Steven entered a number into his calculator.
To this number, he added the square of the original number and the cube
of the original number.
Steven got the answer 182.267
Use a trial and improvement method to find the number that Steven first
entered into his calculator. Show your working.
Show your working

Answer:

Step-by-step explanation:

You want the complete solution (side lengths and angles) for a right triangle with leg lengths a=13 ft and b=16 ft.

Since the two leg lengths are given, it is convenient to use the inverse tangent relation to find one of the acute angles.

  Tan = Opposite/Adjacent

  tan(A) = a/b

  A = arctan(13/16) ≈ 39°

  B = 90° -A = 51°

The hypotenuse can be found using the Pythagorean theorem, or it can be found using trigonometry. We have just computed angle A, so we can use that value to find the hypotenuse of the triangle.

  Cos = Adjacent/Hypotenuse

  Hypotenuse = Adjacent/Cos

  c = b/cos(A) = 16/cos(39.093859°) ≈ 21 . . . . feet

Then the solution is ...

__

Additional comment

Note the calculator is set to DEG mode so the angles are reported in degrees.

The hypotenuse is found using the original full-precision value of the angle, not the rounded value required to answer the problem statement.

Answer: A. To find the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the probability that his height is less than or equal to 72 inches. Since the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, we can use the standard normal distribution to find this probability.

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the height of a male passenger from the given distribution to the standard normal distribution by using the formula:

$z = \frac{x - \mu}{\sigma}$

where $x$ is the height of the male passenger, $\mu$ is the mean height of 69 inches, and $\sigma$ is the standard deviation of 2.8 inches. Substituting these values into the formula gives us:

$z = \frac{72 - 69}{2.8} = \frac{3}{2.8} = 1.0714$

Since the standard normal distribution is symmetric, the probability that a male passenger's height is less than or equal to 72 inches is the same as the probability that his height is greater than or equal to 72 inches. We can find this probability by looking up the value of $z = 1.0714$ in a standard normal table, which gives us a probability of 0.8413. Therefore, the probability that a male passenger can fit through the doorway without bending is 0.8413.

B. To find the probability that the mean height of the 175 men is less than 72 inches, we need to find the probability that the sample mean is less than 72 inches. Since the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, the sample mean will also be normally distributed with a mean of 69 inches and a standard deviation of $\frac{2.8}{\sqrt{175}} = 0.32$. We can use the standard normal distribution to find the probability that the sample mean is less than 72 inches.

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the sample mean from the given distribution to the standard normal distribution by using the formula:

$z = \frac{x - \mu}{\sigma}$

where $x$ is the sample mean, $\mu$ is the mean of 69 inches, and $\sigma$ is the standard deviation of 0.32. Substituting these values into the formula gives us:

$z = \frac{72 - 69}{0.32} = \frac{3}{0.32} = 9.375$

Since the standard normal distribution is symmetric, the probability that the sample mean is less than 72 inches is the same as the probability that the sample mean is greater than 72 inches. We can find this probability by looking up the value of $z = 9.375$ in a standard normal table, which gives us a probability of 0.0000. Therefore, the probability that the mean height of the 175 men is less than 72 inches is 0.0000.

C. When considering the comfort and safety of passengers, the result from part (a) is more relevant than the result from part (b). This is because part (a) tells us the probability that a randomly selected male passenger can fit through the doorway without bending, which is directly relevant to the comfort and safety of the passengers. In contrast, part (b) tells us the probability that the mean height of the 175 men is less than 72 inches, which is not directly relevant to the comfort

D. Women are ignored in this case because the problem only asks about the heights of men. The problem states that the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, and does not provide any information about the heights of women. Therefore, we cannot use the given information to find the probability that a female passenger can fit through the doorway without bending.

Answer:

there are no equations below...

Step-by-step explanation:

answer here!

sry it is a bit messy

Answer:

1) 11001 base 2

2)133 base 5

1) To convert base 10 into base 2

25/2= 12remainder 1

from this point on, the remainders will be replaced by r

12/2= 6r0

6/2=3r0

3/2=1r1

1/2=0r1

The remainders are then written down from the bottom up

= 11001

2) To convert 101011 base 2 into base 5

101011= 1×2⁵ + 0×2⁴+ 1×2³+ 0×2² + 1×2¹ + 1×2⁰

=1×32 + 0×16 + 1×8+ 0×4+1×2+1×1

=32+0+8+0+2+1

=43 base 10

Then convert 43 base 10 to base 5

43/5=8r3

8/5=1r3

1/5=0r1

=133 base 5

Answer: I think its 3.5

Step-by-step explanation:

If UV≅PM then UV≅PM → Definition of congruence, EF≅EF → Reflexive property of congruence, If AB≅LM and LM≅ST then AB≅ST  → Transitive property of congruence.

A statement that is accepted as true without evidence, also referred to as an axiom. Lemmas and theorems are deduced from postulates, which serve as their fundamental building block. For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry.

A) If and only if two segments have equal amounts of each, they are congruent.

If UV≅PM then UV≅PM → Definition of congruence

B) An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.

EF≅EF → Reflexive property of congruence

C) According to the transitive characteristic of congruence, "all sides are congruent to each other if two sides are congruent to the third side."

If AB≅LM and LM≅ST then AB≅ST  → Transitive property of congruence

D) Actually fairly straightforward, equality has the symmetric condition. According to this criterion, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the equation still makes sense.

If AB=XY then XY =AB  → Symmetric property of equality

E) The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.

If 2x-3=13 then 2x=16 → Addition property of equality

Add 3 on both the sides of equation we get

2x-3+3=13+3

⇒ 2x=16

Therefore, the statement If 2x-3=13 then 2x=16 follows addition property of equality.

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Answer:

8 weeks

Step-by-step explanation:

The two equations I got from this are y=16x+42 and y=-70+30x

I graphed both equations online to see what the intersection would be the intersection between both equations is (8,170). I think that this means that in 8 weeks they would both be at 170 dollars, so I think that it will take them 8 weeks to have the same amount of money saved

(if wrong, im sorry..)

The number of weeks it will take them to have saved the same amount of money will be 8.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Sharon began with $42 in her financial balance and added $16 each week. Neil began $70 underwater and kept $30 each week.

Let 'x' be the number of weeks and 'y' be the total amount. Then the equations are given as,

y = 16x + 42              ...1

y = 30x - 70             ...2

From equations 1 and 2, then we have

30x - 70 = 16x + 42

14x = 112

x = 8

The number of weeks it will take them to have saved a similar measure of cash will be 8.

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Amy buys 12 envelopes for 26p each, so the total cost is 12 x 26 = 312p. She pays with a £5 note, which is equal to 5 x 100 = 500p. Therefore, she gets 500 - 312 = 188p in change. This is equal to £1.88.

Mathematics deals with the relationship between two numbers or quantities using the notions of ratio and proportion. Two numbers are compared in a ratio, which is often represented as a fraction. For example, the ratio of pounds to oranges in a basket could be 3:2, implying that there are three apples for every two oranges. Contrarily, proportion is the connection between two ratios. It is an equation, in other words, when two ratios are equal. The ratio of apples to oranges in a basket may be 3:2, whereas the ratio of apples to all the other fruits in the basket might be 9:11. In this case, the two ratios are proportionate since 3/2 = 9/11.

How to solve?

Amy buys 12 envelopes for 26p each, so the total cost is 12 x 26 = 312p. She pays with a £5 note, which is equal to 5 x 100 = 500p. Therefore, she gets 500 - 312 = 188p in change. This is equal to £1.88.

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On solving the provided question, the capital that is placed at 25% for 3 years, to obtain an interest of $ 1620 will be $3,164.06

interest you receive is equal to as - compound interest. Using simple math, you can see how this works: if you have $100 and it earns 5% interest annually, you will have = $105 at the end of the 1st year. You'll have = $110.25 at the conclusion of the 2ndyear.

To calculate, we will use the following

[tex]First, convert R as a percent to r as a decimal[/tex]

r = R/100

r = 25/100

r = 0.25 rate per year,

Then solve the equation for A

[tex]A = P(1 + r/n)^{(nt)}[/tex]

[tex]A = 1,620.00(1 + 0.25/1)^{(1)(3)}[/tex]

A = 1,620.00(1 + 0.25)(3)

A = $3,164.06

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Answer: [tex]-\frac{1}{2}, -\frac{1}{4} , -\frac{1}{6}, -\frac{1}{7} , -\frac{2}{3}[/tex]

Step-by-step explanation:

A simple way to find a rational number is to make sure the fraction is between the given numbers. Below are five examples, but there are many more.

[tex]-\frac{1}{2}, -\frac{1}{4} , -\frac{1}{6}, -\frac{1}{7} , -\frac{2}{3}[/tex]

The two equations that can represent the relationship is

i. x +( x+1) + (x+2) = 42 and

Ii. (x-1) +x + (x+1) = 42 ( option A and C)

Consecutive integers are those numbers that follow each other. They follow in a sequence or in order. For example, a set of natural numbers are consecutive integers.

For example, 4,5,6,7 are consecutive integers. This means that the difference between two consecutive numbers is 1.

If the first number is x, then the second number is (x+1 ) and the third number is (x+3)

The sum of the three number is x +( x+1) + (x+2) = 42

if the second number is x, then the first number is (x-1) and the third number is x+1

Therefore the sum of the three numbers can also be written as (x-1) +x + (x+1) = 42

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The numbers that are located to the right of - 4 on a horizontal number line is

A.) - 1/2

B.) 5 1/2

D.) - 3 2/3

E.) - 1 2/3

G.) 2 /3

H.) - 4

What is number line?

A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.

Given the numbers :

A. -1/2 ; B. 5 1/2 ; C. -4 2/3 ; D. -3 2/3 ; E. -1 2/3 ; F. -5 1/2 ; G. 2/3 ; H. -4

Select which are located to the right of - 4 1/3 on an horizontal number line;

Kindly note that ; numbers located to the right of - 4 1/3 will be greater.

Hence, all numbers in the option greater Than - 4 1/3 are correct.

All positive numbers are located to the right ;

All negative greater than - 4 1/3

A.) - 1/2

B.) 5 1/2

D.) - 3 2/3

E.) - 1 2/3

G.) 2 /3

H.) - 4

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Answer:

66,726

Step-by-step explanation:

Answer:

666,722

Step-by-step explanation:

1 + 59 + 666,662

= 60 + 666,662

= 666,722

i hope this helped

Answer:

Each Girl scored 3.71 points

Each boy scored 12 points

The least number of seats she is setting up 40 seats are needed.

The least number is zero (0). Zero (0) is the smallest natural number and is the additive identity of the set of whole numbers. It is the only number that is neither positive nor negative and is, therefore, regarded as neither odd nor even. Zero (0) is essential in mathematics and is used to represent the absence of a quantity. It is also used to represent the additive identity of real numbers and complex numbers.

Given: Mandy can place 8 seats at each table or 10 seats at each table with no left over.

We have to find the least number of seats needed.

Find the prime factors of 8:

⇒ 8 = 2 x 2 x 2 = 8 = 2³

Find the prime factors of 10:

⇒ 10 = 2 x 5

Find the LCM of 8 and 10:

⇒ 8 = 2³

10 = 2 x 5

LCM = 2³ x 5

LCM = 40

Hence, a minimum of 40 seats are needed.

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Answer:

137

Step-by-step explanation:

triangles always equal 180 degrees for internal angles

20+23-180

Answer:

12? lol

Step-by-step explanation:

<3

The required solution of the given numerals is,
1. 3 + 4k + k < 43, Option D is correct.
2. The oldest Kim could be 7 years old. Option D is correct.

Given that,
Josh is 3 years older than 4 times Kim's age. The sum of their ages is less than 43. Select the correct inequality for the situation, then determine the oldest age Kim could be.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
J = 4k + 3
And
J + K < 43
4K + 3 + K < 43
5k < 40k
k < 8
K could be K = 7

Thus, the required solution of the given numerals is,
1. 3 + 4k + k < 43, Option D is correct.
2. The oldest Kim could be 7 years old. Option D is correct.

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Answer:

answer is c

Step-by-step explanation:

I learned matrix

If two sides of the triangle is congruent then the triangle is known as isosceles triangle.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The two triangular legs and their opposing angles are congruent in an isosceles triangle.

In the given triangle, the sides of a triangle are 10 cm, 8 cm, and 10 cm.

In the triangle, the two sides of the triangle are congruent.

If two sides of the triangle is congruent then the triangle is known as isosceles triangle.

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19.89% is the percentage decrease of the depth of the lake from January to August.

A quantity or ratio can be expressed as a percentage of 100 by using the word "percentage." Comparing two or more numbers and illustrating how significantly one number differs from the other in proportion to the whole is a popular usage for this technique. If a baseball originally costs $12 and is discounted by 20%, for instance, its new price would be $12 x 20/100 = $2.40 less than the original price. In other words, after the reduction, the ball will cost $12 - $2.40 = $9.60. A percentage may often be determined by dividing a quantity by its entirety and multiplying the result by 100. For instance, if a baseball bat costs $100 and is reduced by 30%, its new cost would be $100 x 30/100, which equates to $30 less.

How to solve?

The depth of the lake decreased by 943 - 754.4 = 188.6 feet from January to August.

The percentage decrease is (188.6 / 943) x 100 = 19.89%

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Answer: 37.80

Step-by-step explanation:

The margin of error, a statistic, is a measure of how much random sampling error there is in survey data.

The margin of error exists 0.07728.

A statistic known as the margin of error describes how much random sampling error there is in survey data. Less faith should be placed in a poll's results representing the outcome of a population census as the margin of error increases.

A survey's margin of error, also known as the confidence interval, is a measurement of error in the data, particularly when the sampling method of a survey is used. This indicator lets researchers know to what extent survey findings should be taken as representative of the entire community under study.

Given : n = 36

x-bar = 0.82407

s = 0.00567

Confidence level 95%

The 2 - critical Valve = 2.03

A) Let the equation be

[tex]$S F=\sqrt{\frac{\bar{x}(1-\bar{n})}{n}}[/tex]

substitute the values in the above equation, we get

[tex]$\Rightarrow \sqrt{\frac{(0.82412)(1-0.82412)}{100}}$$[/tex]

S E  = 0.03807

B) Margin of error = (0.03807)(2 × [tex]I_2[/tex])

Margin of error = 0.07728

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The value of underlined digit is Zero ten million

The foundation of our entire number system is place value. In this system, the value of a digit in a number is determined by where it appears in the number. The digits in the numbers 42,316 and 61,432 are different from one another. Each place represents ten times the value of the place to its right in the standard system, also known as the base ten number system (or decimal system).

Given ,

9 ,603 ,450, 503

We know that

1   Thousand

2  Ten thousand

3    Hundred thousand

4   One   Million

5     Ten million

So the value of the underlined digit is 5 ten million

The complete question is : what is the value of the underlined digit 9 ,603 ,450, 503

A) zero ten thousands

B) zero hundred thousands

C) zero one millions

D) zero ten millions

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Answer: 1⋅3+1(−√2)+√2⋅3+√2(−√2)

Step-by-step explanation:

Answer:

x=42

Step-by-step explanation:

Figure A has been scaled by 2/7, so we know that[tex]x * 2/7 = 12.[/tex] Multiplying both sides by 7 gives us [tex]2x = 84[/tex]. Dividing both sides by 2 gives us that x = 42. This is our answer.

Answer: 42

Step-by-step explanation:

2/7x=12

x = 12 * 7/2

x=84/2

x=42

Angle A = 40 degrees

Angle C = 70 degrees

Side AC = 12 cm