Answers
we can subtract the trapezium (white part) formed after from the trapezium (including white and grey) to get area of striped part
area of trapezium is [tex]\frac H2(a+b)[/tex] where $a$ and $b$ are parallel sides.
for bigger trapezium, $h=4$ parallel sides are $5$ and $5$
hence area is $\frac{4(5+5)}{2}=20$
similarily area of white trapezium, $\frac{4(3+3)}{2}=12$
and area of striped part is $20-12=8$
Related Questions
Find the probability of drawing 3 Aces at random from a deck of 52 ordinary playing cards if the cards are:_________
A) Replaced
B) Not Replaced
Answers
Answer:
a. With replacement
1/2197
b. Without replacement
1/5,525
Step-by-step explanation:
Okay, here is a probability question.
The key to answering this question is by knowing the number of aces in a deck of cards.
There is 1 ace per suit, so there is a total of 4 aces per deck of cards.
So, mathematically the probability of picking an ace would be;
number of aces/ total number of cards = 4/52 = 1/13
a. Now since the action is with replacement; that means that at any point in time, the total number of cards would always remain 52 even after making our picks.
So the probability of picking three aces with replacement would be;
1/13 * 1/13 * 1/13 = 1/2197
b. Without replacement
what this action means is that after picking a particular card, we do not return the picked card to the deck of cards.
For the first card picked, we will be having a total of 4 aces and 52 total cards.
So the probability of picking an ace would be 4/52 = 1/13
For the second card picked, we shall be left with selecting an ace out of the remaining 3 aces and the total remaining 51 cards
So the probability will be 3/51 = 1/17
For the third and last card to be picked, we shall be left with picking 1 out of the remaining 2 aces cards and out of the 50 cards left in the deck.
So the probability now becomes 2/50 = 1/25
Thus, the combined probability of picking 3 aces cards without replacement from a deck of cards will be;
1/13 * 1/17 * 1/25 = 1/5,525
Using the binomial and the hypergeometric distribution, it is found that the probabilities are:
a) 0.0005 = 0.05%.
b) 0.0002 = 0.02%.
Item a:
With replacement, hence the trials are independent, and the binomial distribution is used.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.For this problem:
In a deck, there are 52 cards, of which 4 are Aces, hence [tex]p = \frac{4}{52} = 0.0769[/tex]3 cards are drawn, hence [tex]n = 3[/tex].The probability is P(X = 3), then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.0769)^{3}.(0.9231)^{0} = 0.0005[/tex]
0.0005 = 0.05% probability.
Item b:
Without replacement, hence the trials are not independent and the hypergeometric distribution is used.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
Deck of 52 cards, hence [tex]N = 52[/tex].4 of the cards are Aces, hence [tex]k = 4[/tex].3 cards are drawn, hence [tex]n = 3[/tex].The probability is also P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,52,3,4) = \frac{C_{4,3}C_{48,0}}{C_{52,3}} = 0.0002[/tex]
0.0002 = 0.02% probability.
To learn more about the binomial and the hypergeometric distribution, you can take a look at https://brainly.com/question/25783392
write a trinomial that has a factor of X +3 and a GCF of -5x
Answers
Answer:
it is - 15 please mark me brainliest
Let f (x) = x – 4 and g(x) = 6 - x
Evaluate g(f(10)).
Answers
G(f(10))
First solve f(x) by replacing x with 10:
F(x) = x-4 = 10-4 = 6
Now replace x in g(x) with 6
G(x) = 6-x = 6-6 = 0
So g(f(10)) = 0
what is the cost of paving a driveway that is 18m long and 4 m wide, if the paving costs $35 per square metre?
Answers
Answer:
$2520
Step-by-step explanation:
→ Work out the area of the drive way
18 m × 4 m= 72 m²
→ Multiply the area by the cost per square metre
72 m² × $35 = $2520
The cost of paving a driveway that is 18m long and 4 m wide, if the paving costs $35 per square metre is $2520.
