Consider the expression 4a + (-3b), where bis a negative number and a < b. Is the sum positive or negative?
The sum will be negative.
The product of two negative numbers is always positive and if we add two numbers, the sign of the greater number is used in the result.
Here, we are given an expression 4a + (-3b)
Also we are told that a < b and b is a negative number
Mow, since b is a negative number, (-3b) will always be positive. This is because the product of two negative numbers, here -3 and b, will always be positive.
Now, a can be positive or negative. If a is positive, the sum will always be positive. However, if it is negative, the sum can be either positive or negative.
Here, in fact, since a < b, a will always be negative only
Let us take an example, say a = -3 and b = -2
Then the sum becomes 4(-3) + (-3)(-2)
= -12 + 6
= -6
If we observe closely since a and be are both negative and a < b, in absolute terms a will always be greater than b since for negative numbers higher the value, smaller is the number.
Thus, we can conclude that 4a > (-3b) for all values of a and b
and since 4a will always be negative, the sum will also be negative.
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help
.....................
Answer:
1. x = 9
2. x = 4
3 x =
4. x = 10
5. x =
6. x = 11
7. x = -1
8.x =
9. x = -4
10. x =
11. x = 10
12.x = -10
find the intersection of the three sets: A={-2,7,8,11}, B={-2,7,11}, C={-2,8,11}
The intersection of three sets A,B and C is {₋2 , 11}.
Given set A = {₋2,7,8,11}
set B = {₋2,7,11}
set C = {₋2,8,11}
we need to find A∩B∩C.
The components shared by all the sets A, B, and C are given by the intersection of A and B as a set. A ∩ B ∩ C is a notation that can be used to indicate the intersection of A, B, and C.
To obtain A intersection B intersection C, first determine the common elements of sets A and B, or A ∩ B. Then determine the common elements of sets B and C, or B ∩ C. Finally, compute the common elements of these two results.
we first find:
A∩B = {₋2,7,8,11} ∩ {₋2,7,11}
= {₋2,7,11}
then B ∩ C = {₋2,7,11} ∩ {₋2,8,11}
= {₋2 , 11}
now (A∩B) ∩ (B∩C) = {₋2,7,11} ∩ {₋2 , 11}
= {₋2 , 11}
hence we get the intersection of three sets as {₋2 , 11}
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i need help with plotting and answering bottom questions please
a. what fraction of the total goal distance did sarah run? b. tori ran 2 −3 of the total goal distance. who ran farther – sarah or tori?
The total goal distance Sarah run is 7/8.
The distance covered by Sarah is found to be more than Tori.
What is the exponents?A number's exponent indicates what many times a number has been multiplied by itself. For instance, 2×2×2×2 can be composed as 2⁴.
If a fraction does have a negative exponent, we take its reciprocal to make this same exponent positive.
If a fraction does have a negative exponent, we take its reciprocal to create the exponent positive.
Some properties of exponents are-
Law of Product: [tex]a^m \times a^n=a^{m+n}[/tex]Law of Negative Exponent: [tex]a^{-m}=1 / a^m[/tex]Law of Power of a Power: [tex]\left(a^m\right)^n=a^{m n}[/tex]Law of Power of a Product: [tex](a b)^m=a^m b^m[/tex]Law of Quotient: [tex]a^m / a^n=a^{m-n}[/tex]Now, as pet the given question;
Tori has covered 2⁻³ of the total distance;
Thus, it can be written as;
= 1/2³
= 1/8
Lets consider the total distance covered by both of them is 1.
Then, the distance covered by Sarah will be;
= 1 - 1/8
= 7/8
Thus, the distance covered by Sarah is 7/8.
As, 7/8 > 1/8
Therefore, the distance covered by Sarah is more than Tori.
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Find the missing Endpoint
3. What is an equation of the line in slope intercept form? (1 point)
A.y=2x-2
B.y=-2x-2
C.y=-2x+2
D.y=2x+2
Answer:
C. y = 2x + 2
Step-by-step explanation:
There are 2 points on the line (0,2) and (-3,-4)
from (-3,-4) to (0,2), rise over run is 6/3 so slope is 2
You can calculate it too
m = (y2-y1)/(x2-x1)
m = (-4 - 2)/(-3 - 0) = -6/-3 = 2
Using m = 2, x = 0, y = 2
y = mx + b
2 = 2(0) + b
b = 2
therefore
y = 2x + 2
Lucy rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 10.
Answer:
Step-by-step explanation:
Discussion
The numbers on each die are 1 to 6.
They are all equally likely to turn up. There are 36 possibilities in all 6*6
So getting a 10 can be done in 3 ways.
6 + 4 = 10
4 + 6 = 10
5 + 5 = 10
You can't get 10 any other way.
So of the 36 ways of throwing 2 dice, only 3 will work.
Answer
P(10)= 3/36 = 1/12 = 0.0833333...
A sample of hamburger had a total mass of 200. g, of which 30.0 g was found to be fat. what is the percent of fat in this hamburger sample?
The percentage of fat in this hamburger sample is 15 %.
What is percentage ?Percentage is the value per hundredth.
According to the given question a sample of hamburger had a total mass of 200. g, of which 30.0 g was found to be fat.
To find what percentage of the hamburger contains fat we put amount of fat in the numerator and total amount on the denominator and multiply this fraction by 100 to obtain the result in terms of percentage.
∴ (30/200) × 100
= 3000/200
= 30/2
= 15 %.
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The tallest building in the world is the Burj Khalifa tower in Dubai in the United Arab Emirates2. The elevator within the tower descends at a rate of 33 feet per second.3
Suppose you get on the elevator at the observation deck. After
10 seconds, you look at the display and see that you are now
1,490 feet above ground. Use the point-slope formula to find the linear equation for this situation. Let H(t) represent the height of the elevator above the ground t seconds after the elevator begins to descend.
The linear equation to calculate the height is H(t)=33t.
Given that the elevator descends at the speed of 33 feet/second.
If a person gets on the elevator at the observer deck and after 10 seconds he finds himself at 1490 feet above the ground then height descended in 10 seconds= 33×10
= 330 feet
The height of the observer deck from the ground = 1490+330
= 1820 feet
The required equation to calculate the height of above the ground H(t)=33t.
We can calculate the height of the elevator at any instant using the above expression.
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hi please help me ii need this one right now
Answer:the graph is not linear
Step-by-step explanation:
me is needing help ok
Answer:
50.96 days can be rounded to 51
73381
1223
51
Step-by-step explanation:
Too bad I can't see the choices. I will give the numbers both as exact figures rounded to integers and you have to choose the closest to these.
Part A
50.96 days
Part B
6.6043 x 10⁵ gallons at 9 gallons per minute = (6.6043 x 10⁵)/9 = 660,430/9 = 73,381.11 gallons per minute rounded to 73,381 minutes
73,381 minutes = 73,381 /60 = 1223.02 hours 1223 hours
1223 hours = 1223/24 = 50.96 days rounded to 51 days
Hope that helps. Ask if you need further info
Money is borrowed at 18% simple interest. after one year, $610.06 pays off the loan. how much was originally borrowed?
The original amount borrowed was $517.
Simple Interest is the method to calculate the interest charged for a given number of years and given rate , in simple interest the principle remains same for each year.
Simple interest =[tex]\frac{P*R*T}{100}[/tex]
where P= principle, R=rate in % , T= time
We know that Amount= Principle+ Simple Interest........(1)
According to the question
Amount=$610.06
Rate=18%
time = 1yr
Substituting the value in equation (1) we get
[tex]610.06=P+\frac{P*18*1}{100}[/tex]
[tex]610.06=\frac{100P+18P}{100}[/tex]
[tex]610.06=\frac{118P}{100}[/tex]
[tex]61006=118P[/tex]
[tex]P=\frac{61006}{118}[/tex]
[tex]P=517[/tex]
Therefore , The original amount borrowed was $517.
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In a normal distribution the theoretical mean is 30 and the theoretical standard deviation is 5. Find: a) the area below 24, b) the area between 24 and 36, c) the point that has 95% of the area below it.
Answer:
a) P(X < 24) = 0.1151
b) P(24 < X < 36) = 0.7698
c) X value for P(x < X) = 0.95 is X = 38.225
Step-by-step explanation:
a) P(X < 24)
Since μ = 30 and σ = 5 we have:
[tex]\text {z value = } \dfrac{24-30}{5}} = -1.2[/tex]
P(X < 24) = P(Z < -1.2) = 0.1151
You can use a calculator or the standard normal tables to determine P(Z < -1.2)
b) P(24 < X < 36)
First find P(X < 36) using the technique detailed in part a)
For 36, the Z value is
[tex]\dfrac{36-30}{5} = 1.2[/tex]
P(X < 36) = P(z < 1.2) = 0.8849
P(24 < X < 36) = P(X < 36) - P(X < 24) = 0.8849 - 0.1151 = 0.7698
c) X value below which 95% of the area is covered
Using a calculator (or tables) the z value corresponding to P(z < Z) = 0.95 is Z = 1.65(approx)
[tex]\text{We have } \dfrac{X - \mu}{\sigma} = z\\\\\dfrac{X - 30}{5} = 1.645\\\\\text{Multiplying both sides by 5: }\\\\X - 30 = 1.645 \times 5 = 8.225\\\\X = 30 + 8.225 = 38.225[/tex]
So X value is 38.225-
A 2-lb sample of an unknown liquid occupies a volume of 47.6 in.3 for the liquid determine (a) the specific volume, in ft3/lb, and (b) the density, in lb/ft3.
The specific volume is 0.0135 ft^3
The density is 74.07 lb/ft^3
Here,
A 2-lb sample of an unknown liquid occupies a volume of 47.6 in^3.
We have to find the specific volume and density.
What is Specific volume?
Volume is a measure of the amount of space occupied by an object.
Now,
Mass = 2 lb
Volume = 47.6 in^3
= 0.027 ft^3
Hence, Specific volume = volume/ mass = 0.027/2 = 0.0135 ft^3
And, Density = mass/ volume = 2/ 0.027 = 74.07 lb/ft^3
So, The specific volume is 0.0135 ft^3
The density is 74.07 lb/ft^3
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marine biologist captured and tagged 12 seals near Avila Beach. Recapture results found that 27% of the seals were tagged. Approximately how many seals are near Avila Beach
Based on the number of seals that were tagged near Avila Beach, the approximate number of seals near Avila Beach is 44 seals
How many seals are there?The number of seals near Avila beach can be said to be x. If it is x, then the formula is:
12 = 27% x ×
27%x = 12
0.27x = 12
Solving for x then gives:
x = 12 / 0.27
x = 44.44
= 44 seals
In conclusion, there are approximately 44 seals near Avila beach.
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A person invests 10000 dollars in a bank. The bank pays 6.5% interest compounded
annually. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 29500 dollars?
The time it will take for the money in the bank to reach a total of 29500 dollars would be = 30 years.
How to calculate the time for the interest compounded annually?To calculate the time for the interest compounded annually the formula below is used:
Simple interest = principal× time×rate/ 100
Simple interest = principal× time×rate/ 100Simple interest = total amount in the bank - principal amount
= 29500 - 10000
= $19,500
Principal = $10000
Rate = 6.5%
Time = ?
From the given formula, make t that subject of formula;
T = $19,500 ×100/$10000×6.5
T = 1950000/65000
T = 30 years.
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At a concession stand, one hot dog and one hamburger cost $3.75 ; one hot dog and cost $12.25 . Find the cost of one hot dog and the cost of one hamburger .
The function shows that the cost of hotdogs is 1.75 and the cost of hamburger is 1.5.
How to calculate the information?Let hotdogs = h
Let hamburger = x
The expression will be:
h + x = 3.25
h + 7x = 12.25
Subtract the functions
6x = 9
x = 1.5
Therefore, hot dogs will be:
= 3.25 - 1.5
= 1.75
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At a concession stand, one hot dog and one hamburger cost $3.25; one hot dog and seven hamburger cost $12.25. Find the cost of one hotdog and the cost of one hamburger.
8 children have to share two thirds of a watermelon equally what part of the whole watermelon would each child get
Each child would get 1/12 th part of the whole watermelon.
For given question,
8 children have to share two thirds of a watermelon equally .
This means we need to equally distribute 2/3 of whole watermelon to 8 children.
To divide 2/3 part of of a watermelon equally into 8 parts, we need to divide 2/3 by 8.
(2/3) ÷ 8
= [tex]\frac{(\frac{2}{3} )}{8}[/tex]
We know that in 8 = 8/1
So, we rewrite the denominator of above fraction as,
[tex]\frac{(\frac{2}{3} )}{8} \\\\= \frac{(\frac{2}{3} )}{(\frac{8}{1} )} \\\\=\frac{2}{3} \times \frac{1}{8} \\\\=\frac{1}{12}[/tex]
This means, each child will get 1/12 part of the whole watermelon.
Therefore, each child would get 1/12 part of the whole watermelon.
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What are the advantages of the edf scheduling algorithm over the rate-monotonic scheduling algorithm?
When compared to other scheduling methods for real-time systems, EDF is quite effective. It can maintain all work deadlines while increasing CPU utilization to around 100%.
What are the EDF scheduling algorithm and monotonic scheduling algorithm?The earliest deadline first (EDF) algorithm is a dynamic priority scheduling algorithm that is used in real-time systems.
EDF is an optimal algorithm, it will schedule a task set if possible. EDF is also independent of the task's period and can be used to schedule aperiodic tasks because it makes no assumptions about job periodicity. If two jobs have the same absolute deadline, choose one at random.
When compared to fixed priority scheduling techniques such as rate-monotonic scheduling, EDF can guarantee all system deadlines at higher loading. On non-preemptive uniprocessors, EDF is also an optimal scheduling algorithm, but only among scheduling algorithms that do not allow inserted idle time.
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Regression is a statistical technique developed by blaise pascal.
a. false.
b. true.
Blaise Pascal invented the statistical method known as regression. False. The author learned through the reading that adding a bathroom increases home prices more than adding a bedroom does.
What does a statistical regression mean?
A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.What does regression mean?
Regress, from which the word "regression" is derived, means "to go back" in Latin (to something). Regression is the method that, in this way, enables "going back" from muddled, challenging-to-interpret data to a clearer and more understandable meaningful model.Learn more about regression
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Solve the equation
3x/3x-1 + 2/x = 1
Answer:
x= 2/7
Step-by-step explanation:
Multiply both sides by the common denominator
3x^2 +6x−2=3x^2 −x
Move everything to the left side.
3x^2+6x-2-3x^2+x=0
Simply.
7x-2=0
Separate the cosntants and variables.
7x=0+2
Add or subtract zero
7x=2
Then divide both sides by 7.
7x/7=2/7
Cancel out common factors in the numerator and denominator
x=2/7
Answer:
x = 2/7
Step-by-step explanation:
You want to solve the equation 3x/(3x-1) + 2/x = 1.
SolutionIt works nicely to subtract 1 from both sides, then simplify.
[tex]\dfrac{3x}{3x-1}+\dfrac{2}{x}=1\\\\\dfrac{3x}{3x-1}\cdot\dfrac{x}{x}+\dfrac{2}{x}\cdot\dfrac{3x-1}{3x-1}-\dfrac{x(3x-1)}{x(3x-1)}=0\\\\\dfrac{3x^2+6x-2-3x^2+x}{x(3x-1)}=0\qquad\text{combine terms}\\\\\dfrac{7x-2}{x(3x-1)}=0\qquad\text{simplify}\\\\7x-2=0\qquad\text{expression is 0 when numerator is 0}\\\\\boxed{x=\dfrac{2}{7}}\qquad\text{add 2, divide by 7}[/tex]
__
Additional comment
The values x=0 and x=1/3 would make the denominator zero, so are excluded from the domain of the equation. By working the problem this way, we ensure that extraneous solutions do not present themselves.
Use the expression -1/3-(-5/12) show an equivalent addition expression
The equivalent expression to -1/3-(-5/12) is 1/12.
