Find the distance across the lake. Assume the triangles are similar.

Based on the price of the stamp in 1996, and the increase in 2010, the following are true:

The price in 2010 was:

= 3,500 x 225/100

= $7,875

The GST in 2010 is:

= (7,875 / 1.07) x 7%

= $515.19

The GST in 1996 is:

= (3,500 / 1.03) x 3%

= $101.94

The increase in the GMT is:

= (515.19 - 101.94) / 101.94

= 405%

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Answer:

0.1?

58

146,000?

22600

Step-by-step explanation:

So I assume first is 1st decimal place, so that would be the first after the decimal and then the number after has to be 5 or above, which it is. So then its just 0.1

This is easy, look at the decimal, its below .5, so 58.

Same thing for the rest, just look at the digit before.

Answer:

58cm

Step-by-step explanation:

in the simple way the shape is a rectangle so some of the sizes are equal will be added since the perimeter is the distance around it

Answer:

MK intersect LJ at midpoint that's my opinion

Answer:

B. LM = JM = 3 and JK = LK = √17.

Step-by-step explanation:

∠M is a right angle and MK bisects ∠LMJ.

LM = JM = 3 and JK = LK = StartRoot 17 EndRoot.

MK intersects LJ at its midpoint.

The slope of MK is –1 and the slope of LJ is 1.

The range of scores for 95% of the class is 63.8 to 86.6 using the empirical rule.

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations.

The empirical rule specifically states that 68 percent of data will fall inside the first standard deviation, 95 percent will fall within the first two standard deviations, and 99.7 percent will fall within the first three standard deviations.

According to the question,

μ=75.2  and σ=5.7

So, according to the empirical rule, the range of scores for 95% of the class:

μ – 2σ =75.2-2*5.7=63.8

and μ + 2σ=75.2+2*5.7=86.6

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The time taken by the stone to fall in air is 7 seconds and the time taken in water is 5 seconds.

Speed is the distance covered by an object in a fixed period of time. It is measured in m/sec.

The average speed in air is 16m/sec.

The average speed in water is 33m/sec.

The total time taken is 12 seconds.

Total distance covered =  Total time taken * speed at which it covered the distance

Let the time taken to fall in air is t

So, the time taken in water will be 12-t

The total distance is equal to

127 = 16*t + 3(12-t)

127 = 16t + 36 - 3t

127 - 36 = 16t - 3t

91 = 13t

t = 91/13 = 7 seconds

12-t = 12-7 =5 seconds

Therefore, the time taken by the stone to fall in air is 7 seconds and the time taken in water is 5 seconds.

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Answer:

2 22/7 ×r

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...

...

...

...

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Answer:

256 ft^3

Step-by-step explanation:

Volume of pyramid = 1/3  base area * height

                                 = 1/3  96 ft^2   * 8  ft  = 256 ft^3

Answer:

Step-by-step explanation:

The formula for circumference is 2(3.14)r

So, we divide 141.3 by 6.28 and get 22.5

The radius is 22.5 feet.

Answer:

Step-by-step explanation:

2x + 3y = 6

y = x/3 - 3

Since the second equation is already solved for y, we can easily use the substitution method.

Substitute y in the first equation with x/3 - 3

2x + 3(x/3 - 3) = 6

2x + x - 9 = 6

3x = 15

x = 5

Now use the second equation, and x = 5, to solve for y.

y = x/3 - 3

y = 5/3 - 3 = 5/3 - 9/3

y = -4/3

Answer: (5, -4/3)

Answer:

your answer would be B

Step-by-step explanation:  

Answer:

12 units

Step-by-step explanation:

x is to 16    as    9 is to x

x/16 = 9/x     cross multiply

x^2 = 144

x =12

Por lo tanto el número es p/q = 8/64.

Fracción es un número que se puede representar en forma de p/q, donde q no es igual a cero.

It is given that

En su forma más simple, el número es 1/8

Sea el número p/q

p + q = 72 (dado)

p/q = 1/8

q = 8p

p+8p = 72

9p = 72

p = 8

q = 8p

q = 8 * 8 = 64

Por lo tanto el número es p/q = 8/64.

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The approximate value of b in the triangle is D. 9.4 units.

From the information, it should be noted that WZY and XWY are similar triangle.

The corresponding ratio will be:

XW/WZ = XY/WY = WY/ZY

The calculation of WZ using Pythagoras will be 7.81.

This will be substituted into the ratio.

b/7.81 = 6/5

5b = 46.86

b = 9.4 units.

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Probability that no samples are mutated is 0.83, probability that at most one sample is mutated is 0.9812 and probability that more than half the samples are mutated is 0.

Given percentage of rejuvenated mitochondria defective is 1%, and sample size is 18.

Binomial distribution is the probability of exactly x successes on n repeated trials and X can have two outcomes.

P(X=x)=[tex]C_{n,x} p^{x}(1-p)^{n-x}[/tex]

percentage of defective rejuvendated mitochondria=1%

p=0.01

Sample size=18

n=18

a) No samples are mutated

This means P(X=0)=[tex]C_{18,0}(0.01)^{0} (0.99)^{18}[/tex]

=0.83

b) At most one sample is mutated.

P(X<=1)=P(X=0)+P(X=1)

so,

P(X=0)=[tex]C_{18,0} (0.01)^{0} (0.99)^{18}[/tex]

=0.83

P(X=1)=[tex]C_{18,1}(0.01)^{1} (0.99)^{17}[/tex]=

=0.1512

P(X<=1)=0.83+0.1512

=0.9812

c) More than half the samples are mutated.

P(X>9)=P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15)+P(X=16)+P(X=17)+P(X=18)

Using two decimals digits precision all will be 0.

Hence Probability that no samples are mutated is 0.83, probability that at most one sample is mutated is 0.9812 and probability that more than half the samples are mutated is 0.

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Answer:

Krutika

Step-by-step explanation:

Lets convert each person's typing rate to words/min.

Krutika:

80 minutes = 6000 words

1 minute = (6000/80) words

              = 75 words

Typing Rate: 75 words / min

Mark:

60 minutes = 4200 words

1 minute = (4200/60) words

              = 70 words

Typing Rate: 70 words / min

David:

90 minutes = 5850 words

1 minute = (5850/90) words

              = 65 words

Typing Rate: 65 words / min

From the above, we can see Krutika has the fastest rate of words per minute.

Answer:

A) y = –3x+8

Step-by-step explanation:

first off, a negative equation means the graph is downward sloping from left to right –> \. So with this in mind you can immediately eliminate C and D because they are upward sloping graphs. B also doesn't work because it doesn't go through (3,–1). This leaves A as the right answer

the constant number is the number on the y-axis. So, for –3x+2, +2 is the y-coordinate on the y-axis. the slope is -3x meaning down 3, right 1. –3x+8 is the only answer that is perpendicular.

Hello,

x⁴ + 12x³ - 64x² = 0

x²(x² + 12x - 64) = 0

x² = 0 or x² + 12x - 64 = 0

x = 0

∆ = b² - 4ac = 12² - 4 × 1 × (-64) = 400

x1 = (-b -√∆)/2a = (-12 - 20)/2 = -32/2 = -16

x2 = (-b + √∆)/2a = (-12 + 20)/2 = 8/2 = 4

S = {-16 ; 0 ; 4 }

→ factorizacion de x⁴ + 12x³ - 64x² : x(x - 4)(x + 16)

Answer:

2 hours

Step-by-step explanation:

Because if the total round trip took 6 hours then it mustve taken him 2 hours to drive there at 70mph and 4 hours to drive back at 50mph.

Answer:

25

Step-by-step explanation:

The value included in the solution to the given inequality is:

x = -5.

Everything to the left of the circle at x = -2 is shaded, that is, all values less than x = -2, hence the inequality is:

x < -2.

Researching the problem on the internet, the options for the values that belong to the solution are:

-5, -2, 0, 3.

Due to the open circle, -2 is not in the inequality, 0 and 3 are greater than -2, hence they are not in the inequality, then the value included in the solution to the given inequality is:

x = -5.

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The missing values represented by x and y are 8 and 20, that is

(x, y) = (8, 20)

The function y = 16 + 0.5x is a linear equation that can be solved graphically. This means the values of both variables x and y can be found on different points along the straight-line graph.

The ordered pairs simply mean for every value of x, there is a corresponding value of y.

The 2-column table has values for x and y which all satisfy the equation y = 16 + 0.5x. Taking the first row, for example, the pair is given as (-4, 14).

This means when x equals negative 4, y equals 14.

Where y = 16 + 0.5x

y = 16 + 0.5(-4)

y = 16 + (-2)

y = 16 - 2

y = 14

Therefore the first pair, just like the other four pairs all satisfy the equation.

Hence, looking at the options given, we can determine which satisfies the equation

(option 1) When x = 0

y = 16 + 0.5(0)

y = 16 + 0

y = 16

(0, 16)

(option 2) When x = 5

y = 16 + 0.5(5)

y = 16 + 2.5

y = 18.5

(5, 18.5)

(option 3) When x = 8

y = 16 + 0.5(8)

y = 16 + 4

y = 20

(8, 20)

From our calculations, the third option (8, 20) is the correct ordered pair that would fill in the missing values x and y.

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Answer:

70°

Step-by-step explanation:

Due to the fact that the angle is on a straight line, therefore the angle(110°) is equal the inside/opposite to the angle(q°):

q°=180°(since it's on a straight line) -110°

q°= 70°

Step-by-step explanation:

d = price of 1 drink

s = price of 1 sandwich

3d + 5s = 25.05

4d + 2s = 13.8

we can do this by combining both equations so that they is only one variable left.

e.g. multiply equation 1 by 4 and equation 2 by 3, and then subtract equation 2 from equation 1 :

12d + 20s = 100.2

- 12d + 6s = 41.4

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

0 14s = 58.8

s = 58.8/14 = $4.20

3d + 5s = 25.05

3d + 5×4.2 = 25.05

3d + 21 = 25.05

3d = 4.05

d = 4.05/3 = $1.35

so, each drink costs $1.35.

Answer:

Step-by-step explanation:

The domain and range of all linear functions is the set of real numbers.

Answer:

4

Step-by-step explanation:

[tex] \frac{15}{20} = \frac{x + 2}{12 - x} \\ \\ 180 - 15x = 20x + 40 \\ \\ 35x = 140 \\ \\ x = 4[/tex]

Answer:

b=136, c=44, d=44

Step-by-step explanation:

B is the same measure as A. C = D and A+B+C+D=360; C+D=88; C=44; D=44

The multiplicative rate is 9 if the table that shows an exponential function option fourth is correct.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

We have a table that shows an exponential function.

As we know the exponential function:

y = a(b)ˣ

Plug x = 1, y = 6

6 = ab ...1

Plug x = 2, y = 4

4 = ab²  ...2

Divide equations 1 and 2

ab²/ab  = 4/6

b = 2/3

Plug the value of b in the 1 equation.

a(2/3) = 6

a = 9

y = 9(2/3)×

The multiplicative rate = 9

Thus, the multiplicative rate is 9 if the table that shows an exponential function option fourth is correct.

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Answer:

37

Step-by-step explanation:

Let's use the rule GEMDAS (Grouping, Exponents, Multiply, Divide, Add, Subtract) from left to right. Therefore, we will simplify the equation in the parentheses. [tex]2^{3} = 8. (1-8= -7)[/tex]. -(-7) creates a double negative, deeming the 7 positive, because when there is two negatives the number will turn into a positive. [tex]7^{2}[/tex] = 49, -3 x 4= -12. Therefore the final form of the equation will be 49 - 12 = 37.

Let me know if there are mistakes.

[tex]\dfrac{x^2+12x+35}{3x+15}=\dfrac{x^2+12x+35}{3(x+5)}=\dfrac{x^2+5x+7x+35}{3(x+5)}=\dfrac{x(x+5)+7(x+5)}{3(x+5)}=\\=\dfrac{(x+5)(x+7)}{3(x+5)}=\dfrac{x+7}{3}[/tex]

Answer:

(x+7) / 3

Step-by-step explanation:

Factorise the Top half to give  :

x² + 12x+ 35 = (x+5)(x+7)

Factorise the bottom half to give :  

3(x+5)

Cancel (x+5) from top and bottom to give :

(x+7) / 3

So our final answer is Option 3

Hope this helped and have a good day