I dont understand the problem

Answer:

option 2 is correct ans. it can be solved by substitution method.

Answer: Mica spent $70.65

Step-by-step explanation:

Mica's bank balance before shopping = $22.50

Mica's bank balance after shopping = - $48.15

Mica's spending could be calculated by:

Difference between initial and final bank balance.

Hence,

[(Bank balance before shopping - (bank balance after shopping)]

[$22.50 - (-$48.15)]

= $22.50 + 48.15

= $70.65

Step-by-step explanation:To find the interest accumulated over a period of time you use:

A = P [1 + (r/n)]^(nt)

with A = new amount in the account, P = principal, r = percent rate as a decimal, n = how many times you compound during one year, t = time in years.

A = 2000

P = 1500

r = 0.035

n=1

Thus you get:

2000 = 1500 (1+0.035)^t

Divide by 1500:

(4/3) = (1.035)^t

Apply "ln" on both sides:

ln(4/3) = t*ln(1.035)

Calculate the logarithms:

0.28768 = t*0.03440

Divide by 0.03440 on both sides:

t = 8.36 years

So after approximately 8 years and 5 month you will have $2000 or more in the account.

This question is incomplete because it lacks the appropriate options

Complete Question

Which formulas can be used to find the surface area of a regular pyramid

where p is the perimeter of the base, s is the slant height, BA is the base area,

and LA is the lateral area?

Check all that apply.

a) SA = BA + 1/2ps

b) SA = 2BA + 1/2ps

c) SA = BA + LA

d) SA = BA + 2LA

e) SA = 8.LA

Answer:

a) SA = BA + 1/2ps

d) SA = BA + 2LA

Step-by-step explanation:

When finding the surface area of a regular pyramid it is important to take note of two things

A pyramid has a Base area which is always represented by BA.

a) When a regular pyramid has similar ( side)faces, for examples a regular square pyramid, which has the base of a square, the formula to use is

Surface Area = Base Area + 1/2ps

Where p = Perimeter of the side faces

s = Slant height.

b) When the side faces are not so similar , for example, we are given a triangular based pyramid, the formula we would use is given as:

Surface Area = Base Area + Lateral Area.

Therefore, the formulas we can use to find the Surface Areas or a regular pyramid are:

a) SA = BA + 1/2ps

d) SA = BA + 2LA

Answer:

Step-by-step explanation: The answer is A because the two lines must intersect to form an angle take the letter L for example. Letter B is incorrect because Parallel means they don't touch kind of like these two L's: l l And C and D could mean anything meaning they could intersect or not which is an answer too broad for the question.

=====================================================

Explanation:

Rearrange the first equation into [tex]-x^2+y^2 = 16[/tex]

So we have this equivalent system

[tex]\begin{cases}-x^2+y^2 = 16\\\\x^2-y^2=16\end{cases}[/tex]

If you add the terms straight down, then you'll find that the x^2 and y^2 terms add to 0. The right hand side terms add to 16+16 = 32

We are left with the equation 0 = 32, which is a false equation or contradiction. Therefore, there are no solutions. We say the system is inconsistent. The two graphs do not intersect at all as shown in the diagram below. We have two hyperbolas in which the branches extend off to infinity to slowly approach the asymptotes. They never actually get to the asymptotes, but only get closer.

Answer:

B

Step-by-step explanation:

The independent variable is the variable who's variation doesn't depend on the other. Therefore the answer is B because the amount of rooms doesn't depend on the charge, the charge depends of the amount of rooms.

Answer:

Step-by-step explanation:

find the slope

[tex]\frac{4-8}{-5-(-3)} =\frac{-4}{-2} \\\\slope=2\\y=mx+b\\y=2x+b\\[/tex]

take a coordinate to fill in

[tex](-5,4)\\y=-5\\x=4\\-5=2(4)+b\\-5=8+b-8 -8\\-13=b\\[/tex]

this means that the equation is y=2x-13

and if you add m and b

you get :-11

I HOPE THIS HELPS

Answer:

7/2

Step-by-step explanation:

Let $A = (-3,8)$ and $B = (-5,4)$. The midpoint of $\overline{AB}$ is $\left( \frac{(-3) + (-5)}{2}, \frac{8 + 4}{2} \right) = (-4,6)$.

The slope of $\overline{AB}$ is $\frac{8 - 4}{(-3) - (-5)} = 2$, so the slope of the perpendicular bisector of $\overline{AB}$ is $-\frac{1}{2}$. Therefore, the equation of the perpendicular bisector is given by

\[y - 6 = -\frac{1}{2} (x + 4).\]Isolating $y,$ we find

\[y = -\frac{1}{2} x + 4.\]

Answer: 3km/h

Step-by-step explanation:

Johns average speed was 6km/h, so in 3 hours he traveled 18 km.  27-18=9, so Peter ran 9 km in 3 hours.  9/3 = 3, so his average speed was 3km/h

Answer:

3 km/h

Step-by-step explanation:

Distance = speed x time

The distance apart equals to the sum of the distance that John jogged, and the distance that Peter jogged since they go opposite directions.

Hence,

let v be peter's speed

27 = 6x3 + vx3

27 = 18 + 3v

27-18 = 3v

9 = 3v

v = 9/3

v = 3 km/h

Answer:

f(x - n) - shift the graph n units right

f(x + n) - shift the graph n units left

f(x) - n - shift the graph n units down

f(x) + n - shift the graph n units up ----------------------------------------------------------------------------

Answer: shift the graph of y = 2(3)ˣ one unit right and four units up.

Answer:

[tex]\frac{r^{15}}{512}[/tex]

Step-by-step explanation:

Given

[tex](8r^{-5})^{-3}[/tex]

Required

Simplify

This can be simplified using the following law of indices;

[tex](ab)^n = a^{n}b^{n}[/tex]

The equation becomes

[tex](8^{-3})(r^{-5})^{-3}[/tex]

Express [tex]8^{-3}[/tex] as a fraction

[tex](\frac{1}{8^{3}})(r^{-5})^{-3}[/tex]

Simplify [tex]8^3[/tex]

[tex](\frac{1}{8*8*8})(r^{-5})^{-3}[/tex]

[tex](\frac{1}{512})(r^{-5})^{-3}[/tex]

The expression can further be simplified using the following law of indices;

[tex](a^m)^n = a^{mn}[/tex]

[tex](\frac{1}{512})(r^{-5})^{-3}[/tex] becomes

[tex](\frac{1}{512})(r^{-5*-3})[/tex]

[tex](\frac{1}{512})(r^{15})[/tex]

[tex]\frac{r^{15}}{512}[/tex]

Hence, the solution to [tex](8r^{-5})^{-3}[/tex] is [tex]\frac{r^{15}}{512}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer: 1.05x

Step-by-step explanation:

From the question, we are informed to translate into an algebraic expressions: x is increased by 50% and decreased by 30%. This will be calculated thus:

Firstly, we'll increase x by 50%.

= x + (50% of x)

= x + (0.5 × x)

= x + 0.5x

= 1.5x

Then, we'll decrease 1.5x by 30%. This will be:

= 1.5x - (30% × 1.5x)

= 1.5x - (0.3 × 1.5x)

= 1.5x - 0.45x

= 1.05x

The answer is 1.05x.

Answer:

1.05x

Step-by-step explanation:

Answer:

the second description and and expression is correct

Step-by-step explanation:

the first one is wrong because it says 7 minus while it should be minus 7

nine times the difference of a number cubed and three; 9(n³-3)

Paired data in statistics, often referred to the ordered pairs, refers to 2 variables in the individuals of the population that are linked together in the order to determine correlation between them.

Given :

7 less than the quotient of two and a number squared increased by six

7 -  (2/n²)  + 6

9 times the difference of a number cubed and three; 9(n³-3)

8 more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7

twice the difference of a number cubed and eight;  2 n³- 8

To Find: Which description is paired with its correct expression

Solution:

7 less than the quotient of two and a number squared increased by six

7 -  (2/n²)  + 6

Correct Expression is   -7 + (2/n²)  + 6  

nine times the difference of a number cubed and three; 9(n³-3)

Expression is Correct

8 more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7

Correct Expression is  8 + (n²/4) - 7

twice the difference of a number cubed and eight;  2 n³- 8

The correct expression is 2( n³- 8)

Hence the correct answer is :

nine times the difference of a number cubed and three; 9(n³-3)

Statistics is a mathematical body of the science that pertains by the collection or analysis, or interpretation and explanation, or presentation of data, and as a branch of mathematics. Some consider statistics to be the distinct mathematical science rather than a branch of mathematics.

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Answer:

1529.4 m^3

Step-by-step explanation:

We will use the formula V = 1/3*h*B for the volume of the pyramid, where V is volume, h is height, and B is are of the base.

First, since we know h and are looking for V, we need B. To find this, since it has a square base, we multiply b, the base length, by itself. 15.3m * 15.3m = 234.09m^2.

Next, we plug into the formula.

V = 1/3*19.6m*234.09m^2

And simplify:

V= 1/3 * 4,588.164m^3

V= 15.29.3879....

Last, round to the tenth

1529.4 m^3

Answer: 1529.4

Step-by-step explanation:

Answer:

V =2197 ft^3

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the length of a side

V = 13^3

V =2197 ft^3

Answer:

Volume = 2197ft³

Answer:

0 = x, y = 2.

Or x = 2 and y = 1.

Step-by-step explanation:

≤ means less than or equal to.

Answer:

First choice

Step-by-step explanation:

Sum of fractions:

-7/10 + 4/10= - 3/10

the interval required on the line from the left of - 7/10 to the right of -3/10

Which number line would be best to find this sum?

-8/10 to 0

yes, this is good as covers the interval from -7/10 to - 3/10

-3/10 to 3/10

no, it doesn't include the left half of required section

4/10 to 11/10

no, it doesn't include the required interval

0 to 15/10

no, it doesn't include the required interval

Answer:

A

Step-by-step explanation:

Answer:

1/3 < 2/3

Step-by-step explanation:

1/3 compared to 4/6

Simplify 4/6 by dividing the top and bottom by 2

4/5 = 2/3

Since the denominators are the same we compare the numerators

1/3 < 2/3

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}=?\\\\1)\sqrt{8^2+15^2}=\sqrt{289}=17\\2)\sqrt{9^2+40^2}=\sqrt{1681}=41\\3)2\times17=34\\4)\sqrt{34+41}=5\sqrt{3}[/tex]

All Done!

Answer:

Your correct answer is 8.660254

Step-by-step explanation:

√2√82 + 152 + √92 + 402 = 8.660254

Answer:

The value of a + 2z/ 2 in terms of a is (3a+4)/2

Step-by-step explanation:

least of 3 consecutive integers is a, and the greatest is z

if a is the least one

we know that integers differ by value of 1.

example -2, -1, 0, 1,2

they all differ by

then next consecutive integer will be a+1

third integer will be  second integer +1 = a+1 + 1 = a+2

Thus, 3 consecutive integer

a , a+1, a+2

but given that greatest is z

thus, a+2 is greatest and hence

a+2 = z

we have to find   value of a + 2z/ 2 in terms of a

a + 2z/ 2 = a + 2(a+2)/2 = (a+ 2a +4)/2 = (3a+4)/2.

The value of a + 2z/ 2 in terms of a is (3a+4)/2

Answer:

Step-by-step explanation:

(2,6)

Answer:

The solution of the two equations is where both lines intersect

From the graph they intersect at point

(6,2)

So the solution is x = 6 y = 2

Hope this helps you

Answer:

(1) N or n = 20

(2) [tex]\bar X \text{ or } \mu[/tex] = 43.4

(3) σ = 9.78 and s = 10.04.

Step-by-step explanation:

We are given with the following data set below;

{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}

(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.

(2) The formula for calculating Mean of the data, i.e. [tex]\bar X \text{ or } \mu[/tex] is given by;

        Mean  =  [tex]\frac{\sum X}{n}[/tex]

              =  [tex]\frac{51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42}{20}[/tex]

              =  [tex]\frac{868}{20}[/tex]  = 43.4

So, the value of [tex]\bar X \text{ or } \mu[/tex] is 43.4.

(3) The formula for calculating population standard deviation ([tex]\sigma[/tex]) is given by;

        Standard deviation, [tex]\sigma[/tex] =  [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{N} }[/tex]

             =  [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20} }[/tex]

             =  9.78

Similarly, the formula for calculating sample standard deviation (s) is given by;

        Sample Standard deviation, s =  [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex]

             =  [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20-1} }[/tex]

             =  10.04

Answer:

Total weight = 70.5 kg

Step-by-step explanation:

Rectangular frame is made from 5 straight pieces of metal. One of them goes through the diagonal of the rectangle.

2 pieces form the length of the rectangular frame, hence, they have a length of 12 m each

2 pieces from the width of the rectangular frame, hence, they a length of 5 m each

To find the length of the diagonal, we can use Pythagoras Theorem:

Hypotenuse² = Base² + Perpendicular²

Hypotenuse² = 5² + 12²

Hypotenuse² = 169²

Hypotenuse = 13

Hence, the length of the piece of metal placed at the diagonal is 13cm

Find the sum of all lengths of the metal pieces.

Total length = 12 + 12 + 5 + 5 + 13

Total length = 47 m

Total weight = 1.5 × Total length

Total weight = 1.5 kg/m × 47m

Total weight = 70.5 kg

The total weight of the metal in the frame is 70.5 kg

If a rectangular frame is made from 5 straight pieces of metal, with a length of 5m and a width of 12m

Get the diagonal

[tex]d^2= 5^2 + 12^2\\d^2 = 25 + 144\\d^2 = 169\\d= 13m[/tex]

Get the perimeter of the rectangular frame:

Perimeter of the frame = 2(5 + 12) + 13

Perimeter of the frame = 2(17) + 13

Perimeter of the frame = 34 + 13

Perimeter of the frame = 47m

If the weight of the metal is 1.5 kg per metre, the total weight will be expressed as:

Total weight = 47 * 1.5

Total weight = 70.5kg

Hence the total weight of the metal in the frame is 70.5 kg

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Answer:

A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers

I hope that is what your asking...

Answer:

On which number line do the points represent negative seven and one over two and +1? The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of

Step-by-step explanation:

Answer:

From the problem, the answer to the equation is 5 1/10

Step-by-step explanation:

First, let's gather the information from the problem.

a = 4 1/5 (also can be turned into 21/5)

b = 2 7/20 (also can be turned into 47/20)

c = 3 1/4 (also can be turned into 13/4)

Now, plug in the numbers using the improper fractions.

21/5 - 47/20 + 13/4

Turn the denominators into the same number.

84/20 - 47/20 + 65/20

Subtract 84/20 and 47/20.

37/20 + 65/20

Add 37/20 and 65/20.

102/20 or 5 1/10

So, your answer to this equation is 5 1/10.

Answer:

2(d-vt)=-at^2

a=2(d-vt)/t^2

at^2=2(d-vt)

Step-by-step explanation:

Arrange the equations in the correct sequence to rewrite the formula for displacement, d = vt—1/2at^2 to find a. In the formula, d is

displacement, v is final velocity, a is acceleration, and t is time.

Given the formula for calculating the displacement of a body as shown below;

d=vt - 1/2at^2

Where,

d = displacement

v = final velocity

a = acceleration

t = time

To make acceleration(a), the subject of the formula

Subtract vt from both sides of the equation

d=vt - 1/2at^2

d - vt=vt - vt - 1/2at^2

d - vt= -1/2at^2

2(d - vt) = -at^2

Divide both sides by t^2

2(d - vt) / t^2 = -at^2 / t^2

2(d - vt) / t^2 = -a

a= -2(d - vt) / t^2

a=2(vt - d) / t^2

2(vt-d)=at^2

Answer:

678.2

Step-by-step explanation:

To find the surface area you need to use the expression [tex]2\pi rh + 2\pi r^2[/tex]

When you substitute the numbers in you get 678.24

The surface are of the can that has radius of 9 ft. and height of 3 ft is 678.2 ft².

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

The surface area of the can is the sum of the area of the bases of the can and the lateral surface area of the can. Therefore, the total surface area of the can is,

The surface area of can = 2(Area of base) + Lateral surface area of can

                                        = 2(πr²) + 2πrh

                                        = 2[π×(9 ft)²] + (2 × π × 9ft × 3ft)

                                        = 508.8 ft² + 169.4 ft²

                                        = 678.2 ft²

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