Hector's school is holding a fitness challenge. Student are encouraged to exercise at least 2 1/2 hours per week. Hector exercises about the same number of hours each week. During a 4-week period, he exercises for 11 1/2 hours. Hector wants to compare his exercise rate with the fitness challenge rate. How many hours per week does Hector exercise?

Without resorting to L'Hopitâl's rule,

[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac{x-9}{(x-9)(x+9)}=\lim_{x\to9}\frac1{x+9}=\frac1{18}[/tex]

With the rule, we get the same result:

[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac1{2x}=\frac1{18}[/tex]

Answer:

c is the answer

Step-by-step explanation:

-3h = 31

-9h-12h = -3h

54-23= 31

Answer:

[tex]\boxed{C. -3h = 31}[/tex]

Step-by-step explanation:

Hey there!

9h - 12h = 54 - 23

Simplify

-3h = 31

C. -3h = 31

Hope this helps :)

Answer:

B: 54

Step-by-step explanation:

for the first digit: 1 or 3 (2 choices)

for the second digit: 0, 1, or 3 (3 choices)

for the third digit: 0, 1, or 3 (3 choices)

for the forth digit: 0, 1, or 3 (3 choices)

2×3×3×3=54

Answer:

B) 54

Step-by-step explanation:

There are 3 numbers, but in the fourth positon (tens of thousands) if i put the zero no give value, then, in this position only have 2 options:

2*3*3*3 = 54

Answer:

1. Make a list of activities and the number of students:

Watching TV: 32

Talking on the phone: 41

Video games: 24

Reading: 15

2. Then combine the data in a bar graph as shown in the picture

Answer:

a- tulsa to dallas to houston is 235+390 which is 625 miles

b - houston to dallas to tulsa is 390+235 miles which is 625 miles

c - by using reasoning both are same because they are just rewritten differently but the equation is same

please give me brainliest

hope it helps buddy

Answer:

1) The dependent variable is : time to complete the maze

2) The analysis used should be : One -way within-subjects ANOVA ( B )

3) Null hypothesis is ; There will be no difference between any group means

4) Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3

5) degree of freedom for the denominator = 11

6) critical F value = 3.49

Step-by-step explanation:

The dependent variable is the time to complete the maze this is because the time depends on the effects of the stimulant drugs on the rats in the maze .

The analysis used should be : One -way within-subjects ANOVA ( B )

Null hypothesis is ; There will be no difference between any group means

Degrees of freedom for the numerator of the F-ratio ; 4 - 1 = 3

degree of freedom for the denominator = N - k = 16 - 4 = 12. the closest answer from the options is 11

The critical value is 3.49 ,because at degree of freedom = 12 , ∝ = 0.05, and Dfn = 3, from the F -  table the critical value would be 3.49

Answer:

C. 78.5 in^3

Step-by-step explanation:

A soup can is in the shape of a cylinder. The volume of a cylinder can be found using the following formula:

[tex]v=\pi r^2h[/tex]

We know that the height is 4 inches and the radius is 2.5 inches.

r= 2.5 in

h= 4 in

[tex]v=\pi (2.5in)^2*4in[/tex]

Evaluate the exponent.

[tex](2.5 in)^2=2.5 in*2.5in=6.25 in^2[/tex]

[tex]v=\pi *6.25 in^2*4 in[/tex]

Multiply 6.25 in^2 and 4 in.

[tex]6.25 in^2*4 in=25 in^3[/tex]

[tex]v=\pi*25 in^3[/tex]

Multiply pi and 25 in^3.

[tex]v=78.5398163 in^3[/tex]

Round to the nearest tenth. The 3 in the hundredth place tells us to leave the 5 in the tenth place.

[tex]v=78.5 in^3[/tex]

78.5 cubic inches can fill one soup can.

Answer:

1. 5/4

2. 7

Step-by-step explanation:

1) Lets call the width as w

Therefore length would be:

w+4

To find the perimeter you use the formula:

2 (l+w)

Now substitute our values into this formula:

2 (w+4+w)

2( 2w+4)

4w+8

Now make this equal to 13:

4w +8 = 13

4w = 5

w = 5/4

2. In this question we will call length l

Therefore width would be:

l-5

Now we will do the steps we did above:

2 (l+l-5)

2 (2l-5)

4l -10

4l - 10 = 18

4l = 28

l = 7

Answer:

Step-by-step explanation:

[tex] \frac{x + 4}{3} = 2[/tex]

To solve it first of all cross multiply

That's

x + 4 = 6

Move 4 to the right side of the equation

The sign changes to negative

That's

x = 6 - 4

We have the final answer as

Hope this helps you

Answer:

46.2÷m=x

Step-by-step explanation:

u divide the amount of water by the time it takes to fill up(m). Witch will equal the amount per minute (x).

16.5/min

time = m

gallons / minutes = rate

46.2  = 16.5 (m)

46.2 / 16.5 = 16.5 (m) / 16.5

2.8 = minutes

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

Answer:

0

Step-by-step explanation:

0 because there is a $100 duty free exemption.

answer:

For this problem, use the tables and charts shown in this section.  

A United States Citizen returning to the States declares the following items at the customs office:

3 shirts at $8.50 each

2 dresses at $27.50 each

1 pair of gold cuff links at $17.50 per pair

If he has not used his duty free exemption yet, how much duty should he pay?

$0.00 !

$5.00

$10.00

$300

This question is incomplete, here is the complete question:

Specifications for a part for a DVD player state that the part should weigh between 25.2 and 26.2 ounces. The process that produces the parts has a mean of 25.7 ounces and a standard deviation of .25 ounce. The distribution of output is normal. Use Table-A

a) What percentage of parts will not meet the weight specs? (Round your "z" value and final answer to 2 decimal places.

b) Within what values will 95.44 percent of sample means of this process fall, if samples of n = 8 are taken and the process is in control (random)

Answer:

a) What percentage of parts will not meet the weight specs = 4.56%

b) values within which 95.44 percent of sample means of this process falls are;

UCL = 25.88 ounces

LCL = 25.52 ounces

Step-by-step explanation:

Given that;

Mean u = 25.7 ounces

Std deviation = 0.25 ounces

a)

Z-score (Upper) = (X- u) / s = (26.2 - 25.7) / 0.25 = 2

Z-score (Lower) = ( 25.2-25.7 ) / 0.25 = -2

using the T - table

For Z = 2.0

the area in the tail of the curve to the right of the mean (upper) = 0.4772

therefore;

Number of defective = 0.5000 - 0.4772 = 0.0228

These are errors on one side of normal distribution.

To get the total error, we say

Total error = 2 × 0.0228

Total error = 0.0456 ≈ 4.56% ( 2 decimal place )

b)

given that;

n = 8,

standard deviation = 0.25 ounce

Standard deviation of X = Std deviation / √n

= 0.25 /√8 = 0.088

Now for 95.44% of confidence interval, Z = 2

UCL = Mean + Z × Standard deviation of X

= 25.7 + 2 × 0.088

= 25.88 ounces

LCL = Mean - Z × Standard deviation of X

= 25.7 - 2 × 0.088

= 25.52 ounces

Step-by-step explanation:

Hey, there!!

Look this figure, simply we find that;

In triangle ABC,

angle CBD is an exterior angle of a triangle.

and its measure is 90°

Then,

angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.

or, 90°= y + 48°

Shifting, 48° in left side,

90°-48°= y

Therefore, the value of y is 42°.

Hope it helps...

Answer:

Percentage of home team supporters =65%

Percentage of visiting team supporters =35%

Step-by-step explanation:

Total attendees=2,000 people

Home team supporters=1,300

Visiting team supporters=700

What percentage of people attending supported the home team?

Percentage of people attending who supported the home team = home team supporters / total attendees × 100

=1,300/2,000 × 100

=0.65 × 100

=65%

Visiting team supporters = visiting team supporters / total attendees

× 100

=700/2000 × 100

=0.35 × 100

=35%

Alternatively,

Visiting team supporters = percentage of total attendees - percentage of home team supporters

=100% - 65%

=35%

Answer:  see proof below

Step-by-step explanation:

Use the Quotient rule for derivatives:

[tex]\text{If}\ y=\dfrac{a}{b}\quad \text{then}\ y'=\dfrac{a'b-ab'}{b^2}[/tex]

Given: [tex]y=\dfrac{2\sqrtx}{1-x}[/tex]

[tex]\sqrtx[/tex][tex]a=2\sqrt x\qquad \rightarrow \qquad a'=\dfrac{1}{\sqrt x}\\\\b=1-x\qquad \rightarrow \qquad b'=-1[/tex]        

[tex]y'=\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)}{(1-x)^2}\\\\\\.\quad =\dfrac{\dfrac{1-x}{\sqrt x}-(-2\sqrt x)\bigg(\dfrac{\sqrt x}{\sqrt x}\bigg)}{(1-x)^2}\\\\\\.\quad =\dfrac{1-x+2x}{\sqrt x(1-x)^2}\\\\\\.\quad =\dfrac{x+1}{\sqrt x(1-x)^2}[/tex]

LHS = RHS:  [tex]\dfrac{x+1}{\sqrt x(1-x)^2}=\dfrac{x+1}{\sqrt x(1-x)^2}\qquad \checkmark[/tex]

Answer:

7.15 miles

Step-by-step explanation:

4/5 of a mile is equivalent to .8 miles.

32.95

-25.8

7.15

Answer:

Step-by-step explanation:

39.95 - 25.80 = 7.15 miles

Solve

Let's solve your equation step-by-step.

9x−3−8x=7−x

Step 1: Simplify both sides of the equation.

9x−3−8x=7−x

9x+−3+−8x=7+−x

(9x+−8x)+(−3)=−x+7(Combine Like Terms)

x+−3=−x+7

x−3=−x+7

Step 2: Add x to both sides.

x−3+x=−x+7+x

2x−3=7

Step 3: Add 3 to both sides.

2x−3+3=7+3

2x=10

Step 4: Divide both sides by 2.

2x

2

=

10

2

x=5

Answer:

x=5

Answer:

Hope this is easier, good luck.

Answer:

a)2/7

b)1/2

c)9/14

d)6/7

Step-by-step explanation:

The jar contains 4 red marbles, numbered 1 to 4 which means

Red marbles = (R1) , (R2) , (R3) , (R4)

It also contains 10 blue marbles numbered 1 to 10 which means

Blue marbles = (B1) , (B2) , (B3) , (B4) , (B5) , (B6) , (B7) , (B8) , (B9) , (B10) .

We can calculate total marbles = 4red +10 blues

=14marbled

Therefore, total marbles= 14

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10) =7

Total number of Blue marbles = 10

Blue and even marbles = 5

(a) The marble is red

P(The marble is red)=total number of red marbles/Total number of marbles

=4/14

=2/7

(b) The marble is odd-numbered

Blue marbles with odd number= (B1) , (B3) , (B5) , (B7) , (B9) ,

Red marbles with odd number = (R1) , (R3)

Number of odd numbered =(5+2)=7

P(marble is odd-numbered )= Number of odd numbered/ Total number of marbles

P(marble is odd-numbered )=7/14

=1/2

(C) The marble is red or odd-numbered?

Total number of red marbles = 14

Number of red and odd marbles = 2

The marbles that has odd number = (R1) , (R3) ,(B1) , (B3) , (B5) , (B7) , (B9) =7

n(red or even )= n(red) + n(odd)- n(red and odd)

=4+7-2

=9

P(red or odd numbered)= (number of red or odd)/(total number of the marble)

= 9/14

(d) The marble is blue or even-numbered?

