Answer:
a) 0.248
b) 0.434
Explanation:
Given;
Total number of Americans in the poll = 1000
Number of Americans not in favor of the bill = 434
Number of Americans in favor of the bill = 248
Number of Americans that were not sure = 318
a) We can now go ahead and determine the probability that a randomly selected American was in favor of the bill using the below probability formula;
[tex]Probability\text{ of an event occurring = }\frac{Number\text{ of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex][tex]P(\text{Americans in favor of the bill) = }\frac{248}{1000}=0.248[/tex][tex]P(\text{Americans not in support of the bill) = }\frac{434}{1000}=0.434[/tex]Find the standard deviation of the data set.**Round your answer to the nearest hundredth.48, 30, 24, 42, 60, 24
Ok, let's find the standard deviation of the data set:
Step 1: calculate the mean.
(48+30+24+42+60+24)/6=228/6=38
Step 2: calculate the square of the distance from the mean for each piece of data.
|48-38|²=10²=100
|30-38|²=8²=64
|24-38|²=14²=196
|42-38|²=4²=16
|60-38|²=22²=484
|24-38|²=14²=196
Step 3: add the values that resulted from step 2.
100+64+196+16+484+196=1056
Step 4: divide by the number of data.
1056/6=176
Step 5: take the square root.
√176≈13.27
Finally we obtain that the standard deviation is 13.27.
which word best describes the degree of overlap between the 2 data sets
Solution
For this case we can see that the best answer is:
Low
Since we have overlap just in some values representing a low percentage of all the datasets
For the second case we have the following dataset:
27 28 28 29 29 29 30 30 30 31 31 31 33 34
We have 14 values then we can find the median like this:
Median = (30+30)/2= 30
The formula for the volume of a rectangular prism is V = lwh. What is the formula when solved for w?o202IhW=VwV?hVuw=
Formula for the Volume of rectangular prism:
[tex]\begin{gathered} V=l\cdot w\cdot h; \\ l\text{ is long} \\ w\text{ is width} \\ h\text{ is high} \end{gathered}[/tex]They ask you solve the expresion for w, that means that you have to find a expression like w=?
To do that, you should be move l and w to the other side of equation...
Start moving l,
Tell me, what is doing l to w.. what math operation...
??
Exactly, multiply.. the pass to other side to do the oposite operation.. in this case divide..like this..
[tex]\frac{V}{l}=w\cdot h[/tex]we do the same with h.. and thats all.. then we take:
[tex]\frac{V}{l\cdot h}=w[/tex]or the same
[tex]w=\frac{V}{l\cdot h}[/tex]That's your answer
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
We have the expressions:
[tex]y>2x+4[/tex][tex]y+x\le6\Rightarrow y\le6-x[/tex]Now, we will graph:
Since it is an intersection, we will graph the values contained by both inequalities.
Martina purchased a prepaid card for $30. Long distance calls cost 11 cents a minute using this card. Martina used her card only once to .ake a long distance call. If the remaining credit on her card is $28.46, how many minutes did her call last.
we get that
[tex]\begin{gathered} 28.46+0.11t=30 \\ t=\frac{30-28.46}{0.11}=14 \end{gathered}[/tex]so her call last 14 minutes
What is the length of side OR?A:6 unitsB:8 unitsC:10 units D:18 units
The perimeter is the sum of all sides, therefore:
[tex]P=(2x+4)+(x)+(3x+3)[/tex]Since the perimeter is 55 units:
[tex]55=2x+4+x+3x+3[/tex]Add like terms:
[tex]55=6x+7[/tex]Solve for x:
[tex]\begin{gathered} 55-7=6x \\ 48=6x \\ x=\frac{48}{6} \\ x=8 \end{gathered}[/tex]Answer:
x = 8
In circle J with mLHJK 54 and HJ = 13 units find area of sector HJK. Round to the nearest hundredth. K H J
we have a circle first we will calculate the whole area of the circle using the next formula
[tex]A=\pi r^2[/tex]where r= 13 units
[tex]A=\pi(13)^2=530.93\text{ square units}[/tex]Then we have 54° we need to divide between 360 In order to know the part of the circle we have
[tex]\frac{360}{54}=\frac{20}{3}[/tex]so in order to know the area of the sector HJK we will divide the area between 20/3
[tex]A_S=\frac{A}{\frac{20}{3}}=\frac{530.93}{\frac{20}{3}}=79.63[/tex]Five students measured the mass of the rock. Their readings were 95.1g, 97.0g, 96.2g, 96.5g, and 96.7g. Find the mean and median of these measures.
To get the mean of a set of data, the steps are to add all the data and divide by the total number of data.
[tex]\bar{x}=\frac{95.1+97.0+96.2+96.5+96.7}{5}[/tex]Then, solve.
[tex]\bar{x}=\frac{481.5}{5}=96.3[/tex]The mean is 96.3 grams.
On the other hand, the median of a set of data is the middlemost data once the data has been arranged from lowest to highest or vice versa.
Let's arrange the data first.
[tex]95.1,96.2,96.5,96.7,97.0[/tex]Out of the 5 data, the middlemost data would be the third one. Hence, the median is 96.5 grams.
Can you please help me complete. I am reviewing for a final
Given:
Kayakers pulling a raft. One kayaker pulls with a force of F1=(190, 160) and the other kayaker pause with a force of F2=(128, -121)
Required:
We need to find the angle between F1 and F2
Explanation:
[tex]undefined[/tex]Solve (x - 3)^2=5A. X= 5 +- square root sign 3B. X= -3 +- square root sign 5C. X= 3 +- square root sign 5D. X=8 and x= -2
Solving for x, we have:
[tex]\begin{gathered} \mleft(x-3\mright)^2=5 \\ x-3=\pm\sqrt[]{5}\text{ (Taking the square root of both sides)} \\ x=\pm\sqrt[]{5}+3\text{ (Adding 3 to both sides of the equation)} \\ \text{The answer is the option C.} \end{gathered}[/tex]Among all the rectangles that have a perimeter of 134 , find the dimensions of the one whose area is largest. write your answers as fractions reduced to the lowest terms.
Answer:
• Length = 33½ units
,• Width = 33½ units
Explanation:
The perimeter of the rectangle = 134
[tex]\begin{gathered} \text{Perimeter}=2(L+W) \\ 134=2(L+W) \\ L+W=67 \\ \implies L=67-W \end{gathered}[/tex]Using the formula for area:
[tex]\begin{gathered} Area=L\times W \\ =W(67-W) \\ A=67W-W^2 \end{gathered}[/tex]The maximum dimension will occur at the point where the derivative is 0.
[tex]\begin{gathered} A^{\prime}=67-2W=0 \\ 2W=67 \\ W=\frac{67}{2} \\ W=33\frac{1}{2}\text{ units} \end{gathered}[/tex][tex]\begin{gathered} L=67-W \\ =67-33.5 \\ =33\frac{1}{2}\text{ units} \end{gathered}[/tex]The area is maximum when the width and the length are 33½ units.
A building cast a shadow that is 245 ft. in length. If the distance from theshadow to the top of the building is 250 ft, How tall is the building?
You have the next situation:
As the building and its shadow form a angle of 90º (right angle), you use the Pythagoras theorem:
[tex]x=\sqrt[]{h^2-s^2}[/tex]The measure of x is equal to the square root of hypothenusa squared less the shadow measure squared:
[tex]\begin{gathered} x=\sqrt[]{(250ft)^2-(245ft)^2} \\ x=\sqrt[]{62500ft^2-60025ft^2} \\ x=\sqrt[]{2475ft^2} \\ x=49.749ft\approx49.7ft \end{gathered}[/tex]Then, the building is 49.7 feet tallWhich number is less than 0.4?A. 0.57 B. 0.09C. 0.7 D. 0.90 E. 0.5
B. 0.09
Explanations:The only option less than 0.4 in the options is 0.09
All other options (0.57, 0.7, 0.90, 0.5) are greater than 0.4
mrs. Ruiz planted 14 flowers in three plots she planted 4 flowers in 1 blue pot and split the rest equally between 2 red plots add symbols to the equation below then solve the equation to find the number of flowers mrs. Ruiz planet and each of the two red plots
Total numbers of flowers = 14
4 flowers in the blue pot
Then, 14 - 4 = 10 plants
10 plants were equally planted in 2 red pots.
10 = 2r
r = 5 flowers
Mrs Ruiz planted 4 flowers in the blue pot and 5 flowers in each of the red pots.
Asha has $100 on a movie theatergift card. Each time she buys a ticketto a movie it costs her $8.75. Writean equation that Asha can use to findX, the number of tickets she can buyif she wants to keep a $15 balance onthe gift card.
We can write an equation for the balance of the gift card.
We know that if she doesn't buy any ticket (x = 0), the balance will be $100, which is the initial balance.
Each increase in x, is a decrease of 8.75 for the balance. This represents the slope of the equation, as there is not other term.
Then, we can write the equation as:
[tex]y=100-8.75x[/tex]If she wants to know how many tickets she can buy to have a $15 balance (y = 15), we can use the equation as:
[tex]\begin{gathered} y=15 \\ 100-8.75x=15 \\ 100-15=8.75x \\ 85=8.75x \\ x=\frac{85}{8.75} \\ x\approx9.71 \end{gathered}[/tex]She can buy up to 9 tickets (if she buys 10 tickets, she will have less than $15).
Answer:
The equation is y = 100 - 8.75x.
X = 9 tickets for a balance of $15.
NEED HELP ASAP!!! The table shows the relationship between the number of bracelets made and the number of beads used:Number of bracelets Number of beads3 215 357 ?9 63The number of beads used to make 7 bracelets is _______.
49
1) Since this is a proportional relationship, we can fill in the table noticing the factor of proportionality is the same for every row
3 | 21
5 | 35
7 | 49
9 | 63
2) As we can see the factor is 7. So the number of beads used to make 7 bracelets is 49
describe the key features of g(x), including theend behavior, y-intercept, and zeros.g(x) = x^3 - x^2- 4x + 4 than create a graph of the polynomial function
End behavior: You have the leading coefficient (number write in front of the variable with the largest exponent) of +1 and the polynomial degree is odd (3).
For this features the end behavior is: falls to left and rises to right.Y-intercept: The value of g(x) when it cross the y-axis (when x is 0)
Substitute the x in the equation by 0 and evaluate the function:
[tex]\begin{gathered} g(0)=0^3-0^2-4(0)+4 \\ g(0)=4 \end{gathered}[/tex]y-intercept: 4To find the zeros:
Equals the function to 0
[tex]x^3-x^2-4x+4=0[/tex]Factor:
-Factor x²
[tex]x^2(x-1)-4x+4=0[/tex]-Factor -4:
[tex]x^2(x-1)-4(x-1)=0[/tex]-Factor (x-1):
[tex](x-1)(x^2-4)=0[/tex]Write the second factor as a substraction of squares:
[tex]\begin{gathered} (x-1)(x^2-2^2)=0 \\ \\ a^2-b^2=(a+b)(a+b) \\ \\ (x-1)(x+2)(x-2)=0 \end{gathered}[/tex]Equal each factor to 0 and solve x:
[tex]\begin{gathered} x-1=0 \\ x=1 \\ \\ x+2=0 \\ x=-2 \\ \\ x-2=0 \\ x=2 \end{gathered}[/tex]Then, the zeros of g(x) are: x=1, -2, 2if ×=10 what is the value of 2×+5
In order to calculate the value of 2x + 5 if x=10, we would need to substitute in the expression 2x + 5 the variable x with the number 10.
Therefore, 2x + 5 if x=10 would be equal to:
2(10)+5=20+5=25
Therefore, the value of 2×+5 if x=10 would be 25
b.) What does the point (2.1, 18.6) represent? Select]
Based on the information of the graph, you can notice that the point (2.1 , 18.6) corresponds to point B.
The point (2.1 , 18.6) means that for 2.1 free throw attemps per game, there are approximately 18.6 points per game.
Activity 1 of 2Mr. Hall needs lights installed in his house and is trying to decide between two electric companies. ABC Electric's charges can be represented by the equation y = 50x + 75 Two Electricians' charges can be represented by the following table: X: 0 1 2 4Y: 70 130 190 250Complete each of the 2 activities for this Task.Which company charges more per hour?Activity 2 of 2Mr. Hall is estimating he needs about 5 hours of work done. Which company should he choose if he is trying to save money? Show your work or explain your reasoning.
1) Two Electricians' charges more per hour
2) Mr Hall should choose ABC electric to save money
Explanation:ABC Electric's charges :
y = 50x + 75
Two Electricians' charges is shown in the table
To determine which company charges more per hour, let's compare their charages
1) y = 50x + 75
when x = 1 hour
y = 50(1) + 75 = 50 + 75
y = $125
From the table, when x = 1
y = $130
$130 > $125
The charge of Two Electricians' for 1 hour is more than that of ABC Electric's charges
Hence, Two Electricians charges more per hour
2) For 5hours, x = 5
inserting the value for x in ABC electric charges:
y = 50(5) + 75
y = 250 + 75
y = $325
There is no value for x = 5 on the table given
we need to find an equation for it
Equation of line: y = mx + c
Rate of change = slope = change in y/change in x
Using points: (0, 70) and (1, 130)
Rate of change = (130-70)/(1-0) = 60/1
Rate of change = slope = 60
The y-intecept is when x = 0
y-intercept = c = 70
equation for Two Electricians' charges :
y = 60x + 70
when x = 5
y = 60(5) + 70
y = 300 70
y = $370
$370 > $325
ABC electric cost less for 5hrs
Mr Hall should choose ABC electric to save money
Answer the questions below using the given scatter plot. a. The scatter plot shows what kind of association?Circle one. Positive, Negative, Noneb. Finish the following sentence.As the number of peaches sold_________,the price of peaches____________.
a) The scatter plot shows a negative association
b) As the number of peaches sold increases, the price of peaches decreases
The sum of the three angles of a quadrilateral is 310°, what is the measure of the fourth angle?
The sum of the angles in a quadrilateral is 360 degrees. Let x represent the fouth angle. If the sum of the three angles of the quadrilateral is 310, it means that
310 + x = 360
subtracting 310 from both sides,
310 - 310 + x = 360 - 310
x = 50
the measure of the fourth angle is 50 degrees
Gerd is considering an account that earns 6% interest per annum compounded monthly. What is the annual percentage yield (APY)? Give your answer as a percent rounded to the nearest tenth (e.g. 5.1%). Do not include the percentage sign (%) in the answer box below.
Data
Interest = 6%
Annual percentage yield = ?
APY = (1 + r/n)^n -1 12 is because a year has 12 months
6% = 0.06
APY = (1 + 0.06/12) ^12 - 1
APY = (1 + 0.005)^12 - 1
APY = (1.005)^12 - 1
APY = 1.062 - 1
APY = 0.062 or 6.2%
solve the right triangle and round decimal answers to the nearest tenthi know its either option a or c but im not 100% sure which one
Step 1
Name all sides
Hypotanuse = 16 side facing right angle
Opposite = y side facing given angle
Adjacent = x
90 +
Step 2
Find the values of x and y
[tex]\begin{gathered} \theta\text{ = 76} \\ \sin \theta\text{ = }\frac{\text{Opposite}}{\text{Hypotanuse}} \\ \sin 76\text{ = }\frac{y}{16} \\ 0.97\text{ = }\frac{y}{16} \\ \text{Cross multiply} \\ y\text{ = 0.97 x 16} \\ y\text{ = 15.52} \\ y\text{ = 15.5} \end{gathered}[/tex][tex]\begin{gathered} \cos \theta\text{ = }\frac{adjacent}{\text{hypotanuse}} \\ \cos 76\text{ = }\frac{x}{16} \\ 0.24\text{ = }\frac{x}{16} \\ \text{Cross multiply} \\ x\text{ = 0.24 x 16} \\ x\text{ = 3.8}5 \\ x\text{ = 3}.9 \end{gathered}[/tex]help me please..........
The amount each classroom will receive $1,963
mercedes walks 1.93 kilometers to a neighbors house in 23 minutes. assuming she walks at a constant speed write a proportion that represents how many kilometers. y, mercedes can walk in x minutes. then solve your proportion for y
Mercedes can walk 0.083913 km per minute
[tex]y\text{ = 0.083913x}[/tex]
Here, we want to write a proportion and solve it
We want to get the number of kilometers y that mercedes can walk in x minutes
To get the value of y, we simply solve the proportion
Mathematically, the proportion would be;
[tex]\begin{gathered} \frac{y}{x} \\ \\ \end{gathered}[/tex]So, we proceed to divide the number of kilometers walked by the number of minutes
The proportion in this case will be;
[tex]\frac{1.93}{23}\text{ = 0.083913 }[/tex]So, what this means is that she can walk 0.083913 kilometers in a minutes
So if she walks 0.083913 kilometers in a minute, then, the number of kilometers y, walked in x minutes will be;
[tex]y\text{ = 0.083913x}[/tex]The formula gives the volume V of a right cylinder with radius r and height h.V = πr²hSolve for r
The formula that gives the volume V of a right cylinder with radius r and height h is presented below:
[tex]V=\pi r^2h[/tex]Step 1: Divide both sides by πh
[tex]\begin{gathered} \frac{V}{\pi h}=\frac{\pi r^2h}{\pi h} \\ r^2=\frac{V}{\pi h} \end{gathered}[/tex]Step 2: Take the square root of both sides.
[tex]\begin{gathered} \sqrt[]{r^2}=\sqrt[]{\frac{V}{\pi h}} \\ r=\sqrt[]{\frac{V}{\pi h}} \end{gathered}[/tex]Step 3: We can multiply both the numerator and denominator by πh to get:
[tex]\begin{gathered} r=\sqrt[]{\frac{V\pi h}{\pi^2h^2}} \\ =\frac{\sqrt[]{V\pi h}}{\sqrt[]{\pi^2h^2}} \\ r=\frac{\sqrt[]{V\pi h}}{\pi h} \end{gathered}[/tex]The correct option is the last one.
Scott is 72 inches tall. How many feet is Scott? Use a conversion factor to show your work.
Answer
6 feet
Explanation
Note: The conversion rate of inches to feet is given below
1 inches = 0.0833333 foot
Since Scott is 72 inches tall, His height in feet will be
[tex]72\times0.0833333=6\text{ fe}et[/tex]what is the z-score of the value 40 rounded to the nearest tenth?
Remember that
z =(x - μ)/σ
where
μ=43.8
σ=8.7
x=40
substitute
z=(40-43.8)/8.7
z=-0.45.How much of a 30% solution would you need to make 50 mL of a 2% solution?
Answer:
The quantity of a 30% solution you would need to make 50 mL of a 2% solution is;
[tex]3.33\text{ mL}[/tex]Explanation:
Let x represent the quantity of a 30% solution you would need to make 50 mL of a 2% solution.
[tex]\begin{gathered} 30\text{\% of }x=2\text{\% of 50 mL} \\ 0.3\times x=0.02\times50\text{ mL} \\ x=\frac{0.02\times50\text{ mL}}{0.3} \\ x=3.33\text{ mL} \end{gathered}[/tex]Therefore, the quantity of a 30% solution you would need to make 50 mL of a 2% solution is;
[tex]3.33\text{ mL}[/tex]