How to reduce 0.35 to the lowest term

Answer:

Step-by-step explanation:

Let the events be

W = Wednesday

T = Thursday

F = Friday

S = Saturday

The corresponding probability are

P (W) = 0.3

P (T) = 0.4

P (F) = 0.2

P (S) = 0.1

Let Y = number of days beyond wednesday that takes for both magazines to arrive

(so possible Y values are 0, 1 , 2 ,3)

The possible outcome are 4² = 16

(W,W) (W,T) (W,F) (W,S)

(T,W) (T,T) (T,F) (T,S)

(F,W) (F,T) (F,F) (F, S)

(S,W) (S,T) (S,F) (S,S)

The values associated for each of the following as follows

Y(W,W) =0, Y(W,T) =1, Y(W,F)=2, Y (W,S)=3

Y(T,W)=1, Y (T,T)=1, Y (T,F)=2, Y (T,S)=3

Y(F,W)=2, Y (F,T)=2, Y (F,F)=2, Y (F, S)=3

Y(S,W)=3, Y (S,T)=3, Y (S,F)=3, Y (S,S)=3

The probability mass function of Y is

P(Y=0)=0.3(0.3)=0.9

P(Y=1) = P[(W,T) or (T,W) or (T,T)]

= [0.3(0.4) + 0.3(0.4) + 0.4(0.4)]

=0.4

P(Y = 2) = P[(W,F) or (T,F) or (F,W) or (F,T) or (F,F)]

=0.3(0.2) + 0.4(0.2) + 0.2(0.3) + 0.2(0.4) + 0.2(0.2)]

=0.32

P(Y =3) = P[(W,S) or (T,S) or (F,S) or (S,W) or (S,T) or (S,F) or (S,S)]

= [0.3(0.1) + 0.4(0.1) + 0.2(0.1) + 0.1(0.3) + 0.1(0.4) + 0.1(0.2) + 0.1(0.1)]

= 0.19

The average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6 is approximately 0.29 to the nearest hundredth.

To find the average rate of change of the function f(x) = √(x+4) over the interval 2 ≤ x ≤ 6, we need to calculate the change in the function divided by the change in the input variable over that interval.

The change in the function between x = 2 and x = 6 is:

f(6) - f(2) = √(6+4) - √(2+4) = √10 - √6

The change in the input variable between x = 2 and x = 6 is:

6 - 2 = 4

So, the average rate of change of the function over the interval 2 ≤ x ≤ 6 is:

(√10 - √6) / 4

To approximate the answer to the nearest hundredth, we can use a calculator or perform long division to get:

(√10 - √6) / 4 ≈ 0.29

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Answer:

4x^2 - 5.

Step-by-step explanation:

h(x) = x^2 - 5

Replace the x in h(x) by 2x:

h(2x) = (2x)^2 - 5

        =  4x^2 - 5.

Answer:

9u^3 + 6u^2 - 7u + 6

Step-by-step explanation:

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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The operation that has been performed on v to result in the vector that is shown is multiplication by -1.

The vector that is shown is (-2, -1). This can be obtained from vector v = (2, 1) by multiplying it by -1. Multiplying a vector by a negative number reverses its direction.

Multiplication of a vector by a number is performed component-wise. This means that each component of the vector is multiplied by the number. In the case of (-1) * (2, 1), each component is multiplied by -1. This results in the vector (-2, -1).

Here is the mathematical equation:

(-1) * (2, 1) = (-2, -1)

Therefore, the operation that has been performed on v to result in the vector that is shown is multiplication by -1.

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Answer:

proved

Step-by-step explanation:

hope it helped!!!

Answer:

a)  = 13550 paid  by end yr 3                                                                                 b) 36450 * 0. 01 = $364.5 buy down interest by 1%

Step-by-step explanation:

50000 * 0.10 = 5000 paid yr 1 = 5000 /8 = 625 per payment   45000 * 0.10 = 4500 paid yr2  40500 *0. 10 = 4050 paid 40500-4050= 36450 left to pay 50000-36450 = 13550 paid    b) 36450 * 0. 01 = $364.5 buy down interest by 1%

Answer:

127.1

Step-by-step explanation:

This is easy, if you see the hundredth 0.07, that is above 5 so it rounds up to become 0.1 tenth, normally we check for things like 0.003 in the thousandth, but here it is less than 5 so it does nothing, not to mention it wouldnt change the outcome

Answer:

44 cups = 27.5 gallons

Step-by-step explanation:

Using the conversion:

We can find what is 44 cups in gallons.

=> 1 cup = 0.625 gallons

=> 44 x 1 = 0.625 x 44

=> 44 cups = 0.625 x 44 gallons

=> 44 cups = 27.5 gallons

Therefore, 44 cups = 27.5 gallons.

Hoped this helped.

The tree diagram which shows all the possible sandwich combinations is the last tree diagram which shows 8 combinations.

Given that,

Arlo is making a sandwich.

He will choose one type of bread, one type of meat, and one type of cheese.

His choices for bread are wheat (W) and rye (R).

His choices for meat are turkey (T) and ham (H).

His choices for cheese are cheddar (C) and swiss (S).

We can start the combinations with two parts W and R.

For each of this, there will be the combinations of meat and cheese.

The combinations can be :

W - T - C

W - T - S

W - H - C

W - H - S

These 4 combinations will be for R also.

Hence the correct option is the last figure.

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Answer:

12i

Step-by-step explanation:

sqrt(-1) = i, sqrt(144) = 12

Answer:

b

Step-by-step explanation:

The correct option is (b) The data does not contain an outlier. This means that the people at the center were all seniors around the same age.

Outlier in a data set is simply the extremely low data point or an extremely high data point compared to other points in the dataset.

It will stand out from the other values in the dataset.

The line plot shows the ages of people visiting a senior center one afternoon.

The data points are,

70, 70, 70, 75, 75, 80, 80, 85, 90, 90, 95, 95, 95, 100.

If there is an outlier in the set, it would be extremely low or high compared to other points.

But there are no such points.

So there are no outliers.

This means that people visited at the center were all seniors around the same age.

Hence the correct option is (b).

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Answer:

The last step is to simplify the result if it can be done. To simplify a fraction, you have to find the greatest common factor (GCF) of both the numerator and the denominator. The GCF is the largest number that can be evenly divided into both numbers. In the case of 12 and 96, 12 happens to evenly divide into 96.

The value of f(g(2)) from the given functions f(x) and g(x) is 3.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=2x²+1 and g(x)=3x-5.

We need to find f(g(2)).

Put x=2 in the function g(x)=3x-5, we get

g(2)=3×2-5

= 6-5

= 1

So, g(2)=1

Put x=1 in the function f(x)=2x²+1, we get

f(g(2))=2(1)²+1

= 2+1

=3

Therefore, the value of f(g(2)) is 3.

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Step-by-step explanation:

i) 0.0031 (or) 3.1×10^(-3)

ii) 0.0013 (or) 1.3×10^(-3)

I hope It helped you

Answer:

Step-by-step explanation:

the other endpoint: (-13, -21)

When y = ex is used, its range is [2,  ∞] In quadrant 2 of a coordinate surface, a curve approaches y = 1.

The collection of all feasible output values, or y-values, of a function is known as the range in mathematics. It symbolizes the variation between the largest and smallest values in the collection of function output values. For instance, the range of a function f(x) = x2 defined over the domain [-2, 2] would be [0, 4], as the output numbers fall between 0 and 4. In other words, given the domain, the range is the collection of all feasible values for the dependent variable (y-values) of a function (x-values). It is a crucial idea in mathematics, especially when it comes to functions and their graphs, as it aids in describing a function's behavior and potential values.

given

We know that the function's range contains all positive real numbers greater than or equal to 1 because the curve approaches y = 1 in quadrant 2 and increases into quadrant 1.

We can use the fact that the function grows without bound as x gets closer to positive infinity to determine the upper bound of the range. The range therefore encompasses all real positive integers.

Since the function crosses the y-axis at (0, 2), which indicates that the range contains all positive real numbers greater than or equal to 2,

When y = ex is used, its range is [2,  ∞] In quadrant 2 of a coordinate surface, a curve approaches y = 1.

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If y = y(x), then the derivative with respect to x is dy/dx. Differentiating both sides of the given equation gives

d/dx [4x ² + y ²] = d/dx [36]

8x + 2y dy/dx = 0

2y dy/dx = -8x

dy/dx = -4x/y

The turning points of the curve, taken as a function of x, are those points where the derivative vanishes.

-4x/y = 0   ===>   x = 0

This value of x corresponds to two points on the curve,

4×0² + y ² = 36   ===>   y ² = 36   ===>   y = ±6

So there are two turning points, (0, -6) and (0, 6).

Answer:

600

Step-by-step explanation:

(4x5) x (5x6)

First we solve each expression in the parenthesis. 4x5=20 and 5x6=30. Then, since the parenthesis are placed together, we multiply the two values. 20x30=600.

hope this helped!! <3

Answer:

i think 600

Step-by-step explanation:

The statement which best describes Gary’s error is; Gary did not use the greatest common factor in the equation.

This is the largest positive integer or polynomial that is a divisor of several different numbers. For instance, the greatest common divisor of 66, 30 and 18 is 6.

Gary's work:

66 + 36

Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

66 + 36

= 3 (22 + 12)

Gary did not use the greatest common factor in the equation.

The correct answer:

66 + 36

= 6(11 + 6)

Therefore, Gary did not use the greatest common factor in the equation.

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9514 1404 393

Answer:

  (b)  One

Step-by-step explanation:

Specifying the three sides also specifies the angles. Only one such triangle can be made.

Answer:

it is only possible to make one triangle

Step-by-step explanation:

K. 48-24=24

I. 48+24=72×2= (144) so 144

An equation is formed of two equal expressions. The total number of marbles that Ivan had at the first is 40.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of marbles with Katherine be represented by k, while the number of marbles with Ivan is represented by x.

Given that the total number of marbles available with Katherine and Ivan is 96. Therefore, we can write,

k + x = 96

Solving the equation for k,

k = 96 - x

Further, Katherine lost 24 marbles to Ivan during a game and at the end of the game, Ivan had twice as many marbles as Katherine. Therefore, we can write the equation as,

2(k - 24) = (x + 24)

2k - 48 = x + 24

Substituting the value of k,

2(96 - x) - 48 = x + 24

192 - 2x - 48 = x + 24

192 - 48 - 24 = x + 2x

3x = 120

x = 120/3

x = 40

Hence, the total number of marbles that Ivan had at the first is 40.

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Answer: 36 square centimeters

Step-by-step explanation: Hey there! Let's cut the shape in half horizontally. 6 times 4 for the top portion is 24 square centimeters. We subtract 6 cm from the top by 2 cm from the lower part to get the length of the bottom rectangle. We do 4 times 3 for the area of the bottom rectangle which is 12 square centimeters. Finally, we add 24 sq cm and 12 sq cm to get 36 square centimeters. (I tried my best!)

sin²x sec²x +1 = tan²x cosec²x is an Identity and therefore Option C is an Identity.

Trigonometric Identities are based on Trigonometric ratios , these are useful in conversion of the ratios into each other and to solve the problems of Trigonometry.

There are four Identities Given

Among them Option C is an Identity because on solving it

sin²x sec²x +1 = tan²x cosec²x

(sin²x/cos²x) +1 = sin²x / (sin²x cos²x)

sin²x +cos²x = 1

Which is an Identity and

therefore Option C is an Identity.

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Answer:

4n+9

Step-by-step explanation: