Step-by-step explanation:
future value of annuity after 1 year is:
$122× $4.0909=$499.089
=$499.09
Find the sum of the first 9 terms
of the geometric sequence: 0.5, 1, 2,-..
Answer:
S₉ = 255.5
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 0.5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{1}{0.5}[/tex] = 2 , then
S₉ = [tex]\frac{0.5(2^{9}-1) }{2-1}[/tex]
= [tex]\frac{0.5(512-1)}{1}[/tex]
= 0.5(511)
= 255.5
Which angle in this quadrilateral is an obtuse angle?
Angle J
Angle K
Angle L
Angle M
Answer:
Angle L
Step-by-step explanation:
An obtuse angle has a measure between 90° and 180°.
Angles J and K are right angles, so their measures are equal and are 90°. Angle M has measure 64° and is acute.
Only angle L, which measures 116°, has a measure between 90° and 180° and is an obtuse angle.
Answer: Angle L
A softball has a volume of about 29 cubic inches. Find the radius of the softball. Round your answer to the nearest tenth.
The radius of the softball is about _ inches.
The geometry of the softball is a sphere. Then the radius of the softball will be 1.91 inches.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A softball has a volume of about 29 cubic inches.
Then the radius of the softball will be
The geometry of the softball is a sphere.
Then the volume of the sphere is given as
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
where r is the radius of the softball.
Then we have
[tex]\rm r^3 = \dfrac{3V}{ 4 \pi}\\\\r^3 = \dfrac{3 \times 29}{4 \times \pi}\\\\r^3 = \dfrac{87}{12.5664}\\\\r^3 = 6.9232\\\\r \ \ = \sqrt[3]{6.9232}\\\\r \ \ = 1.9059 \approx 1.91 \ in.[/tex]
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Find the range and interquartile range of the data.
2, 4, 8 , 3, 2
Answer:
IQR = 4
Step-by-step explanation:
Q3 = 6
Q1= 2
6-2=4
here it is could you help me.
Answer:
7. D.58
Because 90-32=58 (that cube on the edge means 90degree)
8. A.45
Because 180-135=45
9. C. Because angles are equal
10. C. 95
180-85=95
PLEASE HELP ME !!???! I DONT GET IT
Answer:
see explanation
Step-by-step explanation:
the perimeter (P) is the sum of the 3 sides of the triangle, then
P = 31 + 19.5 + 16.2 = 66.7 units
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 16.2 and h = 13 , then
A = [tex]\frac{1}{2}[/tex] × 16.2 × 13 = 8.1 × 13 = 105.3 units²
pls help me classify each of this?!
First image -Right triangle(One angle is 90 degrees)
Second image-Isosceles triangle(Two equal sides and two equal angles).
Genevieve is in charge of creating a five-digit code to lock and unlock a secure cabinet. she can use any digit from 0 through 9, and she can use each digit as many times as she wants. she knows she wants to start the code with a prime number. how many possible codes that start with a prime number could genevieve create? 40,000 codes 50,000 codes 400,000 codes 500,000 codes
The number of digits is an illustration of combination, and there are 40,000 possible codes that start with a prime number that Genevieve could create
How to determine the number of digits?The given parameters are:
Length = 5
First digit = Prime number (2, 3, 5, and 7)
This means that the first digit can be any of the 4 prime numbers, while the other four digits can be any of the 10 digits 0 - 9
So, the number of codes is
Code = 4 * 10 * 10 * 10 * 10
Evaluate
Codes = 40,000
Hence, there are 40,000 possible codes that start with a prime number that Genevieve could create
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Answer:
40,000
Step-by-step explanation:
i did the k12 test ;)
Help with this volume problem? (please include how you got the answer) will give brainlyest
Answer:
35.28 m
Step-by-step explanation:
Formula for volume of pyramid:
[tex]V=b^2\frac{h}{3}[/tex]
Therefore since,
base - 4.2 m
height - 6 m
Then,
[tex]V=4.2^2\frac{6}{3}[/tex]
[tex]V=35.28m[/tex]
Kavinsky
me podrían ayudar con esto?
