Answer:
b
Step-by-step explanation:
If a negative number times another number is positive, that means that the other number is also negative because multiplying two negative numbers gives you a positive number. Therefore, a - b must be negative. In order for the difference of two numbers to be negative, the number being subtracted must be bigger than the number it's being subtracted from. For example, in 2 - 7, 7 > 2 but 2 - 7 is negative, the same goes for 3 - 8, 4 - 10, etc. Therefore, b must be greater.
A bag contains five tokens numbered 2, 3, 6, 7, and 8. Two tokens are taken in succession out of the bag without replacement. A) Create the probability distribution for "x" being the number of odd numbered tokens drawn. B) What is mean and variance of the probability distribution?
Answer and Step-by-step explanation:
A) Probability of taken two odd numbered token without replacement:
P(3) = 2/5 = 0.4
P(7) = 1/4 = 0.25
Construct a probability distribution:
X 3 7
p(X) 0.4 0.25
B) Mean of the probability distribution:
E(X) = ∑xp
E(X) = 3*0.4 + 7*0.25
E(X) = 2.95
Variance of the probability distribution:
V(X) = [tex]\Sigma X^{2}p - [E(X)]^{2}[/tex]
V(X) = [tex]3^{2}*0.4+7^{2}*0.25 - (2.95)^{2}[/tex]
V(X) = 7.1475
Mean and variance of the probability distribution are 2.95 and 7.145, respectively.
Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.
Answer:
1) The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The joint equations of diagonals are;
5·y = 56 - 6·x and 5·y = 6·x + 14.
Step-by-step explanation:
The equations are;
x² - 7·x + 6 = 0......................(1)
y² - 14·y + 40 = 0.................(2)
Factorizing equation (1) and equation (2) , we get
x² - 7·x + 6 = (x - 6)·(x - 1) = 0
Which are vertical lines at points x = 6 and x = 1
For equation (2) , we get
y² - 14·y + 40 = (y - 10)·(y - 4) = 0
Which are horizontal lines at point y = 4 and y = 10
The region between the four lines x = 6, x = 1, y = 4 and y = 10 describing both equations is a rectangle
2) The points of intersection of the equations are;
(1, 4), (1, 10), (6, 4), and (6, 10)
The end point of the diagonals are;
(1, 10), (6, 4) and (1, 4), (6, 10)
The slope of the diagonals are;
(10 - 4)/(1 - 6) = -6/5 and (4 - 10)/(1 - 6) = 6/5
The equation of one of the diagonals are then, y - 10 = -6/5×(x - 1)
y = -6/5·x + 6/5 + 10 = -6/5·x + 56/5
5·y = 56 - 6·x
The other diagonal is therefore;
y - 4 = 6/5×(x - 1)
y = 6/5·x - 6/5 + 4 = 6/5·x + 14/5
5·y = 6·x + 14.
The joint equations of diagonals are therefore;
5·y = 56 - 6·x and 5·y = 6·x + 14.
5y-5y^2-5+2+2y+3y^2-1
Answer:
7y - 2y² - 4
Step-by-step explanation:
5y - 5y² - 5 + 2 + 2y + 3y² - 1
5y + 2y - 5y² + 3y² - 5 + 2 - 1 (combine like terms)
7y - 2y² - 4
Write a number sentence that
illustrates the associative property
of addition,
Please, someone help.
Answer:
ok so
faf
Step-by-step explanation:
Factor 20x2 + 25x – 12x – 15 by grouping.
1. Group terms with common factors.
2. Factor the GCF from each group.
3. Write the polynomial as a product of binomials.
(20x2 – 12x) + (25x– 15)
4x(5x – 3) + 5(5x – 3)
(5x – 3)(
x +
)
Find the conjugate of 2 - 5i and then calculate the product of the given complex number and its conjugate. (1 point)
Answer:
29
Step-by-step explanation:
conjugate of a+ib=a-ib
conjugate of 2-5i=2+5i
(2+5i)(2-5i)=2²-(5i)²=4-25i²=4-25(-1)=4+25=29
Answer:
29
i had the same question and 29 was the right answer
Find the value of x. Round to the nearest tenth.
15.9
12.4
12.8
16.3
Answer:
x = 15.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 28 = 14/x
x cos 28 = 14
x = 14 / cos 28
x=15.85598
Rounding to the nearest tenth
x = 15.9
90 POINTS! HELP ASAP! Using one of the figures below, explain a strategy for calculating the area of the irregular polygon.
Answer:
area of polygon = 88 sq. units
Step-by-step explanation:
lets make it simple, short and accurate.
area of polygon = total area - total area of triangles
total area = 11 * 12 = 132
triangle 1 = 1/2 * 5 * 5 = 12.5
triangle 2 = 1/2 * 3 * 6 = 9
triangle 3 = 1/2 * 3 * 8 = 12
triangle 4 = 1/2 * 3 * 7 = 10.5
total area of triangle = 12.5 + 9 + 12 + 10.5 = 44
area of polygon = 132 - 44 = 88 sq. units
Answer:
The area of the irregular polygon:
88 units²
Step-by-step explanation:
The irregular polygon is insert in a rectangle
The strategy is:
1 - calculate the rectangle total area
2- calculate the area of each right triangle
3.- substracte the total area of the 4 right triangles from the area of the rectángule
then:
1.-
Ar = 12*11 = 132 units²
Ar = rectangle area
2.-
At₁ = (5*5)/2 = 25/2 = 12.5 units²
At₂ = (6*3)/2 = 18/2 = 9 units²
At₃ = (7*3)/2 = 21/2 = 10.5 units²
At₄ = (8*3)/2 = 24/2 = 12 units²
At total = 12.5 + 9 + 10.5 + 12 = 44 units²
At = right triangle areas
3.-
Ap = 132 - 44 = 88 units²
The graph of a quadratic function intercepts the x-axis in two places and the y-axis in one place. According to the fundamental theorem of algebra, which of the following statements is correct? A. The quadratic function has no real zeros and two complex zeros. B. The quadratic function has one distinct real zero and one distinct complex zero. C. The quadratic function has two distinct real zeros and one distinct complex zero. D. The quadratic function has two distinct real zeros.
Answer: D. The quadratic function has two distinct real zeros.
There are no complex roots as a quadratic's roots are maxed out at 2. The fundamental theorem of algebra says that if you have an nth degree polynomial, then the max number of real roots is n.
This quadratic's roots are distinct because the two x intercepts are in different places. Each x intercept is a root.
With which set of information can you construct a unique triangle?
OA the measurements of all the angles
ОВ.
the lengths of two sides
OC. the measurements of two angles
OD. the lengths of all the sides
OE the measurement of one angle
Answer:
D
Step-by-step explanation:
This would be using the SSS.
Which means knowing three sides.
The other options do not relate to any of the SSS, SAS, ASA, RHS
Hope that helped!!! k
Rewrite the linear equation in general form: y+6= -5/2(x+4)
Answer:
5x+2y = -32Step-by-step explanation:
[tex]The \:standard \: form \:of \: a \:linear \: equation \: is \: Ax+By=C.\\\\Multiply \:both \:sides \:by \:2\\\\2(y+6)=2(\frac{-5}{2}(x+4)) \\\\Simplify\\\\2y+12=-5x-20\\2y+5x=-20-12\\\\2y+5x=-32\\\\Rewrite\:in \:Ax+By+C\:form\\\\= 5x+2y=-32[/tex]
Write rhe set of decimals in order from least to greatest. A) 9.3,3.09,3.9,3.011
Answer:
The digits arranged in order from least to largest is 3.011, 3.09, 3.9, 9.3
Step-by-step explanation:
The arrangement of decimals in order from smallest to largest can be done by taking note of the digit in the unit portion, the tenths, hundredths and thousandths.
The numbers are;
9.3
3.09
3.9
3.011
The largest number is the 9.3
Of the three numbers with 3 as unit, the lowest hundredths is 0.011, therefore, we have;
Therefore, the least (lowest) number = 3.011
The next is the 3.09 as 0.09 is larger than 0.011
Then the second number is 3.9
The digits arranged in order from least to largest is then 3.011, 3.09, 3.9, 9.3.
Find the measure of each side indicated. Round to the nearest tenth.
A) 19.8
C) 24.9
B) 27.2
D) 25.3
Answer:
D. 25.3
Step-by-step explanation:
tan∅ = opposite over adjacent
Step 1: Write equation
tan66.5° = x/11
Step 2: Multiply both sides by 11
11tan66.5° = x
Step 3: Evaluate
x = 25.2983
x ≈ 25.3
Answer:
[tex]\huge\boxed{x = 25.3}[/tex]
Step-by-step explanation:
Tan θ = opposite / adjacent
Where θ = 66.5 , opposite = x and adjacent = 11
Tan 66.5 = x / 11
2.3 * 11 = x
25.3 = x
OR
x = 25.3
The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4. Using the given data, find the mean, median, and mode for this sample. A. mean: 10, median: 8, mode: none B. mean: none, median: 8, mode: 10 C. mean: 8, median: 10, mode: none D. mean: 14, median: 10, mode: 8
Answer: A. mean: 10, median: 8, mode: none
Step-by-step explanation:
Given : The number of patients treated at Dr. Jason's dentist office each day was recorded for seven days: 3, 8, 11, 22, 17, 5, 4.
First we arrange it order.
3, 4, 5, 8, 11, 17, 22
Mean = (Sum of observations) ÷ (Number of observations)
Number of observations = 7
Sum of observations = 3+4+5+8+11+17+22 =70
Mean = 70 ÷7 = 10
Median = Middle-most value
= 8
Mode = Most repeatted value
= none
Hence, the mean, median, and mode for this sample = A. mean: 10, median: 8, mode: none
What is the sign of -xy? Will give the brainlest to who ever answers it
Answer:
positive
Step-by-step explanation:
X is positive since it is to the right of zero
Y is negative since it is to the left of zero
-xy
- ( +) ( -)
negative times positive times negative
negative times negative
positive
Please answer this question now
Answer:
AB = 72°
Step-by-step explanation:
The inscribed angle ADC is half the measure of its intercepted arc, thus
56° = [tex]\frac{1}{2}[/tex] ( m ABC ) ← multiply both sides by 2
112° = ABC
ABC = AB + BC = AB + 40, so
AB + 40 = 112 ( subtract 40 from both sides )
AB = 72°
Simplify.
-4a(3a - 6)
First change the -6 to plus a negative 6.
Then distribute the -4a through the parentheses.
So we have -4a(3a) + -4a(-6).
Remember that -4a(3a) is -12a² and -4a(-6) is 24a.
So the answer is -12a² + 24a.
Answer:
-12a^2 +24a
Step-by-step explanation:
-4a(3a - 6)
Distribute
-4a*3a -4a * -6
-12a^2 +24a
A tent is in the form of a right circular cylinder and cone. The radius of the cone and cylinder is 4 meters. The height of the cylinder and cone are 4.5 meters and 3 meters respectively. Find the outer surface area of the tent. (Assume π = 22 /7)
Answer:
176m²
Step-by-step explanation:
When we are asked to find the outer surface area of a geometric shape, it means to find the Lateral or Curved Surface Area of the shape. We are given two shapes above.
Step 1
Find the Outer surface area of the cone
Outer / Lateral surface area of a cone =
πrl
Where l = √r² + h²
r = 4 m
h = 3m
Outer surface area = 22/7 ×√4² + 3²
= 22/7 × √16 + 9
= 22/7 × √25
= 22/7 × 5
= 62.83185m²
Step 2
Find the outer surface area of a cylinder
= 2πrh
π = 22/7
r = 4m
h = 4.5
π = 22/7
Outer surface area of a cylinder = 2 × 22/7 × 4 × 4.5
= 113.09734m²
Step 3
The Outer Surface Area of the Tent = Outer Surface Area of the cone + Outer Surface Area of the cylinder
= 62.83185m² + 113.09734m²
= 175.92919m²
Approximately ≈ 176m²
Therefore, the outer surface area of the tent = 176m²
How to do this question plz answer my question plz
Answer:
£22.40
Step-by-step explanation:
60% of 12 is 7.2 (you can also write it as 7.20) so you times that by 2 to get 14.4 (you can also write it as 14.40) and [tex]\frac{1}{3}[/tex] of 24 is 8, so you add that to the 14.4 and you get 22.4 (also writen as 22.4) hope this helps!
Help! Will give brainliest.
Answer:
A. You can see which shape the bases are, how many bases there are, how many faces there are, and how many edges there are.
B. The bases are ABC and DEF, and I know because they are two congruent triangles on two opposite sides of the shape.
Calculate YZ if WY = 25, XY = 23, and VZ = 35
Answer:
WY= 25
XY= 23
VZ=36
so,
WY/XY = YZ/VZ
25/23 = YZ/25 (then do cross multiply)
25×25 = 23 × YZ
625= 23 × YZ
625/23= YZ
27,17= YZ
#i'm indonesian
#hope it helps.
Answer:
[tex]\huge \boxed{13.04}[/tex]
Step-by-step explanation:
The triangles are congruent, we can use ratios to solve.
WY/XY = (WY+YZ)/VZ
Let the length of YZ be x.
25/23 = (25+x)/35
Cross multiply.
23(25+x) = 25 × 35
575 + 23x = 875
Subtract 575 from both sides.
575 + 23x - 575 = 875 - 575
23x = 300
Divide both sides by 23.
(23x)/23 = 300/23
x = 13.0434782609...
If 3 cats catch 3 mice in 3 minutes, how long will it take 100 cats to catch 100 mice?
Answer:
100 minutes
Step-by-step explanation:
It takes each of the 3 cats about 1 minute to catch one mouse. If the same goes for the 100 cats, it will take them 100 minutes to catch 100 mice.
Hope that helps.
Answer:
3 min
Step-by-step explanation:
These are all independent actions.
If you put 1 cat in a room with 1 mouse, it will take 3 min to catch the mouse.
If you put 2 cats in a room with 2 mice, they will act independently and it will take 3 min for each one to catch a mouse.
If you put 3 cats in a room with 3 mice, they will act independently and it will take 3 min for each one to catch a mouse.
If you put 100 cats in a room with 100 mice, they will act independently and it will take 3 min for each one to catch a mouse.
Each cat will finish at the same time — 3 min.
Graph a rectangle on the coordinate plane with an area of 250 ft^2. Pretend 1 unit=10 feet.
Answer:
turn the 10 to 5 and divide 250 by 2 which will give you your l and w subract 2 from your l and add 2 to your your w
Step-by-step explanation:
Answer:
Step-by-step explanation:
If the area is to be 250 ft^2, one possible set of dimensions would be
25 ft by 10 ft.
If 1 unit on the coordinate plane represents 10 feet, then the dimensions of the drawing would be 2.5 units by 1 unit.
A conveyor belt carries supplies from the first floor to the second floor, which is 21 feet higher. The belt makes a 60° angle with the ground. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor?
Hey there! I'm happy to help!
LENGTH OF CONVEYOR BELT
We are going to have to use some trigonometry. Let's think of this as a right triangle. The conveyor belt is the diagonal or the hypotenuse, while the ground is and the height of the room make a right angle as the legs.
We have a sixty degree angle between the conveyor belt and the ground. This is means that the 21 foot height is the opposite side of our right triangle. So, we are dealing with the opposite and the hypotenuse, so we will use the sine. The sine of an angle is equal to the opposite length divided by the hypotenuse length.
We will set up the following equation and solve for the length of our conveyor belt (c).
[tex]sin60=\frac{21}{c}[/tex]
We multiply both sides by c.
[tex]c(sin60)=21[/tex]
We divide both sides by sin60.
[tex]c=\frac{21}{sin60}[/tex]
If we evaluate this with a calculator, we get that c is equal to 24.2487113..., or 24 when rounded to the nearest foot.
So, the supplies travel 24 feet from one end to the other.
DURATION OF TRAVEL
We want to find how long it takes the supplies to move across the conveyor belt. We see that every minute, it moves 75 feet. We want to see how many minutes it will take to move 24 feet, as that is the length of the conveyor belt as we previously solved. Let's set up a proportion.
[tex]\frac{feet}{minute} =\frac{75}{1} =\frac{24}{m}[/tex]
We cross multiply, giving us the following equation.
75m=24
We divide both sides by 75.
m=0.32
We want to round to the nearest tenth of a minute, so it will take 0.3 minutes for the supplies to move to the second floor.
Have a wonderful day! :D
I am unable to find the answer to this pleas help me
Answer:
Step-by-step explanation:
[tex]\frac{1}{4}[/tex] of 600 is 150
hope this helps
plz mark as brainliest!!!!!!
Please help!!
can you explain how to do it cause my teacher didnt show us.
math question- If the spinner below is spun 500 times, then how many times could you expect to spin a D
thank you for you trying or helping!!
Answer:
500×4 =2400 I think would help u
What is 12.5% of 72
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
[tex]\sf of \ refers \ to \ multiplication.[/tex]
[tex]12.5\% \times 72[/tex]
[tex]\frac{12.5}{100} \times 72[/tex]
[tex]\sf Multiply.[/tex]
[tex]\frac{900}{100} =9[/tex]
Can someone help me solve parts (a) and (c) please? Thank you!
a) 4x +6
Add up all the sides to calculate perimeter
Answer:
a) 6x + 6
b) 15 x 24
c) see explanation
Step-by-step explanation:
a) 2x + x + 3 + 2x + x + 3 = 6x + 6
b) 6x + 6 = 78
6x = 72
x = 12
2(12) = 24
(12) + 3 = 15
15 x 24
c) 2x(x + 3) = 2x² + 6x
2(12)² + 6(12) = 288 + 72 = 360
15 x 24 is also 360
Theresa volunteers at a food shelf. Today she is filling bags of oranges. When she started, there were 213 oranges. After filling x bags with 3 oranges each, there were fewer than 51 oranges left. How many bags of oranges did Theresa fill? Part c
Answer:
Step-by-step explanation:
So we know that there are 213 oranges and Theresa fills each bag with 3 oranges, so we can represent each bag as 3x. She keeps filling until she reaches 51 oranges.
First. let's write this as an equation, She is starting with 213 oranges and filling x bags with 3 oranges to the point she has less than 51 oranges.
213 - 3x < 51
Now add 3x to both sides,
213 - 3x + 3x < 51 + 3x
213 < 51 + 3x
Now we subtract 51 from both sides,
213 - 51 < 51 - 51 + 3x
162 < 3x
Now we divide both sides by 3,
162/3 < 3x/3
We find the answer,
54 < x
x > 54 bags
There are 10 students on the basketball team. The coach selects 3 of them to go to the basketball clinic. In how many ways can she choose 3 of the 10 students?
[tex]_{10}C_3=\dfrac{10!}{3!7!}=\dfrac{8\cdot9\cdot10}{2\cdot 3}=120[/tex]
Question :-
There are 10 students on the basketball team. The coach selects 3 of them to go to the basketball clinic. In how many ways can she choose 3 of the 10 students?Answer :-
The coach can choose 3 of the 10 students in 120 ways.[tex] \rule{200pt}{3pt}[/tex]
Combinations refers to the number of ways of selecting from a set when the order is not important. The number of combinations of n objects taken r at a time is given by [tex]\sf C(n, r) = \dfrac{n!}{(n - r)!r!}, n \geqslant r[/tex].
Solution :-
As per the provided information in the given question, we have been given that the number of combinations of 10 students taken 3 at a time. We have been asked to calculate the ways that she can choose 3 of the 10 students.
To calculate the ways that she can choose 3 of the 10 students, we will apply the formula below :-
[tex] \qquad \bigstar \: \: \: \boxed{ \sf{ \: \: C(n, r) = \dfrac{n!}{(n - r)!r!} \: \: }}[/tex]
Substitute the given values into the above formula and solve for C:
[tex]\sf:\implies{ C(n, r) = \dfrac{n!}{(n - r)!r!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{(10 - 3)!3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10!}{7!3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8 \cdot \cancel{7!}}{ \cancel{7!}3!}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{10 \cdot 9 \cdot 8}{3 \cdot 2}}[/tex]
[tex]\sf:\implies{ C(10, 3) = \dfrac{720}{6}}[/tex]
[tex]\sf:\implies \bold{ C(10, 3) = 120 \: ways}[/tex]
Therefore :-
The coach can choose 3 of the 10 students in 120 ways.[tex]\\[/tex]
Learn more about combinations at https://brainly.com/question/11955073
Have a great day! <33
Helpppp pleaseee!!! Thank you
