Answer:
54 cm
Step-by-step explanation:
27:9=3
4+5+9=18
3×18=54
Matt buys a new fish tank. The fish tank is in the shape of a cuboid. The diagram shows water in the tank. 30 cm 30 cm 100 cm Matt knows 1000 cm' = 1 litre 1 gallons = 4.5 litres He can keep 2 small fish in the tank for every 1 gallon of water in the tank. Matt thinks he can keep more than 36 small fish in the tank. Is Matt correct?
Answer: Yes, but only if he houses 37, 38, 39, or 40 fish
Anything larger than 40 and he'll need more room.
==========================================================
Explanation:
The tank is 30 cm by 30 cm by 100 cm. The volume is 30*30*100 = 90,000 cm^3 which is shorthand for "cubic centimeters".
We're told that 1000 cm^3 = 1 liter, which means the 90,000 cm^3 converts to (90,000)/(1000) = 90 liters.
The fish tank is 90 liters.
Since 1 gallon = 4.5 liters, this means the 90 liter tank converts to 90/(4.5) = 20 gallons
----------------------------
Your teacher mentions "He can keep 2 small fish for every 1 gallon".
Since the tank is 20 gallons, that means he can keep 20*2 = 40 fish. This value is larger than 36, so Matt is correct to a point. If Matt is thinking 37, 38, 39, or 40 fish then he would be correct. If Matt is wanting more than 40 fish, then he'll need a bigger tank.
In short, he can't have any number over 36 and can only have 4 specific values (the four values mentioned earlier).
So technically, Matt is correct, but strong clarification is needed.
Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with z arbitrary
Write each equation in standard form:
3x + y + 3z = 11
x + 2y + z = 7
-x + y + z = 0
In matrix form, this is
[tex]\begin{bmatrix}3&1&3\\1&2&1\\-1&1&1\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}11\\7\\0\end{bmatrix}[/tex]
and in augmented matrix form,
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\1&2&1&7\\-1&1&1&0\end{bmatrix}\right][/tex]
Now for the row operations:
• Add row 1 to -3 (row 2), and add row 1 to 3 (row 3):
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&-5&0&-10\\0&4&6&11\end{bmatrix}\right][/tex]
• Multiply row 2 by -1/5:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&4&6&11\end{bmatrix}\right][/tex]
• Add -4 (row 2) to row 3:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&6&3\end{bmatrix}\right][/tex]
• Multiply row 3 by 1/6:
[tex]\left[\begin{array}{ccc|c}3&1&3&11\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
• Add -1 (row 2) and -3 (row 3) to row 1:
[tex]\left[\begin{array}{ccc|c}3&0&0&\frac{15}2\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
• Mutiply row 1 by 1/3:
[tex]\left[\begin{array}{ccc|c}1&0&0&\frac52\\0&1&0&2\\0&0&1&\frac12\end{bmatrix}\right][/tex]
Then the solution to the system is (x, y, z) = (5/2, 2, 1/2).
One of the angles of a pair of complementary angles is 50°. Find the ratio of the pair of complementary angles
Answer:
4:5
Step-by-step explanation:
A pair of complementary add up to 90, given that one of them is 50, we can do this: x + 50 = 90
solve it and we get x = 40
40 + 50 = 90, so 40 and 50 are the pair of complementary angles.
As for it's Ratio, we can just get the pair and have it as 40:50 but we can reduce it to 4:5
Blood pressure values are often reported to the nearest 5 mmhg (100, 105, 110, etc.). the actual blood pressure values for nine randomly selected individuals are given below.
108.6 117.4 128.4 120.0 103.7 112.0 98.3 121.5 123.2
Required:
a. What is the median of the reported blood pressure values?
b. Suppose the blood pressure of the second individual is 117.7 rather than 117.4 (a small change in a single value). What is the new median of the reported values?
c. What does this say about the sensitivity of the median to rounding or grouping in the data?
Answer:
Step-by-step explanation:
Arranging the data in the ascending order:
108.6 98.3 103.7 112 117.4 120 121.5 123.2 128.4
The median is the middle value of the data set:
a)
Hence,
median = 117.4
b)
When the value of blood pressure is 117.7 instead of 117.4 then the median will be:
Median = 117.7
c)
This indicates that the median of a well sorted set of data is depends upon the middle value of the data set.
For the given piecewise function, evaluate for the specified value of x.
Answer:
g(-3) = 1
Step-by-step explanation:
The x-value -3 lies within the given interval x ≤ -3, and so the correct piecewise function is x + 4, not -4 or -1. Evaluating x + 4 at x = -3 yields 1.
Thus, g(-3) = 1
The required value of the function g(x) at x = -3 , g(-3) is +1.
Given that,
A function is given with their domain,
g(x) = x + 4 when x≤
g(x) = 4 when -3 < x < 3
g(x) = - 1 when x ≥ 3
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here, Function has been given with their respective limit in which the function is defined,
For the value of g(-3) the value of x = -3 lies in the limit x ≤ -3
So for this limit, we have a function,
g(x) = x + 4
g(-3) = - 3 + 4
g(-3) = +1
The required value of the function g(x) at x = -3 , g(-3) is +1.
learn more about function here:
brainly.com/question/21145944
#SPJ5
Find the product of these complex numbers.
(8 + 5)(6 + 3) =
What is the value of the expression below?
e^In 4
O A. 12
B. 3
C. 4.
D. 8
SUBMI
Answer:
C. 4
Step-by-step explanation:
ln(4) = the power of e to get 4.
and then we put e to the power of that answer, so the result must be 4.
Write the equation of each line in slope intercept form. Slope is -6, and (1,-2) is on the line
What is the value of the expression 10(n-6) when 4=14
Answer:
it's going to be 4n so its going to be 4...
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
Assuming you meant when n=14
10(n-6)
plug in 14 for n
10(14-6)
work out parenthesis first
10(8)=
80
821) The integon which is 15 more than - 55 is
Answer:
-40
Step-by-step explanation:
-55 + 15 = x
-40 =x
what value makes the equation
Answer:
n = .25
Step-by-step explanation:
For the equation to be true, both sides must be equal.
20 * 4 * 3 * n = 5 * 12
240 * n = 60
n = 60/240
n = .25
Answer:
1/4
Step-by-step explanation:
20×n×4×3=5×12
or, 240n=60
or, n=60/240
or, n=1/4
Answered by GAUTHMATH
Find the lengths the missing side
Answer:
Long leg = 10√3Short leg = 10Hypotenuse = 20Step-by-step explanation:
Concept:
Here, we need to know the idea of a special triangle 30-60-90.
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.
The ratio between the corresponding side of each angle is 1 : √3 : 2
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
30-60-90 ⇔ 1 : √3 : 2
Given the side corresponding to 90° is 20
30° : 90° = 1 : 2
30° : 20 = 1 : 2
30° = 10
30° : 60° = 1 : √3
10 : 60° = 1 : √3
60° = 10√3
Hope this helps!! :)
Please let me know if you have any questions
4. Five cards are randomly chosen from a deck of 52 (13 denominations with 4 suits). a. How many ways are there to receive 5 cards from a deck of 52
Answer:
There are 2,598,960 ways to receive 5 cards from a deck of 52.
Step-by-step explanation:
The order in which the cards are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
a. How many ways are there to receive 5 cards from a deck of 52?
[tex]C_{52,5} = \frac{52!}{5!(47)!} = 2598960[/tex]
There are 2,598,960 ways to receive 5 cards from a deck of 52.
An organic farm has been growing an heirloom variety of summer squash. A sample of the weights of 40 summer squash revealed that the mean weight is 402.7 grams and the standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 summer squash exceeds 405.5 grams?
a. 0.3783.
b. 0.0228.
c. 1.0000.
d. 0.5000.
Answer:
b. 0.0228
Step-by-step explanation:
We are given that
n=40
Mean,[tex]\mu=402.7 g[/tex]
Standard deviation, [tex]\sigma=8.8[/tex]g
We have to find the probability hat the mean weight for a sample of 40 summer squash exceeds 405.5 grams.
[tex]P(x>405.5)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}>\frac{405.5-402.7}{\frac{8.8}{\sqrt{40}}})[/tex]
[tex]P(x>405.5)=P(Z>\frac{2.8}{\frac{8.8}{\sqrt{40}}})[/tex]
[tex]P(x>405.5)=P(Z>2.01)[/tex]
[tex]P(x>405.5)=1-P(Z\leq 2.01)[/tex]
[tex]P(x>405.5)=1-0.977784[/tex]
[tex]P(x>405.5)=0.022216[/tex]
Hence, option b is correct.
What is the slope of the line?
-3
-1/3
1/3
3
Answer:
D) 3
Step-by-step explanation:
Rise/run, rise is 3, run is 1
Answer:
3
Step-by-step explanation:
Pick two points on the line
(0,0) and ( 1,3)
The slope is found by
m = ( y2-y1)/(x2-x1)
= ( 3-0)/(1-0)
= 3/1
= 3
Find the equation of the line passing through (4,1) and perpendicular to the line whose equation is 1x-3y-4=0
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Answer:
3x +y -13 = 0
Step-by-step explanation:
The perpendicular line will have the variable coefficients swapped and one of them negated. The new constant will be appropriate to the given point.
3(x -4) +1(y -1) = -0
3x +y -13 = 0
_____
Additional comment
The given equation is in "general form", so that is the form of the equation we have given as the answer. This form is convenient in that the general form equation for a line through the origin, ax+by=0, is easily translated to make it pass through a point (h, k): a(x -h) +b(y -k) = 0. Eliminating parentheses puts the equation back into general form.
PLEASE HELP ASAPPPPPP!!!! (answer in decimal)
Answer:
465/1178 = .395 = 39.5%
Step-by-step explanation:
224 + 245
224+ 387 + 245 + 322
465/1178 = .395 = 39.5%
I need help:/ I’m in college
Step-by-step explanation:
Amount of acid = 14.9% of 331 mL solution
= 0.149×(331 mL)
= 49.3 mL acid
Which similarity statement is true?
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Answer:
(a) ΔWZY ~ ΔWXZ ~ ΔZXY
Step-by-step explanation:
In order for the similarity statement to be correct, the corresponding sides need to be listed in the same order.
A: ΔWZY lists sides in order short leg (WZ), long leg (ZY).
ΔWXZ lists sides in order short leg (WX), long leg (XZ).
ΔZXY lists sides in order short leg (ZX), long leg (XY).
The first similarity statement is correct.
__
You can compare this to an incorrect one, the last one, for example.
ΔYZW lists sides in order long leg (YZ), short leg (ZW).
ΔXZW lists sides in order long leg (XZ), hypotenuse (ZW). Hypotenuse and short leg are not corresponding sides, so the similarity statement is incorrect.
Hello everyone can someone answer this question please
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Answer:
(a) 2
Step-by-step explanation:
Each inch is 2.54 cm, so 5.08 cm is ...
x / (5.08 cm) = (1 in) / (2.54 cm)
x = (1 in)(5.08/2.54) = (1 in)(2)
x = 2 in
5.08 cm equals 2 inches.
Solve the inequality (help please)
Answer:
v<1 23/25
Step-by-step explanation:
The inequality simplifies to 48/25, which is equivalent to 1 23/25.
Two planes are the same altitude. From the airport , one plane is 50 km away in the direction of N°60 E and another is 80 km away in the direction of S50° E .How far apart are the two planes
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Answer:
78.5 km
Step-by-step explanation:
Measured at the airport, the angle between the two planes is ...
180° -60° -50° = 70°
The law of cosines tells us the distance between the planes is ...
d = √(50² +80² -2·50·80·cos(70°)) ≈ √6163.84 ≈ 78.5 . . . km
The planes are about 78.5 km apart.
PLEASE DONT AWNSER ANYTHING RANDOM I REALLY NEED THIS AND DO YOUR OWN AWNSER
Which statements about the box plot are correct? Check all that apply.
A box and whisker plot. The number line goes from 30 to 80. The whiskers range from 34 to 76, and the box ranges from 42 to 70. A line divides the box at 46.
Fifty percent of the data values lies between 34 and 46.
Seventy-five percent of the data values lies between 42 and 70.
It is unlikely that there are any outliers.
The interquartile range is 24.
The range is 36.
Answer:
Fifty percent of the data values lies between 34 and 46.
It is unlikely that there are any outliers.
Step-by-step explanation:
drawing out this box plot and looking online for a picture of the same plot:
From the box plot:
median=46
Q1=42
Q3=70
Q3-Q1= IQR=70-42=28
max=76
min=34
Range=max-min=76-34=42
no outliers seen from boxplot
Answer:
that person is right
Step-by-step explanation:
Y
X
Pls help me you’ll get 29 points
Answer:
x = 60
Step-by-step explanation:
The sum of the angles of a triangle add to 180
x+x+x = 180
3x = 180
Divide by 3
3x/3 =180/3
x = 60
The diameter of the base is the cone measured 8 units. The height measures 6 units.
What is the volume of the cone?
A) 24 π cubic units
B) 32 π cubic units
C)48 π cubic units
D)64 π cubic units
There were 230 shoppers at an electronics store on opening day. The specials that day allowed 21% of shoppers to receive a free set of earbuds and 25% of shoppers to receive $5 off their first purchase. Answer parts a and b.
a. About how many shoppers received a free set of earbuds? Use an equivalent fraction to estimate.
b. About how many shoppers received $5 off their first purchase? Round the number of shoppers to the nearest whole number.
Answer:
a) About 48 of the shoppers, that is [tex]230\frac{21}{100}[/tex] of the shoppers, received a free set of earbuds.
b) About 58 shoppers, that is [tex]\frac{230}{4}[/tex] received $5 off their first purchase.
Step-by-step explanation:
a. About how many shoppers received a free set of earbuds?
21% out of 230. So
[tex]230\frac{21}{100} = 2.3(21) = 48.3[/tex]
About 48 of the shoppers, that is [tex]230\frac{21}{100}[/tex] of the shoppers, received a free set of earbuds.
b. About how many shoppers received $5 off their first purchase?
25% out of 230, so:
[tex]230\frac{25}{100} = 230\frac{1}{4} = \frac{230}{4} = 57.5[/tex]
About 58 shoppers, that is [tex]\frac{230}{4}[/tex] received $5 off their first purchase.
If 400 patrons visit the park in March and 550 patrons visit in April, the total number of patrons who
visited the park over the two months falls into all of the following categories except
O real numbers
O rational numbers
o irrational numbers
Suppose that the functions and g are defined for all real numbers x as follows.
f(x)=x+6
g(x) = 2x + 6
Write the expressions for (f-g)(x) and (fg)(x) and evaluate (f+g)(1).
Answer:
Step-by-step explanation:
Given functions are,
f(x) = x + 6
g(x) = 2x + 6
(f - g)(x) = (x + 6) - (2x + 6)
= -x
(f . g)(x) = f(x) × g(x)
= (x + 6)(2x + 6)
= 2x² + 6x + 12x + 36
= 2x² + 18x + 36
(f + g)(x) = (x + 6) + (2x + 6)
= 3x + 12
(f + g)(1) = 3(1) + 12
= 15
What is the range for the following set of numbers?57, -5, 11, 39, 56, 82, -2, 11, 64, 18, 37, 15, 68
so
82-(-2)
=84
then ur answer is 84
(-1/2^5)×2^3×(3/4^2) [EVALUATE]
Step-by-step explanation:
here's the answer to your question
