A sequence begins with-3. Each term is calculated by multiplying the previous term by -4, then subtracting 1.
Which option correctly represents the sequence described?
A -3, 11, -45, 179, ...
B {-3, -13, -53, -213, ...}
C. {-3, 11, -45, 179, ...}
D -3, -13, -53, -213,...

Answer:

v = 24

Step-by-step explanation:

Ft + mu = mv

v = (Ft + mu)/m = (55*3 + 5*(-9))/5 = 24

Answer:

Step-by-step explanation:

Okay, so, 2 necklaces would be $20.

One hour would be + $2.75

Three hours would be + $8.25

So all the hours together would be $11

Then, you add $20 + $11 to get $31.

The number line for the fractions given are as shown in the attached files

In order for us to represent rational numbers on a number line, we will draw a line and mark a point on it representing rational zero. Positive rational numbers are usually represented to the right of 0 and negative rational numbers are usually represented to the left of 0.

Now, just as any integer can be represented on a number line, rational numbers can also be represented on a number line.

Thus, we have:

For -2/3 and 3/4, we have the number line as attached

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 17160\\ P=\textit{original amount deposited}\dotfill & \pounds 11000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &16 \end{cases}\)

\(17160 = 11000[1+(\frac{r}{100})(16)] \implies \cfrac{17160}{11000}=1+\cfrac{16r}{100}\implies \cfrac{39}{25}=1+\cfrac{4r}{25} \\\\\\ \cfrac{39}{25}=\cfrac{25+4r}{25}\implies 39=25+4r\implies 14=4r\implies \cfrac{14}{4}=r\implies \stackrel{\%\qquad }{\boxed{3.5=r}}\)

Answer:

Step-by-step explanation:

This may be wrong but hear me out, 40+10 is 50 and 11+1 is 12, so 12:50?

The probability of the union of events A, B, and C is 0.7 where P(A)=0.2, P(B)=0.2 and P(C)=0.3.

In set theory, the union of two or more sets is a set that contains all the distinct elements of the sets being considered. Formally, the union of sets A and B, denoted as A ∪ B, is the set of all elements that are in either set A or set B, or in both.

When A, B, and C are mutually exclusive events, it means that they cannot happen at the same time. Therefore, the probability of the union of these events is equal to the sum of their individual probabilities.

In this case, we are given that:

P(A) = 0.2

P(B) = 0.2

P(C) = 0.3

To find the probability of the union of these events, we need to add their probabilities:

P(A ∪ B ∪ C) = P(A) + P(B) + P(C)

Substituting the given probabilities, we get:

P(A ∪ B ∪ C) = 0.2 + 0.2 + 0.3

P(A ∪ B ∪ C) = 0.7

Therefore, the probability of the union of events A, B, and C is 0.7.

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The question is A, B, and C are mutually exclusive. P(A) = 0.2, P(B) = 0.2, P(C) = 0.3. Find P(A ∪ B ∪ C).

P(A ∪ B ∪ C) = ?

Answer:

26°

Step-by-step explanation:

90°+64°+x°=180° (Sum of all the angles in a right angled triangle=180°)

154°+x°=180°

x°=180-154°

x°=26°

The first multiple of 2 greater than 100 is 102.

\(\therefore\) 102 the first multiple of 2 greater than 100.

First we have to know how to express, mathematically, what is a multiple of 2.

Any number multiplied by 2 is its multiple, that is, they are INFINITE.

If we want a multiple of 2 that exceeds the number 100, it is simple to add 2.

\( \bold{100 \: + \: 2 \: = \boxed{ \bold{102}}}\)

\(\therefore\) 102 the first multiple of 2 greater than 100.

Answer:

1) x = 43.33

2) x =  tan⁻¹(4/3)  = 53.13

Step-by-step explanation:

1) Formula: cos(A) = sin(90 - A)

sin(2x - 30) = cos(x - 10)

⇒ sin(2x - 30) = sin(90 - (x - 10))

⇒ sin(2x - 30) = sin(90 - x + 10)

⇒ sin(2x - 30) = sin(100 - x)

⇒ 2x - 30 = 100 - x

⇒ 3x = 130

⇒ x = 130/3

x = 43.33

2) 4sinx . cosx - 3sin²x = 0

⇒ 4sinx . cosx = 3sin²x

⇒ 4cosx = 3sinx

⇒ \(\frac{4}{3} =\frac{sinx}{cosx}\)

⇒ \(tan x = \frac{4}{3}\)

⇒ x =  tan⁻¹(4/3)

⇒ x = 53.13

Answer:

\(\textsf{1)} \quad x \approx 43.33^{\circ}\)

\(\textsf{2)} \quad \boxed{\begin{aligned}x &= \pi n \;\text{radians}\\x&=0.93+\pi n\; \text{radians}\end{aligned}}\quad \boxed{\begin{aligned}x &= 180^{\circ}n\\x&=53.13^{\circ}+180^{\circ} n\; \end{aligned}}\)

Step-by-step explanation:

Given trigonometric equation:

\(\sin(2x - 30^{\circ}) = \cos(x - 10^{\circ})\)

To solve the given trigonometric equation, we can use the following trigonometric identity:

\(\boxed{\begin{minipage}{4 cm}\underline{Trigonometric identity} \\\\$\cos (\theta)=\sin(90^{\circ}-\theta)$\\\end{minipage}}\)

Apply the trigonometric identity to the right side of the equation:

\(\begin{aligned}\sin(2x - 30^{\circ}) &= \cos(x - 10^{\circ})\\\\&= \sin(90^{\circ}-(x - 10^{\circ}))\\\\&= \sin(90^{\circ}-x +10^{\circ})\\\\&= \sin(100^{\circ}-x)\end{aligned}\)

Since the sine function is equal, we can equate the angles:

\(2x - 30^{\circ}=100^{\circ}-x\)

Now simplify and solve for x:

\(\begin{aligned}2x - 30^{\circ}&=100^{\circ}-x\\\\2x - 30^{\circ}+x&=100^{\circ}-x+x\\\\3x - 30^{\circ}&=100^{\circ}\\\\3x - 30^{\circ}+30^{\circ}&=100^{\circ}+30^{\circ}\\\\3x&=130^{\circ}\\\\\dfrac{3x}{3}&=\dfrac{130^{\circ}}{3}\\\\x&=\left(\dfrac{130}{3}\right)^{\circ}\\\\x&\approx 43.3^{\circ}\; \sf (nearest\;tenth)\end{aligned}\)

Therefore, the solution to the equation sin(2x - 30°) = cos(x - 10°) is approximately x = 43.33°.

\(\hrulefill\)

Given trigonometric equation:

\(4 \sin x \cos x-3\sin^2x=0\)

Factor out the common term sin(x):

\(\sin x(4 \cos x-3\sin x)=0\)

According to the zero product property, one of the factors must be equal to zero for the equation to hold.

Set each factor equal to zero and solve for x.

Factor 1

\(\sin x=0\)

According to the unit circle, sin(x) = 0 when x = 0 and x = π.

As the sine function is periodic with a period of 2π, the solutions to sin(x) = 0 are:

\(x=0+2\pi n, \;\;x=\pi + 2\pi n\)

Therefore, x is any multiple of π, where n is an integer:

\(\boxed{x = \pi n}\)

Factor 2

\(\begin{aligned}4\cos x - 3 \sin x & = 0\\\\4 \cos x & = 3 \sin x\\\\\dfrac{4}{3}&=\dfrac{\sin x}{\cos x}\\\\\dfrac{4}{3}&=\tan x\\\\\implies x&=\arctan\left(\dfrac{4}{3}\right)\\\\x&=0.92729...\end{aligned}\)

As the tangent function is periodic with a period of π, the solutions are:

\(\boxed{x=0.92729...+\pi n}\)

where n is an integer.

Therefore, the solutions to the equation 4sin(x)cos(x) - 3sin²(x) = 0 are:

\(\boxed{\begin{aligned}x &= \pi n \;\text{radians}\\x&=0.93+\pi n\; \text{radians}\end{aligned}}\)    \(\boxed{\begin{aligned}x &= 180^{\circ}n\\x&=53.13^{\circ}+180^{\circ} n\; \end{aligned}}\)

(where n is an integer)

Step-by-step explanation:

To eliminate x in the system of equations:

1. Multiply Equation 1 by 9 and multiply Equation 2 by -4, this gives:

Equation 1: 36x -54y = 90

Equation 2: -36x - 8y = -28

2. Add the two equations together to eliminate x:

(36x - 54y) + (-36x - 8y) = 90 - 28

Simplifying, we get:

-62y = 62

3. Solve for y:

y = -1

4. Substitute y = -1 into one of the original equations, say Equation 1:

4x - 6(-1) = 10

Simplifying, we get:

4x + 6 = 10

5. Solve for x:

4x = 4

x = 1

Therefore, the solution to the system of equations is x = 1 and y = -1. We can check that these values are correct by substituting them back into the original equations and verifying that they satisfy both equations.

Answer:

Step-by-step explanation:

This is the general method for doing this problem. First factor these numbers into primes.

72: 2 * 2 * 2 * 3 * 3

84: 2*2 * 3 * 7

Now each number has at least two 2s

Each number has at least one          3

The highest common factor is 2 * 2 * 3 = 12

Given:

Elena has a pet parakeet that weighs 6 when measured in one unit and 170 when measured in a different unit.

6__________ = 170______

To find:

The correct units from grams and ounces for these blanks.

Solution:

We know that, 1 ounce is greater than 1 gram.

1 ounce = 28.3495 grams

Multiply both sides by 6.

6 ounces = 170.097 grams

Approximate the values to the nearest whole number.

6 ounces = 170 grams

Therefore, 6 ounces = 170 grams.

The value of x, y and z in the system equation is (1, 2, 3).

The solution of the equation can be determined by using Cramer's rule as follows;

[-5    -6      0] = [ -17]

[-3     -5     5]    [2   ]

[-6    -5      1]     [-13 ]

The determinant of the matrix is calculate as;

Δ = -5 (-5 + 25) + 6(-3 + 30) + 0(15 + 30)

Δ = 62

The x-determinant of the matrix is calculated as follows;

Δx = -17(-5 + 25) + 6(2 + 65) + 0

Δx = 62

The y-determinant of the matrix is calculated as follows;

Δy = -5(2 + 65) + 17(-3 + 30) + 0

Δy = 124

The z-determinant of the matrix is calculated as follows;

Δz = -5(65 + 10) + 6 (39 + 12) - 17(15 - 30)

Δz =  186

The value of x, y and z is calculated as follows;

x = Δx/Δ = 62/62 = 1

y = Δy/Δ = 124/62 = 2

z = Δz/Δ = 186/62 = 3

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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Answer:

  B.  quadratic

Step-by-step explanation:

You want to know the kind of function that would best fit the points shown on the graph.

The points on the graph demonstrate a slope that starts out positive and decreases through 0 to a slope with a negative value.

A linear function has a constant slope.

An exponential function has a continuously increasing or continuously decreasing slope.

A quadratic function has a slope that changes sign, matching the slope of the curve joining the given points.

The equation that best fits the given data will be quadratic.

<95141404393>

Answer:

All real numbers

Step-by-step explanation:

The parabola is expanding infinitely in both the negative and positive directions. So the x value will be all real numbers.

Answer: i believe it’s 0.28, but tbh i’m on a unit test so i can’t see what’s wrong and what’s right. good luck!

Step-by-step explanation:

Answer:

c- 0.28

Step-by-step explanation:

51% captures a larger portion of the whole compared to half (50%), making 51% of a number more than half of the number.

When we say 51% of a number is more than half of the number, we are comparing two fractions.

Half of a number is represented by 50% (or 0.5), which means dividing the number into two equal parts.

On the other hand, 51% is slightly more than half since it represents a greater proportion.

Since percentages are ratios out of 100, 51% implies that 51 parts out of 100 are taken, while half of the number represents only 50 parts out of 100.

Therefore, 51% captures a larger portion of the whole compared to half (50%), making 51% of a number more than half of the number.

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Answer:

her total cost is $29.45

Step-by-step explanation:

last week - 8 1/2 gallons times $2.30 = $19.55

this week - 4 1/2 gallons times $2.20 = $9.90

$19.55 + $9.90 = $29.45

The total amount Debra ended up paying for the equipment was $28,541.60 and the amount of interest Debra paid on the loan was $14,041.60

(a) To find the total amount Debra ended up paying for the equipment (including the down payment and monthly payments), we need to add the down payment to the total amount of the loan, and then add the total amount of the monthly payments made over the two years.

Total amount of the loan = $14,500 - $1,300 (down payment) = $13,200

Total amount paid = Down payment + Total amount of the loan + Total amount of monthly payments

Total amount paid = $1,300 + $13,200 + ($585.04 x 24) [since there are 24 monthly payments in 2 years]

Total amount paid = $1,300 + $13,200 + $14,041.60

Total amount paid = $28,541.60

Therefore, the total amount Debra ended up paying for the equipment (including the down payment and monthly payments) was $28,541.60.

(b) To find the amount of interest paid on the loan, we need to subtract the total amount borrowed from the total amount paid, and then subtract the down payment. This will give us the total amount of interest paid over the two years.

Total interest paid = Total amount paid - Total amount borrowed - Down payment

Total interest paid = $28,541.60 - $13,200 - $1,300

Total interest paid = $14,041.60

Therefore, the amount of interest Debra paid on the loan was $14,041.60.

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Answer:

1/4 or 0.25

Step-by-step explanation:

The total possibilities of any 7 digit number using 0-9 is :

9×10×10×10×10×10×10=9000000

To work out the total possibilities in this question :

We look at the conditions :

The first digit can only be 5 numbers :

1 , 3 , 5 , 7 , 9

Now we subtract 5 from 9 :

9-5 = 4

Since no repeats for 2 , 3 , 4, 5, 6:

9 , 8 , 7 , 6 , 5,  

5 possibilities for the last digit :

Total possibilities for this code :

4 × 9 × 8 × 7 × 6 × 5 × 5 = 302400

If it begins with 5 that is only 1 possibility for the first digit

1 × 9 × 8 × 7 × 6 × 5 × 5 = 75600

Now we make a fraction :

75600÷302400

Dividing top and bottom by 75600 gives you 1/4 or 0.25

Hope this helped and have a good day

Answer:

Step-by-step explanation:

Comment

The first digit and the last digit are both odd. That tells you that so far what you have is one of 5 digits for the first digit and and one of 4 for the last digit. 4 because you can't repeat the first digit.

5, , , , , ,4

2 digits are gone 8 remain.

5* 8 * 7* 6* 5* 4* 4 = 134400

Part 2

Only one number can go at the beginning, and that is a 5. Everything else remains the same.

1 * 8 * 7 * 6 *5 * 4 * 4 = 26880

P(picking a number beginning with a 5 is  25880 /13440) = 0.2

The word that best describes line segment ID in the image given showing a circle is: a chord.

A chord can simply be described as a line segment in a circle that connects two points on the circumference of a circle to each other.

The largest chord in a circle is a the diameter. A circle can have as many chords as possible.

Considering the image given above, ID is a line segment which connects points I and D which are on the circumference of the circle together. Therefore, ID can best be described as a chord.

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From the information provided;

A commercial is to be played during the 210 minutes of the super bowl. If you had to miss 30 minutes of the game, the probability of seeing beginning of the commercial would be;

The probability of seeing the beginning of the commercial would be 0.1428 (approximately), and when expressed as a percentage, this would be 14.28%.

ANSWER:

The correct answer therefore is 14.3%

Option A is the correct answer

a) The distance of the stone above ground level at time t :

d(t)= -4.9t² + 950

b) It takes 13.92 seconds the stone to reach the ground

c)  With 136.42 m/s velocity the stone strikes the ground.

d) If the stone is thrown downward with a speed of 8 m/s, it will take 13.13 seconds to reach the ground

Here, a  stone is dropped from the upper observation deck of a tower, 950 m above the ground.

(a)  the distance of the stone above ground level at time t would be,

d(t)  = 0.5 (-9.8) t² + v(0) t + d(0)

      = (-4.9)t² + 0t + 950

      = -4.9t² + 950

(b) Now we find the time the stone takes to reach the ground.

i.e., the value of 't' when d = 0

Substituting d(t) = 0 in the above equation.

-4.9t² + 950 = 0

t² = (-950) / (-4.9)

t² = 193.88

t = 13.92 seconds

(c) We need to find the velocity the stone takes to strike the ground

i.e., the velocity when t  = 13.92 seconds

v(t) = v(0) + gt      

v(13.92) = 0 + (9.8)(13.92)

v = 136.42 m/s

(d) here, v(0) = -8 m/s  

Velocity is negative because stone is being thrown downward.

d(t) = 0

(-4.9)t² + v(0) t + d(0) = 0

(-4.9)t² -8t + 950 = 0

Using the quadratic formula we solve above equation for,

t = -14.76, 13.13

We can disregard the negative solution

So, we get t = 13.13 seconds.

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The mean standard deviation of the skittles is calculated to be 0.089

b. The sample proportion of orange Skittles would normally deviate from the true proportion of p = .2 by approximately.089 of a point.

The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.

The standard deviation is calculated from the probability set as follows

Standard deviation = √(p(1 - p)/n)

where

p = probability = 20% = 0.2

n = number of terms = 20

= √(p(1 - p)/n)

= √(0.2 * (1 - 0.2) / 20)

= √(0.2 * (0.8) / 20)

= √(0.16 / 20)

= √(0.008)

= 0.089

this means that the sample will be above the mean by 0.89

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Answer:

The coordinates of ABC are respectively (-2,2), (-2,3), and  (1,2).

Step-by-step explanation:

Dilation About the Origin

Given a point P(x,y), its dilation about the origin by a scale factor of k maps the point to a point P'(kx,ky).

If we are given the dilated point, then we can find the original point by dividing by the scale factor.

Triangle ABC was dilated by a scale factor of 2 about the origin mapping it to triangle A'B'C' with vertices A'(-4,4), B'(-4,6), and C(2,4).

The coordinates of triangle ABC are:

A=(-4/2,4/2) = (-2,2)

B=(-4/2,6/2) = (-2,3)

C=(2/2,4/2) = (1,2)

The coordinates of ABC are respectively (-2,2), (-2,3), and  (1,2).

Answer:

The coordinates of ABC are  (-2,2), (-2,3), and  (1,2).

Step-by-step explanation:

Answer:

5 inches in cm