0.66666667 write this as a fraction.

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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Tthe population of the colony after 2 hours is 64a

From the question, we have the following parameters that can be used in our computation:

Rate = doubles every 20 minutes

Represent the initial population with a

So, we have the following representation

f(t) = a(2)^t

Where t is the number of 20 minutes in the time

The time is given as 2 hours

So, we have

t = 2 hours/20 minutes

Evaluate

t = 6

The function becomes

f(t) = a(2)^6

Evaluate

f(t) = 64a

hence, the population is 64a

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(a). O The entire student body (the 17,000 students) and (b). O the 200 students interviewed are the answers to the above-asked question. This is a multiple-choice question about statistics sampling and population. The inquiry inquires about the problem's population of interest and sample.

The answers to the above statistics-based questions can be stated as,

(a) O The population of interest in this topic is the whole student body of the institution, which has 17,000 students because the student senate wants to know what percentage of all students support changing the grading system.

(b) O The sample in this problem consists of the 200 students who were questioned to determine their attitudes toward the proposed change in the grading system. They represent a subset of the overall student body and are used to estimate the percentage of all students who support the change.

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The probability of hitting a yellow balloon on the first try is 10/25 or 2/5. After hitting the first yellow balloon, there are now 24 balloons left on the board, with 9 of them being yellow. The probability of hitting a yellow balloon on the second try is 9/24 or 3/8. To find the probability of both events happening, we multiply the probabilities together:

P(first yellow) * P(second yellow) = (2/5) * (3/8) = 6/40 = 3/20

Therefore, the probability that the next balloon hit is also yellow given that the first balloon hit is yellow is 3/20.

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The largest value of x for which this solution is defined is 2.45 (approx.).Hence, the required answer is 2.45.

To solve the initial value problem 5x + y y' = 0, y (2) = 5, we need to first solve the differential equation and then plug in the value of y(2) = 5 to find the value of the constant C. Finally, we need to find the largest value of x for which this solution is defined. Steps to solve the initial value problem: Given, 5x + y y' = 0y (2) = 5 Separating the variables and integrating,5x + y y' = 0 => y d y = -5xdx Integrating both sides, we get y²/2 = -5x²/2 + C.... .. (1)Now, we need to find the value of the constant C

To do so, plug in the value of y(2) = 5 in equation (1),5²/2 = -5(2)²/2 + C => C = 15Thus, the solution to the initial value problem is given by, y²/2 = -5x²/2 + 15 => y² = -5x² + 30The solution will be defined only if y² > 0.

Thus, -5x² + 30 > 0 => x < √6 or x > -√6.The largest value of x for which this solution is defined is therefore √6 ≈ 2.45 (rounded to 2 decimal places).Therefore, the largest value of x for which this solution is defined is 2.45 (approx.).Hence, the required answer is 2.45.

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Answer:

\(10\sqrt{14} +8\sqrt{21} + 30\sqrt{3} +36\sqrt{2}\\\)

Step-by-step explanation:

\((2\sqrt{7} + 3\sqrt{6} )(5\sqrt{2} +4\sqrt{3} )\\= 10\sqrt{14} +8\sqrt{21} + 15\sqrt{12} +12\sqrt{18} \\=10\sqrt{14} +8\sqrt{21} + 15\sqrt{4*3} +12\sqrt{9*2} \\= 10\sqrt{14} +8\sqrt{21} + 15*2\sqrt{3} +12*3\sqrt{2} \\=10\sqrt{14} +8\sqrt{21} + 30\sqrt{3} +36\sqrt{2} \\\\\)

Hope this helps!

Answer:

(2√7 + 3√6) x (5√2 + 4√3)

Multiply the parentheses

= 10√14 + 8√21 + 15√12 + 12√18

= 10√14 + 8√21 + 30√3 + 12√18

Answer:

Step-by-step explanation:

There are 540 degrees in a pentagon so take 540-(everything there)= 67

Answer:

yah yeet yeet yah

Step-by-step explanation:

1. The area of two concentric circles with radii 28 cm and 18 cm is 460π cm^2.

2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle is 2 units.

What are concentric circles?

Concentric circles are those that share a common centre but have differing radii. It is described as two or more circles with the same centre, in other words.

The radii of two concentric circles are 28 cm and 18 cm.

The bigger circle has a radius of r1=28 cm and the smaller circle has the radius of r2=18 cm.

Area of two concentric circles is -

A = π[(r1)^2-(r2)^2]

A = π[(28)^2-(18)^2]

A = π[(28+18)(28-18)]

A = π[46 × 10]

A = 460π cm^2

Therefore, the area of concentric circle is 460π cm^2.

The formula for perimeter of the circle is 2πr, and the formula for the area of the circle is πr^2, where r is the radius of the circle.

Now, according to the data given the perimeter and area of the two circles are equal.

So, the equation will be 2πr = πr^2.

2πr = πr^2

2π = πr

r = 2 units

Therefore, the radius is 2 units.

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1. If radii of two concentric circle are 28 cm and 18 cm respectively. Find the area of the concentric circles.

2. If the perimeter and the area of the circle are numerically equal then find the radius of the circle​.

To evaluate dw/dt at t=4, we need to find the derivative of w(x, y) with respect to t and then substitute t=4.

Given:

w(x, y) = e^y - ln(x)

x = t^2

y = ln(t)

First, let's find the partial derivatives of w with respect to x and y:

∂w/∂x = -1/x

∂w/∂y = e^y

Next, let's find the derivatives of x and y with respect to t:

dx/dt = 2t

dy/dt = 1/t

Now, we can use the chain rule to find dw/dt:

dw/dt = (∂w/∂x)(dx/dt) + (∂w/∂y)(dy/dt)

= (-1/x)(2t) + (e^y)(1/t)

Substituting the given values of x and y:

= (-1/(t^2))(2t) + (e^ln(t))(1/t)

= -2/t + t/t

= -2/t + 1

Finally, substituting t=4:

dw/dt = -2/4 + 1

= -1/2 + 1

= 1/2

Therefore, the value of dw/dt at t=4 is 1/2.

So, the answer is: (a) 1/2.

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|x − 37500| ≤ 4500; The salaries range from $33,000 to $42,000

Answer:

B

Step-by-step explanation:

when the arrow is pointing toward the left side that means less than side. When the arrow is pointing towards the right side that means greater than.

Answer:

B, because that symbol means at least so you would go to the negative side which is on the left it has to start from 4 which is correct and this means negative: - The 0 is the origin so from the origin to the left side is negative from the origin to the right side is positive you want to look for negative because it's negative 4.

Answer:

Cross two lines then put one line above the point of intersection and below the point of intersection. straightforward though

Answer:

50,000 in scientific notation is 5 x 10^4

Step-by-step explanation:

10^4 = 10,000 x 5 = 50,000

(a) The sample mean reading for total calcium levels is approximately 9.5300 mg/dl, and the sample standard deviation is approximately 2.6800 mg/dl.  (b) The 99.9% confidence interval for the population mean of total calcium in the patient's blood is approximately 5.3220 mg/dl to 13.7380 mg/dl.

(a) For the patient's total calcium readings, the sample mean is approximately 9.7900 mg/dl and the sample standard deviation is approximately 2.1846 mg/dl. For the candy store startup costs, the sample mean is approximately $109.2222 thousand and the sample standard deviation is approximately $36.6927 thousand. For the weights of wild mountain lions, the sample mean is approximately 95.3333 pounds and the sample standard deviation is approximately 32.2434 pounds. For the percentage of hospitals providing charity care, the sample mean is approximately 61.0360% and the sample standard deviation is approximately 7.8002%.

(b) For the patient's total calcium, a 99.9% confidence interval for the population mean is approximately 6.1257 mg/dl to 13.4543 mg/dl. For the candy store startup costs, a 90% confidence interval for the population average is approximately $80.1 thousand to $138.3 thousand. For the weights of wild mountain lions, a 75% confidence interval for the population average weight is approximately 56.6 pounds to 134.1 pounds. For the percentage of hospitals providing charity care, a 90% confidence interval for the population average percentage is approximately 55.1% to 66.0%.

These confidence intervals provide an estimated range within which the true population parameters (mean, average, weight, percentage) are likely to fall. The higher the confidence level, the wider the interval, indicating greater certainty in capturing the true population parameter. The sample mean represents the best estimate of the population parameter, and the sample standard deviation measures the variability of the data around the mean.

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Answer:

\(f(x) = 30 - 5x \\ f(x) = 0 \\ 30 - 5x = 0 \\ 30 = 5x \\ 5x = 30 \\ x = \frac{30}{5} \\ \purple{\boxed{ \red{x = 6}}}\)

Answer:

height is less than 4 cm

Step-by-step explanation:

We know,

Area of a triangle = \(\frac{1}{2}\) × b × h

Where,

We know A is less than 12 and base is 6cm

\(\frac{1}{2}\) × 6 × h < 12

➨ \(\frac{1}{2}\) × 6h < 12

➨ \(\frac{6h}{2}\) < 12

➨ \(\cancel{\frac{6h}{2}}\) < 12

➨ 3h < 12

➨ h < 4

Height is to be less than 4 cm.

To sketch the region in the plane consisting of points whose polar coordinates satisfy the conditions \(1 < r \leq 2\) and \(\frac{3}{4} \leq \theta \leq \frac{5}{4}\), we can visualize the region as follows:

1. Start by drawing a circle with radius 1. This represents the condition \(r > 1\).

2. Inside the circle, draw another circle with radius 2. This represents the condition \(r \leq 2\).

3. Now, mark the angle \(\theta = \frac{3}{4}\) on the circle with radius 1, and mark the angle \(\theta = \frac{5}{4}\) on the circle with radius 2.

4. Shade the region between the two angles \(\frac{3}{4}\) and \(\frac{5}{4}\) on both circles.

The resulting sketch should show a shaded annular region between the two circles, with angles \(\frac{3}{4}\) and \(\frac{5}{4}\) marked on the respective circles. This annular region represents the set of points whose polar coordinates satisfy the given conditions.

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Answer: A-Bottura cooks food that would be

wasted and serves it to people

Step-by-step explanation: hope this help

Answer:

5/9

Step-by-step explanation:

it's literally telling you the answer and asking you

If they want the odds in favor then it's the odds of the event happening

Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

$35072.78 is the least amount of money needed to build this fence of ideal area if the material used in the fencing costs $31/ft.

In the given question,

A rectangular recreational field needs to be built outside of a gymnasium.

Three walls of fencing are needed and the fourth wall is to be a wall of the gymnasium itself. the ideal area for such a field is exactly 160000 ft^2.

Assuming that the material used in the fencing costs $31/ft, then we have to find the least amount of money needed to build this fence of ideal area.

The given ideal area of rectangular field = 160,000 square feet

We know that the formula of area of rectangle

A = lb

where l = length of rectangle

b = breadth of rectangle

A = area of rectangle

A = 160,000 square feet

Putting the value

lb = 160,000

l = 160,000/b

We have to fence the three wall of this rectangular field

The perimeter of the rectangle is

P = 2(l+b)

We don't have to fence one wall so the perimeter that covered

P= 2(l+b)−b

P= 2l+2b−b

P= 2l+b

Now putting the value of l

P = 2× 160,000/b +b

P = 320,000/b+b

The material cost in fencing $31/ft.

P = 31(320,000/b+b)..........................(1)

Now differentiating with respect to b

P' = 31(−320,000/b^2 +1)..................(2)

For minimum cost that is given the differentiation is zero.

So P' = 0

31(−320,000/b^2 +1) = 0

Dividing by 31 on both side

31(−320,000/b^2 +1)/31 = 0/31

−320,000/b^2 +1 = 0

Subtract 1 on both side

−320,000/b^2 +1−1 = 0−1

−320,000/b^2 = −1

Multiply by −b^2 on both side

−320,000/b^2 ×(−b^2) = −1×(−b^2)

320,000 = b^2

b^2 = 320,000

Taking square root

b = 565.69

Now finding the value of l by putting the value of b in l = 160,000/b

l = 160,000/565.69

l = 282.84

Therefore the minimum cost is

P = 31(320,000/565.69 +565.69)

P = 31(565.69+565.69)

P = 31×1131.38

P = 35072.78

Hence, $35072.78 is the least amount of money needed to build this fence of ideal area if the material used in the fencing costs $31/ft.

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Answer:

Neither

Step-by-step explanation:

In this question, we have to verify if the equations are parallel, perpendicular, or neither to each other.

Turn the first equation into slope-intercept form so we can get a better understanding:

4x - 3y = 9

Subtract 4x from both sides.

-3y = -4x + 9

Divide both sides by -3.

y = 4/3x - 3

Now lets compare both lines:

y = 4/3x - 3

y = 3/4x + 7

Since the slopes have to be the same in order for the lines to be parallel, we can see that the lines are NOT parallel.

We also know that in order for the lines to be perpendicular, one has to be positive and the other has to be negative. In this case, they both are positive. This means that the lines are NOT perpendicular.

This means that our answer would be neither.

Answer:

The scale factor is 1.25 !

Step-by-step explanation:

Take the sides of one triangle and divide them by the sides of the other triangle.

45/36 = 1.25

30/24 = 1.25

35/28 = 1.25

Answer:

To solve this problem, we can use the following equation:

T = 2π√(r/g)

where T is the period (time for one complete revolution), r is the length of the rope, and g is the acceleration due to gravity.

First, we need to find the length of the rope. We can use trigonometry to do this:

sin(12°) = r/1.55m

r = 1.55m * sin(12°) = 0.319m

Next, we need to find g. We can use the value of 9.81 m/s^2 for the acceleration due to gravity.

Now we can plug in our values and solve for T:

T = 2π√(0.319m/9.81 m/s^2)

T ≈ 0.807 s

Therefore, the period of the tetherball's motion is approximately 0.807 seconds.

4/6 = 12/18

8/10 = 16/20

2/5 = 4/10

1/4 = 4/16

Can I get brainiest please.

The number of babies in this problem is classified as an:

For each student, we have an input variable and an output variable, given as follows:

For this problem, we have that the number of babies is predicted according to the size of the stork population, hence the variables are given as follows:

This means that the number of babies can be classified as either the target variable or the outcome, as it is the output of the study, and then either the first and the last options are correct.

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Answer:

x= 115-y

y=115-x
(Please brainlist me)

Step-by-step explanation:

65 + 2x + 2y + 25 + 65 = 360

2x+ 2y = 230

x+y = 115

x= 115-y

y=115-x

Answer:

b = 18 units

Step-by-step explanation:

Answer:

x = 4.5                            x = .5

Step-by-step explanation:

|2x - 5| = 4

The absolute value has two solutions one positive and one negative

2x-5 = 4              2x-5 = -4

Add 5 on each side

2x-5+5 = 4+5         2x-5+5 = -4+5

2x = 9                        2x =1

Divide by 2

2x/2 =9/2                  2x/2 = 1/2

x = 4.5                            x = .5