x = 180

x = 30

3x = 3*30 = 90

The angle that vector makes with the x-axis is closest to [tex]340^\circ[/tex].

What is a vector?

An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.

If the magnitude and direction of two vectors match, they are the same vector. This indicates that if we take a vector and move it to a different point (without rotating it), the vector we finish up with is the same vector we started with.

Given,

[tex]x[/tex]-component of vector = 5.3

[tex]y[/tex]-component of vector = -2.3

angle = [tex]tan^{-1}(\frac{y}{x})[/tex]

angle = [tex]tan^{-1}(\frac{-2.3}{5.3} )[/tex]

angle = [tex]340^\circ[/tex]

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