Answer:
0
Step-by-step explanation:
This would be basically be zero/0 because anything times 0 is just nothing.
Use the function f(x) to answer the questions:
f(x) = 4x2 + 8x − 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)
Step-by-step explanation:
let's start with B :
the best way to find the vertex is by transforming the function into the vertex form :
y = a(x - h)² + k
with (h, k) being the vertex.
when doing all the multiplications, we get
y = a(x²-2hx+h²) + k = ax² - 2ahx + ah² + k
let's compare with the irreducible function
ax² = 4x²
a = 4
-2ahx = 8x
-2×4hx = 8x
-8hx = 8x
-8h = 8
-h = 1
h = -1
ah² + k = -5
4×(-1)² + k = -5
4 + k = -5
k = -9
so, the vertex form is
y = 4(x + 1)² - 9
the vertex is (-1, -9)
if the factor of the (x-h)² term is greater than 0, then the parabola opens upward, and if it is less than zero, the parabola opens downward.
out factor is +4, so it opens upward, and the vertex is a minimum.
A
now we know
y = 4(x + 1)² - 9
for the x-intercepts we need to find the x-values that lead to 0 y values.
so,
0 = 4(x + 1)² - 9
9 = 4(x + 1)²
3 = ± 2(x + 1) = ± (2x + 2)
for +(2x + 2) is then
3 = 2x + 2
2x = 1
x = 1/2
for -(2x + 2) is then
3 = -2x - 2
5 = -2x
x = -5/2
so, the x-intercepts are
(-5/2, 0) and (1/2, 0).
C
I know it is a parabola.
i know 3 points : the vertex and the 2 x-interceot points. i could then also calculate the points for x = 0, 1, -1, 2, -2.
and then draw the graph with a curve ruler connecting the points.
Find the Volume of the Sphere if:
r=10 and pi= 3.1416
Answer:
4188.79
Step-by-step explanation:
formula- [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex] × [tex]r^{3}[/tex]
r= radius
What is the value of 6 n=2 (n-1)!/2
Answer: d- 76.5
Step-by-step explanation:
A quantity with an initial value of 620 grows continuously at a rate of 0.3% per second. What is the value of the quantity after 0.5 minutes, to the nearest hundredth?
Answer:
678.39
Step-by-step explanation:
For this we should probably use the formula A = Pe^rt. The question says that the value grow "continuously" which is our hint that we should use A = Pe^rt rather than A = P(1 +r/n)^nt. Our P = 620 as it is our initial value. e is a constant approx = 2.718. r is our rate, so 0.3% = 0.003, and our t will be in seconds. We need to figure out how many seconds are in .5 minutes, so 30, and that means our t will = 30. Let's plug these in. 620e^(0.003 * 30) = A. This will give us our answer which when rounded to the hundredths = 678.39.
Hope this is helpful.
What is the coefficient of the x2-term of the algebraic expression 2 x 4 + x squared minus x + 7?
-1
1
0
2
Answer:
1
Step-by-step explanation:
If x doesnt have a number in front of it the coefficient is 1. x^2 + 3x + 7 = 1x^2 + 3x + 7 /// same thing
Answer:
i believe its B. 1
Step-by-step explanation:
what does x equal when 6600/80 = x
Answer: 82.5
Step-by-step explanation: 6600 divided by 80 is 82.5
Answer:
82.5
Step-by-step explanation:
A point of sale transaction occurs when a debit card is used to purchase items at a grocery store. please select the best answer from the choices provided. t f
It is a true statement that; "A point of sale transaction occurs when a debit card is used to purchase items at a grocery store."
What is a debit card?
A debit card is a small card that contains a chip which a bank issues to its customers to enable them to perform cashless transactions outside the banking hall.
It is a true statement that; "A point of sale transaction occurs when a debit card is used to purchase items at a grocery store."
