The product of 5 & 10 is equal to a third of a number
Write as an equation and solve.

Answer: D

Step-by-step explanation:

The rationalized form of the surd is;

1) 25/13

2) 144/3

3) 36

We have to note that the term surd would have to refer to an irrational number as we know it.

1) The conjugate of the surd is;

5/4 + √3

Rationalizing we have;

5/4 -  √3 * 5/4 + √3

25/16 + 4√3 - 4√3 -3

25/13

2) The conjugate is √7 - 2

Rationalizing we have;

12/√7 + 2  * 12/√7 - 2

144/7 -2√7 + 2√7 -4

144/3

3) The conjugate of the surd is √2 + √3

Rationalizing we have;

6/ √2 -  √3  * 6/ √2 + √3

36/4 +√6 - √6 - 3

36/1 = 36

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Answer:

Step-by-step explanation:

If there needs to be 4 teachers per 21 students, you would divide the total amount of students by 21 and multiply that answer by 4. SO...:

84 ÷ 21 = 4 groups of 21 students.

4 groups × 4 teachers = 16

*** Answer***

16 TEACHERS

Answer:

$23.646

Step-by-step explanation:

325.80 times 0.07 equals 22.806

12 times 0.07 equals 0.84

Add

Answer:

D 7, -12 is the answer hope this helps✌

Answer:

7, -12

Step-by-step explanation:

x^2+5x-84=0

(x-7)(x+12)=0

u have to always place the opposite for the answers

x= 7

x= -12

The first figure is dilated to form the second figure, the statement according to will be the scale factor is 0.25.

The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is.

A ratio divides two quantities in order to compare them.

As per the given information in the question,

We have two side lengths,

First figure: This represents the object length, which is a diamond with a length equal to 5.8.

Second figure:The picture length is then represented by a small diamond with sides that measure 1.45.

So, the scale factor is,

k = Image length/Object length

k = 1.45/5.8

k = 0.25.

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1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ \(\frac{\frac{4}{25} }{\frac{1}{64} }\)

To find the common ration, multiply thus;

⇒ \(\frac{4}{25}\) × \(\frac{64}{1}\)

⇒ \(\frac{256}{25}\)

= 10. 24

1b. (5/7)^2 × (5/7)^1

= \(\frac{25}{49}\) × \(\frac{5}{7}\)

= \(\frac{125}{343}\)

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= \(\frac{8}{125}\) × \(\frac{4}{25}\)

= \(\frac{32}{3125}\)

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= \(\frac{\frac{1}{4} }{\frac{5}{8} }\)

Take the inverse of the denominator

= \(\frac{1}{4}\) × \(\frac{8}{5}\)

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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The condition numbers for f(x) = sin(x) / (1 + cos(x)) evaluated at x = 1.0001π indicate the sensitivity of the function's output to changes in the input.

In the first paragraph, we summarize that we will evaluate and interpret the condition numbers for the function f(x) = sin(x) / (1 + cos(x)) at x = 1.0001π. The condition numbers provide insight into how sensitive the function's output is to changes in the input.

To calculate the condition numbers, we first find the derivative of f(x) with respect to x, which is [(cos(x)(1 + cos(x))) - sin(x)(-sin(x))] / (1 + cos(x))^2. Evaluating this derivative at x = 1.0001π gives us the slope of the tangent line at that point.

Next, we calculate the absolute value of the product of the derivative and the input value (|f'(x) * x|) at x = 1.0001π. This represents the absolute change in the output of the function due to small changes in the input.

Finally, we divide |f'(x) * x| by |f(x)| to obtain the condition number, which provides a measure of the relative sensitivity of the function. A larger condition number indicates a higher sensitivity to changes in the input.

Interpreting the condition number can be done by comparing it to a threshold. If the condition number is close to 1, the function is considered well-conditioned and changes in the input have minimal impact on the output. However, if the condition number is significantly larger than 1, the function is considered ill-conditioned, and small changes in the input can lead to large changes in the output.

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Answer:

360 cubic inches (remember your units!)

Step-by-step explanation:

the formula for volume of a rectangular prism is length times width times height times depth so you have to do 8 times 5 times 9 witch is 360 cubic inches

The car's altitude remains constant at 50 meters beyond 100 meters, option C is the correct answer: C. As the car travels its altitude increases, but then it reaches a plateau and its altitude stays the same.

The piecewise equation given is:

a = {0.5x if d < 100, 50 if d ≥ 100}

To describe the change in altitude of the car as it travels from the starting point to about 200 meters away, we need to consider the different regions based on the distance (d) from the starting point.

For 0 < d < 100 meters, the car's altitude increases linearly with a rate of 0.5 meters per meter of distance traveled. This means that the car's altitude keeps increasing as it travels within this range.

However, when d reaches or exceeds 100 meters, the car's altitude becomes constant at 50 meters. Therefore, the car reaches a plateau where its altitude remains the same.

Since the car's altitude remains constant at 50 meters beyond 100 meters, option C is the correct answer:

C. As the car travels its altitude increases, but then it reaches a plateau and its altitude stays the same.

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Complete question is below

The change in altitude (a) of a car as it drives up a hill is described by the following piecewise equation, where d is the distance in meters from the starting point. a { 0 . 5 x if d < 100 50 if d ≥ 100

Describe the change in altitude of the car as it travels from the starting point to about 200 meters away.

A. As the car travels its altitude keeps increasing.

B. The car's altitude increases until it reaches an altitude of 100 meters.

C. As the car travels its altitude increases, but then it reaches a plateau and its altitude stays the same.

D. The altitude change is more than 200 meters.

\(\mathrm{Domain\:of\:}\:\sqrt{2-2\sin \left(x\right)}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\in \mathbb{R}\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\)

\(\mathrm{Axis\:interception\:points\:of}\:\sqrt{2-2\sin \left(x\right)}:\quad \mathrm{X\:Intercepts}:\:\left(\frac{\pi }{2}+2\pi n,\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:\sqrt{2}\right)\)

\(\mathrm{Asymptotes\:of}\:\sqrt{2-2\sin \left(x\right)}:\quad \mathrm{None}\)

\(\mathrm{Extreme\:Points\:of}\:\sqrt{2-2\sin \left(x\right)}:\quad \mathrm{Maximum}\left(\frac{3\pi }{2}+2\pi n,\:\sqrt{2-2\sin \left(\frac{3\pi }{2}+2\pi n\right)}\right)\)

9514 1404 393

Answer:

  152 feet

Step-by-step explanation:

A triangle modeling the situation has the unknown length as its hypotenuse, and the given platform height as the side opposite the angle. The relevant trig function is ...

  Sin = Opposite/Hypotenuse

  sin(30°) = (76 feet)/(escalator length)

  escalator length = (76 feet)/sin(30°) = (76/0.5) feet

  escalator length = 152 feet

The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Answer:

B.) \(6^{\frac{1}{2}}\)

Step-by-step explanation:

Use the exponent rule that states \(a^{\frac{1}{m}}=\sqrt[m]{a}\).  For this problem, let

a=6

m=2

So,

\(\sqrt6=6^{\frac{1}{2}}\)

The values of g(-4) = 0

                        g(-2) = 2

                        g(0) = 2

                        g(3) = -1

                        g(4) = -2

What is a function?

In mathematics, a function is a rule which assigns a unique output value to each input value in a given set. It shows a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Functions are typically represented by an equation or a graph, and they play an important role in various fields of mathematics, science, engineering, and technology.

Using the given piecewise defined function:

g(x) = x + 4, −5 ≤ x ≤ −1

         2 − x, −1 < x ≤ 5

We can evaluate g at different values in its domain as follows:

g(−4) = (-4) + 4 = 0

g(−2) = (-2) + 4 = 2

g(0) = 2 - 0 = 2

g(3) = 2 - 3 = -1

g(4) = 2 - 4 = -2

Therefore:

g(-4) = 0

g(-2) = 2

g(0) = 2

g(3) = -1

g(4) = -2

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Answer:

1 I don't know if those are questions but try if they are try the first one a

The difference is: Marginal cost is the money paid for producing one more unit of a good. Marginal revenue is the money earned from selling one more unit of a good.

Marginal cost (MC) is the additional outlay expended by a producer when they fabricate and supply one supplementary unit of an item or service. It symbolizes the replace in total costs caused by producing one extra piece.

Marginal revenue (MR), on the other hand, is the supplementary turnover generated when an establishment deals one more piece of a good or service. It signifies the transformation in complete revenue attained from selling an supplemental product.

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Answer:

D

Step-by-step explanation:

\(2x^2+16x-8=0\)

Simplify:

\(x^2+8x=4\)

Rewrite in the form \((x+a)^2=b\):

\(x^2+8x=4\)

Add \(4^2\) to both sides:

\(x^2+8x+4^2=4+4^2\)

\(x^2+8x+4^2=20\)

\(\left(x+4\right)^2=20\)

\(x+4=\sqrt{20}\) or \(x+4=-\sqrt{20}\)

x = -4±\(\sqrt{20}\)

x= -4±\(2\sqrt{5}\)

99 boys and 1 girl makes 99 percent of boys. To make it 98%, 50 boys must leave the theatre, so there are 49 boys and 1 girl, making 98% of boys.

(a) Making a Type I error in this situation means rejecting the null hypothesis when it is actually true. In other words, concluding that the new additive has a significant effect on drying time when it actually doesn't.

The consequence of a Type I error is that the company would put the new additive on the market and invest in an advertising campaign based on incorrect information. This could lead to wasted resources, loss of reputation if customers are dissatisfied with the product's performance, and financial losses if the product fails to meet expectations.

(b) Making a Type II error in this situation means failing to reject the null hypothesis when it is actually false. In other words, concluding that the new additive does not have a significant effect on drying time when it actually does. The consequence of a Type II error is that the company would miss the opportunity to market and promote a potentially beneficial product. This could result in missed profits and market share, as competitors who successfully introduce similar products gain an advantage.

In summary, a Type I error leads to unnecessary expenditure and potential negative consequences, while a Type II error results in missed opportunities and potential loss of market advantage. Both types of errors have significant implications for the company's resources, reputation, and financial success. It is important for the company to carefully consider the risks associated with each type of error and choose an appropriate level of significance to minimize the likelihood of making incorrect decisions.

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Answer:

$39.22

Step-by-step explanation:

The case costs $37. $37 is 100% of the price of the case.

The tax is 6% of the cost of the case. When you add 6% to 100% you get 106%.

The total price including tax is 106% of the price of the case.

106% of $37 = 1.06 * $37 = $39.22

Answer: $39.22

The equation of the line will be (assuming the y-intercept equal to zero):

y = 2.5*x

We know that we have a linear equation of the form:

y = a*x + b

Such that we know that the line passes through (-3, -7.5), notice that the proposed equation is:

y = 0.5*x

If you evaluate that in -3, you get:

y = 0.5*-3 = -1.5

So this line does not pass through (-3, -7.5).

If we assume that b = 0 in the linear equation, then we can find the value of a as:

-7.5  =  a*-3

a = 7.5/3 = 2.5

Then the linear equation is:

y = 2.5*x

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Answer:

y = 1.4m + 7.4

Step-by-step explanation:

Answer:

Answer

a Geometry :- shapes Are composed of regular lines and curves

b Organic shapes:- Unpredictable, irregular lines that suggest the natural world. Chaotic and unrestrained.

c Texture :-The surface quality of a work of art , for example coarse/fine detailed/lacking details

right answer organic..

i hope this helps you (⁠ ⁠◜⁠‿⁠◝⁠ ⁠)⁠♡

Therefore, An unpredictable and irregular shape is called an organic shape.

These shapes often mimic the forms found in nature, such as the shape of a leaf or a tree branch. Organic shapes lack the symmetry and geometric precision of their counterpart, the geometric shape. In art, organic shapes are commonly used to create a sense of movement, flow, and naturalism in a composition. In design, organic shapes can add visual interest and break up the monotony of straight lines and sharp angles. To sum up, the type of shape composed of unpredictable, irregular lines is an organic shape.

Therefore, An unpredictable and irregular shape is called an organic shape.

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Answer:

Step-by-step explanation:

1500 + (1500 : 100 × 4)

= 1500 + (15 × 4)

= 1500 + 60

= 1560

If we compare price, length and number of plies in each "paper-towel-roll" from six different manufacturers, then "degree-of-freedom" is 5.

The "Degree-of-freedom" is defined as a statistical concept which is used in calculations to account for variability in the data.

In comparing price, length, and "number-of-plies" in each paper "towel-roll" from 6 different manufacturers, the "degree-of-freedom" will depend on the specific statistical test used.

The degree-of-freedom is = "total sample size" - 1,

The total sample-size is the number of different manufacturers, and we know that there are 6 different manufacturers,

So, Degree Of Freedom is = 6 - 1 = 5,

Therefore, the required "degree-of-freedom" is 5.

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To afford a R350,000 deposit for a house in 10 years, your sister will need to invest approximately R1,909.26 per month, assuming a 9% annual nominal return on investment (NACM).

To calculate the monthly investment required, we can use the future value of an ordinary annuity formula:

FV = P × [(1 + r)^n - 1] / r

Where:

FV = Future value (R350,000)

P = Monthly investment

r = Monthly interest rate (9% ÷ 12 = 0.0075)

n = Number of periods (10 years × 12 months = 120)

Rearranging the formula to solve for P, we get:

P = FV × (r / [(1 + r)^n - 1])

Substituting the given values, we have:

P = R350,000 × (0.0075 / [(1 + 0.0075)^120 - 1])

 ≈ R1,909.26

Therefore, your sister would need to invest approximately R1,909.26 per month to accumulate a deposit of R350,000 in 10 years, assuming a 9% annual nominal return on investment.

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Tthe total cost for each club after 7 months will be $123.

To find out when the total cost of each health club will be the same, we can use the equation:

Club A total cost = Club B total cost

18 + 15x = 11 + 16x

Where x is the number of months. We can rearrange the equation to solve for x:

15x - 16x = 11 - 18
-x = -7
x = 7

So the total cost of each health club will be the same after 7 months. To find the total cost for each club, we can plug x = 7 back into the equation:

Club A total cost = 18 + 15(7) = $123

Club B total cost = 11 + 16(7) = $123

So, the total cost for each club after 7 months will be $123.

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Answer:

Plan 1

Step-by-step explanation:

134.97/3=44.99 month

44.99-34.99=10

She will save $10

Answer:

Plan 1 and she would save $120

Step-by-step explanation:

Plan 1 costs $34.99 per month.

For 12 months, it would cost 12 * $34.99 = $419.88

Plan 2 cost $134.97 for 3 months.

A year is 12 months, so it has 4 periods of 3 months.

In one year, this plan would cost 4 * $134.97 = $539.88

She should choose Plan 1.

She will save $539.88 - $419.88 = $120