Answer:
this equation has no solution
Step-by-step explanation:
After the last ice age began, the number of animal species in Australia changed rapidly. The relationship between the elapsed time, t, in years, since the ice age began, and the total number of animal species, S year(t), is modeled by the following function: S year(t)=25,000,000⋅(0.78)t Complete the following sentence about the rate of change in the number of species in decades. Round your answer to two decimal places. Every decade, the number of species decays by a factor of
Answer:
Every decade, the number of species decays by a factor of 0.0834.
Step-by-step explanation:
Let be [tex]S(t) = 25,000,000\cdot 0.78^{t}[/tex], [tex]\forall t \geq 0[/tex]. The decay rate per decay is deducted from the following relation:
[tex]\frac{S(t+10)}{S(t)} = \frac{25,000,000\cdot 0.78^{t+10}}{25,000,000\cdot 0.78^{t}}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{t+10-t}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.78^{10}[/tex]
[tex]\frac{S(t+10)}{S(t)} = 0.0834[/tex]
Every decade, the number of species decays by a factor of 0.0834.
Answer:
28% subtracted
Step-by-step explanation:
khan
whats the square root of 83
Answer:
9.110434
Step-by-step explanation:
√83 ≈ 9.110434
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) → 0.] f(x) = 4 x , a = −2
Answer:
4x
Step-by-step explanation:
The Taylor series of a function f(x) about a value x = a is given by f(x) = f(a) + f'(a)(x - a)/1! + f''(a)(x - a)²/2! + f'''(a)(x - a)³/3! + ... where the terms in f prime f'(a) represent the derivatives of x valued at a.
For the given function, f(x) = 4x and a = -2
So, f(a) = f(-2) = 4(-2) = -8
f'(a) = f'(-2) = 4
All the higher derivatives of f(x) evaluated at a are equal to zero. That is f''(a) = f'"(a) =...= 0
Substituting the values of a = -2, f(a) = f(-2) = -8 and f'(-2) = 4 into the Taylor series, we have
f(x) = f(-2) + f'(-2)(x - (-2))/1! + f''(-2)(x - (-2))²/2! + f'''(-2)(x - (-2))³/3! +...
= -8 + 4(x + 2)/1! + (0)(x + 2)²/2! + (0)(x + 2)³/3! +...
= -8 + 4(x + 2) + 0 + 0
= -8 + 4x + 8
= 4x
How large a sample should be selected to provide a 95% confidence interval with a margin of error of 4? Assume that the population standard deviation is 40. Round your answer to next whole number.
Answer:
The large sample size 'n' = 384.16
Step-by-step explanation:
Explanation:-
Given Margin of error = 4
Given Population standard deviation(σ) = 40
The margin of error is determined by
[tex]M.E = Z_{0.05} \frac{S.D}{\sqrt{n} }[/tex]
[tex]4 = 1.96 \frac{40}{\sqrt{n} }[/tex]
Cross multiplication , we get
[tex]\sqrt{n} = \frac{40 X 1.96}{4}[/tex]
√ n = 19.6
squaring on both sides , we get
n = 384.16
Final answer:-
The large sample size 'n' = 384.16
When 6r − 17r = -66 is solved, the result is: A. 6 B. -6 C. -11 D. 11
Answer:
A
Step-by-step explanation:
6r - 17r = -66
Subtract like terms.
-11r = -66
Divide both sides by -11.
r = -66/-11
r = 6
Answer:
6
Step-by-step explanation:
6r-17r=-66
-11r=-66
r=6
Consider the y-intercepts of the functions. f(x)= 1/5 [x-15] g(x)= (x-2)^2 The y-coordinate of the greatest y-intercept is..
Answer:
4
Step-by-step explanation:
I used Desmos
We will see that the y-intercept of g(x) is larger than the y-intercept of f(x).
How to find the y-intercepts?For a function y = f(x), the y-intercept is the value that takes y when we evaluate in x = 0.
So, for the first function:
[tex]f(x) = (1/5)*|x - 15|[/tex]
The y-intercept is:
[tex]f(0) = (1/5)*|0 - 15| = 15/5 = 3[/tex]
For the second function:
[tex]g(x) = (x - 2)^2[/tex]
The y-intercept is:
[tex]g(0) = (0 - 2)^2 = (-2)^2 = 4[/tex]
Then we can see that g(x) has a greater y-intercept than f(x).
If you want to learn more about y-intercepts:
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solve both equations 8x + 7y = 39 4x – 14y = –68
Answer:
x=1/2, y=5
Step-by-step explanation:
This can be solved using substitution!
Hope this helped!
Answer:
{x,y}={ 1/2, 5)
Step-by-step explanation:
[1] 8x + 7y = 39
[2] 4x - 14y = -68
Solve equation [2] for the variable x
[2] 4x = 14y - 68
[2] x = 7y/2 - 17
// Plug this in for variable x in equation [1]
[1] 8•(7y/2-17) + 7y = 39
[1] 35y = 175
// Solve equation [1] for the variable y
[1] 35y = 175
[1] y = 5
// By now we know this much :
x = 7y/2-17
y = 5
// Use the y value to solve for x
x = (7/2)(5)-17 = 1/2
A soccer player has made 3 of her last 10 field goals, which is a field goal percentage of 30%. How many more consecutive field goals would she need to make to raise her field goal percentage to 50%?
Answer:
x = 4
Step-by-step explanation:
The area of the parallelogram is____________________
the area of the quadrilateral.
What goes in the blank?
Answer:
double
Step-by-step explanation:
Translate into an algebraic expressions: b is decreased by 40% and decreased again by 40% . What is the result ?
Answer:
Result = 9b/25 or 36b/100
Step-by-step explanation:
The number is b
step 1
b is decreased by 40%
value of 40% of b = 40/100 *b = 4b/10
New value after this change = b - 40% decreased value of b = b -4b/10
= (10b-4b)/10 = 6b/10
Step 2 The new value obtained is again decreased by 40%
value of 40% number found in step 1 = 40% of value found in step 1
value of 40% number found in step 1 = 40/100 * 6b/10 = 24b/100
This value (24b/100) is subtracted from value found in step 1(6b/10) as given that value obtained is decreased by 40%
new value found after 40% decrease = 6b/10 - 24b/100
new value found after 40% decrease = 60b/100 - 24b/100= 36b/100
new value found after 40% decrease = 36b/100 = 9b/25
Thus, the result of b is decreased by 40% and decreased again by 40% is 9b/25
The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees based on the region of the country the warehouse is located. She randomly selects 35 employees who work in warehouses on the East Coast (Group 1) and 35 employees who work in warehouses in the Midwest (Group 2) and records the number of parts shipped out from each for a week. She finds that East Coast group ships an average of 1299 parts and knows the population standard deviation to be 350. The Midwest group ships an average of 1456 parts and knows the population standard deviation to be 297.Using a 0.01 level of significance, test if there is a difference in productivity level. What is the p-value? (Round to four decimal places) p-value =
Answer:
The results of the hypothesis test suggests that there is no difference in productivity level of two warehouses (East Coast and the Midwest Coast).
p-value = 0.0473
Step-by-step explanation:
To perform this test we first define the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, we want to test if there is a difference in productivity level of the two warehouses (East Coast and the Midwest Coast).
Hence, the null hypothesis would be that there isn't significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast). That is, there is no difference in the productivity level of two warehouses (East Coast and the Midwest Coast).
The alternative hypothesis is that there is significant evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).
Mathematically, if the average productivity level of the East Coast group is μ₁, the average productivity level of the Midwest group is μ₂ and the difference in productivity level is μ = μ₂ - μ₁
The null hypothesis is represented as
H₀: μ = 0 or μ₂ = μ₁
The alternative hypothesis is represented as
Hₐ: μ ≠ 0 or μ₂ ≠ μ₁
So, to perform this test, we need to compute the test statistic
Test statistic for 2 sample mean data is given as
Test statistic = (μ₂ - μ₁)/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = average productivity level of the East Coast group = 1299 parts shipped
n₁ = sample size of East Coast group surveyed = 35
s₁ = standard deviation of the East Coast group sampled = 350
μ₂ = average productivity level of the Midwest group = 1456 parts shipped
n₂ = sample size of Midwest group surveyed = 35
s₂ = standard deviation of the Midwest group sampled = 297
σ = √[(297²/35) + (350²/35)] = 77.5903160379 = 77.59
We will use the t-distribution as no information on population standard deviation is provided
t = (1456 - 1299) ÷ 77.59
= 2.02
checking the tables for the p-value of this t-statistic
Degree of freedom = df = n₁ + n₂ - 2 = 35 + 35 - 2 = 68
Significance level = 0.01
The hypothesis test uses a two-tailed condition because we're testing in both directions.
p-value (for t = 2.02, at 0.01 significance level, df = 68, with a two tailed condition) = 0.047326
The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.01
p-value = 0.047326
0.047326 > 0.01
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & say that there isn't enough evidence to suggest that there is a difference in productivity level of two warehouses (East Coast and the Midwest Coast).
Hope this Helps!!!
The sugar content of the syrup in canned peaches is normally distributed. A random sample of n=25 cans yields a sample standard deviation of s=6.9 milligrams. Construct a 99% one-sided lower confidence bound for the population variance.
Answer:
99% one-sided lower confidence bound = 26.77
Step-by-step explanation:
We have to calculate a 99% one-sided lower confidence bound for the population variance.
The sample size is n=25.
The degrees of freedom are then:
[tex]df=n-1=25-1=24[/tex]
The critical value of the chi-square for this confidence bound is:
[tex]\chi^2_{0.01, \,24}=42.98[/tex]
Then, the lower confidence bound can be calculated as:
[tex]LB=\dfrac{(n-1)s^2}{\chi^2_{0.01,24}}=\dfrac{24\cdot(6.9)^2}{42.98}=\dfrac{1,142.64}{42.68}=26.77[/tex]
I NEED HELP!!
The chef at a school cafeteria asked 100 male and 100 female students
whether they like peas. 58 of the males said they like peas. 36 of the females
said they dislike peas. Which two-way table correctly shows these results?
Answer:
d
Step-by-step explanation:
The table shows the result of the statement given below.
What is data table?A data table is a range of cells in which you can change values in some of the cells and come up with different answers to a problem.
here, we have,
Given that,
the chef at a school cafeteria asked 100 male and 100 female students whether they like peas.
42 of the males said they like peas. 64 of the females said they dislike peas.
The number of males who like peas=42 and the number of males who dislikes peas=58.
The number of females who like peas=36 and the number of females who dislikes peas=64.
The table shows the result of the statement given below.
To learn more about the data table visit:
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What is the leading coefficient of a cubic polynomial that has a value of −208 when x=1, and has zeros of 5, 5i, and −5i?
Answer:
2
Step-by-step explanation:
We already have the zeros, so we can write the cubic polynomial in this general form:
[tex]y = a(x - x_1)(x - x_2)(x - x_3)[/tex]
Where:
[tex]x_1 = 5[/tex]
[tex]x_2 = 5i[/tex]
[tex]x_3 = -5i[/tex]
So we have that:
[tex]y = a(x -5)(x - 5i)(x + 5i)[/tex]
[tex]y = a(x -5)(x^2 + 25)[/tex]
To find the value of the leading coefficient 'a', we can use the point (1, -208) given:
[tex]-208 = a(1 -5)(1 + 25)[/tex]
[tex]-208 = a(-4)(26)[/tex]
[tex]a = -208 / (-104) = 2[/tex]
So the leading coefficient is 2.
Finding missing angles
Answer:
C. 105° = (5x - 70)°
Step-by-step explanation:
Vertically opposite angles are equal in size.
105° = (5x - 70)°
The correct answer is choice C.
Meant to put the letter C
A dinner at a restaurant was advertised at $60 plus 18% tax. The total bill for this dinner was. Show working plss
Answer:
Total bill = $70.80
Step-by-step explanation:
$60 × 0.18 = $10.80
$60 + $10.80 = $70.80
Hope this helps! :)
Answer:
$70.8
Step-by-step explanation:
Since it is 18 percent tax,we need to find 18% of 60$.In order to do that we need to do 60/1 mutiplied by 18/100 and doing the math 18% of 60 =10.8
Now we have to add 60+10.8=$70.8
Thank you and I hope all you have an amazing day.Hope this helps you.Thank you.
Find the gradient of the line 2y = 8x + 1 =
. Find the y-intercept of the line 4y + 8x = -8 =
Does the point (1 ,12) lie on the line y = 3x + 8 ? =
Does the point (-2 ,10) lie on the line y = 14 + 2x ? =
Answer:
56 46 38 2 12
Step-by-step explanation:
126,720 inche are equal to how many miles ?
Answer:
The answer is
2 milesStep-by-step explanation:
63, 360 inches = 1 mile
126,720 = 126,720 / 63 , 360 × 1 mile
Which is equal to
2 miles
Hope this helps you
Which expression has a positive value?
A - Negative 4 + (negative 5) (negative 6) divided by (negative 3)
B - 8 Left-bracket 10 divided by (2) (negative 2) Right-bracket
C - 3 (negative 64 divided by 8) + 25
D - Negative 2 (negative 5) (negative 3) divided by 10
Answer:
C - 3 (negative 64 divided by 8) + 25 =1
Step-by-step explanation:
Answer:
C is correct answer
Step-by-step explanation:
Which of the following numbers would be used to get the variable by itself in the equation 7x = 12?
Answer:
Divide by 7 or multiply by 1/7
Step-by-step explanation:
7x = 12
Divide each side by 7
7x/7 = 12/7
x = 12/7
We could also multiply each side by 1/7
7x * 1/7 = 12*1/7
x = 12/7
How can (4x⁵/2x²)³ be solved in 2 different ways
We assume that we need to simplify the expression in two different ways.
Answer:
One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.
Second way: Simplify the terms inside parentheses, and then raise the result to the third power.
The result of both ways is the same: [tex] \\8x^{9}[/tex]
Step-by-step explanation:
One way
Raise both, the numerator and denominator, to the third power, and then simplify the expression:
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{64x^{5*3}}{8x^{2*3}})[/tex]
[tex] \\ (\frac{64x^{15}}{8x^{6}})[/tex]
[tex] \\ \frac{64}{8}\frac{x^{15}}{x^{6}}[/tex]
[tex] \\8x^{9}[/tex]
This is the first simplification.
Second way
Simplify the terms inside parentheses, and then raise the result to the third power.
[tex] \\ (\frac{4x^{5}}{2x^{2}})^{3}[/tex]
[tex] \\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}[/tex]
[tex] \\ (2*x^{5-2})^{3}[/tex]
[tex] \\ (2*x^{3})^{3}[/tex]
[tex] \\ (2^{3}*x^{3*3})[/tex]
[tex] \\ (8*x^{9})[/tex]
or [tex] \\ 8x^{9}[/tex].
Explain in your own words why a polynomial can’t be a quadratic if a= 0?
If [tex]a = 0[/tex], then [tex]y = ax^2+bx+c[/tex] turns into [tex]y = 0x^2+bx+c[/tex]. That [tex]0x^2[/tex] term goes away because it turns into 0, and adding 0 onto anything does not change the expression.
So [tex]y = 0x^2+bx+c[/tex] turns into [tex]y = bx+c[/tex] which is a linear equation (b is the slope, c is the y intercept). It is no longer a quadratic as quadratic equations always graph out a curved parabola.
As an example, you could graph out [tex]y = 0x^2+3x+4[/tex] and note how it's the exact same as [tex]y = 3x+4[/tex], both of which are straight lines through the two points (0,4) and (1,7).
Prove that 2x3 + 3x² + x is always divisible by 6 if x is an integer.
PLEASE I NEED THIS ANSWERED ASAP.
USE PROOF BY EXHAUSTION.
Answer: see proof below
Step-by-step explanation:
Proof by exhaustion means to input several numbers that satisfy the claim and if they all prove to be true then you have proven the claim.
Claim: (2x³ + 3x² + x)/(6) ∈ Z (integer)
Let's choose x = {1, 2, 3, 4)
Case 1: x = 1
2(1)³ + 3(1)² + (1) = 12
12/6 = 2
2 ∈ Z [tex]\checkmark[/tex]
Case 2: x = 2
2(2)³ + 3(2)² + (2) = 30
30/6 = 5
5 ∈ Z [tex]\checkmark[/tex]
Case 3: x = 3
2(3)³ + 3(3)² + (3) = 84
84/6 = 14
14 ∈ Z [tex]\checkmark[/tex]
Case 4: x = 4
2(4)³ + 3(4)² + (4) = 180
180/6 = 30
30 ∈ Z [tex]\checkmark[/tex]
Since each case was shown to be true we have proven the claim is true by exhaustion.
What is the equation of a line whose slope is 2 and passes through the point (-6,9)
Answer:
y = 2x + 21
Step-by-step explanation:
Step 1: Write out known variables
y = mx + b
m = 2
y = 2x + b
Step 2: Find b
9 = 2(-6) + b
9 = -12 + b
b = 21
Step 3: Rewrite linear equation
y = 2x + 21
Which of these numbers is prime? 13, 30, 49, 65, 87
Answer:
13
Step-by-step explanation:
factors of 13 : 1, 13
factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
factors of 49: 1, 7, 49
factors of 65: 1, 5, 13, 65
factors of 87: 1, 3, 29, 87
An amusement park has 20 rides. Ethan has enough time to ride 3 rides before the park closes. How many different ways could Ethan pick to ride the 3 rides? PLZZZZ HELLPPPP MEEEE
Answer:
20*19*18 = 6840
UNLESS...............
he is allowed to ride the same ride again , over and over....
then it is 20 x 20 x 20 = 8000
Step-by-step explanation:
Press the attachment it’s a picture of the question. PLEASE HELP ME MY LAST DAY IS TODAY AND I NEED HELP! I WILL GIVE YOU BRAINLIEST
Answer:
210 vegetable in 7 rows
Step-by-step explanation:
first step is to figure out how many vegetable can she grow in one row:
convert feet to inches : 6.25 feet* 12 inches=75 inches
(75/2 1/2) (2 /12 is 3/2 or 2.5)
(75/2.5)= 30 vegetable in one row
in 7 rows : 30*7=210 vegetable in 7 rows
Provided that the ACT scores are reasonably normally distributed with a mean of 18 and standard deviation of 6, what is the proportion of students with a score of 24 or higher
Answer:
0.158655253931 or 15.8%
Step-by-step explanation:
Solve the following system of equations: x − 2y = 14 x + 3y = 9 (1, 12) (−1, −12) (12, −1) (12, 1)
Answer:
work is shown and pictured
answer is c
Answer:
the correct answer among the choices is C
Step-by-step explanation:
HELP ON THIS QUESTION PLEASE
Answer:
slope is m=1. y-intercept is -1
Answer:
Slope is 1 and intercept is -1. Slope can be found by taking the rise and run of 2 points on a graph. and intercept is just when x = 0