Answer:
y=1/3x+4
Step-by-step explanation:
It should be correct as the gradient = 1/3
and the y-intercept = C
= +4
if m<2, then m<1 is...
Answer:
45
Step-by-step explanation:
m<1 and m<2 are complementary angles because the sum of two angles = 90° and since m<1 = m<2
90 ÷ 2 = 45
Find the a. MEAN and b. STANDARD DEVIATION for the data set. Round to two decimal places.
10) Country Number of Television Sets per 100 people
A 124
B 94
C 129
D 109
E 114
A) a. 115
b. 13.69
B)
a. 114
b. 13.69
C)
a. 114
b. 169
D) a. 113
b. 13.69
Provide an appropriate response.
11) If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume?
A) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured.
B) His height measurement is in the same range as about 95% of the other adult males whose heights were measured.
C) He is taller than about 99.7% of the other men whose heights were measured.
D) He is taller than about 95% of the other men whose heights were measured. The scores on a driver's test are normally distributed with a mean of 100. Find the score that is:_____
12) Find the score that is 2 standard deviations below the mean, if the standard deviation is 26.
A) 126
B) 48
C) 152
D) 74
Suppose that prices of a certain model of new homes are normally distributed with a mean of $150,000. Use the 68-95-99.7 rule to find the percentage of buyers who paid:____
13) between $147,700 and $152,300 if the standard deviation is $2300.
A) 34%
B) 95%
C) 99.7%
D) 68%
14) more than $154,800 if the standard deviation is $2400.
A) 95%
B) 2.5%
C) 47.5%
D) 97.5%
A set of data items is normally distributed with a mean of 60. Convert the data item to a z-score, if the standard deviation is as given. 15) data item: 100; standard deviation:_____
a) 10
b) 40
c) 10
d) 4/3
Answer:
Explained below.
Step-by-step explanation:
(10)
The data set is:
S = {124, 94, 129, 109, 114}
The mean and standard deviation are:
[tex]\bar x=\frac{1}{n}\sum x=\frac{1}{5}\times [124+94+...+114]=114\\\\s=\sqrt{\frac{1}{n-1}\sum ( x-\bar x)^{2}}[/tex]
[tex]=\sqrt{\frac{1}{5-1}\times [(124-114)^{2}+(94-114)^{2}+...+(114-114)^{2}]}\\=\sqrt{\frac{750}{4}}\\=13.6931\\\approx 13.69[/tex]
The correct option is B.
(11)
According to the Empirical 95% of the data for a Normal distribution are within 2 standard deviations of the mean.
So, the adult male's height is in the same range as about 95% of the other adult males whose heights were measured.
The correct option is B.
(12)
Let the score be X.
Given:
μ = 100
σ = 26
[tex]X=\mu-2\sigma[/tex]
[tex]=100-(2\times 26)\\=100-52\\=48[/tex]
The correct option is B.
(13)
Let X be the prices of a certain model of new homes.
Given: [tex]X\sim N(150000, 2300^{2})[/tex]
Compute the percentage of buyers who paid between $147,700 and $152,300 as follows:
[tex]P(147700<X<152300)=P(\frac{147700-150000}{2300}<\frac{X-\mu}{\sigma}<\frac{152300-150000}{2300})[/tex]
[tex]=P(-1<Z<1)\\=0.68\\[/tex]
According to the 68-95-99.7, 68% of the data for a Normal distribution are within 1 standard deviations of the mean.
The correct option is D.
(14)
Compute the percentage of buyers who paid more than $154,800 as follows:
[tex]P(X>154800)=P(\frac{X-\mu}{\sigma}>\frac{154800-150000}{2400})[/tex]
[tex]=P(Z>2)\\=0.975\\[/tex]
According to the 68-95-99.7, 95% of the data for a Normal distribution are within 2 standard deviations of the mean. Then the percentage of data above 2 standard deviations of the mean will be 97.5% and below 2 standard deviations of the mean will be 2.5%.
The correct option is D.
(15)
The z-score is given as follows:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
What is the distance between point (6, -1) and point (5, 3) rounded to the nearest tenth?
Answer:
The answer is
4.1 units
Step-by-step explanation:
The distance between two points can be found using the formula
[tex] \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } [/tex]where
( x1 , y1) and ( x2 , y2) are the points
From the question
The points are (6, -1) and (5, 3)
The distance between the points is
[tex] \sqrt{( {6 - 5})^{2} + ({ - 3 - 1})^{2} } [/tex][tex] = \sqrt{ {1}^{2} + ( { - 4})^{2} } [/tex][tex] = \sqrt{1 + 16} [/tex][tex] = \sqrt{17} [/tex]= 4.123105
We have the final answer as
4.1 unitsHope this helps you
need help with this question
Answer:
25) -76
26) -23
27) 21
28) 8
Step-by-step explanation:
25) (-32)-44=-32-44=-76
26) (-12)+(-11)=-12-11=-23
27) 2+15+4=17+4=21
28) 16+(-13)+5=16-13+5=3+5=8
Step-by-step explanation:
Hope it helps u mate
plz mark it as brainlist
A line slope of 2 passes through the point (4,8). What is the equation in slope-intercept form?
A right triangle has vertices (−7,9),(3,9),(−7,−15). Find the perimeter of the triangle.
The perimeter of a triangle is 60 units if the right triangle has the vertices (-7, 9), (3, 9), (-7, -15).
What is meant by perimeter?The perimeter calculation has various practical uses. A calculated perimeter is the length of fencing required to encircle a yard or garden. The circumference (perimeter) of a wheel/circle specifies how far it will roll in one revolution.
If the lengths of the triangle's sides are a, b, and c, the perimeter is the sum of their lengths:
P = a + b + c
The distance formula can be used to calculate any of the side lengths. However, because two of the sides are parallel to the axes, their lengths may be simply calculated by subtracting coordinates.
If the points are designated A, B, and C in that sequence, the two right-angle sides are as follows:
c = AB
= 3 -(-7)
= 10
b = AC
= 9 -(-15)
= 24
The Pythagorean theorem states that the third side of the relation can be found:
a² = b² +c²
a² = 10² +24² = 676
a=√676
a= 26
Now we can plug these numbers into the perimeter formula:
P = a + b + c = 26 + 24 + 10
P = 60
As a result, the perimeter of a triangle is 60 units.
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Which number best represents the slope of the graphed line?
Answer:
the answer is A.
Step-by-step explanation:
for every time you move over one in the x axis you move down 5 on the y axis
If you roll a 6-sided die 4 times, what is the probability of one roll being a multiple of 3? A)2/3 B)16/81 C)145/1296 D)65/81 E)625/1296 (I really need help! Pls answer fast!)
Answer:
671/1296
The probability of rolling at least one six is therefore 1 − 625/1296 = 671/1296 ≈ . 517.
Step-by-step explanation:
Answer:
671/1296
Step-by-step explanation:
pt 2 6-7 Pleaseee Helpp
Answer:
w = 15
Step-by-step explanation:
5
x ___w___ = 3 x 5
5
w = 15
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------
Answer: w = 15~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]\frac{w}{5} = 3[/tex]
Multiply both sides by 5.
[tex]w = 3 \times 5[/tex]
Multiply 3 and 5 to get, you guessed it, 15!2. What is the sum of the three solutions (find the values for x, y, and z, then add the answers)?
2x + 3y − z = 5 x
− 3y + 2z = −6
3x + y − 4z = −8
please show steps
Answer:
x = 30/7 , y = 46/7 , z = 48/7
Step-by-step explanation:
Solve the following system:
{2 x + 3 y - z = 5 x | (equation 1)
2 z - 3 y = -6 | (equation 2)
3 x + y - 4 z = -8 | (equation 3)
Express the system in standard form:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x - 3 y + 2 z = -6 | (equation 2)
3 x + y - 4 z = -8 | (equation 3)
Add equation 1 to equation 3:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x - 3 y + 2 z = -6 | (equation 2)
0 x+4 y - 5 z = -8 | (equation 3)
Swap equation 2 with equation 3:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y - 5 z = -8 | (equation 2)
0 x - 3 y + 2 z = -6 | (equation 3)
Add 3/4 × (equation 2) to equation 3:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y - 5 z = -8 | (equation 2)
0 x+0 y - (7 z)/4 = -12 | (equation 3)
Multiply equation 3 by -4:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y - 5 z = -8 | (equation 2)
0 x+0 y+7 z = 48 | (equation 3)
Divide equation 3 by 7:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y - 5 z = -8 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Add 5 × (equation 3) to equation 2:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+4 y+0 z = 184/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Divide equation 2 by 4:
{-(3 x) + 3 y - z = 0 | (equation 1)
0 x+y+0 z = 46/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Subtract 3 × (equation 2) from equation 1:
{-(3 x) + 0 y - z = -138/7 | (equation 1)
0 x+y+0 z = 46/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Add equation 3 to equation 1:
{-(3 x)+0 y+0 z = -90/7 | (equation 1)
0 x+y+0 z = 46/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Divide equation 1 by -3:
{x+0 y+0 z = 30/7 | (equation 1)
0 x+y+0 z = 46/7 | (equation 2)
0 x+0 y+z = 48/7 | (equation 3)
Collect results:
Answer: {x = 30/7 , y = 46/7 , z = 48/7
Choose the function that correctly identifies the transformation of f(x) = x2 shifted two units down and one unit to the left. g( x) = ( x + 1) 2 + 2 g( x) = ( x - 1) 2 + 2 g( x) = ( x + 1) 2 - 2 g( x) = ( x - 1) 2 - 2
Answer:
g(x)= (x +1)^2 -2
Step-by-step explanation:
What is value of
X+8
Enter your answer in the box
2x-5
B
10
14
Plz help
Answer:
not 100% but i think x may be 23.5
Step-by-step explanation:
The values of (x+8) and (2x-5) are 35 and 49 respectively.
What is a triangle?A triangle is defined as a two-dimensional shape with three sides, three interior angles, and three vertices.
Given a triangle, ABC
We have,
(x+8)/10 = (2x-5)/14
7x+56 = 10x-25
3x = 81
x = 27
X+8 = 35
2x-5 = 49
Hence, The values of (x+8) and (2x-5) are 35 and 49 respectively.
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add or subtract as indicated and write the result in standard form 3i+(-6-i)
A:6-4i
B:-6+2i
C:6-2i
D:-6+4i
Answer:
B: -6+2i
Step-by-step explanation:
3i + (-6 - i) = ⇒ open parenthesis3i - 6 - i = ⇒ simplify-6 + 2i ⇒ answer in standard form of a+bithe projected number of employed writers and authors in 2016 is 153,000. 12.4% of those will have some college experience but no degree, and 84.1% will have a bachelors degree or higher. If this holds true, how many more writers and authors with bachelors degree will be there than those with only some college experience and no degree?
Answer:
Step-by-step explanation:
12.4% 153000 = 12.4/ 100 * 153000 = 0.124 * 153000 = 1897
84.1% 153000 = 84.1/100 * 153000 = 0.841 * 153000 = 128673
The difference (and the answer) is 128673 - 1897 = 126776
Note: 3.5% are not accounted for. They probably just sat down and wrote.
Given that Cos60=sin30=1/2 and cos30=sin60=root3/2.Evaluate tan60-1/1-tan30
Answer:
1/2
Step-by-step explanation:
The value of the given expression is 1 / √3.
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle termed trigonometry.
The given values are cos60=sin30=1/2 and cos30=sin60=√3/2.
Divide sin30 and cos30,
[tex]\dfrac{sin30}{cos30}=tan30 = \dfrac{\dfrac{1}{2}}{\dfrac{2}{\sqrt{3}}}=\dfrac{1}{\sqrt{3}}[/tex]
Divide sin60 and cos60.
[tex]\dfrac{sin60}{cos60}=tan60 = \dfrac{\dfrac{2}{\sqrt{3}}}{\dfrac{1}{2}}= \sqrt3[/tex]
The value of the expression is.
[tex]\dfrac{ tan60-1}{1-tan30}=\dfrac{\sqrt{3}-1}{\sqrt{3}-1}}\times \dfrac{1}{\sqrt{3}}=\dfrac{1}{\sqrt{3}}[/tex]
Therefore, the value of the given expression is 1 / √3.
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determine whether y = 4x+5 and y= 1/4x-2 are perpendicular
Answer:
No, they are not perpendicular
Step-by-step explanation:
Perpendicular lines will have opposite reciprocal slopes, meaning that the slopes will have opposite signs and be the reciprocals of each other.
We can see that the slopes of the lines are not opposite reciprocals.
4 and 1/4 are not opposite reciprocals because they do not have opposite signs.
Please help. Will select brainliest.
Answer:
Heptagon: D
Spetagon: D
Nonagon: B
Describe the relationship between the values of the two 7s in the number 3,772 what equation could you use to help describe the relationship
Answer:
y = 10x, which is the relationship between two 7 in the number 3772
Step-by-step explanation:
In the given number 3772
3 is at thousandth position its value is 3000 numerically
7 is at the hundredth position its value is 700 numerically
next 7 is at tens position its value is 70 numerically
and 2 is at unit position its value is 2 numerically
thus, 3772 can also be written as sum of number based on its position
3000
+700
+ 70
+ 2
___-
= 3772
Thus,
since Third 7 from left has value of 70
and Second 7 from left has value of 700
we know 70*10 = 700
Thus, 70 is 10 times to that 700
Thus, we can say that
value of Second 7 from left = 10*value of Third 7 from left
Thus,
let value of Second 7 from left be y
value of Third 7 from left be x
then
y = 10x, which is the relationship between two 7 in the number 3772
Pre Calc Introduction to Derivatives-Using Limits Help!
Answer:
Attachment 1 : Option A,
Attachment 2 : Option D,
Attachment 3 : Option B,
Attachment 4 : Instantaneous rate of change will be 24
Step-by-step explanation:
"Remember that we can solve such questions by finding the derivative first"
1 : Let's consider this approach a bit differently. If we were to graph this function, we would see that the point (-2,26) would lie on the curve having a negative slope.
The rate of change would thus be negative, eliminating choices b and d. And, the slope of this function would be much greater than 4 due to the coefficient of " 5 " in f(x) = 5x² + 6. Hence our answer will be option a.
2 : f'(5) = - 2 * 5 + 4,
f'(5) = - 10 + 4 = - 6
Your solution is option d.
3 : f'(2) = 12 / 2 + 1 / - 3,
f'(2) = 12 / 3 / - 3 = 4 / - 3,
f'(2) = - 4 / 3
Your solution is option b.
4 : Here again we can apply the power rule, where using constant multiple rule and derivative of a constant, you can quickly find the derivative of g .
g'(t) = 3(2x¹) + 0 = 6t,
And now we can evaluate the derivative at that value of t.
g'(4) = 6(4) = 24 - hence the instantaneous rate of change at t = 4, will be 24
5. Evaluate
a) (-3)²/(-9/4)²
Answer:
16/9
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Exponents
(-3)² = 9
(-9/4)² = 81/16
9/81/16
Step 2: KCF (Keep Change Flip)
9(16/81)
144/81
Step 3: Simplify
144/9 = 16
81/9 = 9
16/9
100 megatons+234 help please
Answer:
we know,
1 megaton=1000kg
100 megaton=100000
now,
total weight=100000+234
=100234.
It is also known that customers will spend an average of $178 on additional maintenance. The standard deviation of the expenses is $50. If a simple random sample of 100 customers is taken: What is the probability that the sample mean will be between 166.75 and $170.50
Answer:
probability that the sample mean will be between 166.75 and $170.50 = 0.42816
Step-by-step explanation:
We are given;
Mean; μ = $178
Standard deviation; σ = $50
Now, we want to find the probability that the sample mean will be between $166.75 and $170.50.
Thus, we'll use the z-score formula;
z = (x - μ)/σ
So;
Lower limit of z is;
z = (166.75 - 178)/50
z = -0.225
Upper limit of z is;
z = (170.50 - 178)/50
z = -0.15
From the z-distribution table attached, the area between -0.225 and -0.15 is;
0.44038 - 0.01222 = 0.42816
In 2003, the population of an African country was about 10.2 million people, which is 1 million more than 4 times the population in 1950. Enter and solve an equation to find the approximate population p (in millions) in 1950. An equation is . The approximate population in 1950 was million people.
Dan invests £11125 into his bank account. He receives 3.3% per year simple interest. How much will Dan have after 4 years? Give your answer to the nearest penny where appropriate.
Answer:
£11564.54
Step-by-step explanation:
100 + 3.3 = 103.3%
103.3% = 1..013
£11125 x 1.013^3 = £11564.54
I hope this helped you!
g In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that: (a) the first question she gets right is the 5th question
Answer:
81 / 1024
Step-by-step explanation:
First, let's find the total number of ways that Nancy can choose random choices for the questions. This would be 4 * 4 * 4 * 4 * 4 = 4⁵ = 1024 because there are 4 choices and 5 questions. In order for first question she gets right to be the 5th question, she has to get the first 4 questions wrong. Therefore, since there are 4 choices for each question and only 1 of them is right, she has 4 - 1 = 3 options for the first 4 questions and only 1 option for the 5th one, so the total number of "successful" ways Nancy can do this would be 3 * 3 * 3 * 3 * 1 = 81. Therefore, the probability is 81 / 1024.
Luke is 5 years younger than 3 times Sydney's age, s. In this situation, what does 3s represent?
0 Luke's age
O Sydney's age
o three times Luke's age
O three times Sydney's age
Answer:
Step-by-step explanation:
'3s' represents 'three times Sydney's age.'
Answer:
three times Sydney's age
Step-by-step explanation:
i took a test on this
A past survey of students taking a standardized test revealed that % of the students were planning on studying engineering in college. In a recent survey of students taking the SAT, % of the students were planning to study engineering. Construct a % confidence interval for the difference between proportions by using the following inequality. Assume the samples are random and independent.
The confidence interval is __
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is [tex]-0.00870 <p_1 -p_2 < -0.007297[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 1068000[/tex]
The first proportion [tex]\r p_1 = 0.084[/tex]
The second sample size is [tex]n_2 = 1476000[/tex]
The second proportion is [tex]\r p_2 = 0.092[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
From the normal distribution table we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] the value is
[tex]Z_{\frac{\alpha }{2} } =z_c= 1.96[/tex]
Now using the formula from the question to construct the 95% confidence interval we have
[tex](\r p_1 - \r p_2 )- z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2} } <p_1 -p_2 < (\r p_1 - \r p_2 )+ z_c \sqrt{ \frac{\r p_1 \r q_1 }{n_1} + \frac{\r p_2 \r q_2 }{n_2} }[/tex]
Here [tex]\r q_1 = 1 - \r p_1[/tex]
=> [tex]\r q_1 = 1 - 0.084[/tex]
=> [tex]\r q = 0.916[/tex]
and
[tex]\r q_2 = 1 - \r p_2[/tex]
=> [tex]\r q_2 = 1 - 0.092[/tex]
=> [tex]\r q_2 = 0.908[/tex]
So
[tex](0.084 - 0.092 )- (1.96)* \sqrt{ \frac{0.092* 0.916 }{1068000} + \frac{0.084* 0.908 }{1476000} } <p_1 -p_2 < (0.084 - 0.092 )+ (1.96)* \sqrt{ \frac{0.084* 0.916 }{1068000} + \frac{0.092* 0.908 }{1476000} }[/tex]
[tex]-0.00870 <p_1 -p_2 < -0.007297[/tex]
A(n) ___
is a numerical summary of a population.
Answer:
parameter
Step-by-step explanation:
A password contains three digits, such as 175. How many different passwords can be formed?
Answer: There are 1000 different passwords.
Step-by-step explanation:
Given: A password contains three digits.
Number of digits from 0 to 9 = 10
Using fundamental principle of counting,
The number of different passwords = (Number of choices for digits) x (Number of choices for digits) x (Number of choices for digits)
= (10) x (10)x (10)
=1000
Hence, there are 1000 different passwords.
20 points! Each month, Sal must pay for car insurance and fuel to drive a vehicle. Sal's parents agree to pay p percent of his car expenses. The cost of car insurance is the same every month, but the cost of fuel depends on d, the number of miles Sal drives. The expression (1−p)(0.10d+60) represents how much Sal must pay toward his monthly car expenses. Which part of the expression represents the percentage of the monthly expenses that Sal must pay? 0.10d + 60 1−p 60 0.10d
Answer:
1 - p
Step-by-step explanation:
The cost of insurance is constant, this is 60.The cost of fuel is 0.10d as d is the number of miles.The only variable left is 1-p which represents the percentage of expensesSo the answer is:
1 - pAnswer:
1-p
Step-by-step explanation:
I took the test and this was the answer.