Dominic has $15 for dinner. His meal costs $13.90. He wants to leave an 18% tip. Does he have enough money? Explain your reasoning

This is about understanding slopes.

Option A is correct.

y = -10x + 6  - - - (eq 1)

y - 36 = 8(x - 4)  - - - (eq 2)

y = mx + c

Where m is slope and c is the y intercept.

Let's expand eq 2 to be in the form of y = mx + c

Thus;

>>y - 36 = 8(x - 4)

>> y - 36 = 8x - 32

>> y = 8x - 32 + 36

>> y = 8x + 4  - - - (eq 3)

Thus, slope of eq 1 is -10 and y-intercept is 6.

Similarly, slope of eq 3 is 8 and y-intercept is 4.

This means y = -10x + 6 has a greater y-intercept than y - 36 = 8(x - 4).

Also, the slope in y - 36 = 8(x - 4) which is 8 will slope to the right while the slope of y = -10x + 6  which is -10 will slope to the left. This means that line represented by y = -10x + 6  has a steeper slope.

This is because the higher the slope, the steeper the line.

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After rewriting both equations in slope-intercept form, we find that the function y = -10x + 6 has a steeper slope and the function y - 36 = 8(x - 4) has a greater y-intercept, making option (b) the correct answer.

The question involves comparing the slopes and y-intercepts of two linear functions, represented by the equations y = -10x + 6 and y - 36 = 8(x - 4). To compare them, we need to write both equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

The first equation, y = -10x + 6, is already in slope-intercept form, with a slope of -10 and a y-intercept of 6. For the second equation, y - 36 = 8(x - 4), we first distribute the 8 to get y - 36 = 8x - 32 and then add 36 to both sides to get the slope-intercept form, y = 8x + 4, which has a slope of 8 and a y-intercept of 4.

Comparing the slopes, -10 for the first equation and 8 for the second, we see that the first equation has a steeper slope because -10 has a greater magnitude than 8. Comparing the y-intercepts, 6 for the first equation and 4 for the second, the first equation has a greater y-intercept. Therefore, the correct statement regarding their slopes and y-intercepts is (b) The function that is represented by the equation y = -10x + 6 has a steeper slope and the function that is represented by the equation y - 36 = 8(x - 4) has a greater y-intercept.

1, 1, 3, 3 - I just did it on e2020 and got it correct

The basic ratio of 30:42 is 5:7. This was found by simplifying the ratio to its lowest terms, which is done by dividing both sides of the ratio by the largest number that can evenly divide both numbers, the greatest common factor (GCF).

The basic ratio of 30:42 is found by simplifying the ratio to its lowest terms. To do this, find the greatest common factor (GCF) of the two terms, which is the largest number that can evenly divide both numbers. In this case, the GCF of 30 and 42 is 6. Therefore, by dividing both sides of the ratio by 6, we get the simplified ratio: 5:7. So, the basic ratio for 30:42 is 5:7.

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The expected number of times the sequence 'qqqq' appears in 1000 random typings of 6 different letters is approximately 0.769 times.

This problem falls under the category of discrete probability in mathematics. The child randomly types one of 6 different letters.

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The volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane is 6 cubic unit.

It is defined as a three-dimensional space enclosed by an object or thing.

It is given that

The solid between the planes z = 3x + 2y + 1 and z = x + y, and above the

triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane.

r(u) = (1, 2)

r(v) = (-2, -1)

|r(u)xr(v)| = 3

The volume of the solid:

∬S(3x + 2y + 1 − x − y)ds = ∫₀¹ ∫(u, 0)(2x + y +1)3 dv du

After solving:

= 3(4/3 - 5 /6 + 3/2)

= 6

Thus, the volume of the solid region. the solid between the planes z = 3x + 2y + 1 and z = x + y, and above the triangle with vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0) in the xy-plane is 6 cubic unit.

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Final answer:

The volume of the solid region between the planes z = 3x + 2y + 1 and z = x + y, above the triangular region in the xy-plane, can be found using a double integral over the triangular area defined by vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0).

Explanation:

To find the volume of the solid region between the planes z = 3x + 2y + 1 and z = x + y, and above the triangular region in the xy-plane, we can use a double integral over the triangular region. The volume is given by the difference between the two planes integrated over the area of the triangle formed by the vertices (1, 0, 0), (2, 2, 0), and (0, 1, 0).

First, define the vertices of the triangle in the xy-plane: A(1, 0), B(2, 2), and C(0, 1).

Second, find the equations of the lines forming the sides of the triangle, which helps in defining the limits of the integral.

Lastly, set up the double integral:

∫∫ (3x + 2y + 1) - (x + y) dA,

after solving, we get volume = 6

where dA is the differential area element in the xy-plane, and the limits of integration are determined by the triangular region.

The integration can be simplified by determining a suitable ordering for dx and dy, often choosing to integrate in x first and then y, or vice versa, based on the geometry of the triangle. The exact bounds for x and y need to be worked out from the equations of the lines defining the triangle's edges.

The result of this integral will give the volume of the solid region bounded by the two planes and above the triangle.

Answer:

a y=.5x

Step-by-step explanation:

please dont look at my name

Solution:

Number of Baseball cards bought by Mohammad each month = 5

As number of baseball cards is represented by T , which are

T = 0,5,10,15,20,25,30,35,40,45,50,55,60   →→  Y axis

Number of months(m) from which Mohammad started buying cards is given as

m = 0,1,2,3,4,5,6,7,8,9,10,11,12   →→     X axis

The given information represented in equation form

T = 5 m

This is a equation of line in two variable passing through origin.

Slope of line = 5 =Amount of baseball card bought each month

Number of cards bought after 6 months = 5 × 6=30

Number of cards bought after 12 months = 5 ×12 =60

Graph is depicted below.

The scale for the T-axis of his graph should go from 0 to at least 60 , and the m-axis of his graph should go from 0 to at least 12 .

Answer:

The answer would be option A the scalene triangle

Answer:

The first triangle, or, A !!

Step-by-step explanation:

Final answer:

The expected waiting time for a bus, E[t], is 8.33 minutes, which is calculated considering the possibility of either bus 51, which has a uniform arrival time between 0 to 30 minutes, or bus 82, which arrives in exactly 10 minutes.

Explanation:

The problem you are dealing with involves finding the expected waiting time, E[t], for either bus 51 or bus 82 to arrive. The expected value of a uniformly distributed random variable on an interval [a, b] is given by the formula (a + b)/2. However, we need to account for the fact that if bus 82 arrives in exactly 10 minutes, then if the 51 bus hasn't arrived by then, you will take the 82 bus.

To compute E[t], if the 51 bus arrives within the first 10 minutes, the expected waiting time is the average of 0 and 10 minutes, which is 5 minutes. If the 51 bus does not arrive within 10 minutes, you will take the 82 bus at exactly 10 minutes. Therefore, the expectation must only account for the time if the 51 bus arrives before the 82. This gives us:

The probability that the 51 bus arrives in the first 10 minutes is 10/30 = 1/3.

The expected waiting time if 51 arrives in the first 10 minutes is 5 minutes.

If the 51 bus does not arrive within 10 minutes, you'll wait exactly 10 minutes for the 82 bus.

So, E[t] = (1/3) * 5 minutes + (2/3) * 10 minutes = (5 + 20)/3 = 25/3 minutes.

Therefore, the expected waiting time E[t] is 8.33 minutes (rounded to two decimal places).

The width is 60 yards and the length, being 80 yards more, is 140 yards.

To find the dimensions of the rectangle when the perimeter is 400 yards and the length is 80 yards more than the width, we can set up two equations based on the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Let the width be w. Then the length is w + 80 yards.

Using the perimeter formula:

400 = 2(w + 80) + 2w

400 = 2w + 160 + 2w

400 = 4w + 160

Subtract 160 from both sides:

240 = 4w

Divide by 4:

w = 60 yards

Now, calculate the length:

l = w + 80 = 60 + 80

l = 140 yards

The width is 60 yards, and the length is 140 yards.

The total number of points = 13.5 points

What is the total amount of points gained?

We are given the scoring method as:

Touchdown pass: 6

Complete pass : 0.5

Incomplete pass : -0.5

Interception : -1.5

Now, we are told that Jeremy's quarterback had the following:

2 touchdowns passes,

16 complete passes,

7 incomplete passes,

2 interceptions.

Thus:

Total points = (2 * 6) + (0.5 * 16) + (-0.5 * 7) + (-1.5 * 2)

Total points = 13.5 points

Answer:

In general the two other decimals are x and y that satisfy x + y = 1.66 where x ≤ .99 and y ≤ .99

One particular pair would be x = 0.99 and y = 0.67

Step-by-step explanation:

If Holland added three decimals that made a sum of 2 and one of them was 0.34, we are going to name x and y to the other 2 decimals.

We are going to write the equation:

[tex]0.34 + x +y= 2\\x+y=2-0.34\\x+y = 1.66[/tex]

So we have that both the other numbers have to sum 1.66, however, we know both numbers are decimals so neither one of them can be greater than 1.

So this problem has many answers and the answers would be all the numbers that satisfy x + y = 1.66 where x ≤ .99 and y ≤ .99

y = 1.66 -0.99 = 0.67.

And our pair of numbers would be 0.99 and 0.67.

y = 1.66 - 0.80 = 0.86

And our pair of numbers would be 0.80 and 0.86

This way, we can find more than 1 answer for the other two decimals.

The function shows exponential growth a stretch of the function f(x) = (1/3)^x .

When the expression of a function is such that it involves the input to be present as the exponent (power) of some constant, then such a function is called an exponential function. Their usual form is specified below. They are written in several equivalent forms.

Given that the exponential function f(x) = 3

The initial value of the function is 2.

The base of the function is 3.

When the intial value is where x=0

where x=0, the value of f(0)=3

The growth is 1/3 but it is decay, that might be correct, or not because it is decay.

It is a stretch of the function f(x)=(1/3) power of x

when x=3, then f(3)=1/9

The function shows exponential growth a stretch of the function f(x) = [tex](1/3)^x[/tex].

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We have a = 2 and b = 3.

To find the exact value of sin(165°) using sum or difference formulas, we notice that 165° can be expressed as the sum of two angles whose sine and cosine values we know exactly, for example, 120° and 45°. The sum formula for sine is sin(A + B) = sin(A)cos(B) + cos(A)sin(B).

Therefore, sin(165°) = sin(120° + 45°) = sin(120°)cos(45°) + cos(120°)sin(45°).

From here, we use the known values:

sin(120°) = sin(180° - 60°) = sin(60°) = √3/2

cos(45°) = √2/2

cos(120°) = cos(180° - 60°) = -cos(60°) = -1/2

sin(45°) = √2/2

Plugging these values into our formula gives:
sin(165°) = ( √3/2)(√2/2) + (-1/2)(√2/2) = (√6 - √2)/4

This fraction can be rewritten to match the given form by factoring out √2 in the numerator:
sin(165°) = √2(√3 - 1)/4

Hence, in the form sin(165°) = √a(√b - 1)/4, we have a = 2 and b = 3.