a certain composer wrote 10 symphonies, 4 piano concertos (music for piano and orchestra), and 35 piano sonatas (music for solo piano). a. how many ways are there to play first a symphony and and then a piano concerto? b. the manager of a radio station decides that on each successive evening (7 days a week), a symphony will be played followed by a piano concerto followed by a piano sonata. for how many nights could this be carried out before exactly the same program would have to be repeated? about how many years would this be? (round to the nearest year).

Answer:

\(5. \: \: 8 + 5(7) = 8 + 35 = 43\)

I hope I helped you^_^

The numerical value "62" is a statistic because it is based on the sample of passengers aboard the Hindenburg airship.

In the given scenario, the numerical value is "62." We are told that there were 97 passengers aboard the Hindenburg airship and that 62 of them survived its explosion.

Since the numerical value is based on the sample (i.e., the passengers aboard the Hindenburg airship), it is a statistic. It describes the proportion of passengers who survived the explosion in the sample.

If we wanted to know the proportion of passengers who survived the explosion in the entire population (i.e., all passengers who have ever traveled on the Hindenburg airship), we would need to determine the parameter.

However, since we do not have data on the entire population, we cannot determine the parameter.

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Option b accurately interprets the slope coefficient in the context of the regression equation provided. b. As x increases by 1 unit, y is predicted to decrease by 17 units.

In the given sample regression equation, the slope coefficient (-17) represents the rate of change in the predicted value of y (y-hat) for each one-unit increase in x. Since the coefficient is negative, it indicates a negative relationship between x and y.

Specifically, for every one-unit increase in x, the predicted value of y is expected to decrease by 17 units. Therefore, option b accurately interprets the slope coefficient in the context of the regression equation provided.

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Answer:

0.03703704

Step-by-step explanation:

https://www.hackmath.net/en/calculator/fraction?input=3+1%2F4+%2B+2+1%2F3

The ordered pairs which are solutions to the system of inequalities given is (10, 2).

Given system of inequalities,

x + 2y ≥ 10

3x - 4y > 12

We have to find the solutions for the system of equations.

Let the equations be,

x + 2y = 10 [equation 1]

3x - 4y = 12 [equation 2]

From [equation 1],

x = 10 - 2y

Substituting in  [equation 2],

3(10 - 2y) - 4y = 12

30 - 6y - 4y = 12

-10y = -18

y = 9/5 = 1.8

x = 10 - 2y = 6.4

The system of equations hold true for (6.4, 1.8).

For (16, 9),

16 + (2 × 9) = 34 ≥ 10 is true.

(3 × 16) - (4 × 9) = 12 not greater than 12.

So this is not true.

For (10, 2),

10 + (2 × 2) = 14 ≥ 10 is true.

(3 × 10) - (4 × 2) = 22 > 12 is true.

Hence the correct ordered pair is (10, 2).

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Answer:

Step-by-step explanation:

The results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

Performing the calculation:

(10.52)(0.6721) = 7.0671992

Rounding to the correct number of significant figures, we have:

(10.52)(0.6721) ≈ 7.07

Next, let's calculate (19.09 - 15.347):

(19.09 - 15.347) = 3.743

Rounding to the correct number of significant figures, we have:

(19.09 - 15.347) ≈ 3.74

Therefore, the results of the calculations are approximately 7.07 and 3.74, respectively, to the correct number of significant figures.

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Step-by-step explanation:

x+(3x+10)=90

4x+10=90

4x=80

x=20 Ans

Answer:

x > -2

Step-by-step explanation:

Answer:

they need to save $630 in order to have enough for the trip

270 + 630 = $900

9514 1404 393

Answer:

  p = (q+4)/3

Step-by-step explanation:

Solve for p.

  \(q-2p=p+4\\\\q=3p+4 \qquad\text{add $2p$}\\\\q-4=3p\qquad\text{subtract 4}\\\\ \dfrac{q+4}{3}=p\qquad\text{divide by 3}\\\\ \boxed{p=\dfrac{q+4}{3}}\)

Step-by-step explanation:

\(8x - 7y = 23\)

\(7y = 8x - 23\)

\(y = \frac{8x}{7} - \frac{23}{7} \)

The maximum height reached by the ball projected upward with an initial velocity of 64 feet per second is 64 feet.

To find the maximum height reached by the ball, we need to determine the vertex of the quadratic function representing the height of the ball as a function of time.

The given equation for the height of the ball is s = -16t^2 + 64t, where s represents the height in feet and t represents time in seconds.

The vertex of a quadratic function in the form of f(t) = at^2 + bt + c is given by the coordinates (t_v, f(t_v)), where t_v is the x-coordinate of the vertex and f(t_v) is the y-coordinate of the vertex. The formula for the x-coordinate of the vertex, t_v, is given by t_v = -b / (2a).

In our case, a = -16 and b = 64. Plugging these values into the formula, we can calculate the x-coordinate of the vertex:

t_v = -b / (2a) = -64 / (2*(-16)) = -64 / (-32) = 2.

