Fill in the blank, rounding the result to exactly three significant digits when necessary

81 m = ___ ft

Answer:

154 legs

Step-by-step explanation:

40-3=37

37 times 4 = 148

3 times 2 ° 6

148+6= 154

Answer: 154 legs

Step-by-step explanation: First, multiply 37×4 because there are 37 cows with 4 legs, which gets you 148. Since there are 3 cows with only 2 legs, do 3×2=6. Finally, add 148 and 6 to get 154 legs.

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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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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.

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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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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If their combined weight is 175 pounds, The amount of Luna weight is D. 82 pounds.

Let x represent the weight of Cooper

Let x +25 represent the weight of Daisy

Let 3x -20 represent the weight of Luna

Hence,

x + (x +25) + (3x -20) = 175

5x +5 =175

Combine like terms

5x = 175 -5

5x =170

Divide both side by 5x

x = 170/5

x =34

Weight of Luna

3x -20  where x= 34

3(32) -20

= 102 -20

= 82 pounds

Therefore the correct option is D.

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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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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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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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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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Answer:

Step-by-step explanation:

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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There are many things obstructing the route so yes. I cannot give a detailed answer as I have not been given the "distance formula" sorry

The rational zeros for F(x)=3x^4-4x^3+x^2+6x-2 are x= -1 and x= 1/3 while the linear factors are (x+1) and (3x-1)

Synthetic division has to do with dividing polynomials.

The process involves:

Step 1: Set up the synthetic division.

Step 2: The leading coefficient should be brought down to the bottom row.

Step 3: Multiply this by the value just written on the bottom row.

Step 4: Then, add the column created in step 3.

This can be illustrated thus:

Given: f(x) = 3x⁴-4x³+x²+6x-2

3x⁴-4x³+x²+6x-2 = 0

We will try x = -1 in f(x). In this case, replace x with -1. This will be:

= 3x⁴-4x³+x²+6x-2 = 0

Since f(-1)= 0 so (x+1) is a factor

Using synthetic division:

-1)....3....-4....1....6....-2

.........3.....-7...8....-2..|..0

Remainder = 0

Quotient = 3x³ -7x² + 8x -2

For 3x³ -7x² + 8x -2,  f(1/3) = 0 so (x- 1/3) is a factor

1/3)....3....-7....8....-2

..........3.....-6...6...|..0

Remainder = 0

Quotient = 3x²-6x+6

= 3(x²-2x+2)

Since there are no more rational zeros or linear factors for x²-2x+2. Therefore, the rational zeros are x= -1 and x= 1/3.

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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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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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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].

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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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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Based on the information given the variance of their​ weights is 119.9200 kg².

What is variance?

The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: σ².

Main body:

n=sample size=10

Standard deviation=10.9508 kg

Using this formula

Variance=(Standard deviation)²

Let plug in the formula

Variance=(10.9508 kg)²

Variance= 119.9200 kg²

Hence the variance of their​ weights is 119.9200 kg².

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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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a. The penalty Lorna must pay is $26.86.

b. The total amount Lorna must pay on February 27 is $2037.74.

Given that,

On December 14, 2017, Lorna Hall's $2,010.88 real estate tax was due. Because of her job loss, Lorna was unable to pay her taxes until February 27, 2018. Late payment fees are assessed at a rate of 6 1/2% regular interest.

We have to find

a. What is the fine Lorna is required to pay

b. How much will Lorna owe in total on February 27.

First,

We know that,

i=p×r×t

Here,

i is interest.

p is principal amount.

r is rate of interest

t is time.

So, p is $2010.88

r is 6 1/2%

t is 17+31+27= 75 days is 75/365

So,

i= 2010.88×6 1/2×75/365

i= $26.86

The penalty Lorna must pay is $26.86.

Second,

We know that,

Total amount= real estate tax due amount+ Penalty pay.

Total amount= $2010.88+$26.86

Total amount= $2037.74

The total amount Lorna must pay on February 27 is $2037.74.

Therefore, a. The penalty Lorna must pay is $26.86.

b. The total amount Lorna must pay on February 27 is $2037.74.

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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

Solution :

[tex]\qquad \sf  \dashrightarrow \: log(x) + 5 \: log(y) - 4 \: log(z) [/tex]

[tex]\qquad \sf  \dashrightarrow \: log(x) + \: log(y {}^{5} ) - \: log(z {}^{4} ) [/tex]

( a log(x) = log(x^a) )

[tex]\qquad \sf  \dashrightarrow \: log( x {y}^{5} ) - log(z {}^{4} )[/tex]

( log (a) + log (b) = log (ab) )

[tex]\qquad \sf  \dashrightarrow \: log( \frac{ x {y}^{5} }{z {}^{4} }) [/tex]

( log (a) - log (b) = log (a/b) )

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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Answer:

1.5 liters

Step-by-step explanation:

Answer:

The ratio shows that there are 14 girls to 30 students in total

Step-by-step explanation:

14 + 16 = 30 that mean that there are 30 students in total, therefore, the ratio shows 14 girls : 30 students

Answer:

x = 147°

Step-by-step explanation:

To find x, we have to find the angle measures in the small triangle.

180 - 61 = 119° (sum of adjacent angles on straight line=180)

The other angle measure in the triangle is 28° because they are vertically opposite angles.

We subtract 119° and 28° to find the angle measure next to x.

180 - 119 - 28 = 33° (sum of angles in a triangle=180)

x = 180 - 33

= 147° (sum of adjacent angles on straight line=180)

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

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The comparison done by Mr Jones means that Test A of standard deviation 7 is closer to the mean scores and Test B of standard deviation 12 is further apart from the mean score

The standard deviation is a statistic measure that expresses how much variance or dispersion there is in a group of numbers.

A high standard deviation suggests that the values are dispersed throughout a wider range,

A low standard deviation suggests that the values tend to be close to the established mean.

A positive value means the standard deviation is above the mean while a negative value means the standard deviation is below the mean

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