Answer:8
Step-by-step explanation:
0.5*10=5
3+5=8
a. Montserrat runs 7.5 kilometers in her 10th training week.
b. by her 15th training week, Montserrat will have run a total of 78.75 kilometers.
To find how many kilometers Montserrat runs in her 10th training week, we can use the arithmetic sequence formula to find the nth term:
[tex]a_n = a_1 + (n - 1) * d[/tex]
where:
[tex]a_n[/tex] is the nth term (the number of kilometers in the nth week),
[tex]a_1[/tex] is the first term (the number of kilometers in the first week, which is 3 km),
n is the number of weeks (in this case, 10), and
d is the common difference (the amount by which the distance increases each week, which is 0.5 km).
[tex]a_{10} = 3 + (10 - 1) * 0.5\\a_{10} = 3 + 9 * 0.5\\a_{10} = 3 + 4.5\\a_{10 }= 7.5 km[/tex]
So, Montserrat runs 7.5 kilometers in her 10th training week.
b. Next, to calculate the total number of kilometers Montserrat will have run by her 15th training week, we use the sum of the first n terms formula:
[tex]S_n = (n / 2) * (a_1 + a_n)[/tex]
where:
[tex]S_n[/tex] is the sum of the first n terms (the total number of kilometers run by the nth week),
[tex]a_1[/tex] is the first term (3 km),
[tex]a_n[/tex] is the nth term (which we found to be 7.5 km in her 10th week),
n is the number of weeks (15 in this case).
[tex]S_{15} = (15 / 2) * (3 + 7.5)\\S_{15} = 7.5 * 10.5\\S_{15} = 78.75 km[/tex]
So, by her 15th training week, Montserrat will have run a total of 78.75 kilometers.
To know more about training:
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if p(x) = x^3 + 1 is divided by (x + 2) , then the remainder is
PLS HELP!
Answer:
[tex]{ \bf{factor : x + 2}} \\ { \tt{divisor = - 2 }} \\ { \bf{f(x) = {x}^{3} + 1 }} \\ { \bf{f( - 2) = {( - 2)}^{3} + 1}} \\ { \bf{remainder = - 7}}[/tex]
In Ethiopia there are 20 premier league soccer teams.
a) In one round how many games are there ?
b) If five of the teams represent one company, find the number of ways pairs of teams representing different companies can play a game.
Answer:
In A Premier League there are 20 soccer teams.
(a)In One Round How Many Games Are There?
20 choose 2 = 20C2 = 190
(b) If five of the teams represent one company, find the
number of ways pairs of teams representing different companies
can play the game.
So there are 4 companies, each having 5 teams.
4 companies choose 2 = 4C2 = 6 ways
Choose a team of the company that's, say, been in business the
longest.
5 teams choose 1 = 5C1 = 5 ways
Choose a team of the other company,
5 teams choose 1 = 5C1 = 5 ways
Answer 6*5*5 = 150 ways.
.can somebody help me.with this question
Answer:
4 and 16
Step-by-step explanation:
Solve:
2(2x + 3) = -6(x + 9)
Answer:
The answer is x = -6
Step-by-step explanation:
Answer:
= − 6
Step-by-step explanation:
Calculate the compound interest a saleswoman would have to pay if she borrows
$54 000 for 9 years at 12% per annum compound interest.
Given:
Principal = $54,000
Time = 9 years
Rate of compound interest = 12% per annum.
To find:
The compound interest.
Solution:
The formula for amount is:
[tex]A=P\left(1+\dfrac{r}{n}\right)^{nt}[/tex]
Where, P is principal, r is the rate of interest in decimal, n is the number of time interest compounded and t is the number of years.
The interest is compounded annually, so [tex]n=1[/tex].
Substituting [tex]P=54000,\ t=9,\ n=1,\ r=0.12[/tex] in the above formula, we get
[tex]A=54000\left(1+\dfrac{0.12}{1}\right)^{1(9)}[/tex]
[tex]A=54000\left(1.12\right)^{9}[/tex]
[tex]A=149746.252902[/tex]
[tex]A\approx 149746.25[/tex]
The amount after 9 years is $149746.25.
Now, the compound interest is:
[tex]C.I.=A-P[/tex]
Where, C.I. is compound interest, A is amount and P is principal.
[tex]C.I.=149746.25-54000[/tex]
[tex]C.I.=95746.25[/tex]
Therefore, the compound interest is $95746.25.
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in second, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of a second
10.17 seconds
hope this helps
The capacity of a fuel tank is 45 litres. Find its
volume.
Answer:
45000 cubic cm
Step-by-step explanation:
Capacity of the fuel tank
= 45 litres
= 45/1000 = 0.045 cubic meters
Or 45* 1000 = 45000 cubic cm
Which of the following systems of linear inequalities is represented by the solution graphed below?
Ranu has 200 stamps and Cathy has 132 stamps. How many stamps must Ranu give Cathy so that they will have the same number of stamps?
Answer:
34
Step-by-step explanation:
let x = number of stamps ranu gives out and the number of stamps cathy receives
200 - x = 132 + x
combine like term s
200 - 132 = 2x
68 = 2x
x = 34
Find the length of "b" to the nearest tenth.
Answer:
11.2
Step-by-step explanation:
(AB) ^2 - (BC) ^2 = b^2 (Pythogoras Theorem)
(15)^2 - (10)^2 = (b) ^2
b^2=225-100
b^2=125
b=root (125)
b=11.18
b=11.2
A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = - 16t^2 + 48t where t equals the time in seconds and the h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? Help please!!!
Answer:
x = 3/2
The axis of symmetry is located at the vertex,
which is the also the highest point in this problem...
the x component of the vertex can be calculated as -b/2a = -48/-32 = 24/16 = 6/4 = 3/2
x = 3/2
Step-by-step explanation:
Sophie is buying fabric to make items for a craft fair. The table shows some combinations of how much of each color fabric she might buy. Which equations model the total yards of fabric Sophie will buy
Answer:
15
Step-by-step explanation:
u add up that then u get the answet
I’ll give brainliest to whoever gets it right. Find the surface area of this prism.
Round to the nearest tenth.
6.72 cm
5.78 cm
12.7 cm
[ ? ]cm
Answer:
493.29[tex]cm^2[/tex]
Step-by-step explanation:
Multiply all values (6.72, 5.78, and 12.7) together, then round to the nearest tenth.
What is the slope of (-2,2) (-4,-4)
Answer:
3
Step-by-step explanation:
slope = (y2-y1)/(x2-x1)
(-4-2)/(-4--2)
-6/-2
3
Answer:
to find slope we use the following methods
Step-by-step explanation:
given
X1 -2
X2= -4
Y1= 2
Y2= -4
slope=y2-Y1 ÷X2-X1
= -4-2÷ -4-(-2)
=-6 ÷-4+2
= -6÷-2
= 3
slop of (-2,2) (-4,-4) = 3
In a village of 1210 people, the ratio of men to women is 6: 5. Find the number of men and women.
Answer:
Men = 660
Women = 550
Step-by-step explanation:
Say the total number of people = x = 1210
Then men = 6/11 x = 660
And women = 5/11x = 550
ute of Change
What is the vertical change from Point A to Point B?
What is the horizontal change from Point A to Point B?
What is the rate of change shown on the graph? Give
the answer as a decimal rounded to the nearest tenth,
if necessary
Answer:
1
2
0.5
Step-by-step explanation:
Determine f(a+h)-f(a)/h for f(x)=x^2+5x
Answer:
2x + 5
ok.. slightly silly question...
you will eventually learn that this formula is the
formula for the "derivative" in calculus....
A[tex]x^{b}[/tex] becomes (a*b) [tex]x^{b-1}[/tex]
2x + 5
Step-by-step explanation:
What is the volume of the cone below?
A. 852 units
B. 3408 units
C. 10,224 units
D. 5112 units
Answer:
B. 3408pi
Step-by-step explanation:
formula volume of cone = 1/3 x pi x r x r x h
volume = 1/3 x pi x 12 x 12 x 71
= 3408pi
The volume of the cone is approximately 10,224 cubic units.
Option C is the correct answer.
What is a cone?It is a shape of a christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is V = (1/3)πr²h,
We have,
The formula for the volume of a cone is V = (1/3)πr²h,
where r is the radius of the base of the cone, h is the height of the cone, and π is a constant approximately equal to 3.14.
Substituting the given values, we get:
V = (1/3)π(12²)(71)
V = (1/3)π(144)(71)
V = (1/3)(3.14)(144)(71)
V = 10,223.04
Rounding this answer to the nearest whole number, we get:
V ≈ 10,224
Therefore,
The volume of the cone is approximately 10,224 cubic units.
Learn more about cones here:
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Which equation is equivalent to the given equation
X2-6x=8
Answer:
Step-by-step explanation:
x^2 －6x-8=0
PLEASE HELP!!!!!!!!!!!!!
Answer:
[tex]\text{C. }\pm \frac{1}{2}[/tex]
Step-by-step explanation:
Start by moving the 2 to the right (so we can multiply both sides by the denominator):
[tex]\frac{1}{2x^2-1}=-2[/tex]
Multiply both sides by [tex]2x^2-1[/tex]:
[tex]1=-2(2x^2-1),\\1=-4x^2+2[/tex]
Move everything to one side:
[tex]4x^2-2+1=0,\\4x^2-1=0,\\4x^2=1,\\x^2=\frac{1}{4},\\x=\boxed{\pm\frac{1}{2}}[/tex]
Answer:
the answer for this is C.
Zach bought a car for $20,000. He
paid a $5,000 down payment and
will pay $450 per month for 5
years. What type of liability is this
for Zach?
A. liquid
B. long-term
C. short term
D. budget
Answer:
The correct answer is B. Long-term.
Step-by-step explanation:
Since Zach has bought a car for $ 20,000 paying a down payment of $ 5,000 and monthly payments of $ 450 per month for 5 years, he will be paying a total of $ 32,000 for that car (5,000 + 450 x 12 x 5). Thus, the responsibility that Zach has incurred forces him to maintain his monthly payment obligation for 5 years, thus becoming a long term liability.
Please help
Expand 3(2x+1)
Answer:
6x + 3
Step-by-step explanation:
3(2x + 1)
=3*2x + 3*1
=6x + 3
20 PTS!! Which best describes the relationship between the line that passes through the points (1, -6) and (3,-2) and the line that
passes through the points (4, 8) and (6, 12)?
A. parallel
B. neither perpendicular nor parallel
C. same line
D. perpendicular
Answer:
A
Step-by-step explanation:
Lines are parallel...
8. The confectionary company "Sugary Sweet" wants to test how sweet and flavorful their participants like their candy. They manipulated three levels of sugar and also two levels of flavor in the candy for their participants to score their preference. State the hypotheses for their study.
Solution :
It is given that a company named "Sugary Sweet" wishes to test about the sweet and the flavorful that their participants like the candy.
There are Two levels of the flavor and three levels of sugar.
Thus it is a Two Way ANOVA test.
A two-way ANOVA test is used to test the effect of any two independent variables on the dependent variable.
[tex]$H_{01} : \text{Mean effect of the sugar are equal}$[/tex]
[tex]$H_{02} : \text{Mean effect of the flavor are equal}$[/tex]
[tex]$H_{01} : \text{There is no interaction between the sugar and the flavor}$[/tex]
Mr cruz is computing his monthly electrical consumption.Basedon his electric bill last month he was able to consume 00150kWh. When he checked his digital electric meter at present, the reading is 00200 kWh. How may killowats hour did Mr dela cruz consume this month? If the minimum charge for the first 10 kWh is P210.00 and the succeding consumed kWh costs P10, how much is Mr. Cruz total bill?
Answer:
610$
Step-by-step explanation:
According to the Question,
Based on his electric bill last month he was able to consume 150kwh. When he checked his digital electric meter at present, the reading is 200 kwh .Thus , Mr. Cruz Consumes 50kwh in this month .
Given, the minimum charge for the first 10 kWh is $210 . & the succeeding consumed kWh costs $10 .
The Total Bill Of Mr. Cruz is ⇒ 210 + (50-10)×10 ⇔ 610$
If the first three Fibonacci numbers are given as [tex]x_{1} =1[/tex], [tex]x_{2}=1[/tex] and [tex]x_{2} = 2[/tex], what is the value of n for which [tex]x_{n} + x_{n+1}=55[/tex]? (see attachment)
Answer:
n = 8
Step-by-step explanation:
Continuing the sequence using
[tex]x_{n}[/tex] + [tex]x_{n+1}[/tex]
x₄ = x₂ + x₃ =1 + 2 = 3
x₅ = x₃ + x₄ = 2 + 3 = 5
x₆ = x₄ + x₅ = 3 + 5 = 8
x₇ = x₅ + x₆ = 5 + 8 = 13
x₈ = x₆ + x₇ = 8 + 13 = 21
x₉ = x₇ + x₈ = 13 + 21 = 34
x₁₀ = x₈ + x₉ = 21 + 34 = 55 ← with n = 8
Answer:
The Fibonacci numbers are
1
1
2
3
5
8
13
21
34
55
The eighth Fibonacci Number is 21, the ninth is 34 and the tenth is 55.
So Fibonacci # 8 + Fibonacci Number #9 = Fibonacci# 10
21 + 34 = 55
If you want to read a little bit more about Fibonacci numbers, try this page: http://www.1728.org/fibonacci.htm
that's my website :-)
Step-by-step explanation:
find the slope of the line (-5,7) (-3,4)(-1,1)(1,-2)
Answer:
-3 is the gradient.
BONUS: y-interspet is -1
Step-by-step explanation:
The gradient is what you mean by slope I am guessing?
well, the line that contains those points will more or less look like the one in the picture below, and we can use any two points from that set to get its slope, say hmmmmm let's use (-5,7) and (1,-2)
[tex](\stackrel{x_1}{-5}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}}\implies \cfrac{-9}{1+5}\implies \cfrac{-9}{6}\implies -\cfrac{3}{2}[/tex]
Where is point B? (im also not good at these at all)
Answer:
[tex]{ \tt{on \: x - axis : 3}} \\ { \tt{on \: y - axis : 0}} \\ = > \: { \tt{x, \: y}} \\ { \boxed{ \bf{substitute \: for \: x \: and \: y}}} \\ \therefore \: { \boxed{ \bf{answer : } \:{ \tt {(3, \: 0)}}}} \\ \\ { \underline{ \blue{ \tt{⚜becker \: jnr}}}}[/tex]
I have a bag of coins.In it, one third is gold, one fifth of them are silver, two seventh are bronze the rest are copper. My bag can only fit 200 coins how many coins do i have in my bag?
Answer:
Copper = x= 36.19
Step-by-step explanation:
The number of copper is unknown
Gold = 1/3
Silver = 1/5
Bronze =2/7
Copper = x
Total coins = 200
Gold = 1/3 of 200
= 1/3 × 200
= 200/3
= 66.67
Silver = 1/5 × 200
= 200/5
= 40
Bronze = 2/7 × 200
= 400/7
= 57.14
Total = gold + silver + bronze + copper
200 = 66.67 + 40 + 57.14 + x
200 = 163.81 + x
200 - 163.81 = x
x = 36.19
Copper = x= 36.19
It's urgent i need help someone help me!
Answer:
x=50, y=20
Step-by-step explanation:
50-20=30, 50+20=70