Given: the fraction 1/8.
Objective is to convert this fraction in to decimal.
[tex]\frac{1}{8}=0.125[/tex]Answer: 0.125
In a raffle where 8000 tickets are sold for $2 each, one prize of $4200 will be awarded. What is the expected value of a single ticket in the raffle?
It is given that 8000 tickets are sold for $2 each, one prize of $4200 will be awarded.
The expected value is determined as
[tex]\frac{1}{8000\times4198}+\frac{7999}{8000\times-2}[/tex][tex]\frac{1}{8000\times4198}-\frac{7999}{8000\times2}=\frac{1}{8000}(\frac{2-33,579,802}{4198\times2})[/tex][tex]\frac{1}{8000}(\frac{-3183600}{796})=\frac{-3183600}{6368000}=-0.499[/tex]The expected value of a single ticket in the raffle is -0.499 dollar.
Given the graph of the function f(x), find x when f(x) =4
x = -1
Explanations:Note:
f(x) is the vertical axis of the graph
x is the horizontal axis of the graph
To get the value of x when f(x) = 4:
Locate the point on the graph that is on the "4" on the vertical axis and trace it downwards to get the value of x.
If that is done, we would observe that x = -1 when f(x) = 4
Find the perimeter (or circumference) and area of the figure. (Where necessary, use 7= 3.14.)
This is a Triangle. The perimeter of a triangle is given by the sum of all sides:
[tex]\begin{gathered} P=a+b+c \\ a,b,c=\text{the sides of the triangle} \\ a=5,b=5,c=6 \\ P=5+5+6=16 \\ P=16units \end{gathered}[/tex]Area of triangle is given by 1/2 * bh
[tex]\begin{gathered} A=\frac{1}{2}bh+\frac{1}{2}bh(For2\text{Triangles)} \\ \Rightarrow A=bh \\ b=6,h=4 \\ A=6\cdot4=24 \\ A=24units^2 \end{gathered}[/tex]Angles X and Y are supplementary. Angle X measures 121.75° and angle Y measures (m − 9)°. Find m∠Y. 125.5° 58.25° 116.5° 67.25°
By the concept of supplementary angles the value of y = 58.25°. That is option C.
What are supplementary angles?Angles that add up to 180 degrees are referred to as supplemental angles. For instance, angle 130° and angle 50° are supplementary angles since the sum of these two angles is 180°. Supplementary angles are two angles that add up to 18 0 180 circ 180. They frequently occur when they are on the same side of a straight line, for example. When two angles sum up to 180 degrees, they are complementary (a Straight Angle). They don't even have to be close to one another for the total to be 180 degrees. Examples: The additional angles of 40° and 140°. Supplementary angles are a pair of angles that always add up to 180 degrees. These two perspectives are referred to as complements of one another.
∠X + ∠Y = 180°
∠Y = 180° - 121.75°
∠Y = 58.25°
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Answer: the answer is B
Step-by-step explanation: i took the test and got it right
A family is driving home from Georgia. The graph shows the distance away 1 point from home, in miles, as a function of time, in hours. Use the graph to estimate the average rate of change from t=0 to t=7.2. **Round answer to 1 decimal place. ***
Basically we need to find the slope:
[tex]\begin{gathered} avg=\frac{f(b)-f(a)}{b-a} \\ \text{Where:} \\ a=0 \\ b=7.2 \\ f(a)=420 \\ f(b)=0 \\ avg=\frac{0-420}{7.2-0}=\frac{-420}{7.2}=-\frac{175}{3}\approx-58.33 \end{gathered}[/tex]I need help solving theses 3 problems I don't understand and need help.
.
From the image;
The two points are (-5, 3) and (-2,-3)
The distance between two points is given by:
[tex]D=\sqrt{(x_2-x_2)^2+(x_2-x_2)^2}[/tex]On substitution
[tex]\begin{gathered} D=\sqrt{(-2--5)^2+(-3-3)^2} \\ \\ D=\sqrt{(3)^2+(-6)^2} \\ \\ D=\sqrt{45} \\ D=6.71units \end{gathered}[/tex]Therefore the distance between two points on the graph is 6.71units
Mama Gianaras pizza comes in two sizes, medium and large. The radius of a medium pizza is 8'' and the large is a 10''. what is the ratio of the circumferences? state answer as a fraction.
Explanation
[tex]\begin{gathered} C_m=2\pi *8 \\ C_l=2\pi *10 \end{gathered}[/tex][tex]\frac{C_m}{C_l}=\frac{2\pi *8}{2\pi *10}=\frac{8}{10}=\frac{4}{5}[/tex]Answer
4/5
members of the starting basketball team weigh 235,210,215,264,and 200 pounds. what is the average weight of starting team.
Consider that the average of any discrete data is defined as,
[tex]\text{Average}=\frac{\text{ Sum of Observations}}{\text{ Number of Observations}}[/tex]Here the data is the weight (in pounds) of the starting basketball team members,
[tex]235,210,215,264,200[/tex]So the corresponding mean wieght of a team member is calculated as,
[tex]\begin{gathered} \text{Average}=\frac{235+210+215+264+200}{5} \\ \text{Average}=\frac{1124}{5} \\ \text{Average}=224.8 \end{gathered}[/tex]Thus, the average weight of starting team member is 224.8 pounds.
you have the numbers 1-24 written on slips of paper. If you choose one slip at random, what is the probability that you will not select a number which divisible by 3?a. 1/3b. 2/3c. 5/8d. 3/8
24 is divisible by 3
21 is divisible by 3
18 is divisible by 3
15 is divisible by 3
12 is divisible by 3
9 is divisible by 3
6 is divisible by 3
3 is divisible by 3
8 numbers are divisible by 3
Total numbers: 24
24-8 = 16 numbers are not divisible by 3
Divide the number that are not divisible by 3 , by the total numbers:
16 /24 = 2/3
the sum of the measures of the angles in a triangle equal
Given:
sum of measure of the angle in a triangle
Sum of three angle is:
[tex]x+y+z=180[/tex]then the sum of the measures of the angle in a triangle is equal to 180.
17. A publisher marks up a textbook by 60%, and a bookstore further marks up the textbook by 25%. What percentage of the original cost do you pay?%
A publisher marks up a textbook by 60%, and a bookstore further marks up the textbook by 25%. What percentage of the original cost do you pay?
Let
x ------> original cost
so
1) publisher marks up a textbook by 60%
cost=1.60x
2) bookstore further marks up the textbook by 25%
cost=1.60x(1.25)=2x
therefore
200%What is the factored form of this expression?x^3 + 27(32 – 3) (3 + 35 + 9)(1 + 3) (12 - 35 + 9)(2 + 3) (1 - 3.5 + 9)(t – 3)(x2 + 3r + 9
We have the following:
[tex]\begin{gathered} x^3+27 \\ x^3+3^3 \end{gathered}[/tex]now,
[tex]x^3+y^3=\mleft(x+y\mright)\mleft(x^2-xy+y^2\mright)[/tex]replacing:
[tex]x^3+3^3=\mleft(x+3\mright)\mleft(x^2-3x+9\mright)[/tex]The answer is the secondo option
Please explain step by step on how to solve As I am brand new to this What is the median of 19,3,7,1,11,19,2,3,17,4,14,12
Answer:
The median is 9
Explanation:
The median of a data set is the value that lies in the middle of the ordered data set.
In this case, we have:
19,3,7,1,11,19,2,3,17,4,14,12
We need to order the list in ascending order:
1, 2, 3, 3, 4, 7, 11, 12, 14, 17, 19, 19
There are 12 values, since is an even number, the median is the average of the pair in the middle.
In this case, the pair in the middle is 7 and 11. The average is:
[tex]\frac{7+11}{2}=\frac{18}{2}=9[/tex]Thus, the median is 9
the boiling point at atmospheric pressure of Ammonia is -28 1/10 °F and of propylene is -5÷ 9/10 °F. what is the difference In their boiling points?
The difference between the boiling points is the subtraction between them. The two boiling points are given in mixed fractions, to subtract them we need to subtract the integer part and the fractional part separately. With this in mind let's solve the problem:
[tex]\begin{gathered} -28\frac{1}{10}-(-53\frac{1}{10}) \\ -28\frac{9}{10}+53\frac{1}{10} \\ 25\frac{8}{10} \\ 25\frac{4}{5} \end{gathered}[/tex]The correct answer is the option "B".
Draw the dilation of ABC using center P and a scale factor of 1/3. Draw the dilation of ABC using center A and a scale factor of 2. Explain how they are similar. 3
Both triangles are similar; while the first is a reduction, the second is an enlargement.
