At a restaurant, the bill comes to $30. If you decide to leave a 10% tip, how much total do you need to pay? Give your answer to the nearest dollar.

The  equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1

To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.

Alternatively, we can use PF = PM to find the equation of the parabola.

vertex is half way between the focus and directrix

It's a downward opening parabola, general form

y= a(x-h)^2 + k

where (h,k) = vertex= (-3,-1)

plug in another point on the parabola to solve for a which gives

am answer with either x coefficient = -1'/4 or =4 Check the math.

one or the other is right another point is the y intercept = 9a-1

Another point is directly to the right of the focus  (-1, -2)  It's 2 down from the directrix and 2 to the right of the focus, equidistant.   plug that point into y= a(x+3)^2 -1 and solve for "a"  

-2 = a((-1+3)^2 -1

-2 = 4a -1

4a = -

a = -1/4

The parabola is y = (-1/4)(x+3)^2 -1

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In linear equation, -1.15  is the value of 21 over 4 − 32 over 5.

What in mathematics is a linear equation?

An algebraic equation B. y=mx+b (where m is the slope and b is the y-intercept) containing simple constants and first-order (linear) components, such as the following, is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.

                                An equation with only one variable is called a univariate linear equation. It contains the expression Ax + B = 0. where A and B are any two real numbers and x is an ambiguous variable with only one possible value. 

(21/4) - (32/5)

=   21 * 5 - 32 * 4/ 20

=  105 -  128/20

= -1.15

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Answer:

C.

Step-by-step explanation:

16 cm² + 9 cm² = 25 cm²

5 cm × 5 cm = 25 cm²

Answer:

  (a)  -3

Step-by-step explanation:

The value of f(x) approaches 3cos(π) = -3 as x approaches π from either direction. The limit is -3.

__

Additional comment

The fact that the function is defined to have a different value at x=π simply means there is a jump discontinuity there. The function is not continuous, because the limit and the function value differ. That doesn't detract from the fact that there is a limit, and it is -3.

Answer:

3.5

Step-by-step explanation:

because its one number less then 3.6

Answer: 9.84*10^6

Step-by-step explanation: Multiply 2.46 by 4

Answer:

Su diferencia es -1.2

Step-by-step explanation:

Analizando la jerarquía de los números esta va de ascendente (mayor) a decendente (menor).

Como se puede ver tu primer número es 1.1 y el que le sigue es -0.1, ahí se podría hacer la primera ecuación que es una resta de números 1.1-0.1=1.2. Vamos a retomar el segundo valor y poner el resultado que nos dio al principio (recordando la ley de los signos:negativo más negativo, pues se suman pero el signo negativo estará presente ahí), para tener sentido aquí hay una explicación.

-0.1-1.2=-1.3 y lo mismo hacemos -1.3-1.2=-2.5

The coordinates of the image of quadrilateral DEFG after being reflected about the origin include the following:

D' = (9, 5).

E' = (-5, -4).

F' = (6, 2).

G' = (-4, -2).

In Geometry, a reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.

Generally speaking, reflecting a point about the origin is a a type of transformation which causes both the x-coordinate and the y-coordinate to become negated (the signs are changed);

(x, y)                              →               (-x, -y)

Ordered pair D  = (-9, -5) →   Ordered pair D' = (9, 5).

Ordered pair E  = (5, 4) →   Ordered pair E' = (-5, -4).

Ordered pair F  = (-6, -2) →   Ordered pair F' = (6, 2).

Ordered pair G  = (4, 2) →   Ordered pair G' = (-4, -2).

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Answer:

A. Reject H0 because the​ P-value is less than or equal to α.

Step-by-step explanation:

Decision:

If the pvalue of the test is less than the significance level, we reject the null hypothesis H0.

Otherwise, we fail to reject the null hypothesis H0.

In this question:

Significance level: 0.01

P-value: 0.0087

0.0087 < 0.01, so we reject H0.

The correct answer is given by option A.

Answer:

2x

Step-by-step explanation:

5, 10, 20, 40, 80

each step is multiplying by 2, therefore the sequence is 2x

Answer:

\(\sqrt{2}\)

Step-by-step explanation:

Angle θ is in standard position and (4,4) is a point on the terminal side of θ.

\(\text{Opposite of }\theta =4 \\\text{Adjacent of }\theta =4 \\$Using Pythagoras Theorem\\Hypotenuse^2=$Opposite^2$+Adjacent^2\\$Hypotenuse^2=4^2+4^2\\$Hypotenuse^2$=32\\Hypotenuse=\sqrt{32}=4\sqrt{2}\)

Now, secant is the inverse of cosine.

Therefore:

\(\sec \theta =\dfrac{Hypotenuse}{Adjacent} \\\sec \theta =\dfrac{4\sqrt{2}}{4} \\\sec \theta =\sqrt{2}\)

1. The hypothesis are given as follows:

2. The critical value is of: t = 2.3974.

3. The test statistic is of: t = 2.35.

4. The decision is: Reject the null hypothesis.

5. The conclusion is: There is enough evidence to conclude that the mean is greater.

At the null hypothesis, it is tested if there is not enough evidence to conclude that the mean in Los Angeles is greater, that is:

\(H_0: \mu \leq 178258\)

At the alternative hypothesis, it is tested if there is enough evidence, hence:

\(H_1: \mu > 178258\)

The t-distribution is used, as we have the standard deviation for the sample but not for the population. Using a t-distribution calculator, with 55 - 1 = 54 df, a right-tailed test, as we are testing if the mean is greater than a value and a significance level of 0.01, the critical value is:

t = 2.3974.

Hence the decision rule is defined as follows:

The test statistic is given by the equation presented as follows:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

\(\overline{x} = 191790, \mu = 178258, s = 42627, n = 55\)

Hence the value of the test statistic is:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{191790 - 178258}{\frac{42627}{\sqrt{55}}}\)

t = 2.35.

The test statistic is greater than the critical value, hence:

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Answer:

70 inches^2

Step-by-step explanation:

7x10=70

The given table does not represent a function. The correct answer is D. No, because one x-value corresponds to two different y-values.

To determine if the table represents a function, we need to check if every x-value corresponds to exactly one y-value. Let's analyze the given table:

x | y

-------

O | 1

X | 4

2 | 3

3 | 2

3 | 5

4 |

5 |

From the table, we can see that the x-values are not unique. Both the values 3 and 4 appear twice in the x-column, but they have different corresponding y-values.

This violates the definition of a function, which states that each input (x-value) should have only one output (y-value).

Therefore, the given table does not represent a function.

The correct answer is D. No, because one x-value corresponds to two different y-values.

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Answer:

alternate interior angles are congruent

Answer:

\(\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}\)

Step-by-step explanation:

To find:

Simplified product of:

\((\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\)

Solution:

First of all, let us have a look at some of the formula:

1. \((a+b) (c+d) = ac+bc+ad+bd\)

2. \(a^b\times a^c =a^{b+c }\)

3. \(\sqrt{a^{2b}} = \sqrt{a^b.a^b}=a^b\)

4. \(\sqrt a \times \sqrt b = \sqrt{a\times b}\)

Now, let us apply the above formula to solve the given expression.

\((\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\\Rightarrow(\sqrt{10x^4})(2\sqrt{15x^4})+(\sqrt{10x^4})(\sqrt{3x^3})-(x\sqrt{5x^2})(2\sqrt{15x^4})-(x\sqrt{5x^2})(\sqrt{3x^3})\\\\\Rightarrow2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\\Rightarrow\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}\)

The answer is:

\(\bold{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}\)

Answer:

Its D

Step-by-step explanation:

The distribution as described in the task content and required to be identified is; a geometric distribution.

By definition and features; a geometric distribution is characterized as follows;

As evident in the given task content; the two possible outcomes are defective and non-defective and the each testing is independent.

Finally, since the probability is same for each trial as described by the approximately 1% defect rate.

Ultimately, the distribution is geometric.

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Answer:

$13.61

Step-by-step explanation:

$18 * 70% = $12.60

$12.60 * 1.08 = $13.61

Answer:

3+jk+k^6

j=2 & k=6

substituting the values, we have

= 3+2(6)+6^3

= 3+12+216

= 231

Ans=231

Step-by-step explanation:

j=2 and k=6

Now

The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).

The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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Answer:

$51.93

Step-by-step explanation:

$48.99 x 1.06 = $51.9294

Answer:. 30 : 48

40:64

Step-by-step explanation: The hint is in the table where the rows highlighted in pink, multiples of 5 and 8, contain the values of the original given ratio, 10:16

Equivalent ratios include any of the corresponding values in columns AND that are in the pink rows.

5:8, 10:16, 15:24, 20:32 . . .

We can see the pattern; pairs of multiples of the factors of the numbers in the original ratio are equivalent ratios.

Domain of the function represented by the graph of a quadratic function y = \(x^2\) – 4 with a minimum value at the point (0,-4) is all real numbers.

The correct answer is option D.

To determine the domain of the quadratic function y = \(x^2\) - 4, we need to consider the x-values for which the function is defined. Since a quadratic function is defined for all real numbers, the domain of this function is "all real numbers."

Let's analyze the given function and its graph to understand why the domain is "all real numbers."

The function y =  \(x^2\) - 4 represents a parabola that opens upward, which means it extends infinitely in both positive and negative x-directions. The vertex of the parabola is at the point (0, -4), indicating that the minimum value of the function occurs at x = 0.

Since there are no restrictions or limitations on the x-values for which the function is defined, the domain is unrestricted and encompasses all real numbers. In other words, the function can be evaluated and calculated for any real value of x, whether it is a negative number, zero, or a positive number.

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Answer:

To solve the equation, factor x 2 + 3 x + 2 using formula x 2 + ( a + b) x + a b = ( x + a) ( x + b). To find a and b, set up a system to be solved. Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution. Since a b is positive, a and b have the same sign.

Step-by-step explanation:

Answer:156

Step-by-step explanation:

Answer: You have six numbers on your ticket. In drawing the first number from the collection of 45, one of those six numbers must be drawn in order for you to still have a chance of winning the big prize. So following the draw, the probability is only 6/45 (or 1/9) that you’re still in the game.

You can now see that on each successive draw the probability steadily drops- to 5/44, 4/43, 3/42, 2/41, and for the last number 1/40. As other answers have stated, there are 8,145,060 possible draws of six numbers and only one makes you a winner.

If you bought ten tickets for every drawing, the odds reach a 50% chance of having won at about 520,550 drawings. Assuming two drawings per week, the chance of winning reaches 50% in about 5,200 years.

Of course, SOMEONE will win and if you don’t play, your chance of winning is zero. It’s kind of fun to occasionally buy lottery tickets just for the dream of winning but don’t spend a lot of money on them.

5.9K viewsView upvotes · Answer requested by Arthur C. Thorpe

7

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Step-by-step explanation:

Answer:

the probability is 3/8

Step-by-step explanation: