Answer:
-3a+3bx+2ab
Step-by-step explanation:
ab=6cm ac=12 calculate the length of cd
Answer:
is that the full question?
Answer:
Solution:-
Given,
ab =perpendicular (p)= 6cm
ac =hypotenuse (h)= 12cm
cd =base (b)= ?
using , Pythagoras theorem we have ,
b²=√h²-p²
or,cd²=√ac²-ab²
= √12²-6²
= √144-36
=√108
=√10.8²
=10.8cm
the length of cd is 10.8 cm
hope it is helpful to you
Which of the following is a like radical to cube rt of 7x
Answer:
[tex]\sqrt[3]{7x}[/tex]
Step-by-step explanation:
Given
[tex]7x[/tex]
Required
The radical statement
Cube root is represented as:
[tex]\sqrt[3]{}[/tex]
Considering [tex]7x[/tex], the expression is:
[tex]\sqrt[3]{7x}[/tex]
2.6.58
The lot in the figure shown, except for the house, shed, and driveway, is lawn. One bag of lawn fertilizer
costs $15.00 and covers 3,000 square feet.
Please help :)
Answer:
50 bags ;
£750
Step-by-step explanation:
The dimension of the rectangular lawn is 500ft by 300 ft
The area of the lawn an e obtained thus :
Area of rectangle = Length * width
Area of rectangle = 500 ft * 300 ft
Area of rectangle = 150000 feets
1 bag of fertilizer covers 3000 feets
The minimum bags of fertilizer required :
Area of rectangle / Area covered by 1 bag of fertilizer
Minimum bags of fertilizer required :
(150,000 / 3000) = 50 bags
50 bags of fertilizer
Cost per bag = 15
Total cost = 15 * 50 = £750
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color green. If 14 buyers are randomly selected, what is the probability that exactly 12 buyers would prefer green
Answer:
The probability that exactly 12 buyers would prefer green
=0.00555
Step-by-step explanation:
We are given that
p=50%=50/100=0.50
n=14
We have to find the probability that exactly 12 buyers would prefer green.
q=1-p
q=1-0.50=0.50
Using binomial distribution formula
[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]
[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]
[tex]P(x=12)=0.00555[/tex]
Hence, the probability that exactly 12 buyers would prefer green
=0.00555
Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occur
Complete question is;
Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 83% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 34% of all defective components. What is the probability that the following occurs?
(a) A defective component will be detected only by the first inspector?
b) A defective component will be detected by exactly one of the two inspectors?
(c) All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?
Answer:
A) 0.17
B) 0.34
C) 0
Step-by-step explanation:
a) We are told that the first inspector(A) detects 83% of all defectives that are present, and the second inspector(B) also does the same.
This means that;
P(A) = P(B) = 83% = 0.83
We are also told that at least one inspector does not detect a defect on 34% of all defective components.
Thus;
P(A' ⋃ B') = 0.34
Also, we now that;
P(A ⋂ B) = 1 - P(A' ⋃ B')
P(A ⋂ B) = 1 - 0.34
P(A ⋂ B) = 0.66
Probability that A defective component will be detected only by the first inspector is;
P(A ⋂ B') = P(A) - P(A ⋂ B)
P(A ⋂ B') = 0.83 - 0.66
P(A ⋂ B') = 0.17
B) probability that a defective component will be detected by exactly one of the two inspectors is given as;
P(A ⋂ B') + P(A' ⋂ B) = P(A) + P(B) - 2P(A ⋂ B)
P(A) + P(B) - 2P(A ⋂ B) ; 0.83 + 0.83 - 2(0.66) = 0.34
C) Probability that All three defective components in a batch escape detection by both inspectors is written as;
P(A' ⋃ B') - (P(A ⋂ B') + P(A' ⋂ B))
Plugging in the relevant values, we have;
0.34 - 0.34 = 0
SCALCET8 3.8.001.MI. A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population consists of two members. Find the population size after seven days. (Round your answer to the nearest whole number.) P(7)
Answer:
A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population · Q: For this discussion, you will work in groups to find the area and answer questions.
Step-by-step explanation:
Consider the quadratic function y = 0.3 (x-4)2 - 2.5
Determine the axis of symmetry, x =
Answer:
[tex]x=4[/tex]
Step-by-step explanation:
We have the quadratic function:
[tex]\displaystyle y=0.3(x-4)^2-2.5[/tex]
And we want to determine its axis of symmetry.
Notice that this is in vertex form:
[tex]y=a(x-h)^2+k[/tex]
Where (h, k) is the vertex of the parabola.
From our function, we can see that h = 4 and k = -2.5. Hence, our vertex is the point (4, -2.5).
The axis of symmetry is equivalent to the x-coordinate of the vertex.
The x-coordinate of the vertex is 4.
Therefore, the axis of symmetry is x = 4.
Expand 5(2x-1) please I need it for homework.
10x-5
Answer:
5(2x-1)
5*2x 5*-1
10x-5
Hey there!
