Points A, B, and C are collinear. Point B is between A and C. Find the length indicated. AB= 5x-15, BC=3x-5, and AC=28. Find AB

Answer:

x²+17x+6=xx+17x+6=(17+x)x +6=17+xx+6= 17+x²+6=23+x²

=>x²+17x+6=23+x²

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

The number of terms in a polynomial helps when performing operations like simplification, factoring, or evaluating expressions.

The polynomial 18x³ - 2x² + 4x - 1 consists of four terms.

In order to determine the number of terms in a polynomial, we count the number of distinct algebraic expressions separated by addition or subtraction operations.

In this polynomial, we have:

Term 1: 18x³ (This is the term with the highest degree, which is 3 in this case, and it includes the coefficient 18.)

Term 2: -2x² (This term has a degree of 2 and a coefficient of -2.)

Term 3: 4x (This term has a degree of 1 and a coefficient of 4.)

Term 4: -1 (This is a constant term with a degree of 0.)

We can see that there are four distinct terms separated by addition and subtraction operations:

18x³, -2x², 4x, and -1.

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Answer:

x= -1/7

Step-by-step explanation:

The p-value of the given hypothesis of proportions is; P = 0.16

We are given;

Population proportion; p = 0.50

Sample proportion; p^ = 52% = 0.52

Sample size; n = 1200

The hypotheses is defined as;

Null hypothesis; H₀: p = 050

Alternative hypothesis; Hₐ: p ≠ 0,50

The formula for the test statistic of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

Plugging in the relevant values gives;

z = (0.52 - 0.5)/√(0.5(1 - 0.5)/1200)

z = 1.386

From online p-value from z-score calculator, we have;

p-value = 0.16

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Answer:

x = 8

Step-by-step explanation:

\(xp = 2 + \frac{3}{5} (12 - 2) \)

I did 12 -2 which equals 10

10 times 3/5 equals 6

6 plus 2 equals 8

Answer:

{√49,-1,0}

Step-by-step explanation:

√49 = 7, because 7*7 = 49

7, -1 and 0 are all integer numbers.

π isn't integer, √20 is not an integer (it's 2√5), 9.5 is not an integer.

Answer:

a) The rate of change associated with the volume of the box is 54 cubic meters per second, b) The rate of change associated with the surface area of the box is 18 square meters per second, c) The rate of change of the length of the diagonal is -1 meters per second.

Step-by-step explanation:

a) Given that box is a parallelepiped, the volume of the parallelepiped, measured in cubic meters, is represented by this formula:

\(V = w \cdot h \cdot l\)

Where:

\(w\) - Width, measured in meters.

\(h\) - Height, measured in meters.

\(l\) - Length, measured in meters.

The rate of change in the volume of the box, measured in cubic meters per second, is deducted by deriving the volume function in terms of time:

\(\dot V = h\cdot l \cdot \dot w + w\cdot l \cdot \dot h + w\cdot h \cdot \dot l\)

Where \(\dot w\), \(\dot h\) and \(\dot l\) are the rates of change related to the width, height and length, measured in meters per second.

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the volume of the box is:

\(\dot V = (6\,m)\cdot (3\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot (3\,m)\cdot \left(-6\,\frac{m}{s} \right)+(6\,m)\cdot (6\,m)\cdot \left(3\,\frac{m}{s}\right)\)

\(\dot V = 54\,\frac{m^{3}}{s}\)

The rate of change associated with the volume of the box is 54 cubic meters per second.

b) The surface area of the parallelepiped, measured in square meters, is represented by this model:

\(A_{s} = 2\cdot (w\cdot l + l\cdot h + w\cdot h)\)

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time:

\(\dot A_{s} = 2\cdot (l+h)\cdot \dot w + 2\cdot (w+h)\cdot \dot l + 2\cdot (w+l)\cdot \dot h\)

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the surface area of the box is:

\(\dot A_{s} = 2\cdot (6\,m + 3\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m+6\,m)\cdot \left(3\,\frac{m}{s} \right) + 2\cdot (6\,m + 3\,m)\cdot \left(-6\,\frac{m}{s} \right)\)

\(\dot A_{s} = 18\,\frac{m^{2}}{s}\)

The rate of change associated with the surface area of the box is 18 square meters per second.

c) The length of the diagonal, measured in meters, is represented by the following Pythagorean identity:

\(r^{2} = w^{2}+h^{2}+l^{2}\)

The rate of change in the surface area of the box, measured in square meters per second, is deducted by deriving the surface area function in terms of time before simplification:

\(2\cdot r \cdot \dot r = 2\cdot w \cdot \dot w + 2\cdot h \cdot \dot h + 2\cdot l \cdot \dot l\)

\(r\cdot \dot r = w\cdot \dot w + h\cdot \dot h + l\cdot \dot l\)

\(\dot r = \frac{w\cdot \dot w + h \cdot \dot h + l \cdot \dot l}{\sqrt{w^{2}+h^{2}+l^{2}}}\)

Given that \(w = 6\,m\), \(h = 6\,m\), \(l = 3\,m\), \(\dot w =3\,\frac{m}{s}\), \(\dot h = -6\,\frac{m}{s}\) and \(\dot l = 3\,\frac{m}{s}\), the rate of change in the length of the diagonal of the box is:

\(\dot r = \frac{(6\,m)\cdot \left(3\,\frac{m}{s} \right)+(6\,m)\cdot \left(-6\,\frac{m}{s} \right)+(3\,m)\cdot \left(3\,\frac{m}{s} \right)}{\sqrt{(6\,m)^{2}+(6\,m)^{2}+(3\,m)^{2}}}\)

\(\dot r = -1\,\frac{m}{s}\)

The rate of change of the length of the diagonal is -1 meters per second.

The value of x is 7 using the concept supplementary.

What is supplementary angle?

Angles that add up to 180 degrees are referred to as supplementary angles.

The image of a transversal angles is added.

Angle 7 = angle 5 since they are vertically opposite angle.

The sum of interior angle on the same side of the transversal is 180 degree.

angle 5 + angle 4 = 180°

Replace angle 5 by angle 7:

angle 7 + angle 4 = 180°

Substitute the value of angle 7  and angle 4:

(7x + 5)° + 126° = 180°

7x+ 131 = 180

Subtract 131 from both sides:

7x  = 49

Divide both sides by 7:

x  = 7

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Answer:

Yes! It is a rational number

Step-by-step explanation:

Irrational numbers:

Pi, which begins with 3.14, is one of the most common irrational numbers

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For the given function the value of limits are

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\) is 5

\(\lim _{x\to 0^+}\left(f\left(x\right)\right)\) is 0

\(\lim _{x\to 0}\left x^2+5\)is 5

The given function is f(x)= x²+5, when x≤0

f(x)=2x when x>0

\(\lim _{x\to 0^-}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0^-}\left x^2+5\)

The given limit is a left hand limit as there is minus in the limits

When we apply x as 0 we get the value 5

Now \(\lim _{x\to 0^+}\left(f\left(x\right)\right)\)

So \(\lim _{x\to 0^+}\left 2x\)

The given limit is a right hand limit as there is positive in the limits

When we apply x as 0 we get 0

Now \(\lim _{x\to 0}\left(f\left(x\right)\right)\)

Which is \(\lim _{x\to 0}\left x^2+5\)

We get 5

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Answer:

Blank 1 would be irrational

Blank 2 would be 5 and 7

Step-by-step explanation:

hope this is correct

Answer:

Irrational & 5 and 7

Step-by-step explanation:

The equation of the line j perpendicular to the given line is 2y + x = 6

Given the equation for line k expressed as y = 2x+8

Slope of the line is expressed as:

mx = 2x

m = 2

The equation of the line j perpendicular to the line will be in the form;

y-y0 = m(x-x0)

Slope of line j = -1/2

Point (x0, y0) = (0, 3)

Substitute the points and the slope into the formula

y - 3 = -1/2(x-0)

2(y - 3) = -x

2y - 6 = -x

2y + x = 6

Hence the equation of the line j perpendicular to the given line is 2y + x = 6

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Answer:

a. Yes

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If the absolute value of the z-score is 2 or larger, X is considered a surprising outcome.

In this question:

\(\mu = 7, \sigma = 3\)

Would you be surprised if it took less than one minute to find a parking space?

We have to find the z-score when X = 1. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1 - 7}{3}\)

\(Z = -2\)

Since Z = -2, the correct answer is:

a. Yes

Answer:

Step-by-step explanation:

Solving in steps:

1. If 3x - 7 > 0

2.  If 3x - 7 < 0

The blanks that are missing in the sequence are -3 and 11

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

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

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Answer:

$13 is discounted from the regular price.

Step-by-step explanation:

20% of 65 is also 0.2 x 65

If you multiply 65 by 0.2 you get $13.

The new price would be $52, with a $13 discount.

Discounted price from the regular price is $52 and the discount is $13 if an item is regularly priced at $65. It is on sale for 20% off the regular price.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

An item is regularly priced at $65. It is on sale for 20% off the regular price.

To find the discounted price from the regular price:

= 20% of 65

= (20/100)65

= 0.2x65

= $13

The new price would be $52, with a $13 discount.

Thus, discounted price from the regular price is $52 and the discount is $13 if an item is regularly priced at $65. It is on sale for 20% off the regular price.

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Answer:

x=122

Step-by-step explanation:

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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By using graph of function y = x² - 5x - 2, the solution of the equation

- 4 = x² - 5x - 2 are,

⇒ (2, - 4) and (3, - 4)

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The equation is,

⇒ y = x² - 5x - 2

⇒ - 4 = x² - 5x - 2

Now, We can draw the graph of function y = x² - 5x - 2 as shown in figure.

Then, For equation - 4 = x² - 5x - 2;

Value of y = - 4

Hence, By the graph of y = x² - 5x - 2 we can see that at y = - 4 there are two value of x;

⇒ x = 2, 3

Thus, By using graph of function y = x² - 5x - 2, the solution of the equation - 4 = x² - 5x - 2 are,

⇒ (2, - 4) and (3, - 4)

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Constructing an angle bisector using only a straightedge and compass involves drawing the Angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle.

To construct an angle bisector using a straightedge and compass, there are several steps that you need to follow. The correct order of steps for constructing an angle bisector of ABC using only a straightedge and compass are listed below:

Step 1: Draw the angle ABC with a straightedge.

Step 2: Place the point of the compass on point B and swing an arc that intersects both lines that make up the angle. Label the two points where the arc intersects the angle as points D and E.

Step 3: Without changing the compass width, place the point of the compass on point D and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point F.

Step 4: Without changing the compass width, place the point of the compass on point E and swing an arc that intersects the ray that extends from point B. Label the point of intersection as point G.

Step 5: Draw the line segment FG with a straightedge. This line segment is the angle bisector of angle ABC.

In summary, constructing an angle bisector using only a straightedge and compass involves drawing the angle, creating two arcs that intersect the angle, and using those arcs to create a line segment that bisects the angle. Following these steps will allow you to construct the angle bisector of ABC accurately.

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Based on the information, the Stafford loan will have a lower balance by $527.14 at the time of repayment

Using the formula for compound interest, the total cost of the loan can be calculated as follows:

Total cost of Stafford loan = $11,650 x (1 + 0.0595/12)^(12*0.5) = $12,652.14

Total cost of PLUS loan = $12,436.41 x (1 + 0.0655/12)^12 = $13,179.28

Therefore, the Stafford loan will have a lower balance at the time of repayment by $527.14 ($13,179.28 - $12,652.14).

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The number of degrees below zero is given by A = 56° F

Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:

If x is positive, then f(x) = x

If x = 0, then f(x) = 0

If x < 0, then f(x) = -x

Given data ,

Let the initial temperature be represented as T

Let the number of degrees below zero be A

Now , the value of T is

T = -56° F

From the modulus function , we get

The value of the modulus function is always non-negative.

So , the measure of A = | T |

A = | -56 |

A = 56° F

Hence , the number of degrees below zero is 56° F

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Answer:

100+50²=2600

Step-by-step explanation:

because 50x2=100 and 50² is 2500. Add those and you get 2600.

The probability that both people picked at random own a dog is 0.0225.

Random selection is a process of choosing items or individuals from a larger population in a way that ensures that each item or individual has an equal chance of being chosen. It is a common method used in research studies to select a representative sample from a larger population. The goal of random selection is to obtain a sample that is representative of the larger population, so that any conclusions drawn from the sample can be generalized to the population as a whole. In random selection, every member of the population has an equal chance of being selected, and the selection process is not influenced by any biases or preferences.

To calculate the probability that both people own a dog, we need to multiply the probability that the first person owns a dog by the probability that the second person owns a dog. Given that the first person own a dog.

The probability that the first person owns a dog is 0.15 or 15%. Then, the probability that the second person also owns a dog, given that the first person does, is 0.15 as well.

So, the probability that both the people owning a dog is:

0.15 x 0.15 = 0.0225 or 2.25%

Therefore, the probability that both people picked at random own a dog is 0.0225 or 2.25% (rounded to 3 decimal places).

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The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

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Answer:

\(x = \frac{2a}{a - 2} \)