To calculate the cost of paving the driveway, you need to find the total area of the driveway and then multiply it by the cost per square meter.
The total area of the driveway can be calculated using the formula:
Area = length × width.
Given that the driveway is 18 meters long and 4 meters wide, the area would be:
Area = 18m × 4m
Area = 72 square meters.
Now, find the cost of paving the driveway by multiplying the area by the cost per square meter:
Cost = Area × Cost per square meter
Cost = 72 square meters × $35/square meter
Cost = $2520.
So, the cost of paying the driveway would be $2520.
To learn more on Area click:
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FACTOR THIS EXPRESSION AS FAR AS POSSIBLE -385y IM GIVING THANKS AND BRAINLIST IF CORRECT. PLEASE HELP ME GUYS
Answers
Answer:
-385y
Step-by-step explanation:
This expression cannot be factored with rational numbers, so -385y is your answer.
How many significant figures does each value contain? 5.6803 kg has significant figures. 0.00047 seconds has significant figures. 0.240 miles has significant figures.
Answers
Answer:
5.6803 has five significant figures.
0.00047 has two significant figures.
0.240 has three significant figures.
What are Significant Figures?Significant figures are numbers that are necessary to express a true value.
Place the values in scientific notation.
[tex]5.6803 * 10^{0} = 5.6803\\\\4.7 * 10^{-4} = 0.00047\\\\2.4 * 10^{-1}=0.240[/tex]
Explanation5.6803
The zero that is within 5.6803 is "trapped," meaning it is in between two nonzero digits. Therefore, all five digits are significant figures.
This answer is also already in scientific notation because 5.6803 satisfies the inequality [tex]1 < x < 10[/tex], which decides if a number is correctly written in scientific notation or not.
0.00047
The zeroes that precede the 4 and the 7 are not significant because they are dropped in scientific notation and are not trapped by other nonzero digits. Therefore, only two digits of this value are significant.
0.240
Since the zero at the end of 0.240 is a trailing zero, it is significant along with the 2 and the 4. The zero that precedes these digits and the decimal point is not significant. Therefore, only three digits of this value are significant.
Therefore:
5.6803 has five significant figures.
0.00047 has two significant figures.
0.240 has three significant figures.
shirley purchased a plot of land for $19,500. the land appreciates about 3.9% each year. what is the value of the land after 5 years
Answers
Answer:
$23,302.50
Step-by-step explanation:
(x2 - 41)2 + (yz - Yı) to the find the length of the segment
62. Use the distance formula d =
from (6,0) and (-5, 4).
Answers
Answer:
√137
Step-by-step explanation:
[tex](x_1, y_1) = (6, 0)\\(x_2, y_2) = (-5, 4)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d = \sqrt{(-5-6)^2+(4-0)^2}\\ d = \sqrt{(-11)^2+(4)^2}\\ d = \sqrt{121+16}\\ d = \sqrt{137}\: or \:11.7[/tex]
Determine the intercepts of the line.
-6x + 3y = -7
z-intercept:
y-intercept:
Answers
Answer:
(7/6, 0) and (0,-7/3)
Step-by-step explanation:
I think you mean x-intercept and y-intercept not z-intercept and y-intercept. The first step is to convert the equation to slope intercept form:
-6x+3y=-7
3y=6x-7
y=6/3x-7/3
y=2x-7/3
Now, to find the x-intercept we find the value of x when y is 0.
0=2x-7/3
7/3=2x
7/6=x so the x-intercept is (7/6,0)
Now, to find the y-intercept we find the value of y when x is 0.
y=2(0)-7/3
y=0-7/3
y=-7/3 so the y-intercept is (0,-7/3)
A rectangular prism has a volume of 864 cubic units. How many cubic unit will fill the volume of the solid if they were packed without any gaps or overlaps
Answers
Answer: 864.
Step-by-step explanation:
The volume of a rectangular prism has a volume equal to:
V = W*L*H
W = width
L = length
H = height
We know that the volume is equal to 864 cubic units.
This means that if we want to fill the prism such that there is no gap or overlap, we should use exactly 864 unit cubes.
Trevor thought there would only be 8 teams in the soccer tournament, but there were 17. What was his percent error?
Answers
Answer:
Around 52.94%
Step-by-step explanation:
We can use the percentage error formula, which is
[tex]\frac{|approx-exact|}{exact}\cdot100[/tex].
The approximated value was 8, however the exact value was 17, so we can substitute inside the equation.
[tex]\frac{|8-17|}{17}\cdot100 \\\\\frac{|-9|}{17}\cdot100 \\\\\frac{9}{17}\cdot100 \\\\0.5294...\cdot100 \\\\52.94[/tex]
Hope this helped!
Rita got three colors of beads, half of them are pink. She used all her pink beads to make some bracelets. If the number of pink beads she used for each bracelet is one eighths of the total number of beads, how many bracelets did she make?
Answers
Answer: she made 4 bracelets.
Step-by-step explanation:
Let x, y, z are the number of three kinds of beads, where x= number of pink beads.
As per given, number of pink beads= half of total beads
[tex]\Rightarrow\ x=\dfrac{1}{2}(x+y+z)\\\\\Rightarrow 2x= x+y+z\\\\\Rightarrow\ x= y+z\ \ \ ...(i)[/tex]
Also, She used all pink beads, Number of pink beads she used for each bracelet= one eighths of the total number of beads
[tex]\dfrac{1}{8}(x+y+z)\\\\=\dfrac{1}{8}(x+x)\ \ \ [ {\text{From (i)}}][/tex]
[tex]=\dfrac{1}{8}(2x)\\\\=\dfrac{x}{4}[/tex]bracelets =
Number of bracelets = (Number of pink beads) ÷ (Number of pink beads used for each bracelet)
[tex]=\dfrac{x}{\dfrac{x}{4}}=4[/tex]
Hence, she made 4 bracelets.
The same amount of trash is dumped into a landfill every day. The function below shows the total number of tons of trash n in the landfill after x days:
n = 2000x + 1000
What does the number 2,000 represent?
Answers
Answer:
Amount of trash added to the landfill everyday
Step-by-step explanation:
If 2000 represents the amount of trash added to the landfill everyday then 1000 is the starting amount.
I got it right on the test. Hope this helped!
is the square root of 2 between 1.4 and 1,5
Answers
Answer:
The square root is around 1.414, so yes, it is between 1.4 and 1.5.
Step-by-step explanation:
Can u guys answer question 2 pls
Answers
Answer:
"2.93BAR
LET X=2.93BAR
10X=29.393BAR
100X=293.93BAR
NOW WE WILL SUBTRACT THE FIRST EQUATION FROM THIRD EQUATION
100X=293.93BAR
X= 2.93BAR
99X=291.00BAR
IT CAN ALSO BE WRITTEN LIKE
X=291/99"
This was an answer from the same question someone else asked.
This answer was given by grvbundela008p3f6id
Step-by-step explanation:
ALGEBRAIC EXPRESSION 11. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7. 12. From the sum of x 2+ 3y 2 − 6xy, 2x 2 − y 2 + 8xy, y 2 + 8 and x 2 − 3xy subtract −3x 2 + 4y 2 – xy + x – y + 3. 13. What should be subtracted from x 2 – xy + y 2 – x + y + 3 to obtain −x 2+ 3y 2− 4xy + 1? 14. What should be added to xy – 3yz + 4zx to get 4xy – 3zx + 4yz + 7? 15. How much is x 2 − 2xy + 3y 2 less than 2x 2 − 3y 2 + xy?
Answers
Answer:
Explained below.
Step-by-step explanation:
(11)
Subtract the sum of (13x - 4y + 7z) and (- 6z + 6x + 3y) from the sum of (6x - 4y - 4z) and (2x + 4y - 7z).
[tex][(6x - 4y - 4z) +(2x + 4y - 7z)]-[(13x - 4y + 7z) + (- 6z + 6x + 3y) ]\\=[6x-4y-4z+2x+4y-7z]-[13x-4y+7z-6z+6x+3y]\\=6x-4y-4z+2x+4y-7z-13x+4y-7z+6z-6x-3y\\=(6x+2x-13x-6x)+(4y-4y+4y-3y)-(4z+7z+7z-6z)\\=-11x+y-12z[/tex]
Thus, the final expression is (-11x + y - 12z).
(12)
From the sum of (x² + 3y² - 6xy), (2x² - y² + 8xy), (y² + 8) and (x² - 3xy) subtract (-3x² + 4y² - xy + x - y + 3).
[tex][(x^{2} + 3y^{2} - 6xy)+(2x^{2} - y^{2} + 8xy)+(y^{2} + 8)+(x^{2} - 3xy)] - [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[x^{2} + 3y^{2} - 6xy+2x^{2} - y^{2} + 8xy+y^{2} + 8+x^{2} - 3xy]- [-3x^{2} + 4y^{2} - xy + x - y + 3]\\=[4x^{2}+3y^{2}-xy+8]-[-3x^{2} + 4y^{2} - xy + x - y + 3]\\=4x^{2}+3y^{2}-xy+8+3x^{2}-4y^{2}+xy-x+y-3\\=7x^{2}-y^{2}-x+y+5[/tex]
Thus, the final expression is (7x² - y² - x + y + 5).
(13)
What should be subtracted from (x² – xy + y² – x + y + 3) to obtain (-x²+ 3y²- 4xy + 1)?
[tex]A=(x^{2} - xy + y^{2} - x + y + 3) - (-x^{2}+ 3y^{2}- 4xy + 1)\\=x^{2} - xy + y^{2} - x + y + 3 +x^{2}- 3y^{2}+ 4xy -1\\=2x^{2}-2y^{2}+3xy-x+y+2[/tex]
Thus, the expression is (2x² - 2y² + 3xy - x + y + 2).
(14)
What should be added to (xy – 3yz + 4zx) to get (4xy – 3zx + 4yz + 7)?
[tex]A=(4xy-3zx + 4yz + 7)-(xy - 3yz + 4zx) \\=4xy-3zx + 4yz + 7 -xy + 3yz - 4zx\\=3xy-7zx+7yz+7[/tex]
Thus, the expression is (3xy - 7zx + 7yz + 7).
(15)
How much is (x² − 2xy + 3y²) less than (2x² − 3y² + xy)?
[tex]A=(2x^{2} - 3y^{2} + xy)-(x^{2} - 2xy + 3y^{2})\\=2x^{2} - 3y^{2} + xy-x^{2} + 2xy - 3y^{2}\\=x^{2}-6y^{2}+3xy[/tex]
Thus, the expression is (x² - 6y² + 3xy).
CAN U PLS HELP ME OUT I WILL GIVE BRAINLIST AND A THANK YOU!!!!!! :)
Answers
Step by step: it is across from 25.
Answer:
Step-by-step explanation:
Vertically opposite angles are equal
x = 25°
Simplify 27^(-2/3) x 25^(1/2) x 5^0 9 5 9/5 5/9
Answers
Answer:
[tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Using the rules of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] ⇔ [tex]\sqrt[n]{a^{m} }[/tex] , [tex]a^{0}[/tex] = 1
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
Given
[tex]27^{-\frac{2}{3} }[/tex] × [tex]25^{\frac{1}{2} }[/tex] × [tex]5^{0}[/tex]
= [tex]\frac{1}{27^{\frac{2}{3} } }[/tex] × [tex]\sqrt{25}[/tex] × 1
= [tex]\frac{1}{9}[/tex] × 5 × 1
=[tex]\frac{5}{9}[/tex]
Find x. A. 22 B. 113–√ C. 222–√ D. 113√3
Answers
Answer:
x = 31.12
Step-by-step explanation:
First find the base (hypotenuse) of the smaller triangle (the isosceles triangle): Its three sides are 11, 11 and b. b can be found using the Pythagorean Theorem: b^2 = 11^2 + 11^2 = 242. Then b = √242, or b = approximately 15.56.
