b only
1.9. (a) Sketch the time functions given. (i) \( 2 e^{-3 t} u(t-5) \) (ii) \( -2 e^{-3 t} u(t-1) \) (iii) \( -5 e^{-a t} u(t-b) \) (iv) \( -K e^{-c(t-a)} u(t-b) \) (b) Use Tables \( 7.2 \) and \( 7.3

Let's denote the ages of the two remaining men as x and x + 3 (since one is 3 years older than the other).

We know that the average age of 6 men is 35 years. So, the sum of their ages is 6 * 35 = 210 years.

We also know that the average age of four of them is 32 years. So, the sum of their ages is 4 * 32 = 128 years.

To find the sum of the ages of the two remaining men, we subtract the sum of the ages of the four men from the sum of the ages of all six men:

210 - 128 = 82 years.

Now, we can set up an equation to solve for the ages of the remaining two men:

x + (x + 3) = 82.

Combining like terms, we get:

2x + 3 = 82.

Subtracting 3 from both sides:

2x = 79.

Dividing both sides by 2:

x = 39.5.

So, one of the remaining men is 39.5 years old, and the other is 39.5 + 3 = 42.5 years old.

Answer:

B. g(x) = RootIndex 3 StartRoot x minus 3 EndRoot + 4

Step-by-step explanation:

edg 2021 .. its correct

The equation that is graphed along with the parent function is \(g(x)=\sqrt[3]{x-3} +4\)

The parent function is a cube root function, represented as:

\(f(x) = \sqrt[3]{x}\)

First, the parent function is horizontally shifted right by 3 units

The rule of this transformation is:

\((x,y) \to (x - 3,y)\)

So, we have:

\(f'(x) = \sqrt[3]{x - 3}\)

Next, the transformed function is vertically shifted up by 4 units

The rule of this transformation is:

\((x,y) \to (x,y+4)\)

So, we have:

\(g(x)=\sqrt[3]{x-3} +4\)

Hence, the equation is \(g(x)=\sqrt[3]{x-3} +4\)

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From the  X coordinate is -0.45 centimeter and Y coordinate is -2.0 cm of the center of mass for the uniform plate.

According to the Question:

Since the plate is uniform, we can divide it into three rectangles, each with a mass proportional to its area and with its barycenter at its geometric center. We will refer to the large piece of 35cm x 10cm; it occupies 63.6% of the total surface and its barycenter is at

(x₁, y₁) = (−5.0cm,−2.5cm).

Now,

The top 20cm× 5cm piece has 18.2 % of the total area; its center of mass is at (x₂, y₂) = (10cm,12.5cm).  

Now,

The bottom 10cm× 10cm piece (section 3) also has 18.2 % of the total area; its center of mass is at (x₃, y₃)​ = (5cm,−15cm).

(a) The x coordinate of the center of mass for the plate is

   \(X_{com} = (0.636)X_1 + (0.182)X_2 + (0.182)X_3\)

            = -0.45 cm

(b) The y coordinate of the center of mass for the plate is

    \(Y_{com} = (0.636)Y_1 + (0.182)Y_2 + (0.182)Y_3\)

             = -2.0 cm.

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Given:

y′=x³+2x⁴−6x⁶ ,

y(1)=−7a)

To find the general solution, integrate the given function with respect to x.

Let us integrate the given function y′=x³+2x⁴−6x⁶ with respect to x.∫y′ dx = ∫ (x³+2x⁴−6x⁶) dxOn integrating we get,y = x⁴/4 + 2x⁵/5 − 6x⁷/7 + C, where C is the constant of integration.b)  Given that y(1) = -7Hence substituting x=1 and y=-7 in the above equation, we get-7 = (1⁴/4) + 2(1⁵/5) - 6(1⁷/7) + C-7 = 1/4 + 2/5 - 6 + C-7 = -142/20 + CC = -7 + 142/20 = -28/20 + 142/20 = 114/20 = 57/10 Therefore the particular solution is, y = x⁴/4 + 2x⁵/5 − 6x⁷/7 + 57/10

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Here is the full question:

Triangle ABC is a right-triangle and sin(53o) = StartFraction 4 Over x EndFraction. Solve for x & round to the nearest whole number.

