Based on the information given, the total number of Goals Scored in all 10 games combined is 11 goals.
How to illustrate the information?It should be noted that in Mathematics, frequency simply has to do with the number of occurence that an event has based on the data or the information that's illustrated.
Based on the information given, it should be noted that the number of goals as well as the frequency are given. This will be illustrated we:
Total number of goals will be:
= (0 × 3) + (1 × 4) + (2 × 2) + (3 × 1)
= 0 + 4 + 4 + 3
= 11 goals
Therefore, 11 goals are scored.
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Write the equation of the line that passes through the points (-6,-1) and (-4,2). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{-4}-\underset{x_1}{(-6)}}} \implies \cfrac{2 +1}{-4 +6} \implies \cfrac{ 3 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +1= \cfrac{3}{2} (x +6) \end{array}}[/tex]
Solve y3 = 1.
y = −1
y = 1
y = ±1
y = 3
The value of the expression y³ = 1 is y = 1.
Expression:
An expression also known as algebraic expression consisting of variables, numbers and an arithmetic operation between them.
Given,
Here we have the expression y³ = 1.
Now, we need to find the value of y.
While we looking into the expression, when we have to find the value of y then we have to move the cube vale to the other side.
When we move the cube to the other side then it will be the cube root of the number.
While we simplify the cube root of the number then we get the result.
Therefore,
y³ = 1
Move the cube to the other side,
y = ∛1
We know that,
∛1 = 1
So, the value of y = 1.
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The standard binet intelligence quotient iq measures intelligence. iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. what percentage of the population has an iq score between 70 and 115?
iq scores have a bell shape distribution with a mean of 100 and standard deviation of 15. 81.855% of the population has an iq score between 70 and 115
What is z-score?
The z score, also referred to as the standard score, serves to calculate how far each data point place is from its mean. In other words, it calculates x's (data point's) deviation in terms of standard deviations.
Using z tables, you may calculate the proportion of the population that is either below or above the score.
Now, according to the question;
IQ scores follow a normal distribution, with a mean of 100 as well as a standard deviation = 15.
A z score is determined as follows:
z = (x - μ)/σ
μ = mean of the distribution
σ = standard distribution of the sampling.
Calculation for the z score for x = 70 and 115
z= (70-100)/15
= -30/15
=-2
and x=115
z = (115 - 100)/15
= 15/15
z = 1.0
Use z-score table, then likelihood that a randomly chosen person's IQ is more than 115 is,
P( -2 < z < 1)= P(z<1) - P(z< -2)
= 0.8413 - 0.02275
= 0.81855
Therefore, the percent of the population has an iq between 70and 115 is 81.855%.
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James took 97 minutes to clean his house. there were 12 rooms in the house, and it took him the same amount of time to clean each room. how much time did he have left after he finished cleaning?
James took 97 minutes to clean his house. there were 12 rooms in the house, and it took him the same amount of time to clean each room. time left after he finished cleaning is 4 hour 36 minutes
James took 97 minutes to clean his house.
there were 12 rooms in the house,
and it took him the same amount of time to clean each room
how much time did he have left after he finished cleaning?
one room clean =97 minutes
12 room clean = 97*12 amount of minutes
= 1164 minutes
= 19hour 24 minutes
James took 19 hour 24 minutes to clean 12 room
amount of time left = 24 hour - 19 hour 24 minutes
= 4 hour 36 minutes
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give h(x)=-2x-3 find h(6)
Answer: h(x)=-15
Step-by-step explanation: First: We plug in h(6) for x. Gives us -2(6)-3. When we solve -12-3. -15.
Answer:
h(6) = 9
Step-by-step explanation:
h(x) = 2x – 3,
Let x = 6
h(6) = 2*6 -3
= 12 -3
= 9
3x + 6x = 45 solve for x
Which of the following expressions is equivalent to x ⅔
Using the conversion of a fractional exponent to a rational expression, the equivalent expression to x^(2/3) is given by:
K. [tex]\sqrt[3]{x^2}[/tex]
How to convert a fractional exponent to a rational expression?A fractional exponent is converted to a rational expression applying the law of indices, in which the numerator, which is the top term of the fraction, will be the power of the base, while the denominator, which is the bottom term of the fraction, represents the root.
The law of indices is illustrated as follows:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
In the context of this problem, the expression is:
x^(2/3).
Hence the coefficients are n = 2 and m = 3, and thus the equivalent expression is:
[tex]x^{\frac{2}{3}} = \sqrt[3]{x^2}[/tex]
Meaning that option K is correct.
What is the missing information?The possible options for the question are missing, and are given by the image at the end of the answer.
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find a polynomial that when added to 5x^2-3x-9 that has the following sum of 0
Answer:
[tex]-5x^2 + 3x+9[/tex]
Step-by-step explanation:
Let the polynomial be p(x).
[tex]p(x)+(5x^2 -3x-9)=0 \\ \\ p(x)=-(5x^2 -3x-9) \\ \\ =-5x^2 + 3x+9[/tex]
3k-8=7
what is the value of k?
Answer:
[tex]\sf{k=5}[/tex]Step-by-step explanation:
[tex]\stackrel\ell{\boxed{\boxed{\begin{minipage}{7cm}\\\begin{aligned}\sf{3k-8=7}\\\downarrow\\\sf{3k=7+8}\\\downarrow\\\sf{3k=15}\\\downarrow\\\boxed{\boxed{\sf{k=5}}}\end{aligned}\end{minipage}}}}}[/tex]
I hope this helps!!
Answer:
5
step by step explaination
first side change -8=+8
7+8
now divide 15 by 3
Then
K=5
Damien played golf on each of the four days of his vacation. His scores on the first three days were 93, 92, and 89, and his average for the four days was 90. What was his score on the fourth day?.
Damien score on the fourth day is 86.
Damien played golf on each of the four days of his vacation and the average for the four days of was 90.
so, his score on the fourth day.
so firstly let, X, be his score on the fourth day. then, the other four day's score is already given so, by using the formula for average.
the average for four numbers is given by, the sum of all numbers divided by the total numbers. so, by using this formula we have
=>(93+92+89+X)/4=90.and ,
on solving this we got,
X=86.
that is our answer.
so, His score on the fourth day is 86
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even if an independent variable has an effect on the dependent variable, it is still possible to obtain a sample mean that is very similar to the original population mean. what outcome is likely if this happens?
even if an independent variable has an effect on the dependent variable, it fail to reject the null hypothesis and make a type II error
Even if a treatment is effective in the real world (it has an effect), it is still possible to obtain a sample mean that is so similar to the population mean that the sample mean doesn't fall in the critical, or rejection, region. If this happens, you are likely to fail to reject the null hypothesis and make a type II error.
Since that sample mean is so similar to the population mean, the treatment effect may not be detected on analysis even though it is in fact significant, this will cause the research to erroneously concluded that the treatment effect is zero and accept the null hypothesis when it is actually not zero. This is a type II error. Type II error in statistics means the non-rejection of a false null hypothesis and type I error is the rejection of a correct null hypothesis.
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Which of the following is an equation of a line that passes through the point
(
−
10
,
2
)
and is perpendicular to the line
4
x
+
5
y
=
15
?
The equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.
What is the equation of a perpendicular line?If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.
The equation is given below.
4x + 5y = 15
5y = −4x + 15
y = −(4/5)x + 3
The slope of the equation is −4/5. Then the slope of the perpendicular line will be 5/4. Then the equation is given as,
y = (5/4)x + c
The equation that passes through (−10, 2) will be
2 = (5/4)(−10) + c
2 = −12.5 + c
c = 14.5
Then the equation of the perpendicular line that passes through (−10, 2) will be y = (5/4)x + 14.5.
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Analyzing Exponential Functions
Compare the table values of f(x)
and g(x).
f(x) = 9x
g(x) = 9/1/2
The outputs of g(x) are the
of f(x).
Rising or growing steadily and quickly: a city in exponential expansion. noun. Mathematics the value of the constant e raised to the power of a given expression, represented as the exponential of 3x, e3x. something that is positive and raised in power.
Explain exponential functions?In the biological sciences, exponential functions are frequently employed to simulate the evolution of a certain quantity over time, such as population number. Experimental data graphs are often created with the quantity on the y-axis and the time on the x-axis.
The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour. After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The values of f(x) and g(x) in the table for various values of f(x) = 9x + 7 and g(x) = 5x
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having trouble coming up with formula
Okay, here we have this:
Considering the provided information, we are going to calculate the speed at which he runs, so we obtain the following:
So we have the following equation:
Distance Traveled Walking + Distance Traveled Running = Total Distance
Distance Traveled Walking + Distance Traveled Running = 20 miles
And taking into account that speed is equal to distance over time, if we take speed to which runs as x we have:
((x/2) mi/h * 2h) + (x mi/h* 1.5h) = 20 miles
x mi+ 1.5x mi= 20 mi
2.5x mi=20mi
x = 20mi/2.5mi
x=8
Finally we obtain that he runs at 8 miles per hour.
which situation is best modeled by an exponential distribution? suppose that, in a strand of dna, mutations occur randomly and independently of other mutations at an average rate of one mutation per 12,400 a. a geneticist is examining a strand of dna. what is the probability that she will observe a mutation within the next 15,000 a? suppose that defects in electrical wire occur randomly and independently of other defects. the average rate is 0.001 defects per cm of wire. what is the probability that a 100 m long spool of wire will contain fewer than two defects? suppose that a traffic light is green for 30 s, yellow for 4 s, and red for 56 s. if cars arrive at the intersection randomly, what is the probability a car will arrive when the light is yellow?
By probability , An average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .
Describe probability using an example?
By dividing the number of positive outcomes by the entire number of possible outcomes, probability—the likelihood that an event will occur—is determined. The most basic illustration is a coin toss. There are just two outcomes when you flip a coin: either it comes up heads or tails.The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.Suppose that, in a strand f DNA ,mutations occur randomly and independently of other mutations .
at an average rate of one mutation per 12,400 A.A geneticist is examining a strand of DNA .
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adriel is younger than jevonte. There ages are consecutive odd integers. Find adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85
Answer:
Step-by-step explanation:
Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85 is 7 years
How to calculate the value?Let the ages be x and x + 2 since they're consecutive odd integers.
We want to find Adriel’s age if the sum of the square of adriel’s age and 4 times jevonte’s age is 85. This will be illustrated as:
x² + 4(x + 2) = 85
x² + 4x + 8 = 85
Collect like terms
x² + 4x + 8 - 85
x² + 4x - 77 = 0
x² + 11x - 7x - 77 = 0
x(x + 12) - 7(x + 11) = 0
x - 7 = 0
x = 0 + 7
Therefore, the age is 7 years.
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Ann bowled 115,121,125,118 and 122 in five games. What must Ann bowl in the sixth game so that she will have an average score of 120 for the six games?
Ann must bowl 119 in the sixth game to have an average score of 120.
What is average?
Average is defined as the mean value that is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
According to question,
155+121+125+118+112+x= 6(120)
601+x=720
x= 720-601
x= 119
Hence, she must bowl 119 in the sixth game.
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what is 7+2b+7b+2 like terms where needed to be simplfied
Answer:
9+9b
Step-by-step explanation:
Answer:
9 +9b
Step-by-step explanation:
Simplify:Like terms are terms that have same variable with same power.
2b and 7b are like terms.
7 and 2 are like terms (constants).
7 + 2b + 7b + 2 = 7 + 2 + 2b +7b
= 9 + 9b
Mimi earned a total of $38 by selling 19
cups of lemonade. How many cups of
lemonade does Mimi need to sell in all to earn
$44?
Answer:
22 cups in total
Step-by-step explanation:
In order to solve this problem we need to know how much money Mimi makes by just selling 1 cup of lemonade. We can find this by dividing
38/19 = 2
Now that we know how much money Mimi makes by just selling 1 cup of lemonade, we can use this to find how many cups she needs to sell in total to earn $44. We can use this equation
2x = 44 (x = cups of lemonade)
Now we solve for x
2x =44
/2 /2
x = 22
So Mimi needs to sell 22 cups in total to earn $44 dollars. Hope this helps :)
----------------------------------------------
Bonus: she need to sell 3 more cups lol incase you need to know
2. Julian is cutting lengths of rope for a class project. Each rope length should be 10
inches long. The specifications allow for a difference of 0.5 inches. Which absolute
value inequality represents the difference between the rope lengths cut and the
specifications?
The absolute value inequality represents the difference between the rope lengths cut and the specifications are | x - 10 | ≤ 0.5.
What is the modulus value?Modulus value always outputs a positive value irrespective of the input value sign.
Julian needed to cut ropes for her school project and their length should be 10 inches long with a difference of 0.5 inches.
∴ The maximum allowable length of the rope should be (10 + 0.5) = 10.5 inches and the minimum allowable length of the rope should be
(10 -0.5) = 9.5 inches.
The absolute value of inequality that represents this condition is,
| x - 10 | ≤ 0.5.
x - 10 ≤ 0.5.
x ≤ 10.5, And
- ( x - 10) ≤ 0.5.
-x + 10 ≤ 0.5.
- x ≤ - 9.5. ( think of moving the terms on either side to make x positive).
x ≥ 9.5.
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Katie has 5 1/3 of potting soil to use in her flowerpots. It takes 1/4 pound of soil to fill one flowerpot. If Katie's flowerpots all hold the same amount of soil, how many flowerpot can she fill?
If Katie has [tex]5\frac{1}{3}[/tex] pounds of plotting soil to use in her flowerpots and it takes 1/4 pounds of soil to fill one flowerpot, then the number of flowerpot that she can fill is 21 pots
The total quantity of potting soil that she has = [tex]5\frac{1}{3}[/tex] pounds
Convert the mixed fraction to the simple fraction
[tex]5\frac{1}{3}[/tex] pounds = 16/3 pounds
The quantity of potting soil that required to fill one flowerpot = 1/4 pounds
Number of flowerpot that she can fill = The total quantity of potting soil that she has / The quantity of potting soil that required to fill one flowerpot
= 16/3 ÷ 1/4
= 16/3 × 4
= 64/3
= 21.33
≈ 21 flowerpot
Hence, if Katie has [tex]5\frac{1}{3}[/tex] pounds of plotting soil to use in her flowerpots and it takes 1/4 pounds of soil to fill one flowerpot, then the number of flowerpot that she can fill is 21 pots
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if you right the number from 1 to 100 how many times would you repeat 3
The number 3 will come 20 times in 1 to 100 .
In mathematics, a number serves as both a unit of measurement and a label.
The first examples are the natural numbers 1, 2, 3, 4, and so forth. Language can express numbers through the use of number terms. Numerals are symbols that are more frequently used to symbolize specific numbers; for example, the number "5" stands in for the number five. Because just a few symbols can be learnt, basic numerals are usually organized into numeral systems, which provide an ordered way to represent any number. The Hindu-Arabic number system, which enables the representation of any number using a combination of 10 fundamental numerical symbols, or "digits," is the most extensively used number system.We know that the number 3 will come up in 3 ,13 ,23,30 , 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93.
Therefore the number 3 will come up 20 times.
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It was hot at the boardwalk. The Real Scoop was doing very well. Russell had just
served up 55 cones, some single scoops, some double scoops, and some triple
scoops. If he served up a total of 103 scoops, how many of the cones were single
scoops, how many were double scoops, and how many were triple scoops?
NEED MORE THEN 2 ANSWERS!! PLEASE
Answer:
Image result for the government
The Federal Government is composed of three distinct branches: legislative, executive, and judicial, whose powers are vested by the U.S. Constitution in the Congress, the President, and the Federal courts, respectively.
Step-by-step explanation:
Li Zhen, Kara and Rose were typing. Li Zhen typed 2 times as fast as Kara. The ratio
of the number of words Kara typed to the number of words Rose typed was 4 : 1.
a) What was the ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed?
Kara typed 48 words.
b) How many words did Li Zhen, Kara and Rose type altogether?
The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed = 8 : 4 : 1
Total numbers of words Li Zhen, Kara and Rose typed = 156 words
What is Ratio ?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Since, it's given that
the number of words Kara typed = 48
number of words Li Zhen typed = 2 x 48
=96words
a) The ratio of the number of words Kara typed to the number of words Rose typed = 4:1
Since, it's given that
the number of words Kara typed = 48
let, the number of words Rose typed = x
then, by equating them we get,
4/1 = 48/x
4x = 48
x = 48/4
x = 12
The ratio of the number of words Li Zhen typed to the number of words Kara typed to the number of words Rose typed :
= 96 : 48 : 12
= 8 : 4 : 1
b) Now we know that,
The number of words Li Zhen typed = 96words
The number of words Kara typed = 48words
The number of words Rose typed = 12words
Then, the total numbers of words Li Zhen, Kara and Rose type altogether
= 96 + 48 + 12
= 156 words
Hence, the total numbers of words Li Zhen, Kara and Rose type altogether is 156 words
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2. Three times one number minus a second is 8, and the sum of
the numbers is 12. Find the numbers.
Answer:
8
Step-by-step explanation:
Let the number be “X"
Solution:
4 + (X/2) = 8
(X/2) = 8-4
(X/2) = 4
X = 4×2
X = 8
THEREFORE THE ANSWER IS “8”
Answer:
This is a simultaneous equation.
Step-by-step explanation:
let the first number be x and second be y
Lets make an equation first:
3x-y = 8 .....(1)
x+y = 12........(2)
Solve by elimination.
Dass
3x+x= 8+12
4x=20
x=5
find y
x+y=12
5+y=12
y=12-5
y= 7
Therefore the two numbers are 5 and 7
Use the figure for #10-13. m/ABD = 127⁰
10. Find m/ABC =
A
II. Find m ZACB =
12. Find m/ ACD =
13. Find m/ CAB
B
D
Answer:
ABC =146.5
ACB=67
ACD=127
CAB=146.5
Step-by-step explanation:
ABD=127
ACD=127
BCD=60 ( Being equilateral triangle)
60+x=127
x=67
ACB=67
CAB=CBA=y (let)
y+y+ACB = 360 ( Sum of int angles of triangle)
2y+67=360
2y=293
y=146.5
CAB=146.5
ABC=146.5
The equation below represents Function A and the graph represents Function B: Function A f(x) = x − 9 Function B graph of line going through ordered pairs negative 1, negative 3 and 2, 3 Which equation best compares the slopes of the two functions? (1 point) Slope of Function B = 2 x Slope of Function A. Slope of Function A = Slope of Function B Slope of Function A = 2 x Slope of Function B Slope of Function B = − Slope of Function A
We will see that the slope of function B is 2, and the slope of function A is 1. This means that the correct equation is:
Slope of function B = 2*Slope of Function A
Which equation compares the slopes?
First, a general linear equation is:
y = a*x + b
Where a is the slope and b the y-intercept.
Here the function A is:
f(x) = x - 9
Then the slope is equal to 1.
We know that function B is a line that passes through (-1, -3) and (2, 3)
Then the slope is:
s = (3 + 3)/(2 + 1) = 6/3 = 2
So the slope of function B is 2, and the slope of function A is 1. Then the equation is:
Slope of function B = 2*Slope of Function A
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3. USE A MODEL To produce a handcrafted rocking chair, a woodworker needs to spend
30 hours on woodworking, and 3 additional hours on painting. The same woodworker
can make a simpler kitchen chair in 24 hours, and it takes an additional 3 hours of
painting. He has a maximum of 192 hours available for woodworking and 21 hours
available for painting in a month. The rocking chair sells for $550, and the kitchen chair
sells for $300. Write a system of inequalities to model this situation as well as a profit
equation, and find the number of rocking chairs and kitchen chairs the woodworker
should make to maximize his revenue for the month.
The woodworker should make atmost 4 rocking kitchen chair and 3 simple kitchen chair to maximize the profit under given conditions of 192 woodworking hours and 21 painting hours.
What is maximum profit?Profit maximization is a process that businesses go through to make sure the best levels of output and prices are realized in order to maximize their returns. The company modifies important variables like sale price, production costs, and output levels in order to achieve its profit objectives.
What is inequality?inequality, A mathematical statement expressing an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to etc.
Given,
Time needed to woodwork a rocking kitchen chair= 30 hours
Time needed to paint a rocking kitchen chair=3 hours
Time needed to woodwork a simple kitchen chair= 24 hours
Time needed to paint a simple kitchen chair=3 hours
Maximum time given by worker= 192 hours for woodwork and 21 hours to paint
Let x and y be the maximum number of chairs created by woodworker of both the types.
so the system of inequality would be,
30x+24y<192 ......(1)
3x+3y<21 ......(2)
To find x and y,
multiply the (2) by 10
30x+30y<210
subtract (1) from (2)
30x+24y-(30x+30y)<192-210
-6y<-18
y<3
3x+3y<21
3x+3*3<21
3x<12
x<4
By this, he can make maximum 4 rocking and 3 simple kitchen chair to earn the maximum profit.
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Tamika's car used 13 gallons to travel 572 miles. How far can she travel on 7 gallons?
Answer:
308
Step-by-step explanation:
Based on the given conditions, formulate: 7 x 572/13
Cross out the common factor: 7 x 44
Calculate the product or quotient: 308
Answer:
308
Step-by-step explanation:
572 divided by 13 is 44 which means there is 44 miles per gallon. So multiply 44 x 7 and you get 308 miles.
Classify each angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles.
The angle pairs can be classified as follows
∠1 and ∠5 → Alternate exterior angles
∠2 and ∠10 → Corresponding angles
∠10 and ∠14 → Alternate interior angles
∠6 and ∠7 → Consecutive interior angles
∠5 and ∠12 → Consecutive interior angles
∠3 and ∠13 → Alternate exterior angles
Classifying angle pairsFrom the question, we are to classify each of the angle pairs as corresponding, alternate interior, alternate exterior, or consecutive interior angles.
Considering the given diagram, and applying the appropriate angle theorems, we can write that
∠1 and ∠5 are alternate exterior angles
∠2 and ∠10 are corresponding angles
∠10 and ∠14 are alternate interior angles
∠6 and ∠7 are consecutive interior angles
∠5 and ∠12 are consecutive interior angles
∠3 and ∠13 are alternate exterior angles
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