b (which is approximately 15.56) is the shorter leg of the large (right) triangle. The trig function needed to solve for x is the cosine:
adjacent side
cos 60 degrees = ----------------------
hypotenuse,
15.56
which becomes (1/2) = ------------
x
Solving this for x, we get: x = 2(15.56) = 31.12
A laundry basket contains 18 blue socks and 24 black socks. What is the probability of randomly picking 2 black socks, with replacement, from the basket?
Answers
Answer:
144/441
Step-by-step explanation:
There are 18+24=42 total socks
There are 24 black socks
So the probability is (24/42)*(24/42)=12/21 * 12/21 = 144/441
Answer:
189
Step-by-step explanation:
44) 93
O 2 remainder of 6
2 remainder of 7
2 remainder of 4
2 remainder of 5
Answers
For the rational equation,[tex]\frac{x^{2}+5x+6}{x+3}=1[/tex] , what is a valid value of x?
Answers
Answer:
-3 or -1 is a valid value for x
Step-by-step explanation:
We start by cross multiplying;
So the expression becomes;
x^2 + 5x + 6 = 1(x + 3)
x^2 + 5x + 6 = x + 3
x^2 + 5x -x + 6-3 = 0
x^2 + 4x + 3 = 0
x^2 + x + 3x + 3 = 0
x(x + 1) + 3(x + 1) = 0
(x + 3)(x + 1) = 0
x + 3 = 0 or x + 1 = 0
x = -3 or x = -1
Figure a is a scale image of figure b. what is the value of x? please answer asap!
Answers
Answer:
[tex]\boxed{x = 20}[/tex]
Step-by-step explanation:
Hey there!
Well to find x we need to set up the following.
[tex]\frac{10}{12.5} = \frac{16}{x}[/tex]
Cross multiply
10x = 200
Divide both sides by 10
x = 20
Hope this helps :)
According to the number line, which statement MUST be true? A) A > 1 B) B > 4 C) C < 4 D) D < 0
Answers
Answer:
The anwser is C) C < 4
......... .
Find the AM and GM for the numbers 18 and 2
Answers
Answer:
Step-by-step explanation:
Solution:
AM =( X_1 + X_2 )/2
=( 18 + 2 )/2
=20/2
=10
Find Geometric mean for data 18,2
Solution:
GM =sqrt( X_1 × X_2 )
=sqrt( 18 × 2 )
=sqrt(36)
=6
What is the justification for step 3 in the solution process?
0.8a - 0.1 a= a - 2.5
Step 1: 0.7a= a - 2.5
Step 2: -0.3a = -2.5
Step 3:
a= 8.3
OA.
the division property of equality
OB
B. combining like terms
O c. the subtraction property of equality
OD. the addition property of equality
Answers
Answer:
c. the subtraction property if equality
Step-by-step explanation:
i just did this and got it right
The justification for step 3 in the solution process is the division property of equality option (A) the division property of equality is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The equation is:
0.8a - 0.1 a = a - 2.5
The above equation represents the linear equation in one variable.
Step 1: 0.7a = a - 2.5 (adding like terms)
Step 2: -0.3a = -2.5 ( subtraction property of equality)
Step 3: a = 8.3 (the division property of equality)
Thus, the justification for step 3 in the solution process is the division property of equality option (A) the division property of equality is correct.
Learn more about the linear equation here:
brainly.com/question/11897796
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Katherine's class is selling raffle tickets for $3 to raise money for charity. Katherine's class raised $504. Which equation would you use to find the number of tickets sold?
Answers
Hey there! I'm happy to help!
Let's represent each ticket with the variable t. For each ticket sold, there will be 3 dollars added to the total. So, if you multiply the number of tickets by 3, you will have your total.
This gives us the following equation.
3t=504
We could use this equation to find the number of tickets sold by dividing both sides of it by 3, which isolates the t, showing us that t=168.
Have a wonderful day!
Answer:
$504 / $3 = t
Step-by-step explanation:
t = total tickets sold
If each ticket cost $3 and the class raised $504, just divide the total amount by the cost.
I hope this helps you! Please tell me if I am wrong!
Sum and Product of zeroes of the quadratic polynomial 16s² - 16s + 4 respectively is:Sum and Product of zeroes of the quadratic polynomial 16s² - 16s + 4 respectively is:
Answers
Answer:
The sum and product of zeroes are 1 and 1/4, respectively.
Step-by-step explanation:
To determine the zeroes of the quadratic polynomial, let equalize the polynomial to zero and solve in consequence:
[tex]16\cdot s^{2}-16\cdot s + 4 = 0[/tex]
By the General Quadratic Formula:
[tex]s_{1,2} = \frac{16\pm \sqrt{(-16)^{2}-4\cdot (16)\cdot (4)}}{2\cdot (16)}[/tex]
[tex]s_{1,2} = \frac{1}{2}[/tex]
Which means that zeroes are [tex]s_{1}=s_{2}=\frac{1}{2}[/tex].
The sum and product of zeroes are, respectively:
[tex]s_{1}+s_{2} =\frac{1}{2}+\frac{1}{2}[/tex]
[tex]s_{1}+s_{2} = 1[/tex]
[tex]s_{1}\cdot s_{2} = \left(\frac{1}{2} \right)^{2}[/tex]
[tex]s_{1}\cdot s_{2} = \frac{1}{4}[/tex]
The sum and product of zeroes are 1 and 1/4, respectively.
Helpppppppppppppppp plzzz
Answers
Answer:
$0.56, or 56¢.
Step-by-step explanation:
According to the picture, there are two dimes, two nickels, a penny, and a quarter.
A penny is worth $0.01.
A nickel is worth $0.05.
A dime is worth $0.10.
A quarter is worth $0.25.
2(0.1) + 2(0.05) + (0.01) + (0.25) = 0.2 + 0.1 + 0.01 + 0.25 = 0.3 + 0.26 = 0.56.
So, Vivian is using $0.56, or 56¢, to buy a toy. That's a cheap one!
Hope this helps!
How to do this question plz answer me step by step plzz plz plz plz
Answers
Answer: 25.6
First, notice that there is 1 adult and 2 children.
A normal adult ticket costs 24. But it's 1/3 off, so 24 * 1/3 = 8 off. That means with the Railcard, it only costs 24 - 8 = 16.
Next, one child ticket costs 12. But it's 60% = 3/5 off, so 12 * 3/5 = 7.2 off. That means with the Railcard, it only costs 12 - 7.2 = 4.8.
Remember there are 2 children, so we multiply by 2 to get 4.8 * 2 = 9.6 for the children.
Final answer: 1 adult + 2 children = 16 + 9.6 = 25.6.
Hope that helped,
-sirswagger21
Answer:
£25.60
Step-by-step explanation:
Adult tickets cost £24 and ⅓ is off the adult tickets according to the Family Railcard. That is:
24 × ⅓ = £8 is removed from the adult tickets. Therefore:
£24 - £8 = £16
Child tickets cost £12 and 60% is off the child tickets according to the Family Railcard. That is:
12 × 60/100 = £7.20 is removed from the child tickets. Therefore:
£12 - £7.20 = £4.80
To find the total cost of Mr. Brown spent:
1 child = £4.80
2 children = ?
4.80 × 2 = £9.60
1 adult = £16
£16 + £9.60
= £25.60
Mr. Brown spent £25.60 in total.
