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3 years ago

Warm-Up

1 answer:

8 0

Answer: x = -5 and x = 3

Explanation:
x = -5
(-5 + 5)(-5 - 3) = 0
(0)(-8) = 0
0 = 0 TRUE

x = 3
(3 + 5)(3 - 3) = 0
(8)(0) = 0
0 = 0 TRUE

(Also, could I have brainliest please?)

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The average spending at Neco's salad bar is $9.03 with a standard deviation of $3.26. The distribution follows t-distribution. T

arlik [135]

Answer:

The difference between these cut-offs is of $1.9.

Step-by-step explanation:

In this question, we have to find the 90% confidence interval, using the t-distribution.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 41 - 1 = 40

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.9}{2} = 0.95$ . So we have T = 1.684

The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.684\frac{3.26}{\sqrt{41}} = 0.95$

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 9.03 - 0.95 = $8.08.

The upper end of the interval is the sample mean added to M. So it is 9.03 + 0.95 = $9.98.

What will be the difference between the upper and lower spending cut-offs which define the middle 90% of the customers if the sample contains 41 customers

$9.98 - $8.08 = $1.9

The difference between these cut-offs is of $1.9.

8 0

3 years ago

Consider the function f(x) = x2 + 2x – 15. What are the x-intercepts of the function?

Rus_ich [418]

Answer:

The x-intercepts of the function are $x = 3$ and $x = -5$ .

Step-by-step explanation:

We are given the function $\displaystyle f(x) = x^2 + 2x - 15$ .

In order to find the x-intercepts of the equation, we need to solve this quadratic. We can use factoring methods to solve it.

The parent function for a quadratic is $f(x) = ax^2 + bx + c = 0$ .

We can use this information to determine what factoring technique we want to use.

There are several different methods, including using the quadratic formula, but because this is easily factorable, we can avoid using it.

We see that our <em>a</em> is equal to 1 (there is no coefficient in front of x²), so we can use the easier of the techniques:

Find what factors of c add up to give you b.
Add to x if positive or subtract from x if negative and set it equal to zero.
Solve for x - these are your x-intercepts.

Therefore, let's determine what our c is: 15.

Now, let's label the factors for 15.

15 cannot be divided by 2 evenly.
15 can be divided by 3 evenly: 15/3 = 5
15 cannot be divided by 4 evenly.
15 can be divided by 5 evenly: 15/5 = 3

Therefore, our two factors are 3 and 5 since they cannot be broken down any further (they are prime numbers - we just performed prime factorization).

Now, we need to pay attention to the sign for c. It's negative, so one of our factors needs to be negative. Therefore, we can test this out:

$5 + -3 = 2$
$-5 + 3 = -2$

Now, we check for which one matches the sign for b. This is positive 2, so our two factors are 5 and -3.

Finally, to factor, we add or subtract the factors from x depending on the sign. If the factor is positive, we add it. If the factor is negative, we subtract it. Therefore, we can set up our equations.

$x + 5 = 0\\\\x = -5$

$x - 3 = 0\\\\x = 3$

Therefore, for when x = 3 or x = -5, the line crosses the x-axis. These are the x-intercepts of the function.

Our answers are x = -5 and x = 3.

4 0

3 years ago

If 2a+2/a=4, what is the value of 2a^2+2/a^2

Arturiano [62]

Answer:

Step-by-step explanation:

2a + 2 / a = 4

2a + 2 = 4a

4a - 2a = 2

2a = 2

a = 1

2a² + 2 / a²

a = 1

2(1²) + 2 / 1²

2 + 2 / 1

8 0

2 years ago

How are reciprocals used in division with rational numbers?

Neko [114]

Answer:

When dividing rational numbers, multiply by the "right" reciprocal. In this case, the "right" reciprocal means to take the reciprocal of the fraction on the right-hand side of the division operator.

8 0

3 years ago

Read 2 more answers

A trapezoid has base lengths of 5 meters and 3.5 meters. If the height of the trapezoid is 4 meters, what is the area of the tra

aev [14]

Answer:

17 m² or 17 square meters

Step-by-step explanation:

A trapezoid has base lengths of 5 meters and 3.5 meters. If the height of the trapezoid is 4 meters, what is the area of the trapezoid?

Area of a trapezoid =1/2(b1 + b2)h

Where

b1 = First base length = 5m

b2 = Second base length = 3.5 m

Height = 4m

= 1/2(5m + 3.5m) × 4m

= 1/2(8.5m) × 4m

= 1/2 × 8.5m × 4m

= 17 m²

Therefore, the area of the trapezoid is 17 m² or 17 square meters

6 0

3 years ago