Money is borrowed at 18% simple interest. after one year, $610.06 pays off the loan. how much was originally borrowed?

Answer: Rotation

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

the 0 is not significant since it is not sandwiched between 2 sigfigs and is not the last digit after a decimal

Domain

[tex]-\infty \: < x < \infty[/tex]

Range

[tex]f\left(x\right)\ge \:-7\:[/tex]

Answer:

first order

Step-by-step explanation:

they're basically a linear function. to make it easier you could just put the coordinates on the side of the table.

Answer:

$2.61

Step-by-step explanation:

So, We have $5.22 for 6 pounds of Bananas.

If we need to find the cost for 3 pounds, we would divide $5.22 by 2 because 6/2=3

In order to do this, we need to turn 5.22 into a whole number, so we multiply by 100

5.22*100=522

Now we divide

522/2 = 261

Now we divide 261 by 100, since we multiplied by 100 earlier.

261/100 =2.61

So our answer is $2.61 for 3 pounds of bananas .

Hope this helps! ^^

Answer:$2.61 for 3 pounds  

Thank for the  brainliest

Step-by-step explanation:first you divided $5.22/6  because the money always goes on the top and you get 0.87, you multiply 0.87 by 3 which is $2.61

Light is about 874052.5 times faster than sound

From the question, we are to determine the magnitude by which light is faster than sound

From the given information,

The speed of light is about 2.998 x 10⁸ meters per second.

and

The speed of sound is about 343 meters per second.

To determine how many rimes faster the speed of light is than the speed of sound, we will divide the speed of light by the speed of sound

That,

The magnitude by which light is faster than sound = (2.998 x 10⁸) / 343

The magnitude by which light is faster than sound = 874052.5

Hence, light is about 874052.5 times faster than sound

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Answer:

x<−2 or x<5

Step-by-step explanation:

x<−2 or x<5

We know either x<−2 or x<5

x<−2(Possibility 1)

x<5(Possibility 2)

The acres of vacant land that the county have now will be 144 acres.

Since 36% has been used, the remaining percentage will be:

= 1 - 36%

= 64%

Therefore, the acres of vacant land that the county has now will be:

= 64% × 225

= 64/100 × 225

= 0.64 × 225

= 144

Therefore, the acres of vacant land that the county have now will be 144 acres.

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Answer:

It's the graph with two dots and no area marked, first image (for me).

Step-by-step explanation:

|x| = 1 means "the distance from x to the 0 point on the axis is exactly 1". There's only 2 numbers x that satisfy that condition: -1 and 1

The second and third image both show an area marked, so it cannot be the right answer, while the first image shows precisely two numbers: -1 and 1

Answer:

40 3/8 bushels of apples

Step-by-step explanation:

13 1/8 bushels and 27 2/8 bushels

13 1/8 + 27 2/8 =

(13 + 27) = 40

(1/8 + 2/8) = 3/8

40 3/8

The equation of the sphere is

[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]

The standard form of the equation of the sphere is :

[tex](x-a)^{2}+(y-b)^{2}+(z-c^{2} )=r^{2}[/tex]

Where A (a, b , c) is the center and r is the radius.

From the question we should first find the radius

r = [tex]\sqrt{(x-a)^{2}+(y-b)^{2}+(z-c)^{2}[/tex]

Point = (x , y , z) = (8 , 3 , -3)

Center = (a, b , c)= (5 , 6 ,5)

Substituting it in the formula

r = [tex]\sqrt{(8-5)^{2}+(3-6)^{2}+(-3-5)^{2} }[/tex]

By further calculation

r = [tex]\sqrt{9+9+64}[/tex]

So, we get

r =[tex]\sqrt{82}[/tex]

Substituting it in the standard form

[tex](x-5)^{2}+(y-6)^{2}+(z-5)^{2}=\sqrt{82}^{2}[/tex]

[tex](x-5)^{2} +(y-6)^{2} +(z-5)^{2}=82[/tex]

[tex]x^{2} +y^{2}+z^{2}+25+36+25-10x-12y-10z=82[/tex]

[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+86-82=0[/tex]

[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]

Therefore, the equation of the sphere is

[tex]x^{2} +y^{2}+z^{2}+-10x-12y-10z+4=0[/tex]

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Answer:

$1020.00

Step-by-step explanation:

15% means 15/100 divide by 100 and you get .15

.15 x 1200 gives us the rebate.  The rebate is 180.  We subtract that from 1200. 1200 -180 = 1020

Another way to think about this, is that we are taking 15% off we are leaving on 85%

.85 x 1200 = 1020

Satisfactory internal control reduces the probability of errors or frauds in the accounts.

What functions may a strong internal control system perform?

Why are internal controls necessary?

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A distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be representing a negatively skewed distribution.

A real-valued random variable's probability distribution's asymmetry can be quantified by looking at how skew it is around its known as skewness.

There are three types of probabilities of a value can be:

Positively skewed

negatively skewed

unskewed

From the given question, the distribution of scores in which almost the entire class scored very high, but a few students scored fairly low would be representing a negatively skewed distribution.

Therefore the correct answer would be an option (D)

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Your question is incomplete, probably the missing part is:

A distribution of scores in which almost the entire class scored very low, but a few students scored fairly high would be ______.

a. normally distributed

b. positively skewed

c. unskewed

d. negatively skewed

Answer:

x = -∛115

Step-by-step explanation:

x^3 - (-115) = 0

= x^3 + 115

Factoring

(a+b) • (a^2-ab+b^2) =

   a^3-a^2b+ab^2+ba^2-b^2a+b^3 =

   a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=

   a^3+0+0+b^3=

   a^3+b^3

(115 isn't a cube.)

Polynomial roots

P: -1, -5, -23, -115, 1, 5, 23, 115

Q: 1

P/Q: -1, -5, -23, -115, 1, 5, 23, 115

Divisor(s): None

In these sets of data, there are no rational roots shown.

Step-by-step explanation(part 2):

x^3 + 115 = 0

x^3 = -115

x  =  ∛-115

Negative numbers will always have real cube roots.

∛ -115 = ∛ -1 × 115  = ∛ -1 × ∛ 115 = (-1) × ∛ 115

Therefore,

x = -∛115

Answer:

310 hamburgers were sold on Saturday

Step-by-step explanation:

1x + 70 =380

    -70   -70     Reverse

1x   =  310

/1         /1          Divide

x =310

The wire that Marlee had left is 20.8 inches.

From the information given, it was stated that Marlee is making jewelry for a class craft show and that she began with 115 inches of wire.

Amount used for rings = 25.75 inches..

Amount given to her by the teacher = 30 1/4 inches.

Amount used for bracelets = 38 1/2

inches.

Amount used for necklace = 60.2 inches

It should be noted to know the wire left, we have to subtract the values that were used and then add the value that her teacher gave her from the original value. This will be calculated thus:

This will be:

= 115 - 25.75 + 30.25 - 38.5 - 60.2

= 20.8 inches

Therefore, in conclusion, the wire that Marlee had will be 20.8 inches left.

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The cost of one sandwich is $5.7

The given parameters are:

Order = 3

Tax = 8% off

Total cost = $20.66

Tip = $5

The cost of one sandwich is calculated as:

Total cost = Order * Cost of One (x) * (1 - tax) + Tip

This gives

20.66 = 3 * x * (1 - 8%) + 5

Subtract 5 from both sides

15.66 = 3 * x * (1 - 8%)

Make x the subject

x = 15.66/[3 * (1 - 8%)]

Evaluate

x = 5.7

Hence, the cost of one sandwich is $5.7

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The value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.

According to the given question.

We have a function h(x) = 18 - 9x + x^4

Here, we have to find the value of h(2). For this we will substiute x = 2 in the function h(x) = 18 - 9x + x^4.

Therefore, the value of h(2) for the function h(x) = 18 - 9x + x^4 is given by

h(x) = 18 - 9x + x^4

h(2) = 18 - 9(2) + 2^4

h(2) = 18 - 18 + 16

h(2) = 16

Hence, the value of h(2) for the function h(x) = 18 - 9x + x^4 is 16.

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Step-by-step explanation:

You want to demonstrate the identity ...

  (1-tan⁴(A))·cos⁴(A) = 1 -2·sin²(A)

Working with the left side, we have ...

  [tex](1-\tan^4(A))\cos^4(A)=1-2\sin^2(A)\\\\(1-\dfrac{\sin^4(A)}{\cos^4(A)})\cos^4(A)=1-2\sin^2(A)\qquad\text{use tangent identity}\\\\\cos^4(A)-\sin^4(A)=1-2\sin^2(A)\qquad\text{multiply it out}\\\\(\cos^2(A) +\sin^2(A))(\cos^2(A)-\sin^2(A))=1-2\sin^2(A)\qquad\text{factor}\\\\1((1-\sin^2(A))-\sin^2(A)) = 1-2\sin^2(A)\qquad\text{use $\cos^2$ identity}\\\\1-2\sin^2(A)=1-2\sin^2(A)\qquad\text{Q.E.D.}[/tex]

__

Additional comment

The referenced identities are ...

  tan = sin/cos

  cos² = 1 -sin²

and the factorization of the difference of squares:

  a² -b² = (a +b)(a -b).

Answer:

yes a product of any number to 0 is equal to 1

Applying the triangle proportionality theorem, the length of line EC is: 7.2 units.

Since lines AC and DE are parallel to each other in the triangle, and DE intersects sides AB and AC, then we would have the following proportion based on the triangle proportionality theorem:

BD/DA = CE/EA

BD = 18 units

DA = 15 units

CE = ?

EA = 6 units

Plug in the values

18/15 = CE/6

(18)(6) = (CE)(15)

108 = CE(15)

Divide both sides by 15

108/15 = CE(15)/15

7.2 = CE

EC = 7.2 units

Therefore, applying the triangle proportionality theorem, the length of line EC is: 7.2 units.

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Answer: the thickness of each sheet of paper is 2in thick.

Step-by-step explanation:

There is none.

If box contains 5 reams of paper, the estimated thickness of 2 sheets of paper is T/1250.

To estimate the thickness of 2 sheets of paper, we can use the given information about the number of reams in the box and the number of sheets in one ream of paper.

First, we know that one ream of paper contains 500 sheets. Since the box contains 5 reams, the total number of sheets in the box is 5 reams × 500 sheets/ream = 2500 sheets.

Next, we can calculate the thickness of one sheet by dividing the total thickness of the reams by the number of sheets. Let's assume the thickness of the 5 reams combined is T.

Thickness of one sheet = T/2500

Now, to estimate the thickness of 2 sheets, we multiply the thickness of one sheet by 2:

Estimated thickness of 2 sheets = (T/2500) × 2 = 2T/2500 = T/1250

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Answer:

130.94

Step-by-step explanation:

'Combine' I assume is to add so here's the answer!

23.8+40+38.94+28.2= 130.94

Answer:

Step-by-step explanation:

Let's open the brackets,

12z - 21 = -21 + 12z (distributive property)

12z - 12z = -21 + 21

0z = 0

z = 0

Answer:

He runs 20% or 1/5 of the total distance the first day

Step-by-step explanation:

We know this due to the fact that 2km / 10km is equal to 1/5 and we then know that 1/5 equates to the percentage equivalence value of 20%

The slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

Slope of the line:

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Given,

The point (9,10) that cuts off the least area from the first quadrant

Here we need to find the slope and y intercept of the line.

A line is passing through a point (9,10) cuts off least area in first quadrant.

The equation of the line passing through point (9,10) and has slope m can be expressed as,

=> y - 10 = m (x - 9)

=> y = m(x - 9) + 10

=> y - mx = - 9m + 10

Divide the terms by - 9m + 10, then we get,

=> (y/- 9m+10) - (mx/ - 9m+10) = 1

=> (mx/9m+10) - (y/9m+10) = 1

It can be rewritten as,

[tex]\implies\frac{x}{\frac{9m-10}{m}} -\frac{y}{10-9m}[/tex]

We know that,

The equation of straight line in intercept form is

=> x/a + y/b = 1

So, the intercept made by the line on x-axis i.e. a and on y-axis i.e. b are:

a = 9m-10/m

b =  10 - 9m

The area of the triangle made by the line in first quadrant can be expressed as,

=> A = 1/2 x (9m-10/m) x (10 - 9m)

=> A = -1/2 (9m-10)²/m-----------------------(1)

Differentiate the equation (1) with respect to m.

[tex]\frac{dA}{dm}=-\frac{1}{2}[\frac{2m(9m-10).9-(9m-10)^2}{m^2}][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[2m.9-(9m-10)][/tex]

[tex]\frac{dA}{dm}=-\frac{9m-10}{2m^2}[18m-9m-10)][/tex]

when we simplify it,

=> dA/dm = -(9m-10)/2m² [9m-10]

Let dA/dm = 0, then

=> 0 = -1/2m² (9m-10)(9m-10)

=> 0 = 1/m² (10-9m)(9m-10)

=> 0 = (10 - 9m) (9m -10)

Therefore, the value of m is,

=> 10 - 9m = 0

=> -9m = -10

=> m = 10/9

And

=> 9m - 10 =0

=> 9m = 10

=> m = 10/9

The line will be in first quadrant and forms a triangle with axes if the slope is negative.

Substitute m = -10/9

Then, b = 10-9m

Then,

=> y = 10 - 6(-10/9)

=> y = 10 + 20/3

=> y = 50/3

So, the slope of the line is -10/9 and the value of y-intercept of the line is 50/3.

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Speed is the constant of proportionality for the relationship between distance and time.

Relationship between these two values is distance is directly proportional to time .

As given,

Distance =400 kilometers

Time=8 hours

Let s, d, and t represents speed, distance and time.

Speed = d / t

           = 400/8

           = 50 km/ hour

           = constant

Hence ,

d = 50t

⇒ d ∝ t

Therefore, speed is the constant of proportionality for the relationship between distance and time.

Relationship between these two values is distance is directly proportional to time .

The complete question is:

An albatross is a large bird that can fly 400 kilometers in 8 hours at a constant speed. using for distance in kilometers and for number of hours, an equation that represents this situation d=50t.

What are two constants of proportionality for the relationship between distance in kilometers and number of hours? What is the relationship between these two values?

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Answer:

What you are looking for is the length of the 'solid diagonal'. First we need to find the length of the base diagonal. That can be done easily using Pythagorean theorem.  52+32−−−−−−√=6. Now this diagonal is a leg of the bigger right triangle whose hypotenuse is the required solid diagonal. You can see this from amd's picture. So apply Pythagorean theorem again.  62+(2.5)2−−−−−−−−−√=37.25−−−−√. You can work that out with a calculator.

In general for a cuboid with dimensions a, b and c(order doesn't matter), the solid diagonal is:  a2+b2+c2−−−−−−−−−−√

Step-by-step explanation:

Answer:

√62+(2.5)2=√37.25.

Step-by-step explanation:

What you are looking for is the length of the 'solid diagonal'. First we need to find the length of the base diagonal. That can be done easily using Pythagorean theorem. &#xA0;52+32=6" role="presentation" style="margin: 0px; padding: 0px; border: 0px; font-style: normal; font-variant: inherit; font-weight: normal; font-stretch: inherit; line-height: normal; font-family: inherit; font-size: 15px; vertical-align: baseline; box-sizing: inherit; display: inline; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;"> 52+32−−−−−−√=6 52+32=6. Now