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The 95% confidence interval for the population mean SAT score is given as follows:

(1340, 1460).

The confidence interval is calculated using the t-distribution, as the standard deviation for the population is not known, only for the sample.

The bounds are obtained according to the equation defined as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

In the context of this problem, the values of these parameters are given as follows:

[tex]\overline{x} = 1400, n = 64, s = 240[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 64 - 1 = 63 df, is t = 1.998.

Then the lower bound of the interval is of:

1400 - 1.998 x 240/sqrt(64) = 1340.

The upper bound of the interval is of:

1400 + 1.998 x 240/sqrt(64) = 1460.

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Answer: it would be 18 candies that are left

Step-by-step explanation:  

I did the math

The expression  -3/10 X (-8/15) is positive

Expression

Expression in mathematics has two or more variables, terms and constants. Also, arithmetic expression contains only numbers and mathematical operators and algebraic expression

The expression has negative sign and from mathematical calculation we already know the following relation:

+ x + = +

positive multiply by positive equals Positive

- x - = +

Negative multiply by Negative equals Positive

+ x - = -

Positive multiply by Negative equal Negative

hence,   - [tex]\frac{3}{10}[/tex] x - [tex]\frac{8}{15}[/tex]

The negative sign multiply by  -3/10 X (-8/15) sign will give positive.

Therefore, the expression  -3/10 X (-8/15) is positive.

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Answer:

The three numbers are 3, 7 and 13

Step-by-step explanation:

Considering the 3 numbers: x, y and z

x + z = 16

z=16-x

3x=z-4

3x=16-x-4

4x=12

x=3

3+z=16

z=16-3

z=13

3+13+y=23

y=23-13-3

y=7

Hope this helps :)

Answer:

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

It is assumed the first column represents x- values and the second column represents y- values.

Inverse variation equation:

Substitute one pair of coordinates, x = 3, y = 10:

Correct choice is B.

Answer:

b) k = 30

Step-by-step explanation:

Formula we use,

→ y = k/x

Now the value of k will be,

→ y = k/x

→ 10 = k/3 || → 6 = k/5

→ k/3 = 10 || → k/5 = 6

→ k = 10 × 3 || → k = 6 × 5

→ [ k = 30 ] || → [ k = 30 ]

Hence, the value of k is 30.

-3 is less than 2

< is the symbol

The simplest expression of the ratio of circles to squares is 5:3.

Describe ratio.

A relationship between two quantities is called a ratio, and it is expressed as one quantity divided by the other.

There are 6 circles and 10 squares.

These steps can be used to determine the ratio of two quantities:

Finding the quantities of both scenarios for which we are calculating the ratio is the first step. There are 10 squares and 6 circles in this instance.

It should be expressed as a fraction, a/b. Thus, we represent it as 10/6.

If you can, make the fraction even simpler. The ultimate ratio will be shown by the simple fraction.

In this case, 10/6 can be reduced to 5/3.

As a result, the simplest expression of the ratio of circles to squares is 5:3.

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A) 3x+9y-1 = 3(x+3y) -1, here distributive property is used the 3 is multiplied with each term inside the bracket.

What is algebraic operations?
Any of the common arithmetic operations, such as addi - tion, subtraction, multiplication, division, raising to a complete number power, and taking roots, are considered basic algebraic operations in mathematics (fractional power). These operations could be applied to numerical data, in which case people are frequently referred to as arithmetic operations. Similar operations can be carried out on factors, algebraic expressions, and, more generally, on components of algebraic structures like groups and fields. Another way to describe an algebraic operation is as a function from the Cartesian power of the a set to the same set. The dot product is an example of an operation that can be described by compounding simple algebraic operations, and is referred to as an algebraic operation.

b) 7x+5y-5y = 7x

Here the Additive inverse of 5y is used which is -5y .

c) (x-4)(x+3) = 0

here distributive property of addition over multiplication is used.

d) 4x+5x = 5x+4x

here commutative property is used.

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The value of the quotient of the polynomial is 2x^2 + 2x + 10 and the remainder is 28

A method for solving a rational number that represents a polynomial divided by a monomial or another polynomial is called "dividing polynomials." In order to divide normally, we place the dividend and the divisor in the exact same manner.

Divide the first term of the dividend by the highest term of the divisor, which in this case is x (i.e., the term with the highest power of x).

Divide the divisor by the outcome you just got (the first term of the eventual quotient).

By following the above rules where

2x3-4x2+3x+2 is divided by the x-3, We get the following equation

where

quotient is 2x2+2x+10

and the remainder is 28

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The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

The function is given below.

f(x) = 28x² - 7

For the zeroes of the function, put f(x) = 0, then we have

f(x) = 0

28x² - 7 = 0

x² = 1/4

x = ± 1/2

The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.

