Find all solutions of sqrt(3)tan(3x) = 0

Answer:

3.75 hours

Step-by-step explanation:

Using the relation

Distance = speed × time

Change Jasmine's speed into an improper fraction

9 [tex]\frac{3}{10}[/tex] = [tex]\frac{93}{10}[/tex], then

distance = [tex]\frac{93}{10}[/tex] × [tex]\frac{5}{2}[/tex] = [tex]\frac{93}{4}[/tex] miles

To calculate Lucy's time over the same distance use

Time = [tex]\frac{distance}{speed}[/tex]

Change speed to an improper fraction

6 [tex]\frac{1}{5}[/tex] = [tex]\frac{31}{5}[/tex], hence

time = [tex]\frac{\frac{93}{4} }{\frac{31}{5} }[/tex]

       = [tex]\frac{93}{4}[/tex] × [tex]\frac{5}{31}[/tex] ( cancel 93 and 31 )

      = [tex]\frac{3(5)}{4}[/tex]

      = [tex]\frac{15}{4}[/tex] = 3.75 hours

Final answer:

It took Lucy approximately 160.17 minutes to bike the trail.

Explanation:

Jasmine finished the bike trail in 2.5 hours at an average rate of 9 3/10 miles per hour. Lucy biked the same trail at a rate of 6 1/5 miles per hour. To find out how long it took Lucy to bike the trail, we can use the formula:

Time = Distance / Rate

Since the distance is the same for both Jasmine and Lucy, we can set up an equation:

2.5 = Distance / 6 1/5

To solve this equation, we first need to convert 2.5 into a fraction. 2.5 is the same as 2 1/2. So, the equation becomes:

2 1/2 = Distance / 6 1/5

To make the equation easier to work with, we can convert 2 1/2 into an improper fraction: 2 1/2 = 5/2. The equation now becomes:

5/2 = Distance / 6 1/5

To solve for Distance, we can use cross-multiplication:

(5/2)(6 1/5) = Distance

Simplifying the right side of the equation:

(5/2)(31/5) = Distance

(5/1)(31/5) = Distance

31 = Distance

So, the distance of the bike trail is 31 miles. Now, we can find out how long it took Lucy to bike the trail by using the formula Time = Distance / Rate:

Time = 31 / 6 1/5

Once again, let's convert 31 into a fraction: 31 = 31/1. The equation now becomes:

Time = 31/1 / 6 1/5

To divide fractions, we can multiply by the reciprocal of the second fraction. So, the equation becomes:

Time = 31/1 * 5 1/6

Now, we can convert 5 1/6 into an improper fraction: 5 1/6 = 31/6. The equation now becomes:

Time = 31/1 * 31/6

To multiply fractions, we can multiply the numerators together and the denominators together. So, the equation becomes:

Time = (31*31) / (1*6)

Calculating the numerator and denominator separately:

Time = 961 / 6

So, it took Lucy approximately 160.17 minutes to bike the trail.

Answer:

1.7 seconds, and

3.3 seconds

Step-by-step explanation:

We simply need to plug in 8 into h and solve for t:

[tex]h=-15Cos(\frac{2\pi}{5}t)\\8=-15Cos(\frac{2\pi}{5}t)\\-\frac{8}{15}=Cos(\frac{2\pi}{5}t)\\\frac{2\pi}{5}t=Cos^{-1}(-\frac{8}{15})\\\frac{2\pi}{5}t=2.13\\t=\frac{2.13}{\frac{2\pi}{5}}\\t=1.70[/tex]

Since cosine is negative in the 3rd quadrant as well, we need to figure out the 3rd quadrant equivalent of 2.13 radians.

First, π - 2.13 radians = 1.01 radians.

Then, we add 1.01 to π radians, so we get 4.15 radians

Solving from the last part, we have:

[tex]t=\frac{4.15}{\frac{2\pi}{5}}\\t=3.3[/tex]

also, t = 3.30 seconds

*Note: we put the calculator mode in radians when solving

So, t = 1.7 seconds & 3.30 seconds

A=f(18)=110(.8855)^18=12.3mg

===========================================================

Explanation:

Plug in t = 18 to get

f(t) = 110*(0.8855)^t

f(18) = 110*(0.8855)^18

f(18) = 110*(0.112045)

f(18) = 12.32495

f(18) = 12.32

The answer is approximate. I rounded to two decimal places (aka to the nearest hundredth).

The fractions 3/4 and 6/8 are equivalent. They are essentially the same when reduced to their lowest terms, both representing the same part of a whole.

The statement that is true about the fractions 3/4 and 6/8 is that they are equivalent fractions. The student's question is about the comparison of the fractions 3/4 and 6/8. When these two fractions are examined, it becomes clear that they are, in fact, equivalent.

This is because when you divide the numerator and the denominator of 6/8 by their highest common factor, which is 2, you get 3/4. Therefore, 3/4 and 6/8 are equivalent fractions and represent the same part of the whole.

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Answer:

It is 2 1/2

Step-by-step explanation:

I hope the answer is 7/4

8/32 is the answer to your problem

The equivalent fraction of given fraction is  [tex]\frac{8}{32}[/tex].

Given fraction is,  [tex]\frac{4}{16}[/tex]

It is observed that both numerator and denominator of given fraction is divisible by 4.

Simplest form of  [tex]\frac{4}{16}[/tex] is,

                          [tex]\frac{4}{16}=\frac{4*1}{4*4} =\frac{1}{4}[/tex]

Equivalent fraction that has a denominator of 32 is,

                  [tex]\frac{1}{4}=\frac{1*8}{4*8}=\frac{8}{32}[/tex]

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Answer:There will be 10 grams left because you subtract half of the current amount from it every 9 years.

Step-by-step explanation:

Starting with 40 grams of europium which has a half-life of 9 years, after the first half-life, there would be 20 grams left, and after the second half-life (a total of 18 years), there would be 10 grams remaining.

The question is about calculating the amount of a radioactive substance that remains after a certain period of time has passed, which is based on the substance's half-life. Given that the half-life of europium is 9 years, after one half-life (9 years) 50% of the substance would remain, and after two half-lives (18 years) only 25% would remain. Since we started with 40 grams of europium, we apply this decay process step by step:

Therefore, after 18 years, there will be 10 grams of the radioactive europium left.

Answer:

- 9 1/4

Step-by-step explanation:

Get a common denominator for the fractions

-5 3/4 - 3 1/2 *2/2

-5 3/4 - 3 2/4

-5 3/4 + -3 2/4

Add them together

-8 5/4

We have an improper fraction

-( 8 + 1 1/4)

- (9 1/4)

- 9 1/4

Answer:

the mean high temperature is 71 degrees and the mean low is 31 degrees

Step-by-step explanation:

Answer:   [tex]\bold{\dfrac{241}{500}}[/tex]

Step-by-step explanation:

[tex]0.482 = \dfrac{482}{1000}\\\\\\\dfrac{482}{1000}\div \dfrac{2}{2}=\dfrac{241}{500}[/tex]

Answer:

241/500 is The answer

Step-by-step explanation:

1) 0.482 = 482/1000

2) Divide by 2 on both side

0.482 = (482/2)/(1000/2) = 241/500

Hopes this helps!

Answer:

The lateral area is [tex]298.7\ units^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of the regular octagonal pyramid is equal to the area of its eight triangular lateral faces

The lateral area is equal to

[tex]LA=8[\frac{1}{2}(b)(l)][/tex]

we have

[tex]b=6.6\ cm[/tex]

To find the slant height apply the Pythagoras Theorem

[tex]l^{2}=8^{2} +8^{2}\\l^{2}=128\\l=\sqrt{128}\ units[/tex]

Find the lateral area

substitute the values

[tex]LA=8[\frac{1}{2}(6.6)(\sqrt{128})]=298.7\ units^{2}[/tex]

The answer is 298.7 cm²

Answer:

[tex]L=15\ m[/tex]

Step-by-step explanation:

we know that

The perimeter of rectangle is equal to

[tex]P=2L+2W[/tex]

In this problem we have

[tex]P=42\ m[/tex]

[tex]W=6\ m[/tex]

substitute in the formula and solve for L

[tex]42=2L+2(6)[/tex]

simplify

[tex]21=L+(6)[/tex]

[tex]L=21-6=15\ m[/tex]

Answer:6

Step-by-step explanation:

500/12 is 41 so therefore you do 48/12 is 6.

Answer:

1 19/125

Step-by-step explanation:

1.) 12/500 = 0.024

2.) 0.024 * 48 = 1.152

3.) 1.152 converted to a fraction is 144/125, or 1 19/125

Answer:

Use the quadratic formula

Step-by-step explanation:

Use the quadratic formula

For a quadratic function of the form:

[tex]ax ^ 2 + bx + c[/tex]

Where a, b and c are the real coefficients of the polynomial

Then, for

[tex]2x^2+4x-7=0\\a = 2\\b = 4\\c = -7[/tex]

The solutions are:

[tex]x_1 = \frac{-b+\sqrt{b^2-4ac}}{2a}\\\\x_2 = \frac{-b-\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x_1 = \frac{-4+\sqrt{4^2-4(2)(-7)}}{2(2)}\\\\x_2 = \frac{-4-\sqrt{4^2-4(2)(-7)}}{2(2)}\\\\x_1 = \frac{-2+3\sqrt{2}}{2}\\\\x_2 = \frac{-2-3\sqrt{2}}{2}[/tex]

I need help to please?

Answer:

x = 15

Step-by-step explanation:

➷ population = 100,000 x 1.03^5

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

Step-by-step explanation:

[tex]y-1<2x\qquad\text{add 1 to both sides}\\\\y<2x+1\\\\\text{Substitute the coordinates of the points and check the inequality:}\\\\a.\ (3,\ 7)\\7<2(3)+1=6+1=7\qquad\text{FALSE}\\\\b.\ (1,\ 8)\\8<2(1)+1=2+1=3\qquad\text{FALSE}\\\\c.\ (2,\ 7)\\7<2(2)+1=2+1=5\qquad\text{FALSE}\\\\d.\ (3,\ -11)\\-11<2(3)+1=6+1=7\qquad\text{TRUE}[/tex]

The coefficient of the variable is equal to 1

A coefficient is a value that is attached to a variable. It is the number always in front for a variable eg x, y or v in this case.

Data given;

The coefficient of the variable (v) is 1 because if it is greater than 1, or less than one and cannot be equal to zero, it would be attached.

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Step-by-step explanation:

Do you mean:

(6^5/7^3)^2?

If so, you will get

6^10/7^6 or about 513.954016

It is to be note that  (6⁵ / 7³)² simplifies to become approximately 514.64

To simplify the expression (6⁵ / 7³)², we start by evaluating the exponents first.

6⁵ means 6 raised to the power of 5, which is 6 * 6 * 6 * 6 * 6 = 7776.

7³ means 7 raised to the power of 3, which is 7 * 7 * 7 = 343.

Now, we substitute these values back into the expression  -

(7776 / 343)² = (22.6666666667)² = 514.64197531

Therefore, it is right to state that (6⁵ / 7³)² simplifies to 514.64197531 which is approximately, 514.64.

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54 or it 180 i got 54 by adding 30 and 24in and got 180 by multiplying

Answer: 360 sq inches

Step-by-step explanation: The formula for finding the area of a triangle is 1/2*bh. So, plug-in your numbers: 1/2*(30*24). Then multiply the value in the perentheses which is 720 and then you multiply that by 1/2 (0.5) or you can divide it by 2. When you divide it by 2 or multiply it you would get 360.

In the fifth generation 1024 people learnt the art of quilling​.

In the fifth generation 1024 people learnt the art of quilling​.

In total 5 generations total (16+ 64 + 256 + 1024) = 1364  people learnt the art of quilling​.

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Using the exponential growth formula, it is determined that by the end of five generations, 4096 people will know the art of quilling, starting with one teacher teaching four students, and each subsequent student teaching four others.

The question involves an exponential growth scenario where Amanda teaches the art of quilling to four students, and then these students each teach four others, and so on for five generations. To find out how many people will know the art of quilling by the fifth generation, we use the formula for exponential growth: Total = a(1 + r)^n, where a is the initial amount (number of people who know the art at the beginning), r is the rate of increase (each person teaches 4 others means the rate is 4), and n is the number of generations.

The initial teacher, Amanda, is not counted in the first generation of students she teaches, so we begin with 4 students as our initial amount (a=4). Thus, the calculation for five generations becomes: Total = 4(4)^5. The formula simplifies to 4 * 1024 = 4096 people. Therefore, by the end of five generations, 4096 people will know the art of quilling.

Answer:

Option B. [tex]33,493.3\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=40/2=20\ cm[/tex] ----> the radius is half the diameter

[tex]\pi=3.14[/tex]

substitute the values

[tex]V=\frac{4}{3}(3.14)(20)^{3}=33,493.3\ cm^{3}[/tex]

Answer:

x = 149

Step-by-step explanation:

Lines m and n are parallel lines as shown by the double arrows on each line.

The angles marked x and 149 deg are corresponding angles of parallel lines cut by a transversal.

Postulate:

If parallel lines are cut by a transversal, then corresponding angles are congruent.

According to the postulate above, since the angles marked 149 and x are corresponding angles, they are congruent.

x = 149

Answer:

X=149

Step-by-step explanation:

Lines m and n are parallel. You know this because the 2 marks on both lines mean that they are the same and parallel.

Final answer:

To find the empty space in the can of tennis balls, calculate the volume of one tennis ball and multiply by three (since there are typically three balls per can), then subtract from the volume of the can. There are 43.54 inches³ of empty space in the can, after rounding to the nearest hundredth.

Explanation:

To calculate the empty space inside the can of tennis balls, we first need to determine the volume of one tennis ball and then the volume of the can. Given the radius of each tennis ball is 1.5 inches, we use the formula for the volume of a sphere:

V_ball = 4/3 π r³

Substitute with r = 1.5 inches and π = 3.14:

V_ball = 4/3 × 3.14 × (1.5 inches)³

V_ball = 4/3 × 3.14 × 3.375 inches³

V_ball = 14.13 inches³ (rounded to the nearest hundredth)

Next, we calculate the volume of the can, using the formula for the volume of a cylinder:

V_can = π r² h

Substitute with r = 1.75 inches and h = 9 inches:

V_can = 3.14 × (1.75 inches)² × 9 inches

V_can = 3.14 × 3.0625 inches² × 9 inches

V_can = 85.93 inches³ (rounded to the nearest hundredth)

The empty space within the can is therefore the volume of the can minus the volume of three tennis balls (assuming the can holds three balls):

Empty space = V_can - 3 × V_ball

Empty space = 85.93 inches³ - 3 × 14.13 inches³

Empty space = 85.93 inches³ - 42.39 inches³

Empty space = 43.54 inches³ (rounded to the nearest hundredth)

Therefore, there are approximately 43.54 inches³ of empty space inside the can.

Answer:

x = 2

Step-by-step explanation:

These are 2 secant lines intersecting a circle. This problem can be solved using secant-theorem.

Simply put, the secant theorem tells us that the outer segment (outside the circle) times the total length of secant line (outer and inner segment) is equal to that of the other secant line's product of outer and total.

For this diagram, according to the theorem, it should be:

DE * CE = AE * BE

Hence we have:

[tex]DE * CE = AE * BE\\(1+x+4)*(x+4)=(11+x+1)*(x+1)\\(x+5)*(x+4)=(x+12)*(x+1)\\x^2+9x+20=x^2+13x+12\\20-12=13x-9x\\8=4x\\x=\frac{8}{4}=2[/tex]

The value of x is 2

Hey there!

The first thing we can do is find the number of third in 4.

We can do this by multiplying 4 by 3 since there are 3 thirds in a whole.

4 x 3 = 12

So, 4 = 12/3

If she studies for 2/3 an hour each night, then we can divide 12 by 2 to figure out how many 2/3 go into 12/3.

12 ÷ 2 = 6

So, she studied for 6 days.

Hope this helps!

Answer:

C

Step-by-step explanation:

The point slope form of a line is [tex]y - y_1 = m(x-x_1)[/tex]. If the point is (2,5) then the equation will be [tex]y - 5=m(x-2)[/tex]. Only option C matches this equation.

Answer:

Hiro factored them correctly.

Step-by-step explanation:

The factors of 14 are 1, 2, 7, and 14.

7 * 2 = 14

10 and 4 make the product of 14.

10 + 4 = 14

Bilial factored 14y3 correctly.

Hiro factored 14y2 as (7y2)(2y)
Bilial factored 14y3 as (10y)(4y2)

To determine which one factored 14y3 correctly, we need to compare their factorizations to the original expression: 14y3. Hiro's factorization (7y2)(2y) does not match the original expression, as it is missing a y term. On the other hand, Bilial's factorization (10y)(4y2) matches the original expression.

Therefore, "Bilial factored 14y3 correctly."

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