4 The pet store has 6 fish tanks.
Each tank has 7 goldfish and 5
Tetras. What is the total
number of fish (f) in the tanks?
x
= f
_= f
f
​

Answer:

4/21

Step-by-step explanation:

In this case, carry out the indicated operations from left to right:

8      1

---- * --- = 4/21

7       6

Use the half-angle identities.

[tex]\sin^2x=\dfrac{1-\cos2x}2[/tex]

[tex]\implies\sin^4x=\left(\dfrac{1-\cos2x}2\right)^2=\dfrac{1-2\cos2x+\cos^22x}4[/tex]

[tex]\cos^2x=\dfrac{1+\cos2x}2[/tex]

[tex]\implies\sin^4x=\dfrac{1-2\cos2x+\frac{1+\cos4x}2}4=\dfrac{3-4\cos2x+\cos4x}8[/tex]

sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.

Rewrite sin^4(x) in terms of cosine by using the Pythagorean identity for trigonometric functions, which relates sin^2(x) and cos^2(x):

sin^2(x) + cos^2(x) = 1

Now, solve for sin^2(x):

sin^2(x) = 1 - cos^2(x)

Now, square sin^2(x) to get sin^4(x):

(sin^2(x))^2 = (1 - cos^2(x))^2

sin^4(x) = (1 - cos^2(x))^2

So, sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.

for such more question on trigonometric functions

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Answer:

-2

Step-by-step explanation:

the coefficient is the number in front of the variable.

Answer:

the population would be 30.28 billion by 2020

Step-by-step explanation:

y=6.08 + 1.21x

y = 6.08 + 1.21(20)

y = 6.08 + 24.2

y = 30.28

Answer:

1/2

Step-by-step explanation:

3+7+10=20

20/2=10=1/2

Answer: Equivalent

Step-by-step explanation:

[tex]y=-\dfrac{1}{3}x+\dfrac{2}{3}\\\\\text{Multiply by 3 to clear the denominator: }3y = -x + 2\\\text{Add x to both sides: }x+3y=2\\\text{Multiply both sides by 2: }2x+6y=4[/tex]

When given a system of equations, the definitions of the solution are:

In the given system, the equations are the same which means they have INFINITE solutions --> The system is Consistent & Dependent = Equivalent.

Answer:

[tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69

Step-by-step explanation:

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

[tex]f(t)=A(1+r)^t[/tex]

where

[tex]f(t)[/tex] is the final population after [tex]t[/tex] years

[tex]A[/tex] is the initial population

[tex]r[/tex] is the growth rate in decimal form

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

We know from our problem that the initial population is 5000, the final population is 10000, and the time is 10 years, so [tex]A=5000[/tex], [tex]f(t)=10000[/tex], and [tex]t=10[/tex].

Let's replace the values and solve for [tex]r[/tex]:

[tex]f(t)=A(1+r)^t[/tex]

[tex]10000=5000(1+r)^{10}[/tex]

Divide both sides by 5000

[tex]\frac{10000}{5000} =(1+r)^{10}[/tex]

[tex]2=(1+r)^{10}[/tex]

Take root of 10 to both sides

[tex]\sqrt[10]{2} =\sqrt[10]{(1+r)^{10}}[/tex]

[tex]\sqrt[10]{2} =1+r[/tex]

Subtract 1 from both sides

[tex]\sqrt[10]{2}-1=r[/tex]

[tex]r=\sqrt[10]{2}-1[/tex]

[tex]r=1.0718-1[/tex]

[tex]r=0.0718[/tex]

We can conclude that the growth rate of our exponential equation is [tex]r=0.0718[/tex]. The closest value from your given choices is C)r=0.69

Answer:

[tex]\sqrt{5}\cdot\sqrt[3]{5} =\sqrt[6]{5^3} \cdot\sqrt[6]{5^2} =\sqrt[6]{5^5} =5^{(5/6)}[/tex]

Step-by-step explanation:

The rules of exponents apply, even when they are fractional exponents:

[tex]a^b\cdot a^c=a^{b+c}\\\\\sqrt[b]{x^a}=x^{(a/b)}[/tex]

Answer:

the number of sheet available is 75, 000

you take the total number of pages available = 8 x 75,000

= 600,000 pages

then each notebooks contains 200 pages

= 600,000 / 200

= 3000 notebooks can be made

Step-by-step explanation:

Answer:

3000 notebooks

Step-by-step explanation:

75,000*8=600000

600000/200=3000

Theoretically, each letter should have the same probability of occurring since there are 15 of each. There are 5 letters that can be drawn, so there is a total of 75 balls, and each letter has a probability [tex]\dfrac{15}{75}=\dfrac15[/tex] of being drawn.

This means one would expect a theoretical frequency of [tex]\dfrac{1250}5=250[/tex], i.e. any given letter should get drawn 250 times, which means the answer is D.

Answer:

252 D-O

Step-by-step explanation:

250 and theoretically 252

Answer:

The surface area of the rectangular pyramid is [tex]SA=109.50\ m^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the rectangular prism is equal to the area of the rectangular base plus the area of the four triangular faces

so

[tex]SA=(8)(5)+2[14.75]+2[\frac{1}{2}(8)(5)][/tex]

[tex]SA=40+29.50+40[/tex]

[tex]SA=109.50\ m^{2}[/tex]

Answer:

109.5

Step-by-step explanation:

Answer:

The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).

Step-by-step explanation:

Given : Sample size(n)= 144

Sample mean [tex]\mu= 22 ug/m^3[/tex]

Standard deviation [tex]\sigma=3.5 ug/m^3[/tex]

To find : 99.7% confident that actual concentration of fine particulates at the school is?

Solution :

The formula for confidence interval is

[tex]CI=\mu \pm z\times\dfrac{\sigma}{\sqrt{n}}[/tex]

Substituting the values in the formula,

[tex]CI=22 \pm 3\times\dfrac{3.5}{\sqrt{144}}[/tex]

[tex]CI=22 \pm 3\times\dfrac{3.5}{12}[/tex]

[tex]CI=22 \pm 3\times 0.2916[/tex]

[tex]CI=22 \pm 0.8748[/tex]

[tex]CI=22+0.8748, 22-0.8748[/tex]

[tex]CI=22.8748, 21.1252[/tex]

Therefore, The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).

Answer:

21 ug/m^3 - 23 ug/m^3

Step-by-step explanation:

Just got it right

Answer:

The factorization of [tex]729x^{15} +1000[/tex] is [tex](9x^{5} +10)(81x^{10} -90x^{5} +100)[/tex]

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form [tex](a^{3} +b^{3} )[/tex] or [tex](a^{3} -b^{3})[/tex]. It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of [tex]729x^{15} +1000[/tex] by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation [tex]729x^{15} +1000[/tex], and the exponent of the letter x is divided by 3.

[tex]\sqrt[3]{729x^{15}} =9x^{5}[/tex]

[tex]1000=10^{3}[/tex] then [tex]\sqrt[3]{10^{3}} =10[/tex]

So, we got that

[tex]729x^{15} +1000=(9x^{5})^{3} + (10)^{3}[/tex] which has the form of [tex](a^{3} +b^{3} )[/tex] which means is a sum of cubes.

Sum of cubes

[tex](a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})[/tex]

with [tex]a= 9x^{5}[/tex] y [tex]b=10[/tex]

2.) Solving the sum of cubes.

[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )[/tex]

[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)[/tex]

.

Here is the answer:...

Answer:

- Solve for y

- Subtract  2 x  from both sides of the equation then divide by  5 .

-y = 1 − 2 x 5

Step-by-step explanation:

Pie. It’s pie 3.14.... the name of that sign is pie

Answer:

That symbol represents pi.

Step-by-step explanation:

Pi is used by mathematicians to represent the ratio of a circle's circumference to its diameter.  It is approximately equal to 3.14159. Hope this helps!

Answer:

the probability is very high 86% > 14%

Step-by-step explanation:

55+20+11= 86%/100% 100-86=14% chance there will not be any rain or lightning

hope this helps!!

Answer:

- 864

Step-by-step explanation:

In the case of a 2 × 2 matrix the determinant may be defined as:

|A| = [tex]\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right][/tex]= ad-bc

Given in the question a matrix

[tex]\left[\begin{array}{cc}-30&-6\\6&30\\\end{array}\right][/tex]

(-30)(30) - (-6)(6)

-900 + 36

- 864

Answer:

Option A: -30

For Odyssey

**If you are on the pre-test then you might wanna take your time because they can suspect if you are cheating**

Answer: b) -5 ≤ y ≤ 1

Step-by-step explanation:

y = 3 cos (4x) - 2

     ↓                 ↓

amplitude       vertical shift

The amplitude is 3 which gives a range of -3 to 3 but there is also a shift down of 2 units so the new range is: -3 - 2 = -5 to 3 - 2 = 1

-5 ≤ y ≤ 1

Answer:

Point S coordinates= (-4,5)

Step-by-step explanation:

If you would just move the point 5 PLACES TO THE RIGHT, you would get -4, 5, which is the correct answer.

Answer:

14n-16

Step-by-step explanation:

Given

[tex]2n - 7 + 3(4n - 3)\\[/tex]

Simplification requires the expression to be in its shortest and concise form. The brackets are opened and addition or subtractions are performed

So,

Multiplying 3 inside bracket

[tex]2n - 7 + 12n - 9[/tex]

Combining alike terms:

[tex]2n+12n-7-9[/tex]

Performing addition and subtractions:

[tex]14n-16[/tex]

Hence the simplified form is:

14n-16 ..

The answer is:

The area that the want to cover with new grass will be:

[tex]Area_{grass}=8x^{2} -12x-22[/tex]

If we want to calculate what is the ara of the region of the backyard that they want to cover with new grass, we need to calculate the area of the backyard, calculate the area of the swimming pool and its patio, and the last step is to subtract the area of the swimming pool and its patio to the total area of the backyard.

So, to calculate the areas, we need to use the following formula:

[tex]Area=Length*Width[/tex]

Also, we need to remember how the distributive property works, since we are going to need it.

We have that:

[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]

We are given the following information:

For the backyard we have:

[tex]Length=3x-2\\Width=3x+1[/tex]

For the swimming pool and its patio:

Since there it's not mentioned, let be the first expression the length, and the second one, the width.

[tex]Length=x+4\\Width=x+5[/tex]

Then, calculating we have:

Backyard:

[tex]Area_{backyard}=(3x-2)*(3x+1)=9x^{2}+3x-6x-2=9x^{2}-3x-2[/tex]

Swimming pool and patio:

[tex]Area_{swimmingpool}=(x+4)*(x+5)=x^{2}+5x+4x+20=x^{2}+9x+20[/tex]

Now, calculating the area that they want to cover with new grass, we have:

[tex]Area_{grass}=Area_{backyard}-Area_{swimmingPool}\\\\Area_{grass}=(9x^{2}-3x-2)-(x^{2}+9x+20)\\\\Area_{grass}=9x^{2} -x^{2} -3x-9x-2-20\\\\Area_{grass}=8x^{2} -12x-22[/tex]

Hence, we have that the area that the want to cover with new grass will be:

[tex]Area_{grass}=8x^{2} -12x-22[/tex]

Have a nice day!

Answer:

(x-2)(x+4)

Step-by-step explanation:

So it would be A.

Explanation: The middle number is 2 and the last number is -8.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 2

Multiply together to get -8

Can you think of the two numbers?

Try -2 and 4:

-2+4 = 2

-2*4 = -8

Fill in the blanks in

(x+_)(x+_)

with -2 and 4 to get...

(x-2)(x+4)

Answer:

(x−2)(x+4)

A. (x+4)(x-2). The factorization of the quadratic equation x²+2x-8 given by the graph is (x+4)(x-2).

From the graph shown in the image we can see the parabola's cut points, in the y-axis is -4 and the x-axis is 2, then we write the product changing the signs (x+4)(x-2) = x²+2x-8

Answer:

Step-by-step explanation:

Lateral Area:

The formula of a Lateral Area of a cone:

[tex]L.A.=\pi rs[/tex]

r - radius

s - slant height

We have r = 5m and s = 12m. Substitute:

[tex]L.A.=\pi(5)(12)=60\pi\ m^2\\\\\pi\approx3.14\to L.A.\approx(6)(3.14)=188.4\ m^2[/tex]Surface Area:

The formula of a Surfaace Area of a cone:

[tex]S.A.=B+L.A.[/tex]

In the base we have the circle with the radius r = 5m.

The formula of an area of a circle"

[tex]A_O=\pi r^2[/tex]

Substiute:

[tex]B=\pi(5^2)=25\pi\ m^2\approx(25)(3.14)=78.5\ m^2[/tex]

[tex]S.A.=60\pi+25\pi=85\pi\ m^2\approx188.4+78.5=266.9\ m^2[/tex]

Answer: B=27

Step-by-step explanation:

10.8 x 5=54/2= 27

Answer:

26in.^2 the first choice

Step-by-step explanation:

Just did the QC

Answer:

147

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

here a = 3 and d = 9 - 3 = 15 - 9 = 6, hence

[tex]a_{25}[/tex] = 3 + (24 × 6) = 3 + 144 = 147

Answer:

90

Step-by-step explanation:

add them all up and divide by how many there are

The answer is 90.

Add all the numbers then average them out by how many numbers there are.

solution here,

slope(m)=(y2-y1)/(x2-x1)

=(5-1)/(1-0)

=4/1 =4

Answer:

The correct answer is D) 4

Step-by-step explanation:

I took the test and this was correct!

Answer:

the pattern would be W

Step-by-step explanation:

W should be the answer. Hope I helped you lots please count me brainy

Answer:

Area of Trapezoid is 88 Units^2

Step-by-step explanation:

Area of trapezoid = (a+b)/2 * h

where a and b are lengths of each base and h is the height of trapezoid.

In the question given:

a= 17 (because a is the upper base and value will be 17)

b= 27 (because b is the lower base and value will be 17+5+5 = 27)

h= 4

Area of trapezoid = (a+b)/2 * h

                             = (17 +27)/ 2 * 4

                             = 22 * 4

                             = 88 Units^2

Area of Trapezoid is 88 Units^2

Answer:

The perimeter is 22.

Step-by-step explanation:

The perimeter formula (it sometimes varies) is 2(b+h)

b being base (in this example, 6)

h being height (in this example, 5)

So now, with substitution, we are left with:

2(6+5)

Which simplifies down to:

2(11)

22