I remember doing this but I don’t seem to remember
Which expression is equivalent to
(x-1)^2 x^2+-6
———— * ————
x^2-x-12 x^2+6x-5
If no denominator equals 0?
The expression is equivalent to (x - 2)(x - 5)/(x - 4)(x - 1), as long as the denominators do not equal 0.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.
We can begin by factoring the denominators of both fractions as follows:
[tex]x^{2}[/tex]- x - 12 = (x - 4)(x + 3)
[tex]x^{2}[/tex]- + 6x - 5 = (x - 1)(x + 5)
Substituting these expressions, the given expression becomes:
[(x - 1)(x-1) [tex]x^{2}[/tex]-+ (-6)]/[(x - 4)(x + 3)] * [(x + 5)/(x - 1)(x + 5x - 5)]
Simplifying, we can cancel out the (x - 1) and (x + 5) terms in the numerator and denominator:
[(x - 1) * [tex]x^{2}[/tex]- + (-6)]/[(x - 4)(x + 3)] * [1/(x - 5)]
Expanding the numerator:
( [tex]x^{3}[/tex]- [tex]x^{2}[/tex]- - 6)/( [tex]x^{2}[/tex]- - x - 12) * [1/(x - 5)]
Factoring the numerator:
( [tex]x^{2}[/tex]- + x - 6)(x - 5)/( [tex]x^{2}[/tex]- - x - 12)
Factoring again:
(x + 3)(x - 2)(x - 5)/(x - 4)(x + 3)(x - 1)
Canceling out the (x + 3) terms:
(x - 2)(x - 5)/(x - 4)(x - 1)
Therefore, the expression is equivalent to (x - 2)(x - 5)/(x - 4)(x - 1), as long as the denominators do not equal 0.
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divide 70 into the ratio of 2:5
Answer:
20 : 50
Step-by-step explanation:
sum the parts of the ratio , 2 + 5 = 7 parts
divide 70 by 7 to find the value of one part of the ratio
70 ÷ 7 = 10 ← value of 1 part of the ratio , then
2 parts = 2 × 10 = 20
5 parts = 5 × 10 = 50
then
50 divided in the ratio 2 : 5 is 20 : 50
Lim (x,y)->(0,0) f (x,y) = L if f (x,y) gets close to l as we approach (0,0) along the x-axis (y = 0) and along the y-axis (x = 0)?
If f(x,y) gets close to L as we approach (0,0) along the x-axis (y = 0) and along the y-axis (x = 0), the limit of f(x,y) as (x,y) approaches (0,0) is L.
We can follow these steps:
Step 1: Approach (0,0) along the x-axis (y = 0)
Evaluate the limit of f(x,0) as x approaches 0. If the limit exists and is equal to L, proceed to step 2.
Step 2: Approach (0,0) along the y-axis (x = 0)
Evaluate the limit of f(0,y) as y approaches 0. If the limit exists and is equal to L, proceed to step 3.
Step 3: Conclude the limit
If both the limits in steps 1 and 2 exist and are equal to L, then the limit of f(x,y) as (x,y) approaches (0,0) is L. Otherwise, the limit does not exist.
So, if f(x,y) gets close to L as we approach (0,0) along the x-axis (y = 0) and along the y-axis (x = 0), the limit of f(x,y) as (x,y) approaches (0,0) is L.
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Obtain the derivative of the following function using the addition and subtraction rule:
F(x) = 5x10 - 2x2 + x - 1
Answer:
Step-by-step explanation:
To obtain the derivative of F(x) = 5x^10 - 2x^2 + x - 1 using the addition and subtraction rule, we can take the derivative of each term separately and then add or subtract the resulting derivatives.
The derivative of 5x^10 is:
(5x^10)' = 50x^9
The derivative of -2x^2 is:
(-2x^2)' = -4x
The derivative of x is:
(x)' = 1
The derivative of -1 is:
(-1)' = 0
Putting these derivatives together using the addition and subtraction rule, we get:
F'(x) = (50x^9) - (4x) + (1) + (0)
Simplifying this expression, we get:
F'(x) = 50x^9 - 4x + 1
Therefore, the derivative of F(x) = 5x^10 - 2x^2 + x - 1 using the addition and subtraction rule is F'(x) = 50x^9 - 4x + 1.
Which temperature is colder, -145°C or -130°C? Explain or show your work on a number line.
Answer:
Step-by-step explanation:
-145c is lower because it’s further left on a numberline
a sample of 1200 computer chips revealed that 53% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that more than 50% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.10 level to support the company's claim? state the null and alternative hypotheses for the above scenario.
The null hypothesis is that the proportion of computer chips that do not fail in the first 1000 hours of use is equal to 50%. The alternative hypothesis is that the proportion is greater than 50%.
At the 0.10 level of significance, we will reject the null hypothesis if the test statistic is greater than 1.28. The test statistic can be calculated using the formula:
[tex]z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$[/tex]
where [tex]\hat{p}$[/tex] is the sample proportion, [tex]p_0$[/tex] is the hypothesized proportion under the null hypothesis, and $n$ is the sample size.
In this case, we have [tex]\hat{p} = 0.53$, $p_0 = 0.50$, and $n = 1200$.[/tex] Substituting these values into the formula, we get:
[tex]z = \frac{0.53 - 0.50}{\sqrt{\frac{0.50(1-0.50)}{1200}}} = 2.77$[/tex]
Since the test statistic is greater than 1.28, we reject the null hypothesis and conclude that there is sufficient evidence at the 0.10 level to support the company's claim that more than 50% of computer chips do not fail in the first 1000 hours of their use.
Therefore, the null hypothesis is equal to 50%, and the alternative hypothesis is 50%. The test statistic is 2.77, which is greater than the critical value of 1.28 at the 0.10 level of significance, so we reject the null hypothesis and conclude that there is sufficient evidence to support the company's claim.
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The value of x is__?
The measure of is angle 1 is__?
The measure of angle 2 is __?
The measure of angle 3 is __?
The measure of angle 4 is __?
The measure of angle 5 is __?
The measure of angle 6 is __?
The measure of angle 7 is __?
The measure of angle 8 angles 2 and 3 are____ angles.
The value of x is 24
The measure of is angle 1 is 101°
The measure of angle 2 is 79°
The measure of angle 3 is 101°
The measure of angle 4 is 101°
The measure of angle 5 is 79°
The measure of angle 6 is 79°
The measure of angle 7 is 101°
The measure of angle 8 is 79°
What are angles on a parallel line?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
3x +19 = 5x-29 ( opposite angle)
collect like terms
5x-3x = 29+19
2x = 48
x = 24
angle 1 = 180-(3×24+7)
= 180- 79
= 101°
angle 2 = 3x+7 = 79°( opposite angles)
angle 3 = 101° ( opposite angles)
angle 4 = angle 1 = 101° ( corresponding angles)
angle 5 = 79° ( corresponding angles)
angle 6 = angle 5 = 79°( opposite angle)
angle 7 = angle 4 = 101 ( corresponding angles)
angle 8 = angle 7 = 79 ( opposite angle )
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14. Ella is making a corner bench
seat. She plans to outline the seat
cushion in a decorative ribbon.
How much ribbon will she need?
3.6 ft
6.25 ft
4.8 ft
Answer:
14.65
Step-by-step explanation:
3.6 ft + 6.25+4.8=14.65
Solve For X Question 1
Answer:
x=52
Step-by-step explanation:
Set equal to 180
x-30+3x+2=180
solve for x
4x-28=180
4x=208
x=52
plug in to check
1. Use the following information and the map of downtown Seattle to answer questions one and two. Harrison St, Thomas St, and Denny Way are parallel. On Broad St, the distance between Mercer St and Denny Way is 0.7 miles. The distance between those same streets on Aurora Ave is 0.45 miles.
a) On Aurora Ave the distance between Thomas St to Denny Way is 0.2 miles. What is the distance
between these two streets on Broad St? Round your answer to the nearest tenth of a mile.
The distance between these two streets on Broad St is 0.3 miles.
