Step-by-step explanation:
4/6
=2/3
That's what I could show you
if cosA=3√2/5,then show that cos2A=11/25
Answer:
Step-by-step explanation:
Cos 2A = 2Cos² A - 1
[tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]
The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 8 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 8 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is 9.582 and the standard deviation of the differences is 15.9274. Calculate a 90% confidence interval to estimate the average difference in scores between the two courses.1) (13.73,-0.65).2) (-10.359,-4.021).3) (-9.259,-5.121).4) (-13.745,-0.635).5) (13.745, -0.635).
Answer:
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
Step-by-step explanation:
We have the standard deviation for the differences, 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 = 8 - 1 = 7
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 7 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 1.8946
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 1.8946\frac{15.9274}{\sqrt{8}} = 10.67[/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 9.582 - 10.67 = -1.088
The upper end of the interval is the sample mean added to M. So it is 9.582 + 10.67 = 20.252
The 90% confidence interval to estimate the average difference in scores between the two courses is (-1.088, 20.252).
PLEASE HELP!!! Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question. A number line going from negative 9 to positive 1.
Answer:
is it going to be 10.5
Step-by-step explanation:
I do not have any explanation
Answer: 0 (zero)
Step-by-step explanation:
Start Learning & start growing! edge2023
*DROPS THE MIC*
Solve for x. The triangles are similar.
What is the correct line graph for y=3x+5?
Answer:
The equation y=−3x+5 is in slope intercept form, and represents a straight line in which -3 is the slope, and 5 is the y -intercept.
13, 5, 4, 9, 7, 14, 4 The deviations are _____.
A. "5, -3, -4, 0, 1, 6, 4"
B."5, -3, -4, 1, -1, 6, -4"
C."6, -3, -4, 1, 2, 6, -4"
D."-5, 3, 4, -1, 1, 6, 4 "
Answer:
B."5, -3, -4, 1, -1, 6, -4"
Step-by-step explanation:
We are given that
13,5,4,9,7,14,4
We have to find the deviation.
Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]
Using the formula
[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]
[tex]Mean,\mu=\frac{56}{7}=8[/tex]
Deviation=[tex]x_i-\mu[/tex]
[tex]x_i-\mu[/tex]
13 5
5 -3
4 - 4
9 1
7 -1
14 6
4 - 4
Hence, option B is correct.
If the mean, median, and mode are all equal for the set (10, 80, 70, 120, x}, find the value of x.
X
(Simplify your answer. Type an integer or a decimal.)
Question Viewer
Answer:
x=70
Step-by-step explanation:
First, we know that the mode is the number that is the most common. As each value in the set so far only has one of each number, we know that x must be one of the current numbers, making that the mode.
Next, because x is the mode and has to be the median as well, and our number line so far is
(10, 70, 80, 120), x must be either 70 or 80 to make it the median. This is because if x is 10 or 120, we would end up with (10, 10, 70, 80, 120) with 70 as the median or (10, 70, 80, 120, 120) with 80 as the median.
Finally, to calculate the mean, we have
mean = sum / count
The mean must be x, as it is equal to the mode, so we have
x = (10+70+80+120 + x)/5 (as there are 5 numbers including x)
multiply both sides by 5 to remove the denominator
5 * x = 10+70+80+120+x
5 * x = 280 + x
subtract x from both sides to isolate the x and the coefficient
4 * x = 280
divide both sides by 4 to get x
x= 70
We see that x is 70 or 80 and is one of the current numbers, checking off all boxes.
ASAP What is the rule for this relation? i will give brainliest
Answer:
your selected answer is right
A tree cast a shadow of 30m long and a 2m stick casts one that is 3m long. As show in the below diagram how tall is the tree?
Answer:
20 mStep-by-step explanation:
We have similar triangles here.
BC║DE, AB║AD and AC║AE ⇒ ΔADE ~ ΔABCThe ratio of corresponding sides of similar triangles is same:
BC/DE = AC/AEBC / 2 = 30/3BC / 2 = 10BC = 2*10BC = 20 mTake the similar triangles,
→ ∆ADE ≈ ∆ABC
Now we can find,
The height of the tree in meters,
→ BC/DE = AC/AE
In this equation BC is the height of tree,
→ BC/2 = 30/3
→ BC/2 = 10
→ BC = 10 × 2
→ BC = 20
Hence, the height of the tree is 20 m.
Geometry PLS HELP due soon
Answer:
(3) [tex]x = 7.5[/tex] and [tex]y = 51[/tex]
(4) [tex]x = 6[/tex]
Step-by-step explanation:
Question 3
Required
Solve for x and y
We have:
[tex]16x - 18 + 10x +3 = 180[/tex] --- angle on a straight line
Collect like terms
[tex]16x + 10x = 180 + 18 - 3[/tex]
[tex]26x = 195[/tex]
Solve for x
[tex]x = 195/26[/tex]
[tex]x = 7.5[/tex]
Also:
[tex]16x - 18 = 2y[/tex] ---- opposite angles
So, we have:
[tex]16 * 7.5 - 18 = 2y[/tex]
[tex]120 - 18 = 2y[/tex]
[tex]102 = 2y[/tex]
Divide by 2
[tex]51 = y[/tex]
[tex]y = 51[/tex]
Question 4:
Required
Solve for x
We have:
[tex]11x - 2 + 5x - 4 = 90[/tex] ---- angle at right-angled
Collect like terms
[tex]11x + 5x = 90 +2 + 4[/tex]
[tex]16x = 96[/tex]
Divide by 16
[tex]x = 6[/tex]
A business woman wants to open a coffee stand across the street from a competing coffee company. She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers. Suppose she takes a random sample of 31 days. Identify the following to help her decide whether to open her coffee stand, rounding to the nearest whole number when necessary:
μ =_____customers per day
σ =_____customers per day
n =____
μ-x =____
σ-x =_____customers per day
Answer:
μ = 170 customers per day
σ = 45 customers per day
n = 31
[tex]\mu_x = 170[/tex]
[tex]\sigma_x = 8[/tex]
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.
She notices that the competing company has an average of 170 customers each day, with a standard deviation of 45 customers.
This means that [tex]\mu = 170, \sigma = 45[/tex]
Suppose she takes a random sample of 31 days.
This means that [tex]n = 31[/tex]
For the sample:
By the Central Limit Theorem, the mean is [tex]\mu_x = 170[/tex] and the standard deviation is [tex]\sigma_x = \frac{45}{\sqrt{31}} = 8[/tex]
The width of a rectangle is 2 cm less than its length. The perimeter is 52 cm. The length is:
14 cm.
12 cm.
9 cm.
None of these choices are correct.
Answer: 14 cm
Step-by-step explanation:
Rectangle:
Length = xWidth = x - 2x + x + (x - 2) + (x - 2) = 52
2x + 2(x - 2) = 52
2x + 2x - 4 = 52
4x = 52 + 4
4x = 56
x = 14
Chloe has a small dog and a large dog. Each day, the small dog eats 3/4 cup of dog food, and the large dog 2 1/2 cups of dog food. In one week, how much more dog food does the large dog eat than the small dog ?
A. 1 3/4 cups
B. 8 3/4 cups
C. 12 1/4 cups
D. 22 3/4 cups
Answer:
A
Step-by-step explanation:
small dog eats 3/4 cup each day
large dog eats 1 cup each day
~after 1 week (x7)~
small dog = 5.25 cups
large dog = 7 cups
(7-5.25=1.75)
= therefore 1 and 3/4 cups
A student-faculty government committee of 4 people is to be formed from 20 student
volunteers and 5 faculty volunteers.
a. If one person from the group of volunteers is chosen at random to draw the names
out of a hat, what is the probability that the person drawing the names is a student?
b. How many ways can the committee of four be formed if there are no restrictions on
composition.
C. How many ways can two of the students be chosen?
d. How many ways can 2 faculty be chosen?
e. What is the probability that the random selection of the four-person committee will
result in two students and two faculty?
the answer is c i just had this question your welcome
TZ is a midsegment, which of the following statements CANNOT be true
Answer:
Option C: QT < TR
Step-by-step explanation:
From the triangle, we can see that UX bisects RS into two equal parts and so it is a perpendicular bisector.
TZ Is a mid segment and it means that T bisects QR into 2 equal parts as well as QS into 2 equal parts.
Thus;
QT = QR
And QZ = SZ
So Option C is not correct because QT = QR
The graph of f(x) with the graph of w(x)=(x-6)^2
Answer:
A
Step-by-step explanation:
graph is 6 units to the right
if it had been (x+6)^2
it would have been 6 units to left
Will give brainliest answer
Answer: 2/5x to the second.
may I have the brainiest? pls
Question 3
A 70kg patient has approximately 8 pints of blood. The patient donates 470mL of blood.
Approximately what fraction of his body's blood is this? (one pint = 568mL)
Step-by-step explanation:
Given that,
The mass of a patient = 70 kg
A 70kg patient has approximately 8 pints of blood.
The patient donates 470mL of blood.
We know that,
1 pint = 568 mL
8 pints = 4544 mL
Required fraction,
[tex]\dfrac{470}{4544}=0.1\\\\=\dfrac{1}{10}[/tex]
So, the required fraction is approximately [tex]\dfrac{1}{10}[/tex].
Lolz please help me I would gladly appreciate it
Pentagon has sum of 540°
A line passes through the point (-9, 4) and has a slope of 2/3.
Write an equation in slope-intercept for this line.