5(2x - 1)
= 5(2x) + 5(-1)
= 10x - 5
Therefore, your answer should be: 5x - 5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
You are making a committee from the class and need to have 6 students on it. There are 32 students in the class.
answer in permutations
Answer:
32P6
Step-by-step explanation:
nPr
n=32
r=6
An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.
Weight % of Total Underweight 2.5 Satisfactory 90.0 Overweight 7.5a) What is the probability of selecting and finding that all three bags are overweight?b) What is the probability of selecting and finding that all three bags are satisfactory?
Answer:
a) 0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.
b) 0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory
Step-by-step explanation:
The condition of the bags in the sample is independent of the other bags, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
a) What is the probability of selecting and finding that all three bags are overweight?
2.5% are overweight, which means that [tex]p = 0.025[/tex]
3 bags means that [tex]n = 3[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.025)^{3}.(0.975)^{0} = 0.000016[/tex]
0.000016 = 0.0016% probability of selecting and finding that all three bags are overweight.
b) What is the probability of selecting and finding that all three bags are satisfactory?
90% are satisfactory, which means that [tex]p = 0.9[/tex]
3 bags means that [tex]n = 3[/tex]
This probability is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.9)^{3}.(0.1)^{0} = 0.729[/tex]
0.729 = 72.9% probability of selecting and finding that all three bags are satisfactory
A storage box with a square base must have a volume of 80 cubic centimeters. The top and bottom cost $0.20 per square centimeter and the sides cost $0.10 per square centimeter. Find the dimensions that will minimize cost. (Let x represent the length of the sides of the square base and let y represent the height. Round your answers to two decimal places.) x
Answer:
Box dimensions:
x = 3.42 cm
y = 6.84 cm
C(min) = 14.04 $
Step-by-step explanation:
We need the surface area of the cube:
S(c) = 2*S₁ ( surface area of top or base) + 4*S₂ ( surface lateral area)
S₁ = x² 2*S₁ = 2*x²
Surface lateral area is:
4*S₂ = 4*x*h V(c) = 80 cm³ = x²*h h = 80/x²
4*S₂ = 4*80/x
4*S₂ = 320 / x
Costs
C (x) = 0.2* 2*x² + 0.1 * 320/x
Taking derivatives on both sides of the equation we get:
C´(x) = 0.8*x - 32/x²
C´(x) = 0 0.8*x - 32/x² = 0
0.8*x³ - 32 = 0 x³ = 32/0.8
x³ = 40
x = 3.42 cm
h = 80/(3.42)² h = 6.84 cm
To find out if x = 3.42 brings a minimum value for C we go to the second derivative
C´´(x) = 64/x³ is always positive for x > 0
The C(min) = 0.4*(3.42)² + 32/(3.42)
C(min) = 4.68 + 9.36
C(min) = 14.04 $
Lorena and Julio purchased a home for $205,950. Their loan amount was $164,760, and the assessed value is now $200,500. Their tax rate is 1.5%. How much will their monthly taxes be?
Answer:
Monthly taxes = $250.63 (Approx.)
Step-by-step explanation:
Given:
Amount of purchase = $205,950
Loan amount = $164,760
Assessed value = $200,500
Tax rate is 1.5%
Find:
Monthly taxes
Computation:
Tax always calculated on Assessed value
Annual tax amount = 200,500 x 1.5%
Annual tax amount = 3,007.5
Monthly taxes = Annual tax amount / 12
Monthly taxes = 3,007.5 / 12
Monthly taxes = 250.625
Monthly taxes = $250.63 (Approx.)
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
Use the button on your calculator to complete this
problem.
V=
cm3
Answer:4778.3 cm^3
Step-by-step explanation: The formula for volume of a cone is V=1/3h pi r^2. By plugging in the height and the radius we get our answer.
Answer:
4778.4 :)
Step-by-step explanation:
In the figure below. JLM is similar to JKN if JM=14 inches what is the length of JN
Answer:
Hello good evening friend
Solve. SHOW ALL YOUR WORK
2.51 * .2
77/ 1.2
Answer:
0.502
64.1666
Step-by-step explanation:
Detained explanation of the product operation and division operation is attached below.
2.51 * 0.2 = 0.502
(after multiplying) the number of decimal places of the town values is added and counted from the right in the product to place the data Comal point appropriately.
77/1.2 ; values were multiplied by 10 in other to obtain inter values for the denominator.
please answer me as soon as posible
Answer:
yes your answer is right
Answer:
Yes it's Perfectly correct
What are the domain and range of the function f(x) = 3^x + 5?
a. domain: (negative infinity, infinity); range: (0, infinity)
b. domain: (negative infinity, infinity); range: (5, infinity)
c. domain:(0, infinity); range: (negative infinity, infinity)
d. domain: (5, infinity); range: (negative infinity, infinity)
PLEASE RESPOND QUICKKK THANK YOUU
Answer:
b. domain: (negative infinity, infinity); range: (5, infinity)
Step-by-step explanation:
Answer:
B. Domain: (negative infinity, infinity);
Range: (5, infinity)
One-ninth of all sales at a local Subway are for cash. If cash sales for the week were $690, what were
Subway's total sales?
Select one:
O a. $22,600
O b. $2,611
O c. $6,210
O d. $2,610
e. None of these
Answer:
c. $6,210Step-by-step explanation:
Total sales = x
x*1/9 = 690x = 690*9x = 6210Correct choice is C
fill in the blink
Given ,Simplify ,BC=EF ,Multiplication Property of Equality ,Substitution Property of Equality AC=DF DE+EF=DF Reflexive Property of Equality Transitive Property of Equality ,Segment Addition Postulate, Division Property of Equality ,Addition Property of Equality, Distributive Property, Subtraction Property of Equality
Answer:
see below
Step-by-step explanation:
[tex] \displaystyle AB = DE[/tex]
[given]
[tex] \displaystyle \boxed{BC = EF}[/tex]
[given]
[tex] \displaystyle AB + BC = AC[/tex]
[segment addition Postulate]
[tex] \displaystyle \boxed{DE+ EF=DF}[/tex]
[segment addition Postulate]
[tex] \rm\displaystyle DE+ BC = AC \: \: \text{and} \: \: DE+ BC = DF[/tex]
[Substitution Property of Equality]
[tex] \displaystyle \boxed{AE= DE}[/tex]
[Proven]
HELP HELP HELP MATH⚠️⚠️⚠️⚠️⚠️
Find four consecutive integers with the sum of 2021
Answer:
This problem has not solution
Step-by-step explanation:
lets the integers be:
x
x+1
x+2
x+3
so:
x+(x+1)+(x+2)+(x+3)=2021
x+x+x+x+1+2+3=2021
4x+6=2021
4x=2021-6=2015
x=2015/4=503.75
x is not a integer
Choose the system of inequalities that best matches the graph below.
Answer:
"D" is the correct answer
Step-by-step explanation:
I need help nowww!! 16 points
Answer:
A: x = 0
B: x = All real numbers
Step-by-step explanation:
A.
Any number to the power of (0) equals one. This applies true for the given situation; one is given an expression which is as follows;
[tex](6^2)^x=1[/tex]
Simplifying that will result in;
[tex]36^x=1[/tex]
As stated above, any number to the power of (0) equals (1), thus (x) must equal (0) for this equation to hold true.
[tex]36^0=1\\x=0[/tex]
B.
As stated in part (A), any number to the power (0) equals (1). Therefore, when given the following expression;
[tex](6^0)^x=1[/tex]
One can simplify that;
[tex]1^x=1[/tex]
However, (1) to any degree still equals (1). Thus, (x) can be any value, and the equation will still hold true.
[tex]x=All\ real \ numbers[/tex]
In the diagram below, POR is a diameter, <QPR is a°,<PRS is (4a+12)°. find the value of a
Answer:
22=4
Step-by-step explanation:
0977-=ytb
Drag the label to the correct location on the image
9514 1404 393
Answer:
-∞ < y ≤ 12
Step-by-step explanation:
The range is the vertical extent of the graph of the function. Here the function values range from -∞ to a maximum of about 12. An appropriate description is ...
-∞ < y ≤ 12
For a popular Broadway music the theater box office sold 356 tickets at $80 a piece275 tickets at $60 a piece and 369 tickets at $ 45 a piece. How much money did the box office take in?
Answer:
Step-by-step explanation:
356 * 80 = 28 480
275 * 60 = 16 500
369 * 45 = 16 605
sum = $ 61 585
Help me or ill fail plz
Answer:
1,108 in²
Step-by-step explanation:
SA = (12×20) + (2×20×5 + 2×12×5) + (2×½×12×9)
+ (2×20×11)
= 240+320+108+440
= 1,108 in²
rotation 180 degrees about the origin.
Answer:
Click the rotate 'button' twice.
Observe.
The rotate button is rotating the image about the orgin.
Answer:
Click the rotate 'button' twice.
Observe.
The rotate button is rotating the image about the orgin.
Step-by-step explanation:
14. 14. If f(x)= sec^2x, thenf'(x)=
Answer:
1 (2) f(x) = 1 (3) 1< f(x) < 2 (4) f(x) greater than or equal to 2
Step-by-step explanation:
We know AM ≥ GM
(cos2x+sec2x )/2 ≥ √(cos2x sec2x)
(cos2x+sec2x ) ≥ 2√(cos2x (1/cos2x)
f(x) ≥ 2
Hence option (4) is the answer.
Let v=-9i+j and w=-i-6j find 8v-6w
Answer:
78i+52j
Step-by-step explanation:
8(9i+2j)-6(-i-6j)
72i+16j+6i+36j
=78i+52j
What is the domain of the function f(x) = (-5/6)(3/5)superscript x
Answer:
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x[/tex]
Required
The domain
There are no undefined points such as denominator of x or square roots.
Hence, the domain is:
[tex]-\infty < x < \infty[/tex]
