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2 years ago

Need the answer to this thank you!

Mathematics

1 answer:

Sholpan [36]2 years ago

7 0

Answer:

n = 4

Step-by-step explanation:

Use the explicit formula of a arthmetic sequence: an = a1 + d(n - 1)

a1 = -70

d = -10

an = -100

Do all of the steps and plug all the numbers with the formula.

So -100 = -70 - 10(n - 1)

-100 = -70 - 10n + 10

-100 = -60 - 10n

-100 + 60 = -40

-40 = -10n

-40/-10n = -10n/10

n = 4

So the final answer is n = 4. Just follow all of the steps and you will understand how I got my answer. Hope it helped!

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A die with six faces has the number 1 painted on three of its faces, the number 2 painted on 2 of its faces, and number 3 on one

salantis [7]

Answer:

a) S = {1, 2, 3}

b) P(odd number) = $\frac{2}{3}$

c) No

d) Yes

Step-by-step explanation:

a) The sample space is the set of all possible outcomes. By definition, the elements of a set should not be repeated. Hence, the sample space S = {1, 2, 3}

However, the sample is not equiprobable because each element has different probabilities.

b) P(odd number) = $\frac{number of odd digits}{number of faces}=\frac{4}{6}=\frac{2}{3}$

Note that the odd numbers are 1 (on three faces) and 3 (on one face).

c) The fact the die has been biased does not change the possible outcomes. It only changes the probability of getting any given number.

d) Because the 3-face has been loaded, this probability changes. In fact, it is calculated thus:

Let's assume the probability for 1 or 2 is $x$ . Then that of 3 is $2x$ (because it is twice the others). The sum of probabilities must be 1.

$x+x+x+x+x+2x=1$

$7x=1$

$x=\frac{1}{7}$

P(odd number) = $3\times$ Prob(1) + Prob(3)

= $3\times\frac{1}{7}+\frac{2}{7}$ = $\frac{5}{7}$

7 0

2 years ago

I need help with this i cant get it whats 7|x|=42 is it -6 or just 6

alexdok [17]

7x =42
x=42÷7=6
not -6

8 0

2 years ago

Which expression represents the following calculation? Add the product of 7 and 5 to the quotient of 288 and 18.

Nataly_w [17]

Answer: 288/18+7x5

Step-by-step explanation:

6 0

2 years ago

A radio station signal covers a circular area out from the signal tower. It gets weaker the farther away your are. The local sta

valentinak56 [21]

Answer:

1. We would hear better at Dunkin's since its distance from the radio station is the shortest.

2. McDonald's is out of range of the radio station since its distance is greater than the range of the radio station.

Step-by-step explanation:

1) Will we hear it better at Zaxby's (2,-4), McDonalds (4, -4), or Dunkin' (-3,3). Show work to support your decision and explain your reasoning.

We need to find the distance of each point from the tower.

The shorter the distance from the radio station the better the signal.

The distance between two points (x₁, y₁) and (x₂, y₂) is given by d = √[(x₂ - x₁)² + (y₂ - y₁)²].

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

Since Dunkin's distance, d₃ = 4.24 is the least distance from the radio station and is within range of 5 miles, we would hear better at Dunkin's.

2) Are any of these location outside the range of the radio station? If so, which one(s). Defend your decision mathematically.

The radio station is outside of range if its distance is greater than 5 miles. That is, d > 5 miles.

So, we calculate the distance of each point from the radio station.

With (x₁, y₁) = (0, 0) the location of local station WDHS

For Zaxby's distance located at (2, -4) = (x₂, y₂)

So, d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(2 - 0)² + (-4 - 0)²]

= √[(2)² + (-4)²]

= √[4 + 16]

= √20

= √(5 × 4)

= √5 × √4

= 2√5

= 4.47 miles

For McDonald's distance located at (4, -4) = (x₂, y₂)

So, d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - 0)² + (-4 - 0)²]

= √[(4)² + (-4)²]

= √[16 + 16]

= √32

= √(16 × 2)

= √16 × √2

= 4√2

= 5.66 miles

For Dunkin's distance located at (-3, 3) = (x₂, y₂)

So, d₃ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-3 - 0)² + (-3 - 0)²]

= √[(-3)² + (-3)²]

= √[9 + 9]

= √18

= √(9 × 2)

= √9 × √2

= 3√2

= 4.24 miles

So, for each of the distances calculated above, only McDonald's distance, d₂ = 5.66 miles > 5 miles.

So, McDonald's is out of range of the radio station.

5 0

3 years ago

Suppose that the consumer price index (CPI), which measures the cost of a typical package of consumer goods, stood at 113.5 in

notka56 [123]

Answer:

Equation: y=2x+113.5

CPI in 1992 and 2001 are 117.5 and 135.5 respectively.

Step-by-step explanation:

Let x equal 0 correspond to 1990.

The cost of a typical package of consumer goods, stood at 113.5 in 1990 and 133.5 in 2000.

It is given that the data can be modeled by a straight. So, the line passes through (0,113.5) and (10,133.5).

The equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-113.5=\dfrac{133.5-113.5}{10-0}(x-0)$

$y-113.5=2(x)$

$y=2x+113.5$ .... (1)

Therefore, the best liner equation that models the CPI is y=2x+113.5.

Note: The given options are incorrect.

We need to estimate the CPI in 1992 and 2001.

Substitute x=2 in equation (1), to find the CPI in 1992.

$y=2(2)+113.5=117.5$

Substitute x=11 in equation (1), to find the CPI in 2001.

$y=2(11)+113.5=135.5$

Therefore, the CPI in 1992 and 2001 are 117.5 and 135.5 respectively.

8 0

3 years ago

Need the answer to​ this thank you!

Need the answer to this thank you!