20 POINTS! You are planning to use a ceramic tile design in your new bathroom. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 9 centimeters, what will be the exact area of each hexagonal shape?
Answer:
210.33 cm^2
Step-by-step explanation:
We know that 6 equilateral triangles makes one hexagon.
Also, an equilateral triangle has all its sides equal.
If the tile of each side of the triangular tile measure 9 cm, then the height of the triangular tiles can be gotten using Pythagoras's Theorem.
The triangle formed by each tile can be split along its height, into two right angle triangles with base (adjacent) 4.5 cm and slant side (hypotenuse) of 9 cm. The height (opposite) is calculated as,
From Pythagoras's theorem,
[tex]hyp^{2} = adj^{2} + opp^{2}[/tex]
substituting, we have
[tex]9^{2} = 4.5^{2} + opp^{2}[/tex]
81 = 20.25 + [tex]opp^{2}[/tex]
[tex]opp^{2}[/tex] = 81 - 20.25 = 60.75
opp = [tex]\sqrt{60.75}[/tex] = 7.79 cm this is the height of the right angle triangle, and also the height of the equilateral triangular tiles.
The area of a triangle = [tex]\frac{1}{2} bh[/tex]
where b is the base = 9 cm
h is the height = 7.79 cm
substituting, we have
area = [tex]\frac{1}{2}[/tex] x 9 x 7.79 = 35.055 cm^2
Area of the hexagon that will be formed = 6 x area of the triangular tiles
==> 6 x 35.055 cm^2 = 210.33 cm^2
-50 POINTS- (5/5) Which scatter plot represents the following data?
Answer:
B is plotted correctly
Step-by-step explanation:
A point (1,2) is plotted at (1,3)
B is plotted correctly
C point (1,2) is plotted at (1,3)
D point (1,2) is plotted at (1,3)
Answer:
B.
Step-by-step explanation:
According to the table, there is a point at (0, 5), and a point at (1, 2).
A: The scatterplot has a point at (0, 5), but a point at (1, 3).
B: The scatterplot has points at (0, 5) and (1, 2).
C: The scatterplot has a point at (0, 5), but a point at (1, 3).
D: The scatterplot has a point at (0, 5), but a point at (1, 3).
Hope this helps!
Find the probability that when a couple has four children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
Answer:
The probability that at least, one of the four children the couple has is a boy is 0.8.
Step-by-step explanation:
Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..
Note that it is possible to have the following for 4 children:
1. 4 boys, 0 girls
2. 3 boys, 1 girl
3. 2 boys, 2 girls
4. 1 boy, 3 girls
5. 0 boys, 4 girls.
To have at least, one boy, out of the 5 options, only 4 is possible.
1. 4 boys, 0 girls.........YES
2. 3 boys, 1 girl ...........YES
3. 2 boys, 2 girls.........YES
4. 1 boy, 3 girls.............YES
5. 0 boys, 4 girls..........NO
The probability is therefore,
(Probability of event = 4) ÷ (Total possible outcome = 5)
P = 4/5 = 0.8
Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is false. A sampling distribution is normal only if n30. B. The statement is false. A sampling distribution is normal if either n30 or the population is normal. C. The statement is true. D. The statement is false. A sampling distribution is never normal.
The statement is false. A sampling distribution is normal if either n > 30 or the population is normal.
==========================================
Explanation:
If the underlying population is normally distributed, then so is the sample distribution (such as the distribution of sample means, aka xbar distribution).
Even if the population isn't normally distributed, the xbar distribution is approximately normal if n > 30 due to the central limit theorem. Some textbooks may use a higher value than 30, but after some threshold is met is when the xbar distribution is effectively "normal".
Choice A is close, but is missing the part about the population being normal. If we know the population is normal, then n > 30 doesn't have to be required.
nick cut a circular cookie into 5 equal slices. what is the angle measure of each slice?
Using concepts of circles, it is found that the angle measure of each slice is of 72º.
--------------------------------------------
The cookies have circular formats.A complete circle, which is the format of a cookie, has an angular measure of 360º.If it is divided into a number n of equal slices, the angles will be 360 divided by n.--------------------------------------------
5 equal slices, thus:
[tex]\frac{360}{5} = 72[/tex]
The angle measure of each slice is of 72º.
A similar problem is given at https://brainly.com/question/16746988
One model of the length LACL of a person's anterior cruciate ligament, or ACL, relates it to the person's height h with the linear function LACL=0.04606h−(41.29 mm) This relationship does not change significantly with age, gender, or weight. If a basketball player has a height of 2.13 m, approximately how long is his ACL?
Answer:
The [tex]L_{ACL}[/tex] of the player is [tex]L_{ACL} = 56.82 \ mm[/tex]
Step-by-step explanation:
From the question we are told that
The relationship between the length [tex]L_{ACL}[/tex] to the height is
[tex]L_{ACL} = 0.04606h - (41.29 \ mm)[/tex]
The height of the basketball player is [tex]h = 2.13 \ m = 2130 \ mm[/tex]
Substituting the value of height of the basket ball player in to the model we have the [tex]L_{ACL}[/tex] of the player is
[tex]L_{ACL} = 0.04606 (2130) - (41.29 ) \ mm[/tex]
[tex]L_{ACL} = 56.82 \ mm[/tex]
what is sum of all palindromic numbers from 1 to 100
Answer:
540
Step-by-step explanation:
0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99
Answer:
540
Step-by-step explanation:
Hey there!
Well we need to first find all the palindromic numbers,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99
Add
= 540
Hope this helps :)
8/2(2+2)
What is the answer?
Answer:
16
Step-by-step explanation:
[tex]\frac{8}{2} x (2+2) = \frac{8}{2} x 4 = \frac{8 x 4}{2} = \frac{32}{2} = 16[/tex]
Answer: 16
PEMDAS
P: Parenthesis
E: Exponents
M: Multipcaction
D: Divison
A: Addition
S: Subtraction
PEMDAS can be also known as Please Excuse My Dear Aunt Sally
P: (2+2)
E: N/A (There are no exponents)
M: 4×4
D: 8÷2
A: 2+2
S: N/A (There is nothing to subtract)
How did we get 4×4? We divided 8÷2 which got us 4. Then we added 2+2 and we also got 4. Then we multiplied 4×4 which got us 16. That's how 16 is our answer.
Use the number line below, where RS = 6y + 2, ST = 3y + 7, and RT = 14y - 11.
a. What is the value of y?
b. Find RS, ST, and RT.
Answer:
a) y = 4
b) RS = 26, ST = 19, RT = 45
Step-by-step explanation:
From the line given, the following vector equation is true, RS + ST = RT since R, S and T lies in the same straight line.
Given RS = 6y + 2, ST = 3y + 7, and RT = 14y - 11
On substituting this values into the equation above we will have;
6y+2+(3y+7) = 14y-11
6y+2+3y+7 = 14y-11
Collect the like terms
6y+3y-14y = -11-7-2
9y-14y = -20
-5y = -20
y = 20/5
y = 4
Since RS = 6y + 2
RS = 6(4)+2
RS = 24+2
RS = 26
ST = 3y + 7
ST = 3(4)+7
ST = 12+7
ST = 19
Also, RT = 14y - 11
RT = 14(4)-11
RT = 56-11
RT = 45
Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
The portfolio beta is [tex]\alpha = 1.354[/tex]
Step-by-step explanation:
From the question we are told that
The first investment is [tex]i_1 = \$ 25,000[/tex]
The first beta is [tex]k = 0.8[/tex]
The second investment is [tex]i_2 = \$ 40,000[/tex]
The second beta is [tex]w = 1.7[/tex]
Generally the portfolio beta is mathematically represented as
[tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]
substituting values
[tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]
[tex]\alpha = 1.354[/tex]
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times. What is the probability that the toast lands buttered side down?
Step-by-step explanation:
Given that,
A piece of buttered toast falls to the floor 17 times. The toast landed buttered side up 6 times.
It means that the total number of outcomes are 17
We need to find the probability that the toast lands buttered side down. Favourable oucome is 17-6 = 11
So, probability is given by :
[tex]P(E)=\dfrac{\text{favourable outcomes}}{\text{total no of outcomes}}[/tex]
[tex]P(E)=\dfrac{11}{17}[/tex]
So, the probability that the toast lands buttered side down is 11/17.
find the value of x? please help
Answer:
49
Step-by-step explanation:
With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!
idk how to put the picture but can someone just tell me the points where the two dots go plz will give good rate nd say thx plz answer fast
Graph -8x-y=8
Answer:
(-1,0) and (0,-8)
Step-by-step explanation:
Hey there!
Well first we’ll graph -8x - y = 8,
Look at the image below
By lookig at the image below we can tell the 2 points are at,
(-1,0) and (0,-8)
Hope this helps :)
Gina, Sam, and Robby all rented movies from the same video store. They each rented some dramas, comedies, and documentaries. Gina rented 11 movies total. Sam rented twice as many dramas, three times as many comedies, and twice as many documentaries as Gina. He rented 27 movies total. If Robby rented 19 movies total with the same number of dramas, twice as many comedies, and twice as many documentaries as Gina, how many movies of each type did Gina rent?
Hi there! :)
Answer:
Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Step-by-step explanation:
To solve, we will need to set up a system of equations:
Let x = # of dramas, y = # of comedies, and z = # of documentaries:
Write equations to represent each person:
Gina:
x + y + z = 11
Sam:
2x + 3y + 2z = 27
Robby:
x + 2y + 2z = 19
Write the system:
x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Begin by subtracting the third equation from the second:
2x + 3y + 2z = 27
x + 2y + 2z = 19
-----------------------
x + y = 8
If x + y = 8, plug this into the first equation:
(8) + z = 11
z = 11 - 8
z = 3
We found the # of documentaries Gina rented, now we must solve for the other variables:
Subtract the top equation from the third. Substitute in the value of z we solved for:
x + 2y + 2(3) = 19
x + y + (3) = 11
-------------------------
y + 3 = 8
y = 5
Substitute in the values for y and z to solve for x:
x + 5 + 3 = 11
x + 8 = 11
x = 11 - 8
x = 3.
Therefore, Gina rented 3 dramas, 5 comedies, and 3 documentaries.
Answer:
B- x + y + z = 11
2x + 3y + 2z = 27
x + 2y + 2z = 19
Step-by-step explanation:
I took the quiz
This graph shows the US unemployment rate from August 2010 to November 2011.
Sample Unemployment Rate
Graph
Unemployment Rate
10%
80%
6%
Unemployment Rate
Aug 10
Jan 11
Jun 11
Nov 11
This graph suggests unemployment in the United States
O will continue to fall.
O will continue to rise.
O will remain the same.
O will only change a little.
Answer: Will continue to rise
Step-by-step explanation:
Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.
The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.
This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.
Answer:
EDGE 2021
Step-by-step explanation:
1) 4%
2) Increase
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs.
Answer: 1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar for both recipes.
Step-by-step explanation:
Dante is baking two recipes.
A cookie recipe, that needs 1.5 cups of sugar.
A brownie recipe, that needs 1.25 cups of sugar.
So the total sugar that he needs is:
The sugar for the cookies + the sugar for the brownies:
The equation is:
1.5 cups of sugar + 1.25 cups of sugar = 2.75 cups of sugar.
What is the slope of the line shown below?
A. -3/2
B. 3/2
C. 2/3
D. -2/3
Answer:
2/3
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= (1- -7)/(9 - -3)
= ( 1+7)/( 9+3)
= 8/12
Simplifying
= 2/3
Answer:
C. 2/3
Step-by-step explanation:
You can use the equation: [tex]y_{2} - y_{1}/x_{2} - x_{1}[/tex] to find the slope.
y2 is equal to the y coordinate of the second point: 1
y1 is equal to the y coordinate of the first point: -7
x2 is equal to the x coordinate of the second point: 9
x1 is equal to the x coordinate of the first point: -3
So if you plug these values into the equation, you will get:
1 - (-7)/ 9- (-3)
= 1 + 7/ 9 + 3
= 8/12
= 2/3
Suppose you are standing such that a 32-foot tree is directly between you and the sun. If you are standing 140 feet away from the tree and the tree casts a 160-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 160 ft 140 ft 32 ft
Answer:
Height = 4 feet
Step-by-step explanation:
To determine how tall I can be we take the difference between the shadow cast by the 32-feet tree and the distance away from the tree
But the tree is 32 feet tall but on shadow it's 160
So lemme determine how long I'll be in my shadow first
Distance away from tree= 140 feet
Length of shadow cast by tree
= 160 feet
Length of shadow= 160-140
Length if shadow= 20 feet
My height= x
X/20= 32/160
X= 20*32/260
X = 4 feet
Height = 4 feet
Which of the following is the solution set of the given equation? (x - 3) - 2(x + 6) = -5 a) {-4} b) {8} c) {-10}
Answer:
x = -10
Step-by-step explanation:
(x - 3) - 2(x + 6) = -5
Distribute
x-3 -2x-12 = -5
Combine like terms
-x -15 = -5
Add 15 to each side
-x-15+15 = -5+15
-x=10
Multiply each side by -1
x= -10
Answer:
c
Step-by-step explanation:
The distance between two cities on a map is 4 centimeters. If the scale is 0.5 cm:1 km, how many kilometers apart are the actual cities?
Answer:
8 km
Step-by-step explanation:
1 km
4 cm x -------- = 8 km
0.5 cm
The actual cities are 8 km apart from each other at the scale 0.5 cm = 1 km.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
The distance between two cities on a map = 4 centimeters.
Also, the scale
0.5 cm = 1 km
To find actual distance between cities, use ratio properly,
0.5 cm = 1 km
1 cm = 2 km
4 cm = 8 km
The distance between the actual cities is 8 km.
To learn more about Ratio on :
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The MCAT is the admission exam that medical schools use as one of the criteria for accepting students. The exam is based on a scale of 0-45. The following data shows the MCAT scores for nine students.
32 36 29 31 30 35 34 26 30
The 35th percentile of this data set is:________
a. 31
b. 32
c. 31.5
d. 30
Answer:
d. 30
Step-by-step explanation:
The computation of the 35th percentile of this data set is shown below:
Before that first we have to series the number in ascending number
S. No Numbers
1 26
2 29
3 30
4 30
5 31
6 32
7 34
8 35
9 36
Now use the formula
Here n = 9
Percentile = 100
[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]
= 3.5th
= 3th + 0.5 (4th - 3th)
= 3th + 0.5 (30 - 30)
= 3th + 0
= 30
PLZ answer quick i will give brainliest if right no explanation needed Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms. Joe had already reserved and paid for 161616 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900. Let B represent the number of additional blocks that Joe reserves. 1) Which inequality describes this scenario? Choose 1 answer: a: 16+8B≤50 b: 16+8B≥50 c: 16+B≤50 d: 16+B≥50 2) What is the least amount of additional money Joe can spend to get the rooms they need?
Answer:
16 + 8b ≥ 50
4500
Step-by-step explanation:
He needs at least 50 rooms and has already reserved 16
They are in groups of 8
16 + 8b ≥ 50
Subtract 16 from each side
16+8b-16 ≥ 50 -16
8b≥ 34
Divide by 6
8b/8 ≥ 34/8
b≥ 4.25
We need to round up since we need at least 50
b = 5 since we want the least amount of rooms
Each block is 900
5*900 = 4500 more that he will have to spend
_Thirty-two holes are drilled in rows on a metal block. The number of rows is more than the number of holes in each
row. Find the number of row. (a)7 (b)25(c)67
(d)4 (e) 12
_
Answer:
D
Step-by-step explanation:
Let the number of rows be x
And the numbers of holes in each be y
xy = 32
x and y must be factors of 32
From options stated
4 is the only factor of 32
Hence option D is correct
Variable g is 8 more than variable w. Variable g is also 2 less than w. Which pair of equations best models the relationship between g and w? g = 8w g = w + 2 w = g + 8 w = g − 2 w = 8g w = g + 2 g = w + 8 g = w − 2
Answer: g = w + 8 g=w-2
Step-by-step explanation:
We could represent the word phrases by the equations.
g = w + 8
g = w - 2
Answer:
g = w + 8
g = w - 2
Step-by-step explanation:
Assuming that g and w exists, then we can show the relation as described:
"Variable g is 8 more than variable w."
g = w + 8
"Variable g is also 2 less than w."
g = w - 2
These are the two equations of the described relationship between g and w.
Note that g could not actually exist in the real number system:
g = w + 8
g = w - 2
w + 8 = w - 2
w - w = -2 - 8
0 != -10
This is impossible within the real number system.
Cheers.
In a survey of 15000 students of different schools, 40% of them were found to have tuition before the see examination. Among them 50% studied only mathematics ,30% only science and 10% studied others subject. how many student studied mathematics as well as science.
Answer: 600 students.
Step-by-step explanation:
Ok, we start with 15,000 students.
40% of them had tuition, so the actual number of them that had tuition is:
15,000*0.40 = 6,000.
Now we want to find the number of students that studied math and science.
50% only studied math,
30% only studied science
10% studied other subjects.
So 50% + 30% + 10% did NOT studied both math and science
90% is the percentage that did not study math and mathematics as well as science, then the other 10% did.
Then, out of the 6,000 students that had tuition, 10% studied math and science, the total number is:
6,000*0.10 = 600
simplify the following expression by combining like terms 2x+7x^2-5x+8x^2
Answer:15x^2-3x
Step-by-step explanation:
16
Select the correct answer.
If function g is defined by the equation Y-3X = -14, which equation represents the function in function notation?
OA. gx) = 3X - 14
OB. gx) = -3X - 14
OC. g(x) = 3X + 14
OD. gx) = -3X + 14
Reset
Next
Answer: A) g(x) = 3x - 14
Step-by-step explanation:
Solve the equation for y and replace y with g(x):
y - 3x = -14
y = 3x - 14
g(x) = 3x - 14
A boutique wants to make at least $127 profit from purses this week. The boutique earns $7 profit from each purse. How many purses must be sold?
Answer:
19 purses
Step-by-step explanation:
Set up an inequality where x represents the number of purses:
127 [tex]\geq[/tex] 7x
Solve for x by dividing each side by 7:
18.14 [tex]\geq[/tex] x
Round up to 19 because purses have to be whole
So, 19 purses have to be sold.
Suppose that the function g is defined, for all real numbers, as follows.
find g(-5) g(1) g(4)
=================================================
Explanation:
The piecewise function shows that we have two cases. Either x = 1 or [tex]x \ne 1[/tex].
If x = 1, then g(x) = 3 as shown in the bottom row. This is why g(1) = 3.
If [tex]x \ne 1[/tex], then g(x) = (1/4)x^2-4
Plug x = -5 into this second definition
g(x) = (1/4)x^2-4
g(-5) = (1/4)(-5)^2-4
g(-5) = (1/4)(25)-4
g(-5) = 25/4 - 4
g(-5) = 25/4 - 16/4
g(-5) = 9/4
Repeat for x = 4
g(x) = (1/4)x^2-4
g(4) = (1/4)(4)^2-4
g(4) = (1/4)(16)-4
g(4) = 4-4
g(4) = 0
The value of the function at x = -5, x = 1, and x = 4 will be 2.25, 3, and 0, respectively.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
g(x) = (1/4)x² - 4, x ≠ 1
g(x) = 3, x = 1
The value of the function at x = -5 will be given as,
g(-5) = (1/4)(-5)² - 4
g(-5) = 25 / 4 - 4
g(-5) = 6.25 - 4
g(-5) = 2.25
The value of the function at x = 4 will be given as,
g(4) = (1/4)(4)² - 4
g(4) = 16 / 4 - 4
g(4) = 4 - 4
g(4) = 0
The value of the function at x = 1 will be given as,
g(1) = 3
The value of the function at x = -5, x = 1, and x = 4 will be 2.25, 3, and 0, respectively.
More about the function link is given below.
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Caleb made 6 quarts of trail mix for his camping trip. Each week,he ate 4 pints of the trail mix. How many weeks did Caleb have trail mix?
Sry if this is too much
Answer:
3 weeks
Step-by-step explanation:
6 quarts = 12 pints
12 divided by 3 = 4
Step-by-step explanation:
1 quart = 2 pints
6 quarts = 2 x 6 = 12 pints
12 ÷ 4 = 3
He can have 3 weeks
