Janis wants to carpet her living room. Which means 15 feet by 12 feet. She picked out a nice style that Cost $2 per square foot How much will it cost.
Pls help

To find the height of the square pyramid, we can use the Pythagorean theorem. The slant height of the pyramid (s) is the hypotenuse of a right triangle formed by the height (h), half the length of the base (b/2), and the slant height.

Using the Pythagorean theorem:

s^2 = (b/2)^2 + h^2

We are given that the length of one of the base sides (b) is 23.8 and the slant height (s) is 89.3.

Plugging in the values:

89.3^2 = (23.8/2)^2 + h^2

Simplifying:

h^2 = 89.3^2 - (23.8/2)^2

h^2 = 7950.49 - 141.64

h^2 = 7808.85

Taking the square root of both sides:

h = √7808.85

h ≈ 88.37

Therefore, the height of the square pyramid is approximately 88.37 inches.[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

Based on the data, we can infer that the park with the highest fee is Coaster City.

To find the value of each park we must take into account the different tables that show the value of each park. In this case we must find the unit value of each park as follows:

Park 1:

Park 2:

Park 3:

In accordance with the above, we can infer that the 2 Coaster City park is the one with the highest rate.

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Answer: Amplitude is 108 degrees

Step-by-step explanation:

To determine the amplitude of the tip of King Arthur's Sword, we need to understand the shape of the sword's blade, which consists of a regular hexagon and a regular pentagon.

A regular hexagon has six equal sides and six equal angles, each measuring 120 degrees. The regular pentagon, on the other hand, has five equal sides and five equal angles, each measuring 108 degrees.

Since the tip of the sword is formed by the meeting point of the hexagon and pentagon, it will be at the apex of the pentagon. The apex of the pentagon will have an angle of 108 degrees.

I hope this helps!!!

The degrees of freedom is 21, the critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas and chi-square test statistic is 27.

The null and alternative hypotheses can be stated as follows:

Null Hypothesis (H0): The population variance is equal to 14.

Alternative Hypothesis (Ha): The population variance differs from 14.

To find the critical values of χ2 with α = 0.05, we need to determine the degrees of freedom first.

For a sample variance, the degrees of freedom (df) is given by (n - 1), where n is the sample size.

In this case, n = 22, so the degrees of freedom is 21.

Using a chi-square table or statistical software, we can find the critical values for a chi-square distribution with 21 degrees of freedom and α = 0.05.

The critical values correspond to the points where the chi-square distribution curve separates the rejection and non-rejection areas.

To determine the test statistic χ2 value, we need to calculate the chi-square test statistic using the given information.

The chi-square test statistic is calculated as:

χ2 = (n - 1) ×(sample variance) / (population variance)

Plugging in the values, we have:

χ2 = (22 - 1) × 18 / 14

=27

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Answer:

8x is your answer.

Step-by-step explanation:

The photo shows how it's solved.

Answer:

The median is the middle value in the set. Since there are 5 values in this set, the middle value is the third value, which is 6.

Therefore, the median of the set {2, 4, 6, 8, 10} is 6.

Answer:

x = 12

Step-by-step explanation:

sin45 = x/17         (sin = opposite/hypotenuse)

x = (sin45)(17) = 12.02 ≈ 12

The transformed vertices are;

A''  => (-7, -1)

B''  => (-7, 4)

C''=> (-9,4)

D''=> (-9, -1)

Here, we have,

given that,

we have to translate by (x,y) => (x-5, y+4)

so, the rectangle will be transformed as;

the transformed vertices are;

A' => ( 4-5, 3+4) => (-1, 7)

B' => (9-5, 3+4) => (4,7)

C'=>(9 -5, 5 +4 ) => (4, 9)

D'=> (4 -5, 5+4 ) => (-1, 9)

now, For clockwise rotation of a triangle by 90 degree, then x coordinate is similar to the y coordinate of original point and y coordinate is negative times of x coordinate of original point.

So (x,y) changes to (-y,x).

the transformed vertices are;

A'' => ( 4-5, 3+4) => (-1, 7) => (-7, -1)

B'' => (9-5, 3+4) => (4,7) => (-7, 4)

C''=>(9 -5, 5 +4 ) => (4, 9) => (-9,4)

D''=> (4 -5, 5+4 ) => (-1, 9)=> (-9, -1)

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The two other positive angles of rotation that take Point A to Point B on the unit circle is (5π/6) and (5π/6) + 2π .

Given data ,

To find two other positive angles of rotation that take Point A to Point B, we need to consider the angle values that yield the same coordinates as (1, 0) after rotating counterclockwise.

The position of Point A is (1, 0) on the unit circle.

Now, let's find the coordinates of Point B after rotating (7π/6) radians counterclockwise.

To rotate counterclockwise by (7π/6) radians, we can subtract (7π/6) from the angle of Point A. So, the angle for Point B would be:

Angle of Point B = 0 - (7π/6) = - (7π/6)

Now , for positive angles of rotation, we can add multiples of 2π to the angle of Point B while keeping the same coordinates. Adding 2π to the angle gives us:

Angle of Point B = - (7π/6) + 2π = (5π/6)

Hence , two other positive angles of rotation that take Point A to Point B are (5π/6) and (5π/6) + 2π. Both of these angles yield the same coordinates as Point B, which is (1, 0) on the unit circle.

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The probability of accepting the whole shipment is 0.9093. Therefore, almost all such shipments will be accepted.

The probability that the whole shipment will be accepted is calculated as follows;

First, we calculate the probability of having at most 3 batteries that do not meet specifications out of the 40 randomly tested batteries.

Assuming:

We can use the binomial probability formula to calculate the probability:

[tex]P(X \leq k) = \sum (from\: i = 0 \:to\: k) [(nCi) * p^{i} * q^{(n-i)}][/tex]

P(X ≤ 3) = [(⁴⁰C₀) * (0.03⁰) * (0.97⁴⁰] + [(⁴⁰C₁) * (0.03¹) * (0.97³⁹)] + [(⁴⁰C₂) * (0.03²) * (0.97³⁸)] + [(⁴⁰C₃) * (0.03³) * (0.97³)]

P(X ≤ 3) = 0.9093.

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The amplitudes of functions are a) 8 and b) 6.

Given are the functions we need to determine the amplitude of function,

a) y = 8 Sin (x/2) + 3

b) y = 6 Cos x + 2

So,

To determine the amplitude of a trigonometric function, you can follow these steps:

For a sine function of the form y = A×sin(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

For a cosine function of the form y = A×cos(Bx + C) + D:

The amplitude is equal to the absolute value of the coefficient A.

Let's apply these steps to the given functions:

a) y = 8×sin(x/2) + 3

The coefficient of sin in this function is 8, so the amplitude is |8| = 8.

Therefore, the amplitude of function a) is 8.

b) y = 6×cos(x) + 2

The coefficient of cos in this function is 6, so the amplitude is |6| = 6.

Therefore, the amplitude of function b) is 6.

Hence the amplitudes of functions are a) 8 and b) 6.

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Answer:

44 m2

Step-by-step explanation:

The area of the rhombus can be divided into 4 equal triangles.

The area of one triangle is A=bh/2

so:

A = 5.5*2

A = 11 squared m

Since there are four (4) triangles in the rhombus we just need to multiply 11 by 4 so:

A = 11 * 4

A = 44 squared m

Answer:

The volume is 423.33 cubic millimeters.

Step-by-step explanation:

The formula for volume of a cylinder is given by:

V = πr^2h, where

Step 1:  Find radius, r, of the cylinder:

The diagram shows us the diameter, d, of the circle is 7 mm.  Since the diameter is twice the radius, r, we can find r by dividing the diameter by 2:

r = d / 2

r = 7 / 2

r = 3.5 mm

Thus, the radius of the cylinder is 3.5 mm.

Step 2:  Plug in values and round to the nearest hundredth to find the volume, V, of the cylinder:

Now we can plug in 3.5 for r and 11 for h to find V, the volume of the cylinder.  We can round at the end.

V = π(3.5)^2(11)

V = π(12.25)(11)

V = 134.75π

V = 423.3296101

V = 423.33 mm^2

Thus, the volume of the cylinder is 423.33 cubic millimeters.

Here is your answer!

Answer:

[tex](x - 5)^2 + (y + 2)^2 = 5[/tex]

Step-by-step explanation:

The equation of a circle with a center at (h, k) and radius r is given by:

[tex]\bold{(x - h)^2 + (y - k)^2 = r^2}[/tex]

In this case, the center is at (5, -2) and the point that the circle passes through is (4, 0).

The distance between the center and the point is:

[tex]\sqrt{(5 - 4)^2 + ((-2) - 0)^2} = \sqrt{1 + 4} = \sqrt{5}[/tex]

Therefore, the equation of the circle is:

[tex](x - 5)^2 + (y + 2)^2 = \sqrt{5}^2[/tex]

Simplifying the equation, we get:

[tex]\bold{(x - 5)^2 + (y + 2)^2 = 5}[/tex] is a required equation

The given triangle is a right angled triangle, therefore the rules of basic Trigonometry can be used here to find the solution.

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin(45 \degree) = \frac{opposite \:\: side}{hypotenuse} [/tex]

[ sin 45° = 1/√2 ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{ \sqrt{2} } = \frac{b}{x} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = b \sqrt{2} \: \: cm[/tex]

So, the side HG is b√2 cm long

The thermal energy of the first rock is twice the Thermal energy of the second rock.

The thermal energy of an object is directly proportional to its mass. Therefore, if the first rock has twice the mass of the second rock, it will also have twice the thermal energy.

Thermal energy is a measure of the internal energy of an object, which includes the kinetic energy of its particles. In this case, since both rocks are made of the same material and are at the same temperature, we can assume that their particles have the same average kinetic energy per particle.

The thermal energy of an object can be calculated using the formula:

Thermal energy = Mass * Specific heat capacity * Change in temperature

Since the specific heat capacity and the change in temperature are the same for both rocks (as they are made of the same material and are at the same temperature), we can simplify the comparison of their thermal energies based on mass alone.

Let's denote the mass of the second rock as "m" (arbitrary unit). Since the first rock has twice the mass, its mass can be represented as "2m".

Therefore, the thermal energy of the first rock is:

Thermal energy of the first rock = (2m) * Specific heat capacity * Change in temperature

And the thermal energy of the second rock is:

Thermal energy of the second rock = m * Specific heat capacity * Change in temperature

Comparing the thermal energies:

Thermal energy of the first rock / Thermal energy of the second rock = (2m) * Specific heat capacity * Change in temperature / (m) * Specific heat capacity * Change in temperature

The specific heat capacity and the change in temperature cancel out, leaving us with:

Thermal energy of the first rock / Thermal energy of the second rock = 2m / m = 2

Therefore, the thermal energy of the first rock is twice the thermal energy of the second rock.

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Answer:

A. 11.2

Step-by-step explanation:

But this has nothing to do with 5.6 × 2. Erase that! Lol.

You have a right triangle here. The only thing to do with the circle is that there are two radii (plural of radius) shown. So they have to be the same measure.

The unmarked "bottom" of the triangle, the short leg, is a radius, so it too, is 8.4.

The hypotenuse of the right triangle, the side on the right, the longest side is 5.6 + 8.4.

The hypotenuse is 14.

Let's do some Pythagorean Theorem.

Leg^2+ leg^2=hypotenuse^2

you know,

a^2 + b^2 = c^2

fill in what we know.

8.4^2 + b^2 = 14^2

simplify.

70.56 + b^2 = 196

subtract 70.56

b^2 = 125.44

squareroot both sides

b = 11.2

The area of shaded sector is,

⇒ Area of sector =  15.35 feet²

We have to given that,

In circle O,

⇒ Radius = 4 feet

And,  the central angle a measures 110°.

Since, We know that;

Area of sector = (θ/360) πr²

Where, θ is central angle and r is radius of circle,

Here., r = 4 and θ = 110°

Substitute the given values, we get;

Area of sector = (θ/360) πr²

Area of sector = (110/360) π (4)²

Area of sector = (0.30) π x 16

Area of sector =  4.89 x 3.14

Area of sector = 15.35 feet²

Thus, The area of shaded sector is,

⇒ Area of sector = 36π units²

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Answer:

[a] 12 units

Step-by-step explanation:

The answer is (D) 44 units

1. The formula for the area of a rhombus is A= [tex]\frac{d_{1} d_{2}}{2}[/tex]

2. Fill in the information we know:

3. Now work backward:

4. Solve it:

Hence 44 units (D) is your answer

The expression (r-s)(x) is 4x² - x + 5, (r.s)(x) is 4x³ - 20x² and value of (r-s)(-1) is 10.

To find the expression (r-s)(x), we subtract the function s(x) from the function r(x):

(r-s)(x) = r(x) - s(x)

Substituting the given functions, we have:

(r-s)(x) = 4x² - (x-5)

Simplifying further:

(r-s)(x) = 4x² - x + 5

To find the expression (r.s)(x), we multiply the functions r(x) and s(x):

(r.s)(x) = r(x) × s(x)

Substituting the given functions, we have:

(r.s)(x) = (4x²)×(x-5)

Expanding and simplifying:

(r.s)(x) = 4x³ - 20x²

Now, let's evaluate (r-s)(-1) by substituting x = -1 into the expression (r-s)(x):

(r-s)(-1) = 4(-1)² - (-1) + 5

(r-s)(-1) = 4 - (-1) + 5

(r-s)(-1) = 4 + 1 + 5

(r-s)(-1) = 10

Therefore, (r-s)(-1) equals 10.

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Answer:

Step-by-step explanation:

Given the following quadratic sequences, you want the value of x and the expression for the n-th term.

One way to determine x is to look at the differences between terms. The "second difference" is constant for a quadratic sequence, and the third difference is zero.

The quadratic equation for the n-th term can be found by solving for its coefficients. The three known values of the sequence can give rise to three linear equations in the three unknown coefficients. These can be solved by your favorite method. We use this approach in the following.

First differences are the differences between each term and the one before:

  {6, x-5, 35-x}

Second differences are the differences of these:

  {x -11, 40 -2x}

Third differences are zero:

  51 -3x = 0   ⇒   x = 17

The value of x is 17.

The expression for the n-th term of the sequence can be written as ...

  an = a·n² +b·n +c

We are given values of a1, a2, and a4. This lets us write 3 equations for a, b, and c. The solution of those is shown on the first line of the first attachment. (The second line shows the evaluation of this quadratic equation for n=3. It gives 17, which we already knew.)

  an = 3n² -3n -1

The last line of the first attachment shows us the expression for the third differences. The value of that is zero, so ...

  -3x +60 = 0   ⇒   x = 20

The value of x is 20.

As in the above problem, the matrix of equations for the quadratic coefficients can be reduced to give the coefficient values. That tells us the n-th term of this sequence is ...

  an = 3n² -4n +5

The last line in the second attachment tells us this expression for the n-th term properly computes the 3rd term (x), as above.

__

Additional comments

You can also use quadratic regression to find the coefficients of the formula for the quadratic sequence. This is shown in the 3rd attachment.

If you're trying to avoid using a calculator, you can write the equations out and solve them in an ad hoc way. In case you cannot tell, the equations for the coefficients of an = a·n² +b·n +c for the first problem are ...

You can also use the first values of the sequence (p), first difference (q), second difference (r) to write the quadratic:

  an = p +(n -1)(q +(n -2)/2(r))

For (p, q, r) = (-1, 6, 6), this is an = -1 +(n -1)(3n) . . . . . . for the first sequence.

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Answer:

5:52

Step-by-step explanation:

Answer: 5:52

Step-by-step explanation:

Answer:

Step-by-step explanation:

first, to find if they are perpendicular, we would have to determine their slopes.

y=-2x-1, we know that the slope is -2 (due to y=mx+b, where m is the slope)

y=-2x+6, we also know that the slope is -2.

since the slope is equal, it would be parallel.

However, if the slopes were negative reciprocals, (e.g. 1/2 & -2) they would be perpendicular.

If the slopes were neither negative reciprocals or equal, it would be neither.

There is 90% confidence that the population mean number of books people read is between 11.55 and 13.25.

To construct a 90% confidence interval for the mean number of books people read, we can use the following formula:

Confidence Interval = x ± (Z * (s / √n))

Where:

x = sample mean (12.4 books)

s = sample standard deviation (16.6 books)

n = sample size (1017)

Z = Z-score

Since the sample size is large (n > 30), we can assume the sampling distribution is approximately normal.

We can use the standard normal distribution to find the Z-score for a 90% confidence level.

The Z-score for a 90% confidence level is approximately 1.645.

Now we can calculate the confidence interval:

Confidence Interval = 12.4 ± (1.645  (16.6 / √1017))

Confidence Interval ≈ 12.4 ± (1.645  (16.6 / √1017))

Confidence Interval ≈ 12.4 ± (1.645  (16.6 / 31.95))

Confidence Interval ≈ 12.4 ± (1.645 x 0.518)

Confidence Interval ≈ 12.4 ± 0.85

There is 90% confidence that the population mean number of books people read is between 11.55 and 13.25.

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The measure of unknown angles,

∠1  = ∠4 = 110 degree

∠2 = ∠3 = 70 degree

Labeling the figure,

Then from figure we have,

⇒ x + 40 + x = 180

⇒     2x + 40 = 180

Subtract 40 both sides,

⇒            2x  = 140

Divide both sides by 2

⇒              x  = 70

From figure,

⇒ ∠1 + 70 = 180

⇒         ∠1 = 180 - 70

⇒         ∠1 = 110 degree

And from figure,

⇒ ∠1 + ∠2 = 180

⇒ 110 + ∠2 = 180

⇒          ∠2 =  70 degree

Since,

∠2 = ∠3 = 70 degree

And  ∠1  = ∠4 = 110 degree

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The correct answer is 86.08, as the octagon is given and the apothem given here is 13 units. The calculation after putting the value in formula is  86.08.

An octagon is a polygon with eight sides and eight angles. It is a two-dimensional geometric shape.  Each angle in a regular octagon measures 135 degrees, and all sides of a regular octagon are of equal length.

The formula is given below,

P= side length ×n

Apothem of octagon =13 units,

side length is = tan (360° / (2 × 8)) = (n/2) ÷ 13

= tan (360° / (2 × 8)) = n/26

tan 22.5°= n/26

n/26 =  0.4142

n = 10.76

perimeter of octagon = 8 ×  10.76 = 86.08

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The total amount of money shared by Lee and Olivia is £132 and  Lee and Olivia shared £84 and £48, respectively.

Lee has 7/11 of the total money, which means Lee has (7/11) × x amount of money.

When Lee gives Olivia £18, they have the same amount of money.

So Olivia's share becomes equal to Lee's share.

Therefore, we can set up the following equation:

(7/11) × x - £18 = (1/2)×x

To solve this equation, we can simplify it:

7x/11 - £18 = x/2

Multiplying both sides of the equation by 22 (the least common multiple of 11 and 2) to eliminate the denominators:

14x - 22 × £18 = 11x

14x - 396 = 11x

Subtracting 11x from both sides:

14x - 11x - 396 = 0

3x - 396 = 0

Adding 396 to both sides:

3x = 396

Dividing both sides by 3:

x = 396/3

x = 132

To find Lee and Olivia's individual shares, we can substitute this value back into the initial conditions:

Lee's share = (7/11)× £132 = £84

Olivia's share = £132 - £84 = £48

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The test statistic χ² is approximately 1.47.

We have,

To test independence for the contingency table, we need to calculate the test statistic.

The most commonly used test statistic for testing independence in a 2x2 contingency table is the chi-square test statistic.

The chi-square test statistic (χ²) is calculated using the formula:

χ² = Σ [(Observed - Expected)² / Expected]

Where:

Σ represents the sum over all cells of the contingency table.

Observed is the observed frequency in each cell.

Expected is the expected frequency in each cell if the variables were independent.

First, we calculate the expected frequencies for each cell. To do this, we use the formula:

Expected frequency = (row total x column total) / grand total

Grand total = sum of all frequencies = 36 + 17 + 15 + 11 = 79

Expected frequency for the cell "Closed roof - Win" = (53 * 51) / 79 = 34.49

Expected frequency for the cell "Closed roof - Loss" = (53 * 28) / 79 = 18.51

Expected frequency for the cell "Open roof - Win" = (26 * 51) / 79 = 16.51

Expected frequency for the cell "Open roof - Loss" = (26 * 28) / 79 = 9.49

Now, we can calculate the test statistic using the formula:

χ² = [(36 - 34.49)² / 34.49] + [(17 - 18.51)² / 18.51] + [(15 - 16.51)² / 16.51] + [(11 - 9.49)² / 9.49]

Calculating each term and summing them up:

χ² ≈ 0.058 + 0.482 + 0.58 + 0.35 ≈ 1.47

Therefore,

The test statistic χ² is approximately 1.47.

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The height of the tallest triangle on the actual bridge is 12 feet.

If James made a model of a truss bridge with a scale of 1 inch = 4 feet, we can use this information to find the height of the tallest triangle on the actual bridge.

Let x be the height of the tallest triangle on the actual bridge. Since the scale of the model is 1 inch = 4 feet, the height of the tallest triangle on the model can be converted to feet by multiplying by 4. Therefore, the height of the tallest triangle on the model is:

9 inches * (1 foot / 12 inches) * 4 = 3 feet

We can use the similarity of triangles to set up a proportion to find x. The corresponding sides of similar triangles are proportional. In this case, the height of the triangle on the model corresponds to the height of the triangle on the actual bridge, and the scale factor from the model to the actual bridge is 1/4 (since 1 inch on the model represents 4 feet on the actual bridge). Therefore, we have:

height of triangle on model / height of triangle on actual bridge = scale factor

3 feet / x = 1/4

Multiplying both sides by x, we have:

3 feet = (1/4) x

Multiplying both sides by 4, we have:

12 feet = x

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