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2 years ago

Find the range of the function in the image.

Mathematics

1 answer:

bixtya [17]2 years ago

3 0

Answer:

0 < f(x) ≤ 3/4, or (0, 3/4]

Step-by-step explanation:

x² - x + 1 = x² - x + 1/4 + 3/4 = (x - 1/2)² + 3/4

It is always positive and has a minimum value of 3/4 at x = 1/2

So f(x) is always positive (not equal zero) and has a maximum value of 3/4

Then the range is 0 < f(x) ≤ 3/4, or (0, 3/4]

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Two sides of a triangle have lengths of 18 and 29 units. if the third side has an integer length, what is the positive differenc

Andru [333]

Triangular inequality: Length of third side must be less than the sum of the lengths of the other 2 sides.
x < 18 + 29
x < 47

so Maximum length of third side is 46 units.

Also 29 < 18 + x
x > 11 so minimum length = 12

Difference = 46-11 = 35

3 0

3 years ago

Your bill at a restaurant was $29.54, which included the tax at a rate of 7.4%. What was the price before tax? Decimals allowed

tatiyna

Let's think about what happens when you find the price after tax. Let the price before tax be $p$ . The tax rate is $7.4 \% = .074$ , so the tax part of the total price is $.074p$ . Adding that onto the original price, we see that

$p + .074p = \$29.54$
$1.074p = \$29.54$

So, we can just divide each side by $1.074$ to get the original price, which rounded to two decimal places is $\bf \$27.50$ .

3 0

3 years ago

Find the sum of the first 90 terms of the sequence -4,-1,2,5,8

telo118 [61]

Answer:

1655

Step-by-step explanation:

Note the common difference d between consecutive terms of the sequence

d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3

This indicates the sequence is arithmetic with sum to n terms

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ]

Here a₁ = - 4, d = 3 and n = 90, thus

$S_{90}$ = $\frac{90}{2}$ [ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655

4 0

3 years ago

Compare.<br><br> 140/130 _____ 104%

Gnoma [55]

Answer:

140/130 > 104%

Step-by-step explanation:

When you convert 140/130 to a decimal, you get 1.07 which is 107%. 107% is greater than 104%, so 140/130 is > 104%

8 0

3 years ago

A report states that the mean yearly salary offer for students graduating with a degree in accounting is $48,743. Suppose that a

Shtirlitz [24]

Answer: Reject H0. We do not have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,743

Step-by-step explanation:

The relevant t-test for this situation would be:

$\frac{49870-48743}{\frac{3300}{\sqrt{50} } }$

Which is (49870-48743) ÷ standard error

standard error = standard deviation ÷√sample size

From the t-test, we obtain the value = 2.41...

Using α = 0.05, our critical value is 1.96. As 2.41 is larger than 1.96, we reject our null hypothesis that the mean salary offer is higher than $48,743

5 0

4 years ago