Answer: 9 feet
Step-by-step explanation:
From the information given, we have already been given the equation which is x(x-3)=54. Therefore we will find the value of x which will be:
x(x-3)=54
x² - 3x - 54
x² - 9x + 6x - 54
x(x - 9) + 6(x - 9)
Therefore,
(x - 9) = 0
x = 0 + 9
x = 9
The length is 9 feet
The width will be:
x - 3 = 9 - 3 = 6 feet
nen,
Problem: Two towns, A and B, located along the coast of the Pacific Ocean are 30
km apart on a north-south line. From a ship, the line of sight of town A is W30°N,
while that of town B is S400W.
1. How far is the ship from town A?
2. How far is the ship from town B?
Answer:
Step-by-step explanation:
From the picture attached,
m∠COB = 90° - m∠BOS
= 90° - 40°
= 50°
tan(30°) = [tex]\frac{AC}{OC}[/tex]
[tex]\frac{1}{\sqrt{3}}=\frac{AC}{OC}[/tex]
AC = [tex]\frac{OC}{\sqrt{3}}[/tex] ------(1)
Similarly, tan(50°) = [tex]\frac{BC}{OC}[/tex]
BC = OC[tan(50°)] -------(2)
Now AC + BC = 30 cm
By substituting the values of AC and BC from equation (1) and (2),
[tex]\frac{OC}{\sqrt{3}}+OC(\text{tan}50)=30[/tex]
(1.769)OC = 30
OC = 16.96
1). cos(30°) = [tex]\frac{OC}{AO}[/tex]
[tex]\frac{\sqrt{3}}{2}= \frac{16.96}{OA}[/tex]
[tex]OA=19.58[/tex] cm
Therefore, distance between the ship and town A is 19.58 cm.
2). cos(50°) = [tex]\frac{OC}{OB}[/tex]
0.6428 = [tex]\frac{16.96}{OB}[/tex]
OB = 26.38 cm
Therefore, distance between the ship and town B is 26.38 cm.
pls how can u convert 9ml to cm cube
Answer:
There is no conversion necessary. It's a 1 to 1 ratio.
ml = [tex]cm^{3}[/tex]
so, 9ml is 9[tex]cm^{3}[/tex]
Answer:
9ml = 9cm³
Step-by-step explanation:
1ml = 1cm³
Therefore,
9ml = 9cm³
Identify an equation in point-slope from for the line perpendicular to y=-4x-1 that passes through (-2, 4)
Answer:
y - 4 = ¼(x + 2)
Step-by-step explanation:
Point-slope form equation is given as y - b = m(x - a). Where,
(a, b) = a point on the line = (-2, 4)
m = slope = ¼ (sleep of the line perpendicular to y = -4x - 1 is the negative reciprocal of its slope value, -4 which is ¼)
✔️To write the equation, substitute (a, b) = (-2, 4), and m = ¼ into the point-slope equation, y - b = m(x - a).
y - 4 = ¼(x - (-2))
y - 4 = ¼(x + 2)
None of the options are correct
oludonts c) 2x + y = 2
2x + 2y = 0
Answer:
[tex]x = 2[/tex]
[tex]y = -2[/tex]
Step-by-step explanation:
Given
[tex]2x + y = 2[/tex]
[tex]2x + 2y = 0[/tex]
Required
Solfe for x and y
Subtract both equations
[tex]2x- 2x + y - 2y = 2 -0[/tex]
[tex]-y = 2[/tex]
Divide by -1
[tex]y = -2[/tex]
Substitute [tex]y = -2[/tex] in [tex]2x + 2y = 0[/tex]
[tex]2x+2 *-2 = 0[/tex]
[tex]2x-4 = 0[/tex]
[tex]x - 2 = 0[/tex]
Collect like terms
[tex]x = 2[/tex]
sec theta root under 1- cos square theta = tan theta
Answer:
Step-by-step explanation:
012345678910
'yl\f[pt;]p;d[k;ell-=;q'[;
Answer:
see explanation
Step-by-step explanation:
Assuming you mean
secθ × [tex]\sqrt{1-cos^20}[/tex]
= [tex]\frac{1}{cos0}[/tex] × sinθ [ sin²θ + cos²θ = 1 , so sinθ = [tex]\sqrt{1-cos^20}[/tex] ]
= [tex]\frac{sin0}{cos0}[/tex]
= tanθ
= right side , thus verified
Công ty T vừa đưa vào sản xuất một loại sản phẩm mới với định mức giờ máy là 2 giờ/sản phẩm. Tài liệu về sản phẩm trong năm như sau (đồng):
Chi phí nguyên vật liệu trực tiếp/sp
30.000
Chi phí nhân công trực tiếp/sp
27.000
Chi phí sản xuất chung/sp
12.000(25% là biến phí)
Bao bì/sp (ở khâu SX)
5.000
Lương quản lý và bán hàng
83.300.000
Quảng cáo
34.700.000
Chí phí khác bằng tiền
30.000.000
Vốn đầu tư bình quân
1.200 triệu
ROI mong muốn
16%
Tổng số giờ máy hoạt động cho sản xuất
40.000 giờ
Yêu cầu:
1. Hãy định giá bán theo biến phí?
2. Để sản xuất sp mới này, Cty tự chế tạo 1 chi tiết để lắp vào sản phẩm với thông tin như sau:
- Biến phí sản xuất của Chi Tiết = 40% biến phí sp
- KH TSCĐ cho việc sản xuất chi tiết là 42.000.000đ
- Chi phí quản lý chung phân bổ cho việc sản xuất chi tiết là 19.040.000đ.
Có một doanh nghiệp khác đến chào hàng chi tiết với giá chỉ bằng 70% so với giá thành cty tự sản xuất và đảm bảo đủ số lượng, chất lượng theo yêu cầu. Các phương tiện sản xuất chi tiết có thể cho thuê 13.000.000đ/năm. Cty nên tự sản xuất hay mua ngoài?
Answer:
??????
Step-by-step explanation:
Can someone help me with this? Thanks!
9514 1404 393
Answer:
x ∈ {5, 7}(5,7)Step-by-step explanation:
The graph shows the function value is zero for x=5 and x=7. These are the elements of the solution set.
x ∈ {5, 7}
__
The graph is below the x-axis between these points, so that is the region where f(x) < 0
5 < x < 7 . . . . . for f(x) < 0
In interval notation: (5, 7).
She decides that ordering that many cars would not be economically feasible at this time and asks her sales manager to randomly choose one of the models for the sales lot. What is the probability that he chooses the 4-door, special edition model, with four-wheel drive?
The probability that he chooses the 4-door, special edition, four-wheel drive model is (44)=
P(4S4)=
Answer:
The probability that he chooses the 4-door, special edition, four-wheel drive model is P( 454) = 1 (Enter your answer as reduced fraction.) ...Step-by-step explanation:
The probability that he chooses the 4-door, special edition, four-wheel drive model is (44)=P(4S4)=What is the value of x
Answer:
[tex]6x+3+69=180[/tex]
[tex]6x=180-72[/tex]
[tex]6x=108[/tex]
[tex]x=18[/tex]
--------------------------
hope it helps..
have a great day!!
The answer to this 6th grade summer school math question is
Answer 7.84
Hw help ASAP PLZZZZZZ
Answer:
Your answer is C. X = 29/8c
Step-by-step explanation:
2/3(cx + 1/2) - 1/4 = 5/2
2cx/3+1/3-1/4=5/2
2cx3+1/12=5/2
2cx/3=5/2-1/12
2cx/3=29/12
(3)2cx/3=29/12(3)
2cx= 31/4
(2c)2cx=29/4(2c)
X=29/8c
Your answer is C. X = 29/8c
a woman bought some large frames for
$12 each and some small frames for $5
each. If she bought 20 frames for $156
find how many of each type she bought.
Answer:
8 pairs of large glasses and 12 pairs of small ones
Step-by-step explanation:
Let's say the number of large frames she buys is l, and the number of small frames is s. She buys 20 frames of assorted sizes, but they can only be small or large. Therefore, s + l = 20.
Next, the total cost of large frames is 12 dollars for each frame. Therefore, the total cost for the large frames is equal to 12 * l. Similarly, the total cost for the small frames is equal to 5 * s. The total cost of all frames is equal to 156, so
12* l + 5 * s = 156
s + l = 20
In the second equation, we can subtract l from both sides to get
s = 20 - l
We can then plug that into the first equation to get
12 * l + 5 * (20-l) = 156
12 * l + 100 - 5*l = 156
subtract both sides by 100 to isolate the variable and its coefficient
12 * l - 5 * l = 56
7 * l = 56
divide both sides by 7 to isolate the l
l = 8
The woman buys 8 pairs of large glasses. The number of small glasses is equal to 20-l=20-8=12
I need help :)What’s m
Answer:
[tex] \large{ \tt{❃ \: S \: O \: L \: U \: T \: I \: O \: N : }}[/tex]
[tex] \large{ \tt{⇢m \: \angle \: GHI= m \: \angle \: GHQ + m \: \angle \: QHI}}[/tex]
[tex] \large{ \tt{➝14x + 6 = 3x - 3 + 130 \degree}}[/tex]
[tex] \large{ \tt{➝14x + 6 = 3x + 127}}[/tex]
[tex] \large{ \tt{➝ \: 14x - 3x = 127 - 6}}[/tex]
[tex] \large{ \tt{➝ \: 11x = 121}}[/tex]
[tex] \large{ \tt{➝ \: x = \frac{121}{11} }}[/tex]
[tex] \large{ \tt{➝ \: x = 11}}[/tex]
[tex] \large{ \tt{✣ \: REPLACING \: VALUE}} : [/tex]
[tex] \large{ \tt{✺ \: m \: \angle \: GHI = 14x + 6 = 14 \times 11 + 6 = \boxed{ \tt{160 \degree}}}}[/tex]
Our final answer : 160° . Hope I helped! Let me know if you have any questions regarding my answer! :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
Answer:
See attachment showing the rise and run
Slope = 1
Step-by-step explanation:
In the diagram attached below, the rise is represented by the blue line, while the run is represented by the red line.
Rise = 4 units
Run = 4 units
It's a positive slope because the line slopes upwards from left to right
Slope = rise/run = 4/4
Slope = 1
A student takes an exam containing 16 true or false questions. If the student guesses, what is the probability that he will get exactly 14 questions right
Answer:
0.001831055
Step-by-step explanation:
Here, n = 16, p = 0.5, (1 - p) = 0.5 and x = 14
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)
We need to calculate P(X = 14)
P(x =14) = 16C14 * 0.5^14 *(1-0.5)^2
= 120 * 0.5^14 *(1-0.5)^2
= 0.001831055
At a coffee shop, the first 100 customers'
orders were as follows.
Medium Large
Small
Hot
5
48
22
Cold
8
12
5
What is the probability that a customer ordered
a small given that he or she ordered a hot
drink?
Rounded to the nearest percent, [? ]%
Well formatted distribution table is attached below :
Answer:
7%
Step-by-step explanation:
The probability that a customer ordered a small Given that he or she ordered a hot drink ;
This is a conditional probability and will be represented as :
Let :
P(small drink) = P(S)
P(hot drink) = P(H)
Hence, the conditional probability is written as :
P(S|H) = P(SnH) / P(H) = 5 / (5+48+22) = 5/75 = 0.0666 = 0.0666 * 100% = 6.67%
I need some help please!
Answer:
See below
Step-by-step explanation:
Given :-
y || zTo Prove :-
m∠5 + m∠2 + m∠6 = 180°Proof :-
Here we are required to prove that ,
[tex]\rm\implies m\angle 5 + m\angle 6 + m\angle 2 = 180^o [/tex]
And here it's given that , y || z . Therefore ,
∠3 = ∠6 ( alternate interior angles )∠1 = ∠5 ( alternate interior angles )Now we know that the measure of a straight line is 180°. Therefore ,
[tex]\rm\implies m\angle 1 + m\angle 2 + m\angle 3 = 180^o \\\\\implies\boxed{\rm m\angle 5 + m\angle 6 + m\angle 2 = 180^o} [/tex]
From 1 and 2 .Hence Proved !
You own a small storefront retail business and are interested in determining the average amount of money a typical customer spends per visit to your store. You take a random sample over the course of a month for 12 customers and find that the average dollar amount spent per transaction per customer is $116.194 with a standard deviation of $11.3781. Create a 90% confidence interval for the true average spent for all customers per transaction.1) ( 114.398 , 117.99 )2) ( 112.909 , 119.479 )3) ( -110.295 , 122.093 )4) ( 110.341 , 122.047 )5) ( 110.295 , 122.093 )
Answer:
(110.295, 122.093).
Step-by-step explanation:
We have the standard deviation for the sample, which means that 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 = 12 - 1 = 11
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 11 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.7959
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.7959\frac{11.3781}{\sqrt{12}} = 5.899[/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 116.194 - 5.899 = 110.295
The upper end of the interval is the sample mean added to M. So it is 116.194 + 5.899 = 122.093
So
(110.295, 122.093).
2.According to www.city-data, the mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000. Check the three assumptions associated with the Central Limit Theorem. What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009
Answer:
0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
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.
The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.
This means that [tex]\mu = 192723, \sigma = 42000[/tex]
Sample of 75:
This means that [tex]n = 75, s = \frac{42000}{\sqrt{75}}[/tex]
What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?
1 subtracted by the p-value of Z when X = 190000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}[/tex]
[tex]Z = -0.56[/tex]
[tex]Z = -0.56[/tex] has a p-value of 0.2877
1 - 0.2877 = 0.7123
0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.
Allie rode her bike up a hill at an average speed of 12 feet/second. She then rode back down the hill at an average speed of 60 feet/second. The entire trip took her 2 minutes. What is the total distance she traveled. [Hint: use t = time traveling down the hill]
Answer:
The total distance Allie traveled was 0.81 miles.
Step-by-step explanation:
Since Allie rode her bike up a hill at an average speed of 12 feet / second, and she then rode back down the hill at an average speed of 60 feet / second, and the entire trip took her 2 minutes, to determine what is the total distance she traveled, the following calculation must be performed:
12 + 60 = 72
72 x 60 = 4320
1000 feet = 0.189394 miles
4320 feet = 0.8181818 miles
Therefore, the total distance Allie traveled was 0.81 miles.
11
5
у
х
Find the value of x.
A) 4rad5
B) 8rad5
C) 6
D) 16
Answer:
Option A, 4rad5
Step-by-step explanation:
x² = 5*(5+11)
x² = 5*16
x² = 80
x = 4√5
Answered by GAUTHMATH
F (x) = 1/3 x for x=4
Answer:
4/3
Step-by-step explanation:
Substitute in 4.
(1/3)4
Multiply
4/3
I hope this helps!
Simplify:
-5x+6y-9y+4x
Answer:
-x-3y
Step-by-step explanation:
-5x+6y-9y+4x
-5x+4x+6y-9y
-x-3y
Yess again pls help!
Tyyy
Simplify the following expression.
3^{0}
Answer:
Anything to the power of zero (with the exception of zero itself) is equal to one.
So 3⁰ = 1
if 18 : 6 = x : 3 then what is 5 + 3x
Answer:
32
Step-by-step explanation:
18 : 6 = 3
therefore, x : 3 has to equal 3.
X : 3 = 3
X = 3 × 3
X = 9
To verify:
18 : 6 = 9 : 3
3 = 3
It's true that X = 9, so now just replace the X with 9 in the next equation
5 + 3(9) = 32
Answer:
32
Step-by-step explanation:
18 : 6 = x : 3
Product of means = Product of extremes
6 * x = 3*18
x = [tex]\frac{3*18}{6}[/tex]
x = 3*3
x = 9
Now plugin x = 9 in the expression
5 + 3x = 5 + 3*9
= 5 + 27
= 32
The five-number summary of a data set is: 0, 4, 6, 14, 17
An observation is considered an outlier if it is below:
An observation is considered an outlier if it is above:
Answer:
Outlier therefore could only be values below - 12.75
or could only be values above + 121.125
Step-by-step explanation:
0, 4, 6, 14, 17
inner quartile range of 0 - 17 is 1/2 of 17 subtracted from the higher number = 17 - 1/2 of 8.5 = 8.5 - 4.25 = 4.25 - 4.25 x 3
= 4.25 to 12.75 for inner quartile
inner quartile range is 12.75-4.25 = 8.5
We then 1.5 x 8.5 to show the outlier
= 12.75 meaning there is no outlier if is below.
Lower quartile fences = 4.25 - 1.5 = 2.75
or -1.5 x 8.5 (the range) = -12.75
Upper quartile fence = 12.75 + 1.5 = 14.25 x 8.5 = 121.125 this would be an outlier if it is 12.75 higher than 121.125 or 12.75 lower than 5.50.
Outlier therefore could only be values below - 12.75
or could only be values above + 121.125
An observation is considered an outlier if it exceeds a distance of 1.5 times the interquartile range (IQR) below the lower quartile or above the upper quartile. The values of the lower quartile - 1.5 x IQR and upper quartile + 1.5 x IQR are known as the inner fences.
An observation is an outlier if it falls more than above the upper quartile or more than below the lower quartile. The minimum value is so there are no outliers in the low end of the distribution. The maximum value is so there are no outliers in the high end of the distribution.
What is the cost, in dollars, of 16 onions if 3 onions weigh 1.5 lb and the price of onions is 33 cents per kilogram
Answer:
The cost of 16 onions is $ 1.20.
Step-by-step explanation:
To determine what is the cost, in dollars, of 16 onions if 3 onions weigh 1.5 lb and the price of onions is 33 cents per kilogram, the following calculation must be performed:
1.5 pounds = 0.68 kilos
0.68 / 3 = 0.22666 kilos each onion
16 x 0.22666 = 3.626 kilos
0.33 x 3.626 = 1.20
Therefore, the cost of 16 onions is $ 1.20.
Use a Maclaurin series to obtain the Maclaurin series for the given function.
f(x)= 14x cos(1/15x^2)
Answer:
[tex]14x cos(\frac{1}{15}x^{2})=14 \sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]
Step-by-step explanation:
In order to find this Maclaurin series, we can start by using a known Maclaurin series and modify it according to our function. A pretty regular Maclaurin series is the cos series, where:
[tex]cos(x)=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{2k}}{(2k)!}[/tex]
So all we need to do is include the additional modifications to the series, for example, the angle of our current function is: [tex]\frac{1}{15}x^{2}[/tex] so for
[tex]cos(\frac{1}{15}x^{2})[/tex]
the modified series will look like this:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15}x^{2})^{2k}}{(2k)!}[/tex]
So we can use some algebra to simplify the series:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}(\frac{1}{15^{2k}}x^{4k})}{(2k)!}[/tex]
which can be rewritten like this:
[tex]cos(\frac{1}{15}x^{2})=\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]
So finally, we can multiply a 14x to the series so we get:
[tex]14xcos(\frac{1}{15}x^{2})=14x\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k}}{(2k)!15^{2k}}[/tex]
We can input the x into the series by using power rules so we get:
[tex]14xcos(\frac{1}{15}x^{2})=14\sum _{k=0} ^{\infty} \frac{(-1)^{k}x^{4k+1}}{(2k)!15^{2k}}[/tex]
And that will be our answer.
4+4+8+8+422+33+65520222222+222
Answer:
4+4+8+8+422+33+65520222222+222= 65,520,222,923
