Answer: B. (all numbers less than or equal to -3 will satisfy the inequality)
Step-by-step explanation:
Hi, to answer this question we have to solve the inequality for x:
7 - 5x > 3x + 31
7-31 > 3x +5x
-24 > 8x
-24/8 > x
-3 > x
x < -3
So, the correct option is:
B. (all numbers less than or equal to -3 will satisfy the inequality)
Feel free to ask for more if needed or if you did not understand something.
If the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 2), (negative 1, 2). (–4, –7) (–4, 2) (2, –7) (2, 11)
Answer:
A ( -4, -7)
Step-by-step explanation:
if you translate -1, three units to the left u get -4 and then when u go nine units down u get -7 do it on a grid and u will see wut im talkin about : )
Answer:
A.
Step-by-step explanation:
38. Convert 85 to a number in base eight.
O 95 (base eight)
O 105 (hase eight)
O 115 (base eight)
O 125 (base eight)
Answer:
divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125
In a class Vidya ranks 7th from the top. Divya
is 7 ranks ahead of Medha and 3 ranks
behind Vidya. Sushma who is 4th from the
bottom is 32 ranks behind Medha. How many
students are there in the class?
Answer:
52 students
Step-by-step explanation:
From the question above, we have the following information:
a) Vidya ranks 7th from the top.
Mathematically,
Vidya = 7th student
b) Divya 3 ranks behind Vidya.
Divya = Vidya + 3
Hence, Mathematically:
Divya = 7 + 3 = 10
Divya = 10th student
c) Also, Divya is 7 ranks ahead of Medha.
Mathematically,
Medha = 10 + 7= 17
Medha= 17th student
d)Sushma is 32 ranks behind Medha
Mathematically,
Sushma = Medha + 32
= 17 + 32 = 49
Sushma is the 49th student
Therefore, since, Sushma is 4th from the bottom, total number of students is:
49 + 3 = 52 students
The perimeter of a rectangle is 141 feet, and the length is twice the width. What are the dimensions ?
Answer:
The width is 23.5 ft and the length is 47 ft
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w)
141 = 2(l+w)
The length is twice the width
l = 2w
141 = 2 ( 2w+w)
141 = 2( 3w)
141 = 6w
Divide each side by 6
141/6 = 6w/6
23.5 = w
l = 2w = 2(23.5) = 47
The width is 23.5 ft and the length is 47 ft
Answer:
[tex]\boxed{Width = 23.5 \ feet}[/tex]
[tex]\boxed{Length = 47 \ feet}[/tex]
Step-by-step explanation:
Let Length be l and Width be w
Perimeter = 2(Length) + 2(Width)
Condition # 1:
2l+2w = P
=> 2 l + 2 w = 141
Condition # 2:
=> l = 2w
Putting the second equation in the first one
=> 2(2w)+2w = 141
=> 4w + 2w = 141
=> 6w = 141
Dividing both sides by 6
=> Width = 23.5 feet
Given that
=> l = 2w
=> l = 2(23.5)
=> Length = 47 feet
Answer the problem below
Answer:
D. 4z^3
Step-by-step explanation:
First, you see what cubed is 64, which is 4, so you know it is either A or D, but it can not be A because it is not z to the power 5 but x to the power of 3
Hope this helps, if you want me to explain more, feel free to ask questions.
Have a good day! :)
Answer:
4 z^3
Step-by-step explanation:
( 64 z^9) ^ 1/3
Rewriting 64 as 4^3
( 4^3 z^9) ^ 1/3
We know that ( ab) ^c = a^c * b^c
4^3 ^ 1/3 z^9 ^ 1/3
We know that a^ b^c = a^ ( b*c)
4^(3 * 1/3) z^ (9 * 1/3)
4 ^ ( 1) z^ ( 3)
4 z^3
Determine how many litres of water will fit inside the following container. Round answer and all calculations to the nearest whole number.
Answer:
[tex]\approx[/tex] 11 litres of water will fit inside the container.
Step-by-step explanation:
As per the given figure, we have a container formed with combination of a right angled cone placed at the top of a right cylinder.
Given:
Height of cylinder, [tex]h_1[/tex] = 15 cm
Diameter of cylinder/ cone, D = 26 cm
Slant height of cone, l = 20 cm
Here, we need to find the volume of container.[tex]\\Volume_{Container} = Volume_{Cylinder}+Volume_{Cone}\\\Rightarrow Volume_{Container} = \pi r_1^2 h_1+\dfrac{1}{3}\pi r_2^2 h_2[/tex]
Here,
[tex]r_1=r_2 = \dfrac{Diameter}{2} = \dfrac{26}{2} =13\ cm[/tex]
To find the Height of Cylinder, we can use the following formula:
[tex]l^2 = r_2^2+h_2^2\\\Rightarrow h_2^2 = 20^2-13^2\\\Rightarrow h_2^2 = 400-169\\\Rightarrow h_2^2 = 231\\\Rightarrow h_2=15.2\ cm \approx 15\ cm[/tex]
Now, putting the values to find the volume of container:
[tex]Volume_{Container} = \pi \times 13^2 \times 15+\dfrac{1}{3}\pi \times 13^2 \times 15\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 15+\pi \times 13^2 \times 5\\\Rightarrow Volume_{Container} = \pi \times 13^2 \times 20\\\Rightarrow Volume_{Container} = 10613.2 \approx 10613\ cm^3[/tex]
Converting [tex]cm^{3 }[/tex] to litres:
[tex]10613 cm^3 = 10.613\ litres \approx 11\ litres[/tex]
[tex]\approx[/tex] 11 litres of water will fit inside the container.
At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?
Answer:
5,000 passengers
Step-by-step explanation:
1. Find out how many trains leave each hour.
6 min – 60/6 = 10 x 200 passengers = 2000
10 min – 60/10 = 6 x 200 passengers = 1200
12 min – 60/12 = 5 x 200 passengers = 1000
15 min – 60/15 = 4 x 200 passengers = 800
2. Add it all up.
2000 + 1200 + 1000 + 800 = 5000 passengers
Answer:
5000
Step-by-step explanation:
6 minute train leaves 10 times
10 x 200 = 2000 passengers
10 minute train leaves 6 times
6x200 = 1200
12 minute train leaves 5 times
5x200 =1000
15 minute train leaves 4 times
4x200 =800
2000+1200+1000+800=5000
assuming more than 1 train can be at the station at once
Solve the equation using the zero-product property. (2x − 8)(7x + 5) = 0 x = –2 or x = 7 x = –4 or x = x = 4 or x = x = 4 or x =
Answer:
x = 4 or x = - [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Given
(2x - 8)(7x + 5) = 0
Equate each factor to zero and solve for x
2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4
7x + 5 = 0 ⇒ 7x = - 5 ⇒ x = - [tex]\frac{5}{7}[/tex]
A total of $10,000 is invested in two mutual funds. The first account yields 5% and the second account yields 6%. How much was invested in each account if the total interest earned in a year is $575?
Answer:
$2,500 was invested in the first account while $7,500 was invested in the second account
Step-by-step explanation:
Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments
Now, since we do not know the amount invested , we shall be representing them with variables.
Let the amount invested in the first account be $x and the amount invested in the second account be $y
Since the total amount invested is $10,000, this means that the summation of both gives $10,000
Mathematically;
x + y = 10,000 ••••••(i)
now for the $x, we have an interest rate of 5%
This mathematically translates to an interest value of 5/100 * x = 5x/100
For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100
The addition of both interests, gives 575
Thus mathematically;
5x/100 + 6y/100 = 575
Multiplying through by 100, we have
5x + 6y = 57500 •••••••••(ii)
From 1, we can have x = 10,000-y
let’s substitute this into equation ii
5(10,000-y) + 6y = 57500
50,000-5y + 6y = 57500
50,000 + y = 57500
y = 57500-50,000
y = 7,500
Recall;
x = 10,000-y
so we have;
x = 10,000-7500 = 2,500
What does the denominator of the fraction \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction mean?
Answer: It represents that 2 will be divided into 3 equal parts.
Step-by-step explanation:
Numerator is the top number in a fraction. It represents the total item it has to divide.Denominator is the bottom number in a fraction. it represents the number of equal parts the item is divided into.The given fraction : [tex]\dfrac{2}{3}[/tex]
here, Numerator = 2
Denominator = 3
It represents that 2 will be divided into 3 equal parts.
List some typical benefits an employee might receive on top of their wage?
Answer:
paid vacation
paid medical
401k
Write each of the following expressions without using absolute value.
|a−7|−|a−9|, if a<7
PLEASE HELP!!!! D:
=======================================================
If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that
[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]
Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.
---------
So we have,
|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2
As long as a < 7, the result of |a-7| - |a-9| will always be -2.
---------
As an example, let's say a = 0
|a-7| - |a-9| = |0-7| - |0-9|
|a-7| - |a-9| = |-7| - |-9|
|a-7| - |a-9| = 7 - 9
|a-7| - |a-9| = -2
I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.
What is the slope of the line in the graph? A.2 B.1/2 C.-2 D.-1/2
Step-by-step explanation:
bhdjdjsjshhdfhfbtvyvyvjdjshdjfy
Solve the inequality for y.
y - 9x > 6
please help!!!!!!!
Answer:
y>9x+6
Step-by-step explanation:
y-9x+(9x)>6+(9x)
y>9x+6
Scarlett Squirrel teaches a hula dancing class to young squirrels. 141414 squirrels showed up to class on Monday, 101010 squirrels on Tuesday, 888 squirrels on Wednesday, 101010 squirrels on Thursday, and 121212 squirrels on Friday. Find the mean number of the squirrels
Answer:
93107
Step-by-step explanation:
add all of the numbers together
divide by 5 since there are 5 numbers
you would get 92106.8
so round that up since you cannot have 1/8 of a squirrel
Hope this helps!!
An item is selling for $7,000. This item gets a discount and it is now $4,900. What percentage was the discount?
Answer:
30%Step-by-step explanation:
Discount =$7000-$4900
Discount% =
[tex] \frac{2100}{7000} \times 100 \\ = \frac{210000}{7000 } \\ = \frac{210}{7} = 30[/tex]
On a coordinate plane, a graph shows Street on the x-axis and Avenue on the y-axis. A line is drawn from Tia to Lei. Tia is at (4, 8) and Lei is at (12, 20). Tia lives at the corner of 4th Street and 8th Avenue. Lei lives at the corner of 12th Street and 20th Avenue. The fruit market is Three-fourths the distance from Tia’s home to Lei's home.
Answer:
(10, 17)
Step-by-step explanation:
It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.
Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)
From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.
y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.
The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.
x: 4+6 = 10
y: 8+9=17
The fruit market is at point (10,17)
What is graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates
[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]
[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]
Tia is at P(4, 8) and Lei is at Q(12, 20).
The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1
So,
[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]
Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.
Learn more about graph here:
brainly.com/question/16608196
#SPJ5
Please help me with this question!! TRIGONOMETRY
Work Shown:
sin(angle) = opposite/hypotenuse
sin(35) = 10/x
x*sin(35) = 10
x = 10/sin(35)
x = 17.434467956211 make sure your calculator is in degree mode
x = 17.4
Answer:
[tex]\boxed{17.4}[/tex]
Step-by-step explanation:
sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
sin (35) = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{sin(35)}[/tex]
x = 17.4344679562...
x ≈ 17.4
Six friends went to a restaurant and agreed to share the bill equally. However, two people forgot their wallets so the other four friends' portions of the bill went up by $7 each. How many dollars was the total bill?
Answer:
The total bill was $84
Step-by-step explanation:
Ok so we know a few things, we know that the total cost of the bill is divisible by both 6 and 4, and we know that if we call the total cost of the bill x and the amount each person would pay if it was divided for 6 people y we can write these equations:
[tex]\frac{x}{6}=y[/tex]
[tex]\frac{x}{4}=y+7[/tex]
Now we can substitute the first equation into the second and solve for x
[tex]\frac{x}{4}=\frac{x}{6}+7\\\frac{x}{4}-\frac{x}{6}=7\\\frac{x}{12}=7\\x=7*12=84[/tex]
Therefore, the total bill was $84
sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the 0.025 significance level. H0: μ ≥ 220 H1: μ < 220 Is this a one- or two-tailed test? One-tailed test Two-tailed test
Answer: (upside down fancy u) q5
Step-by-step explanation:
Simply apply the law of conservative (upside down fancy u)
im stuck on this question helm me out I will mark you as brainliest
Answer: it is =4176000000000000
Step-by-step explanation:
(2.9)(100000)(7.2)(10^2)
5(10^−8)
=
(290000)(7.2)(10^2)
5(10^−8)
=
2088000(10^2)
5(10^−8)
=
(2088000)(100)
5(10^−8)
=
208800000
5(10^−8)
=
208800000
5(1/100000000)=
208800000/1
20000000
=4176000000000000
hope i helped
-lvr
Use De Morgan's laws to write negations for the statement. Sam is an orange belt and Kate is a red belt.
A. Sam is an orange belt or Kate a red belt.
B. Sam is not a red belt and Kate is not an orange belt.
C. Sam is not an orange belt and Kate is not a red belt.
D. Sam is not a red belt or Kate is not an orange belt.
E. Sam is not an orange belt or Kate is not a red belt.
Answer:
C. Same is not an orange belt and Kate is not a red belt.
Step-by-step explanation:
The negation for the statement is Sam is not an orange belt or Kate is not a red belt.
What is Negation of De- Morgan's Law?The negation of a conjunction is equivalent to the disjunction of the negation of the statements making up the conjunction. To negate an “and” statement, negate each part and change the “and” to “or”.
Given statement:
Sam is an orange belt and Kate is a red belt.
Now, to make the negation we have to consider the rule "To negate an “and” statement, negate each part and change the “and” to “or”."
So, the negation statement would be
Sam is not an orange belt or Kate is not a red belt.
Learn more about De Morgan's laws here:
https://brainly.com/question/13317840
#SPJ2
if 12 1/2% of a sum of money is $40, what is the TOTAL sum of money?
Answer:
$320
Step-by-step explanation:
Let the total sum of money be $x.
Therefore,
12 1/2% of x = 40
25/2% * x = 40
0.125 * x= 40
x = 40/0.125
x = $320
Thus, total sum of money is $320.
Carrie can inspect a case of watches in 5 hours.James can inspect the same case of watches in 3 hours.After working alone for 1 hour,Carrie stops for lunch.After taking a 40 minute lunch break,Carrie and James work together to inspect the remaining watches.How long do Carrie and James work together to complete the job?
Will mark brainlist if it correct and well explained
Answer:
It takes Carrie and James an hour and a half to finish the job.
Step-by-step explanation:
assuming they have to inspect ONE case of watches.
Carrie can inspect 1/5 case in one hour.
James can inspect 1/3 case in one hour.
Carrie worked alone for 1 hour, so she finished 1/5 of a case.
She leaves 4/5 case to finish.
She had lunch.
After that, Carrie and James worked together for x hours to finish the job.
When they work together, the finish 1/5+1/3 = 8/15 case per hour.
So time to finisher the remaining case
Time = 4/5 / (8/15)
= 4/5 * 15/8
= 3/2 hours
= an hour and a half.
An electronics company designed a cardboard box for its new line of air purifiers. The figure shows the dimensions of the box.
The amount of cardboard required to make one box is___square inches.
a)130
b)111
c)109
d)84
Answer:
130
Step-by-step explanation:
just did test on plato/edmentum..it was correct
84 (the answer above) is incorrect
Answer:
Hi sorry for late respond but the answer in 130!!
Step-by-step explanation:
What is the margin of error for 95% confidence for a sample of size 250 where p = 0.45?
A. 0.0541
B. 0.0775
C. 0.0706
D. 0.0617
Answer:
0.0617
Step-by-step explanation:
so the formula is 1.96[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
P is the proportion (.45) and n is the sample size (250). Inserting these into the problem, we get 1.96[tex]\sqrt{\frac{.45(1-.45)}{250} }[/tex]. Solving this out, you should solve the inside of the square root to get .00099. Take the square root of this, and multiply by 1.96 to get your answer!
This method applies to any problems with the same basic format. Good luck!
The sum of ages Afful and Naomi is 34. In 5 years time , Afful will be 2 times the age on Naomi now. How old are they now.
Answer:
Afful is 21 and Naomi is 13.
Step-by-step explanation:
Let [tex]A[/tex] represent the age of Afful and [tex]N[/tex] represent the age of Naomi.
The sum of their ages is 34. In other words:
[tex]A+N=34[/tex]
In 5 years time, Afful will be two times the age of Naomi now. In other words:
[tex]A+5=2N[/tex]
Solve for the system. Substitute.
[tex]A+N=34\\A=34-N\\34-N+5=2N\\39=3N\\N=13\\\\A=34-N\\A=34-(13)\\A=21[/tex]
Afful is currently 21 and Noami is currently 13.
Answer:
Naomi=x
Afful=2x
In 5 years time= +5
So Naomi=x+5
and and Afful=2x+5
=x+5+2x+5=34
=3x+10=34
Subtract 10 on both sides
3x=24
Divide 3 on both sides
X=8
Check:
X=8
Naomi=16
In 5 years
=16+5=21
Naomi=8+5=13
13+21=34
Hope this helps
Step-by-step explanation:
If you had a cube with a side length of 4, how can your write the calculations in exponential form? What are 2 other ways to read the exponent verbally?
Answer: 4^3
(Four cubed or Four to the power of 3)
Step-by-step explanation:
Select all that apply. If x^2+b/ax+c/a=0 ; then: The sum of its roots = -b/a? The difference of its roots =-b/a? The product of its roots = c/a?The division of its roots = c/a? I can select multiple.
Answer:
The first and the thirdStep-by-step explanation:
[tex]x^2+\frac bax+\frac ca=0\\\\ ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\qquad\quad x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x_1+x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}+\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-2b}{2a}=\dfrac{-b}a\\\\\\x_1\cdot x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\cdot\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\\\\{}\ \ =\dfrac{b^2-b\sqrt{b^2-4ac}+b\sqrt{b^2-4ac}-(\sqrt{b^2-4ac})^2}{2a}=\dfrac{b^2-(b^2-4ac)}{4a^2}=\\\\{}\ \ =\dfrac{b^2-b^2+4ac}{4a^2}=\dfrac{4ac}{4a^2}=\dfrac{c}{a}[/tex]
[tex]x_1-x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}-\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-2\sqrt{b^2-4ac}}{2a}=\frac{-\sqrt{b^2-4ac}}{a}\\\\\\x_1\div x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}\div\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}\,\cdot\,\frac{2a}{-b+\sqrt{b^2-4ac}}=\\\\=\frac{-b-\sqrt{b^2-4ac}}{-b+\sqrt{b^2-4ac}}=\frac{b+\sqrt{b^2-4ac}}{b-\sqrt{b^2-4ac}}=\frac{b^2+2\sqrt{b^2-4ac}+b^2-4ac}{b^2-b^2+4ac}=\frac{2b^2+2\sqrt{b^2-4ac}-4ac}{4ac}=[/tex]
[tex]=\frac{b^2+\sqrt{b^2-4ac}-2ac}{2ac}[/tex]
Which expression is equivalent to
-21/4over -2/3
Answer:
[tex]\frac{9}{4}/\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]-2\frac{1}{4}[/tex] is equilavalent to [tex]-\frac{9}{4\\}[/tex].
[tex]-\frac{2}{3}[/tex] can stay put.
The equation is division so neither answers #2 and #3 are the correct ones because when dividing fractions the second fraction has to be flipped in order to continue multiplying instead.
In addition, when two negatives are put together the answer must always be positive.
Hence the answer is [tex]\frac{9}{4}/\frac{3}{2}[/tex].