Are
12/20
and
equivalent fractions?
22/30
Α. No
B. Yes, because both fractions are divisible by 2
C. Yes, because the difference between the denominator and numerator in each fraction is 8.
D. Yes, because they can both be simplified

Answer:

a) The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.

b) Antonio is expected to make a profit of 37445.17 in 7 months from now.

Step-by-step explanation:

a) The equation described on statement represents a geometrical progression, which is defined as:

[tex]y = C_{o}\cdot (1+ r)^{x}[/tex] (1)

Where:

[tex]C_{o}[/tex] - Initial amount, measured in monetary units.

[tex]r[/tex] - Rate, dimensionless. (The progression is increasing when [tex]r > 0[/tex], and decreasing when [tex]-1 < r < 0[/tex])

[tex]x[/tex] - Time, measured in months.

[tex]y[/tex] - Profit, measured in monetary units.

Given that [tex]y = 150,210\cdot (0.82)^{x}[/tex], we calculated the rate below:

[tex]1+r = 0.82[/tex]

[tex]r = 0.82-1[/tex]

[tex]r = -0.18[/tex]

The negative sign indicates that progression is decreasing in time and decreases by 18 percent each month.

b) If we know that [tex]x = 7[/tex], then the expected amount for Antonio in 7 months from now is:

[tex]y = 150,210\cdot (0.82)^{7}[/tex]

[tex]y = 37445.17[/tex]

Antonio is expected to make a profit of 37445.17 in 7 months from now.

Answer:

domain: [-4, ∞)

range: [-6, ∞)

Step-by-step explanation:

look at the graph. for domain, you want the x-values included in the interval. the endpoint at -4 means that the domain begins at -4. since the graph extends to positive infinity, then include that in domain with an parentheses not bracket since there's no endpoint.

for range, do the same thing but for y-values.

The domain and the range of a function are the possible x and y values it can take

The domain

From the graph, the x-value starts at x = -4, and it continues to the right.

The dot at x = -4, means that -4 is inclusive of the x values.

The arrow at the other end means that, the value increases to infinity.

So, the domain of the function is: [tex][-4, \infty)\\[/tex]

The range

From the graph, the y-value starts at y = -6, and the curve open upwards

The arrow at the other end means that, the value increases to infinity.

So, the range of the function is: [tex][-6,\infty)[/tex]

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Answer:

I dont get itt

Step-by-step explanation:

Answer:

thank for the free point

The midpoint of the line segment with the endpoints is (4, 1)

The endpoints are given as:

E= (-2,8) and F = (10, -6)

The midpoint of the line segment with the endpoints is calculated as

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have:

Midpoint = 0.5 * (-2 + 10, 8- 6)

Evaluate the sum

So, we have:

Midpoint = 0.5 * (8, 2)

Evaluate the products

So, we have:

Midpoint = (4, 1)

Hence, the midpoint of the line segment with the endpoints is (4, 1)

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Answer:

They are equal

Step-by-step explanation:

Answer:

$0.98

Step-by-step explanation:

First, add $8.75 & $4.35.

8.75 + 4.35 = $13.10 in total

Then find the tax by multiply 7.5% (3/40) times 13.10.

3/40 * 131/10

393/400 = 0.9825, which rounds down to $0.98 in tax

Answer:

[tex]x = \frac{9}{14} [/tex]

Step-by-step explanation:

6 (5x - 7) = -3 (4x + 7) + 6

30x - 42 = -12x - 21 + 6

30x - 42 = -12x - 15

30x + 12x = -15 + 42

42x = 27 ÷ 42

x = 27/42

simplify with factor 3

[tex]x = \frac{9}{14} [/tex]

Answer:

No, it isn't.

Step-by-step explanation:

The point on y = 5 should be on y = 7, and the point on x = 5 should be on x = 7. The attachment shown is what the graph should look like.

Answer:

you get 0.4 litres for every dollar

Answer:

hen he deposited some more money and his account balance was $28.

Step-by-step explanation:

Answer:7

Step-by-step explanation:

Answer: 3x + 15

Step-by-step explanation:

In order to use the distributive property, you simply multiply the number on the outside by both the number inside the parenthesis

So, in this case, we would multiply 3 by X and 3 by 5

3 times x = 3x

3 times 5 =15

Your new equation is then made by adding these two together

3x+15

Answer 3x + 15

Answer:

A and C

Step-by-step explanation:

First because "AAS" is when we know two angles and one side (which is not between the angles). To solve an AAS triangle. use the three angles add to 180° to find the other angle. then The Law of Sines to find each of the other two sides.

And then C because all angles have to equal to the other angle pattern

Answer:I = prt

p = 7430

r = 5%....turn to decimal = 0.05

t = 3

I = (7430)(0.05)(3)

I = 1114.50 <===

Step-by-step explanation:

Answer:

I = prt

p = 7430

r = 5%....turn to decimal = 0.05

t = 3

I = (7430)(0.05)(3)

I = 1114.50 <===

Step-by-step explanation:

Answer:

ggg if fdrsyviinoiv fcvui I tzhvii u u y

Considering the definition of scale, the length of the Mississippi River on the map is 96.667 cm.

The scale of a cartographic representation, or map scale, is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map.

Scale is the relationship between a real object (for example, the surface of the Earth or a portion of it) and the representation that is made of it.

The scale is represented as a fraction as follows: measured on the map/measured in reality

In this case, you know that:

Considering the definition of scale, you can calculate the length of the Mississippi River on the map as follow:

5 cm/ 120 miles= measured on the map/2320 miles

(5 cm/ 120 miles)× 2320 miles= measured on the map

96.667 cm= measured on the map

Finally, the length of the Mississippi River on the map is 96.667 cm.

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Answer:

7.77%

Step-by-step explanation:

When dealing with calculating a sequence of probabilities for an specific event such as this one you simply need to multiply the seperate probabilities of each part of the event happening together. Which in this case would be 21% and 37%. We first need to convert these percentages into decimal form by dividing each of them by 100. Once we have the decimal form we multiply them together to find the answer.

21% / 100 = 0.21

37% / 100 = 0.37

0.21 * 0.37 = 0.0777   ... multiply by 100 to get percent form

0.0777 * 100 = 7.77%

Finally, we can see that the probability that a first-year student requires both a developmental math course and a developmental English course is 7.77%

The probability that a first year student requires both a development math course and a developmental English course is 7.77%

Since The probability that a first year student entering a certain private college needs neither a developmental math course nor a developmental English is 61% while 21% require a developmental math course and 37% require a developmental English course.

So, the probability is

[tex]= 0.21 \times 0.37[/tex]

= 7.77%

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The acute angle that satisfies the equation is 18.6 degrees

The equation is given as

csc Theta = 3.1297

Rewrite properly as

csc(∅) = 3.1297

In trigonometry

csc(∅) = 1/sin(∅)

So, we have

1/sin(∅) = 3.1297

This means that

sin(∅) = 1/3.1297

Evaluate the expression

sin(∅) = 0.3195

Take the arc sin of both sides

∅ = sin-1(0.3195)

Evaluate the arcsin expression

So, we have

∅ = 18.6

Hence, the acute angle that satisfies the equation is 18.6 degrees

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Answer:

The zeros of the function:

[tex]x=5.53 ,[/tex]  [tex]x=3.22[/tex]  

Step-by-step explanation:

Given the function

[tex]f\left(x\right)=2x^2-17.5x+35.6[/tex]

To find zeros, put f(x)=0

[tex]0=2x^2-17.5x+35.6[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]

[tex]0\cdot \:10=2x^2\cdot \:10-17.5x\cdot \:10+35.6\cdot \:10[/tex]

[tex]0=20x^2-175x+356[/tex]

switch sides

[tex]20x^2-175x+356=0[/tex]

subtract 356 from both sides

[tex]20x^2-175x+356-356=0-356[/tex]

[tex]20x^2-175x=-356[/tex]

divide both sides by 20

[tex]\frac{20x^2-175x}{20}=\frac{-356}{20}[/tex]

[tex]x^2-\frac{35x}{4}=-\frac{89}{5}[/tex]

[tex]\mathrm{Add\:}a^2=\left(-\frac{35}{8}\right)^2\mathrm{\:to\:both\:sides}[/tex]

[tex]x^2-\frac{35x}{4}+\left(-\frac{35}{8}\right)^2=-\frac{89}{5}+\left(-\frac{35}{8}\right)^2[/tex]

applying perfect square

[tex]\left(x-\frac{35}{8}\right)^2=\frac{429}{320}[/tex]

[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]

solving

[tex]x-\frac{35}{8}=\sqrt{\frac{429}{320}}[/tex]

[tex]x=\frac{\sqrt{2145}}{40}+\frac{35}{8}[/tex]

[tex]x=5.53[/tex]

also solving

[tex]x-\frac{35}{8}=-\sqrt{\frac{429}{320}}[/tex]

[tex]x=-\frac{\sqrt{2145}}{40}+\frac{35}{8}[/tex]

[tex]x=3.22[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]

[tex]x=5.53 ,[/tex]  [tex]x=3.22[/tex]  

Therefore, the zeros of the function:

[tex]x=5.53 ,[/tex]  [tex]x=3.22[/tex]  

Answer:

12

Step-by-step explanation:

Answer:I’m pretty sure I got this one right too

Step-by-step explanation:

The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.

"In a two-dimensional coordinate system, any vector can be broken into x -component and y -component according to axis."

We can assume, east as the positive x- axis and north as the positive y-axis, respectively.

Similarly, west as the negative x- and south as the negative y-axis, respectively.

Therefore, the x- and y-components of the speeds.

Now, for the airplane:

x-component: - 500 × cos(45°) mph = - 353.55 mph

y-component: 500 × sin(45°) mph = 353.55 mph

For the wind:

y-component: -40 mph

Therefore, sum of the x-components = -353.55 mph

Similarly, sum of the y-components = (353.55 - 40) mph = 313.55 mph

Now, the actual speed =

[tex]\sqrt{(-353.55)^{2} + (313.55)^{2}}[/tex] mph

= [tex]\sqrt{223313.6}[/tex] mph

= 472.56 mph

Now, the direction of the airplane is:

tan(Ф) = [tex]\frac{313.55}{- 353.55}[/tex]

⇒ Ф = tan⁻¹( [tex]\frac{313.55}{- 353.55}[/tex])

⇒ Ф = - 41.57°

The actual speed of the airplane is 472.56 mph in the direction of 41.57° north of west.

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Answer:

4 2/3

Step-by-step explanation:

When dividing fractions you multiply the recipricol of the second term by the first.

1/3 x 5/1 = 5/3.

2 x 1 = 3

5/3 = 1 2/3

3 + 1 2/3 = 4 2/3.

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The simplest form of the resultant fraction when 2 1/3 divided 1 1/5

is 1 17/18.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given are two fractions 2 1/3 divided by 1 1/5.

We know,

2 1/3.

= (2×3 + 1)/3.

= 7/3 and similarly 1 1/5 is 6/6.

So, 7/3 divided by 6/5.

= (7/3)/(6/5).

= (7/3)×(5/6).

= 35/18.

= 1 17/18.

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Answer:

Step-by-step explanation:The largest fraction is 5/8

Answer:

.007 is in the thousandths place.

Step-by-step explanation:

In decimals it goes tenths, houndredths, thousandths, and so on.

Answer:

To the left, the constant is plus 5.

To the right, the constant is plus 42.

Step-by-step explanation:

Answer:

-x^2-2x+3

1/2x^2-2x-1

Step-by-step explanation: