Pls help. I'm stuck on this question

Find the sum of each series, if it exists<br>91 + 85 + 79 + … + (29)

Natali [406]

Answer:

651.

Step-by-step explanation:

Note: In the given series it should be -29 instead of 29 because 29 cannot be a term of AP whose first term is 91 and common difference is -6.

Consider the given series is

$91+85+79+...+(-29)$

It is the sum of an AP. Here,

First term = 91

Common difference = 85 - 91 = -6

Last term = -29

nth term of an AP is

$a_n=a+(n-1)d$

where, a is first term and d is common difference.

$-29=91+(n-1)(-6)$

$-29-91=(n-1)(-6)$

$\dfrac{-120}{-6}=(n-1)$

$20=(n-1)$

$n=20+1=21$

Sum of AP is

$Sum=\dfrac{n}{2}[\text{First term + Last term}]$

$Sum=\dfrac{21}{2}[91+(-29)]$

$Sum=\dfrac{21}{2}[62]$

$Sum=651$

Therefore, the sum of given series is 651.

5 0

2 years ago

Help me with this question

Maksim231197 [3]

Answer:

3m/s

Step-by-step explanation:

Your welcome

4 0

3 years ago

PLEASE HELP ME <br>...This is my homework and I don't understand how to do it.

musickatia [10]

The probability that a point chosen at random lies in the shaded region is 0.28

<h3>Calculating the area of a shaded region and probability</h3>

From the question, we are to find the probability that a point chosen at random lies in the shaded region.

The shaded region is a triangle.

The probability that a point chosen at random lies in the shaded region = Area of the triangle / Area of the circle

First, we will calculate the unknown side of the triangle

Let the unknown side be x.

Then, from the <em>Pythagorean theorem</em>, we can write that

12² = 6² + x²

144 = 36 + x²

x² = 144 - 36

x² = 108

x = √108

x = 6√3

From formula,

Area of a triangle = 1/2 × base × height

Area of the triangle = 1/2 × 6 × 6√3

Area of the triangle = 18√3 square units

Now, we will determine the area of the circle

Area of a circle = πr²

Where r is the radius

From the given information,

Diameter of the circle = 12

But,

Radius = Diameter / 2

Therefore,

r = 12/2

r = 6

Thus,

Area of the circle = 3.14 × 6²

Area of the circle = 113.04 square units

Now,

The probability that a point chosen at random lies in the shaded region = 18√3 / 113.04

The probability that a point chosen at random lies in the shaded region = 0.2758

The probability that a point chosen at random lies in the shaded region ≈ 0.28

Hence, the probability is 0.28

Learn more on Calculating area of a shaded region here: brainly.com/question/23629261

#SPJ1

4 0

1 year ago

2. A particular resource class must perform at a level consistent with the rest of the school to avoid being discontinued. On th

Natali5045456 [20]

Answer:

$t=\frac{71.86-78}{\frac{17.52}{\sqrt{14}}}=-1.311$

$p_v =P(t_{13}$

If we compare the p value and a significance level assumed for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the scores is NOT significant less than 78.

Step-by-step explanation:

Data given and notation

$\bar X=71.86$ represent the sample mean

$s=17.52$ represent the standard deviation for the sample

$n=14$ sample size

$\mu_o =78$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean is less than 78, the system of hypothesis would be:

Null hypothesis: $\mu \geq 78$

Alternative hypothesis: $\mu < 78$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{71.86-78}{\frac{17.52}{\sqrt{14}}}=-1.311$

Calculate the P-value

First we need to find the degrees of freedom given by:

$df=n-1=14-1=13$

Since is a one-side left tailed test the p value would be:

$p_v =P(t_{13}$

Conclusion

If we compare the p value and a significance level assumed for example $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the actual true mean for the scores is NOT significant less than 78.

3 0

3 years ago

19/2 - 11/2 as an improper fraction

rjkz [21]

Answer:9 1/2 and 5 1/2

I hope that’s what your looking for

8 0

3 years ago