Sophia asked 50 people which drinks they liked from tea, coffee and milk.
all 50 people like at least one of the drinks.
19 people like all three drinks.
16 people like tea and coffee but do not like milk.
21 people like coffee and milk.
24 people like tea and milk.
40 people like coffee.
1 person likes only milk.

sophia selects at random one of the 50 people.
work out the probability that this person likes tea.

The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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The composite result function of ( f ° g )(x) in the given functions f( x ) = x² + 9 and g( x ) = x² - 9 is x⁴ - 18x² + 90.

A function is simply a relationship that maps one input to one output.

Given the data in the question;

First, we set up the composite result function f(g(x)).

f( x ) = x² + 9

f( g(x) ) = f( x² - 9 ) = ( x² - 9  )² + 9

f( g(x) ) = ( x² - 9  )² + 9

Expand the parenthesis

f( g(x) ) = ( x² - 9 )( x² - 9 )  + 9

f( g(x) ) = ( x²( x² - 9 ) -9( x² - 9 ) + 9

f( g(x) ) = x⁴ - 9x² - 9x² + 81 + 9

Collect and add like terms

f( g(x) ) = x⁴ - 18x² + 81 + 9

f( g(x) ) = x⁴ - 18x² + 90

Therefore,  ( f ° g )(x) in the given functions is x⁴ - 18x² + 90.

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Step-by-step explanation:

\(f(x) = ln( \frac{1}{x} ) \)

To find the derivative, notice we have a function 1/x inside of another function, ln(x)

We use what we call the chain rule,

It states that

derivative of a '

\( \frac{d}{dx} f(g(x)) = f '(g(x)) \times \: g '(x)\)

Here f is ln(x)

f is 1/x

So first, we know that

\( \frac{d}{dx} ( ln(x) = \frac{1}{x} \)

so

\(f'(g(x)) = \frac{1}{ \frac{1}{x} } \)

We know that

\(g'(x) = - \frac{1}{ {x}^{2} } \)

So we have

\(x \times - \frac{1}{ {x}^{2} } = \frac{ - 1}{x} \)

Becca made a total of 24 rolls and 12 biscuits.

Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.

Becca made 2 trays of rolls and biscuits, with 12 rolls and 6 biscuits in each tray. To find the total number of rolls and biscuits, we need to multiply the number of rolls and biscuits per tray by the number of trays, and then add them together:

Total rolls = 2 trays × 12 rolls per tray = 24 rolls

Total biscuits = 2 trays × 6 biscuits per tray = 12 biscuits

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Answer:

Step-by-step explanation:

Part 1: x represents her bank account

Part2: 135-x=y

Part 3: I'm not sure how long she's worked there, but it would look like: 7.85x=y. X representing number of hours

Answer:

$4.76

Step-by-step explanation:

It costs $2.80 to make a sandwich at the local deli shop and the deli sells it at a price that is 170% of the cost.

We have to find 170% of the cost of making each sandwich ($2.80):

170/100 * 2.80 = $4.76

The sandwich sells for $4.76

Answer:

ben

Step-by-step explanation:

Answer:

Step-by-step explanation:

y= 3.50m + 35

y= 4.25m

4.25m = 3.50m + 35

.75m = 35

m = about 47 movies

Answer:

24 / 7

Step-by-step explanation:

y - 4(2y - 5) = -4

y - 8y + 20 = -4

-7y = -24

7y = 24

y = 24/7,

y = 3 and 3/7

or

y = 3.428571 all recurring

(they are all the same value in different forms I would just write 24/7)

The value of the function (f/g)(x) is (x+5)/(3x+5) if f(x) = 3x² + 10x - 25

g(x) = 9x²-25.

The earliest known attempt to the concept of function may be traced back to the works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. The concept of a function was codified in terms of set theory at the end of the nineteenth century, which substantially expanded its realms of applicability.

Given,

f(x) = 3x² + 10x - 25

g(x) = 9x² - 25

To find (f/g)(x) divide f(x) by g(x)

(f/g)(x)=(3x²+ 10x-25)/(9x²-25)

We have to factorize both the numerator and denominator

For the numerator

3x²+10x-25

3x²+15x-5x-25

3x(x+5)-5(x +5)

(3x-5 )(x+5)

For the denominator

9x² - 25

(3x)² - 5²

We have to use the formula,

a²- b² = (a+b)(a-b)

(3x)²-5² = (3x+5)(3x-5)

Therefore,

(f/g)(x)=(3x-5)(x+5)/(3x+5)(3x-5)

By simplifying we get,

(f/g)(x)=(x+5)/(3x+5)

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Answer:

24 cups or 6 quarts

Step-by-step explanation:

2 x 2 = 4  4 + 2 = 6

6 x 4 = 24

Since none of the 13 classmates had been given math homework between the original survey and Kelly's second survey, the sum of the values in the second data set is the same as the sum of the values in the original data set. Therefore, the change in the means can be determined without calculating the mean of either data set by considering the number of data points in each set.

