Explain why receiving a 15% discount is the same as finding 85% percent of the original cost of an item. Then, explain how the mathematical properties and equivalent expressions helped them understand and solve the problem. Please answer!!

Answer:

30.

Step-by-step explanation:

6 = 2 * 3

5 = 5

LCM = 2 * 3 * 5 = 30.

Answer:

The graph is decreasing everywhere, the second option.

Step-by-step explanation:

Took the test.

Answer: 3.01 is less than 3.10

Step-by-step explanation:

Answer: 3.01 is less than 3.01

Step-by-step explanation:

3.10 is .09 more than 3.01

Answer:

11.GBJ JBD  12.AD GE  13.GBC GBA  14.FCD JBE (is obtuse)

Step-by-step explanation:

Answer:

11.GBJ JBD  12.AD GE  13.GBC GBA  14.FCD JBE (is obtuse)

Step-by-step explanation:

Step-by-step explanation:

The question refers to numerical approximation methods used for integration: the Trapezoidal, Midpoint, and Simpson's Rules. Answers for specific n-values and error calculations require a calculator or programming tool and are not provided here. The processes, however, involve application of respective formulae and comparison of approximations against the desired accuracy level.

Solution:

The question is related to approximating the value of an integral using numerical methods, specifically using the Trapezoidal Rule (Tn), Midpoint Rule (Mn), and Simpson's Rule (Sn). Additionally, it asks about the corresponding estimation errors which are defined as differences between the true integral value and the approximations.

Part (a)

To find T10, M10, and S10 for ∫₀π (21 sin x) dx, we would use respective formulae. Unfortunately, without a calculator or computational tool, it's not practical to perform these calculations here in this answer.

Part (b)

The actual errors ET, EM, and ES compare to the theoretical error bounds given by the respective theorems for each rule. Again, without the approximated values from part (a), we cannot calculate these errors.

Part (c)

Choosing n so that the approximations are accurate to within 0.00001 is a trial and error process where you start with n and continue to increase it until the approximation is within the desired accuracy. This typically requires use of a computational tool or programming.

Please note, these answers can vary depending on the specific constants and functions used in the integration.

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Step-by-step explanation:

4.

22+4x= 90

4x=90-22

4x=68

x°=17°

7.

(x-5)°+29°=180°

x-5+29=180

x= 180-24

x=156°

10.

(x+3)°+49°=90°

x= 90-52°

x=38°

Answer:

[tex]\bold{\frac{(cosx-sinx)}{(sinx)}}=\bold{\frac{cosx-sinx}{sinx}}[/tex]

Step-by-step explanation:

[tex]\frac{cos^2x-sin^2x}{sin^2x+sinxcosx}=cotx-1[/tex]

We're going to start by manipulating the left side of the equation and making it the same form as [tex]cotx-1[/tex].

Start by applying the difference of two squares formula to the numerator, like so:

Now simplify the denominator by expanding the [tex]sin^2x[/tex].

The denominator can even be further simplified since both addends (when added together = a sum) have the common factor of [tex]sinx[/tex]. Factor it out.

Cancel out the common factor [tex](cosx+sinx)[/tex].

Since this is the furthest simplified that the left side can be manipulated, let's see if can try to manipulate the right side to also look like [tex]\frac{(cosx-sinx)}{(sinx)}[/tex].

Start by expressing [tex]cotx-1[/tex] with [tex]sinx[/tex] and [tex]cosx[/tex], since we know that cotangent is simply [tex]\frac{x}{y} \rightarrow\frac{cosx}{sinx}[/tex].

We can simplify this expression to look like our expression we found by manipulating the left side [tex](\frac{(cosx-sinx)}{(sinx)})[/tex] by making the 1 have a common denominator of [tex]sinx[/tex].

To do this, multiply 1 by [tex]\frac{sinx}{sinx}[/tex]. Now the expression should look like:

Since they have a common denominator we can write the expression under one fraction, like so:

This looks exactly the same as what we manipulated the left side to be [tex](\frac{(cosx-sinx)}{(sinx)})[/tex], just without parentheses. I put both expressions in bold. Therefore, this identity proves to be true as we just proved it.

Answer:

see explanation

Step-by-step explanation:

Using x = 5, then

x² = 5² = 5 × 5 = 25

[tex]1^{5}[/tex] = 1 × 1 × 1 × 1 × 1 = 1

[tex]5^{1}[/tex] = 5

Answer:

a transformation could be a rotation, reflection, and/or a translation.

Step-by-step explanation:

In geometry, transformation refers to the movement of objects in the coordinate plane.

Therefore, a transformation could be a rotation, reflection, and/or a translation.

Answer: x = - 19

y = 55

Step-by-step explanation:

y = - 3x - 2 (1)

5x + 2y = 15 (2)

substitute y = - 3x - 2 into equation (2)

equation (2) becomes

5x + 2 (-3x - 2) = 15

5x + ( - 6x - 4) = 15

opening the bracket

5x - 6x - 4 = 15

collecting like terms

5x - 6x = 15 + 4

-x = 19

x = - 19

substituting x = - 19 into equation 1

y = - 3x - 2

y = - 3 (-19) - 2

y = 57- 2

y = 55

Answer:

x= 19/11

y=35/11

Step-by-step explanation:

Answer: Eleventh Grade

Step-by-step

The ratio of tenth graders to the school's total population is 86:255 = 33.7%.

The ratio of eleventh graders to the school's total population is 18:51 = 35.3%.

Since the probability of a student being in either tenth, eleventh, or twelfth grade = 1 = 100% (that is, certainty), then the probability of a randomly drawn student being in twelfth grade is (100-33.7-35.3)% = 31.0%.

When randomly choosing one student from the whole school, it is most likely (35.3%) that the student is in the eleventh grade.

Answer:

32k13

Step-by-step explanation:

32k13 Multiply the number add the the exponent

To simplify the expression 4k9×8k3×k, combine the coefficients and add the exponents of the same variable k to get 32k13.

To simplify the expression 4k9×8k3×k, we can combine the coefficients and add the exponents of the same variable k.

4k9×8k3×k = (4×8)k(9+3+1) = 32k13

Therefore, the simplified expression is 32k13.

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The volume of the larger cone divided by the volume of the smaller cone is 25.

A cone is a three-dimensional object that is made up of a circular base and a vertex.

Volume of a cone = 1/3(πr²h)

Assumed dimensions of the smaller cone:

Volume = 1/3(π x 9 x 10) = 30π

Assumed dimensions of the larger cone:

Volume = 1/3(π x 225 x 10) = 750π

Ratio of the volumes = 750π / 30π = 25

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Answer:

A, 25 is correct

Step-by-step explanation:

i got it right on edge 2023

Answer: 38.45

Step-by-step explanation:

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=21.98 \end{cases}\implies 21.98=2\pi r\implies \cfrac{21.98}{2\pi }=\boxed{r} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2\qquad \qquad A=\pi \left( \boxed{\cfrac{21.98}{2\pi }} \right)^2\implies A=\cfrac{21.98^2}{2^2\pi }\implies A\approx 38.445[/tex]

Answer:

y=3 x=1

Step-by-step explanation:

Let's solve your equation step-by-step.

2x+1=4x−1

Step 1: Subtract 4x from both sides.

2x+1−4x=4x−1−4x

−2x+1=−1

Step 2: Subtract 1 from both sides.

−2x+1−1=−1−1

−2x=−2

Step 3: Divide both sides by -2.

−2x

−2

=

−2

−2

x=1

then

y=(2)(1)+1

Answer:

y=3

Answer:

Vertical angles are angles opposite each other where two lines cross. Vertical angles are very specific - you have two intersecting lines to form two sets of vertical angles that are across from each other and congruent. Both supplementary angles and complementary angles are much broader - they do not even have to be touching or near each other, but they could be.

Answer:

This will be your answer. Good luck! :)

Step-by-step explanation:

'Desmos Graphing Calculator' is extremely helpful to anyone who needs help in math involving functions and solving equations. Take the time to learn how it works and it'll be your best friend. Free, reliable, and saves time!

Final answer:

Yes, a data set can have two modes, which occurs when two different values appear with equal and highest frequency, making the set bimodal.

Explanation:

Yes, there can be two modes in a data set. The mode is the most frequent value or values in a set of data. When a data set has exactly two modes, it is called bimodal. This phenomenon occurs when two different numbers appear with equal frequency and more often than any other numbers in a set. For example, in the data set 2,5,6,7,9,9,11,11,12,13, both 9 and 11 appear twice and more frequently than any other values, making them both modes of the data set.

Length = 12 m and width = [tex]\frac{7}{2}[/tex] m.

Solution:

Let the width of the rectangle be w.

Length of the rectangle = 2w + 5

Area of the rectangle given = 42 m²

Area of the rectangle = length × width

length × width = 42

(2w + 5) × w = 42

[tex]2w^2+5w=42[/tex]

Subtract 42 from both sides, we get

[tex]2w^2+5w-42=0[/tex]

Using quadratic formula,

[tex]$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

Here, [tex]a=2, b=5, c=-42[/tex]

[tex]$w=\frac{-5 \pm \sqrt{5^{2}-4 \cdot 2(-42)}}{2 \cdot 2}[/tex]

[tex]$w=\frac{-5 \pm \sqrt{25+336}}{4}[/tex]

[tex]$w=\frac{-5 \pm \sqrt{361}}{4}[/tex]

[tex]$w=\frac{-5 \pm19}{4}[/tex]

[tex]$w=\frac{-5+19}{4}, w=\frac{-5-19}{4}[/tex]

[tex]$w=\frac{14}{4}, w=\frac{-24}{4}[/tex]

[tex]$w=\frac{7}{2}, w=-6[/tex]

Dimension cannot be in negative, so neglect w = –6.

Width of the rectangle = [tex]\frac{7}{2}[/tex] m

[tex]$L=2(\frac{7}{2} )+5=12 \ m[/tex]

Hence length = 12 m and width = [tex]\frac{7}{2}[/tex] m.

Two expressions are equivalent if we can arrange one of them in order to match the other.  If we evaluate the two expressions for certain values in the input, we must get the same value in the output. In this exercise, we have the following expression:

[tex]a-2.87[/tex]

There are infinitely many equivalent expressions. We can write some of them:

[tex]\bullet \ 2a-a-2.87 \\ \\ \bullet \ a-1-1.87 \\ \\ \bullet \ 5a-4a-5.87+3[/tex]

Because when simplifying these expressions we get:

[tex]a-2.87[/tex]

Answer:

51 inches

Step-by-step explanation:

area = base x height

8.5 x 6 = 51

51 inches

Solution:

Given that,

We have to find the multiplicative inverse of [tex]9^3[/tex]

By multiplicative inverse,

The product of a number and its multiplicative inverse is 1

Given number is: [tex]9^3[/tex]

Let "x" be the required multiplicative inverse

Therefore,

[tex]9^3 \times \text{ multiplicative inverse of } 9^3 = 1[/tex]

[tex]9^3 \times x = 1\\\\x = \frac{1}{9^3}[/tex]

Thus the multiplicative inverse of [tex]9^3[/tex] is [tex]\frac{1}{9^3}[/tex]

Answer:

The correct table is A.

Correct statement and question:

Sarah sells beaded necklaces she makes a profit of $4 on every necklace she sells which table represents the profit Sarah makes.

A.

Necklaces Sold Profit $

 4                           16

 6                           24

 8                           32

10                          40

B.  

Necklaces Sold Profit $

 4                           8

 6                           10

 8                           12

10                          14

C.

Necklaces Sold Profit $

 4                           4

 6                           8

 8                           12

10                          16

D.

Necklaces Sold Profit $

 4                           16

 6                           20

 8                           24

10                          28

Source:

North Carolina Practice Test

Step-by-step explanation:

If Sarah makes a profit of $ 4 on every necklace she sells, then:

4 necklaces = 4 * 4 = $ 16

6 necklaces = 6 * 4 = $ 24

8 necklaces = 8 * 4 = $ 32

10 necklaces = 10 * 4 = $ 40

The correct table is A.

Answer:

B.

Step-by-step explanation:

We see (-10) repeating six times. This means the product would be 6(-10). To simplify this, 6 × (-10) = -60.

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the function f(x)=6+x

F(x) is dependent on x,

When x=1

f(x)=6+x

f(x)=6+1,

f(x)=7

When x=2

f(x)=6+x

f(x)=6+2

f(x)=8.

This will continue like this till we get to x=15

So when x=15

We will substitute x=15 into the function f(x)

f(x)=6+x

f(x)=6+15

f(x)=21

Then, the answer is 21.

Answer: 17

Step-by-step explanation:

To solve 6+x when x = 15,

Step 1: Substitute 15 into x

Step 2: Sum 6 and 15

6+15= 17.

Answer:

It's form. Linear is a normal line, exponential is a curvy line, and quadratic is a u shape with the vertice on the y-axis line, making half of the u on the left quadrant and the other half on the right quadrant

Step-by-step explanation:

first is linear, second is exponential and third is quadratic

Answer:

quadratic needs to have a degree of 2, linear equations are in form y=mx+b and do not have exponents

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

you have 600 = 8 and you want to break it down into just 1 hour so you divide both sides by 8

600/8 = 75

Final answer:

The student was traveling at a speed of 75 miles per hour.

Explanation:

To calculate the speed in miles per hour when a student has traveled 600 miles in 8 hours, you divide the total distance by the total time taken. The formula to find speed is:

Speed = Distance / Time

So, if we plug in the values we have:

Speed = 600 miles / 8 hours = 75 miles per hour

Therefore, the student was traveling at a speed of 75 miles per hour.

Answer: im not sure but a)15 B)24 c)zoo in a different city

Step-by-step explanation:

There are 15 reptiles in the zoo. To keep the ratio 4:3, if the zoo adds 12 more mammals, they will need to add 9 more reptiles. The first zoo has a larger ratio of mammals to reptiles (4:3) compared to the second zoo (6:5).

To answer the question, let's solve each part step by step:

Answer:$1636.4

Step-by-step explanation:

Selling price(sp)=$1800

Profit%=10%

Cost price(cp)=?

Profit%=(sp-cp)/cp x 100

10=(1800-cp)/cp x 100

Cross product

10cp=100(1800-cp)

Open brackets

10cp=180000-100cp

Collect like terms

10cp+100cp=180000

110cp=180000

Divide both sides by 110

110cp/110 = 180000/110

cp=1636.4

Cost price is $1636.4

Answer: Cost Price = $1, 636.36

Step-by-step explanation:

Given from the question Selling price (SP)= $1800; Profit%= 10%= 10/100 = 0.1

Cost price(CP)= ??

Profit% is derived by the formula

=(SP-CP)/ CP x 100

0.1 = (1800 - CP)/CP x 100

Then we cross multiply

0.1 x 100 x CP = 1800 - CP

10 CP = 100(1800 - CP)

Open the bracket

10 CP=180000 - 100CP

Divide both sides by 10

CP = 180000 - 100CP/10

CP = 18000 - 10CP

Combine like terms

CP + 10CP = 18000

11CP = 18000

Divide both sides by 11

CP = 18000/11

CP = $1, 636.36