[tex]X[/tex] is the random variable for lifespan of a protozoan and [tex]X\sim\mathcal N(48,10.2^2)[/tex]. Let [tex]\bar X[/tex] be the mean of a sample from this distribution, so that [tex]\bar X\sim\mathcal N\left(48,\left(\dfrac{10.2}{\sqrt{49}}\right)^2\right)[/tex].
For the sake of clarity, I'm denoting a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] by [tex]\mathcal N(\mu,\sigma^2)[/tex].
We have
[tex]P(\bar X\ge49)=P\left(\dfrac{\bar X-48}{\frac{10.2}{\sqrt{49}}\ge\dfrac{49-48}{\frac{10.2}{\sqrt{49}}\right)\approx P(Z\ge0.6863)\approx0.2463[/tex]
(where [tex]Z[/tex] follows the standard normal distribution)
To the nearest hundredth, what is the value of x?
42.16
43.11
52.07
54.26
Answer:
52.07
Step-by-step explanation:
We know that the sin of an angle is equal to the opposite side divided by the hypotenuse
sin 51 = opposite side/ hypotenuse
sin 51 = x/67
Multiply each side by 67
67 sin 51 = x
52.06877942=x
To the nearest hundredth
52.07 =x
In the first quadrant, you start at 5,4 and move 2 unit's left what point will you end up on
You end up on Point (3, 4)
Answer:
you will end up on (3,4)
Step-by-step explanation:
If you roll two fair six-sided dice, what is the probability that the sum is 444 or higher?
Answer:
11/12
Step-by-step explanation:
Final answer:
To find the probability of rolling a sum of 444 or higher with two fair six-sided dice, calculate the sum probabilities for 444, 455, and 466, then add them together.
Explanation:
If you roll two fair six-sided dice, what is the probability that the sum is 444 or higher?
To calculate this probability, we need to first determine the total possible outcomes when rolling two dice and then find the favorable outcomes where the sum is 444 or higher.
The sum can range from 2 to 12 when rolling two dice, so we can find the probabilities for sums 444, 455, and 466, then add these probabilities up to get the final answer.
Please help with this question, I will give the brainliest if correct! The question is in the picture.
Answer:
Resolved.
Step-by-step explanation:
Answer:
The Answer is B. I had this a few months ago. Good luck with Apex!
The current understanding of created "kinds" is:
similar to species
no variation
related to higher taxonomic orders
similar to Linnaean "fixity of species"
Correct option is A. The term 'kinds' likely refers to informal groupings of organisms and may align with 'species' or higher taxonomic orders. Organisms are classified into a hierarchical system, where species represent closely related organisms capable of interbreeding, but higher levels like genus and family involve organisms that share broader similarities.
The question pertains to the concept of biological classification and how created "kinds" are understood within that framework. The term "kinds" is not particularly scientific and may refer to informal groupings of organisms. However, it could be inferred that the student is asking about how closely these "kinds" align with scientifically recognized categories such as species or higher taxonomic orders (like genus, family, order, etc.).
According to the Linnaean system introduced by Carl Linnaeus, organisms are classified in a hierarchical structure based on shared physical characteristics. This system organizes living organisms into a hierarchy of taxa, with species being the most specific level and kingdoms being the most general. Species are groups of organisms that are very similar and capable of interbreeding, while higher taxonomic levels, such as genus and family, group together organisms that share fewer, but still significant, similarities.
The concept of a species can be complex, as there can be significant variation within what we consider a single species, making the categorization sometimes controversial and subject to scientific debate. Moreover, as our understanding of evolution and phylogeny has advanced, the classification system has evolved to reflect these new insights, leading to changes in how organisms are grouped.
need some help plz-(7-9z)+8(3z-4)
Simplify brackets
-7 + 9z + 8(3z - 4)
Expand
-7 + 9z + 24z - 32
Collect like terms
(-7 - 32) + (9z + 24z)
Simplify
-39 + 33z
Regroup terms
= 33z - 39
what is the molariry of a solution that contains 1.22 mol of hydrogen chloride if the total volume of the solution is 1,251 mL?
Your molarity would be 0.975 M HCl because it’s moles of solute divided by liters of solvent
The answer would be 0.975
Suppose the side lengths are multiplied by 2. Describe the change in the perimeter
Answer:
The perimeter would also be multiplied by 2.
Step-by-step explanation:
The perimeter would also be multiplied by 2. Suppose the sides of a triangle are 5, 10 and 13. The perimeter would be the sum of the side lengths or 5 + 10 + 13 = 28 ft.
Multiply each side length so 5*2 = 10, 10*2 = 20 and 13*2 = 26. Find the perimeter by finding their sum, 10 + 20 + 26 = 56.
Divide the new perimeter by the old perimeter to find a scale factor.
56/28 = 2.
The new perimeter is exactly 2 times bigger since 2*28 = 56.
Identify the area of the rhombus.
Answer:
[tex]A=240\ m^{2}[/tex]
Step-by-step explanation:
we know that
A rhombus is a parallelogram with four congruent sides, the diagonals are perpendicular bisectors of each other
The area of a rhombus is equal to
[tex]A=\frac{1}{2}(D1*D2)[/tex]
where
D1 and D2 are the diagonals
In this problem we have
[tex]D1=16\ m[/tex]
Applying the Pythagoras Theorem find D2
[tex]17^{2} =(D2/2)^{2}+(16/2)^{2}[/tex]
[tex](D2/2)^{2}=17^{2}-(16/2)^{2}[/tex]
[tex](D2/2)^{2}=225[/tex]
[tex](D2/2)=15[/tex]
[tex]D2=30\ m[/tex]
Find the area of the rhombus
[tex]A=\frac{1}{2}(16*30)=240\ m^{2}[/tex]
One fifth of the twenty five people in the bakery made a preorder how many did not make a preorder
One fifth is five people. Twenty five minus five is twenty. So twenty people did not preorder.
Estimate the difference. 10 1/9 - 5 14/15 simplest form
Answer: 188/45 or 4 8/45.
Step-by-step explanation:
1. Change the mixed numbers to improper fractions.
10 1/9 = 91/9
5 14/15 = 89/15
2. Now, we must find a common denominator by finding the LCM (Least Common Multiple). In this case, it would be 90. 9 x 10 = 90 and 15 x 6 = 90. The numerators must equal the denominators, so we would multiply 91 by 10 and 89 by 6.
Our new fractions are 910/90 and 534/90.
3. Subtract the fractions. 910/90 - 534/90 = 376/90.
4. Simplify. 376 and 90 are both divisible by 2, so our answer will be 188/45 or 4 8/45.
Describe the sequence of transformations from quadrilateral ABCD to A'B'C'D A: -8,8 B: 8,-2 C: 4,-8 D: 4,-2 A': 2,-10 B': 8,-10 C': 2,-6 D: 8, -5?
Answers:
See below
Step-by-step explanation:
First transformation
Reflection about the line y = 6.
This inter-converted Points A and C and Points B and D.
The coordinate transformations were (Fig. 1):
A: (-8, 8) ⟶ (-8, 4)
B: (-2, 8) ⟶ (-2, 4)
C: (-8, 4) ⟶ (-8, 8)
D: (-2, 4) ⟶ (-2, 8)
Second transformation
Translation 10 units to the right and 14 units down.
The coordinate transformations were (Fig. 2):
A: (-8, 4) ⟶ (2, -10)
B: (-2, 4) ⟶ (8, -10)
C: (-8, 8) ⟶ (2, -6)
D: (-2, 8) ⟶ (8, -6)
The transformations were:
Reflection about the line y = 6 Translation 10 units to the right and 14 units downWhich expression is equivalent to
1/100c^3d^4
1/100c^6d^9
1/10c^3d^4
1/10c^6d^9
Answer:
1/10c^3d^4
Step-by-step explanation:
A cube root is an operation which splits expressions and numbers within it into 3 groups of the exact same size. These groups when multiplied by themselves make the expressions and numbers under the root. For example, ∛27 = 3 since 3*3*3 = 27.
Take each part under the cube root and split it into three equal groups.
1/ 1000 = 1/10 * 1/10 * 1/10 so ∛1/1000 = 1/10
c^9 = c^3*c^3*c^3 so ∛c^9 = c^3
d^12 = d^4*d^4*d^4 so ∛d^12 = d^4
Together ∛1/1000 c^9 d^12 = 1/10 * c^3 * d^4
A duplex generates $1,400 rent for each of its two units per month. The property has been recently appraised for $350,000. What is this property's GIM? 4.8, 9.6, 10.4, or 20.83??
Answer:
10.4
Step-by-step explanation:
To get the property's gross income multiplier (GIM), you divide its appraised value by its gross annual rental income.
Rental income = 2 × $1400/1 month × (12 months/1 yr)
= $33 600/yr
GIM = $350 000/$33 600 = 10.4
The property's GIM is 10.4.
Which of the following quantities would be acceptable representations of weight? Check all that apply. a.12.0 lb b.0.34 g c.120 kg d.1600 kN e.0.34 m f.411 cm
Answer:
a.12.0 lb; b.0.34 g; c.120 kg
Step-by-step explanation:
To measure weight using the English system of measurements, we use ounces, pounds, tons, etc.
To measure weight using the metric system, we use grams, milligrams, kilograms, etc.
This means that pounds, grams and kilograms are all acceptable representations of weights.
Kilonewtons (kN) measure force, not weight.
Meters and centimeters (m and cm) measure length, not weight.
Answer:
a.12.0 lb
d.1600 N
Step-by-step explanation:
THe weight of objects is the force with which each object is attracted by the gravitational force where they are located, for example on earth gravitational force is equal to 9.81 m/[tex]s^{2}[/tex], so an object that is 1 kg of mass, would have a weight of 9.81 Newtons, pounds are also a measure of force.
Derive these identities using the addition or subtraction formulas for sine or cosine:
a. sin a sin b = 1 / 2(cos(a – b) – cos(a + b))
b. sin a cos b = 1 / 2(sin(a + b) + sin(a – b))
Answer:
Step-by-step explanation:
cos(a-b)-cos(a+b)=2(sina x sinb)
using formulae of cos (a-b) & cos(a+b)
cos a cos b + sina sinb - cosa cosb + sina sinb=2 sina sinb
2 sina sinb = 2 sina sinb
proved!
What is the area of a sheet of binder paper? (Binder paper is 8 1/2 inches by 11 inches.) 88 inches 88 1/2 in2 93 1/2 in2 94 in2
Answer:
93 1/2 in^2.
Step-by-step explanation:
The Area = 8 1/2 * 11
= 17/ 2* 11
= 187/2
= 93 1/2 in^2.
Answer:
The area of the binder paper is 93 1/2 in^2 :)
Step-by-step explanation:
A toaster has four slots for bread. Once the toaster is warmed up, it takes 35 seconds to make 4 slices of toast, 70 seconds to make 8 slices, and 105 seconds to make 10 Slices. How long do you think it will take to make 20 slices?
In order to make 20 slices of toast, given the constants provided, it would take approximately 175 seconds total. This is calculated based on the established rate of 4 slices of toast per 35 seconds.
Explanation:The subject of this question is mathematics, specifically focusing on patterns and ratios. Given that it takes 35 seconds to make 4 slices of toast, we can establish a consistent rate of toast production. Because the toaster can toast 4 slices at a time, every 35 seconds, 4 more slices are ready. If we want to make 20 slices of toast, we can calculate this as follows: 20 slices ÷ 4 slices per 35 seconds = 5 times. Therefore, 5 times multiplied by the 35 seconds it takes to toast a set of 4 slices gives us 175 seconds. So, to toast 20 slices, it would take approximately 175 seconds.
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To make 20 slices of toast, it will take 210 seconds.
Explanation:To find out how long it will take to make 20 slices of toast, we can determine the time required to make 1 slice of toast and then multiply it by 20.
From the given information, we can create a pattern to determine the time required:
4 slices take 35 seconds8 slices take 70 seconds10 slices take 105 secondsWe can observe that doubling the number of slices doubles the time required. Therefore, 20 slices will take twice the time required for 10 slices, which is 105 seconds. So, it will take 210 seconds to make 20 slices of toast.
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Find the radius of convergence, R, of the series. ∞ (−1)n (x − 6)n 4n + 1 n = 0 R =
Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I =
The radius of convergence of [tex]\sum\limits^{\infty}_{n=0} \frac{(-1)^n(x-6)^n}{4n+1}[/tex] is 1, and the interval notation is (5,7)
The radius and interval of convergenceThe series is given as:
[tex]\sum\limits^{\infty}_{n=0} \frac{(-1)^n(x-6)^n}{4n+1}[/tex]
The ratio test of a series states that:
[tex]L = \lim_{n \to \infty} |\frac{a_{n+1}}{a_n} |[/tex]
If L < 1, then [tex]\sum a_n[/tex] converges If L > 1, then [tex]\sum a_n[/tex] divergesIf L = 1, then [tex]\sum a_n[/tex] is inconclusiveBy applying the ratio test considering that the series converges, we have:
[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4(n+1)+1} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]
Open the bracket
[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+4+1} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]
Evaluate the sum
[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+5} \div \frac{(-1)^n(x-6)^n}{4n+1}|[/tex]
Express as product
[tex]\lim_{n \to \infty} | \frac{(-1)^{n+1}(x-6)^{n+1}}{4n+5} \times \frac{4n+1}{(-1)^n(x-6)^n}|[/tex]
Expand the exponents
[tex]\lim_{n \to \infty} | \frac{(-1)^{n} \times (-1)^1 (x-6)^{n} \times (x-6)}{4n+5} \times \frac{4n+1}{(-1)^n(x-6)^n}|[/tex]
Cancel out the common factors
[tex]\lim_{n \to \infty} | \frac{(-1)(x-6)(4n+1)}{4n+5} |[/tex]
Factor out (-1)(x - 6)
[tex]|x-6|\lim_{n \to \infty} | \frac{(4n+1)}{4n+5} |[/tex]
Assume the limit to infinity is 1, the equation becomes
[tex]|x- 6| < 1[/tex] --- condition for convergence series
Split
[tex]-1 < x - 6 < 1[/tex]
Add 6 to both sides
[tex]5 < x < 7[/tex]
Rewrite as interval notation
(5,7)
Hence, the radius of convergence is 1, and the interval notation is (5,7)
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The radius of convergence, R, of the given series is 1. The interval of convergence, I, is [7,5). These are found using the Ratio Test to determine where the series converges, and then checking behavior at the endpoints.
Explanation:To find the radius and interval of convergence of a series, we typically use the Ratio Test, where we consider the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term. If this limit L is less than 1, the series converges absolutely; if it is greater than 1, the series diverges; if it equals 1, the test is inconclusive.
From the given series ∞ (−1)n (x − 6)n (4n + 1)/n, let a(n) be the nth term, so a(n+1) = (−1)^(n+1) (x − 6)^(n+1) (4*(n +1) + 1)/(n+1). Thus, we find |a(n+1)/a(n)| = |(x-6) * (4n+1) / (4n+5)|. In the limit as n approaches infinity, this becomes |x-6|. The series converges where this is less than 1, hence the radius of convergence, R, is 1.
For the interval of convergence, I, we need to check the points x = 7 and x = 5 (the endpoints of the interval centered at 6 with radius 1). Substituting these into the original series, we can use the Alternating Series Test and find the series converges for x = 7 and diverges for x = 5. Hence, the interval of convergence is I = [7,5).
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If f(x)=-3x+8,find (f)5 A.-7 B.5 C.-5 D.7
Answer:
A.-7
Step-by-step explanation:
f(x)=-3x+8,
f(5) means let x=5
f(5) = -3(5) +8
f(5) = -15+8
f(5) = -7
Given (x, y ) = (5, 15). Find tan θ.
a.3
b.1/3
c.5
d.1/5
Answer:
Step-by-step explanation:
You wouldn’t put y over x Which is 15/3 you would divide which gives you five. So your tan theta would be 5
Answer:
it's definitely 3 on odyssey. tan theta= y/x =3.
Step-by-step explanation:
Julian has 3 pounds of ham to make 12 sandwiches.Which statement about Julian's sandwiches are true? A) Each sandwich has more than 1 pound of ham B)Julian will have 1/2 pound of ham left over C)Each sandwich has 1/4 pound of ham D) Each sandwich has 4 pounds of ham
Answer:
C. Each Sandwich has 1/4 pounds of ham
Step-by-step explanation:
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test. Find the percent of students that scored below Jake. Round your answer to the nearest whole number. (Include a step by step description of the process you used to find that percentage.)
*You will need to find the z-score using the z-score formula, the probability using the table, then change the probability to a percent.
Subtract the mean from Jake's score:
520 - 500 = 20
No divide that by the standard deviation:
20/60 = 0.33
This means Jake scored 0.33 standard deviations above the mean.
Now using the Z-table find 0.33: 0.33 = 0.6293 = 62.93% of students scored below Jake.
Rounded to nearest whole number = 63%
Answer:
63% of students
Step-by-step explanation:
Z = (X - μ) / σ
Z = 520 - 500 / 60
Z = 0.33
ON THE Z-TABLE
0.33 = 0.6293
62.93% = 63% of students answer
Noah made the following table to record the height of each person in his family.
How much taller is his dad than his mom?
Name Height (in feet)
Dad 6 1/12
Mom 5 7/12
Sadie 5 1/2
Sam 5 1/8
Noah 4 7/8
1 1/2 feet
1/2 foot
1/3 foot
1 1/3 foot
Answer:1/2 feet
Step-by-step explanation:
6 1/12 - 5 7/12 = 6/12 = 1/2
how many real number solutions does the equation have? 0= -4x^2 +7x +8
A)two solutions
B)one solutions
C)no solutions
D)infinitely many solutions
Answer:
should be A. Two-Solutions
How many sums????????????????? EXPLAIN!
Answer: 7
Step-by-step explanation:
The 1st spinner can land on 2, 3, 4, or 5
The 2nd spinner can land on 2 or 3
The 3rd spinner can land on 6, 7, or 8
1st spinner + 2nd spinner + 3rd spinner:
2 + 2 + 6 = 10, 2 + 2 + 7 = 11, 2 + 2 + 8 = 12 --> 3 different sums
2 + 3 + 6 = 11, 2 + 3 + 7 = 12, 2 + 3 + 8 = 13 --> 1 different sum
This pattern follows where the only new sums are as follows:
3 + 3 + 8 = 14
4 + 3 + 8 = 15
5 + 3 + 8 = 16
This makes a total of 7 different sums.
The equation of the parabola whose focus is at (7, 0) and directrix at x = -7 is:
y = (1/28)x²
x = (1/28)y²
x = -(1/28)y²
the answer is x=(1/28)y^2
The equation of the parabola with focus at (7, 0) and directrix at x = -7 is x = (1/28)y².
The general equation of a horizontally opening parabola, using the distance between the vertex and the focus or directrix as the value of 'p'.
To find the equation of a parabola with a focus at (7, 0) and a directrix at x = -7, we first note that the vertex of the parabola is midway between the focus and the directrix. This puts the vertex at the origin (0, 0), and the parabola opens to the right since the focus is to the right of the vertex.
The general form of the equation for a parabola that opens horizontally (left or right) is
[tex](y - k)^2 = 4p(x - h)[/tex], where (h, k) is the vertex and p is the distance from the vertex to the focus.
If the parabola opens to the right (as in this case), the equation will be
[tex](y - 0)^2 = 4*(7)(x - 0)[/tex]
y² = 28x.
However, to match the format of the original options given to the student, we divide every term by 28, leading to the equation x = (1/28)y², which is the correct parabolic equation for the given focus and directrix.
Evaluate the exponential expression: (2x)2nd power −3y2nd power =___, if x = 5 and y = 3.
A.73
B.125
C.-73
D.-125
ANSWER
A. 73
EXPLANATION
The given expression is
[tex](2{x})^{2} - 3{y}^{2} [/tex]
We substitute x=5 and y=3 to obtain:
[tex](2 \times 5)^{2} - 3{(3)}^{2} = {10}^{2} - 3 \times 9[/tex]
This simplifies to,
[tex] = 100 - 27[/tex]
[tex] = 73[/tex]
The correct choice is A.
25% of the students at school a got a score greater than 25 but less or an equal to 28
Answer:
28 >= 0.25x > 25
Step-by-step explanation:
25% of x
1) Greater than 25: 25%x > 25
2) Less than and equal to 28: 25%x <= 28
25%x = 25/100 * x = 0.25x
1 and 2:
28 >= 0.25x > 25
//I hope this is what you are looking for. Not sure it's right
NEED HELP FAST PLEASE HELP
Answer:
B
Step-by-step explanation:
The easiest way to do this is to look at the -1 first. That shifts the small horizontal graph downwards. So that little line is below the x axis as answer B would show you.
The next thing to notice is that the graph is at +6 which is what you might expect because the x carries a minus with it. B and C both do that. I'm not sure what D does but I think it is on the left side of the y axis and that makes it wrong. A also looks like it is on the left side of the y axis and it is not correct either.
The difference between B and C has to be that 2 in front of the cubic. I think the vertical part of the cubic in B is closer to a vertical line through 6. If that is the case B is the answer.
Graph
Red: y = (-x + 6)^3
Blue: y = 2*(-x + 6) Notice that this is closer to a vertical line at x = 6. That's the function of the 2
Green: y = 2*(x +6)^3 - 1 Notice it is shifted down.