We can use proportions to solve the problem.
Let's assume x is the distance between Thomas St and Denny Way on Broad St.
We know that on Aurora Ave, the distance between Thomas St and Denny Way is 0.2 miles, and on Broad St, the distance between Mercer St and Denny Way is 0.7 miles.
So, we can set up the following proportion:
0.2/0.45 = x/0.7
Simplifying, we get:
x = (0.2/0.45) * 0.7
x = 0.3111 miles
Rounded to the nearest tenth, the distance between Thomas St and Denny Way on Broad St is 0.3 miles.
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simplify (x-y/√x-√y)-√x
It’s asking me to write a quadratic equation in that form with the roots
Answer:
x^2-11x+28=0
Step-by-step explanation:
(x-7)(x-4)=0
= x^2-7x-4x+28=0
= x^2-11x+28=0
The sum of three consecutive odd
numbers is 39. What is the largest of
these numbers?
Answer:
2145
Step-by-step explanation:
Given: Sum of three consecutive odd integers = 39
Calculation:Let x, x + 2, x + 4 be the three consecutive odd integers.
Sum of three consecutive odd integers = 39
⇒ x + (x + 2) + (x + 4) = 39
⇒ 3x + 6 = 39
⇒ 3x = 33
⇒ x = 11
∴ The integers are 11, 13 and 15.
∴ Their product = 11 × 13 × 15 = 2145
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So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.
In this case, the bounce heights form a geometric sequence with a common ratio of 2/3. , the ball reaches a height of [tex]8[/tex] feet on the third bounce,
What is the geometric sequence?The definition of a geometric sequence is a set of numbers where each term is created by multiplying the preceding term by a fixed factor.
If the bounce heights form a geometric sequence with common ratio "r", we can write:
27 = initial height
[tex]18 = 27r[/tex]
[tex]12 = 18r = 27 \times r^2[/tex]
Solving for "r", we get:
[tex]r = 2/3[/tex]
So, the fourth bounce height would be:
[tex](12) \times (2/3) = 8[/tex]
Therefore, the ball reaches a height of 8 feet on the third bounce, not the fourth bounce as stated in the original statement.
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Answer the question below in the screenshot, thanks! (please answer quickly, I'm on edge so I can't move on!)
The exact answer on Edge is
"Use the product of powers property to simplify the numerator by removing the parentheses. Follow the order of operations by removing the innermost parentheses first. Cube the quantity to get the product of 2 to the third power, r to the 6th power, and t to the third power, or 2^3r^6t^3 in the numerator. "
a manufacturer knows that their items have a normally distributed length, with a mean of 14.7 inches, and standard deviation of 4.8 inches. if 25 items are chosen at random, what is the probability that their mean length is less than 12.4 inches?
The probability that the mean length of the 25 items is less than 12.4 inches is approximately 0.0009
We can solve this problem by using the Central Limit Theorem (CLT), which states that the sample mean of a large enough sample size from any distribution with a finite mean and variance will follow a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, the population mean is 14.7 inches, the population standard deviation is 4.8 inches, and the sample size is 25. Thus, the mean of the sample means is also 14.7 inches, and the standard deviation of the sample means is 4.8 inches / sqrt(25) = 0.96 inches.
To find the probability that the mean length of the 25 items is less than 12.4 inches, we can standardize the sample mean using the z-score formula
z = (x - mu) / (sigma / sqrt(n))
where x is the sample mean we want to find the probability of (in this case, 12.4 inches), mu is the population mean (14.7 inches), sigma is the population standard deviation (4.8 inches), and n is the sample size (25).
Substituting these values, we get
z = (12.4 - 14.7) / (4.8 / sqrt(25)) = -3.13
We can then use a standard normal distribution table or calculator to find the probability that a standard normal variable is less than -3.13, which is approximately 0.0009.
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if the original length and width of the paper is twice its current length and width, calculate the original area, in cm, of the paper in terms of a and b.
Answer:
[tex]4a^{2} + 4ab[/tex]
Step-by-step explanation:
as I can see in the image posted by you,
current length = a + b
current width = a
according to the condition, original paper length and width was twice of their current values,
original length = 2(a+b)
original width = 2a
therefore,
original area = 2(a+b) * 2a
original area = 4(a+b)a
original area = [tex]4a^{2} + 4ab[/tex]
Hopefully you found the answer helpful
A bakery can make 3 cheesecakes for every 4 blocks of cream cheese. Which
table represents the relationship between the number of cheesecakes the
bakery makes and the number of blocks of cream cheese the bakery uses?
A
C
Cheesecakes
3
6
12
Cheesecakes
3
9
12
Cream Cheese
(blocks)
4
7
13
Cream Cheese
(blocks)
4
16
20
B
D
Cheesecakes
3
9
12
Cheesecakes
9
10
11
Cream Cheese
(blocks)
4
12
16
Cream Cheese
(blocks)
12
13
14
Since this bakery can make 3 cheesecakes for every 4 blocks of cream cheese, a table that represent the relationship between the number of cheesecakes the bakery makes and the number of blocks of cream cheese the bakery uses is: B. table B.
What is a proportional relationship?In Mathematics, a proportional relationship produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represent the number of blocks of cream cheese.x represent the number of cheesecakes.k is the constant of proportionality.In order to have a proportional relationship, the variables representing the number of blocks of cream cheese and the number of cheesecakes must have the same constant of proportionality:
Constant of proportionality, k = y/x
Constant of proportionality, k = 4/3 = 8/6 = 12/9 = 16/12
Constant of proportionality, k = 4/3.
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What are the solutions to the system of conics?
y^2/4−x^2/2=1
y^2=8(x+1)
Drag the ordered pairs into the box to correctly complete the table.
The cοmplete table with the οrdered pairs is:
(2-√6,2√(6-2√6)) (2+√6,2√(6-2√6)) (2+√6,-2√(6-2√6))
(2-√6,2√(6+2√6)) (2+√6,-2√(6+2√6)) (2+√6,2√(6+2√6))
What is quadratic equatiοn?A quadratic equatiοn is a secοnd-degree pοlynοmial equatiοn in οne variable οf the fοrm: [tex]ax^2 + bx + c = 0.[/tex]
Tο find the sοlutiοns tο the system οf cοnics, we can use substitutiοn tο eliminate οne variable and οbtain a quadratic equatiοn in the οther variable. Then, we can sοlve this quadratic equatiοn tο find the pοssible values οf the remaining variable.
Frοm the given system οf cοnics:
[tex]y^2/4 - x^2/2 = 1 ...(1)[/tex]
[tex]y^2 = 8(x + 1) ...(2)[/tex]
We can eliminate [tex]y^2[/tex] frοm equatiοn (1) by multiplying bοth sides by 4:
[tex]y^2 - 2x^2 = 4[/tex]
Substituting the value οf [tex]y^2[/tex] frοm equatiοn (2), we get:
[tex]8(x + 1) - 2x^2 = 4[/tex]
Simplifying and rearranging, we get:
[tex]x^2 + 2x - 2 = 0[/tex]
We can sοlve this quadratic equatiοn using the quadratic fοrmula:
[tex]x = (-2 \± \sqrt{(2^2 - 4(1)(-2))}) / (2(1))[/tex]
x = (-2 ± √12) / 2
x = -1 ± √3
Substituting these values οf x in equatiοn (2), we can find the cοrrespοnding values οf y:
When x = -1 + √3, we get:
[tex]y^2[/tex] = 8((-1 + √3) + 1) = 8√3
y = ±2√(2√3)
Therefοre, the sοlutiοns are:
(-1 + √3, 2√(2√3)) and (-1 + √3, -2√(2√3))
When x = -1 - √3, we get:
[tex]y^2[/tex] = 8((-1 - √3) + 1) = -8√3
This equatiοn has nο real sοlutiοns fοr y.
Therefοre, the cοmplete table with the οrdered pairs is:
(2-√6,2√(6-2√6)) (2+√6,2√(6-2√6)) (2+√6,-2√(6-2√6))
(2-√6,2√(6+2√6)) (2+√6,-2√(6+2√6)) (2+√6,2√(6+2√6))
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Wendy asked 40 students on the school football team if they ever injured themselves while playing sports. Fifteen football team members responded "Yes. " Wendy concluded that 375 of the 1,000 students in her school have injured themselves playing sports
Wendy's conclusion is invalid as she cannot generalize her findings as sample size is too small to represent the entire school population accurately.
Wendy's assessment is incorrect. This is due to the fact that she is unable to extrapolate from a sample of just 40 students who play football for the school. The sample size is insufficient to provide an accurate representation of the student body as a whole. Also, the football players might be more prone to injuries than those who don't participate in sports, which could further skew the results.
Moreover, Wendy did not choose the football team members using a random sample approach. Instead, she restricted her questions to those students who were already on the football team, thereby introducing sample bias. She might have unintentionally left out pupils who don't participate in athletics but may nonetheless have hurt themselves while doing other physical activities.
Wendy's assertion that 375 of the school's 1,000 kids have sustained sports-related injuries is therefore unfounded. Wendy would need to employ a more representative and random sampling technique that includes students from various sports teams as well as those who do not play sports in order to draw a reliable conclusion. She would also require a larger sample size to obtain a more accurate representative of the total student body.
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Complete Question: Wendy questioned the 40 members of the varsity football team about their experiences with sports-related injuries. "Sure," fifteen football players answered. Wendy came to the conclusion that 375 of the 1,000 pupils at her school had had sports-related injuries. Decide if Wendy's conclusion is true or not.
Hank pours himself a jar full of
milk to drink with his pie. The jar is 6"
high and 3" in diameter. What is
the volume of the jar?
Answer:
13.5pi inches^3
Step-by-step explanation:
the jar is a cylinder.
the volume of a cylinder is the height * base area, and the base area is a circle. the area of a circle is pi*r^2.
the radius is half the diameter, so it is 1.5.
the area of the circle is pi * 1.5^2 = 2.25pi.
multiply this by the height, and we get 13.5pi. the units is cubic inches, or inches^3.
z varies directly as x^2. If z= 8 when x= 2, find z when x= 6.
Thus, the value of z = 72, when x = 6 for the given condition that z varies directly with the square of x.
Define about the direct proportion:The connection among two variables is known as a direct proportion when their ratios are comparable to a fixed value.
To the contrary, a direct proportion occurs when a change in one quantity prompts a commensurate change in the other amount, or when a change in one quantity prompts a change in the other quantity.The proportional sign (∝) is used to represent a direct proportion. For instance, the sentence "x ∝) y" can be used to indicate the relationship between two variables x and y.Given data:
z varies directly as x².
z= 8 when x= 2.
So,
z ∝ x²
z = k x²
k = z/ x² (k is the constant of proportionality)
z= 8 when x= 2.
k = 8/(2)²
k = 2
Now, when x = 6
z = k x²
z = 2 * (6)²
z = 72
Thus, the value of z = 72, when x = 6 for the given condition that z varies directly with the square of x.
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Are angles C and D supplementary angles: B. No.
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees. Mathematically, a supplementary angle can be calculated by using this mathematical equation:
C + D = 180
Where:
C and D are measure of the angles subtended.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of the given angles are not supplementary angles:
58 + 102 = 160° ≠ 180°
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considering the following scenario, which method would be most appropriate when calculating the margin of error for the population mean? a research scientist wants to know how many times per hour a certain strand of virus reproduces. she obtains information from 14 strands of this particular virus and finds the mean to be 7.4 . the population is assumed to be normally distributed.
The method that is most appropriate when calculating margin-of-error for population mean is (b) Student's t-distribution.
When calculating the margin of error for the population mean, the most appropriate method depends on the sample size.
If the sample size is large (n > 30) and the population standard deviation is known, then a normal z-distribution can be used to calculate the margin of error.
If the sample size is small (n < 30) or the population standard deviation is unknown, then Student’s t-distribution should be used to calculate the margin of error.
In this case, we are told that the information was obtained from 14 strands of this particular virus. Since n < 30, we should use Student’s t-distribution to calculate the margin of error.
Therefore, the correct option is (b).
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The given question is incomplete, the complete question is
Considering the following scenario, which method would be most appropriate when calculating the margin of error for the population mean?
A research scientist wants to know how many times per hour a certain strand of virus reproduces. she obtains information from 14 strands of this particular virus and finds the mean to be 7.4 . the population is assumed to be normally distributed.
(a) Normal z-distribution
(b) Student's t-distribution
(c) More advanced statistical techniques
Write an algebraic expression with four terms, using only the variables a, b, and c.
Answer:
2a + 3b - 6bc + c
Step-by-step explanation:
For our terms, we will use a, b, c, and bc terms.
Now, here is what I came up with.
[tex]2a+3b-6bc+c[/tex]
Examine the loan amortization table for a $210,000, 15-year mortgage with an APR of 3.8%. The borrower paid an extra $100 each month towards the principal.
Determine the missing amounts.
Using a loan amortization calculator, we can generate a table that shows the borrower's monthly payments, the interest paid, the principal paid, and the remaining balance after each payment.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9."
Using a loan amortization calculator, we can generate a table that shows the borrower's monthly payments, the interest paid, the principal paid, and the remaining balance after each payment. Here is the loan amortization table for the $210,000, 15-year mortgage with an APR of 3.8%, assuming the borrower pays an extra $100 towards the principal each month:
Month Payment Interest Paid Principal Paid Extra Principal Paid Remaining Balance
1 $1,529 $662 $297 $100 $209,703
2 $1,529 $657 $301 $100 $209,402
3 $1,529 $652 $306 $100 $209,096
4 $1,529 $647 $311 $100 $208,783
5 $1,529 $642 $316 $100 $208,463
6 $1,529 $637 $321 $100 $208,137
7 $1,529 $632 $326 $100 $207,803
8 $1,529 $627 $331 $100 $207,463
9 $1,529 $622 $336 $100 $207,116
10 $1,529 $617 $341 $100 $206,762
11 $1,529 $611 $347 $100 $206,411
12 $1,529 $606 $352 $100 $206,052
13 $1,529 $601 $357 $100 $205,686
14 $1,529 $596 $362 $100 $205,322
15 $1,529 $590 $368 $100 $204,950
16 $1,529 $585 $373 $100 $204,570
17 $1,529 $580 $378 $100 $204,182
18 $1,529 $574 $384 $100 $203,787
19 $1,529 $569 $389 $100 $203,383
20 $1,529 $563 $395 $100 $202,972
21 $1,529 $558 $400 $100 $202,552
22 $1,529 $552 $406 $100 $202,125
23 $1,529 $547 $411
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Leeze is making labels in the shape of parallelograms. Each label has an area of 18 square centimeters and a base of 6 centimeters. What is the height of each label?
The height of the parallelogram is 3 cm.
What is area?
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.
What is a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. This means that opposite sides of a parallelogram are parallel and have the same length. Additionally, opposite angles of a parallelogram are congruent (i.e., have the same measure). Some common properties of parallelograms include:
The opposite sides of a parallelogram are equal in length.
The opposite angles of a parallelogram are equal in measure.
The consecutive angles of a parallelogram are supplementary (i.e., they add up to 180 degrees).
The diagonals of a parallelogram bisect each other (i.e., they intersect at their midpoint).
Here the given ,
Area of the parallelogram = 18 square centimeters.
Base b = 6 cm
Area of parallelogram = bh square unit
=> 18=6*h
=> h= 18/6 = 3 cm
Hence the height of the parallelogram is 3 cm.
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Step-by-step explanation:
VOLUME of pyramid = 1/3 base area * height
Base area is a square = 3 x 3
= 1/3 ( 3x3) * 16 = 48 in^3
a quality control inspector has drawn a sample of 14 light bulbs from a recent production lot. suppose 20% of the bulbs in the lot are defective. what is the probability that less than 9 but more than 7 bulbs from the sample are defective? round your answer to four decimal places.
The probability that less than 9 but more than 7 bulbs from the sample are defective is 0.8944.
The formula to find the probability of x number of defective bulbs in a sample of n bulbs is as follows:
P(x) = [[tex]n \choose x[/tex] * p^x * (1-p)^(n-x)], where [tex]n \choose x[/tex] is the combination of n and x.
So, The probability of x < 9 defective bulbs in a sample of 14 bulbs is given as follows:
P(x<9) = P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6) + P(x=7)
Therefore, the probability that less than 9 bulbs from the sample are defective is
P(x<9) = [[tex]14 \choose0[/tex] * (0.2)^0 * (0.8)^14] + [[tex]14 \choose1[/tex] * (0.2)^1 * (0.8)^13] + [[tex]14 \choose2[/tex] * (0.2)^2 * (0.8)^12] + [[tex]14 \choose3[/tex] * (0.2)^3 * (0.8)^11] + [[tex]14 \choose4[/tex] * (0.2)^4 * (0.8)^10] + [[tex]14 \choose5[/tex] * (0.2)^5 * (0.8)^9] + [[tex]14 \choose6[/tex] * (0.2)^6 * (0.8)^8] + [[tex]14 \choose7[/tex] * (0.2)^7 * (0.8)^7]= 0.8962
Similarly, the probability that more than 7 bulbs from the sample are defective is:
P(x>7) = P(x=8) + P(x=9) + P(x=10) + P(x=11) + P(x=12) + P(x=13) + P(x=14)
Therefore, the probability that more than 7 bulbs from the sample are defective is
P(x>7) = [[tex]14 \choose8[/tex] * (0.2)^8 * (0.8)^6] + [[tex]14 \choose9[/tex] * (0.2)^9 * (0.8)^5] + [[tex]14 \choose10[/tex] * (0.2)^10 * (0.8)^4] + [[tex]14 \choose11[/tex] * (0.2)^11 * (0.8)^3] + [[tex]14 \choose12[/tex] * (0.2)^12 * (0.8)^2] + [[tex]14 \choose13[/tex] * (0.2)^13 * (0.8)^1] + [[tex]14 \choose14[/tex] * (0.2)^14 * (0.8)^0]= 0.0005
Therefore, the probability that less than 9 but more than 7 bulbs from the sample are defective is:
P(8≤x≤7) = P(x<9) - P(x≤7)
P(8≤x≤7) = P(x<9) - [P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) + P(x=6) + P(x=7)]= 0.8962 - 0.0018= 0.8944 (rounded to four decimal places)
Therefore, more than 7 out of the sample have a probability of failure, but less than 9 out of the sample probably have a failure.
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The test statistic of z=−1.91 is obtained when testing the claim that p=1/2. a. Using a significance level of α=0.10, find the critical value(s). b. Should we reject H 0 or should we fail to reject H 0 ? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. a. The critical value(s) is/are z= (Round to two decimal places as needed. Use a comma to separate answers as needed.) b. Choose the correct conclusion below. A. Reject H 0 . There is sufficient evidence to warrant rejection of the claim that p=1/2. B. Fail to reject H 0 . There is sufficient evidence to warrant rejection of the claim that p=1/2. C. Fail to reject H 0 . There is not sufficient evidence to warrant rejection of the claim that p=1/2. D. Reject H n . There is not sufficient evidence to warrant rejection of the claim that p=1/2.
a. The critical value(s) is/are z = -1.645, 1.64
b. Fail to reject H0.
How to determine critical valueThere is not sufficient evidence to warrant rejection of the claim that p = 1/2. The test statistic of z = -1.91 is obtained when testing the claim that p = 1/2.
We want to know whether to reject H0 or fail to reject H0 using a significance level of α = 0.10.
Using the standard normal distribution table, the critical value(s) are z = ± 1.645 (rounded to two decimal places).
Since -1.91 is less than -1.645, we fail to reject H0.
In other words, there is not sufficient evidence to warrant rejection of the claim that p = 1/2.
Therefore, the correct conclusion is "Fail to reject H0.
There is not sufficient evidence to warrant rejection of the claim that p = 1/2."
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