A researcher collected sample data for 12 middle-aged women. The sample had a mean serum cholesterol
level (measured in milligrams per one hundred milliliters) of 192.4, with a standard deviation of 5.9.
Assuming that serum cholesterol levels for middle-aged women are normally distributed, find a 90%
confidence interval for the mean serum cholesterol level of all women in this age group. Give the lower limit
and upper limit of the 90% confidence interval.

The regular price of the running shoes is $80.

Let's denote the regular price of the running shoes as P. We know that during the sale, the price is reduced by 20%, which means the sales price is 80% (100% - 20%) of the regular price.

Given that the sales price is $64, we can set up the equation:

0.8P = $64

To find the regular price P, we divide both sides of the equation by 0.8:

P = $64 / 0.8

P = $80

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To create a consistent and dependent system with the equation x - y = -2, we need to find another equation that has the same solution as this equation.

We can manipulate the equation x - y = -2 to get y = x + 2.

Now, we can substitute y = x + 2 into each of the given equations to see which one creates a dependent system:

6x + 2y = 15 becomes 6x + 2(x + 2) = 15, which simplifies to 8x = 11. This equation has no solution, so it does not pair with x - y = -2 to create a dependent system.

-3x + 3y = 6 becomes -3x + 3(x + 2) = 6, which simplifies to 0 = 0. This equation has infinitely many solutions and pairs with x - y = -2 to create a dependent system.

-8x - 3y = 2 becomes -8x - 3(x + 2) = 2, which simplifies to -11x = -8. This equation has a unique solution, so it does not pair with x - y = -2 to create a dependent system.

4x - 4y = 6 becomes 4x - 4(x + 2) = 6, which simplifies to -4 = 6. This equation has no solution, so it does not pair with x - y = -2 to create a dependent system.

Therefore, the equation -3x + 3y = 6 can pair with x - y = -2 to create a consistent and dependent system.

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By adding the formed equations, Schuyler will receive $7.05 in change.

What is addition?

Addition is a basic arithmetic operation in mathematics that involves combining two or more numbers to form a sum.

To find the total cost of the almonds and walnuts, we need to calculate the cost of each separately and then add them together.

The cost of 0.4 pound of almonds is:

0.4 x $9.95 = $3.98

The cost of 0.6 pound of walnuts is:

0.6 x $14.95 = $8.97

The total cost of the almonds and walnuts is:

$3.98 + $8.97 = $12.95

Schuyler gives the cashier $20, so the amount of change she will receive is:

$20 - $12.95 = $7.05

Therefore, Schuyler will receive $7.05 in change.

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Answer: To find d(L(x))/dx, we need to differentiate L(x) with respect to x using the derivative rules.

d(L(x))/dx = d/dx (sinx - cosx)

= cosx + sinx

Therefore, the correct answer is option A, cosx+sinx.

Step-by-step explanation:

Answer:

6 and 2/3

Step-by-step explanation:

4 divided by 3/5 is the same as 4 divided by 0.6

4 divided by 0.6 equals 6.6 repeating...

or

6 and 2/3

Answer: 12

Step-by-step explanation: 2 x 6 = 12 = the third side

The quantity of pounds of dog food that Mrs. Evans should buy that would be enough for her dog = 720 ounces.

The total number of days the food is required to last = 90 days.

The quantity of dog food in ounce the dog eat per day = 4 × 2 = 8 ounces.

Therefore the quantity of pounds that will be enough for the dog for the whole 90 days would be = ?

That is;

1 day = 8 ounces

90 days = X

Make X the subject of formula;

X = 90× 8

= 720 ounces

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The evaluation of the functions using piecewise function gives:

f(-9) =  8

f(0) =  2

f(6) =  7

f(-6) =  4

f(3) =  4.5

f(9) = -6

To evaluate the functions using piecewise function, we have to the condition they satisfy. That is:

For f(-9), x = -9. Thus, x≤ -6. So use f(x) = (-4/3)x - 4 to evaluate f(-9). That is:

f(-9) =  (-4/3)*(-9) - 4

f(-9) =  8

For f(0), x = 0. Thus, -6 x ≤ 6. So  use f(x) = (5/6)x + 2 to evaluate f(0). That is:

f(0) = (5/6)*0 + 2

f(0) =  2

For f(6), x = 6. Thus, -6 x ≤ 6. So use f(x) = (5/6)x + 2 to evaluate f(6). That is:

f(6) = (5/6)*6 + 2

f(6) =  7

For f(-6), f(x) = (-4/3)x - 4:

f(-6) = (-4/3)*(-6) - 4

f(-6) =  4

For f(3), f(x) = (5/6)x + 2:

f(3) = (5/6)*3 + 2

f(3) =  4.5

For f(9), x = 9. Thus, x > 6. Use f(x) = -2x + 12:

f(9) = -2*9 + 12

f(9) = -6

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The area in square centimeters, of the trapezoid below is equal to 84.4 cm².

In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):

Area of trapezoid, A = ½ × (a + b) × h

Where:

a and b represent the base areas of a trapezoid.

h represent the height of a trapezoid.

By substituting the given side lengths into the formula for the area of a trapezoid, we have the following:

Area of trapezoid, A = ½ × (7.9 + 13.2) × 8

Area of trapezoid, A = 84.4 cm².

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Therefore, the value of f(m-2) is 5/(m-2) + 2, and the value of function g(1/2) is 2.

In mathematics, a function is a rule or correspondence between two sets, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function is often represented by a formula, equation, or graph.

Here,

1. To find f(m-2), we substitute (m-2) for x in the expression for f(x):

f(m-2) = 5/(m-2) + 2

So the value of f(m-2) is 5/(m-2) + 2.

2. To find g(1/2), we substitute 1/2 for x in the expression for g(x):

g(1/2) = -2(1/2) + 3

So the value of g(1/2) is -1 + 3, which simplifies to 2.

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Answer:

A nonlinear line is a line that is not straight. So the answers for these question include B and D

B and D  are not straight lines and they are increasing

Step-by-step explanation:

Hope this helps! =D

Mark me brainliest! =D

Using simple mathematical operations we can conclude that Adriel will earn $2,10,000 after 29 years working at the job.

The order of operations is a rule that outlines the proper steps to take when analyzing a mathematical equation.

The steps that we can memorize using PEMDAS include parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right), and so on.

So, we know that:

Adriel will earn $65,000 this year.

She will get a raise of $5,000 each year.

Then, her salary after 29 years would be:

= (5000 * 29) + 65,000

= 1,45,000 + 65,000

= $2,10,000

Therefore, using simple mathematical operations we can conclude that Adriel will earn $2,10,000 after 29 years working at the job.

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Answer: 5

Step-by-step explanation:

the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color.

How to solve the question?

To find the least number of rows, we need to determine the greatest common divisor (GCD) of 56 and 120, since each row must have the same number of blocks. We can use the Euclidean algorithm to find the GCD:

120 = 2 x 56 + 8

56 = 7 x 8 + 0

Therefore, the GCD of 56 and 120 is 8. This means that each row must have 8 blocks, and there will be a total of (56+120) = 176 blocks to be arranged.

Since each row can have either only yellow or only black blocks, we need to determine which color will have the greater number of rows. To do this, we can divide the total number of blocks by the number of blocks in each row:

Yellow blocks:

Number of rows = 56 ÷ 8 = 7 rows

Black blocks:

Number of rows = 120 ÷ 8 = 15 rows

Since there are more black blocks, we will use 15 rows of black blocks. Each row will have 8 blocks, so there will be a total of (15 x 8) = 120 black blocks.

We can then use the remaining 56 yellow blocks to create rows of only yellow blocks. Each row will have 8 blocks, so there will be a total of (56 ÷ 8) = 7 yellow rows.

Therefore, the total number of rows will be 15 + 7 = 22 rows. This is the least number of rows that James' brother can make while arranging the blocks in rows such that each row has the same number of blocks and contains only one color

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The arc length generated by a radius r is S = 11πr

The formula for arc length is given by:

S = θr

where θ is the central angle in radians and r is the radius of the circle.

For a full revolution, a radius r revolves around the center of the circle at an angle of 2 radians. Therefore, the central angle for 5 1/2 revolutions would be:

θ = (5 1/2) * 2π radians

θ = 11π radians

So, the arc length generated by a radius r rotating 5 1/2 revolutions is:

S = θr

S = 11πr

Note that if the radius is not given, then the arc length cannot be determined.

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Answer:

Step-by-step explanation:

64 - 16= 48

[tex]\sqrt{48}[/tex]

[tex]\sqrt{3*16}[/tex]

4[tex]\sqrt{3}[/tex]

Option 2 is the correct answer, that is, the equation of the given circle is (x+3)² + (y - 6)² = 4 with center at (-3,6) and radius 2.

The distance formula is a mathematical formula used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem as:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

where  (x₁, y₁) and (x₂, y₂) are the x and y coordinates of the said two points. This formula works for any two points in a two-dimensional space with a Cartesian coordinate system.

To answer this we need to know the equation of a circle.

Let (a,b) be the center of a circle with radius r, then the equation of the circle can be written as:

(x - a)² + (y - b)² = r²

We see that from the given graph center of the circle is the point (-3,6) and radius will be 2.

We can now substitute these information in the circle equation,

(x - -3)² + (y - 6)² = 2²

(x+3)² + (y - 6)² = 4

That is the equation of the given circle is (x+3)² + (y - 6)² = 4.

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1) The value of given random variable having mean 20 and variance 25 is (a) 0.1587, (b) 0.0228 and (c) 0.5328.

2) The z-score corresponding to a probability of a) 0.95 is 1.645, b) 0.05 is -1.645 and c) 0.1515 is -1.04.

The mean is a measure of central tendency, which represents the average value of a set of numbers. It is calculated by adding up all the values in the set and then dividing by the total number of values.

1) (a) We can standardize the random variable X using the formula z = (X - μ) / σ, where μ is the mean and σ is the standard deviation. Therefore,

z = (15 - 20) / 5 = -1

Using a standard normal distribution table or calculator, we can find P(Z < -1) = 0.1587.

(b) Similarly, we have

z = (30 - 20) / 5 = 2

Using the standard normal distribution table or calculator, we can find P(Z > 2) = 0.0228.

(c) To find P(18 ≤ X ≤ 25), we can again standardize the random variable:

z1 = (18 - 20) / 5 = -0.4

z2 = (25 - 20) / 5 = 1

Then we can use the standard normal distribution table or calculator to find P(-0.4 ≤ Z ≤ 1) = 0.5328.

2) (a) Since we are given that X is a standard normal random variable, we can use the standard normal distribution table or calculator to find the value of a such that P(X < a) = 0.95. From the table, we find that the z-score corresponding to a probability of 0.95 is 1.645. Therefore,

a = μ + σ * z = 0 + 1 * 1.645 = 1.645

(b) Similarly, we can find the value of b such that P(X ≤ b) = 0.05 using the standard normal distribution table or calculator. From the table, we find that the z-score corresponding to a probability of 0.05 is -1.645. Therefore,

b = μ + σ * z = 0 + 1 * (-1.645) = -1.645

(c) We want to find the value of c such that P(X > c) = 0.8485. Since the normal distribution is symmetric about the mean, we know that P(X > c) = 1 - P(X < c), so we can find the value of c such that P(X < c) = 1 - 0.8485 = 0.1515. From the standard normal distribution table, we find that the z-score corresponding to a probability of 0.1515 is -1.04. Therefore,

c = μ + σ * z = 0 + 1 * (-1.04) = -1.04.

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Option B

One dimensional objects

Answer:

B. One-dimensional objects

A line segment can "grow" from one-dimensional objects. A line segment is a one-dimensional figure that has two endpoints and connects them with a straight path. One-dimensional objects include lines and curves, and a line segment can be a part of a longer line or curve.

Three-dimensional objects (A) are made up of length, width, and height and cannot "grow" into a line segment, but a line segment can be a part of a three-dimensional object, such as an edge or a diagonal.

Zero-dimensional objects (C) are points, which do not have any length, width, or height. A line segment cannot "grow" from a point, but a point can be one of the endpoints of a line segment.

The equation that helps her is $65 + 5m = $500. D'angela must save $87 each month for the next 5 months to reach her goal of having $500 in her savings account.

A group of equations that must be solved simultaneously is referred to as a system of equations. The variables in the equations are interconnected, and the set of values for the variables that satisfy all of the system's equations is the solution. Depending on whether the equations feature linear or nonlinear interactions between the variables, a system of equations can be either linear or nonlinear. A vast range of phenomena, including physical systems, economic systems, and social systems, are modelled using systems of equations, which appear in many branches of mathematics and science.

Let us suppose the amount of money saved by her = m.

The, for 5 months the amount saved is = 5m.

Given an initial deposit of $65, we have the equation of total amount as:

T = $65 + 5m

Now, she needs to save $500 thus,

$65 + 5m = $500

5m = $500 - $65

5m = $435

m = $87

Hence, D'angela must save $87 each month for the next 5 months to reach her goal of having $500 in her savings account.

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The complete question is:

The training wheel has an area approximately 286.34 square inches smaller than the regular wheel.

The area of a circle is given by the formula A = πr², where A is the area of the circle and r is the radius of the circle. Since we have the radii of both wheels, we can use this formula to find their respective areas.

The area of the training wheel is A₁ = π(3)² = 9π square inches.

The area of the regular wheel is A₂ = π(10)² = 100π square inches.

To find the difference in their areas, we can subtract A₁ from A₂:

A₂ - A₁ = 100π - 9π = 91π

So the difference in their areas is 91π square inches. To round to the nearest hundredth, we can use the approximation π ≈ 3.14:

91π ≈ 286.34 square inches

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Answer:

64cm³

Step-by-step explanation:

( 4 x 4 x 4) cm x cm x cm

Answer:

  (b)  $21,495.64

Step-by-step explanation:

You want to know the value of $15,000 after it has earned continuously compounded interest at 17.99% for 2 years.

The value of an account earning interest at annual rate r compounded continuously is ...

  A = P·e^(rt)

where P is the initial account value, and t is the number of years.

In this problem, we have P=15000, r=0.1799, and t=2, so the amount due will be ...

  A = $15,000·e^(0.1799·2) ≈ $21,495.64 . . . choice B

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Answer:

2011: 0.3×750= 225

therefore, 750-225=525

2012: 0.15 × 525= 78.75

therefore, 525 + 78.75= 603. 75

bag of coffee: mass (kg)

1: 55

603.75: x

x= 55 × 603.75

=33206.25 Kg

33206.25÷1000= 332.0625

tonne: shillings

1:7900

332.0625: x

hence, x= 2623293.75 shillings

8690× 332.0625= 2885623. 125 shillings

The area of the triangle is 87.6 cm².

The area of the triangle can be found as follows:

Therefore,

area of a triangle = 1 / 2 bh

where

Therefore,

b = 17 cm

h = 10.3 cm

Hence,

area of a triangle = 1 / 2 × 17 × 10.3

area of a triangle = 1 / 2 × 175.1

area of a triangle = 87.55

area of a triangle = 87.6 cm²

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The required polynomial  [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex].

What is a polynomial ?

A polynomial is a mathematical expression that consists of variables and coefficients, combined by addition, subtraction, and multiplication, but not division by a variable.

To write a polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex], we need to include their conjugates as well. This is because complex roots always come in conjugate pairs.

The conjugate of  [tex]i\sqrt{6[/tex] is  [tex]-i\sqrt{6[/tex], so our polynomial function will have the following zeros: -1, 1,  [tex]i\sqrt{6[/tex], and  [tex]-i\sqrt{6[/tex].

To find the polynomial function, we can use the fact that the product of the factors of a polynomial is equal to the polynomial itself. So, we can start by multiplying out the factors:

[tex](x+1)(x-1)(x-i\sqrt6)(x+i\sqrt6)[/tex]

Expanding this out gives:

[tex](x^2-1)(x^2+6)[/tex]

Multiplying these two expressions gives:

[tex]x^4+5x^2-6[/tex]

So the polynomial function of least degree with integral coefficients that has zeros of -1, 1, and [tex]i\sqrt{6[/tex] is [tex]f(x) = x^4+5x^2-6[/tex]

To verify that this polynomial has the desired zeros, we can factor it using the difference of squares:

[tex]x^4+5x^2-6 = (x^2-1)(x^2+6) = (x-1)(x+1)(x^2+6)[/tex]

And the quadratic factor has no real roots, so it must be the factorization [tex](x-i\sqrt6)(x+i\sqrt6)[/tex].

Therefore, [tex]f(x) = x^4+5x^2-6[/tex] has the zeros -1, 1, [tex]i\sqrt6[/tex], and [tex]-i\sqrt6[/tex], as required.

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A feature of function gif g(x) = f(x-4) is D. horizontal asymptote of y = 4

A horizontal asymptote is a straight line on a graph that a function approaches but never touches as the independent variable (usually denoted as x) increases or decreases without bound. In other words, the function gets closer and closer to the horizontal line as x becomes very large or very small, but it never actually touches or crosses it.

A function can have at most two horizontal asymptotes - one on the left side of the graph and one on the right side. The horizontal asymptotes of a function are determined by the highest degree of the polynomial in the numerator and the denominator of the function.

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The expression for the velocity is v(t) = 30m/s

(a) x(t) = 30t

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 30t, we have:

v(t) = d/dt (30t)

= 30

So the expression for velocity is v(t) = 30 m/s.

(b) x(t) = 7sin(30)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = 7sin(30), we have:

v(t) = d/dt (7sin(30))

= 7cos(30) * d/dt (30t)

= 3.5cos(30)

So the expression for velocity is v(t) = 3.5cos(30) m/s.

(c) x(t) = ecos(701)

The velocity is the derivative of the position function with respect to time:

v(t) = dx/dt

Since x(t) = ecos(701), we have:

v(t) = d/dt (ecos(701))

= -e sin(701) * d/dt (701t)

= -701e sin(701t)

So the expression for velocity is v(t) = -701e sin(701t) m/s.

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Answer:

x = -14 and x = 12

Step-by-step explanation:

Let x be the width of the rectangular room in feet. Then, according to the problem, the length of the room is 2 feet longer than the width, or x + 2 feet.

The area of a rectangle is given by the formula A = length × width, so we have:

A = (x + 2) × x = x^2 + 2x

We are also given that the area of the room is 168 square feet, so we set A = 168 and get:

x^2 + 2x = 168

This is a quadratic equation in standard form, where 1x^2 + 2x - 168 = 0. We can solve this equation by factoring or using the quadratic formula. This will give us the value(s) of x, which represents the width of the room. Once we have the width, we can find the length by adding 2 feet to it.

And x is :  -14 and 12

The experimental probability of tossing a 3 is 22% ( option D).

Experimental probability, which is also known as Empirical probability, is based on actual experiments and adequate recordings of the occurring of events. An experiment can be repeated a fixed number of times and each repetition is known as a trial. The formula for the experimental probability is defined by;

Probability of an Event P(E) = Number of times an event occurs / Total number of events

From the table it is visible that the occurrence of tossing 3 is 11 times.

So by the definition of experimental probability the possibility is 11/50

As the table given is the result for tossing a number cube 50 times.

In 50 times the possibility is 11

In 1 time the possibility is 11/50

In 100 times the possibility is (11×100)/50

                                              = 22

Hence, the experimental probability of tossing a 3 is 22%.

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