Find the surface area of the regular pyramid. Write your answer as a decimal.

A pentagonal pyramid. The base is labeled, Area of base is 84.3 square centimeters. The triangular faces have base 7 centimeters and height 9 centimeters.


cm2

Answer:

I think answer is D but it could be wrong not sure

There are 5040 different passwords that can be created from the word "Alabama" when using all the letters.

To calculate the number of different passwords that can be created from the word "Alabama," we need to consider the total number of permutations.

The word "Alabama" contains 7 letters. To find the number of different passwords, we need to calculate the number of permutations of these 7 letters.

The formula to calculate permutations is given by:

nPr = n! / (n - r)!

Where n is the total number of items (letters in this case), and r is the number of items selected (length of the password).

For the word "Alabama," let's assume we want to create passwords of length 7, using all the letters.

n = 7 (number of letters in "Alabama")

r = 7 (length of the password)

Using the formula, we can calculate the number of permutations:

7P7 = 7! / (7 - 7)!

= 7! / 0!

= 7! / 1

= 7 × 6 × 5 × 4× 3 × 2 × 1

= 5040

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In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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The polygons are not similar because they do not have a constant similarity ratio

From the question, we have the following parameters that can be used in our computation:

The polygons

To check if the polygons are similar, we divide corresponding sides and check if the ratios are equal

So, we have

Scale factor = 150/100 = 151/100

Scale factor = 1.5 = 1.51 --- false

Hence, the polygons are not similar

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The meaning of the amount his classmates spend on clothes is,

If the amount spent on clothes per month by all his classmates is leveled, that amount would be $46.

We have to given that,

The amount of money everyone spends buying snacks each month has a mean of $46.

Mean = Sum of observations / Total number of observation

Hence, It means that average amount of money spend by everyone is $46.

And, If the amount spent on snacks per month by all his classmates is leveled, that amount would be $46.

So, if some one paid more amount than $38, whereas some one paid less amount than $38.

It will be nullify by leveling the amount by all his classmate while calculating the mean.

So, Option 'D' is correct.

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The coordinates of P' after rotating triangle PQR counterclockwise by 270 degrees about the origin are P'(-3, 1).

To rotate a point counterclockwise about the origin, you can use the following rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

In this case, we want to rotate the triangle PQR 270 degrees counterclockwise. We can calculate the coordinates of each point after the rotation.

For point P(-1, -3):

x' = (-1) * cos(270°) - (-3) * sin(270°)

y' = (-1) * sin(270°) + (-3) * cos(270°)

We can simplify these equations using the values of cosine and sine for 270 degrees:

x' = (-1) * 0 - (-3) * (-1)

y' = (-1) * (-1) + (-3) * 0

Simplifying further:

x' = 0 - 3

y' = 1 + 0

x' = -3

y' = 1

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The measure of arc MN include the following: B. 45°.

In Mathematics and Geometry, the theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, the value of arc MN can be calculated as follows:

37= 1/2(arc MN + 29)

37(2) = arc MN + 29

74 = arc MN + 29

arc MN = 74 - 29

arc MN = 45 degrees.

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To multiply the given binomials, we use the distributive property. So, the multiplication of the given binomials (2√3x - 2) and (3√3x + 5) is 18x + 4√3x - 10.

Using the distributive property which is given as: (a+b) (c+d) = a*c + a*d + b*c + b*d.

To multiply the binomials (2√3x - 2) and (3√3x + 5), we need to apply the distributive property which will result in four different terms.

Using the distributive property: (2√3x - 2) (3√3x + 5)= (2√3x * 3√3x) + (2√3x * 5) - (2 * 3√3x) - (2 * 5)= 6√(3x*3x) + 10√3x - 6√3x - 10= 6√9x² + (10-6)√3x - 10= 6 * 3x + 4√3x - 10= 18x + 4√3x - 10.

Therefore, the multiplication of the given binomials (2√3x - 2) and (3√3x + 5) is 18x + 4√3x - 10.

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There is a unique solution (x = 0, y = 5) that satisfies both equations, the system of equations has one solution. There is a unique solution (x = 0, y = 5) that satisfies both equations, the system of equations has one solution.

To determine the number of solutions for the given system of equations:

y = -2x + 5

4y + x - 20 = 0

We can solve the system of equations using various methods such as substitution, elimination, or graphing. Let's solve it using the elimination method:

First, we'll multiply the first equation by 4 to make the coefficients of x in both equations equal:

4y = -8x + 20

4y + x - 20 = 0

Next, we'll subtract equation 1 from equation 2 to eliminate the y term:

(4y + x - 20) - (4y = -8x + 20)

This simplifies to:

x = 0

Now, we substitute this value of x back into the first equation to find the value of y:

y = -2(0) + 5

y = 5

we have found the values x = 0 and y = 5, which satisfy both equations simultaneously.

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The required answer is: it is not possible to determine Alvin's average paddling rate based on the given information.

Given that table of terms Distance, Rate and  Time

Against the current d r - 2 km/hr 8 hours

With the current d r + 2 km/hr 3 hours

To set up an equation to solve for Alvin's average paddling rate, we can use the formula: rate = distance/time.

For the first row : (r - 2 km/hr) = d/8.

For the second row: (r + 2 km/hr) = d/3.

To solve for r, we can equate the rates against the current and solve for r.

(r - 2 km/hr) = (r + 2 km/hr)

Simplifying the equation, we get: r - 2 = r + 2.

By solving this equation, we find that the "r" terms cancel out, resulting in -2 = 2, which is not a true statement. This indicates that there is no solution for Alvin's average paddling rate in this scenario.

Therefore, it is not possible to determine Alvin's average paddling rate based on the given information.

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This example demonstrates a two-step inequality where we first express the savings equation and then solve for the variable 'w' to determine the number of weeks needed to reach the savings goal.

Liam is saving money to buy a new video game console. He has already saved $50 and is saving $10 per week from his allowance. He wants to determine how many weeks it will take for his savings to reach at least $150.

Let:

number of weeks Liam saves = w

total amount of money he saves = S

Step 1: Express the first step of the problem as an inequality.

Liam saves $10 per week, so the amount of money he saves after w-weeks is 10w. We can write the first step of the inequality as:

10w + 50 ≥ 150

Step 2: Solve the inequality.

To isolate 'w', we can subtract 50 from both sides of the inequality:

10w ≥ 150 - 50

10w ≥ 100

Finally, divide both sides of the inequality by 10 to solve for 'w':

w ≥ 10

Therefore, it will take Liam at least 10 weeks to save enough money to reach $150 for the video game console.

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The midline of the graphed function is y = 3.

For a sinusoidal function, we define the midline as the value that the function takes when the sinusoidal term is equal to zero.

So, for example in:

f(x) = k*sin(x) +M

The midline is the line y = M

so this is a line that goes through the middle of the graph.

On the given graph, we can see that the maximum value is at:

y = 5

The minimum is at:

y = 1

The midline is right between these two, at:

M = (5 + 1)/2 = 3

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The function which is modeled by the graph is y=2x+4.

We have to find the function in the given graph.

The line is passing through the points (-1, 2) and (0, 4).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope = 4-2/0+1

=2

Now let us find the y intercept.

4=2(0)+b

b=4

So the function is y=2x+4.

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Answer:

the dean bought more of swiss than cheddar because hee only bought  1.5 pounds of cheddar and 1.7 of swiss

Step-by-step explanation:

The value of y is 48.

To find the value of y in this scenario, we need to use the fact that the angle bisector of ∠JSL splits it into two congruent angles.

Let's denote one of these congruent angles as ∠HSL and the other as ∠LSJ. Since ∠JSL is bisected, we have:

m∠JSL = m∠HSL + m∠LSJ

Given that m∠JSL = (4y - 10)° and m∠HSL = m∠LSJ = ∠HSJ = (y + 43)°, we can substitute these values into the equation:

4y - 10 = (y + 43) + (y + 43)

Simplifying the equation:

4y - 10 = 2y + 86

Subtracting 2y from both sides:

2y - 10 = 86

Adding 10 to both sides:

2y = 96

Dividing both sides by 2:

y = 48

Therefore, the value of y is 48.

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Answer:

[tex]\Huge \boxed{\text{13.66$\%$}}[/tex]

Step-by-step explanation:

To find the rate, we need to use the following formula:

[tex]\LARGE \boxed{ \boxed{\text{Rate = $\frac{\text{Portion}}{\text{Base}}$$\times$100}}}[/tex]

Where "Portion" is the part of the whole and "Base" is the whole.

Now, let's plug in the given values:

[tex]\large \text{Rate = $\frac{\text{50}}{\text{366}}$$\times$100 = 13.66 (Rounded to the nearest tenth of a percent)}[/tex]

Therefore, the rate is 13.66% (rounded to the nearest tenth of a percent).

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Answer:

y= -3/2x+1

Step-by-step explanation:

slope intercept is y = mx + b form

so the answer is y= -3/2x+1

We transformed 630 square yards to square inches, resulting in a value of 816,480 square inches.

To convert 630 square yards to square inches, we can utilize the following unit multipliers:

1 yard = 3 feet (since there are 3 feet in a yard)

1 foot = 12 inches (since there are 12 inches in a foot)

1 square yard = 1 yard × 1 yard = 3 feet × 3 feet = 9 square feet

1 square foot = 12 inches × 12 inches = 144 square inches

Now, we can set up the conversion using the unit multipliers:

630 square yards × (9 square feet / 1 square yard) × (144 square inches / 1 square foot) = 630 × 9 × 144 square inches

Simplifying the calculation:

630 × 9 × 144 square inches = 816,480 square inches

Therefore, 630 square yards is equal to 816,480 square inches.

By using the four unit multipliers and converting yards to feet and then to inches, we successfully transformed 630 square yards to square inches, resulting in a final value of 816,480 square inches.

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The value of p is -3.

To rewrite the equation 2x² + 12x = -13 in the form 2(x - p)^2 + q = 0, we need to complete the square. Let's go through the steps:

2x² + 12x = -13

First, let's move the constant term to the right side:

2x² + 12x + 13 = 0

Next, divide the equation by the leading coefficient (2) to simplify:

x² + 6x + 6.5 = 0

To complete the square, we take half of the coefficient of x (6) and square it to get 9.

Then, we add and subtract 9 to the equation:

x² + 6x + 9 - 9 + 6.5 = 0

(x + 3)² - 3² + 6.5 = 0

(x + 3)² - 9 + 6.5 = 0

(x + 3)² - 2.5 = 0

Comparing this equation with 2(x - p)² + q = 0, we can see that p = -3 and q = -2.5.

Therefore, the value of p is -3.

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The matrix corresponding to the vertices of the triangle after the rotation is given as follows:

[0 -1 -2]

[0 -3 1]

The five more known rotation rules are given as follows:

The vertices of the original triangle are given as follows:

(0,0), (-3,1) and (1,2).

The rotation rule is given as follows:

(x,y) -> (-y, x).

Hence the vertices of the rotated figure are given as follows:

(0,0), (-1, -3) and (-2, 1).

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The area of the shaded region is 61.76 square feet.

The given figure has a rectangle and circle.

Let us find the area of both rectangle and circles.

The length of rectangle is 14 ft and width is 8 ft.

Area = length × width

=14×8

=112 square feet.

The diameter of the circle is 8 feet because diameter is equal to width of rectangle.

Radius =diameter/2

= 4 ft.

Area of circle =πr²

=3.14×4²

=3.14×16

=50.24

To find the area of shaded region subtract area of circle from area of rectangle.

Shaded area = 112-50.24

=61.76 square feet.

Hence, the area of the shaded region is 61.76 square feet.

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Answer:

A = 153.86

Step-by-step explanation:

A = πr^2

A = 3.14 (7)^2

A = 3.14 (49)

A = 153.86

Answer:

Because the P-value < α = 0.05, the correct decision is to reject H0.

Step-by-step explanation:

When the p-value is less than our given significance level, it's outside the rejection region, so there is strong evidence that suggest the null hypothesis is not true and that the alternate hypothesis is favored instead.

The perimeter (P) by multiplying the side length by 4:
P = 4 * (4√2) = 16√2
The answer: b. 16√2

To find the perimeter of a square with a diagonal length of 8 feet, first, you need to determine the side length. In a square, the diagonal length (d) is related to the side length (s) through the Pythagorean theorem as follows:

d = s√2

Now, plug in the given diagonal length (8 feet) and solve for s:

8 = s√2
s = 8/√2
s = 4√2 (simplified by multiplying both numerator and denominator by √2)

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As per the given equation, when a = 3 and b = -2, the value of the expression [tex]b^2[/tex] - 4ab is 28.

When a = 3 and b = -2, we replace the given values into the formula and make the necessary calculations to evaluate the expression b² - 4ab.

Now,

[tex](-2)^2 - 4 * 3 * (-2)[/tex]

4 - 4 * 3 * (-2)

Multiplying -4 and 3 gives us -12, so the expression becomes:

4 - (-12) * (-2)

Multiplying -12 and -2 gives us 24, so the expression further simplifies to:

4 + 24

Adding 4 and 24 together yields:

28

Therefore, when a = 3 and b = -2, the value of the expression b² - 4ab is 28

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Your question seems incomplete, the probable complete question is:

Using quadratic formula, Evaluate b²-4ab when a= 3, b = -2

Using synthetic division, P(a)= 9.

To find P(a) using synthetic division and the remainder theorem, we will substitute the value of a into the polynomial p(x) = x^3 + 4x^2 - 5x + 6 and perform synthetic division.

First, let's set a = 2 and write the polynomial as p(x) = x^3 + 4x^2 - 5x + 6. Now, we set up the synthetic division table:

2 | 1 4 -5 6

|_____________

1 6 7 9

The numbers in the first row of the table are the coefficients of the polynomial p(x), and the second row represents the result after each step of the synthetic division. The number at the bottom right corner, 9, is the remainder.

According to the remainder theorem, P(a) is equal to the remainder when p(x) is divided by (x - a). In this case, a = 2, so P(2) is equal to the remainder, which is 9.

Therefore, P(2) = 9.

In summary, using synthetic division and the remainder theorem, we find that P(2) for the polynomial p(x) = x^3 + 4x^2 - 5x + 6 is equal to 9.

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An inequality that represents the state's hourly wage requirement include the following: C. m ≥ $9.25 per hour.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Assuming the variable m represent the state's hourly wage requirement. Additionally, each interval on the number line represent 0.25 per hour.

Since the shaded circle (dot) is located at point 9.25 and the arrows points or increases to the right, an inequality that represents the state's hourly wage requirement is m ≥ $9.25 per hour.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The percentage of age-groups has more male customers than female customers is approximately 50%.

The given graph depicts a company's customer analysis based on gender and age group.

Male percentage is more between the age 30-34, 45-49, 50-54 and 55-59.

Here, percentage = 20/41 ×100

= 0.487×100

= 48.7%

≈ 50%

Therefore, option B is the correct answer.

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The statement that best describes the effect on the graph of y=(x-9)² if the equation is changed to y = (x + 9)² is:O C. The graph moves left 18 units.

The graph shifts horizontally when the equation is modified from y = (x - 9)2 to y = (x + 9)2. The graph's points' x-coordinates are impacted by the inclusion of 9 inside the brackets.

The graph is moved 9 units to the left by adding 9 to the x-coordinate. As a result, the phrase "The graph moves left 18 units" is the most correct way to describe the effect on the graph.

Therefore the correct option is C.

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The probability that a randomly selected permutation of the letters A, A, B, C, S, U would spell "abacus" is:  

(A) 1/720

Probability is the likelihood of a desired event happening. Mathematically:

Probability = Number of occurrence / Number of possible outcomes

The number of permutations of 6 letters is:

6! =720

Out of these 720 permutations, only one spells "abacus" (based on the arrangement of letters).

Thus, the probability that a randomly selected permutation of the letters A, A, B, C, S, U would spell "abacus" is:  

1/720

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