What is the average rate of change of the function on the interval from x = 0 to x = 5?


f(x)=

1/2^(3)x

Answer:

  24/7 = 3 3/7 inches

Step-by-step explanation:

The triangle can be represented by a line in the first quadrant with y-intercept 8 and x-intercept 6. Then its equation is ...

  x/6 +y/8 = 1 . . . . . intercept form of the equation of the line

  4x + 3y = 24 . . . . multiply by 24 to get standard form

Since the square will have the origin as one corner, and all sides are the same length, the opposite corner will lie on the line y=x. Then we're solving the system ...

  4x +3y = 24

  y = x

to find the side length.

__

By substitution for y, this becomes ...

  4x +3x = 24

  7x = 24

  x = 24/7 = 3 3/7

The length of the side of the square is 3 3/7 inches.

The question involved finding the side length of a square inscribed in a right triangle. The correct approach uses additional geometry to set up a system of equations resulting from segments on the legs of the triangle equal to the side length of the square. Solving these equations reveals that the side length of the square is 2 inches.

The student is seeking to find the length of the side of a square inscribed in a right triangle with legs measuring 6 inches and 8 inches. To determine this, one can use the Pythagorean theorem which relates the legs of a right triangle to its hypotenuse. However, in this scenario, the side of the square also acts as a 'leg' of two smaller right triangles within the original triangle. The length of the square, let's call it 's', plus the square's length (again 's') will equal the longer leg of the triangle (8 inches); similarly, 's' plus the length from the corner of the square to the right angle of the triangle (which is also 's') will equal the shorter leg (6 inches).

Therefore, we have two equations: 2s = 8 and 2s = 6. Since both cannot be true with the same value of 's', we realize that the premise of the question must be reconsidered. The actual process involves a bit more geometry, using the fact that the segments along the legs that are not part of the square must be equal respectively, leading to a system of equations to solve for the length of the side of the square. Let's denote these segments as 'x'; hence the equations are s + x = 6 and s + x = 8. Subtracting these equations from the original leg lengths gives us x = 6 - s and x = 8 - s. As these segments are equal, we can set them equal to each other, getting 6 - s = 8 - s, which simplifies to s = 2 inches.

Answer: the speed of the plane is 7.4 miles per minute.

the speed of the wind is 0.93 miles per minute.

Step-by-step explanation:

Let x represent the speed of the plane.

Let y represent the speed of the wind.

Distance of Las Cruses, NM from Dallas, TX is 600 miles.

Distance = speed × time

One plane flies from Dallas to Las Cruses in 1 hr 12 min(72 minutes). Assuming the plane flew in the same direction with the wind, then

600 = 72(x + y)

600 = 72x + 72y - - - - - - - - 1

Another plane with the same air speed flies from Las Cruses to Dallas in 1 hr 30 min(90 minutes). Assuming it flew in opposite direction to that of the wind, then

600 = 90x - 90y - - - - - - - 2

Adding equation 1 and equation 2, it becomes. 1200 = 162x

x = 1200/162 = 7.4 miles per minute.

x + y = 600/72 = 8.33

y = 8.33 - x = 8.33 - 7.4 = 0.93 miles per minute

Answer:

Hi am sitting in my post office waiting for you to come over and then I’ll come over to you

Step-by-step explanation:

Inside the post office office became offices when offices are offices

Answer:

D) q + d = 330

0.25q + 0.1d = 6

Step-by-step explanation:

Let q= numbers of quarters

d = number of dimes

q + d = 33 ...........(1)

q = 33 - d

xq + yd = 6 ..........(2)

We will consider the options to know the correct answer

From option A

q +d = 6

25q + 10d = 33

This is wrong

Option B

q + d = 60

0.25q + 0.1d = 33

This is also wrong

Option C

q+d = 33

25q + 10d = 6

Put q = 33 -d in equation 2

25(33 - d) + 10q = 6

825 - 25d + 10d = 6

825 - 15d = 6

-15d = 6-825

-15d = -819

d = -819/-15

d= 54.6

This is also wrong because d exceeds the combination.

Option D

q+d = 33

0.25q + 0.1d = 6

Put q = 33 -d in equation 2

0.25(33 - d) + 0.1d = 6

8.25 - 0.25d + 0.1d = 6

8.25 - 0.15d = 6

-0.15d = 6 - 8.25

-0.15d = -2.25

d = -2.25/ -0.15

d = 15

q = 33 - 15

q = 18

This is correct

Answer:

It's D.

Step-by-step explanation:

Edge 2020;)

Answer:

Step-by-step explanation:

let width=x

length=x+3

x(x+3)=54

x²+3x-54=0

x²+9x-6x-54=0

x(x+9)-6(x+9)=0

(x+9)(x-6)=0

x=-9,6

x=-9 (rejected)

as width can't be negative.

hence width=6 units

Answer:

The measure of an interior angle in a regular triangle is 60 degrees

Step-by-step explanation:

we know that

A regular triangle has three equal sides and three equal interior angles

Remember that the sum of the interior angles in a triangle must be equal to 180 degrees

so

Divide 180 by 3 to determine the measure of each interior angle

[tex]\frac{180^o}{3}=60^o[/tex]

A regular triangle is called equilateral triangle

therefore

The measure of an interior angle in a regular triangle is 60 degrees

Their headquarters contains 28000 employees.

Step-by-step explanation:

Given,

Total number of employees = 30000

Let,

Number of employees in headquarters = x

Number of employees in overseas branch = y

According to given statement;

x+y=30000     Eqn 1

x = 14y             Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex]14y+y=30000\\15y=30000\\[/tex]

Dividing both sides by 15

[tex]\frac{15y}{15}=\frac{30000}{15}\\y=2000[/tex]

Putting y=2000 in Eqn 2

[tex]x=14(2000)\\x=28000[/tex]

Their headquarters contains 28000 employees.

Keywords: linear equation, division

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The overseas branch has 2,000 employees, and since the headquarters has 14 times as many employees, it contains 28,000 employees.

We need to determine the number of employees at the headquarters of a company given that the headquarters has 14 times as many employees as the overseas branch, and the total number of employees in both buildings is 30,000.

Let's denote the number of employees in the overseas branch as x. Then, the number of employees in the headquarters is 14x. According to the problem, the total number of employees in both buildings is:

x + 14x = 30,000

Combining the terms:

15x = 30,000

To find x, we divide both sides by 15:

x = 30,000 / 15

x = 2,000

This means the overseas branch has 2,000 employees.

Now, since the headquarters contains 14 times as many employees as the overseas branch, we calculate:

14x = 14 * 2,000 = 28,000

Therefore, their headquarters contains 28,000 employees.

Answer:

Building is 56.58 feet long.

Step-by-step explanation:

Consider the provided information.

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads.

When the photograph is taken, the angle of elevation of the sun is 30°.

By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.

As we know: [tex]\tan\theta=\frac{opp}{adj}[/tex]

The value of tan 30 degrees is [tex]\frac{1}{\sqrt{3} }[/tex]

[tex]\tan30=\frac{h}{98}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{h}{98}[/tex]

[tex]h=\frac{98}{\sqrt{3}}[/tex]

[tex]h=56.58[/tex]

Hence, Building is 56.58 feet long.

Answer:

56.58 feet long

Step-by-step explanation:

Consider the provided information.

An aerial photograph from a U-2 spy plane is taken of a building suspected of housing nuclear warheads.

When the photograph is taken, the angle of elevation of the sun is 30°.

By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph, scientists determine that the shadow of the building in question is 98 feet long.

As we know:

The value of tan 30 degrees is

Hence, Building is 56.58 feet long.

Answer:No, the hat will not fit into the box.

Step-by-step explanation:

The length of the hat is 27 inches long. The only box available is 15-by-20-by-15 inches. This represents the height , width and length of the box

Since all sides of the box are lesser than 27 inches, then the hat will not fit into the box.

Answer:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{0.8^2}{1.0^2}=0.64[/tex]

[tex]p_v =P(F_{15,10}<0.64)=0.2105[/tex]

Since the [tex]p_v > \alpha[/tex] we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.  

Step-by-step explanation:

Data given and notation  

[tex]n_1 = 11 [/tex] represent the sampe size for the Old

[tex]n_2 =16[/tex] represent the sample size for the New

[tex]\bar X_1 =6.25[/tex] represent the sample mean for Old

[tex]\bar X_2 =5.95[/tex] represent the sample mean for the New

[tex]s_1 = 1.0[/tex] represent the sample deviation for Old

[tex]s_2 = 0.8[/tex] represent the sample deviation for New

[tex]\alpha=0.05[/tex] represent the significance level provided

Confidence =0.95 or 95%

F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:

[tex]F=\frac{s^2_2}{s^2_1}[/tex]

Solution to the problem  

System of hypothesis

We want to test if the variation for New sample it's lower than the variation for the Old sample, so the system of hypothesis are:

H0: [tex] \sigma^2_2 \geq \sigma^2_1[/tex]

H1: [tex] \sigma^2_2 <\sigma^2_1[/tex]

Calculate the statistic

Now we can calculate the statistic like this:

[tex]F=\frac{s^2_2}{s^2_1}=\frac{0.8^2}{1.0^2}=0.64[/tex]

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_2 -1 =16-1=15[/tex] and for the denominator we have [tex]n_1 -1 =11-1=10[/tex] and the F statistic have 15 degrees of freedom for the numerator and 10 for the denominator. And the P value is given by:

P value

Since we have a left tailed test the p value is given by:

[tex]p_v =P(F_{15,10}<0.64)=0.2105[/tex]

And we can use the following excel code to find the p value:"=F.DIST(0.64,15,10,TRUE)"

Conclusion

Since the [tex]p_v > \alpha[/tex] we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.  

if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is 1.56. The option (d) is correct.

To test whether the new seed results in less variability in individual potato length compared to the old seed, we can perform an F-test for comparing variances.

The F-test statistic for comparing two variances is given by:

[tex]\[ F = \frac{s_1^2}{s_2^2} \][/tex]

where [tex]\( s_1^2 \)[/tex] is the variance of the old seed and [tex]\( s_2^2 \)[/tex] is the variance of the new seed. The larger variance should be the numerator to ensure the F-value is greater than or equal to 1.

Given data:

- Old Seed:

[tex]- \( n_1 = 11 \)\\ - \( \bar{x}_1 = 6.25 \) inches\\ - \( s_1 = 1.0 \) inch[/tex]

- New Seed:

[tex]- \( n_2 = 16 \)\\ - \( \bar{x}_2 = 5.95 \) inches\\ - \( s_2 = 0.80 \) inch[/tex]

First, calculate the variances:

- Variance of old seed, [tex]\( s_1^2 = (1.0)^2 = 1.0 \)[/tex]

- Variance of new seed, [tex]\( s_2^2 = (0.80)^2 = 0.64 \)[/tex]

Since [tex]\( s_1^2 \)[/tex] (old seed) is larger than [tex]\( s_2^2 \)[/tex] (new seed), we use:

[tex]\[ F = \frac{s_1^2}{s_2^2} = \frac{1.0}{0.64} \][/tex]

Now, calculate the F-value:

[tex]\[ F = \frac{1.0}{0.64} = 1.5625 \][/tex]

The calculated test statistic is approximately 1.56. Therefore, the correct answer is (d) 1.56.

The complete question is:

The Russet Potato Company has been working on the development of a new potato seed that is hoped to be an improvement over the existing seed that is being used. Specifically, the company hopes that the new seed will result in less variability in individual potato length than the existing seed without reducing the mean length. To test whether this is the case, a sample of each seed is used to grow potatoes to maturity. The following information is given: Old Seed - Number of Seeds = 11, Average length = 6.25 inches , Standard Deviation = 1.0 inches New Seed - Number of Seeds = 16, Average length = 5.95 inches Standard Deviation = 0.80 inches. On this data, if the hypothesis test is conducted using a 0.05 level of significance, the calculated test statistic is:

(a) 1.25

(b) 0.80

(c) 0.64

(d) 1.56

Answer:

Part a) Is a growth function

Part b) The function's percent rate of change is 160%

Step-by-step explanation:

we have

[tex]f(x)=0.3(2.6^x)[/tex]

This is a exponential function of the form

[tex]f(x)=a(b^x)[/tex]

where

a is the initial value or y-intercept

b is the base of the exponential function

If b> 1---> we have a growth function

if b< 1---> is a decay function

r is the percent rate of change

b=(1+r)

In this problem we have

[tex]a=0.3[/tex]

[tex]b=2.6[/tex]

The value of b >1

so

Is a growth function

Find the value of r

[tex]r=b-1=2.6-1=1.6[/tex]

convert to percentage

[tex]r=1.6*100=160\%[/tex]

Answer:

Total money made by carnival booth selling popcorn and cotton candy = $2024

Step-by-step explanation:

Money made by carnival booth selling popcorn = $88

Money made by selling cotton candy was 22 times the money made by selling popcorn.

Thus, money made selling cotton candy = [tex]22\times \$88=\$1936[/tex]

Total money made by carnival booth selling popcorn and cotton candy = [tex]\$88+\$1936=\$2024[/tex]

Final answer:

To find the distance that the tornado traveled, rearrange the equation S = 93log(d) + 65 to solve for d. The equation to find the distance is d = 10^(65/93), where d is the distance in miles.

Explanation:

To find the distance that the tornado traveled, we can rearrange the equation S = 93log(d) + 65 to solve for d.

First, subtract 65 from both sides of the equation: 130 - 65 = 93log(d). Now, divide both sides by 93: 65/93 = log(d). Finally, take the inverse logarithm of both sides to find d: 10^(65/93) = d.

Therefore, the equation to find the distance that the tornado traveled is d = 10^(65/93), where d is the distance in miles.

We can find the value of [tex]\( d \)[/tex]. This equation is the one that would be used to determine the distance traveled by the tornado corresponding to a wind speed of 130 miles per hour.

To find the distance that the tornado traveled when the wind speed is known, we need to solve the given equation for [tex]\( d \)[/tex]. The original equation is  [tex]\[ S = 93\log d + 65 \][/tex]

Given that [tex]\( S = 130 \)[/tex] miles per hour, we substitute this value into the equation:

[tex]\[ 130 = 93\log d + 65 \][/tex]

Now, we need to isolate [tex]\( \log d \)[/tex]:

[tex]\[ 130 - 65 = 93\log d \] \[ 65 = 93\log d \][/tex]

Next, we divide both sides by 93 to solve for [tex]\( \log d \)[/tex]:

[tex]\[ \frac{65}{93} = \log d \][/tex]

To find [tex]\( d \)[/tex], we need to use the inverse of the logarithm function, which is the exponential function. The base of the logarithm is 10 (common logarithm) because it is not specified otherwise. Thus, we have:

[tex]\[ 10^{\frac{65}{93}} = d \][/tex]

This is the equation that could be used to find the distance[tex]\( d \)[/tex] that the tornado traveled when the wind speed is 130 miles per hour.

To find the numerical value of [tex]\( d \)[/tex], we calculate:

[tex]\[ d = 10^{\frac{65}{93}} \][/tex]

The correct matches are the intersection for common elements in both sets, union for all elements in either set, compound inequality for multiple inequalities, element for a set member, and set for a grouped collection of objects.

To match the terms with their definitions, we need to understand the concepts represented by each term. Here is the correct matching:

These definitions are essential to understanding basic concepts in set theory, a foundation for probability and other areas of mathematics. Recognizing these definitions helps in identifying the relationships between sets and the outcomes of events, especially when working with Venn diagrams and calculating probabilities.

Answer:

(B) I only

Step-by-step explanation:

450y = n³

y = n³ / 450 = n³ / (3² * 2 * 5²)

in order to keep y and n be positive integer, the minimal requirement for n³ is n³ = (3³ * 2³ * 5³)

y = n³ / 450

  = n³ / (3² * 2 * 5²)

  = (3³ * 2³ * 5³) / (3² * 2 * 5²)

  = 3*2²*5

∴ I. y / (3*2²*5) =  ((3³ * 5³ * 2³) / (3² * 5² * 2)) / (3*2²*5) = 1 ... that keep answer as the smallest positive integer .... Correct answer

II.   y / (3²*2*5) =  ((3³ * 5³ * 2³) / (3² * 5² * 2)) / (3²*2*5) = 2/3 ...not integer

III.  y / (3²*2*5) =  ((3³ * 5³ * 2³) / (3² * 5² * 2)) / (3*2*5²) = 2/5 ...not integer

Answer: The correct answer is neither

Step-by-step explanation:

for DeltaMath.

Answer:

C. 9

Step-by-step explanation:

it's multiple choice so plug each value in

A = -26

B = -34

C = 22

D = 46

so the answer is c

Answer:

The area of a rhombus is [tex]18\sqrt{3}[/tex] square units.

Step-by-step explanation:

Side length of rhombus = 6 units.

Interior angle of rhombus = 120°

another Interior angle of rhombus = 180°-120° = 60°.

Draw an altitude.

In a right angled triangle

[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]

[tex]\sin (60)=\frac{h}{6}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{h}{6}[/tex]

Multiply both sides by 6.

[tex]3\sqrt{3}=h[/tex]

The height of the rhombus is [tex]3\sqrt{3}[/tex].

Area of a rhombus is

[tex]Area=base\times height[/tex]

[tex]Area=6\times 3\sqrt{3}[/tex]

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

Therefore, the area of a rhombus is [tex]18\sqrt{3}[/tex] square units.

Area of Rhombus is 31.176 unit² (Approx.)

Length of rhombus side = 6 unit

Angle = 120°

Area of Rhombus

Area of Rhombus = Side²(Sin θ)

Area of Rhombus = 6²(Sin 120)

Area of Rhombus = 36(0.866)

Area of Rhombus = 31.176 unit² (Approx.)

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Answer:

[tex]x<-\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{7-2x}{-4} +2<-x[/tex]

Subtract 2 from both sides

[tex]\frac{7-2x}{-4} <-x-2[/tex]

mutliply both sides by -4, flip the inequality

[tex]7-2x >4x+8[/tex]

Add 2x on both sideds

[tex]7>6x+8[/tex]

Subtract 8 from both sides

[tex]-1>6x[/tex]

Divide both sides by 6

[tex]x<-\frac{1}{6}[/tex]

To solve for x, the given inequality (7 - 2x) / (-4) + 2 < -x can be simplified by isolating the variable on one side of the inequality. The value of x is found to be x < -15/2, making option C) x greater than negative one over six the correct answer choice.

The given inequality is:

(7 - 2x) / (-4) + 2 < -x

To solve for x, we need to isolate it on one side of the inequality. Let's simplify the equation step by step:

(7 - 2x) / (-4) + 2 < -x

7 - 2x + 8 < -4x (Added 2 to both sides)

15 - 2x < -4x

15 < 2x - 4x (Moved -2x to the right side)

15 < -2x

-15/2 > x

So the value of x in the inequality is x < -15/2. Therefore, the correct answer is option C) x greater than negative start fraction one over six end fraction.

Answer:

It prints 65 copies in 1  minute.

It takes 80 minutes to print 5200 copies.

Step-by-step explanation:

In 5 minutes the machine prints 325 copies and it can print at that steady state.

We have to find the number of copies it prints in  1 minute.

So ,number of copies in 1 minute = [tex]\frac{number of copies in 5 minute}{5}[/tex]

                                          = [tex]\frac{325}{5}[/tex]

                                           = 65

Hence it prints 65 copies in 1  minute.

The time taken to print 5200 copies = [tex]time to make 1 copy \times 5200[/tex]

                                            = [tex]\frac{1}{65} \times 5200[/tex]

                                             = 80 minutes

Answer:

  angle measures are 32°, 53°, 95°.

Step-by-step explanation:

The problem statement asks you to report the angle measures after telling you what they are. The mention of side lengths (without any numbers for them) seems irrelevant.

  "The measures of the angles of the triangle are 32, 53, 95."

Answer:

The volume of the marble is 47 ml

The volume of the water is 100 ml

Step-by-step explanation:

we know that

The volume of the marble is equal to the change in water level

so

To find out the volume of the marble subtract 100 ml from 147 ml

[tex]147-100=47\ ml[/tex]

The volume of the water no change

The volume of the water is 100 ml

Answer:

c =$607

200 ft deep

Step-by-step explanation:

A sale transaction closes on April 15th. The day oIf a lot contains 48,000 square feet and is 240’ wide, how deep is the lot? closing belongs to the seller. Real estate taxes for the year, not yet billed, are expected to be $2,110. According to the 365-day method, what is the seller's share of the tax bill?

a. $626

b. $675

c. $607

d. $721

Since there are 90 days between january and March, we add that to the 15 days in April. which will give us 105 days.

Applying the 365-day method,

therefore 2110/365

5.78*105

606.98

approximately=$607

b. the day golf contains 48000 square feet

then 48000 divided by how wide it is

48,000 sq ft ÷ 240' = 200'

For this case we have to:

x: Variable that represents Tyler's age

y: Variable that represents Tiffany's age

According to the data of the statement we can propose the following equations:

[tex]x = y + 4\\x + 10 = 2y[/tex]

To solve we substitute the first equation in the second equation:

[tex]y + 4 + 10 = 2y\\14 = 2y-y\\14 = y[/tex]

So, Tiffany is 14 years old.

Then Tyler has:

[tex]x = 14 + 4\\x = 18[/tex]

Tyler is 18 years old.

Answer:

Tyler: 18 years old

Tiffany: 14 years old

Answer:

  (a) 74√3 N

  (b) 37√3 N

  (c) 111 N

Step-by-step explanation:

(a) The moment about the hinge produced by the beam is the product of the weight of the beam and the distance of its center from the wall. The tension in the wire counteracts that moment.

The tension in the wire acts at a horizontal distance from the wall that is twice the distance to the beam's center, so the tension's vertical component is only half the weight of the beam.

Since the wire is at a 30° angle to the wall, the horizontal component of the tension is 1/√3 times the vertical component. Altogether, the tension in the wire is (2/√3) times half the beam's weight, or 74√3 N.

__

(b) The horizontal force at the hinge counteracts the horizontal component of the tension in the wire, so is 111/√3 N = 37√3 N.

__

(c) The vertical component of the force at the hinge is half the beam weight, so is 111 N.

a) The tension in the wire is 192.3 N. b) The horizontal component of the force of the hi-nge on the beam is 96.1 N. c) Vertical component of the force of the hi-nge on the beam is 55.5 N.

(a) To find the tension in the wire, we can use a torque balance around the hi-nge. The torques due to the weight of the beam and the tension in the wire are equal and opposite, so we have:

T * L * cos(30°) = W * L/2

where:

T is the tension in the wire

L is the length of the beam

W is the weight of the beam

Solving for T, we get:

T = W * cos(30°) / 2

Substituting the known values, we get:

T = 222 N * cos(30°) / 2

= 192.3 N

Therefore, the tension in the wire is 192.3 N.

(b) The horizontal component of the force of the hi-nge on the beam is equal to the tension in the wire multiplied by the sine of the angle between the wire and the beam. This angle is 30°, so we have:

[tex]F_h[/tex] = T * sin(30°)

Substituting the known values, we get:

[tex]F_h[/tex] = 192.3 N * sin(30°)

= 96.1 N

Therefore, the horizontal component of the force of the hi-nge on the beam is 96.1 N.

(c) The vertical component of the force of the hi-nge on the beam is equal to the weight of the beam minus the tension in the wire multiplied by the cosine of the angle between the wire and the beam. This angle is 30°, so we have:

[tex]F_v[/tex] = W - T * cos(30°)

Substituting the known values, we get:

[tex]F_v[/tex] = 222 N - 192.3 N * cos(30°)

= 55.5 N

Therefore, the vertical component of the force of the hi-nge on the beam is 55.5 N.

To learn more about horizontal component here:

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Answer:6

Step-by-step explanation:

Let digit be r=abc

if tens digit of [tex]\frac{r}{10}[/tex] is 3.2

i.e. [tex]\frac{r}{10}[/tex] is written as ab.c

so tens digit is a=3

If the hundreds digit of 10r is 6

i.e. 10r is written as abc0

its hundreds digit is b=6

thus tens digit of abc is b=6

To find the tens digit of the integer r, we use the information that the hundreds digit of 10r is 6, indicating that the tens digit of r is also 6.

The question is asking to determine the tens digit of a positive integer r. To solve this, we need to analyze the given facts separately:

From statement 2 alone, we can determine that the tens digit of the positive integer r is 6.

Answer:

y = 0

Step-by-step explanation:

When the degree of the denominator of a rational function is greater than the degree of the numerator, then the equation of the horizontal asymptote is

y = 0

here degree of numerator is 1 and degree of denominator is 2

Degree of denominator > degree of numerator, thus

y = 0 ← equation of horizontal asymptote

Answer:

Least common denominator = 32

Step-by-step explanation:

We are given the following in the question:

Lina wants to find the least common denominator of two fractions so she can add them.

[tex]\dfrac{4}{32}\text{ and }\dfrac{5}{8}[/tex]

To find the LCM of the fractions:

[tex]8 = 2\times 2\times 2\\32 = 2\times 2\times 2\times 2\times 2\\\text{Common factors = }2\times 2\times 2\\LCM = 2\times 2\times 2\times 2\times 2 = 32[/tex]

The fractions can be added in the following manner:

[tex]\dfrac{4}{32} + \dfrac{5}{8}\\\\=\dfrac{4\times 1}{32\times 1} + \dfrac{5\times 4}{8\times 4}\\\\= \dfrac{4}{32} + \dfrac{20}{32}\\\\=\dfrac{4+20}{32}\\\\=\dfrac{24}{32}[/tex]

Answer:

(B) 0.8+0.0025y

Step-by-step explanation:

Total houses =80

First y houses was painted at the rate of x hours per week

Remaining houses was painted at 1.25x hours per week

Remaining houses= 80-y

Rate = quantity/ time

Time = quantity/ rate

Time for the first painting = y/x

Time for the second painting = 80-y/1.25x

Total time y/x + 80-y/1.25x

= 0.25y +80/1.25x

If it was being painted at the original rate

Time = 80/x

The time to paint in this scenario as a fraction of the time it will take to paint in the original rate.

(0.25y+80/1.25x) /(x/80)

=( 0.25y +80)/100

=0.0025y +0.8

Answer: Driven gear will have 50 teeth, and driver gear will have 42 teeth

Step-by-step explanation: First we have to know the formula of gear ratio which is started below

(No of teeth on driven)/(No of teeth on driver)

Note: we should all know in the combination of a gear system, we have two gears, the driver gear and the driven gear

So since the least amount of teeth for any gear is 50, we assume the no of teeth on the driven is 50

And no of teeth on the driver is x

50/x = 1.1839323

Cross multiply

x x 1.1839323 = 50

x = 50/1.1839323

x = 42.23

To the nearest whole number = 42

So therefore, number of teeth on the driver gear is 42

To approximate the gear ratio of 1.1839323 with gear teeth not exceeding 50, gears with 42 and 50 teeth can be used, resulting in an actual ratio of approximately 1.1904762, which is a close approximation to the desired value.

To find the number of teeth on each gear for a ratio as close to 1.1839323 as possible with a maximum of 50 teeth on a gear, we can start by recognizing that gear ratios are a form of fraction. Since the ratio must not exceed the limit of 50 teeth on each gear, the numbers must be integers within this boundary. The ratio can be approximated by finding two numbers close to the target ratio when divided, while not exceeding the maximum teeth number of 50 for either gear.

For an initial approximation, we can multiply the ratio by a number that will give us an integer closest to 50. For example, multiplying 1.1839323 by 42 (because 50 / 1.1839323 is approximately 42.245) gives us approximately 49.725, which we can round to 50. Thus, the other gear would have 42 teeth (as we multiplied by 42 to stay within the boundary of 50 teeth on a gear).

Now, to check the obtained ratio, we divide 50 by 42, which gives us approximately 1.1904762. This is a very close approximation to the desired ratio of 1.1839323. Therefore, the gears should have 42 and 50 teeth, respectively, to best approximate the desired gear ratio.

Answer:

Aaron needs 2 more rolls to complete the path.

Step-by-step explanation:

Given:

Total rolls Aaron has = 4

Part of path covered by using [tex]\frac{3}{4}[/tex] of a roll = [tex]\frac{1}{8}[/tex]

So, in order to find the number of rolls required to cover the complete path is given using the unitary method.

Rolls used for [tex]\frac{1}{8}[/tex] of a path = [tex]\frac{3}{4}[/tex]

Therefore, rolls used to cover the whole path is given by dividing the rolls used for one-eighth of the path and the path covered. This gives,

[tex]=\frac{3}{4}\div \frac{1}{8}[/tex]

[tex]=\frac{3}{4}\times \frac{8}{1}[/tex]

[tex]=\frac{3\times 8}{4\times 1}[/tex]

[tex]=\frac{24}{4}[/tex]

[tex]=6\ rolls[/tex]

Now, rolls required to complete the path is 6. But Aaron has only 4 rolls.

So, he will need 6 - 4 = 2 rolls more to complete the path.

Aaron can cover 6 portions of the path with his 4 rolls. Since the path has 8 portions, he needs 2 more rolls of rope to complete the path.

In this question, Aaron uses 3/4 of a roll for 1/8 of the path. Therefore, he will need one roll for (1/8) / (3/4) = 2/3 of the path. Now, we want to know how many rolls he needs for the complete path. The full path will be 1/(2/3) = 3/2 = 1.5 times bigger than the amount of path he can cover with one roll. Since he has four rolls to start with, he can cover 4 * 1.5 = 6 portions of the path. But to cover a full path, he would need 8 portions (as 1/8 of the path corresponds to one portion). So, he needs 8 - 6 = 2 more rolls.

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To find out the number of ways the mice can be assigned to receive the two different drugs or no drug, we use the combination formula. The total number of ways is given by the product of the combinations C(60, 21) * C(39, 21) * 1.

In this problem, we are given a group of 60 mice and we need to find the number of ways the mice can be assigned to receive drug A, drug B, or no drug. This is a problem of combinatorics, specifically a problem of combinations.

We have 60 mice and we want to choose 21 for the drug A. The number of ways to do this is given by the combination formula C(n, k) = n! / [k!(n-k)!], where 'n' is the total number of items, 'k' is the number of items to choose, and '!' represents the factorial function. So for drug A, it will be C(60, 21).

Then, from the remaining 39 mice, we need to choose 21 for drug B. The number of ways we can do this is C(39, 21).

Finally, the remaining 18 mice will serve as the control group. Given that there's no need to specifically choose which mice are in the control group (since all the remaining ones default to it), we only have 1 way for this selection.

 Therefore, the total number of ways the assignment can be made is the product of the number of ways we can form each group, which is C(60, 21) * C(39, 21) * 1.

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The number of ways the assignment of treatments to the mice can be made is 10278857927713471414080000.

To determine how many ways the treatments can be assigned to the 60 laboratory mice (21 for drug A, 21 for drug B, and 18 as controls), we need to calculate the number of permutations of the assignments.

The total number of mice is 60, consisting of:

- 21 mice for drug A

- 21 mice for drug B

- 18 mice as controls

The number of ways to assign treatments is the number of permutations of these groups within the total set of mice. This can be calculated using the multinomial coefficient:

[tex]\[ \frac{60!}{21! \times 21! \times 18!} \][/tex]

Where:

- 60!  is the factorial of 60 (total number of mice)

- 21! is the factorial of 21 (number of mice for drug A)

- 21! is again the factorial of 21 (number of mice for drug B)

- 18! is the factorial of 18 (number of control mice)

Let's compute this step-by-step:

1. Calculate 60!:

[tex]\[ 60! = 60 \times 59 \times 58 \times \ldots \times 2 \times 1 \][/tex]

2. Calculate 21!:

[tex]\[ 21! = 21 \times 20 \times \ldots \times 2 \times 1 \][/tex]

3. Calculate 18!:

[tex]\[ 18! = 18 \times 17 \times \ldots \times 2 \times 1 \][/tex]

Now, plug these into the formula:

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = \frac{60 \times 59 \times \ldots \times 2 \times 1}{(21 \times 20 \times \ldots \times 2 \times 1) \times (21 \times 20 \times \ldots \times 2 \times 1) \times (18 \times 17 \times \ldots \times 2 \times 1)} \][/tex]

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = \frac{83209871127413901442763411832233643807541726063612459524492776964096000000000000000}{51090942171709440000} \][/tex]

[tex]\[ \frac{60!}{21! \times 21! \times 18!} = 10278857927713471414080000 \][/tex]