olivia and kieran share money in the ratio 2:5. Olivia gets £42. how much did kieran get?

Answers

Answer 1

[tex] \huge \: \tt \green{Answer} [/tex]

Olivia and kieran share ratio 2 : 5

[tex] \texttt{olivia's share \: of \: money = £42 }= \frac{2}{7} \\ [/tex]

Total Amount of Money = Olivia's share of money × Reciprocal of olivia's share

[tex] \tt \: = > 42 \times \frac{7}{2} \\ \\ = > 147[/tex]

Kieran's share of Money =

[tex] = > 147 \times \frac{5}{7} \\ \\ = > \sf{ \pink{£105}}[/tex]


Related Questions

What are inequalities?

Answers

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

Answer:

In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.

There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:

Greater than: x > y (read as "x is greater than y")

Less than: x < y (read as "x is less than y")

Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")

Less than or equal to: x ≤ y (read as "x is less than or equal to y")

Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.

Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.

Step-by-step explanation:

You run 3 laps around a rectangular field. The field is 100 meters long and 97 meters wide. How many meters do you run?

Answers

The distance around the rectangular field can be calculated using the formula:

distance = 2(length + width)

In this case, the length is 100 meters and the width is 97 meters. So the distance around the field is:

distance = 2(100 + 97) = 2(197) = 394 meters

Since you run 3 laps around the field, the total distance you run is:

total distance = 3 × distance around the field
total distance = 3 × 394 meters
total distance = 1182 meters

Therefore, you run 1182 meters in total.

Question 1: 10 pts

A triangle has a base length of 2ac² and a height 6 centimeters more than the base

length. Find the area of the triangle if a = 4 and c = 2.

608 cm²

224 cm²

1,216 cm²

576 cm²

Answers

The area of the triangle with the given base and height where a = 4 and c = 2 is: 608 cm²

What is the Area of a Triangle?

Area = 1/2(base)(height).

Given the parameters:

Base length = 2ac² cmHeight = 2ac² + 6 cm

If a = 4 and c = 2, then:

Area = 1/2(base)(height) = 1/2(2ac²)(2ac² + 6)

Area = 1/2(2 × 4 × 2²)(2 × 4 × 2² + 6)

Area = 1/2(32)(38)

Area = 608 cm²

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Consider the line that passes through the point and is parallel to the given vector. (4, -1, 9) ‹-1, 4, -2› symmetric equations for the line. -(x - 4) = y+1/ 4​ = − z−9 /2​ . (b) Find the points in which the line intersects the coordinate planes.

Answers

The symmetric equations of the line passing through a point and parallel to a vector are -(x - 4) = y + 1/4 = -(z - 9)/2. The line intersects the xy-, xz-, and yz-planes at (5, -9/4, 0), (15/4, 0, 23/2), and (0, -17/4, 11/2), respectively.

To find the symmetric equations of the line, we first need to find the direction vector of the line. Since the line is parallel to the vector <4, -1, 9>, any scalar multiple of this vector will be a direction vector of the line. So, let's choose the parameter t and write the vector equation of the line:

r = <4, -1, 9> + t<-1, 4, -2>

Expanding this vector equation component-wise, we get:

x = 4 - t

y = -1 + 4t

z = 9 - 2t

These equations can be rearranged to get the symmetric equations of the line:

-(x - 4) = y + 1/4 = -(z - 9)/2

To find the points in which the line intersects the coordinate planes, we substitute the corresponding variables with 0 in the equations for the line.

For the xy-plane, we set z = 0 and solve for x and y:

-(x - 4) = y + 1/4 = -(-9)/2

x = 5, y = -9/4

So, the line intersects the xy-plane at the point (5, -9/4, 0).

For the xz-plane, we set y = 0 and solve for x and z:

-(x - 4) = 0 + 1/4 = -(z - 9)/2

x = 15/4, z = 23/2

So, the line intersects the xz-plane at the point (15/4, 0, 23/2).

For the yz-plane, we set x = 0 and solve for y and z:

-(-4) = y + 1/4 = -(z - 9)/2

y = -17/4, z = 11/2

So, the line intersects the yz-plane at the point (0, -17/4, 11/2).

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Marcos had $60 in his savings account in January. He continued to add money to his account and by June, the value of the savings account had increased by 50%. How much money is in Marcos's account in June?

Answers

Answer: 90$

Step-by-step explanation:  50% of 60 is 30 so 60+30=90

Drag each tile to its equivalent measure, rounded to the nearest tenth.
Options: 19.8, 10.2, 22.7, 15.4

Measure Equivalent
4 in. _____ Cm
7 kg _____lb
6 gal _____L
65 ft _____ m

Answers

The correct matches are: 4 in. → 10.2 cm   ,   7 kg → 15.4 lb

6 gal → 22.7 L   and  65 ft → 19.8 m.

What are conversions?

Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.

For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.

Here are the conversions:

1 inch = 2.54 cm (approx.)

1 kg = 2.205 lb (approx.)

1 gal = 3.785 L (approx.)

1 ft = 0.3048 m (approx.)

Using these conversions, we can find the equivalent measures:

4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm

7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb

6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L

65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m

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for a given positive integer n, output all the perfect numbers between 1 and n, one number in each line.

Answers

Perfect numbers between 1 and n (where n is a positive integer) are 6, 28, 496, 8128.

A positive integer that is the sum of its appropriate divisors is referred to as a perfect number. The sum of the lowest perfect number, 6, is made up of the digits 1, 2, and 3. The digits 28, 496, and 8,128 are also ideal.

Perfect numbers are whole numbers that are equal to the sum of their positive divisors, excluding the number itself. Examples of perfect numbers include 6 (1 + 2 + 3 = 6), 28 (1 + 2 + 4 + 7 + 14 = 28) and 496 (1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496).

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The complete question is:

What are all the perfect numbers between 1 and n (where n is a positive integer)?

Just needing help here

Answers

Based on the graph given, the function is not continuous at x = 1.

What is function?

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. A function is typically represented using functional notation as f(x), which means that the output value of the function f corresponds to the input value x.  Functions can take many forms and can be represented graphically or algebraically. They are used to describe many real-world phenomena, including physical systems, economic trends, and social behavior. Functions are important in mathematics because they provide a framework for understanding relationships between variables and for solving problems in various areas of mathematics, science, and engineering.

Here,

At x = 1, there is a "hole" or a point of discontinuity in the graph where the function is undefined. This is because the function has a removable discontinuity at x = 1, meaning that the limit of the function exists at x = 1 but the function is not defined at that point.

Therefore, the value of x at which the function is not continuous is: 1

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i need the answer to this question

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The measure of angle BAC is 55°, which is closest to option B (50°).

What is a tangent angle?

The ratio of the length of the side directly opposite an acute angle to the side directly adjacent to the angle is known as the tangent in trigonometry. Only triangles with straight angles can have this.

Let's give the angles shown in the diagram the following labels:

Angle ACD = 55°

Angle ABD = 35°

Angle BCD = 90°

To determine the size of angle ABC, we can use the knowledge that a triangle's total angles equal 180°. Because the straight line formed by angles ABD and BCD, we have:

[tex]Angle ABC = 180° - Angles ABD and BCD.[/tex]

[tex]Angle ABC = 180° - 35° - 90°Angle ABC = 55°[/tex]

Given that triangle ABC has two angles, we can use the knowledge that a triangle's total of angles equals 180° to determine the size of angle BAC:

[tex]Angle BAC = 180° - Angle ABC - Angle ACBAngle BAC = 180° - 55° - 70°Angle BAC = 55°[/tex]

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It is most similar to option B (50°) when the angle BAC is 55°.

What is a tangent angle?

The tangent in trigonometry is the length of the side directly opposite an acute angle divided by the length of the side directly next to the angle.

This property can only be found in triangles with straight angles.

Let's give the angles shown in the diagram the following labels:

Angle ACD = 55°

Angle ABD = 35°

Angle BCD = 90°

We can use the fact that a triangle's total number of angles is 180° to calculate the size of angle ABC. due to the fact that the straight line created by angles ABD and BCD

Triangle ABC has two angles, so we can use the fact that a triangle's sum of angles is 180° to calculate the size of angle BAC.

Therefore, the BAC measurement is 55°, which is closest to option B's 50°.C is 55°, which is closest to option B (50°).

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Use the power of a power property to simplify the numeric expression.

(91/4)^7/2

Answers

Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8


Using the power property to simplify the numeric expression.

Given the expression

(9¹⁺⁴)⁷⁺²

To simplify this expression using the power of a power property, we need to multiply the exponents:

(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)

Simplifying the exponents in the parentheses:

(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8

Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).

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The circle graph below represents the favorite fruit of 300 people How many prefer oranges? b. How many prefer pineapples? c. How many prefer blueberries? d. How many prefer apples? e. How many prefer strawberries?​

Answers

Hey!
A: 50% Of people = 150 people prefer oranges.

B: 10% Of people = 15 people prefer pineapple.

C: 15% Of people = 20 people prefer blueberries.

D: 5% Of people = 5 people prefer apples.

E: 20% Of people = 22 people prefer strawberries

Mason earns $8.10 per hour and worked 40 hours. Noah earns $10.80 per hour. How many hours would Noah need to work to equal Mason’s earnings over 40 hours?

Answers

Answer:

Noah would need to work 30 hours to equal Mason's earning for 40 hours

Step-by-step explanation:

Mason;

8.10 x 40 = 324

324 ÷ 10.80 = 30 hours.

Helping in the name of Jesus.

Answer:

30 hours

Step-by-step explanation:

40 times 8.10 is 324 and 324 divided by 10.8 is 30 hours

determine, without actually computing the z transform, the rocs for the z transform of the following signals:

Answers

The ROC of a given signal's Z-transform can be determined without actually computing the Z-transform by identifying the maximum and minimum magnitude of the signal and checking for any poles of the Z-transform within the resulting annular region.

Let's take a signal as an example, suppose x[n] = {1, -2, 3, -4, 5}. In order to determine the ROC of its Z-transform, we are firstly required to first look for any regions in the complex plane where the sum of the absolute values of the Z-transform is found finite. It can be done by looking for the maximum and minimum magnitude of x[n] and denote them as R1 and R2 respectively. Then, the ROC of the Z-transform will be the annular region between R1 and R2, excluding any poles of the Z-transform that lie within this annular region.

In this case, the maximum absolute value of x[n] is 5 and the minimum is found being 1. So, the ROC of the Z-transform will be the annular region between |z| = 1 and |z| = 5. We can denote this as 1 < |z| < 5. We also need to check if there are any poles of the Z-transform within this annular region. Since we haven't actually computed the Z-transform, we cannot determine the exact location of any poles.

However, we can check for any values of z that would make the Z-transform infinite. For example, if x[n] is a causal signal (i.e., x[n] = 0 for n < 0), then the ROC cannot include any values of z for which |z| < 1, since this would make the Z-transform infinite.

So, the ROC of the Z-transform for the given signal x[n] can be written as 1 < |z| < 5, assuming that x[n] is a causal signal.

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The complete question is :

Can you explain how to determine the ROCs (regions of convergence) for the Z-transform of a given signal without actually computing the Z-transform? Please provide an example signal with random data and demonstrate how to find its ROCs using this method.

3. Factor 72x³ +72x² +18x.

Answers

The expression's fully factored form is:[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]

Factored value is what?

Factored Value, also known as "trended value," is the base annual value plus a yearly inflation factor based on a variation in the cost if live that is not to exceed 2% and is set by the State Agency of Equalization.

What is a factored expression example?

Rewriting an expression as the sum of factors is referred to as factor expressions or factoring. For instance, 3x + 12y may be expressed as 3 (x + 4y), which is a straightforward equation. The computations get simpler in this method. Three or (x + 4y) were examples of factors.

We can factor out [tex]18x[/tex] from each term to simplify the expression:

[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{3} + 4x^{2} + 1)[/tex]

An expression enclosed in parentheses can now be calculated by grouping or factoring.

[tex]4x^{3} + 4x^{2} + 1 = (4x^{2} + 1)(x + 1)[/tex]

The expression's properly factored version has the following result,

[tex]72x^{3} + 72x^{2} + 18x = 18x(4x^{2} + 1)(x + 1)[/tex]

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if the sum of a number and eight is doubled​, the result is seven less than the number. Find the number.

Answers

Answer:

Step-by-step explanation:

Let's call the number we're looking for "x".

The problem tells us that "if the sum of a number and eight is doubled, the result is seven less than the number", which can be translated into an equation:

2(x+8) = x-7

Now let's solve for x:

2x + 16 = x - 7

2x - x = -7 - 16

x = -23

Therefore, the number we're looking for is -23.

-6(4p+5) > 34-8p HELP ASAP

Answers

Answer:

p < -4

Step-by-step explanation:

-6(4p+5) > 34 - 8p

-24p - 30 > 34 - 8p

-16p - 30 > 34

-16p > 64

p < -4

Question 15 (2 points)
A standard deck of cards contains 4 suits of the same 13 cards. The contents of a
standard deck are shown below:

Standard deck of 52 cards
4 suits (CLUBS SPADES, HEARTS, DIAMONDS)
13 CLUBS
13 SPADES
13 HEARTS
DIAMONDS

If a card is drawn at random from the deck, what is the probability it is a jack or ten?

0
4/52- 1/13
8/52 = 2/13
48/52- 12/13

Answers

Answer: 2/13

Step-by-step explanation:

There are four jacks and four tens in a standard deck of 52 cards. However, the jack of spades and the ten of spades are counted twice since they are both a jack and a ten. Therefore, there are 8 cards that are either a jack or a ten, and the probability of drawing one of these cards at random is:

P(Jack or Ten) = 8/52 = 2/13

So the answer is 2/13.

Step-by-step explanation:

a probability is airways the ratio

desired cases / totally possible cases

in each of the 4 suits there is one Jack and one 10.

that means in the whole deck of cards we have

4×2 = 8 desired cases.

the totally possible cases are the whole deck = 52.

so, the probability to draw a Jack or a Ten is

8/52 = 2/13

the position vector r describes the path of an object moving in the xy-plane. position vector point r(t)

Answers

a) Velocity vector v(t) = i - 2tj, Speed s(t) = sqrt(1 + 4t²), Acceleration vector a(t) = -2j. b) Velocity vector v(1) = i - 2j, Acceleration vector a(1) = -2j

This problem is about finding the velocity, speed, and acceleration vectors of an object moving in the xy-plane, described by a position vector r(t). We can find the velocity vector by taking the derivative of the position vector, and the speed by taking the magnitude of the velocity vector. The acceleration vector can be found by taking the derivative of the velocity vector. We can then evaluate the velocity and acceleration vectors at a given point by plugging in the coordinates of the point. This problem requires basic vector calculus and understanding of the relationship between position, velocity, speed, and acceleration vectors.

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Complete question is attached below

In a double slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0cm. The distance between adjacent maxima when the slit separation is cut in half decreases to 0.50cm. The speed of light in a certain material is measured to be 2.2x10^8 m/s.

Answers

The index of refraction of the material used in double slit experiment is 1.36.

The distance between adjacent maxima on a screen in a double-slit experiment is given by:

d sinθ = mλ

where d is the slit separation, θ is the angle between the screen and the line connecting the slits and the maxima, m is the order of the maximum, and λ is the wavelength of light.

The distance between adjacent maxima changes from 1.0cm to 0.50cm when the slit separation is cut in half, which means that the wavelength of light is also halved. Therefore, the ratio of the two wavelengths is:

λ1/λ2 = 2/1 = 2

The speed of light in the material is given as 2.2x10^8 m/s. The speed of light in a vacuum is c, so the index of refraction of the material is given by:

n = c/v

where v is the speed of light in the material. Therefore:

n = c/2.2x10^8 m/s = 1.36

The index of refraction of the material is 1.36.

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_____The given question is incomplete, the complete question is given below:

In a double slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0cm. The distance between adjacent maxima when the slit separation is cut in half decreases to 0.50cm. The speed of light in a certain material is measured to be 2.2x10^8 m/s. what is the index refraction of this material?

Determine the interval(s) over which the graph of f left parenthesis x right parenthesis equals short dash x to the power of 6 minus 6 x to the power of 5 plus 12 x minus 2 is concave up or concave down.

Answers

Answer:

gdiduusuehfuehvv

Step-by-step explanation:

bbzbhshxhdhhd are the best and my mom I WINNNNNN you want it to be over with you guys to come in and your mom are doing ghhdhhsuwuwhsh and your family are doing well and your family are doing well and your family are doing well and your family are doing well and your family and my wife was the best and I WINNNNNN and my mom are doing ghhdhhsuwuwhsh and what is the only ones I WINNNNNN with the kids I WINNNNNN and I will be over and I can do i and eat early for you and Darshanie and I WINNNNNN and my friend and your mom and my mom ever had a great day I love ever and your mom are the kids I will get you a great mom and I will send you a link and I WINNNNNN with the only ones I WINNNNNN with you don't need me I can get it and I will be over and your mom and your mom I will send it out tomorrow night I will send it out tomorrow night with you guys and I can send the best ones that have to do i I will send you and Darshanie and your mom I will send it and your family and I WINNNNNN and my friend are doing errands to run out to do i you guys and I WINNNNNN you want me I will send you and Darshanie is done now we have a great day for a great mom I will be over there and I WINNNNNN you and everyone and my friend and my friend and what time do the kids have a whole new world we live together I will be home tomorrow night with the only one that has to wait until the way home tomorrow morning to run out of wo you guys to run out with the best ones that w with the kids I will get you guys want me when we good day for you it

A teacher has a large yellow bulletin board in her classroom. She decides to use purple paper to frame a smaller rectangle inside the original board. The paper will create a border that is x inches wide. The teacher's bulletin board plan and dimensions are shown below.
Look at the picture then choose the answer from the options below:
Select the true statement about the expression.

A.
The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.
B.
The term 4x2 represents the area, in square inches, of the entire bulletin board.
C.
The factor (48 − 2x) represents the height, in inches, of the bulletin board including the decorative border.
D.
The term -288x represents the area, in square inches, of the decorative border.

Answers

Option A: The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.

How to obtain the area of a rectangle?

To obtain the area of a rectangle, you need to multiply the dimensions of the rectangle, which are the length and the width.

Hence the formula for the area of the rectangle is given as follows:

Area = Length x Width.

The area of the uncovered region is given by the total area subtracted by the area of the covered region.

Then the dimensions for the uncovered region are given as follows:

96 - 2x.48 - 2x.

The area of the covered region is given as follows:

4x².

The area of the entire region is given as follows:

4x² - 288x + 4608.

Hence the correct statement is given by option A.

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right triangle that i’m confused on please help

Answers

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

LI Annexure A shows Rhandzu's grade 11 school timetable for 2023. Learners are given 5 minutes to change from one lesson to the other. Use ANNEXURE A to answer the questions that follow. 1.1.1 Determine how l
ong the second break is. 1.1.2 How many subjects is Rhandzu doing? 1.1.3 Determine the number of days in an eight-day cycle that Rhandzu has Mathematical Literacy. Explain why it is important to schedule breaks on the time-table. 1.1.4​

Answers

The answer of the given question based on determining the second break in the break is  1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long , 1.1.2 Rhandzu is doing 8 subjects , Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle.

What is Sepedi Home Language?

Sepedi is  Bantu language spoken in South Africa by Pedi people. It is one of the 11 official languages of South Africa and is primarily spoken in  northern parts of  country, like Limpopo, Gauteng, and Mpumalanga provinces.

Sepedi is also known as Sesotho sa Leboa and is closely related to Sesotho (Southern Sotho) and Setswana (Tswana). Sepedi Home Language refers to  study of Sepedi as  first language or mother tongue in South African schools. It is an important subject in South African education system, as it helps to preserve and promote use of indigenous languages and cultural heritage.

1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long.

1.1.2 Rhandzu is doing 8 subjects, which are English Home Language, Mathematics, Life Orientation, Physical Sciences, Life Sciences, Agricultural Sciences, Mathematical Literacy, and Sepedi Home Language.

1.1.3 Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle. Therefore, in an eight-day cycle, Rhandzu would have Mathematical Literacy on Day 3, Day 7, Day 3 again, and Day 7 again.

It is important to schedule breaks on the time-table because they allow students to rest and recharge between lessons. Breaks can also help students to stay focused and engaged during lessons by giving them time to process and reflect on what they have learned. Additionally, breaks can provide opportunities for social interaction and physical activity, which can have a positive impact on students' well-being and academic performance.

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The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long , Rhandzu is doing 8 subjects , Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle.

What is Sepedi Home Language?

Sepedi is  Bantu language spoken in South Africa by Pedi people. It is one of the 11 official languages of South Africa and is primarily spoken in  northern parts of  country, like Limpopo, Gauteng, and Mpumalanga provinces.

Sepedi is also known as Sesotho sa Leboa and is closely related to Sesotho (Southern Sotho) and Setswana (Tswana). Sepedi Home Language refers to  study of Sepedi as  first language or mother tongue in South African schools. It is an important subject in South African education system, as it helps to preserve and promote use of indigenous languages and cultural heritage.

1.1.1 The second break is from 11:25 AM to 11:40 AM, which means it is 15 minutes long.

1.1.2 Rhandzu is doing 8 subjects, which are English Home Language, Mathematics, Life Orientation, Physical Sciences, Life Sciences, Agricultural Sciences, Mathematical Literacy, and Sepedi Home Language.

1.1.3 Rhandzu has Mathematical Literacy on Day 3 and Day 7, which means it is a 4-day cycle. Therefore, in an eight-day cycle, Rhandzu would have Mathematical Literacy on Day 3, Day 7, Day 3 again, and Day 7 again.

It is important to schedule breaks on the time-table because they allow students to rest and recharge between lessons. Breaks can also help students to stay focused and engaged during lessons by giving them time to process and reflect on what they have learned. Additionally, breaks can provide opportunities for social interaction and physical activity, which can have a positive impact on students' well-being and academic performance.

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How do I solve? I don’t understand

Answers

Step-by-step explanation:

Use the 110 to find the 70 degree angle   (they form a straight line = 180°)

   then 70 + 64 + R angle = 180°    ( sum of angles of a triangle)

        then  :    R angle = 46°

then the R angle + 2x-10 = 90°    ( because the two lines are perpendicular)

(2x -10)°   + 46 °  = 90 °

x = 27

main Street tea company blends black tea that sells for $3.45 a pound with Earl Gray tea that sells for $2.15 a pound to produce 80 lb of mixture that they sell for $2.75 a pound how much of each kind of tea does the mixture contain rounding to the nearest pound​

Answers

36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.

Let x and y be the amount of tea that sells fo 3.45 and 2.15 a pound respectively:

x+y=80....................eq 1

3.45x+2.15y=2.75(80)......eq 2

:

rewrite eq 1 to x=80-y and plug that value into eq 2

:

3.45(80-y) +2.15y=2.75(80)

:

276-3.45y+2.15y=220

:

-1.3y=56

:

y=43.07 pounds of $2.15 tea

:

28x=80-43.07=36.93 pounds of $3.45 tea

Let a= the pounds of the more expensive tea needed

Let b= the pounds of the less expensive tea needed

(1) a+%2B+b+=+80

(2) 345a+%2B+215b+=+80%2A275 (in cents)

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

In words, (2) says.

(lbs of 'a' tea x price/lb) + (lbs of 'b' tea x price/lb) =

(lbs of mixture x price/lb of mixture)

-------

Multiply both sides of (1) by 215 and then.

subtract from (2)

345a+%2B+215b+=+80%2A275

-215a+-+215b+=+-80%2A215

130a+=+80%2A60

130a+=+4800

a+=+36.92

and, from (1)

(1) a+%2B+b+=+80

36.92+%2B+b+=+80

b+=+80+-+36.92

b+=+43.08

36.92 lbs. of the $3.45 tea and 43.08 lbs. of the $2.15 tea are needed.

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The mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations.

Let's denote the amount of black tea in pounds by "x" and the amount of Earl Gray tea in pounds by "y".

Since the total amount of mixture is 80 lb, we have:

x + y = 80 ----(1)

We also know that the mixture sells for $2.75 a pound, so the total revenue from selling 80 lb of mixture is:

80 x $2.75 = $220

On the other hand, the cost of the mixture is the sum of the costs of the black tea and the Earl Gray tea, which is:

3.45x + 2.15y

Since the company wants to make a profit, the revenue must be greater than the cost, so we have:

3.45x + 2.15y < $220

We can simplify this inequality by dividing both sides by 0.1:

34.5x + 21.5y < 2200 ----(2)

Now we have two equations with two unknowns (equations (1) and (2)), which we can solve using substitution or elimination.

Substitution method:

From equation (1), we have:

y = 80 - x

Substituting this into equation (2), we get:

34.5x + 21.5(80 - x) < 2200

Simplifying and solving for x, we get:

x < 34.5

Rounding x to the nearest pound, we get x = 34.

Substituting this value into y = 80 - x, we get y = 46.

Therefore, the mixture contains 34 pounds of black tea and 46 pounds of Earl Gray tea.

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In the diagram below, MN is parallel to JK. If MN=10,LK=7.2, JL=13.2, and LN=6.find the length of JK. Figures are not necessarily drawn to scale.

Answers

The length of JK is 18.333.

Since MN is parallel to JK, the angles formed by JLN and MLK are equal. Therefore, we can use the Triangle Proportionality Theorem, which states that if a line parallel to one side of a triangle divides the other two sides proportionally, then the triangles are similar.

Using the Triangle Proportionality Theorem, we can set up the following proportion:

[tex]$\frac{LK}{JL} = \frac{MN}{LN}$[/tex]

Therefore,

[tex]$\frac{7.2}{13.2} = \frac{10}{6}$[/tex]

We can cross-multiply to solve for JK:

[tex]$7.2 \cdot 6 = 13.2 \cdot 10$\\$43.2 = 132$\\$JK = \frac{132}{7.2} = 18.333$[/tex]

Therefore, the length of JK is 18.333.

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A company reported the following:
$275,270
Preferred dividends
$20,390
Shares of common stock outstanding
36,000
Market price per share of common stock
$118.87
Calculate the company's price-earnings ratio. Round your answer to two decimal places.
Net income

Answers

The company's price-earnings ratio for a company that reported net income of $275,270 with $20,390 for preferred dividends and 36,000 shares of common stock, is 16.79.

What is the price-earnings ratio?

The price-earnings ratio represents the per-dollar amount that an investor can expect to invest in a company in order to receive $1 of that company's net earnings.

The price-earnings (P/E) ratio is also referred to as the price multiple.

The price-earnings (P/E) ratio compares the market price with the earnings per share.

Net income = $275,270

Preferred Dividends = $20,390

Net income available to Common Stockholders = $254,880 ($275,270 - $20,390)

Number of common stock outstanding = 36,000 shares

Market price per share of common stock = $118.87

Earnings per share (Common Stock) = $7.08 ($254,880/36,000)

Price-earnings ratio = Market price per share/Earnings per share

= 16.79 ($118.87/$7.08).

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I will mark you brainiest!

Determine the MOST PRECISE name for the quadrilateral below.
A) rhombus
B) parallelogram
C) square
D) trapezoid
E) kite

Answers

The answer is A, rhombus.

What is the limit of (n!)^(1/n) as n approaches infinity?

Note: n! means n factorial, which is the product of all positive integers up to n.

Answers

Answer:

Step-by-step explanation:

To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:

n! ≈ (n/e)^n √(2πn)

where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.

Using this approximation, we can rewrite (n!)^(1/n) as:

(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)

Taking the limit as n approaches infinity, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)

Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:

lim [√(2πn)]^(1/n) = 1

For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:

lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1

Therefore, combining the two terms, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1

Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.

Answer:1

Step-by-step explanation:

GUYS PLEASE HELP MATH!!

Answers

Answer:

4.3

Step-by-step explanation:

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