Given the legs of a right triangle are 8 and 4, what is the measure of the hypotenuse?

98% confidence interval for the mean rate = [4.1437 , 4.4983]

We are given the interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia for one day ;

4.751, 4.373, 4.177, 4.676, 4.425, 4.228, 4.125, 4.251, 3.951, 4.192, 4.291, 4.414

Now, Firstly we will find the Mean of the above data, Xbar ;

Mean, Xbar = ∑ x ÷ n =

4.751 + 4.373 + 4.177 + 4.676 + 4.425 + 4.228 + 4.125 + 4.251 + 3.951 + 4.192 + 4.291 + 4.414 ÷ 12 = 4.321

Standard deviation, s = √ ∑(x - x bar)²÷ n-1 = 0.226.

Now, the pivotal quantity for the 98% confidence interval for the mean rate is;

P.Q = x bar - ц ÷ n - 1 ≈ tn - 1

where, Xbar = sample mean

s = sample standard deviation

n = sample size = 12

So, 98% confidence interval for the mean rate, μ is ;

P(-2.718 < t₁₁ <2.718) = 0.98

P(-2.718 <Xbar - μ σ√ⁿ < 2.718) = 0.98

P(Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar +  2.718 * ₈÷ √ⁿ ) = 0.98

98% confidence interval for μ = (Xbar - 2.718 * ₈÷ √ⁿ < μ Xbar +  2.718 * ₈÷ √ⁿ ) = 0.98

[4.321 - 2.718 * 0.226 ÷ √₁₂ , 4.321 + 2.718 * 0.226 ÷ √₁₂

                                  = [4.1437 , 4.4983]

Therefore, 98% confidence interval for the mean rate = [4.1437 , 4.4983]

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The statements about the function that are true include:

g(0) = 0

g(1) = -1

g(-1) = 1

From the information, the points include:

(x1, y1) = (-2, 2, 5).

(x2, y2) = (0, 0)

(x3, y3) = (2, 3, 5).

It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in the graph.

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Answer:

jupiter, Saturn, Uranus, neptune are all distance from sun

Step-by-step explanation:

Answer:

AU:

Merc-0.39

Venus-0.72

Earth- 1

Mars- 1.52

Jupiter - 5.20

Uranus - 19.1

Neptune - 30

Years:

Merc-0.24

Venus-0.61

Earth- 1

Mars- 1.88

Uranus - 84?(maybe)

Neptune - 165

Step-by-step explanation:

Edge

Answer:

x=9

Step-by-step explanation:

3/4x+2 1/4=9

3/4x=9-2 1/4

3/4x=6 3/4

4(3/4x)=4(6 3/4)

3x=27

x=9

Answer:

x = 9

Step-by-step explanation:

3/4 x + 2 1/4 = 9      subtract 2 1/4 from both sides of the equation

3/4  x = 6 3/4           now divide both sides by 3/4

x = 9

Triangle A was dilated by a scale factor of 1/3 and reflected over the x axis to form triangle A'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

Triangle A was dilated by a scale factor of 1/3 and reflected over the x axis to form triangle A'

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Answer:

b d e

Step-by-step explanation:

Answer:

1, 5

Step-by-step explanation:

-16/4=-4

10/5=2

1/2=1/2

-1/-3=1/3

-1/4/1/2=-1/2

The negative ones are your answer.

By using the concepts of relations and functions and based on the table given, the function presents the following relationship:

x → f(x)

7 → 95

Functions are relations between an input set named domain (x) and an output set named range (f(x)), that is:

x → f(x)

After a quick observation, for x = 7, then f(7) = 95. In more graphically manner, the function present the respective relation:

7 → 95

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Answer:

B) f≥0.2(375,000) +7,200

Step-by-step explanation:

≥ means 'at least'

Answer:

z = 6[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the altitude- on- hypotenuse theorem

(leg of large Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

z² = 8 × (8 + 1) = 8 × 9 = 72 ( take square root of both sides )

z = [tex]\sqrt{72}[/tex] = [tex]\sqrt{36(2)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex] = 6[tex]\sqrt{2}[/tex]

Answer:

[tex]z = 6 \sqrt{2} [/tex]

Step-by-step explanation:

The solution is in the image

The logarithm base 10 of the number 10 is 1

We have to find logarithm base 10 of number 10.

Therefore, using logarithm rule

logₐ a = 1

Hence,

log₁₀ 10 = 1

Therefore, logarithm base 10 of the number 10 is 1

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Answer:

1

Step-by-step explanation:

The reportable square footage for Kinsey's home = 2150square feet.

The main floor of Kinsey's home is 1,425 square feet.

The upper level is 875 square feet with one unfinished bedroom that measures 150 square feet.

The finished basement is 1,425 square feet with 7.5-foot ceilings.

That means the square footage of the upper floor plus the main floor (minus the unfinished laundry area).

Kinsey should report square feet (1425+875- 150)

= 2150square feet.

Hence, The reportable square footage for Kinsey's home = 2150square feet.

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Answer:

could u send a photo please

The value of the expression when evaluated is: 162.

To evaluate the expression, 6x^4y^3, substitute x = -1 and y = 3 into the expression and solve.

6(-1^4) × 3^3

6(1) × 27

6 × 27

162

The value of the expression, 6x^4y^3, is: 162.

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Answer:

108 km/hr

Step-by-step explanation:

45 minutes = 3/4 hours

1) Distance = speed × time

= 60 × 3/4

= 45 km

2) 20 minutes = 1/3 hours. So, 3/4 - 1/3 = 5/12 hours.

speed = distance / time

= 45 / 5/12

= 108 km/hr

Answer: 38.2 degrees

Step-by-step explanation:

[tex]b^2 = a^2 + c^2 - 2ac \cos B\\\\5^2 = 3^2 + 7^2 - 2(3)(7) \cos B\\\\25 = 58-42 \cos B\\\\-42 \cos B=-33\\\\\cos B=\frac{33}{42}\\\\B \approx 38.2^{\circ}[/tex]

The magnitude and direction of line UV is 19.7° South of West for 8.1 miles

The magnitude of the vector line UV is given by the length of the line UV,

d = √[(x₂ - x₁)² + (y₂ - y₁)²] where

Substituting the values of the variables intot he equation, we have

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

d = √[(-2 - 2)² + (-4 - 3)²]

d = √[(-4)² + (-7)²]

d = √[4² + 7²]

d = √[16 + 49]

d = √65

d = 8.06 miles

d ≅ 8.1 miles

So, the magnitude of vector line UV is 8.1 miles

The direction of the vector line UV is given by Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)] where

Substituting the values of the variables into the equation, we have

Ф = tan⁻¹[(y₂ - y₁)/(x₂ - x₁)]

Ф = tan⁻¹[(-4 - 3)/(-2 - 2)]

Ф = tan⁻¹[(-7)/(-4)]

Ф = tan⁻¹[7/4]

Ф = tan⁻¹[1.75]

Ф = 60.26°

Ф ≅ 60.3°

Its bearing from the north-south line is α = 90° - Ф

= 90° - 60.3°

= 19.7°

So, its direction is 19.7° South of West

So, the magnitude and direction of line UV is 19.7° South of West for 8.1 miles

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For the function f(x) = 4|x - 3| + 4, we have that:

The x-intercept of a function is the value of x when y = f(x) = 0, hence:

0 = 4|x - 3| + 4

4|x - 4| = -4

|x - 4| = -1

The absolute value cannot be negative, hence the function has no x-intercepts.

The x-intercept of a function is the value of y = f(x) when x = 0, hence:

f(0) = 4|0 - 3| + 4 = 12 + 4 = 16.

The y-intercept is of y = 16.

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Step-by-step explanation:

[tex] \frac{x}{12} = \frac{x + 4}{5 + 12} \\ [/tex]

[tex] \frac{x}{12} = \frac{x + 4}{17} \\ [/tex]

Now cross multiply...

[tex]12(x + 4) = 17x[/tex]

[tex]12x + 48 = 17x[/tex]

[tex]12x - 17x = - 48[/tex]

[tex] - 5x = - 48[/tex]

Now divide both term by same number

[tex] \frac{ - 5x}{ - 5} = \frac{ - 48}{ - 5} \\ [/tex]

[tex]x = 9.6[/tex]

The solution of the equations will be the point of intersection of the two lines

A line is the shortest distance between two points. The equation of a line in standard form is given as Ax + By = C

According to the question, we are to pot the following lines.

4y +3x = 0

4y - x = 16

The solution of the equations will be the point of intersection of the two lines as attached.

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Answer:

0.1359

Step-by-step explanation:

There are 1,16,280 different recital programs possible.

Given: A pianist plans to play 4 pieces at a recital from her repertoire of 20 pieces and is carefully considering which song to play first, second, etc.

It means the repetition of pieces is not allowed.

When repetition is not allowed, then the number of ways to arrange n things where r things taken together is given by:-

[tex]^{n} P_{r} =\frac{n!}{(n-r)!}[/tex]

Now, the number of different recital programs are:-

[tex]^{20} P_{4} =\frac{20!}{(20-4)!}=\frac{20*19*18*17*16!}{16!}=116280[/tex]

Hence, there are 1,16,280 different recital programs possible.

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Answer:

-20

Step-by-step explanation:

-5-5-5-5=-20

Answer:

I would say b since this would tell him how many people are wiling to join a health club

Hope This Helps!!!

Answer:

16 Liters of the correct answer.

Emil started his lemonade stand with 12 litres of Lemonade.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that:-Emil is running a lemonade stand. He sells half of his lemonade in the morning, a quarter of what was left at lunchtime, and a third of what was left in the afternoon.

When he closes for the day, he has 4 litres of lemonade left. Let the total lemonade he started with is x litres. Now we will form an expression from the given data to calculate the value of x.

x - (x/2) -(1/4)(x/2) - ( 1/4)(x/2)(1/3) = 4

x - ( x/2) - (x/8) - ( x/24) = 4

[ 24x -12x -3x - x][24] = 4

8x  =  96

x = 12 liters

Therefore Emil started his lemonade stand with 12 liters of Lemonade.

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[tex]f(x )= - 2x[/tex]

[tex]g(x) = \frac{1}{2} x {}^{2} + 5[/tex]

#1

Domain

Range

#2

Domain

Range

#3

Its graphed

Domain=Range=(-oo,oo)

#4

Domain

Range

[-3,-oo) or (-oo,-3]

Answer:

y = [tex]\frac{7}{6}[/tex] x - 3

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 = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (9, 2 ) and (x₂, y₂ ) = (3, - 5 )

m = [tex]\frac{-5-2}{3-9}[/tex] = [tex]\frac{-7}{-6}[/tex] = [tex]\frac{7}{6}[/tex]

• Parallel lines have equal slopes , so

m = [tex]\frac{7}{6}[/tex] is the slope of the parallel line

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = [tex]\frac{7}{6}[/tex] x - 3 ← equation of parallel line

Hey there!

[tex] \\ [/tex]

[tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}[/tex]

[tex] \\ [/tex]

To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.

Let the line that we are trying to determine its equation be [tex] \: \sf{d_1} \: [/tex] and the line that is parallel to [tex] \: \sf{d_1} \: [/tex] be [tex] \: \sf{d_2} \: [/tex] .

[tex] \sf{d_2} \:[/tex] passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:

[tex] \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{y_2} - \orange{y_1}}{\red{x_2} - \blue{x_1 }}} [/tex]

[tex] \\ [/tex]

⇒Subtitute the values :

[tex] \sf{(\overbrace{\blue{9}}^{\blue{x_1}}\: , \: \overbrace{\orange{2}}^{\orange{y_1}}) \: \: and \: \: (\overbrace{\red{3}}^{\red{x_2}} \: , \: \overbrace{\green{-5}}^{\green{y_2}} )} [/tex]

[tex] \implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}[/tex]

[tex] \sf{\bold{The \: slope \: of \: both \: lines \: is \: \dfrac{7}{6}}} [/tex].

Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:

Slope-Intercept Form:

[tex] \sf{y = mx + b} \\ \sf{Where \: m \: is \: the \: slope \: of \: the \: line \: and \: b \: is \: the \: y-intercept.} [/tex]

[tex] \implies \sf{y = \bold{\dfrac{7}{6}}x + b} [/tex] [tex] \\ [/tex]

We know that the coordinates of the point (0 , -3) verify the equation since it is on the line [tex] \: \sf{d_1} \: [/tex]. Now, replace y with -3 and x with 0:

[tex] \implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Therefore, the equation of the line [tex] \: \bold{d_1} \: [/tex] is [tex] \green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}} [/tex]

[tex] \\ [/tex]

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a. Find the graph in the attachment

b. As h increases, e tends to 90°

Since you are standing 22 feet from a tall building that has a glass elevator on the exterior wall facing you. You watch the elevator as it ascends to the top of the building.

The height h (in feet) of the elevator above the ground can be modeled by h = 22tane.

To plot the graph, we see that the function is the tangent function.

The tangent function has the value -∞ ≤ tanx ≤ +∞ for -90° ≤ x ≤ 90°

Since e is our angle of elevation and e ≥ 0, that is 0 ≤ e ≤ 90°. So, we choose the range of values for which tane ≥ 0. So, 0 ≤ tane ≤ +∞

So, we plot h = 22tane for 0 ≤ e ≤ 90°

Find the graph in the attachment

From the graph, we seet that at high h or as h increases, e tends to 90°

So, as h increases, e tends to 90°

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The largest possible error in the area of the circle is of 44%.

The area of a circle of radius r is given by:

[tex]A = \pi r^2[/tex]

With a diameter of 20 cm = radius of 10 cm, the area in cm² is given by:

[tex]A = \pi \times 10^2 = 100\pi[/tex]

With the error, with a diameter of 20 x 1.2 = 24 cm = radius of 12 cm, the area in cm² is given by:

[tex]A = \pi \times 12^2 = 144\pi[/tex]

The error is given by:

[tex]E = 144\pi - 100\pi = 44\pi[/tex]

The percent error is the error divided by the initial amount, multiplied by 100%, hence:

[tex]P = \frac{44\pi}{100\pi} \times 100\% = 44\%[/tex]

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Answer:

No, the ratio is not the same.

Step-by-step explanation:

75 total (large tank) / 25 total (small tank) = 3

25 angelfish (large tank) / 5 angelfish (small tank) = 5

The ratio of angelfish to total fish is not the same. When we scale up from the small tank to large tank in terms of total fish, we have a factor of 3. However, when we scale up from the small tank to large tank in terms of angelfish, we have a factor of 5. For the ratio to be the same, these factors would need to be identical.

Using proportions, it is found that the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Each lb has 0,0005 tons. Hence the total weight in tons that we want to put in the elevator is:

T = (175 + 240 + 80 x 50) x 0.0005 = 2.2075 tons.

Hence, the elevator will be safe, as the total weight of 2.2075 tons is less than the maximum load restriction of 2.5 tons.

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