What year was math invented?

Answers

Answer 1

Answer:

Around 3000 BC

Answer 2

Answer:

It is difficult to pinpoint a specific year or time period in which math was "invented," as math is a fundamental aspect of human thought and has likely been present in some form since ancient times.

The study of mathematics has a long and rich history, dating back to ancient civilizations in Mesopotamia, Egypt, Greece, and India. These early societies developed mathematical concepts and techniques to aid in practical tasks such as measuring land, calculating the volume of objects, and tracking the movement of celestial bodies.

As human civilizations developed and advanced, so too did the study of mathematics. Over time, new mathematical concepts and techniques were developed and refined, leading to the development of more advanced branches of mathematics such as algebra, geometry, trigonometry, and calculus.

In summary, math has a long and complex history, and it is difficult to pinpoint a specific year or time period in which it was "invented." It has likely been present in some form since ancient times and has evolved and developed over the course of human history.

Step-by-step explanation:

SELF EXPLANATORY

Related Questions

Which of the following is NOT valid for proving that triangles are congruent? (A) AAA, (B) ASA (C) SAS, (D) HL

Answers

Answer:

A) AAA

Step-by-step explanation:

This proved similarity, but not necessarily congruency. If the angles are the same in a triangle, they could be smaller and larger versions of themselves. They will have the same shape, but not necessary the same size. The side lengths will be proportional. If the scale factor between the two triangles is 1 , then the triangles would be congruent, but they could have any scale factor greater or less than 1 too.

HELPP 65 POINTS I NEED THEM ALL

It can be expensive to go to the movie theater. The scatter plot shown here gives the average cost in

U.S. dollars of a movie ticket in the U.S. for each year from 1980 to 2013. Using this data, how much do

you think a movie ticket will cost in the years 2020 and 2030? Download the worksheet and complete it.

1. How has the cost of a movie ticket changed over the last 30 years? What has been the general

trend? How can you tell this from the graph? (2 points)

2. What years did the cost of movie ticket decrease compared to the year before? How can you tell

from the graph when the price is decreasing? (2 points)

Student Name:

Predicting Movie Ticket Costs Activity

3. There was a time where the cost of a movie ticket stayed relatively the same over several years.

For what years did the cost stay relatively the same? How can you tell this from the graph? (2

points)

4. The graph could be divided up into three different periods of relatively consistent ticket price

change: The years 1980 – 1988, 1989 – 1993 and 1994 – 2011. Can you find a typical rate of

change in the price of a ticket for each of these time periods? In other words, on average, by

how much did the price of a ticket increase by each year during each of these time periods?

(2 points)

5. Predict the cost of a ticket in 2012 – 2015. Plot your predictions and give your actual predictions

for each year below. How did you determine how much a ticket would cost each year? (2 points)

6. What might have been the cost of a ticket during the years 1975 – 1979? Plot your estimates on

the grid and give your actual predictions for each year below. How did you determine how much

a ticket would cost each year? (2 points)

Predicting Movie Ticket Costs Activity

7. Find a line of best fit to represent the data. Let y = ticket price and x = the number of years since

1980 (1980 is year zero, 1981 is year one). Approximate a line to represent the data, a slope, a y-intercept and equation that models your line of best fit. (2 points)

8. Use your equation (or graph or a table) to predict the cost of a movie ticket in the years 2020

and 2030. Be sure to show how you came to each answer. (2 points)

Answers

Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.

What do you mean by rates?

A rate in mathematics is the comparison of two related values expressed in different units. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

1. Perhaps in other parts of the country, ticket prices are much cheaper. So, the average of all of the ticket prices turns out to be less.

2. From 1988 to 1989 the cost of a ticket decreased. Also from 1991 to 1992 the cost decreased a little. The graph slants a little downward.\

3. From 1990 to 1994 the cost stayed pretty much the same. Those years on the graph look almost level... not sloping upward or downward.

4. 1980-1988 price increased from about $2.75 to about $4.25 $1.50 over 8 years = $0.19 per year 1989-1993 price increased from about $4.00 to about $4.20 = $0.20 over 4 years = $0.05 per year 1994-2011 price increased from about $4.20 to about $8.00 $3.80 over 7 years = $0.54 per year

5. Maybe 2012 will be $8.20, 2013 will be $8.30, 2014 will be $8.50, 2015 will be $8.60 ish
Maybe I should make the price go up about $0.17 cents per year ... on average.