Let's begin by listing out the information given to us:
A(5,6), B(5,10), C(8,3)
A scale factor of 1 / 3 means the triangle will be smaller (reduction):
[tex]$$\begin{gathered}P=(2,3) \\A B=4 \Rightarrow A^{\prime} B^{\prime}=\frac{4}{3} \\B C=\sqrt{58} \Rightarrow B^{\prime} C^{\prime}=\frac{\sqrt{58}}{3} \\A C=\sqrt{18} \Rightarrow A^{\prime} C^{\prime}=\frac{\sqrt{18}}{3}=\sqrt{6}\end{gathered}$$[/tex]
A scale factor of 2 means the triangle will be bigger (enlargement):
[tex]$$\begin{gathered}A^{\prime \prime}=2 A=2(5,6)=(10,12) \\B^{\prime \prime}=2 B=2(5,10)=(10,20) \\C^{\prime \prime}=2 C=2(8,3)=(16,6)\end{gathered}$$[/tex]
Both triangles are similar; while the first is a reduction, the second is an enlargement
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A line passes through (10, 3) and (13, -6). What is the equation of the line in standard form?A. 3x - y = 1B. 3x + y = 27C. 3x + y = 33D. 3x - y = 27
In general, given two points on a line, we can find its equation by using the formula below
[tex]\begin{gathered} (x_1,y_1),(x_2,y_2) \\ \Rightarrow y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{gathered}[/tex]Therefore, in our case,
[tex]\begin{gathered} (10,3),(13,-6) \\ \Rightarrow y-3=\frac{-6-3}{13-10}(x-10) \\ \Rightarrow y-3=-\frac{9}{3}(x-10) \\ \Rightarrow y-3=-3(x-10) \\ \Rightarrow y-3=-3x+30 \\ \Rightarrow3x+y=33 \end{gathered}[/tex]Thus, the answer is 3x+y=33, option C.
how many square inches, 1 in. by 1 in., fit in an area if 1 square foot, 1 ft by 1 ft?
We have the following:
We must convert square feet to square inches
We have that 1 foot is equal to 12 inches
[tex]1ft^2\cdot\frac{(12in)^2}{(1ft)^2}=144in^2[/tex]Which means that one square foot equals 144 square inches.
Whats the correct answer answer asap
Answer:
the answer is c- best known mass
hello I'm in the 7th grade and i need help with these word problems are you able to help and explain it to me so I can understand .. the title is called word Ratios
a) 12 goats ate 3 pizzas. To find goat per pizza, dividing the number of goats by the number of pizzas:
[tex]\frac{12\text{ goats}}{3\text{ pizzas}}=4\text{ }\frac{goat}{pizza}[/tex]b) 20 banks are robbed for a total of $50,000. To find the money per bank, divide the total money by the number of banks.
[tex]\frac{50,000}{20}=2500\text{ }\frac{\text{\$}}{bank}[/tex]c) In 86 years, 9 drops have formed. To find years per drop, divide the years by the number of drops.
[tex]\begin{gathered} \frac{86\text{ years}}{9\text{ drops}} \\ 9.6\text{ }\frac{years}{drop} \end{gathered}[/tex]d) 3 hippos eat 5 pumpkins
To find the number of pumpkins per hippo, divide 5 by 3.
[tex]\begin{gathered} \frac{5\text{ pumpkins}}{3\text{ hippos}}=1.7\text{ }\frac{pumpkins}{hippos} \\ \end{gathered}[/tex]On a map, the distance from Falls City, Texas to Pleasanton, Texas measure 2 centimeters. What is the actual distance if the scale on the map shows that 1 centimeter is equal to 30 kilometers?
1 cm --------------------- 30 km
2 cm -------------------- x
x = (2 x 30) / 1
x = 60 / 1
x = 60
Result: the distance between these cities is 60 km.
Find the coordinates of the centroid.F(1,5) G(-2,7) H(-6,3)
The coordinates of the centroid is
[tex](-\frac{7}{3},5)[/tex]Explanation:The coordinates of the centroid of a triangle is given as:
[tex](\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})[/tex]Using the above formula, we have:
[tex]\begin{gathered} C=(\frac{1+(-2)+(-6)}{3},\frac{5+7+3}{3}) \\ \\ =(-\frac{7}{3},\frac{15}{3}) \\ \\ =(-\frac{7}{3},5) \end{gathered}[/tex]Given the function h described by h(x) = x + 2, find each of the following.h(0)=h(-7)=h( - 13)=h(10) =h(d + 4)=
Given the function h described by h(x) = x + 2, find each of the following:
h(0) = 0 + 2 = 2
h(-7) = -7 + 2 = -5
h( -13) = -13 + 2 = -11
h (10) = 10 + 2 = 12
h (d + 4) = d + 4 + 2 = d + 2 + 6
Use a calculator to help answer the question, Show that the point (6,1) is equidistant from points (9,0) and (3,0).The distance from (6,1) to (9,0) and the distance from (6,1) to (3,0) are both [ ] . Thus, (6,1) is equidistant from the two points.
First find the distance from (3,0) to (6,1)
We will use the distance formula
d = sqrt( (x2-x1)^2 + ( y2-y1)^2)
= sqrt( ( 6-3)^2 + ( 1-0)^2)
= sqrt( 3^2 + 1^2)
= sqrt( 9+1)
= sqrt(10)
Now we can find the distance between ( 6,1) and (9,0)
We will use the distance formula
d = sqrt( (x2-x1)^2 + ( y2-y1)^2)
= sqrt( ( 9-6)^2 + (0-1)^2)
= sqrt( 3^2+ (-1)^2)
= sqrt( 9+1)
= sqrt(10)
The distance is sqrt(10)
[tex]\sqrt[]{10}[/tex]The lenath of an instant message conversation is normally distributed with a mean of 5 minutes and a standard deviation of .7 minutes. What is the probability that a conversation lasts longer than 6 minutes?
To solve this problem we can use a z-table. First, we convert our score to a z-score using the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where mu represents the mean and sigma represents the standard deviation.
Using this formula in our problem, we have:
[tex]z=\frac{6-5}{0.7}=\frac{10}{7}\approx1.429[/tex]This z-score represents the position where the phone call is equal to 6 minutes. On a z-table, we're going to find the area between the mean and this z-score, since we want the probability that a conversation lasts longer than 6 minutes, we want the area above it. To calculate this area, we're going to subtract the value given on the z-table from 0.5.
The value on the z-table is:
Then, our probability is:
[tex]P(x>6)=0.5-0.4236\approx0.077[/tex]The answer is 0.077.
in the following geometric sequence, find (i) the 7th term; (ii) the nth term:-1/3, 3/4, -9/8, .....
Given the geometric sequence:
[tex]-\frac{1}{2},\frac{3}{4},\frac{-9}{8},\ldots.[/tex]The common ratio will be:
[tex]r=\frac{3}{4}\div-\frac{1}{2}=\frac{3}{4}\cdot-2=-\frac{3}{2}[/tex]The general rule of the geometric sequence will be:
[tex]a_n=a_1\cdot r^{n-1}[/tex]so, a7 will be:
[tex]a_7=-\frac{1}{2}\cdot(-\frac{3}{2})^{7-1}=-\frac{1}{2}\cdot(-\frac{3}{2})^6=-\frac{729}{128}[/tex]And an will be:
[tex]a_n=(-\frac{1}{2})\cdot(-\frac{3}{2})^{n-1}_{}[/tex]Cost for assembling a smart phone is given in formula C(q) = 500 - 2q. Where C is cost, and q is cost for parts. If cost for parts equal $75, find total cost to assemble 1500 smart phones.
The total cost to assemble 1, 500 smart phones, given the cost formula, can be found to be $525,000
How to find the cost of the smart phones?The total cost of a smart phone is found by the formula, C(q) = 500 - 2q.
Here q is the cost of parts which is 75.
The assembly cost of a single phone is therefore:
= 500 - 2(75)
= 500 - 150
= $350
If there are 1, 500 smart phones, the total cost would be:
= 350 x 1, 500
= $525,000
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what is the absolute value of -435 and 72
The absolute value of 72 is the distance between 72 and 0 on a number line.
There will be 72 point on the number line if we count. So,
Mrs. Roberts bought 4 student movietickets and one adult ticket that cost $12.Write an expression to represent the totacost of the tickets. Let s represent eachstudent ticket
Total cost = 4s+12
student's ticket price = s
Number of students tickets= 4
Adult's tickets price = $12
Number of Adult's tickets = 1
Total cost = (number of students tickets x price of each student's ticket) + ( number of adult tickets x price of each adult ticket)
Total cost of the tickets (y)= 4s + 1(12)
y = 4s+12
Michael rented a truck for one day. There was a base fee of $20.99, and there was an additional charge of 85 cents for each mile driven. Michael had to pay$134.89 when he returned the truck. For how many miles did he drive the truck?
Let the number of miles Michael drove the truck be m.
Then, the cost of the drive is given by the expression,
[tex]20.99+0.85m[/tex]The actual cost is given as $134.89
Hence, we must have that
[tex]\begin{gathered} 20.99+0.85m=134.89 \\ \text{ Subtracting 20.99 from both sides we have} \\ 0.85m=113.9 \\ \text{ Dividing both sides by 0.85 we have} \\ m=\frac{113.9}{0.85}=134 \end{gathered}[/tex]Thus the number of miles is 134 miles
Which expression has a coefficient of 6? A. 2x + 6 B. 3x - 6 C. 2(x + 6) D. 6x + 3
A coefficient is a number that is multiplied by the variable.
From the given options, the variable is x, and the option that has the coefficient 6 is option D. 6x+3.
Since the number multiplied by the variable x is 6 in option D.