Hey there!
4x - 16 + 2x + 16 = 180 (linear pair)
4x + 2x - 16 + 16 = 180
6x = 180
x = 180/6
x = 30.
Hope it helps ya!
PLEASE HELP!
A poll is given, showing 45% are in favor of a new building project.
If 4 people are chosen at random, what is the probability that exactly 3 of them favor the new building project?
The probability that exactly 3 out of 4 people chosen at random favor the new building project is 0.2904.
This problem can be solved using the binomial probability formula. Let X be the number of people who favor the new building project out of the 4 chosen at random. Then X follows a binomial distribution with parameters n = 4 and p = 0.45.
The probability of having exactly k people who favor the new building project out of 4 is given by:
P(X = k) = (4 choose k) * \(0.45^{k}\) * \(0.55^{4-k}\)
where (4 choose k) is the binomial coefficient.
To find the probability that exactly 3 of the 4 people favor the new building project, we substitute k = 3 in the above formula and evaluate:
P(X = 3) = (4 choose 3) * \(0.45^{3}\) * \(0.55^{1}\)
= 0.290384375
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Gravity acceleration at the Earth surface is 9.81 m/s². What is the acceleration in inches/s² (rounded to the nearest tenth) ?
Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².
To convert the acceleration from meters per second squared (m/s²) to inches per second squared (in/s²), we need to use the conversion factor between the two units.
1 meter is equal to 39.37 inches.
To convert the units, we can set up the following conversion factor:
1 m/s² = (39.37 in/m)^2 = 1550.0031 in/s²
Now, we can multiply the given acceleration in m/s² by the conversion factor to obtain the acceleration in in/s²:
Acceleration in in/s² = 9.81 m/s² * 1550.0031 in/s²
Acceleration in in/s² ≈ 15222.7568 in/s²
Rounded to the nearest tenth, the acceleration in inches per second squared is approximately 15222.8 in/s².
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Select the correct answer. Which statement best describes the zeros of the function h(x) = (x – 6)(x2 + 8x + 16)? A. The function has two distinct real zeros. B. The function has three distinct real zeros. C. The function has one real zero and two complex zeros. D. The function has three complex zeros.
We can see here that the statement that best describes the zeros of the function h(x) = (x – 6)(x² + 8x + 16) is: C. The function has one real zero and two complex zeros.
What is a function?In mathematics, a function is a special type of relation. A relation is a set of ordered pairs, where each ordered pair consists of two elements.
To determine the zeros of the function h(x) = (x - 6)(x^2 + 8x + 16),
we can set the function equal to zero and solve for x.
Setting h(x) = 0, we have:
(x - 6)(x^2 + 8x + 16) = 0
Setting x - 6 = 0, we find:
x = 6
Setting x^2 + 8x + 16 = 0,
we can attempt to factor or use the quadratic formula.
Therefore, the function:
h(x) = (x - 6)(x^2 + 8x + 16) has one real zero (x = 6) and two complex zeros.
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the times for completing one circuit of a bicycle course are normally distributed with a mean of 62.9 minutes and a standard deviation of 6.1 minutes. an association wants to sponsor a race but will cut the bottom 25% of riders. in a trial run what should the cutoff time be
In a trial run the cutoff time should be 58.78 minutes.
What is standard deviation?The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability. When data points are closely spaced from the mean, there is a little variation, and when they are far spaced from the mean, there is a large variation. The standard deviation determines how much the data deviate from the mean.
Given a normal distribution:
Mean = 62.9 minutes
Standard deviation = 6.1 minutes
To cut the bottom 25% riders
Using the relation:
Z score = (score - mean) / standard deviation
Z score for the bottom 25% corresponds to
- 0.674(using tables or calculator)
Hence,
-0.674 = (score - 62.9) / 6.1
-0.674 * 6.1 = score - 62.9
-4.1114 = score - 62.9
-4.1114 + 62.9 = score
Score = 58.78
Hence, in a trial run the cutoff time should be 58.78 minutes.
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Use synthetic division to solve (x cubed minus x squared minus 17 x minus 15) divided by (x minus 5). What is the quotient?
x squared + 4 x + 3
x squared minus 6 x + 13 minus StartFraction 80 Over x minus 5 EndFraction
x cubed + 4 x squared + 3 x
x squared minus 6 x + 13 minus StartFraction 80 Over x + 5 EndFraction
Answer: A
Step-by-step explanation:
The quotient is x² + 4x +3. Then the correct option is A.
What is the quotient?A quotient in mathematics is the amount created by dividing two numbers. In mathematics, the term "quotient" is frequently used to refer to the integer portion of a division, as well as to a fraction or a ratio.
The quotient is calculated as:-
x - 5 ) x³ - x² - 17x -15 ( x² + 4x + 3
-x³ + 5x²
_________________
4x² - 17x - 15
-4x² + 20x
_________________
3x -15
-3x + 15
_________________
0
Hence, the quotient is x² + 4x +3.
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Suppose that the function g is defined, for all real numbers, as follows. Find g(-5) ,g (-2), and g(-1)
If the function g(x) is defined for all real-numbers, then the value of g(-5) is 7/2, g(-2) is -1 and g(-1) is 0.
A piecewise function is a function that is defined by different rules or formulas on different parts of its domain. The piecewise function "g(x)" is given as :
g(x) = {-(1/2)x + 1, for x<-2
= {-(x+1)², for -2≤x≤1
= {4 for x>1
We have to find the value of g(-5) ,g (-2), and g(-1),
For x = -5, the number -5 is less than -2, so the first function "-(1/2)x + 1" will be used,
⇒ g(-5) = -(1/2)(-5) + 1 = 5/2 + 1 = 7/2,
For x = -2, the number -2 lies in the interval "-2≤x≤1", so second function
"-(x+1)²" will be used,
⇒ g(-2) = -(x+1)² = -(-2+1)² = -(-1)² = -1,
For x = -1, the number -1 lies inn the interval "-2≤x≤1", so second function "-(x+1)²" will be used,
⇒ g(-1) = -(x+1)² = -(-1+1)² = -(0)² = 0,
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Given f(x)= 3x+2, what is the Inverse Function?
Answer:
Step-by-step explanation:
For this case we must determine the inverse of the following function:
\(f(x)=3x-2\)
Step 1:
We would write
\(y=f(x)\) or \(y=3x-2\)
Step 2:
We clear x:
\(y+2=3x\)
\(\frac{y+2}{3}=x\)
Step 3:
"x" and "y" are exchanged:
\(y=\frac{x+2}{3}\)
The inverse is:
\(f^{-1}(x)=\frac{x+2}{3}\)
Find the Taylor Polynomial 3P x (up to3
x ) for( ) x
f x e , centered at0x ?
We have to find the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$.
The Taylor Polynomial is given by:
(x)=∑
k=0
n
k!
f
(k)
(a)
(x−a)
k
where $f^{(k)}(a)$ is the $k$th derivative of $f(x)$ evaluated at $a$.
Using this formula, we can find the Taylor Polynomial as follows:
\begin{align*}
f(x) &= e^x \
f'(x) &= e^x \
f''(x) &= e^x \
f'''(x) &= e^x \
\end{align*}
Evaluating each derivative at $x=0$, we get:
\begin{align*}
f(0) &= e^0 = 1 \
f'(0) &= e^0 = 1 \
f''(0) &= e^0 = 1 \
f'''(0) &= e^0 = 1 \
\end{align*}
Substituting these values into the formula for the Taylor Polynomial, we get:
\begin{align*}
P_3(x) &= \frac{f(0)}{0!}(x-0)^0 + \frac{f'(0)}{1!}(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3 \
&= 1 + x + \frac{x^2}{2} + \frac{x^3}{6}
\end{align*}
Therefore, the Taylor Polynomial of $f(x)=e^x$ up to the third degree, centered at $x=0$, is $P_3(x) = 1 + x + \frac{x^2}{2} + \frac{x^3}{6}$.
The graph below represents a rock climbers height as she acends a hill. Part A- The above graph is (circle one) linear/ nonlinear. Part B- Is the above graph a function? Explain.
Answer:
Part A: its linear
Part B: it is a function
Step-by-step explanation:
Find the solution set of the inequality and what is the number? 16x − 7 ≤ − 71 A. C. ≤ D. ≥ E. =
x ≤ − 4
Step-by-step explanation:
Answer:
x ≤ -4
Step-by-step explanation:
16x − 7 ≤ − 71
Add 7 to both sides.
16x ≤ -64
Divide both sides by 16.
x ≤ -4
Find the X and Y
Help ASAP please!!!
You go to the store to buy a new TV that is $430. If the tax is 6% of that price, what is the total cost of the TV including tax? PLEASE HELP ME
Answer:
455.8?
Step-by-step explanation:
$430 (tax: x,-,+) = 455.8.
tax: 25.8
Sorry if this is wrong.
Have a great day/night.
2. Given that the indicated lines in figure 10.30(a) are parallel, determine the unknown angles without actually measuring them. Explain your reasoning briefly.
The opposie angles are equal
c is opposite to a, so
\(c=a=34^o\)The angle p is opposite to that of n, so
\(p=118^o\)The total angle of rotation in a line is 180°. so,
\(o=180-118=62\)This o is the oppsite to m, and hence m=o.
similarly,
\(d=180-34=146\)And hence, b=d=146
let f(x) = 9x - 2 and g(x) = -x + 3. find f(g(x)). a. -9x - 2 b. -9x + 5 c. -9x + 25 d. -9x + 27
Answer:
See below.
Step-by-step explanation:
\(f(x)=9x-2 \text{ and } g(x)=-x+3\\f(g(x))=f(-x+3)\\f(-x+3)=9(-x+3)-2\\\text{Distribute and Simplify}\\-9x+27-2\\=-9x+25\\\text{Therefore, f(g(x))=-9x+25}\\\text{The answer is C}\)
Given AC=LN and BA=ML, which statement must be true?
Answer: BC<MN
Step-by-step explanation:
Answer: BC <MN
Step-by-step explanation: i just took the test on eginuity
Jason has 75 feet of wallpaper border. He wants to put a wallpaper border around his rectangular bedroom that measures 12 fee by 14 feet. he multiplies 12×14= 168 to get an exact answer of how much border he needs. He concludes that he does not have enough water for the whole job. Full picture below
Let's summarize the facts:
the tape is 75 feet long
the bedroom is 12 feet by 14 feet.
1. Tell how you can critique Jason’s reasoning.
If you want to Critique Jason's reasoning, you could a) ask yourself the same questions that Jason did and see if you would come with the same answers and used the same analysis or b) analyse Jason's answer to see if he did a mistake or missed an important detail and made a thought mistake
2. Critique Jason’s reasoning
I will use the option b from above:
?
Jason first multiplied 12 x 14 = 168. This multiplication is correct, but what did he get? He needed to get the perimeter of the bedroom because it was only the wallpaper border, not the wallpaper itself - so getting the perimeter was needed, but this we get by the formula (2* *(length width), not length* width - as Jason did.
So, Jason made a mistake here! his actual answer should be 2*(12+14) =2*26=52, so the tape of 75 feet would have been enough!
3. Jason uses an overestimate to decide how many rolls of wallpaper he needs for another’s room. Explain why his reasoning to use an overestimate does or does not make sense
Using an overestimate is often a good idea- in case some of the tape gets damaged, he will have some left. However, since his calculations are wrong by a lot (he multiplies rather than adds and multiplies by 2), his overestimate will be a lot higher than would be practical - he would be left with a lot of leftovers and spend too much money. So his reasoning does not make sense
9 ft
4.7 ft
6.5 ft
6.5 ft
Find the area of the triangle.
Answer: 21.15 ft²
Step-by-step explanation:
We can use the formula for the area of a triangle:
(b×h)/2
In this case, the base is 9 and the height is 4.7.
So, we substitute the variables with the numbers in this problem.
(9 × 4.7)/2
9 × 4.7 = 42.3
42.3/2 = 21.15
So, our final answer is 21.15 ft²
BRAINLIEST (statistics) (please help fast)
Data were collected from a typing class with 10 students. The class had an average of 56 words per minute (WPM) with a standard deviation of 7 WPM. The teacher realized that the data from one student who typed 70 WPM was not entered. If this student’s results were included in the data set, what effect would it have on the standard deviation?
