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Maru [420]
3 years ago
14

Pls help. I'm stuck on this question

Mathematics
1 answer:
Sav [38]3 years ago
7 0
547.66666666666666667
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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
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