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Answer:

[tex]\displaystyle a_1 = 44[/tex]

Step-by-step explanation:

Recall the direct formula for an arithmetic sequence:
[tex]\displaystyle a_n = a_1 + d(n-1)[/tex]

Where d is the common difference.

Therefore, we can write the following two equations:
[tex]\displaystyle \left \{ {a_4 = 107 = a_1 + d(4-1)\atop {a_8 = 191 = a_1 + d(8-1)}} \right.[/tex]

Solve the system. Simplifying yields:
[tex]\displaystyle 107 = a_1 + 3d\text{ and } 191 = a_1 + 7d[/tex]

Subtracting the two equations into each other yields:
[tex]\displaystyle \begin{aligned} (191) - (107) & = (a_1 + 7d) - (a_1 + 3d) \\ \\ 84 & = 4d \\ \\ d & = 21 \end{aligned}[/tex]

Using either equation, solve for the initial term:

[tex]\displaystyle \begin{aligned} 107 & = a_1 + 3(21) \\ \\ a_1 & = 107-63 \\ \\ & = 44\end{aligned}[/tex]

In conclusion, the initial term is 44.

Answer:

[tex]\huge\boxed{\bf\:a_{1} = 44}[/tex]

Step-by-step explanation:

In the given arithmetic series,

We know that,

[tex]\boxed{a_{n} = a + (n - 1)d}[/tex]

Therefore,

[tex]a_{4} = a + 3d = 107 -----(1)\\a_{8} = a + 7d = 191 -----(2)[/tex]

By solving the two equations (1) & (2)....

[tex]\:\:\:\:a + 7d = 191 \\-\underline{a + 3d = 107 }\\ \underline{\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:4d = 84\:\:\:\:\:\:\:\:}}\\\\\\\\4d = 84\\d = 84 \div 4\\\boxed{d = 21}[/tex]

Now, we have the value of the common difference (d). To find [tex]a_{1}[/tex] or a, let's substitute the value of 'd' in (1).

[tex]a + 3d =107\\a + 3(21)=107\\a + 63 = 107\\a = 107 - 63\\\boxed{\bf\:a_{1} = 44}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

The interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.

According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.

[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]

Here, we had  where mean of distribution of X is \mu  and standard deviation from mean of distribution of X is \sigma

The amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1400 hours and a standard deviation of 50 hours. Thus,

[tex]\mu=1300\\\sigma=90[/tex]

Using the empirical rule, the interval of hours represents the lifespan of the middle 68% of light bulbs is,

[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(1300- 90 < X < 1300+ 90) = 68\%\\P(1210 < X < 1390) = 68\%[/tex]

Thus, the interval of hours represents the lifespan of the middle 68% of light bulbs, using the empirical rule is, 1210 hours to 1390 hours.

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Answer:

Your Answer is D.

Step-by-step explanation:

There isn't much to explain but look at the graph.

The slope of m = rise/run.

m = 1/2

b = -3/2

y = mx + b

Answer:20%

Step-by-step explanation:

Solution for 600 is what percent of 3000:

600:3000*100 =

( 600*100):3000 =

60000:3000 = 20

Now we have: 600 is what percent of 3000 = 20

Question: 600 is what percent of 3000?

Percentage solution with steps:

Step 1: We make the assumption that 3000 is 100% since it is our output value.

Step 2: We next represent the value we seek with x.

Step 3: From step 1, it follows that $100%=3000.

Step 4: In the same vein, x%=600.

Step 5: This gives us a pair of simple equations:

$100%=3000(1).

x%=600(2).

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

100% / %=3000/600

Step 7: Taking the inverse (or reciprocal) of both sides yields

x%/100%=600/3000

--->=20%

Therefore, $600 is $20% of $3000.

Answer:

-11

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

If he runs five times a week and his route is 2 7/10 then you do 5x2 7/10

The probability that the first pencil is green and the second pencil is yellow is 0.16.

Probability determines the odds that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the first pencil is green and the second pencil is yellow = (number of green pencils / total number of pencils) x (number of yellow pencils / total number of pencils)

5/17 x 9/17 = 0.16

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Answer:

5.99 days.

Step-by-step explanation:

If you are asking how many days he can rent the car then this is the correct answer.

So first multiply 275 x .06 to get how much money he will spent on the mileage. Which is $16.50. Then subtract that from $450 which is $433.50 and divided by $72.37.

Answer:

addition, subtraction, multiplication

Step-by-step explanation:

If you add two polynomials, the result is a polynomial. If you subtract two polynomials, the result is a polynomial. If you multiply two polynomials, the result is a polynomial.

Answer:

Fraction 8/20

Step-by-step explanation:

So only 12 people don't use sugar so if we were to put a fraction for people who don't put sugar then it would be.

12/20

The 20 stands about how many people their are and the 12 stands for how many people don't put sugar.

So now we are supposed ot do peope who put sugar so it would look like this

8/20

How I got the 8 is that I took the 20 people and subtrack it with the people who don't get sugar which is 8 and 8 people use sugar so theirs our answers.

8/20

Answer:

86 5/8 square feet

Step-by-step explanation:

[tex]10 \frac{1}{2} \times 8\frac{1}{4} = \frac{21}{2} \times \frac{33}{4} = \frac{693}{8} = 86 \frac{5}{8} [/tex]

Answer:

b

Step-by-step explanation:

Answer:

79/156

Step-by-step explanation:

we know that cosx is the adjacent side over the hypotenuse.

hence, we can find the opposite side using the pythagorean theorem.

sqrt(13^2 - 5^2)

therefore, the opposite side is 12

opposite: 12

adjacent: 5

hypotenuse: 13

not that cot is adjacent over opposite while sin is opposite over hypotenuse.

So,

12/13 - 5/12

the answer is 79/156

Answer:

A) (x, y) → (x - 8, y)

Step-by-step explanation:

(3, 7) →  (-5, 7)

Without adding or subtracting any values, we can immediately tell that the y-value did not change, but the x-value did. With this, we are left with choices A and D.

A) (x, y) → (x - 8, y)

   (3, 7) → (3 - 8, y)

   (3, 7) → (-5, 7)

This matches our problem, and therefore, A is the correct answer.

Hope this helps!

Answer:

A) (x, y) → (x-8, y)

Explanation:

Present Point: (3, 7)

Future Point: (-5, 7)

The change be: (x, y)

Solve:

(3, 7) + (x, y) → (-5, 7)

change side

(x, y) → (-5, 7) - (3, 7)

simplify the following

(x, y) → (-8, 0)

Therefore, we identify this using (x - 8, y)

Answer:

379.94 cm2 correct me if im wrong

We know that,

[tex] \rightarrow \: z = \frac{x - \mu}{\sigma} \\ [/tex]

inserting the given values in the formula

[tex]\rightarrow \: z = \frac{27.87 - 30}{1.9} \\\rightarrow \: z = - 1.121[/tex]

Area that's left to z = -1.121

Area that's left to -1.121 = 0.1311

= 13.11%

Hence ,

13.11% of the watermelons weigh less than 27.87 pounds

To find the number of watermelons,

We'll find 13.11% of 400

= 13.11% x 400

= 13.11/100 x 400

= 52.44

hence , approx 52 watermelons would be lesser than 27.87 pounds

Answer:

where is the shape ???????

The set of transformations that would map the red triangle to the blue triangle are translation by 2 units up and 4 units left

From the graph, we have the following highlights:

This means that the transformation is 2 units up and 4 units left

Hence, the set of transformations that would map the red triangle to the blue triangle are translation by 2 units up and 4 units left

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Answer:

  2 solutions

Step-by-step explanation:

In order to answer a question "based on the graph," we need to have a graph of the equation. A graph provided by a graphing calculator is attached.

The cubic intersects the x-axis at two distinct points.

There are two (2) distinct real solution to the equation. (x = -1, x = 2).

Answer:

A. 17

Step-by-step explanation:

The "mean" is the same as an average.

To find the mean, add all the numbers.

Then divide that sum by the total numbers you added.

18+23+9+16+30+16+7=119.

119/7= 17.  (We divided by 7 because we added 7 numbers)

Hope this helps!

your answer would be 254 I just did it and I got it right ✨

Answer:

Q2: J. all real numbers.

Q4: [tex]f(3)=-20[/tex]

Q15: [tex]y=-3x+5[/tex]

Step-by-step explanation:

Q2: J. All real numbers.

Range: It can be [tex]y\geq 1[/tex].

It can't be [tex]y\geq 2[/tex].

Domain: It can't be [tex]x\geq 1[/tex] because it is going from (-∞,+∞)

Q4:

[tex]f(x)=-2x^2+x-5,f(3)=?[/tex]

Plugin x with 3 into the equation.

[tex]f(3)=-2(3)^2+(3)-5\\f(3)=-2*9+3-5\\f(3)=-18+3-5=-20\\f(3)=-20[/tex]

Q15: point-slope form.

[tex]y-(y_1)=m(x-x_0)[/tex], plugin [tex](2,-1)=(x_0,y_0)[/tex] and m=-3

[tex]y-(-1)=-3(x-(2))\\y+1=-3(x-2)\\y+1=-3x+6\\y=-3x+5[/tex]

Based on the curve ; The graph is:

       B. The curve is a many-to-one function.

Function--

A function is a relation in which each element is mapped to a single element i.e. no element is mapped to two different elements.

Also, the graph of a function satisfies the vertical line test i.e. any line passing through the domain and parallel to the y-axis should intersect the graph exactly once.

and one-to-one function--

A one-to-one function is such that no two elements have the same image i.e. any line passing through the co-domain and parallel to the x-axis should intersect the graph at most once.

Hence, by looking at the graph we see that the graph is not a straight line.

Hence, it is not a linear function.

           Hence, the correct answer is:

                   Option: B

Answer:

So this is what hello means :):):):):):):)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

38 cm

Step-by-step explanation:

The perimeter of the figure is the sum of the lengths of all its sides.

We have two unknown length, so let's find their lengths first.

x= 10 -6= 4 cm

y= 9 -2= 7cm

Let's add all the lengths together to find the perimeter:

Perimeter

= 9 +10 +2 +6 +7 +4

= 38 cm

Answer:

First one: median= 98

Second one: median= 105

Thrid one: median= 103

Step-by-step explanation:

The median is the middle number.