Standard deviation - The value of x is 1.96.
What is standard normal distribution?
A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.
As given, for a standard normal distribution, 95% of the data points are contained in the interval [ -x , x ].
The standard normal distribution, commonly known as the z-distribution, is a unique type of normal distribution in which the mean and standard deviation are both equal to 1. By transforming its values into z-scores, any normal distribution can be standardised. Z-scores indicate how far away from the mean each number is from.
Hence, from the standard normal table, the value of x = 1.96 for 95% confidence level.
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A family buys a studio apartment for $200,000. They pay a down payment of $20,000. a. Their down payment is what percent of the purchase price? b. What percent of the purchase price would an $80,000 down payment be?
Answer:A. 20% B.45%
A= 40,000/40,000/200000=.2 Or 20%b. 90,000/200000=.45
Step-by-step explanation:
hope i helped!
A line passes through the points (2,20) and (9,27) Write a linear function rule in terms of x and y for this line.
The linear function rule of the equation is y = x + 18
How to determine the linear function rule?From the question, the points on the line are given as
(2, 20) and (9, 27).
So, we have the following ordered pairs
(x, y) = (2, 20) and (9, 27).
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (2, 20) and (9, 27).
Substitute the known values in the above equation
So, we have the following equation
Slope = (27 - 20)/(9 - 2)
Evaluate the above quotient
Slope = 1
The equation is then calculated as
y = Slope(x - X) + Y
Substitute the known values in the above equation
So, we have the following equation
y = 1 * (x - 2) + 20
So, we have
y = x + 18
Hence, the equation of the line is y = x + 18
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johnny the gambler tosses 6 fair six-sided dice numbered 1 through 6. in order to win the jackpot, he needs a 5 or 6 on exactly 3 of the dice. what are johnny's chances to win?
The probability of Johnny winning is [tex]20 *(\frac{2^3}{3^6} )[/tex].
Given data;
Johnny throws six equal dice with six sides and the numbers 1 through 6 on them. He needs a 5 or 6 on precisely 3 of the dice to take home the prize. What are Johnny's odds of winning?
The probability of 5 or 6 = 2/6
= 1/3
The probability of not 5 or 6 = 4/6
= 2/3
The total probability of getting in exactly 3 chances;
⇒ ⁶C₃ * (1/3)³ * (2/3)³
⇒ [tex]20 *(\frac{2^3}{3^6} )[/tex]
Hence, the chances for Johnny to win are [tex]20 *(\frac{2^3}{3^6} )[/tex].
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25 is what percent of 872
25 is 2.87 percent of 872.
First, let us understand the percentage:
A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.
To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.
We need to find 25 is what percent of 872.
Let 25 be x percent of 872.
So,
872 * x % = 25
872 * x / 100 = 25
872x = 25 * 100
x = 25 * 100 / 872
x = 2.87 %
So, 2.87 % of 872 is 25.
Thus, 25 is 2.87 percent of 872.
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98. XYZ Corporation hired 6 people as
summer workers. Of these 6 people, 3 will
be hired as permanent employees in the
fall. If 2 of the 6 people are male, how
many of the possible groups of 3 people
hired in the fall will include only 1 male?
E. 4
F. 6
G. 12
H. 24
Answer:
G. 12
Step-by-step explanation:
You want the number of ways 1 male and 2 females can be chosen from a group of 2 males and 4 females.
MalesFrom a group of 2 males, there are 2 ways that 1 male can be chosen. (He can be one, or the other.
FemalesFrom a group of 4 females, there can be 4C2 = 4!/(2!(2!)) = 4·3/2 = 6 ways that 2 females can be chosen.
Possible groupsThe total number of possible groups is the product of the numbers of groups of males and of females:
possible groups = 2 · 6 = 12
G. There are 12 possible groups of 3 people.
__
Additional comment
If the males are {a, b} and the females are {A, B, C, D}, the 12 possible groups are ...
aAB aAC aAD aBC aBD aCD bAB bAC bAD bBC bBD bCD
<95141404393>
(22-23)
-Jeva
7
#7 of 9 -
Ms. Smith opened a bank account to save money. The balance of the account is modeled by the function
f(x) = 4,000 (1.06)*, where x is the number of years since the account is opened. According to the function,
what is happening to the balance of the account each year?
A The balance of the account increases by 1.06% each year.
B The balance of the account decreases by 6% each year.
C The balance of the account decreases by 1.06% each year.
D The balance of the account increases by 6% each year.
<6)
The changes in his account is that (d) The balance of the account increases by 6% each year.
How to determine the occurrence in his account?The function of the account balance is given as
f(x) = 4,000 (1.06)*
The above function is an exponential growth function
Such that the growth factor (b) is the number in bracket
This is represented as
b = 1.06
The percentage growth rate (r) is calculated as:
r = b - 1
Substitute known values
r = 1.06 - 1
Evaluate the difference
r = 0.06
Express as percentage
r = 6%
This implies that the balance increases by 6% each year.
So, the true statement is (d)
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Graph the step function. (5 points - 1 point for each part of the graph)
Answer:
Step-by-step explanation:
is √3 a rational or irrational
Irrational Number
Step-by-step explanation:
Alternatively, 3 is a prime number or rational number, but √3 is not rational number.
Here, the given number √3 is equal to
1.73205080756 which gives the result of non
terminating and non recurring decimal and keep on extending , and cannot be expressed as fraction ..,
Therefore √3 is Irrational Number.
Which expressions are equivalent to g16? Check all that apply.
The equivalent expressions are (6^(-4) )^(-4), (6^(-2) )^(-8) and (6^8 )^2
Using exponent property, we have
[tex](a^{m})^{n} = a^{m*n}[/tex]
The given expressions is 6^16
From the question, we have
(6^0 )^16=6^(0×16)
⇒6^0 ≠ 6^16
(6^8 )^8=6^(8×8)
⇒6^64 ≠ 6^16
(6^(-4) )^(-4)=6^(-4x-4)
⇒6^16
(6^(-2) )^(-8)=6^(-2×-8)
⇒6^16
(6^(-1) )^16=6^(-1×16)
⇒6^(-16)≠6^16
(6^8 )^2=6^(8×2)
⇒6^16
Multiplication:
In mathematics, multiplying the numbers is used to find the product of two or more numbers. We frequently perform one of the basic mathematical operations. The simplest basic application is to use multiplication tables. Mathematicians multiply two integers to express the repetitive addition of one number to another. It is possible to contain natural numbers, fractions, integers, whole numbers, and other forms of numbers. M would either be added to itself 'n' times or subtracted from itself when M is multiplied by n.
Complete question:
Which expressions are equivalent to 6^16?
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PLEASSEEEEEE HELP MEEEE
determine the percentage of gross domestic product that went toward healthcare in 2009 using the given function
does this underestimate or overestimate the percent displayed by the graph
cording to the model when will 18.4% of domestic gross product go towards healthcare around to nearest year
The percentage in 2009, calculated from the logarithmic function is given as follows:
16.5%.
Which underestimates the graphed amount by 0.4%.
According to the model, the year in which 18.4% of the domestic gross product will go towards healthcare is:
2020.
What is the function?The logarithmic function in the context of this problem is given as follows:
f(x) = 1.2ln(x) + 15.2.
In which x is the number of years since 2006.
2009 is three years after 2006, hence the percentage is obtained as follows:
f(3) = 1.2ln(3) + 15.2 = 16.5%.
The percentage on the graph is given by:
16.9%.
Hence the function underestimates the graphed amount by 0.4%.
The year in which 18.4% of the domestic gross product will go towards healthcare is x for which f(x) = 18.4, hence:
18.4 = 1.2ln(x) + 15.2.
1.2ln(x) = 3.2
ln(x) = 3.2/1.2
ln(x) = 2.67.
ln and the exponential are inverse functions, hence:
x = e^2.67 = 14.4.
2006 + 14 = 2020.
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factorise fully 7x^3-35
Answer: 7(x^3-5)
Step-by-step explanation:
the common number between 7 and 35 is seven( 7*1=7, 7*5=35)
so with the 7 outside the parenthesis we end up having inside the parenthesis x^3 and 5 because x=1 and 7*1=7 and the 5 because 7*5=35 so if we distribute the seven we would get the original answer
Answer:
[tex]7(x^3-5)[/tex]
Step-by-step explanation:
Given expression:
[tex]7x^3-35[/tex]
To factor the given expression, begin by rewriting 35 as 7 · 5:
[tex]\implies 7x^3-7 \cdot 5[/tex]
Now factor out the common term 7:
[tex]\implies 7(x^3-5)[/tex]
What is the slope of the line on this graph? Please help me.
Answer:
2/3
Step-by-step explanation:
the slope is rise over run so y/x
Find the value of *p* using Cos. Answer with explanation and I will give brainlist.
Answer:
The angle is approximately 111.199 degrees.
Step-by-step explanation:
Cosine is adjacent over hypotenuse.
The hypotenuse is the longest side of the triangle.
In this cos the hypoteneuse is a. However, we can only use cos on right triangles and on the angles that are not 90 degrees. In this case, p would be the 90 degree angle if we could use cosine.
In this case, you need the law of cosines, not cosine. The law of cosine says [tex]c=\sqrt{a^2+b^2-2 a b cosp}[/tex] where c is the side opposite to the angle, a and b are the sides adjacent to the angle, and p is the angle. The law of cosine works for all the triangles.
Plugging in the numbers:
[tex]5.3=\sqrt{3.6^2+2.8^2-2*3.6*2.8* cosp}\\5.3^2=20.8-20.16* cosp}\\7.29=-20.16*cosp\\cos^{-1}\frac{7.29}{ -20.16}=p\\p=111.198929[/tex]
add an animal rescue 80% of the animals are dogs and 20% of the animals are cats. If the average age of the dogs is six months and the average age of the cat is three months what is the average age of all the animals?
The average age of all the animals at the animal rescue center is 5.4 months .
In the question ,
it is given that ,
at an animal rescue center .
percent of dogs that are present in the animal rescue = 80%
percent of cats that are present in the animal rescue = 20%
let suppose that there are total of 100 animals in the animal rescue .
So , the number of dogs = 80
and the number of cats = 20
also given that ,
the average age of dogs = 6 months
the average age of cats = 3 months .
So , the average age of all the animals can be calculated by
Average age = (80×6 + 20×3)/100
= (480 + 60)/100
= 540/100
= 5.4 months
Therefore , The average age of all the animals at the animal rescue center is 5.4 months .
At an animal rescue 80% of the animals are dogs and 20% of the animals are cats. If the average age of the dogs is six months and the average age of the cat is three months what is the average age of all the animals ?
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300 large pretzels cost $171. What is the unit price per pretzel?
Answer:
The unit price per pretzel is 57 cents (fifty-seven cents) each!
Step-by-step explanation:
Step One: Divide
Since the price is 171 dollars for 300 large pretzels, and you want to find the price of each pretzel, divide the price by the amount of pretzels.
171 / 300 = 0.57
Step Two: Convert
The answer is 0.57, but since you want to know the unit price, you need to convert it to dollars, and that's simple.
0.57 of a dollar is 57 cents.
Step Three: Get your Answer
Your answer is 57 cents per pretzel! You can double-check this by multiplying 0.57 by 300, getting 171.
Hope my answer helped you!
10x+5y=5x+20 solve for y
The value of y in the expression is y= - (x + 4) or, y= (x -4)
ExpressionAlgebraic expression in mathematics is a phrase that include coefficients, unknown variables operations, and constants
To solve for y in the equation 10x+5y=5x+20 we apply algebraic rule;
Step 1: Collect the like terms by moving the unknown 'ý' to the left side of the equation
5y =5x -10x+20
Step 2: Evaluate the the expression 5y =5x -10x+20
5y = -5x + 20
Step 3: Divide both sides by 5
[tex]\frac{5y }{5}[/tex] = [tex]\frac{-5x +20}{5}[/tex]
y = -5x/5 + 20/5
y = - (x + 4) or, y= (x -4)
Therefore, the value of y in the expression is y= - (x + 4) or, y= (x -4)
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2
Determine the volume of the rectangular
prism, if each cube represents 1 unit.
The volume of the rectangular prism is 12 cubic inches
It is given that Each cube represent 1 unit
The base length of the rectangular prism = 4 inches
The base width of the rectangular prism = 3 inches
The height of the rectangular prism = 1 inches
The volume of the rectangular prism = The base length of the rectangular prism × The base width of the rectangular prism × The height of the rectangular prism
Substitute the values in the equation
The volume of the rectangular prism = 4 × 3 × 1
= 12 cubic inches
Hence, the volume of the rectangular prism is 12 cubic inches
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Linear Equation Word Problems
The Bike Rental Shop charges $12 plus $9 an hour for renting a bike. Darnell paid $57 to rent a bike. How many hours did he pay to have the bike checked out?
Answer: 5 hours.
Step-by-step explanation: First you need to subtract the $12 fee from the total to find out how many hours he paid for. 57-12=45. So if he paid $45 at $9 per hour, 45 divided by 9 equals 5.
3. What is m ∠ E?
(x + 10)
E
(4x - 35)°
Using the corresponding angle theorem, the value of m∠E is 155.
In the given question we have to find the value of m∠E.
As we know that,
According to the corresponding angle theorem, if a transversal meets two parallel lines, the corresponding angles must be congruent.
So from the figure
4x−35=x+10
Add 35 on both side we get
4x=x+10+35
4x=x+45
Subtract on both side
4x−x=x+45−x
3x=45
Divide by 3 on both side we get
x=15
So the value of x+10
=15+10
=25
As we know that value the angle of straight line is 180.
So m∠E+25=180
Subtract 25 on both side we get
m∠E=180−25
m∠E=155
Hence, the value of m∠E is 155.
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Write the equation of the line perpendicular to
y = 5/3x + 1 and passing through the point (-10, 3)
The equation of the line is y = (-3/5)x - 3
The equation of the line given
y = (5/3)x + 1
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Comparing the given equation
slope of the line m = 5/3
The slope of the perpendicular line = -1/m
= -1 ÷ 5/3
= -3/5
The line is passing through the point (-10, 3)
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values in the equation
y - 3 = (-3/5)(x - (-10))
y - 3 = (-3/5)x - 6
y = (-3/5)x - 6 + 3
y = (-3/5)x - 3
Hence, the equation of the line is y = (-3/5)x - 3
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Write the expression without brackets and then simplify.
a) 6 + 5(3x – 2)
The expression when the brackets are removed is 15x - 4
How to rewrite the expression without the brackets?From the question, we have the following expression that can be used in our computation:
6 + 5(3x - 2)
The above expression has brackets
So, we start by expanding the brackets
Solving further, we have
6 + 5(3x - 2) = 6 + 15x - 10
Collect the like terms
This gives
6 + 5(3x - 2) = 15x - 10 + 6
Evaluate the like terms
So, we have
6 + 5(3x - 2) = 15x - 4
Hence, the expression is 15x - 4
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CHALLENGE btw it hard
Answer:
25%
Step-by-step explanation:
Lets find how many people were at the pool at the 4th week.
1060 - 110 + 145 - 247 =
848
Use percent error formula,
[tex]\frac{v_a-v_e }{v_e}[/tex]
Actual - Estimate over Estimate
Actual (1st week): 1060
Estimate (4th week): 848
Plug into formula.
[tex]\frac{1060-848}{848}[/tex]
Simplify.
[tex]\frac{212}{848}[/tex]
Divide.
0.25
Multiply by 100 and write with a percentage sign.
0.25*100 = 25
25%
Answer:
The percent decrease is 20%
Step-by-step explanation:
First week : 1060 people
Second week: 1060 - 110 = 950 people
Third week : 950 + 145 = 1095 people
Fourth week: 1095 - 247 = 848 people
Make 1060 the whole (100%), we need to figure out 848 percent
848 x
1060 100
848 x 100 = 84800
84800 divided by 1060 = 20
From 1060 people to 848 people is a 20% decrease
Kim downloads game and music apps. She spends of 3/4 her money on game apps. Kim spends $0.98 on music apps. How much does Kim spend on game apps?
The amount of money spend on music from the fractional value is $1.30;
What are fractions?
Fractions are referred to as the components of a whole in mathematics. A single object or a collection of objects might be entire. When we cut a piece of cake in real life from the entire cake, the part represents the percent of the cake. The word "fraction" is derived from Latin. "Fractus" means "broken" in Latin. The fraction was expressed verbally in earlier times. It was afterward presented in numerical form.
A piece or sector of any quantity is another name for the fraction. It is indicated by the sign "/," such as a/b. For instance, in the fraction 2/4, the lower part represents the denominator, and the top part the numerator.
In the given question, we have:
spends 3/4 of her money on game apps
spends $0.98 on music apps.
So, we can assume the total amount to be K;
So, The fraction of money spend on music is K/4;
According to the question, we have:
[tex]\frac{1}{4} \times k[/tex] = $0.98;
⇒K = $3.92;
So, The total amount with Kim is $1.30;
Hence,
The amount of money spend on music is $1.30;
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which of the following is a heuristic commonly used in problem solving? group of answer choices regression analysis local minimization means-end analysis local maximization functional fixedness
The commonly used technique in problem solving is means-end analysis
One typical heuristic is to define subproblems or subgoals. Means-ends analysis, which entails determining how to close the gap between a goal and the actual situation, is another frequently employed heuristic. You can divide a problem into smaller problems and deal with each one separately by using means-ends analysis.
Heuristic problem-solving entails what?
A problem-solving heuristic is a non-formal, speculative process that, in certain circumstances, produces a solution but not in others. The strategy can be either more or less successful than employing an algorithm because the results of applying a heuristic are unpredictable.
So,therefore the means-end analysis is commonly used technique in problem solving
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three boys and three boys are lined up in a row. what is the probability of all three girls being together
The probability that all three girls are together is 0.03
Here we will use the string method
Consider 3 girls as a single element, and consider the other 3 boys as 3 separate elements
So total we have 4 element
So the arrangement of 4 elements is given by 4!
Arrangement of girls inside a single element given by 3!
So the way of getting all girls together is given by 4! × 3! = 24 × 6 =144
Total way of arranging 7 people given by 7! = 5040
Probability = Required cases / Total cases
= 144 / 5040
= 0.03
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Brianna and Gavin used partial quotients to show 552 divided by 23
willing to give extra points ( 50 more!)
Briannas work:
Step 1: Subtract (20×23) from 552 to get 92.
Step 2: Subtract (4×23) from 92 to get 0.
Step 3: Add partial quotients.
Gavins work:
Step 1: Subtract (10×23) from 552 to get 322.
Step 2: Subtract (10×23) from 322 to get 92.
Step 3: Subtract (2×23) from 92 to get 46.
Step 4: Subtract (2×23) from 46 to get 0.
Step 5: Add the partial quotients.
Which student(s) correctly calculated the quotient? Explain your answer
The student that correctly used partial quotients to show 552 divided by 23 was Gavin.
What is the purpose of partial quotients?The purpose of partial quotients is to facilitate division as by using partial quotients students can easily divide big numbers by using easy multiples first and then adding the multiplers to find the final divisiors. The recommended numbers to use are 5 or 10.
Which student used this method correctly?Based on the information provided, it can be conclude Gavin was better at applying this method because he used only easy multiples (10, 2) to make the number easier to divide, while Brianna completed the process only through to steps, which is not recommended when applying this method.
In conclusion, Gavin was the one who correctly used the method and calculated the result.
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The diameter of holes for a cable harness is known to have a normal distribution with a standard deviation of 0. 01 inch. A random sample of size 10 yields an average diameter of 1. 5045 inch. Find the 99% and 95% two-tailed/two-sided confidence intervals on the mean diameter and explain the difference of the interval between the two confidence levels.
For the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.
As given in the question,
Confidence interval for population mean is given by:
[tex]\bar{x}[/tex] ± z × ( σ / √n)
Where,
σ = population standard deviation.
n= sample size
[tex]\bar{x}[/tex] = Sample mean
Given values from the random sample size are :
σ = 0.01 inches
n= 10
[tex]\bar{x}[/tex] = 1.5045
Critical value confidence interval (using x-value table)
z for 99% = 2.576 and Significance level = 0.01
z for 95% = 1.960 and Significance level = 0.05
99% two-sided confidence interval on the mean hole diameter is equal to :
[tex]\bar{x}[/tex] ± z × ( σ / √n)
= 1.5045 ± 2.576 × ( 0.01 / √10)
= 1.5045 ± 0.00815 (approximately)
= 1.5045 - 0.00815 , 1.5045 + 0.00815
= ( 1.49635 , 1.51265 )
95% two-sided confidence interval on the mean hole diameter is equal to :
[tex]\bar{x}[/tex] ± z × ( σ / √n)
= 1.5045 ± 1.960 × ( 0.01 / √10)
= 1.5045 ± 0.00620 (approximately)
= 1.5045 - 0.00620 , 1.5045 + 0.00620
= ( 1.4983 , 1.5107 )
Therefore, for the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.
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The product of -8 and -4 is -32 it is false hope you like it and please give me a five star rating thank you very much hope this helps
Answer:
The answer is false.
Step-by-step explanation:
If you do not already know this, a negative and a negative equals a positive. Therefore, instead of –8 • –4 = –32, the correct answer would be –8 • –4 = 32.
Hope that helps! Have an amazing rest of your day! Brainliest welcome! :)
Answer: is false.
hope this helps
have a good day
Step-by-step explanation:
A child's height is 59.3 inches, what is the height of the child in feet? Round your answer to the nearest tenth.
1 ft = 12 in
what is an equation of the line that passes through the point (-3,-1) and is perpendicular to the line x-2y=6
An equation of the line that passes through the point (-3, -1) and is perpendicular to the line x - 2y = 6 is y = -2x - 7.
How to determine an equation of this line?Mathematically, the standard form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.Next, we would rewrite the given equation representing a line in standard form:
x - 2y = 6
2y = x - 6
y = x/2 - 6
Therefore, slope (m) = 1/2
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
1/2 × m₂ = -1
m₂ = -2
At point (-3, -1), an equation of this line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
y - (-1) = -2(x - (-3))
y + 1 = -2(x + 3)
y + 1 = -2x - 6
y = -2x - 6 - 1
y = -2x - 7
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