9514 1404 393
Answer:
4. n = 4
5. P(A|B) = 0.75
Step-by-step explanation:
4. The coefficient of x will depend on n. The expansion is ...
(5 +nx)^2(1 +3/5x)^n = (25 +10nx +n^2·x^2)(1 +3/5nx +...)
So, the x-term of the expansion is ...
25(3/5nx) +(10nx)(1) = 25nx
The problem statement tells us that is 100x, so we have ...
25nx = 100x
n = 100x/(25x) = 4 . . . . . divide by the coefficient of n
The value of n is 4.
__
5. For the conditional probability formula, we need to know P(A∩B).
P(A∩B) = P(A) +P(B) -P(A∪B)
P(A∩B) = 0.5 +0.4 -0.6 = 0.3
Then the conditional probability is ...
P(A|B) = P(A∩B)/P(B) = 0.3/0.4
P(A|B) = 0.75
I don’t understand the problem or question
Answer:
Part A
a. Could be a parallelogram but cannot be a rectangle
Part B
c. 100°
Step-by-step explanation:
Part A
The polygon constructed by Andrew = Four sided polygon having no right angles
From the given four sided polygon (quadrilateral) options, the options which can have no right angles are the parallelogram, and rhombus
The rectangle, and square both have 4 right angles
Therefore, the polygon can be either a parallelogram or a rhombus, but cannot be either a rectangle or square
The correct option is therefore, 'His polygon could be a parallelogram but cannot be a rectangle'
Part B
The given parameters of the rhombus EFGH are;
Angle E = 3·x + 5, angle H = 4·x
The characteristics of a rhombus are;
The sum of the interior angles of a rhombus = 360°
The opposite angles of a rhombus are equal
The sum of the adjacent angles = 180° (The adjacent angles are supplementary)
Therefore, in the rhombus EFGH, we have;
Angle E, and angle H are supplementary angles
∴ Angle E + angle H = 180°
Substituting the values of angle E and angle H gives;
3·x + 5 + 4·x = 180°
7·x = 180° - 5 = 175°
x = 175°/7 = 25°
Angle H = 4·x
∴ Angle H = 4 × 25° = 100°
Angle H = 100°
Angle F = angle H = 100°
Therefore, angle F = 100°
Convert 150 base 10 to a binary
number.
Answer:
10010110
Step-by-step explanation:
A binary number is basically a number in base 2. So, each place represents a power of two. The ones place represents 1 or 2^0, the tens represents 2 or 2^1, the hundreds represents 4 or 2^2 and so on. To find the highest place needed to make in the number in binary, we find the greatest power of two that is below 150. In this case, it is 128. We can start by writing 128 in binary:
10000000
Now, we subtract 128 from 150 and find the largest power of two that is smaller than the difference. The largest power of 2 smaller than 22 is 16, so we put a one in the place for 2^4:
10010000
We can subtract 16 from 22 to get what is leftover to continue the process. We get 6, and the largest power of 2 smaller is 4. We can place a one in the hundreds place to represent it:
10010100
What is left is 6-4 or 2, which is just 2^1, so we can place it in the tens place:
10010110
a) Model this situation with a linear system:
To rent a car, a person is charged a daily rate and a fee for each kilometre driven. When Chena
rented a car for 6 days and drove 320 km, the charge was $286.00. When she rented the same car
for 10 days and drove 900 km, the charge was $605.00.
b) Determine the daily rate and the fee for each kilometre driven.
Answer:
The daily rate is $ 29 and the fee for each kilometer driven is $ 0.35.
Step-by-step explanation:
Since to rent a car, a person is charged a daily rate and a fee for each kilometer driven, and when Chena rented a car for 6 days and drove 320 km, the charge was $ 286.00, while when she rented the same car for 10 days and drove 900 km, the charge was $ 605.00, to determine the daily rate and the fee for each kilometer driven the following calculation must be performed:
286 = 6 days and 320 km
320/6 = 53,333 km
286/6 = $ 47,666
Thus, the value of 1 day and 53,333 km is $ 47,666.
605 = 10 days and 900 km
900/10 = 90 km
605/10 = $ 60.5
Thus, the value of 1 day and 90 km is $ 60.5.
90 - 53,333 = 36,666
60.5 - 47.666 = 12.833
12,833 / 36,666 = value per kilometer traveled
0.35 = value per kilometer traveled
(286 - (0.35 x 320)) / 6 = X
(286/112) / 6 = X
174/6 = X
29 = X
(605 - (0.35 x 900)) / 10 = X
(605 - 315) / 10 = X
290/10 = X
29 = X
Therefore, the daily rate is $ 29 and the fee for each kilometer driven is $ 0.35.
Which best describes the relationship between the line that passes through the points (-6, -1) and (-11, 1) and the line
that passes through the points (-3, -8) and (-5, -13)?
A. perpendicular
B. parallel
C. neither perpendicular nor parallel
D. same line
Answer: A. perpendicular
Step-by-step explanation: First, you have to determine the slope of both lines and you can do so using the slope formula: (y2 - y1)/(x2 - x1). You should get the slope -2/5 for the first line and 5/2 for the second. Because one line has a slope that is the negative reciprocal of the other, these lines are perpendicular.
Will give branliest
Find l.
l= [?] in
Suppose the hypotenuse of a right triangle is 13 cm and one of the legs is 10 cm. Use the Pythagorean Theorem to find the measure of the triangle’s other leg.
Answer:
3
Step-by-step explanation:
Pythagorean rule
[tex]hyp = opp + adj \\ therefore. \\ opp = hyp - adj \\ and \\ adj = hyp - opp[/tex]
opp=13-10
opp=3
give me one secondddd..
Answer:
mark me as a brainleast
Step-by-step explanation:
iam not undeerstand on your qiestion write it beautiful words
Simplify variable expressions involving like terms and the distributive property
Answer:
gracias por los puntos xd
what is the value of J
Answer:
Step-by-step explanation:
Since all 3 of these angle come off a straight line, they all add up to equal 180. Thus,
2j + 32 + 6j - 2 + 30 = 180 and
8j + 60 = 180 and
8j = 120 so
j = 15
m∠RST =______because they are __________ (Fill in the blanks)
Answer:
∠RST = ∠SRU because they are alternate angles.
Step-by-step explanation:
Hope it helps .
The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle. The two acute angles along the straight angle are congruent to each other. The overlapping part of the legs is labeled 12. The part of the overlapping side that extends above the smaller triangle is labeled 3. The leg of the smaller triangle that is a ray of the straight angle is labeled 3 x plus 1. The leg of the larger angle that is a ray of the straight angle is labeled 4 x.
Answer:
The two triangles are similar.
What is the value of x?
Enter your answer in the box.
x=
The value of x is 7 units.
What is Similarity of Triangles?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.
Given :
AD = 6 units , BD = 8 units, m∠ABC = m∠DBE = 90° and
∠DEB ≅ ∠ACB
Now, AB = AD + BD
= 8 + 6 = 14 units
Now, In ΔABC and ΔDBE,
∠DBE = ∠ABC ( Each of 90° )
∠DEB = ∠ACB ( given )
So, By using AA postulate of similarity of triangles , ΔABC ~ ΔDBE
Now, proportion of the corresponding sides will be equal.
AD/ DB= BC/ BE
14/8 = 3x/ 2x-2
4x= 28
x= 7
Hence, the value of x is 7 units.
Learn more about similarity of Triangle here:
https://brainly.com/question/11923416
#SPJ6
Which segments have equal
lengths?
The segment that has equal length are known as congruent segment
Answer: corresponding segments
Step-by-step explanation:
Use the figure below, If m
Answer:
m anglw ABD answers is 50 degree
Sarah accepted a new job at a company with a contract guaranteeing annual raises. Sarah's salary after working for nn years can be determined using the equation S=90000+3500n.S=90000+3500n. What is the slope of the equation and what is its interpretation in the context of the problem?
Answer:
Slope = 3500
Sarah's salary will increase by 3500 per year
Step-by-step explanation:
Given that Sarah's salary after working n years is given as :
S=90000+3500n
The equation given is similar to a linear equation :
y = bx + c ;
Where, b = slope of the linear equation
Therefore, relating the equation to that of a linear model ; the slope, b is equivalent to 3500 in Sarah's salary equation.
Slope is simply described as the rate of change, the change in y per unit change in x ;
Therefore, this means Sarah's salary will increase by 3500 per year
i need help as soon as possible please and thank you
Step-by-step explanation:
yes that's the answer
can you please give me brainliest
and use DESMOS app for drawing graphs
I need the answers and it's due today, please help
Answer:
1. 3
2. 1
3. 2
4. 4
5. 5
Step-by-step explanation:
Math a challenging subject, sigh...
Write the slope-intercept form of the linear equation that has a slope of 3
and a y-intercept of -1.
Answer:
y = 3x - 1
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope
b = y-intercept
Emily has pledged to start a healthy lifestyle and so she started walking to keep fit. On Monday, she walked 2/4 of a mile, and on Tuesday she walked 5/6 of a mile. How far did she walk in her first two days of exercise?
Quickkkkkk
Answer:
1 [tex]\frac{1}{3}[/tex] miles.
Step-by-step explanation:
2/4 + 5/6 = ?
We must convert these fractions to the same denominator so we can add fractions. Least common multiple of 4 and 6 is 12.
2/4 = 6/12
5/6 = 10/12
6/12 + 10/12 = 16/12
16/12 = 4/3
4/3 = 1 [tex]\frac{1}{3}[/tex]
The profit for a car company can be represented by the function P=−0.5 x² +4 x+ 12,
where P is the profit in hundred thousands of dollars and x represents the number of cars sold in thousands. What is the maximum profit the company can make?
Answer:
3x+12
Step-by-step explanation:
-0.5x*2+4x+12
Multiply 0.5x*2=x
= -x+4x+12
Add similar elements -x+4x+12
= 3x+12
If a triangle has one interior angle measuring 102°, what is a possible pair of measurements for the other two
interior angles
it edmentum guided notes so it has to be a writing answer
Answer:
a2+a3=78
a2 and a3 must both be positive numbers that add up to 78
so a2 = a3 = 39
a1=102, a2=39, a3=39
Step-by-step explanation:
a1=102
a1+ a2 + a3=180 (all interrior angles of a triangle add up to 180)
a2+a3=78
a2 and a3 must both be positive numbers that add up to 78
write a linear equation in one variable for each of the following situations:
Answer:
i. y = 4
ii. p = 45
iii. m = 5
Step-by-step explanation:
(a) In triangle PQR, PQ = QR. So that,
Perimeter = PQ + PR + QR
40 = (2y + 3) + (5y - 2) + (2y + 3)
= 2y + 3 + 5y - 2 + 2y + 3
40 = 9y + 4
40 - 4 = 9y
36 = 9y
y = [tex]\frac{36}{9}[/tex]
y = 4
(b) The age of Rahim's father is p years. Since he is 29 years older than Rahim, we have;
p = 16 + 29
p = 45
Rahim's father is 45 years old.
(c) Cost of a chair = RM 5.90
Cost of m chairs = RM 5.90 x m
= RM 5.90m
Amount paid = RM 50 - RM 20.50
= RM 29.50
Thus,
RM 5.90m = RM 29.50
5.90m = 29.50
m = [tex]\frac{29.50}{5.90}[/tex]
= 5
m = 5
The number of units of chairs bought is 5.
Solve for b in the literal equation y = 12x + 12b.
b=
Answer:
[tex]b = \frac{y-12x}{12}[/tex]
Step-by-step explanation:
subtract 12x from both sides, then divide by twelve.
What is the area of this figure? Round to the tenth if necessary.
Answer:
b) 850.1 centimeters.Step-by-step explanation:
To find the area of this figure, we must first find the areas of the shapes that compose this figure.
This figure is made up of a rectangle and a semicircle.
Remember: To find the area of a semicircle, multiply the radius by itself twice, then multiply the product pi, lastly divide the product by 2.
[tex]a=\pi r^2/2[/tex]
3.14 will be used for pi!
To find the area of a rectangle, multiply the length by the width. The product is the area of the rectangle.
[tex]a=lw[/tex]
Now, let's solve.
The diameter of the semicircle is 32 centimeters.
To find the radius of a semicircle, divide the diameter by 2.
[tex]32/2=16[/tex]
The radius of the semicircle is 16 centimeters.
Now that we have the radius, we can find the area of the semicircle.
[tex]\pi 16^2/2=401.92[/tex]
The area of the semicircle is 401.92 centimeters.
Furthermore, we find the area of the rectangle.
[tex]14*32=448.[/tex]
The area of the circle is 448 centimeters.
Next, we add the areas of both shapes to find the area of this figure.
[tex]401.92+448[/tex]
[tex]=849.92[/tex]
The final step is to round 849.92 to the nearest tenth.
Even though 849.92 to rounded to the nearest tenth is 849.9, there is no answer choice for this. The closest one to this answer is choice 'b.'
I, therefore, believe the area of this figure is 850.1 centimeters.
CAN SOMEONE PLEASE ANSWER THESE TWO QUESTIONS?! I NEED HELP!
Answer:
B ; A
Step-by-step explanation:
1) The first operation that we have to do is the division
2) we have to added up the the fishes
A rectangle measures 15 cm by 10 cm is given, if the length of side is
increased by 20%, find the increase of area in percentage.
Answer:
20 % increase in Area
Step-by-step explanation:
1. Original Rectangle Area = 150cm ²
2. 20% of 15 is 3
3. Increased length is equal to 18
4. Increased Rectangle Area = 180cm ²
5. Ten percent of 150 = 15.
6. 15x2(ten percent) = 30. Which give us 150+30 equal to 180.
7. 2 ten percent equals 20%
8. Answer is 20%.
Let $z$ and $w$ be complex numbers satisfying $|z| = 5, |w| = 2,$ and $z\overline{w} = 6+8i.$ Then enter in the numbers \[|z+w|^2, |zw|^2, |z-w|^2, \left| \dfrac{z}{w} \right|^2 \]below, in the order listed above. If any of these cannot be uniquely determined from the information given, enter in a question mark. Don't even know where to start.
I got 49 for the first one, 100 for the second one, 9 for the 3rd one, and 6.25 for the 4th one. But it was wrong, so I don't know how to do this question.
Answer:
1st entry: 41
3rd entry: 17
Step-by-step explanation:
The 1st and 3rd entry are incorrect.
We will use the following for the 1st and 3rd:
[tex]|z+w|=|z|^2+|w|^2+2R(z\overline{w})[/tex]
[tex]|z-w|=|z|^2+|w|^2-2R(z\overline{w})[/tex]
where [tex]R(z\overline{w})[/tex] means 'real part of [tex]z\overline{w}[/tex]'.
Let's do part 1 now)
25+4+2(6)
29+12
41
Let's do part 3 now)
25+4-2(6)
29-12
17
the pythagorean theorem equation
Answer:
(Altitude)^2+(Base)^2=(Hypotenuse)^2
Write an equation for the line that passes through E(4, -3) and is parallel to the line
0 = 5x - 7y - 27 Write the equation in general form.
Answer:
y= 5x/7 -27/7
if they are parallel there gradient is the same
m1=m2
y-y1=m(x-x1)
plug in the gradient and points E
y-(-3)=5/7( x-4)
y= 5/7(x) -20/7 +3
final answer
y= 5/7(x) +1/7
Kate is 1 year and six months younger than her sister. If her sister is 14 years and 2 months old, how old is Kate?
Answer:
Kate is 13years and 4 months old,I suggest.