Answer:
X=10.8 and X=1.1
Step-by-step explanation:
Δ= b^2-4ac
= (-6)^2-4(1)(3)
=24
X1=
[tex] \frac{6 + \sqrt{24} }{ {1}^{2} } [/tex]
=10.8
X2=
[tex] \frac{6 - \sqrt{4} }{ {1}^{2} } [/tex]
=1.1
About 32% of the population in a large region are between the ages of 40 and 65, according to the country's census. However, only 2% of the 2100 employees at a company in the region are between the ages of 40 and 65. Lawyers might argue that if the company hires people regardless of their ages, the distribution of ages would be the same as through they had hired people at random from the surrounding population. Check whether the condoms for using the one proportion z-test are met.
The conditions for using a one proportion z-test are likely met as the sample of 2100 employees is assumed to be randomly selected, independent, and satisfies the success-failure condition, allowing for comparison of the company's age distribution with the surrounding population.
To check whether the conditions for using a one proportion z-test are met, we need to ensure that the following conditions are satisfied:
1. **Random Sample**: The sample of 2100 employees should be selected randomly from the population.
2. **Independence**: The selection of one employee should not influence the selection of another. This condition is typically assumed to be met if the sample size is less than 10% of the population size.
3. **Success-Failure Condition**: The number of successes (employees aged between 40 and 65) and failures (employees not aged between 40 and 65) in the sample should each be at least 10.
Let's check each condition:
1. **Random Sample**: If the company's hiring process is unbiased and follows fair employment practices, then this condition is likely met.
2. **Independence**: With 2100 employees selected, it's reasonable to assume that this condition is met, especially if the population of potential employees is large.
3. **Success-Failure Condition**: We have:
- Number of successes: [tex]\(2100 \times 0.02 = 42\)[/tex]
- Number of failures: [tex]\(2100 - 42 = 2058\)[/tex]
Both 42 and 2058 are greater than 10, so the success-failure condition is met.
Since all three conditions are satisfied, the company's distribution of ages among its employees can be analyzed using a one proportion z-test to compare it with the population distribution.
Create a real-world problem involving three lengths that form a right triangle
Give the measurement of the “legs”, then solve for the missing hypotenuse
Answer:
Bob was looking for a shade sail that was big enough and wide to cover his hotube. The legs were 6 by 8 but he didnt know how long the hypotinuce was. So he use pythagorean theorm to sove fot the unknown side.
A^2 + B^2 = C^2 --> 6^2 + 8^2 = C^2 --> he square rooted the 6 and 8 and got (36 + 64 = c^2) 100 to get c he had to squar root that. He found out that the missing side was 10 inch long.
Step-by-step explanation:
Solve the equation 51 = x(3.50 + 5.50)
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Evaluate 0.1m+8-12n0.1m+8−12n0, point, 1, m, plus, 8, minus, 12, n when m=30m=30m, equals, 30 and n=\dfrac14n= 4 1 n, equals, start fraction, 1, divided by, 4, end fraction
Answer:
8
Step-by-step explanation:
We are required to evaluate:
0.1m+8-12n
When [tex]m=30, n=\frac{1}{4}[/tex]
Substituting these values into the expression, we have:
[tex]0.1m+8-12n=0.1(30)+8-12(\frac{1}{4})\\=3+8-\frac{12}{4}\\=3+8-3\\=8[/tex]
After evaluating the expression the value is 8.
Evaluating the Expression
To evaluate the expression 0.1m + 8 - 12n when m = 30 and n = \frac{1}{4}, we need to follow these steps:
Substitute m and n into the expression:
0.1(30) + 8 - 12 [tex]\left(\frac{1}{4}\right)[/tex]
Calculate 0.1(30):
0.1 [tex]\times[/tex] 30 = 3
Calculate 12[tex]\left(\frac{1}{4}\right):[/tex]
12 [tex]\times \frac{1}{4}[/tex] = 3
Substitute these values back into the expression:
3 + 8 - 3
Simplify the expression:
3 + 8 = 11
11 - 3 = 8
Thus, the value of the expression is 8.
A solid right pyramid has a square base. The length of the
base edge is 4 cm and the height of the pyramid is 3 cm.
What is the volume of the pyramid?
12 cm
16 cm
32 cm
48 cm
4 cm
Mark this and return
Savo and Exit
Next
Submit
Answer:
The volume of the pyramid is 16 cm³.
Step-by-step explanation:
The volume of squared-base pyramid is given by the formula:
[tex]V=A\times \frac{h}{3}[/tex]
Here,
V = volume of the squared-base pyramid
A = area of the square base
h = height of the pyramid.
The information provided is:
a = side of square = 4 cm
h = 3 cm
Compute the area of the square base as follows:
[tex]A=a^{2}\\=4^{2}\\=16\ \text{cm}^{2}[/tex]
Compute the volume of squared-base pyramid as follows:
[tex]V=A\times \frac{h}{3}[/tex]
[tex]=16\times \frac{3}{3}\\\\=16[/tex]
Thus, the volume of the pyramid is 16 cm³.
A survey of athletes at a high school is conducted, and the following facts are discovered: 68% of the athletes are football players, 26% are basketball players, and 23% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player
Answer:
71% probability that the athlete is either a football player or a basketball player
Step-by-step explanation:
We solve this problem building the Venn's diagram of these probabilities.
I am going to say that:
A is the probability that an athlete is a football player.
B is the probability that an athlete is a basketball players.
We have that:
[tex]A = a + (A \cap B)[/tex]
In which a is the probability that an athlete plays football but not basketball and [tex]A \cap B[/tex] is the probability that an athlete plays both these sports.
By the same logic, we have that:
[tex]B = b + (A \cap B)[/tex]
23% of the athletes play both football and basketball.
This means that [tex]A \cap B = 0.23[/tex]
26% are basketball players
This means that [tex]B = 0.26[/tex]. So
[tex]B = b + (A \cap B)[/tex]
[tex]0.26 = b + 0.23[/tex]
[tex]b = 0.03[/tex]
68% of the athletes are football players
This means that [tex]A = 0.68[/tex]. So
[tex]A = a + (A \cap B)[/tex]
[tex]0.68 = a + 0.23[/tex]
[tex]a = 0.45[/tex]
What is the probability that the athlete is either a football player or a basketball player
[tex]A \cup B = a + b + (A \cap B)[/tex]
[tex]A \cup B = 0.45 + 0.03 + 0.23 = 0.71[/tex]
71% probability that the athlete is either a football player or a basketball player
Answer:
71%
Step-by-step explanation:
Applying Venn's diagram
probabilty that an athlete plays either football or basketball
P ( A ∪ B ) = a + b + ( A ∩ B ) equation 1
note:
P ( A ) = a + ( A ∩ B )
( A ∩ B ) = 23% = 0.23
a = P( A ) - 0.23 = 0.68 - 0.23 = 0.45
P ( B ) = b + ( A ∩ B )
b = P ( B ) - ( A ∩ B ) = 0.26 - 0.23 = 0.03
back to equation 1
P ( A ∪ B ) = 0.45 + 0.03 +( 0.23 )
= 0.48 + ( 0.23 ) = 0.71 = 71%
P( A ) = probability of football players
P ( B ) = probability of basketball players
a = probability of playing football but not basketball
b = probabilty of playing basketball but not football
Is 237.5 less than or greater than 2 8/24
Alright!
In order to properly compare these numbers, they need to look the same!
Lets change 2 8/24 into a decimal.
To do this, we need to convert it into an improper fraction
Follow these steps:
[tex]2 \frac{8}{24} \\[/tex]
We multiply the whole number (2) by the denominator (24) and then add the numerator (8). The improper fraction will keep the same denominator (24) at the end.
2 × 24 = 48
48 + 8 = 56
[tex]\frac{56}{24}[/tex]
Now, lets use a calculator to see what 56/24 is!
56 ÷ 24 = 2.33
237.5 is GREATER than [tex]2 \frac{8}{24} \\[/tex]
Hope I helped! Comment if you have questions :)
16.
(a)
Simply
3b + 5b - 2
Combine like terms
1. Add 3b and 5b (combine like terms)
2. After adding you are supposed to get 8b
3. The -2 would stay as it is because we can't add it to 8b
4. So the answer would be 8b-2
30 square root the nearest tenth
Answer:
Step 1: Calculate
We calculate the square root of 30 to be:
√30 = 5.47722557505166
Step 2: Reduce
Reduce the tail of the answer above to two numbers after the decimal point:
5.47
Step 3: Round
Round 5.47 so you only have one digit after the decimal point to get the answer:
5.5
To check that the answer is correct, use your calculator to confirm that 5.52 is about 30.
Answer:
I think its 5.5
Step-by-step explanation:
We feed the okapi about 5,024 cubic centimeters of pellets and hay each day. How many times a day would we have to fill the container shown below
Answer:
Step-by-step explanation:
10 * 4 = 40 times
It’s 5024 Divide by 314 which equals 16 you got it wrong but good try
Step-by-step explanation:
Emily has a spinner that has 5 equal sections: red, blue, green, purple, and orange. She spins the spinner 150 times. About how many times should Emily expect the spinner to land on either purple or orange? *
20 points
2
20
40
60
Answer:
60
Step-by-step explanation:
morgan has $28.75 on a gift card. she buys seven cups of coffee and has $20 left write and solve an equation to determine the cost of one cup of coffee.
Step-by-step explanation:
28.75-20=8.75
8.75/7= 1.25
each cup costs $1.25
What is the standard deviation of the data? Round to the nearest whole number.
Answer:
Where's the data?
Step-by-step explanation:
A canal is 10 miles long. It had a lock every 2/3 mile. How many locks are on the canal?
To find the number of locks on the canal, divide the length of the canal by the distance between each lock. The canal is 10 miles long and there is a lock every 2/3 mile. Therefore, there are 15 locks on the canal.
Explanation:To find the number of locks on the canal, we need to divide the length of the canal by the distance between each lock. The canal is 10 miles long and there is a lock every 2/3 mile. We can divide 10 by 2/3 to find the number of locks.
Using the rule of dividing by a fraction, we can rewrite the expression as 10 ÷ \(\frac{2}{3}\). This is equivalent to multiplying by the reciprocal of the fraction, so the expression becomes 10 × \(\frac{3}{2}\). Now we can multiply 10 by 3 and divide by 2 to get the answer.
10 × 3 = 30
30 ÷ 2 = 15
Therefore, there are 15 locks on the canal.
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I paid $15 for 6 pounds of gasoline . What was the price PER gallon ?
Answer:
$2.50 per gallon
Step-by-step explanation:
The times a fire department takes to arrive at the scene of an emergency are normally distributed with a mean of 6 minutes and a standard deviation of 1 minute. For about what percent of emergencies does the fire department arrive at the scene in between 4 minutes and 8 minutes ?
Answer:
Step-by-step explanation:
Let x be the random variable representing the times a fire department takes to arrive at the scene of an emergency. Since the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 6 minutes
σ = 1 minute
the probability that fire department arrives at the scene in case of an emergency between 4 minutes and 8 minutes is expressed as
P(4 ≤ x ≤ 8)
For x = 4,
z = (4 - 6)/1 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
For x = 8
z = (8 - 6)/1 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.98
Therefore,
P(4 ≤ x ≤ 8) = 0.98 - 0.23 = 0.75
The percent of emergencies that the fire department arrive at the scene in between 4 minutes and 8 minutes is
0.75 × 100 = 75%
Help number 8 Please help
Answer: V = 97.08 or B.
Step-by-step explanation: Hope this helps.
Answer:
its answer is 30.9[tex]\pi inch^{3}[/tex]
Step-by-step explanation:
given
radius (r) = 3 inch
height (h) =10.3 inch
Now
Volume of cone
= 1/3 * [tex]\pi[/tex]* [tex]r^{2} *h[/tex]
= 0.33 * 3 * 3 * 10.3 [tex]\pi[/tex]
= 30. 9[tex]\pi[/tex] inch ^3
Which graph represents this system?
2 x minus 5 y = negative 5. y = two-fifths x + 1.
Answer:
The answer is the first graph.
Step-by-step explanation:
I did it on edge. I got it wrong the first time because I used an answer from this question. Because of that, I reported it. Now I have the correct answer lol.
The slope and the intercept for the lines 2 x minus 5 y = negative 5 and y = two-fifths x + 1 are the same thus the line will coincide so, option A is the correct graph.
What is a graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given:
2 x minus 5 y = negative 5 and y = two-fifths x + 1,
Write the above phrase in mathematical form,
2x - 5y = -5 and y = 2 / 5 x + 1
5y = 2x + 5 and y = 2 / 5 x + 1
y = 2 / 5 x + 1 and y = 2 / 5 x + 1
As we can see here, the slope and the intercept are the same so, the lines are collinear.
Thus, the line will coincide.
To know more about Graph:
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Which of the following phrases are equations?
Choose 2 answers:
© b = 9
© 7+ 19 = 26
© a +9 > 72
©
X
+Y-
Colo
Answer:
d
Step-by-step explanation:
The two phrases that are equations are 'b = 9' and '7 + 19 = 26' because both have an equals sign, indicating that two expressions are set equal to each other.
An equation is a mathematical statement that asserts the equality of two expressions, and it is characterized by the presence of an equals sign '='. From the given options, the two phrases that qualify as equations are b = 9 and 7 + 19 = 26. These both show a relationship where two expressions are set equal to each other.
The phrase a +9 > 72 is not an equation, but an inequality because it uses a greater than symbol '>' instead of an equals sign. The last option provided seems to be typos or irrelevant content and does not constitute an equation.
Five pumpkin pies sit in front of 12 hungry people. If they finish the pies, and each person eats the same amount find the unit rate in the pumpkin pie per person
Answer:
The rate is 0.42 pumpkin pies per person
Step-by-step explanation:
In this question, we are to calculate the amount of pie eaten per person.
This is a rate question.
We have 5 pies and 12 hungry people who ate the same amount of pies as the next person.
The unit rate which is pumpkin pie person is mathematically calculated by dividing the number of pumpkins pies by the number of persons
Mathematically that would be 5/12 = 0.42 pies per person approximately
Determine whether the set of data shown below displays exponential behavior right yes or no explain why or why not. Please help
Answer:
yes
Step-by-step explanation:
you need to see the differences of the numbers
Sharon bought a mixture of nuts that was made up of pecans, walnuts and cashews in a ratio by weight of $2:3:1$, respectively. If she bought $9$ pounds of nuts, how many pounds of walnuts were in the mixture? Express your answer as a decimal to the nearest tenth.
Answer:4.5
Step-by-step explanation:
2+3+1=6, 3 divided by 6 equals to 1/2. 1/2 times 9 equals 4.5 pounds of walnuts
Answer:
4.5
Step-by-step explanation:
Since the pecan to walnut to cashew ratio is 2:3:1, it follows that the walnut ratio to all of the nuts is equal to 3/2+3+1. Thus, there were 1/2 x 9 = 4.5 pounds of walnuts in the mixture.
HURRY!!!!!!
What is:
a=sr (25²-25/2²)
Answer:
24.8746859277
Step-by-step explanation:
sqrt(625 - 25/4)
sqrt[(2500-25)/4]
sqrt(2475/4)
sqrt(618.75)
24.8746859277
Answer:
24.87
Step-by-step explanation:
The parent function h(x)=log3(x) is transformed into j(x)=2log3(x+3)−7. Using complete sentences, describe ALL transformation that occurred.
Answer:
The function is vertically scaled (expanded) by a factor of 2.The scaled function is translated left 3 units and down 7 units.Step-by-step explanation:
When a function f(x) is transformed by ...
g(x) = a·f(x -h) +k
it has been vertically scaled by a factor of "a" and translated to the right and up by amounts h and k, respectively.
Here, we have a=2, h=-3, and k=-7. The means ...
The function has been vertically expanded by a factor of 2, translated left 3 units, and translated down 7 units.
Find the height of the rectangular prism below if the volume is 334.8 meters cubed
Answer:
Step-by-step explanation:
Volume of rectangular prism = 334.8 cubic meter
length * width * height = 334.8
18 * 6 * height = 334.8
[tex]height= \frac{334.8}{6*18}\\[/tex]
= 3.1 m
Find the area of the semicircle. Round your answer to the nearest whole number.
Answer:
2513
Step-by-step explanation:
A=πr^2
A=π40^2
A=π x 1600
A=5026
5026÷2=2513
Answer:
its 628
Step-by-step explanation:
(x^2−1)(3x−4)(3x+4) what is the product
Answer:
9x^4-25x^2+16
Step-by-step explanation:
(x^2−1)(3x−4)(3x+4)=(*)
(x^2−1)((3x)^2−4^2) =
(x^2 - 1)(9x^2-16)=
x^2*9x^2 - x^2*16 - 1*9x^2 +16=
9x^4-16x^2-9x^2+16=
9x^4-25x^2+16
(*) (A-B)(A+B) =A^2 - B^2
Major arc JL measures 300°.
Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Major arc J L is 300 degrees.
Which describes triangle JLM?
right
obtuse
scalene
equilateral
Answer:
The answer is D. Equilateral
Step-by-step explanation:
Answer on edg
The triangle ΔJLM is an equilateral triangle. Then the correct option is D.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In an isosceles triangle, two angles and their opposite sides are equal.
In an equilateral triangle, all the angles and sides of the triangle are congruent.
Circle M is shown. Line segments MJ and ML are radii.
Tangents JK and LK intersect at point K outside the circle.
Major arc JL is 300 degrees.
Then the measure of the minor arc will be
Major arc + minor arc = 360°
300° + minor arc = 360°
Minor arc = 60°
Then the measure of angle ∠MLJ will be
Minor arc = ∠LMJ = 60°
Then the sides MJ and ML congruent, then their opposite angles are also congruent.
∠MJL = ∠MLJ
Then the measure of the angle ∠MLJ will be
∠MJL + ∠MLJ + ∠LMJ = 180
∠MLJ + ∠MLJ + 60° = 180°
2∠MLJ = 120°
∠MLJ = 60°
All the angles of the triangle are congruent.
Then the correct option is D.
More about the triangle link is given below.
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The general manager of a fast food restaurant chain must select 6 restaurants from 11 for a promotional program. How many different possible ways can this selection be done?
Answer:
Step-by-step explanation:
This question will be solved using the combination formula which is nCr because the order is unimportant and we need the selection.
11C6
11!/(11-6)!*6!
= 462
Therefore the manager can select the restaurant in 462 ways.
Answer:
462
Step-by-step explanation:
There 6 slots available to fill in the restaurants options
- For the 1st slot, there are 11 ways to choose
- For the 2nd slot, there are 10 ways to choose
- For the 3rd slot, there are 9
- For the 4th slot, there are 8
- For the 5th slot, there are 7
- For the last 6th, there are 6 ways
So in total there would be 11*10*9*8*7*6 = 332640 ways to choose. But since the order of these 6 slots don't matter, there are actually 6! = 720 ways to order these 6 slots. So the actual number of possible ways is
332640 / 720 = 462
I have to give the answer in by 8pm
Answer:
15
Step-by-step explanation:
TV = TU+UV
= 12 + 3
TV = 15