The height of
the
glass
is 7cm and radius is 3cm if the glass is half filled with water find the height of the water.find the area of the water

Answer:

Hundredths: \(\frac{6}{10}\)

6 × 10 = 60 & 10 × 10 = 100

(multiply both the numerator and denominator by 10)

Decimal: 0.6

6 ÷ 10 =

good luck, hope this helps :)

Answer:

Step-by-step explanation:

12,787

a. ^p^ represents the proportion of adults who chose chocolate pie, ^q^ represents the proportion of adults who did not choose chocolate pie, n represents the sample size, E represents the margin of error, and p represents the population proportion.

b. The value of α for a 99.99% confidence level is 0.0001.

a. ^p^ represents the sample proportion of adults who chose chocolate pie, ^q^ represents the proportion of adults who did not choose chocolate pie (1 - ^p^), n represents the sample size of 1500, E represents the margin of error of ±3 percentage points (0.03), and p represents the population proportion of adults who choose chocolate pie.

b. To find the value of α for a 99.99% confidence level, we need to subtract the confidence level from 100% to get the level of significance, which is 0.0001. This means that there is a 0.0001 probability of rejecting the null hypothesis when it is actually true.

The level of significance (α) is used to determine the critical value for the test statistic, which is then used to determine whether or not to reject the null hypothesis.

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The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:it is the fist car

Step-by-step explanation:

Because im so fudgen smart

Answer:

5/32

Step-by-step explanation:

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Holy will take 13/5 or 2.6 hours to finish the bookcase.

The relation between time and work is

Work Done = Time Taken × Rate of Work ·

or, Rate of Work = 1 / Time Taken ·

or, Time Taken = 1 / Rate of Work ·

Now it is given that,

Time taken by Fritz to build a bookcase =  8 hours

So, Bookcase build by Fritz in 1 hour = 1/8

Similarly,

Time taken by Holly to build a bookcase =  10 hours

So, Bookcase build by Holly in 1 hour = 1/10

So, bookcase build in 3 hours

Fritz = 3/8

Holly = 3/10

Total bookcase build in 3 hours =  3/8 + 3/10 =  27/40

So. remaining work =  1 - 27/40 =  13/40

Thus, Time taken by Fritz to complete the bookcase =  8 * (13/40) hours

                                                                                         =  13/5 or 2.6 hours

Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.

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The number ¾1868O 12O 64 in base 10 notation is approximately equal to 2129.16.

The given number is in base 8 (octal) notation, which means each digit can represent any number from 0 to 7. To convert this number to base 10 (decimal) notation,

we need to multiply each digit by the corresponding power of 8 and then add up the products:

38^3 + 18^2 + 68^1 + 88^0 + 18^-1 + 28^-2 + 68^-3 + 48^-4 = 2016 + 64 + 48 + 1 + 0.125 + 0.03125 + 0.001953125 + 0.000244140625 = 2129.15722656

Therefore, the number ¾1868O 12O 64 in base 10 notation is approximately equal to 2129.16.

Alternatively, we can convert the number to base 2 (binary) notation and then to base 16 (hexadecimal) notation, which is equivalent to the given number.

In binary notation, each digit can represent either 0 or 1, and 3 digits correspond to each digit in octal notation. Thus, we have:

011 100 110 100 000 010 110 100

Grouping the digits into groups of 4, we can convert the binary number to hexa decimal notation:

0111 0011 0100 0000 0110 1100

7 3 4 0 6 C

Therefore, the number ¾1868O 12O 64 in hexadecimal notation is 73406C, which is equivalent to the given number in octal notation.

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Answer:

Slope = 1

Step-by-step explanation:

(5,7) (-4,-2) Answer:1

Approximating the sum of the series by the tenth partial sum, we have the following result:

∑ (n=1 to ∞) 1/n^5 ≈ s10 = 1/1^5 + 1/2^5 + 1/3^5 + ... + 1/10^5 ≈ 1/1 + 1/32 + 1/243 + ... + 1/100,000 ≈ 0.8413 (rounded to four decimal places).

In this approximation, we sum the reciprocals of the fifth powers of natural numbers from 1 to 10. The tenth partial sum, denoted as s10, represents the sum of the series up to the 10th term. By evaluating each term and adding them together, we obtain the approximate value of 0.8413. This approximation provides an estimation of the sum of the series while considering a finite number of terms, allowing for a simplified calculation of the overall sum.

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Approximating the sum of the series by the tenth partial sum, we have the following result:

∑ (n=1 to ∞) 1/n^5 ≈ s10 = 1/1^5 + 1/2^5 + 1/3^5 + ... + 1/10^5 ≈ 1/1 + 1/32 + 1/243 + ... + 1/100,000 ≈ 0.8413 (rounded to four decimal places).

In this approximation, we sum the reciprocals of the fifth powers of natural numbers from 1 to 10. The tenth partial sum, denoted as s10, represents the sum of the series up to the 10th term. By evaluating each term and adding them together, we obtain the approximate value of 0.8413. This approximation provides an estimation of the sum of the series while considering a finite number of terms, allowing for a simplified calculation of the overall sum.

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The answer is either 2 cups or slightly more than 2 cups of fluid to rehydrate himself.

Rehydration means replenishing the fluids and electrolytes lost from the body due to various reasons, such as sweating during exercise, diarrhea, vomiting, fever, etc.

It is important to maintain proper hydration levels to keep the body functioning properly.

Here we have

Bert goes to the gym and works out strenuously for about 45 minutes. after his exercise session, he weighs himself and notices that he has lost a pound.  

It is recommended to drink about 16-20 ounces (2-2.5 cups) of fluid for every pound lost during exercise.

Since Bert lost one pound during his workout, he should drink about 16-20 ounces (2-2.5 cups) of fluid to rehydrate his body.

Therefore,

The answer is either 2 cups or slightly more than 2 cups of fluid to rehydrate himself.

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The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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The correct answer is 51, which is the next closest value to 30 after 41. the answer is option D, 51.

To find the approximate difference in tenths between 12 and 15, we need to subtract 12 from 15 and then convert the answer into tenths.

This can be done as follows:15 - 12 = 3Then, to convert the answer into tenths, we need to multiply by 10, which gives 3 x 10 = 30

Therefore, the approximate difference in tenths between 12 and 15 is 30. The answer choice closest to this is 20, but it is not correct since it is too low.

The answer choice that is closest to 30 is 41, but it is too high.

The key takeaway from this problem is to be careful when converting between units. In this case, we needed to convert the difference from 3 to 30 by multiplying by 10, which is equivalent to moving the decimal point one place to the right.

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The correct answer is B. The sample mean being greater than 30 is not a requirement for testing a claim about a population mean with σ known.

The requirements are that either the population is normally distributed or n > 30 or both, the value of the population standard deviation is known, and the sample is a simple random sample. The hypothesis test for a population mean with σ known involves calculating the z-score by subtracting the population mean from the sample mean and dividing it by the standard deviation of the sampling distribution.

If the calculated z-score falls within the rejection region, we reject the null hypothesis and conclude that the sample mean is significantly different from the population mean. It is important to ensure that all the requirements are met before conducting the hypothesis test to obtain accurate and reliable results.

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Answer:

C, and x=30

Karen had a gift card for $150. She bought 3 gifts for her sisters. The gifts cost the same amount, x. After paying for the gifts, her gift card had a balance of $60.

Step-by-step explanation:

Answer:

a) I=9,5

b) x=43

c) I is same for every  value of y and x if the relationship is proportional.

Step-by-step explanation:

The constant of proportionality I can be found as: \(\mathbf{I=\frac{y}{x}}\)

a)

We are given: x= 29, y=275.5 we need to find constant of proportionality I

Using formula:

\(\mathbf{I=\frac{y}{x}}\\I=\frac{275.5}{29}\\I=9.5\)

So, constant of proportionality I = 9.5

b)

Now, we need to find x when y is 408.5.

Using the above formula we can find x

\(I=\frac{y}{x}\\9.5=\frac{408.5}{x}\\x=\frac{408.5}{9.5}\\x=43\)

c)

A relationship is proportional if for every value of x and y we have a relation: \(\mathbf{I=\frac{y}{x} }\) where I is constant. The value of I is same for every value of y and x.

If a relationship is not proportional then for every value of x and y we have don't have a relation: \(\mathbf{I=\frac{y}{x} }\) where I is constant. The value of I is different for every value of y and x.

The vertex form of the quadratic equation is:

y = (x - 3)² - 16

To complete squares we need to use the perfect square trinomial:

(a + b)² = a² + 2ab +b²

The given quadratic can be rewritten as:

y = x² - 2*3*x - 7

We can add and subtract 3²  = 9 to get:

y = x² - 2*3*x + 9 - 9- 7

y = (x - 3)² - 16

That is the quadratic equation in vertex form, wehre the vertex is (3, -16)

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The given logical expression (((P→Q)↔(¬Q∨R))∧(P→¬R))→¬((S∨R)←(¬R∧P)) simplifies to ¬((R→(¬Q∧(S∨¬P)))∨(P∧(¬Q∨R))) using logical equivalences.

To simplify the given expression, we can use logical equivalences to rewrite it.

We start by applying the equivalence of ↔ (if and only if) to (P→Q)↔(¬Q∨R). This becomes ((P→Q)∧(¬Q∨R))∨(¬(P→Q)∧¬(¬Q∨R)).

We then simplify (P→Q)∧(¬Q∨R) to (¬P∨Q)∧(¬Q∨R).

Next, we use the implication P→¬R to simplify it to ¬P∨¬R.

We substitute the simplified expressions from step 2 and step 3 into the original expression. (((¬P∨Q)∧(¬Q∨R))∨(¬(¬P∨Q)∧¬(¬Q∨R)))→¬((S∨R)←(¬R∧P)).

We use the equivalence of ← (left implication) to simplify (S∨R)←(¬R∧P) to (¬R∧P)→(S∨R).

Finally, we simplify the expression further and obtain ¬((R→(¬Q∧(S∨¬P)))∨(P∧(¬Q∨R))) as the simplified form.

The second given expression (R∨(¬Q∧(S∨¬P)))→(P∧(¬Q∨R)) remains unchanged.

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Answer:

Step-by-step explanation:

y = 4 + 3x

3x + 4 = y

     - 4 - 4

3x = y - 4

/ 3      / 3

x = 1/3y - 4/3

Answer:

Depends on your sales tax rate where you live.

Lets call your sales tax rate X%

then it would be multiplied b y the $850 and that would be added back to the $850.

Example:

If your sales tax rate were 10%

then it would be .10 x $850 =$85

Now add the $85 to the $850 and your total would be $945

P.S. Some localities offer sales tax free weekends for school supplies.

Step-by-step explanation:

From the question, the sum of each of the geometric sequence are;

1)  31 3/4

2) 340

3) 11/16

4) -6, 12, -24

We have that;

Sn = a(1 -\(r^n\))/1 - r

Sn = 16(1 \(- (1/2)^7\))1 - 1/2

Sn = 16(1 - 1/128)/1/2

Sn = 16(127/128) * 2

Sn = 31 3/4

2) Un = a\(r^n\) -1

256 = \(4(4)^n-1\)

64 =\(4^n-1\)

\(4^3 = 4^n-1\)

n = 4

Sn= \(4(4^4 - 1)\)/4 - 1

Sn = 340

3) Since we have a5 then n = 5

Sn = 1(1 - (\(-1/2)^5\))/1 -(-1/2)

Sn = 33/32 * 2/3

= 11/16

4) 30= a(1 -\((-2)^4\))/1 - (-2)

30 = a(-15)/3

30 = -5a

a = 30/-5

a = -6

Then the first three terms are;

-6, 12, -24

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The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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