2/3 of a number is 12. What is 1/2 the number?​

Answer:

A. x = 4

I hope this helps!

Answer:

1=27

2=65

3=115

4=

Step-by-step explanation:

I am still working on four i will put it in the comments

Answer:

take away the 15 and 8

Step-by-step explanation:

12 plus 5 =17

Answer:

15÷(8-5)+12=17

Step-by-step explanation:

Use PEMDAS to solve

15÷(8-5)+12=17

first-parentheses

(8-5)=3

rewrite equation

15÷3+12=17

next-divide

15÷3=5

rewrite equation

5+12=17

and finally-add

5+12=17

:)

Hope This Helps

(brainliest please, if possible)

Answer:

Red balls =  84     Blue balls =  140

Step-by-step explanation:

Ok so there are 225 marbles

And ratio here is Red : Blue = 3 : 5

So Red marbles = 3x whereas Blue marbles = 5x

Therefore,

3x + 5x = 225

8x = 225

x = 28.125 = 28

Red balls = 28*3 = 84     Blue balls = 28*5 = 140

(Pls check whether total no of balls is 224)

Answer: 7/8 or 0.875

Step-by-step explanation:

28

32

​  

Reduce the fraction  

28/32

​  

 to lowest terms by extracting and canceling out 4.

7/8

the simplest form of given fraction 28/32 is 7/8.

Given that:

Fraction: 28/32

To write the fraction 28/32 in its simplest form, to find the greatest common divisor (GCD) of the numerator (28) and the denominator (32) and then divide both the numerator and denominator by that GCD.

Step 1: Find the GCD of 28 and 32.

The factors of 28 are 1, 2, 4, 7, 14, and 28.

The factors of 32 are 1, 2, 4, 8, 16, and 32.

The largest common factor between 28 and 32 is 4.

Step 2: Divide both the numerator and denominator by the GCD (4).

28 ÷ 4 = 7

32 ÷ 4 = 8

Hence, the simplified fraction is 7/8.

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The given statement "A successful proof can indeed turn a conditional statement into a theorem.'' is true because a successful proof can transform a conditional statement into a theorem by providing a logical and rigorous demonstration of its truth based on the given hypothesis.

In mathematics, a conditional statement is a proposition that asserts a relationship between two or more mathematical objects or concepts. It consists of a hypothesis and a conclusion.

A conditional statement is typically expressed in the form "If A, then B," where A represents the hypothesis and B represents the conclusion.

To establish a conditional statement as a theorem, one needs to provide a valid proof that demonstrates the truth of the statement. A proof is a logical argument that follows a series of logical deductions from axioms, definitions, and previously established theorems.

When a proof is successfully constructed for a conditional statement, it provides rigorous justification for the truth of the conclusion based on the given hypothesis.

By demonstrating the logical validity and coherence of the argument, the proof confirms the truth of the conditional statement and establishes it as a theorem.

The process of proving a conditional statement involves carefully reasoning through logical steps, utilizing mathematical principles and logical inference rules.

It requires precise and accurate reasoning, ensuring that each step in the proof is valid and consistent with the underlying mathematical framework.

Once a conditional statement has been proven, it is elevated to the status of a theorem. Theorems are fundamental results in mathematics that have been rigorously proven and hold true within a given mathematical system.

They serve as building blocks for further mathematical investigations and form the foundation of mathematical knowledge.

In summary, a successful proof can transform a conditional statement into a theorem by providing a logical and rigorous demonstration of its truth based on the given hypothesis.

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Answer:

\(9^4\) = \(6561\)

The sample in this example is D) the small group of college students who are observed. The correct option is D.

The researcher has identified college students as her group of interest, but it is not feasible or practical to observe or study all college students. Therefore, she needs to select a subset of college students, which is known as a sample. In this case, she has chosen to observe a small group of local college students, which is the sample. It is important to note that the sample needs to be representative of the larger population of interest, in this case, all college students, in order for the results to be applicable to the larger group.

While the sample in this example is only a small group of local college students, the researcher would need to ensure that they are representative of all college students in order for the results to be generalizable.

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The probability that a woman tests positive given that she has breast cancer is 7/8 and the probability that a woman tests negative for breast cancer given that her test result is negative is 923/1000.

Probability is the possibility of happening an event.

Since 14 of 16 have breast cancer test positive, the probability is:

p = 14/16

p = 7/8

Therefore, the probability that a woman tests positive given that she has breast cancer is 7/8.

The number of women who test negative is:

2000 - 154

= 1846

Therefore, 1846 out of 2000 women test negative.

The probability of a woman testing negative is:

p = 1846/2000

p = 923/1000

Therefore, The probability that a woman tests negative for breast cancer given that her test result is negative is 923/1000.

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1/4 of all the students in the orchestra are girls who play string instruments.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's assume there are a total of 100 students in the school orchestra. Then, according to the problem, 2/5 of them are string players.

The number of string players is:

2/5 x 100 = 40

Out of these 40 string players, 5/8 are girls.

The number of girls who play string instruments is:

5/8 x 40 = 25

Therefore, the fraction of all the students in the orchestra who are girls who play string instruments is:

25/100 = 1/4

Therefore, 1/4 of all the students in the orchestra are girls who play string instruments.

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The cannonball will have moved approximately 24.2 meters horizontally from the cannon when it hits the hill.

To find the horizontal distance the cannonball travels before hitting the hill, we need to determine the point where the path of the cannonball intersects with the incline of the hill. We can do this by setting the equations of the cannonball's path and the incline of the hill equal to each other and solving for x.

Setting -0.05x^2 + 5x + 1 = 0.725x, we can rearrange the equation to form a quadratic equation: -0.05x^2 + 4.275x + 1 = 0.

Using the quadratic formula x = (-b ± √(b^2 - 4ac))/(2a), where a = -0.05, b = 4.275, and c = 1, we can solve for the two possible values of x.

Calculating the discriminant, b^2 - 4ac, we get 4.275^2 - 4(-0.05)(1) = 18.20625. Since the discriminant is positive, we have two real solutions.

Applying the quadratic formula, we find x ≈ -2.6 and x ≈ 24.2. Since we are interested in the positive value, the cannonball will have moved approximately 24.2 meters horizontally from the cannon when it hits the hill.

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The equation of the line is x - 3y + 1 =0.

What is the meaning perpendicular line?

A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle.

Given equation of line is

y=−3x + 5

Now compare the given equation with y = mx +c

m = -3 and c = 5.

The slope perpendicular line of the given line is = -1/m

= 1/3

The equation of line passes through the point (x₁, y₁) with slope m is

y - y₁ = m (x - x₁)

Putting m = 1/3, y₁ = 2, and x₁ = 5 in the above equation:

y - 2 = 1/3 (x - 5)

3y - 6 = x - 5

x - 3y + 1 =0

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The future value of the monthly deposit which earns 0.475 monthly interest will be $10,944.67 after 16 months.

The future value can be determined using the future value annuity formula or an online finance calculator.

The future value represents the periodic deposits compounded periodically at an interest rate.

N (# of periods) = 16 months

I/Y (Interest per year) = 5.7% (0.475% x 12)

PV (Present Value) = $0

PMT (Periodic Payment) = $660

Results:

Future Value (FV) = $10,944.67

The sum of all periodic payments = $10,560.00

Total Interest = $384.67

Thus, using an online finance calculator, the future value of the monthly deposits is $10,944.67.

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Answer:

w = 12

Step-by-step explanation:

Create formula:

540 = 40w - 60 where 540 is the cost of the camera, 40 is the amount saved, w is the number of weeks, 60 is the amount owed

Solve for w

540 = 40w - 60: subtract 60

480 = 40w: divide by 40

w = 12

Answer:

1.  26

2. 15

3. 14

4. \(\sqrt{50}\) or \(5\sqrt{2}\)

5. \(\sqrt{11} \\\)

6. \(\sqrt{245}\)  or \(7\sqrt{5}\)

I think most of these answers are correct

Answer:

negative 5. or -5

Step-by-step explanation:

f(-1)= (-1)2-3

2 times -1= -2

-2-3= -5

f= -5

Answer:

A: y = -4/5x + 3/2 i believe is the correct answer

Step-by-step explanation:

The given system of equations do not have a solution since their related line equations have the same slope.

The given system of equations is:

-x + 5y = 3   .......... (1)

2x - 10y = 4   ........(2)

In Equation (1), add both sides by (-5y)

-x + 5y + (-5y) = 3 + (-5y)

-x = -3 - 5y

Multiply by (-1)

x = 3 + 5y

Substitute x = 3 + 5y into equation (2)

2x - 10y = 4

2.(3 + 5y) - 10y = 4

6 + 10y - 10y = 4

6 = 4 (False)

Since the last equation is false, we might suspect that the given system of solution does not have solutions.

We need to check the slope of both equations:

-x + 5y = 3

⇒ 5y = x + 3

⇒ y = 1/5 x + 3/5

2x - 10y = 4

⇒ -10 y = -2x + 4

⇒ y = (2/10) x - 4/10

⇒ y = 1/5 x - 2/5

We can see that both equations have the same slope, i.e. 1/5.

Hence, they do not have solutions since the lines are parallel to each other.

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According to the question we have  approximately 99.74 percent of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

To answer this question, we will use the normal distribution formula and z-score.

First, we need to find the z-score for the lower limit of $1.20:

z = (1.20 - 1.50) / 0.10 = -3

Next, we need to find the z-score for the upper limit of $1.80:

z = (1.80 - 1.50) / 0.10 = 3

Now, we can use a z-table to find the area under the curve between these two z-scores.

The area to the left of z = -3 is 0.0013, and the area to the left of z = 3 is 0.9987.

To find the area between these two z-scores, we subtract the area to the left of z = -3 from the area to the left of z = 3:

0.9987 - 0.0013 = 0.9974

Therefore, approximately 99.74% of customers are willing to pay between $1.20 and $1.80 for a pint of frozen yogurt.

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Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

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The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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Answer:

p=2

Step-by-step explanation:

3.2*2.5=8

10-8=2

Answer:

10x(2x+1)

Step-by-step explanation:

20x^2+10x

2*10*x*x + 10 *x

Factor out the common terms

10x(2x+1)

The correct interpretation regarding the solution of the compound inequality is given as follows:

Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.

To solve a compound inequality involving the or operation, we solve each inequality, then apply the union operation to their solutions.

In this problem, the following inequalities help us find the miles x in which the drivers are never pulled over.

The solutions are found as follows:

2x - 18 ≥ 122

2x ≥ 140

x ≥ 140/2

x ≥ 70.

5x + 15 < 250.

5x < 235

x < 235/5

x < 47.

Hence the correct option is given by:

Drivers located below mile marker 47 or at mile marker 70 or above never get pulled over.

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a. The mass of the wire is 4π√5.

b. The coordinates of the center of mass at  (0, 0, 8π/3).

c. The moment of inertia about the z-axis is 16π√5.

A. To find the mass of the wire, we need to integrate the density function over the length of the wire:

M = ∫ρ(t)ds = \(\int\limits^{2\pi} _0\) ρ(t) ||r'(t)|| dt

where ||r'(t)|| is the magnitude of the derivative of r(t):

||r'(t)|| = ||-2sin(t)i + 2cos(t)j + 4k|| = √(4sin²(t) + 4cos²(t) + 16) = 2√5

Substituting in the values, we get:

M = \(\int\limits^{2\pi} _0\) 1 * 2√5 dt = 4π√5

Therefore, the mass of the wire is 4π√5.

B. The coordinates of the center of mass (x, y,z) can be found using the following formulas:

x = (1/M) ∫ρ(t)x(t)ds

y = (1/M) ∫ρ(t)y(t)ds

z = (1/M) ∫ρ(t)z(t)ds

We can simplify the expressions using the parameterization of the helix:

x(t) = 2cos(t)

y(t) = 2sin(t)

z(t) = 4t

Substituting the values, we get:

x = (1/4π√5)  \(\int\limits^{2\pi} _0\) 2cos(t) * 2√5 dt = 0

y = (1/4π√5)  \(\int\limits^{2\pi} _0\)2sin(t) * 2√5 dt = 0

z = (1/4π√5)  \(\int\limits^{2\pi} _0\) 4t * 2√5 dt = 8π/3

Therefore, the center of mass is located at (0, 0, 8π/3).

C. The moment of inertia about the z-axis can be found using the formula:

Iz = ∫ρ(t)(x² + y²)ds

Using the same parameterization as before, we get:

Iz =  \(\int\limits^{2\pi} _0\) 1 * (4cos²(t) + 4sin²(t)) * 2√5 dt

= \(\int\limits^{2\pi} _0\) 8√5 dt

= 16π√5

Therefore, the moment of inertia about the z-axis is 16π√5.

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Answer:

the answer is 6.28 her total is 34.83

Answer:

the answer is 6.28 hope it helps

Answer: (2x^2 - 3y^2)(2x^2 + 3y^2)(4x^2 + 9y^2)

Step-by-step explanation:

Formula to remind: \((A^2 - B^2) = (A-B)(A+B)\)

\(16x^4 - 81y^4 = (4x^2 - 9y^2)(4x^2 + 9y^2) = (2x^2 - 3y^2)(2x^2 + 3y^2)(4x^2 + 9y^2)\)

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

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