Find x if angle 1 = 2x+10 and angle 2 = 3x-6

In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy  the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).

Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.

From the question, p = number of pounds Juan will buy.

candy=costs $8 per pound

$20/$4 = 5 pounds

p>5

at least 5 pounds

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The measure of angle R,if R is a point of tangency is 37°.

We have been given a diagram of a circle. We are asked to find the measure of angle R.

Since QR is the tangent of our given circle, so measure of angle Q will be 90 degrees as radius is perpendicular to tangent at point of tangency.

We will use angle sum property to solve for angle R as:

53 + 90 + R = 180

R = 180 - 143

R = 37°

Therefore, based on the information, it should be noted that the measure of angle R,if R is a point of tangency is 37°.

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Answer:

9x-2

Step-by-step explanation:

f^-1(x)=1/f(x)=9x-2

Answer:

419.099 is less than 419.045

Step-by-step explanation:

Answer:

419.099 is greater

Step-by-step explanation:

Answer:

f(g(9)) = 945/16

Step-by-step explanation:

To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).

g(x) = x + 3/4

f(x) = x² - 4x - 3

f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3

f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3

f(g(x)) = x² - 5/2x + 9/16 + 3 - 3

f(g(x)) = x² - 5/2x + 9/16

Now, put a 9 wherever there is an x in f(g(x)).

f(g(9)) = (9)² - 5/2(9) + 9/16

f(g(9)) = 81 - 5/2(9) + 9/16

f(g(9)) = 81 - 45/2 + 9/16

f(g(9)) = 117/2 + 9/16

f(g(9)) = 945/16

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Option A is correct. The value of function (f/g)(x) is found to be  \(\sqrt[3]{3x}\)/(3x+2) where the condition is that  x ≠  -2/3.

In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

The new function obtained by performing f first and then g is the combination of two functions g and f.

Given:

f(x) = \(\sqrt[3]{3x}\)

g(x) = 3x + 2

(f/g)(x) =  \(\sqrt[3]{3x}\)/(3x+2)

Also, the denominator should not be equal to 0.

So, 3x + 2 ≠ 0

     x ≠  -2/3

Therefore, the value of function  is found to be  \(\sqrt[3]{3x}\)/(3x+2) where the condition is that  x ≠  -2/3. So, Option A is correct

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Answer:

D.

Step-by-step explanation:

the suggested relation can be described as y=15x. Then the correct answer is D) Yes, the points are on the line that passes through the origin.

The number of turns the wheel makes is 1.93 ≈ 2.

What is Turns?

This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.

formular for calculating Turns:

Turns =         Lenght

              Circumference

Circumference of a circle, C= πD

Where,

Diameter=D

            π =22/7

Calculating Circumference;

C= 22  * 66

            7

    =207.4

From the question:

D= 66cm

L  =400m

Calculating Turns:

Turns =  Lenght

              Circumference

          =   400m

               207.4

      Turns =1.93

Turns =1.93≈ 2

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Answer:

Alternative hypothesis is that Worker productivity is higher with automatic dispensers.

The Rank for  Group1  is 115.5 and Group 2 is 55.5.

Conclusion is that Worker productivity is higher with automatic dispensers.

Step-by-step explanation:

The null and alternative hypotheses are

H0: Group1 ≤ Group2   against the claim

Ha: Group1 > Group2

Alternative hypothesis is that Worker productivity is higher with automatic dispensers.

Calculations:

                                        Group1               Group2

Sample Mean   x `       139.22               114.67

Sample size n                   9                         9

Sample SD                     18.21                  11.937

Rank                               115.5                       55.5

U                                      10.5                          70.5

The Rank for  Group1  is 115.5 and Group 2 is 55.5.

1. H0 hypothesis

As p-value < alpha  and Z lies in the critical region, H0 is rejected.

The randomly selected value of Group1's population is considered have greater productivity  than the randomly selected value of Group2's population.

2. P-value

The p-value equals 0.0046.

3. Test statistics

Z= u-μ+c/σ

The critical region for one tailed test for z at 0.01 significance level is

z > 2.33.

The test statistic Z equals 2.6063, which lies in the critical region of acceptance z> 2.326

4. Conclusion

As the calculated test statistic lies in the critical region H0 is rejected and it is concluded that

Worker productivity is higher with automatic dispensers.

Answer:

Therefore, any data value less than -27.5 or greater than 117.5 is an outlier. In Bayo's data, there are two values that are considered outliers: 5 and 80.

Step-by-step explanation:

To determine if there are any outliers in Bayo's data, we need to first find the median and interquartile range (IQR) of the dataset.

The median of the data is the middle value when the data is arranged in order:

{5, 10, 10, 50, 55, 60, 65, 70, 70, 75, 75, 80}

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1) of the dataset. Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.

Q1 = median({5, 10, 10, 50, 55, 60}) = 32.5

Q3 = median({65, 70, 70, 75, 75, 80}) = 72.5

IQR = Q3 - Q1 = 40

To identify outliers, we can use the rule that any data value outside the range of Q1 - 1.5 × IQR to Q3 + 1.5 × IQR is considered an outlier.

Q1 - 1.5 × IQR = 32.5 - 1.5 × 40 = -27.5

Q3 + 1.5 × IQR = 72.5 + 1.5 × 40 = 117.5

Therefore, any data value less than -27.5 or greater than 117.5 is an outlier. In Bayo's data, there are two values that are considered outliers: 5 and 80.

Yes, there are outliers in Bayo's data.

We have,

To identify outliers, we need to first find the median of the data set.

The median is the middle value when the data is arranged in order.

Arranging the data set in order gives:

{5, 10, 10, 50, 55, 60, 65, 70, 70, 75, 75, 80}

The median is the middle value, which is 65.

Next, we need to find the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1).

To find Q1, we need to find the median of the data values below the median.

{5, 10, 10, 50, 55, 60}

The median of this set is 30.

To find Q3, we need to find the median of the data values above the median.

{70, 70, 75, 75, 80}

The median of this set is 75.

So,

Q1 = 30 and Q3 = 75, and IQR = Q3 - Q1 = 75 - 30 = 45.

Any data values that are more than 1.5 times the IQR away from the median are considered outliers.

1.5 × 45 = 67.5

So,

Any data values less than 65 - 67.5 or greater than 65 + 67.5 are outliers.

The values less than 65 - 67.5 = -2.5 are not possible in this context, so we only need to consider values greater than 65 + 67.5 = 132.5.

The only value greater than 132.5 in the data set is 80, so 80 is an outlier.

Therefore,

The outlier in Bayo's data is 80.

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Answer:

djsushf sjsushsjd sjdusbs

Step-by-step explanation:

iahsjsidjdjdudjdbdjdid

Answer:

10 hours

Step-by-step explanation:

380 - 80 = 300

30 : 1 = 300 : x

x = 300 / 30

x = 10

Answer:

i have a fixed mindset

Step-by-step explanation:

if i want something i will work on it no matter how hard or long it will take me i will persevere and be positive

Answer:

c = 18

Step-by-step explanation:

Given

\(\frac{c}{3}\) = \(\frac{30}{5}\) = 6

Multiply both sides by 3

c = 3 × 6 = 18

The y-coordinate of -3f(x-1) when x = 0 is -63

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

The table of values

So, we have

-3f(x - 1)

When x = 0, we have

y = -3f(0 - 1)

This gives

y = -3f(-1)

From the table, we have

y = -3 * 21

Evaluate

y = -63

Hence, the y-coordinate is -63

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The total amount that Fanfare realized from the sale of games and fruit salad is $1,270.

The total revenue realized from the sale of games and fruit salad is a function of the units sold and the unit prices.

For instance, multiplying the unit price of games by the number of games sold gives $568 ($1 x 568).  The same applies to the fruit salad sales.

Then the totals for the two categories are added to get the total revenue realized from the Fanfare.

The unit price of games = $1

The unit price of fruit salad = $9

The number of games sold = 568

The number of fruit salad sold = 78

                          Games      Fruit Sald    Total

Quantity sold       568               78

Unit price              $1                $9

Total revenue    $568           $702       $1,270

Thus, the total amount that Fanfare realized from the sale of games ($568) and fruit salad ($702) is $1,270.

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Time series forecasts are developed based on time series analysis, which comprises methods for analyzing time series data to extract meaningful statistics and other characteristics of the data.

One of the most often used data science techniques in business, finance, supply chain management, production, and inventory planning is time series forecasting.

A time component is often present in prediction difficulties, necessitating the extrapolation of time series data or time series forecasting. Another crucial field of machine learning (ML) is time series forecasting, which may be viewed as a supervised learning issue.

It can be subjected to ML techniques including regression, neural networks, support vector machines, random forests, and XGBoost. Using models created from historical data to anticipate future observations is known as forecasting.

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In order to calculate the expected value of one policy, we can use the formula below:

When the holder of the policy dies before 70 years old (probability of 3%), the company will earn $765 but will lose $27400. If the holder dies after 70 years old, the company will earn $765.

So the expected value is:

Since the expected value is negative, that means the company should expect to have a loss of $57 for each insurance policy sold.

Therefore the correct option is the second one, and the expected loss is $57 per policy.

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

Ok so since this is an area question we should begin with writing the correct formula for it. This says it's rectangular pool so we'll be using our rectangle formula, which is...

\(A=lw\)

Now we plug in what we know...

\(length=30\frac{1}{3} \\width=12\frac{1}{2}\)

Now we solve...

\(A=lw\\A=(30\frac{1}{3})(12\frac{1}{2})\\A=379\frac{1}{6}\)

So the area is.... \(379\frac{1}{6}\) feet ²

or if you want an improper fraction....\(\frac{2275}{6}\) feet²

or a decimal... \(379.1666667=379.17\) feet².

9514 1404 393

Answer:

  12 ft

Step-by-step explanation:

Let the width of the room be represented by w. Then the length is (2w-2), and the area is ...

  A = LW

  264 = (2w-2)w

  132 = w² -w . . . . . . . divide by 2, eliminate parentheses

  132.25 = w² -w +.25 . . . . . add (-1/2)² to complete the square

  √132.25 = w -0.5 . . . . . take the square root

  0.5 +11.5 = w = 12 . . . . . add 0.5; use the positive root

The width of the living room is 12 feet.

Answer:

Based on the 68-95-99.7 Rule, approximately 68% of the individuals in the population have an IQ between 85 and 115. Values in this particular interval are the most frequent. Approximately 95% of the population has IQ scores between 70 and 130. Approximately 99.7% of the population has IQ scores between 55 and 145.

The domain of the rational function h(x) = (x - 3)/(x² - 4) is equal to (-∞, -2)  ∪ (-2, 2) ∪ (2, ∞).

The possible points that would lie on h(x) = x² - x + 1 are (3, 7).

True: (1, -1) is a point of the graph of f(x) = -2(x + 1)² + 7.

In Mathematics, a domain is the set of all real numbers for which a particular function is defined.

From the graph of h(x) = (x - 3)/(x² - 4), the domain in interval notation and set builder notation is as follows;

Domain = (-∞, -2)  ∪ (-2, 2) ∪ (2, ∞)

Domain = {x|x ≠ 2, -2}.

Next, we would determine possible x-value for the given quadratic function as follows;

h(x) = x² - x + 1

7 = x² - x + 1

7 - 1 = x² - x

6 = x² - x

x² - x - 6 = 0.

x² - 3x + 2x - 6 = 0.

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x = 3 or x = -2.

For second quadratic function f(x) = -2(x + 1)² + 7, we have:

f(x) = -2(x + 1)² + 7

-1 = -2(1 + 1)² + 7

-1 = -2(2)² + 7

-1 = -8 + 7

-1 = -1 (True).

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Answer:

a= 2 and b= 8

Step-by-step explanation:

a=5/9×18=10

b=4/9×18=8, then a-b=10-8=2

b=4/9×18=8