6. 1979 maybe $2.52
1978 maybe $2.36
1977 maybe $2.19
1976 maybe $2.02
975 maybe $1.85
I figured that the price was going down, on average, at about $0.17 per year.

7. one possibility might be y=$5.30/31 x + $2.70 or y = 0.17x+2.7.

8.Using the equation that we fit to this data y = 0.17x + 2.7 we get 0.17(40) + 2.7= $9.50 for the year 2020 and for the year 2030 we get 0.17(50)+2.7 $11.20

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Answer:

Step-by-step explanation:

its b like this the aetter number g

find f(2), f(3), f(4), and f(5) if f is defined recursively by f(0) = f(1) = 1 and for n = 1, 2, …

Answers

As a set of inputs with one output for each, a function is defined as a relationship between them.

What is meant by functions?

An equation, rule, or law in mathematics that establishes the link between the independent variable and the dependent variable (the dependent variable). Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.

We have given, f(0) = 3 for all parts.

a) f(n+1) = -2 f(n)

For f(1) put f(n) = f(0), f(0+1) = -2 f(0)

f(1) = -2(3) = -6

For f(2) put f(n = 1), f(1+1) = -2 f(1)

f(2) = -2(-6) = 12

For f(3) put f(n) = f(2), f(2+1) = -2 f(2)

f(3) = -2(12) = -24

For f(4) put n = 3, f(3+1) = -2 f(3)

f(4) = -2(-24) = 48

For f(5) put n = 4, f(4+1) = -2 f(4)

f(5) = -2(48) = -96

b) f(n+1) = 3, f(n) + 7

For f(1) put n = 0, f(0+1) = 3 f(0)+7

f(1) = 3(3)+7 = 16

For f(2) put n = 1, f(1+1) = 3 f(1)+7

f(2) = 3(16)+7 = 55

For f(3) put f{n}=f{2}, f(2+1)=3 f(2)+7

f(3) = 3(55) + 7 = 172

For f(4) put n = 3, f(3+1) = 3 f(3)+7

f(4) = 3(172)+7 = 523

For f(5) put n = 4, f(4+1) = 3 f(4)+7

f(5) = 3(523)+7 = 1576

c) f(n+1) = f(n)²-2 f(n)-2

For f(1) put n = 0, f(0+1) = f(0)²-2 f(0)-2

f(1) = 3²-2(3)-2 = 1

For f(2) put n = 1, f(1+1) = f(1)²-2 f(1)-2

f(2) = 1²-2(1)-2 = -3

For f(3) put n = 2, f(2+1) = f(2)² - 2 f(2) - 2

f(3) = -3² - 2(-3) - 2 = 13

For f(4) put n = 3, f(3+1) = f(3)² - 2 f(3) - 2

f(4) = 13² - 2(13) - 2 = 141

For f(5) put n=4, f(4+1) = f(4)² - 2 f(4) - 2

f(5) = 141² - 2(141) - 2 = 19597

d) f(n+1)[tex]=3^{\frac{f(n)}{3}}$[/tex]

For f(1) put n = 0, f(0+1) [tex]$=3^{\frac{f(0)}{3}}$[/tex]

f(1) = [tex]3^{\frac{3}{3}}[/tex] = 3

For f(2) put n = 1, f(1+1) [tex]=3^{\frac{f(1)}{3}}$[/tex]

f(2) [tex]=3^{\frac{3}{3}}[/tex] = 3

For f(3) put n = 2, f(2+1) [tex]=3^{\frac{f(2)}{3}}$[/tex]

f(3) [tex]=3^{\frac{3}{3}}[/tex] = 3

For f(4) put n = 3, f(3+1) [tex]$=3^{\frac{f(3)}{3}}$[/tex]

[tex]$f(3)=3^{\frac{3}{3}}=3$[/tex]

For f(4) put n = 3, f(3+1) = [tex]$3^{\frac{f(3)}{3}}$[/tex]

f(4) [tex]$=3^{\frac{3}{3}}[/tex] = 3

For f(5) put n = 4, f(4+1) = [tex]3^{\frac{f(4)}{3}}$[/tex]

f(5) [tex]=3^{\frac{3}{3}}[/tex] = 3

The complete question is:

Find f( 1 ) , f( 2 ) , f( 3 ) , f( 4 ) , and f( 5 ) if f(n) is deﬁned recursively by f( 0 ) = 3 and for n = 0 , 1 , 2 ,... a) f(n + 1 ) = − 2 f(n) . b) f(n + 1 ) = 3 f(n) + 7. c) f(n + 1 ) = f(n) 2 − 2 f(n) − 2. d) f(n + 1 ) = 3 f( slader

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f(2)=4, f(3)=7, f(4)=19, f(5)=40

What is a function?

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially provided the contemporary concept of function in 1837.

Given, the function is f(n+1) = f(n) + 3f(n-1)

Calculating f(2) by substituting n=1 in the above equation.

f(2) = f(1) + 3f(0)

⇒f(2) = 1 + 3

⇒f(2) = 4

f(3) is calculated by substituting n=2

f(3) = f(2) + 3f(1)

⇒f(3) = 4 + 3

⇒f(3) = 7

f(4) is calculated by substituting n=3

f(4) = f(3) + 3f(2)

⇒f(4) = 7 + 12

⇒f(4) = 19

f(5) is calculated by substituting n=4

f(5) = f(4) + 3f(3)

⇒f(5) = 19 + 21

⇒f(5) = 40

f(2)=4, f(3)=7, f(4)=19, f(5)=40

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Plss help only question 12

Answers

Answer:

Step-by-step explanation:

Let's try negative number for n.

n = -3

(n+1)/n

(-3 + 1)/-3 => -2/-3

=> 0.66

Which is less than 1, so therefore the original statement is false

in triangle ABC, AB = 5, BC = 6, and AC= 7 , the the nearest degree, what is the measurment of angle ABC
how can i find it

Answers

Answer:

∠ ABC ≈ 78°

Step-by-step explanation:

using the Cosine rule in Δ ABC

cos ABC = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]

where a is the side opposite ∠ A , b is the side opposite ∠ B and c the side opposite ∠ C

here a = BC = 6 , b = AC = 7 and c = AB = 5 , then

cos ABC = [tex]\frac{6^2+5^2-7^2}{2(6)(5)}[/tex] = [tex]\frac{36+25-49}{60}[/tex] = [tex]\frac{12}{60}[/tex] , then

∠ ABC = [tex]cos^{-1}[/tex] ( [tex]\frac{12}{60}[/tex] ) ≈ 78° ( to the nearest degree )

which expression is not equivlent to 8 + ( n - 4)

Answers

Answer: The expression which is not equivalent to (8 + (n - 4)) is (12+n) and this can be determined by using the arithmetic operations.

Given :

Expression - 8 + (n - 4)

To simplify the given expression following steps can be used:

Step 1 - Rewrite the given expression.

= (n - 4) + 8

Step 2 - Now, remove the parenthesis in the given expression.

= n - 4 + 8

Step 3 - Now, write 8 as the addition of 4 and 4.

= n - 4 + 4 + 4

Step 4 - Subtract 4 by 4.

= n + 4

5x+2y-2z=-57
3x-10y-z=-11
Y=-2

Answers

First up is 5x+2y-2z=-57

5x+2y-2z=-57 /You gotta subtract 27 and 2z from both sides

5x+2y-2z- (2y-2z)=-57- (2y-2z) Then simplify-5x =-57-2y+2z

Then divide by both sides:

Answer is: x=-57-2y+2z / over 5

Thomas increased the amount of water she gives her plants from 2 cups to 2 1/2 cups. By what percentage did Thomas increase the amount of water?

Answers

Ok so any % change is simply just final over initial. It would also be helpful to convert your fractions into decimals. So, 2.5/2 will give you 1.25. Move the decimal to the right twice, you get 125. So now it’s at 125% of the FULL value, so subtract 100 and it increased by 25%. :)

He sold a car for 247,250 at a profit of 15%, what was the price of the car?

Answers

Answer: Cost Price = 21,50,000

Step-by-step explanation:

Solve for x, please help finals are in a day and I have a D in this class(Geometry)

Answers

Answer:

x = 2

Step-by-step explanation:

In order to find the value of x, first we need to prove ∆ABC and ∆ADE as similar ∆s.

So, let's prove:

In ∆ABC and ∆ADE,

[tex]\angle ABC \cong \angle ADE....(each \: 90\degree)[/tex]

[tex]\angle BAC \cong \angle DAE....(common \: \angle s)[/tex]

[tex]\implies \triangle ABC \sim \triangle ADE[/tex] (By AA postulate)

[tex]\implies \frac{AB}{AD}=\frac{BC}{DE}....(csst) [/tex]

[tex]\implies \frac{2}{2+x}=\frac{1}{2}[/tex]

[tex]\implies {2+x}=4[/tex]

[tex]\implies {x}=4-2[/tex]

[tex]\implies {x}=2[/tex]

Suppose IQ scores were obtained for 20 randomly selected sets of twins. The 20 pairs of measurements yield x=98.13, y=100.6, r=0.904, P-value=0.000, ŷ=14.68+0.88x, where x represents the IQ score of the twin born first. Find the best predicted value of ModifyingAbove y with caret given that the twin born first has an IQ of 104? Use a significance level of 0.05.

Answers

The best-predicted value of Modifying Above y with caret given that the twin born first has an IQ of 104 is 106.2.

The dependent variable's predicted value in basic linear regression is given by the equation = b0 + b1x.

In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X. (the error is the difference between the predicted value and the actual value of y).

Use regression equation

ŷ=14.68+0.88x

plug in IQ, which is x

y = 14.68 + 0.88(104)

= 106.2

Hence, the answer is 106.2

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A body moving at an initial velocity of 30m|s and accelerates at 60m|s in 12s & then is uniformly decelerated to rest if the total time taken is 16s find the distance in metres during acceleration

Answers

Using equation of motion to calculate the distance covered during acceleration is 540m

What is Distance

Distance is the total length between two points, while displacement is the length between two points, but it also takes into account the direction of the motion. Distance is a scalar quantity, while displacement is a vector quantity.

In this problem, we can either draw a velocity - time graph or proceed to solve using equations of motions.

We are required to calculate the distance covered during the period of acceleration.

Data;

Initial velocity (U) = 30 m /sFinal velocity (V) = 60 m/sTime = 12s

a = v - u / t

a = acceleration

a = (60 - 30) / 12

a = 30 / 12

a = 2.5 m/s²

But we have another equation as

v² = u² + 2as

s = distance

60² = 30² + 2*2.5*s

x = 540

The distance covered is 540m

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what are the solutions of the equation x4 3x2 2 = 0? use u substitution to solve. and x = ±1 and x = ±i and x = ±i and x = ±1

Answers

The solutions of the equation is found for the values of x = ±√2i or x = ±i.

Explain the term imaginary number?A number that produces a negative square root is referred to as an imaginary number. Fundamentally, an imaginary number is indeed the square root of such a negative number does not have a concrete value.

An equation x⁴ + 3x² + 2 = 0, has been presented to us.

We are asked to discover the solutions of our supplied equation using substitution.

Our provided equation can be rewritten as: x⁴ + 3x² + 2 = 0

Considering that: u = x²

u² + 3u + 2 = 0

Factorizing the equation;

(u + 2)(u + 1)

or, u = - 2 and u = -1.

When we re-substitute the value of u, we obtain:

x² = -2 or x² = -1

x = ±√-2 or x = ±√-1

x = ±√(-1).2 or x = ±√-1

Now we shall employ imaginary unit i. That is a fact i² = -1.

x = ±√i².2 or x = ±√i²

x = ±√2i or x = ±i

Consequently, the solution obtained for the equation are- x = ±√2i or x = ±i.

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sales at a fast-food restaurant average $6,000 per day. the restaurant decided to introduce an advertising campaign to increase daily sales. to determine the effectiveness of the advertising campaign, a sample of 49 days of sales were taken. they found that the average daily sales were $6,300 per day. from past history, the restaurant knew that its population standard deviation is about $1,000. the restaurant wishes to test whether sales have increased as a result of the advertising campaign. if the level of significance is 0.05, what is the decision?

Answers

Answer: The null and alternative hypothesis 6000 > 6000 This is an one tailed test Test statistic 6300 = 1000 n= 49 Thus , test statistic is = 2.1 Q1. At 0.025 le

Step-by-step explanation:

Help please
Multiply.
-2w(-5-w)

Answers

Answer:

[tex]10w + 2w^{2}[/tex]

Step-by-step explanation:

To solve this, we have to apply the distributive property and simplify:

(-2w x -5) + (-2w x -w)

[tex]10w + 2w^{2}[/tex]

Answer:

[tex]10w + 2w {}^{2} [/tex]

Which of the following is the value of discriminant for √ 2x² − 5x+ √ 2 = 0?

Answers

Answer:

The value of the discriminant is 17.

Step-by-step explanation:

⭐What is the discriminant?

[tex]b^2-4ac[/tex]it is the radicand (the value inside of the radical) of the quadratic formula

Thus, we have to substitute the values a, b, and c from the quadratic equation we are given into the discriminant formula.

Let's identify what a, b, and c are.

[tex]y = ax^2 + bx + c[/tex]

[tex]y = \sqrt{2}x^2 -5x + \sqrt{2}[/tex]

a = [tex]\sqrt{2}[/tex]

b = -5

c = [tex]\sqrt{2}[/tex]

Now, substitute these values into the discriminant formula.

[tex]b^2 - 4ac =[/tex]

[tex](-5)^2 - 4(\sqrt{2}*\sqrt{2}) =[/tex]

[tex]25 -4(2) =[/tex]

[tex]25-8 =[/tex]

= 17

∴ The value of the discriminant is 17.

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Spontaneous dental hydroplosion is a disease makes your teeth spontaneously turn into liquid. To investigate whether a new drug can prevent the onset of this disease, Jim Halpert decided to perform a study in which half of the fourteen employees at Dunder Mifflin Scranton received the drug and the other half received a placebo. Neither Jim nor the employees were told who received which treatment, and the number of times a subjectâs teeth turned into liquid was recorded. This is an example of (A) A double-blind experiment. (B) A matched-paired experiment. (C) An experiment, but neither double-blind or matched-pair. (D) An observational study. In order to make thorough conclusions, the most important condition for statistical inference is usually that (A) the population distribution follows a Normal distribution exactly. (B) the data does not contain outliers. (C) the data follows the asymmetric, single-peaked distribution. (D) the data can be treated as a random sample from the population of interest. A study was taken at the large senior living retirement community, The Senior Living Community, found that the average age of residents is 73 years with a standard deviation of 6.1 years. A simple random sample of 100 residents is selected and the sample mean age !Ì("x-bar") of these residents is calculated. you know that the random variable X has approximately a normal distribution because of (A) the central limit theorem. (B) the 68-95-99.7 rule. (C) the population that youâve sampled from does not have a Normal distribution. (D) the law of large numbers.

Answers

For the study for investing the result of drugs in a particular diseases,

(1)This is an example of double blind experiment. So,correct option is option A

(2) The Correct option is option (C) i.e. the data can be treated as a random sample from the population of interest.

(3) The random variable X has approximately a normal distribution because of Central Limit Theorem i.e the Correct option is option (A).

Here , Spontaneous hydrostatic collapse is a disease in which teeth spontaneously turn into fluid. Jim Halpert decided to perform a study to find out if new drugs can prevent the development of this disease.

1. Since, neither researcher nor the employees were told who received which treatment, this is an example of a double-blind experiment.

2. In order to make thorough conclusions, the most important condition for statistical inference is usually that data can be treated as a random sample from the population of interest.

3. The sample mean age, X-bar of these residents has approximately a normal distribution because of the central limit theorem. Hence, we get all required answers for asking questions.

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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=99(1.04)^4

Answers

The percentage rate of increase or decrease of the function y=99(1.04)^4 is 4%

What is an exponential function?

This is a type of function that are of 3 main parts

the starting or initial value

base function

the exponents

Considering the given problem, y=99(1.04)^4

the starting = 99

the base = 1.04

the exponents = x

The base is what determines increase or decrease with a base of 1.04 shows a percentage increase is 4%

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Write a polynomial function that meets the stated condition.

The zeros are -2/3 and , and the constant term of the polynomial is -10.

Answers

The polynomial that has a factor (3x + 2) and the constant term negative 10 will be p(x) = 3x - 8.

How to get polynomials with zeroes?

Let a, b, c, and d are the zeroes of the polynomial.

Then the polynomial is given as,

⇒ (x - a)(x - b)(x - c)(x - d)

The degree of the polynomial will be greater than or equal to the number of zeroes.

The zeros are -2/3. Then the factor of the polynomial is given as,

x = - 2/3

3x = - 2

3x + 2 = 0

The polynomial that has a factor (3x + 2) and the constant term negative 10 will be given as,

p(x) = 3x + 2 - 10

p(x) = 3x - 8

The polynomial that has a factor (3x + 2) and the constant term negative 10 will be p(x) = 3x - 8.

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what is s for the following function

Answers

Step-by-step explanation:

you just need to put the value for t into the equation and then solve for s.

t = 3s + 2

t = 11

11 = 3s + 2

3s = 11 - 2 = 9

s = 3

t = 17

17 = 3s + 2

3s = 17 - 2 = 15

s = 5

t = 23

23 = 3s + 2

3s = 23 - 2 = 21

s = 7

t = 29

29 = 3s + 2

3s = 29 - 2 = 27

s = 9

what is the slope of the line whose equation is -3x 8y = -10.

Answers

Given a line with the equation -3x+8y=-10, its slope can be calculated using the slope intercept form of the line that is 3/8.

What is slope?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies). The slope of a line in mathematics indicates how steep a line is. It is also referred to as the gradient. The "change in y" over the "change in x" of a line is referred to as the slope.

Here,

-3x+8y=-10

y=mx+c

where m=slope of line

8y=3x-10

y=3x/8-10/8

slope=3/8

The slope of given line whose equation is -3x+8y=-10 is 3/8 using slope intercept form of line.

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He fits all of his boxes exactly into a larger box with a volume of 1,152
cubic inches. How many gift boxes are in the larger box? Explain how you know.

Enter the correct numbers in the boxes to complete the statement and equation.

Answers

on solving the provided the question, we got know that - width = 6 in, length = 16 in, and height = 12 in

Waht is factor?

Decomposing or decomposing an entity (number, matrix, polynomial, etc.) into another entity or product of coefficients, the multiplication of which yields the original number, matrix, etc. is known in mathematics as factorization or factorization .

A rectangular prism with the dimensions l, w, and h has the following volume:

[tex]V = l * w * h[/tex]

[tex]V = 1152 in^3\\[/tex]

[tex]l = 2w + 4\\h = 18 - w[/tex]

[tex]So,\\ V = l * w * h\\ \\ 1152 = (2w + 4) * w * (18 - w)1152 = (2w^2+ 4w) * (18 - w)\\ 1152 = 36w^2 + 72w - 2 w^3 - 4w^2\\ -2w^3 + 36w^2 - 4w^2 + 72w = 1152\\ -2w^3 + 32w^2 + 72w = 1152\\ -2w^3+ 32w^2 + 72w - 1152 = 0\\ -w^3+ 16w^2 + 36w - 576 = 0\\ w^3 - 16w^2 - 36w + 576 = 0\\ (w^3 - 36w) - (16w^2 - 576) = 0\\[/tex]

[tex]Factor:\\ w * w^2 - w * 36 - (16 * w^2 - 16 * 36) = 0\\ w(w^2 - 36) - 16(w^2 - 36) = 0\\(w - 16)(w^2 - 36) = 0\\(w - 16)(w^2 - 6^2) = 0\\(w - 16)(w - 6)(w + 6) = 0\\[/tex]

So,

w - 16 = 0, or w - 6 = 0, or w + 6 = 0.

w = 16, or w = 6, or w = -6.

Since width cannot be zero, w = –6.

l = 2 * 16 + 4 = 32 + 4 = 36 and h = 18 - 16 = 2 if w = 16

However, because the width must be smaller than the height (h > w), w 16.

l = 2 * 6 + 4 = 12 + 4 = 16 and h = 18 - 6 = 12 if w = 6, respectively.

Consequently, w = 6 in, l = 16 in, and h = 12 in

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A group of friends wants to go to the amusement park. They have no more than $280
to spend on parking and admission. Parking is $20, and tickets cost $40 per person,
including tax. Write and solve an inequality which can be used to determine a, the
number of people who can go to the amusement park.

Answers

[tex]\boxed{20+40a \leq 280}\\\\1+2a \leq 14\\\\2a \leq 13\\\\a\leq \frac{13}{2}[/tex]

However, since there must be a whole number of people, this rounds down to [tex]\boxed{a \leq 6}[/tex]

if line segment c b. bisects ∠acd, what additional information could be used to prove δabc ≅ δdbc using sas? select three options.

Answers

A) m∠ABC = 125° and AB ≅ DB ; B) ΔACD is isosceles with base AD ; D) CD = 52 cm.

What exactly are triangles?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the three sides' end-to-end connections at a point. The triangle's three angles add up to 180 degrees in total.

Knowing that ACD is isosceles with base AD indicates that AC and DC are congruent. As a result, we have two sides that are at an angle, or SAS.

A congruent relationship exists between AC and CD if we know that CD = 52 cm. As a result, we are left with two sides that include an angle.

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according to statistics reported on cnbc, a surprising number of motor vehicles are not covered by insurance. sample results, consistent with the cnbc report, showed 46 out of 200 vehicles were not covered by insurance. Develop a 95% confidence interval for the population proportion

Answers

The 95% confidence interval for the given population proportion is between 0.1716 to 0.2884.

How to find the confidence interval for a population proportion?

The confidence interval for a population proportion is calculated by the formula,

[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]

Where [tex]\bar{p}[/tex] is the sample proportion and α is the level of significance.

Calculation:

It is given that,

The statistics reported on CNBC projects, a surprising number of motor vehicles are not covered by insurance. The sample results are

The sample size n = 200;

The number of successes = 46

So, the sample proportion [tex]\bar{p}[/tex] = 46/200 = 0.23

For a 95% confidence interval, the level of significance is

α = 1 - 95/100 = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Then, the z-score for the value 0.025 is

[tex]z_{\alpha/2}[/tex] = 1.96 (from the table)

Thus, the confidence interval is

[tex]C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }[/tex]

⇒ C.I = 0.23 ± (1.96) × [tex]\sqrt{\frac{0.23(1-0.23)}{200} }[/tex]

⇒ C.I = 0.23 ± 1.96 × 0.0298

⇒ C.I = 0.23 ± 0.0584

So, the upper limit is 0.23 + 0.0584 = 0.2884 and the lower limit is 0.23 - 0.0584 = 0.1716.

Therefore, the 95% confidence interval for the given population proportion lies between 0.1716 to 0.2884.

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7. There are 84 people going camping.
a) A bus can take 42 people. How many buses
would be needed?
b) A van can take 12 people. How many vans
would be needed?
c) A car can take 4 people. How many cars
would be needed?

Answers

Answer: A) 2 buses B) 7 vans C) 21 cars

Step-by-step explanation:

You divide 84 by the number of people the vehicle can take.

For a. 84/42=2, so you need 2 buses.

For b. 84/12=7, so you need 7 vans

For c. 84/4=21, so you need 21 cars

Which equation represents a circle with a diameter of 10 units that is centered at (3,-7)

Answers

The equation of the given circle is

[tex](x - 3)^2 + (y + 7)^2 = 25[/tex]

What is a circle?

Circle is a two dimensional round figure in which every point on the figure maintains a fixed distance from a point known as the center of the circle.

The fixed distance is called the radius of the circle.

Diameter of circle = 10 units

Radius of the circle = [tex]\frac{10}{2}[/tex] = 5 units

Coordinates of center = (3, -7)

Equation of circle = [tex](x - 3)^2 + (y - (-7))^2 = 5^2[/tex]

[tex](x - 3)^2 + (y + 7)^2 = 25[/tex]

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(d) Use function notation to write g in terms of f.
1. g(x) = (x − 10)2
f(x)= x2
answer: g(x)= f(____)
2. g(x)= -x3-2
f(x)= x3
answer: g(x)= -f(____) + (____)
3. g(x)= -(x+6)2+2
f(x)= x2
answer: g(x)= -f(____) + (____)
4. g(x) = (x + 2)3 − 8
f(x)= x2
answer: g(x)= f(____) + (____)
5. g(x) = 8 − |x + 4|
f(x)= |x|
answer: g(x)= ____ - f(____)
6. g(x) = |−x + 5| + 7
f(x)= |x|
answer: g(x)= f(____) + (____)
7.

f(x)= √x
answer: g(x)= f(____) + (____)

Answers

The value of g in terms of f is:

[tex]x^{4} -20x^{2} +100[/tex]

[tex]x^{9} -2[/tex]

[tex]-x^{4} -12x^{2} -34[/tex]

[tex]8-||X|+4|[/tex]

[tex]|-|x|+5|+7[/tex]

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).