Simplify 9a - 2(a-3)

Answer:

i) Consecutive interior angles

ii) Supplementary angles

iii) The two oars are parallel by consecutive interior angles theorem

Step-by-step explanation:

i) m∠1  and m∠2 lie between two line and on the same side of the line passing through the two lines. Therefore, they are consecutive interior angles

ii)x = 10

m∠1 = 6x + 18

= 6(10) + 18

= 60 + 18

= 78

m∠2 = 9x + 12

= 9(10) + 12

= 90 + 12

= 102

m∠1 + m∠2 = 72 + 108 = 180

Since m∠1 and m∠2 add to 180, they are supplementary angles.

iii) The two oars are parallel

consecutive interior angle theorem:

If  a transversal cuts through two line and the consecutive interior angles are supplimentary, then the two lines are parallel

15 is the value of x that will make the linear equation true .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                            The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

x + 5= 20

X = 20 - 5

x = 15

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Answer:

  A

Step-by-step explanation:

It looks like you can make the short table ...

(recipe, ounces, servings, ounces/serving)

(A, 28, 14, 28/14 = 2.00)

(B, 9, 12, 9/12 = 0.75)

(C, 1.3, 1, 1.3/1 = 1.30)

Recipe A uses the most flour per serving of pizza.

Answer:

A

Step-by-step explanation:

Limit of the function ln(n³)/10n is \(\lim_{n \to \infty}\) (3/n) and the sequence will be divergence in nature.

In Arithmetic, divergence and curl are the two fundamental procedure on the vector field. Both are significant in math as it assists with fostering the higher-layered of the central hypothesis of analytics. For the most part, uniqueness makes sense of how the field acts towards or away from a point. Likewise, curl is utilized to quantify the rotational degree of the field about a specific point.

We have a\(_n\)=ln(n³)/10n

Apply n'th term test for divergence, which states that,

If \(\lim_{n \to \infty} a_n\) !=0 , then ∑a\(_n\) diverges

Apply L'Hospital's rule,then \(\lim_{n \to \infty} ln(n^3)/10n\), Test L'Hospital condition:0/0

=\(\lim_{n \to \infty}\) d [ln(n³)/10n] / dn

=\(\lim_{n \to \infty}\)  (1/n³) ×3n²(since differentiation of ln(x) is 1/x)

=\(\lim_{n \to \infty}\)(3/n)

If n tends to infinite then the function tends to zero because 1/n tends to zero.

But,By the limit chain rule we know that 1!=0.So,according to the postulate of the divergence test criteria,we got that  the given function will diverges.

Hence, limit of the function is \(\lim_{n \to \infty}\)(3/n) and function will diverges.

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(Complete question) is:

determine the convergence or divergence of the sequence with the given nth term. if the sequence converges, find its limit- ln(n³)/10n.

Answer:

234 Square Inches

Step by Step Explanation:

To find the area of a parallelogram, we must first find the height. In this case, it is 18. Then, we must find the base. In this case, it is 13. Then, we multiply base x height for our final answer of 234.

Base - 13

Height - 18

18 x 13 = 234.

Easy enough?

The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.

Please find attached the graph of the residual plot for the data created with MS Excel

A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.

The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158

The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;

Area (in²)    \({}\)              Residuals

x-value

5 \({}\)                             -1.0178

10 \({}\)                           -0.2718

24 \({}\)                           0.605

46 \({}\)                           0.7874

53 \({}\)                           0.7018

78 \({}\)                           0.0758

84 \({}\)                           -0.129

100 \({}\)                         -0.7538

The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option

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Using the periodicity of the tangent function we can see that:

tan(-4π/3) = -√3

Ok, we know that the trigonometric functions have a period of 2π, that means that we can rewrite the expression:

tan(-4π/3)

as:

tan(-4π/3 + 2π)

The argument can be rewritten as:

tan(-4π/3 + 2π) = tan(2π/3)

Using a table for the tangent function we can see that it is equal to -√3, that is the value of the tangent.

