Answer:
5 b^ 3 √ a
Step-by-step explanation:
Break up the radicand up into a product of known factors assuming positive real numbers.
A note card company has found that the marginal cost per card of producing x note cards is given by the function below, where C'(x) is the
marginal cost, in cents, per card. Find the total cost of producing 900 cards, disregarding any fixed costs.
C'(x) = -0.05x + 77, for x S 1000
The total cost is
cents
Answer:
49,050cents
Step-by-step explanation:
Given the expression for calculating the marginal cost per card of producing x note cards expressed as
C'(x) = -0.05x + 77
On intergrating the marginal cost, we will get the total cost
C(x) = -0.05x²/2 + 77x
Substitute x = 900 into the resulting expression
C(900) = -0.05(900)²/2 + 77(900)
C(900) = -20,250+69,300
C(900) = 49,050
Hence the total costs in cents is 49,050cents
a 40 foot ladder is leaning against a building and forms a 29.32° angle with the ground. How far away from the building is the base of the latter? Round your answer to the nearest hundred
9514 1404 393
Answer:
34.88 feet
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
We want to find the length of the side adjacent to the measured angle. The hypotenuse is the ladder length.
cos(29.32°) = distance/(40 ft)
distance = (40 ft)cos(29.32°) ≈ 34.876°
The base of the ladder is about 34.88 feet from the building.
_____
Additional comment
It extends about 19.59 feet up the side of the building.
Which equation represents a line that passes through (4,1/3) and has a slope of 3/4?
Oy- 3/4= 1/3(x-4)
Oy-1/3= 3/4(x-4)
Oy- 1/3= 4(x-3/4)
Oy-4 = 3/4(x-1/3)
Step-by-step explanation:
With this kind of problem, we're looking at an equation in the form
y - y1 = m(x - x1)
(m = slope)
so we can substitute m, y1, and x1 with the values we're given.
y - y1 = m(x - x1)
y - 1/3 = 3/4(x - 4)
Answer:
y - 1/3 = 3/4(x - 4)
A 10-sided die is rolled. Find the probability of rolling an even number. The set of equally likely outcomes is shown below. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The probability of rolling an even number on a 10-sided die is:
Answer:
1/2
Step-by-step explanation:
There are ten sides on this die. As stated in your question, there are five even numbers and five odd numbers. If we take the amount of even numbers over the total, you get 5/10, which simplifies to 1/2.
The probability of rolling an even number on a 10 - sided die is 1/2 or 0.5
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the data set be S = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }
So , the number of elements in the data set = 10 elements
Now , in order to get an even number when dolling the dice ,
The set of possible outcomes P = { 2 , 4 , 6 , 8 , 10 }
The number of elements in the data set P of outcomes = 5 elements
So , the probability of getting an even number from the data set when rolling a 10 sided dice is P ( x ) =
number of elements in the data set P of outcomes / number of elements in the data set
The probability of getting an even number from the data set when rolling a 10 sided dice is P ( x ) = 5 / 10
The probability P ( x ) = 1/2
= 0.5
Hence , The probability of rolling an even number on a 10 - sided die is 1/2 or 0.5
To learn more about probability click :
https://brainly.com/question/17089724
#SPJ2
which equation is equivalent to 8+2(x-1)=5
Answer:
8+2x-2 = 5
2x+6 =5
2x = -1
Step-by-step explanation:
8+2(x-1)=5
Distribute
8+2x-2 = 5
Combine like terms
2x+6 =5
Subtract 6
2x+6-6=5-6
2x = -1
Find the volume of the figure. If necessary, round the answer to the nearest whole number.
Answer:
V = 108 ft³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Rectangular Prism Formula: V = lwh
l is lengthw is widthh is heightStep-by-step explanation:
Step 1: Define
Identify variables
l = 4 ft
w = 3 ft
h = 9 ft
Step 2: Find Volume
Substitute in variables [Volume of a Rectangular Prism Formula]: V = (4 ft)(3 ft)(9 ft)Evaluate [Order of Operations]: V = 108 ft³find the value of n . 80×π×n=1100000
Answer:
110000/8π
Step-by-step explanation:
Divide 1100000 by 80 and cancel 0. Then divide pi
An advertising firm wanting to target people with strong desires for success conducted a study to see if such people differed in the types of television shows they watched. Randomly selected participants recorded the shows they watched for a week, then their desire for success was assessed, and finally they were divided into two groups. Low Success seekers watched 8 comedies, 15 romances, 6 documentaries, 13 dramas, and 3 news shows. High Success seekers watched 3 comedies, 3 romances, 9 documentaries, 7 dramas, and 8 news shows.
1. Use the five steps of hypothesis testing.
2. Sketch the chi-square distribution. Be sure your sketch gives a rough indication of its shape and shows the cutoff score and the sample's score.
3. Explain the logic of what you have done to a person who is familiar with the logic and steps of hypothesis testing for the t test and analysis of variance, but who knows nothing about chi-square tests.
4. Figure a measure of effect size and indicate whether it is small, medium, or large.
Answer:
Blablabla
Step-by-step explanation:
Bababa
Expand and simplify the following expressions. a. (2 − 3)( − 6)
Answer:
your answer should be six I hope this help
Answer:
the should be 6
Step-by-step explanation:
(2-3)(-6)
-12+18
=6
A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 6 students' scores on the exam after completing the course: 6,16,19,12,15,14.
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval.
Answer:
The critical value is [tex]T_c = 2.5706[/tex].
The 90% confidence interval for the average net change in a student's score after completing the course is (9.04, 18.30).
Step-by-step explanation:
Before building the confidence interval, we need to find the sample mean and the sample standard deviation:
Sample mean:
[tex]\overline{x} = \frac{6+16+19+12+15+14}{6} = 13.67[/tex]
Sample standard deviation:
[tex]s = \sqrt{\frac{(6-13.67)^2+(16-13.67)^2+(19-13.67)^2+(12-13.67)^2+(15-13.67)^2+(14-13.67)^2}{5}} = 4.4121[/tex]
Confidence interval:
We have the standard deviation for the sample, so the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.5706, that is, the critical value is [tex]T_c = 2.5706[/tex]
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.5706\frac{4.4121}{\sqrt{6}} = 4.63[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 13.67 - 4.63 = 9.04.
The upper end of the interval is the sample mean added to M. So it is 13.67 + 4.63 = 18.30.
The 90% confidence interval for the average net change in a student's score after completing the course is (9.04, 18.30).
Please help me please please help ASAP
Step-by-step explanation:
70 + 45 = 115
180 - 115 = 65
angle c = 65
use sohcahtoa
cos angle = adjacent
hypotenuse
cos 65 = 2.5
b
b cos 65 = 2.5
use the calc for further answers
hope that helped
find the value of the trigonometric ratio
Answer:
ur box cannot be opend repain the window
Step-by-step explanation:
please mark this answer as brainlist
(ii). nth term of: 10+4-2...
9514 1404 393
Answer:
an = 10 -6(n -1)
Step-by-step explanation:
The series is an arithmetic series with a first term of 10, and a common difference of 4-10 = -6. The n-th term of an arithmetic series is given by ...
an = a1 +d(n -1) . . . . . for first term a1 and common difference d
__
For the parameters this series has, the n-th term is ...
an = 10 -6(n -1)
Kayla parks her car at the corner of Ogilvie and Montreal Rd. She walks 80m East and then turns 30° to the left towards her office building and continues walking for another 100m until she reaches her building. She then takes the elevator to her office 60m above ground level and looks out the window. She can see her car from here. How far is it from where she is to her car in a direct line?
9514 1404 393
Answer:
184 m
Step-by-step explanation:
The direct distance from Kayla's car (C) to the door of her office building (B) can be found using the Law of Cosines. The interior angle of the triangle at the turning point is 180° -30° = 150°, so the distance is ...
t² = b² +c² -2bc·cos(T)
t² = 80² +100² -2·80·100·cos(150°) = 30256.406
The direct distance from her window to the car can be found from the Pythagorean theorem. The legs of the right triangle are the distance from the car to the building (CB) and the height from the building entrance to the window (BW).
CW = √(t² +60²) ≈ 184.001
The direct line distance from Kayla to her car is 184 meters.
_____
For the first computation, we used the usual notation for a triangle, where capital letters (CTB) are the vertices and angles, and corresponding lower-case letters are their opposite sides.
In 20P4 how many choices are
there for vice-president from a
state of four officers?
Note: The vice president is the second officer
to be elected.
Acellus
Explanation:
There are 20 choices for president, and 20-1 = 19 choices for vice president. You count down by 1 each time you fill a seat. So that means you'll have 19-1 = 18 choices for the third seat, and 18-1 = 17 choices for the fourth seat.
Find the missing length indicated
Answer:
x = 15
Step-by-step explanation:
x = √{(25-16)×25}
x = √(9×25)
x = √225
x = 15
Answered by GAUTHMATH
Aku has less than 3 times as many mangoes as Alaba and half as many mangoes as Amina if alaba has x mangoes the interns of x then how many mangoes do aku alaba and Amina have in combined
Answer:
I have no clue my bad bro.
What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39
Answer:
B.17
Step-by-step explanation:
B.17
B.17
B.17
B.17
Find the slope and the y-intercept of the line with the given equation.
f(x) = 7 -4/5x
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The slope is
(Type an integer or a simplified fraction.)
B. The slope is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The y-intercept is
(Simplify your answer. Type an ordered pair, using integers or fractions.)
B. There is no y-intercept.
Answer:
The slope is -4/5
The y intercept is (0,7)
Step-by-step explanation:
f(x) = 7 -4/5x
Rewriting
y = -4/5x +7
This is in slope intercept form
y = mx+b where m is the slope and x is the y intercept
The slope is -4/5
The y intercept is (0,7)
A sample of 375 college students were asked whether they prefer chocolate or vanilla ice cream. 210 of those surveyed said that they prefer vanilla ice cream. Calculate the sample proportion of students who prefer vanilla ice cream.
Answer:
The sample proportion of students who prefer vanilla ice cream is 0.56.
Step-by-step explanation:
Sample proportion of students who prefer vanilla ice cream:
Sample of 375 students.
Of those, 210 said they prefer vanilla ice cream.
The proportion is:
[tex]p = \frac{210}{375} = 0.56[/tex]
The sample proportion of students who prefer vanilla ice cream is 0.56.
Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, evaluate the researcher's hypothesis that the instructional program affects students' knowledge. What is the correct cutoff score(s)
Answer:
The solution according to the problem given is provided below in the explanation segment.
Step-by-step explanation:
According to the question,
[tex]H_o: \mu_1=\mu_2[/tex]
[tex]H_a: \mu_1 \neq \mu_2[/tex]
Level of significance,
[tex]\alpha = .05[/tex]
The test statistics will be:
⇒ [tex]Z = \frac{(\bar x_1 - \bar x_2)}{\sqrt{\frac{\sigma_1^2}{n_1} +\frac{\sigma_2^2}{n_2} } }[/tex]
[tex]=\frac{(38-35)}{\sqrt{\frac{(3)^2}{30} +\frac{(5)^2}{30} } }[/tex]
[tex]=2.82[/tex]
The p-value will be:
= [tex]0.0024[/tex]
Lily wants to put a ribbon border around two round clocks. Each clock has a diameter of 24 centimeters. Using 3.14 for π, approximately how many meters of ribbon does Lily need?
Answer:
1.5 meters
Step-by-step explanation:
You need to use circumference for this problem and the formula is dπ.
Plug in:
24π
Solve with pi:
24×3.14 = 75.36
Since there is two clocks, multiply:
75.36 × 2 = 150.72
In 1 meter there is 100 centimeters so divide
150.75 ÷ 100 = 1.5
So you will need 1.5 meters of ribbon.
Write an absolute value equation to satisfy the given solution set shown on a number line.
Answer:
|x + 6| = 2
Step-by-step explanation:
For a general absolute value equation:
| f(x) | = b
We can rewrite it as:
f(x) = b
f(x) = -b
with b > 0.
Because in the number line we have only two points graphed, this means that our absolute value equation has two solutions.
And we can conclude that one solution comes from the equation:
f(x) = b
And the other solution comes from the equation:
f(x) = -b
And thus, f(x) is a linear equation, that we can simply write as:
x - c
Then our equations can be rewritten as:
x - c = b
x -c = -b
Now let's look at the graph, we can see that the two solutions are:
x = -8
and
x = -4
Let's input each one of these in one of our above equations (the order does not matter).
-4 - c = b
-8 - c = -b
The larger value of x, (x = -4) needs to be in the equation with the positive value of b.
From the first equation we can get:
b = -4 - c
now we can replace the variable "b" in the second equation by "-4 - c" to get:
-8 - c = -(-4 - c)
-8 - c = 4 + c
-8 - 4 = c + c
-12 = 2c
-12/2 =c
-6 = c
Now that we know the value of c, we can input it in the equation:
b = -4 - c
to find the value of b
b = -4 - (-6) = -4 + 6 = 2
b = 2
Then the absolute value equation is:
|x - (-6) | = 2
|x + 6| = 2
Hey guys if you could help ASAP thank you
Answer:
Step-by-step explanation:
The answer is B
if you have 2^3 * 2*4 to find out what that equals, leave the base (2) alone and add the powers. You get 2^(3 + 4) = 2^7
Let's see if that works.
2^3 = 8
2^4 = 16
8 * 16 = 128
Now what is 2^7?
2^7 = 128 just as it should
Now returning to your question
3^7.869 = answer B You leave the base alone (7) and add the powers. The 8 is 8/10
The 6 is 6/100
The 9 is 9 / 1000 Just add the fractions and keep the 7 and the 3.
How can you minimize the risk from your investments?
A.
by investing in a stock with the highest volatility
B.
by investing in a stock with maximum returns
C.
by investing in a variety of investment options
by common sense I can tell is C.) by investigating in a variety of investment options!
while doing business I rather have multiple options than one! but that is personal you may have your own thought!
Answer:
C. by investigating in a variety of investment options
Explanation:
diversification reduces investment risk
(it is obviously not a as volatility is high degree of variation which is negative)
A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug. Each rat will be given a different dosage of the drug. The oncologist will then measure the growth rate of the cancerous tumor. What best describes the input and output variables that will be used in this experiment?
The input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.
Given information:
A medical researcher is using rats to do an experimental test to determine the appropriate dosage for a new cancer drug.
Each rat will be given a different dosage of the drug.
The oncologist will then measure the growth rate of the cancerous tumor.
Now, in the experiment, the oncologist tries to study or calculate the growth rate of a cancerous tumor. So, the output that he/she will get will be the growth rate of the cancerous tumor.
The experiment is done on the rate by giving them a dosage of the drug. The dosage can vary based on the study criterion. So, the amount of dosage of the drug should be the input of the experiment.
Therefore, the input of the experiment is the amount of dose of the drug and the output is the growth rate of the cancerous tumor.
For more details, refer to the link:
https://brainly.com/question/5527886
Find f′ in terms of g′
f(x)=x2g(x)
Select one:
f′(x)=2xf′(x)+2xg′(x)
f′(x)=2xg′(x)
f′(x)=2x+g′(x)
f′(x)=x2g(x)+2x2g′(x)
f′(x)=2xg(x)+x2g′(x)
f(x)g(x) if you find the derivative of two products, you get f(x)g’(x)+f’(x)g(x). Let’s say x^2 = f(x).
(x^2)(g’(x))+2x(g(x)) so it would be your last option, 2x(g(x))+x^2(g’(x))
Find the inequality represented by the graph
I'm using khan academy btw
Answer:
Step-by-step explanation:
slope of line through (0,0) and (4,3) =(3-0)/(4-0)=3/4
eq. of line is y-0=3/4(x-0)
y=3/4 x
put x=4
y=2
2=3/4×4
2=3
which is true if 2<3
2<3
so y<3/4 x
Point D is 8 units away from the origin along the x-axis, and is 6 units away along the y-axis. Which of the following could be the coordinates of Point D
Answer:
The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Now we know that point D, which we can write as (x, y), is at a distance of 8 units from the origin.
Where the origin is written as (0, 0)
We also know that point D is 6 units away along the y-axis.
Then point D could be:
(x, 6)
or
(x, -6)
Now, let's find the x-value for each case, we need to solve:
[tex]8 = \sqrt{(x - 0)^2 + (\pm6 - 0)^2}[/tex]
notice that because we have an even power, we will get the same value of x, regardless of which y value we choose.
[tex]8 = \sqrt{x^2 + 36} \\\\8^2 = x^2 + 36\\64 - 36 = x^2\\28 = x^2\\\pm\sqrt{28} = x\\\pm 5.29 = x[/tex]
So we have two possible values of x.
x = 5.29
and
x = -5.29
Then the points that are at a distance of 8 units from the origin, and that are 6 units away along the y-axis are:
(5.29, 6)
(5.29, -6)
(-5.29, 6)
(-5.29, -6)
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.03 0.02 1 0.06 0.20 0.07 2 0.05 0.14 0.33 (a) What is P(X
Answer:
[tex]P(x = 1) = 0.33[/tex]
[tex]P(y = 2) = 0.42[/tex]
Step-by-step explanation:
Given
y
x [tex]\begin{array}{cccc}P(x,y) & {0} & {1} & {2} & {0} & {0.10} & {0.03} & {0.02} & {1} & {0.06} & {0.20} & {0.07} & {2} & {0.05} & {0.14} & {0.33}\ \end{array}[/tex]
Solving (a)
[tex]P(x = 1)[/tex]
To do this, we simply add all data where x = 1
So, we have:
[tex]P(x = 1) = P(x=1|y=0) + P(x=1|y=1) + P(x=1|y=2)[/tex]
[tex]P(x = 1) = 0.06 + 0.20 + 0.07[/tex]
[tex]P(x = 1) = 0.33[/tex]
Solving (b)
[tex]P(y = 2)[/tex]
To do this, we simply add all data where y = 2
So, we have:
[tex]P(y = 2) = P(x=0|y=2) + P(x=1|y=2) + P(x=2|y=2)[/tex]
[tex]P(y = 2) = 0.02 + 0.07 + 0.33[/tex]
[tex]P(y = 2) = 0.42[/tex]
