Jacob is twice as heavy as Ken Linda is half as heavy as Ken Giver 3 children is at least 35 kg. a By letting Linda's mass be x, write an inequality for the total mass of the 3 children b. Hence, find the minimum mass of Ken Monica wanted to buy x notebooks at $3.50 each and 15 rulers at $(x+0.20) each She had a budget of $105 only c. Write an inequality for Monica's total expenditure . Hence, how many notebooks can she buy at most? ​

Answer:

x=3

Step-by-step explanation:

7+4(5/4x-1)=18

7+5x-4=18

3+5x=18

5x=15

x=3

Answer:

x = 3

Step-by-step explanation:

18 = 7 + 4(\(\frac{5}{4}\)x - 1)

18 = 7 + 5x - 4

18 = 3 + 5x

15 = 5x

x = 3

Answer:

7.14%

Step-by-step explanation:

Any comparison with the increase or decrease in price has to be compared to the ORIGINAL price. (at the beginning of the month.)

The price increased from $3.50 to $3.75, an increase of $0.25

To find what percent it is use:\(\frac{change}{original}\)×100%

\(\frac{0.25}{3.50}\)×100%

Answer:

7.1428571% increase

7  1/7 % increase

Step-by-step explanation:

To find the percent increase ( we know this is an increase since the amount went up), take the new amount and subtract the original amount

3.75 - 3.50 = .25

Divide by the original amount

.25 / 3.50

.071428571

Multiply by 100 %

7.1428571%

7 1/7 %

The solution to the differential equation D²y(t) + 12 Dy(t) + 36y(t) = 2 \(e^{(-5t)}\), with initial conditions y(0) = 1 and Dy(0) = 0, is \(y(t) = (1 + 6t) e^{(-6t)}\).

To solve the given differential equation using the classical method, we can assume a solution of the form \(y(t) = e^{(rt)}\) and find the values of r that satisfy the equation. We then use these values of r to construct the general solution.

Using the classical method:

Substitute the assumed solution \(y(t) = e^{(rt)}\) into the differential equation:

D²y(t) + 12 Dy(t) + 36y(t) = \(2 e^{(-5t)}\)

This gives the characteristic equation r² + 12r + 36 = 0.

Solve the characteristic equation for r by factoring or using the quadratic formula:

r² + 12r + 36 = (r + 6)(r + 6)

= 0

The repeated root is r = -6.

Since we have a repeated root, the general solution is y(t) = (c₁ + c₂t) \(e^{(-6t)}\)

Taking the first derivative, we get Dy(t) = c₂ \(e^{(-6t)}\)- 6(c₁ + c₂t) e^(-6t).\(e^{(-6t)}\)

Using the initial conditions y(0) = 1 and Dy(0) = 0, we can solve for c₁ and c₂:

y(0) = c₁ = 1

Dy(0) = c₂ - 6c₁ = 0

c₂ - 6(1) = 0

c₂ = 6

The particular solution is y(t) = (1 + 6t) e^(-6t).

Using the Laplace transform method:

Take the Laplace transform of both sides of the differential equation:

L{D²y(t)} + 12L{Dy(t)} + 36L{y(t)} = 2L{e^(-5t)}

s²Y(s) - sy(0) - Dy(0) + 12sY(s) - y(0) + 36Y(s) = 2/(s + 5)

Substitute the initial conditions y(0) = 1 and Dy(0) = 0:

s²Y(s) - s - 0 + 12sY(s) - 1 + 36Y(s) = 2/(s + 5)

Rearrange the equation and solve for Y(s):

(s² + 12s + 36)Y(s) = s + 1 + 2/(s + 5)

Y(s) = (s + 1 + 2/(s + 5))/(s² + 12s + 36)

Perform partial fraction decomposition on Y(s) and find the inverse Laplace transform to obtain y(t):

\(y(t) = L^{(-1)}{Y(s)}\)

Simplifying further, the solution is:

\(y(t) = (1 + 6t) e^{(-6t)\)

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Answer:

<1 = 12.71 degrees

<2 = 77.29 degrees

Step-by-step explanation:

<1 = x

<2 = 6x - 1

x + 6x - 1 = 90 degrees

7x = 90 - 1

x = 89/7

x = 12.71

The dimensions that maximize the printed area are a width of 30cm and a height of 255.6cm.