Number of Blue and even marbles = 5

Total number of Blue marbles = 10

Number of blue that are even= 5

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10)

=7

n(Blue or even )= n(Blue) + n(even)- n(Blue and even)

= 10+7-5 =12

Now , the probability the marble is blue or even numbered can be calculated as

P(blue or even numbered)= (number of Blue or even)/(total number of the marble)

= 12/14

= 6/7

Answer:

Step-by-step explanation:

x^2+20=4 first isolate the variable by subtracting 20 on both sides.

x^2=-16 again isolate the variable but this time you square root both sides.

[tex]\sqrt{x}^2[/tex]=[tex]\sqrt{-16[/tex] then simplify

x= ±4

Answer:

No, it's not enough

Step-by-step explanation:

Given

Tilling Dimension = 4m by 2m

Tile Dimension = 400mm by 400mm

Required

Determine the 45 tiles is enough

First;

The area of the tiling has to be calculated

[tex]Area = Length * Breadth[/tex]

[tex]Area = 4m * 2m[/tex]

[tex]Area = 8m^2[/tex]

Next, determine the area of the tile

[tex]Area = Length * Breadth[/tex]

[tex]Area = 400mm * 400mm[/tex]

Convert measurements to metres

[tex]Area = 0.4m* 04m[/tex]

[tex]Area = 0.16\ m^2[/tex]

Next, multiply the above area result by the number of files

[tex]Total = 0.16m^2 * 45[/tex]

[tex]Total = 7.2m^2[/tex]

Compare 7.2 to 8

Hence, we conclude that the 45 tiles of 400mm by 400 mm dimension is not enough to floor his bathroom

Answer:

$7,415.99

Step-by-step explanation:

Hello, please consider the following.

[tex]P\cdot (1+\dfrac{10.5\%\cdot 9}{12})=A = 8000 \\\\P = \dfrac{8000}{(1+\dfrac{31.5}{400})}=\dfrac{8000}{1.07875}\\\\=7415.990730...[/tex]

So it gives $7,415.99

Thank you.

Answer:

See below.

Step-by-step explanation:

It depends on the sentence or phrase. If the sentence includes an operation of numbers or something related to comparing numbers, then maybe it can be translated into symbols. If the sentence or phrase has nothing to do with quantities, or operations or comparison of quantities, then probably it can't.

Examples:

1) The boy went for a walk.

There's nothing to translate into symbols in this case.

2) I had $10 in my bank account, then I deposited n dollars. Now I have $30 in my account.

In this case, I can translate the sentence into an equation.

10 + n = 30

Answer:

The first table on the list:

x 1   2  3  4    5

y 5 10 15 20 25

Step-by-step explanation:

A linear equation is when the slope is the exact same between each point.  The way we find slope is by finding the change in "y" over the change in "x".

x-values: 1, 2/y-values: 5, 10---[tex]\frac{10-5}{2-1}[/tex]=5/1=5

x-values: 2, 3/y-values: 10, 15---[tex]\frac{15-10}{3-2}[/tex]=5/1=5

x-values: 3, 4/y-vaues: 15, 20---[tex]\frac{20-15}{4-3}[/tex]=5/1=5

x-values: 4, 5/y-values: 20, 25---[tex]\frac{25-20}{5-4}[/tex]=5/1=5

The slope for each change in points is 5, which means that this table represents a linear function.

The only table that represents a linear function is; Table 1

A linear function is one that has the same slope for every coordinate point.

Looking at the tables, the one with same slope for all points is table 1 and we will prove that as follows;

Slope = 5/1 = 5

Slope = 10/2 = 5

Slope = 15/3 = 5

Slope = 20/4 = 5

slope = 25/5 = 5

In conclusion, only table 1 represents a linear function.

Read more about Linear function at; https://brainly.com/question/15602982

Answer:

There is not sufficient sample evidence to support the claim that the population mean is not equal to 88.9.

