Ten times a number, x, is one-half the sum of the number and three.
Which answer represents this situation?

Step-by-step explanation:

4x³ = 36x

4x³ - 36x = 0

4x(x² - 9) = 0

4x(x + 3)(x - 3) = 0

Hence x = 0, x = -3 or x = 3.

Answer:

The volume of the sphere is 32 π /3 cm^3

Step-by-step explanation:

Mathematically, the volume of a sphere can be calculated using the formula below;

V = 4/3 * pi * r^3

Now since we have the radius and diameter = 2 * radius

radius = diameter/2 = 4/2 = 2

Substituting this value into the volume equation;

V = 4/3 * pi * 2^3 = 32pi/3

Answer:

The correct answer is A

Step-by-step explanation:

Answer:

C. f(x) = 5x² - 4x + 7

Step-by-step explanation:

Quadratic functions have a square (x²) in them. Answer B has this as well, however, the coefficient is 0 which would turn x² to 0.

The expression of 0.785 in the form p/q is 157/200

The ratio is defined as a way of dividing a variable by another variable.

Given the decimal number 0.785, to convert to fraction, we will place divide 785 by 1000 (since the decimal is on thousandth)

0.785 = 785/1000

Express in its simplest form

785/1000 = 157/200

Hence 0.785 written in the form p/q is 157/200 where p = 157 and q = 200.

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Answer: 20

Step-by-step explanation: to find f, you divide 10 by 0.5 to see what’s left. When you divide it you get 20. To check your work multiply 0.5 by 20 and you’ll see that it equals 10.

Answer:

umm i think it is B.

Step-by-step explanation:

Answer:

y=4x+2

Step-by-step explanation:

y=mx+b

replace m for 4 and b for 2

To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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Answer:

Yes

Step-by-step explanation:

Answer:

Ricky get $4 than Sam.

Step-by-step explanation:

.25x80=20

80-20=60

.30×80=24

80-24=56

Answer:

7x = 6

Step-by-step explanation:

  2x - 3y = 10

+ 5x + 3y = -4

------------------------

  7x         = 6

Given:

The two functions are:

\(f(x)=\sqrt{32x}\)

\(g(x)=\sqrt{2x}\)

To find:

The \((f\cdot g)(x)\). Assume \(x\geq 0\).

Solution:

We have,

\(f(x)=\sqrt{32x}\)

\(g(x)=\sqrt{2x}\)

Now,

\((f\cdot g)(x)=f(x)\cdot g(x)\)

\((f\cdot g)(x)=\sqrt{32x}\cdot \sqrt{2x}\)

\((f\cdot g)(x)=\sqrt{32x\times 2x}\)

\((f\cdot g)(x)=\sqrt{64x^2}\)

\((f\cdot g)(x)=8x\)

Therefore, the correct option is A.

The area of the polygon is approximately 497.41 square centimeters.

A polygon is a two-dimensional geometric shape that is made up of straight lines connected end to end to form a closed shape. A polygon must have at least three sides, and each side must intersect with exactly two other sides.

The exterior angle of a regular polygon is equal to 360 degrees divided by the number of sides. So, if the exterior angle is 20 degrees, the number of sides can be found by dividing 360 by 20, which gives us 18.

Each interior angle of a regular polygon can be found using the formula:

Interior angle = (n - 2) x 180 / n

where n is the number of sides. For an 18-sided polygon, the interior angle is:

(18 - 2) x 180 / 18 = 160 degrees

Apothem = (Side length) / (2 x tan(π/n))

where n is the number of sides. Plugging in the values, we get:

Apothem = (6) / (2 x tan(π/18)) = 6 / (2 x 0.32492) ≈ 9.2367 cm

Finally, we can use the formula for the area of a regular polygon:

Area = (1/2) x Apothem x Perimeter

where Perimeter is just the side length multiplied by the number of sides. Plugging in the values, we get:

Perimeter = Side length x Number of sides = 6 x 18 = 108 cm

Area = (1/2) x 9.2367 x 108 ≈ 497.41 cm²

Therefore, the area of the polygon is approximately 497.41 square centimeters.

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Answer:  1.2

Step-by-step explanation:

Let X denotes the grades on a  language midterm at Oak Academy.

As per given ,

X follows normal distribution ( because it has symmetric graph)

\(\mu=67,\ \ \ \ \sigma= 2.5\)

Formula for z : \(z=\dfrac{X-\mu}{\sigma}\)

For X = 70, we have

\(z=\dfrac{70-67}{2.5}=\dfrac{3}{2.5}=1.2\)

Hence, the z-score for Ishaan's exam grade = 1.2

z-scores are the corresponding standard normal variate's values for normal variates' values. The z-score for Ishaan's grade is 1.2

If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.

If we have

\(X \sim N(\mu, \sigma)\)

(X is following normal distribution with mean \(\mu\) and standard deviation \(\sigma\) )

then it can be converted to standard normal distribution as

\(Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)\)

(Know the fact that in continuous distribution, probability of a single point is 0, so we can write

\(P(Z \leq z) = P(Z < z) )\)

Also, know that if we look for Z = z in z tables, the p-value we get is

\(P(Z \leq z) = \rm p \: value\)

For the given case, if we suppose the random variable X's values as scores of the grades on given language midterm at Oak Academy, then, as it is symmetric around value 67, with σ = 2.5, thus,

\(X = N(\mu = 67, \sigma = 2.5)\)

Its given that Ishaan scored X = 70

The standard normal variate conversion of X is given by:

\(Z = \dfrac{X- \mu}{\sigma} = \dfrac{X - 67}{2.5}\)

Thus, z-scores for Ishaan's score is: \(Z = \dfrac{70 - 67}{2.5} = \dfrac{3}{2.5} = 1.2\)

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Answer:

5/6

Step-by-step explanation:

1/2 + 1/3 You first multiply 1/2 by 3 and 1/3 by 2

3/6 + 2/6 then you add

5/6

Step-by-step explanation:

1/2 + 2/3

find the LCM of 2 and 3

LCM =6

1/2 + 2/3

(you'll divide 6 by the denominator and multiply by the numerator)

denominator= the figure down(2 &3)

numerator= the figure up (1 & 2)

= 3/6 +4/6

=7/6

Answer:

area = 16 cm²

Step-by-step explanation:

area = length x width

area = 4 cm x 4 cm = 16 cm²

Answer: Since the radius of the circle is perpendicular to AB, AB is tangent to the circle.

Step-by-step explanation:

Answer:

perpendicular and tangent

Step-by-step explanation:

The size of angle ACB in triangle ABC is approximately 35.5 degrees.

To calculate the size of angle ACB, we can use the Law of Cosines, which states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle.

The formula for the Law of Cosines is:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where:

c is the side opposite to angle C (in this case, side AB with length 7cm)

a and b are the other two sides (in this case, sides AC and BC with lengths 6cm and 8cm, respectively)

C is the angle we want to find (angle ACB)

Plugging in the given values, we have:

7^2 = 6^2 + 8^2 - 2 * 6 * 8 * cos(C)

Simplifying the equation, we get:

49 = 36 + 64 - 96 * cos(C)

49 = 100 - 96 * cos(C)

96 * cos(C) = 100 - 49

96 * cos(C) = 51

cos(C) = 51 / 96

To find the angle ACB, we need to take the inverse cosine (also known as arccos) of the value we just calculated:

C = arccos(51 / 96)

Using a calculator, we find that C is approximately 35.5 degrees.

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Answer:

8 d)

Step-by-step explanation:

2x -10 = 3x +6 -4x +8

3x=24

x=8

Answer:

x = 8 (d)

Step-by-step explanation:

Expand

2x -  10 = 3x + 6 - 4x + 8

Collect like terms

2x - 3x + 4x = 6 + 8 + 10

3x = 24

Divide both sides by 3 to make x on its own

x = 8

Answer:

We can use synthetic division to divide the polynomial p(x) by (x+2):

-2 | 1 0 -19 -30

| -2 4 -10

|__________________

1 -2 -15 -40

The result is a quadratic polynomial x^2 - 2x - 15 with a remainder of -40.

Therefore, we can factor p(x) as:

p(x) = (x+2)(x^2 - 2x - 15)

The quadratic factor can be factored further as:

p(x) = (x+2)(x-5)(x+3)

So the complete factorization of p(x) is:

p(x) = (x+2)(x-5)(x+3)

There are no points outside the control limits, since all of the weekly sample means are within the range of 4.7 to 5.3 degrees Celsius (the mean of 5 degrees Celsius plus or minus 0.3 degrees Celsius).

Given a population X with normal distribution with mean μ=79 and standard deviation σ=7

You have to calculate the probability of X greater than or equal to 93, symbolically:

To calculate this probability you have to "transform" this value to the standard normal distribution. You have to use the standard normal or Z distribution because it is tabulated, i.e. its values and accumulated probabilities are known.

To translate a value of any normal distribution to a value of the standard normal distribution you have to subtract the mean and divide by the standard deviation.

The standard normal distribution is defined as:

Calculate the Z value

So the probability you have to calculate is

Now the tables of the standard normal distribution indicate the accumulated probabilities, to determine the probability above a determined value, you have to subtract the probability accumulated until that value to the total probability.

Remember that for any distribution of probability, the total probability is always 1. So under The normal distribution or the standard normal distribution, the total area of under the curve is 1

In the Z table (right entry) look for the corresponding value of the probability

So

The probability of X is greater than or equal to 93 is 0.023

Answer:

24

Step-by-step explanation:

if he splits 1 yard into 6 pcs for 6 bracelets 4 times, thats 24 pieces of yarn that are 1/6 of a yard long meaning he can make 24 bracelets

Answer:

Step-by-step explanation:

» the lines PS and RT intersect each other at Q

also, ∠PQT and ∠SQR are opposite angles

Then

the angles ∠PQT and ∠SQR are vertical angles.

………………………………………………………………………

» the lines PS and RT intersect each other at Q

also, ∠PQR and ∠SQT are opposite angles

Then

the angles ∠PQR and ∠SQT are vertical angles.

Answer: 4

Step-by-step explanation:

4x - y = -4

add 4 to both sides

4x - y + 4 = 0

add y to both sides

4x + 4 = y

Answer:

B) Rotation

Step-by-step explanation:

The arrows at the end of each line imply a line, not a line segment. Since the they both pass through the origin, they rotate about the origin, hence B) Rotation.

Answer:

A I'm about 89% certain that's a vertical translation

Answer: 3.12

Step-by-step explanation:

The answer to the nearest tenth of a second is 40.0 seconds.

To solve this problem, we need to know the length of the perimeter of a baseball field. According to official regulations, the distance between each base is 90 feet, so the perimeter of a baseball field is 360 feet.

Now, we can use the formula distance = rate x time, where distance is 360 feet, and rate is 9 feet per second. We can solve for time by dividing both sides of the equation by the rate:

time = distance / rate
time = 360 / 9
time = 40 seconds

Therefore, it takes you 40 seconds to run the perimeter of the baseball field. To find the answer to the nearest tenth of a second, we need to round the answer. Since the next decimal place after the tenths is a hundredth, we need to look at the second decimal place. If it is 5 or greater, we round up, otherwise, we round down. In this case, the second decimal place is 0, so we round down. Therefore, the answer to the nearest tenth of a second is 40.0 seconds.

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Answer:

Step-by-step explanation:

okay so it’s gonna be 11.400