the cake is regular price at $9 and is on sale for 25%. how much would you save with the discount

Part b.

In this case, we have the following function:

First, we need to solve for x. Then, by applying natural logarithm to both sides, we have

By the properties of the logarithm, it yields

By moving log5 to the left hand side, we have

By moving log2.4 to the left hand side, we obtain

Therfore, the answer is

Part C.

In this case, the given function is

and we need to solve x. Then, by raising both side to the power 10, we have

By moving 17 to the left hand side, we get

Therefore, the answer is

x-intercepts

1) In a quadratic equation, the Real solutions correspond to the points in which the parabola intercepts the x-axis.

2) Note that when the roots are not real solutions, then we'd have complex numbers and the parabola wouldn't intercept the x-axis.

3) Therefore, the answer is: x-intercepts

A lineal equation has the next form:

where m is the slope and is calculated as follow:

For this case

y1=20

y2= 25

x1=12

x2= 5

so:

then the equation will be:

Using one of the points we calculate the b

we are going to use y=25 x=5

Clearing the b we get:

b=200/7 or b=28.57

A lineal equation has the next form:

where m is the slope and is calculated as follow:

For this case

y1=20

y2= 25

x1=12

x2= 5

so:

then the equation will be:

Using one of the points we calculate the b

we are going to use y=25 x=5

Clearing the b we get:

b=200/7 or b=28.57

Answer

Option B is correct.

Percent of students that scored above 86% = 18%

Explanation

To find the percentage of students that scored above 86%, we will need to add the percent of the bars for all the scores greater than 86%.

For 87%, the bar is 8%

For 88%, the bar is 5.8%

For 89%, the bar is 2.2%

For 90%, the bar is 2%

So,

Percent of students that scored above 86% = 8 + 5.8 + 2.2 + 2 = 18%

Hope this Helps!!!

Given:

Domain:

Answer:

**NEED USEFUL ANSWER ASAP, H.W QUESTION**

Given that hotter blackbodies produce more energy than cooler blackbodies, why do cooler red giants have much higher luminosities than much hotter white dwarfs?

Step-by-step explanation:

she spent 525 on Food

she spent 750 on rent

she spent 775 on others

she spent 450 on fun

Explanation

to find the value of the percentage of any number just use this formula

so

to find the values, apply the formula

Step 1

a) food :21 %

so

it means she spent 525 on Food

Step 2

b) Rent:30 %

so

it means she spent 750 on rent

Step 3

c)other:31 %

so

it means she spent 775 on others

Step 4

d)Fun:18 %

so

it means she spent 450 on fun

I hope this helps you

`Answer:

h(x) = -x^2/2 - 4x + 32

Explanation:

The standard form of a quadratic equation is expresssed as

ax^2 + bx+c

Writing the given equation h(x)= -1/2 (x+4)^2 +10 in stabdard form will give;

h(x)= -1/2 (x+4)^2 +10

h(x)= -1/2 (x^2+8x+16)+40

h(x)= -x^2/2 - 4x - 8 + 40

h(x) = -x^2/2 - 4x + 32

Hence the equation in standard form is expressed as h(x) = -x^2/2 - 4x + 32

A rational value that is less than zero is -√4.

An irrational value greater than five is 5 1/9.

A rational value between 10 and 20 is √225.

A rational number is a number that can be expressed as a fraction of two integers. A rational number can either be a positive number, negative number, whole number, decimal or fraction.  Examples of rational numbers are 100, -0.5.

A irrational number is a number that cannot be expressed as a fraction of two integers. An irrational number can either be a positive number, negative number, whole number, decimal or fraction.  Examples of irrational numbers are 22/7, 1-/9.

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Let's convert the given equation first into a vertex form.

where (h, k) is the vertex.

The vertex form of the equatio that we have is:

Hence, the vertex of the equation is at the origin (0, 0).

Since "a" is negative, our parabola is opening downward.

Let's identify two points to the left of the vertex. Let's say at x = -1. Replace "x" with -1 in the equation.

Hence, we have a point to the left of the parabola at (-1, -2).

Let's say x = -2. Replace "x" with -2 in the equation.

Hence, we also have another point to the left of the parabola at (-2, -8).

If our x is to the right of the vertex, say, x = 1. Replace "x" with 1 in the equation.

We have a point to the right of the parabola at (1, -2).

If x = 2, let's replace "x" with 2 in the equation.

Hence, we also have another point to the right of the parabola at (2, -8).

The graph of this equation is:

Given the number

We can express it in scientific notation below;

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.

Therefore, in the given question, we will have;

Answer: Option C

The length of rectangle is : 6ft .

Width of rectangle is : 5.5ft .

The area of rectangle is :

A = l × w

Here given,

length is 5ft less than twice the width,

So the equation can be represented in terms of length as,

l = 2w - 5

Given area = 33sqft

By substituting value of length,

33 = (2w - 5) × w

By applying distributive property,

33 = 2w² - 5w

= 2w² - 5w - 33

By factoring the equation:

(2w - 11)(w + 3) = 0

To find value of zeros,

2w - 11 = 0

2w = 11

w = 5.5

Similarly,

w + 3 = 0

w = -3

Since width cannot be negative , the width will be:

the width = 5.5 ft.

Also find length by substituting value of width in equation,

33 = 5.5l

33/5.5 = l

l = 6 ft.

∴ The  length = 6ft, and width = 5.5ft.

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Answer:

The two lines are parallel.

Explanation:

We have the equations:

Let's solve the first one for y, so we get the same formatting on both euqations:

SInce the two lines have the same slope, 2/5, the two lines are parallel.

Given the folllowing equation:

You need to solve for "x" in order to find its value. To do this, you can follow the steps shown below:

1. You can apply the Addition property of equality by adding 0.04 to both sides of the equation:

2. Now you need to add the like terms on the left side of the equation:

3. Finally, you can apply the Division property of equality by dividing both sides of the equation by 0.41:

The answer is:

Answer:

The expression is c-6. She gave away 6 cards so subtract 6 from the original number which is c.

Since the critical value of the test is greater than the absolute value of the test statistic, there is not enough evidence to conclude that the proportion is different of 20%.

At the null hypothesis, it is tested if the proportion is of 20%, that is:

[tex]H_0: p = 0.2[/tex]

At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:

[tex]H_1: p \neq 0.2[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

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

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

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

[tex]p = 0.2, n = 200, \overline{p} = \frac{38}{200} = 0.19[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.19 - 0.2}{\sqrt{\frac{0.2(0.8)}{200}}}[/tex]

z = -0.35.

|z| < 1.96, hence there is not enough evidence to conclude that the proportion is different of 20%.

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AB in 1:3 ratio, Find a pointwhere on one side there is 1/4 of AB and in the other side 3/4 of AB:

Given:

Population in 2000 = 572 thousand

Rate of growth per year = 1.15%

Let's solve for the following:

(a) Explicit formula for the population years after 2000.

Where:

In year 2000, t = 0

To write the explicit formula, apply the exponantial growth function formula:

Where:

a is the initial amount

r is the growth rate.

Thus, we have:

Therefore, the explicit formula for the population years after 2000 is:

(b) What will be the district's population in 2025.

Where:

In the year 2000, t = 0

In the year 2025, t will be = 25

To find the population in 2025, substitute 25 for t in the explicit formula for evalaute:

The population in 2025 if the trend continues will be approximately 761 thousand.

(c) When does the model predict the population to exceeed 800 thousand.

Substitute 800 for Pt and solve for t.

We have:

Divide both sides by 572:

Take the natural logarithm of both sides:

Divide both sides by 0.01143:

When t = 29, the year is 2000 + 29 = 2029

Therefore, using this model, DC's population will exceed 800 thousand in the year 2029.

ANSWERS:

The polar coordinates for each point are given as follows:

a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]

b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]

Suppose we have a point with Cartesian coordinates given as follows:

(x,y).

The polar coordinates will be found as follows:

For item a), the Cartesian coordinates are as follows:

(-4, 4).

Hence the polar coordinates will be given as follows:

For item a), the Cartesian coordinates are as follows:

(3, 3sqrt(3)).

Hence the polar coordinates will be given as follows:

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Volume of sandbox (to be built) = 50,445 cubic inches

A sandbox is the shape of a cuboid and is calculated by the formula

Volume = Length * Width * Height

Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?

50,445 = 59 * 57 * h

Make h the subject of the formula, we have:

h = 50445 / (59 * 57) = 15 in

The measurement that cannot be taken directly in 2-D is depth

What do you mean by measurement?

Measurement is the quantification of an object's or event's properties for comparison with other objects or occurrences. Measurement, in other terms, is the act of establishing how large or little a physical amount is in comparison to a fundamental reference quantity of the same sort. The scope and use of measurement are context and discipline dependent. Measurements do not apply to nominal qualities of things or events in natural sciences and engineering, which is compatible with the recommendations of the International Bureau of Weights and Measures' International lexicon of metrology. However, measures in other domains, such as statistics and the social and behavioral sciences, can have numerous levels.

The measurement that cannot be taken directly in 2-D is depth

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The change of base formula states that:

this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.

In this case we have:

Then, using the change of base formula, we have:

Once we have the expression we just evaluate the expression on the right to get the appoximation we need:

it would be 75 ur welcome

To solve this equation, we need to subtract both, 9c - 3c:

Dividing by 6 at both sides of the equation

Then

Then the answer C = 8. (Option D)

Okay, here we have this:

We need to identify the x-value at which the-following function touches but does not cross the x-axis in the following function: 3x^3- 18^2 + 27x. So, considering that if is a zero with even multiplicity, the graph touches the x-axis and bounces off of the axis. And if it is a zero with odd multiplicity, the graph crosses the x-axis at a zero.

According with this let's

The two ships are 1933.32 ft apart

Given:

The height of the lighthouse = 350 ft

The angles of depression to the ships are 4 degree and 6.5 degree

To find:

the distance between the two ships

To determine the distance, we will use an illustration of the situation

First we will find the value of y as we need to know this value to get x

To get y, we will apply tan ratio (TOA)

Next is to find x using tan ratio (TOA):

The value of x nodes given quadrilateral ​is 80° which is determined by the measure of the supplemental interior angle.

A quadrilateral is a polygon with four sides. This also indicates that a quadrilateral has four vertices and four angles.

Exterior Angle is defined as an angle produced on the outside of a polygon by extending the sides of the polygon.

First, we have to find the measure of the supplemental interior angle

Here take the exterior angle1 = 100° and  exterior angle2 = 60°, find its interior angles

⇒ 100 + int.1 = 180 ⇒ int.1 = 180 - 100 = 80°

⇒ 60 + int.2 = 180 ⇒ int.2 = 180 - 60 = 120°

Since the sum of all interior angles of a polygon = 360°

As per the given figure,

x + 80 + x + 120 = 360

2x = 360 - 200

2x = 160

x = 80°

Therefore, the value of x nodes given quadrilateral ​is 80°.

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Given data:

The diameter of cylinder is d=12 cm.

The height of the cylinder is h= 27 cm.

The dimension of the aquarium is V=(35 cm)(40 cm)( 42 cm).

The volume of the cylinder is,

The volume of the aquarium is,

The number of cylinders that can be pour into aquarium is,

Thus, the number of cylinders that can be pour into aquarium is 19.25.