5. How long is the diagona of a 12 ft-by-16 ft rectangular garden?
A. 6 ft
B. 14 ft
C. 18 ft
D. 20 ft
Answers
Answer:
The correct answer is option D, 20ft
Step-by-step explanation:
After drawing the picture below, you can just use pythagorean theorem to solve for the diagonal, or the hypotenuse in this case;
(Length)² + (Width)² = (Diagonal)²
(16)² + (12)² = (Diagonal)²
256 + 144 = (Diagonal)²
400 = (Diagonal)²
[tex]\sqrt{400}[/tex] = [tex]\sqrt{Diagonal^{2} }[/tex]
20 = Diagonal
Hope this helps!
Answer:
D. 20 ft
Step-by-step explanation:
Use pythagorus! We can imagine the rectangle is split into 2 equal triangles, one side of the triangle being 12, and the width being 16.
Pythagorus theorum is used to calculate the hypotenuse (long side) of a right-angled triangle. This is the formula:
[tex]\sf{a^{2}+b^{2} = c^{2} }[/tex]
So, we do 12^2 (squared) + 16^2 =
144 + 256 = 400
Now, we have to find the square root of 400, which is equal to
20
So our answer is 20ft
Hope this makes sense! If you need further explanation, do let me know...
- profparis
Related Questions
A shopkeeper bought 30 pens for 150 and sold 20 of them for 140. Find his profit or loss percentage
Answers
Answer:
Because the cost price of 30 pens = Rs. 150
So, the cost price of 1 pen = 150/30 =5
so, the cost price of 20 pens =
Rs. 5 x 20 = 100
Cp is Rs. 100
Sp is Rs. 140
So, profit = 140-100 = Rs. 40
Profit % = (Profit x 100)xCp
=(40 x 100)/100
= 4000/100
= 40% profit
Step-by-step explanation:
The rectangles below have the same perimeter.
Answers
AS BASICALLY IF I TELL U THE CORRECT ANSWER OF ORANGE RECTANGLE IS16ML2
Answer:
16 mi squared
Step-by-step explanation:
Gray perimeter :16 (5,5,3,3)
Orange perimeter :16 (4,4,4,4)
Area of Gray :15 (5x3)
Area of Orange :16(4x4)
Solve the inequality.
7x ≥ –7
A.x ≤ –1
B.x ≥ 14
C.x ≥ –1
D.x > –14
Answers
25 76
Step-by-step explanation:
Answer: C ( x ≥ -1 )
Step-by-step explanation:
Here is an expression.
1} :
Which situation could the expression model?
O A. A bag of almonds weighs 13 pounds. When of
the bag of almonds remain, how many pounds do
the almonds weigh?
B. How many cup servings of yogurt are in 1 cups
of yogurt?
o C. A student made 6 bows from 1 yards of ribbon.
How many bows can be made from yard of
ribbon?
OD. A girl has 1 cups of soup. She eats of the soup.
How many cups of soup remain?
Answers
Answer:
b
Step-by-step explanation:
is the situation could the expression model.
4x + 9y - 9 = 0
y intercept =
Answers
The school newspaper wants to do an article about DLDs at DHS by interviewing the Dacula Leadership Team. They wish to get quotes from 8 of the 30 seniors on DLT. 18 of the senior DLT members are athletes, while 12 are non-athletes. Determine the probability that the newspaper staff receives quotes from exactly 3 athletes. Round to two decimal places.
Answers
The binomial distribution is applicable when only two outcomes are possible. The probability that the newspaper staff receives quotes from exactly 3 athletes is 0.1238.
What is Binomial distribution?A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,
[tex]P(x) = ^nC_x p^xq^{(n-x)}[/tex]
Where,
x is the number of successes needed,
n is the number of trials or sample size,
p is the probability of a single success, and
q is the probability of a single failure.
Given that 18 of the senior DLT members are athletes, therefore, the probability of a DLT member being an athlete is,
[tex]P = \dfrac{18}{30} = \dfrac{6}{10} = 0.6[/tex]
Also, 12 of the senior DLT members are non-athletes, therefore, therefore, the probability of a DLT member being a non-athlete is,
[tex]q = \dfrac{12}{30} = \dfrac{4}{10} = 0.4[/tex]
Now, using the binomial distribution the probability that the newspaper staff receives quotes from exactly 3 athletes can be written as,
[tex]P(x) = ^nC_x p^xq^{(n-x)}\\\\P(x=3) = ^8C_3\cdot (0.6)^3\cdot (0.4)^{(8-3)}\\\\P(x=3) = ^8C_3\cdot (0.6)^3\cdot (0.4)^{(5)}\\\\P(x=3) = 0.1238[/tex]
Hence, the probability that the newspaper staff receives quotes from exactly 3 athletes is 0.1238.
Learn more about Binomial Distribution:
https://brainly.com/question/14565246
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What is 79,300 written in scientific notation?
O
A. 7.93 x 104
OB. 7.93 x 105
O Ос C. 79.3 x 104
OD. 79.3 x 105
Answers
Answer:
A. 7.93 x 104
Step-by-step explanation:
Use the regression calculator to compare the teams’ number of runs with their number of wins. a 2-column table with 9 rows. column 1 is labeled r with entries 808, 768, 655, 684, 637, 619, 613, 609, 563. column 2 is labeled w with entries 93, 94, 66, 81, 86, 75, 61, 69, 55. the equation of the trend line is
Answers
The equation of the trend line is ŷ = 0.15x - 23.21
How to determine the average rate of change of the trend line?The points are given as:
hr =>808, 768, 655, 684, 637, 619, 613, 609, 563
w => 93, 94, 66, 81, 86, 75, 61, 69, 55.
Using a graphing calculator, we have the following calculation summary:
Sum of X = 5956Sum of Y = 680Mean X = 661.7778Mean Y = 75.5556Sum of squares (SSX) = 50569.5556Sum of products (SP) = 7547.1111The regression equation is represented as:
ŷ = bX + a
Where:
b = SP/SSX
b = 7547.11/50569.56
b = 0.14924
a = MY - bMX
a = 75.56 - (0.15*661.78)
a = -23.20961
This gives
ŷ = 0.14924X - 23.20961
Approximate
ŷ = 0.15x - 23.21
Hence, the equation of the trend line is ŷ = 0.15x - 23.21
Read more about trend lines at:
https://brainly.com/question/2589459
Answer:
D.) y = 0.15 - 23.21
Step-by-step explanation:
I took the assignment
Measuring the height of a tree is usually more difficult than measuring the diameter of the tree. Therefore, many researchers use regression models to predict the height of a tree from its diameter measured at 4 feet 6 inches from the ground. The following computer output shows the results of a linear regression based on the heights, in feet, and the diameters, in inches, recorded from 31 felled trees.
Estimate Std Error t-value Pr(>|t|)
Intercept 62. 031 4. 383 14. 15 0. 0000
Diameter 1. 054 0. 322 0. 2028 3. 27
Required:
What is a 95 percent confidence interval for the slope of the population regression line?
Answers
Measuring the height of a tree is usually more difficult than measuring the diameter of the tree, confidence interval for the slope is mathematically given as
C=(0.396, 1.712)
What is a 95 percent confidence interval for the slope of the population regression line?Generally, the equation for the confidence interval is mathematically given as
[tex]C=\beta-tn-2, \alpha /2 (S.E)[/tex]
Where
[tex]\beta=1.054[/tex]
Therefore
C=(1.054-t29, 0.025*0.322)
C=(0.396, 1.712)
In conclusion, the 95 percent confidence interval is
C=(0.396, 1.712)
Read more about Confidence interval
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The Dolphins' hockey coach kept track of how many goals the team scored in the first half of their season.
Answers
Answer:
the median is 3 for your question
solve the system of linear equations by graphing
x+y=18
y=x+12
Answers
Answer:
it equals =204 y=12
Nikkita sold her old textbooks for $54 a piece. When she was done, she had $324, but she still had 8 textbooks left. How many textbooks did she start with?
Answers
Answer:
14 :D
Step-by-step explanation:
First we must divide!!
324/54 = 6
Now we add :)
6 + 8 = 14
Have an amazing day!!
Please rate and mark brainliest!!
What are the approximate dimensions of the rug? round each dimension to the nearest tenth of a foot. 10.4 feet by 7.4 feet 11.1 feet by 8.1 feet 13.4 feet by 10.4 feet 14.1 feet by 11.1 feet
Answers
Step-by-step explanation:
10.4feet by 7.4feet11.1 feet by 8.1 feet
10m^2n+30mn^2+5mn
factor the polynomial
Answers
[tex] \: [/tex]
Explanation :
So, here we are to factor the polynomial :
[tex]\\ \longrightarrow \sf \qquad10m^2n+30mn^2+5mn\\ \\[/tex]
[tex] \longrightarrow \sf \qquad5mn(2m+6n + 1)\\ \\[/tex]
Some points to know :
Factorisation is the reverse process of multiplucation.The Factorisation is the process of finding two or more expressions such that their product is the given expressionAnswer:
[tex]\boxed{5\left(6mn^{2}+mn+2\left(m^{n}\right)^{2}\right)}[/tex]
Step-by-step explanation:
[tex]10m ^ { 2n } +30mn ^ { 2 } +5mn[/tex]
Factor out the common factor: 5
[tex]=5\left(2m^{2n}+6mn^{2}+mn\right) [/tex]
[tex]=5\left(6mn^{2}+mn+2\left(m^{n}\right)^{2}\right)[/tex]
=》This expression cannot be further simplified.
___________
Hope it helps ⚜
Which equation could be used to calculate the sum of the geometric series? one-third two-ninths startfraction 4 over 27 endfraction startfraction 8 over 81 endfraction startfraction 16 over 243 endfraction
Answers
The equation could be used to calculate the sum of the geometric series is [tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]
Sum of geometric sequenceGeometric sequence are sequence that increase expoentially. The formula for calculating the sum of an exponential sequence is expressed as:
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
where
a is the first termn is the number of termsr is the common ratioFrom the given sequence
a= 1/3
r = 2/9 * 3 = 2/3
Substitute into the formula
[tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]
Hence the equation could be used to calculate the sum of the geometric series is [tex]S_n=\dfrac{\frac{1}{3} (1-(\frac{2}{3} )^n)}{1-\frac{2}{3} }[/tex]
Learn more on geometric series here; https://brainly.com/question/24643676
Answer:
A
Step-by-step explanation:
edge
Please help me and you will get the brainiest answer.
Answers
Answer:
the right answer is c(5) . because the last digit of the second number is 2 . every number that its last digit is 2 squared , the last digit of the result will always be 4 . also , in every number that its last digit is five , the result will also always be 5 . so if the last digit of the first number is 5 this equasion is correct (because the last digit of the answer is 9 )(5+4)
hope that helped
I’ve worked out that the 1st term is -5 but can’t work out the rest. I thought it was -77 but it’s wrong
Answers
1st term: 3(1) - 8 = 3-8= -5
10th term: 3(10) - 8= 30-8= 22
100th term: 3(100)-8= 300-8= 292
Explanation:
Substitute the term number (e.g. 10) in the place of n
Hope this helped! :)
Answer:
-5, 22, 292
Step-by-step explanation:
Subbsittutoin mehtod
(i) n = 1 , 3n - 8
= 3 x 1 - 8
= -5
(ii) n = 10 , 3n - 8
= 3 x 10 - 8
=22
(iii) n = 100 , 3n - 8
= 3 x 100 - 8
= 300 - 8
= 292
.divide the problem.
Answers
Answer:
[tex]x - 2x - 15 \: divided \: by \: x - 3[/tex]
according to the above x²-2x-15 divided by the number below x-3 first I cancel out the x[tex]x - 2x - 15 \: divided \: by \: - 3[/tex]the we solve the next x-5 divided by x²-9 then as usual rule out the x[tex] - 5 \: divided \: by \: x - 9[/tex]now we only have x-2x-15 divided by-3 divided by-5÷x-9 now our next step is to again single the equations out [tex]x - 2x - 15 \: divided \: by \: - 3 \: lets \: rue \\s \: rule \: out \: - 3 \: and \: 15 \: giving \: us \: x - 2x - 5[/tex]now the next -5 divided by x-9 here there's nothing to rule out therefore the sign "÷" is changed to "×" cancel out the -5 and therefore we have [tex]x - 2x = x - 9 \: as \: final \: answer[/tex]pls help i need answer pls
Answers
Answer:
The answer is B.
Step-by-step explanation:
There isn't much to explain.
3/6 people like chocolate ice cream and x/600 where x is the number of people who like chocolate ice cream.
[tex]\frac{3}{6}=\frac{x}{600} \\[/tex]
Cross multiply to solve for x.
6*x = 3*600
6*x = 1800
x = 300
300 people like chocolate ice cream so about half of people like chocolate ice cream compare to 3/6 the same.
Please help me with this :)))))
If
Answers
Answer:
c) x = 20, angle COD = 70 °
Step-by-step explanation:
(x+50)° + 90° +20° = 180°
x + 160° = 180°
x = 180°- 160°
x = 20
Angle COD = (x+50)° = (20 +50)° = 70°
Hope this helps
Use the Fundamental Counting Principle to find the total number of possible outcomes.
Beverage
Size Small, Medium, Large
Flavor
Orange juice, Apple juice,
Lemonade, Milk
Answers
Answer:
There are 12 possible outcomes.
Step-by-step explanation:
For each of the three sizes of beverages, there are four flavors. So there are 3 * 4, or 12, possible outcomes.
Just need a bit off help! 10 points for each question and another 10 for the help so 50 points
Answers
Answer:
84, do 252/3
7.5, do 180/24
0.45, do 9/20
1.4, do 11.2/8
11. Write down three different whole numbers so that: • the median of the three numbers is 13, the range of the three numbers is 5.
Answers
Step-by-step explanation:
Let the numbers be a, b, c in ascending order.
Mean is 7, i.e. (a+b+c)/3 = 7 or a+b+c=21
Median(middle number) is 5, i.e. b=5
Range is 8, i.e. c-a=8 or c=8+a
Solving the above three equations simultaneously, we have
a+5+8+a=21
a=4, hence c=12
Therefore the three numbers are 4, 5 and 12
Help if you can
Please no links or false answers
Answers
Answer:
1st option
Step-by-step explanation:
given a quadratic function in standard form
f(x) = ax² + bx + c ( a ≠ 0 ) , then
• if a > 0 , the function opens up and has a minimum
• if a < 0 , the function opens down and has a maximum
here a = [tex]\frac{1}{2}[/tex] > 0
then f(x) opens up and has a minimum
Answer:
Option A, open up and have a minimum
Step-by-step explanation:
Step 1: Determine if it opens up or down
Since the value of a is 1/2 which means that it's positive which also means that it opens up. When a parabola opens up, that means that it has a minimum.
The picture attached to this answer shows an example of how a graph would look when using this equation. If a was -1/2 then the parabola would be facing down and would have a maximum.
Answer: Option A, open up and have a minimum
HELPPPPPP FRENNN HELPPP frenss!!! HURRY
Answers
Answer:
x=6 y=2
Step-by-step explanation:
y=2
so 6x+9(2)=-24
6x+18=-24
6x=42
x=6
The graph shows the relationship between the distance a bicyclist travels and the time in hours.
100
90
80
70
Distance (mi)
60
50
40
30
20
.
10
Time (h)
Answers
Calculate the sale price on a mobile phone with a marked price of $145, and a
discount of 53%
Answers
$68.15
P=Original price=145
D=Discount=53%
Sales=S
S=P-PD
S=145-(145×53%)
Please answer this I’m struggling rn :(
Answers
Answer:
The answer is on a picture⊙﹏⊙Step-by-step explanation:
Have a great day✧◝(⁰▿⁰)◜✧What is the length of side PQ in this figure?
Answers
Answer:
[tex]\sqrt{52[/tex]
Step-by-step explanation:
hope it helps! im not completely sure but its the best answer!
What is the solution to the inequality |2n +5| > 1?
Answers
Answer:
the answer is C
Step-by-step explanation: