Answers
Answer:
P(x < 84) = 0.3085 or approximately 31%============
Hello to you from Brainly team!
GivenMean grade μ = 86,Standard deviation σ = 4,Grade limit x = 84.To find Probability of that a randomly selected grade is less than 84 or P(x < 84).SolutionFind z-score using relevant equation:
z = (x - μ)/σSubstitute values and calculate:
z = (84 - 86)/4 = - 0.5Using the z-score table find the corresponding P- value.
P(x < 84) = 0.30854 or approximately 31%Answer:0.30854
Step-by-step explanation:Solution:
Given:
Using the z-scores formula;
From the z-scores table, the probability is;
Therefore, the probability that the grade is less than 84 is 0.30854
Related Questions
(4) A taxi service charges Rs.100 as an initial fee and Rs.50 for each kilometer travelled. Write an algebraic expression for the total amount that has to be paid for a journey of x meters.
Answers
Answer:
f(x) = 50x + 100
Explanation:
The term "Rs. 100" is constant. The term "Rs. 50" keeps changing per km.
Linear equation: y = mx + b, where 'm' is rate of change, 'b' is constant
Equation built:
f(x) = 50x + 100
This will determine the cost for journey of x meters.
Suppose you start with a full tank of gas (17 gallons) in your truck. After driving 3 hours, you now have 3 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is the gas left in the tank changing
Answers
Step-by-step explanation:
in 3 hours the truck used 17 - 3 = 14 gallons.
that means it used
14 gallons / 3 hours = 14/3 gallons / hour
and that means it is using
14/3 × x gallons in x hours
y = 17 - (14/3 × x)
the gas left in the tank is decreasing by 14/3 gallons per hour.
The slope of the line is -2 use the coordinates (4,-6) to find the point-slope equation of the line
Answers
Answer: [tex]y+6=-2(x-4)[/tex]
Step-by-step explanation:
See attached image.
Quick algebra 1 assignment for 50 points!
Only answer if you know the answer, tysm!
1. Create 5 questions referencing “Zeros and Intercepts”Below is an example of one.
——————————————————————
Example :
Given: h(x) = -2x + 10
What are the x-intercepts and y-intercepts of h?
a. x-intercepts of (0,5) and y-intercepts of (10,0)
b. x-intercepts of (10,0) and y-intercepts of (0,5)
c. x-intercepts of (5,0) and y-intercepts of (0,10)
d. x-intercepts of (0,10) and y-intercepts of (5,0)
——————————————————————
2. Answer each question and write a brief step by step process on how you got the answer to each of your questions.
Answers
x intercept:-
put y =0
-2x+10=0-2x=-10x=5(5,0)
y intercept
put x=0
y=-2(0)+10y=10(0,10)
option C
Question 1: Given a(x) = x + 5, what are the x-intercepts and y-intercepts of a?
a. x-intercept at (-5,0), y-intercept at (0,5)
b. x-intercept at (5,0), y-intercept at (0,-5)
c. x-intercept at (0,5), y-intercept at (5,0)
Answer: a
The x-intercept is the place where the graph touches the x-axis. Since the equation for the x-axis is just y=0, we can put in 0 for y to get it.
0 = x + 5
x = -5
Since x is -5 and y is 0, the x-intercept is at (-5,0).
The y-intercept is the place where the graph touches the y-axis. Since the equation for the y-axis is just x=0, we can put in 0 for x to get it.
y = 0 + 5
y = 5
Since x is 0 and y is 5, the y-intercept is at (0,5).
Question 2: Given b(x) = 2x + 1, what are the x-intercepts and y-intercepts of b?
a. x-intercept at (0.5, 0), y-intercept at (0, 2)
b. x-intercept at (-0.5,0), y-intercept at (0, 1)
c. x-intercept at (0, -0.5), y-intercept at (1,0)
Answer: b
The x-intercept is the place where the graph touches the x-axis. Since the equation for the x-axis is just y=0, we can put in 0 for y to get it.
0 = 2x + 1
x = -0.5
Since x is -0.5 and y is 0, the x-intercept is at (-0.5,0).
The y-intercept is the place where the graph touches the y-axis. Since the equation for the y-axis is just x=0, we can put in 0 for x to get it.
y = 2(0) + 1
y = 1
Since x is 0 and y is 1, the y-intercept is at (0,1).
Question 3: Given c(x) = 3x - 2, what are the x-intercepts and y-intercepts of c?
a. x-intercept at (-2,0), y-intercept at (0,2/3)
b. x-intercept at (0, 2), y-intercept at (3/2, 0)
c. x-intercept at (2/3, 0), y-intercept at (0, -2)
Answer: c
The x-intercept is the place where the graph touches the x-axis. Since the equation for the x-axis is just y=0, we can put in 0 for y to get it.
0 = 3x - 2
x = [tex]\frac{2}{3}[/tex]
Since x is 2/3 and y is 0, the x-intercept is at (2/3,0).
If the equation is in the form y = mx + b, the y-intercept will be b. The y-intercept also crosses the graph x = 0, so the y-intercept is (0, -2).
Question 4: Given d(x) = -x + 1, find the x-intercepts and y-intercepts of d.
a. x-intercept at (0, 1), y-intercept at (1,0)
b. x-intercept at (1, 0), y-intercept at (0, -1)
c. x-intercept at (1,0), y-intercept at (0,1)
Answer: c
The x-intercept is the place where the graph touches the x-axis. Since the equation for the x-axis is just y=0, we can put in 0 for y to get it.
0 = -x+1
x = -(-1) = 1
Since x is 1 and y is 0, the x-intercept is at (1,0).
If the equation is in the form y = mx + b, the y-intercept will be b. The y-intercept also crosses the graph x = 0, so the y-intercept is (0, 1).
Question 5: Given f(x) = -7x+5, find the x-intercepts and y-intercepts of f.
a. x-intercept at (-5/7, 0), y-intercept at (0, -7/5)
b. x-intercept at (5, 0), y-intercept at (0, 5/7)
c. x-intercept at (5/7, 0), y-intercept at (0, 5)
Answer: c
The x-intercept is the place where the graph touches the x-axis. Since the equation for the x-axis is just y=0, we can put in 0 for y to get it.
0 = -7x+5
x = -5/-7= 5/7
Since x is 5/7 and y is 0, the x-intercept is at (5/7,0).
If the equation is in the form y = mx + b, the y-intercept will be b. The y-intercept also crosses the graph x = 0, so the y-intercept is (0, 5).
Find the equation of the linear function represented by the table below in slope-intercept form.
Answers
Answer:
y=-2x+5
Step-by-step explanation:
For every increase in x, y decreases by 2
so the slope is -2
You can solve for the y-intercept by going backward, 1-1=0, 3+2=5
the y-intercept is (0,5)
Using the slope intercept equation format, the answer is y-2x+5
Determine the period.
Answers
Answer:
[tex]5 \cos( \frac{2\pi x}{7} ) [/tex]
The period of the given graph is 2π.
A period is the amount of time between two waves, whereas a periodic function is one whose values recur at regular intervals or periods. In other terms, a periodic function is one whose values recur after a specific interval.
This specific time span indicated above is the function's period.
The length of one function wave is referred to as the period.
The sine and cosine functions have a period of 2π radians, or 360 degrees. The period of the tangent function is π radians, or 180 degrees.
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The graphs below have the same shape. What is the equation of the red
graph?
Answers
Answer:
[tex]G(x) = 6-x^{4}[/tex]
Step-by-step explanation:
The red graph is the blue graph translated up 3 units, so the answer is [tex]G(x) = 6-x^{4}[/tex].
PLEASE IM BEGGING U so hard to understand T_T
Answers
Answer:
[tex]b^{2} +7b+7[/tex] with remainder 1
please can someone tell me how to get the answer
Answers
The number of three-digit number you can make is 8
How to determine the number of digits?The usable digits are given as:
4 and 9
Since the two digits can be repeated, then we have
First = 2
Second = 2
Third = 2
So, we have:
Total = 2 * 2 * 2
Evaluate
Total = 8
Hence, the number of three-digit number you can make is 8
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Does this graph represent a function? What is the domain and range of the graph? On a coordinate plane, a line goes through (negative 2, 2) to (0, 0) and another line goes from (0, 0) through (2, 2).
a. Yes; domain: all real numbers; range: y = 0
b. Yes; domain: all real numbers; range: y greater-than-or-equal-to 0
c. No; domain: all whole numbers; range: y less-than-or-equal-to 0
d. Yes; domain: all real numbers; range: y greater-than 0
Answers
The domain and the range of the function are given as follows:
b. Yes; domain: all re.al numbers; range: y greater-than-or-equal-to 0.
What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.Since each input is related to only one output values, the graph is a function. It is defined for all values of x, assuming only non-negative values, hence the correct option is:
b. Yes; domain: all re.al numbers; range: y greater-than-or-equal-to 0.
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Rank--from first to last--the following steps for finding the bottleneck and capacity in a process with rework.
Answers
Steps for finding the bottleneck and capacity in a process with rework:
atevaluateevaluate---What is the bottleneck and capacity in a process with a rework?In production and project management, a bottleneck is a process in a chain of processes whose restricted capacity reduces the capacity of the entire chain. A bottleneck causes production stalls, supply overstock, customer pressure, and low employee morale.To evaluate a reworked process, a weighted average processing time must be calculated. Because the processing time for rework differs from the initial processing time, a weighted average processing time must be computed. The resource's capacity is divided by its weighted average processing time.Steps for determining the bottleneck and capacity in a reworked process:atevaluateevaluate---Therefore, steps for finding the bottleneck and capacity in a process with rework:
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An allergy medication is successful in treating 60% of all patients who use it. The medication is given to 200 patients. Let X
Answers
The mean is μ=140.
The standard deviation is σ = 6.4807.
The probability that X (number of successful treatments) is 128 or less is 0.0322.
What is normal distribution curve?In statistics, a normal distribution's probability density function is represented by a symmetrical bell-shaped curve. The likelihood that the random variable will fall between two values that define a vertical portion of the curve is represented by the area of the section.
According to the question,
An allergy medication is successful in treating 70%
The medication is given to 200 patients.
Thus,
The random variable X is a binomial random variable with n = 200 (there were 200 patients).
The probability that a medication is successful in treating a randomly selected patient is 0.7.
p = 0.7 (the medication was successful in 70% cases).
Step 1: Use the formulas for mean and standard deviation of a binomial random variable X.
[tex]\begin{gathered}\mu=E(X)=n \cdot p \\\sigma=\sqrt{n \cdot p \cdot(1-p)}\end{gathered}[/tex]
Substitute values of 'n' and 'p' to get the result,
[tex]\begin{gathered}\mu=200 \cdot 0.7=140 \\\sigma=\sqrt{200 \cdot 0.7 \cdot 0.3}=\sqrt{42}=6.4807 .\end{gathered}[/tex]
Thus, the mean is obtained as 140.
The standard deviation is 6.4807.
Step 2: find P(X≤128)
As a result, the prerequisites for a normal approximation to the binomial distribution are satisfied.
[tex]$n \cdot p=200 \cdot 0.7=140 \geq 10$$$n \cdot(1-p)=200 \cdot 0.3=60 \geq 10 .$$[/tex]
[tex]\begin{aligned}P(X \leq 128) & \approx P\left(Z \leq \frac{128-n \cdot p}{\sqrt{n \cdot p \cdot(1-p)}}\right)=P\left(Z \leq \frac{128-200 \cdot 0.7}{\sqrt{200 \cdot 0.7 \cdot(1-0.7)}}\right) \\&=P(Z \leq-1.85)=0.0322\end{aligned}[/tex]
Therefore, the probability that X is 128 or less. is 0.0322.
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The complete question is-
An allergy medication is successful in treating 70% of all patients who use it. The medication is given to 200 patients. Let X = number of successful treatments. What are the mean and standard deviation of X? Use the normal curve to approximate the probability that X is 128 or less.
What is the surface area of pyramid with a square base of 5km and slant of 4.7km
Answers
The surface area of pyramid is 47km^2
A regular pyramid has a base that is a regular polygon and a vertex that is above the center of the polygon.
A pyramid is named after the shape of its base. A rectangular pyramid has a rectangle base. A triangular pyramid has a triangle base.
Given that the base of the pyramid is 5 km and the slant height is 4.7km
We need to find the surface area of pyramid
We know that
The lateral surface of pyramid = 4 *(1/2* length of base * slant height)
= 2*5*4.7
=47km^2
Hence the surface area of the pyramid is 47km^2
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[tex]what must be added to 4x2+3xy-7 to get x2-5xy
Answers
4x² + 3xy - 7 + (y) = x² -5xy
y = -3x² - 8xy + 7
The correct answer is -3x² -8xy + 7
Find the h.c.f of {x}^{3} + {y}^{3} \: and \: \: {x}^{2} - xy + {y}^{2}x 3 +y 3 andx 2 −xy+y 2
Answers
Factorize the sum of cubes:
[tex]x^3 + y^3 = (x+y) (x^2 - xy + y^2)[/tex]
so [tex]x^2-xy+y^2[/tex] is a factor of [tex]x^3+y^3[/tex]. Then the HCF is [tex]\boxed{x^2 - xy + y^2}[/tex].
The top of the John Hancock Building is a rectangle whose length is 60 ft more than the width. The perimeter is 520 feet. What is the length?
Group of answer choices
a. L = 160 ft
b. L = 40 ft
c. L = 100 ft
d. L = 80 ft
Answers
Answer:
160 ft
Step-by-step explanation:
We have
2(length + width)= perimeter
than,
let, width =x
now,
2(x+60+x) = 520
or, 2x+60 = 260
or, 2x = 200
or, x = 100
so length is 100+60 = 160
PLS HELP ME QUICKLY PLSSS IM BEGGINGG
Answers
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "GRAPHS." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
If the discriminant of a quadratic equation is 2, then the equation has Select an answer . If the discriminant of a quadratic equation is 4, then the equation has Select an answer . If the discriminant of a quadratic equation is 0, then the equation has Select an answer .
Answers
1) If the discriminant is greater than 0, the quadratic equation has 2 real solutions. Here D is grater than 0 . the quadratic equation has two real, distinct (different) roots.
2) If the discriminant of a quadratic equation is 4, then there are two real roots.
3) A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.
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Labor productivity is normally measured by Part 2 A. the educational level of workers. B. the change in the amount of leisure. C. dividing total real domestic output by the number of workers or by the number of labor hours. D. the percentage change in GDP.
Answers
Labor productivity is normally measured by (c) dividing total real domestic output by the number of workers or by the number of labor hours.
What is Labour productivity?The total volume of production (measured in terms of Gross Domestic Product, GDP) produced per unit of labor (measured in terms of the number of employed workers or hours worked) during the course of a specific time reference period is what is referred to as labor productivity.Divide the total output by the total labor hours to find the labor productivity of a nation.What is labour productivity in India?
A measurement of labor output is labor productivity. Hourly productivity metrics are used. The actual Gross Domestic Product (GDP) produced by labor in an hour is what is referred to as labor productivity in macroeconomics. An important component of a business's overall growth is labor productivity.Learn more about labour productivity
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Someone help me pls and thank you
Answers
Answer:
4,11
Step-by-step explanation:
11-4=7
11*4=44
To find the actual integers, factor 44 and experiment with each pair of factors, an example being 2 and 22.
2*22=44
However, if you subtract 2 from 22, you get 20, not 7.
22-2-20
identify the steps for proving AD ==DC
Answers
Answer:
using pythagoras theorem
Consider the graph of the function f(x)=2^x which statements describe key features of function g if g(x)=3f(x)?
it's multiple choice, select all the correct answers:
y-intercept at (0,1)
y-intercept at (0,3)
horizontal asymptote of y=3
x-intercept at (3,0)
horizontal asymptote of y=0
no x-intercept
Answers
Answer:
y-intercept at (0,3)horizontal asymptote of y=0no x-interceptStep-by-step explanation:
The y-intercept of f(x) is (0,1), so the y-intercept of g(x) is (0,3).
f(x) has a horizontal asymptote at y=0. and so does g(x).
f(x) does not have an x-intercept, and neither does g(x).
Answer:
y-intercept at (0, 3)
horizontal asymptote of y = 0
no x-intercept
Step-by-step explanation:
Definitions
y-intercept: the point(s) at which the curve crosses the y-axis (when x=0).
x-intercept: the point(s) at which the curve crosses the x-axis (when y=0).
Asymptote: a line that the curve gets infinitely close to, but never touches.
Given function:
[tex]f(x)=2^x[/tex]
Properties of function f(x):
y-intercept at (0, 1)As x → -∞, y → 0 therefore there is a horizontal asymptote at y=0 and no x-intercept (since the curve never crosses the x-axis).As x → ∞, y → ∞[tex]\textsf{If }g(x)=3f(x):[/tex]
[tex]\implies g(x)=3(2)^x[/tex]
Properties of function g(x):
y-intercept at (0, 3)As x → -∞, y → 0 therefore there is a horizontal asymptote at y=0 and no x-intercept (since the curve never crosses the x-axis).As x → ∞, y → ∞Therefore the true statements are:
y-intercept at (0, 3)horizontal asymptote of y = 0no x-interceptA man bought 42 stamps, some 13¢ and some 18¢. How many of each kind did he buy if the cost was $6.66? If x represents the number of 13 cent stamps and y the 18 cent stamps, which system represents the problem?
Answers
Answer:
18 stamps of 13 cent
24 stamps of 18 cent
Step-by-step explanation:
we have to solve the following system:
x + y = 42 equation (1)
13x + 18y = 666 equation (2)
(1) ⇒ y = 42 - x
We substitute y by 42 - x in equation (2) :
13x + 18(42 - x) = 666
⇔ 13x + 756 - 18x = 666
⇔ -5x + 756 = 666
⇔ -5x = 666 - 756
⇔ -5x = -90
⇔ x = 18
…………………………
Then
y = 42 - x
= 42 - 18
= 24
Which of these tables represents a function
Answers
The table that represents a function is:
C. YWhat is a Function?A function is an expression that represents the relationship between two variables. The variables in this case are the dependent and independent variables.
To identify a function, you need to note that no variable of x should be equal to y.
The formular is represented this way: y = f(x). The table that satisfies this condition is the Y table.
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Help me pleaseeeeeeeeeeeeeeeeeeeee
Answers
Answer:
a = 16.52 cmb = 23.85 cm=========================
Given AB = 22 cmm∠A = 42°m∠B = 75°To findSide length of a and bSolutionThe law of sines is:
a/sin A = b/sin B = c/sin CStep 1Find the value of ∠C using the angle sum theorem:
m∠A + m∠B + m∠C = 180°42° + 75° + C = 180°117° + C = 180°C = 180° - 117°C = 63°Step 2Find side a:
Note, the sides of a triangle are marked as:
a = BC, b = AC, c = AB (opposite to respective angle).Use two pairs with one unknown:
a/sin A = c/sin CSubstitute values and solve for a:
a/ sin 42° = 22/sin 63°a = 22*sin 42°/sin 63°a = 16.52 cm (rounded)Step 3Find side b, similar to finding side a:
b/ sin 75° = 22/sin 63°b = 22*sin 75°/sin 63°b = 23.85 cm (rounded)Answer:
a = 16.5 cm (nearest tenth)
b = 23.8 cm (nearest tenth)
Step-by-step explanation:
Definition
A, B and C are the angles and a, b and c are the sides opposite the angles.
From inspection of the triangle:
A = 42°B = 75°c = 22 cmInterior angles of a triangle sum to 180°:
⇒ A + B + C = 180°
⇒ 42° + 75° + C = 180°
⇒ C = 180° - 117°
⇒ C = 63°
To find the missing side lengths a and b, use the Sine Rule:
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
Substitute the given values into the Sine Rule formula:
[tex]\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
Finding side a:
[tex]\implies \sf \dfrac{a}{\sin 42^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf a=\dfrac{22\sin 42^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf a=16.52162239...[/tex]
Therefore, side a is 16.5 cm (nearest tenth).
Finding side b:
[tex]\implies \sf \dfrac{b}{\sin 75^{\circ}}=\dfrac{22}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf b=\dfrac{22\sin 75^{\circ}}{\sin 63^{\circ}}[/tex]
[tex]\implies \sf b=23.84984577...[/tex]
Therefore, side b is 23.8 cm (nearest tenth).
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40 boys and 28 girls stand in a circle, hand in hand, all facing inwards. Exactly 18 boys give their right hand to a girl. How many boys give their left hand to a girl
Answers
Answer:
28-18=10
Step-by-step explanation:
10 boys give their left hand
hope it helps
sry if im wrong
There are 10 boys who give their left hand to a girl in the given scenario.
In a circle, the total number of students is equal to the sum of the number of boys and girls.
Therefore, in this case, there are 40 boys + 28 girls = 68 students in total.
Since exactly 18 boys give their right hand to a girl, there are 18 boys who are connected to girls in a clockwise direction. As the remaining boys are connected in a counterclockwise direction, the number of boys giving their left hand to a girl can be determined by subtracting 18 from the total number of girls.
Thus, the number of boys giving their left hand to a girl is 28 - 18 = 10 boys.
Therefore, there are 10 boys who give their left hand to a girl in the given scenario.
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please help me with this im struggling
Answers
=======================================================
Explanation:
Triangle ABC is similar to triangle DEF. The order of the lettering is important because it tells us how the letters pair up.
A and D are the 1st letters, so they pair upB and E are the 2ndletters, so that's another pairC and F are the 3rd letters, which is the final pair of pointsBased on that, we can determine how the segments pair up
AB and DE correspond to each other. The segments are composed of the 1st and 2nd points.BC and EF correspond as well. The segments use the 2nd and 3rd points.AC and DF correspond also. They use the 1st and 3rd points.We want to find how long EF is, which means we'll involve BC = 17 since it is paired with it.
The diagram shows that AC = 14 and DF = 3, which is another pair we'll use
--------------------------
The key takeaway is that
AC = 14 and DF = 3 pair up togetherBC = 17 and EF also pair up togetherThose two facts lead to the steps below
[tex]\frac{AC}{DF} = \frac{BC}{EF}\\\\\frac{14}{3} = \frac{17}{EF}\\\\14*EF = 3*17\\\\14*EF = 51\\\\EF = \frac{51}{14}\\\\EF \approx 3.642857\\\\EF \approx 3.6\\\\[/tex]
The proportion in step 1 is valid due to the similar triangles, and because of the corresponding side pairs mentioned. In step 3, I cross multiplied.
Answer:
3.6 cm
Step-by-step explanation:
Similar Triangle Theorem
If two triangles are similar, the ratio of their corresponding sides is equal.
Given triangles:
ΔABC and ΔDEFTherefore the corresponding sides are:
AC and DF, BC and EF, AB and DETo find the measure of side EF, use the Similar Triangle Theorem:
[tex]\implies \sf AC:DF=BC:EF[/tex]
[tex]\implies \sf \dfrac{AC}{DF}=\dfrac{BC}{EF}[/tex]
[tex]\implies \sf \dfrac{14}{3}=\dfrac{17}{EF}[/tex]
[tex]\implies \sf EF=17 \cdot \dfrac{3}{14}[/tex]
[tex]\implies \sf EF=\dfrac{51}{14}[/tex]
[tex]\implies \sf EF=3.642857...[/tex]
[tex]\implies \sf EF=3.6\:cm\:\:(nearest\:tenth)[/tex]
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You have a set of 10 cards: five red and five blue. Each group of five colored cards is numbered one through five. What is the probability of drawing a red four and then a blue four, while replacing the card between the drawings?
1/100
1/10
1/20
1/90
Answers
The probability of drawing a red four and then a blue four is:
P = 1/100
How to get the probability?
We know that there are 10 cards in total, then the probability of drawing a red four (there is only one of these cards) is:
p = 1/10
Now we put the red four again, the probability of getting a red blue is computed in the same way:
q = 1/10
The probability for both events happening consecutively is:
P = p*q = (1/10)*(1/10) = 1/100
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A bike shop offers three kinds of cycles—tricycles, bicycles, and unicycles. Together, the cycles in the shop have a total of 98 wheels and 46 seats. (Tricycles have 3 wheels, bicycles have 2 wheels, and unicycles have 1 wheel. All cycles have 1 seat.) There are twice as many bicycles as tricycles. How many of each type of cycle are in the shop?
Answers
Answer:
There are 13 tricycles, 26 bicycles, and 7 unicycles.
Step-by-step explanation:
Let t=the number of tricycles, b=the number of bicycles, and u=the number of unicycles.
Equation to find the number of wheels:
3t+2b+u=98
This can be found because we know that each tricycle has 3 wheels, so we multiply the number of tricycles by 3. This can be done with bicycles and unicycles as well.
Equation to find the number of seats:
t+b+u=46
We know that there are two times as many bicycles as there are tricycles, this can be represented by the equation b=2t.
We can plug this into our number to wheels equation to get:
3t+2(2t)+u=98
3t+4t+u=98
7t+u=98
u=-7t+98
We can also put this into out number of seats equation to get:
t+2t+u=46
3t+u=46
u=-3t+46
Set the equations equal to each other to get:
-7t+98=-3t+46
-4t+98=46
-4t=-52
t=13
b=2t
b=2(13)
b=26
b+t+u=46
26+13+u=46
39+u=46
u=7
There are 13 tricycles, 26 bicycles, and 7 unicycles.
make x the subject. show work!
Answers
Answer:
[tex]x = \frac{b}{6a} - c[/tex]
Step-by-step explanation:
Steps are as below:
(I will refer A as 'a' and B as 'b')
[tex]a = \frac{b}{c + x} - 5a \\ a + 5a = \frac{b}{c + x} \\ 6a = \frac{b}{c + x} \\ 6a(c + x) = b \\ 6ac + 6ax = b \\ 6ac = b - 6ax \\ b - 6ax = 6ac \\ - 6ax = 6ac - b \\ 6ax = - (6ac - b) \\ 6ax = b - 6ac \\ x = \frac{b - 6ac}{6a} \\ x = \frac{b}{6a} - \frac{6ac}{6a} \\ x = \frac{b}{6a} - c[/tex]