Hannah is solving 42×19. Hannah says, “That’s easy! I can just break up the numbers and do 40×10=400 and 2×9=18.” Is Hannah correct? In the space below, show or explain why he’s correct or incorrect.
Answers
No, Hannah is incorrect.
We are given the expression 42*19.
Hannah got the solution by multiplying 40*10 and 2*9 and then adding the values.
This can be done by using distributive property, which is given by:-
(a + b)(c + d) = ac + ad + bc + bd
We can write,
42*19 = (40 + 2)(10 + 9) = 40*10 + 40*9 + 2*10 + 2*9
Hence, the answer is not just 40*10 + 2*9 but 40*10 + 40*9 + 2*10 + 2*9.
Hannah did not add the remaining 40*9 + 2*10 to calculate the answer.
That is why Hannah was incorrect.
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Related Questions
Please help
graph x<2.
Answers
Answer:
Bottom right
Step-by-step explanation
Answer:
first answer is correct
Find all the points having an x coordinate of 1 whose distance from the point (-3,-2) is 5
Answers
The possible coordinates of the other points are (1, -1) and (5, 1)
How to calculate the coordinates of the points?From the question, we have
Distance = 5 unitsPoints = (-3, -2) and (1, y)Where (1, y) represents the other points
The distance between the points is then calculated using the following distance formula
d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
Where x and y are the coordinates of the two points
Substitute the known values in the above equation
So, we have
d = √[(-3 - 1)²+ (-2 - y)²]
Evaluate
d = √[16+ (-2 - y)²]
The distance is 5 units
So, we have
√[16+ (-2 - y)²] = 5
Square both sides
16+ (-2 - y)² = 25
This gives
(-2 - y)² = 9
Square root of both sides
-2 - y = +/-3
So, we have
y = -2+/-3
Evaluate
y = -1 and y = 5
Hence, the coordinates are (1, -1) and (5, 1)
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Write an equation and solve.You bought a magazine for $5 and 4 erasers. You spent a total of $25. How much did each eraser cost?
Answers
Let the magazine be m and the eraser be e. Then the total cost is 25.
The equation can now be shown as follows;
[tex]\begin{gathered} 25=m+4e \\ 25=5+4e \\ Subtract\text{ 5 from both sides of the equation;} \\ 20=4e \\ \text{Divide both sides of the equation by 4} \\ 5=e \end{gathered}[/tex]Therefore each eraser cost $5
1. What is the slope of a line Parallel to y=-2/3x - 7*3/2-3/2O 2/3-2/3
Answers
Question:
Solution:
The definition of parallel lines tells us that if two lines are parallel, they have the same slope. On the other hand, the slope-intercept form of a line is given by the following formula:
y = mx+b
where m is the slope of a line. In this case, the slope of the given line would be m = -2/3. Then the correct answer would be:
[tex]-\frac{2}{3}[/tex]X=
////////////////////////
Answers
Answer: [tex]x=90[/tex]
Step-by-step explanation:
Using the alternate exterior angles theorem,
[tex]180-x=x\\\\180=2x\\\\x=90[/tex]
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
The volume of a gas V held at a constant temperature in a closed container varies inversely with its pressure P. If the volume of a gas is 800 cubic centimeters when the pressure is 450 millimeters of mercury (mm Hg), find the volume when the pressure is 200 mm Hg.
Step 2:
This is an application of Boyle's law which states that:
Boyle’s law is a gas law that states that the pressure exerted by a gas (of a given mass, kept at a constant temperature) is inversely proportional to the volume occupied by it. In other words, the pressure and volume of a gas are inversely proportional to each other as long as the temperature and the quantity of gas are kept constant.
[tex]\begin{gathered} Mathematically,\text{ we have that:} \\ V\text{ }\propto\text{ }\frac{1}{P} \\ Then,\text{ we have that:} \\ V\text{ =}\frac{k}{P}\text{ \lparen where k is a constant \rparen} \end{gathered}[/tex][tex]when\text{ V = 800 cubic centimetres , then P = 450 mm Hg}[/tex][tex]\begin{gathered} 800\text{ =}\frac{k}{450} \\ cross-multiply,\text{ we have that:} \\ \text{k = 800 x 450 = 360,000} \end{gathered}[/tex][tex]\begin{gathered} Then,\text{ the equation connecting V and P =} \\ \text{ V }=\frac{360,000}{P} \end{gathered}[/tex]Next:
[tex]when\text{ P = 200 mm Hg, we have that:}[/tex][tex]\begin{gathered} V\text{ = }\frac{360,000}{200} \\ \text{V = 1800 cubic centimetres } \end{gathered}[/tex]CONCLUSION:
The volume when the pressure is 200 mm Hg is:
[tex]V\text{ = 1800 cubic centimetres}[/tex]there is an ongoing debate about how many spaces should be placed after a period in typed documents. alana read about a study where 100100100 participants all read the same document typed in courier new font. half of the participants were randomly assigned the document with one space after each period, and the other half were given the document with two spaces after each period. participants who read the document with two spaces after each period were able to finish reading significantly faster than those with one space after each period. alana concluded that using two spaces after each period will help people read all documents faster. why is alana's conclusion not appropriate?
