what is the angle of x when the other is 51

Answer:

X≈ 2,37 cm

x= (-11+√637)/6 cm

Step-by-step explanation:

Answer:

y-intercept is (0,3) and the slope is 3

Step-by-step explanation:

Answer: the slope is 3x while 3 is the y-intercept.

Step-by-step explanation:

Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:

Square both sides of the equation to eliminate the square root:

√y = (6/p)x - (2/q)

√y^2 = (6/p)x - (2/q)^2

Simplifying the right-hand side, we get:

y = (36/p^2)x - (4/q) + 4/q^2

Rearrange the equation to the form y = mx + c:

y = (36/p^2)x + (4/q^2 - 4/q)

So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).

Step-by-step explanation:

Answer:

three times

Step-by-step explanation:

They would each need to sell 5 bicycles to make the same amount of money and if they both sell 5 bicycles, they would each make $500.

What do you mean by finding the break-even point ?

The key concept used here is the idea of finding the break-even point between two scenarios. In this case, the break-even point is the number of bicycles that Jim and Tom each need to sell in order to make the same amount of money. This is found by setting their total earnings equal to each other and solving for the number of bicycles. Once the break-even point is found, the total earnings for that number of bicycles can be calculated by plugging it back into the original equations. This concept is commonly used in business and finance to determine the minimum level of sales needed to cover costs and make a profit.

Calculating the number of bicycle and money :

To make the same amount of money, Jim and Tom would have to each sell the same number of bicycles, let's call it "b".

So Jim would make a total of:

250 + 50b dollars

Tom would make a total of:

400 + 20b dollars

To find the value of "b" where they both make the same amount of money, we can set the two expressions equal to each other and solve for "b":

250 + 50b = 400 + 20b

30b = 150

b = 5

Therefore, they would each need to sell 5 bicycles to make the same amount of money.

To find out how much they would make, we can substitute "b=5" into either of the expressions above:

Jim:

250 + 50(5) = $500

Tom:

400 + 20(5) = $500

Therefore, if they both sell 5 bicycles, they would each make $500.

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[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:

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.

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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Answer:

2125 ft/min

33,000 ft

y = -2125x + 33,000

Step-by-step explanation:

A. -2125 feet per minute. You get this number when you divide 17,000 by 8 (rise over run). You could also use the formula y2-y/x2-x1 with the points (0, 33,000) and (8, 17,000).

B. 33,000 feet is the height of the plane before it starts descending, so it must be the starting value.

C. Plug in the values you got for A and B into the slope formula y = mx + b

y = -2125x + 33,000

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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(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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​

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.

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

There are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.

There are a total of 6 outcomes for the rolling cube and 3 outcomes for picking a card. To find the total number of outcomes, we can use the multiplication rule of counting:

Total number of outcomes = number of outcomes for picking a card x number of outcomes for rolling a cube

Total number of outcomes = 3 x 6 = 18

Therefore, there are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.

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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:

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  

Answer:

7/12 pizzas have been eaten

Step-by-step explanation:

3 + 4= 7

7/12

7-12=5

5 pizzas left

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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The missing value to find the length of BC is 9x.

The distance formula is a formula for calculating the separation in coordinates between two places. It is provided by and deduced from the Pythagorean theorem by:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

The distance formula is used to compute distances between objects or places in many disciplines, including geometry, physics, and engineering.

The distance formula is given as:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the values of the coordinates of B and C we have:

distance = √((7x - (-2x))² + (-1y - (-4y))²)

distance = √((9x)² + (3y)²)

distance = √(81x² + 9y²)

distance = 3√(9x² + y²)

Hence, the missing value to find the length of BC is 9x.

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The solutions for the systems of inequalities are:

a) (0, -100), (0, -150), (0, -1000)

b)  (0, 50), (0, 55) , (0, 1,204).

When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.

The first one is:

y ≤ x - 8

y < -3x - 9

Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:

-100  ≤ 0 - 8 = -8

-100 < - 3*0 - 9 = -9

Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.

For the second system:

y > 5x + 1

y > 3

Let's do the same thing, x = 0 and y gets really large values, like y = 50

50 > 5*0 + 1 = 1  this is true.

50 > 3   this is true.

so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).

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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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Pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

We can write quadradic equation as [tex]y=1+x^2[/tex]

Where y is number οf dοts and x is step number.

Then if x=0 and y=1

If x = 1 and y = 2

If x = 2 and y = 5

If x = 3 and y = 10

Hence Patten B fοllοws the quadratic realatiοnship.

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Using  the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)

We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:

-4x + y = 3 (Equation 1)

5x - 2y = -9 (Equation 2)

Solving Equation 1 for y, we get:

y = 4x + 3

Now, we substitute this expression for y into Equation 2 and solve for x:

5x - 2(4x + 3) = -9

5x - 8x - 6 = -9

-3x = -3

x = 1

We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:

-4(1) + y = 3

y = 7

Therefore, the solution to the system of equations is (x, y) = (1, 7)

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When a point is rotated, it must be rotated around a point.

See attachment for the image of the rotation about point K

We should note the following:

In order to construct triangles, you will need a protractor, a pair of compasses and a ruler. To draw the triangle, three properties must be taken into account: length, angle and shape

The given parameters are:

ΔEFG

The angle of rotation is

∅ = 180⁰

The above angle of rotation means that:

The translated triangle will be 180 degrees from ΔEFG about point K.

It also means that:

ΔEFG and ΔE'F'G' will be equidistant from point K

See attached image for ΔE'F'G'

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Combining these, we have[tex]$6 \times 6 = \boxed{36}$[/tex] different arrangements of the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex] in a row where the sum of any adjacent numbers is even.

Products intended for exporting after processing into goods or processed products are referred to as "basic products," as are goods planned for export after processing. Samples 1 - 3 Samples 2 - 3.

We may start by noting that at minimum one of the neighboring numbers must be even for the sum of both numbers to be even. This means that a even numbers (2, 4, 6) as well as the odd numbers (1, 3, 5) should be arranged in the appropriate positions.

Let's start by thinking about the even positions. The second, fourth, and sixth places are the only even positions. We can choose any variant of the 3 even numbers to occupy these spots, giving us[tex]$3! = 6$[/tex] ways.

Let's now think about the unusual positions. The first, third, and fifth positions are the only ones that are odd. We have an additional [tex]$3! = 6$[/tex]ways to fill these spots by using any combination of the 3 odd numbers.

Consider the odd locations now. The first, third, and fifth places are the three odd positions. We have an additional[tex]$3! = 6$[/tex]ways by using any permutation of the three odd numbers to fill these positions.

Together, this give us [tex]$6 \times 6[/tex] = [tex]\boxed{36}$[/tex] different ways to arrange the numbers [tex]${}1,$ ${}2,$ ${}3,$ ${}4,$ ${}5,$ $6$[/tex]in a row so that the sum of any two adjacent numbers is even.

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Answer:

4m + 6

Step-by-step explanation:

Since the length is twice as long your equation should look like this

2(2m + 3) = L

which would be 4m + 6 as the length of the rectangle

Answer:

[tex]\frac{11}{8}[/tex]

Step-by-step explanation:

3(2k+3)=6-(3k-5)

6k +9=6-3k+5

6k+3k=6+5

8k=11

k=[tex]\frac{11}{8}[/tex]

Answer: I think it is k=2/9

Step-by-step explanation:

Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.

Perimeter is the total distance around the outside of a closed 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 all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.

Here,

The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:

2 × (length + width) = 2 × (175 m + 96 m) = 542 m

Therefore, the cost of fencing the garden at 17.50 per meter is:

Cost of fencing = length of fence × cost per meter

= 542 m × 17.50

= 9485

Hence, the cost of fencing the garden is ₹9485.

To find the cost of plowing the garden, we need to first calculate its area, which is given by:

Area = length × width

= 175 m × 96 m

= 16800 m²

Therefore, the cost of plowing the garden at 4.50 paise per square meter is:

Cost of plowing = area of garden × cost per square meter

= 16800 m² × 0.045

= 756

Hence, the cost of plowing the garden is ₹756.

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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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