2x + y - 3z , x = 2/5 , y = 2/3 , z = 1/6 what does it equal
29/30
2x + y - 3z
2 x 2/5 + 2/3 - 3x1/6
4/5 + 2/3 - 3/6
x 3 x 5
12/15 + 10/15 - 3/6
22/15 - 3/6
x2. x5
44/30 - 15/30
= 29/30
Hope this helps!
it takes 3 eggs to make two dozen cookies. About what fraction of an egg are in two cookies
keeping in mind that two dozen cookies is just 24 cookies, then
[tex]\begin{array}{ccll} eggs&cookies\\ \cline{1-2} 3 & 24\\ x& 2 \end{array} \implies \cfrac{3}{x}=\cfrac{24}{2}\implies \cfrac{3}{x}=12\implies 3=12x \\\\\\ \cfrac{3}{12}=x\implies \cfrac{1}{4}=x[/tex]
A hotel is building a large new aquarium for their lobby. They know the length from the top corner to the opposite bottom corner is 13 feet long, the height is 12 feet and the length is 4 feet. Solve for the width and then determine the volume in cubic feet of water it will take to fill the aquarium
Answer:
3 ft, 144 ft³Step-by-step explanation:
Find the width as below
l² + w² + h² = d², where l- length, w- width, h- height, d- the distance between top and bottom cornersSubstitute the values and solve for w
4² + w² + 12² = 13²w² + 160 = 169w² = 9w = 3 feetNow find the volume
V = lwhV = 4*3*12 = 144 ft³Answer:
width = 3ft
volume = 144 ft³
Step-by-step explanation:
Pythagoras Theorem
[tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
The diagonal of the base of the aquarium, its height, and the length from the top corner to the opposite bottom corner forms a right triangle. As we know two of the lengths, we can use Pythagoras Theorem to calculate the unknown length (diagonal of base).
Given:
a = height of aquarium = 12 ftb = diagonal of basec = top corner to opposite corner = 13 ft[tex]\implies \sf 12^2+b^2=13^2[/tex]
[tex]\implies \sf b=\sqrt{13^2-12^2}[/tex]
[tex]\implies \sf b=5[/tex]
Now we know the length of the diagonal of the base, we can again use Pythagoras Theorem to find the width of the aquarium.
Given:
a = length of aquarium = 4 ftb = width of aquarium c = diagonal of base = 5 ft[tex]\sf \implies 4^2+b^2=5^2[/tex]
[tex]\sf \implies b=\sqrt{5^2-4^2}[/tex]
[tex]\sf \implies b=3[/tex]
Therefore, the width of the aquarium is 3 ft.
As the aquarium is modeled as a rectangular prism:
[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf width \times length \times height\\ \implies \textsf{Volume of aquarium} & = \sf 3\:ft \times 4\:ft \times 12\:ft\\& = \sf 144 \:\:ft^3\end{aligned}[/tex]
Which ordered pairs match the mapping diagram? O (1, 0), (7, 2), (3, 1), (-1, 1), (-7, -6) (0, 1), (2, 7), (3, 4), 4, 1), -6, 7) O(0, 1), (0, 4), (0, 7), (2, 7), (6, 7) (0 1), (2, 7), 3, 4), (4, 1), (6, 7)
Answer:
I've done this b4
(0, 1), (2, 7), (3, 4), (-4, 1) , (-6, 7)
How does your Web browser get a file from the Internet? Your computer sends a request
for the file to a Web server, and the Web server sends back a response. For one
particular Web server, the time X (in seconds) after the start of an hour at which a
randomly selected request is received has the uniform distribution shown in the figure. in
The probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour is 0.0833 or 8.33%.
How does your Web browser get a file from the Internet?Your computer sends a request for the file to a Web server, and the Web server sends back a response.
For one particular Web server, the time X (in seconds) after the start of an hour at which a randomly selected request is received has the uniform distribution shown in the figure.
The probability of finding value less than the X is,
[tex]P(X < x)=\dfrac{x-a}{b-a}[/tex]
Here, a and b are two bonds of uniform distribution.
The probability distribution of X can be modeled by a uniform density curve on the interval from 0 to 3600 seconds, as shown in the given figure.
The probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour has to be found out. Thus,
[tex]P(X < x)=\dfrac{300-0}{3600-0}\\P(X < x)=0.0833\\P(X < x)=8.33\%[/tex]
Thus, the probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour is 0.0833 or 8.33%.
Learn more about the probability distribution here;
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I need help with this
your older sister tells you that you seem to be short for your age. in school, your teacher measured your height and that of your classmates to compute for your BMI. you teacher tells you that your height belongs to the 9th decile in the class. assuming you and your classmates have similar ages, would you agree with what your sister says? why?
Answer:
No.
Step-by-step explanation:
No, because the 9th decitile is equal to the 90th decitile, and so that means that you're tall.
A city council is considering funding a proposal to create a new city park. The council members will fund the proposal if they conclude that more than 60 percent of the city residents support the proposal. A survey of 2,000 randomly selected city residents will be conducted to investigate the level of support for the proposal. Let X represent the number of city residents in the sample who support the proposal. Assume that X is a binomial random variable.
A. Determine the mean and standard deviation of the random variable X, assuming that 60 percent of city residents support the proposal
B. Assume that 60 percent of city residents support the proposal. Use a normal approximation and the mean and standard deviation from part a to determine the values of k1 and k2 (the left and right boundaries of the middle .997 area)
C. The survey was conducted, and 1293 of the 2000 city residents supported the proposal. Do your answers in part b and the survey support the funding of the proposal? Justify your answer.
The mean and standard deviation of the random variable X if 60 percent of city residents support the proposal is 1200 and 21.9 respectively.
How to calculate the mean?From the information given, the mean of the binomial variable x will be:
= 2000 × 60%
= 2000 × 0.6
= 1200
The standard deviation will be:
= ✓n × ✓p(1 - p)
= ✓1200 × ✓0.4
= ✓480
= 21.9
Also, the mean and standard deviation to determine the values of k1 and k2 will be -3 and 3.
Lastly, the test statistic will be:
= (0.65 - 0.60)/(✓0.60 × (0.40) /2000
= 0.05/✓0.24/2000
= 0.05/0.011
= 4.55
The z value at 5% significance level is 1.64. This supports the funding of the proposal.
Learn more about mean on:
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what is the greatest common factor of 15, 5, and 50
Answer:
Therefore, the GCF of 15 and 50 is 5.
Step-by-step explanation:
Solution:
The greatest number that divides 15 and 50 exactly is their greatest common factor, i.e. GCF of 15 and 50.
⇒ Factors of 15 and 50:
Factors of 15 = 1, 3, 5, 15
Factors of 50 = 1, 2, 5, 10, 25, 50
Therefore, the GCF of 15 and 50 is 5.
Are the triangles similar? If so, how do you know?
A soccer player gets 2 points for a goal and 1 point for an assist. If the combined number of goals and assists that a player has is 24, and the total number of points that the player has is 42, which system of equations can be used to determine the number of goals and assists the player has? Assume g represents the number of goals and a represents the number of assists.
g + a = 24. g + 2 a = 42.
g + a = 24. 2 g + a = 42.
g + a = 42. g + 2 a = 24.
g + a = 42. 2 g + a = 24.
Answer:
g + a = 24. 2 g + a = 42.
Step-by-step explanation:
Each goal gets 2 points and each assist gets 1 point
If # of goals = g , and you get 2 points for each goal, then points acquired by goals can be represented by 2g
If # of assists = a, and you get 1 point for each assist, then points acquired by assists can be represented by a
The total # of points the player had was 42. This means that 2g + a = 42 (this is the first equation)
We are also told the player scored a total of 24 goals and assists. If g = # of goals and a = of assists, then g + a = 24 (this is the second equations)
So the two equations are g + a = 24. 2 g + a = 42.
Answer:
g + a = 24. 2 g + a = 42.
Step-by-step explanation
trust
What is the perimeter, rounded to the nearest tenth? 24.2 ft 28.3 ft 48.5 ft 56.8 ft
Answer:
48.5 ft
Step-by-step explanation:
Suppose the correlation coefficient between a student's homework score & their test score is found to be
0.92.
0.92.
What conclusion can you make about the relationship between a student's homework & test scores based on the correlation coefficient?
A
Students score an average of 92%92% on their homework & tests
B
A student's homework & test score have a strong association
C
There is a difference of 0.920.92 points from a student's homework & test grades
D
Only 92%92% of students pass on their homework & test scores
Answer:
A
Step-by-step explanation:
2x - 5 = 3 what does X equal to?
Given the following construction, which of the following can you now create?
Select ALL that apply.
options:
square
equilateral triangle
rhombus
the midpoint of segment AB
perpendicular bisector of segment AB
square is the correct answer
what is point?
(in mathematics)
Step-by-step explanation:
a microscopic membrane of lipids and proteins which forms the external boundary of the cytoplasm of a cell or encloses a vacuole, and regulates the passage of molecules in and out of the cytoplasm
thx for ur poi.nts buddy
kese h.o aap
2. How do you know if two ordered pairs lie along the same vertical line?
Their x-coordinates are the same.
The line always has the equation x = -2.
Their y-coordinates are the same.
The line always passes through the origin.
Answer:
1st option
Step-by-step explanation:
A verical line parallel to the y- axis has equation
x = c ( c is the value of the x- coordinates the line passes through )
thus the x- coordinates are the same
You have 31 coins consisting of nickels and
dimes. The coins total $2.25. How many coins
are nickels? How many are dimes?
Answer:
There are 14 dimes and 17 nickels.
Step-by-step explanation:
Let x be number of nickels and let y be number of dimes.
Given that the total is $2.25 and there are 31 coins, we know that:
[tex]0.05x +0.10y = 2.25[/tex]
[tex]x+y = 31[/tex]
Solving for x yields:
[tex]x=31-y[/tex]
We then proceed by plugging that back into the previous equation:
[tex]0.05(31-y)+0.10y=2.25[/tex]
[tex]1.55 - 0.05y +0.10y = 2.25\\[/tex] --> Distribute
[tex]1.55 +0.05y=2.25[/tex] --> add y's together
[tex]0.05y=0.7[/tex] --> subtract 1.55
[tex]y=14[/tex] --> divide by 0.05
Therefore, x must equal 17, which means you have 14 dimes and 17 nickels.
marty's dog eats about 5 pounds of dog food every four days. what is the rate the dog eats his food in pounds per day?
Answer:
5/4 pounds
Step-by-step explanation:
Using unitary method:
4 days-------5 pounds
1 day---------5/4 pounds
Solve for x (literal equations):
c=b-bx show work
Answer:
x = [tex]\frac{b-c}{b}[/tex]
Step-by-step explanation:
c = b - bx ( add bx to both sides )
bx + c = b ( subtract c from both sides )
bx = b - c ( divide both sides by b )
x = [tex]\frac{b-c}{b}[/tex]
i need to find volume of this triangular pyramid
Answer:
135 Cubic Inches
Step-by-step explanation:
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!
Use the line plot to answer the questions, and describe how you figured out the answer to each question. 80 POINTS IF ANSWERD AND GIVING BRAINLIEST
How many boxes did Lamar sell?
How many more boxes did John sell than Suzy?
How many more boxes would Lizzy have to sell to equal how many Mark sold?
X = 5 boxes
figure out the X for each person
Lizzy = 5 XLizzy sold: 5 * 5 = 25 boxes
Suzy = 1 XSuzy sold: 5 * 1 = 5 boxes
John = 3 XJohn sold: 5 * 3 = 15 boxes
Mark = 8 XMark sold: 5 * 8 = 40 boxes
Lamar = 4 XLamar sold: 5 * 4 = 20 boxes
→ How many boxes did Lamar sell?
Answer: 20 boxes
→ How many more boxes did John sell than Suzy?
Answer: 10 boxes
workout: 15 boxes - 5 boxes = 10 boxes more
→ How many more boxes would Lizzy have to sell to equal how many Mark sold?
Answer: 15 boxes
workout: 40 boxes - 25 boxes = 15 boxes more
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here we go ~
Each Cross (X) represents 5 boxes
Now, let's move on to questions :
1. How many boxes Lamar sell ~-) 4 Cross = 4 × 5 = 20 boxes
2. How many more boxes did John sell than Suzy ?-) (4× Cross) - (1 × cross)
-) (3 × 5) - (5)
-) 25 - 5 = 10more boxes than Suzy
How many more boxes would Lizzy have to sell to equal how many Mark sold ?-) (8 × Cross) - (5 × Cross)
-) (8 × 5) - (5 × 5)
-) 40 - 25
-) 15 more boxes to be sold to get equal to the number of boxes mark sold.
a rectangular shoebox has a volume of 160 cubic inches. the base of the shoebox measures 8 inches by 5 inches. how long is the shoebox?
i do not know this answer
A large box of crackers away 20 Oz if James needs 3 pounds of crackers for a party how many boxes of crackers should he buy
Answer:
James will need to buy 3 boxes of crackers for the party.
Step-by-step explanation:
remember: 16oz=1 pound
If James needs 3 pounds of crackers, and each box is 20oz, that means each box is a little over 1 pound. (1.25 pounds to be exact). So, we know that he needs to buy 3 boxes of crackers. This is because 20×3=60 ounces which is 3.75 pounds. Meaning, 3 boxes is the correct answer since we can't cut a box in half.
(2,132 x 10 -15 - (4,695 x 10 )
Answer:
25,645
________________________________________________________
SolveFirst, find 4,695 × 10
[tex]4,695 * 10 = 46,950[/tex]
Next, do 2,132 × 10
[tex]2,132 * 10 = 21,320[/tex]
Now, subtract by 15.
[tex]21,320 - 15 = 21,305[/tex]
Lastly, subtract by the product you found earlier.
[tex]46,950 - 21,305 = 25,645[/tex]
________________________________________________________
Questions?Ask in comments box.
PLEASE ANSWER THIS QUICKLY!
Consider the circle shown.
1. What is the length of the minor arc DE? (EXPRESS YOUR ANSWER AS A SIMPLIFIED FRACTION IN TERMS OF PI).
2. What is the length of the major arc DGE? (EXPRESS YOUR ANSWER AS A SIMPLIFIED FRACTION IN TERMS OF PI).
Answer:
minor arc DE: (23/9)π
Major arc DGE:(49/9)π
Step-by-step explanation:
This is a simple problem.
First solve the circumference of the circle: 2π (4).
then use the length formula
L=(x*c)/360
and then plug in, so first we use 115 as x(which is degrees) to find de
so
L = (115* 2π (4))/360
and you will get (23/9)π
To get the major arc you have to get the outside angle, so 360-115, and you do the same thing but with 245 as x.
Hope this helps and im correct!
Work out
21
% of
£
944.13
Give your answer rounded to 2 DP. I need right awnsers you can use calculators
Answer: £198.27
Step-by-step explanation:
944.13x0.21=198.2673Rounded to 2 decimal places that is 198.279. The value of U.S. postage stamps increases -5% per year. The current price is 55€. Estimate what the price will be in 20 years
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &\$0.55\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &20\\ \end{cases} \\\\\\ A=0.55(1 + 0.05)^{20}\implies A=0.55(1.05)^{20}\implies A\approx 1.46[/tex]
.If Rashard wants to earn $300 interest in 2 years from an account that earns an annual simple
interest rate of 8%, how much must he invest initially?
Answer:
$ 1875
Step-by-step explanation:
Richard invests some amount P. He want the money he invested to gain an interest of $300.
A = P(1 + n×i)
A = P + 300
i = 0.08
n = 2
P + 300 = P(1 + 2×0.08)
P + 300 = P(1.16)
300 = 1.16P - P
300 = 0.16P
300/0.16 = 0.16P/0.16
P =300/0.16
P = $1875
Richard should invest $1875 if he wants an interest of $300 in 2 years.