8. If3:8=c:56, the value of c will be

Answer:

The largest interval is    [tex]-\infty < 0 < 5[/tex]

Step-by-step explanation:

From the question the equation given is  

       [tex](x-5)y'' + 3y = x \ \ \ y(0) = 0 \ , y'(0) = 1[/tex]  

Now dividing the both sides of this equation by (x-5)

         [tex]y'' + \frac{3y}{(x-5)} = \frac{x}{x-5}[/tex]

Comparing this equation with the standard form of 2nd degree differential which is

        [tex]y'' + P(x)y' + Q(x) y = R(x)[/tex]

We see that

        [tex]Q(x) = \frac{3y}{(x-5)}[/tex]

        [tex]R(x) = \frac{x}{(x-5)}[/tex]

So at x =  5  [tex]Q(x) \ and \ R(x)[/tex] are defined for this equation because from the equation of [tex]Q(x) \ and \ R(x)[/tex]  x =  5 give infinity

This implies that the largest interval which includes x = 0 , P(x) , Q(x) , R(x ) is  

       [tex]-\infty < 0 < 5[/tex]

This because x = 5 is not defined in y domain

Answer:

a. 23.02 %

b. 49%

c. W

Step-by-step explanation:

Solution:-

- A multi-variable function for the percentage of fish in the lake that are intolerant to the pollution is given as:

                     [tex]P ( W , R , A ) = 49 - 1.61W - 1.41R - 1.38A[/tex]

Where,

             W: percentage of wetland

             R: percentage of residential area

             A: percentage of agriculture

- We are to evaluate the percentage of fish intolerant to pollution in the case where W = 3 , R = 15 , A = 0. We will plug in the values in the modeled function P ( W , R , A ) as follows:

                     [tex]P ( 3 , 15 , 0 ) = 49 - 1.61*3 - 1.41*15 -1.38*0\\\\P ( 3 , 15 , 0 ) = 23.02\\[/tex]

- To determine the maximum percentage of fish that will be intolerant to pollution we will employ the use of critical points. The critical point that is defined by the linear relationship between P and all other parameters ( W, R , A ). The maximum value occurs when W = R = A = 0.

                   [tex]P ( 0 , 0 , 0 ) = 49 - 1.61*0 -1.41*0 - 1.38*0 = 49[/tex]

- Hence, the maximum value of the function is 49%.

- The linear relationship between each induvidual parameter ( R, W , A ) and the function ( P ) is proportional in influence. The extent of influence can be quantized by the constant multiplied by each parameter.

- We see that that ( 1.61*W ) > ( 1.41R ) > ( 1.38A ). The greatest influence is by parameter ( W ) i.e the influence of percentage of wetlands .

Answer:

a) 10.38% probability that the sample mean will be more than 59 pounds.

b) 67.72% probability that the sample mean will be more than 56 pounds.

c) 22.10% probability that the sample mean will be between 56 and 57 pounds.

d) 1.46% probability that the sample mean will be less than 53 pounds.

e) 0% probability that the sample mean will be less than 49 pounds.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 56.8, \sigma = 12.2, n = 49, s = \frac{12.2}{\sqrt{49}} = 1.74285[/tex]

a. More than 59 pounds

This is 1 subtracted by the pvalue of Z when X = 59. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{59 - 56.8}{1.74285}[/tex]

[tex]Z = 1.26[/tex]

[tex]Z = 1.26[/tex] has a pvalue of 0.8962.

1 - 0.8962 = 0.1038

10.38% probability that the sample mean will be more than 59 pounds.

b. More than 56 pounds

This is 1 subtracted by the pvalue of Z when X = 56. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{56 - 56.8}{1.74285}[/tex]

[tex]Z = -0.46[/tex]

[tex]Z = -0.46[/tex] has a pvalue of 0.3228.

1 - 0.3228 = 0.6772

67.72% probability that the sample mean will be more than 56 pounds.

c. Between 56 and 57 pounds

This is the pvalue of Z when X = 57 subtracted by the pvalue of Z when X = 56. So

X = 57

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{57 - 56.8}{1.74285}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a pvalue of 0.5438

X = 56

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{56 - 56.8}{1.74285}[/tex]

[tex]Z = -0.46[/tex]

[tex]Z = -0.46[/tex] has a pvalue of 0.3228.

0.5438 - 0.3228 = 0.2210

22.10% probability that the sample mean will be between 56 and 57 pounds.

d. Less than 53 pounds

This is the pvalue of Z when X = 53.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{53 - 56.8}{1.74285}[/tex]

[tex]Z = -2.18[/tex]

[tex]Z = -2.18[/tex] has a pvalue of 0.0146

1.46% probability that the sample mean will be less than 53 pounds.

e. Less than 49 pounds

This is the pvalue of Z when X = 49.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{49 - 56.8}{1.74285}[/tex]

[tex]Z = -4.48[/tex]

[tex]Z = -4.48[/tex] has a pvalue of 0.

0% probability that the sample mean will be less than 49 pounds.

Answer:

????????????????????????

Answer:

(-∞,∞)

Step-by-step explanation:

It's just a line

Answer:

INFINITIE, INFINITIE

Step-by-step explanation:

Answer:

f(x) = 2x^4 - 3

Step-by-step explanation:

First multiplying by 2 giving f(x) = 2x^4 stretches it vertically by factor 2.

Then subtract 3 to move it down 3 units:

f(x) = 2x^4 - 3.

Answer:

g(x)=2x^4-3

Step-by-step explanation:

Answer:

2.33% probability that three are cinnamon and two are peppermint

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the candies are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

3 cinnamon, from a set of 6.

2 peppermint, from a set of 5. So

[tex]D = C_{6,3}*C_{5,2} = \frac{6!}{3!(6-3)!}*\frac{5!}{2!(5-2)!} = 200[/tex]

Total outcomes:

5 candies, from a set of 6+5+7 = 18. So

[tex]T = C_{18,5} = \frac{18!}{5!(18-5)!} = 8568[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{200}{8568} = 0.0233[/tex]

2.33% probability that three are cinnamon and two are peppermint

Answer:

[tex](4x-3)(3x^2)+2)[/tex]

Step-by-step explanation:

Answer:

The greatest common factor for the first parenthesis is 3 and the greatest common factor for the second parenthesis is 2

Step-by-step explanation:

Hope this helps plz mark brainliest!

Answer:

C.

Step-by-step explanation:

60° in Radians = 1.047

Using Formula

s=rθ

s= 7(1.047)

s ≈ 7.36

Answer: g(x) = -f(x)

Step-by-step explanation:

When we have a point (x, y) and we reflect it over the x-axis, the end result of the reflection is the point (x, -y)

In this case we have a function reflected, and we know that we can write a function as (x, f(x))

So when we reflect it, the result will be (x, g(x)) = (x, -f(x))

So we have g(x) = -f(x)

Answer:

1 5/6 gallons

Step-by-step explanation:

1. 5 1/2 = 11/2 gallons

2. She uses: 1/3 x 11/2 = 11/6 gallons

3. so: 11/6 = 1 5/6 gallons

I'M MARIE!!!

Answer:

[tex]\hat p=\frac{92}{1500}=0.0613[/tex] estimated proportion of unemployed

[tex]z=\frac{0.0613 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1500}}}=2.01[/tex]  

Step-by-step explanation:

Information given

n=1500 represent the random sample taken

X=92 represent the number of people unemployed

[tex]\hat p=\frac{92}{1500}=0.0613[/tex] estimated proportion of unemployed

[tex]p_o=0.05[/tex] is the value to value to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true proportion is lower than 0.05 or no and the system of hypothesis are::  

Null hypothesis:[tex]p \geq 0.5[/tex]  

Alternative hypothesis:[tex]p < 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{0.0613 -0.05}{\sqrt{\frac{0.05(1-0.05)}{1500}}}=2.01[/tex]  

Answer: D) 180 Minutes

Step-by-step explanation:

If every hour is equal to 60 minutes and the movie (Lord of the Rings) was 3 hours longs...then we just have to multiply....

60 x 3 = 180

I hope this helps!

Answer:

68% of the lengths of pregnancies fall between 250 days and 282 days.

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 = 266

Standard deviation = 16.

What is the proportion of the lengths of pregnancies that fall between 250 days and 282 days?

250 = 266 - 16

So 250 is one standard deviation below the mean.

282 = 266 + 16

So 282 is one standard deviation above the mean.

By the Empirical Rule, 68% of the lengths of pregnancies fall between 250 days and 282 days.

Answer:

[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]

And we can find this probability with this difference and using the normal standard table or excel:

[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]

So then we will have approximatetly 68.26% of the values between 250 and 282 days

Step-by-step explanation:

Let X the random variable that represent the The length of human pregnancies from conception to birth, and for this case we know the distribution for X is given by:

[tex]X \sim N(266,16)[/tex]  

Where [tex]\mu=266[/tex] and [tex]\sigma=16[/tex]

We are interested on this probability

[tex]P(250<X<282)[/tex]

And the best way to solve this problem is using the normal standard distribution and the z score given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

If we apply this formula to our probability we got this:

[tex]P(250<X<282)=P(\frac{250-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{282-\mu}{\sigma})=P(\frac{250-266}{16}<Z<\frac{282-266}{16})=P(-1<z<1)[/tex]

And we can find this probability with this difference and using the normal standard table or excel:

[tex]P(-1<z<1)=P(z<1)-P(z<-1)= 0.8413-0.1587= 0.6826[/tex]

So then we will have approximatetly 68.26% of the values between 250 and 282 days

Answer:

PQ AND SR on ED

Step-by-step explanation:

Based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.

The vertical angles theorem is a theorem that states that when two lines intersect and form vertically opposite angles, each pair of vertical angles has the same angle measures. A pair of vertically opposite angles are always equal to each other.

For the given situation,

Angles PTQ and STR are vertical angles and congruent.

Line segments T P, T Q, T R, and T S are radii.

So, T P = T Q = T R = T S.

The two sides T P = T Q and T R = T S and [tex]\angle PTQ = \angle RTS[/tex],

then by SAS similarity theorem two triangles,

Δ PTQ ≅ Δ STR.

When two triangles are congruent, then the corresponding arc are also congruent.

The congruent central angles intercept congruent arcs PQ and SR.

Hence we can conclude that based on vertical angle theorem, arcs that are congruent is option (B) arc P Q and arc S R is the correct answer.

Learn more about vertical angle theorem here

https://brainly.com/question/17702030

#SPJ2

Answer:

P= $3.5x -$30

Step-by-step explanation:

Let the number of roses Thomas bought and sold be x.

Hence the total selling price would be;

$3.5 × x= $3.5x

The profit = selling price-expenses

P= $3.5x -$30

Answer:

60, 62, 64

Step-by-step explanation:

Let x, (x + 2) & (x+ 4) be three consecutive even integers.

[tex] \therefore \: x + (x + 2) + (x + 4) = 186 \\ \therefore \:3x + 6 = 186 \\ \therefore \:3x = 186 - 6 \\ \therefore \:3x = 180 \\ \therefore \:x = \frac{180}{3} \\ \therefore \:x = 60 \\ \implies \\ x + 2 = 60 + 2 = 62 \\ x + 4 = 60 + 4 = 64[/tex]

Hence, the three consecutive even integers are 60, 62 and 64.

Answer:

z=2

Step-by-step explanation:

56-35z+17=3

73-35z=3

-35z=-70

z=2

Answer:

Gasoline is a petroleum-derived product comprising a mixture of liquid aliphatic and aromatic hydrocarbons, ranging between C4 and C12 carbon atoms with the boiling range of 30–225°C. It is predominantly a mixture of paraffins, naphthenes, aromatics and olefins. hope that helps love!

Answer:

Answer is below

Step-by-step explanation:

Gasoline has an initial boiling point at about 35 °C or 95 °F and a final boiling point of about 200 °C or 395 °F.

Answer:

Step-by-step explanation:

There are four options given above.

P specifies the probability that a couple turns their head to the right when kissing. P is 0.5 because the probability of turning right when kissing is 75÷150 = 1/2 = 0.5

Assuming that the given confidence intervals are an instance of a random interval computed upon observing the given data,

The correct statements are statements 1 and 4

Answer:

Step-by-step explanation:

item 4 Find the perimeter of the window. Round your answer to the nearest tenth. 90 cm

You did not state the diameter or radius of the window

so, i will use 90cm as the diameter of the window

First, I'd calculate the half circumference of the window.

The formula for circumference is [tex]c = 2\pi r[/tex],

Half of it would just be [tex]c/2 = r\pi[/tex]

Since our diameter is 90 cm, our radius is 45 cm.

Circumference =

[tex]=45\pi \\= 141.37 cm[/tex]

circumference is also the same with perimeter

Answer:

141.4cm

Step-by-step explanation:

=>

please give barinlist

Answer:

S20 ≈ 4.942

Step-by-step explanation:

Sum of a geometric series is expressed as Sn = a(1-rⁿ)/1-r if r<1

a is the first term

r is the common ratio

n is the number of terms

Given the geometric series

1 + 0.8 + 0.8^2 +0.8^3 + ... + 0.8^{19}

Given a = 1,

r = 0.8/1 = 0.8²/0.8 = 0.8

n = 20 (The total number of terms in the series is 20)

Substituting this values in the formula above.

S20 = 1(1-0.8^20)/1-0.8

S20 = 1-0.01153/0.2

S20 = 0.9885/0.2

S20 ≈ 4.942

Answer: choice A

Step-by-step explanation:

The shaded area represents the complement of B.

Bc or B’ is the complement of B and B’=1-B or B’=S-B

The probability that Events A and B occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B), which in this example would be equal to B.

The probability that Events A or B occur is the probability of the union of A and B. The probability of the union of Events A and B is denoted by P(A ∪ B), which in this example is equal to S.

Answer:The transformation is described as a rotation of 180 degrees clockwise around the origin.

Step-by-step explanation:

Answer:

V=3

Step-by-step explanation:

2(v-1)+8=6(2v-4)

2V-2+8=12v-24(calculate)

2v+6=12v-24(move terms)

2v-12v=-24-6(collect like terms)

-10v=-30(devide both sides by-10)

V=3

hi I hope this helps.

Answer:

Future value = $755.61 ( to the nearest cent)

Step-by-step explanation:

The formula for calculating the future value of an invested amount compounded periodically for a number of years is given as:

[tex]FV = PV (1+\frac{r}{n} )^{n*t}[/tex]

where:

FV = future value = ???

PV = present value = $575

r = interest rate in decimal = 5.5% = 0.055

n = number of compounding periods per year = quarterly = 4

t = time of investment = 5 years

∴ [tex]FV = 575 (1+\frac{0.055}{4} )^{4*5}[/tex]

[tex]FV = 575 (1+0.01375)^{20}\\FV = 575 (1.01375 )^{20}\\FV = 575 * 1.3141\\FV = 755.607[/tex]

∴ Future value = $755.61 ( to the nearest cent)

Answer:

This is the answer EDGE 2020