The expression that must be equivalent to the one give must be 1/3x - 2
Equivalent ExpressionEquivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable. Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In this problem, we just need to simply the expression to get the answer to this.
1/3(x + 6) - 4
Step 1 : Expand or open the bracket
1/3x + 2 - 4
Step 2: Simplify the expression.
1/3x + 2 - 4 = 1/3x - 2
The equivalent expression must be 1/3x - 2
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for what value of x does the function have an output of -7, given that g(x)=-3x+8
Answer:
-5
Step-by-step explanation:
-7=3x+8-7-8=3x-15=3x divide two sides by 3x= -5The half-life of radium is 1690 years. If 30 grams are present now, how much will be present in 720 years?
Using the properties of half-life we calculate that approximately 22.33 grams of radium will be present after 720 years.
The half-life of radioactive element radium = 1690 years.
Time = 720 years
the formula for calculating half life is given by:
[tex]N(t)&=N_{0}\left({\frac {1}{2}}\right)^{\frac {t}{t_{1/2}}[/tex]
Now we substitute the values to find the N(t) which is the amount of radium left after 720 years.
t = 720
half life = 1690
N₀ (initial mass) = 30gm
[tex]N(t)&=30\left({\frac {1}{2}}\right)^{\frac {720}{1690}[/tex]
N(t) = 22.329 gm
N(t) ≈ 22.33 gm
The half-life of a substance is the amount of time required for it to reach that point. The phrase is widely used in nuclear physics to describe how quickly unstable atoms decay radioactively or how long stable atoms remain.
Additionally, a broader definition of the term is used to characterize any exponential decay (or, very infrequently, nonexponential decay). For instance, a term used in the medical sciences is the biological half-life of drugs and other compounds in the human body.
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14. Reflection: in the line y=x
Rotation: 180 about the origin
The image of the end points X(-3 , 1) and Y(4 , -5) is
X'' = (-1 , 3) and Y'' = (5 , -4).
Given, a line segment with end points X(-3 , 1) and Y(4 , -5)
We have to find the image of the points after the given composition,
Reflection in the line y = x.
Rotation 180° about the origin.
After the reflection the image of the points X and Y be,
X' = (1 , -3) and Y' = (-5 , 4)
Now, after the rotation of the points of 180° about the origin be,
X'' = (-1 , 3) and Y'' = (5 , -4)
Hence, the image of the end points X(-3 , 1) and Y(4 , -5) is
X'' = (-1 , 3) and Y'' = (5 , -4).
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Consider the following data: x −7 −6 −5 −4 −3 P(X=x) 0.2 0.1 0.2 0.2 0.3 Step 1 of 5 : Find the expected value E(X). Round your answer to one decimal place.
The expected value of the given discrete distribution is presented as follows:
E(X) = -4.7.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's respective probability.
The distribution in this problem, which contains the outcomes and their probabilities, is presented as follows:
P(X = -7) = 0.2.P(X = -6) = 0.1.P(X = -5) = 0.2.P(X = -4) = 0.2.P(X = -3) = 0.3.Hence the expected value of the distribution is calculated as follows:
E(X) = -7 x 0.2 - 6 x 0.1 - 5 x 0.2 - 4 x 0.2 - 3 x 0.3 = -4.7.
(each value from the distribution above, that is, -7, -6, -5, -4 and -3 was multiplied by it's respective probability and then these values were added).
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Seven people work at an office. Every day they draw straws to decide who will have to pick up lunch for the office. Janice has just joined the office (so there are now eight people). She knows that it's unlikely she will have to pick up lunch on her first day, and on the second day as well. How many days must past before it becomes probable that Janice will have had to pick up lunch at least once?
Given the frequency and number of possible outcomes, the number of days that must pass before it becomes probable that Janice will have had to pick up lunch at least once is 8.
Note that the probability of any of the staff at the office picking the food is 1/8.
Even if She does not pick up lunch on her first day or second, the number of days that must pass to make sure that Janice picks up lunch AT LEAST once is 1 in 8 days.
What is probability?The formula to compute the probability of an event is equivalent to the ratio of favorable outputs to the total number of outputs. It is to be noted that probabilities always range between 0 and 1.
The expression is given as:
P (E) = f/O; where
P(E) is the Probability of an event E happening;
f = The number of possible outcomes for an event (frequency)
n = Total number of outputs that are likely
Hence,
P(E) = 1/8
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One way that a company can raise money for expansion is to sell stock. When you buy a share of a company's stock, you become a shareholder, or part owner, of that company. The cost of a share is often represented in points, where each points represents one dollar. When a stock gains points, its shares increase in value, and when a stock loses points, its shares decrease in value. For instance, if a stock gains three points one day, each share of its stock is worth three dollars more than it was the day before. Positive decimal numbers are used to represent gains, and negative decimal numbers are used to represent losses.
On Monday, the closing value of a share of stock in Company ABC, was 74.01. On Tuesday, it closed at 73.67, and on Wednesday, it closed at 74.32. On Thursday, the change in stock value was -1.48. And, on Friday, Company ABC's stock gained 0.89 points. Answer the following questions based on Company ABC's stock performance this week.
One shareholder owns 13 shares of Company ABC's stock. What was the total value of their stock in this company at the close of Tuesday? $
equation if he started his day on Wednesday with 75 end he ended with 74.32 he lost -0.68 of his share hope this helped there a lot of extra information in the question
An equation is written as expressions, connected by an equals signal ("=").[2] The expressions on the two facets of the equals signal are referred to as the "left-hand side" and "right-hand side" of the equation. Very regularly the right-hand side of an equation is assumed to be zero. Assuming this doesn't lessen the generality, as this can be realized through subtracting the right-hand side from each facets.
The most common sort of equation is a polynomial equation (commonly known as also an algebraic equation) wherein the 2 facets are polynomials. the edges of a polynomial equation incorporate one or greater terms
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simplify the expresion (5÷5)+5×(5²- 5)
Answer: 101
Step-by-step explanation: 1+5x20 then 100+1= 101
please help me due today
Answer: B
Step-by-step explanation: I believe this is correct. The arrows on both run all trough the x-axis, so it would be negative infinity to positive infinity. Then, you go from open circle ( ( ) -3 to closed circle ( } ) 4.
Help me please will be highly appreciated
Answer:
500- p=1100
400- p=800
300- p=500
200- p=200
Step-by-step explanation:
you multiply the 3 by the different numbers then subtract 400
hope it helps
Answer:
middle column P = 3(500) + -400 Last column 1100
P = 3(400) + (-400) 800
P = 3(300) + (-400) 500
P = 3(200) + -(400) 200
Step-by-step explanation:
1)
1500 -400 = 100
2)
1200 - 400 = 800
3)
900 - 400 = 500
4)
600 - 400 = 200
Simplify the power (3x^2 y)^4
Answer:
(3x^2 y)^4
first apply the index power to all the numbers.
3^4= 81
then you multiply the two indices.
x^2 x 4= x^8
y^4
the answer is:
81 x^8 y^4
What is the simplified form of |-10-(-20)|-|-6+2|+|12-6|
Answer:
12
Step-by-step explanation:
|-10+20| - |-4| + |6|
10 - 4 + 6
12
It would make my day if you helped me with this!! :D
Find the coordinates of the image of a point (x, y) after a reflection in the y-axis, and after the composition when the first reflection is followed by a reflection in the x-axis.
The coordinates of the first image are (_ , _) and of the second image are (_ , _).
What type of rotation results in the same image as a reflection in the y-axis followed by a reflection in the x-axis?
45° rotation
90° rotation
135° rotation
180° rotation
270° rotation
360°rotation
The image after the first reflection is (-x, y)
The image after the second reflection is (-x, -y)
This is equivalent to a rotation of 180°.
What are the coordinates after the reflections?
First, we start with a reflection across the y-axis. This type of reflection only changes the sign of the x-value of our point.
So, if we start with the point (x, y), the image after the reflection is:
(-x, y)
Now we apply a reflection across the x-axis, this one changes the sign of the y-value, then the image after the reflection is:
(-x, -y)
Notice that a change in both signs is equivalent to a 2 quadrant motion, which is equivalent to a rotation of 180°.
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Factor 3x+11y if the expression cannot be factored
The expression 3x+11y cannot be factorized.
What is factorization?
To factorise an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse. The same way, as the product of their factors, are the algebraic expressions written in algebra. The only difference is that in an algebraic expression, variables and integers are combined to perform mathematical operations like addition or subtraction.
Here the given expression 3x+11y didn't have any common factors.
The given expression has two variables 3x and 11y and they didn"t have any common terms.
Hence the expression 3x+11y cannot be factored.
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Suppose that the volume of water in the rain barrel decreased by 4
58
gallons in 4 minutes. What will be the change in the volume of water after 1 minute.
The change in the volume of water after 1 minute is 1 5/32 gallons.
How to calculate the change in volume?Given that the volume of water in the rain barrel decreased by 4 5/8 gallons in 4 minutes.
The change after 1 minute will be:
= Total volume of water / Number of minutes
= 4 5/8 ÷ 4
= 37/8 ÷ 4
= 37/8 × 1/4
= 37 / 32
= 1 5/32
The change is 1 5/32 gallons.
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According to a recent survey of 43 million citizens in the United States, 8 million were planning to start a new degree program or continue their education in the next year. According to this data, what is the probability that a random U.S. citizen you meet is not planning to start a new degree program or continue their education in the next year? (Round to four decimal places.)
The probability of people not planning a new degree = [tex]\frac{35}{43}[/tex]
What is probability ?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
And while solving these type of question we calculate the probability of a particular event.
The survey has 43 million people
Given is 8 million were planning to start a new degree program
Thus the probability of people planning a new degree program = 8 million divided by 43 million
Thus the probability of people not planning a new degree = 1 - [tex]\frac{8 million}{43 million}[/tex]
which is equal to [tex]\frac{35,000,000}{43,000,000}[/tex]
which on solving further will give us:
P ( people not planning a new degree ) = [tex]\frac{35}{43}[/tex]
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An x-ray machine for animals costs 125,000. If the loan is for 10 years, and the interest paid is $65,625, what is the interest rate on the loan?
The interest rate on the loan is 5.25%.
How to calculate the rate?It should be noted that the formula for calculating the simple interest is given as:
Interest = (Principal × Rate × Time) / 100
In this case,
Interest = 65625
Principal = 125000
Time = 10
Interest = (Principal × Rate × Time) / 100
65625 = (125000 × R × 10)/100
Cross multiply
6562500 = 1250000R
Divide
R = 6562500 / 1250000
R = 5.25
The rate is 5.25%
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How many values of x must be excluded in the expression (x+9)(x-5)?
The number of values of x to be excluded is 2.
To find out the values of x that must be excluded in the expression
(x+9)(x-5) as follows:
The value of x is 2.
We are given to find the number of value of x that must be excluded in the expression below:
E = (x+9)(x-5)
We have to exclude those values of x for which the expression E becomes undefined.
Since E is a rational expression, so the becomes undefined only when the denominator becomes 0.
That is,
(x+9)(x-5) = 0
= x+9 = 0 x-5 = 0
= x = -9 x = 5
Therefore, we need to exclude the values x = -9 and x =5.
So, there are two values of x to be excluded from the given expression.
Hence the answer, the number of values of x to be excluded is 2.
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Two cubes have sides of length 5 cm and 6cm. What is the ratio of their respective surface areas?
If two cubes have sides of length 5 cm and 6cm. The ratio of their respective surface areas is 36 : 25.
How to find the ratio of the surface area?Using this formula to find the ratio
Ratio of their surface area = a /a'
Where:
a = 6
a' =5
Let plug in the formula
Ratio of their surface area = 6a² /6a'²
Ratio of their surface area = 6(6)² / 6(5)²
Ratio of their surface area = 36 / 25
Ratio of their surface area = 36 : 25
Therefore the ratio is 36 : 25.
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Which Form is the following equation in?
y = −7(x + ²)² + 11 Vertex Form Standard Form Factored Form
Answer:
Factored form is the form of the equation.
During a football game the parents of the Devils football players sell nachos and popcorn to raise money for
new uniforms. They charge $8.50 for nachos, and $6.00 for a bag of popcorn. The parents collect $883.50 in
sales during the game. They sell a total of 126 items. Set up a system of equations and solve to determine
how many nachos and bags of popcorn were sold.
Number of nachos sold:
Number of bags of popcorn:
The equation is 8.50x + 6y = 883.50
Number of nachos sold is 51
Number of bags of popcorn sold is 75
Given,
The cost for nachos = $8.50
The cost of a bag of popcorn = $6.00
The total amount collected = $883.50
Total number of items sold = 126
We have to find an equation and solve to determine the number of nachos and bags of popcorn sold;
Here,
x be the number of nachos sold
y be the number of bags of popcorn sold
Then,
x + y = 126
x = 126 - y
Now,
8.50x + 6y = 883.50
Solve the equation using x as 126 -y.
That is,
8.50(126 - y) + 6y = 883.50
1071 - 8.50y + 6y = 883.50
1071 - 2.50y = 883.50
1071 - 883.50 = 2.50y
y = (1071 - 883.50) / 2.50
y = 187.50/2.50
y = 75
Now.
x = 126 - y
x = 126 - 75
x = 51.
Therefore,
The equation is 8.50x + 6y = 883.50
Number of nachos sold is 51
Number of bags of popcorn sold is 75
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See the question above. I don’t understand how I was wrong to do the LCM of 50 and 60, which is 300, so that’s the distance where the friends will meet, and d/s = time, so 300/50 and 300/60 are 6 and 5, and the average of that is 5.5, but the real answer seems to be approx. 18.2? Please solve the question AND explain my mistake.
Answer:
Step-by-step explanation:
so this is a combined work problem, both of the people are moving towards each other. They are both doing some of the work to move towards each other.
one is moving at 50 , the other at 60 , directly towards each other. Now change the problem to one moving at 50+60 =110 at a destination 200 away
now you can solve this pretty easily , i'm guessing
200/110 = 1.818181
or approx. 1.82 hours
got it?
Julie had $20.00 in her pocket. She spent $7.40. About what percent of her money does she still have?
63%
First, we have to take 20.00 - 7.40 which gets us 12.60.
Then, we use the formula where we put the 12.60 on top of a fraction bar, and the 20.00 on bottom.
We do 12.60 x 100 which makes 1260.
Lastly, we divide that by the 20.00 which gets us 63.
So, Julie has 63% of her money left.
I hope this helped!!!
In the figure, m is parallel to n and mZ4= 114°. Find the measures of the other angles.
Answer:
∠2 = ∠4 = ∠6 = ∠8 = 114°
∠1 = ∠3 = ∠5 = ∠7 = 66°
Step-by-step explanation:
You want to know the measures of all of the angles where transversal t crosses parallel lines m and n. ∠4 is given as 114°.
Congruent anglesWhere a transversal crosses parallel lines, all of the acute angles are congruent, and all of the obtuse angles are congruent. The obtuse and acute angles form linear pairs, so are supplementary.
In the given figure, the acute angles are numbered using odd numbers, and the obtuse angles are numbered using even numbers.
