Answers
The stem-and-leaf diagram is:
Stem Leaf
0 9
1 0, 5, 5, 8
2 1, 4, 8
3 0, 3, 5, 6, 6
4 2, 3, 4, 5, 5, 6, 7, 7, 8
5 1, 4, 5, 6, 8, 8, 8, 8, 9, 9, 9, 9,9,9
The mode is 59
The range is 50
The median is 45.50
The interquartile range is 6.5.
What is a stem-and-leaf plot?A stem-and-leaf plot is a table that is used to display numerical data. A stem-and-leaf plot has two column, one for the stem and the other for the leaf. The stem is the first number in the digit while the leaf is the last number. For example in the number 59, 5 would be the stem and 9 would be the leaf.
Mode is the number that occurs most frequently in a dataset. The mode is 59 because it appears 6 times in the dataset.
Range is the difference between the highest number and the lowest number
Range = 59 - 9 = 50
Median is the number at the center of the dataset.
Median = (n + 1) / 2
37 / 2 = 18.5th term = (45 + 46) / 2 = 45.5
The interquartile range is the difference between the third quartile and the first quartile.
Third quartile = 3/4(n + 1)
3 / 4 x 37 = 27.75 term = 58
First quartile = 1/4 x (n + 1)
1/4 x 37 = 9.25term = (50 + 53) / 2 = 51.5
Interquartile range = 58 - 51.5 = 6.5
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Related Questions
Select all the equations where x = -2 is a solution.
(Select all that apply.)
a. 3x - 5 = 1
b. 19 = 2(x-6)+3
c. 5 + 3x = -1
d. 2(x+5)=x+8
e. 4x = 4 + 2x
Answers
the leters c and d are correct for this equation
#2 The number of bacteria in a refrigerated food is given by N(T)=20T2-20T+120 for -2T14 Tand where T is the temperature of the food in Celsius.
(a)Explain the meaning of -2T14 in this context
(b)Determine the temperature the number of bacteria will be minimal?
(c)Find number of bacteria in a above
(d) Sketch a graph
Answers
From the given quadratic function, it is found that:
a) The interval -2 ≤ T ≤ 14 gives the range of the temperature of the food in Celsius.
b) The number of bacteria will be minimal for a temperature of 0.5 ºC.
c) The minimum number of bacteria is of 115.
d) The graph that models the situation is sketched at the end of the answer.
What does the quadratic function models in this problem?The quadratic function is given as follows:
N(T) = 20T² - 20T + 120, -2 ≤ T ≤ 14.
In which:
T is the temperature in Celsius of the food.N(T) is the number of bacteria in the food.The function has a domain of -2 ≤ T ≤ 14, meaning that these are the possible temperatures of the food.
For a concave up quadratic function, the minimum value happens when the input is of:
Tm = -b/2a.
For this problem, the coefficients of the quadratic function are as follows:
b = -20, a = 20.
Hence the temperature in which the number of bacteria will be minimal is of:
Tm = 20/40 = 0.5 ºC.
The number of bacteria with this temperature is given by the numeric value of the function when T = 0.5, that is, each instance of T in the function is replaced by 0.5, hence:
N(0.5) = 20(0.5)² - 20(0.5) + 120 = 115 bacteria.
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What is the best estimate of 31 3/4 X 4 1/7 = ? Help Me?!!
Answers
The best estimate of fraction is 131.445.
What is fractions?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is [tex]\frac{1}{2}[/tex]
Given Data
31[tex]\frac{3}{4}[/tex] × 4[tex]\frac{1}{7}[/tex]
Solving mixed fractions
[tex]\frac{127}{4}[/tex] × [tex]\frac{29}{7}[/tex]
31.75 × 4.14
Multiplying
131.445
The best estimate of fraction is 131.445.
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If the measure of 43 is 70 degrees, what is the measure of <6?
A. 20; ∠s 3 and 6 are complementary angles
B. 70; ∠ s 3 and 6 are alternate interior angles
C. 110; ∠ s 3 and 6 are supplementary angles
D. 180; ∠ s 3 and 6 are same-side interior angles
Answers
Answer:
b
Step-by-step explanation:
angle 3 and angle 6 are alternate interior angles which makes the congruent
Find the distance from the point A(−2, 3) to the line y = 12x+1. Round your answer to the nearest tenth.
Answers
When adding and subtracting with significant digits, it's important to consider decimal places in the numbers being added.
TRUE or FALSE?
Answers
Answer:
false
Step-by-step explanation:
can some one help i will give 100 points and brainliest can you show your work step by step?
Answers
suppose abc is a right triangle with sides a, b, and c and right angle at c. use the pythagorean theorem to find the unknown side length. then find the values of the six trigonometric functions for angle b. rationalize the denominators when applicable.
Answers
The unknown length is 28. the values of the six trigonometric functions for angle b that is tan B = 7/24
From the question,
we are given
a = 96 and c = 100, to get the unknown side 'b',
we will substitute the given values into the formula above;
c² = a²+b²
100² = 96² +b²
b² = 100² - 96²
b² = 10,000 - 9216b²
= 784b = √784b = 28
Hence, the unknown length is 28.
To get tanB, we will use the SOH, CAH, TOA trigonometry identity.
According to TOA,
tan B = opposite/adjacenttan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)
Given, b = 28 and a = 96tan B = 28/96tan B = 4*7/4*24
tan B = 7/24
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The question is incomplete. Here is the complete question.
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.
$10,000 for 5 years at 4% interest
Answers
Simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
As given in the question,
Simple Interest:
The simple interest is an amount that is paid for loan or borrowed money over a certain period at a fixed percentage of borrowed money.
Principal amount:
Principal amount is the money that is taken as loan or borrowed.
Formula of Simple Interest:
Simple interest = Principal amount × Rate × Time
Since,
Principal amount = $10,000
Rate = 4% per year
Time = 5 years
Then,
Simple interest = 10,000 × 4 × 5
Simple interest = $ 12000
Total value after 5 years = $ 12000
Principal amount = $ 10000
Interest Earned = (Total value) - (Principal amount)
Interest Earned = $ 12000 - $ 10000
Interest Earned = $ 2000
Therefore, simple interest earned on the principal amount $10,000 for 5 years at 4% interest per year will be $12,000.
The complete question is:
Fabian is taking out a loan in the amount of $10,000. His choices for the loan are a 5-year loan at 4% rate of interest .What is the amount of simple interest and interest earned Fabian would have to pay?
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PLS HELP QUICK!!!
help me solve 3<2p-3≤ 12 and graph the solution
Answers
The solution to the given inequalities is 3 < p and p ≤ 7.5. That is 3 < p ≤ 7.5.
The graph of the solution is shown below.
Solving Linear InequalitiesFrom the question, we are to solve the given inequalities
The given inequalities are
3 < 2p - 3 ≤ 12
We will solve the inequalities separately
That is
3 < 2p - 3 and 2p - 3 ≤ 12
Solve 3 < 2p - 3
3 < 2p - 3
3 + 3 < 2p
6 < 2p
6/2 < p
3 < p
Solve 2p - 3 ≤ 12
2p ≤ 12 + 3
2p ≤ 15
p ≤ 15/2
p ≤ 7.5
Hence,
Joining the two solutions together, the solution is 3 < p ≤ 7.5.
The graph is shown below.
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Please answer the question in the photo
Answers
Answer: 8
Step-by-step explanation:
180 degrees in a triangle, so 180 - 92 - 48 = 40
So, the missing angle is 40, which is equal to 5t, so
40 = 5t
t = 8
In Exercises 7-10, determine whether the table represents a linear or nonlinear function. Explain. (See Exam
8.
7.
X
X
y
4
y 16.8
1
5
2
12.6
10
8 12
7.4
3
15
16
1.2
4
20
10.
x 5
y
-9
X
y
-1
35
7
-3
9
-1
11
3
0
1
2
20 5 -10 pls help me
Answers
Answer:
every number has a correlating value
Step-by-step explanation:
What is the equation for the line that passes through the coordinates (-4,-12)and(16,3)
Answers
The equation of the line that passes through these coordinates is 3x-4y= 36
How to calculate slope?
If you have the coordinates of two points on a line, you can use the slope formula to determine that line's slope. m=(y2-y1)/(x2-x1), or the ratio of the change in the y values to the change in the x values, is the slope formula.
To find the equation of the line we first have to find the slope which is represented by m.
The slope or m is given by : y₂ - y₁ / x₂ - x₁
thus, m= 3-(-12)/ 16-(-4)
m= 3+12/ 16+4 = 15/20
m= 3/4
The equation of a slope is y-y₁=m (x-x₁)
y- (-12) = 3/4 (x- (-4))
y+12 = 3/4 (x+4)
On solving it further we get:
4y+48= 3x+12
3x-4y= 36
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CARD #9:
V (2,2) U(6,2) T(2,10)
Triangle TUV will be dilated by a
scale factor of 2.
Isaac says
that T will be
located at
(4, 20).
Isabelle says
that T' will be
located at (4, 12).
Answers
Isaac's statement that T will be located at (4, 20) is correct
How to determine the correct statement?The coordinates of the triangle are given as
V (2,2) U(6,2) T(2,10)
The transformation is given as
Scale factor of 2, across the origin
The transformation can be described by (x, y) --> (2x, 2y)
There are four types of transformation, and they are:
DilationRotationReflectionTranslationThe representation of the types of transformation are:
Dilation: k(x, y)Rotation: rotation by anglesReflection: reflection across linesTranslation: (x + h, y + k)By comparing the rules of the above types of transformation, we have
(x, y) --> (2x, 2y)
For point T, we have
(2, 10) --> (2 x 2, 2 x 10)
Evaluate
(2, 10) --> (4, 20)
When the above is compared to the student's result, we have
Isaac = (2, 10) --> (4, 20)
Hence, the correct statement about the transformation is Isaac's statement is correct
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pls pls help whoever gets it right gets marked brainliest
Answers
Answer:
Step-by-step explanation:
B
Interior angle + exterior angle of a triangle = 180
On the axes below, make an appropriate scale and graph exactly one cycle of the trigonometric function y=16sin 1/2 x
Answers
For the given trigonometric function y =16sin1/2 x the graph shows the amplitude of 16 , graph of exactly one cycle is with period 4π , with no vertical and phase shift.
As given in the question,
Given trigonometric function :
y = 16sin 1/2 x
Attached graph of the given trigonometric function with
Amplitude = 16
Period = 4π
Vertical shift = None
Phase shift = none
Table for the required trigonometric function values which represent appropriate scale and graph exactly one cycle of the trigonometric function
x : 0 π 2π 3π 4π
y : 0 16 0 -16 0
Therefore, graph of trigonometric function y =16sin1/2 x shows the amplitude of 16 , graph of exactly one cycle is with period 4π , with no vertical and phase shift.
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What is the truth value for the following conditional statement?
p: false
q: true
~p~q
OTF F
OTF-T
OFF-T
OFT F
Answers
This is the right response: T F- F.
What is the explanation:
If the answer to the following question is p, then 2 + 2 = 4.
which is accurate, meaning that this statement has a truth value of True.
The following assertion q illustrates q: 7 + 1 Equals 7.
This is untrue, making the statement's truth value Untrue
As far as we are aware, "pq (p implication q)" means that the truth value of the implication is False only when the truth value of statement p is True.
The truth table reveals that the truth value of pq will be False
So T F → F
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Why can it help to line up the decimal
points before comparing and ordering
numbers with decimals?
Answers
Answer: Why it makes sense: When we compare or order decimals we need to compare place values just like we do with whole numbers. When the edges are “jagged” it makes it harder to compare each decimal place. Adding a zero in an empty place value makes it easier to compare the numbers.
Step-by-step explanation:
Answer:
you need to line them up to tell what place value each are in. if u don't the you won't known exactly what the product is equivalent to.
The value for x that makes the equation 4×-2+3×-7=51 true
Answers
The value of x that makes the equation true is 60/7.
The given equation is:-
4x - 2 + 3x - 7 = 51
The given equation is a linear equation in one variable.
Linear equation in one variable
A linear equation in one variable is of the form of ax + b = 0, where a and b are any two integers and x is an unknown variable having only one solution. Example : 5x + 3 = 10.
We have to find the value of x that makes the equation true.
Simplifying the given equation, we get
(4x + 3x) - (2 + 7) = 51
7x - 9 = 51
7x = 51 + 9
7x = 60
x = 60/7
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On 1st January 2017, Samantha and Dyfan invested money into different
savings accounts.
They did not make any further payments into their accounts or withdraw any
money from their accounts.
Dyfan invested £3000 in a savings account that paid interest at a rate of
1.02% every 3 months.
Interest is paid on the last day of each 3-month period.
Calculate the date when Dyfan will first have over £3600 in his account.
Input note: give your answer in the form DD/MM/YY
(4 marks)
(8
Answers
The number of years when Dylan would have over £3,600 in his account is 18 June, 2021.
When would Dylan have over £3,600?The time that If the account earns interest every 3 months, it means that the value increases quarterly or 4 times a year. The account would increase at an exponential rate. This means that both the amount invested and the interest that has already been earned would increase in value 4 times a year.
The formula that can be used to determine the time is:
Time = In(FV / PV) / r
Where:
FV = future value
PV = present value
r = interest rate
t = In (£3,600 / £3,000) / 0.0102
t = In 1.2 / 0.0102 = 17.87 / 4 = 4.468 years
4 years = 2017 + 4 = 2021
0.468 x 12 = 5.616 months
January + 5 months = June
0.616 x 31 = 19 days
18 June, 2021
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Estimate the quotient of 41 ÷ 7.94.
4
5
6
7
Answers
Is the function linear? (actual answers please, i know someone could easily say yes or no)
Answers
Answer:
Obviously yes...
Step-by-step explanation:
Because there is not a single curve, hence the fn is linear.
Had it been if there are some curves, it may result in having more than one zeroes...
Cuz there's no curve it has only one zero, which made the fn linear..
Thanks.
Rewrite in simplest terms: −4(8f+g)+9g−5(−2g+6f)
Answers
-32f - 4g + 9g + 10g - 30f
simplify
-62f + 15g
When Riley left her house in the morning, her cell phone battery was partially
charged. The charge remaining in Riley's battery, as a percentage, can be modeled by
the equation B = 40 - 5t, where t is the number of hours since Riley left her
house. What is the x-intercept of the equation and what is its interpretation in the
context of the problem?
Answers
Riley's phone had a 50% charge when she left her home in the morning. Equation B = 40 - 5t. The x-intercept of the equation is (8,0). After 8 hours, Riley battery has no charge left in it ( since Riley left her house).
Given that,
Riley's phone had a 50% charge when she left her home in the morning. Equation B = 40 - 5t, where t is the number of hours since Riley left her residence, can be used to predict the percentage of charge still in Riley's battery.
We have to find what is the equation's x-intercept and how is it interpreted in the problem's context.
The equation B=40-5t can be used to model Lauren's battery charge remaining as a percentage when t is the number of hours since she left her home.
Put B = 0 to determine the x-intercept. (In this case, the independent variable is "t," as x signified the independent variable).
0=40-5t
5t=40
t=40/5
t=8
Therefore, the x-intercept of the equation is (8,0).
After 8 hours, Riley battery has no charge left in it ( since Riley left her house).
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9. Describe and correct the error in performing the operation.
X 4x²(3x - 2x² + 7) = 12x³ - 8x + 28x²
Answers
Answer:
12[tex]x^{3}[/tex]-8[tex]x^{4}[/tex]+ 28[tex]x^{2}[/tex]
Step-by-step explanation:
the second term should not be -8x, it should be -8[tex]x^{4}[/tex]
The product of powers principle tells us that when we are multiplying powers with the same bases, we add the exponents. 4[tex]x^{2}[/tex](2[tex]x^{2}[/tex]) is 8 but then we add the exponents 2 + 2 = 4
need help on this question
Answers
The coordinates of the vertex B' is (2,3)
Given,
The vertices of triangle ABC are
A = (-4,4)
B = (-2,3)
C = (-5,2)
and, reflected across the y-axis to produce the image of triangle A'B'C'
To find the coordinate of the vertex B'
Now, According to the question
For reflection across y-axis, the rule is:
(x, y) → (-x, y)
So, the image of B is:
(-2, 3) → (-(-2), 3)
(-2,3) → (2, 3)
Hence, The coordinates of the vertex B' is (2,3)
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Find the volume of this solid.
Answers
Answer:
128m²
Step-by-step explanation:
separate the two solids.The cube and the cuboid
find the volume of the cube i.e.5³=115m²
find the volume of the cuboid i.e 1×1×3=3m²
add the two volumes
Answer:
128m²
Explanation:
Add all volumes, 5+5+4+6+3, then times that by the volume below.
Which diagram shows parallel lines cut by a transversal?
Answers
the lines is cut by one common line
Polly used 15/16 pounds of sugar to make 5 batches of cupcakes for a party. She uses the same amount of sugar to make each batch of cupcakes. How many pounds of sugar are in each batch? (I have my answer, but have no clue how to show it visually.
Answers
Based on the number of batches of cupcakes, the pounds of sugar in each batch can be found to be 3 / 16 pounds
Find out more below
How to find the pounds of sugar?The total number of pounds of sugar that Polly used was 15/16 pounds of sugar and she used these to make 5 batches of cupcakes.
Each of this batches of cookies used the same amount of sugar so the amount of sugar per batch of cookie is:
= Total number of pounds of sugar used / Number of batches of sugar
Solving for the pounds of sugar gives:
= 15/16 ÷ 5
= 15/16 x 1/5
= 15 / 80
= 3 / 16 pounds
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One of your friends is working on their math homework. They decide to translate the phrase "subtract 3 from 5" like this:
3-5
Which statements below give a reason why your friend's expression is incorrect?
Select ALL that apply.
A.The expression is written with the wrong operation.
B.in subtraction, order matters and the expression in the incorrect order.
C.the expression should be written as an addition expression with the 5 being added to the 3
D. The expression was written in the order from the phrase which is incorrect
Answers
Answer:
B
Step-by-step explanation:
When you are taking 3 away from 5 it would be 5-3, when you are taking 5 away from 3 it would be 3-5, but in this case it is not so the answer would be B as the order is incorrect.