Need help (100 easy points)

Answer:

Step-by-step explanation:

2r+4<8

subtract 4 from both sides

2r<4

divide by two

no need to reverse the sign since you are not dividing by a negative number

r<2

Answer:

  1/3

Step-by-step explanation:

Your choice of answer must be consistent with the instructions.

The only answer with no exponent is the correct one:

  1/3

__

The rules of exponents tell you ...

  (a^b)(a^c) = a^(b+c)

  3^(-4) × 3^3 = 3^(-4+3) = 3^-1

and

  a^-b = 1/a^b

so

  3^-1 = 1/3^1 = 1/3 . . . . written without an exponent

The given expression is 4(8x + 5). This is a product of a coefficient and a binomial expression. In mathematics, a binomial is a polynomial with two terms.

They are represented as ax + b or a + bx or (a + b) etc. Given expression is 4(8x + 5). We can simplify this by applying the distributive property. It is given as follows; The distributive property of multiplication states that a(b + c) = ab + ac To simplify the given expression, we need to multiply the coefficient 4 with each term in the parentheses.

It can be done as follows; 4(8x + 5) = 4*8x + 4*5 We multiply 4 with 8x and 4 with 5 to obtain; 32x + 20 This is the main answer. Therefore, the simplified form of 4(8x + 5) is 32x + 20. To simplify the given expression 4(8x + 5), we can use the distributive property. According to this property, the product of a number with the sum of two or more terms is equal to the sum of the products of that number with each term of the sum. In other words, a(b + c + …) = ab + ac + … In the given expression, 4 is multiplied with the binomial (8x + 5). Hence,

4(8x + 5) = 4*8x + 4*5

= 32x + 20

Hence, the simplified form of 4(8x + 5) is 32x + 20.

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The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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Step-by-step explanation:

\(f(x) = \frac{1}{3} x - 5\)

\(y = \frac{1}{3} x - 5\)

\(x = \frac{1}{3} y - 5\)

\(x + 5 = \frac{1}{3} y\)

\(3x + 15 = y\)

\(3x + 15 = f {}^{ - 1} (x)\)

The domain of the inverse is the range of the original function

The range of the inverse is the domain of the original.

This the domain and range of f is both All Real Numbers

Answer:

2/3 pounds of peanuts and

1/3 pound of cashews for every 1 pound of the mixture.

Step-by-step explanation:

Let x = the pounds of peanuts

Let 1-x = the pounds of cashews.

3x + 4.5(1 - x) = 3.5  Distribute the 4.5

3x + 4.5 - 4.5x = 3.5  Combine like terms

-1.5x + 4.5 = 3.5  Subtract 4.5 from both sides

-1.5x = -1  Divide both sides by -1.5

x = 2/3  This is the pounds of peanuts

1-x

1 - 2/3 = 1/3  This is the pounds of cashews.

Answer:

w=3.33

Step-by-step explanation:

you should solve carefully surely u will get that answer...it won't be easy to solve it using phone that is y I didn't send solution

Answer:

measure of arc QR = 28.8°

Step-by-step explanation:

Full circle = 100% = 360°

Measure of arc QR = percentage covered by arc QR / 100 × 360

arc QR covers 8%

Therefore:

measure of arc QR = 8/100 × 360°

measure of arc QR = 0.08 × 360°

measure of arc QR = 28.8°

The normal probability plot suggests the data is approximately normally distributed. The sample standard deviation of given data is 3.13. The 95% confidence interval for the population standard deviation is (1.85, 6.28). The investment manager's desire for a population standard deviation below 6% is validated by the confidence interval.

To construct a normal probability plot, we first need to sort the data in ascending order:

6.6, 6.7, 8.7, 9.6, 10.0, 10.3, 11.3, 12.4, 12.4, 13.8, 14.9, 15.9

Then we can plot the ordered data against the expected values of a normal distribution with the same mean and standard deviation as the sample. The plot shows that the points follow a roughly straight line, which suggests that the data is roughly normally distributed.

To determine the sample standard deviation, we can use the formula:

s = sqrt[(∑(xi - x)²) / (n - 1)]

where xi is the rate of return for each year, x is the sample mean, and n is the sample size.

Sample mean:

x = (13.8 + 15.9 + 10.0 + 12.4 + 11.3 + 6.6 + 9.6 + 12.4 + 10.3 + 8.7 + 14.9 + 6.7) / 12 = 11.433

Sample standard deviation:

s = sqrt[((13.8 - 11.433)² + (15.9 - 11.433)² + ... + (6.7 - 11.433)²) / (12 - 1)]

= 3.059

Therefore, the sample standard deviation is 3.059.

To construct a 95% confidence interval for the population standard deviation of the rate of return, we can use the formula:

CI = [(n - 1) * s² / χ²(α/2, n-1), (n - 1) * s² / χ²(1-α/2, n-1)]

where n is the sample size, s is the sample standard deviation, χ² is the chi-square distribution, and α is the level of significance (1 - confidence level).

For a 95% confidence level and 11 degrees of freedom (n - 1), α = 0.05/2 = 0.025. From the chi-square distribution table with 11 degrees of freedom, we can find the critical values as follows:

χ²(0.025, 11) = 2.201 and χ²(0.975, 11) = 23.337

Plugging in the values, we get:

CI = [(12 - 1) * 3.059² / 23.337, (12 - 1) * 3.059² / 2.201]

= [1.946, 26.557]

Therefore, we can say with 95% confidence that the population standard deviation of the rate of return is between 1.946 and 26.557.

The investment manager wants to have a population standard deviation for the rate of return below 6%. The confidence interval (1.946, 26.557) does not validate this desire, as it includes values above 6%. Therefore, based on the sample data, the investment manager cannot be confident that the population standard deviation is below 6%.

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The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

Given that,

We have to find why i squared is equal to negative 1.

We know that,

The imaginary numbers are denoted as i.

We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.

The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.

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1)

Volume of sphere is 113.1 ft³.

Given radius of sphere 3 ft.

Volume of sphere is 4/3× π ×r³

Substitute the value of radius in the formula of Volume of Sphere,

Volume of Sphere= 4/3×π×r³

                             = 4/3×22/7×3³

                             = 4/3×22/7×27

                             = 113.1 ft³

Hence the given sphere has volume of 113.1 ft³ rounded to the nearest tenth.

2)

Volume of cone is 94.3 yd³

Given diameter of base of cone and height of cone.

Diameter of base = 6 yd

Radius = diameter/2

Radius= 3 yd

Height of cone = 10 yd

Volume of cone = 1/3×π×r²×h

r = radius of base of cone

h = height of cone

Substitute the values of radius and height in the formula,

Volume of cone = 1/3×π×r²×h

                          = 1/3×22/7×3³×10

                          = 660/7

                          = 94.3 yd³

Hence volume of cone rounded to the nearest tenth is 94.3 yd³.

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Answer:

3/8

Step-by-step explanation:

slope = rise/run = 3/8

Answer:

x = 3 +√43, x = 3 - √43

Step-by-step explanation:

x^2 - 6x - 34 = 0

move the 34 across

x^2 - 6x = 34

take -6 and divide by two, then square it

(-6/2)^2 = 9

add the product to your equation

x^2 - 6 + 9 = 34 + 9

solve

(x - 3)^2 = 43

x - 3 = ± √43

x = 3 ± √43

The correct option is (B) generated randomly from probability distributions.

The values for random variables in a Monte Carlo simulation are generated randomly from probability distributions.

A frequency distribution that has been idealized is a probability distribution. An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each possible value of a variable appears. The probability of occurrence of a value determines how frequently it appears in a sample.

A random variable can have any number of alternative values and likelihoods within a particular range, and a probability distribution is a statistical function that captures all of these possibilities. This range will be constrained by the minimum and maximum possible values, but the location of the possible value on the probability distribution will rely on a number of other variables.

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The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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The type of triangle is △STR is isosceles triangle.

A triangle is a flat shape bounded by three sides. In another sense, a triangle is formed by three line segments called sides and each side intersects with two other sides.

When classified from its angles, triangles consist of acute triangles, right triangles, and obtuse triangles. Even so, the sum of the angles of a triangle is always 180 degrees. Based on the classification of its sides, triangles consist of equilateral triangles, arbitrary triangles, and acute triangles.

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Answer: 8575/2

Step-by-step explanation:

The standard deviation for the random variable X, the number of wins, is approximately 0.10341.

Probability of winning a certain lottery \(= 1/51,949\)

560 times were played overall.

Let X represent the random variable that represents the number of victories out of 560 plays.

The probability of winning in one play is \(p = 1/51,949\). The probability of not winning in one play is \(q = 1 - p\)

\(q = (51,949 - 1) / 51,949\)

\(q = 51,948 / 51,949.\)

What X should actually be is:

\(E(X) = np\)

\(E(X) = 560 * (1/51,949)\)

\(E(X) = 0.010793\)

The variance of X is:

\(Var(X) = npq\)

\(Var(X) = 560 * (1/51,949) * (51,948/51,949)\)

\(Var(X) = 0.010699\)

The value of X's standard deviation is

\(SD(X) = \sqrt{Var(X)}\)

\(SD(X) = \sqrt{0.010699}\)

\(SD(X) = 0.10341\)(approx)

Therefore, the standard deviation for the random variable X, the number of wins, is approximately 0.10341.

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

the answer for this problem is 5xy(3x-2y)

Answer:

5xy(3x-2y)

Step-by-step explanation:

since xy are common terms they can be taken out

Answer:

135 grams of Zinc

Step-by-step explanation:

zinc:copper

3:14

3/14=x/630

x=135

Hence the two events are dependent.

In first event lacy draws a heart from a standard deck of 52 cards.After that Without replacing the first card, she then proceeds to draw a second card and gets a club. so the probability of second event is dependent on the result of first event.

given that a deck has 52 cards.

the total number of clubs in a deck = 13

Actually the probability of drawing a club is

\( \frac{13}{52} \)

but she draws a heart from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card and gets a club.

now the total number of cards in a deck=51

the probability of getting a club is

\( \frac{13}{51} \)

so the probability is changed based on the result of first event.

Hence the two events are dependent.

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The calculation that will be performed first in the formula =D1+C1/F3 is option a. C1/F3 because in the order of operations, division is performed before addition.

In the formula =D1+C1/F3, the calculation that will be performed first is: a. C1/F3. This is because, according to the order of operations (PEMDAS/BODMAS), division should be performed before addition.

1. Perform the division operation: C1/F3
2. Perform the addition operation: D1 + (result from step 1)

So, The calculation that will be performed first in the formula =D1+C1/F3 is option a. C1/F3 because in the order of operations, division is performed before addition.

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Answer:

-1 is 1 to the left of zero. Positive one is 1 to the right of zero

Step-by-step explanation:

Answer:

4x+6y or 2*(2x+3y)

Step-by-step explanation

4x+6y

if you want to factorize it

2*(2x+3y)

Answer:

You just estimated

Step-by-step explanation:

Answer:

The total mechanical energy is 0.712 J.

Step-by-step explanation:

A blue 573 g mobile is moving on a metal rail. If on the mobile, the spring exerts a force to the right of modulus 0.85 N and in the indicated position the kinetic energy of the mobile-spring system is 0.47 J and its elastic potential energy is 0.242 J. Determine the mechanical energy of the system mobile-spring in the position shown as indicated in the figure.

The total mechanical energy is given by the sum of the kinetic energy and the potential energy.

Kinetic energy = 0.47 J

Potential energy = 0.242 J

The total mechanical energy is

T = 0.47 + 0.242 = 0.712 J