The nth term Tn = n - 12 illustrates an arithmetic progression
The sum of the first 25 terms is 25
How to determine the sum of the terms?The nth term is given as:
Tn = n - 12
Calculate the first term
a = 1 - 12
a = -11
Calculate the second term
T2 = 2 - 12
T2 = -10
Calculate the common difference (d)
d = T2 - a
d = -10 + 11
d = 1
The sum of n terms is then calculated as:
Sn = n/2(2a + (n - 1) * d)
So, we have:
S25 = 25/2(-2 * 11 + (25 - 1) * 1)
Evaluate
S25 = 25
Hence, the sum of the first 25 terms is 25
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A dodgeball has a volume of approximately 113.04 cubic inches. Find the circumference of the ball. Use
3.14 for O.
14
Answer:
18.84 inches.
Step-by-step explanation:
Volume = 4/3 π r^3 = 113.04
r^3 = 113.04 / 4/3 * 3.14
r^3 = 27
r = 3 inches,
So the circumference = 2 * 3.14 * 3
= 18.84 inches.
separate into real and imaginary parts and find the multiplicative inverse of √2+i/√2-i (only 2 is in the √
The multiplicative inverse for √2-i = 1/(√2+1) and The multiplicative inverse is √2+1 = 1/(√2-1)
Real and Imaginary Numbers/Complex NumbersGiven Data
First expression = √2+iSecond expression = √2-iFor√2+i
the real part is is √2 and the imaginary part is i
The multiplicative inverse is √2+1 = 1/(√2-1)
rationalising the denominator we have
= 1/√2-1 * √2-1/√2-1
= √2-1/(√2-1)*(√2-1)
= √2-1/(2-√2-√2+1)
= √2-1/(-2√2+3)
For√2-i
the real part is is √2 and the imaginary part is -i
The multiplicative inverse is √2-1 = 1/(√2+1)
Rationalising the denominator we have
= 1/√2+1 * √2+1/√2+1
= √2+1/(√2+1)*(√2+1)
= √2+1/(2+√2+√2+1)
= √2+1/(2√2+3)
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Hey y’all! Can I please have some help??? :)
Answer:
Rhombi and Squares
Step-by-step explanation:
1) KY (pythagorean Thm) 5² + x² = 13² ...= 12
2) PK Diagonals bisected. also = 12
3) Diagonals of rhombi are perpendicular. <YKZ = 90
4) 67. Alternate interior angles are congruent.
5) 3. Diagonals are bisected and congruent for squares.
6) 45° . Angles are bisected by diagonals.
7) 90° . All angles of squares are right angles.
8) 6. Diagonals are bisected. So 3 is doubled to 6.
9) I need graph paper.. hol'up
Consider nick draws 3 cards from a pack of 52 cards. What is the probability of getting no kings?
The probability of getting no kings is 0.7826
What is the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.
The random experiment follows a hypergeometric distribution with,
N = 52 since there are 52 cards in a deck.
k = 4 since there are 4 kings in a deck.
n = 3 since we randomly select 3 cards from the deck.
x = 0 since we want no kings.
The probability of getting no kings is;
[tex]\rm = \dfrac{^4C_0 \times ^{48}C_3}{^{52}C_3}\\\\=\dfrac{1 \times 17296}{22100}\\\\= 0.78[/tex]
Hence, the probability of getting no kings is0.7826.
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What value completes this expression?
4m + ____m = 4m (1 + 6)
Answer:
24
Step-by-step explanation:
4(1)m + 4(6)m
= 4m + 24m
Drag the measurements to the containers to show equal length.
The measurements that show equal length is 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.
Hence:
15 yd = 15 yd * 36 in per yd = 540 in
195 ft = 195 ft * 12 in per ft = 2340 in
5280 yd = 5280 yd * 3 ft per yd = 15840 ft
The measurements that show equal length is 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
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Solve the system by substitution.
y= 4x + 22
y= -7x
(__,__)
Answer:
y=14, and x=-2(-2,14)Step-by-step explanation:
Isolate the term of x and y from one side of the equation.
y=4x+22 and y=-7x
y=-7x=4x+22
Solve.
-7x=4x+22
x=2
Substitute.
y=-7x, x=-2
y=-7(-2)
Solve.
Multiply.
y=14
(-2,14)
Therefore, the final answer is (-2,14).
I hope this helps you! Let me know if my answer is wrong or not.
There is a bag a filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and
then it iS not replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
Answer:
3/7Step-by-step explanation:
Given
Red = 4, Blue = 3Total number of marbles is
3 + 4 = 7Probability of getting 2 of the same color is
P(2 same) = P(red, red) + P(blue, blue)Probability of 2 reds is:
P(red, red) = 4/7*3/6 = 2/7Probability of 2 blues is:
P(blue, blue) = 3/7*2/6 = 1/7Required probability is
P(2 same) = 2/7 + 1/7 = 3/7Which statement about the asymptotes is true with respect to the graph of this function f(x)= 3x^2-3/x^2-4
Answer:
D. The graph has two vertical asymptotes and one horizontal asymptote.
Step-by-step explanation:
Sunny made a deposit into an account that
earns 6% simple interest. After 7 years, Sunny
had earned $420. How much was his initial
deposit?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$420\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &7 \end{cases} \\\\\\ 420 = (P)(0.06)(7)\implies \cfrac{420}{(0.06)(7)}=P\implies 1000=P[/tex]
Q1. If you draw a triangle with angles that measure 25 degrees and 60 degrees, what will be the measure of the third angle?
Q2. If angle 1 and angle 2 are supplementary, and angle 1 measures 80 degrees, what is the measure of angle 2?
Answer:
Q1. 95 degrees
Q2. 100 degrees
Step-by-step explanation:
When you create a triangle, all angle measures must equal 180 degrees.
So, using that information, take 180 and subtract both of the other values.
180 - 25 = 155
155 - 60 = 95
When two angles are supplementary, the sum of their angle measures equal 180, or a straight angle.
Using that information, take 180 and subtract 80.
180 - 80 = 100
Find the area of the rectangle.
l=10 in, w=7.5 in
Answer:
It should be 75 inches
Step-by-step explanation:
Given: Line segment A B is parallel to line segment D C and Measure of angle 2 equals measure of angle 4
Prove: Line segment A D is parallel to line segment B C
A parallelogram has points A B C D. Angle D A B is angle 1, Angle A B C is angle 2, Angle B C D is angle 3, and angle C D A is angle 4.
A 2-column table with 7 rows. Column 1 is labeled statements and has entries line segment A B is parallel to line segment D C, measure of angle 2 = measure of angle 4, angle 1 and angle 4 are supplements, question mark, measure of angle 1 + measure of angle 2 = 180 degrees, angle 1 and angle 2 are supplements, line segment A D is parallel to line segment B C. Column 2 is labeled reasons with entries given, given, same side interior angles theorem, definition of supplementary angles, substitution, definition of supplementary angles, converse same side interior angles theorem.
m∠1 = m∠4
m∠2 = m∠3
m∠1 + m∠4 = 180°
m∠2 + m∠3 = 180°
Answer: m∠1 + m∠4 = 180°
Step-by-step explanation:
If angles 1 and 4 are supplementary, their measures must add to 180 degrees.
Find the missing side. Round your answer to the nearest tenths.
X=
Answer:
16.5 ≈ x
Step-by-step explanation:
We have a right triangle where we know 1 side, 1 angle and we need to find another side. We can use trigonometric functions to find the missing side.
The tangent function definition is
tan α = opposite side/ adjacent side
In our problem
tan 70° = x/ 6, multiply both sides by 6 to isolate x
6 · tan 70° = x, use the calculator (make sure is set in degrees)
16.4848 ≈ x , round to the nearest tenths
16.5 ≈ x
Jack rides in a motorboat against a river current for 36 km. Then he returns to his starting point by floating down river on a raft.Tommy travels 9 hours less on the motorboat than on the raft. Find the speed of the river current if the speed of the motorboat in still water is 15 km/h.
The speed of the river current if the speed of the motorboat in still water is 15 km/h is 3 km/h.
SpeedLet x be the speed of the current in km/h units
Speed of the boat traveling against the current= (15-x) km/h
Time spent traveling 36 miles against the current=36/15-x hours
Time spent rafting36miles (with the current) =35/x hours
Equation=36/x-36/15-x=9
Multiply both sides by x×(15-x)
36×(15-x) - 36x = 9x×(15-x)
540 - 36x - 36x=135x-9x²
9x²-207x+540=0
x²-23x+60=0
(x-3)×(x-30) = 0
Roots are x= 3 and x= 30
Since 15-x must be positive, the only root x = 3 survives
Hence:
Speed =3 km/h
Inconclusion the speed of the river current if the speed of the motorboat in still water is 15 km/h is 3 km/h.
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Plss help i need this asap
(will give brainliest)
(this is not from a test)
Answer:
90
Step-by-step explanation:
im not sure but im pretty sure it would be 90 dont come at me if it not:(
Answer:
360°/3=120°
which is the size of each exterior angle.
Step-by-step explanation:
An equilateral triangle has 3 lines of symmetry, but of more importance in this case, it has rotational symmetry of order 3. This means that in a rotation of 360° the same image appears 3 times.
360°/3=120° which is the size of each exterior angle.
The triangle rotates through the exterior angle so that the next vertex can be in the same position as the previous one.
IN the same way, a square will rotate through 360/4=90°
A pentagon will rotate through 360/5=72°
for the figure to map onto itself.
Graph the image of the figure using the transformation given
Answer:
See the explanation
Step-by-step explanation:
Please see the photo
A path of 0.5 meter wide runs round within a square garden of side 15 m.Find it's perimeter ?
Answer:
:))
Step-by-step explanation:
Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and six have a master’s degree. If the department chairperson selects three applicants at random for an interview, find the probability that all three have a PhD
Using the hypergeometic distribution, it is found that there is a 0.0175 = 1.75% probability that all three have a PhD.
The applicants are chosen without replacement, hence the hypergeometric distribution is used to solve this question.
What is the hypergeometric distribution formula?The formula is:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.In this problem, the values of the parameters are as follows: N = 20, k = 6, n = 3.
The probability that all three have a PhD is P(X = 3), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,20,3,6) = \frac{C_{6,3}C_{14,0}}{C_{20,3}} = 0.0175[/tex]
0.0175 = 1.75% probability that all three have a PhD.
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Which system of equations
Answer:
The answer is J.
Step-by-step explanation:
Because y= 2x-3 as shown on the graph and on the chart it shows y=-x+3
ylinder has a base radius of 9 feet and a height of 4 feet. What is its volume in cubic feet, to the nearest tenths place?
Answer:
Formula for volume of cylinder;
V = π[tex]r^{2}[/tex]h
Where 'π' represents pi(22/7 or 3.14), and 'r' is the radius which is squared, and 'h' is the height.
Plug in your values:
V = π[tex]r^{2}[/tex]h
V = 3.14(9^2) x 4
V = 3.14(81) x 4
V = 254.34 x 4
V = 1,017.36^3 feet or 1,017.36 cubic feet.
Line M is represented by the following equation: x + y = −1 What is most likely the equation for line P so the set of equations has infinitely many solutions? (4 points) Group of answer choices x − y = 1 2x + 2y = 4 2x + 2y = −2 2x + 2y = 2
The most likely equation for line P so the set of equations has infinitely many solutions is 2x + 2y = -2.
How to know an equation with infinitely many solutions?If a linear equation has the same variable term and the same constant value on both sides of the equation, it has infinitely many solutions.
Therefore, let's check for the equation with the same terms and constant with the equation :
x + y = -1
Hence, the most likely equation of line p is as follows:
2x + 2y = -2
divide both sides by 2
2x/ 2 + 2y / 2 = -2 / 2
x + y = - 1
The equation of the line will be 2x + 2y = -2
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pls help ill give brainliest and 5 starts
Answer:
For number 1: Plate boundaries.
For number 2: Geography.
For number 4: Plate.
For number 5: Plate tectonics
Hope this helps.
-Mark me brainliest & 5 star-
PLSS HELPP IMPORTANT
(WILL GIVE BRAINLIEST)!
Answer:
c. It is a reflection around the x-axis and a reflection around the y-axis
Step-by-step explanation:
1) The sum of the digits in a 2 digit number is 7. Reversing the digits increases the number by 9. What is the number?
Answer:
34
Step-by-step explanation:
Sum of two numbers = 7
1+6
2+5
3+4
34+9=43
Brandon paid $70 for 20 gallons of
gasoline. How much did he pay per
gallon?
Answer:
$3.50
Step-by-step explanation:
For this question, you just take the price paid and divide it by the number of gallons. In this case, you get $3.50 per gallon.
Which expression is equivalent to 8/6?
•/14
•/48
•/96
•/384
Answer:
./48
Step-by-step explanation:
wich expression shows a way to factor 15+18
how many solutions are there to the system of equations graphed below if the lines are parallel
Answer:
your answer would be zero
Step-by-step explanation:
Parllel lines never crosses or intercept, which means they have 0 solutions
Can the sides of a triangle have lengths 2, 1, and 2?
yes
no
Submit
Answer:
YES
Step-by-step explanation:
Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (Any side of a triangle is always shorter than the sum of the other two sides)
1+2 >2
2+2>1