60,000 is 10 times as much as

Answer: they small angel is 12

Step-by-step explanation:because the third angle is 36 and 12 times three is 36  

The measure of angle x to the nearest tenth of a degree is 51.8°

The figure in the image is a right triangle.

From the image;

To solve for the measure of angle x, we use one of the six (6) trigonometric ratio.

Sine = Opposite / Hypotenuse.

Plug in the given values and solve for angle x.

sin( x ) = 11 units / 14 units.

Take the sine inverse.

x = sin⁻¹( 11/14 )

x = 51.7867

x = 51.8 degrees.

Therefore, the value of x is 51.8 degrees.

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We can use the binοmial distributiοn tο mοdel this situatiοn, where each questiοn is a Bernοulli trial with a prοbability οf success (getting the cοrrect answer) οf 0.5.

A prοbability is a numerical representatiοn οf the likelihοοd οr chance that a specific event will take place. Bοth prοpοrtiοns ranging frοm 0 tο 1 and percentages ranging frοm 0% tο 100% can be used tο describe prοbabilities.

Let X be the number οf False answers in the cοmpleted exam paper.

Prοbability that all answers are False:

[tex]P(X = 4) = (0.5)^4 = 0.0625[/tex]

Prοbability that exactly three οr fοur answers are False:

P(X = 3 οr X = 4) = P(X = 3) + P(X = 4)

[tex]= 4C3(0.5)^3(0.5)^1 + (0.5)^4[/tex]

= 0.25 + 0.0625

= 0.3125

Prοbability that at least οne answer is True (which is the cοmplement οf the event that all answers are False):

P(at least οne True) = 1 - P(all False) = 1 - 0.0625 = 0.9375

Prοbability that the last answer is True:

This prοbability can be calculated using cοnditiοnal prοbability, where we find the prοbability that the last answer is True given that we knοw that at least οne answer is True:

P(last answer is True | at least οne True) = P(last answer is True and at least οne True) / P(at least οne True)

P(last answer is True and at least οne True) = P(last answer is True) = 0.5

P(at least οne True) = 0.9375 (calculated in part 3)

Sο, P(last answer is True | at least οne True) = 0.5 / 0.9375 = 0.5333 (rοunded tο fοur decimal places).

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Answer: We can simplify the given expression as follows:

9√64 - 2√125

Since √64 = 8, we can substitute to get:

9(8) - 2√125

Since √125 = √(25 × 5) = √25 × √5 = 5√5, we can substitute again to get:

9(8) - 2(5√5)

Simplifying further:

72 - 10√5

Therefore, the expression 9√64 3 − 2√125 simplifies to 72 - 10√5.

Step-by-step explanation:

When x = 5, y =  9 / 11

When x = 0, y = -1 / 6

when x = -6, y = -13

When x = 5

we would have

[tex]y = \frac{2(5) - 1}{5 + 6}[/tex]

y = 10 - 1 / 11

y = 9 / 11

when the value of x = 0

[tex]y = \frac{2(0) - 1}{0 + 6}[/tex]

y = -1 / 6

When the value of x = -6

[tex]y = \frac{2(-6) - 1}{-6 + 6}[/tex]

y = -12 - 1 / 0

y = -13 / 0

y = -13

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Answer:

b

Step-by-step explanation:

my brain

Answer:

0

Step-by-step explanation:

Expected Value = (Probability of winning) x (Amount won) + (Probability of losing) x (Amount lost)

In this case, the probability of winning is 1/6 (since there is only one way to roll a 3 out of six possible outcomes), and the probability of losing is 5/6 (since there are five other outcomes that do not result in a win).

The amount won is $15, and the amount lost (i.e., the cost of playing the game) is $3.

Therefore, the expected value is:

Expected Value = (1/6) x $15 + (5/6) x (-$3)

Expected Value = $2.50 - $2.50

Expected Value = $0

The height of the can should be approximately 7 inches to have a surface area as close to 100 square inches as possible.

What is cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of the same size and shape, and a curved lateral surface connecting the bases.

The formula for the surface area of a cylinder is:

where r is the radius of the base, h is the height, and π is approximately 3.14.

In this case, the radius is given as 2 inches, and we want to find the height that will give us a surface area as close to 100 square inches as possible. So we need to solve for h in the equation:

100 = 2π(2)² + 2π(2)h

Simplifying this equation:

100 = 8π + 4πh

92 = 4πh

h = 23/π

h ≈ 7.32

Rounding this answer to the nearest inch, we get:

h ≈ 7 inches

Therefore, the height of the can should be approximately 7 inches to have a surface area as close to 100 square inches as possible.

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From the table, we see that Julia rolled the die 100 times, and the number of times she rolled a 3 was 45.

The best estimate of the probability of rolling a 3 can be found by dividing the number of times a 3 was rolled by the total number of rolls:

P(rolling a 3) = Number of times 3 was rolled / Total number of rolls

P(rolling a 3) = 45 / 100

P(rolling a 3) = 0.45 or 45%

Therefore, based on Julia's experimental results, the best estimate of the probability of rolling a 3 on her biased die is 0.45 or 45%.

The rate of change is $1.25 per premium movie watched.

A. $1.25 / 1 premium movie

The rate of change in this scenario is the increase in cost for each additional premium movie watched.

In this case, the rate of change is constant, since the cost per premium movie remains the same regardless of the number of premium movies watched.

Therefore, the rate of change is simply the additional cost per premium movie, which is $1.25.

So, for example, if you watched 10 premium movies, the total cost would be:

$35 + (10 * $1.25) = $47.50

And if you watched 20 premium movies, the total cost would be:

$35 + (20 * $1.25) = $60.00

rate of change = (60 - 47.5) / (20 - 10) = 1.25

In both cases, the rate of change is still $1.25 per premium movie watched.

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Answer:

-10x+18=-15x-18+5x

-10x+18=-10x-18

18=-18

Since the equation is inconsistent and has no solution, there is no value of x that would make it true.

Step-by-step explanation:

The answer is [tex]\sqrt{58} = 7.62[/tex]

So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).

Use the Pythagorean theorem:

[tex]c^2 = a^2 + b^2[/tex]

[tex]a = 3[/tex]

[tex]b = 7[/tex]

[tex]c^2 = 3^2 + 7^2[/tex]

[tex]c^2 = 9 + 49[/tex]

[tex]c^2 = 58[/tex]

[tex]c = \sqrt{58}[/tex]

[tex]c = 7.62[/tex]

Answer:

I think the answer is 63%

Step-by-step explanation:

9/10 * 7/10 = 63/100 = 63%

(I am not fully sure.)

Answer:

7+2=3x-2+2

9/3=3x/3

3=x

The transformations that compares the functions y = 1/x and y = 5/(x + 6) are

What are transformations?

Transformations are mathematical operations that are performed to change the shape or value of a graph, function or image.

Since we have the functions

We want to see how the graphs of

We proceed as folows.

Looking at the functions

We compare the transformations and see that

So, the functions compare by

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Answer:

144ft^2

Step-by-step explanation:

Answer:

144^2 feet

Step-by-step explanation:

To find the area you would multiply length x width for your answer. I hope this helps!

Answer:

To prove that every bounded sequence contains a convergent subsequence, we will use the Bolzano-Weierstrass theorem.

Bolzano-Weierstrass theorem: Every bounded sequence in Euclidean space has a convergent subsequence.

Proof: Let (a_n) be a bounded sequence in Euclidean space, which means that there exists some M > 0 such that |a_n| <= M for all n. We will use the bisection method to construct a subsequence that converges to some limit L.

Step 1: Divide the interval [-M, M] into two subintervals, [-M, 0] and [0, M]. Since (a_n) is bounded, at least one of these intervals contains infinitely many terms of the sequence. Let's call the interval that contains infinitely many terms I_1.

Step 2: Divide I_1 into two subintervals of equal length, and again, at least one of these subintervals must contain infinitely many terms of the sequence. Let's call the interval that contains infinitely many terms I_2.

Step 3: Repeat this process for each subinterval, dividing it into two subintervals of equal length and choosing the one that contains infinitely many terms of the sequence. We obtain a sequence of nested intervals I_1 ⊃ I_2 ⊃ I_3 ⊃ ... that contain infinitely many terms of the sequence.

Step 4: Since the length of each interval is decreasing and they are nested, the intersection of all the intervals is a single point L. By construction, every term of the sequence (a_n) belongs to one of the intervals I_k, which means that there exists a subsequence (a_nk) that converges to L.

Therefore, every bounded sequence in Euclidean space has a convergent subsequence, as required.

Step-by-step explanation:

Answer:

To find out how many patients smoke, you can multiply the total number of patients by the percentage of smokers:

8500 x 25% = 2125

Therefore, there were 2125 patients who smoke last month in the trust.

Step-by-step explanation:

2125 of the patients are smoker.

Percentages are fractions with 100 as the denominator. It is the relation between part and whole where the value of whole is always taken as 100.

Given that, there were 8500 patients in total last month in the trust. 25% of these are smokers.

We need to find the number of the patients who smoke.

So,

25% of 8500

= 0.25 × 8500

= 25 × 85

= 2125

Hence, 2125 of the patients are smoker.

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Answer:

105 mi

Step-by-step explanation:

distance = speed x time

total distance = (62 mi/hr)(1.5 hr) + (24 mi/hr)(0.5 hr) = 105 mi

30 min = 0.50 hr

Answer: B) 2

Step-by-step explanation:

In the image, we see a box and whisker plot. The middle line represents the median. Looking at the numbers on the side, and the placement of the middle line, we can see that the median in this situation is 2.

According to the tax tables below, Melvin would have to pay in federal income taxes if filing separately $5,131 and Sylvia $6,750. The total would be $11,881

To identify how much Melvin and Sylvia have to pay in taxes, we must look carefully at the table. In this, the different incomes are classified and on the right side are shown how much the tax is depending on the condition of the citizen. These options are: single, married filling jointly, married filling separately and head of a household.

In accordance with the above, we must look at which number coincides in the row of married filling separately with the value of the income of each one of them. According to the above, Melvin has to pay 5,131 in taxes while Sylvia has to pay 6,750.

Note: This question is incomplete. Here is the complete information:

Melvin and Sylvia are married with no children, and they're filing their federal income tax return. Melvin had a gross income of $35,750 last year, while Sylvia had a gross income of $41,700.

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Starting with the angle of -270°, adding 360° gives us 90° (which is a coterminal angle with -270°).

If we rotate 180° counter-clockwise from 90°, we end up at the angle of 270°. Therefore, the new measurement of the coterminal angle is 270°.

I hope this helps :)

The 5 foot 5 tall lady will cast a shadow of approximately 4.4 ft.

Given that, a 6 foot 2 man casts a shadow of 5 feet. Also, a lady is 5 foot 5 and we find the shadow she casted.

We can solve this problem by setting up a proportion:

The height and shadow length are proportional, so we can write:

6 feet 2 inches : 5 feet = 5 feet 5 inches : x

where x is the length of the shadow cast by the lady.

To solve for x, we can cross-multiply:

(6 feet 2 inches) × x = (5 feet) × (5 feet 5 inches)

To simplify the calculation, we can convert all the lengths from feets to inches:

Note: 1 ft = 12 in

(74 inches) × x = (60 inches) × (65 inches)

Now we can solve for x:

x = (60 inches)  × (65 inches) / (74 inches)

x = 3900/74

x = 52.70 inches

Convert back to ft

x = 4.4 ft

Therefore, the lady will cast a shadow of approximately 4.4 ft.

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Answer:

Step-by-step explanation:

a. To find the rate at which the x-coordinate of the bug is increasing when the bug is at the point (4, 16), we need to differentiate the equation y=x with respect to time t:

dy/dt = dx/dt

Since the bug is moving along the right side of the parabola y=x, the bug's position can be described by the equation y=x^2. Taking the derivative of both sides with respect to time t, we get:

2y(dy/dt) = 2x(dx/dt)

Simplifying and plugging in the given values for y and dy/dt:

2(16)(9) = 2(4)(dx/dt)

dx/dt = 36 cm/min

Therefore, the x-coordinate of the bug is increasing at a rate of 36 cm/min when the bug is at the point (4, 16).

b. The equation y=x^2 can be rewritten as x=sqrt(y). Differentiating both sides with respect to time t, we get:

dx/dt = 1/(2sqrt(y)) * dy/dt

Substituting y=16 and dy/dt=9, we get:

dx/dt = 1/(2sqrt(16)) * 9

dx/dt = 9/8 cm/min

c. We can use the same equation from part (a) to find the rate at which the y-coordinate of the bug is increasing when the bug is at the point (4, 16):

2y(dy/dt) = 2x(dx/dt)

Substituting y=16, x=4, and dx/dt=36, we get:

2(16)(dy/dt) = 2(4)(36)

Solving for dy/dt:

dy/dt = 18 cm/min

Therefore, the y-coordinate of the bug is increasing at a rate of 18 cm/min when the bug is at the point (4, 16).

d. Let D be the distance the bug is from the origin. We can use the Pythagorean theorem to relate D to x and y:

D^2 = x^2 + y^2

Substituting y=x^2, we get:

D^2 = x^2 + x^4

Taking the derivative of both sides with respect to time t, we get:

2D(dD/dt) = 2x(dx/dt) + 4x^3(dx/dt)

Simplifying and substituting x=4, dx/dt=36, and y=16:

2sqrt(16+16^2)(dD/dt) = 2(4)(36) + 4(4^3)(36)

Solving for dD/dt:

dD/dt = (836 + 44^3*36) / (2sqrt(16+16^2))

dD/dt = 72/(sqrt(17))

Therefore, the distance between the bug and the origin is increasing at a rate of 72/(sqrt(17)) cm/min when the bug is at the point (4, 16).

The Tοtal number οf tickets tο play will be 15.

Mathematical expressiοns with inequalities οn bοth sides are knοwn as inequalities. In an inequality, we cοmpare twο values as οppοsed tο equatiοns. In between, the equal sign is changed tο a less than (οr less than οr equal tο), greater than (οr greater than οr equal tο), οr nοt equal tο sign.

At a schοοl fair, there are different games tο play that each require 5 tickets tο play.

Jοrdan wants a bag οf pοpcοrn that requires 26 tickets and tο use the rest οf the tickets tο play games.

Jοrdan has 101 tickets.

Fοr tickets tο play will be 101-26 = 75

Sο the Tοtal number οf tickets tο play will be 75/5 = 15.

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