Answer:
[tex] Ways = 3*5*7= 105[/tex]
And that's equivalent to:
[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]
Where C represent the term combinatory defined as:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
And then the number of ways to select the three books are 105, and the best option would be:
b). 105
Step-by-step explanation:
For this case we can use the multplication principle of counting or sometimes called the product rule.
We have a total of 3 novels, 5 biographies and 7 self-help books. And we can find the number of ways that a person can select the three books with theis product:
[tex] Ways = 3*5*7= 105[/tex]
And that's equivalent to:
[tex] Ways= (3C1) (5C1) (7C1) =3*5*7=105[/tex]
Where C represent the term combinatory defined as:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
And then the number of ways to select the three books are 105, and the best option would be:
b). 105
We want to see in how many different ways a person can select one book from 3 novels, one book from 5 biographies and one book from 7 self-help books, the correct option is b: 105.
To get the numbe of different ways, the first thing we need to do is find the selections.
Here we have 3 selections:
Novel selection.Biography selectionSelf-help selection.Now we need to find the number of options for each of these selections, and just multiply the numbers of options.
we have:
Novel selection: 3 optionsBiography selection: 5 optionsSelf-help selection: 7 optionsNumber of different ways of selecting = 3*5*7 = 105
So the correct option is b.
If you want to learn more, you can read:
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A sphere has a diameter of 18 inches. What is the volume of this sphere? Use ≈ 3.14 and round your answer to the nearest tenth.
Answer:
3053.63 cu. inches
Step-by-step explanation
Volume = 4/3 pi r^3
Answer:
[tex]v \: \: ≈
3053.62 {in}^{3}
[/tex]
Step-by-step explanation:
[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times \pi \times {9}^{3} \\ ≈
3053.62806
[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Factor completely. 25+70x+49x^2
Answer:
(5+7x)^2
Step-by-step explanation:
25+70x+49x^2
This is a perfect square trinomial
a^2 +2ab + b^2 = (a+b)^2
5^2 *2*5*7x+ (7x)^2 = (5+7x)^2
A factory makes bicycles.Out of 300 bicycles, 2 were found to have defective brakes
A.what is the experimental probability that the next bike manufactured will have defective brakes?
B. Predict how many bikes out of 2,100 will have defective brakes.
Answer:
A. 2/300=1/150
B.1/315,000
Step-by-step explanation:
B. 1/150*2100=1/315000
pls help me with this and show any work
Answer: 9.5 (D.)
Step-by-step explanation:
SOCAHTOA
the sin of an angle is equal to the opposite side over the hypotenuse.
angle: 32
opposite side: x
hypotenuse: 18 m
1. sin32 = x/18
2. 18(sin32) = x
3. 9.5 = x
if you are confused with how it went from 18(sin32) to 9.5, you can plug 18(sin32) into your calculator.
Prove
sec2x - tan2x = tan(45-x)
Pls Help!!!TQ
Step-by-step explanation:
sec(2x) − tan(2x)
Write in terms of sine and cosine:
1/cos(2x) − sin(2x)/cos(2x)
(1 − sin(2x)) / cos(2x)
Use double angle formulas:
[ 1 − 2 tan x / (1 + tan²x) ] / [ (1 − tan²x) / (1 + tan²x) ]
Multiply by reciprocal:
[ 1 − 2 tan x / (1 + tan²x) ] × [ (1 + tan²x) / (1 − tan²x) ]
Distribute 1 + tan²x:
(1 + tan²x − 2 tan x) / (1 − tan²x)
Factor:
(1 − tan x)² / ((1 − tan x) (1 + tan x))
Simplify:
(1 − tan x) / (1 + tan x)
Rewrite using 1 = tan(45°):
(tan(45°) − tan x) / (tan(45°) + tan x)
Use angle difference formula:
tan(45° − x)
A study randomly assigned adult subjects to one of three exercise treatments: (1) a single long exercise period five days per week; (2) several ten-minute exercise periods five days per week; and (3) several ten-minute periods five days per week using a home treadmill. The study report contains the following summary statistics about weight loss (in kilograms) after six months of treatment: Does the type of exercise treatments influence weight loss significantly? Use α = 5%. Treatment Mean Std. Dev. n Long periods 10.2 4.2 10 Multiple short periods 9.3 4.5 10 Multiple short periods with treadmill 10.2 5.2 10 The test statistic is:
Answer:
Step-by-step explanation:
Hello!
For this study adult subjects were randomly assigned to three different exercise treatments establishing three different groups:
Group 1: Single long exercise period five days per week
Group 2: Several 10' exercise periods five days per week
Group 3: Several 10' exercise periods five days per week using a home treadmill
All subjects were weighed before and after 6 months of training and their weight loss was determined.
The objective of this study is to determine if there is any difference between the treatments, meaning, if the weight loss is the same regarding the type of exercise or if the type of exercise has some influence over it.
To test this you have to conduct an ANOVA, with the hypothesis:
H₀: μ₁= μ₂= μ₃
H₁: At least one μi differs from the others. ∀ i=1, 2, 3
α: 0.05
The statistic is:
[tex]F= \frac{MS_{Tr}}{MS_{Er}} ~~F_{k-1; n-k}[/tex]
Normally it is better to have the raw data to conduct the analysis using statistical software, but it is not impossible to calculate the statistic using the descriptive statistics for each group.
As you know the statistic is calculated as the ratio between the mean square of the treatments (between groups) and the mean squares of errors.
Each means square is calculated as the sum of squares by the degrees of freedom of the category: SS/Df
So first you need to determine the SS and Df of treatments and errors, then the MS and finally the value of F.
Treatments:
> The degrees of freedom between treatments are k-1 (k represents the number of treatments):
DfTr: 3-1= 2
>The sum of squares is:
SSTr: ∑ni(Ÿi - Ÿ..)²
Ÿi= sample mean of sample i ∀ i= 1,2,3
Ÿ..= grand mean is the mean that results of all the groups together.
So the Sum of squares of treatments (SSTr) is the sum of the square of the difference between the sample mean of each group and the grand mean.
To calculate the grand mean you can sum the means of each group and dive it by the number of groups:
Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ k = (10.2+9.3+10.2)/3= 29.7/3= 9.9
SSTr= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (10.2 - 9.9)² + (9.3 - 9.9)² + (10.2 - 9.9)²= 0.54
> The Means Squares is:
MSTr= SSTr/DFTr= 0.54/2= 0.27
Errors
>Degrees of freedom of error DfEr= N-k Where N is the total of observations of the experiment (N= n₁+n₂+n₃) and k is the number of treatments.
DfEr= N-k= 30-3= 27
>The mean square error (MSEr) is the estimation of the variance error (σ[tex]_{e}^2[/tex] → S[tex]_{e}^2[/tex]), you have to use the following formula:
[tex]S_{e}^2= \frac{(n_1-1)S^2_1+(n_2-1)S_2^2+(n_3-1)S^2_3}{N-k}= \frac{(9*17.64)+(9*20.25)+(9*27.04)}{27}= \frac{584.37}{27}= 21.643[/tex]
Finally you calculate the statistic:
[tex]F_{H_0}= \frac{MS_{Tr}}{MS_{Er}}= \frac{0.27}{21.643}= 0.012[/tex]
This test is One-tailed right, meaning that you'll reject to high values of the statistic and there is one critical value:
[tex]F_{k-1;N-k;1-\alpha }= F_{2;27;0.95}= 3.35[/tex]
Using the critical value approach, the decision rule is:
If [tex]F_{H_0}[/tex] ≥ 3.35, reject the null hypothesis.
If [tex]F_{H_0}[/tex] < 3.35, do not reject the null hypothesis.
The calculated value is less than the critical value, the decision is to not reject the null hypothesis.
So at a 5% significance level, there is not enough evidence to conclude that the treatments influence significantly in weight loss. The population mean weight loss is the same for the treatments "Single long exercise period five days per week", "Several 10' exercise periods five days per week" and "Several 10' exercise periods five days per week using a home treadmill"
I hope this helps!
solve for c 45 = 3c
Answer:
c=15
Step-by-step explanation:
45=3c,divide
c=15
What is the product?
5/
3
23
42
52
4
54
5
44
Answer:
5,10,15,20,25,30,25,40,45,50,55,
Step-by-step explanation:
Li is using a cone shaped cup with a diameter of 7 and 3/8 cm and a height of 10 cm. Find the total volume of the cup. Round to the nearest tenth.
Answer:
The volume of the cup is of 142.2 cubic centimeters.
