One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the
third angle is 50 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.

Answer:

10.4

Step-by-step explanation:

cosine rule=\(a^{2}=b^{2} +c^{2} -2bc*cosa\)

                \((2\sqrt{3}) ^{2}=(x+2)^{2} +x^{2} -2(x+2)x*cos60\\12=x^{2} +4x+4+x^{2} -2x^{2} -4x*\frac{1}{2}\\2x-8=0\\x=4\\Area=\frac{1}{2}absinc\\ = \frac{1}{2}*6*4*sin60\\\\ =6\sqrt{3}\\=10.4(3 sig.fig)\)

The t value will be the result that is  58.851995039

The t-statistic for the observed correlation coefficient of 0.951 can be calculated to determine if it is statistically significant. Using the T.INV() spreadsheet function and the appropriate degrees of freedom.

We can test the null hypothesis of no correlation at the 5% significance level. Additionally, the T.DIST() function can be used to calculate the p-value of the t-statistic.

To calculate the t-statistic, we need to know the sample size (n) and the observed correlation coefficient (r). In this case, we have 37 monthly observations and a correlation coefficient of 0.951. The t-statistic can be calculated using the formula t = r x sqrt((n - 2) / (1 - r^2)). Plugging in the values, we find t = 0.951 x sqrt((37 - 2) / (1 - 0.951^2)).

By comparing this t-statistic to the critical value at the desired significance level (5% in this case), we can determine if the null hypothesis of no correlation can be rejected. Additionally, the p-value can be calculated using the T.DIST() function to determine the probability of obtaining a t-statistic as extreme as the observed value. If the p-value is less than the chosen significance level, the null hypothesis can be rejected.

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Answer : \(22.000\) x \(10x^{3}\)

Step-by-step explanation:

Answer:22 x 10^3

Step-by-step explanation:

Given that the absolute value of the price elasticity of demand for Good X is 0.5, this indicates that the demand for Good X is inelastic. Now, let's analyze the effect of a 10 percent decrease in the price of Good X.

1. Calculate the percentage change in quantity demanded: Multiply the price elasticity of demand (0.5) by the percentage change in price (-10%).
  0.5 * (-10%) = -5%

2. Since the result is negative, this implies that the quantity demanded will increase by 5% due to the 10% decrease in price. This corresponds to option (b) in your list.

3. To determine the effect on revenues, we'll consider both the price and quantity changes. The price decreased by 10%, and the quantity demanded increased by 5%.

4. Calculate the new revenue: Initial revenue (100%) + price change (-10%) + quantity change (5%) = 95% of the initial revenue.

This means that there will be a 5% increase in revenues from the sale of Good X after the price decrease, which corresponds to option (c) in your list. So, the correct answer is (b) A 5% increase in the quantity demanded of Good X, and (c) A 5% increase in revenues from the sale of Good X.

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The cause-specific mortality rate from tuberculosis in Sample City in 2018 is approximately 1.7 per 1,000 population.

To calculate the cause-specific mortality rate from tuberculosis in Sample City in 2018, we need to divide the number of deaths caused by tuberculosis by the population size and then multiply the result by a constant factor (e.g., 1,000 or 100,000) to express it per a specific unit of population.

Given information:

Population of Sample City: 200,000

Number of deaths resulting from tuberculosis: 340

Cause-specific mortality rate from tuberculosis = (Number of deaths resulting from tuberculosis / Population) * Constant factor

Let's calculate the cause-specific mortality rate:

Cause-specific mortality rate = (340 / 200,000) * 1,000

Calculating the value:

Cause-specific mortality rate = 0.0017 * 1,000

≈ 1.7

Therefore, the cause-specific mortality rate from tuberculosis in Sample City in 2018 is approximately 1.7 per 1,000 population.

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Answer:

Step-by-step explanation:

\((x-h) ^2+(y-k) ^2 =r^2\)

The above equation is the general standard equation for the circle centered at (h,k) with radius r

Given that the equation of the circle is

\((x-2) ^2+(y+3) ^2 =25\)

Comparing this with the general equation we can get the center and the radius as

\((x-h) ^2+(y-k) ^2 =r^2\\(x-(2)) ^2+(y-(-3)) ^2 =5^2\)

We can now see that

h= 2

k= -3 and

r= 5

Answer:

25

Step-by-step explanation:

(a) The recursive definition of the sequence {on} is:

a₁ = 0 (base case)

an = 1 + (-1)ⁿ⁻¹ + an-1 (recursive rule)

(b) f(2) = 2, f(3) = 4, and f(4) = 4.

(a) Recursive definition of the sequence {on}:

To define the sequence {on} recursively, we need to provide the base case and the recursive rule.

Base case: a₁ = 1 + (-1)¹ = 1 - 1 = 0

Recursive rule: For n > 1, an = 1 + (-1)ⁿ⁻¹ + an-1

So, the recursive definition of the sequence {on} is:

a₁ = 0 (base case)

an = 1 + (-1)ⁿ⁻¹ + an-1 (recursive rule)

(b) Finding the values of f(2), f(3), f(4):

Given the recursive definition of the function f, we can use it to find the values of f(2), f(3), and f(4).

f(0) = -1 (given)

f(1) = 2 (given)

Using the recursive rule, we can calculate the values of f(2), f(3), and f(4):

f(2) = 1 + (-1)¹ + f(1) = 1 - 1 + 2 = 2

f(3) = 1 + (-1)² + f(2) = 1 + 1 + 2 = 4

f(4) = 1 + (-1)³ + f(3) = 1 - 1 + 4 = 4

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The smallest allowable thickness of the Styrofoam would be 0.98 times the desired thickness.

To find the smallest allowable thickness of the Styrofoam for facade insulation, we need to consider the 2% error allowed.

Let's assume the desired thickness is represented by x.

Since the error allowed is 2%, we can calculate the maximum acceptable error as (2/100) * x.

To find the smallest allowable thickness, we subtract the maximum acceptable error from the desired thickness: x - (2/100) * x.

Simplifying this expression, we get x(1 - 2/100) or x * 0.98.

Therefore, the smallest allowable thickness of the Styrofoam would be 0.98 times the desired thickness.

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Answer:

There is no solution

Step-by-step explanation:

\(\frac{1}{4} x-13= \frac{1}{4} x + \frac{13}{4}\)

subrtact 1/4 X from each side

-13=13/4 is not true, so no solution

The answer is C.) (0, 5)

Explaintion is in the pictures

I believe this is the answer if it isn't I'm sorry for wasting your time by answering.

Hope this helps!

\(Answer: \large\boxed{Cos(\theta_{1} )=\frac{84}{85}}\)

Step-by-step explanation:

Thinking about a triangle in Quadrant IV, we can imagine sin as opposite/hypotenuse. Therefore, the hypotenuse is 85 and the opposite angle is -13. To find the adjacent angle, we use the pythagorean theorum,

\(a^2+b^2=c^2\)

\(-13^2+b^2=85^2\)

\(169+b^2=7225\)

\(b^2=7056\)

\(b=\sqrt{7056}\)

\(b=\pm84\)

Taking only the positive number, the adjacent angle is 84

Now that we have all 3 sides, we can find the cosine.

Cosine is adjacent/hypotenuse

Therefore,

\(Cos(\theta_{1} )=\frac{84}{85}\)

See the attached picture:

Answer:

3-4 no 4-3=1

Step-by-step explanation:

this is the anwers

the length of the arc of the curve f(x) = 4x^2 + 5 on [2, 5) is approximately 24.79 units.

the surface area generated by revolving about the z-axis the curve f(x) = 2x^3 + 20/x on [1, 6] is approximately 1220.37 square units.

the volume of the solid formed by revolving D about the x-axis is approximately 5.58 cubic units.

the volume of the solid formed by revolving D about the y-axis is approximately 13.89 cubic units.

To find the length of the arc of the curve f(x) = 4x^2 + 5 on [2, 5), we need to use the formula for arc length:

L = ∫[a,b] sqrt(1 + [f'(x)]^2) dx

Taking the derivative of f(x), we get:

f'(x) = 8x

Plugging in f'(x) into the formula for arc length, we get:

L = ∫[2,5) sqrt(1 + (8x)^2) dx

Using a substitution of u = 1 + (8x)^2, we get:

du/dx = 16x

dx = du/16x

Substituting these into the integral, we get:

L = ∫[321, 1601) sqrt(u)/16x du

L = (1/128) ∫[321, 1601) u^(-1/2) du

L = (1/64) [u^(1/2)] [321, 1601)

L ≈ 24.79

Therefore, the length of the arc of the curve f(x) = 4x^2 + 5 on [2, 5) is approximately 24.79 units.

---

To find the surface area generated by revolving about the z-axis the curve f(x) = 2x^3 + 20/x on [1, 6], we need to use the formula for surface area of revolution:

A = ∫[a,b] 2πf(x) sqrt(1 + [f'(x)]^2) dx

Taking the derivative of f(x), we get:

f'(x) = 6x^2 - 20/x^2

Plugging in f(x) and f'(x) into the formula for surface area, we get:

A = ∫[1,6] 2π[2x^3 + 20/x] sqrt(1 + (6x^2 - 20/x^2)^2) dx

Using a substitution of u = 6x^2 - 20/x^2 + 1, we get:

du/dx = 12x + 40/x^3

dx = du/(12x + 40/x^3)

Substituting these into the integral, we get:

A = 2π ∫[7,217] (u-1)^(1/2)/6 du

Using a substitution of v = u - 1 and multiplying by 2π/6, we get:

A = π/3 ∫[6,216] v^(1/2) dv

A = π/3 [v^(3/2)/ (3/2)] [6,216]

A ≈ 1220.37

Therefore, the surface area generated by revolving about the z-axis the curve f(x) = 2x^3 + 20/x on [1, 6] is approximately 1220.37 square units.

---

To find the volume of the solid formed by revolving D about the x-axis, we need to use the formula for volume of solid of revolution:

V = ∫[a,b] π[f(x)]^2 dx

We can see that the region D is formed by the intersection of y

= 5x and y = x, so the bounds of integration are from x = 0 to x = 1.

Plugging in f(x) = (5x - x)^2 = 16x^2 into the formula, we get:

V = ∫[0,1] π(16x^2) dx

V = (16π/3) ∫[0,1] x^2 dx

V = (16π/3) [x^(3)/3] [0,1]

V = (16π/9)

Therefore, the volume of the solid formed by revolving D about the x-axis is approximately 5.58 cubic units.

---

To find the volume of the solid formed by revolving D about the y-axis, we need to use the formula for volume of solid of revolution:

V = ∫[a,b] π[f(x)]^2 dy

Since we have y = 5x and y = x, we can solve for x in terms of y to get the bounds of integration:

x = y/5 and x = y

So the bounds of integration are from y = 0 to y = 5.

Plugging in f(y) = (5y/4)^2 - (y/4)^2 = 24y^2/16 into the formula, we get:

V = ∫[0,5] π(24y^2/16)^2 dy

V = π(36/256) ∫[0,5] y^4 dy

V = (9π/64) [(y^5)/5] [0,5]

V = (1125π/256)

Therefore, the volume of the solid formed by revolving D about the y-axis is approximately 13.89 cubic units.

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Answer:

58.480766068854

Step-by-step explanation:

hope it will help you

Answer:

2 Tetrahedrons combined create an Octahedron.

Step-by-step explanation:

Despite the lack of information.

The Plato Polyhedrons are Tetahedron, Cube (Hexaedron), Dodecahedron, Octahedron and Icosahedron. They are regular ones, made up by regular plane figures.

An Octahedron can be built by combining two pyramids. Each Tetrahedron is made up by 4 equilateral triangle.

The solution to the linear function M(x) = 180 is of x = -5.

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

In this problem, the function is defined as follows:

M(x) = 120 - 12x.

M(x) represents the balance remaining on the gift card after x movie tickets priced at $12 are purchased.

The domain of the situation is given as follows:

x ≥ 0. {discrete}

As the number of tickets cannot assume negative neither decimal values.

The equation is:

M(x) = 180.

The solution is calculated as:

120 - 12x = 180

12x = -60

x = -60/12

x = -5.

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Answer:

23.225%

Step-by-step explanation:

Runtime in June (x1) = 7:45 = (7 * 60) + 45 = 465

Runtime in September (x2) = 5:57 = (5*60)+57 = 357

Percentage change in Runtime :

[|x2 - x1|÷ x1] * 100%

[|357 - 465| ÷ 357] * 100%

108 / 465 * 100%

0.23225 * 100%

= 23.225%

Answer:

12/12 is greater

Step-by-step explanation:

12/12= 1

4/6=0.66667

Answer:

12/12 because 4/6 as a decimal is 0.6 and 12/12 is 1.

Step-by-step explanation:

Answer:

\(\frac{-4+6}{2} , \frac{3+2}{2} =1,4\\\\\frac{6+6}{2} ,\frac{5+(-1)}{2} =6,2\\\\\frac{-4+6}{2} ,\frac{3+(-1)}{2} =1,1\)

Step-by-step explanation:

hope it helps have a nice day!!

Answer:

a) $520

b) $580

c) Interest amount is same each year

Step-by-step explanation:

Given - Georgie put $500 in her savings account, earning interest at a rate of 4% each year. She did not make any more deposits or withdrawals.

To find - a) How much money was in the account after one year?

              b) How much money was in the account after 4 years?

              c) Was the amount of money earned in interest the same or different each year?

Proof -

Here given that,

Principal amount = $500

rate of interest = 4% = 4/100 = 0.04

Now,

a)

Amount =  P [ 1 + RT ]

             = 500 [ 1 + 0.04(1)]

             = 500 [ 1 + 0.04] = 520

⇒Amount = $520

b)

Amount =  P [ 1 + RT ]

             = 500 [ 1 + 0.04(4)]

             = 500 [ 1 + 0.16] = 580

⇒Amount = $580

c)

In 2nd year,

Amount =  P [ 1 + RT ]

             = 500 [ 1 + 0.04(2)]

             = 500 [ 1 + 0.08] = 540

⇒Amount = $540

Now,

Interest in 1st year = 520 - 500 = 20

Interest in 2nd year = 540 - 520 = 20

So,

The interest amount  is same each year

The amount paid as a car loan is $19,500 at 6% compounded annually of the principal amount of $15,000.

The Amount is calculated by \(A=P(1+\frac{r}{n} )^{nt}\)

where A is the Amount

P is the Principal

r is the Interest rate (in decimals)

n is the frequency at which the interest is compounded per year

t is the Time duration

According to the question,

Principal = $15,000

interest rate = 6% compound annually

Since interest is compounded annually, n =1

Time duration = 6 years

Therefore,

\(A= 15,000*(1+\frac{0.06}{1})^{1*5}\\ = 15,000*(1+0.06)^{5}\\= 15,000*(1.06)^{5}\\= 15,000*1.3\\= 19,500\)

Hence, the amount paid is $19,500.

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Step-by-step explanation:

33+22+90=145

180-145=35

x=180-35

x=145

Answer:

24.

Step-by-step explanation:

The pattern is clearly going up by twos.

So continuing the pattern,

1, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

1 2  3   4 5   6   7   8   9   10  11    12   13

Using the plus 4 method, the 95% confidence interval for the difference in proportion of individuals developing a cold after viral exposure between the Echinacea and the placebo is (-0.158, 0.397). Based on this confidence interval, we can conclude that there is no significant difference in the proportion of individuals developing a cold between the Echinacea and the placebo groups.

To determine the 95% confidence interval for the difference in the proportion of individuals developing a cold between the Echinacea and placebo groups, we can use the plus 4 method for small sample sizes.

First, we calculate the proportions of individuals who developed a cold in each group.

In the placebo group, out of 103 subjects, 88 developed a cold, giving a proportion of 88/103 ≈ 0.854.

In the Echinacea group, out of 48 subjects, 44 developed a cold, giving a

proportion of 44/48 ≈ 0.91

Next, we add 2 to the number of successes and 2 to the total number of observations in each group to apply the plus 4 adjustment.

This gives us 90 successes out of 107 observations in the placebo group (0.841) and 46 successes out of 52 observations in the Echinacea group (0.885).

To calculate the 95% confidence interval, we can use the formula:

\(CI = (p1 - p2) \pm Z \times \sqrt{(p1(1-p1)/n1} + p2(1-p2)/n2)\)

where p1 and p2 are the adjusted proportions, n1 and n2 are the respective sample sizes, and Z is the critical value for a 95% confidence interval (approximately 1.96).

Substituting the values into the formula, we get:

\(CI = (0.841 - 0.885) \pm 1.96 \times \sqrt{((0.841(1-0.841)/107) + (0.885(1-0.885)/52))}\)

Calculating the values within the square root and the overall expression, we can find the lower and upper bounds of the confidence interval.

Interpreting the results, if we repeat this experiment many times and construct 95% confidence intervals, we can expect that approximately 95% of these intervals will contain the true difference in proportions

In this case, if the interval contains 0, it suggests that there is no significant difference between Echinacea and placebo in terms of the proportion of individuals developing a cold after viral exposure. However, if the interval does not include 0, it indicates a significant difference, suggesting that Echinacea may have an effect on reducing the likelihood of developing a cold.

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The expression which is equivalent to the given expression; 3(-5h-9) + 2 as required in the task content is; -15h + 25.

It follows from the task content that the expression which is similar to the given expression; 3(-5h-9) + 2 is to be determined.

Since the given expression is; 3(-5h-9) + 2; we have that;

By solving the parentheses by the distributive property;

-15h - 27 + 2

= -15h - 25.

Ultimately, the equivalent expression is; -15h - 25.

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Answer:

This is gebber gabber but yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

Refers to the attachment given below!

The external financing need when sales increase by 4 percent is equal to -$1473.

Total assets value = $48,900

Total debt = $21,750

Long term debt = $18,100

Equity = $27,150

Dividend paid = $1,925

Net income = $5,500

Sales increase by 4%

Calculate the increase in sales,

Increase in sales

= 4% of total sales

= 4% x (total assets - net working capital)

Net working capital

= Current assets - Current liabilities

= (Total assets ) - (Total debt - Long-term debt)

= $48,900  - ($21,750 - $18,100)

= $9050

Increase in sales

= 4% x ($48,900 - $9050)

= $1594

Total funds required for the increase in sales,

= Increase in sales + Increase in net working capital + Increase in total costs - Increase in retained earnings

Increase in net working capital

= Net working capital x Sales growth rate

= $9050 x 4%

= $362

Increase in total costs

= Total costs x Sales growth rate

= (Total assets - Owners' equity) x Sales growth rate

= ($48,900 - $27,150) x 4%

= $870.

Increase in retained earnings

= Net income x (1 - Dividend payout ratio)

= $5,500 x (1 - ($1,925/$5,500))

= $3575

Total funds required

= $1594 + $362 + $870 - $3575

= -$749

Calculate the external financing needed,

External financing needed

= Total funds required - Increase in long-term debt

Increase in long-term debt

= Long-term debt x Sales growth rate

= $18,100 x 4%

= $724

External financing needed

= -$749 - $724

= -$1473

Therefore, the external financing need is -$1473represents that the company does not require any external financing to support the increase in sales by 4%.

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