The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for larger vehicles. The amount collected can be modeled by the equation , where x represents the number of small vehicles and y represents the number of larger vehicles. If the number of larger vehicles washed was 50, how many small vehicles were washed in total?
a.55
b.60
c.130
d.150

Answer:

Whittingham's time through the 200 m was 5.55 seconds.

Step-by-step explanation:

Huber's peed = 200m / 6.509s = 30.72m/s

1 meter per second = 3.6 km per hour

30.72 m/s =  [tex]30.72\times36.=110.6[/tex] km/hr

Sam's speed is 110.6 + 19 = 129.6 km/hr

1 km per hour = 0.2778 meter per second.

So, 129.6 km/hr = [tex]129.6\times0.2778[/tex]= 36m/s

So, Sam Whittingham's time through the 200 m was =

[tex]\frac{200}{36}= 5.55[/tex] seconds.

Final answer:

Chris Huber's average speed was 30.73 m/s. Sam Whittingham beat this by 19.0 km/h, or 5.28 m/s, totaling to an average speed of 35.01 m/s. Whittingham's time for the 200m stretch was thus approximately 5.71 seconds.

Explanation:

To calculate Sam Whittingham's time through the 200 m stretch, we first need to find Chris Huber's average speed during his record-setting ride. Huber's time was 6.509 seconds for a 200 meter stretch, giving us an average speed of 200 m / 6.509 s ≈ 30.73 m/s. Whittingham beat Huber's record by 19.0 km/h. Since 1 km/h is approximately 0.27778 m/s, a 19.0 km/h increase translates to 19.0 km/h * 0.27778 m/s/km/h ≈ 5.28 m/s. Therefore, Whittingham's average speed was 30.73 m/s + 5.28 m/s = 35.01 m/s.

To find Whittingham's time for the 200 m stretch, we divide the distance by his average speed.
Time = Distance / Speed
Time = 200 m / 35.01 m/s ≈ 5.71 seconds.

Therefore, Sam Whittingham's record-breaking time through the 200-meter distance was approximately 5.71 seconds.

Answer:

The answer to your question is: lost 70 games; played 154 games

Step-by-step explanation:

Data

Won 84 games

Won 14 more games than it lost

There was no toes.

# of games did the team lose?

# of games did it play?

Process

             games lost = games won - 14

             games lost = 84 - 14

             games lost = 70

# of games played = games won + games lost

# games played = 84 + 70

                           = 154

Answer: d 6000 bytes

Step-by-step explanation: The web server will acknowledge 6000 bytes of information after receiving 4 packets of data from the PC. This is because 1 packet of data has a size of 1500 bytes. In a situation where the web server receives 4 of these, it is 1500 multiplied by 4 which is 6000 bytes. The window size of 6000 is there to try distract you from calculating the answer correctly, it serves as a misguidance.

The byte of information that the web server acknowledge is 6000 bytes.

From the information given, were told that the web server is utilizing a window size of 6,000 bytes when sending data and a packet size of 1,500 bytes.

The byte of information that'll be received will be:

= 1500 × 4

= 6000 bytes

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Answer:

The answer to your question is letter: c) √106 units

Step-by-step explanation:

data

B (5, 3)

D (-4 , -2)

Formula

d = √((x2-x1)² + (y2-y1)²)

dBD = √(-4-5)² + (-2-3)²)

dBD = √(-9)² + (-5)²

dBD = √81 +25

dBD = √106 units

Answer:

  D)  26 miles per gallon

Step-by-step explanation:

To find miles per gallon, divide miles by gallons:

  Lily's miles/gallon = (52 miles)/(2 gallon) = 26 miles/gallon

_____

Comment on the answer choices

Unless Lily's car manufactures gas, her mileage will not be negative miles per gallon.

Answer: There are 241 red candies in the bowl. 482 Green candies in bowl.

Step-by-step explanation:

241 (is the answer) x2= 482. There's TWICE as many green as there is red, since there is 241 red candies, we multply that by two (482). Now let's add to check if it is correct. 241+482= is indeed 723.

Answer:

red = 241

green = 482

Step-by-step explanation:

The total = 723

red candies = x

green candies = y

⇒ x + y =723

There are twice as many green candies as red candies.

this means: y = 2x

x + y = 723

x +2x = 723

3x = 723

x = 241

y = 723 - 241 = 482

To control this y = 2x ⇒ 482 = 2 * 241

This means that there 241 red candies and 482 green candies.

Answer:

  8

Step-by-step explanation:

The coordinates of Preston's house are ...

  2J -E = P = 2(-5, 3) -(3, -2) = (-13, 8)

The y-coordinate of P is 8.

Answer:

D

Step-by-step explanation:

[tex]4=r cos \theta\\-4=r sin \theta\\square ~and~add\\16+16=r^2(cos^2 \theta+sin^2\theta)\\r^2=32\\ r=4\sqrt{2} \\divide \\tan \theta=-1\\as x is positive ,y is negative ,so \theta lies in 4th quadrant.\\tan \theta=-1=-tan 45=tan(360-45)=tan 315\\\theta=315°\\\\co-ordinates~ are~(r,theta) ~or~(-r,\theta+ -180°)\\hence ~co-ordinates~are(4\sqrt{2} ,315°),(-4\sqrt{2} ,135°)[/tex]

A square has all 4 sides equal, so divide the amount of fence available by 4 to get the length of one side of the square

600/4 = 150

Now since the creek is being used for one side, add one side of the square to the other side to get a rectagle 150 by 300 feet.

Area = 150 x 300 = 45,000 square feet.

The maximum possible area of the pasture is;

A_max = 45000 ft²

Available fencing; Perimeter = 600 feet

Number of sides to fence; 3 sides of rectangle

Perimeter of rectangle; P = 2L + 2W

But we are told one of the edges is the creek.

Thus, New perimeter = L + 2W

thus, we have;  L + 2W = 600

L = 600 - 2W

Let's put 600 - 2W for L in the area equation to get;

A = (600 - 2W)W

A = 600W - 2W²

Thus;

dA/dW = 600 - 4W

At dA/dW = 0, we have;

600 - 4W = 0

4W = 600

W = 600/4

W = 150 ft

Let's put 150 for W in L = 600 - 2W

L = 600 - 2(150)

L = 600 - 300

L = 300 ft

 Therefore, Maximum possible area of pasture = 300 × 150 = 45000 ft²

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Answer:

20/100

Step-by-step explanation:

20 over 100 due to 100 percent is a whole and you are taking 20 percent so 20 will be ur numerator and 100 for you dominator

Answer:

  20 1/4 ft

Step-by-step explanation:

Subtracting the four given lengths from 75 feet will tell you how much is left.

  75 - (12 1/3 +16 1/6 +11 3/4 +14 1/2) = 75 -54 3/4 = 20 1/4

Gabriel has 20 1/4 ft of material left for his 5th banner.

After adding the lengths of the first four banners, we subtract that number from the total material Gabriel originally had. Gabriel has 20 13/24 feet of material left for the fifth banner.

To determine the amount of material left for the fifth banner, we first have to add the lengths of the four banners that Gabriel has already made. These lengths are 12 1/3 ft., 16 1/6 ft., 11 3/4 ft., and 14 1/2 ft. We add these four values together:

12 1/3 + 16 1/6 + 11 3/4 + 14 1/2 = 54 11/24 ft.

Gabriel originally had 75 feet of material, so to find out how much is left for the fifth banner, we subtract the total length of the first four banners from the original amount:

75 - 54 11/24 = 20 13/24 ft.

So, Gabriel has 20 13/24 ft. of material left for the fifth banner.

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Answer:

Option C is the answer.

Step-by-step explanation:

Given diameter is = 2 miles

So, radius will be = 1  mile

Let t represents the number of hours it took Johanna to walk completely around the lake.

Now, the circumference is given as: [tex]2\pi r[/tex]

So, circumference = [tex]2(3.14)(1)[/tex] = 6.28 miles

Johanna's speed = 3 miles/ hour

We know the formula [tex]Time=Distance / Speed[/tex]

t = [tex]6.28/3[/tex]

t = 2.09 hours

This is greater than 2, but less than 2.5, therefore, 2.0 < t < 2.5 is the answer.

Answer:

Option D. x = 4

Step-by-step explanation:

we have

[tex]f(x)=\frac{1}{x-3}+1[/tex]

[tex]g(x)=2\sqrt{x-3}[/tex]

we know that

The solution of the system

f(x)=g(x)

is the x-coordinate of the intersection point both graphs

using a graphing tool

The intersection point is (4,2)

see the attached figure

therefore

The solution is x=4

Answer:

for plato its d

Step-by-step explanation:

i got it

Answer: True.

Step-by-step explanation:

Let [tex]\mu[/tex] be the population mean.

Given : Null hypothesis = [tex]H_0:\mu=160[/tex]

Alternative hypothesis =[tex]H_1:\mu<160[/tex]

Since , the alternative hypothesis is left-tailed, then the test is a left-tailed test.

The sample mean ([tex]\overlien{x}[/tex]) of the 80 students who were weighed was found to be 142 pounds and the p-value was 0.03.

We know that p-value gives that probability that if the null hypothesis is true, than the sample mean ([tex]\overlien{x}[/tex]) will be at least as small as the actual mean ([tex]\mu[/tex]).

It means that if the mean of all students’ weight is 160 lbs, then there would be only a 3% chance that a randomly selected group of 80 students would have a mean weight of less than 142 lbs.

Hence, the answer is "True".

Final answer:

The statement is true; a p-value of 0.03 indicates a 3% chance of observing a sample mean weight of 142 lbs or less if the true mean weight of all college students is 160 lbs, suggesting strong evidence against the null hypothesis.

Explanation:

The statement provided is true: if the null hypothesis is true (that college students' average weight is 160 lbs), there would only be a 3% chance that a random sample of 80 students would have a mean weight of 142 lbs or less. This small p-value (0.03) typically indicates strong evidence against the null hypothesis, suggesting that the average weight of college students is indeed less than the average American.

In other words, a p-value is the probability that we observe a sample statistic as extreme as the one measured (or more extreme) given that the null hypothesis is true. Taking another example to illustrate the concept: if the null hypothesis assumes no difference in the average height between male and female students, and we observe a sample where the difference is 4 inches with a p-value of 0.04, this means there's a 4% chance we would see at least this large a difference if in reality there was no difference at all.

Answer:-13/4

Step-by-step explanation:

Move 3/4 to the left:

-2/5-3/4=-20/8-6/8

-26/8=n

-13/4=n

The first one is the answer

The question revolves around basic algebra and setting up an equality equation based on the given information. In this case, from the facts given, we can state Mai's earnings (x) in terms of Noah's earnings plus an additional amount (y), resulting in the equation x = w + y.

The subject of this problem is algebra, specifically involving variables and the concept of equality. In this problem, Noah earned an amount we will denote as w dollars over the summer. Mai, on the other hand, earned x dollars, and it's said that this is an amount of y dollars more than Noah did.

We can express Mai's earnings in terms of Noah's earnings by adding the extra amount to what Noah earned, which gives us the following equality equation:

x = w + y

This equation means that Mai's earnings (x) are equal to the sum of Noah's earnings (w) and the additional amount (y).

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Answer:

x=8

Step-by-step explanation:

6. an odd-degree polynomial function.

   f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

Step by step explanation;

6. The graph represent an odd-degree polynomial function.

The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;

f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

Answer:

End behavior: [tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]  and [tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]

The function has odd-degree.

The number of real zeros in 5.

Step-by-step explanation:

From the given graph it is clear that the graph approaches towards negative infinite as x approaches towards negative infinite.

[tex]f(x)\rightarrow -\infty\text{ as }x\rightarrow -\infty[/tex]

The graph approaches towards positive infinite as x approaches towards positive infinite.

[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow \infty[/tex]

For even-degree the polynomial has same end behavior.

For odd-degree the polynomial has different end behavior.

Since the given functions has different end behavior, therefore the graph represents an odd-degree polynomial function.  

If the graph of a function intersects the x-axis at a point then it is a zero of the function.

If the graph of a function touch the x-axis at a point and return then it is a zero of the function with multiplicity 2. It means, the function has 2 equal zeros.

The graph intersect the x -axis at 3 points and it touch the x-axis at origin. So, the number of zeros is

[tex]N=3+2=5[/tex]

The number of real zeros is 5.

let's bear in mind that B is the midpoint and thus it cuts a segment into two equal halves.

[tex]\bf \underset{\leftarrow \qquad \textit{\large 10x-6}\qquad \to }{\boxed{A}\stackrel{4x+2}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\underline{4x+2}}{\rule[0.35em]{10em}{0.25pt}\boxed{C}}} \\\\\\ AC=AB+BC\implies 10x-6=(4x+2)+(4x+2)\implies 10x-6=8x+4 \\\\\\ 2x-6=4\implies 2x=10\implies x=\cfrac{10}{2}\implies x= 5 \\\\[-0.35em] ~\dotfill\\\\ AC=(4x+2)+(4x+2)\implies AC=[4(5)+2]+[4(5)+2] \\\\\\ AC=22+22\implies AC=44[/tex]

This is a geometry problem, specifically involving the calculation of lengths using the properties of midpoints. A midpoint divides a line into two equal lengths. The problem is solved by equating the length of AB to half of AC to determine the value of x, which is then substituted back into the equation for AC to find its length.

The solution to your problem involves understanding that Point B is the midpoint of AC. A midpoint essentially divides a line into two equal lengths. Therefore, AB is equal to BC which can also be referred to as (AC/2). If AB = 4x+2 and AC = 10x-6, then to solve for the value of x, you would need to equate (4x+2) to (10x-6)/2. After solving this equation, the value of x can then be substituted back into the equation of AC to get the length of AC.

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Answer:

y - 1 = -4(x - 7).

Step-by-step explanation:

Point-slope equation is:

y - y1 = m(x - x1)  where m = the slope and (x1, y1) is a point on the line.

Here m = -4 , x1 = 7 and y2 = 1, so:

y - 1 = -4(x - 7).

An equation of the line in point-slope form is: D. y - 1 = -4(x - 7).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

x and y represent the data points.

m represent the slope.

At data point (7, 1) and a slope of -4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -4(x - 7)  

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Answer:

a) Δ ABC is rotated around the origin by angle 180° and then translated 1

unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 180° then its image

 is (-x , -y)

- If the point (x , y) translated horizontally to the right by h units

 then its image is  (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

 then its image is  (x - h , y)

- If the point (x , y) translated vertically up by k units

 then its image is  = (x , y + k)

- If the point (x , y) translated vertically down by k units

 then its image is  (x , y - k)

* Lets solve the problem

∵ Δ ABC change its place from 2nd quadrant to the 4th quadrant

  and reverse its direction Point A up and its image A" down

∵ No change in its size

∴ Triangle ABC rotates 180° clockwise around the origin

# Remember : There is no difference between rotating 180° clockwise

  or  anti-clockwise around the origin

∵ The vertices of Δ ABC are:

# A = (-3 , 5)

# B = (-3 , 2)

# C = (-1 , 2)

∵ If point (x , y) rotated about the origin by angle 180° then its image

 is (-x , -y)

∴ A'' = (3 , -5)

∴ B'' = (3 , -2)

∴ C'' = (1 , -2)

∴ Triangle ABC rotates 180° around the origin to form ΔA"B"C"

∵ The vertices of Δ A'B'C are:

# A' = (4 , -2)

# B' = (4 , 1)

# C' = (2 , 1)

- By comparing the x-coordinates and y-coordinates of points of

 Δ A''B''C'' and Δ A'B'C' we will find that every x-coordinate add by 1

 and every y-coordinate add by 3

∵ 4 - 3 = 1 and 2 - 1 = 1 ⇒ x- coordinates

∵ -2 - (-5) = -2 + 5 = 3 and 1 - (-2) = 1 + 2 = 3 ⇒ y-coordinates

∴ ΔA''B''C'' translates to the right 1 unite and up 3 units to form

  Δ A'B'C'

a) Δ ABC is rotated around the origin by angle 180° and then

   translated 1 unite to the right and 3 units up

b) R (O , 180°) and T (x + 1 , y + 3)

Answer:

25 seconds

Step-by-step explanation:

Hi there!

In order to answer this question, first we need to know how many bolts per second are produced by each machine, this can be known by dividing the number of bolts by the time it takes.

For machine A:

[tex]A = \frac{120 bolts}{40 s}= 3 \frac{bolts}{s}[/tex]

For machine B:

[tex]B = \frac{100 bolts}{20 s}= 5 \frac{bolts}{s}[/tex]

So, if the two machines run simultaneously, we will have a rate of prodcution of bolts equal to the sum of both:

[tex]A+B=(3+5)\frac{bolts}{s}=8\frac{bolts}{s}[/tex]

Now, we need to know how much time it will take to producee 200 bolts, to find this out we need to divide the amount of bolts by the production rate:

[tex]t = \frac{bolts}{ProductionRate}= \frac{200 bolts}{8 \frac{bolts}{s} }[/tex]

The bolts unit cancell each other and we are left with seconds

[tex]t = \frac{200}{8} s = 25 s[/tex]

So it will take 25 seconds to produce 200 bolts with machine A and B running simultaneously.

Greetings!

Answer:

25 seconds.

Step-by-step explanation:

We have been given that Machine A produces bolts at a uniform rate of 120 every 40 seconds.

Bolts made by Machine A in one second would be [tex]\frac{120}{40}=3[/tex] bolts.

Machine B produces bolts at a uniform rate of 100 every 20 seconds.

Bolts made by Machine B in one second would be [tex]\frac{100}{20}=5[/tex] bolts.

The speed of making bolts in one second of both machines running simultaneously would be [tex]3+5=8[/tex] bolts per second.

[tex]\text{Time taken by both Machines to make 200 bolts}=\frac{200\text{ bolts}}{8\frac{\text{bolts}}{\text{Sec}}}[/tex]

[tex]\text{Time taken by both Machines to make 200 bolts}=\frac{200\text{ bolts}}{8}*\frac{\text{Sec}}{\text{bolts}}[/tex]

[tex]\text{Time taken by both Machines to make 200 bolts}=25\text{ Sec}[/tex]

Therefore, the both machines will take 25 seconds to make 200 bolts.

Answer:

Step-by-step explanation:

y - 1 = 2(x + 8)

y - 1 = 2x + 16

y = 2x + 17

An equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1) is: B. y - 1 = 2(x + 8).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

At data point (-8, 1) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 2(x - (-8))

y - 1 = 2(x + 8)

In slope-intercept form, the equation of the line is given by;

y - 1 = 2x + 16

y = 2x + 16 + 1

y = 2x + 17

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Complete Question:

Which equation is the equation of the line, in point-slope form, that has a slope of 2 and passes through the point (−8, 1)?

A. y - 1 = 2(x - 8)

B. y - 1 = 2(x + 8)

C. y - 8 = 2(x + 1)

D. y - 8 = 2(x - 1)

Relatively prime means there are no number greater than 1 that divides them both.

Find the GCF for each set:

A. 68 and 119

68: 1 , 2, 4, 17, 34,68

119: 1, 7, 17

Both numbers can be divided by 1 or 17 so are not relative.

B.

40 and 395

are both divisible by 1 and 5 so are not relative.

C. 119 and 715

Are both only divisible by 1, so are relative.

D. 63 and 56

Are divisible by both 1 and 7 so are not relative.

The answer is C. 119 and 715

Hey!

---------------------------------------------------------

Question #1:

= 6n^2 - 2n - 3 + 5n^2 - 9n - 6

= 6n^2 + (-2n) + (-3) + 5n^2 + (-9n) + (-6)

= (6n^2 + 5n^2) + (-2n + -9n) + (-3 + -6)

= (11n^2) + (-11n) + (-9)

Answer: 11n² + (-11n) + (-9)

---------------------------------------------------------

Question #2:

= 8c^2 - c + 3 + 2c^2 - c + 2

= 8c^2 + (-c) + 3 + 2c^2 + (-c) + 2

= (8c^2 + 2c^2) + (-c + -c) + (3 + 2)

= (10c^2) + (-2c) + (5)

Answer: 10c² + (-2c) + 5

---------------------------------------------------------

Hope This Helped! Good Luck!

Answer:

1. 11n^2-11n-9

2. 10c^2-2c+5

Step-by-step explanation:

1. 6n^2+5n^2 = 11n^2

-2n-9n = -11n

-3-6=-9

2. 8c^2+2c^2 = 10c^2

-c-c= -2c

3+2=5

Answer:

For 2 months

Step-by-step explanation:

Let after x months the cost of each health club is same,

Now, In club A,

Membership fees = $ 19,

Monthly fees = $ 21,

So, the total fees for x months = membership fees + total monthly fees for x months

= 19 + 21x

In Club B,

Membership fees = $ 23,

Monthly fees = $ 20,

So, the total fees for x months = membership fees + total monthly fees for x months

= 23 + 20x

Thus, we can write,

19 + 21x = 23 + 20x

21x - 20x = 23 - 21

x = 2

Hence, for 2 months the total cost of each health club would be same.

Approximately [tex]\(8.51 \times 10^8\)[/tex] ice cream cones are purchased in one year, given a rate of 1.7 thousand cones per minute over [tex]\(5.3 \times 10^5\)[/tex] minutes.

To find the total number of ice cream cones purchased in one year, we can multiply the rate of purchase per minute by the total number of minutes in a year.

Given: Purchase rate = 1.7 thousand ice cream cones per minute, and there are [tex]\(5.3 \times 10^5\)[/tex] minutes in a year.

[tex]\[ \text{Total cones in one year} = \text{Rate per minute} \times \text{Minutes in a year} \][/tex]

[tex]\[ \text{Total cones} = 1.7 \times 10^3 \, \text{cones/minute} \times 5.3 \times 10^5 \, \text{minutes} \][/tex]

Now, multiply the coefficients and add the exponents:

[tex]\[ \text{Total cones} = 8.51 \times 10^8 \, \text{ice cream cones} \][/tex]

Therefore, approximately [tex]\(8.51 \times 10^8\)[/tex] ice cream cones are purchased in one year.

Final answer:

By multiplying 1.7 × 10³ cones per minute by 5.3 × 10⁵ minutes per year, the total number of cones purchased in one year is approximately 9.01 × 10⁸ cones.

Explanation:

To calculate the total number of ice cream cones purchased in one year, we can use scientific notation and multiplication. First, convert the number of ice cream cones bought per minute into scientific notation:

1.7 thousand cones per minute = 1.7 × 10³ cones/minute

Next, multiply this by the total number of minutes in a year, also given in scientific notation:

5.3 × 10⁵ minutes/year

The calculation will look like this:

(1.7 × 10³ cones/minute) × (5.3 × 10⁵ minutes/year) = (1.7 × 5.3) × (10³× 10⁵) = 9.01 × 10⁸ cones/year

The approximation for the number of cones purchased in one year is 9.01 × 10⁸ cones.

Answer:

Step-by-step explanation:

72/6=13

Answer:

Each person picked 12 bananas.

Step-by-step explanation:

Given,

Total numbers of banana = 72,

The number of persons = 6,

If each person picks equal number of bananas,

Then,

[tex]\text{Total bananas picked by each person}=\frac{\text{Total bananas}}{\text{Total persons}}[/tex]

[tex]=\frac{72}{6}[/tex]

= 12

The component of A that is parallel to B can be found using the equation A_parallel to B = (A.B)/|B|. Therefore, the component of A parallel to B is A_parallel to B = Scalar product / |B|

The component of A that is parallel to B can be found using the equation:

Aparallel to B = (A.B)/|B|

where A.B is the dot product of vectors A and B and |B| is the magnitude of vector B.

Since the scalar product is equal to the magnitude of B times the component of A parallel to B, we can rewrite the equation as:

Scalar product = |B| * Aparallel to B

Therefore, the component of A parallel to B is:

Aparallel to B = Scalar product / |B|

Answer:

13 over 3

Step-by-step explanation:

Hi Jakeyriabryant! I hope you’re fine!

I hope I have understood the problem well.

If so, what the exercise raises is the following equality:

(x-1) / 5 = 2/3

From this equation you must clear the "x".

First, we pass the 5 that is dividing on the side of the x, to the other side and passes multiplying

(X – 1) / 5 = 2/3  

(X – 1) = (2/3)*5

X – 1 = 10/3

Then we pass the one that is subtracting from the side of the x, to the other side and passes adding

X  = 10/3 + 1

Remember that to add or subtract fractions they must have the same denominator or a common denominator (in this case we can write 1 as fraction 3/3). Then,

X = 10/3 + 3/3

X = 13/3

I hope I've been helpful!

Regards!

The solution to the equation 2/3 = (x-1)/5 is x = 13/3. This is achieved by cross-multiplying, then isolating x.

To solve for x in the equation 2/3 = (x-1)/5, you will need to isolate the variable 'x'. This requires you to perform the same mathematical operation on both sides of the equation in order to maintain balance. Here we have a situation that involves proportions. Solve it by cross-multiplying:

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Answer:  d. This study is best described as an experiment.

e. The explanatory variable is whether or not fertilizer X was used.

f. The response variable is the average height for each group of 10 plots.

Step-by-step explanation:

Given : A crop scientist is conducting research with a drought resistant corn hybrid.

She is interested in determining if using fertilizer X will increase plant height.

She prepares 20 single acre plots and randomly assigns 10 to have normal soil while the other 10 are planted with fertilizer X.

This study is best describe as an experiment because the scientist is experimenting about the increase in plant height with an generation of  20 single acre plots not like an observational study where the observer just observe the study without any influence.

Here the fertilizer is used to see the change in the plant height.

So, the explanatory variable is whether or not fertilizer X was used and the response variable is the average height for each group of 10 plots.