Answer:
infinite number of solutions
Step-by-step explanation:
Given
8(x - 3) = 8x - 24 ← distribute left side
8x - 24 = 8x - 24
The expressions on both sides are equal
Hence any real value of x is a solution
That is there are an infinite number of solutions
The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid?
36 times the square root of 3
36
18 times the square root of 3
18
Recall that the area of an equilateral triangle with side length [tex]s[/tex] is [tex]\dfrac{\sqrt3}4s^2[/tex].
In the [tex]x-y[/tex] plane, the base is given by two equations:
[tex]x^2+y^2=9\implies y=\pm\sqrt{9-x^2}[/tex]
so that for any given [tex]x[/tex], the vertical distance between the two sides of the circle is
[tex]\sqrt{9-x^2}-\left(-\sqrt{9-x^2}\right)=2\sqrt{9-x^2}[/tex]
and this is the side of length of each triangular cross-section for each [tex]x[/tex]. Then the area of each cross-section is
[tex]\dfrac{\sqrt3}4(2\sqrt{9-x^2})^2=\sqrt3(9-x^2)[/tex]
and the volume of the solid is
[tex]\displaystyle\int_{-3}^3\sqrt3(9-x^2)\,\mathrm dx=\boxed{36\sqrt3}[/tex]
What is the domain of this graph?
[tex](-\infty, +\infty)[/tex]
Hope this helps.
r3t40
The sum of 5 consecutive even numbers is 310. What are the numbers?
These 5 numbers can be written as [tex]x,x+2,x+4,x+6,x+8[/tex], so their sum is
[tex]x+(x+2)+(x+4)+(x+6)+(x+8)=5x+20=310[/tex]
[tex]\implies5x=290[/tex]
[tex]\implies x=58[/tex]
Then the numbers are 58, 60, 62, 64, and 66.
URGENT!!! 100PTS!!!
A sporting equipment company wants to sell a new bicycle helmet. They have developed a function, shown below, where total profit, p, can be determined based on sale price, s.
What will be the total profit if the sale price of the helmet is $60?
p(s)=-24s^(2)+2200s-18000
$112,560
$27,600
$111,120
$236,400
$14,240
Answer:
112560
Step-by-step explanation:
The total profit is the sale price of the helmet is $ 60 is:
$ 27,600
Step-by-step explanation:p denote the total profit and s denote the sale price.
The total profit in terms of the sale price is given by the function :
[tex]p(s)=-24s^2+2200s-18000[/tex]
Now we are asked to find the value of p when the s=60
when s=60 we have:
[tex]p(60)=-24\times (60)^2+2200\times 60-18000\\\\\\p(60)=-24\times 3600+132000-18000\\\\\\p(60)=-86400+132000-18000\\\\\\p(60)=27600[/tex]
Hence, the total profit when sale price is $ 60 is:
$ 27,600
The position of an object at time t is given by s(t) = 1 - 10t. Find the instantaneous velocity at t = 10 by finding the derivative.
I know I have to use the differential quotient formula:
f(x-h) - f(x) / h
Answer:
-10
Step-by-step explanation:
Velocity is the derivative of position. Derivative is defined as:
f'(x) = lim(h->0) [ f(x+h) - f(x) ] / h
s(t) = 1 - 10t
s(t+h) = 1 - 10(t+h)
Plugging in:
s'(t) = lim(h->0) [ 1 - 10(t+h) - (1 - 10t) ] / h
s'(t) = lim(h->0) (1 - 10t - 10h - 1 + 10t) / h
s'(t) = lim(h->0) (-10h) / h
s'(t) = lim(h->0) -10
s'(t) = -10
v(t) = -10
So at t=0, v(0) = -10.
The instantaneous velocity at [tex]t = 10[/tex] is 10.
The instantaneous Velocity of the object at a time [tex]t[/tex] is determined by mathematical concept of Derivative, whose description is shown below:
[tex]v = \lim_{h \to 0} \frac{s(t+h) - s(t)}{h}[/tex] (1)
Where:
[tex]h[/tex] - Time difference.
[tex]s(t)[/tex] - Function position evaluated at time [tex]t[/tex].
If we know that [tex]s(t) = 1 - 10\cdot t[/tex], then the instantaneous Velocity of the object is:
[tex]v = \lim_{h \to 0} \frac{1-10\cdot (t+h)-1+10\cdot t}{h}[/tex]
[tex]v = \lim_{h \to 0} \frac{10\cdot h}{h}[/tex]
[tex]v = \lim_{h \to 0} 10[/tex]
[tex]v = 10[/tex]
As instantaneous velocity is a constant function, it means that objects travels at constant velocity. Hence, we conclude that the instantaneous velocity at [tex]t = 10[/tex] is 10.
