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scZoUnD [109]
3 years ago
14

What is the solution to the system of equations below? 5 x + 2y = -3 3x + 6y = 6

Mathematics
1 answer:
Orlov [11]3 years ago
3 0
Eqn (1)*3: 15x + 6y = -9 -> Eqn (3)
Eqn (3) - Eqn (2): 12x = -15
x = -5/4 = -1 1/4
Eqn (2): -15/4 + 6y = 6
6y = 9 3/4
y = 1 5/8

x = -1 1/4
y= 1 5/8
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Daily-high temperature measurements for 40 consecutive days are recorded for a particular city. The mean daily-high temperature
Vesnalui [34]

Answer:

t=\frac{21.5-22}{\frac{1.5}{\sqrt{40}}}=-2.108    

p_v =P(t_{39}  

Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean temperature actually its NOT significant less then 22 at 1% of signficance.  

(D) P-val=0.021, fail to reject the null hypothesis

Step-by-step explanation:

1) Data given and notation  

\bar X=21.5 represent the mean for the temperatures

s=1.5 represent the sample standard deviation

n=40 sample size  

\mu_o =22 represent the value that we want to test

\alpha=0.01 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 check if the mean is less than 22C, the system of hypothesis would be:  

Null hypothesis:\mu \geq 22  

Alternative hypothesis:\mu < 22  

If we analyze the size for the sample is > 30 and we don't know the population deviation so 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{21.5-22}{\frac{1.5}{\sqrt{40}}}=-2.108    

P-value

We can calculate the degrees of freedom like this:

df=n-1=40-1=39

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

p_v =P(t_{39}  

Conclusion  

If we compare the p value and the significance level given \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the mean temperature actually its NOT significant less then 22 at 1% of signficance.  

The best option would be:

(D) P-val=0.021, fail to reject the null hypothesis

5 0
3 years ago
Use the polynomial 3x^2−4x^11+4x^4−2x^10−5+^8x^8 to answer the question. 
Anit [1.1K]

Answer: 11

<u>Step-by-step explanation:</u>

3x² - 4x¹¹ + 4x⁴ - 2x¹⁰ - 5 + 8x⁸

To find the degree, look for the largest exponent.  <em>11</em>

If you put this polynomial in standard form (from largest to smallest exponent), the first term will give you the degree of the polynomial and the leading coefficient.

- 4x¹¹ - 2x¹⁰ + 8x⁸ + 4x⁴ + 3x² - 5

4 0
3 years ago
Read 2 more answers
Please please help. I have a bunch of these and I don’t understand it at all
shtirl [24]
The correct option is: Option (B) \sum_{i=1}^{7} (5i-2)

Explanation:

First thing is that the difference between each number in the series with the next number is 5. It means it must be the multiple of 5. There are two options that contain multiples of 5: Option B and Option D. Now in the option D, the upper limit is 6. If we put 6 in the expression: 5(6)-2, the last term would be 28. However in the series given in the question, the last term is 33. Hence 5(7) - 2 = 35 - 2 = 33 which is Option B.

When i=1: 5(1)-2 = 3
When i=2: 5(2)-2 = 8
When i=3: 5(3)-2 = 13
.
.
When i=7: 5(7)-2 = 35-2 = 33
Hence the correct option is (B).
3 0
3 years ago
For his troops' popcorn fundraiser sale, Mike sold caramel corn for $10, buttered microwave popcorn for $8, and lightly buttered
erastovalidia [21]
Mike sold 99 bags of caramel corn,60 bags of buttered popcorn,and 109 bags of lighted buttered corn
 
8 0
3 years ago
Pts
ladessa [460]

Answer:

<u>In week 20, Seth will have 80 cards and Matt will have 60.</u>

Step-by-step explanation:

Let's find out the amount of cards that Math and Seth will have in week 20, using the information shown in the graph and table:

Amount of cards Seth has in week 20 = 20 * 4 = 80

The equation to find out the amount of cards, c, Seth has in week w:

c = 4w

Amount of cards Matt has in week 20 = 20 + (2 * 20) = 20 + 40 = 60

The equation to find out the amount of cards, c, Matt has in week w:

c = 20 + 2w

<u>In week 20, Seth will have 80 cards and Matt will have 60.</u>

8 0
3 years ago
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