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Answer:

The original price of the shoes was of 2200 pesos

Step-by-step explanation:

She bought the shoes for 1866 pesos.

She receibed a discount of 70 pesos, so the cost, with the discount, is 1866 + 70 = 1936 pesos.

The pair was bought at 12% off, that is, 1936 pesos is 100 - 12 = 88% of the original price. Then

\(0.88x = 1936\)

\(x = \frac{1936}{0.88}\)

\(x = 2200\)

The original price of the shoes was of 2200 pesos

The equation for the line in the graph given is 7x - 4y - 28 = 0. The points in the given graph are (0, -7) and (4, 0).

Consider two points (x1, y1) and (x2, y2).

When a line passing through these points is calculated as

y - y1 = (y2 - y1)/(x2 - x1) × (x - x1)

The given line in the graph passes through the points (0, -7) and (4, 0). (By taking x = 0, we get y = -7 and y = 0, we get x = 4)

x1 = 0, x2 = 4, y1 = -7, y2 = 0

Then, the equation of the line is

y - y1 = (y2 - y1)/(x2 - x1) × (x - x1)

⇒ y + 7 = (0 + 7)/(4 - 0) × (x - 0)

⇒ y + 7 = 7/4 (x)

⇒ 4y + 28 = 7x

⇒ 7x - 4y - 28 = 0

Therefore, the equation of the given line in the graph is 7x - 4y - 28 = 0.

And the points that lie on the line are (0, -7) and (4, 0).

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Answer:

Explanation:

Here, we want to calculate the probability that all three have only cell phone service

The probability that a household has only cell phone service is 50% which is the same as 1/2 or 0.5

The probability that all three have only cell phone services will be:

The probability that all three households only have cell phone service is approximately 0.2307 or 23.07%. The probability that at least one household has only cell phone service is approximately 0.7693 or 76.93%.

To calculate the probability that all three households only have cell phone service, we need to consider the total number of households and the number of households with only cell phone service.

Let's assume there are a total of 100 households in the region.

According to the study, 62% of households no longer have a landline and only have cell phone service. This means that 62 households out of 100 have only cell phone service.

To calculate the probability that all three households only have cell phone service, we need to calculate the probability of selecting a household with only cell phone service for each selection.

For the first household, the probability of selecting a household with only cell phone service is 62/100.

For the second household, since one household has already been selected, there are now 99 households remaining, out of which 61 have only cell phone service. Therefore, the probability of selecting a household with only cell phone service for the second selection is 61/99.

Similarly, for the third household, since two households have already been selected, there are now 98 households remaining, out of which 60 have only cell phone service. Therefore, the probability of selecting a household with only cell phone service for the third selection is 60/98.

To calculate the probability that all three households only have cell phone service, we multiply the probabilities of each selection:

(62/100) * (61/99) * (60/98) = 0.2307

Therefore, the probability that all three households only have cell phone service is approximately 0.2307 or 23.07%.

To calculate the probability that at least one household has only cell phone service, we can use the complement rule. The complement of the event 'at least one household has only cell phone service' is 'no household has only cell phone service.'

The probability that no household has only cell phone service can be calculated by subtracting the probability that all three households have cell phone service from 1:

1 - 0.2307 = 0.7693

Therefore, the probability that at least one household has only cell phone service is approximately 0.7693 or 76.93%.

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Step-by-step explanation:

Step 1: Find the mean x of the data values.

X = (ix₁) / n

x = (12 + 3 + 9 + 2 + 0 + 0 + 3) / 7

x = 29 / 7

x ≈ 4.14 (rounded to two decimal places)

Step 2: Calculate the squared differences from the mean for each data value [(x₁ - x)²].

For each data value, subtract the mean and square the result.

Squared Differences:

(12 - 4.14)² ≈ 53.43

(3 - 4.14)² ≈ 1.31

(9 - 4.14)² ≈ 23.09

(2 - 4.14)² ≈ 4.34

(0 - 4.14)² ≈ 17.11

(0 - 4.14)² ≈ 17.11

(3 - 4.14)² ≈ 1.31

Step 3: Calculate the variance (s²) of the data values.

s² = ((x₁ - x)²) / (n - 1)

s² = (53.43 + 1.31 + 23.09 + 4.34 + 17.11 + 17.11 + 1.31) / (7 - 1)

s² ≈ 117.70 / 6

s² ≈ 19.62 (rounded to two decimal places)

Step 4: Calculate the standard deviation (s) of the data values.

s = √s²

s = √19.62

s ≈ 4.43 (rounded to two decimal places)

Step 5: Find the range of the data values.

Range = Maximum value - Minimum value

Range = 12 - 0

Range = 12

Therefore, the results are:

The standard deviation is approximately 4.43 (rounded to two decimal places).

The variance is approximately 19.62 (rounded to two decimal places).

The range is 12.

The equivalent expression of (1.3³/1.2⁴)⁻⁶ is the expression 1.2²⁴/1.3¹⁸

An equation shows the relationship between two or more numbers and variables.

Given the expression:

(1.3³/1.2⁴)⁻⁶

Applying the law of negative exponents:

= (1.2⁴/1.3³)⁶

Further simplifying gives:

= (1.2⁴⁽⁶⁾/1.3³⁽⁶⁾)

= 1.2²⁴/1.3¹⁸

(1.3³/1.2⁴)⁻⁶ is equal to 1.2²⁴/1.3¹⁸

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The search results are unrelated to the question of finding the reflection image of (5, -3) across the y-axis. To find the reflection image of a point across the y-axis, we need to change the sign of the x-coordinate of the point. Therefore, the reflection image of (5, -3) across the y-axis is (-5, -3).

Answer:

Step-by-step explanation:

You want the coordinates of the vertices of QRST after it has been translated right 2 units, then reflected across the y-axis. The original coordinates are Q(1, 5), R(3, -1), S(0, 0), T(-2, 3).

The problem statement is written as a composition of the transformations Ry and T(2,0). A composition of functions is generally executed right to left, meaning the translation will be done first, then the reflection.

The numbers in the translation vector are added to the coordinates:

  (x, y) ⇒ (x+2, y+0)

Reflection over the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

Then the composition of transformations is ...

  (x, y) ⇒ (-(x+2), y)

  Q(1, 5) ⇒ Q'(-3, 5)

  R(3, -1) ⇒ R'(-5, -1)

  S(0, 0) ⇒ S'(-2, 0)

  T(-2, 3) ⇒ T'(0, 3)

Answer:

Following are the solution to this question:

Step-by-step explanation:

C'(t) was its time, in years, or t shift of cash per unit. That C'(1980) meaning, therefore, becomes the change of cashier's population to t = 1980.  

They could either use t = 1970 or t = 1990 to approximate the C'(1980) price. When using t = 1970:

\(C'(1980) = \frac{[C(1980) - C(1970)]}{[1980 - 1970]}\\\\\)

              \(= \frac{(571 - 265)}{10}\\\\ = \$ \ 30.6 \\\)

t = 1990:

\(C'(1980) = \frac{[C(1980) - C(1990)]}{[1980 - 1990]}\)

              \(= \frac{(571 - 1063)}{ -10} \\\\= \$ \ 49.2\)

The cοrrect answer is: the predicted number οf elephants in the regiοn in 1995.

An expοnential functiοn is a mathematical functiοn in which an independent variable appears in the expοnent.

In the given expressiοn, 3652(1.045)b, the cοnstant 3652 represents the predicted number οf elephants in the regiοn in the base year, which is 1995.

This can be determined by setting b=0, which gives:

\(3652(1.045)^0 = 3652(1) = 3652\)

Hence, the correct answer is: the predicted number of elephants in the region in 1995.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

Step-by-step explanation:

(4x - 9) + 12 = 2x - 5           Remove the brackets

4x - 9 + 12 = 2x - 5             Combine the left

4x + 3 = 2x - 5                    Subtract 2x from both sides

4x - 2x + 3 = - 5                 Combine

2x + 3 = - 5                         Subtract 3 from both sides

2x + 3 -3 = - 5 -3                Combine

2x = - 8                               Divide by 2

x = -8/2

x = -4

Answer: circle

Step-by-step explanation:

The set of points on a given plane which is equidistant from a fixed point that is called the center​ simply describes a circle.

We should note that the straight line that goes through the centre of a circle is referred to as the diameter while half of the diameter is the radius which is drawn from the center of the circle.

Answer:

x = -3 + 2 i or x = -3 - 2 i

Step-by-step explanation:

Solve for x:

x^2 + 6 x + 13 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 13 from both sides:

x^2 + 6 x = -13

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 9 to both sides:

x^2 + 6 x + 9 = -4

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x + 3)^2 = -4

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x + 3 = 2 i or x + 3 = -2 i

Hint: | Look at the first equation: Solve for x.

Subtract 3 from both sides:

x = -3 + 2 i or x + 3 = -2 i

Hint: | Look at the second equation: Solve for x.

Subtract 3 from both sides:

Answer: x = -3 + 2 i or x = -3 - 2 i

Answer: 8 bags.

Step-by-step explanation:

It is given that, a make-your-own ice pop kit says to pour 4 fluid ounces of juice into each bag.

We need to find the number of ice pop bags we can fill with 1 quart of juice.

We know that,

1 quart = 32 ounces

We have  32 ounces of juice and each bag contains 4 fluid ounces.

\(\text{Number of ice pop bags}=\dfrac{\text{Total juice}}{\text{Juice contained in each bag}}\)

\(\text{Number of ice pop bags}=\dfrac{32}{4}\)

\(\text{Number of ice pop bags}=8\)

Therefore, 8 ice pop bags we can  fill with 1 quart of juice.

Answer:

8 bags

Step-by-step explanation:

The last expression finally simplifies to cot β + tan α using quotient identity in trigonometric identities.

We want to verify the trigonometric  identity;

cos (α - β)/(cos α sin β) = cot β + tan α

Now, according to trigonometric identities in mathematics, we know that;

cos (α - β) = (cos α cos β) + (sin α sin β)

Thus, plugging that back into our left hand side of the main question gives;

[(cos α cos β) + (sin α sin β)]/(cos α sin β)

Rewriting this expression by separating the denominator gives;

[(cos α cos β)/(cos α sin β)] + [(sin α sin β)]/(cos α sin β)

Using quotient identities, this can be simplified to;

cot β + tan α

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The congruence theorems or postulates that could be given as reasons why ACDE=AOPQ are:

Note that in the diagram, there has been given one side that is congruent to its other corresponding side and as such, it has remove the option or postulates that needs the HL and SAS sides.

Conclusively, when all three angles are said to be congruent and when they have one side (known as the hypotenuse), one can use the congruence theorems or postulates of  AAS, HA and ASA.

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The piecewise function for this problem is defined as follows:

B.

The function is a piecewise function, as the function has different definitions based on the input of the function.

The different definitions for the graph are given as follows:

To the left of x = 0, we have a linear function with intercept of 2 and slope of 2, hence it is given as follows:

y = 2x + 2, x ≤ 0.

To the right of x = 0, we have a linear function with intercept of 4 and slope of -4/3, hence it is given as follows:

y = -4/3x + 4, x > 0.

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From the test the person wants, and the sample data, we build the test hypothesis, find the test statistic,  and use this to reach a conclusion.

This is a two-sample test, thus, it is needed to understand the central limit theorem and subtraction of normal variables.

