Ann, Ben, and Cindy were eating strawberries. The ratio of the numbers of berries they ate is 5:5:7. If Cindy ate 30 strawberries less than Ann and Ben together, what is the total number of strawberries the three of them ate?
Answer:

Answer:

A

Step-by-step explanation:

5/18 = 0.2777 = 0.27° so when you divided thd no. it is 0.277777 and 7 is repeat .

Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

The approximate amount of interest earned on the investment is c. $720.37.

The formula to calculate compound interest is given by:

\(A = P(1 + r/n)^{nt}\)

Where:

A = the final amount (including principal and interest)

P = the principal amount (initial investment)

r = annual interest rate (as a decimal)

n = number of times interest is compounded per year

t = number of years

In this case, the principal amount (P) is $2,000, the annual interest rate (r) is 6.2% (or 0.062 as a decimal), the interest is compounded quarterly (n = 4), and the investment is held for 5 years (t = 5).

Plugging these values into the formula, we can calculate the final amount (A):

\(A = 2000(1 + 0.062/4)^{4*5}\\A ≈ $2,720.37\)

To calculate the interest earned on the investment, we subtract the principal amount from the final amount:

Interest = A - P

Interest ≈ $2,720.37 - $2,000

Interest ≈ $720.37

Therefore, the approximate amount of interest earned on the investment is $720.37. So the correct answer is c. $720.37.

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Answer:

<FGH and <JKL are supplementary

<AED and <BEC are complementary

Step-by-step explanation:

For supplementary angles, the sum of the pair of angles must be 180degrees

Given;

<FGH = 109degrees

<JKL = 71degrees

Taking the sum

<FGH + <JKL

= 109 + 71

= 180

Since the sum of the angles is 180, hence <FGH and <JKL are supplementary

Similarly;

Given

<AED = 45degrees

<BEC = 45degrees

Taking the sum

<AED + <BEC

= 45 + 45

=90degrees

Since the sum of complementary angles is 90degrees, hence <AED and <BEC are complementary

Positional numeration is a system of representing numbers using positional notation. In this system, each digit represents a multiple of the base of the number system, which is usually 10 in our decimal system. The number 3.15569 x 10^7 in positional numeration is 31,556,900.

The value of a digit is determined by its position, with the rightmost digit representing the ones place, the next digit to the left representing the tens place, and so on. To convert the given number, 3.15569 x 10^7, into positional numeration, we first need to express it in scientific notation. In scientific notation, a number is expressed as a product of a coefficient and a power of 10. In this case, the coefficient is 3.15569, and the power of 10 is 7. Therefore, the given number can be expressed as: 3.15569 x 10^7

To convert this number into positional numeration, we can simply multiply the coefficient by the power of 10. This can be done by moving the decimal point of the coefficient 7 places to the right, since 10^7 is a power of 10 with exponent 7. The resulting number is: 31,556,900

Therefore, the number 3.15569 x 10^7 in positional numeration is 31,556,900. It is important to remember that positional numeration is a system of representing numbers using positional notation based on the base of the number system, which is usually 10 in our decimal system.

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In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.

The load from the structural element is transferred to the foundation at a bearing point, which is often a concentrated load point.

To avoid structural failure, settling, or excessive deflection of the part, it is crucial to make sure the bearing point is properly designed and supported.

Since the bearing of C from A is 050°, we can find the bearing of A from C by adding 180° to 50°, which gives us:

Bearing of A from C = 50° + 180° = 230°

Therefore, In the context of engineering and construction, a bearing point refers to a specific location or area. The bearing of A from C is 230°.

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Complete question -

Answer:1=157 2=23 3=157 4=23 5=157 6=23 7=157 8=23

Step-by-step explanation:

theyre congruent

Answer: The answer is 60p.

Step-by-step explanation:

1) You first simplify what is in parenthesis.

         (6p+9p) = (15p)

2) Next, you multiply (15p) by 4.

        4(15p) = 60p

3) You simplified the expression of

        4(6p+9p) to 60p.

The derivatives of the given functions are as follows: u'(x) = cos(x), v'(x) = \(5x^4\), and f'(x) = \((u'(x)v(x) - u(x)v'(x))/v(x)^2 = (cos(x)x^5 - sin(x)(5x^4))/(x^{10})\).

To find the derivative of u(x), we differentiate sin(x) using the chain rule, which gives us u'(x) = cos(x). Similarly, to find the derivative of v(x), we differentiate x^5 using the power rule, resulting in v'(x) = 5x^4.

To find the derivative of f(x), we use the quotient rule. The quotient rule states that the derivative of a quotient of two functions is given by (u'(x)v(x) - u(x)v'(x))/v(x)^2. Applying this rule to f(x) = u(x)/v(x), we have f'(x) = (u'(x)v(x) - u(x)v'(x))/v(x)^2.

Substituting the derivatives we found earlier, we have f'(x) = \((cos(x)x^5 - sin(x)(5x^4))/(x^10)\). This expression represents the derivative of f(x) with respect to x.

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Answer:

Nancy types the fastest

Answer:

Nacy

Step-by-step explanation:

Jake types 24 wpm

Sam types 22 wpm

Nacy types 25 wpm

In 9 minutes Jake would type 216 words

In 9 minutes Sam would type 198 words

In 9 minutes Nacy  would type 225 words.

Given this information Nacy types the fastest

Hope this helps :)

Exact Form:

1/27

Decimal Form:

0.037 (with a line over 037)

Answer:

it lies in the middle term in the arranged data set the medium class interval is corresponding were the medium Value falls

Step-by-step explanation:

I hope it will help

The simplified form of the trigonometric expression is:  \($-\cos(2\alpha) + \cos^2(\alpha)$\).

To simplify the trigonometric expression \($\sin^4(\alpha) - \cos^4(\alpha) + \cos^2(\alpha)$\), we can use some trigonometric identities.

First, let's recall the identity for the difference of squares:

\($a^2 - b^2 = (a + b)(a - b)$\)

Now, let's rewrite the expression using this identity:

\($\sin^4(\alpha) - \cos^4(\alpha) = (\sin^2(\alpha) + \cos^2(\alpha))(\sin^2(\alpha) - \cos^2(\alpha))$\)

Since \($\sin^2(\alpha) + \cos^2(\alpha) = 1$\) (by the Pythagorean identity), we can simplify further:

\($(\sin^2(\alpha) + \cos^2(\alpha))(\sin^2(\alpha) - \cos^2(\alpha)) = 1(\sin^2(\alpha) - \cos^2(\alpha))$\)

Now, we can use the identity \($\sin^2(\alpha) - \cos^2(\alpha) = -\cos(2\alpha)$\) to simplify:

\($1(\sin^2(\alpha) - \cos^2(\alpha)) = -\cos(2\alpha)$\)

Finally, adding \($\cos^2(\alpha)$\) to the expression:

\($-\cos(2\alpha) + \cos^2(\alpha)$\)

Therefore, the simplified form of the trigonometric expression \($\sin^4(\alpha) - \cos^4(\alpha) + \cos^2(\alpha)$\) is \($-\cos(2\alpha) + \cos^2(\alpha)$\).

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Complete question:

Simplify the trigonometric expression. \($$\sin ^4(\alpha)-\cos ^4(\alpha)+\cos ^2(\alpha)$$\).

Answer: 5.19 cm.

Step-by-step explanation: Area= l*w so then that also means that l=area/width. So you can divide 6.12 by 1.18 to get 5.19cm.

Answer:

p = 16x² + 38y

Step-by-step explanation:

x + 10y + x + 10y + 8x² - x + 9y + 8x² - x + 9y

Simplify:

16x² + 38y

good luck, i hope this helps :)

Answer:

\(\huge\boxed{\bf\:1}\)

Step-by-step explanation:

\(\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\)

Take \(\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 }\) & factorise it at first.

\(\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \\= \frac{\left(x-3\right)\left(x-1\right)}{\left(x-4\right)\left(x-3\right)}\\= \frac{x-1}{x-4}\)

Now factorise the next set : \(\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\).

\(\frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{\left(x-4\right)\left(x+6\right)}{\left(x-1\right)\left(x+6\right)}\\= \frac{x-4}{x-1}\)

Now, multiply the two simplified results.

\(\frac{ x ^ { 2 } -4x+3 }{ x ^ { 2 } -7x+12 } \times \frac{ x ^ { 2 } +2x-24 }{ x ^ { 2 } +5x-6 } ^ { }\\= \frac{x-1}{x-4}\times \frac{x-4}{x-1} \\= \frac{\left(x-1\right)\left(x-4\right)}{\left(x-4\right)\left(x-1\right)} \\= \boxed{\bf\: 1}\)

\(\rule{150pt}{2pt}\)

Centre ( - 10 , 7 )

Radius -> 4 unit

No, milliliters (mL) and centiliters (cl) are not the same units of measurement. They are both units of volume, but with different scales.

A milliliter (mL) is a unit of volume in the metric system, equal to one-thousandth of a liter (1 mL = 0.001 L). Milliliters are commonly used to measure the volume of liquids, such as medicine or cooking ingredients.

A centiliter (cl) is also a unit of volume, and it is equal to one hundredth of a liter (1 cl = 0.01 L). Centiliters are less commonly used than milliliters and are generally used in the same contexts where milliliters are used.

In conclusion, mL and cl are different units of volume and cannot be used interchangeably. Milliliters are smaller units than centiliters, so when converting between the two, a conversion factor of 10 must be used. For example, 1 cl = 10 mL.

