in triangle abc, the length of side ab is 16 inches and the length of side bc is 24 inches. which of the following could be the length of side ac?

Answer:

Step-by-step explanation:

m∠O = 90° - 34° = 56°

cos M = [tex]\frac{MN}{MO}[/tex]  ⇒  MO = [tex]\frac{12}{cos34}[/tex] ≈ 14.5 cm

tan M = [tex]\frac{ON}{MN}[/tex]  ⇒  ON = 12 × tan 34° ≈ 8.1 cm  

Therefore, the length of the diagonal of the rectangle is approximately 193.57 cm or 49.43 cm, depending on which value of x is used.

Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of its four sides.

Here,

(i) Let the length of the rectangle be y cm.

Then, the perimeter of the rectangle is given by:

2(x + y) = 112

x + y = 56

y = 56 - x

(ii) The area of the rectangle is given by:

Area = length x breadth

597 = yx

Substituting y = 56 - x, we get:

597 = x(56 - x)

597 = 56x - x²

x² - 56x + 597 = 0

(iii) Using the quadratic formula,

x = (-(-56) ± √((-56)² - 4(1)(597))) / (2(1))

x = (56 ± √(3136 - 2388)) / 2

x = (56 ± √(748)) / 2

x = (56 ± 2√(187)) / 2

x = 28 ± √(187)

Therefore, the two solutions are x = 28 + √(187) and x = 28 - √(187).

(iv) The length of the rectangle is y = 56 - x.

Using Pythagoras theorem, the length of the diagonal of the rectangle is given by:

d² = y² + x²

d² = (56 - x)² + x²

d² = 3136 - 112x + 2x²

d = √(3136 - 112x + 2x²)

Substituting the value of x from part (iii) into the above equation, we get:

d = √(3136 - 112(28 ± √(187)) + 2(28 ± √(187))²)

d = √(3136 - 3136 ± 112√(187) + 56 ± 56√(187) + 2(187))

d = √(37400 ± 168√(187))

d ≈ 193.57 cm (rounded to 2 decimal places) or d ≈ 49.43 cm (rounded to 2 decimal places)

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By answering the presented question, we may conclude that In general, expressions it is often most convenient to choose numbers that are powers of ten. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Tavon may have chosen to multiply both sides of the equation by 10 because he wanted to remove the decimal point and work with integers. Then he can use his knowledge of integer multiplication and division to solve the equations more easily.

Tavon may have used a different number and removed the decimal point. For example, you could multiply both sides by 100 or 1000 instead of 10. However, you should carefully choose a number that is manageable and does not overcomplicate the problem. Multiplying by larger numbers complicates the calculations, and multiplying by smaller ones does not eliminate the decimal point entirely. In general, it is often most convenient to choose numbers that are powers of ten. 

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a. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{17}}$.

b. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{51}}$.

c. You would need to know that the population distribution of X, teacher salaries, is normal in order to answer the questions regarding any sample size.

d. Assuming a sample size of 51, the probability that the sampling error is within $1000 is approximately 0.84 or 84%.

e. Assuming a sample size of 51, the 90th percentile for the average teacher's salary is approximately $54488.

f. Assuming that teacher's salaries are normally distributed, the 90th percentile for an individual teacher's salary is approximately $56396.

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You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.

The given expression is equivalent to

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

[tex]a(b+c)=a\times b+a\times c[/tex]

(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2\times x=2x[/tex])

The given expression is [tex]6g-18h[/tex]

We know that we can write

[tex]6=2\times3[/tex]

[tex]18=2\times9=3\times6[/tex]

Thus,

[tex]6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)[/tex]

[tex]6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)[/tex]

[tex]6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)[/tex]

All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.

Thus,

The given expression is equivalent to

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Answer:C & D

Step-by-step explanation:

(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.

To perform a t-test for the population mean difference, follow these steps:

(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.

Mean difference = (Sum of differences) / Number of pairs

Using the given data gives:

Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5

Subtracting gives:

Mean difference = (3 - 1 - 1 + 3 + 7) / 5

Solving gives:

Mean difference = 11 / 5

Dividing gives:

Mean difference = 2.2

(b) Calculate the standard deviation of the differences:

To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.

Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]

Solving gives:

Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)

Solving gives:

The sum of squared differences = 48.36

The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]

Solving gives:

The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]

Rounded to three decimal places

The standard deviation of the differences ≈ 3.47

c) Calculate the test statistic:

The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))

Let's assume the null hypothesis is that there is no difference between the two fertilizers

(i.e., mean difference = 0).

[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]

Substituting [tex]\sqrt 5 = 2.236[/tex]

t = 2.2 / (3.47 / 2.236)

Rounded to two decimal places

t ≈ 1.378

So, the test statistic is approximately 1.378.

The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma

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​

Answer:

y = 3x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (- 1, - 6 )

m = [tex]\frac{-6-6}{-1-3}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 6 )

6 = 3(3) + c = 9 + c ( subtract 9 from both sides )

- 3 = c

y = 3x - 3 ← equation of line

The option B is the correct option.

Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. The correct option is B.What is natural induction?The concept of natural induction is based on the notion of logical implication, in which the validity of the subsequent statement is demonstrated using the initial statement. Suppose, for example, you want to show that P(2) is valid. A hypothesis is a statement that is proven using induction; it is the statement that P(n) is valid for a natural number n.Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. Therefore, option B is the correct option.

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In the given elementary matrix, the corresponding elementary row operation is multiplication of the second row of a given matrix with a scalar of 5. The given matrix is an elementary matrix because it can be obtained by multiplying an identity matrix by an elementary matrix. The inverse of the given matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix.

The given elementary matrix is:
[1 0 0]
[0 0 5]
[0 1 0]

The corresponding elementary row operation for this matrix is multiplication of the second row of a given matrix with a scalar of 5. This means that if we have a matrix A and we multiply the second row of A with a scalar of 5, we get a new matrix B which is represented by the above elementary matrix.

The inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]

The inverse of a given elementary matrix can be obtained by applying the inverse of the corresponding elementary row operation to an identity matrix. In this case, the inverse of the given elementary matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix. This gives us the above inverse matrix.

Therefore, the corresponding elementary row operation for the given matrix is multiplication of the second row of a given matrix with a scalar of 5 and the inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]

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Answer:

D. 24 ft

Step-by-step explanation:

Congruent means equal. Since ABCD and PQRS are congruent they are the same.

Answer:

D

Step-by-step explanation:

The result of each trigonometric functions are:

a) sin X = 7√149 / 149

b) sin Z = 10√149 / 149

c) cos X = 10√149 / 149

d) cos Z = 7√149 / 149

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows

sin X = YZ / XZ = 7 / √149

cos X = XY / XZ = 10 / √149

sin Z = XY / XZ = 10 / √149

cos Z = YZ / XZ = 7 / √149

To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:

sin X = 7√149 / 149

cos X = 10√149 / 149

sin Z = 10√149 / 149

cos Z = 7√149 / 149

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The given question is incomplete, the complete question is:

Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.

When a double cone is sliced at the apex by a plane perpendicular to the base of the cone, the resulting conic section is a parabola.

Option B is the correct answer.

We have,

A parabola is a type of conic sect ion that can be defined as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).

In the case of slicing a double cone at the apex, the resulting conic section will have the characteristic shape of a parabola.

The slicing plane intersects both sides of the double cone, creating a curved shape that opens upward or downward, depending on the orientation of the cone.

The vertex of the parabola corresponds to the point of intersection of the slicing plane with the double cone.

Therefore,

When a double cone is sliced at the apex by a plane perpendicular to the base, a parabola is formed.

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The complete question:

Which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?

A. Circle

B. Parabola

C. Ellipse

D. Hyperbola

To find the point on the given plane that is closest to the given point (5,6,2), we can use Lagrange multipliers.

Let f be the function that represents the plane x-y+z=3 and let g be the function that represents the point (5,6,2). Then, the point on the plane closest to (5,6,2) is the point that minimizes g=x2+y2+z2. We can use the method of Lagrange multipliers to solve this problem.

Let lambda be the Lagrange multiplier. Then, we need to solve the system of equations given by:
x2+y2+z2-2x-2y-2z=0x-y+z-3=0

By solving this system of equations, we obtain the point 13/14x=7/7y=11/7z=5/7, which is the closest point on the plane to the given point (5,6,2).

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In mathematics, a logarithm is a mathematical operation that determines how many times a given number (known as the base) must be multiplied by itself to produce another given number.

Logarithms are used to simplify complex calculations involving exponents and to convert between exponential and logarithmic expressions.

The logarithm of a number x to a given base b is represented as logb(x). For example, log10(100) = 2 because 10 multiplied by itself twice equals 100.

Logarithms have a wide range of applications in various fields, including mathematics, physics, engineering, finance, and computer science. They are particularly useful in scientific calculations involving large numbers, where working with exponents can become cumbersome. Logarithms are also used in the study of exponential growth and decay, as well as in the analysis of data sets with a wide range of values.

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Answer:

20.864

Step-by-step explanation:

8.15 x 4 is 32.6. I used a calculator but what I would do if I were solving on paper would be to double it, and then double it again.

Then, we divide 32.6 by five to get 6.52. I did this with a calculator, but if I were solving on paper, I would divide by 10 (move decimal point), and then double it.

Finally, we muliply 6.52 by 3.2. I did this with a calculator and got 20.864, but if I was doing this on paper, I would just solve using standard form!

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Answer:

To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.

For last week's test, the ratio of correctly spelled words to total words is:

16/20 = 0.8

For this week's test, the ratio of correctly spelled words to total words is:

13/15 ≈ 0.867

Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.

Answer:

7/12 pizzas have been eaten

Step-by-step explanation:

3 + 4= 7

7/12

7-12=5

5 pizzas left

Answer:

Use the quadratic formula to solve. Show work describe solution.

Step-by-step explanation:

The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.

The quadratic formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.

For example, let's say we have the equation 2x^2 + 5x - 3 = 0.

Here, a = 2, b = 5, and c = -3.

Plugging these values into the quadratic formula, we get:

x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)

Simplifying the expression inside the square root:

x = (-5 ± sqrt(49)) / 4

x = (-5 ± 7) / 4

We get two solutions:

x = (-5 + 7) / 4 = 1/2

x = (-5 - 7) / 4 = -3

So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.

These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.

From the survey of 50 people 20 people like chocolate.

A survey was conducted with 50 people, out of which 30 liked chocolate, 20 liked vanilla, and 10 liked both. The question is asking how many people like chocolate.

To determine the number of people who like chocolate only, we subtract the number of people who like both flavors from the total number of people who like chocolate.

The number of people who like chocolate alone = total number of people who like chocolate - the number of people who like both

= 30 - 10= 20

This means that out of the 50 people surveyed, 20 individuals like chocolate, while 10 people enjoy both chocolate and vanilla.

Therefore, 20 people like chocolate.

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Answer:

To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:

r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5

Now we can substitute the center and radius into the standard form equation:

(x - 4)^2 + (y + 2)^2 = 5^2

Simplifying and expanding the right-hand side, we get:

Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.

Probability that X = 5:Since, Joe selects only 4 bags of lettuce. X can't be 5.P(X=5) = 0Hence, the probability that X = 0 is 0.3164 and the probability that X = 5 is 0.

The given problem can be solved using the concept of binomial distribution.

In the given question, there are 48 bags of lettuce out of which 12 bags are contaminated with listeria.

Joe selects 4 bags of lettuce. X is the random variable which represents the number of contaminated bags of lettuce selected by Joe. X can take values from 0 to 4. (as Joe selects only 4 bags).

Part A)Number of ways to select 4 bags of lettuce out of 48:This can be solved using the concept of combinations. The formula to calculate the number of combinations is[tex]:nCr = n! / r!(n-r)![/tex]Here, n = 48 and r = 4.

Number of ways = 48C4 = 194,580

Part B)Probability that X = 0:This can be calculated using the formula for the binomial distribution :

[tex]P(X = r) = nCr * p^r * q^(n-r)[/tex]

Here, p = probability of selecting contaminated bag = 12/48 = 0.25q = probability of selecting non-contaminated bag = 1-0.25 = 0.75Also, n = 4 and r = [tex]0P(X=0) = 4C0 * 0.25^0 * 0.75^4= 0.3164[/tex]

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Answer:

The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:

(10a-6) + (7a+4) + (7a+4) + (10a-6)

Simplifying the expression:

= 34a - 4

Therefore, the perimeter of the quadrilateral is 34a - 4.

[tex]x=\textit{Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~x\implies \cfrac{20}{100}(x)\implies 0.2 (x) \\\\\\ y=\textit{Liters of solution at 50\%}\\\\ ~~~~~~ 50\%~of~y\implies \cfrac{50}{100}(y)\implies 0.5 (y) \\\\\\ \textit{600 Liters of solution at 21\%}\\\\ ~~~~~~ 21\%~of~600\implies \cfrac{21}{100}(600)\implies 126 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{acid only}}&\stackrel{\textit{Liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.2&0.2x\\ \textit{2nd Sol'n}&y&0.5&0.5y\\ \cline{2-4}&\\ mixture&600&0.21&126 \end{array}~\hfill \begin{cases} x + y = 600\\\\ 0.2x+0.5y=126 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=600}\implies x=600-y \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.2(600-y)+0.5y=126}\implies 120-0.2y+0.5y=126 \\\\\\ 120+0.3y=126\implies 0.3y=6\implies y=\cfrac{6}{0.3}\implies \boxed{y=20} \\\\\\ \stackrel{\textit{since we know that}}{x=600-y}\implies \boxed{x=580}[/tex]

Answer:

(3480 - 600)/2 = 1440cm

Step-by-step explanation:

Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.

In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Here,

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the given coordinates, we have:

x1 = 0, y1 = 5

x2 = 2, y2 = 0

slope = (0 - 5) / (2 - 0)

slope = -5/2

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Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.

There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.

To calculate this, the total number of possibilities can be found by using the formula nPr,

where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]

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When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.

The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.

Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.

The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.

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Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect and the statistics is misleading.

Inferential statistics and descriptive statistics are two disciplines of statistics with distinct applications.

Summarizing and characterizing gathered data is the focus of descriptive statistics. It uses techniques including graphical presentations, measurements of variability, and measures of central tendency, such as mean, median, and mode (e.g., histograms, box plots). The purpose of descriptive statistics is to shed light on a sample's or population's properties, such as its distribution, dispersion, and shape.

Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect.

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Answer:

three times

Step-by-step explanation: