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Answer:

g(-5) = 8(-5) - 24 = -40 - 24 = -64

g(5) = 8(5) - 24 = 40 - 24 = 16

y = 8x - 24

8x = y + 24

x = (1/8)(y + 24) = (1/8)y + 3

g^-1(x) = (1/8)x + 3, -64 < x < 16

Answer:

To factor the polynomial 40x^3 + 70x^2 + 30x, we can first factor out the greatest common factor of the terms, which is 10x:

10x(4x^2 + 7x + 3)

Next, we can factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to give 4 × 3 = 12 and add to give 7. These numbers are 4 and 3:

10x(4x + 3)(x + 1)

Therefore, the factored form of the polynomial is:

10x(4x + 3)(x + 1)

Answer:

If 45% of the fruit on a table are apples, then 55% of the fruit are oranges (since the total percentage must add up to 100%).

The probability of selecting a piece of fruit that is not an apple is equal to the percentage of oranges on the table, which is 55%.

Therefore, the probability of selecting a piece of fruit that is not an apple is 55%.

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  [tex]9 \frac{1}{10}[/tex]   to a decimal number:

⇒ [tex]9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}[/tex]

⇒ [tex]\frac{91}{10}[/tex]  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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Answer:

28%

Step-by-step explanation:

Let's assume that there are 2x girls and 3x boys in the school, as given the ratio of girls to boys is 2:3. Therefore, the total number of students in the school is 5x.

According to the problem, 25% of the girls have school dinners. So, the number of girls having school dinners is 0.25*2x = 0.5x.

Similarly, 30% of the boys have school dinners. So, the number of boys having school dinners is 0.3*3x = 0.9x.

Therefore, the total number of students having school dinners is 0.5x + 0.9x = 1.4x.

The percentage of students having school dinners can be found by dividing the total number of students having school dinners by the total number of students in the school and multiplying by 100%.

So, the percentage of students having school dinners is (1.4x/5x) * 100% = 28%.

Hence, the total percentage of students at the school who have school dinners is 28%.

To verify the answer, let's consider a numerical example.

Let's assume there are 200 students in the school, out of which 2/5 (i.e., 40%) are girls and 3/5 (i.e., 60%) are boys.

According to the problem, 25% of the girls have school dinners, which is 0.25 * 2/5 * 200 = 20 students.

Similarly, 30% of the boys have school dinners, which is 0.3 * 3/5 * 200 = 36 students.

Therefore, the total number of students having school dinners is 20 + 36 = 56.

The percentage of students having school dinners is (56/200) * 100% = 28%.

Hence, the answer is verified.

Here is the code that can be used to find the MLE of M allele in the 206th row of Mourant dataset using the HardyWeinberg package in R:

# Load HardyWeinberg package

library(HardyWeinberg)

# Load Mourant dataset

data(Mourant)

# Extract the genotype counts for the 206th row

counts <- Mourant[206, 2:4]

# Calculate the MLE of M allele frequency

mle <- hw_mle(counts)

# Extract the MLE of M allele frequency

mle_M <- mle$p[2]

Note that the code assumes that the Mourant dataset is already installed and loaded in R. If the dataset is not installed, you can install it by running install.packages("HardyWeinberg") in R.

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Answer:

51.1 to nearest tenth of a degree.

Step-by-step explanation:

Sin x = 7/9

x = 51.05756 degrees

On solving the provided question ,we can say that In order to find holes in a mathematical proof or the boundaries of a theory or hypothesis, counterexamples might be helpful.

A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.

Evidence is utilised to back up a claim or argument in a direct proof. A direct proof's objective is to connect known facts or presumptions logically to the desired conclusion in order to show that a certain assertion is true. Direct proofs sometimes take the form of a series of logical stages that are combined to get the desired result.

A counterexample, on the other hand, is a solitary instance that refutes a claim or argument. A counterexample presents a particular situation in which a claim is wrong in order to demonstrate that the claim is not always true. In order to find holes in a mathematical proof or the boundaries of a theory or hypothesis, counterexamples might be helpful.

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The values of the variables are;

x = 7

y = -9

From the information given, we have that;

5x−y=44

−3x−y=−12

Using the elimination method of solving simultaneous equations

Subtract equation (2) from equation (1), we get;

5x - y - (-3x - y) = 44 - (-12)

Now, expand the bracket

5x - y+ 3x + y = 56

collect the like terms

5x + 3x = 56

add the terms

8x = 56

Make 'x' the subject of formula

x= 7

Now, substitute the value of x in equation (2)

-3x - y = -12

-3(7) - y = -12

expand the bracket

-21 - y= - 12

collect like terms

-y = 9

y = -9

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The scale factor of HOPE to RSTU is 1.5

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

The shape

From the shape, we have the following parameters

Side length of HOPE = 8

Corresponding side length of RSTU = 12

Using the above as a guide, we have the following:

Scale factor of the dilation = Corresponding side length of RSTU/ Side length of HOPE

So, we have

Scale factor of the dilation = 12/8

Evaluate

Scale factor of the dilation = 1.5

Hence, the scale factor of the dilation is 1.5

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The genotype ratio is:  1   TT : 1   Tt : 0  tt

The phenotype ratio is :  4   Tall :   0   Short

100 percent of the offspring will be tall.

Genotypic ratio is the ratio between the genetic makeup among the offspring population.

On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.

The given test cross is between a homozygous tall parent and a heterozygous tall parent.

Using a Punnett square,

The result will be as shown below.

                     T                   t

          T        TT                 Tt

           T       TT                 Tt

Genotype :  1   TT : 1   Tt : 0  tt

Phenotype :  4   Tall :   0   Short

100 percent of the offspring will be tall.

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Inequality in standard form:

5x² - 40x - 45 ≤ y ≤ x² + 8x + 9 and y ≤ x² - 8x - 9 and y ≥ 5x² + 40x + 45

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal.

To find the inequality that represents the shaded region, we can first simplify each inequality and then combine them using "and" or "or" operators as necessary.

Starting with each inequality:

y ≥ x² + 8x + 9: This is a parabola that opens upwards and has a vertex at (-4,1). The inequality means that all points above or on the parabola are included in the shaded region.

y ≥ x² - 8x - 9: This is a parabola that opens upwards and has a vertex at (4,-1). The inequality means that all points above or on the parabola are included in the shaded region.

y ≤ 5x² - 40x - 45: This is a parabola that opens upwards and has a vertex at (4,-125). The inequality means that all points below or on the parabola are included in the shaded region.

y ≥ 5x² + 40x + 45: This is a parabola that opens upwards and has a vertex at (-4,-125). The inequality means that all points above or on the parabola are included in the shaded region.

Combining the inequalities using "and" or "or" operators:

Since all of the inequalities have "y ≥" or "y ≤" in them, we know that the shaded region is above or below some combination of the parabolas. Specifically, the shaded region is above the first two parabolas and below the second two parabolas. Therefore, we can use "and" to combine the inequalities as follows:

y ≥ x² + 8x + 9 and y ≥ x² - 8x - 9 and y ≤ 5x² - 40x - 45 and y ≤ 5x² + 40x + 45

This gives us the final inequality in standard form:

5x² - 40x - 45 ≤ y ≤ x² + 8x + 9 and y ≤ x² - 8x - 9 and y ≥ 5x² + 40x + 45

Note that we flipped the direction of the inequality for the last term (y ≥ 5x² + 40x + 45) to make it consistent with the other three inequalities.

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The distance from point C to A that is AC = 7.5 cm and CB = 10.5 cm.

While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Let us suppose the distance between C to A = x.

Now, for C to B we have = 3 + x

Given, AB = 18

Thus,

AC + CB = AB

x + (x + 3) = 18

2x + 3 = 18

2x = 15

x = 7.5

Now, CB = 3 + x = 3 + 7.5 = 10.5

Hence, the distance from C to A that is AC = 7.5 cm and CB = 10.5 cm.

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If the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.

Graph is a data structure composed of nodes (vertices) and edges. It is a non-linear data structure that is used to represent relationships between objects, events, or ideas. Graphs are widely used in computer science, mathematics, engineering, and other fields for representing various types of data. Graphs can be used to represent a wide variety of data sets, including networks, social relationships, and even biological systems. Graphs can also be used to identify patterns, trends, and correlations in data.

The graph below shows the relation between time (hours) and distance (km) for a train trip that lasted from 0 to 7 hours.

The line of best fit is a linear line with a positive slope, indicating that the distance travelled increases as the time spent travelling increases. Therefore, it can be estimated that if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be calculated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis, which is approximately 90 km.

In conclusion, if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.

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Complete questions as follows-
On the grid below, draw a graph of the relationship between  and  for a trip that lasted from 0to 7 hours.  8Time (hours) If the train was traveling nonstop, how many  would it travel in 5.5 hours?

When both t and d are zero, we can immediately see that c = 0 because the train begins at rest. Additionally, the rate of change is the constant speed, making m = 95. Thus, d = 95t is the necessary relationship.

A graph is a type of data structure that consists of edges and nodes (vertices). It is a non-linear data structure intended to depict connections between things, occasions, or concepts. Graphs are frequently used to represent numerous forms of data in computer science, mathematics, engineering, and other disciplines. A wide range of data sets, including networks, social relationships, and even biological systems, can be represented using graphs. Graphs can also be used to spot trends, correlations, and patterns in data.

The necessary equation should be d = mt +c,

Where the arbitrary real constants m and c are used.

When t = 1, d = 95

so that 95= m+c ---> (1)

Also, when t=2, d = 190,

hence 190 = 2m+c ---> (2)

When the first equation is taken out and the second equation is added back in,

we get 2m+c-m-c = 190-95 or, m = 95.

When this value of m is substituted in the first equation,

we get 95 = 95+c so that c = 95-95 = 0.

Thus, the require3d equation is d = 95t. Since 95*3 = 285 and 95*4= 380, All of the given facts are satisfied by this equation.

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The complete question and graph attached below,

Answer:

[tex]y =- \frac{3}{10} x + \frac{17}{20}[/tex]

Step-by-step explanation:

We are given the line 6x+20y=17, and we want to write it in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept, hence the name.

As we can see, in slope-intercept form, y is by itself on one side. So, we should solve the equation for y.

To do that, we can start by subtracting 6x from both sides.

6x + 20y = 17

-6x             -6x

_________________

20y = -6x + 17

Now, we should divide both sides by 20 to isolate y.

20y = -6x + 17

÷20   ÷20

_______________

[tex]y=-\frac{6}{20} x + \frac{17}{20}[/tex]

This can be simplified to:

[tex]y =- \frac{3}{10} x + \frac{17}{20}[/tex]

The correct option is D, the x-intercept is 2pi

To find this, we need to solve the equation:

y = cos(x/2) = 0

Remember that the cosine function is zero for the arguments pi and (3/2)pi.

Then the x-intercepts are:

x/2 = pi

x/2 = (3/2)pi

Solving these:

x = 2pi

x = 3pi

From these the one that appears in the options is 2pi, at option D.

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Answer:

325

Step-by-step explanation:

the product being multiplication is 65 * 5

A student who does not have a sister has a 2/9 chance of having a brother.

What exactly is probability?

Probability is a measure of an event's possibility or chance of occurring. It's a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of an occurrence is estimated by dividing the number of possible outcomes by the number of ways the event might occur.

Consider the following events:

"Has a brother"

"Doesn't have a sister," says B.

The probability of occurrence A given event B is written as P(A|B). We can use Bayes' theorem to write:

P(A|B) equals P(B|A) * P(A) / P(B).

where P(B|A) represents the probability of not having a sister given that the student has a brother, P(A) represents the probability of having a brother (equal to the proportion of students who have a brother), and P(B) represents the probability of not having a sister (equal to the proportion of students who do not have a sister).

We can use the table values to fill in the blanks:

P(B|A) = 2 / (5 + 2) = 2/7

P(A) = (5 + 2) / (5 + 2 + 9 + 7) = 7/23

P(B) = (2 + 7) / (5 + 2 + 9 + 7) = 9/23

Plugging these values into the formula, we get:

P(A|B) = (2/7) * (7/23) / (9/23) = 2/9

Therefore, A student who does not have a sister has a 2/9 chance of having a brother.

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Answer:

What we know from the problem:

therefore tangent will be positive.

Adjacent Side = 1

Hypotenuse Side = 7

We need to find out:

Opposite Side = b

Using the Pythagorean Theorem: a² + b² = c²

1² + b² = 7²

b = 4√3

Lastly:

Tangent = Opposite/Adjacent

4√3 ÷ 1 = 4√3

Tangent = 4√3

Answer:

Step-by-step explanation:

The inequality is graphed on the number line is

Inequality can be graphed on a number line by shading the appropriate region of the number line.

To graph an inequality x > -7, follow these steps:

Plot the critical points on the number line. The critical points are the values of x that make the inequality true with an equal sign. For example, to graph the inequality x > -7, we plot the critical point x = -7 on the number line.

Determine the direction of the shading or line. If the inequality is "greater than" or "greater than or equal to," shade to the right of the critical point..

If the inequality includes "or equal to," use a closed circle at the critical point. If the inequality does not include "or equal to," use an open circle at the critical point.

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The percent of the total time teens spend using the Internet and doing chores is the time they spend listening to the radio is 55.56%.

Time spent using the internet = 4 hours

Time spent doing chores = 4 hours

The time spent listening to the radio = 10 hours

The total time spent during the week is 4 + 4 + 10 = 18 hours

The percentage of this total time that is spent listening to the radio is:

(10 hours / 18 hours) x 100% =55.56%

This is basic arithmetic operations and is used in calculation of numbers.

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The equation that represents the town's population after 6 years is:

P = 2.33 × 10¹ (1.07)⁶

What is the rate?

In mathematics, the rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.

The initial population is 2.33 × 10¹.

After one year, the population will be:

P₁ = 2.33 × 10¹ + 0.07 × 2.33 × 10¹

P₁ = 2.33 × 10¹ (1 + 0.07)

After two years, the population will be:

P₂ = P₁ + 0.07 P₁

P₂ = P₁ (1 + 0.07) = 2.33 × 10¹ (1 + 0.07)²

After three years, the population will be:

P₃ = P₂ + 0.07 P₂

P₃ = P₂ (1 + 0.07) = 2.33 × 10¹ (1 + 0.07)³

And so on, until after six years:

P₆ = 2.33 × 10¹ (1 + 0.07)⁶

Simplifying the expression, we get:

P₆ = 2.33 × 10¹ (1.07)⁶

Therefore, the equation that represents the town's population after 6 years is:

P = 2.33 × 10¹ (1.07)⁶

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The correct postulate that states a line is determined by two points is:

• Postulate 2: Through any two different points, exactly one line exists.

Postulate 2 states that if you have two distinct points, you can uniquely determine a line that passes through both of them. In other words, any two points in space define a line, and there is only one line that can pass through those two points.

This postulate is a fundamental concept in Euclidean geometry, which is the study of geometry based on the work of the ancient Greek mathematician Euclid.

This postulate is often used as a basic assumption or starting point in geometric proofs and constructions. It implies that a line is uniquely defined by just two points, and any additional points on that line can be determined by extending it infinitely in both directions.

It also implies that two distinct points always lie on exactly one line, and no more than one line can pass through them.

Postulate 2 is a fundamental principle in geometry and serves as the basis for many geometric theorems and proofs.

It helps establish the relationship between points and lines in Euclidean space, and it is used to reason about the properties and behavior of lines and points in geometric constructions, proofs, and demonstrations.

therefore, The correct postulate that states a line is determined by two points is:

• Postulate 2: Through any two different points, exactly one line exists.

