Step-by-step explanation:
r = 32/40 = 0.8
S10 = 40(1- (0.8)^10)/ (1- 0.8)
= 40(1 - 0.107) / 0.2
= 200(1.107)
= 221
Justin runs each lap in 8 minutes. He will run at most 10 laps today. What are the possible numbers of minutes he will run today?
Reduce to Standard form : (a) -21/91 (b) 32/(-256)
Answer:
a) -3/13
b) -1/8
Step-by-step explanation:
a) - (21 / 7) / (91 / 7) = 3/13
b) (32 / 32 ) / - (256 / 32) = -1/8
which two intergers have a difference of 24 and a quotient of -7
Answer:
21 and -3
Step-by-step explanation:
Hope this helps!!! :)
Please someone help me I rlly don’t get this I’ll give you like 40 points
Answer:
Step-by-step explanation:
H(n)=91x(-1/7) n-1
do not know
Hope it helps the answer is the 2nd one have a great day
How many triangles can you make with 60,60,60 degrees? how do you know?
Answer:
3 triangles can be make with 60,60,60 degrees.
Jack is taller than Pater and Bill is shorter than Jack. what is accurate?
Bill is taller than Peter
kiristen is paid 8.25 per hour. How much would her paycheck be for 39 hours? show your work
Answer: $321.75
Step-by-step explanation:
8.25*39=321.75
Answer:
$321.75
Step-by-step explanation:
She is payed 8.25 per hour. Per hour basically means 1 hour. If she is payed 8.25 every hour, you just need to multiply because there are a total of 39 hours.
Tina had $40. She spent 1/4 of her money on a new purse. She paid her mother$5 she borrowed she spent $5.75 on hair ribbons. How much change she had left?
Answer:
$19.25
Step-by-step explanation:
4/4-1/4=3/4
=3/4×40
=30-5
=25-5.75
=$19.25
The first term of a geometric sequence is 5 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?
Step-by-step explanation:
s1 = 5
s2 = s1 × -2 = 5×-2 = -10
s3 = s2 × -2 = -10 × -2 = 20
...
now, we could do all that manually.
but there is also a formula for geometric sequence.
in fact, there are 2 - one for finite and one for infinite sequences.
and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.
since we need the sum of the first 5 terms, which of the 2 do you think we need ?
of course, finite, because 5 is a normal number we can "touch". it is not infinity.
so, the formulas for finite sums of geometric sequences are :
if |r| < 1, Sn = a(1 - r^n)/(1 - r)
if |r| > 1, Sn = a(r^n - 1)/(r - 1)
if r = 1, Sn = na
if r = -1, then Sn = a or 0 depending on if n is odd or even.
the sequence is in general
s1 = a
sn = sn-1 × r
in our case a = 5, r = -2.
so, what form of the formula do we need ?
|-2| = 2, and 2 > 1, so ...
S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =
= 5 × 11 = 55
quick check, as the 5 terms are
5
-10
20
-40
80
and their sum is : 55
correct !
What next number 3 4 6 9 13 18 24
Answer:
I think it 31
Step-by-step explanation:
Answer:
31
Step-by-step explanation:
3+1=4
4+2=6
6+3=9
9+4=13
13+5=18
18+6=24
24+7=31
you start with one 3+1=4but everytime you add you add an extra 1
Determine the largest power of 10 that is a factor of the following numbers (equivalently, the number of terminal 0's, using ordinary base 10 representation):(a) 50!.
(b) 1000!.
The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.
(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.
There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.
Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.
(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:
⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249
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What is the solution set of the equation (x – 2)(x – a) = 0?
A –2 and a
B –2 and –a
C 2 and a
D 2 and –a
E 2 only
2. What is the smallest mass you could measure with this balance beam?
From the given measure, let's find the smallest mass you could measure.
From the tape, we can see the third line has the smallest measure = 10 g
On the third measure, 1 line represents 0.2 g
Hence, the smallest mass you can measure is 2/10.
Therefore, we have:
\(\frac{2}{10}=\frac{1}{5}\)Therefore, the smallest mass you could measure with balance beam is 1/5 g.
ANSWER:
\(\frac{1}{5}\text{ g}\)Find the exact value of sin G.A. √1010B. 3√1010C. 4√10D. 160
Given the Right Triangle EFG, you know that:
\(\begin{gathered} EF=4 \\ EG=12 \end{gathered}\)By definition:
\(sin\theta=\frac{opposite}{hypotenuse}\)Since, in this case:
\(\theta=G\)You can identify that:
\(\begin{gathered} opposite=EF=4 \\ hypotenuse=FG \end{gathered}\)In order to find the hypotenuse of the Right Triangle, you need to use the Pythagorean Theorem, which states that:
\(c=\sqrt{a^2+b^2}\)Where "c" is the hypotenuse, and "a" and "b" are the legs of the Right Triangle.
You can set up that:
\(\begin{gathered} c=FG \\ a=EG=12 \\ b=EF=4 \end{gathered}\)Therefore:
\(FG=\sqrt{12^2+4^2}=4\sqrt{10}\)Now you can determine that:
\(sinG=\frac{4}{4\sqrt{10}}\)Simplify:
\(sinG=\frac{1}{\sqrt{10}}\)You can multiply the numerator and the denominator by:
\(\sqrt{10}\)In order to Rationalize the denominator:
\(sinG=\frac{1\cdot\sqrt{10}}{\sqrt{10}\cdot\sqrt{10}}\)\(sinG=\frac{1\cdot\sqrt{10}}{(\sqrt{10})^2}\)\(sinG=\frac{\sqrt{10}}{10}\)Hence, the answer is: Option A.
What is the slope? (IXL)
Answer:
2/5x
Step-by-step explanation:
[character limit thing]
Answer:
2/5
Step-by-step explanation:
rise over run
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Pam, the CEO of Zettabyte Tek, set up a $750,000 education fund. She wants to give each employee who takes a computer security class a $350 reimbursement toward the cost of the class. You can use a function to describe the amount of money left in the fund after x employees receive the reimbursement.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.
The formula for this linear function is f(x) = mx + b, where m is the slope (in this example, -350), and b is indeed the y-intercept (750,000 in this case).
What does a simple equation represent?An equation expressing the connection between the expressions on either side of a sign. Normally, it has an equal sign and just one variable. such as: 2x - 4 is equal to 2. The variable x is present in the example above.
Workers who complete the computer security course will each receive a reimbursement of $350.
We deduct $350x from of the initial $750,000 to determine how much money will remain inside the education fund once x employee gets the reimbursement.
Thus, f(x) = 750,000 - 350x is the equation again for function that describes that amount of money still in the fund when x employees receive the refund.
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Given that √3 = 1.7321 , find correct to 3 places of decimals , the value of √192 - 1 / 2√48 - √75
Step-by-step explanation:
the value of root three is given already so the question is asking you to round it of to the nearest 1000 which means there should be three numbers after the decimal point.
Let (-3, 4) be a point on the terminal side of 0. Find the exact values of sin 0, csc 0, and cot 0.
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4 using trigonometric ratio.
Trigonometric ratio calculation.
We know that the point (-3, 4) is on the terminal side of the angle θ, and we can use the Pythagorean theorem to find the value of the hypotenuse:
r² = x² + y²
r² = (-3)² + 4²
r² = 9 + 16
r² = 25
r = 5
Now we can find the values of sin θ, csc θ, and cot θ:
sin θ = y/r = 4/5
csc θ = r/y = 5/4
cot θ = x/y = -3/4
Therefore, sin θ = 4/5, csc θ = 5/4, and cot θ = -3/4.
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Write an equation of a parabola with a vertex at the origin and a diretrix at y=5.
The equation of the parabola with a vertex at the origin and a directrix at; y = 5 as described in the task content is; x² = -20y.
How to write equation of a parabola with a vertex at the origin?It follows from the task content that the vertex of the parabola is at the origin while it's directrix is the line; y = 5.
Therefore, it follows that the focus of the parabola is; f = -5, since; (f - k) = (k - 5) where, k = 0.
Ultimately, a = 1/4(f-k).
a = 1/4(-5-0) = -1/20.
Recall, the vertex form equation of a parabola takes the form;
y = a(x - h)² + k; where (h, k) is the vertex.
Therefore, since the vertex is at the origin; we have;
y = (-1/20) (x -0)² + 0
y = -x²/20
20y = -x²
Ultimately, the required equation of the parabola is;
x² = -20y.
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Answer:
\(y = -\frac{1}{20} x^{2}\)
Step-by-step explanation:
\(y = \frac{1}{4(f-k)}(x - h)^{2} + k\) Use the equation of the parabola. The vertex is at the origin, then (h, k) is (0, 0). Substitute 0 for h and k in the equation.
\(y = \frac{1}{4(f-0)} (x-0)^{2} + 0\) Simplify.
\(y = \frac{1}{4f} x^{2}\)
The directrix is given \(y = 5\). The distance from the focus to the vertex equals the distance from the vertex to the directrix, so
\(f - k = k - 5\\f = -5\) Substitute -5 for f in the equation of the parabola above.
\(y = \frac{1}{4 * - 5} x^{2}\) Simplify.
\(y = - \frac{1}{20} x^{2}\)
BRAINLIEST FOR CORRECT ANSWER PLEASE HELP ASAP
Answer:
A is the correct point;)
Benjamin has $400, and makes $50 per week. Bill has $800 and spends $25 every week. What week will they have the same amount of money, and how
much money will that be?
Answer:
They won't
Step-by-step explanation:
Benjamin makes 50 per week, and Bill spends 25 per week, here's a table with each week for 10 weeks.
Ben 400, Bill 800Ben 450, Bill 775Ben 500, Bill 750Ben 550, Bill 725Ben 600, Bill 700Ben 650, Bill 675Ben 700, Bill 650Ben 750, Bill 625Ben 800, Bill 600Ben 850, Bill 575Question 8 The site from which an airplane takes off is the origin. The x axis points east; the y axis points straight up. The position and velocity vectors of the plane at a later time are given by = (1.61 x 10'i +3.00 x 10°j)m and 7 = +(150î - 21ị) m The plane is most likely just touching down. in level flight in the air. taking off. ascending descending < Previous
The plane is most likely taking off.The two vectors provided, position and velocity, indicate that the plane is moving eastward with a velocity of 150 m/s and is ascending with a vertical velocity of 21m/s.
This indicates that the plane is taking off, and not just touching down, ascending, or in level flight.
The position and velocity vectors of the plane indicate that the plane is moving in an eastward direction with a velocity of 150 m/s, and is also ascending with a vertical velocity of 21 m/s. This indicates that the plane is taking off, and not just touching down, ascending, or in level flight. This means that the plane is most likely taking off from the origin and is in the process of gaining altitude.
the complete question is :
( figure attached below )
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HELPPPP I WILL GIVE POINTS AND BRAINLIEST
Answer:
11 mm, 21 mm, and 16 mm.
Step-by-step explanation:
since 11+21>16, 11+ 16>21>11, You can form a triangle with 11,21,16
Can some one help me plz
Answer:
1b
1
Step-by-step explanation:
-10(-2)
Please show work!!
Answer:
20
Step-by-step explanation:
a negative times anegative is a postive
-10× -2= +20
which one doesn't belong fractions answers 1/4 , 40% , 3/2 , or 1/6
Answer:
40%.
Step-by-step explanation:
-1/4, 3/2, and 1/6 are fractions, but 40% is not.
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Fill in the banks if you had this question before!!
An equation for the total cars and trucks for dealership A is: x + y = 164.
An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.
The number of cars that dealership A sold is: 98 cars.
The number of trucks that dealership B sold is: 66 trucks.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of cars sold.Let the variable y represent the number of trucks sold.Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;
x + y = 164.
Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;
2x + 0.5y = 229.
By solving the systems of linear equations simultaneously, we have:
2x + 0.5(164 - x) = 229
1.5x + 82 = 229
x = 98 cars.
For the y-value, we have;
2(98) + 0.5y = 229
0.5y = 229 - 196
y = 33/0.5
y = 66 trucks.
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Selected financial data for Amberjack Corporation follows.
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Define Decimal place?
A decimal number is a number that consists of a whole number and a fractional part separated by a point. For example – 3.5, 6.79, 78.32 etc. In the figure given above, the decimal point separates the whole number 42 from the fractional part . In words, it is written as Forty Two Point Eight Five.One decimal place to the left of the decimal point is the ones place. One decimal place to the right of the decimal place is the tenths place. Keep your eye on the 9 to see where the decimal places fall.Rounding a decimal number to two decimal places is the same as rounding it to the hundredths place, which is the second place to the right of the decimal point. For example, 2.83620364 can be round to two decimal places as 2.84, and 0.7035 can be round to two decimal places as 0.70.To learn more about decimal place refers to:
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4b - 3(6 + 2b) = 12
i
Answer:
-15
Step-by-step explanation:
4b - 3(6 + 2b) = 12
4b - 18 - 6b = 12
4b - 6b = 12 + 18
-2b = 30
b = 30/-2
b = -15
(1 3/4)²
help please
Answer:
\( \frac{49}{16} \: or \: 3 \frac{1}{16} \)