To find the required linear model using least-squares regression, we first calculate the slope and y-intercept of the line that best fits the given data.
(a) We can use the formula for the slope and y-intercept of a least-squares regression line:
slope = r * (std_dev_y / std_dev_x)
y_intercept = mean_y - slope * mean_x
where r is the correlation coefficient between the two variables, std_dev_y and std_dev_x are the standard deviations of the dependent and independent variables, respectively, and mean_y and mean_x are the means of the dependent and independent variables, respectively.
Using the given data, we can calculate:
n = 5
sum_x = 10055
sum_y = 20884
sum_xy = 41938251
sum_x2 = 20125
sum_y2 = 46511306
mean_x = sum_x / n = 2011
mean_y = sum_y / n = 4177
std_dev_x = sqrt((sum_x2 / n) - mean_x^2) = 1.5811
std_dev_y = sqrt((sum_y2 / n) - mean_y^2) = 164.6483
r = (sum_xy - n * mean_x * mean_y) / (std_dev_x * std_dev_y * (n - 1)) = 0.9941
slope = r * (std_dev_y / std_dev_x) = 102.9552
y_intercept = mean_y - slope * mean_x = -199456.2988
Therefore, the linear model for these data is:
y = 102.9552x - 199456.2988
(b) To estimate the number of federal credit unions in the year 2017, we plug in x = 7 (corresponding to the year 2017) into the linear model and round to the nearest integer:
y = 102.9552(7) - 199456.2988 = 4605.0896
Rounding to the nearest integer, the estimated number of federal credit unions in the year 2017 is 4605.
To know more about standard deviations refer here:
https://brainly.com/question/23907081
#SPJ11
The function of f(x) = 3x + 6,000 represents the amount of money a tablet is being sold for, where x is the number of tablets being manufactured. The function g(x) = 20x - 400 represents the cost of production, where x is the number of tablets being manufactured. The function g(x) = 20x - 400 represents the cost of production, where x is the number of tablets being manufactured. What is (f - g)(300)? Explain.
A. $1,300 is the cost of manufacturing 300 tablets
B. $12,500 is the cost of manufacturing 300 tablets.
C. $1,300 is the profit made from 300 tablets.
D. $12,500 is the profit made from 300 tablets.
Answer:
(f - g)(300) = $1,300 is the profit made from 300 tablets
Step-by-step explanation:
(f - g)(300) is the profit made from 300 tablets
(f - g)(x) = (3 x + 6,000) - (20 x - 400)
- Simplify it
(f - g)(x) = 3 x + 6,000 - 20 x + 400
- Add like terms
(f - g)(x) = -17 x + 6,400
Substitute x by 300
(f - g)(300) = -17(300) + 6,400
(f - g)(300) = -5,100 + 6,400
(f - g)(300) = $1,300
The profit is $1,300
An integrated transcriptomic and epigenomic analysis identifies CD44 gene as a potential biomarker for weight loss within an energy-restricted program
An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program: TRUE
What is an integrated transcriptomic and epigenomic analysis?Because of the interindividual variability in response to weight-loss treatments, new predictive biomarkers are needed to improve the efficacy of weight-loss programs. The goal of this work is to find new genes that distinguish individual responses to a weight-loss dietary regimen by combining mRNA expression and DNA methylation arrays.Different expression and DNA methylation profiles were found in LR versus HR. The integrative analysis of the array data found four genes that were differentially methylated and expressed between groups: CD44, ITPR1, MTSS1, and FBXW5. In LR, CD44 expression was higher and DNA methylation levels were lower than in HR.Therefore, the statement "an integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program" is TRUE.
Know more about weight loss here:
https://brainly.com/question/1519447
#SPJ4
Complete question:
An integrated transcriptomic and epigenomic analysis identifies the CD44 gene as a potential biomarker for weight loss within an energy-restricted program. TRUE or FALSE
The sum of three numbers is 69. If the second number is equal to the first diminished by 8, and the third number is 5 times the first. What are the numbers?
If x represents the first number, then which of the following equations could be used to solve the problem?
69 = 7x - 8
x = 6x - 8
69 = 6x - 8
Answer:
[tex]69 = 6x - 8[/tex]
Step-by-step explanation:
All 3 numbers must sum to 69, so we can draw out the second option [tex]x = 6x - 8[/tex]
Let the first number be x, adding 5x to the first x would give you 6x for the sum of the first and third numbers, therefore you can remove [tex]69 = 7x - 8[/tex] from your considerations as it includes 7x not 6x.
This leaves you with the one final answer [tex]69 = 6x - 8[/tex]
What is the solution to the inequality?
A. y > 32
B. y > 2
C. y < 2
D. y < 32
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
An inequality [tex]\sf{-\cfrac{y}{4}+7 > -1}[/tex]✏[tex]\bigstar\textsf{To\quad find:-}[/tex]✏
y -- ?▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪▪
✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex]✏
First, subtract both sides by 7:-
[tex]\sf{-\cfrac{y}{4} > -1-7}}[/tex]
[tex]\sf{-\cfrac{y}{4} > -8}[/tex]
Now multiply both sides by 4:-
[tex]\sf{-y > -8*4}[/tex]
[tex]\sf{-y > -32}[/tex]
last step:-
[tex]\sf{y < 32}[/tex]
`hope it was helpful to u ~
[tex] \implies \: \sf{ - \dfrac{y}{4} \: + \: 7 \: > \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 7 \: - 1} \\ \\ \implies \: \sf{ - \dfrac{y}{4} \: > \: - 8} \\ \\ \implies \: \sf{ \cancel- \: \dfrac{y}{4} \: > \: \cancel- \: 8} \\ \\ \implies \: \sf{ \dfrac{y}{4} \: < \: 8} \\ \\
\implies \: \sf{ y \: < \: 8 \times 4} \\ \\ \implies \: \bf{ y \: < \: 32}[/tex]
A board of directors consists of fourteen men and six women. A four-member search committee is randomly chosen to recommend a new company president. What is the probability that all four members of the search committee will be women
Answer:
probability of all the four women chosen over people needed in a committee=4 over 4 =1
Which function has a vertex at the origin?
O f(x) = (x+4)²
Of(x) = x(x-4)
Of(x)=(x-4)(x + 4)
Of(x) = -x²
Answer:
(d) f(x) = -x²
Step-by-step explanation:
For the vertex of the quadratic function to be at the origin, both the x-term and the constant must be zero. That is, the function must be of the form ...
f(x) = a(x -h)² +k . . . . . . . . . . vertex form; vertex at (h, k)
f(x) = a(x -0)² +0 = ax² . . . . . vertex at the origin, (h, k) = (0, 0)
Of the offered answer choices, the only one with a vertex at the origin is ...
f(x) = -x² . . . . . a=-1
If the area of the rectangle avove is 180 spuare inches, then x =
Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.
Hence, option A is the correct answer.
This question is incomplete, the missing diagram is uploaded along this answer below.
What is the value of x?Area of a rectangle is expressed as; A = l × b
Given that;
Length of the rectangle l = 20inBreadth b = xArea A = 180in²A = l × b
180in² = 20in × x
x = 180in² / 20in
x = 9in
Given the dimension of the length and area of the rectangle, the dimension of the breadth x is 9in.
Hence, option A is the correct answer.
Learn more about area of rectangle here: brainly.com/question/12019874
#SPJ1
URGENT PLEASE ANSWER THESE QUESTIONS
a) The fire is out of the reach of helicopter 1.
b) Only helicopter 3 can be sent to stop the fire.
What helicopter does stop the fire?
We have both the location of the fire and the initial position of the three helicopters set on a Cartesian plane. The locations are listed below:
Fire - (x, y) = (- 3, - 5)Helicopter 1 - (x, y) = (1, 4)Helicopter 2 - (x, y) = (- 2, 3)Helicopter 3 - (x, y) = (4, - 2)The distance is found by the straight line distance formula, an application of Pythagorean theorem:
a) [tex]d = \sqrt{[1 - (- 3)]^{2}+[4-(-5)]^{2}}[/tex]
[tex]d = \sqrt{4^{2}+9^{2}}[/tex]
[tex]d = \sqrt{97}[/tex]
d ≈ 9.849
The fire is out of the reach of helicopter 1.
b) Helicopter 2
[tex]d = \sqrt{[- 2 - (- 3)]^{2}+[3 - (- 5)]^{2}}[/tex]
[tex]d = \sqrt{1^{2}+8^{2}}[/tex]
[tex]d = \sqrt{65}[/tex]
d ≈ 8.062
Helicopter 3
[tex]d = \sqrt{[4 - (- 3)]^{2}+ [- 2 - (-5)]^{2}}[/tex]
[tex]d = \sqrt{7^{2}+3^{2}}[/tex]
[tex]d = \sqrt{58}[/tex]
d ≈ 7.616
Only helicopter 3 can be sent to stop the fire.
To learn more on Pythagorean theorem: https://brainly.com/question/26183488
#SPJ1
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes
respectively: (a) 3 /2 and 5
The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10
What is a quadratic polynomial?A quadratic polynomial is a polynomial of the form ax² + bx + c
How to find the quadratic polynomial?For any given quadratic polynomial we have
x² - (sum of zeros)x + (products of zeros) = 0
Given that the sum and product of its zeroes respectively 3/2 and 5,
We have that
sum of zeroes = 3/2 and product of zeros = 5Substituting the values of the variables into the equation, we have
x² - (sum of zeros)x + (products of zeros) = 0
x² - (3/2)x + (5) = 0
x² - (3/2)x + (5) = 0
Multiplying through by 2, we have
2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2
2x² - 3x + 10 = 0
So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10
Learn more about quadratic polynomial here:
https://brainly.com/question/7784687
#SPJ1
what is the coefficient of (3y^2 + 9)5
The coefficient of (3y² + 9)5 is 15.
A polynomial is of the form a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ.
Here, x is the variable, aₙ is the constant term, and a₀, a₁, a₂, ..., and aₙ₋₁, are the coefficients.
a₀ is the leading coefficient.
In the question, we are asked to identify the coefficient of (3y² + 9)5.
First, we expand the given expression:
(3y² + 9)5
= 15y² + 45.
Comparing this to the standard form of a polynomial, a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ₋₁x + aₙ, we can say that y is the variable, 15 is the coefficient, and 45 is the constant term.
Thus, the coefficient of (3y² + 9)5 is 15.
Learn more about the coefficients of a polynomial at
https://brainly.com/question/9071229
#SPJ1
a. Use the properties of right triangles and AABC to prove the Law of Sines.
b. Find the length of BC, rounded to the nearest tenth of a unit.
In your final answer for parts A and B, Include all of the necessary steps and calculations.
The Law of sines defines that in a triangle, (Sin A)/a = (Sin B)/b = (Sin C)/c and as per law of sines the length of BC is 24.
The given triangle is ΔABC, we split the given triangle into two right-angled triangle ΔABD and ΔBCD.
In the triangle ΔABD,
sin θ = opposite side/hypotenuse
sin A=BD/AB
BD=(sin A)/AB
And in the triangle ΔBCD,
sin θ = opposite side/hypotenuse
sin B=BD/BC
BD=(sin B)/BC
Hence, BD=(sin A)/AB=(sin B)/BC
Let say, (sin A)/a=(sin B)/b
As per law of sine, (sin A)/a=(sin B)/b
Then,
(sin 46°)/a=(sin 31°)/17
a=(17 × sin 46°)/(sin 31°)
a=23.74
a=24
Hence, the value of BC, rounded to the nearest tenth of a unit is 24.
Learn more about law of sine at
https://brainly.com/question/13983159
#SPJ1
plss help!!
1. Abigail is 8 years older than Cynthia. Twenty years ago Abigail was three times as old as Cynthia. How old is each now?
2. Three years ago Tom was twice as old as Jean. And in two years the sum of their ages will be 28 years. Find their present ages.
3. Bill is 5 years older than Sue is, and the sum of their ages is 67 years. How old is Bill and Sue?
4. The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digits, and the tens digit equals to the sum of the other two. Find the number.
5. The units digit is twice the tens digit. If the number is doubled, it will be 12 more than the reversed number. Find the number.
Answer:
1. a = 32, c = 24
Step-by-step explanation:
a = c+8
a-20 = 3(c-20)
(c+8)-20 = 3c-60
c = 24
a = 24+8
a = 32
2. t = 15, j = 9
t-3 = 2(j-3)
t-3 = 2j-6
t = 2j-3
t + 2 + j + 2 = 28
(2j-3)+ 2 + j + 2 = 28
3j + 1 = 28
3j = 27
j = 9
t-3 = 2(9-3)
t-3 = 2(6)
t-3=12
t = 15
3. b=36, s=31
b = s + 5
b+s = 67
(s+5)+s = 67
2s+5 = 67
2s = 62
s = 31
b = 31+5
b = 36
4. 231
h + t + u = 6
(with h=hundreds digit, t=tens digit, u=units digit)
h = 2u
t = h+u
t = (2u) + u
(2u) + (2u +u) + u = 6
6u = 6
u = 1
h = 2
t = 3
the number is 231
5. 48
u = 2t
the 2-digit number is 10t+u
2(10t+u) = 10u+t+12
2(10t + 2t) = 10(2t) + t + 12
20t + 4t = 20t + t + 12
24t = 21t + 12
3t = 12
t = 4
u = 2*4
u = 8
the number is 48
Jean estimates that her friend complete a new level of a game on the first try 20% of the time. she conducts a simulation to predict how manytimes out of 80 her friend would complete a new level on the first try. jin uses a random number generator. every digit that is eight or nine representatives complete in the level. what is the problem ability that her friend completes a new level on the first try written as a percent
The friend's probability of beating the next level on her first attempt are 22.5 percent.
Describe probability.
To forecast how likely occurrences are to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment.
This idea is used to discuss the probability or likelihood of an event happening.
The frequency of the number 8 is seven.
The frequency of the number 9 is 11.
The full list of frequencies is provided as
10 + 9 + 6+ 7 + 8 + 12 + 4 + 6 + 7 + 11 = 80
7 + 11 = 18
18/80 is the probability.
= 0.225 x 100
22.5 percent
Click here to learn more about probability:
brainly.com/question/251701
#SPJ4
HELP!!!!!!QUICK!!!!!!!
Jake started biking to the coffee shop traveling 8 mph, after some time the bike got a flat so Jake walked the rest of the way, traveling 4 mph. If the total trip to the coffee shop took 9 hours and it was 60 miles away, how long did Jake travel at each speed
Jake travel to the coffee shop by bike with speed of [tex]8mph[/tex] is [tex]56mile[/tex] and when bike got a flat so Jake walked [tex]4mile[/tex]
How to find the speed by biking and walking ?
let [tex]b[/tex] = time spent biking
then [tex]8-b[/tex] =time spent walking
Write distance equation
[tex]dist=speed *time[/tex]
So bike distance [tex]+[/tex] walk distance [tex]=60mile[/tex]
[tex]8b+4(8-b)=60\\8b+32-4b=60\\4b=60-32\\b=28/4\\\\b=7hrs[/tex]
Then [tex]8-7=1 hrs[/tex] spent walking.
For cross check the answer find that actual distance for each
[tex]8(7)=56mi\\4(1)=4mi\\-------\\total distance=60mile[/tex]
Learn more about distance and speed here :
https://brainly.com/question/28045840
#SPJ4
choose the equation that satisfies the data in the table
Answer:
B is the answer
Step-by-step explanation:
Triangles A B C and T P Q are shown. Sides A C and T Q are congruent. Angles B C A and P Q T are congruent. Which statements are true about additional information for proving that the triangles are congruent? Select two options.
If Angle A ≅ Angle T, then the triangles would be congruent by ASA
If Angle B ≅ Angle P, then the triangles would be congruent by AAS.
How to Identify congruency statements?We are told that;
Sides AC and TQ are congruent.
Angles BCA and PQT are congruent.
Thus, we can say that;
Side AC and side TQ are congruent.
Angle BCA and angle PQT are congruent too.
Since angle A and angle T are congruent, it means the congruency theorem used will be ASA(Angle - Side - Angle) Theorem.
Lastly, if angle B were to be congruent to angle P, it means the congruency theorem used will be AAS(Angle - Angle - Side) Theorem.
The missing options are;
A) If AngleA ≅ AngleT, then the triangles would be congruent by ASA.
B) If AngleB ≅ AngleP, then the triangles would be congruent by AAS.
C) If all the angles are acute, then the triangles would be congruent.
D) If AngleC and AngleQ are right angles, then triangles would be congruent.
E) If BC ≅ PQ, then the triangles would be congruent by ASA.
Read more about congruency at; https://brainly.com/question/1675117
#SPJ1
pls i need help on this quick pls
Answer:
Answer should be 15
Step-by-step explanation:
25 divided by 15 is 1.6666666667 so if use that multiply 9 you'll get 15.
Answer:
Step-by-step explanation:
A^2 + B^2=C^2
30^2 -25^2= 16.5
answer= 16.5
1) (x-y)(y-2)(x+2) / 2x^2+4yz+6 =
2) 4(x+y)(x-y)(y-x) / t+d+m =
3) ( √25+√9 / 2 ) + √21675 =
4) (9x^2+3x+27)(3+6y)(4+6y) / 1+2a+38+4c+2000z =
5) (x^2+6x+5) / (x+2)(x+6) =
^^^Simplify
6) (xy/m) + (xm/y) - (m/x) = 63 x=
Isolate
Could anyone help me with these?
See below for the solution to each expression
How to solve the expressions?Expression 1
The expression is given as:
(x-y)(y-z)(x+z)/(2x^2+4yz+6)
Expand the numerator
(x^2 - y^2 -xz + yz)(x + z)/(2x^2+4yz+6)
Further, expand the numerator
(x^3 - xy^2 - x^2z + xyz + x^2z - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Evaluate the like terms
(x^3 - xy^2 + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Hence, the equivalent expression of (x-y)(y-z)(x+z)/(2x^2+4yz+6) is (x^3 - xy^2 + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)
Expression 2
The expression is given as:
4(x+y)(x-y)(y-x)
Apply the difference of two squares
4(x^2 - y^2)(y - x)
Expand the expressions in the brackets
4(x^2y - x^3 - y^3 + xy^2)
Open the bracket
4x^2y - 4x^3 - 4y^3 + 4xy^2
Hence, the equivalent expression of 4(x+y)(x-y)(y-x) is 4x^2y - 4x^3 - 4y^3 + 4xy^2
Expression 3
The expression is given as:
(√25+√9/2) + √21675
Take the square roots of 25, 9 and 21675
(5 +3/2) + 5√867
Evaluate the sum
13/2 + 5√867
Hence, the equivalent expression of (√25+√9/2) + √21675 is 13/2 + 5√867
Expression 4
The expression is given as:
(9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z
Factor out 3 and 2 from the numerator
3(3x^2 +x + 9) * 3(1 + 2y) * 2(2 + 3y)/1+2a+38+4c+2000z
This gives
18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z
The expression cannot be further simplified.
Hence, the equivalent expression of (9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z is 18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z
Expression 5
The expression is given as:
(x^2+6x+5)/(x+2)(x+6)
Factorize the numerator
(x + 1)(x + 5)/(x + 2)(x + 6)
Hence, the equivalent expression of (x^2+6x+5)/(x+2)(x+6) is (x + 1)(x + 5)/(x + 2)(x + 6)
Expression 6
6) (xy/m) + (xm/y) - (m/x) = 63
Factor out x
x(y/m + m/y) - m/x = 63
Evaluate the sum
x(y^2 + m^2)/y - m/x = 63
Multiply through by xy
x^2(y^2 + m^2) - my = 63xy
Add my to both sides
x^2(y^2 + m^2) = 63xy + my
The above implies that the variable x cannot be isolated from the equation
Read more about expressions at:
https://brainly.com/question/723406
#SPJ1
Can someone help me please
The domain of the function will therefore be 0≤x<∞
Domain of a functionDomain of a function are the independent value for which a function exists. Given the function below;
f(x) = [tex]\sqrt[4]{x}[/tex]
Since the value in the root cannot be negative hence the domain of the function will be all positive real numbers.
The domain of the function will therefore be 0≤x<∞
Learn more on domain here: https://brainly.com/question/25959059
#SPJ1
Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.
Answer:
? = 120°
Step-by-step explanation:
the central angle is the same as the arc that subtends it , that is
? = 120°
Can you help me,pls
Answer:
x^4 +2 +x^-4
Step-by-step explanation:
The square of a binomial is a form worthy of memorization.
(a +b)² = a² +2ab +b²
ApplicationHere, you have a binomial with a=x² and b=1/x². Using these values in the pattern, we have ...
[tex]\left(x^2+\dfrac{1}{x^2}\right)^2=(x^2)^2+2(x^2)\dfrac{1}{x^2}+\left(\dfrac{1}{x^2}\right)^2\\\\=\boxed{x^4+2+\dfrac{1}{x^4}}[/tex]
Consider the function shown on the graph.
45-
12
9.
6
3
-13.
999
-6-
-9
-12-
-15-
(3, 0)
23
(8, 15)
((7,0)
5 6 7 8 9
X
Which function does the graph represent?
Of(x) = (x+3)(x + 7)
Of(x)=(x-3)(x-7)
Of(x)=3(x-3)(x-7)
Of(x)= 11(x+3)(x + 7)
Answer:
(c) f(x) = 3(x -3)(x -7)
Step-by-step explanation:
The correct function can be chosen by looking at the x-intercepts and the behavior around the vertex.
X-interceptsThe graph crosses the x-axis at x=3 and x=7. Each x-intercept x=p gives rise to a factor (x -p). These two x-intercepts mean the function will have factors ...
(x -3)(x -7) . . . . . . . . eliminates choices A and D
Vertex behaviorThe vertical scale factor of the quadratic is easily found by looking at the function behavior near the vertex. Specifically, the scale factor is the change in y-value at a distance of 1 unit either side of the vertex.
Here, the y-value at the vertex (x=5) is -12. The y-value at x=4 and x=6 is -9, three units up from the value at the vertex. This means the vertical scale factor (leading coefficient) is 3. (This eliminates choice B.)
EquationPutting these observations together, we have determined the equation of the function to be ...
f(x) = 3(x -3)(x -7) . . . . . . matches choice C
A river flows at 2m/s . Juan's boat can travel twice as fast down the river as it can go up the river. how fast the boat go in still water?
Using proportions, it is found that the boat can go 6 m/s in still water.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, we have that:
Down the river, the speed is v + 2.Up the river, the speed is v - 2.He goes twice as fast down the river, hence:
v + 2 = 2(v - 2).
v + 2 = 2v - 4
2v - v = 2 + 4
v = 6.
The boat can go 6 m/s in still water.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Calculate x for each of the following right angled triangles.
Give your answer as a simplified surd (or integer).
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
(a) x = 6.5 cm (b) x = 10 cm(c) x = 7 cm(d) x = 7.9 cmStep-by-step explanation:
To find an unknown side of a right angled triangle we use a theorum called pythagorus theorum..
Formula :(Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2
(h)^2 = (p)^2 + (b)^2
therefore,(a) hypotenuse = x cm, base = √30 cm, perpendicular = √12 cm.
by formula,→ h^2 = p^2 + b^2
→ (x)^2 = (√12)^2 + (√30)^2
→ x^2 = 12 + 30
→ x^2 = 42
→ x = √42
→ x = 6.480...
→ x = 6.5 cm. (approx)
___________________________(b) hypotenuse = √300 cm, base = √200 cm,perpendicular = x cm.
by formula,→ h^2 = p^2 + b^2
→ (√300)^2 = (x)^2 + (√200)^2
→ 300 = x^2 + 200
→ x^2 = 300 – 200
→ x^2 = 100
→ x = √100
→ x= 10 cm.
___________________________(c) hypotenuse = √66 cm, base = √17 cm,perpendicular = x cm.
by formula,→ h^2 = p^2 + b^2
→ (√66)^2 = (x)^2 + (√17)^2
→ 66 = x^2 + 17
→ x^2 = 66 – 17
→ x^2 = 49
→ x = √49
→ x = 7 cm.
___________________________(d) hypotenuse = x cm, base = 5√12 cm,perpendicular = 2√3 cm.
by formula,→ h^2 = p^2 + b^2
→ (x)^2 = (2√3)^2 + (5√12)^2
→ x^2 = 12 + 50
→ x^2 = 62
→ x = √62
→ x = 7.874...
→ x = 7.9 cm. (approx)
___________________________Hope it helps you!!A local salesman receives a base salary of $975 monthly. He also receives a commission of 6% on all sales over $1200. How much would he have to sell in a month if he needed to have a monthly income of $2500
He has to sell in a month $26616.67.
Given that a local salesman receives a base salary of $975 monthly and he also receives a commission of 6% on all sales over $1200.
A numerical assertion wherein two articulations are delivered equivalent to each other is known as an algebraic condition.
Let the Sales amount be s.
We have:
Sales over 1,200 is written as
s-1200
6% is also 0.06 as a decimal,
so according to question, we have
0.06(s - 1200) + 975=2500
Now, we will apply the distributive property a(b+c)=ab+ac, we get
0.06s-0.06×1200+975=2500
Further, we want to simplify the left-hand side, we get
0.06s-72+975=2500
0.06s+903=2500
Furthermore, we will subtract 903 from both sides, we get
0.06s+903-903=2500-903
0.06s=1597
Now, we will divide both sides with 0.06, we get
0.06s/0.06=1597/0.06
s=26616.67
Hence, he have to sell in a month if he needed to have a monthly income of $2500 is $26616.67.
Learn more about algebraic equation from here brainly.com/question/4344214
#SPJ4
10 points + BRAINEST
[tex]\textbf{Heya !}[/tex]
basic math tips -»
"of" means multiply
[tex]\sf{\cfrac{1}{10}\cdot\cfrac{5}{1}}[/tex]
multiply the numerators and denominators times each other -»
[tex]\sf{\cfrac{5}{10}}[/tex]
reduce:-
[tex]\sf{\cfrac{1}{2}}[/tex]
`hope it was helpful to u ~
Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of sines, what is the measure of side c? Round your answer to the nearest whole number, if necessary.
b = 11 cm
B = 80°
C = 54°
Answers
13 cm
15 cm
17 cm
9 cm
The measure of side c is 9 cm. The correct option is the last option 9 cm
Law of SinesFrom the question, we are to determine the measure of side c
From the law of sines, we have that
[tex]\frac{c}{sinC} =\frac{b}{sinB}[/tex]
From the given information,
b = 11 cm
B = 80°
C = 54°
Putting the parameters into the equation, we get
[tex]\frac{c}{sin54^\circ} =\frac{11}{sin80^\circ}[/tex]
[tex]c =\frac{11\times sin54^\circ}{sin80^\circ}[/tex]
c = 9.03647
c ≈ 9 cm
Hence, the measure of side c is 9 cm. The correct option is the last option 9 cm
Learn more on Law of sines here: https://brainly.com/question/15140698
#SPJ1
Which expression belongs
For the expression to be equal to the original one, we have;
[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]
How to Simplify Algebraic Expressions?
We are given the algebraic expression;
(5x² + 25x + 20)/(7x)
Now, looking at the numerator, a common factor to all terms is 5. Thus, we will factorize it out to get;
5(x² + 5x + 4) = 5((x + 1)(x + 4))
Now, we see that the expression that simplifies the algebra is given as;
[(x² + 2x + 1) * ( )]/[( ) * (7x² + 7x)]
Now, the numerator and denominator can be factorized to get;
[(x + 1)(x + 1) * ( )]/[( ) * 7x(x + 1)]
Thus, x + 1 will cancel out to get;
[(x + 1) * ( )]/[( ) * 7x]
For the expression to be equal to the original one, we have;
[(x + 1) * 5(x - 1)(x + 4)]/[(x - 1) * 7x]
Read more about Algebraic Expressions at; https://brainly.com/question/723406
#SPJ1
Does this graph represent a function? Why or why not?
A. No, because it is not a straight line.
• B. Yes, because it passes the vertical line test.
C. Yes, because it is a curved line.
• D. No, because it fails the vertical line test.
SUBMIT
Answer:
B. Yes, because it passes the vertical line test.
Step-by-step explanation:
Vertical line test - if a vertical line passes through more than one pone, the relation is not a function
Any vertical line will only pass through one point, so this relation is a function
The relation is a function because it passes the vertical line test