Answer:
a + b = 27
=> a = 27 - b
ab = 50
So, (27 - b) x b = 50
27b - b^2 = 50
b^2 - 27b + 50 = 0
Solving, b = 25, 2
Hence,
Case 1: b = 25, a = 2
Case 2, b = 2, a = 25
Answer:
2, 25
Step-by-step explanation:
Let the numbers be x and y :
x + y = 27xy = 50Rearrange the first equation so it is equal to one variable :
y = 27 - xSubstitute the value in the second equation :
x(27 - x) = 5027x - x² = 50x² - 27x + 50 = 0(x - 25)(x - 2) = 0x = 2, 25There are 2022 kangaroos and some koalas living across seven parks. in each park the number of kangaroos is equal to the number of koalas in all the other parks. how many koalas live in the seven parks in total
Answer:
337
Step-by-step explanation:
I remember this from UKMT maths challenge.
Let the number of kangaroos in each of the seven parks be , , , , , and with the
corresponding number of koalas being , , , , , and . The question tells us that the
number of kangaroos in any park is equal to the sum of the numbers of koalas in the other six
parks. Therefore we have
= + + + + + ,
= + + + + + ,
= + + + + + ,
= + + + + + ,
= + + + + + ,
= + + + + + ,
= + + + + + .
Adding these equations, we obtain
+ + + + + + = 6( + + + + + + ).
The total number of kangaroos in the seven parks is 2022. Hence
+ + + + + + = 2022.
Therefore
2022 = 6( + + + + + + )
and hence the total number of koalas in the seven parks is
+ + + + + + = 2022 ÷ 6 = 337.
PLEASE HELP!!!!
y = 1.4 (1.02)
a =
b=
r(as a percentage)
Answer:
a = 1.4 then b = (1+0.02) and r = 2%
4.
Suppose events A and B are independent and P(A and B) is 0.2
Which statement could be true?
(1) P(A) = 0.4, P(B) = 0.3, P(A or B) = 0.5
(2) P(A) = 0.8, P(B) = 0.25
(3) P(A/B) = 0.2, P(B) = 0.2
(4) P(A) = 0.15, P(B) = 0.05
Answer: answer choice 2) P(A) = 0.8, P(B) = 0.25
Step-by-step explanation:
The True statement is P(A) = 0.8, P(B) = 0.25.
The correct option is (B).
What is Conditional Probability?Conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.
1. 0.4 ·0.3≠ 0.2,
2. 0.8 · 0.25 = 0.2
3. P(A|B)= P(A)= 0.2
0.2 ≠ 0.2 · 0.2
4. 0.2 ≠ 0.15 · 0.05
Hence. the only condition is satisfied is (B).
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please solve this problem using the pythagorean theorem, and give me the right answer and I will give you brainliest. :)
Answer:
6.5
Step-by-step explanation:
9.1^2-6.4^2 is 41.85
square root of that is 6.469...
the food bill for meal at a restaurant is $12. THe sales tax is 6.5%, and you leave 15% tip. Wat is the total cost of the meal? PLEASE ANSWER FAST
Answer:
Step-by-step explanation:
12*6.5%=0.72
12+15%=13.8
0.72+13.8=14.52
What is the remainder of (x3+5x2−32x−7)÷(x−4) ? Enter your answer in the box.
Answer:
x^2+5x-36-7/x
Step-by-step explanation:
assuming x^3 and 5x^2
The density of iron is 7.8 g/cm3. an iron beam has a volume of 10,504 cm³. what is the mass of the iron beam? enter your answer as a decimal in the box.
Under the assumption of uniform iron beam and definition of uniform density, the total mass of the iron beam is equal to 81931.2 grams.
How to determine the mass of the iron beam
Let suppose that the iron beam has an uniform density, the mass of the iron beam (m), in gram, is equal to the product of its density (ρ), in grams per cubic centimeter, and its volume (V), in cubic centimeters:
m = ρ · V (1)
If we know that ρ = 10504 cm³ and V = 7.8 g/cm³, then the mass of the iron beam is:
m = (7.8 g/cm³) · (10504 cm³)
m = 81931.2 g
Under the assumption of uniform iron beam and definition of uniform density, the total mass of the iron beam is equal to 81931.2 grams.
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Which of these strategies would eliminate a variable in the system of equations? 5x + 3y = 9
4x - 3y = 9 Choose all answers that apply: (Choice A) A Subtract the top equation from the bottom equation. (Choice B) B Add the equations. (Choice C) C Subtract the bottom equation from the top equation.
Answer:
(Choice B) Add the equations
Step-by-step explanation:
The equations that were given are:
[tex]5x + 3y = 9 \\ 4x - 3y = 9[/tex]
If we add the equequatiothen the y variable would be eliminated:
[tex] +3y + (-3y) = 0[/tex]
A train left a station at noon going at 40 mph. A second train left at 3 pm going in thte same direction at 6o mph. At what time iwll the second train catch up with the first
Answer:
9PM
Step-by-step explanation:
3pm - 40x3=120 Miles Travelled (Noon Train)
3pm - 60x0=0 Miles Travelled (3pm Train)
4pm - 40x4=160 Miles Travelled (Noon Train)
4pm - 60x1=60 Miles Travelled (3pm Train)
5pm - 40x5=200 Miles Travelled (Noon Train)
5pm - 60x2=120 Miles Travelled (3pm Train)
6pm - 40x6=240 Miles Travelled (Noon Train)
6pm - 60x3=180 Miles Travelled (3pm Train)
7pm - 40x7= 280 Miles Travelled (Noon Train)
7pm - 60x4=240 Miles Travelled (3pm Train)
8pm - 40x8 = 320 Miles Travelled (Noon Train)
8pm - 60x5=300 Miles Travelled (3pm Train)
9pm - 40x9 = 360 Miles Travelled (Noon Train)
9pm - 60x6= 360 Miles Travelled (3pm Train)
A cube of side 3cm contains a sphere within it.if the sphere touches each face of the cube,find the volume of the space between the cube and the sphere
Answer:
6.86cm^3
Step-by-step explanation:
In order to do this problem you must first find the volume of the cube and subtract the volume of the sphere within it.
Volume of a cube is S^3
using the given 3×3×3= 27cm^3 volume of cube
volume of a sphere is 4/3 pir^3
4/3 × pi x 1.5^3 = 14.14cm^3 volume of sphere
now simply subtract
27-14.14= 6.86 cm^3
2. What is the new correction equation using the Equal Values Method for the following system below?
y=2x+1
y = 6-3x
Answer:
new equation: 2x +1 = 6 -3x
solution: (x, y) = (1, 3)
Step-by-step explanation:
The Equal Values Method of solving a system of equations has you equate the two expressions that are equal to the same variable or expression. Here, we have two expressions that are equal to y.
equationThe next step is to set them equal to each other:
2x +1 = 6 -3x
__
solutionThis equation can be solved by adding 3x -1 to both sides to get ...
5x = 5
Then dividing both sides by 5 gives ...
x = 1
Substituting into either expression for y gives its value:
y = 2x +1 = 2(1) +1 = 3
The solution to the system is (x, y) = (1, 3).
Which equation is equal to y = 2x + 3 ?
the options are
y + 3 = 2x
y - 3 - 2x = 0
2x + y = 3
y + 2x = -3
The equation y = 2x + 3 is a linear equation, and the equivalent equation of y = 2x + 3 is y - 3 - 2x = 0
How to determine the equal equation?The equation is given as:
y = 2x + 3
Subtract 3 from both sides
y - 3 = 2x
Subtract 2x from both sides
y - 3 - 2x = 0
The above means that the equation y - 3 - 2x = 0 is equal to the equation y = 2x + 3
Hence, the equivalent equation of y = 2x + 3 is y - 3 - 2x = 0
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How do I find the domain range and function of the graph
Answer:
D = {-3, -2, -1, 1, 4}
R = {-5, -1, 0, 2}
Step-by-step explanation:
You have correctly described the process of finding the domain and range by the way you filled in the blanks at the top of the sheet.
__
The domain is the set of x-values of the points on the graph:
D = {-3, -2, -1, 1, 4}
The range is the set of (unique) y-values of the points on the graph:
R = {-5, -1, 0, 2}
The dot plot below represents how long it takes students in an 8th grade math
class to get to school every morning.
COMMUTE TIME
......
...
:
...
G...
-
10
20
25
30
35
40
45
Minutes
What was the shortest commute time?
minutes
ann
Answer:
5 minutes
Step-by-step explanation:
Solve the following...
[tex]1 \cfrac{1}{5} \times 2\cfrac{1}{3} [/tex]
Let's see
[tex]\\ \rm\Rrightarrow 1\dfrac{1}{5}\times2\dfrac{1}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6}{5}\times \dfrac{7}{3}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{6(7)}{5(3)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{42}{15}[/tex]
[tex]\\ \rm\Rrightarrow2 \dfrac{12}{15}[/tex]
The sum of three consecutive intergers is 189 what are the integers
Answer:
62, 63, 64
Step-by-step explanation:
The middle integer of three consecutive integers will be the average of them. That is, it will be their sum, divided by 3.
__
The middle integer is 189/3 = 63.
The three consecutive integers are 62, 63, 64.
_____
Additional comment
If you'd like to write an equation that tells you the same thing, let x represent the middle integer. Then the lower one is x-1, and the upper one is x+1. Their sum is ...
(x-1) +x +(x+1) = 189
3x = 189 . . . . . . . . . . . . simplify
x = 189/3 = 63 . . . . . . . divide by the coefficient of x
(x-1) = 63-1 = 62 . . . . . . find the other two integers
(x+1) = 63+1 = 64
What is the volume of a sphere with a radius of 6 mm? sphere v = four-thirds pi r cubed v = 216pi mm3 v = 288pi mm3 v = 512pi mm3 v = 648pi mm3
Answer:
[tex]V =288 \pi \ mm^3[/tex]
Step-by-step explanation:
[tex]V =\frac{4}{3} \pi r^{3}[/tex]
[tex]=\frac{4}{3} \pi \left( 6\right)^{3}[/tex]
[tex]=\left( \frac{4}{3} \right) \times \pi \times 216[/tex]
[tex]=\left( \frac{4}{3} \right) \times 216\times \pi[/tex]
[tex]=288\times \pi[/tex]
Answer:
IT IS B
Step-by-step explanation:
SOURCE: TRUST ME BRO
Someone please helppp
your friend house is 6.4 miles north and 12 miles west of your bank. how far is your friends house from your bank
Answer:
the answer is 76.8
Step-by-step explanation:
multiple of the number
Use the binomial formula to find the coefficient of the q22p² term in the expansion of (q-2p)24.
7
X
Ś
?
What is the area of this triangle in the coordinate plane?
25.0 units²
27.5 units²
50.0 units²
55.0 units²
Answer:
B.) 27.5²
Explanation:
This should be the triangle per say:
The Area of a Triangle can be found by using the formula- 1/2 x base x height.
In this case: 1/2 x 11 x 5
This equals 27.5².
Hopefully this may help.
The cosine of an angle a is 0.8. what is the value of sin (a)
If you live in a state that needs to collect $18 million in property taxes and has a tax rate of 2.77%, what is that state's
taxable value?
O $650 million
O $65 million
O $6 million
O $499,000
Answer:
la respuesta es 65 millones
An ice cream shop will allow you to build your own sundae. You must choose from vanilla, chocolate, or strawberry ice cream. You must choose with or without bananas, with or without nuts, and must pick between chocolate and caramel syrup. How many sundaes can you build?
Answer: 24
Step-by-step explanation: 3*2*2*2=24
You can build 24 sundaes
Rita has a circular hot tub. the hot tub has a circumference of 25.12 feet. it is 3.5 feet deep.
how much water can the hot tub hold?
Volume is a three-dimensional scalar quantity. The amount of water that the tub can hold is 4,981.75 litres.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the circumference of the tub is 25.12 feet, therefore, the radius of the circumference of the tub will be,
Circumference = 2πr
25.12 = 2×π×r
r = 3.9979ft ≈ 4ft
Now, the volume of the tub will be,
Volume = πr²h = π×(4²)×3.5 = 175.929 ft³
Since 1 ft³ is equal to 28.3168 litres, therefore, the amount of water that a tub can store is
Volume of water = 175 × 28.3168 = 4,981.75 litres
Hence, the amount of water that the tub can hold is 4,981.75 litres.
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what is the slope of the line 6x+5y=10 ?
Answer:
[tex]-\dfrac 65[/tex]
Step-by-step explanation:
[tex]~~~~~~~6x +5y = 10\\\\\implies 5y = 10-6x\\\\\implies y = \dfrac 15(10-6x)\\\\\implies y=-\dfrac65x+2\\\\\text{It is now in slope-intercept form(y=mx+c), where m is the slope.}\\ \\\text{Hence,}~ m = -\dfrac 65[/tex]
what is the area in square centimeters of the isosceles trapezoid below?
The first sequence rule is multiply by 4 starting from 7. The second sequence rule is add 5 starting from 8. What is the first number that appears in both sequences?
28
56
112
225
Answer:
28
Step-by-step explanation:
28 is the number that appears first for both.
For first sequence:
7 × 4 = 28 × 4 = 112 × 4 = 448
For second sequence:
8 + 5 = 13 + 5 = 18 + 5 = 23 + 5 = 28
giving the following sequence: 21, 24.5, 28 write an equation for the nth term
Answer:
tₙ = (3.5x + 17.5)
evauleate 150-(2+x)^3 when x is 2
Answer:
Down below
Step-by-step explanation:
150 - (2 + x)^3
150 - (2 + 2)^3
150 - (4)^3
150 - 64
= 86
I would check my math but I believe this is correct.
Answer:
86
150-(2+x)^3
⇒ x = 2
2 + 2 = 4
4^3(4 • 4 • 4) = 64
150 - 64 = 86
What is the mean absolute deviation of 1, 2, 2, 3, 5, 6, 6, 8, 8, 9
Answer:
5
Step-by-step explanation:
1+2+2+3+5+6+6+8+8+9/10=5
