12.) During the first 3 weeks of training, a runner runs 20 miles, 22 miles, and 21 miles. How many miles must she run during the fourth week to have
a mean of at least 22 miles per week?
10 miles
15 miles
20 miles
25 miles
Answers
20+22+21+25=88
88 divided by 4 is 22.
She just run 25 miles in the 4th week
Since the runner wants to have an average of 22 miles per week in 4 weeks, then the total miles that she must run will be:
= 22 × 4
= 88 miles
We will then add the total number of miles for the first 3 weeks. This will be:
= 20 + 22 + 21
= 63 miles
Then, the number of miles needed for the 4th race will be:
= 88 miles - 63 miles
= 25 miles
Therefore, she must run 25 miles in the 4th week.
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Related Questions
In the coordinate plane, which of the following functions dilates by a factor of 3
about the point (9, 6)?
A. (, ) = (3 + 9, 3 +6)
B. (, ) = (3( + 9), 3( + 6))
C. (, ) = (9+ 3( − 9), 6 + 3( −6))
D. (, ) = (9+ 3(9− ), 6+ 3(6 − ))
Answers
Solve the following LP formulation and determine the number of Surplus units in constraint B.
Answers
SOLUTION
From the what is given
\(\begin{gathered} x+y\le5 \\ x\ge3 \\ 2y\le8 \\ x\ge0 \\ y\ge0 \end{gathered}\)We have the graph as shown below
We are told that the MAX is
\(5x+2y\)Substituting these required points into the equation, our maximum becomes
\(\begin{gathered} 5x+2y \\ \text{For (3, 2)} \\ 5(3)+2(2)=15+4=19 \\ \text{For }(3,\text{ 0)} \\ 5(3)+2(0)=15+0=15 \\ \text{For (5, 0)} \\ 5(5)+2(0)=25+0=25 \end{gathered}\)We can see that the maximum is 25 at for units of 5, that is x = 5
But we are told in (B) that
\(x\ge3\)Hence the surplus unit is
\(5-3=2\)Hence the answer is 2
Help-
This is due today
Answers
Step-by-Step Explanation:
We know that volume of a cube is the edge raised to 3. (edge^3)
Therefore when the edge is “y”,
The Volume of the Cube = y^3
When y = 9, the Volume of the Cube is
= 9 * 9 * 9
= 81 * 9
= 729
Therefore, Volume of Cube is 729 feet^3
Let $n$ be a positive integer.
(a) There are $n^2$ ordered pairs $(a,b)$ of positive integers, where $1 \le a,$ $b \le n.$ Using a counting argument, show that this number is also equal to
\[n + 2 \binom{n}{2}.\]
(b) There are $n^3$ ordered triples $(a,b,c)$ of positive integers, where $1 \le a,$ $b,$ $c \le n.$ Using a counting argument, show that this number is also equal to
\[n + 3n(n - 1) + 6 \binom{n}{3}.\]
Answers
Alternatively, we can count the number of ordered pairs $(a,b)$ by dividing into cases based on the value of $a.$ For each $a,$ there are $n$ choices for $b$ (namely, $b$ can be any integer between 1 and $n,$ inclusive). Thus, the total number of ordered pairs is $\sum_{a=1}^n n = n^2.$
On the other hand, we can also count the number of ordered pairs $(a,b)$ by first choosing two distinct integers from the set $\{1,2,\ldots,n\}$ and then ordering them. There are $\binom{n}{2}$ ways to choose two distinct integers from the set, and once we have chosen them, there are two ordered pairs corresponding to them (namely, $(a,b)$ and $(b,a)$). Thus, the total number of ordered pairs is $2\binom{n}{2}.$
Since we have counted the same quantity in two different ways, we must have
\[n^2 = 2\binom{n}{2} + n.\]
(b) We can count the number of ordered triples $(a,b,c)$ in three ways.
First, we can simply note that there are $n$ choices for each of $a,$ $b,$ and $c,$ giving a total of $n^3$ ordered triples.
Alternatively, we can count the number of ordered triples $(a,b,c)$ by dividing into cases based on the values of $a$ and $b.$ For any given pair $(a,b),$ there are $n$ choices for $c,$ so the total number of ordered triples is $\sum_{a=1}^n \sum_{b=1}^n n = n^3.$
On the other hand, we can also count the number of ordered triples $(a,b,c)$ by first choosing three distinct integers from the set $\{1,2,\ldots,n\}$ and then ordering them. There are $\binom{n}{3}$ ways to choose three distinct integers from the set, and once we have chosen them, there are $3! = 6$ ordered triples corresponding to them (namely, $(a,b,c),$ $(a,c,b),$ $(b,a,c),$ $(b,c,a),$ $(c,a,b),$ and $(c,b,a)$). Thus, the total number of ordered triples is $6\binom{n}{3}.$
Finally, we can count the number of ordered triples $(a,b,c)$ by dividing into cases based on how many of $a,$ $b,$ and $c$are equal. If all three are equal, there are $n$ choices for each of $a,$ $b,$ and $c,$ giving a total of $n$ ordered triples. If exactly two are equal, there are $3n(n-1)$ choices for $(a,b,c)$ (namely, we can choose the two equal values in $n$ ways, and then choose the distinct value in $n-1$ ways). If all three are distinct, there are $6\binom{n}{3}$ choices for $(a,b,c)$ (as before). Thus, the total number of ordered triples is
\[n + 3n(n-1) + 6\binom{n}{3}.\]
Since we have counted the same quantity in three different ways, we must have
\[n^3 = n + 3n(n-1) + 6\binom{n}{3}.\]
Find the OL length
Please
Answers
Answer:
M N o 3 9:Ol length-P∆kon-60+39-99
121, 50 boys and 50 girls with add (attention deficit disorder) were selected for an oxperiment to test a new drug for the treatment of aldod, half of the boys and half of the giris were selected sordedow to selected he new drag, and the other halt or each group received a placebo. a reduction in symptoms of add was measured for each subject. the basic design of this experiment is: (a) completely randomized (b) completely randomized with one factor, gender (c) randomized block, blocked by gender and drug (d) randomized block, blocked by drug (e) randomized block, blocked by gender
Answers
The basic design of this experiment is a randomized block design, blocked by gender and drug. In a randomized block design, subjects are first divided into blocks based on a characteristic that is believed to be related to the response variable.
In this case, the characteristic is gender, which is likely to influence the response to the drug. Then, within each block, the subjects are randomly assigned to the treatment groups.
Randomized block designs are used when there is a known factor that is likely to influence the response variable, and it is important to control for this factor in the analysis. By blocking on gender, we can ensure that each treatment group has an equal number of boys and girls, which will make it easier to compare the effect of the drug between the two genders.
In this particular experiment, we also need to control for the effect of the drug itself, since we are comparing the effect of the new drug to a placebo. Therefore, we block on both gender and drug to ensure that each treatment group has an equal number of boys and girls, and an equal number of subjects receiving the new drug and the placebo.
Overall, a randomized block design is a powerful tool for controlling the effects of known factors on the response variable, and can lead to more accurate and precise estimates of treatment effects.
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how do i solve this?
Answers
Step-by-step explanation:
it is a quadrilateral.
the sum of all angles in a quadrilateral is always 360°.
so,
360 = x + x + 2x + 7 + 2x + 5 = 6x + 12
348 = 6x
x = 348/6 = 58°
that's it.
helppppppppppp i hv 5 mins
Answers
Answer: 342.5 miles
Step-by-step explanation:
Distance = Speed x Time
Speed(mph) Time(hr) Distance(miles)
55 x 3.5 = 192.5
60 x 2.4 = 150
Total Distance (miles) = 342.5 miles
Solve the triangle. Round decimal answers to the nearest tenth.
Answers
The value of
1. angle B = 66°
2. a = 14.3
3. b = 24.1
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
angle B = 180-(81+33)
B = 180 - 114
B = 66°
Using sine rule;
sinB/b = SinC /c
sin66/b = sin81/26
0.914/b = 0.988/26
b( 0.988) = 26 × 0.914
b = 23.764/0.988
b = 24.1
sinC/c = sinA /a
sin81/26 = sin33/a
0.988/26 = 33/a
a = 26×sin33/0.988
a = 14.3
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in how many ways 7 people be seated at around a table if; a) they can sit anywhere, b) two particular people must not sit next to each other?
Answers
Answer:
I’d say the two people that can’t sit next to each other but to choose a different seat, if they find themselves seated next to each other they could ask someone next to them to switch seats with them. The 7 people can sit anywhere but the 2 particular people could sit away from the other.
Step-by-step explanation:
I hope I helped! ^.^’
What does Sin Cos Tan mean?
Answers
"Sine, Cosine, and Tangent" (often abbreviated as "sin, cos, tan") are basic trigonometric functions that are used to describe the relationship between the angles and sides of a right triangle. These functions have many applications in mathematics, science, and engineering, including solving problems related to triangles, circles, and waves.
Sine is defined as the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse (the longest side). In mathematical notation, sin θ = opposite/hypotenuse, where θ represents the angle in question.
Cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In mathematical notation, cos θ = adjacent/hypotenuse.
Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side. In mathematical notation, tan θ = opposite/adjacent.
It is important to note that sine, cosine, and tangent can be used to find the values of unknown sides and angles in a right triangle, given the known values. These functions can also be used in more advanced mathematical concepts, such as calculus and vector calculus.
In summary, sine, cosine, and tangent are essential tools for solving problems involving triangles and circles, and they have numerous applications in various fields of mathematics, science, and engineering.
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Please help I’ll give brainliest
Answers
Answer:
v = 27,000 mm³
Step-by-step explanation:
v = s³
v = 30³
v = 27,000 mm³
Solve for x, using a
tangent and a secant line.
145°
35°
x = [?]°
![Solve for x, using atangent and a secant line.14535x = [?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/gIXfLZShQibRDkBhtrgV4R3AvRo6I3ZS.png)
Answers
Check the picture below.
![Solve for x, using atangent and a secant line.14535x = [?]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/3boSNnke7VcLrcV3Gs7RfliyaoLv39yA.png)
Please help! I need the answer immediately, atleast 15 minutes under!
Answers
The question according to the equation will be a board that is 1/4 yard long cut into 2 equal pieces. Hence, option A is correct.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
The given equation in the question is,
1/4 ÷ 2 = 1/8
It can be clearly seen that 1/4 divided by 2 is mentioned in the question and the product obtained is 1/8.
It means that 1/4 is divided into 2 equal pieces and the length of each piece is 1/8.
So, the question will be a board that is 1/4 yard long cut into 2 equal pieces. How long is each piece?
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Ricky has 648 baseball cards he wants to put them in an album if each page of the album holds 12 cards how many pages are needed to hold all of his cards
Answers
54 pages are needed to hold all of his cards , if Ricky has 648 baseball cards he wants to put them in an album if each page of the album holds 12 cards
Ricky has 648 cards , and each page of the album holds 12 cards. Which means, if each page holds 12 cards; One page will hold 12 cards, the second page, another 12 cards and so on.
Hence, 2 pages will hold 12+12 cards which is 24 cards. 3 pages will hold, 12+12+12 = 36 cards
Now, to get how much pages will hold 648 cards, we divide 648 by 12
648/12= 54 pages
Hence, if Ricky has 648 baseball cards he wants to put them in an album if each page of the album holds 12 cards then 54 pages are needed to hold all of his cards
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A linear function has an x-intercept of 8 and a y-intercept of 4 . which of these is an equation of the linear function?
Answers
y = (-1/2)x + 4 is the equation for the linear function with an x-intercept of 8 and a y-intercept of 4.
How to find the slope of the line ?We are aware that lines might have several kinds of equations; the typical form is
The equation of a line in slope-intercept form is Ax + By + c = 0, and
y = mx + b.
m is the slope, and b is the y-intercept.
The y-intercept, or (0,b), is the point where the line crosses the y-axis at x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.
Given, An x-intercept for a linear function is 8, and a y-intercept is 4.
The two points on the line are therefore (8, 0) and (0, 4).
Slope(m) is now equal to (4 - 0)/(0 - 8).
m slope = 4/8.
slope(m) equals -1/2.
With a y-intercept of 4, it represents the value of b in the equation y = mx + b.
Consequently, the equation is y = (-1/2)x + 4 is linear.
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2.3 × 2² ÷ 2- 8·9 help please
Answers
Answer:
67.4
Step-by-step explanation:
Tanvi opened a savings account and deposited $400.00 as principal. the account earns 13%
interest, compounded annually. what is the balance after 7 years?
p(1+)",
use the formula a = p 1 + where a is the balance (final amount), p is the principal
(starting amount), r is the interest rate expressed
as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
round your answer to the nearest cent.
Answers
The amount of the money after 7 years with a rate of 13% with an initial amount of $400 will be $ 941.04.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
Tanvi opened a savings account and deposited $400.00 as principal.
The account earns 13% interest, compounded annually.
Then the balance after 7 years will be
We know the compound interest formula.
A = P (1 + r)ⁿ
We have
P = $ 400
r = 13%
n = 7 years
Then we have
A = 400 x (1 + 0.13)⁷
A = 400 x 1.13⁷
A = 400 x 2.3526
A = $ 941.04
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For a population with µ = 65 and σ = 4, what is the X value corresponding to z = -2.25?
a. X = 74
b. X = 56
c. X = 71
d. X = 60
Answers
The X value corresponding to z = -2.25 is X = 56.
What is z - score?A z score is a statistical indicator that shows how far a raw score is from a distribution's mean. Give the z-score formula. The z-score is calculated using the formula z = (x -μ)/σ.
To find the corresponding X value for a given z-score, we use the formula:
X = µ + (z * σ)
Given µ = 65, σ = 4, and z = -2.25, we can calculate the X value:
X = 65 + (-2.25 * 4)
X = 65 - 9
X = 56
Therefore, the X value corresponding to z = -2.25 is X = 56.
The correct answer is b. X = 56.
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After applying a discount of 8% on a toy, it is sold for $216.20. Find the original price of the toy.
Answers
92%=216.20 then 2.35x8%=18.80 then 18.80+216.20=235 the answer is 235
how do you solve 6 – 5c = -29
Answers
Answer: C = 7
Step-by-step explanation:
6 -5c = -29 make the variable be by itself by subtracting 6 on both sides.
-5c = -35 divide -5 on both sides, when dividing if both numbers are negative they become positive.
c = 7
When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial? mc030-1. Jpg.
Answers
The expression that can be added to both sides of the given quadratic equation to change it to a perfect square trinomial is \(\frac{b^2}{4a^2}\) .
The standard form of perfect square trinomial is given as:
\(ax^2 + bx + c\)
here,
a = coefficient of x² .
b = coefficient of x.
c = constant .
Given the quadratic equation:
\(x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?\)
The above equation is needed to be changed to a perfect square trinomial.
To change the quadratic equation into the perfect square, the squared of half the value of the coefficient of degree one variable can be added to both sides of the equation.
Therefore, the term to be that is needed to be added to the given quadratic equation is \(\frac{b^2}{4a^2}\) .
Now, the quadratic equation can be written as:
\(x^{2} + \frac{b}{a} x + \frac{ b^{2}}{4a^{2}} = \frac{-c}{a} + \frac{ b^{2}}{4a^{2}}\)
Therefore, \(\dfrac{b^2}{4a^2}\) should be added to both sides to convert it into the perfect polynomial.
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The given question is incomplete. Probably the complete question is:
When deriving the quadratic formula by completing the square what expression can be added to both sides of the given equation to create a perfect square trinomial?
\(x^2 + \dfrac{b}{a}x\ +\ ?= -\dfrac{c}{a}\ +\ ?\)
The graph shows the cost, C, of renting a concert hall for t hours.
Answers
This way to go all the way to t just did this for Brainly
Pls help this is confusing :/
Use matrices to determine the coordinates of the vertices of the rotated figure. Then graph the pre-image and the image of the same coordinate grid. \(Rot_{270}\) for ΔUVW with vertices U(-3,8), V(8,4), and W(6,-8) This is for pre-calculus!
Answers
The coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.
What is a transformation?A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
The types of transformation.In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on the information provided, triangle UVW would be rotated counterclockwise through an angle of 270 degree at origin to produce triangle U'V'W', we have:
\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\)
Therefore, the image of triangle UVW would be given by this matrix:
\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\) \(\left[\begin{array}{ccc}-3&8&6\\8&4&-8\end{array}\right]\)
Image = \(\left[\begin{array}{ccc}8&4&-8\\3&-8&-6\end{array}\right]\)
Based on the image above, we can logically deduce that the coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.
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Answer:
hi friend
Step-by-step explanation:
use the alternating series estimation theorem or taylor's inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error. question 2 options: -1.739 < x < 1.599 -1.669 < x < 1.669 -0.669 < x < 2.669
Answers
we can apply the appropriate theorem to determine the range of values of x for which the approximation is accurate to within the given error.
WithoutWithout the given approximation or error, it is difficult to provide an exact answer to this question. However, we can use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values of x for which the given approximation is accurate to within a given error bound.
The Alternating Series Estimation Theorem states that the error in approximating a convergent alternating series is bounded by the absolute value of the next term in the series. Taylor's Inequality is a more general form of this theorem that can be applied to non-alternating series as well.
To estimate the range of values of x, we would need to know the specific function being approximated, the center of the series expansion, and the error bound. Once we have this information, we can apply the appropriate theorem to determine the range of values of x for which the approximation is accurate to within the given error.
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ten days after it was launched toward mars in december 1998, the mars cli- mate orbiter spacecraft (mass 629 kg) was 2.87 x 106km from the earth and traveling at 1.20 x 104km/h relative to the earth
Answers
The kinetic energy of the Mars Climate Orbiter spacecraft is approx 3.31 x 10^7 joules.
To determine the kinetic energy of the Mars Climate Orbiter spacecraft, we can use the formula:
Kinetic energy = (1/2) * mass * velocity^2
Given:
Mass of the spacecraft (m) = 629 kg
Velocity of the spacecraft (v) = 1.20 x 10^4 km/h
First, we need to convert the velocity from km/h to m/s:
1 km = 1000 m
1 h = 3600 s
Velocity in m/s = (1.20 x 10^4 km/h) * (1000 m/km) / (3600 s/h) ≈ 333.33 m/s
Now, we can calculate the kinetic energy:
Kinetic energy = (1/2) * (629 kg) * (333.33 m/s)^2
Kinetic energy ≈ 3.31 x 10^7 joules
Therefore, the kinetic energy of the Mars Climate Orbiter spacecraft is approximately 3.31 x 10^7 joules.
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could the standard deviation of a data set ever be negative? what
about the IQR? explain your reasoning
Answers
No, the standard deviation of a data set can never be negative. The standard deviation is a measure of the dispersion or spread of data points from the mean.
It is calculated by taking the square root of the variance, which is the average of the squared differences between each data point and the mean.
Since the variance involves squaring the differences, it ensures that all values are positive. Taking the square root of the positive variance yields a positive value, which is the standard deviation. Thus, the standard deviation is always non-negative.
Similarly, the Interquartile Range (IQR) cannot be negative. The IQR is a measure of statistical dispersion that represents the range between the first quartile (25th percentile) and the third quartile (75th percentile) of a dataset. It provides insights into the spread of the central 50% of the data.
Like the standard deviation, the IQR involves calculating the difference between specific percentiles. Since percentiles represent ordered values in a dataset, the difference between them is non-negative, ensuring that the IQR is also non-negative.
In summary, both the standard deviation and the IQR are measures of dispersion that involve calculating differences between values in a dataset, ensuring that they cannot be negative.
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Please help me find the length of the line!
Answers
Answer:
The length of the segment is 10.
Step-by-step explanation:
Think of the segment as the hypotenuse of a right triangle.
Draw the legs and label the lengths.
See the picture below.
The length of the hypotenuse is c.
c^2 = a^2 + b^2
c^2 = 6^2 + 8^2
c^2 = 36 + 64
c^2 = 100
c = 10
Answer: 10
Mr. and Mrs. Sanchez want to invest money for their child’s college education. They have decided to invest $2000 initially. If the investment is in an account that earns 8% annual interest, compounded yearly for 10 years, how much will their investment be worth at the end of the 10th year?
Answers
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.08}{1}\right)^{1\cdot 10}\implies A=2000(1.08)^{10} \implies A \approx 4317.85\)
i need help solving this
Answers
Answer:
slope =m = -1/5
c = -6
y = mx+c