Doing this:

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

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

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

Proportion 1: Jet-ski users

86.5% out of 400, thus:

\(p_1 = 0.865\)

\(s_1 = \sqrt{\frac{0.865*0.135}{400}} = 0.0171\)

Proportion 2: boaters

92.8% out of 250, so:

\(p_2 = 0.928\)

\(s_2 = \sqrt{\frac{0.928*0.072}{250}} = 0.0163\)

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

Hypothesis:

Test the claim that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

At the null hypothesis, it is tested that the proportions are the same, that is, the subtraction is 0. So

\(H_0: p_1 - p_2 = 0 \rightarrow p_1 = p_2\)

At the alternative hypothesis, it is tested that the proportions are different, that is, the subtraction is different of 0. So

\(H_1: p_1 - p_2 \neq 0 \rightarrow p_1 \neq p_2\)

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

Test statistic:

The test statistic is:

\(z = \frac{X - \mu}{s}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis.

This means that \(\mu = 0\)

From the samples:

\(X = p_1 - p_2 = 0.865 - 0.928 = -0.063\)

\(s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0171^2 + 0.0163^2} = 0.0236\)

The value of the test statistic is:

\(z = \frac{X - \mu}{s}\)

\(z = \frac{-0.063 - 0}{0.0236}\)

\(z = -2.67\)

The value of the test statistic is z = -2.67.

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

p-value of the test and decision:

The p-value of the test is the probability that the proportion differs by at at least 0.063, which is P(|z| > 2.67), given by 2 multiplied by the p-value of z = -2.67.

Looking at the z-table, z = -2.67 has a p-value of 0.0038.

2*0.0038 = 0.0076.

The p-value of the test is 0.0076 < 0.05(standard significance level), which means that there is enough evidence to conclude that the proportion of people who wear life vests while riding a jet ski is not the same as the proportion of people who wear life vests while riding in a boat.

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The individual that will be paying the most for their purchase is: B.edgar paid with a credit card and paid the minimum payment each month

The individual that will pay the most according to the data provided is Edgar. Edgar's payment is spread out to the longest length of time. So, he will have to pay the added dues for extending his payment.

Usually, the person who pays cash pays the least amount while the person who pays in installments is charged for additional time spent in making the payment.

Complete Question:

Each of the following people bought a watch that costs $300. Which of the following people will pay the most for their purchase A.Sarah paid cash B.edgar paid with a credit card and paid the minimum payment each month C.susan paid with a credit card and paid the minimum payment plus 30 each month D. Sean paid with a credit card and paid the full balance the first of the month

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To determine the surface area of the glass surfaces, we will determine the area of each rectangle and sum them.

The area of a rectangle is given by the following formula:

Now, the rectangles that compose the total surface area of glass have dimensions:

Therefore, the total area adding up the areas of the rectangles is:

Now, the area covered by the plastic lid is the area of a rectangle of dimensions

Therefore, the surface area of the plastic surface is:

The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The image of the triangle ABC is shown in the image below attached.

According to Euclidean geometry, triangles can be constructed by means of three non-colinear points. Two points are collinear when they can be contained by a line. The image of the triangle is the result of a rigid transformation known as translation:

P'(x, y) = P(x, y) + T(x, y)

Where:

First, write the original points of the triangle:

A(x, y) = (- 8, 8), B(x, y) = (- 8, 3), C(x, y) = (- 4, 4)

Second, determine the image of each point:

A'(x, y) = (- 8, 8) + (10, - 6)

A'(x, y) = (2, 2)

B'(x, y) = (- 8, 3) + (10, - 6)

B'(x, y) = (2, - 3)

C'(x, y) = (- 4, 4) + (10, - 6)

C'(x, y) = (6, - 2)

Third, graph both the original and resulting triangle.

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Answer:

Each pencil cost $0.51

Step-by-step explanation: