Given nth term of an AP = 7-4n
Put n = 1 then t1 = 7-4(1) = 7-4 = 3
Put n = 2 then t2 =7-4(2) = 7-8 = -1
Common difference = t2-t1 = -1-3 = -4
at which value will the graph of y=csc x have a zero
Answer:
y = csc(x) does not have any zero.
Step-by-step explanation:
If we have:
y = f(x)
a zero of that function would be a value x' such that:
y = f(x') = 0
Here we basically want to solve:
y = csc(x) = 0
First, remember that:
csc(x) = 1/sin(x)
now, the values of sin(x) range from -1 to 1.
So we want to solve:
1/sin(x) = 0
notice that a fraction:
a/b = 0
only if a = 0.
Then is easy to see that for our equation:
1/sin(x) = 0
The numerator is different than zero, then the equation never will be equal to zero.
Then:
y = csc(x) = 1/sin(x)
Does not have a zero.
if x-y =2 and xy=15, find the value of x cube - y cube.
Answer:
5³ = 125 : -3³ = -27Step-by-step explanation:
let x= 5 and y= 3x - y = 25 - 3 = 2xy = 155 × 3 = 15x³ = ? : -y³ = ?5³ = 125 : -3³ = -27[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
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 tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than 60,000 miles. The manufacturer tests 250 tires and finds the mean life for these tires to be 64,500 miles.What is the alternative hypothesis being tested in this example
Answer:
The alternative hypothesis being tested in this example is that the tire life is of more than 60,000 miles, that is:
[tex]H_1: \mu > 60,000[/tex]
Step-by-step explanation:
A tire manufacturer has a 60,000 mile warranty for tread life. The company wants to make sure the average tire lasts longer than 60,000 miles.
At the null hypothesis, we test if the tire life is of at most 60,000 miles, that is:
[tex]H_0: \mu \leq 60,000[/tex]
At the alternative hypothesis, we test if the tire life is of more than 60,000 miles, that is:
[tex]H_1: \mu > 60,000[/tex]
Can you please help me
9514 1404 393
Answer:
1/63
Step-by-step explanation:
There are various ways the question "how much larger" can be answered. Here, we choose to answer it by telling the difference between the two fractions:
4/9 -3/7 = (4·7 -9·3)/(9·7) = 1/63
The larger fraction is 1/63 unit larger than the smaller fraction.
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).
Find the sum of the geometric series given a1=2, r=−3, and n=8.
Answer:
S₈ = - 3280
Step-by-step explanation:
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{}(r^{n}-1) }{r-1}[/tex]
Here a₁ = 2, r = - 3 and n = 8 , then
S₈ = [tex]\frac{2((-3)^{8}-1) }{-3-1}[/tex]
= [tex]\frac{2(6561-1)}{-4}[/tex]
= [tex]\frac{2(6560)}{-4}[/tex]
= [tex]\frac{13120}{-4}[/tex]
= - 3280
What are the values of a, b, and c in the quadratic equation 0 = one-halfx2 – 3x – 2?
a = one-half, b = 3, c = 2
a = one-half, b = –3, c = –2
a = one-half, b = 3, c = –2
a = one-half, b = –3, c = 2
Answer:
b
Step-by-step explanation:
ax^2+bx+c=0
1/2x^2-3x-2=0
Answer:
B
Step-by-step explanation:
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)
The difference of two numbers is 8. If the sum of the smaller number and the square of the larger number is 148, what is the smaller number?
Answer:
C
Step-by-step explanation:
Hello people can you please help me on this
Step-by-step explanation:
Step 1: Complete the first equation
0.1 is a tenth, therefore if we have 15.3 then we have 153 tenths.
Step 2: Complete the second equation
15.3 / 3 = 5.1
0.1 is a tenth, therefore if we have 5.1 then we have 51 tenths.
Step 3: Complete the third equation
15.3 / 3 = 5.1
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
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11. The unit digit in the expression (31 + 132 + 143 + 414 + 515 +156 + 61) i (A) 4 (B) 3 (C) 2 . (D) 1
Answer:
Step-by-step explanation:
[tex]we \ add \ \ only \ \ units \ we \ do \ not \ need \ the \ rest \\\\ \bf (3\underline 1 + 13\underline2 + 14\underline3 + 41\underline4 + 51\underline5 +15\underline6 + 6\underline1)= \\\\ 1+2+3+4+5+6+1=2\underline 2 \\\\ Answer: C) \ 2[/tex]
5x + 2y + 19 = 0 3x + 4y + 17 = 0
Answer:
x = -3; y = 2
Step-by-step explanation:
5x + 2y + 19 = 0
3x + 4y + 17 = 0
-10x - 4y - 38 = 0
3x + 4y + 17 = 0
-7x - 21 = 0
x = -3
5(-3) + 2y = -19
2y = -4
y = -2
Answer: x = -3; y = 2
What is (4n + 3n2 + 2) - (n - 6n
+1) simplified?
A -3n2 + 3n-2 C 9n2 + 3 + 2
B 3n2 + 3n + 2 D 9n2 + 3n + 1
C 9n2 + 3n + 2
D 9n2 + 3n + 1
Step-by-step explanation:
4n + 3n2 + 2 + n + 6n – 1 Expand with – 1
3n2 + 4n + n + 6n + 2 – 1 Grouped liked terms
3n2 + 11n – 1
The pie chart shows the favorite type of book of the more than 50,000 high school students. About what percent of favorite type of book is drama? About what percent is mystery?
Complete the statements based on the information.
About
% of high school students chose dramas as their favorite type of book.
About
% of high school student chose mysteries as their favorite type of book.
Ans:
50%
25%
Thus, 50% of high school students chose dramas as their favorite type of book and 25% of high school students chose mysteries as their favorite type of book.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
The pie chart shows the favorite type of book of more than 50,000 high school students.
As we know,
A circular statistical visual with slices illustrating a normal probability plot is named a pie chart. Each slice's arc length in a pie chart matches to the quantity it displays.
Thus, 50% of high school students chose dramas as their favorite type of book and 25% of high school students chose mysteries as their favorite type of book.
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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 rectangle is 19 inches long and 6 inches wide find it’s area
Step-by-step explanation:
how to find the area
multiply the length times the width
19 × 6 = 114 inches squared
The area of the rectangle is 114 square inches if the length and breadth of the rectangle are 19 inches and 6 inches.
A rectangle is one of the elementary geometric figures. It is a quadrilateral with a pair of equal and parallel sides. All angles of a rectangle are right angles.
The length of the rectangle is given as 19 inches.
The breadth of the rectangle is given as 6 inches.
The area of the given rectangle is given as:
Area = length × breadth
Area = 19 × 6
Area = 114 square inches
Thus, the area of the given rectangle is 114 square inches.
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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))
6. Find the missing side. Round to the nearest tenth
Answer:
x = 7.6
Step-by-step explanation:
We know the opposite side and the adj side and this is a right triangle
tan theta = opp / adj
tan 66 = 17/x
x tan 66 = 17
x = 17 /tan 66
x=7.56888
To the nearest tenth
x = 7.6
tanØ=Perpendicular/Base
tan66=17/xx=17/tan66x=7.57x=7.6Find the value of x on this triangle
Answer:
x = 35
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
x^2 + 12^2 = (x+2)^2
FOIL
x^2+144=x^2+4x+4
Subtract x^2 from each side
144= 4x+4
Subtract 4 from each side
140 = 4x
Divide by 4
35 =x
x^ 3 +x^ 2 +4x/x^ 2 +x-2
into partial
fractions
Answer:
x + (4/ x-2) + (2/ x-1)
Step-by-step explanation:
x + (6x/ x^2 + 2x - x -2)
x + (6x/ (x + 2) X (x - 1))
(6x/ (x + 2) X (x - 1))
(A/ x+2) + (B/ x-1)
(6x/ (x + 2) X (x - 1)) = (A/ x+2) + (B/ x-1)
6x = Ax + Bx - A + 2B
6x = (A+B)x + (-A+2b)
{0 = -A+2B
{6 = A+B
(A,B) = (4, 2)
(4/ x+2) + (2/ x-1)
x + (4/ x-2) + (2/ x-1)
If a ∥ b and b ⊥ y, then _____
Answer:
a ⊥ y
Step-by-step explanation:
since b is parallel to a & perpendicular to y , line y will eventually cut across line a at a 90 degree angle as well
Answer:
a ⊥ y
Step-by-step explanation:
Look at the image given below.
Hi !I need help with this question
I have doubt it be 270 degrees.
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
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
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.
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]
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
A warehouse contains ten printing machines, two of which are defective. A company selects seven of the machines at random, thinking all are in working condition. What is the probability that all seven machines are nondefective?
Answer:
0.0667 = 6.67% probability that all seven machines are nondefective.
Step-by-step explanation:
The machines are chosen from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
10 machines means that [tex]n = 10[/tex]
2 defective, so 10 - 2 = 8 work correctly, which means that [tex]k = 8[/tex]
Seven are selected, which means that [tex]n = 7[/tex]
What is the probability that all seven machines are nondefective?
This is P(X = 7). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 7) = h(7,10,7,8) = \frac{C_{8,7}*C_{2,0}}{C_{10,7}} = 0.0667[/tex]
0.0667 = 6.67% probability that all seven machines are nondefective.