The standard deviation would be noticeably larger.
The standard deviation would be noticeably smaller.
The standard deviation would be about the same, perhaps a little larger.
The standard deviation would be about the same, perhaps a little smaller.
Answer: The STandard deviation would be noticably A is the answer
Step-by-step explanation:
Theprofit(indollars)earnedbysellingwappletreesisrepresentedby w2 − 4w + 14. The profit (in dollars) earned by selling w pear trees is
represented by 2w + 10. Write a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.
The profit earned by selling w pear trees is 2w + 10
To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:
\((w^2 - 4w + 14) - (2w + 10)\)
Simplifying the expression:
\(w^2 - 6w + 4\)
Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).
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Question 2
No calculations are necessary to answer this question.
3/01
3/02
$1.7420 $1.7360
Date
July GBP Futures
Contract Price
O long; long
Based on the closing prices of July GBP Futures Contract over the 3-day period in March 20XX as shown above, you shou
position on 3/01 and a position on 3/02.
O long; short
O short; short
3/03
short; long
$1.7390
The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.
Part 1 of 2
Evaluate the function f(x)=x-7 at the given value of the variable.
a. f(13)
b. f(3)
Answer:
a)
b)-4
Step-by-step explanation:
a) f(13) = 13-7=
b) f(3)= 3-7= -4
HElP ME PLEASE AnYONE
Answer:
\(y=2x+3\)
Step-by-step explanation:
We know that \(m=\frac{5-3}{1-0}=2\) and that the \(y\) intercept is 3.
Answers:
1/53 ; your car travels 53 miles every 1 hour.
OR
53/1; your car travels 53 miles every 1 hour.
Answer:
1/53 I believe because it says I believe sorry if I am wrong hope you get it right
Put these numbers in order from greatest to least. 16/25, 4/16, -8, -11/20
help me find the slope please
Answer:
3/4
Step-by-step explanation:
Ok, so I see that the x-intercept is (4,0), while the y-intercept is(-3,0)
Slope is rise/run
Between these two points, the line rose 3 and horizontally went 4 units to the right. Therefore, the slope is 3/4.
Feel free to tell me if I did anything wrong! :)
Also, if you're still confused, I could explain it another way.
Question 1-2
What is the value of a³ + b (6 + c), when a = 2, b = 3, and c = 4?
Answer:
\(\huge\boxed{\sf 38}\)
Step-by-step explanation:
Given expression:= a³ + b (6 + c)
Put a = 2, b = 3 and c = 4
= (2)³ + 3 (6 + 4)
= 8 + 3(10)
= 8 + 30
= 38\(\rule[225]{225}{2}\)
Answer:
Step-by-step explanation:
the requied answer is 38.
according to the question the value of a=2,b=3,c=4.
here,
to find the value of a³ + b (6 + c)we have to do it in steps:
step 1: solve the bracket (6+4) =10.
step 2: solve the value of a³ =8.
now put these values ,
=8+3(10)
=38.
Using The table of values find a Y intercept. Find a slow. What is the equation?
answer:
y = -2/5x + 4
give me examples of equivalent expressions of square root 54 with a radican of 3
i need help with this problem.
Sue decided to make more orange flavored desserts and picked more oranges. She used 1/6 gal less juice to make popsicles than to make candy. She used 1/3 gal more juice to make candy than to make sorbet. If she used 1/2 gal of juice to make the popcicles, how much juice did she use to make the sorbet? (Write your fraction answer like this. 1/2) Fill in the blank. Sue used_____ gallons of juice to make sorbet. *
Answer: 1/2
Step-by-step explanation:
ach ant has 6 legs. How many legs do 3 ants have?
Ants 1 2 3
Legs 6 ?
Answer:
Step-by-step explanation:
the answer is 18 I think?
Answer:
18
Step-by-step explanation:
6 (legs) x 3 (ants) = 18 legs
It can also be represented as 6+6+6 (18)
hope this helps :)