the cost $C of transporting goods is directly proportional to the distance, d km. Given that C=100 when d=60 find

a) an equation connecting C and d

b) the cost of transporting goods for 45km

c) the distance if the cost of transporting goods is $120

Answer:

Yes, they are equal.

Step-by-step explanation:

Because these are both right triangles, we know that one angle is similar. And seeing that side MO is the hypotenuse of both triangles, by the SA theorem we know that the two are equal. Or because we know that this is a reactangle or square by the four equal angles, we know that because this triangle is split in half, the triangle have to be equal.

-Hope this

Therefore , the solution of the given problem of unitary method comes out to be a 2-liter soda costs $4.98 and a platter of nachos costs $11.99.

The measurements taken from this femtosecond section must be multiplied by two in order to complete the task using the unitary variable technique. In essence, the characterised by a group and the hue groups are both removed from the unit approach when a desired object is present. For example, 40 pens with a expression price will indeed cost Inr ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality.

Here,

Let's use "N" for the price of a platter of nachos and "S" for the price of a 2-liter soda.

The first aspect of the issue reveals that:

=> 5N + 2S = 67.87

The second component of the issue reveals the following to us:

=>2N + S = 27.94

=> S = 27.94 - 2N

When we use this expression in place of S in the first equation, we obtain:

=> 5N + 2(27.94 - 2N) = 67.87

When we simplify and account for N, we obtain:

=> 5N + 55.88 - 4N = 67.87\sN = 11.99

We can determine S by substituting this number for N in the second equation:

=> 2(11.99) + S = 27.94\sS = 4.98

As a result, a 2-liter soda costs $4.98 and a platter of nachos costs $11.99.

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In this context, we will explore the benefit and step of budgeting on home pay. By creating a budget and sticking to it, She (Henley) can ensure that she is effectively managing her income and achieving her financial goals.

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The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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1. The probability of finding 1 toy in the 24 packages is 0. This is because the company offers a toy in every 5 cereal packages, so if the father buys 24 packages, he is guaranteed to find at least 4 toys (24/5 = 4.8, rounded down to 4). Therefore, the probability of finding only 1 toy is 0.

2. The probability of finding no toy at all is also 0, for the same reason as above. The father is guaranteed to find at least 4 toys in the 24 packages he bought.

3. The mean number of toys in the 24 packages is 4.8, which is the result of 24/5. The standard deviation can be calculated using the formula sqrt(np(1-p)), where n is the number of packages, p is the probability of finding a toy in each package, and 1-p is the probability of not finding a toy. In this case, n=24, p=1/5, and 1-p=4/5. Plugging these values into the formula gives us:

Standard deviation = sqrt(24*(1/5)*(4/5)) = 1.732

So the mean number of toys in the 24 packages is 4.8, and the standard deviation is 1.732.

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The intersection point of ℓ and Q is (1, 1, 2.5) is not in any of the option.

To find the intersection point of ℓ and Q, we need to find a point that lies on both the line and the plane. We can do this by finding the equation of the line and the equation of the plane, and then solving for the point where they intersect.

First, let's find the equation of the line ℓ. We can use the formula for a line passing through two points:

(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1) = (z - z1) / (z2 - z1)

Plugging in the points (1, 1, 1) and (2, 0, 1), we get:

(x - 1) / (2 - 1) = (y - 1) / (0 - 1) = (z - 1) / (1 - 1)

Simplifying, we get:

x - 1 = -y + 1 = 0

So the equation of the line is x + y = 2.

Next, let's find the equation of the plane Q. We can use the formula for a plane passing through three points:

| x - x1  y - y1  z - z1 |
| x2 - x1  y2 - y1  z2 - z1 | = 0
| x3 - x1  y3 - y1  z3 - z1 |

Plugging in the points (0, 0, 0), (1, 2, 2), and (1, 0, 1), we get:

| x   y   z |
| 1   2   2 | = 0
| 1   0   1 |

Expanding the determinant, we get:

x(2 - 0) - y(2 - 1) + z(0 - 2) = 0

Simplifying, we get:

2x - y - 2z = 0

So the equation of the plane is 2x - y - 2z = 0.

Now we can solve for the intersection point of the line and the plane by substituting the equation of the line into the equation of the plane:

2(x + y) - y - 2z = 0

2x + 2y - y - 2z = 0

2x + y - 2z = 0

Since x + y = 2, we can substitute 2 for x + y:

2(2) + y - 2z = 0

4 + y - 2z = 0

y - 2z = -4

Now we can solve for y in terms of z:

y = 2z - 4

And substitute this back into the equation of the line:

x + (2z - 4) = 2

x = 2 - 2z + 4

x = 6 - 2z

Now we have two equations with two unknowns:

y = 2z - 4
x = 6 - 2z

We can solve for z by setting the two equations equal to each other:

2z - 4 = 6 - 2z

4z = 10

z = 2.5

And then solve for x and y:

y = 2(2.5) - 4 = 1
x = 6 - 2(2.5) = 1

So the intersection point of ℓ and Q is (1, 1, 2.5).

The correct answer is none of the options given.

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The percent notation is 55%.

Percentage is the fraction of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentage is %. In order to convert a fraction to percentage notation, multiply by 100.

Percent notation = fraction that attended the wedding x 100

= 11/20 x 100 = 55%

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Answer:

We can use trigonometry to solve this problem.

A is the taller platform, B is the shorter platform, and x is the length of the zipline cable that we want to find.

We can see that the angle between the horizontal and the zipline cable is 12 degrees, so we can use the tangent function to find x:

Therefore, the length of the zipline cable, rounded to the nearest foot, is 209 ft.

Answer:

9*5*7 = 315 week

9*5 = 40 day

Step-by-step explanation:

hope it helps

Answer:

9 songs/day × 5 days = 45 songs/day

45 songs/day × 7 days/week = 315 songs this week

The solution to the inequality 5(3y+1)<15 in interval notation is (-∞, 2/3).

To solve the inequality 5(3y+1)<15, we need to isolate the variable y on one side of the inequality. Here are the steps to do so:
1. Start with the given inequality: 5(3y+1)<15
2. Distribute the 5 on the left side: 15y+5<15
3. Subtract 5 from both sides: 15y<10
4. Divide both sides by 15: y<10/15
5. Simplify the fraction: y<2/3

Now, we can write the solution in interval notation. Interval notation uses parentheses or brackets to indicate the range of values that satisfy the inequality. In this case, the solution is all values of y less than 2/3, so we use the notation (-∞, 2/3).

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To solve this problem, we first need to find a common denominator for the fractions in the parentheses.

The common denominator for 12 and 8 is 24, so we can rewrite the fractions as (14/24) and (9/24). Then, we can add these fractions together to get (14/24) + (9/24) = (23/24). Next, we can subtract this fraction from (3/8) by finding a common denominator for 8 and 24, which is 24. We can rewrite (3/8) as (9/24) and then subtract (23/24) from it to get (9/24) - (23/24) = (-14/24). Finally, we can simplify this fraction to get (-7/12).

So, the final answer is:
(3/8) - ((7/12) + (3/8)) = (3/8) - ((14/24) + (9/24)) = (9/24) - (23/24) = (-14/24) = (-7/12)

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The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.

The given data set is,

14, 13, 13.5, 16, 14, 15.5, 14.5.

Hence, We get;

Order of data is,

⇒ 13, 13.5, 14, 14, 14.5, 15.5, 16.

Here, minimum is 13

Maximum is 16

Median is 14

Lower quartile range(Q1) is 13.5

Upper quartile range(Q3) is 15.5

Therefore, The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

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Using the triangle proportionality theorem, the length of CD is calculated as: 12 cm.

The triangle proportionality theorem states that if a line is parallel to one side of a triangle, it divides the other two sides proportionally.

To calculate the length of the line, recall the triangle proportionality theorem which states that:

Given the following:

AB = 10 cm

AC = 15 cm

BE = 8 cm

CD = ?

Based on the triangle proportionality theorem, we have:

AC/AB = CD/BE

Substitute:

15/10 = CD/8

Cross multiply:

10CD = 120

CD = 120/10

CD = 12 cm

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The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C

The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.

This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.

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Answer: I speak a little spanish but hopefully this helps:)

Los vectores son muy utilizados en muchos ámbitos de la vida cotidiana porque permiten conocer magnitudes y representarlas a partir de su módulo, sentido y dirección. Suelen usarse para: Marcar recorridos.

Step-by-step explanation:

This means that for each hour worked, Jean earns $12, and the total earnings y increase linearly with the number of hours x worked.

In mathematics, an equation is a statement that two expressions are equal. It contains an equals sign (=) between two expressions, which are usually composed of variables, constants, and mathematical operations.

For example, the equation:

2x + 3 = 7

states that the sum of two times x and three is equal to seven. This equation can be solved to find the value of x that satisfies it.

Equations can be used to model and solve a wide range of problems in mathematics and science, including algebraic, geometric, and physical problems.

Assuming that Jean earns a fixed hourly rate, we can use the equation:

y = kx

where y is the total earnings, x is the number of hours worked, and k is the hourly rate.

For example, if Jean earns $12 per hour, the equation would be:

y = 12x

This means that for each hour worked, Jean earns $12, and the total earnings y increase linearly with the number of hours x worked.

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In quadrilateral EFGH, sides FG and EH are congruent because they each have a length of 7.07

The area of quadrilateral EFGH is closest to 30 square units.

From the question, we have the following parameters that can be used in our computation:

The quadrilateral EFGH

This quadrilateral is a rectangle

From the figure, we can see that the following side lengths

EF = 3√2 = 4.24

EH = 5√2 = 7.07

So, we have

Area = 3√2 * 5√2

Evaluate

Area = 30

Hence, the area is 30 square units

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The solution to the system of equations is (0,1).

To solve the system of equations using elimination, we need to eliminate one of the variables. In this case, we will eliminate x by multiplying the first equation by -2 and the second equation by 6.

First equation: 6x+3y=3
Second equation: 2x+7y=7

Multiply the first equation by -2: -12x-6y=-6
Multiply the second equation by 6: 12x+42y=42

Now we can add the two equations together to eliminate x:
-12x-6y=-6
+12x+42y=42
_______________
0x+36y=36

Now we can solve for y:
36y=36
y=1

Now we can plug y back into one of the original equations to solve for x:
6x+3(1)=3
6x+3=3
6x=0
x=0

So the solution to the system of equations is (0,1).

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Answer:

One example of a sequence is the Fibonacci sequence, which starts with 0 and 1, and each subsequent term is the sum of the two preceding terms:

0, 1, 1, 2, 3, ...

To write the explicit formula for the nth term of the Fibonacci sequence, we can use Binet's formula:

Fn = [((1 + sqrt(5))/2)^n - ((1 - sqrt(5))/2)^n]/sqrt(5)

where Fn is the nth term in the sequence.

To write the recursive formula for the Fibonacci sequence, we can use the definition:

F0 = 0, F1 = 1, and Fn = Fn-1 + Fn-2 for n ≥ 2.

So the first five terms of the Fibonacci sequence are:

F0 = 0

F1 = 1

F2 = 1 (0 + 1)

F3 = 2 (1 + 1)

F4 = 3 (1 + 2)

F5 = 5 (2 + 3)

The explicit formula for the nth term in the sequence is:

Fn = [((1 + sqrt(5))/2)^n - ((1 - sqrt(5))/2)^n]/sqrt(5)

The recursive formula for the nth term in the sequence is:

Fn = Fn-1 + Fn-2 for n ≥ 2, with F0 = 0 and F1 = 1.

The equation 7y = 4x - 7.

An equation is a statement that asserts the equality of two mathematical expressions. It contains an equals sign (=) and typically has variables, constants, and mathematical operations on both sides.

Equations are used in many areas of mathematics, science, and engineering to represent relationships between variables and to solve problems. In algebra, equations are often used to solve for the values of variables that make the equation true.

We have;

y = 4/7x - 1

Multiplying through by 7

7y = 4x - 7

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The complete sentence would be: "For 4x^(2)+6x+2=0, a=4, b=6, and c=2."

To complete the sentence, we need to identify the values of a, b, and c in the given equation. The equation is in the form of ax^(2)+bx+c=0, where a, b, and c are the coefficients of the respective terms.

Therefore, to fill in the blanks in the sentence, we can simply match the coefficients in the given equation with the corresponding letters:

a = 4, because the coefficient of the x^(2) term is 4
b = 6, because the coefficient of the x term is 6
c = 2, because the constant term is 2

So the complete sentence would be: "For 4x^(2)+6x+2=0, a=4, b=6, and c=2."

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Answer:

x= 27.4

Step-by-step explanation:

a triangle's angles always equal 180 so

34.6+118+x=180

add 34.6 and 118 to get

152.6+x=180

subtract both sides by 152.6 to get

x=27.4

The correct option regarding the amount of coins is given as follows:

c 4 nickels, 10 dimes, 4 quarters

The amounts are obtained by a system of equations, for which the variables are given as follows:

Amy has 18 coins consisting of nickels, dimes, and quarters, hence:

x + y + z = 18.

She has the same amount of nickels as quarters, hence:

x = z.

Thus:

2x + y = 18

y = 18 - 2x.

She has a total of $2.20 worth of coins, hence:

0.05x + 0.1y + 0.25z = 2.2

0.3x + 0.1y = 2.2

Since y = 18 - 2x, the value of x is obtained as follows:

0.3x + 0.1(18 - 2x) = 2.2

0.1x = 0.4

x = 0.4/0.1

x = 4.

Hence the remaining values are given as follows:

Meaning that option c is correct.

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The equation when solved for the price of a lightbulb, y, is: [tex]y=7 - \frac{4}{5} x[/tex]

A statement that shows the equality of the two expressions is known as an equation. Mathematical operations including addition, subtraction, multiplication, division, and exponentiation are included, along with one or more variables, constants, and other operations.

To solve the equation 4x + 5y = 35 for the price of a lightbulb, y, we need to isolate y on one side of the equation. Here are the steps:

Subtract 4x from both sides of the equation:

4x + 5y - 4x = 35 - 4x

Simplifying, we get:

5y = 35 - 4x

both sides divided by 5 in the equation:

(5y)/5 = (35 - 4x)/5

Simplifying, we get:

y = (35/5) - (4/5)x

y = 7 - (4/5)x

Therefore, the equation when solved for the price of a lightbulb, y, is: [tex]y=7 - \frac{4}{5} x[/tex]

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Answer:

B is correct

Step-by-step explanation:

The points all go downhill as you move from left to right. We can draw a straight line that is fairly close to all of them. This is known as the regression line. The regression line having a negative slope tells us the linear association is negative. This means the correlation coefficient r is negative, so,  (r = -1 is not possible as not all points fall on the same straight line)

Answer:

Step-by-step explanation:

Both angles are equal so,

1+16x =17x-3

16x-17x= -3-1

-x = -4

x = 4

Answer:

y-intercept: 3

equation: y = -x + 3

Step-by-step explanation:

For problem #6: (-2,5) and (2,1)

Slope m = (y2 - y1)/(x2 - x1)

=>m = (1 - 5)/(2 - -2) = -4/4 = -1

Slope-intercept form is y = mx + b

Given m = -1, y = 1, x = 2

=> 1 = -1(2) + b

=> 1 = -2 + b

=> b = 1 + 2  = 3

equation: y = -x + 3

since b is the y-intercept => 3