Step-by-step explanation:

We are given the following hypothesis below;

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 88.9      {means that the population mean is equal to 88.9}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 88.9     {means that the population mean is different from 88.9}

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 = 81.3

             s = sample standard deviation = 13.4

            n = sample size = 7

So, the test statistics =  [tex]\frac{81.3-88.9}{\frac{13.4}{\sqrt{7} } }[/tex]   ~ [tex]t_6[/tex]

                                     =  -1.501

The value of t-test statistics is -1.501.

Also, the P-value of the test statistics is given by;

                    P-value = P([tex]t_6[/tex] < -1.501) = 0.094

Since the P-value of our test statistics is more than the level of significance as 0.094 > 0.01, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 88.9.

Answer:

Step-by-step explanation:

Perimeter of a rectangle = 2l + 2w

Area of a rectangle = l × w

where

l is the length

w is the width

From the question

The length of a rectangle six times its width which is written as

l = 6w

Area = 150cm²

Substitute these values into the formula for finding the area

That's

150 = 6w²

Divide both sides by 6

w² = 25

Find the square root of both sides

width = 5cm

Substitute this value into l = 6w

That's

l = 6(5)

length = 30cm

So the perimeter of the rectangle is

2(30) + 2(5)

= 60 + 10

Hope this helps you

Answer:

the interest is 195dollars

Answer:

0.4

Step-by-step explanation:

we are required to find the probability that the ring is within 12 meters from nthe car.

we start by defining a random variable x to be the distance from the car. the car is the starting point.

x follows a normal distribution (0,30)

[tex]f(x)=\frac{1}{30}[/tex]

[tex]0<x<30[/tex]

probabilty of x ≤ 12

= [tex]\int\limits^a_ b{\frac{1}{30} } \, dx[/tex]

a = 12

b = 0

[tex]\frac{1}{30} *(12-0)[/tex]

[tex]\frac{12}{30} = 0.4[/tex]

therefore 0.4 is the probability that the ring is within 12 feet of your car.

Answer:

The critical value for two tailed test at alpha=0.1 is ± 1.645

The calculated  z= 9.406

Step-by-step explanation:

Formulate the hypotheses as

H0: p1= p2 there is no difference between the population scrap rates between the old and new cutting methods

Ha : p1≠ p2

Choose the significance level ∝= 0.1

The critical value for two tailed test at alpha=0.1 is ± 1.645

The test statistic is

Z = [tex]\frac{p_1- p_2}\sqrt pq(\frac{1}{n_1} + \frac{1}{n_2})[/tex]

p1= scrap rate of old method = 62/200=0.31

p2= scrap rate of new method = 36/400= 0.09

p = an estimate of the common scrap rate on the assumption that the two rates are same.

p = n1p1+ n2p2/ n1 + n2

p =200 (0.31) + 400 (0.09) / 600

p= 62+ 36/600= 98/600 =0.1633

now q = 1-p= 1- 0.1633= 0.8367

Thus

z= 0.31- 0.09/ √0.1633*0.8367( 1/200 + 1/400)

z= 0.301/√ 0.13663( 3/400)

z= 0.301/0.0320

z= 9.406

The calculated value of z falls in the critical region therefore we reject the null hypothesis and conclude that the 10% significance level that the scrap rate of the new method is different from the old method.

Answer:

C) 100 cm²

Step-by-step explanation:

(14*6)/2*10

20/2*10

10*10

100

The area of the given shaded part of the rectangle is 100 square meters as shown.

The entire space filled by a triangle's three sides in a two-dimensional plane is defined as its area.

The fundamental formula for calculating the area of a triangle is A = 1/2 b h.

The area of the shaded part = area of the rectangle -  area of the triangle

The area of the shaded part = 14 × 10 - (1/2) × 8 × 10

The area of the shaded part = 140 - 80/2

The area of the shaded part = 140 - 40

Apply the subtraction operation, and we get

The area of the shaded part = 100 meters²

Thus, the area of the given shaded part of the rectangle is 100 square meters.

Learn more about the triangles here:

https://brainly.com/question/17997149

#SPJ3