The length of a rectangle is 3x +2 and the width of the rectangle is 6x-1. Express the

We invested $10000 into two bank accounts. One account earns 14% per year, the other account earns 8% per year. How much did we

Blababa [14]

Answer:

$7,300 was invested in the 14% account while $2,700 was invested in the 8% interest account

Step-by-step explanation:

Let the amount invested in first account be $x while the amount for second account is $y

Mathematically;

x + y = 10,000 •••••••••(i)

Interest on first account

= 14% of x = 14/100 * x

Interest on second account

= 8% of y= 8/100 * y

Adding all together will give total

14/100 * x + 8/100 * y = 1238

Multiply through by 100

14x + 8y = 123800 •••••••(ii)

From equation 1, x = 10,000 - y

Insert this into second equation

14(10,000-y) + 8y = 123,800

140,000 - 14y + 8y = 123,800

140,000 - 6y = 123,800

6y = 140,000 - 123,800

6y = 16,200

y = 16,200/6

y = $2,700

Recall

x + y = 10,000

x = 10000 - y

x = 10,000 - 2,700

x = $7,300

3 0

3 years ago

Can anyone explain how to find surface area? BRAINLIEST FOR BEST EXPLAINTION!

Wittaler [7]

Surface Area of a Cube = 6 a 2

(a is the length of the side of each edge of the cube)

In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac
(a, b, and c are the lengths of the 3 sides)

In words, the surface area of a rectangular prism is the area of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.

The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.

Surface Area of Any Prism

(b is the shape of the ends)

Surface Area = Lateral area + Area of two ends

(Lateral area) = (perimeter of shape b) * L

Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

Surface Area of a Sphere = 4 pi r 2

(r is radius of circle)

Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h

(h is the height of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r 2) + (2 pi r)* h

In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.

You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.

The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(pi r 2) + (2 pi r)* h

6 0

3 years ago

What is an equation of a line,in point-slope from, that passes through (1, -7) and has a slope of -2/3

il63 [147K]

Answer:

y + 7 = - $\frac{2}{3}$ (x - 1)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

Where m is the slope and (a, b) a point on the line

Here m = - $\frac{2}{3}$ and (a, b) = (1, - 7), thus

y - (- 7) = - $\frac{2}{3}$ (x - 1), that is

y + 7 = - $\frac{2}{3}$ (x - 1) ← in point- slope form

3 0

3 years ago

A loaf of bread costs $1.40 and the markup is 30% of the selling price. Find the selling price.

andreev551 [17]

Answer:

The selling price after the markup is $1.82

Step-by-step explanation:

$1.40 * .30 =

Multiply $1.40 times .30 (which is same as 30%)

$1.40 * .30 = $0.42

Add $1.40 and $0.42

= $1.82

Hope this helps.

6 0

3 years ago

4. The data shows the number of siblings each student in a 9th-grade class has.

antiseptic1488 [7]

Answer:

The correct option is Mean and standard deviation.

Step-by-step explanation:

The data set provided, arranged in ascending order is:

S = {0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 4}

Now, it is provided that Macy was absent when the data was collected and the class guessed she had 4 siblings. When she returned, they found out she actually has 9 siblings.

So, the new data set is:

X = {0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 9}

The mean of a data set is the average value representing the entire data.

$\bar X=\frac{1}{n}\sum X_{i}$

The median is the middle value of the data set.

The inter-quartile range is the difference between the first and the third quartile.

The standard deviation is the value that represents how dispersed the data values are.

$SD=\sqrt{\frac{1}{n}\sum (X_{i}-\bar X)^{2}}$

From all the above statistic, the mean and standard deviation are the only ones that uses all the observations in the data set to compute their value.

So, on changing one of the 4s by a 9, the set of measures that will be affected are the mean and standard deviation.

Thus, the correct option is Mean and standard deviation.

3 0

3 years ago