Tracy is designing a desk decoration which is part of a
sphere 8 cm in diameter.
The decoration is 7 cm high.
The diagram shows a cross-section of the decoration.
The equation of the circle is x² + y² = 16
a Write down the equation of the base.
b Solve these simultaneous equations and find the diameter of the base.

Answer

62

Step-by-step explanation:

The given equation represents a sinusoidal voltage source with amplitude 15V and frequency 500 Hz. The circuit connected to this voltage source needs to be analyzed to find the essential nodes.

To find the essential nodes, we need to analyze the circuit connected to the given voltage source. Essential nodes are the points in the circuit where the voltage cannot be determined by using Kirchhoff's laws alone. They are the points where the circuit needs to be divided into separate parts and analyzed separately. The number of essential nodes in a circuit depends on the complexity of the circuit and the number of independent loops. Conclusion: The given equation represents a sinusoidal voltage source with amplitude 15V and frequency 500 Hz. To find the essential nodes in the circuit connected to this voltage source, we need to analyze the circuit. The number of essential nodes in a circuit depends on the complexity of the circuit and the number of independent loops. Therefore, without additional information about the circuit, we cannot determine the number of essential nodes.

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The expressions 10x-7 and 7-10x represent the statement "seven less than ten times a number".

The verbal expression "seven less than ten times a number" can be written mathematically in different ways, depending on the intended meaning. One possible expression is:

10x - 7

In this expression, "10x" represents ten times a number, and "-7" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting 7 from the product of 10 and the number x.

Another possible expression is 7 - 10x

In this expression, "10x" represents ten times a number, and "7 - 10x" represents seven less than that quantity. Thus, the entire expression represents the result of subtracting the product of 10 and the number x from 7.

If the focus is on finding the result of subtracting 7 from ten times a number, the first expression is more appropriate. If the focus is on finding the result of subtracting the product of 10 and a number from 7, the second expression is more appropriate.

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The required bunny hopped 32 units on the number line and bunny's average speed was 6.4 units per minute.

The distance the bunny hopped is the absolute value of the difference between its starting point and ending point on the number line:

\(\begin{align*}\left|-66 - (-34)\right| &= \left| -66 + 34\right| \&= \left|-32\right| \&= 32\end{align*}\)\($\begin{align*}\left|-66 - (-34)\right| &= \left| -66 + 34\right| \&= \left|-32\right| \&= 32\end{align*}$\)

So the bunny hopped 32 units on the number line.

To find the bunny's average speed, we need to know the formula:

\($\text{Average Speed} = \frac{\text{Distance Traveled}}{\text{Time Elapsed}}$$\)

We know that the bunny traveled 32 units and that it took 5 minutes to do so, so we can substitute those values into the formula:

\($\begin{align*}\text{Average Speed} &= \frac{\text{Distance Traveled}}{\text{Time Elapsed}} \&= \frac{32}{5} \&= 6.4\end{align*}$\)

Therefore, the bunny's average speed was 6.4 units per minute.

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The expected number of coins that are heads at the end after Jennifer has tossed 64 fair coins and those that landed on tails were tossed again is 32. the expected number of coins that are heads at the end is 48.

Here is a detailed explanation:Jennifer tosses 64 coins, and each coin has an equal chance of landing on either heads or tails. Thus, the probability that any one coin lands on heads is 0.5, and the probability that it lands on tails is also 0.5.When Jennifer tosses the 64 coins, some of them will land on tails.

Those coins will be tossed again. However, the probability of getting heads or tails for these coins is still 0.5 since the coins are fair.Therefore, the probability that a coin that has already been tossed and landed on tails to land on heads the second time is also 0.5.

The same applies to the third toss. The probability that a coin will land on heads or tails is 0.5.The total number of coins that land on tails during the first toss is given by

64*0.5 = 32.

Since these coins are tossed again, the expected number of coins that land on tails for the second toss is given by

32*0.5 = 16.

The remaining coins that landed on heads during the first toss are not affected. Thus, the expected number of coins that landed on heads during the first toss is

64 - 32 = 32.

The total number of coins that landed on heads during the first toss is given by 32.

Adding the expected number of coins that land on heads during the second toss (16),

the expected number of coins that land on heads is

32 + 16 = 48.

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The range or the given data is calculated as 10.2 . Range is the difference between minimum value and maximum value.

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we can make use of the formula for range in statistics which is given as follows:[\large Range = Maximum\ Value - Minimum\ Value\]

To find the range in the following data 1.0, 7.0, 4.8, 1.0, 11.2, 2.2, 9.4, we need to arrange the data in either ascending or descending order, but since we only need to find the range, it is not necessary to arrange the data.

From the data given above, we can easily identify the minimum value and maximum value and then find the difference to get the range.

