Lucy has a bag of marbles. She shares one third of them with Carol, keeping one quarter for herself. Amrita joins them, so Lucy gives the rest of the marbles to her. If Carol has seven more marbles than Lucy, how many does Amrita have?

The statement "there exists a function f such that f(x) < 0, f'(x) > 0, and f''(x) < 0 for all x" is True.

1. f(x) < 0: This means the function is always negative.
2. f'(x) > 0: This means the function is always increasing.
3. f''(x) < 0: This means the function is always concave down.

A function that satisfies all these conditions is f(x) = -e^x.

1. For all x, f(x) = -e^x is always negative because e^x is always positive and the negative sign in front makes it negative.
2. The first derivative of f(x) is f'(x) = -e^x, which is always positive because e^x is always positive and the negative sign cancels out.
3. The second derivative of f(x) is f''(x) = e^x, which is always negative because e^x is always positive.

Therefore, the statement is true.

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If 150 town residents were asked about their age and yogurt , then the probability that a randomly selected customer prefers Swirl if age is at least 25 years old is 0.66 .

let X be = the selected customer that prefers swirled yogurt or is at least 25 years old ;

The sum of all the customers that are "at least 25 years old" = 21 + 30 + 24 = 75 ;

the sum of all the customers that " like Swirl Yogurt" is = 24 + 24 = 48 ;

the total number of residents = 150 students ;

So , the probability is calculated as : ( 75+48 -24)/150 = 0.66 .

Therefore , the required probability is 0.66 .

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The given question is incomplete , the complete question is

The 150 residents of the town of wonderland were asked their age and whether they preferred vanilla, chocolate, or swirled frozen yogurt. the results are displayed next.

     Age                               Chocolate      Vanilla      Swirl

under 25 years old                  22                 29             24

at least 25 years old                21                  30             24

What is the probability a randomly selected customer prefers Swirl Yogurt given he or she is at least 25 years old ?

Answer:

636.9

Step-by-step explanation:

684+615+648+598+654+612+606+621+642+689

=6369

6369÷10=636.9

Hello and Good Morning/Afternoon:

Let's take this step-by-step:

Let's find the slope:

 \(\hookrightarrow \text{Slope} = \frac{y_2-y_1}{x_2-x_1}=\frac{1--3}{-4--4} =\frac{4}{0}=\) undefined

If the slope is undefined:

  ⇒ the equation is of the form 'x = a'

      \(\hookrightarrow \text{a is the x-coordinate shared by both coordinates}\)

Thus the equation is x= -4

Answer: x= -4

Hope that helps!

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Answer:

C. 4x = 12

Step-by-step explanation:

You and three friends= you + 3 friends=4 people

Pizza= 12 pieces

Each person eats equal pieces of pizza

x= number of pieces each person ate

Equation

4x=12

Divide both sides by 4

x=12/4

=3

x=3

Therefore, each person ate 3 pieces of pizza each

Check:

4x=12

4(3)=12

12=12

Answer:

Where is the answers, they might help.

Answer:

Any number multiplied by 0 is 0

Step-by-step explanation:

imagine math answer.

t = 0:0.001:0.2;

xa = 5 * cos(120 * pi * t + pi/6);

plot(t, xa); This MATLAB code will plot the signal \( x_{a}(t) = 5 \cos(120 \pi t + \pi / 6) \) for \( 0 \leq t \leq 0.2 \).

To plot the given signal \( x_{a}(t) = 5 \cos(120 \pi t + \pi / 6) \) for \( 0 \leq t \leq 0.2 \) using MATLAB, follow these steps:

Step 1: Define the time axis

```matlab

t = 0:0.001:0.2; % time vector from 0 to 0.2 with a step of 0.001

```

Step 2: Define the signal equation

```matlab

xa = 5 * cos(120 * pi * t + pi/6);

```

Step 3: Plot the signal

```matlab

plot(t, xa);

xlabel('Time (s)');

ylabel('Amplitude');

title('Signal xa(t)');

```

Step 4: Customize the plot (optional)

You can customize the plot by adjusting the axis limits, adding a grid, legends, etc., based on your preference.

