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3 years ago

The graph of h (x) = StartAbsoluteValue x minus 10 EndAbsoluteValue + 6 is shown. On which interval is this graph increasing

Mathematics

2 answers:

k0ka [10]3 years ago

7 0

Answer:

x≥10 or x∈[10, ∞)

Step-by-step explanation:

The graph we are given is h(x) = |x-10|+6, which has the shape of a V. The vertex is at (10, 6), so to the right of the vertex, the graph is increasing.

Therefore, the graph increases during the interval x≥10 or x∈[10, ∞).

devlian [24]3 years ago

4 0

The answer is 10 because there is not negative number so the absolute value of a positive number is that number

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Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year many small plots of equal size but

podryga [215]

Answer:

(a) 0.653

(b) 0.0198

(c) Yes, after testing we conclude that the population variance of annual wheat production for the first plot is larger than that for the second plot.

Step-by-step explanation:

(a) We are give the sample of one year annual production of wheat (in pounds) ;

4.46, 4.21, 4.40, 4.81, 2.81, 2.90, 4.93, 3.54, 4.16, 4.48, 3.26, 4.74, 4.97, 4.02, 4.91, 2.59

For calculating sample variance, firstly we will calculate mean of the above data;

Mean of above data, $X_1bar$ = Sum of all values ÷ n (no. of values)

= $\frac{4.46 + 4.21+4.40+.......+4.91+2.59}{16}$ = 4.074

Sample Variance, $s_1^{2}$ = $\frac{\sum (X-X_1bar)^{2} }{n-1}$ = $\frac{(4.46-4.074)^{2}+(4.21-4.074)^{2}+.........+(4.91-4.074)^{2}+(2.59-4.074)^{2} }{16-1}$ = 0.653

(b) Another sample for annual wheat production (in pounds);

3.89, 3.81, 3.95, 4.07, 4.01, 3.73, 4.02, 3.78, 3.72, 3.96, 3.62, 3.76, 4.02, 3.73, 3.94, 4.03

Mean of above data, $X_2bar$ = Sum of all values ÷ n (no. of values)

= $\frac{3.89+3.81+3.95.......+3.94+4.03}{16}$ = 3.88

Sample Variance, $s_2^{2}$ = $\frac{\sum (X-X_2bar)^{2} }{n-1}$ = $\frac{(3.89-3.88)^{2}+(3.81-3.88)^{2}+.........+(3.94-3.88)^{2}+(4.03-3.88)^{2} }{16-1}$ = 0.0198

(c) Now, we have to test the claim that population variance of annual wheat production for the first plot is larger than that for the second plot i.e.;

Null Hypothesis, $H_0$ : $\sigma_1^{2} = \sigma_2^{2}$ or $H_0$ : $\frac{\sigma_1^{2} }{\sigma_2^{2} } = 1$

Alternate Hypothesis, $H_0$ : $\sigma_1^{2} > \sigma_2^{2}$ or $H_0$ : $\frac{\sigma_1^{2} }{\sigma_2^{2} } > 1$

The test statistics used here is;

$\frac{s_1^{2} }{s_2^{2} }* \frac{\sigma_1^{2} }{\sigma_2^{2}}$ ~ $F_n__1-1_,n_2-1$ where, $n_1 = 16$ and $n_2 =16$

Test Statistics = $\frac{0.653 }{ 0.0198}* 1$ ~ $F_1_5_,_1_5$

= 32.98

Since, we are not provided with any significance level so we assume it to be 5% and at this level, the F table gives critical value of 2.4282.

<em>Since our test statistics is higher than the critical value and it falls in the rejection region so we have sufficient evidence to reject null hypothesis and conclude that the population variance of annual wheat production for the first plot is larger than that for the second plot.</em>

8 0

3 years ago

Integral from 0 to 5 of x^2 + 3 dx

Alla [95]

Answer:

=170/3 or (decimal 56.67)

Step-by-step explanation:

Steps

∫⁵ x²+3dx

⁰

Apply the Sum Rule: ∫fx) + gx) dx = ∫f(x)dx +-∫ g(x)

∫⁵ x² dx +∫⁵ 3dx

⁰ ⁰

∫⁵ x² dx=125/3

⁰

∫⁵ 3dx=15

⁰

125/3+15

=170/3

4 0

2 years ago

Please please help me with my math

densk [106]

Answer:

Step-by-step explanation:

In functions like this, its best to pay attention to the end points of the rays.

On the lower line:

it ends at x -1

because it is a closed circle, that means x can also equal -1.

x≤-1

On the upper line:

it starts at -1

it is an open circle, meaning x cannot be -1

x>-1

7 0

2 years ago

I need to learn about percent, proportion, and mixture word problems

oksano4ka [1.4K]

Answer:

Percent:

There are many formulas for percentage problems. You can think of the most basic as X/Y = P x 100. The formulas below are all mathematical variations of this formula.

X and Y are numbers and P is the percentage:

Find P percent of X

Find what percent of X is Y

Find X if P percent of it is Y

Mixture:

Solving a percent mixture problem can be done using the equation Ar = Q, where A is the amount of a solution, r is the percent concentration of a substance in the solution, and Q is the quantity of the substance in the solution.

Proportion:

Many "proportion" word problems can be solved using other methods, so they may be familiar to you. For instance, if you've learned about straight-line equations, then you've learned about the slope of a straight line, and how this slope is sometimes referred to as being "rise over run". But that word "over" gives a hint that, yes, we're talking about a fraction. And this means that "rise over run" can be discussed within the context of proportions.

Step-by-step explanation:

Hope This Helps!

4 0

3 years ago

Which polynomial is prime? x2 – 36 x2 16 x2 – 7x 12 x2 – x – 20.

miskamm [114]

Answer:

start with what you know

Step-by-step explanation:

makes you smarter

5 0

3 years ago