Answer:
y=(2/3)x+10
Hope it helps!
My graph isn't really clear
The slope-intercept of the line that passes through the point (-9, 4) and has a slope of 2/3 will be y = (2/3)x + 10.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A line is given as y = mx + c
Here m is the slope,
Put m = 2/3 and (-9, 4)
4 = (2/3)(-9) + c
c = 10
Thus equation will be y = (2/3)x + 10.
Hence "Y = (2/3)x + 10 is the slope-intercept of the line passing through the point (-9, 4), which has a slope of 2/3".
For more about the linear function,
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find out the Range coefficient of the range
marks number of students
20-29 8
30-39 12
40-49 20
50-59 7
60-69 3
Answer:
0.4494
Step-by-step explanation:
Given :
marks number of students
20-29 8
30-39 12
40-49 20
50-59 7
60-69 3
The range Coefficient is obtained thus :
Range Coefficient = (Xm - Xl) / (Xm + Xl)
Where ;
Xm = Mid value of highest class = (60+69)/2 = 64.5
Xl = Mid value of lowest class = (20+29)/2 = 24.5
Range Coefficient = (64.5 - 24.5) / (64.5 + 24.5)
Range Coefficient = 40 / 89 = 0.4494
Amy worked 37.5 hours last week.
She is paid £11.50 per hour.
Her total deductions last week were £116.30.
What was Amy’s net pay last week?
£
2.6.5 A plant physiologist grew birch seedlings in the green-house and measured the ATP content of their roots. (See Example 1.1.3.) The results (nmol ATP/mg tissue) were as follows for four seedlings that had been handled identically.39 1.45 1.19 1.05 1.07 Calculate the mean and the S
Answer:
[tex](a)\ \bar x = 1.19[/tex]
[tex](b)\ \sigma_x = 0.18[/tex]
Step-by-step explanation:
Given
[tex]n = 4[/tex]
[tex]x: 1.45\ 1.19\ 1.05\ 1.07[/tex]
Solving (a): The mean
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x = \frac{1.45 + 1.19 + 1.05 + 1.07}{4}[/tex]
[tex]\bar x = \frac{4.76}{4}[/tex]
[tex]\bar x = 1.19[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}[/tex]
So, we have:
[tex]\sigma_x = \sqrt{\frac{(1.45 -1.19)^2 + (1.19 -1.19)^2 + (1.05 -1.19)^2 + (1.07 -1.19)^2}{4 - 1}}[/tex]
[tex]\sigma_x = \sqrt{\frac{(0.1016}{3}}[/tex]
[tex]\sigma_x = \sqrt{0.033867}[/tex]
[tex]\sigma_x = 0.18[/tex]
Simplify this plz thanks
Answer:
[tex]\frac{1}{g^{5nd+10v+20dv} }[/tex]
Step-by-step explanation:
Jen recently rode her bicycle to visit her friend who lives 6 miles away. On her way there, her average speed was & miles per hour faster than on her way home. If jen
spent a total of 2 hours bicycling find the two rates.
Answer:
(1) +t+=+1.2+ hrs
Step-by-step explanation:
what is the value of digit 6 in9.78265.
Answer: uhh I think 60?
Step-by-step explanation:
the answer is 6p because after any value place is zero hoped I helped
Find the area of the shaded region. Round to the nearest tenth. 11.1m 130°
Area = [ ? ] m²
The area of the shaded region is 294.5 m².
What is the area of the entire circle?The area of the entire circle is calculated as follows;
A = πr²
where;
r is the radius of the circleA = π ( 11.1² )
A = 387.1 m²
The area of the sector is calculated as follows;
A = ( θ/360 ) πr²
A = ( 130/360 ) x π ( 11.1² )
A = 139.8 m²
The area of the triangle is calculated as follows;
A = ¹/₂ ( sinθ )r²
A = ¹/₂ ( sin 130 ) (11.1²)
A = 47.2 m²
Area of the unshaded region is calculated as;
A' = 139.8 m² - 47.2 m²
A' = 92.6 m²
The area of the shaded region is calculated as follow;
A'' = 387.1 m² - 92.6 m²
A'' = 294.5 m²
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What is the value of x?
Answer:
Step-by-step explanation:
the ratio of 24 to 36 is the same as x to 12
[tex]\frac{24}{36}[/tex] = [tex]\frac{x}{12}[/tex]
then
12*([tex]\frac{24}{36}[/tex])=x
[tex]\frac{24}{3}[/tex] = x
8 = x
that's it :)
Please help asap I needs someone to find the addition property added
A
Step-by-step explanation:
you can notice that at step 2 9 is added on both sides that is the addition property of equality
The sum of two six-digit numbers is a seven-digit number
Answer
500,000 + 500,000 = 1,000,000
Step-by-step explanation: