Answer:
1
Step-by-step explanation:
The number of terms in the polynomial;
7b^7
The number of terms in this polynomial is simply 1
Since the two are together, they are treated as a single term in the polynomial.
Take for example a quadratic polynomial;
3x^2 + 2x + 1
This is a polynomial with 3 terms.
All multiplications are treated as a single unit.
This is the case in terms of what we have too
Find x and y. Give reasons to justify your solution. AB is a straight line.
Answer:
x=8 degrees y=21 degrees
Step-by-step explanation:
Determine which postulate or theorem can be used to prove that
APQS= ARQS.
Answer:
sss
Step-by-step explanation:
as you seen your puestion it says they are similar by side if you ask me by what because your given is side
There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. b How many ways can we choose a Senator from a chosen state? HELP AS SOON AS POSSIBLE
Answer:
i dont get it, can you please rephrase it?
A rectangle has an area of 524.4m2. One of the sides is 6.9m in length. Work out the perimeter of the rectangle. PLEASE ANSWER!!! SOON ASAP
Answer:
165.8 mSolution,
Area of rectangle= 524.4 m^2
Length(L)= 6.9 m
Breadth(B)=?
Now,
[tex]area = length \times breadth \\ or \: 524.4 = 6.9 \times b \\ or \: 524.4 = 6.9b \\ or \: b = \frac{524.4}{6.9} \\ b = 76 \: m[/tex]
Again,
Perimeter of rectangle:
[tex]2(l + b) \\ = 2(6.9 + 76) \\ = 2 \times 82.9 \\ = 165.8 \: m[/tex]
Hope this helps...
Good luck on your assignment.....
Answer:
The perimeter of the rectangle is 165.8cm
Step-by-step explanation:
Area of a rectangle = length × width
Area = 524.4m²
length = 6.9m
524.4 = 6.9 × width
width = 524.4 / 6.9
width = 76m
Perimeter of a rectangle =
2(length ) + 2(width)
length = 6.9m
width = 76m
Perimeter = 2( 6.9) + 2(76)
= 13.8 + 152
The final answer is
= 165.8cm
Hope this helps you
What is the explicit formula for this sequence?
5, 10, 20, 40, 80, 160,...
O A. an = 5 + 5(n-1)
O B. an = 2(5)(n-1)
O c. an = 5(2)"
D. an = 5(2)(n = 1)
Step-by-step explanation:
The above sequence is a geometric sequence
For an nth term in a geometric sequence
[tex] a(n) = a ({r})^{n - 1} [/tex]
where
n is the number of terms
a is the first term
r is the common ratio
From the question
a = 5
r = 10/5 = 2
Therefore the explicit formula for this sequence is
[tex]a(n) = 5( {2})^{n - 1} [/tex]
Hope this helps you
Grey’s Labs is testing a new growth inhibitor for a certain type of bacteria. The bacteria naturally grows exponentially at a rate of 4.7% each hour. The lab technicians know that the growth inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. The current sample contains 90 bacteria. Once a standard tube contains more than 270 bacteria, the sample will stop growing. So, to analyze the effect of the inhibitor over longer spans of time, the lab technicians move the bacteria to larger containers, essentially increasing the container size at a constant rate. This adaptation accommodates 100 more bacteria each hour. The research team wants to track the number of bacteria over time given these two conditions. Select the two inequalities they can use to model this situation.
P ≥ 90e^(0.047t)
P ≤ 270 + 100t
P ≤ 270 – 100t
P ≤ 0.047e^(90t)
P ≤ 90e^(0.047t)
Answer:
The two inequalities are;
P ≤ 90e^(0.047t)
P ≤ 270 + 100·t
Step-by-step explanation:
The parameters given for the testing of the new growth inhibitor are;
The growth rate of the bacteria = 4.7% exponentially
The growth inhibitor lowers the growth rate
The population of bacteria after time, t = P
The increase in the number of bacteria per unit time in the 100
The maximum number of bacteria in the standard tube = 270
Therefore, the number of bacteria after the first filling of the tube is P ≤ 270 + 100·t
The equation for exponential growth is [tex]A_0 e^{kt}[/tex]
Where:
A₀ = Initial population = 90
k = Percentage growth rate as percentage
t = Time
The equation for the population of bacteria under the influence of the inhibitor is therefore;
P ≤ [tex]90 \times e^{0.047 \cdot t}[/tex] which is P ≤ 90e^(0.047t).
Answer:
P≤270+100t
P≤90e^(0.047t)
Combine like terms: ab-a2+42-5ab+3a2+10
Answer:
-4AB+2A2+52
Step-by-step explanation:
1. FIRST WE PUT THE LIKE TERMS TOGETHER (REARRANGE THE PROBLEM)
AB-5AB-A2+3A2+42+10
2. SIMPLIFY ALL LIKE TERMS
-4AB+2A2+52
YOUR DONE!!!!!!
HOPE I HELPED
CAN I GET BRAINLIEST PLS? (DESPERATELY TRYING TO LEVEL UP)
-ZYLYNN JADE
15.) In a laboratory, the count of bacteria in a certain
experiment was increasing at the rate of 2.5% per
hour. Find the bacteria at the end of two hours if the
count initially was 4,80,000.
PLZ answer it's urgent plz
Answer:
Step-by-step explanation:
given,
initial count of bacteria(P)=4,80,000 ,
increasing rate of bacteria(R)=2.5%,
time(T)= 2 hours
amount(A)=p(1+R/100)^T
A=480000(1+2.5/100)^2
A=480000*(1681/1600)
A=504300
therefore, the bacteria at the end of 2 hours is 504300(approx)
Answer:
itchkirdcbn
Step-by-step explanation:
86rfbbcgui6g....
Please answer this question now
Answer:
61
Step-by-step explanation:
Definition of conguency
*figure on the right is rotated a bit
1)How many pinches of salt would be in 24 servings?
2) How many eggs would be needed to serve 18 people?
3) If you only had 33g of flour, how much of the other
ingredients would you need?
4) If 2 eggs were used, how many grams of flour would be
needed?
5) How much flour would be needed if 900ml milk is used?
HELP!!
Answer:
1. 2 pinch of salt
2. 3/2 egg =1.5 eggs
3. 33g of flour=1/3 pinch of salt
33g of flour=1/3 tbsp of oil
33g of flour=1/3 egg
33g of flour=100ml of milk
4. 24 servings
5. 300g of flour
Step-by-step explanation:
12 servings
Plain flour=100g
Salt=a pinch
Oil= 1 tbsp
Egg=1
Milk=300 ml
1. Pinches of salt in 24 servings
24
12 servings=1 pinch of salt
24 servings=24/12*1 pinch of salt
=2*1 pinch of salt
=2 pinch of salt
2. Egg needed for 18 servings
12 servings=1 egg
18 servings=18/12 * 1 egg
=3/2* 1 egg
=3/2 egg
3. If there are 33 grams of flour,
The other ingredients will be
33g/100g=1/3
The other ingredients will be 1/3 of the original measurement
Salt=a pinch
33g of flour=1/3 pinch of salt
Oil= 1 tbsp
33g of flour=1/3 tbsp of oil
Egg=1
33g of flour=1/3 egg
Milk=300 ml
33g of flour=1/3 of 300ml
=1/3*300
=300/3
=100ml of milk
4. If two eggs were used, grams of flour needed is
1 egg =12 servings
2 eggs=2* 12 servings
=24 servings
5. Flour needed if 900ml milk is used
100g flour=300ml of milk
900ml of milk=300ml * 3
Therefore,
900ml of milk=100g of flour *3
900ml of milk=300g of flour
PLEASE HELP! ! ! PLEASEEE!!
Answer:
4^2
Step-by-step explanation:
4^4 times 4^3 is equal to 4^7 since you just add the exponents. Then, when dividing, you subtract the exponents, so 4^7/4^5 is 4^2. I hope this is helpful!
Answer:
the answer is
Step-by-step explanation:
4 to the power of 2
you add 4 and 3 which is 7
and 7 subtract 5 which is
4 to the power of 2
A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. Find the probability of rolling a number greater than 10
Answer:
2/12
Step-by-step explanation:
You have 12 possible outcomes. Greater than 10 gives you 2 outcomes. 2/12
Answer:
1/6
Step-by-step explanation:
There are 12 equally likely outcomes, so the total number of possible outcomes is 12.
There are 2 numbers greater than 10: 11 and 12.
The number of desired outcomes is 2.
p(event) = (number of desired outcomes)/(total number of possible outcomes)
p(greater than 10) = 2/12 = 1/6
Complete the table of values below: x -3 -2 -1 0 1 2 3 How the graph relates to y=2x y=2x Answer Answer Answer Answer Answer Answer Answer Not applicable y=-2x Answer Answer Answer Answer Answer Answer Answer multiplied by Answer y=(3)(2x)
Answer:
The values of x are:
x : -3, -2, -1, 0, 1, 2, 3
Let's solve each by putting each value of x into each equation:
a [tex]y = 2^x[/tex]
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. [tex]y = -2^x[/tex]
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. [tex]y = (3)(2^x)[/tex]
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Input these values into the table.
Answer:
a y = 2^x
> x = -3
=> y = 2^(-3) = 1/8
> x = -2
=> y = 2^(-2) = 1/4
> x = -1
=> y = 2^(-1) = 1/2
> x = 0
=> y = 2^0 = 1
> x = 1
=> y = 2^1 = 2
> x = 2
=> y = 2^2 = 4
> x = 3
=> y = 2^3 = 8
b. y = -2^x
> x = -3
=> y = -2^(-3) = -1/8
> x = -2
=> y = -2^(-2) = -1/4
> x = -1
=> y = -2^(-1) = -1/2
> x = 0
=> y = -2^0 = -1
> x = 1
=> y = -2^1 = -2
> x = 2
=> y = -2^2 = -4
> x = 3
=> y = -2^3 = -8
c. y = (3)(2^x)
> x = -3
=> y = 3 * 2^(-3) = 3 * 1/8 = 3/8
> x = -2
=> y = 3 * 2^(-2) = 3 * 1/4 = 3/4
> x = -1
=> y = 3 * 2^(-1) = 3 * 1/2 = 3/2
> x = 0
=> y = 3 * 2^0 = 3 * 1 = 3
> x = 1
=> y = 3 * 2^1 = 3 * 2 = 6
> x = 2
=> y = 3 * 2^2 = 3 * 4 = 12
> x = 3
=> y = 3 * 2^3 = 3 * 8 = 24
Step-by-step explanation:
a) A square has an area of 64 cm?
Find the perimeter of the square.
(2)
64cm?
I
(3)
b) The diagram shows a right-angled triangle and a parallelogram.
The area of the parallelogram is 5 times
the area of the triangle and its perpendicular
height is h cm.
24 cm
Find the value of h.
h cm
+
7 cm
30 cm
Total marks: 5
Answer:
perimeter of square =34cm
Step-by-step explanation:
its 64..area
normally we find area by calculating side ×side
so 8×8
=64
so its 34cm....Find the value of x in the following
a) x:2 = 10:4 b) 3:x= 6:8
Answer:
a) x = 5
b) x = 4
Step-by-step explanation:
a) x:2 = 10:4
Product of extremes = Product of means
=> x*4 = 10*2
=> 4x = 20
Dividing both sides by 4
=> x = 5
b) 3:x = 6:8
Product of extremes = Product of Means
=> 3*8 = 6*x
=> 24 = 6x
Dividing both sides by 6
=> x = 4
Answer:
a. X= 5b. X= 4Solution,
[tex]a. \: \: \frac{x}{2} = \frac{10}{4} \\ \: \: or \: x \times 4 = 10 \times 2 \: ( \: cross \: multiplication) \\ \: \: or \: 4x = 20 \\ or \:x = \frac{20}{4} \\ \: \: \: x = 5[/tex]
[tex]b. \: \frac{3}{x} = \frac{6}{8} \\ or \: 6 \times x = 3 \times 8 \: ( \: cross \: multiplication) \\ or \: 6x = 24 \\ \: or \: x = \frac{24}{6} \\ x = 4[/tex]
Hope this helps...
Good luck on your assignment
Find the slope of the line that passes through (–7, 1) and (7, 8)
Answer:
slope= 1/2x
Step-by-step explanation:
For this line, you can count it going up 7 and to the right 14. Next, to calculate the slope, you take the change in y over the change in x, and you take those numbers (7 and 14) and divide 7 by 14 to get the slope, which simplifies to 1/2x, the slope.
Answer:
1/2
Step-by-step explanation:
The slope formula is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
where (x1,y1) and (x1, y2) are 2 points the line passes through.
We are given the points:
(-7,1) and (7,8). Match the corresponding variables with the points.
x1= -7
y1= 1
x2= 7
y2= 8
Substitute these values into the formula.
[tex]m=\frac{8-1 }{7--7 }[/tex]
Solve the numerator first. Subtract 1 from 8.
[tex]m=\frac{7 }{7--7 }[/tex]
Now solve the denominator. Subtract -7 from 7, or add 7 and 7.
[tex]m=\frac{7}{7+7}[/tex]
[tex]m=\frac{7}{14}[/tex]
This fraction can be simplified. Both 7 and 14 can be divided evenly by 7.
[tex]m= \frac{(7/7)}{(14/7)}[/tex]
[tex]m=\frac{1}{2}[/tex]
The slope of the line is 1/2.
I am between 8 o clock in the morning and 3:00 in the afternoon .My number of minutes is odd i am more than half an hour away from the next o clock i am closer to 5pm than to 5am what time am i ?
Answer:
1:00 PM
Step-by-step explanation:
According to the conditions given in the question, i confirm that the time time asked here is 1:00 PM.
at 1:00 PM, its 5 minutes (odd), clearly, more than half an hour away from the next o clock. It is closer to 5 PM than 5 AM.
can i get help with these questions
Calculate $\frac{1}{2} \cdot \frac{2}{4} \cdot \frac{3}{6} \cdot \frac{4}{8} \cdot \frac{5}{10} \cdot \frac{6}{12}$
Explanation:
Each fraction reduces to 1/2, so we have six copies of 1/2 being multiplied together. A shortcut to repeated multiplication like this is to use exponents
So you're really computing (1/2)^6 to get
(1/2)^6 = (1^6)/(2^6) = 1/64
Answer:
2.35*2/3=47/30
Step-by-step explanation:
could someone please answer the questions in the photo
Answer:
10. A dice has 6 sides each from 1-6, rolling each time can give 6 different possible results, hence the chances of rolling a 2, 3, and 5 will be 1/6 respectively.
To roll a 2, 3, and 5 in order, which are independent events,
the required probability will be
= 1/6 x 1/6 x 1/6
= 1/216
11. Using Pythagoras theorem,
8² + B² = 15²
B =√161
=12.689
13. Area of trapezoid= (upper base+ lower base)(height)/2
= (16+23)(3)/2
= 58.5 m²
Answer:
Answers:
Question #10:
Rolling a die three times gives 6 · 6 · 6 possibilities this makes 216 possibilities in total. Rolling the die in the order 2, 3, 5 is only one so the answer is: [tex]\frac{1}{16}[/tex].
Question #11:
Since the triangle is a right triangle we can use the pythagorean theorem:
[tex]B^{2}[/tex] + [tex]8^{2}[/tex] = [tex]15^{2}[/tex]
Working backwards we get that B is equal to 225 minus 64 which gets the square root of 161 or [tex]\sqrt{161}[/tex].
Question #12:
First we can start with finding the area of the rectangle in the trapezoid:
3 · 16 = 48
Next the two right triangles. 21 - 16 = 5 That is the length of the additional two triangles. Dividing 5 by two gets the base of one of them, but if we don't divide it by two we will be able to solve for both at the same time:
3 · 5 = 15
[tex]\frac{15}{2}[/tex] = 7.5
7.5 + 48 = 55.5
6 more than 3 times a number
Answer:
6+3x
Step-by-step explanation:
Have a good day and stay safe!
Answer:
Let the number be x
The above statement is written as
6 + 3xHope this helps you
HELP PLEASE ASAP PLEASE HELP ASAP
Answer:
angle 3 and angle 4 are equal because the diagonals/2 are equal. Angle 4 equals angle 1 due to opposite interior angles thereom. 90 degrees minus 37=53 degrees which is angle 2. Since angle 2 is equal to the angle GKH, 53+53=106 and 180-106=74 degrees, and due to vertical angles, angle 7 is 74 degrees.
A zoo has a menagerie containing four pairs of different animals, one male and one female for each. The zookeeper wishes to feed the animals in a specific pattern: each time he feeds a single animal, the next one he feeds must be a different gender. If he starts by feeding the male giraffe, how many ways can he feed all the animals?
Answer:
144
Step-by-step explanation:
We will use permutations to solve this problem
There are 4 pairs each having a male and a female.
The total number of sample points is 4! = 4*3*2*1= 24
He chooses the male first then the number of sample space he is left with are 3! = 3*2*1=6
The total number of ways he can select is 4! 3! = 24 * 6= 144
Another way of finding it out is
he has 4 pairs each having a male and a female so he chooses 1st male then he would choose from this
4 female choices*3 male choices * 3 female choices *2 male choices *2 female choices *1 male choices *1 female choices *= 4*3*3*2*2*1*1= 144
The zookeeper can feed all the animals in 144 ways
The number of different animals is given as:
[tex]n = 4[/tex]
The number of ways to feed any of the 4 male animals is:
[tex]Ways = 4![/tex]
Expand
[tex]Ways = 4 \times 3 \times 2 \times 1[/tex]
[tex]Ways = 24[/tex]
From the question, we understand that the female of the particular animal cannot be selected (yet).
So, there are 3 female animals left.
The number of ways to feed any of the 3 female animals is:
[tex]Ways = 3![/tex]
Expand
[tex]Ways = 3 \times 2 \times 1[/tex]
[tex]Ways = 6[/tex]
So, the number (n) of ways to feed all the animals is:
[tex]n = 24 \times 6[/tex]
[tex]n = 144[/tex]
Hence, he can feed all the animals in 144 ways
Read more about permutation at:
https://brainly.com/question/11706738
20 pts!! ANSWER SOON PLEASE!! WILL GIVE BRAINLIEST!!Would you rather paint 3/4 of a circle or a circular ring? Using area, explain your reasoning. Include calculations in your reasoning.
Answer:
Both/Neither.
Step-by-step explanation:
For the circle, the area is π(6)^2= 36π. 3/4 of that is 27π. Now, for the ring, area of outer circle is 36π. The area of inner circle is 9π. So, area of ring is 27π. That means, both will take the same amount of paint.
Find the measure of the unknown acute angle. Round your answer to the nearest degree.
Answer:
d. x° = 27°, y° = 63°
Step-by-step explanation:
To choose the correct answer, you only need to know that the smaller angle is opposite the shorter side. x° is opposite the shorter side so will have a smaller measure than y°.
The correct choice is ...
d. x° = 27°, y° = 63°
_____
If you want to actually go to the trouble to determine the angles exactly, you can use the tangent relation:
Tan = Opposite/Adjacent
tan(x°) = 4/8
x° = arctan(1/2) ≈ 26.56°
x° ≈ 27°
y can be computed as the complement of this, or can be computed in similar fashion:
tan(y°) = 8/4
y° = arctan(2) ≈ 63.43°
y° ≈ 63°
Alejandra can husk 8 ears of corn in 24 minutes. At this rate, how many ears of corn can she husk in 33 minutes?Jonah bicycled 12 miles in 4 hours. What is the unit rate?
Answer:
Step-by-step explanation:
If she can husk 8 in 24mins
⟩ 8 = 24
Let x = ears of corn in 33mins
⟩ 8 = 24
x = 33
If less more divide
⟩ 24x = 8×33
⟩ x = 264÷24
⟩ x = 11 mins
Derive the equation of the parabola with a focus at (6, 2) and a directrix of y = 1. f(x) = −one half(x − 6)2 + three halves f(x) = one half(x − 6)2 + three halves f(x) = −one half(x + three halves)2 + 6 f(x) = one half(x + three halves)2 + 6
Answer:
Second choice.
f(x) = 1/2(x - 6)^2 + 3/2.
Step-by-step explanation:
The distance of a point (x, y) from the focus = the distance of the point from the directrix, so:
(x - 6)^2 + (y - 2)^2 = (y - 1)^2
x^2 - 12x + 36 + y^2 - 4y + 4 = y^2 - 2y + 1
x^2 -12x + 39 = 2y
y = f(x) = 1/2 (x^2 - 12x + 39)
I see you want the answer in vertex for so it is:
f(x) = 1/2 [ (x - 6)^2 - 36) + 39)
f(x) = 1/2(x - 6)^2 + 3)
f(x) = 1/2(x - 6)^2 + 3/2.
A parabola is a plane that is approximately U-shaped.
The equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
The given parameters are:
[tex]\mathbf{Focus = (6,2)}[/tex]
[tex]\mathbf{Directrix: y = 1}[/tex]
First, equate the directrix to 0
[tex]\mathbf{y - 1 = 0}[/tex]
The equation is then calculated as:
[tex]\mathbf{(x - a)^2 + (y - b)^2 = (y- 1)^2}[/tex]
Where:
[tex]\mathbf{(a,b) = (6,2)}[/tex]
So, we have:
[tex]\mathbf{(x - 6)^2 + (y - 2)^2 = (y- 1)^2}[/tex]
Expand
[tex]\mathbf{x^2 - 12x +36 + y^2 - 4y + 4 = y^2 - 2y + 1}[/tex]
Subtract y^2 from both sides
[tex]\mathbf{x^2 - 12x +36 - 4y + 4 =- 2y + 1}[/tex]
Collect like terms
[tex]\mathbf{x^2 - 12x +36 + 4 - 1 =4y - 2y}[/tex]
[tex]\mathbf{x^2 - 12x +39 =2y}[/tex]
Divide through by 2
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +39)}[/tex]
Express 39 as 36 + 3
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36 + 3)}[/tex]
Factor out 3/2
[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36) + \frac 32}[/tex]
Expand the bracket
[tex]\mathbf{y = \frac{1}{2}(x^2 - 6x - 6x +36) + \frac 32}[/tex]
Factorize
[tex]\mathbf{y = \frac{1}{2}(x(x - 6) - 6(x -6)) + \frac 32}[/tex]
Factor out x - 6
[tex]\mathbf{y = \frac{1}{2}((x - 6) (x -6)) + \frac 32}[/tex]
Express as squares
[tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
Hence, the equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]
Read more about equations of parabola at:
https://brainly.com/question/4074088
Farmer Hanson is putting together fruit baskets. He has 240 apples and 150 pears. What is the largest number of baskets he can put together so that he can have the same number of apples and same number of pears in each basket considering no fruit is left out?
Answer: 30 baskets.
Step-by-step explanation:
You need to find the Greatest Common Factor (GCF).
240 (apples) = 2 x 2 x 2 x 2 x 3 x 5
150 (pears) = 2 x 3 x 5 x 5
GCF (240, 150) = 2 x 3 x 5
= 30
You can make 30 baskets containing 240/30 = 8 apples and 150/30 = 5 pears.
Answer:
30 baskets
Step-by-step explanation:
Some pupils were asked which their favourite school subject was, from a choice of maths, english and science. Soe of the results are shown in the table. How many pupils in total chose English as their favourite subject?
Answer:
[tex]\boxed{26 pupils}[/tex]
Step-by-step explanation:
Girls for English:
20 + English + 12 = 36
English + 32 = 36
English = 36-32
English = 4 (For girls)
Total for Science:
12+7 = 19
Total for English:
25 + English + 19 = 70
English + 44 = 70
English = 70-44
English = 26 pupils
There are 26 pupils (20 Boys and 6 Girls) who chose English as their favorite subject.
The table shows data about the favorite subject of some of the students.
The following things can be observed from the given table:
Girls who like maths are 20, who like science are 12 and total girls are 38. So, the number of girls who like English will be [tex]38-20-12=38-32=6[/tex]. So. 6 girls like English subject.Out of 25 students who like maths, 20 are girls. So, 5 students are boys who like maths.Total students who like science are 12 girls and 7 boys. So, the sum of students will be 19.Total number of students participated in the survey is 70.So, the total number of students of English subject can be calculated as,
[tex]70-25-19=70-44\\=26[/tex]
So, out of 26 students, 6 are girls and 20 will be boys who love English subject.
Therefore, there are 26 pupils (20 Boys and 6 Girls) who chose English as their favorite subject.
For more details, refer to the link:
https://brainly.com/question/21976671
The time (in minutes) taken for a dose of a certain drug to be effective as a sedative on lab animals is normally distributed with mean =1 and variance 2=0.01. What is the proportion of animals for which the time taken is between 1 and 1.1 minutes?
Answer:
Step-by-step explanation:
Let x be the random variable representing the time (in minutes) taken for a dose of a certain drug to be effective as a sedative on lab animals. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 1
σ = √variance = √0.01 = 0.1
the probability that the time taken for a randomly selected animal is between 1 and 1.1 minutes is expressed as
P(1 ≤ x ≤ 1.1)
For x = 1,
z = (1 - 1)/0.1 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 1.1
z = (1.1 - 1)/0.1 = 1
Looking at the normal distribution table, the probability corresponding to the z score is 0.84
Therefore,
P(1 ≤ x ≤ 1.1) = 0.84 - 0.5 = 0.34
The the proportion of animals for which the time taken is between 1 and 1.1 minutes is 0.34