(A + B)3's binomial expansion has (D) 1, 3, 3, 1 coefficients.
What are coefficients?A coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or an expression.
It is typically a number, but it can also be any expression.
They may also be referred to as parameters if the coefficients are variables in and of themselves.
A coefficient is, in other words, the numerical factor of a term that contains both constants and variables.
For instance, the coefficient in the expression 2x is 2.
So, we have: (a + b)3
Since we have nothing before (a + b)3.
Then the coefficient will be 1 here.
If we have 3 after (a + b) then the coefficient will be 3.
Therefore, (A + B)3's binomial expansion has (D) 1, 3, 3, 1 coefficients.
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Correct question:
What are the coefficients for the binomial expansion of (a + b)3?
a. 1, 4, 6, 4, 1
b. 1,1
c. 1, 2,1
d. 1,3,3, 1
If you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test. True False
If you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test. This statement is True.
What is partial F-test?
A partial F-test is used to determine whether or not there is a statistically significant difference between a regression model and some nested version of the same model.
A nested model is simply one that contains a subset of the predictor variables in the overall regression model.
Partial F-test is a statistical analysis used in multivariate linear regression to determine independent variables are to be considered when fitting a multivariate linear regression mode.
This is necessary because if too many variables are considered, then the model would be too complex. On the other hand, if too few variables are used, then we may get a very weak fit.
Hence if you have more than one quadratic predictor in your model, you can test them all at the same time using the partial F-test.
The given statement is true.
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your subject-matter expert tells you that her most likely estimate to complete her task is 40 hgours. the task starts on thrusday, january 20, at 8 a.m.
The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.
Given that,
Your subject-matter expert informs you that she believes it will take her 40 hours to finish the work. The project begins on January 20 at 8 a.m. The staff only works throughout the weekdays, eight hours a day.
We have to find when will the assignment be completed.
We know that,
This simple table explains the answer
Thursday, January 20, at 4 p.m. - 8 hours worked
Friday, January 21, at 4 p.m. - 16 hours worked
Monday, January 24, at 4 p.m. - 24 hours worked
Tuesday, January 25, at 4 p.m. - 32 hours worked
Wednesday, January 26, at 4 p.m. - 40 hours worked
Therefore, The correct answer is Wednesday, January 26, at 4 p.m when your subject-matter expert informs you that she believes it will take her 40 hours to finish the work.
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Solve for x.
Please help
The value of x will be;
⇒ x = 3
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The triangle is shown in figure.
Now,
All the sides are given in figure.
By definition of proportionality, we get;
⇒ 3 / (6x - 2 - 10) = (3 + 5) / (6x - 2)
Solve for x as;
⇒ 3 / (6x - 12) = 8 / (6x - 2)
⇒ 3 (6x - 2) = 8 (6x - 12)
⇒ 18x - 6 = 48x - 96
⇒ 96 - 6 = 48x - 18x
⇒ 90 = 30x
⇒ 30x = 90
⇒ x = 90/30
⇒ x = 3
Thus, The value of x will be;
⇒ x = 3
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what is 4 1/3 multplyed by 6?
Answer:
26!
Step-by-step explanation:
let's firstly convert the mixed fraction to improper fraction.
[tex]\stackrel{mixed}{4\frac{1}{3}}\implies \cfrac{4\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{13}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{13}{3}\cdot 6\implies \cfrac{13}{3}\cdot \cfrac{6}{1}\implies \cfrac{13}{1}\cdot \cfrac{6}{3}\implies \cfrac{13}{1}\cdot\cfrac{2}{1}\implies \text{\LARGE 26}[/tex]
What is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle ABC?.
2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'
Given,
Triangles ABC and A'B'C' are similar
For ABC;- (x₁, y₁) = (0, 2) and (x₂, y₂) = (2, 2)
For A'B'C' ;- (x₁, y₁) = (-4, -1) and (x₂, y₂) = (1, -1)
We have to find the scale factor of the dilation;
Here,
Find the distance AB and distance A'B' with the formula
Distance, d = [tex]\sqrt{(y_{2} -y_{1})^{2} +(x_{2} -x_{1} )^{2} }[/tex]
Then,
a) Distance of AB
d AB = [tex]\sqrt{(2-2)^{2}+(2-0)^{2} }[/tex]
d AB = [tex]\sqrt{0^{2} +2^{2} }[/tex]
d AB = √4
Distance of AB = 2 units
b) Distance of A'B'
d A'B' = [tex]\sqrt{(-1+1)^{2} +(1+4)^{2} }[/tex]
d A'B' = [tex]\sqrt{0^{2} +5^{2} }[/tex]
d A'B' = √25
Distance of A'B' = 5 units
Now,
Scale factor;
Scale factor = Distance of AB / Distance of A'B'
Scale factor = 5/2
Scale factor = 2.5
Therefore,
2.5 is the scale factor of the dilation triangle ABC was dilated and translated to form similar triangle A'B'C'
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These expressions are equivalent. True or False?
2x−3(x−4) = 5x+12
the answer is -6x and the equation is equivalent
Alan has a guessing game on his computer.
He estimates that the probability of winning each game is 0.35
Alan decides to play 20 of these games.
How many of these games should he expect to win?
Answer:7
Step-by-step explanation:
100/20 = 5
35/5 = 7
How do you solve an equation in slope intercept form without graphing?.
To solve a system of linear equations without graphing, you can use the substitution method.
How do you solve a system of equations without graphing?
To solve a system of linear equations without graphing, you can use the substitution method. This method works by solving one of the linear equations for one of the variables, then substituting this value for the same variable in the other linear equation and solving for the other variable.
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in 2017, the united states had a population of 320 million people, a crude birth rate (cbr) of 11.8 and a crude death rate (cdr) of 8.5. the net migration rate (the difference between the number of persons entering and leaving a country during the year per 1,000 persons) was 3.9 per 1,000 people. use the formula below to calculate the national population growth rate for the united states in 2017. show your work and clearly label each step.
Therefore, the national population growth rate in the United States in 2017 was 0.72%.
What is growth rate?Growth rate is a metric for determining how quickly a variable has changed over time. It is usually represented as a percentage and is frequently used to calculate the rate of change in economic indicators such as GDP or the rate of inflation. Growth rate may also be used to quantify the rate of change in biological or population processes, such as the growth of an organism's population or the expansion of the size of a tumour. In general, a high growth rate is positive and indicates that a variable is increasing quickly, whereas a low growth rate is considered negative and suggests that a variable is increasing more slowly or may even be decreasing.
How to solve?
Population growth rate = (CBR - CDR + net migration rate) / 10
Population growth rate = (11.8 - 8.5 + 3.9) / 10
Population growth rate = (11.8 - 8.5) + 3.9 / 10
Population growth rate = 3.3 + 3.9 / 10
Population growth rate = 3.3 + 3.9
Population growth rate = 7.2 / 10
Population growth rate = 0.72 %
Therefore, the national population growth rate in the United States in 2017 was 0.72%.
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Translate the phrase -19y and 20y is -6 into an algebraic equation.
Answer:
-19y+20y=-6
Step-by-step explanation:
and means plus so its would be -19y+20y
is=equal sign so -19y+20y=-6
Marty is a competitive eater who can eat approximately one hot dog every 20 seconds. If his next competition gives contestants 15
minutes to eat as many hot dogs as they can, approximately how many hot dogs will Marty
eat?
Answer:
45 hotdogs
Step-by-step explanation:
if he eats 1 hot dog every 20 seconds he will eat 3 hotdogs in a minute (20x3=60seconds aka a minute) so you multiply that by 15 and you get 45
all the real zeros of the given polynomial are integers. find the zeros. (enter your answers as a comma-separated list. enter all answers including repetitions.) p(x)
The zeros of the polynomial P(x) = x³ + 7x² - x - 7 is 1 , - 1 , - 7 .
What is zeros of the polynomial ?In algebraic expressions, exponents may have rational values. A polynomial, on the other hand, is an algebraic assertion with a whole number exponent on any variable. The places where a polynomial turns 0 are referred to as its zeros.
P(x) = x³ + 7x² - x - 7
Now we have to find one zero of given polynomial.
By hit and trial, we get
P(-7) = (-7)³ + 7 (-7)² - (-7) - 7
= 0
Hence we get one zero = -7
So, -7 is the roots of the equation.
Now, by factorisation :
P(x) = x³ + 7x² - x - 7
= x² ( x+7 ) - 1 ( x+3 )
= (x² - 1) ( x+7 )
= ( x-1 )( x+1 )( x+7)
Hence the zeros of the polynomial is 1 , - 1 , - 7.
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THE RIGHT QUESTION ISAll the real zeros of the given polynomial are integers. Find the zeros. (Enter your answers as a comma-separated list. Enter all answers including repetitions.)
P(x) = x3 + 7x2 − x − 7
in a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that group of answer choices the estimated mean of y is 2 when x1 equals zero. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, holding x2 constant. the relationship between x1 and y is significant. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, without regard to x2.
In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that B. the estimated mean of y increases by 2 units for each increase of 1 unit of x1, holding x2 constant
What is a multiple regression?Multiple regression is a statistical technique for examining the relationship between a single dependent variable and a number of independent variables. The goal of multiple regression analysis is to use known independent variables to predict the value of a single dependent variable.
Multiple regression predicts the value of one dependent variable by taking into account the values of the available multiple independent variables. For example, suppose a researcher decides to study the performance of students at a school over time.
In this case, the correct option is B.
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Which expression is equivalent to log subscript 5 baseline (startfraction x over 4 endfraction) squared? 2 log subscript 5 baseline x + log subscript 5 baseline 4 2 log subscript 5 baseline x + log subscript 5 baseline 16 2 log subscript 5 baseline x + 2 log subscript 5 baseline 4 2 log subscript 5 baseline x + log subscript 5 baseline 4.
The required expression for
[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.
Given,
In the question:
The expression is given as:
Log subscript 5 baseline (startfraction x over 4 endfraction) squared
To find the which expression is equivalent?
Now, According to the question:
The expression is given as:
[tex]log_5(\frac{x}{4} )^2[/tex].
We know that from the properties of logarithm, the following identities
[tex]log m^n = n log m...(1)\\\\log\frac{m}{n} = log m - log n .....(2)[/tex]
Now, [tex]log_5(\frac{x}{4} )^2[/tex] = 2 log [tex]\frac{x}{4}[/tex] (using 1 identity)
Again, Using (2) identity we get,
[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.
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consider a blackbody of surface area a that cools down with time according to the time-dependent tem- perature function t(t)
The blackbody surface area cools down the area according to time dependent temperature (t)
Radiation that is incident on an object is partially absorbed and partially reflected. At thermodynamic equilibrium, the rate at which an object absorbs radiation is the same as the rate at which it emits it.
Therefore, a good absorber of radiation - any object that absorbs radiation, is also a good emitter. A perfect absorber absorbs all electromagnetic radiation incident on it; such an object is called a blackbody.
The temperature (T) of the object that emits radiation, or the emitter, determines the wavelength at which the radiated energy is at its maximum. For example, the Sun, whose surface temperature is in the range between 5000 K and 6000 K, radiates most strongly in a range of wavelengths about 560 nm in the visible part of the electromagnetic spectrum. The body, when at its normal temperature of about 300 K, radiates most strongly in the infrared part of the spectrum.
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add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
The correct response is 110.
Consider two numbers that are inside 1000.
324 and 434 are these two numbers.
As a result, for any number abc, the terms a, b, and c each have a place value of 100, 10, and 1.
We will therefore add the corresponding digits and multiply them by their place value when adding the two numbers abc and def.
In order to add 324 and 434, we will
(3+4)×100 + (2+3)×10 + (4+4)×1
The solution is 700+50+8=758.
This is equivalent to (324 + 434 = 758)
Similar steps apply for subtraction; simply choose the larger number and continue the same procedures, changing the + sign in the inner bracket to a -.
(4-3)×100 + (3-2) (3-2)×10 + (4-4)×1
Therefore, the correct response is 110.
This equals (434-324) = 110.
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which sampling method is conducted when every 50th person registered to vote in a given state is selected from list of voters
Cluster Sampling method , is the required method .
Because the population is split into two separate groups in two different ways.
In a given problem, a survey says that a sample is selected by dividing the population into the gifts of votes, and we need to figure out how to sample. This is called cluster sampling. Analysts are run using a sample her cluster.
Cluster Sampling Method:
In cluster sampling, researchers divide the population into smaller groups called clusters. Then randomly select from these clusters to form a sample. Cluster sampling is a probabilistic sampling technique commonly used to study large populations, especially those that are geographically dispersed.
How to cluster the samples
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What does find the mean of these numbers mean?.
The mean of the numbers means that it is average of the given numbers.
According to the question,
We have the following information:
Mean of the numbers
We know that the mean of a given data set means that we add all the numbers in data set and divide the obtained result by the total numbers.
For example, we have a following data set:
2,5 and 8
Total numbers in the set = 3
Now, the mean of these numbers will be:
Mean = (2+5+8)/3
Mean = 15/3
Mean of the numbers = 5
So, in other words, it can be expressed as the average of the numbers.
Hence, the mean of the numbers means that it is average of the given numbers.
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Which is a way to solve the equation 4x = 128 if you do not know a power of 4 that equals 128?.
When you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is; Find intersections on the graph of y = 4ˣ and y = 128.
Define the term mathematical equation?The explanation of an equation in arithmetic is a mathematics statement that indicates the equality of two mathematical expressions.For instance, the equation 3x + 5 = 14 is composed of the two equations 3x + 5 and 14, whose are separated by the 'equal' sign.Consider the given equations;
y = 4ˣ and y = 128
Since, the power of 4 equals 128 is unknown.
Thus, draw the graph of equation y = 128. and y = 4ˣ .
Consider the intersected point from the graph.
Thus, when you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is;
Find intersections on the graph of y = 4ˣ and y = 128.
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A rectangular playground i to be fenced in uing a wall on one ide and 210 meter of fencing for the other three ide. The area A(x) in quare meter of the playground i a function of the length x in meter of the ide parallel to the wall. A. Write an expreion for A(x)
The function of the length 'x' in meters of the side parallel to the wall is A(x) = x/2(210 - x)
What are perimeter and area?
While area describes the space it occupies, perimeter describes how far the shape's edge extends. A shape's perimeter is its entire circumference. The region that an object's shape defines as its area.
Given, perimeter (P) = 210 meters ........... (i)
Let the length parallel to the wall be 'x' and the width be 'y'
So, the perimeter of the fence is
P = 2y + x ............... (ii)
From eq. (i) & (ii), we get
210 = 2y + x
or, y = 1/2(210 - x)
The area of the wall is calculated as:
A = xy
or, A = x * 1/2(210 - x)
or, A = x/2(210 - x)
Rewrite as
A(x) = x/2(210 - x)
Hence, the function of the length 'x' in meters of the side parallel to the wall is A(x) = x/2(210 - x)
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Which congruence theorem can be used to prove that the triangles are congruent two sides and non-included right angle?.
According to the Side-Angle-Side Theorem (SAS), two triangles are congruence if their two sides and the angle between them are equal to those of another triangle's two sides and angle.
What in mathematics is a congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Is congruent the same as equal?If and only if two segments have equal amounts of each, they are congruent. If and only if all of the corresponding angles and sides are congruent, two triangles are said to be congruent.
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explanation+answer please
Answer:
-1
Step-by-step explanation:
if the input is 4 you just go through the cycles
4 then subtract 7
4-7
-3
Then divide by 3
-3/3
-1
Hopes this helps please mark brainliest
PLEASE HELP ASAP .................... I will mark brainiest.
Answer:
x>3
Step-by-step explanation:
the answer is x>3 because I took this test in class
select the correct answer from each drop-down menu. consider circle c with diameter de. diameter shows a circle centered at c. points d and e lies on the circumference of the circle. point e is labeled (13, 11) and point d is labeled (minus 3, 3). the equation of circle c is ( )2 ( )2
The equation of the circle , with diameter DEis (x - 5)² + (y - 7)² = 80
An equation is an expression that appears as the relationship between two or more variables and numbers. since the standard equation for a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. It is given that the diameter of the circle is at D(-3, 3) and E(13, 11). So the coordinate of the center is:
h = (13 + (-3))/2 = 5
k = (3 + 11)/2 = 7
(h, k) = (5, 7) and the Radius is diameter / 2 = 8√5 ÷ 2 = 4√5.
the equation will be : (x - 5)² + (y - 7)² = (4√5)² => (x - 5)² + (y - 7)² = 80
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Answer:
(x - 5)² + (y - 7)² = 80
Step-by-step explanation:
Construct the lowest-degree polynomial given the zeros below. Then, choose the intervals that contain the coefficients of the polynomial in the form x3 + bx? + cr + d. -4 + 4i and 4 I A. b€ (-2.3, 2.2),c € (-3, 10), and d € (-22, -15] B. be[-2.3, 2.2),c € (-14, -6), and d € [11, 19] C. be[-5.4, -1],ce 1-3, 10), and d e [123, 134] D. 6 € (2.1, 5.3],c el-3, 10), and d e f-138, -126] E. None of the above.
Option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].
Here, we are given a polynomial of the form [tex]x^{3}[/tex] + b[tex]x^{2}[/tex] + cx + d
The zeroes of the polynomial are ( -4 + 4i ) and 4
The third root of the cubic equation will be (-4 - 4i) which is the conjugate of (-4 + 4i)
This means that for x = ( -4 + 4i ), ( -4 - 4i ) and 4, the polynomial is equal to 0.
Further, the sum of zeroes of a cubic equation
= -(coefficient of [tex]x^{2}[/tex] )/(coefficient of [tex]x^{3}[/tex])
Thus, -4 + 4i + 4 - 4 - 4i = -b
b = 4
Similarly, the sum of the product of zeroes taken 2 at a time = c
⇒ (-4 + 4i)(-4- 4i) + 4(-4 + 4i) + 4(-4- 4i) = c
c = 16 -16[tex]i^{2}[/tex] - 16 + 16i - 16 - 16i
c = 16 + 16 - 32
c = 0
Further, product of zeroes = -d
-d = (-4 + 4i) (-4- 4i) 4
d = -(16 + 16i - 16i -16[tex]i^{2}[/tex]) 4
d = -(16 + 16)4
d = -128
Thus, we get that option D is the correct answer, intervals of the coefficients are- b ∈ (2.1, 5.3], c ∈ (-3, 10), and d ∈ (-138, -126].
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a deck of cards contains red cards numbered 1,2,3,4, blue cards numbered 1,2,3,4,5,6 and green cards numbered 1,2,3,4,5,6,7,8,9. if a single card is picked at random, what is the probability that the card is blue? give your answer as a fraction.
if a single card is picked and if it is blue card then the probability is 6 / 19 .
What is probability ?Probability means possibility of happening of event, it varies from 0 to 1.
Generally it helps us in determining odds of this situation. Probability expresses that situation.
Probability is defined as the the number of favourable outcomes to the total number of outcomes.
Red Cards = 1, 2, 3, 4
Blue Cards = 1, 2, 3, 4, 5, 6
Green Cards= 1, 2, 3, 4, 5, 6, 7, 8, 9.
Now,
Total number of cards = 19
P ( Blue card ) = [tex]\frac{Number of blue cards}{Total number of cards}[/tex]
= 6 / 19
Hence, if a single card is picked and if it is blue card then the probability is 6 / 19 .
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A car is moving at a constant speed and travels 48 4/5 miles in 4/5 of an hour. How many miles will this car travel in three hours?
The car travels 183 miles distance in 3 hours.
What is ratio?Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
Distance travelled by car in 4/5 hour = 48⁴/₅ miles or 244/5 miles.
To find distance travelled by car in 3 hours, use ratio property,
4/5 hours = 244/5 miles
⇒1 hour = 61 miles
⇒3 hours = 61×3 = 183 miles
The distance covered by car in 3 hours is 183 miles.
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Mrs. Stevens bought 5 identical gifts for her children. Each gift was valued at $80. She paid 1/2 of the total cost and financed the remaining balance through her credit union for 18 months at 9 % interest. What was the total amount of money she borrowed?
The total amount of money that she borrowed would be= $227.
What is a credit union?A credit union could be defined as the union that identifies am individual as their members and there offer financial assistance to such an individual.
The number of gifts bought by Mr Steven = 5 identical gifts.
The price for each gift = $80
The total money that Mr Steven spent on gift = 5×80 = $400.
The amount paid was 1/2 of total cost = 1/2×400 = $200
The amount of money she borrowed for her credit union is calculated using simple interest formula;
si = P*T*R/100
si = 200×1.5 × 9/100
si = 2700/100
si = $27
The amount borrowed= 200+27 = $227.
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What is the opportunity cost for the congo to produce diamonds? 6 thousand units of corn one-sixth of a thousand units of corn 4 thousand units of corn one-fourth of a thousand units of corn.
The opportunity cost for the Congo to produce additional diamonds is; 4 thousand units of corn.
What is the Opportunity Cost?Opportunity costs are defined as the benefits of an alternative decision when the decision maker is made to reject the alternative.
For example, the opportunity cost of going to college would be the earnings forgone.
The opportunity cost is calculated as the lost benefit when an alternative decision is not followed up.
Fractionally, we can say that the opportunity cost of producing one product A) to another (B) = Units of B/Units of A.
From the attached table, we can deduce the following;
United States opportunity cost to produce diamonds = 60/10 = 6
United States opportunity cost to produce corns = 10/60 = 1/6
Congo's opportunity cost to produce diamonds = 20/5 = 4
Congo's opportunity cost to produce corn = 5/20 = 1/4
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in short-track speed skating, the track has straight sections and semicircles 16 m in diameter. assume that a 65 kg skater goes around the turn at a constant 12 m/s .
The horizontal force exerted on the skater 1170 N.
The diameter of the semicircular portion of the track is 16 m.
Therefore its radius is
r = 8 m.
The tangential velocity of the skater is 12 m/s.
Therefore the angular speed is
ω = v/r = (12 m/s)/(8 m) = 1.5 rad/s
The horizontal force on the skater is due to centripetal acceleration of
a = r*ω² = (8 m)*(1.5 rad/s)² = 18 m/s².
The force acting on the 65-kg skater is
F = m*a = (65 kg)*(18 m/s²) = 1170 N
Therefore, the horizontal force exerted on the skater 1170 N. The correct answer is 1170 N.
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#SPJ4
