Answer:
5 in x 5 in
Step-by-step explanation:
The area of the rectangle is given by:
[tex]A=x*y=25\\y=\frac{25}{x}[/tex]
Where x and y are the length and width of the rectangle.
The perimeter is:
[tex]P=2x+2y\\P=2x+2*\frac{25}{x}\\ P=2x+\frac{50}{x}[/tex]
The value of x for which the derivate of the perimeter function is zero is the length that yields the smallest perimeter:
[tex]P=2x+\frac{50}{x} \\\\P'=2-\frac{50}{x^2} =0\\2x^2=50\\x=5\ in[/tex]
The value of y is:
[tex]y=\frac{25}{5}\\y=5\ in[/tex]
Therefore, the dimensions that yield the smallest perimeter are 5 in x 5 in.
A baseball player has a batting average of 0.25. What is the probability that he has exactly 2 hits in his next 7 at bats
Answer:
The probability that he has exactly 2 hits in his next 7 at-bats is 0.3115.
Step-by-step explanation:
We are given that a baseball player has a batting average of 0.25 and we have to find the probability that he has exactly 2 hits in his next 7 at-bats.
Let X = Number of hits made by a baseball player
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r}; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 7 at-bats
r = number of success = exactly 2 hits
p = probability of success which in our question is batting average
of a baseball player, i.e; p = 0.25
SO, X ~ Binom(n = 7, p = 0.25)
Now, the probability that he has exactly 2 hits in his next 7 at-bats is given by = P(X = 2)
P(X = 2) = [tex]\binom{7}{2}\times 0.25^{2} \times (1-0.25)^{7-2}[/tex]
= [tex]21 \times 0.25^{2} \times 0.75^{5}[/tex]
= 0.3115
H 0 : μ ≥ 25 H 1 : μ < 25 Your sample consists of 28 subjects, with a mean of 23.2 and standard deviation of 8.6. Calculate the test statistic, rounded to 2 decimal places.
Answer:
The test statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=23.6[/tex] represent the sample mean
[tex]s=8.6[/tex] represent the sample standard deviation
[tex]n=28[/tex] sample size
[tex]\mu_o =25[/tex] represent the value that we want to test
t would represent the statistic
System of hypothesis
We want to test if the true mean is lower than 25, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 25[/tex]
Alternative hypothesis:[tex]\mu < 25[/tex]
The test statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{23.2-25}{\frac{8.6}{\sqrt{28}}}=-1.11[/tex]
Quick and easy geometry thanks please help !!!!!
Answer:
Midpoint of segment AB= (-0.5, 0)
Step-by-step explanation:
The midpoint coordinates of the midpoint has the x coordinate on .5 and the y coordinate on 0.
Please tell me the answer to c ignore the question b thank you
Answer:
c).[tex] {1000}^{m} \div {100}^{n} \\ \\ {10}^{3m} \div {10}^{2n} [/tex]
Since they have the same base and are dividing we subtract the exponents
That's
[tex] {10}^{3m - 2n} [/tex]
So
z = 3m - 2nHope this helps you
Answer:
[tex]\boxed{ z = 3m-2n}[/tex]
Step-by-step explanation:
=> [tex]1000^m / 100^n[/tex]
=> [tex](10)^{3m} / (10)^{2n}[/tex]
Using rule of exponents [tex]a^m/a^n = a^{m-n}[/tex]
=> [tex]10 ^{3m-2n}[/tex]
Comparing it with [tex]10^z[/tex], we get
=> z = 3m-2n
Mike tabulated the following values for heights in inches of seven of his friends: 65, 71, 74, 61, 66, 70, and 72. Mike wishes to construct a 95% confidence interval. What value of t* should Mike use to construct the confidence interval? Answer choices are rounded to the hundredths place.
Answer:
a) 95% confidence intervals are
(64.188, 72.652)
b) Mike use
(t₀.₀₂₅ , ₆)= 2.4469
Step-by-step explanation:
Step(i):-
Given data
x : 65 71 74 61 66 70 72
Mean of 'x'
x⁻ = ∑ x / n
[tex]x^{-} = \frac{65+71+74+61+66+70+72}{7} = 68.42[/tex]
x : 65 71 74 61 66 70 72
x - x⁻ : -3.42 2.58 5.58 -7.42 -2.42 1.58 3.58
(x-x⁻)² : 11.69 6.65 31.13 55.05 5.85 2.49 12.81
∑((x-x⁻)²) = 125.67
Variance
S² = ∑((x-x⁻)²) / n-1 = [tex]\frac{125.67}{6} = 20.945[/tex]
Standard deviation S = √20.945 =4.576
Step(ii):-
95% confidence intervals are determined by
[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } , x^{-} +t_{\alpha } \frac{S}{\sqrt{n} })[/tex]
Degrees of freedom
ν =n-1 = 7-1 =6
[tex]t_{\frac{\alpha }{2} , n-1 } = t_{(\frac{0.05}{2} , 6)}[/tex] = (t₀.₀₂₅ , ₆)= 2.4469
[tex](68.42 - 2.4469 \frac{4.576}{\sqrt{7} } , 68.42 +2.4469\frac{4.576}{\sqrt{7} })[/tex]
( 68.42 - 4.232, 68.42 + 4.232)
(64.188, 72.652)
Conclusion:-
95% confidence intervals are
(64.188, 72.652)
Answer:
64.19 to 72.67
Step-by-step explanation:
Mrs. Nestler enjoys listening to classical music. She has the following audio CDs by her favorite composers in her collection: 4 by Bach, 6 by Beethoven, 3 by Brahms, and 2 by Handel. If she selects 4 CDs randomly from her collection without replacing them, what is the probability that she will choose one by each composer.
Answer:
10.55% probability
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the CDs are chosen is not important. So we use the combinations formula to solve this question.
1 Bach CD, from a set of 4.
1 Beethoven CD, from a set of 6.
1 Brahms CD, from a set of 3.
1 Handel CD, from a set of 2.
So, D=144
4 CDs from a set of 4+6+3+2 = 15.
So, T= 1365
p= D/T= 144/1365 = 0.1055
10.55% probability that she will choose one by each composer
the number 12,16, n, 23, 30 have a mean of 22.6 the value of n
Answer:
32
Step-by-step explanation:
Mean = Average = The data values added together/ the number of data values.
The mean of 5 numbers is 22.6=
[tex]\frac{12+16+n+23+30}{5} = 22.6[/tex]
Multiply both sides by 5. 22.6 becomes 113
12+16+23+30+n=113
n+81 = 113
n= 32
The value of n is 32.
What is the arithmetic mean?The arithmetic mean of m values [tex]x_1,x_2,..., x_m[/tex] is
[tex]\frac{x_1+x_2+...+x_m}{m}[/tex]
How to solve for n?The given
mean = [tex]\frac{12+16+n+23+30}{5}=22.6[/tex]
⇒12+16+n+23+30=22.6×5=113
⇒n=113-81=32
Hence, n=32
To learn more about the arithmetic mean visit- https://brainly.com/question/15196910?referrer=searchResults
#SPJ2
What is the perimeter of the equilateral triangle if one side is 6 feet?
Answer:
18 feet
Step-by-step explanation:
Equilateral triangles have 3 equal sides.
If one side is 6 feet, the other two are also 6 feet.
Perimeter is all the sides added.
6 + 6 + 6
= 18
Store pays $56 for a GPS navigation system the markup is 25% what price will the store sell it for
[tex]\text{We need to find how much the store will sell a GPS navigation system}\\\\\text{We know that the store paid \$56 for it}\\\\\text{We also know that they will mark up the price by 25\%}\\\\\text{We can find 25\% of 56}\\\\56\cdot0.25=14\\\\\text{We can now add that to the original price to get the price the store}\\\text{will sell it for}\\\\56+14=70\\\\\boxed{\$70}[/tex]
WILL GIVE BRAINLIEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter.
Answer:
Perimeter = 317 m
Step-by-step explanation:
Given track is a composite figure having two semicircles and one rectangle.
Perimeter of the given track = Circumference of two semicircles + 2(length of the rectangle)
Circumference of one semicircle = πr [where 'r' = radius of the semicircle]
= 25π
= 25 × 3.14
= 78.5 m
Length of the rectangle = 80 m
Perimeter of the track = 2(78.5) + 2(80)
= 157 + 160
= 317 m
Therefore, perimeter of the track = 317 m
Please help ill mark you the brainlist The scale on a map indicates that 1 cm represents 50 km. If two cities are 400 km apart, then how far apart would the cities be on this map?
Answer:
8 cm
Step-by-step explanation:
divide 400 by 50 which is 8.
An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample of 8 school districts is selected, and the daily salaries are 60, 56, 60, 55, 70, 55, 60, and 55. Is there enough evidence to support the educator’s claim at 10% level of significance? (HELP: The sample mean is 58.88, and the sample standard deviation is 5.08)
Answer:
[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value would be given by:
[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60
Step-by-step explanation:
Information given
60, 56, 60, 55, 70, 55, 60, and 55.
We can calculate the mean and deviation with these formulas:
[tex]\bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
Replacing we got:
[tex]\bar X=58.875[/tex] represent the mean
[tex]s=5.083[/tex] represent the sample standard deviation for the sample
[tex]n=8[/tex] sample size
[tex]\mu_o =60[/tex] represent the value that we want to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is less than 60, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 60[/tex]
Alternative hypothesis:[tex]\mu < 60[/tex]
The statistic would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626[/tex]
The degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
The p value would be given by:
[tex]p_v =P(t_{(7)}<-0.626)=0.275[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60
An airline allows passenger 33 kg of luggage cost to lower the weight of a suitcase by 25% to stay within the limit how much does suitcase originally way
Answer:
The suitcase originally weighed 44kg.
Step-by-step explanation:
1- 0.25= 0.75 (multiplier)
33÷0.75=44
The suitcase originally weighed 44kg
A circle is represented by the equation x2+y2=445. a) State the radius. b) Find y if point A(-9,y) is on this circle.
Answer:
R= sqrt 445
Y = 19
Step-by-step explanation:
Radius is the square root of 445
Find y
So, First step is to substitute what you have
-9^2 + y^2 = 445
81 + y^2 = 445
-81 -81
y^2 =364
Y is about 19
Let me know if I'm incorrect
Hope this helps :)
The lengths of adult males' hands are normally distributed with mean 190 mm and standard deviation is 7.4 mm. Suppose that 45 individuals are randomly chosen. Round all answers to 4 where possible.
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For the group of 45, find the probability that the average hand length is less than 189.
Find the third quartile for the average adult male hand length for this sample size.
For part b), is the assumption that the distribution is normal necessary?
Answer:
a. The distribution of the sample means is normal with mean 190 mm and standard deviation 1.1031 mm.
b. The probability that the average hand length is less than 189 is P(M<189)=0.1823.
c. The third quartile for the average adult male hand length for this sample size is M_75=190.7440.
d. The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Step-by-step explanation:
We have a normal distribution, with mean 190 and standard deviation 7.4.
We take samples of size n=45 from this population.
Then, the sample means will have a distribution with the following parameters:
[tex]\mu_s=\mu=190\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{7.4}{\sqrt{45}}=\dfrac{7.4}{6.7082}=1.1031[/tex]
The probability that the sample mean is less than 189 can be calculated as:
[tex]z=\dfrac{M-\mu}{\sigma/\sqrt{n}}=\dfrac{189-190}{7.4/\sqrt{45}}=\dfrac{-1}{1.1031}=-0.9065\\\\\\P(M<189)=P(z<-0.9065)=0.1823[/tex]
The third quartile represents the value of the sample where 75% of the data is to the left of this value. It means that:
[tex]P(M<M^*)=0.75[/tex]
The third quartile corresponds to a z-value of z*=0.6745.
[tex]P(z<z^*)=0.75[/tex]
Then, we can calculate the sample mean for the third quartile as:
[tex]M=\mu_s+z^*\sigma_s=190+0.6745\cdot 1.1031=190+0.7440=190.7440[/tex]
The assumption of normality is not necessary as the sampling distribution will tend to have a bell shaped independently of the population distribution.
Square ABCD is shown below with line EF and passing through the center:
Answer: B) contain the points E and F
Step-by-step explanation:
Dilation of 2 means to multiply both the x- and y-coordinates by 2
see image below
The only option that is true that E'F' contains points E and F
Answer:
contains the points E and F
Step-by-step explanation:
The center of dilation is an invariant point. It doesn't move, regardless of the dilation factor.
Likewise, any line through the center of dilation will not move. It is not rotated or translated by dilation--it simply is stretched (or compressed) along its length. It is still an infinite line, and it still goes through all of the points it went through before dilation.
The line through the center of dilation that contains points E and F, after dilation, ...
contains the points E and F.
Need help please show how to complete
Answer:
Step-by-step explanation:
P= 2*10+2*6=20+12= 32 mP= 4*7 = 28 cm P= 8+10+12 =30How many multiples of 4, that are smaller than 1,000, do not contain any of the digits 6, 7, 8, 9 or 0?
Answer:
44
Step-by-step explanation:
11×4
hope it helped!
Simon swapped of 2/5
his 40 marbles for 9 of
Saqib's. How many has
Simon got now?
Answer:
33
Step-by-step explanation:
2/5x40=16
40-16=24
24+9=33
33 marbles
2/5 is .4
Multiply .4 by 40 to get 16
Subtract 16 from 40 to get 24
Add 9 to 24 to get 33
Hope it helps <3
(If it does, please mark brainliest, only need 1 more to get rank up :) )
<1 and <3 are complementary and <1= <2 Which one of these statements will always be true?
A. M<2 = m<3
B. <2 and <3 are complementary
C. M<1= m<3
D. <2 and <3 are supplementary
Answer:
B. ∠2 and ∠3 are complementary
Step-by-step explanation:
The substitution property of equality lets you put ∠2 in place of ∠1 in the statement ...
∠1 and ∠3 are complementary.
∠2 and ∠3 are complementary . . . . using ∠2 for equal ∠1 in the above
Answer: ∠2 and ∠3 are complementary
Step-by-step explanation:
A traffic helicopter pilot 300 feet above the road spotted two antique cars. The angles of depression are 7.5° and 9º. How far apart are the cars? Round to the nearest tenth.
Answer:
384.6 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the trig relation involving sides adjacent and opposite the angle. Here, the road distance is adjacent to the angle of depression, and the altitude is opposite. So, you have ...
Tan = Opposite/Adjacent
tan(7.5°) = (300 ft)/(distance to car 1)
tan(9°) = (300 ft)/(distance to car 2)
Solving for the distances, we have ...
distance to car 1 = (300 ft)/tan(7.5°) ≈ 2278.73 ft
distance to car 2 = (300 ft)/tan(9°) ≈ 1894.13 ft
Then the separation between the cars is ...
distance apart = 2278.73 ft - 1894.13 ft
distance apart = 384.6 ft
Select the two values of x that are roots of this equation.
x2 + 2x- 6 = 0
A. X= -1 - 7
B. x= -1+ 7
C. x = -1 - 2-17
2
D. x = -1 + 2-17
Answer:
x = 2, -3
Step-by-step explanation:
[tex]x^2 + 2x- 6 = 0\\=>x^2 +3x - 2x- 6 = 0\\=>x(x+3) - 2(x +3) = 0\\=> (x-2)(x+3) = 0\\\\[/tex]
(x-2) = 0 or (x+3) = 0
x = 2 or x = -3
Thus, two values of x are x = 2, -3
Note: The options given are incorrect.
Answer:
a and b.
Step-by-step explanation:
i’m assuming that the 7 is square root of seven.
ap3x verified
At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequality models this situation?
Answer:
T < -25
Step-by-step explanation:
Was correct on TTM
The set G 5 {1, 4, 11, 14, 16, 19, 26, 29, 31, 34, 41, 44} is a group under multiplication modulo 45. Write G as an external and an internal direct product of cyclic groups of prime-power order.
Answer: G = (19) × (26) × (16)
Step-by-step explanation:
The isomorphism classes of Abelian groups of order 12 are Z₄ ⊕ Z₃ and Z₂ ⊕ Z₂ ⊕ Z₃
SO Let us calculate the orders of some of the elements of G
We have
4² = 16,
4³ = 64
= 19,
and
4^4 = 19.4
= 76
= 31.
furthermore,
4^5 = 31.4
= 124
= 34
and
4^6 = 34.4
= 136
= 1
Hence, 4 and 34 each have order 6, 16 and 31 each have order 3, and 19 has order 2.
Next, we calculate
11² = 121
= 31
and
11³ = 11.3
= 341
= 26
this is the calculation needed.
26² = 11^6
= 31³
= 1
since we already showed that 31 has order 3. This means that 26 has order 2
Since G has two distinct elements of order 2, it cannot be isomorphic to . We conclude
that G = Z₂ ⊕ Z₂ ⊕ Z₃
Finally, we will express as an internal direct product.
The previous calculations show that
(19) = { 1, 19 }
and (26) = { 1, 26 }
are cyclic subgroups of G of order 2 with trivial intersection. We have
(19) × (26) = { 1, 19, 26, 44 }
since
(16) = { 1, 19, 26, 44 }
has trivial intersection with (19) × (26), conclude that
G = (19) × (26) × (19)
Xavier and Yifei have been married for exactly 37 years.Yifei is four years older than Xavier. Now the sum of their ages is 124. How old was Yifei when theywere married?a) Set up and write an equation that represents
Answer:
Xavier's age = 23
Yifei's age = 27
Step-by-step explanation:
Represent Yifei's age with Y and Xavier's age with X;
Given that the sum of their ages is 124;
X + Y = 124
Also, given that Yifei is 4 years older
Y = X + 4
Required
Find their age when they got married
From the parameters above, we've been able to form a simultaneous equation
[tex]X + Y = 124[/tex]
[tex]Y = X + 4[/tex]
Substitute X + 4 for Y in the first equation
[tex]X + X + 4 = 124[/tex]
[tex]2X + 4=124[/tex]
Subtract 4 from both sides
[tex]2X + 4 - 4 = 124 - 4[/tex]
[tex]2X = 120[/tex]
Divide both sides by 2
[tex]\frac{2X}{2} = \frac{120}{2}[/tex]
[tex]X = 60[/tex]
Substitute 60 for X in the second equation
[tex]Y = X + 4[/tex] becomes
[tex]Y = 60 +4[/tex]
[tex]Y = 64[/tex]
To get their ages when they got married; we simply subtract 37 from their current ages
Xavier's age = 60 - 37
Xavier's age = 23
Yifei's age = 64 - 37
Yifei's age = 27
A simple random sample of size nequals15 is drawn from a population that is normally distributed. The sample mean is found to be x overbarequals18.3 and the sample standard deviation is found to be sequals6.3. Determine if the population mean is different from 24 at the alpha equals 0.01 level of significance. Complete parts (a) through (d) below.
(a) Determine the null and alternative hypotheses. Upper H 0: ▼ p sigma mu ▼ less than not equals equals greater than 24 Upper H 1: ▼ sigma mu p ▼ greater than not equals equals less than 24
(b) Calculate the P-value.P-valueequals nothing (Round to three decimal places as needed.)
(c) State the conclusion for the test.
A. Do not reject Upper H 0 because the P-value is less than the alphaequals0.01 level of significance.
B. Do not reject Upper H 0 because the P-value is greater than the alphaequals0.01 level of significance.
C. Reject Upper H 0 because the P-value is less than the alphaequals0.01 level of significance.
D. Reject Upper H 0 because the P-value is greater than the alphaequals0.01 level of significance.
(d) State the conclusion in context of the problem. There ▼ is not is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.
Answer:
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24
(b) The P-value is 0.004.
(c) Reject Upper H 0 because the P-value is less than the alpha = 0.01 level of significance.
(d) There is sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.
Step-by-step explanation:
We are given that a simple random sample of size n = 15 is drawn from a population that is normally distributed. The sample mean is found to be x overbar = 18.3 and the sample standard deviation is found to be s = 6.3.
Let [tex]\mu[/tex] = population mean
(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24 {means that the population mean is 24}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24 {means that the population mean is different from 24}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = 18.3
s = sample standard deviation = 6.3
n = sample size = 15
So, the test statistics = [tex]\frac{18.3-24}{\frac{6.3}{\sqrt{15} } }[/tex] ~ [tex]t_1_4[/tex]
= -3.504
The value of t-test statistics is -3.504.
(b) Now, the P-value of the test statistics is given by;
P-value = P( [tex]t_1_4[/tex] < -3.504) = 0.002 or 0.2%
For the two-tailed test, the P-value is calculated as = [tex]2 \times 0.002[/tex] = 0.004 or 0.4%.
(c) Since the p-value of the test statistics is less than the level of significance as 0.002 < 0.01, so we will reject our null hypothesis.
(d) This means that we have sufficient evidence at the alpha equals 0.01 level of significance to conclude that the population mean is different from 24.
The pront for a company this year was $100,000. Each year the profit increases at a rate
of 1.2% per year. Which function shows the company's profit as a function of time in
years?
Answer:
f(t) = 100,000 ⋅ 0.012 t
Step-by-step explanation:
Please please please please help me. i will do anything, anything!! please
Answer:
[tex]d \approx 2.2[/tex]
Step-by-step explanation:
It is the same process as in previous problems.
Once the origin is the point (0, 0):
[tex]d=\sqrt{(x_{1}-x_{2})^2 + (y_{1}-y_{2})^2}[/tex]
[tex]d=\sqrt{(2-0)^2 + (-1-0)^2}[/tex]
[tex]d=\sqrt{2^2 + (-1)^2}[/tex]
[tex]d=\sqrt{5}[/tex]
[tex]d \approx 2.2[/tex]
Answer:
2.2
Step-by-step explanation:
The distance formula
[tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex] with
[tex]x_1=0\\y_1=0\\x_2=2\\y_2=-1[/tex]
[tex]\sqrt{(0-2)^2+(0-(-1))^2}=\sqrt{2^2+1^2}=\sqrt{5}[/tex]
[tex]\sqrt{5} =2.2360...=2.2[/tex]
Solve this rational equation:
Х
1
x – 4
+
=
2
x2 - 6x + 8
x – 2
Hey there! :)
Answer:
x = -1.
Step-by-step explanation:
[tex]\frac{1}{x-4}+ \frac{x}{x-2}= \frac{2}{x^{2}-6x+8 }[/tex]
Make each fraction have a common denominator:
[tex]\frac{1(x-2)}{x^{2}-6x+8}+ \frac{x(x-4)}{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]
Simplify:
[tex]\frac{x-2}{x^{2}-6x+8}+ \frac{x^{2}-4x }{x^{2}-6x+8}= \frac{2}{x^{2}-6x+8 }[/tex]
Disregard the denominator and solve the numerators:
x - 2 + x² - 4x = 2
Combine like terms:
x² - 3x - 2 = 2
x² - 3x - 4 = 0
Factor:
(x - 4)(x + 1)
***Only one of these solutions works because if x = 4, the denominator of the first fraction would be 0, which is undefined. Therefore, the only possible solution is x = -1.
Given a triangle with: a =
150, A = 75°, and C = 30°
Using the law of sines gives: c = 0
Answer:
[tex] c = 77.6 [/tex]
Step-by-step explanation:
You may have entered the measure of a side as the measure of an angle.
[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin 75^\circ}{150} = \dfrac{\sin 30^\circ}{c} [/tex]
[tex] c\sin 75^\circ = 150 \sin 30^\circ [/tex]
[tex] c = \dfrac{150 \sin 30^\circ}{\sin 75^\circ} [/tex]
[tex] c = 77.6 [/tex]
You are correct. Good job!