We were told that Aubrey paints 4 square feet of her house each minute.
Recall that 1 minute = 60 seconds.
The statement can be written as
Aubrey paints 4 square feet of her house each 60 seconds
If x represents the number of square feets that she paints in 20 seconds, it means that
4 = 60
x = 20
By cross multiplying, it becomes
60 * x = 4 * 20
60x = 80
x = 80/60
x = 1.333
Rounding to the nearest tenth, it becomes 1.3 square feet
She paints 1.3 square feet in 20 seconds
Use the given cost table for the same product from two different companies to create alinear system. Then solve the system to determine when the cost of the product will be thesame and what the price will be.Two online spice retailers sell paprika by the pound using the following pricing chart.Paprika (lb)iSpicei(x)SpiceMagics(x)1$19.75$65.252$34.50$49.25$76.50$87.7534$64.00$99.00i(x) =x + 5Sim)s(x) = 11.25x +forBoth iSpice and Spice Magic charge $pounds of paprika.
g(n) = 2n+6
c(n) = 2.25n+4
Both Chef Mate and Grocery Gourmet charge $22 for 8 ounces of vanilla extract.
From the question, we have
g(n) = 2n+6
c(n) = 2.25n+4
g(n) = c(n)
2n+6 = 2.25n+4
0.25n = 2
n = 8
g(n) = 2n+6
=2*8+6
=22
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ9
A ferris Wheel has a radius of 65 feet. What is the circumference of the wheel?
Circumference of the wheel = 408.2 ft
Explanation:radius = 65 ft
Circumference of the wheel = circumference of a circle
Circumference of a circle = 2πr
π = 3.14
Circumference of a circle = 2 × 3.14 × 65
Circumference of a circle = 408.2 ft
Circumference of the wheel = 408.2 ft
Three teachers handed out mathand science textbooks for theirclasses. Two teachers had21 students each, and the lastteacher had 22. How manytextbooks were handed outaltogether?
Given Data:
The number of teachers is, 3.
Two teachers had 21 students each.
The last teacher had 22.
Since, two teachers had 21 students each, the number of textbooks handed out by these two teachers can be calculated as,
[tex]21\times2=42[/tex]Therefore the total number of text books handed out is,
[tex]42+22=64[/tex]Thus, 64 textbooks were handed out altogether.
Identify the center of the circle defined by the equation (x + 4)² + (y - 1)² = 32
Answer:
The centre of the circle is (-4,1).
Explanation
Given the equation of the circle:
[tex]\mleft(x+4\mright)^2+(y-1)^2=32[/tex]Comparing with the standard form of the equation of a circle:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ Where\; Centre=(h,k) \end{gathered}[/tex]We see that:
[tex]\begin{gathered} x-h=x+4 \\ \implies h=-4 \\ \text{Also:} \\ y-k=y-1 \\ \implies k=1 \end{gathered}[/tex]The centre of the circle is (-4,1).
6in 4in 3in 8in 3in 4in area of irregular figures
Are The Ratios 2:4 and 1:3 equivalent?Yes or No
The ratio 2:4 is equivalent to and 1:3 if both numbers are obtained by the same multiplication:
Since
1 x 2 = 2 and
3 x 2 = 6 (instead of 4)
then they are NOT equivalent
Lora rents a car while spending her vacation traveling in Brazil. When she returns the car, she has driven 1350 miles and used about 54 gallons of gas. If gas costs an average of $4.969 per gallon, estimate how much she spent on fuel.
Given:
distance Lora has driven = 1350 miles
amount of gas she used = 54 gallons
cost of gas per gallon = $4.969
The amount she spent o fuel can be calculated using the formula:
[tex]\text{Amount she has spent on fuel = cost per gallon }\times\text{ amount of fuel she has used }[/tex]Substituting we have:
[tex]\begin{gathered} \text{Amount she has spent on fuel = \$5 }\times\text{ 5}5 \\ =\text{ }275 \end{gathered}[/tex]Answer:
Hence, Lora has spent $275 on fuel by estimate
The following triangles are scaled copies of each other. What is the scale factor? The scale factor is? What is the length of x? What is the length of y?
If we divide corresponding sides, we can obtain the scale factor:
24/6 = 4
Lenght of x
x/8 =4
Solve for x
x=4 (8)
x= 32
Lenght of y:
36/y=4
Solve for y
36/4=y
9=y
A new model of shirt at the clothing store comes in 4 colors: black, white, red, and blue
The data provided of the 16 sold shirts can be used to count the frequency of each color.
The results are shown below:
White = 5
Black = 2
Blue = 4
Red = 5
We can check the total is 5 + 2 + 4 + 5 = 16
Now we are ready to draw the bar graph, where each color must have a height that equals its frequency.
[tex] {a}^{12} {b}^{ - 9} \ \: {c}^{ - 6} [/tex]what is the answer ?
We have the following expression:
[tex](a^{12}b^{-9})\frac{c^{-6}}{\square}[/tex]Now let's recall two properties of the exponents that will help to solve this exercise:
[tex]x^{-1}=\text{ }\frac{1}{x}\Rightarrow4^{-3\text{ }}=\text{ }\frac{1}{4^3}[/tex]Then we have:
[tex]a^{12}c^6/b^9[/tex]Now, we have all the exponents with positive sign
The base of the exponents is different (a,b and c), therefore there is no additional step we can take
Student became unresponsive. Closing the session
What is the slope of LaTeX: f\left(x\right)=3x-1
To find the slope of the expression:
[tex]f(x)=y=3x-1[/tex]We need to remember that this is the Slope-intercept Form of the line equation:
[tex]y=mx+b[/tex]Where
m = slope
b is the y-intercept.
Therefore, the slope of the line equation above is m = 3.
How to find the distance of a circle given points (-2.1,1.5) and (0.8771,0)
Given:
There are given the two points of the circle:
[tex](-2.1,1.5)\text{ and (0.8771,0)}[/tex]I would like to know the answer for this question it’s very confusing
As the first step, let us say that the velocity of the boat in relation to a fixed point in the map of this travel is equal to its velocity in relation to the water PLUS the water velocity in relation to the fixed point WHEN it is in the same direction (travel downstream), and MINUS when traveling in the opposite direction (upstream).
From this, we will remember the definition of velocity by:
[tex]V=\frac{\Delta S}{\Delta t}[/tex]The ΔS is the distance ran by the boat, which is 60 miles. Δt is 4h for the upstream case, and 3h for the downstream case.
From this, we say that the value of V is for the boat in relation to the water (which is what we need here) and v for the water. Now, we have the following system of equations.
[tex]\begin{gathered} V-v=\frac{60}{4}=15 \\ V+v=\frac{60}{3}=20 \\ \\ V-v=15 \\ V+v=20 \end{gathered}[/tex]Now, to proceed with the solution, we will sum up the equations, which will result in the following:
[tex]\begin{gathered} V-v+(V+v)=15+20 \\ 2V=35 \\ V=\frac{35}{2} \\ \\ V=17.5mph \end{gathered}[/tex]From the solution developed above, we are able to conclude that the rate of the boat in still water, what is the velocity the boat reaches in relation to the water, is equal to 17.5 miles per hour.A committee has seven men and four women. If four people are selected to go to a conference, what is the chance that the group is two men and two women?
Given:
A committee has seven men and four women.
four people are selected to go to a conference
We will use the combinations as follows
the number of ways to choose the four people are:
[tex]7C4+7C3+7C2+7C1+7C0[/tex]The rule of combinations is:
[tex]\text{nCr}=\frac{n!}{(n-r)!\cdot r!}[/tex]so, the number of ways will be:
[tex]35+35+21+7+1=99[/tex]The number of ways to make a group of two men and two women will be:
[tex]7C2=21[/tex]So, the chance that the group is two men and two women =
[tex]\frac{21}{99}=\frac{7}{33}[/tex]so, the answer will be 7/33
If f(5)=2 and g(5)=9, what is (f+g)(5)
Answer:
11
Step-by-step explanation:
You have an equation [tex]f(x)[/tex] and you set [tex]x=5[/tex], and the result is 2.
You have another equation [tex]g(x)[/tex] and you set [tex]x=5[/tex], and the result is 9.
Therefore, if you add both equations, represented by [tex](f+g)(x)[/tex], and you set [tex]x=5[/tex], the result is simply 2 + 9 = 11.
For questions 6 – 10, find the unknown side length. number 10
10) Given:
hypotenuse = 20
angle = 45°
To find:
length of s
angle = 45
opposite = side opposite the angle = s
To find the value of s, w will apply sine ratio (SOH)
[tex]sin\text{ 45 = }\frac{opposite}{hypotenuse}[/tex][tex]\begin{gathered} sin\text{ 45 = }\frac{s}{20} \\ s\text{ = 20sin45} \\ sin\text{ 45 = }\frac{\sqrt{2}}{2} \\ \\ s\text{ = 20}\times\frac{\sqrt{2}}{2} \\ s\text{ = 10}\sqrt{2}\text{ \lparen exact answer\rparen} \end{gathered}[/tex][tex]\begin{gathered} s\text{ = 20sin45} \\ s\text{ = 20\lparen0.7071\rparen} \\ s\text{ = 14.142 \lparen decimal approximation\rparen} \end{gathered}[/tex]What is the image of (-8, -1) when it isreflected across the line y=x?A (-1, -8) C (1,8)B(1-1)D8
Give the object with a coordinate (-8,-1)
The transformation of an object with coordinate (x,y) reflected across the line y=x is given by
T(x,y) => (y,x)
So for the question given
If (-8,-1) is reflected across the line y = x
Then
T(-8,-1) => (-1, -8)
Answer = (-1,-8)
For the rectangle shown below, which can be used to find the value of x?A. 3^2 + x^2 = 15^2B. (x + 3)^2 = 15^2C. 3^2 + 15^2 = x^2D. 3 + 15 = x^2
Since the rectangle is composed of 2 right triangles, we can apply the Pythagorean theorem to one of the triangles:
c^2 = a^2 +b^2
Where:
c= hypotenuse (longest side) = 15
a & b = the other two legs of the triangle ( x , 3 )
Replacing:
15^2 = 3^2 + x ^2
Solve for x
225 = 9 + x^2
225-9 = x^2
216 = x^2
√216 = x
x= 14.69
So, to find the value of x, we can use:
A. 3^2 + x^2 = 15^2
Paxton did the following multiplication problem. Where should he put the decimal point in his product? 9.18 % 73 2754 64260 67014 6.701.4 67.014 6.7014 670.14
We have the multiplication of 9.18 * 7.3 and want to know where the decimal point has to be.
In the multiplication we have to sum the decimal position of the numbers and taht is the position of the decimal point of the result.
In this case, the decimal point of 9.18 is 2 places and for 7.3 is one place, so the final result will have 2+1=3 places. The decimal point has to be 3 places.
The number is 67014 and the decimal point is three places from rigth, 67.014
Write a polynomial function of least degree with the given zeros: -2, 1,4
Since we want a polynomial p(x) with zeros -2,1 and 4, we have the following expression:
[tex]p(x)=(x-(-2))(x-1)(x-4)[/tex]If we multiply these factors we get:
[tex]\begin{gathered} p(x)=(x+2)(x-1)(x-4) \\ \Rightarrow p(x)=(x^2+x-2)(x-4) \\ \Rightarrow p(x)=x^3-4x^2+x^2-4x-2x+8 \\ p(x)=x^3-3x^2-6x+8 \end{gathered}[/tex]Therefore, the polynomial function with the given zeros is p(x)=x^3-3x^2-6x+8
1593 concert tickets were sold for a total of $22,491. If students paid $11 and nonstudents paid $17, how many student tickets were sold?
765 student tickets were sold
Explanation:Let the number of student tickets be represented by x
Let the number of nonstudent tickets be represented by y
1593 concert tickets were sold
x + y = 1593....................(1)
The total amount made = $22491
Cost of each student ticket = $11
Cost of each nonstudent ticket = $17
This can be interpreted mathematically as:
11x + 17y = 22491...............(2)
Mulitipy equation (1) by 17
17x + 17y = 27081...........(3)
Subtract equation (2) from equation (3)
6x = 4590
x = 4590/6
x = 765
765 student tickets were sold
In JKL, LJ K L and mZK = 26Find mZJ.
From the information given, we can draw a triangle.
A rough drawing of the triangle is shown below:
if given the function y=-3x+5,what is the output if f(x)=4
To solve this problem, we have to evaluate when f(x) = 4. Remember that y = f(x)
[tex]\begin{gathered} y=-3x+5\rightarrow f(x)=-3x+5 \\ 4=-3x+5 \end{gathered}[/tex]Then, we solve for x
[tex]\begin{gathered} 4-5=-3x \\ -3x=-1 \\ x=-\frac{1}{-3} \\ x=\frac{1}{3} \end{gathered}[/tex]Hence, th
How many weeks are in 259 days
SOLUTION
We want to find the number of weeks in 259 days
Now, 7 days make a week. So to get the number of weeks in 259 days, we divide the 259 by 7, we get
[tex]\frac{259}{7}=37[/tex]So the answer is 37 weeks
find the median of 79,27,24,11,14,11
To get the median of the distribution, we need to re-arrange the data in either ascending or descending order
Re-arranging the data in ascending order, we have
11, 11, 14, 24, 27, 79
There are two numbers that falls in the midle of the distribution, that is 14 and 24
The median = (14 + 24)/2 = 38/2
=19
The answer is 19
Given the function h(x) = x^2 + 3x - 1 determine the average rate of change of the function over the interval -7 ≤ x ≤ 5
Given:
[tex]x^2+3x-1[/tex]Find: average rate of change of the function over the interval -7 ≤ x ≤ 5
Explanation: the average rate of change of the function is
[tex]\begin{gathered} \frac{f(b)-f(a)}{b-a} \\ \end{gathered}[/tex][tex]\begin{gathered} f(b)=f(5)=5^2+15-1 \\ =25+15-1 \\ =39 \\ f(a)=f(-7)=(-7)^2-21-1 \\ =49-22 \\ =27 \end{gathered}[/tex][tex]\frac{f(b)-f(a)}{b-a}=\frac{39-27}{5-(-7)}=\frac{12}{12}=1[/tex]Final answer: the required answer is 1.
9) A notebook costs $3.50 and a binder costs $6.70. Jessica bought m binders. She also bought 4 fewernotebooks than binders. Write an algebraic expression for the total amount she spent.
Explanation:
We are told that a notebook costs $3.50 and a binder costs $6.70
If we represent the number of notebooks to be n and binders to be m
Also, we are told that she bought 4 fewer notebooks than binders
Then, we can say that
[tex]n=m-4[/tex]The total amount spent can be obtained using the basic principle
[tex]Amount=cost\text{ per unit}\times quantity\text{ sold }[/tex]Therefore
we have
[tex]Total\text{ Amount}=3.50(n)+6.70(m)[/tex]But, we have established that n = m-4
Thus
[tex]Total\text{ amount =3.5\lparen m-4\rparen+6.7\lparen m\rparen}[/tex]The total amount in terms of the binders will be
[tex]\begin{gathered} 3.5m-14+6.7m \\ 3.5m+6.7m-14 \\ 10.2m-14 \end{gathered}[/tex]Thus,
we can also express the total amount in terms of the binders as
[tex]Total\text{ amount }=10.2m-14[/tex]How many quarts of pure antifreeze must be added to 3 quarts of a 50% antifreeze solution to obtain a 60% antifreeze solution?quart(s) of pure antifreeze must be added(Round to the nearest tenth as needed.)
Initially we have 3 quarts of a 50% antifreeze solution
We want to obtain a 60% antifreeze solution by adding x quarts of pure antifreeze
Therefore we can set the following equation,
[tex]1x+0.5*3=0.6*(x+3)[/tex]where x are the quarts of pure antifreeze added
let's solve for x
[tex]\begin{gathered} x+1.5=0.6x+1.8 \\ x-0.6x=1.8-1.5 \\ 0.4x=0.3 \\ x=\frac{0.3}{0.4} \\ x=0.75 \end{gathered}[/tex]rounding to the nearest tenth, 0.8 quarts of pure antifreeze must be added
If we consider only the cost of gasoline, how much does it cost ( in dollars) to drive each mile ? Round to the nearest cent.
Given:
The cost of gasoline, c=$2.20/gallon.
The car gets x=26 miles per gallon.
The cost to drive each mile if gasoline costs $2.20/gallon is
[tex]\begin{gathered} T=\frac{c}{x} \\ =\frac{\frac{2.20\text{ dollars}}{1\text{ gallon}}}{\frac{26\text{ miles}}{1\text{ gallon}}} \\ =\frac{2.20\text{ dollars}}{1\text{ gallon}}\times\frac{1\text{ gallon}}{26\text{ miles}} \\ =0.08 \end{gathered}[/tex]Therefore, the two fractions for obtaining the solution is,
[tex]\begin{gathered} \frac{2.20\text{ dollars}}{1\text{ gallon}} \\ \frac{1\text{ gallon}}{26\text{ miles}} \end{gathered}[/tex]The cost in dollars to drive each mile is $0.08 per mile (rounded to nearest cent).
Select the correct answer. 3(r + 4) – 2(1 - 1) Which is the simplified form of the expression OA. - 1 OB. 67 101 + 9 O C. 3 Tot + 5 2 76 OD. 15 + 101 Undo Next
We have the expression:
[tex]3(\frac{7}{5}x+4)-2(\frac{3}{2}-\frac{5}{4}x)[/tex]We simplify it as follows:
[tex]\frac{21}{5}x+12-3+\frac{5}{2}x\Rightarrow(\frac{21}{5}x+\frac{5}{2}x)+(12-3)[/tex][tex]\Rightarrow\frac{67}{10}x+9[/tex]From this, we have that the solution is the B option.