[tex] \Large \mathbb{SOLUTION:} [/tex]
[tex] \begin{array}{l} \text{Let }r\text{ be the rate of the boat in still water and} \\ c\text{ be the rate of the current.} \\ \\ \text{So } \\ \begin{aligned} \quad&\bullet\:\text{Rate Upstream}= r - c \\ &\bullet\:\text{Rate Downstream}= r - c\end{aligned} \\ \\ \text{We know that }\text{Rate} = \dfrac{\text{Distance}}{\text{Time}}. \end{array} [/tex]
[tex] \begin{array}{l} \bold{Equations:} \\ \\ \begin{aligned} &\quad\quad \quad r - c = \dfrac{104}{4} = 26\quad (1) \\ \\ & \quad \quad \quad r + c = \dfrac{200}{4} = 50\quad (2)\\ \\ & \text{Adding (1) and (2), we get} \\ \\ &\quad\quad 2r = 76 \implies \boxed{r = 38\ \text{kph}} \\ \\ &\text{Using (2), it follows that} \\ \\ & \quad \quad c = 50 - r \implies \boxed{c = 12\ \text{kph}} \end{aligned} \end{array} [/tex]
need help solving this equation right now please
9514 1404 393
Answer:
(5, -6)
Step-by-step explanation:
x-coordinates measure the distance to the right of the y-axis. Moving a point 4 units to the right adds 4 to its x-coordinate.
y-coordinates measure distance up from the x-axis. Moving a point 4 units down subtracts 4 from its y-coordinate.
(1, -2) +(4, -4) = (1 +4, -2 -4) = (5, -6) . . . . image of translated point
6( n - 2) in word form please c:
Answer:
six in parenthesis n minus two
Step-by-step explanation:
2 ways could be:
A. N minus two then multiply by six
B. Six times parentheses n minus two end parentheses
14. The area of 10 square plots is 160 ares. Find the length in metres of the side of each plot (3mks)
Answer:
Step-by-step explanation:
1 are = 100 m²
Assuming the ten squares are congruent, the area of each square is 160/10 = 16 are
16 are × 100 m²/are = 1600 m²
each side is √1600 = 40 m
The length of side of plot is 40 meters.
What is area?The total space occupied by a flat (2-D) surface or shape of an object is known as area.
Draw a square on a piece of paper with a pencil. It has two dimensions. The term "area" refers to the area that the shape occupies on the paper.
Now picture your square as being comprised of smaller unit squares. The number of unit squares required to cover a 2-D shape's total surface area is used to calculate its area.
Given the area of 10 square plot is 160 are,
here 1 are = 100 m²
area of 10 square plot = 160 x 100 = 16,000 m²
area of 1 square plot = 16000/10 = 1600 m²
area of square is "a²"
where a is side of square
area = a² = 1600 m²
a = √1600
a = 40 m
Hence the length of side of each plot is 40 meters.
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A composite figure is made up of one simple figure.
True or
False
Answer:
False
Step-by-step explanation:
A composite figure would be any irregular shapes and can be made up of multiple shapes
Two sides of a triangle have lengths 13 m and 19 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)
Answer:
The third side is increasing at an approximate rate of about 0.444 meters per minute.
Step-by-step explanation:
We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.
Let the angle between the two given sides be θ and let the third side be c.
Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.
First, convert the degrees into radians:
[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]
Hence, dθ/dt = π/90.
From the Law of Cosines:
[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]
Since a = 13 and b = 19:
[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]
Simplify:
[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]
Take the derivative of both sides with respect to t:
[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]
Implicitly differentiate:
[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]
We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:
[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]
Substitute:
[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]
Solve for dc/dt:
[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]
Evaluate. Hence:
[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]
The third side is increasing at an approximate rate of about 0.444 meters per minute.
9514 1404 393
Answer:
0.444 m/min
Step-by-step explanation:
I find this kind of question to be answered easily by a graphing calculator.
The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...
c = √(a² +b² -2ab·cos(C))
Since C is a function of time, its value in degrees can be written ...
C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest
Using a=13, and b=19, the length of the third side is ...
c(t) = √(13² +19² -2·13·19·cos(60° +2t°))
Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...
0.443855627418 m/min ≈ 0.444 m/min
_____
Additional comment
At that time, the length of the third side is about 16.823 m.
__
c(t) reduces to √(530 -494cos(π/90·t +π/3))
Then the derivative is ...
[tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]
A perfect correlation is denoted by:
A. +1.0 and -1.0
B. +1.00
C. -1.00
D. .50
A perfect correlation is denoted by:
A. +1.0 and -1.0
I need help with C,D,E,F,G thank you
Answer:
D = 120 Degrees , E : x = 14 , F: <JHK = 21, G: Summplementary Angle is 96 Degrees
Step-by-step explanation:
4X+2X = 180
6X=180
X=30
<ABD = 4X = 4(30) = 120
1. Given the line of best fit y = 6.2x + 13, what is the residual for the point (10,80)? (1 pt)
A. 75
B. 5
C. 499
D. 55
Answer:
c
Step-by-step explanation:
The residual for the point line (10,80) is option A 75. at the given line which best fits y = 6.2x + 13.
What is a straight line graph?The graph follows a straight line equation shows a straight line graph.
equation of a straight line is y=mx+cy represents vertical line y-axis.x represents the horizontal line x-axis. m is the slope of the lineslope(m)=tan∅=y axis/x axis.
c represents y-intercepts (it is the point at which the line cuts on the y-axis)Straight line graphs show a linear relationship between the x and y values.
solving the equation:-
y = 6.2x + 13
putting value of X = 10
Y = 6.2 * 10 + 13
Y = 62 + 13
Y = 75
Hence the line best fit = 75.
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Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 11? The graph of y = f(x) will shift up 11 units. The graph of y = f(x) will shift right 11 units. The graph of y = f(x) will shift left 11 units. The graph of y = f(x) will shift down 11 units.
Answer:
The graph of y = f(x) will shift down 11 units
Step-by-step explanation:
Social media is popular around the world. Statista provides estimate of the number of social media users in various countries in as well as the projections for . Assume that the results for surveys in the United Kingdom, China, Russia, and the United States are as follows.
Use Social Media United Kingdom China Russia United States
Yes 480 215 343 640
No 320 285 357 360
Required:
a. Conduct a hypothesis test to determine whether the proportion of adults using social media is equal for all four countries. What is the p-value? Using a .05 level of significance, what is your conclusion?
b. What are the sample proportions for each of the four countries? Which country has the largest proportion of adults using social media?
c. Using a 0.05 level of significance, conduct multiple pairwise comparison tests among the four countries. What is your conclusion?
Answer:
Kindly check explanation
Step-by-step explanation:
The data table :
Use of SM _UK _China _ Russia _US _ col total
Yes ______480 __215 ___343 __640 _ 1678
No _______320 _ 285 ___357__ 360 _ 1322
Row Total__ 800 _500 __ 700_ 1000_ 3000
H0 : p1 = p2 = p3 = p4
H1 : p1 ≠ p2 ≠ p3 ≠ p4
Test statistic :
χ² = Σ(observed - Expected)² / Expected
Expected value of each cell = (Row total * column total) / N
N = grand total
Expected Values:
447.467 _279.667 _ 391.533 _ 559.333
352.533 _ 220.333 _ 308.467 _ 440.667
χ²=(2.36536+14.9527+6.01605+11.6337+3.00232 18.9793+7.63611+14.7665) = 79.352
Degree of freedom, df = (row-1)*(column-1) = (2 - 1) * (4 - 1) = 1 * 3 = 3
Using the Pvalue from Chisquare calculator :
Pvalue(79.352, 3) = 0.00000000001
Decision region :
Reject H0 ; If Pvalue < α
α = 0.05
Since 0.000000001 < 0.05 ; Reject H0 and conclude that not all population proportion are equal.
Sample proportion :
Phat = number of yes, x / total
For UK, Phat = 480/800 = 0.6
For China , Phat = 215/500 = 0.43
For Russia , Phat = 343/700 = 0.49
For US, Phat = 640/1000 = 0.64
Find the 97th term of the arithmetic sequence 17, 26,35,...
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An ice cream truck started the day with 454545 ice cream sandwiches. During a stop at a busy park they sold sss ice cream sandwiches. After the stop, the truck had 212121 ice cream sandwiches remaining.
Write an equation to describe this situation.
How many ice cream sandwiches did the truck sell at the park?
Answer:
45- s= 21
s= 45- 21
=24
so the answer is 24
In performing a one-way ANOVA, ________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response and its corresponding treatment mean.
Answer: SS Error
Step-by-step explanation:
The SS Error refers to the sum of the squares of the deviations of the observations, from their mean. It is simply the total variance from the observations on the study.
In performing a one-way ANOVA, the SS Error measures the variability of the observed values around their respective means and this is done through the summation of the squared differences between each observed value of the response and its corresponding treatment mean.
There are10 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, howmany different slates of candidates are possible
Answer:
The answer is "720"
Step-by-step explanation:
The amount of different slates candidates:
[tex]n=\frac{N!}{(N-k)!}\\\\[/tex]
[tex]=\frac{10!}{(10-3)!}\\\\=\frac{10!}{7!}\\\\=\frac{10\times 9 \times 8 \times 7! }{7!}\\\\=10\times 9 \times 8\\\\=90\times 8\\\\=720[/tex]
The number of people attending graduate school at a university may be
modeled by the quadratic regression equation y = 8x2 - 40x+6, where x
represents the year. Based on the regression equation, which year is the best
prediction for when 1206 people will attend graduate school?
A. Year 15
B. Year 18
C. Year 24
D. Year 20
Answer:
15 years
Step-by-step explanation:
Given the quadratic regression model:
y = 8x² - 40x+6 ; where
y = Number of people attending graduate school ;
x = number of years
The value of x when y = 1206
The equation becomes :
1206 = 8x² - 40x+6
1206 - 6 = 8x² - 40x
1200 = 8x² - 40x
Divide through by 8
150 = x² - 5x
x² - 5x - 150 = 0
x² - 15x + 10x - 150 = 0
x(x - 15) + 10(x - 15)
x - 15 = 0 or x + 10 = 0
x = 15 or x = - 10
Number of years can't be negative,
Hence, x = 15 years
The salt content in snack bags of pretzels is Normally distributed, with a mean of 180 mg and a standard deviation of 15 mg. Eighty four percent of bags have a salt content higher than which value?
Find the z-table here.
165.2 mg
179.2 mg
187.0 mg
194.9 mg
I think its (A), 165.2mg
Answer: Yes you are correct. The answer is choice A
============================================================
Explanation:
If you used the z-table, you should find that P(Z < 1) = 0.84 approximately.
So by symmetry, P(Z > -1) = 0.84 approximately as well.
We'll convert the z score z = -1 into its corresponding x score
z = (x-mu)/sigma
-1 = (x-180)/15
-15 = x-180
x-180 = -15
x = -15+180
x = 165
We don't land on any of the answer choices listed, but we get fairly close to 165.2, which is choice A. So you are correct.
I have a feeling that the table you have is probably more accurate than the one I'm using, so it's possible that you'd land exactly on 165.2 when following the steps above.
Answer:
194.9
Step-by-step explanation:
ON EDG
What is the distance between (8, -3) and (4, - 7)?
Choose 1 answer:
Will GIVE YOU BRAINLIEST
Step-by-step explanation:
We'll find the distance using the all-famous "Distance Formula." You'll probably come across it quite a bit, so it's best to have it written down somewhere.
The Distance Formula: [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
Our points are (8, -3) and (4, -7), so we'll plug in those numbers accordingly.
For reference:
x2 = 4
x1 = 8
y2 = -7
y1 = -3
The calculation:
(substitute)
[tex]\sqrt{(4-8)^2+((-7)-(-3))^2 }[/tex]
(simplify)
[tex]\sqrt{(-4)^2+(-4)^2 }[/tex]
(square things)
[tex]\sqrt{16+16 }[/tex]
(add)
[tex]\sqrt{32}[/tex]
Answer:
[tex]\sqrt{32}[/tex]
Answer:
[tex]\boxed {\boxed {\sf C. \sqrt{32}}}[/tex]
Step-by-step explanation:
The distance between 2 points can be determined with the following formula.
[tex]d= \sqrt{(x_2-x_1)^2+ (y_2-y_1)^2[/tex]
In this formula, (x₁, y₁) and (x₂, y₂) are the 2 points. We want to find the distance between the points (8, -3) and (4, -7). If we match the value with its corresponding variable, then we see:
x₁= 8 y₁= -3 x₂= 4 y₂ = -7Substitute the values into the formula.
[tex]d= \sqrt{(4-8)^2+(-7--3)^2[/tex]
Solve inside the parentheses.
(4-8) = -4 (-7 - -3) = (-7+3)= -4[tex]d= \sqrt {(-4)^2+(-4)^2[/tex]
Solve the exponents.
(-4)² = -4 * -4 = 16[tex]d= \sqrt {16+16[/tex]
Add.
[tex]d= \sqrt {32}[/tex]
This radical can be simplified, but since it is an answer choice, we can leave it as is.
The distance between the points (8, -3) and (4, -7) is √32 and choice C is correct.
Suppose the following data represent the ratings (on a scale from 1 to 5) for a certain smart phone game, with 1 representing a poor rating. The discrete probability distribution for the random variable x is given below:
Star Frequency
1 2140
2 2853
3 4734
4 4880
5 10,715
Required:
Construct a discrete probability distribution for the random variable X
Answer:
[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]
Step-by-step explanation:
Given
The above table
Required
The discrete probability distribution
The probability of each is calculated as:
[tex]Pr = \frac{Frequency}{Total}[/tex]
Where:
[tex]Total = 2140+ 2853 + 4734 + 4880 + 10715[/tex]
[tex]Total = 25322[/tex]
So, we have:
[tex]P(1) = \frac{2140}{25322} = 0.0845[/tex]
[tex]P(2) = \frac{2853}{25322} = 0.1127[/tex]
[tex]P(3) = \frac{4734}{25322} = 0.1870[/tex]
[tex]P(4) = \frac{4880}{25322} = 0.1927[/tex]
[tex]P(5) = \frac{10715}{25322} = 0.4231[/tex]
So, the discrete probability distribution is:
[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]
Find hypotenuse,perpendicular and base
Answer:
Consider the angle Ф.
the line opposite to Ф is the perpendicular -> PQ = 5cm
The base is the line with whom the perpendicular has 90° angle -> PR = 12cm
Finally, hypotenuse is the line opposite to the 90° which is QR= 13cm
Answer:
hypotenuse = QR = 13 cm
Perpendicular = PQ = 5 cm
Base = PR = 12 cm
exchange rate for rand is 7 for $1 how any dollars would u receive is u exchange 21 rand
Answer:
$3
Step-by-step explanation:
7 rands for $1
7×3=21
21 rands for $3
Answer:
$3
Step-by-step explanation:
7 rand = 1 dollar
Divide both sides by 7 rand.
1 = (1 dollar)/(7 rand)
Notice that the fraction (1 dollar)/(7 rand) equals 1, so multiplying by it will not change the amount, just the units.
21 rand * (1 dollar)/(7 rand) =
= 21/7 dollar
= 3 dollar = $3
What is the unit rate for $7.30 for 5 pounds.
Answer:
1.46 dollars per pound
Step-by-step explanation:
Take the total cost and divide by the number of pounds
7.30 dollars / 5 pounds
1.46 dollars per pound
Answer:
1.46
Step-by-step explanation:
Unit rate is the amount for only one pound. To do this, divide 7.30 and 5.
Divide:
7.3 / 5 = 1.46
Each pound is $1.46
Hope this helped.
write the number 16, 107, 320 in expanded
form.
398383i4irujidifififif
Solve for x
Answer options:
A) 6
B) 3
C) 5
D) 4
Answer:
it should be 3
Step-by-step explanation:
I hope this help
PLEASE HELP LOOK AT PICTURE
Ivan caught a total of 7 2/5 pounds of fish one day. Of the fish caught, 4 5/8 pounds were sea bass and the rest were mackerel. He gave away 1 7/8 pounds of mackerel. How many pounds of mackerel did he have left.
Given:
Total fish (Sea bass and mackerel) = [tex]7\dfrac{2}{5}[/tex] pounds
Sea bass = [tex]4\dfrac{5}{8}[/tex] pounds
He gave away [tex]1\dfrac{7}{8}[/tex] pounds of mackerel.
To find:
The remaining mackerel.
Solution:
We know that,
Mackerel = Total fish - Sea bass
[tex]\text{Mackerel}=7\dfrac{2}{5}-4\dfrac{5}{8}[/tex]
[tex]\text{Mackerel}=\dfrac{37}{5}-\dfrac{37}{8}[/tex]
[tex]\text{Mackerel}=\dfrac{296-185}{40}[/tex]
[tex]\text{Mackerel}=\dfrac{111}{40}[/tex]
He gave away [tex]1\dfrac{7}{8}[/tex] pounds of mackerel. So, the remaining mackerel is:
[tex]\text{Remaining Mackerel}=\dfrac{111}{40}-1\dfrac{7}{8}[/tex]
[tex]\text{Remaining Mackerel}=\dfrac{111}{40}-\dfrac{15}{8}[/tex]
[tex]\text{Remaining Mackerel}=\dfrac{111-75}{40}[/tex]
[tex]\text{Remaining Mackerel}=\dfrac{36}{40}[/tex]
[tex]\text{Remaining Mackerel}=\dfrac{9}{10}[/tex]
Therefore, the remaining Mackerel is [tex]\dfrac{9}{10}[/tex] pounds or 0.9 pounds.
Answer:
The amount of Mackerel left is 9/10.
Step-by-step explanation:
total fish = 7 2/5 pounds
sea bass = 4 5/8
The amount of mackerel =
[tex]7\frac{2}{5}-4\frac{5}{8}\\\\=\frac{37}{5}-\frac{37}{8}\\\\=\frac{296-185}{40}\\\\=2 \frac{31}{40}[/tex]
Mackerel left =
[tex]2 \frac{31}{40}-1\frac{7}{8}\\\\= \frac{111}{40}-\frac{15}{8}\\\\=\frac{111-75}{40}\\\\=\frac{36}{40}\\\\=\frac{9}{10}[/tex]
HELP ME PLSSS SUMMER SCHOOL A HARD
Answer:
y=2x+8
Step-by-step explanation:
Hope this helps
which point lies on the line defined by 7x - 7y = -43
Answer:
(-6,0) and (0,-6) are the points on the graph
Question 13 (Essay Worth 8 points)
Write the sum using summation notation, assuming the suggested pattern continues.
3, -12, 48, -192, + …
Is this sequence arithmetic or geometric? Explain your answer.
9514 1404 393
Answer:
geometric sequence
Step-by-step explanation:
The terms of the sequence have a common ratio of -12/3 = -4, so the sequence is geometric. The general term is ...
an = 3(-4)^(n-1)
so the sum can be written as ...
[tex]\displaystyle\sum_{n=0}^\infty3(-4)^n[/tex]
(Note the summation starts at n=0, corresponding to a first term of 3.)
Instruction: Find the average rate of change for the scenario below.
A rocket is 1 mile above the earth in 30 seconds and 5 miles
above the earth in 150 seconds. What is the rockets rate of
change in miles per second?
Rate of Change
miles/second
Answer:
Step-by-step explanation:
Use the coordinates (30, 1) and (150, 5) to solve this. Time is always an x thing, while things like distance and weight and value are y things. Put them into the slope formula:
[tex]m(\frac{miles}{sec})=\frac{5-1}{150-30}=\frac{4}{120}=\frac{1}{30}[/tex] This translates to:
The rocket is ascending at a constant rate of 1 mile every 30 seconds; or, conversely, for every 30 seconds the rocket is flying, it is traveling 1 mile.
a farmers field is 440 feet long and the length is 4 times the width of the field how wide is the field
Answer:
110 feet
Step-by-step explanation:
Take x as the width of the field.
4x = 440 feet
x = 440 feet ÷ 4
x = 110 feet
So, the field is 110 feet wide #
