Answer:
constant term = 6
Step-by-step explanation:
if you multiply the constant terms within each factor together you get the constant term of the expansion of p(x) , that is
constant term = 3 × 2 × 1 = 6
The mean mark for the class was 70% there are 30 students in class 20 of whom are boys the mean mark for the mark in test was 62% work out mean for the girls.
The mean mark of the girls is 86.
How is the mean mark calculated?You must first add up all the numbers (3 + 11 + 4 + 6 + 8 + 9 + 6 = 47) before you can determine the mean. The amount is then divided by the number of scores utilized (47 / 7 = 6.7).
Given information:
The number of total students in the class is 30
Given number of boys in the class is 20
Then, the number of girls will be = 30-20
=10
The mean mark of the class = 70×30
= 2100
The guy's average grade is = 62.
Then, mark for the boys = 62×20
= 1240
The mark for the girls = 2100-1240
= 860
Then the mean mark of the girls will be =860/10
= 86
Hence, the mean mark for the girls is 86
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If the simple interest on $6,000 for 5 years is $2,400 then what is the interest rate?
The interest rate will be 8%.
What is Simple interest?
A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Principal amount = $6,000
Time = 5 years
Simple interest = $2,400
Now,
We know that;
⇒ Simple interest = PRT
Where, P is principal amount, R is interest rate and T is time.
Substitute all the values, we get;
⇒ Simple interest = PRT/100
⇒ 2400 = 6,000 x R x 5/100
⇒ 2400/30,000 = R/100
⇒ R = 0.08 x 100
⇒ R = 8%
Thus, The interest rate will be 8%.
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Which equivalent equation is the result of applying the distributive property in thegiven equation?10y + 14 = 2(y-9)
Answer
[tex]10y+14=2y-18[/tex]Explanation
The distributive property tells us that:
[tex]a(x+y)=ax+ay[/tex]Thus, we can apply this property to our given equation in the right side:
[tex]10y+14=2(y-9)[/tex][tex]10y+14=(2\cdot y-2\cdot9)[/tex][tex]10y+14=2y-18[/tex]There are f flavors of ice cream at the shop. Dominic has sampled 7 of them. Choose the expression that shows the number of flavors Dominic has not sampled.
In linear equation, Jen planned to spent 3.75 hours paddleboarding.
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).Dominic has sampled = 7
flavors of ice cream at shop = f
the expression that shows the number of flavors Dominic has not sampled
= 7 * f = 7f
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Given: A = B,
CD LAB
Prove: CD bisects ACB
C
A
D
B
As AD = DB, CD bisects ∠ACD
In Δ ACD and ΔBCD
We need to prove that CD bisects ACB
∠A = ∠B
side AC = CB (as angle A and angle B are same)
CD is ⊥ AB
So, ∠ADC = ∠BDC
By SAS Δ ACD and ΔBCD are congurent
In congurent triangles, corresponding angles and sides are equal
So, in Δ ACD and ΔBCD
ACD = DCB
Therefore, as AD = DB, CD bisects ∠ACD
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A yearbook has 32 pages, and each page has 8 pictures on it. Estimate how manypictures are in the yearbook.
To find how many picture are in the yearbook, multiply the number of pages of the yearbook by the number of pictures on one page. This is 32 times 8:
[tex]32\cdot8=256[/tex]There are 256 picture in the yearbook.
what is the 1/3 of 24
ANSWER:
8
STEP-BY-STEP EXPLANATION:
They ask us for 1/3 of 24, what we must do multiply both values, just like that
[tex]\frac{1}{3}\cdot24=8[/tex]Which means that 1/3 of 24 is 8
11 The table below shows pairs of values that satisfy a linear function.2 -53 64 175 286 397 50What is the y-intercept of the graph of this function?
10)
we get the points from the table are (2,12) and (8,0).
Consider the line equation.
[tex]y=mx+b[/tex]where b is the y=intercept.
Substitute x=2 and y=12, we get
[tex]12=m(2)+b[/tex][tex]12=2m+b[/tex][tex]12-b=2m[/tex][tex]\frac{12-b}{2}=m[/tex]Substitute x=8 and y=0 in the line equation, we get
[tex]0=8m+b[/tex]Substitute m value in this equation to find the value of b.
[tex]0=8(\frac{12-b}{2})+b[/tex][tex]0=4(12-b)+b[/tex][tex]0=4\times12-4b+b[/tex][tex]0=48-3b[/tex][tex]3b=48[/tex]Dividing both sides by 3, we get
[tex]b=\frac{48}{3}=16[/tex]Hence the y-intercept is 16.
11)
we get the points from the table are (2,-5) and (4,17).
Consider the liner function.
[tex]y=mx+b[/tex]where b is the y-intercept.
Substitute x=2 and y=-5, we get
[tex]-5=2m+b[/tex][tex]-5-b=2m[/tex][tex]\frac{-5-b}{2}=m[/tex][tex]m=\frac{-5-b}{2}[/tex]Substitute x=4 and y=17 in the equation, we get
[tex]17=4m+b[/tex]Substitute the value of m in this equation to find the value of b.
[tex]17=4(\frac{-5-b}{2})+b[/tex][tex]17=2(-5-b)+b[/tex][tex]17=-10-2b+b[/tex][tex]17+10=-b[/tex][tex]b=-27[/tex]Hence the y-intercept is -27.
Round 31.212 to the nearest hundredth.
☐
Answer:
31.21
Step-by-step explanation:
Estimate the sum or difference, by rounding each number to its largest place (front-end rounding)–36.673+39.999
Answer:
0
Explanation:
Given the difference:
[tex]-36.673+39.999[/tex]In front-end rounding, we consider the number with the largest place value.
In -36.673, the number with the largest place value is 3.
The digit after 3 us 6, so we round up as follows:
[tex]-36.673\approx-40[/tex]Likewise, In 39.999, the number with the largest place value is 3.
The digit after 3 us 9, so we round up as follows:
[tex]39.999\approx40[/tex]Therefore:
[tex]-36.673+39.999\approx-40+40=0[/tex]The diffrence is 0 using front-end rounding.
I don't understand this
Answer:
∠F = 29
Step-by-step explanation:
There is a property of angle of triangles.
Exterior angle = Sum of opposite interior angles
58 = x + x
58 = 2x
2x = 58
x = 58/2
x = 29
∠F = x = 29
5.5/x=1.375/11
find x
Answer:x=44
Step-by-step explanation:
please help me dhdjjdjejejejdjejejejejejkenensndd
Answer: area=8cm
Step-by-step explanation:
Answer:
a) Area of shape = 8 square cm.
Step-by-step explanation:
Area of composite shape:
Area of shape = area of rectangle + 2* area of triangle
Rectangle:l = 3 cm ; w = 2 cm
[tex]\sf \boxed{\text{Area of rectangle = l *w}}[/tex]
= 3 * 2
= 6 cm²
Triangle:
b = 2 cm
h = 1 cm
[tex]\sf \boxed{\text{Area of triangle=$\dfrac{1}{2}*b*h$}}[/tex]
[tex]\sf = \dfrac{1}{2}*2*1\\\\\\ = 1 \ cm^2[/tex]
Area of two triangles = 2 *1
= 2 cm²
Area of shape = 6 + 2
= 8 cm²
b) Area of rectangle ABCD = 4 * 2
= 8 cm²
Make a table of the values for the function Y=3/5x-1
Answer:
plug the the x values in the chart into the formula one at a time and plug it into a calculator to get your y values.
example: y= -3/5(10)-3 —-> -9 y value
Step-by-step explanation:
-1.25(z+8)=-6
Please help; find z
Answer:
z = -3.2
Step-by-step explanation:
-1.25(z + 8) = -6
-1.25z - 10 = -6
+10 +10
-----------------------
-1.25z = 4
÷(-1.25) ÷(-1.25)
--------------------------
z = -3.2
I hope this helps!
60 feet per second = how many kilometers per hour?
For solving this problem we have to know the transformations between feeds and kilometers and seconds to hours:
[tex]\begin{gathered} 1\operatorname{km}=3280.84ft \\ 1h=3600\text{ seg} \end{gathered}[/tex]Now we can make the transformation:
[tex]60\frac{ft}{seg}=60\frac{1}{3280.84}\frac{3600}{1}=65.8\frac{\operatorname{km}}{h}[/tex]2. The following data set is given:5041414546364436513736494345454136Construct a dot plot:
As given by the question
There are given that the numbers;
[tex]50,\text{ 41, 41, 45, 46, 36, 44, 36, 51, 37, 36, 49, 43, 45, 45, 41, 36.}[/tex]Now,
First make a table of numbers and their frequency.
So,
[tex]\begin{gathered} \text{Number}\rightarrow\text{frequency} \\ \text{ }36\rightarrow4 \\ \text{ 37}\rightarrow1 \\ \text{ }44\rightarrow1 \\ \text{ 45}\rightarrow3 \\ \text{ 46}\rightarrow1 \\ \text{ 49}\rightarrow1 \\ \text{ 50}\rightarrow1 \\ \text{ 51}\rightarrow1 \\ \text{ 41}\rightarrow3 \\ \text{ 43}\rightarrow1 \end{gathered}[/tex]Now,
From the dot plot of the given numbers and their frequency.
So,
The dot plot of the given number is shown below:
A bag contains 15 cards numbered 1 through 15. A card is randomly chosen from the bag. What is the probability that the card has an odd number on it? Write your answer as a fraction in simplest form.
There are 15 cards numbers are from 1 to 15.
From the numbers 1 to 15:
• 8 numbers, are ,odd
,• 7 numbers, are ,even,
The probability is the possibility of an event occuring.
Probability of event to happen P(A) = Number of favourable outcomes/Total Number of outcomes
Thus, the probability of an odd card is:
total number of odd cards/total number of cards
= 8/15
the Correct Answer is:
[tex]\frac{8}{15}[/tex]I need help please with [tex]6409 \div 61[/tex]. I know the answer is 105.06the problem is it has to be written as a a whole number with a fraction. we put 105 and 3/50 but its saying it's wrong.
Given the expression
[tex]\frac{6409}{61}[/tex]Next is to know how many 61 can go in 6409. Using the calculator, you can see that it is 105 with a remainder of 4
We will then have to express the fraction in the form:
[tex]Q\text{ +}\frac{R}{D}[/tex]Q is the quotient = 105
R is the remainder = 4
D is the divisor = 61
Substituting these values into the expression we will have:
[tex]\begin{gathered} \frac{6409}{61}=105+\frac{4}{61} \\ \frac{6409}{61}=105\frac{4}{61} \end{gathered}[/tex]Hence the solution written as a whole number and fraction is 105 4/61
Lines AB, CD, and LK intersect as shown in the figure below. AB I CDKA
The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent.
Given that:
[tex]\begin{gathered} m\angle\text{LRB}=86\degree,\text{ its alternate exterior angle is }m\angle\text{CSK} \\ \\ \text{Therefore,} \\ m\angle\text{CSK}=m\angle\text{LRB} \\ m\angle\text{CSK}=86\degree\text{ (final answer)} \end{gathered}[/tex]An irregular figure is shown on the coordinate plane below. Part A: Find the area of the irregular figure above. Answer:__________________________ square units
In the present question, we will calculate the area of each of the three regular figures that are parts of the irregular figure. They are:
A: a rectangle 4x3
B: a rectangle 9x3
C: a rectangle 3x5
The area of each rectangle is just the multiplication of the two sides, and the area of the irregular figure is the sum of them. From this, we calculate:
[tex]\begin{gathered} A_A=4\times3=12\text{ square units} \\ A_B=9\times3=27\text{ square units} \\ A_C=3\times5=15\text{ square units} \\ \\ A_{\text{Total}}=A_A+A_B+A_C \\ A_{\text{Total}}=12+27+15=54\text{ square units} \end{gathered}[/tex]From the solution presented above, we are able to conclude that the area of the irregular figure is 54 square units.Which of the following represents vector vector t equals vector PQ in trigonometric form, where P (–13, 11) and Q (–18, 2)?
SOLUTION
The coordinate of the vector P and Q are
[tex]\begin{gathered} P(-13,\text{ 11)} \\ \text{And } \\ Q(-18,2) \end{gathered}[/tex]To find the vector PQ. we have
[tex]\begin{gathered} t=\bar{PQ} \\ PQ\text{ is having the coordinate } \\ PQ=(-18-(-13),2-11)=(-5,-9) \end{gathered}[/tex]To find the vector, we use
[tex]\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \text{Where } \\ x=-5,y=-9 \\ r=\sqrt[]{(-5)^2+(-9)^2}=\sqrt[]{25+81}=\sqrt[]{106}=10.296 \end{gathered}[/tex]Then we obtain the angle using
[tex]\begin{gathered} \text{tan}\theta=(\frac{y}{x})_{} \\ \text{Substituting the value of x and y, we have } \\ \tan \theta=(\frac{9}{5})=\tan \theta=(1.8) \end{gathered}[/tex]Hence
[tex]\begin{gathered} \tan \theta=1.8 \\ \theta=\tan ^{-1}(1.8) \\ \theta=60.945 \end{gathered}[/tex]Hence
The vector in trigonometry form will be
[tex]\begin{gathered} t=r(i\cos \theta+j\sin \theta) \\ \text{Then} \\ t=10.296\cos 60.945i+10.296\sin 60.945j \end{gathered}[/tex]Therefore
t= 10.296 cos 60.945 i + 10.296 sin 60.945j
Answer: Option C(third option ).
I don’t under stand help
Xavier Knox's annual salary is $61,100. He is paid semimonthly. His personal exemptions total $4,000. How
much does his employer deduct from each of Knox's paychecks for state income tax of 3.5 percent?
a. $166.54
c.
b. $83.27
$83.13
d. $166.26
The amount that Xavier Knox's employer deducts from his paychecks for state income tax is b. $83.27
How to find the state income tax?First find his taxable income:
= Annual salary - Personal exemptions
= 61, 100 - 4, 000
= $57, 100
The state income tax per year is:
= 57, 100 x 3.5% state income tax rate
= $1, 998.50
The semimonthly state income tax deducted is:
= 1, 998.50 / (12 months x twice a month)
= $83.27
In conclusion, on a semimonthly basis, $83.27 is deducted for state income tax.
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What is the common difference for the arithmetic sequence?
3.2, 5, 6.8, 8.6, 10.4
help me please!
Answer:
the difference is 1.8
Step-by-step explanation:
5-3.2=1.8
6.8-5=1.8
8.6-6.8=1.8
ect
Rides, r Cost, c5 $25.506Use the table shown to answer problems10-11.10. A state fair charges $8 for generaladmission and $3.50 for each ride. Usethe pattern in the table to find the cost of7 rides and 10 rides. Then write anequation for the pattern.11. Find the cost c for 18 rides.$29.0078$36.0010C= 8 + 3.50rUse the operation symbols in the math palette as needed. Type an equation. Use integers or decimals for anynumbers in the equation.)11. Find the cost c for 18 rides.
We want to know the cost for 7 rides and for 10 rides. We see that for each ride the price increases by $3.50. And thus the price for 7 rides will be:
[tex]29.00+3.50=32.50[/tex]And the price for 10 rides will be:
[tex]36.00+3.50+3.50=39.50+3.50=43.00[/tex]Now, for finding the equation we use that the state fair charges $8 for a general admission, and $3.50 for each ride. This can be written as:
[tex]y=8+3.50x[/tex]where x represents the number of rides.
For example, if we want to know the cost for 18 rides, we replace the value of x by 18, and we get:
[tex]\begin{gathered} y=8+3.50(18) \\ =8+63 \\ =71 \end{gathered}[/tex]Then, the cost for 18 rides is $71.
there are 55 stickers in each box how many stickers are in 7 boxes
find linear approxmiation f(x)=x^3+5x^2+4 at a=1
The linear approximation of the function is given by a³ - 3a² +4 + 10ax
The given function is f(x)=x³+5x²+4
Let us find the linear approximation.
L(a) = f(a) + f'(a)(x-a)
let us differentiate the function
f'(x) = 2x²+10x
Let us find the value of the function at the exact point a
f'(a) = 2a²+10a
f(a) = a³+5a²+4
L(a) = f(a) + f'(a)(x-a)
L(a) = a³ + 5a² + 4 + 2a² + 10a (x-a)
L(a) = a³ + 7a² +4 + 10ax - 10a²
L(a) = a³ - 3a² +4 + 10ax
The use of a line to approximate the value of a function at a point is the definition of a linear approximation of either a function. When we see a curve (of a function) and a point on it, we immediately think of the tangent line concept.
If the equation of the tangent line is discovered at the supplied point, one can roughly calculate the value of something similar to the function at every location that is very close to the supplied point using the equation of the tangent line. This concept is also known as the tangent line approximation because the tangent line is utilized. Additionally called linear approximation.
Therefore the linear approximation of the function is given by
a³ - 3a² +4 + 10ax .
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draw the lewis structure for nh3. what are the approximate bond angles, in degrees, around the n atom?
Trigonal pyramidal is the NH3 molecule's molecular shape. The hydrogen atoms are attracted to the lone pair of electrons on the nitrogen atom, which causes the NH3 bond angle to be 107 degrees.
What is Hybridisation?The process of merging two atomic orbitals to produce a new variety of hybridized orbitals is described as hybridization.
Usually, this mixing creates hybrid orbitals with entirely distinct energies, forms, and other characteristics.
Atomic orbitals with the same energy level are principally responsible for hybridization.
However, if the energies of the orbitals are equivalent, the process can involve both fully filled and partially filled orbitals.
We can better understand bond formation, bond energies, and bond lengths by using the hybridization concept, which is an extension of valence bond theory.
Hence, Trigonal pyramidal is the NH3 molecule's molecular shape. The hydrogen atoms are attracted to the lone pair of electrons on the nitrogen atom, which causes the NH3 bond angle to be 107 degrees.
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Find the distance between the points J(-8, 0) and K(1, 4).
The distance between two points of coordinates (x₁, y₁ ) and (x₂, y₂) is calculated using the formula:
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