You need 320 mL of a 65% alcohol solution. On hand, you have a 60% alcohol mixture. How much of the 60% alcohol mixture and pure alcohol will you need to obtain the desired solution?

You will need
____ mL of the 60% solution
and
_____ mL of pure alcohol.

Answer:

Simplify:

[tex](8\frac{2}{3} )^4[/tex]

Step-by-step explanation:

[tex](8\frac{2}{3})^4 =(\frac{26}{3} )^4=\frac{456976}{81}[/tex]

Answer:

The answer is

650/81

Step-by-step explanation:

I think this is a better representation

Of the given expression

(8 2/3^4)

To solve the problem let us perform a step by step operation

Step one

Let's us solve the bracket terms first

=(8 2/3^4)

3⁴= 3*3*3*3=81

=(8 2/81)

=Simplifying we have

=((81*8)+2)/81

=(648+2)/81

=650/81

Let P = Patrick's age

P + 8 = 18

The equation is P + 8 = 18

Let P = Patrick's age

An equation is a mathematical statement this is made up of expressions related with the aid of the same signal. for instance, 3x – five = 16 is an equation. Solving this equation, we get the price of the variable x as x = 7.

A one-step equation is an algebraic equation you may resolve in the most effective one step. You've got solved the equation when you get the variable through itself, and not using numbers in the front of it, on one side of the same signal.

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Answer: $212.5

Step-by-step explanation:

250% = 2.5

So we multiply 85.00 by 2.5

85*2.5=212.5

So it is $212.5

Answer:

your answer is  $212.5

Step-by-step explanation:

Answer:

Its C. XD sorry i just answered this.

Step-by-step explanation:

Hope this helped again! :3

Answer:

Each path in the diagram is a possible outcome with a probability of 1/4. The sum of all paths should equal 1.

 The answer is C.

Answer:

1.958 * 10^-5 seconds  or 0.00001958 seconds.

Step-by-step explanation:

3740 = 3.74 * 10^3  in scientific notation.

Time = distance / speed.

= 3. 74 * 10^3 / 1.91 * 10^8

= 1.958 * 10^-5 seconds.

It takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away using the speed of sound in telephone cables.

To find the time it takes for sound to travel a certain distance, we can use the formula time = distance / speed. In this case, the speed of sound along the telephone cable is 1.91 * 10^8 ms⁻¹ and the distance is 3740m.

So the time = 3740 / 1.91 * 10^8 = 1.96 * 10^-5 seconds.

Therefore, it takes Tetsuo's voice approximately 1.96*10^-5 seconds to travel from his office phone in Tokyo to his wife's phone 3740m away.

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Answer: [tex]\frac{1}{8}[/tex] or [tex]1:8[/tex]

Step-by-step explanation:

First, you can convert the mixed number [tex]1\ \frac{1}{2}[/tex] into a decimal number. To do this, you need to divide the numerator (which is 1)  by the denominator (which is 2) of the fraction:

[tex]\frac{1}{2}=0.5[/tex]

Now you must add 0.5 to the whole number part. Then:

[tex]1+0.5=1.5[/tex]

In order to find the ratio of cleaner to water, you must divide 1.5  cups of cleaner by 12 cups of water.

Therefore, the ratio is:

[tex]ratio=\frac{1.5}{12}=\frac{1}{8}[/tex] or [tex]1:8[/tex]

Answer:

157.65

Step-by-step explanation:

38*4.1=155.8

155.8+1.85=157.65

For this case we must find the value of the following expression:

[tex]1.85 + 38 * 4.1 =[/tex]

According to the PEMDAS algebraic resolution method, multiplications must be made before the addition. So, we have:

[tex]1.85 + 155.8 =[/tex]

Adding we have:

157.65

Answer:

157.65

Answer:

y^2+12-7y

Step-by-step explanation:

(y-3)(y-4)

I will split it up for us

y*y= y^2

-3*y= -3y. \

y*-4= -4y. / -7y

-3*-4= 12

y^2+12-7y

The product of (y-3)(y-4), is y^2 - 7y + 12.

To find the product of (y-3)(y-4), we will use the FOIL method, which stands for First, Outer, Inner, Last. This method is used to multiply two binomials.

First: Multiply the first terms of each binomial: y × y = y^2.

Outer: Multiply the outer terms: y × -4 = -4y.

Inner: Multiply the inner terms: -3 × y = -3y.

Last: Multiply the last terms of each binomial: -3 × -4 = 12.

Adding these products together, we get: y^2 - 4y - 3y + 12. Simplifying by combining like terms, the final product is: y^2 - 7y + 12.

Answer:

4x^2(5x^4 / 2x^2)= 10 x^4

Step-by-step explanation:

We want factorize the expression 4x^2(5x^4 / 2x^2)

And to do this, we need to remember key properties of exponents.

Those are:

[tex]x^{m} / x^{n} = x^{m-n}[/tex]

[tex]x^{m} * x^{n} = x^{m+n}[/tex]

So

4x^2(5x^4 / 2x^2)= 4x^2(5/2 x^2)=10 x^4

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

We have the points (0, 2) → b = 2 and (4, 6).

Calculate the slope:

[tex]m=\dfrac{6-2}{4-0}=\dfrac{4}{4}=1[/tex]

Substitute the values of the slope and the y-intercept to the equation of a line:

[tex]y=1x+2[/tex]

Answer:

y=x+2

Step-by-step explanation:

Answer:

2 is the only even prime number.

Step-by-step explanation:

Two is the only even prime number. It's the only even number that can be divided by only itself (2) and one.

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

10u+t=18+10t+u

(If this doesn't match one of the equations, please post your options so I can put it in the form of one of your options.)

Step-by-step explanation:

Let there be a number [tu] where t is the tens and u is ones digit.

t+u=16.

Now we reverse the number [ut] is 8 more than [tu].

[ut]=18+[tu]

So [ut]=10u+t because u is the tens  and t is the ones digit

and [tu]=10t+u because t is the tens and u is the ones digit.

The equation you are looking for is

10u+t=18+10t+u.

Let's solve it just for fun:

Subtract u on both sids:

9u+t=18+10t

Subtract 10t on both sides:

9u-9t=18

Divide both sides by 9:

u-t=2

The system is:

u-t=2

u+t=16

--------------add!

2u  =18

u=9

If u=9 and u+t=16, then t=7.

To the original number is 79.

The new number is 97 (is this 18 more than the other; yep).

Answer:

97.

Step-by-step explanation:

Answer:

(L + 10)/(L + 16) = 0.8

Step-by-step explanation:

She needs to answer L more questions to get a grade of 80%.

When she answers L more questions correctly, she will have answered L + 10 questions correctly.

The total number of questions will be L + 16.

L + 10 must be 80% of L + 16

(L + 10)/(L + 16) = 0.8

Cheryl must use the equation 0.80 = (10 + I) / (16 + I) to determine how many consecutive questions she needs to answer correctly to reach her goal of 80% accuracy on her test.

Cheryl has answered 16 questions on her online test with 10 correct responses. To achieve her goal of 80% accuracy, she must determine how many additional questions she must answer correctly in a row.

To find the necessary total number of correct answers (T) for 80% accuracy, we use the equation:

0.80 = (10 + I) / (16 + I)

where I represents the number of consecutive questions Cheryl answered correctly after the initial 16 questions.

The height of the triangle is approximately [tex]4.35\text{ mm}[/tex]

Step-by-step explanation:

The area of a triangle can be calculated by using the Heron's formula.

Heron's formula:  

Suppose a triangle has sides [tex]a'[/tex], [tex]b'[/tex] and [tex]c'[/tex], then the semi-perimeter [tex]S[/tex] of the triangle is represented by the expression,

[tex]S=\frac{a'+b'+c'}{2}[/tex]

The area [tex]A[/tex] of the traingle is formulated below.

[tex]\fbox {\begin\\A=\sqrt{s(s-a')(s-b')(s-c')}\end{minispace}}[/tex]

To calculate the area of the triangle with sides [tex]9 \text{ mm}[/tex] , [tex]6 \text{ mm}[/tex] and [tex]12 \text{ mm}[/tex], first find the semi-perimeter.

[tex]S=\frac{9+6+12}{2}\\S=\frac{27}{2}\\S=13.5 \text{ mm}[/tex]

Now, the area of the triangle is calculated below.

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}\\A=\sqrt{13.5(13.5-9)(13.5-6)(13.5-12)}\\A=\sqrt{13.5 \times 4.5 \times 7.5 \times 1.5}\\A=\sqrt{\frac{135}{10}\times\frac{45}{10}\times\frac{75}{10}\times\frac{15}{10}} \\A=\sqrt{\frac{(15\times3\times3) \times (15\times3) \times (15\times5) \times15}{100\times100}}\\A=\frac{15\times15\times3\sqrt{15 } }{100} \\A=2.25\times3\times3.87\\A=26.122[/tex]

Area A of a triangle with a altitude P and one side as base B on which the altitude P is drawn, can be calculated as,

[tex]\fbox{\begin\\A= \left[\frac{1}{2}(B)(P)\right]\\\end{minispace}}[/tex]

Now, the area of the same triangle can also be calculated as,

[tex]A=\frac{1}{2}(12)(x)\\A=6x[/tex]

In the above calculations, area of the triangle is calculated in two ways.

Therefore, both the areas can be equated to obtain the altitude [tex]x[/tex].

[tex]6x=26.122\\x=\frac{26.122}{6}\\x=4.35[/tex]

Thus, the height of the triangle is evaluated as [tex]\fbox{4.35 \text{ mm}}[/tex].

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1. Prove that AB2+BC2=AC2https://brainly.com/question/1591768

2. Which undefined term is needed to define an angle? https://brainly.com/question/3717797

3. Look at the figure, which trigonometric ratio should you use to find x? https://brainly.com/question/9880052

Answer Details

Grade: Junior High School

Subject: Mathematics

Chapter: Area of triangle

Keywords: area of triangle, heron's formula, base multiplied by height, base multiplied by perpendicular, base multiplied by altitude, right triangle, altitude corresponding to base, area of right triangle

Answer:

4.3 mm

Step-by-step explanation:

I got it correct on founders edtell

Answer:

D. More Than 1 Solution

Step-by-step explanation:

Let the system of equations be:

[tex]a_1x+b_1y=c_1...(1)[/tex]

[tex]a_2x+b_2y=c_2...(2)[/tex]

If the graph of equation (1) and (2) are the same, then the two graphs coincide with each other.

What that means is that; the two graphs intersects at infinitely many points.

Therefore the system must have infinitely many solutions.

In other words the system has more than one solution.

NB: At least one solution means exactly one solution and/or more than one solution. But lines that coincide cannot have exactly one solution.

Answer:

-3

Step-by-step explanation:

If a line is perpendicular to another the product of their slope should equal -1. The slope of the first equation is -1 and -1*1=-1 so the slope of the second equation is 1. That means that the equation looks like y=x+b. We know that when x is 4 y is 1. So plugging in those values you get 1=4+b, subtracting 4 you get -3=b. So the y-intercept is -3

Answer:

[tex]\large\boxed{\dfrac{(x^6y^8)^3}{x^2y^2}=x^{16}y^{22}}[/tex]

Step-by-step explanation:

[tex]\dfrac{(x^6y^8)^3}{x^2y^2}\qquad\text{use}\ (ab)^n=a^nb^n\ \text{and}\ (a^n)^m=a^{nm}\\\\=\dfrac{(x^6)^3(y^8)^3}{x^2y^2}=\dfrac{x^{(6)(3)}y^{(8)(3)}}{x^2y^2}=\dfrac{x^{18}y^{24}}{x^2y^2}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\=x^{18-2}y^{24-2}=x^{16}y^{22}[/tex]

Answer: [tex]x^{16}\ y^{22}[/tex]

Step-by-step explanation:

The given expression : [tex]\dfrac{(x^6y^8)^3}{x^2y^2}[/tex]

Using identity , [tex](a^m)^n=a^{mn}[/tex] , we have

[tex]{(x^6y^8)^3=x^{6\times3}\ y^{8\times3}\\\\=x^{18}\ y^{24}[/tex]

Now, [tex]\dfrac{(x^6y^8)^3}{x^2y^2}=\dfrac{x^{18}\ y^{24}}{x^2\ y^2}[/tex]

( its also an equivalent expression to given expression.)

Using identity , [tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex] , we have

[tex]\dfrac{x^{18}\ y^{24}}{x^2\ y^2}=x^{18-2}\ y^{24-2}\\\\=x^{16}\ y^{22}[/tex]

Hence, the expression is equivalent to given expression :

[tex]x^{16}\ y^{22}[/tex]

The astronaut is experiencing approximately 6.21 g's in the centrifuge.

a. To find the angular velocity of the centrifuge in radians per second, we first need to convert the number of revolutions per minute to revolutions per second. Since there are 60 seconds in a minute, the angular velocity (ω) can be calculated as follows:

Angular velocity (ω) = (Number of revolutions per minute) / 60

Given that the centrifuge makes 72 complete revolutions in 2 minutes:

ω = 72 / 2 / 60 = 1.2 revolutions per second

Next, to find the distance an astronaut travels around the center each second, we can use the formula for the circumference of a circle:

Circumference = π × diameter

Circumference = π × 70 feet

Circumference ≈ 220 feet

Distance traveled each second = Circumference × ω

Distance traveled each second = 220 feet × 1.2 revolutions per second ≈ 264 feet

So, the angular velocity of the centrifuge is approximately 1.2 radians per second, and an astronaut travels around the center approximately 264 feet each second.

b. The acceleration (a) of an object moving in circular motion with a constant velocity (v) and a radius (r) is given by the formula:

[tex]a = v^2 / r[/tex]

Since the astronaut is moving at a constant velocity around the center of the centrifuge, we can use the same formula to find their acceleration. The velocity of the astronaut is the distance traveled each second (264 feet) and the radius of the centrifuge is half of its diameter (70 feet / 2 = 35 feet):

Acceleration (a) = (264 feet per second)^2 / 35 feet ≈ 198.86 feet per second squared

So, the astronaut's acceleration is approximately 198.86 feet per second squared.

c. To find how many g's the astronaut is experiencing in the centrifuge, we need to compare their acceleration with the acceleration due to gravity on Earth (32 feet per second squared). One g is equivalent to the acceleration due to gravity.

Number of g's = Acceleration (astronaut) / Acceleration due to gravity on Earth

Number of g's = 198.86 feet per second squared / 32 feet per second squared ≈ 6.21 g's

So, the astronaut is experiencing approximately 6.21 g's in the centrifuge.

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Answer:

5

Step-by-step explanation:

[tex]\tt a_n=a_{n-1}-5\\\\ a_1=20\\a_2=a_1-5=20-5=15\\a_3=a_2-5=15-5=10\\a_4=a_3-5=10-5=5[/tex]

The value of x = -1

The value of y = -5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be A

The value of A is

y = 3x - 2   be equation (1)

Let the second equation be B

The value of B is

x - y = 4   be equation (2)

On simplifying equation (2) , we get

Adding y on both sides of the equation , we get

x = y + 4   be equation (3)

Substituting the value of x in equation (1) , we get

y = 3x - 2

y = 3 ( y + 4 ) - 2

y = 3y + 12 - 2

y = 3y + 10

Subtracting y on both sides of the equation , we get

2y + 10 = 0

Subtracting 10 on both sides of the equation , we get

2y = -10

Divide by 2 on both sides of the equation , we get

y = -5

Substitute the value of y in equation (3) , we get

x = y + 4

x = -5 + 4

x = -1

Therefore , the value of x is -1 and the value of y is -5

Hence , The value of x = -1

The value of y = -5

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Final answer:

To solve the equations using substitution, isolate y from the first equation, substitute it into the second, solve for x, and then use the value of x to find y. The solution to the system is x = -1 and y = -5.

Explanation:

To solve the system of equations by substitution, we will first isolate y in one of the equations and then substitute it into the other equation.

Step 1: Isolate y in the first equation.

We have y = 3x - 2. This equation is already solved for y, so we can use it as our substitution.

Step 2: Substitute y into the second equation.

Our second equation is x - y = 4. We substitute y with 3x - 2 to get x - (3x - 2) = 4.

Step 3: Solve for x.

Now, we simplify and solve for x:

x - 3x + 2 = 4

-2x + 2 = 4

-2x = 4 - 2

-2x = 2

x = -1

Step 4: Substitute x back into the first equation to solve for y.

Using x = -1 in the first equation y = 3x - 2, we get:

y = 3(-1) - 2

y = -3 - 2

y = -5

Therefore, the solution to the system of equations is x = -1 and y = -5.

Answer:

So (L,W) possibilities are:

(1,4),(4,1),(2,3),(3,2)

That makes 4 possibilities.

Step-by-step explanation:

The perimeter of a rectangle is P=2L+2W where L is the length and W is the width.

We have that P=10, so 10=2L+2W.

10=2L+2W

10=2(L+W)  By factoring using the distributive property.

2(5)=2(L+W)  I factored 10 as 2(5).

If 2(5)=2(L+W), then 5=L+W.

Whole numbers are {0,1,2,3,4,5,6,7,8,9,10,...}. They are your counting numbers and 0.

I think they want natural numbers {1,2,3,4,...}.  This is also just called the counting numbers. The reason I think they want this because if one of the dimensions is 0, we won't actually have a rectangle.

So now looking for numbers from this set that satisfy: L+W=5.

L+W=5

1+4=5

4+1=5

2+3=5

3+2=5

So (L,W) possibilities are:

(1,4),(4,1),(2,3),(3,2)

That makes 4 possibilities.

Answer:

1/3x+4 ≤ 2x+12

Step-by-step explanation:

x ≤ -24/5

Answer:

4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

Step-by-step explanation:

Given  : The sum of one third a number and 4 is at the most the sum of twice that number and 12.

To find : Write expression .

Solution : We have given statement

According to question :

Let the number = x

One third of a number = [tex]\frac{1x}{3}[/tex].

Sum of one third of number and 4 =  4 +  [tex]\frac{1x}{3}[/tex].

Twice a number  =  2x

Sum of twice that number and 12 =  2x +  12

So,  sum of one third a number and 4 is at the most the sum of twice that number and 12.

4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

greater than equal to sign for at most.

Therefore, 4 +  [tex]\frac{1x}{3}[/tex] ≤ 2x +  12.

Answer:

3^9 * 11^9

Step-by-step explanation:

33^9 =

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

(33)^9 = (3*11)^9 = 3^9 * 11^9

Final answer:

The measure of the other angle that is complementary to a 13º angle is 77º.

Explanation:

If two angles are complementary, it means they add up to 90 degrees. In this case, one angle is given as 13º. To find the measure of the other angle, we subtract the given angle from 90º because complementary angles sum up to 90 degrees.

So, if we let x represent the measure of the other angle, the equation becomes:

13° + x = 90°

To find x, we subtract 13 from both sides:

The calculation would be:

90º - 13º = 77º.

Therefore, the measure of the other angle is 77º.

Hence, the correct answer is:

B. 77

Answer:

23.09 meters.

Step-by-step explanation:

Sin(60) = opposite / hypotenuse =  pole / steel wire

pole = 20 m

angle = 60 degrees.

sin(60) = 20/ hypotenuse       multiply both sides by the hypotenuse

hypotenuse * sin(60) = 20      divide by sin(60)

hypotenuse = 20 / 0.866        do the division    

hypotenuse = 23.09

The steel wire = 23.09 meters.

Answer:

Option B 125°

Step-by-step explanation:

In this problem we need to calculate the measure of angle ∠6

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

see the attached figure to better understand the problem

∠6=(1/2)[arc AB+arc CD]

(arc AB+arc CD)=360°-(60°+50°)=250°

substitute

∠6=(1/2)[250°]=125°

Answer:

[tex]x\leq10[/tex]

Step-by-step explanation:

we know that

The algebraic expression of the phrase "It is at most ten" is equal to

[tex]x\leq10[/tex]

All real numbers less than or equal to 10 (the number 10 is included)

The solution of this inequality is the interval -----> (-∞,10]

Answer:

B

Step-by-step explanation:

Answer:

Id say 35

Sorry of im wrong :{

Answer:

Area of the triangle is 25.9 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- In Δ ABC

∵ m∠ B = 9° 20' = 9 + 20/60 = (28/3)°

∵ b = 2.92 feet

- b is the side opposite to angle B

∵ m∠ C = 80° 40' = 80 + 40/60 = (242/3)°

- Lets find c the side opposite to angle C by sing the sine rule

∵ [tex]\frac{b}{sinB}=\frac{c}{sinC}[/tex]

∴ [tex]\frac{2.92}{sin(28/3)}=\frac{c}{sin(242/3)}[/tex]

- By using cross multiplication

∴ [tex]c=\frac{2.92(sin(242/3)}{sin(28/3)}=17.77[/tex]

- The area of the triangle = 1/2 (b)(c)sin∠A

∵ The sum of the interior angles of a triangle is 180°

∴ m∠ A + m∠ B + m∠ C = 180°

∵ m∠ B = (28/3)°

∵ m∠ C = (242/3)°

∴ m∠ A + 28/3 + 242/3 = 180

∴ m∠ A + 90° = 180° ⇒ subtract 90 from both sides

∴ m∠ A = 90°

∴ Area of the triangle = 1/2 (2.92)(17.77) sin(90)

∵ sin(90) = 1

∴ Area of the triangle = 1/2 (2.92)(17.77) = 25.9 feet²

* Area of the triangle is 25.9 feet²

Answer: G.

Step-by-step explanation: When reading the choices F & J will make you say : "Well F is not true because look at the amount of men compared to women. And J, the choice is unbiased doesn't refers to any kind of opinion based reponse so I'll cross 'em off immediatly". The leave you with G & H H is true but it's also opinion based reponse, and G told you that more men are surveyed than women an it's true because look at the sport section! High off top! But still more than women even if the minivans section is little of men but women also so fair and square!

- I'm sorry this is so long. Just comment if you have questions :)