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astraxan [27]
2 years ago
12

Find a1 when d= - 1 and a7= -2

Mathematics
1 answer:
Pie2 years ago
5 0

Answer:

  • a₁ = 4

Step-by-step explanation:

<u>Given</u>

  • d = - 1
  • a₇ = - 2

<u>Find</u> a₁

Use the nth term equation of AP

  • aₙ = a₁ + (n - 1)d

Apply to the given case and solve for a₁

  • - 2 = a₁ + 6(- 1)
  • - 2 = a₁ - 6
  • a₁ = 6 - 2
  • a₁ = 4
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Please help :) worth more than 10 points :) Find the area of the triangle.
olga_2 [115]

13 m ...?.........;;;;;;;;;

5 0
3 years ago
The following data were collected from 12 rain gauges in a park. Build a 95% CI for the mean rainfall at the park.
dybincka [34]

Answer:

Critical values:t_{\alpha/2}=-2.201 t_{1-\alpha/2}=2.201

95% confidence interval would be given by (3.646;4.472)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The data is:

4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87

2) Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}

=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

On this case the average is \bar X= 4.059

=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

The sample standard deviation obtained was s=0.6503

3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. The degrees of freedom are given by:

df=n-1=12-1=11

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,11)" for t_{\alpha/2}=-2.201

"=T.INV(1-0.025,11)" for t_{1-\alpha/2}=2.201

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}  

And we can use Excel to calculate the limits for the interval

Lower interval : "=4.059 -2.201*(0.6503/SQRT(12))" =3.646

Upper interval :  "=4.059 +2.201*(0.6503/SQRT(12))" =4.472

So the 95% confidence interval would be given by (3.646;4.472)

8 0
3 years ago
Find the maximum production level p = 100x^{0.34}y^{0.66} if the total cost of labor (at $72 per unit) and capital (at $40 per u
Anton [14]

Maximum production p=552728

Step-by-step explanation:

The equation for maximum production is : p=100x^{0.34} y^{0.66}

The number of units of labor is x @$72

The number of units of capital is y @$40

The total cost of labor and capital is limited to $270,000, this can be written as;

72x+40y ≤ $270,000

Graphing the inequality to find values of x and y ,from the graph;

x=3750 units

y=6750  units

Applying the expression for maximum production

p=100*x^{0.34}* y^{0.66} \\\\p=100*3750^{0.34} *6750^{0.66} \\\\p=552727.56\\\\p=552728

Learn More

Inequalities graphs :brainly.com/question/11386040

Keywords: maximum, production,cost, labor,limited to,capital ,unit

#LearnwithBrainly

6 0
3 years ago
Help me check my answer!
astra-53 [7]

Step-by-step explanation:

ah, here you go.

come on, now. you know this now ...

again, mutually exclusive attributes in the table (no overlap here) allow us to add the numbers for a total :

4+2+12+10 = 28 students in total.

how many of those 28 fulfill our desired criteria (has a brother) ?

well, it is the sum of the column "has a brother", as it does not matter, if there is also a sister or not.

so, it is 4 + 12 = 16

therefore, the probability to pick a student randomly, who has a brother is

16/28 = 4/7 = 0.571428571...

5 0
2 years ago
I need help pls !!!!!!
swat32

\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}

Actually Welcome to the Concept of the Trigonometry.

here, we use the Linear pair property of the adjacent angles.

We know that, all the adjacent angles in a linear pair add to get 180°

so we get as,

=> (n+6) +90°+(2n+3) =180°

=> (n+6) +(2n+3) =180-90

=> 3n+9 = 90

=> 3n= 90-9

=> 3n = 81

hence, n = 81/3

=> n = 27°

thus the value of n is 27° .

4 0
3 years ago
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