Triangle A B C is shown. Angle A C B is a right angle and angle B A C is 53 degrees. The length of B C is 4 centimeters, the length of A C is y, and the length of hypotenuse A B is x.

Which equation correctly use the value of x to represents the cosine of angle A?

cos(53o) = StartFraction 4 Over x EndFraction cos(53o) = StartFraction y Over 5 EndFraction cos(53o) = StartFraction x Over 4 EndFraction cos(53o) = StartFraction 5 Over y EndFraction

Answer:

cos(53°) = StartFraction y Over 5 EndFraction

Step-by-step explanation:

From the information above:

The sketch of the triangle is drawn and attached in the diagram below.

To find x using the sine rule,

We know that:

\(Sin \theta = \dfrac{opposite}{hypothenuse}\)

∴

\(Sin (53^0) = \dfrac{4}{x}\)

Making x the subject of the formula:

\(x = \dfrac{4}{Sin \ 53^0}\)

\(x = \dfrac{4}{0.7986}\)

\(x \simeq 5\)

Now, the equation that correctly uses the value of x can be determined by finding the cosine of ∠ A.

Recall that:

\(Cos \theta = \dfrac{adjacent}{hypothenuse}\)

\(Cos \ 53^0 = \dfrac{y}{x}\)

where; x = 5

\(Cos \ 53^0 = \dfrac{y}{5}\)

Thus, the equation that correctly uses the value of x to represent the cosine of angle A is:

cos(53°) = StartFraction y Over 5 EndFraction

Answer:

simple answer B

Step-by-step explanation:

Given that the test's p-value is 0.0562>0.05, there is enough data to conclude that the machines' manufacturer should perform a new calibration.

A statistic employed in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

Here,

x=4.88 cm

μ=5 cm

σ=0.44 cm

n=49

The test statistic,

=(4.88-5)/(0.44/7)

z=-1.909

The p-value of the test is the probability that the sample mean is different by at least 4.88 - 5 = 0.12 from the target value, which is P(|z| > -1.909), which is 2 multiplied by the p-value of z = -1.909

At z=-1.909, p-value=0.0281

2*0.0281=0.0562

The test's p-value is 0.0562>0.05, indicating that there is enough data to conclude that the machines' manufacturer should perform a recalibration.

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The reliability of a two-component product if the components are in parallel, with individual reliabilities of 0.95, and 0.80 is 0.99. The answer is option b.

The probability that a specific object will carry out its intended function for a specific amount of time under a specific set of circumstances without experiencing any failures is known as reliability.

The reliability definition is based on four criteria: function, fulfillment likelihood, duration, and environment. Maintainability and reliability are related because when a machine or product malfunctions, there may be a way to get it back into working order.

When we use the phrase "talking reliability-smart," we mean that any of the aspects that shape the device in parallel can be considered. This does not necessarily imply that they are physically parallel (in all circumstances), as parallel capacitors have a certain behavior in the circuit and may malfunction if one of them fails.

Parallel forms reliability is a measure of reliability obtained by giving the same set of people different versions of an assessment tool (each version must contain items that probe the same construct, talent, knowledge base, etc.

The complete question is given below:-

What is the reliability of a two-component product if the components are in parallel, with individual reliabilities of 0.95, and 0.80?

a. 0.875

b. 0.99

c. 0.95

d. 0.76

e. 0.80

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The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

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Answer:

The answer is D.

Step-by-step explanation:

Answer:

The choice D)

\(2 \sqrt{2} \)

Step-by-step explanation:

Sin = Opposite/ hypotenuse

\( \sin(45) = \frac{x}{4} \\ \\ \frac{1}{ \sqrt{2} } = \frac{x}{4} \\ \\ \sqrt{2} x = 4 \\ \\ x = \frac{4}{ \sqrt{2} } \\ \\ x = \frac{4}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } \\ \\ x = \frac{4 \sqrt{2} }{2} = 2 \sqrt{2} \\ \\ \\ x = 2\sqrt{2} \)

I hope I helped you^_^

The expression that is equivalent to 8y + 5x - 3y + 7 - 2x is 5y + 3x + 7

From the question, we have the following parameters that can be used in our computation:

8y + 5x - 3y + 7 - 2x

Collect the like terms in the expression

So, we have the following representation

8y + 5x - 3y + 7 - 2x = 8y  - 3y + 5x - 2x + 7

Evaluate the like terms in the expression

So, we have the following representation

8y + 5x - 3y + 7 - 2x = 5y + 3x + 7

Hence, the expression that is equivalent to 8y + 5x - 3y + 7 - 2x is 5y + 3x + 7

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The sequence an = ln(3n^2 + 4) − ln(n^2 + 4) converges to ln(3) as n approaches infinity.

To find the limit of the sequence an = ln(3n^2 + 4) − ln(n^2 + 4) as n approaches infinity, we can use algebraic manipulation and properties of limits

an = ln(3n^2 + 4) − ln(n^2 + 4)

= ln[(3n^2 + 4)/(n^2 + 4)]

= ln[3 + 4/n^2]/[1 + 4/n^2]

= ln(3) + ln[1 + (4/n^2)] − ln[1 + (4/n^2)]

= ln(3)

As n approaches infinity, the expression inside the natural logarithm approaches 3, so the limit of the sequence is ln(3):

\(\lim_{n \to \infty} a_n\)  = ln(3)

Therefore, the sequence converges to ln(3).

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The given question is incomplete, the complete question is:

A) Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)

an = ln(3n^2 + 4) − ln(n^2 + 4)

lim n→∞ an = ?

Answer:

3.92yd

Step-by-step explanation:

pi r²÷2

pi 2.5²÷2=3.92

Required function g(h(x)) is 6 x - 9.

A function is a relationship between a set of outputs referred to as the range and a set of  inputs referred to as the domain, with the condition that each input is contain  to exactly one output. An input x corresponding to a function f output, which is represented by f(x).

We can combine two functions so that the outputs of one function become the inputs of the other if we have two functions is known as composite function . A composite function is defined by this action,that the function g f(x) = g(f(x)) is known as a composite function. This is occasionally referred to as a function of a function. g f can also be written as g o f instead.

We have, h(x)=3 x-5 and g(x)=2 x+1.

So, g(h(x)) = g(3 x - 5) = 2(3 x - 5) + 1 = 6 x - 9.

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It is true that one method of conducting a survey involves selecting a sampling of a representative group of people. This is called survey sampling.

Survey sampling is defined as a statistical method that involves selecting and surveying individuals from a particular group of people. The population that is chosen to survey could be based on a range of attributes. The target audience could be a general group like the United States' population or a more specific group, like young adults, voters in California, or male pet owners from New England.

Survey sampling involves three steps, which are:

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Answer:

50/277 is also the same as 50 ÷ 277, so just divide those two numbers.

50 ÷ 277 = 0.181

Now we find out 0.181 to the nearest hundredth

To the nearest hundredth when rounding the answer will be 0.18

So your answer is 0.18

Hope I helped! :)

The equation after recognizing the properties after solving the equation is 5 = 42x

The definition of a equation which is in algebra form is a mathematical statement that describes the equality of two mathematical expressions. A mathematical phrase with two equal sides and an equal sign is known as an equation.

The point-slope form, standard form, and slope-intercept form are the three main types of equations which are linear.

the equation given is

2/3 - x + 1/6 = 6x

by taking the L.C.M

2/3 - (6x+1)/6 = 6x

(4-6x+1)/6 = 6x

4-6x+1 = 36x

5 = 36x+6x

5 = 42x

by recognizing the properties the equation after solving the equation given is 5 =42x

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- 57m + 9

Hi there !

−7(9m − 2) + (−5 + 6m) =

= -7×9m - 7×(-2) - 5 + 6m

= - 63m + 14 - 5 + 6m

= - 57m + 9

Good luck !

Answer: I don't understand your question

Step-by-step explanation:

my explanation is at the top

No, It is not possible for consecutive interior angles to be congruent.

If the transversal line crosses the two lines as parallel to one another, the consecutive interior angles are supplementary rather than congruent and add up to 180 degrees.

Parallel internal angles are additional (the consecutive interior angles postulate) External angles that follow each other are supplemental (the consecutive exterior angles theorem) Congruent alternate interior angles (the alternate interior angles theorem)

The pair of non-adjacent internal angles that are located on the same side of the transversal are referred to as consecutive interior angles. The term "consecutive" describes events that take place side by side. On the internal side of a transversal, two consecutive interior angles are situated next to one another.

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An expression with (-1) as its base that will produce a positive product is (-1)^2

The base of the expression is given as:

Base = -1

So, the expression can be represented as:

Expression = Base^n

Substitute the known values in the above equation

Expression = (-1)^n

For the expression to have a positive product, the value of n must be even.

Say n = 2

So, we have:

Expression = (-1)^2

Hence, an expression with (-1) as its base that will produce a positive product is (-1)^2

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Answer:

which person shake 5 times which mean 25 times

Answer:

Step-by-step explanation: 1

1. Nobody shook hands than 8 people so numbers going to be 0, 1, 2, 3, 4, 5, 6, 7, 8

2. The person shook 8 times married with the person shook 0 time

3. The person shook 7 times married with the person shook 1 time

4. The person shook 6 times married with the person shook 2 time

5. The person shook 5 times married with the person shook 3 time

6.  Therefore, only person left is the one shook 4 times, which is Jack's wife

7. Jack's wife shook 4 times so Jack shook 4 times

Answer:

Step-by-step explanation:

a- 0.4a

The training heart rate function, T(M) for a person with a resting heart rate of 62 beats per minute is 0.6M.

a. The maximum heart rate function, M() for a person a years of age. M(x) is 220 - x.

The formulas provided are:

T(M, R) = R + 0.6(M - R)M(z) = 220 - z

where R is the resting heart rate, M is the maximum heart rate, and z is the age.

Using the formula T(M, R) = R + 0.6(M - R), we can find the training heart rate function, T(M), for a person with a resting heart rate of 62 beats per minute:

T(M, R) = R + 0.6(M - R)T(M, 62) = 62 + 0.6(M - 62)T(M, 62) = 62 + 0.6M - 37.2T(M, 62) = 24.8 + 0.6M

Therefore, the training heart rate function for a person with a resting heart rate of 62 beats per minute is T(M) = 24.8 + 0.6M.

To find the maximum heart rate function, M(x), for a person a years of age, we can use the formula M(z) = 220 - z:

M(z) = 220 - z

M(a) = 220 - a

Therefore, the maximum heart rate function for a person a years of age is M(x) = 220 - x.

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Answer: $210

Step-by-step explanation:

Find 75 percent of 120

75% of 120 = 90

120 and 90 together

120 + 90 = $210

Your answer is 210

Out of the given differential equations, only equation 3 is separable, and equation 4 is linear. The rest are nonlinear and neither separable nor linear.

The first-order differential equation dy/dx + exy = x2y2 is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term x2y2 in the equation makes it nonlinear, and the term exy makes it non-separable.

The differential equation y + ex * sin(x) = x3y' is neither separable nor linear. It is a nonlinear ordinary differential equation. The presence of the term ex * sin(x) and the term y' (derivative of y) make it nonlinear, and the term y makes it non-separable.

The differential equation ln(x) - x2y = xy' is separable but not linear. The terms ln(x) and x2y make it nonlinear, but it can be separated into two parts, one containing x and y and the other containing x and y'. Therefore, it is separable.

The differential equation dy/dx + cos(y) = tan(x) is linear but not separable. The terms cos(y) and tan(x) make it nonlinear, but it can be written in the form dy/dx + P(x)y = Q(x), where P(x) = cos(y) and Q(x) = tan(x). Therefore, it is a linear differential equation.

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Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be the entire. 480 is the value for given fraction.

Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be the entire. When we carve an element of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin.  

3/4 of 640 = 480

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Your question is incomplete but most probably your full question was,

How do i figure out 3/4 of 640 fraction

Answer:

Step-by-step explanation:

Let's start with some conversions

Remember that when you go to the negative side of the reals, the number that looks like it should be the largest, when negative is the smallest.

Answers

The smallest number of these three is -10.909

The second smallest is -10.777... repeat

The third smallest is -√113 which is -10.6301

The Largest one of the four is 10.7

Solution:

Note that:

Solving the inequality one by one.

The inequality is 0 < x < 3.