Since the calculated t-value (2.24) is greater than the critical value (2.074), we reject the null hypothesis and conclude that there is convincing evidence that the average food intake is different for the patients in the treatment group. In other words, playing solitaire while eating lunch seems to have an effect on the amount of food consumed.
To determine whether there is convincing evidence that the average food intake is different for the patients in the treatment group, we can conduct a two-sample t-test. The null hypothesis is that the means of the two groups are equal, and the alternative hypothesis is that they are different.
H0: μa = μb
Ha: μa ≠ μb
where μa is the mean amount of biscuits consumed in the treatment group and μb is the mean amount of biscuits consumed in the control group.
We can use the following formula to calculate the test statistic:
t = (Xa - Xb) / √[(Sa²/n) + (Sb²/n)]
where Xa and Xb are the sample means, Sa and Sb are the sample standard deviations, and n is the sample size.
Plugging in the values from the question, we get:
t = (52.1 - 27.1) / √[(45.1²/22) + (26.4²/22)]
= 2.24
Using a two-tailed t-distribution with 22 degrees of freedom and a significance level of 0.05, the critical values are ±2.074.
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Suppose that the weights of 2700 registered female Great Danes in the United States are
distributed normally with a mean of 133 lb. and a standard deviation of 6.4 lb.
Approximately how many of the Great Danes weigh less than 126.6 lbs.? SHOW WORK!
Answer:
To solve this problem, we can use the cumulative distribution function (CDF) of the normal distribution.Given:
Mean (μ) = 133 lb
Standard Deviation (σ) = 6.4 lb
Weight (X) = 126.6 lb
We can use the formula for the standard normal distribution to calculate the z-score:
z = (X - μ) / σ
Plugging in the values, we get:z = (126.6 - 133) / 6.4 = -0.984375
Now, we can use a standard normal distribution table or a calculator with a built-in normal distribution function to find the cumulative probability (P) associated with the z-score of -0.984375.
Using a standard normal distribution table, we find that the cumulative probability for a z-score of -0.984375 is approximately 0.1611.
So, approximately 16.11% of the registered female Great Danes in the United States weigh less than 126.6 lbs.
Step-by-step explanation:
A man has three children whose ages are 9 years, 12 years and 24 years. Find the ratio of their ages
The ratio of ages of a man who has three children whose ages are 9 years, 12 years, and 24 years is 1:4/3:8/3.
To find the ratio of the ages of the man's three children, we need to divide their ages by their greatest common factor (GCF). The GCF of 9, 12, and 24 is 3. So, we divide each age by 3:
9 ÷ 3 = 3
12 ÷ 3 = 4
24 ÷ 3 = 8
Therefore, the ratio of their ages is 3:4:8. This means that for every 3 years the youngest child ages, the middle child ages 4 years, and the oldest child ages 8 years. We can simplify the ratio by dividing all three numbers by their GCF of 3, which gives us the simplified ratio of 1:4/3:8/3.
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If one were testing whether a particular sample was drawn from a population with a particular mean and the standard deviation of the entire population was known, one would use the _____ to statistically answer the question
"If one were testing whether a particular sample was drawn from a population with a particular mean and the standard deviation of the entire population was known, one would use the Z-test to statistically answer the question". Option A is correct.
In statistical hypothesis testing, when the standard deviation of the entire population is known and you want to determine if a particular sample was drawn from a population with a specific mean, the appropriate test to use is the Z-test.
The Z-test is used when the population standard deviation is known and the sample size is large enough to satisfy the assumptions of normality. It compares the observed sample mean to the hypothesized population mean and determines the likelihood of obtaining such a sample mean if the population mean is actually equal to the hypothesized value.
By calculating the Z-score and comparing it to the critical value, you can make a statistical inference about whether the sample is likely to have been drawn from the specified population.
Option A holds true.
The complete question:
If one were testing whether a particular sample was drawn from a population with a particular mean and the standard deviation of the entire population was known, one would use the ______test to statistically answer the question.
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what type of angle is ABC
Answer:
right angle
Step-by-step explanation:
the sign you find in the angle ABC means that it is a right angle, therefore 90°
Raymond and his wife have a traditional IRA, and they plan to deposit $100 per month for the next 4 years. What is the future of their IRA if the interest is compounded semi annually at a rate of 4%? The factor, according to the future value of ordinary annuities table, is 8.58297 at 2% interest, and 8 compounding periods.
a. $2510.18
b. $4800.29
c. $5149.78
d. $8582.97
The future value of the IRA is given as $5149.78. Option C
How to solve for the IRARaymond and his wife plan to deposit $100 per month,
semi-annual period, deposit = $100 × 6
= $600
[tex]FV = P * [(1 + r)^n - 1] / r[/tex] = 8.58297
We have to define the terms in the formula
FV is the future value of the IRA,
P is the payment per period ($600),
r is the interest rate per period (2% or 0.02 as a decimal),
n is the number of periods (8).
FV = $600 * 8.58297
FV = $5,149.78
The futire value is given as FV = $5,149.78
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18. Which numbers are plotted on the number line?
A-3, 1, 4
B
-2.5, 0.5, and 2
C -1.5, 0.5, and 2
D 0.5, 1.5, and 2
T
3
2
T
O
↑ ?
←+
O
It should be noted that a number line is a picture of a graduated straight line that serves as visual representation of the real numbers.
What is number line?In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
Positive numbers are plotted to the right of the origin while negative numbers are plotted to the left of the origin. Arrows are put on the ends of the horizontal line to show that the line continues to infinity.
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A study by the Pew Research Center1 reports that in 2010, for the first time, more adults aged 18 to 29 got their news from the Internet than from television. In a random sample of 1500 adults of all ages in the US, 66% said television was one of their main sources of news. Does this provide evidence that more than 65% of all adults in the US use television as one of their main sources for news? A randomization distribution for this test shows Sâ¢Eâ¢=â0.013.
Based on the random sample, there is not enough evidence to conclude that more than 65% of all adults in the US use television as one of their main sources of news.
To answer your question, we will perform a hypothesis test using the given information.
Step 1: State the hypotheses.
H0 (null hypothesis): p = 0.65 (65% of all adults in the US use television as one of their main sources for news)
Ha (alternative hypothesis): p > 0.65 (more than 65% of all adults in the US use television as one of their main sources for news)
Step 2: Determine the sample proportion (p-hat) and sample size (n).
p-hat = 0.66 (66% from the random sample of 1500 adults)
n = 1500
Step 3: Calculate the test statistic (z) using the formula:
z = (p-hat - p) / sqrt[(p * (1-p)) / n]
z = (0.66 - 0.65) / sqrt[(0.65 * (1-0.65)) / 1500]
z = 0.01 / 0.013 (given Sâ¢Eâ¢=â0.013)
z ≈ 0.77
Step 4: Find the p-value corresponding to the test statistic.
Using a z-table or calculator, we find the p-value for z = 0.77 is approximately 0.2206. Since this is a one-tailed test, we will use this p-value directly.
Step 5: Compare the p-value to the significance level (α) and make a decision.
Assuming a common significance level (α) of 0.05, our p-value (0.2206) is greater than α. Therefore, we fail to reject the null hypothesis (H0).
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Testing the effects of radiation on the growth of tardigrades there were 3 levels, 1, 2, and 3.Sample size-2 per level Mean Variance Level 3 (highest radiation) 83.74 14Level 2 (medium level) 65.83 16Level 1(Lowest radiation) 56.76 23 Assume all variances the same a. If the means are the same, each mean has the same mean, and a variance of sigma2/2, so we can build 2 estimates of variance, we can i. Calculate Meantot=(mean1+mean2+mean3)/3, and var1-2* (sum(meani- meantot)A2)/2 ii. Calculate Var2=generalize the pooled estimate of variance from the outside the book, class notes (lecture 18), Calculate it. iii. Calculate Var1/Var2"F with 2 and 3 degrees of freedom (why 3 df)b. Test if the 2 estimates of variance are the same c. If Var1>>Var2, what does that mean about the means of the data
a. To compare these two estimates of variance, we calculate the F statistic as Var1/Var2 with 2 and 3 degrees of freedom (why 3 df is because we have 3 levels). b. We reject the null hypothesis that the variances are equal and conclude that they are significantly different. c. It does not necessarily mean that the means of the data are significantly different.
a. To test the effects of radiation on the growth of tardigrades, we experimented with 3 levels of radiation: 1, 2, and 3. For each level, we had a sample size of 2 and calculated the mean and variance. The mean and variance for each level are as follows:
Level 3 (highest radiation): Mean = 83.74, Variance = 14
Level 2 (medium level): Mean = 65.83, Variance = 16
Level 1 (lowest radiation): Mean = 56.76, Variance = 23
If the means are the same, each mean has the same mean and variance of sigma2/2, we can build 2 estimates of variance. The first estimate (Var1) is calculated using the formula: Var1 = 2 * (sum(meaning - meant)²) / 2, where meant is the overall mean of the data. The second estimate (Var2) is a pooled estimate of variance, which can be calculated using the formula taught in class (lecture 18).
b. We can test if the 2 estimates of variance are the same by comparing the F statistic we calculated in part a to the critical F value from the F distribution table with 2 and 3 degrees of freedom at a given significance level (e.g. 0.05). If the calculated F statistic is greater than the critical F value, we reject the null hypothesis that the variances are equal and conclude that they are significantly different.
c. If Var1>>Var2, it means that there is a larger variation within each level of radiation compared to the variation across all levels. This could be due to experimental error or other factors that are not related to radiation. It does not necessarily mean that the means of the data are significantly different.
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What is the size of x when the opposite is 4.9 the hypotenuse is 7.2 i need to work out x which is where it meets with the hypotenuse and adjacent?
Answer:
Step-by-step explanation:
10
Pls give me an explanation on this lol. My teacher sucks .. it’s geometry circle stuff. It’s probably ready but she doesn’t teach well
Answer: 25
Step-by-step explanation:
You have 2 secants, i have attached an image that may help with the rules for secants
Multiply short length * full = other short length* full
What is the short length, 3
Full length of that line is x.
3x=5(10+5) simplify
3x=75
x=25
To negate a conjunction, negate each of the component statements and change and to
The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.
To negate a conjunction, which is a statement of the form "p and q", we need to negate each of the component statements and change "and" to "or". The negation of "p and q" is "not p or not q", which means that "p and q" is false if either "p" or "q" is false.
For example, if we have the statement "John will go to the beach and he will go to the park", we can negate it by saying "It is not the case that John will go to the beach and he will go to the park", which can be written symbolically as "not (John will go to the beach and he will go to the park)". Using the rule for negating a conjunction, we can rewrite this statement as "John will not go to the beach or he will not go to the park".
Note that this is different from the negation of a disjunction, which is a statement of the form "p or q". The negation of "p or q" is "not p and not q", which means that "p or q" is false if both "p" and "q" are false.
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During the sale, Ronald paid $77
for a hammock.
What was the original price rounded to the nearest penny? sorry forgot the picture on the other one
Answer:
$96.25
Step-by-step explanation:
$77 x 25% = $19.25
$77 + $19.25 = $96.25
An experiment to compare the spreading rates of five different brands of yellow interior latex paint available in a particular area used 4 gallons (J = 4) of each paint. The sample average spreading rates (ft2/gal) for the five brands were x1. = 462.0, x2. = 502.8, x3. = 427.5, x4. = 469.3, and x5. = 532.1. The computed value of F was found to be significant at level α = 0.05. With MSE = 450.8, use Tukey's procedure to investigate significant differences between brands. (Round your answer to two decimal places.)
W= ?
Which means differ significantly from one another? (Select all that apply.)Which means differ significantly from one another? (Select all that apply.)
x1. and x2.
x1. and x3.
x1. and x4.
x1. and x5.
x2. and x3.x2. and x4.
x2. and x5.
x3. and x4.
x3. and x5.
x4. and x5.
There are no significant differences.
Tukey's procedure to investigate significant differences between brands is x3. and x5.
x4. and x5.
To use Tukey's procedure to investigate significant differences between brands, we need to calculate the value of W and compare it with the critical value from the Studentized Range Distribution.
The formula for W is:
W = q(α, 5, 15) * √(MSE/4)
where q(α, 5, 15) is the critical value from the Studentized Range Distribution with α = 0.05, k = 5 (number of brands), and df = 15 (total degrees of freedom). Using a table or calculator, we find:
q(0.05, 5, 15) = 3.07
Plugging in the given values, we get:
W = 3.07 * √(450.8/4) ≈ 17.99
Since the computed value of F was found to be significant at level α = 0.05, we can conclude that there are significant differences between at least some of the brands. To determine which brands differ significantly from one another, we can use the formula:
|xi. - xj.| ≥ W / √(2MSE/4)
where xi. and xj. are the sample averages for any two brands i and j. If this inequality is satisfied, then we can say that the two brands differ significantly from one another.
Calculating the absolute differences between all pairs of sample averages and comparing them with the right-hand side of the inequality above, we get:
|462.0 - 502.8| = 40.8 ≥ 8.99 → Significant
|462.0 - 427.5| = 34.5 < 8.99 → Not significant
|462.0 - 469.3| = 7.3 < 8.99 → Not significant
|462.0 - 532.1| = 70.1 ≥ 8.99 → Significant
|502.8 - 427.5| = 75.3 ≥ 8.99 → Significant
|502.8 - 469.3| = 33.5 < 8.99 → Not significant
|502.8 - 532.1| = 29.3 < 8.99 → Not significant
|427.5 - 469.3| = 41.8 ≥ 8.99 → Significant
|427.5 - 532.1| = 104.6 ≥ 8.99 → Significant
|469.3 - 532.1| = 62.8 ≥ 8.99 → Significant
Using the critical value W, we can conclude that brands 1, 2, 4, and 5 differ significantly from one another. Therefore, the correct answer is:
x1. and x2.
x1. and x5.
x2. and x3.
x3. and x4.
x3. and x5.
x4. and x5.
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Consider a hypothetical two way layout where two drugs A and B are each taken in quantities 0g, 1g or 2g. And our measurements are years of remaining life.
In this hypothetical two-way layout, we are studying the effects of two drugs A and B on remaining life. The drugs are each taken in quantities of 0g, 1g or 2g, resulting in a total of 9 possible treatment combinations.
Our outcome of interest is years of remaining life. To analyze this data, we would likely use a two-way ANOVA to assess the main effects of each drug and the interaction effect between the two drugs. This analysis would allow us to determine if there is a significant difference in remaining life between the different drug doses and if the effect of one drug is influenced by the dose of the other drug.
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(a)At what age did the infant weigh 11 pounds?
(b)What was the infant’s weight at birth?
(c)Paul the alien uses the function y=5/4 x+7 to model the situation. What weight does
the model predict for an infant of 16 months?
(d)What does the number 5/4 in Part (c) mean in the context of the situation?
(e)What does the number 7 in Part (c) mean in the context of the situation? Answer:
The solution to the linear equation graph problems are:
a) 20 months
b) 7 pounds
c) 27 pounds
d) Rate of change of weight per month
e) Weight of the infant at birth
How to solve Linear Equation Word Problems?The general form of the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
a) The corresponding age at which the infant weighed 11 pounds from the graph is: 20 months
b) The infants weight at birth is the age at 0 years which in this case is 7 pounds
c) Paul's function is given as:
y = ⁵/₄x + 7
Thus, at 16 months, the weight is:
y = ⁵/₄(16) + 7
y = 27 pounds
d) What the number 5/4 represents in the model is the rate of change of weight per month.
e) The number 7 in part c denotes the weight at birth.
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You deposit $6000 in a savings account that earns 4.5% annual interest compounded mon
a. Write a functions that represents the balance (in dollars) of your savings account after t years.
b. What is the balance of the account after 6 years to the nearest cent?
a. A function that represents the balance (in dollars) or the future value of the savings account after t years is C. s(t) = 6,000(1 + 0.045/12)^12t.
b) The balance (future value) of the account after 6 years, to the nearest cent, is $7,855.82.
How the future value is computed?The future value can be computed using the FV formula or function below:
s(t) = 6,000(1 + 0.045/12)^12t
s(t) = 6,000(1 + 0.045/12)^12(6)
= $7,855.8186
= $7,855.82
This future value can also be computed using an online finance calculator as follows:
N (# of periods) = 72 months (6 years x 12)
I/Y (Interest per year) = 4.5%
PV (Present Value) = $6,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $7,855.82
Total Interest = $1,855.82
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help please what are the features of the function f(x) = -(1/3)^x +5 graphed below (it's all in the picture)
The requried features of the given function has been shown below.
The function f(x) = -(1/3)^x +5 has the following features:
Domain: The domain of the function is all real numbers.
Range: The range of the function is y ≤ 5. In other words, the function has a maximum value of 5, which is approached but never reached as x approaches negative infinity.
x-intercept: The x-intercept is where the graph of the function intersects the x-axis. The x-intercept is approximately -3.96.
y-intercept: The y-intercept is where the graph of the function intersects the y-axis. The y-intercept is (0, 4).
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"Q4) Suppose a researcher has access to a listof all pilots who are members of the Air Line Pilots Association.If this list is used as a frame for the study, she can randomlyselect a sample of pilot"
If a researcher has access to a list of all pilots who are members of the Air Line Pilots Association and she wishes to conduct a study, she can use this list as the frame for selecting a random sample of pilots. By doing so, she can ensure that the sample is representative of the larger population of pilots who are members of the association.
Suppose a researcher wants to conduct a study on pilots who are members of the Air Line Pilots Association. The researcher has access to a list of all these pilots, which serves as the frame for the study. In order to randomly select a sample of pilots, the researcher can follow these steps:
1. Assign a unique number to each pilot on the list.
2. Determine the sample size required for the study based on the research objectives.
3. Use a random number generator or a random sampling technique (e.g., simple random sampling) to select the desired number of pilots from the list.
4. Once the sample has been chosen, the researcher can proceed with the study by contacting the selected pilot members and collecting the necessary data.
This method ensures that the sample is representative of the entire population of pilots in the Air Line Pilots Association and helps maintain the validity of the research findings. This is important because it allows her to draw conclusions about the population based on the sample data. The sample should be selected in a random and unbiased manner to ensure that it is a true representation of the population. The researcher can then use the data collected from the sample to make inferences about the population of pilots who are members of the Air Line Pilots Association.
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What is the surface area of the rectangular prism?
5 m
10 m
2 m
The surface area of the rectangular prism is 160 square meters
What is the surface area of the rectangular prism?From the question, we have the following parameters that can be used in our computation:
5 m by 10 m by 2 m
The surface area of the rectangular prism is calculated as
Area = 2 * (5 * 10 + 5 *2 + 10 * 2)
Evaluate
Area = 160
Hence, teh area is 160 square meters
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The number of calls coming in to an office follows a Polsson distribution with mean 5 calls per hour. What is the probabllity that there will be exactly 7 calls within the next hour ? O a. 0.071 O b. 0.104 Oc. 0.090 Od 0.123 Which of the following statements Is False? O a. Using the normal curve, the P(Z < 1.28) is approximately 0.9 O b. Using the standard normal curve, the area between z=0 and z = 3.50 is about 0.50 Oc. In the normal distribution, the total area under the curve is equal to one (1) O d. The mean of any normal distribution is always zero
The false statement is option d. The mean of a standard normal distribution is zero, but the mean of any normal distribution can vary and is not always zero.
The number of calls coming in to an office follows a Poisson distribution with a mean of 5 calls per hour. To find the probability of exactly 7 calls within the next hour, we can use the formula for the Poisson probability:
P(X = k) = (e^(-λ) * (λ^k)) / k!
Where λ is the mean (5 calls per hour), k is the number of calls we're interested in (7), and e is the base of the natural logarithm (approximately 2.71828).
P(7 calls) = (e^(-5) * (5^7)) / 7! ≈ 0.104
So the probability of exactly 7 calls within the next hour is 0.104 (option b).
For the false statement among the given options:
a. Using the normal curve, the P(Z < 1.28) is approximately 0.9
b. Using the standard normal curve, the area between z=0 and z = 3.50 is about 0.50
c. In the normal distribution, the total area under the curve is equal to one (1)
d. The mean of any normal distribution is always zero
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What is the range of the equation shown in the graph?
The range of the graphed function is y ≤ 1, or written in interval form, it is:
(-∞, 1]
What is the range of the function?The range is the set of the possible outputs of the function, so we need to look at the vertical axis (also called the y-axis).
Here we can see that we have the maximum at y = 1, and then the function goes down. (We can assume it will go to negative infinity, this is beacuse we can see arrow points at the ends, which means that the function keeps going downwards)
Then the range is:
y ≤ 1
Or (-∞, 1] in interval form.
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The serving size for a snack is 3 1/5 grams. What amount of servings are in 16.8 grams of the snack?
The amount of servings are in 16.8 grams of the snack is: 5 servings
How to solve Algebra Word Problems?Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.
We are told that:
Serving Size for a snack = 3¹/₅ grams = 16/5 grams
In 16.8 grams, we can write as 168/10 or 84/5
Thus:
The amount of servings are in 16.8 grams of the snack is:
84/5 ÷ 16/5
= 84/5 * 5/16
= 84/16
= 21/4
= 5.25
Approximately 5 servings
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A large number of insects are expected to be attracted to a certain variety of rose plant. A commercial insecticide is advertised as being 99
% efective. Suppose 2000
insects infest a rose garden where the insecticide has been applied, and let X=
number of surviving insects. Evaluate an approximation to the probability that fewer than 100
insects survive
There is a very low probability of fewer than 100 insects surviving in the rose garden.
Given that the insecticide is advertised as being 99% effective, it means that 1% of the insects are not affected by the insecticide. Therefore, the probability of an insect surviving the insecticide is 0.01.
Let's assume that the number of surviving insects, X, follows a binomial distribution with parameters n = 2000 and p = 0.01. We want to find the probability that fewer than 100 insects survive, i.e., P(X < 100).
Since the number of trials is large (n = 2000) and the probability of success is small (p = 0.01), we can approximate the binomial distribution with a Poisson distribution with parameter λ = np = 2000*0.01 = 20.
Using the Poisson distribution, we can calculate the probability of fewer than 100 insects surviving as:
P(X < 100) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 99)
= e^(-20) * (20^0/0!) + e^(-20) * (20^1/1!) + e^(-20) * (20^2/2!) + ... + e^(-20) * (20^99/99!)
We can use a calculator or a software program to calculate this sum, which gives us an approximation of 0.0000386 or 0.00386%.
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Prepare journal entries to record transactions a through h.
a. Raw materials purchased on credit, $82,000.
b. Direct materials used, $37,500. Indirect materials used, $17,200.
c. Direct labor used, $30,000. Indirect labor used, $10,000. (Record using Factory Wages Payable.)
d. Paid cash for other actual overhead costs, $7,125.
e. Applied overhead at the rate of 125% of direct labor cost.
f. Transferred cost of jobs completed to finished goods, $54,400.
g. Sales of jobs on credit was $77,000.
h. Cost of jobs sold was $54,400.
View transaction list
Journal entry worksheet
help please
What is the volume for 25 in? Look at the picture.
Step-by-step explanation:
to find to multiply it 3 times
V=length x width x height
V=25in x 25in x 25in
V=15,625 cubic inches
Answer:
[tex]V = 15,625 in^3[/tex]
Step-by-step explanation:
The formula for the area of a square is if x is the length of a side
V = x^3
V =25^3
V = 25 · 25 · 25
V = 625 ·25
V = 15,625 in^3
Select True or False for each statement.
1. (1/64)^–⅚ = 32 True
2. √12 - 2/5 × √75 = 4√3 = False
3. √9a + √98b -a+√2b = 2a+10√b = 0 =True
4. 1/(√5-√6)² = 11-2√30/241 = False
How did we arrive at these assertions?1. (1/64)^–⅚ = 32
write in exponential form
2⁵ = 2⁵, hence, true
2. √12 - 2/5 × √75 = 4√3
Simplify the expressions
2√3-2√3 = 4√3
Eliminate the opposites
0 = 4√3
The statement is false
3. √9a + √98b -a+√2b = 2a+10√b = False
Evaluate
3a + √98b-a + √2b = 2a+10√b
Collect like terms
2a + √98b+ √2b = 2a+10√b
Cancel equal terms
98b+ √2b = 10√b Simplify the equation
98b+28b+2b = 100b
Collect like terms
128b = 100b
Move the variable to the left
128b 100b = 0
28b = 0
Divide both sides
b = 0
4. 1/(√5-√6)² = 11-2√30/241 = False
The approximate value of 1 / (√5-√6)² is 21.95445 and the approximate value of 11-2√30/ 241 is 0.000188999, meaning 1/(√5-√6)² ≠ 11-2√30/241
1/(√5-√6)² = 11-2√30/241, so equality is false
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What is the mapping formula expressed by the vector that translates JKLM to J’K’L’M’.
(x,y) → (x - 2, y - 3)
(x,y) → (x +1, y - 4)
(x,y) → (x +1, y + 4)
(x,y) → (x - 2, y +3)
Answer:
The answer to your problem is, D. (x,y) → (x - 2, y +3)
Step-by-step explanation:
We can see that the vector that translates JKLM to J'K'L'M' is given by the difference between the coordinates of J and J', and the difference between the coordinates of K and K'.
The differences can be called, "a" and "b", respectively. Then we can write:
a = J' - J = (-1) - 0 = -1
b = K' - K = 3 - (-1) = 4
Which can conclude to the mapping formula expressed by the vector that translates JKLM to J'K'L'M' is:
(X,Y) → (X - 1, Y + 4)
Thus the answer to your problem is, D. (x,y) → (x - 2, y +3)
How many different selections of 4 books can be made from 10 different books, if (i) there is no restriction (ii) two particular books are always selected (iii) two particular books are never selected
There are 210 different selections of 4 books that can be made from 10 different books with no restriction. There are 28 different selections of 4 books that can be made from 10 different books if two particular books are always selected. There are 70 different selections of 4 books that can be made from 10 different books if two particular books are never selected.
(i) If there is no restriction, then we can choose any combination of 4 books from the 10 different books. This is a combination problem, and the formula for combinations is:
n C r = n! / r!(n-r)!
where n is the total number of items to choose from, and r is the number of items we want to choose.
So, in this case, we have n = 10 and r = 4. Plugging these values into the formula, we get:
10 C 4 = 10! / 4!(10-4)! = 210
(ii) If two particular books are always selected, then we only need to choose the remaining 2 books from the remaining 8 books. We can do this using the same combination formula, but with different values of n and r:
n = 8 (since we only have 8 books to choose from)
r = 2 (since we want to choose 2 books)
Plugging these values into the formula, we get:
8 C 2 = 8! / 2!(8-2)! = 28
(iii) If two particular books are never selected, then we need to choose 4 books from the remaining 8 books. Again, we can use the same combination formula:
n = 8
r = 4
Plugging these values into the formula, we get:
8 C 4 = 8! / 4!(8-4)! = 70
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Find the measure of the missing angle.
Answer: 41 degrees
Step-by-step explanation:
118 + 21 = 139
180 - 139 = 41
A graphic designer wanted to create a new logo for a company that will be printed on a large signage. The logo is a rectangle that has a semicircular piece removed. If the designer wanted that the area of the logo is approximately 90.64 ft², will it be possible for him to make the desied logo in a 14ft by 8.5ft rectangle?