2/3 of the students in a class passed their math test. If 16 of students passed the test, how many students are in the class

Answer:

Step-by-step explanation:

SQR-PRQ-SRP

SP/RP=RP/PQ

QP/QR=RQ/SQ

The measure of angle B is 82°

What is angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

∠A = 180° - 143°

     = 37°

∠A + ∠B + ∠C = 180°

37° + ∠B + 61° = 180

∠B = 180 - 61 - 37

     = 82°

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The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

What is a peripheral coordinate?

A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.

To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:

[tex]r=\sqrt{(x^2 + y^2 + z^2)} = \sqrt{((-2)^2 + (2\sqrt3)^2 + 4^2)} = \sqrt{(4 + 12 + 16)} = \sqrt32 = 4\sqrt2[/tex]

θ = [tex]tan^{-1}(y/x) = tan^{-1}(2\sqrt3/(-2)) = tan^{-1}((-\sqrt3)/1) = -60^o[/tex]

φ = [tex]cos^{-1}(z/r) = cos^{-1}(4/4\sqrt2) = cos^{-1}(1/\sqrt2) = \degree 45 ^o[/tex]

So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

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The spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

What is a peripheral coordinate?

A peripheral coordinate is a set of three coordinates (r, θ, φ) that describes the position of a point in space in relation to a fixed origin. r is the distance from the origin to the point, θ is the angle between the positive x-axis and the projection of the point onto the xy-plane, and φ is the angle between the positive z-axis and the line connecting the point to the origin.

To find the spherical coordinates of a point whose rectangular coordinates are (-2, 2√3,4), we can use the following formulas:

[tex]r=\sqrt{x^2+y^2+z^2} = \sqrt{(-2)^2+(2\sqrt{3})^2+4^2}=4\sqrt{2}[/tex]

θ = [tex]tan^{-1}(y/x)=tan^{-1}(2\sqrt{3}/(-2))=60^o[/tex]

φ = [tex]cos^{-1}(z/r)=tan^{-1}(4/4\sqrt{4})=45^o[/tex]

So, the spherical coordinates of the point are (r, θ, φ) = (4√2, -60°, 45°).

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The solution to the system of equations is x = 4 and y = 2.

We would use the elimination method to solve the system of equations:

Let's eliminate the variable y by adding equations 1 and 2:

4x + 8y = 24

2x + y = 19

.

.

.,

6x + 9y = 43

Now we can eliminate the variable x by subtracting equation 3 from the above equation:

6x + 9y = 43

3x + y = 15

.

.

.

3x + 8y = 28

We now have an equation with one variable: 3x + 8y = 28. We can solve for x by dividing both sides by 3:

x = (28 - 8y) / 3

Now we can substitute this expression for x into one of the original equations and solve for y. Let's use equation 4:

4x + 2y = 12

Substituting x = (28 - 8y) / 3:

4((28 - 8y) / 3) + 2y = 12

If we simplify:

Finally, we can use this value of y to find x by plugging it into the expression we found earlier:

x = (28 - 8(2)) / 3

x = (28 - 16) / 3

x = 12 / 3

x = 4.

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5 half-dozens he should buy to make enough cookies.

What is an average?

Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or a figure that lies halfway between two extremes.

Here, we have

If 108 students eat 2 cookies on average, there will need to be 108× 2 = 216 cookies.

There are 15 cookies per pan, meaning there need to be {216}/{15} = 14.4 pans.

However, since half-recipes are forbidden, we need to round up and make{216}/{15} = 15 pans.

1 pan requires 2 eggs, so 15 pans require 2×15 = 30 eggs.

Since there are 6 eggs in a half dozen,

we need 30/6 = 5 half-dozens of eggs.

Hence, 5 half-dozens he should buy to make enough cookies.

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The surface area that can be painted with one complete rotation of the roller is 226.19 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 3 inches

h = height of the cylinder = width = 12 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(3 inches)(12 inches)

SA = 226.19 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².

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Answer:

Step-by-step explanation:

The smallest possible multiple of 13 dollars greater than 500 dollars would be 507 which is 13*39 (i assume you mean whole numbers when you say positive numbers, if not the other answer would be 13*38.461)

The equation of the line that passes through the point (3, 2) and is perpendicular to 3x + 5y = 15 is y = (5/3)x - 3

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line is y = m(1)x + c

The line passes through (3, 2) and is perpendicular to 3x + 5y = 15.

This means,

3x + 5y = 15

5y = -3x + 15

y = (-3/5)x + 3

m(2) = (-3/5)

Now,

m(1) x m(2) = -1

m(1) = -1 / ((-3/5)

m(1) = 5/3

Now,

(3, 2) = (x, y)

y = m(1)x + c

2 = (5/3) x 3 + c

2 = 5 + c
c = 2 - 5

c = -3

Thus,

The equation of the line is y = (5/3)x - 3.

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The price of the sales tax on the elephant could be 0.75$

What is percentage ?

percentage can be defined as the product of ratio of given value and total value and hundred.

Given

he sells a stuffed elephant for $14.95,

the sales tax is 5% of the sale price .

So,

as the tax is 5% of the given value.

so we are here multiplying the given value to the 5/100

we get,

The amount of the tax could be

 = 14.95*5/100

 = 0.7475

≈ 0.75 (rounded)

Hence the  price of the sales tax on the elephant could be 0.75$

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By using formula and solving we get the item is on sale for $76.

What is selling price?

The selling price is the amount of money that a seller asks for in exchange for a product or service. It is also known as the "list price" or "retail price" and it is the price at which an item is intended to be sold. Selling price is usually set by the manufacturer or the retailer, taking into account the cost of production, distribution, and marketing, as well as competition and market demand. The selling price is usually higher than the cost of production, which includes the cost of the materials, labor, and overhead expenses.

The formula to calculate the selling price of a product or service depends on the information available and the desired level of accuracy. However, there are a few common formulas used to calculate the selling price based on different factors.

Cost-plus pricing formula: This formula calculates the selling price by adding a markup percentage to the cost of the product or service.

The formula is: Selling price = Cost + (Cost x Markup percentage)

If the original price of an item was $95 and it is now on sale for 20% off, we can calculate the sale price using the following formula:

Sale price = Original price x (1 - Discount percentage)

In this case, the discount percentage is 20%, so we can express it as 0.2. Therefore, the formula becomes:

Sale price = $95 x (1 - 0.2)

To calculate the sale price, we need to multiply the original price by (1 - 0.2) which is (1-0.2) = 0.8

Sale price = $95 x 0.8

Sale price = $76

So, the item is on sale for $76.

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The option 1 "Simple random sampling, because the people in the sample are accessible and available" is correct for the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.

In the given question, we have to find which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country.

As we know that, you must carefully consider how you will choose a sample that is representative of the group as a whole if you want to make accurate conclusions from your data. It is known as a sampling method.

Every individual in the population has an equal chance of being chosen in a simple random sample. The entire population should be included in your sampling frame.

You might utilize instruments like random number generators or other methods that just rely on chance to carry out this kind of sampling.

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The complete question is:

Which sampling method is the most appropriate in studying the opinions of stay-at-home mothers in all towns across the country?

(1) Simple random sampling, because the people in the sample are accessible and available

(2) Stratified sampling, because there are specific subgroups to investigate

(3) Systematic sampling, because of the ease in selecting every nth person

(4) Cluster sampling, because the studied population is spread across a wide area such that simple random sampling would be difficult to implement

(5) All the above sampling methods

The expression when Buffalo New York had 2ft of snow on the ground before a snowstorm is 2 - 0.25h.

From the information, Buffalo New York had 2ft of snow and we want to find the. expression based on the information given.

An expression have at least two terms which have to be related by through an operator.

Since Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. The expression will be:

2 - (25% × h)

= 2 - 0.25h

h = number of hours.

The expression is 2 - 0.25h.

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Complete question

Buffalo New York had 2ft of snow on the ground before a snowstorm during the storm snow fell at an average rate of 25% in every hr. Illustrate the expression

The basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, section, and segment.

the surface or circumference of a circle, ball, and other object measured in a straight line The radius and diameter of a circle are equal. The length of such a line. whatever radiating or radial component. A circle's chord is the line segment that connects any two locations on the circle's circumference. It should be remembered that a circle's diameter is defined as the lengthiest chord that runs across the center of the circle.

Here,

given

The letter "C" should be in the center.

radius=r=AC=CB

Diameter=d=2r=AB.

Therefore , the solution to the given problem of circle comes out to be ,the basic parts of a circle include its diameter, circumference, radius, arc, chord, tangent, tangent, sector, and segment.

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Answer:

Step-by-step explanation:

The factors of (x^3 +  y^3) are ( x +  y )(x^2 - x . y +  y^2).

In order to find the factors of  (x^3 +  y^3), you need to apply the sum of cubes formula:

(x^3 +  y^3) = ( x +  y )(x^2 - x . y +  y^2)

(x^3 +  y^3) = ( x +  y )(x^2 - x y +  y^2)

Therefore, in order to find the factor of the given expression, you just simply need to learn the sum of cubes formula.

Similarly, the difference of cubes formula is as follows:

(x^3 -  y^3) = ( x -  y )(x^2 + x y +  y^2)

Which gives factors of (x^3 -  y^3).

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There are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.

A number system is defined as a system of writing to express numbers.

The factorial 4! is 24

Factorial value of 3!=6

Factorial value 2!=2

Factorial value 1!=1

4! x 3! x 2! x 1! =24×6×2×1=288

288 can be written as a product 2 and 144 which are perfect squares.

So 2 and 144 are the divisors of 4! x 3! x 2! x 1!

Hence, there are 2 divisors of 4! x 3! x 2! x 1! which are perfect squares.

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Spiders are arachnids with eight legs, as do all arachnids. Spiders differ from insects in that they have only six legs.

Crabs and prawns are also members of the phylum Arthropoda, which includes spiders. Spiders walk on eight legs, but they also have two additional legs that they utilise as hands. The front legs are called pedipalps, or palps for short.

Proteins are secreted by glands on spiders, which aid in the formation of the web. For a number of objectives, including prey capture, prey detection, tunnel lining, egg sacs, and prey wrapping, spiders can create a variety of webs or silks.

Spiders are venomous carnivores who hunt their prey with poison.In Everglades National Park, arachnids such as spiders, scorpions, mites, ticks, whip scorpions, and pseudoscorpions are all common.

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[tex]4(x+7) \leqslant 4(2x+8)\implies 4x+28\leqslant 8x+32\implies 28\leqslant 4x+32 \\\\\\ -4\leqslant 4x\implies \cfrac{-4}{4}\leqslant x\implies \boxed{-1\leqslant x}[/tex]

notice, in the division by "4" we didn't flip the inequality sign, because the division was by a positive value, we only flip it when the division involves a negative value.

Answer:

x > 3

Step-by-step explanation:

6x - 2 - 3x + 9 > 16

3x + 7 > 16

3x > 9

x > 3

Answer:

-2 i think hope this helps

Step-by-step explanation:

The length of the wood altogether is 340 inches

Robert is building a deck

Each piece of the wood measures 42.5 inches

Robert has 8 boards

The length of the wood altogether is

= 42.5 × 8

= 340

Hence the length of the wood is 340 inches

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The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

In mathematics, a ratio is a comparison of two or more numbers that demonstrates how large one number is relative to the other. The divisor or number that is dividing is known as the consequent, while the dividend or number being divided is known as the antecedent. A ratio divides two numbers to compare them.

Given that the Total number of athletes are 2+4+7+1+6+5+7+4+4+8+15+10

= 73

Ratio of 5:73 represent the athletes in a particular grade with specific games to total number of athletes in the school.

There are on one event is where 5 athletes are, that is 8th grade baseball players.

So the correct answer is The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.

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Using PEMDAS to solve the algebraic expression, the value is 2

Mathematical operations are operations that involve the manipulation of numbers, variables, and/or equations. Examples of mathematical operations include addition, subtraction, multiplication, division, exponentiation, and root extraction.

In this problem, we can use PEMDAS to solve this algebraic expression.

[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3 (1/3)] + [6(3/4) + 5(1/2)] / 26 ÷ 3(5/7)] - 0.05

This will become;

[10.2 / 34] + [12.25 / 7] - 0.05

Dividing and adding the numbers will give us;

(0.3 + 1.75) - 0.05 = 2

The value is 2

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The sales team must sell 8 more computers than they sold last month to receive the bonus.

Last month the sales team of Electronic Mania sold 27 computers.

If they sold 30% more computer than they sold last month, they would get a bonus.

First we find the 30 percent if 27

27 × 30/100

= 8.1

Let m be the total number of computers sold.

So, the total number of computers sold would be,

m = 27 + 8.1

m = 35.1

m ≈ 35

Therefore, they need to sell 35 computers in total.

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Answer:

y = 2x + 10

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 10) ← 2 points on the line

m = [tex]\frac{10-0}{0-(-5)}[/tex] = [tex]\frac{10}{0+5}[/tex] = [tex]\frac{10}{5}[/tex] = 2

the line crosses the y- axis at (0, 10 ) ⇒ c = 10

y = 2x + 10 ← equation of line

The subtraction of the given number would be = 386

Subtraction is defined as one of the major arithmetic operations that is used to remove a value from another given values.

The subtraction of the value 340 from 726 would be = 386.

That is; 726 - 340 = 386

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Answer:

2.50 × 19 = 47.5

Therefore, she would get $47.5 if she sold 19 cups.

The probability that Sabreena is going to lose is given as 0.5833

Probability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.

A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.

If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7

In this case, the odds of Sabreena winning are 5:7,

so the probability of winning is 5/(5+7)

the probability of not winning is 1 -  5/12

The probability of not winning is approximately 0.5833

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