Answer:
[tex]x < -2[/tex].
Step-by-step explanation:
It is given that [tex]3x + 6 < 12[/tex] and [tex]6x + 24 < 12[/tex].
For [tex]3x + 6 < 12[/tex],
[tex]3x < 12-6[/tex]
[tex]3x < 6[/tex]
Divide both sides by 2.
[tex]x < 2[/tex] ...(i)
For [tex]6x + 24 < 12[/tex],
[tex]6x< 12-24[/tex]
[tex]6x< -12[/tex]
Divide both sides by 6.
[tex]x < -2[/tex] ...(ii)
From (i) and (ii), we get
[tex]x < 2\text{ and }x<-2[/tex]
[tex]\Rightarrow x<-2[/tex]
Therefore, the required answer is [tex]x < -2[/tex].
The area of a triangle is 25 square Inches, base Inches. What is its helght (a) ? Use the formula A triangle = 1/2 ba
50 inches
5 inches
62.5 inches
10 inches
125 inches
Answer:
50/b in
Step-by-step explanation:
Use the area formula A = (1/2)(base)(height).
Here the area A is given and is 25 in^2; the base is not given, so use 'b.'
Then, since A = (1/2)(base)(height),
(height) = 2A/(base) = 2(25 in^2)/b = 50/b in
Which equation has no solution?
4(x + 3) + 2x = 6(x + 2)
5+2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 612 + x) = 2(3x + 8)
Answer:
[tex]4(x + 3) + 2x = 6(x + 2)[/tex][tex]5 + 2(3 + 2x) = x + 3(x + 1)[/tex]Step-by-step explanation:
[tex]5(x + 3) + x = 4(x + 3) + 3 \\ 5x + 15 + x = 4x + 12 + 3 \\ 5x + x - 4x = 12 + 3 - 15 \\ 2x = 0[/tex]
Divide both sides of the equation by 2
2x/2 = 0/2
x = 0
(4+612+x)=2(3x+8)
4+612+x=6x+16
4+612-16=6x-x
600=5x
Divide both sides of the equation by 5
600/5 = 5x
120 = x
Answer:
Its B. 5+2(3 + 2x) = x + 3(x + 1)
Step-by-step explanation:
I just took the test on edge
a bucket full of milk is 80cl,how many litres are in 15 of such
Answer:
1.2 liters
Step-by-step explanation:
1 bucket has a volume of 80 cL.
15 buckets have a volume of 15 * 80 cL = 120 cL
1 L = 100 cL
120 cL * (1 L)/(100 cL) = 1.2 L
16. The difference of two numbers is 3 and the
difference of their square is 69. Find the
numbers.
Make a system of equations.
[tex]x-y=3[/tex]
[tex]x^2-y^2=69[/tex]
[tex]x=y+3[/tex]
[tex](y^2+6y+9)-y^2=69[/tex]
[tex]6y+9=69[/tex]
[tex]6y=60[/tex]
[tex]y=10[/tex]
[tex]x=10+3[/tex]
[tex]x=13[/tex]
[tex]x=13,y=10[/tex]
Hope this helps.
頑張って!
Consider the region bounded by the curves y=x2 and y=9. Find the volume of the solid formed when this region is rotated around the x-axis.
Answer:
V = 36Π cubic Centimetres
Step-by-step explanation:
Step(i):-
Volume of the solid
The Volume of the solid formed by revolving the region bounded by the curve y = f(x) and rotated around the x-axis defined by
[tex]V = \pi \int\limits^a_b {[f(x)]^{2} } \, d x[/tex]
Step(ii):-
Given two curves are y = x² and y = 9
The point of intersection of two curves
y = x²...(i)
and y = 9 ...(ii)
Equating both equations , we get
x² - 9 =0
⇒ x² - 3² =0
⇒ (x+3)(x-3) =0
⇒ x+3=0 and x-3=0
x = 3 ⇒ y = 9
x = -3 ⇒y = 9
The point of intersection ( -3,9) and (3,9)
Step(iii):-
[tex]V = \pi \int\limits^a_b {[(f(x)]^{2} } \, -[g(x)]^{2})d x[/tex]
The limits x- varies from -3 to 3
[tex]V =\pi (\int\limits^3_3 {x^{2} } \, dx +\int\limits^3_3{9} \, dx[/tex]
[tex]V =\pi (\frac{x^{3} }{3} -9 x)^{3} _{-3}[/tex]
[tex]V= \pi ( \frac{27}{3} - 9(3) - (\frac{-27}{3} -9(-3))[/tex]
V = π ( |-36| = 36Π cubic Centimetres
Final answer:-
The volume of the solid
V = π ( |-36| = 36Π cubic Centimetres
Simplify the expression to a polynomial in standard form:
(3x − 2)(22 - 2x + 1)
Please answer
Answer:
[tex]-6x^2 + 73x - 46[/tex]
Step-by-step explanation:
(3x-2)(22-2x+1)
simplify (22-2x+1)
(3x-2)(23-2x)
distribute
69x - 6x^2 - 46 + 4x
simplify
[tex]-6x^2 + 73x - 46[/tex]
A cafeteria worker knows that it takes 3 bottles of juice to serve a table of 18 students. How many bottles of juice are needed for 24 students? How many bottles of juice are needed for 42 students?
Answer:7
Step-by-step explanation:
quik math
A triangle has sides with lengths of 2x - 7, 5x - 3, and 2x - 2. What is the perimeter of the triangle
Answer:
3x
Step-by-step explanation:
f(x) = 2x2 + 5x + 20
Find f(-9)
Answer: f(-9)=137
Step-by-step explanation:
To find f(-9), you plug in -9 into x.
f(-9)=2(-9)²+5(-9)+20 [solve parenthesis]
f(-9)=2(81)-45+20 [multiply]
f(-9)=162-45+20 [subtract]
f(-9)=117+20 [add]
f(-9)=137
3/2•3/2•3/2•3/2 rewrite product in exponential form
Answer:
1.5^4
Step-by-step explanation:
The product for this expression is 1.5 multiplied by itself 4 times. This means you raise it to the fourth power, thus giving you 3/2^4 or 1.5^4.
What are the subsets of real numbers -7
The subsets of real numbers are known as:
rational numbers (decimals that don't repeat)irrational numbers (decimals that repeat)integers (a number that isn't a fraction)whole numbersnatural numbers (a positive number)Best of Luck!
The length of Tom’s rectangular classroom floor is 8 feet longer than 2 times the
width. The perimeter of his classroom floor is 124 feet. Write and solve an
equation to find the length of his classroom.
Answer:
Length= 44 feet
Width= 18 feet
Step-by-step explanation:
Let the length= x
Let the width = y
Length is 8 feet longer than 2 times the
width.
X= 8+2y
The perimeter of his classroom floor is 124 feet
Perimeter= 2(x+y)
124= 2x+2y
But x= 8+2y
124= 2x+2y
124= 2(8+2y) +2y
124= 16 +4y +2y
124-16= 6y
108= 6y
18 = y
Width= 18 feet
X= 8+2y
X= 8 +2(18)
X= 8+36
X= 44
Length= 44 feet
On the game show « the price is right », the highest winning amount was $262,743. The next largest winning amount was only 81.4012% of the highest. What was the second highest winning amount rounded to the nearest dollar?
Answer:
The second highest winning amount was of $213,876
Step-by-step explanation:
Given that the main prize of "The price is right" won is $ 262,743, and that the second highest prize in the history of said program is 81.4012% of said value, to obtain said number the following calculation must be performed:
(262,743 / 100) x 81.4012 = X
2,627.43 x 81.4012 = X
213,875.95 = X
Therefore, rounded to the nearest dollar, the second highest prize in the program was $213,876.
All 4 questions please
Answer:
π = S/2πrhv = √2E/mb = (-7a+c)/2x =3y-1Step-by-step explanation:
1.
[tex]S = 2\pi rh\\Divide\:both\sides\:of\:the\:equation\:by\:2rh\\\\\frac{S}{2rh} = \frac{2 \pi rh}{2 rh} \\\\\pi = \frac{S}{2rh}[/tex]
2.
[tex]E = \frac{1}{2} mv^2\\\\E = \frac{mv^2}{2} \\\\Cross\:multiply\\\\2E =mv^2\\Divide\:both\:sides\:of\:the\:equation\:by\:m\\\frac{2E}{m} = \frac{mv^2}{m} \\\\\frac{2E}{m} =v^2\\Square\:root\:both\:sides\:of\:the\:equation\\\sqrt{\frac{2E}{m} } = \sqrt{v^2} \\\\\sqrt{\frac{2E}{m} } =v\\\\v =\sqrt{\frac{2E}{m} }[/tex]
3.
[tex]7a+2b =c\\Isolate\:b\\\\2b =c-7a\\2b= -7a+c\\Divide\:both\:sides\:of\:the\:equation\:by \:2\\\frac{2b}{2} =\frac{-7a+c}{2} \\\\b = \frac{-7a+c}{2}[/tex]
4.
[tex]y = \frac{1}{3} (x+1)\\\\y = \frac{x+1}{3}\\\\Cross\:multiply \\3y =x+1\\Isolate \:x\\3y -1=x\\\\x =3y-1[/tex]
How do I factor 4x^2-12x^3?
Please help what is the area?
Answer: 70 square units
Solve and check the solution 5/8 = 1/2(a + 2) please help me
Answer:
[tex]a=-\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]\frac{5}{8}=\frac{1}{2}\left(a+2\right)\\\\Switch\: sides\\\frac{1}{2}\left(a+2\right)=\frac{5}{8}\\\\\mathrm{Multiply\:both\:sides\:by\:}2\\2\times\frac{1}{2}\left(a+2\right)=\frac{5\times\:2}{8}\\\\Simplify\\a+2=\frac{5}{4}\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\a+2-2=\frac{5}{4}-2\\\\Simplify\\a=-\frac{3}{4}[/tex]
Check[tex]\frac{5}{8} = \frac{1}{2}\left(-\frac{3}{4}+2\right) \\\\\mathrm{Multiply\:fractions}:\\\\\quad \:a\times\frac{b}{c}=\frac{a\:\times \:b}{c}\\\\\frac{5}{8}=\frac{1\times \left(-\frac{3}{4}+2\right)}{2}\\\\\frac{5}{8}=\frac{1\times\left(-\frac{3}{4}+2\right)}{2}\\\frac{5}{8}=\frac{-\frac{3}{4}+2}{2}\\\\\mathrm{Join}\:-\frac{3}{4}+2:\quad \frac{5}{4}\\\frac{5}{8}=\frac{\frac{5}{4}}{2}\\\\\frac{5}{8}=\frac{5}{4\times\:2}\\\\\frac{5}{8}=\frac{5}{8}[/tex]Which of the following statements best describes adjacent angles
Answer:
The correct answer to this would be D, adjacent angles share a side.
Step-by-step explanation:
Adjacent angles share a common side as well as a common vertex.
I hope this helps :)
The statement that best describes adjacent angles is that adjacent angles share a side.
What is a vertex ?A vertex is where two non parallel lines meet.For example a triangle has 3 vertex.We can also say that vertex is a point where two non parallel lines meet to form an angle.
According to the given question the best description of adjacent angle is that they share a side.
We can say that adjacent angles are those angles which are placed next to each other.
Adjacent angle also share a common vertex but they do not overlap each other.
learn more about vertex here :
https://brainly.com/question/12563262
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Is 8.73 a rational number
Answer:
Yes
Step-by-step explanation:
8 73/ 100=8.73
What information can you obtain about the scores in a regular frequency distribution table that is not available from a grouped table.
A. The number and width of the class intervals
B. The exact frequency for each category on the scale of measurement
C. The overall frequency for each class interval
Answer: B. The exact frequency for each category on the scale of measurement
Step-by-step explanation: The main difference between a grouped table and regular frequency distribution exists in the fact that ; grouped table takes in a defined range of (X) values, that is takes more than one individual value per group and takes the frequency of all scores or values in the group, hence giving the frequency of the scores in the interval rather than the frequency of each individual score. On the other hand, the regular frequency distribution treats values or scores individually and then takes the frequency of each score. This way a regular frequency distribution enables us to know the exact number or distribution of each individual score.
The information in a regular frequency distribution table that is not available from a grouped table is (b) the exact frequency for each category on the scale of measurement
There are several similarities between a regular frequency table, and a grouped frequency table.
However, both frequency tables have a major difference.
This difference is in the frequency of the data they represent
While a regular frequency table shows the exact frequency of each data element, a grouped frequency table cannot show the exact frequency of each data element.
Hence, the true option is (b)
Read more about frequency distribution table at:
https://brainly.com/question/1094036
Find the circumference of a circle with radius of 18 in. Leave your answer in terms of pi.
A. 18 pi in.
B. 324 pi in.
C. 54 pi in.
D. 36 pi in.
Answer:
36pi. in. answer is D
Step-by-step explanation:
C = 2(18)pi= 36pi in
5/8x3/5
help please
Answer:
3/8
Step-by-step explanation:
reduce the numbers with the greates componentes factor. 5 and then calculate the product
20 POINTS AND BRAINLIEST Ed has 93 marbles. In which sequence can he arrange them in to use all the marbles?
Answer:
A.) asequence with six terms that starts with 1 and has a common ratio of 2
Convert 1 million seconds into years (round to 3 decimal places)
Answer:
that would be 0.032 because 1 million secs is 11 days 13 hours 46 minutes and 40 secs
Answer:
0.032 years.
Step-by-step explanation:
1 year = 365 * 24 * 60 * 60 = 31,536,000 seconds.
= 1000000 / 31,536,000
= 0.03170979
Tecside real estate, inc. is a research firm that tracks the cost of apartment rentals in southwest virginia. in mid-2002, the regional average apartment rental rate was $895 per month. assume that, based on the historical quarterly surveys, it is reasonable to assume that the population standard deviation is $225. in a current study of apartment rental rates, a sample of 180 apartments in the region provided the apartment rental rates.a. do the sample data enable tecside real estate, inc. to conclude that the population mean apartment rental rate now exceeds the level reported in 2002? the sample mean is $915 and the sample standard deviation is $227.50. make your decision based on α=0.10.b. what is the p-value?
Answer:
The decision is to fail to reject the null hypothesis
This means that the population mean apartment rental rate now does not exceeds the level reported in 2002
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$895[/tex]
The population standard deviation is [tex]\sigma = \$225[/tex]
The sample size is [tex]n = 180[/tex]
The sample mean is [tex]\= x = \$ 915[/tex]
The sample standard deviation is [tex]s = \$ 227.50[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu \le \$ 895[/tex]
The alternative hypothesis is [tex]H_a : \mu > \$895[/tex]
The test statistics is evaluated as
[tex]t = \frac{\= x- \mu}{\frac{\sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 915 - 895}{ \frac{225}{ \sqrt{180} } }[/tex]
=> [tex]t =1.193[/tex]
So from z-table the p-value is obtained, the value is
[tex]p-value = P(Z > t) = P(Z > 1.193 ) = 0.11643[/tex]
So From the value obtained we see that
[tex]p-value > \alpha[/tex] so we fail to reject the null hypothesis
A company says their cough syrup, called Cough-Up, is real effective and that 7 out of 10 doctors prefer it over any competitors. Using the given ratio, answer the following questions If there are 40 doctors, how many prefer Cough-Up? Your answer
Answer:
40÷10=4
7×4=28
18 doctors
Hi! I really need help with figuring out how to do #2, I just don't get how it's done and really need an explanation! thanks in advance :)
Answer:
18
Step-by-step explanation:
g(3)+f(4)
=3²+1+2×4
=9+1+8
=18
A lab technician needs 60mL of 25% acid solution for a certain experiment , but he has only 10% solution and 40% solution. How many milliliters of the 10% and the 40% solutions should he mix to get what he needs?
Answer:
10%: 30 mL40%: 30 mLStep-by-step explanation:
The needed concentration is exactly halfway between the available concentrations, hence they must be mixed equally.
He should mix 30 mL each of the 10% and 40% solutions.
_____
The first step in solving any problem is to look at the given information, and at what is being asked for. Here, the mix that is being asked for is exactly halfway between the given concentrations, so you know without any further contemplation that the mix will be 50%/50% of each.
__
If the mix were something else, there are several ways the problem can be solved. I like to use a diagram that puts the available concentrations on the left in a column with the highest on top, the needed concentration in the next column in the middle, and the differences of these numbers on the diagonals in the right column.
Example: if the needed mix is 15%, the diagram would look like ...
40 5
15
10 25
The numbers on the right tell you the proportions required (5:25 = 1:5). For this example, you need 1 part 40% solution and 5 parts 10% solution to make a mix that is 15%. That's a total of 6 parts, so each "part" is 10 mL for 60 mL of solution.
We chose this example so every number in the diagram is different, so you could see how the instructions for use apply.
__
Another way to solve this is to let a variable represent the amount needed of the highest concentration. If we let that variable be x, for the given problem, we can write the equation for the amount of acid in the mix as ...
40%(x) + 10%(60 -x) = 25%(60)
0.30x = 9 . . . . . . . . subtract 6, simplify
x = 9/0.30 = 30 . . . . . mL of 40% solution
A company assigns to each of its employees an ID code that consists of one or two uppercase letters followed by a digit from 0 through 9. How many employee codes does the company have available?
Answer:
7020 codes
Step-by-step explanation:
For one upper case letter:
There are 26 letters in this scenario
For two upper case letters:
There are 26 * 26 letters in this scenario. Essentially, there are 676 letters in this scenario.
For one upper case letter:
There are 10 digits that can be applied to it. So therefore, there are 26 * 10 codes in this case.
That means, there are 260 codes for one upper case letter.
For two upper case letters:
There are 10 digits that can be applied to it. That is to day, there are 676 * 10 codes in this case.
This means, for two upper case letters, there are 6760 codes.
Finally, we add up the number of codes for one upper case letter, and that of two upper case letters together. As such, we have
6760 + 260 = 7020.
The company has 7020 codes available.
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The following boxplot is of the birth weights (in ounces) of 160 infants born in a local hospital The following boxplot is of the birth weights (in ounces) of 160 infants born in a local hospital
About 40 of the birth weights were below?
A) 92 ounces B) 102 ounces C) 112 ounces D) 122 ounces
This question is Incomplete because it lacks the diagram of the box plot. Please find attached the diagram of the box plot
Answer:
B) 102 ounces
Step-by-step explanation:
Looking at the attached diagram, we can see the box plot it divided into different segment
The median weight of the babies = 110 ounces
The maximum weight of the babies is between = 140 and 130, approximately let's say 135 ounces
The minimum weight is 80 ounces
Then the box in the middle is divided into 3
It has the First Quartile
Median
And third Quartile
Since we have 160 infants born in the local hospital, about 40 of the birthweights we fall into
= 40/160 = 1/4
1/4 represents the first Quartile
Looking at the box plot, 40 of the birthweights were below 102 ounces.