A rock thrown into a still pond causes a circular ripple. If the radius of the ripple is increasing at 2 feet per second, how fast is the area changing when the radius is 10 feet

Answer:

C

Step-by-step explanation:

The x's can not completely cancel each other out so they are still included but you have to divide the numbers, exponents and whole numbers.

Answer:

first one

Step-by-step explanation:

Answer:

bisector

Step-by-step explanation:

PQ bisected RS and created two congruent segments

Answer 9 3/7

Step-by-step explanation:

\( \frac{30}{7} \times \frac{11}{5} \\ = \frac{330}{35} \\ = 9 \frac{15}{35} \)

SIMPLIFIED WE GET:

\(9 \frac{3}{7} \)

THE LAST OPTION IS THE ANSWER

Answer:

$255.00

Step-by-step explanation:

If you deposit $250 for only a year, and the interest per year is $5 dollars, then you would add $250+$5, getting $255.

Answer:

$255.00

Step-by-step explanation:

There will be two hundred fifty-five dollars in the account. The balance equals the principal plus the interest.

The value of x is 42.

To determine the value of x, we need to analyze the given information regarding the scale factor between Figure A and Figure B.

The scale factor is expressed as the ratio of the corresponding side lengths or dimensions of the two figures.

Let's assume that the length of a side in Figure B is represented by 'x'. According to the given information, Figure A is a scale copy of Figure B with a scale factor of 2/7. This means that the corresponding side length in Figure A is 2/7 times the length of the corresponding side in Figure B.

Applying this scale factor to the length of side x in Figure B, we can express the length of the corresponding side in Figure A as (2/7)x.

Given that the length of side x in Figure B is 12, we can substitute it into the equation:

(2/7)x = 12

To solve for x, we can multiply both sides of the equation by 7/2:

x = (12 * 7) / 2

Simplifying the expression:

x = 84 / 2

x = 42

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Answer:

between 49-55.

\(\huge\color{purple}\boxed{\colorbox{black}{Answer ☘}}\)

in ∆ABE

\( \tan(theta) = \frac{p}{b} \\ \tan(60) = \frac{h}{x} \\ \sqrt{3} = \frac{h}{x} \\ h = \sqrt{3}x\)

Now, in ∆CDE

\( \tan(theta) = \frac{p}{b} \\ \tan(30) = \frac{h}{80 - x} \\ \frac{1}{ \sqrt{3} } = \frac{ \sqrt{3}x }{80 - x} (from \: (1)) \\ = > 3x = 80 - x \\ 4x = 80 \\ x = 20\)

distance of pole CD from E = 80 - x = 60m

distance of pole AB from E = x = 20m

\(h = \sqrt{3} x = 20 \sqrt{3}m\)

Step-by-step explanation:

well, we have several right-angled triangles here.

the main one from the point in the street to the 2 tops of the poles.

and the 2 side ones of the poles to the point on the street.

we know the angle above the point in the street is 90 degrees, because the other 2 angles of the main triangle are 30 and 60 degrees. and the sum of all angles in a triangle must always be 180 degrees.

as the angles up are 30 and 60 degrees, so are their mirrored twins at the tops of the poles as part of the main triangle.

the Hypotenuse of the main triangle is the connection between the tops of the poles, and is also 80m long.

so, now that we have established the "picture", we can use the law of sine to get all the other side lengths.

a/sin(A) = b/sin(B) = c/sin(C)

where the sides are always opposite of the correlated angles.

so, we know,

80/sin(90) = 80 = a/sin(30) = 2a = b/sin(60)

a = 80/2 = 40m (the connection from the point in the street to the top of the pole under 60°)

b = 80×sin(60) = 69.2820323... m (the connection from the point in the street to the top of the second pole under 30°).

now we use the same principle on the side lengths of the 2 side triangles. their Hypotenuses are the 2 sides we just calculated.

let's start with the one with the round number as Hypotenuse : 40m

40/sin(90) = street distance / sin(30) = 2× street distance

street distance = 40/2 = 20m

that means the street distance of the point in the street to the other pole is 80-20 = 60m

for the pole height(s) we now just use regular Pythagoras

c² = a² + b²

with c being the Hypotenuse.

40² = 20² + pole height²

1600 = 400 + pole height²

1200 = pole height²

pole height = 34.64101615... m

Answer:

130 degree

Step-by-step explanation:

all angles of add quadrilateral is 360

so

100⁰ + 95⁰+ 35⁰ + b⁰ = 360⁰

230⁰ + b⁰ = 360⁰

b⁰ = 360⁰ - 230

b⁰ = 130⁰

Answer:

$261,500

Step-by-step explanation:

What amount should Nash report as its December 31 inventory?

Item                                                             Amount

Goods on hand as per physical count    $208,000

(+) Goods purchased from Swifty             $30,000

Corporation FOB shipping point    

(+) Goods sold to Marigold Corp               $23,500

FOB destination (at cost value)

Ending inventory                                        $261,500

Notes:

1) In case of FOB shipping point, the ownership of goods is transferred to the buyer when the goods are shipped and hence in the case of purchases from Swifty corporation, the goods should be included in the inventory of Nash's Trading Post as the goods are shipped and are in transit.

2) In case of FOB destination, the ownership of goods is transferred to the buyer when the goods reaches to the buyer, hence in the case of sales made to Marigold Corp, the goods are still in transit and the ownership is not transferred to Marigold Corp, hence Nash's Trading Post should included that goods in its inventory.

Answer:

9cm r=2x3x9= 54. Find the volume of the cube. Include units. 5cm ... Not to scale. Work out the volume of the prism. Area of front. 3x5=15. 3cm 4x8=32. 10cm.

Step-by-step explanation:

Answer:

  470 cm³

Step-by-step explanation:

You want the volume of a prism with an L-shaped base.

The volume of a prism is given by ...

  V = Bh

where B is the area of the base, and h is the distance between bases.

The base is has an L-shape. Its area can be found by extending the horizontal line to divide the figure into two rectangles.

The top rectangle is 4cm × 5cm, so has an area of ...

  A = LW = (4 cm)(5 cm) = 20 cm²

The bottom rectangle is 9 cm × 3 cm, so has an area of ...

  A = LW = (9 cm)(3 cm) = 27 cm²

Then the total base area is ...

  B = (top rectangle area) + (bottom rectangle area)

  B = (20 cm²) +(27 cm²) = 47 cm²

Then the volume is ...

  V = Bh = (47 cm²)(10 cm) = 470 cm³

The volume of the prism is 470 cm³.

Answer:The 99% confidence interval is

To find the 99% confidence interval for the mean systolic blood pressure (SBP) level, we use the formula:

CONFIDENCE INTERVAL = Mean ± Z * (Standard Deviation / √n)

Where:

Mean is the sample mean of SBP

Z is the Z-score corresponding to the desired confidence level

Standard Deviation is the population standard deviation

Explanation:

Given that the sample size is 13 and the standard deviation is 10, we need to calculate the sample mean and the Z-score for the 99% confidence level.

First, we calculate the sample mean:

Mean = (129 + 134 + 142 + 114 + 120 + 116 + 133 + 142 + 138 + 148 + 129 + 133 + 140) / 13

= 1724 / 13

≈ 132.62

Next, we need to determine the Z-score for a 99% confidence level. The Z-score can be found using a Z-table or a statistical calculator. For a 99% confidence level, the Z-score is approximately 2.576.

Now, we can calculate the confidence interval:

Confidence Interval = 132.62 ± 2.576 * (10 / √13)

132.62 ± 2.576 * (10 / 3.6056)

≈ 132.62 ± 2.576 * 2.771

≈ 132.62 ± 7.147

Therefore, the 99% confidence interval for the mean SBP level is approximately (125.47, 139.77).

Answer:

n = 3200

Step-by-step explanation:

200 = 1000 - \(\frac{n}{4}\) ( subtract 1000 from both sides )

- 800 = - \(\frac{n}{4}\) ( multiply both sides by 4 to clear the fraction )

- 3200 = - n ( multiply both sides by - 1 )

n = 3200

Answer:

See the attached image for work.

1) The slope is 4.

2) The slope is 2.

Answer:

on the first one the rise is 20 and the run is 5. 5 divided by 20 is 4 so the slope is 4. I haven't answered the second one yet, sorry.

Answer:

Step-by-step explanation:

SOLVING

================================================================

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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Answer:

d, -3

Step-by-step explanation:

Answer:

3/7

Step-by-step explanation: hope this helps :)

Answer:

3/7 is the simplest

Step-by-step explanation:

30/70: given

15/35: divided by 2

3/7: divided by 5

The graph of Linear Equation is always a straight line .

The null and alternative hypotheses for testing the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the 0.005 significance level can be stated as H0: pM ≥ pF H1: pM < pF

In this case, pM represents the proportion of men who own cats, and pF represents the proportion of women who own cats. The null hypothesis (H0) states that the proportion of men who own cats is greater than or equal to the proportion of women who own cats. The alternative hypothesis (H1) states that the proportion of men who own cats is less than the proportion of women who own cats.

To test these hypotheses, statistical analysis can be performed using appropriate methods, such as conducting a hypothesis test for the difference in proportions between the two groups. The significance level of 0.005 indicates that the researcher wants to have strong evidence against the null hypothesis before rejecting it.

The sample data should be collected and analyzed to determine if there is sufficient evidence to support the claim that the proportion of men who own cats is smaller than the proportion of women who own cats. This can be done by calculating the test statistic, comparing it to the critical value, and calculating the p-value. If the p-value is less than 0.005, the null hypothesis can be rejected in favor of the alternative hypothesis.

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Answer:

your answer would be 9. hope this helps!

Answer:

-Dividing 3,024 by 336 would give you 9:

\(3,024 \div 336 = 9\)

The equation you provided, -3 - 4 = -4 - 3, does not imply that subtraction of integers is commutative. In fact, subtraction of integers is not a commutative operation.

The equation you presented demonstrates the property of additive inverse, where the negative of a number is the additive inverse of that number. In this case, both sides of the equation result in the same value (-7), but it does not illustrate commutativity.

To show an example of a commutative operation, we can look at addition of integers:

For example:

3 + 4 = 7

4 + 3 = 7

In this case, the order of the integers being added does not change the result, illustrating the commutative property of addition.

However, subtraction does not exhibit this property. For instance:

3 - 4 = -1

4 - 3 = 1

In this case, swapping the order of the subtraction operation changes the result, indicating that subtraction is not commutative.

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The probability of getting a return of 200% or more in a single year is approximately 0.0000317 or 0.00317%.

Assuming that the returns from holding small-company stocks are normally distributed, the probability of doubling or tripling your money in a single year can be estimated using the normal distribution formula.

To calculate the probability of doubling your money, you need to find the number of standard deviations away from the mean that represents a return of 100%. If we assume that the average return for small-company stocks is 10% per year with a standard deviation of 20%, we can use the formula:

Z = (100% - 10%) / 20% = 4.5

Using a normal distribution table or calculator, we can find that the probability of getting a return of 100% or more in a single year is approximately 0.0000317 or 0.00317%.

Similarly, to calculate the probability of tripling your money, you need to find the number of standard deviations away from the mean that represents a return of 200%. Using the same formula as above, we get:

Z = (200% - 10%) / 20% = 9.5

Using a normal distribution table or calculator, we can find that the probability of getting a return of 200% or more in a single year is approximately 0.000000002 or 0.0000002%.

It's important to note that these calculations are based on assumptions and estimates, and actual returns may vary significantly. Investing in small-company stocks involves significant risks, and investors should carefully consider their investment goals, risk tolerance, and overall financial situation before making any investment decisions.

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Answer:

\(h=\frac{1452}{7\pi }\)

Step-by-step explanation:

\(84=\pi \left(\frac{7}{11}\right)^2h\\\mathrm{Switch\:sides}\\\pi \left(\frac{7}{11}\right)^2h=84\\\frac{49\pi }{121}h=84\\\)

\(\mathrm{Multiply\:both\:sides\:by\:}121\\121\cdot \frac{49\pi }{121}h=84\cdot \:121\\49\pi h=10164\\\mathrm{Divide\:both\:sides\:by\:}49\pi \\\frac{49\pi h}{49\pi }=\frac{10164}{49\pi }\\h=\frac{1452}{7\pi }\\or\\h=66.0266\)

Answer:

h=66

Step-by-step explanation:

84=22/7 *(7/11)^2*h

84=22/7*49/121*h

84=(22*49/7*121) * h   ( we simplify by 7  and 11)

84=2*7/11 *h

84=14/11 *h

84=14h/11

:14

6=h/11

h=6*11

h=66

The size of the sample space for this experiment is 8.

Informally, the collection of all potential values that an event set may take is referred to as the sample space. A formal definition of sample space is the biggest set in the sigma-algebra, which is the set of probable occurrences for a given random variate.

The set of all potential outcomes or results of an experiment or random trial is referred to as the sample space in probability theory. The potential ordered outcomes, or sample points, are listed as elements in a set that is used to represent a sample space.

Rolling a die has 6 outcomes and rolling a coin has 2 outcomes.

Sample = {HT, TH, 1, 2, 3 , 4, 5 ,6 }

Size of sample size = 8

The size of the sample space for this experiment is 8.

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The expression for r in terms of R is: r = (1-R²) / R²

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 multiplied by itself gives 9:

3 x 3 = 9

The square root symbol is √, and the number under the symbol is called the radicand. So, √9 is read as "the square root of 9."

Starting with the given equation:

R = √(r-1) / √(r+1)

Let's first clear the square roots by squaring both sides:

R² = (r-1) / (r+1)

Now, let's multiply both sides by (r+1) to eliminate the denominator on the right-hand side:

R²(r+1) = r-1

Expanding the left-hand side:

R²r + R² = r-1

Subtracting R²r from both sides:

R² - R²r = -1

Factoring out R² on the left-hand side:

R²(1-r) = -1

Dividing both sides by (1-r):

R² = -1 / (1-r)

Finally, we can take the square root of both sides and multiply by -1 to isolate r:

r = -1 / R² + 1

Therefore, the expression for r in terms of R is:

r = (1-R²) / R²

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Make r the subject of the following:

R= √(r-1) / √(r+1)

Answer:

3

Step-by-step explanation:

11-8

8-5=3

5-2=3

y=3x+14

so,the slope is 3

Answer:

is b i think

hope my answer help you

Answer:

n has to be negative

The dimensions of the largest rectangle that can be formed if all the sides (including the partition) sum to 600 units are 150 units x 150 units. This solution yields an area of 22,500 square units.

To find the dimensions of the largest rectangle that can be formed if all the sides (including the partition) sum to 600 units, we can use the concept of optimization. Let's assume that the rectangle has a length of L and a width of W, with a partition dividing it into two smaller rectangles.
Since all the sides (including the partition) sum to 600 units, we can express this mathematically as:
L + W + 2x = 600
where x represents the length of the partition. Rearranging the equation, we get:
L + W = 600 - 2x
The area of a rectangle is given by the formula A = L x W. To find the largest possible area of the rectangle, we need to maximize this function.
Substituting the above equation into the area formula, we get:
A = (600 - 2x - W) x W
Expanding and simplifying, we get:
A = 600W - 2W^2 - Wx
To find the maximum value of A, we can differentiate it with respect to W and set it equal to zero:
dA/dW = 600 - 4W - x = 0
Solving for W, we get:
W = (600 - x)/4
Substituting this value of W back into the equation for A, we get:
A = (600 - x)^2/16
To maximize A, we need to minimize x. Since x represents the length of the partition, this means that the partition should be as small as possible. Therefore, the largest rectangle that can be formed will be a square with sides of 150 units, and the partition will have a length of zero.
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