Answer: g=18
Step-by-step explanation:
g*4=72
g=72/4
g=18
In a survey of women in a certain country (ages 20−29), the mean height was 63.7 inches with a standard deviation of 2.75 inches. Answer the following questions about the specified normal distribution.
(a) What height represents the 95th percentile?
(b) What height represents the first quartile?
a) The height that represents the 95th percentile is approximately 68.1 inches.
b) the height that represents the first quartile is approximately 65.5 inches.
Percentile and Quartile Heights(a) To find the height that represents the 95th percentile, we need to find the z-score that corresponds to this percentile and then use that to find the corresponding height.
The z-score for the 95th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.95, so the area to the right is 0.05. From the standard normal distribution table, the z-score corresponding to an area of 0.05 is approximately 1.645.
Now we can use the formula for z-scores to find the corresponding height:
z = (x - mu) / sigma
where x is the height we want to find, mu is the mean height (63.7 inches), sigma is the standard deviation (2.75 inches), and z is the z-score we just calculated (1.645).
Rearranging the formula, we get:
x = mu + z * sigma
Plugging in the values, we get:
x = 63.7 + 1.645 * 2.75 ≈ 68.1
Therefore, the height that represents the 95th percentile is approximately 68.1 inches.
(b) To find the height that represents the first quartile, we need to find the z-score that corresponds to the 25th percentile and then use that to find the corresponding height.
The z-score for the 25th percentile can be found using a standard normal distribution table or calculator. The area to the left of the z-score is 0.25, so the area to the right is 0.75. From the standard normal distribution table, the z-score corresponding to an area of 0.75 is approximately 0.67.
Using the formula for z-scores and the same values for mu and sigma, we get:
x = mu + z * sigma = 63.7 + 0.67 * 2.75 ≈ 65.5
Therefore, the height that represents the first quartile is approximately 65.5 inches.
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100 Points!!! Algebra question, only looking for answer to last two. Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Photo attached. Thank you!
1) y = -3x and y = -3x + 2: inconsistent system of equations.
2) y = x - 5 and -2x + 2y = - 10: consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.
Explain about the consistent and inconsistent system of equations?If there is at least one solution, an equation system is considered consistent. If there is no solution, a system is inconsistent.If one equation is a multiple of the other in a pair of equations that have two variables, both equations are dependant. Every point in dependent systems is a potential solution, giving them an endless number of solutions.The given equation are:
The graph for each system of equations is plotted.
1) y = -3x and y = -3x + 2
From the graph 1 it is shown that the lines for the each equation form the parallel lines.
Thus, system of equations are inconsistent.
2) y = x - 5 and -2x + 2y = - 10
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
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Use the quadratic formula to solve the equation 2 - 5x-9=0
The answer is x = 5±√61/2, I really hope this helps (:
If lines, KI and LY, intersect at point A and m/KAY=4x+39, m/LAI=12x-9, what is m/YAI?
Answer:
0 degrees
Step-by-step explanation:
To find m/YAI, we need to first find the measure of angle KAI, which is the sum of angles KAY and LAI. Then, we can find the measure of angle YAI by subtracting the measure of angle KAI from 180 degrees.
Using the angle addition postulate, we know that:
m/KAY + m/LAI = m/KAI
Substituting the given values, we get:
4x + 39 + 12x - 9 = m/KAI
Simplifying the expression, we get:
16x + 30 = m/KAI
Now, we need to solve for x. To do this, we can use the fact that angles KAY and LAI are supplementary (add up to 180 degrees) since they form a straight line. Thus:
m/KAY + m/LAI = 180
Substituting the given values, we get:
4x + 39 + 12x - 9 = 180
Simplifying the expression, we get:
16x + 30 = 180
Subtracting 30 from both sides, we get:
16x = 150
Dividing both sides by 16, we get:
x = 9.375
Now that we know x, we can substitute it back into the equation we found earlier:
16x + 30 = m/KAI
16(9.375) + 30 = m/KAI
150 + 30 = m/KAI
m/KAI = 180
So, we know that angle KAI measures 180 degrees. To find m/YAI, we need to subtract the measure of angle KAI from 180 degrees:
m/YAI = 180 - m/KAI
m/YAI = 180 - 180
m/YAI = 0
Therefore, we can conclude that the measure of angle YAI is 0 degrees. This means that YAI is not an angle, but a line segment, and it does not have a measure in degrees.
State any excluded values of a domain and identify the type of break in the graph at the value of x
f(x)=x+7/x-2
Answer:
The excluded value in the domain is x = 2 because the denominator of the rational function becomes zero at this value of x, which results in division by zero.
At x = 2, there is a vertical asymptote, which means that the graph of the function approaches positive or negative infinity as x approaches 2 from either side.
rewrite the following without an exponet. 3^-4
Answer:i think -81
Step-by-step explanation:3x (-3) = -9. -9x(-3)=27. 27x(-3)= -81
Which of the following values of x makes this inequality true? Circle all that apply
5 + x > 5
A.1/2
B. -10
C. -5
D. 0.000003
E. 1.5
Answer:
A. 1/2
D. 0.000003
E. 1.5
Step-by-step explanation:
The inequality 5 + x > 5 can be simplified as follows:
5 + x > 5
x > 5 - 5
x > 0
Find the area of the shaded sector of the circle
Answer:
32.67 square meters
Step-by-step explanation:
finding the area of the shaded region.
area of sector = (θ/360°) x πr²
where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.
Substituting the given values into the formula, we get:
area of sector = (60°/360°) x π(14m)²
area of sector = (1/6) x 3.14 x 196m²
area of sector = 32.67m² (rounded to two decimal places)
Therefore, the area of the section is 32.67 square meters
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers
T.A. =
To clear all your answers and start over, click the trashcan icon. Remember to always be accurate, professional, and friendly in your responses.
To answer a student question on Brainly, first, carefully read the question and understand what is being asked. Then, click on an item from the list or group of pictures provided at the bottom of the problem. Hold down the mouse button and drag the item into the correct position in the answer box.
Release the mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Simply click the garbage button to start anew after clearing all your answers. Always be sure to respond with accuracy, professionalism, and friendliness.
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If the graph of a polynomial function P(x) has -intercepts at x = - 4, x = 0, x * 1 point
= 5, which of the following must be true for P(x)?
• (x + 5) is a factor of the polynomial.
• (x-4) is a factor of the polynomial.
•' The degree of the polynomial is 3.
• The degree of the polynomial is greater than or equal to 3.
(x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
What is a functiοn ?Functiοn can be define in which it relates an input tο οutput.
If the graph οf a pοlynοmial functiοn P(x) has x-intercepts at x = -4, x = 0, and x = 5, then we knοw that the factοrs οf P(x) are (x + 4), x, and (x - 5). This is because a pοlynοmial has x-intercepts where the value οf P(x) is equal tο zerο, and this οccurs when each factοr is equal tο zerο.
Therefοre, we can cοnclude that (x + 4) and (x - 5) are factοrs οf the pοlynοmial P(x), but x is nοt necessarily a factοr. This is because x is a linear factοr with a zerο intercept, but it cοuld be cancelled οut by anοther factοr in the pοlynοmial.
Thus, the cοrrect statement is:
(x + 5) is nοt necessarily a factοr οf the pοlynοmial.
(x-4) is a factοr οf the pοlynοmial.
The degree οf the pοlynοmial is 3 οr greater since the pοlynοmial has three x-intercepts. Hοwever, we cannοt determine the exact degree οf the pοlynοmial withοut additiοnal infοrmatiοn.
Therefοre, (x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.
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please help!!
angle relationships in circles
Answer:60
Step-by-step explanation:
30x2=60
video
Let the region R be the area enclosed by the function f(x) = ln (x) + 1 and
g(x)=x-1. If the region R is the base of a solid such that each cross section
perpendicular to the a-axis is a semi-circle with diameters extending through the
region R, find the volume of the solid. You may use a calculator and round to the
nearest thousandth.
The volume of the solid is approximately 0.558 cubic units.
To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.
We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:
d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2
The radius of each semi-circle is half of the diameter, which is:
r(a) = (ln(a) - a + 2) / 2
The area of each semi-circle is π times the square of its radius, which is:
[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]
To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:
V = ∫[e,2] A(a) da
V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]
V ≈ 0.558 (rounded to the nearest thousandth)
Therefore, the volume of the solid is approximately 0.558 cubic units.
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I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. Royalty would be great.
By adding fractions that represent each of the amounts of cupcakes, we can see that you need 9 cupcakes for you and your friends.
How many halves they need in total?Her we know that you want 3 halves of a cupcake for yourself, 8 halves for your friend, and 7 halves for your other friend.
So we just need to add all of these fractions, to do so, we need to solve the follwing opeartion:
3*(1/2) + 8*(1/2) + 7*(1/2)
3/2 + 8/2 + 7/2
All of these have the same denominator so we can directly add them up:
3/2 + 8/2 + 7/2 = (3 + 8 + 7)/2
(3 + 8 + 7)/2 = 18/2
18/2 = 9
You need 9 cupcakes for you and your friends.
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Complete question:
"I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. How many halves we need in total?"
A truck is traveling due north at 60km/hr approaching a crossroad. On a perpendicular road a police car is traveling west toward the intersection at 75km/hr. Both vehicles will reach the crossroad exactly one hour. Find the vector currently representing the displacement of the truck with respect to the police car.
Displacement d=
In the given problem, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.
How to Solve the Problem?To solve this problem, we can use vector addition. Let's assume that the police car is at the origin, and let the positive x-axis point west and the positive y-axis point north. Then, the initial position of the truck can be represented by the vector (-d, 0), where d is the distance between the police car and the crossroad.
Since the truck is traveling due north, its velocity vector is (0, 60). Similarly, the velocity vector of the police car is (-75, 0). We know that both vehicles will reach the crossroad at the same time, which means that their displacement vectors will have the same magnitude and direction.
Let's call the displacement vector we're looking for "D". Using the formula for displacement, we can write:
D = vt
where v is the average velocity of both vehicles, and t is the time it takes for them to reach the crossroad (which is one hour). The average velocity is given by the vector sum of the velocities of the truck and the police car:
v = (0, 60) + (-75, 0) = (-75, 60)
Substituting in the values for v and t, we get:
D = (-75, 60) * 1 = (-75, 60)
Therefore, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.
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One of outstanding journal recently published an article indicating differences in perception of gender equality on the job between men and women. The article claimed that women perceived the gender equality problem to be much more compared to men. One question asked of both men and women was: "Do you think gender equality is a major problem in the workplace?" 60% of the women responded "Yes", compared to men about 25%. Assuming W designates women's responses and M designates men's, what hypothesis should journal test in order to show that its claim is TRUE?
The journal could use a one-tailed hypothesis test with a significance level (α) of 0.05 to determine whether there is a significant difference between the proportion of women and men.
What is p value?In statistics, the p-value is a measure of the evidence against the null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming that the null hypothesis is true. In other words, the p-value is the probability of obtaining the observed results, or more extreme results, if the null hypothesis were true.
Given by the question.
To test the claim that women perceive the gender equality problem to be much more compared to men, the journal could test the following hypothesis:
Hypothesis: The proportion of women who perceive gender equality to be a major problem in the workplace (W) is significantly greater than the proportion of men who perceive gender equality to be a major problem in the workplace (M).
H0: W = M (there is no significant difference in perception of gender equality between men and women)
Ha: W > M (women perceive gender equality to be a major problem more than men do)
who perceive gender equality to be a major problem in the workplace. They could calculate the p-value and compare it to α. If the p-value is less than α, they would reject the null hypothesis and conclude that the proportion of women who perceive gender equality to be a major problem in the workplace is significantly greater than the proportion of men who perceive it to be a major problem.
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The two top concert tours in 2016 were concert A and concert B. Based on average ticket prices, it cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B. Three tickets for concert B cost a total of $687. How much did an average ticket cost for each tour?
The average ticket cost for each concert is given as follows:
Concert A: $188.83.Concert B: $95.67.How to obtain the ticket costs?The ticket costs are obtained by a system of equations, for which the variables are given as follows:
Variable a: cost for Concert A.Variable b: cost for Concert B.It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:
6a + 6b = 1707
a + b = 284.5.
Three tickets for concert B cost a total of $687, hence the cost for concert B is of:
3b = 687
b = 287/3
b = $95.67.
Replacing into the first equation, the cost for concert A is given as follows;
a = 284.5 - 95.67
a = $188.83.
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A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1728 mailboxes this week. If each mailbox has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the value 3.14 for X, and round up your answer to the next square meter.?
Answer:
1759 square meters
Step-by-step explanation:
You want the surface area of a cuboid with a half-cylinder top.
Lateral areaThe lateral area of the figure is the product of the length of the mailbox (0.45 m) and the perimeter of the end. The perimeter of the end is the sum of the lengths of the straight sides and half the circumference of a circle with diameter 0.3 m.
P = 0.3 + 2·0.4 + π/2(0.3) = 1.571 . . . . . meters
LA = Ph = (1.571 m)(0.45 m) = 0.70695 m²
End areaThe end area is twice the area of the rectangular portion of the end, plus the area of a circle 0.3 m in diameter.
EA = (0.3 m)(0.4 m) + 3.14(0.3/2 m)² = 0.31065 m²
Total areaThe total area of 1 mailbox is ...
LA +EA = 0.70695 m² +0.31065 m² = 1.0176 m²
Then the area of 1728 mailboxes is ...
1728 × 1.0176 m² ≈ 1758.4 m² ≈ 1759 m²
About 1759 square meters of aluminum will be needed for the 1728 mailboxes.
__
Additional comment
This presumes there is no waste in cutting the semicircular shape from the supplied aluminum.
HELP ME!!! Find the percent equivalent to 14 over 35. 21% 40% 42% 50%
Answer:
The answer is 40% :) Hope this helps!
Each of the lists below is in order from least to greatest
and has one number missing. List an example of a value
that could correctly complete the blank in each list.
I. -0.65,
2.
4.
/
3. 1.2%, 10%,
1
20'
12 13
4'5'2'2
,-0.6, -0.5, -0.4
6.2%,
/
1
16.7%, 40%
10.45
Answer:
-0.63
1/7
15%
10%
Step-by-step explanation:
hope this helps
1. Identify and clearly label the slope and y-intercept for each equation in slope intercept form. Choose the correct answer from the choices below.
Y=-5
A. Slope is-5 and the y-intercept is (0,0)
B.Slope is zero and the y-intercept is (0,-5)
C. Slope is zero and the y-intercept is (0,0)
D. Slope is -5 and the y-intercept is (0,-5)
Slope is zero and the y-intercept is (0,-5)
What is slope ?
In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.
In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.
The formula for calculating slope is:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Comparing the equation Y = -5 to y = mx + b, we can see that:
The slope, m, is 0, since there is no x-term in the equation.
The y-intercept, b, is -5, since that is the constant value in the equation.
Therefore, the correct answer is:
B. Slope is zero and the y-intercept is (0,-5)
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Find the rule x = 8 y = 10 x = 9 y = 12
The equation of the rule that relates x and y is y = 2x - 6.
What is the equation's rule?Anything on one side of the equals sign in a calculation must equal anything on the other side of the equals sign. So long as we maintain the balance on both sides of the equals symbol, we can do whatever we want to an equation.
We can create a system of equations using the provided values (8, 10) and (9, 12) in order to determine the rule that connects x and y. One approach is as follows:
The slope of the line connecting the two locations can be determined first:
m = (y2 - y1)/(x2 - x1) = (12 - 10)/(9 - 8) = 2/1 = 2
The point-slope version of the equation of a line can then be used, using either of the two points:
y - y1 = m(x - x1)
For example, using the first point (8, 10):
y - 10 = 2(x - 8)
Simplifying:
y - 10 = 2x - 16
y = 2x - 6
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In 1993, the life expectancy of males in a certain country was 65.2 years. In 1998, it was 67.7 years. Let E represent the
life expectancy in year t and let t represent the number of years since 1993. Determine the linear function E(t) that fits
the data. Use the function to predict the life expectancy of males in 2006.
The predicted Iife expectancy οf maIes in 2006 is 71.7 years.
What is Iinear equatiοn?A Iinear equatiοn is a mathematicaI equatiοn that describes a straight Iine in a twο-dimensiοnaI pIane.
Tο find the Iinear functiοn E(t) that fits the data, we need tο find the equatiοn οf the Iine that passes thrοugh the twο given pοints: (0, 65.2) and (5, 67.7), where t = 0 cοrrespοnds tο the year 1993 and t = 5 cοrrespοnds tο the year 1998.
Using the sIοpe-intercept fοrm οf a Iinear equatiοn, we have:
E(t) = mt + b
where m is the sIοpe οf the Iine and b is the y-intercept.
We can find the sIοpe by using the fοrmuIa:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (0, 65.2) and (x2, y2) = (5, 67.7):
m = (67.7 - 65.2)/(5 - 0) = 0.5
Sο the equatiοn οf the Iine is:
E(t) = 0.5t + b
Tο find the y-intercept, we can use οne οf the given pοints. Let's use (0, 65.2):
65.2 = 0.5(0) + b
b = 65.2
Therefοre, the Iinear functiοn E(t) that fits the data is:
E(t) = 0.5t + 65.2
Tο predict the Iife expectancy οf maIes in 2006, we need tο find t when the year is 2006:
t = 2006 - 1993 = 13
Sο we can use t = 13 in the equatiοn:
E(13) = 0.5(13) + 65.2
E(13) = 6.5 + 65.2
E(13) = 71.7
Therefοre, the predicted Iife expectancy οf maIes in 2006 is 71.7 years.
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What is the domain of the square root function graphed below?
Interpret the data in the circle graph. If 560 books were sold at the book fair, find the number of the books that were mystery books.
If 560 books were sold at the book fair,
(Type a whole number.)
of the books were mystery books.
Circle graph
Fantasy 8%
Science
Fiction
12%
Comic 15%
Other 5%
Mystery 20%
-Fictic
Answer:
112
Step-by-step explanation:
According to the circle graph, the mystery books make up 20% of all books sold. So, we can calculate the number of mystery books sold as follows:
Number of mystery books = 20% of 560
= (20/100) x 560
= 112
Therefore, the number of mystery books sold at the book fair was 112.
you randomly draw 2 cards from a standard deck of 52 cards. what is the probability you draw a heart, don't replace it, and pull a club?
PLEASE ANSWER BY 7:00AM Pacific Standard Time!!!!!! 17 pointz
Step-by-step explanation:
There are 52 cards and 13 are hearts
first card heart is then 13 /52 = 1/4 chance
now there is only 51 cards and 13 are clubs
second card club is then 13 / 51 chance
13/52 * 13/ 51 = 169 / 2652 = 13/204 = .0637 chance of Heart - Club
Solve the problems. Show your work.
7
1. Mr. Nguyen had 7/8
pint of water in his water bottle. Then, he drank 2/3
pint. How much water is left in the bottle?
Answer:
7/8 - 2/3 = 5/8 pint of water left in the bottle.
A company makes 140 bags. 47 of the bags have buttons but no zips. 48 of the bags have zips but no buttons. 22 of the bags have neither zips nor buttons. How many bags have zips on them?
Required number of bags which have zips on them are 71.
Here given, A company makes 140 bags.
So, total number of bags = 140
It is also given, 47 of the bags have buttons but no zips 48 of the bags have zips but no buttons.
So, number bags which have buttons but no zips = 47 and number bags which have zips but no buttons = 48
and numbers of bags which have neither zips nor buttons = 22.
If we subtract number of bags which have no zips from total number of bags then we will get total number of bags which have zips
So, number of bags have zips on them
[tex] = 140 - 47 - 22 = 71[/tex]
Therefore, 71 bags have zips on them.
This is a problem of Subtraction.
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To solve using square roots, your quadratic must be in which format?
Answer:
0=-ax^2+bx+c
Step-by-step explanation:
Ella has an offer to buy an item with a sticker price of $12,300 by paying $420 a month for 36 months. What interest rate is Ella being offered?
Answer:
To calculate the interest rate, we can use the formula for the present value of an annuity:
PV = PMT x [(1 - (1 + r)^(-n)) / r]
where:
PV = present value
PMT = monthly payment
r = interest rate per period
n = number of periods
In this case, we have:
PV = $12,300 (the sticker price)
PMT = $420
n = 36 (36 months)
Substituting these values into the formula, we get:
12,300 = 420 x [(1 - (1 + r)^(-36)) / r]
Simplifying this equation algebraically is not possible, so we need to use numerical methods to solve for r. One way to do this is to use a financial calculator or spreadsheet program, which can find the interest rate that makes the equation true. Using Excel's RATE function, for example, we get:
=RATE(36,-420,12300)
This gives us an interest rate of approximately 3.33% per month or 39.96% per year.
Therefore, Ella is being offered an interest rate of 3.33% per month or 39.96% per year.
What is the center and radius of a circle with the following equation
Answer:
Center: (1, -3); radius: 2
Step-by-step explanation:
(x - h)² + (y - k)² = r²
(x - 1)² + (y + 3)² = 4
(x - 1)² + (y - (-3))² = 2²
Center: (1, -3); radius: 2