So, the x-coordinate of the vertex is 2 seconds. To find the y-coordinate (height) of the vertex, we substitute t = 2 into the equation:

s = -16(2)^2 + 64(2) = -64 + 128 = 64.

Therefore, the maximum height reached by the ball is 64 feet.

It's important to note that in this context, we assume that the upward direction is positive, and the height is measured relative to the ground level. The ball reaches its maximum height when its vertical velocity becomes zero, which occurs at the vertex of the quadratic function representing the height-time relationship.

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Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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To tile the bathroom, it would cost the amount of $20. To carpet the bedroom and living room, it would cost $72.

To calculate the cost of tiling the bathroom, we need to multiply the number of squares in the bathroom (4 x 2 = 8) by the cost per square foot ($5). 8 x $5 = $40. To calculate the cost of carpeting the bedroom and living room, we need to multiply the number of squares in the bedroom (5 x 4 = 20) and the living room (7 x 4 = 28) and add them together (20 + 28 = 48). Then multiply the total number of squares (48) by the cost per square yard ($18). 48 x $18 = $864.

To calculate the cost of tiling the bathroom, we need to multiply the number of squares in the bathroom (4 x 2 = 8) by the cost per square foot ($5). 8 x $5 = $40. This is the total cost of amount of tiling the bathroom. To calculate the cost of carpeting the bedroom and living room, we need to multiply the number of squares in the bedroom (5 x 4 = 20) and the living room (7 x 4 = 28) and add them together (20 + 28 = 48). Since each square in the blueprint has a side length of 1/4 inch, we need to convert this measurement to square feet (1/4 inch = 0.00694 square feet) and then multiply 48 x 0.00694 = 0.33456 square yards. Finally, multiply the total number of square yards (0.33456) by the cost per square yard ($18). 0.33456 x $18 = $72. This is the total cost of carpeting the bedroom and living room.

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9514 1404 393

Answer:

  2.05 pounds

Step-by-step explanation:

The total amount of dough Yahir is using is ...

  3.4 lbs + 4.8 lbs = 8.2 lbs

The amount used for each of 4 pizzas will be ...

  (8.2 lbs)/4 = 2.05 lbs . . . . for one pizza

Answer:

6\(x^{2}\) + 1

Step-by-step explanation:

\(\frac{6x^{3}+ 2x-x }{x}\)   combine 2x -x = x

\(\frac{6x^{3} + x}{x}\)

\(\frac{x(6x^{2} + 1) }{x}\)  the x's cancel out

6\(x^{2}\) + 1

Given:

Initial population = 100 algae

Growth rate = 30% per day.

Time = 5 days

To find:

The future amount of population.

Solution:

The exponential growth model is

\(y=a(1+r)^t\)

where, a is the initial value, r is the rate of interest in percent and t is time period.

Substituting the given values, we get

\(y=100(1+\dfrac{30}{100})^5\)

\(y=100(1+0.30)^5\)

Now, solve this.

\(y=100(1.30)^5\)

\(y=100(3.71293)\)

\(y=371.293\)

Therefore, the future value is 371.293 algae.

Answer:

Future amount rounded = 371

Step-by-step explanation:

I = Initial population = 100 algae

R = Growth rate = 30% per day.

T = Time = 5 days

\(Future Amount = I(1+r)^{t\\\)

\(Future Amount = 100(1+0.30)^{5}\)

\(Future Amount = 100(1.30)^{5}\)

Future Amount = 371.293 = 371

Answer:

x = 30

m<Y = 60

m<Z = 60

m<X = 60

Step-by-step explanation:

All of this should add up to 180 so...

2x + 2x + 3x - 30 = 180 (collect like terms)

7x - 30 = 180 (add 30 on both sides)

7x = 210 (divide by 7 on both sides)

x = 30

PLUG IN

2(30) = 60

3(30) - 30

90 - 30 = 60

m<Y = 60

m<Z = 60

m<X = 60

equilateral triangle

Hope this helps ya! Keep smiling!

Answer:

[See Below]

Step-by-step explanation:

____________________

✦ Solve:

____________________

So your answer would be:

____________________

~Hope this helps Mate. If you need anything feel free to message me.

\(-Your~ Friendly~ Answerer,~Shane\) ☺

Answer:

  3. 79.9 mm²

  4. 6.4 in

  5. 177.5 mi²

  6. 60.3°

Step-by-step explanation:

Given various quadrilaterals and their dimensions, you want to find missing dimensions.

In all cases, one or more area formulas and trig relations are involved. The trig relations are summarized by the mnemonic SOH CAH TOA. The relevant relation for these problems is ...

  Tan = Opposite/Adjacent

It is also useful to know that 1/tan(x) = tan(90°-x).

The formula for the area of a trapezoid is ...

  A = 1/2(b1 +b2)h

The relevant formula here for the area of a parallelogram is ...

  A = bs·sin(α) . . . . . where α is the angle between sides of length b and s

Using the area formula above, we find the area to be ...

  A = (21 mm)(9 mm)·sin(155°) ≈ 79.9 mm²

The area is about 79.9 square mm.

The given figure shows two unknowns. We can write equations for these using the area formula and using a trig relation.

If we draw a vertical line through the vertex of the marked angle, the base of the triangle to the right of it is (b2-4). The acute angle at the top of that right triangle is (121°-90°) = 31°. The tangent relation tells us ...

  tan(31°) = (b2 -4)/h   ⇒   h = (b2 -4)/tan(31°)

Using the area formula we have ...

  A = 1/2(b2 +4)h

and substituting for A and h, we get ...

  20.8 = 1/2(b2 +4)(b2 -4)/tan(31°)

  2·tan(31°)·20.8 = (b2 +4)(b2 -4) = (b2)² -16 . . . . . multiply by 2tan(31°)

  (b2)² = 2·tan(31°)·20.8 +16 . . . . . . . add 16

  b2 = √(2·tan(31°)·20.8 +16) ≈ 6.4 . . . . . . take the square root

Base 2 of the trapezoid is about 6.4 inches.

To find the area, we need to know the height of the trapezoid. To find the height we can solve a triangle problem.

If we draw a diagonal line parallel to the right side through the left end of the top base, we divide the figure into a triangle on the left and a parallelogram on the right. The triangle has a base width of 10 mi, and base angles of 60° and 75°.

Drawing a vertical line through the top vertex of this triangle divides it into two right triangles of height h. The top angle is divided into two angles, one being 90°-60° = 30°, and the other being 90°-75° = 15°. The bases of these right triangles are now ...

and their sum is 10 mi.

The height h can now be found to be ...

  h·tan(30°) +h·tan(15°) = 10

  h = 10/(tan(30°) +tan(15°))

Back to our formula for the area of the trapezoid, we find it to be ...

  A = 1/2(b1 +b2)h = 1/2(20 +10)(10/(tan(30°) +tan(15°)) ≈ 177.5

The area of the trapezoid is about 177.5 square miles.

The final formula we used for problem 5 can be used for problem 6 by changing the dimensions appropriately.

  A = 1/2(b1 +b2)(b1 -b2)/(tan(90-x) +tan(90-x))

  112 = 1/2(20+12)(20-12)/(2·tan(90-x)) = (20² -12²)·tan(x)/4

  tan(x) = 4·112/(20² -12²)

  x = arctan(4·112/(20² -12²)) = arctan(7/4) ≈ 60.3°

Angle x° in the trapezoid is about 60.3°.

__

Additional comment

There is no set "step by step" for solving problems like these. In general, you work from what you know toward what you don't know. You make use of area and trig relations as required to create equations you can solve for the missing values. There are generally a number of ways you can go at these.

A nice scientific calculator has been used in the attachment for showing the calculations. A graphing calculator can be useful for solving any system of equations you might write.

The second attachment shows a graphing calculator solution to problem 5, where we let y = area, and x = the portion of the bottom base that is to the left of the top base. Area/15 represents the height of the trapezoid. This solution also gives an area of 177.5 square miles.

Answer: x can equal 9 or -1

Step-by-step explanation:

Answer:

3(6 - 4) + 7²

3 x 2 + 7²

3 x 2 + 49

6 + 49

= 55

Answer:

Here's the exponential equation to model the card's value:

y = 98.70 * 2^x

where x is the number of years after Mr. Olsen purchased the card.

To find the value of the card after 5 years:

x = 5

y = 98.70 * 2^5 = 98.70 * 32 = $3162.40

So, Mr. Olsen can expect the card's value to be $3162.40 5 years after he purchased it.

Step-by-step explanation:

Answer:

Step-by-step explanation:

m

Answer:

Has one to one correspondence

Monique needs 30 fluid ounces of orange juice to keep the ratio same.

Ratio is the quantity of certain type of amount out of the total amount of all types is quantities.

According to the given question
The fruit punch is made up of 32 fluid ounces of pineapple juice and 48 fluid ounces of orange juice.

∴ The total Mixed juice is

(32 + 48) = 80 fluid ounces of mixed juice.

The ratio of pineapple juice juice to the orange juice is

32:48

= 2x:3x

Now Monique has 20 fluid ounces of pineapple juice

∴2x = 20

    x = 10

So, to keep the ratio of pineapple juice to the orange juice same she needs 3x or 30 fluid ounces of orange juice.

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Answer:

The matrix that represents the number of each type of house available in Tampa is D) Matrix with 1 row and 3 columns consisting of elements 24, 12, and 18. This matrix shows that there are 24 1-bedroom houses, 12 2-bedroom houses, and 18 3-bedroom houses available in Tampa.

We can see here that the solutions to the triangles are:

1. 62.2°.

2. 35.9°

3. 61.9°

4. 53.1°

We can see here that using trigonometric ratio formula, we find the values of x.

We see the following:

1. Cos x = 7/15 = 0.4666

x = \(cos^{-1}\) 0.4666 = 62.2°.

2. Sin x = 27/46 = 0.5869

x° = \(sin^{-1}\)  0.5869  = 35.9°

3. Sin x = 30/34 = 0.8823

x° = \(sin^{-1}\) 0.8823 = 61.9°

4. Tan x = 8/6 = 1.3333

x° = 1.3333 = 53.1°

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