If a test of a hypothesis has a type I error probability (alpha) of 0.01, it means that there is a 1% chance of rejecting the null hypothesis when it is actually true.
When conducting hypothesis testing, we are trying to make an inference about a population based on sample data. There are two types of errors that can occur:
Type I Error: This occurs when we reject the null hypothesis (H0) when it is actually true. In other words, we falsely conclude that there is a significant effect or relationship when there is none in the population. The probability of committing a Type I error is denoted as alpha (α) and is often set before conducting the test.
In this case, if the type I error probability (alpha) is 0.01, it means that we are willing to tolerate a 1% chance of incorrectly rejecting the null hypothesis when it is actually true. We set the significance level at 0.01, which represents the maximum acceptable level of making a Type I error.
Type II Error: This occurs when we fail to reject the null hypothesis (H0) when it is actually false. In other words, we fail to detect a significant effect or relationship when one exists in the population. The probability of committing a Type II error is denoted as beta (β).
It is important to strike a balance between Type I and Type II errors based on the context and consequences of the study. The choice of the significance level (alpha) reflects the trade-off between the risks of making Type I and Type II errors.
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The correct statement is: "If the null hypothesis is true, you reject it 1% of the time."
In hypothesis testing, the Type I error refers to rejecting the null hypothesis when it is actually true. The significance level, often denoted by α (alpha), determines the probability of making a Type I error.
A significance level of 0.01 means that there is a 1% chance of rejecting the null hypothesis when it is true. This signifies that even if the null hypothesis is correct, there is still a small probability (1%) of observing a result that is extreme enough to lead to the rejection of the null hypothesis.
- Type I error: Rejecting the null hypothesis when it is true.
- α (alpha): The probability of making a Type I error.
- Significance level of 0.01: There is a 1% chance of making a Type I error, or rejecting the null hypothesis when it is true.
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If a test of hypothesis has a Type I error probability (alpha) of 0.01. it means that If the null hypothesis is false, you don't reject it 1% of the time. if the null hypothesis is true, you reject it 1% of the time. if the null hypothesis is true, you don't reject it 1% of the time. if the null hypothesis is false, you reject it 1% of the time.
Which of the following assessment types has the greatest effect on your overall grade?
A. Discussion
B. Quiz
C. Quick check
D. Test
Question: "Which of the following assessment types has the greatest effect on your overall grade?"
Answer: "Out of all the assessment types, 'tests' have the greatest effect on your overall grade as a student. Hence, Option D would be the best choice."
The assessment types has the greatest effect on your overall grade is test.
The following information should be considered;
Here the test should have the highest impact on the overall grade. Since discussion, quiz and the quick check does not have much impact than the test.learn more: https://brainly.com/question/26115859?referrer=searchResults
for a lunch box, you can choose 2 entrees and 1 side. there are 3 choices of sides. there are 6 choices for the entrees and you can not choose the same entree twice. in total, how many different ways are there to make a lunch box?1 point d. 9 e. 90 f. 45 (3 x 6 x 5 / 2)
The number of different ways to make a lunch box can be determined by multiplying the number of choices for each component: entrees and side.Therefore, the correct answer is (E) 90.
For the entrees, there are 6 choices, and since you cannot choose the same entree twice, the second entree will have 5 choices remaining.For the side, there are 3 choices.
To calculate the total number of different ways, we multiply these numbers together: 6 entree choices multiplied by 5 entree choices divided by 2 (since the order of the entrees doesn't matter) multiplied by 3 choices for the side.This gives us a total of 90 different ways to make a lunch box.Therefore, the correct answer is (E) 90.
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An article suggests that a Poisson process can be used to represent the occurrence of structural loads over time. Suppose the mean time between occurrences of loads is 0.4 year.
(a) How many loads can be expected to occur during a 2-year period?
loads
(b) What is the probability that more than eight loads occur during a 2-year period? (Round your answer to three decimal places.)
(c) How long must a time period be so that the probability of no loads occurring during that period is at most 0.2? (Round your answer to four decimal places.)
yr
(a) The number of loads that can be expected to occur during a 2-year period can be found using the mean time between loads and the length of the time period. The mean number of loads that occur in a time period of length t can be found using the formula: mean number of loads = λt, where λ is the mean number of loads per unit time.
In this case, λ = 1/0.4 loads/year, so the mean number of loads that occur in a 2-year period is:
mean number of loads = λ * 2 years = 1/0.4 * 2 = 5
So, we can expect 5 loads to occur during a 2-year period.
(b) The probability that more than eight loads occur during a 2-year period can be found using the Poisson distribution. The Poisson distribution gives the probability of a specific number of events occurring in a given time period, given the average rate of events per unit time. In this case, the Poisson distribution can be used to find the probability that more than 8 loads occur in a 2-year period:
P(more than 8 loads) = 1 - P(8 or fewer loads) = 1 - (P(0) + P(1) + ... + P(8))
Where P(k) is the Poisson probability of exactly k loads occurring in a 2-year period. The Poisson probability of exactly k loads occurring can be found using the formula:
P(k) = (λt)^k * e^-λt / k!
So, substituting the values of λ = 1/0.4 and t = 2 into this formula, we can find the probability that more than 8 loads occur:
P(more than 8 loads) = 1 - (P(0) + P(1) + ... + P(8)) = 1 - (0.135 + 0.270 + 0.405 + 0.541 + 0.678 + 0.814 + 0.947 + 1.078 + 1.206) = 1 - 6.590 = -5.59
Since the probability of an event cannot be negative, this result is not meaningful. The probability that more than 8 loads occur during a 2-year period is greater than 1, which is not possible. This indicates that the assumption that the loads follow a Poisson process may not be valid.
(c) To find the time period for which the probability of no loads occurring is at most 0.2, we can solve for t in the equation:
P(0) = (λt)^0 * e^-λt / 0! = e^-λt = 0.2
Taking the natural logarithm of both sides:
-λt = ln(0.2)
And dividing both sides by -λ:
t = -ln(0.2) / λ = 3.5695 / (1/0.4) = 14.2780 years
So, the time period must be at least 14.2780 years in order for the probability of no loads occurring to be at most 0.2.
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Please help!ill mark you the brainlist!!!!
Answer:
D 58
Step-by-step explanation:
because it is half of 116 which is the whole angle, so if it bisects it is half
Answer:
d) 58
Step-by-step explanation:
Now by my knowledge that should be correct, but if not I'm sorry and I tried. But, I do hope it helps.
0 0
U
To conduct an experiment, researches randomly select five students from a class of 18. How many different groups of five students are possible? groups
Answer:
8568 ways
Step-by-step explanation:
We have to in this particular case the order to find a 5 person group out of a class of 18, when order does not matter, we use combinations. In this case n = 18 and r = 5.
We have that the combination formula is:
nCr = n! / (r! * (n-r)!)
replacing we have:
18C5 = 18! / (5! * (18-5)!)
18C5 = 8568
What it means in total are 8568 ways of arms groups.
Consider the two vectors d = (1,-1,2) and 7 = (-1, 1, a) where a is the last digit of your exam number. (a) Give a unit vector in the direction of a. (b) Computea and ab. (c) Give an equation for the plane perpendicular to a and b containing the point (3.5, -7).
The equation for the plane perpendicular to vectors a and b and containing the point (3.5, -7) is -(y + 7) - (3 + a²)z = 0.
To solve the given problem, we will first find the unit vector in the direction of vector a. Then, we will compute the dot product of vectors a and b. Finally, we will find the equation of the plane perpendicular to vectors a and b that contains the point (3.5, -7).
(a) Finding the unit vector in the direction of a:
To find the unit vector in the direction of vector a, we divide the vector a by its magnitude. The magnitude of vector a can be calculated as:
|a| = √((-1)² + 1² + a²) = √(2 + a²)
Dividing vector a by its magnitude, we get:
a = (-1/√(2 + a²), 1/√(2 + a²), a/√(2 + a²))
(b) Computing a and ab:
To compute a and ab, we will calculate the dot product between vectors a and b:
a · b = (-1)(-1) + (1)(1) + (a)(a) = 2 + a²
Therefore, a = 2 + a² and ab = 2 + a².
(c) Finding the equation of the plane perpendicular to a and b containing the point (3.5, -7):
The equation of a plane can be written in the form Ax + By + Cz = D, where (A, B, C) is the normal vector to the plane. Since the plane is perpendicular to vectors a and b, the normal vector will be the cross product of a and b.
The cross product of vectors a and b can be calculated as:
n = a × b = ((1)(-1) - (1)(-1), (2)(-1) - (1)(-1), (-1)(1) - (1)(2 + a²))
= (0, -1, -1 - 2 - a²)
= (0, -1, -3 - a²)
The equation of the plane perpendicular to vectors a and b and containing the point (3.5, -7) can be written as:
0(x - 3.5) - 1(y + 7) - (3 + a²)(z - 0) = 0
Simplifying the equation, we get:
-(y + 7) - (3 + a²)z = 0
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Rachana has a set of ten mugs the set up is made of 3 different mugs
If Rachana randomly selects two mugs from the set, the probability that she gets two different mugs is 0.1556 or 15.56%.
To solve this problem, we can use the concept of combinations. Since there are 10 mugs in the set, there are 10 choose 2 = 45 ways to select two mugs without considering order.
Out of these 45 ways, we need to count the number of ways Rachana can select two different mugs. Since there are 3 different types of mugs, Rachana can choose any one of the three types for the first mug. There are 10 mugs in the set, out of which 3 belong to the chosen type. Therefore, the probability of choosing a mug of the chosen type is 3/10.
For the second mug, Rachana can choose from the remaining 9 mugs. Since she needs to choose a different type of mug, she can choose any one of the 2 remaining types. There are 7 mugs left from the other 2 types. Therefore, the probability of choosing a mug of a different type is (7/9) * 2/3 = 14/27.
Therefore, the probability of selecting two different mugs is the product of the probabilities of selecting a mug of the chosen type and a mug of a different type. This is given by (3/10) * (14/27) = 7/45, which is approximately 0.1556 or 15.56%.
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Complete question is:
Rachana has a set of ten mugs the set up is made of 3 different mugs. If Rachana randomly selects two mugs from the set, what is the probability that she gets two different mugs?
Tara owns a pizza shop. She sells pizzas for $6.00 plus a $10 delivery fee.If you are having a party and you have $58 how many pizzas can you buy?
Answer:
You can buy 8 pizzas
Step-by-step explanation:
$58 - $10 = $48
$48/$6 = 8
HELP WORTH 10
solve for the values of x and y
3x + 2y =9
y= 2x + 8
Answer: x=-1
Step-by-step explanation:
3x+2(2x+8)=9
Answer:
3x+2y=9
3x+2(2x+8)=9
3x+4x+16=9
7x=-7
x=-1
y=2(-1)+8
y=-2+8
y=6
Step-by-step explanation:
Draw two cards without replacement from a well-shuffled standard deck of 52 cards. find the probability distribution of the number of diamonds drawn. enter exact answers (fractions).
There are 13 diamonds in the deck (as well as other colors). Since there are 52 cards, the probability of getting a diamond on the first draw is 13/52. After the first card is drawn, all that's left are his 12 diamonds. Therefore, the probability of drawing a diamond is 12/51 (note that he has only 51 cards left after pulling/removing the first card since there are no replacement cards). The overall probability is the product of two possibilities. The odds of drawing diamonds from the original deck are 13/52 times the odds of drawing diamonds from his remaining 51 cards. Assuming the first card drawn is a diamond, 12/51.
P=13/52*12/51=1/4*4/17=1/17.
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Error Analysis Sarah said the vertex of the function f(x) = (x + 2)² is (2, 6). Is she correct? Explain.
No, Sarah's claim that the vertex of the function\(f(x) = (x + 2)^2\) is (2, 6) is incorrect. The correct vertex of the function f(x) = (x + 2)² is (-2, 0)
Comparing the given function \(f(x) = (x + 2)^2\) with the general form, we can see that the function has a transformation of shifting 2 units to the left (h = -2) and no vertical shift (k = 0). Therefore, we expect the vertex to be at the point (-2, 0).
To find the vertex explicitly, we can set the derivative of the function equal to zero and solve for x. The derivative of\(f(x) = (x + 2)^2\) is\(f'(x) = 2(x + 2).\)Setting f'(x) = 0, we find x = -2. Plugging this value into the original function, we get f(-2) = (0)² = 0. So, the vertex is indeed located at (-2, 0).
In conclusion, the correct vertex of the function \(f(x) = (x + 2)^2\) is (-2, 0), not (2, 6). Sarah's claim is incorrect, likely due to a misunderstanding of the vertex form of the quadratic function.
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The diameters of trees at a nursery are Normally
distributed with a mean of 2.5 inches and a standard
deviation of 0.5 inches.
X-
Calculate the Z-score for a tree that has a diameter of
1.83 inches. Round the Z-score to the nearest
hundredth, if necessary.
The Z-score for a tree that has a diameter of 1.83 inches
is about...?
Answer:
-1.34
Step-by-step explanation:
Explain what it means for x and y to vary directly
Answer:
(Some textbooks describe direct variation by saying " y varies directly as x ", " y varies proportionally as x ", or " y is directly proportional to x . ") This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.
I need major help, again TvT
Answer:
Step-by-step explanation:
first graph the y-intercept. when x=0, y=-3, so graph a point at (0,-3). since this is a straight line, we only need to graph one more point to find the line. since the slope is -1/5, we can plug in 5 for x to find integer points. when x=5, y=-1/5*5 -3 = -1-3=-4. so another point on the line is (5,-4). then just connect the two points to find the line
Answer:
here's the answer
Step-by-step explanation:
plot the coordinates according to the picture shown. hope this helps!
This year (2022), Evan graduated from college and took a job as a deliveryman in the city. Evan was paid a salary of $73,650 and he received $700 in hourly pay for part-time work over the weekends. Evan summarized his expenses as follows:
Cost of moving his possessions to the city (125 miles away) $ 1,200
Interest paid on accumulated student loans 2,890
Cost of purchasing a delivery uniform 1,490
Cash contribution to State University deliveryman program 1,345
Calculate Evan's AGI and taxable income if he files single. Assume that interest payments were initially required on Evan's student loans this year.
To calculate Evan's AGI (Adjusted Gross Income) and taxable income if he files as a single taxpayer, we need to consider his income and deductible expenses.
Calculate Evan's total income:
- Salary: $73,650
- Part-time hourly pay: $700
Total income = Salary + Part-time pay = $73,650 + $700 = $74,350
Deductible expenses:
- Moving expenses: $1,200
- Student loan interest: $2,890
- Uniform cost: $1,490
- Cash contribution: $1,345
Total deductible expenses = $1,200 + $2,890 + $1,490 + $1,345 = $6,925
Calculate AGI:
AGI = Total income - Total deductible expenses
AGI = $74,350 - $6,925 = $67,425
Evan's taxable income is equal to his AGI since there were no other deductions mentioned in the question.
Therefore, Evan's AGI is $67,425, and his taxable income is also $67,425.
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Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.
We have,
Income:
Salary: $73,650
Part-time work pay: $700
Total income: $73,650 + $700 = $74,350
Deductible Expenses:
Cost of moving possessions: $1,200
(This deduction applies if the move meets certain distance and time requirements. Since the move was 125 miles away, it meets the distance requirement.)
Interest paid on student loans: $2,890
Cost of purchasing a delivery uniform: $1,490
Cash contribution to State University deliveryman program: $1,345
Total deductible expenses:
$1,200 + $2,890 + $1,490 + $1,345
= $6,925
Now we can calculate Evan's AGI and taxable income:
AGI (Adjusted Gross Income)
= Total income - Deductible expenses
AGI = $74,350 - $6,925 = $67,425
Taxable Income = AGI - Standard Deduction
For a single filer in 2022, the standard deduction is $12,550.
Taxable Income = $67,425 - $12,550 = $54,875
Therefore,
Evan's AGI is $67,425 and his taxable income is $54,875 if he files as a single taxpayer.
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What is the image of the point (0, 9) after a rotation of 90° counterclockwise about
the origin?
Answer: -9,0
Step-by-step explanation:
AB = 8m
BC =15m
Determine the length of the diagonal AC and BD
Length =15cm
Breath =8cm
Diagonal =
(length)
2
−(breath)
2
=
(15)
2
+(8)
2
=17cm
What is the value of (x - y) (x - y) if xy = 12 and x² + y² = 25?
In order for us to determine the value of (x - y)(x - y), we have to solve for the value of x and y first. To do that, we can use the substitution method. Here are the steps.
1. Rewrite equation 1 xy = 12 in terms of "y" by dividing both sides of the equation by x.
\(\frac{xy}{x}=\frac{12}{x}\Rightarrow y=\frac{12}{x}\)So, equation 1 becomes y = 12/x.
2. Replace the value of y in equation 2 with 12/x.
\(\begin{gathered} x^2+y^2=25 \\ x^2+(\frac{12}{x})^2=25 \end{gathered}\)Then, solve for x.
\(x^2+\frac{144}{x^2}=25\)Add the terms on the left side of the equation. Use x² as the GCD.
\(\frac{x^4+144}{x^2}=25\)Cross multiply.
\(\begin{gathered} x^4+144=25x^2 \\ x^4-25x^2+144=0 \end{gathered}\)Then, we factor the quartic polynomial. In order to factor, just answer the question "what are the factors of 144 that add to -25?".
The factors are -16 and -9. Hence, we can rewrite the equation as:
\(x^4-16x^2-9x^2+144=0\)Then, divide the equation into two groups.
\((x^4-9x^2)-(16x^2-144)=0\)Then, factor out x² in the first group and factor out 16 in the second group.
\(x^2(x^2-9)-16(x^2-9)=0\)Since x² - 9 is a common factor on both groups, we can just rewrite it as:
\((x^2-16)(x^2-9)=0\)Then, equate each factor to zero. Then, solve for x.
\(\begin{gathered} x^2-16=0 \\ x^2=16 \\ x=\pm4 \end{gathered}\)\(\begin{gathered} x^2-9=0 \\ x^2=9 \\ x=\pm3 \end{gathered}\)Therefore, there are 4 possible values of x. These are +4, -4, +3, and -3.
Since xy = 12, then:
1. At x = 4, y = 3.
2. At x = -4, y = -3.
3. At x = 3, y = 4.
4. At x = -3, y = -4.
Let's plug the pairs of x and y in the expression (x - y)(x - y) and solve.
\(\begin{gathered} 1.\text{ }(4-3)(4-3)=(1)(1)=1 \\ 2.\text{ }(-4--3)(-4--3)=(-1)(-1)=1 \\ 3.\text{ }(3-4)(3-4)=(-1)(-1)=1 \\ 4.\text{ }(-3--4)(-3--4)=(1)(1)=1 \end{gathered}\)On all pairs, the value of (x - y)(x- y) is 1. Hence, the answer is 1.
How long is 140 kilometers in miles ?
87.0 miles are equal to 140 kilometres.
0.62137119223733 miles make up one kilometre.
87.0 miles are equal to 140 kilometres multiplied by 0.62137119223733.
We must first determine the rate of conversion between kilometres and miles in order to convert 140 kilometres to miles. By multiplying the number of kilometres by 0.62137119223733, we can determine the equivalent number of miles. One kilometre is equal to 0.62137119223733 miles. In this instance, 87.0 miles are equal to 140 kilometres. We can calculate the number of miles by taking the initial number of kilometres (140) and multiplying it by the conversion factor (0.62137119223733). (87.0). To confirm the calculation, we can change the miles to kilometres conversion, which should get the same result (140).
Hence, 87.0 miles are equal to 140 kilometres.
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Question
Subtract.
73 7/10 − 25 5/8
Enter your answer in the box as a mixed number in simplest form.
In this unit, you explored different reasons and incentives to save, such as saving for a down payment on a large purchase, financial security for emergencies, and tax advantages. Imagine that it’s 10 to 15 years into the future, and you’ve secured your dream job. Which reasons or incentives to save money resonate the most with you? Explain your reasoning.
Answer:
Financial Freedom
Step-by-step explanation:
In my personal opinion, the biggest reason/incentive for saving would be Financial Freedom. This is the ability to not have to depend on a full-time job in order to survive and be able to live off of the passive income being produced by the money that you saved. If you save enough money and invest it correctly you can live off of the interest that is being generated from those investments. This allows you to not have to work a full-time job and instead free's up your time to pursue meaningfull hobbies or even travel. I believe that is true freedom and it is something that motivates me to save money.
is a parallelogram. is the midpoint of . and trisect .
Let ⃗⃗⃗⃗⃗ = ⃗ and ⃗⃗⃗⃗⃗ = . Show your work on the diagram as well.
Answer:
option 6b):) is correct
Which of the following statements is not true about a rational function of the form f(x) where g and h are polynomial functions? O A. The graph of a rational function will never intersect a vertical asymptoto. OB. A rational function may have many vertical asymptotes. Ос. If the degree of gism and the degree of his n such that , then will have a horizontal asymptote with equation where is the leading coefficient of a and bm is the leading coefficient of h. D. A rational function mav have many horizontal asymptotes.
The statement that is not true about a rational function of the form f(x) where g and h are polynomial functions is D. A rational function may have many horizontal asymptotes.
A rational function is defined as the ratio of two polynomial functions, where g and h are polynomials and h is not the zero polynomial. The graph of a rational function can have vertical asymptotes, which occur when the denominator of the function is equal to zero. However, a rational function can intersect a vertical asymptote if the numerator is also equal to zero at that point.
Regarding vertical asymptotes, statement A is true. The graph of a rational function will never intersect a vertical asymptote, as long as the function is defined at that point.
Statement B is also true. A rational function may have multiple vertical asymptotes if the denominator has multiple factors that result in the function being undefined at different points.
Statement C is also true. If the degrees of g and h are m and n, respectively, and m is less than or equal to n, then the rational function will have a horizontal asymptote with an equation of y = (a/b).
However, statement D is not true. A rational function can have at most one horizontal asymptote, and this occurs when the degree of g is equal to the degree of h. The equation of the horizontal asymptote is y = (a/b), where a is the leading coefficient of g and b is the leading coefficient of h.
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The sum of the measures of the interior angles of a polygon is 5 times the sum of the measures of the exterior angles. How many sides does the polygon have
Answer:
polygon has 12 sides
Step-by-step explanation:
the sum of the exterior angles of a polygon is 360°
the sum of the interior angles of a polygon is
sum = 180° (n - 2 ) ← n is the number of sides
given the sum of the interior angles is 5 times sum of exterior angles, then
sum = 5 × 360° = 1800° then
180° (n - 2) = 1800 ( divide both sides by 180 )
n - 2 = 10 ( add 2 to both sides )
n = 12
Thus the polygon has 12 sides
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds of coffee.
Step-by-step explanation:
Equation
y = -7.37x + 80
substitute 57.89 for y
57.89 = -7.37 + 80 Subtract 80 from both sides
57.89 - 80 = -7.37 + 80 - 80
-22.11 = -7.37x Divide both sides by -7.37
3 = x
3 pound of coffee
Helping in the name of Jesus.
Answer:
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Step-by-step explanation:
Let's first find out how much money Rita spent on coffee:
$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee
Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:
$7.37x = $22.11
Solving for x, we can divide both sides by $7.37:
x = 3
Therefore, Rita bought 3 pounds of coffee.
What is the slope of the line represented by the equation y- 6 = 2(x+3)?
Answer: 2
Step-by-step explanation:
remember y=mx^2+c
where m = gradient = slope
∴ expand and simplify y-5=2(x+3)
y-5=2x+6
y=2x+11
m=2 ∴ slope: 2
Jane belongs to a book club. She pays a flat fee of $8 to ship any number of books. She is able to purchase
the books for $10 each. Which of the following choices shows the expression that represents
1. Jane's situation and
2. how much it would cost her if she bought 8 books?
a. 10+8b, the cost would be $88.
b. 8+10b, the cost would be $88.
C. 8+10b, the cost would be $74.
d. 10+8b, the cost would be $74.
Answer:
b.8+10b,the cost would be $88
Step-by-step explanation:
if she buys 8 books worth $10 each
so 8×10= 80
plus $8 for shipment
so $80 +$8 =$88
Whats the measure of angle J rounded to the nearest tenth?
The measure of angle J, m∠J = 41.2°.
angle mwasurement:
We can use trigonometry to find the measure of ∠J. Since we know the lengths of the two sides adjacent to ∠J (GH and GJ), we can use the tangent function, which is defined as the opposite side divided by the adjacent side:
tan(J) = opposite/adjacent = GH/GJ
We can solve for J by taking the inverse tangent (or arctan) of both sides:
J = \(tan^{-1}\)(GH/GJ)
Substituting the given values, we get:
J = \(tan^{-1}\)(14/16)
Using a calculator, we find:
J ≈ 41.186
Rounded to the nearest tenth, the measure of angle J is 41.2°.
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Perform the calculation and record the answer with the correct number of significant figures. (34.123 + 1.70)/(98.7654 - 2.565)
The calculation and record the answer with the correct number of significant figures. The final answer is 0.3724, accurate to four significant figures.
When performing calculations with significant figures, it is important to consider the precision of the numbers involved. In this case, we are adding 34.123 and 1.70, which gives us 35.823. The subtraction of 2.565 from 98.7654 gives us 96.1994.
To find the final result, we divide 35.823 by 96.1994, resulting in 0.372352. However, we must round the answer to the appropriate number of significant figures. Since 2.565 has the least number of significant figures (four), we round our answer to four significant figures as well.
Performing the calculation, we have:
(34.123 + 1.70) = 35.823
(98.7654 - 2.565) = 96.1994
Dividing the sum by the difference, we get:
35.823 / 96.1994 = 0.372352
Considering significant figures, we look at the least precise number, which is 2.565, with four significant figures. Therefore, our final answer should also have four significant figures.
Rounding the result to four significant figures, the answer is 0.3724.
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A laptop is on sale for 18% off the original price of $450. What is the sale price?
Answer: 369
Step-by-step explanation:
This is becuase 18% of 450 is 81, and 18% off means you subract the 81 leaving 369.