Answer:
x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Step-by-step explanation:
Solve for x over the real numbers:
x - 2 + x/x + 1 - 1/x = -1
x - 2 + x/x + 1 - 1/x = x - 1/x:
x - 1/x = -1
Bring x - 1/x together using the common denominator x:
(x^2 - 1)/x = -1
Multiply both sides by x:
x^2 - 1 = -x
Add x to both sides:
x^2 + x - 1 = 0
Add 1 to both sides:
x^2 + x = 1
Add 1/4 to both sides:
x^2 + x + 1/4 = 5/4
Write the left hand side as a square:
(x + 1/2)^2 = 5/4
Take the square root of both sides:
x + 1/2 = sqrt(5)/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
x = sqrt(5)/2 - 1/2 or x + 1/2 = -sqrt(5)/2
Subtract 1/2 from both sides:
Answer: x = sqrt(5)/2 - 1/2 or x = -1/2 - sqrt(5)/2
Please answer this correctly
Answer:
2 cups more was given to the flower with the most water because 5 cups - 3 cups = 2 cups.
Answer:
2 cups
Step-by-step explanation:
The most water was 5 cups and the least was 3 cups. So:
5-3=2 cups more
Suppose a company's revenue function is given by R(q) = - q^3 + 220q^2 and its cost function is given by C(q) = 500 + 13q, where q is hundreds of units sold/produced, while R(q) and C(q) are in total dollars of revenue and cost, respectively.
A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.)
MP(q) =
B) How many items (in hundreds) need to be sold to maximize profits? (Round your answer to two decimal places.)
Answer:
A) MP(q) = -3q² + 440q - 13
B) 146.64 units.
Step-by-step explanation:
The profit function is given by the revenue minus the cost function:
[tex]P(q) = R(q) - C(q)\\P(q) = -q^3+220q^2-500-13q[/tex]
A) The Marginal profit function is the derivate of the profit function as a function of the quantity sold:
[tex]P(q) = -q^3+220q^2-500-13q\\MP(q) = \frac{dP(q)}{dq} \\MP(q)=-3q^2+440q-13[/tex]
B) The value of "q" for which the marginal profit function is zero is the number of items (in hundreds) that maximizes profit:
[tex]MP(q)=0=-3q^2+440q-13\\q=\frac{-440\pm \sqrt{440^2-(4*(-3)*(-13))} }{-6}\\q'=146.64\\q'' = - 0.03[/tex]
Therefore, the only reasonable answer is that 146.64 hundred units must be sold in order to maximize profit.
A factory received a shipment of 10 generators, and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.
Answer:
A) 0.026
B) 0.130
Step-by-step explanation:
Complete Question
A factory received a shipment of 10 generators and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.
(A) If a sample of 4 generators is selected, find the probability that all in the sample are defective.
(B) If a sample of 4 generators is selected, find the probability that none in the sample is defective.
Solution
A) This is a binomial distribution problem
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = number of generators to be picked = 4
x = Number of successes required = number of defective generators required = 4
p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40
q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60
P(X = 4) = ⁴C₄ (0.40)⁴ (0.6)⁴⁻⁴ = 0.0256 = 0.026 to 3 d.p.
B) n = total number of sample spaces = number of generators to be picked = 4
x = Number of successes required = number of defective generators required = 0
p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40
q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60
P(X = 0) = ⁴C₀ (0.40)⁰ (0.6)⁴⁻⁰ = 0.1296 = 0.130 to 3 d.p.
Hope this Helps!!!
Bernard bought 8gal of paint. Convert the volume to liters. Round to the nearest tenth
Answer:
In one gallon of paint there are about 3.8 liters so 8 gallons is about 30.3 liters.
Felicia walks 3 blocks west, 4 blocks south, 3 more blocks west, then
2 blocks south again. How far is Felicia from her starting point?
blocks
Answer:
Round $0.6683 to the nearest cent
Answer:
0.67
Step-by-step explanation:
0.668 is close to 0.67 than 0.66
Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?
(5m+100) (2m+10) what’s the value of m
Answer:
m=-30
Step-by-step explanation:
5m+100=2m+10
We want to get the variable on one side of the equation. First we subtract 100 from both sides.
5m=2m-90
Subtract 2m from both sides.
3m=-90
Divide both sides by 3.
m=-30
Tony rode his bicycle 3 7/10 miles to school. What is this distance written as a decimal?
Answer:
the distance written as a decimal is 3.7
37/10 = 3,7
Achievements :)
Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication a at what time will you need to stop the infusion
Answer:
6 PM
Step-by-step explanation:
125 mg --- 300 mL
500 mg --- x mL
x = 500*300/125 = 1200 mL solution contains 500 mg
rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
You need to stop infusion at 6 PM
It is found that You need to stop infusion at 6 PM.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication.
125 mg = 300 mL
500 mg = x mL
x = 500*300/125
x = 1200 mL
Here solution contains 500 mg
The rate = 100 mL/h
1200 mL* 1h/100 mL = 12 h
6AM + 12 h = 6 PM
Therefore, You need to stop infusion at 6 PM.
Learn more about the unitary method;
https://brainly.com/question/23423168
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Which ordered pair is the solution of the system of equations? 3x+2y=4, -2+2y=24
Answer:
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
y = 13
Step-by-step explanation:
→You can use the substitution method. First, make y by itself in (-2 + 2y = 24):
-2 + 2y = 24
2y = 26
y = 13
→Then, plug in 13 for y into the other equation:
3x + 2y = 4
3x + 2(13) = 4
3x + 26 = 4
3x = -22
x = -7.33 OR x = [tex]\frac{-22}{3}[/tex]
HELP PLEASE
Find the solution set.
(x - 11)(x - 11) = 0
Answer:
x = 11
Step-by-step explanation:
You are solving for the solution of the variable given (x). Set each parenthesis equal to 0 and simplify:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Add 11 to both sides:
x - 11 = 0
x - 11 (+11) = 0 (+11)
x = 0 + 11
x = 11
Do the same for the other set:
x - 11 = 0
x - 11 (+11) = 0 (+11)
x = 0 + 11
x = 11
~
While filing your income tax, you report annual contributions of $100 to a public radio station, $300 to PBS (television station), $150 to a woman’s shelter, and $450 to other charitable organizations.
Find your monthly expense.
Hey there! I'm happy to help!
Let's add up all of these contributions.
100+300+150+450=1000
However, this is annual. We want monthly. So, we simply divide by 12.
1000/12≈83.33
Therefore, the monthly expense is $83.33
I hope that this helps! Have a wonderful day!
Chris has been hired to assess a new version of a college entrance exam. He randomly assigns 100 high school juniors to take the new exam and 100 high school juniors to take the old exam. So that the participants were unaware of the two versions, the new exam was administered in the school gym while the old exam was administered in the school auditorium. The students taking the exam in the gym complained about the smell, the temperature and the uncomfortable seats. The students taking the exam in the auditorium made no complaints. Chris calculated a statistically significant difference between the two versions of the exam (t(198)= 3.1, p< 0.005) and concluded that the new exam was not a valid substitute for the old exam. There is a problem with validity. Which validity is weak in this example?
a. external validity
b. construct validity
c. statistical validity
d. internal validity
Answer:
Internal validity
Step-by-step explanation:
The internal validity here is weak
Internal validity describes the extent to which an evidence weighs the cause and effect claim. In this study, the internal validity that brought about failure in the new exam is mainly due to the environment where the exam was written and not the new exam itself.
So this validity is weak in claiming that the new exam is not a good substitute for the old exam.
Putting them in the same good environment might help the researchers to draw a better conclusion.
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
64
Step-by-step explanation:
If the mean is 15, the sum of 5 numbers is:
5*15 = 75Minimum value for the first four numbers would be:
1, 2, 3, 4Then the fifth number is:
75 - (1+2+3+4) = 75 - 10 = 65So the maximum difference is:
65 - 1 = 64write this small number in standard form. 0.00078
Answer:
78/100000
Hope it helps you
please help !!!
Find the probability that x = -10
Answer:
20%
Step-by-step explanation:
Use the table provided... it says -10 is .2 which is the same as 20%
Answer:
0.20
Step-by-step explanation:
requires decimal not percentage
The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 38 hours and the median is 34.2 hours. Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours. Step 2 of 5 : Approximately how many families are in the sample? Round your answer to the nearest integer.
Answer:
There are approximately 171 families in the sample.
Step-by-step explanation:
Percentile meaning:
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours.
This means that 24 is 14% of the total number of families.
Approximately how many families are in the sample?
Using a rule of three.
24 - 0.14
x - 1
0.14x = 24
x = 24/0.14
x = 171.4
Rounding to the nearest integer
There are approximately 171 families in the sample.
URGENT!! EASY IM DUMB MY LAST QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
18. Using the diagram below as reference, write a paragraph proof to prove that the symmetric property of congruence exists for any two angles. (IMAGE BELOW)
Given: ∠A is congruent to ∠B
Prove: ∠B is congruent to ∠A
Plan: Show that ∠A and ∠B have the same measure, thus ∠B and ∠A have the same measure under symmetry for equality. Conclude with ∠B being congruent to ∠A.
Answer:
Below.
Step-by-step explanation:
Since A is congruent to B, you can conclude that B is congruent to A by the Reflexive Property of Congruence.
Can anybody please help me with this one??
Answer:
[tex]the \: answer \: is \: d.(x + 4) {}^{2} = 8(y + 4)[/tex]
A bread machine produces 159 loaves of bread per hour. The machine operates 10 hours per day. How many loaves of bread does it produce per day? _____ loaves
Answer:
It can produce 1590 loaves of bread per day.
Step-by-step explanation:
Given that the bread machine operates only 10 hours per day. So in order to calculate how many loaves can be produce a day, you have to multiply it by 10 :
[tex]1hour = 159loaves[/tex]
[tex]10hours = 159 \times 10[/tex]
[tex]10hours = 1590loaves[/tex]
What is the value of the discriminant for the quadratic equation?
6x^2 - 2x + 5 = 0
Answer: -116 is value of discriminant
If 6 newborn babies are randomly selected, how many different gender sequences are possible?
Answer:
720
Step-by-step explanation:
6!
6x5x4x3x2x1=720
Which set of three angles could represent the interior angles of a triangle? A 26 degrees, 51 degrees, 103 degrees B 29 degrees, 54 degrees, 107 degrees C 35 degrees, 35 degrees, 20 degrees D 10 degrees, 90 degrees, 90 degrees
Answer:
it is option A
Step-by-step explanation:
Find the measure of angle x in the figure below: A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 56 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 51 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 72 degrees. The interior angle on the left is labeled as x.
Answer:
[tex]x=35^\circ[/tex]
Step-by-step explanation:
From the diagram which I have drawn and attached below:
[tex]56^\circ+y+51^\circ=180^\circ$ (Sum of Angles on a Straight Line)\\y=180^\circ-(56^\circ+51^\circ)\\y=73^\circ[/tex]
Next, in the triangle, the sum of the three interior angles:
[tex]y+x+72^\circ=180^\circ\\$Since y=73^\circ\\73^\circ+x+72^\circ=180^\circ\\x=180^\circ-(73^\circ+72^\circ)\\x=35^\circ[/tex]
The value of angle x is 35 degrees.
Answer 5x + 8 − 3x = −10
Answer:
-9
Step-by-step explanation:
5x+8-3x = -10
Combine like terms
2x+8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
Answer:
-9
Step-by-step explanation:
5x + 8 - 3x = -10
Combine like terms
2x + 8 = -10
Subtract 8 to both sides
2x = -18
Divide both sides by 2
x = -9
A bag contains some number of marbles. It is known that 20 of them are red. When 15 marbles are drawn, without replacement, we get 6 red. Assuming E(X)=6 red, what is the total number of marbles in the bag?
Answer:
The total number of marbles in the bag is 50.
Step-by-step explanation:
Here, we have n trials, without replacement. So the hypergeometric distribution is used.
The mean of the hypergeometric distribution is:
[tex]E(X) = \frac{n*k}{N}[/tex]
In which n is the number of items in the sample, k is the number of items in the population that are classified a success and N is the size of the population.
15 marbles are drawn:
This means that [tex]n = 15[/tex]
A bag contains some number of marbles. It is known that 20 of them are red.
This means that [tex]k = 20[/tex], since a success is drawing a red marble.
Assuming E(X)=6 red, what is the total number of marbles in the bag?
We have to find N when [tex]E(X) = 6[/tex]
So
[tex]E(X) = \frac{n*k}{N}[/tex]
[tex]6 = \frac{15*20}{N}[/tex]
[tex]6N = 300[/tex]
[tex]N = \frac{300}{6}[/tex]
[tex]N = 50[/tex]
The total number of marbles in the bag is 50.
You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h = 130 and a square base with side s = 870
To impress your Egyptian subjects, find the volume of the pyramid.
Answer:
32799000 cubic units
Step-by-step Explanation:
Height if the Pyramid=130 Units
Side Length of square base=870 Units
Volume of a Pyramid=[tex]\frac{1}{3}[/tex]* Base Area*Height
Since the base is a square,
Area of a Square of side length s[tex]=s^2[/tex]
Therefore:
Volume[tex]=\frac{1}{3}*870^2*130[/tex]
=32799000 cubic units
The volume of your pyramid is 32799000 cubic units.
Answer:
V = 3.28x10⁷
Step-by-step explanation:
The volume of a pyramid is given by:
[tex] V = \frac{1}{3}bh [/tex]
Where:
b: is the base of the pyramid
h: is the height of the pyramid = 130
The base of the square base of the pyramid is given by:
[tex] b = s^{2} [/tex]
Where:
s: is the side of the square base = 870
Thus, the base of the square base of the pyramid is:
[tex] b = s^{2} = (870)^{2} = 7.56 \cdot 10^{5} [/tex]
Now, the volume of a pyramid is:
[tex] V = \frac{1}{3}bh = \frac{1}{3}(7.56 \cdot 10^{5})*130 = 3.28 \cdot 10^{7} [/tex]
Therefore, the volume of the pyramid is 3.28x10⁷.
I hope it helps you!
Can someone help me with this I don’t know if I’m right so
2. A manufacturer produces light bulbs at a Poisson rate of 300 per hour. The probability that a light bulb is defective is 0.012. During production, the light bulbs are tested, one by one, and the defective ones are put in a special can that holds up to a maximum of 50 light bulbs. On average, how long does it take until the can is lled
Answer:
On average it will take 13 hrs 53 minutes before the van is filled
Step-by-step explanation:
The first thing we need to do here is to find find the number of defective light bulbs
Using the poisson process, that would be;
λ * p
where λ is the poisson rate of production which is 300 per hour
and p is the probability that the produced bulb is defective = 0.012
So the number of defective bulbs produced within the hour = 0.012 * 300 = 3.6 light bulbs per hour
Now, let X be the time until 50 light bulbs are produced. Then X is a random variable with the parameter (r, λ) = (50, 3.6)
What we need to find however is E(X)
Thus, the expected value of a gamma random variable X with the parameter (x, λ) is;
E(X) = r/λ = 50/3.6 = 13.89
Thus the amount of time it will take before the Can will be filled is 13 hrs 53 minutes