Answers
Alana's conclusion from the study is not appropriate.
Why is Alana's conclusion from the study is not appropriate?
In this study, there was no attempt made to research the alternative fonts. Alana reads about the study that includes only courier new font and arrives at a conclusion.The study in inconsistent with the standard scientific methods as it is not inclusive of all factors and possibilities and is thus inappropriate.What is an appropriate study?
The achievement of the research objectives is ensured by an appropriate study design. The important element of appropriate studies known as formulated research are missing from observational studies.Observational studies are in which the outcome is not tried to be altered through analysis unlike appropriate studies.This describes an investigation of a specific phenomenon that meets all requirements and adheres to the scientific method.To learn more about appropriate studies, refer:
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Marty graphs the hyperbola (y+2)2/36−(x+5)2/64=1 .
How does he proceed?
Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Marty first identifies the center of the hyperbola as Response area, and that the hyperbola opens Response area. Since a = Response area, the coordinates of the vertices are Response area.
The slopes of the asymptotes of this parabola are ± Response area, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Response area.
Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through the vertices, approaching the asymptotes.
Answers
To construct the graph of the hyperbola, the procedure is as follows:
Marty first identifies the center of the hyperbola as (-5,2), and that the hyperbola opens up and down. Since a = 6, the coordinates of the vertices are (-5, -4) and (-5, 8).The slopes of the asymptotes of this parabola are a = ± 3/4, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are y - 2 = ± 3/4(x + 5).Equation of an hyperbolaThe equation of a vertical hyperbola with center (x*, y*) is given according to the following equation:
(y - y*)²/a² - (x - x*)²/b² = 1.
A vertical hyperbola opens up and down.
In this problem, the equation is:
(y + 2)²/36 - (x + 5)²/64 = 1.
Hence the center is:
(-5, 2).
The value of coefficient a is:
a² = 36 -> a = 6.
Then the vertices of the hyperbola are:
(-5, 2 - 6) = (-5,-4).(-5, 2 + 6) = (-5,8).The slopes of the asymptotes of the parabola are given as follows:
±a/b.
Hence:
a/b = 6/8 = 3/4.-a/b = -6/8 = -3/4.Since the asymptotes pass through the center, the equation is:
y - 2 = ± 3/4(x + 5).
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which two county libraries charge the same penalty per week
Answers
Answer:
where's the rest of the question⁉️
a box contains 2828 red balls, 2020 green balls, 1919 yellow balls, 1313 blue balls, 1111 white balls, and 99 black balls. what is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 1515 balls of a single color will be drawn?
Answers
7069 are the minimum number of balls that must be drawn without replacement to complete the requirement that all balls of a single color be drawn.
First of all, we’ll look at the worst possible scenario and determine the minimum number of balls needed. We know that the color we are looking for is not blue, nor white, nor black (as there are less than 1515 of the same color when talking about those). In our worst possible scenario, we’ll first pull out all the blue, white, and black balls. Add them up. That means that we’ll definitely pull out 2523 balls( 1111 white + 1313 blue + 99 black). We are not done yet. From all the given balls, we are left with red, green, and yellow colored balls. In our worst scenario, we’ll pull out 1514 balls of every single color, and then we’ll finish it with one color (it doesn’t matter which). Since, we have 3 different colors left, that’s 3*1515+1 = 4545+1 = 4546 that is 4546 more balls.
To finish, we simply add the first 2523 balls with 4546, yielding 2523+4546 = 7069 balls.
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The graph shows g(x), which is a transformation of f(x)= 1x1. Write the function rule for
g(x).
Answers
The most appropriate choice for function will be given by -
g(x) = -|x| is the correct function
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
f(x) = |x| is the given function.
f(x) has been transformed to g(x) according to the graph given in the figure
In the figure, the range is negative real number.
So the transformation g(x) = - |x|
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In Emily's physics class, she had to solve the equation 9 = 12at2 + ut for u. Each step of her work is shown below.
Use the drop-down menus to explain each step.
Answers
The equation of u when it is the subject is u = 9/t - 12at
How to determine the solution for the equation for u?From the question, the original equation is given as
9 = 12at2 + ut
Next, we rewrite the equation to show the exponents
This is represented as
9 = 12at² + ut
To solve further, we simply isolate the variable term ut
This is done by subtracting 12at² from both sides of the equation
So, we have the following equation
9 - 12at² = 12at² - 12at² ut
Evaluate the like terms in the equation
So, we have
9 - 12at² = ut
Lastly, divide both sides of the equation by t
So, we have
(9 - 12at²)/t = ut/t
Evaluate the quotients
9/t - 12at = u
Make us the subject
u = 9/t - 12at
Hence, the solution for the equation for u is u = 9/t - 12at
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PLS HELP!!!
The tables show the cat population on two islands over several years. Describe mathematically, as precisely as you can, how the
cat population on each island is changing.
year
01 2 3
number of cats on Meow Island 2 6 18, 54 162
2 3 4
number of cats on Purr Island 2 6 10 14 18
B I
year
Type your response in the space below.
Type here
01
t
Answers
Step-by-step explanation:
Meow island get's their population multiplied by 3 per year
Purr island get's and additional 4 cats per year
The population of cats on each island in the mathematical form is:
Meow island:
f(0) = 2
And,
f(x) = 3f(x - 1)
Where x is the number of years from x = 1, 2, 3 ,,,,
Purr island:
y = 4x + 2
Where x is the number of years from x = 0, 1, 2, 3 ,,,,
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
We will make ordered pair of number of years x and number of cats y as
(x, y).
Meow island:
We see that the number of cats is increasing 3 times the previous number of cats.
So,
f(0) = 2
And,
f(x) = 3f(x - 1)
Where x is the number of years from x = 1, 2, 3 ,,,,
Purr island:
(0, 2), (1, 6), (2, 10), (3, 14) ....
The equation for the table.
y = mx + c
m = (6 - 2) / (2 - 1) = 4/1 = 4
(0, 2) = (x, y)
2 = 4 x 0 + c
c = 2
Now,
y = 4x + 2
Thus,
The population of cats on each island in mathematical form is given above.
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Please help!
Write an equation that represents the function graphed in blue by using transformations from y = |x| , which is graphed in green.
Answers
Answer:
-1/4*|X-1|Step-by-step explanation:
Let the green graph be G and the blue graph, be B:
1) Be cognate of the fact that the function in blue is completely negative, while the upper green graph is positive
Note: First, we should note that the blue function must therefore be a transformation of the Green function.
This means B takes the form:
y = (s)*a*|X+b|
We are required to find a, b, and s, where s is the sign.
2) From (1), we can deduce that, if graph G was transformed into B, then the first transformation begins by reflecting G along the X-axis (multiplying by -1).
Therefore, s = -1
3) From (2), it follows that the first transformation produces the following effect:
y = |X| transformed to y = -|X|
and B now takes the form y = -a*|X+b|
4) We notice again that the apexes of both functions do not touch. This means G was not only reflected along the X-axis but was also shifted or translated along the X-axis.
5) Building from (4), we notice that the Blue function takes a value of 0 when x is 1. If we put this in the general equation for B;
Finding b:
y = -a*|X+b| implies;
0= -a*|1+b|
|1+b| = 0/-a
|1+b| = 0
1+b = 0
b = -1and y becomes:
y = -a*|X-1|Finding a:
Notice also that when the x is 5, the Blue function now takes a value of -1. If we put this in a general equation for B;
y = -a*|X-1|
-1 = -a*|5-1|
-1 = -a*|4|
-4a = -1
a = 1/4The general equation for blue, B:y = -1/4*|X-1|Blaise M.
SAMANTHA HAS $27 TO RENT A BIKE FROM CYCLES RUS. SHE
HAS TO PAY A $IO FEE PLUS $2 FOR EVERY HOUR SHE HAS THE
BIKE. WRITE AND SOLVE AN INEQUALITY TO FIND THE
MAXIMUM NUMBER OF HOURS SAMANTHA CAN RENT THE BIKE.
Answers
Answer:
2 hours
Step-by-step explanation:
10+10= 20, so $20 fee
2+2= 4, so a fee for every hour she has the bike.
20+4= $24, so 2 hours maximum
If you tried adding another hour (which would be $12) that would equal $36 which is over her budget.
A recipe calls for 3 ⅜ cups of flour. How can you express that mixed number as a fraction?
Answers
To convert a mixed number to a fraction, you must multiply the denominator (8) by the number beside the fraction (3).
8 x 3 = 24.
Next, you add the numerator (3) to your answer!