Step-by-step explanation:
The cone volume is given by the following equation:
[tex]V = \frac{\pi r^{2}h}{3}[/tex]
In which r is the radius, which is half the diameter, and h is the height.
In this question:
Dimensions in cm, so the volume will be in cubic centimers.
Height of 10 cm, so [tex]h = 10[/tex]
Diameter of [tex]7 + \frac{3}{8} = \frac{7*8 + 3}{8} = \frac{59}{8} = 7.375[/tex]
So the radius is [tex]r = \frac{7.375}{2} = 3.6875[/tex]
Volume of the cup:
[tex]V = \frac{\pi*(3.6875)^{2}*10}{3} = 142.4[/tex]
The volume of the cup is of 142.2 cubic centimeters.
Solve
x^2-4=77
E2020
Answer:
Step-by-step explanation:
Answer:
x = 9 or x = -9
Step-by-step explanation:
x² - 4 = 77
then
x² - 4 + 4 = 77 + 4
then
x² = 81
then
x² - 81 = 0
then
x² - 9² = 0
then
(x - 9)(x + 9) = 0
then
x - 9 = 0 or x + 9 = 0
then
x = 9 or x = -9
__________________________
:)
A group of kinesiology students wanted to know if individuals who took group fitness classes lost more weight than individuals who worked out on their own. They obtained a sample of 70 individuals who wanted to lose weight. The first 35 participants to show up for the study were assigned to the group fitness condition; they attended a group fitness class twice a week. The second 35 participants were assigned to the individual workout condition; they worked out alone in the gym twice a week. Change in weight over a 15 week period was recorded and compared for the two groups.
Is this an observational or experimental study?
Answer:
Experimental.
Step-by-step explanation:
It is an independent measure design. Multiple experimental groups are used in an independent measures design, which is a research method and participants are only in one group. Each participant is only in one condition of the independent variable during the experiment.
suppose you roll two dice. find the probability of rolling a sum of 11.
Answer:
1/18
Step-by-step explanation:
There are 36 different possible combinations. There are only two ways of rolling a sum of 11.
2/36 = 1/18
Alex has 3 more quarters than dimes in his pocket, for a total of $5.25.
Which equation could be used to determine the number of dimes, x, in his.
pocket? *
Answer:
the equation used to determine the number of dimes in his pocket is an "algebraic equation" (3/4)x = 5.25
and the value of x = 7
Step-by-step explanation:
We are being told that:
Alex has 3 more quarters than dimes in his pocket, for a total of $5.25.
Let the value for the dimes in his pocket be x:
So he has 3 more quaters than x
We know that a quarter is 1/4
3 more quaters than x = (3/4) x
(3/4)x = 5.25
3x = 5.25 * 4
3x = 21
x = 21/3
x = 7
Thus, the equation used to determine the number of dimes in his pocket is an "algebraic equation" (3/4)x = 5.25
and the value of x = 7
Ted likes to run long distances. He can run 20 km in 95 minutes.He wants to know how many kilometers he will go if he runs the same pace for 285 minutes. How far will Ted run in 285 minutes
Last Thursday was costume day at Emmet's school. 108 out of the 120 students at the school wore a costume. What percentage of the students wore a costume?
Answer:
90%
Step-by-step explanation:
100%=120 pupils
108pupils
108 x 100= 10800/120=90 %
Entomologists are biological scientists who study insects. Entomologists studying tree crickets have found that they chirp at different rates depending on the temperature. The number of chirps per minute, C , that the tree cricket makes is linearly dependent on the temperature, T , in Fahrenheit. The crickets do not chirp at all if the temperature is 40 degrees and at 60 degrees they chirp about 92 times per minute.
A) Express the number of chirps, C , as a function of the temperature, T . Use function notation, and round decimals to one decimal place.
B) How many chirps per minute will crickets make at 75 degrees?
Step 1
Find the rate change at which the crickets are chirping.
Step 2
Find the function
Nancy hears a report that the current national average price of gasoline is $3.14. She averages the prices of stations near her home.she finds the average price of gas to be $2.95. Why are the averages different?
Answer:
Nancy's ambient locality might be having more suppliers, higher supply of Gasoline
Step-by-step explanation:
National average price of gasoline = $3.14
Stations near Nancy's home have an average price = $2.95
Gasoline price near Nancy's house is lesser than national average price level. Number of gasoline stations near her house might be more. It implies increase in its supply. This leads to competition among sellers & reduces the price level.
An electronics store offers students a discount
of 10% on purchases of computers. They
estimate that of computer sales are to
students. The average sale per customer is $498
and the store's profit is $80 before the discount.
What is the expected profit on the sale of a
computer?
show work
Answer:
83.9357% increase for the buyer
Step-by-step explanation:
If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?
[Hint: Place your coordinates in the blank with no parentheses and a space after the comma in the form: x, y]
Parallelogram ABCD is shown.
A is at negative 4, 1.
B is at negative 3, 2.
C is at 0, 2.
D is at negative 1, 1.
Answer:
(Fill in the blank)
Answer:
-4, 1
Step-by-step explanation:
A (-4, 1)
reflected over y-axis –> (4, 1)
reflected over x-axis –> (4, -1)
rotated 180º –> (-4, 1)
The range of F(x)= 7•4^x is all positive real numbers
Answer:
its true
Step-by-step explanation:
MARKING BRAINLIEST!!!
Answer:quadratic formula
Step-by-step explanation:
Answer:
Completing the square.
Step-by-step explanation:
x^2-8x+(-4)^2=22 can be rewritten as (x-4)^2=22. therefore, the best method would be completing the square.
Movie executives want to know if a movie watcher’s heart rate increases when they watch certain types of movies. Subjects in the experiment were given a free movie ticket and randomly assigned to watch one of four movies: an action-adventure film, a horror film, a romantic comedy, or an animated children’s film. They measured the average heart rate of all subjects while watching the assigned film.
Which of the following is the most appropriate statistical test to use to test if the average heart rate of the movie watchers was different for the four types of movies?
A. Matched pairs t-test
B. Chi-squared test for independence
C. ANOVA
D. Two-sample t-test
E. Inference for regression
Answer:
The correct option is C
Step-by-step explanation:
ANOVA is the correct option because it can be used to carry out comparison of average of more than two groups
XYZ Inc. produces two types of paper towels?regular and super-soaker. Regular uses 2 units of recycled paper per unit of production, and super-soaker uses 3 units of recycled paper per unit of production. The total amount of recycled paper available per month is 10,000. Let X1 be the number of units of regular produced per month and X2 the number of units of super-soaker produced per month. The appropriate constraint/s will be:_________
A) 2X1 + 3X2 = 10000
B) 180X1 + 80X2 geq 360
C) 2X1 + 3X2 geq 10000
D) 2X1 = 3X2
E) A, B, and C
Answer:
The appropiate constraint is:
[tex]2X_1+3X_2\leq10,000[/tex]
Step-by-step explanation:
There is only one restriction in this problem, and that is the available units of recycled paper per month.
There is a total of 10,000 units.
Regular paper (X1) uses 2 units per unit of production and Super-soaker (X2) uses 3 units per unit of production.
The total units used for both types of paper are:
[tex]2X_1+3X_2[/tex]
This amount has to be equal or smaller than the available (10,000 units):
[tex]2X_1+3X_2\leq10,000[/tex]
The appropriate constraint/s for the units of production being made by XYZ Inc is;
2X₁ + 3X₂ ≤ 10000
We are told that;
X₁ is the number of units of regular produced per month
X₂ the number of units of super-soaker produced per month.
we are told that;
Regular uses 2 units of recycled paper per unit of production. This is 2X₁
Also, we are told that super-soaker uses 3 units of recycled paper per unit of production. This is 3X₂.
We are now told that The total amount of recycled paper available per month is 10,000.
This means that;
2X₁ + 3X₂ ≤ 10000
The symbol less than or equal to is used because it is not possible for the 10000 to be exceeded as that is the amount available and also it's possible less than the 10000 may be used.
Read more at;https://brainly.com/question/24279865
factoring area models x2 + 6x + 5
Answer:
factored is (x+1)(x+5)
Step-by-step explanation:
gradpoint
a bag contains a mixture of almonds walnuts and cashews there's an equal quantity of each nut. If a nut is chosen randomly out of the bag what is the probability that an almond will be selected or that a cashew will be selected
Answer:
P(either almond or cashew) = ⅔
Step-by-step explanation:
We are told that the bag contains a mixture of almonds walnuts and cashews of equal number.
Since the 3 nuts are equal in number, they will have a ratio of 1:1:1.
So, when a nut is chosen randomly,
Probability of choosing almond = 1/3
Probability of choosing cashew = 1/3
Thus,
Probability of choosing either almond or cashew in a random selection will be the sum of their individual probability.
So,
P(either almond or cashew) = ⅓ + ⅓ = ⅔
Find the product.
y4 · y6
The answer is [tex]y^{4+6}[/tex] = [tex]y^{10}[/tex]
a bag of sweets contains only two different flavours strawberry and orange. the probability that a sweet is strawberry is 0.8 what is the probability that a sweet is orange falvour
Answer:
0.2
Step-by-step explanation:
total = 1.0
strawberry = 0.8
1-0.8 =0.2
Answer:
0.2 is the probability of orange sweet.
A Pew Internet poll asked cell phone owners about how they used their cell phones. One question asked whether or not during the past 30 days they had used their phone while in a store to call a friend or family member for advice about a purchase they were considering. The poll surveyed 1003 adults living in the United States by telephone. Of these, 462 responded that they had used their cell phone while in a store within the last 30 days to call a friend or family member for advice about a purchase they were considering.
A) Identify the sample size and the count.
B) Calculate the sample proportion.
C) Explain the relationship between the population proportion and the sample proportion.
Answer:
Given:
n = 1003
[tex] p' = \frac{462}{1003} = 0.4606 [/tex]
q = 1 - 0.4606 = 0.5394
a) The sample size and count.
Here the sample size is the number that took part in the poll. It is denoted as n = 1003.
The count is the number that answered yes. Count = 462
b) The sample proportion.
The formula for sample proportion is: [tex] p' = \frac{x}{n} [/tex]
Therefore, sample proportion =
[tex] p' = \frac{462}{1003} = 0.4606 [/tex]
c) The relationship between population proportion and sample proportion.
Since the sample size is greater than 30 (n>30), the sample size is large. Hence, for a large sample, the population proportion is approximately equal to the sample proportion.
This means the population proportion, p = 0.4606
Answer:
A) Sample size n=1003
Count x=462
B) Sample proportion p=0.46
C) The population proportion can be estimated with a confidence interval, with the information given by the sample proportion.
The 95% confidence interval for the population proportion is (0.429, 0.491).
Step-by-step explanation:
A) The sample size include all the adult that answer the poll. The sample size is then n=1003.
The count is the number of adults that answer Yes in this case. The count is x=462.
B) The sample proportion can be calculated dividing the count by the sample size:
[tex]p=\dfrac{x}{n}=\dfrac{462}{1003}=0.46[/tex]
C) The population proportion is not known. It can only be estimated with the information given by samples of that population. The statistical inference is the tool by which the sample information can be used to estimate the population characteristics.
With the sample proportion p we can estimate a confidence interval for the population proportion.
We can calculate a 95% confidence interval.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.46*0.54}{1003}}\\\\\\ \sigma_p=\sqrt{0.00025}=0.0157[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0157=0.031[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.46-0.031=0.429\\\\UL=p+z \cdot \sigma_p = 0.46+0.031=0.491[/tex]
The 95% confidence interval for the population proportion is (0.429, 0.491).
We have 95% that the population proportion is within this interval
6i4+6i3−2i2+−49−−−−√ rewritten in a+bi form
Answer:
[tex]8+i[/tex]
Step-by-step explanation:
We are given that an expression
[tex]6i^4+6i^3-2i^2+\sqrt{-49}[/tex]
We have to rewrite in the form of a+bi
[tex]6(i^2)^2+6i^3-2i^2+\sqrt{-49}[/tex]
We know that
[tex]i^2=-1[/tex]
[tex]i^3=-i[/tex]
[tex]\sqrt{-1}=i[/tex]
Using the identity
Then, we get
[tex]6-6i-2(-1)+7i[/tex]
[tex](6+2)+(7-6)i[/tex]
[tex]8+i[/tex]
This is required form of a+ib
There are three choices for a drink three choices for an entree and two choices for dessert find the total number of possible outcomes of ordering one drink one entree and one dessert
Answer:
It is 18
Step-by-step explanation:
Hope this helps have a wonderful day
The possible outcomes of ordering be 18.
What is combination?A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Drink = 3 choice
Entree= 3 choices
Dessert = 2 choice
So, Using tree method
drink 1 2 3
Entree 1 2 3 1 2 3 1 2 3
Dessert 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
So, the possible outcomes of ordering be 18.
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