Answers
ANSWER
[tex]200[/tex]EXPLANATION
From the given data;
The ratio of the grandmother who buys lunch : all grandmother is;
[tex]\begin{gathered} 35:50 \\ =7:10 \end{gathered}[/tex]To calculate the corresponding values of grandmothers who buys lunch and all grandmother;
For the 3rd column;
When all grandmother is 150.
The grandmothers who buy lunch will be;
[tex]70+35=105[/tex]Hence the ratio;
[tex]105:150[/tex]also, the next column;
[tex]105+35=140[/tex]For all grandmother, add 50 to 150
[tex]50+150=200[/tex]Hence, the ratio equals;
[tex]140:200[/tex]The next column for grandmothers who buy lunch;
[tex]140+35=175[/tex]For all grandmother;
[tex]200+50=250[/tex]The ratio;
[tex]175:250[/tex]About 200
Related Questions
What is fºg(x) if f(x) = 2x + 7 and g(x)=-3x+4?
Answers
Answer
(f o g) (x) = -6x + 15
Explanation
We are given that
f(x) = 2x + 7
g(x) = -3x + 4
(f o g)(x) means writing the formula for f(x), but replacing the x with g(x)
(f o g) (x) = f[g(x)] = 2[g(x)] + 7 = 2(-3x + 4) + 7 = -6x + 8 + 7 = -6x + 15
Hope this Helps!!!
1. 3/4 + 5/6 + 1/4 + 1/62. 3/4 + 1/4 +5/6 +1/6
Answers
1. 3/4 + 5/6 + 1/4 + 1/6
The first step is to find the lowest common multiple(LCM) of the numbers in the denominators. The LCM is 12. We would divide each denominator by 12 and multiply the result by the numerator. The common denominator would be 12. Thus, we have
(3 * 3 + 5 * 2 + 1 * 3 + 1 * 2)/12
= (9 + 10 + 3 + 2)/12
= 24/12
= 2
A relation is shown (2,7), (0.1), (8, 9), (12, 18), (?, ?)} Select all ordered pairs that could replace the missing ordered pair to make the relation a function. •(-2,9)•(8,-18)•(7,-2)•(-8,0)•(0,0)
Answers
In order to be a function, the input values (x) must have only one output value (y)
So:
Possible pairs.
(-2,9)
(7,-2)
(-8,0)
is 4.5m equivalent to 0.45 km ?
Answers
EXPLANATION
4.5 is not equivalent to 0.45km because as 1km is equivalent to 1000 meters, then 0.45km is equivalent to 450 meters.
peter scores 125 marks in a test and it is equivalent to 31.25%.what is the total mark for the test?
Answers
Let TM denote the total marks for the test.
Then the 31.25% of total marks is given by the expression,
[tex]\begin{gathered} =\frac{31.25}{100}\cdot TM \\ =0.3125TM \end{gathered}[/tex]Given that the value of this 31.25% of total marks is 125,
[tex]\begin{gathered} 0.3125TM=125 \\ TM=\frac{125}{0.3125} \\ TM=400 \end{gathered}[/tex]Thus, the total mark for the test is 400.
six more than a number Is negative nine write a algebraic equation and solve
Answers
-15
Explanation
Step 1
let x represent the number
now, traslate into math terms
a)six more than a number is negative nine
[tex]\begin{gathered} \text{Number}\rightarrow x \\ \text{six more than a nubmer}\rightarrow x+6 \\ \text{six more than a number is negative nine}\rightarrow x+6=-9 \end{gathered}[/tex]hence, we got the equation
[tex]x+6=-9[/tex]Step 2
now, solve the equation
[tex]x+6=-9[/tex]we need isolate x without affect the expression, The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same
hence, subtract 6 in both sides
[tex]\begin{gathered} x+6=-9 \\ x+6-6=-9-6 \\ x=-15 \end{gathered}[/tex]therefore, the number is -15
I hope this helps you
The retail price for a book was $30. It was marked down 20% on Black Friday. The next day, it was marked back up 30%. What was the percent increase on the original price?
Answers
We have a retail price that is marked down 20% one day and then marked up 30%.
The original price is P=30, so a marked down price P' will be:
[tex]P^{\prime}=(1-0.2)\cdot P=0.8\cdot P=0.8\cdot30=24[/tex]Then, if we mark up 30% this price will be:
[tex]P^{\prime\prime}=(1+0.3)\cdot P^{\prime\prime}=1.3\cdot24=31.20[/tex]Now we can compare the increase in price as:
[tex]\begin{gathered} 1+i=\frac{P^{\prime\prime}}{P} \\ i=\frac{P^{\prime\prime}}{P}-1 \\ i=\frac{31.20}{30}-1 \\ i=1.04-1 \\ i=0.04 \\ i=4\% \end{gathered}[/tex]Answer: the percent increase on the original price is 4%.
What is the equation of the line that passes through (1,2) and is parallel to the line whose equation is 2x+y-1=01. 2x-y-4=02. 2x+y-4=03. 2x+y+4=0
Answers
STEP - BY - STEP EXPLANATION
What to find?
Equation of a line.
Given:
Passes through point ( 1, 2)
Parallel to line 2x+ y - 1 =0
Step 1
Write the parallel line equation in slope - intercept form.
That is; In the form y=mx + b
[tex]y=-2x+1[/tex]Step 2
Determine the slope of the line.
Comparing the equation above with the general equation y=mx + b
[tex]slope(m)=-2[/tex]Step 3
Find the slope of the new equation.
Slope of parallel line are equal, hence slope(m) = -2
Step 4
Find the intercept(b) of the new equation by substituting (1,2) and m=-2 into y=mx + b
x=1 and y=2
Where b is the intercept.
[tex]2=-2(1)+b[/tex][tex]\begin{gathered} 2+2=b \\ \\ b=4 \end{gathered}[/tex]Step 5
Form the new equation by substituting the value of m and b into y=mx + b.
[tex]y=-2x+4[/tex]Step 6
Re-arrange the equation.
[tex]2x+y-4=0[/tex]ANSWER
Second option
2x+y-4=0
Find the equation of the line through the given points (-1, 0) and (5, 5)
Answers
5x - 6y = -5
Explanations:The equation of the line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
y - y₁ = m (x - x₁)
where m is the slope of the line and is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
For the line passing through the points (-1, 0) and (5, 5)
[tex]\begin{gathered} x_1=-1,y_1=0,x_2=5,y_2=5 \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{5-0}{5-(-1)} \\ m\text{ = }\frac{5}{6} \end{gathered}[/tex]Substitute the values of x₁, y₁, and m into the equation of the line:
y - y₁ = m (x - x₁)
[tex]\begin{gathered} y\text{ - 0 = }\frac{5}{6}(x\text{ - (-1))} \\ y\text{ = }\frac{5}{6}\text{ (x + 1)} \\ y\text{ = }\frac{5}{6}x\text{ + }\frac{5}{6} \end{gathered}[/tex]6y = 5x + 5
5x - 6y = -5
The equation of the line is:
5x - 6y = -5
3. A cylindrical can has a height of 5 inches and adiameter of 4 inches. What is the approximatevolume of the can?A. 20 cubic inchesB. 100 cubic inchesC. 200 cubic inchesD. 314 cubic inches
Answers
Solution:
Given a cylinder with
Height = 5 in
Diameter = 4in
We want to determine the volume of the cylinder.
[tex]\begin{gathered} Volume\text{ of cylinder = }\pi r^2h \\ Where\text{ r=radius, h=height } \end{gathered}[/tex][tex]For\text{ this question, r=}\frac{4}{2}=2inches[/tex][tex]\begin{gathered} Volume\text{ = }\pi(2^2)(5) \\ Volume=\text{ 62.84cubic inches} \end{gathered}[/tex]The volume of the of the can is 62.84 cubic inches
this is an assignment that has four different parts so if you can help me with the four of them it would be great if not you can just do one. the first one says function A and B or linear function and are shown or described below. which function has the greater rate of change function a has a greater rate of change or function B has a greater rate of change.the second part says function A and B are linear functions and are shown or described below function 8 is defined by the equation y equals 4x + 2 function B has a table with x and y 4x I has numbers 1 2 4 and then the y side has 17 22 and 32.explain how you know which function has a greater rate of change.the third part of this says function A and B are linear functions and are shown or described below. function A is defined by the equation y equals 4x + 2.function B is represented in the table below there is a graph with an x side and a y side in the x aidw it has numbers 1 2 4 in the y side it has numbers 17 22. 32 the question says which function has a greater y intercept function a has the greatest y-intercept or function B has a greater y intercept
Answers
Function A
y=4x+2
Function B (table)
Slope intercept form:
y=mx+b
Where:
m= slope
b= y-intercept
For function a, the slope (rate of change) is 4.
For function B, apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where: (from the table)
(x1,y1) = (1,17)
(x2,y2) = (2,22)
Replacing:
[tex]m=\frac{22-17}{2-1}=\frac{5}{1}=5[/tex]rate of change A =4
rate of change B =5
Function B has a greater rate of change.
• Y-intercept
For the first equation the y-intercept is 2
y= mx+b
b= y intercept
The y-intercept is the value of x where y=0
for the second function, first, we have to wind the equation.
y=mx+b
so far we have _
y= 5x+b
replace x,y for a coordinate point from the table, for example (1,17), and solve for b
17=5(1)+b
17=5+b
17-5=b
12=b
So:
y intercept A = 2
y-intercept B = 12
Function B has a greater y-intercept
Which of the following shows V-16 simplified and written as a complex number?
Answers
Given:
[tex]\sqrt[]{-16}[/tex]Sol:.
[tex]\begin{gathered} \sqrt[]{-16} \\ =\sqrt[]{16}\times\sqrt[]{-1} \\ =\sqrt[]{4^2}\times\sqrt[]{-1} \\ =4i \end{gathered}[/tex]What is this question it’s math I just really don’t understand
Answers
ANSWER :
The value of a is a = -36
EXPLANATION :
From the problem, we have :
[tex]\frac{a}{9}=-4[/tex]cross multiply :
[tex]\begin{gathered} a=-4(9) \\ a=-36 \end{gathered}[/tex]wich set of side lengths forms a right angle?2 3 134 6 109 12 1815 36 39
Answers
To find if the length form a righ triangle we need to take the first two length, and check that we get the third length by using the Pythagorean Theorem:
[tex]undefined[/tex]can you show me how to do this on the graph aswell
Answers
Solution:
The system of inequalities is given below as
[tex]\begin{gathered} 3x+2y\leq6 \\ 4x-y\leq8 \end{gathered}[/tex]Step 1:
Put x=0 and find y
[tex]\begin{gathered} 3x+2y=6 \\ 3(0)+2y=6 \\ 2y=6 \\ \frac{2y}{2}=\frac{6}{2} \\ y=3 \\ (0,3) \end{gathered}[/tex]Put y=0 and find x
[tex]\begin{gathered} 3x+2y=6 \\ 3x+2(0)=6 \\ 3x=6 \\ \frac{3x}{3}=\frac{6}{3} \\ x=2 \\ (2,0) \end{gathered}[/tex]Step 2:
Put x= 0 and find y
[tex]\begin{gathered} 4x-y=8 \\ 4(0)-y=8 \\ -y=8 \\ y=-8 \\ (0,-8) \end{gathered}[/tex]Put y=0 and find x
[tex]\begin{gathered} 4x-y=8 \\ 4x-0=8 \\ \frac{4x}{4}=\frac{8}{4} \\ x=2 \\ (2,0) \end{gathered}[/tex]By using a graphing calculator, we will have
THE PURPLE REGION IS THE REGION TO BE SHADED
4. A busload of campers stopped at a local organic dairy stand for ice cream. They ordered 91cones, some soft-serve at $2.25 each and the rest hard-pack at $0.75 each. The total bill was$158.25. How many of each type of cone were ordered? (10 points)
Answers
Let the number of soft-serve be x and the number of hard-pack be y.
The total number of cones ordered is 91. Thus,
[tex]x\text{ + y =91 --- equation 1}[/tex]The price of soft-serve is $2.25 each. Thus, for x number of soft-serve, we have
[tex]2.25\text{ }\times\text{ x =\$2.25x}[/tex]Similarly, the price of hard-pack is $0.75 each. Thus, for y number of hard-pack, we have
[tex]0.75\text{ }\times\text{ y= \$0.75y}[/tex]The total bill was $158.25. This implies that
price of x soft-serve + price of y hard-pack = total bill
[tex]2.25x\text{ + 0.75y = 158.25 ----- equation 2}[/tex]Solve for x and y simultaneously in equations 1 and 2.
[tex]\begin{gathered} x\text{ + y = 91 ---- equation 1} \\ 2.25x\text{ + 0.75y = 158.25 ---- equation 2} \end{gathered}[/tex]Solve by the method of substitution.
From equation 1,
[tex]\begin{gathered} x+y=91 \\ \Rightarrow y=91-x\text{ ---- equation 3} \end{gathered}[/tex]Substitute equation 3 into equation 2.
[tex]\begin{gathered} 2.25x\text{ + 0.75y = 158.25} \\ 2.25x\text{ + 0.75(91-x) = 158.25} \\ \text{open brackets} \\ 2.25x\text{ + 68.25-0.75x = 158.25} \\ \text{collect like terms} \\ 2.25x-0.75x\text{ = 158.25-68.25} \\ 1.5x=90 \\ \text{divide both sides by the coefficient of x, which is }1.5 \\ \frac{1.5x}{1.5}=\frac{90}{1.5} \\ \Rightarrow x=60 \\ \end{gathered}[/tex]Substitute the value of 60 for x in either equation 1, 2 or 3.
Substitution into equation 3, we have
[tex]\begin{gathered} y=91-x \\ \Rightarrow y=91-60 \\ y=31 \end{gathered}[/tex]Hence,
the number of soft-serve ordered is 60,
the number of hard-pack is 31.
I need help with my math
Answers
By definition, when two figures are similar the ratios of the lengths of their corresponding sides are equal and their corresponding angles are congruent.
Knowing that the rectangles shown in the exercise are similar, you can set up the following proportion:
[tex]\frac{24}{16}=\frac{x}{6}[/tex]Then, you have to solve for the variable "x" in order to find its value. You get that this is:
[tex]\begin{gathered} (6)(\frac{24}{16})=x \\ \\ \frac{144}{16}=x \\ \\ x=9 \end{gathered}[/tex]The answer is:
[tex]x=9[/tex]6. You draw one card from a standard deck.(a) What is the probability that you do not select a diamond? (b) What is the probability that you do not select a face card? (c) What is the probability that you do not select an Ace? (d) What is the probability that you do not select a Jack or a King?
Answers
a.
We have 13 diamond cards.
The total of cards in a standard deck is 52
P(not a diamond) = 1 - P(Diamond)
= 1 - 13/52
= 3/4
b.
There are 12 faces cards
P(not a face card) = 1- P(face card)
= 1 - 12/52
= 10/13
c.
There are 4 ace cards
P(not an Ace) = 1-P(Ace)
= 1 - 4/52
= 12/13
d.
We have 4 jack cards and 4 king cards. 4+4 =8 j and k cards
P(not j or k) = 1 - P(j or k)
=1 - 8/52
= 44/52
As a percentage, $6.50 is equal to% of $10.00.
Answers
Take $10.00 as 100%
Use a rule of three to find which percentage is $6.50
[tex]\begin{gathered} \frac{x}{6.50}=\frac{100}{10.00} \\ \\ \end{gathered}[/tex]Solve x:
[tex]\begin{gathered} x=6.50\times\frac{100}{10.00} \\ \\ x=65 \end{gathered}[/tex]Then, $6.50 is the 65% of 10.00It is recommended that you save 12% of your salary for retirement. If I saved $6,600 this year, what was my total salary?
Answers
Let x represent the total salary. If the amount saved is $6600 and this is 12% of the total salary, it means that
12% of x = 6600
Recall, percentage is expressed in term of 100. It becomes
12/100 * x = 6600
0.12x = 6600
x = 6600/0.12
x = 55000
The total salary was $55000
(0,2) and(8,0) Write an equation in standard form of the line that passes through the given points
Answers
To find the equation of a line that pasess through two ponit, we'll first have to calculate the slope, using the formula:
[tex]m=\frac{y_2-y^{}_1}{x_2-x_1}[/tex]Therefore,
[tex]m=\frac{0-2}{8-0}\rightarrow m=\frac{-2}{8}\rightarrow m=-\frac{1}{4}[/tex]Then, we use the point-slope form equa with the slope we just found and the point (8,0)
[tex]\begin{gathered} y-0=-\frac{1}{4}(x-8)\rightarrow y=-\frac{1}{4}x+2\rightarrow y-2=-\frac{1}{4}x \\ \rightarrow-4y+8=x\rightarrow8=x+4y \\ \text{Therefore, the equation of the line is:} \\ x+4y=8 \end{gathered}[/tex]The question is in the image. They all are functions, right? I believe I am correct on that part. I’m struggling on the domain and range, and the intervals
Answers
The graph of question 8 is a function
The function in number 8 is defined for all real values except at x = 0. Hence, the domain of the function is given by the interval
(- ∞, 0) ∪ ( 0, ∞)
Also, the range of the function is given by the interval
( 0, ∞)
From the image of question 8, we can see that the function increases on the interval from x = - ∞ to x = 0.
That is the function is increasing on the interval
(- ∞, 0)
Also, the function is decreasing on the interval from x =0 to x=∞
Hence the function is decreasing on the interval
( 0, ∞)
Sketch and graph the function pls I need help sorry it’s a terrible graph but y’all got computer graphs
Answers
Given the function:
[tex]-3x^2-12x-10[/tex]In order to graph the quadratic function, we find some points on the parabola.
Vertex
Using the vertex formula:
[tex]\begin{gathered} \text{Vertex}=(-\frac{b}{2a},\frac{4ac-b^2}{4a}) \\ =(-\frac{-12}{2\times-3},\frac{4(-3)(-10)-(-12)^2}{4\times-3}) \\ =(-2,2) \end{gathered}[/tex]y-intercept
When x=0
[tex]\begin{gathered} y=-3(0)^2-12(0)-10=-10 \\ \implies(0,-10) \end{gathered}[/tex]Next, look for one point to the right of the vertex and one to the left.
When x=-1
[tex]\begin{gathered} y=-3(-1)^2-12(-1)-10=-3+12-10=-1 \\ \implies(-1,-1) \end{gathered}[/tex]Similarly, when x=-3
[tex]\begin{gathered} y=-3(-3)^2-12(-3)-10=-27+36-10=-1 \\ \implies(-3,-1) \end{gathered}[/tex]Similarly, when x=-4
[tex]\begin{gathered} y=-3(-4)^2-12(-4)-10=-48+48-10=-10 \\ \implies(-4,-10) \end{gathered}[/tex]The graph showing the points (-2,2), (0,-10), (-1,-1), (-3,-1) and (-4,-10) is attached below:
$1,030 at 4% compounded semiannually for 2 Years. please can you give the process to do it because i have problem about the process of that kind of work.
Answers
EXPLANATION
Let's see the facts:
Initial Amount = $1,030
Interest rate = 4% = 0.04 (in decimal form)
Compounding rate = Semiannually = 2 times by year
Time= 2 years
As we already know, the Formula to calculate the Principal is as follows:
[tex]P=I(1+\frac{r}{n})^{nt}[/tex]Substituting terms:
[tex]P=1030(1+\frac{0.04}{2})^{2\cdot2}[/tex]Adding numbers:
[tex]P=1,030(1.02)^4[/tex]Simplifying the power:
[tex]P=1,030\cdot1.0824=1,114.87[/tex]The Amount obtained is $1,114.87
calculate the area of the circle with radius = 3 ¼ydhelp me
Answers
We have the following:
The formula for the area of the circle is as follows
[tex]A=\pi\cdot r^2[/tex]replacing:
[tex]\begin{gathered} A=(3.14)\cdot(3\frac{1}{4})^2 \\ A=33.17 \end{gathered}[/tex]Therefore the area of the circle is 33.17 square yards.
Rachel is getting a sundae where the cost is proportional to the weight of the sundae she makes. Last time Rachel went she bought a 12-ounce sundae for $4.20. This time she buys a 17-ounce sundae. Let c be the cost of the sundae. Set up and solve a proportion for c.( Please show your work on how this problem is solved so i can understand it.)
Answers
12 Oz sundae is $4.20
The cost is given by the following eqation
[tex]c=\frac{\text{Last time price}}{\text{Last time weight}}\cdot w[/tex]where,
c is the cost of the sundae
w is the weight of the sundae
last time price = $4.20
last time weight = 12 Oz
Solving:
[tex]c=\frac{4.20}{12}\cdot w[/tex]Simplify
[tex]c=0.35\cdot w[/tex]if the sundae is 17 Oz , then the price would be: $5.95
[tex]c=0.35\cdot17=5.95[/tex]i need to graph it and i can use 2 points only please help noo
Answers
Answer:
Plotting the graph by selecting the two points using the parabola tool.
Explanation:
Given the function;
[tex]h(x)=-x^2+3[/tex]To find the vertex, it is the lowest or the highest point on the parabola.
[tex]\begin{gathered} At\text{ the vertex h'(x)=0} \\ h^{\prime}(x)=-2x=0 \\ -2x=0 \\ x=0 \end{gathered}[/tex]So, the vertex will be at x=0;
[tex]\begin{gathered} h(0)=-0^2+3 \\ h(0)=3 \\ (0,3) \end{gathered}[/tex]We can then identify one other point on the parabola;
[tex]\begin{gathered} at\text{ x=3} \\ h(x)=-x^2+3 \\ h(3)=-(3)^2+3 \\ h(3)=-9+3 \\ h(3)=-6 \\ (3,-6) \end{gathered}[/tex]Plotting the graph by selecting the two points using the parabola tool.
Solve the system graphically and check the solution. X+2y=2. 2x+4y=4
Answers
In order to find the solution graphically, you can solve both equations for y:
x + 2y = 2
y = -1/2 x + 1
2x + 4y = 4
y = -1/2 x + 1
The graph of the previous equations are:
As you can notice, the equations correspond to the same line. It means that the two lines have the same points and then, there are infinite solutions to the system.
((4x^5y)/(16xy^4))^3 Solve and Explain.
Answers
The given question is indices. we will be using laws of indices to solve it. This are some of the laws;
[tex]\begin{gathered} a^m\times a^n=^{}a^{m+n} \\ \frac{a^m}{a^n}=a^{m-n} \\ (a^m)^n=a^{mn} \end{gathered}[/tex]Given the expression;
[tex](\frac{4x^5y}{16xy^4})^3[/tex]Simplify using the laws as shown;
[tex]\begin{gathered} =(\frac{4}{16}\times\frac{x^5}{x}\times\frac{y}{y^4})^3 \\ =(\frac{1}{4}^{}x^{5-1}y^{1-4})\text{ }^3 \\ =(\frac{1}{4}^{}x^4y^{-3})\text{ }^3 \\ =\text{ }(\frac{1}{4}^{})^3(x^4)^3(y^{-3})\text{ }^3 \\ =\text{ }\frac{1}{64}x^{12}y^{-9} \end{gathered}[/tex]Hence the simplified form of the expression is;
[tex]\frac{1}{64}x^{12}y^{-9}[/tex]Put the quadratic into vertex form and state the coordinates of the vertex. y= x² – 2x – 3 Vertex Form: y = Vertex: Submit Answer
Answers
The Vertex form of a Quadratic equation is:
[tex]f(x)=a\mleft(x-h\mright)^2+k[/tex]Where the vertex of the parabola is:
[tex](h,k)[/tex]Given the following Quadratic equation:
[tex]y=x^{2}-2x-3[/tex]You can write in Vertex form by completing the square. The steps are:
1. You need divide the coefficient of the x-term by 2, square it and add it to both sides of the equation. Notice that:
[tex](\frac{2}{2})^2=1^2=1[/tex]Then:
[tex]y+(1)=x^{2}-2x-3+(1)[/tex]2. Move the term to the left side:
[tex]y+3+(1)=x^2-2x+(1)[/tex]3. Simplifying and factoring:
[tex]y+4=(x-1)^2[/tex]4. Solve for "y":
[tex]y=(x-1)^2-4[/tex]Now you can identify that:
[tex]\begin{gathered} h=1 \\ k=-4 \end{gathered}[/tex]The answer is:
a. Vertex form:
[tex]y=(x-1)^2-4[/tex]b. Vertex:
[tex](1,-4)[/tex]