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Answer: It is a true statement.
A transaction is an agreement between a buyer and a seller to exchange goods, services or financial instruments.
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Have a great day and God bless! :)
What is an equation of the line that passes through the point (-4,-6) and is
parallel to the line 33 – y = 6?
Hey there!
33 - y = 6
33 - 1y = 6
-1y + 33 = 6
-y + 33 = 6
SUBTRACT 33 to BOTH SIDES
-y + 33 - 33 = 6 - 33
SIMPLIFY IT!
-y =6 - 33
-y = 6 - 33
-1y = -27
DIVIDE -1 to BOTH SIDES
-1y/-1 = -27/-1
SIMPLIFY IT!
y = -27/-1
y = 27
Therefore, your answer is: y = 27
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
I guess question is wrong :
What is an equation of the line that passes through the point (-4,-6) and is parallel to the line 33 x– y = 6?
3x - y = 6
[tex]m = \frac{ - a}{b} [/tex]
[tex]m = \frac{ - 3}{ - 1} [/tex]
[tex]m = 1[/tex]
Lines are parallel :
m1 = m2
[tex]x - x1 = m(y - y1)[/tex]
[tex]x + 4= 1(y + 6)[/tex]
[tex]x + 4= y + 6[/tex]
[tex]x - y= 6 - 4[/tex]
[tex]x - y - 2 = 0[/tex]
Can you answer this for me ty :)
Four girls and six boys are in a Spanish club. Three of the people will be chosen at random to represent the group in a photograph.What is the probability that one girl and two boys will be chosen
Answer:
18/125
Step-by-step explanation:
4 add 6 is 10
4/10 chance for a girl
6/10 chance for a boy
2 boys and a girl is 4/10, 6/10, 6/10
4/10 multiplied by 6/10 multiplied by 6/10 is:
144/1000
This can be simplified to 72/500
This can be simplified to 36/250
This can be simplified to 18/125
The ice cream stand offers chocolate, vanilla, and strawberry ice cream. Find the approximate probability the next three customers order vanilla, chocolate, and then strawberry.
Answer: 1/3 im not sure tho
Step-by-step explanation:
The points P (22, 15), Q (−13, c) and R (k, 24) all lie on a circle, centre (2, 0). Find the radius of the circle and the possible values of the constants c and k.
Answer:
r = 25c = 20k = 9 or k = -5Step-by-step explanation:
Circle of center A(2, 0) and radius r.
P (22, 15), Q(−13, c) and R (k, 24) all lie on a circle,
[tex]r=AP=\sqrt{\left( 22-2\right)^{2} +\left( 15-0\right)^{2} }[/tex]
[tex]=25[/tex]
Q(−13, c) lies on the circle then ,
[tex]AQ=r\Longrightarrow AQ^{2}=r^{2}\Longrightarrow (-13-2)^{2}+(c-0)^2=25^2=625[/tex]
[tex]\Longrightarrow 225+c^{2}=625[/tex]
[tex]\Longrightarrow c=20[/tex]
R (k, 24) lies on the circle then ,
[tex]AR=r\Longrightarrow AR^{2}=r^{2}\Longrightarrow (k-2)^{2}+(24-0)^2=25^2=625[/tex]
[tex]\Longrightarrow (k-2)^{2}+576=625[/tex]
[tex]\Longrightarrow (k-2)^{2}=49[/tex]
[tex]\Longrightarrow k-2=7\ \ or \ \ k-2=-7[/tex]
[tex]\Longrightarrow k=9\ \ or \ \ k=-5[/tex]
Three less than the quotient of a number and 4 is 18. What is the number? Let n be the unknown number.
Answer:
n = 84
Step-by-step explanation:
18 + 3 = 21, so that means the quotient of the number and 4 is 21.
21 * 4 = 84
CHECK:
84 / 4 = 21
21 - 3 = 18
Amanda created a table to help her represent the sample space of spinning a spinner and flipping a coin.
Result of spin
Result of coin toss Red Green Yellow Blue
Heads Red, heads Green, heads Yellow, heads Blue, heads
Tails Red, tails Green, tails Yellow, tails Blue tails
What is the probability that the result of the spin is blue and the coin lands heads up?
two over eight
three over eight
one over eight
four over eight
Answer:
[tex]\sf \dfrac{1}{8}[/tex]
Step-by-step explanation:
Spinner choices: Red, Green, Yellow, Blue
Coin choices: Heads, Tails
[tex]\large\begin{array}{| c | c | c | c | c |}\cline{1-5} & \sf Red & \sf Green & \sf Yellow & \sf Blue\\\cline{1-5} \sf Heads & RH & GH &YH & BH \\\cline{1-5} \sf Tails &RT & GT& YT& BT\\\cline{1-5}\end{array}[/tex]
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(blue)=\dfrac{1}{4}[/tex]
[tex]\implies \sf P(heads)=\dfrac{1}{2}[/tex]
[tex]\implies \sf P(blue)\:and\:P(heads)=\dfrac{1}{4} \times \dfrac{1}{2}=\dfrac{1}{8}[/tex]
A marine biologist compared two large pools that could be used for a new dolphin training arena. Pool A held 2 x 1010 gallons, and pool B held 2 x 108 gallons. How many times more gallons will the larger pool hold than the smaller pool?
4
20
100
200
Answer:
20
Step-by-step explanation:
HELPPP PLEASEEEEE
Tyrion creates a set of nesting shapes as a toy set for his baby nephew. The outer figure is a
cube with an edge length of 20 centimeters. The middle figure is a square pyramid with an
identical square base and the same height as the cube. The innermost figure is a cone with a
diameter and height equal to the edge of the cube. Calculate the difference of volumes
between cube and cone. Round your answers to the nearest whole cubic centimeter.
Answer:
5906
Step-by-step explanation:
The difference in volumes between cube and cone is 5190.52 cubic units.
How to find the volume of a cube?Suppose that:
The side length of the considered cube is L units.
Then, we get:
The volume of that cube = L³ cubic units.
The outer figure is a cube with an edge length of 20 centimeters.
The volume of that cube = L³ cubic units.
= 8000 cubic units.
The volume of that cone
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
The height is 20 cm and the radius will be
[tex]D = 20\sqrt{2} \\ = 28.2\\\\r = D/2\\ = 14.1[/tex]
volume of that cone
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
= [tex]V = \dfrac{1}{3} (3.14) (14.1)^3 (20) \: \rm unit^3[/tex]
= 59190.52 cubic units
Therefore, the difference in volumes bbetween cube and cone is 5190.52 cubic units.
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______ is the cost for the use of money.
Answer:
do you have a pic?
Step-by-step explanation:
Laura's yard is in the shape of a square and a half-circle. 12 m What is the approximate area of Laura's yard? A 57 m2 B 144 m2 C 201 m2 D 257 m2
Answer:
B 144
Step-by-step explanation:
Simplify the expression. Write your answer as a power.
Answer:
2/3 to the power 8
Step-by-step explanation:
Power : 2 + 6 = 8
One spinner has three equally sized sectors labeled R, S, and T. A second spinner has two equally sized sectors labeled 3 and 5. Each spinner is spun once. What is the sample space of outcomes
The total number of outcomes will be 6. Then the sample space will be {(3,R), (3,S), (3,T), (5,R), (5,S), (5,T)}
What are Sets?Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as a curly bracket {..}.
One spinner has three equally sized sectors labeled R, S, and T.
A second spinner has two equally sized sectors labeled 3 and 5.
Then the total number of the event will be
Total event = 3 × 2
Total event = 6
Then the sample space will be
[tex]\rm Sample = \left\{\begin{matrix}3,R & 3,S & 3,T \\\\5,R & 5,S & 5,T \\\end{matrix}\right.[/tex]
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