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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Which expression is a trinomial of degree 1?
Answer:
A
Step-by-step explanation:
Answer:
"C"
trinomial means three parts, degree 1 means highest exponent is 1
x & y are of degree 1 and there are three parts
Step-by-step explanation:
Question 9 of 10
Which polynomial represents the difference below?
(8x2 +9) - (3x2 + 2x + 5)
Step-by-step explanation:
= (8x² + 9) - (3x² + 2x + 5)
= 8x² + 9 - 3x² - 2x - 5
= 5x² - 2x + 4
what is energy efficiency
Answer:
The goal to reduce the amount of energy used to provide products and services; saving the earth vibes.
Find all solutions to the equation in the interval [0, 2pie] Enter the solutions in increasing order.
sin 2x = sin x
=============================================
Work Shown:
sin(2x) = sin(x)
sin(2x) - sin(x) = 0
2*sin(x)*cos(x) - sin(x) = 0
sin(x)*(2cos(x) - 1) = 0
sin(x) = 0 or 2cos(x)-1 = 0
sin(x) = 0 or cos(x) = 1/2
Using the unit circle, the solutions to sin(x) = 0 are x = 0, x = pi, x = 2pi
Also, the solutions to cos(x) = 1/2 are x = pi/3, x = 5pi/3
So the entire solution set on the interval [0,2pi] is {0, pi/3, pi, 5pi/3, 2pi} when written in increasing order.
All solutions to the equation in the interval [0, 2[tex]\pi[/tex]] is {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}.
What is solution to an equation?A solution is an assignment of values to the unknown variables that makes the equality in the equation true.
As sin2x = 2 sinx cosx,
sin2x = sinx is equivalent to
2 sinx cosx = sinx or 2 sinx cosx − sinx = 0 or
sinx (2cosx − 1) = 0 i.e.
either sinx = 0 and x = 0, π, 2π
or 2cosx − 1 = 0 i.e. cosx = [tex]\frac{1}{2}[/tex] i.e. x = [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]
Hence, solution to an equation is x = {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}
Learn more about solution to an equation here
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A square fits exactly inside a circle with each of the vertices being on the circumference of the circle. The square has sides length of X cm. The area of the circle is 56cm^2. Work out the value of x. Give your answer correct to 3sf
Answer: The value of x is 5.970.
Step-by-step explanation:
Given: The square has sides length of X cm.
Let r be the radius of the circle.
The square fits exactly inside a circle with each of the vertices being on the circumference of the circle.
Then diagonal of square = diameter of circle
i.e. [tex]\sqrt{2}x= 2r[/tex] [Diagonal of square = [tex]\sqrt{2}[/tex](side)]
i.e. [tex]r=\dfrac{x}{\sqrt{2}}[/tex]
area of circle =[tex]\pi r^2[/tex]
i.e. [tex]56=\frac{22}{7}(\frac{x}{\sqrt{2}})^2[/tex]
[tex]56=\frac{22}{7}\times\frac{x^2}{2}\\\\\Rightarrow\ x^2= \dfrac{7}{11}\times56\\\\\Rightarrow\ x^2=35.636\\\\\Rightarrow\ x=\sqrt{35.636}\approx5.970[/tex]
Hence, the value of x is 5.970.
What am I doing wrong? I've tried every conceivable answer, I thought I was good at this type of math but this program keeps proving me wrong. Please help.
Answer:
Step-by-step explanation:
A new bank customer with $3,000 wants to open a money market account. The bank is offering a simple interest rate of 1.8%. How much interest will the customer earn in 10 years? b. What will the account balance be after 10 years?
Answer: See explanation
Step-by-step explanation:
The Simple Interest will be calculated as:
= P × R × T
= $3000 × 1.8% × 10.
= $3000 × 0.018 × 10
= $540
The interest that the customer earn in 10 years is $540.
Then, the account balance after 10 years will be:
= Principal + Interest
= $3000 + $540
= $3540
Therefore, the account balance will be $3540
Solve for the class width if R = 40 and I = 7.
A. 5
B. 6
C. 8
D. 7
Answer:
A.5
Step-by-step explanation:
divide 40 by 7 which is equal to 5
2. Out of 500 students appearing in an examination, the number of students who passed in mathematics only is twice the number of students who passed in science only. If 120 students passed in both subjects and 140 students failed in both subjects, then Find the ratio of the students who passed in mathematics to the students who passed in science.
Answer:
60 to 60
Step-by-step explanation:
It says 120 students passed in both and mathematics is only twice so 120 divided by 2 is 60
An arrow is shot vertically upward from a platform 19ft high at a rate of 163ft/sec. When will the arrow hit the ground? Use the formula: h=−16t2+v0t+h0. (Round your answer to the nearest tenth.)
Answer: 10.3 s
Step-by-step explanation:
Given
The height of the arrow is given by [tex]h=-16t^2+v_ot+h_o[/tex]
At [tex]t=0, h=19\ ft[/tex]and [tex]v_o=163\ ft/s[/tex]
When arrow hits ground, h becomes 0 i.e.
[tex]\Rightarrow 0=-16t^2+163t+19\\\Rightarrow 16t^2-163t-19=0\\\\\Rightarrow t=\dfrac{163\pm \sqrt{(-163)^2+4(16)(19)}}{2(16)}\\\\\Rightarrow t=-0.115,10.30\ s[/tex]
Neglecting the negative value of t
So, the arrow hits the ground after 10.30 s
6. You begin work at 8:30 am. You take an unpaid lunch break from 11:45 am to 12:30 pm
You also take two 15-minute unpaid coffee breaks during the day. Your work day ends
at 5:00 pm. How many hours are you paid?
a) Express your answer in hours and minutes.
b) Express your answer as a decimal in hours only.
Answer:
7 hours 15 minutes
7.25 hours
Step-by-step explanation:
Break from 11:45 am to 12:30 pm = 45 minutes
Two 15-minute unpaid coffee breaks during the day = 30 minutes
Total break hours = 45 minutes + 30 minutes
= 1 hour 15 minutes
Total work day hours from 8:30 am to 5:00 pm = 8 hours 30 minutes
How many hours are you paid?
Total hours paid = Total work day hours - Total unpaid break hours
= 8 hours 30 minutes - 1 hour 15 minutes
= 7 hours 15 minutes
b) Express your answer as a decimal in hours only
7 hours 15 minutes as a decimal
15 minutes to hour = 60 minutes/15 minutes
= 1/4
= 0.25 hours
7 hours 15 minutes as a decimal = 7 hours + 0.25 hours
= 7.25 hours
find the value of √(6-3√5)
Answer:
There is no answer
Step-by-step explanation:
because 3√5=6,7082039232 > 6
So 6-3√5 < 0
But √x always >0
So there is no answer
5(4)-4/2 ??
Some know how to respond
Answer:
19 1/2??? Read explanation
Step-by-step explanation:
I am not sure entirely by your formatting when you put it into Brainly but since 5x4=20 and 20-1/2 = 19 1/2, the answer would be 19 1/2 but I am not sure due to the format.
Hope this helps and if it does, don't be afraid to rate my answer as well as maybe give it a "Thanks"? (Or even better a "Brainliest"). And if it’s not correct, I am sorry for wasting your time, and good luck finding the correct answer :)
Answer:
18
20 -2 = 18
Step-by-step explanation:
10.)A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet and a height of 12 inches. The pool is filled with water to 2/3 of its height. Determine and state the volume of the water in the pool, to the nearest cubic foot. One cubic foot equals 7.48 gallons of water. Determine and state, to the nearest gallon, the number of gallons of water in the pool.
Answer:
165.47≈165 Gallons of Water
Step-by-step explanation:
According To the Question,
Given, A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet (or) 6.5 feet (radius is 3.25 feet) and a height of 12 inches(1 feet).The pool is filled with water to 2/3 of its height (H= 2/3 feet) .
Volume of Cylinder = π×R²×H , now put values, we get
Volume = 3.14×3.25²×2/3
Volume = 22.122 foot³ .
And, One cubic foot equals 7.48 gallons of water
Thus, 22.122 cubic foot equals to 165.47≈165 gallons of water .
Helppppppppppp:)))))))))
Hi there!
We are given the set of ordered pairs below:
[tex] \large \boxed{(3, - 1),(2, - 2),(0,2),(2,1)}[/tex]
1. What is the domain?
Domain is a set of all x-values in one set of ordered pairs. So what are the x-values that I am talking about? In ordered pairs, we define x and y which both have relation to each others which we can write as (x,y). That's right, the domain is set of all x-values from ordered pairs.Therefore, we gather only x-values from (x,y). Hence, the domain is {3,2,0,2}. Whoops! Something is not right. As we learn in Set Theory that we don't write the same or repetitive in a set. Hence, the actual domain is {0,2,3}
2. What is the range?
Because domain is set of all x-values. Then what do you think the range is? That's right! The range is set of all y-values. If you got this right before looking up the underlined words then a handclap for you! So how do we find range? Simple, we just do like finding the domain in the Q1, except we gather the y-values in (x,y) instead and make sure that we don't write same number!Therefore, gather y-values from the ordered pairs. Hence, the range is {-2,-1,1,2}
3. Is the relation a function?
All functions are relations but not all relations are functions. Function is a set of ordered pairs where domain is not repetitive or in a set, there cannot be more than one same value. Consider the following relation: (1,1),(1,2) - Oh, looks like in a set of ordered pairs, there are two same domains which make it only a relation, and not a function. On the other hand, (1,1),(2,2) - Looking good! No same or repetitive domain, making it indeed a function.Consider the domain from Q1 and see if there are two same values of x in a set. Looks like the relation is not a function since there are same x-values which are 2 in a set, making it only a relation. Hence, the relation is not a function.
These are all 3 answers along with an explanation. Let me know if you have any doubts regarding Relations and Functions.
From the Q1's answer, there are two bold texts, please choose the second bold text to answer (the one with underline) and not the first one (the one with same 2's).
Good luck on your assignment, have a nice day!
The function f(x) = 4x + 8 represents the distance traveled by a herd of elephants in miles. The function g(x) = x − 1 represents the time the herd traveled in hours. Solve f divided by g of 4, and interpret the answer.
Answer:
[tex](f/g)(4)=8[/tex]
Interpretation: 4 elephants traveled at a speed of 8 miles per hour
Step-by-step explanation:
Given
[tex]f(x) = 4x + 8[/tex]
[tex]g(x) = x -1[/tex]
Required
[tex](f/g)(4)[/tex]
This is calculated as:
[tex](f/g)(4)=\frac{f(4)}{g(4)}[/tex]
We have:
[tex]f(x) = 4x + 8[/tex]
[tex]f(4) = 4 * 4 + 8 =24[/tex]
[tex]g(x) = x -1[/tex]
[tex]g(4) = 4 - 1 = 3[/tex]
So:
[tex](f/g)(4)=\frac{f(4)}{g(4)}[/tex]
[tex](f/g)(4)=\frac{24}{3}[/tex]
[tex](f/g)(4)=8[/tex]
Answer:
Answer:C) 8; The elephants’ rate in miles per hour
Step-by-step explanation:
First write the question as an equation that can be solved to give you a numerical answer.
[f(4)=4(4)+8] / [g(4)=(4)-1]
Then solve the equation.
24/3=8
Finally use background information to give you the context.
Since the problem gives you the function for distance and the function for time then it can be concluded that the context will be the elephants’ rate in miles per hour
Step-by-step explanation:
HELP PLEASE!!!!!
A car owner decides to upgrade from tires with a diameter of 24.3 in to tires with a diameter of 26.1 in. If she doesn't update the onboard
computer, how fast will she actually be traveling when the speedometer reads 65 mph?
Although we want to solve for the linear speed of the upgraded tires, we do not have enough information for that. To fill up the formula v = rw, we only have the upgraded tires
r. but we do not know yet their w. However, since the speedometer counts rotations per hour and uses that to get the v of older tires, we can use that information to find the w
of the upgraded tires. Thus, let us solve first for w using the radius of the old tires and the reading of the speedometer.
Note: Do not forget that you are given the diameter and must still use that to get the radius. Also, do not forget that the diameter is given in inches, and you must convert that to miles, in order to be able to
cancel the time units. (1 mi = 63, 360 in)
Answer:
8yr7xy9c8ze6X9yc9y8d58f99ff68g
find the value of k if the line 2x-y+k=0 may touch the circle x^2 + y^2=5
Answer:
k = ±4
Step-by-step explanation:
Equation of the circle is:
x² + y² = 5
This means from the general form of equation of a circle;
Centre coordinates is (0, 0) and radius is; √5.
The line 2x - y + k = 0 touches the circle. Thus, perpendicular distance from centre of the circle to this line is equal to the circle radius;
Thus;
|((2 - 0) - (1 × 0) + k)|/(√(2² + 1²)) = √5
|(1 + k)|/√5 = √5
Multiply both sides by √5 to get;
|1 + k| = 5
|k| = 5 - 1
k = ±4
Volume How many fluid ounces are in each size?
1 cup = 8 oz. 1pint = 2 cups. 1 quart = 2 pints. 1 gallon = 4 quart
Half gallon = __________fl oz.
What is the product of 4xy and y^2 + 2x
Answer:
C
Step-by-step explanation:
4xy(y^2 + 2x) Remove the brackets (distributive law)
4xy^3 + 8x^2y
You have to turn the two terms around to see the correct answer. That's perfectly alright when dealing with addition of pluses.
8x^2y + 4xy^3
A city has a 20% chance of having a flood in any given decade. The table shows the results of a simulation using random numbers to find the experimental probability that there will be a flood in the city in at least 1 of the next 5 decades. In the table below, 1 represents a decade with a flood. The numbers 2 to 5 represents a decade without a flood.
Answer:
4/10=40%
Step-by-step explanation:
What is the value of x?
OA 73°
OB. 71°
OC. 70°
OD. 68°
Answer:
OB.71
Step-by-step explanation:
correct me if I'm wrong
Answer:C.70
Step-by-step explanation:
3
If x=
)
X Х
find the value of x-2
3
2.
Step-by-step explanation:
Answer
Open in answr app
Correct option is
B
±2
x=3+22 x1=3+221×3−223−22
=3−22
(x−21)2=x+x1−2
=3+22+3−22−2=4
So, x−x1=4=±2 Ans
Please answer these graph questions for the following! (✿◡‿◡)
a) how far did he go before stopping?
b) which part of the journey is the traveling the fastest a, b, c, or d?
c)what was his speed on the last section of his journey (d)?
Answer:
60
a
30
Step-by-step explanation:
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Please help ASAP
Will give Brainliest
Want explanation
Answer:
1.73 or 3+√6/√3+√2
Step-by-step explanation:
1. Simplify the Numerator...3+ the square root of 6 cannot be simplified, so the answer is 5.45
2. Simplify the Denominator.
[tex]17 \sqrt{3} - 2 \sqrt{4} \sqrt{4} \sqrt{2} + 3 \sqrt{9} \sqrt{2} - 4 \sqrt{4} \sqrt{4} \sqrt{3} = 17 \sqrt{3} - 8 \sqrt{2} + 9 \sqrt{2} - 16 \sqrt{3} = \sqrt{3} + \sqrt{2} = 3.15[/tex]
3. Divide. 5.45/3.15= 1.73
Complete the proof that
Answer:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
ΔSCW ≅ ΔTUW [tex]{}[/tex] Given
[tex]\overline {SV}[/tex] ≅ [tex]\overline {TU}[/tex] [tex]{}[/tex] CPCTC
[tex]\overline {SW}[/tex] ≅ [tex]\overline {TW}[/tex] [tex]{}[/tex] CPCTC
[tex]\overline {WV}[/tex] ≅ [tex]\overline {UW}[/tex] [tex]{}[/tex] CPCTC
∠SVW ≅ ∠TUW [tex]{}[/tex] CPCTC
SU = SW + UV [tex]{}[/tex] Additive property of Length
TU = TW + VW [tex]{}[/tex] Additive property of Length
SU = TW + VW [tex]{}[/tex] Substitution
SU = TV [tex]{}[/tex] [tex]{}[/tex] Transitive property
ΔSTV ≅ ΔTSU [tex]{}[/tex] SAS
∠TSV ≅ ∠STU [tex]{}[/tex] CPCTC
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
ΔSCW ≅ ΔTUW [tex]{}[/tex] Given
[tex]\overline {SV}[/tex] ≅ [tex]\overline {TU}[/tex] [tex]{}[/tex] Congruent Parts of Congruent Triangles are Congruent
[tex]\overline {SW}[/tex] ≅ [tex]\overline {TW}[/tex] [tex]{}[/tex] Congruent Parts of Congruent Triangles are Congruent
[tex]\overline {UV}[/tex] ≅ [tex]\overline {VW}[/tex] [tex]{}[/tex] Congruent Parts of Congruent Triangles are Congruent
∠SVW ≅ ∠TUW [tex]{}[/tex]Congruent Parts of Congruent Triangles are Congruent
SU = SW + UV [tex]{}[/tex] Additive property of Length
TU = TW + VW [tex]{}[/tex] Additive property of Length
SU = TW + VW [tex]{}[/tex] Substitution
SU = TV [tex]{}[/tex] Transitive property
ΔSTV ≅ ΔTSU [tex]{}[/tex] Side-Angle-Side rule of congruency
∠TSV ≅ ∠STU [tex]{}[/tex] Congruent Parts of Congruent Triangles are Congruent
Please help ASAP !!!
Answer:
C
Step-by-step explanation:
the domain is for which values of x is that function defined (is that a valid function).
the range is what values that function can produce based on all the different x-values as input.
so, checking option A
that means all x values are negative.
that means all values inside the square root are negative.
the resulting function values are a discussion class of numbers and not part of the interval of (0, infinity).
so, it cannot be A.
checking option B
the domain range includes the value 6 for x.
but that would make this function for x=6 an invalid expression of 1/0
so, it cannot be B.
checking option C
the value range for x (domain) is x>6 (and excluding x=6).
and the result range is all positive numbers including 0.
there is no violation of any function principle.
the answer is C.
checking option D
similar to C, but the result range is defined as all numbers, negative and positive.
but for the domain the function can never produce negative numbers.
so, it is not D.
Find the slope of a line through the points (0,0) and (2, 9). Round your
answer to 1 decimal place.
SLope = y2-y1 / x2-x1
Answer:
Slope = 4.5
Step-by-step explanation:
We need to find the slope of a line through the points (0,0) and (2, 9).
We know that, the slope of a line is given by :
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have, x₁ = 0, x₂ = 2, y₁ = 0 and y₂ = 9
Put all the values,
[tex]m=\dfrac{9-0}{2-0}\\\\m=4.5[/tex]
So, the slope of the line is 4.5.
help pls i need this asap
Answer:
I got 45 degrees
Step-by-step explanation:
knowing that where T is is 90 degrees and a triangle always= 180 degrees I just split 90 in half and got 45. I could be wrong but I hope this helps :)
Write the equation of a line passing through (4,1) and parallel to y = 3/2x + 3.
Answer:
y = 3/2x - 5
Step-by-step explanation:
y = 3/2x + b
1 = 3/2(4) + b
1 = 6 + b
-5 = b
