find the number that is exactly halfway between 5 and 17

Answer:

amount owed = $7434.57

Step-by-step explanation:

To solve this problem, we have to use the following formula:

[tex]\boxed{A = P(1 + \frac{r}{n})^{nt}}[/tex],

where:

• A = final amount

• P = principal (initial) amount

• r = annual interest rate

• n = amount of times the interest is compounded per time period

• t = number of years the money is kept for

In this case, the principal amount, P = $5000 and the money is owed for two years, so t = 2. The annual interest rate, r = 0.20 (20% = [tex]\frac{20}{100}[/tex] = 0.2). The interest is compounded monthly, which means it is compounded 12 times per year. Therefore, n = 12.

Using the above information and formula, we can calculate the amount owed after 2 years:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

   [tex]= 5000(1 + \frac{0.2}{12})^{12 \times 2}[/tex]

   [tex]=[/tex] $7434.57

Therefore, the amount Edgar owes after 2 years is $7434.57.

9514 1404 393

Answer:

 2×10¹

Step-by-step explanation:

For division, mantissas divide, and exponents subtract.

Answer:

2*10^1

Step-by-step explanation:

Process

When you divide powers, they can be subtracted -- numerator - denominator in powers

The numbers divide the way you normally would if the question is 6/3 = 2

Numerator power = 3

denominator power = 2

Solution

6*10^3/ 3*10^2 = (6/3) * 10^(3 -2) = 2 * 10^1 = 20

20 = 2 * 10^1

24.

[tex](6x+3y)-\frac{z^{2}}{(2x)}[/tex]

[tex](6(3)+3(4))-\frac{(6)^{2}}{(2(3))}[/tex]

a) Solve parenthesis.

[tex](18+12)-\frac{(6)^{2}}{6}\\ \\30-\frac{(6)^{2}}{6}[/tex]

b) Solve the exponent.

[tex]30-\frac{36}{6}[/tex]

c) Divide.

[tex]30-6[/tex]

d) Subtract.

[tex]24.[/tex]

The student enrollment the previous year is 630 students.

Sine the percentage given is 10% decrease, us implies that the percentage for the previous year will be x

Based on the information given, this will be illustrated as:

x - (20% × x) = 504

x - 0.2x = 504

0.8x = 504.

Divide.

x = 504 / 0.8

x = 630

There were 630 students.

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The probability that the second ball drawn is yellow is of:

0.2926 = 29.26%.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

In this problem, the possible outcomes to obtain a yellow ball on the second draw are:

Then the probability of an yellow ball on the second draw is given as follows:

p = (3/11) x (3/11) + (8/11) x (3/10) = 0.2926 = 29.26%.

The problem asks for the probability that the second ball drawn is yellow.

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Perimeter of triangle FBC is 19.24 units

Area of triangle FBC is 100.62 square units

Given,

The triangle with vertices;

F(-3, 5)

B(3, 2)

C(1, -2)

We have to find the perimeter and area of the triangle;

Formula for getting distance from vertices;

D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

Here,

D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

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

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

= [tex]\sqrt{36+9}[/tex]

= √45

D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1 -3 )^{2}+(-2-2)^{2} }[/tex]

= [tex]\sqrt{(-2)^{2} +(-4)^{2} }[/tex]

= [tex]\sqrt{4+16}[/tex]

= √20

D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]

= [tex]\sqrt{(1-(-3) )^{2}+(-2 -5)^{2} }[/tex]

= [tex]\sqrt{4^{2}+(-7)^{2} }[/tex]

= [tex]\sqrt{16+49}[/tex]

= √65

That is,

Now,

Perimeter of triangle FBC = FB + BC + FC

= √45 + √20 + √65

= 19.24 units

Next,

Area of triangle FBC = 1/2 × BC × FB²

= 1/2 × √20 × √45²

= 100.62 square units.

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The percentage of computers not working is 10%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that there are three of the 30 computers are out of service.

The percentage of the computers which are out of service will be calculated as,

P = 3 / 30

P = 0.1

P = 0.1x 100

P = 10%

Therefore, the percentage of computers not working is 10%.

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The probability that at least 40 rolls are necessary is 4/15.

What is probability?

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No of out comes=40

No. of total possible outcome=150

Therefore probability P= 40/150

                                    P=4/15

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The function that represents the graph f(x) = -3|x| is f(x) = -3|x| - 5

How to find the function of the graph ?

To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.

As it is already given in the question that the function

f(x) = -3|x|

We will use transformation rules to solve the given question

f(x)→f(x-a) ⇒ Graph shifted to right by a units

f(x)→f(x+a) ⇒ Graph shifted to left by a units

f(x)→f(x) - a ⇒ Graph shifted downwards by a units

f(x)→f(x) + a ⇒ Graph shifted upwards by a units

When it is translated 5 units down

Then we subtract 5 outside of the given function

∴ f(x) = -3 |x| - 5

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Equation of parabola in vertex form is :

[tex](x-h)^{2} = 4a(y-k)[/tex]

[tex](x-0)^{2} = 4a(y-180)[/tex]

it passing through (1,164)

∴ [tex](1-0)^2=4a(164-180)[/tex]

[tex]1 = 4a(-16)[/tex]

⇒ [tex]-64a = 1[/tex]

⇒ [tex]a = -\frac{1}{64}[/tex]

∴ [tex](x-0)^2 = 4 \times \frac{1}{-64} (y-180)[/tex]

[tex]x^2 = -\frac{1}{16}(y-180)[/tex]

[tex]-16x^2 = y-180\\y = -16x^2+180\\[/tex]

Here, the equation of parabola in vertex form is:

[tex]y = -16(x^2)+180 ,\ for \ x\geq 0[/tex]

What is Parabola?

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface.

What is cone?

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the Centre of base) called the apex or vertex.

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1) The interest if it is compounded using simple interest is $240

2) The interest if it is compounded annually is $249.73

3) The interest if it is compounded semiannually is $252.325

4) The interest if it is compounded quarterly is $253.650

5) The interest if it is compounded monthly is $254.543

6) The interest if it is compounded daily is $254.978

7) The interest if it is compounded hourly is $254.993

8) The interest if it is compounded every minute is $254.993

9) The interest if it is compounded continuously is $254.993

10) The difference in interest between simple interest and interest compounded continuously is $14.993

Compound interest is the addition of interest to the principal sum of a loan or deposit, or interest on interest plus interest.

Given, P=2000

r=4%

r=4/100

r=0.04

t=3 years

1) Simple interest⇒ A=P(1+rt)

=2000(1+3(0.04)

=2000(1+0.12)

=2240

S.I= 2240-2000

S.I=$240

2) Compound interest(yearly)

1st year= 2000(4/100)=80

2nd year=2080(4/100)=83.2

3rd year=(2080+83.2)(4/100)=86.528

P=2163.2+86.528

P=2249.728

C.I=2249.728-2000

C.I=249.728≈$249.73

3) Compounded semiannually

A= P(1+(R/200))²ⁿ

A=2000(1+(4/200))⁶

A=2000(1.12616)

A=2252.325

C.I= 2252.325-2000

C.I=$252.325

4) Compounded quarterly

A=P(1+(R/400))⁴ⁿ

A=2000(1+(4/400))¹²

A=2253.650

C.I=2253.650-2000

C.I=$253.650

5) Compounded monthly

A=P(1+(R/1200))³⁶

A=2000(1+(4/1200))³⁶

A=2254.543

C.I= 2254.543-2000

C.I=$254.543

6) Compounded daily

A=P(1+(R/36500))³⁶⁵ⁿ

A=2000(1+(4/36500))¹⁰⁹⁵

A=2254.978

C.I=2254.978-2000

C.I=$254.978

7) Compounded hourly

A=P(1+(R/876000))²⁶²⁸⁰

A=P(1+(4/876000))²⁶²⁸⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

8) Compounded every minute

A=P(1+(R/52560000))¹⁵⁷⁶⁸⁰⁰

A=P(1+(4/52560000))¹⁵⁷⁶⁸⁰⁰

A=2254.993

C.I=2254.993-2000

C.I=$254.993

9) Compounded continuously

A= [tex]Pe^{rt}[/tex]

A=2000([tex]e^{0.04*3}[/tex])

A=2254.993

C.I=2254.993-2000

C.I=$254.993

10) The difference in interest between simple interest and interest compounded continuously is

254.993-$240=$14.993

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The number of rotations is 172.

Rotation is a circular movement about the specific axis or point of rotation. The two most prevalent directions for rotation are clockwise and counterclockwise, or anti-clockwise.

Rotation simply means going around a central point. Any point on the shape has a constant distance from the center.

Given, the clockwise rotation is by 62,000°.

To find the number of rotation (n),

[tex]n = \frac{62000}{360}[/tex]

n = 172.2

Therefore, the number of rotations is 172.

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Answer:

(10, -1)

Step-by-step explanation:

x + 2x = 3x

-y + y = 0

11 + 19 = 30

3x = 30

3/3 x = 30/3

x = 10

10 - y = 11

y = -11 + 10

y = -1

The equations for early pay, deposit plus and daily pay is y = 110, y = 6x + 30 and y = 9x respectively.

An equation is an expression showing the relationship between two or more numbers and variables.

Let y represent the total cost for swimming x numbers of days.

Early Pay: Pay $110.00 before Memorial Day; swim any number of days. Hence:

y = 110

Deposit Plus: $30.00 deposit plus $6.00 per day. Hence:

y = 6x + 30

Daily Pay: $9.00 per day. Hence:

y = 9x

The equation for early pay is y = 110

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The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)

In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.

Horizontal translation

g(x) = f(x - k), where k > 0 for a translation in + x direction.

Vertical translation

g(x) = f(x) + k, where k > 0 for a translation in + y direction.

After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down.  Then, we find the following transformation formula:

g(z) = f(z) - 2

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The two possible solutions of the given quadratic equation are -

x =  +√6 +5 and x =  -√6 +5

For the given question;

(x - 5)² - 6 = 0

Bring constant on other side.

(x - 5)² = 6

Taking square root both side.

√ (x - 5)² = √6

(x - 5) = ±√6

Separate the constant and variables.

x =  ±√6 +5

There are two possible solution.

x =  +√6 +5 and x =  -√6 +5

Thus, the two possible solutions of the given quadratic equation are -

x =  +√6 +5 and x =  -√6 +5.

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Answer:

x=19/24

Step-by-step explanation:

3/8=15/5x-2

3/8= 3x -2 |*8

3=24x-16

24x=19

x=19/24

23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.

No. of players = 29

No. of coaches = 4

Total fabric used for headbands = 773.85 inches

Total no. of people for headbands = 29 + 4

                                                          = 33

Fabric used for headband for 1 person = 773.85/33

                                                                 = 23.45 inches

Total fabric used for wristbands = 279.56 inches

Total no. of people for wristbands = 29

Fabric used for headband for 1 person = 279.56/29

                                                                 = 9.64 inches

Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.

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They joined together to resist the attempts of Europeans to change them.

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Value of BC is 36  in triangle's similarity .

What is  the triangle's similarity?

ΔABC and ΔPQR are similar .

so all sides are equal in ratio .

let BC is x .

 AB/BC = PQ/QR

 18/x = 2/4

    18 * 4 = 2 * x

       x = 18 * 4/2

        x = 18 * 2

         x = 36

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The Total Probability is 4/663 and 35/2652

What is Probability?

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. An event's probability is a number between 0 and 1.

Solution:

We know that there are 52 cards in a deck of cards.

So, probability of getting a king = 4/52 = 1/13

And probability of getting a 7 after drawing a king is 4/51,

this is because one card is drawn out from the deck and there are only 51 cards left in the deck.

Total Probability = 1*4/13*51 = 4/663

In the secon case, there are two possibilities,

It can be the kling drawn might be of spade or not

Case 1: When King drawn is of Spade

Probaility of drawing a King of Spade = 1/52

Probability of drawing a Spade after King of Spade is drawn = 11/51

Total Probaility = 1*11/52*51 = 11/2652

Case 2: When King drawn is not of Spade

Probability of drawing a King not of Spade = 2/52

Probability of drawing a Spade after drawing the King = 12/51

Total Probability = 2*12/51*52 = 24/2652

Total Probability of drawing a king and spade = 11/2652 + 24/2652 = 35/2652

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We get 2 complex answers

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared.

Given that F(x) = 3x2 - 40x + 180

Set F(x) to 0, and you get ax2 + bx + c = 3x2 -40x + 180.

[-b +/- (b2 -4ac)(1/2)] is the quadratic formula. / 2a.

The stuff under the square root / radical (b2 - 4ac) is the KEY to your answer, and it determines whether you have two real, one real, or two imaginary answers. The discriminant is the term (b2 - 4ac).

Obviously, if (b2 - 4ac) > 0, you have two real answers, because the square root of a positive number is also a (positive) real number. And -b multiplied by a real number (and divided by 2a) yields two (real) answers.

If (b2 - 4ac) = 0, you have one correct answer because the square root of 0 is zero. And -b multiplied by a 0 real number (and divided by 2a) yields 1 (real) answer.

(b2 - 4ac) 0 yields two fictitious answers, because the square root of a negative number is a fictitious number. And -b multiplied by an imaginary number (and divided by 2a) yields two (complex) answers.

In this case, (b2 - 4ac) = ((-40)2 - 4(3)(180)) = 1600 - 2160 0 As a result of the discriminant is negative, the quadratic formula yields two complex answers.

Therefore we get two complex answers

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Answer:

[tex]x=\dfrac{20 +2\sqrt{35}\:i}{3}, \quad x=\dfrac{20 -2\sqrt{35}\:i}{3}[/tex]

2 imaginary answers.

Step-by-step explanation:

Given quadratic function:

[tex]f(x) =3x^2 - 40x + 180[/tex]

The zeros of a quadratic function can be found when f(x) = 0:

[tex]\implies 3x^2 - 40x + 180=0[/tex]

[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]

Therefore:

Substitute the values of a, b and c into the quadratic formula and solve for x:

[tex]\implies x=\dfrac{-(-40) \pm \sqrt{(-40)^2-4(3)(180)}}{2(3)}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{1600-2160}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{-560}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{16 \cdot 35 \cdot -1}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm \sqrt{16}\sqrt{35}\sqrt{-1}}{6}[/tex]

[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\sqrt{-1}}{6}[/tex]

Apply the imaginary number rule [tex]\sqrt{-1}=i[/tex]:

[tex]\implies x=\dfrac{40 \pm 4\sqrt{35}\:i}{6}[/tex]

[tex]\implies x=\dfrac{20 \pm 2\sqrt{35}\:i}{3}[/tex]

Therefore, the solution is 2 imaginary answers.

Imaginary numbers

Since there is no real number that squares to produce -1, the number [tex]\sqrt{-1}[/tex] is called an imaginary number, and is represented using the letter [tex]i[/tex].  

An imaginary number is written in the form [tex]bi[/tex], where [tex]b \in \mathbb{R}[/tex].

To find the arithmetic mean (average) of a group of numbers add the numbers and divide by the total number of items we added.

(12+16+10+8+14+15)/6

= 75/6

= 12.5 (answer is already rounded to nearest tenth)

Answer:

612.5

Step-by-step explanation:

Area is the length times the width

a = 70x35

a = 2450  Divide this number by 4

612.5

The total weight of the metal bar is 45.002 grams.

Given:

While mining, Peter found a large metal bar that contained 33 grams of gold.

Peter also determined that the bar was 73.33% gold.

73.33% = 33 grams

divide by 73.33 on both sides

73.33%/73.33 = 33/73.33 grams

1% = 0.45002 grams

Multiply on 100 on both sides

1%*100 = 0.45002*100

100% = 45.002 grams.

Therefore the total weight of the metal bar is 45.002 grams.

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Louie can choose the vessel for exhibition using combination in 3003 ways

information from the question include

Louie is studying ceramics and he is to submit 5 vessels

He has 15 vessels

The problem will be solved using combination

combination is method of choosing or making selection when order does not matter

Louie can choose any 5 of his vessel with no particular order

The formula is ₁₅C₅

₁₅C₅ = 15! / {5!(15 - 5)! )

= 15! / {5! * 10!}

= 3003 ways

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Answer:

↓ ↓ ↓

Step-by-step explanation:

7) Name of plane to piano CIJ:-

8) Name a segment parallel to BC:-

9) Which segment  is not skew to EK:-

______________________

Hope this helps!

Have a great day!

Answer:

Scale of the map is 1 cm corresponds to an actual distance of 1.5 km

Step-by-step explanation:

According to the question,

4.2 cm on the map corresponds to an actual distance of 6.3 km.

So,

[tex] \rm 1 \: cm \: will \: correspond \\ \rm to \: a \: distance= \dfrac{6.3}{4.2} \: km \\ \rm = 1.5 \: km[/tex]

Scale of the map is represented by 1 cm corresponds to an actual distance of 1.5 km

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

According to the question we are given that 4.2 cm on the map corresponds to an actual distance of 6.3 km.

Similarly on the map, 4.2 cm corresponds to an actual value of 6.2km distance, this means

Thus 6.2km is the same as (6.2×1000)m = 6200m

therefore, the scale of the map is

= 4.2/6200

= 1/1476.2

that is, 1cm : 1476.2 cm

= 1cm: 1.5km

Scale of the map is represented by 1 cm corresponds to an actual distance of 1.5 km

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Mean absolute deviation is the variation in a data set and is the average distance between each value and mean.

It is calculated by finding the difference between each data value and mean and then finding average of that.

So, let data set be x1,x2,x3,x4...xN.

mean of the data set is [tex]\bar{x}[/tex].

then mean absolute deviation will be

[tex]M.A.D=\sum\limits^N_{n=0}\frac{ {x_n-\bar{x}}}{N}[/tex]

Thus, mean absolute deviation shows how much the data vary in the data set.

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It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX

Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:

Diagonal WY bisects angles ZWX and ZYX because:

all corresponding parts of both triangles are congruent. (Option A).

If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.

Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.

If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).

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