Given the three points A(8,1,3), B(-6,-4,3) and C(9,-8,3) let L1 be the line through A and B and let L2 be the line through C parallel to (-6,2,-8)T. Find the distance between L1 and L2. Exact the exact value of the distance in the box below.

We can use trigonometry to solve this problem.

Let's call the distance we are looking for "x". We can use the sine function, which relates the opposite side of a right triangle to its hypotenuse:

sin(51°) = opposite/hypotenuse

We know that the hypotenuse is the length of the ladder, which is 3.8m. We can solve for the opposite side (x) by rearranging the equation:

x = sin(51°) * 3.8m

x ≈ 2.98m

So the bottom of the ladder is about 2.98 meters away from the wall. Rounded to the nearest tenth, the answer is 3.0 meters.

Coordinates of the vertices of the pre-image are (-4, 4), (-1, 9), and (1, 9).

And the graph is given below.

A transformation of a triangle can refer to any process that changes the size, position, or shape of a triangle.

Translation involves moving the triangle without changing its shape or size. To translate a triangle, you can simply move it in any direction by a certain distance, without rotating or flipping it.

Here we have

From the graph

The coordinates of the triangle are (1, 1) (4, 6), and (6, 3)

Given T < -5, 3 > (x, y)

Hence, the coordinates of the pre-image are

(1, 1) => (1 - 5,  1 + 3)  = (-4, 4)  

(4, 6) => (4 - 5, 6 + 3) = (-1, 9)

(6, 3) => (6 - 5,  3+3) = (1, 6)

Hence,

Coordinates of the vertices of the pre-image are (-4, 4), (-1, 9), and (1, 9).

And the graph is given below.

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(a) (6, H, 7) is not a possible outcome because the sum of the two numbers rolled on the number cube cannot be 7 if the first number rolled is 6.

(b) (T, 3, 4) is a possible outcome because the first outcome is tails, the second outcome is 3, and the third outcome is 4.

(c) (6, H, 6, T) is not a possible outcome because the third outcome cannot be both 6 and T at the same time.

(d) (1, T, 1) is a possible outcome because the first and third outcomes are both 1 and the second outcome is tails.

(e) (H, H, 3) is not a possible outcome because the third outcome cannot be 3 if the first two outcomes are both heads.

What is Probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

Since each of the three people orders a different flavor, the first person has 6 choices, the second person has 5 choices (since one flavor has already been chosen), and the third person has 4 choices (since two flavors have already been chosen). The total number of outcomes is the product of these numbers:

6 × 5 × 4 = 120

Therefore, there are 120 possible outcomes.

(part 1) There are 10 options for the first digit, 9 options for the second digit (since one digit has already been chosen), and 8 options for the third digit (since two digits have already been chosen). The total number of combinations is the product of these numbers:

10 × 9 × 8 = 720

Therefore, there are 720 possible locker combinations.

(part 2) If you absolutely choose 9 as your first digit, then there are only 9 options for the first digit. The second and third digits can still be any of the remaining 9 digits (since digits cannot repeat). Therefore, the number of possible combinations is:

1 × 9 × 8 = 72

The theoretical probability of getting HH on two coin flips is (1/2) × (1/2) = 1/4 = 0.25. The experimental probability of getting HH after 100 trials is 25/100 = 0.25. Since the experimental probability is equal to the theoretical probability, we can say that the experimental probability of getting HH is equal to the theoretical probability.

The possible outcomes of rolling a standard number cube are 1, 2, 3, 4, 5, and 6. The possible outcomes of flipping a coin are heads (H) or tails (T).

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When the angle of elevation to the plateau's top is 20°, we are therefore 34.22 metres distant from the plateau's foot.

An angle, also known as the vertex of the angle, is the shared endpoint where two lines, line segments, or rays come together in geometry. Angles are commonly expressed as degrees or radians. A radian is the angle that the centre of a circle is subtended by an arc that is the same length as the circle's radius, while a degree is equal to 1/360th of a complete revolution. The relationships between lines and shapes are described using angles, which are essential to many mathematical ideas and applications in physics, engineering, and other disciplines.

given

Trigonometry can be used to resolve this issue. Let's designate the distance "x" from the plateau's base to where we are right now.