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20,000 = 1750 e^(0.6t)

Divide both sides by 1750:

11.43 = e^(0.6t)

Take the natural log of both sides:

ln(11.43) = 0.6t

Divide both sides by 0.6:

t ≈ 6 years

So it will take approximately 6 years (rounded to the nearest year) for the town's population to reach 20,000.
To find the number of years it takes for the population to reach 20,000, we need to solve the equation for t, using the given equation:

20,000 = 1750 * e^(0.6 * t)

Step 1: Divide both sides of the equation by 1750:
20,000 / 1750 ≈ 11.43 = e^(0.6 * t)

Step 2: Take the natural logarithm (ln) of both sides:
ln(11.43) ≈ 2.435 ≈ 0.6 * t

Step 3: Divide both sides by 0.6 to isolate t:
2.435 / 0.6 ≈ t

Step 4: Calculate t:
t ≈ 4.06

Approximately, it will take 4 years (rounded to the nearest year) for the town's population to reach 20,000.

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The expected value of X is 297/35 and the variance of X is 774/1225.

Let's define the indicator random variable Xi as follows:

Xi = 1, if the i-th roll results in a new number (that hasn't been rolled before).

Xi = 0, otherwise.

Then, X is the sum of these indicator variables, that is:

X = X1 + X2 + X3

We know that E[Xi] = 1/p, where p is the probability of rolling a new number on the i-th roll, given that i - 1 distinct numbers have already been rolled. Since there are i - 1 distinct numbers already rolled, the probability of rolling a new number on the i-th roll is (6 - i + 1)/6.

Thus, we have:

E[Xi] = 6/(6-i+1) = 6/(7-i)

Using the linearity of expectation, we can find the expected value of X:

E[X] = E[X1] + E[X2] + E[X3] = 6/7 + 6/6 + 6/5 = 297/35

To find the variance of X, we need to calculate the variance of each Xi:

Var(Xi) = E[Xi^2] - E[Xi]^2

We know that:

E[Xi^2] = 1(6-i+1)/6 + 0(i-1)/6 = (7-i)/6

So, we have:

Var(Xi) = (7-i)/6 - (6/(7-i))^2

Using the linearity of variance, we can find the variance of X:

Var(X) = Var(X1) + Var(X2) + Var(X3)

= (4/6) - (6/7)^2 + (3/6) - (6/6)^2 + (2/6) - (6/5)^2

= 774/1225

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Answer: 3/2

Step-by-step explanation:

\(\frac{7-1}{5-1}=\frac{6}{4}=\frac{3}{2}\)

The 3rd option is correct

Answer:

A) $425.92

Step-by-step explanation:

The new price percentage with relation to the previous can be determined by dividing \(p = \frac{484}{550}\). Once we calculate p, we can multiply it by 484, which is equivalent to applying the same discount, thus \(\frac{484}{550}484=425.92\)

The total number of visitors visited to Mr. carl burl's exhibition in first three hours are 16.

For the given question-

The graph for the number of visitors who visited his exhibit in the first 8 hours of opening day is show -

The number of customers vising in first three hours are-

Total visitors = 1st hour + 2nd hour + 3rd hour

Total visitors = 4 + 5 + 7

Total visitors = 16

Thus, the total number of visitors visited to Mr. carl burl's exhibition in first three hours are 16.

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The complete question with diagram is attached,

mr. carl burl, an artist, has recorded the number of visitors who visited his exhibit in the first 8 hours of opening day. he has made a scatter plot to depict the relationship between the number of hours and the number of visitors.

How many visitors came to his exhibition in first three hours.

The area is equal to 324π square units.

To find the area of a circle with radius 18 units, we can use the formula for the area of a circle, which is given by A = πr^(2), where r is the radius.

Given that the radius is 18 units, we can plug this value into the formula:

A = π(18)^2

Now, square the radius:

A = π(324)

Next, multiply 324 by π:

A = 324π

Therefore, the area of the circle with radius 18 units is 324π square units.

Now, let's compare the options with the given options:

a) 18π units^(2)- This is incorrect, as we calculated the area to be 324π square units.

b) 36π units^(2)- This is also incorrect, as our calculated area is 324π square units.

c) 9π units^(2)- This is incorrect, as our calculated area is 324π square units.

d) 324π units^(2)- This is the correct option , as we calculated the area to be 324π square units.

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Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Initial investment (PV)= $7,000

Interest rate (i)= 2.5%

To calculate the future value after x years, we need to use the following formula:

FV= PV*(1 + i)^x

Now, for 9 years:

x= 9

FV= 7,000*(1.025^9)

FV=$8,742.04

Answer:

A

Step-by-step explanation:

We have the function:

\(f(x)=2x+5\)

And we want to find f(11).

So, we can substitute 11 for our function and evaluate. Therefore:

\(f(11)=2(11)+5\)

Evaluate:

\(f(11)=22+5=27\)

Hence, our answer is A.