solve 2(x+3)=x-4
solve 4(5x-2)=2(9x+3)​

As of 1995, the human population was expected to double within 50 years. If we calculated r for the human population, we would get 1.39. statement is False.

To determine whether the statement is true or false, we need to calculate the doubling time (DT) based on the given growth rate (r) and see if it aligns with the expected doubling time of 50 years.

The formula to calculate the doubling time (DT) for a population with a constant growth rate (r) is:

DT = ln(2) / r

where ln is the natural logarithm (base e).

If the expected doubling time is 50 years, then:

DT = 50 years.

Now, we can calculate the value of r:

r = ln(2) / DT

Plugging in the values:

r = ln(2) / 50 ≈ 0.01386

Comparing the calculated value of r (approximately 0.01386) with the given value of 1.39, we can see that they are not the same.

Therefore, the statement is False. The calculated value of r (0.01386) does not match the given value of 1.39, and it would not result in the human population doubling within 50 years. In reality, with a growth rate of 1.39, the population would grow at an unsustainable rate, leading to an even faster increase in population over time.

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straightforward random sampling With simple random sampling (SRS), each sampling unit of a population has an equal chance of being included in the sample.

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Sides of the given Right angle Triangle are 7.5,12.5,10.

The Pythagoras Theorem defines the relationship between a triangle's perpendicular, hypotenuse, and base. The right-angled triangle theorem is another name for this. The Pythagoras theorem states that a triangle is said to be right-angled if the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be said in the following way:

If Angle equals 90° then Hypotenuse = Perpendicular∧2+ Base∧2.

The base is the side that the right angle is connected to, the neighboring side of the right angle is connected to the hypotenuse by the perpendicular, and the side that the angle is opposite to is known as the hypotenuse. The legs of the hypotenuse are another name for the base.

Given

Tan(B) = [tex]\frac{3}{4}[/tex]=[tex]\frac{NE}{BE}[/tex]

⇒BE=10;

NB^2=NE^2+BE^2;

⇒NB^2=156.25

⇒NB=12.5

Sides of the given Right angle Triangle are 7.5,12.5,10.

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Answer:

Step-by-step explanation:

a°=180°-36°=144° b°=180°-113°=67°

a°=144° and b°=67°

144+67=211

36+113=149

149+211=360

He has enough cans to create the pyramid i.e. 91 cans.

What is a pyramid?

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces unite at a common point known as the apex and have a polygonal base. The bases are joined to the peak to create a pyramid. The lateral face is a triangle face formed by the connection of each edge of the base to the apex.

Each layer of the pyramid contains the square of the layer number.

Let's find out :

[tex]1^{2}[/tex] = 1, [tex]2^{2}[/tex] = 4, [tex]3^{2}[/tex] = 9, [tex]4^{2}[/tex] = 16, [tex]5^{2}[/tex] = 25, [tex]6^{2}[/tex] = 36

So, the total number of cans required = 1+4+9+16+25+36

                                                              = 91 cans

Hence, he has enough cans to create the pyramid.

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Answer:

-13???

Step-by-step explanation:

Answer: −28+15=-13

Step-by-step explanation: -28 + 15 = -13

The pairs of days and heights that could also be included in the table is given as follows:

The slope-intercept linear function that defines the plant's height after x days is given as follows:

y = mx + b.

The coefficients of the function are given as follows:

Then, considering the table given at the end of the answer, the equation that gives the height after x days is of:

y = 2x + 10.

The possible pairs are given at the beginning of the answer, for example, on day 9, the expected height is of:

y = 2(9) + 10 = 28 in.

The table is given by the image shown at the end of the answer.

The problem is incomplete, hence the pairs were calculated considering the table at the end of the answer. For a different table, you should follow the same procedure, identifying the equation and then testing the pairs.

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Aligned Dim constraint option allows you to create a dimensional constraint that has extension lines perpendicular to an angled surface.

In CAD software, a constraint is a restriction or limitation placed on geometric properties by a designer or engineer: An entity in a design model that keeps its structure when the model is altered is referred to as type 203. In addition to relative length and angle, these properties may also include size, shift, and displacement.

The term "plural form constraints" refers to the delineations of geometrical characteristics between two or more entities or solid modelling bodies; these delimiters are definitive for properties of hypothetical physical position and motion, or displacement in parametric design. However, a CAD programme vendor may use different terminology than another.

CAD software for solid modelling, computer-aided architectural design (including building information modelling), computer-aided engineering, assembly modelling, and other CAD subfields frequently uses constraints.

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Answer: 1578

Step-by-step explanation:

The answer is 1578

Answer:

1578.8333

Step-by-step explanation:

The amount of compound interest on #640.00 borrowed for 4years at 3% is #163, 840

The formula for determining compound interest is given as;

Compound interest = P ( 1 + r/n)^nt

Where;

Now, substitute the values

Compound interest = 640( 1 + 3/1)^(4×1)

expand the bracket

Compound interest = 640( 1 + 3)^4

Compound interest = 640(4)^4

find the exponential value

Compound interest = 640(256)

Multiply the value

Compound interest = #163, 840

Hence, the value is  #163, 840

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Data set: Factor A: Brand of Car Factor B: Type of Fuel Response Variable: Fuel Efficiency Levels of Factor A: 4 (Toyota, Honda, Ford, Chevrolet) Levels of Factor B: 2 (Gasoline, Diesel) Value of n: 3 (3 replicates per combination or treatment)

The data set has two factors: Brand of Car and Type of Fuel. The response variable is Fuel Efficiency, which is the value that is being measured in response to the two factors. There are four levels of Factor A (Toyota, Honda, Ford, Chevrolet) and two levels of Factor B (Gasoline, Diesel). Finally, the value of n is 3, meaning there are 3 replicates or treatments per combination of the two factors.

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When x0 x 0, log x is NOT defined (undefined). As a result, when x is in [(−∞,0]), log x is undefined.

1)  We are aware that only when x is positive is a logarithmic function, log x, defined. i.e., x>0 . Therefore, when x0 x 0, log x is NOT defined (undefined). As a result, when x is in [(−∞,0]), log x is undefined.

2) Order from smallest to largest:

     [tex]log^{200}_{20} < log 100 < log^{5}_{40} < log^{3}_{60} < log^{2}_{16}[/tex]

3)

           [tex]\(2A=A(1+\frac{0.09}{52})^{n}\\\\ 2=(1+\frac{0.09}{52})^{n}\\\\ log2=log(1+\frac{0.09}{52})^{n}\\\\ log2=nlog(1+\frac{0.09}{52})\\\\ n=log2\div log(1+\frac{0.09}{52})\\\)[/tex]

log(2)/log(1+0.09/52 = 400.831511360387616 weeks

400.831511360387616/52 = 7.708298295392069538

7.7 years

Hence, It take 7.7 years for deposit to double.

4)

a)

          [tex]S= 86 \ log d+112\\\\S= 86 log 50 +112\\\\S = 86*1.7+112\\\\S= 258.2[/tex]

          S = 258.2 mph

b)

S = 258.2 mph ;  find d

258 =86 log10 (d) + 112

146 = 86 log10 (d)

 1.7 = log10 (d)

 d = 50.118

Change from Log Form to Exponential Form

50.118 miles = d   Rounded is 181 miles

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Answer:  The correct answer is 0.1246135 kilograms

Step-by-step explanation:

1,000 grams = 1 kilogram

Therefore 124.6135 grams / 1000 = 0.1246135 kilograms

Answer:

124.6135 grams to the nearest kilogram would be none if you want to round how you are supposed to, or one if round to the next number up.

Step-by-step explanation:

What is 124.6135 grams compared to kilograms? Well, it's simple. A single kilogram has kilo in it. Kilo is a prefix meaning thousand, so therefor, a kilo gram is a thousand grams. since you have 124.6135 grams if you divide that by a thousand, you get 0.1246135. And using the rounding rule five or more, raise the score, four or less, let it rest; 1 is less than four so it would be zero.

Answer:

Below

Step-by-step explanation:

Find the slope between the two given points

  (y1-y2) / (x1-x2)     <====  does not matter which you assign as point 1 or 2

(-3-5) / (0-4) = -8/-4 = 2

now set up equation using point-slope form  (use either point)

  y-5  = 2 (x-4)      re-arrange

   y -5  = 2x - 8

   2x - y  = 3

In a simple linear regression analysis, the correlation coefficient (r) and the slope (m) Always have the same sign.

What is linear regression?

Predictive analysis and modelling frequently use linear regression. It can be used, for instance, to measure the proportional effects of diet, age, and gender (the predictor variables) on height (the outcome variable).

A correlation coefficient is a metric that expresses a correlation, or a statistical relationship between two variables, in numerical terms.

Two columns of a given data set of observations, also known as a sample, or two parts of a multivariate random variable with a known distribution may serve as the variables.

Hence, in a simple linear regression analysis, the correlation coefficient (r) and the slope (m) Always have the same sign.

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Answer:

(3,-1)

Step-by-step explanation:

you have a graph and poin is (0,1) you have 0+3 to make 2 on the horizontil line and they y = -2 so you go down 2 to make (3,-1)

Answer:

(3, -1)

Step-by-step explanation:

Graphical Translation is about shifting the coordinates by a certain value towards the left/down (x and y coordinates respectively) for negative signs and towards the right/up (x and y coordinates respectively) for positive signs.

Eg. x is shifted by + 3 units, y is shifted by - 1 unit from the point (9 , 3) , the resulting coordinate will be:

(9 + 3, 3 - 1) = (12, 2)

Given from the question:

x is shifted by + 3 units and y is shifted by - 2 units,

Therefore, the resulting coordinates will be:

(0 + 3, 1 - 2) = (3, -1).

Thus , probability of very last passenger getting seat comes out to be

P = 0.5 .

Mathematics' field of probability deals with numerical representations of the possibility that an event will take place or that a statement is true. An event's probability is a number between 0 and 1, with 1 generally denoting certainty and 0 generally denoting impossibility.

Here,

If everyone chose at random, you would only have a 1/100 chance of receiving your own seat on a plane with 100 seats. However, in the context of this riddle, each participant does not make a random selection; rather, they only do so if all available seats have been occupied.

This indicates that half of the scenarios will resolve themselves (i.e., someone takes the mystery ticket holder's assigned seat allowing every subsequent passenger to take their assigned seat), while the other half will not resolve themselves and you will be seated in the incorrect location, making the probability of any plane occupancy equal to half.

Thus , probability of very last passenger getting seat comes out to be P = 0.5 .

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Yes, Since  a and b are independent event then therefore, a and b are mutually exclusive events.

             P(a) +P(b) = 0.5+0.5

therefore, P(a ∪b) = 1.0

Mutually exclusive events are events that do not occur at the same time. For example, when you toss a coin, the result is either heads or tails, but you cannot get both results. Such events are also called disjoint events because they do not occur at the same time. If A and B are mutually exclusive events, their probabilities are given by P(A or B) or P(A U B).

According to the question:

P(a) = 0.5 and P(b)=0.5

therefore,

    P(a) +P(b) = P(a ∪ b)

⇒ 0.5 +0.5 = 1.0

Therefor a and b are mutually exclusive events.

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The probability of winning is 0.01 is -2  is the expected profit of this game.

What is probability?

Expected profit of the game =expected value received from this game- cost to play the game

=100*0.01-3

= -2

Hence, the probability of winning is 0.01 is -2 is the expected profit of this game.

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Answer:

#1. The zeros of the function g(x) are −3/2, 1, and 3 (all with multiplicity 1).

#2. The zeros of the function h(x) are −1 and −2 (both with multiplicity 2).

The probability that next ice cream cone sold is a chocolate chip ice cream cone is 0.052. The result is obtained by dividing the chocolate chip ice cream cone sold by the total ice cream from the previous week data.

Probability is a numerical description of how possible an event to happen. Probability of an event can be expressed as

P(A) = n(A) / n(S)

Where

The previous week data shows that

To estimate the probability that will happen in the future, we use the data happened in the past.

The probability that the ice cream cone sold for chocolate chip variant is

P(A) = n(A) / n(S)

P(A) = 52 / 997

P(A) = 0.052

Hence, the probability of next selling a chocolate chip ice cream cone is 0.052.

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Answer: 52/997

Step-by-step explanation: I checked on khan

Yes, three equations are needed to find the values of three variables. Then only it will have a unique solution. The  solution of three variable equation is also known as the ordered triple.  

There must be 3 equations, If there are 3 variables.

Lets consider  A,B,C as our equations and x, y, and z as the variables.

We will now follow these following steps:

1) By using C, first write z in terms of x and y. Then, Replace z with its equivalent in B.

2) Then write y in terms of x.

3) In A, replace y with its equivalent and replace z with its equivalent then solve A for x. Now you should know the value of x. You should have written y in terms of x so plug x and you will find y.

4)Finally, you should have written z in terms of x and y so you can find the value of z.

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The constant of  proportionality is 5 for the relation between x and y.

What is proportional relationship?

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of the constant.

Given table is

x(days)         5    10   15   20

y(swings)      1      2     3    4

Since y is increasing with increase of days(x).

Thus the relation between y and x is in direct proportional.

Assume the relation be x ∝ y

x = ky, where k is constant proportionality.

Putting x = 5 and y = 1:

5 = k × 1

k = 5

Putting x = 10 and y = 2:

10 = k × 2

k = 5

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Answer:

Step-by-step explanation: Are you talking about negative numbers? If so, the answer is -9.5

If you aren't talking about negative numbers, then your answer is -3.9

Hope this helps.

Answer:

They each brought $22 to the fair

Step-by-step explanation:

8+3=11

11*2=22

Answer=22

Answer:

Jill paid 26.73$, and Jane paid 16.20$ with tax in total 42.93$

Step-by-step explanation:

[tex]24.75$ * 0.08$= 1.98$\\15$ * 0.08$= 1.2$\\24.75$ + 1.98$=26.73$\\15$ + 1.20$= 16.20$\\26.73$ + 16.2$= 42.93$[/tex]

The algebraic expression for 8 less than a number is x - 8

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations

Let the number be x.

The algebraic expression for 8 less than a number will be:

x - 8.

The expression is x - 8.

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The complete statements are

The complete question is added at the end of this solution

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

Garrick's plant:

Zan's plant:

Garrick's plant is shorter than Zan's plant and the difference in heights is

Actual difference = 100 mm - 10 mm = 90 mm

Measured difference = 88 mm - 8 mm = 80 mm

The percentage errors are calculated using

Percentage errors = Difference/Actual measurement * 100%

So, we have

Garrick's actual error = (10 - 8)/10 *100% = 20%

Zan's actual error = (100 - 88)/10 * 100% = 12%

Hence, Garrick's measurement was 20% off and Zan's was 12% off.

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The constant of proportionality is 0.25

Using the unitary approach, you can solve problems by first figuring out the value of a single unit, then multiplying that value by the number of units you need.

According to the given information

Applying Unitary Method

Pages have a direct relationship with time.

N ∝ t

N = k × t

k is constant of proportionality

Time taken to read 15 pages = 60 minutes

Time taken to read 1 page = [tex]\frac{15}{60}[/tex]

                                            = 1/4

1/4 is constant of proportionality

k = 0.25

The constant of proportionality is 0.25

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