What three ratios are equivalent to 5:9

The lines that are perpendicular to 3x – y = 10, are y = –1/3x + 17 and x + 3y = 27.

The correct option is B and C.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

Given:

We have a linear equation,

3x – y = 10.

Arranging to the slope-intercept form.

y = 3x - 10.

The slope of the lines that are perpendicular to line y = 3x - 10,

= negative reciprocal of 3

= -1/3

Therefore, the required lines are y = –1/3x + 17 and x + 3y = 27.

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a) True, b) False, c) False, d) True, e) False, f) False, g) True

a) The statement is true. The symbol "∅" represents the empty set, which does not contain any elements. Since 0 is not an element of the empty set, the statement "0 ∈ ∅" is false.

b) The statement is false. The symbol "{0}" represents a set containing the element 0. The empty set, represented by "∅", does not contain any elements. Therefore, the empty set is not an element of the set {0}.

c) The statement is false. The symbol "{0}" represents a set containing the element 0. However, the empty set, represented by "∅", does not contain any elements. Therefore, the set {0} is not a subset of the empty set.

d) The statement is true. The empty set, represented by "∅", does not contain any elements. Every set is a subset of the empty set, including the set {0}.

e) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not an element of itself. Therefore, the statement "{0}∈{0}" is false.

f) The statement is false. The symbol "{0}" represents a set containing the element 0. In this case, {0} is not a proper subset of itself. Therefore, the statement "{0}⊂{0}" is false.

g) The statement is true. The symbol "{∅}" represents a set containing the empty set. In this case, {∅} is a subset of itself because it contains the element ∅. Therefore, the statement "{∅} ⊆ {∅}" is true.

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by simplifying the number by 2 & 4 we get

=> 75:4

=> 37.5:2

=> 18.75:1

the simplest form of the numbers in ratio is 18.75 : 1...

hope this helps u out and Mark the brainliest :)

A trader sold 100 boxes of fruit at GH¢8. 00 per box, 800 boxes at GH¢6. 00 per box and 600 boxes at GH¢4. 00 per box, the average selling price per box is GH₵ 5.33.

Average selling price per box = (Total sales revenue) / (Total boxes sold)

There are 3 different types of fruit boxes sold. So, we need to find the total revenue from each type of fruit box sold and add them together. Similarly, we need to find the total boxes sold of all the types of fruit boxes sold and add them together. Lastly, divide the total revenue by the total boxes sold to find the average selling price per box.

1. For 100 boxes sold at GH₵ 8.00 per box, the total sales revenue is:

GH₵ 8.00 × 100 = GH₵ 8002.

For 800 boxes sold at GH₵ 6.00 per box, the total sales revenue is

GH₵ 6.00 × 800 = GH₵ 4,8003.

For 600 boxes sold at GH₵ 4.00 per box, the total sales revenue is

GH₵ 4.00 × 600 = GH₵ 2,400

Total sales revenue from all types of fruit boxes sold = GH₵ 800 + GH₵ 4,800 + GH₵ 2,400= GH₵ 8,000

Total boxes sold from all types of fruit boxes sold = 100 + 800 + 600= 1,500

Average selling price per box = (Total sales revenue) / (Total boxes sold)= GH₵ 8,000 / 1,500= GH₵ 5.33.

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Steps to solve:

2/3m = 1/2

~Multiply 3/2 to both sides

m = 3/4

Best of Luck!

Answer:

SAS (Side Angle Side)

Step-by-step explanation:

It is SAS because both triangles are congruent due to 2 congruent sides and one congruent angle, thus being SAS.

The largest possible domain of W(t) is [0, 300].

Levi has 5 hours to work on a research paper and he can type 80 words per minute. The function W(t) = 80t represents the number of words Levi produces in t minutes of typing. We want to find the largest possible domain of W(t). The domain of W(t) is the set of all possible input values of t that make the function W(t) defined. So, we need to find out the maximum number of minutes Levi can work for. We know that he has 5 hours to work, and there are 60 minutes in one hour.

Therefore, he has a total of: 5 hours × 60 minutes/hour = 300 minutes Thus, the domain of W(t) is the set of all real numbers between 0 and 300 inclusive. We include 0 because Levi can type for 0 minutes (i.e. he hasn't started typing yet), and we include 300 because that's the maximum number of minutes he has available to type in. Hence, the largest possible domain of W(t) is [0, 300].

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Answer:

64/27

Step-by-step explanation:

The value of angle x in decimal place is 57.8°.

A decimal number's digits are assigned a place value according to a chart that displays decimal place values. A digit in a number's place value is, as far as we are aware, its numerical value. The correct placement of each digit in a decimal number is therefore determined using decimal place value charts, just like with other place value diagrams. In this chart, the place values of the digits before and after the decimal point are shown.

Draw the altitude of the triangle

We know that

sinθ =  Opposite / Hypotenuse

sin 38° = y/11

y = 11 sin 38°

y = 6.77

sin(x) = y/8

sin(x) = 6.77/8

sin(x) = 0.84625

sin(x) = 57.8°

Thus, the value of angle x in decimal place is 57.8°.

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The probability that student chosen at random is 16 years is 0.28.

The table shows the distribution of student by age in a high school with 1500 students. Therefore, the probability that randomly chosen student is  16 years can be found as follows:

Therefore,

probability = number of favourable outcome to age / total number of possible outcome

Hence,

probability that student chosen at random is 16 years =  420 / 150

probability that student chosen at random is 16 years = 0.28

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Answer:

5

Step-by-step explanation:

5 x 8 = 40

3.50 x 4 = 14

Answer:

343

Step-by-step explanation:

Given :

Numerator

Denominator

Fraction

The number of people on the bus after the second stop is 10 fewer than the number of people on the bus before the 2:30 PM stop.

In conclusion, the number of people on the bus after the second stop is 10 fewer compared to the number of people on the bus before the 2:30 PM stop.

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The form of the partial fraction decomposition for the rational function "(18x - 29)/((x - 6)(5x - 4))" is A/(x - 6) + B/(5x - 4) .

The partial fraction decomposition is defined as a way to write a rational function as a sum of simpler fractions.

The general form of the partial fraction decomposition for a rational function with distinct linear factors in the denominator is:

⇒ R(x)/[(x - a)(x - b)(x - c) ...] = A/(x - a) + B/(x - b) + C/(x - c) + ...

where R(x) = numerator of the rational function, and A, B, C, etc. are constants .

The function is (18x - 29)/((x - 6)(5x - 4)) ,

the denominator (x-6)(5x-4) is already expressed in the factor form ,

So , we can write in partial fraction decomposition as :

⇒ (18x - 29) / ((x - 6)(5x - 4)) = A/(x - 6) + B/(5x - 4)

where A and B are constants that we are not required to solve .

Therefore , the form of partial fraction decomposition for this rational function is "A/(x - 6) + B/(5x - 4)" .

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The given question is incomplete , the complete question is

Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. (18x - 29)/(x-6)(5x-4)

The coefficients for the expression are:

C₂ = C₀/2

C₃ = C₀/6

C₄ = C₀/24

C₅ = C₀/120

C₆ = C₀/720

To solve the given differential equation y' = xy using the power series substitution y = ∑ Cₙxⁿ, we will first find the derivative of y, then substitute both y and y' into the given equation, and finally determine the coefficients.

Step 1: Find the derivative of y.

y = ∑ Cₙxⁿ

y' = ∑ nCₙxⁿ⁻¹

Step 2: Substitute y and y' into the given equation.

∑ nCₙxⁿ⁻¹ = x ∑ Cₙxⁿ

Step 3: Match the coefficients on both sides of the equation.

For n = 1, C₁ = C₀.

For n = 2, 2C₂ = C₁ => C₂ = C₀/2.

For n = 3, 3C₃ = C₂ => C₃ = C₀/6.

For n = 4, 4C₄ = C₃ => C₄ = C₀/24.

For n = 5, 5C₅ = C₄ => C₅ = C₀/120.

For n = 6, 6C₆ = C₅ => C₆ = C₀/720.

So, the coefficients are:

C₂ = C₀/2

C₃ = C₀/6

C₄ = C₀/24

C₅ = C₀/120

C₆ = C₀/720

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Answer:

yes, this triangle contain a right angle ,and it is B, because CB is the base and AB is the height.

The All are equivalent expression except 2/4 - 1/2 given in the question.

A mathematical expression known as an algebraic expression is one that includes variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division. Generally speaking, two of something are regarded as being equivalent. Similar to this, equivalent mathematical expressions are those that are true even when they appear to be different. When the values are put into the formula, however, both expressions yield the same result.

Expression Equivalent

X - 2/4 Equivalent to 1/2 X - 1

2/4 - X Equivalent to X - 1/2

2/4 - 1/2 Not Equivalent to 1/2 X - 1 or X - 1/2

X + 1/2 Equivalent to X - 1/2

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Answer:

7/16

Step-by-step explanation:

5/8-3/16=7/16

The probability associated with obtaining a particular value of z is referred to as its statistical probability or simply its probability. It represents the likelihood of observing a specific value of z in a given statistical distribution.

The probability of a specific value of z can be calculated using various statistical methods, depending on the distribution being considered. In statistics, z represents a standard score or a z-score. It is a measure of how many standard deviations a particular value is away from the mean of a distribution. The probability associated with a specific value of z is determined by the characteristics of the distribution, such as its shape, mean, and standard deviation. Different distributions, such as the normal distribution or the t-distribution, have different methods for calculating probabilities associated with specific values of z.

The probability associated with a particular value of z can be useful in hypothesis testing, confidence interval estimation, or determining the likelihood of an event occurring. By understanding the probability distribution of z-values, statisticians can make informed decisions and draw conclusions based on data analysis.

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Answer:

b stands for the y-intercept

Step-by-step explanation:

I hope this helps you out! :-)

Answer:

B= y intercept

Step-by-step explanation:

Answer:

\(Fraction = \frac{2}{15}\)

Step-by-step explanation:

Given

Wall = 30 inches

Concrete = 16 inches

Brick = 10 inches

Limestone = 4 inches

Required

Fraction of the wall that is limestone

The fraction of limestone is calculated as follows;

\(Fraction = \frac{Size\ of\ limestone}{Size\ of\ wall}\)

Substitute 4 for size of limestone and 30 for size of size of wall

The formula becomes

\(Fraction = \frac{4}{30}\)

Divide numerator and denominator by 2

\(Fraction = \frac{4/2}{30/2}\)

\(Fraction = \frac{2}{15}\)

The fraction can not be further simplified; hence, the fraction of limestone is \(\frac{2}{15}\)

Answer:

2/15

Step-by-step explanation:

Fractions can be found by dividing the part by the whole.

part/whole

In this problem, the part is the limestone portion of the wall and the whole is the total width of the wall.

limestone/total

16 inches are concrete, 10 inches are brick and 4 inches are limestone. The total width is 30 inches.

limestone = 4

total = 30

4/30

This fraction can be simplified. Both the numerator and denominator can be evenly divided by 2.

(4/2) / (30/2)

2/ (30/2)

2/15

This fraction cannot be simplified further, therefore it is our answer.

2/15 of the wall is limestone.

As a result of answering the given question, we may state that Because equation 18 transactions exceed his goal of 16 transactions per hour, the clerk will complete 16 transactions in 1 hour.

In mathematics, an equation is a statement stating the equality or two expressions. An equation consists of two sides split by an algebraic equation (=). For illustration, the argument "2x + 3 = 9" argues that the statement "2x + 3" is equal to the value "9". The goal of equation solving is to find the value or values of the variable(s) to make the equation true. Simple or complex equations, regular or nonlinear, and including one or more factors are all possible. For example, the equation "x2 + 2x - 3 = 0" has the variable x raised to the second power. Lines are used in many fields of mathematics, including algebra, calculus, or geometry.

There are three sets of 20 minutes in an hour, thus if the clerk continues to work at his current rate, he will finish:

6 transactions in 20 minutes multiplied by 3 sets is 18 transactions in 1 hour.

Because 18 transactions exceed his goal of 16 transactions per hour, the clerk will complete 16 transactions in 1 hour.

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The number of miles she drove the van for is 250 miles

From the question, we are to determine the number of miles Shelly drove the van

The given equation which shows the relationship between the number of days she rented the van, d, and the number of miles she drove the van, m is

20d + 0.7m = 235

Now, if she rented the van for 3 days, that is, d = 3

Putting the value of d = 3 into the equation to determine the value of m

We get

20(3) + 0.7m = 235

60 + 0.7m = 235

0.7m = 235 - 60

0.7m = 175

m = 175 / 0.7

m = 250

Hence, the number of miles she drove the van for is 250 miles

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Answer:

15

Step-by-step explanation:

24-9

Surface area of the Triangular Prism is 4488  \(mm^{2}\)

A polyhedron with three faces connecting matching sides, a triangle base, and a translated copy is known as a triangular prism. If the sides of a right triangular prism are not rectangular, the prism is oblique.

A triangular prism is a prism that has three rectangular sides and two triangular bases. A pentahedron, that is.

Characteristics of triangle prism

A triangular prism's total surface area is another name for its surface area. A triangular prism's total surface area is equal to the sum of its faces' surface areas. Three rectangle and two triangle faces make up a triangular prism. The bases are the triangle faces, whereas the lateral faces are described as being rectangular. When a triangular prism's bases are arranged horizontally, the top and bottom (faces) of the prism are referred to as such.

Perimeter of the Triangel of the prism = 30 + 30 + 36 = 96 mm

Length of the prism = 34 mm

Base of the triangle = 36 mm

Surface area of the Triangular Prism is = (perimeter of the triangle * length of prism) + (base area)

= 96*34 + 34*36 = 4488  \(mm^{2}\)

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The value of integral of ∫ cos 5 x cos 2 x dx is  (1/2) [1/3 sin(3x) + 1/7 sin(7x)] + C.

We can use the trigonometric identity formula:

cos(a)cos(b) = (1/2)[cos(a-b) + cos(a+b)] Here a and b dontes to the two angles, to write by substituting the values of a and b.

cos 5 x cos 2 x = (1/2)[cos(5x-2x) + cos(5x+2x)]

= (1/2)[cos(3x) + cos(7x)]

Therefore, we have:

∫ cos 5 x cos 2 x dx = (1/2) ∫ [cos(3x) + cos(7x)] dx

Using the power rule and the fact that the integral of cos(x) is sin(x) + C, we get:

∫ cos 5 x cos 2 x dx = (1/2) [1/3 sin(3x) + 1/7 sin(7x)] + C

where C is the constant of integration.

The value of integral is (1/2) [1/3 sin(3x) + 1/7 sin(7x)] + C.

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Answer:

990.56

Step-by-step explanation:

because, Distance=velocity× time