We must first determine the height we are at right now. Since we are aware of the slope angle, we can accomplish this using the tangent function:

tan(20°) Means adjacent/opposite

h is the height we are presently at, so tan(20°) = h/x.

To find h, we can change this equation as follows:

h Equals x * tan(20°)

x² + h² = 40^2

If you replace h = x * tan(20°):

x² + (x*tan(20°))

x² = 40²

Simplifying:

x² + 0.364x²= 1600

1.364x² = 1600

x² = 1171.61

x ≈ 34.22

When the angle of elevation to the plateau's top is 20°, we are therefore 34.22 metres distant from the plateau's foot.

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The value of x is 18 and y is 16. The solution has been obtained by using concept of similar triangles.

If two triangles have the same number of corresponding sides and corresponding angles, they are said to be similar. Similar figures are objects that have the same shape but various sizes, like two or more figures.

We are given that in ΔABC and ΔBDC,

∠ABC ≅ ∠BDC  (right angles)

BC ≅ BC  (common side)

∠ACB ≅ ∠BCD (common angle)

So,  ΔABC ≅ ΔBDC.

We know that in similar triangles, the ratio of the corresponding sides is same.

So,

AC / BC = BC / CD

Now, by substituting the given values in the relation, we get,

⇒18/a = a/16

We are given proportion as x/a = a/y.

On comparing both, we get

x = 18 and y = 16

Hence, the value of x is 18 and y is 16.

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The common factors are \[(x+5)\], so the LCM is (x+5)²(x+6) of the given polynomials. The Least Common Multiple (LCM) of the two given polynomials can be found by factoring them and then finding the common factors:

\[ x²+10 x+25 = (x+5)(x+5) \]
\[ x²+11 x+30 = (x+5)(x+6) \]

To determine the LCM of the given polynomials, we need to factor each polynomial and then multiply the factors together, taking the highest power of each factor.

First, let's factor each polynomial:

\[ x²+10 x+25 = (x+5)(x+5) \]
\[ x²+11 x+30 = (x+5)(x+6) \]

Now, let's find the LCM by multiplying the highest power of each factor together:

LCM = (x+5)(x+5)(x+6) = (x+5)²(x+6)

So, the LCM of the given polynomials is (x+5)²(x+6) in factored form.

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Answer:

a. x = 11; mAB = 34°

b. x = 25.5; mAB = 46°

c. x = 17; mAB = 46°

d. x = 11; mAB = 17

Step-by-step explanation:

Elena plans on running a total of 5 miles.

Mile, any of several distance measurements, such as the statutory mile (5,280 ft) (1.609 km). It comes from of the Romans lire passus, also referred as the "1000 steps," which was equal to 5,000 Romans feet. Unit of length is a related topic. See all relevant material The "old London" mile was eight furlongs when it was first established in 1500.

The term mille passus, which translates to "a hundred paces" in Latin and meant a length of 1,000 rates of speed or 5,000 Rome feet, was originally used by the Romans. It is equivalent to around 1,480 metres, or 1,618 contemporary yards.

We are aware that she has covered 2 miles, or 40% of a total distance, in her run thus far:

[tex]2=0.4x[/tex]

To find x,

[tex]2=0.4x[/tex]

[tex]x=\frac{2}{0.4}[/tex]

[tex]x=5[/tex]

Therefore, Elena plans to run a total distance of 5 miles.

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6%=300

300 x 5 = 1500

5k add £1500

=

6500

Answer:Next year, he will have 5% more than that. To find our total value at the end of the year, .

Step-by-step explanation:

Answer:

working on it

Step-by-step explanation:

$120,000

The formula for an exponential function passing through the points (-2,--) and (2, 75) is: y = 75 * 2x + 2. To answer the question about the house valued at $120,000, the value of the house is not related to an exponential function. Therefore, the answer is that the value of the house is $120,000.

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The GCF (greatest common factor) of the first two terms of the polynomial 3p^(3)+9p^(2)+5p+15 is 3p^(2). This is because both terms have a common factor of 3p^(2) that can be factored out.

The GCF of the last two terms of the polynomial is 5. This is because both terms have a common factor of 5 that can be factored out.

Therefore, the polynomial can be factored as follows:

3p^(2)(p+3) + 5(p+3)

Now, we can factor out the common factor of (p+3) to get the final factored form of the polynomial:

(3p^(2)+5)(p+3)

So, the GCF of the first two terms is 3p^(2) and the GCF of the last two terms is 5.

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The value conversion of polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x² to standard form is [tex]x^4[/tex] - 2x³ - x² + 1/7.

To rewrite the polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x² in standard form, we need to arrange the terms in decreasing order of their degree, with the highest degree term first.

Rewrite the polynomial with the terms in descending order of degree:

[tex]x^4[/tex] - 2x³ - x² + 1/7

Combine any like terms:

There are no like terms to combine in this polynomial.

Rewrite the polynomial in standard form:

The polynomial in standard form is:

[tex]x^4[/tex] - 2x³ - x² + 1/7

Therefore, the polynomial -2x³ + 1/7 + [tex]x^4[/tex] - x^2 in standard form is [tex]x^4[/tex] - 2x³ - x² + 1/7.

It is important to remember to always arrange the terms in descending order of degree when writing a polynomial in standard form.

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The distribution is  X ~ N(46, 19), the probability that a randomly selected student's time will be between 42 and 44 minutes is 0.04147. the probability that the average time studying for the 50 students is between 42 and 44 minutes is 0.1601.

a. X ~ N(46, 19)

b. e is not defined in the problem, so it does not have a distribution.

c. z ~ N(0, 1) (standard normal distribution)

d. To find the probability that one randomly selected student's time will be between 42 and 44 minutes, we first standardize the values:

z = (44 - 46) / 19 = -0.1053

z = (42 - 46) / 19 = -0.2105

Using a standard normal table or calculator, we can find the area under the standard normal curve between these two z-scores:

P(-0.2105 < z < -0.1053) = 0.04147

Therefore, the probability that a randomly selected student's time will be between 42 and 44 minutes is 0.04147.

e. To find the probability that the average time studying is between 42 and 44 minutes, we need to use the central limit theorem. Since we have a large enough sample size (n = 50) and the population standard deviation is known, we can use the following formula to standardize the sample mean:

z = (x - μ) / (σ / √n)

Substituting the given values:

z = (44 - 46) / (19 / √50) = -0.7443

z = (42 - 46) / (19 / √50) = -1.4886

Using a standard normal table or calculator, we can find the area under the standard normal curve between these two z-scores:

P(-1.4886 < z < -0.7443) = 0.1601

Therefore, the probability that the average time studying for the 50 students is between 42 and 44 minutes is 0.1601.

f. The total study time for the 50 students follows a normal distribution with mean 5046 = 2300 minutes and standard deviation √5019 ≈ 39.70 minutes. To find the probability that the total study time is more than 2200 minutes, we standardize the value:

z = (2200 - 2300) / 39.70 = -2.5189

Using a standard normal table or calculator, we can find the area under the standard normal curve to the right of this z-score:

P(z > -2.5189) = 0.99411

Therefore, the probability that the randomly selected 50 students will have a total study time more than 2200 minutes is 0.99411.

g. The assumption of normality is necessary for parts e) and f) because we are using the normal distribution and the central limit theorem to approximate the probabilities. Without the normal assumption, we would need to use different methods for probability calculations.

h. We need to find the least total time that corresponds to the top 15% of the distribution. Using a standard normal table or calculator, we can find the z-score that corresponds to the 85th percentile:

z = 1.0364

We can then use the formula for the total study time:

x = μ + z(σ / √n)

Substituting the given values:

x = 4650 + 1.0364(19*√50) ≈ 4652.78

Therefore, the least total time that a group can study and still receive a sticker is approximately 4652.78 minutes.

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Answer: See attached.

Step-by-step explanation:

    Since the first equation uses a ≤ symbol, we know we will use a solid line. This is because it is less than and equal to. Then, we will graph it as a regular slope-intercept line.

    This line has a slope of 5 and a y-intercept of -2. This means we will start at (0, -2) and move five units up for every unit right, or five units down for every unit left.

    For the next equation, it uses a > symbol so we will use a dashed line. This is because it is not equal to, only greater than. Same as the previous. We will graph it as a slope-intercept line, but using a dashed line instead of a solid line.

    This line has a slope of -2 and a y-intercept of positive 5. This means we will start at (0, 5) and move two units down for every unit right, or two units up for every unit left.

Answer: 1 1/4

Step-by-step explanation:

1/4 * 3 = 3/4

3/4 + 1/2 =

3/4 + 2/4 = 5/4 = 1 1/4

the answer to the question Simplify. Express your answer z^(4)*z*z" is z^(6).

To simplify the expression z^(4)*z*z, we need to use the rules of exponents. Specifically, we need to use the rule that states that when we multiply expressions with the same base, we can add the exponents. In other words, a^(b)*a^(c) = a^(b+c).

Using this rule, we can simplify the given expression as follows:

z^(4)*z*z = z^(4+1+1) = z^(6)

So, the simplified expression is z^(6).

In conclusion, the answer to the question "Simplify. Express your answer z^(4)*z*z" is z^(6).

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Step-by-step explanation:

Refer to pic............

Answer:

1st choice

Step-by-step explanation:

(r² -4r + 5 - r² -2r + 8) / (r - 4)

= (-6r + 13) / (r - 4)

The correct classification for the expression 2x+2 is a Linear binomial.(3)


A monomial is an algebraic expression with only one term. A binomial is an algebraic expression with two terms. A trinomial is an algebraic expression with three terms.

A quadratic expression is an expression with a term that has a degree of 2. A linear expression is an expression with a term that has a degree of 1.

In the given expression, 2x+2, there are two terms (2x and 2) so it is a binomial. The highest degree of the terms is 1 (in the term 2x), so it is a linear expression. Therefore, the correct classification for the expression is a Linear binomial.

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complete question

Classify 2x+2 in one of the following

1.Quadratic monomial

2.Linear monomial

3.Linear binomial

4.Quadratic trinomial

Answer:

Step-by-step explanation:

x = number of small boxes

x-4 = number of large boxes

total number of eggs in the large boxes = 12(x-4) = 12x - 48

total number of eggs she buys = 6x + 12x - 48 = 18x - 48 = 6(3x - 8)

The requried equation represents the volume of the gas in terms of temperature is V = 22 + 225T.

The equation model is defined as the representative of the given case in the form of an equation using variables and constants.

Here,
Let's denote the volume of the gas as V and temperature as T.

From the given information, we know that at 0°C temperature (i.e. T = 0), the volume of the gas is 22 liters.

For every 1°C increase in temperature, the volume of the gas increases by 225 liters.

Therefore, we can write the equation as:

V = 22 + 225T

This equation represents the volume of the gas in terms of temperature.

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The estimated value of the standard deviation using the range rule of thumb is 0.875 degrees F

The range rule of thumb is used to estimate the standard deviation of a data set using the range of the data. In this case, the range of the data is 3.5 degrees F. Using the range rule of thumb, the standard deviation of the data can be estimated by taking the range (3.5) and dividing it by 4, which gives us an estimated standard deviation of 0.875 degrees F.

This estimated value is within 0.2 degrees F of the actual standard deviation of the data (0.72 degrees F).

To compare this result to the actual standard deviation of the data, we subtract the estimated value from the actual value and take the absolute value of the result. This gives us the difference between the two values:

|0.72 - 0.875| = 0.155

Since the difference between the estimated and actual standard deviations is less than 0.2 degrees F, we can say that the range rule of thumb provides a reasonable approximation of the standard deviation for this data set.

In conclusion, the estimated value of the standard deviation using the range rule of thumb is 0.875 degrees F, and this value is within 0.2 degrees F of the actual standard deviation of 0.72 degrees F.

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The product of the two given binomials can be expressed as the trinomial 2561104x³ + 684636x² + 87719x + 736, which is in its simplest form.

In this case, we will multiply the first two binomials (12x+1)(21x+1) and then multiply the second two binomials (65x+32)(56x+23). We will then multiply the two resulting expressions to get the final trinomial.

To multiply (12x+1)(21x+1), we can use the distributive property of multiplication, which states that a(b+c) = ab + ac. Therefore, we have:

(12x+1)(21x+1) = 12x(21x) + 12x(1) + 1(21x) + 1(1) = 252x² + 12x + 21x + 1 = 252x² + 33x + 1

Similarly, to multiply (65x+32)(56x+23), we have:

(65x+32)(56x+23) = 65x(56x) + 65x(23) + 32(56x) + 32(23) = 3640x² + 1495x + 1792x + 736 = 3640x² + 3287x + 736

Now, to find the product of the two expressions, we can multiply them using the distributive property again:

(252x² + 33x + 1)(3640x² + 3287x + 736) = 252x²(3640x²) + 252x²(3287x) + 252x²(736)

   • 33x(3640x²) + 33x(3287x) + 33x(736)

   • 1(3640x²) + 1(3287x) + 1(736)

Simplifying this expression by combining like terms, we get:

= 917280x⁴ + 1573824x³ + 684636x² + 87719x + 736

This final expression has four terms, but it can be simplified further to a trinomial by combining the first two terms using the associative property of addition. We have:

917280x⁴ + 1573824x³ + 684636x² + 87719x + 736 = (917280x⁴ + 1573824x³) + (684636x² + 87719x + 736) = 2561104x³ + 684636x² + 87719x + 736

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Complete Question:

Express the product of(12x+1)(21​x+1) and(65x+32)(56​x+23​) as a trinomial in simplest form

Answer:

First, we need to calculate Danielle's commission on the merchandise she sold:

Commission = 7.25% of $4,100 = 0.0725 x $4,100 = $296.25

Next, we need to calculate her total earnings for the week:

Total earnings = Base salary + Commission

Total earnings = $725 + $296.25

Total earnings = $1,021.25

Therefore, Danielle earned $1,021.25 last week.

Answer:

1,021.25

Step-by-step explanation:

The hypothesis of this research is that there is a positive correlation between the independent variables (hours slept on the night of the test, hours spent studying the week before the test, and student's IQ) and the dependent variable (test scores). As such, the null hypothesis states that there is no relationship between the independent variables and the dependent variable, while the alternative hypothesis states that there is a relationship between the independent variables and the dependent variable. Symbolically, this can be written as:

H0: There is no relationship between the independent variables and the dependent variable

H1: There is a relationship between the independent variables and the dependent variable

Given the hypothesis, the independent variable (number of hours of sleep, number of hours spent studying, and IQ) are quantitative and discrete, and the dependent variable (test scores) is ratio, an f test is the most appropriate statistical test to use. An f test will allow us to compare the independent variables to see if there is a statistically significant difference between the independent variables and the dependent variable. By using an f test, we can determine if the independent variables are actually associated with the dependent variable and how strong that association is.

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The answer is x=26.

To solve the equation x-5=21 using the addition property of equality, we need to isolate the variable x on one side of the equation. The addition property of equality states that if we add the same value to both sides of an equation, the equation will remain true.

Step 1: Add 5 to both sides of the equation to cancel out the -5 on the left side.
x-5+5=21+5

Step 2: Simplify both sides of the equation.
x=26

Step 3: Check the solution by substituting the value of x back into the original equation.
26-5=21
21=21

The solution checks out, so the answer is x=26.

In conclusion, the solution to the equation x-5=21 using the addition property of equality is x=26.

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The answer should be 10 1/2 ft

Here is my work below:

The series converges.

To test the series 3 + 3/5 + 3/5^2 + 3/5^3 + … =∑n=0[infinity] 3/5^n,

we can use the ratio test.

Specifically, we can look at the ratio of each successive term.

Let an+1/an = 3/5n+1/3/5n = 1/5. Since this is less than 1, the series converges.

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