suppose a die is tossed 1000 times, and the following frequencies are obtained for the number of pips up when the die comes to a rest. x1 x2 x3 x4 x5 x6 163 178 142 150 183 184 using the chi-squared goodness of fit test, assess whether we have evidence that this is not a symmetrical die. record the standardized residuals.

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:

Step-by-step explanation:

a) 1012⁵ can be written as:

1012⁵ = 15¹² + 05¹¹ + 1*5¹º

= 5¹² + 5¹º

= 3125 + 625

= 3750

(b) 101⁵ can be written as:

101⁵ = 15⁴ + 05³ + 1*5²

= 5⁴ + 5²

= 625 + 25

= 650

(c) 1.1⁵ can be written as:

1.1⁵ = 15¹ + 15º

= 5¹ + 5º

= 25 + 5

= 30

(d) 10.21⁵ can be written as:

10.21⁵ = 15² + 05¹ + 25º + 15⁻¹

= 5² + 2*5º + 5⁻¹

= 25 + 10 + 0.2

= 35.2

(e) 210⁵ can be written as:

210⁵ = 25⁴ + 15²

= 2*625 + 25

= 1250 + 25

= 1275

The equivalent expression for the given expression is 29/3.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given mixed fraction [tex]9\frac{2}{3}[/tex].

There are equivalent improper fractions for all mixed numbers. By multiplying the integer by the denominator and then adding the numerator, they are transformed. The numerator will not change.

Convert mixed fraction to improper fraction as follows

Improper fraction = [(Numerator × Denominator)+Numerator]/Denominator

[(9×3)+2]/3

=[27+2]/3

= 29/3

Therefore, the equivalent fraction for the given mixed fraction is 29/3.

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To determine if the mean reduction in blood pressure is different between the two groups, you can use a statistical test such as a two-sample t-test. This test compares the means of two groups and determines whether the difference between the means is statistically significant.

To conduct the t-test, you will need the following information:

Once you have this information, you can use a statistical software or calculator to perform the t-test and determine the p-value. The p-value is a measure of the probability that the difference between the means is due to chance.

If the p-value is less than the level of significance (5% in this case), then the difference between the means is statistically significant and you can conclude that there is a significant difference in the mean reduction in blood pressure between the two groups.

If the p-value is greater than the level of significance, then the difference between the means is not statistically significant and you cannot conclude that there is a difference in the mean reduction in blood pressure between the two groups.

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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.

Answer:

Step-by-step explanation:

Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.

Let s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...

  s +(s -42) = 244

Add 42 and simplify

  2s = 286

  s = 143 . . . . . divide by 2

  hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs

143 sodas and 101 hot dogs were sold.

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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Answer:

The two locker numbers are 80 and 69.

Hope it helps!

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.

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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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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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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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:

  (c)  x = -1/11(y -3)²

Step-by-step explanation:

You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).

The directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.

The vertex form of the equation is ...

  x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)

Here, we have ...

  p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix

and

  (h, k) = (0, 3)

so the equation is ...

  x = 1/(4(-11/4))(y -3)² +0

  x = -1/11(y -3)²

The interest accrued in the first four years is $1.69 and a half years is $0.21.

What is interest rate?

The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given:

Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college.

The rate is 4.3%.

We have to find the interest accrued in the first four-and-a-half years.

First to find the interest for first four years.

p = $9.800,  r  = 4.3% = 0.043,  t = 4

⇒ I = P x r x t

   I = 9.800 x 0.043 x 4

   I = 1.6856

   I = $1.69

Now to find the interest for a half years.

p = $9.800 ,  r = 4.3% = 0.043,  t = 1/2

I = p x r x t

I = 9.800 x 0.043 x 1/2

I = 0.2107

I = $0.21

Hence, the interest accrued in the first four years is $1.69 and a half years is $0.21.

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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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There is no property named 'left' for the circle. So the answer is 'c'.

Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.

The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.

Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.

Width is another term for diameter of the circle, although it is not commonly used.

Left is the only term which does not have any role in the properties of circles.

Hence, the term 'left' is not a valid property of circles.

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The number of square feet each lot measure is 54, 450 square feet.

Five acres of land were divided into 4 lots of equal size. The number of square feet each lot measure can be calculated as follows:

1 acre = 43,560 square ft

5 acres = ?

cross multiply

number of acres = 5 × 43,560

number of acres = 217800 square feet.

Therefore, the lots is divide into 4 equal lots.

Hence,

measure of each lot =  217800 / 4

measure of each lot = 54, 450 square feet.

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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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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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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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The number of djembe drums you sold is 8

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

Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.

Earning = $326

Also, we have:

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

So, we have

12 * 14 + 6 * 5 + x * 16 = 326

Evaluate the products

198 + 16x = 326

Evaluate the iike terms

16x = 128

So, we have

x = 8

Hence, the number of djembe drums is 8

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Complete question

You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

Find the number of djembe drums you sold.

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.

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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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 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:

A. 110°

Step-by-step explanation:

according to the theorems,

m∠1=m∠6=m∠9=m∠14=110°;

m∠2=m∠5=m∠10=m∠13=70°;

m∠3=m∠8=m∠11=m∠16=70°;

m∠4=m∠7=m∠12=m∠15=110°.

all the details are in the attachment.

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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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: