Upon graduation from​ college, Warren Roberge was able to defer payment on his ​$22,000 student loan for 3 months. Since the interest will no longer be paid on his​ behalf, it will be added to the principal until payments begin. If the interest is 6.94 ​% compounded monthly ​, what will the principal amount be when he must begin repaying his​ loan?

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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To find the number of hours Carla worked, we'll set up and solve equations based on the information given.

To solve this problem, we'll set up an equation based on the information given.

Let x be the number of hours Carla worked last week and y be the number of hours she worked this week.

According to the problem, 15 more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15:

2x + 15 = 3y - 15

Next, we'll set up another equation based on the fact that Carla worked the same number of hours each week:

x = y

We can now solve this system of equations to find the value of y, which represents the number of hours Carla worked this week:

Substituting y for x in the first equation: 2y + 15 = 3y - 15

Combining like terms: 15 = y - 15

Adding 15 to both sides: 30 = y

So, Carla worked 30 hours this week.

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:

C. $25

Step-by-step explanation:

We will find,

The slope of the function using [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].

Taking the points (1,40) and (2,55).

Slope = [tex]\frac{55-40}{2-1}[/tex]

i.e. Slope = [tex]\frac{15}{1}[/tex]

i.e. Slope = 15

Substituting the slope and point (1,40) in the equation [tex]y=mx+b[/tex],

We have, [tex]40=15\times 1+b[/tex]

i.e. [tex]b=40-15[/tex]

i.e. b= 25

Thus, the equation of the linear function is [tex]y=15x+25[/tex].

This linear function represents the cost of the comic book since Lucy purchased it, where x= years.

So, the initial value of the comic book is when x= 0.

So, [tex]y=15\times 0+25[/tex] i.e. y= 25

Hence, the cost of the book when Lucy purchased it was $25.

Answer:

The answer be 25

Step-by-step explanation:

Answer:18.75 gallons

Step-by-step explanation:

Answer:

The answer would be option A the scalene triangle

Answer:

The first triangle, or, A !!

Step-by-step explanation:

Answer:

5040

Step-by-step explanation:

To Find : How many different 4-digit personal identification numbers are possible if no digit can be used twice?

Solution :

Since we are given that no digit can be used twice

SO, when one digit is used so next digit will be chosen from the remaining digit an so on .

the digits can be 0,1,2,3,4,5,6,7,8,9

Since these are 10 in number

out of these 10 we need to choose 4 but no digit can be used twice

⇒[tex]_{10}\textrm{C}_1 *_{9}\textrm{C}_1 *_{8}\textrm{C}_1*_{7}\textrm{C}_1  [/tex]

Formula : [tex]_{n}\textrm{C}_r=\frac{n!}{r!(n-r)!}[/tex]

thus using this formula

⇒[tex]\frac{10!}{1!(10-1)!} *\frac{9!}{1!(9-1)!}*\frac{8!}{1!(8-1)!}*\frac{7!}{1!(7-1)!}[/tex]

⇒[tex]\frac{10!}{9!} *\frac{9!}{8!}*\frac{8!}{7!}*\frac{7!}{6!}[/tex]

⇒[tex]10*9*8*7[/tex]

⇒[tex]5040[/tex]

Thus  different 5040 number of 4-digit personal identification numbers are possible if no digit can be used twice

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.

-6 -(-4) = -6 +4 = -2

 So answer is:

A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.

Answer:

The correct option is B) A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.

Step-by-step explanation:

Consider the provided expression.

−6 − (−4)

Open the parentheses and change the sign.

−6 − (−4)

−6 + 4

Subtract the numbers.

−2

Now draw this on number line.

First draw a number line is shown from −10 to 0 to 10. with scale of 2 unit on either side of the number line. Draw an arrow pointing from 0 to −6 Which show −6. Above this, another arrow pointing from −6 to −2 which shows −6 − (−4) = −2. A vertical bar is shown at the tip of the arrowhead of the top arrow.

The required number line is shown in the figure 1.

Hence, the correct option is B) A number line is shown from negative 10 to 0 to positive 10. There are increments of 2 on either side of the number line. The even numbers are labeled on either side of the number line. An arrow pointing from 0 to negative 6 is shown. Above this, another arrow pointing from negative 6 to negative 2 is shown. A vertical bar is shown at the tip of the arrowhead of the top arrow.

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).

Answer: 8.

Step-by-step explanation: since the y coordinates are the same number and they are both positive you move to the x coordinates and you subtract them since they are both negative and you'd get a positive 8. Have a Blessed Day! :D

To find the distance between two points in a coordinate plane, you can use the distance formula. In this case, the distance between point G (-4, 1) and point H (-12, 1) is 8 units.

To find the distance between two points in a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem and is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, the coordinates of point G are (-4, 1) and the coordinates of point H are (-12, 1).

So, substituting the values into the distance formula:

distance = sqrt((-12-(-4))^2 + (1-1)^2)

Simplifying that expression, the distance between point G and point H is 8 units.

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.

Answer:

The slope of the function is 5.

Step-by-step explanation:

Remember that to calculate the slope of any function you just need the equation of the function on slope form: y=mx+c or any two points in the graph that are result of the function, in this case we have a table, and we will use the first two points:

(-4,-16)

(-2.-6)

So the formula for slope is:

[tex]\frac{y2-y1}{x2-x1}[/tex]

We insert the values of our two points:

[tex]\frac{y2-y1}{x2-x1} \\\frac{-6-(-16)}{-2-(-4)}\\\frac{10}{2}\\  Slope=5[/tex]

So the slope of the function is 5.

The final mark you can get by substitute the 6 to the x  which you get the total of 38 because you have to calculate the perimeter of the isosceles triangle. You both literally helped me to get the full marks on Mathswatch Thank you!

Taking square root on both sides, that becomes 2x - 5 = (+/-) √11

Then:

2x = (+/-)√11 + 5

x = [5 +/- √11 ] / 2

x = 5/2 +/- (√11)/2

That is, x = 5/2 +(√11)/2 and x = 5/2 - (√11)/2

The solution is Option B.

The value of x = 2

The value of y = -2

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

The value of A is

5x + 2y = 6   be equation (1)

Let the second equation be B

The value of B is

3x + y = 4   be equation (2)

Now , on simplifying the equations , we get

Multiply equation (2) by 2 , we get

6x + 2y = 8   be equation (3)

Subtracting equation (1) from equation (3) , we get

x = 8 - 6

x = 2

So , the value of x = 2

Substituting the value of x in equation (2) , we get

3x + y = 4

3 ( 2 ) + y = 4

6 + y = 4

Subtracting 6 on both sides of the equation , we get

y = -2

So , the value of y = -2

Hence , the solution to the system of equations is x = 2 and y = -2

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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.

Answer:

C. [tex](0,-5)[/tex]

Step-by-step explanation:

We have been given a graph of system of equation on coordinate plane. We are asked to find the solution for the system of equations.

We know that we can find solution of a system of linear equations by graphing. The solution of the system is the point, where both lines intersect.

Upon looking at our given graph, we can see that both lines intersect at point [tex](0,-5)[/tex] that is at y-axis.

Therefore, the solution to the system of equations is [tex](0,-5)[/tex] and option C is the correct choice.

Answer:

a y=.5x

Step-by-step explanation:

please dont look at my name