24 + 3 = 27.
Lastly, put this number over your original denominator (8).
Therefore, the answer is 27/8!! I hope this helped!! <33
6 divided by 396 long divison attatch work !
Answers
Spoonhead's
heart beats 48 times
per minute. How many times will
his heart beat in two hours?
Answers
Answer:5760
Step-by-step explanation:
48 beats per min and its 120 min in 2 hours so multiply 120×48=5760
4. Find all values of x that make the statement true.
Answers
By solving ( 3 / x - 4) = (x - 5) / x equation we get ,
x = 10 and x = 2 .
Solution:
Given ( 3 / x - 4) = (x - 5) / x,
3x = (x - 5) (x - 4)
By solving this equation,
3x = x( x - 5 ) - 4( x- 5)
3x = x² - 5x - 4( x - 5)
3x = x² - 5x - 4x + 20
3x = x² - 9x + 20 = 0
3x - x² + 9x -20 = 0
12x - x² - 20 = 0
-x² + 12x -20 = 0
-1(x(x - 2 ) - 10( x - 2 )) = 0
-1( x - 10) ( x - 2) = 0
x - 10 = 0
x - 2 = 0
∴ x = 10
x = 2
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Make up a word problem to solve for system of equations. Be creative
Answers
Consider the following problem.
A student library has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student academic meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.
The conditions of this problem give rise to the following system of equations
[tex]x\text{ +y + z = 24}[/tex][tex]4x\text{ + 6y + 10z = 148}[/tex][tex]\frac{1}{2}x\text{ + }\frac{1}{4}y+\frac{1}{3}z\text{ = 9}[/tex]Multiplying the second equation by 1/2 and the third equation by 12, we get:
[tex]x\text{ +y + z = 24}[/tex][tex]2x\text{ + 3y + 5z = 74}[/tex][tex]6x\text{ + 3}y+4z\text{ = 108}[/tex]Now, multiply the first equation by -2 and add it to the second equation. In this way we obtain:
[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]6x\text{ + 3}y+4z\text{ = 108}[/tex]Multiply the first equation by -6 and add it to the last equation. In this way we obtain:
[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]\text{ -3y -2z = -36}[/tex]Finally, the process is completed by adding the second multiplied by 3 to the third equation.
[tex]x\text{ +y + z = 24}[/tex][tex]y+3z\text{ =26}[/tex][tex]7z\text{ = 42}[/tex]then, if we perform back substitution we get the desired solutions:
[tex]x=10[/tex][tex]z=6[/tex]and
[tex]y=8[/tex]We can conclude that the correct answer is:
Answer:Problem:
A student cafeteria has 24 tables, X tables with 4 seats each, Y tables with 6 seats each, and Z tables with 10 seats each. The total seating capacity of the cafeteria is 148. For a special student meeting, half of the X tables, 1/4 of the Y tables, and 1/3 of the Z tables will be used, for a total of 9 tables. Determine X, Y, and Z.
System of equations:
[tex]x\text{ +y + z = 24}[/tex][tex]4x\text{ + 6y + 10z = 148}[/tex][tex]\frac{1}{2}x\text{ + }\frac{1}{4}y+\frac{1}{3}z\text{ = 9}[/tex]Solution for this system of equations:
[tex]x=10[/tex][tex]y=8[/tex][tex]z=6[/tex]Select the value that make the inequality w≥6 true
Answers
Answer:
Every number that is greater than 6
2.a statewide real estate sales agency, farm associates, specializes in selling farm property in the state of nebraska. its records indicate that the mean selling time of farm property is 90 days. because of recent drought conditions, the agency believes that the mean selling time is now greater than 90 days. a statewide survey of 100 farms sold recently revealed that the mean selling time was 94 days, with a standard deviation of 22 days. at the .10 significance level, has there been an increase in selling time?
Answers
The increase in the selling price is 1.818.
Test statistic:
A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.
The given values are:
a = 0.1
x = 94
μ = 90
The formula for test statistic will be:
t = ((x- μ) / ([tex]\frac{s}{vn}[/tex])
Now put the values in the given equation we have:
t = (94-90) / ([tex]\frac{22}{10}[/tex])
= 4/2.2
= 1.818
Therefore the increase in the selling price is 1.818.
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we have a coin which, with equal odds, is either weighted so that heads has .75 probability, or weighted so that heads has .25 probability. we flip the coin twice and observe two heads. what is the conditional probability that the coin is weighted toward heads with .75 probability?
Answers
The Conditional Probability that the coin is weighted towards heads is 0.25/0.75 . Conditional probability is the result of Bayes’ Theorem .
A coin is tossed twice . So, total outcomes are { HH , TH , HT, TT} that is 4 .
Probability= favourable outcomes / total outcomes
Probability of getting two heads = ¼ = 0.25
Favourable outcomes are { HH , HT, TH}
Probability of getting at least one head = ¾ = 0.75
Conditional probability is measure of the probability of an event occurring, given that another event has already occurred.
Formula , P(A|B) = P(A and B)/ P(B)
Here, p(A|B) is conditional probability of A given B
P(B) is probability of event B occur
P(A and B) is probability of both events A and B occur
We have to find conditional probability that coin is weighted towards heads and it is = Probability of getting both heads / probability of getting at least one head
= ¼ / ¾ = 0.25 / 0.75
Which is required result .
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1.39 to 1 decimal point
Answers
Answer: 1.4 or just 1
Step-by-step explanation:
But we are going to a decimal point then go to 1.4, cause the 9 makes the 3 round-up. :)
Answer: 1.4
Step-by-step explanation:
I believe you're asking what 1.39 rounded to the nearest tenths place is, in that case it is 1.4
What is Y=2x+5 solved
Answers
The answer of the linear equation for Y=2x+5 is x = (y-5)/2.
What is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Now in this equation, x is a variable, A is a coefficient, and B is constant.
The given linear equation is,
Y=2x+5
Now, solve this linear equation for x
Take 5 to LHS it will change sign to -ve
y-5 = 2x
Next, take coefficient of x below to LHS
(y-5)/2 = x
Now, swap the sides
x = (y-5)/2
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Hello! I think I have this correct but want to make sure.
Answers
Solution;
y=5x
Explanation;
[tex]\begin{gathered} y\propto x \\ y=kx \\ k=\frac{y}{x} \\ when\text{ x=1 and y=5;} \\ k=\frac{5}{1}=5 \\ Therefore; \\ y=5x \end{gathered}[/tex]how to find the inverse of f(x) = 3x - 7
Answers
To get the inverse of this function you need two steps. First, we leave the variable [tex]x[/tex] alone in the function. Finally, write [tex]f^{-1}(x)[/tex] where you see the letter [tex]x[/tex] and [tex]x[/tex] where you see the letter [tex]y[/tex].
First step:Leave the variable [tex]x[/tex] alone.
[tex]y=3x-7[/tex][tex]y+7=3x[/tex][tex]\frac{y+7}{3}=x[/tex]Last step:Make lettering according to the rule above.
[tex]\frac{x+7}{3} =f^{-1}(x)[/tex]Hello I just need help with A and B on my homework I was able to complete C
Answers
ANSWERS
a) 58
b) 62.2
EXPLANATION
a) The median is the middle value. It separates the data set in two. To find the median we have to put the data in order, from least to greatest:
[tex]44,49,53,54,58,74,74,74,80[/tex]The number of data is odd, this means that the median will be one of the values of the data set and not a mean between two of them. If there are 9 values, the median is the 5th value - so we have 4 values to the left and 4 values to the right.
The first 4 values are 44,49,53,54, so the median is 58.
b) The mean is the sum of all values of the data set divided by the amount of data:
[tex]\bar{x}=\frac{44+49+53+54+58+74+74+74+80}{9}=\frac{560}{9}=62.2222\ldots[/tex]Rounded to one decimal place, the mean is 62.2
TEST SCORES The average test score in a class is 74%. Half of the class scored within 7 points of the average.
One student received a score of x%. Which shows an expression that could be used to determine how far the student's score is from the average?
A. |74-7|
B. |x|-74
C. |x-74|
D. 74-|7|
Answers
It is to be noted that the absolute expression that shows how far the student's score is from the average is given as: "| x - 74| (Option C)
What is the justification for the above result?The student obtained a score of x% based on the question. As a result, x% might be larger or lower than the average score of 74%.
To establish how distant the student's score is from the average, we must subtract the student's score from the average score; i.e. (x - 74)
This difference, however, might be negative: as a result, the absolute value of (x - 78) must be calculated, yielding |x - 74|.
As a result, the phrase that may be used to assess how distant the student's score is from the average is as follows: |x - 74| which is the same as option c - An Absolute expression.
Absolute expressions are or modulus of a real number x, abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.
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PLEASE HELP ASAP! What is the rate of change (slope) and the initial value (y-axis) for this table?
Answers
Answer: m = 24
Step-by-step explanation:
The right side of the table is the x value, and the left side is the y value.
Pick two points, I will pick (1,35) and (3,83).
Once you pick the points, input them in the rise over run formula:
y2-y1/x2-x1
83-35/3-1 = 48/2 = 24