12. A teacher weighed 148 lbs. in 1999 and weighs 190 lbs. In 2020. What was the rate ofchange in weight?
Answers
Given,
The weight of the teacher in 1999 is 148 lbs.
The weight of the teacher in 2020 is 190 lbs.
The rate of change in weight is,
[tex]\begin{gathered} \text{Rate of change=}\frac{190-148}{2020-1999} \\ =\frac{42}{21} \\ =2 \end{gathered}[/tex]The teacher gained 2 pounds per year.
Hence, option A is correct.
Related Questions
Determine if the following ordered pairs are solutions to the equation 3x + y = 12.
(2,5)
(4,0)
(0,6)
Is (2,5) a solution to the equation 3x+y=12? Select the correct choice below and fill in the answer box to complete your
choice.
OA. Yes, because when 2 is substituted for x and 5 is substituted for y, simplifying the left side results in.
equals the right side.
OB. No, because when 2 is substituted for x and 5 is substituted for y, simplifying the left side results in
does not equal the right side.
A. Yes, because when 4 is substituted for x and 0 is substituted for y, simplifying the left side results in
equals the right side.
which
Is (4,0) a solution to the equation 3x + y = 12? Select the correct choice below and fill in the answer box to complete your
choice.
OB. No, because when 4 is substituted for x and 0 is substituted for y, simplifying the left side results in
does not equal the right side.
which
which
which
Is (0,6) a solution to the equation 3x+y=12? Select the correct choice below and fill in the answer box to complete your
choice.
OA. Yes, because when 0 is substituted for x and 6 is substituted for y, simplifying the left side results in
which
Answers
We can conclude that (4,0) is the solution of the equation 3x + y = 12 with the correct option (A).
What exactly are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, the ordered pair of the equation 3x + y = 12:
(A) When (2,5):
3x + y = 123(2) + 5 = 126 + 5 = 1211 ≠ 12(B) When (4,0):
3x + y = 123(4) + 0 = 1212 + 0 = 1212 = 12(C) When (0,6):
3x + y = 123(0) + 6 = 120 + 6 = 126 ≠ 12Therefore, we can conclude that (4,0) is the solution of the equation 3x + y = 12 with the correct option (A).
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The graph of y=-2 is is transformed to become y=√2+3-2 Which of the following statements best describes the effect this transformation has on the graph of y=√CA The graph is translated 2 units right and 5 units up.C. The graph is translated Sumits left and 2 units up.OC. The graph is slated Sumits left and 2 units down.C. The graph is translated 2 unitsSunits down.
Answers
We know that transformations on functions are given by:
Now, we notice that we get the second function if we perform the following things:
Add 5 to the radicand.
Subtract 2 to the whole function.
Comparing this with the table above we conclude that this transformation is described bt:
The graph is translated 5 units to the left and 2 units down.
Therefore, the answer is B
In 2011, an earthquake in Chile measured 8.3 on the Richter scale. How many times more intense was thisearthquake then than the 2011 earthquake in Papa, New Guinea that measured 7.1 on the Richter scale? Roundthe answer to the nearest integer.
Answers
SOLUTION:
Step 1:
In this question, we are given that:
In 2011, an earthquake in Chile measured 8.3 on the Richter scale. How many times more intense was this earthquake then than the 2011 earthquake in Papa, New Guinea that measured 7.1 on the Richter scale?
Round the answer to the nearest integer.
Step 2:
From the question, we are to use this formula:
Now, we have that:
[tex]\begin{gathered} M_2-M_1=\log (\frac{I_2}{I_1}) \\ \text{where M}_2=\text{ 8.3} \\ \text{and} \\ M_1=\text{ 7. 1} \end{gathered}[/tex]Hence, we have that:
[tex]\begin{gathered} \text{8. 3 - 7. 1 = log ( }\frac{I_2}{I_1}) \\ 1.2=log_{10}\text{ (}\frac{I_2}{I_1}) \\ (\frac{I_2}{I_1})\text{ = }10^{1.2} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex](\frac{I_2}{I_1})=10^{1.\text{ 2}}[/tex]I am creating a study guide and need step by step explanation for this question please
Answers
After other workers taken 1 banana, 2 oranges and 1 pear then total fruits left in the basket
[tex]11[/tex]Now the number of oranges left is 4.
So the probability of picking an orange from the basket is
[tex]\frac{4}{11}[/tex]After she took 1st orange then the number of oranges left 3
So the probability of picking an orange for the 2nd time is
[tex]\frac{3}{10}[/tex]Now the number of oranges left is 2, and the total number of fruits is 9. So the probability of picking third fruit also orange is
[tex]\frac{2}{9}[/tex]Express M in terms of B and n: B = 3Mn 2
Answers
We are given the expression B=3Mn/2 and told to express M in terms of B and n. This means that we should apply mathematical operations on both sides of the equation so we "isolate " M on one side of the equality sign. We begin with the given equation
[tex]B=\frac{3\cdot M\cdot n}{2}[/tex]First, we multiply both sides by 2, so we get
[tex]2\cdot B=3\cdot M\cdot n[/tex]Next, we divide by 3 on both sides, so we get
[tex]\frac{2\cdot B}{3}=M\cdot n[/tex]Finally, we divide both sides by n, so we get
[tex]\frac{2\cdot B}{3\cdot n}=M[/tex]In this case, we have succesfully expressed M in terms of B and n
A package of 8-count AA batteries costs $6.16. A package of 20-count AA batteries costs $15.60. Which statement about the unit prices
is true?
The 8-count pack of AA batteries has a lower unit price of $0.77 per battery.
The 20-count pack of AA batteries has a lower unit price of $0.77 per battery.
The 20-count pack of AA batteries has a lower unit price of $0.78 per battery.
Answers
Answer:
it would be within the range of $0.77 <x< $0.78
Find the length of the third side. If necessary, round to the nearest tenth. 12 5 x=what is the missing number x?
Answers
Step 1
Longest side is the hypotanuse = x
opposite = 5
Adjacent = 12
Apply pythagorus theorem
[tex]\begin{gathered} \text{Opposite}^2+Adjacent^2=Hypotanuse^2 \\ 5^2+12^2=x^2 \\ \\ 25+144=x^2 \\ x^2\text{ = 169} \\ x\text{ = }\sqrt[\square]{169} \\ x\text{ = 13} \end{gathered}[/tex][tex]undefined[/tex]What is the slope between (2,-1 ) and ( 5,4 )
Answers
the slope will be 5/3 because:
[tex]\frac{4-(-1)}{5-2}=\frac{5}{3}[/tex]What are the unknown angles?
Answers
A= 53°
B= 53°
C=127°
Explanation:
To find angle a, it is the same as the 53° angle given because they are corresponding angles. (Same place but on different lines)
To find angle b, we know that it is across from angle a. These types of angles are called alternate interior angles and they are always equal just like corresponding angles. So, therefore, angle b must equal angle a which is 53°.
To find angle c we know that a straight line equals 180°. Subtract the known 53 from 180 to figure out the degree of angle c.
180-53=127
Angle c=127°
You can always check your answer by making sure the line adds up to 180°
b is 53
c is 127
Christine is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of Math is Fun she sells. Suppose that x and y are related by the equation 70x + 1700= y.Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number. What is the change in Christine’s total pay for each copy of Math is Fun she sells? What is Christine’s total pay if she doesn’t sell any copies of Math is Fun?
Answers
From the information given, the equation relating her total pay (in dollars), y to the number of copies of Math is Fun she sells, x is expressed as
y = 70x + 1700
This is a linear equation. The slope intercept form of a linear equation is expressed as
y = mx + b
where
m = slope or rate of change
b = y intercept of the value of y when x = 0
By comparing both equations,
m = 70
b = 1700
a) Thus, the change in Christine’s total pay for each copy of Math is Fun she sells 70 dollars per copy
b) Christine’s total pay if she doesn’t sell any copies of Math is Fun is the value of y when x = 0. thus,
Christine’s total pay if she doesn’t sell any copies of Math is Fun = $1700
find the sum of the first 44 terms of the following series. to the nearest integer 10,14,18,...
Answers
The first term is a=10.
The number of terms is n=44.
The common difference is d=4.
The formula for the sum of n terms is,
[tex]S=\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]Determine the sum of first 44 terms of the series.
[tex]\begin{gathered} S=\frac{44}{2}\lbrack2\cdot10+(44-1)4\rbrack \\ =22\cdot\lbrack20+172\rbrack \\ =22\cdot192 \\ =4224 \end{gathered}[/tex]So answer is 4224.
15 points?Solve for A 5/A = P A = ???? That’s all it saysPlease state what A is.
Answers
In the picture below, angle 2 = 130 degrees, what is the measurement of angle 8?
Answers
Answer:
130°
Step-by-step explanation:
Alternate interior angles are equal in measure.
[tex] - x \div 4 \geqslant 2[/tex]That's the Math problem
Answers
6x + 14y what is the letter y in this problem?
Answers
The value of letter y in this problem is y = 6x / -14
How to solve the equationThe equation says that 6x + 14y
To solve the equation that we have here, we would have to equate to 0
such that we would have the equation as 6x + 14y = 0
6x + 14y = 0
then we would have
6x = - 14y
remember that when positives crosses over we would have it turn as negative.
Next we would have to divide through by - 14 in order to get the value of y
hence we would have
-14y / -14 = 6x / -14
then we would have y as
y = 6x / -14
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point).
Questions
1. (1) How many observations are collected? (2) How many variables are collected? (3) write
I
down quantitative variables (4) write down qualitative variables
2. Describe the data visually
2.1.(1) Make a frequency tables and histogram for the “Hour” variable (bin limit = 1), and (2)
describe the shapes of the histogram
2.2.(1) Make a frequency tables and histogram for the “Type” variable, and (2) prepare a 2-D
pie chart and write down the title of chart
2.3.(1) Make a frequency tables and histogram for the “Weekday” variable, and (2) prepare a 2-
D pie chart and write down the title of chart
2.4.(1) Make a frequency tables and histogram for the “Location” variable, and (2) prepare a 2-D
pie chart and write down the title of chart
2.5.(1) Make a scatter plot of the data for the “Time” and “Hour variables, placing “Hour" on the
X-axis and "Time" on the Y-axis. Add titles and modify the default colors, fonts, etc., to make
the scatter plot easy to understand. (2) Describe the relationship (if any) between X and Y.
Weak? Strong? Negative? Positive? Linear? Nonlinear?
2.6.(1) Make a dot plot of the “Hour" variable for the “Deposit Type" variable. (2) Make a dot
plot of the "Hour" variable for the "Withdraw Type” variable. (3) Compare the shapes of both
charts
Answers
1). 68 observations
1.2) 8 variables
1.3) Quantitative Variables: Type, Time, Date, DayCode, Hour, and Amount
1.4) Qualitative Variables: Location, Weekday
Question 1) Let's examine that table to find out the number of collected observations. Counting each row, we have 68 observations. Each one informing the type, time, date, day code, weekday, Location, Hour, and Amount
1.2) We have then 8 variables namely (type, time, date, day code, weekday, Location, Hour, and Amount)
1.3) The Quantitative Variables are the ones whose entries are numerical, so examining then we can state that:
Type, Time, Date, DayCode, Hour, and Amount each and every one of them receives a numerical entry.
1.4) Qualitative or Categoricals variables are the ones whose entry is not a numerical one. So we can enlist the following ones as Qualitative:
Location
Weekday
Hence the answers are:
1). 68 observations
1.2) 8 variables
1.3) Quantitative Variables: Type, Time, Date, DayCode, Hour, and Amount
1.4) Qualitative Variables: Location, Weekday
Jeff has a job at baseball park selling bags of peanuts .he get paid $12 a game and 1.75 per bag of peanuts they sell .how many bags if peanuts does he need to sell in order to earn $54 in one
Answers
Let x be the number of peanut bags Jeff sells. Since he earns $1.75 per bag the total amount he earns for selling x bags is:
[tex]1.75x[/tex]Now, to this we have to add the $12 he gets paid, then the total amount he earns is:
[tex]1.75x+12[/tex]To find out how many bags he has to sell to earn $52 we equate the expression above with the amount and solve for x:
[tex]\begin{gathered} 1.75x+12=54 \\ 1.75x=54-12 \\ 1.75x=42 \\ x=\frac{42}{1.75} \\ x=24 \end{gathered}[/tex]therefore he has to sell 24 bags to earn $54.
Columbia Mirror and Glass pays Janet Murphy a $1120 monthly salary plus a 14% commission on merchandise she sells each month. Assume Janet's sales were $94,100 for last month. Calculate the following amounts: 1. Amount of Commission: Х ? SUD si 2. Gross Pay:
Answers
Monthly salary = $1120
Comission percentage = 14%
Janet's sales = $94,100
1. Amount of commission
Multiply the sales amount (94,100) by the Commission percentage in decimal form (divided by 100).
94,100 x (14/100) =
94,100 x 0.14 = $13,174
2. Gross pay
Add the amount of commission and the monthly salary:
13,174+1120 = $14,294
What is 16.02+8.5+14 ?? i want to know for a home work
Answers
Given:
[tex]16.02\text{ + 8.5 + 14}[/tex]To solve,
Step 1:
Express each value to a common decimal place.
We can express each value to two decimal places.
Thus, we have
[tex]16.02+8.50+14.00[/tex]Step 2:
Sum up the values.
Hence, 16.02 + 8.5 + 14 gives 38.52.
The sum of 19 and twice a number
Answers
Answer:
2x+19
Step-by-step explanation:
Let x be the number
2x+19
if you can tee the picture well please tell me
Answers
Since they give us the equation they have gotten for the line of best fit, we use it to estimate what thye answer is when x = 25:
Use:
y = 1.708 x - 4.011
then when x = 25:
y = 1.708 (25) - 4.011
y = 38.689
I don't read if the want you to round the answer to a given number of decimals, but if you try exactly the number we got (with the three decimals) that would be the most exact.
In the diagram below, if the measure of < C = 45 °, and side AB = 6.8, then side BC = _____.
Answers
Solution
Since
[tex]\begin{gathered} \tan45=\frac{6.8}{BC} \\ \\ \Rightarrow BC=\frac{6.8}{\tan45}=6.8\text{ since}\tan45=1 \end{gathered}[/tex]The correct option is A.
Please help meSolve using A=PertThe half life gets me each time.
Answers
In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. What is the probability that a randomly selected student will be taller than 71 inches tall, to the nearest thousandth?
Answers
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Answer:
0.010
Step-by-step explanation:
We solve the above question using z score formula
z = (x-μ)/σ, where
x is the raw score = 63 inches
μ is the population mean = 70 inches
σ is the population standard deviation = 3 inches
For x shorter than 63 inches = x < 63
Z score = x - μ/σ
= 63 - 70/3
= -2.33333
Probability value from Z-Table:
P(x<63) = 0.0098153
Approximately to the nearest thousandth = 0.010
Therefore, the probability that a randomly selected student will be shorter than 63 inches tall, to the nearest thousandth is 0.010.
Find the area of the shaded circles. Leave your answer in terms of pi or round to the nearest 10th
Answers
step 1
Find out the area of the complete circle
[tex]A=\pi\cdot r^2[/tex]we have
r=10 units
substitute
[tex]\begin{gathered} A=\pi\cdot10^2 \\ A=100\pi\text{ unit2} \end{gathered}[/tex]Remember that the area of the complete circle subtends a central angle of 360 degrees
so
Applying proportion
Find out the area of the circle with a central angle of 330 degrees
100pi/360=x/330
solve for x
x=(100pi/360)*330
x=91.67pi unit2What is the solution set of x² + 5x - 5 = 0?
Answers
The solution of x² + 5x - 5 = 0 is :
x = 0.854 and -5.854 .
Solution:
Here given equation,
x2 + 5x - 5 = 0
To solve the given equation use quadratic formula,
Using the quadratic formula,
x = [-b ± [tex]\sqrt{b2 - 4ac}[/tex] ] /2a
Here,
a = 1, b = 5 and c = -5
By substituting,
x = [-5 ± [tex]\sqrt{52 - 4(1)(-5)}[/tex] ] /2(1)
= [-5 ± √[tex]\sqrt{25 + 20}[/tex]] /2
= [-5 ± √45] /2
= [-5 ± 6.708] /2
So,
x = (-5 - 6.708)/2
= -11.708/2
= -5.854
= (-5 + 6.708)/2
= 1.708/2
= 0.854
∴ the solutions of equation is : 0.854 and -5.854.
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Any equation that can be rearranged in standard form as follows, where x stands for, is referred to be a quadratic equation in algebra.
What constitutes the x2 + 5x - 5 = 0 solution set?
We must figure out the equation's answer. The answers to the problem are thus 0.854 and -5.854. x^2 + 5x - 5 = 0
It is impossible to factor a quadratic equation like this one. It can be resolved either by completing the square or by applying the quadratic formula.
x = (-b +-sqrt(b2 - 4ac))/2a is the quadratic formula, where an is the coefficient of the x2, b is the coefficient of the x, and c is the constant.
a = 1, b = 5, c = -5
x = (-5 +- sqrt(25+20))/2
x = (-5 +- sqrt(45))/2
x = (-5 + - 3 sqt 5))/2
x = (-5 + 3sqrt5)/2 as well as x = (-5 - 3sqrt5)/2.
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The angle of depression from the top of a sheer cliff to point A on the ground is 35º. If point A is280 feet from the base of the cliff, how tall is the cliff? Round the answer to the nearest tenth of afoot.
Answers
In this case, to calculate the tall of the cliff, consider the distance from the base of the cliff to the point A, as a hypotenuse of a right triangle.
The tall of the clift is given by:
h = 280 sin(35)
h = 280(0.573)
h = 160.60
Hence, the tal of the clift is 160.60 feet
2. Using Vièta's theorem, find the solutions to the equation. a) x^2 - 3x + 2 = 0 b) x^2 + 2x - 15 = 0.
Answers
Given:
[tex]\begin{gathered} x^2-3x+2=0 \\ x^2+2x-15=0 \end{gathered}[/tex]Required:
We need to find the solution by Vièta's theorem.
Explanation:
Compare 1st equation with
[tex]ax^2+bx+c=0[/tex]we get
[tex]\begin{gathered} a=1 \\ b=-3 \\ c=2 \end{gathered}[/tex]Vièta's theorem is
[tex]\begin{gathered} x_1+x_2=-\frac{b}{a} \\ x_1x_2=\frac{c}{a} \end{gathered}[/tex][tex]\begin{gathered} x_1+x_2=3 \\ x_1x_2=2 \end{gathered}[/tex]now solve this equation and we get
[tex]\begin{gathered} x_1=1 \\ x_2=2 \end{gathered}[/tex]because addition of 1 and 2 is 3 and multiplication is 2
Now for 2nd equation
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-15 \end{gathered}[/tex]apply Vièta's theorem
[tex]\begin{gathered} x_1+x_2=-2 \\ x_1x_2=-15 \end{gathered}[/tex]by this
[tex]\begin{gathered} x_1=3 \\ x_2=-5 \end{gathered}[/tex]because addition of 3 and -5 is -2 and multiplication is -15
Exercises Complete the following: 11. Find the intercepts and (a) 9x² - 164 = 144 (c) 25x - 4y = 100 (e) x² + y² = 1 29x² + 16y² = 144
Answers
The intercepts for a function can be on either of the two axis, y or x.
when finding the intercepts of x, means that y = 0
when finding the intercepts of y, means that x = 0
finding the x intercepts
[tex]\begin{gathered} -x^2+(0)^2=1 \\ -x^2=1 \\ x^2=-1 \\ x=\sqrt[]{-1} \end{gathered}[/tex]since the solution for the square root of -1 has not any solution on the real numbers, we can say that there is no intercept over the x axis.
finding the y intercepts
[tex]\begin{gathered} -(0)^2+y^2=1 \\ y^2=1 \\ y=\pm\sqrt[]{1} \\ y=1;y=-1 \end{gathered}[/tex]there are 2 intercepts on the y axis, these are at y=1 and y=-1
information can be proven by graphing the function
write the simplest polynomial equation with the given roots. -1, 2i please answer quickly
Answers
The polynomial equation with root of -1 and 2i is,
[tex]\begin{gathered} (x+1)(x+2i)(x-2i)=(x+1)(x^2-(2i)^2) \\ =(x+1)(x^2-4i^2) \\ =(x+1)(x^2+4) \\ =x^3+4x+x^2+4 \\ =x^3+x^2+4x+4 \end{gathered}[/tex]So simplest polynomial is,
[tex]x^3+x^2+4x+4[/tex]