Answer:
[tex]m = \frac{1}{12}[/tex]
Step-by-step explanation:
Given
[tex](x,y) = (36,6)[/tex]
[tex]f(x) = \sqrt x[/tex] ----- the equation of the curve
Required
The slope of f(x)
The slope (m) is calculated using:
[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]
[tex](x,y) = (36,6)[/tex] implies that:
[tex]a = 36; f(a) = 6[/tex]
So, we have:
[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]
[tex]m = \lim_{h \to 0} \frac{f(36 + h) - 6}{h}[/tex]
If [tex]f(x) = \sqrt x[/tex]; then:
[tex]f(36 + h) = \sqrt{36 + h}[/tex]
So, we have:
[tex]m = \lim_{h \to 0} \frac{\sqrt{36 + h} - 6}{h}[/tex]
Multiply by: [tex]\sqrt{36 + h} + 6[/tex]
[tex]m = \lim_{h \to 0} \frac{(\sqrt{36 + h} - 6)(\sqrt{36 + h} + 6)}{h(\sqrt{36 + h} + 6)}[/tex]
Expand the numerator
[tex]m = \lim_{h \to 0} \frac{36 + h - 36}{h(\sqrt{36 + h} + 6)}[/tex]
Collect like terms
[tex]m = \lim_{h \to 0} \frac{36 - 36+ h }{h(\sqrt{36 + h} + 6)}[/tex]
[tex]m = \lim_{h \to 0} \frac{h }{h(\sqrt{36 + h} + 6)}[/tex]
Cancel out h
[tex]m = \lim_{h \to 0} \frac{1}{\sqrt{36 + h} + 6}[/tex]
[tex]h \to 0[/tex] implies that we substitute 0 for h;
So, we have:
[tex]m = \frac{1}{\sqrt{36 + 0} + 6}[/tex]
[tex]m = \frac{1}{\sqrt{36} + 6}[/tex]
[tex]m = \frac{1}{6 + 6}[/tex]
[tex]m = \frac{1}{12}[/tex]
Hence, the slope is 1/12
In the parallelogram below, solve for x.
D (9x + 5)
E
G
F (13 - 43y
Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
Given
[tex]\angle D = 9x + 5[/tex]
[tex]\angle F = 13x -43[/tex]
Required
Find x
To find x, we make use of:
[tex]\angle D =\angle F[/tex] --- opposite angles of a parallelogram
So, we have:
[tex]9x + 5 =13x -43[/tex]
Collect like terms
[tex]9x - 13x = -5-43[/tex]
[tex]-4x = -48[/tex]
Divide by -4
[tex]x = 12[/tex]
In a sociology class there are 14 men and 10 women. 3 students are randomly selected to present a topic. What is the probability that at least 1 of the 3 students selected is female? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
0.8015
Step-by-step explanation:
Hope I'm correct lol
How many edges are there?
9514 1404 393
Answer:
24
Step-by-step explanation:
The front face is an 8-sided star, so has 8 edges. We presume the back face is the same, so it also has 8 edges. Each of the front vertices is connected by an edge to each of the corresponding back vertices, so there are 8 more edges connecting front and back.
The total number of edges is 8 + 8 + 8 = 24.
If path has 56 marbles and he gave Sandra 34 how many marbles will he have left?
Answer:
22
Step-by-step explanation:
You just subtract them
56-34
= 22
Evaluate S8 for the series 1+3+6+9+12.........
Answer:
S8 is 64
Step-by-step explanation:
[tex]{ \boxed{ \bf{S_{n} = \frac{n}{2} [2a + (n - 1)d]}}}[/tex]
n is number of terms; n = 8
a is the first term; a = 1
d is the common difference: d = 3-1; d = 2
[tex]{ \sf{S_{8} = \frac{8}{2}[(2 \times 1) + (8 - 1) \times 2 ]}} \\ \\ { \sf{{S_{8}} = 4(2 + 14)}} \\ { \sf{S_{8}}} = 4 \times 16 \\ { \sf{S_{8}}} = 64[/tex]
In a large midwestern university (the class of entering freshmen is 6000 or more students), an SRS of 100 entering freshmen in 1999 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 2000. In 2001, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 and p2 be the proportion of all entering freshmen in 1999 and 2001, respectively, who graduated in the bottom third of their high school class.
Required:
Is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced, as a result of the tougher admission standards adopted in 2000, compared with the proportion in 1999
Answer:
The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.
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]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
1999:
20 out of 100 in the bottom third, so:
[tex]p_1 = \frac{20}{100} = 0.2[/tex]
[tex]s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04[/tex]
2001:
10 out of 100 in the bottom third, so:
[tex]p_2 = \frac{10}{100} = 0.1[/tex]
[tex]s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03[/tex]
Test if proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
At the null hypothesis, we test if the proportion is still the same, that is, the subtraction of the proportions in 1999 and 2001 is 0, so:
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternative hypothesis, we test if the proportion has been reduced, that is, the subtraction of the proportion in 1999 by the proportion in 2001 is positive. So:
[tex]H_1: p_1 - p_2 > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]X = p_1 - p_2 = 0.2 - 0.1 = 0.1[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.1 - 0}{0.05}[/tex]
[tex]z = 2[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of at least 0.1, which is the p-value of z = 2.
Looking at the z-table, the p-value of z = 2 is 0.9772.
1 - 0.9772 = 0.0228.
The p-value of the test is 0.0228, which is less than the standard significance level of 0.05, which means that there is evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 2001 has been reduced.
Which of these graphs represents the inequality x > 5?
Answer:
A is correct.
x>5 means all numbers greater than BUT not equal to 5.
The open circle means "not equal".
So, A is correct.
Hope this helps!
Answer:
Graph A.
Step-by-step explanation:
Answer: x > 5 means all x values greater than 5
thus, the graph that best shows that x is greater than 5 is graph A.
Explanation: because x isn't being itself I mean by x isn't just 5 but greater than 5 (graph a)
graph b shows x being less than 5 which is wrong
graph c shows x being greater than 5 but being equal to 5 because of the bold circle
graph d shows everything wrong about x. first it's not suppose to be less than and second x isn't equal to 5
therefore the answer graph A.
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doomdabomb: all brainliest and thanks are appreciated
and would mean a lot to me, thanks!
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 ladder? Round your answer to the nearest hundredth.
45.88 feet
34.88 feet
22.47 feet
19.59 feet
Answer:
34.88
Step-by-step explanation:
I took the test
The distance between the building and the ladder is 34.88 foot, the correct option is B.
What is a Right Triangle?A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.
The ladder forms a right triangle with the building and the ground,
The length of the triangle is 40 foot
The angle made by the ladder is 29.32 degree
By using Trigonometric Ratios
cos 29.32 = Base / Hypotenuse
cos 29.32 = Base / 40
Base is the distance between the building and the ladder.
Base = 34.88 foot
To know more about Right Triangle
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2y-x=6 and y=2x+7 graphed equals how many solutions
Answer:
One solution
BRAINLIEST, PLEASE!
Step-by-step explanation:
2y - x = 6
2y = x + 6
y = x/2 + 3
y = 2x + 7
After graphing, they have one solution at (-2.667, 1.667).
Why is the value of -9 is not-3
Answer:
Because it's a negative.
Step-by-step explanation:
The value of a positive number is still a positive number.
I need to solve this, showing work would be appreciated!
Answer:
e) cannot be determined
Step-by-step explanation:
there is no way you can find out angle 2 if there is no angle 1 first
hope this helps!
There are 45 applicants for two Software
Maker positions.
I
3. Find the minimum number of students needed to guarantee that five of them belong to the same class (Freshman, Sophomore, Junior, Senior)
Answer:
100
Step-by-step explanation:
well you can put 5 students in each class guaranteed 5 times over so it would make sense because 5 for each class 9th-12th 5 times over again and again will eventually give you the answer of 100 5•20
If we take 5 students are in each class.
Then let minimum number of students be x
ATQ
1/20()x = 5
x = 5 × 20
x = 100
Answer: 100 people
Must click thanks and mark brainliest
which of the following illustrates commutative property of addition? 17+4=4+17
9514 1404 393
Answer:
17 +4 = 4 +17
Step-by-step explanation:
The only expression shown here illustrates that property.
Find an equation of the plane orthogonal to the line
(x,y,z)=(0,9,6)+t(7,−7,−6)
which passes through the point (9, 6, 0).
Give your answer in the form ax+by+cz=d (with a=7).
The given line is orthogonal to the plane you want to find, so the tangent vector of this line can be used as the normal vector for the plane.
The tangent vector for the line is
d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩
Then the plane that passes through the origin with this as its normal vector has equation
⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0
We want the plane to pass through the point (9, 6, 0), so we just translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,
(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0
Simplifying this expression and writing it standard form gives
⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0
7 (x - 9) - 7 (y - 6) - 6z = 0
7x - 63 - 7y + 42 - 6z = 0
7x - 7y - 6z = 21
so that
a = 7, b = -7, c = -6, and d = 21
An equation of the plane orthogonal to the line 7x - 7y - 6z = 21.
The given line is orthogonal to the plane you want to find,
So the tangent vector of this line can be used as
The normal vector for the plane.
The tangent vector for the line is,
What is the tangent vector?A tangent vector is a vector that is tangent to a curve or surface at a given point.
d/dt (⟨0, 9, 6⟩ + ⟨7, -7, -6⟩t ) = ⟨7, -7, -6⟩
Then the plane that passes through the origin with this as its normal vector has the equation
⟨x, y, z⟩ • ⟨7, -7, -6⟩ = 0
We want the plane to pass through the point (9, 6, 0), so we just
translate every vector pointing to the plane itself by adding ⟨9, 6, 0⟩,
(⟨x, y, z⟩ - ⟨9, 6, 0⟩) • ⟨7, -7, -6⟩ = 0
Simplifying this expression and writing it in standard form gives
⟨x - 9, y - 6, z⟩ • ⟨7, -7, -6⟩ = 0
7 (x - 9) - 7 (y - 6) - 6z = 0
7x - 63 - 7y + 42 - 6z = 0
7x - 7y - 6z = 21
So that, a = 7, b = -7, c = -6, and d = 21.
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Which is the best way to accumulate wealth: a) Save your money by putting it into a savings account at the bank. b) Invest as much money as you can, at the end of each year, (A lump sum) into some sort of long term investment vehicle. c) Contribute to a monthly annuity as early as possible for the long term. d) Invest monthly into an investment vehicle that pays the minimum return.
Choose a, b, c, or d and state four reasons why.
Answer:
save your money by putting it into a savings account at the bank
54
What value of b will cause the system to have an
infinite number of solutions?
y = 6x - b
-3х+ 1/2y=-3
b=
Answer:
Does the answer help you?
Find the length of the arc.
A. 539π/12 km
B. 9π/3 km
C. 9π/2 km
D. 18π km
Answer:
b because it is I found out cus I took test
The length of the arc 9π/2 km.
The answer is option C.9π/2 km.
What is the arc of the circle?
The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.
⇒angle= arc/radius
⇒ 135°=arc/6km
⇒ arc =135°*6km
⇒arc=135°*π/180° * 6km
⇒arc = 9π/2 km
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Evaluate the equation
Answer:
3 +4 i
Step-by-step explanation:
x + sqrt(yz)
Let x = 3 y=2 and z = -8
3 + sqrt(2*-8)
3+ sqrt(-16)
3 + sqrt(16) sqrt(-1)
We know sqrt(-1) = i
3 +4 i
Ahmad Conan deposited 60 quarters, 53 dimes, 44 nickels, and 50 pennies into his checking account. The total of the checks he deposited equaled $17 less than twice his total deposit. If Ahmad received 2 twenty-dollar bills in cash, what was his total deposit?
Answer:
40 $
Step-by-step explanation:
He first deposited 60 quarters=15$, 53 dimes=5.3$, 44 nickels=2.2$, and 50 pennies=0.5$ Total 23$
23$+17$=2*(total deposit)
so total deposit = 20
"If Ahmad received 2 twenty-dollar bills in cash" - does not mean that he deposited those 40$
so total deposit = 20$
The most frequently occuring value in a set is called the
Answer:
Step-by-step explanation:
The mode is the correct answer
. Parul purchased 9 bottles each containing 750 ml of orange juice. What is the total quantity of orange juice she purchased? If you give me correct answer I will make u brainlist and also give 5 rates and thanks
answer me
hi
9x750 = 630 +450= 1080 ml
so 1.08 liter.
X < -3 graph line
How do you graph
X < -3
Is it A,B,C,D ?
Answer:
Option B
Step-by-step explanation:
x<-3 means the values of x will be less than -3, do the dot will be blank and towards the left side of -3
What happens to the median of the data set
{2, 4, 5, 6, 8, 2, 5, 6} if the number 10 is added to the data set?
A. The median does not change.
B. The median increases by 2.
C. The median decreases by 0.25.
D. The median increases by 1.
Answer:
A. The median does not change.
Step-by-step explanation:
Original data set,
Put the numbers in order from smallest to largest
2,2, 4, 5, 5, 6,6, 8
Median is the middle number
2,2, 4, 5, 5, 6,6, 8
It is between the two 5's
(5+5)/2 = 10/2 = 5
New data set
Put the numbers in order from smallest to largest
2,2, 4, 5, 5, 6,6, 8,10
Median is the middle number
2,2, 4, 5, 5, 6,6, 8,10
The middle number is 5
Answer:
The answer is A
Step-by-step explanation:
PLEASE HELP!!!
The following data are the distance from the workplace ( in miles) for the 5 employees of a small business.
10,17,12,14,12
Assuming that these distance constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
Answer:
stdev= 2.366431913
Step-by-step explanation:
10 stdev= 2.366431913
17
12
14
12
Reason Can you subtract a positive integer from a positive integer
and get a negive result? Explain your answer.
Answer:
No
Step-by-step explanation:
No matter the situation, when you multiply a negative by a negativeyou get a positive and a positive by a positive you get a positive. but if its two different like a negative and a positive then its NEGITIVE.
let's say you have 23 and you're multiplying by 2.
It's always increasing so it doesnt ever reach the negitive numbers.
compare the following rational number
[tex] \frac{4}{5} and \frac{7}{5} [/tex]
Answer:
7/5 is greater than 4/5
Answer:
[tex]\frac{4}{5}[/tex] < [tex]\frac{7}{5}[/tex]
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
A team of 15 basketball players needs to choose two players to refill the water cooler.
Permutation/Combination:
Answer:
Answer:
Permutation ; 210 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 players from 15 ; since order does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
15P2 = 15! ÷ (15 - 2)!
15P2 = 15! ÷ 13!
15P2 = (15 * 14) = 210 ways
You and your friend decide to get your cars inspected. You are informed that 83% of cars pass inspection. If the event of your car's passing is independent of your friend's car. please help me with d! an explanation with steps would be nice but mandatory
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
The student body of 290 students wants to elect a president and vice president.
Permutation/Combination:
Answer:
Answer:
Permutation. ; 83810 ways
Step-by-step explanation:
Permutation and combination methods refers to mathematical solution to finding the number of ways of making selection for a group of objects.
Usually, selection process whereby the order of selection does not matter are being treated using permutation, while those which takes the order of selection into cognizance are calculated using combination.
Here, selecting 2 members (president and vice president) from 290 ; since order of arrangement does not matter, we use permutation ;
Recall :
nPr = n! ÷ (n - r)!
Hence,
290P2 = 290! ÷ (290 - 2)!
290P2 = 290! ÷ 288!
290P2 = (290 * 289) = 83810 ways