Since both data sets have the same number of data points, the change in the means will be zero. This is because the mean is calculated by dividing the sum of the values by the number of data points, and since the sum of the values is the same in both data sets, the means will also be the same.

In other words, if the mean of the first data set is x, then the sum of the values in the first data set is 13x (since there are 13 classmates), and the sum of the values in the second data set is also 13x (since none of the values have changed). Therefore, the mean of the second data set will also be x, and the change in the means will be zero.

If lisa is on her way home in her car, she has driven 24 miles so far, which is three-fourths of the way home, Lisa's total drive is 32 miles.

Let's represent the total length of Lisa's drive as x. We know that she has driven 24 miles so far, which is three-fourths of the total length. We can write this information as:

24 = (3/4) x

To find x, we need to isolate it on one side of the equation. We can start by multiplying both sides by 4/3 to get rid of the fraction:

24 * (4/3) = x

Simplifying, we get:

32 = x

We can say that Lisa has already driven 24 miles, which is three-fourths of the total distance. To find the total distance, we use the equation 24 = (3/4) x, where x represents the total distance.

To solve for x, we multiply both sides of the equation by 4/3 to cancel out the fraction, giving us 32 = x. Therefore, Lisa's total drive is 32 miles.

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No, because 3n could be equal to or less than n + 3 (option D)

To determine the correct option, we test with different numbers

let n = -3, -1, 0, 3, 4

From the above, we can see that depending on the value of n, 3n can be greater than or less than n + 3.

No, because 3n could be equal to or less than n + 3 (option D)

The answer is D: no, because 3n could be equal to or less than n + 3. Hope this helps! :)

Answer:

28 - 3=25

3/5×25

5

hope that helps

Answer:

Step-by-step explanation:

b/c they end up in the same place but take different ways of getting there...  90 + 270 adds up to a full circle of 390 so b/c one goes in the positive direction and one goes in the negative, the both get to the same location, :)

The kilogrammes of calcium found in 173 pounds of calcium is = 78.5 kg. That is option A.

First convert the 173 pounds of calcium to gramma

1 lb(pounds) = 454 g;

Therefore 173 pounds = 173 ×454

                                    = 78,542g

But,             1000 g = 1kg

Therefore, 78542g = 78542  ÷1000

                                = 78.542

                                =78.5kg.

Therefore, the kilogrammes of calcium found in 173 pounds of calcium is = 78.5kg.

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Answer:

PB = 15

Step-by-step explanation:

A midpoint is a point in the center of a line. Since P is the midpoint of AB, the length of AP = PB. Therefore, if AP = 15, PB = 15.

Answer:

yes every person has an equal chance of being selected

Step-by-step explanation:

To determine the amount of dirt removed, one would need to consider factors such as the dimensions of the area where the dirt was excavated,

the depth of the excavation, and the type of soil being removed. This information would be necessary to calculate the volume of dirt removed.

Construction companies typically use surveying and engineering techniques to measure the volume of material being excavated.

This may involve taking measurements and using mathematical formulas to calculate the volume of the removed dirt.

In conclusion, without specific data or measurements, it is not possible to determine the exact amount of dirt that was removed by the construction company.

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Answer:

a +d = a2

Step-by-step explanation:

-2 - (-9) =

-2+9=7

a + d = a2

Answer: 5t + (10x2) i believe. I don’t know what the question was but i’m guessing they wanted to know the equation..!

Step-by-step explanation: first ... add all the people up in the family which is 5 then you times that by a variable and since they bought all of them t- shirts the variable will be ‘t’ so that’s 5t then take 10x2 since they bought two pairs of sandals which cost $10 for each pair and your equation will be 5t + (10x2)

Answer:

Because 20% of $10 will not be the same as 20% of a larger number

Step-by-step explanation:

120% of 10= 1.2(10)=$12

So we added $2 on the mark up.

Marking 20% off of $12 means the price will be 80% of 12= .8(12)= $9.60

This was a reduction of $2.40 which is 20% of $12

Answer:

Step-by-step explanation:

20% of 10 is $2

Marked up: 10+2 = $12

Marked down: 20% of 12 is 2.40 = 12-2.40 = $ 9.60

20% of 10 is not the same as 20% of 12.

Factor the polynomial by factoring out the greatest common factor, 7x2 + 5 - x = 6x2 + 10

x = -5

Soultion:

→ 7 × 2 + 5 - x = 6 × 2 + 10

Multiply.

→ 14 + 5 - x = 12 + 10.

Combine like terms.

→ 19 - x = 24

Isolate x (I'm going to add x and subtract 24 from both sides to avoid changing signs)

Answer

→ = x = -5

The profits would reach 413 thousand dollars in the year 9181.

The linear relationship between two variables is displayed by linear regression. The slope formula that we previously learnt in prior classes, such as linear equations in two variables, is similar to the equation of linear regression.

To find the linear regression equation that represents the given set of data, we can use the least squares method. Let's denote the year as x and the profits as y. We'll calculate the slope (m) and the y-intercept (b) of the regression line using the formulas:

m = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)

b = (Σy - mΣx) / n

where n is the number of data points, Σ represents the sum, Σxy represents the sum of the products of x and y, Σx represents the sum of x values, and Σy represents the sum of y values.

Let's calculate the values:

n = 5

Σx = 1999 + 2000 + 2001 + 2002 + 2003 = 10005

Σy = 112 + 160 + 160 + 173 + 226 = 831

Σxy = (1999 * 112) + (2000 * 160) + (2001 * 160) + (2002 * 173) + (2003 * 226) = 1072103

Σ(x²) = (1999²) + (2000²) + (2001²) + (2002²) + (2003²) = 40100245

Now, we can calculate the slope and y-intercept:

m = (5 * 1072103 - 10005 * 831) / (5 * 40100245 - 10005²) ≈ 0.0561

b = (831 - 0.0561 * 10005) / 5 ≈ -100.784

Therefore, the linear regression equation is approximately y = 0.0561x - 100.784.

To estimate the year in which the profits would reach 413 thousand dollars, we can substitute y = 413 into the equation and solve for x:

413 = 0.0561x - 100.784

0.0561x = 513.784

x ≈ 9181.155

Rounding to the nearest whole year, the profits would reach 413 thousand dollars in the year 9181.

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We have two samples, A and B, so we need to construct a 2 Samp T Int using this formula:

In order to use t*, we need to check conditions for using a t-distribution first.

Since 2/3 conditions aren't met, we can still proceed with the problem but keep in mind that the results will not be as accurate until more data is collected or more information is given in the problem.

Solve for t*:

We need the tail area first.

Next we need the degree of freedom.

The degree of freedom can be found by subtracting the degree of freedom for A and B.

The general formula is df = n - 1.

Use a calculator or a t-table to find the corresponding t-score for df = 5 and tail area = .05.

Now we can use the formula at the very top to construct a confidence interval for two sample means.

Substitute the variables into the formula: \(\displaystyle \overline {x}_1 - \overline {x}_2 \ \pm \ t^{*} \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2} }\).

Simplify this expression.

Adding and subtracting 3.73139 to and from -16 gives us a confidence interval of:

If we want to interpret the confidence interval of (-20.5707, -11.4293), we can say...

We are 90% confident that the interval from -20.5707 to -11.4293 holds the true mean of items sold at locations A and B.

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

To simplify the expression (w^4 * z^8) / (w^2 * y^2 * z^4), we can use the rules of exponents to combine like terms and simplify.

First, let's simplify the numerator:

w^4 * z^8

Since we are dividing, we can subtract the exponents:

w^(4 - 2) * z^(8 - 4) = w^2 * z^4

Now, let's simplify the denominator:

w^2 * y^2 * z^4

To divide, we subtract the exponents:

w^(2 - 2) * y^(2 - 2) * z^(4 - 4) = w^0 * y^0 * z^0

Any number (except 0) raised to the power of 0 is equal to 1:

w^0 * y^0 * z^0 = 1 * 1 * 1 = 1

Therefore, the simplified expression is:

(w^4 * z^8) / (w^2 * y^2 * z^4) = w^2 * z^4 / 1 = w^2 * z^4

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The simplified exponential expression is given as follows:

\(\frac{w^2z^4}{y^2}\)

The exponential expression for this problem is defined as follows:

\(\frac{w^4 \times z^8}{w^2 \times y^2 \times z^4}\)

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.

Hence the exponent of w is given as follows:

4 - 2 = 2.

The exponent of y is given as follows:

0 - 2 = -2 -> y² in the denominator.

The exponent of z is given as follows

8 - 4 = 4.

Hence the simplified expression is given as follows:

\(\frac{w^2z^4}{y^2}\)

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Answer:

total change is 8505

Step-by-step explanation:

hope that helped

Answer: The third one.

Step-by-step explanation:

A translation of six units down will change the value of the y-coordinate. In this case, you would take the y-coordinates of each point and subtract by 6 units. Your x-coordinate values will not change. The first option and the last option can automatically be omitted due to a change in the value of the x-coordinate. The second option shows a translation of 6 units UP, so the right value changed, but not the right way.

The third option has a 6 unit decrease in the y-coordinate, along with no change to your x-coordinate, making C) your correct answer.