Which equation is equivalent to the given equation.

Answer:

The formula is:

[tex]a_n=1.2(\frac{5}{2})^{n-1}[/tex]

Step-by-step explanation:

The geometric sequences are those in which the division between the terms [tex]a_{n + 1}[/tex] and [tex]a_n[/tex] of the sequence are equal to a constant common reason called "r"

The geometrics secencias have the following form:

[tex]a_n=a_1(r)^{n-1}[/tex]

Where [tex]a_1[/tex] is the first term of the sequence

In this sequence we have the following terms

1.2, 3, 7.5, 18.75

Then notice that:

[tex]\frac{3}{1.2}=\frac{5}{2}\\\\\frac{7.5}{3}=\frac{5}{2}\\\\\frac{18.75}{7.5}=\frac{5}{2}[/tex]

Then:

[tex]r=\frac{5}{2}[/tex]  and [tex]a_1=1.2[/tex]

Finally the formula is:

[tex]a_n=1.2(\frac{5}{2})^{n-1}[/tex]

Answer:

Answer: "f(x) = 1.2(2.5)x-1"

Step-by-step explanation:

Answer:

Number the boxes on the left 1–8 from top to bottom. Then their correct order on the right is 3, 7, 8, 4, 6, 5, 2, 1

Step-by-step explanation:

Trade the cube root for a 1/3 power:

(875x^5y^9)^(1/3)

Distribute the 1/3 power:

(125·7)^(1/3)·x^(5/3)·y^(9/3)

Further distribute the powers, rewrite the improper fractions:

125^(1/3)·7^(1/3)·x^(3/3+2/3)·y^3

Write 125 as a cube and simplify 3/3:

(5^3)^(1/3)·7^(1/3)·x^(1+2/3)·y^3

Simplify the cube root of a cube and the x term:

5·7^(1/3)·x·x^(2/3)·y^3

Group the terms with fractional exponents:

5·x·y^3·(7^(1/3)·x^(2/3))

Factor out the 1/3 exponent:

5xy^3·(7x^2)^(1/3)

Trade the 1/3 exponent for a cube root symbol:

5xy^3·∛(7x^2)

Answer:

width = (x-1)

Step-by-step explanation:

The volume of the prisms is defined in the problem as

Volume = x^3 + 9x^2 + 6x − 16

Volume  = width*height* length

And we know that,

length = (x+2)

height = (x+8)

We can find the roots of the equation, which happen to be

x = -8

x = -2

x = 1

(See image below)

This means that the volume can be represented as

Volume = x^3 + 9x^2 + 6x − 16 = (x+8)(x+2)*(x-1)

Therefore,

The width = (x-1)

Answer:

Surface area = [tex]261.6cm^2[/tex]

Volume = [tex]281.2cm^3[/tex]

Step-by-step explanation:

To find the surface area of our cone, we are using the formula for the surface area of a cone:

[tex]A=\pir(r+\sqrt{h^2+r^2} )[/tex]

where

[tex]A[/tex] is the surface area

[tex]r[/tex] is the radius

[tex]h[/tex] is the height

Notice that the height, radius, and slant height make a right triangle, so to find the height, [tex]h[/tex], we can use the Pythagorean theorem:

[tex]s^2=r^2+h^2[/tex]

[tex]14^2=4.5^2+h^2[/tex]

[tex]196=20.25+h^2[/tex]

[tex]h^2=196-20.25[/tex]

[tex]h^2=175.75[/tex]

[tex]h=\sqrt{175.75}[/tex]

[tex]h=13.26[/tex] cm

We have all we need now to find the surface area of our cone:

[tex]A=\pir(r+\sqrt{h^2+r^2} )[/tex]

[tex]A=\pi(4.5)(4.5+\sqrt{13.26^2+4.5^2} )[/tex]

[tex]A=261.6cm^2[/tex]

Now, to find the volume of our cone, we are using the formula for the volume of a cone:

[tex]V=\frac{\pi r^2h}{3}[/tex]

where

[tex]V[/tex] is the volume

[tex]r[/tex] is the radius

[tex]h[/tex] is the height

Replacing values

[tex]V=\frac{\pi (4.5^2)(13.26)}{3}[/tex]

[tex]V=281.2cm^3[/tex]

We can conclude that the surface area of our cone is 261.6 square centimeters and its volume is 281.2 cubic centimeters.

Answer:

Surface area [tex]= 261.405 cm^2\\[/tex]

Volume of the cone [tex]= 177.19 cm^3\\[/tex]

Step-by-step explanation:

Slant height of cone [tex]= (r + \sqrt{r^2 + h^2}) \\[/tex]

Height of the cone will be derived from this slant height

[tex]14 = 4.5 + \sqrt{4.5^2 + h^2} \\9.5 = \sqrt{4.5^2 + h^2}\\90.25 = 20.25 + h^2\\h = 8.36\\[/tex]

Surface Area of Cone

[tex]= \pi r (r + l)\\= (3.14) (4.5) (4.5 + 14)\\= 261.405[/tex]

Volume of the cone

[tex]= \frac{1}{3} \pi r^2h\\= \frac{1}{3} (3.14)(4.5^2) (8.36)\\= 177.19 cm^3\\[/tex]

Answer:

11.1803

Step-by-step explanation:

Answer:

The square root of 125 is 11.1803398875

Step-by-step explanation:

You know that 10 times 10 is 100. You would then go up from there to 11. If you need to round it, do it to the hundredths place though.

for (A^x)^y = A^xy

Thus for (3^-5)^-2 = 3^n

n = -5×-2 =10

Answer:

n=10

Step-by-step explanation:

We know that a^b^c = a^(b*c)

3 ^-5^-2 = 3^(-5*-2)

             = 3^(10)

3^n = 3^10

n = 10

B. Interquartile Range

Answer:

20

Step-by-step explanation:

This reads mathematically exactly how it is stated in words.  The word "is" means =, the word "of" means multiply, and "what number" is x.  Therefore, the equation from that looks like this:  16 = .80x.  Don't forget that you cannot use a percent in an equation without first changing it to its decimal equivalency.  Solve that for x by dividing both sides by .80 to get that x = 20

The number that when 80 % is found of it, would give the result of 16 is the number 20.

To determine the number that 16 is 80% of, you can set up an equation using algebra.

Let's represent the unknown number with the variable "x." The equation can be written as:

16 = 80% of x

To solve for "x," we need to isolate it on one side of the equation.

Since 80% is equivalent to 0.8 as a decimal, we can rewrite the equation as:

16 = 0.8x

To solve for "x," divide both sides of the equation by 0.8:

16 / 0.8 = 0.8x / 0.8

Simplifying the equation:

20 = x

Therefore, the number that 16 is 80% of is 20.

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[tex]\text{Hey there!}[/tex]

[tex]\text{Decimals can run out 100}[/tex]

[tex]\text{So,}\frac{0.0487\%}{1}\times\frac{100}{100}[/tex]

[tex]\text{Cross multiply: .0487}\times100=4.87\\ 100\times1=100[/tex]

[tex]\text{We get:}\frac{4.87}{100}[/tex]

[tex]\text{We could get rid of the 100 value because it is labeled as: per}[/tex]

[tex]\text{But, you can keep the 4.87 because it is the percentage of .0487}[/tex]

[tex]\boxed{\boxed{\text{Answer:C.) 4.87\%}}}[/tex] [tex]\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Final answer:

Decimal .0487 converts to 4.87% when we move the decimal point two places to the right. The correct answer is C, 4.87%.

Explanation:

To convert the decimal .0487 into a percent, we need to move the decimal point two places to the right, in accordance with the process described for converting decimals to percents. This gives us 4.87%, which means the correct answer is option C.

Answer:

Rational number/integer

Answer:

12 parts of fruit juice

To maintain the 2:3 ratio of soda to fruit juice, if you use 8 cups of soda, you would need 12 cups of fruit juice.

The punch recipe calls for 2 parts soda to 3 parts fruit juice. If you are using 8 cups of soda, you need to determine how much fruit juice is required using the given ratio. To do this, we can set up a proportion:

Soda: 2 parts
Fruit juice: 3 parts

If 2 parts are represented by 8 cups of soda, then 1 part would be 4 cups of soda (since 8 divided by 2 equals 4). Therefore, for 3 parts of fruit juice, we need 3 times 4 cups, which is 12 cups of fruit juice.

Here is the calculation:
2 parts : 3 parts
8 cups : x cups
x =  rac{3}{2} times 8 cups
x = 3 times 4 cups
x = 12 cups

So, you will need 12 cups of fruit juice to maintain the proper ratio if using 8 cups of soda.

Answer:

[tex]\large\boxed{(81m^6)^\frac{1}{2}=9m^3}[/tex]

Step-by-step explanation:

[tex]81=9^2\\\\m^6=m^{3\cdot2}=(m^3)^2\qquad\text{used}\ (a^n)^m=a^{nm}\\\\\left(81m^6\right)^\frac{1}{2}=\bigg(9^2\left(m^3\right)^2\bigg)^\frac{1}{2}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\left(9^2\right)^\frac{1}{2}\bigg(\left(m^3\right)^2\bigg)^\frac{1}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=9^{2\cdot\frac{1}{2}}\left(m^3\right)^{2\cdot\frac{1}{2}}=9^1(m^3)^1=9m^3[/tex]

Other method:

[tex]Use\ a^\frac{1}{n}=\sqrt[n]{a}\to a^\frac{1}{2}=\sqrt[2]{a}=\sqrt{a}\\\\\left(81m^6\right)^\frac{1}{2}=\sqrt{81m^6}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\ \text{and}\ (a^n)^m=a^{nm}\\\\=\sqrt{81}\cdot\sqrt{m^{3\cdot2}}=9\sqrt{(m^3)^2}\qquad\text{use}\ \sqrt[n]{a^n}=a\to\sqrt{a^2}=a\\\\=9m^3[/tex]

You would get paid $1.25 per hour, you divide 50 by 40 and get 1.25. Hope this helps ʅ（◞‿◟）ʃ

the answers is 1.25

enjoy good grades!!!!!

Answer:

2n-12 ( n is the unknown number)

Answer:

12-2n

Step-by-step explanation:

12 less which means you have to subtract 12 from twice a number n so 2 times n

so 12-2n

Answer: [tex]P=61.93\°[/tex]

Step-by-step explanation:

You know that:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

And the arctangent is:

[tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]

You can observe a right triangle in the figure.

Since you need to find the measure of the angle P, then:

[tex]\alpha=P\\opposite=15cm\\adjacent=8cm[/tex]

Knowing this, you can substitute these values into [tex]\alpha=arctan(\frac{opposite}{adjacent})[/tex]:

[tex]P=arctan(\frac{15cm}{8cm})[/tex]

Therefore, the measure of the angle P to the nearest hundreth is:

[tex]P=61.93\°[/tex]

Answer:

B

Step-by-step explanation:

Put in order smallest to largest:

43, 46, 48, 50, 50, 51, 52, 55, 57, 57, 58

Identify the median (middle number).  That's 51.  So we can split this into a lower half and an upper half:

Lower half: 43, 46, 48, 50, 50

Upper half: 52, 55, 57, 57, 58

The lower quartile starts at the median of the lower half: 48.

The upper quartile ends at the median of the upper half: 57.

So the answer is B.

Answer:

4(2y−9)

Step-by-step explanation:

lets factor out "4" out of the equation 8y-36

so u will get: 4(2y−9)

hope this helps

Answer:

Step-by-step explanation:

1 represent a candy bar with a  coupon and numbers 2 through 5 represent a candy bar without a coupon.

Now we are asked to find the probability that, if she buys 7 candy bars, more than 2 will include a coupon.

Total number of outcomes=16

Number of favorable outcomes(i.e. the outcome which have more than 2 one) = 3

( Since the outcomes are:  2113415 4341112   1455141 )

Hence, the probability is the ratio of Number of favorable outcomes to the total number of outcomes.

i.e.  [tex]Probability=\dfrac{3}{16}\\\\\\Probability=0.1875[/tex]

The equation that can be used to find the total distance the plane will travel in h hours is d = 400 × h

Total distance traveled by the plane = d miles

Total hours traveled = h hours

total speed of the plane = 400 miles per hour

Distance traveled = speed × time

d = 400 × h

d = 400h

Therefore, the equation that can be used to find the total distance the plane will travel in h hours is d = 400 × h

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The correct option is 3. [tex]\ d = 400 \times h[/tex]

To determine the total distance \(d\) an airplane will travel given its speed and time, we use the formula:

[tex]\[\text{Distance} = \text{Speed} \times \text{Time}\][/tex]

Given:

[tex]\text{Speed of the airplane} = \text{400 miles per hour}[/tex]

[tex]Time = \(h\) hours[/tex]

Plugging in the values:

[tex]\[d = 400 \times h\][/tex]

Answer:

C

Step-by-step explanation:

We know it's direct variation using the direct variation equation.

[tex]y=kx[/tex]

Where k is the constant.

Since 7 times x is the y values, [tex]k=7[/tex]

Now we can substitute 7 into k of the direct variation equation.

[tex]y=7x[/tex]

Answer:

The number of permutations of the letters in the word SMART are 120

Step-by-step explanation:

Permutations are events of multiplicative type, where the number of possibilities decreases and if the order of a permutation is an arrangement of a set of objects in a defined order.

The number of possible permutations when taking objects from the set of elements will be, following the same reasoning: [tex]P_{n} =n![/tex]

The number of permutations of the letters in the word SMART is:

[tex]P_{5} =5!=5.4.3.2.1=120[/tex]

.

Answer: $235,62

Step-by-step explanation:

You need to use the formula for calculate the volume of a cylinder:

[tex]V=\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that  the cylindrical container has a diameter of 0.5 feet and a height of 5 feet (Remember that the radius if half the diameter):

[tex]r=\frac{0.5ft}{2}=0.25ft\\\\h=5ft[/tex]

Then, you need to substitute these values into  [tex]V=\pi r^2h[/tex] to get the  volume of the cylindrical container:

 [tex]V=\pi (0.5ft)^2(5ft)[/tex]

[tex]V=3.92ft^3[/tex]

Since the gas costs $60 per cubic foot, you need to multiply the volume of the container by $60 to get  the total value of the gas in the container if it's filled completely. Then:

[tex]total\ value=(3.92)(\$60)=$235,62[/tex]

Answer:

C

Step-by-step explanation:

The scale factor is a quantity that "scales" another quantity.

Since, the dimensions of large is "3 times" that of the smaller box, the scale factor is 3.

This means, that we can multiply any dimension (length, width, or height) of the small box by 3 to get respective dimension of large box.

Remember, to get area, we need to multiply by scale factor squared. To get volume, we need to multiply by scale factor cubed.

Since, surface area is given of smaller box, we need to multiply by scale factor squared (3^2 = 9) to get surface area of larger box.

Hence, 79 * 9 = 711 cm^2

C is the correct answer.

Answer:

tan(5x/8)

Step-by-step explanation:

given expression

[tex]\frac{tan(1/2x)+tan(1/8x)}{1-tan(1/2x)tan(1/8x)}[/tex]

Using the trigonometric identity

tan(a+b)= [tex]\frac{tan(a) + tan(b)}{1-tan(a)tan(b)}[/tex]

here a= 1/2x and b=1/8x

putting the values we get

=tan(1/2x+1/8x)

=tan(5/8x)!

Answer:

b

Step-by-step explanation:

The correct answer should be x=4, y=2 or (4, 2)

Answer:

B.2152

Step-by-step explanation:

To solve this we are using the standard exponential growth equation:

[tex]y=a(1+b)^x[/tex]

where

[tex]y[/tex] is the final value after [tex]x[/tex] years

[tex]a[/tex] is the initial value

[tex]b[/tex] is the growing rate in decimal form

[tex]x[/tex] is the time in years

We know from our problem that the GNP is growing 4.8% per year, so [tex]b=\frac{4.8}{100} =0.048[/tex]. We also know that the GDP in 1994 was $5.9 billion and the desired GNP is $10 trillion, so [tex]a=5,900,000,000[/tex] and [tex]y=10,000,000,000,000[/tex].

Replacing values

[tex]y=a(1+b)^x[/tex]

[tex]10,000,000,000,000=5,900,000,000(1+0.048)^x[/tex]

[tex]10,000,000,000,000=5,900,000,000(1.048)^x[/tex]

Divide both sides by 5,900,000,000:

[tex]\frac{10,000,000,000,000}{5,900,000,000} =(1.048)^x[/tex]

Take natural logarithm to both sides

[tex]ln(1.048)^x=ln(\frac{10,000,000,000,000}{5,900,000,000})[/tex]

[tex]xln(1.048)=ln(\frac{10,000,000,000,000}{5,900,000,000})[/tex]

Divide both sides by ln(1.048)

[tex]x=\frac{ln(\frac{10,000,000,000,000}{5,900,000,000})}{ln(1.048)}[/tex]

[tex]x[/tex] ≈ 158

We now know that Canada's GNP will reach $10 trillion after 158 years from 1994, so to find the year we just need to add 158 years to 1994:

1994 + 158 = 2512

We can conclude that the correct answer is B.2152

For this case we have the following functions:

[tex]f (x) = x + 7\\g (x) = \frac {1} {x}[/tex]

We must find [tex](f_ {0} g) (x):[/tex]

By definition:

[tex](f_ {0} g) (x) = f (g (x))[/tex]

So, evaluating g(x) in f(x) we have:

[tex](f_ {0} g) (x) = f (g (x)) = \frac {1} {x} +7[/tex]

ANswer:

[tex]\frac {1} {x} +7[/tex]

Option D

Answer:

Part 1) The measure of the remaining angle is [tex]60\°[/tex]

Part 2) Is a 10 sided polygon (decagon)

Part 3) Yes, is possible for a triangle to have angles measures of 1°, 2° and 177°

Step-by-step explanation:

Part 1)

we know that

The sum of the measures of the interior angles of a polygon is equal to the formula

[tex]S=(n-2)180\°[/tex]

where

n is the number of sides of polygon

In this problem we have a hexagon

so

n=6 sides

Substitute

[tex]S=(6-2)180\°=720\°[/tex]

Let

x-----> the measure of remaining angle of the hexagon

[tex]6*(110\°)+x\°=720\°[/tex]

[tex]x=720\°-660\°=60\°[/tex]

Part 2) The sum of the measures of the interior angles of a polygon is [tex]1440\°[/tex]. What kind of polygon is it?

we know that

The sum of the measures of the interior angles of a polygon is equal to the formula

[tex]S=(n-2)180\°[/tex]

where

n is the number of sides of polygon

In this problem we have

[tex]S=1440\°[/tex]

substitute in the formula and solve for n

[tex]1440\°=(n-2)180\°[/tex]

[tex]n=(1440\°/180\°)+2=10\ sides[/tex]

therefore

Is a 10 sided polygon (decagon)

Part 3) Is it possible for a triangle to have angles measures of 1°, 2° and 177° ?

we know that

In any triangle the sum of the measures of the interior angles must be equal to 180 degrees

In this problem we have

1°+ 2°+ 177°=180°

therefore

Yes, is possible for a triangle to have angles measures of 1°, 2° and 177°

La letra C puede ser la respuesta correcta pero tengo mis dudas.

The probability of x = 5 successes in n = 8

trials for the probability of success p = 0.3 IS A.) 5.6

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