Beth and her father have a large model railroad in their basement. Beth figured out that the equation y = 260/3x relates the length of an item on her model railroad to the length of the real thing, where x is the size on the model and y is the real object’s size. Beth’s uncle has a different model railroad in his home. It has a different scale. He put together the following table for Beth.

I DONT GET IT

#1

100+200+300..10000

Now

[tex]\\ \rm\Rrightarrow S_{100}=\dfrac{100}{2}(100+10000)=50(10100)=505000[/tex]

#2

[tex]\\ \rm\Rrightarrow x^2+(x+1)^2=21[/tex]

[tex]\\ \rm\Rrightarrow x^2+x^2+2x+1=21[/tex]

[tex]\\ \rm\Rrightarrow 2x^2+2x=20[/tex]

[tex]\\ \rm\Rrightarrow x^2+x-10=0[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm\sqrt{1-40}}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm\sqrt{-39}}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{-1\pm \sqrt{39}i}{2}[/tex]

Answer:

  150 in³

Step-by-step explanation:

We want to find half the volume of a rectangular pyramid. The volume of the whole pyramid is given by the formula ...

  V = 1//3LWH

  V = 1/3(5 in)(15 in)(12 in) = 300 in³

Then the volume of the half that is not filled with marbles is ...

  1/2V = 1/2(300 in³) = 150 in³

150 cubic inches of marbles are needed to finish filling the container.

Answer:

i)  Using log law:  [tex]\log_aa=1[/tex]

[tex]\implies \log_55+1=1+1=2[/tex]

ii) [tex]\log \left(\dfrac{15}{8}\right)+4 \log 2-\log 3[/tex]

Using log law [tex]a \log b=\log b^a[/tex]:

[tex]\implies \log \left(\dfrac{15}{8}\right)+\log 2^4-\log 3[/tex]

[tex]\implies \log \left(\dfrac{15}{8}\right)+\log 16-\log 3[/tex]

Using log law [tex]\log a-\log b=\log (\frac{a}{b})[/tex]:

[tex]\implies \log \left(\dfrac{15}{8}\right)+\log\left(\dfrac{16}{3}\right)[/tex]

Using log law  [tex]\log a+\log b=\log(ab)[/tex]:

[tex]\implies \log \left(\dfrac{15}{8}\cdot \dfrac{16}{3}\right)[/tex]

[tex]\implies \log 10[/tex]

Using log law:  [tex]\log_aa=1[/tex]

[tex]\implies \log_{10} 10=1[/tex]

iii) Take log of base 10:

[tex]\log_{10}(\sqrt{8.357}\times0.895^2)[/tex]

[tex]\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)[/tex]

Log tables

The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation.

The mantissa is found using the log tables and is always prefixed by a decimal point.

The row is the first two non-zero digits of the number, and the column is the 3rd digit of the number

Use the log tables to find [tex]\log_{10}(8.357)[/tex]:

8.357 = 8.357 × 10⁰

⇒ characteristic = 0

log table:  row 83, column 5 ⇒ mantissa 9217

(as there is a 4th digit) Mean difference 7 = 4

mantissa + mean difference = 9217 + 4 = 9221 ⇒ 0.9221

characteristic + mantissa = 0 + 0.9221 = 0.9221

Therefore, [tex]\log_{10}(8.357)=0.9221[/tex]

Use the log tables to find [tex]\log_{10}(0.895)[/tex]:

[tex]0.895 = 8.95\times 10^{-1}[/tex]

⇒ characteristic = -1

log table: row 89, column 5 ⇒ mantissa 9518⇒ 0.9518

characteristic  + mantissa = -1 + 0.9518= -0.0482

Therefore, [tex]\log_{10}(0.895)=-0.0482[/tex]

Therefore,

[tex]\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)[/tex]

[tex]\implies \dfrac12 \cdot 0.9221+2\cdot-0.0482[/tex]

[tex]\implies 0.36465[/tex]

Therefore,

[tex]\log_{10}(\sqrt{8.357}\times0.895^2)=0.36465[/tex]

Using [tex]\log_ab=c \implies a^c=b[/tex]

[tex]\implies \sqrt{8.357}\times0.895^2=10^{0.36465}[/tex]

[tex]\implies \sqrt{8.357}\times0.895^2=2.3155[/tex]

Answer:

[tex]x[/tex] =[tex]\frac{-2}{3}[/tex]   or   [tex]x[/tex] = -1

Step-by-step explanation:

quadratic formula⇒ -b ±[tex]\sqrt{b^{2} -4ac}[/tex] / 2a

15[tex]x[/tex]² + 22[tex]x[/tex] = -8

15[tex]x[/tex]² + 22[tex]x[/tex] +8 = 0

taking a=15, b=22 & c=8;

[tex]x[/tex] = (-22 ± [tex]\sqrt{ - 22^{2} 4 × 15 × 8}[/tex])/ 2 x 15 ⇒ (Pls note that the A~s are multiplications.. unable to insert symbols in equations)

  = (-22 ± [tex]\sqrt{484 - 480}[/tex]) / 30

  = (-22 ± [tex]\sqrt{4}[/tex]) / 30

  = (-22 ± 2) / 30

[tex]x[/tex] = [tex]\frac{-22 + 2}{30}[/tex]  or  [tex]x[/tex] =[tex]\frac{-22 - 2}{30}[/tex]

[tex]x[/tex] = -[tex]\frac{-20}{30}[/tex]    or [tex]x[/tex] = [tex]\frac{-30}{30}[/tex]

[tex]x[/tex] =[tex]\frac{-2}{3}[/tex] or [tex]x[/tex] = -1

Step-by-step explanation:

Go and learn numbers , it will be 1 2 3 4 5

Answer:

It is 3

•°•°•°

Math is poop

[tex] \sf \dashrightarrow \: - \frac{2}{5} - ( - \frac{3}{10} ) - ( - \frac{4}{7} )[/tex]

When there is a - in front of an expression in parentheses, change the sign of each term in the expression to +

[tex] \sf \dashrightarrow \: - \frac{2}{5} + \frac{3}{10} + \frac{4}{7} [/tex]

Calculate the LCM of denominators

[tex] \sf\frac{ - 28 + 21 + 40}{70} [/tex]

Calculate the difference

[tex] \bf \underline{ \underline \frac{33}{70} }[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-2}{5}-\left(-\dfrac{3}{10}\right)-\left(-\dfrac{4}{7}\right)[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-2}{5}+\dfrac{3}{10}+\dfrac{4}{7}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-28+21+40}{70}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{-7+40}{70}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{33}{70}[/tex]

Answer:

x = 8/3

Step-by-step explanation:

1. Subtract 7 from both sides.

-3x + 7 = -1

-7 -7

-------------------

-3x = -8

2. Divide both sides by -3

-3x = -8

---- ----

-3 -3

x = 8/3

The equation of the function in the form y=mx+b is y = 110x-2020

The standard equation of a line is expressed as:

y = mx + b

where:

m is the rate of change or slope

b is the intecept

Using the coordinate points

Determine the slope

m = 550/5

m = 110

For the intercept

280 + 110(20) + b

280 = 2200 + b

b = 180 - 2200

b = -2020

Hence the equation of the function in the form y=mx+b is y = 110x-2020

Learn more on rate of change here: https://brainly.com/question/8728504

The area of the garden enclosed by the fencing is

A(x, y) = xy

and is constrained by its perimeter,

P = x + 2y = 200

Solve for x in the constraint equation:

x = 200 - 2y

Substitute this into the area function to get a function of one variable:

A(200 - 2y, y) = A(y) = 200y - 2y²

Differentiate A with respect to y :

dA/dy = 200 - 4y

Find the critical points of A :

200 - 4y = 0   ⇒   4y = 200   ⇒   y = 50

Compute the second derivative of A:

d²A/dy² = -4 < 0

Since the second derivative is always negative, the critical point is a local maximum.

If y = 50, then x = 200 - 2•50 = 100. So the farmer can maximize the garden area by building a (100 ft) × (50 ft) fence.

Answer:

[tex]\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10[/tex]

General Formulas and Concepts:
Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                           [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                 [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                     [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:                                                   [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Area of a Region Formula:                                                                               [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

y = 2x + 3

x-interval [3, 4]

x-axis

See attachment for graph.

Step 2: Find Area

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

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Learn more about integration: https://brainly.com/question/26401241

Learn more about calculus: https://brainly.com/question/20197752

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

r = 3

Step-by-step explanation:

Answer:

Ocupa los miles.

Step-by-step explanation:

400,000

30,000

2,000

70

9

Hey there!

12: 1, 2, 3, 4, 6, & 12

30: 1, 2, 3, 5, 6, 10, 15, & 30

75: 1, 3, 5, 15, 25, & 75

LIKE TERMS: 1 and 3

GCF: 3

Therefore, your answer is: 3

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

C .6 inches

Step-by-step explanation:

I'm not sure of my answer

Considering the discrete distribution, it is found that the desired measures are given as follows:

a) 0.86.

b) 0.57.

c) 0.45.

d) 0.14.

e) 0.43.

f) 3.02.

g) 1.31.

According to the table, it is given by:

P(X = 1) = 0.14.

P(X = 2) = 0.29.

P(X = 3) = 0.12.

P(X = 4) = 0.31.

P(X = 5) = 0.14.

Item a:

[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - P(X = 1) = 1 - 0.14 = 0.86[/tex]

Item b:

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - P(X = 1) - P(X = 2) = 1 - 0.14 - 0.29 = 0.57[/tex]

Item c:

P(X > 3) = P(X = 4) + P(X = 5) = 0.31 + 0.14 = 0.45.

Item d:

P(X < 2) = P(X = 1) = 0.14.

Item e:

[tex]P(X \leq 2) = P(X = 1) + P(X = 2) = 0.14 + 0.29 = 0.43[/tex].

Item f:

The mean is given by the sum of each outcome multiplied by it's respective probability, hence:

E(X) = 0.14(1) + 0.29(2) + 0.12(3) + 0.31(4) + 0.14(5) = 3.02.

Item g:

The standard deviation is given by the square root of the sum of the difference squared of each observation and the mean, multiplied by it's respective probabilities, hence:

[tex]\sqrt{V(X)} = \sqrt{0.14(1-3.02)^2 + 0.29(2-3.02)^2 + 0.12(3-3.02)^2 + ... + 0.14(5-3.02)^2} = 1.31[/tex]

More can be learned about discrete probability distributions at https://brainly.com/question/24855677

Step-by-step explanation:

To find a, the leading coeffiecent of the quadratic is a.

So a is 2.

To find b, we must use the formula

[tex] - \frac{b}{2a} [/tex]

[tex] \frac{ - ( - 3)}{2(2)} = \frac{3}{4} [/tex]

So b=3/4.

To find c, plug in 3/4 into the function,

which we get

[tex]2( \frac{9}{16} ) - 3( \frac{3}{4} ) + 21[/tex]

[tex] \frac{9}{8} - \frac{9}{4} + 21 = \frac{9}{8} - \frac{18}{8} + 21 = - \frac{9}{8} + 21 = 19.875[/tex]

So c=19.875

Answer:

85%

Step-by-step explanation:

Johny answered [tex]\frac{17}{20}[/tex] questions correctly. To change this into percent, just multiply both the numerator and denominator by the number that makes the denominator equal 100. In this case, 5 would make 20 equal 100, so we multiply both the top and bottom by 5.

[tex]\frac{17}{20} *\frac{5}{5}=\frac{85}{100}[/tex]

Your numerator will be your percentage if the denominator is 100.

Answer:

Bobby has 45 beads

Step-by-step explanation:

Let x be the number of beads Bobby has.

Then, (x + 30) is the number of beads Alvin has.

Then, 3 (x + 30) is the number of beads Cathy has.

3 (x + 30) + (x + 30) + x = 345

3x + 90 + x + 30 + x = 345

5x + 120 = 345

5x = 225

x = 45

Therefore, Bobby has 45 beads.

Answer:

a starting value of -1/2 so its starts at -1/2 so lets see which ones start at that

not a

not b

yes c

this isn't a function

and no change so

not a

not b

yes c

yes d(not a function)

c

Hope This Helps!!!

50 % =20 Learners

100%= x

x=100/50

=2

=2×20

=40 learners

was this helpful?

Answer:

Given:

[tex] \: [/tex]

To Find:

[tex] \: [/tex]

Solution:

Let,

So,

length will be 2b + 3

[tex] \: [/tex]

As, we know:

[tex] \bigstar \quad {\underline{ \boxed{ \green{Perimeter = 2 ( length + breadth ) }}}} \quad \bigstar[/tex]

➝ 2[(2b + 3) + b)] = 252

➝ 2( 3b + 3 ) = 252

➝ 6b + 6 = 252

➝ b + 1 = 42

➝ b = 41

[tex] \: [/tex]

Now putting the value of b in second equation:

➝ l = 2(41) + 3 = 85

[tex] \: [/tex]

Hence,

[tex] \: [/tex]

Check:

2( l+b ) = 252

➝ 2( 85 + 41 )

➝ 2( 126 )

➝ 252

[tex] \: \: \: \: \: \: { \sf{ \mathbb{ \pink{Formula's \: for \: Perimeter}}}}[/tex]

★ Triangle = Sum of all sides

★ Square = 4 × Side

★ Rectangle = 2( l + b )

★ Circle = 2πr

the answer is 15!

Hope this helps!

Answer:

d) 4w - 2

Step-by-step explanation:

(7w-5) and (-3w+3)

(7w-5) + (-3w+3)

1(7w-5) + 1(-3w+3)

7w - 5 - 3w + 3

Combine like terms:

7w - 5 - 3w + 3

7w - 3w - 5 + 3

4w - 2

Hope this helps!

Answer:

Not worth 40 points. Poster is a liar.

R=15 --> 30/2 , H=320

Anyways, because you lied, I won't show my work.

Volume= 72,000pi or 226194.6711

Answer:

Step-by-step explanation:

sorry I tried but it is hard