for which of the three intervals do you have the most confidence that the interval captures the population mean

Answer:

[tex]\frac{7}{10}[/tex]

Step-by-step explanation:

c. A greater proportion of adolescent girls with anorexia nervosa live in the South than live in the other regions when compared to the general US population.

Null Hypothesis, [tex]H_{0}[/tex] : All proportions are the same  

Alternative Hypothesis, [tex]H_{1}[/tex]: At least two of the proportions are not the same

The alternative and null are both population-based assertions. The reason for this is that the purpose of hypothesis testing is to draw conclusions about a population from a sample.

The null and alternative hypotheses are two competing claims that researchers weigh the evidence for and against using a statistical test:

Null hypothesis: There’s no effect on the population.

Alternative hypothesis: There’s an effect on the population.

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After 81 minutes of driving the distance to destination is 32.8 miles.

Th function that has two variables with first order term is called linear function.  While plotting on the XY coordinate system we get a straight line.

Why do we use linear equation in this problem?

as per question, distance to destination is a linear function of total driving time so we use the equation of straight-line having slope m and y intercept b for determining unknown values.

given, distance to destination in miles is a linear function of total driving time in minutes.

y=mx+b

in the equation, y denotes the distance to destination in miles

                 x is the total driving time in minutes

         m is the slope of linear equation

      b is the y intercept

Milan has 68 miles to his destination after 37 minutes of driving

68 = mx37+b

he has 45.6 miles to destination after 65 minutes of driving

45.6=mX65+b

solving the two equations by addition method

slope, m= -0.8

from the above two equation

we get b=97.6

now, after 81 minutes of driving the distance to destination, y=mx+b

                                               y= -0.8x81+97.6

                               distance = 32.8 miles

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After the markup in the price, the new cost of goldfish will be equal to $4.45.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Cost of goldfish = $3.45

Markup = 29%

So, the price increase will be,

(3.45 × 29)/100

= 100.05/100

= 1.0005

So, the new price is,

$3.45 + $1.0005

= $4.4505 ≈ $4.45

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We get 3y= √(x+2) after vertically stretches by 3 and translated 2 unit left.

If a function is multiplied by a positive value that greater than 1, the graph of function is called vertically stretched graph. Here vertically stretches means the factor 3>1 and we need to multiply the y value by 3.

Translation of a graph means move the graph from one position to another position without changing its size, shape or orientation. Here, the graph is translated 2 units left so we need to add 2 with the x value.

We are given a graph, y= √X

Hence, after transformation the graph became 3y= √(x+2)

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Using the two column proof, we have been able to prove that;

ΔPQR ≅ ΔTSR by AAS Congruency Postulate

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Thus, the two column proof required is as follows;

Statement 1: PR ≅ TR

Reason 1: Given

Statement 2: ∠PQR ≅ ∠TSR

Reason 2: Given

Statement 3: ∠PRQ ≅ ∠TRS

Reason 3: Opposite angles

Statement 4: ΔPQR ≅ ΔTSR

Reason 4: AAS Congruency postulate

AAS congruency postulate is one of the 5 major triangle congruency postulates that is defined as Angle-Angle-Side. This tells us that two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

We can also say that Opposite angles are defined as the angles that are directly opposite each other where two lines cross. The intersection point in this regards is called the vertex, which is the point where the lines connect to form the angle. Opposite angles are also referred to as vertical angles

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44 seconds will pass before the planes are at the same altitude.

What do you mean by algebraic expression?

An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

There are three main types of algebraic expressions:

Monomial Expression

Binomial Expression

Polynomial Expression

An algebraic expression with only one term is called a monomial.

It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.

Let x seconds will pass before the planes are at the same altitude.

Plane A, 3500 + 45.5x

Plane B, 2609 + 65.75x

x is number of seconds of time

When altitudes equal

3500 + 45.5x = 2609 + 65.75x

3500 - 2609 = 65.75x - 45.5x

891 = 20.25x

891/20.25 = x

44 = x

Therefore, 44 seconds will pass before the planes are at the same altitude.

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Answer: 12

Step-by-step explanation:

Since we are given what v and w are, we can directly plug them in to solve the expression.

w²+1v        [plug in v and w]

(3)²+1(3)     [exponent]

9+1(3)        [multiply]

9+3            [add]

12

The expression is equal to 12.

The two equations that equal Willie's number are given as follows:

Jennie's number is unknown, hence we use the variable x to refer to her number.

Robbie picked a number that is nine more than four times Jennie's number, hence:

y = 9 + 4x.

(using y to refer to Robbie's number).

Willie picked a number that is two less than three times Robbie's number, hence:

n = 3y - 2.

