An ounce is 1/16 of a pound. How many ounces are in 8 3/4 pounds?

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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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.

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

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

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.

Answer:18.75 gallons

Step-by-step explanation:

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.

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.

-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.

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:

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:

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 monthly interest rate on this annuity is approximately 0.4318%.

To find the monthly interest rate on the annuity, we need to use the present value formula for an annuity:

PV = A * (1 -[tex](1+r)^{(-n)[/tex]) / r

Where PV is the present value, A is the monthly payment, r is the monthly interest rate, and n is the total number of payments. In this case, PV = $90,000, A = $850, and n = 15 (since the professor's remaining life expectancy is 15 years).

By plugging in these values and solving for r, we can find the monthly interest rate on the annuity.

$90,000 = $850 * (1 - [tex](1+r)^{-15)[/tex] / r

After solving this equation, we find that the monthly interest rate on this annuity is approximately 0.4318%.

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The monthly interest rate is approximately 0.58%.

To determine the monthly interest rate on the annuity, we need to solve for the rate that equates the present value of the annuity payments to the initial payment of $90,000. The payments of $850 are made for the expected life of 15 years, which translates to 180 monthly payments.

The present value (PV) of an annuity can be calculated using the formula:

[tex]PV = Pmt * [(1 - (1 + r)^{-n}) / r][/tex]

Where:
Pmt = $850 (monthly payment)
r = monthly interest rate
n = 180 (total number of payments)

Given PV = $90,000, we need to solve for r:

$90,000 = $850 × [(1 - (1 + r)^-180) / r]

This requires solving the equation iteratively or using a financial calculator, as it's a non-linear equation. By trial and error or using a financial calculator or spreadsheet:

We find that r ≈ 0.0058 or 0.58%

Thus, the monthly interest rate on this annuity is approximately 0.58%.

Answer:

a y=.5x

Step-by-step explanation:

please dont look at my name

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!

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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