Find the unit rate.
48words
2minutes
What is the answer?

The the length of LJ is approximately 3.5.OptionD) is correct.

To find the length of LJ, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides of the triangle.

Let's denote the length of JL as x. Then, we can set up the following proportion:

sin(23°) / LJ = sin(89°) / KL

where KL is given as 9.

We can simplify this proportion by using the fact that sin(89°) = cos(1°) (since the sine of the complement of an angle is equal to the cosine of the angle), and by using a calculator to find the values of sin(23°) and cos(1°):

0.3919 / LJ = 0.0175 / 9

Multiplying both sides by x and then dividing both sides by 0.0175, we get:

LJ = 0.3919*9/ 0.0175

x ≈ 3.5

Therefore, the length of LJ is approximately 3.5.OptionD) is correct.

To know more about triangle visit:

brainly.com/question/2773823

#SPJ1

The given vector is:

It is required to find the direction of the given vector.

Recall that the direction θ of a vector is the angle it forms with the horizontal, or, in the coordinate plane, with the positive x-axis.

For a vector given in component form j = , the direction is calculated using the tangent ratio:

Substitute y=8 and x=4 into the formula:

The direction of the vector is about 63.43º counterclockwise from the east.

Answer:

It is.

Step-by-step explanation:

1.5cm is in the plan.

1.92m is in real life.

We need to convert m to cm so 1.92m=192cm

The ratio is 1:128.

1.5cm in plan as is 192 cm in real life.We write that as the ratio of: 1.5 : 192.

We need to prove that it is the actual scale so we equal this ratio(1.5:192) and the other ratio(1:128):

1.5 : 192 = 1 : 128

Then we multiply the numbers that are in and out of the equation like this:

1.5 * 128 = 192 * 1

192 = 192 It is proven beacuse the numbers are equal. The scale of the house is 1:128

Answer:

a

The 95% confidence interval is   \(0.5753<  p <0.62474\)  

b

 This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

c

 The margin of error is   \(E =    0.02474 \)  

d

 The confidence interval becomes wider

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 1506

    The sample proportion is  \(\^ p = 0.60\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

     \(E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)

=>   \(E =    1.96 * \sqrt{\frac{0.60 (1- 0.60)}{1506} } \)    

=>   \(E =    0.02474 \)  

Generally 95% confidence interval is mathematically represented as  

      \(\^ p -E <  p <  \^ p +E\)

=>   \(0.60 - 0.02474 <  p <0.60 + 0.02474\)  

=>   \(0.5753<  p <0.62474\)  

This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

Generally the level of confidence varies directly with the critical value of \(\frac{\alpha }{2}\) and this in turn varies directly with the margin of error which when sample proportion is constant it determines the width of the confidence interval so when the level of confidence increases the confidence interval becomes wider  

Answer:

(2/7*-6)-1/7*-5)

=-12/7--5/7

=7/7

=1

Step-by-step explanation:

i think the answer is positive

Michael will draw solid lines to indicate visible boundaries in an orthographic projection. The solid lines are usually thick and dark, with a thickness of 0.5-0.6 mm, to make them easily visible and distinguishable from other lines in the drawing.

The line used to represent visible lines are called the solid lines. These lines are connected together from start to finish and have varying thickness depending on the boundary represented.

While orthographic projection is a technique used in engineering, architecture, and design to represent a three-dimensional object in two dimensions.

Learn more about line thickness at

https://brainly.com/question/31262058

#SPJ1

In a case whereby Another company is advertising 59$ for their service plan ,The customer bill using Percentages can be expressed as   $67.85.

In math, a percentage is a number or ratio expressed as a fraction of 100. It is denoted by the symbol %. Percentages are commonly used in many areas of math and science, such as statistics, finance, and physics. They are a useful way to express proportions, ratios, and rates in a standardized and easily understandable format.

The equation can be set up as ;

59 * (1+ 15%)

59 * (1.15)

=67.85

Therefore, the customer bill is $67.85

Learn more about Percentages at:

https://brainly.com/question/24877689

#SPJ1

Answer:

1x10^-6

Step-by-step explanation:

\(1*10^{-6}\)

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

For more such questions on GCF

https://brainly.com/question/902408

#SPJ8

Step-by-step explanation:

The expression you provided involves taking the square root of a negative number, which results in an imaginary number. In standard real number arithmetic, the square root of a negative number is undefined. However, in the realm of complex numbers, we can define a square root of negative numbers using the imaginary unit "i," where i is defined as the square root of -1.

Let's break down the expression step by step:

√(-25) / √9

The square root of -25 can be written as √(-1 * 25), which can further be simplified as √(-1) * √25.

√(-1) is equal to "i," and the square root of 25 is 5.

So, the expression becomes:

i * 5 / √9

The square root of 9 is 3.

Now, we can simplify further:

i * 5 / 3

Thus, the simplified expression is (5i) / 3, where "i" represents the imaginary unit.

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

<95141404393>

Answer:

The the best college to go to is the one where you feel comfortable.

Step-by-step explanation:

It is so important to understand the sence of what is actually "the best" college to go to.

You can look at that from a viriety of perspectives, and it is debatable to just go for the college which holds the highest rank on some site.

There are a lot of factors to consider, and what is generally considered the best college does not necassarilly the right one for you.

Ask your loved ones for advice and if you can take a look at yourvtop thee collages.

The the best college to go to is the one where you feel comfortable.

Answer:

3.1072325059538586

Step-by-step explanation:

If you do 3.1072325059538586 x 3.1072325059538586 x 3.1072325059538586, you get 30.

Answer: The session was 1 hour long.

75% of an hour is 45 minutes.

Answer:

Step-by-step explanation:

Under her cell phone plan, Mei Mei pays a flat cost of $46 per month and $5 per gigabyte. She wants to keep her bill under $70 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Mei Mei can use while staying within her budget.

The

inequality

for the required

condition

will be 46+5x<70 as she want to keep the

bill

under $70 according to question. Also she can buy 5 gg that is number of

gigabytes

in a month.

What is inequality?

An

inequality

in mathematics is a relationship that makes a non-equal

comparison

between two numbers or other

mathematical

expressions. It is most commonly used to compare the

sizes

of two numbers on a

number

line.

How to solve the inequality?

To solve an inequality, follow these steps: Remove fractions by

multiplying

all terms by the fractions' least common

denominator

.

Simplify

the

inequality

by combining like terms on each side.

Subtract

or add

amounts

to get the unknown on one side and the numbers on the other.

according to the question,

$46 is the fix cost that she has to pay.

$5 is the cost of gg she buys that is variable.

let us assume that x gigabytes she can buy in a month.

$70 is the maximum bill amount she want.

so the inequality would be,

46+5x<70

5x<70-46

5x<26

x<26/5

x<5.2

so, she can

buy

5 gg at

maximum

in a month with the inequality 46+5x<70 for the given conditions.

to know more about inequality,

https://brainly.com/question/28865837

#SPJ13

Answers:

x = 6

Each angle is 45 degrees

The diagram is shown below

=========================================================

Explanation:

Vertical angles are always congruent

Set the two expressions equal to each other and solve for x.

5x+15 = 3x+27

5x-3x = 27-15

2x = 12

x = 12/2

x = 6

As a way to check the answer, replace x with 6 in each expression. We should get the same thing on both sides

5x+15 = 3x+27

5*6+15 = 3*6+27

30+15 = 18+27

45 = 45

Each angle is 45 degrees, so the answer is confirmed.

---------

The diagram is shown below. There are infinitely many ways to draw out the diagram. In the version I drew, the angles aren't vertically aligned but instead they are opposite one another in this X configuration. So the vertical angles could be vertically aligned, but they don't have to be.

In short: draw an X shape and mark any two opposite angles to form the vertical angles.

Answer:

the required differential equation is dA/dt - \(\frac{2A}{t+500}\) = 6  

A(0) = 50lb

Step-by-step explanation:

Given the data in the question;

A(t) is the mass of the salt in in the tank at time t

the new volume of the solution in the tank increases by one gallon each minute

so

dA/dt = ( Rate in) - ( Rate out)

dA/dt = ( 3 gal/min × 2 lb/gal ) - ( 2 gal/min × \(\frac{A}{t+500}\) lb/gal )

dA/dt = 6 - \(\frac{2A}{t+500}\)

dA/dt - \(\frac{2A}{t+500}\) = 6  

A(0) = 50lb

Therefore,  the required differential equation is dA/dt - \(\frac{2A}{t+500}\) = 6  

A(0) = 50lb

Answer:

B displays correct solutions for x² +9x +12 = 6

step-by-step explanation:

\(\rightarrow \sf x^2 + 9x + 12 = 6\)

\(\rightarrow \sf x^2 + 9x +12 -6 = 0\)

\(\rightarrow \sf x^2 + 9x + 6 =0\)

use the formula:   \(\sf \bold{x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a } \ \ when \ \ \ ax^2 + bx + c = 0}\)

\(\rightarrow \sf x = \dfrac{ -9 \pm \sqrt{(-9)^2 - 4(1)(6)}}{2(1)}\)

\(\rightarrow \sf x = \dfrac{ -9 \pm \sqrt{57}}{2}\)

\(\rightarrow \sf x = \dfrac{ -9}{2} +\dfrac{\sqrt{57}}{2}\)   ;  \(\sf x = \dfrac{ -9}{2} -\dfrac{\sqrt{57}}{2}\)

Answer:

a) response variable

Step-by-step explanation:

The response variable is the variable that depends on other variables such as the independent or explanatory variable, it is the variable that is being tested. The response variable is also called the dependent variable.

In linear regression, the y variable is referred to as the response variable while the x variable is referred to as the explanatory or independent variable.

In this case the y variable is "the number of times they cough in a day" and this variation depends on the x variable "number of cigarettes a person smokes in a day".

Answer:

3(x+7)=57

Step-by-step explanation:

3 is being multiplied by "the sum of a number(or x) and 7". So, we write it as 3(x+7). That is equal to 57, so that makes the expression 3(x+7)=57.

-hope it helps

Equivalent expressions are expressions that have the same values.

The expression is \(3(x + 7) = 57\) and the number is 12

Represent the number with x.

So, the sum of a number (x) and 7 would be represented as: x + 7

Three times the sum would be represented as: 3(x + 7)

This expression is equivalent to 57.

So, we have:

\(3(x + 7) = 57\)

Divide both sides of the equation by 57

\(x + 7 = 19\)

Subtract 7 from both sides of the equation

\(x + 7 - 7 = 19 - 7\)

\(x = 12\)

Hence, the number is 12

Read more about equivalent expressions at:

https://brainly.com/question/2972832

Answer:

0

Step-by-step explanation:

x < 4 means all numbers less than 4, excluding 4 itself.

4.5 > 4.

5 > 4.

so 0 is the solution

Answer:

4

Step-by-step explanation:

interval notation ( negative infinity, 4)

Answer:

Problem 9:  One solution

Problem 10:  Infinitely many solutions

Problem 11: One solution

Problem 12:  No solution

Step-by-step explanation:

Solving one-variable equations

When solving a one variable equation, there are two steps:

During Step 1 of that process, usually one will be combining like-terms to take two terms that contain x, and merging them into one term that contains x.  However, occasionally, the like terms contain x will completely cancel, leaving an equation with no variable left in it.

At that point, there are one of two possibilities:

If the remaining equation is true, it doesn't matter what the value of x is, the equation will be true.  This means there are infinitely many solutions (any value of x will make the equation true).

Similarly, if the remaining equation is false, it doesn't matter what the value of x is, the equation will be false.  This means there are no solutions (no values of x that will make the equation true).

Problem 9

\(3-x=x-3\)

Add "x" to both sides to move the x-term on the left side of the equation from the left, to the right side, and group like terms.

\(3=2x-3\)

We were able to combine like terms containing the x into a single term.  This equation will have one solution.

The remaining work is unnecessary to answer the question, but shows that there is one solution, the steps to find it, and what it is.

\(6=2x\)

\(3=x\)

Problem 10

\(4x-8=4(x-2)\)

Use the distributive property on the expression on right hand side of the equation ...

\(4x-8=4x-8\)

Observe that at this point, the entire left hand side of the equation EXACTLY matches that of the entire right hand side of the equation.

They are not just equal, they are exactly the same.

Attempting to move the term with x on the left hand side to the right hand side will require subtracting 4x from both sides, but combining like terms will cancel all terms with x on both sides....

\(-8=-8\)

Since negative eight is ALWAYS equal to negative eight, no matter what value you choose for x, the equation must be true because each side is the same exact expression.  This means there are infinitely many solutions.

Problem 11

\(5(1-x)=5+5x\)

Apply the distributive property on the expression on left hand side of the equation ...

\(5-5x=5+5x\)

Add 5x to both sides of the equation to move the terms with x on the left side to the right side of the equation, and combine like terms...

\(5=5+10x\)

Again, we were able to combine like terms containing the x into a single term.  This equation will have only one solution:

Subtract 5 from both sides...

\(0=10x\)

Divide both sides by 10...

\(0=x\)

Problem 12

\(x+2(x-7)=3x-7\)

Apply the distributive property on the expression on left hand side of the equation ...

\(x+2x-14=3x-7\)

Combine like terms on the left hand side of the equation...

\(3x-14=3x-7\)

To move the term with x from the left side to the right side, subtract 3x from both sides, and combine like terms...

\(-14=-7\)

Here, when combining like terms, the x all canceled out, and negative 14 is not equal to negative 7.  So, there is no solution so this equation.

Step-by-step explanation:

I don't even get the question pls forgive me

Given

G'H'T'I' is the rotation image of GHIJ.

To find the centre of rotation, angle of rotation and direction of rotation.

Now,

It is given that,

From the figure, it is clear that the rotation is in clockwise direction, and the figure GHIJ is reflected about 90 degrees.

The question is incomplete, complete version is written in the comment section below :

Answer:

Kindly check explanation

Step-by-step explanation:

1 / 4 (16 + 12x) = 28

Opening the bracket :

1/4 * 16 + 1/4 * 12x = 28

4 + 3x = 28

Subtract 4 from both sides :

4 + 3x - 4 = 28 - 4

3x = 24

Divide both sides by 3

3x / 3 = 24 / 3

x = 8

The equation that represents the total cost of the membership will be y = 5x + 265.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A local rec center offers a yearly membership for $265. The center offers aerobics classes for an additional $5 per class.

Let 'x' be the number of aerobics classes and 'y' be the total cost. Then the equation is given as,

y = 5x + 265

The equation that represents the total cost of the membership will be y = 5x + 265.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ1

Answer:

C=(F-32)×5/9

C=(70-32)×5/9

C=38×5/9

C=21.1111

C=21°C

The blanks that are missing in the sequence are -3 and 11

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

The blanks in the sequence

When listed out, we have

_, _, 25, 39

Assuming that the sequence, is an arithmetic sequence, then we have

Common difference = 39 - 25

Common difference = 14

This means that

Previous term = 25 - 14 = 11

Firs term = 11 - 14 = -3

So, the missing terms are -3 and 11

Read more about sequence at

https://brainly.com/question/30499691

#SPJ1

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

For more questions on probability

https://brainly.com/question/251701

#SPJ8

9514 1404 393

Answer:

  (3, 4)

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  Q = (A + B + C)/3

  Q = ((1, 1) +(4, 5) +(4, 6))/3 = (1+4+4, 1+5+6)/3 = (9, 12)/3

  Q = (3, 4)

The centroid is (3, 4).