(using n to refer to Willie's number).

Considering the expression for y, the second expression that describes Willie's number is given as follows:

n = 3(9 + 4x) - 2

n = 12x + 25.

The problems asks foir the two expressions that equals Willie's number.

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The probability of selecting a white rabbit on the second draw, given that the first rabbit selected was a black rabbit is 3/5.

P(B∩W) = 1/4  getting a black and a white rabbit

P(B) = 5/12  getting a black rabbit

 P(W/B)

= P(B∩W) / P(B)

= (1/4) / (5/12)

= 12/20

= 3/5

Therefore, the conditional probability is 3/5.

Conditional probability is the chance of an event A occurring when another event B in relation to A has previously occurred. P(A|B) represents it. As seen in the picture above, S represents sample space, and A and B represent events.

The potential of an event or outcome occurring based on the existence of a preceding event or outcome is known as conditional probability. It is computed by multiplying the preceding event's probability by the renewed probability of the next, or conditional, occurrence.

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Given that x is a normal variable with mean = 47 and standard deviation = 6.4, find the following probabilities.

Generally, To solve these problems, we can use the standard normal distribution table or a computer program to find the desired probabilities.

First, we need to standardize the given values of x by subtracting the mean and dividing by the standard deviation. This gives us a standard normal random variable, denoted by Z, with a mean of 0 and a standard deviation of 1.

(a) P(x ≤ 60) = P(Z ≤ (60 - 47)/6.4) = P(Z ≤ 1.5625). From the standard normal distribution table or a computer program, we find that P(Z ≤ 1.5625) = 0.9356.

(b) P(x ≥ 50) = P(Z ≥ (50 - 47)/6.4) = P(Z ≥ 0.46875). From the standard normal distribution table or a computer program, we find that P(Z ≥ 0.46875) = 0.6744.

(c) P(50 ≤ x ≤ 60) = P(0.46875 ≤ Z ≤ 1.5625) = P(Z ≤ 1.5625) - P(Z ≤ 0.46875) = 0.9356 - 0.6744 = 0.2612.

Therefore, the probabilities are as follows:

(a) P(x ≤ 60) = 0.9356 (b) P(x ≥ 50) = 0.6744 (c) P(50 ≤ x ≤ 60) = 0.2612

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Answer:

4/15 cups of soda per hour

Step-by-step explanation:

1 1/4 = 5/4 and if 5/4 hours yielded 1/3 cups, you would have to multiply 1/3 by the reciprocal to find the hourly rate

1         4             4

-   *     -      =      --

3        5             15

The function f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex] is continuous at x = 2.

Given that,

We need to follow the following steps:

The function is:

f(x) = 3x^4 − 5x + ^3√(x^2 + 4)

The function is continuous at point x=2 if:

The function f(x) exists at x=2.

The limit on both sides of 2 exists.

The value of the function at x=2 is the same as the value of the limit of the function at x = 2.

Therefore:

The value of the function at x = 2 is:

f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex]

f(2) = 3[tex](2^{4} )[/tex] - 5[tex](2^{3} )[/tex] + 3[tex]\sqrt{2^{2} +4}[/tex]

f(2) = 3*16 - 5*8 + 3 [tex]\sqrt{8}[/tex]

f(2) = 48 - 40 + 3*2.82

f(2) = 8 + 8.46

f(2) = 16.46

The limit of the f(x) is the same at both sides of x=2, that is, the evaluation of the limit for values coming below x = 2, or 1,0.5  is the same that the limit for values coming above x = 2, or 3 , 4 , 5 etc.

For this case:

[tex]lim_{x -2} f(x)[/tex] = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex]

[tex]lim_{x -2} f(x)[/tex] = 16.46

Since

f(2) = 16.46

And

[tex]lim_{x -2} f(x)[/tex] = 16.46

Therefore,

The function f(x) = 3[tex]x^{4}[/tex] - 5[tex]x^{3}[/tex] + 3 [tex]\sqrt{x^{2} +4}[/tex] is continuous at x = 2.

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Answer:

The two locker numbers are 80 and 69.

Hope it helps!

The value of x = 2nπ,  (n ∈ Z) and

[tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex],  (n ∈ Z)

What are Trigonometric Identities?

Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables  being on both sides of an equation. Geometrically, these identities involve certain trigonometric functions(  similar as sine, cosine, tangent ) of one or  further angles.

According to question

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + cos(x) - 1 = 0

{ cos(2x) = 1 - 2sin²(x) }

cos(x) = 1 - 2sin²(x/2)

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + 1 - 2sin²(x/2) - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2) + 1 - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2)  = 0

⇒ sin(x/2)(- 2sin(x/2) + 1)  = 0

⇒ sin(x/2) = 0 , x = 2nπ (n ∈ Z)

and

⇒ sin(x/2) = 1/2 , [tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex] (n ∈ Z)

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Answer:

y=-2x/3

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes.

An example of opposite reciprocals: -1/2 and 2

-1*2=-2

The reciprocal of -2 is -1/2.

In order to solve for slope, isolate y:

3x - 2y = 7  ==> solve for y

3x = 7 + 2y  ==> add 2y on both sides to make y positive

3x - 7 = 2y  ==> isolate y by subtracting 7 on both sides

y = (3x - 7)/2  ==> divide both sides by 2 in order to isolate y

y = 3x/2 - 7/2  ==> distribution

Hence, the slope is 3/2  <== 3x/2.

Now, find the perpendicular slope:

-1*3/2=-3/2

The reciprocal of -3/2 is -2/3 ==> the slope of the perpendicular equation

Now, find the equation of the line that passes through (3, -2):

y=mx+b  ==> slope-intercept equation

-2=-2/3 * (3) + b  ==> plugin (x=3, y=-2) and m=-2/3 which is the slope.

-2 = 3 * (-2/3) + b  ==> solve for b

-2 = -6/3 + b

-2 = -2 + b

b = 0 ==> -2 + 0 = -2

y=-2x/3+0  ==> plugin the slope -2/3 and b=0.

y=-2x/3+0  ==> y=-2x/3

Hence, the equation is y=-2x/3.

Answer:

Here is the answer

Step-by-step explanation:

If 40% of the students in the class are female, then there are 40/100 * 120 = 48 female students.

If 70 male students passed with a 100% pass rate, then the pass rate for male students is 100%.

If the pass rate for male students is 100%, then the pass rate for female students must also be 100%. This is because the pass rate is calculated as the number of students who pass divided by the total number of students, and if all the male students pass, then the pass rate for male students must be 100%.

Therefore, the pass rate for female students at a 100% rate is also 100%.

The expression equivalent to "20 divided by 1 plus 4" is 20 ÷ 1 + 4.

The rules of PEDMAS can be understood by the full form of the name. B stands for bracket, O for of, D for division, M for multiplication, A for addition and S stands for subtraction. For a mathematical expression involving the combination of any of these operators the priority will be given to the letter that comes first.

The given statement for the problem is, " 20 divided by 1 plus 4".

It can be written in the form of expression as follows,

The sign of plus is given as '+'.

And, for divide it is '÷'.

Now, 20 divided by 1 plus 4 can be written as,

20 ÷ 1 + 4

Which is evaluated  by BODMAS to give,

20 + 4 = 24.

Hence, the expression for the given case is 20 ÷ 1 + 4 which is equal to 24.

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Answer:

Below

Step-by-step explanation:

2^9 possibilities =512

9 possibles with only ONE tails  (9 C 1)

36 possibles with TWO tails     ( 9 C 2)

45 out of 512       45/512 = .088  

Answer:m

Step-by-step explanation:

Inverse of the equation y = [tex]2x^2-8[/tex] is [tex]y = \pm \sqrt{\frac{x+8}{2} }[/tex]

What do you mean by inverse function?

Let f and g be two functions. If

f(g(x)) = x and g(f(x)) = x,

g is the reciprocal of f, and f is the reciprocal of g.

Some functions don't have inverses Let f be a function.

If the horizontal line crosses the graph of f more than once, then f has no inverse.

If no horizontal line crosses the graph of f more than once, then f is the inverse.

Given equation:

y = [tex]2x^2-8[/tex]

To find the inverse of the function find the value of the x in terms of y

[tex]2x^2-8=y[/tex]

[tex]2x^2=y+8[/tex]

[tex]x^{2} =\frac{y+8}{2}[/tex]

x = [tex]\pm \sqrt{\frac{y+8}{2} }[/tex]

Therefore, inverse of the equation y = [tex]2x^2-8[/tex] is [tex]y = \pm \sqrt{\frac{x+8}{2} }[/tex]

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Answer: 2 complete games

Step-by-step explanation:

add shoes and game charge

$10.00 + 2.75 = 12.75 <— that’s 1 complete game

subtract it from $30.00

$30.00 - 12.75 = 17.25.

A complete game costs 12.75. so, Kim had enough money for one more game.

17.25 - 12.75 = $4.50 remaining after 2 complete games

Answer: 7 games

Step-by-step explanation: if it charges 10 for shoes, then you already subtract 10 from 30. 30-10=20. then, to find out how many games she can play, divide 2.75 from 20. 20/2.75=7.272727.... Since you can't pay for half of a game, it would be 7 games.

There are 21 days for there to be 150 frogs in the pond.

There are 37 days for there to be 1400 frogs in the pond.

What is exponential growth?

Quantity increases over time through a process called exponential growth. When a quantity's instantaneous rate of change with respect to time is proportional to the quantity itself, it happens.

Given:

There are currently 25 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days.

The exponential equation for the given problem is,

[tex]A(t) = Ar^t^/^1^0[/tex]

To find the number of days for there to be 150 frogs in the pond.

Here,

A(t) = 250, A = 25, r = 3

⇒

[tex]250 = 25(3)^t^/^1^0\\10 = 3^t^/^1^0\\t = 20.97[/tex]

t ≈ 21

Hence, there are 21 days for there to be 150 frogs in the pond.

Now to find how long for there to be 1400 frogs in the pond, we solve:

[tex]1400 = 25(3)^t^/^1^0\\56 = (3)^t^/^1^0\\t = 36.64[/tex]

t ≈ 37

Hence, there are 37 days for there to be 1400 frogs in the pond.

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The value of the expression is 3st² - s² is 315.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

Given expression is 3st² - s².

For s = 3 and t = 6, find the value of the expression 3st² - s².

To find the value of the expression, replace s by 3 and t by 6:

3st² - s²

= 3×3×6² - 3²

= (9 × 36) - 9

= 324 - 9

= 315

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The required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.

A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept.

The equation of the line's general form is:

y = MX + c

Where, m = slope, c = y-intercept and slope = ( y₂ - y₁ ) / ( x₂ - x₁ ).

Determine the line's slope:

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope = ( -2-2) / (2+7 )

Slope= -4/9

The y-intercept is determined as follows:

y = MX + c

2 = -4/9x 2+c

c = -8/9

The lines' equation:

y = MX + c

y = -4/9x - 8/9

Therefore, the required equation of the line which contains the points (−7,2) and (2,−2) is y = -4/9x - 8/9.

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Answer:

½

pa brainliest po thanks

Answer:

Step-by-step explanation:

6 small rectangles, 3 are shaded and three are not, so half,

your answer is 1/2 (one half)

The correct statements regarding the transformations to the volumes are given as follows:

1. A cone's radius increases x 3: -> The cone's volume will increase x 9.

2. A cone's height increases x 3: -> The cone's volume will increase x 3

3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.

4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.

The volume of a cone of radius r and height h is given as follows:

V = πr²h/3.

Then the scale factors are considered as follows:

The volume of an sphere of radius r is given as follows:

V = 4πr³/3.

Then when the radius is multiplied by 3, the volume is multiplied by 27, as 3³ = 27, and the radius is cubed in the equation.

The volume of a cylinder of radius r and height h is given as follows:

V = πr²h.

Then if the radius is multiplied by 6, the volume is multiplied by 36, as the variable r is squared in the equation for the volume.

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In the case where a=78, b=716, c=0.8, and d=14, the simplest form of a mixed number is -117/640.

The smallest equivalent fraction of the number is the form that is the simplest. How to find the most basic form: In the numerator and denominator, look for shared factors. Examine the fraction to see if one of the numbers is a prime number.

The term "reduced form" refers to the fraction's simplest form. As an illustration, the simplest form of a fraction with a common component of 1 is 34 However, while 2/4 can be further condensed and expressed as 12, it is not the most basic form.

When the top and bottom of a fraction cannot be any smaller while remaining whole numbers, it is said to be in its simplest form.

b a + c d

b= -7/16

a= 7/8

c= 08.(4/5)

d= 1/4

It can therefore be calculated as follows.

-7/16×7/8 + 4/5×1/4

-49/128 + 1/5

-246+128/640

= -117/640

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Answer: x = 70

Step-by-step explanation:

You can simply solve for x by simplifying both sides of the equation, then isolating the variable

Solve, x/7 - 2 = 8, for x.

x/7 = 10, added the value of 2 to both sides of the equation.

x=70, multiplied the value of 7 to both sides of the equation.

Thus the value of x is equal to 70.

Observing the nature of the provided equation and the degree of the polynomial , The answer is Cubic.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The highest degree of a polynomial's monomials (individual terms) with non-zero coefficients is referred to as the polynomial's degree in mathematics.

Expression : [tex]8x^{3}-1[/tex]

Degree of polynomial =3

The expression is a Cubic Expression.

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Observing the nature of the provided equation and the degree of the polynomial , The answer is Cubic.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The highest degree of a polynomial's monomials (individual terms) with non-zero coefficients is referred to as the polynomial's degree in mathematics.

Expression : 8x³ - 1

Degree of polynomial =3

The expression is a Cubic Expression.

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