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3 years ago

What is the solution to the compound inequality 3x − 8 ≥ −5 and 2x − 7 < 5?

Mathematics

2 answers:

AURORKA [14]3 years ago

6 0

<h2>Answer:</h2>

The solution to the compound inequality is given by:

$1\leq x$

<h2>Step-by-step explanation:</h2>

The compound inequality is given by:

$3x-8\geq -5$ and

$2x-7$

On solving the first inequality i.e.

$3x-8\geq -5$

on adding both side of the inequality by 8 we get:

$3x\geq -5+8\\\\i.e.\\\\3x\geq 3$

Now on dividing both side of the inequality by 3 we get:

$x\geq 1$

The second inequality is given by:

$2x-7$

On adding both side of the inequality by 7 we get:

$2x$

on dividing both side of the inequality by 2 we get:

$x$

Hence, the solution of the compound inequality is:

$1\leq x$

maksim [4K]3 years ago

5 0

1<x<6 or its x>1 and x>6

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-3y^2 + -6y + -17

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2 years ago

Out of 50 basketball players trying to make a team, 5 will be chosen. 36 of the 50 are seniors and the remaining players are jun

AveGali [126]

Answer: 5503680

Step-by-step explanation:

The coach wants 2 senior out of 36 so he have

C₃₆,₂ = 36!/( 36 - 2 )! = 36*35*34!/34! = 36 * 35 = 1260

possibilities

Now he also wants 3 juniors out of 14

C₁₄,₃ = 14!/ (14- 3)! = 14*13*12*11!/11! = 14*13*12 = 2184

Now for each pair of senior (from 1260 outcomes) coach has 2184 possiblities therefore

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2184 * 1260 = 2751840 possibilities to choose from

Again as there are 2 senior to choose for captain we have to multiply by 2 to get the total ways the team could be

2751840*2 = 5503680

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2 years ago

A contractor developed a multiplicative time-series model to forecast the number of contracts in future quarters, using quarterl

dusya [7]

There is a missing content in the question.

After the statements and before the the options given; there is an omitted content which says:

Referring to Table 16-5, in testing the coefficient of X in the regression equation (0.117) the results were a t-statistic of 9.08 and an associated p-value of 0.0000. Which of the following is the best interpretation of this result?

Answer:

C. The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05).

Step-by-step explanation:

From the given question:

The resulting regression equation can be represented as:

$\hat Y = 3.37 + 0.117 X - 0.083 Q_1 + 1.28 Q_2 + 0.617Q_3$

where;

the estimated number of contracts in a quarter X is the coded quarterly value with X = 0

the first quarter of 2010 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise

Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise

Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise

Our null and alternative hypothesis can be stated as;

Null hypothesis :

$H_0 :$ The quarterly growth rate in the number of contracts is not significantly different from 0% (? = 0.05)

$H_a:$ The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

The decision rule is to reject the null hypothesis if the p-value is less than 0.05.

From the missing omitted part we added above; we can see that the t-statistics value = 9.08 and the p-value = 0.000 .

Conclusion:

Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e

The quarterly growth rate in the number of contracts is significantly different from 0% (? = 0.05)

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3 years ago

What is the value of h when the function is converted to vertex form?

Dmitrij [34]

Answer: The value of 'h' is 3.

Step-by-step explanation: Given that the vertex form of a function is given by

$g(x)=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the value of 'h' when the following function is converted to the vertex form.

$g(x)=x^2-6x+14~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (ii), we have

$g(x)=x^2-6x+14\\\\\Rightarrow g(x)=x^2-2\times x\times 3+3^2-3^2+14\\\\\Rightarrow g(x)=(x-3)^2-9+14\\\\\Rightarrow G(x)=(x-3)^2+5.$

Comparing it with the vertex form (i), we get

$h=3.$

Thus, the value of 'h' is 3.

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3 years ago

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satela [25.4K]

Answer:

$K=-2J+24$

Step-by-step explanation:

Trend line passes through the points (6,12) and (4,16).

Find the slope of the line:

$m=\dfrac{K_2-K_1}{J_2-J_1}=\dfrac{16-12}{4-6}=\dfrac{4}{-2}=-2$

Write the equation of the line in the form $K=mJ+b,$ where the slope $m=-2:$

$K=-2J+b$

This line passes through the point (6,12), then its coordinates satisfy the equation:

$12=-2\cdot 6+b\\ \\12=-12+b\\ \\b=12+12\\ \\b=24\\ \\K=-2J+24$

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3 years ago