Answer: 2/3
Step-by-step explanation:
N is the total number of students
M is the number of students thta like math
S is the number of students that like science.
We know that half of the elements in M also are elements from S
And a third of the elements of S also are elements of M
And because those elements are common elements for both sets, we should have that:
M/2 = S/3
then we have that:
M = (2/3)*S
The ratio is 2/3
this means that the number of students that like math is 2/3 times the number of students that like science.
The ratio of the number of students who like math to the number of students who like science is 2/3
What is ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
For the given case, we can assume the real quantities by variables.
Let we have:
M = Number of students who like mathsS = Number of students who like science.By given information, we have:
M/2 students like science too.S/3 students like maths too.Since the statement "M/2 students like science too" and "S/3 students like maths too" are same thing, so they're taking about same students who like math and science both, thus:
[tex]\dfrac{M}{2} = \dfrac{S}{3}\\\\\text{Multiplying both the sides by 2/S}\\\\\dfrac{M}{S} = \dfrac{2}{3}[/tex]
Thus, the ratio needed (ratio of number of students liking math to the number of students liking science) is M/N = 2/3
Learn more about ratios here:
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if you were to roll a standard 6 sided game die 60 times, approximately how many times would you expect to roll each of the six faces?
Answer:
1/10(1 out of every 10)
Step-by-step explanation:
6/60 = 1/10
Find the sum of the first 10 terms if a(n) = n^2 - n +1
Answer:
The formula to find the sum of the first n terms of our sequence is n divided by 2 times the sum of twice the beginning term, a, and the product of d, the common difference, and n minus 1. The n stands for the number of terms we are adding together.
Triangle MNO is reflected over the x-axis and then translated up 4 and right 3. On a coordinate plane, triangle O M N has points (1, 3), (2, 1), (negative 1, 2). Triangle O prime M prime N prime has points (4, 1), (5, 3), (2, 2). How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?
Answer: the answer is i think* A, Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
Step-by-step explanation: it's the only one that makes sense im takin the test
Answer:
A, Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.
Step-by-step explanation:
I took the test hope this helps!!!!!!!!!!!!!!
5x + 7y = 2 and -2x + 7y = 9
Answer:
conclusion one solution (-1 , 1)
Step-by-step explanation:
hello :
5x + 7y = 2 ...(*)
-2x + 7y = 9....(**)
by(*) and (**) calculate 7y
7y = 2-5x
7y = 9+2x
9+2x = 2-5x
2x+5x = 2-9
7x=-7 so : x= - 1
put this value in expression : 7y = 9+2x
7y = 9+2(-1)
7y =7
y =1
conclusion one solution (-1 , 1)
Alannah is a student who is not old enough to work, but would like to make some money. She
decides to make her own hand sanitizer to sell to her family and neighbors. She makes 2
different size bottles: large and small. The small bottle sells for $5.00 and the large sells for
$12.00. On her first day, she sold all 45 of the hand sanitizer bottles she had made and
collected $435. how many small bottles of hand sanitizer did Alannah sell? how many large bottles of hand sanitizer did Alannah sell?
Answer:
15 small bottles
30 large bottles
Step-by-step explanation:
Let the number of small bottle sold=s
Let the number of large bottle sold=l
She sold all 45 of the hand sanitizer bottles, therefore:
s+l=45The small bottle sells for $5.00
The large sells for $12.00
She collected a total of $435
5s+12l=435We solve the two equations simultaneously to obtain s and l.
From the first equation, s=45-l
Substitute s=45-l into 5s+12l=435
5(45-l)+12l=435
225-5l+12l=435
7l=435-225
7l=210
Divide both sides by 7
l=30
Recall: s=45-l
Therefore, s=45-30=15
Allanah sold 15 small bottles and 30 large bottles of hand sanitizer.
What is the solution for a in the following question? 2b-a=5
Answer:
5
Step-by-step explanation:
so you can think of it as b is 5 and 2 times by 5 is 10. you can then make 10 - 5 which is 5. so a is 5
In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t > 0. Determine a differential equation for the amount A(t) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t).)
Answer: equation = dA/dt = K₁ (M - A) - K₂A
Step-by-step explanation:
Let us follow this carefully to get our equation right.
From the question we are told to (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t) ).
The Rate of memorizing the material is ∝ [Total amount to be memorized] - [Amount memorized]
remember using A for A(t).
where A rep the amount memorized at a time t and M is the Total amount memorized.
so we have that dA/dt ∝ M - A
which is dA/dt = K₁ (M - A) ---------------(*)
remember it was stated that forgetfulness is taken into account
Forgetfulness, F ∝ A
F = K₂A --------------- (**)
which implies the rate of memorization is decreased as a result of forgetting;
this leads to
dA/dt = K₁ (M - A) - K₂A
The rate of differential equation is ⇒ dA/dt = K₁ (M - A) - K₂A
cheers i hope this helped!!!!
what’s the measure of the angle theta?
Answer:
∅ = 50°
Step-by-step explanation:
YOU NEED A CALCULATOR TO SOLVE THIS!
You need to use Law of Sines
[tex]\frac{a}{sinA} =\frac{b}{sinB} = \frac{c}{sinC}[/tex]
Here you will be doing [tex]\frac{a}{sinA} =\frac{c}{sinC}[/tex]
a and c are the lengths, while A and C are the angles
[tex]\frac{3.46}{sinA} = \frac{2.54}{sin43}[/tex] you want to get the denominators out from underneath so multiply both sides by sinA and sin43
[tex]3.46sin43 = 2.54sinA[/tex]
Now you want to get sinA alone so divide both sides by 2.54
[tex]\frac{3.46sin43}{2.54} = sinA[/tex] now get A alone
[tex]sin^{-1} (\frac{3.46sin43}{2.54}) = A[/tex] put that into the calculator
[tex]49.61741033 = A[/tex]
The following data gives the monthly sales (in thousands of dollars) for different advertising expenditures (also in thousands of dollars) and sales commission percentages. Sales 245 138 352 322 228 275 560 366 Advertising 16.5 18.0 22.3 18.4 19.0 19.5 30.0 18.6 Commission 10.5 2.0 4.0 3.5 4.5 1.8 9.0 8.5 1. What amount of sales would this model predict for advertising expenditures of 25,000 and sales commission of 8%? [Show your code in "R Code" section. Show the answer in "Answer" section. Leave "Comments" section blank.] 2. Find the correlation coefficients for advertising expenditure and commission compared to sales. Explain the results of these findings. [Show your code in "R Code" section. Show the answer in "Answer" section. Leave "Comments" section blank.] 3. At the 5% level of significance, are advertising expenditure or sales commission percentage significant? Why? [Show your code in "R Code" section. Show the answer in "Answer" section. Include the mathematical notations of two sets of null and alternate hypotheses and the phrase "advertising expenditure" or "sales commission percentage" or "both" along with a justification in a few sentences in "Comments" section.]
Answer:
Check the explanation
Step-by-step explanation:
Use the below R Code
Sales=c(245,138,352,322,228,275,560,366)
Advertising=c(16.5,18,22.3,17.4,19,20,32,18.6)
Commission=c(10.5,2,4,3.5,4.5,1.8,9,8.5)
data=as.data.frame(cbind(Sales,Advertising,Commission))
model1=lm(Sales~Advertising+Commission, data = data)
dat2=data.frame(Advertising=25,Commission=8)
predict(model1,dat2)
The predicted value of Sales for 25000 dollar on Advertising and 8% on Commission is 424685 dollars approximately (rounded to 0 decimal places)
Ella drew 40 different pictures for an art show. Twenty of them include a dog in the picture. If she shuffles the pictures and picks one at random to give to her friend, what is the probability that she will pick one that includes a dog?
A.
0.2
B.
0.05
C.
0.1
D.
0.5
Answer:
0.05
Step-by-step explanation:
Which of these numbers of simulations of an event would be most likely to produce results that are closest to those predicted by probability theory?
A. 50
B. 60
C. 30
D. 40
Answer:
60. Got it wrong, but oh well.
Step-by-step explanation:
A random sample of 8989 eighth grade students' scores on a national mathematics assessment test has a mean score of 282282. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280280. Assume that the population standard deviation is 3838. At alphaαequals=0.050.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).
Answer:
[tex]t=\frac{282-280}{\frac{38}{\sqrt{89}}}=0.497[/tex]
Now we can calculate the p value for the test
We are conducting a right tailed test so then the p value is given by:
[tex]p_v =P(z>0.497)=0.310[/tex]
Since the p value is higher than the significance level we have enough evidence to conclude that the true mean is not significantly higher than 280 so then the administrator claim is not true
Step-by-step explanation:
Data provided
[tex]\bar X=282[/tex] represent the mean for the assesment test
[tex]\sigma=38[/tex] represent the population deviation
[tex]n=89[/tex] sample size
[tex]\mu_o =280[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to determine if the mean score for the state's eighth graders on this exam is more than 280, so then the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 280[/tex]
Alternative hypothesis:[tex]\mu > 280[/tex]
Since we know the population deviation we can use a z test for the true mean and the statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info given by the problem we got:
[tex]t=\frac{282-280}{\frac{38}{\sqrt{89}}}=0.497[/tex]
Now we can calculate the p value for the test
We are conducting a right tailed test so then the p value is given by:
[tex]p_v =P(z>0.497)=0.310[/tex]
Since the p value is higher than the significance level we have enough evidence to conclude that the true mean is not significantly higher than 280 so then the administrator claim is not true
To determine if there is enough evidence to support the administrator's claim, we need to perform a hypothesis test. By comparing the z-score to the critical value at α=0.05, we can reject the null hypothesis and conclude that there is enough evidence to support the administrator's claim.
Explanation:To determine if there is enough evidence to support the administrator's claim, we need to perform a hypothesis test. The null hypothesis (H0) is that the mean score for the state's eighth graders is <=280. The alternative hypothesis (Ha) is that the mean score is >280.
To conduct the test, we can calculate the z-score using the formula z = (x - μ) / (σ / sqrt(n)), where x is the sample mean, μ is the hypothesized population mean (280), σ is the population standard deviation (38), and n is the sample size (8989). Plug in the given values, we get z = (282 - 280) / (38 / sqrt(8989)) = 3.055.
Next, we compare the z-score to the critical value at α=0.05. For a one-tailed test, the critical value is 1.645. Since 3.055 > 1.645, we reject the null hypothesis and conclude that there is enough evidence to support the administrator's claim that the mean score for the state's eighth graders on this exam is more than 280.
You fill an aquarium with water. The water is 22 inches deep. The water evaporates at a rate of 2 inches per week. a. Write an equation that approximates the depth y of water in the aquarium c weeks after you fill it. b. After two weeks, you have not yet refilled the aquarium. What is the depth of the water?
The equation for water depth in the aquarium after evaporation is y = 22 - 2c.
a. Equation: The equation approximating the depth y of water in the aquarium c weeks after filling it is y = 22 - 2c.
b. Depth after Two Weeks: Substitute c = 2 into the equation, y = 22 - 2(2) = 18 inches.
Find f(-2) for the function fwd) = 3x - 2x +7
Answer:
23
Step-by-step explanation:
Maybe you want to evaluate ...
f(x) = 3x^2 -2x +7
for x = -2.
Put the value of x where x is, then do the arithmetic.
f(-2) = 3(-2)^2 -2(-2) +7 = 3(4) +4 +7
f(-2) = 23
Which choice could represent the volume of a cake pan
Answer:
3150^3
Step-by-step explanation:
A group of 4 people share 1/2 pounds of almonds how many pounds of almonds does each person get choose an equation you can use to answer the question
Answer:
1/2 x 1/4=1/8
Step-by-step explanation:
On one day a Plumber Joe earned $80 on a plumbing job. Out of his earnings he spent $6.85 on tea and snacks, $5.50 on food and $21.40 on tools. Before reaching home that evening his boss sent Plumber Joe $22 on "cash app", which his boss said was a tip from his early morning plumbing job. How much did he save on that day?
Answer:
Joe saved 68.25
Step-by-step explanation:
Subtract 6.85 from 80, you get 73.15
Subtract 5.50 from 73.15 and you get 67.65.
Subtract 21.40 from 67.65 and you get 46.25.
Add 22 to that amount, you get 68.25.
P.S
Have an Amazing Day! I Hope this Helps and Good Luck!!
~Faker/Tosrel
Lisa rides a bicycle 30 miles every 5 hours at this rate how many hours did Lisa ride is she rode 150 miles
Answer:
25 hours
Step-by-step explanation:
30 times 5 is 150 and 5 times 5=25
Please answer! Will mark as Brainliest if correct.
Pedro, Lena, Harriet, and Yermin each plot a point to approximate the square root of 0.50.
(See picture)
Whose point is the best approximation of the square root of 0.50?
A: Pedro
B: Lena
C: Harriet
D: Yermin
Answer:Harriet
Step-by-step explanation:
Answer:
The aNSWER IS d
Step-by-step explanation: i JUST DID THE TEST
Help please I really do need help
Answer:
P'(-6, -4)
Step-by-step explanation:
The (x, y) coordinates of the plotted point P are (-2, 2).
Putting those values into the translation formula, you get ...
(x, y) ⇒ (x -4, y -6)
(-2, 2) ⇒ (-2 -4, 2 -6) = (-6, -4)
The coordinates of the translated point P' are ...
P'(-6, -4)
Determine whether the data described below are qualitative or quantitative and explain why. The postal codes of survey respondents Choose the correct answer below. A. The data are quantitative because they consist of counts or measurements. B. The data are quantitative because they don't measure or count anything. C. The data are qualitative because they don't measure or count anything. D. The data are qualitative because they consist of counts or measurements.
Answer:
C
Step-by-step explanation:
Postal code numbers are qualitative data because on these numbers, we can't perform any calculations.
The data are qualitative because they don't measure or count anything.
The correct option is C.
What is qualitative data?
Information that cannot be quantified, tallied, or simply stated using numbers is referred to as qualitative data.
Given:
The postal codes of survey respondents.
Here, no numbers are given.
Data visualization technologies like word clouds, idea maps, graph databases, timelines, and infographics are used to communicate the information that is gathered from text, audio, and visual sources.
And the data can not be calculated.
Therefore, Postal code numbers are qualitative data.
To learn more about the qualitative data;
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When calculating the successive discounts of 15% and 10% on a $100 item,
а. take 10% of $85
b. take 10% of $90
C. take 15% of $85
d. take 25% of $100
Answer:
A. Take 10% of $85
Step-by-step explanation:
Taking away 15% from $100 leaves you with $85 to take the second discount away from (10%)
Commercial real estate prices and rental rates suffered substantial declines in 2008 and 2009. These declines were particularly severe in Asia; annual lease rates in Tokyo, Hong Kong, and Singapore declined by 40% or more. Even with such large declines, annual lease rates in Asia were still higher than those in many cities in Europe. Annual lease rates for a sample of 30 commercial properties in Hong Kong showed a mean of 1,114 per square meter with a standard deviation of 230. Annual lease rates for a sample of 40 commercial properties in Paris showed a mean lease rate of 989 per square meter with a standard deviation of 195. On the basis of the sample results, can we conclude that the mean annual lease rate is higher in Hong Kong than in Paris? Develop appropriate null and alternative hypotheses. At the 5% level of significance, what is your conclusion?
Answer:
Conclusion
The average rental rate in Hong Kong are higher than in Paris
Step-by-step explanation:
From the question we are told that
The sample size for Hong Kong is [tex]n_1 = 30[/tex]
The mean for Hong Kong is [tex]\mu_h = 1,114 \ m^2[/tex]
The standard deviation for Hong Kong is[tex]s = 230[/tex]
The sample size for Paris is [tex]n_2 = 40[/tex]
The mean for Paris is [tex]\mu_p = 989 \ m^2[/tex]
The standard deviation for Paris is [tex]s_p = 195[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The Null Hypothesis is
[tex]H_o : \mu_1 - \mu_2 = 0[/tex]
The alternative hypothesis is
[tex]H_a: \mu_1 - \mu_2 >0[/tex]
The test statistics is mathematically represented as
[tex]t = \frac{\mu _1 - \mu_2 - d }{\sqrt{(\frac{s^2}{n1} )+(\frac{(s_p^2}{n_2} )}}[/tex]
Substituting values
[tex]t = \frac{1114 - 989 - 0 }{\sqrt{(\frac{230^2}{30} )+(\frac{(195^2}{40} )}}[/tex]
[tex]t = 2.399[/tex]
Since the value of the test statistics is higher than the significance level then there is enough evidence to conclude that the average rental rate in Hong Kong are higher than in Paris
Using the t-distribution, it is found that since the test statistic is more than the critical value, there is enough evidence to conclude that the mean annual lease rate is higher in Hong Kong than in Paris.
At the null hypothesis, it is tested if the average is not higher in Hong Kong, that is, the result of the subtraction if not greater than 0.
[tex]H_0: \mu_H - \mu_P \leq 0[/tex]
At the alternative hypothesis, it is tested if it is higher, that is:
[tex]H_1: \mu_H - \mu_P > 0[/tex]
The standard errors for both samples are:
[tex]s_H = \frac{230}{\sqrt{30}} = 42[/tex]
[tex]s_P = \frac{195}{\sqrt{40}} = 30.83[/tex]
The distribution of the differences has mean and standard deviation given by:
[tex]\overline{X} = \mu_H - \mu_P = 1114 - 989 = 125[/tex]
[tex]s = \sqrt{s_H^2 + s_P^2} = \sqrt{42^2 + 30.83^2} = 52.1[/tex]
The test statistic is:
[tex]t = \frac{\overline{X} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence, the value is:
[tex]t = \frac{125 - 0}{52.1}[/tex]
[tex]t = 2.4[/tex]
The critical value, for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 30 + 40 - 2 = 68 df, is [tex]t^{\ast} = 1.67[/tex]
Since the test statistic is more than the critical value, there is enough evidence to conclude that the mean annual lease rate is higher in Hong Kong than in Paris.
A similar problem is given at https://brainly.com/question/16402495
What is bigger 2 gallons or 16 quarts?
Answer:
16 quarts
Step-by-step explanation:
16 quarts is bigger than 2 gallons because every 4 quarts equals 1 gallon.
What is there area to this?
Answer:
The total area of the figure is 52 in²
Step-by-step explanation:
This figure requires you to find the area of the square and the triangle separately, and then subtract the area of the triangle from the area of the square.
Find the area of the square
l=8in
A=l²
A=8²
A=64 in²
The area of the square is 64 in²
Find the area of the triangle
b=8in
h=3in
A=(bh)/2
A=(8*3)/2
A=24/2
A=12 in²
The area of the triangle is 64 in²
Now we need to subtract the areas
64-12=52 in²
The total area of the figure is 52 in²
Can someone help me ...
What is the area of the parallelogram below?
A. 7 in
B. 14 in
C. 15 in
D. 12 in
Answer:
D. 12 in²
Step-by-step explanation:
The area of a parallelogram is given by the formula ...
A = bh
Substituting the given values for the length of the base (b) and the height (h), we have ...
A = (4 in)(3 in)
A = 12 in²
The area is 12 square inches.
Answer:
D 12
Step-by-step explanation:
I just did the lesson and got it right.
A circle has a radius of 5. An arc of 162 degrees. What is the length of the arc?
Answer:
242
Step-by-step explanation:
Answer:
14.14 units
Step-by-step explanation:
Klan Academy- I checked and it was correct.
100 POINTS.
PLEASE PROVIDE STEPS
Step-by-step explanation:
12 ∫ (cot⁴(3x) csc²(3x)) dx
If u = cot(3x), then du = -3 csc²(3x) dx. So -⅓ du = csc²(3x) dx.
12 ∫ u⁴ (-⅓ du)
-4 ∫ u⁴ du
-⅘ u⁵ + C
Substituting back:
-⅘ cot⁵(3x) + C
Evaluate between x=0 and x=π/12. cot(0) is undefined, so the integral does not exist.
Answer:
12 ∫ (cot⁴(3x) csc²(3x)) dx
If u = cot(3x), then du = -3 csc²(3x) dx. So -⅓ du = csc²(3x) dx.
12 ∫ u⁴ (-⅓ du)
-4 ∫ u⁴ du
-⅘ u⁵ + C
Substituting back:
-⅘ cot⁵(3x) + C
Evaluate between x=0 and x=π/12. cot(0) is undefined, so the integral does not exist.
Step-by-step explanation:
Eastman Company purchased a delivery truck for $35,000 on January 1, 2008. The truck was
assigned an estimated useful life of 5 years and has a residual value of $10,000. Compute
depreciation expense using the double-declining-balance method for the years 2008 and 2009
BE 3
Answer:
The depreciation expense of the truck in 2008 and 2009 are $14,000 and $8,400 respectively.
Step-by-step explanation:
The double declining depreciation method depreciates assets twice as fast as the traditional declining balance method.
The method records larger depreciation expenses during the earlier years of an asset’s useful life, and smaller ones in later years.
As a result, companies opt for the method for assets that are likely to lose most of their value early on, or which will become obsolete faster.
For double declining depreciation method,
- Divide “100%” by the number of years in the asset’s useful life, this is the straight-line depreciation rate.
- Then, multiply that number by 2 and that is the Double-Declining Depreciation Rate. - In this method, depreciation continues until the asset value declines to its salvage value.
Number of useful lives = 5 years.
- Divide 100% by 5 years
100% / 5 = 20%
- Then, multiply that percentage by 2
20% x 2 = 40%
The Double-Declining Depreciation rate is 40%.
Value of the truck at the start of 2008 = $35,000
Depreciation in 2008 = 40% × 35000 = $14,000
Book Value of the truck at the start of 2009 = $35000 - $14000 = $21000
Depreciation in 2009 = 40% × 21000 = $8,400
Hope this Helps!!!