Evaluate.
16 ÷ (2 + 1/2) ^2
A) 2 14/25
B) 4 1/4
C) 6 2/5
D) 8 1/4

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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Answer:

x=11

Step-by-step explanation:

(3x-1)+(6x-8)= 90

9x- 9= 90

+9 +9

9x=99

/9 /9

x=11

Answer:

B

Step-by-step explanation:

B is the answer to your question

Answer: -6P - 10

Step-by-step explanation:

STEP 1.   -12 - 6P + 2

STEP 2.   -6P + ( -12 + 2 )

STEP 3.   -6P - 10

The parametric equations are mathematically given as

(x(t), y(t), z(t))= (2-4t, 1-t, t)

Generally, To express the parametric point from A (2,1,0) to B(-2,0,1) in parametric form, we can use the following equation:

P(t) = (2-4t, 1-t, t)

To find the parametric equations for a point moving from A to B, we can use the following formula:

x = x₁ + t(x₂ - x1)

y = y₁ + t(y₂ - y₁)

z = z₁ + t(z₂ - z₁)

Where (x₁, y₁, z₁) is the starting point (A), (x₂, y₂, z₂) is the ending point (B), and t is a parameter that varies from 0 to 1.

Using this formula, the parametric equations for a point moving from A (2,1,0) to B(-2,0,1) are:

x = 2 + t(-2 - 2)

= 2 - 4t

y = 1 + t(0 - 1)

= 1 - t

z = 0 + t(1 - 0)

= t

These equations describe the motion of a point that starts at A, moves along the line segment from A to B, and arrives at B when t = 1.

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The complete Question was found

Find parametric equations for the line. (Use the parameter t.)

The line through points A (2,1,0) to B(-2,0,1)

(x(t), y(t), z(t))= \((\square)\)

Any line that is perpendicular to a given line y = ax + b must have slope -1/a

For the lines -x - 5y = 7 and 5x - y = -9, first, we rewrite them in the slope-intercept form:

y = -x/5 - 7/5

y = 5x + 9

We can check that the slope of the first line is the negative inverse of the slope of the second line. Therefore, the lines are perpendicular.

Answer:

g(-3x) = -9x - 3

Step-by-step explanation:

Step 1: Define function

g(x) = 3x - 3

g(-3x) = x = -3x

Step 2: Substitute

g(-3x) = 3(-3x) - 3

g(-3x) = -9x - 3

Answer:

sale price of video game

Step-by-step explanation:

Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) \(\times\) $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) \(\times\) (23/40) = 92/360 = 23/90

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The class of the equation and the cross section equation are;

The equation is a hyperboloid of two sheets

The cross sections are;

Equation at z = 0 is; y²/8 - x²/8 = 1

Equation at y = -4 is; x²/8 + z² = 1

Equation at y = 0 is; x²/8 + z² = -1

Equation at y = 4 is; x²/8 + z² = 1

Equation at x = 0 is; y²/8 - z² = 1

An equation is a mathematical statement which indicates the equivalence two expressions by joining them with the '=' sign.

The equation can be presented as follows;

y² = x² + 8·z² + 8

y² - x² - 8·z² = 8

y²/8 - x²/8 - z² = 1

The above equation is the equation of an hyperboloid of two sheets, where;

a² = 8, b² = 1, and c² = 8

Please find attached the diagram of the surface, created with an online 3D graphing tool.

The equation for the cross section at z = 0, can be obtained by plugging in z = 0, into the equation as follows;

y²/8 - x²/8 - 0 = 1

y²/8 - x²/8 = 1

The above equation is the equation of an hyperbola in the xy plane

The equation for the cross section at y = -4, can be obtained by plugging in y = -4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 4²/8 = -1

- x²/8 - z² = -1

x²/8 + z² = 1

The above is an equation of an ellipse in the xz plane

The equation for the cross section at y = 0, can be obtained by plugging in y = 0, into the equation as follows;

0²/8 - x²/8 - z² = 1

- x²/8 - z² = 1

Therefore; x²/8 + z² = -1

The equation for the cross section at y = 4, can be obtained by plugging in y = 4, into the equation as follows;

4²/8 - x²/8 - z² = 1

- x²/8 - z² = 1 - 2 = -1

x²/8 + z² = 1

The above equation is the equation of an ellipse in the xz plane

The equation for the cross section at x = 0, can be obtained by plugging in x = 0, into the equation as follows;

y²/8 - 0²/8 - z² = 1

y²/8 - z² = 1

The equation is the equation of an hyperbola in the yz plane

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Answer:

7

Step-by-step explanation:

Lets use Pemdas for this

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

First you always do parenthesis, (47+4^2)

Then Exponents 4^2 this means 4x4 and 4x4=16

So (47+16)= 63

so we have 63/3^2

We go to exponents before division according to pemdas

3^2=3x3=9

63/9

63/9=7

Answer:

x=8

Step-by-step explanation:

you distribute and solve

\( - 13 = \frac{w}{9} - 6 \\ - 13 + 6 = \frac{w}{9} \\ - 7 = \frac{w}{9} \\ w = - 63\)

so only -63 is the solution, the rest three are NOT solution for this equation.

Answer:

B

Step-by-step explanation:

The secant of the angle A is 13/4

The given parameter is:

\(\tan(A) = -\frac{\sqrt{153}}{4}\)

Using the trigonometry identity, we have:

\(\sec^2(A) = \tan^2(A) + 1\)

This gives

\(\sec^2(A) = (-\frac{\sqrt{153}}{4})^2 + 1\)

Evaluate the exponent

\(\sec^2(A) = \frac{153}{16} + 1\)

Evaluate the sum

\(\sec^2(A) = \frac{169}{16}\)

Take the square root of both sides

\(\sec(A) = \pm \frac{13}{4}\)

Secant in quadrant IV is positive.

So, we have:

\(\sec(A) = \frac{13}{4}\)

Hence, the secant of angle A is 13/4

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Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

Answer:

I think 3/6 or 3/12

Step-by-step explanation:

because either way we are adding 1/6+2/6=3/6

Answer:

4 are eating sandwhiches and 2 are eating salads

Step-by-step explanation:

1/6 of 12 is 2 2/6 of 12 is 4

Using the inequality concept, the expression models the number of days Samuel can afford to rent while staying within his budget is 11x + 18 ≤  40

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

A rental car company charges $22 per day to rent a car and $0.08 for every mile driven

The maximum amount to spend = $80

Fixed charge per day $22

Charge per mile = $0.08

The inequality which represents the number of days Can be expressed thus :

(Charge per day × number of days) + (charge per mile × number of miles) ≤  80

22x + 0.08× 450 ≤ 80

22x + 36 ≤  80

Divided by 2 both sides of an inequality,

11x + 18 ≤  40

Hence, the required inequality expression is 11x + 18 ≤  40

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Answer:

Step-by-step explanation:

m = (y2-y1) / (x2-x1)

m = (-8-0) / (-5-5) = 4/5  

note that it does not matter which points you chose to be second or first

then use slope point equation again it does not matter which point from the slope you use

y - y1 = m ( x - x1 )

y - 0 = 4/5 ( x - 5)

y = 4/5x -4

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Where the friend made the error was in step 2. She should have squared the 4 first before multiplying by 2. The correct answer is 44

We want to simplify the mathematical expression;

2(10 - 6)² + 3*4

The correct steps are as follows;

Step 1; Using BODMAS Acronym, let us deal with the bracket first to get;

2(4)² + 3*4

Step 2; Still dealing with the bracket, we will now have;

2(16) + 3*4

Step 3; Still dealing with the bracket, we will now have; 32 + 3*4

Step 4; Next sign to be used is multiplication sign and as such we now have; 32 + 12

Step 5; Using the addition sign, we now have 44

Thus, where the friend made the error was in step 2. She should have squared the 4 first before multiplying by 2.

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answer my questions plz

Answer:

1unit scale on map is equal to 100.16 km in real life

Step-by-step explanation:

since in map 12.cm =1262km in real life

1cm=(1262/12.6) km

therefore it gives us 100.158km which is approximately 100.16 km .

Answer:

6 days

Step-by-step explanation:

This question becomes much easier when written out per day (shown below). The question tells us that she is reducing her run by half every day, so all we need to is divide the previous day by 2 to get the current day. She starts out with 26 miles so this is our day 1 value.

Day 1 = 26 miles

Day 2 = 13 miles (26÷2=13)

Day 3 = 6.5 miles (13÷2=6.5)

Day 4 = 3.25 miles (6.5÷2=3.25)

Day 5 = 1.625 miles (3.25÷2=1.625)

Day 6 = 0.8125 miles (1.625÷2=0.8125)

We can see that by day 6, her total running amount is less that 1 mile, so the final answer is 6 days.

Numbers between 2.6×10^-1 and 29.5% are

2.6 × 10^-1 in exponential form written in decimal as 0.26

29.5% in percentage written in decimal as 0.295

2/7 in fraction written in decimal as 0.2857

2.8%  in percentage written in decimal as 0.028

0.2875 already in decimal form

the problem asks of numbers from 0.26 to 0.295

comparing the numbers shows that the numbers in this range are

0.2875 and 2/7

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Answer: The total distance covered by the car is 331 9/16 km.

Step-by-step explanation:

We know that, speed= distance/time taken

Therefore, distance = speed x time taken

= 132 5/8 x 2 1/2

= 5/2 x 1061/8

= 5305/16

= 331 9/16 km

Therefore, total distance is 331 9/16 km.

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Greetings.

The answer is 5.

Explanation:

\(\frac{x-6}{3}\)

We want to know the value when x = 21. Therefore, substitute x = 21 in the expression.

\(\frac{21-6}{3}\)

Evaluate 21-6 = 15

\(\frac{15}{3}\)

Therefore, the answer is 5.

The probability of Event E occurring before Event F with independent trials of an experiment is given by P(E)/[P(E) + P(F)].

The probability of E occurring before F with independent trials of an experiment can be calculated using the formula P(E)/[P(E) + P(F)]. This formula is derived from the principle that the probability of an event is the sum of its individual probabilities, and the probability of a mutually exclusive event is the sum of the probabilities of the individual events minus the probability of their intersection. Thus, the formula for the probability of E occurring before F is P(E) divided by the sum of P(E) and P(F). This gives us the probability of E occurring before F with independent trials of the experiment as P(E)/[P(E) + P(F)].

The probability of Event E occurring before Event F with independent trials of an experiment is given by P(E)/[P(E) + P(F)].

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Answer:  6 * 24 = 144 ways.

Step-by-step explanation:

Solution:

Given word => DANGER.

The condition is that vowels can't occupy odd places so, we will let them occupy even places.

A total number of arrangements will be = 6 * 24 = 144 ways.

Answer: 6x24 = 144 ways.