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Answer:

the remaining mass is 7.3 g

Step-by-step explanation:

a=30g

t=200 years

h=98 years

f(98)=a([tex](\frac{1}{2})^ \frac{t}{h}[/tex]

f(98)=30([tex](\frac{1}{2})^ \frac{200}{98}[/tex]

f(98)=7.3

A comparison of multiple treatments and the use of the double-blind method are two fundamental components of all statistically designed experiments. (6) Compare various treatments; assign patients to treatments at random.

What is double-blind method?

A kind of clinical experiment in which neither the participants nor the researcher is aware of the treatment or intervention that each participant is receiving until the trial is complete.

                      This reduces the likelihood of skewed study outcomes.

What is a sample of a double-blind study?

Imagine, for instance, that researchers are looking into the effects of a novel medication.

                            The participants in a double-blind study would not be aware of who was receiving the real medication and who was receiving a placebo, and neither would the researchers who interact with them.

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The complete question is -

Two essential features of all statistically designed experiments are (2 Points) O use enough subjects; always have a control groups O always have a placebo group; use the double - blind method O use a block design; use chance to assign subjects to treatments O compare several treatments; use the double - blind method O compare several treatments; use chance to assign subjects to treatments.

The total change in the stock market from the beginning of the day to the end of the day is 89.75

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

At the beginning of the day, the stock market goes up 30 1/2 points.

At the end of the day, the stock market goes down 120 1/4 points.

The total change in the stock market from the beginning of the day to the end of the day.

= 120(1/4) - 30(1/2)

= 481/4 - 61/2

= 120.25 - 30.5

= 89.75

Thus,

The total change in the stock market from the beginning of the day to the end of the day is 89.75

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Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.

Based on the expected value, Rosie's statement is correct.

The expected value, denoted as E(X), represents the average or mean value of a random variable, in this case, the sum of points in a given turn when rolling the five dice.

Tom's statement, "A player will most likely get 17.5 points in any given roll," is not accurate. The expected value of 17.5 points does not necessarily mean that a player is most likely to get exactly 17.5 points in any single roll. Instead, it indicates that over many rolls, the average value of points earned in a turn is 17.5 points.

On the other hand, Rosie's statement, "Over 100 turns, we can expect a total of about 175 points," is correct. Since the expected value is 17.5 points per turn, over 100 turns, we can expect the total sum of points to be approximately 100 turns × 17.5 points/turn = 1750 points.

In summary, the expected value of 17.5 points represents the average outcome over multiple rolls, and based on this value, Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.

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The complete question:

Tom and Rosie are designing a game. In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=5 points, and the highest is 6+6+6+6+6=30 points.

They let X represent the sum in a given turn, and they find the expected value of X is E(X) = 17.5 points.

Tom says, "A player will most likely get 17.5 points in any given roll."

Rosie says, "Over 100 turns, we can expect a total of about 175 points."

Whose statement is correct based on the expected value?

Answer:

3

Step-by-step explanation:

Answer:

For the first graph:

Domain: -∞ [tex]\leq[/tex] x [tex]\leq[/tex] ∞

Range: y [tex]\geq[/tex] 3

For the second graph:

Domain: 0 [tex]\leq[/tex] x [tex]\leq[/tex] 4

Range: y [tex]\leq[/tex] 64

Step-by-step explanation:

For the second graph, I'm assuming that that point are stopping at (0,0) and (4,0) that's why I wrote that for the domain. If it doesn't stop, then the domain would be the same and the first graph.

The divide rule will be;

⇒ Divisor = (Dividend - Remainder) / Quotient

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Vocabulary Use the terms divisor, dividend, quotient, and remainder.

Now,

If we have to find the divisor , then we can use the divide rule as;

⇒ Divisor = (Dividend - Remainder) / Quotient

Thus, The divide rule will be;

⇒ Divisor = (Dividend - Remainder) / Quotient

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Answer:

5cm. 8cm

Step-by-step explanation:

Label all the vertices then use Pythagorean theorem

c² = a² + b²

If an 80% confidence interval for a proportion is found to be (0.27, 0.33), then the sample proportion would be 0.30

Sampling is frequently used to estimate the proportion of a population that has a given attribute, such as the proportion of all faulty goods coming off an assembly line or the proportion of all individuals visiting a retail store who make a purchase before leaving. The percentages for the population and sample are written as p and p, respectively. Thus, if 43% of individuals visiting a business make a purchase before departing, p = 0.43; if 78 people enter the store and make a transaction, p=78/200=0.39.

The sample proportion is a random variable because it differs from sample to sample in ways that are impossible to anticipate in advance.

How to solve?

For this case the confidence interval is given by:

(0.27; 0.33)

We can find the estimaed proportion in the following way:

p = (0.27 + 0.33)/2 = 0.30

then the sample proportion would be 0.30

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Answer:

12 miles

Step-by-step explanation:

72 x [tex]\frac{10}{60}[/tex] = 12

Answer:

Step-by-step explanation:

First of all let's look at the side lengths of both figures.

Let's see how the corresponding sides relate:-

[tex]\sf 6*\cfrac{1}{3} =3[/tex]

[tex]\sf 3*\cfrac{1}{3} =1[/tex]

We can see that all sides scale by the same factor of 1/3.

Therefore, YES A is a scaled copy of Figure B.

______________________

Hope this helps!

Have a great day!

The exact value of sin(u + v), obtained using trigonometric identities is for sine and cosine is 16/65

Trigonometric identities are equations that involve trigonometric functions that are valid for all values of the input variable.

The possible value of sin(u) obtained from a similar question posted online is; sin(u) = 5/13

Both u and v are in quadrant II

The trigonometric identity of the addition formula for the sine of the sum of two angles, indicates;

sin(u + v) = sin(u)·cos(v) + sin(v)·cos(u)

sin(u) = 5/13

cos(v) = -4/5

sin(v) = √(1 - (cos(v))²)

Therefore;

sin(v) = √(1 - (-4/5)²) = 3/5

cos(u) = √(1 - (sin(v))²)

Therefore;

cos(u) = √(1 - (5/13)²) = 12/13

Therefore;

sin(u + v) = (5/13) × (-4/5) + (3/5) × (12/13) = 16/65

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There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

What are qualitative and quantitative variables?

The variables are classified as qualitative or quantitative as follows:

Qualitative variables assume labels as values.

Quantitative variables assume numbers as values.

The relevance of the variables according to association and correlation are given as follows:

Qualitative variables can have association.

Quantitative variables can have correlation.

The variables in this problem are given as follows:

Television watching -> yes/no -> qualitative.

Crimes committed -> yes/no -> qualitative.

As they are qualitative variables, they can have association, and thus there is no correlation between the two variables

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If mean of 11 numbers is 7 one of the numbers, 13, is deleted then the mean of remaining 10 numbers is 6.4

The mean of 7 numbers = 11

We know,

Mean = Sum of the terms / Number of terms

Substitute the values in the equation

11 = Sum of the terms / 7

The sum of the terms = 11 × 7

= 77

Number 13 is deleted

Sum of the terms = 77 - 13

= 64

Number of terms = 11 - 1

= 10

The mean = Sum of the terms / Number of terms

Substitute the values in the equation

= 64 / 10

= 6.4

Hence, the mean of the remaining 10 numbers is 6.4

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Answer: the answer is A,B,E

Step-by-step explanation:

Answer: The answer is (four/seven)

Yes, because it forms a straight line.

Arithmetic; it's a linear function.

Step-by-step explanation:

2023 Edgen

To maximize the profit 29.6 units must be produced.

What is the maxima or minima?

The maxima and minima of a function collectively referred to as extrema in mathematical analysis, are the highest and lowest values of the function, either on the whole domain or within a specific range.

We have given,

The revenue function is,

R(x)=3x

Cost function,

C(x)=0.05x^2+0.04x+10,

Where

x = number of units produced.

Thus, profit = revenue - cost

P(x) = 3x - (0.05x^2+0.04x+10)

= -0.05x^2 + 2.96x - 10

Differentiating with respect to x,

P'(x) = -0.1x + 2.96

Again differentiating with respect to x,

P''(x) = -0.1

For maxima or minima,

P'(x) = 0,

0 = -0.1x + 2.96

-0.1x = -2.96

x = 2.96/0.1

For x = 29.6,

P''(x) = negative,

Hence, to maximize the profit 29.6 units must be produced.

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The solution is y will increase by 2 units with every unit increase in x1

A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.

X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.

In the above question:-

Interpretation of b1=2

it means that y will increase every 2 units for every unit increase in x1

holding x2 constant.

Hence option B is the correct answer.

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The probability that the number 6 will appear between 150 and 200 times inclusively is 0.926.

In the given question, one thousand independent rolls of a fair die will be made.

We have to compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.

Let n=1000 are independent trails.

The probability of success is constant, p=1/6

The probability of success is not constant,

q=1-1/6 = 5/6

let X be the number of times the die shows a 6.

μ = np

μ = 1000*1/6

μ = 166.7

σ=√npq

σ=√1000*1/6*5/6

σ=√5000/36

σ=11.785

Now we used the correlation continuity for finding the probability that number 6 will appear between 150 and 200 times is

P(150≤X≤200)=P(X≤200)-P(X<150)

P(150≤X≤200)=P(Z≤(200+0.5-166.7)/11.785)-P(Z≤(150-0.5-166.7)/11.785)

P(150≤X≤200)=P(Z≤2.87)-P(Z≤-1.46)

P(150≤X≤200)=0.998-0.072

P(150≤X≤200)=0.926

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