Answer:
P=1
Step-by-step explanation:
P(even or less than 6) = P(even)+P(less than 6) -P(even ∩ less than 6)
P(even)=3/6 (numbers 2,4, and 6)
P(less than 6) =5/6 (numbers 1,2,3,4, and 5)
P(even ∩ less than 6)=2/6 (numbers 2 and 4)
(3/6)+(5/6) -(2/6) = (3+5-2)/6 = 6/6=1
There are twelve shirts in my closet. Five are red, four are blue, and three are green. What is
the probability that I choose a red or blue shirt to wear tomorrow?
O 65%
0 75%
0 80%
60%
58%
Answer:
the probability that I chose red or blue is 75%
75%
List the angles in order from the smallest to the largest.
Answer:
D. <S, <R, <T
Step-by-step explanation:
Recall: On a triangle, the bigger an angle measure the longer the side opposite it and vice versa.
In ∆RST,
The longest side, SR = 22, is opposite to <T
Therefore, <T is the biggest angle.
Medium side, ST = 21, is opposite to <R, therefore,
<R is the medium angle measure
The smallest angle measure <S is opposite to the shortest side, RT.
Angels I'm order form the smallest to largest will be:
<S, <R, <T
We know that the remainder Rn will satisfy |Rn| ⤠bn + 1 = 1 (n + 1)9n + 1. We must make n large enough so that this is less than 0.0001. Rounding to five decimal places, we have b2 = _________ , b3 =_________and b4 =__________
This question is incomplete, the complete question is;
We know that the remainder R[tex]_n[/tex] will satisfy | R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex].
We must make n large enough so that this is less than 0.0001.
Rounding to five decimal places,
we have b₂ = _________ , b₃ =_________and b₄ =__________
Answer:
b₂ = 0.00617, b = 0.00046 and b₄ = 0.00004
Step-by-step explanation:
Given the data in the question;
| R[tex]_n[/tex] | ≤ b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]
Now,
b[tex]_{ n + 1[/tex] = 1 / ( n + 1 )9[tex]^{ n + 1[/tex]
b₂ = b[tex]_{ 1 + 1[/tex] = 1 / ( 1 + 1 )9[tex]^{ 1 + 1[/tex] = 1 / (2)9² = 1 / 162 = 0.00617 { 5 decimal places }
b₃ = b[tex]_{ 2 + 1[/tex] = 1 / ( 2 + 1 )9[tex]^{ 2 + 1[/tex] = 1 / (3)9³ = 1 / 2187 = 0.00046 { 5 decimal places }
b₄ = b[tex]_{ 3 + 1[/tex] = 1 / ( 3 + 1 )9[tex]^{ 3 + 1[/tex] = 1 / (4)9⁴ = 1 / 19683 = 0.00004 { 5 decimal places }
Therefore, b₂ = 0.00062, b = 0.00046 and b₄ = 0.00004
Using the following distribution, calculate the following measures of central tendency:
State Proportion of Residents Without Health Insurance Louisiana 0.19 New Jersey 0.13 New York 0.16 Pennsylvania 0.11 Rhode Island 0.09 South Carolina 0.13 Texas 0.25 Washington 0.14 Wisconsin 0.10
N = 9
Identify the variable:
Identify the median:
Identify the mean:
How would you describe the shape of the distribution:
Answer:
(a) Residents
(b) [tex]Median = 0.13[/tex]
(c) [tex]\bar x = 0.14[/tex]
(d) Right skewed
Step-by-step explanation:
Given
The data of residents without health insurance
Solving (a): The variable
The variable is the residents
Solving (b): The median
First, we sort the data
[tex]Sorted: 0.09, 0.10, 0.11, 0.13, 0.13, 0.14, 0.16, 0.19, 0.25[/tex]
So, the median position is:
[tex]Median = \frac{n + 1}{2}[/tex]
[tex]Median = \frac{9 + 1}{2}[/tex]
[tex]Median = \frac{10}{2}[/tex]
[tex]Median = 5th[/tex]
The 5th element of the dataset is: 0.13
So:
[tex]Median = 0.13[/tex]
Solving (c): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
[tex]\bar x = \frac{0.09+ 0.10+ 0.11+ 0.13+ 0.13+ 0.14+ 0.16+ 0.19+ 0.25}{9}[/tex]
[tex]\bar x = \frac{1.3}{9}[/tex]
[tex]\bar x = 0.14[/tex]
Solving (d): The shape of the distribution
In (b) and (c), we have:
[tex]Median = 0.13[/tex]
[tex]\bar x = 0.14[/tex]
By comparison, the mean is greater than the median.
Hence, the shape is: right skewed.
every student from different schools planted as many plants of their number if they planted 4225 plants how many students were there
Answer:
65 students.
Step-by-step explanation:
Given that :
Every student planted as many plant as their number ;
Then let the number of student = x
Then the number of plant planted by each student will also = x
The total number of plants planted by all the students = 4225
The Number of students can be obtained thus ;
Total number of plants = Number of plants * number of plants per student
4225 = x * x
4225 = x²
√4225 = x
65 = x
Hence, there are 65 students
Find the value for the side marked below.
Round your answer to the nearest tenth.
у
100
49°
y = [?]
Answer:
y = 75.5
Step-by-step explanation:
Reference angle (θ) = 49°
Hypotenuse = 100
Opposite = y
Apply trigonometric function, SOH. Which is:
Sin θ = Opp/Hyp
Plug in the values
Sin 49 = y/100
100*Sin 49 = y
y = 75.5 (nearest tenth)
Part 1: Joe and Hope were both asked to factor the following polynomial completely. Is one of them correct? Both of them? Neither of them? Explain what each of them did was correct and/or incorrect.
Part 2:
Find all the values of k so the the quadratic expression factors into two binomials. Explain the process used to find the values.
3x^2 + kx - 8
If we simplify, both Joe and Hope factored the polynomial correctly but Joe didn't complete it fully.
The first binomial can be further factored:
8x + 12 = 4(2x + 3)Part 2The quadratic expression needs to have two roots in order to be factored as two binomials.
The discriminant must be positive or zero:
D = b² - 4ac ≥ 0We have a = 3, b = k, c = -8
So we get following inequality:
k² - 4*3*(-8) ≥ 0k² + 96 ≥ 0Since k² is positive for any value of k, the solution is any value of k:
k ∈ RHope this attachment helps you.
If f(x) = 4^x-8 and g(x) = 5x+6, find (f + g)(x)
A. (F+g)(x) = -4^x - 5x + 2
B.(F+g)(x) = 4^x + 5x - 2
C.(F+g)(x) = 4^x - 3x + 6
D.(F+g)(x) = 9x - 2
Hey there!
We are given two functions - one is Exponential while the another one is Linear.
[tex] \large{ \begin{cases} f(x) = {4}^{x} - 8 \\ g(x) = 5x + 6 \end{cases}}[/tex]
1. Operation of Function
(f+g)(x) is a factored form of f(x)+g(x). We can common factor out x. Therefore:[tex] \large{(f + g)(x) = f(x) + g(x)}[/tex]
2. Substitution
Next, we substitute f(x) = 4^x+8 and g(x) = 5x+6.[tex] \large{(f + g)(x) = ( {4}^{x} - 8) + (5x + 6)}[/tex]
3. Evaluate/Simplify
Cancel out the brackets and combine like terms.[tex] \large{(f + g)(x) = {4}^{x} - 8 + 5x + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 8 + 6} \\ \large{(f + g)(x) = {4}^{x} + 5x - 2}[/tex]
4. Final Answer
(f+g)(x) = 4^x+5x-2SOMEONE HELP PLEASE! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
a mountain railway AB is of length 864m and rises at an angle of 120° to the horizontal.A train is 856m above sea level when it is at A calculate the height above sea level of the train when it reaches B
9514 1404 393
Answer:
1604 m
Step-by-step explanation:
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
Here, the "opposite" is the elevation of point B above point A, and the "hypotenuse" is the length of the railway. Then the total height of point B is ...
B = 856 + 864·sin(120°)
B = 856 +864(√3)/2 = 856 +432√3 ≈ 1604.246
The height of the train at point B is about 1604 m above sea level.
Find the equation of the line tangent to y = sin(x) going through х = pi/4
Answer:
[tex]\displaystyle y - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2} \bigg( x - \frac{\pi}{4} \bigg)[/tex]
General Formulas and Concepts:
Algebra I
Coordinates (x, y)
Functions
Function Notation
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate y₁ - y coordinate m - slopePre-Calculus
Unit CircleCalculus
Derivatives
The definition of a derivative is the slope of the tangent lineDerivative Notation
Trig Derivative: [tex]\displaystyle \frac{d}{dx}[sin(u)] = u'cos(u)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = sin(x)[/tex]
[tex]\displaystyle x = \frac{\pi}{4}[/tex]
Step 2: Differentiate
Trig Derivative: [tex]\displaystyle y' = cos(x)[/tex]Step 3: Find Tangent Slope
Substitute in x [Derivative]: [tex]\displaystyle y' \bigg( \frac{\pi}{4} \bigg) = cos \bigg( \frac{\pi}{4} \bigg)[/tex]Evaluate [Unit Circle]: [tex]\displaystyle y' \bigg( \frac{\pi}{4} \bigg) = \frac{\sqrt{2}}{2}[/tex]Step 4: Find Tangent Equation
Substitute in x [Function y]: [tex]\displaystyle y \bigg( \frac{\pi}{4} \bigg) = sin \bigg( \frac{\pi}{4} \bigg)[/tex]Evaluate [Unit Circle]: [tex]\displaystyle y \bigg( \frac{\pi}{4} \bigg) = \frac{\sqrt{2}}{2}[/tex]Substitute in variables [Point-Slope Form]: [tex]\displaystyle y - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{2} \bigg( x - \frac{\pi}{4} \bigg)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Problem is in the picture below
Answer:
68.1
Step-by-step explanation:
If those angles are congruent, then all side lengths follow the same ratio.
So the smaller triangle side length of 9 over the small side length of the bigger triangle 21.5, is the ratio for all the sides.
9/21.5 = unknown side / 48
unknown side = 48 * 9/21.5
So to find the length of CD, multiply 48 by our ratio to get ~ 20.1
Add that to our 48 and we get 68.1
PUWID, du then solve.
Timothy's father will build a shed for his tools. It will be a square with a
1 side that measures 8 m. What is the area of the shed?
1. What is asked?
testy
Answer:
The area of the shed=[tex]64m^2[/tex]
Step-by-step explanation:
We are given that
Side of square =8m
We have to find the area of the shed.
To find the area of shed we will find the area of square.
We know that
Area of square=[tex]side\times side[/tex]
Using the formula
Area of square=[tex]8\times 8[/tex]
Area of square=[tex]64m^2[/tex]
Area of shed=Area of square
Area of shed=64 square m
Hence, the area of the shed=[tex]64m^2[/tex]
express the ratio as a fraction in the lowest terms 100cm:5m
Step-by-step explanation:
we know that 1m=100cm
so 1m:5m(final)
1:5
Answer:
1/5
Step-by-step explanation:
Since 100cm = 1m
then
100cm:5m becomes 1m:5m
which in fraction is 1/5
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.4 in/s. At what rate is the volume of the cone changing when the radius is 140 in. and the height is 186 in.
Answer:
The volume is increasing at a rate of 27093 cubic inches per second.
Step-by-step explanation:
Volume of a cone:
THe volume of a cone, with radius r and height h, is given by:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
In this question:
We have to differentiate implictly is function of t, so the three variables, V, r and h, are differenciated. So
[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.4 in/s.
This means that [tex]\frac{dr}{dt} = 1.4, \frac{dh}{dt} = -2.4[/tex]
Radius is 140 in. and the height is 186 in.
This means that [tex]r = 140, h = 186[/tex]
At what rate is the volume of the cone changing?
[tex]\frac{dV}{dt} = \frac{\pi r^2}{3}\frac{dh}{dt} + \frac{2\pi rh}{3}\frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{\pi (140)^2}{3}(-2.4) + \frac{2\pi 140*186}{3}1.4[/tex]
[tex]\frac{dV}{dt} = -0.8\pi(140)^2 + 62*2\pi*1.4*140[/tex]
[tex]\frac{dV}{dt} = 27093[/tex]
Positive, so increasing.
The volume is increasing at a rate of 27093 cubic inches per second.
What was the original price of the car? Show all work
Answer:
I got u, it is litearly 16540/83.8 = $19737.5
Step-by-step explanation:
its very simple sincen 100-16.2=83.8
Which of the following indicates that Triangle ABC and Triangle DEF are similar?
Answer:
D
Step-by-step explanation:
The symbol ~ means similarity (same shapes, not same size)
List all factors of the number 52. SHOW ALL WORK!!!
Answer:
Factors of number 52
Factors of 52: 1, 2, 4, 13, 26 and 52.
Negative Factors of 52: -1, -2, -4, -13, -26 and -52.
Prime Factors of 52: 2, 13.
Prime Factorization of 52: 2 × 2 × 13 = 22 × 13.
Sum of Factors of 52: 98.
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated samplingg distribution.
The amounts of time employees of a telecommunications company have worked for the company are normally distributed with a mean of 5.5 years and a standard deviation of 2.1 years. Random samples of size 17 are drawn from the population and the mean of each sample is determined.
a. 1.33 years, 2.1 years
b. 5.5 years, 0.12 years
c. 5.5 years, 0.51 years
d. 1.33 years, 0.51 years
Answer:
c. 5.5 years, 0.51 years
Step-by-step explanation:
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]
Mean of 5.5 years and a standard deviation of 2.1 years.
This means that, for the population, [tex]\mu = 5.5, \sigma = 2.1[/tex]
Random samples of size 17.
This means that [tex]n = 17[/tex]
Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.
The mean is the same as the mean for the population, that is, 5.5 years.
The standard deviation is:
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{17}} = 0.51[/tex]
This means that the correct answer is given by option c.
Question 3
Solve In(x + 1) = 1.
A) X= 2
B) x = e + 1
C)x= e
D)x= e-1
Answer:
D) x = e - 1
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural Logarithms ln and Euler's number eSolving logarithmic equationsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle ln(x + 1) = 1[/tex]
Step 2: Solve for x
[Equality Property] e both sides: [tex]\displaystyle e^{ln(x + 1)} = e^1[/tex]Simplify: [tex]\displaystyle x + 1 = e^1[/tex][Equality Property] Isolate x: [tex]\displaystyle x = e - 1[/tex]Hi, Friends,
please help me solve this problem.
Q. terms of a geometric sequence are found by the formula Tn = ar n-1 If a = 3 and r = 2 , find the 4 terms of the sequence.
9514 1404 393
Answer:
3, 6, 12, 24
Step-by-step explanation:
It helps if the formula is properly written.
Tn = a·r^(n-1)
Fill in the given values for a, r, and use n = 1 to 4.
T1 = 3·2^(1-1) = 3
T2 = 3·2^(2-1) = 6
T3 = 3·2^(3 -1) = 12
T4 = 3·2^(4 -1) = 24
__
Additional comment
The value a=3 tells you the first term is 3. The value r=2 tells you each term is 2 times the previous one. Knowing this, you can write down the sequence based on your knowledge of multiplication tables (×2). You can use the formula as we did above, but it isn't necessary.
3, 6, 12, 24, ...
Will give brainliest answer
Answer:
not equivalent
equivalent
not equivalent
Step-by-step explanation:
25 is by itself already 5²
therefore
[tex] {25}^{m} = {5}^{2m} [/tex]
when we divide one time by 5, we simply take away 1 from the power making it
[tex] {5}^{2m - 1} [/tex]
the other options are wrong
[tex] {25}^{m - 1} [/tex]
would be right, if we have
[tex] {25}^{m} \div 25[/tex]
but we don't.
and
[tex] {25}^{2m - 1} [/tex]
would even square
[tex] {25}^{m} [/tex]
and then divide by 25. no, the original excision is nothing like that.
What is the domain of this function y= 1/ square root 2-x
Answer:
Domain:
( − ∞ , 2 ] , { x | x ≤ 2 }
Range:
[ 0 , ∞ ) , { y | y ≥ 0 }
SCC U of 1 pt 3 of 1 1.2.11 Assigned Media A rectangle has a width of 49 centimeters and a perimeter of 216 centimeters. V The length is cm.
Answer:
The length is of 59 cm.
Step-by-step explanation:
Perimeter of a rectangle:
The perimeter of a rectangle with width w and length l is given by:
[tex]P = 2(w + l)[/tex]
Width of 49 centimeters and a perimeter of 216 centimeters:
This means that [tex]w = 49, P = 216[/tex]
The length is cm.
We have to solve the equation for l. So
[tex]P = 2(w + l)[/tex]
[tex]216 = 2(49 + l)[/tex]
[tex]216 = 98 + 2l[/tex]
[tex]2l = 118[/tex]
[tex]l = \frac{118}{2}[/tex]
[tex]l = 59[/tex]
The length is of 59 cm.
20. In the image, ABC has measure 58°. What is the measure of ABD?
A. 116°
OB. 29°
O C. 58
OD. There is not enough information to determine LABD.
Answer:
Option B, 29°
Step-by-step explanation:
The diagram is a angle bisecting diagram which divides the 58° angle into two 29° angles.
Answered by GAUTHMATH
Translate the sentence into an inequality.
The sum of 5 and c is greater than – 22.
what da hell the answer ?
Answer:
5 + c > -22
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
InequalitiesStep-by-step explanation:
Step 1: Define
Sum of 5 and c is greater than -22
↓ Identify
Sum = addition
5 + cIs greater than = inequality
>Add them all together:
5 + c > -22
Which point represents the unit rate?
A
B
C
D
Answer:
Point C represents the unit rate
Step-by-step explanation:
ok i think you guys can do it
[tex] {64}^{ \frac{2}{3} } \div {27}^{ \frac{5}{3} } \times 54 \\ = > \: {({2}^{3} )}^{ \frac{2}{3} } \div ({{3}^{3}})^{ \frac{5}{3} } \times 54 \\ = > \: {2}^{2} \div {3}^{5} \times 54 \\ = > \: 4 \div 243 \times 54 \\ = > \: 4 \div 13122 \\ = > \: \frac{4}{13122} \\ = > \: \frac{2}{6561} [/tex]
Hope it helps!!!!!!!!!!
a garden has more roses than daisies, and it has 9 daisies.furthermore, each flower in the garden has more then 3 petals.Let r represent the number of roses and let P represent the total number of petals in the garden. let’s compare the expressions P and 3(r+9). which statement is correct
Answer:
There is not enough info to tell
Step-by-step explanation:
Khan acadamey
Write a compound inequality to represent all of the numbers between -4 and 6.
Answer:
-4 < x < 6
Step-by-step explanation:
