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Drupady [299]
2 years ago
14

Let x be a real number. Find the lowest possible value of |5x^2 - 16| + |10x - 2|.

Mathematics
1 answer:
BlackZzzverrR [31]2 years ago
4 0

Since the equations are for absolute value this means any negative number used the answer would become positive, so to get the lowest value possible x would need to equal 0, which would eliminate the x variable from the equations.

Replace x with 0 and solve:

|5(0)^2 - 16| + |10(0) - 2|

Simplify:

|0 - 16| + |0 - 2|

|-16| + |-2|

Combine:

|-18|

Absolute Value = 18

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Listed below are annual data for various years. The data are weights​ (metric tons) of imported lemons and car crash fatality ra
anyanavicka [17]

Answer:

Because the​ P-value is _(<u>0.02)  less </u> than the significance level 0.05​, there <u> is </u> sufficient evidence to support the claim that there is a linear correlation between lemon imports and crash fatality rates for a significance level of α=0.05.

C. The results suggest that imported lemons cause car fatalities.

Step-by-step explanation:

Hello!

The study variables are:

X₁: Weight of imported lemons.

X₂: Car crash fatality rate.

The objective is to test if the imported lemons affect the occurrence of car fatalities. To do so you are asked to use a linear correlation test.

I've made a Scatterplot with the given data, it is attached to the answer.

To be able to use the parametric linear correlation you can use the parametric test (Person) or the nonparametric test Spearman. For Person, you need your variables to have a bivariate normal distribution. Since one of the variables is a discrete variable (ratio of car crashes) and the sample is way too small to make an approximation to a normal distribution, the best test to use is Spearman's rank correlation.

This correlation coefficient (rs) takes values from -1 to 1

If rs = -1 this means that there is a negative correlation between the variables

If rs= 1 this means there is a positive correlation between the variables

If rs =0 then there is no correlation between the variables.

The hypothesis is:

H₀: There is no linear association between X₁ and X₂

H₁: There is a linear association between X₁ and X₂

α: 0.05

To calculate the Spearman's correlation coefficient you have to assign ranks to the observed values of each variable, from the smallest to the highest). Then you have to calculate the difference (d)between the ranks and the square of that difference (d²). (see attachment)

The formula for the correlation coefficient is:

rs= 1 - \frac{6* (sum of d^2)}{(n-1)n(n+1)}

rs= 1 - \frac{6* (40)}{4*5*6}

rs= -1

For this value of the correlation coefficient, the p-value is 0.02

Since the p-value (0.02) is less than the significance level (0.05) the decision is to reject the null hypothesis. In other words, there is a linear correlation between the imported lemons and the car crash fatality ration, this means that the modification in the lemon import will affect the car crash fatality ratio.

Note: the correlation coefficient is negative, so you could say that there is a correlation between the variables and this is negative (meaning that when the lemon import increases, the car crash fatality ratio decreases)

I hope it helps!

4 0
3 years ago
When 4x + 4x + 1 = 33 is solved, the result is:
butalik [34]

Answer:

x = 4

Step-by-step explanation:

1. 8x+1 = 33 and the 4x together

2. 8x = 32 subtract 1 from each side

3. x = 4 Divide both sides by 8

6 0
2 years ago
Read 2 more answers
Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if the product of the numbers is 10, the sum of the square
professor190 [17]

Answer:

The sum of two numbers is 7.

Step-by-step explanation:

Given : the product of the numbers is 10, the sum of the squares of the numbers is 29, and the sum of the cubes of the numbers is 133.

Using identity (x+y)(x^2-xy+y^2)=x^3+y^3 and given details, we have to find the sum of two numbers.

Since, given that the product of the numbers is 10 that is xy=10

Also, given the sum of the squares of the numbers is 29 that is x^2+y^2=29

and the sum of the cubes of the numbers is 133 that is x^3+y^3=133

Using, the given identity (x+y)(x^2-xy+y^2)=x^3+y^3,

Substitute, the given values, we have,

(x+y)(29-10)=133

Simplify , we get,

(x+y)(19)=133

Divide both side by 19, we have,

(x+y)=7

Thus, the sum of two numbers is 7.

7 0
3 years ago
Read 2 more answers
|x|-8=5 help me pls some one help me
MariettaO [177]
The answer is X=13 because 13-8=5
6 0
3 years ago
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How can you use the sign of the points to determine location? please help and i will give brainliest :D
Vladimir [108]

To determine the location of a point on a graph, the first number of the ordered pair is a x-coordinate which means the first number you would look for would be the horizontal line, or the x-axis. The second number is the y-coordinate which means that you would look on the vertical line, or the y-axis. You would go on the horizontal line first, then from there go up to the y-coordinate and place your point. (I'm sorry if it's long but you can try to shorten it.)

Hope this helped!

Have a nice day!

8 0
3 years ago
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