Emma solved a problem on graphing linear inequalities as shown below. She made a mistake. What mistake did she make? What should she have done instead? Explain her error and explain how you would do the problem correctly. (Hint: solve the problem first and see what your graph looks like, then see if you can identify the error).
Graph the following linear inequality to show all possible solutions.
m= 1/4 b=(-2)

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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I hope this helps you.

Answer: A. He should focus on his student loan debt and give himself a deadline of five years. This statement specifies a particular type of debt and sets a time-bound goal, making it both specific and timely.

Step-by-step explanation:

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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Step-by-step explanation:

A = π r²

r = 3 inches

A = 3.14 × (3)²

A = 3.14 × 9

A = 28.29 square inches

Answer: 0.0972

Step-by-step explanation:

To find the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10, we need to find the probabilities of each event separately and then multiply them together.

First, let's find the probability of the first roll being a total of at least 7. There are a total of 36 possible outcomes when rolling a pair of dice (6 sides on each die, so 6 x 6 = 36). To get a total of at least 7, the following outcomes are possible:

7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)

8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)

9: (3, 6), (4, 5), (5, 4), (6, 3)

10: (4, 6), (5, 5), (6, 4)

11: (5, 6), (6, 5)

12: (6, 6)

There are 21 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 7 in the first roll is:

P(at least 7) = 21/36

Next, let's find the probability of the second roll being a total of at least 10. The following outcomes are possible:

10: (4, 6), (5, 5), (6, 4)

11: (5, 6), (6, 5)

12: (6, 6)

There are 6 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 10 in the second roll is:

P(at least 10) = 6/36

Now, to find the probability that both events happen, we multiply the probabilities of each event:

P(first roll at least 7 and second roll at least 10) = P(at least 7) * P(at least 10) = (21/36) * (6/36)

P(first roll at least 7 and second roll at least 10) = 126/1296

So, the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10 is 126/1296, or approximately 0.0972 (rounded to four decimal places).

The probabilities of randomly entering each room in the maze shown at right are:

P(A) = 5/18

P(B) = 1

The probabilities can be determined from the formulas below:

P(A) = 1/3 * 1/2 * 1 + 1/3 * 1/3

P(B) = 1/3 * 1 + 1/3 * 1 + 1/3 *1

To calculate the probabilities, we need to simplify the expressions and do the arithmetic.

Using the formulas you provided:

P(A) = (1/3 * 1/2 * 1) + (1/3 * 1/3) = 1/6 + 1/9 = 5/18

P(B) = (1/3 * 1) + (1/3 * 1) + (1/3 * 1) = 1

Therefore, the probabilities, evaluated to their simplest form, are:

P(A) = 5/18

P(B) = 1

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Answer:

The surface area is 65.94 ft

Answer:

a) Let’s assume that the moose population, p, changes linearly with time t (in years since 1991). We can use the given data to find the slope of the line that represents the population change. The slope is (5850-4330)/(1999-1991) = 190 moose/year. The equation of the line is p = 190(t) + 4330.

b) According to this model, the moose population in 2002 would be p = 190(2002-1991) + 4330 = 6490 moose.

Step-by-step explanation:

Answer:

x and y are the variables.

Step-by-step explanation:

1. The critical value, according to the z-table, is roughly 2.33. 2. There is enough data to support the alternative hypothesis and reject the null hypothesis.

A null hypothesis is a claim that assumes there is no meaningful difference between two or more variables in a population or that any difference that is detected is the result of chance in statistical hypothesis testing. Typically, it is indicated by H0. A statement that rejects the null hypothesis and assumes that the variables being compared have a substantial difference is known as an alternative hypothesis, or Ha. In contrast to the null hypothesis, which the researcher is attempting to refute, the alternative hypothesis is what the researcher is attempting to prove.

1. We can use a z-table or a calculator to determine the critical value for a right-tailed z-statistic test with a sample size of 100 and a significance level of 0.01. The z-score that equates to the 0.99 probability level, which is the complement of the 0.01 significance level, is the critical value. The crucial value, according to the z-table, is roughly 2.33.

2. We compare the estimated z-statistic value, z = 2.88, to the crucial value, 2.33. The estimated value of z falls in the rejection zone of the null hypothesis because it exceeds the crucial value. As a result, we find that there is enough data to support the alternative hypothesis and reject the null hypothesis.

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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 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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The surface area of the pyramid is 113 cm².

A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.

The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.

To find the surface area of the pyramid, we need to find the area of each face and then add them up.

Area of the base:

The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:

Area of base = length × width = 7 cm × 5 cm = 35 cm²

Area of the four triangular faces:

Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:

Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²

Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²

There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:

Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face

= 2 × 19 cm² + 2 × 20 cm²

= 78 cm²

Total surface area:

Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:

Total surface area = area of base + total area of four triangular faces

= 35 cm² + 78 cm²

= 113 cm²

Therefore, the surface area of the pyramid is 113 cm²

.

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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:

The volume of a cube with a length of 11 meters is 33 m³.

To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.

A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.

This can be written in mathematical notation as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.

In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:

Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks

Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks

Now we can use the Pythagorean theorem to find the distance between their houses:

Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks

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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.

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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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:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

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.

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:

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]​

Answer:

-2.5

Step-by-step explanation:

follow BIMDAS.

like my answer if you find it helpful

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: 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: