The pitcher that has the lowest number of runs allowed per inning is Randy.
Which pitcher has the lowest number of runs per inning?In order to determine the pitcher that has the lowest number of runs per innings, divide the number of runs of each player by the number of innings of that player.
Division is the mathematical operation that is used to calculate the quotient of two or more numbers. It entails grouping a number into equal parts using another number.
Number of runs per innings = number of runs / number of innings
Number of runs per innings for Randy : (2 / 3) = 0.667
Number of runs per innings for Felix : (4 / 5) = 0.80
Number of runs per innings for Johan: (5 / 7) = 0.714
Here is the complete question:
A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.
Which pitcher has the lowest number of runs allowed per inning?
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Write an equation of the parabola in vertex form.
Amusement Park Ride
Height (feet)
YA(0, 180)
(1, 164)
160
80
0 2 4
Time (seconds)
Equation:
Equation of parabola in vertex form is :
[tex](x-h)^{2} = 4a(y-k)[/tex]
[tex](x-0)^{2} = 4a(y-180)[/tex]
it passing through (1,164)
∴ [tex](1-0)^2=4a(164-180)[/tex]
[tex]1 = 4a(-16)[/tex]
⇒ [tex]-64a = 1[/tex]
⇒ [tex]a = -\frac{1}{64}[/tex]
∴ [tex](x-0)^2 = 4 \times \frac{1}{-64} (y-180)[/tex]
[tex]x^2 = -\frac{1}{16}(y-180)[/tex]
[tex]-16x^2 = y-180\\y = -16x^2+180\\[/tex]
Here, the equation of parabola in vertex form is:
[tex]y = -16(x^2)+180 ,\ for \ x\geq 0[/tex]
What is Parabola?
A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface.
What is cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the Centre of base) called the apex or vertex.
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F(x)=3x^4-4x^3+x^2+6x-2
The rational zeros for F(x)=3x^4-4x^3+x^2+6x-2 are x= -1 and x= 1/3 while the linear factors are (x+1) and (3x-1)
How to determine the rational zeros and linear factors?Synthetic division has to do with dividing polynomials.
The process involves:
Step 1: Set up the synthetic division.
Step 2: The leading coefficient should be brought down to the bottom row.
Step 3: Multiply this by the value just written on the bottom row.
Step 4: Then, add the column created in step 3.
This can be illustrated thus:
Given: f(x) = 3x⁴-4x³+x²+6x-2
3x⁴-4x³+x²+6x-2 = 0
We will try x = -1 in f(x). In this case, replace x with -1. This will be:
= 3x⁴-4x³+x²+6x-2 = 0
Since f(-1)= 0 so (x+1) is a factor
Using synthetic division:
-1)....3....-4....1....6....-2
.........3.....-7...8....-2..|..0
Remainder = 0
Quotient = 3x³ -7x² + 8x -2
For 3x³ -7x² + 8x -2, f(1/3) = 0 so (x- 1/3) is a factor
1/3)....3....-7....8....-2
..........3.....-6...6...|..0
Remainder = 0
Quotient = 3x²-6x+6
= 3(x²-2x+2)
Since there are no more rational zeros or linear factors for x²-2x+2. Therefore, the rational zeros are x= -1 and x= 1/3.
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Ms. Jones is comparing two sets of scores. For Test A, the standard deviation is 7, and for Test B, the standard deviation is 12. This means that
The comparison done by Mr Jones means that Test A of standard deviation 7 is closer to the mean scores and Test B of standard deviation 12 is further apart from the mean score
What is standard deviation?The standard deviation is a statistic measure that expresses how much variance or dispersion there is in a group of numbers.
A high standard deviation suggests that the values are dispersed throughout a wider range,
A low standard deviation suggests that the values tend to be close to the established mean.
A positive value means the standard deviation is above the mean while a negative value means the standard deviation is below the mean
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A random sample of 10 subjects have weights with a standard deviation of 10.9508 kg What is the variance of their weights? Be sure to include the appropriate units with the result
Based on the information given the variance of their weights is 119.9200 kg².
What is variance?
The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other. This symbol is frequently used to represent variation: σ².
Main body:
n=sample size=10
Standard deviation=10.9508 kg
Using this formula
Variance=(Standard deviation)²
Let plug in the formula
Variance=(10.9508 kg)²
Variance= 119.9200 kg²
Hence the variance of their weights is 119.9200 kg².
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1) While mining, Peter found a large metal bar that contained 33 grams of gold. Peter also
determined that the bar was 73.33% gold. What was the total weight of the metal bar in
grams? Round your answer to the nearest whole number if necessary.
The total weight of the metal bar is 45.002 grams.
Given:
While mining, Peter found a large metal bar that contained 33 grams of gold.
Peter also determined that the bar was 73.33% gold.
73.33% = 33 grams
divide by 73.33 on both sides
73.33%/73.33 = 33/73.33 grams
1% = 0.45002 grams
Multiply on 100 on both sides
1%*100 = 0.45002*100
100% = 45.002 grams.
Therefore the total weight of the metal bar is 45.002 grams.
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I need to find the measure
Answer:
x = 147°
Step-by-step explanation:
To find x, we have to find the angle measures in the small triangle.
180 - 61 = 119° (sum of adjacent angles on straight line=180)
The other angle measure in the triangle is 28° because they are vertically opposite angles.
We subtract 119° and 28° to find the angle measure next to x.
180 - 119 - 28 = 33° (sum of angles in a triangle=180)
x = 180 - 33
= 147° (sum of adjacent angles on straight line=180)
How many legs do 40 cows have if 3 cows only have 2
Answer:
154 legs
Step-by-step explanation:
40-3=37
37 times 4 = 148
3 times 2 ° 6
148+6= 154
Answer: 154 legs
Step-by-step explanation: First, multiply 37×4 because there are 37 cows with 4 legs, which gets you 148. Since there are 3 cows with only 2 legs, do 3×2=6. Finally, add 148 and 6 to get 154 legs.
please give brainliest!
What expression has the same value as 2(5x + 2) - (3y)2x – 4x
Answer:
10x+6xy+4
Step-by-step explanation:
2(5x+2)-(3y) 2x-4x
By removing the bracket
10x+4-6xy+12xy
10x+4+6xy
10x+6xy+4
2. Draw the image of RST under the dilation with scale factor 5/3 and center of dilation (2, -2) . Label the image R'S'T' .
Answer:
Step-by-step explanation:
Using the graph below, determine the employee's hourly wage.
Using the graph, the hourly wage of the employees is: $8 per hour.
How to Determine Hourly Wage From a Graph?Slope of a proportional graph is the unit rate between two variables, x and y, and it is calculated as: k = y/x.
To find the unit rate or slope of the graph, use any point on the graph (x, y).
The unit rate of the graph in the image above is the hourly wage of the employees.
Using any point on the line, say, (13, 104), we can find the slope/unit rate. Therefore:
Unit rate/slope, k = 104/13
Unit rate/slope, k = 8
Therefore, the hourly wage is: $8 per hour.
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Which function represents the graph of f (x) = -3 |x| after it is translated 5 units down?
The function that represents the graph f(x) = -3|x| is f(x) = -3|x| - 5
How to find the function of the graph ?
To ascertain whether a graph accurately depicts a function, use the vertical line test. The graph is a function if a vertical line drawn across it is moved and hits it only once at any given time. If there are multiple points where the vertical line intersects the graph, the graph is not a function.
As it is already given in the question that the function
f(x) = -3|x|
We will use transformation rules to solve the given question
f(x)→f(x-a) ⇒ Graph shifted to right by a units
f(x)→f(x+a) ⇒ Graph shifted to left by a units
f(x)→f(x) - a ⇒ Graph shifted downwards by a units
f(x)→f(x) + a ⇒ Graph shifted upwards by a units
When it is translated 5 units down
Then we subtract 5 outside of the given function
∴ f(x) = -3 |x| - 5
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water faucet leaked 3/5 liters of water over the course of 2/5 hours. How many liters would it have leaked in 1 hour please tell me the answer
Answer:
1.5 liters
Step-by-step explanation:
Three of the 30 computers are out of service. What percent of the computers are not working?
The percentage of computers not working is 10%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that there are three of the 30 computers are out of service.
The percentage of the computers which are out of service will be calculated as,
P = 3 / 30
P = 0.1
P = 0.1x 100
P = 10%
Therefore, the percentage of computers not working is 10%.
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rita class has 14 girls and 16 boys how does the ratio 14:30 describe ritas class
Answer:
The ratio shows that there are 14 girls to 30 students in total
Step-by-step explanation:
14 + 16 = 30 that mean that there are 30 students in total, therefore, the ratio shows 14 girls : 30 students
the mean absolute deviation of Mr. Zimmerman's class is 0.46 What does this mean
Mean absolute deviation is the variation in a data set and is the average distance between each value and mean.
It is calculated by finding the difference between each data value and mean and then finding average of that.
So, let data set be x1,x2,x3,x4...xN.
mean of the data set is [tex]\bar{x}[/tex].
then mean absolute deviation will be
[tex]M.A.D=\sum\limits^N_{n=0}\frac{ {x_n-\bar{x}}}{N}[/tex]
Thus, mean absolute deviation shows how much the data vary in the data set.
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My friend is hoping to move to your town but is concerned because she doesn’t have a car. Do you think this will present a big problem for her? Use the distance formula in some way to justify your response.
There are many things obstructing the route so yes. I cannot give a detailed answer as I have not been given the "distance formula" sorry
Solve-ns16 Which of the following must be true about the inequality and the resulting graph? Select three
options.
ns<-24
n>-24
The circle is open.
The circle is closed.
The arrow points right.
By using the concept of inequality, the correct options are
2nd, 4th and 5th option
What is linear inequation?
Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by [tex]> , < . \geq, \leq[/tex]
A one degree inequation is known as linear inequation.
Here,
The given inequation is
[tex]\frac{-2}{3}n \leq 16[/tex]
Now,
[tex]\frac{-2}{3}n \leq 16\\n \geq -16 \times \frac{3}{2}\\n \geq -24\\[/tex]
Since n is greater than or equal to 24, the arrow will point towards right
The circle will be closed as there is an equality
So the correct options are 2nd, 4th and 5th option
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Complete Question
The complete question has been attached here
reduce 12/16 to simplest terms
Answer: 3/4
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 12 and 16 is 4
Divide both the numerator and denominator by the GCD
12 ÷ 4
16 ÷ 4
Reduced fraction: 3/4
Therefore, 12/16 simplified to lowest terms is 3/4.
Answer:.
Step-by-step explanation:
Louie is studying ceramics, and he was asked to submit 5 vessels from his collection to exhibit at the fair. He has 15 vessels that he thinks are show worthy. In how many ways can the vessels be chosen?
Louie can choose the vessel for exhibition using combination in 3003 ways
How to determine the number of Louie can choose the ceramicinformation from the question include
Louie is studying ceramics and he is to submit 5 vessels
He has 15 vessels
The problem will be solved using combination
combination is method of choosing or making selection when order does not matter
Louie can choose any 5 of his vessel with no particular order
The formula is ₁₅C₅
₁₅C₅ = 15! / {5!(15 - 5)! )
= 15! / {5! * 10!}
= 3003 ways
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Lorna Hall’s real estate tax of $2,010.88 was due on December 14, 2017. Lorna lost her job and could not pay her tax bill until February 27, 2018. The penalty for late payment is 612% ordinary interest. (Use Days in a year table.) a. What is the penalty Lorna must pay? (Round your answer to the nearest cent.) b. What is the total amount Lorna must pay on February 27? (Round your answer to the nearest cent.)
a. The penalty Lorna must pay is $26.86.
b. The total amount Lorna must pay on February 27 is $2037.74.
Given that,
On December 14, 2017, Lorna Hall's $2,010.88 real estate tax was due. Because of her job loss, Lorna was unable to pay her taxes until February 27, 2018. Late payment fees are assessed at a rate of 6 1/2% regular interest.
We have to find
a. What is the fine Lorna is required to pay
b. How much will Lorna owe in total on February 27.
First,
We know that,
i=p×r×t
Here,
i is interest.
p is principal amount.
r is rate of interest
t is time.
So, p is $2010.88
r is 6 1/2%
t is 17+31+27= 75 days is 75/365
So,
i= 2010.88×6 1/2×75/365
i= $26.86
The penalty Lorna must pay is $26.86.
Second,
We know that,
Total amount= real estate tax due amount+ Penalty pay.
Total amount= $2010.88+$26.86
Total amount= $2037.74
The total amount Lorna must pay on February 27 is $2037.74.
Therefore, a. The penalty Lorna must pay is $26.86.
b. The total amount Lorna must pay on February 27 is $2037.74.
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2. Kira has three dogs, Luna, Cooper, and Daisy.
Cooper weighs 25 pounds less than Daisy. Luna
weighs 20 pounds less than three times Cooper.
If their combined weight is 175 pounds, how
much does Luna weigh?
A. 59 pounds
B. 74 pounds
C. 78 pounds
D. 82 pounds
If their combined weight is 175 pounds, The amount of Luna weight is D. 82 pounds.
How to determine the weight?Let x represent the weight of Cooper
Let x +25 represent the weight of Daisy
Let 3x -20 represent the weight of Luna
Hence,
x + (x +25) + (3x -20) = 175
5x +5 =175
Combine like terms
5x = 175 -5
5x =170
Divide both side by 5x
x = 170/5
x =34
Weight of Luna
3x -20 where x= 34
3(32) -20
= 102 -20
= 82 pounds
Therefore the correct option is D.
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log x + 5 log y -4 log z rewrite as a single logarithm
Solution :
[tex]\qquad \sf \dashrightarrow \: log(x) + 5 \: log(y) - 4 \: log(z) [/tex]
[tex]\qquad \sf \dashrightarrow \: log(x) + \: log(y {}^{5} ) - \: log(z {}^{4} ) [/tex]
( a log(x) = log(x^a) )
[tex]\qquad \sf \dashrightarrow \: log( x {y}^{5} ) - log(z {}^{4} )[/tex]
( log (a) + log (b) = log (ab) )
[tex]\qquad \sf \dashrightarrow \: log( \frac{ x {y}^{5} }{z {}^{4} }) [/tex]
( log (a) - log (b) = log (a/b) )
Carl is making accessories for the soccer team. He uses 773.85 inches of fabric on headbands for 29 players and 4 coaches. He also uses 279.56 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
23.45 inches fabric was used on a headband and 9.64 inches fabric was used on a wristband for each player.
No. of players = 29
No. of coaches = 4
Total fabric used for headbands = 773.85 inches
Total no. of people for headbands = 29 + 4
= 33
Fabric used for headband for 1 person = 773.85/33
= 23.45 inches
Total fabric used for wristbands = 279.56 inches
Total no. of people for wristbands = 29
Fabric used for headband for 1 person = 279.56/29
= 9.64 inches
Hence, fabric for headband is 23.45 inches and for wristband is 9.64 inches.
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Graph the solution set to the inequality: 8x - 7y ≥ 42
Answer:
How do I show you the graph because I have it
Step-by-step explanation:
What is the CLOCKWISE equivalent to a CLOCKWISE rotation by an angle of 62,000 degrees?
The number of rotations is 172.
Explain rotationRotation is a circular movement about the specific axis or point of rotation. The two most prevalent directions for rotation are clockwise and counterclockwise, or anti-clockwise.
Rotation simply means going around a central point. Any point on the shape has a constant distance from the center.
Given, the clockwise rotation is by 62,000°.
To find the number of rotation (n),
[tex]n = \frac{62000}{360}[/tex]
n = 172.2
Therefore, the number of rotations is 172.
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NO LINKS!! Please help me with this probability question Part 1j
Answer:
[tex]\textsf{b)} \quad \text{P}(A\;\text{and}\;B)=\dfrac{1}{5}[/tex]
Step-by-step explanation:
Given:
[tex]\text{P}(A)=\dfrac{1}{4}[/tex]
[tex]\text{P}(B)=\dfrac{1}{4}[/tex]
[tex]\text{P}(A|B)=\dfrac{4}{5}[/tex]
Conditional Probability Formula
[tex]\text{P}(A \cap B)=\text{P}(B)\;\text{P}(A|B)[/tex]
Substitute the given values into the formula:
[tex]\begin{aligned}\implies \text{P}(A \cap B)&=\dfrac{1}{4} \cdot \dfrac{4}{5}\\\\&=\dfrac{4}{20}\\\\&=\dfrac{1}{5}\end{aligned}[/tex]
(A) find the perimeter of triangle BCF, to the nearest hundredth
(B) find the area of triangle BCF
Perimeter of triangle FBC is 19.24 units
Area of triangle FBC is 100.62 square units
Given,
The triangle with vertices;
F(-3, 5)
B(3, 2)
C(1, -2)
We have to find the perimeter and area of the triangle;
Formula for getting distance from vertices;
D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
Here,
Length of FB; F(-3, 5), B(3, 2)D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(3 -(-3) )^{2}+(2 -5 )^{2} }[/tex]
= [tex]\sqrt{6^{2} +(-3)^{2} }[/tex]
= [tex]\sqrt{36+9}[/tex]
= √45
Length of BC; B(3, 2), C(1, -2)D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(1 -3 )^{2}+(-2-2)^{2} }[/tex]
= [tex]\sqrt{(-2)^{2} +(-4)^{2} }[/tex]
= [tex]\sqrt{4+16}[/tex]
= √20
Length of FC; F(-3, 5), C(1, -2)D = [tex]\sqrt{(x_{2} -x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
= [tex]\sqrt{(1-(-3) )^{2}+(-2 -5)^{2} }[/tex]
= [tex]\sqrt{4^{2}+(-7)^{2} }[/tex]
= [tex]\sqrt{16+49}[/tex]
= √65
That is,
Length of side FB = √45 unitsLength of side BC = √20 unitsLength of side FC = √65 unitsNow,
Perimeter of triangle FBC = FB + BC + FC
= √45 + √20 + √65
= 19.24 units
Next,
Area of triangle FBC = 1/2 × BC × FB²
= 1/2 × √20 × √45²
= 100.62 square units.
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Please help I need to find X
Answer:
x=17
Step-by-step explanation:
8x+20 is equal to 11x-31 because l parallel to m.
8x+20=11x-31
3x=51
x=17
Answer:
[tex]\sf x=17^o[/tex]Step-by-step explanation:
L || m
[tex]\sf (8x+20)^o=(11x-31)^o[/tex]
[ Corresponding angles]
[tex]\sf 8x+20=11x-31[/tex]
[tex]\sf 8x-11x=-31-20[/tex]
[tex]\sf -3x=-51[/tex]
[tex]\sf \cfrac{-3x}{-3}=\cfrac{-51}{-3}[/tex]
[tex]\sf x=17^o[/tex]
__________________
Hope this helps!
Have a great day!
i. Can you
3. Two cards are randomly dealt from a deck. Find the probability that the first is a king and the
second is a 7. Find the probability that the first is a king and the second is a spade.
The Total Probability is 4/663 and 35/2652
What is Probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. An event's probability is a number between 0 and 1.
Solution:
We know that there are 52 cards in a deck of cards.
So, probability of getting a king = 4/52 = 1/13
And probability of getting a 7 after drawing a king is 4/51,
this is because one card is drawn out from the deck and there are only 51 cards left in the deck.
Total Probability = 1*4/13*51 = 4/663
In the secon case, there are two possibilities,
It can be the kling drawn might be of spade or not
Case 1: When King drawn is of Spade
Probaility of drawing a King of Spade = 1/52
Probability of drawing a Spade after King of Spade is drawn = 11/51
Total Probaility = 1*11/52*51 = 11/2652
Case 2: When King drawn is not of Spade
Probability of drawing a King not of Spade = 2/52
Probability of drawing a Spade after drawing the King = 12/51
Total Probability = 2*12/51*52 = 24/2652
Total Probability of drawing a king and spade = 11/2652 + 24/2652 = 35/2652
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in 2017 , sharjah unfurled the worlds largest flag measuring 70m in length and 35m in width.the flag broke the guiinness world record for the largest flag hoisted on a fixed flagpole . there are 4 colours that occupy almost the same area in the flag . based on the above information , how much area will the black part occupy
Answer:
612.5
Step-by-step explanation:
Area is the length times the width
a = 70x35
a = 2450 Divide this number by 4
612.5