The length of a side of a triangle is in the extended ratio of 3:5:7. The perimeter of the triangle is 120cm. What are the lengths of the sides?

Answer:

486 and 2187

Step-by-step explanation:

the nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ × [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

(1)

here a₁ = 2 and r = 3 , then

a₆ = 2 × [tex]3^{5}[/tex] = 2 × 243 = 486

(2)

here a₁ = [tex]\frac{1}{3}[/tex] and r = 3 , then

a₉ = [tex]\frac{1}{3}[/tex] × [tex]3^{8}[/tex] = [tex]\frac{1}{3}[/tex] × 6561 = 2187

Answer: Luz has 37 juice boxes.

Step-by-step explanation:

3 packages x 10 juice boxes = 30 juice boxes

30 + 7 = 37 juice boxes.

37 = 3 x 10 + 7 x 1

Due to length restriction, we kindly invite to check the explanation for further details on profit and risk minimization.

In this problem we find the case of a person that invests a lot of money, distributed in two investments. We need to determine how much money must be invested in each plan to earn a desired return:

R = (C - c) · (r₁ / 100) + c · (r₂ / 100)

Where:

Part A - If we know that R = 9300, C = 91000, r₁ = 10 and r₂ = 11, then the amount invested in the most risky investment:

9300 = (91000 - c) · (10 / 100) + c · (11 / 100)

930000 = (91000 - c) · 10 + c · 11

930000 = 910000 - 10 · c + 11 · c

c = 20000

The person must invest $ 20000 in the least risky investment and $ 71000 in the most risky investment.

Part B - The use of two accounts gives a reasonable equilibrium between profit and risk minimization.

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Because smaller denominators result in larger fractional pieces, the denominators for the numbers 6 and 8 are 6 and 8, respectively. Therefore, 5/6 will be greater than 5/8.

As you saw, you may compare fractions with the same denominator by examining their numerators. As you can see below, 3/4 is larger than 1/4.

The fraction grows as the numerator gets bigger. Due to the fact that it represents a portion of a whole, the fraction 5/8 can never be a whole number. The fraction 5/8 represents 5 of the 8 parts that make up the whole.

Although the decimal 0.625 is equivalent to 5/8, it still does not make a whole. You may represent 5/8 as that. The complete response is provided below. Because smaller denominators result in larger fractional pieces, the denominators for the numbers 6 and 8 are 6 and 8, respectively. Therefore, 5/6 will be greater than 5/8.

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The null hypothesis states that there is no difference in the intensity of any discomfort experienced while counting money versus paper. Money-related groups have a M = 7.56 and SS = 42.22 mean.

The null hypothesis assumes that any differences you see between the chosen attributes in a set of data are due to chance. For instance, if the predicted profits from the gambling game genuinely equal zero, then any discrepancy between the data's average profits and zero results from chance.

Here,

According to the null hypothesis, there is no difference in how painful anything feels while counting money versus paper. The mean for the group relating to money is

=>  M = 7.56 and SS = 42.22.

=> M = 11.33 and SS = 38 for the paper group.

=> t(16) is equal to 3.57,

=> the standard error is 1.06, and the pooled variance is 5.01.

=>The critical values for df = 16 are 2.921.

Reject the null hypothesis and draw the conclusion that there is a notable variation in the level of discomfort felt after counting money versus counting paper.

=> d = 3.77/2.24 = 1.68

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There is no sufficient evidence to keep up the claim that the bags are underfilled.

We are given;

n = 27 bags

Sample mean;X = 402 gram

Population mean;μ = 404 gram

Variance = 676

We know that, standard deviation(σ) = √variance

Thus;

σ = √676

σ = 26

The hypotheses are;

Null hypothesis; H0: μ = 404

Alternative hypothesis; HA: μ < 404

Let's find the z-score from the formula;

z = (X - μ)/(√σ/n)

z = (402 - 404)/√(26/27)

z = -2.04

The z-distribution table attached, we have a p-value of 0.02068

This is less than the significance value of 0.01 and we will reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that the bags are underfilled.

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The complete question is:

A manufacturer of chocolate chips would like to know whether its bag-filling machine works correctly at the 404-gram setting. It is believed that the machine is underfilling the bags. A 27-bag sample had a mean of 402 grams with a variance of 676. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Is there sufficient evidence to support the claim that the bags are underfilled?

The simplified form of the expression is 4x² - 3x + 2

Answer:

[tex]4x^{2} - 3x + 2[/tex]

Step-by-step explanation:

[tex](2x^{2} + x) - (-2x^{2} + 4x - 2)\\\\2x^{2} + x + 2x^{2} - 4x - 2\\\\\\4x^{2} -3x+2[/tex]

The graph of the linear function y = -3x is attached below.

A linear function is a type of mathematical function that describes a straight line relationship between two variables. It is defined by an equation of the form:

y = mx + b

where y is the dependent variable (output), x is the independent variable (input), m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis).

In a graph, a linear function will always be a straight line. The slope (m) tells you how steep the line is, and the y-intercept (b) tells you where the line crosses the y-axis. The slope-intercept form is y = mx + b

The linear function given is y = -3x

From the table of values;

f(x) = -3x

f(-1) = -3(-1)

f(-1) = 3

f(0) = -3(0)

f(0) = 0

f(1) = -3(1)

f(1) = -3

Plotting this on a graph, our slope is -3 and since it doesn't have a            y - intercept, the graph passes through the origin.

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Answer:

17＋p＝36

Step-by-step explanation:

people already on bus ＋ additional people＝limited people

17＋p＝36

p＝36-17

p＝19

Answer:

graph the line -2x+3 as a dotted line and shade in below that line.

Step-by-step explanation:

Linear inequalities are an inequality... which contain linear equations. To graph these linear inequalities it helps to first just graph the linear equation and then based on the inequality whether it's less than, less than or equal to, greater than, or greater than or equal to we would draw above or below this line and with a solid or dotted line.

So we're given the equation: [tex]y < -2x+3[/tex] it helps to first just graph the -2x + 3, which we can do by starting at the y-intercept of 3 and then going down 2 and going right 1 as defined by the slope -2. Likewise we can go up 2 and go left 1 from the y-intercept to define points to the left of the y-axis.

Now from here we look at the inequality: [tex]y < -2x+3[/tex], it's telling us y values less than -2x + 3, so we want to be below the line we just graphed, so shade below the line. One thing to note is it's a less than and not a less than or equal to so the line it self is not included, meaning we draw a dotted line.

I included a desmos graph which further illustrates how this would look.

Answer:

The dimensions of the garden are not provided in the question, so it is not possible to determine the area for which Jane needs to buy mulch. Without knowing the dimensions, there is not enough information to answer the question.

Step-by-step explanation:

perpendicular means the opposite inverse of a slope

so the slope of the other line is -7/2

y = -7/2x + b

from the given point (-4,6)

6 = (-7 *4)/2 + b

6 = -14 +b

b = 20

y = -7/2x + 20

The estimate of the total number of litter complaints for planet Yellow is:

Between 3,835 and 20,800 complaints.

The average number of complaints about litter from the sample of 250 cities is 3.2 ± 0.59. This means that the actual number of complaints could be anywhere from 2.61 to 3.79. To estimate the total number of complaints for all 6,500 cities on planet Yellow, we need to multiply the sample average by the number of cities.

If we assume the lower end of the sample average (2.61), then the total number of complaints would be:

2.61 x 6,500 = 17,065

If we assume the upper end of the sample average (3.79), then the total number of complaints would be:

3.79 x 6,500 = 24,935

So the total number of complaints for planet Yellow is estimated to be between 17,065 and 24,935, which is equivalent to the range of:

Between 3,835 and 20,800 complaints.

Answer:

The future value of the annuity is $14,170.

The total amount invested is $39,000.

The interest earned is $14,170 - $39,000 = -$24,830

Step-by-step explanation:

The future value of the annuity can be calculated using the formula:

FV = P * (1 + r)^n

where FV is the future value, P is the annual payment, r is the annual interest rate, and n is the number of years.

In this case, the annual payment is $13,000, the annual interest rate is 3%, and the number of years is 3. So, the calculation is:

FV = $13,000 * (1 + 0.03)^3

FV = $13,000 * 1.09

FV = $14,170

So, the future value of the annuity is $14,170.

How much was invested?

The annual payment is $13,000. We multiply that by the number of years of the investment, 3 years. The total amount invested is $39,000.

How much interest was earned?

We can calculate the interest earned by subtracting the total amount invested from the future value.

The interest earned is $14,170 - $39,000 = -$24,830

So, the future value of the annuity is $14,170, the total amount invested is $39,000 and the interest earned is -$24,830.

Answer:

Step-by-step explanation:

1/2*1/5=1/10

1/10x=6

x=6*10

x=60

Answer: 20 and 40

Step-by-step explanation: i how how to do math

Answer:

B.20

E.40

Step-by-step explanation:

The common multiples are 20 and 40.

Answer:

5 cookies and 4 brownies

Step-by-step explanation:

First, let's assign variable for cookies and brownies:

x= cookies

y= brownies

Now, let's create an equation with the information given to us:

[Note: "#of brownies + 8" equals the number of cookies because, in the question, we are told He bought 8 more cookies than brownies ]

cost of a brownie * #of brownies +  cost of a cookie * (#of brownies + 8 ) = $7.50

1.25y + 0.5x = 7.5

Since we want to solve the problem graphically, let's solve our equation for y, so it can be graphed:

1.25y + 0.5x = 7.5   [Subtract 0.5x from both sides]

1.25y = -0.5x + 7.5   [Divide both sides by 1.25 so we just get y]

y = -0.4x + 6

This equation will be used to determine what we can buy at the bakery with $7.50.

Now, we will graph the equation (see attached image). What we will see is that as x increases, y decreases. This makes sence, since the number of brownies (y) you can buy with your budget decreases as the number of cookies (x) you buy increases. Lastly, since we can't buy a fraction of a cookie, we want to find a coordinate on the line that has both a natural [see definition if confused] x and y value. To do this, we will look at the graph and see if a x value of 1 gives us a natural y value. If not, we go on to 2 and see if it gives us a natural y value. This continues until you find both a natural x and y value. This will happen at x=5 and y=4. This answer tells us that, with $7.50, Qasim and his children bought 5 cookies and 4 brownies.

*Natural number: Positive, whole numbers

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The value of Sin2θ in 4th the quadrant is -8/5

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled

Given that, cosθ = √5/5, we need to find sin2θ

According to SOH, CAH, TOA;

cos θ = adjacent/hypotenuse

Finding the opposite

5² = opp² + √5²

opp²  = 25 - 5

opp² = 20

opp = 4√5

Sinθ = opp/hyp

Sin = 4√5/5

Sin2θ = 2sinθcosθ

Sin2θ = 2 × 4√5/5 ×√5/5

Sin2θ = 8/5

Since, the quadrant is 4th so, Sin2θ = -8/5

Hence, the value of Sin2θ in 4th the quadrant is -8/5

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The difference between the median and the range in the data set shown below is option A. 5.

What is mean ?

Mean can be defined as the ratio of sum of given observations and total number of observations.

The calculation is as follows:

Median is 7

As two numbers in the middle should be 8 and 6.

Now

= 8+ 6

= 14

It should be divided by 2 so it comes 7.

The range should be

= 13- 1

= 12

Now  the difference is  

= 12-7

= 5

Therefore, The difference between the median and the range in the data set shown below is option A. 5.

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Answer:

80 months

Step-by-step explanation:

If the present monthly heating costs average $300, but the insulation is expected to reduce heating costs by 10%, then there will be a monthly saving of 10%:

[tex]\implies \rm Monthly\;saving=10\%\;of\;\$300 =\dfrac{10}{100} \times \$300=\$30[/tex]

To calculate how many months it will take to recover the cost of the insulation, divide the cost of installing the insulation by the monthly saving:

[tex]\implies \rm Number\;of\;months=\dfrac{\$2400}{\$30}=80[/tex]

Therefore, it will take 80 months to recover the cost of the insulation.

Answer:

80 months

Step-by-step explanation:

The expected monthly savings from the insulation are: $300 × 10% = $30.

So, the number of months required to recover the cost of the insulation, $2400, is $2400/$30 = 80 months.

From the given triangle, the value of sin Θ is 3/√34.

To find the value of sin Θ, we have to know the definition of sin Θ first. Sin Θ can be calculated using formula of:

sin Θ = the front side : the hypotenuse

Based on the given triangle, we need to find the lenght of hypotenuse first to be able to find the value of sin Θ. The hypotenuse of the given triangle is:

h = √(5² + 3²)

h = √(25 + 9)

h = √34

The exact value of sin Θ is:

sin Θ = 3 / √34

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An Inequality for the statement is -4y ≤ -2/3.

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given statement,

Number y multiplied by -4 is no more than -2/3

which means

- 4 y is less or equal to -2/3 and can be written as inequality

-4y ≤ -2/3

Hence, -4y ≤ -2/3 is the Inequality for the given statement.

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Answer:

You're right

Step-by-step explanation:

I don't think it can be anything else

16.25 percent the total number of students on the honor roll decreased.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, last year at a certain high school, there were 140 boys on the honor roll and 100 girls on the honor roll.

This year, the number of boys on the honor roll decreased by 25% and the number of girls on the honor roll decreased by 6%.

So, the number of boys = 140 - 25% of 140

= 140 - 0.25×140

= 140 - 35

= 105

The number of girls = 100 - 6% of 100

= 96

Total number of students last year = 140+100

= 240

Total number of students this year = 105+96

= 201

Difference = 240-201

= 39

Now, percentage decrease = 39/240 ×100

= 0.1625×100

= 16.25%

Hence, 16.25 percent the total number of students on the honor roll decreased.

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By the synthetic division method, the polynomial x³ - 2x - 8 dividing by x - 2 will get a remainder -4.

Given the polynomial,

x³ - 2x - 8

dividing a polynomial by x - 2

Solution will be :

Coefficients are required for Synthetic Division.

As a result, the coefficients are :

1, 0, -2, -8

as well as we have x-2

2   1   0  -2   8

          2   4    4              

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

      1    2   2   -4

By synthetic division, the remainder is now -4.

Substituting  the polynomial in x = 2 the Remainder theorem yields the required remainder.

  = 2³ -2 x 2 - 8

  = 8 -4 -8

  = -4

Which is equivalent to synthetic division. Therefore the correct division is option B.

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Answer:

  B.  y = 5x

Step-by-step explanation:

You want to find the proportional relationship among the answer choices.

The hint shows you the proportional relationship is expressed by an equation that has a multiplier for x, with no added constants, and no exponents.

You find the answer to this question by matching the answer choices to the given form. There is only one match:

  y = 5x

The role of the media in a democracy is essential for a free and informed society.

Democracy is a form of government in which power is held by the people through their elected representatives. It is based on the principle of political equality and rule of law, where all citizens have an equal say in the decisions that affect their lives. It is a system of government in which citizens have the right to vote, stand for office, and participate in decision-making processes that shape their communities and the nation as a whole.

The media acts as a watchdog for the government, keeping them accountable and ensuring that the people are aware of the decisions being made. It also provides a platform for citizens to express their opinions and to discuss important issues. Additionally, the media can help to educate the public on important topics, such as politics, economics, and social issues. This helps to ensure that citizens are well informed and can make informed decisions when voting or engaging in other forms of political participation.

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let's say the front of the coin is T and the back is h

Step-by-step explanation:

th

tt

ht

hh

The equations of the tangent to the curve when x = 1 are;

[tex]y = 5\frac{1}{3}\cdot x - 1\frac{1}{3}[/tex]

[tex]y = 1\frac{1}{3} - \frac{1}{3} \cdot x[/tex]

The tangent to a curve at a point, is the line that best fits the rate of change of the curve at the specified point.

The equation to be differentiated in the question is; y² - 5·x·y + 4·x = 0

The derivative of the above equation using the differentiation of a product is as follows;

2·y·y' - (5·y + 5·x·y') + 4 = 0

2·y·y' - 5·y - 5·x·y' + 4 = 0

2·y·y' - 5·x·y' - 5·y + 4 = 0

y'·(2·y - 5·x) - 5·y + 4 = 0

The slope of the curve, therefore is; y' = (5·y - 4)/(2·y - 5·x)

At x = 1, we get;

y² - 5·y + 4 = 0

(y - 4)·(y - 1) = 0

At x = 1, y = 4 and y = 1

Therefore;

At (1, 4), y' = (5 × 4 - 4)/(2 × 4 - 5 × 1) = 16/3

The equation of the tangent is therefore;

y - 4 = (16/3)·(x - 1)

y = 16/3)·x - 16/3 + 4 = 16/3)·x - 4/3

The tangent at (1, 4) is; y = (16/3)·x - 4/3 = (5 1/3)·x - 1 1/3

At (1, 1), y' = (5 × 1 - 4)/(2 × 1 - 5 × 1) = 1/-3 = -1/3

The equation is therefore;

y - 1 = (-1/3)·(x - 1)

y = (-1/3)·x + 1/3 +  1 = 4/3 - (1/3)·x

The equation of a second tangent is; y = 4/3 - (1/3)·x = (1 1/3) - (1/3)·x

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Answer:

The firm's 2021 tax liability can be calculated as follows:

EBT (Earnings Before Taxes) = $168,300

Taxes = EBT * Corporate Tax Rate = $168,300 * 0.21 = $35,253.