Solve the rational inequality, and write the solution in interval notation.
x+1x−3≤0

Answer: banana- 88

Orange-55

Apple-143

Step-by-step explanation:

220 divided by 5, times 2,

that’s the banana trees

220 divided by 4, that’s the oranges

Add the answers together

Take the answer away from 220 that’s the apples

Answer:

X = 9

Step-by-step explanation:

Vertical angles equal to each other, the example shows vertical angles.

6x + 2 = 54

-2 -2

6x/6 = 54/6

X = 9

Hope this helps you have a nice day!

The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

know more about Distributive Property here:

https://brainly.com/question/2807928

#SPJ8

Using congruent angles theorem, we can find that the angles that are adjacent to ∠LSP are ∠4 and ∠6.

Angles with an equal measure are considered congruent angles. They appear everywhere, including in isosceles and equilateral triangles, as well as when a transversal connects two parallel lines.

The term "adjacent angles" refers to angles that do not overlap but share a common arm (side). When two rays intersect at a shared endpoint, an angle is created. Angles that are always located next to one another are called neighbouring angles. Two neighbouring angles are referred to as a linear pair of angles when their sum is 180 degrees.

Now, according to the question,

The angles that are adjacent to ∠LSP must share a common vertex and a common arm.

Now, the common arm between ∠4 and ∠LSP is line LM.

The common arm between ∠6 and ∠LSP is line NP.

And all have a common vertex.

Hence, the angles that are adjacent to ∠LSP are ∠4 and ∠6.

To know more about congruent angles, visit:

https://brainly.com/question/16448127

#SPJ1

9514 1404 393

Answer:

  $6.55

Step-by-step explanation:

The cost will be multiplied by 1 +3% = 1.03 each year, so after 30 years, the cost will be ...

  $2.70 × 1.03^30 ≈ $6.55

a) The group of points labeled X are the non-outlier scores, while point Y is an outlier score.

b) The association between the variables is positive.

There are two possible classifications for the associations between variables, as follows:

For this problem, the variables are given as follows:

As the number of assignments submitted increases, the test scores also increases, hence there is a positive relationship between these two variables.

The point Y is an outlier, as the student got a considerably worse grade than expected, meaning that combined with his low score on the assignments, the student may have considerable difficulties in the subject.

The graph is given by the image shown at the end of the answer.

More can be learned about association between variables at https://brainly.com/question/16355498

#SPJ1

Answer:21

Step-by-step explanation:

7 ➗ 1/3

when dividing fractions you have to change the divide sign to multiplication

and the denominator at the right hand side will become the numerator,the previous numerator at the right hand side will become denominator

7 x 3/1=21

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: x=11

Explanation: See below!

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer:

Step-by-step explanation:

\(\sqrt{x - 2} + 8 = x\\ \sqrt{x - 2} = x - 8\\x - 2 = (x - 8)^2\\x - 2 = x^2 - 16x + 64\\x^2 - 17x + 66 = 0\\(x^2 - 11x) - (6x - 66) = 0\\x(x - 11) - 6(x - 11) = 0\\(x - 6)(x - 11) = 0\\x - 6 = 6 >> x = 6\\x - 11 = 0 >> x = 11\)

Answer:

$19

Step-by-step explanation:

5% discount = 100% - 5% = 95% = 0.95

0.95(20) = 19

$19

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer: 19 dollars

Step-by-step explanation:

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

For more such questions on line.

https://brainly.com/question/280216

#SPJ8

Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

The equation of the line in slope-point form is:

y - 7 = -4/5(x + 6)

The equation of a line in slope-point form is given by:

y - y₁ = m(x - x₁)

where:

(x₁, y₁) represents the coordinates of a point on the line.

m represents the slope of the line.

m = (y₂ - y₁)/(x₂ - x₁)

(x₁, y₁) represents the coordinates of the 1st point on the line

where (x₂, y₂) represents the coordinates of the 2nd point on the line

We have

(x₁, y₁) = (-6, 7)

(x₂, y₂) = (4, -1)

m = (y₂ - y₁)/(x₂ - x₁)

m = (-1 - 7) / (4 - (-6))

m = -8/10

m = -4/5

Using y - y₁ = m(x - x₁):

y - 7 = -4/5(x - (-6))

y - 7 = -4/5(x + 6)

Learn more about equation of a line on:

brainly.com/question/12626026

#SPJ1

Answer:

xy=6

Step-by-step explanation:

sin θ= opposite side÷ hypotenuse

sin 30°= xy÷12

sin 30°=1/2

Therefore,

1/2=xy÷12

1/2×12=xy

xy=6

Answer:

5(5x-3)

Step-by-step explanation:

The common factor in this expression is 5 so divide 5 to all the values

25/5=5

-15/5= -3

Put these values into parenthesis and leave the 5 on the left side and out of the parenthesis

5(5x-3)

Answer:

5(5x - 3)

Step-by-step explanation:

The greatest common factor here is 5. Divide each term by 5 and simplify.

25x/5 = 5x

15/5 = 3

Therefore, the answer is 5(5x - 3).

Answer:

38.6

Step-by-step explanation:

Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

for such more questions on investigate

https://brainly.com/question/32310280

#SPJ8

The percentage of vehicles whose speeds are between 52 miles per hour and 70 miles per hour is 75%.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will fall within three standard deviations of the mean.

Given, The mean speed of a sample of vehicles along a stretch of highway is 64 miles per​ hour, with a standard deviation of 4 miles per hour.

\(\mu = 64\) and \(\sigma = 4\).

Now, 52 is 3 standard deviations away from the mean so 50% of the data falls into this category and 70 is 1.5 standard deviations away from the mean and 25% of the data falls into this category.

Therefore, 75% of the vehicles would fall into this category.

learn more about the empirical rule here :

https://brainly.com/question/28234946

#SPJ1

The definite integrals associated with the piecewise function have the following values:

Case 1: 1.5

Case 2: - 2 + 0.5π

Case 3: 5.5

In this problem we find the representation of a piecewise function formed by four parts, whose definite integrals must be determined by means of the following formulas:

\(I = \int\limits^b_a {f(x)} \, dx\)

Graphically speaking, the definite integral is equal to the area below the curve.

Case 1

I = 0.5 · 2² - 0.5 · 1²

I = 1.5

Case 2

I = - 2 · 1 + 0.5π · 1²

I = - 2 + 0.5π

Case 3

I = - 0.5 · 0.5 · 1 + 0.5 · 1.5 · 3 + 1 · 3

I = - 0.25 + 2.75 + 3

I = 5.5

To learn more on definite integrals: https://brainly.com/question/14279102

#SPJ1

2 by 7 + – is equals to 1 so we can say that x.

x=1-2/7

x=7/7-2/7

x=5/7

The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

Learn more about coordinates here:

https://brainly.com/question/13118993

#SPJ1

Answer:

\(\frac{8-\sqrt{6} }{2}\)

Step-by-step explanation:

To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator, which in this is 2 - √6.

We can write the expression:

\(\frac{3\sqrt{6}+5 }{2+\sqrt{6}} *\frac{2-\sqrt{6}}{2-\sqrt{6} }\)

We can use the special product of the difference of squares to simplify the denominator:

\((2 + \sqrt{6})(2-\sqrt{6}) = 2^2 - (\sqrt{6})^2 =4 - 6 = -2\)

We can use distributive for the numerator:

\((3\sqrt{6}+5)(2-\sqrt{6})=6\sqrt{6} -18+ 10-5\sqrt{6} =\sqrt{6} -8\)

Now we can rewrite the fraction:

\(\frac{\sqrt{6}-8 }{-2} =\frac{8-\sqrt{6} }{2}\)

Answer:

The probability that more than 4 calls will be received during the noon hour, on some particular Thursday is 0.9113.

Step-by-step explanation:

The random variable X can be defined as the number of incoming phone calls during the noon hour on Thursdays.

The random variable X describes a finite number of occurrences of an event in a fixed time interval.

The random variable X follows a Poisson distribution with parameter λ = 8.2.

The probability mass function of X is:

\(P(X=x)=\frac{e^{-8.2}(8.2)^{x}}{x!};x=0,1,2,3...\)

Compute the probability of more than 4 calls as follows:    

\(P(X>4)=1-P(X\leq 4)\)

                \(=1-\sum\limits^{4}_{x=0}{\frac{e^{-8.2}(8.2)^{x}}{x!}}\\\\=1-[0.00027+0.00225+0.00923+0.02524+0.05174]\\\\=1-0.08873\\\\=0.91127\\\\\approx 0.9113\)

Thus, the probability that more than 4 calls will be received during the noon hour, on some particular Thursday is 0.9113.

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

For more such questions on probability visit:

https://brainly.com/question/251701

#SPJ8

Answer:

3 is your answer im pretty sure:)))

Step-by-step explanation:

The mode will not change.

Given data,

58,60,53,54,60,35,58,60

Outlier is the value in a set of data that much higher or lower than other values in data.

from given data, outlier is 35.

Mode is the value in a set of data that occurs more frequently in set of data.

from given data, 60 occurs more frequently.

Hence, 60 is the mode of data.

If outlier is removed from the data set then it will not affect the mode of the data

Thus, the mode will not change.

To learn more about outlier of data set refer here

https://brainly.com/question/12982142

#SPJ9

Answer:

$35.97

Step-by-step explanation:

Given:

Dimensions of homecoming float = 9 ft \(\times\) 16 ft

Area covered by a quart of paint = 53 sq ft

Cost of a quart of paint = $11.99

To find:

Cost of painting the homecoming float = ?

Solution:

First of all, let us find the area of homecoming float which is to be painted.

Area = Length \(\times\) Width = 9 \(\times\) 16 = 144 sq ft

Quart needed to cover 53 sq ft = 1

Quart needed to cover 1 sq ft = \(\frac{1}{53}\)

Quart needed to cover 144 sq ft = \(\frac{1}{53}\times 144 = 2.716 \approx 3\)

So, 3 quarts will be needed.

Cost of 1 quart = $11.99

Cost of 3 quarts = $11.99 \(\times\) 3 = $35.97

Answer: 4000

Step-by-step explanation:

Two sets are disjoint if they have no element in common

Looking at the given options, for the last one,

Edmonton is located in canada. Since it is not in the united states, there is nothing common between the people living there and the united states. Thus, the disjoint set is

People who live in Edmonton. People who live in the united states