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Answer:

8

Step-by-step explanation:

x^2-4x=32

Subtract from both sides:

x^2-4x-32=32-32

Simplify the expression

x^2-4x-32=0

To find the coefficients, use the standard form of a quadratic equation:

ax^2+bx+c=0

x^2-4x-32=0

a coefficient =1

b coefficient =-4

c coefficient =-32

Find the factors which product equals to coefficient a multiplied by coefficient c:

a coefficient ∙ c coefficient = 1 ∙ -32 = -32

List the factors of -32:

1, 2, 4, 8, 16, 32

Because the product of coefficient a and coefficient c equals a negative number (-32) one factor needs to be positive and the other one negative.

From the list of factors, find a pair which sum equals to the b coefficient.

b coefficient = -4

This pair doesn't work.

1*-32=-32

2*-16=-32

2-16=-14

Found it - this pair does the trick:

4*-8=-32

4-8=-4

The product of 4 and -8 equals to coefficient a(1) multiplied by coefficient c (-32) and their sum equals to coefficient b (-4).

The engineer should consider a sample size of 325 electronic components to be 90% sure that the mean width will be within ± 0.3 mm.

To determine the required sample size, we can use the formula for the margin of error (ME) in the context of the normal distribution:

ME = (Z * σ) / √n

Where:

ME = Margin of error

Z = Z-score, which corresponds to the desired level of confidence (in this case, 90%)

σ = Standard deviation (3.3 mm in this problem)

n = Sample size

First, we need to find the Z-score corresponding to a 90% confidence level. This can be found using a Z-table or statistical software. The Z-score for a 90% confidence interval is approximately 1.645.

Now, we will rearrange the formula to solve for the sample size (n):

n = (Z * σ / ME)^2

We are given that the margin of error should be within ± 0.3 mm:

n = (1.645 * 3.3 / 0.3)^2

n ≈ (18.015)^2

n ≈ 324.54

Since we cannot have a fraction of a component, we round up to the nearest whole number to ensure the desired level of confidence:

n ≈ 325

The engineer should consider a sample size of 325 electronic components to be 90% sure that the mean width will be within ± 0.3 mm.

North Division’s direct fixed expenses for February is $34000.

Segment margin = Contribution margin - Direct fixed expenses

We are given that the North Division's segment margin for February is $18,000, and its contribution margin is $52,000. Let X represent the North Division's direct fixed expenses:

$18,000 = $52,000 - X

Solving for X, we get:

X = $52,000 - $18,000

X = $34,000

Therefore, the North Division's direct fixed expenses for February is $34,000.

The answer is: Multiple Choice $34,000.

Hence, North Division’s direct fixed expenses for February is $34000.

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Complete question:

American Manufacturing Incorporated operates two divisions with the following selected information for the month of February: North Division South Division Sales $ 120,000 $ 90,000 Contribution margin $ 52,000 $ 40,000 Segment margin $ 18,000 $ 12,000 North Division’s direct fixed expenses for February is: Multiple Choice $34,000. $96,000. $60,000. $78,000.

Upon answering the query we can say that  As a result, in rectangle  AC is 75 units long.

A rectangle is a quadrilateral with four right angles in the Euclidean plane. It is also known as an equiangular quadrilateral since each of its angles is equal. A straight angle is an additional alternative for the parallelogram. A square has four sides that are the same length. A quadrilateral with a rectangle-like form has equal parallel sides and four 90-degree vertices. Due of this, it is occasionally referred to as a "equirectangular rectangle". Due to its opposing sides' equal and parallel lengths, a rectangle is occasionally referred to as a parallelogram.

The diagonals of a rectangle are of equal length. As a result, we have:

[tex]AC = BD\\3x + 15 = 4x - 5\\15 = x - 5\\x = 20\\[/tex]

Now, we can change the equation for AC to use this value of x:

[tex]AC = 3x + 15\\AC = 3(20) + 15\\AC = 60 + 15\\AC = 75\\[/tex]

As a result, AC is 75 units long.

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