To move at 100 km/hour at its end, the length of the minute hand that has an angular velocity of 2·π radians per hour, has to be approximately 15.92 kilometers
What is angular velocity?Angular velocity is the rate and direction of rotation of a body about an axis.
The required linear speed of the minute hand = 100 km/hour
The formula to convert angular speed to linear speed is presented as follows;
[tex]\omega = \dfrac{v}{r}[/tex]Which gives;
[tex]r = \dfrac{v}{\omega}[/tex]The angular speed of the minute hand = 2·π rad/hour
The required length of the minute hand is therefore;
[tex]r = \dfrac{100 \ km/hour}{2\cdot \pi/hour} = \dfrac{50}{\pi}\, km \approx 15.92 \, km[/tex]
The length of the minute hand that that give a motion of 100 km/hour at the end is approximately 15.92 km
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A regular polygon has 16 sides. If one of its angles measures (5h − 29)°, what is the value of h?
Answer:10.3
Step-by-step explanation:
16(5h-29)=360
80h-464=360
80h-464+464=360+464
80h/80=824/80
h=10.3
If tan(A+B) = -4 and tan B=5/3, find tan A.
The value of tan A = 1
What are trigonometric ratios?Trigonometric ratios are the ratios of sides of a right-angle triangle. The six trigonometric ratios of a right angle triangle are Sin, Cos, Tan, Cosec, sec and cot.
The trigonometric ratios relate the sides of the triangle with the angles of the triangle.
tan(A+B) = -4, tan B = 5/3
But tan(A + B) = [tex]\frac{tan A + tanB}{1-tanAtanB}[/tex]
Substituting the values of tan(A +B) tan B
-4 = [tex]\frac{tan A + 5/3}{1 - 5/3tanA}[/tex]
multiply numerator and denominator by 3, you have
-4 = [tex]\frac{3tanA + 5}{3 -5tanA}[/tex]
-4(3-5tanA) = 3tanA +5
-12 +20tanA = 3tanA +5
collect like terms
20tanA - 3tanA = 5 +12
17tanA = 17
tan A = 17/17
tanA = 1
In conclusion, the value of tanA = 1
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10. Each term in a sequence is generated by
multiplying the previous term by 3 and then
adding 2. If the first term is -3, what will the 6th
term be?
a. -487
b. -165
C. -57
d. 57
e. 165
2
The 6th term is -487 i.e, option(a)
What is a Sequence ?
A sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence.
There are 4 types of sequence, arithmetic sequences, geometric sequences, quadratic sequences and special sequences.
Given, the 1st term = -3
According to question, we get the term by multiplying the previous term by 3 and then adding 2.
Now, calculate the other terms.
so, the 2nd term will be
-3 * 3 + 2 = -7
3rd term
-7 * 3 + 2 = -19
4th term
-19 * 3 + 2 = - 55
5th term
-55 * 3 + 2 = -163
6th term
-163 * 3 + 2 = -487
Hence, the 6th term is -487 i.e, option(a)
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help meeeeeeeeeeeeeee pleaseee
The recommended screen size for the television is 59.85 inches.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, the expression for the size of the television is given as:
S = 0.228x² + 8.154x - 8.3
where x = 7 feet
S = 0.228x² + 8.154x - 8.3
S = 0.228(7)² + 8.154(7) - 8.3
S = 11.172 + 57.078 - 8.4
S = 59.85
The size is 59.85 inches.
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a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus. she wants to know if anxiety levels were higher in the fearful stimulus condition. if the same participants are observed in each group, then what type of statistical design is appropriate for this study? group of answer choices a one-way between-subjects anova a one-way within-subjects anova an independent t-test a dependent t-test
Using the theories of statistical design, we got that both related sample t test and one-way within-subjects ANOVA is the appropriate statistical design for the study in which a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus.
Statistical design of experiments and the response surface methodology has become a standard tool for the medium development. There are several applications reported in literature, such as the production of antibiotics, secondary metabolites, and enzymes.
Applications of statistical design of experiment shown in the Table 1 and several other studies use exclusively of the response surface method with quadratic polynomial models and the central composite design with on average 20–30 experiments. In most cases, the important components were identified by fractional factorial design or by the Plackett–Burman design with 10–15 experiments. Methods for narrowing optimal variable range are only infrequently applied.
Hence, when a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus and wants to know if anxiety levels were higher in the fearful stimulus condition and if the same participants are observed in each group, then the appropriate statistical design is that both related sample t test and one-way within-subjects ANOVA .
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Determine the period.
Answer:
shopkeeper sells a book at INR 960 for a profit of 20% and another book at INR 720 for a loss of 10%. Find the total profit/loss of the shopkeeper
60+16=x-16+16 x=? This math book hates me
Answer: 76
Step-by-step explanation: simplify equation
60+16=x-16+16 (cancel out 16 and add 60+16)
76=x
60+16=x-16+16
76=x
x=76
when the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. what is the original number?
The original number from the given decimal number is 0.02.
Define the term reciprocal of the number?A multiplicative inverse of such a number is referred to as the reciprocal. In other words, 1 divided by a number is the definition of the reciprocal. Any given number multiplied by its reciprocal would always yield the value 1. By swapping the values of a numerator and denominator, one can find exact reciprocal of a fraction.For the given question;
Moving a decimal point 4 places towards the right corresponds to multiplying the given integer by 10,000 if it is x.
This results in:
10000x = 4.(1/x)
Simplifying.
x² = 4/10000
x > 0.
Taking square root of the number.
x = 2/100
x = 0.02
Thus, the original number from the given decimal number is 0.02.
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Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job. How much total money would Taub have after 7 weeks of saving? Also, write an expression that represents the amount of money Taub would have saved in w weeks.
Total savings after 7 weeks:
Total savings after w weeks:
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a phrase : Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job.
Taub will have a total of -
70 + 7 x 10 = $140
The expression that represents the amount of money Taub would have saved in [w] weeks is -
y = 70 + 10w
Therefore -
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
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an srs of 29 students at uh gave an average height of 5.5 feet and a standard deviation of .3 feet. construct a 90% confidence interval for the mean height of students at uh. a) [4.250, 6.950] b) [5.405, 5.595] c) [4.990, 6.010] d) [4.000, 7.300] e) [5.482, 5.518] f) none of the above
1 trillion = 1,000 billion
There are about 40 trillion cells in the human body.
Each cell consists of about 100 trillion atoms.
About how many atoms are there in the human body altogether?
Give your answer in standard form.
The number of atoms in standard form is 4 × 10²⁵ atoms
What is standard form?Standard form is number written in the form a × 10ⁿ where 1 ≤ a < 10 and n is an integer
How to find how many atoms are there in the human body altogether in standard form?Since there are about 40 trillion cells in the human body. and each cell consists of about 100 trillion atoms, we have that
40 trillion cells = 40 trillion × 1 cell
Also, 1 cell = 100 trillion atoms.
So, 40 trillion × 1 cell = 40 trillion × 100 trillion atoms.
Now, we know that 1 trillion = 1000 billion
So, Number of atoms = 40 trillion × 100 trillion atoms
= 40 × trillion × 100 × 1 trillion atoms.
= 40 × 1000 billion × 100 × 1000 billion atoms.
= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.
We know that 1 billion = 1000000000
So,
= 40 × 1000 × 100 × 1000 × 1 billion × 1 billion atoms.
= 40 × 1000 × 100 × 1000 × 1000000000 × 1000000000 atoms
= 40000000000000000000000000
= 4 × 10000000000000000000000000
= 4 × 10²⁵ atoms
So, the number of atoms in standard form is 4 × 10²⁵ atoms
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NEED HELP ASAP!!!!!!!!!!!!!!
The number of solutions each polynomial has is 1, 5 and 3
What is a polynomial?In mathematics, a polynomial is an equation made up of coefficients and indeterminates, sometimes referred to as variables. Only addition, subtraction, multiplication, and powers of positive-integer variables may be used to solve it. An example of a polynomial with one undetermined x is x2 4x + 7.
Polynomials are often employed in both mathematics and science. In fundamental chemistry and physics, economics, and social science, for example, they are used to define polynomial functions. They are also employed in calculus and numerical analysis to approximate other functions. From straightforward word problems to intricate scientific conundrums, polynomial equations are utilized to represent a broad variety of topics. polynomials' usage in complex maths.
The number of solutions of a polynomial is equal to the highest degree of the polynomial.
So,
1) y = -6x -9
Has 1 solution as highest degree = 1
2) y = 2x⁵-x⁴ +2x³-6x²+2x+4
Has 5 solutions as highest degree = 5
3) y = -4x³-10x² +7x+5
Has 3 solutions as highest degree = 3
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37, 38, 39, and 40 show that the series is convergent. how many terms of the series do we need to add in order to find the sum to the indicated accuracy?
In order to find the sum to the indicated accuracy we need to add
5 terms as the series is said to be convergent.
Given Series is Σ(-1/3)^n / n where error is less than 0.0005
= Σ (-1)^n / n3^n
For this series, we will use ratio test
if [tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = L < 1 then series in convergent,
Let an = (-1)^n / n3^n , an+1 = (-1)^n+1 / (n+1)3^n+1
[tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = [tex]\lim_{n \to \infty} | ((-1)^n+1 / (n+1)3^n+1)(n3^n/(-1)^n) |[/tex]
By solving we get,
[tex]\lim_{n \to \infty} |an + 1 / an |[/tex] = 1/3 < 1
Then given series is convergent.
By alternating series estimation theorem we have,
|Rn|=|S-Sn| <= an+1
an+1 <= 0.0005
1 / (n+1)3^n+1 <= 0.0005
(n+1)3^n+1 >= 2000
2 * [tex]3^{2}[/tex] >[tex]\neq[/tex] 2000 (n=1)
4 * [tex]3^{4}[/tex] >[tex]\neq[/tex] 2000 (n=3)
6 * [tex]3^{6}[/tex] >= 200 (n=5)
So required terms is n=5
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Just 2 questions.
Explaining the Converse of the Pythagorean Theorem
Task 1
Part A
The Pythagorean Theorem states that for any given right triangle, a2 + b2 = c2. Using the Pythagorean Theorem, what should be the relationship between the areas of the three squares?
Task 2
Part E What does this show about the relationship between the two triangles?
The Pythagorean Theorem indicates the following relationship between the squares and triangles.
Part A
The relationship between the areas of the squares is that the area of the large square is the sum of the areas of the other two squares.Part E
The point that the length c on one triangle is equal to the length n on the other triangle and that the other two sides of both triangles are congruent, the two triangles are congruent by SSS congruency rule.What is the Pythagorean Theorem?Pythagoras theorem can be stated as follows; The square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.
Part A
The possible squares in the question are the three squares arranged on the three sides of the triangle, and having a side length which is the same as the length of the side of the triangle to which the square is attached
The relationship between the three squares of side length a, b, and c according to Pythagorean theorem is; a² + b² = c²
Therefore, the area of the largest square that is located on the hypotenuse side of the triangle is equal to the sum of the areas of the other two squares.
Part E
The length of the sides of the triangles, obtained from a similar question on the site are; a, b, and c and a, b, and n
It was shown that c² = n²
Therefore;
c = n
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Write the equation of the line in fully simplified slope-intercept form.
ANSWER ASAP
WILL GIVE BRAINLIEST
The equation of the line in fully simplified slope - intercept form is 5x + 4y = 12 .
In the question ,
a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .
to find the equation , we need minimum two points ,
So , from the given graph ,
we can find that
when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 3 ,
the first point is (0 [tex],[/tex] 3) .
when x [tex]=[/tex] 4 , the value of y [tex]=[/tex] -2 ,
the second point is (4 [tex],[/tex] -2) .
the slope can be calculated by
slope = (-2-3)/(4-0)
= -5/4
So , the equation of the line passing through point (4,-2) with slope -5/4 , in the slope intercept form is
(y -(-2)) = (-5/4)(x-4)
y + 2 = (-5/4)x + 5
y = (-5/4)x + 5 - 2
y = (-5/4)x + 3
Simplifying further , we get
4y = -5x + 12
5x + 4y = 12
Therefore , The equation line in fully simplified slope - intercept form is 5x + 4y = 12 .
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Carly works 6 hours each day for 4 days a week
she earns £360 each week
How much does Carly earn each hour
Answer:
the answer is £15
Step-by-step explanation:
Carly works 6 hours for four days 6x4= 24
so she worked for 24 hours we know that she makes £360 per week.
so we divide 360 by 24 which gives us the total of
£15 per hour
Aaliyah was given a gift card for a coffee shop. Each morning, Aaliyah uses the card to
buy one cup of coffee. The original amount of money on the gift card was $30 and
each
сир of coffee costs $2. Make a table of values and then write an equation for A,
in terms of x, representing the amount money remaining on the card after buying a
cups of coffee.
The equation in terms of x, which represents the amount of money left on the gift card of Aaliyah upon buying a cup of coffee is; A = 30 - 2x dollars.
Define the term equation?A single mathematical phrase is referred to as a term. It could be a single number (negatively or positively), a single variable (a letter), or a combination of variables multiplied but still never added or eliminated. Variables with such a number ahead of them are used in some words. A coefficient is the number that appears ahead of a phrase.The original value of the gift card was $30.
Coffee costs $2 per cup.
Let 'x' be the number of cup of coffee purchased by Aaliyah.
Total cost be 'A' be paid by her.
Thus, the equation in terms of x, which represents the amount of money left on the gift card upon buying a cup of coffee is;
A = 30 - 2x dollars.
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an experiment consists of tossing a fair die until a 6 occurs four times. what is the probability that the process ends after exactly stack exchange
The experiment will end after 4th time.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .hence, after 4th trial experiment will stop.
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Find the value of x. Then find the measure of each labeled angle
(3x+6)
(4x-12)
answer:
x = 18, 60.
step-by-step explanation:
evaulating (3x+6) = (4x-12) and solving for x gives us x = 18. you didn't include the angle, so i can't give you that. but
(3x+6) = 60
(4x-12) = 60
if those were your angles, you would have an equilalateral triangle (all sides/angles even) and your missing angle would also be 60.
Please help !!! I don’t understand 25 points !
Answer: Triangle VUT:
84:70:42
Triangle RSQ:
30:25:15
Final simplified answer: 2.8:2.8:2.8
Scale factor of 2.8
Step-by-step explanation:
Each triangle's sides are a part of the ratio, then you divide each side by the corresponding one (84 by 30, and 70 by 25) to get your scale factor.
Tim and Jessica plan to rent a camper van for a vacation. The van costs $183 per day.
The rental includes 120 miles for free and then charges $0.39 per mile.
The total price Tim and Jessica paid to rent the camper van is $598.74. Write an
equation that models the cost of the van rental in terms of miles traveled, m.
Create an equation
The equation that represents the cost of the van rental is $598.74 = 136.20 + $0.39m .
What is the equation that represents the cost?The equation that would model the cost of the van rental is a linear equation. A linear equation is an equation that has one variable that is raised to the power of one.
The general form of linear equations is: y = a + bx
Where:
a = intercept
b = slope
The form of the equation that models the cost is:
Total cost = cost of renting the van + [cost per mile x (m - 120 miles)
$598.74 = $183 + [$0.39 x (m - 120)
$598.74 = $183 + $0.39m - 46.80
$598.74 = 136.20 + $0.39m
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Justify each step of the solution by stating the property that was used to get to each step. (4 points - 1 point each correct answer)
Given: 2(10 - 13x) + 9x) = -34x + 60
Step 1: 20 + 26x + 9x = -34x + 60
Step 2: -17x = -34x + 40
Step 3: 17x = 40
Step 4: x = 40/17
Sample Answer
Step 1: _____ property
Step 2: ______ property
Step 3: ______ property
Step 4: ______ property
The ratio of the number of beads collected by Jane to the number of beads collected by Jill is 7: 3. Jane gave some beads to Jill. Is it possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill? Explain why you think so
yes , it is possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill and The number of beads Jane has is 7t/4 and Jill has 3t/4 bead's
The ratio of Jane's beads to Jill's beads is 7: 3
Let x be the number of beads Jane has
y be the number of beads Jill has
x/y = 7/3
When Jane's gives t of her beads away both will have the same number of beads so
x - t = y
substituting in the first equation
x/ ( x- t) =7/3
3x= 7x-7t
4x= 7t
x= 7t/4
y= 7t/4 -t
= 3t/4
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an envelope contains eight bills: ones, fives, tens, and twenties. two bills are drawn at random without replacement. what is the probability that their sum is $ or more?
Using the concepts of probability, we got 0.5 is the probability of drawing the sum $20 or more when two bills are drawn randomly without replacement.
We have an envelope contains 8 bills;
Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.
When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.
Total outcomes = 2 x 2 x 2 x 2 = 16
Total possible outcomes, more than 20;
(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases
That is,
The total possible outcomes is 8.
Now,
The probability of bill to be $20 or more = Possible outcome / Total outcome
Probability = 8/16 = 1/2=0.5
Hence, When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 0.5.
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(Complete question)
an envelope contains eight bills: 2 ones, 2 fives, 2 tens, and 2 twenties. two bills are drawn at random without replacement. what is the probability that their sum is $20 or more?
The goals in a hockey rink are 6 feet wide. A hockey player is standing 25 feet directly in front of the left side of one of the goals.
a) what is the maximum angle at which the player can shoot the puck to make it in the goal?
b) if the player skates forward 5 feet, how wide of a range of angles can the player shoot the puck to make it in the goal?
c) describe what happens to the maximum angle as the player gets closer to the goal
The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.
a)
The given condition makes a right-angle triangle as shown below,
The tan function,
tanθ = 6/25
θ = 14.50°
b)
When a player is 5 feet closer means (20 feet far)
tanθ = 6/20
θ = 16.70°
c)
As the player gets closer the angle becomes more and more.
Hence "The maximum angle when a player is 25 feet far is 14.50° while when 5 feet closer it will be 16.70° and as a player gets closer angle increases".
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Which equation is equivalent to y = 3x-6?
0 3x-2y = 6
000
2x+3y = -6
=
O 3x-2y = 12
2x-3y = 18
The equivalent equation for the expression y = 3x-6 is none.
Equivalent equation:
If the two equations are said to be equivalent when they have the same solution set. Then it is called as Equivalent equation.
Given,
Here we have the expression y = 3x-6
Now, we need to find the equivalent equation.
In order to find the equivalent equation, we have to take some sample values for x,
The sample value of x as 1, 2, 3
Now, we have to apply these values on the given expression first,
Then we get,
x = 1 => y = 3(1) - 6 = -3
x = 2 => y = 3(2) - 6 = 0
x = 3 => y = 3(3) -6 = 9
Now, we have to apply these to the given equation and which has the same value of the given expression,
x = 1 => 3(1) - 2y = 6 = -2y = 6 - 3 => y = -3/2
x = 2 => 3(2) - 2y = 6 = -2y = 6 - 6 => y = 0
x = 3 => 3(3) - 2y = 6 = -2y = 6 - 9 => y = 3/2
This is not equal one.
Move on to the second one,
x = 1 => 2(1) + 3y = -6 => 3y = -6 - 2 => y = -8/3
x = 2 => 2(2) + 3y = -6 = 3y = -6 - 4 => y = -10/3
x = 3 => 2(3) + 3y = -6 = 3y = -6 - 6 => y = -4
This is not a equivalent one.
Move on to the third expression,
x = 1 => 3(1) - 2y = 12 = -2y = 12 - 3 => y = -9/2
x = 2 => 3(2) - 2y = 12 = -2y = 12 - 6 => y = -3
x = 3 => 3(3) - 2y = 12 = -2y = 12 - 9 => y = -3/2
This is not a equivalent one.
Finally we have to use the last one, then we get,
x = 1 => 2(1) - 3y = 18 => -3y = 18 - 2 => y = -16/3
x = 2 => 2(2) - 3y = 18 => -3y = 18 - 4 => y = -14/3
x = 3 => 2(3) - 3y = 18 => -3y = 18 - 6 => y = -4
Therefore, none of them are the equivalent one.
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Tiara, a quality assurance inspector at a chocolate factory, checks for product quality using a random sample of 18 pieces of chocolate from a batch of 60, with 17 white chocolates and 43 dark chocolates. Let p be the proportion of white chocolates in the sample
The 10% criterion is not followed in Part A. The typical condition is not satisfied in component B.
What is proportion?A proportion is a component, piece, or amount that is compared to a total. It might be 0 or 1, or any number between 0 and 1. It can be stated numerically or as a percentage. In official statistics, one example would be the proportion of the Canadian population residing in a certain province.
Here,
The chocolate chunks' data are as follows:
The sample size (n = 18) of chocolates
The batch contains 17 pieces of white chocolate.
The batch contains 43 dark chocolates.
Given the percentage of white chocolates in the sample, we have;
p = 17/60 = 0.28, the proportion of white chocolates in the batch
Part A
Because sampling samples without replacing them does not result in independent Bernoulli trials, the 10% condition stipulates that the sample size should be less than or equal to 10% of the population.
Because the stated sample size, n = 18, is 18/60100 = 30% > 10% of the batch, the 10% condition is not satisfied in the current case.
Part B
The normal approximation can be assumed when we have;
n·p > 10 and n·p·(1 - p) > 10
By plugging in the values for 'n' and 'p', we have;
p = 0.28 = 17/60
n·p = 18 × 17/60 = 5.1 < 10
n·p·(1 - p) = 18 × 17/60 × (1 - 17/60) = 3.655 < 10
Therefore the normal condition is not met.
Part A does not adhere to the 10% requirement. Component B does not meet the normal condition.
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(giving brainliest)
Two friends, Sophia and Ruby, took summer jobs. the equation y=23.9x represents ruby's earnings in dollars and cents, y, for working x hours. Sophia earned 1098.20 in 38 hours.
sophia earns $___ per hour (less/more) than ruby.
By performing some simple mathematical operations, we know that Sophia earns $366 per hour.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations. Parentheses, Exponents, Multiplication, Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).So, to calculate how much Sophia earns in 1 hour:
Total earnings are 1098.20.Total working hours are 38.Now, calculate earnings per hour:
1098.20/38366.06Rounding off: $366
Therefore, by performing some simple mathematical operations, we know that Sophia earns $366 per hour.
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Complete question:
Two friends, Sophia and Ruby, took summer jobs. the equation y=23.9x represents ruby's earnings in dollars and cents, y, for working x hours. Sophia earned 1098.20 in 38 hours.
sophia earns $___ per hour
under what circumstances would a score that is 10 points below the mean be considered to be an extreme value? select one: a. when the mean is much greater than 10 b. when the mean is much less than 10 c. when the standard deviation is much greater than 10 d. when the standard deviation is much less than 10
The correct option d. when the standard deviation is much less than 10.
Describe the term standard deviation?The term "standard deviation" (or "σ") applies to a measurement of the data's dispersion from the mean. A low standard deviation indicate that the data are grouped around the mean, although a large standard deviation indicates that the data are more dispersed.When a value is 10 points beyond the norm, it is said to be an extreme value or an outlier.
When a point deviates significantly from the mean in comparison to other points, it is referred to as an outlier. Z-scores can be used to establish this. Remember the z-score formula:
z = (x - μ) / σ
μ = mean σ = standard deviationx = point of interestThe outlier should have a very big magnitude z-score. We are aware that the score in this issue is 10 points just below mean, we can say:
A lesser value of would raise the magnitude of a z-score, increasing it to the maximum extent achievable.
Therefore, this point would be an outlier whether its standard deviation was drastically lower than 10.
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7. Eugene earns $2,700 monthly. He is going to be receiving a 3.5% raise. With this new raise, he
Inelieves he will earn more than $2,800 a month. Is Eugene correct in his thinking? Why or why
rot? Justify your reasoning.
Answer: No
Step-by-step explanation: to find out how much more money Eugene will be making we need to isolate the increased value provided by the raise and then add it to his already existing earnings. We do this by multiplying $2700 by 3.5%.
We would write this as 2700 x .035
This is because 100% can be converted to 1, for example if Eugene got a 100% raise we would multiply 2700 by 1 (which changes nothing) then add 2700 and 2700 together.
Since Eugene is only getting a 3.5% raise we would write it as .035 instead of 1
Now that we have our equation we first need to simplify. In this case it means we remove the two zero's from 2700 to make it 27. To make sure the answer does not get messed up will make the other side of the equation larger by moving everything two decimal points (one for each removed zero) like this.
27 x 3.5
This is much easier to work with but I will still show the steps I am using to prevent confusion.
27 x .5 = 13.5
27 x 3 = 20 x 3 + 7 x 3
20 x 3 = 60
7 x 3 =21
60+21 =81
81+13.5=94.5
Since 2700 + 94.5 = 2794.5 Eugene will not make more than $2800 dollars a month after his raise.