The f'(x) has two x-intercepts, but f''(x) is always positive, indicating that f(x) has no relative extrema. This means that the function is either always increasing or always decreasing, and there are no maximum or minimum points.
The function f(x) =
[tex](1/3)x^3 - (2/7)x^2 - 1x[/tex]
has no relative extreme points. To find the relative extreme points of a function, we need to find the critical points where either the derivative f'(x) is equal to zero or the second derivative f''(x) is equal to zero.
Taking the derivative of f(x), we get f'(x) = x^2 - (4/7)x - 1. Setting f'(x) equal to zero and solving for x, we get x =
[tex](2 ± \sqrt{} (30))/7[/tex]
Upon further analysis of the second derivative f''(x) = 2x - (4/7), we see that it is always positive for all values of x.
There are no relative extreme points as the function f(x) does not have any points where the slope is zero and the curvature changes from positive to negative or vice versa.
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PLEASE HELP ITS URGENT I INCLUDED THE GRAPH AND WROTE THE PROBLEM DOWN ITS THE IMAGE I HAVE ATTACHED!!!
Answer:
Ive attached a picture
Step-by-step explanation:
In a flower garden, there are 6 tulips for every 7 daisies. If there are 48 tulips, how many daisies are there?
Answer:
56, There are 56 daisies.
Step-by-step explanation:
Which is a factor !!! See picture below
Answer: A: (x+3)
Step-by-step explanation:
Lets simplify this first:
[tex]2x^2 + 2x - 12[/tex]
[tex]2(x^2 + x - 6)[/tex]
we can factor this into:
[tex]2(x+3)(x-2)[/tex]
so, from the options, we can see that option A is correct.
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 53.9 for a sample of size 24 and standard deviation 5.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.
_______ < μ < _________ please teach using calculator method
We can be 90% confident that the true mean reduction in systolic blood pressure for the population is between 51.433 and 56.367.
To estimate the confidence interval for the true mean reduction in systolic blood pressure, we can use the formula:
CI = X ± Zα/2 * (σ/√n)
where X is the sample mean, Zα/2 is the critical value of the standard normal distribution for a given level of confidence (α), σ is the population standard deviation, and n is the sample size.
In this case, X = 53.9, σ = 5.6, n = 24, and we want a 90% confidence interval, so α = 0.1 and Zα/2 = 1.645 (using a standard normal distribution table or calculator).
Substituting the values, we get:
CI = 53.9 ± 1.645 * (5.6/√24)
CI = 53.9 ± 2.467
CI = (51.433, 56.367)
Therefore, we can be 90% confident that the true mean reduction in systolic blood pressure for the population is between 51.433 and 56.367.
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Most problems involving the Intermediate Value Theorem will require a three step process:
Most problems involving the Intermediate Value Theorem will require a three-step process:
1. Verify that the function f is continuous on the closed interval [a,b].
2. Find two points, say p and q, in the interval [a,b] such that f(p) and f(q) have opposite signs.
3. Apply the Intermediate Value Theorem, which guarantees the existence of a root of the equation f(x) = 0 in the interval [p,q].
Most problems involving the Intermediate Value Theorem require a three-step process:
Step 1: Verify the conditions for the Intermediate Value Theorem (IVT)
To apply the IVT, ensure that the function is continuous on a closed interval [a, b]. If it's continuous, you can proceed to the next step.
Step 2: Determine the values of the function at the endpoints
Evaluate the function at the given interval's endpoints, f(a) and f(b).
Step 3: Apply the Intermediate Value Theorem
If there is a value 'c' between f(a) and f(b) such that f(a) < c < f(b) (or f(a) > c > f(b)), then by the IVT, there exists a value x in the interval (a, b) such that f(x) = c.
Keep in mind these steps when solving problems involving the Intermediate Value Theorem.
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define a method that recieves 2 ints as input parameters and returns true or false depending on whether or not the first nubmer is twice the second
Python Program to Find Whether a Number is a Power of Two. The function power of two is defined. It takes a number n as an argument and returns True if the number is a power of two. If n is not positive, False is returned. If n is positive, then n & (n – 1) is calculated.
To define a function that receives two numbers as input parameters and returns true or false depending on whether or not the first number is twice the second, follow these steps:
1. Define the function with a name, e.g., "is_twice," and specify the two input parameters, e.g., "num1" and "num2."
2. Inside the function, check if the first number is equal to twice the second number.
3. Return True if the condition is met; otherwise, return False.
Here's the function definition:
```python
def is _ twice (num1, num2):
if num1 == 2 * num2:
return True
else:
return False
```
Now you can call this function with two numbers as input parameters, and it will return true or false based on the condition mentioned.
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If X is an exponential random variable with parameter λ, and c>0, show that cX is exponential with parameter λ/c.CDF Method:Let X be a continuous random variable and let Y=g(X)be a function of that random variable, where g(X) is some function of X. Let fX(x) be the probability density function (PDF) of X and fY(y) be the PDF of Y. Recall that the cumulative distribution function (CDF) of X is defined as the probability that X is less than or equal to some value x, for any real value of x. Mathematically,FX(x)=P(X≤x)Similarly, FY(y)=P(Y≤y).To find the distribution of Y, we can use the CDF method. We start by expressing the CDF of Y (FY(y)) in terms of X. We do this by using the fact that Y=g(X)and then solving the resulting inequality for X. Mathematically,FY(y)=P(Y≤y)=P(g(X)≤y)=⋯=P(X ???⋯)We isolate X in the inequality and we get an inequality which can be changed into CDF terms (the CDF of X).After we find the CDF of Y, we can differentiate it to get the PDF of Y. Recall that for any random variable, the first derivative of its CDF is equal to its PDF. In mathematical terms,fY(y)=ddyFY(y)We do this using the CDF of Y we obtained earlier. After completing this step, you will have the PDF of Y.
We have shown that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.
To show that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ, and c>0, we will use the CDF method:
1. Define the transformation: Let Y = cX be a function of the random variable X, where c > 0.
2. Find the CDF of Y: We want to find P(Y ≤ y), which is equal to P(cX ≤ y) or P(X ≤ y/c).
3. Express CDF of Y in terms of X: Since P(X ≤ y/c) is the CDF of X at y/c, we have FY(y) = FX(y/c).
4. Find the PDF of X: The exponential distribution has the PDF fX(x) = λ * exp(-λx) for x ≥ 0.
5. Differentiate the CDF of Y to find its PDF: To find fY(y), we differentiate FY(y) with respect to y. Using the chain rule, we have:
fY(y) = d(FX(y/c))/dy = fX(y/c) * (1/c)
6. Substitute the PDF of X: Now, we replace fX(y/c) with its exponential form λ * exp(-λ(y/c)):
fY(y) = (λ * exp(-λ(y/c))) * (1/c)
7. Simplify the expression: fY(y) = (λ/c) * exp(-λ(y/c))
This is the PDF of an exponential distribution with parameter λ/c. Therefore, cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.
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draw the graph of polynomial function
The graph of the polynomial function that passes through the points P(−2,2) and Q(1,0) is added as an attachment
Drawing the graph of polynomial functionFrom the question, we have the following parameters that can be used in our computation:
The graph passes through the points P(−2,2) and Q(1,0)
Assuming the graph is a linear function
So, we have
y = mx + c
Where
c = y when x = 0 and m = slope
This gives
-2m + c = 2
m + c = 0
Subtract the equations
So, we have
-3m = 2
m = -2/3
Solving for c, we have
-2/3 + c = 0
Evaluate
c = 2/3
So, the equation is f(x) = -2/3x + 2/3
See attachment for the graph
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Complete question
Draw the graph of polynomial function f(x) containing the points P(−2,2) and Q(1,0)
Give the reason(s) for each step needed to show that the following argument is valid.[p ∩ (p → q) ∩ (s ∪ r) ∩ (r → ¬p)] → (s ∪ t)1. p2. p→q3. q4. r → ~p5. q → ~r6. ~r7. s ∪ r8. s9. ∴ s ∪ t
The given argument is valid.
To show that the following argument is valid, we will use the given terms and follow a step-by-step explanation.
Argument: [p ∩ (p → q) ∩ (s ∪ r) ∩ (r → ¬p)] → (s ∪ t)
Steps:
1. p (Premise)
2. p → q (Premise)
3. q (From 1 and 2 using Modus Ponens: If p is true and p → q is true, then q is true)
4. r → ~p (Premise)
5. q → ~r (From 1 and 4 using the Contrapositive: If p is true and r → ~p is true, then q → ~r is true)
6. ~r (From 3 and 5 using Modus Ponens: If q is true and q → ~r is true, then ~r is true)
7. s ∪ r (Premise)
8. s (From 6 and 7 using Disjunction Elimination: If ~r is true and s ∪ r is true, then s is true)
9. ∴ s ∪ t (From 8 using Disjunction Introduction: If s is true, then s ∪ t is true)
By following these steps, we have shown that the given argument is valid.
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An angle measures 83.2° less than the measure of its supplementary angle. What is the measure of each angle?
Find the circumferences of of both circles to the nearest hundredth.
The value of circumferences of both circles to the nearest hundredth are 28.27 ft and 44ft.
Since, We know that;
The circumference of a form is the space surrounding its edge. Find the circumference of various forms by summing the lengths of their sides.
Given two coincide circles, the Radius of the smaller circle is 4.5ft.
Since the diameter is 9 ft.
Since, the bigger circle is 2.5 ft wider than the smaller circle,
Thus, the radius of the bigger circle = 4.5 + 2.5
Hence, the radius of the bigger circle = 7
From the formula for the circumference of a circle:
Circumference = 2π × radius
Thus,
The circumference of the yellow(bigger) circle is about = 2 x pi x 7
The circumference of the yellow(bigger) circle is about = 44 ft
The circumference of the purple(smaller) circle is about = 2 x pi x 4.5
The circumference of the purple(smaller) circle is about = 28.274 ft
therefore, The circumference of the yellow circle is about 44 ft. The circumference of the purple circle is about 28.27ft.
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The Circumference of the yellow circle is about 44 ft.
The circumference of the purple circle is about 28.27ft.
We have,
Radius of the smaller circle is 4.5ft
and radius of the bigger circle = 4.5 + 2.5 = 7 ft
Now, Circumference of Bigger circle (yellow) = 2 x π x r
= 2(3.14)(7)
= 44 ft
and, Circumference of Smaller circle (Purple) = 2 x π x r
= 2(3.14)(4.5)
= 28.274 ft
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For a four strokes engine, the camshaft that controls the valves a timing rotates at a. Double the engine rotational speed b. Half the engine rotational speed
c. Same engine rotational speed
d. none of the options
The correct answer is option (c) same engine rotational speed.
In a four-stroke engine, the camshaft rotates at half the speed of the crankshaft. The camshaft controls the opening and closing of the engine valves, which allows for the intake of fuel and air and the expulsion of exhaust gases.
When the engine rotational speed is doubled, the crankshaft will rotate twice as fast, but the camshaft will still rotate at half the speed of the crankshaft. This means that the camshaft will still rotate at the same speed as before, and the valve timing will remain the same.
Similarly, when the engine rotational speed is halved, the camshaft will still rotate at half the speed of the crankshaft. This means that the camshaft will still rotate at the same speed as before, and the valve timing will remain the same.
Therefore, the correct answer is option (c) same engine rotational speed.
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A serving of crackers has 1. 5 grams of fat. How many grams of fat are in 3. 85 servings
The approximately grams is 5.78 of fat in 3.85 servings of crackers. The nutritional information on food packages typically lists the amount of nutrients, including fat, in grams per serving.
We used grams in this calculation to measure the amount of fat in the serving of crackers and in the total number of servings.
To determine the grams of fat in 3.85 servings of a food item, you would need to know the amount of fat in one serving of that food and multiply it by 3.85.
For example, if one serving of the food contains 10 grams of fat, then the total amount of fat in 3.85 servings would be:
10 grams of fat/serving x 3.85 servings = 38.5 grams of fat
So, there would be 38.5 grams of fat in 3.85 servings of that food item. Please note that the actual amount of fat may vary depending on the specific food item and its nutritional content.
It's always best to refer to the nutrition label or consult a reliable source for accurate and up-to-date nutritional information
To calculate the total grams of fat in 3.85 servings of crackers, you can multiply the amount of fat in one serving by 3.85.
One serving of crackers has 1.5 grams of fat.
Total grams of fat in 3.85 servings of crackers = 1.5 grams of fat per serving x 3.85 servings
= 5.78 grams of fat.
Therefore, there are approximately 5.78 grams of fat in 3.85 servings of crackers.
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An online poll asked: "Do you believe the Loch Ness monster exists?" Among 21,466 responses, 62% were "yes." Use a 0.10 significance level to test the claim that most people believe that the Loch Ness monster exists. How is the conclusion affected by the fact that Internet users who saw the question could decide whether to respond?
Identify the null and alternative hypotheses for this test. Choose the correct answer below.
OA H_{0} / p = 0.5 H_{1} / p > 0.5
OB. H_{0} / p = 0.5 H_{1} :p ne0.5
OC. H_{0} / p = 0.5 H_{1} / p < 0.5
OD. H_{0} / p > 0.5 H_{1} / D = 0.5
Who are more likely to respond to an online poll about the Loch Ness monster may not be representative of the general population, and may have different beliefs about its existence.
The correct answer is: H0: p <= 0.5, H1: p > 0.5
Explanation:
The null hypothesis (H0) is that the proportion of people who believe that the Loch Ness monster exists is less than or equal to 0.5. The alternative hypothesis (H1) is that the proportion is greater than 0.5.
This is a one-tailed test, since we are only interested in whether the proportion is greater than 0.5.
The fact that Internet users who saw the question could decide whether to respond may affect the conclusion of the test, as it introduces potential bias into the sample. Those who are more likely to respond to an online poll about the Loch Ness monster may not be representative of the general population, and may have different beliefs about its existence.
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Which relationships have the same constant of proportionality between y and x as in the equation y=1/3x?
Therefore, any equation of the form y = kx, where k is a constant, has the same constant of proportionality as the equation y = (1/3)x.
Proportionality, equivalence between two ratios in mathematics. A and B are in the same ratio as C and D in the formula a/b = c/d. When one of a proportion's four quantities is unknown, a proportion is often built up to resolve the word problem.
According to the principle of proportionality, any incidental human casualties and property damage must not outweigh the tangible benefits to the military that may be expected from the destruction of a military objective.
The equation y = (1/3)x represents a proportional relationship between y and x with a constant of proportionality of 1/3.
Any equation of the form y = kx, where k is a constant, represents a proportional relationship between y and x with a constant of proportionality of k.
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NEED HELP ASAP!!!!!
(1)
Abe has $550 to deposit at a rate of 3%.what is the interest earned after one year?
(2)
Jessi can get a $1,500 loan at 3%for 1/4 year. What is the total amount of money that will be paid back to the bank?
(3)
Heath has $418and deposit it at an interest rate of 2%.(What is the interest after one year?)( How much will he have in the account after 5 1/2 years?)
(4)
Pablo deposits $825.50 at an interest rate of 4%.What is the interest earned after one year?
(5)
Kami deposits $1,140 at an interest rate of 6%. (What is the interest earned after one year?) (How much money will she have in the account after 4 years?)
1) Interest amount = $16.5
2) Interest amount = $4.125
3) Interest amount = $8.36
And, After 5 1/2 years;
Interest amount = $22.99
4) Interest amount = $33.02
5) Interest amount = $45.6
Now, We can simplify as;
1) Principal amount = $550
Rate = 3%
Time = 1 year
Hence, We get;
Interest amount = 550 x 3 x 1 / 100
= $16.5
2) Principal amount = $1500
Rate = 3%
Time = 1/4 year
Hence, We get;
Interest amount = 1500 x 3 x 1 / 100 x 4
= $4.125
3) Principal amount = $418
Rate = 2%
Time = 1 year
Hence, We get;
Interest amount = 418 x 2 x 1 / 100
= $8.36
And, After 5 1/2 years;
Interest amount = 418 x 11 x 1 / 100 x 2
= $22.99
4) Principal amount = $825.5
Rate = 4%
Time = 1 year
Hence, We get;
Interest amount = 825.5 x 4 x 1 / 100
= $33.02
5) Principal amount = $1140
Rate = 6%
Time = 1 year
Hence, We get;
Interest amount = 1140 x 6 x 1 / 100
= $68.4
And, After 5 4 years;
Interest amount = 1140 x 4 x 1 / 100
= $45.6
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The quality control inspector of a factory manufacturing screws found that the samples of screws are normally distributed with a mean length of 5.5 cm and a standard deviation of 0.1 cm.
If the distribution is normal, what percent of data lies between 5.3 centimeters and 5.7 centimeters?
A. 95%
B. 99.7%
C. 68%
D. 34%
In this case, the mean is 5.5 cm and the standard deviation is 0.1 cm. So, one standard deviation below the mean is 5.4 cm and one standard deviation above the mean is 5.6 cm. Therefore, about 68% of the data falls between 5.4 cm and 5.6 cm, which includes the range of 5.3 cm to 5.7 cm.
Your question involves a normal distribution with a mean (µ) of 5.5 cm and a standard deviation (σ) of 0.1 cm. You want to find the percentage of data between 5.3 cm and 5.7 cm.
First, we need to standardize the scores using the z-score formula: z = (x - µ) / σ
For 5.3 cm: z1 = (5.3 - 5.5) / 0.1 = -2
For 5.7 cm: z2 = (5.7 - 5.5) / 0.1 = 2
Now, referring to a standard normal distribution table or using a calculator, we find the area between these z-scores:
This can be determined using the empirical rule, also known as the 68-95-99.7 rule, which states that for a normal distribution:
- About 68% of the data falls within one standard deviation of the mean
- About 95% of the data falls within two standard deviations of the mean
- About 99.7% of the data falls within three standard deviations of the mean
P(-2 < z < 2) = P(z < 2) - P(z < -2) = 0.9772 - 0.0228 = 0.9544
Converting it to a percentage, we get 95.44%, which is approximately 95%.
So, the answer is A. 95%.
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What is the value of M?
70 is the answer
Step-by-step explanation:
two points are selected randomly on a line of length 18 so as to be on opposite sides of the midpoint of the line. in other words, the two points x and y are independent random variables such that x is uniformly distributed over [0,9) and y is uniformly distributed over (9,18] . find the probability that the distance between the two points is greater than 7 . answer:
The probability that the distance between the two randomly selected points on a line of length 18, which are on opposite sides of the midpoint, is greater than 7 is 1/3.
Let the midpoint of the line be M. Since x is uniformly distributed over [0,9) and y is uniformly distributed over (9,18], the probability of selecting any point in [0,9) is 1/2 and the probability of selecting any point in (9,18] is also 1/2.
Let A be the event that the distance between x and M is less than or equal to 7, and let B be the event that the distance between y and M is less than or equal to 7.
Therefore, the probability of A is the ratio of the length of [0,9) and the length of the entire line, which is 9/18 or 1/2. Similarly, the probability of B is also 1/2.
Now, the probability that the distance between the two points is greater than 7 is the complement of the probability that either A or B occurs, which is 1 - P(A or B).
Using the formula for the probability of the union of two events, we have P(A or B) = P(A) + P(B) - P(A and B).
Since A and B are independent events, P(A and B) = P(A) * P(B) = 1/4.
Therefore, P(A or B) = 1/2 + 1/2 - 1/4 = 3/4.
Finally, the probability that the distance between the two points is greater than 7 is 1 - 3/4 = 1/4 or 0.25, which is equivalent to 1/3 when expressed as a fraction in the simplified form.
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Fourteen of the 32 marbles in the bag were blue. The rest
were red. What was the ratio of red marbles to blue
marbles in the bag?
Answer: 18/14 or 18:14
Step-by-step explanation: this is relatively simple you have 32 in all and 14 are blue so 32-14=18 now you know there are 18 red marbles now to set up the ratio 18/14 or 18:14 (to check your work add 18+14=32)
The length of a cell phone is
1.4
1.4 inches and the width is
4.4
4.4 inches. The company making the cell phone wants to make a new version whose length will be
1.96
1.96 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
The width of the new phone is 6.16 inches.
How to find the width of the new phone?The length of a cell phone is 1.4 inches and the width is 4.4 inches. The company making the cell phone wants to make a new version whose length will be 1.96 inches.
The side length of the new phone are proportional to the old phone. Therefore, the width of the new phone can be calculated as follows:
let
x = width of the new phone
1.4 / 1.96 = 4.4 / x
cross multiply
1.4x = 4.4 × 1.96
1.4x = 8.624
divide both sides by 1.4
x = 8.624 / 1.4
x = 6.16
Therefore,
width of the new phone = 6.16 inches
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If P(A)= 0.3, P(B)=0.4, and P(A or B)=0.7, are A and B mutually exclusive? Use a table or the formula to answer the question. a [ Select] > they [Select ] 2 mutually exclusive because the P(A and B) [ Select ] equal to [ Select ]
This means that if event A occurs, event B cannot occur and vice versa.
A and B are mutually exclusive events if they have no outcomes in common. In other words, if A occurs, then B cannot occur and vice versa. Mathematically, if A and B are mutually exclusive events, then P(A and B) = 0.
Using the given probabilities, we can check if A and B are mutually exclusive by using the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Substituting the given probabilities, we get:
0.7 = 0.3 + 0.4 - P(A and B)
Simplifying, we get:
P(A and B) = 0.3 + 0.4 - 0.7 = 0
Since P(A and B) = 0, we can conclude that A and B are mutually exclusive events. This means that if event A occurs, event B cannot occur and vice versa.
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Zahra is a company specializing in high-end cosmetics. Its signature nail polish color is Soft Lilac. On a certain day, the company's factory had 5300 bottles of nail polish, and 1400 of those bottles were Soft Lilac. On that day, the inventory manager took a sample of 14 bottles of nail polish in the factory. She found that 3 of those bottles were Soft Lilac. For the inventory manager's sample, find and write with proper notation the population proportion and sample proportion of bottles that were Soft Lilac. Write the proportions as decimals (not percentages) rounded to two decimal places.
The population proportion (P) can be found by dividing the number of Soft Lilac bottles by the total number of bottles in the factory:
P = 1400 Soft Lilac bottles / 5300 total bottles
P ≈ 0.26 (rounded to two decimal places)
The sample proportion (p) can be found by dividing the number of Soft Lilac bottles in the sample by the total number of bottles in the sample:
p = 3 Soft Lilac bottles / 14 total bottles in the sample
p ≈ 0.21 (rounded to two decimal places)
So, the population proportion (P) of Soft Lilac bottles in Zahra's factory is approximately 0.26, and the sample proportion (p) of Soft Lilac bottles in the inventory manager's sample is approximately 0.21.
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Please help me with this my quiz. Thank you :)
Due tomorrow
Answer: yello
Step-by-step explanation:
On Friday, Daniel wrote a check for $158. The following Monday he deposited $60 into his bank account. On
Wednesday the bank informed him that he had overdrawn his account by $8. If Daniel made no other
transactions between Friday and Wednesday, what was his balance before he wrote the check on Friday?
Daniel's balance before he wrote the check on Friday was $248.
What was Daniel's balance before he wrote the check on Friday?To solve this problem, we can start by subtracting the $60 deposit from the $158 check, which gives us a balance of $98 before the check was cashed.
Since the account was overdrawn by $8 on Wednesday, we can subtract $8 from the balance to get $90.
Finally, we must add back the $158 check that was cashed which will give a balance of:
= $158 + $90
= $248
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A restaurant serves 10 different entrees, 6 of which contain meat. What is the ratio of vegetarian to non-vegetarian items?
Answer:
4/6 which is 2:3
Explanation:
the vegterian is 10-6=4
the non vegterian or eat meat is 6
and their ratio is 4/6
2:3
Is (7,-45) and (-8, -30) a solution to y=3x-6
Answer: No
Step-by-step explanation:
If you substitute the x and y values from the coordinates into eh equations, they will not add up.
Answer:
(-8,-30) is a solution
Step-by-step explanation:
Help me solve this please and thanks!
Answer:
9 x 9 x 9
Step-by-step explanation:
its obvious
understand subtraction as an unknown-addend problem. for example, subtract 10-8 by finding the number that makes 10 when added to 8.
To understand subtraction as an unknown-addend problem means to view subtraction as finding the missing number in an addition problem.
In the example given, subtracting 10-8 means finding the number that needs to be added to 8 to make 10. This is essentially an addition problem with an unknown addend.
To solve the problem, one needs to think about what number added to 8 will result in 10. This can be done by counting up from 8 until you reach 10, which is a difference of 2. Therefore, 10-8=2, and the missing number is 2.
In general, to subtract any two numbers using this method, you can start with the smaller number and count up until you reach the larger number. The difference between the two numbers is the missing addend. For example, to subtract 15-7, you would start with 7 and count up to 15, which is a difference of 8. So 15-7=8.
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The diameters of bolts produced on a certain machine are normally distributed with a mean of 0.62 cm and a standard deviation of 0.04 cm. Find the probability that a randomly selected bolt will have a diameter greater than 0.60 cm.
The probability that a randomly selected bolt will have a diameter greater than 0.60 cm is approximately 0.6915.
We know that the diameters of bolts produced on a certain machine are normally distributed with a mean (μ) of 0.62 cm and a standard deviation (σ) of 0.04 cm.
Let X be the diameter of a bolt. Then, X ~ N(μ, σ) = N(0.62, 0.04).
We need to find the probability that a randomly selected bolt will have a diameter greater than 0.60 cm.
P(X > 0.60) = P((X - μ)/σ > (0.60 - 0.62)/0.04) (standardizing X)
= P(Z > -0.5) (where Z ~ N(0,1) is the standard normal distribution)
Using the standard normal distribution table or calculator, we can find that P(Z > -0.5) is approximately 0.6915.
Therefore, the probability that a randomly selected bolt will have a diameter greater than 0.60 cm is approximately 0.6915.
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