Step 5: Display the plot

```matlab

grid on;

legend('xa(t)');

```

By running the MATLAB code, you will obtain a plot of the signal \( x_{a}(t) \) with the time axis ranging from 0 to 0.2 seconds. The amplitude of the signal is 5, and it oscillates with a frequency of 60 Hz (120 cycles per second) and a phase shift of \(\pi/6\) radians. The plot will show the waveform of the signal over the specified time interval, allowing you to visualize the behavior of the signal over time.

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19 has an infinite number of multiples since we can multiply 19 by any positive integer to get a new multiple.

A multiple of number is product of that number and  other integer.

To find the multiples of 19, we need to multiply 19 by every positive integer. So, the multiples of 19 are:

19 × 1 = 19

19 × 2 = 38

19 × 3 = 57

19 × 4 = 76

19 × 5 = 95

19 × 6 = 114

19 × 7 = 133

19 × 8 = 152

19 × 9 = 171

19 × 10 = 190

and so on.

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Answer:

-15

Step-by-step explanation:

We proceed as follows;

In this question, we want to fill in the blank so that we can have the resulting expression expressed as the product of two different linear expressions.

Now, what to do here is that, when we factor the first two expressions, we need the same kind of expression to be present in the second bracket.

Thus, we have;

2a(b-3) + 5b + _

Now, putting -15 will give us the same expression in the first bracket and this gives us the following;

2a(b-3) + 5b-15

2a(b-3) + 5(b-3)

So we can have ; (2a+5)(b-3)

Hence the constant used is -15

Answer:

16 (NOT SURE )

Step-by-step explanation:

False.A sample is a subset of the entire set of elements in which a researcher is interested.

A sample is a subset of the entire set of elements in which a researcher is interested. The sample is typically selected to represent the characteristics of the larger population from which it is drawn.

By studying the sample, researchers can make inferences about the larger population. However, the sample is not the entire set of elements, but rather a smaller subset selected for study.

In research, the population refers to the entire set of elements that a researcher is interested in studying. This could be a group of people, animals, objects, or events that share common characteristics.

For example, if a researcher is interested in studying the effects of a new drug on patients with a certain disease, then the population would be all patients with that disease.

However, it is not always possible or practical to study the entire population. This is where sampling comes in. A sample is a smaller subset of the population that is selected to represent the characteristics.

By studying the sample, researchers can make inferences about the larger population.

For example, if a researcher wants to study the average height of people in a certain city, it would be impractical to measure the height of every single person in the city.

Instead, the researcher could select a representative sample of people and measure their height, then use statistical methods to estimate the average height of the entire population.

In summary, while the population refers to the entire set of elements in which a researcher is interested, a sample is a smaller subset of that population that is selected for study.

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The coordinates of the foot of the perpendicular drawn from the point (6, 3) to the line by segment joining (4,1) and (8,3). is (6.4, 2.2)

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of the line passing through (4,1) and (8,3) is:

y - 1 = [(3 - 1)/(8 - 4)](x - 4)

y = 0.5x - 1

The line perpendicular to y = 0.5x - 1 has a slope of -2. It passes the point (6, 3), hence:

y - 3 = -2(x - 6)

y = -2x + 15

The line y = 0.5x - 1 and y = -2x + 15 intersect at point (6.4, 2.2)

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\(\large \underline\mathcal{ » \: QUESTION \: : }\)

6. What is the domain of this function?

(0, 2), (1, 3), (2, 4), (3,5), (4,6)

the domain is the set of all the values x of while the range is the set of all the value of y

\( \tt \:1.) (0, 2), (1, 3), (2, 4), (3,5), (4, 6)\)

\( \tt \: DOMAIN = ({{0,1,2,3,4}})\)

\( \tt \: RANGE (2,3,4,5,6)\)

Answer:

\(10x - 7x + 3 \)

\( = 3x + 3\)

The answer is C. 3x + 3

Probabilities are used to determine the chances of events

The value of t is 16

The number of bricks is given as t

Let the number of red bricks be x.

So, the number of blue bricks would be t - x

So, the probability values are:

\(\frac{x -1}{t - 1} = \frac 13\) --- when the both bricks are red

\(\frac{x}{t - 1} = \frac 25\) --- when only the second brick is red

Divide both equations

\(\frac{x -1}{t - 1} \div \frac{x}{t - 1} = \frac 13 \div \frac 25\)

Divide

\(\frac{x -1}{x} = \frac 13 \div \frac 25\)

This gives

\(\frac{x -1}{x} = \frac 13 *\frac 52\)

Evaluate the product

\(\frac{x -1}{x} = \frac 56\)

Cross multiply

\(6x - 6 = 5x\)

Collect like terms

\(6x - 5x = 6\)

\(x = 6\)

Recall that:

\(\frac{x -1}{t - 1} = \frac 13\)

So, we have:

\(\frac{6 -1}{t - 1} = \frac 13\)

\(\frac{5}{t - 1} = \frac 13\)

Cross multiply

\(t -1 =15\)

Add 1 to both sides

\(t = 16\)

Hence, the value of t is 16

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x+5 is not a factor f(x) = x³ - 4x² + 3x + 7

A polynomial is an expression consisting of indeterminate (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and natural powers of variables. An example of a polynomial of a single indeterminate x is x2 − 4x + 7.

Using  the remainder theorem so if a polynomial p(x) is divided by x-a the remainder obtained is p(a) therefore X= -5

Substituting -5 in the function and if the result is 0 then is a factor

(-5)^3 - 4(-5)^2 + 3(-5) + 7 = -233

Therefore x+5 is not a factor

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By using combination, it can be obtained that

Number of simple random samples of size 3 that can be selected from a population of size 7 = 35

What is combination?

Combination determines the number of arrangements that can be made from a collection of objects when the order of arrangement is not taken into account.

Here, concept of combination is used

Number of simple random samples of size 3 that can be selected from a population of size 7 = \({7 \choose 3}\) = 35

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The difference quotient of the function f(x) = 4x² - 5x is 8x + 4h - 5.

The formula for difference quotient is expressed as:

\(\frac{f(x+h)-f(x)}{h}\)

Given the function in the question:

f(x) = 4x² - 5x

To solve for the difference quotient, we evaluate the function at x = x+h:

First;

f(x + h) = 4(x + h)² - 5(x + h)

Simplifying, we gt:

f(x + h) = 4x² + 8hx + 4h² - 5x - 5h

f(x + h) = 4h² + 8hx + 4x² - 5h - 5x

Next, plug in the components into the difference quotient formula:

\(\frac{f(x+h)-f(x)}{h}\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - (4x^2 - 5x)}{h}\\\\Simplify\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - 4x^2 + 5x)}{h}\\\\\frac{(4h^2 + 8hx - 5h)}{h}\\\\\frac{h(4h + 8x - 5)}{h}\\\\8x + 4h -5\)

Therefore, the difference quotient is 8x + 4h - 5.

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Answer:

The fear of a local outbreak of the virus, limited staffing due to health concrens from the administration who run the school.

Step-by-step explanation:

In simple linear regression, the predictor variable is the independent variable, which is used to predict the value of the dependent variable. It is also referred to as the explanatory variable, as it is used to explain the variability in the response variable.

For example, in a study that examines the relationship between the hours studied and exam scores, the predictor variable is the number of hours studied, and the dependent variable is the exam score.

The predictor variable is plotted on the x-axis, while the dependent variable is plotted on the y-axis in a scatter plot. The relationship between the predictor and the dependent variable is represented by a straight line, which is determined by the regression equation.

The slope of the line represents the change in the dependent variable for each unit change in the predictor variable.

In summary, the predictor variable is the variable that is used to predict or explain the changes in the dependent variable in simple linear regression.

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The polynomial function of least degree with integral coefficients is equal to f(x) = x³ - 4x² + x + 6 with the given zeros 3, 2, -1.

As given in the question,

Given zeros of the polynomial function are :

3, 2, -1

⇒ ( x - 3 ) =0 or ( x - 2 ) = 0 or ( x + 1 ) = 0

Polynomial function of the given factors  ( x - 3 ) =0 or ( x - 2 ) = 0 or

( x + 1 ) = 0 is given by :

f (x ) = ( x - 3 )( x - 2 )( x + 1 )

⇒ f(x) = ( x² - 3x - 2x + 6 ) ( x + 1 )

⇒ f(x) = ( x² - 5x + 6 ) ( x + 1 )

⇒ f(x) = x³ + x² -5x² - 5x + 6x + 6

⇒f(x) = x³ - 4x² + x + 6

Therefore, the required polynomial function of least degree with integral coefficients using given zeros is equal to f(x) = x³ - 4x² + x + 6.

The complete question is:

Write a polynomial function of least degree with integral coefficients that has the given zeros 3, 2, -1?

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Answer:

1.3455

Step-by-step explanation:

A 15% increase is a multiplication by 1.15

So a 15% and a 17% increase is a multiplication of 1.15*1.17 = 1.3455

Answer:

0.9545

Step-by-step explanation:

Let an integer be x.

If x is increased by 15%, then the value of the number would be

115/100x=1.15x

If 1.15x is decreased by 17%, then the value of the number would be:

(100-17)/100×1.15x

83/100×1.15x=0.9545x

Answer:

d=7.4

d= =square 1.

Step-by-step explanation:

Answer:

7.4 meters

Step-by-step explanation:

Solve for the radius:

\(A=\pi r^2\)

\(42.71=\pi r^2\)

\(\frac{42.71}{\pi}=r^2\)

\(\sqrt{\frac{42.71}{\pi}}=r\)

Solve for the diameter:

\(d=2r\)

\(d=2\sqrt{\frac{42.71}{\pi}}\)

\(d\approx7.4\)

Therefore, the diameter of the circle is about 7.4 meters

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. The given statement is True.

A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.

The given statement is true and can be observed in the given image below.

Hence, the given statement is True.

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The probability that Steve will get a nine on the next card he is dealt is 4/47.  Steve and Cathy are playing a card game with a standard deck of 52 playing cards. After Cathy is dealt an ace and a four and Steve is dealt a jack, there are 49 cards left in the deck. Out of the remaining cards, there are three aces.

If Steve gets an ace on the next card he is dealt, he will win. The probability of this happening is 3/49, as there are three aces left in the deck out of a total of 49 cards remaining.

After Steve gets a two and Cathy gets a five, there are now 47 cards left in the deck. The probability of Steve getting a nine on the next card he is dealt is 4/47, as there are four nines left in the deck out of a total of 47 cards remaining.

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If the time series in an exponential smoothing model exhibits a negative trend, the correct option is: C) forecast will overshoot the actual values

Exponential smoothing is a time series forecasting method that uses a weighted average of past observations, with the weights decreasing exponentially as the observations get older.

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From the given information, we know that the expression that models the population of amoebas with respect to time is:

Where x is the number of hours. by replacing 9 for x, we can find the population after 9 hours, like this:

Then, the population of amoebas after 9 hours is 5832.

Answer:

Step-by-step explanation: Since the purpose of solving two-step equations is to determine the value of x, the multiplication or division of the coefficient attached to x must be the last step. Because of this, you must use inverse operations to solve two-step equations. This means adding and subtracting first, then multiplying and dividing.

We shall apply the method of break apart and distribute to solve the question as follows;

Break apart 54 into multiples of 6;

Divide each part by 6

Note that you may break apart the number 54 into bigger multiples of 6 (e.g, 30 and 24 OR, 36 and 18)

Hey there!

Your mean is known as your average / total. To find your mean you have to ADD the total numbers you have in your data plot then DIVIDE it by the total number you have in your set.

FORMULA:

sum of numbers ÷ total numbers = mean

YOUR EQUATION:

MEAN = 6 + 14 / 2

MEAN = 20 / 2

MEAN = 10

Therefore, your answer is: 10

Good luck on your assignment & enjoy day!

~Amphitrite1040:)

Answer:

10

(6+14)/2 = 10

Step-by-step explanation: