Answer:
The length of the hypotenuse is 8 units
Step-by-step explanation:
Recall the notation SOH CAH TOA. This means that in aright angled triangle,
Sin A = a/c where a is the length of the opposite side and c is the length of the hypotenuse.
Given that sinA=1/2 and a = 4, the hypotenuse c
sin A = 4/c
1/2 = 4/c
cross multiply
c * 1 = 4 * 2
c = 8 units
When 10 gallons of gasoline are put into a car's tank, the indicator goes from 1/8 of a tank to 3/4. What is the total capacity of the gasoline tank?
Answer: 16 gallons
Step-by-step explanation:
Since the the indicator goes from 1/8 of a tank to 3/4, we need to know the difference and this will be:
= 3/4 - 1/8
= 6/8 - 1/8
= 5/8
Therefore, 10 gallons represents 5/8 of the total capacity. Therefore, the total capacity will then be:
5/8 of x = 10
5x/8 = 10
5x = 10 × 8
5x = 80
x = 80/5
x = 16
Therefore, the total capacity is 16 gallons
38% of students taking exam P will pass the exam. 5% of students are taking exam P having used ADAPT. 79% of the students using ADAPT pass the exam. What is the probability of passing the exam if a student does not use ADAPT
Answer:
the probability of passing the exam if a student does not use ADAPT is 0.3584
Step-by-step explanation:
Given the data in the question;
Probability a student will pass = 38% = 0.38
Probability a student have used ADAPT = 5% = 0.05
P(passed | used ADAPT) = 79% = 0.79
Now lets use table
Used ADAPT Not use ADAPT Total
Passed [0.05×0.79] = 0.0395 [0.38 - 0.0395] = 0.3405 0.38
Not Passed [0.05-0.0395] = 0.0105 [0.62 - 0.0105] = 0.6095 0.62
Total 0.05 0.95
Now, the probability of passing the exam if a student does not use ADAPT will be;
⇒ P(passed and Not used ADAPT) / P( did not use ADAPT)
⇒ 0.3405 / 0.95
⇒ 0.3584
Therefore, the probability of passing the exam if a student does not use ADAPT is 0.3584
Which of the following graphs shows a pair of lines that represents the equations with the solution (3, −6)? (1 point)
Given:
The solution of two equation is (3,-6).
To find:
The graphs that shows a pair of lines that represents the equations with the solution (3, −6).
Solution:
In first graph, both line intersect each other at point (-6,3). So, the solution of the pair of lines is (-6,3).
In second graph, both line intersect each other at point (-3,6). So, the solution of the pair of lines is (-3,6).
In third graph, both line intersect each other at point (3,-6). So, the solution of the pair of lines is (3,-6).
In forth graph, both line intersect each other at point (6,-3). So, the solution of the pair of lines is (6,-3).
Therefore, the correct option is C.
Someone help me solve please
Answer:
48.37 degrees
Step-by-step explanation:
c = AB = sqrt((9-7)² + (2-7)²) = sqrt(4+25) = sqrt(29)
b = AC = sqrt((5-7)² + (3-7)²) = sqrt(4+16) = sqrt(20)
a = BC = sqrt((5-9)² + (3-2)²) = sqrt(16+1) = sqrt(17)
A = angle at A
B = angle at B
C = angle at C
cos(A) = (b²+c²-a²)/(2bc) = (20+29-17)/2sqrt(20)sqrt(29) =
= 32/48.16637832... = 0.664363839...
A = acos(0.664363839...) = 48.366461... degrees
What is blank -3/4 = 2/3
Answer:
Blank = 17/12
Step-by-step explanation:
Blank = 2/3 + 3/4
Blank = 8/12 + 9/12
Blank = 17/12
Please find the general limit of the following function:
[tex]\lim_{x \to 9}(x^2 + 2^7 + (9.1 \times 10))[/tex]
Answer:
The general limit exists at x = 9 and is equal to 300.
Step-by-step explanation:
We want to find the general limit of the function:
[tex]\displaystyle \lim_{x \to 9}(x^2+2^7+(9.1\times 10))[/tex]
By definition, a general limit exists at a point if the two one-sided limits exist and are equivalent to each other.
So, let's find each one-sided limit: the left-hand side and the right-hand side.
The left-hand limit is given by:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))[/tex]Since the given function is a polynomial, we can use direct substitution. This yields:
[tex]=(9)^2+2^7+(9.1\times 10)[/tex]
Evaluate:
[tex]300[/tex]
Therefore:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1 \times 10))=300[/tex]
The right-hand limit is given by:
[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))[/tex]
Again, since the function is a polynomial, we can use direct substitution. This yields:
[tex]=(9)^2+2^7+(9.1\times 10)[/tex]
Evaluate:
[tex]=300[/tex]
Therefore:
[tex]\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]
Thus, we can see that:
[tex]\displaystyle \lim_{x \to 9^-}(x^2+2^7+(9.1\times 10))=\displaystyle \lim_{x \to 9^+}(x^2+2^7+(9.1\times 10))=300[/tex]
Since the two-sided limits exist and are equivalent, the general limit of the function does exist at x = 9 and is equal to 300.
Step-by-step explanation:
Hey there!
Please look your required answer in picture.
Note: In left hand limit always take a smaller near number of the approaching number. For example as in the solution I took the 8.99,8.999 as it is smaller than 9 but very near to it.
And in right hand limit always take a smaller and just greater near number than the approaching number. For example, I took 9.01,9.001 which a just greater but very near to 9.
Hope it helps!
Which values for A and B will create many solutions for this system of equations? 4x-Ay=15 -4x+6y=B
Answer:
A = 6; B = -15
Step-by-step explanation:
To have an infinite number of solutions, both equations must be the same.
4x - Ay = 15
-4x + 6y = B
The only coefficient we see in both equations is the coefficient of the x term. We have -4x and 4x. Multiply both sides of the second equation by -1.
4x - Ay = 15
4x - 6y = -B
For the equation to be equal, we need each term of one equation to be equal to the corresponding term of the other equation.
4x and 4x are equal.
-Ay must equal -6y
-Ay = -6y
-A = -6
A = 6
15 must equal -B
-B = 15
B = -15
Answer: A = 6; B = -15
Yo-yo yo answer for brainlest
Using the predicate symbols shown and appropriate quantifiers, write eachEnglish language statement as a predicate wff. (The domain is the whole world).
S(x): x is aspy novel
L(x): x is long
M(x): x is a mystery
B(x, y): x is better than y
a. All spy novels are long
b. Not every mystery is a spy novel
c. Only mysteries are long.
d. Spy novels are better than mysteries.
e. Only spy novels are better than my
Answer:
a. All spy novels are long. S (L)
b. Not every mystery is a spy novel S (x,M)
c. Only mysteries are long M ( L)
d. Spy novels are better than mysteries S B(x, y)
e. Only spy novels are better than mystery S B(x)
Step-by-step explanation:
Spy novels and mystery novels both are long. There is a domain function representing mystery novels is better than spy novels. The spy novel can be long and and better than mystery novels. The symbol representation for spy novel and mystery novel is given in the domain function.
Could anyone help me please?
9514 1404 393
Answer:
4
Step-by-step explanation:
In order to evaluate f(g(-1)), you first need to find g(-1).
The graph of g(x) crosses the line x = -1 at y = 1, so g(-1) = 1.
The second step is evaluating f(1). The graph of f(x) crosses the line x=1 at y=4, so f(1) = 4.
f(g(-1)) = f(1) = 4
A flower store has an inventory of 25 roses, 15 lilies, 30 tulips, 20 gladiola, and 10 daisies. A customer picks one of the flowers at random.
What is the probability that the flower is not a rose?
Answer: 75/100
Step-by-step explanation:
the total number of flowers= 25+15+30+20+10
= 100
so probability that the flower is not a rose is= 75/100
Note: i got 75 by subtracting 100 by 25
HELP HURRY PLS I really really need help
Answer:
a big number
Step-by-step explanation:
I have been stuck on this forever plz help
What is the surface area of this cylinder
Answer:
1865.16 m^2
Step-by-step explanation:
first let 's find radius of a circle
radius=diameter/2
=18/2
=9 m
area of a cylinder=2πrh+2πr2
=2*3.14*9*24 + 2*3.14*(9)^2
=1356.48 + 2*3.14*81
=1356.48 + 508.68
=1865.16 m^2
Answer:
1866.11 m²
Step-by-step explanation:
Formula = 2πrh + 2πr²
Surface area = 2 * 3.14 * 9 * 24 + 2*3.14* 81 ≈ 1866.11
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Need help with this Equation
Answer:
15/17
Step-by-step explanation:
sine is opposite/hypotenuse
Pls help I’ll brainlest ASAP
Answer:
D
Step-by-step explanation:
because in standard form the first number is only up to 10 and above 10 it is decimal places e.g.6.12×10^5
hope this helps u understand :)
Hello. I need help with creating a normal distribution for a pre-made dataset in excel? I mainly confused with the steps to complete the process.
Let's say your data is all in column A. Furthermore, we'll say we have 21 items in this column. Make sure this data column is sorted from smallest to largest. If this isn't done, then weird things will happen when it comes to connecting the dots later on.
Column B will be used later, but for now, let's move to cell C1. In this cell, type =AVERAGE(A1:A21)
The equal sign is important to tell Excel that we have a function here, and not just plain text. As the function implies, we're finding the average (aka mean) of values A1,A2,...,A20,A21. This computes the arithmetic mean.
In cell D1, type in =STDEV(A1:A21) to compute the sample standard deviation
There's nothing special about C1 or D1. We just need something off to the side. Think of it like scratch work.
-------------------------
Now move back to column B. In cell B1, type =NORMDIST(A1,$C$1,$D$1,FALSE)
The $C$1 and $D$1 refer to cells C1 and D1 respectively. The dollar signs lock in those rows and columns so they don't change. We don't want the mean and standard deviation to alter. The "False" at the end tells Excel that we don't want a cumulative normal distribution.
The first parameter A1 is the x value. Much like the curve y = x^2, we plug in various x values to find corresponding y values. We'll plot various (x,y) points to connect them with a curve. The more points, the more accurate the curve. Instead of the x^2 function, we're using the NORMDIST function.
Once cell B1 is filled out, click on the bottom right corner of the cell. You should see a very small square at this corner. Dragging this square down until you reach cell B21 will fill in the remaining 20 cells with the formula mentioned in bold; however, the A1 will change depending on what row you're on. Everything else stays the same hence the use of the dollar signs.
-------------------------
In figure 1 below, I'm showing an example of what I've discussed so far. Figure 1 shows the formulas in each cell. This is before they are evaluated.
Figure 2 shows what the formulas evaluate to. The data in column A can be anything you want. I randomly generated the data values between 2 and 17.
Once column B is figured out, you would insert a chart of (x,y) scatter points. Make sure to connect the dots so that a curve forms. This will complete the normal distribution graph. Again, the data in column A must be sorted or else the dots won't be connected properly.
To be perfectly honest, Excel doesn't really do a good job at drawing curves like this. In my opinion, programs like GeoGebra are better suited for the task. Though spreadsheet programs like Excel are still used in a lot of settings, which is why this is good practice.
The rectangular ground floor of a building has a perimeter of 780 ft. The length is 200 ft more than the width. Find the length and the width.
The length is ___ and the width is ___
Answer:
perimeter of the rectangular ground floor
=2(length+width)
length=X+200
width=X
=2(X+200+X)
=4x+400
4x+400 =780
4x =780-400
4x =380
x =95
width=95 feet
length=95+200
=295 feet
Add and subtract the values. Express your answer in scientific notation. (5.4 times 10 Superscript 5 Baseline) + (2.9 times 10 Superscript 5 Baseline) minus (1.1 times 10 Superscript 4) 7.2 times 10 Superscript 5 8.19 times 10 Superscript 5 8.41 times 10 Superscript 5 9.4 times 10 Superscript 5
The correct answer is option B which is 8.19 x 10⁵.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
The given expression will be written as :-
E = ( 5.4 x 10⁵ ) +( 2.9 x 10⁵ ) - ( 1.1 x 10⁴ )
E = ( 5.4 x 10⁵ ) +( 2.9 x 10⁵ ) - ( 0.11 x 10⁵ )
E = ( 5.4 + 2. 89 -0.11 ) x 10⁵
E = 8.19 x 10⁵
Therefore the correct answer is option B which is 8.19 x 10⁵.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
In circle S, angle QTR is an inscribed angle.
What is the measure of angle QRS?
angle QRS = 51°
Step-by-step explanation:
The diagram for the question has been attached to this response.
From the diagram, some circle theorems can be applied.
Circle theorem:
The angle subtended by an arc of a circle at the centre is twice the angle subtended by it at any other point on the remaining part of the circle.
From the diagram, QR is the arc and therefore:
∠QSR = 2 x ∠ QTR
Since ∠QTR = 39°
=> ∠QSR = 2 x 39°
=> ∠QSR = 78°
Other theorem:
(i)The base angles of an isosceles triangle are equal.
Triangle QSR is an isosceles triangle, therefore, angles SQR and QRS are equal. i.e
∠SQR = ∠QRS
(ii) The sum of angles of a triangle is 180°. i.e
∠SQR + ∠QRS + ∠QSR = 180°
Since ∠SQR = ∠QRS and ∠QSR = 78°
=> ∠QRS + ∠QRS + 78° = 180°
=> 2(∠QRS) = 180° - 78°
=> 2(∠QRS) = 102°
Divide both sides by 2
=> ∠QRS = 51°
Therefore, angle QRS = 51°
Find m < RMQ if mQR = 54
9514 1404 393
Answer:
27°
Step-by-step explanation:
The inscribed angle is half the measure of the arc it intercepts.
∠M = 1/2 arc QR = 1/2(54°)
∠M = 27°
Melinda is selling her paintings. The graph depicits the profit she makes given the selling price of the paintings. What is the approximate average rate of change in profit per dollar selling price, when the selling price yields $0 profit to a selling price that yield the maximum profit
Answer:
The average rate of change is 28.57
Step-by-step explanation:
Given
See attachment for graph
Required
The average rate of change from 0 to maximum profit
At 0, we have:
[tex](x_1,y_1) = (32,0)[/tex]
At maximum, we have:
[tex](x_2,y_2) = (60,800)\\\\[/tex]
The average rate of change (m) is calculatd as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{800 - 0}{60 - 32}[/tex]
[tex]m = \frac{800}{28}[/tex]
[tex]m = 28.57[/tex] --- approximated
A random sample of vehicle mileage expectancies has a sample mean of x¯=169,200 miles and sample standard deviation of s=19,400 miles. Use the Empirical Rule to estimate the percentage of vehicle mileage expectancies that are more than 188,600 miles.
____%
Answer: 16%
Step-by-step explanation:
HALP!!! FIND ALL THREE ANGLES WILL MARK BRAINLIEST FOR LEGITIMATE ANGLES
Answer:
Step-by-step explanation:
2x+3+2x-12+4x-11=180 degree (sum of interior angles of a triangle)
8x-20=180
8x=180+20
x=200/8
x=25
Now , substitute the value of x.
Chicago=2x+3
=2*25+3
=50+3
=53 degree
Austin=2x-12
=2*25-12
=50-12
=38 degree
Atlanta=4x-11
=4*25-11
=100-11
=89 degree
what are point slope equations that pass through points (5,6) and (1,1)
Plz help i need a correct answer asap
Given that ſ-, f(x) dx = 4, S f(x) dx = -3, and $129(x) dx = 8, find the following.
S; f(x) dx
b. (f(x) dx
c. Lt, [F(x) +2g(x)] dx
| 0111869 +296) de
Multiple Choice: Choose the correct simplified expression for (3x - y) (W+p-3).
Answer:
answer this 5-y this the answer thanks for
Answer:
3xw+3xp+3y-9x-yw-yp
(I have no idea how it's ordered on your test)
Step-by-step explanation:
(3x-y)(w+p-3)
Multiply.
3xw+3xp-9x-yw-yp+3y
Reorder.
3xw+3xp+3y-9x-yw-yp
(me looking at this long a** expression like o.O)
---
hope it hope
U.S. women aged 20 or over have a mean HDL cholesterol levels of 55mg/dl with a standard deviation of 15 mg/dl. Assume that the distribution is Normal. What proportion of women have HDL below 45 mg/dl or less?
Answer:
0.2514 = 25.14% of women have HDL below 45 mg/dl or less.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean HDL cholesterol levels of 55mg/dl with a standard deviation of 15 mg/dl.
This means that [tex]\mu = 55, \sigma = 15[/tex]
What proportion of women have HDL below 45 mg/dl or less?
This is the p-value of Z when X = 45. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{45 - 55}{15}[/tex]
[tex]Z = -0.67[/tex]
[tex]Z = -0.67[/tex] has a p-value of 0.2514
0.2514 = 25.14% of women have HDL below 45 mg/dl or less.
6.) Ms. Speer is scuba diving. She descends 5 feet below sea level. She descends the same distance 4 more times. What is Ms. Speer's final elevation? *
Answer:
-25 feet
Step-by-step explanation:
First she descends 5 feet below sea level
She then descends the SAME DISTANCE ( so 5 feet ) 4 MORE TIMES
So feet descended = 4 * 5 + 5
4 * 5 = 20
20 + 5 = 25
Her final elevation will be -25 feet
( it's important that we add a negative sign because she is descending meaning going down )
4x – 26 = 18 pls answer fast
Answer:
X = 11
Step-by-step explanation:
4x - 26 = 18
Add 26 on both sides to get 4x alone.
4x - 26 + 26 = 18 + 26
4x = 44
44 divided by 4 is 11.
Therefore X is 11.
Answer: x=11
Step-by-step explanation:
Add 26 to both sides
4x-26+26=18+26
4x=44
Divide by 4 and get 11
x=11