how to solve this proportion​

The required formula to find the missing angles in the triangle is x + x + 10 = 130

The sum of angles in a triangle gives us 180°, Mathematically, this gives :

50 + x + (x + 10) = 180

50 + x + x + 10 = 180

x + x + 60 = 180

x + x + 10 = 180 - 50

x + x + 10 = 130

Therefore, the required formula is x + x + 10 = 130

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Answer: -1.4,1 1/25,1.25

Step-by-step explanation:

-1.4,1 1/25,1.25

1 1/25=

1+0.04=1.04

Order: -1.4, 1.04, 1.25 ==> -1.4,1 1/25,1.25

Answer:

0.018

Step-by-step explanation:

Probability of (The test will accurately identify a steroid user) = 90% = 0.9

Probability of (generating a false positive(probability of testing positive and he/she is not a steroid user)= 5% = 0.05

Probability of ( actual steroid users) = 0.1% = 0.001

Probability of not been a steroid user = 1 - 0.001 = 0.999

Probability that( he/she actually was using steroid and if an athlete tests positive) = 0.001 × 0.9 / 0.001 × 0.9 + 0.5 × 0.999

= 0.009/0.009 + 0.4995

= 0.009/0.5085

= 0.017699115

Approximately = 0.018

To earn an average score of 90, the score on the fourth test needs to be 98.

The core value of a set of data is expressed mathematically as the average of a list of data. It is defined mathematically as the ratio between the total number of units in the list and the sum of all the data. The term "mean" in statistics also refers to the average of a particular set of numerical data.

Given the score of the first three tests as:

91, 84, 87.

The average is given by the following formula:

Average = Sum of scores ÷ total number of tests

Let us suppose the score of fourth test as x.

Given that A = 90:

90 = (91 + 84 + 87 + x) ÷ 4

x = 98

Hence, the score on the fourth test must be equal to 98, to get an average score of 90.

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Answer:

11.405

Step-by-step explanation:

When rounding numbers, check the digit to the right of the one you're rounding to:

If a = 14.6 is rounded to 1 decimal place then:

If b = 3.25 is rounded to 2 decimal places then:

Therefore, to find the maximum value of a - b, subtract the smallest value of b from the largest value of a:

\(\implies \sf a_{max}-b_{min}=14.649999...-3.245=11.405\)

Answer:

2p-8

Step-by-step explanation:

Know you're amazing and smart!

Answer:

Step-by-step explanation:

4p+8-2p-16 combine like terms

2p-8

Answer:

1+tan2x=sec2x.

Explanation: Change to sines and cosines then simplify.

Answer:

-7

Step-by-step explanation:

8-15 = -7 but since it's an absolute value, it is 7 and then you add the negative sign in front since it is not in the absolute value.

Answer and Step-by-step explanation: The graph is shown in the attachment.

a. ΔR on [1,2] is mathematically expressed as:

ΔR = R(2) - R(1)

which means difference of population of rabbits after 2 months and after 1 month.

\(R(1) = 100(\frac{2}{5}.1 )\)

\(R(1) = 100(\frac{2}{5} )\)

R(2) = \(100(\frac{2}{5}.2 )\)

\(R(2) = 100(\frac{4}{5} )\)

\(\Delta R = 100(\frac{4}{5} )-100(\frac{2}{5} )\)

\(\Delta R = 100[\frac{4}{5} - \frac{2}{5} ]\)

\(\Delta R=\) 40

Difference of rabbits between first and second months is 40.

b. R(0) = 100(\(\frac{2}{5} .0\))

R(0) = 0

Initially, there no rabbits in the population.

c. R(10) = \(100(\frac{2}{5}.10 )\)

R(10) = 400

In 10 months, there will be 400 rabbits.

d. R(t) = 500

\(500=100(\frac{2}{5}.t )\)

\(\frac{500}{100}=\frac{2}{5}.t\)

\(t = \frac{500.5}{100.2}\)

t = 12.5

In 12 and half months, population of rabbits will be 500.

A. The system of equations in standard form is: 4x + 5y = 540 and 3x + 5y = 440.

B. The y-intercept of the equation representing the prices on Saturday night is 108, and the y-intercept of the equation representing the prices at the matinee on the second day is 88.

A) Let's define the variables:

Let x represent the number of children attending.

Let y represent the number of adults attending.

On Saturday night:

The equation for the revenue generated on Saturday night is:

4x + 5y = 540 (since children's tickets cost $4 and adults' tickets cost $5, and the total revenue is $540).

Matinee on the second day:

The equation for the revenue generated at the matinee is:

3x + 5y = 440 (since children's tickets cost $3 and adults' tickets still cost $5, and the total revenue is $440).

Therefore, the system of equations in standard form is:

4x + 5y = 540

3x + 5y = 440

B) Let's rewrite the system of equations in slope-intercept form:

On Saturday night:

4x + 5y = 540

Rearranging the equation, we get:

5y = -4x + 540

Dividing both sides by 5, we get:

y = (-4/5)x + 108

The y-intercept of this equation is 108.

Matinee on the second day:

3x + 5y = 440

Rearranging the equation, we get:

5y = -3x + 440

Dividing both sides by 5, we get:

y = (-3/5)x + 88

The y-intercept of this equation is 88.

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The function, \(\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }\) has a limit that is undefined (does not exist) as x approaches 0. The correct option therefore option b;

b. As x approaches 0, the limit of p(x) does not exist

The given function is presented as follows;

\(\displaystyle { p(x) = \frac{ {cos}^{2}x }{sin(2 \cdot x)} }\)

Required;

The limit of the function as x approaches (zero) 0

Solution;

The limit of a function at a given point within the domain of the function is the value of the function as the function's argument approaches a.

Therefore, the limit of the given function at the point x = 0 is given by the function's value as the argument of the function, x approaches 0.

cos²(0) = 1

sin(2×0) = sin(0) = 0

Therefore;

\(\displaystyle { p(x) = \frac{ {cos}^{2}0 }{sin(2 \times 0)} = \frac{ 1 }{0} = \infty}\)

Therefore, the limit of the function does not exist as x approaches 0

The correct option is therefore, option b

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Answer:

4th option

Step-by-step explanation:

Given

j(x) = \(5^{x-3}\) , then

j(x + h) = \(5^{x+h-3}\)

\(\frac{j(x+2)-j(x)}{h}\)

= \(\frac{5^{x+h-3}-5^{x-3} }{h}\) ← factor out \(5^{x-3}\) from each term on the numerator

= \(\frac{5^{x-3}(5^{h}-1) }{h}\)

The value of j(x+h)-j(x) / h is 5^{x-3}(5^h-1)/h if j(x) = 5^{x − 3} option fourth is correct.

It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

\(\rm j(x) = 5^{x-3}\)

First fine the value of j(x+h) for this simply plug x+h in the j(x), we get:

\(\rm j(x+h) = 5^{x+h-3}\)

Put the values of j(x) and j(x+h) in the below expression, we get;

\(=\rm \frac{j(x+h)-j(x)}{h}\)

\(=\rm \frac{5^{x+h-3}-5^{x-3}}{h}\)

\(=\rm 5^{x-3}\frac{5^{h}-1}{h}\)  or

\(=\rm \frac{5^{x-3}(5^{h}-1)}{h}\)

Thus, the value of j(x+h)-j(x) / h is 5^{x-3}(5^h-1)/h if j(x) = 5^{x − 3} option fourth is correct.

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Answer:

1 is good number 2 is wrong number 3 is good

Step-by-step explanation:

your welcome im juss writting more so it wont say issa short question!!

Answer:

9 is thr answer

Step-by-step explanation:

pls mark me as brianliest

Answer:

9.9 is the answer

Step-by-step explanation:

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The height of the cylindrical piece of pure gold with density and mass of 19.32 g/cm³ and 1699.48g, having a radius of 2cm is 7cm.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Also, density is expressed mathematically as;

p = m / v

Given that;

First, we determine the volume of the cylinder.

Density = Mass / Volume

Volume = Mass / Density

Volume = 1699.48g / 19.32g/cm³

Volume = 87.9648 cm³

Next, we determine the height.

V = π × r² × h

87.9648 = 3.14 × (2)² × h

87.9648 = 3.14 × 4 × h

87.9648 = 12.56 × h

h = 87.9648 / 12.56

h = 7cm

Therefore, the height of the cylinder is 7cm.

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The surface area of the cylindrical pottery vase is 177.55 in².

Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,

SA of a cylinder = 2π×radius(h+r)

= 2×3.14×2.15(2.15+11)

= 177.55 in²

Hence, the surface area of the cylindrical pottery vase is 177.55 in².

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Answer:

Step-by-step explanation:

Answer:

A = 1.02 P

Step-by-step explanation:

A = P + 0.02P

Formula in Factorized form

(Taking P common)

A = P(1+0.02) [The required factorized from]

Then,

A = 1.02 P

Answer:

The box plot

Step-by-step explanation:

Answer:

X = 13

Step-by-step explanation:

Add 7 to both sides

2x = 26

divide by 2

x = 13

Answer:

depends

Step-by-step explanation:

see it really does show

Answer:

y = \(\frac{3}{4}\) x + 14

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 = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, - 2) and (x₂, y₂ ) = (5, 4) ← 2 points on the line

m = \(\frac{4-(-2)}{5-(-3)}\) = \(\frac{4+2}{5+3}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\) , then

y = \(\frac{3}{4}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, 4 )

4 = \(\frac{3}{4}\) (5) + c = \(\frac{15}{4}\) + c ( subtract \(\frac{15}{4}\) from both sides )

4 - \(\frac{15}{4}\) = c , then

c = \(\frac{16}{4}\) - \(\frac{15}{4}\) = \(\frac{1}{4}\)

y = \(\frac{3}{4}\) x + \(\frac{1}{4}\) ← equation of line

Answer:

You have to apply Indices Law :

\( {a}^{m} \div {a}^{n} ⇒ {a}^{m - n} \)

So for this question :

\( \frac{ \sqrt[3]{x} }{ {x}^{ \frac{1}{8} } } \)

\( = \sqrt[3]{x} \div {x}^{ \frac{1}{8} } \)

\( = {x}^{ \frac{1}{3} } \div {x}^{ \frac{1}{8} } \)

\( = {x}^{ \frac{1}{3} - \frac{1}{8} } \)

\( = {x}^{ \frac{5}{24} } \)

Answer:

35.6

Step-by-step explanation:

By the Pythagorean Theorem:

\( {x}^{2} + {91.3}^{2} = {98}^{2} \)

\(x = \sqrt{ {98}^{2} - {91.3}^{2} } = 35.6\)

Answer:The answer is 27.04

Step-by-step explanation:

The solution is in the attached

Answer:

Based on the diagram, we can see that the triangle formed by the line segment with length 8 and the two dashed line segments is a right triangle with a 45° angle. This means that the other two angles of the triangle are also 45° each.

Using the properties of 45°-45°-90° triangles, we know that the length of the hypotenuse is equal to the length of either leg times the square root of 2. Therefore, we have:

x = 8 / sqrt(2) = 8 * sqrt(2) / 2 = 4 * sqrt(2)

So the value of x is option B: 8√2 / 2 or simplified, 4√2.

Answer:

45.5

Step-by-step explanation:

You do the linear length multiplied by the longitudinal length

The distance across the lake is 320 ft.

Given is a scenario of a lake, a survey crew has laid out the concept of similar triangles to find the distance across the lake.

The figure shows the base of the larger triangles is the distance across the lake. [please refer to the figure attached]

The dimensions of the imaginary triangles are 30 ft, 30 ft, 40 ft and 240 ft, 240 ft, x ft.

Here, x is the distance across the lake which we are asked to find.

Using the definition of the similar triangles,

Two triangles are considered similar if their corresponding angles are equal, and the ratios of the lengths of their corresponding sides are equal.

So,

\(\frac{240}{30} = \frac{x}{40}\)

\(x = \frac{240 \times 40}{30}\)

x = 320

Hence the distance across the lake is 320 ft.

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1. The volume of the pyramid is 320ft³

3. The volume of the pyramid is 2395.83cm³

5. The volume of the pyramid is 1200in³

The volume of a rectangular pyramid can be calculated using the formula:

V = (1/3) * base area * height

Where:

1. The volume of the pyramid is calculated as;

V = 1/3 * 8 * 12 * 10 = 320ft³

3. The volume of the pyramid is;

V = 1/3 * (25 * 12.5) * 23 = 2395.83cm³

5. The volume of the pyramid is;

V = 1/3 * (15 * 15) * 16 = 1200in³

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The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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