The value of the test statistic for the test H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9 is

The money at the end of 4 years will be $1034.

What is compound interest ?

The interest on the initial investment as well as the interest that has accrued on that investment are both referred to as compound interest, or "compounding interest."

Given, P = $1,000

          Rate (r) = 0.85% p.a.

          time (t)  = 4 years

We know that, Amount = P ( 1 + r/100 )^t

The money in account after 4 years will be :

           = P ( 1 + r/100 )^t

           = $1,000 × ( 1 + 0.85/100 )^4

           = $1,000 × 1.0085^4

           = $1,000 × 1.0344

           = 1034 (approx).

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The derivative of function y =eu is dy/dx = dy/du × du/dx

                                        Derivative refers to the rate of change of a variable with respect to any independent variables.

The function that has such a differentiable element which is also a function of other variable is termed as composite function. The method of differentiating composite function is called chain rule for differentiation.

In the above question, y is a composite function as y is a function of u and at the same time u is a function of x.

given, y =eu, where u is differentiable function of x, let u = g(x)

now, y =eu is differentiated using chain rule and we get dy/dx = dy/du×du/dx

hence, the derivative is dy/dx = dy/du×du/dx

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The correct answer is the quotient of six and Nineteen times a number. Option C

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner. It provides a unique representation of every number and represents the arithmetic and algebraic structure of the figures

Given 6/19n

6/9  can be written as the quotient of six and nineteen multiply by a number

Quotient means that you divide something by another

A quotient means a ratio or one quantity being divided by another, or in algebraic terms (a/b).

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A box of truffles costs $4.00 each

A box of peanut brittle costs $4.00 each

What is the algebra of equation?

A mathematical statement in which two expressions are rendered equal to one another is known as an algebraic equation. A variable, coefficients, and constants make up an algebraic equation in most cases.

Here, we

Let t = boxes of truffles and p = peanut brittle

53t + 54p = 428...(1)

67t + 54p = 484...(2)

On solving equations (1) & (2), we get

14t = 56

t = 4

53t + 54p = 428

53(4) + 54p = 428

212 + 54p = 428

54p = 216

p = 4

Hence,

A box of truffles costs $4.00 each

A box of peanut brittle costs $4.00 each

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The random large boulders around central park in new york city got to central park They were carried by glaciers and dropped as glacial erratics.

There have been four kinds of bedrock in Manhattan, including the Manhattan schist and the Hart-land shirts, which are metamorphosed sedimentary rocks found in outcrops. Some of these are made out of igneous rocks that developed billions of years ago. It happened during the period of the Grenville progeny and occurred during the formation of the ancient mega continent.

Various glaciers have covered the region of Central Park in the past, the much more recent being the Wisconsin glacier that developed about around 12,000 years ago.

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The required equation of the line is 9/4x with a slope of 9/4 and a y-intercept of 0.

The value of the steepness or the direction of a line in a coordinate plane is known as a line's slope, often referred to as a line's gradient. With a line's equation or the coordinates of a point along the straight line, slope can be computed using a variety of ways.

The slope of a line indicates the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The letter "m" is typically used to signify slope.

The slope of the line is a tangent angle made by line with horizontal.

i.e. m = tan x, where x in degrees.

Let the given values be m = 9/4 and c = 0

Standard equation of the line, y = mx + c

substitute the values in the above equation, we get

y = 9/4x + 0

y = 9/4x

Therefore, the required equation of the line exists 9/4x.

The complete question is:

Which linear equation represents a line with a slope of 9/4 and a y-intercept of 0?

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Answer:

(-4,4)

Midpoint= (x2 + x1 /2, y2+y1 /2)

Step-by-step explanation:

the coordinates of the midpoint between points A and B are

((xa + xb)/2, (ya + yb)/2)

in our case

((-2 + -6)/2, (0 + 8)/2) = (-8/2, 8/2) = (-4, 4)

By adding up all the possible ways to distribute the coupon and subtracting it from the possible ways to distribute the 10 coupons to the 15 men, we can determine the total number of ways at least a woman can receive a coupon.

- The entire number of options for dividing the coupons among the 20 customers is the same as the total number of ways to choose a subset of 10 items from a set of 20.

In other terms, 20/10 = 20!/ 10!10 is the combinatorial number of 20 and 10.

- We must use the same calculation as above, but with a set of 15 items rather than 20, to get the total number of alternatives for distributing the coupons among the 15 males.

We now have 15/10, which is 15!/10!5! possibilities.

To ensure that at least one woman receives a coupon, we have 20/10 - 15/10 distribution options.

A combination is made up of r items chosen without replacement from a set of n items, where the order is irrelevant.

The amount of circular permutations of n other objects, taken r at a time, is nPr 2r if clockwise and anti-clockwise configurations are not considered to be distinct. Combinations are various groups or choices made from a variety of items, either all or some of them.

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The number of combination possible = 15625

When the numbers are repeating

The number of possible combinations = 13800

Given that a certain combination lock requires three selections of numbers

Total possible numbers = 25

Part a

Total number of combinations possible = 25 × 25 × 25

Multiply the numbers

= 15625 possible combinations

Part b

The given condition is no number may be used twice

Total number of combinations possible = 25 × 24 × 23

Multiply the numbers

= 13800 possible combinations

Therefore, when the number are repeating, the possible combinations are 15625 and when the numbers are not repeating the possible combinations are 13800

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(A)  The probability that, after 11 weeks, the supply of gasoline will be below 20000 gallons is 0.2643.

(B) 52854.8 gallons should be the weekly delivery so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%.

Given,

u = 50000

s = 10000

n = 11

Starting supply = 74000

Weekly delivery = 47000

Total supply for 11-week = 74000 + 11*47000

                                        = 591000

(A) If more than 20,000 gallons of gasoline are purchased overall in these 11 weeks, the supply will fall below that amount.

591000 - 20000 = 571000

We need to find, P(T > 571000) = P(z > [tex]\frac{571000-11(50000)}{\sqrt{1110000} }[/tex])

                                                    = P(z > 0.63)

                                                    = 1 - 0.7357

                                                    = 0.2643

(B) Unknown schedule delivery = A

     Total gasoline should be more than = 74000 + 11*A - 20000

     Probability = 05%

    z-value corresponding it = 2.575

    P(T > 74000 + 11*A - 20000) = 0.05

    [tex]\frac{74000+11A-20000-11(50000)}{\sqrt{1110000} } = 2.575[/tex]

                                        A = 52854.8

Hence, 52854.8 gallons should be the weekly delivery be so that after 11 weeks the probability that the supply is below 20000 gallons is only 0.5%.

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The angle, to the degree, that the string makes with the ground is

34.33.

A right-angled triangle can be formed by the string, the height of the kite, and the horizontal distance along the ground to a point directly beneath the kite.

The string represents the hypotenuse (200 feet), and the height (120 feet) represents the opposite side.

The trigonometric ratio sin can be used to calculate the angle between the string and the ground.

sinθ= Perpendicular/hypotenuse

sinθ=120/200

=0.6

Now sin(0.6) = 0.5646

sinθ=0.5646

therefore ,θ

=sin⁻¹(0.5646)

=34.33°

Heights and Distances is a study of Trigonometry applications. It has many real-world applications, such as measuring the height of an object, the depth of an object, the distance between two celestial objects, and so on.

Trigonometric formulas and ratios are useful in the study of heights and distances.

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A dictator

Step-by-step explanation:

The required elementary matrix E such that EA = B is

[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].

Any matrix obtained by performing a single elementary row operation on the identity matrix is called an elementary matrix.

The elementary operations are as follows:

1. Interchange the two rows of a matrix

2. Multiply a row of a matrix by the non-zero scalar k.

3. Add k-times of a row into another row of the matrix.

Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.To perform an elementary row operation on A, an n×m matrix, take the following steps:

1. To find E, the elementary row operator, apply the operation to an n×n identity matrix.

2. To carry out the elementary row operation, premultiply A by E.

We want to interchange the first and second rows of A, a 3×3 matrix to  get B. To create the elementary row operator E, we interchange the first and second rows of the identity matrix I3:

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex] is changed to  [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].

So, [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex][tex]\left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right][/tex]

Thus, the required elementary matrix E such that EA = B is

[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]

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The Perimeter of the Pathway around the pool is 38.4m

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Length of the Pathway = 12m + 80cm + 80cm = 12m + 1.6m = 13.6m

Breadth of the Pathway = 4m + 80cm + 80 cm = 4m + 1.6m = 5.6m

Perimeter of Rectangle = 2(l+b)

Perimeter = 2(13.6 + 5.6)

Perimeter = 2(19.2)

Perimeter = 38.4m

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The point (11,11) will lie on the graph of the function f(x) = IxI

What is coordinate?

The x-coordinate informs us of a point's separation from the y-axis, which is the vertical axis. The abscissa is another term for the x-coordinate. The y-coordinate shows how far a point is from the horizontal axis, or x-axis. The term "ordinate" also applies to the y-coordinate.

the function: f(x) = IxI

The function will have every positive and negative integer contained within itself.

So coordinates of another point with the same y value (11,11) will lies on the graph so as (-11,11).

Hence point (11,11) will lie on the graph of the function f(x) = IxI

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We know that the required zero of the given polynomial 3x²+4x²-7=0 is (B) x = 1.

A polynomial is a mathematical formula that involves only the operations of addition, subtraction, multiplication, and powers of positive integers of the variables and is composed of coefficients and indeterminates.

An example of a polynomial with a single indeterminate x is x² - 4x + 7.

So, we have the equation:

3x²+4x²-7=0

Now, calculate the zero of the polynomial as follows:

When x = 0:

P(x) = 3x² + 4x² - 7 = 0

P(0) = 3(0)² + 4(0)² - 7

P(0) = - 7

Not zero

When x = 1:

P(x) = 3x² + 4x² - 7 = 0

P(1) = 3(1)² + 4(1)² - 7

P(1) = 3 + 4 - 7

P(1) = 0

Zero of the polynomial.

Therefore, we know that the required zero of the given polynomial 3x²+4x²-7=0 is (B) x = 1.

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The equation K = 4a + 9ab solved for a is a = K /(4 + 9b). (Option D)

In mathematics, an equation refers to a formula that expresses the equality of two mathematical expressions by connecting them with the equals sign =.

The given equation is K = 4a + 9ab.

In order to solve for a, the a variable must be isolated at one side of the equation and the other variables must be collected on the other sides.

On the right-hand side, as both terms contain the variable a, hence factoring it,

K = a(4 + 9b)

Dividing both sides by (4 + 9b) to isolate a,

a = K /(4 + 9b)

Note: The question is incomplete. The complete question probably is: Solve the equation for a in K = 4a + 9ab. A) a = K(4 + 9b) B) a = 4(K + 9b) C) a = (4 + 9b)/K D) K /(4 + 9b)

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To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Mr. Dyer received 1,080 votes.

Ratio of votes = 4:3:2

Total votes = 4 + 3 + 2 = 9

Total votes cast = 2,700

Mr. Dyer's votes = (4/9) x 2,700 = 1,080 votes

The ratio of votes cast for Mr. Dyer, Ms. Frau and Mr. Borak was 4:3:2 respectively. This means that for every 9 votes cast, 4 votes were for Mr. Dyer, 3 votes were for Ms. Frau and 2 votes were for Mr. Borak. Since none of the 2,700 voters cast more than one vote, the total votes cast for each candidate would be 2,700. To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Therefore, Mr. Dyer received 1,080 votes (4/9 x 2,700).

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Under coverage of the population will be the most noticeable bias in distributing the survey at his point in time.

Undercoverage bias happens when segments of the target population are entirely executed or loses represented in the sample than they are in the population. This means that these segments are executes from the sampling process. Non response bias occurs when parts of the sampled population are unable or refuse to respond.

Undercoverage occurs when an element of the target population is not represented on the survey frame and therefore not given any chance of selection in the survey sample; that is the element has zero probability of selection into the sample. It refers to a type of sampling bias that occurs when a piece of information from your sample responses goes missing or uncovered in the results. This significant entity goes unselected or has zero chance of getting in your representing sample.

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If an object travels according to a distance function, d(t), and d' (c) < 0, then at t = c we know that the velocity is positive.

The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument. Calculus relies heavily on derivatives. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function depending on one of its variables. The most prominent example is velocity, which is the rate of change of displacement with respect to time. Differentiation is used to calculate the rate of change of values in real time. For example, if we want to find the velocity of an automobile, we may use differentiation.

Here,

if first derivative is < 0 then, the value is positive.

If an item moves according to a distance function, d(t), and d' (c) <0, we know that the "velocity is positive" at t = c.

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The probability that the first is red and the second is white is 4/21 or 0.190476.

The total number of marbles in the jar is 4 red, 7 white and 10 blue. This means there is a total of 21 marbles.

The probability of selecting a red marble first is 4/21 (4 out of 21 marbles are red).

The probability of selecting a white marble second is 7/20 (7 out of the remaining 20 marbles are white).

The probability of selecting a red marble first and a white marble second is 4/21 x 7/20 = 28/420 = 4/60 = 0.190476

The probability of selecting two marbles at random from the jar is calculated by multiplying the individual probabilities of selecting each marble. The probability of selecting the first marble is 4/21 (4 out of 21 marbles are red) and the probability of selecting the second marble is 7/20 (7 out of the remaining 20 marbles are white). Thus, the probability of selecting a red marble first and a white marble second is 4/21 x 7/20 = 28/420 = 4/60 = 0.190476.

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Answer:

$47.25

Step-by-step explanation:

When the price goes down by 30%, you pay 70% of the original price.

When the price goes down by 10%, you pay 90% of the original price.

0.9 × 0.7 × $75 = $47.25

Answer: 9 visits

Step-by-step explanation:

Let x =  number of visits to the rink

19.95 + 6.95x ≤ 82.5

6.95x ≤ 82.50 - 19.95

6.95x ≤ 62.55

x ≤ 62.55/6.95

x≤ 9

The answer is to the 7 1/3 th mark.

Consider the provided question,

Since, in wide cylinder, water rises to 4th mark while in narrow cylinder same amount of water rises to 6th mark.

So, 6th mark on narrow cylinder = 4th mark on the wide cylinder which implies that 3rd on narrow cylinder = 2th mark on the wide cylinder

From the above,

Since, 3rd on narrow cylinder = 2th mark on the wide cylinder that means 1 mark on narrow cylinder is equal to 2/3 the of the 1st mark of the wider cylinder.

Hence the 11th mark of the narrow cylinder is equal to the

11 * 2/3 = 22/3  = 7 1/3 mark of the wider cylinder.

Hence, the correct answer is option to the 7 1/3th mark.

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Answer:

i

Step-by-step explanation:

1. Multiply the Numerator and the Denominator by the Complex Conjugate of the Denominator:

  [tex]\frac{1+i}{1-i}*\frac{1+i}{1+i}=\frac{1+2i+i^{2}}{1-i^{2}}[/tex]

  Remember that i² = -1:

  [tex]\frac{1+2i+i^{2}}{1-i^{2}}=\frac{2i}{2}[/tex]

2. Simplify

Answer:

the quadrilateral is a trapezium,

area of trapezium ABCD = AB(AD + BC)/2

By distance formula,

AD = 5 units

BC = 9 units

AB = 6 units

area = 6(5+9)/2

=6×7

=42

option D is correct

The zero of the polynomial 3x² - 8x + 5 is 1

The correct answer option is option C.

3x² - 8x + 5

check all options:

When x = 0

3x² - 8x + 5

substitute x = 0 into the equation

3(0)² - 8(0) + 5

3(0) - 0 + 5

0 - 0 + 5

= 5

When x = -1

3x² - 8x + 5

3(-1)² - 8(-1) + 5

3(1) + 8 + 5

3 + 8 +5

= 16

When x = 1

3x² - 8x + 5

3(1)² - 8(1) + 5

3(1) - 8 + 5

3 - 8 + 5

= 0

Consequently, 1 is the zero of the given Polynomial.

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Answer:

1. x = 30

2. ∠1 = 30°

3. ∠2 = 60°

4. ∠3 = 120°

Step-by-step explanation:

⭐What are supplementary angles?

⭐What are complementary angles?

Set up the equations for the situation:

∠1 + ∠2 = 90

∠2 + ∠3 = 180

x + 2x = 90 . . . (1)

2x + ∠3 = 180 . . . (2)

First, solve for "x" in equation 1:

x + 2x = 90

3x = 90

∴ x = 30

Next, substitute "x" into ∠1 and ∠2 to solve for ∠1 and ∠2:

∠1 = x

∴ ∠1  = 30°

∠2 = 2x

∠2 = 2(30)

∴ ∠2  = 60°

Finally, substitute "x" into equation 2 to solve for ∠3:

2x + ∠3 = 180

2(30) + ∠3 = 180

60 + ∠3 = 180

∴ ∠3 = 120°

The percent error of Oliver's estimate will be 7.1%. Then the correct option is B.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

In science class, Oliver gauges the volume of an example to be 52 mL. The genuine volume of the example is 56 mL.

The percent error of Oliver's estimate is given as,

P = [(56 - 52) / 56] x 100

P = (4 / 56) x 100

P = 0.071 x 100

P = 7.1%

The percent error of Oliver's estimate will be 7.1%. Then the correct option is B.

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