Considering the given stem-and-left plot, the median = second quaritle of the data set is of 84.5.
What is the median of a data-set?The median of a data-set is the 50th percentile, that is, the value that separates the bottom 50% of scores from the upper 50% of scores.
This data-set has even cardinality of 26, hence the median is the mean of the 13th and 14th scores, which, considering the key for the stem-and-leaf plot, are 84 and 85, hence:
Me = (84 + 85)/2 = 84.5.
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The ratio of the number of laps Andy swam to the number of laps Ben swam
on the first day of a swimming lesson was 5: 6. The ratio of the number of
laps Andy swam to the number of laps Ben swam on the second day of the
swimming lesson was 9: 5. If Ben swam 33 laps on both days, how many laps
did Andy swim on the second day of the swimming lesson?
Answer:
10
Step-by-step explanation:
Use the graph of the parabola to fill in the table
(a) The parabola opens downward.
(b) The axis of symmetry is at x = -2.
(c) The vertex is at (-2,0).
(d) The x-intercepts is (-2,0), and the y-intercept is at (0,-1).
What is the midpoint of AB?
Answer: Point G.
Step-by-step explanation:
Count the number of spaces between points A and B. Then divide that number by 2 and count that many spaces from one point.
14/2=7
I hope this helps!! Pls mark brainliest :)
Find the compound interest on $4000 for 2 years and 3months at 2% per annum,
compounded annually.
Answer:
CI = $182.25
Step-by-step explanation:
Compound interest formula:
[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex] ,
where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).
Using formula:
CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]
CI = $182.25
Question 6 of 10
sin 30º = √3/2 and cos 30º = 1/2
O A. True
OB. False
In one month, a farmer produces 300 pounds of corn. In the
following month he produces 35% more. How many pounds of corn
does he produce in the second month?
The pounds of corn in the second month is 390
How to determine the amount?We have:
First month, a = 300
Rate, r = 35%
The pounds of corn in the second month is calculated using:
Pound = a * (1 + r)
So, we have:
Pound = 300 * (1 + 30%)
Evaluate the sum
Pound = 300 * 1.3
Evaluate the product
Pound = 390
Hence, the pounds of corn in the second month is 390
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Which of the following is a correctly written algebraic equation?
2 + 0.2x
5b - 5x + 2
a - 3x=0
3(x/5)
Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The best buy is (d) a 9 oz box of rice $1.25
How to determine the best buy?The best buy is the product that has the least unit rate.
The unit rate is calculated as:
Unit = Price/Weight
So, we have:
Box 1:
Unit rate = $0.90/6 oz = $0.150 per oz
Box 2:
Unit rate = $1.93/12 oz = $0.161 per oz
Box 3:
Unit rate = $2.42/16 oz = $0.151 per oz
Box 4:
Unit rate = $1.25/9 oz = $0.139 per oz
The least unit price is $0.139 per oz for box 4
Hence, the best buy is (d) a 9 oz box of rice $1.25
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A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
Answer:
1/(7^5)=1/16807
Step-by-step explanation:
Assuming 7-key mean zero up to 7,
# of possible codes = 17^5 = 16807
=====
Probability of first try correct = 1/7^5
Jack and Susan bought together 28 books. Susan bought 11 books. Which one of the
following equations represents the number of books bought by Jack? Let x be the
number of books bought by Jack.
Answer:
11 + x = 28
Step-by-step explanation:
The number of books they bought must add to 28.
100 points (08 03)Consider the following set of equations: Equation A: y = 2x + 4 Equation B: y = 3x + 1 Which of the following is a step that can be used to find the solution to the set of equations? 08 03 ) Consider the following set of equations : Equation A : y = 2x + 4 Equation B : y = 3x + 1 Which of the following is a step that can be used to find the solution to the set of equations ?
Answer:the equations are
y = x + 4 and y = 3x + 6
Now we can use substitution method to solve the system
So we can substitute value of y from one equation into other
So we get
x+4 = 3x+6
So Option B is correct
Step-by-step explanation:
Answer:
2x + 4 = 3x + 1
Explanation:
Equation A: y = 2x + 4
Equation B: y = 3x + 1
Simultaneously solving :
⇒ y = y
⇒ 2x + 4 = 3x + 1
⇒ 2x - 3x = 1 - 4
⇒ -x = -3
⇒ x = 3
Solve for y :
⇒ y = 2x + 4
⇒ y = 2(3) + 4
⇒ y = 10
which of the following are identities? check all that apply A. cot^2x+1=csc^2x B.tan^2=1-sec^2x C.sin2^x=1=cos^2x D.sin^2x+cos^2x=1
Find x and y please help
Answer:
x is 130°,y is 60°
Step-by-step explanation:
x is corresponding to 130° therefore they are equal to find y since the angle on a straight line is 180° you subtract 180 from 130 and get 50 then you have gotten the other interior angle then add both interior angles and subtract by180 then you get the y
Answer:
X = 130° Y = 60°both the lines are parallel
therefore, X= 130° ( if two lines are parallel their corresponding angles are equal)
Y + 70° = X ( sum of tow interior angle is equal to exterior)
Y + 70= 130
Y = 130 - 70
Y = 60°
What are the solution(s) to the quadratic equation x² - 25 = 0?
h
O x=5 and x =
-5
−5
x = 25 and x = -25
x = 125 and x = -125
Ono real solution’s
Answer:
x = ±5
Step-by-step explanation:
x² - 25 = 0
x² = 25
√x² = √25
x = ±5
Check:
5² - 25 = 0
-5² - 25 = 0
25 - 25 = 0
Number of Potatoes
36
24
12
5
10
Number of Pounds
x
15
Use the graph to find the unit rate.
potatoes per pound
I keep putting in the formula but I keep getting the answer wrong
Answer:
314 in² (nearest whole number)
Step-by-step explanation:
Radius of a regular polygon: The distance from the center of the polygon to any vertex. The radius of a hexagon is equal to the length of one side.
Therefore, from inspection of the given diagram:
radius = 11 in ⇒ side length = 11 inTo find the area of a regular polygon, we first need to calculate the apothem. The apothem is the line drawn from the center of the polygon to the midpoint of one of its sides.
[tex]\textsf{Length of apothem (a)}=\dfrac{s}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]
where:
s = length of one siden = number of sidesGiven:
s = 11 inn = 6Substitute the given values into the formula and solve for a:
[tex]\implies \textsf{a}=\dfrac{11}{2 \tan\left(\frac{180^{\circ}}{6}\right)}=\dfrac{11\sqrt{3}}{2}[/tex]
Area of a Regular Polygon
[tex]\textsf{A}=\dfrac{n\:s\:a}{2}[/tex]
where:
n = number of sidess = length of one sidea = apothemGiven:
n = 6s = 11[tex]\textsf{a}=\dfrac{11\sqrt{3}}{2}[/tex]Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{6 \cdot 11 \cdot \dfrac{11\sqrt{3}}{2}}{2}[/tex]
[tex]\implies \sf A=314.3672216...[/tex]
[tex]\implies \sf A=314\:\:in^2\:\:(nearest\:whole\:number)[/tex]
pls someone help me asap :)
Answer:
right angle
acute
acute
obtuse
obtuse
Step-by-step explanation:
Since angle <ABC is a straight line, the angle is 180 degrees. This means all the angles in between should also add up to 180 degrees. Using this knowledge you can solve for the value of angle <FBE which is going to be equal to 180 - (40 + 25 + 50) = 65.
< DBF = <DBE + <EBF
< DBF = 25 + 65 = 90 (right angle)
<EBD = 25 (given) (acute)
<DBC = 50 (given) (acute)
<ABE = <ABF + <FBE
<ABE = 40 + 65
<ABE = 105 (obtuse)
<CBF = <CBD + <DBE + <EBF
<CBF = 50 + 25 + 65
<CBF = 140 (obtuse)
function F(x)=x+1 and g(x)=5x+1 find the f(4)=g(x+1)
The function of f(4) = g(x+1) gives the value of x that is -1/5.
What is the function addition?It is the addition of two functions similar to the addition of any two polynomial functions.
Given;
F(x)=x+1
g(x)=5x+1
We need to find f(4)=g(x+1)
First substitute x = 4 in f(x)
F(x)=x+1
F(4) = 4 + 1
F(4) = 5
Now substitute x = x + 1 in g(x)
g(x)=5x+1
g(x + 1) = 5(x + 1) + 1
g(x + 1) = 5(x + 1) + 1
g(x + 1) = 5x + 5 + 1
g(x + 1) = 5x + 6
Then ,
F(4) = g(x + 1)
5 = 5x + 6
5x = 5 - 6
5x = -1
x = -1/5.
The function of f(4) = g(x+1) gives the value of x that is -1/5.
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Which formula finds the probability that a point on the grid below will be in the blue area? A grid contains 20 squares. 10 squares are shaded blue. P (blue) = StartFraction total number of squares over number of blue squares EndFraction P (blue) = StartFraction number of blue squares over total number of squares EndFraction P (blue) = StartFraction number of blue squares over number of white squares EndFraction P (blue) = StartFraction number of white squares over number of blue squared EndFraction
The formula that finds the probability that a point on the grid below will be in the blue area is represented by the option:
P (blue) = StartFraction number of blue squares over the total number of squares EndFraction.
The probability = 1/2.
The probability of an event defines the chance of the occurrence of that event. It is given by the ratio of the total number of outcomes favorable to the event to the total number of outcomes in the experiment.
If we suppose an event to be A, the total number of possible outcomes favorable to A be n, and the total number of outcomes in the experiment be S, then the probability of event A can be given as:
P(A) = n/S.
In the question, we are asked to find the formula that defines the probability that a point on the grid will be in the blue area, where the grid contains 20 squares, 10 of them being shaded blue.
We take the event that the chosen point is in the blue area as A.
The total number of outcomes favorable to this event A can be given by n, which will be equal to the number of blue squares = 10
The total number of outcomes in the experiment can be given by S, which will be equal to the number of squares = 20.
Now, the formula for the probability of event A can be written as
P(A) = n/S = 10/20 = 1/2.
The formula that finds the probability that a point on the grid below will be in the blue area is represented by the option:
P (blue) = StartFraction number of blue squares over the total number of squares EndFraction.
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What is the measure of complemnt angle
a)42° b) 35°
Answer:
90°
Step-by-step explanation:
A complement angle is the same as a right angle
Hii!
___________________________________________________________
Answer:
[tex]\sf 48\textdegree[/tex][tex]\sf 55\textdegree[/tex]Step-by-step explanation:
The sum of complementary angles is always 90 degrees.
We can find the complements of these two angles by setting up an equation.
x+42=90
Subtract 42 from both sides
x=48
This problem can be solved the same way!
x+35=90
Subtract 35 from both sides
x=55
--
Hope that this helped! Best wishes.
--
Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard
Prove: An odd number squared is
an odd number.
(2n + 1)² = [?]n² + [ ]n +
=
[](2n² + 2n) + [ ]
= an odd
Considering the result of the expression of the square of the sum, 2(2n² + 2) is always an even number, then when 1 is added it will always be an odd number.
What is the square of the sum notable product?It is given as follows:
(a + b)² = a² + 2ab + b².
In this problem, the expression is:
(2n + 1)² = (2n)² + 2(2n)(1) + 1²
= 4n² + 4n + 1
= 2(2n² + 2) + 1
The term 2(2n² + 2) will always be even(multiplication by 2), and when 1 is added to an even number it will always be odd, hence it is proved that an odd number squared is an odd number.
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height of 24cm with a radius of 7cm. What is the total surface area of the cone?
Answer:
the answer to this problem is 703.7 in^2
I should have payed more attention but can someone please guide me through this and build me up an answer.
Answer:
arc QM = 38°
Step-by-step explanation:
the inscribed angle NQM is half the measure of its intercepted arc NM , so
arc NM = 2 × 90° = 180°
the sum of the arcs in a circle = 360° , then
QN + NM + MQ = 360° , that is
142° + 180° + QM = 360°
322° + QM = 360° ( subtract 322° from both sides )
QM = 38°
BRAIN WARM UP MATHS?
We can make 64 different equations using the power of ten.
What is the power of a number?The power of a number identifies how many times that particular number is multiplied by itself.
Here, let us assume that the different equations = x
Using a power of 10, we have 10x making a total of 640.
10x = 640Divide both sides by 10
10x/10 = 640/10
x = 64
Therefore, we can conclude that we can make 64 different equations using the power of ten.
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Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?
Answer:
28 feet
Step-by-step explanation:
Area of a rectangle is :
A = L × W
We are given A and a expression for L, so let's substitute :
448 = (2W-4) × W
Now we expand the left side :
2W²-4w = 448
Subtract 448 from both sides :
2W²-4W-448 = 0
Divide everything by 2 :
W²-2W-224 = 0
Now we factorise :
Find 2 numbers that multiply to give -224 and add to give -2 :
-16 and 14
Rewrite -2W with -16W and +14W :
W² - 16W + 14W -224 = 0
W(W-16) +14(W-16) = 0
(W+14)(W-16) = 0
W = -14 , W = 16
Only take positive value since this is lengths :
W = 16
Now we substitute W into the expression to find L :
L = (2W -4)
L = 2(16) - 4
L = 32 - 4
L = 28
Units will be feet since it is a length
Hope this helped and have a good day
Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβtanβsecβcotβ?
Select the correct answer below:
secβcotβ
tanβ
cotβtanβ
tanβcscβsecβ
Answer:
[tex]\tan(\beta)[/tex]
Step-by-step explanation:
For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.
[tex]{\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}[/tex] and [tex]{\sec(\theta)}={\dfrac{1}{\cos(\theta)}[/tex]
Recall the following reciprocal identity:
[tex]\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}[/tex]
So, the original expression can be written in terms of only sines and cosines:
[tex]\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)[/tex]
[tex]\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }[/tex]
[tex]\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}[/tex]
[tex]\sin(\beta) *\dfrac{1 }{\cos(\beta) }[/tex]
[tex]\dfrac{\sin(\beta)}{\cos(\beta) }[/tex]
Working toward one of the answers provided, this is the tangent function.
The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to [tex]\tan(\beta)[/tex].
find sin(x/2), cos (x/2), and tan(x/2) from the given information.
Sin(x)= 15/17, 0 < x <90
sin(x/2)= ?
cos(x/2)=?
tan(x/2)= 0.6
I need help with sin and cos. I know what tan is.
Step-by-step explanation:
sin(x/2) = sqrt((1 - cos(x))/2)
cos(x/2) = sqrt((1 + cos(x))/2)
tan(x/2) = sin(x/2)/cos(x/2)
sin(x) = 15/17
so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.
via Pythagoras we get the 3rd, horizontal side :
17² = 15² + side²
289 = 225 + side²
64 = side²
side = 8
cos(x) = 8/17
sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =
= 0.514495755...
cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =
= 0.857492926...
tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =
= 3/5 = 0.6
If f(x) = x² - 2x, find:
f(6) = [?]
will give brainliest answer !!
Answer:
[tex] \boxed{f(6) =2 4}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x) = x² - 2x[/tex]
Solution:
ATP,it is that x = 6. So substitute 6 on the function.
[tex]f(6) = 6 {}^{2} - 2(6)[/tex]
Simplifying using PEMDAS,we obtain:
[tex]f(6) = 6 \times 6- 12[/tex]
[tex]f(6) = 36 - 12[/tex]
[tex] \boxed{f(6) =2 4}[/tex]
Hence,f(6) = 24.
Answer this! Thanks so much in advance (:
Answer:
ai) m = 17, applicable past x = 23/17; aii) m = 4; applicable past 3 dad jokes
Step-by-step explanation:
to calculate slope you use the (y2 - y1) / (x2 - x1) equation
so for the first one
(62 - 11) / (5 - 2)
51 / 3 = 17
the equation for this is y = 17x + b
plug in values to find b
11 = 34 + b
b is -23
y = 17x - 23
because distance cannot be negative we must find when x is exactly 0 to find where it is applicable
17x = 23
x = 23/17
for the second one we can subtract again
(10 - 2) / (5 - 3)
8 / 2
4 is the slope
like before we must find b and then find where y is 0
y = 4x + b
2 = 12 + b
b = -10
y = 4x - 10
4x = 10
x = 5/2
since you cannot have 1/2 a dad joke we round up from 2 1/2 to 3
