For what values of b are the vectors \langle -46, b, 10 \rangle and \langle b, b^2, b \rangle orthogonal

Answer:12.5 seconds

Step-by-step explanation:hconsidering Runner 1 with a speed of 10m/s

and Runner 2 with a speed of 4 m/s

the equation of displacement for a uniform movement is

x=V*t

so x1=V1*t

and x2=V2*t

and the problem condition is x2=x1+75m

so we proceed to solve the equations.

from equation 2 t=x2/V2

substituting in equation 1 we have

x1=V1(x2/V2) and then the 3 equation

x1=V1((x1+75m)/v2

finally x1=75*(V1/(V2-V1)) =75*(10/(10-4))=125m

then t=(x1/v1)=125/10=12.5 seconds

Answer:

12.5 seconds

Step-by-step explanation:

Speed of the first person = 10 meter per second

Speed of the second person = 4 meter per second

Relative velocity of faster person = 10 - 4 = 6 meter per second

since distance between both the person is = 75 meter.

Therefore, time to cover this distance by faster person = [tex]\frac{Distance}{Speed}[/tex]

[tex]\frac{75}{6}[/tex]

= 12.5 seconds.

Faster runner catches the slower runner after 12.5 seconds.

Check the picture below.

make sure your calculator is in Degree mode.

The angle that the ladder makes with the ground would be 66.42 degrees.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are given that  ladder is leaning against a building. The ladder is 10m long and it is sitting on the ground 4m out from the building.

The side adjacent to the angle is given, and the hypotenuse of the triangle is the unknown.

The cosine relation applies

 Cos = Adjacent/Hypotenuse

We are given the hypotenuse = ladder length

Cos (∅)= (4 )/10

Cos (∅)≈ 2/5

(∅)≈ [tex]Cos^{-1}[/tex]2/5

(∅) = 66.42

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Answer:

38

Step-by-step explanation:

1/3+1/4=7/12

7/12*24=12

24+12=26

Answer:

They are intersecting line segments ⇒ answer b

Step-by-step explanation:

* Lets explain the types of the lines

- Parallel lines lie in the same plane and never intersect each other

- Intersecting lines are lines that meet each other in exactly one point

- Skew lines are lines that are in different planes and never intersect

* Now lets solve the problem

- The line segments that cut sides of a wedge of apple pie

∵ The wage of apple pie could represent a plane

∵ The line segments cut the sides of the wedge

∴ The lines are in the same plane

∵ Skew lines are in different planes and never intersect

∴ The lines can not be skew

∵ The line segments that cut sides of the wage must be intersected

   at exactly one point

∵ Parallel lines never intersected

∴ The lines can not be parallel lines

∴ They are intersecting line segments

Answer: 11,658.45

Step-by-step explanation:

First multiply 305 x 620 to determine the square footage

divide that answer by 16.22 to get your answer

The required amount of electricity produced by a field of solar panels which is 305 feet by 620 feet, is 3,067,202 watt.

Given that,
A field of solar panels yields 16.22 watts per square foot.
T0 determines the amount of electricity produced by a field of solar panels that is 305 feet by 620 feet.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
A field of solar panels yields 16.22 watts per square foot.
The amount of electricity produced by a field of solar panels is 305 feet by 620 feet,
= 16.22 * 305 * 620
= 3,067,202 watt,

Thus the required amount of electricity produced by a field of solar panels that is 305 feet by 620 feet, is 3,067,202 watt.

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Answer:

  24

Step-by-step explanation:

The greatest common divisor of 72 and 96 is 24. Robert can make any number of bags that is a divisor of 24. If he wants to make the largest number possible, then he can make 24 bags with 4 balloons and 3 pieces of candy in each one.

__

  72 = 2³·3²

  96 = 2⁵·3

The greatest common divisor is the product of the common factors: 2³·3 = 24.

Total shoppers 255.

Number of shoppers who did not shop at the store = 20+70 = 90

Probability = 90/255 = 0.353

Answer:

It's a bit unclear with the table this way, but I count fifteen points, fifteen lines of the table, each a pair of numbers.

That's 15 degrees of freedom in the data.   When modeling, each parameter in the model uses up one degree of freedom, so you'd use a smaller number of degrees of freedom when calculating t statistics, etc.

Answer:

See explanation

Step-by-step explanation:

I wouls say to my friend that he is incorrect, because there are infinitely many pairs of numbers with a difference of 12.

For example,

[tex]13-1=12\\ 14-2=12\\15-3=12\\16-4=12\\...[/tex]

Here we can increase the first and the second number by 1 and get their difference equal to 12 after this operation.

The same is possible with negative numbers:

[tex]-1-(-13)=12\\ -2-(-14)=12\\-3-(-15)=12\\ ...[/tex]

Actuall, we can do this with decimals too

[tex]12.5-0.5=12\\ \\13.4-1.4=12\\ \\12\dfrac{1}{8}-\dfrac{1}{8}=12\\...[/tex]

Such pairs of numbers are infinitely many (because there are infinitely many real numbers) and we cannot find all possible numbers with difference of 12.

Answer:

  (3 7/8, -1 3/4)

Step-by-step explanation:

The midpoint is the average of the end point coordinates:

  ((5 1/2, -4 3/4) +(2 1/4, 1 1/4))/2

  = (7 3/4, -3 1/2)/2 = (3 7/8, -1 3/4)

Answer:

The answer is letter d

Step-by-step explanation:

This problem is a basic combinatory statistical problem:

Right now Washington uses 3 numerical digits (ranging from 0 to 9 each) and three letters (ranging from A to Z). So each number can be one in 10 and each letter can be one in 26 (the amount of numbers that the alphabet has).

Given n= the amount of possible licence plates and a= the amount of numbers ranging from 0 to 9 (10 possibilities) and b= the amount of letters ranging from A to Z (26 possibilities)

n=a*a*a*b*b*b=17.576.000

So if we switch one a to a b, we increment the amount of possible outputs, that is why when switching all the numbers to letters we exponentially increase the amount of possible license plantes.

Answer:

  (x, y) = (-1, -3)  or  (4, 12)

Step-by-step explanation:

A graphing calculator can show the solutions to this system.

__

You can equate expressions for y and solve for x.

  3x = x^2 -4

  x^2 -3x = 4 . . . . add 4-3x

  x^2 -3x +2.25 = 6.25 . . . . complete the square by adding (-3/2)^2 where -3 is the coefficient of x.

  (x -1.5)^2 = 2.5^2 . . . . . . rewrite as squares

  x -1.5 = ±2.5 . . . . . . . . . . take the square root

  x = 1.5 ± 2.5 = -1, +4

  y = 3x = -3, +12, respectively

Solutions are ...

  (x, y) = (-1, -3) . . . . and . . . . (4, 12)

Answer:

x + y = 4 or y = -x + 4

Step-by-step explanation:

0 = -1[4] + b

4 = b

y = -x + 4

If you want it in Standard Form:

y = -x + 4

+x +x

_________

x + y = 4 >> Line in Standard Form

* Since the rate of change [slope] is -1 and that parallel lines have SIMILAR SLOPES, -1 remains the same.

I am joyous to assist you anytime.

Answer:

The answer to your question is: 2.26%

Step-by-step explanation:

Data

densities    2.49 g/cm3,  2.56 g/cm3, 2.72 g/cm3

accepted value = 2.65 g/cm3

Process

            mean = (2.49 + 2.56 + 2.72) / 3 = 7.77 / 3

                      = 2.59 g/cm3

% error = | approx. - exact| / exact x 100

% error =  | 2.59 - 2.65 | / 2.65 x 100

% error = | -0.06| / 2.65 x 100

% error = 0.06/2.65 x 100

% error = 2.26 %

To find the percent error of Ari’s average measurement, find the average of the three measurements and use the formula: |(Accepted Value - Experimental Value)| / Accepted Value * 100%.

To find the percent error of Ari’s average measurement, we first need to calculate the average of the three measurements. Adding 2.49, 2.56, and 2.72 and dividing by 3 gives us an average density of 2.59 g/cm3.

To find the percent error, we use the formula:

Percent Error = |(Accepted Value - Experimental Value)| / Accepted Value * 100%

Substituting in the values, we get:

Percent Error = |(2.65 - 2.59) / 2.65| * 100%

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Answer:

the easyiest way for me to explain why the answer is A 0.077

Step-by-step explanation:

first add all your numbers it comes up to 1112 then youre going to take that number and put it aside then you dived 86 (the total for anyone at least 31+) and it gices you 0.077

Answer:

27.32 m

Step-by-step explanation:

We are given that

Height of window from the ground=18 m

Height of rock  form the ground=2 m

Speed of thrown rock=30 m/s

We have to find the horizontal distance from the window from which rock was release.

Difference between window and rock=18-2=16 m

Initial vertical velocity component=[tex]30sin40^{\circ}=19.28 [/tex]m/s

Initial horizontal velocity component=[tex]30cos 40^{\circ}=22.98 m/s[/tex]

If the rock is reached to maximum height

Then, maximum height=[tex]\frac{v^2}{2g}=\frac{(19.28)^2}{2\times 9.8}=18.9731 m[/tex]

Time taken by rock to reach maximum height=[tex]\frac{v}{g}=\frac{19.28}{9.8}=1.96775 s[/tex]

Distance between window and maximum height at which rock reached=18.9731-16=2.973 m

Time to drop 2.973 m=[tex]\sqrt{\frac{2h}{g}}=\sqrt{\frac{2\cdot 2.973}{9.8}}=0.77893 s[/tex]

Time to be at 16 m=1.96775-0.77893=1.189 s

Horizontal distance=[tex]1.189\times 22.98=27.32 m[/tex]

Hence, horizontal distance of rock from the window from which rock was released=27.32 m

The rock was released approximately 71.1 meters horizontally from the window. This calculation is based on the rock's initial speed of 30.0 m/s, launch angle of 40.0°, and the fact that it struck the window on its upward trajectory with no air resistance.

To solve this problem, we can use the kinematic equations of motion. We need to find the horizontal distance the rock was released from the window.

1. First, we can find the time it takes for the rock to reach its maximum height. We can use the following kinematic equation:

[tex]\[v_y = u_y + at\][/tex]

  Where:

  - [tex]\(v_y\)[/tex] is the final vertical velocity (0 m/s at the maximum height),

  - [tex]\(u_y\)[/tex] is the initial vertical velocity (30.0 m/s, since it's thrown vertically),

  - \(a\) is the vertical acceleration due to gravity (-9.81 m/s²),

  - \(t\) is the time.

  Rearrange the equation to solve for t:

 [tex]\[0 = 30 - 9.81t\]\\\\[/tex]

[tex]\[t = \frac{30}{9.81} \approx 3.06 \, \text{s}\][/tex]

2. Now, we can find the horizontal distance using the horizontal motion equation:

 [tex]\[d_x = u_x \cdot t\][/tex]

  Where:

  - [tex]\(d_x\)[/tex] is the horizontal distance we want to find.

  - [tex]\(u_x\)[/tex] is the horizontal component of the initial velocity                                    
[tex](30.0 m/s * cos(40°)).[/tex]

  - \(t\) is the time calculated in step 1.

  Plug in the values:

[tex]\[d_x = (30 \cdot \cos(40°)) \cdot 3.06 \approx 71.1 \, \text{m}\][/tex]

So, the rock was released approximately 71.1 meters horizontally from the window.

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Answer:

The sample standard deviation is 393.99

Step-by-step explanation:

The standard deviation of a sample can be calculated using the following formula:

[tex]s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex]

Where:

[tex]s=[/tex] Sample standart deviation

[tex]N=[/tex] Number of observations in the sample

[tex]{\displaystyle \textstyle {\bar {x}}}=[/tex] Mean value of the sample

and [tex]\sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex] simbolizes the addition of the square of the difference between each observation and the mean value of the sample.

Let's start calculating the mean value:

[tex]\bar {x}=\frac{1}{N}  \sum_{i=1}^{N}x_{i}[/tex]

[tex]\bar {x}=\frac{1}{15}*(180+1600+90+140+50+260+400+90+380+110+10+60+20+340+80)[/tex]

[tex]\bar {x}=\frac{1}{15}*(3810)[/tex]

[tex]\bar {x}=254[/tex]

Now, let's calculate the summation:

[tex]\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=(180-254)^2+(1600-254)^2+(90-254)^2+...+(80-254)^2[/tex]

[tex]\sum_{i=1}^{N}(x_{i}-\bar {x}) ^{2} }=2173160[/tex]

So, now we can calculate the standart deviation:

[tex]s=\sqrt[ ]{\frac{1}{N-1} \sum_{i=1}^{N}(x_{i}-{\displaystyle \textstyle {\bar {x}}}) ^{2} }[/tex]

[tex]s=\sqrt[ ]{\frac{1}{15-1}*(2173160)}[/tex]

[tex]s=\sqrt[ ]{\frac{2173160}{14}}[/tex]

[tex]s=393.99[/tex]

The sample standard deviation is 393.99

To find the sample standard deviation, use the formula standard deviation = √[ Σ(x - μ)² / (n - 1) ]. Follow the steps: find the mean of the data set, subtract the mean from each value and square the result, add all the squared deviations together, divide by (n - 1), and finally, take the square root of the result.

To find the sample standard deviation, you can use the formula:

standard deviation = √[ Σ(x - μ)² / (n - 1) ]

where Σ represents the sum of the values, x is each value in the data set, μ is the mean of the data set, and n is the number of values in the data set.

Step 1: Find the mean of the data set. Add all the values together and divide by the number of values (15 in this case). This gives you a mean of 179.3333.

Step 2: Subtract the mean from each individual value in the data set, square the result, and add all the squared values together. This gives you a sum of squared deviations of 977733.3333.

Step 3: Divide the sum of squared deviations by (n - 1), where n is the number of values in the data set. Since there are 15 values, you divide by 14 to get 69838.0952.

Step 4: Take the square root of the result from Step 3. This gives you a sample standard deviation of approximately 264.1046.

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Answer:

  10.5 miles

Step-by-step explanation:

Let b represent the distance traveled by boat. The relation between speed, distance, and time is ...

  time = distance / speed

We are told the total time and the total distance so we have ...

  b/7 + (14-b)/2 = 3.25

  2b +7·14 -7·b = 14·3.25 . . . multiply by 14

  3.75·14 = 5b . . . . . . . . . . . .add 5b-14·3.25

  b = 10.5 . . . . . . . . . . . . . . . divide by 5

They traveled 10.5 miles by boat.

_____

Check

10.5/7 +3.5/2 = 1.5 +1.75 = 3.25 . . . . the answer checks OK

They spent 1.75 hours walking 3.5 miles to the dock and 1.5 hours traveling 10.5 miles by boat.

we know that Bob can do the whole job in 14 hours, how much of the work has he done in 1 hour only?  well since he can do the whole lot in 14 hours in 1 hour he has only done 1/14 th of the job.

we know that James can do it in 18 hours, a bit slower, so in 1 hour he has done only 1/18 th of the job.

let's say it takes both of them working together say "t" hours, so in 1 hour Bob has done (1/14) of the work whilst James has done (1/18) of the work, the whole work being t/t or 1 whole, so for just one hour that'd 1/t done by both Bob and James.

[tex]\bf \stackrel{Bob}{\cfrac{1}{14}}~~+~~\stackrel{James}{\cfrac{1}{18}}~~=~~\stackrel{total~for~1~hour}{\cfrac{1}{t}} \\\\\\ \stackrel{\textit{using an LCD of 126}}{\cfrac{9+7}{126}=\cfrac{1}{t}}\implies \cfrac{16}{126}=\cfrac{1}{t}\implies 16t=126\implies t=\cfrac{126}{16} \\\\\\ \stackrel{\textit{7 hrs, 52 minutes and 30 seconds}}{t=\cfrac{63}{8}\implies t=7\frac{7}{8}}\implies \stackrel{\textit{rounded up}}{t=7.88}[/tex]

Answer:

12 seconds

Step-by-step explanation:

75 t=66t+108

75t-66t=108

9t=108

t=108/9=12

Answer:

The answer to your question is: 12 seconds

Step-by-step explanation:

Lion v = 75 ft/s

wildebeest = 66 ft/s and is 108 feet behind the lion

t = time = ?

Formula

v = d/ t    solve for d   d = vt

Process

lion      d = 75t

wildebeest =   d = 108 + 66t

Now

                    75t = 108 + 66t

solve for t     75t - 66t = 108

                     9t = 108

                       t = 12 s

Answer:

-46 feet/min

Step-by-step explanation:

Initial elevation = 1,380 ft

Final Elevation = 0 feet

Change in elevation

= Final elevation - Initial Elevation

= 0 - 1,380

= - 1,380 feet

Given that the journey took 30 min,

rate of descent = Change in elevation / time

= -1,380 / 30

= - 46 feet/min

[tex]\bf (\stackrel{x_1}{-6}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{(-6)}}}\implies \cfrac{-8}{-3+6}\implies -\cfrac{8}{3}[/tex]

Answer:

c

Step-by-step explanation:

it is the total cost for the lawn servic3

Answer:

B

Step-by-step explanation:

f(x)= the total of the equation

The constant term is the $25 which is what they charge along with the hours determined by x

Answer:

  42 = the number of hats Paula can knit from one yard of yarn

Step-by-step explanation:

The way this problem is written, the constant 42 is the multiplier of yards to get hats. That is, it has units of hats per yard, so represents the number of hats that can be knit from 1 yard of yarn.

_____

Comment on the problem

It seems more likely that the proportion should be written as ...

  y = 42h

or

  h = y/42

Then the constant would be the number of yards of yarn required for each hat.

The value of 5 in 5,476,807,139 is five billion, as it is positioned in the billions place. This is explained by the concept of place value.

The value of 5 in the number 5,476,807,139 refers to its place value in the numerical system. In this case, the 5 is in the billions place. This means that, in terms of place value, that 5 actually represents [5 × 1,000,000,000], which is 5,000,000,000 or five billion. The concept of place value is important in mathematics, it tells you how much each digit in a number is worth according to its position.

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Answer:

2 yard loss

Step-by-step explanation:

When the team gains yards we use a positive value, and when the team loses yards we use a negative value. So the operation would be 2 -5 -3 +4 = -2, this means that the team had a 2 yard loss.

Answer:

A, B, C, D, E

Step-by-step explanation:

AB ≅ AC and AD bisects ∠A

This is given information from the diagram and the statement.

∠BAD ≅ ∠CAD

This is from the definition of angle bisector.

AD ≅ AD

This is reflective property of congruence.

ΔABD ≅ ΔACD

From the previous three statements, side-angle-side congruence tells us the triangles are congruent.

∠B ≅ ∠C

Corresponding parts of congruent triangles are congruent.

Answer:

A.

B.

C.

D.

E.

refer to the attachment

Answer:

y = [tex]\frac{1}{2}[/tex] x + 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, 3)

m= [tex]\frac{3-1}{4-0}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, 1) ⇒ c = 1

y = [tex]\frac{1}{2}[/tex] x + 1 ← equation of line

Answer:

The height that make the surface area as small as possible is 10 cm

Step-by-step explanation:

Let

L -----> the length of the base of the box

W -----> the width of the base of the box

H ----> the height of the box

we know that

The volume of the box is equal to

[tex]V=LWH[/tex]

we have

[tex]V=4,500\ cm^3[/tex]

so

[tex]4,500=LWH[/tex] ----> equation A

[tex]L=2W[/tex] ------> equation B

substitute equation B in equation A

[tex]4,500=(2W)WH[/tex]

[tex]4,500=2W^2H[/tex]

Solve for H

[tex]H=\frac{2,250}{W^{2}}[/tex] -----> equation C

The surface area of a open box is equal to

[tex]SA=2(L+W)H+LW[/tex] ----> equation D  

Substitute equation B and equation C in equation D

[tex]SA=2(2W+W)(\frac{2,250}{W^{2}})+(2W)W[/tex]

[tex]SA=6W(\frac{2,250}{W^{2}})+2W^2[/tex]

[tex]SA=6(\frac{2,250}{W})+2W^2[/tex]

[tex]SA=\frac{13,500}{W}+2W^2[/tex]

Convert to function notation

[tex]f(W)=\frac{13,500}{W}+2W^2[/tex]

Find the derivative

[tex]f'(W)=-\frac{13,500}{W^2}+4W[/tex]

set equal to zero

[tex]f'(W)=0[/tex]

[tex]0=-\frac{13,500}{W^2}+4W[/tex]

Solve for W

[tex]\frac{13,500}{W^2}=4W[/tex]

[tex]W^3=\frac{13,500}{4}[/tex]

[tex]W=15\ cm[/tex]

Find the value of L (equation B)

[tex]L=2(15)=30\ cm[/tex]

Find the value of H (equation C)

[tex]H=\frac{2,250}{15^{2}}=10\ cm[/tex]

therefore

The height that make the surface area as small as possible is 10 cm