To find the growth factor, b, we can use the formula for exponential growth: n = ln(M)/ln(b), where n is the number of years, M is the final population, and b is the growth factor.
Explanation:To find the growth factor, b, we can use the formula for exponential growth: n = ln(M)/ln(b), where n is the number of years, M is the final population, and b is the growth factor. In this case, the final population is 1573 bears. Let's solve for b: n = ln(1573)/ln(b). To isolate b, we can take the exponential of both sides: b^n = 1573. Now we can solve for b by taking the nth root of 1573. The growth factor, b, is the value that, when raised to the power of the number of years, gives us the final population of bears.
Which expression can be written as x + 4 = x^2? Assume x > 0
The shoe store has twice as many black shoes as it does brown shoes. The total number of shoes is 66. How many brown shoes are there?
To solve the problem, denote the number of brown shoes as x, and the black shoes as 2x, as the store has twice as many black shoes. The total number of shoes is x + 2x = 66. Solving this gives us x (brown shoes) as 22.
Explanation:The subject is concerning a mathematical problem involving ratios. In the given problem, it is stated that the shoe store has twice as many black shoes as brown shoes, and the total number of shoes is 66. Here's a step-by-step process to solve it:
Let's denote the number of brown shoes as x. Therefore, due to the problem stating that there are twice as many black shoes, the number of black shoes will be 2x.The total number of shoes is the sum of the brown shoes (x) and the black shoes (2x), thus the equation becomes: x + 2x = 66.Solving this equation gives us:3x = 66.Divide both sides of the equation by 3 to isolate x, which gives us x = 22.Therefore, there are 22 brown shoes in the store.
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DATA MANAGEMENT GRADE 12! HELP
Between periods at a hockey game, some fans are selected to shoot a puck at the net from each of 10 m, 15 m and 30 m, with winnings of $50, $100 and $1000 per goal scored, respectively. The chance of scoring from each position has been estimated to be 60%, 20% and 2%, respectively. What is the expected payout per fan? Question 6 options: $140 $70 $2300 $26 620
What is the answer to this?
Write the sum using summation notation, assuming the suggested pattern continues.
2 - 12 + 72 - 432 + ...
Answer:
[tex]\displaystyle \sum_{k=1}^{n}2(-6)^{k-1}[/tex]
Step-by-step explanation:
we have to write the sum using summation notation of the following series:
2-12+72-432+...
which could also be written as:
2+(-12)+72+(-432)+...
We observe that first term=2
second term=2×-6
Third term=2×-6×-6
Fourth term=2×-6×-6×-6
nth term=[tex]2\times (-6)^{n-1}[/tex]
Hence, the series sum= [tex]\displaystyle \sum_{k=1}^{n}2(-6)^{k-1}[/tex]
________ probability is used when we know the number of possible outcomes of the event of interest and the total number of possible outcomes in the sample space.
If EF = HG and HG = 16, find the diameter of K
Answer:
Diameter of the circle K = 20 units
Step-by-step explanation:
Given that : EF = HG
Also, HG = 16 units
⇒ EF = 16 units
Now, any line drawn perpendicular to the chord always bisects the chord
⇒ KI will bisect the chord EF
⇒ EI = 8 units
Now, in ΔEIK using Pythagoras theorem we have :
⇒ EK² = 8² + 6²
⇒ EK² = 100
⇒ EK = 10 units
So, Radius of the circle K = 10 units
Now, Diameter of the circle K = 2 × 10
= 20 units
given that (6,-8) is on graph f(x), find the corresponding point for the function f(-1/2x)
Kite DCFE is inscribed in circle A shown below:
If the measure of arc DEF is 266°, what is the measure of ∠DEF?
Numerical Answers Expected!
Answer:
133 degrees
Step-by-step explanation:
Given is a picture of a kite DCFE inscribed in circle A
The vertices of the kite D, C, E and F lie on the circle.
A is the centre.
Arc DEF = 266 degrees
This means the subtended angle of arc DEF at the centre = Angle DAF = 266
By theorem on circles, we have central angle of any arc is twice the angle subtended by the arc on the remaining part of the circumference
Hence
Angle DEF = 1/2 angle DAF
i.e. DEF =[tex]\frac{266}{2} =133[/tex]
133 degrees
Class a has x students and class b has y students. the average of class a is 85 and class b is 90. when the scores of class a and b are combine the average is 88, what is the ratio of x to y
Which expression gives the same result as ∑4i=0(5)(1/3)i?
The symbol, ∑ is a summation sign that drills us to sum the elements of a sequence. The variable of summation is represented by an index that is placed under the summation sign and is often embodied by i. The index is always equal to 1 and adopt values beginning with the value on the right hand side of the equation and finishing it with the value over head the summation sign. So in the expression ∑4i = 0(5)(1/3)i will be the same as:
∑4i = 0(5)(1/3)i
= (1/3)⁰ + (1/3)¹ + (1/3)² + (1/3)³ + (1/3)⁴ + (1/3)⁵
= 364/243
A committee consisting of 6 people is to be selected from eight parents and four teachers. find the probability of selecting three parents and three teachers.
Answer with explanation:
→Total Number of People which are in the group =8 parents + 4 Teacher=12 People
→Probability of an Event
[tex]=\frac{\text{Total Favorable Outcome}}{\text{Total Possible Outcome}}[/tex]
→Probability of selecting three parents and three teachers
= Selecting 3 parents from 8 Parents +Selecting 3 teacher from 4 teacher
As order of Arrangement is not Important ,so we will use the concept of Combinatorics.
→→ Required Probability
[tex]=\frac{_{3}^{8}\textrm{C}\times _{3}^{4}\textrm{C}}{_{6}^{12}\textrm{C}}\\\\=\frac{\frac{8!}{3!\times 5!}\times \frac{4!}{3!\times 1!}}{\frac{12!}{6!\times 6!}}\\\\=\frac{56 \times 4}{7\times 4 \times 3\times 11}\\\\=\frac{8}{33}[/tex]
URGENT!!
what is this graph considered:
A: Bimodal Skewed
B: Bimodal Symmetric
C: Unimodal Skewed
D:Uniform
E: Unimodal Symmetric
The next four batters on a baseball team have hitting percentages of 0.400,0.325, o.250, and 0.300, respectively The team currently has two outs. If any player gets an out, the next player or players will not get an opportunity to bat. What is the probability that the fourth player will have an opportunity to bat?
B for online school yuhp
20 POINTS
Robinson's home run hitting distance is normally distributed with a mean of 394 feet and a standard deviation of 35 feet. He wanted to find the probability that his home runs traveled at least 380 feet. He calculated the z-score to be −0.40 and looked up the probability on the Standard Normal Probabilities table. He found that the table stated his probability as 0.3446. Determine whether Robinson made an error in his calculation and explain.
I need step by step instructions
Answer:
he made an error, the probability that his homeruns traveled at least 380 feet is 65.54%
Step-by-step explanation:
let´s see the Robinson's calculation:
using the formula for normal distribution:
Z = (x-μ)(σ/[tex]\sqrt{n}[/tex]) [1]
where:
x is raw measurement
μ is the mean
σ is the standar deviation
n is the size of sample
in this case x = 380, μ = 394, σ = 35, n = 1.
then using the equation [1] he calculated the Z score:
[tex]Z = \frac{380-394}{\frac{35}{\sqrt{1}}}\\\\Z = -\frac{14}{35}\\\\Z = -0.4\\\\[/tex]
and it's correct but his answer is wrong because he confuse the term at least.
at least means that the probability be greater than 380 feet, not less than 380 feet.
so he looked the Z score in a table of normal distribution (this table has been attached) and effectively this value is 0.3446. but as I told you this probability is for x < 380.
therefore, the probability that his homeruns traveled at least 380 feet is:
[tex]P(x > 380) = 1 - P(x < 380)\\\\P(x > 380) = 1 - 0.3446\\\\P(x > 380) = 0.6554 \ or \ 65.54 \%[/tex]
please see the table attached.
The measure of an angle is 60° less than nineteen times the measure of its supplement. what is the measure of the angle?
The measure of the angle will be;
⇒ 60°
What is Supplementary angle?The sum of two or more angle is 180 degree then the angle is called the Supplementary angle.
Given that;
The statement is,
''The measure of an angle is 60° less than nineteen times the measure of its supplement.''
Let measure of an angle = x
So, The measure of its supplement = 180° - x
Hence, We can formulate;
⇒ x = (180 - x) - 60°
Solve for x as;
⇒ x = 180 - x - 60
⇒ x + x = 120
⇒ 2x = 120
⇒ x = 120/2
⇒ x = 60°
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(05.05)On the coordinate plane below, what is the length of AB?
A coordinate plane is shown with the following points A at negative 9, 4; B at 5, 4; C at 5, negative 5; D at negative 9, negative 5. All points are connected to create a rectangle.
8 units
9 units
14 units
15 units
Answer:
14 units
Step-by-step explanation:
both points have the same y-coordinate, so therefore, the line is horizontal from x = -9 and x = 5 9 (plus I did the 5.05 math quiz segment two 6th grade)
1. A ladybug lands on the end of a pinwheel that is spinning at a steady speed. The equation y = –7 sin (0.4πx) + 11 gives the height of the ladybug y, in centimeters, above the ground x seconds after landing. What is the diameter of the pinwheel
What is the arc length when Θ = pi over 3 and the radius is 5 cm?
Answer:
Arc length = 5.23 cm
Step-by-step explanation:
Given : Radius = 5 cm
Angle = [tex]\theta=\frac{\pi}{3}[/tex]
To find : Arc length(A)
Solution: The formula of arc length is
A = radius × angle(in radian)
[tex]A= 5\times\frac{\pi}{3}[/tex]
⇒[tex]\frac{5\pi}{3}[/tex]
A ⇒15.70/3 = 5.23 cm
What can you say about the nature of any other zeros of the quadratic equation which has one complex zero? Explain your answer.
Hosting a breakfast for 25 people you plan to serve scrambled eggs the grocery store sells eggs in cartons and each carton can feed people. how many cartoons of eggs must you buy to ensure each guest a serving
The number of egg cartons required to serve 25 people with scrambled eggs is 3 cartons, assuming each carton serves 12 people and we cannot purchase partial cartons.
To calculate the number of egg cartons needed to serve scrambled eggs to 25 people, we first need to know how many people each carton can serve. However, it appears there's a typo or missing information in the question regarding the number of people an egg carton can serve. Assuming that one egg carton can serve a certain number of people, we'd use that information to determine the total number of cartons required.
If we refer to the related information provided about pancakes - where one egg is needed for 8 pancakes - we can draw a parallel for eggs for scrambled eggs. If one egg serves one person in the case of scrambled eggs, and typically there are 12 eggs in a carton, then one carton would serve 12 people.
Using this assumption, since we have 25 people to serve, we can calculate the number of cartons needed as follows:
25 people
Since we cannot purchase a partial carton, we would need to round up to the nearest whole number. Therefore, we would need to purchase 3 cartons of eggs to ensure each guest has a serving.
The table below shows some values of f(x) and g(x) for different values of x: x f(x) = 2x + 24 g(x) = 5(0.5)x −2 20 −1 0 5 1 2.5 2 28 complete the chart and determine the solution of the equation f(x) = g(x). a x = −2 b x = −1 c x = 1 d x = 20
Answer:
answer is A
Step-by-step explanation:
Which is an undefined term that is useful for defining a circle?
a. angle
b. distance
c. line
d. segment
True or false the rules of two dimensional geometry can be applied to three dimensional solids
Answer:
the answer is TRUE.
Step-by-step explanation:
we can coclude that the three-dimensional geometry is more or less the extension of a two-dimensional geometry as many of the same principles imply.
two points determine a straight line no matter whether the points are two-dimensional or three-dimensional.
hence the following statements holds true that the rules of two dimensional geometry can be applied to three dimensional solids.
Answer:
The answer is false.
Step-by-step explanation:
The lengths of the sides of a right triangle are a and b, and the hypotenuse is
c. find the area of the triangle. a=2 squareroot 3; c=4 a = sq. ft.
Answer:
Area is 2√3 ft².
Step-by-step explanation:
Given,
A right triangle having sides,
a = 2√3 ft,
c = 4 ft,
Where, c is the hypotenuse of the triangle,
If b is the other leg of the triangle,
By the pythagorean theorem,
[tex]c^2=a^2+b^2[/tex]
[tex]4^2=(2\sqrt{3})^2+b^2[/tex]
[tex]16=12+b^2[/tex]
[tex]4=b^2[/tex]
[tex]\implies b = 2[/tex]
Hence, the area of the given triangle is,
[tex]A=\frac{1}{2}\times a\times b[/tex]
[tex]=\frac{1}{2}\times 2\sqrt{3}\times 2[/tex]
[tex]=\frac{4\sqrt{3}}{2}[/tex]
[tex]=2\sqrt{3}\text{ square ft}[/tex]
If a seed is planted, it has a 90% chance of growing into a healthy plant. if 7 seeds are planted, what is the probability that exactly 4 don't grow?
Answer:
0.098415
Step-by-step explanation:
The way the question is worded is odd and you should probably actually include “don’t grow into a healthy plant” or something. You can use the binomial distribution. Suppose ∼Bin(6,0.1) so the probability that k trees don’t grow into a healthy plant is
Pr( = ) = (6 / ) 0.16^ 0.9^6−
Then the probability that two don’t grow into healthy plants is
Pr( = 2) = (6/2) 0.1^2 0.9^4
this is equal to 0.098415
To calculate the probability of exactly 4 out of 7 seeds failing to grow, use the binomial probability formula with n = 7, p = 0.10, and k = 4. The calculation involves combinations and exponentiation.
Explanation:The question is asking for the probability of exactly 4 seeds out of 7 failing to grow. Given that each seed has a 90% chance of growing into a healthy plant, which means each seed has a 10% (1 - 0.90) chance of not growing. To solve this, we can use the binomial probability formula: P(X = k) = C(n, k) * (pk) * ((1 - p)n - k), where n is the number of trials, p is the probability of success, and k is the exact number of successes. In this case, n = 7, p = 0.10 and k = 4. So, we get:
P(X = 4) = C(7, 4) * (0.104) * (0.907 - 4)
The calculation of this probability requires the use of combinations and exponentiation, providing the specific likelihood of having exactly 4 seeds out of 7 not growing into a healthy plant.
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The following table shows the expressions that represent the sales of 4 companies: Company A B C D Sales 170(1.04)x 330(1.80)x 250(0.06)x 120(1.09)x Rank the company sales by smallest to largest percent of increase and select the correct answer below.
To rank the company sales by smallest to largest percent of increase, calculate the percent of increase for each company, which in this case is 0% for all companies.
Explanation:To rank the company sales by smallest to largest percent of increase, we need to calculate the percent of increase for each company. The percent of increase can be found by subtracting the initial value from the final value, dividing that number by the initial value, and then multiplying by 100.
For company A: Percent of increase = ((170(1.04)x - 170(1.04)x) / (170(1.04)x)) * 100 = 0%For company B: Percent of increase = ((330(1.80)x - 330(1.80)x) / (330(1.80)x)) * 100 = 0%For company C: Percent of increase = ((250(0.06)x - 250(0.06)x) / (250(0.06)x)) * 100 = 0%For company D: Percent of increase = ((120(1.09)x - 120(1.09)x) / (120(1.09)x)) * 100 = 0%Since all the percent of increase values are 0%, the company sales can be ranked in any order, as there is no change in sales for any of the companies.
Find the product.
(-5a ^2)^3 · a ^5
-15a^10
-125a^11
15a^6
-125a^10
The distance between points (3, 7) and (x1, y1) is the square root of (x1 - 3)2 + (y1 - 7)2. True or false?
Answer:
True
Step-by-step explanation:
By the distance formula,
The distance between two points [tex](a_1, b_1)[/tex] and [tex](a_2, b_2)[/tex] is,
[tex]d=\sqrt{(a_2-a_1)^2+(b_2-b_1)^2}[/tex]
Here, [tex]a_1=3[/tex], [tex]b_1=7[/tex], [tex]a_2=x_1[/tex] and [tex]b_2=y_1[/tex]
Thus, the distance would be,
[tex]d=\sqrt{(x_1-3)^2+(y_1-7)^2}[/tex]
= the square root of [tex](x_1 - 3)^2 + (y_1 - 7)^2[/tex]
This needs to contain only positive exponents