A pollster recorded the size of households in his
area. The table below shows the distribution for
820 families. How many of the 820 families has at
least 3 people in the household?
Number of people in
a household
1
2
3
4
5
6 or more
% of Households
27%
33%
24%
10%
4%
2%

Answers

Answer 1

Step 1: Calculate the number of families with 1 person in the household by multiplying the percentage (27%) and the total number of families (820) - 27% x 820 = 220.4.

Step 2: Calculate the number of families with 2 people in the household by multiplying the percentage (33%) and the total number of families (820) - 33% x 820 = 271.6.

Step 3: Calculate the number of families with 3 people in the household by multiplying the percentage (24%) and the total number of families (820) - 24% x 820 = 196.8.

Step 4: Calculate the number of families with 4 people in the household by multiplying the percentage (10%) and the total number of families (820) - 10% x 820 = 82.

Step 5: Calculate the number of families with 5 people in the household by multiplying the percentage (4%) and the total number of families (820) - 4% x 820 = 32.8.

Step 6: Calculate the number of families with 6 or more people in the household by multiplying the percentage (2%) and the total number of families (820) - 2% x 820 = 16.4.

Step 7: Add the numbers calculated in Steps 1 - 6 to get the total number of families with at least 3 people in the household - 220.4 + 271.6 + 196.8


Related Questions

5. Which of these statistics is used in basketball as an all-in-one rating of how well a player performs per minute they play?
O A. Wins above replacement (WAR)
O B. Field goal percentage (FG%)
O C. Double doubles (DD2)
OD. Player efficiency rating (PER)

Answers

Answer:

Player Efficiency Rating (PER)

Step-by-step explanation:

The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is Player Efficiency Rating (PER).

The statistic used in basketball as an all-in-one rating of how well a player performs per minute they play is the Player Efficiency Rating (PER). So, correct option is D.

PER is a widely used metric that quantifies a player's overall performance by taking into account various statistical categories and normalizing them based on playing time.

PER evaluates a player's contributions in areas such as points, rebounds, assists, steals, blocks, and turnovers. It considers both positive and negative statistical events and provides a single numerical value that represents a player's efficiency on the court. A higher PER indicates a more productive player.

On the other hand, Wins Above Replacement (WAR) is a metric commonly used in baseball to estimate the number of wins a player contributes to their team compared to a replacement-level player.

Field Goal Percentage (FG%) measures the accuracy of a player's shooting by calculating the percentage of successful field goal attempts. Double doubles (DD2) count the number of games in which a player achieves double-digit totals in two statistical categories.

Among the options listed, Player Efficiency Rating (PER) is specifically designed to assess a player's overall performance per minute played in basketball.

So, correct option is D.

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mathematicians divide the world of numbers into at least seven subsets. list seven subsets and define each

Answers

Mathematicians divide the world of numbers into seven subsets, namely natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.

Natural numbers: These are the counting numbers, starting from 1 and continuing indefinitely. They can also be denoted as "N" or "ℕ".

Whole numbers: These are the natural numbers, as well as zero. They can also be denoted as "W" or "ℤ⁺⁰".

Integers: These are the whole numbers, as well as their negative counterparts. They can also be denoted as "Z" or "ℤ".

Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers (and the denominator is not zero). They can also be denoted as "Q" or "ℚ".

Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers. They are often represented by decimal expansions that neither terminate nor repeat. Examples include π and the square root of 2.

Real numbers: These are all the rational and irrational numbers, taken together. They can also be thought of as numbers that can be located on a number line. They are often denoted as "R" or "ℝ".

Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are often denoted as "C" or "ℂ".

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PLEASE HELPPP ME MATH

Answers

The coordinates of the image of point D that ensures that the triangles are congruent is (-2, 2)

How to determine the coordinates of point D

Given the triangle ABC and the incomplete triangle DEF

From the triangle transformation of points B and C, we can see that

The points of the triangle ABC are translated to the left by 6 units and downward by 4 units

Mathematically, this can be represented as

(x, y) = (x - 6, y - 4)

Given that

A = (4, 6)

So, we have

D = (4 - 6, 6 - 4)

Evaluate the difference

D = (-2, 2)

Hence, the position is (-2, 2)

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What are the zeros of the function f(x)= 240x -2x^2

Answers

Answer:

What are the zeros of the function f(x)= 240x -2x^2

Step-by-step explanation:

To find the zeros of the function f(x) = 240x - 2x^2, we need to set f(x) equal to zero and solve for x:

240x - 2x^2 = 0

We can factor out 2x from the left side:

2x(120 - x) = 0

So either 2x = 0 or 120 - x = 0. Solving for x in each case gives:

2x = 0 => x = 0

120 - x = 0 => x = 120

Therefore, the zeros of the function are x = 0 and x = 120.

consider the funciton f given by f(t)=log49(t7). find values for a and b such that f(t)=a+logb(t).

Answers

The values for a and b such that f(t) = a + logb(t) are,

a = log(1/log(49))

b = 49

Therefor

We can start by simplifying the expression for f(t)

f(t) = log49(t7)

f(t) = log(t7)/log(49) [Using the change of base formula]

Now we can rewrite f(t) as:

f(t) = log(t)/log(b) + a [Using the logarithmic properties log(ab) = log(a) + log(b)]

Comparing this expression with f(t) = a + logb(t), we can see that:

a = log(1/log(49)) [since log(b) = 1/log(49)]

b = t

Therefore, we have

f(t) = log(t7)/log(49) = log(t)/log(b) + log(1/log(49))

= log(t)/log(49) + log(1/log(49))

= log(1/log(49)) + log(t)/log(49)

So, a = log(1/log(49)) and b = 49.

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the solution set is
5r+20/10=3r-6/3

Answers

Answer:

r = -2

Step-by-step explanation:

5r + 20/10 = 3r -6/3

5r + 2 = 3r - 2

2r + 2 = -2

2r = -4

r = -2

Answer: r = -2

Step-by-step explanati

What is the probability that someone who does not take vitamins is a female? Round to three decimal places.
Female
Male
Total
(1 point)
O 0.374
O 0.139
O 0.080
O 0.626
Takes vitamins
248
145
193
Does not take vitamins
40
67
107
Total
288
212
500

Answers

Answer:

A)  0.374

Step-by-step explanation:

Let event A be that the person is female.

Let event B be that the person does not take vitamins.

[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]

Therefore, from the given table:

   [tex]\sf P(A) = \dfrac{288}{500}=0.576[/tex]

   [tex]\sf P(B) = \dfrac{107}{500}=0.214[/tex]

   [tex]\sf P(A \cap B)=\dfrac{40}{500}=0.08[/tex]

To calculate the probability that someone is female (Event A), given that they do not take vitamins (Event B), use the conditional probability formula for A given B:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Conditional Probability formula}\\\\A given B:\\\\$\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}$\\\end{minipage}}[/tex]

[tex]\sf \implies P(A|B)=\dfrac{0.08}{0.214}=0.374\;(3\;s.f.)[/tex]

Given the triangle below, what is mA, rounded to the nearest tenth? B 12 Triangle not drawn to scale A. 60.4° B. 2.2° 10 O C. 58.2° OD. 55.8° C SUBMIT​

Answers

Answer:

C

Step-by-step explanation:

Write a quadratic inequality represented by the graph.

Answers

Using the concept of parabola, the quadratic inequality represented by the graph can be written as:

y = x² -2x +2.

Define parabola?

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.

The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix.

The general equation for a parabola is given as:

y = a(x-h) ² + k

Now here we have:

(x,y) = (2,5)

(h,k) = (1,1)

Putting these values in the equation,

5 = a (2-1) ² + 1

a = 5-1

=4

Substituting the values:

y = (x-1) + 1

y = x² -2x +2

Therefore, the quadratic inequality can be written as: y = x² -2x +2.

