Answer:
Hey there!
q is 1, and n=-2.
q-n=1-(-2), which is 3.
n-q=-2=1, which is -3.
q is 1.
Thus, the least value is n-q, and the greatest value is q-n. Closest to zero would be q.
Let me know if this helps :)
Answer:
Least: n-q
Greatest: q-n
Closest to zero: q
) A random sample of size 36 is selected from a normally distributed population with a mean of 16 and a standard deviation of 3. What is the probability that the sample mean is somewhere between 15.8 and 16.2
Answer:
The probability is 0.31084
Step-by-step explanation:
We can calculate this probability using the z-score route.
Mathematically;
z = (x-mean)/SD/√n
Where the mean = 16, SD = 3 and n = 36
For 15.8, we have;
z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4
For 16.2, we have
z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4
So the probability we want to calculate is;
P(-0.4<z<0.4)
We can get this using the standard normal distribution table;
So we have;
P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)
= 0.31084
Use the Pythagorean theorem to find the length of the hypotenuse in the triangle shown below.4,3
Answer:
5
Step-by-step explanation:
a^2 + b^2 = c^2
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
c = 5
Answer:
5Step-by-step explanation:
[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]
Solve the equation for x by graphing.-4x-1 5x=4
Answer: Undefined
Step-by-step explanation:
slope is undefined
no y intercept
This line is vertical
If the solutions for a quadratic equation are -2 and 5 what is the equation
Answer:
f(x) = x^2 - 3x -10
Step-by-step explanation:
If the solutions are {-2, 5}, the factors of the quadratic are (x + 2) and (x - 5).
The equation is f(x) = (x + 2)(x - 5) = x^2 - 3x -10
a vegetable garden and he's around the path of seemed like a square that together are 10 ft wide. The path is 2 feet wide. Find the total area of the vegetable garden and path
Answer:
Garden: 36 square feet
Path: 64 square feet
Step-by-step explanation:
Let's first find the total area. The total area will be 100 square feet since the side length is 10. Since the path is 2 feet wide and on all sides, that means that the inside square will have a side length of 6. That means that the vegetable garden is 36 square feet. The path will be 100 - (the garden), and the garden is 36 square feet, which means the outer path will be 64.
3. A jogger runs 4 miles on Monday, 5 miles on
Tuesday, 3 miles on Wednesday, and 5 miles on
Thursday. He doesn't run on Friday. How many
miles did he run in all?
Answer:
17 miles
Step-by-step explanation:
4+5+5+3=17
The height of the plant is given by the equation h = 0.5d + 4. Rewrite this as a function rule where f(x) is the height, in centimeters, and x is the time, in days. Use the rule to complete the table, and then use the drawing tools to create the graph representing this relationship.
Answer:
Here's what I get
Step-by-step explanation:
h = 0.5d + 4
A function rule tells you how to convert an input value (x) into an output value (y).
Your function rule is
ƒ(x) = 0.5x + 4
An easy way to represent your function is to make a graph.
The easiest way to make a graph is to make a table containing some inputs and their corresponding outputs.
Here's a typical table.
[tex]\begin{array}{cc}\textbf{x} &\textbf{y} \\0 & 4 \\2 & 5 \\4 & 6 \\6 & 7\\6 & 8 \\\end{array}[/tex]
The graph is like the one below.
Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.05 significance level to test for a difference between the measurements from the two arms. What can be concluded?
Right_arm(mm_Hg) Left_arm(mm_Hg)
149 166
136 179
129 190
137 148
139 138
Data was entered in SPSS using the paired t-test approach!!
a. In this example, μd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the measurement from the right arm minus the measurement from the left arm. What are the null and alternative hypotheses for the hypothesis test?
b.) Identify the test statistic.
c.) Identify the P-value.
d.) What is the conclusion based on the hypothesis test?
Answer:
There is a significant difference in the systolic blood pressure measurements between the two arms.
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or paired samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
In this case a paired t-test is used to determine whether there is a difference in the systolic blood pressure measurements between the two arms.
The SPSS output is attached below.
(a)
The hypothesis for the test can be defined as follows:
H₀: There is no difference in the systolic blood pressure measurements between the two arms, i.e. d = 0.
Hₐ: There is a significant difference in the systolic blood pressure measurements between the two arms, i.e. d ≠ 0.
(b)
Consider the SPSS output.
The test statistic value is t = 0.871.
(c)
Consider the SPSS output.
The p-value of the test is:
p-value = 0.433.
(d)
The significance level of the test is, α = 0.05.
Decision rule:
If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.
p-value = 0.433 > α = 0.05
The null hypothesis will not be rejected at 5% level of significance.
Conclusion:
Thus, it can be concluded that there is a significant difference in the systolic blood pressure measurements between the two arms.
AB is dilated from the origin to create A'B' at A' (0, 8) and B' (8, 12). What scale factor was AB dilated by?
Answer:
4
Step-by-step explanation:
Original coordinates:
A (0, 2)
B (2, 3)
The scale is what number the original coordinates was multiplied by to reach the new coordinates
1. Divide
(0, 8) ÷ (0, 2) = 4
(8, 12) ÷ (2, 3) = 4
AB was dilated by a scale factor of 4.
Question:
A school's band members raised money by selling magazine subscriptions and shirts. Their profit from selling shirts was per shirt minus a one-time set-up fee. Their profit from selling magazine subscriptions was per subscription. They made exactly the same profit from shirts as they did from magazines. They also sold the same number of shirts as magazine subscriptions. How many shirts did they sell?
Jamie has a jar of coins containing the same number of nickels, dimes and quarters. The total value of the coins in the jar is 13.20. How many nickels does Jamie have?
The gasoline gauge on a van initially read ⅛ full. When 15 gallons of gasoline were added to the tank, the gauge then read ¾ full. How many more gallons would be needed to fill the tank?
Answer:
Question 1: 40 shirts and 40 magizines
Question 2: $4.4
Question 3: 6 gallons
Answer:
hello
Step-by-step explanation:
Gulnaz plans to use less than 26 eggs while baking. She uses 5 eggs for each cake that she bakes, and 3 eggs for each quiche that she bakes.
Write an inequality that represents the number of cakes (C)left parenthesis, C, right parenthesis and quiches (Q)left parenthesis, Q, right parenthesis Gulnaz can bake according to her plan.
Answer:
5(x) +3(y)<26
Step-by-step explanation:
Let x represent the number of cakes she will bake and let you know represent the nymber of quiche she will bake.
She will use less than 26 eggs while baking and 5 eggs for each cake and 3 eggs for each quiche.
The inequality representing the above statement iz given below.
5(x) +3(y)<26
In how many years will
The Compounds interest
onRs. 14,000 be Rs. 4, 634 at 10%
p.a?
Answer:
3 years
Step-by-step explanation:
A = P(1 + r)^t
A = I + P
A = 14,000 + 4,634 = 18,634
18,634 = 14,000(1 + 0.1)^t
18,634/14,000 = 1.1^t
log (18,634/14,000) = log 1.1^t
log (18,634/14,000) = t * log 1.1
t = [log (18,634/14000)]/(log 1.1)
t = 3
the length of a mathematical text book the is approximately 18.34cm and its width is 11.75 calculate ?
the approximate perimeter of the front cover?
the approximate area of the front cover of the book?
Answer:
Perimeter=60.18cm
Area=215.495cm^2
Step-by-step explanation:
Given:
Length of book=18.34cm
Breadth=11.75cm
Solution:
Perimeter=2(l +b)
P=2(18.34+11.75)
P=2 x 30.09
P=60.18cm
Area=l x b
A=18.34 x 11.75
A=215.495 cm^2
Thank you!
The perpendicular bisectors of ΔKLM intersect at point A. If AK = 25 and AM = 3n - 2, then what is the value of n?
Answer:
n = 9 is the answer.
Step-by-step explanation:
Given a Triangle [tex]\triangle KLM[/tex] with its perpendicular bisectors intersecting at a point A.
AK = 25 units and
AM = 3n -2
To find:
Value of n = ?
Solution:
First of all, let us learn about perpendicular bisectors and their intersection points.
Perpendicular bisector of a line PQ is the line which divides the line PQ into two equal halves and is makes an angle of [tex]\bold{90^\circ}[/tex] with the line PQ.
And in a triangle, the perpendicular bisectors of 3 sides meet at one point and that point is called Circumcenter of the triangle.
We can draw a circle from circumcenter so that the circle passes from the three vertices of the triangle.
i.e.
Circumcenter of a triangle is equidistant from all the three vertices of the triangle.
In the given statement, we are given that A is the circumcenter of the [tex]\triangle KLM[/tex].
Please refer to the attached image for the given triangle and sides.
The distance of A from all the three vertices will be same.
i.e. AK = AM
[tex]\Rightarrow 25 = 3n-2\\\Rightarrow 3n =25+2\\\Rightarrow 3n =27\\\Rightarrow \bold{n = 9}[/tex]
Therefore, n = 9 is the answer.
I cant seem to get the second one right...
Rx=1 means to reflect the given point on the line of x= 1
The mapping for the reflection on line x is x = k
(-2,7) = (-2(1) - -2,7) = (4,7)
The missing value is 7
The domain of the following relation has how many elements?
[(1/2, 3.14/6), (1/2, 3.14/4), (1/2, 3.14/3), (1/2,3.14/2)]
a. 0
b. 1
c. 4
Answer:
b. 1
Step-by-step explanation:
All first coordinates are 1/2.
Answer: b. 1
Find the area of the shape shown below.
2
2
4
Hurry and answer plz!!!!
1
Answer:
7 square units
Step-by-step explanation:
We can break down this complex shape into smaller shapes.
I've broken it down into a rectangle, a square, and a triangle (See attached picture)
Let's first find the area of the triangle. To do this we use the formula [tex]\frac{bh}{2}[/tex]. The base is 1 (because the top is 2, and 1 is already used on the triangle - 2-1 = 1.) and the height is 2 (because 4 is already used on the left, and 2 was used on the right so 4-2=2).
[tex]\frac{2\cdot1}{2} = \frac{2}{2} = 1[/tex].
Now let's find the area of the top square - we can just square 2 which is 4.
To find the area of the bottom rectangle, we can multiply it's two side lengths of 2 and 1 = 2.
Adding these all together gets us 4+2+1 = 7.
Hope this helped!
3 ratios that are equivalent to 6:12
Answer:
1:3
2:4
3:6
Step-by-step explanation:
we can divide both sides by 6 and get 1:2
we can divide both sides by 3 and get 2:4
we can divide both sides by 2 and get 3:6
Answer:
12:24, 3:6, 2:4
Step-by-step explanation:
What we are looking for here is a ratio that, when you divide/multiply the same constant on both parts of the ratio, you get 6:12.
6:12 is the same thing as 1:2, so we can find ratios equivalent to 1:2 (the first value will be half the second).
Hope this helped!
find the h.c.f of 186,310,434
186|2
93|3
31|31
1
310|2
155|5
31|31
1
434|2
217|7
31|31
1
[tex]186=2\cdot3\cdot31\\310=2\cdot5\cdot31\\434=2\cdot7\cdot31\\\\\text{hcf}(186,310,434)=2\cdot31=62[/tex]
Find the remainder in the Taylor series centered at the point a for the following function. Then show that limn→[infinity]Rn(x)=0 for all x in the interval of convergence.
f(x)=cos x, a= π/2
Answer:
[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
Step-by-step explanation:
From the given question; the objective is to show that :
[tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x in the interval of convergence f(x)=cos x, a= π/2
Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]
where;
[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-a)^{n+1}}[/tex]
is a remainder at x and c happens to be between x and a.
Given that:
a= π/2
Then; the above equation can be written as:
[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-\dfrac{\pi}{2})^{n+1}}[/tex]
so c now happens to be the points between π/2 and x
If we recall; we know that:
[tex]f^{(n+1)}(c) = \pm \ sin \ c \ or \ cos \ c[/tex] (as a result of the value of n)
However, it is true that for all cases that [tex]|f ^{(n+1)} \ (c) | \leq 1[/tex]
Hence, the remainder terms is :
[tex]|R_n (x)| = | \dfrac{f^{(n+1)}(c)}{(n+1!)}(x-\dfrac{\pi}{2})^{n+1}| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
If [tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x and x is fixed, Then
[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]
please help
-3(-4x+4)=15+3x
Answer:
x=3
Step-by-step explanation:
● -3 (-4x+4) = 15 + 3x
Multiply -3 by (-4x+4) first
● (-3) × (-4x) + (-3)×(4) = 15 + 3x
● 12 x - 12 = 15 +3x
Add 12 to both sides
● 12x - 12 + 12 = 15 + 3x +12
● 12 x = 27 + 3x
Substract 3x from both sides
● 12x -3x = 27 + 3x - 3x
● 9x = 27
Dividr both sides by 9
● 9x/9 = 27/9
● x = 3
Find the 14th term in the sequence 1, 1/3, 1/9, … Find the sum of the first 10 terms of the sequence above.
Answer:
This is a geometric progresion that begins with 1 and each term is 1/3 the preceeding term
Let Pn represent the nth term in the sequence
Then Pn = (1/3)^n-1
From this P14 = (1/3)^13 = 1/1594323
5. The sum of the first n terms of a GP beginning a with ratio r is given by
Sn = a* (r^n+1 - 1)/(r - 1)
With n = 10, a = 1 and r = 1/3, S10 = ((1/3)^11 - 1)/(1/3 - 1) = 1.500
What is the quotient of 35,423 ÷ 15?
Answer: 2361.53
Step-by-step explanation:
Use long division and round.
(The 3 is repeated)
Can somebody explain how trigonometric form polar equations are divided/multiplied?
Answer:
Attachment 1 : Option C
Attachment 2 : Option A
Step-by-step explanation:
( 1 ) Expressing the product of z1 and z2 would be as follows,
[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]
Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,
cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],
sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]
cos(3π / 2) = 0,
sin(3π / 2) = - 1
Let's substitute those values in our expression,
[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]
And now simplify the expression,
[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]
The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.
( 2 ) Here we will apply the following trivial identities,
cos(π / 3) = [tex]\frac{1}{2}[/tex],
sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],
cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],
sin(- π / 6) = [tex]-\frac{1}{2}[/tex]
Substitute into the following expression, representing the quotient of the given values of z1 and z2,
[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒
[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]
The simplified expression will be the following,
[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]
The solution will be option a, as you can see.
Evaluate
1+5.3
2
please answer quickly
Answer:
1+5.3=6.3
Step-by-step explanation:
not sure what your asking for with the 2
explain what your looking for with the 2 and maybe we can help you further
(I have to do it the way I did it because the 2 in the question is confusing)
Answer:
For expression 1 + 5.32: 6.32
For expression 1 + 5.3 × 2: 11.6
Step-by-step explanation:
If the expression is 1 + 5.32:
Add 1 to 5.32: 1 + 5.32 = 6.32If the expression is 1 + 5.3 × 2:
5.3 × 2 = 10.6Plug in 10.6: 1 + 10.61 + 10.6 = 11.6
Tanθ - cosecθ secθ (1-2 cos²θ) = cotθ
Answer:
I thinksomething is wrong.
I'm getting another proving it's-tan thita.
I hope this is the one you are searching for..
Help me please thank y’all
x= 30 degrees
Step-by-step explanation:
there's 180 degrees in a triangle. You can see 60 degrees right there. Theres a 90 degree angle right next to it. 180-150=30
Please help me with this ,
Answer:
(a) -2.3°/min
(b) -2.9°/min
Step-by-step explanation:
The average rate of change is the ratio of the difference in R values to the difference in the corresponding t values.
(a) m = (157.6 -226.6)/(30 -0) = -69/30 = -2.3 . . . degrees per minute
__
(b) m = (61.6 -119.6)/(70 -50) = -58/20 = -2.9 . . . degrees per minute
John painted his most famous work, in his country, in 1930 on composition board with perimeter 101.14 in. If the rectangular painting is 5.43 in. taller than it is wide, find the dimensions of the painting.
Answer:
22.57 x 28
Step-by-step explanation:
10.86 + 4x = 101.14
-10.86 -10.86
4x = 90.28
/4 /4
x = 22.57
5.43 + 22.57 = 28
22.57
4. Solve the system of equations. (6 points) Part I: Explain the steps you would take to solve the system by eliminating the x-terms. (1 point) Part II: Explain the steps you would take to solve the system by eliminating the y-terms. (2 points) Part III: Choose either of the methods described in parts I or II to solve the system of equations. Write your answer as an ordered pair. Show your work. (3 points)
Answer:
The system of equations you want to be solved is not given. I would however give an example with which the method of elimination will be shown, and can be used in solving problems of the nature.
Step-by-step explanation:
Consider the system of equations:
x + y = 7 ................................(1)
2x - y = 8 ..............................(2)
To eliminate x:
First multiply (1) by 2 to have
2x + 2y = 14 ...........................(3)
Next, subtract (2) from (3) to have
3y = 6
y = 6/3 = 2
To eliminate y:
Add (1) and (2) to have
3x = 15
x = 15/3 = 5
Therefore, (x, y) = (5, 2).