Is The slope of a line perpendicular to y = 2x + 1 is -2.
d
Answer:
-1/2
Step-by-step explanation:
The slopes of perpendicular lines are negative reciprocals
the negative reciprocal of 2 is -1/2
Substance A decomposes at a rate proportional to the amount of A present. a) Write an equation that gives the amount A left of an initial amount A0 after time t. b) It is found that 8 lb of A will reduce to 4 lb in 4.6 hr After how long will there be only 1 lb left?
a) Choose the equation that gives A in terms of A0, t, and k, where k > 0.
b) There will be 1 lb left after 14 hr (Do not round until the final answer. Then round to the nearest whole number as needed.)
Answer:
(a) [tex]A = A_0 * e^{kt}[/tex]
(b) There will be 1lb left after 14 hours
Step-by-step explanation:
Solving (a): The equation
Since the substance decomposes at a proportional rate, then it follows the following equation
[tex]A(t) = A_0 * e^{kt}[/tex]
Where
[tex]A_0 \to[/tex] Initial Amount
[tex]k \to[/tex] rate
[tex]t \to[/tex] time
[tex]A(t) \to[/tex] Amount at time t
Solving (b):
We have:
[tex]t = 4.6hr[/tex]
[tex]A_0 = 8[/tex]
[tex]A(4.6) = 4[/tex]
First, we calculate k using:
[tex]A(t) = A_0 * e^{kt}[/tex]
This gives:
[tex]A(4.6) = 8 * e^{k*4.6}[/tex]
Substitute: [tex]A(4.6) = 4[/tex]
[tex]4 = 8 * e^{k*4.6}[/tex]
Divide both sides by 4
[tex]0.5 = e^{k*4.6}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.5) = \ln(e^{k*4.6})[/tex]
This gives:
[tex]-0.6931 = k*4.6[/tex]
Solve for k
[tex]k = \frac{-0.6931}{4.6}[/tex]
[tex]k = -0.1507[/tex]
So, we have:
[tex]A(t) = A_0 * e^{kt}[/tex]
[tex]A(t) = 8e^{-0.1507t}[/tex]
To calculate the time when 1 lb will remain, we have:
[tex]A(t) = 1[/tex]
So, the equation becomes
[tex]1= 8e^{-0.1507t}[/tex]
Divide both sides by 8
[tex]0.125= e^{-0.1507t}[/tex]
Take natural logarithm of both sides
[tex]\ln(0.125)= \ln(e^{-0.1507t})[/tex]
[tex]-2.0794= -0.1507t[/tex]
Solve for t
[tex]t = \frac{-2.0794}{-0.1507}[/tex]
[tex]t = 13.7983[/tex]
[tex]t = 14[/tex] --- approximated
The profits in hundreds of dollars, P(c), that a company can make from a product is modeled by a function of the price, c, they charge for the product: P(c) = –20c2 + 320c + 5,120. What is the maximum profit the company can make from the product?
Answer:
6400
Step-by-step explanation:
Given the profit function ;
P(c) = –20c2 + 320c + 5,120
The maximum value is given by :
f(h) ; where, h = - b /2a
From P(C) ; a = - 20 ; b = 320
h = - b / 2a = - 320 / 2(-20) = - 320 / 40 = 8
c = h
P(8) = –20(8)² + 320(8) + 5,120
P(8) = - 1280 + 2560 + 5120
= 6400
Answer:
B.) $640,000
Step-by-step explanation:
HELP!!
What are extraneous solutions to rational and radical equations? How do they arise? How do we check if a solution is extraneous? Use these equations as examples to help you explain:
Answer:
In general, extraneous solutions arise when we perform non-invertible operations on both sides of an equation. ... Squaring (or raising to any other even power) is a non-invertible operation. Solving equations involving square roots involves squaring both sides of an equation
Step-by-step explanation:
I hope this will help u
three-fifths of a number increased by ten
Answer: [tex]\frac{3}{5} x+10[/tex]
Step-by-step explanation:
three-fifths of a number means multiply three-fifths by a variable [tex]\frac{3}{5} x[/tex]
increased by 10 means addition +10
together it is [tex]\frac{3}{5}x +10[/tex]
Rewrite the following subtraction problem as an addition problem.
Answer:
x+129=592
Step-by-step explanation:
add 129 to each side
Use the calculator to evaluate each expression. Round your answers to the nearest hundredth.(GIVING BRAINLEST TO BEST ANSWER)
Answer:
tan 43 =.93
cos 67=.39
sin 39=.63
Step-by-step explanation:
tan 43 = .932515086=.93
cos 67=.390731128=.39
sin 39=.629320391=.63
Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = (1 + 8x)^(1/2) (g(x), f(u)) = (1 + 7x, u^1/3)Find the derivative dy/dx. dy/dx = _______.
By the chain rule, you have
dy/dx = dy/du * du/dx
For the function y = f(x) = (1 + 8x)^(1/2), you're taking
y = u ^(1/2)
u = 1 + 8x
These have derivatives
dy/du = 1/2 u ^(-1/2)
du/dx = 8
which means
dy/dx = 4u ^(-1/2) = 4 (1 + 8x)^(-1/2)
determine the general term of this sequence 2;10;18;26;.........;394
Answer:
Tn=8n-6
Step-by-step explanation:
this is arithmetic sequence so first we check our difference by saying
T2-T1=T3-T2
10-2=18-10
so difference =8 nd a=2
Formula for arithmetic is Tn=a + (n-1)d
then substitute Tn=2 + (n-1)(8)
Tn=2 + 8n-8
Tn=8n-6
y=x+9x solve for x. Please and Thank you.
Answer:
x=y/10
Step-by-step explanation:
y=10x
y/10=x
x=y/10
Hope this is helpful
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {\: x = \frac{y}{10}}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
[tex]y = x + 9x\\[/tex]
[tex]➺ \: y = 10x\\[/tex]
[tex]➺ \: x = \frac{y}{10}\\ [/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
simplify: 6x²+35x-6÷ 2x²-72
Step-by-step explanation:
this will be the answer of the question where quotient is 3 and the remainder is 35x + 210
Answer:
[tex]\frac{6x - 1}{2(x - 6)}[/tex]
Step-by-step explanation:
[tex]6x^2 + 35x - 6 \ \div \ 2x^2 - 7 2\\\\6x^2 + 36x - x - 6 \ \div \ 2(x^2 - 36)\\\\6x(x + 6) - 1(x + 6) \ \div \ 2(x^2 - 6^2)\\\\(6x - 1)(x + 6) \ \div \ 2(x- 6)(x+ 6) \ \ \ \ \ \ \ \ \ \ [ \ x^2 -a^2 = (x-a)(x+a) \ ]\\\\\frac{(6x - 1)(x + 6) }{2(x- 6)(x+ 6)} = \frac{6x - 1}{2(x-6)}[/tex]
what do you call the middle value in the set of the data or quantities a mean b. median c.mode d.range
Answer:
median is the middle value
mean is the average
mode is the one that occurs most
range is the highest number - lowest number
Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 2 and a mean diameter of 200 inches.
If 83 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches? Round your answer to four decimal places.
Answer:
0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Standard deviation of 2 and a mean diameter of 200 inches.
This means that [tex]\sigma = 2, \mu = 200[/tex]
83 shafts
This means that [tex]n = 83, s = \frac{2}{\sqrt{83}}[/tex]
What is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches?
Mean between 200 - 0.2 = 199.8 inches and 200 + 0.2 = 200.2 inches, which is the p-value of Z when X = 200.2 subtracted by the p-value of Z when X = 199.8.
X = 200.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{200.2 - 200}{\frac{2}{\sqrt{83}}}[/tex]
[tex]Z = 0.91[/tex]
[tex]Z = 0.91[/tex] has a p-value of 0.8186
X = 199.8
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{199.8 - 200}{\frac{2}{\sqrt{83}}}[/tex]
[tex]Z = -0.91[/tex]
[tex]Z = -0.91[/tex] has a p-value of 0.1814
0.8186 - 0.1814 = 0.6372
0.6372 = 63.72% probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.2 inches.
Which of these four sets of side lengths will form a right triangle? set 1 set 2 set 3 set 4
Answer:
hey um I cant see the picture
Determine the validity of each the following arguments. If the argument is one of those listed in the text, name it.
a. She uses e-commerce or she pays by credit card.
b. She does not pay by credit card.
c. She uses e-commerce
Answer:
Step-by-step explanation:
We will design a truth table to determine the validity of the provided arguments.
As a result, we have the following presumption:
Assume "p" stands for "she shops online(e-commerce)" and "q" stands for "she pays with a credit card."Also, she utilizes e-commerce or pays with a credit card, resulting in "p Vs q".She doesn't pay with a credit card, therefore -commerce becomes "™q → p".Now;
p q ™q p Vs q ™q →p
T T F T T
T F T T T
F T F T T
F F T F F
Conclusion:
The given arguments are valid.
A company wants to estimate, at a 95% confidence level, the proportion of all families who own its product. A preliminary sample showed that 30.0% of the families in this sample own this company's product. The sample size that would limit the margin of error to be within 0.047 of the population proportion is:
Answer:
The sample size is of 366.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A preliminary sample showed that 30.0% of the families in this sample own this company's product.
This means that [tex]\pi = 0.3[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The sample size that would limit the margin of error to be within 0.047 of the population proportion is:
This is n for which [tex]M = 0.047[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.047 = 1.96\sqrt{\frac{0.3*0.7}{n}}[/tex]
[tex]0.047\sqrt{n} = 1.96\sqrt{0.3*0.7}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.3*0.7}}{0.047}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3*0.7}}{0.047})^2[/tex]
[tex]n = 365.2[/tex]
Rounding up:
The sample size is of 366.
In most acceptance sampling plans, when a lot is rejected, the entire lot is inspected and all defective items are replaced. When using this technique the AOQ: worsens (AOQ becomes a larger fraction). improves (AOQ becomes a smaller fraction). is not affected, but the AQL is improved. is not affected. falls to zero.
Answer:
When using this technique, the AOQ:
improves (AOQ becomes a smaller fraction).
Step-by-step explanation:
AOQ simply means Average Outgoing Quality, which improves with inspection. It is a part of an organization's Acceptance Sampling Plan, usually designed to meet product quality and risk level targets. The plan draws samples from a population of items. Then it tests the samples. It only accepts the entire population if the sample is considered good enough. It also rejects the population when the sample is poor enough. In the plan, information about sample size and critical acceptance or rejection numbers are clearly indicated. Acceptance sampling is common in most business environments because it has been found to be more economical than doing 100% inspection of incoming production input and output.
What is the measure of each exterior angle of the right triangle?
x =
y =
z =
Answer:
x = 90
y = 134
z = 136
Step-by-step explanation:
Sum of interior angles of a triangle are 180
Linear angles are 180
So 180 - 90 = 90
180 - 44 = 136
180 - 90-44 = 46
180 - 46 = 134
qual é a raiz quadrada de 84
Please Help
Greatly appreciated!!
Answer:
D
Step-by-step explanation:
[tex](x_{1}, y_{1}) \ =[/tex] (-2, 1) ; m = 4/5
y - y1 = m(x - x1)
[tex]y - 1 = \frac{4}{5}(x- [-2])\\\\y - 1 =\frac{4}{5}(x + 2 )[/tex]
For every 1 litre of water used to make a medicine, 200 ml of sucrose and 300ml of saline solution are used. Express the amount of water, sucrose and saline solution needed as a ratio in its simplest form
10:2:3
Hope this helps! :)
Answer:
10:2:3
water:sucrose:saline
Step-by-step explanation:
Determine the equation of the circle shown in the graph.
Answer:
B.
Step-by-step explanation:
The equation of a circle with center at (h, k) and radius r is
[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]
We have center at (-5, 0). That makes h = -5, and k = 0.
The radius is 3, so r = 3.
[tex] (x - (-5))^2 + (y - 0)^2 = 3^2 [/tex]
[tex] (x + 5)^2 + y^2 = 9 [/tex]
Answer: B.
Answer:
B
Step-by-step explanation:
The equation of a circle has the form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the center of the circle and r is the radius.
From the graph, we can see that the center of the circle is at (-5, 0). So, (h, k) is (-5, 0), where h = -5 and k = 0.
And by counting, we can determine that the radius of the circle is three units. Hence, r = 3.
Substitute the information into the equation:
[tex](x-(-5))^2+(y-(0))^2=(3)^2[/tex]
Simplify. Therefore, our equation is:
[tex](x+5)^2+y^2=9[/tex]
Our answer is B.
What is the scale factor of this dilation?
Step-by-step explanation:To find the scale factor for a dilation, we find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image. The ratio of these distances gives us the scale factor.
John throws a biased four-sided dice.
The probabilities of getting each number are summarised in the table below.
Number
1
2
3
4
Probability
0.2
x
0.2
0.2
Work out the probability that the dice lands on 2.
Answer:
0.4
Step-by-step explanation:
0.2+0.2+0.2=0.6
1.0-0.6=0.4
This isn't 0.2 like the others which is why it's a biased dice like it says.
If you are selling your house with a local realtor who requires a 5 % commission fee, what can you expect to pay the realtor if your house sells for $182,000?
Answer: $9100
Step-by-step explanation:
Since the local realtor will get a commission of 5% whenever the house is sold, then the amount they the realtor will be paid when the house is old for $182000 will be calculated thus:
= 5% × $182000
= 5/100 × $182000
= 0.05 × $182000
= $9100
The realtor will be paid $9100.
A.85
B.98
C.102
D.34
Answer:
C. 102Step-by-step explanation:
[tex]{hope it helps}}[/tex]
Công thức tính hiệu suất
Answer:
Công thức tính hiệu quả công việc là tỷ lệ giữa đầu ra và đầu vào được biểu thị bằng phần trăm. ... Công thức hiệu quả công việc là hiệu quả = đầu ra / đầu vào, và bạn có thể nhân kết quả với 100 để tính hiệu quả công việc theo tỷ lệ phần trăm.
construct a scale of A-sharp major on a treble staff in ascending order only
Answer: In the picture from the basic music theory website's page on a-sharp major scale
Step-by-step explanation: music theory
Which matrix represents the solution to the system of equations below?
2a+b+c=2
-a+ - =-4
a-25+2c=6
1
0
0
2
1
0
-2.
0
0
1
0
1
0
0
1
0
1
0
- 2
0
0
1
0
2
1
1
2.
-4
Answer:
The one that's include a rows 2 1 1 2
Answer:
A
Step-by-step explanation:
they wanted the reduced echelon form.
On Edge. btw
How do I solve this and do the explanation of it
Answer:
180-66
114
hope it helps mark as brainlist