A square pyramid has a base that measures 8 inches on each side. The
height of the pyramid is 11.5 inches. What is the volume of the pyramid?
Answer as numbers only, round to the tenths place

The trigonometric identity has been proven as 1 in the space below

Given the identity:

tan(1/2x) (2cot(x) + tan(1/2x)) = 1

To prove this identity, let's start by expressing cot(x) in terms of tan(x):

cot(x) = 1 / tan(x)

Now, replace cot(x) in the given identity:

tan(1/2x) (2(1/tan(x)) + tan(1/2x)) = 1

Now, let's use the double angle formula for tan(x):

tan(x) = 2 * tan(1/2x) / (1 - tan^2(1/2x))

Replace tan(x) in the equation:

tan(1/2x) (2(1/(2 * tan(1/2x) / (1 - tan^2(1/2x))) + tan(1/2x)) = 1

Simplify the equation:

tan(1/2x) ((1 - tan^2(1/2x)) + tan(1/2x) * tan(1/2x)) = 1

Now, notice that the expression in the parentheses is equal to 1:

(1 - tan^2(1/2x)) + tan^2(1/2x) = 1

So, we can simplify the equation further:

tan(1/2x) * 1 = 1

This directly leads us to the original identity:

tan(1/2x) = 1

Thus, the trigonometric identity is proven.

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Answer:

19

Step-by-step explanation:

5 + 4^2 - 6/3

= 5 + 16 - 2

= 21 - 2

= 19

Answer:

formula= 6ssquare

Step-by-step explanation:

where s is the length of the cube on each side

Answer:

Step-by-step explanation:

the answer is 0.01

The base of the exponential form  is 10 and the power is -2 therefore the answer is 0.01 if the power was 2 the answer would have been 100

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Answer:

C

Step-by-step explanation:

We are given that FGH is a triangle, which means that...

Angle F + Angle G + Angle H = 180

Start by substituting the given angle measurements into the equation:

4x+2+13x-7+3x+5=180

Combine like terms

20x=180

Divide both sides by 20 to isolate x

x=9

Plug 9 back in for x to solve for each angle

Angle F = 4(9)+2=36+2=38

Angle G = 13(9)-7=117-7=110

Angle H = 3(9)+5=27+5=32

Step-by-step explanation:

line passes through the point (5,0) and another one (0,3)

equation of the line passing through two points is

x-x1/x2-x1=y-y1/y2-y1

so

x-5/0-5=y-0/3-0

(x-5)*3=y*(-5)

3x-15+5y=0

this is the equation of the line shown in the graph

Answer:

please mark my brain list answer

Answer:

s = ut + 1/2 at²

2.4 = 4.9t²

t = 0.70

distance = speed x time

d = 24 x 0.7

d = 16.8 m

The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)

We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)

a) \((a^2 - b^2)\)

We can write the transpose of this matrix as

\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.

b) (A+B)(A-B)

Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)

Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)

Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.

c) ABA

Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

d) ABAB

Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)

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Step-by-step explanation:

radius=6cm.

π=22 over 7

circumference=2πr

circumference=2×22 over7×6

circumference=51.04cm

The p value is calculated as 0.116

Null u = 70

alternate u ≠ 70

The alternate is a two tailed test

the test statistic calculation

t = x - u / s/√n

x = 85 + 77 + 82 + 68 + 72 + 69 / 6

= 75.5

standard deviation s = \(\sqrt{\frac{(85- 75.5)^2+(77- 75.5)^2+...(69- 75.5)^2}{6-1} }\)

= 7.01

Test stat = (75.5 - 70) / 7.01/√6

= 1.92

degree of freedom = 6 - 1 = 5

this is 2 tailed

p value using excel = tdist( 1.8, 5 , 2)

= 0.116

We fail to reject the null hypothesis because it is greater than the level of significance

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The only solution to the given equation is x = 4.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

We can solve the given equation by subtracting 5 from both sides and then taking the square root of both sides:

x² - 8x + 16 = 5

x² - 8x + 11 = 0

(x - 4)² = 0

x - 4 = 0

x = 4

Therefore, the only solution to the given equation is x = 4.

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Answer: B. false

Step-by-step explanation:

An equilateral triangle has 3 equal sides

Isosceles triangle has two equal sides.

Which means that equilateral triangles cannot become isosceles.

Answer:

False

Step-by-step explanation:

An equilateral triangle has all three sides equal

An isosceles triangle has at least 2 sides equal

An equilateral triangle is a special isosceles triangle

Answer:

Step-by-step explanation:

cos A = \(\frac{\sqrt{8} }{3}\)

The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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Answer:

A $6.20

Step-by-step explanation:

first multiply 7.90 x3 and subtract 17.50 from the answer and you should get A

Using percentage error, the measured weight is 0.5% less than the expected weight.

The percentage error serves as a gauge for how closely a computed or experimental result matches the true or accepted value. It is determined as the true or accepted value multiplied by 100% times the absolute difference between the experimental or calculated value and the true or acceptable value.

The formula for percentage error is:

Percentage Error = (|experimental value - true value| / true value) x 100%

The weight of the distilled water can be calculated by subtracting the weight of the graduate from the combined weight of the graduate and water:

weight of water = 100.28 g - 85.49 g = 14.79 g

To calculate the percentage error, you can use the formula:

(measured weight - actual weight) / actual weight * 100%

The actual weight of 15 mL of distilled water is 15 g, so the percentage error is:

(14.79 g - 15 g) / 15 g * 100% = -0.5%

So, the deviation from the expected weight of 5 g is -0.5%, which means the measured weight of the distilled water is 0.5% less than the expected weight.

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Answer:

≈ 0.97

Step-by-step explanation:

Given that :

Number of green gum drops = 30

Number of Blue gum drops = 1

Total number of gum drops :

(Number of blue + number of green gum drops)

(30 + 1) = 31

Probability = Required outcome / Total possible outcomes

P(green gum drops) = number of green drops / total number of gum drops

P(green gum drops) = 30 / 31 = 0.967 ≈ 0.97

The point x will be drawn slightly to the right of the midpoint between the last two tick marks.

Answer:

x= 20

Step-by-step explanation:

5.70x3x=17.1x

17.1x+4.05x=21.15x

21.15x=423

423/21.15=20

x=20

Hope this is the answer you were looking for.

9514 1404 393

Answer:

  0

Step-by-step explanation:

The two expressions for her salary can be equated:

  2h +4 = 4 +4h

  0 = 2h . . . . . . . . subtract 2h+4 from both sides

  h = 0 . . . the husband's salary is zero dollars per month

Answer:

$2000

Step-by-step explanation:

We want to divide 849 by 24

By making the long division the result will be :

35 and the reminder = 9

The long division will be as shown in the following picture :

Answer:

Step-by-step explanation:

Credit scores are made of credit history, payment history, debt ratio, and types of credit which is therefore denoted as option A.

This is referred to as a numerical expression based on a level analysis of a person's credit files, to represent the creditworthiness of an individual.

It is a prediction of how likely you are to pay a loan back on time based on information from your credit reports and has different components such as the credit history, payment history, debt ratio, etc.

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Answer:

D

Step-by-step explanation:

you can express them in all the above form

Answer:

C. g(x) + (-3x + 1)2

Step-by-step explanation:

did the test for it

Answer:

I think is B

Step-by-step explanation:

Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and

after 11 steps, the mixture contains less than 9% vinegar.

What is concentration?

Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.

a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:

\(C(1) = C(0) * \frac{1 - 0.14}{1}\)

where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:

C(2) = C(1) * \(\frac{1 - 0.14}{1}\)

Substituting the formula for C(1), we get:

C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)

or, more generally:

\(C(n) = C(0) * (0.86)^n\)

b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:

\(C(0) * (0.86)^n < 0.09\)

Dividing both sides by C(0), we get:

\((0.86)^n < 0.09\)

Taking the natural logarithm of both sides, we get:

n * ln(0.86) < ln(0.09)

Dividing both sides by ln(0.86), we get:

n > ln(0.09) / ln(0.86)

Using a calculator, we get:

n > 10.7

Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.

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(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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