Stefan is making meringue with eggs whites and sugar. he uses 50 grams of sugar for every egg white.

if Stefan is making 10 egg whites. how many grams of sugar does he use?

The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

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9514 1404 393

Answer:

  $7.50

Step-by-step explanation:

The monthly interest rate is 3%/12 = 1/4%. The dollar amount of interest earned in 3 months is ...

  I = Prt = $1000(0.0025/mo)(3 mo) = $1000(0.0075) = $7.50

Erna Corporation is evaluating between giving an extra dividend versus a share repurchase. Either way, $515000 will be spent. The current earnings are $2.50 per share, and the stock is currently selling for $50 per share. There are 4000 shares outstanding.

Ignoring taxes and other imperfections, we shall compute the amount of dividends that can be given to shareholders.Suppose the company decided to distribute the entire $515000 as a dividend. The dividend per share would be equal to the total dividend amount divided by the number of shares outstanding. Then:$515000/4000 = $128.75 per share dividendIf the company decided to use the $515000 to buy back shares of stock, the amount of shares that can be repurchased would be equal to the repurchase amount divided by the market price per share.

Then:$515000/$50 = 10300 shares repurchasedThe effect of the two methods on the market price per share would depend on the market conditions, but the two methods should have an equal effect. The dividend would decrease the market price per share by the amount of the dividend, while the share repurchase would increase the market price per share by reducing the number of shares outstanding.

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In bayes theorem, you have some starting information, then you collect some new information so that you can UPDATE the original probabilities so you now have better information.

The Bayes' theorem, commonly referred to as the Bayes' rule, is a mathematical formula used in statistics and probability theory to calculate the conditional probability of events. The Bayes theorem essentially describes the likelihood of an event based on prior knowledge of any circumstances that might be relevant to the event.

P(A|B) = \(\frac{ P(A) P(B|A)}{P(B)}\)

So it is always the case of conditional probability.

Hence, the original probability is always updated in case of Baye's theorm.

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Answer:

12x³ - 8x² - 54x - 36

Step-by-step explanation:

The polynomial is the product of the factors, that is

(- 4x - 6)(- 3x² + 5x + 6)

Each term in the second factor is multiplied by each term in the first factor, that is

- 4x(- 3x² + 5x + 6) - 6(- 3x² + 5x + 6) ← distribute both parenthesis

= 12x³ - 20x² - 24x + 18x² - 30x - 36 ← collect like terms

= 12x³ - 8x² - 54x - 36

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For a. 10.2,

For b. 70,

For c. 0.15,

For d. 4,

For e. 13.02,

For f. 45.4

The area of the triangle is 31.54 square units

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

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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Answer:

-40

Step-by-step explanation:

-7 x 7 + 9 x (-1) / (-1)

-49 + 9 x (-1) / (-1)

-49 - 9 / (-1)

-49 + 9

= -40

To find the probability of drawing a face card or a red card, we first need to determine the total number of favorable outcomes and then divide it by the total number of possible outcomes (52 cards in a deck).

A face card can be a King, Queen, or Jack, and there are 12 face cards in a deck (3 face cards x 4 suits). There are 26 red cards in a deck (13 cards from hearts suit and 13 cards from diamonds suit). However, we must subtract the red face cards from the total, as they are already included in the 12 face cards. There are 6 red face cards (3 face cards x 2 red suits).

So, the total number of favorable outcomes is 12 face cards + 26 red cards - 6 red face cards = 32 cards.

The probability of drawing a face card or a red card is the number of favorable outcomes divided by the total number of possible outcomes: 32/52 ≈ 0.6154, or approximately 61.54%.

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Answer:

The statements about arcs and angles that are true in the figure are;

1) ∠EFD ≅ ∠EGD

2) \(\overline{ED}\cong \overline{FD}\)

3) mFD = 120°

Step-by-step explanation:

1) ∠ECD + ∠CEG + ∠CDG + ∠GDE = 360° (Sum of interior angle of a quadrilateral)

∠CEG = ∠CDG = 90° (Given)

∠GDE = 60° (Given)

∴ ∠ECD = 360° - (∠CEG + ∠CDG + ∠GDE)

∠ECD = 360° - (90° + 90° + 60°) = 120°

∠ECD = 2 × ∠EFD (Angle subtended is twice the angle subtended at the circumference)

120° = 2 × ∠EFD

∠EFD = 120°/2 = 60°

∠EFD ≅ ∠EGD

∠ECD = 120°

∠EGD = 60°

∴∠EGD ≠ ∠ECD

2) Given that arc mEF ≅ arc mFD

Therefore, ΔECF and ΔDCF are isosceles triangles having two sides (radii EC and CF in ΔECF and radii EF and CD in ΔDCF

∠ECF = mEF = mFD = ∠DCF (Given)

∴ ΔECF ≅ ΔDCF (Side Angle Side, SAS, rule of congruency)

\(\\ \overline{EF}\cong \overline{FD}\) (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)

∠FED ≅ ∠FDE (base angles of isosceles triangle)

∠FED + ∠FDE + ∠EFD = 180° (sum of interior angles of a triangle)

∠FED + ∠FDE = 180° - ∠EFD = 180° - 60° = 120°

∠FED + ∠FDE = 120° = ∠FED + ∠FED (substitution)

2 × ∠FED  = 120°

∠FED = 120°/2 = 60° = ∠FDE

∴ ∠FED = ∠FDE = ∠EFD =  60°

ΔEFD  is an equilateral triangle as all interior angles are equal

\(\\ \overline{EF}\cong \overline{FD}\cong \overline{ED}\) (definition of equilateral triangle)

\(\overline{ED}\cong \overline{FD}\)

3) Having that ∠EFD = 60° and ∠CFE = ∠CFD (CPCTC)

Where, ∠EFD = ∠CFE + ∠CFD (Angle addition)

60° = ∠CFE + ∠CFD = ∠CFE + ∠CFE (substitution)

60° = 2 × ∠CFE

∠CFE =60°/2 = 30° = ∠CFD

\(\overline{CF}\cong \overline{CD}\) (radii of the same circle)

ΔFCD is an isosceles triangle (definition)

∠CFD ≅ ∠CDF (base angles of isosceles ΔFCD)

∠CFD + ∠CDF + ∠DCF = 180°

∠DCF = 180° - (∠CFD + ∠CDF) = 180° - (30° + 30°) = 120°

mFD = ∠DCF (definition)

mFD = 120°.

Answer:

1,3,5

Step-by-step explanation:

right on edge 2022

Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.

Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.

The information that her account is losing $15 every day can then be put to use. We can write this as:

Rate of change = -$15 per day

The negative symbol signifies a declining amount on her account.

Therefore, Miss Carol's bank account is losing money at a daily rate of

$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.

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Solution

The average number of beats per second is calculated as;

The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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Based on the information provided, it can inferred that letter A is equivalent to 4.

The image shows B + B+ A = A. This is only possible if letter adding 2 letters B is equal to 10. Now 10/2 = 5. This means B = 5.

It is known 5 + A + A = A. This is only possible is A is 4. 5 + 4+ 4 + 1 (from the previous addition) = 4 (+2 that is added in the next column).

Note: This question is incomplete below I add the missing image.

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Answer:

1/4+1/32

Step-by-step explanation:

1/4+1/4=1/2

1/32+1/32=1/16

I hope this helps:

Based on the constant rate of change, it will take Lamonte 4.5 hours to earn $107.55.

The constant rate of change refers to the ratio of an output value to an input which remains constant in all variables.

The constant rate of change is called a slope in a linear function or the unit rate.

The constant rate of change implies that the dependent variable changes (increasing or decreasing) as the other comparable or independent variable changes similarly.

Time (hours)  Earnings (dollars)   Unit Rate

       3                      $71.70            $23.90 ($71.70/3)

      11                   $262.90           $23.90 ($262.90/11)

    28                   $669.20           $23.90 ($669.20/28)

Total earnings = $107.55

Unit rate her hour = $23.90

The number of hours required = 4.5 hours ($107.55/$23.90)

Thus, using the constant rate of change or unit rate, Lamonte must work 4.5 hours to have total earnings of $107.55.

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Answer:

In 4 hours the guy walked 2 miles

Step-by-step explanation:

the 4 represents the hours and the 2 represents the miles

Answer:

Yes because it equals 10

Step-by-step explanation:

Answer:

10 so yes

Step-by-step explanation:

calculator

When performing a hypothesis test on the population mean (μ) when the population standard deviation (σ) is known, the null hypothesis (H0) can never be rejected if the sample mean falls within the acceptance range determined by the chosen significance level and the critical values.

In hypothesis testing for the population mean when the population standard deviation is known, the null hypothesis (H0) represents the claim or assumption that the population mean is equal to a specific value. The alternative hypothesis (Ha) states that the population mean is not equal to the specific value.

To determine whether to reject or fail to reject the null hypothesis, we compare the sample mean to the expected value under the null hypothesis. If the sample mean falls within the acceptance range determined by the chosen significance level and the critical values, we do not have sufficient evidence to reject the null hypothesis. The acceptance range is defined by the margin of error around the expected value, and it indicates the range of values that can be considered reasonably close to the expected value.

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The number of zero-dimensional objects are: 5

A point is said to have zero dimensions. This means that there are no length, height, width, or volume. Its only property will definitely be its' location. Thus, we could possibly have a collection of points, such as the endpoints of a line or the corners of a square, but then it would still be a zero-dimensional object.

Now, we are given a square based pyramid object but then going by the definition of zero-dimensional objects earlier stated, we can see that they are points and we have 5 points here which denotes 5 zero-dimensional object.

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The given integrals are improper because they involve either an infinite interval of integration, an integrand that approaches infinity, or a discontinuity within the interval of integration. Each integral has specific reasons that make it improper.

(a) The integral √(2/82) dx is improper because the interval of integration extends to infinity. When integrating over an infinite interval, the limits are not finite.

(b) The integral √(1+x²³) dx is improper because the integrand approaches infinity as x approaches ±∞. When the integrand becomes unbounded, the integral is considered improper.

(c) The integral √(x²e^(x²)) dx is improper because the integrand has a discontinuity at x = 0. Integrals with discontinuous functions within the interval of integration are classified as improper.

(d) The integral f/4 cot(x) dx is improper because the integrand has singularities where cot(x) becomes undefined, such as when x = kπ, where k is an integer. Integrals with singularities in the integrand are considered improper.

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The correlation between two variables is an important measure that helps us understand the relationship between them. In Scenario 3-2, if the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would not change the correlation (r) between wine consumption and heart disease death rate.

The correlation coefficient (r) measures the strength and direction of the relationship between two variables. If the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would change the units in which the death rate is expressed, but it would not change the underlying relationship between wine consumption and heart disease death rate.

In other words, regardless of the units in which the death rate is expressed, the correlation between wine consumption and heart disease death rate would remain the same. This is because the correlation measures the relationship between two variables, not the units in which they are expressed. It is important to note that expressing the death rate in different units may make it easier or more difficult to understand the relationship between two variables, but it does not change the underlying correlation.

In conclusion, the correlation (r) between wine consumption and heart disease death rate would not change if the death rate were expressed as deaths per 1,000 people instead of as deaths per 100,000 people.

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Answer:

Step-by-step explanation:

4th

(a) Approximately 68% of pregnancies have lengths between 251 days and 279 days.

(b) Approximately 95% of pregnancies have lengths between 237 days and 293 days.

We have given that,

lengths of human pregnancies are normally distributed with a mean of 265 days and a standard deviation of 14 days,

(a)

To find the length of 68% of pregnancies  we know the formula,

days ± standard deviation

Therefore

265 - 14 = 251

265 + 14 = 279

Hence approximately 68% of pregnancies have lengths between 251 days and 278 days.

(b)

From the section (a) 68% of pregnancies have lengths between 251 days and 278 days.

Now we will check for 95%

so the formula is

days ± 2× standard deviation

⇒ 265 - 2 × 14 = 237

and 265 + 2 × 14 = 293

Therefore approximately 95% of pregnancies lengths between 237 days and 293 days.

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Factor

what 2 numbers multily to get -12and add to get -4

-6and -2

(x-6)(x+2)=0

ser to zero

x-6=0

x=6

x+2=0

x=-2

6>-2

w=6

-2=z

3w+2z

3(6)+2(-2)

18-4

14

value is 14

option D

The truth value of the given proposition is "false".

The truth value of the given proposition can be evaluated using the following steps:

Convert the binary representation of the numbers to decimal:

0 = 0

~1 = -1 (invert the bits of 1 to get -2 in two's complement representation and add 1)

10 = 2

Apply the comparison operator "=" between the left and right sides of the equation:

(0 = -1) = 2

Evaluate the left side of the equation, which is false, because 0 is not equal to -1.

Evaluate the right side of the equation, which is true, because 2 is a nonzero value.

Apply the comparison operator "=" between the results of step 3 and step 4, which yields:

false = true

Therefore, the truth value of the given proposition is "false".

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The value of 16.023-5.58 = 10.4430 rounded off to the correct number of significant figures.

To perform the calculation and round the answer to the correct number of significant figures for the expression 16.023-5.58, follow these steps: First, subtract the given values of 16.023 and 5.58.16.023 - 5.58 = 10.443. The difference value is 10.443.

Now, round the answer to the correct number of significant figures by identifying the least significant digit that has been given in the question.

Here, the least significant figure is 2. The next digit after 2 is 3 which is greater than or equal to 5, so round up the digit. Therefore, rounding off 10.443 to the nearest thousandth gives 10.4430.

Thus, the value of 16.023-5.58 = 10.4430 rounded off to the correct number of significant figures.

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The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

15%

Step-by-step explanation:

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Answer:

15%

Step-by-step explanation:

anything out of 100 and is 2 digits will be the same number.

example: 72/100 = 72%

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Mrs. Downey is responsible for paying at most $50 of the unauthorized charge for the $1,124 watch.

We have,

The Truth-in-Lending Act is a federal law in the United States that provides certain protections to consumers in credit transactions.

One of the provisions of this act is the limitation of liability for unauthorized charges on a stolen credit card.

According to the Truth-in-Lending Act,

If a credit card is stolen and unauthorized charges are made on it, the cardholder's liability for those charges is limited to a maximum of $50.

This means that even if the thief charged a significant amount, such as $1,124 for a watch, the cardholder is only responsible for paying up to $50 of that unauthorized charge.

So,

The maximum liability for unauthorized charges on a stolen credit card is $50.

Therefore,

Mrs. Downey is responsible for paying at most $50 of the unauthorized charge for the $1,124 watch.

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