Benji's total score is -2.
What is the total of negative numbers?If two numbers are negative, their sum will also be negative. When two negative numbers are added together, their value is further diminished, hence the sum of the two negative numbers is always negative.
Given:
Benji has four -0.5 cards.
According to the question, we have to determine his total score which will be equal to adding scores on all four cards.
As we are adding negative scores, upon adding them place a negative sign in front of the sum.
The total score of Benji = (-0.5) + (-0.5) + (-0.5) + (-0.5)
= -2
Therefore, his total score is -2.
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Find the first four terms of the binomial series for the function shown below
(1+x^3)^-1/5
The first four terms of the binomial series are 1, x³/5, (12/25)x⁶ and respectively.
The binomial provided to us is (1+x^3)^-1/5.
To find out the first four terms of the binomial, we shall first extend the standard binomial (1+x)^n.
[tex](1+x)^n = 1 + nx + [n(n - 1)/2!] x^{2} + [n(n - 1)(n - 2)/3!] x^{3} +...[/tex]
As we can see here,
The value of x = x³,
The value of n = -1/5.
We get,
[tex](1+x^{3})^{-\frac{1}{5} } = 1 - \frac{1}{5} (x^{3} ) + [\frac{-1}{5} (\frac{-1}{5} -1)/2!]x^{6} + [\frac{-1}{5} (\frac{-1}{5} -1)(\frac{-1}{5} -2)/3!]x^{27} +[/tex]
From the expansion, we can see,
First term = 1
Second term = x³/5
Third term = (12/25)x⁶
Fourth term = (-13/125)x²⁷
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(5-9i)-(2-6i)+(3-4i)
Hello! So...
We are given the following:
[tex](5-9i)-(2-6i)+(3-4i)[/tex]
_____________________________________________
1. Simplify the given expression.
[tex](5-9i)-(2-6i)+(3-4i)=5-9i-(2-6i)+3-4i[/tex]
_____________________________________________
2. Group the like terms.
[tex]-9i-4i(-2-6i)+5+3[/tex]
_____________________________________________
3. Add similar elements ( [tex]-9i-4i=-13i[/tex] ).
[tex]=-13i-(2-6i)+5+3[/tex]
_____________________________________________
4. Add the numbers ( [tex]5+3=8[/tex] ).
[tex]-13i-(2-6i)+8[/tex]
_____________________________________________
5. Remove the parentheses ( [tex]-(a+bi)=-a-bi[/tex] ).
[tex]-13i+-2-(-6)i+8[/tex]
_____________________________________________
6. Group the like terms.
[tex]-13i-(-6)i-2+8[/tex]
_____________________________________________
7. Add similar elements ( [tex]-13i-(-6)i=-7i[/tex] ).
[tex]-7i-2+8[/tex]
_____________________________________________
8. Add the numbers ( [tex]-2+8=6[/tex] ).
[tex]-7i+6[/tex]
_____________________________________________
9. Rewrite in standard complex form.
[tex]6-7i[/tex]
^Hence, our solution.
_______________________________________________________
Hope this helps! If so, lmk! If you need anything else, feel free to comment below and I'll see what else I can do to assist you further. But for now, thank you for your time and good luck!
What is the sum of the first 5 numbers in the series 1+2+4+8+16+32+...?16313263
Given data:
The series is 1 + 2 + 4 + 8 + 16 + 32 + ....
The given series is G.P because the common ratio for GP is,
[tex]C\mathrm{}R\text{ = }\frac{a_2}{a_1}[/tex]Here, the common ratio is 2.
Sum of the first five numbers ,
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]Here, a is first term that is 1
r is common ratio that is 2
n is the number
Therefore, sum is given as
[tex]S_5=\frac{1(2^5-1)}{2-1}[/tex][tex]\begin{gathered} S_5=\frac{32-1}{1} \\ \text{ = 31} \end{gathered}[/tex]Thus, the sum of first five terms is 31
The correct option is (2).
An angle measures 88.8° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:Hence, the measure of angle whose measure is 32∘ less than its supplement is 74∘.
Step-by-step explanation:
95 divided by 60 step by step
For
f(x) = 3
x
and
g(x) = x4 + 2,
find the following.
(a)
(f ∘ g)(x)
(b)
(g ∘ f)(x)
(c)
f(f(x))
(d)
f 2(x) = (f · f)(x)
Answer:
f(3) = (3)4 + 2
Step-by-step explanation:
y = (3)4 + 2
y = 12 + 2
y = 14
The depth of a local lake averages 26 ft, which is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|. What is the difference between the depths in February and July?
21 feet
23 feet
8 feet
13 feet
The difference between the depths in February and July is D. 13 feet.
How to illustrate the information?From the information illustrated, it was stated that the depth of a local lake average 26 ft is represented as |−26|. In February, it measured 5 ft deep, or |−5|, and in July, it was 18 ft deep, or |−18|.
Therefore, it should be noted that the depth in July is -18.
Therefore, the difference between the depths in February and July will be:
= -5 - (-18)
= -5 + 18
= 13
Therefore, the depth is 13 feet.
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Please help me correct my problem
Answer:
you accidentally put x+6 for the 1st part
Use the given special right triangle to find the value of cos 7 21 XV3 3 T
We have:
[tex]\cos (\frac{\pi}{6})=\frac{\sqrt[]{3}}{2}[/tex]And
[tex]\cos (\frac{\pi}{3})=\frac{1}{2}[/tex]After that, we proceed as follows:
[tex]\sin (\frac{\pi}{3})=\frac{x\sqrt[]{3}}{2x}\Rightarrow\sin (\frac{\pi}{3})=\frac{\sqrt[]{3}}{2}[/tex][tex]\cos (\frac{\pi}{3})=\frac{x}{2x}\Rightarrow\cos (\frac{\pi}{3})=\frac{1}{2}[/tex][tex]undefined[/tex]Circle whether the point is a solution to the inequality. Show work to support the answer.y ≤ 1/3x + 4 is (-6,2) a solution?Yes/No
Answer:Explanation:
Yes
The point is a solution if it satisfies the inequality.
In this case, the inequality is y ≤ (1/3)x + 4, so replacing (x, y) = (-6, 2), we get:
y ≤ (1/3)x + 4
2 (1/3)(-6) + 4≤
2 ≤ -2 + 4
2 ≤ 2
Since 2 is equal to 2, the inequality is satisfied and (-6, 2) is a solution.
So, the answer is Yes.
Using truth tables
24) All businessmen wear suits.
Aaron wears a suit.
Therefore, Aaron is a businessman.
A) Valid
B) Invalid
hello! here is my question! the histogram shows the range of salary for employees at a company . if the mediansalary increased by $10,000 per year, what would be the new median salary?
Increasing amount = $10000
Median = Middle value = $40000
then
New median salary = $40000 + $10000 = $50000
Then answer is
OPTION C) $50-59 thousand
I need help on this question please and thank you
It is proved that the line c is parallel to line d.
What is defined as the supplement angles?If two angles add up to 180 degrees, they are described as supplementary angles. When supplementary angles are combined, they establish a straight angle (180 degrees). In other words, if Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary. Supplementary angles can be either adjacent or not. As a result, there are two kinds of supplementary angles. Every one of these kinds of supplementary angles is discussed further below.supplementary angles adjacentNon-contiguous supplementary anglesFor the given question;
Angle 2 and angle 3 are supplement;
∠2 + ∠3 = 180 ......eq 1
See from figure.
∠4 = ∠3 (vertically opposite angles)
Thus, replacing ∠3 with ∠4 in eq 1.
∠2 + ∠4 = 180 (linear pair)
As ∠2 and ∠4 form the linear pair. Thus, line c is parallel to line d.
Therefore, line c proved to be parallel to line d.
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Graph the line y = kx + 1 given that point M belongs to the line.
M(1, 3)
Please help 25 points
The graph of the line y=kx+1 given that the point M(1,3) belongs to the line is shown below .
In the question ,
it is given that
the line y=kx+1 has point (1,3) on it ,
which means that the point (1,3) will satisfy the equation y=kx+1 .
So, substituting x=1 and y=3 , we get
3=k*1+1
3-1=k
k=2
Hence , the equation of the line becomes y=2x+1 .
On comparing the equation with point slope form of the the line, y=mx+c ,
we get , the slope of the line = 2 and y intercept of the line = 1 .
the graph of the line y=2x+1 is shown below .
Therefore , the graph of the line y=kx+1 given that point M(1,3) belongs to the line is shown below .
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In a certain science experiment, it was required to estimate the nitrogen
content of the blood plasma of a certain colony of rats at their 37th day of age.
A sample of 9 rats was taken at random and the following data was obtained
(grams per 100cc of plasma):
0.98, 0.83, 0.99, 0.86, 0.90, 0.81, 0.94, 0.92, and 0.87.
Find the estimates for the average content and the variation in nitrogen
content in the colony.
The estimates for the average content is 0.9.
The variation in nitrogen content in the colony is 0.0036.
What is the average of a data set?
The average of a data set or the mean of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The sum of the data set is calculated as follows;
total = 0.98 + 0.83 + 0.99 + 0.86 + 0.9 + 0.81 + 0.94 + 0.92 + 0.87
total = 8.1
The estimated average of the nitrogen content = 8.1/9 = 0.9
The deviation of each data from the mean;
= (0.98 - 0.9), (0.83 - 0.9), (0.99 - 0.9), (0.86 - 0.9), (0.9 - 0.9), (0.81 - 0.9), (0.94 - 0.9), (0.92 - 0.9), (0.87 - 0.9)
= 0.08, -0.07, 0.09, -0.04, 0, -0.09, 0.04, 0.02, -0.03
The sum of the square of each data from the mean;
= (0.08)² + (-0.07)² + (0.09)² + (-0.04)² + (0.0)² + (-0.09)² + (0.04)² + (0.02)² + (-0.03)²
= 0.032
The variation of the data sample = (0.032)/9 = 0.0036
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Use Gaussian elimination or Gauss-Jordan elimination.
Mike works a total of 58 hr per week at his two jobs. He makes $7 per hour at job A and $8 per hour at job B. If his total
pay for one week is $424 before taxes, then how many hours does he work at each job?
Mike works 40 hours at job A and 18 hours at job B.
What are simultaneous equations?Simultaneous equations are two or more algebraic equations that share the same unknown variables and have the same solution for each of them. This suggests that the equations are simultaneous and have a single solution.
Given:
Mike makes $7 per hour at job A and $8 per hour at job B.
Let x be the number of hours Mike spends working at job A and y be the number of hours he spends working at job B.
Since he works a total of 58 hours per week,
x + y = 58
His total pay for one week is $424.
7x + 8y = 424
Solving both equations simultaneously we get,
From the first equation, we have, y = 58 - x
Putting the value of y in the second equation,
7x + 8(58 - x) = 424
7x + 464 - 8x = 424
8x - 7x = 464 - 424
x = 40
So, now calculate y = 58 - 40 = 18
Therefore, Mike spends 40 hours working at job A and 18 hours working at job B.
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Balloon
1 reached
a height of X meters.
Balloon
2 reached a height of 7 times balloon 1.
Balloon 3 reached a height of half that of balloon 1.
Balloon 4 reached a height of 30 metres more than balloon 1.
The total height reached by all the balloons was 550 metres.
(a)
Formulate an algebraic expression to model the heights reached by balloons 2, 3
(b)
Find the heights reached by balloons 1, 2, 3 and 4.
Algebraic expression for Height of Balloon 2 = 7x and Height of Balloon 3 = x/2.
Heights reached by balloons 1, 2, 3 and 4 will be 54.73, 383.11, 27.36, 84.73 respectively.
We have the following given information as per the question
Balloon 1 reaches x m.
Balloon 2 reaches a height of 7 times balloon 1
∴ Balloon 2 reaches 7x m.
Balloon 3 reaches a height of half that of balloon 1.
∴ Balloon 3 reaches [tex] \frac{x}{2} [/tex] m.
Balloon 4 reaches a height of 30 meters more than balloon 1.
∴ Balloon 4 reaches ( x + 30 ) m.
Now As given The total height reached by all the balloons was 550 meters.
∴ Height of Balloon 1 + Height of Balloon 2 + Height of Balloon 3 + Height of Balloon 4 = 550 meter
∴ x + 7x + [tex] \frac{x}{2} [/tex] + (x + 30 ) =550
∴ 9.5x + 30 = 550
∴ 9.5x = 550 - 30
∴ 9.5x = 520
∴ x = 520/9.5
∴ x = 54.73 meter
(a) Algebraic expression to model the heights reached by balloons 2, 3 will be
Height of Balloon 2 = 7x = 7(54.73) = 383.11 meter
Height of Balloon 3 = x/2 = 54.73 / 2 = 27.36 meter
(b) The heights reached by balloons 1, 2, 3 and 4 will be as follows
Height of Balloon 1 = x = 54.73 meter.
Height of Balloon 2 = 7x = 7(54.73) = 383.11 meter
Height of Balloon 3 = x/2 = 54.73 / 2 = 27.36 meter
Height of Balloon 4 = x + 30 = 54.73 + 30 = 84.73 meter
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Jessie incorrectly said the rate 1/4 1/16 can be written as the unit rate 1/64 what is the correct unit rate
Correct Unit rate is 4 pounds per gallons.
What is unit rate?An item's unit rate is its price for one of it. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate. A unit rate is a ratio between two separate units with one as the denominator. Examples include miles/hour, kilometers/hour, meters/sec, salaries/month, etc.
Given Data
[tex]\frac{1}{4}[/tex] pounds = [tex]\frac{1}{16}[/tex] gallons
Rate = [tex]\frac{1}{4}[/tex] pounds ÷ [tex]\frac{1}{16}[/tex] gallons
Rate = [tex]\frac{1}{4}[/tex] × 16
Rate = 4
Unit rate is 4 pounds per gallons.
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assume that each of the n trails
Given,
The value of n is 8.
The value of x is 0.
The value of p is 0.6.
The binomial expression is,
[tex]P(X=x)=^nC_x\times(p)^x\times(1-p)^{n-x}[/tex]Subsituting the values then,
[tex]\begin{gathered} P(X=0)=^8C_0\times(0.6)^0\times(1-0.6)^{8-0} \\ P(X=0)=\frac{8!}{0!\times8!}\times1\times(0.4)^8 \\ P(X=0)=1\times1\times(0.4)^8 \\ P(X=0)=0.000655 \\ P(X=0)=0.0007 \end{gathered}[/tex]ence, the probability is 0.0007.
4: (x+5)=1:2
[tex]4 \div x + 5 = 1 \div 2[/tex]
4 is to (x + 5) and 1 is to 2
Step-by-step explanation:
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I Need help with this
STEP - BY - STEP EXPLANATION
The product of two irrational numbers is an irrational number
a.True
b.False
False, The product of two irritational numbers is either rational or irrational numbers.
A rational number is a number expressed in the form of p/q where p and q are integers and q should not be zero. Example: 2/5, 24
Whereas an irrational number is a number that is not rational in nature means it neither be expressed in the form of p/q nor in ratio terms. Example: √12, √3
Product of two irrational numbers: √2* √2 = 4 (which is a rational number)
Product of again two irrational numbers: √2*√3= √6 ( which is an irrational number)
Therefore, the product of two irrational numbers can be rational or irrational numbers.
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The product of two irrational numbers is an irrational number is false because it is either a rational or irrational number.
What is a rational number?A rational number is defined as a numerical representation of a part of a whole that represents a fraction number.
It can be a/b of two integers, a numerator a, and a non-zero denominator b.
The product of two irrational numbers √3 ×√3 = 3
This is a rational number.
Again, the product of two irrational numbers: √5 ×√3 = √15
This is an irrational number.
As a result, the product of two irrational integers can be both rational and irrational.
Thus, the product of two irrational numbers is an irrational number is false because it is either a rational or irrational number.
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Brian is working his way through school. He works two part-time jobs for a total of 22 hours a week. Job A pays $6.10 per hour, and Job B pays $7.30 per hour. How many hours did he work at each job the week that he made $148.60.
Let a be the number of hours that Brian works at Job A in one week and b be the number of hours that he works at Job B .in one week
Since Brian worked 22 hours per week and he made $148.60, we can set the following system of equations:
[tex]\begin{gathered} a+b=22, \\ 6.10a+7.30b=148.60. \end{gathered}[/tex]Subtracting b from the first equation we get:
[tex]\begin{gathered} a+b-b=22-b, \\ a=22-b\text{.} \end{gathered}[/tex]Substituting the above equation in the second one we get:
[tex]6.10(22-b)+7.30b=148.60.[/tex]Applying the distributive property we get:
[tex]\begin{gathered} 6.10\times22-6.10\times b+7.30b=148.60, \\ 134.20+1.20b=148.60. \end{gathered}[/tex]Subtracting 134.20 from the above equation we get:
[tex]\begin{gathered} 134.20+1.20b-134.20=148.60-134.20, \\ 1.20b=14.40. \end{gathered}[/tex]Dividing the above equation by 1.20 we get:
[tex]\begin{gathered} \frac{1.20b}{1.20}=\frac{14.40}{1.20}, \\ b=12. \end{gathered}[/tex]Substituting b=12 in a=22-b we get:
[tex]a=22-12=10.[/tex]Answer:
Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at and t = x for the graph below. Evaluate A(x) for x = 1,2,3, and 4
Answer:
• A(1)=4
,• A(2)=8
,• A(3)=13
,• A(4)=17.5
Explanation:
The graph is given below:
The area, A(x) represents the area bounded by the graph, the horizontal axis, and the vertical lines at t=0 and t = x.
(a)A(1)
Area, A(1) is the area of a trapezoid in which: a=3, b=5 and h=1
[tex]\begin{gathered} \text{ Area of a trapezoid}=\frac{1}{2}(a+b)h \\ A(1)=\frac{1}{2}(3+5)(1)=\frac{1}{2}\times8=4\text{ square units} \end{gathered}[/tex](b)A(2)
.
[tex]A(2)=2\times A(1)=2\times4=8\text{ square units}[/tex](c)A(3)
.
[tex]\begin{gathered} A(3)=A(2)+(5\times1) \\ =8+5 \\ =13\text{ square units} \end{gathered}[/tex](d)A(4)
[tex]\begin{gathered} A(4)=A(3)+\text{ Area of shape 4} \\ =13+\frac{1}{2}(5+4)(1) \\ =13+\frac{9}{2} \\ =13+4.5 \\ =17.5\text{ square units} \end{gathered}[/tex]
This year nelson planted 6 more than one fifth of the tomato plants he planted last year. which expression represents the number of tomato plants he planted this year?
a 1/5x-6
b 1/5x+6
c 5x+6
d 5x-6
The expression to represent the number of tomato plants he planted this year 1 / 5 x + 6.
How to represent expression?This year Nelson planted 6 more than one fifth of the tomato plants he planted last year.
The expression that can be used to represent the number of tomato plant he planted this year can calculated as follows:
Therefore,
let
x = number of tomato he planted last year.
Hence, the final expression is as follows:
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The graph of a 3rd degree polynomial is shown below. Use the Fundamental Theorem of Algebra to determine the number of real and imaginary zeros.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\texttt{real roots : 2 }[/tex]
[tex]\qquad \tt \rightarrow \: imaginary \: \: roots = 1[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The given polynomial is a 3rd degree polynomial so it has a total of three roots.
And we know, where the curve (of polynomial) cuts the x - axis is its real root. so, from the graph we can infer that the given polynomial has 2 real roots [ as it cuts the x - axis at two points, i.e x = -2 and x = 1 ]
Hence, Number of real roots = 2
Number of imaginary roots = total roots - real roots
i.e 3 - 2 = 1
So, number of imaginary roots = 1
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Brandon mows the neighbor's yard to earn extra cash during the summer. He estimates that he mows 1/4 an acre every 1/2 hour. How many acres does he mow each hour?
zymiyas, this is the solution:
Brandon mows 1/4 an acre every 1/2 hour, therefore:
1/2 hour * 2 = one hour
1/4 * 2 = 2/4 or 1/2 an acre
Brandon will mow 1/2 an acre every hour
Use substitution to find the solution to the system ofequation.-4x + y = 6-5x – y = 21
Let:
[tex]\begin{gathered} -4x+y=6_{\text{ }}(1) \\ -5x-y=21_{\text{ }}(2) \end{gathered}[/tex]From (1), solve for y:
[tex]y=6+4x_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} -5x-(6+4x)=21 \\ -5x-6-4x=21 \\ -9x-6=21 \\ -9x=21+6 \\ -9x=27 \\ x=\frac{27}{-9} \\ x=-3 \end{gathered}[/tex]Replace the value of x into (3):
[tex]\begin{gathered} y=6+4(-3) \\ y=6-12 \\ y=-6 \end{gathered}[/tex]What is the mathematical model of different dimensions but same volume?
Prism is the mathematical model with different dimensions but same volume.
As given in the question,
Mathematical model represent different dimensions but same volume.
Prism is the mathematical model with different dimensions but same volume.
To prove it consider two different dimensions of prism.
Prism 1
length = 4cm
Width = 4cm
Height = 4cm
Surface area of the prism1 = 2( 4×4 + 4×4 +4×4)
= 2(48)
= 96cm²
Volume of prism1 = 4×4×4
= 64cm³
Prism 2
length = 8cm
Width = 2cm
Height = 4cm
Surface area of the prism1 = 2( 8×2 + 2×4 +4×8)
= 2(56)
= 112cm²
Volume of prism1 = 8×2×4
= 64cm³
Therefore, prism is the mathematical model with different dimensions but same volume.
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Find the slope and y-intercept for the line.
Slope=
y-intercept = (0,
slope= 1/4
y intercept= -5