the expression x^2-8x+6 can be written in the form (x-p)^2+q

The area of the object is 40 square centimeters

The correct answer is an option (B)

We know that the formula for the area of trapezoid is,

A = ((a + b)/2) × h

where a and b are the two parallel bases

h is the height of the trapezoid

From the attached figure, first we determine the length of the two parallel bases.

Let us assume that 'a' represents the length of the upper base and 'b' represents the length of the bottom side of the trapezoid

We can observe that a = 2x

so the length of a = 6 centimeters

And b = 2z

So, the length of b = 2(5)

                              = 10 cm

Here, the height h of the trapezoid is given by y = 5 cm

Using above formula for the area of trapezoid, the area of the object would be,

A = ((a + b)/2) × h

A = ((6 + 10)/2) × 5

A = (16/2)  × 5

A = 40 cm²

Therefore, the correct answer is an option (B)

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Find the complete question below.

The type of sequence is a geometric sequence with a common ratio of 1/3

To determine whether the given sequence is a geometric sequence, we need to check if there is a common ratio between any two consecutive terms.

The common ratio, denoted by "r", is calculated by dividing any term of the sequence by its preceding term.

Let's check if there is a common ratio between any two consecutive terms of the given sequence:

15/45 = 1/3

5/15 = 1/3

5/3 / 5 = 1/3

Since the ratio between any two consecutive terms is the same (1/3), the sequence is a geometric sequence.

To find the explicit formula for a geometric sequence, we use the formula:

an = a1 * r^(n-1)

So, we have

an = 45* (1/3)^(n-1)

For the recursice sequence, we have

an = a(n - 1) * 1/3

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To compute the number of 12 letter combinations of the 26 letters in the alphabet, we can use the formula for combinations, which is:

nCr = n! / r!(n-r)!

where n is the total number of items (26 letters in this case), r is the number of items to choose (12 letters in this case), and ! means factorial (the product of all positive integers up to that number).

Using this formula, we can plug in the numbers:

26C12 = 26! / 12!(26-12)!
= (26 x 25 x 24 x 23 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15) / (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
= 9,675,700

Therefore, there are 9,675,700 possible 12 letter combinations of the 26 letters in the alphabet.

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The median number of goals scored is 1, and the mean number of goals scored is 2. The median is less than the mean, indicating a right-skewed distribution.

To find the median, we need to first put the numbers in order

0, 0, 1, 1, 1, 3, 3, 4, 5

There are an odd number of values, so the median is the middle value, which is 1.

To find the mean, we add up all the values and divide by the number of values

(0 + 0 + 1 + 1 + 1 + 3 + 3 + 4 + 5) / 9 = 2

So the mean number of goals scored is 2.

Since the median (1) is less than the mean (2), we can say that the distribution is skewed to the right. This is because the high value of 5 pulls the mean up, while the median is not affected as much by outliers.

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Answer:

1

1

1

2

2

2

2

Step-by-step explanation:

The expression that represents the area of the rectangular patio in factored form is: area = [(t + 4)(t + 21) / 2(t + 7)(t + 2)]

An expression is a grouping of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division in mathematics.

Exponents, functions, and other mathematical symbols may also be included.

In mathematical equations and formulas, expressions are used to represent numbers, calculations, and relationships.

The length of the rectangular patio is given by the expression:

length = (t^2 + 19t + 84) / (4t - 4)

The width of the rectangular patio is given by the expression:

width = (2t - 2) / (t² + 9t + 14)

The area of the rectangular patio is given by the product of its length and width:

area = length x width

By substituting, we get:

area = [(t² + 19t + 84) / (4t - 4)] x [(2t - 2) / (t² + 9t + 14)]

We can factor the numerator and denominator of both fractions to simplify the expression:

area = [(t + 4)(t + 21) / 4(t - 1)] x [2(t - 1) / (t + 7)(t + 2)]

We can then simplify the expression by canceling out the common factors of (t - 1) in the numerator and denominator:

area = [(t + 4)(t + 21) / 4] x [2 / (t + 7)(t + 2)]

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There is not enough evidence to conclude that Devon's true proportion of good serves is greater than 72%.

The correct conclusion for Devon to reach is: Because the P-value of 0.06 > a (where a = 0.05), Devon should fail to reject H0. There is no convincing evidence that the proportion of services that are good is more than 72%.

The null hypothesis, H0, states that the true proportion of good serves for Devon is equal to 72%. The alternative hypothesis, Ha, states that the true proportion of good serves for Devon is greater than 72%.

The P-value is the probability of obtaining a test statistic as extreme or more extreme than the observed data, assuming that the null hypothesis is true. In this case, the P-value is 0.06, which means that if the true proportion of good serves for Devon is actually 72%, there is a 6% chance of observing a sample of 50 serves with 42 or more good serves.

Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis.  

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The 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03)

To find the 68% confidence interval for systolic blood pressure in women, we can use the standard formula:

Confidence Interval = Mean ± (Z * (Standard Deviation / √n))

Where:

Mean = 123.4 (sample mean)

Standard Deviation = 19.9 (sample standard deviation)

n = 1000 (sample size)

Z = Z-score corresponding to the desired confidence level (in this case, 68% corresponds to 1 standard deviation on each side of the mean)

To find the Z-score, we can refer to the standard normal distribution table or use a calculator. For a 68% confidence level, the Z-score is 1.

Plugging in the values, we get:

Confidence Interval = 123.4 ± (1 * (19.9 / √1000))

Calculating the square root of 1000, we have:

Confidence Interval = 123.4 ± (1 * (19.9 / 31.62))

Simplifying further, we get:

Confidence Interval = 123.4 ± (0.6301)

Therefore, the 68% confidence interval for systolic blood pressure in women, based on the given sample, is approximate: (122.77, 124.03).

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The square was translated 2 units downwards.

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

The square was translated 2 units downward since all the y-coordinates of the vertices of the image square are 2 units less than the corresponding y-coordinates of the vertices of the pre-image square.

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The perimeter of the rectangle is 8 1/4 feet. the correct answer is A.

Perimeter is the total length of the sides of a two-dimensional shape. In a rectangle, opposite sides are equal in length, so the perimeter can be found by adding the lengths of all four sides. To find the perimeter of a rectangle, we use the formula:

Perimeter = 2(length + width)

In this case, the length is given as 3 1/4 feet and the width is given as 7/8 feet. To find the perimeter, we substitute these values into the formula:

Perimeter = 2(3 1/4 + 7/8)

To simplify, we need to convert the mixed number to an improper fraction and find a common denominator for the fractions:

Perimeter = 2(13/4 + 7/8)

Perimeter = 2(26/8 + 7/8)

Perimeter = 2(33/8)

Now we can simplify the expression by multiplying 2 by the fraction:

Perimeter = 66/8

We can reduce this fraction by dividing both the numerator and denominator by 2:

Perimeter = 33/4

Therefore, the perimeter of the rectangle is 8 1/4 feet, which is answer choice A.

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The balance of the CD after 6 years will be $678.35.

To calculate the balance of the CD after 6 years, we need to use the formula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:
A = the balance after 6 years
P = the initial deposit of $500
r = the annual interest rate of 2.25%
n = the number of times the interest is compounded per year (biweekly = 26 times per year)
t = the number of years (6)

Plugging in the values, we get:

A = [tex]500(1 + 0.0225/26)^{(26*6)[/tex]
A = 500(1.001727)¹⁵⁶
A = 500(1.3567)
A = $678.35

Therefore, the balance of the CD after 6 years will be $678.35.

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Answer:

answer choice C

Step-by-step explanation:

The playground is a rectangle.

To find the area of a rectangle, we use the formula:

Area = Length x Width

The length is 25 yards.

The width is 68 yards.

Plugging these into the area formula:

Area = 25 x 68 = 1,700 square yards

Of the options, the closest choice is:

1,710 square yards

The area is 1,710 square yards.

Emir earned approximately $207.05 doing odd jobs.

Let x be the amount that Emir earned doing odd jobs. We can use the formula for compound interest, A = P(1+r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have P = x, r = 0.1, n = 12 (since interest is compounded monthly), t = 9, and A = 400. Solving for x, we get:

x = A/(1+r/n)^(nt) = 400/(1+0.1/12)^(12*9) ≈ $207.05

Therefore, Emir earned approximately $207.05 doing odd jobs.

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The calculated value of the expression 3 - (-1) + (-1) - 3 using a calculator is 0

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

The expression 3 - (-1) + (-1) - 3

We can add the numbers using a calculator

So, we have the following representation

Value = 3 - (-1) + (-1) - 3

Using the above as a guide, we have the following:

Value = 0

This means that the value of the expression 3 - (-1) + (-1) - 3 using a calculator is 0

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The length of BD is √(65)) and the slope of BD is 1/7.

What does Quadrilateral means ?

In geometry, a quadrilateral is a four-sided polygon with four sides (sides) and four angles (vertices). The word is derived from the Latin words quadri, the form of four, and latus, meaning "side". Different types of quadrilaterals include trapezoid, parallelogram, rectangle, rhombus, square, kite

 To find the slope of the diagonal BD of  square ABCD, you must first  find the coordinates of points B and  D. Since ABCD is a square, all sides are the same length and the diagonals bisect each other at 90 degrees.  

The midpoint M of AC is the intersection of the diagonals, so we can find the coordinates of M by taking the average of the x-coordinates and the average of the y-coordinates:

M = ((4 +3)/2, (9+ 2)/2) = (3.5, 5.5)

Since BD bisects AC, the coordinates of the midpoint M are also the coordinates of both B and D. Hence we have:

B = D = (3.5, 5.5)

The slope of the line passing through points A and C is:

m_AC = (2-9)/(3-4) = -7

Since the diagonals of the square are perpendicular, the slope of BD is the negative inverse of m_AC:

m_BD = -1/m_AC = 1/7

We can use the Pythagorean theorem to find the length of BD. Let x be the length of BD. Then we have:

AC² + BD² = 2x²

Since AC is the diagonal of the square, its length is:

AC = square((3-4)²+ (2-9)²) = square(65)

Substituting this into the above equation  and solving for x, we get:

√(65) x² = 2x²

x² = square(65)

x = square (square(65))

Therefore, the length of BD is √(65) and the slope of BD is 1/7.

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189*365=68985

68985/15= $4599

Step-by-step explanation:

or $5000 if you round up

Answer:

113 or 401: see below for explanation

Step-by-step explanation:

x = 8

The way you wrote it with the " * " symbol, it means the multiplication of 6x and 2. This is what I did in the line below.

6x × 2 + 17 = 6 × 8 × 2 + 17 = 48 × 2 + 17 = 113

If by " * " you actually meant an exponent, such as 6x², then here is the calculation using 2 as an exponent. For exponent, we normally use ^, such as 6x^2 to mean 6x².

6x² + 17 = 6 × 8² + 17 = 6 × 64 + 17 = 384 + 17 = 401

The standard deviation of X to be approximately 0.4852. The correct answer is option (A).

To calculate the standard deviation of X, we need to first calculate the probability of drawing a red marble on the first draw, which is 11/29. The probability of not drawing a red marble on the first draw is 18/29. The probability of drawing a red marble on the second draw, given that we did not draw a red marble on the first draw, is 11/29. Using the formula for the geometric distribution, which models the number of trials until the first success, we can calculate the expected value of X, which is 1/p, where p is the probability of success (11/29 in this case).

Therefore, the expected value of X is 29/11. To calculate the standard deviation of X, we use the formula sqrt(q/p^2), where q is the probability of failure (18/29) and p is the probability of success (11/29). Plugging in these values, we get the standard deviation of X to be approximately 0.4852.  Therefore, the correct answer is option A, 0.4852.

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The intervals where f is decreasing are given as follows:

None of the above.

Hence the decreasing intervals of the function are given as follows:

Which are none of the options given in the problem.

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In the surface area, the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here we know that the tin is in the shape of cylinder.

Now to find the amount we need to determine the surface area of the cylinder.

Now Height h = 5 cm, Diameter = 4 cm then radius r = d/2 = 4/2 = 2 cm.

Now using formula then,

Surface  Area  = 2[tex]\pi\\[/tex]r(h+r) square unit.

=> Surface area = [tex]2\times3.14\times2(5+2)=2\times3.14\times2\times7[/tex] = 87.92 [tex]cm^2[/tex]

Hence the amount of tin needed to make a milk can is 87.92 [tex]cm^2[/tex].

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The equation of the line that is parallel to the graph of 2x-3y=7 and contains the point (-3, -3) is expressed as: y = (2/3)x - 1.

To find the equation of a line that is parallel to the graph of 2x - 3y = 7, we need to determine the slope of the given line. We can rewrite the equation in slope-intercept form:

2x - 3y = 7

-3y = -2x + 7

y = (2/3)x - 7/3

This implies that the slope of this line is m = 2/3.

Thus, the equation of the line we are to find will take the following form:

y = (2/3)x + b

where b is the y-intercept of the line.

To find the y-intercept (b), substitute (x, y) = (-3, -3) and m = 2/3 into y = mx + b:

-3 = (2/3)(-3) + b

-3 = -2 + b

b = -1

Substitute m = 2/3 and b = -1 into y = mx + b:

y = (2/3)x - 1

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Karen's last class will end at three in the afternoon.

Given that Kevin has three classes in a row, each lasting two hours, we can calculate the total duration of his classes. Three classes, each two hours long, amount to a total of 6 hours.

Since Kevin's first class starts at seven in the morning, we add 6 hours to that time, resulting in the conclusion of Karen's last class at three in the afternoon.

Understanding schedules and timetables is essential for effective time management. In academic settings, students often have multiple classes with varying durations throughout the day.

Calculating the end time of a class or event based on its start time and duration helps individuals plan their activities and allocate their time efficiently.

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a) The divergence of F is -4x - 2y,

b) The curl of F is (-2(x+y), 0, -2x).

A) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:

div(F) = ∇ · F = ∂(yz)/∂x + ∂(-5xz)/∂y + ∂(-4xy)/∂z

= 0 - 5z - 4x

= -5z - 4x

To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:

curl(F) = ∇ × F = ( ∂(-4xy)/∂y - ∂(-5xz)/∂z, ∂(yz)/∂z - ∂(4xy)/∂x, ∂(-yz)/∂x - ∂(-5xz)/∂y )

= (-5z, y, -5x)

B) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:

div(F) = ∇ · F = ∂(-x²)/∂x + ∂(-(x+y)²)/∂y + ∂(0)/∂z

= -2x - 2(x+y)

= -4x - 2y

To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:

curl(F) = ∇ × F = ( ∂(0)/∂y - ∂(-(x+y)²)/∂z, ∂(0)/∂z - ∂(-x²)/∂x, ∂(-(x+y))/∂x - ∂(-x²)/∂y )

= (-2(x+y), 0, -2x)

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The expression for AB in terms of x and √3 is:

AB = x√3.

An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.

In the given question,

In a right triangle ABC, if sin B = 0.5, then we know that:

sin B = opposite / hypotenuse

So, we can write:

0.5 = AB / CB

We also know that:

CB² = AB² + AC²

Substituting the value of AC, we get:

CB² = AB² + (3x)²

CB² = AB² + 9x²

Now, we can substitute the value of CB² from the first equation:

(AB / 0.5)² = AB² + 9x²

4AB² = AB² + 9x²

3AB² = 9x²

AB² = 3x²

The expression for AB in terms of x and √3 is:

AB = x√3

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Answer:

Step-by-step explanation:

3.) The volume of the triangular prism = 6,480 mi³

The surface area of the triangular prism = 1,872mi²

To determine the surface area of the given triangular prism, the formula that should be used is given as follows:

Surface area = bH + (b1+b2+b3)×l

where ;

b= 8 mi

b1 = 18 mi

b2 = 24 mi

b3 = 30 mi

Height = 18 mi

length = 24 mi

Surface area = 8×18 + ( 18+24+30)× 24

= 144 + 1728

= 1,872mi²

To calculate the volume of a triangular prism, the formula the should be used is given as follows;

Volume = 1/2 × b× h × L

where;

b = 24 ni

h = 18 mi

l = 30 mi

volume = 1/2 ×24×18×30

= 6,480 mi³

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Answer:

we know that given triangle is right angled triangle.

➢ By using Phythagoras Theorem:-

[tex] \sf \longrightarrow \: (AC)^2 = (AB)^2 + (BC)^2[/tex]

[tex] \sf \longrightarrow \: ( \sqrt{80} )^2 = (x)^2 + (8)^2[/tex]

[tex] \sf \longrightarrow \: 80 = (x)^2 + (8)^2[/tex]

[tex] \sf \longrightarrow \: 80 \: = x^2 \: + \: 8^2[/tex]

[tex] \sf \longrightarrow \: 80 \: = x^2 \: + \: 64[/tex]

[tex] \sf \longrightarrow \: 80 \: - 64 = x^2 \:[/tex]

[tex] \sf \longrightarrow \: 16 = x^2 \:[/tex]

[tex] \sf \longrightarrow \: x^2 \: = 16[/tex]

[tex] \sf \longrightarrow \: x \: = \sqrt{16} [/tex]

[tex] \sf \longrightarrow \: x \: = 4 \: units [/tex]

The average rate of change for the function f(x) = x² + 6x between x = 0 and x = 7 is 13.

To find the average rate of change for the given function f(x) = x² + 6x between x = 0 and x = 7, you can follow these steps: Calculate the value of the function at the given points.
f(0) = 0² + 6(0) = 0
f(7) = 7² + 6(7) = 49 + 42 = 91

Use the average rate of change formula, which is (f(b) - f(a)) / (b - a), where a and b are the given points.

Substitute the values into the formula:
Average rate of change = (f(7) - f(0)) / (7 - 0) = (91 - 0) / 7 = 91 / 7 = 13

Therefore the average rate of change for the function f(x) = x² + 6x between x = 0 and x = 7 is calculated to be 13.

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Therefore, Jamison made $96.30 in tips on Friday night.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.

Here,

Jamison made $42.80 in tips on Thursday night.

To find out how much he made in tips on Friday night, we need to multiply the Thursday amount by 2 1/4, which is the same as multiplying it by 9/4.

$42.80 x 9/4 = $96.30

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The critical value t Subscript c for a confidence level of 0.90 and sample size of 26 is 1.708. A t-value greater than or less than 1.708 in absolute value would lead to rejection of the null hypothesis at the 0.10 level of significance.

To find the critical value t Subscript c for the confidence level c=0.90 and sample size n=26, we can use a t-distribution table or calculator.

Since we have a sample size of n=26, we have n-1 = 25 degrees of freedom. Using a t-distribution table or calculator with 25 degrees of freedom and a confidence level of 0.90, we get

t Subscript c = 1.708

Therefore, the critical value t Subscript c for the confidence level c=0.90 and sample size n=26 is 1.708. This means that if we calculate the t-value from our sample data and it is greater than or less than 1.708 in absolute value, we can reject the null hypothesis at the 0.10 level of significance.

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