80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible. This can be obtained by converting the given statements into algebraic equation.
Find the required equation for the given question:Here in the question it is given that,
Athlete trains for 80 min each day,that is each day the athlete spends 80 min.
We have to assume the variable d the number of days the athlete spends training.Finally we have to find an equation that relates the number of days d that the athlete spends training when the athlete trains for 400 min.So we can write that,
400 min is the time spent by the athlete
400 min = number of days × time spent by the athlete in one day
400 min = d × 80
⇒ 80d = 400
Hence 80d = 400 is the equation that relates the number of days d that an athlete spends training when the athlete trains for 400 min given that athlete trains for 80 min each day for as many days as possible.
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Select all the correct answers. If the measure of angle 0 is 5(pi)/4, which statements are true?
The Measure of the reference angle is 45
cos(0)= √ 2/2
tan(0)=1
sin(0)=√ 2/2
the measure of the referance angle is 30
the measure of the referance angle is 60
Finding the equivalent angle of [tex]\theta[/tex], the correct statements are given as follows:
The Measure of the reference angle is 45.[tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].[tex]\tan{\theta} = 1[/tex][tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, the given angle is as follows:
[tex]\theta = \frac{5\pi}{4}[/tex]
It is on the third quadrant, as it is between pi and 1.5 pi, hence the equivalent on the first quadrant, also known as the reference angle, is given by:
[tex]\frac{5\pi}{4} - \pi = \frac{5\pi}{4} - \frac{4\pi}{4} = \frac{\pi}{4}[/tex]
The angle of 45º has equal sine and cosine, and tangent of 1, hence the correct statements are:
The Measure of the reference angle is 45.[tex]\cos{\theta} = \frac{\sqrt{2}{2}}[/tex].[tex]\tan{\theta} = 1[/tex][tex]\sin{\theta} = \frac{\sqrt{2}{2}}[/tex].More can be learned about equivalent angles at https://brainly.com/question/24787111
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Answer:
The measure of the reference angle is 45 degrees
tan(theta) = 1
Step-by-step explanation:
Find the value of x.
50°
(5x + 30)%
21⁰
Distributions of data can be characterized along three aspects or dimensions. Which aspect represents the spread or distribution of the data?
The distributions of data can be characterized along three aspects or dimensions, namely location, spread, and shape. The spread (variance, range, interquartile range) aspects represent variation of the data or the spread of the data distributions.
About the Distribution of Data:
The idea of a distribution is fundamental to illustrating any output from a production process. Any manufacturing process output will not always produce the same value when it is measured, leading to distributions.
The measured values will naturally disperse around a central tendency value. A distribution is the name given to this dispersion around a core value. It is characterized by 3 aspects - location, spread, and shape.
Mean or median represent the location of the distribution numerically. Most common numerical measures that represent the spread are variance, range, and interquartile range. Skewness or kurtosis tell about the shape of the distribution.
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How do you expressed the difference in the measures of center as a multiple of the measure of variation in a box plot when the IQ ours are different
hich is the best approximation for the solution of the system of equations?
y = A system of equations. y equals negative StartFraction 2 over 5 EndFraction x plus 1. y equals 3 x minus 2.x + 1
y = 3x – 2
the solution of the system of linear equations is:
x = 6/11
y = -4/11
How to solve the system of equations?
Here we have the system of equations:
y = (-5/2)*x + 1y = 3x - 2To solve the system, we can see that y is already isolated in both sides, then we get:
(-5/2)*x + 1 = 3x - 2
Now we can solve this for x:
(-5/2)*x + 1 = 3x - 2
2 + 1 = 3x + (5/2)*x
3 = (6/2)*x + (5/2)*x
3 = (11/2)*x
(2/11)*3 = x
6/11 = x
To get the value of y, we evaluate any of the lines in x = 6/11
y = 3*(6/11) - 2 = 18/11 - 2 = 18/11 - 22/11 = -4/11
Then the solution of the system of linear equations is:
x = 6/11
y = -4/11
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Kathy needs money for her trip to Europe. If she has $300$ US dollars in the bank but wants to withdraw half of it in British pounds and half of it in euros, how many more euros than pounds will she have
Kathy has 22 more Euros than British pounds.
Linear equation is an algebraic equation that is a representation of the straight line. Linear equations are composed of variables and constants. These equations are of first-order, that is, the highest power of any of the involved variables i.e. 1. It can also be considered as a polynomial of degree 1. Linear equations containing only one variable are called homogeneous equations. The corresponding variable is called the homogeneous variables.
For instance,
x + 2y = 3 is a linear equation in two variables.x + y + z = 8 is in three variables.x + y2 = 1 is not a linear equation because the highest power of y is 2.300 / 2 = 150 dollars.
150 /1.64 = 91.46 British pounds
150 /1.32 =113.64 Euros
113.64 - 91.46 =22.18 ≅ 22
Thus Kathy has 22 more Euros than British pounds.
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Use the recursive formula to find the first five terms in the arithmetic sequence.
Answer:
is 54, 45, 36, 27, 18
Step-by-step explanation:
Recursive formulas give us two pieces of information:
1. The first term of the sequence
2. The pattern rule to get any term from the term that comes before it
In the formula given,
n is any term number
f(n) is the nth term
This means
f(1) is the first term
f(f-1) is the term before the nth term
To find the first five numbers in this arithmetic sequence, we know the formula has given us these two pieces of information:
1. The first term is 54
2. The rule to get any term from its previous term is -9
So, we know the sequence for this formula is 54, 45, 36, 27, 18 because starting off with 54, then minus 9 from every sum gives us the following equations
54-9=45
45-9=36
36-9=27
27-9=18
In the circle below, if AD is a diameter, and the length of chord BC = 36, find the length of the segment BP.
Answer:
b. 18
Step-by-step explanation:
The perpendicular bisector of a chord is a diameter of the circle. Conversely, if the diameter is perpendicular to a chord, it also bisects it.
Segment lengthsBC = BP +PC
BC = 2×BP . . . . . . . BP = PC
BP = BC/2 = 36/2 = 18 . . . . . . . divide by 2; substitute given values
The length of segment BP is 18 units.
Research that analyzes a portion of an entire population is carried out on a(n):____.
a. sample.
b. population.
c. census.
d. survey
Option (a) Sample
Sample is the research that analyzes a portion of an entire population.
A sample is a condensed, controllable portion of a bigger group. It is a subgroup of people with traits from a wider population. When populations are too big for a statistical test to include every potential participant or observation, samples are utilized.
By permitting researchers to obtain the same results from a sample as they would from the population, sampling helps researchers save money. Non-random sampling is much less expensive than random sampling since it reduces the expense of locating participants and obtaining their data.
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number 7 please and don t care abt others lol
Answer:
The question does not make a lot of sense to me but I think this is how its supposed to be done
so there are 15 shirts
2 are sold at 3.90, 2 x 3.90 = 7.8
15-2= 13 t shirts
13 sold at 4.70, 13 x 4.70 = 61.1
amount of money made is = 7.8 + 61.1
= 68.9
PLEASE HELP IM SO STUCK
Answer:
y-9=-4(x+2)
Step-by-step explanation:
The point-slope formula is:
y-y1=m(x-x1)
m=-4 and use the point (-2, 9)
x1 y1
Plug in the information.
y-9=-4(x+2)
This is the equation written in point-slope form using the point (-2, 9).
Hope this helps!
2(x+1)=10 what's x please best example
Answer:
x = 4
Step-by-step explanation:
1.Distribute
2. Subtract 2 from both sides
3. Simplify
4. Divide both sides by same factor
5. Simplify
x = 4
Answer: 4
Step-by-step explanation:
We have to try getting x by itself to solve for it. Since we have two sides that are equal to each other, we can add, subtract, multiply, and divide anything on both sides to try to isolate x.
[tex]2(x+1)=10[/tex]
We can first divide the left side and the right side by 2. This would remove the 2 being multiplied on the outside.
[tex]\frac{2(x+1)}{2}=\frac{10}{2}\\x+1=10\div 2\\x+1=5[/tex]
Now, we have a + 1 on the left side that we need to remove to get x by itself. If we are adding something, we can remove that by subtracting the same thing. Hence, we can subtract 1 from both sides to remove the + 1.
[tex]x+1=5\\x+1-1=5-1\\x+0=4\\x=4[/tex]
After all that simplifying, we get that x equals 4.
Compute the surface area obtained by rotating the curve y = 3 x , for x is in [1, 125] about the y-axis
Answer:
Given,
y=x³ ,0≤x≤2
We have to find the surface area of the surface by rotating the curve about the x axis.
For rotation about the x axis, the surface area formula is given by-
s=2π∫ᵇₐ y√1+(y)² dx
y=x³
y'=3x²
By rotating the curve y=x³ about the x axis in the interval [0,2]
s=2π∫₀²(x³)√1+(3x²)² dx
let u=1+9x⁴
du=36x³dx
dx/36x³
Substituting u and du in the integral,
s= 2π∫₀²(x³)√u du/36x³
s= 2π∫₀²√u du
s= 2π/36.2/3[u.3/2]₀²
s= π/27[(145)³/²-(1)³/²]
s= π/27 [1746.03-1]
s= π/27 [1745.03]
s= 64.67π
s= 64.67(3.14)
s=203.06 square units.
therefore, the exact surface area is 203.06 square units.
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Answer:
In order to find the surface area obtained by rotating the curve we need to find surface area for rotation along x axis then substituting values in the integral.
Given: y=3x, for x is in [1,125] about the y axis.
y=x³ ,0≤x≤2
Lets find the surface area of the rotating curve,
Finding surface area for rotation along x-axis,
s=2π∫ᵇₐ y√1+(y)² dx
y=x³
y'=3x²
By rotating the curve y=x³ about the x axis in the interval [0,2]
s=2π∫₀²(x³)√1+(3x²)² dx
Assuming u =1+9x⁴
du=36x³dx
=dx/36x³
Substituting respective values of u and du in the integral,
s= 2π∫₀²(x³)√u du/36x³
s= 2π∫₀²√u du
s= 2π/36.2/3[u.3/2]₀²
s= π/27[(145)³/²-(1)³/²]
s= π/27 [1746.03-1]
s= π/27 [1745.03]
s= 64.67π
s= 64.67(3.14)
s=203.06 square units.
hence, the surface area is 203.06 square units.
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Q11) kelly puts $350 in a savings account. the savings account accrues interest at a flat rate of 1.05% a month. how much will the account be worth in 7 months ?
The account be worth in 7 months is 375.725 .
What is the amount in simple interest?Amount (A) is the total money paid back at the end of the time period for which it was borrowed. The total amount formula in case of simple interest can also be written as: A = P(1 + RT)
Here, A = Total amount after the given time period.
Given that,
P = $350, R = 1.05%, T = 7 month
The simple interest equation uses "t" as years, but is just cycles, using an APR rate.
now, if we never mind "t" as years and just use it as an interest cycle, then we can say the rate is 1.05% and the period is 7 cycles.
A = P(1 + RT)
= 350(1+1.05%×7)
= 350(1+0.0105×7)
= 350(1+0.0735)
= 350×1.0735
A = $375.725
Hence, The account be worth in 7 months is 375.725 .
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A person spends 1/5 of his salary on rent, 3/7 on food, 1/3 on other expenses and saves the rest. If she earns $21,000 per month, how much does she save per year?
Answer:
$9600 saving / year
Step-by-step explanation:
1/5 of $21000 = 21000 / 5 = $4200 / month on rent
3/7 of $21000 = (21000 / 7) x 3 = $9000 / month on food (shocking right :) food is expensive)
1/3 of $21000 = 21000 / 3 = $7000 on other expenses / month
total savings/month = salary/month - rent/month - food/month - other expenses/month
total savings/month = 21000 - 4200 - 9000 - 7000
total savings/month = $800
BUT the question asks for savings per year. therefore, we must multiply the savings per month by total months per year (12)
800 x 12 = $9600
the person's total savings per year, with a salary of $21000 per month, is equal to $9600 per year
Determine the 95% confidence interval for the difference of the sample means. then complete the statements.
Answer:
Confidence Level z*-value
90% 1.645 (by convention)
95% 1.96
98% 2.33
99% 2.58
Step-by-step explanation:
the difference in sample means is 0.1, and the upper end of the confidence interval is 0.1 + 0.1085 = 0.2085 while the lower end is 0.1 – 0.1085 = –0.0085.
Please help I need the answer
The maximum value of P = x + 6y subject to the constraints is 9
How to determine the maximum value?The objective function is given as:
P = x + 6y
The constraints are given as:
2x + 4y ≤ 10
x + 9y ≤ 12
x≥0 y≥0
Rewrite 2x + 4y ≤ 10 and x + 9y ≤ 12 as equations
2x + 4y = 10
x + 9y = 12
Divide 2x + 4y = 10 through by 2
x + 2y = 5
Subtract x + 2y = 5 from x + 9y = 12
x - x + 9y - 2y = 12 - 5
Evaluate the difference
7y = 7
Divide by 7
y = 1
Substitute y = 1 in x + 2y = 5
x + 2(1) = 5
Solve for x
x = 3
So, we have
(x, y) = (3, 1)
Substitute (x, y) = (3, 1) in P = x + 6y
P = 3 + 6 * 1
Evaluate
P = 9
Hence, the maximum value of P = x + 6y subject to the constraints is 9
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factor the gratest common factor: -5k^2+20k-30
Answer:
±5
Step-by-step explanation:
-5k²+20k-30
if u look at the equation ±5 are the greatest common factors so we ±5(±k²±4k±6)
In the diagram below, if arc AB measures 62 ° and arc DC measures 102 °, find the measure of < APD.
The measure of angle < APD = 98°. That is option D
Calculation of the missing angleAngle APB = 62°
Angle DPC = 102°
But length AD = BC
Therefore, angle APD = BPC
Also, the angle at a point = 360°
The sum of the angles given = 102 + 62 = 164°
The remaining angle = 360 - 164 = 196°
Therefore angle APD = 196/2 = 98°
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Under his cell phone plan, christopher pays a flat cost of $59 per month and $3 per gigabyte. he wants to keep his bill at $62.90 per month. how many gigabytes of data can he use while staying within his budget?
The number of gigabytes of data that Christopher can use while staying within his budget exists 1.3 gigabytes.
How many gigabytes of data can he utilize while staying within his budget?The number of gigabytes of data that Christopher can use while staying within his budget is 1.8 gigabytes.
Based on the information, we get
59 + (3 × g) = 62.90
59 + 3g = 62.90
simplifying the equation, we get
3g = 62.90 - 59
3g = 3.9
Divide both sides by 3, and we get
3g/3 = 3.9/3
g = 1.3
The number of gigabytes of data that Christopher can use while staying within his budget exists 1.3 gigabytes.
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please answer my question
Considering the box-plots, the means for the data-sets are given as follows:
Data-set A: 5.5Data-set B: 5.What does a box-plot shows?Each shows the number of times each measure appears.
Hence, the mean of data-set A is given as follows:
mA = (3 + 4 x 3 + 5 x 2 + 6 x 2 + 7 x 3 + 8)/(1 + 3 + 2 + 2 + 3 + 1) = 5.5.
For data-set B, the mean is:
mB = (2 x 4 + 2 x 5 + 2 x 6)/(2 + 2 + 2) = 5.
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If a writer writes 5,000 words per day to their novel, spending at least 6 hours to do so, and their goal is 120,000, how many days and hours total would it take to achieve their goal? The best explanation and answer gets Brainliest!
Answer:
6 days
Step-by-step explanation:
if they are writing at 5,000 words per 6 hours, we divide 120,000 by 5,000 and then multiply by 6: 120,000/5,000 = 24, 24*6 = 144 total hours
There are 24 hours in a day: 144/24 = 6
I reallly badly need help
Answer:
You can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°
Step-by-step explanation:
The above is a cyclic quadrilateral.
What is a cyclic quadrilateral?A Cyclic quadrilateral is having all the vertices of a quadrilateral ( four sided figure) inside a circle, that is a quadrilateral inscribed in a circle.
To find either x or y, we should note:
The sum of opposite angles of a cyclic quadrilateral is 180° or Angles in opposite segment are supplementary.
Therefore,
2x + 2x + 4= 180
4x = 180 - 4
4x = 176
x = 44°
To find y
3y + 8 + y = 180°
4y = 180 - 8
4y = 172
y = 43°
Therefore, you can find either x or y by applying the Theorem which states that sum of opposite angles of a cyclic quadrilateral is 180°
Instructions: Find the length of the arc. Round your answer to the nearest tenth.
Answer:
7
Step-by-step explanation:
The length of the arc can be calculated via a simple proportion:
2 pi r : 360° = x : 45°
Where r is the radius of the circumference and x the length of the arc we want to know. Isolating the x:
x = (2 pi r : 360) * 45 = (2 pi * 9 : 180) * 45 = 18 pi : 360 * 45 = 18pi : 8 = 7
Which statement is true about the value of Dante’s assets and liabilities?
He has $50,000 more in assets than in liabilities.
He has $50,000 more in liabilities than in assets.
He has $110,000 more in liabilities than in assets.
He has $160,000 more in assets than in liabilities.
Answer: te correct answer is A
Step-by-step explanation:
He has $50,000 more in assets than in liabilities.
Answer:
1. He has $50,000 more in assets than in liabilities.
Step-by-step explanation:
Which type of function describes f(x)? exponential logarithmic polynomial rational
The category of the function f(x) shown in the graph is a (B) linear function.
What are linear functions?In mathematics, the word linear function refers to two distinct but related concepts.In calculus and related fields, a linear function is one whose graph is a straight line, that is, a polynomial function of degree zero or one.
To find which type of function describes f(x):
How do determine the graph?
A linear graph is any graph that is represented by a straight line.Because the graph is represented by a straight line, the above statement implies that it is a linear graph.Therefore, the category of the function f(x) shown in the graph is a (B) linear function.
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The complete question is given below:
Which type of function describes f(x)?
(A)exponential
(B) linear
(C) logarithmic
(D) polynomial
(E) rational
Which inequality explains why these three segments cannot be used to construct a triangle? ef fd > de ed ef < df ed ef > df ef fd < de
We have the segments EF, FD, and DE.
Therefore, the correct answer is
ED + EF < DF
EF + FD < DE
What is Triangle Inequality Theorem?
The Triangle Inequality Theorem states that the totality of any side of a triangle must be greater than the measure of the third side in this problem.
We have the segments EF, FD, and DE.
To construct a triangle three inequalities must be met
case 1: EF + FD > DE
case 2: FD + DE > EF
case 3: EF + DE > FD
Therefore, the correct answer is
ED + EF < DF
EF + FD < DE
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please help! look at the photo linked
Answer:
3; 1
Step-by-step explanation:
when there are six spots we can see that there are 2 eyes
so
divide both sides by 2
6:2
6 / 2 : 2 / 2
3 : 1
that is your answer
Determine the factors of x2 − 8x − 12. (x − 6)(x 2) (x 3)(x − 4) prime (x 6)(x − 2)
The polynomial cannot be factored in because it exists prime. Since 112 exists not a perfect square number so we cannot estimate the factors of the given equation.
What is a quadratic equation?
In a quadratic equation ax² + bx + c = 0
when (b² - 4ac) exists a perfect square only then we can factorize the equation.
In the given equation x² - 8x - 12 we have to determine the value of
b² - 4ac
From the equation, we get b = -8 and c = -12
b²- 4ac = (-8)² - 4(1)(-12)
= 64 + 48 = 112
Since 112 exists not a perfect square number so we can not estimate the factors of the given equation.
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A graph titled Population of Old Town has Time (years after 2000) on the x-axis, and number of people on the y-axis. A line goes through points (4, 7,000) and (6, 6,500). What is the slope for this scenario? -500 -250
The slope of the scenario is calculated as: -250.
How to Find the Slope Value?Slope (m) = change in y / change in x = (y2 - y1)/((x2 - x1).
Given the points:
(4, 7,000) = (x1, y1)
(6, 6,500) = (x2, y2)
Plug in the values
Slope (m) = (6,500 - 7,000) / (6 - 4)
Slope (m) = (-500) / (2)
Slope (m) = -250
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