Answer:
The answer is obtained by dividing 13.5 by 1.125 (1 1/8th) = 12 miles per gallon
what should she use as her common denominator
why does gradient normal x gradient tangent = -1 ??
Answer:
Gradient normal x gradient tangent = -1 is a mathematical expression that relates the normal and tangent vectors of a curve in three-dimensional space. The gradient of a scalar function is a vector that points in the direction of the greatest rate of increase of the function. The normal vector is perpendicular to the surface defined by the function, and the tangent vector is a vector that lies on the surface and points in the direction of the curve.
In mathematics, the cross product of two vectors is a vector that is orthogonal to both vectors, and the magnitude of the cross product is equal to the product of the magnitudes of the two vectors multiplied by the sine of the angle between them. In this case, the normal and tangent vectors of a curve form an orthogonal basis, meaning that they are perpendicular to each other. The expression gradient normal x gradient tangent = -1 says that the magnitude of the cross product of the normal and tangent vectors is equal to -1. This means that the normal and tangent vectors form a right-handed coordinate system, where the cross product is negative because the normal vector points in the opposite direction to the positive z-axis.
Find the sum of the infinite geometric sequence.
If the answer is not an integer, enter it as a fraction in simplest form.
The sum of the infinite geometric sequence is 3 3/4
How to find the sum of the infinite geometric sequence.From the question, we have the following parameters that can be used in our computation:
The geometric sequence
In the geometric sequence, we have
First term, a = 3/5¹⁻¹
a = 3
Also, we have
Common ratio, r = 1/5
The sum of the infinite geometric sequence is calculated as
Sum = a/(1 - r)
So, we have
Sum = 3/(1 - 1/5)
Evaluate
Sum = 3 3/4
Hence, the sum of the infinite geometric sequence is 3 3/4
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What is the value of u
u=______°
Answer:
u=94 Hope that helps. Mark as brainliest it helps
The mean cost of a five pound bag of shrimp is 40 dollars with a standard deviation of 8 dollars.
If a sample of 49 bags of shrimp is randomly selected, what is the probability that the sample mean would be less than 37.4 dollars? Round your answer to four decimal places.
Answer:
The mean of the sample distribution of the sample mean is the same as the population mean, which is 40 dollars. The standard deviation of the sample distribution of the sample mean (also called the standard error) is given by:
standard error = standard deviation / sqrt(sample size) = 8 / sqrt(49) = 8 / 7
To find the probability that the sample mean would be less than 37.4 dollars, we need to standardize the sample mean using the standard error and then look up the probability from a standard normal distribution table. The z-score for a sample mean of 37.4 dollars is:
z = (37.4 - 40) / (8 / 7) = -1.225
Looking up this z-score in a standard normal distribution table, we find that the probability of getting a sample mean less than 37.4 dollars is 0.1103 (rounded to four decimal places). Therefore, the probability that the sample mean would be less than 37.4 dollars is 0.1103.
give thanks, your welcome <3
Step-by-step explanation:
A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape.
389 357 359 364 375 424 326 395 402 373
374 371 365 367 365 326 339 393 392 369
374 359 357 403 335 397
A normal probability plot of the n 26 observations on escape time given above shows a substantial linear pattern; the sample mean and sample standard deviation are 371.08 and 24.45, respectively. (Round your answers to two decimal places.)
Required:
a. Calculate an upper confidence bound for population mean escape time using a confidence level of 95%.
b. Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.
Answer:
The upper confidence bound for population mean escape time is: 379.27
The upper prediction bound for the escape time of a single additional worker is 413.64
Step-by-step explanation:
Given that :
sample size n = 26
sample mean \(\bar x\) = 371.08
standard deviation \(\sigma\) = 24.45
The objective is to calculate an upper confidence bound for population mean escape time using a confidence level of 95%
We need to determine the standard error of these given data first;
So,
Standard Error S.E = \(\dfrac{\sigma }{\sqrt{n}}\)
Standard Error S.E = \(\dfrac{24.45 }{\sqrt{26}}\)
Standard Error S.E = \(\dfrac{24.45 }{4.898979486}\)
Standard Error S.E = 4.7950
However;
Degree of freedom df= n - 1
Degree of freedom df= 26 - 1
Degree of freedom df= 25
At confidence level of 95% and Degree of freedom df of 25 ;
t-value = 1.7080
Similarly;
The Margin of error = t-value × S.E
The Margin of error = 1.7080 × 4.7950
The Margin of error = 8.18986
The upper confidence bound for population mean escape time is = Sample Mean + Margin of Error
The upper confidence bound for population mean escape time is = 371.08 + 8.18986
The upper confidence bound for population mean escape time is = 379.26986 \(\approx\) 379.27
The upper confidence bound for population mean escape time is: 379.27
b. Calculate an upper prediction bound for the escape time of a single additional worker using a prediction level of 95%.
The standard error of the mean = \(\sigma \times \sqrt{1+ \dfrac{1}{n}}\)
The standard error of the mean = \(24.45 \times \sqrt{1+ \dfrac{1}{26}}\)
The standard error of the mean = \(24.45 \times \sqrt{1+0.03846153846}\)
The standard error of the mean = \(24.45 \times \sqrt{1.03846153846}\)
The standard error of the mean = \(24.45 \times 1.019049331\)
The standard error of the mean = 24.91575614
Recall that : At confidence level of 95% and Degree of freedom df of 25 ;
t-value = 1.7080
∴
The Margin of error = t-value × S.E
The Margin of error = 1.7080 × 24.91575614
The Margin of error = 42.55611149
The upper prediction bound for the escape time of a single additional worker is calculate by the addition of
Sample Mean + Margin of Error
= 371.08 + 42.55611149
= 413.6361115
\(\approx\) 413.64
The upper prediction bound for the escape time of a single additional worker is 413.64
out of 80,000 seats in a cricket stadium 12% seats were there occupied by vips and 39040 seats by general public what percentage of the stadium remained un occupied?
Answer:
% of unoccupied seats = 63.2 %
Step-by-step explanation:
Total seats = 80, 000
VIP seats = 12 % of 80, 000
\(= \frac{12}{100} \times 80000\\\\= 9600\)
General Seats = 39040
Remaining seats = 80000 - 9600 - 39040 = 50, 560
Percentage of un-occupied seats,
\(= \frac{50560}{80000} \times 100 = 63.2 \%\)
Answer:
THE NUMBER OF SEATS OCCUPIED BY VIPS=80000×12/100
=9600
occupied seats=9600+39040
=48640
number of unoccupied seats=80000-48640
=31360
percentage of unoccupied seats=31360/80000×100%
=39.2%
Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any resulting triangle(s).b=5 c=6 B=20 degreesA) single triangle is produced, where C degrees=___. A degrees=___ a=____B) Two triangles are produced, where the triangle with the smaller angle C has C1= ___ A1=____ and a1=____ / Triangle with the larger angles has C2=___ A2=___ and a2=____C) No triangles are produced
Using the Law of Sines, we get an angle of 2.41 degrees and no triangles are produced.
Option (C) is the correct one.
Given, Two sides and an angle are given below.
we have to determine whether the given information results in one triangle, two triangles, or no triangle at all.
If b = 5, c = 6 and B = 20 degrees in the triangle.
On using the concept of Laws of Sines, we get
sinA/a = sinB/b = sinC/c
sin 20°/5 = sin C/6
0.34/5 = sin C/6
0.007 = sin C/6
sin C = 0.042
C = 2.41
So, the angle C be 2.41 degrees.
which implies that no triangle can be formed or produced with the given data of the triangle.
Hence, No triangles are produced.
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cual de estos tipos de mentalidad puede contribuir a superar situaciones de no inclusión porque
La mentalidad de crecimiento, ya que a diferencia de la mentalidad fija, nos permite ver en otras personas la mentalidad de mejorar y perseverar.
Which statements about f(x) = −(x − 7)2 + 4 are true?
Select all that apply.
Answer:
x=9
Step-by-step explanation:
f(x) = −(x − 7)2 + 4
(substitute f(x) = 0)
0= −(x − 7)2 + 4
(distribute 2 into brackets)
0= −(2x - 14) + 4
(remove brackets and change the sign of each expression inside the brackets)
0= - 2x + 14 + 4
(add the numbers)
0= - 2x + 18
(move variable to the other side and change its sign)
2x = 18
(divide both sides by 2)
x = 9
The given expression is quadratic, parabolic graph, relative maxima and real zeros. The correct options are (a), (c) and (f).
What is a quadratic equation?The general form of a quadratic equation is given as ax^2 + bx + c = 0.
Here, a ≠ 0 and b and c are integers.
The degree of a quadratic equation is 2.
The given expression is f(x) = -(x - 7)² + 4
Since the degree of the expression is 2, it is quadratic.
The graph of the given equation will be parabolic.
By comparing from the general vertex form (x - h)² + k, its vertex can be found as (7, 4).
Axis of symmetry is x = 7.
y-intercept can be obtained by plugging x = 0 as,
-(0 - 7)² + 4 = 53.
Maxima or minima can be found as below,
f'(x) = 0
⇒ -2(x - 7) = 0
⇒ x = 7
In order to find the solution write the expression as follows,
-(x - 7)² + 4 = 0
⇒ -x² + 14x - 49 + 4 = 0
⇒ x² - 14x + 45 = 0
⇒ x = 5,9
Thus, the equation has real solutions.
Hence, the properties of the given equation are derived as quadratic, parabolic graph, relative maxima and real zeros.
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. A cocoa blender makes a profit of 30% be selling a super mix cocoa at Kshs.650 for 250 grams tin. He makes a super mix cocoa by blending two varieties of cocoa., A and which cost him Kshs. 1 800 and Kshs.2 400 per kg respectively. B In what proportion the cocoa types A and B mixed? were (3 marks)
Answer:
The cost price of 250 grams of super mix cocoa is Kshs.650/1.3=Kshs.500.
The cost price of 1 kg of super mix cocoa is Kshs.500*4=Kshs.2000.
If x kg of cocoa A is mixed with (1-x) kg of cocoa B, then the cost price of the mixture is Kshs.1800x+Kshs.2400(1-x).
Therefore, Kshs.1800x+Kshs.2400(1-x)=Kshs.2000.
Solving for x, we get x=2/3.
Therefore, the cocoa types A and B are mixed in the proportion 2:1.
A study was performed with a random sample of 5 people from a certain city. What population would be appropriate for generalizing conclusions from the study, assuming the data collection methods used did not introduce biases?
The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
High sample size is typically crucial in order to be able to draw generalizations from a sample, aside from avoiding bias. Since the sample size is modest, it will thus be possible to draw general conclusions about the study utilizing a larger sample, in my opinion.
The size of the sample has a significant impact on whether an experiment is legitimate. The central limit theorem states that as sample size rises, the sample mean approaches the population means value.
Because of this, generalizing from just five samples regarding a population of city dwellers won't produce a result that can be generalized.
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A report included the following information on the heights (in.) for non-Hispanic white females.
Sample Sample Std. Error
Age Size Mean Mean
20–39 868 65.9 0.09
60 and older 934 64.3 0.11
(a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use μ20–39 − μ60 and older.) , Interpret the interval
(b) Let μ1 denote the population mean height for those aged 20–39 and μ2 denote the population mean height for those aged 60 and older. Interpret the hypotheses H0: μ1 − μ2 = 1 and Ha: μ1 − μ2 > 1.
Carry out a test of these hypotheses at significance level 0.001. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
(c) Based on the P-value calculated in (b) would you reject the null hypothesis at any reasonable significance level? Explain your reasoning.
(d) What hypotheses would be appropriate if μ1 referred to the older age group, μ2 to the younger age group, and you wanted to see if there was compelling evidence for concluding that the population mean height for younger women exceeded that for older women by more than 1 in.?
Following are the solution to the given points:
In point a:
When 95% are confidence interval:
\(=( \mu_{20-39} - \mu_{60})+(-z_{0.025})((0.09)^2+(0.11)^2)^{0.5} \\\\= (65.9-64.3)+(-1.96) \times 0.14213\\\\=(1.3214, 1.8786)\)
In point b:
\(H_0: \mu_1 - \mu_2 =1\\\\ H_a: \mu_1 - \mu_2 > 1\)
In the Z test statistic:
\(= \frac{((65.9-64.3)-1)}{((0.09)^2+(0.11)^2)^{0.5}} \\\\= 4.22 \\\\\to p= 0.000012\)
In point c:
The rejection value of the null hypothesis as \(p< 0.001\)
In point d:
\(H_0: \mu_2 -\mu_1 = 1 \\\\H_a: \mu_2 - \mu_1 > 1\)
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A survey found that women's heights are normally distributed with mean 63.6 in and standard deviation 2.5 in. A branch of the military requires women's heights to be between 58 in and 80 in.
a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too tall?
b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements?
Answer:
(A)
Step-by-step explanation:
The survey follows of women's height a normal distribution.
The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.
The new height requirements would be 57.7 to 68.6 inches
The given parameters are:
\mathbf{\mu = 63.5}μ=63.5 --- mean
\mathbf{\sigma = 2.5}σ=2.5 --- standard deviation
(a) Percentage of women between 58 and 80 inches
This means that: x = 58 and x = 80
When x = 58, the z-score is:
\mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
This gives
\mathbf{z_1= \frac{58 - 63.5}{2.5}}z
1
=
2.5
58−63.5
\mathbf{z_1= \frac{-5.5}{2.5}}z
1
=
2.5
−5.5
\mathbf{z_1= -2.2}z
1
=−2.2
When x = 80, the z-score is:
\mathbf{z_2= \frac{80 - 63.5}{2.5}}z
2
=
2.5
80−63.5
\mathbf{z_2= \frac{16.5}{2.5}}z
2
=
2.5
16.5
\mathbf{z_2= 6.6}z
2
=6.6
So, the percentage of women is:
\mathbf{p = P(z < z_2) - P(z < z_1)}p=P(z<z
2
)−P(z<z
1
)
Substitute known values
\mathbf{p = P(z < 6.6) - P(z < -2.2)}p=P(z<6.6)−P(z<−2.2)
Using the p-value table, we have:
\mathbf{p = 0.9999982 - 0.0139034}p=0.9999982−0.0139034
\mathbf{p = 0.9860948}p=0.9860948
Express as percentage
\mathbf{p = 0.9860948 \times 100\%}p=0.9860948×100%
\mathbf{p = 98.60948\%}p=98.60948%
Approximate
\mathbf{p = 98.61\%}p=98.61%
This means that:
The height of 98.51% of women that meet the height requirement are between 58 inches and 80 inches.
So, many women (outside this range) would be denied the opportunity, because they are either too short or too tall.
(b) Change of requirement
Shortest = 1%
Tallest = 2%
If the tallest is 2%, then the upper end of the shortest range is 98% (i.e. 100% - 2%).