Total area of the poster = Area of printed area + Area of top/bottom margins + Area of side margins

15360 = xy + 2(10cm)(x) + 2(6cm)(y)

Simplifying this equation:

xy + 20x + 12y = 7680

xy = 7680 - 20x - 12y

To maximize the printed area, we need to find the values of x and y that satisfy this equation while also maximizing the value of xy.

To solve for y in terms of x, we can rearrange the equation as follows:

y = (7680 - 20x)/x - 12

Then we can substitute this expression for y into the equation for xy:

xy = x[(7680 - 20x)/x - 12] = 7680x/x - 20x²/x - 12x

Simplifying this expression,:

xy = 7680 - 20x² - 12x

Take the derivative of this expression with respect to x and set it equal to zero:

d(xy)/dx = -40x - 12 = 0

Solving for x:

x = -12/(-40) = 0.3m

Substituting this value back into the expression for y:

y = (7680 - 20(0.3))/0.3 - 12 = 255.6cm

Therefore, the dimensions are a width of 30cm and a height of 255.6cm.

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Answer:

110

Step-by-step explanation:

lets assume y is the angle next to x which should complete to form a 360.

50 + 25 + 35 + y = 360

y = 250

x + y = 360

x + 250 = 360

x = 110

Answer:

110

Step-by-step explanation:

lets assume y is the angle next to x which should complete to from a 360.

50 + 25 + 35 + y = 360

y = 250

x + y = 360

x + 250 = 360

x = 110

Answer:

25

Step-by-step explanation:

x^2 + 10x + 25   = (x+5)^2

Answer:

$684.38

Step-by-step explanation:

A = Pi / (1 − 1/(1 + i)ⁿ)

where A is the annuity (monthly payment),

P is the present value (the loan),

i is the interest rate per compounding,

and n is the number of compoundings.

P = 35400

i = 0.06 / 12 = 0.005

n = 5 × 12 = 60

A = (35400) (0.005) / (1 − 1/(1 + 0.005)⁶⁰)

A = 684.38

Answer:

-17(-)-18=-17+18=1 or -17+18=1

Step-by-step explanation:

if -17 is one number you Add 18.

-17(-)-18=-17+18=1

The lowest possible number of balls blind man need to pick to ensure that he picked two different colors balls is equal to 48.

Number of green balls = 44

Number of blue balls = 65

Number of yellow balls = 14

Number of red balls = 2

To ensure the blind man picks two balls of different colors.

Maximum number of balls he can pick of a single color before he is guaranteed to have picked two of different colors.

All the blue and red balls have a rough surface.

All the green and yellow balls have a smooth surface.

Treat them as two distinct groups.

Let us consider the worst-case scenario,

where the blind man picks all the balls of one group before picking any ball of the other group.

Here, he could pick all 44 green balls or all 14 yellow balls before picking any blue or red ball.

Similarly, he could pick both red balls before picking any blue ball.

To ensure he has picked two balls of different colors, he needs to pick at least,

(44 green balls + 1 yellow ball) or 3 balls (2 red balls + 1 blue ball)

= 48 balls whichever is higher.

Therefore, the lowest possible number of balls he needs to pick to ensure he has picked two balls of different colors is 48.

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Answer:

3.7

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

There are 8 equal slices so each slice is 1/8th of the whole pizza

1/8+1/8=2/8 he ate right away

2/8+1/8 for what he ate before going to sleep

2/8+1/8=3/8

Answer:

3

Step-by-step explanation:

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

7 pages

Step-by-step explanation:

21/3=7/3

18÷6=3

7/3×3=7

Answer:

You would have $343.37 at the end of the 2 years.

Step-by-step explanation:

Interest earned is like bonus money the bank pays you just for keeping money

\(\mathrm{Compund\:Interest\:Formula}:\quad A = P { \left( 1+ \dfrac{ r }{ n } \right) }^{ nt }\)

P: the starting balance of the account (also called initial deposit, or principal)

A: the new balance in the account after N years.

t: the number of years or time

r: the interest rate, (in decimal form)

n: the number of times the interest is compounded each year.

Annually = each year = 1

P =$300, r = 7%, t = 2, n = 1, A = ?

Substitute the numbers into the "Compound Interest Formula".

\(A = 300 { \left( 1+ \dfrac{ 0.07 }{ 1 } \right) }^{ 1 \times 2 }\)

\(\mathrm{Anything\:divided\:by\:1\:gives\:itself}\)

\(A = 300 { \left( 1+0.07 \right) }^{ 1 \times 2 }\)

\(\mathrm{Add\:1\:and\:0.07\:to\:get\:1.07}\)

\(A = 300 \times { 1.07 }^{ 1 \times 2 }\)

\(\mathrm{Multiply\:1\:and\:2\:to\:get\:2}\)

\(A = 300 \times { 1.07 }^{ 2 }\)

\(\mathrm{Calculate\:1.07\:to\:the\:power\:of\:2\:and\:get\:1.1449}\)

\(A = 300 \times 1.1449\)

\(\mathrm{Multiply\:300\:and\:1.1449\:to\:get\:343.47}\)

\(A = 343.47\)

So you would have $343.37 at the end of the 2 years.

Look at the chart

\(\mathrm{Year}\quad \mathrm{Year\: Interest}\quad \mathrm{Total\:Interest}\quad \mathrm{Balance}\\\quad1\quad\quad\quad $21.00\quad\quad\quad\quad $21.00\quad\quad\quad\quad $321.00\\\quad2\quad\quad\quad $22.47\quad\quad\quad\quad $43.47\quad\quad\quad\quad $343.47\)

Answer:

No solutions

Step-by-step explanation:

y = 2x + 7

(y = 2x + 5)-1 = -y = -2x - 5

-y = -2x - 5

y = 2x + 7

0 = 2

In simple linear regression, the predictor variable is the independent variable, which is used to predict the value of the dependent variable. It is also referred to as the explanatory variable, as it is used to explain the variability in the response variable.

For example, in a study that examines the relationship between the hours studied and exam scores, the predictor variable is the number of hours studied, and the dependent variable is the exam score.

The predictor variable is plotted on the x-axis, while the dependent variable is plotted on the y-axis in a scatter plot. The relationship between the predictor and the dependent variable is represented by a straight line, which is determined by the regression equation.

The slope of the line represents the change in the dependent variable for each unit change in the predictor variable.

In summary, the predictor variable is the variable that is used to predict or explain the changes in the dependent variable in simple linear regression.

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We use ANOVA to test for differences between population means by examining the amount of variability between the samples relative to the amount of variability within the samples. Hence, it is TRUE

The statistical analysis tool known as analysis of variance (ANOVA) divides the observed aggregate variability present in a data set into two categories: systematic variables and random components. The random factors have no statistical impact on the presented data set, whereas the systematic factors do. The ANOVA test is used by analysts to ascertain how independent factors in a regression analysis affect the dependent variable.

ANOVA basically stands for analysis of the variance.

Hence, according to above statements, given fact is true.

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Answer:

b.

Step-by-step explanation:

30×0.5×63 = 945

this is not a square number. therefore, the sqrt(945) is a number of infinite digit positions after the decimal point without repeating pattern.

so, it is a prime example of an irrational number.

At x = 1, the coordinates are (1, 4)

They represent the proportionality of 1 teaspoon of cumin and 4 teaspoons of chili powder.

The graph is proportional because as x increases, y al

9514 1404 393

Answer:

  see below

Step-by-step explanation:

The term y/2 tells you that any integer solution must include an even value of y. That is, y=3 cannot be part of an integer solution.

When we use the ordered pair (x, y) = (2, -4) in the equation, we get ...

  6(2) -(-4)/2 = 12 +2 = 14 . . . . . satisfies the equation

Of the two points offered, only (2, -4) is a solution.

The value of the unknown number is 4/3. To solve this equation, let's assign a variable to represent the unknown number.

Let's say the unknown number is represented by "x".
The equation can be written as:
1/2 + 6x = 7x - 5/6
To solve for x, we can start by getting rid of the fractions. We can do this by multiplying every term in the equation by 6 to eliminate the denominators.
6 * (1/2) + 6 * 6x = 6 * (7x) - 6 * (5/6)
3 + 36x = 42x - 5
Now, let's combine like terms and simplify the equation:
42x - 36x = 3 + 5
6x = 8
Finally, we can solve for x by dividing both sides of the equation by 6:
x = 8/6
Simplifying the fraction, we get:
x = 4/3


The sum of 1/2 and 6 times the number is equal to 5/6 subtracted from 7 times the number. To solve for the unknown number, we assigned the variable "x" to represent it. We eliminated the fractions by multiplying every term in the equation by 6 to get rid of the denominators. After simplifying and combining like terms, we found that the value of the unknown number is 4/3.

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Answer:

\(8^{\frac{x}{3} }\)

Step-by-step explanation:

43 is the quotient

=======

\(\rightarrow \sf \dfrac{690}{16}\)

\(\rightarrow \sf 43\dfrac{2}{16}\)

=========

In a mixed fraction like: \(\sf a \dfrac{b}{c}\)

Answer:

43

Step-by-step explanation:

To find the quotient of 690/16, the first step is to simplify the expression so that it would be easier to simplify.

\(\rightarrowtail \dfrac{690}{16} = \dfrac{345}{8}\)

Now, let's simplify the expresssion using long division.

(Refer to image attached)

According to the image, we can tell that quotient is 43. Keep in mind that the quotient is the number obtained at the top.

a)  P(X=330) is approximately 0.0002. b)P(X>340) is approximately 0.0294. c) P(335≤X≤345) is approximately 0.6415. d) P(X=300) is approximately 0.0004 of given probabilities

To find the probabilities using Excel's function options, we can use the binomial distribution function, which is provided as BINOM.DIST in Excel.

a) P(X=330):

=BINOM.DIST(330, 400, 0.8, FALSE)

The first argument is the specific value (330), the second argument is the total number of trials (400), the third argument is the probability of success (0.8), and the fourth argument FALSE indicates that we want the probability for a specific value.

The result is approximately 0.0002.

Therefore, P(X=330) is approximately 0.0002.

b) P(X>340):

=1 - BINOM.DIST(340, 400, 0.8, TRUE)

Since we want the probability of X being greater than 340, we can subtract the cumulative probability of X up to 340 from 1. We use the TRUE argument to indicate that we want the cumulative probability.

The result is approximately 0.0294.

Therefore, P(X>340) is approximately 0.0294.

c) P(335≤X≤345):

=BINOM.DIST(345, 400, 0.8, TRUE) - BINOM.DIST(334, 400, 0.8, TRUE)

To find the probability of X being between 335 and 345 (inclusive), we subtract the cumulative probability of X up to 334 from the cumulative probability of X up to 345.

The result is approximately 0.6415.

Therefore, P(335≤X≤345) is approximately 0.6415.

d) P(X=300):

=BINOM.DIST(300, 400, 0.8, FALSE)

The first argument is the specific value (300), the second argument is the total number of trials (400), the third argument is the probability of success (0.8), and the fourth argument FALSE indicates that we want the probability for a specific value.

The result is approximately 0.0004.

Therefore, P(X=300) is approximately 0.0004.

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Answer: - 17 C

Step-by-step explanation: 7 - 8 is negative 1 and twice as much of 8 is 16. -1 minus 16 is negative 17 (-17).