Answer:
a)Randomization condition: Satisfied, as the subjects were randomly selected.
10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).
Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.
b) The 90% confidence interval for the population proportion is (0.68, 0.70).
Step-by-step explanation:
a) Evaluating the necessary conditions:
Randomization condition: Satisfied, as the subjects were randomly selected.
10% condition: Satisfied, as the sample size is less than 10% of the population (U.S. adults).
Sample size condition: Satisfied, as the product between the smaller proportion and the sample size is bigger than 10.
[tex]n(1-p)=4,726\cdot (1-0.69)=4,726\cdot 0.31=1,465>10[/tex]
b) We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.69.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.69*0.31}{4726}}\\\\\\ \sigma_p=\sqrt{0.000045}=0.007[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.007=0.01[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.69-0.01=0.68\\\\UL=p+z \cdot \sigma_p = 0.69+0.011=0.70[/tex]
The 90% confidence interval for the population proportion is (0.68, 0.70).
What is the value of the discriminant for the quadratic equation?
6x^2 - 2x + 5 = 0
Answer: -116 is value of discriminant
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
write this small number in standard form. 0.00078
Answer:
78/100000
Hope it helps you
If 6 newborn babies are randomly selected, how many different gender sequences are possible?
Answer:
720
Step-by-step explanation:
6!
6x5x4x3x2x1=720
(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
Can someone help me with this I don’t know if I’m right so
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 tree that is 10 feet tall is growing at a rate of 2 foot each year. A tree that is 14 feet tall is growing at a rate of 2/3 foot each year. What is the number of years it will take for both trees to be the same height, and what will their height be?
Answer:
after three years
Step-by-step explanation:
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
Can anybody please help me with this one??
Answer:
[tex]the \: answer \: is \: d.(x + 4) {}^{2} = 8(y + 4)[/tex]
What’s the correct answer for this question?
Answer:
B.
Step-by-step explanation:
A cone with a radius of 1-unit will be obtained by rotating the 3-D figure.
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.
What is the solution to this equation?
10x - 3(x- 6) = x + 30
O A. x = 8
O B. x = 2
C. X= 4
[tex]answer \\ 2\\ solution \\ 10x - 3(x - 6) = x + 30 \\ or \: 10x - 3x + 18 = x + 30 \\ or \: 10x - 3x - x = 30 - 18 \\ or \: 7x - x = 12 \\ or \: 6x = 12 \\ or \: x = \frac{12}{6} \\ x = 2 \\ hope \: it \: helps[/tex]
Answer:
x=2
Step-by-step explanation:
10x - 3(x- 6) = x + 30
Distribute
10x -3x+18 = x+30
Combine like terms
7x + 18 = x+30
Subtract x from each side
6x+18 = 30
Subtract 18 from each side
6x = 30-18
6x = 12
Divide by 6
6x/6 = 12/6
x =2
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.
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!!!
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:
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.
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 $83.33
I hope that this helps! Have a wonderful day!
Find the measure of angle x in the figure below: A triangle is shown. At the top vertex of the triangle is a horizontal line aligned to the base of the triangle. The angle formed between the horizontal line and the left edge of the triangle is shown as 56 degrees, the angle formed between the horizontal line and the right edge of the triangle is shown as 51 degrees. The angle at the top vertex of the triangle is labeled as y, and the interior angle on the right is labeled as 72 degrees. The interior angle on the left is labeled as x.
Answer:
[tex]x=35^\circ[/tex]
Step-by-step explanation:
From the diagram which I have drawn and attached below:
[tex]56^\circ+y+51^\circ=180^\circ$ (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.
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
~
Answer pls need help
The pressure p(in lbs/in^2) that a 160 pound persons shoe exerts on the ground when walking varies inversely with the area A(in in^2) of the sole of the shoe when the shoes have a sole area of 40 in^2 The pressure is 4 lbs/in^2 find equation that relates these variables
A=
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]
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 = 64What is X:
3x−22=44
5/6 = 10/2x−3
Answer:
x = 22
x = 4,6
Step-by-step explanation:
3x - 22 = 44
3x = 44 + 22
3x = 66
x = 66/3
x = 22
5/6 = 10/2x - 3
5/6 + 3 = 10/2x
5/6 + 18/6 = 10/2x
23/6 = 10/2x
23/6 * 2 = 10x
46 = 10x
x = 46/10
x = 4,6
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!
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:
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?
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]
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
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;
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