6. Find the distance from A to B for the hexagonal nut shown below: А 1.50 in BYo I've asked tutors and they have been unable to answer, after all it's only given one side and I need some help.
Answers
Let
x ------> the length side of the regular polygon
we have a regular hexagon
that means
the interior angle of this polygon is
180(6-2)/6=120 degrees
A regular hexagon can be divided into 6 congruent equilateral triangles
see the attached figure to better understand the problem
in the right triangle of the figure
we have that
sin(60)=0.75/x
solve for x
x=0.75/sin(60)
Remember that
[tex]\sin (60^o)=\frac{\sqrt[]{3}}{2}[/tex]substitute
[tex]\begin{gathered} x=0.75\colon\frac{\sqrt[]{3}}{2} \\ \\ x=\frac{1.50}{\sqrt[]{3}}\cdot\frac{\sqrt[]{3}}{\sqrt[]{3}}=\frac{1.50\sqrt[]{3}}{3}=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Part 2
Find the distance AB
Applying the Pythagorean Theorem
AB^2=1.5^2+x^2
substitute the value of x
AB^2=2.25+(3/4)
AB^2=3
[tex]AB=\sqrt[]{3}\text{ in}[/tex]the distance AB is the square root of 3 inches
Related Questions
which number is divisible by "644532"
Answers
Answer:
2
Step-by-step explanation: 2 can be divided by 644532
tell whether you can prove that each quadrilateral is a parallelogram. Explain.
Answers
WE know that in any quadrilateral the interior sum of its angles is 360. The missing angle in this case is:
[tex]360-121-59-59=121[/tex]Now, we also know that if the oposite angles in a quadrilateral are equal then the quadrilateral is a parallelogram.
Therefore the figure shown is a parallelogram.
Find the total amount in the compound interest account $2650 is compounded annually at a rate of 11% for 1 year
Answers
The compound interest formula is:
[tex]A\text{ = P}(1+i)^t[/tex]where:
A is the final amount including the principal
P is the principal amount
i is the interest rate (as a decimal)
t is time in years
Replacing with P = $2650, i = 0.11, and t = 1, we get:
A = 2650*(1 + 0.11)
A = 2650*1.11
A = $2941.5
Please tell me if these are correct if theyre not please help and tell me which ones are the right answers
Answers
Answer:
They're correct
Step-by-step explanation:
A random variable X follows a normal distribution with a mean of 150 and a standard deviation of sigma. If we know that P(120 < X < 180) = 0.95, then, according to the 68-95-99.7 rule, the value of sigma is approximately:
a.
20
b.
15
c.
40
d.
30
e.
60
Answers
The value of sigma according to the 68-95-99.7 rule is 15.
What is the 68-95-99.7 rule?This is the informal term that is used in statistics to remember the percentage of values that are in the interval of a distribution in statistics.
We have the mean = 150
the interval is given as P(120 < X < 180)
based on this rule, 95 percent of the data lies in the u - 20 and u + 20 region
Such that we would have
u - 2α < x < u + 2α = 0.95
we have
u - 2α = 120
150 - 2α = 120
2α = 150 - 120
2α = 30
divide through by 2
α = 15
Sigma is given as 15
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Find the area of the triangle. 30 cm 15 cm cm2
Answers
Area of the triangle is 225 sq. cm.
Given:
The base of the triangle is, b = 30cm.
The height of the triangle is, h = 15cm.
The objective is to find the area of the triangle.
The formula to find the area of the triangle is,
[tex]A=\frac{1}{2}\times b\times h[/tex]Now, substitute the given values in the above formula.
[tex]\begin{gathered} A=\frac{1}{2}\times30\times15 \\ A=225cm^2 \end{gathered}[/tex]Hence, the area of the triangle is 225 sq. cm.
Exercise 2 Find a formula for Y in terms of X
Answers
Given:
y is inversely proportional to square of x.
The equation is written as,
[tex]\begin{gathered} y\propto\frac{1}{x^2} \\ y=\frac{c}{x^2}\ldots\ldots\ldots c\text{ is constant} \end{gathered}[/tex]Also y = 0.25 when x = 5.
[tex]\begin{gathered} y=\frac{c}{x^2} \\ 0.25=\frac{c}{5^2} \\ 25\times0.25=c \\ c=\frac{25}{4} \end{gathered}[/tex]So, the equation of y interms of x is,
[tex]y=\frac{25}{4x^2}[/tex]When x increases,
[tex]\begin{gathered} \lim _{x\to\infty}y=\lim _{x\to\infty}(\frac{25}{4x^2}) \\ =\frac{25}{4}\lim _{x\to\infty}(\frac{1}{x^2}) \\ =0 \end{gathered}[/tex]Hence, the value of x increases then y decreases.
Simplify the numerical expression (3^2 * 5^-1)^2
Answers
Simplify the numerical expression
[tex](3^2\cdot5^{-1})^{2}[/tex][tex]\begin{gathered} (9\cdot\frac{1}{5})^{2}= \\ (\frac{9}{5})^{2}= \\ \frac{81}{25} \end{gathered}[/tex]A car used 15 gallons of gasoline when driven 315 miles. Based on this information, which expression should be used to determine the unit rate of miles per gallon of gasoline?
Answers
Given trhat a car used 15 gallons of gasoline to cover 315 miles.
The expression that will be used to determine the unit rate of miles per gallon of gasoline is:
[tex]\frac{315\text{ miles}}{15\text{ gallons}}[/tex]ANSWER:
[tex]\frac{315\text{ miles}}{15\text{ gallons}}[/tex]it says i need to find the shortest distance between the point and the line for geometry honors, how would i figure it out
Answers
The given line equation is,
[tex]3x-y=-6[/tex]The given point is ,
[tex](5,1)[/tex]The graph will look like this,
let us rewrite the line equtaion as ,
[tex]3x-y+6=0[/tex]now, let us compare with the general equation of line,
[tex]Ax+By+C=0[/tex]then, A= 3,B=-1 and c= 6.
let us use the formula,
[tex]\begin{gathered} d=\frac{|Ax+By+c|}{\sqrt[]{A^2+B^2}} \\ d=\frac{|3\times5+(-1)\times1+6|}{\sqrt[\square]{3^2+(-1)^2}} \\ d=\frac{|15-1+6|}{\sqrt[\square]{9+1}} \\ d=\frac{20}{\sqrt[\square]{10}} \\ d=6.32 \end{gathered}[/tex]The shortest distance is 6.32 .
Find the quotient.8 / (1 1/3) (Type a whole number or a fraction.)
Answers
In order to calculate the result of this division, let's first convert the mixed number 1 1/3 into a fraction:
[tex]1\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}[/tex]Now, calculating the division, we have:
[tex]\frac{8}{\frac{4}{3}}=8\cdot\frac{3}{4}=2\cdot3=6[/tex]So the result is 6.
Jenny wants to earn $1,300by the end of the summer. How much more will she need to earn to meet her goal?
Answers
The most appropriate choice for subtraction of natural numbers will be given by-
Jenny needs $1172.95 to earn her goal.
What is subtraction?
At first, it is important to know about natural numbers.
Natural numbers are integers which are greater than or equal to 1
One of the operations on natural number is subtraction
The process of reducing one number from another number is called subtraction. Subtraction is used to find the difference between two numbers. The larger number is called minuend and the smaller number is called subtrehend.
Amount of money Jennyy had before = $127.05
Amount of money Jenny wants to earn = $1300
Amount of money Jenny needs to earn her goal = $(1300 - 127.05)
= $1172.95
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Complete Question
Jenny wants to earn $1,300 by the end of the summer. How much more will she need to meet her goal?
(Jenny had $127.05 before.)
18. Yvonne paid $18.72 for 8 gallons of gas. How much would she have spent on gas if she had only needed 5 gallons of gas?
Answers
As given by the question
There are given that $18.72 for 8 gallons of gas.
Now,
Since, $18.72 for 8 gallons of gas;
Then,
First calculate the price of one-gallon gas
So,
[tex]\frac{18.72}{8}=2.34[/tex]The price og one g
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online.Grocery OptionsStoreOnlineTotalWomen231235Men221537Total452772What percent of the people surveyed shop at a local grocery store? Round your answer to the nearest whole number percent
Answers
Given:
A survey stopped men and women at random to ask them where they purchased groceries, at a local grocery store or online. Grocery Options
Store Online Total
Women 23 12 35
Men 22 15 37
Total 45 27 72
Required:
To find the percentage of the people surveyed shop at a local grocery store.
Explanation:
The total number of people is 75.
And the total number of people surveyed shop at a local grocery store is 45.
Now the percentage of the people surveyed shop at a local grocery store is,
[tex]=\frac{45}{72}\times100[/tex][tex]\begin{gathered} =62.5\% \\ \\ \approx63\% \end{gathered}[/tex]Final Answer:
63% of the people surveyed shop at a local grocery store.
The cargo of the truck welghs no more than 2,800 pounds.Use w to represent the weight (in pounds) of the cargo.
Answers
We know that
• The truck weighs no more than 2,800 pounds.
This problem is about inequalities.
"no more" indicates an inequality sign, specifically, it shows that we should use "less than or equal to", because this sign indicates the same as the problem do.
Therefore, the expression of the truck weight is
[tex]w\leq2,800[/tex]The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.A. 7/12B. 4/7C. 7/11D. 4/11
Answers
We have a reason for 7:4,
i.e. the total probability of winning is 7+4=11
If the horse has a probability of winning of 7 between 11
We can say that the Pw of the horse is as follows
[tex]\frac{7}{11}[/tex]The answer is the option C
A teacher determines the linear equation y=12x + 40 best models the number of points a student should earn on a test, y, if the student studies for x hours. Which statement is true
Answers
Given the equation:
y = 12x + 40
Where x represents the number of hours and y represents the number of points the student should earn.
To find the correct statement substitute the number of hours and points given for x and y respectively. If the left hand side of the equation equals the right hand side then the statement is the true.
We have:
1. A student who studies for 3 hours should earn about 76 points.
x = 3
y = 76
Substitute 3 for x and 76 for y.
y = 12x + 40
76 = 12(3) + 40
76 = 36 + 40
76 = 76
This statement is true.
2.
I need help with this practice problem solving It is trigonometry I will send another picture with the graph that is included in the problem, it asks to use the graph to solve
Answers
Given the function
[tex]f(x)=\sin (\pi x+\frac{\pi}{2})[/tex]The graph of the function is as shown below:
Solve the inequality and graph the solution set.3 ≤ 4x + 1 < 9
Answers
Okay, here we have this:
Considering the provided inequality, we are going to solve it and graph the solution set, so we obtain the following:
3 ≤ 4x + 1 < 9
3 -1≤ 4x + 1 -1< 9-1
2 ≤ 4x < 8
2/4 ≤ 4x/4 < 8/4
1/2 ≤ x < 2
In interval notation the solution set will be: [1/2, 2)
And if we plot this solution interval we get:
Where the solution set will be the purple part.
A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked. Suppose that x and y are related by the equation y=53 + 2x. Answer the questions below. Note that a change can be increased or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What was the road’s length when the crew started working?What is the change per day in the road’s length?
Answers
Given the equation:
[tex]y=53+2x[/tex]Where y represents the total length of the road (in miles), and x represents the number of days the crew has worked.
(a) What was the road’s length when the crew started working?
When the crew started working we have x = 0. Then:
[tex]\begin{gathered} y=53+2\cdot0 \\ \therefore y=53\text{ miles} \end{gathered}[/tex]The road's length is 53 miles.
(b) What is the change per day in the road’s length?
The change per day in the road's length is 2 miles/day.
Find the equation of the linear function x 1 2 3 4 y 1 6 11 16
Answers
We solve as follows:
*We determine first the slope (m), that is:
[tex]m=\frac{6-1}{2-1}\Rightarrow m=5[/tex]Now, using the slope and one point of the line, we replace in the following expression:
[tex]y-y_1=m(x-x_1)[/tex]We can use any point of the line, but I will be using the point (1, 1), that is:
[tex]y-1=5(x-1)[/tex]Now, we solve for y:
[tex]\Rightarrow y-1=5x-5\Rightarrow y=5x-4[/tex]Find the area round to two decimal places as needed
Answers
To find the area of an obtuse triangle you have to multiply the base of the triangle by the vertical height and divide the result by 2 following the formula:
[tex]A=\frac{b\cdot h}{2}[/tex]The base of the triangle is b= 7 miles and the height is h= 8 miles, using these lengths calculate the area as follows:
[tex]\begin{gathered} A=\frac{7\cdot8}{2} \\ A=\frac{56}{2} \\ A=28mi^2 \end{gathered}[/tex]The area of the triangle is 28 square miles.
Susan has a job selling cars, and earns 1.25% commission on the first $100,000 in sales,The commission increases to 4.95% on the next $200,000. Last month her total sales were$387,000. How much was her commission if she received 7.25% for any sales over $300,000
Answers
Solution:
Susan earns a commission based on car sales made.
Given:
Total sales made for the month = $387,000
Her commission is calculated based on levels and commision rate for each level.
On the first $100,000, she earns 1.25% commission.
Total sales at this level is $100,000
[tex]\begin{gathered} \text{Commision made on the first \$100,000 is;} \\ \frac{1.25}{100}\times100000=\text{ \$1,250} \\ =\text{ \$1,250} \end{gathered}[/tex]On the next $200,000, she earns 4.95% commission.
Total sales at this level is $300,000
[tex]\begin{gathered} \text{Commision made on the next \$200,000 is;} \\ \frac{4.95}{100}\times200000=\text{ \$9,900} \\ =\text{ \$9,900} \end{gathered}[/tex]On the next $87,000, total sales at this level is $387,000. She earns 7.25% commission for sales above $300,000.
[tex]\begin{gathered} \text{Commision made on the next \$87,000 is;} \\ \frac{7.25}{100}\times87000=\text{ \$6,}307.50 \\ =\text{ \$6,}307.50 \end{gathered}[/tex]Therefore, Susan's total commission received for the month is;
[tex]\begin{gathered} \text{ \$1250 + \$9900 + \$6307.50} \\ =\text{ \$17,457.50} \end{gathered}[/tex]Hence, her commission received in total for the sales made is $17,457.50
Sales representatives of a new line of computers predict that sales can be approximated by the function (0= 1350 + 6101n(31+ e), where is measured in years.What are the predicted sales in 15 years? Round your answer to the nearest whole number
Answers
It is predicted that sales over time can be approximated by the function:
[tex]S(t)=1350+610\ln(3t+e)[/tex]It is required to find the predicted sales in 15 years to the nearest whole number.
To do this, substitute t=15 into the given function:
[tex]S(15)=1350+610\ln(3\cdot15+e)=1350+610\ln(45+e)[/tex]Evaluate and round to the nearest whole number as required:
[tex]S(15)=1350+610\ln(45+e)\approx3708[/tex]The sales in 15 years is about 3708.
you have a table that shows a linear relationship, when can you read the value for b,in y = mx + rectly from the table without drawing a graph or doing any calculations? Complete the explanati there is a point ( (select) vy) in the table, then y = b because at the y-Intercept the value of x select) (select) 0 y
Answers
y=mx+b
Where:
m= slope
b= y-intercept
b= has coordinate points (0,y) where the line crosses the y-axis.
So:
If there is a point (0,y) in the table y=b because at the y-intercept the value of x is 0.
114. If plane X averages 800 mph and plane Y averages 400 mph, how manyhours will plane X travel before it overtakes plane Y if plane Y has a 2 hourand 30 minute head start?a.1b. 2c. 5d. 72
Answers
To determine the time taken for the plane X to travel:
If plane X averages 800 mph and plane Y averages 400 mph
Distance column is found by multiplying the rate
by time.
The time taken for plane Y to travel = 2hr 30 minutes = 2.5hrs head start
Be sure to distribute the 400(t +2.5)for Plane Y,
and Plane X to distribute 800t
As they cover the same distance
[tex]\begin{gathered} Dis\tan ce\text{ is equal ,} \\ 800t=400(t+2.5) \\ 800t=400t+1000 \\ 800t-400t=1000 \\ 400t=1000 \\ t=\frac{1000}{400} \\ t=2\frac{1}{2}hr \end{gathered}[/tex]Therefore the plane X will travel for 2 1/2 hours
Hence the correct answer is Option B
Rosa needs to build a wall. She has to start the wall with one postand then every 5.75 feet put another post. The wall will be166.75 feet long. How many posts will she need?
Answers
For every 5.75 feet, here is one post.
Determine the number of posts in a wall of 166.75 feet.
[tex]\begin{gathered} p=\frac{166.75}{5.75} \\ =29 \end{gathered}[/tex]So 29 posts needed for the wall.
Sketch the graph of each line.
24)
y=3/5x-4
Answers
The graph of the given line is attached below.
We are given the line:-
y = (3/5)x - 4
We will find the x and y intercepts of the line to plot in the graph.
As the equation is already in the slope intercept form, we can write,
The y-intercept of the line is -4.
Hence, the coordinates of the point will be (0,-4).
To find the x - intercept of the line we will put y = 0 in the given line.
0 = (3/5)x - 4
4 = 3x/5
x = 20/3
The coordinates of the point will be (20/3,0).
We can plot these points to get the desired graph.
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calculate the slope of a line passing through the given points (5,-2) and (5,-3)
Answers
Given the points (5,-2) and (5,-3), we can find the slope of the line that passes through them with the following formula:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{-3-(-2)}{5-5}=\frac{-1}{0} \end{gathered}[/tex]since we have that the slope is not defined, the line that passes through the points (5,-2) and (5,-3) is the vertical line x=5
Fifteen strips, 11/4" wide, are to be ripped from a sheet of plywood. If 1/8" is lost with each cut, how much of the plywood sheet is used in making the 15 strips? (Assume 15 cuts are necessary.)
Answers
The size of the plywood sheet used is;
[tex]\frac{37}{8}^{\doubleprime}[/tex]Here, we want to get the size of the part of the plywood sheet lost
From the question, we are told that 1/8 inches is lost
The size lost would be;
[tex]\frac{1}{8}\times\text{ 15 = }\frac{15}{8}[/tex]This is the size that was lost
To get the total part of the plywood used, we simply add the width of all the strips to the amount of the plywood lost
We have this as;
[tex]\frac{11}{4}\text{ + }\frac{15}{8}\text{ = }\frac{22+15}{8}\text{ = }\frac{37}{8}[/tex]