If d(3) = 4 and d(x)= 7x - k, what is k?

The probable reason that 37 runners broke the four-minute mile barrier within one year after Roger Bannister originally did in 1954 was due to the psychological barrier being broken.

Before Bannister's accomplishment, many believed that running a mile under four minutes was impossible for a human being. However, once Bannister proved it could be done, it changed people's beliefs about what was possible and opened up new possibilities.

This change in belief and perception likely inspired other runners to push themselves harder and believe that they too could achieve this feat, leading to a rapid increase in the number of people breaking the four-minute mile barrier. Additionally, advances in training techniques and equipment may have also played a role in this increase.

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Therefore, the probability that a person with blue hair isn't invited is 49/50 or approximately 0.98.

Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. In other words, probability represents the proportion of times an event is expected to occur in a large number of repetitions of the same situation. For example, the probability of rolling a six on a fair six-sided die is 1/6, since there is one favorable outcome out of six possible outcomes.

Here,

Assuming that the invitation is randomly given to one of the 50 friends, the probability that a person with blue hair isn't invited can be found as follows:

Let B be the event that a friend has blue hair, and let I be the event that the friend is not invited. Then, we need to find the probability of the event not(B ∩ I), which represents the event that a person with blue hair isn't invited.

We can use the formula for conditional probability to express this as:

P(not(B ∩ I)) = P(not(I) | B) * P(B)

where P(B) is the probability of a friend having blue hair, and P(not(I) | B) is the conditional probability of not being invited given that the friend has blue hair.

From the given information, we know that there are 12 friends with blue hair out of 50 total friends. Therefore, P(B) = 12/50.

To find P(not(I) | B), we need to know the number of friends with blue hair who are not invited. This number is not given, so we have to make an assumption.

If we assume that the invitation is given randomly without any bias towards or against friends with blue hair, then the probability of a friend with blue hair not being invited is the same as the probability of any friend not being invited, which is:

P(not(I)) = 1 - P(I) = 1 - 1/50 = 49/50

Then, the conditional probability we need is:

P(not(I) | B) = P(not(I) ∩ B) / P(B)

P(not(I) | B) = P(not(I)) / P(B)

P(not(I) | B) = (49/50) / (12/50)

P(not(I) | B) = 49/12

Now we can substitute these values into the formula for P(not(B ∩ I)):

P(not(B ∩ I)) = P(not(I) | B) * P(B)

P(not(B ∩ I)) = (49/12) * (12/50)

P(not(B ∩ I)) = 49/50

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Answer:

Step-by-step explanation:

a is (5,1)

b is (-5,-1)

c is (5,-1)

Answer:

Therefore you have to run every mile in ~ 8 minutes.

Step-by-step explanation:

10 miles - 3 miles = 7 miles left.

1 hour 20 minutes - 24.7 minutes= 80 minutes - 24.7 minutes

                                                       = 55.3 minutes left

Therefore, you have 55.3 minutes left to run 7 miles. But since you want to finish in LESS than 1 hour and 20 minutes, subtract the .3.  

So:

7 miles = 55 minutes

1 mile        x minutes

x minutes= 55 x 1 ÷ 7 miles

x minutes = 7.85

x minutes = ~ 8 minutes

Therefore you have to run every mile in ~ 8 minutes.

Hope this helps!

A full circle is 360 degrees.

The arc length would be 48/360 of the full circumference.

12 x 48/360 = 576/360 = 1.6

The portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

To calculate the portfolio weights for stock A and stock B, we need to determine the total value of the portfolio and the proportion of each stock's value within that total.

The total value of the portfolio can be calculated as follows:

Total value = (Number of shares of stock A × Price per share of stock A) + (Number of shares of stock B × Price per share of stock B)

Total value = (135 × $84) + (110 × $82)

Total value = $11,340 + $9,020

Total value = $20,360

Now, we can calculate the portfolio weights for each stock:

Weight of stock A = (Value of stock A ÷ Total value) × 100%

Weight of stock A = (($84 × 135) ÷ $20,360) × 100%

Weight of stock A = $11,340 ÷ $20,360

Weight of stock A ≈ 0.5569 or 55.69%

Weight of stock B = (Value of stock B ÷ Total value) × 100%

Weight of stock B = (($82 × 110) ÷ $20,360) × 100%

Weight of stock B = $9,020 ÷ $20,360

Weight of stock B ≈ 0.4431 or 44.31%

Therefore, the portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.

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Answer:

The image A'(4, 6) is the result of dilation of the original point A(2, 3) by a scale factor 2 with a center at the origin.

Therefore, we conclude that If A (2, 3) maps to A' (4, 6) under a certain enlargement:

Step-by-step explanation:

We know that when any object is dilated by a certain scale factor, it gets reduced or enlarged. The reduction or enlargement depends upon the scale factor.

If the scale factor > 1, the image is an enlargement.

If the scale factor < 1, the image is reduced.

For example, if a point P(x, y) is dilated by a scale factor of 2 with a center at the origin, the image P' will have the coordinates (2x, 2y).

As scale factor 2 > 1, so the image P' is enlarged.

Given the point

A(2, 3)

Rule of dilation by a scale factor 2 with a center at the origin

P(x, y) → P'(2x, 2y)

A(2, 3) → A'(2(2), 2(3)) = A'(4, 6)

It is clear that image A' has the coordinates (4, 6). i.e. A'(4, 6).

In other words, the image A'(4, 6) is the result of dilation of the original point A(2, 3) by a scale factor 2 with a center at the origin.

Therefore, we conclude that If A (2, 3) maps to A' (4, 6) under a certain enlargement:

In the given word problem, the rate of change is the change in the cost of the ice cream concerning the change in the number of scoops.

That is, the rate of change is the ratio of the change in the cost of ice cream and the change in the number of scoops. Let's first calculate the initial rate of change or slope of the given deal: When we buy a waffle cone, the cost is $3, and we can buy one scoop of ice cream for $1.50.So, for one scoop of ice cream, the total cost would be 3 + 1.50 = $4.50.

We can represent the cost of one scoop of ice cream with the help of a linear equation: y = mx + b. Here, the slope or the rate of change, m = Change in cost of ice cream/ Change in the number of scoops= 1.5/1= 1.5Therefore, the rate of change of the ice cream with respect to the number of scoops is $1.50/scoop.

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Answer:

138

Step-by-step explanation:

$ 11.50 x 12 = 138

It would take approximately 52.49 hours to fill the empty tank with only Inlet B running. The correct answer is 52.49 hours .

To find the time it would take to fill the empty tank with only Inlet B running, we can first determine the rate at which both Inlet A and Inlet B fill the tank.

Let's say the rate at which Inlet A fills the tank is A gallons per hour, and the rate at which Inlet B fills the tank is B gallons per hour.

We know that Inlet A fills the tank in 22 hours, so the rate of Inlet A can be calculated as:
Rate of Inlet A = 8,000 gallons / 22 hours = 363.64 gallons per hour (approx.)

When both Inlet A and Inlet B are used, the tank fills in 15.5 hours. Therefore, the combined rate of Inlet A and Inlet B can be calculated as:
Rate of Inlet A + Rate of Inlet B = 8,000 gallons / 15.5 hours = 516.13 gallons per hour (approx.)

To find the rate of Inlet B, we subtract the rate of Inlet A from the combined rate:
Rate of Inlet B = Rate of Inlet A + Rate of Inlet B - Rate of Inlet A = 516.13 gallons per hour - 363.64 gallons per hour = 152.49 gallons per hour (approx.)

Now, to find the time it would take to fill the empty tank with only Inlet B running, we divide the tank capacity by the rate of Inlet B:
Time = 8,000 gallons / 152.49 gallons per hour = 52.49 hours (approx.)

Therefore, it would take approximately 52.49 hours to fill the empty tank with only Inlet B running.

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It would take approximately 52.5 hours to fill the empty tank with only Inlet B running.

To find out how long it would take to fill the empty tank with only Inlet B running, we need to determine the rate at which Inlet B fills the tank.

First, let's calculate the rate at which Inlet A fills the tank. In 22 hours, Inlet A can fill the tank, which has a capacity of 8,000 gallons. Therefore, the rate of Inlet A can be calculated as 8,000 gallons divided by 22 hours, which equals 363.64 gallons per hour.

Next, let's calculate the combined rate of Inlet A and Inlet B. In 15.5 hours, both Inlet A and Inlet B together fill the tank. Since the combined rate is the sum of the individual rates, we can calculate it as 8,000 gallons divided by 15.5 hours, which equals 516.13 gallons per hour.

To find the rate of Inlet B, we subtract the rate of Inlet A from the combined rate. Therefore, the rate of Inlet B is 516.13 gallons per hour minus 363.64 gallons per hour, which equals 152.49 gallons per hour.

Finally, we can calculate the time it would take to fill the empty tank with only Inlet B running. Since the rate of Inlet B is 152.49 gallons per hour, and the tank has a capacity of 8,000 gallons, we can divide 8,000 gallons by 152.49 gallons per hour. This gives us approximately 52.47 hours, which can be rounded to 52.5 hours.

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Answer: 3.6

20

8.25

Step-by-step explanation:

7 - 10 = 3

-6 - -8 = 2

\(\sqrt{3^{2} +2^{2} } =3.6\)

The statistic that the value 24.7 represents in this context is the median of the gas mileages for the cars tested.

Popular magazine that tests cars and trucks for mileage on the road and around the city. They report that 50% of the cars tested had mileages below 24.7 mpg on the road, and the other 50% had mileages above 24.7 mpg. The 24.7 mpg statistic represents the median of the gas mileages for the cars tested. This is because the median is the middle value when the data is arranged in ascending order, and in this case, it separates the lower 50% from the upper 50% of the mileages.

The median is the value that separates the data set into two halves. In this case, the magazine reports that 50% of the cars tested had mileages below 24.7 mpg on the road and the other 50% of the cars tested had mileages above 24.7 mpg. This means that 24.7 mpg is the exact middle value of the distribution of the gas mileages for the cars tested.

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The solution to given problem is  since E(Wu) < Wr, there will be no migration from rural areas .

The subject of probability in mathematics is concerned with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, with 1 typically signifying certainty and 0 typically signifying impossibility.

Here,

Since ,the rural wage is $2 per day. Urban modern sector employment can be obtained with .24 probability and pays $4 per day. The urban traditional sector pays $1 per day.

As long as the rural pay (Wr) differs from the anticipated urban wage (E(Wu)), according to the Harris-Todaro model, there will be movement between rural and urban areas.

Here, Wr equals $2.00.

Determine the anticipated urban wage now.

E(Wu) = p

*Wum+(1-p)

*Wut

Where p is the likelihood of finding employment in the urban modern sector, which is 0.25, and Wum is the wage for such employment, which is $4.00.

Wut = $1.00 in wages for jobs in the typical urban sector.

Hence, E(Wu) = 0.24*$4.00+0.76*$1.00 = $1.72

Since E(Wu) < Wr, there will be no migration from rural areas .

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Answer:

y= -1/3x+3

Step-by-step explanation:

Old homework answers.

Answer:

A

Step-by-step explanation:

A is the right answer because I took the quiz.

Answer:

f(x)= (-4)/(5-X)

Step-by-step explanation:

Let's do

\(\\ \sf\longmapsto 3.76(4.8)\)

\(\\ \sf\longmapsto \dfrac{376}{100}\times \dfrac{48}{10}\)

\(\\ \sf\longmapsto \dfrac{18048}{1000}\)

\(\\ \sf\longmapsto 18.048\)

3.76 x 4.8 = 376/100 × 48/10 = 18048/1000 = 18.048

Answer: 18.048

Ok done. Thank to me :>

Answer: 0.31

Step-by-step explanation:

0.3158 is closer too 0.3100 than 0.3000 or 0.3

Rounding 0.3058 to the nearest hundredth gives us 0.31.

Given that a number we need to round it to the nearest hundredth,

To round 0.3058 to the nearest hundredth, we need to look at the digit in the thousandth place (the third decimal place).

Step 1: Look at the digit in the thousandth place. In this case, the digit is 5.

Step 2: Determine if the digit is 5 or greater. If the digit is 5 or greater, we round up. If the digit is less than 5, we round down.

Since the digit in the thousandth place is 5, we round up.

Step 3: Round up the number in the hundredth place. In this case, the number in the hundredth place is 0.

Rounding up 0 to the nearest hundredth gives us 1.

Therefore, rounding 0.3058 to the nearest hundredth gives us 0.31.

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The functions f(x) and g(x) are defined differently based on the value of x. For x less than or equal to 1, f(x) is equal to 3x + 4, while for x greater than 1, f(x) is equal to (1/3)x + 8. This indicates that the two functions have different rules or formulas depending on the value of x.

The function f(x) is defined piecewise, meaning it has different expressions for different intervals of x. For x less than or equal to 1, f(x) is given by 3x + 4. This means that for values of x in this range, the function f(x) will produce outputs according to the equation 3x + 4. On the other hand, for x greater than 1, f(x) is given by (1/3)x + 8.

This means that for values of x in this range, the function f(x) will produce outputs according to the equation (1/3)x + 8. The difference in the rules or formulas for f(x) depending on the value of x distinguishes it from a typical linear function.

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(a) We first need to obtain two direction vectors on the plane. These direction vectors will be given by the difference between the coordinates of pairs of points on the plane. Let us choose the direction vectors AB and AC as shown below.

AB= ( 6−1,4−1,−5+1)=(5,3,−4)

AC= (−4−1,−2−1,3+1)

=(−5,−3,4)

A point on the plane, A, is given as (1,1,−1).

Using the vector equation of a plane, the equation of the plane, p, can be found as follows.

p → . ( A → − A → 0 ) = 0

where A→0 is a vector perpendicular to the plane.

A→0= AB × AC

       =〈5,3,−4〉 × 〈−5,−3,4〉

       =〈0,−36,−12〉

Normalizing A→0 yields;

A→0= 1 6 〈0,−36,−12〉 =〈0,−6,−2〉

Thus the equation of the plane is given by;

p: 0(x−1)−6(y−1)−2(z+1)=0

or x−3y+z−5=0

(b) Let vector w be the cross product of vectors u and v.

w→ = u→ × v→ = 〈 2, 2, −1 〉 × 〈 2, 0, 6 〉 = 〈 12, -14, -4 〉

Therefore,

w→ = 〈 12, -14, -4 〉 is the vector that is orthogonal to both u→ and v→ .

We can verify this by taking the dot product of w→ with u→ and v→. u→ · w→

= (2)(12) + (2)(-14) + (-1)(-4)

= 0v→ · w→

= (2)(12) + (0)(-14) + (6)(-4)

= 0

Therefore, we can conclude that w→ = 〈 12, -14, -4 〉 is the vector that is orthogonal to both u→ and v→.

The dot product of any two orthogonal vectors is always equal to 0.

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The other piece of evidence that supports the author's main point is, "Schools already teach math skills, which are used to count money". Thus, option third is correct.

The evidence for a proposition is what backs up that assertion. It is commonly seen as proof that the supported statement is correct. The function of evidence and how it is conceived differs by discipline.

The point for the given chart is "Students should learn money skills in school". The evidences of the given point are as follows:-

"Having money skills will help students become successful adults."

"Schools already teach math skills, which are used to count money."

Therefore, it can be concluded that option third is correct.

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Answer:

Sydney is 42 years old

Step-by-step explanation:

57 - 15 = 42

Answer: -20

Step-by-step explanation: 16 x 1/4 - 4x 6

According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)

Quadrilateral

Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.

If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.

Here we need to find the coordinate of D'.

In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.

While we looking into the graph, we have identify the point of

A (0,0), B(-4, 3), C(1,5) and D(2,3)

Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).

According to this rule, the new coordinates are written as,

A(0,0) = A'(0,0)

B'(-4,3) = B'(-3,-4)

C(1,5) = C'(5, -1)

D(2,3) = D' (3, -2)

Therefore, the new coordinate of D' is (3, -2).

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Answer:

They are similar by the definition of similarity in terms of a dilation

Step-by-step explanation:

The given vertices of triangle ΔABC are;

A(1, 5), B(3, 9), and C(5, 3)

The vertices of triangle ΔDEF are;

D(-3, 3), E(-2, 5), and F(-1, 2)

Therefore, we get;

The length of segment, \(\overline{AB}\) = √((9 - 5)² + (3 - 1)²) = 2·√5

The length of segment, \(\overline{BC}\) = √((9 - 3)² + (3 - 5)²) = 2·√10

The length of segment, \(\overline{AC}\) = √((5 - 3)² + (1 - 5)²) = 2·√5

The length of segment, \(\overline{DE}\) = √((5 - 3)² + (-2 - (-3))²) = √5

The length of segment, \(\overline{EF}\) = √((2 - 5)² + (-1 - (-2))²) = √10

The length of segment, \(\overline{DF}\) = √((2 - 3)² + (-1 - (-3))²) = √5

∴ \(\overline{AB}\)/\(\overline{DE}\) = 2·√5/(√5) = 2

\(\overline{BC}\)/\(\overline{EF}\) = 2·√10/(√10) = 2

\(\overline{AC}\)/\(\overline{DF}\) = 2·√5/(√5) = 2

The ratio of their corresponding sides are equal and therefore;

ΔABC and ΔDEF are similar by the definition of similarity in terms of dilation.

Answer:

fg(x) = √143x+121

Step-by-step explanation:

in such function we go right to left

given = f(x) = √11x   and g(x) = 13x + 11

fg(x) =

f( 13x + 11 )

√11( 13x + 11 )

√143x+121

therefore found fg(x) = √143x+121

Answer:

The answer to this is B, $135.

Step-by-step explanation:

I took the test.

Answer:

$135 is the correct answer, I took the test and got it right

Step-by-step explanation:

Answer:

Pears = $ 0.60 each and apples $0.75 each.

Step-by-step explanation:

4a+3p = 4.80

3a+5p = 5.25 (I will solve it by addition)

3(4a+3p=4.80) plus

-4(3a+5p=5.25) =

12a+9p=14.40 plus

-12a-20p= -21

-11p = - 6.6

p = -66/-11

p = 0.60

Apples:

4a + 3(0.60) = 4.80

4a + 1.80 = 4.80

a = (4.80-1.80)/4

a = 0.75