Conn Math increase by 3 , each week
Conn Sci increase doubling number, every week
Then now fill table
. Week. 1. Conn Math. Conn Sci
. Week 1. 25. 25
. Week 2. 28. 50
. Week 3. 31. 75
. Week 4. 34. 100
Now part. B
A linear model is when data fits in a straight line
hence Then
Then
First model of Conn Math is
Visitors. = 25 + 3 W
Second model for Conn Sci
Visitors = 25 x
[tex](3x^{2} -x+1)-(6x^{2} -x+2)[/tex]
Answer:
−3x2−1
Step-by-step explanation:
−3x2−1 Is the answer to this equatiom
If the two expressions are equivalent, find value of x
1. Subtract 1/x in both sides of the equation:
[tex]\begin{gathered} \frac{5}{x}-\frac{1}{x}-\frac{1}{3}=\frac{1}{x}-\frac{1}{x} \\ \\ \frac{4}{x}-\frac{1}{3}=0 \end{gathered}[/tex]2. Add 1/3 in both sides of the equation:
[tex]\begin{gathered} \frac{4}{x}-\frac{1}{3}+\frac{1}{3}=0+\frac{1}{3} \\ \\ \frac{4}{x}=\frac{1}{3} \end{gathered}[/tex]3. Multiply both sides of the equation by x:
[tex]\begin{gathered} x\cdot\frac{4}{x}=x\cdot\frac{1}{3} \\ \\ 4=\frac{x}{3} \end{gathered}[/tex]4. Multiply both sides of the equation by 3:
[tex]\begin{gathered} 4\cdot3=\frac{x}{3}\cdot3 \\ \\ 12=x \\ \\ \text{ Rewrite} \\ x=12 \end{gathered}[/tex]Then, the value of x is 12In △GHI, m∠G = (9x - 2), m∠H = (3x - 19), and m∠I = (3x + 6)". Find m∠G.
Answer:
m∠G = 115 degrees
Explanation:
The sum of the angles in a triangle is 180 degrees.
In triangle GHI:
[tex]\begin{gathered} m\angle G+m\angle H+m\angle I=180\degree \\ \implies9x-2+3x-19+3x+6=180\degree \end{gathered}[/tex]First, solve for x:
[tex]\begin{gathered} 9x+3x+3x-2-19+6=180\degree \\ 15x-15=180\degree \\ 15x=180+15 \\ 15x=195 \\ x=\frac{195}{15} \\ x=13 \end{gathered}[/tex]Therefore, the measure of angle G is:
[tex]\begin{gathered} m\angle G=9x-2 \\ =9(13)-2 \\ =117-2 \\ m\angle G=115\degree \end{gathered}[/tex]The measure of angle G is 115 degrees.
question 13Consider the following data: 12, 15, 13, 10, 15, 10. Answer the following questicwrite final answers only. [T/I - 4]#1) What is the mean of the data?#2) What is the median of the data?#3) What is the mode of the data?#4) What is the range of the data?
Solution:
Given:
The data;
[tex]12,15,13,10,15,10[/tex]Question 1:
To get the mean:
The mean of a set of numbers, sometimes simply called the average, is the sum of the data divided by the total number of data.
[tex]\begin{gathered} \text{Mean}=\frac{\text{ sum of data}}{n\text{ umber of data}} \\ \text{Mean}=\frac{12+15+13+10+15+10}{6} \\ \text{Mean}=\frac{75}{6} \\ \text{Mean}=12.5 \end{gathered}[/tex]Therefore, the mean is 12.5
Question 2:
To get the median:
The median of a set of numbers is the middle number in the set (after the numbers have been arranged from least to greatest)
If there is an even number of data, the median is the average of the middle two numbers.
[tex]\begin{gathered} R\text{ earranging the data given in rank order,} \\ 10,10,12,13,15,15 \end{gathered}[/tex]
The data indicates an even number of data. There are 6 numbers in the set.
Hence, the median is the mean of the middle two numbers.
[tex]\begin{gathered} \text{The middle two numbers are;} \\ 12\text{ and 13} \\ \text{Hence, the median is the mean of 12 and 13} \\ \text{Median}=\frac{12+13}{2} \\ \text{Median}=\frac{25}{2} \\ \text{Median}=12.5 \end{gathered}[/tex]Therefore, the median is 12.5
Question 3:
To find the mode:
The mode of a set of numbers is the number that occurs the most. Hence, the mode of a set of numbers is the number with the highest frequency.
If a set of data has two modes, the data is said to be bimodal.
[tex]\begin{gathered} 10,10,12,13,15,15 \\ \\ \text{From the above, 10 appears twice} \\ 15\text{ also appears twice} \\ \\ \text{Hence, the mode is 10 and 15. The data has two modes, it is a bimodal data.} \end{gathered}[/tex]
Therefore, the modes are 10 and 15.
Question 4:
The range is the difference between the highest and lowest values in a set of numbers.
[tex]\begin{gathered} 10,10,12,13,15,15 \\ \text{Lowest number=10} \\ \text{Highest number=15} \\ \\ \text{Hence, range=highest number-lowest number} \\ \text{Range}=15-10 \\ \text{Range}=5 \end{gathered}[/tex]Therefore, the range is 5.
Translate into proportion 16.4 is 45% of what number ?
Given:
16.4 is 45%
[tex]\begin{gathered} 16.4\times\frac{45}{100}=\frac{b}{1} \\ \frac{16.4}{b}=\frac{100}{45} \end{gathered}[/tex]Hence, the required option is D.
What is the value of x?
The value of x =20 when the angles given are 3x° and (x+40)°.
Given that,
There a picture with 2 lines.
The angles given are 3x° and (x+40)°.
We have to find the x value.
We the alternative angles are equal in an intersecting angles.
Angles that are in opposition to a transversal connecting two lines are known as alternate angles.
x +40=3x
Taking 40 to right side.
x= 3x-40
Taking 3x to left side.
x-3x=-40
Subtracting x ad 3x
-2x=-40
Divide by -2.
x=20
Therefore, the value of x =20 when the angles given are 3x° and (x+40)°.
To learn more about angle visit: https://brainly.com/question/28451077
#SPJ9
the radius of a circle is 9 feet. what is the diameter? give the exact answer in simplest form.
The diameter of a circle equals twice the radius of that circle.
Then:
[tex]\begin{gathered} D=2\times r \\ =2\times9ft \\ =18ft \end{gathered}[/tex]Therefore, the diameter of the circle is:
[tex]18\text{ feet}[/tex]Answer:
18 feetStep-by-step explanation:
The radius is always 2 times the diameter. Since the radius is [tex]9 ~feet[/tex], the diameter is [tex]9\cdot2=\boxed{18}~feet[/tex]
Is this correct? If not can u show me how to do it
Given
[tex]k(x+y)=2x-4[/tex]Notice that it is the equation of a line.
Then, since it crosses (10,-2), set x=10 and y=-2 in the given equation, as shown below
[tex]\begin{gathered} x=10,y=-2 \\ \Rightarrow k(10-2)=2*10-4 \\ \Rightarrow k(8)=20-4 \\ \Rightarrow k=\frac{16}{8}=2 \\ \Rightarrow k=2 \end{gathered}[/tex]Thus, the answer is k=2.
If ∠2 = 50° and lines a and b are parallel, which of the following angles cannot be determined? *-∠1-∠3-∠4-∠8-None of the above
If you have the angle 2, you can deduce its the supplement,which is the angle 4. In this case the supplement is equal to 130°.
Angle 2 and angle 6 are corresponding angles, so they have the same measure.
Angle 4 and angle 8 are corresponding, so they have the same measure.
Angle 2 and angle 1 are vertically opposite angles, so they have the same measure.
Angle 5 and angle 6 are vertically opposite angles, so they have the same measure.
Angle 7 and angle 8 are vertically opposite angles, so they have the same measure.
Angle 4 and angle 3 are vertically opposite angles, so they have the same measure.
Therefore the answer is None of the above.
identify the rate, base and portion.17% of what number is 60?
For the given question which is;
17% of what number is 60?
We shall begin by determining the value of the number. Let us call the number a.
We can now set up the following equation;
[tex]\begin{gathered} 17\text{ \% of a}=60 \\ 0.17\times a=60 \end{gathered}[/tex]We now divide both sides by 0.17;
[tex]\begin{gathered} \frac{0.17a}{0.17}=\frac{60}{0.17} \\ a=352.9411 \\ \text{Rounded to the nearest whole number,} \\ a=353 \end{gathered}[/tex]So we now have;
"17% of 353 is 60."
The rate is the variable that represents part of the whole and that is 17
The base is the whole number itself which is a 100% value and that is 353
The portion is that part of the whole (base) made up of 17% and that is 60."
ANSWER:
Rate is 17%
Base is 353
Portion is 60
If Martha is x years old and her mother is 5 times older and the sum of their age is 88, how old is Martha?
Let Martha age = x years old
Since her mother's age is 5 times her age, then
Her mother = 5(x) = 5x years old
Since the sum of their ages is 84, then
Add x and 5x, then equate the sum by 84
[tex]\begin{gathered} x+5x=84 \\ 6x=84 \end{gathered}[/tex]Divide both sides by 6 to find x
[tex]\begin{gathered} \frac{6x}{6}=\frac{84}{6} \\ x=14 \end{gathered}[/tex]Martha is 14 years old
x-2Question 8 of 15Use the remainder theorem to find P (2) for P (x)=xª − 3x³ +x−9.-(2,01 mismoSpecifically, give the quotient and the remainder for the associated division and the value of P (2)_Quotient =RemainderP (2)=
8)
The remainder theorem states that when a polynomial P(x) is divided by a linear polynomial x-b, the remainder is given by r=P(b).
Thus, in our case,
[tex]P(2)=2^4-3(2)^3+2-9=16-24+2-9=-15[/tex]Then, the Remainder theorem states that if we divide P(x) by x-2, the remainder will be -15.Calculating the quotient of P(x)/(x-2),
Hence, the answers are[tex]\begin{gathered} Q(x)=x^3-x^2-2x-3 \\ Remainder=-15 \\ P(2)=-15 \end{gathered}[/tex]Question 8 of 10Which of these is a geometric sequence?O A. 2, 3, 5, 9, 17,...O B. 5, 2, 3, 4, ...O C. 2, 4, 6, 8, 10, ...
We have that in a geometric sequence, the common ratio are equal in geometric sequence, this is:
[tex]\frac{second\text{ term}}{first\text{ term}}=\frac{third\text{ term}}{second\text{ term}}[/tex]Next, check options:
A. 2, 3, 5, 9, 17
Common ratio
[tex]undefined[/tex]Given f(x)=2x-1 and g(x) =x^2 -2A) f(5)B) f(g(3))C) f(a+1) - f(a)D) g(2f(-1))E) g(x+h) -g(x)/h
2x + h
Explanation:
Given the following functions
f(x) = 2x - 1
g(x) = x^2 - 2
We are to simplify the expressionn:
[tex]\frac{g(x+h)-g(x)}{h}[/tex]Substitute the given functions into the expression and simplify
[tex]\begin{gathered} \frac{\lbrack(x+h)^2-2\rbrack-(x^2-2)}{h} \\ \frac{\lbrack\cancel{x^2}^{}+2xh+h^2-\cancel{2}-\cancel{x^2}^{}+\cancel{2}}{h} \\ \frac{2xh+h^2}{h} \end{gathered}[/tex]Factor out "h" from the numerator to have:
[tex]\begin{gathered} \frac{\cancel{h}(2x+h)}{\cancel{h}} \\ 2x+h \end{gathered}[/tex]Hence the simplified form of the expression is 2x + h
using the rule of s-14 - (-2) = -12
We will have:
[tex]-14-(-2)=-12\Rightarrow-14+2=-12\Rightarrow-12=-12[/tex]Section 5.2-12. Solve the following system of equations by substitution or elimination. Enter your answer as (x,y).3x-3y = -6-x+2y = 8
the Given the simultaneous equations
[tex]\begin{gathered} 3x-3y=-6\text{ ------(1)} \\ -x+2y=8\text{ -------(2)} \end{gathered}[/tex]Solving the above equations by substitution method:
Step 1:
From equation 2, make x the subject of the formula
[tex]\begin{gathered} -x+2y=8 \\ \text{making x the subject of formula, we have} \\ x=2y-8\text{ -------(3)} \end{gathered}[/tex]Step 2:
Substitute equation 3 into equation 1
[tex]\begin{gathered} \text{From equation,} \\ 3x-3y=-6 \\ \text{Thus, we have} \\ 3(2y-8)-3y=-6 \\ \text{opening the brackets, we have} \\ 6y-24-3y=-6 \\ \text{collecting like terms, we have} \\ 6y-3y=-6+24 \\ 3y=18 \\ \text{divide both sides by the coefficient of y.} \\ \text{The coefficient of y is 3. Thus,} \\ y=\frac{18}{3}=6 \end{gathered}[/tex]Step 3:
Substitute the value of y in either equation 1 or 2.
[tex]\begin{gathered} \text{From equation 2,} \\ -x+2y=8 \\ \text{Thus,} \\ -x+2(6)=8 \\ -x+12=8 \\ \text{collecting like terms, we have} \\ -x=8-12 \\ -x=-4 \\ x=4 \end{gathered}[/tex]Thus, the values of (x, y) are (4, 6)
A(0,3) B(1,6) C(4,6) D(5,3) rotate it around the origin 270 degrees clockwise
Please answer with the coordinates.
♥
The rule for a rotation by 270° about the origin is (x,y)→(y,−x)
so i guess A?
♥
what are the similarities between rate and ratio
A rate is a specific type of ratio. A rate is a comparison of two numbers with different units, whereas a ratio compares two numbers with the same unit.
For example, in a bowl, there are 12 fruits: 8 oranges and 4 apples. This means the ratio of oranges to apples is 8:4.
If we simplify the ratio, we can see that the ratio of oranges to apples is 2:1, because:
[tex]\frac{8}{4}=\frac{4\cdot2}{4\cdot1}=\frac{2}{1}=\frac{2}{1}[/tex]Then, there are 2 oranges in the bowl for every apple.
On the other hand, suppose we want to distribute the fruits to 3 people. We can use a rate to find out how many fruits correspond to each person because we have 2 different units:
[tex]\begin{gathered} \frac{12\text{ fruits}}{3\text{ people}}=\frac{x}{1\text{ person}} \\ \text{ Apply cross product} \\ 12\text{ fruits}\cdot1\text{ person}=x\cdot3\text{ people} \\ \text{ Divide by 3 people from both sides} \\ \frac{12\text{ fruits}\cdot1\text{ person}}{3\text{ people}}=\frac{x\cdot3\text{ people}}{3\text{ people}} \\ \frac{12\text{ fruits}}{3}=x \\ 4\text{ fruits }=x \end{gathered}[/tex]Now, we know that each person corresponds to 4 fruits, in other words, the rate is 4 fruits/person.
Therefore, we can see the similarities between rate and ratio are:
• Both are a comparison of two numbers.
,• Both can be written as fractions.
,• Both reduce to the lowest form.
Find the area of the triangle below. Be sure to include the correct unit in your answer. bu
The area of the triangle = 0.5 x base x height
For the given triangle:
Base = 25 ft
The corresponding height to the base = 7 ft
So, the area =
[tex]0.5\cdot25\cdot7=87.5[/tex]So, the area of the triangle = 87.5 ft^2
What number is 75% of 96?
Answer
The number is 72
Explanation
75% of 96 is
[tex]\begin{gathered} =\frac{75}{100}\times\frac{96}{1} \\ =\frac{7200}{100} \\ =72 \end{gathered}[/tex]Solve for y and show steps 75-3.5y-4y=4y+6
Solve for y;
[tex]\begin{gathered} 75-3.5y-4y=4y+6 \\ \text{Collect like terms, which means the values with y would be moved to one side} \\ \text{And the values without y would be moved to the other side} \\ 75-6=4y+4y+3.5y \\ \text{Note that when a positive value moves to the other side of the equation} \\ It\text{ becomes a negative value, and vice versa} \\ 69=11.5y \\ \text{Divide both sides by 11.5} \\ \frac{69}{11.5}=\frac{11.5y}{11.5} \\ 6=y \end{gathered}[/tex]The answer is y equals 6
A new cell phone costs $108.99 in the store. What would your total cost be if the sale tax is 7.5% ? Round your answer to the nearest cent, if necessary.
to calculate the tax we need to multiply the % by the price of the cellphone
7.5%=0.075
108.99*0.075=8.17
and the total cost is:
$108.99 + $8.17= 117.16
So the answer is: $
Please help me solve the following problem:A conic kettle has a cover which height is 30% of its total height. The height is 2 cm less than the diameter of the base, which has an area of 380 squared cm. Which is the volume capacity of the kettle?
If a conical kettles has a solid cover whose volume is 30% of the total volume, and it's height is 2 cm less than the radius of it's base, which has an area of 380cm², then the volume of the kettle is 798.6cm³.
As per the question statement, a conical kettles has a cover whose volume is 30% of the total volume, and it's height is 2 cm less than the radius of it's base, which has an area of 380cm²,
And we are required to calculate the volume capacity of the kettle.
To solve this question, first we need to know the formula to calculate the volume of a cone, which goes as, [Volume (V) = {π * r² * (h/3)}],
Where, "r" is the radius of the base of the cone,
And, "h" is the height of the cone.
Now, the height of our concerned cone is 2 cm less than the radius of it's base, and the area of the base is 380cm². Assuming that the height of the cone be "h" and the radius of it's base be "r", we get that,
[r = (h - 2)]...(i)
And, [(π * r²) = 380]
Or, [{(22/7) * r²} = 380]
Or, [(r²) = {(380 * 7)/22]
Or, [(r²) = 120.9090]
Or, (r = √120.91)
Or, (r = 10.9959)
Or, (r ≈ 11 cm)
Therefore, using the value for "r" in equation (i), we will get,
[h = (11 - 2)cm = 9cm]
And finally substituting these values of "h" and "r" in the above mentioned formula to calculate the volume of a cone,, we get,
[V = {π * (11)² * (9/3)}]
Or, [V = {(22/7) * 121 * 3}]
Or, [V = (7986/7)]
Or, (V = 1140.85714 cm³)
Or, (V ≈ 1140.86 cm³)
Since the cover of the kettle occupies 30% of the volume of the total structure of the conical kettle with it's cover, the volume capacity of the kettle is [(100 - 30)% = 70%] of the volume of the total structure of the conical kettle with it's cover, that is,
[1140.86 * (70/100)]cm³ = (1140.86 * 0.7)cm³ = 798.6cm³
Volume: The volume of any object is the three-dimensional space, occupied by the existence of that very object.To learn more about Volumes of Cones, click on the link below.
https://brainly.com/question/28262307
#SPJ9
Vance bought 2 packages of large beads
and 1 package of medium beads. He
bought 2 packages of large buttons and 2
packages of medium buttons. How many
more beads than buttons did Vance buy?.
The no. of more buttons than beads that Vance bought is 1 (medium package)
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
How to solve algebraic expressions?A General Rule for Equation Solving
B Remove parenthesis from either side of the equation and combine similar phrases to make it simpler.
C To separate the variable term on one side of the equation, use addition or subtraction.
D To find the variable, use division or multiplication.
Given:- The no: of package of large beads is 2
The no: of the package of medium beads is 1
The no: of the package of large buttons is 2
The no: of the package of medium buttons is 2
Hence large packages
2(buttons)-2(beads)=0
For medium packages
2(buttons)-1(beads)=0
therefore, the no of more buttons than beads is 1 medium package
Learn more about algebraic expressions, visit :
https://brainly.com/question/4344214
#SPJ1
Can you pls help me with this question thank you
The Solution:
The difference of c and 7 is either:
[tex]\begin{gathered} c-7\text{ } \\ \text{ or} \\ 7-c \end{gathered}[/tex]Multiplying the result by 10, we get
[tex]\begin{gathered} 10(c-7) \\ \text{ or} \\ 10(7-c) \end{gathered}[/tex]We are asked not to simplify any part of the expression.
So, the correct answer is:
[tex]\begin{gathered} 10(c-7) \\ or \\ 10(7-c) \end{gathered}[/tex]
Find 3 ratios that are equivalent to the given ratio. 3 6 Find 3 ratios that are equivalent to the given ratio. g B. 18 9 DA. 24 6 D. 18 C. 6 24 1 F. 2 12 O E. 18 OH. 6 12 g G. 12
Find the circumference and area of the circle. Express answers in terms of and then round to the nearest tenth. Find the circumference in terms of . C = _
Solution:
Given the circle with its radius, r;
[tex]r=11cm[/tex]Thus, the circumference, C, of a circle is;
[tex]C=2\pi r[/tex]Then;
[tex]\begin{gathered} C=2\pi(11)cm \\ \\ C=22\pi cm \end{gathered}[/tex]ANSWER:
[tex]C=22.0\pi cm[/tex]Also, the area, A, of the circle is;
[tex]A=\pi r^2[/tex]Then;
[tex]\begin{gathered} A=\pi(11)^2 \\ \\ A=121\pi cm^2 \end{gathered}[/tex]ANSWER:
[tex]A=121.0\pi cm^2[/tex]From the diagram below, we can tell that Δ ABC is similar to ____.
From the diagram, we get that
[tex]\measuredangle ABD\cong\measuredangle ADB.[/tex]By the reflexive property of congruence, we know that:
[tex]\measuredangle A\cong\measuredangle A.[/tex]Therefore, by the Angle-Angle criterion:
[tex]\Delta ABC\sim\Delta ADB.[/tex]Answer: [tex]\Delta ADB.[/tex]help me havig a hard time .
What is the conversion factor?
It is a number used to change one unit to another when it is multiplied.
Jenna wants to know how many pounds correspond to 50 tons, she does know that 1 ton = 2,000lb. Then she has the following equivalence:
50 tons ⇄ ??
1 ton ⇄ 2,000 lb
We know that if we divide both sides of the equivalence we will have the same result:
[tex]\frac{50\text{tons}}{1\text{ton}}=\frac{?\text{?}}{2000lb}[/tex]Multiplying both sides by 2000lb we have that
[tex]undefined[/tex]Which transformations can be used to carry ABCD ontoitself? The point of rotation is (3, 2). Check all that apply.yB1 23 4 5 6A. Translation four units to the rightB. Dilation by a factor of 2C. Rotation of 180°D. Reflection across the line x = 3
C. Rotation of 180°
D. Reflection across the line x = 3
Explanation:The point of rotation = (3, 2)
From the diagram:
The center of the rectangle = (3, 2)
Note that:
The point of rotation = The center of the rectangle
Therefore, the rectangle ABCD will be reflected across its center, x =3 and y = 2
Also note that ABCD has two lines of symmetry. Therefore, a rotation by 180 degrees will carry ABCD back to itself