Justine is trying to read the most pages of all students in her Language Arts class by the end of the year. The table shows the pages Justine read, and the time she read them in.Which of the following would be the best equation for the function of the values for Justine's reading?A.h = 40pB.p = 7hC.40p = hD.p = 40h
Answers
Given
Hours (h) = 1, 2, 3, 4, 5, 6, 7
Pages (p) = 40, 80, 120, 160, 200, 240, 280
Procedure
[tex]\begin{gathered} \frac{\text{pages}}{\text{hours}}=\frac{40}{1}=\frac{80}{2} \\ \frac{p}{h}=40 \\ p=40h \end{gathered}[/tex]
The answer would be p = 40h
Related Questions
(statistics) urgently need help with question 32, is it valid or not valid & is the argument sound or not?
Answers
From the Venn diagram shown above we notice that the conclusion is false. This comes from the fact that even if all queens are women not all women are quenss.
The area of the parallelogram below is square meters. 9 m 7 m 2m
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Answer:
63 square meter
Explanation:
Area of the parallelogram = Base * Height
From the given diagram;
Base = 9m
Height = 7m
Area of the parallelogram = 9m * 7m
Area of the parallelogram = 63 square meter
Use diagram to find the following 1. m angle RVS = 2. M angle TVU =
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The pie chart provides the following information;
[tex]\begin{gathered} m\angle RVS=(10x-10)^o \\ m\angle RVU=(8x-14)^o \\ m\angle UVT=8x^o \\ m\angle TVS=(5x+12)^o \end{gathered}[/tex]The sum of angles in a circle is 360 degrees.
Thus, we have;
[tex]\begin{gathered} (10x-10)^o+(8x-14)^o+8x^o+(5x+12)^o=360^o \\ 31x^o-12^o=360^o \\ 31x^o=360^o+12^o \\ 31x^o=372^o \\ x^o=\frac{372^o}{31} \\ x^o=12^o \end{gathered}[/tex]Then;
(a)
[tex]\begin{gathered} m\angle RVS=(10x-10)^o_{} \\ m\angle RVS=10(12)-10 \\ m\angle RVS=110^o \end{gathered}[/tex](b)
[tex]\begin{gathered} m\angle TVU=8x^o \\ m\angle TVU=8(12) \\ m\angle TVU=96^o \end{gathered}[/tex]a boat is heading towards a lighthouse, whose beacon light is 117 feet above the water. the boats crew measures the angle of elevation to tye beacon 3. what is the ships horizontal distnace from the lighthouse( and the shore)? round your answer to the nearest hundreth of a foot if necessary.
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So,
We could draw the situation of the problem as follows:
We want to find the horizontal distance, which we will call "x".
To find it, we could use the trigonometric ratio: tan(a).
This ratio relations the opposite side of the angle given (a) and its adjacent side. So, we could write:
[tex]\tan (3)=\frac{117}{x}[/tex]Now, if we solve for x:
[tex]x=\frac{117}{\tan (3)}[/tex]This is, x = 2232.49 ft
In 1960, the world record for the men's mile was 3.91 minutes. In 1980, the record time was 3.81 minutes. a, write the linear model that represents the world record (in minutes) for the men's mile as a function of the number of years, t , since 1960. y=___b, use the model to estimate the record time in 2000 and predict the record time in 2020.2000:___ minutes2020:___ minutes
Answers
To first answer this question, we need to find the slope of the linear equation. We have the following information:
x1 = 1960, y1 = 3.91
x2 = 1980, y2 = 3.81
Then
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3.81-3.91}{1980-1960}=-0.005[/tex]Then, we have that the linear model will be:
[tex]y-y1=m\cdot(x-x1)\Rightarrow y-3.91=-0.005\cdot(x-1960)_{}[/tex]Or
[tex]y=-0.005\cdot(x-1960)+3.91\Rightarrow y=-0.005x+13.71[/tex]This is the linear model.
Then, to use the model to estimate the record time in 2000 and in 2020, we have:
[tex]y=-0.005\cdot(2000)+13.71\Rightarrow y=3.71[/tex]And
[tex]y=-0.005\cdot(2020)+13.71\Rightarrow y=3.61[/tex]Therefore, the linear model is y = -0.005x + 13.71.
The estimation for the record time in 2000 is 3.71 minutes.
The estimation for the record time in 2020 is 3.61 minutes.
This is a linear model.
given two numbers 9 * 10 to the 8 power, and 30,000,000, which one is larger and by how much. 3 times larger or 30 times larger
Answers
The first number is 9 * 10^8
The second number = 30,000,000 = 3 * 10^7
so, the larger number is 9 * 10^8 because the power of 10 is the larger than the other number
To find how much is larger, divide 9 * 10^8 by 3 * 10^7
so,
so, it is 30 times larger
solve the equation -8y + 8 = 37y - 7
Answers
you must first get the variables on the same side of the equal sign. It yields,
[tex]-8y-37y+8=-7[/tex]if we also pass the constant 8 to the right hand side, we have
[tex]-8y-37y=-7-8[/tex]Hence, the left and right hand sides are equal to
[tex]-45y=-15[/tex]hence, we have
[tex]y=\frac{-15}{-45}[/tex]since minus times minus is plus, we obtain
[tex]y=\frac{15}{45}[/tex]and it can be reduced to
[tex]\begin{gathered} y=\frac{15}{15\cdot3} \\ y=\frac{1}{3} \end{gathered}[/tex]Finally, the answer is
[tex]y=\frac{1}{3}[/tex]Answer:
y= 1/3
Step-by-step explanation:
Write an equivalent expression by distributing the "-" sign outside the parentheses: -k-(-6.2m +1)
Answers
In order to get the required expression you take into account that when you eliminate a prenthesis preceded by a minus sign, terms inside the parenthesis change their sign.
Then, for the following expression, you have:
- k - (-6.2m + 1)
- k + 6.2m - 1 that is, signs inside the parenthesis have changed
see, I got an answer but my teacher showed us the websites answer and I'm confused.
Answers
First let's remember what a Rational number is. A Rational number is that one that can be written in this form (as a fraction):
[tex]\frac{a}{b}[/tex]Where "a" is the numerator and "b" is the denominator.
Integers include negative numbers and, positive numbers and zero. For example, these are Integers:
[tex]4,2,-3,-8[/tex]An Integer is always a Rational number, because it can be written as a fraction with denominator 1:
[tex]\frac{4}{1},\frac{2}{1},\frac{-3}{1},\text{ }\frac{-8}{1}[/tex]Then:
A Rational number that is not an Integer is different from a Rational number that is an Integer, because the first one must be written with a denominator. For example:
[tex]\frac{1}{2}[/tex]but the second one can written showing only the numerator (because it is know that all Integers have denominator 1):
[tex]4=\frac{4}{1}[/tex]Therefore, all Integers are Rational numbers, but a Rational number is not always an Integer.
Ignore c. I only need help with a and b
Answers
Part A.
The composition of f ang g is given by
[tex](f\circ g)(x))=f(g(x))=\frac{(3x+7)-7}{3}[/tex]where we have inserted 3x-7 in the place of x in function f. Then, we have
[tex](f\circ g)(x))=f(g(x))=\frac{3x+7-7}{3}=\frac{3x}{3}=x[/tex]Therefore, the answer is
[tex](f\circ g)(x))=x[/tex]Part B
Similarly to the previous case, we have
[tex](g\circ f)(x))=g(f(x))=3(\frac{x+7}{3})-7[/tex]which gives
[tex](g\circ f)(x))=g(f(x))=x+7-7=x[/tex]then, the answer is
[tex](g\circ f)(x))=x[/tex]Part C.
In the first case, x belongs to the domain of g and g(x) belongs to the domain of f. Then, the domain of the composition (fog)(x) is all real numbers.
Similarly, in the second case, x belongs to the domain of f and f(x) belongs to the domain of g. Then, the domain of the composition (gof)(x) is all real numbers. Then, the domains are the same (all real numbers).
Quadratic Functions in Standard FormCaroline wrote these steps to graph f(x) = 2x2 + 4x + 5 on note cards, but they gotmixed up. Help Caroline by re-writing the steps in the correct order. Use the notecards to complete the steps below.
Answers
1.- Determine the vertex...
2.- The axis of symmetry...
3.- The y-intercept...
4.- Plot a point...
5.- Plot another point...
The above is the correct order of the cards, now the reason for that first you have to find the vertex. Now, the axis of symmetry is a straight line that passes through the vertex. Later you have to find another 2 points reflected by the symmetry axis and finally construct the graph.
Identify the slope and the y-intercept of each line and use them to write an equation of the graph
Answers
Notice that the line passes through the point (0,1) and the point (3,-1). Then, we have the following:
[tex]\begin{gathered} y-\text{intercept: (0,1)} \\ \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{-1-0}{3-0}=-\frac{1}{3} \\ m=-\frac{1}{3} \end{gathered}[/tex]now we can find the equation of the line using the slope and the y-intercept:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-1=-\frac{1}{3}(x-0) \\ \Rightarrow y=-\frac{1}{3}x+1 \end{gathered}[/tex]therefore, the equation of the line is y=-1/3x+1
In professor Johnson's literature class there are 267 students. At a random check Prof.Johnson notices that 22 students among 59 students did not complete their essays.Can you estimate how many students in Prof. Johnson's class did not finish theiressay?Question 71 pts
Answers
We have a class of a total of 267 students.
The professor has a sample of 59 students, where 22 of them did not complete their essays.
This equals a proportion of:
[tex]p=\frac{22}{59}\approx0.373[/tex]If this sample is representative of the class, we can use this proportion to estimate how many students did not complete the essay.
To do that we multiply the total number of students by the proportion we have just calculated:
[tex]X=N\cdot p=267\cdot0.373\approx99.59\approx100[/tex]Answer: it can be estimated that approximately 100 students did not finish their essay.
what is f(-2) if f (x)= 1/2xa. -2b. -1c. 0d. 1
Answers
EXPLANATION
If x=-2 the f(-2) = (1/2)(-2) = 1
So, f(-2) = 1
The right option is d. 1
Find the next three terms of the given sequences below. Type your answer on the blank.1. 12, 18, 24, 30, 36,2.90, 81, 72, 63, 543.100, 90, 80, 70,
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We have three arithmetic sequences. Arithmetic sequences have a common difference between each consecutive terms. We just have to calculate the common difference of each sequence and then add to the last term to get the following terms.
item a)
The common difference is
[tex]18-12=6[/tex]The next three terms are
[tex]\begin{gathered} 36+6=42 \\ 42+6=48 \\ 48+6=54 \end{gathered}[/tex]42, 48 and 54.
item b)
The common difference is
[tex]81-90=-9[/tex][tex]\begin{gathered} 54+(-9)=45 \\ 45+(-9)=36 \\ 36+(-9)=27 \end{gathered}[/tex]The next three terms are 45, 36 and 27.
item c)
The common difference is
[tex]90-100=-10[/tex][tex]\begin{gathered} 70+(-10)=60 \\ 60+(-10)=50 \\ 50+(-10)=40 \end{gathered}[/tex]The next three terms are 60, 50 and 40.
I need help with my math
Answers
SOLUTION:
Step 1:
An adult's ticket costs $11
A child's ticket costs $6
The number of Adult's tickets sold is x
The number of Children's tickets sold is y
The total number of tickets sold is 60
The total amount of sales made is $460
Step 2:
We need to form two equations based on the information given in the question;
[tex]undefined[/tex]The point (-3, - 5) is on the graph of a function. Which equation must be true regarding the function? A. f(-3) = -5B. f(-3, -5) = -8C. f(-5) = -3D. f(-5, -3) = -2
Answers
SOLUTION
The correct option is A
Points with coordinates (x,y) on a graph can also be expressed thus:
[tex]f(x)=y[/tex]So with the above explanation, we can answer the question.
The point (-3,-5) on the graph means that x=-3 and y=-5
So it can be expressed as a function in the form:
[tex]\begin{gathered} f(x)=y \\ x=-3\text{ and y=-5} \\ f(-3)\text{ =-5} \end{gathered}[/tex]The correct option is A
What is the measurement of DC? How do you know ?
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The vertices B, C and D form a right triangle.
Knowing 2 sides of the tright triangle, like BD and BC, we can find the length ofthe third side, DC, using the Pythagorean theorem: the sum of the squares of the length of the legs, DC and BC, is equal to the square of the length of the hypotenuse BD.
[tex]DC^2+BC^2=BD^2[/tex]Replacing with the values, we can calculate DC:
[tex]\begin{gathered} DC^2+60^2=100^2 \\ DC^2+3600=10000 \\ DC^2=10000-3600 \\ DC^2=6400 \\ DC=\sqrt[]{6400} \\ DC=80 \end{gathered}[/tex]Answer:
The correct options are
A: 80
B: Pythagorean theorem
what is 5.8x10² in standard notation?
Answers
Answer:
[tex]5.8\text{ }\times\text{ 10}^2[/tex]Explanation:
Here, we want to write the given number in standard notation
The form we have given, is the scientific notation
To write in the standard form, we consider the scientific notation as they are the same
We have the standard notation as:
[tex]5.8\text{ }\times\text{ 10}^2\text{ = 5.8 }\times\text{ 10}^2[/tex]a store is having a sale on almonds and Jelly Beans .For 3 pounds of almonds and 8 pounds of jelly beans the total cost is 34 dollars. For 5 pounds of almonds and 2 pounds of jelly beans. the cost is 17 dollars. Find the cost of each pound of almonds and each pound of jelly beans
Answers
We have a system of equation problem
x= cost of almonds per pound
y= cost of the jelly beans per pound
For the first equation, we have
3 pounds of almonds
8 pounds of jelly beans
total $34
so the equation is
3x+8y=34
For the second equation we have
5 pounds of almonds
2 pounds of jelly beans
total $17
so the equation is
5x+2y=17
so our system of equation is
[tex]\begin{gathered} 3x+8y=34 \\ 5x+2y=17 \end{gathered}[/tex]In order to solve the system we will multiply the second equation by -4
[tex]-4(5x+2y=17)=-20x-8y=-68[/tex]then we sum the equation above with the first equation
[tex]3x-20x+8y-8y=34-68[/tex]then we sum similar terms and isolate the x to find the value of x
[tex]\begin{gathered} -17x=-34 \\ x=\frac{-34}{-17} \\ x=2 \end{gathered}[/tex]then we substitute the value of x=2 in the first equation and we find the value of y
[tex]\begin{gathered} 3(2)+8y=34 \\ 6+8y=34 \\ 8y=34-6 \\ 8y=28 \\ y=\frac{28}{8} \\ y=3.5 \end{gathered}[/tex]The solution is
x= $ 2 cost of each pound of almond
y= $3.50 cost of each pound of jelly beans
use the elimination to solve each system of equations exercise number 4)
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To solve this system of linear equations using the elimination method, first, add both equations:
[tex]\begin{gathered} 8x+5y=38\Rightarrow\text{ Equation 1} \\ -8x+2y=4\Rightarrow\text{ Equation 2} \end{gathered}[/tex][tex]\begin{gathered} 8x+5y=38 \\ -8x+2y=4\text{ +} \\ --------- \\ 0x+7y=42 \\ 7y=42 \end{gathered}[/tex]Now solve for y dividing by 7 on both sides of the equation:
[tex]\begin{gathered} \frac{7y}{7}=\frac{42}{7} \\ y=6 \end{gathered}[/tex]Finally, replace the value of y in any of the initial equations, for example in equation 1
[tex]\begin{gathered} 8x+5y=38 \\ 8x+5(6)=38 \\ 8x+30=38 \\ \text{ Subtract 30 from both sides of the equation} \\ 8x+30-30=38-30 \\ 8x=8 \\ \text{ Divide by 8 from both sides of the equation} \\ \frac{8x}{8}=\frac{8}{8} \\ x=1 \end{gathered}[/tex]Therefore, the solution of the system of equations is
[tex]\begin{cases}x=1 \\ y=6\end{cases}[/tex]Find the measure of Z CFD.СF5m + 116T3m + 80D
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I need help with this practice problem solving Make sure to read the instructions, answer by filling in the three boxes
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Solution
[tex](-2\sqrt{3}-2i)^4[/tex]Therefore the correct answer is
The polar form of a complex number
[tex]128\text{ cis }\frac{2\pi}{3}[/tex]The rectangular form of a complex number
[tex]-128+128\sqrt{3}i[/tex]how do you solve 0.27÷0.9?
Answers
Given:
[tex]0.27\div0.9[/tex]To divide the decimals, we must take care of the decimal points
So, we will divide it as follows:
[tex]0.27\div0.9=\frac{27}{100}\div\frac{9}{10}=\frac{27}{100}\times\frac{10}{9}=\frac{27}{9}\times\frac{10}{100}=3\times\frac{1}{10}=0.3[/tex]So, the answer will be 0.27 ÷ 0.9 = 0.3
Solve the system graphically and check the solution. 2x+y=4. Y-2x=6
Answers
Answer:
[tex]\begin{gathered} x\text{ = -0.5} \\ y\text{ = 5} \end{gathered}[/tex]Explanation:
Here, we want to solve the system of linear equations graphically, then we proceed to check for the solution
To do this, we have to plot the graph of the two equations on the same plot, the point at which these lines intersect would be the solution to the system of linear equations
We have the plot shown as follows:
From what we have on the plot, the solution to the system is x = -0.5 and y =5 . The reasonn for this is that it is at this point that both lines intersect
Now, let us check the solution:
We can check the solution by substituting -0.5 for x and 5 for y in both equations
For the first one:
[tex]\begin{gathered} 2(-0.5)\text{ + 5 = 4} \\ -1\text{ + 5 = 4} \\ 4\text{ = 4} \end{gathered}[/tex]We can see that th solution works for the first equation
For the second one, we proceed with the same substitution process
We have this as:
[tex]\begin{gathered} 5-2(-0.5)\text{ = 6} \\ 5\text{ + 1 = 6} \\ 6\text{ = 6} \end{gathered}[/tex]We can see the solution works for the second equation too
In ACDE, mZC = (4x – 16), m D = (6x - 1)", and mZE = (4x - 13). Find mZC.
Answers
Explanation:
We can do a diagram of triangle CDE:
The sum of the measures of the interior angles of any triangle is 180º. We can write an equation:
[tex]\begin{gathered} m\angle C+m\angle D+m\angle E=180º \\ (4x-16)+(6x-1)+(4x-13)=180 \\ (4x+6x+4x)+(-16-1-13)=180 \\ 14x-30=180 \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 14x=180+30 \\ 14x=210 \\ x=\frac{210}{14} \\ x=15 \end{gathered}[/tex]And with x = 15, replace into the expression for the measure of angle C to find it:
[tex]m\angle C=4x-16=4\cdot15-16=60-16=44º[/tex]Answer:
m
The board of directors of a company must have select a president, a secretary and a treasurer in how many possible ways can this be accomplished if there are 22 members on the board
Answers
Given
Total number of members = 22
Find
Possible ways of selection of president, a secretary and a treasurer
Explanation
As we know , the number of possible ways of selection is given by
[tex]N=^nP_r[/tex]there are three members required so , r = 3
now , substitute the values in above equation
[tex]\begin{gathered} N=^{22}P_3 \\ N=\frac{22!}{(22-3)!} \\ \\ N=\frac{22!}{19!} \\ \\ N=22\times21\times20 \\ N=9240 \end{gathered}[/tex]Final Answer
Possible ways of selection of president, a secretary and a treasurer = 9240
One thermos of hot chocolate uses 2/3 cup of cocoa powder. How many thermoses can nalli make with 3 cups of cocoa powder?
Answers
In order to determine the number of thermos, divide by 3 by 2/3, as follow:
[tex]\frac{\frac{3}{1}}{\frac{2}{3}}=\frac{3\cdot3}{1\cdot2}=\frac{9}{2}=4.5[/tex]the previous result means that nalli can make four and one hal thermoses with 3 cups of cocoa powder.
Question 3 1 Marge is making a chocolate cake to surprise the best nend. She needs 3 1/2cups of four but she only has 1/3cup. How much more flour does she need?
Answers
Answer:
19/6 cups
Explanation:
First, we need to transform the mixed number into a fraction as:
[tex]3\frac{1}{2}=\frac{3\cdot2+1}{2}=\frac{7}{2}[/tex]Now, we need to subtract 1/3 from 7/2, so:
[tex]\frac{7}{2}-\frac{1}{3}=\frac{7\cdot3-2\cdot1}{2\cdot3}=\frac{21-2}{6}=\frac{19}{6}[/tex]Therefore, she needs 19/6 cups more
TA Write in simplest form (improper not accepted): 7[tex] 7 \frac{7}{14} [/tex]
Answers
We are given the following fraction
[tex]\frac{7}{14}[/tex]We are asked to write it in the simplest form.
Notice that the number 14 is a multiple of number 7.
That is 7 times 2 is equal to 14.
Which means that 7 divided by 14 must be equal to 2
So the fraction becomes
[tex]\frac{7}{14}=\frac{1}{2}[/tex]Therefore, the simplest form of the given fraction is 1/2
Please note that the simplest form means that it cannot be further simplified.