Here are the ingredients needed to make 12 shortcakes.
50g of sugar
200g of butter
200g of flour
10ml of milk.
How many shortcakes does Dan make?

As the function f is defined piecewise with different rules on different intervals, we need to check the continuity of f at each point of its domain.

In order for a function to be continuous, it needs to be defined and have no breaks, jumps, or holes in its graph. Let's consider the function f with a positive constant k.

The function f can be written as:

f(x) = {

kx^2, if x < 2,

4k - 3x, if x >= 2

}

To determine the value of k for which f is continuous, we need to ensure that the two cases defined for f match at the point x = 2.

When x < 2, the function is defined as kx^2. At x = 2, this becomes k(2)^2 = 4k.

When x >= 2, the function is defined as 4k - 3x. At x = 2, this becomes 4k - 3(2) = 4k - 6.

For the function f to be continuous, the values of 4k and 4k - 6 must be equal at x = 2. Therefore, we have the equation 4k = 4k - 6.

Simplifying the equation, we find that -6 = 0, which is not true for any value of k.

Since the equation has no solution, it means that there is no specific value of k for which f is continuous. However, we can note that for all positive values of k, the function will still be defined in both cases and continuous within each individual case. Therefore, the function f will be continuous for all positive values of k.

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Mr. Adam Bought 15 cookies and 10 muffins.

Variables to represent the number of muffins and cookies that Mr. Adam bought. We'll let x be the number of muffins and y be the number of cookies. Then we can set up two equations based on the information given:

Equation 1: x + y = 20   (the total number of muffins and cookies is 20)

Equation 2: 0.5y = 1.5x + 5   (the cost of the cookies is $5 more than the cost of the muffins)

Let's simplify Equation 2 by dividing both sides by 0.5:

y = 3x + 10

Now we can use substitution to solve for one of the variables. We can rearrange Equation 1 to solve for x:

x = 20 - y

Then we can substitute this expression for x in Equation 2:

y = 3(20 - y) + 10

Simplifying this equation, we get:

y = 50 - 3y

Adding 3y to both sides, we get:

4y = 50

Dividing both sides by 4, we get:

y = 12.5

This means that Mr. Adam bought 12.5 cookies. However, we can't have a fraction of a cookie, so let's check whether our solution makes sense in the context of the problem.

If Mr. Adam bought 12.5 cookies, he must have bought 7.5 muffins (since x + y = 20). But we can't have a fraction of a muffin either.

Therefore, it's likely that there was an error in the problem setup. One possibility is that Mr. Adam actually bought a total of 25 muffins and cookies (instead of 20). In this case, the equations would be:

Equation 1: x + y = 25

Equation 2: 0.5y = 1.5x + 5

Following the same steps as before, we would get:

y = 15 and x = 10

Therefore, Mr. Adam bought 15 cookies and 10 muffins.

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Answer:

A histogram would be the most appropriate graph to display the distribution of scores and identify clusters and gaps.

Step-by-step explanation:

So the equation of the tangent line to the graph of y = x + cos x at the point (0, 1) is y = x + 1.

To find the equation of the tangent line to the graph of y = x + cos x at the point (0, 1), we need to find the slope of the tangent line at that point. The slope of the tangent line is given by the derivative of the function y = x + cos x evaluated at x = 0:

y' = 1 - sin x

y'(0) = 1 - sin 0 = 1

So the slope of the tangent line at the point (0, 1) is 1. Using the point-slope form of the equation of a line, we can write the equation of the tangent line as:

y - 1 = 1(x - 0)

Simplifying, we get:

y = x + 1

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Answer: 22

Step-by-step explanation:

Ok, so the way I do it I multiply then divide.

For Monday I did: ?/220=55/100. what you would do is multiply across then divide by the other number, so 220x55 which is 12100 then you will divide it by 100. So 121 people voted on Monday

For Tuesday: Using the same method. ?/220=45/100 you will multiply 45x220 giving you 9900 then you will divide by 100 giving you 99. 99 people voted on Tuesday.

So to find the DIFFERENCE you need to subtract, so 121-99 leaving you with 22. Also, if you are confused how on where I got 100 from you put the percentage over 100, because percentages go from 0%-100% so you put the partial percentage over the maximum (100)  

The ant population will reach 38.2 thousand in about 3.25 years, assuming a growth rate of 5% per year.

To answer this question, we need to know the growth rate of the ant population. Let's say the growth rate is 5% per year. This means that each year, the population will increase by 5% of its current size. To calculate the population size after a certain number of years, we can use the formula:

P = P0 * (1 + r)^t

where P is the population size after t years, P0 is the initial population size, r is the growth rate as a decimal, and t is the number of years.

Assuming the initial population size is 30 thousand, we can plug in the values to find when the population will reach 38.2 thousand:

38.2 = 30 * (1 + 0.05)^t

Solving for t, we get t = 3.25 years. However, it's important to note that the actual growth rate may be different, so this calculation is just an estimate.

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The resulting confidence interval will give you the range of values within which the true slope of the line is likely to fall, with a 90% level of confidence.

To find a 90% confidence interval for the slope of the true line describing the association between Math and Verbal scores, we would need to conduct a regression analysis on the data. This would allow us to estimate the slope of the line and calculate a confidence interval around that estimate.

Assuming that we have already conducted the analysis and obtained the necessary statistics, let's say that our estimate for the slope is 0.8 with a standard error of 0.2. Using a t-distribution with n-2 degrees of freedom (where n is the sample size), we can calculate a 90% confidence interval around our estimate by multiplying the standard error by the appropriate t-value (in this case, 1.645) and adding and subtracting the resulting value from our estimate.

Thus, our 90% confidence interval for the slope would be (0.8 - (1.645*0.2), 0.8 + (1.645*0.2)) = (0.452, 1.148). This means that we can be 90% confident that the true slope of the line describing the association between Math and Verbal scores falls somewhere within this interval.

In this context, our confidence interval tells us how uncertain we are about the true relationship between Math and Verbal scores. Specifically, it tells us that there is a 90% chance that the true slope of the line falls within the range of 0.452 to 1.148. This means that we cannot be absolutely certain about the direction or strength of the relationship between these two variables, but we can be reasonably confident that it falls within this range.

a) To find a 90% confidence interval for the slope of the true line describing the association between Math and Verbal scores, follow these steps:

Step 1: Obtain the data for both Math and Verbal SAT scores.

Step 2: Perform a linear regression analysis to obtain the sample slope (b) and its standard error (SE).

Step 3: Determine the critical value (t) for the 90% confidence level. This can be found using a t-table or a calculator with the appropriate degrees of freedom (n-2, where n is the number of data points).

Step 4: Calculate the margin of error by multiplying the standard error (SE) by the critical value (t).

Step 5: Create the confidence interval by adding and subtracting the margin of error from the sample slope (b).

The resulting confidence interval will give you the range of values within which the true slope of the line is likely to fall, with a 90% level of confidence.

b) In this context, the 90% confidence interval for the slope means that we are 90% confident that the true slope of the line describing the association between Math and Verbal scores falls within the calculated range. This gives us an indication of the strength and direction of the relationship between the two variables. If the interval contains only positive values, it suggests a positive association between the scores; if it contains only negative values, it suggests a negative association; and if it includes zero, we cannot conclude that there is a significant association between Math and Verbal scores at the 90% confidence level.

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The measure of arc:

16: m FE = 100 degree

17: mBC = 50 degree

18: mCE = 130 degree

19: mCFE = 230 degree

In  the figure,

mFE = ∠FGE = 100 degree

mBC = ∠AGB = 50 degree

Now,

mCE  = mCD +mDE

         =  90 + (180 - mBC - mCD)

         =  90 + ( 180 - 90 - 50)

         = 130 degree

And mAF = 180 - mAB - mFE

                =  180 - 50 - 100

                = 30 degree

Now,

mCFE = 50+50+30+100

          = 230 degree

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Answer: 4.97

Step-by-step explanation:

h(0.1) means value of h(x) when x = 0.1

Plug in x = 0.1 into h(x): h(0.1) = -3*(0.1)^2+5 = -3*0.01+5 = -0.03+5 = 4.97

Answer:

14

Step-by-step explanation:

Ok, 60! is a really big number

[tex]x!=x(x-1)(x-2)...1[/tex]

So we have 60*59*58...*1

2 times 5 is 10 which makes a terminal zero (ending zero)

We need to count how many fives and twos are in 60!

There are 60/5=12 5^1's

There are 60/25=2 5^2's

So 12+2=14

There are way more 2's than fives so we take the lesser number

So the answer is 14

*Note that 60/25 is not 2, we need an integer rounded down

Answer:

All Real Numbers

Step-by-step explanation:

I will be using x instead of θ as a variable:

1.) [tex]1+tan^2[/tex]x is equal to [tex]sec^2[/tex]x, so we can substitute [tex]sec^2[/tex]x for [tex]1+ tan^2[/tex]x.

2.) Now, since [tex]csc^2[/tex]x is equal to [tex]\frac{1}{sin^2x}[/tex], and [tex]sec^2[/tex]x is equal to [tex]\frac{1}{cos^2x}[/tex], we can just move [tex]cos^2x[/tex] to the numerator and [tex]sin^2x[/tex] to the denominator. [tex]\frac{cos^2x}{sin^2x}[/tex] is equal to [tex]cot^2x[/tex]

3.) Since we have [tex]cot^2x[/tex] = [tex]cot^2x[/tex] , the answer is All Real Numbers.

Answer:

Cylinder:  π r² h

Cone:  V=1/3hπr²

Sphere: V = 4/3 πr³

One-third of the volume of a cylinder

Step-by-step explanation:

Your welcome

To simplify the expression (x+5)(x^2-25)(x+5)^2(x-5)^2, we can begin by factoring the expressions:

(x+5) = (x+5)

(x^2-25) = (x-5)(x+5)

(x+5)^2 = (x+5)(x+5)

(x-5)^2 = (x-5)(x-5)

Now, we can substitute these factorized expressions back into the original expression:

(x+5)(x^2-25)(x+5)^2(x-5)^2 = (x+5)(x-5)(x+5)(x-5)(x+5)(x+5)(x-5)(x-5)

Simplifying further, we can combine like terms:

(x+5)(x-5)(x+5)(x-5)(x+5)(x+5)(x-5)(x-5) = (x+5)^3(x-5)^3

Therefore, the simplified expression is (x+5)^3(x-5)^3.

As for the domain of this expression, it includes all real numbers because there are no restrictions or limitations on the values that x can take. Therefore, the domain is (-∞, ∞).

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Answer:

2 there we have the second quadrant

Answer:

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

Both angles PQS and PRS intercept same arc PS, hence they have same measure:

Substitute values and solve for x:

Plug in the value of x into either angle measure:

The intercepted arc is twice the inscribed angle measure:

Answer:

Step-by-step explanation:

To change the number 40.505734 to two significant figures, we need to round it to the nearest value with two significant figures.

Looking at the third digit after the decimal point (5), we see that it is greater than or equal to 5. Therefore, we need to round up the second digit after the decimal point (0) by adding 1 to it.

Thus, the number 40.505734 rounded to two significant figures is 41.

The statistical unit for John's study is A. the 35 countries. John is trying to estimate the average literacy rate across all countries, and he randomly selected 35 countries to research their literacy rates. The statistical unit in this case is the individual country, as each country's literacy rate is being used to calculate the average.

The statistical unit for John's study is A. the 35 countries. This is because John's study is based on a sample of 35 countries that he randomly selected. The sample is used to estimate the average literacy rate for all countries. The sample size of 35 countries is large enough to provide a representative sample of the population of countries. If John had selected only a few countries or individuals, his estimate of the average literacy rate would not have been reliable. However, by selecting a sample of 35 countries, John can make a more accurate estimation of the average literacy rate for all countries. In conclusion, the statistical unit for John's study is the sample of 35 countries that he researched to estimate the average literacy rate for all countries.

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The volume of the tool box is 2,052 cubic inches.

To find the volume of a rectangular solid, we need to multiply its length, width, and height. In this case, the length is 19 inches, the width is 12 inches, and the height is 9 inches. So, we can use the formula:

Volume = length x width x height

Volume = 19 in. x 12 in. x 9 in.

Volume = 2,052 cubic inches

Therefore, the volume of the tool box is 2,052 cubic inches.

Conclusion: The tool box has a volume of 2,052 cubic inches, which means it can hold that much space or stuff inside it.
The volume of the toolbox is 2052 cubic inches.


To calculate the volume of a rectangular solid, you multiply the length, width, and height of the solid. In this case, the dimensions of the toolbox are 19 inches (length), 12 inches (width), and 9 inches (height).

Step 1: Multiply the length, width, and height:
Volume = Length × Width × Height

Step 2: Substitute the given dimensions:
Volume = 19 inches × 12 inches × 9 inches

Step 3: Perform the multiplication:
Volume = 2052 cubic inches

The volume of the rectangular solid toolbox with sides of 19 inches, 12 inches, and 9 inches is 2052 cubic inches.

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The baby bird's initial height above the ground would be 10 meters when it jumped.

I understand you would like to know the height of the baby bird above the ground when it jumped, using the function "f" that models its height (in meters) as a function of time (in seconds).
To find the bird's initial height above the ground when it jumped, we need to evaluate the function f at the time when the bird just jumped, which is at time t = 0 seconds.
Step 1: Plug t = 0 into the function f(t).
f(0) = (height of the bird at time t = 0 seconds)
Since you didn't provide the specific function f, I cannot give you the exact height value. However, once you have the function f(t), simply substitute t = 0 and calculate f(0) to find the bird's initial height above the ground when it jumped.
For example, if the function were f(t) = 10 - 2t, you would do:
f(0) = 10 - 2(0) = 10
the baby bird's initial height above the ground would be 10 meters when it jumped. Make sure to use your given function f(t) to find the accurate height for your problem.

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The maximum height above the ground attained by the bird is 16 meters

The curve showing the travel path of the bird from a tree is a parabola.

Examining the graph attached in the problem, the maximum height reached with is same as the vertex of the parabola, is at point (2, 16)

hence we can say that the height reached by the bird is equal to 16 m

The attached graph shows the point marking the height the bird traveled

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The valid statement about the value of the correlation coefficient (r) is:

"The correlation between the height and BMI of 10th graders is 0.82."

The reason this statement is valid is that the correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It can range from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

In the given statement, it is mentioned that the correlation coefficient between height and BMI of 10th graders is 0.82. This indicates a strong positive correlation between height and BMI, suggesting that as height increases, the BMI tends to increase as well.

The other statements provided do not represent valid examples because they either contain incorrect values for the correlation coefficient (e.g., r = 3.1) or provide correlation coefficients that are not correctly interpreted (e.g., stating a correlation coefficient in terms of dollars).

Therefore, the statement about the correlation between the height and BMI of 10th graders having a correlation coefficient of 0.82 is the valid statement.

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The correct matrices are:

Matrix:

7 1 5

1 5 7

5 7 1

Matrix:

9   18  27

27 -9  18

18  27 9

Matrix:

8 1 6

6 8 1

1 6 8

Matrix:

7 1 5

1 5 7

5 7 1

[tex]Diagonal elements of A^2 are: 7^2 + 1^2 + 5^2[/tex]

Matrix:

9   18  27

27 -9  18

18  27 9

[tex]Diagonal elements of A^2 are: 9^2 + 27*18 + 18*27 or (-9)^2[/tex]

Matrix:

8 1 6

6 8 1

1 6 8

[tex]Diagonal elements of A^2 are: 8^2 + 6*1 + 1*6[/tex]

Matrices play an instrumental role in mathematics due to their versatility as an array of numbers or symbols arranged in rows and columns within a rectangular configuration.

The extensive application extends beyond just math into other areas like computer science or physics.

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Answer:

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

To calculate the variance for this set of data, you simply need to square the sample standard deviation.

In this case, the sample standard deviation is 7.79.

The variance for this set of data is 60.68.

For the given data with standard deviation of 7.79, the variance is 60.68.

The given sample standard deviation for the number of new vehicles sold per month for a sample of 6 car dealerships is 7.79, we have to calculate the variance for this set of data. The formula to calculate variance is:

Var(X) = s2 = (Σ(X - μ)2) / N

Where, X = each value of the dataset, μ = mean of the dataset, N = total number of values in the dataset

Given that,

Standard deviation (s) = 7.79, Sample size (n) = 6, Variance (s²) = ?

We know that, variance = (standard deviation)²

Variance = 7.79²

Variance = 60.6841 ≈ 60.68

Hence, the variance for the given set of data is 60.68 (approx).

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Answer:

1.6

Step-by-step explanation:

12.8/8 = 1.6

15.2/9.5 = 1.6

Scale factor = 1.6

Answer: 3/10

Step-by-step explanation:

First find the probability of it landing on an even number:

There are 5 even numbers from 1-10

Therefor the probability is 5/10

Next find the probability that it spins a number greater than 4:

There are 6 numbers greater than 4 from 1-10

6/10  

To find the probability of 1 and 2, multiply

5/10 * 6/10 = 3/10

Answer:

130

Step-by-step explanation:

To meet the requirements of a 98% confidence level and a margin of error of 3%, you should interview at least 314 individuals in the workforce.

To determine the sample size needed for the survey, we can use the formula:

n = (z^2 * p * (1-p)) / E^2

Where:

n is the required sample size

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

p is the estimated proportion from the pilot survey

E is the desired margin of error

In this case, the desired confidence level is 98% which corresponds to a z-score of approximately 2.33 (rounded to 3 decimal places). The estimated proportion from the pilot survey is 7/45 = 0.1556, and the desired margin of error is 3% which is equivalent to 0.03.

Substituting these values into the formula:

n = (2.33^2 * 0.1556 * (1-0.1556)) / 0.03^2 ≈ 313.085

Rounding up to the next whole number, the required sample size is 314.

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Answer:(3,9)

Step-by-step explanation:

Simplifying the expression, 7x + 9 - 3x + 4, we can combine the like terms to get: 4x + 13.

Like terms are terms that have the same degree or are of the same variable, for example, 3x and 7x are like terms, 9 and 4 are like terms as well because they are constants.

Given the expression, 7x + 9 - 3x + 4, we can simplify the expression by combining like terms as shown below:

Rearrange the expression:

7x - 3x + 9 + 4 [note that 7x and 3x are like terms while 9 and 4 are also like terms]

Combine like terms:

4x + 13

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The coordinates of the vertices of A’B’C’ are A' = (1, 3), B' = (3, 4) and C' = (4, 1)

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

The graph

The coordinates of the vertices of A’B’C’ are the coordinates of the locations of the the vertices A', B' and C'

Using the above as a guide, we have the following:

From the graph, we have the coordinates of the vertices of A’B’C’ to be

A' = (1, 3)

B' = (3, 4)

C' = (4, 1)

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Answer:

8 decimeter are 800 millimeters

Step-by-step explanation:

Just multiply the length value by 100

Hope this helps :)

Pls brainliest...

Answer: 8 decimeters equals 800 millimeters.

Step-by-step explanation:

We know that,

1 decimeter = 100 millimeter

Therefore, To convert decimeters to millimeters, we have to multiply it by 100.

Hence, mm= dm*100

                   = 8*100

                   = 800

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