Terms from two sequences are given in tables below. Which of the following statements are true? Select all that apply.
Answers
As per the terms from the two sequences given in tables as attachment hereby along with the question statement, the following statements from the provided options are true.
(i) [(a₁) > (g₂)]
(iv) Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ).
As per the question statement and the reference tables attached thereby along with the question, we are provided with terms from the two sequences in table format, and five statements based on the sequences.
We are required to determine which statements among the five, are true.
To solve this question, we will use the trial-and-error method, where we will consider individual statement and assess it's honesty.
First statement is [(a₁) > (g₂)], which is true. As we can see from the table, that, [(a₁) = 10] and [(g₂) = 4], i.e., (10 > 4), or, [(a₁) > (g₂)].
Second statement is that, "The constant difference for (aₙ) is 10" which is False. We can clearly see from the table that, (a₁ = 10), (a₂ = 15), (a₃ = 20), (a₄ = 25) and so on, and [(25 - 20) = (20 - 15) = (15 - 10) = 5], i.e.,
[(a₄ - a₃) = (a₃ - a₂) = (a₂ - a₁) = 5]. Hence, the common difference for (aₙ) is 5, and not 10.
Third statement is that, "(aₙ) can be modelled by a linear function, and (gₙ) can be modelled by an exponential function" which is true for the first part, but false for the second, making the complete statement false as whole.
From the left hand side table, we can see that, (a₂ = 15) and (a₁ = 10),
Or, [a₂ = (10 + 5)]
Or, [a₂ = (a₁ + 5)]
Similarly, (a₃ = 20),
Or, [a₃ = (15 + 5)]
Or, [a₃ = (a₂ + 5)]
That is, we can generalise (aₙ) as
[aₙ = {(aₙ₋₁) + 5}] where, (n = 2, 3, 4, 5...) and (a₁ = 10).
Hence, (aₙ) can be modelled by a linear function.
But from the right hand side table, we can see that, (g₂ = 4) and (g₁ = 2),
Or, [g₂ = (2 * 2)]
Or, [g₂ = 2g₁]
Similarly, (g₃ = 8),
Or, [g3 = (2 * 4)]
Or, [g₃ = 2g₂], it goes on for (gₙ).
Therefore, we can generalise (gₙ) as
[gₙ = 2*(gₙ₋₁)] where, (n = 2, 3, 4, 5...) and (g₁ = 2).
Here, (gₙ) can also modelled as a linear function and not as a exponential function (which goes in the form of "xⁿ").
Coming to the fourth statement, "Initially (aₙ) is greater than (gₙ), and as "n" gets larger, (gₙ) is greater than (aₙ)" is true, as from both the tables,
For (n = 5), [aₙ = a₅ = (a₄ + 5) = (25 + 5) = 30],
And [gₙ = g₅ = (2 * g₄) = (2 * 16) = 32], which is greater than 30,
Or, [(g₅) > (a₅)].
Similarly, for (n = 6), (a₆ = 35) while (g₆ = 64), i.e., [(g₆) > (a₆)], and it continues for greater values of "n".
Coming to the last statement, that [a₁₀ > g₆], is false. As we can observe from the both the tables and their sequence,
For (n = 5), (aₙ = 50), for (n = 6), (aₙ = 35), for (n = 7), (aₙ = 40), for (n = 8), (aₙ = 45), for (n = 9), (aₙ = 50) and for (n = 10), (aₙ = 55),
While on the other hand, for (n = 5), (gₙ = 32) and for (n = 6), (gₙ = 64).
Since (64 > 55), therefore, [(g₆) > (a₁₀)].
Sequence: In mathematics, a sequence is an enumerated collection of objects in a particular order, and repetitions being allowed.To learn more about Sequence, click on the link below.
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Related Questions
14.2 cm correct 1 decimal place
Answers
The 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.
What is rounding off the number?Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.
It is given that:
14.2 cm correct 1 decimal place
14.2
Rounded to the nearest 0.1 or
the Tenths Place.
Rounded to the nearest tenth place. The 2 in the tenth place rounds down to 2 or stays the same because the digit to the right in the hundredth place is 14.2
Thus, the 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.
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The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).
Write a translation rule that maps point D(7,-3) onto point D'(2,5)
PLLS HELP if you do it in simple words and step by step i will give brainliest
Answers
Answer:
translates up 8 and 5 left
Step-by-step explanation:
To find the distance (x) it translate up, -3 + x = 5 where x = 8
To find the distance (x) it translate left, 2 + x = 7 where x = 5
Answer:
(x, y) → (x-5, y+8)
Step-by-step explanation:
A translation is a type of transformation that moves a figure up, down, left or right.
Calculate the change in the coordinates by subtracting the coordinates of point D from the coordinates of point D':
[tex]\implies (x_{D'}-x_D, y_{D'}-y_D)[/tex]
[tex]\implies (2-7, 5-(-3))[/tex]
[tex]\implies (-5, 8)[/tex]
Therefore, to map point D onto point D', move 5 units left and 8 units up.
Therefore, the translation rule that maps point D(7, -3) onto point D'(2, 5) is:
(x, y) → (x-5, y+8)Q.4 Find the median class.
Size of the shoe No. of pair sold
3 4
4 18
5 25
6 12
7 5
8 1
Answers
Answer: Median = 5
=====================================================
Explanation
Given Table of Data
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Size of the shoe} & \text{No. of pair sold}\\\cline{1-2}3 & 4\\\cline{1-2}4 & 18\\\cline{1-2}5 & 25\\\cline{1-2}6 & 12\\\cline{1-2}7 & 5\\\cline{1-2}8 & 1\\\cline{1-2}\end{array}[/tex]
The second column is the set of frequencies. Adding up those frequencies gets us
4+18+25+12+5+1 = 65
There are 65 total shoes.
Divide this in half
65/2 = 32.5
There are 32 values below the median, and 32 values above it. That's 32+32 = 64 values so far. When including the median value itself we have 32+1+32 = 65 values total. This only works when the sample size is odd.
---------------------------
What we'll do is add up the partial sums of the frequency values.
The goal is to get to a sum of 33, or larger, because the median is in the 33rd slot.
Adding the first two frequencies gets us 4+18 = 22. This is not 33 or larger, so we move on.
Adding the first three frequencies gets us 4+18+25 = 22+25 = 47 which is 33 or larger.
What this tells us is that the median corresponds to the third row of the table, since we added the first three frequencies to get to 33 or larger.
The median must be 5.
c) Suppose that you take a random sample of 5,000 people from the U.S. population.Make a table that shows the expected number of people in your sample who come fromeach of the four age groups
Answers
In order to determine the number of people in the sample for each age group, here are the steps:
1. Determine what proportion in the entire population the population of each group. To get the proportion, simply divide the population of each respective group by the entire population.
2. To get the number of samples for each group, multiply the proportion by 5,000 and round the answer to the nearest whole number.
Now, let's apply the steps above in each group.
Let's start with ages under 18.
[tex]\begin{gathered} Proportion:74,181,467\div308,745,538=0.240267333 \\ Number\text{ }of\text{ }Samples:0.240267333\times5,000=1,201.33\approx1,201 \end{gathered}[/tex]Hence, we are expected to have 1,201 people aged under 18 in the sample.
For those aged 18 - 44,
[tex]\begin{gathered} Proport\imaginaryI on:112,806,642\div308,745,538=0.3653709224 \\ Number\text{ }of\text{ }Samples:0.3653709224\times5,000=1,826.85\approx1,827 \end{gathered}[/tex]Hence, we are expected to have 1,827 people aged 18-44 in the sample.
For those aged 45 - 64,
[tex]\begin{gathered} Proportion:81,489,445\div308,745,538=0.2639372395 \\ Number\text{ }of\text{ }Samples:0.2639372395\times5,000=1,319.68\approx1,320 \end{gathered}[/tex]The expected number of samples for people aged 45-64 is 1,320.
Lastly, for aged 65 and over,
[tex]\begin{gathered} Proportion:40,267,984\div308,745,538=0.1304245051 \\ Number\text{ }of\text{ }Samples:0.1304245051\times5,000=652.12\approx652 \end{gathered}[/tex]The expected number of samples for people aged 65 and over is 652.
To summarize, we have:
Age under 18 ⇒ 1,201 samples
18 - 44 ⇒ 1,827 samples
45 - 64 ⇒ 1,320 samples
65 and over ⇒ 652 samples
.
the weight of items produced by a machine is normally distributed with a mean of 7 ounces and a standard deviation of 3 ounces. what percentage of items will weigh between 4.3 and 8.65 ounces? a. 47.52%
Answers
27.80% is percentage of items .
What percentage means?
Percentage ,a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.Mean = 7
standard deviation = 3 ounces
Required % = p (5.6<x < 7.1 ) × 100 = ?
z = x - μ/σ = 5.6 - 7/2
z = 7.1 - 7/2 = 0.05
∴ P(5.6 < x < 7.1 ) = p ( - 0.7 < z < 0.05 )
p( z < 0.05 ) - p ( z < - 0.7)
= 0.51994 - 0.24196 ≅ 0.2780
So, required % = 0.2780 × 100
= 27.80%
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R obery and dora need to write 4,300,000,000 using scentific notation robert wrote 4,300,000,000=4.3 10 9 whick descrbes. Whose number is correct and the reason it is
Answers
The number 4,300,000,000 in scientific notation is 4.3x10⁹.
What is a number?
A number is a quantitative entity that may be used to tally, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.
The number 4,300,000,000 in scientific notation is 4.3x10⁹.
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Find the measure of the exterior angle.
Answers
The measure of the exterior angle is a = 54
Where is the exterior angle?
The angle formed by a polygonal side and its extended neighboring side.The angle at all between the side of a shape and a line that extends from the next side is known as the exterior angle. The result of adding the interior and outside angles is a 180° straight line. "Supplementary Angles" is what they are.the exterior angle 2a = a + 10 + 44
2a = a + 54
2a - a = 54
a = 54
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The front suspension system of a passenger car typically has coiled springs attached to the front wheels. a typical spring has a spring constant k of about 82,000 k/m
Answers
If the front suspension system of a car has coiled springs of spring constant(k) of about 82,000N/m attached to the front wheels, then the force required to compress this spring by 1.2 cms will be 984N.
As per the question statement, the front suspension system of a passenger car has coiled springs attached to the front wheels and a typical spring has a spring constant "k" of about 82,000 k/m.
We are required to calculate the force required to compress this spring by 1.2 cms
To solve this question, we will need to apply the formula to calculate the force to compress a spring, which is known as the Hooke's Law. So, as per the Hooke's Law, the force (F) required to compress a spring of spring constant (k) by "x" units, can be represented as
[F = (k * x)]
Now comparing the RHS of the Hooke's Law equation with the data provided in the question statement, we get, (k = 82000 N/m) and
(x = 0.012 m), and using these values in the Hooke's law equation, we get, the force required to compress a spring of spring constant(k) of about 82,000N/m by 1.2 cms will be (82000 * 0.012)N = 984 N.
Spring Constant: The magnitude of force required to compress or stretch a spring by unit distance, is known as it's spring constant, and it varies from spring to spring, typically being based on the constituent elements of the spring.To learn more about Spring Constants, click on the link below.
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which is closest to 8? 7.5 , 7 6/10 , 7 2/5 , 7.02?
Answers
Answer:7 6/10 is the answer if you turn a fraction into a decimal like so
7.5=7.5, 7 6/10=7.6, 7 2/5=7.4, 7.02=7.02 i hope i helped
Step-by-step explanation:
Answer: [tex]7\frac{6}{10}[/tex] is closest to 8.
Step-by-step explanation:
[tex]7\frac{6}{10} =\frac{70}{10} +\frac{6}{10} = \frac{76}{10} = 7.6[/tex]
[tex]7\frac{2}{5} = \frac{35}{5} +\frac{2}{5} =\frac{37}{5} =7.4[/tex]
7.02 < 7.4 < 7.5 < 7.6
7.02 < [tex]7\frac{2}{5}[/tex] < 7.5 < [tex]7\frac{6}{10}[/tex]
what is the height of the candle after 7 hours
Answers
Let
y -----> candle heigh in centimeters
x ----> burning time in hours
In this problem we have the ordered pairs
(5,22.5) and (17,16.5)
step 1
Find out the slope
m=(16.5-22.5)/(17-5)
m=-6/12
m=-1/2 -----> is negative because is a decreasing function
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=-1/2
point (5,22.5)
substitute
22.5=-(1/2)(5)+b
solve for b
b=22.5+2.5
b=25
therefore
y=-(1/2)x+25
step 3
For x=7 hours
substitute in the equation
y=-(1/2)(7)+25
y=-3.5+25
y=21.5 cmA car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 1/35 of a gallon of gas to go 1 mile
Answers
Answer:
525 miles is that was what was being asked
Step-by-step explanation:
sorry I don't know the quest but the car can travel a total of 525 miles with 15 gallons in the tank
15 times 35=525
450 x 670 - 80 x 500 = ?
Answers
Answer:
261 500
Step-by-step explanation:
450x670-80x500
301500-80x500
301500-40000
261500
Given f(x)= -6x+7, what are f(3) and f(-5). show your work please!!
f (3)=
f (-5)=
Answers
Answer:
f(3) = -11
f(-5) = 37
Step-by-step explanation:
f(x) = -6x + 7
We want to find f(3) and f(-5)
To do so we substitute the input with any x in the equation and evaluate.
f(3) = -6x + 7
==> substitute all x's with the input, 3
f(3) = -6(3) + 7
==> multiply -6 and 3
f(3) = -18 + 7
==> add -18 and 7
f(3) = -11
f(-5) = -6x + 7
==> substitute all x's with the input -5
f(-5) = -6(-5) + 7
==> multiply -6 and -5
f(-5) = 30 + 7
==> add 30 and 7
f(-5) = 37
How many seconds does it take for lighting to strike 7250
Answers
Answer:
Pues hablemos primero de lo que sucede antes de apagar la luz y usemos como ejemplo el viaje de un solo fotón.
Un fotón proveniente de un bombillo de luz blanca se dispara en línea recta hacia la pared. El material que cubre la pared, en este caso la pintura, tiene ciertas propiedades físicas y la energía del fotón es absorbida por un electrón de algún átomo de esa superficie. Ocurre una excitación del electrón, el cual ahora tiene más energía de la que normalmente tiene en su estado fundamental, y para regresar a su estado fundamental emite parte de esa energía como un nuevo fotón, este último de menor energía (frecuencia) que el anterior. La frecuencia dependerá del material y esa nueva frecuencia es la que da color a la pared. La luz blanca está compuesta por fotones de distintas frecuencias. Los de baja frecuencia son absorbidos y lo que se emite es en forma de calor, lo cual no puedes ver con tus ojos. Los de alta frecuencia tienen suficiente energía para que la energía que se re-emite sea visible y posiblemente sea re-emitida, cada vez con menos energía. Uno habla de que la luz “rebota” en el objeto. (Aunque “rebotar” no es necesariamente la acción correcta, voy a usar el término para simplificar).
Ahora digamos que ese fotón que “rebotó” en la pared rebota en otra pared y otra pared. Ese fotón es solo visible si en ese rebotar llega a tu ojo antes de que su energía sea demasiado baja. No podemos ver el calor ni las microondas que son fotones de baja energía. Al final la energía se va a convertir en calor, el cual es invisible al ojo humano.
Ese es el trayecto de un solo fotón. El bombillo produce un flujo de fotones en todas direcciones. Hay que recordar que esos fotones viajan a la velocidad de la luz. Cuando el bombillo se apaga, se interrumpe el flujo de fotones. Si se movieran a la velocidad del agua en una manguera, verías el flujo rebotando por varios segundos hasta que los fotones que más han rebotado desaparecen de tu vista por aquello de la baja frecuencia energética. Pero al viajar a la velocidad de la luz, el tamaño de la habitación se hace irrelevante y nuestra experiencia es prácticamente instantánea.
¿A donde va la luz? La luz no sale de la habitación sino que la calienta.
7/6 x 3 how to slove
Answers
The expression given: 7/6 x 3 can be calculated to get 7/2
what is multiplication?This is a basic math operation that helps to determine the product of two or more numbers.
The numbers given here include a whole number and a fraction
What is a fraction?A fraction refers to classification of numbers to be represented as having a stroke dividing the two groups of numbers.
The numbers on top is referred to as numerators while the numbers below is referred to as the denominator
in the question the fraction is 7/6: The numerator is 7 while the denominator is 6
how to solve the multiplication problem= 7/6 * 3
= 7/2
= 3.5
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suppose that your boss must choose three employees in your office to attend a conference in jamaica. because all 18 of you want to go, he decides that the only fair way is to draw names out of a hat. what is the probability that you, sharon, and robert are chosen? enter a fraction or round your answer to 4 decimal places, if necessary.
Answers
The probability that I, Sharon, and Robert are chosen is 0.0012
What is the formula for calculating combinations?
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.
The total number of employees=18
The Boss must choose 3 employees to attend the conference.
The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex] .
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations,.
So, [tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}[/tex]
[tex]^{18}C_{3}=\frac{18!}{(15)! 3!}[/tex]
[tex]^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]
[tex]^{18}C_{3} =816[/tex]
The probability that I, Sharon, and Robert are chosen is [tex]\frac{1}{816}[/tex] = 0.0012
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The probability that I, Sharon, and Robert are chosen is 0.0012
What is the formula for calculating combinations?
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.
The total number of employees=18
The Boss must choose 3 employees to attend the conference.
The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex] .
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations,.
So,
[tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}^{18}C_{3}=\frac{18!}{(15)! 3!}^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]
[tex]^{18}C_{3}=816[/tex]
The probability that I, Sharon, and Robert are chosen is = 0.0012
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You bring 1.5 dozen bagels to school.
A dozen bagels cost $5.98.
You used a coupon that took $1.00 off the total.
Answers
Because you do 5.98 plus half of 5.98 and then minus a dollar
What dose 10x+9-6x=-19 mean
Answers
Answer:
it algebra
Step-by-step explanation:
10x-6x=4x
Then the equation becomes
4x+9=-19
Then you subtract the 9 from -19
4x=-28
Now you have to separate the 4 from x
4x/4 and -28/4
So now you get
X=-7
Simplify the expression (2 − 5i)(3 + 7i) − (4 + 3i) and please be sure to explain your steps!
Answers
Answer:
2-33i
Step-by-step explanation:
(2 − 5i)(3 + 7i) − (4 + 3i) |Set up equation|
6+14i-15i-35i-(4+3i) |Multiply the numbers in the parentheses together using the distributive property|
6-1i-35i-(4+3i) Subtract like terms
6-36i-(4+3i) Subtract like terms
6-4-36i+31 Open parentheses and put like terms together
2-33i Answer
Hope this helped!
help me wwqưqưeqưeqưeqưeqưeqư
Answers
Answer:
Step-by-step explanation:
So, what you need to do is find out the formula for this question. And your answer will come out to be x=32
2
Write the decimal as a percent. .065
A
65%
B
650%
C
6.5%
D
.65%
Answers
The value of percent of the decimal .065 is 6.5 %.
We are provided with the value .065 .
The ratio or a number expressed as a fraction of 100 is referred to as percentage. It is denoted using the percent sign % .
We have, .065 . We need to convert this value in the percentage. certain steps need to be followed to convert this value in the percentage. These steps are mentioned below;
.065
Multiply this above mentioned value by 100 to convert it into percent.
.065 × 100
= 6.5 %
So, percent of the decimal value is 6.5 %.
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Find the values of the constant p q and r in such that when the polynomial f(x)=x^3 +px^2+ qx+ r is divided by (x+2),(x-1),and (x-3) the remainders are respectively -48,0 and 2 hence actoreise f(x) completely
Answers
In the polynomial expression f(x) = x³ + px² + qx +r, the values of p is 1/5, q is -66/5 and r is 12.
Polynomial:
Polynomial means an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Given,
Here we have the polynomial f(x) = x³ + px² + qx +r
And it is divisible by (x+2),(x-1),and (x-3) the remainders are respectively -48,0 and 2.
Here we need to find the value of p, q and r.
Let us consider that the equations,
x + 2 = 0 then x = -2
x - 1 = 0 then x = 1
x - 3 = 0 then x = 3.
Now, apply these values on the polynomial expression then we get,
f(-2) = (-2)³ + p(-2)² + q(-2) +r = -48
f(-2) = -8 + 4p - 2q +r = -48
f(-2) = 4p - 2q +r = -48 + 8
f(-2) = 4p - 2q + r = -40 ----------------------(1)
Apply the value of x as 1, then we get
f(1) = (1)³ + p(1)² + q(1) +r = 0
f(1) = 1 + p + q + r = 0
f(1) = p + q + r = -1 ----------------------(2)
Apply the value of x as 3, then we get
f(3) = (3)³ + p(3)² + q(3) + r = 2
f(3) = 27 + 9p + 3q + r = 2
f(3) = 9p + 3q + r = -25 ----------------------(3)
Now we have to solve the equation (2) and (1), then we get,
=> (4p -p) + (-2q - q) + (r - r) = -40 - (-1)
=> 3p -3p = -39
Divide it by 3, then we get
=> p - q = -13 ----------------------(4)
Similarly, solve equations (2) and (3), then we get,
=> (9p - p) + (3q - q) + (r - r) = -25 - (-1)
=> 8p + 2q = -24
Divide it by 2, then we get,
=> 4p + q = -12 ---------------------------(5)
Solve the equations (4) and (5), then we get,
=> (4p + p) + (q - q) = -12 - (-13)
=> 5p = 1
=> p = 1/5
Apply the value of p on equation (4), then we get the value of q as,
=> (1/5) - q = -13
=> -q = -13 -1/5
=> -q = -66/5
Apply the value of p and q on equation (2), then we get,
=> 1/5 + (-66/5) + r = -1
=> -65/5 + r = -1
=> -13 + r = -1
=> r = 12
Therefore, the value of p is 1/5, q is -66/5 and r is 12.
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after paying 5.12 salad , kamauri has 27.10
Answers
The amount of money that Kamauri has at first will be 32.22.
How to calculate the cost?From the information, it was stated that after paying 5.12 for salad, Kamauri has 27.10.
Based on the information given, the total amount of money that he had at first will be the addition of the cost of salad and the change left.
This will be illustrated as:
= 5.12 + 27.10
= 32.22
The amount is 32.22.
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After paying 5.12 for salad, Kamauri has 27.10. What was the total amount of money that he had at first?
There are integers that are not rational
numbers. (True or false)
There are whole numbers that are not rational
numbers. (True or false
There are integers that are not whole numbers.(true or false)
All rational numbers are integers. (True or false)
Answers
A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043
Explain about the integers?Integers, as opposed to fractions or decimals, are all whole numbers plus their antipodes. For instance, numbers include -3, -2, -1, 0, 1, 2, 3,... On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.
False. An integer is a whole number.
False. For instance, 1/2 is not a whole number but is a rational number.
False. For instance, -3 is not a whole number but is an integer.
True. Rational numbers include all integers.
Answers:
False
False
False
True
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I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
Answers
Answer: 5.13
Step-by-step explanation:
1) Set up the equation
3.8(1.35)
2) Solve
5.13
Select all sequence(s) of translations and reflections that were performed to show the two figures in each pair are
congruent. Image is shown with dashed lines.
*Remember to map the pre-image to the image. Select all that apply.
Answers
The sequence(s) of translations and reflections that were performed to show given two figures are congruent:
- Translate triangle ABC down and then reflect across vertical line.
- Reflect triangle ABC across vertical line and then translate down.
- ΔABC ≅ ΔDEF
In this question, we have been given a triangle and its image.
We need to select all sequence of translations and reflections that performed to show given figures in each pair are congruent.
From figure, we can see that the image of vertex A is vertex D, the image of vertex B is vertex E and the image of vertex C is vertex F.
In we translate the triangle ABC down and then reflect across vertical line then the image would be DEF.
We can do the same transformation by reflecting triangle ABC across the vertical line and then translating it down.
From above, we can conclude that, ΔABC ≅ ΔDEF
Therefore, the sequence(s) of translations and reflections that were performed to show given two figures are congruent:
- Translate triangle ABC down and then reflect across vertical line.
- Reflect triangle ABC across vertical line and then translate down.
- ΔABC ≅ ΔDEF
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Which of the following is the center and radius of the circle?
x² + y2 + 10x-6y + 15 = 0
Answers
The most appropriate form for equation of circle will be given by-
Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units
What is equation of circle?
A round figure whose all points on the boundary maintains a fixed distance from a point known as the centre of the circle and the fixed distance is called the radius of the circle.
If radius of a circle is doubled, we will obtain the diameter of the circle.
Equation of circle
[tex](x-a)^2 + (y-b)^2 = r ^2[/tex]
where (a, b) is the centre of the circle and r is the radius of the circle.
Here,
[tex]x^2 + y^2 + 10x-6y + 15 = 0[/tex]
[tex]x^2 + 2\times x\times 5 + 5^2 -5^2 +y^2 -2\times y\times 3 + 3^2 - 3^2 + 15 = 0\\(x+5)^2 + (y-3)^2-25-9+15=0\\(x+5)^2 + (y-3)^2-19=0\\(x+5)^2 + (y-3)^2=19\\ (x+5)^2 + (y-3)^2=\sqrt{19}^2\\[/tex]
Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units
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Which expression is equivalent to 2x^ 2 -2x+7^ prime ?
Answers
The expression which is equivalent to; 2x² - 2x + 7 as required in the task content is; 2 (x - 0.5)² + 6.5.
Which expression is equivalent to 2x² - 2x + 7 as required in the task content?It follows from the task content that the expression which is equivalent to; 2x² - 2x + 7 is to be determined.
Therefore, since the expression whose equivalent is to be determined is; 2x² - 2x + 7; we have;
2x² - 2x + 7
By completing the square method; we have;
2(x² - x) + 7
2 {(x - 0.5)² - 0.25} + 7.
2 (x - 0.5)² - 0.5 + 7
2 (x - 0.5)² + 6.5
Therefore, the required expression which is equivalent to the given expression is; 2 (x - 0.5)² + 6.5.
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HELP PLS! How does the graph of g(x) = (x + 2)3 − 6 compare to the parent function of f(x) = x3?
Answers
It is to be noted that the graph of g(x) = (x+2)³ -6 compares to the parent function f(x) = x³ in that g(x) is shifted 2 units to the left and 6 units down. See the explanation below.
What is a parent function?A parent function in mathematics is the simplest function in a family of functions that retains the concept of the whole family.
Here is how the transformation of a function can occur
Any change can occur during the transformation of a function.
Typically, they can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.
If the initial function is y = f(x), and the horizontal axis represents inputs and the vertical axis represents outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)A function sets the value of one set's elements to the value of another set's specified element.
Given that the parent function is f(x)=x³, while the transformed function is g(x)=(x+2)³ - 6. Therefore, the transformation of the parent function that results in the transformed function is that g(x) is shifted 2 units to the left and 6 units down.
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The transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
A change can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.
If the initial function is y = f(x), and the horizontal axis shows the inputs and the vertical axis shows outputs, then:
Horizontal shift would be Left shift by c units; y=f(x+c) and Right shift by c units; y=f(x-c)
Vertical shift would be Up by d units; y = f(x) + d and Down by d units; y = f(x) - d
Stretching would be as Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given that the parent function is; f(x)=x³,
And the transformed function is; g(x)=(x+2)³ - 6.
Hence, the transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.
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Raj has put soup into the freezer to cool down. The soups tempature started at
170 °f and decreased at a rate of 30 °f per hour.
Answers
Answer:
If the same cup of 190∘F soup is instead placed into a freezer set at 30∘F, what is the time required for the soup to cool from 190∘Fto135∘F in this situation?