Please see this question related to instantaneous Velocity: https://brainly.com/question/17727430
The athlete’s salary, in thousands, for the first two years is $400 and $400(1.05). The approximate salary, in thousands, earned each year for the first five years is $400, $420, $441, $463, and $486. Explain how you can evaluate the fifth partial sum. What does the fifth partial sum represent?
Answer:
Add the five terms.
Use the formula for the fifth partial sum.
The fifth partial sum represents the total amount of money the athlete earns over the first five years.
Step-by-step explanation:
Add the five terms.
Use the formula for the fifth partial sum.
The fifth partial sum represents the total amount of money the athlete earns over the first five years.
Answer: The fifth partial sum = 2210
The fifth partial sum represent the sum of the first 5 terms in the sequence.
Step-by-step explanation:
We know that he partial sum of a sequence gives the sum of the first n terms in the sequence.
Thus, the fifth partial sum represent the sum of the first 5 terms in the sequence.
The given geometric sequence : $400, $420, $441, $463, and $486.
Now, the fifth partial sum of the above sequence will be :
[tex]S_5=\$400+ \$420+ \$441+ \$463+\$486=\$2210[/tex]
Henry runs 5 miles an hour. He takes a break for 5 minutes every mile. In the 5th hour , how far he will be from the starting point?
Answer:
Step-by-step explanation:
4 miles = 1hour
5miles = 1hour and 25 minutes
10miles = 2 hours and 50 min
15miles = 4hours and 15min
x miles = 5 hours
20 miles = 5 hours
tell me if i got it wrong sry
A model rocket is fired from the ground at time t=0, and it’s height is given in cm by the formula h=-490t^2 +1470t where t is measured in seconds.
Write an equation to find when the height of the rocket is 980 cm.
Solve the equation by factoring.
Explain why there are two solutions to this problem.
Step-by-step explanation:
h = -490t² + 1470t
When h = 980:
980 = -490t² + 1470t
Simplifying:
0 = -490t² + 1470t - 980
0 = t² - 3t + 2
Factoring:
0 = (t - 1) (t - 2)
t = 1, 2
There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.
The rocket reaches a height of 980 cm at 1 second and 2 seconds. The equation is factored to find these solutions, symbolizing the ascent and descent of the rocket.
To find when the height of the rocket is 980 cm, we set the height formula equal to 980 cm:
h = -490t² + 1470t = 980.
We then solve the equation by factoring:
-490t² + 1470t - 980 = 0
Divide by -10:
t²- 3t + 2 = 0
Factor:
(t - 1)(t - 2) = 0
Setting each factor to zero gives us the solutions:
t = 1 second
t = 2 seconds
There are two solutions because the rocket reaches 980 cm twice: once on its way up and once on its way down. This is demonstrated by the positive and negative components of the parabolic trajectory represented by the quadratic equation.
Please help. what is the quotient of 4m^12/x-1÷x^2/8m^3 assume x ≠ 0 and m≠0
Answer:
[tex]\frac{32m^{15}}{x^3-x^2}[/tex]
Step-by-step explanation:
The given expression is: [tex]\frac{4m^{12}}{x-1}\div \frac{x^2}{8m^3}[/tex]
We multiply by the reciprocal of the second fraction:
[tex]\frac{4m^{12}}{x-1}\times \frac{8m^3}{x^2}[/tex]
We cancel out the common factors to get;
[tex]\frac{32m^{12+3}}{x^2(x-1)}[/tex], where [tex]x\ne0[/tex] and [tex]m\ne0[/tex]
We simplify to get:
[tex]\frac{32m^{15}}{x^3-x^2}[/tex]
Answer:
To simplify all that its D
Step-by-step explanation:
Any number that can be written as a ratio of two integers
Final answer:
A number that can be expressed as a ratio of two integers is called a fraction. Ratios compare quantities and can be written in various forms, like fractions or with a colon. Proportions represent the equivalence of two ratios and are widely used in both mathematics and science.
Explanation:
Any number that can be written as a ratio of two integers is known as a fraction. A fraction is a type of ratio where one integer, the numerator, is divided by another integer, the denominator. For instance, 5/8 is a fraction because it represents 5 parts out of a total of 8.
A ratio can compare any two quantities, not just parts of a whole. These can be written as fractions, with a colon, or with the word 'to'. Examples include 2/3, 2:3, . Ratios are often used to compare dimensions, such as on a map where a unit scale is provided. For example, a map might state that 1 inch represents 100 feet, which is a ratio written as 1 inch/100 ft. Ratios are also essential in the health sciences, for instance, when describing solutions with a certain proportion like 1:1000.
In more complex applications, proportions are used to express equivalences between two ratios. For example, 1/2 is equivalent to 3/6, and this relationship forms a proportion. Proportions are useful in various fields, for setting up equivalencies and solving for unknown quantities.
Find the value of x.
Answer:
[tex]\large\boxed{2\sqrt7}[/tex]
Step-by-step explanation:
Look at the picture.
ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{AC}{AD}=\dfrac{AB}{AC}[/tex]
We have
[tex]AC=x,\ AD=2,\ AB=2+12=14[/tex]
Substitute:
[tex]\dfrac{x}{2}=\dfrac{14}{x}[/tex] cross multiply
[tex]x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7[/tex]
The cost of 3 slices of pizza is $4.89. What is the cost of each slice of pizza? $1.63 $1.89 $2.45 $2.88
1.63
4.89 divided by 3 = 1.63
1.63 just divided the total by 3
Write the english phrase as an algebraic expression. then simplify the expression. let x represent the number. the difference between five times a number and one more than three times the number.
Answer:
5x-(3x+1) or 2x-1
Step-by-step explanation:
The difference (subtraction) between five times x (5x) and one more (+1) than three times x (3x.) 5x-(3x+1)
Simplified, 5x-3x-1=2x-1.
Brian and Christina started keeping track of their workouts. Brian did 85 sit-ups the first week and 90 sit-ups each week after that. Christina did 65 sit-ups the first week and 90 sit-ups each week after that. How many sit-ups will each person have done after 5 weeks?
After 5 weeks, Brian will have completed 445 sit-ups, and Christina will have completed 425 sit-ups.
To calculate the total number of sit-ups Brian and Christina will have done after 5 weeks, we can use arithmetic progressions since the number of sit-ups increases by the same amount each week after the first.
For Brian:
Week 1: 85 sit-upsWeeks 2 to 5: 4 weeks x 90 sit-ups each week = 360 sit-upsTotal after 5 weeks: 85 + 360 = 445 sit-upsFor Christina:
Week 1: 65 sit-upsWeeks 2 to 5: 4 weeks x 90 sit-ups each week = 360 sit-upsTotal after 5 weeks: 65 + 360 = 425 sit-upsTherefore, after 5 weeks, Brian will have done 445 sit-ups and Christina will have done 425 sit-ups.
If BC = 6 and AD = 5, find DC.
A) 4
B) 4.5
C) 7.2
We have three similar triangles, because each has a right angle and shares an angle. Let's write the angles in order: opposite to short leg, long leg, hypotenuse.
CAB similar to BAD similar to CBD
Or as ratios,
CA:AB:CB = BA:AD:BD = CB:BD:CD
We also know
AC = AD + CD
(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD
(AD+CD)/CB=CB/CD
We have CB=6, AD=5 and seek x=CD.
[tex](5 + x)/6 = 6/x[/tex]
[tex]x(x+5) = 36[/tex]
[tex]x^2 +5x - 36 = 0[/tex]
[tex](x+9)(x-4) = 0[/tex]
We reject the negative root and conclude x=4
Answer: 4
From opposite to the short leg, long leg, and hypotenuse DC is A) 4
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
Because each triangle has a right angle and shares an angle, we have three comparable triangles. The angles should be written from opposite to the short leg, long leg, and hypotenuse.
CAB is similar to BAD similar to CBD
CA : AB : CB = BA : AD : BD = CB : BD : CD
We also know
AC = AD + CD
(AD + CD) : AB : CB = BA : AD : BD = CB : BD : CD
(AD + CD)/CB = CB/CD
We have CB = 6, AD = 5, and x = CD.
∴ (5 + x)/6 = 6/x.
x(5 + x) = 36.
5x + x² = 36.
x² + 5x - 36 = 0.
x² + 9x - 4x - 36 = 0.
x(x + 9) - 4(x + 9) = 0.
(x + 9)(x - 4) = 0.
x = - 9 Or x = 4. (length can not be negative).
learn more about triangles here :
https://brainly.com/question/2773823
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Jack estimates that the cost per mile, in dollars, for operating a certain truck is between 15% and 21% of the number of miles driven. This is shown by the system of inequalities below, where x represents the number of miles driven and y represents the cost of operating the truck.
y ≥ 0.15x
y ≤ 0.21x
Based on this information, which statement is true?
A) If Jack drives over 15 miles, it will cost 15 · 0.15 to operate the truck.
B) If Jack drives less than 21 miles, it will cost 21 · 0.21 to operate the truck.
C) If Jack drives the truck 100 miles, it will cost either $15 or $21.
D) If Jack drives 200 miles, it will cost anywhere between $30 and $42.
Answer:
D) If Jack drives 200 miles, it will cost anywhere between $30 and $42
Step-by-step explanation:
The cost is said to be a range of possibilities. The first three answer choices seem to assume the cost is at one extreme or the other. They incorrectly interpret the statement of cost.
Type the correct answer in each box. If necessary, round your answers to the nearest hundredth.
The vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). The perimeter of ∆ABC is
units, and its area is
square units.
Answer:
Perimeter = 32.44 units
Area = 30 square units
Step-by-step explanation:
Given
Vertices
A(2,8), B(16,2) and C(6,2)
WE have to determine the lengths of all sides before finding the perimeter and area.
The formula of modulus is:
[tex]d = \sqrt{(x_{2}- x_{1})^{2} +(y_{2}-y_{1})^{2}}\\AB=\sqrt{(16-2)^{2} +(2-8)^{2}}\\=\sqrt{(14)^{2} +(-6)^{2}}\\=\sqrt{196+36}\\ =\sqrt{232}\\=15.23\\\\BC=\sqrt{(6-16)^{2} +(2-2)^{2}}\\=\sqrt{(-10)^{2} +(0)^{2}}\\=\sqrt{100+0}\\ =\sqrt{100}\\=10\\\\AC=\sqrt{(6-2)^{2} +(2-8)^{2}}\\=\sqrt{(4)^{2} +(-6)^{2}}\\=\sqrt{16+36}\\ =\sqrt{52}\\=7.21\\\\[/tex]
So the perimeter is:
[tex]Perimeter=AB+BC+AC\\=15.23+10+7.21\\=32.44\ units[/tex]
Using hero's formula,
[tex]s=\frac{perimeter}{2}\\s=\frac{32.44}{2}\\ s=16.22\\Area=\sqrt{s(s-a)(s-b)(s-c)}\\=\sqrt{16.22(16.22-15.23)(16.22-10)(16.22-7.21)}\\=\sqrt{(16.22)(0.99)(6.22)(9.01)}\\=\sqrt{899.91}\\=29.99\ square\ units[/tex]
Rounding off will give us 30 square units ..
Answer:
30 square units
Step-by-step explanation:
PLEASE HELP ASAP 40 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
B
Step-by-step explanation:
2 || 1 - 4 6 - 4
2 -4 4
==================
1 -2 2
x^2 - 2x + 2 with no remainder.
Looks like the answer is B
Note: Note that the two in x - 2 changes sign. That always happens when using synthetic division as long the number in front of the x is positive.
Help with this question, please!!
Answer:
V = 135π in³A = 105π in²Step-by-step explanation:
Area of a circle is ...
A = πr² . . . r is the radius
Area of a sphere is ...
A = 4πr²
Lateral area of a cylinder is ...
A = πdh = 2πrh . . . h is the height
Volume of a cylinder is ...
V = πr²h
Volume of a sphere is ...
V = (4/3)πr³
___
The area of the composite figure is the sum of the areas ...
total area = base circle area + cylinder lateral area + 1/2 sphere area
= πr² + 2πrh + (1/2)4πr² = (πr)(r +2h +2r)
= πr(3r +2h)
For the given dimensions, r=3 in, h = 13 in, this is ...
total area = π(3 in)((3·3 +2·13) in) = 105π in²
___
The volume of the composite figure is the sum of the volumes ...
total volume = cylinder volume + 1/2 sphere volume
= πr²h + (1/2)(4/3)πr³ = πr²(h + 2/3r)
= π(3 in)²((13 +2/3·3) in) = 135π in³
Use the substitution method to solve the system of equations.Choose the correct ordered pair.
Hello there! The answer is B. (3, 21).
So you want to be able to substitute one of the equations into the other. We can't do this right now since both of the equations are y = something, so we need to change the second equation to x = something so we can plug it in to the value of x in the first equation.
y = x + 18 can translate to x = y - 18. Now, plug "y - 18" into x in the first equation.
y = 10(y-18) - 9 and solve.
y = 10y - 180 - 9
-9y = - 180 - 9
-9y = -189
y = 21.
Now we have our y value, but we need our x value. Well, remember that y = x + 18? So, since y is 21, what plus 18 is equal to 21? The answer is 3, making our x value 3.
If x = 3 and y = 21, the ordered pair is (3, 21) or option B. I hope this was helpful and have a great day! :)
Hello
10x-9=x+18
10x-x=18+9
9x=27
x=3
10x-9=30-9=21
(3,21)
Good Luck
Goodbye ♥
Identify the equation of the circle X that passes through (−3,−5) and has center (4,−7). HELP ASAP!!
Answer:
(x - 4)² + (y + 7)² = 53
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (4, - 7), so
(x - 4)² + (y + 7)² = r²
The radius is the distance from the centre to a point on the circle.
Use the distance formula to calculate r
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (4, - 7) and (x₂, y₂ ) = (- 3, - 5)
r = [tex]\sqrt{(-3-4)^2+(-5+7)^2}[/tex]
= [tex]\sqrt{(-7)^2+2^2}[/tex] = [tex]\sqrt{49+4}[/tex] = [tex]\sqrt{53}[/tex]
Hence r² = ([tex]\sqrt{53}[/tex] )² = 53
(x - 4)² + (y + 7)² = 53 ← equation of circle
What is the simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15?
Answer:
It cannot be simplified any further.
The simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15 is (y-4)/(y-5) .
Simplifying the equation(y^2-y+12)/(y^2-2y-15) factor both the numerator and denominator...
(y^2-4y-3y+12)/(y^2-5y+3y-15)
(y(y-4)-3(y-4))/(y(y-5)+3(y-5))
((y-4)(y-3))/((y-5)(y+3)) so the (y+3) and (y-3) cancel leaving
(y-4)/(y-5)
(y-4)/(y-5) the simplified form of the quantity y−squared plus 7y plus 12 over the quantity y−squared minus 2y minus 15.
To learn more about Simplifying the equation refer:https://brainly.com/question/26779637
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The stock market lost 777.68 points in one day. It ended at 10,364.45 points on the same day. How many points did the stock market start with on that day
Answer:
jnd8663393765422345678
Step-by-step explanation:
nhbkjnm.l,n aels ewdlasmjDQLKd
a custodian pours 1/8 gallon of cleaning solution into each pail of water that she uses. how many pails of water and cleaning solution can the custodian make using 16 gallons of cleaning solution?
Find the volume of solution in two of these pails
Answer:
The custodian can make 128 pails.
Step-by-step explanation:
first, you convert 1/8 to 0.125.
then, you divide 16 by 0.125 to get 128.
The tallest living man at one time had a height of 265 cm. The shortest living man at that time had a height of 109.1 cm. Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm. Which of these two men had the height that was more extreme?
Answer:
tallest man height is more extreme.
Step-by-step explanation:
Given:
Heights of men at that time had a mean of 173.73 cm and a standard deviation of 8.65 cm.
Concept used:
Convert height into z scores for comparison of deviation from the mean.
Solution:
Tallest man height = 265 cm
[tex]Z_{tall} =\frac{265-173.73}{8.65} \\=10.55[/tex]
Shortest man height = 109.1 cm
[tex]Z_{short} =\frac{109.1-173.73}{8.65} \\=-7.47[/tex]
Thus we find that tallest man is 10.55 std deviations from the mean to the right and shortest man is 7.47 std deviations from the mean to the left.
Hence tallest man height is more extreme.
The tallest living man at one time had a more extreme height compared to the shortest living man at that time.
Explanation:In this question, we are given the heights of the tallest and shortest living men at a specific time, as well as the mean and standard deviation of heights at that time. To determine which man had a more extreme height, we need to compare their heights to the mean and see how many standard deviations away they are.
The tallest man had a height of 265 cm, which is 265 - 173.73 = 91.27 cm above the mean.
The shortest man had a height of 109.1 cm, which is 173.73 - 109.1 = 64.63 cm below the mean.
Since the tallest man's height is significantly farther away from the mean compared to the shortest man's height, we can conclude that the tallest man had a more extreme height.
WILL GIVE BRAINLIEST AND 25 POINTS HURRY (has to be correct tho !)
Answer:
i am assuming 2 and 5 because they are the only ones that are not like the others
Step-by-step explanation:
Answer:
Angles 2 and 5
Step-by-step explanation:
Supplement angles are the angles which up to 180 degrees.
And all the angles shown are Vertically opposite angles and these angles are always the same.
Vertically opposite angles:
Angles 2 and 5
Angles 1 and 3
Angles 6 and 4
As shown in the picture, Angle 2 is 90 degrees and angle 5 being a vertically opposite angle, angle 5 is 90 degrees too.
90 + 90 = 180 degrees.
Kim and Casey want to compare the prices of their favorite snack nexus determine which is less expensive the table below shows the price of each box of snack mix and the number of ounces in each box.One box cost $3.84 for 24 ounces and the other box is $4.48 for 32 ounces which is the cheapest
Answer:
The box of 32oz is cheaper by 2 cents per ounce.
Step-by-step explanation:
1. 3.84/24 ($0.16/oz)
2. 4.48/32 ($0.14/oz)
___
Hope this helps you! :)
The price of the box of 15 stickers is $6. The price of the box of 25 stickers is $8. All prices are without tax, and the price of the boxes is the same. .How much would a box of 50 stickers cost?
Answer:
A box of 50 stickers would cost $13
Explanation:
1- getting the equation representing the price:
We have two variables; the number of stickers and the price of the box
We can note that the price is the dependent variable (y) while the number of stickers is the independent one (x)
We are given that:
A box of 15 stickers cost $6..........> first point is (15,6)
A box of 25 stickers cost $8 ........> second point is (25,8)
The general equation of the linear line is:
y = mx + c
where m is the slope and c is the y-intercept
i. getting the slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{25-15}=0.2[/tex]
The equation now became: y = 0.2x + c
ii. getting the y-intercept:
To get the y-intercept, use any of the given points and substitute in the equation we got in part i. I will use the point (15,6)
y = 0.2x + c
6 = 0.2(15) + c
c = 6 - 0.2(15) = 3
The final equation is:
y = 0.2x + 3
where y is the price of the box and x is the number of stickers it contains
2- getting the price of a box with 50 stickers:
To get the price of a box of 50 stickers, simply substitute with x = 50 in the equation we got from part 1
This is done as follows:
y = 0.2(50) + 3 = 13
Therefore, a box of 50 stickers will cost $13
Hope this helps :)
Male and female students were surveyed about dancing and playing sports. They had the following preferences: Do you prefer dancing or playing sports? Playing sports Dancing Row totals Male students 0.25 0.27 0.52 Female students 0.17 0.31 0.48 Column totals 0.42 0.58 1 Which of the following is a two-way conditional frequency table for gender? (2 points) Do you prefer dancing or playing sports? Playing sports Dancing Row totals Male students 0.48 0.52 1 Female students 0.35 0.65 1 Do you prefer dancing or playing sports? Playing sports Dancing Row totals Male students 25% 27% 52% Female students 17% 31% 48% Column totals 42% 58% 100% Do you prefer dancing or playing sports? Playing sports Dancing Male students 0.60 0.47 Female students 0.40 0.53 Column totals 1 1 Do you prefer dancing or playing sports? Playing sports Dancing Row totals Male students 50 54 104 Female students 34 62 96 Column totals 84 116 200
The option that shows a two-way conditional frequency table is option B as shown in the image attached.
What is a two-way conditional frequency table?A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:
Gender.Preferred activity.Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.
Which option is correct?The correct option is option B because it meets the following requirements:
It displays the two variables: gender and preferred activities.It uses frequency values such as 0.48 rather than percentages or the number of people, which would be incorrect.The row totals are displayed in a third column than in a new row.Learn more about variables in: https://brainly.com/question/787279
Answer:
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.48 0.52 1
Female students 0.35 0.65 1
Step-by-step explanation:
This is the answer
Given: F(x) = 3x and G(x) = x 2 + 1 Find (F + G)(x).
3x³ + 1
x² + 3x + 1
3x² + 1
For this case we have the following functions:
[tex]f (x) = 3x\\g (x) = x ^ 2 + 1[/tex]
We must find (f + g) (x). By definition of operations with functions we have to:
(f + g) (x) = f (x) + g (x)
So we have to:
[tex](f + g) (x) = 3x + (x ^ 2 + 1)\\(f + g) (x) = x ^ 2 + 3x + 1[/tex]
Answer:
[tex](f + g) (x) = x ^ 2 + 3x + 1[/tex]
Option B