Luisa's restaurant Bill comes to $75.50 and she leaves a 15% tip what is Luisa's total restaurant bill

Which of the following is the minimum value of the equation y = 3x^2 − 4x − 2?

KonstantinChe [14]

Answer:

-3 1/3

Step-by-step explanation:

The quadratic

... y = ax² +bx +c

has its extreme value at

... x = -b/(2a)

Since a = 3 is positive, we know the parabola opens upward and the extreme value is a minimum. (We also know that from the problem statement asking us to find the minimum value.) The value of x at the minimum is -(-4)/(2·3) = 2/3.

To find the minimum value, we need to evaluate the function for x=2/3.

The most straightforward way to do this is to substitue 2/3 for x.

... y = 3(2/3)² -4(2/3) -2 = 3(4/9) -8/3 -2

... y = (4 -8 -6)/3 = -10/3

... y = -3 1/3

_____

<em>Confirmation</em>

You can also use a graphing calculator to show you the minimum.

5 0

3 years ago

ΔMNO is shown.

JulijaS [17]

Answer:

ABC - AAS

DEF - not enough information

GHI - not enough information

JKL - SAS

Step-by-step explanation:

SAS postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

AAS postulate states that if two angles and the non-included side one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

HL postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

ASA postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

SSS postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

1. In triangles MNO and ABC, there are two congruent sides and non-included angle - AAS

2. In triangles MNO and DEF, there are two congruent sides - there is not enough information

3. In triangles MNO and GHI, there are three congruent angles - there is not enough information

4. In triangles MNO and JKL, there are two congruent sides and included angle - SAS

5 0

3 years ago

The top of the Boulder Dam has an angle of elevation of 1.2 radians from a point on the Colorado River. Measuring the angle of e

Nana76 [90]

Answer:

382.925 feets

Step-by-step explanation:

The solution diagram is attached below :

Converting radian measurement to degree :

radian angle * 180/π = degree angle

1.2 * 180/π = 68.755°

0.9 * 180/π = 51.566°

Height of dam is h:

Using trigonometry :

Tan θ = opposite / Adjacent

Tan 68.755° = h / x

h = x Tan 68.755° - - - (1)

Tan 51.566° = h / (155+x)

h = (155+x) tan 51.566° - - - (2)

Equate (1) and (2)

x Tan 68.755 = (155+x) Tan 51.566

x Tan 68.755 = 155tan 51.566 + x tan 51.566

x Tan 68.755 = 195.32311 + x Tan 51.566

x Tan 68.755 - x Tan 51.566 = 195.32311

x(tan 68.755 - tan 51.566) = 195.32311

x * 1.3120110 = 195.32311

1.3120110x = 195.32311

x = 195.32311 / 1.3120110

x = 148.87307

Using :

h = x Tan 68.755

h = 148.87307 * tan(68.755)

h = 382.92539

h = 382.925 feets

5 0

3 years ago

5. The superintendent of the local school district claims that the children in her district are brighter, on average, than the g

anygoal [31]

Answer:

We conclude that children in district are brighter, on average, than the general population.

Step-by-step explanation:

We are given the following data set:

105, 109, 115, 112, 124, 115, 103, 110, 125, 99

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{1117}{10} = 111.7$

Sum of squares of differences = 642.1

$S.D = \sqrt{\frac{642.1}{49}} = 8.44$

We are given the following in the question:

Population mean, μ = 106

Sample mean, $\bar{x}$ = 111.7

Sample size, n = 10

Alpha, α = 0.05

Sample standard deviation, s = 8.44

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 106\\H_A: \mu > 106$

We use one-tailed(right) t test to perform this hypothesis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{111.7 - 106}{\frac{8.44}{\sqrt{10}} } = 2.135$

Now,

$t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = 1.833$

Since,

$t_{stat} > t_{critical}$

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.

We conclude that children in district are brighter, on average, than the general population.

4 0

2 years ago

Mean, median, mode or standard deviation best represents the data

pickupchik [31]

Answer:

mean

Step-by-step explanation:

7 0

2 years ago