prove that if f is a continuous and positive function on [0,1], there exists δ > 0 such that f(x) > δ for any x E [0,1] g

Answer:

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]

Step-by-step explanation:

Given

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100})[/tex]

Required

Simplify

For clarity, group the expression in threes

[tex]((\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the first group [Divide 8 by 4]

[tex]((\frac{3}{1})*(\frac{2}{9})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 9 by 3]

[tex]((\frac{1}{1})*(\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex]((\frac{2}{3})*(\frac{15}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 15 by 3]

[tex]((\frac{2}{1})*(\frac{5}{16}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 16 by 2]

[tex]((\frac{1}{1})*(\frac{5}{8}))*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{5}{8})*((\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the second group [Divide 35 and 25 by 5]

[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{7}{36})*(\frac{48}{49}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 49 by 7]

[tex](\frac{5}{8})*((\frac{24}{5})*(\frac{1}{3})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[Divide 24 by 3]

[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{1}{1})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{5}{8})*((\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Merge the first and second group

[tex]((\frac{5}{8})*(\frac{8}{5})*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](1*(\frac{4}{7}))*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}))[/tex]

Evaluate the last group [Divide 99 by 9]

[tex](\frac{4}{7})*((\frac{63}{64})*(\frac{80}{9})*(\frac{11}{100}))[/tex]

[Divide 63 by 9]

[tex](\frac{4}{7})*((\frac{7}{64})*(\frac{80}{1})*(\frac{11}{100}))[/tex]

[Divide 64 and 80 by 8]

[tex](\frac{4}{7})*((\frac{7}{8})*(\frac{10}{1})*(\frac{11}{100}))[/tex]

[Divide 10 and 4 by 2]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{5}{1})*(\frac{11}{100}))[/tex]

[Divide 100 by 5]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{1}{1})*(\frac{11}{20}))[/tex]

[tex](\frac{4}{7})*((\frac{7}{4})*(\frac{11}{20}))[/tex]

[tex](\frac{4}{7})*(\frac{7}{4})*(\frac{11}{20})[/tex]

[tex]1*(\frac{11}{20})[/tex]

[tex]\frac{11}{20}[/tex]

Hence;

[tex](\frac{3}{4})*(\frac{8}{9})*(\frac{15}{16})*(\frac{24}{25})*(\frac{35}{36})*(\frac{48}{49})*(\frac{63}{64})*(\frac{80}{81})*(\frac{99}{100}) = \frac{11}{20}[/tex]

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

= x/2-3 + 4x²+x+4

= ..........

Answer:

30 cm

Step-by-step explanation:

let x be the lenght of the two sides of equal lenghts, so the other is x+3

and the perimeter is x+x +x +3

P=3x+3

P=3(x+1)

93=3(x+1)

31=x+1

x=30

so the shorter sides are of 30 centimeters and the longest is 33

Answer: 22,103

Step-by-step explanation:

Compound interest is the interest calculated on the initial principal and the accumulated interest.

The amount in the account at the end of two years is $22,050.

Compound interest is the interest calculated on the initial principal and the accumulated interest.

We have,

Principal = $20,000

Rate = r = 5%

It is compounded yearly.

Time = t = 2 years.

The formula for the amount having compound interest:

A = P [tex]( 1 + \frac{r}{n} )^{nt}[/tex]

A = 20,000 [tex](1 + \frac{5}{100\times1})^{2\times1}[/tex]

A = 20,000 ( 1 + 5/100 )²

A = 20,000 ( 105/100 )²

A = (20,000 x 105 x 105) / (100 x 100)

A = 2 x 105 x 105

A = $22,050

Thus the amount in the account at the end of two years is $22,050.

Learn more about compound interest here:

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Answer:

Step-by-step explanation:

To find the approximate value of y when

x = 13 and z = 195 we must first find the relationship between them

The statement

y varies jointly with x and z is written as

where k is the constant of proportionality

From the question

y = 2

x = 11

z = 110

We have

2 = 11(110)k

2 = 1210k

Divide both sides by 1210

[tex]k = \frac{1}{605} [/tex]

So the formula for the variation is

[tex]y = \frac{1}{605} xz[/tex]

When

x = 13

z = 195

y is

[tex]y = \frac{1}{605} (13)(195)[/tex]

[tex]y = \frac{507}{121} [/tex]

y = 4.1900

We have the final answer as

Hope this helps you

Answer:

[tex]18\sqrt2[/tex]

Step-by-step explanation:

To simplify:

[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 }[/tex]

First of all, let us write 18 and 162 as product of prime factors:

[tex]18 = 2 \times \underline{3 \times 3}\\162 = 2 \times \underline{3 \times 3} \times \underline{3 \times 3}[/tex]

The pairs are underlined as above.

While taking roots, only one of the numbers from the pairs will be chosen.

Now, taking square roots.

[tex]\sqrt{18} =3 \sqrt2[/tex]

[tex]162 = 3 \times 3 \times \sqrt 2 = 9 \sqrt2[/tex]

So, the given expression becomes:

[tex]2 \sqrt{18}+ 3 \sqrt2+ \sqrt{162 } = 2 \times 3\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow 6\sqrt2 + 3\sqrt2 +9\sqrt2\\\Rightarrow \sqrt2(6+3+9)\\\Rightarrow \bold{18\sqrt2}[/tex]

So, the answer is:

[tex]18\sqrt2[/tex] or 18 StartRoot 2 EndRoot

Answer:

its B. 18 sqrt(2)

Step-by-step explanation:

just took test

[tex](f\circ g)(2)=\dfrac{1}{4\cdot2+9}=\dfrac{1}{17}\\\\(f+g)(2)=\dfrac{1}{2}+4\cdot2+9=\dfrac{1}{2}+17=\dfrac{1}{2}+\dfrac{34}{2}=\dfrac{35}{2}[/tex]

Answer:

[tex]x > -1[/tex] or

[tex]x > 2[/tex] or

[tex]x > 3[/tex]

Step-by-step explanation:

Given

[tex](x + 1)(x - 2) (x - 3) > 0[/tex]

Required

Solve; with steps

[tex](x + 1)(x - 2) (x - 3) > 0[/tex]

Start by splitting the inequality as follows

[tex]x + 1 > 0[/tex] or [tex]x - 2 > 0[/tex] or  [tex]x - 3 > 0[/tex]

Solve the inequalities one after the other

Solving: [tex]x + 1 > 0[/tex]

Subtract 1 from both sides

[tex]x + 1 - 1 > 0 - 1[/tex]

[tex]x > -1[/tex]

Solving: [tex]x - 2 > 0[/tex]

Add 2 to both sides

[tex]x - 2 +2 > 0 +2[/tex]

[tex]x > 2[/tex]

Solving: [tex]x - 3 > 0[/tex]

Add 3 to both sides

[tex]x - 3 +3> 0+3[/tex]

[tex]x > 3[/tex]

Hence, the solution to the inequality is

[tex]x > -1[/tex] or

[tex]x > 2[/tex] or

[tex]x > 3[/tex]

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = expected outcome of event /total outcome

Since the population consists of 100 elements, the total outcome of event = 100.

If random sample of 20 element is drawn from the population, the expected outcome = 20

On the first selection, the probability of any particular element being selected = 20/100 = 1/5

Answer:

The 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Step-by-step explanation:

The complete question is:

Salaries of 42 college graduates who took a statistics course in college have a​ mean, [tex]\bar x[/tex] of, $64, 100. Assuming a standard​ deviation, σ of ​$10​,016 construct a ​99% confidence interval for estimating the population mean μ.

Solution:

The (1 - α)% confidence interval for estimating the population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

The critical value of z for 99% confidence interval is:

[tex]z_{\alpha/2}=z_{0.01/2}=z_{0.005}=2.57[/tex]

Compute the 99% confidence interval for estimating the population mean μ as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=64100\pm 2.58\times\frac{10016}{\sqrt{42}}\\\\=64100+3987.3961\\\\=(60112.6039, 68087.3961)\\\\\approx (60112.60, 68087.40)[/tex]

Thus, the 99% confidence interval for estimating the population mean μ is ($60,112.60, $68087.40).

Answer:

I noticed that to babysit my cousin was the chore that doled out the most, and I wonder why pet my dog is even a chore. Do they not love their pets?

Answer:

X is uniformly distributed.

Step-by-step explanation:

Uniform Distribution:

This is the type of distribution where all outcome of a certain event have equal likeliness of occurrence.

Example of Uniform Distribution is - tossing a coin. The probability of getting a head is the same as the probability of getting a tail. The have equal likeliness of occurrence.

Answer:

A. 10%

B. Lower limit= 21

Upper limit = 39

Step-by-step explanation:

Mean = 30

SD = 3

a. COV = SD/|x| × 100

= 3/30 × 100

= 10%

= 0.1

B. For 88.9 chevbychev interval:

= (1 - 1/K²) = 0.889

= 1/K² = 1 - 0.889

= 1/K² = 0.111

= K² = 1/0.111

= K² = 9

= K = √9

K = 3

Lower limit = 30 - 3(3)

Lower limit = 21

Upper limit = 30 + 3(3)

Upper limit = 39

Therefore lower limit is 21 and upper limit is 39

Answer:

9  3  -7  -13

4  -4  11  8

0  9  2  -4

Step-by-step explanation:

9  3  -7  -13

4  -4  11  8

0  9  2  -4

Answer: 9  3  -7  -13

4  -4  11  8

0  9  2  -4

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) Putting 6 into the first (left) machine will give an output of ...

  y = √(6 -5) = √1 = 1

Putting 1 into the second (right) machine will give an output of ...

  y = 1² -6 = -5

This answers the second question, but not the first question.

__

If we put 6 into the right machine first, we get an output of ...

  y = 6² -6 = 30

Putting 30 into the left machine, we get an output of ...

  y = √(30 -5) = √25 = 5 . . . . . the desired output.

The input must go into the right machine first, then its output goes into the left machine to get a final output of 5 from an input of 6.

__

b) The left machine cannot produce negative outputs, so achieving an output of -5 with the arrangement used in part A is not possible. (green curves in the attached graph)

However, as we have shown above, inputting 6 to the left machine first, following that by processing with the right machine, can produce an output of -5. (purple curve in the attached graph)

Answer:

1. cups of coffee sold

2.Y = 605.7 - 5.943x

3. -0.952

4. 70.84

Step-by-step explanation:

1. the dependent variable in this question is the cups of coffee sold

2. least square estimation line

Y = a+bx

we have y as the cups of coffee sold

x as temperature.

first we will have to solve for a and then b

∑X = 450

∑Y = 960

∑XY = 61600

∑X² = 35500

∑Y² = 221800

a = ∑y∑x²-∑x∑xy/n∑x²-(∑x)²

a = 960 * 35500-450*61600/6*35500-450²

a = 6360000/10500

= 605.7

b = n∑xy - ∑x∑y/n∑x²-(∑x)²

= 6*61600 - 450*960/6*35500 - 450²

= -5.943

the regression line

Y = a + bx

Y = 605.7 - 5.943x

3. we are to find correlation coefficient

r = n∑xy - ∑x∑y multiplied by√(n∑x²-(∑x)² * (n∑y² - (∑y)²)

= 6*61600 -960*450/√(6*35500 - 450²)*(6*221800 - 960²)

=-62400/√4296600000

= -62400/65548.5

= -0.952

4. we have to predict sales of a 90 degree day fro the regression line

Y = 605.7 - 5.943x

y = 605.7 - 5.943(90)

y = 605.7 - 534.87

= 70.84

Answer:

16.50

Step-by-step explanation:

Constant of proportionality = no of gallons of water per 1 minute.

In the first row, we have 16.50 gallons of water per 1 minute.

In the 2nd row, we have 24.75 gallons of water in 1.5 minutes. In 1 minute, we will have 24.75 ÷ 1.5 = 16.50 gallons

In the 3rd row, we have 33 gallons in 2 minutes. In 1 minute, we will have 33 ÷ 2 = 16.50 gallons.

We can see that there seems to be the same constant of proportionality for the 2nd and 3rd row, which is 16.50.

Thus, a relationship between gallons of water (w) and time (t), considering the constant, 16.50, can be written as: [tex] w = 16.50t [/tex]

This means the constant of proportionality, 16.50, is same for all rows.

Answer:

box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35

Step-by-step explanation:

The scores of the students represented on the dot plot are:

1 dot => 24

3 dots => 26, 26, 26

3 dots => 27, 27, 27

5 dots => 28, 28, 28, 28, 28

3 dots => 30, 30, 30

3 dots => 32, 32, 32

1 dot => 35

Quickly, we can ascertain 3 values from these data points of which we can use to find out which box plot represents the dot plot data.

The minimum score = 24

The maximum score = 35

The median score is the 10th value, which is the middle value of the data point = 28

Therefore, we can conclude that: "box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35".

Answer:

(a). x = 80°

(b). x = 7.2 units

Step-by-step explanation:

Angle formed between the tangents from a point outside the circle measure the half of the difference of intercepted arcs.

(a). Here the intercepted arcs are,

    Measure of major arc = 360° - 100°

                                        = 260°

    Measure of minor arc = 100°

   x° = [tex]\frac{1}{2}[m(\text{Major arc})-m(\text{Minor arc})][/tex]

       = [tex]\frac{1}{2}(260-100)[/tex]

    x = 80°

(b). If a secant and tangent are drawn form a point outside the circle, then square of the measure of tangent is equal to the product of the measures of the secant segment and and its external segment.

x² = 4(4 + 9)

x² = 4 × 13

x² = 52

x = √52

x = 7.211 ≈ 7.2 units

Answer:

Below

Step-by-step explanation:

● 8 ÷ (3-x)

Dividing by 3-x is like multiplying by 1/(3-x)

● 8 × (1/3-x)

● 8 /(3-x)

Answer:

300.05 miles

Step-by-step explanation:

initial fee= $39.99

final bill = $ 100

cost =$ 0.20 per mile

remaining amount = $ 60.01

solution,

she drive = remaining amount / cost

=60.01/0.20

=300.05 miles

Answer:

500 miles

Step-by-step explanation:

Let us use cross multiplication to find the unknown amount.

Given:

1) Cost for 1 mile=$0.20

2)Cost for x miles=$100

Solution:

No of miles                             Cost

1) 1                                             $0.20

2)x                                             $100

By cross multiplying,

100 x 1= 0.20x

x=100/0.20

x=500 miles

Thank you!

Answer:

less than

Step-by-step explanation:

If the normality requirement is not satisfied​ (that is, ​np(1​ - p) is not at least​ 10), then a​ 95% confidence interval about the population proportion will include the population proportion in​ _less than__ 95% of the intervals.

The confidence interval consist of all reasonable values of a population mean. These are value for which the null hypothesis will not be rejected.

So, let assume that If the 95%  confidence interval contains the value for the hypothesized mean, then the sample mean  is reasonably close to the hypothesized mean. The effect of this is that the p- value is going to be greater than 0.05, so we fail to reject the null hypothesis.

On the other hand,

If the 95%  confidence interval do not contains the value for the hypothesized mean, then the sample mean  is far away from the hypothesized mean. The effect of this is that the p- value is going to be lesser than 0.05, so we reject the null hypothesis.

Complete Question

A research center claims that ​30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that​ country, ​34% say that they would travel into space on a commercial flight if they could afford it. At ​, is there enough evidence to reject the research center's claim

Answer:

Yes there is  sufficient evidence to reject the research center's claim.

Step-by-step explanation:

From the question we are told that

     The population proportion is  p = 0.30

      The sample proportion is  [tex]\r p = 0.34[/tex]

       The  sample size is  n = 700

The null hypothesis is  [tex]H_o : p = 0.30[/tex]

 The  alternative hypothesis is  [tex]H_a : p \ne 0.30[/tex]

Here we are going to be making use of  level of significance  =  0.05 to carry out this test

Now we will obtain the critical value of  [tex]Z_{\alpha }[/tex] from the normal distribution table , the value is  [tex]Z_{\alpha } = 1.645[/tex]

 Generally the test statistics is mathematically represented as

            [tex]t = \frac{ \r p - p }{ \sqrt{ \frac{ p (1-p)}{n} } }[/tex]

substituting values

              [tex]t = \frac{ 0.34 - 0.30 }{ \sqrt{ \frac{ 0.30 (1-0.30 )}{ 700} } }[/tex]

              [tex]t = 2.31[/tex]

Looking at the values of t  and  [tex]Z_{\alpha }[/tex] we see that [tex]t > Z_{\alpha }[/tex] hence the null hypothesis is rejected

 Thus we can conclude that there is  sufficient evidence to reject the research center's claim.

Answer:

6.25

Step-by-step explanation:

2.5 *2.5=6.25

Answer:

6.25cm^2.

Step-by-step explanation:

To find the area of a square, you multiply the two sides, 2.5✖️2.5.

This gives the area of 6.25cm^2.

Hope this helped!

Have a nice day:)

Answer:

Step-by-step explanation:

[tex]-3\left(x+1\right)=-3\left(x+1\right)-5\\\\\mathrm{Add\:}3\left(x+1\right)\mathrm{\:to\:both\:sides}\\\\-3\left(x+1\right)+3\left(x+1\right)=-3\left(x+1\right)-5+3\left(x+1\right)\\\\\mathrm{Simplify}\\\\0=-5\\\\\mathrm{The\:sides\:are\:not\:equal}\\\\\mathrm{No\:Solution}[/tex]

Answer:

40 minutes

Step-by-step explanation:

If it takes her 8 minutes to mow 1/6 of it, we can find the total amount of time it  will take by multiplying 8 by 6, since 1/6 times 6 is 1 (1 represents the whole lawn mowed)

8(6) = 48

The question asks for how many more minutes it will take, so subtract 48 by 8.

48 - 8 = 40

= 40 minutes

Answer:

40 minutes

Step-by-step explanation:

We can use ratios to solve

8 minutes          x minutes

------------------- = ----------------

1/6 yard                 1 yard

Using cross products

8 * 1 = 1/6 x

Multiply each side by 6

8*6 = 1/6 * x * 6

48 = x

48 minutes total

She has already done 8 minutes

48-8 = 40 minutes

Answer:

Simple Interest : $ 4400

Step-by-step explanation:

We want to calculate the interest on $ 10,000, at 5.5% interest rate per year, over a course of 8 years.

We can use the simple interest formula here, or :

I = P × r × t,

Where P is the principle amount, $ 10,000, r is the interest rate, 5.5% each year, or in decimal form 5.5 / 100 = 0.055. t is the time, 8 years.

Simple Interest : 10000 × 0.055 × 8 =  $4400.00

Then again the interest can be added to the principal amount ( $10,000 ) to receive some new amount after 8 years, which is $ 14,000. However the simple interest earned in 8 years at a rate of 5.5% should be $4400.

The simple interest earned on the amount is $4,400

Interest is the total amount that would be paid or earned from making an investment or taking a loan over a period of time.

Simple Interest  = principal x time x interest rate

principal = amount borrowed = $10,000

time = 8 years

Interest rate = 5.5%

10,000 x 0.055 x 8 = $4,400

To learn more about simple interest, please check: https://brainly.com/question/9352088?referrer=searchResults

Answer:

[tex]\large \boxed{\sf No}[/tex]

Step-by-step explanation:

There are 365 days in 1 year.

The average person lives for about 78 years.

Multiply 78 by 365 to find the value in days.

[tex]78 \times 365= 28470[/tex]

The average person lives for about 28470 days.