A pillow that usually costs $18 is marked down 25%. Use the table to find the pillow’s new price.

Fill in the missing amounts to solve the problem.

100 percent is an 18 dollar original price, 25 percent markdown is a, and new price is b.

a =
b =

Answer:

\(x>-6\)

Step-by-step explanation:

\(-4x-12<12\)

\(-4x-12+12<12+12\) (Add \(12\) to both sides of the inequality to isolate \(x\))

\(-4x<24\) (Simplify)

\(\frac{-4x}{-4}<\frac{24}{-4}\) (Divide both sides of the inequality by \(-4\) to get rid of \(x\)'s coefficient)

\(x>-6\) (Simplify, don't forget to flip the sign of the inequality when multiplying or dividing by a negative number)

Hope this helps!

The simplified value the expression "㏑e^(2x-5)", by applying the properties of logarithmic and exponential function is 2x-5.

An exponential-function is a function of the form f(x) = aˣ, where a is a constant called the base and x is the variable. The base "a" is positive and not equal to 1.

A logarithmic function is called inverse of an exponential-function.

The inverse properties of logarithmic and exponential functions tell us that ㏑eˣ = x for any value of x.

So, we can simplify ㏑e^(2x-5) as :

⇒ ㏑e^(2x-5) = 2x - 5

Therefore, the simplified expression is 2x-5.

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The given question is incomplete, the complete question is

Apply the inverse properties of logarithmic and exponential functions to simplify the expression. ㏑e^(2x-5)

The values of k for which the augmented matrix follows the consistent  linear system are all the real numbers except 2 i.e. R- {2}

The linear equations become consistent when it has unique or infinitely many solutions. We have to find k according to the linear system which is consistent.

Consider the given matrix,

\(\left[\begin{array}{ccc}1&k&-4\\4&8&2\end{array}\right]\)

After dividing R2 by 2,

\(\left[\begin{array}{ccc}1&k&-4\\2&4&1\end{array}\right]\)

Now the linear equations will be,

x+ky = -4

2x+4y = 1

For infinitely many solutions it should be coincident lines so a1/a2=b1/b2=c1/c2 which is not going to happen for any value of k.

Therefore it should follow the condition of a unique solution i.e.

a1/a2\(\neq\)b1/b2

1/2\(\neq\)k/4

k\(\neq\)2

Therefore the value of k other than 2  i.e R-{2} will satisfy the linear equations.

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Answer:

A = a/2^2 + b/2^2          where b = 26 - a     (a/2 and b/2 sides of square)

A = a^2 / 4 + 1/4 (a^2 - 52 a + 676)

4 * A= 2 a^2 - 52 a + 676

4 dA / da =4 a - 52 = 0

Area will be minimized when   a = 13 and b = 13

Check:  

 n A

13 13 0 84.5

12 14 1 85

11 15 2 86.5

10 16 3 89

9 17 4 92.5

8 18 5 97

7 19 6 102.5

6 20 7 109

5 21 8 116.5

4 22 9 125

3 23 10 134.5

2 24 11 145

1 25 12 156.5

0 26 13 169

The solutions of the quadratic equation x^2 + 3x - 10 = 0 are x = 4 and x = -1.

The solution of the quadratic equation x^2 + 3x - 10 = 0 can be found by using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

Where (a, b, and c) are 1, 3, and -10

So, the solutions of the equation x^2 + 3x - 10 = 0 are:

x = (-3 ± √(3^2 - 4(1)(-10)) ) / 2(1)

x = (-3 ± √(9 + 40)) / 2

x = (-3 ± √49) / 2

x = (-3 ± 7) / 2

x = (4, -1)

Complete question:

Which of the following is the solution of the quadratic equation x^2 - 3x − 10 = 0?

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Answer:

7x - 6 - y

Step-by-step explanation:

Simplify:

-Chetan K

To calculate the corresponding values for the triangle in the larger circle, we need to use the fact that all circles are similar. This means that the corresponding sides of the circles are proportional, and their corresponding angles are congruent. We can use this property to find the missing values.

