Answers
Answer:
tanx·secx
Step-by-step explanation:
To simply this, you can begin by factoring sin x out of the numerator to become:
[tex]\frac{sinx (sin^{2}x +cos^{2} x)}{cos^{2} x}[/tex]
Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:
[tex]\frac{sinx}{cos^{2}x }[/tex]
First of all, we can convert [tex]\frac{sinx}{cosx}[/tex] to tanx. However, we have a remaining [tex]\frac{1}{cosx}[/tex] which, using reciprocal identities, will become sec x.
Finally, we get our answer as tanx·secx.
Related Questions
Use what you have learned about filing income taxes to complete these sentences.
If a citizen pays too much in taxes throughout the year, then after filing a tax return, he or she will receive a .
Employers supply a each January to help citizens file their tax returns.
Taxes returns can by filed either by mail or
Answer: refund, w-2, online
Answers
Answer:
See Explanation
Step-by-step explanation:
The W-2 form is a form which an employer must send to an employee and the Internal Revenue Service (IRS) at the end of each year. Every January, the employee should receive a Form W-2 Wage and Tax Statement from his/her employer. The contents of this form are the amount of money made by the employee during the previous year and how much was paid as tax.
Therefore, Employers supply a w-2 each January to help citizens file their tax returns.When a citizen gets their W-2 form for the previous year, they can use it to decide if they qualify for a tax refund which could be in cash or used towards the next years' tax.
If a citizen pays too much in taxes throughout the year, then after filing a tax return, he or she will receive a refund.Finally,
Taxes returns can by filed either by mail or online.Answer:
1. refund
2. w-2
3. online
The cost, not including tax, of paper and pens
at the card store is $21.79. The tax is 9% of
the selling price. What is the total cost of the
pens and pencils including tax?
Answers
At a high school, the cafeteria staff provides optional comment cards to students eating in the cafeteria. Students who wish to make a comment can obtain and fill out a comment card and return it to a drop box in the front office. At the end of the semester, the staff analyzes the responses and finds that 72% of the students who filled out a comment card recommend major changes to the food selection. What conclusions can the cafeteria staff draw from these responses?A) Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes. B) The cafeteria staff should not use the results to draw any conclusions since some students may not have filled out a comment card, which is non-response. C) If the students recorded their grade level with their response, the staff could make the original sample a stratified sample and use the responses to learn what proportion of each grade recommends major changes to food selection. D) The responses were from a voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions. E) The opportunity to fill out comment cards should be offered to students at all high schools in the school district to get a larger sample size, which will make the results more reliable,
Answers
Answer:
A) Since all of the students had an opportunity to respond, this is evidence that a majority of all the students supports major changes.
Step-by-step explanation:
Since all the students were given equal opportunity then the response suggest that a major change is required by the students.
Answer: d
Step-by-step explanation: the responses were from voluntary response sample, so the cafeteria staff should not use the results to draw any conclusions
A research company desires to know the mean consumption of milk per week among males over age 25. A sample of 650 males over age 25 was drawn and the mean milk consumption was 3.4 liters. Assume that the population standard deviation is known to be 1.3 liters. Construct the 95% confidence interval for the mean consumption of milk among males over age 25. Round your answers to one decimal place.
Answers
Answer:
[tex]3.3\leq x\leq 3.5[/tex]
Step-by-step explanation:
The 95% confidence interval can be calculated as:
[tex]x'-z_{\alpha/2}\frac{s}{\sqrt{n}} \leq x\leq x'+z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
Where [tex]x[/tex] is the mean consumption of milk, [tex]x'[/tex] is the sample mean, [tex]s[/tex] is the population standard deviation, [tex]n[/tex] is the size of the sample, [tex]\alpha[/tex] is 5% and [tex]z_{\alpha /2}[/tex] is the z-value that let a probability of [tex]\alpha /2[/tex] on the right tail.
So, replacing [tex]x'[/tex] by 3.4 liters, [tex]s[/tex] by 1.3 liters, n by 650 and [tex]z_{\alpha /2}[/tex] by 1.96, we get that the 95% confidence interval is equal to:
[tex]3.4-(1.96*\frac{1.3}{\sqrt{650}})\leq x\leq 3.4+(1.96*\frac{1.3}{\sqrt{650}}) \\3.4-0.1\leq x\leq 3.4+0.1\\3.3\leq x\leq 3.5[/tex]
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.
Margin of error = z × σ/√n
Where
σ = population standard Deviation
n = number of samples
From the information given
x = 3.4
σ = 1.3
n = 650
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, confidence level of 95% is 1.96
Margin of error = 1.96 × 1.3/√650 = 0.1
Confidence interval = 3.4 ± 0.1
The lower end of the confidence interval is
3.4 - 0.1 = 3.3 litres
The upper end of the confidence interval is
3.4 + 0.1 = 3.5 litres
Sam is creating a homemade lava lamp using an empty 0.6-liter water bottle. He fills the 1.25 bottle with deciliters of colored water, and plans to fill the rest of the bottle with oil. How many milliliters of oil will he need?
Answers
Answer:
475 milliliters of oil
Step-by-step explanation:
1 liter =1000 milliliters
1 deciliter =100 milliliters
To make it easier, we convert all our units to milliliters.
Volume of the water bottle =0.6 liter
=0.6 X 1000 =600 milliliters
Volume of colored water = 1.25 deciliters
=1.25 X 100 =125 milliliters
Therefore:
Volume of oil needed to fill the bottle = 600-125
=475 milliliters
Sam will need to add 475 milliliters of oil to the 0.6-liter bottle after adding 1.25 deciliters of colored water to create his homemade lava lamp.
Explanation:The question involves calculating the volume of oil needed to fill the remainder of a 0.6-liter bottle after adding some colored water. To solve this, we need to convert the measurements into the same units and perform subtraction. In this case, we convert deciliters to milliliters, as we know that 1 deciliter is equivalent to 100 milliliters. The student has filled the bottle with 1.25 deciliters of colored water, which is 1.25 × 100 milliliters = 125 milliliters of water.
Since the bottle can hold 0.6 liters, which is equal to 600 milliliters, the amount of oil required will be the total bottle capacity minus the volume of colored water already added. Thus, we calculate 600 milliliters (bottle capacity) – 125 milliliters (water added) to find the volume of oil needed.
So, Sam will need 600 mL – 125 mL = 475 milliliters of oil to fill the rest of his homemade lava lamp.
The operations manager of a manufacturer of television remote controls wants to determine which batteries last the longest in his product. He took a random sample of his remote controls and tested two brands of batteries. Here are the number of minutes of continuous use before the batteries failed for each brand. Is there statistical evidence of a difference in longevity between the two batteries?
Answers
Answer:
There is not enough evidence to support the claim that the longevity of the two brand of batteries differs.
Step-by-step explanation:
The question is incomplete:
The sample data for each battery is:
Battery 1: 106 111 109 105
Battery 2: 125 103 121 118
The mean and STD for the sample of battery 1 are:
[tex]M_1=\dfrac{1}{4}\sum_{i=1}^{4}(106+111+109+105)\\\\\\ M_1=\dfrac{431}{4}=107.75[/tex]
[tex]s_1=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s_1=\sqrt{\dfrac{1}{3}\cdot [(106-(107.75))^2+(111-(107.75))^2+(109-(107.75))^2+(105-(107.75))^2]}\\\\\\ s_1=\sqrt{\dfrac{1}{3}\cdot [(3.06)+(10.56)+(1.56)+(7.56)]}\\\\\\ s_1=\sqrt{\dfrac{22.75}{3}}=\sqrt{7.58333333333333}\\\\\\s_1=2.754[/tex]
The mean and STD for the sample of battery 2 are:
[tex]M_2=\dfrac{1}{4}\sum_{i=1}^{4}(125+103+121+118)\\\\\\ M_2=\dfrac{467}{4}=116.75[/tex]
[tex]s_2=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{4}(x_i-M)^2}\\\\\\s_2=\sqrt{\dfrac{1}{3}\cdot [(125-(116.75))^2+(103-(116.75))^2+(121-(116.75))^2+(118-(116.75))^2]}\\\\\\ s_2=\sqrt{\dfrac{1}{3}\cdot [(68.06)+(189.06)+(18.06)+(1.56)]}\\\\\\ s_2=\sqrt{\dfrac{276.75}{3}}=\sqrt{92.25}\\\\\\s_2=9.605[/tex]
This is a hypothesis test for the difference between populations means.
The claim is that the longevity of the two brand of batteries differs.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is α=0.05.
The sample 1, of size n1=4 has a mean of 107.75 and a standard deviation of 2.754.
The sample 2, of size n2=4 has a mean of 116.75 and a standard deviation of 9.605.
The difference between sample means is Md=-9.
[tex]M_d=M_1-M_2=107.75-116.75=-9[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{2.754^2+9.605^2}{4}}\\\\\\s_{M_d}=\sqrt{\dfrac{99.841}{4}}=\sqrt{24.96}=4.996[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-9-0}{4.996}=\dfrac{-9}{4.996}=-1.8014[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=4+4-2=6[/tex]
This test is a two-tailed test, with 6 degrees of freedom and t=-1.8014, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t<-1.8014)=0.122[/tex]
As the P-value (0.122) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the longevity of the two brand of batteries differs.
The following represent statistics of weekly salaries at the Harper Publishing Company.
Mean = $470 Median = $475 Mode = $460 Standard deviation = $30
First Quartile = $450 Third Quartile = $485 79th Percentile = $545 P67 = $483
Answers
Answer:
1) The most common salary is $460.
2) The salary that half of the employees surpassed is $475
3) The percentage of employees with salaries below $485 is 75%
4) 75% of the employees have a salary above $450.
5) The salary that stands 3 standard deviations below the mean is $380
6) 33% of the employees have a salary above $483.
7) The salary that stands 2 standard deviations above the mean is $530
Step-by-step explanation:
Hello!
1. What is the most common salary?______________
The measure that allows you to know which one is the most common value (i.e. the most frequent/observed number) in a data set is the mode. According to the given statistics, the most common salary is $460.
2. What salary did half the employees surpass?_________________
The measure that divides the sample in exactly a half (bottom 50% from the top 50%) is the median. In this example the salary that half of the employees surpassed is $475.
3. About what percent of employee's salaries is below $485?__________________
As you can see in the descriptive statistics, the third quartile (Q₃) is $485.
The Q₃ is the value that divides the bottom 75% of the sample from the top 25%. So the percentage of employees with salaries below $485 is 75%
4. What percent of the employees are above $450?___________________
The first quartile (Q₁) is the value that separates the bottom 25% of the sample from the top 75%. In this case Q₁= $450, which means that 75% of the employees have a salary above $450.
5. What salary is 3 standard deviations below the mean?____________________
The mean is $ 470 and the standard deviation is $30, the salary that stands 3 standard deviations below the mean is
X[bar]-3S= $470-3*$30= $380
6. About what percent of employee's salaries is above $483?__________________
P₆₇= $483, this value is the 67th percentile and means that 67% of the employees have a salary below $483.
If 67% are below $483, then 100 - 67= 33% of the employees have a salary above $483.
7. What salary is 2 standard deviations above the mean?______________________
The mean is $ 470 and the standard deviation is $30, the salary that stands 2 standard deviations above the mean is
X[bar]+2S= $470+2*$30= $530
I hope you have a SUPER day!
Mr. Hobbs has 10 blue markers, 6 black markers, and 8 red markers
on his desk. What fraction of black markers can be found on Mr.
Hobbs' desk?
Select one:
1.3/9
2.5/12
3.1/4
4.1/3
Answers
Answer:
4
Step-by-step explanation:
Im not completely sure
What are the most bags Mrs. Dupree can make? Will choose brainliest and will report absurd answers
Answers
Answer:
B. 4 bags
Step-by-step explanation:
The number of bags that will have the same quantities of the different gifts is the Greatest Common Divisor of the numbers of gifts.
GCD(24, 32, 44) = 4
Mrs. Dupree can make at most 4 identical bags.
___
How to find the GCD
The GCD can be found by looking at factors:
24 = 4·632 = 4·844 = 4·114 is the largest common factor of these numbers.
__
The GCD can also be found using Euclid's algorithm. In that algorithm, the larger number is divided by the smaller, with the remainder replacing the larger number after each step. If the remainder is zero, the smaller number is the GCD.
The GCD of several numbers can be found by finding the GCD of a pair, then of that value and the next number:
GCD(24, 32, 44) = GCD(GCD(24, 32), 44) = GCD(8, 44) = 4
_
32/24 = 1 r 8 . . . . first step in Euclid's algorithm for GCD(24, 32)
24/8 = 3 r 0 ⇒ GCD(24, 32) = 8
Then
44/8 = 5 r 4
8/4 = 2 r 0 ⇒ GCD(8, 44) = 4 = GCD(24, 32, 44)
Multiply and simplify: (6x + 3y)(6x − 3y)
Answers
Answer:
36x² - 9y²
Step-by-step explanation:
We see that the given expression (6x + 3y)(6x - 3y) looks just like the expression (a + b)(a - b). When multiplied out, this is a difference of squares identity that I highly recommend you memorise:
(a + b)(a - b) = a² - b²
Here, a = 6x and b = 3y, so plug these in:
(6x + 3y)(6x - 3y) = (6x)² - (3y)² = 36x² - 9y²
Answer:
36x² - 9y²
Step-by-step explanation:
(6x + 3y)(6x − 3y)
(6x)² - (3y)²
36x² - 9y²
If 15 bahs are equal to 24 rahs, and 9 rahs are equal in value to 15 yahs, how many bahs are equal in value to 1000 yahs?
Answers
Answer:
375
Step-by-step explanation:
b : r = 15 : 24
r : y = 9 : 15 = 3 : 5 = 24 : 40
Then ...
b : r : y = 15 : 24 : 40
The number of bahs equivalent to 1000 yahs is ...
bahs = (15/40)(1000) = 375
375 bahs are equal in value to 1000 yahs.
The monthly demand equation for an electric utility company is estimated to be p equals 59 minus (10 Superscript negative 5 Baseline )x, where p is measured in dollars and x is measured in thousands of killowatt-hours. The utility has fixed costs of $3 comma 000 comma 000 per month and variable costs of $27 per 1000 kilowatt-hours of electricity generated, so the cost function is Upper C (x )equals 3 times 10 Superscript 6 Baseline plus 27 x. (a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) Suppose that the rising fuel costs increase the utility's variable costs from $27 to $41, so its new cost function is Upper C 1 (x )equals 3 times 10 Superscript 6 Baseline plus 41 x. Should the utility pass all this increase of $14 per thousand kilowatt-hours on to the consumers?
Answers
Answer:
a) The price that maximizes profit is p =$43.
b) The utility shouldn't pass all this increase on the consumers because this would mean a decrease in the profits. They should pass only $7 to consumers price.
Step-by-step explanation:
We have an electric utility company which has a demand function defined by:
[tex]p=59-10^{-5}x[/tex]
where p is the price and x is the the energy in thousands of kWh.
The cost of the company is defined as:
[tex]C(x)=3\cdot 10^6+27x[/tex]
We have to calculate the price that maximizes the utility's profit R(x).
We can define the profit as:
[tex]R(x)=p\cdot x-C=(59-10^{-5}x)\cdot x-(3\cdot 10^6+27x)\\\\R(x)=-10^{-5}x^2+(59-27)x-3\cdot10^6\\\\R(x)=-10^{-5}x^2+32x-3\cdot10^6[/tex].
To maximize R, we have to derive it and equal to zero
[tex]\dfrac{dR}{dx}=0\\\\\\\dfrac{dR}{dx}=-2\cdot10^{-5}x+32=0\\\\\\x=(32/2)\cdot 10^5=16\cdot 10^5=1.6\cdot 10^6[/tex]
The price that maximizes the profit is then:
[tex]p=59-10^{-5}x=59-10^{-5}(16\cdot 10^5)=59-16=43[/tex]
b) When the unit cost rise from $27 to $41, the utility profit function changes.
We have to calculate the new price that maximizes profit, and then we will know if the rise in cost was transferred to price completely.
The new profit function is:
[tex]R(x)=p\cdot x-C=(59-10^{-5}x)\cdot x-(3\cdot 10^6+41x)\\\\R(x)=-10^{-5}x^2+(59-41)x-3\cdot10^6\\\\R(x)=-10^{-5}x^2+18x-3\cdot10^6[/tex]
To maximize R, we have to derive it and equal to zero
[tex]\dfrac{dR}{dx}=0\\\\\\\dfrac{dR}{dx}=-2\cdot10^{-5}x+18=0\\\\\\x=(18/2)\cdot 10^5=9\cdot 10^5[/tex]
We calculate the new price as:
[tex]p=59-10^{-5}x=59-10^{-5}(9\cdot 10^5)=59-9=50[/tex]
The new price is $7 dollars above the previous maximizing price, so the rise in unit cost is only transferred 50% to the price.
The utility shouldn't pass all this increase on the consumers because this would mean a decrease in the profits. They should pass only $7 to consumers price.
The right rectangular prism below is made up of 8 cubes. Each cube has an edge length of 12inch.
What is the volume of this prism?
Answers
Answer:
13824 cubic inches
Step-by-step explanation:
So all we need to do is:
1) Find the volume of 1 cube of the 8
2) Multiply that by 8, because 8 of them make the prism.
SO 1)
the volume of cube = side * side * side = 12*12*12 = 1728
SO 2)
the volume of prism = vol(cube) * 8 = 1728 * 8 = 13824
ANSWER: 13824 cubic inches ;)
After getting trounced by your little brother in a children's game, you suspect the die he gave you to roll may be unfair. To check, you roll it 60 times, recording the number of times each face appears. Do these results cast doubt on the die's fairness? Full data set Face Count Face Count 1 14 4 15 2 5 5 14 3 11 6 1 a) If the die is fair, how many times would you expect each face to show? nothing b) To see if these results are unusual, will you test goodness-of-fit, homogeneity, or independence? A. Independence B. Homogeneity C. Goodness-of-fit c) State your hypotheses. A. Upper H 0: The die is unfair. Upper H Subscript Upper A: The die is fair. B. Upper H 0: The die is fair. Upper H Subscript Upper A: The die produces outcomes that are less than the expected value. C. Upper H 0: The die is fair. Upper H Subscript Upper A: The die is unfair. D. Upper H 0: The die is fair. Upper H Subscript Upper A: The die produces outcomes that are greater than the expected value. d) Check the conditions. Is the counted data condition met? No Yes Is the randomization condition met? Yes No Is the expected cell frequency condition met? Yes No e) How many degrees of freedom are there? nothing
Answers
Answer:
Given:
Face ____________Count
1_________________14
4_________________15
2_________________5
5_________________14
3_________________11
6_________________1
a) I rolled the die 60 times and my values are recorded.
Assuming the die is fair, each face is expected to show 10 times.
[tex] 60* \frac{1}{6} = 10 [/tex]
b) To check if my results are unusual hypothesis test is used to address this. In this case the test is called goodness of fit.
c) For the null and alternative hypothesis :
The null hypothesis states , the die is fair (the number of times each face appear is equal)
The alternative hypothesis states the die is not fair.
H0 : p = 0.6
H1 : p ≠ 0.6
d)
The number of times the die is rolled is recorded.
The number of times the die is rolled is independent because the outcomes are independent.
Here the expected value of observation is more than five because the null hypothesis expects each die roll to be 10. Thus, the condition is satisfied.
e) Number of degrees of freedom for this test is n-1.
n = 6 (total faces in a die)
Therefore, degrees of freedom =
6-1 = 5
−15x + 60 ≤ 105 AND 14x + 11 ≤ −31
Answers
Answer:
X=-3
Step-by-step explanation:
Which choice are equivalent to the fraction below? Check all that apply 6^7/6^5
Answers
Answer:36
Step-by-step explanation:u
6^7/6^5
6^(7-5)
6^2
6x6=36
Jenny is 12 years older than Nancy. Five years ago Jenny was three times as old as Nancy. How old is each now?
Answers
Answer:
Jenny = 23 | Nancy = 11
Step-by-step explanation:
A car that normally sells for $20,000 is on sale for $16,000. What percent of the original price of the car is the final price?
Answers
Answer:
80%
Step-by-step explanation:
20000. take out 3 zeros from both numbers and you get 20 and 16. 20 is 4 times 5 and 16 is 4 times 4 if 20 is 100% then 4 over 5 is 80%
Find the error in the student’s calculation.
a. The student should have simplified the exponent first.
b. The student did not subtract 3 and 8 correctly.
c. The student should not have multiplied 8 and -2.
d. The student did not make an error.
Answers
Answer:
The answer is A
Step-by-step explanation:
When doing an equation you always have to follow this order: exponents, parentheses, multiply/divide, then addtion/subtraction
A truck that can carry no more than 7200 lb is being used to transport refrigerators and upright pianos. Each refrigerator weighs 250 lb and each piano weighs 525 lb. Write and graph an inequality to show how many refrigerators and how many pianos the truck could carry. Will 14 refrigerators and 9 pianos overload the truck? Explain. Let x be the number of refrigerators in the truck and y be the number of pianos in the truck. Write an inequality to show how many refrigerators and how many pianos the truck could carry.
Answers
Answer:
x250+y525=7200 the answer is no
Step-by-step explanation:
what shape would you get if you cut off one of the corners of a rectangular prism
Answers
Cutting off one corner of a rectangular prism creates a bicapped trigonal prismatic shape.
When you cut off one of the corners of a rectangular prism, you would get a shape known as a bicapped trigonal prismatic. This shape is formed by twisting one face of a cube relative to another, folding opposing faces towards one another, and distorting the original rectangular prism.
Type the expressions as radicals.
Answers
[tex] \sqrt{ {q}^{3} } [/tex]
Step-by-step explanation:
[tex] {q}^{ \frac{3}{2} } = ( {q}^{3} )^{ \frac{1}{2} } = \sqrt{ {q}^{3} } \\ [/tex]
Brent’s after-school game club has 12 members from which a six-member team is created. Miguel’s after-school sports club has 10 members from which a six-member team is created. Which student’s club has more possible combinations for his six-member team?
Answers
Answer:
Brent
Step-by-step explanation:
More numbers = More combinations
Answer:
Brent’s club has more possible team combinations because there are more members to choose from.
Step-by-step explanation:
I completed it on edg 2020
tina has a doll which she can dress with a hat, a scarf and a jacket.
she has 3 different colour hat, 4 different colour scarves and 5 different colour jackets
Tina chose a hat a scarf and a jacket for her doll
how many combinations of hat scarf and jacket can she choose
Answers
Answer:
60 combinations
Step-by-step explanation:
3 × 4 × 5 = 60
Hope i helped!
Tina can choose from 60 different combinations of hat, scarf, and jacket for her doll.
To find the total number of combinations Tina can choose for her doll's outfit, you can use the multiplication principle.
Tina has 3 choices for the hat, 4 choices for the scarf, and 5 choices for the jacket.
To find the total number of combinations, multiply the number of choices for each item together:
3 (choices for the hat) × 4 (choices for the scarf) × 5 (choices for the jacket) = 60
Tina can choose from 60 different combinations of hat, scarf, and jacket for her doll.
for such more question on combinations
https://brainly.com/question/28065038
#SPJ3
A rectangular sheet of paper is folded diagonally. What is the length of XY?
15 in
8 in
OA) 23 in.
OB) 19 in.
OC) 15 in.
OD) 17 in.
Answers
Answer:
17 inches
Step-by-step explanation:
corse hereo Joe has two drawers containing socks. The first contains three pairs of red socks, two pairs of black socks, and one pair of white socks. The second drawer contains two pairs of red socks, one pair of black socks, and two pairs of white socks. Each morning Joe flips a fair coin and picks two socks at random from the first drawer if heads is flipped; if tails is flipped he instead picks two socks at random from the second drawer. Joe is observed leaving his house this morning wearing one red and one black sock. What is the probability he flipped heads today?
Answers
Answer:
P(H/A) = 0.6716
Step-by-step explanation:
Let's call H the event that Joe flipped heads, T the event that Joe flipped tails and A the event that Joe wear one read and one black sock.
So, the probability that he flipped heads given that Joe wears one read and one black sock is calculated as:
P(H/A) = P(H∩A)/P(A)
Where P(A) = P(H∩A) + P(T∩A)
On the other hand, nCx gives the number of combinations in which we can select x elements from a group of n elements. nCx is calculated as:
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
So, the probability that Joe wear one red and one black sock given that he picks the socks from the first drawer is:
[tex]\frac{6C1*4C1*2C0}{12C2}=0.3636[/tex]
Because he need to choose one red sock from the 6 that are in the first drawer, one black sock from the 4 that are in the first drawer and 0 white socks. Additionally there are 12C2 ways to choose a pair of socks.
Therefore the probability P(H∩A) that that Joe flipped heads and Joe wear one read and one black sock is:
P(H∩A) = 0.5*0.3636 = 0.1818
Because there is a probability of 0.5 to flipped heads and the probability that Joe wear one red and one black sock given that he flipped heads is 0.3636.
At the same way, the probability that Joe wear one red and one black sock given that he picks the socks from the second drawer is:
[tex]\frac{4C1*2C1*4C0}{10C2}=0.1778[/tex]
Therefore the probability P(T∩A) that that Joe flipped tails and Joe wear one read and one black sock is:
P(T∩A) = 0.5 * 0.1778 = 0.0889
Finally, P(A) and P(H/A) is equal to:
P(A) = 0.1818 + 0.0889 = 0.2707
P(H/A) = 0.1818/0.2707 = 0.6716
Please help 6th grade math ! :)
Answers
Answer:
2.50 per two bottles of sprite
Step-by-step explanation:
Box measure 4 units by 2.5 by 1.5 units what is the greatest number of cubes side length o 1/2 unit can be pack inside the box
Show details
Answers
Answer:120
Step-by-step explanation:
Volume=length x width x height
volume of box=4x2.5x1.5
Volume of box=15
Length of side of cube=1/2=0.5
Volume of cube=0.5x0.5x0.5
Volume of cube=0.125
Number of cube that can pack inside there box=15 ➗ 0.125=120
θ is an acute angle. Find the value of θ in radians.
sin(θ)=1
Write your answer as an integer or as a decimal rounded to the nearest hundredth.
Answers
The value of θ in radians when sin(θ) = 1 is π/2, approximately equal to 1.57 rounded to the nearest hundredth.
To find the value of θ in radians when sin(θ) = 1, we know that sine is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
Since the sine of an acute angle cannot exceed 1, and sin(θ) = 1, this indicates that θ must be a 90-degree angle, or π/2 radians.
In radians, π represents the ratio of the circumference of a circle to its diameter, and π/2 corresponds to one-fourth of the circumference, which equals a right angle.
Therefore, the value of θ in radians is π/2, or approximately 1.57 rounded to the nearest hundredth.
help. If 20 men can survive for 24 days on 15 cans of rations, how many cans will be needed for 16 men to survive for 36 days?
Answers
Answer: 29 cans.
Step-by-step explanation:
20 can survive 24 days with 15 cans.
If X is the number of days that a man can survive with one can of rations.
so X is in the units can/day
then we have that:
24/15*X = 20
X = 20*15/24 = 12.5
This means that a man can live 12.5 days with a can of food.
then, for 16 men and 36 days we have:
(36/C)*12.5 = 16
C = (36/16)*12.5 = 28.1215
And we can not have a 0.1215 of a can, so we should round it up to 29 cans.