So, Minimum Value = 1.0

Maximum Value = 11.2

Range = Maximum Value - Minimum Value

                  = 11.2 - 1.0

                     = 10.2

Therefore, the range of the given data is 10.2.

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The roots of the polynomial functions are

(a) x = -1 or x = -1.2 and x = -0.16

(b) x = -1/7 or x = 2

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

a) y = (x + 1)(5x² + 7x + 1)

b). y = (7x + 1) (2x - 4)

The roots of the polynomial functions are calculated by setting the functions to 0

So, we have

(x + 1)(5x² + 7x + 1) = 0

(7x + 1) (2x - 4) = 0

Using the zero product property, we have

x + 1 = 0 or 5x² + 7x + 1 = 0 and

7x + 1 = 0 or 2x - 4 = 0

When evaluated, we have

x = -1 or x = -1.2 and x = -0.16

x = -1/7 or x = 2

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Complete question

For each polynomial function below, determine all of the roots.

a) y = (x + 1)(5x² + 7x + 1)

b). y = (7x + 1) (2x - 4)

Answer:

Step-by-step explanation:

Hope it helped you

Answer:

1. [A] More than 205

2. [B] less than 10

3. [B] less than 0.2

Step-by-step explanation:

1. The value of 25 · (8.5) is:

a. More than 205

b. Less than 205

Solve:

25 · (8.5) = 212.5

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2. The value of (9.93) · (0.984) is:

a. More than 10

b. Less than 10

(9.93) · (0.984) = 9.77112

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

3. The value of (0.24) · (0.67) is:

a. More than 0.2

b. Less than 0.2

(0.24) · (0.67) = 0.1608

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~lenvy~

2/5th of a number is 40% of that number.

In order to calculate the percentage of a given number that is equal to 2/5 of that number, we must first convert the fraction to percentage form, which is as follows:

= 2/3 * 100

= 0.4 * 100

= 40%

We will use the following example to validate the aforementioned process:

Assume that it is 50.

First, 2/5 of 50 equals 2/5 * 50, or 20.

Second, 40% of 50 equals 40/100 * 50 = 0.4 * 50 = 20.

The equality of the two results is evident.

2/5 of a number is therefore 40% of that number.

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The question is incomplete;

\dfrac25 start fraction, 2, divided by, 5, end fraction of a number is what percentage of that number?

The cost percentage is 3.61 %.

A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting.

A percentage is calculated by dividing a value or a number by its sum, then multiplying the result by 100. The percentage calculation formula is ( value / total value) × 100%.

The cost of all ingredients mixed in the stew is $2.76.

The total sales is $435.98.

57 gallons of stew are sold per week.

Therefore, the total sales per week is

= $2.76 × 57 = $157.32

Hence, the cost percentage of food is:

= ( 2.76 × 57 ) / 435.98

= 157.32 / 435.98

= 0.361

= 3.61 %

The cost percentage of the food is 3.61 %.

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Answer:

3x+20

Step-by-step explanation:

The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

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Answer:

earplugs

Step-by-step explanation:

Because sound waves absorb most sound, the sound is coming from the earplugs which creates the most sound waves rather than water, tissue paper, and air.

Answer:

Water

Step-by-step explanation:

In linear equation, 1875  does Hoppy weight .

What are instances of linear equations?

A = 42b = 56c

a : b : c  = 42 : 100 : 75

total Mr Flopsy weights = 2500

then  Hoppy weight =  75 = 2400/100 * 75

                                  = 1875

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She have 18 color pencils.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Number of Marcus violet have = 3

She has six times as many colored pencils as Marcus.

Now,

Since, Number of Marcus violet have = 3

Hence, Number of Marcus she have = 3 x 6

                                                        = 18

Thus, She have 18 color pencils.

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Answer:

Find two numbers that multiply to equal the original number; write them as numbers that branch off the original one. ..

.If either number is prime, circle it and end that branch.

Continue branching off non-prime numbers into two factors; whenever a branch reaches a prime number, circle it and close the branch.

The type of experiment design described in the scenario is: B) Stratified.

In this design, the population is divided into homogeneous groups (in this case, males and females) called strata. Then, within each stratum, participants are randomly assigned to different treatment groups (treatment and control groups).

This approach ensures that each stratum is represented equally in both treatment groups, allowing for comparisons within each group and reducing potential confounding variables.

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Answer:

D and E

Step-by-step explanation:

Let's double check:

D. 9 ÷ 3 = 3

E. 4 × 9 = 36

---------------------------------------------------------------------------------------------------------------

Have a great summer :)

Answer:

the answers would be A, D, and E

Step-by-step explanation:

just replace the Cs with the number 9 and solve from there.

for example c/3=3 would say 9/3=3

Answer:

3 in.

Step-by-step explanation:

volume = ⅓πr²h

⅓πr²h=12π

r²h=36

r²=9

r = 3 inches

Answer:3 4/5

Step-by-step explanation:

Answer:

3 4/5

Step-by-step explanation:

Thus, we need a sample size of at least 22 to obtain a 90 percent confidence interval for the mean protein content of meat with an estimate within 2 pounds of the true mean value.

To obtain a 90 percent confidence interval for the mean protein content of meat with an estimate within 2 pounds of the true mean value, we need to calculate the required sample size. The formula for the required sample size is:

n = (Zα/2 * σ / E)^2

where n is the required sample size, Zα/2 is the z-score for the desired confidence level (in this case 90%), σ is the standard deviation of the population (in this case 7 pounds, the square root of the variance), and E is the margin of error (in this case 2 pounds).

Plugging in the values, we get:

n = (1.645 * 7 / 2)^2
n = 21.16

Therefore, we need a sample size of at least 22 to obtain a 90 percent confidence interval for the mean protein content of meat with an estimate within 2 pounds of the true mean value. It is important to note that this assumes that the sample is drawn randomly and is representative of the population.

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Answer:

angle 1= 110 degrees

Step-by-step explanation:

A line = 180 degrees

Since angle 1 and 4 make a line then both of them have to equal 180 degrees.

So, you would just subtract 180-70(angle 4)= 110 which gives you angle 1.

You could do the same with angle 4 and 3, angle 3 and 2, and angle 2 and 1 since they all form a line.

The extreme values of the function f(x, y) = xy(2y^2 x^4 − y^4) on the circle x^2 + y^2 = 1 are approximately ±0.235

To find the extreme values of the given function f(x, y) = xy(2y^2 x^4 − y^4) on the circle x^2 + y^2 = 1, we can use the method of Lagrange multipliers.

First, we write down the Lagrangian function L(x, y, λ) as follows:

L(x, y, λ) = xy(2y^2 x^4 − y^4) + λ(x^2 + y^2 − 1)

Then, we take the partial derivatives of L with respect to x, y, and λ and set them equal to zero:

∂L/∂x = y(2y^2 x^4 − y^4) + 2λx = 0

∂L/∂y = x(6y^3 x^4 − 4y^3) + 2λy = 0

∂L/∂λ = x^2 + y^2 − 1 = 0

Simplifying the first two equations, we get:

2y^5 x^4 − y^5 + 2λxy = 0

6y^4 x^4 − 4y^4 + 2λxy = 0

Dividing these equations, we obtain:

3x^4 = 2y^2

Substituting this back into the equation x^2 + y^2 = 1, we get:

3x^4 + x^2 = 1

This is a quartic equation in x^2. We can solve it using numerical methods to get the two possible values of x:

x ≈ ±0.681

y ≈ ±0.732

Plugging these values into the equation 3x^4 = 2y^2, we get:

y ≈ ±0.524

Now we can calculate the corresponding values of the function f(x, y) = xy(2y^2 x^4 − y^4):

f(x, y) ≈ ±0.235

Therefore, the extreme values of the function f(x, y) on the circle x^2 + y^2 = 1 are approximately ±0.235, and they are attained at the points (±0.681, ±0.732) and (±0.732, ±0.681).

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Answer:x=20

Step-by-step explanation:

Answer:

I think is x=-20

I might have calculated wrong

Answer:

30

Step-by-step explanation:

500 g = 1/2 kg => 2 weeks he loses 1 kg

105 - 90 = 15 kg

So he needs to take 30 weeks in total. ( 15 * 2)

Let weeks be x

So

Answer:

c divided by 1/3

Step-by-step explanation:

if you plug in a number for c and solve for each of the equations you will find that c is false so it can't be used. for example if i use the number 30 for c, i get 10 for every single equation except for the last one

Answer:

36-x≥24

Step-by-step explanation:

Answer:

The Correct answer is

57°

The probability of choosing the first chip white and the second chip red is 1/15.

In order to find the probability of choosing the first chip white, then the second chip red (without replacement), the total number of ways the chips can be chosen will be considered.

The probability of choosing the first chip white and the second chip red is given by;

P(white, red) = P(white) * P(red | white is chosen first)

Where, P(red | white is chosen first) is the probability that the second chip drawn is red given that a white chip is drawn first.

The probability of choosing a white chip as the first chip is 2/10 or 1/5. Without replacing the first chip, there are now 9 chips remaining, of which 3 are red chips.

Hence, the probability of choosing a red chip given that a white chip was drawn first is 3/9 or 1/3.

Using the above information,

P(white, red) = P(white) * P(red | white is chosen first)P(white, red) = (2/10) * (1/3) = 1/15

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