So, we have:
Shortest = 1% to 98%
This means that:
The p values are: 1% to 98%
Using the z-score table
When p = 1%, z = -2.32635
When p = 98%, z = 2.05375
Next, we calculate the x values from \mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
Substitute \mathbf{z = -2.32635}z=−2.32635
\mathbf{-2.32635 = \frac{x - 63.5}{2.5}}−2.32635=
2.5
x−63.5
Multiply through by 2.5
\mathbf{-2.32635 \times 2.5= x - 63.5}−2.32635×2.5=x−63.5
Make x the subject
\mathbf{x = -2.32635 \times 2.5 + 63.5}x=−2.32635×2.5+63.5
\mathbf{x = 57.684125}x=57.684125
Approximate
\mathbf{x = 57.7}x=57.7
Similarly, substitute \mathbf{z = 2.05375}z=2.05375 in \mathbf{z= \frac{x - \mu}{\sigma}}z=
σ
x−μ
\mathbf{2.05375= \frac{x - 63.5}{2.5}}2.05375=
2.5
x−63.5
Multiply through by 2.5
\mathbf{2.05375\times 2.5= x - 63.5}2.05375×2.5=x−63.5
Make x the subject
\mathbf{x= 2.05375\times 2.5 + 63.5}x=2.05375×2.5+63.5
\mathbf{x= 68.634375}x=68.634375
Approximate
\mathbf{x= 68.6}x=68.6
Hence, the new height requirements would be 57.7 to 68.6 inches
Solve the following quadratic inequality x^2+x-6>0
Answer:
x < -3 or x > 2
Step-by-step explanation:
x² + x - 6 > 0
Convert the inequality to an equation.
x² + x - 6 = 0
Factor using the AC method and get:
(x - 2) (x + 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x - 2 = 0
x = 2
x + 3 = 0
x = -3
So, the solution is x < -3 or x > 2
Factorise the given expression compleyely.
1. 2x(4-7)+(-7+4)
Answer:
The answer is:-
(2x+1)(4-7)
A blue bag has 2 times as many marbles as a red bag. The blue bag has 6 marbles.
How many marbles are in the red bag?
Answer:
3
Step-by-step explanation:
What is the solution of the equation x^2 - 2x + 4 = 0?
Answer: x = 1+-i√3
Step-by-step explanation:
the first one
which graph represents a function?
I can determine a function by drawing a vertical line. If this line pass trought the graph only one time, it's a function.
The only function there is the last one. (Right bottom)
The figure shows segment A D with two points B and C on it in order from left to right. The length of segment A B is 22 units, the length of segment B C is 19 units, and the length of segment C D is 11 units.
The total length of the segment AD will be 52 units.
The complete question is given below:-
The figure shows segment A D with two points B and C on it in order from left to right. The length of segment A B is 22 units, the length of segment BC is 19 units, and the length of segment C D is 11 units. What will be the total length of the segment AD?
What is the length?The measure of the size of any object or the distance between the two endpoints will be termed the length. In the question the total length is AD.
Given that:-
Segment AD with two points B and C on it in order from left to right. The length of segment AB is 22 units, the length of segment BC is 19 units, and the length of segment C D is 11 units.The total length will be calculated as:-
The total length will be equal to the sum of all the segments of line AD. It will be the sum of AB, BC and CD.
AD = AB + BC + CD
AD = 22 + 19 + 11
AD = 52 units
Therefore the total length of the segment AD will be 52 units.
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The length of a rectangle is twice the width. The area of the rectangle 88 is square units. Notice that you can divide the rectangle into two squares with equal area. How can you estimate the side length of each square? Estimate the length and width of the rectangle.
Answer:
Width of the rectangle = 6.325 units
Length of the rectangle = 12.65 units
Side length of the square the 6.325 units.
Step-by-step explanation:
The length of a rectangle is twice the width. The area of the rectangle is 80 square units.
The area of the rectangle = Length × Width
Length = 2W
80 square units = 2W × W
80 = 2W²
W² = 80/2
W² = 40
W = √40
Width of the rectangle = 6.3245553203 units
Approximately = 6.325 units
Length = 2 × Width
= 2 × 6.325
= 12.65 units
• Notice that you can divide the rectangle into two squares with equal area. How can you estimate the side length of each square?
We you divide a rectangle into 2 squares,
The length is divided into two.
Hence, the length of the rectangle = 12.65 units
12.65 units ÷ 2 = 6.325 units.
Hence, the side length of the square the 6.325 units.
The length and width of the rectangle are 13.26 units and 6.63 units if the length of a rectangle is twice the width.
What is a rectangle?It is defined as two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is given that:
The length of a rectangle is twice the width. The area of rectangle 88 is square units.
As we know:
The area of the rectangle = Length×Width
L = 2W
88 = 2W × W
88 = 2W²
W² = 44
W = √44 = 6.63 units
L = 2 × Width
= 2×6.63
= 13.26 units
Thus, the length and width of the rectangle are 13.26 units and 6.63 units if the length of a rectangle is twice the width.
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A password with 6 characters is randomly selected from the 26 letters of the alphabet.
What is the probability that the password does not have repeated letters, expressed to the nearest tenth of a percent?
We can see here that the probability that the password does not have repeated letters, expressed to the nearest tenth of a percent is = 9.8%.
What is probability?Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.
The probability of an event can be calculated using the following formula:
Probability = Favorable Outcomes / Total Outcomes
The number of possible passwords is:
26 × 26 × 26 × 26 × 26 × 26 = 308,915,776.
The number of passwords with no repeated letters is
26P6 = 30,260,000.
The probability of a password having no repeated letters is
= 30,260,000 / 308,915,776 = 0.09779 = 9.78%.
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a box contains 5 green pencils and 7 yellow pencils. two pencils are chosen at random from the box without replacement. what is the probability they are different colors
Answer:
A box contains 5 green pencils and 7 yellow pencils.
Two pencils are chosen at random from the box without replacement.
=> There are two cases:
1st pick green & 2nd pick yellow: P = 5/12 x 7/11 = 0.265
1st pick yellow & 2nd pick green: P = 7/12 x 5/11 = 0.265
Add up both cases, the probability they are different colors:
P = 0.265 + 0.265 = 0. 53
Hope this helps!
:)
20 students each rolled dice 5 times each to measure the median. Here is the data in the picture attached. What can we infer from this graph by looking at the median data?
A. when rolling a dice multiple times, the median is less likely to fall between numbers 1 and 6.
B. it's not possible to tell the likelihood of where the median is going to be when measuring probability since rolling dice is completely randomized, etc.
C. some other response
We can deduce that option A is likely to be true based on the given graph of rolling dice median data.
What is the median?The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median.
The graph illustrates that the median value of the rolls is closer to the center of the possible outcomes (numbers 3, 4, and 5) than the extremes (numbers 1 and 6).
This implies that when rolling a dice several times, the median is less likely to fall between the numbers 1 and 6.
However, because rolling the dice is a random process, there is always a degree of uncertainty in predicting the outcomes.
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(18 POINTS!!!) When Katie installed a fence along the 200-
fixed perimeter of her rectangular backyard,
she left an op an opening for a gate. What is
the value of x, if the equation
2(x+ 60) + 2(300) = 200
Answer:
-260
Step-by-step explanation:
Answer:
x = -260
Step-by-step explanation:
I need a lot of help please help me not doing good
Answer:
What do you need help with?
Triangle RST with (2,0), s(-2,-3), and t(-2,3) reflected over the y axis. Find the coordinates and vertices
I
Step-by-step explanation:
The coordinates and vertices
which reflected over the y- axis are
r(-2,0) , s(2,-3) , and t(2,3).
Please help me quickly I don’t need the explanation I just need the answer I’m sorry I just need a fast
Notice that the area is equivalent to the area of the complete rectangle minus the area of the 3km x 4km rectangle.
\(A=TA-AS\text{.}\)Now, the area of a rectangle is given by the following formula:
\(A=\text{width}\cdot\text{lenght.}\)Therefore:
\(A=9km\cdot16km-3km\cdot4km\text{.}\)Simplifying the above result, we get:
\(A=(144-12)km^2=132km^2.\)Answer:
\(132km^2.\)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.
7. Identify the axis of symmetry of the parabola.
y = -1
-8-6-4 P
-2/
X = 1
X = -1
y4
8
y = 1
6-
4-
2+
CO
+
4 68 X
Q
Answer:
The answer is y=-1 (answer is C).