The length of a rectangle is twice its width. If the perimeter of the rectangle is 30m, find its area.

Complete question is;

A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:

Do the results support the manufacturer's claim?

Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed

Answer:

We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

Step-by-step explanation:

For the first sample, we have;

Mean; x'1 = 1160 ft

standard deviation; σ1 = 32 feet

Sample size; n1 = 19

For the second sample, we have;

Mean; x'2 = 1130 ft

Standard deviation; σ2 = 30 ft

Sample size; n2 = 11

The hypotheses are;

Null Hypothesis; H0; μ1 = μ2

Alternative hypothesis; Ha; μ1 > μ2

The test statistic formula for this is;

z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]

Plugging in the relevant values, we have;

z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]

z = 2.58

From the z-table attached, we have a p-value = 0.99506

This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.

Answer:

a. 539.54

b. No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.

c. 540

d. 25.54%

Step-by-step explanation:

Given that:

A polling company reported that 53​% of 1018 surveyed adults said that secondhand smoke is "very harmful."

Complete parts​ (a) through​ (d) below.

a. What is the exact value that is 53​% of 1018​?

The 53% of 1018 is :

=[tex]\dfrac{53}{100} \times 1018[/tex]

= 0.53 × 1018

= 539.54

b. Could the result from part​ (a) be the actual number of adults who said that secondhand smoke is ''very harmful"? Why or why​ not?

No, the result from part (a) could not be the actual number of adult who said that secondhand smoke are very harmful because a count of people must result into a whole number.

c. What could be the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful"?

Since, a count of people must result into a whole number, the actual number of adults who said that secondhand smoke is secondhand smoke "very harmful" can be determined from the approximation of the exact value into whole number which is 539.54 [tex]\approx[/tex] 540.

d. Among the 1018 ​respondents, 260 said that secondhand smoke is  is "not at all harmful.''  What percentage of respondents said that secondhand smoke is  "not at all harmful"?

Since 260 respondents out of 1018 respondents said that the second hand smoke is not harmful, then the percentage of the 260 respondents is :

= [tex]\dfrac{260}{1018} \times 100 \%[/tex]

= 25.54%

Answer:

0.05m^2

Step-by-step explanation:

5 divided by 100

Answer:

3.25 + 5.50S ≤ 30

Step-by-step explanation:

Given:

Chocolate milk cost $3.25.

Maximum bill that Benjamin wants = $30

Cost of a stack pancake(44) = $5.50

Let number of stacks of pancakes bought = S

Benjamin will spend all the money available on 1 chocolate milk and S number of stacks of pancakes.

Cost of 1 pancake = $5.50

Cost of S number of stacks of pancakes = S*5.50

=5.50S

Total money spent =$3.25+5.50S

The total money spent should either be lesser than or equal to $30

The inequality is

3.25 + 5.50S ≤ 30

Largest number of pancakes Benjamin can afford

3.25 + 5.50S ≤ 30

5.50S ≤ 30-3.25

5.50S ≤ 26.75

Divide both sides by 5.50

S ≤ 4.86

1 stack=44 pancakes

4.86 stacks= 4.86 *44

=213.84 pancakes

Answer:

3.25+5.50S≤30

and 16 pancakes

Step-by-step explanation:

Answer:

Yes you can

Step-by-step explanation:

To eliminate the denominator

Answer:

No

Step-by-step explanation:

We cannot be certain that x + 3 > 0

If it was negative then the sign of the inequality would change.

To solve find the critical values of the numerator/ denominator, that is

x = 2 and x = - 3

The domain is the split into 3 intervals

(- ∞, - 3 ), (- 3, 2), (2, + ∞ )

Use test points from each interval to determine valid solution

Answer:

The angle of elevation is not properly represented

Step-by-step explanation:

Given

The question in the attachment;

Required

Determine the error

See attachment for proper representation of the angle of elevation;

Solving further (From the Attachment)

[tex]Tan22 = \frac{x}{3000}[/tex]

Multiply both sides by 3000

[tex]x = 3000 * tan22[/tex]

[tex]x = 3000 * 0.4040[/tex]

[tex]x = 1212[/tex]

The cliff is about 1212 feet high

Answer:

hello attached is the missing part of your question and the answer of the question asked

answer : 0.2951

Step-by-step explanation:

Given data:

number of persons allowed in the elevator = 15

weight limit of elevator = 2500 pounds

average weight of individuals = 152 pounds

standard deviation = 26 pounds

probability that an individual selected weighs more than 166 pounds

std = 26 ,  number of persons(x) = 15, average weight of individuals(u) = 152 pounds

p( x > 166 ) = p( x-u / std,  166 - u/ std )

                  = p (  z > [tex]\frac{166-152}{26}[/tex] )

                  = 1 - p( z < 0.5385 )

p( x > 166 ) = 1 - 0.70488 = 0.2951

Answer:

Population parameters

Step-by-step explanation:

Population parameters usually find from the average values, ​​in a simple way we can say that finding the average value comes in the Population Parameters.

In the given question, car manufacturing companies provide sample of average.

So, given scenario is a type of "Population parameters".

Answer:

ray is the answer for this

opposite rays form a line because they provide the two opposite directions in which the line extends infinitely.

Opposite rays are two rays that have the same endpoint but extend in opposite directions. When these opposite rays are extended infinitely in both directions, they form a straight line. A line is a set of points that extends infinitely in both directions, and opposite rays provide the two distinct directions in which the line can be extended.

The concept of opposite rays is derived from the concept of a line. A line can be defined as a straight path that extends infinitely in both directions. Opposite rays are a pair of rays that share a common endpoint and extend infinitely in opposite directions along this line.

For example, consider a line segment AB. If we extend one side of the line segment from point A and the other side from point B, we obtain two opposite rays: one from point A to infinity and the other from point B to infinity. Together, these opposite rays form the line on which the line segment AB lies.

Learn more about lines at:

https://brainly.com/question/24607467

#SPJ6

Answer:

240 candidates

Step-by-step explanation:

40% candidates failed, i. e. out of every 100 candidates 40 failed.

40 failed ----------------------------- 100 total students

1 failed --------------------------------100/40 total students, given 160 failed therefore

160 failed ----------------------------(100/40) x 160 total students

Total students = (100/40) x 160 = 400

Number of candidates passed = (total candidates) - (total candidates failed)

                                                   = 400 - 160 = 240 candidates

Answer:

[tex]\bold{\dfrac{11}{16}}[/tex]

Step-by-step explanation:

Given four tiles with numbers:

1, 4, 5 and 8

Tile chosen once and then replaced, after that another tile chosen:

All possibilities are:

{(1, 1) ,(1, 4) ,(1, 5) ,(1, 8)

(4, 1) ,(4, 4) ,(4, 5) ,(4, 8)

(5, 1) ,(5, 4) ,(5, 5) ,(5, 8)

(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }

Total number of possibilities = 16

When the sum is greater than 7, the possibilities are:

{(1, 8)

(4, 4) ,(4, 5) ,(4, 8)

(5, 4) ,(5, 5) ,(5, 8)

(8, 1) ,(8, 4) ,(8, 5) ,(8, 8) }

Number of favorable cases = 11

Formula for probability of an event E is:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Hence, the required probability is:

[tex]\Rightarrow \bold{\dfrac{11}{16}}[/tex]

Answer:11/16

Step-by-step explanation:i took the test

Answer:

[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]

Step-by-step explanation:

18d + 12

The greatest common factor is 6, So we need to factor out 6

=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]

Answer:

6(3d+2)

Step-by-step explanation:

6 is the gcd of the two terms.

Answer:

35 or 25

Step-by-step explanation:

Answer:

[tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex] converges.

Step-by-step explanation:

The convergence analysis of this sequence is done by Ratio Test. That is to say:

[tex]r = \frac{a_{n+1}}{a_{n}}[/tex], where sequence converges if and only if [tex]|r| < 1[/tex].

Let be [tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex], the ratio for the expression is:

[tex]r =-\frac{3}{n+1}[/tex]

[tex]|r| = \frac{3}{n+1}[/tex]

Inasmuch [tex]n[/tex] becomes bigger, then [tex]r \longrightarrow 0[/tex]. Hence, [tex]a_{i} = \frac{(-3)^{i}}{4\cdot i!}[/tex] converges.

Answer:

Step-by-step explanation:

Answer:

[tex]\huge\boxed{r<8}[/tex]

Step-by-step explanation:

[tex]5 > r - 3[/tex]

Adding 3 to both sides

[tex]5 + 3 > r[/tex]

[tex]8 > r\\OR \\r < 8[/tex]

Answer: D. r<8

Step-by-step explanation:

[tex]5>r-3[/tex]

add 3 to both sides

[tex]r-3+3<5+3[/tex]

[tex]5+3=8[/tex]

simplify

[tex]r<8[/tex]

Answer:

The 95% confidence interval is  [tex]0.3795 < p < 0.4405[/tex]

Step-by-step explanation:

From the question we are told that

     The sample size is  [tex]n = 1000[/tex]

      The  number of approved loan is  k =  410

Generally the sample proportion is mathematically represented as

       [tex]\r p = \frac{k}{n}[/tex]

substituting values

      [tex]\r p = \frac{410}{1000}[/tex]

       [tex]\r p = 0.41[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

       [tex]\alpha = 100 - 95[/tex]

        [tex]\alpha = 5\%[/tex]

       [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is  

         [tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p(1- \r p)}{n} }[/tex]

substituting values

        [tex]E = 1.96 * \sqrt{\frac{ 0.41(1- 0.41)}{1000} }[/tex]

        [tex]E = 0.03048[/tex]

The 95% confidence interval for p is mathematically represented  as

     [tex]\r p - E < p < \r p + E[/tex]

substituting values

     [tex]0.41 - 0.03048 < p < 0.41 + 0.03048[/tex]

    [tex]0.3795 < p < 0.4405[/tex]

Answer:

There are 24 avocados in each crate.

Step-by-step explanation:

This is a division problem.

8640/360 = 24

There are 24 avocados in each crate.

Answer:

reject null hypothesis if calculated t value > 2.624

Step-by-step explanation:

n = 15

To calculate degree of freedom, n -1 = 14

The claim says ud>0

The decision rule would be to reject this null hypothesis if the test statistics turns out to be greater than the critical value.

With df =14

Confidence level = 0.01

Critical value = 2.624 (for a one tailed test)

If the t value calculated is > 2.624, we reject null hypothesis.

Using the t-distribution and it's critical values, the decision rule is:

At the null hypothesis, we test if the mean is not greater than 0, that is:

[tex]H_0: \mu \leq 0[/tex]

At the alternative hypothesis, we test if the mean is greater than 0, that is:

[tex]H_1: \mu > 0[/tex].

We then have to find the critical value for a right-tailed test(test if the mean is more than a value), with 15 - 1 = 14 df and a significance level of 0.01. Using a t-distribution calculator, it is [tex]t^{\ast} = 2.624[/tex].

Hence, the decision rule is, according to the test statistic t:

A similar problem is given at https://brainly.com/question/13949450

Answer:

9x -9

9(x - 1)

4(3x-3) - 3x + 3

Step-by-step explanation:

4(2x + x-3) - 3x + 3

Combine like terms

4(3x-3) - 3x + 3

Distribute

12x -12 -3x+3

Combine like terms

9x -9

Factor out 9

9(x-1)

Answer:

9

18

Step-by-step explanation:

x = 2:

4(4 + 2 - 3) - 6 + 3 = 12 - 6 + 3 = 9

x = 3:

4(6 + 3 - 3) - 9 + 3 = 24 - 9 + 3 = 18

Answer:

Option (D)

Step-by-step explanation:

By applying Sine rule in the right ΔABD,

Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

Sin(60)° = [tex]\frac{\text{BD}}{\text{AB}}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{\text{BD}}{7\sqrt{3}}[/tex]

BD = [tex]7\sqrt{3}\times \frac{\sqrt{3} }{2}[/tex]

     = [tex]\frac{21}{2}[/tex]

Now by applying Cosine rule in the right ΔBDC,

Cos(45)° = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]\frac{1}{\sqrt{2}}=\frac{\frac{21}{2}}{x}[/tex]

x = [tex]\frac{21}{2}\times \sqrt{2}[/tex]

x = [tex]\frac{21\sqrt{2}}{2}[/tex]

Therefore, Option (D) is the correct option.

Answer:

$34000

Step-by-step explanation:

We can set up a systems of equations, assuming [tex]h[/tex] is the husbands income and [tex]w[/tex] is the wife's income.

h + w = 84000

h = 2w - 18000

We can substitute h into the equation as 2w - 18000:

(2w - 18000) + w = 84000

Combine like terms:

3w - 18000 = 84000

Add 18000 to both sides

3w = 102000

And divide both sides by 3

w = 34000

Now that we know how much the wife earns, we can also find out how much the husband earns by substituting into the equation.

h + 34000  = 84000

h = 50000

Hope this helped!

Answer:

That's your answer

x= 125

3x= 375

2x-1= 249

Answer:

The sample size is 50 and population proportion under null hypothesis is 25%  ( A )   meets the requirement

Step-by-step explanation:

when applying the central limit theorem on sample proportions in one sample proportion test .The conditions needed to be satisfied are np > 10, and   n( 1-p ) > 10

A)  sample size ( n ) = 50

population proportion = 25%

np = 50 * 0.25 = 12.5 which is > 10 ( 1st condition met )

n( 1 - p ) = 50( 1 - 0.25 ) = 37.5 which is > 10 ( second condition met )

B ) sample size (n) = 70

population proportion = 90%

np = 70*0.9 = 63 which is > 10 ( 1st condition met )

n(1-p) = 70 ( 1 - 0.9 ) = 7 which is < 10 ( second condition not met )

C) sample size ( n ) = 50

population proportion = 15% = 0.15

np = 50 * 0.15 = 7.5 which is < 10 ( 1st condition not met )

n ( 1 - p ) = 50 ( 1 - 0.15 ) = 50 * 0.85 = 42.5 which is > 10 ( second condition met )

D) sample size ( n ) = 200

population proportion = 4% = 0.04

np = 200 * 0.04 = 8 which is < 10 ( 1st condition not met )

n ( 1 - p ) = 200 ( 1 - 0.04 ) = 192 which is > 10 ( second condition met )

hence : The sample size of 50 with population proportion under null hypothesis of 25%  meets the requirement

Answer: b. False

Step-by-step explanation:

Hence, the given statement is absolutely false.

Answer:

40.5

Step-by-step explanation:

diameter^2 = (3 +6)^2 + (5+4)^2

or, d^2 = 9^2 + 9^2

or, d^2 = 81 +81

or,d^2 =162

or d=√ 162

• d= 81

then radius = d/2

r = 81/2

•r= 40.5 ans

Answer: 247.92 euros

Step-by-step explanation:

Given, Varia is required pay $3,500 (in US dollars) per year to the university.

If she must pay in euros , then we convert $3,500 into euros.

Current rate : 1 US dollar = 0.85 euro

Then,  $3,500 = ( 0.85 x 3500) euros

= 2975 euros

She can expect 2975 euros to pay per year.

Also, [tex]2975\div 12\approx247.92[/tex]   [ 1 years = 12 months]

Hence, She can expect 247.92 euros to pay per month to the university.

Answer:

It is not symmetric, but skewed left. Data appears more to be on the left side.

Step-by-step explanation:

The smallest value is 24 and the largest is 43 . The difference between these two values is 19 which can be divided into into intervals of 4.

19/4= 4.75 It will be rounded to 5.

The class interval can of 5. Starting from 20 we get class intervals and frequency distribution as

Class Intervals          Data                                        Frequency      

20-24                           24                                              1

25- 29                           28,                                            1

30-34                            34,30,34,30,33,31,                   6

35-39                         35,36,39,37,35,36,39,37,           14

                                         38,39,35,35,36,36

40-44                                43,40,41                                3

The class intervals are inclusive of both upper and lower limits. The difference between the lower limits of two consecutive classes or upper limits of two consecutive classes must be the same.

As we see the difference here is that of 5 between the two upper or lower limits of consecutive classes.

The histogram is attached which shows the class intervals along x- axis and data frequency along y- axis.

Errors:   Both of your upper bounds are wrong

               You subtracted the upper bound from the upper bound

Step-by-step explanation:

605 kg to the nearest 5 kg

lower bound is 602.5 (because it rounds up to 605)

upper bound is 607.4 (because it rounds down to 605)

Note: 607.5 would round up to 610

78 kg rounded to the nearest 1 kg

lower bound is 77.5 (because it rounds up to 78)

upper bound is 78.4 (because it rounds down to 78)

Note: 78.5 would round up to 79

Upper Bound - Lower bound is the maximum weight remaining on the elevator

607.4 - 77.5 = 529.9

529.9 ≤ 530 so YES the elevator is safe.

Answer:

C

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

Here r = 18 cm , thus

A = π × 18² = 324π ≈ 1017.9 cm² → C

Answer:

C.) 1017.9 cm²

Step-by-step explanation:

For a given circle

radius (r) = 18 cm

Now,

Area of Circle

= πr²

= 3.14 × (18)² cm

= 3.14 × 324 cm

= 1017.9 cm²