a youth chorus has 30 members. there are 14 boys in the chorus. what is the ratio of boys to girls in simplest form? 715 7 over 15 87 8 over 7 815 8 over 15 78

Answer:

y

2

​

=−

2

z

​

+7

Steps for Solving Linear Equation

z=18−2×2−2y2

Multiply 2 and 2 to get 4.

z=18−4−2y

2

​

Subtract 4 from 18 to get 14.

z=14−2y

2

​

Swap sides so that all variable terms are on the left hand side.

14−2y

2

​

=z

Subtract 14 from both sides.

−2y

2

​

=z−14

Divide both sides by −2.

−2

−2y

2

​

​

=

−2

z−14

​

Dividing by −2 undoes the multiplication by −2.

y

2

​

=

−2

z−14

​

Divide z−14 by −2.

y

2

​

=−

2

z

​

+7

Step-by-step explanation:

the given equation defines a paraboloid that lies below the plane z=0. Specifically, it is situated above the xy-plane, which means that the z-values of all points on the surface are greater than or equal to zero.

we can break down the equation z=18-2x^2-2y^2. This equation represents a paraboloid with its vertex at (0,0,18) and axis of symmetry along the z-axis. The first term 18 is the z-coordinate of the vertex and the last two terms -2x^2 and -2y^2 determine the shape of the paraboloid.

Since the coefficient of x^2 and y^2 terms are negative, the paraboloid is downward facing and opens along the negative z-axis. Therefore, all points on the paraboloid have z-values less than 18. Additionally, since the paraboloid is situated above the xy-plane, its z-values are greater than or equal to zero.

the paraboloid defined by the equation z=18-2x^2-2y^2 is situated below the plane z=0 and above the xy-plane. Its vertex is at (0,0,18) and it opens along the negative z-axis.

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Answer:

option C

Step-by-step explanation:

2, 4, 6

i don't know whether it is correct or not...

The value of x in function cos(3pi/2+2x/3)=1/2 is  x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.

Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.

In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).

The slant side is called hypotenuse.

From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.

From that angle (suppose its measure is θ),

\(\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}\\\cos(\theta) = \dfrac{\text{Length of Base }}{\text{Length of Hypotenuse}}\\\\\tan(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of base}}\\\\\cot(\theta) = \dfrac{\text{Length of base}}{\text{Length of perpendicular}}\\\\\sec(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of base}}\\\\\csc(\theta) = \dfrac{\text{Length of Hypotenuse}}{\text{Length of perpendicular}}\\\)

We are given;

6sinx=5, 6cosx=7, sin2x=0, sin(x+pi/3)+1=0, cos(2x/3-pi/4)=\(\sqrt{2} /2\), cos2x-1=0, 2sin3x=-1, cos(3pi/2+2x/3)=1/2

Now,

1. 6sinx=5

sinx=5/6

x=0.98511078

2. sin2x=0

x=n*pi/2

3. sin(x+pi/3)+1=0

x-intercept= (pi/6+2n*pi)

y-intercept= (0, \(\sqrt{3}\)/2 -1)

4. cos(2x/3-pi/4)=\(\sqrt{2}/2\)

x= (pi/4+n*pi, pi+n*pi)

6. cos2x-1=0

x=n*pi

7. 2sin3x=-1

x= 7pi/18 + 2pi*n/3, 11pi/18+2pi*n/3

8. cos(3pi/2+2x/3)=1/2

x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n

For any value of integer n

Therefore, the answer of trigonometric function will be x= pi/4 + 3pi*n, 5pi*/4 + 3pi*n.

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Answer:

Step-by-step explanation:

x + 2) = 2(x + 2)2 - 6(x + 2)

           = 2(x2 + 4x + 4) - 6(x + 2)

           = 2x2 + 8x + 8 - 6x - 12

           = 2x2 + 2x - 4

If a significant result is yielded by a repeated-measures analysis of variance, post - hoc tests would be used to determine which levels of the independent variable significantly differ from each other.

What is the purpose of a post hoc test?

When an analysis of variance (ANOVA) F test indicates that there are significant differences between three or more group means, post hoc (Latin for "after this") tests are employed to identify the precise discrepancies.

When an experiment's findings show that the dependent variable has a substantial effect size You can infer it from this, right?

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Whenever a probability sample is drawn from a population, it is not enough to simply report the sample's descriptive statistics, for these measures contain a certain degree of error due to the sampling process.

Thus the answer is ‘ true’.

A population is any entire group that has at least one trait in common that is relevant to a given issue or experiment in statistics.

A probability sample is one that is drawn using a method of random selection that is compatible with the known odds for each member of the population to be selected, and that takes these probabilities into account when generating estimates from the sample.

If the chosen sample does not accurately reflect the total population of data, there has been a sampling error, which is a statistical error resulting from sampling.

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Answer:

See attached image for the table.

Step-by-step explanation:

The table shows all 4 possible truth values for statements p and q .

p  v  q  is true if one or both of the p, q are true.

Finally, an implication (if-then) is true in every case except when the first statement (hypothesis) is true and the second (conclusion) is false.

Step-by-step explanation:

solution file attached

Answer:

6

Step-by-step explanation:

She had 20 chocolate pieces and her friends ate 7/10 of them.

20 x 0.7 = 14

20 - 14 = 6 pieces left over

Hope this helps <3

1.) 3x

2.) area

3.) six

4.) 3/2

:)

Answer:

The height of the pyramid can be represented as

3x

The

area

of an equilateral triangle with length

The area of the hexagon base is

six

The volume of the pyramid is

3/2

Step-by-step explanation:

Answer:

6 units

Step-by-step explanation:

JK + KL = JL

3x + 5x-6 = 4x+2

8x-6 = 4x+2

subtract 4x from each side to get:

4x - 6 = 2

add 6 to each side to get:

4x = 8

x = 2

JK = 3x and x=2 so JK = (3)(2) or 6

The numerical length of JK = 6

What is Line Segment?

" A line segment is a line section that can link two points. "

We know that point K is divide line JL

Given that JL = 4x+2

                 KL = 5x-6

                JK = 3x

So,  Equation is JK+KL = JL

                           3x+5x-6 = 4x+2

                           8x-6 = 4x+2

                            8x-4x = 2+6

                            4x = 8

                              x = 8/4

                             x = 2

So , numerical length of JK = 3x

                                        JK = 3×2

                                         JK = 6

Hence , length of JK is 6

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At the end of the fifth day, a bricklayer has laid 324 bricks on the job.

Multiplication is a mathematical arithmetic operation.

It is also a process of adding the same types of expression to some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given, a bricklayer lays 4 bricks on the first day on the job.

On each day thereafter, he lays three times the number of bricks he laid on the previous day.

And he continued his pattern.

Let x be the number of bricks he laid in the previous day.

Then according to the question,

The number of bricks in total is = 3x

For the second day, x =4

Number of the bricks he laid on the second day = 12

Now the x =12 for the third day.

Number of the bricks he laid on the third day = 36

Now x = 36 for the fourth day.

Number of the bricks he laid on the fourth day = 108

Now the x = 108 for the fifth day.

Number of the bricks he laid on the fifth day = 324

Therefore, 324 bricks he has laid at the end of the fifth day.

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The parametric equations for the portion of the cone are: r(t) = t, θ(t) = t, z(t) = 2√2t where t is a parameter that ranges from 0 to √8.

To parametrize the portion of the cone z - √(8x^2 + 8y^2) with 0 ≤ z ≤ √8, we can use cylindrical coordinates. Let's denote the parameters as r, θ, and z.

We know that x = rcosθ, y = rsinθ, and z = z.

Substituting these values into the equation of the cone, we have:

z - √(8(rcosθ)^2 + 8(rsinθ)^2) = 0

Simplifying the expression inside the square root, we get:

z - √(8r^2(cos^2θ + sin^2θ)) = 0

z - √(8r^2) = 0

z - 2√2r = 0

From this equation, we can express z in terms of r as:

z = 2√2r

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The value of x in the parallelogram is 21.

To find the value of x in the parallelogram, we can equate the lengths of the opposite sides of the parallelogram. In this case, we have side AD equal to 36 and side BC equal to 2x - 6.

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

36 = 2x - 6

To solve for x, we can isolate it on one side of the equation. Adding 6 to both sides of the equation, we get:

36 + 6 = 2x

To simplify, we have:

42 = 2x

Finally, we can solve for x by dividing both sides of the equation by 2:

x = 42/2

Evaluating the expression on the right side, we find:

x = 21

Therefore, the value of x in the parallelogram is 21.

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Answer:

14

Step-by-step explanation:

Answer:

t + 4/10 >1

t + 4>1*10

t >10 - 4

t > 6

Answer:

Yes, at positive x coordinates

Step-by-step explanation:

Find the equation of g(x)

Given ordered pairs of g(x):  (-1, -22)  (0, -20)  (1, -18)

\(\sf let\:(x_1,y_1)=(0,-20)\)

\(\sf let\:(x_2,y_2)=(1,-18)\)

\(\sf slope\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-18-(-20)}{1-0}=2\)

Point-slope form of linear function: \(\sf y-y_1=m(x-x_1)\)

\(\implies \sf y-(-20)=2(x-0)\)

\(\implies \sf y=2x-20\)

Substitute the equation of g(x) into the equation of the circle and solve for x

Given equation:  \(y^2+x^2=100\)

\(\implies (2x-20)^2+x^2=100\)

\(\implies 4x^2-80x+400+x^2=100\)

\(\implies 5x^2-80x+300=0\)

\(\implies x^2-16x+60=0\)

\(\implies x^2-10x-6x+60=0\)

\(\implies x(x-10)-6(x-10)=0\)

\(\implies (x-6)(x-10)=0\)

Therefore:

\((x-6)=0 \implies x=6\)

\((x-10)=0 \implies x=10\)

So the linear function g(x) will intersect the equation of the circle at positive x coordinates.

a. The length of the hypotenuse is √5

b.  If it has one leg of length 1 and a hypotenuse of length 3,  the length of the other leg is √8

a. To find the length of the hypotenuse in a right triangle with legs of length 1 and 2, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

In this case, the legs have lengths 1 and 2, so we have:

Hypotenuse² = Leg1²+ Leg2²

Hypotenuse² = 1² + 2²

Hypotenuse² = 1 + 4

Hypotenuse² = 5

Taking the square root of both sides, we find:

Hypotenuse = √(5)

Therefore, the length of the hypotenuse in this right triangle is √(5).

For the second part of the question, if a right triangle has one leg of length 1 and a hypotenuse of length 3, we can again use the Pythagorean theorem to find the length of the other leg.

Let's assume the length of the other leg is x. We have:

Hypotenuse² = Leg1² + Leg2²

3² = 1² + x²

9 = 1 + x²

x² = 9 - 1

x² = 8

Taking the square root of both sides, we find:

x = √(8)

Therefore, the length of the other leg in this right triangle is √(8).

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Answer:

1. C 2.B .  

Step-by-step explanation:

answer : 1. A+ 5/4 +19/4 ,,,,, 2. 14/4 = 7/2

Hope it helps :)

Answer:

What is the equation that models this scenario?

✔ A + 5/4 = 19/4

and

How many pounds of apples did Angelica buy?

✔ 14/4 = 7/2

Step-by-step explanation:

Hope this helps!! :)

The other number is 4.35 ( rounded to tenth place)

The Geometric Mean (GM) is the average value or mean that, by taking the product of a set of numbers' values as its root, indicates the set's central tendency.

For example: for a given set of two numbers such as 8 and 1, the geometric mean is equal to √(8×1) = √8 = 2√2.

Given:

The geometric mean of 23 and other value is 10.

Let the other number be x.

Use the geometric mean property,

GM = √ab

Put the value of GM and a

So, 10 = √23x

x=100/23

x=4.347

The geometric mean of 23 and 4.35 is 10.

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In total 180 chairs are ordered for the cost $6000.

The total cost of chairs=$6,000.

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Let x be the chairs ordered each at $20 and y be the chairs ordered each at $40.

Then equation will be 20x+40y=6000-------(1)

Given that, twice as many $20 chairs as $40 chairs were ordered.

That is 2x=y⇒2x-y=0--------(2)

Multiply equation (2) by 40.

That is 80x-40y=0--------(3)

By adding equation (2) and (3) we get

20x+40y+80x-40y=6000

⇒100x=6000

⇒x=60

Substitute x=60 in equation (2)

That is, 2x=y

⇒y=120

Total number of chairs=x+y=60+120=180 chairs.

Hence, in total 180 chairs are ordered for the cost $6000.

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Answer: 4 points

Step-by-step explanation:

The minimum number of points needed to define two distinct planes is 4 points. Two distinct planes can be defined by 4 points under the conditions that the two distinct planes intersect at a line, and two points exist on that line that are shared between the planes.

Answer:

One line of intersection (three points of intersection)

Step-by-step explanation:

When two planes intersect, they don't form points of intersection, but they form a line of intersection.

From equation of a line,

\({ \tt{ax + by + cz = 0}}\)

x, y, z are points of intersection

Answer:

17cm is the answer

Step-by-step explanation:

27×2 = 54

88 - 54 = 34

34 ÷ 2 = 17

Answer:

no

Step-by-step explanation:

By the Side-Angle-Side Similarity Theorem (SASS), if two sides of a triangle are in proportion with the corresponding sides of another triangle, and the included angles are congruent, then the triangles are similar.

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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Answer:

8m

Hope this answers the question. Have a nice day.

The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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The number of ways a club with n members can select a President and a Vice President, where the two positions must be held by different people, is given by option C) n² - n.

To determine the number of ways the choice can be made, we need to consider the following:

1. Selection of the President: Since the club has n members, there are n options to choose from for the President position.

2. Selection of the Vice President: After selecting the President, we need to choose a different person for the Vice President position. Since we have already selected one person for the President position, there are (n - 1) options left to choose from for the Vice President.

To calculate the total number of ways, we multiply the number of options for each position. Therefore, the total number of ways is n * (n - 1) = n² - n.

Option C) n² - n accurately represents the number of ways the club can select a President and Vice President, ensuring that the two positions are held by different people.

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The options reasonable to his needs is 15 carbon black freshwater fish hooks and 3 vivd color spinnerbaits. they cost a combined 15 dollars, which Josh has.

or 9 carbon black freshwater fish hooks and 2 vivid color spinnerbaits. they cost a combined 9.55 dollars, which Josh has.

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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