∠2 = ∠4 = ∠6 = ∠8 = 114°
∠1 = ∠3 = ∠5 = ∠7 = 180° -114° = 66°
Please help! (Will give a good amount of points)
The two way table to display the relative frequency by row is:
Lasagna orders
veggie meat total
Tomato sauce 44.871% 55.128% 100%
cream sauce 76.67% 23.33% 100%
Given:
Tomato sauce = 35 veggie + 43 meat
= 78
cream sauce = 46 veggie + 14 meat
= 60
veggie % in tomato sauce = 35 * 100/78 = 3500/75 = 44.871%
meat % in tomato sauce = 43 * 100 / 78 = 4300/78 = 55.128%
veggie % in cream sauce = 46 * 100 / 60 = 4600/60 = 76.67%
meat % in cream sauce = 14 * 100 / 60 = 1400/60 = 23.33%
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The function f(x) is graphed below. What is true about the graph on the interval from point e to point f?
Answer: It is positive and increasing
Step-by-step explanation:
From point e to f it is clearly going up, and is part of the positive side of the graph.
hey please solve this
Answer:
∴ x = 70°, y = 70°, z = 40°
Step-by-step explanation:
x = 180° - 110° (adjacent angles on a straight line)
= 70°
Since triangle PQR is an isosceles triangle,
∴ y = x = 70°
∴ z = 180° - 70° - 70° (angle sum of a triangle)
= 40°
A funicular carries passengers up an embankment to an observation point. If the length of the track is 51.1 meters and the angle of inclination is 35 degrees 7, determine the height of the embankment.
The height of the embankment is 8.19 meters
How to determine the height of the embankment.Information from the question
the length of the track is 51.1 meters
the angle of inclination is 35 degrees
The height of the embankment is worked using SOH CAH TOA
The direction of movements describes a right angle triangle of
opposite = x meters
hypotenuse = 10 miles
The height is calculated using cos, CAH let the height be x
cos 35 = adjacent / hypotenuse
cos 35 = x/ 10
x = 10 * cos 35
x = 8.19 meters
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A baseball player makes an annual salary of 3,200,000.
A charitable organization states that for $120 it can send 1 child to school in a developing country for 1 year. The baseball player decides to donate 10% of his annual salary to this organization. Calculating it would be 320,000,
About how many children could his donation send to school for 1 year?
Answer: 2,666 children
Step-by-step explanation:
This player makes $3.2 M per year. 10% of his salary is $320,000
($320,000) / ($120/child) = 2,666 children
Which describes the slope of this line?
The slope of the line in the image is a zero slope.
What is the Slope of a Line?The slope of a line can be defined as the ratio of a line's vertical change to the line's horizontal change, which is rise/run or change in y / change in x.
What is the Slope of Horizontal Line?An horizontal line has horizontal change but no vertical change. Therefore, no matter the horizontal change of the line, the slope of a horizontal line would always be zero. Therefore, horizontal lines have zero slope.
The line in the image is a horizontal line, therefore, the slope is neither positive nor negative, but a zero slope.
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An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 75 type K batteries and a sample of 46 type Q batteries. The type K batteries have a mean voltage of 8.51, and the population standard deviation is known to be 0.344. The type Q batteries have a mean voltage of 8.87, and the population standard deviation is known to be 0.644. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1 be the true mean voltage for type K batteries and μ2 be the true mean voltage for type Q batteries. Use a 0.05 level of significance.
Step 3 of 4 : Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places.
The decision rule for rejecting the null hypothesis, considering the t-distribution, is of:
|t| < 1.9801 -> do not reject the null hypothesis.|t| > 1.9801 -> reject the null hypothesis.What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean voltage for these two types of batteries is different, that is, the subtraction of the sample means is of zero, hence:
[tex]H_0: \mu_1 - \mu_2 = 0[/tex]
At the alternative hypothesis, it is tested if there is enough evidence to conclude that the mean voltage for these two types of batteries is different, that is, the subtraction of the sample means different of zero, hence:
[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]
We have a two-tailed test, as we are testing if the mean is different of a value.
Considering the significance level of 0.05, with 75 + 46 - 2 = 119 df, the critical value for the test is given as follows:
|t| = 1.9801.
Hence the decision rule is:
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