Answer:
[tex]Perimeter = 11 + \sqrt{13}[/tex]
Step-by-step explanation:
To find the perimeter of WXYZ we need to find the length of all four sides: WX, XY, YZ and WZ.
To find the length of each side, we can use the formula for the distance of two points:
[tex]distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So we have that:
[tex]WX = \sqrt{(2 - 4)^2 + (3 - 6)^2} = \sqrt{13}[/tex]
[tex]XY = \sqrt{(4 - 7)^2 + (6 - 6)^2} = 3[/tex]
[tex]YZ = \sqrt{(7 - 7)^2 + (6 - 3)^2} = 3[/tex]
[tex]WZ = \sqrt{(2 - 7)^2 + (3 - 3)^2} = 5[/tex]
The perimeter is:
[tex]Perimeter = WX + XY + YZ + WZ[/tex]
[tex]Perimeter = \sqrt{13} + 3 + 3 + 5 =11 + \sqrt{13}[/tex]
The computer hardware company requires all of its chips purchased from its supplier of computer chips to meet specifications of 1.2 cm with the margins of error of plus and minus 0.1 cm. Based on the computer chip supplied last month, the mean length of a computer chip was 0.9 cm. What are the elements that the production manager should consider in determining his company's ability to produce chips that meet specifications
Answer:
Step-by-step explanation:
The computer hardware company requires all of the chips purchased from its supplier of computer chips to meet the specification of 1.2 centimeters, with error margins of -0.1cm and +0.1cm
This means that the required length of computer chips is between 1.1cm - 1.3cm
Where 1.1cm = [1.2 - 0.1]
1.3cm = [1.2 + 0.1]
Based on the computer chips supplied last month, mean length was 0.9cm. This means that most of the chips were (in length) less than the lower boundary of 1.1cm.
The element that the production manager should consider in determining his company's ability to produce chips that meet specification is:
- The length of the chips.
The length of the chips his production team produces should be tailored to meet the length specification of his client.
Could you please help me with this problem.
Answer:
x=6√2please see the attached picture for full solution...
Hope it helps...
Good luck on your assignment....
A real estate agent is showing homes to a prospective buyer. There are ten homes in the desired price range listed in the area. The buyer has time to visit only four of them. If four of the homes are new and six have previously been occupied and if the four homes to visit are randomly chosen, what is the probability that all four are new
Answer:
0.48% probability that all four are new
Step-by-step explanation:
The homes are chosen "without replacement", which means that after a home is visited, it is not elegible to be visited again. So we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
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]
In this question:
Total of 10 homes, so N = 10.
We want 4 new, so x = 4.
In total, there are 4 new, so k = 4.
Sample of four homes, so n = 4.
Then
[tex]P(X = 4) = h(4,10,4,4) = \frac{C_{4,4}*C_{6,0}}{C_{10,4}} = 0.0048[/tex]
0.48% probability that all four are new
The calculated probability is "0.0048".
Probability calculation:From a total of [tex]N=10\ \ \text{homes},\ r=4[/tex] are completely new while 6 are not.
Let X indicate the series of innovative dwellings in a sample of[tex]n=4[/tex] homes.
X is the next step. Algebraic distribution for parameters[tex]N=10, r=4, \ \ and\ \ n = 4[/tex] Only integer values in this range: can be given to a hypergeometric random variable.
[tex]\to [ \max {(0,\,n+r-N)}, \min {(n,\,r)} ] = [ 0, 4 ] \\\\ \to P( X = 4) \\\\ \to N=10\\\\ \to r=4\\\\ \to n = 4[/tex]
[tex]\to \bold{P(X=k) = \dfrac{\binom{r }{ k}{\binom{N-r} {n-k}}}{\binom{N}{n}}} \\\\\to P(X =4 ) = \dfrac{\binom{r }{ 4}{\binom{N-r} {n-4}}}{\binom{N}{n}} \\\\[/tex]
[tex]= \dfrac{\binom{4 }{ 4}{\binom{10-4} {4-4}}}{\binom{10}{4}}\\\\= \dfrac{\binom{4 }{ 4}{\binom{6} {0}}}{\binom{10}{4}} \\\\= \dfrac{ 1 \times 1}{210} \\\\= \dfrac{ 1}{210} \\\\= \dfrac{1}{210} \\\\= 0.004762[/tex]
Using the excel function:
[tex]\text{HYPGEOM.DIST( k, n, r, N. cumulative)}[/tex] for calculating the [tex]P_{X} (4)[/tex]:
[tex]\to \text{HYPGEOM.DIST( 4, 4, 4, 10, FALSE) = 0.0047619047619}[/tex]
[tex]\to P(X= 4 ) = \frac{1}{210} = { 0.0048 }[/tex]
Find out more information about the probability here:
brainly.com/question/2321387
A wall is in the shape of a trapezium. The first level of the wall is made up of 50 bricks where as the top level has 14 bricks. If the levels differ from each other by 4 bricks, determine the number of;
(i)levels of the bricks.
(ii)bricks used to make the wall.
Answer:
i). 10 levels of the bricks
ii). 320 bricks
Step-by-step explanation:
First level contains number of bricks = 50
Second level will contain = 50 - 4 = 46 bricks
Similarly, 3rd level will contain number of bricks = 46 - 4 = 42
Therefore, sequence formed for the number of bricks in each level of the wall will be,
50, 46, 42........14
This sequence is an arithmetic sequence having,
First term 'a' = 50
Common difference 'd' = 46 - 50 = (-4)
Last term of the sequence [tex]T_{n}[/tex]= 14
i). Expression representing last term will be,
[tex]T_{n}=a+(n-1)d[/tex]
Here [tex]T_{n}[/tex] = nth term
a = first term
n = number of term (Number of level of the wall)
d = common difference
By substituting these values in the formula,
14 = 50 + (n - 1)(-4)
14 - 50 = (-4)(n - 1)
-36 = -4(n - 1)
9 = (n - 1)
n = 9 + 1
n = 10
ii). Number of bricks used in the wall = Sum of the sequence
Expression for the sum of an arithmetic sequence is,
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_n=\frac{10}{2}[2\times 50+(10-1)(-4)][/tex]
= 5(100 - 36)
= 320 bricks
To solve the system given below using substitution, it is best to start by
solving the second equation for y.
5x + 2y = 33
6y + x = 3
true or false
Answer:
False, it is easier to isolate x.
Step-by-step explanation:
6y+x=3
x=3-6y
A contractor is considering whether he should take on a project that promises a profit of $8800 with a probability of 0.83 or a loss (due to bad weather, strikes, etc.) of $2900 with a probability of 0.17. What is the expected profit for the contractor
Answer: 6811
Step-by-step explanation:
in this problem the values are 8800 and -2900 and the respective probabilities are 0.83 and 0.17
--
so the expected profit o# sum = (x*P(x))=8800*(0.83)+(-2900)*(0.17)=6811
Please answer this correctly
Answer:
20-39 ⇒ 5
40-59 ⇒ 3
60-79 ⇒ 5
80-99 ⇒ 10
Answer:
20-39: 5
40-59: 3
60-79: 5
80-99: 10
Step-by-step explanation:
If you just added up, you can find all the values.
Look at this expression.
Can you put it in the simplest form?
The denominator contains negative exponents. Using the negative exponent rule, multiply the denominator by -1 and then reverse the fraction and multiply.
The denominator becomes x^3y^4
The problem then becomes -3x^6y^4 times x^3y^2
When multiplying exponents add them together:
The final answer is -3x^9y^6
What is the remainder when the product of the 5 smallest prime numbers is divided by 42?
Answer:
21
Step-by-step explanation:
The 5 smallest prime numbers are 1, 2, 3, 5, and 7.
So when multiplied it equals 105.
Divide by 42 and you get 2 21/42
So you have a remainder of 21
Find the product
2y2(3x + 5z)
Answer:
6xy^2+10y^2z is the answer
in a bag there are 2 red, 3 yellow, 4 green, 6 blue marbles.
what is the probability of p (blue)?
Answer:
2/5
Step-by-step explanation:
2 red, 3 yellow, 4 green, 6 blue marbles. = 15 marbles
P( blue) = blue / total
=6/15
=2/5
Heidi looks at the donkeys and
tourists. She counts 50 heads
and 114 legs.
How many donkeys are there?
o
ANSWER:
O The retired question
Answer:
7 donkeys
Step-by-step explanation:
Given
A system consisting of donkeys and tourists
Heads = 50
Legs = 114
Required
Calculate number of donkeys.
Represent donkeys with D and tourists with T.
By means of identification; donkeys and tourists (human) both have 1 head.
This implies that
Number of Heads = D + T
50 = D + T ----- Equation 1
While each donkey have 4 legs, each tourists have 2 legs.
This implies that
Number of legs = 4D + 2T
114 = 4D + 2T ---- Multiply both sides by ½
114 * ½ = (4D + 2T) * ½
57 = 4D * ½ + 2T * ½
57 = 2D + T ----- Equation 2
Subtract equation 1 from 2
57 = 2D + T
- (50 = D + T)
---------------------
57 - 50 = 2D - D + T - T
7 = D
Recall that D represents the number of donkeys.
So, D = 7 implies that
The total number of donkeys are 7
The mean temperature for the first 4 days in January was 7°C. The mean temperature for the first 5 days in January was 9°C. What was the temperature on the 5th day?
Answer:
If the mean was 7 for the first 4 days that means the sum of temperatures of the first 4 days was 7 * 4 = 28. Similarly, the sum of temperatures of the first 5 days was 9 * 5 = 45 so that means that the temp. on the 5th day was 45 - 28 = 17°C.
Answer:
11 C
Step-by-step explanation:
To find the mean (average), you have to add all and divide by 2, so if you reverse this, you get (7 + X)/2 = 9 , 9 * 2 - 7 = 11
There are three highways in the county. The number of daily accidents that occur on these highways are Poisson random variables with respective parameters 0.3, 0.5, and 0.7.
Required:
Find the expected number of accidents that will happen on any of these highways today.
Answer:
50% Chance
Step-by-step explanation:
So Pr(0.3, 0.5, and 0.7) = (30% + 50% + 70%) / 300
= 1/2
I’ll mark Brainlyist to the correct answer
Rewrite 8 log3 x^7 in a form that does not use exponents.
8log3 x^7 = ( )log3 x
Answer:
(56 )log3 x
Step-by-step explanation:
We know that log a^b = bloga
8log3 x^7 = (7*8 )log3 x = 56 log3 x
Answer:
56 log3 x
Step-by-step explanation:
8 log3 x^7 can be rewritten as log3 x^(7*8) = log3 x^56 or 56 log3 x
At a department store, Kendra has a debt greater than $25.00. Which could be Kendra’s balance? A.Negative 32 dollars B.Negative 22 dollars C.Negative 19 dollars D.Negative 11 dollars
Answer:
A. Negative 32 dollars
Step-by-step explanation:
Kendra has a debt. Doubt means that the balance is Negative.
If the debt is greater than 25 USD . Kendra's debt has to be more negative than 25 . Amoung all other numbers only debt 32 is more negative than 25.
Answer:
I think it would be 32
Step-by-step explanation:
So she can pay the debt off
Write an expression to represent: Eight more than the product of two and a number x.
Answer:
8 + 2x
Step-by-step explanation:
You are adding 8 to 2 times an unknown number.
find the value of ∛27
Answer:
3
Step-by-step explanation:
3^3 = 27
How can knowing how to represent proportional relationships in different ways be useful to solving problems
Answer:
appropriately writing the proportion can reduce or eliminate steps required to solve it
Step-by-step explanation:
The proportion ...
[tex]\dfrac{A}{B}=\dfrac{C}{D}[/tex]
is equivalent to the equation obtained by "cross-multiplying:"
AD = BC
This equation can be written as proportions in 3 other ways:
[tex]\dfrac{B}{A}=\dfrac{D}{C}\qquad\dfrac{A}{C}=\dfrac{B}{D}\qquad\dfrac{C}{A}=\dfrac{D}{B}[/tex]
Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.
I find this most useful to ...
a) put the unknown quantity in the numerator
b) give that unknown quantity a denominator of 1, if possible.
__
The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.
Example:
x/4 = 3/2
Usual method:
2x = 4·3
x = 12/2 = 6
Multiplying by the denominator:
x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step
__
Example 2:
x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...
x/1 = 4/2 . . . . . . written with 1 in the denominator
x = 2 . . . . simplify
Of course, this is the same answer you would get by multiplying by the denominator, 4.
The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.
If the volume of a cube is
64 cubic feet, what is the
surface area of the cube in
square feet?
Answer:
96 ft^2
Step-by-step explanation:
volume=l^3
l=4
4x4x4=64
Surface area (4x4)=16
16x6=96
Answer:
SA =96 ft^2
Step-by-step explanation:
The volume of a cube is given by
V = s^3
64 = s^3
Take the cube root of each side
64 ^ 1/3 = s^3 ^ 1/3
4 =s
The side length si 4
The surface area of a cube is
SA = 6 s^2
SA = 6 * 4^2
SA = 6 * 16
SA =96 ft^2
3 of 8 The following are the ages (years) of 5 people in a room: 14, 14, 18, 18, 22 A person enters the room. The mean age of the 6 people is now 16. What is the age of the person who entered the room?
Answer:
[tex]\boxed{\sf \ \ age = 10\ \ }[/tex]
Step-by-step explanation:
Hello,
let's write the mean computation, we note x the age of the additional person
[tex]\dfrac{14+14+18+18+22+x}{6}=16[/tex]
[tex]<=> 14+14+18+18+22+x = 6*16=96\\\\<=> x = 96 - ( 14+14+18+18+22)= 10[/tex]
So the age of the person is 10
hope this helps
Answer:
10
Step-by-step explanation:
The mean is the sum of terms divided by number of terms.
Let x be the age of the person who entered the room.
(14+14+18+18+22+x)/6 = 16
(x + 86)/6 = 16
x + 86 = 96
x = 10
The age of the person who entered the room is 10.
Calculate the length of the
circumference of a circle with
radius of 1.6m
Answer:
C = 10.05
Step-by-step explanation:
Formula: C = 2[tex]\pi[/tex]r
circumference = ?
Solution:
C = 2[tex]\pi[/tex](1.6 m) (multiply)
C = 3.2[tex]\pi[/tex]m
C = 3.2(3.14) m (multiply)
C = 10.048
Rounded off (If needed): 10.05
Let's list the elements of these sets and write whether thoy are empty
(null), singleton, finite or Infinito sots.
a) A = {prime number between 6 and 7)
b) B = {multiples of 2 less than 20}
Answer:
a. They are empty set.
b. they are finite set.
Solution,
a. A={ prime number between 6 and 7}
There are not any number between 6 and 7.
So there will be no Elements.
A={ }
It is empty set.
Empty set are those set which doesn't contain any Element.
b.B={multiples of 2 less than 20}
B={2,4,6,8,10,12,14,16,18}
It is a finite set.
Finite set are those set which we can count easily.
Hope this helps...
Good luck on your assignment...
What is the square root of -1?
Step-by-step explanation:
Zero has one square root which is 0. Negative numbers don't have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.
What is -5/4 to the 2nd power?
Answer:
[tex]\frac{25}{16}[/tex]
Step-by-step explanation:
[tex](-\frac{5}{4})^2\\\\ \text {Apply power of a fraction rule: } (\frac{a}{b})^x=\frac{a^x}{b^x}\\\\(-\frac{5}{4})^2 = \frac{-5^2}{4^2}=\frac{25}{16}\\\\\boxed{(-\frac{5}{4})^2=\frac{25}{16}}[/tex]
What is the slope of the line represented by the equation y = 4/5x - 3?
in
Answer:
[tex]\boxed{\sf \ \ \ \dfrac{4}{5} \ \ \ }[/tex]
Step-by-step explanation:
when the equation is like y = ax + b
the slope is a
in this case we have
[tex]y \ = \ \dfrac{4}{5}x\ \ - \ 3[/tex]
so the slope is
[tex]\dfrac{4}{5}[/tex]
Two sides of a triangle measure 5 in. and 12 in. Which could be the length of the third side?
Answer: 10.9
Step-by-step explanation:
You would use Pythagorean theorem:
5x5+12x12=c
5x5=25
12x12=144
Now, 25+144=169
Now find the square root of 169 which is 13 which isn't an answer choice, which means your prolly after a leg.
I assume 12 is the hypotenuse
A(squared)+5x5=12x12
A+25=144
144-25=119
Square root of 119=10.9
So I'm going to go with answer 10 in or 11 if you round.
Answer:
i think its c
Step-by-step explanation:
The populations and areas of four states are shown.Which statement regarding these four states is true?
Carla earns $564 for 30 hours of work. Which represents the unit rate?
a) $30 per hour
b) $168 per hour
c) $18.80 per hour
d) $5.30 per hour
Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified?
Answer:
[tex]j^4k[/tex]
Step-by-step explanation:
[tex]3j^4k-2jk^3+jk^3-2j^4k+jk^2\\2j^4k-2j^4k-2jk^3+jk^3+jk^3\\j^4k[/tex]
Answer:
4
Step-by-step explanation:
give me brainliest