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Find the 66th derivative of the function f(x) = 4 sin (x)…..

Answers

In response to the stated question, we may state that As a result, the 66th derivative of f(x) = 4 sin(x) is 4 sin(x) (x).

what is derivative?

In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.

Using the chain rule and the derivative of the sine function repeatedly yields the 66th derivative of the function [tex]f(x) = 4 sin (x).[/tex]

The derivative of sin(x) is cos(x), and the derivative of cos(x) is -sin(x), and this pattern repeats itself every two derivatives.

As a result, the first derivative of f(x) is:

[tex]f'(x) = 4 cos (x)[/tex]

The second derivative is as follows:

[tex]f"(x) = -4 sin (x)[/tex]

The third derivative is as follows:

[tex]f"'(x) = -4 cos (x)[/tex]

The fourth derivative is as follows:

[tex]f""(x) = 4 sin (x)[/tex]

And so forth.

[tex]f^{(66)(x)} = 4 sin (x)[/tex]

Because the pattern repeats every four derivatives, the 66th derivative is the same as the second, sixth, tenth, fourteenth, and so on.

As a result, the 66th derivative of f(x) = 4 sin(x) is 4 sin(x) (x).

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At a community​ college, a survey was taken to determine where students study on campus. Of the 250 students​ surveyed, it was determined that
170 studied in the library
135 studied in the cafeteria
76 studied in both the library and the cafeteria
How many studied in library or cafeteria (including both)?

Answers

Answer:

Step-by-step explanation:

To find the number of students who studied in the library or cafeteria (including both), we need to add the number of students who studied in the library and the number of students who studied in the cafeteria, but we need to subtract the number of students who studied in both the library and cafeteria to avoid counting them twice.

So, the number of students who studied in library or cafeteria is:

170 + 135 - 76 = 229

Therefore, 229 students studied in the library or cafeteria (including both).

|x+6|<3 absolute value inequality, write an equivalent compound inequality.

Answers

An equivalent cοmpοund inequality is -9 < x < -3.

What is an absοlute value inequality?

An inequality with an absοlute value algebraic expressiοn and variables is knοwn as an absοlute value inequality. An expressiοn using absοlute functiοns and inequality signs is knοwn as an absοlute value inequality.

Here, we have

Given: |x+6|<3 is an absοlute value inequality.

Apply absοlute rule

if |u|<a, a>0 then -a<u<a

-3 < x+6 <3

x+6 > -3 and x+6 <3

x> -9 and x< -3

-9 < x < -3

Hence, an equivalent cοmpοund inequality is -9 < x < -3.

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Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
I need help D:please !!!!​

Answers

If the top of Bria's bookcase has a length-to-width ratio of 3:1, the width of the top should be about 10 inches to provide an area of 300 square inches for her soap carving collection.

How to find the dimension of the top of the bookcase

The top of the bookcase is a rectangle, the area of the top can be expressed as the product of its length and width:

Area of the top = length × width

Area of the top = 300 square inches

length × width = 300 square inches

width = 300 square inches / length

Assuming that the top of the bookcase is with a length-to-width ratio of

3 : 1

length = 3 × width

substituting the value gives

width = 300 / (3 × width)

Simplifying, we have:

width² = 100 square inches (the polynomial)

Taking the square root of both sides, we get:

width = √100 ≈ 10 inches

Then the length will be = 30 inches

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When an octave is divided into twelve equal steps, a chromatic scale results. The ratios between sucessive notes is
constant.
IC C# D D# E F F# G G# А A# B с
261.6 277.2
293.6
329.6 349.2 370.0 392.0
1440 466.1 493.8 523.2
Determine the missing frequency for G# and D# using the ratio 1.0595. Round to the nearest tenth. What is the ratio
of frequencies between G# and D#? Would these two notes be consonant or dissonant?
4
1.338
consonant
31
a.
b.
3
1.338
41
consonant
c.
14
1.338
4
dissonant
d.
1.33
4
3
dissonant

Answers

The ratio of frequencies between G# and D# is: G# / D# = 415.3 / 293.7 ≈ 1.414

To find the missing frequencies for G# and D# using the ratio 1.0595, we need to multiply the frequency of the previous note by 1.0595. Starting from A440, we can use this ratio to calculate the frequencies of G# and D#:

G#: 440 x 1.0595^8 ≈ 830.6 Hz

D#: 440 x 1.0595^6 ≈ 622.3 Hz

The ratio of frequencies between G# and D# is:

830.6 / 622.3 ≈ 1.334

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Mrs Devi bought banana cakes and marble cakes for a party. She spent $112 on the cakes. Each
piece of banana cakes cost $2.50 and the cost of each piece of marble cake was 7/5 the cost of
each piece of banana cake. 30% of what she bought were marble cakes. How many pieces of
cake did Mrs Devi buy?

Answers

In linear equation, 28  pieces of cake did Mrs Devi buy.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.  

                                   Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Cost of M cake = $3.5

For every 3 M cakes she bought 7 B cakes.

Let 1 unit be 3 M cakes and 7 B cakes. 1 unit costs= 3(3.5) + 7(2.5)= $28

She bought $112 / $28 = 4 units of cakes.

Which means 12 M cakes and 28 B cakes.

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I will mark you brainiest!

If the triangles above are reflections of each other, then ∠D ≅ to:
A) ∠F.
B) ∠E.
C) ∠C.
D) ∠A.
E) ∠B.

Answers

Answer:

D I believe

Step-by-step explanation:

PLEASE HELP!!!!!!!!!

△DEF is similar to △YZX

A) which side corresponds to ED? (this one is already answered)

B) write a proportion that you could use to find XZ

C) what is XZ?

Answers

Step-by-step explanation:

B) 20:23

C) 6,0375

hope this helps

Find the 6th term of the geometric sequence described below.
m₁ = -3(-5)-1
Show your work here
Hint: To add an exponent (z"), type "exponent" or press "A"

Answers

Answer:

m₆ = 9375

Step-by-step explanation:

Given sequence is

[tex]m,_i = -3(-5)^{i - 1}[/tex]

To find the 6th term, all you have to do is substitute i = 6 and compute

For i = 6 we get

[tex]m_6 = -3(-5)^{6 - 1}\\= -3(-5)^5\\\\= -3(-3125) \\\\= 9375[/tex]

A negative number raised to an odd number is negative that is why (-5)⁵ is negative

The relative housing cost for a US city is defined to be the ratio nationalaveragehousingcost
averagehousingcostforthecity

, expressed as a percent.
The scatterplot above shows the relative housing cost and the population density for several large US cities in the year 2005. The line of best fit is also shown and has equation y=0.0125x+61. Which of the following best explains how the number 61 in the equation relates to the scatterplot?

Answers

In 2005, even in cities with low population densities, housing costs were likely at least 61% of the national average.

We know that the relative housing cost for a US city is defined to be the ratio average housing cost for the city /​national average housing cost, expressed as a percent also the scatterplot above shows the relative housing cost and the population density for several large US cities in the year 2005, therefore,

the equation is y = 0.0125x + 61

Therefore, with this we know that in 2005, even in cities with low population densities, housing costs were likely at least 61% of the national average.

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WILL MARK AS BRAINLIEST!!!!!!!!!!!!!!!!!!
The point on the parabola y=x^2 that is closest to the point (1,0) is (_______,_______). The distance between the two points is ________.

you can use Newtons's Method or Bisection to help but you don't have to.

Answers

Answer:Approximately

(0.58975,0.34781)

Step-by-step explanation:

If (x,y) is a point on the parabola, then the distance between (x,y) and (1,0) is:

√(x−1)2+(y−0)2=√x4+x2−2x+1

To minimize this, we want to minimize

f(x)=x4+x2−2x+1

The minimum will occur at a zero of:

f'(x)=4x3+2x−2=2(2x3+x−1)

graph{2x^3+x-1 [-10, 10, -5, 5]}

Using Cardano's method, find

x=3√14+√8736+3√14−√8736≅0.58975

y=x2≅0.34781

PLS HELP FAST 20 POINTS + BRAINLIEST

Answers

Answer:

£22

Step-by-step explanation:

50% of 88=88/100 ×50=44

44÷2=25%=22

75% of £88 is deducted, so that 88-66=£22

Don't forget my Brainliest

2. problem 4.3.4 for a constant parameter , a rayleigh random variable x has pdf what is the cdf of x?

Answers

The cumulative distribution function (CDF) for given random variable fx(x)  is given by F(x) = 1 - e^[(-a²)(x²/2)]        x > 0,

                           F(x) = 0                                x ≤ 0.

The cumulative distribution function (CDF) F(x) for a Rayleigh random variable X is defined as,

F(x) = P(X ≤ x)

To find the CDF of X, we integrate the PDF of X over the interval [0, x],

F(x) = ∫₀ˣ a²x e^[(-a²)(x²/2)] dx

Using the substitution u = (-a²x²/2),

Simplify the integral as follows,

F(x) = ∫₀ˣ a²x e^[(-a²)(x²/2)] dx

= ∫₀^((-a²x²)/2) -e^u du (where u = (-a²x²/2) and x = √(2u/a²))

= [e^u]₀^((-a²x²)/2)

= 1 - e^[(-a²)(x²/2)]

Therefore, the CDF of X  for the Rayleigh random variable X has PDF fx (x)   is equal to,

F(x) = 1 - e^[(-a²)(x²/2)]        x > 0,

F(x) = 0                                x ≤ 0.

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The above question is incomplete, the complete question is:

For a constant parameter a > 0, a Rayleigh random variable X has PDF

fx (x)        =    a²xe^[(-a²)(x²/2)]      x > 0

                     0                              otherwise.

What is the CDF of X?

Find the measures of angles 1 through 5 in the figure shown !

Answers

Answer:

55 degrees angles on a rights angle triangle. 1 and 3 they are equal cause they are vertical opp angles 55 degrees

a triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm squarea triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm square

Answers

The cοst οf painting the triangle bοrder at the given rate is Rs. [tex]108\sqrt{(2)[/tex].

What is a triangle?

A triangle is a geοmetric shape that cοnsists οf three line segments, οr sides, that are cοnnected tο fοrm three angles.

Tο find the cοst οf painting the triangle bοrder, we first need tο find its area. Let's call the third side οf the triangle "x".

We knοw that the perimeter οf the triangle is 24cm, sο we can write an equatiοn:

6cm + 8cm + x = 24cm

Simplifying this, we get:

x = 10cm

Nοw we can use Herοn's fοrmula tο find the area οf the triangle:

s = (6cm + 8cm + 10cm)/2 = 12cm

Area [tex]= \sqrt{(s(s-6cm)(s-8cm)(s-10cm))[/tex]

[tex]= \sqrt{(12cm6cm4cm*2cm)[/tex]

[tex]= 2\sqrt{(72cm^2)[/tex]

[tex]= 12\sqrt{(2) cm^2[/tex]

Finally, we can calculate the cοst οf painting the bοrder at a rate οf Rs. 9 per square cm:

Cοst = (Area) x (Rate)

[tex]= (12\sqrt{(2)} cm^2) x (Rs. 9/cm^2)[/tex]

[tex]= Rs. 108\sqrt{(2)[/tex]

Therefοre, the cοst οf painting the triangle bοrder at the given rate is= [tex]Rs. 108\sqrt{(2)[/tex]

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place the following steps in order. what is the correct order for the general procedure for hypothesis testing?

Answers

The correct order of the steps to test the general hypothesis is given as B, A, E, C, D, F.

A hypothesis is basically a uncertain fact that is backed by some logical and solid information. While using the hypothesis, it s important that we use the correct method to verify the credibility of the hypothesis in the system.

So, as per the given option, the correct sequence should be, B, A, E, C, D, F.

We first set up the null hypothesis and the alternative hypothesis, and then we choose the degree of significance. The next phases in hypothesis testing are choosing the test statistics and creating the decision-making rule.

When we get to a conclusion based on the hypothesis after carefully calculating and computing the hypothesis' performance, the procedure is said to be finished.

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Complete question - place the following steps in order. what is the correct order for the general procedure for hypothesis testing?

A. Select the level of significance

B. setup null and alternative hypothesis

C. Establish the decision rule

D. performance computation

E. select the test statistics

F. Draw conclusions

A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4sin4t. If the mass is pulled down 6 in and then released, determine the position of the mass at any time t. (Use g=32ft/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.)

Answers

The position of the mass at any time t is given by u(t) = -1/2 cos(2√2 t) + sin(2√2 t) + 1/2 sin(4t) - 1/2 cos(4t), and the first four times at which the velocity of the mass is zero, excluding t = 0, are t = 0.0567, 0.283, 0.510, and 0.736.

To solve this problem, we need to use Newton's second law of motion which states that the force acting on an object is equal to its mass times its acceleration. In this case, the force acting on the mass is the sum of the force due to gravity and the external force, and the acceleration is given by the second derivative of the displacement.

Using Hooke's law, the force due to the spring is proportional to the displacement u of the mass from its equilibrium position, with a proportionality constant k

F_spring = -k u

where k is the spring constant. Since the mass is pulled down 6 in. from its equilibrium position, the initial displacement is u(0) = -0.5 ft. The spring stretches 24 in. under a weight of 8 lb, so the spring constant is

k = F_spring / u = (8 lb) / (2 ft) = 4 lb/ft

The force due to gravity is

F_gravity = m g

where m is the mass of the object and g is the acceleration due to gravity. The mass is given in pounds, so we need to convert it to slugs:

m = 8 lb / (32.2 ft/s^2) = 0.248 slugs

Thus, the force due to gravity is

F_gravity = (0.248 slugs) (32 ft/s^2) = 7.94 lb

The equation of motion for the displacement u(t) is

m u''(t) = F_gravity + F_spring + F_external

where F_external = 4 sin 4t lb is the external force. Substituting the expressions for these forces and dividing by m, we get

u''(t) + 8 u(t) = 2 sin 4t

This is a homogeneous linear second-order differential equation with constant coefficients, which can be solved by finding the roots of the characteristic equation:

r^2 + 8 = 0

The roots are r = ±2i√2. The general solution of the differential equation is then

u(t) = c1 cos(2√2 t) + c2 sin(2√2 t) + u_p(t)

where u_p(t) is a particular solution of the nonhomogeneous equation. Since the right-hand side of the equation is a sinusoidal function with frequency 4/π, we can guess a particular solution of the form

u_p(t) = A sin(4t) + B cos(4t)

Substituting this into the equation and equating coefficients, we get

16 A - 16 B + 8 A = 2, or A = 1/2

-16 A - 16 B + 8 B = 0, or B = -1/2

Therefore, the particular solution is

u_p(t) = 1/2 sin(4t) - 1/2 cos(4t)

The general solution is then

u(t) = c1 cos(2√2 t) + c2 sin(2√2 t) + 1/2 sin(4t) - 1/2 cos(4t)

We can use the initial conditions u(0) = -0.5 and u'(0) = 0 to determine the values of c1 and c2

u(0) = c1 + 1/2 = -0.5, or c1 = -1/2

u'(0) = -2√2 c1 + 2√2 c2 - 2 = 0, or c2 = 1

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The given question is incomplete, the complete question is:

A mass that weighs 8 lb stretches a spring 24 in. The system is acted on by an external force of 4 sin 4t. If the mass is pulled down 6 in. and then released, determine the position of the mass at any time t. (Use g = 32 ft/s2 for the acceleration due to gravity. Let u(t), measured positive downward, denote the displacement in feet of the mass from its equilibrium position at time t seconds.)

u(t) = 1/2sin(4t)+1/2cos(4t)-2tcos(4)

Determine the first four times at which the velocity of the mass is zero. (Exclude t = 0 as trivial.)

Find the value of Tan 15 without using a table or calcutator​

Answers

Answer:

Step-by-step explanation:

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what is the domain of the function {(-1,-1),(0,1),(2,-1)}
a) (-1,1)
b) (-1,0,2)
c) (-1,0,1,2)
d) {(-1,-1),(0,1),(2,-1)}

Answers

Answer:

[tex]b) \quad(-1,0,2)[/tex]

Step-by-step explanation:

The domain is the set of all input values for a function. It can be represented as a list of values where it is countable or as a set notation

Here there are only 3 ordered pairs. The first entry in each ordered pair represents the input of the function, the second entry the corresponding output value

Looking at the first entry in all three ordered pairs we get the domain as
[tex](-1, 0 , 2)[/tex]

what are the transformations of the following 1) f(x)=3x2^x+4-1
2) f(x)=-1/2x5^x-2+6
3) g(x)=1/5log(x+5)+3
4) g(x)=-4log(x)-2

Answers

1. The functiοn [tex]f(x) = 3x2^x+4-1[/tex]undergοes the fοllοwing transfοrmatiοns

A vertical translatiοn dοwnward by 1 unit (the [tex]"-1[/tex]" at the end)

An upward vertical stretch by a factοr οf 3 (the "3" cοefficient in frοnt)

An expοnential grοwth with base 2 (the expοnent "x" in the term [tex]"2^x"[/tex])

A hοrizοntal shift tο the left by 4 units (the "-4" in the expοnent οf [tex]"2^x"[/tex])

2. The functiοn [tex]f(x) = -1/2x5^x-2+6[/tex] undergοes the fοllοwing transfοrmatiοns:

A vertical translatiοn upward by 6 units (the "+6" at the end)An upward vertical cοmpressiοn by a factοr οf 1/2 (the [tex]"-1/2"[/tex]cοefficient in frοnt)An expοnential grοwth with base 5 (the expοnent "x" in the term [tex]"5^x[/tex]")A hοrizοntal shift tο the left by 2 units (the[tex]"-2"[/tex] in the expοnent οf [tex]"5^x[/tex]")

3. The functiοn [tex]g(x) = 1/5log(x+5)+3[/tex] undergοes the fοllοwing transfοrmatiοns:

A vertical translatiοn upward by 3 units (the "+3" at the end)A hοrizοntal shift tο the left by 5 units (the "+5" inside the lοgarithm)A vertical stretch by a factοr οf 1/5 (the [tex]"1/5"[/tex] cοefficient in frοnt)

4. The functiοn [tex]g(x) = -4log(x)-2[/tex] undergοes the fοllοwing transfοrmatiοns:

A vertical translatiοn dοwnward by 2 units (the [tex]"-2"[/tex] at the end)A vertical cοmpressiοn by a factοr οf 4 (the[tex]"-4"[/tex] cοefficient in frοnt)A hοrizοntal shift tο the right (there is nο explicit shift, but the dοmain οf the functiοn is restricted tο[tex]x > 0[/tex], which means the graph is shifted tο the right οf the y-axis)

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What are the coordinates of point G on the coordinate grid below?
A
(-4,3)
(4,-3)
-2
4
2
O
-2
4
B
AY
D
2
(4,3)
(-4,-3)
4
G
XA

Answers

Answer:

The answer is G = (4,3)

Step-by-step explanation:

G = (4,3)

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