In triangle ABC, angle B is a right angle. Give me measures of side BC and hypotenuse AC so that the measure of Angle A is greater than 75 degrees

Answer:

x = 14°

t = 12.367 ~ 12.4

r = 2.999 ~ 3

Step-by-step explanation:

1st we can find x by sum theory which is the sum of all side equal to 180° .

x + 90° + 76° = 180 °

x + 166° = 180°

x= 180° - 166°

x = 14° ... So the unknown angle is 14°

and we also can solve hypotenus t and adjecent r by using sin amd cos respectively by angle 76° .

sin(76) = 12/t

sin(76) t = 12 ....... criss cross it

t = 12 / sin(76) ....... divided both side by sin(76)

t = 12.367 ~ 12.4 ....... result

And

cos(76) = r / 12.4

r = cos(76) × 12.4 .......criss cross

r = 2.999 ~ 3 ....... amswer and i approximate it

Rectangle: w = 5.5cm, l = 11cm. Shortest side is width.

The photo takes up 30% of the framed area.

To calculate the percentage of the frame that is taken up by the photo, we first need to calculate the dimensions of the framed photo. If the photo measures 4 inches by 6 inches, the dimensions of the framed photo will be 8 inches by 10 inches (adding 2 inches to each side).

To calculate the area of the frame, we need to subtract the area of the photo from the area of the framed photo. The area of the photo is 4 inches x 6 inches = 24 square inches. The area of the framed photo is 8 inches x 10 inches = 80 square inches. So, the area of the frame is 80 square inches - 24 square inches = 56 square inches.

To calculate the percentage of the frame that is taken up by the photo, we divide the area of the photo by the area of the framed photo and multiply by 100.

24 square inches / 80 square inches x 100 = 30%

Therefore, the photo takes up 30% of the framed area.

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The measure of the other side of the right triangle is given as follows:

12 cm.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the other side has the length given as follows:

5² + x² = 13²

25 + x² = 169

x² = 144

x = 12.

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6.2 × 10⁴ in decimal notation is simply 62,000.

In scientific notation, a number is expressed as the product of a decimal number between 1 and 10 and a power of 10.

Now, let's talk about converting a number in scientific notation to decimal notation. Decimal notation simply means expressing a number in the standard way, using digits and a decimal point. To convert a number in scientific notation to decimal notation, we just need to evaluate the product of the decimal number and the power of 10.

In the case of 6.2 × 10⁴, the decimal number is 6.2, and the power of 10 is 4. To evaluate the product, we simply move the decimal point in 6.2 four places to the right, since the power of 10 is positive. This gives us:

6.2 × 10⁴ = 62,000

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Complete Question:

Convert to decimal notation: 6.2 × 10⁴

Using a table is similar to using a double number line because the relation between the corresponding would never change.

Given that,

To explain how using a table is similar to using a double number line and how it is different.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,

Let assuming some values, in tabulated form,

x     y

1     -1

2    -2

3    -3

Now calibrating the x and y in the number line

x =  1   2   3

     ----------

y = -1   -2  -3

     -----------

When comparing the corresponding relationship it remains the same, where it is a table or number line.

Thus, using a table is similar to using a double number line because the relation between the corresponding would never change.

The average rate of change of DVD sales is 723.1 billion dollars.

The average rate of change of an equation can be determine by using the formula below:

average rate of change = (f(x₂)- f(x₁)) / [x₂- x₁]

From the given information of the DVD sales:

f(x) = -158.8x² + 2469.9x + 3010.5

x₁ = 2001 - 1999 = 2

x₂ = 2008 - 1999 = 9

average rate of change =  ([-158.8(9)² + 2469.9(9) + 3010.5] - [-158.8(2)² + 2469.9(2) + 3010.5]) / (9-2)

                                      = (12376.8 - 7315.1)/(7)

                                      = 723.1 billion dollars

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Complete Question

Check image attached

The Fourier series Using the complex form of f(x) is

f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25

where k is an integer.

To find the Fourier series of the function f(x) over the interval [-1, 1], we first note that f(x) is periodic with period T = 0.5. We can then write f(x) as a Fourier series of the form

f(x) = a0/2 + ∑[n=1, ∞] (ancos(nπx) + bnsin(nπx))

where

a0 = (1/T) ∫[0,T] f(x) dx

an = (2/T) ∫[0,T] f(x)*cos(nπx) dx

bn = (2/T) ∫[0,T] f(x)*sin(nπx) dx

Since f(x) = 0 for x < -0.25 and x > 0.25, we only need to consider the interval [-0.25, 0.25]. We can break this interval into subintervals of length 0.5 centered at integer values k

[-0.25, 0.25] = [-0.25, 0.25] ∩ [1.5, 2.5] ∪ [-0.25, 0.25] ∩ [0.5, 1.5] ∪ ... ∪ [-0.25, 0.25] ∩ [-1.5, -0.5]

For each subinterval, the Fourier coefficients can be calculated as follows

a0 = (1/0.5) ∫[-0.25, 0.25] f(x) dx = 1/2

an = (2/0.5) ∫[-0.25, 0.25] f(x)*cos(nπx) dx = 0

bn = (2/0.5) ∫[-0.25, 0.25] f(x)sin(nπx) dx = 2(-1)^k/(nπ)

Therefore, the Fourier series of f(x) is

f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25

where k is an integer.

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The measure of the smaller acute angle of the triangle to the nearest tenth of a degree is 28.3 degrees.

Let's denote the smaller acute angle of the triangle as θ. We can use the tangent function to find the measure of this angle:

tan(θ) = opposite/adjacent

In this case, the opposite side is the length of the short leg (17) and the adjacent side is the length of the long leg (32). So we have:

tan(θ) = 17/32

Using a calculator, we can take the inverse tangent (tan^-1) of both sides to solve for θ:

θ = tan^-1(17/32) ≈ 28.3 degrees

So the measure of the smaller acute angle of the triangle is approximately 28.3 degrees.

Here's a diagram to illustrate the triangle:

            / l

         /    l

  17 /       l opposite

    /         l

  /  θ       l

/_______l

    adjacent

      32

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Chelsey is correct that we use the same slope as the radius to write the equation of the tangent line, even though the slope of the radius is undefined at the points of tangency.

The perimeter will be 20 ✓2 units.

The area will be 50 units²

Chelsey is correct, and the reason is that a tangent line to a circle at a given point is always perpendicular to the radius of the circle at that point. This means that the slope of the tangent line and the slope of the radius at the point of tangency are negative reciprocals of each other.

Chelsey is correct that we use the same slope as the radius to write the equation of the tangent line.

The perimeter will be:

= 4 × BC

= 20 ✓2

The area will be:

= BC²

= (5✓2)²

= 50

It should be noted that BCDE is a square as EBC is 90°.

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The area of ΔRST, to the nearest square inch is,

Area = 29,17,735.54 square inches

We have,

In ΔRST, s = 990 inches, ∠S=8° and ∠T=60°.

Apply sine rule formula,

sin S / s = sin T / t

sin 8° / 990 = sin 60° / t

0.14 / 990 = 0.87 / t

0.14t = 990 x 0.87

0.14t = 861.3

t = 6,152 inches

Here, ∠R = 180° - (8 + 60)°

∠R = 180 - 68

∠R = 112°

sin S / s = sin R / r

sin 8° / 990 = sin 112° / r

0.14 / 990 = 0.92 / r

0.14r = 0.92 x 990

0.14r = 910.8

r = 910.8 / 0.14

r = 6505 inches

We use the formula

Heron's formula = √s(s - a)(s - b)(s - c)

Where s = a + b + c/2

Solving for s

s = 990 + 6505 + 6,152 /2

s = 6823.5

Solving for the area of the triangle

= √6823.5 × (6823.5 - 990) × (6823.5 - 6,152) × (6823.5 - 6505)

= √6823.5 x 5833.5 x 671.5 x 318.5

= 29,17,735.54 square inches

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The population density is 87.4, under the condition that a study report shows that in 2010 the population of the United States was counted to be  308,745,538 people and the land area is approximately 3,531,905 square miles.

Now to evaluate  the population density of the United States in 2010, here we have to use the principles of division
Population density = Population / Land area

Staging  the values from the study
Population density = 308,745,538 / 3,531,905
The evaluated Population density = 87.4 people per square mile

Then, the United State's population density in 2010 was  evaluated as 87.4 people per square mile.

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The complete question is
A study reports that in 2010 the population of the United States was 308,745,538 people and the land area was approximately 3,531,905 square miles. ​Based on the study, what was the population density, in people per square mile, of the United States in 2010? ​Round your answer to the nearest tenth. ​

The equation relates the sound level, in decibels (dB), of a noise with an intensity of I to the smallest sound intensity that can be heard by the human ear, which is approximately 1 x 10^-12 watts/meter2.

Using this equation and the given maximum intensity of a car horn (0.01 watts/meter2), we can find the maximum sound level in decibels:

Sound level = 10 log (0.01/1 x 10^-12)
Sound level = 10 log (1 x 10^10)
Sound level = 100 dB

Therefore, the value that is closest to the maximum sound level in decibels of a car horn is 100 dB.

Answer: So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.

Step-by-step explanation:

Unfortunately, I cannot see the scatter plot you are referring to. However, I can explain how to use a trend line to predict the number of pages in a book with 19 chapters.

A trend line is a line that represents the general direction or tendency of the data in a scatter plot. To use a trend line to predict the number of pages in a book with 19 chapters, you would first need to determine the equation of the trend line.

This equation usually takes the form y = mx + b, where y is the dependent variable (in this case, the total number of pages), x is the independent variable (in this case, the number of chapters), m is the slope of the line, and b is the y-intercept (the value of y when x is 0).

Once you have the equation of the trend line, you can plug in the value x = 19 and solve for y to get the predicted number of pages in a book with 19 chapters.

For example, if the equation of the trend line is y = 50x + 200, then the predicted number of pages for a book with 19 chapters would be:

y = 50(19) + 200

y = 950

So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.

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Answer:

Step-by-step explanation:

There are 12 possible cards you can choose.

There are 3 possible results for the spinner.

There are 2 possible results for the coin toss.

When doing all 3 events:

      Total possibilities [tex]=12\times 3 \times 2=72.[/tex]

SOLUTION:   72

The correct option regarding the data is B. Mean = 8.2, median = 9, mode = 9, midrange = 7; skewed to the left.

A histogram has score on the x-axis, and frequency on the y-axis. A score of 4 has a frequency of 1; 5, 1; 6, 2; 7, 3; 8, 5; 9, 7; 10, 6.

It shtbe noted that Mean = 8.2, median = 9, mode = 9, midrange = 7; skewed to the left.

This statement describes a distribution with a mean equal to the median and a mode that is likely less than the mean and the median. The fact that the distribution is skewed to the left indicates that the tail of the distribution is longer on the left side, and that there may be some low outliers that are pulling the mean towards the left.

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Answer:

C

Step-by-step explanation:

Since the rate is linear, we can subtract a larger amount of minutes by a smaller one and a larger cost by a smaller one.

For example:

20 - 15 = 5

3.40 - 3.05 = 0.35

Since you want to find the amount it takes per minute, you divide the 5 by 5 to make it one minute. You also divide the 0.35 by 5 in which you get 7.

Por lo tanto, el tercer carro que recibirá boletos de ambos colores ocupará la posición número 18 en la fila.

Hola, entiendo que quieres saber en qué posición de la fila se encontrará el tercer carro que recibirá boletos de ambos colores (verde y azul). Para esto, vamos a analizar la situación:

- La primera persona entrega un boleto verde cada 2 carros.
- La segunda persona entrega un boleto azul cada 3 carros.

Un carro que recibe boletos de ambos colores será aquel que ocupa una posición que es múltiplo común de 2 y 3. El mínimo común múltiplo (MCM) de 2 y 3 es 6. Por lo tanto, cada 6 carros, habrá uno que reciba boletos de ambos colores.

Para encontrar el tercer carro que recibirá boletos de ambos colores, simplemente multiplicamos el MCM (6) por la cantidad de carros que buscamos (3):

6 × 3 = 18

Por lo tanto, el tercer carro que recibirá boletos ición número 18 en la fila.

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Answer:

a= 2.9cm

Step-by-step explanation:

area =25 so 17a=50

50/17=2.941176...

The maximum profit will be realized by producing and selling 2.5 kilograms of whatchamacallits.

The maximum profit, in hundreds of dollars, will be $500.

To find the maximum profit, we need to first calculate the profit function P(x), which is the difference between the revenue and the cost functions:

P(x) = R(x) - C(x)
P(x) = 450x - (50x + 1000)
P(x) = 400x - 1000

To find the amount of kilograms that should be produced and sold to realize a maximum profit, we need to find the value of x that maximizes the profit function.

We can do this by taking the derivative of the profit function and setting it equal to zero:

P'(x) = 400
400 = 0

Since the derivative is a constant value, there is no critical point or inflection point. Therefore, the profit function is increasing at a constant rate, and the maximum profit will be achieved at the highest possible value of x.

To find that value, we can set the profit function equal to zero and solve for x:

P(x) = 400x - 1000 = 0
400x = 1000
x = 2.5

Therefore, the maximum profit will be realized by producing and selling 2.5 kilograms of whatchamacallits.

To find the maximum profit itself, we can substitute this value of x into the profit function:

P(2.5) = 400(2.5) - 1000 = 500

So the maximum profit, in hundreds of dollars, will be $500.

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The frog will travel a total distance of 1650 cm before she cannot jump anymore. None of the options given are correct.

To find the total distance the frog will travel, we need to add up the distances of all her jumps. Given that her first jump is her longest at 300 cm and her second jump is 270 cm, we can assume that each subsequent jump is shorter than the one before it.

The difference between the first jump and the second jump is 30 cm. So let's assume that the common difference between each jump is 30 cm. So the frog takes a total of 10 jumps before she cannot jump anymore.

The total distance the frog will travel is:

300 + 270 + (240 + 210 + 180 + 150 + 120 + 90 + 60 + 30) = 1650 cm

So here none of the options are correct.

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To find the measure of angle 1 when AB is tangent to circle P at point B, we must consider some properties of tangents and circles.

A tangent line to a circle is a line that touches the circle at exactly one point, known as the point of tangency. In this case, line AB is tangent to circle P at point B. A crucial property of tangents is that they are perpendicular to the radius of the circle at the point of tangency. Therefore, the radius PB of circle P is perpendicular to tangent AB at point B.

Now, let's examine angle 1. If angle 1 is the angle formed by the tangent AB and the radius PB at point B, then it is a right angle due to the aforementioned property. In this case, the measure of angle 1 is 90 degrees.

However, if angle 1 is not directly formed by the tangent and radius, more information is needed to determine its measure. For example, if angle 1 is an angle inside the circle, you would need to know the measure of other angles or lengths of chords within the circle to calculate it.

In summary, if angle 1 is formed by tangent AB and radius PB at point B, its measure is 90 degrees because tangents are perpendicular to the radius at the point of tangency. If angle 1 is not formed by the tangent and radius, additional information is required to determine its measure.

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The probability that a randomly selected house with 2 bathrooms has 3 is: 0.8.

So, the fourth option is correct.

We have given that,

The two-way table shows the number of houses on the market in the Castillos’ price range.

A 6-column table has 4 rows.

The first column has entries 1 bathroom, 2 bathrooms and 3 bathrooms, in total.

The second column is labeled 1 bedroom with entries 67, 0, 0, 67.

The third column is labeled 2 bedrooms with entries 21, 6, 18, 45.

We are only considering the houses that have 2 bathrooms.

There are a total of 30 of these houses.

Out of these 30, 24 have 3 bedrooms.  

What is the formula for probability?

The probability of an event can only be between 0 and 1 and can also be written as a percentage.

This makes the probability 24/30, which is 0.8.

Therefore, the probability that a randomly selected house with 2 bathrooms has 3 is: 0.8.

So, the fourth option is correct.

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Number of balls ≈ [tex]1.03 * 10^9[/tex]

To calculate how many table tennis balls can fit into the coin building, we need to first figure out the volume of the building and the volume of the table tennis ball.

Then, we can divide the volume of the building by the volume of the ball to get an estimate of the number of balls that can fit inside.

The volume of a table tennis ball can be calculated using the formula for the volume of a sphere, which is:

V = (4/3)πr³

where V is the volume, π is pi (approximately 3.14), and r is the radius of the ball. In this case, the radius is given as 0.04m, so we can plug that in and get:

V = (4/3) x 3.14 x 0.04³

[tex]V =2.14 * 10^{-5} m^3[/tex]

Next, we need to find the volume of the coin building. The building has a width of 20m and a height of 110m, but we don't know its depth.

Let's assume that the building is a rectangular prism with a depth of 10m. Then, we can calculate its volume using the formula:

V = l x w x h

where l is the length, w is the width, and h is the height. Plugging in the given values, we get:

V = 20 x 10 x 110

V = 22000 m³

Now, we can divide the volume of the building by the volume of the ball to get an estimate of how many balls can fit inside:

Number of balls ≈ [tex]V_building / V_ball[/tex]

Number of balls ≈ 22000 / 2.14 x [tex]10^-5[/tex]

Number of balls ≈ [tex]1.03 * 10^9[/tex]

So we can estimate that approximately 1.03 billion table tennis balls can fit into the coin building.

As for the accuracy of this prediction, it's important to keep in mind that we made some assumptions and estimations in our calculations.

For example, we assumed that the building is a rectangular prism with a depth of 10m, which may not be completely accurate.

Additionally, we rounded some of our values and used approximations for pi.

Therefore, our estimate should be considered as a rough approximation rather than an exact calculation. Nonetheless, it gives us an idea of the scale of the building and how many objects it can hold.

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Step-by-step explanation:

For this given problem we have the following statements and reasons:

1) SD is vertical to HT,

Reason: Given

2) SDH and SDT are right angles

Reason: Right angle congruence theorem

3) SH=≈ST

Reason: Given

4) BD=≈BD

Reason: Reflexive property

5) SHD=≈STD

Reason: SAS