Hazel is playing hide-and-seek with Audrey and Jamal. Audrey is hiding 6 meters south of Hazel, and Jamal is hiding 8 meters east of Audrey. How far apart are Hazel and Jamal?

We can write g in terms of f as: g(x) = f(x) - 3 = x² - 3

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range. In simpler terms, a function is a set of rules that takes an input value and produces a corresponding output value.

To write g in terms of f, we can use function composition, which involves plugging the function f(x) into g(x) wherever we see x.

So, we have:

g(x) = f(x) - 3

where f(x) = x².

Substituting f(x) into g(x), we get:

g(x) = (x²) - 3

Therefore, we can write g in terms of f as:

g(x) = f(x) - 3 = x² - 3.

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One such tool that enables us to visualise the given math issue using various-sized rectangles or bars is the bar model.

A bar model in mathematics is a visual representation of a subject or problem where the known and unknown quantities are represented by bars or boxes. To answer issues involving the four operations of addition, subtraction, multiplication, and division, bar models are most frequently utilised.

To help kids "see" mathematical structure, the bar model is utilised in teaching for mastery. It is not a method for solving issues, but rather a strategy to uncover the mathematical underpinnings of a problem and obtain knowledge and clarity to aid in its resolution.

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Image attached below,

There is a 0.00567 percent chance that 4 out of the 5 auto damage claims were submitted by individuals under the age of 25.

An expression that has been raised to any finite power can be expanded using the binomial theorem. A binomial theorem is a potent expansionary technique with uses in probability, algebra, and other fields.

A binomial expression is an algebraic expression with two terms that are not the same. For instance, a+b, a3+b3, etc.

Let n = N, x, y, R, then the binomial theorem holds.

(x + y)n = nΣr=0 where, nCr xn - r yr

The likelihood of an event happening is gauged by probability. Several things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. A crucial subject for pupils in class 10, probability explains all the fundamental ideas of the subject. A sample space has an overall probability of 1 for all events.

This is a binomial probability problem, where each automobile damage claim is a Bernoulli trial with a probability of success (a claim made by someone under the age of 25) of p=0.70. We want to find the probability of getting exactly 4 successes out of 5 trials.

The probability of getting exactly k successes out of n trials in a binomial experiment with probability of success p is given by the binomial probability formula:

P(k successes out of n trials) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^(n-k)[/tex]

where (n choose k) = n! / (k! * (n-k)!) is the number of ways to choose k items out of n items.

In this case, we have n=5 and p=0.70. So, the probability of getting exactly 4 successes out of 5 trials is:

P(4 out of 5 claims made by someone under 25) = (5 choose 4) * [tex]0.70^4[/tex] *[tex](1-0.70)^(5-4)[/tex]

P(4 out of 5 claims made by someone under 25) = 5 * [tex]0.70^4[/tex] *[tex]0.30^1[/tex]

P(4 out of 5 claims made by someone under 25) = 0.00567 (rounded to 5 decimal places)

Therefore, the probability that exactly 4 of the 5 automobile damage claims were made by people under the age of 25 is approximately 0.00567.

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Answer: Let's say that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is 6 meters longer than the width, which means that the length is (x + 6) meters.

The formula for the area of a rectangle is:

Area = Length x Width

We are given that the total area of the rectangle is 16m². Substituting the expressions for length and width, we get:

(x + 6) x = 16

Expanding the product and rearranging, we get a quadratic equation:

x² + 6x - 16 = 0

We can solve this equation by factoring or by using the quadratic formula. Factoring, we get:

(x + 8) (x - 2) = 0

This equation is satisfied when either x + 8 = 0 or x - 2 = 0. Therefore, the possible values for the width are x = -8 or x = 2. However, since the width of a rectangle cannot be negative, we reject the solution x = -8.

Therefore, the width of the rectangle is x = 2 meters. The length is 6 meters longer than the width, so the length is (2 + 6) = 8 meters.

Therefore, the dimensions of the rectangle are 2 meters by 8 meters.

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

the description is very confusing and lacks any hint about the behavior of the curve before the change.

but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.

I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.

now they pay the driver. $0.25 per mile.

this has to come out of their profit.

so, the Y (profit) values all go down by 0.25.

therefore, the y-intercept is going down too.

that eliminates C. and D.

for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).

so, the line must be in a form

y = ax + b

with "b" <> 0.

and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).

because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.

and that eliminates A, leaving B. as the right answer.

Answer:

Step-by-step explanation:

Answer:

You can make 12 possible sundaes with these toppings.

Step-by-step explanation:

Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:

1. Fudge & Chocolate Sprinkles

2. Fudge & Rainbow Sprinkles

3. Marshmallow & Chocolate Sprinkles

4. Marshmallow & Rainbow Sprinkles

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

4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.

Answer:

Phn10x12

Step-by-step explanation:

PEANUTS CASHEWS MIXTURE Number of Grams (g) 12 X 12+ X Price per grams Php 10.00 Php 8.00 Php 9.00 Total Price Phn10x12 = Php 120 8x 9 [12+x]​

The per square meter cost of steel will be $32. The solution has been obtained by using the cylinder.

What is a cylinder?

The cylinder, one of the most basic curvilinear geometric shapes, has long been considered to be a three-dimensional solid. It is regarded as a prism with a circle as its basis in elementary geometry.

We are given that the height of cylinder is 8 m and diameter is 10 m.

So, the radius is 5 m.

Now, using the surface area formula, we get

⇒ S = 2πrh + 2π[tex]r^{2}[/tex]

⇒ S = 2π * 5 * 8 + 2π * [tex]5^{2}[/tex]

⇒ S = 2 * 3.14 * 5 * 8 + 2 * 3.14 * 25

⇒ S = 251.2 + 157

⇒ S = 408.2 square meter

Now, it is given that the total cost of the steel will be $13,062.40.

So, per square meter cost will be:

⇒ Cost = [tex]\frac{13,062.40}{408.2\\}[/tex]

⇒ Cost = $32

Hence, the per square meter cost of steel for the cylinder will be $32.

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Part a: The Weight corresponding to the given z score: z = -1 is 2.4 kilograms.

Part b: The Weight corresponding to the given z score: z = 1.34 is 3.921 kilograms.

The relationship between a value and a group of values' mean is described by the Z score or standard score. It gauges how far a data point deviates from the mean.

the procedure of standardising or normalising a raw score to get a standard score. The most popular name for the standard scores is Z Scores.

Given that for the normal distribution.

Weight corresponding to the given z score-

Part A: z = -1

Z score :

z = (x - μ)/σ

-1 = (x - 3.05)/0.65

x - 3.05 = -0.65

x = -0.65 + 3.05

x = 2.4

Thus, the Weight corresponding to the given z score: z = -1 is 2.4 kilograms.

Part b: z = 1.34

z = (x - μ)/σ

1.34 = (x - 3.05)/0.65

x - 3.05 = 1.34*0.65

x = 0.871 + 3.05

x = 3.921

Thus, the Weight corresponding to the given z score: z = 1.34 is 3.921 kilograms.

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Answer:

40%

Step-by-step explanation:

We Know

You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble.

4 + 3 + 2 + 1 = 10 marbles total

What is the probability of drawing a red marble out of the bag?

We Take

(4 ÷ 10) x 100 = 40%

So, 40% of drawing a red marble out of the bag.

Answer:

x and y are the variables.

Step-by-step explanation:

Answer: There are a total of 6 x 6 = 36 possible outcomes when rolling a pair of dice. We can count the number of outcomes where the sum of the dice is odd or a multiple of 3.

For the sum to be odd, we can have:

A 1 on one die and an even number on the other, or

A 3 on one die and an even number on the other, or

A 5 on one die and an even number on the other, or

A 2 on one die and an odd number on the other, or

A 4 on one die and an odd number on the other, or

A 6 on one die and an odd number on the other.

There are a total of 18 outcomes that satisfy this condition.

For the sum to be a multiple of 3, we can have:

A 1 on one die and a 2 on the other, or

A 1 on one die and a 5 on the other, or

A 2 on one die and a 1 on the other, or

A 2 on one die and a 4 on the other, or

A 3 on one die and a 3 on the other, or

A 4 on one die and a 2 on the other, or

A 4 on one die and a 5 on the other, or

A 5 on one die and a 1 on the other, or

A 5 on one die and a 4 on the other, or

A 6 on one die and a 3 on the other.

There are a total of 10 outcomes that satisfy this condition.

However, we have counted twice the outcomes that satisfy both conditions (i.e., the outcomes where the sum is both odd and a multiple of 3). There are 5 such outcomes: (1,2), (1,5), (5,1), (5,4), and (4,5).

Therefore, the total number of outcomes where the sum of the pair of dice is odd or a multiple of 3 is 18 + 10 - 5 = 23.

The probability of getting one of these outcomes is therefore 23/36.

Step-by-step explanation:

Answer:

-2.5

Step-by-step explanation:

follow BIMDAS.

like my answer if you find it helpful

The statement "About 16% of the students scored 74 or below" is true for the given normal distribution of test scores with an average of 78 and a standard deviation of 4.

Standard deviation is a measure of the amount of variation or dispersion of a set of values from their mean (average) value. It is calculated as the square root of the variance of a set of data. A smaller standard deviation indicates that the values are tightly clustered around the mean, while a larger standard deviation indicates that the values are more spread out.

In the given question,

About 16% of the students scored 74 or below is true. This is because of the empirical rule for normal distributions, which states that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. So, if the average score is 78 and the standard deviation is 4, a score of 74 falls one standard deviation below the mean, which represents about 16% of the total data.

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Answer:

About 97.5%  of the students scored 86 or below.

Step-by-step explanation:

Answer: The height of the object at any time t is given by the function s(t) = -16t² + 64. When the object reaches the ground, its height will be 0. So we need to solve the equation:

-16t² + 64 = 0

Dividing both sides by -16, we get:

t² - 4 = 0

Adding 4 to both sides, we get:

t² = 4

Taking the square root of both sides (and remembering to include both the positive and negative roots), we get:

t = ±2

Since time cannot be negative, the only valid solution is:

t = 2

Therefore, it will take the object 2 seconds to reach the ground.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The equation for the volume of a sphere is [tex]\frac{4}{3}[/tex][tex]\pi r^3[/tex].

[tex]\frac{4}{3} \pi r^3 = 33.5[/tex]

[tex]r^3 = \frac{33.5*3}{4\pi} \\r = \sqrt[3]{\frac{33.5*3}{4\pi} }\\r = 2\\2 * r = 2 * 2 = 4[/tex]

Answer: Let the two numbers be x and y. We know that:

x*y = 2420 ---(1)

LCM(x, y) = 110 ---(2)

We can write the LCM as:

LCM(x, y) = (x*y)/HCF(x, y)

Substituting the given values, we get:

110 = (x*y)/HCF(x, y)

Multiplying both sides by HCF(x, y), we get:

HCF(x, y) * 110 = x*y

Substituting equation (1), we get:

HCF(x, y) * 110 = 2420

Dividing both sides by 110, we get:

HCF(x, y) = 2420/110

HCF(x, y) = 22

Therefore, the HCF of the two numbers is 22.

Step-by-step explanation:

Answer:

f(x) - g(x) = 2x² + 6x - 4

Step-by-step explanation:

f(x) - g(x)

= 3x² + x - 3 - (x² - 5x + 1) ← distribute parenthesis by - 1

= 3x² + x - 3 - x² + 5x - 1 ← collect like terms

= 2x² + 6x - 4

In the exponential function F(x) = ab^x, the variable x is an exponent.

In the exponential function F(x) = ab^x, the variable x is an exponent.

The function F(x) represents a value that grows or decays exponentially with respect to x.

The base b is a positive constant that determines the rate of growth or decay, and the coefficient a determines the initial value of the function.

The variable x can be any number

However, it is always the exponent that determines the value of the function F(x) for a given input x.

Therefore, the correct answer is A. an exponent.

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Answer:

Vertex: (-2, -1)

Axis of Symmetry: x = -2

Y-intercept: (0, 3)

Min/Max: Min

Domain: All Real

Range: y ≥ -1

Step-by-step explanation:

Given the graph:

Answer:

So, the answers to the question is:

Vertex: (-2, -1)

Axis of Symmetry: x = -2

Y-intercept: (0, 3)

Min/Max: Min

Domain: All Real

Range: y ≥ -1

The relation that is a function is D: {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}.

A function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, for a relation to be a function, each input can only be related to one output.

In relation D, each input (x-value) has a unique output (y-value), meaning that each x-value is only paired with one y-value. In contrast, relations A, B, and C have repeated x-values with different y-values, which means that they are not functions.

In relation A, the input -1 is paired with two different outputs (2 and 3). In relation B, both inputs 0 and -1 are each paired with two different outputs. In relation C, both inputs 0 and -3 are each paired with two different outputs. Therefore, only relation D satisfies the definition of a function.

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The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).

The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.

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By answering the presented question, we may conclude that Finally, the expressions fourth column represents the value of the expression A ⋀ ~B for each possible combination of truth values of A and B.

To create a truth table for A ⋀ ~B, we first need to list all possible combinations of truth values for A and B, and then calculate the value of the expression A ⋀ ~B for each combination.

A B ~B A ⋀ ~B

True True False False

True False True True

False True False False

False False True False

In the above truth table, the first column lists all possible truth values of A, and the second column lists all possible truth values of B. The third column represents the negation of B, which is denoted as ~B. Finally, the fourth column represents the value of the expression A ⋀ ~B for each possible combination of truth values of A and B.

Therefore, the truth table for A ⋀ ~B is:

A B A ⋀ ~B

True True False

True False True

False True False

False False False

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The surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that consists of two congruent parallel bases in the shape of circles or ellipses, and a curved surface that connects the bases. The height of a cylinder is the perpendicular distance between the bases. A cylinder is a type of prism, and it can be classified as either a right cylinder or an oblique cylinder depending on whether or not its axis is perpendicular to its bases. Right cylinders have circular bases and their axis is perpendicular to the bases, while oblique cylinders have elliptical bases and their axis is not perpendicular to the bases.

Now,

Let the radius of cylinder M be r and its height be h. Then, the radius and height of cylinder N are both 2r, since the radius is equal to the height.

Since the cylinders are similar, their dimensions are proportional, which means:

(height of N) / (height of M) = 5/3

(radius of N) / (radius of M) = (2r) / r = 2

Using the formula for the surface area of a cylinder, we can write:

Surface area of cylinder M: 2πr² + 2πrh

Surface area of cylinder N: 2π(2r)² + 2π(2r)(5/3)h

We are told that the surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. So we can set up the equation:

2π(2r)² + 2π(2r)(5/3)h = 2πr² + 2πrh + 256

Simplifying and solving for h, we get:

4r² + 20rh/3 = r² + rh + 128

3r² - rh - 128 = 0

(3r + 32)(r - 4) = 0

Since the height of the cylinder cannot be negative, we take the positive solution r = 4. Then, the height of cylinder M is (3/5)(4) = 12/5, and the height of cylinder N is 2(4) = 8.

Using the formulas for surface area, we can find the surface areas of both cylinders:

Surface area of cylinder M: 2π(4)² + 2π(4)(12/5) = 131.95 square feet

Surface area of cylinder N: 2π(2(4))² + 2π(2(4))(8) = 319.77 square feet

Therefore, the surface area of cylinder M is approximately 131.95 square feet and the surface area of cylinder N is approximately 319.77 square feet.

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We can use the trigonometric identities to find the exact values of the expressions.

First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:

cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25

cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)

Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):

sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425

cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85

Finally, we can use the quotient identity for tangent to find tan(alpha + beta):

tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85

Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.

The two possible locations for the fourth vertex are (4, -4) and (-3, -1).

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

To find the location of the fourth vertex of the square, we need to use the fact that a square has four equal sides and four right angles.

The first two vertices given are (4, 3) and (-3, 3), which lie on a horizontal line segment of length 7.

The third vertex is (-3, -4), which is 7 units away from the first two vertices and lies on a vertical line segment.

Since the square has four equal sides, the distance between the third vertex and the fourth vertex must also be 7 units.

And since the square has four right angles, the fourth vertex must be located on a vertical line passing through the first two vertices or on a horizontal line passing through the third vertex.

So, there are two possible locations for the fourth vertex:

(4, -4): This point is located 7 units below the first vertex (4, 3) on the vertical line passing through it.

(-3, -1): This point is located 7 units to the right of the third vertex (-3, -4) on the horizontal line passing through it.

Therefore, the two possible locations for the fourth vertex are (4, -4) and (-3, -1).

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We know that the angle bisector theorem and the specified requirements are satisfied if BC = 16, CZ = 8, and BZ = 24. The angle bisector theorem is also satisfied if BC = 8, which also makes CZ = 16/3 and BZ = 112/9.

The opposite side of a triangle is divided into two portions that are proportional to the sides they are on if the angle is bisected by a line, according to the angle bisector theorem.

The angle bisector theorem, which asserts that if a line bisects a triangle's angle, it divides the opposite side into two segments that are next sides to each other, can be used to solve this problem.

Let BC and BZ both equal x. The angle bisector theorem provides us with:

AC/AB = CZ/BZ

16/(16+x) = 16/y

We solve y in terms of x, and as a result,

y = 16(16+x)/16 = x+16

Upon substitution, we discover—

16/(16+x) = 16/(x+16)

If we cross-multiply, we obtain:

16(x+16) = 16(16+x)

Simplifying, we get:

16x + 256 = 256 + 16x

In light of the fact that 16x cancels on both sides, we are left with:

256 = 256

As a result, there exist an endless number of BC and BZ values that could satisfy the requirements.

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The logarithm of the expression [tex]5^{(-3log_{5} 2 )} * 2^{(log_{2}3)}[/tex] is log(3/8).

Mathematical functions called logarithms let us change the scale at which numbers are expressed. They specifically aid in the transformation of numbers stated in exponential form into numbers expressed in standard form. The exponent to which the base must be raised in order to obtain a given number is given by the logarithm of the number to the specified base. For instance, since 23 = 8, the logarithm base 2 of 8 is 3. Natural logarithms, which are logarithms to the base e (about 2.718), and common logarithms, which are logarithms to the base 10, are the two types of logarithms that are most frequently used.

The given logarithmic expression is:

[tex]5^{(-3log_{5} 2 )} * 2^{(log_{2}3)}[/tex]

Using the properties of logarithm we have:

[tex]5^{(-3log_{5} 2 )} 2^{(log_{2}3)}\\= (5^{(log_{5}2)})^{(-3)} * 3\\= 2^{(-3)} * 3\\= 3/8[/tex]

Hence, the logarithm of the expression [tex]5^{(-3log_{5} 2 )} * 2^{(log_{2}3)}[/tex] is log(3/8).

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Step-by-step explanation:

data given

men 330 ,days30

men? ,days11

from

men(m) are inversely proportional todays (d)

m=k/d

330×30=k

k=9900

now,

m=9900/11m

m=900

data given

friends 20, time 2hours

friends 30, time?

from

friends (f) are inversely proportional to time (t)

f=k/t

k=20×2

k=40

now,

t=40/30

t=1.3(1:18)