Consider an integer n greater than 1. where c^n=d. which number is an nth root of the other number? explain

Answer:

18 Square inches

Step-by-step explanation:

Surface Area of original prism: 54 square inches

Surface Area of similar prism:

1/3 x 54

=18 square inches

Answer:

0.5

Step-by-step explanation:

The two figures are similar

find the linear scale factor of the two figures

=L/l ......... 10/4

=2.5

use the linear scale factor to find the other side

2.5= 5/n

2.5n=5 divide both sides by 2.5

n=0.5

The number of vendors selling maize or gari Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. 16 sell wheat and maize, 10 sale gari and rice, 42 sell maize, and 6 sell gari.

To assess the trading strategies used by traders to complete a trade transaction, mathematical analysis is employed. Moreover, probability theory is used to evaluate the usefulness of money management strategies.

Out of 59 dealers, 26 exclusively sell gari, 8 only offer rice, and 15 only sell maize. Ten sell rice and gari, sixteen sell rice and maize, and forty-two sell maize.

Determine the quantity of dealers selling gari of corn using the formula below:

P(G ∪ R ∪ M) = P(G) + P(R) + P(M) - P(G ∩ R) - P(R ∩ M) - P(G ∩ M) + P(G ∩ R ∩ M)

59 = 26 + 8 + 15 - 10 - 16 - P(G ∩ M) + 42

59 - 42 = 49 - 26 - P(G ∩ M)

P(G ∩ M) =  - 17 + 23

P(G ∩ M) = 6

Hence, there are 6 dealers selling gari or corn.

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For the given right triangles the value of side b is  [tex]4\sqrt{3}=6.9[/tex]  meanwhile the value of side c is  [tex]2.5\sqrt{2} =3.5[/tex].

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem. The Pythagorean Theorem says (hypotenuse)²= (leg1)²+(leg2)². And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) .

The question asks the values of the side lengths b and c. The variables b and c represent one of the sides of the right triangles.

     sin (60)=b/8

     [tex]\frac{\sqrt{3}}{2}=\frac{b}{8} \\ \\ 2b=8\sqrt{3} \\ \\ b=4\sqrt{3}=6.9[/tex]

     [tex]\frac{\sqrt{2}}{2}=\frac{c}{5} \\ \\ 2c=5\sqrt{2} \\ \\ c=\frac{5}{2} \sqrt{2}\\ \\ c=2.5\sqrt{2}=3.5[/tex]

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a)The probability that daily production is less than 27.6 liters is given by the equation P ( x < 27.6 ) = 0.014179

b) The probability that daily production is more than 49.4 liters is given by the equation P ( x > 49.4 ) = 0.02275

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the probability that daily production is less than 27.6 liters be represented as P

Now , the equation will be

a)

The observed value of x = 27.6 L

The mean of the sample μ = 39 L

The standard deviation of the sample σ = 5.2 L

Now , z-score is calculated using the formula:

z = (x - μ)/σ

Substituting the values in the equation , we get

z = ( 27.6 - 39 ) / 5.2

z = -2.19231

Now ,the p value from the z table is

P ( x < 27.6 ) = 0.014179

And , the probability is P ( x < 27.6 ) = 0.014179 = 1.418 %

Therefore , the probability that daily production is less than 27.6 liters is given by P = 1.418 %

b)

The observed value of x = 49.4 L

The mean of the sample μ = 39 L

The standard deviation of the sample σ = 5.2 L

Now , z-score is calculated using the formula:

z = (x - μ)/σ

Substituting the values in the equation , we get

z = ( 49.4 - 39 ) / 5.2

z = 2

Now ,the p value from the z table is

P ( x < 49.4 ) = 0.97725

P ( x > 49.4 ) = 1 - P( x < 49.4 ) = 0.02275

And , the probability is P ( x > 49.4 ) = 0.02275 = 2.275 %

Therefore , the probability that daily production is more than 49.4 liters is given by P₁ = 2.275 %

Hence , the probabilities are solved

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The factorization of the given quadratic equation by grouping is (2y + 1) (4y + 1)

Factorization is a method of finding factors for any quadratic expression, polynomial, or algebraic expression.

For a polynomial of the form ax^2 + bx + c, rewrite the middle term as a sum of two terms whose product is a×c = 8 × 1 = 8 and whose sum is b = 6.

Given that:

8y² + 6y + 1

8y² + 2y + 4y + 1

Factor out the greatest common factor from each group.

2y(4y + 1) + 1(4y + 1)

(2y + 1) (4y + 1)

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The number of phones and accessories sold are 8 and 24 respectively.

Indigo works as a salesperson at an electronics store and sells phones and phone accessories. Indigo earns a $8 commission for every phone she sells and a $4 commission for every accessory she sells. On a given day, Indigo made a total of $160 in commission from all accessory and phone sales and she sold 3 times as many accessories as phones.

Therefore, the number of phones and accessories she sold can be calculated as follows:

Using equation,

let

x = number of phone sold

y = number of accessories sold.

Therefore,

8x + 4y = 160

y = 3x

Therefore,

8x + 4(3x) = 160

8x + 12x = 160

20x = 160

x = 160 / 20

x = 8

Hence,

y = 3(8) = 24

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Answer: m = 20.23 - 16.09

Step-by-step explanation:

This trade will create a win-win situation for both players, leaving them both better off than they were before.

Capacity in math is the maximum amount that a container or figure can hold. It is typically measured in liters, gallons, or quarts and is determined by the size of the container or figure. Capacity is a measure of volume and is used in a variety of math problems, including those involving capacity conversion, calculating the amount of liquid that can be stored in a container, and determining the amount of material needed to fill a given area.

A trade that will leave both players better off is for Amber to produce all of the apples and Johnny to produce all of the pears. This way, Amber can produce 24 apples in a day and Johnny can produce 32 pears in a day, which is more efficient than if they both tried to produce both items. Amber has a higher capacity for producing apples while Johnny has a higher capacity for producing pears. Therefore, this trade makes the most sense.

The trade will leave both players better off because of the increased efficiency in production. Amber can produce 24 apples in a day and Johnny can produce 32 pears in a day, which is more efficient than if they both tried to produce both items. This means that they will both have more resources to spend on other things. They will also be able to divide their time more evenly between the two tasks, allowing them to be more productive and efficient.

In addition, the trade will also benefit both players in terms of their preferences. Amber will be able to spend a full day producing apples, which she prefers, and Johnny will be able to spend a full day producing pears, which he prefers. This trade will create a win-win situation for both players, leaving them both better off than they were before.

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If  a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting

a) 0 defective resistors: 0.3164

b) 1 defective resistor: 0.4219

c) 3 defective resistor: 0.0469

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

Probability

First step is to calculate the probability for a defective resistor and non-defective resistor:

Probability=3/12

Probability =0.25

Non-defective resistor:

Probability=(1-0.25)

Probability=0.75

Now  let find the probabilities for defective resistors from 0 to 3

P(0)=1(0.75)^4 ×(0.25)^0

P(0)=0.3164

P(1)=4(0.75)^3× (0.25)^1

P(1)=0.4219

P(2)=6(0.75)^2× (0.25)^2

P(2)=0.2109

P(3)=4(0.75)^0×(0.25)^3

P(3)=0.0469

P(4)=1(0.75)^0 × (0.25)^4

P(4)=0.0039

Hence,

a. P(0)=0.3164

b. P(1)=0.4219

c. P(3)=0.0469

Therefore If  a package contains 12 resistors, 3 of which are defective. If 4 are selected, the probability of getting 0 defective resistors: 0.3164, 1 defective resistor: 0.4219, 3 defective resistor: 0.0469.

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Hello :3

Answer:

(-8,-5)

Hope this helps! :)

Answer:

b = -10

Step-by-step explanation:

Two vectors are orthogonal if and only if their dot product is zero. The dot product of v and w is given by:

(v · w) = (5i + 2j) · (4i + bj) = 5 * 4 + 2 * b = 20 + 2b.

For v and w to be orthogonal, we need the dot product to be zero, which means 20 + 2b = 0, so:

2b = -20

b = -10

Therefore, b = -10 makes the vectors v and w orthogonal.

Answer:

January 2nd

Step-by-step explanation:

subtract 5 from February and 30 from January

Answer:

The watch loses 5 seconds per hour. It is 5 minutes slow. 5 minutes is 300 seconds(5 x 60). 300 seconds therefore represents 300/5 hours=60 hours. From Tuesday 10.30 AM backwards 60 hours(2 1/2 days) brings you to 10.30 PM on Sunday evening as the date and time the watch was last set.

Step-by-step explanation:

The answer choice which is equivalent to sec (x) among the given answer choices is; 1 / cos(x).

It follows from the task content that the answer choice which is equivalent to sec (x) is to be determined among the given answer choices.

From trigonometric ratios concept, it follows that the inverses of the 3 basic trigonometric ratios are as follows;

1 / sin x = csc (x)

1 / cos x = sec (x)

1 / tan x = cot (x)

On this note, it follows that the answer choice which is equivalent to sec (x) is; 1 / cos x.

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Answer:

4

Step-by-step explanation:

The maximum number of cases of vegetables that he can buy can be calculated by dividing the maximum budget of $50 by the cost of a single case of vegetables, which is $10.68:

$50 ÷ $10.68 = 4.67 cases

Since you can't buy fractional cases, the maximum number of cases he can buy would be 4. Round down to the nearest whole number, the maximum number of cases he can buy is 4.

The value of the variable x is 99 and y is 22 in the given transversal of parallel lines.

There are several different kinds of lines that can exist in geometry, including parallel, perpendicular, intersecting, and so on. A transversal is a different line that we have in addition to that. A road crossing two or more other roads or a railway crossing several other lines are examples of this. These convey the fundamental concept of a transversal. If two or more other lines in the Euclidean plane are parallel, transversals are crucial in determining this. Learn the definition of a transversal line in this article, along with how it can be used to create angles with both parallel and non-parallel lines. Study additional geometrical ideas here.

Given,  I || h

Using the same internal property of transversal

81 + x = 180° (angle sum property)

x = 180 - 81

x = 99°

For (3y + 33), vertical opposite angle rule can be applied so

x = (3y + 33)

3y + 33 = 99°

3y = 99 - 33

3y = 66

y = 66/3

y = 22°

Thus, The value of the variable x is 99 and y is 22 in the given transversal of parallel lines.

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Correct question:

In the figure below, I || h. Find the values of y and x.

The domain of the graphed function is interpret as follows:

The domain represents a 10-month period of flower production.

The domain of a function is composed by the set containing all the possible input values for the function, hence it is composed by all the values of x assumed by the function.

The input variable, represented by the x-axis, is defined as follows:

Number of Months.

Hence the correct option is given by the fourth option, as x ranges from 0 to 10.

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The density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]

The density function of [tex]U = Y1^2 +Y2^2[/tex]  is given by the formula [tex]f_U(u) = (1/2π)∫_0^∞ f_Y1(y_1)f_Y2(√(u-y_1^2)) dy_1[/tex]. This can be calculated as follows:

Let u ≥ 0, then

[tex]f_U(u) = (1/2π)∫_0^∞ (1/√(2π))e^(-(y_1^2/2))(1/√(2π))e^(-(√(u-y_1^2)^2/2)) dy_1[/tex]

[tex]= (1/2π)∫_0^∞ (1/2π)e^(-u/2) dy_1= (1/2π)e^(-u/2) ∫_0^∞ (1/2π) dy_1= (1/2π)e^(-u/2)[/tex]

Therefore, the density function is given by [tex]f_U(u) = (1/2π)e^(-u/2).[/tex]

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The solutions to each recurrence relation can be expressed as a linear combination of terms:

For (a) The solution to (x - 1)(x + 2) = 0 is

For (b) The solution to (x - 4)(x - 4) = 0 is

For (c) The solution to (x - 4)(x - 4)(x + 5) = 0 is

For (d) The solution to (x - 4)(x - 4)(x + 5)^4 = 0 is

These linear combinations of terms can be used to describe the general solution to each recurrence relation, but the actual coefficients in the linear combination are not given and depend on the base cases of the recurrence relation.

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Answer:

1

Step-by-step explanation:

The two equations have one solution. This is because when the two equations are graphed, the lines intersect in only one point. Therefore, the system only has one solution.

The independent variable is distance from the left end of the radio dial and its unit is centimeters.

Scatter plots are used to observe and plot relationships between two numeric variables graphically with the help of dots. The dots in a scatter plot shows the values of individual data points.

The given coordinate points are (53, 1.54), (60, 2.17), (70, 2.95), (80, 3.62), (100, 4.75)

Here,

1.a) The independent variable is distance from the left end of the radio dial and its unit is centimeters.

b) The dependent variable is frequency and its units is kilohertz.

2. a) A scatter plot of the data is given below in the attachment.

b) The distance from the left end of the radio as the frequency gets higher is increases.

c) The distance from the left end of the radio as the frequency gets smaller is decreases.

Therefore, the independent variable is distance from the left end of the radio dial and its unit is centimeters.

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The appropriate answer to that same previous information is y ≥ -(x-50)² + 25

According to analysts, inequality promotes political dysfunction and slows down economic progress. Because wealthy households typically spend a smaller share of their earnings than do poorer households, concentrated riches lower the amount of demand within the economy. The economy may suffer if low-income families have fewer possibilities.

Assume that the equation is y = a(x-h)² + k

y - a (x-50)² + 625

Put (61,504) in the equation

504 = a(61 - 50)² + 625

504 = a.121+625

121a = -121

a = -1

y = -(x-50)² + 625

Hence, y ≥ - (x-50)² + 625

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Step-by-step explanation:

Start by dividing it by a prime number and just go from there. The included pictures will show how :) Because the end result is all prime numbers it is prime factorization.

Nomusa's statement is not valid because her monthly tax is not equal to R502.34.

A medical fund is a type of financial arrangement that individuals, families, or organizations set up to pay for medical expenses. The purpose of a medical fund is to help cover the cost of medical treatments, procedures, or medications that may not be covered by insurance. There are different types of medical funds, including personal savings accounts, health savings accounts (HSAs), flexible spending accounts (FSAs), and crowdfunding platforms that allow people to raise money for medical expenses. These funds can be used to pay for a variety of medical expenses, including doctor visits, surgeries, prescription drugs, and medical equipment. The goal of a medical fund is to provide individuals and families with a source of financial support for medical expenses, and to help reduce the financial burden associated with medical care.

Gross salary is the total amount of money earned by an individual before any deductions or taxes have been taken out.

2.3 Nomusa's monthly taxable income can be determined as follows: Gross salary = R28 500; 7.5% pension deduction = R28 500 x 7.5% = R2,137.5; Monthly taxable income = Gross salary - pension deduction = R28 500 - R2,137.5 = R26,362.5

2.4 Based on Nomusa's annual taxable income of R26,362.5 x 12 = R316,350, she falls in tax bracket 4, with a taxable income between R305,850 and R423,300.

2.5 Nomusa's monthly tax can be calculated as follows: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R316,350 - R195,850) = 26% x R120,500 = R31,230; Total tax = R35,253 + R31,230 = R66,483; Monthly tax = Total tax ÷ 12 = R66,483 ÷ 12 = R5,540.25.

2.6 To determine whether Nomusa's statement is valid, we would have to calculate her monthly tax if she were 10 years younger, and compare it to the stated amount of R502.34: If she were 10 years younger, she would not be eligible for the secondary tax threshold, so her monthly tax would be the same as calculated in 2.5: R5,540.25. This amount is not equal to R502.34, so Nomusa's statement is not valid.

2.7 If Nomusa joins a medical fund and includes her husband and two grandchildren, she would qualify for the following monthly medical credits: For herself: R310; For her husband: R310; For each grandchild: R209; Total monthly medical credit = R310 + R310 + 2 x R209 = R936.

2.8 To calculate Nomusa's brother's monthly tax, we can use the same process as in 2.5: 18% of the first R195,850 = R35,253; 26% of the portion of taxable income over R195,850 = 26% x (R45,980.17 - R195,850) = 26% x (R26,129.17) = R6,792.19; Total tax = R35,253 + R6,792.19 = R42,045.19; Monthly tax = Total tax ÷ 12 = R42,045.19 ÷ 12 = R3,503.77, which is approximately R11,024.11.

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The ranges of each equation for the domain {-2,0,2} are given as follows:

The domain is the set of input values for each equation, hence the range will be the set of output values for the given domain.

For the equation y = -x, the range is obtained as follows:

Hence the range is:

{-2, 0, 2}.

The same procedure is applied to the other equations, the range is the set containing the numeric value of the function for each input value.

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Answer:

x-2y =6

x-2y =6

= 6-2y=x=4