Answer:
There is not enough evidence to support the claim that single people who own pets are generally happier than single people without pets. (P-value=0.0509).
Step-by-step explanation:
We have to calculate the difference for every pair, and applied the hypothesis test to this sample of differences.
Non-pet Pet --> Difference (d)
A 11 13 --> 2
B 9 8 --> -1
C 11 14 --> 3
D 13 13 --> 0
E 6 12 --> 6
F 9 11 --> 2
The claim is that single people who own pets are generally happier than single people without pets. In the context of the sample, it means that the difference between the metric of happiness between the pet and the non-pet subjects is bigger than 0.
The mean and standard deviation of the sample of differences is:
[tex]M=\dfrac{1}{6}\sum_{i=1}^{6}(2+(-1)+3+0+6+2)\\\\\\ M=\dfrac{12}{6}=2[/tex]
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{6}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{5}\cdot [(2-(2))^2+(-1-(2))^2+(3-(2))^2+(0-(2))^2+(6-(2))^2+(2-(2))^2]}\\\\\\ s=\sqrt{\dfrac{1}{5}\cdot [(0)+(9)+(1)+(4)+(16)+(0)]}\\\\\\ s=\sqrt{\dfrac{30}{5}}=\sqrt{6}\\\\\\s=2.449[/tex]
Then we perform an hypothesis test for the population mean.
The claim is that single people who own pets are generally happier than single people without pets.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_d=0\\\\H_a:\mu_d> 0[/tex]
The significance level is 0.05.
The sample has a size n=6.
The sample mean is M=2.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.449.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2.449}{\sqrt{6}}=0.9998[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{2-0}{0.9998}=\dfrac{2}{0.9998}=2.0004[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=6-1=5[/tex]
This test is a right-tailed test, with 5 degrees of freedom and t=2.0004, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2.0004)=0.0509[/tex]
As the P-value (0.0509) is bigger 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 single people who own pets are generally happier than single people without pets.
Answer:
Step-by-step explanation:
Null hypothesis : [tex]H_0:\mu_d=0[/tex]
Alternative hypothesis: [tex]H_0:\mu_d>0[/tex]
Level pf significance [tex]\alpha =0.05[/tex]
Test statistic [tex]t = \frac{\bar d- \mu}{s_d/\sqrt{n} }[/tex]
Mean of difference
[tex]\bar d = \frac{\sum d_i}{n} = 12/6 = 2[/tex]
Standard deviation of difference
[tex]s_d=\sqrt{\frac{\sum (d_i- \bar d)}{n-1} } \\\\=\sqrt{\frac{30}{6.1} } \\\\=2.441[/tex]
Test statistic
[tex]t = \frac{\bar d- \mu}{s_d/\sqrt{n} }[/tex]
[tex]=\frac{2-0}{2.449/\sqrt{6} } \\\\=2.00[/tex]
Degree of freedom
df = n - 1
6-1 = 5
This test is a right-tailed test, with 5 degrees of freedom and t=2.0004, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t>2.0004)=0.0509[/tex]
As the P-value (0.0509) is bigger 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 single people who own pets are generally happier than single people without pets.
What is the product? [-3 4 2 +5] * [3 -2 1 0]
Answer:
So the answer is the first one
1,664 flound ounces = gallons
Answer:
1,664 fluid ounces = 13 gallons
Step-by-step explanation:
In a random sample of 49 people who work out in the morning it is found that they exercise an average of 4.1 hours per weeks with a standard deviation of 0.7 hours. In a random sample of 54 people who exercise in the afternoon or evening it is found they exercise an average of 3.7 hours with a standard deviation of 0.5 hours. Test the claim that people who exercise in the morning have a mean exercise time greater than those who work out in the afternoon or evening at a 5% level of significance. a. Identify the parameter and label all given information. b. Identify the null hypothesis and the alternative hypothesis and identify the claim. c. Find the critical value(s). d. Compute the test statistic and/or find the p-value. e. State the conclusion that addresses the original claim. Upload
Answer:
a) [tex] \mu_m -\mu_a [/tex]
[tex]\bar X_{m}=4.1[/tex] represent the mean for the morning
[tex]\bar X_{a}=3.7[/tex] represent the mean for the afternoon
[tex]s_{m}=0.7[/tex] represent the sample standard deviation for the morning
[tex]s_{a}=0.5[/tex] represent the sample standard deviation for afternoon
[tex]n_{m}=49[/tex] sample size for the morning
[tex]n_{a}=54[/tex] sample size for the afternoon
b) Null hypothesis:[tex]\mu_{m} \leq \mu_{a}[/tex]
Alternative hypothesis:[tex]\mu_{m} > \mu_{a}[/tex]
c) [tex] t_{\alpha}= 1.66[/tex]
d) [tex]t=\frac{4.1-3.7}{\sqrt{\frac{0.7^2}{49}+\frac{0.5^2}{54}}}}=3.307[/tex]
The p value would be:
[tex]p_v =P(t_{101}>3.307)=0.00065[/tex]
e) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the mean for people in the morning have a mean exercise time is greater than the mean for those who work out in the afternoon or evening at the 5% of significance
Step-by-step explanation:
Part a
[tex]\bar X_{m}=4.1[/tex] represent the mean for the morning
[tex]\bar X_{a}=3.7[/tex] represent the mean for the afternoon
[tex]s_{m}=0.7[/tex] represent the sample standard deviation for the morning
[tex]s_{a}=0.5[/tex] represent the sample standard deviation for afternoon
[tex]n_{m}=49[/tex] sample size for the morning
[tex]n_{a}=54[/tex] sample size for the afternoon
t would represent the statistic
[tex]\alpha=0.05[/tex] significance level
The parameter of interest is:
[tex] \mu_m -\mu_a [/tex]
Part b
We want to verify if the people who exercise in the morning have a mean exercise time greater than those who work out in the afternoon or evening, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{m} \leq \mu_{a}[/tex]
Alternative hypothesis:[tex]\mu_{m} > \mu_{a}[/tex]
The statistic is given by:
[tex]t=\frac{\bar X_{m}-\bar X_{a}}{\sqrt{\frac{s^2_{m}}{n_{m}}+\frac{s^2_{a}}{n_{a}}}}[/tex] (1)
Part c
Based on the significance level[tex]\alpha=0.05[/tex] and the degrees of freedom given by:
[tex] df = 49+54-2= 101[/tex]
We can find the critical value in the t distribution iwth 101 degrees of freedom who accumuate 0.05 of the area in the right and we got:
[tex] t_{\alpha}= 1.66[/tex]
Part d
[tex]t=\frac{4.1-3.7}{\sqrt{\frac{0.7^2}{49}+\frac{0.5^2}{54}}}}=3.307[/tex]
The p value would be:
[tex]p_v =P(t_{101}>3.307)=0.00065[/tex]
Part e
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the mean for people in the morning have a mean exercise time is greater than the mean for those who work out in the afternoon or evening at the 5% of significance
What is x to the nearest tenth?
Answer:
x= 13.7 (nearest tenth)
Step-by-step explanation:
Please see attached picture for full solution.
PLEASE HELP ME PLEASE LOOK AT THE PICTURE I NEED AN ANSWER ASAP
Answer:
1st one is 2. 2nd one is 5. 3rd one is less than. 4th one is, is smaller
Step-by-step explanation:
1. Michel buys a leash for his dog. The leash is 6 ft 3 inches. How long, in inches, is the leash?(1 ft = 12 inches)
A) 48 inches
B) 51 inches
C) 72 inches
D) 75 inches
2. What is the area of a triangular garden with base of 6 ft and a height of 9 ft? (A = 1/2BH)
A) 27 square feet
B) 48 square feet
C) 54 square feet
D) 24 square feet
Answer:
1 = D 75 inches
2 = A 27
Step-by-step explanation:
1 - 6.3 times 12 = 75.6
2 - 6 times 9 = 54
54/2 = 27
:)
Meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories. Use the 68-95-99.7 rule to answer the following questions. NOTE. This web site 68-95-99.7 rule graphically depicts the 68-95-99.7 rule and may help with the following questions. a. What is the approximate percentage of the Chipotle meals that have more than 471 calories
Answer:
The approximate percentage of the Chipotle meals that have more than 471 calories is 95%.
Step-by-step explanation:
We are given that meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories.
Let X = Chipotle meals having calories
So, X ~ Normal([tex]\mu=1075, \sigma^{2} =302^{2}[/tex])
Now, the 68-95-99.7 rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.So, the approximate percentage of the Chipotle meals that have more than 471 calories is given by;
[tex]\frac{X-\mu}{\sigma} = \frac{471-1075}{302}[/tex]
= -2
Since, it is stated above that 95% of the data values lies within two standard deviation points which means 95% values lies between -2 and 2 z score values.
SO, the approximate percentage of the Chipotle meals that have more than 471 calories is 95%.
How would you simplify a negative square root?
Provide a detailed explanation, with an example, to receive full credit.
Answer:
To simplify
√(-x) = √((x)(-1)) = √((x)(i^2))
√(-x) = √(i^2) × √x = i√x
For example;
Simplify √-9
√-9 = √(-1×9) = √-1 × √9
√-9 = √(i^2) × √9 = i × 3
√-9 = 3i
Step-by-step explanation:
Given a negative square root √(-x);
From our knowledge of complex numbers, we know that
i^2 = -1 and vise versa
To simplify
√(-x) = √((x)(-1)) = √((x)(i^2))
√(-x) = √(i^2) × √x = i√x
For example;
Simplify √-9
√-9 = √(-1×9) = √-1 × √9
√-9 = √(i^2) × √9 = i × 3
√-9 = 3i
Step-by-step explanation:
The square root of a number A, is a number B such that, when it is multiplied by itself, the result is A.
If A × A = B
Then √B = A.
Now the multiplication of two numbers gives a positive number if both numbers are positive, or both numbers are negative.
2 × 2 = -2 × -2 = 4
3 × 3 = -3 × - 3 = 9
And so on.
So, the square root of 4 = 2 or -2
The square root of 9 = 3 or -3
But if one of the numbers is positive while the other is negative, then the result is negative.
2 × -2 = -4
3 × -3 = -9
Clearly, √(-4) ≠ 2 ≠ -2
√(-9) ≠ 3 ≠ -3
It is impossible to find the square root of negative numbers on the real line. This gives rise to the introduction of Complex Number.
Let i² = -1, then we have that
√(-1) = i.
This is the idea of Complex number, and it helps solve the problem of the negative square roots, and every negative number can be written as the multiplication of -1 and the inverse of the number.
-A = -1 × A
So, √(-A) = √(-1 × A)
= √(-1) × √A
= i × √A
= i√A
Example, to simplify √(-16)
√(-16) = √(-1 × 16)
= √(-1) × √16
= i × ±4
= ±4i
The students in Mr. Sanchez's class are converting distances measured in miles to kilometers. To estimate the number of kilometers, Abby takes the number of miles, doubles it, then subtracts 20% of the result. Renato first divides the number of miles by 5, then multiplies the result by 8. Write an algebraic expression that shows the process that both students used. Abby's expression: Renato's expression:
Step-by-step explanation:
Abby’s Expression:
Double m, giving 2m. She then takes 20% of the result, which we can write 0.2(2m). Finally she subtracts this from 2m, giving 2m−(0.2)2m
2m − (0.2)2m
Renato’s Expression:
Divide m by 5, giving m ÷ 5 = m/5, and then multiplies the result by 8, giving:
8(m/5)
Help me with this question
Answer:
14 ft
Step-by-step explanation:
After the sides are folded up, the depth of the box is 2 ft, so the area of the square bottom is ...
(200 ft^2)/(2 ft) = 100 ft^2
The edge dimension of the bottom is then ...
√(100 ft^2) = 10 ft
Each side adds 2+2=4 ft to the bottom dimension in each direction, so the original square piece of metal was 14 ft square.
Rihanna planned a rectangular courtyard for a park and made a scale drawing using inches as the unit of measurement. She originally planned for the length of the actual courtyard to be 54 feet, but she decided to change it to 72 feet. If the length of the courtyard is 18 inches in her scale drawing, which statement about the change of scale is true?
Answer:
I think it changed from 36x to 48x
Depending on how you look at it, it could have changed from 3x to 4x or 36x to 48x.
If they said it was 18 feet instead of 18 inches, it would be 3x or 4x, but they had it as inches.
18 inches = 1.5 feet
72/1.5 = 48
54/1.5 = 36
So originally, it would have been a scale of 1 in : 36in , but it changed to 1 in : 48 in
Sorry if this was confusing.
Answer:
One inch represented 3 feet in the first scale, but now 1 inch now represents 4 feet in the second scale. Otherwise known as D
I got 100% on my quiz.
Step-by-step explanation:
a study studied the birth weights of 1,999 babies born in the United States. The mean weight was 3234 grams with a standard deviation of 871 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1492 grams and 4976 grams. Write only a number as your answer. Round your answer to the nearest whole number.
Answer:
1899
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 3234
Standard deviation = 871
Percentage of newborns who weighed between 1492 grams and 4976 grams:
1492 = 3234 - 2*871
So 1492 is two standard deviations below the mean.
4976 = 3234 + 2*871
So 4976 is two standard deviations above the mean.
By the Empirical Rule, 95% of newborns weighed between 1492 grams and 4976 grams.
Out of 1999:
0.95*1999 = 1899
So the answer is 1899
Prove the identity:
sin ((x))-(y)) / cos (x) sin (y) = tan (x) cot (y) - 1
Answer:
Below.
Step-by-step explanation:
sin ((x))-(y)) / cos (x) sin (y)
sin x cos y - cos x sin y
= ----------------------------------
cos x sin y
sin x cos y
= ---------------- - 1
cos x sin y
But tan x = sin x / cos x and cot y = cos y / sin y
So the above = tan x cot y - 1.
Find the mass of lamina bounded by circles x2 + y2 = 1 and x2 + y2 = 4in the first quadrant if the density is (x2 + y2). Could please anyone solve this...
Since density is equal to mass per unit volume, mass is equal to density times volume. So we split up the lamina into tiny regions with "volume" (area) equal to dA, multiplied by the density, and integrated over the entirety of the lamina.
This is best done in polar coordinates:
[tex]\begin{cases}x=u\cos v\\y=u\sin v\end{cases}\implies\mathrm dA=\mathrm dx\,\mathrm dy=u\,\mathrm du\,\mathrm dv[/tex]
so that [tex]x^2+y^2=u^2\cos^2v+u^2\sin^2v=u^2[/tex].
The lamina is then the set of points
[tex]L=\left\{(u,v)\mid1\le u\le2\land0\le v\le\dfrac\pi2\right\}[/tex]
Now compute the integral: the mass of the lamina is
[tex]\displaystyle\iint_L(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^2u^3\,\mathrm du\,\mathrm dv=\frac\pi2\int_1^2u^3\,\mathrm du=\frac{15\pi}8[/tex]
The ACT is an achievement test given nationally with normally distributed scores. Tim
scored a 24 on the mathematics portion of his ACT. The mean for the mathematics portion of
the ACT was 22.0 and the standard deviation was 5.1. What percent of the population scored
higher than Tim on the mathematics portion of the ACT?
Answer:
34.83% of the population scored higher than Tim on the mathematics portion of the ACT
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 22, \sigma = 5.1[/tex]
Tim scored 24. What percent of the population scored higher than Tim on the mathematics portion of the ACT?
The proportion is 1 subtracted by the pvalue of Z when X = 24. The percentage is the proportion multiplied by 100.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 22}{5.1}[/tex]
[tex]Z = 0.39[/tex]
[tex]Z = 0.39[/tex] has a pvalue of 0.6517
1 - 0.6517 = 0.3483
34.83% of the population scored higher than Tim on the mathematics portion of the ACT
what is equal to 12/10
Answer:
6/5, or 1.2
Step-by-step explanation:
The right answer is 6/5
Look at the attached picture
Hope it will help you
Good luck on your assignment
Which is the completely factored form of 4X cubed +10 X squared minus 6X
Answer:
2x(2x - 1)(x + 3)
Step-by-step explanation:
4x^3 + 10x^2 - 6x =
Factor out the common factor 2x.
= 2x(2x^2 + 5x - 3)
Factor the trinominal.
= 2x(2x - 1)(x + 3)
Answer:
[tex]=2x\left(2x-1\right)\left(x+3\right)[/tex]
Step-by-step explanation:
[tex]4x^3+10x^2-6x\\\mathrm{Factor\:out\:common\:term\:}2x:\quad 2x\left(2x^2+5x-3\right)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\x^3=x^2x\\=4x^2x+10xx-6x\\\mathrm{Rewrite\:}6\mathrm{\:as\:}2\cdot \:3\\\mathrm{Rewrite\:}10\mathrm{\:as\:}2\cdot \:5\\\mathrm{Rewrite\:}4\mathrm{\:as\:}2\cdot \:2\\=2\cdot \:2x^2x+2\cdot \:5xx-2\cdot \:3x\\\mathrm{Factor\:out\:common\:term\:}2x\\=2x\left(2x^2+5x-3\right)\\\mathrm{Factor}\:2x^2+5x-3:\quad \left(2x-1\right)\left(x+3\right)[/tex]
[tex]2x^2+5x-3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(2x^2-x\right)+\left(6x-3\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-x\mathrm{:\quad }x\left(2x-1\right)\\2x^2-x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=2xx-x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(2x-1\right)\\\mathrm{Factor\:out\:}3\mathrm{\:from\:}6x-3\mathrm{:\quad }3\left(2x-1\right)\\6x-3\\\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2\\=3\cdot \:2x-3[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}3\\=3\left(2x-1\right)\\=x\left(2x-1\right)+3\left(2x-1\right)\\\mathrm{Factor\:out\:common\:term\:}2x-1\\=\left(2x-1\right)\left(x+3\right)\\=2x\left(2x-1\right)\left(x+3\right)[/tex]
Marc drives his car 500 miles using 20 gallons of gas. How many miles per gallon does his car get
Answer:
25 miles per gallon
Step-by-step explanation:
We want to find miles per gallon so take the miles and divide by the gallons
500 miles / 20 gallons
25 miles per gallon
Answer:
[tex]= 25 \: \: \: miles \: \: \: per \: \: \: gallon \\ [/tex]
Step-by-step explanation:
You have to find miles per gallon.
So to solve that you have to divide miles by gallon.
[tex] \frac{500}{20} \\ = 25 \: \: \: miles \: \: \: per \: \: \: gallon[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The ratio of Adriana's age to her aunt's age is 7:10. In 2 years the sum of their ages will be 123. How old is Adriana's aunt now?
Answer:
70.35Step-by-step explanation:
The sum of 7 and 10 is 17. So 123 / 17 = 7.235 (roughly)
7.235 x 10 (for Adriana's aunt's age) equals 72.35
And to double check: We can find adriana's age by doing. 7.235 x 7 = 50.645. If we add 50.645 and 72.35 we get 122.995 which is roughly 123 and the reason why it is not 123 on the dot is because 123 / 17 is roughly 7.235 the full expanded one is: 7.23529411765
You may try checking with the full number without estimating but i am sure of my answer
5-5+x*7=14
What is x=
A carpenter bought some tools to build chairs. The cost of the materials for each chair was the same. The total cost y (tools and materials) to make x chairs is shown in the graph below. The cost of the tools was $_____ and the cost of materials for one chair was $________
Answer:
Cost of tools: $100
Cost for each chair: $25
Step-by-step explanation:
You can see that before 1 chair, the cost is at 100. This means that the cost of the tools is $100. Another way to determine this is to see that at 1 chair, the cost is $125. At 2, it's $150, and at 3 it's $175, etc. This tells you that the cost to produce each chair is $25, but it also tells you that the tools cost 100 dollars, since the total cost at 1 chair is $125, and each chair only costs $25.
Hope this helps!
Answer:
100,25
Step-by-step explanation:
triangle ABC a = 4 and m angle C=30 If the area of the triangle is 6 what is the length of side b
Answer:
6m = b
Step-by-step explanation:
The area of triangle when angle and sides are given = 1/2* sin angle*ab
Area = 1/2 * sin 30 * 4*b
Area = 6m²
6 = 1/2 * sin 30 * 4*b
(6*2)/(sin 30 * 4)= b
12/(0.5*4) = b
12/2 = b
6m = b
If Triangle M N O is congruent to triangle N M O, what statement best describes triangle MON?
The triangle is scalene.
The triangle is equilateral.
The triangle is isosceles and possibly equilateral.
The triangle is isosceles but definitely not equilateral.
Answer:
The answer is c
Step-by-step explanation:
The statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.
The congruent triangles are:
Triangle MNO and Triangle NMO
The above means that:
Sides MN and NO or MN and MO are equal
So, the triangles are isosceles triangles
However, it is possible that sides NO and MO are congruent
Hence, the statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.
Read more about congruent triangles at:
https://brainly.com/question/1675117
Pls help me
(-7a2 9a3x3 :(-3ax3)] : ( 10a) -(-20a b) : (-5a²b)
Answer:
(-21a^5×b)/(2+4b)
Step by step explanation:
The question isn't complete and clear as we were not told what to determine from the expression.
Looking at the question, we can tell we are to simplify the expression.
[(-7a² × 9a³x³) :(-3ax³)] : [( 10a) -(-20a b) : (-5a²b)]
First we would work with expressions in each parenthesis (bracket).
Then we would work on the answer we derive after opening the parenthesis.
See attachment for detail
i’m confused on the split circle part; do i count it as a full circle?
Answer:
Below.
Step-by-step explanation:
Yes - those are 2 semicircles so their combined area = πr^2
= 3^2π
= 9π.
Yes.. You can count it as full circle.
Answer:
3.9 squre inch
Step-by-step explanation:
Two semicircles are inscribed in a square of side 6 in. Both the semicircles if combined together will form a full circle.
Area of the yellow region would be half of the areas of the difference between area of square and area of two semicircles each with radius 3 inches.
Therefore,
Area of yellow region
[tex] = \frac{1}{2} (area \: of \: square - 2 \times area \: of \: semicircle) \\ \\ = \frac{1}{2} ( {6}^{2} - 2 \times \frac{1}{2} \pi {r}^{2} ) \\ \\ = \frac{1}{2} ( {6}^{2} - 3.14 \times {3}^{2} ) \\ \\ = \frac{1}{2} ( 36 - 3.14 \times 9 ) \\ \\ = \frac{1}{2} ( 36 - 28.26 ) \\ \\ = \frac{1}{2} \times 7.74 \\ \\ = 3.87 \: {in}^{2} \\ \\ = 3.9 \: {in}^{2}[/tex]
Find the product. (3x 2 - 5x + 3)(3x - 2)
Answer:
9x^3-21x^2+19x-6
Step-by-step explanation:
First you have to distribute the first equation into the second since the two are being multiplied:
(3x^2-5x+3)(3x-2)
9x^3-6x^2-15^2+10x+9x-6
(simplify)
9x^3-21x^2+19x-6
9x^3-21x^2+19x-6
First you have to distribute the first equation into the second since the two are being multiplied:
(3x^2-5x+3)(3x-2)
9x^3-6x^2-15^2+10x+9x-6
(simplify)
9x^3-21x^2+19x-6 is the answer to the question
Find the point based on the parametric
equations. t = 3
X = 1 - 2t
y = 4t + 1
Answer:
(-5,13)
Step-by-step explanation:
because t=3
[tex]x = 1 - 2 \times 3 = - 5 \\ y = 4 \times 3 + 1 = 13[/tex]
Please help me understand this!!
Step-by-step explanation:
3 + 15 + 75 + 375 + 1,875
This is a geometric series. The first term is 3, the common ratio is 5, and the number of terms is 5.
∑₁⁵ 3 (5)ⁿ⁻¹
∑₀⁴ 3 (5)ⁿ
3 + 12 + 48 + 192 + 768
This is a geometric series. The first term is 3, the common ratio is 4, and the number of terms is 5.
∑₁⁵ 3 (4)ⁿ⁻¹
∑₀⁴ 3 (4)ⁿ
4 + 32 + 256 + 2048 + 16,384
This is a geometric series. The first term is 4, the common ratio is 8, and the number of terms is 5.
∑₁⁵ 4 (8)ⁿ⁻¹
∑₀⁴ 4 (8)ⁿ
2 + 6 + 18 + 54 + 162
This is a geometric series. The first term is 2, the common ratio is 3, and the number of terms is 5.
∑₁⁵ 2 (3)ⁿ⁻¹
∑₀⁴ 2 (3)ⁿ
Find the GCF.
6m3n and 8mn2
Answer:
[tex]2mn[/tex]
Step-by-step explanation:
[tex]6m^3n,\:8mn^2[/tex]
Find the GCD of [tex]6,\:8[/tex]:
[tex]6[/tex]
[tex]=2\cdot \:3[/tex]
[tex]8[/tex]
[tex]=2\cdot \:4[/tex]
[tex]=2\cdot \:2\cdot \:2[/tex]
So the prime factor common to 6, 8 is:
[tex]2[/tex]
So the factor common to [tex]6m^3n,\:8mn^2[/tex]:
[tex]=2mn[/tex]
Carole ordered 4 dresses for $80 each, a $25 sweater, and a coat. The cost of the items without sales tax was $430. What was the cost of the coat?
Explanation:
The equation for the total cost of the clothes is 4×80+25+c=430, where c is the cost of the coat.
320 + 25 + c = 430
345 + c = 430
345 - 345 + c = 430 - 345
c = 85
The cost of the coat was $85.
Answer:
$85 for the coat
Step-by-step explanation:
1 dress = $80
4 dress =$80×4
=$320
sweater=$25
coat=?
4 dresses plus the sweater cost :
$320+$25=$345
The cost of all the item $430
cost of the coat :
$430-$345=$85
