find the area of the quadrilateral ABCD in which ab=5cm,bc=4.5cm,cd=3.5cm,da=4cm and ac=6.5cm
Answers
Answer:
A(ABCD) ≈ 17.285 cm²
Step-by-step explanation:
Heron formulaA = √s(s - a)(s - b)(s - c)
s = (a + b + c)/2
a ; b ; c = the sides of the triangle
A(ABCD) = A(ABC) + A(ACD)A(ABC) = √s(s - AB)(s - BC)(s - AC)s = (AB + BC + AC)/2 = (5cm + 4.5cm + 6.5cm)/2 = 16cm/2 = 8 cm
A(ABC) = √8(8 - 5)(8 - 4.5)(8 - 6.5)
= √8×3×3.5×1.5
= √126
≈ 11.225 cm²
2. A(ACD) = √s(s - AC)(s - CD)(s - AD)
s = (AC + CD + AD)/2 = (6.5cm + 3.5cm + 4cm)/2 = 14cm/2 = 7 cm
A(ACD) = √7(7 - 6.5)(7 - 3.5)(7 - 4)
= √7×0.5×3.5×3
= √36.75
≈ 6.060 cm²
3. A(ABCD) = 11.225cm² + 6.060cm² = 17.285 cm²
Related Questions
a box of tickets has an average of 100, and an SD of 20. Four hundred draws will be made at random with replacement from this box. a) Estimate the chance that the average of the draws will be in the range 80 to 120. b) estimate the chance that the average of the draws will be in the range 99 to 101
Answers
Answer:
(a) The probability that the average of the draws will be in the range 80 to 120 is 1.
(b) The probability that the average of the draws will be in the range 99 to 101 is 0.6827.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
As the sample selected is quite large, i.e. n = 400 > 30, then the sampling distribution of sample means will be approximately normally distributed.
Compute the mean and standard deviation of sample mean as follows:
[tex]\mu_{\bar x}=\mu=100\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{400}}=1[/tex]
So, [tex]\bar X\sim N(100, 1)[/tex]
(a)
Compute the probability that the average of the draws will be in the range 80 to 120 as follows:
[tex]P(80<\bar X<120)=P(\frac{80-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{120-100}{1})[/tex]
[tex]=P(-20<Z<20)\\\\=P(Z<20)-P(Z<-20)\\\\=(\approx1)-(\approx0)\\\\=1[/tex]
Thus, the probability that the average of the draws will be in the range 80 to 120 is 1.
(b)
Compute the probability that the average of the draws will be in the range 99 to 101 as follows:
[tex]P(99<\bar X<101)=P(\frac{99-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{101-100}{1})[/tex]
[tex]=P(-1<Z<1)\\\\=P(Z<1)-P(Z<-1)\\\\=0.6827[/tex]
Thus, the probability that the average of the draws will be in the range 99 to 101 is 0.6827.
Which sign makes the statement true?
11
20
? 61%
>
<
Submit
ASAP
Answers
11/20 =.55
61% = .61
.55<.61
PLEASE ANSWER QUICKLY: Two boxes have the same volume. One box has a base that is 5cm by 5cm. The other box has a base of 10cm by 10cm. How many times as tall is the box with the smaller base than the larger base?
Answers
Answer: 4 times as large
Step-by-step explanation:
The volume of a rectangular prism(box) can be calculated as base area*height. Because the base of one is 100 and the other 25, simply do 100/25 = 4, to determine that the box with the smaller base must be 4x as tall as the other box.
Hope it helps <3
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1).
Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.)
Answers
Answer:
[tex]P(X_i=2) =\dfrac{1}{6}[/tex]
[tex]P(X_i=-1) =\dfrac{5}{6}[/tex]
Step-by-step explanation:
Given the numbers on the chips = 1, 1, 3 and 5
Miguel chooses two chips.
Condition of winning: Both the chips are same i.e. 1 and 1 are chosen.
Miguel gets $2 on winning and loses $1 on getting different numbers.
To find:
Probability of winning $2 and losing $1 respectively.
Solution:
Here, we are given 4 numbers 1, 1, 3 and 5 out of which 2 numbers are to be chosen.
This is a simple selection problem.
The total number of ways of selecting r numbers from n is given as:
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
Here, n = 4 and r = 2.
So, total number of ways = [tex]_4C_2 = \frac{4!}{2!\times 2!} = 6[/tex]
Total number of favorable cases in winning = choosing two 1's from two 1's i.e. [tex]_2C_2 = \frac{2!}{2! 0! } = 1[/tex]
Now, let us have a look at the formula of probability of an event E:
[tex]P(E) = \dfrac{\text{Number of favorable ways}}{\text{Total number of ways}}[/tex]
So, the probability of winning.
[tex]P(X_i=2) =\dfrac{1}{6}[/tex]
Total number of favorable cases for -1: (6-1) = 5
So, probability of getting -1:
[tex]P(X_i=-1) =\dfrac{5}{6}[/tex]
Please refer to the attached image for answer table.
Answer:
two = 1/6
and -1 = 5/6
Step-by-step explanation:
What is 3.41 (where the .41 is repeating) written as a fraction?
Please help!!
Answers
Answer:
41/99
Step-by-step explanation:
There are two types of non terminating decimals. These are: Simple and Mixed
The one that you wrote up here is Simple, Since 41 is the only number that goes on repeating itself.
And mixed non terminating decimal is like 0.352 whereas 52 keeps repeating itself.
So when you change a non terminating decimal the denominator is always 9. But it depends on the decimal whether it is simple or mixed.
Since the decimal you wrote is simple and 2 digits keep on repeating themselves the denominator will be 99.
And the numerator will be the decimal number that keeps repeating itself without the repeating bar.
Therefore, the answer is 41/99.
Hope it helps ;) ❤❤❤
A group conducted a poll of 2022
likely voters just prior to an election. The results of the survey indicated that candidate A would receive 49
%
of the popular vote and candidate B would receive 46
%
of the popular vote. The margin of error was reported to be 5
%.
The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means.
Answers
Answer:
Step-by-step explanation:
number of likely voters = 2022
candidate A = 49%
candidate B = 46%
margin of error = 5%
using the concept of a confidence interval to explain
from the result of the poll conducted candidate A scored 49% of the votes while Candidate B scored 46% therefore the difference between the two voters is 3%.
also the margin of error is 5% which is higher than the 3% difference between the candidates. this margin error means that the 5% can vote for either candidate A or candidate B .which makes the results TOO CLOSE TO CALL
what is the initial value for g(x) = 3(1/4)^(x-2) - 3
Answers
Answer: g(1) = 9
Step-by-step explanation:
g(x) = 3(1/4)^(x-2) - 3
g(1) = 3(1/4)^(1-2) - 3
g(1) = 3(1/4)^(-1) - 3
g(1) = 3(4) - 3
g(1) = 12 - 3
g(1) = 9
what is the value of y in the figure below? (Picture provided)
Answers
30 degrees= x
60 degrees= x root 3
90 degrees= 2x
In this case since you know 90 degrees is 14 then you would have to find c which is 7 when you divide it by 2
A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Material for the base costs $20 per square meter. Material for the sides costs $12 per square meter.
Answers
Answer:
$ 327.08
Step-by-step explanation:
Let x = width of the container,
Then Length of the container = 2x
Let h = height of the container,
volume of the container can be calculated as length × width × height
= 2x × x × h
= 2x² h
Then we can say Volume =
= 2x² h=10
If we simplify inorder to get h
We have h= 5/x²
Then the area= (2L×h) +(2xh)
Where L is lenght
x= wish
h= height
= 2× 2x × h+ x× h
= 4x× 5/x + 2x × 5/x
Area = 30/x
Now, the area of the base = length × width
But from question, for the base costs $20 per square meter. Material for the sides costs $12 per square meter
Then the cost C(x)= 2x²× 20+30/x ×12
C(x)= 40x²+35/x²
If we differenciate wrt x we have
C(x)= 80-360/x²
If we equate C(x)=0the
80=360/x²
x= 1.651
If substitute to C(x)= 40x²+35/x²
C(x) = 40(1.651)² + 35/(1.651)²
We have cost= 327.08
How many cubes are there . A - 26 B - 27 C - 28 D - 29 E - 30 or F - 31
Answers
Answer is 31 because you have to count the ones under and behind
6) Which expressions are equivalent to 12x + 36y? Choose ALL that apply.
12(x + 3y)
9(3x + 4y)
6(2x + 6y)
4(3x + 9y)
2(6x + 24y)
3(4x + 12y)
Answers
the 1st one
third one
fourth one
the last one
each of the equation has one of the common factor out
12(x + 3y), 6(2x + 6y), 4(3x + 9y) and 3(4x + 12y) are the equivalent expressions of 12x + 36y.
What is Expression?An expression is combination of variables, numbers and operators.
Equivalent expressions are expressions that work the same even though they look different.
The given expression is 12x + 36y.
Twelve times of x plus thirty six times of y.
When we solve each expression we have to get 12x + 36y.
1. 12(x + 3y)- Equivalent expression
By distributive property
=12x+36y
2. 9(3x + 4y)- Not Equivalent expression.
27x+36y
3. 6(2x + 6y)- Equivalent expression
12x+36y
4. 4(3x + 9y)-Equivalent expression
5. 2(6x + 24y)- Not Equivalent expression.
12x+48y
6. 3(4x + 12y)-Equivalent expression
12x+36y
Hence, 12(x + 3y), 6(2x + 6y), 4(3x + 9y) and 3(4x + 12y) are the equivalent expressions of 12x + 36y.
To learn more on Expressions click:
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Jane exchanged £100 for 216 Swiss francs. After buying a meal and a present to take home,she had 70 francs left.How much is this in £?
Answers
Answer:
£32.4
Step-by-step explanation:
£100 = 216 Swiss francs
x = 70 francs
70 x 100=7000/216=32.4
using the order of operations, which operation should be performed first? 3(7+2²) - 5 A:7+ 2 B: 2² C: 3 x 7 and 3 x 2 D: 11 - 5
Answers
Answer:
B: 2²
Step-by-step explanation:
3(7+2²) - 5
PEMDAS says parentheses first
Then we do the order of operations inside the parentheses
Exponents are the first thing inside the parentheses
Please help me i give 40 points and five more to who say me the answers
Answers
Answer:
Step-by-step explanation:
A frequency table can be used to group a raw data. It shows the quantity of each variable in the data.
The required answers to the question can be found in the attachments to this answer.
Which relation is a function of x? {(1, 2), (7, 6), (3, 2), (1, 0), (5, 6)} A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 0, 0, 0. Column 2 is labeled y with entries 2, negative 6, 9, negative 7. x = 3 y squared minus 7 On a coordinate plane, a graph curves up, then curves down, and then curves up again. please comment i cant see answers thank you! :)
Answers
Answer: The answer is D . The graph
Step-by-step explanation: It was the answer given on Edge.
Answer:
d
Step-by-step explanation:
The double number line shows that Faye can sort 150 recyclable items in 3 minutes. Based on the ratio shown in the double number line, how many recyclable items can Faye sort in 4 minutes? items
Answers
Answer:
200 Recyclables Items
Step-by-step explanation:
The first step is to find the common ratio using this formula
Common ratio= Numbers of recyclable items/Number of minutes it takes to sort the recyclable item
Let plug in the formula
Common ratio =150/3 = 50
This means that we have 50 Recyclables Items per minute.
Now let calculate how many recyclable items that Faye can sort in 4 minutes
This means we are going to multiply 4 minutes by the 50 recyclable items per minutes
Hence,
4 * 50 = 200 Recyclables Items
Therefore Based on the ratio shown in the double number line, this means that Faye can sort 200 recyclable item in 4 minutes
Answer: 200
Step-by-step explanation: Since 150 divided by 3 is 50 add a 50 to 150 and you get 200
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?
Answers
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
Hope is the coach of the Wilson High School girls' soccer team. There are 3 minutes left in the game they are currently playing, and they are losing by 1 goal. In the past, when losing by 1 goal, Hope has pulled a defender out of the game and replaced her with a forward a total of 9 times. When in the same position, she has left the defender in the game 10 times. In the situations when Hope has pulled her defender, the team has lost 4 times, tied 2 times, and won 3 times. In situations when she has left her defender in the game, the team has lost 1 time, tied 3 times, and won 6 times. Based on the information above, if the goal is to either tie or win the game, should Hope pull the defender or leave her in the game?
Answers
Answer:
Hope should not pull her defender.
Step-by-step explanation:
When Hope has pulled her defender:
The team had lost 4 times, tied 2 times, and won 3 times.
Hence, the total number of times she meets her goal is:
6 times (Since the goal is to either tie or win the game )
Hence, the probability that she meets her goal is = 6/9=2/3=0.66
When she left her defender in the game:
The team has lost 1 time, tied 3 times, and won 6 times.
Hence, the total number of times she meets her goal is: 9
Hence, the probability that she meets her goal is: 9/10=0.9
As the probability of meeting her goal is more when she left her defender in the game is more.
Hence, Hope should not pull her defender.
A car can go from rest to 90 km⁄h in 10 s. What is its acceleration?
Answers
Answer:
2.5 m/s^2
Step-by-step explanation:
Answer:
2.5 m/s²
Step-by-step explanation:
First, convert to SI units.
90 km/h × (1000 m/km) × (1 h / 3600 s) = 25 m/s
a = Δv / Δt
a = (25 m/s − 0 m/s) / 10 s
a = 2.5 m/s²
Find the value of f(-1)g(-1)
Answers
Answer:
4
Step-by-step explanation:
f(-1) = (-1)^2 +1 = 1 + 1 = 2
g(-1) = 3(-1) +5 = -3 +5 = 2
f(-1)g(-1) = (2)(2) = 4
Please help me with this question.
Answers
Answer:
75% (I think)
Step-by-step explanation:
1/4 of babies have no hair
2/4 of babies have little hair
1/4 of babies have a lot of hair
Jeff's sister drives 14 miles to her collage his brother only drives 5/7/10 miles to his collage how much farther does Jeff's sister drive than his brother
Answers
Answer:
8.3miles
Step-by-step explanation:
Here Jeff's sister drives 14 miles
his brother only drives 57/10 miles then the question is only asking the difference between their distance of driving to school knowing fully well that Jeff's sister drive farther than his brother, then we find the difference between their drives which is done bow
14miles -57/10 miles
= 83/10
= 8.3miles
Therefore, Jeff's sister drive 8.3miles farther than his brother
Which values for h and k are used to write the function f of x = x squared + 12 x + 6 in vertex form?
h=6, k=36
h=−6, k=−36
h=6, k=30
h=−6, k=−30
Answers
Answer:
h=−6, k=−30
Step-by-step explanation:
did on edge
Considering the equation of the parabola, the coefficients of the vertex are:
h=−6, k=−30
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](h,k)[/tex]
In which:
[tex]h = -\frac{b}{2a}[/tex]
[tex]k = -\frac{b^2 - 4ac}{4a}[/tex]
In this problem, the equation is:
[tex]f(x) = x^2 + 12x + 6[/tex]
Hence the coefficients are a = 1, b = 12, c = 6, thus:
[tex]h = -\frac{12}{2} = -6[/tex]
[tex]k = -\frac{120}{4} = -30[/tex]
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
find the value of x in the triangle shown below
Answers
Answer:
46°
Step-by-step explanation:
We can tell that this triangle is an isosceles triangle because 2 of it's sides are the same, therefore, two of it's angles are the same.
Looking at it, we can assume that the two angles not defined (x and the other one) are the two angles that are the same because they look similar.
Now, the angles of all triangles add up to 180°. So, we can subtract 88° from 180 to see what the two angles add up to.
[tex]180-88=92[/tex]
So both of these angles add up to 92 degrees. Since there are two, we divide 92 by 2.
[tex]92 \div 2 = 46[/tex]
Hope this helped!
the angle of elevation of the top of a tree from a point 27m away on the same horizontal ground as the foot on the tree is 30 degrees .find the height of the tree.
Answers
Answer:
The height of the tree = 15.59m
Step-by-step explanation:
let's make the height of the tree = x
tan30=x/27
x = 27 x tan30
x = 15.59m
The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below.
On a coordinate plane, a graph of a function is in quadrants 1 and 4. The function goes through the x-axis at (2, 0), (3, ), and (4.5, 0).
How many roots of f(x) are rational numbers?
0
1
2
3
Mark this and return
Answers
Answer:
it'd be 3! :)
Step-by-step explanation:
took quiz
to be sure, the graph goes like
/ , then a hill like shape, then goes U, and then goes up
The number of rational roots of the equation are 3.
What is the root of an equation?The root of an equation are the solutions to an equation. The equation as shown is a cubic equation hence will have three roots shows as (2, 0), (3, 0), and (4.5, 0).
It thus implies from the foregoing that the number of rational roots of the equation are 3.
Learn more about root of an equation:https://brainly.com/question/12029673
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PLEASE HELP I WILL REWARD BRAINLY. PLEASE ONLY ANSWER IF YOU KNOW HOW TO SOLVE THIS PROBLEM. PLEASE INCLUDE INSIGHTFUL EXPLAINATION AND THOUGHT PROCESS: A woman and her two children are playing on a seesaw. This seesaw has seats that can move to different distances from the fulcrum. Riders can also add seats to the seesaw. The woman weighs 145lb, her son weighs 95lb, her daughter weighs 70lb, each seat weighs 5 pounds. Question: The woman is on the left side of the seesaw, 60 inches from the fulcrum. The daughter and son both get on the right side. The son sits 60 inches from the fulcrum. Where should the daughter sit to balance the seesaw. Please explain your process and give correct answer.
Answers
Answer: 40 inches
Step-by-step explanation:
The woman weight and the seat will be: 145lb + 5lb = 150lb,
her son weight and the seat will be: 95lb + 5lb = 100lb
her daughter weight and the seat will be: 70lb + 5lb = 75lb
Given that the woman is on the left side of the seesaw, 60 inches from the fulcrum. The moment of the woman will be 150 × 60 = 9000
The daughter and son both get on the right side.
If the son sits 60 inches from the fulcrum, his moment will be:
100 × 60 = 6000
The sum of the moment of the son and daughter must be equal to the moment of their mother.
Let the position of the daughter = X
The moment of the daughter will be:
75 × X = 75X
Equate the moment of the mother to the sum of the moment of her children
9000 = 6000 + 75X
Collect the like terms
75X = 9000 - 6000
75X = 3000
X = 3000/75
X = 40
The position the daughter should sit to balance the seesaw is 40 inches away from seasaw to the right.
factor the equation using zero product property. x2+7x=-6
Answers
Answer:
x = -6 x = -1
Step-by-step explanation:
We want to solve using the zero product property
x^2+7x=-6
Add 6 to each side
x^2 +7x +6 = 0
Factor
What 2 numbers multiply to 6 and add to 7
( x+6) (x+1) =0
Using the zero product property
x+6 =0 x+1 =0
x+6-6 =0-6 x+1-1 = 0-1
x = -6 x = -1
pls help !!!! i do not know or understand this at all
Answers
Answer:
(3, -3)
Step-by-step explanation:
Given functions:
f(x)= x² - 5x + 3and
f(x)= -3Solution is the Intersect which is found by equalizing the two functions:
x² - 5x + 3= -3Solving for x:
x² - 5x + 6=0x² - 2x -(3x -6) =0x(x-2) - 3(x-2)=0(x-2)(x-3)= 0x= 2 and x= 3As both values of x for the first function reveal f(x) = -3, the pairs are:
(2, -3) and (3, -3)if x= y^2/y^3 +1, what is the value of y in terms of x?
Answers
Answer:
1/(x-1)
Step-by-step explanation:
here,x=y^2/y^3 +1
x-1=y^2-3
x-1=y^-1
y=1/(x-1)
So, the value of y in terms of x is 1/(x-1)
I Hope this will be helpful for you