First, let's find the radius of circle B. Since the ratio of the corresponding sides of the circles is 4.25, we can find the radius of circle B as follows:

R_B = 4.25 * R_A = 4.25 * 2.9 = 12.33 cm

Now, we can use the radius of circle B to find the lengths of the sides of triangle BSH. Since triangle BSH is also similar to triangle AOG, we can use the same ratio of 4.25 to find the lengths of the corresponding sides. We have:

BS = 4.25 * OA = 4.25 * 3.2 = 13.6 cm

BH = 4.25 * OG = 4.25 * 2.6 = 11.05 cm

To find the length of SH, we can use the fact that the sum of the lengths of the sides of a triangle is equal to its perimeter. We have:

Perimeter of triangle BSH = BS + SH + BH = 13.6 + SH + 11.05 = 24.65 cm

Therefore, the perimeter of triangle BSH is 24.65 cm.

To find the measure of angle LSBH, we can use the fact that the corresponding angles of similar triangles are congruent. Since angle AOG is a right angle, we know that angle BSH is also a right angle. Therefore, we have:

angle LSBH = angle BSH - angle LBS = 90 - 64 = 26 degrees

Therefore, the measure of angle LSBH is 26 degrees.

To find the area of triangle BSH, we can use Heron's formula, which gives the area of a triangle in terms of its side lengths. We have:

s = (BS + SH + BH)/2 = 24.65/2 = 12.325 cm

Area of triangle BSH = sqrt(s(s-BS)(s-SH)(s-BH)) = sqrt(12.3250.0251.275*0.075) = 0.167 cm^2

Therefore, the area of triangle BSH is 0.167 cm^2.

To find the length of the circumference of circle B, we can use the formula for the circumference of a circle, which is given by:

C_B = 2piR_B = 2pi12.33 = 77.42 cm

Therefore, the length of the circumference of circle B is approximately 77.42 cm.

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\(\textcolor{blue}{\small\textit{If you have any further questions, feel free to ask!}}\)

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Answer:

60

Step-by-step explanation:

10 x 6 is what?

Took the test :p

\(\huge\text{Hey there!}\)

\(\large\boxed{\text{describes the length from 0 that a given number is on the number}} \\\large\boxed{\text{line, without considering the direction it is going in}}\)

\(\large\boxed{\mathsf{|-\dfrac{10}{3}}|}\\\large\boxed{\mathsf{\rightarrow -3.33333333333}}\\\\\large\boxed{\text{The absolute value}}\\\large\boxed{\mathsf{= \dfrac{10}{3}}}\\\large\boxed{\mathsf{\rightarrow 3.33333333333}}}\\\\\huge\boxed{\mathsf{Therefore, your\ answer is: \mathsf{\dfrac{10}{3}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

The first equations' answer is 21 and the second answer is 34

Hope this helps and please mark as brainliest!!

Answer:

5

Step-by-step explanation:

used a cal

Answer:

5

Step-by-step explanation:

-30 / -6 = 5

-6 * x = -30

(drop the negatives)

30 / 6 = 5

-6 * 5 = -30

The magnetic field $H$ in the interface between region 1 and region 2 is $2.7a$ mWb/m$^2$, and the angle it makes with the positive $x$-axis is $\arctan(\frac{1.8}{2.7}) = \boxed{33^\circ}$.

The magnetic field in region 1 is given by $B = 2.5a_x + 6a_z$ mWb/m$^2$, and the magnetic field in region 2 is given by $B = 4.2a_x + 1.8a_z$ mWb/m$^2$. The interface between the two regions is defined by $z = 0$.

We can use the boundary condition for magnetic fields to find the magnetic field at the interface:

B_1(z = 0) = B_2(z = 0)

Substituting the expressions for $B_1$ and $B_2$, we get:

2.5a_x + 6a_z = 4.2a_x + 1.8a_z

Solving for $H$, we get:

H = 2.7a

The angle that $H$ makes with the positive $x$-axis can be found using the following formula:

tan θ = \frac{B_z}{B_x} = \frac{1.8}{2.7} = \frac{2}{3}

The angle θ is then $\arctan(\frac{2}{3}) = \boxed{33^\circ}$.

The first step is to use the boundary condition for magnetic fields to find the magnetic field at the interface. We can then use the definition of the tangent function to find the angle that $H$ makes with the positive $x$-axis.

The boundary condition for magnetic fields states that the magnetic field is continuous across an interface. This means that the components of the magnetic field in the two regions must be equal at the interface.

In this case, the two regions are defined by $z = 0$, so the components of the magnetic field must be equal at $z = 0$. We can use this to find the value of $H$ at the interface.

Once we have the value of $H$, we can use the definition of the tangent function to find the angle that it makes with the positive $x$-axis. The tangent function is defined as the ratio of the $z$-component of the magnetic field to the $x$-component of the magnetic field.

In this case, the $z$-component of the magnetic field is 1.8a, and the $x$-component of the magnetic field is 2.7a. So, the angle that $H$ makes with the positive $x$-axis is $\arctan(\frac{1.8}{2.7}) = \boxed{33^\circ}$.

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Answer:

\(x=7\)

Step-by-step explanation:

Angles opposite congruent sides in a triangle are congruent.

\(6=2x-8 \\ \\ 2x=14 \\ \\ x=7\)

Answer:

\(\boxed{ \{7, 6, 5, 3 \} }\)

Step-by-step explanation:

The domain is all possible values for x.

The range is all possible values for f(x) or y.

The domain given is {-3, -2, -1, 1}.

Plug x as {-3, -2, -1, 1} and find the f(x) or y values.

\(f(-3)=-(-3)+4=7\\f(-2)=-(-2)+4=6\\f(-1)=-(-1)+4=5\\f(1)=-(1)+4=3\)

The range is {7, 6, 5, 3}, when the domain is {-3, -2, -1, 1}.

Step-by-step explanation:

Image 1:

Blank 1: (0,5)

Blank 2: (5,0)

Blank 3: (0,-5)

Blank 4: (-5,0)

Image 2:

C, Both B and D only have one line of symmetry. Choice A has more than 2 because you can evenly split the kite by its vertices and its lengths.

Image 3:

B, a regular quadrilateral is named this way because it contains both the point and linear symmetry. By definition, a regular quadrilateral must have 4 equal sides and angles and must have its diagonals bisect each other.

Image 4:

B, Point symmetry only. This is because when flipped upside down, the shape would still look the same. This would not be rotational symmetry because it does not look 100% like the original after rotating it to a certain degree.

The probability of getting exactly 2 jacks in a hand of 11 cards is approximately \(1.277 * 10^(-7).\)

To find the probability of getting 2 jacks in a hand of 11 cards from a well-shuffled 52-card deck, we can use the concept of combinations.

First, let's calculate the number of ways to choose 2 jacks from the deck. Since there are 4 jacks in the deck, the number of ways to choose 2 jacks is given by the combination formula:

C(4, 2) = 4! / (2! ×(4-2)!) = 6

Next, let's calculate the number of ways to choose the remaining 9 cards from the remaining 48 cards in the deck:

C(48, 9) = 48! / (9! ×(48-9)!) = 25,179,390

To find the probability, we divide the number of favorable outcomes (choosing 2 jacks and 9 other cards) by the total number of possible outcomes (choosing any 11 cards from the deck):

Probability = (6 ×25,179,390) / C(52, 11)

C(52, 11) = 52! / (11! × (52-11)!) = 23,581,386,680

Probability = (6 ×25,179,390) / 23,581,386,680

Probability = 1.277 ×10⁷

So, the probability of getting exactly 2 jacks in a hand of 11 cards is approximately 1.277 ×10⁷

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The probability of getting 2 jacks in a hand of 11 cards is approximately 0.0104 or 1.04%.

The probability of getting 2 jacks in a hand of 11 cards from a well-shuffled standard 52-card deck can be calculated by using the concept of combinations.

Step 1: Determine the total number of possible hands of 11 cards from a deck of 52 cards. This can be calculated using the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of cards in the deck (52) and r is the number of cards in the hand (11).

Step 2: Determine the number of ways to choose 2 jacks from the 4 available jacks in the deck. This can be calculated using the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of jacks (4) and r is the number of jacks in the hand (2).

Step 3: Calculate the probability by dividing the number of favorable outcomes (getting 2 jacks) by the total number of possible outcomes (getting any 11 cards). This can be calculated as the ratio of the number of ways to choose 2 jacks to the number of possible hands of 11 cards.

So, the probability of getting 2 jacks in a hand of 11 cards is:

P(2 jacks) = (Number of ways to choose 2 jacks) / (Total number of possible hands of 11 cards)

P(2 jacks) = C(4, 2) / C(52, 11)

Simplifying the calculation, the probability is:

P(2 jacks) = (4! / (2!(4-2)!)) / (52! / (11!(52-11)!))

P(2 jacks) = (4! / (2! * 2!)) / (52! / (11! * 41!))

P(2 jacks) = (24 / (4 * 2)) / (52! / (11! * 41!))

P(2 jacks) = 24 / 8 * (11! * 41!) / 52!

P(2 jacks) ≈ 0.0104 or 1.04%

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The center of the circle is (-3, -4), and its radius is sqrt(9) = 3.

To determine the center and radius of the circle within the given equation x^(2)+y^(2)+6x+8y=-16, we need to complete the square for both x and y.

First, let's complete the square for x by adding (6/2)^2 = 9 to both sides of the equation:

x^(2) + 6x + 9 + y^(2) + 8y = -16 + 9

Simplifying this equation, we get:

(x + 3)^(2) + y^(2) + 8y = -7

Next, we complete the square for y by adding (8/2)^2 = 16 to both sides of the equation:

(x + 3)^(2) + (y + 4)^(2) = 9

Now we can see that the equation is in standard form: (x - h)^(2) + (y - k)^(2) = r^(2), where (h, k) is the center of the circle and r is its radius.

Therefore, the center and radius are (-3, -4) and 3 respectively.

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Answer:

The area of the triangle is 70.805 ft squared

Step-by-step explanation:

The examples of a function from Z to Z that are f(x) = 2x, g(x) = x², h(x) = 3x and k(x) = x³

Example 1: One-to-One but not Onto Function

Consider the function f: Z to Z defined by f(x) = 2x, where Z represents the set of integers. This function is one-to-one (injective) but not onto (surjective).

However, this function is not onto. For a function to be onto, every element in the codomain must have a corresponding element in the domain. In this case, not all integers in the codomain Z have a preimage in the domain Z. For instance, there is no integer x such that f(x) equals 1 or f(x) equals 3, as the function only produces even integers. Thus, the function f is not onto.

Example 2: Onto but not One-to-One Function

Consider the function g: Z to Z defined by g(x) = x², where Z represents the set of integers. This function is onto (surjective) but not one-to-one (injective).

However, the function g is not one-to-one. A function is one-to-one if distinct elements in the domain map to distinct elements in the codomain. In this case, there are multiple domain elements that map to the same codomain element. For instance, both -2 and 2 map to the same output 4, as (-2)² = 2² = 4. Therefore, the function g is not one-to-one.

Example 3: Both Onto and One-to-One Function (Not the Identity Function)

Consider the function h: Z to Z defined by h(x) = 3x, where Z represents the set of integers. This function is both onto (surjective) and one-to-one (injective), but it is not the identity function.

Additionally, the function h is onto. For any integer y in the codomain Z, we can find an integer x in the domain Z such that 3x = y. For example, if we choose y = 6, we can set x = 2, as 3 * 2 = 6. This shows that every element in the codomain has a corresponding element in the domain, fulfilling the onto property.

Example 4: Neither Onto nor One-to-One Function

Consider the function k: Z to Z defined by k(x) = x³, where Z represents the set of integers. This function is neither onto (surjective) nor one-to-one (injective).

Moreover, the function k is not one-to-one. It fails the one-to-one property because different elements in the domain can map to the same output in the codomain. For example, both -2 and 2 map to the same output -8, as (-2)³ = 2³ = -8. Therefore, the function k is not one-to-one.

By examining these four examples, you can observe the distinct combinations of properties that a function from Z to Z can possess. It is important to explore these properties to understand the behavior and characteristics of various functions.

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Answer:

5/6

Explanation

Probabaility is the likelihood or chance that an event will occur. Mathematically;

Probabiblity = Expected outcome/Total outcome

Since a pair of dice is rolled;

Total outcome for n dice = 6^n

For a pair of dice, total outcome is 6^2 = 36

For the expected outcome

If we got different numbers on both dice, the outcomes wil be 30 since the only periods we will have the same value are [(1, 1), (2,2), (3,3), (4,4), (5,5), (6,6)] which is 6 outcomes

getting different numbers on both dice = 36 - 6 = 30

Probability of getting different numbers on both dice = 30/36

Probability of getting different numbers on both dice = 5/6

Answer:

Ashley

Step-by-step explanation:

Ashley:

12n (n=5) = 60+2u (u=10)=80

4 quarters equal a dollar

$1.80

Beto:

10n (n=5)= 50+ 4u (u=10) = 90

3 quarters equal .75

$1.65

The correct statements regarding the compound interest balance function in this problem are given as follows:

The balance, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which the parameters are listed as follows:

For this problem, the function is given as follows:

\(A = 4500\left(1 + \frac{0.035}{12}\right)^{12t}\)

Hence the balance after three months is given as follows:

\(A = 4500\left(1 + \frac{0.035}{12}\right)^{12 \times \frac{3}{12}}\)

A = $4,539.49.

(as the time is measured in years, 3 months = 3/12 of an year).

After six months, the balance is given as follows:

\(A = 4500\left(1 + \frac{0.035}{12}\right)^{12 \times \frac{6}{12}}\)

A = $4,579.33.

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When measuring height, it is necessary to represent both the vertical position and the separation between the minimum and maximum place or location. Rachel is 5 feet 6 inches tall, the tall is her cousin exists 2 feet 9 inches.

In math, tall can be defined as the vertical distance from the top to the base of the object. Tall is the distance between an object's highest and lowest points.

The measurement of an object's height from the base to the top is known as tall. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Rachel/Cousin = Rachel's shadow / Cousin's shadow

5 feet 6/x = 2/1

simplifying the above equation, we get

5ft 6 = 2x

x = 5ft 6/2

x = 66in/2

x = 33 in

x = 2ft 9inch

Therefore, the value of x = 2ft 9inch.

Rachel is 5 feet 6 inches tall, the tall is her cousin exists 2ft 9inch.

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An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.

An investment strategy with an expected return of 14 percent and a standard deviation of 8 percent means that the investment has a higher potential for return, but also a higher risk.

The standard deviation is a measure of the variation or dispersion of a set of data values. In this case, the standard deviation of 8 percent indicates the degree of variation in the investment returns. A higher standard deviation means that the investment returns are more spread out and there is a higher chance of extreme values, both positive and negative.

In terms of investment strategy, it is important to consider the trade-off between risk and return. While a higher expected return is desirable, it often comes with a higher level of risk. Therefore, it is important to carefully consider the standard deviation and the potential risks associated with an investment before making a decision.

In conclusion, an investment strategy with an expected return of 14 percent and a standard deviation of 8 percent has the potential for higher returns, but also comes with a higher level of risk. It is important to carefully consider the trade-off between risk and return before making an investment decision.

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Step-by-step explanation:

-33 + -20 is -53. and I don't how

Answer:

The correct answer is B. 20,000

Step-by-step explanation:

To determine the man's total monthly salary, we can set up a simple equation using the given information. Let's denote the total monthly salary as "x."

According to the information provided, 33% of the man's monthly salary is equal to Birr 6600. We can express this relationship mathematically as:

0.33x = 6600

To solve for "x," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 0.33:

x = 6600 / 0.33

Evaluating the right side of the equation gives:

x ≈ 20,000

Therefore, the man's total monthly salary is approximately Birr 20,000.

Hence, the correct answer is B. 20,000.

Answer:

m∠1 = 131°

m∠2 = 49°

m∠3 = 112°

Step-by-step explanation:

We find the m∠2 using Vertical Angles Theorem

We find the m∠1 using Definition of a Line

We find the m∠3 also using Vertical Angles Theorem

Answer:

20

Step-by-step explanation:

Answer:

20 times

Step-by-step explanation:

6 x 10^5 = 600000

3 x 10^4 = 30000

600000/30000 = 20

There are 5²⁵ possible ways to select 25 cans of soda from 5 types, while there are [5¹⁸] (25 choose 7) possible ways to select 25 cans with at least 7 Dr. Peppers, and only [3²²] (25 choose 3) possible ways to select 25 cans with only 3 Dr. Peppers available.

(a) Since there are five types of soda and we are selecting 25 cans, we can choose any type of soda for each can. Therefore, the number of ways to select 25 cans of soda is 5²⁵.

(b) If we must include at least seven Dr. Peppers, then we can choose the remaining 18 cans from any of the five types of soda (including Dr. Pepper). We can choose 7 Dr. Peppers in (25 choose 7) ways. Therefore, the number of ways to select 25 cans of soda with at least seven Dr. Peppers is (25 choose 7) [5¹⁸].

(c) If there are only three Dr. Peppers available, then we must choose all three Dr. Peppers and select the remaining 22 cans from the four types of soda (excluding Dr. Pepper). We can choose the remaining 22 cans in 4²² ways. Therefore, the number of ways to select 25 cans of soda with only three Dr. Peppers available is 3 [4²²].

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Complete question:

From an unlimited selection of five types of soda, one of which is Dr. Pepper, you are putting 25 cans on a table.

(a) Determine the number of ways you can select 25 cans of soda.

(b) Determine the number of ways you can select 25 cans of soda if you must include at least seven Dr. Peppers.

(c) Determine the number of ways you can select 25 cans of soda if it turns out there are only three Dr. Peppers available.

Answer:

126

Step-by-step explanation:

I = prt

I = (600)(0.07)(3)

I = 126

Answer: 126