[tex]a {}^{2} + ab - 2 {b}^{2} [/tex]
[tex] = (a - b) {}^{2} [/tex]
Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12)
Here, 12 is the mode.
Step-by-step explanation:
Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12) ?
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode.
So let's talk in brief:-
First, we arrange it in ascending order.
3,3,6,6,9,9,12,12,12,12
and now as we see that we get 12 as the most repeated ones.
reference link-
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Three quarters of a cake was eaten at a party .how much cake is left?
Hi! ◈
Answer:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
1/4 of the cake was left
Step-by-step explanation:
Since the total cake is [tex]\sf{\dfrac{4}{4}}[/tex], all we should do is subtract 3 from 4
[tex]\sf{\dfrac{4-3}{4}}=the \ cake \ that \ was \ left[/tex]
_____________________
[tex]\sf{\dfrac{1}{4} \ of \ the \ cake \ was \ left}[/tex]
Hope this made sense to you !!
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CalligrxphyHow do u solve for X?
Answer:
x = 70
Step-by-step explanation:
x and 2x - 30 are supplementary angles , sum to 180° , then
x + 2x - 30 = 180 ( add 30 to both sides )
3x = 210 ( divide both sides by 3 )
x = 70
Answer:
2x - 30 and x degrees should add up to 180 degrees
2x - 30 + x = 180
3x = 210
x = 70 degrees
The correct answer would be D
Please help me solve this
If the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.
Given sample mean of 51, sample size of 21, sample standard deviation be 15 and confidence level be 95%.
We are required to find the upper bound and lower bound.
We have to use t test as the sample size is less than 30.
Margin of error is the difference between calculated figures and real figures.
Margin of error= standard deviation* critical value of t
Critical value of t at 0.05 significance level with degree of freedom 20 [21-1] is 1.7247.
Margin of error=1.7247*15/4.5826
(4.5826 is the square root of 21)
=5.6454
Upper bound=51+5.6454
=56.6454
Lower bound=51-5.6454
=45.3546
After rounding off they will be 56.65 and 45.35.
Hence if the sample mean is 51,sample size is 21 , sample standard deviation is 15 and confidence level is 95% then the lower bound is 45.35 and upper bound is 56.65.
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a x = ±5
b. x = ±5i
C. x = ±3√√5
d. x = ±3√3
e. x = ±3i√√3
f. x= ±3i√√5
1. x^2+45=0
2. x^2=-25
3. x^2-25=0
4. x^2-45=0
5. x^2=27
6. x^2+27=0
Match the items
Answer:
1f, 2b, 3a, 4c, 5d, 6e
see image
Step-by-step explanation:
Solve the equations by getting x all by itself on one side. Then, square root to get rid of the exponent.
Any problem where you square root a negative will give you an i in the answer. This is because sqrt(-1) is i. Because i^2 = -1
Also, when you are simplifying square roots for your final answer, look for a perfect square number inside of the radical. Like Sqrt45 can be broken down to
Sqrt9•sqrt5
And because 9 is a perfect square, sqrt9 simplifies to just 3. See image.
for this graph, mark the statements that are true.
Answer:
C,D
Step-by-step explanation:
C: Range refers to the y axis and all values shown on this graph (and even beyond the graph) are greater than 0
D: The domain refers to the x-axis. The line goes on forever both to the right and the left therefore meaning all x values are used.
In 1996 an outbreak of a disease affected 10 people in a large community. By 1997, the number of those infected had grown to 40. Find an exponential growth function that fits the data.
Answer: The initial population is 18 and 1 year(t=1) later it is 38
Step-by-step explanation:
38 = 18 * e^(1*k), where k is the growth rate
e^(1*k) = 38/18
Take the natural log(ln) of both sides of the = k = ln(38/18) = 0.747
P(t) = 18 * e^(0.747*t), where P(t) is the population affected at time t(years since 1996)
Question Find the area of a trapezoid whose height is 6 ft and whose bases are 9.7 ft and 6.3 ft.
Answer:
48 Square feet
Step-by-step explanation:
A=((a+b)/2)*h,
((6.3+9.7)/2)*6=48ft^2
Let m = X^2 + 3.
What is (x^2+3)^2+7x^2+21=-10 in terms of m?
OR
Let m=x^2+3m=x
2
+3m, equals, x, squared, plus, 3.
Which equation is equivalent to (x^2+3)^2+7x^2+21=-10(x
2
+3)
2
+7x
2
+21=−10left parenthesis, x, squared, plus, 3, right parenthesis, squared, plus, 7, x, squared, plus, 21, equals, minus, 10 in terms of mmm ?
The Equation in terms of m, m^2+7m+10=0
What is substituting in the equation ?
substituting means changing or replacing the values in the given equation.
Calculation:
Given equation is (x^2+3)^2+7x^2+21=-10
and m= X^2 + 3.
make the given equation in the form X^2 + 3,
now,
(x^2+3)^2+7x^2+21=-10
(x^2+3)^2+7(x^2+3)=-10
where,
X^2 + 3= m
after putting the value or replacing the values
we get, m^2+7m=-10
m^2+7m+10=0
the above equation is in the form of "m".
The Equation in terms of m, m^2+7m+10=0
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Answer:
m^2+7m+10=0
Step-by-step explanation:
Give brainly lol
What fraction with a denominator of 32 is equal to 1/2?
Answer:
[tex]\frac{16}{32}[/tex]
Step-by-step explanation:
given
[tex]\frac{1}{2}[/tex] ← multiply numerator and denominator by 16 (2 × 16 = 32 )
= [tex]\frac{16}{32}[/tex]
Dana believes that she needs to study for at least 14 hours to be prepared for her monthly accounting test. If she can study for 4 hours per day, what is the minimum number of days that she should allow to study for the test?
Find cos B, sinB,tanb
Using right triangle relations, we will get:
tan(B) = 1.05sin(B) = 0.735cos(B) = 0.7How to find the value of the trigonometric equations?
We assume that bot triangles are equivalent, then the angle B will be the same as the angle Z.
Now remember the relations:
tan(θ) = (opposite cathetus)/(adjacent cathetus).sin(θ) = (opposite cathetus)/(hypotenuse)cos(θ) = (adjacent cathetus)/(hypotenuse).If we step on angle B, we have:
opposite cathetus = 29.4adjacent cathetus = 28hypotenuse = 40.6Replacing that, we get:
tan(B) = 29.4/28 = 1.05sin(B) = 29.4/40.6 = 0.735cos(B) = 28/40.6 = 0.7If you want to learn more about trigonometric functions:
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A carnival ferris wheel with a radius of 7m rotates once every 16 seconds. The bottom of the wheel is 1m above the ground.
Find the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel.
Please use math tools to state your answer - see hint. Or attach your work as ONE easy to read file.
The equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds is y(t) = 14sin(πt/8) + 1
The equation of the function that gives the height of the ferris wheel
Since the motion of the ferris wheel is periodic,it follows a sinusoidal function form.
So, the general form of a sine function y(t) is
y(t) = Asin(2πt/T) + K where
A = amplitude, T = period, t = time and K = vertical shiftNow since radius of 7m, the maximum value from its lowest point is at y = 2r + 1 = 2 × 7 + 1 = 14 + 1 = 15 at sin(2πt/T) = 1 which is the maximum value for sinФ = 1.
Since the bottom of the wheel is 1m above the ground, its minimum value is y = 1 at t = 0.
Also, it rotates once every 16 seconds, so its period T = 16 s.
So, y(t) = Asin(2πt/T) + K
y(t) = Asin(2πt/16) + K
y(t) = Asin(πt/8) + K
At maximum value
15 = Asin(πt/8) + K
15 = A + K (1)
At minimum value
1 = Asin(πt/8) + K
1 = A(0) + K
1 = 0 + K
K = 1
Substituting K into (1), we have
15 = A + 1
15 - 1 = A
14 = A
A = 14
So, y(t) = Asin(πt/8) + K
y(t) = 14sin(πt/8) + 1
So, the equation of the function that gives a rider's height above the ground in meters as a function of time, in seconds, with the rider starting at the bottom of the wheel is y(t) = 14sin(πt/8) + 1
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Here are the gold medal times for the women’s 100-meter freestyle (swimming) in every other Summer Olympics:
The least-squares regression line equation is y = -0.28x + 610.31
The scatter plot of the dataTo plot the scatter plot of the data, we represent the x-axis with year and we represent the y-axis with time
Next, we plot the scatter plot using the dataset
See attachment for the scatter plot
Describe the relationship between the variables in the graph.From the attached scatter plot, we can see that the relationship between the variables in the graph is approximately linear.
This is so because the points appear to be on a straight line
Find the correlation coefficient.To do this, we make use of a graphing calculator, with the following summary:
X Values
∑ = 21608Mean = 1964.364∑(X - Mx)2 = SSx = 10062.545Y Values
∑ = 686.41Mean = 62.401∑(Y - My)2 = SSy = 842.83X and Y Combined
N = 11∑(X - Mx)(Y - My) = -2806.684R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -2806.684 / √((10062.545)(842.83)) = -0.9638
Hence, the correlation coefficient is -0.9638
Find the least-squares regression line.To do this, we make use of a graphing calculator, with the following summary:
Sum of X = 21608Sum of Y = 686.41Mean X = 1964.3636Mean Y = 62.4009Sum of squares (SSX) = 10062.5455Sum of products (SP) = -2806.6836The least-squares regression line equation is
y = bx + a
Where
b = SP/SSX = -2806.68/10062.55 = -0.27892
a = MY - bMX = 62.4 - (-0.28*1964.36) = 610.30872
So, we have
y = -0.27892x + 610.30872
Approximate
y = -0.28x + 610.31
Hence, the least-squares regression line equation is y = -0.28x + 610.31
The estimated gold medal time for 1924 and for 1976.We have:
y = -0.28x + 610.31
Substitute 1924 and 1976 for x
y = -0.28 * 1924 + 610.31 = 71.59
y = -0.28 * 1976 + 610.31 = 57.03
Are these estimates reliable?
Yes, the estimates are reliable
Are they reasonable?
Yes, the estimates are reasonable
Why are your answers in Question 5 different than the times given in the table?The results are different because the answers in 5 are estimated from the formula while the table are the actual values
Find the estimated gold medal time for 2022 and for 2200.We have:
y = -0.28x + 610.31
Substitute 2022 and 2200 for x
y = -0.28 * 2022 + 610.31 = 44.15
y = -0.28 * 2200 + 610.31 = -5.69
Are these estimates reliable?
No, the estimates are not reliable
Are they reasonable?
The estimate in 2022 is reasonable, while the estimate in 2200 is not reasonable
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A tennis ball can in the shape of a right circular cylinder holds six tennis balls snugly. If the radius of a tennis ball is 3.4 cm, what percentage of the can is not occupied by tennis balls?
The percentage of the can that is not occupied by tennis balls is 33.33%.
PercentageGiven:
Radius of cylinder=3.4cm
First step
Height of cylinder=3.4×2×6
Height of cylinder=40.8 cm
Second step
Volume of cylinder=(3.4)^2×40.8
Volume of cylinder=471.648
Volume of tennis=6×4/3×(3.4)^3
Volume of tennis=314.432
Third step
Percentage=471.648-314.432/471.648×100
Percentage=33.33%
Therefore the percentage of the can that is not occupied by tennis balls is 33.33%.
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WILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
The correct order of reasons that complete the proof about the rectangle and square is that D. definition of congruence, distance formula if two consecutive sides of a rectangle are congruent, then it's a square.
What is congruence?It should be noted that congruence simply means an agreement or a correspondence between shapes.
In geoemtry, it should be noted that figures are said to be congruent if it is possible to superpose one of them on another.
It should be noted that the opposite sides of a rectangle are parallel while in a square, all the sides that are given are equal.
Therefore, the correct order of reasons that complete the proof about the rectangle and square is the definition of congruence, and that if two consecutive sides of a rectangle are congruent, then it's a square.
In conclusion, the correct option is D.
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126.8 is 63 2/5% of what?
Answer:
200
Explanation:
126.8 x 100
126.8/63.4 = 200
Solve for x. Round your answer to the nearest tenth if necessary. Figures are
not necessarily drawn to scale.
T
63°
72°
18
19
45
630
37
72°
W
45°
X
X
Answer:
18/19= X/37 because 18 and x are both between 72 and 45 degrees
Multiply 18 and 37 then divide by 19 to get answer
Step-by-step explanation:
Shawn averages 10,142 steps every day. If there were 31 days in the month, about how many steps did he take in that month.
Answer:
314402 steps
Step-by-step explanation:
10142 x 31
A perimeter of a movie screen is 56 meters. the area is 171 square meters what are the dimensions of the screen
Using the formula for the perimeter and area of rectangle, the dimensions are: Length = 19 m; width = 9 m.
What is the Perimeter and Area of a Rectangular Shape?Perimeter = 2(length + width)
Area = (length)(width).
Let x represent the length and y the width, therefore:
2(x + y) = 56 --> eqn. 1
xy = 171 --> eqn. 2
Rewrote eqn. 1
x + y = 56/2
x = 28 - y
Substitute x = (28 - y) into eqn. 2
171 = (28 - y)y
171 = 28y - y²
171 - 28y + y² = 0
y² - 28y + 171 = 0
Factorize
(y - 9)(y - 19)
y = 9 and y = 19
Therefore, the dimensions are: Length = 19 m; width = 9 m.
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a right triangle has side lengths of 6, 10, and x. find x if it is the hypotenuse
X= root 6^2 + 10^2
X=2 root 34
So, x is 11.66 to 2d.p
(root means square root)
Hope this helps!
Answer:
x = 11.66
Step-by-step explanation:
Hello!
We can use the Pythagorean theorem to solve for the hypotenuse.
Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
a = legb = legc = hypotenusePlug the values of 6 and 10 into the formula to solve.
Find the Hypotenuse[tex]a^2 + b^2 = c^2[/tex][tex]6^2 + 10^2 = c^2[/tex][tex]36 +100 = c^2[/tex][tex]136 = c^2[/tex][tex]c = \sqrt{136[/tex][tex]c \approx 11.66[/tex]The hypotenuse is approximately 11.66.
What The What The???
Considering a geometric sequence, the pattern is given as follows:
1, 2, 4, 8, 16, 32, 64.
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The first term and common ratio are given as follows:
[tex]a_1 = 1, q = 2[/tex].
Hence the remaining terms are:
[tex]a_4 = 2^{4-1} = 8[/tex][tex]a_5 = 2^{5-1} = 16[/tex][tex]a_7 = 2^{7-1} = 64[/tex]More can be learned about geometric sequences at https://brainly.com/question/11847927
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The double number line shows that Toni can type 180 words in 2 minutes.
A double number line with 6 equally spaced tick marks. The line labeled Time, minutes, reads from left to right: 0, an unlabeled tick mark, 2, three unlabeled tick marks. The line labeled Words, reads from left to right: 0, an unlabeled tick mark, 180, three unlabeled tick marks.
A double number line with 6 equally spaced tick marks. The line labeled Time, minutes, reads from left to right: 0, an unlabeled tick mark, 2, three unlabeled tick marks. The line labeled Words, reads from left to right: 0, an unlabeled tick mark, 180, three unlabeled tick marks.
Based on the ratio shown in the double number line, how many words can Toni type in 3 minutes?
_words
The number of words that Toni can type in 3 minutes is 270 words per minute.
How to work with ratios?We are given 180 words in 2 minutes. This means;
Toni can type 180/2 = 90 words per minute (90wpm).
Using the above same ratio/rate, it means that in 3 minutes, Toni would be able to type:
90 * 3 = 270 words per minute.
Thus, we conclude that the number of words that Toni can type in 3 minutes is 270 words per minute.
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Vrite the equation of a line in the slope-intercept form that has a slope of 4
and contains the point (4, 12).
Answer:
y= 4x -4
Step-by-step explanation:
Slope-intercept form is given by y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is 4, m= 4.
Substitute the value of the slope into the equation:
y= 4x +c
The value of c can be found by substituting any point in which the line passes through into the equation above.
When x= 4, y= 12,
12= 4(4) +c
12= 16 +c
Subtract 16 from both sides:
c= 12 -16
c= -4
Thus, the equation of the line is y= 4x -4.
Additional:
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https://brainly.com/question/27941697jerome wants to bake two batches of muffins. He can bake two batches of chocolate chip (C), two batches pumpkin, or one batch of each.
The situation presented can be represented using the following letters CC, CP, PC, and PP.
How many combinations are possible in this situation?The possible combinations are:
Two batches of chocolate chip or CC.Two batches of pumpkin or PP.One batch of chocolate chip and another of pumpkin of CP.One batch of pumpkin and another of chocolate chip or PC.Based on this, the option that represents the situation is:
CC, CP, PC, and PP.
Note: This question is incomplete; here is the missing section:
What is the sample space of the event described above?
Answer choices:
a. CC, CP, PC, PP
b. CC, PP
c. CC, CP, PC
d. C, P
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Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20.
What is the length of Line segment S R?
9 units
12 units
15 units
18 units
The length of the line segment SR is 15 units.
How to find the length of a line segment?In Δ SRQ as seen in the attached image, we see that;
∠SRQ is a right angle
SQ is the hypotenuse
RT ⊥ SQ
Thus, by triangular rules, we know that;
(RQ)² = TQ × SQ
RQ = 20 units and TQ = 16 units
Thus;
(20)² = 16 × SQ
400 = 16 × SQ
SQ = 400/16
SQ = 25 units
By using Pythagoras theorem in Δ SRQ, we have;
(SR)² + (RQ)² = (SQ)²
RQ = 20 units and SQ = 25 units
Thus;
(SR)² + (20)² = (25)²
(SR)² + 400 = 625
(SR)² = 225
SR = √225
SR = 15 units
The length of the line segment SR is 15 units.
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pls help I dont understand this
Answer:
D
Step-by-step explanation:
The coconut milk is in a can but he doesn’t know how much the can holds.
The can is 12 cm high and the diameter is 8 cm.
Using the formula V = π r2 h, work out how much coconut milk is in the can.
Use 3 as a value for π.
Give your answer using the correct units.
A 28-metrelong guy wire is attched to a point 24 m up the side of a tower. How far from the base of the tower is the guy wire attached
The distance between the guy and the wire attached is 14.42m
Pythagoras theoremThe square of the longest side is equal to the sum of the square of other two sides.
In order to determine the length of base of the tower, we will use the expression below:
b² = 28² - 24²
b² = 208
b = 14.42
Hence the distance between the guy and the wire attached is 14.42m
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In the figure below, the radius of the larger circle is 6,8 and the radius of the smaller circle is 4.5. Which of the following best approximates the area of the shaded region? Note: The figure is not drawn to scale. O 14.45 O 16.62 O 25.99 O 81.65 O 145.27
A circle is a figure bounded by a curved side which is referred to as circumference. Thus the area of the shaded region is option D. 81.65.
A circle is a figure bounded by a curved side which is referred to as circumference. Some of its parts are radius, diameter, sector, arc, etc.
The area of a circle can be determined by the given expression:
Area = π[tex]r^{2}[/tex]
where r is the radius of the circle and π = [tex]\frac{22}{7}[/tex]
So, the area of the shaded region can be determined as:
Area of the shaded region = area of the larger circle - area of the smaller circle
Area of the shaded region = π[tex](6.8)^{2}[/tex] - π[tex](4.5)^{2}[/tex]
= π (46.24 - 20.25)
= [tex]\frac{22}{7}[/tex] x 25.99
= [tex]\frac{571.78}{7}[/tex]
Area of the shaded region = 81.683
Thus the appropriate answer to the question is option D. 81.65.
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