How to calculate the expression?From the information, the expression given is -1/3-(-5/12).
Therefore, this will be computed thus:
= -1/3-(-5/12)
= - 1/3 + 5/12
= 5/12 - 1/3
= 5/12 - 4/12
= 1/12
Therefore, the equivalent expression to -1/3-(-5/12) is 1/12.
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solve the equation for the given variable. justify each step.
9x + 2y = 5; y
1/15s - 2/3t = -2; s
Answer: y=[tex]\frac{5-9x}{2}[/tex]
s=-30+10t
Step-by-step explanation:
9x + 2y = 5; y
9x-9x+2y = 5-9x
2y=5-9x
y=[tex]\frac{5-9x}{2}[/tex]
1/15s - 2/3t = -2; s
(1/15s - 2/3t = -2)*15 ==> Get rid of fraction by multiplying both sides by 15
s - 30/3 t=-30
s-10t=-30
s=-30+10t
PLEASE HELP ME ILL RATE U 5 STARS PLEASEE
Ali and Leila are analyzing the following points. Ali thinks that most of the points are in
quadrant 2 because there are many x-values that are negative. Leila disagrees. Who is
correct?
(−3, 6), (−2, 4), (−3, −1), (−1, −6), (−4, −5), (−2, −7), (−5, −9), (−8, −9), (−12, −3), (2, 4),
(3, 2) and (4, 1).
Answer: Ali is correct because all of the negatives are mostly in quadrant 2.
Step-by-step explanation:
graph g(x) = -3|x+5|-1. Describe the transformations of the parent function f (x) =|x| that produce the graph g(x).
Answer:
horizontal shift 5 units left
Vertical shift 1 unit down
reflection on the x-axis: Reflected
Vertical stretch: stretched
Step-by-step explanation:
A pet groomer gave 9 baths, 15 nail trims, 8 brush-outs, and 5 ear cleanings.
For every 5 nail trims, the groomer gave 3.
Based on the baths, nail trims, brush-outs, and ear cleanings the pet groomer gave, for every 5 nails, the groomer gave 3 baths.
What is the ratio?The pet groomer gave out a total of 15 nail trims. To find out the service that the pet groomer gave 3 of for every 5 nail trims, find out the number that takes 15 nail trims to 5 nail trims and then use this number to divide the number of the other services given.
The service that comes to a quantity of 3 would be the answer.
= 15 nail trims / 5
= 3
Use 3 to divide the rest. When baths are divided by 3 we get:
= 9 / 3
= 3 baths
In conclusion, for every 5 nail trims, the groomer gave out 3 baths.
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2r−2p= n solve for p. has to be answered such as n-2r line under (division) equals p.
The solution of the given linear equation 2r−2p= n in two variables for p is r -n/2.
According to the given question.
We have a linear equation in two variables 2r - 2p = n.
Here we have to solve the given linear equation 2r - 2p = n in two variables for p.
So, the solution of the equation 2r - 2p = n for p is given by
2r - 2p = n
⇒ 2(r - p) = n (taking 2 as a common)
⇒ r - p = n/2 (dividing both the sides by 2)
⇒ r - n/2 - p = 0 (subtracting n/2 from both the sides)
⇒ r - n/2 = p (adding p both the sides)
⇒ p = r -n/2
Hence, the solution of the given linear equation 2r−2p= n in two variables for p is r -n/2.
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Find the value of sin c
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{\sqrt{95}}\\ \end{cases} \\\\\\ c=\sqrt{7^2~~ + ~~(\sqrt{95})^2}\implies c=\sqrt{49+95}\implies c=\sqrt{144}\implies c=12 \\\\[-0.35em] ~\dotfill\\\\ sin(C )=\cfrac{\stackrel{opposite}{\sqrt{95}}}{\underset{hypotenuse}{12}}\implies sin(C)\approx \text{\LARGE 0.81}[/tex]
- Three times a number increased by 15 is
equal to 30. What is the number?
plify.
Answer:
x = 5
Step-by-step explanation:
3x + 15 = 30 Subtract 15 from both sides of the equation
3x = 15 Divide both sides by 3
x = 5