A mathematics professor created a test that was supposed to be mostly easy except for two challenging problems, the highest grade was 93.
Data is encoded in a dot or tiny circle using a dot plot. The distribution of numerical variables is depicted on a number line in the dot plot, where each dot represents a value.
Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots represents the numerical value of each variable, it is comparable to a bar graph or a simplified histogram. Small amounts of data are shown using dot plots.
Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money. Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range.
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Mark's model train can go 1/3 laps around its track in 2 mins. If it runs at the same speed,
1. How many laps can the train go in 9 mins?
2. Rate needed?
3. Unit rate?
4 Interpretation of unit rate?
In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.
What is the average rate of change?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.
Given, Mark's model train can go 1/3 laps around its track in 2 mins. If it runs at the same speed,
Since,
In 2 mins Mark's model train can go = 1/3 laps
Thus,
In 1 min Mark's model train can go = 1/3/2 laps
In 1 min Mark's model train can go = 1/6 laps
In 9 mins Mark's model train can go = 9/6 laps
In 9 mins Mark's model train can go = 1.5 laps
Therefore, In 9 mins Mark's model train can go 1.5 laps and unit rate is 1/6 laps per minute.
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Based on the information in the model, which equation represents the Pythagorean theorem?
From the given figure, equation represents the Pythagorean theorem is 13²=12²+5². Therefore, option D is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.
From the given figure, area of a largest square is 169 square units, area of a larger square is 144 square units and the area of a smaller square is 25 square units.
We know that, the area of a square is side².
Now, the side(a) of a largest square is side²=169
So, a=13 units
The side(b) of a larger square is side²=144
So, b=12 units
The side(c) of a smaller square is side²=25
Then, c=5 units
Here, a, b and c form a right angle triangle.
By using Pythagoras theorem, we get
a²=b²+c²
13²=12²+5²
Therefore, option D is the correct answer.
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The intruction booklet for a cd player ay that the player ue about 0. 2 of electricity per hour if electricity cot 0. 30 per hour hour how much doe it cot to run a player for an hour
If the instruction booklet for a CD player says that player uses 0.2 kilowatt of electricity per hour and electricity costs $0.30 per kilowatt hour, then the cost to run the player for an hour is $0.06 .
The cost of running a CD player for an hour can be calculated by multiplying (the amount of electricity it uses) by (the cost per kilowatt hour) .
According to the instruction booklet, the player uses 0.2 kilowatt of electricity per hour.
So, if electricity costs $0.30 per kilowatt hour, then
it would cost ⇒ 0.2 × $0.30 = $0.06 .
Therefore , it will take $0.06 to run the player for an hour.
The instruction booklet for a CD player says that player uses 0.2 kilowatt of electricity per hour. If electricity costs $0.30 per kilowatt hour, how much does it cost to run the player for an hour ?
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i really do need help with this
On applying the supplementary angle rule, the value for x is obtained as 10°, and the angle 7x° is obtained as 70°.
What is a supplementary angle?
The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.
The line segment is given which has a ray diving the line segment.
Since it is a straight line, the total angle on it will be 180°.
The two angles given are 110° and 7x°.
Apply the supplementary angle rule =
On a straight line sum of two angles = 180°
Substitute the values in the equation -
110° + 7x° = 180°
Collect the like terms -
7x° = 180° - 110°
Apply the arithmetic operation of subtraction -
7x° = 70°
Apply the arithmetic operation of division -
x = 70/7
x = 10°
Now the angle 7x° = 7(10°) = 70°
Therefore, the angle value is obtained as 70°.
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3. If f(x)=x² - 2x + 7, evaluate the following:
f(-5)
ƒ (0)
f (1)
f(-5) = 42
f(0) = 7
f(1) = 6
What is a function?A function is a relationship that has a set of inputs and outputs. An example of a function is f(x) = x. The "(x)" in the parenthesis represents the input while the x on the left side represents the output. To compute the values of an output you plug in the input and replace all the variables with the input. E.g. to find f(1) we would replace all "x"s with 1 giving us f(1) = 1
Answering the questionGiven f(x) = x² - 2x + 7 we want to find f(-5) , f(0) and f(1)
We can find these values by simply plugging in the values of the inputs and replacing all x's for them.
If f(x)= x² - 2x + 7
Then,
f(-5) = (-5)² - 2(-5) + 7 simplify exponents
f(-5) = 25 - 2(-5) + 7 multiply -2 and -5
f(-5) = 25 + 10 + 7 add all values
f(-5) = 42
f(0) = (0)² - 2(0) + 7 simplify exponents
f(0) = 0 - 2(0) + 7 multiply 0 and -2
f(0) = 0 - 0 + 7 add all values
f(0) = 7
f(1) = (1)² - 2(1) + 7 simplify exponent
f(1) = 1 - 2(1) + 7 multiply -2 and 1
f(1) = 1 - 2 + 7 add and subtract the values
f(1) = 6
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The math seems easy but I've been staring at this question for so long that I'm kinda lost LOL
According to the information and the graph, the best place for Lois Lane to stand to receive the keys from Superman is in the middle of the Krytonite cage because it is the closest place to the point where superman is standing.
At what point should Lois Lane be located?
The point where Lois Lane should stand is in the middle of the cage because there he will have a better chance of receiving the Kronite keys that he has. Additionally, this point is the closest to the point where Superman is standing so he wouldn't have to go near the krionite and could throw the keys from there.
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Write an exponential function y=abx whose graph passes through the points (1,2) and (3,50) .
Answer:
y = 0.4·5^x
Step-by-step explanation:
You want an exponential function y = a·b^x that passes through the points (1, 2) and (3, 50).
SetupThe given point values give two equations in two unknowns when used in the given exponential form:
y = a·b^x
2 = a·b^1
50 = a·b^3
SolutionDividing the second equation by the first, we find b:
50/2 = (ab^3)/(ab)
25 = b^2 . . . . . simplify
5 = b . . . . . . . . . square root
Then the value of 'a' can be found from the first equation:
2 = a·5
a = 2/5 = 0.4
Exponential functionUsing these values of 'a' and 'b', we have the exponential function ...
y = 0.4·5^x
__
Additional comment
The exponential regression function of your calculator can tell you the same thing.
Find the domain for which the functions f(x)=2x^2−1 and g(x)=1−3x are equal.{-2,2}{2,1/2}{-2,1/2}none of these
The domain for which functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal:{-2, 1/2}
When the functions f(x) = 2x² - 1 and g(x) = 1 - 3x are equal,
f(x) = g(x)
2x² - 1 = 1 - 3x
2x² + 3x -1 - 1 = 0
2x² + 3x - 2 = 0
We solve above quadratic equation to find the value of x.
2x² + 3x - 2 = 0
2x² + 4x - x - 2 = 0
2x(x + 2) - 1(x + 2) = 0
(x + 2)(2x - 1) = 0
x + 2 = 0 OR 2x - 1 = 0
x = -2 OR x = 1/2
This means, for x = -2 as well as x = 1/2 the functions f(x)=2x^2−1 and g(x)=1−3x are equal.
Thus, the required domain is: {-2, 1/2}
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what method of probability assessment would most likely be used to assess the probability that a major earthquake will occur in california in the next three years?
Seismic hazard analysis is a method of probability assessment that would most likely be used to assess the probability that a major earthquake will occur in California in the next three years.
Seismic hazard analysis is a method used to assess the probability of earthquakes occurring in a specific location, and it involves analyzing the historical records of earthquakes, geological data, and the tectonic plate movements in the area. This method is used to predict the likelihood of future earthquakes and their potential magnitude and intensity.
In the case of California, a seismic hazard analysis would likely be used to assess the probability of a major earthquake occurring in the next three years. The data collected from this analysis would help the government and the public prepare for potential earthquakes and minimize the damage caused by such events.
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Help! See the image below! :)) thank you!!
(a) The answer is The Allen family earns $24,000 more than the Reed family.
(b) The answer is The Allen family earns more than about 87% of families in their county.
Which of the following must be true about the Allen family's income?The other options do not necessarily have to be true. It is possible for the Read family to earn more than the Allen family, but if the $24,000 difference is given, then the Read family must earn less. It is also possible for both families to earn more than the median income, or for both to have incomes in the bottom half of incomes in their county, but this is not necessarily true based on the information given.(b) The answer is (O) The Allen family earns more than about 87% of families in their county.The first option, The Allen family earns less than about 87% of families in their county, cannot be determined based on the information given. The second option, The Allen family earns about 87% of the highest income in their county, is not necessarily true. The third option, The Allen family earns more than about 87% of families in their county, is the only one that is logically consistent with the information given in the problem. The fourth option, The Allen family earns about 13% of the highest income in their county, cannot be determined based on the information given.To learn more about income refer:
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Today, everything at a store is on sale. The store offers a 20% discount.
1. The regular price of a T-shirt is $16. What is the discount price?
2. Write an expression for the discount price of x dollars.
3. The discount price of a hat is $20. What is the regular price?
Answer:
1. $16-20%= 12.8 US$
2. $x-20%=x
3. >>>>>?
Step-by-step explanation:
A 20% discount means that you subtract 20% of the normal price. Suppose the normal price is $100. 20% of this is $20. Subtract this from $100 and you have the new price---$80.
Note that "subtracting 20%" is the same as multiplying by 0.8----the general formula is:
discount price = normal price * (1-d) , where d is the decimal equivalent of the percentage discount.
From the example above:
discount price = normal price * (1-d) = 100(0.8)
to go the other way, simply rearrange the formula:
normal price = discount price / (1-d)
C=/5(F−32)
The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 95 degree Celsius.
II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III. A temperature increase of 95 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius
a. I only
b. II only
c. III only
d. Iand II only
At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.
What is meant by Fahrenheit ?Fahrenheit is named for German scientist Daniel Gabriel Fahrenheit, who was born there in 1686 as part of the Polish-Lithuanian Commonwealth. He was the first to develop a constant, accurate method of measuring temperature. At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.
To assist us remember that we go from colder to hotter as we walk up the scale on our thermometer, let's label it. In other terms, a higher number of degrees Fahrenheit is hotter than a lower number.
[tex]$$\begin{aligned}& \text { Given:- } \mathrm{C}=\frac{5}{9}(\mathrm{~F}-32) \\& \Rightarrow \mathrm{F}=\frac{9}{5} \mathrm{C}+32\end{aligned}$$[/tex]
(I) If [tex]$F^{\prime}=F+1$[/tex]
[tex]$$\begin{aligned}\mathrm{C}^{\prime} & =\frac{5}{9}\left(\mathrm{~F}^{\prime}-32\right) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}+1-32) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}-32)+\frac{5}{9} \times 1 \\\mathrm{C}^{\prime} & =\mathrm{C}+\frac{5}{9}\end{aligned}$$[/tex]
Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of [tex]$\frac{5}{9}$[/tex] degree Celsius.
Therefore, statement I exists true.
(II) If [tex]$\mathrm{C}^{\prime}=\mathrm{C}+1$[/tex]
[tex]$$\begin{aligned}& \mathrm{F}^{\prime}=\frac{9}{5} \mathrm{C}^{\prime}+32 \\& \mathrm{~F}^{\prime}=\frac{9}{5}(\mathrm{C}+1)+32 \\& \mathrm{~F}^{\prime}=\left(\frac{9}{5} \mathrm{C}+32\right)+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+1.8\end{aligned}$$[/tex]
Therefore, a temperature increase of 1 degree Celsius exists equivalent to a temperature increase of 1.8 degrees Fahrenheit.
Therefore, statement II exists true.
[tex]$$\begin{aligned}& \text { (III) If } F^{\prime}=F+\frac{5}{9} \\& C^{\prime}=\frac{5}{9}\left(F^{\prime}-32\right) \\& C^{\prime}=\frac{5}{9}\left(F+\frac{5}{9}-32\right) \\& C^{\prime}=\frac{5}{9}(F-32)+\frac{5}{9} \times \frac{5}{9} \\& C^{\prime}=C+\frac{25}{81}\end{aligned}$$[/tex]
Therefore, a temperature increase of [tex]$\frac{5}{9}$[/tex] degree Fahrenheit exists equivalent to a temperature increase of [tex]$\frac{25}{81}$[/tex] degree Celsius.
Therefore, statement III exists false.
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describe fully the transformation
Answer: The transformation is a reflection over the line x=0. The original square OABC is reflected over the line x=0 and the only invariant point is (0,2).
Step-by-step explanation:
This transformation is a reflection over the line with equation y = 2. The original square OABC is reflected over this line, mapping point A to C and C to A, while the only invariant point is (0, 2).
INTEGRALS HELP PLEASE I’LL GIVE U A CROWN
Answer:
Step-by-step explanation:
The definite integral of the function (2x - 3) with respect to x can be found using the antiderivative, also known as indefinite integration.
The antiderivative of (2x - 3) is:
x^2 - 3x + C, where C is the constant of integration.
For the definite integral, we need to find the antiderivative over a given interval. To calculate the definite integral, we need to evaluate the antiderivative at the limits of the interval and subtract the values.
So, for example, if the interval is from a to b, the definite integral is given by:
∫_a^b (2x - 3) dx = (x^2 - 3x) |_a^b = (x^2 - 3x) evaluated at b - (x^2 - 3x) evaluated at a.
The definite integral of the function y³ (2y² – 3) with respect to y can be found in a similar way. The antiderivative of y³ (2y² – 3) can be found using power rule of integration.
The antiderivative of y³ (2y² – 3) is:
(1/4) y⁴ - 3y² + C, where C is the constant of integration.
The definite integral of the function can then be found by evaluating the antiderivative at the limits of the interval and subtracting the values, as described above.
Answers in image.
Step-by-step explanation:
To solve the questions, use the power rule to solve.
Translate the line segment with endpoints (0, 0) and (5, 4) up 3 units and left 2 units. What are the new endpoints? PLEASEEE HELPPPPPP I NEED IT
The translated points are P' ( -2 , 3 ) and Q' ( 3 , 7 )
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the points be represented as P and Q
Now , the coordinates of point P = P ( 0 , 0 )
And , the coordinates of the point Q = Q ( 5 , 4 )
when the points are translated up 3 units and left 2 units
The coordinates of the translated point will be ( x , y ) to ( x - 2 , y + 3 )
Substituting the values in the equation , we get
The coordinates of the translated point P' = P' ( -2 , 3 )
The coordinates of the translated point Q' = Q' ( 3 , 7 )
Hence , the translated points are P' ( -2 , 3 ) and Q' ( 3 , 7 )
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Alan sold t-shirts and hats at a festival. His total profit was $125. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. How many t-shirts did he sell?
Write an equation that could be used to answer the question above. First chose the appropriate form. Then fill in the blanks with the numbers 125, 5, 40. Let x represent the number of t-shirts.
A. _x + _ = _
B. _x - _ = _
Answer:
17
Step-by-step explanation:
First you have to subtract 125-50 since we are trying to find the amount he made from selling t-shirts. That equals 85. So now we divide 85 by 5 and that gives us 85.
Answer:
Step-by-step explanation:
a._x+_=_
5x+40=125
-40 -40
5x=85
/5
x=17
he sold 17 shirts
Please Help! I Have Limited Time! A student is measuring the length of an icicle, y, every hour, x. The icicle is currently 9 inches long and is melting at a rate of 0.6 inches per hour. Find and interpret the slope for this relationship.
A. 9; the length of the icicle when the student first measures it.
B. −9; the length of the icicle when the student first measures it.
C. 0.6; for every additional hour, the length of the icicle increases by 0.6 inches.
D. −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches.
Answer:
D
Step-by-step explanation:
The correct answer is D. −0.6; for every additional hour, the length of the icicle decreases by 0.6 inches.
The slope of a line represents the rate of change of one variable with respect to the other variable. In this case, the length of the icicle (y) is changing with respect to time (x). The slope of the line represents the change in the length of the icicle (y) for every additional hour (x).
Since the icicle is melting at a rate of 0.6 inches per hour, the length of the icicle decreases by 0.6 inches for every additional hour. The slope of the line representing this relationship is -0.6. This means that for every additional hour, the length of the icicle decreases by 0.6 inches.
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Before catching the bud for school, Steven , Andy , and Chad went to the fridge and grabbed a 25 ounce juice to split evenly between them. How much orange justice did each person get? Write your answer as a proper fraction or mixed number
Answer:
8 and 1/3
Step-by-step explanation:
First, let's understand the situation. There is a 25 oz juice that is to be split 3 ways. To determine the amount of jucie each person gets, we will take the total amount of juice and divide it by the number of kids, 3. When we do this, we get 25/3. Since this fraction can;t be simplified into a whole number, we will need to turn 25/3 into a mixed number. To do this, we need to know how many times 3 goes into 25. 3 goes into 25 8 times with a remainder of 1. This remainder is put over 3, giving us the final answer, 8 and 1/3.
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let u = (1, 0, 1) and v = (0, 2, 2). find a vector w that is orthogonal to both u and v. find a vector x which is orthogonal to u and lies in the same plane defined by u and v.
A vector w that is orthogonal to both u and v is w = (-1,-1,-1) and a vector x which is orthogonal to u and lies in the same plane defined by u and v is x = (-1,2,1).
The vectors are
u = (1, 0, 1)
v = (0, 2, 2)
If the scalar product of two vectors is equal to zero, then the vectors are orthogonal.
If we let let w = (a, b, c)
Then (u, w) ≥ 0
1×a + 0×b + 1×c = 0
a + c = 0
Subtract c on both side, we get
a = -c
and (v, w) = 0
0×a + 2×b + 2×c = 0
2b + 2c = 0
2(b + c) = 0
b + c = 0
b = -c
Then w = (-c, -c, -c)
If c=1
Then the orthogonal vector
w = (-1,-1,-1)
Let x = (x, y, z)
x is now orthogonal to u.
That is (u, x) = 0
1×x + 0×y + 1×z = 0
x + z = 0
x = -z
u × v = [tex]\begin{vmatrix}\hat{i} & \hat{j} & \hat{k}\\ 1 & 0 & 1\\ 0 & 2& 2\end{vmatrix}[/tex]
u × v = [tex]\hat{i}\begin{vmatrix} 0 & 1\\ 2& 2\end{vmatrix}-\hat{j}\begin{vmatrix} 1 & 1\\ 0& 2\end{vmatrix}+\hat{k}\begin{vmatrix} 1 & 0\\ 0& 2\end{vmatrix}[/tex]
u × v = [tex]\hat{i}[/tex](-2) - [tex]\hat{j}[/tex](2) + [tex]\hat{k}[/tex](2)
u × v = -2i-2j+2k
The given condition x lies on the plane u and v
(-2, -2, -2), x ≥ 0
-2x - 2y + 2z = 0
[x = -z]
2z - 2y + 2z = 0
-2y = -4z
y = 2z
That is x = (-z, 2z, z)
Now put z = 1
x = (-1,2,1)
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eucalyptus trees, common in california and the pacific northwest, grow better with more water. scientists in north africa, analyzing where to plant trees, found that the volume of wood that grows on a square kilometer, in meters cubed, is approximated by where is rainfall in centimeters per year, and . calculate the average rate of change of with respect to over the interval .
The average rate of change of V with respect to r over the interval [85,110] is 0.76 meters cubed per year per centimetre of rainfall.
V(r) = 0.2r² − 20r + 600
The average rate of change of V with respect to r over the interval [85,110] can be calculated by finding the derivative of V(r) and evaluating it at the midpoint of the interval, then dividing the result by the length of the interval. The derivative of V(r) is:
dV/dr = 0.4r - 20
The midpoint of the interval [85,110] is (85 + 110)/2 = 97.5. Evaluating the derivative at the midpoint, we get the following:
dV/dr = 0.4 × 97.5 - 20 = 19.0
The length of the interval is 110 - 85 = 25, so the average rate of change is:
The average rate of change = (dV/dr)/(110 - 85) = 19.0/25 = 0.76
So, the average rate of change of V with respect to r over the interval [85,110] is 0.76 meters cubed per year per centimetre of rainfall.
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--The given question is incomplete; the complete question is
"Eucalyptus trees, common in California and the Pacific Northwest, grow better with more water. Scientists in North Africa, analyzing where to plant trees, found that the volume of wood that grows on a square kilometre, in meters cubed, is approximated by V(r)=0.2r²−20r+600 where r is rainfall in centimetres per year, and 60≤ r ≤120. Calculate the average rate of change of V with respect to r over the interval [85,110]."--
There are 12 Year 13 pupils in a football club, out of a total of 35 pupils.
Write this proportion as a percentage.
Give your answer correct to 1 decimal place when appropriate.
Answer:
Step-by-step explanation:
The proportion of Year 13 pupils in the football club is 12/35. To convert this to a percentage, we need to multiply it by 100.
12/35 * 100 = 34.285714285714285 (approximately 34.3% when rounded to 1 decimal place)
Answer:
[tex] \frac{13}{35} \times \frac{100}{100} = 37.14\%[/tex]
This polygon is a regular hexagon. The sum of the measures of all the interior angles in this polygon is 720°.
What is m∠A?
Answer:
120
Step-by-step explanation:
720/6 =120
Based on the information in the model, which equation represents the Pythagorean theorem?
Answer:
i believe it is the last option.
Step-by-step explanation:
square units are units of area, so you'll want to find the SIDES and use those.
144 squared units would be 12 units per side.
25 would be 5, 169 would be 13.
pythagorean theorem is a^2 + b^2 = c^2, generally c is shown as the hypotenuse.
12^2 + 5^2 = 13^2 would be the last option given.
an automobile insurer has found that repair claims are normally distributed with a mean of $530 and a standard deviation of $490.
There is a 68% chance that a repair claim will be between $40 and $1020.
The normal distribution is a continuous probability distribution that is symmetric around the mean, with mean and variance being the same. In this case, the mean is $530 and the standard deviation is $490. This means that the repair claims are normally distributed, with the majority of the claims being between $530-$490 and $530+$490. This gives us a range of $40-$1020.
The normal distribution is often used to describe random variables because it is the most common probability distribution. In this case, it implies that the repair claims are randomly distributed around the mean of $530. The standard deviation of $490 indicates that there is a 68% chance that a repair claim will be within one standard deviation of the mean. In this case, that means that there is a 68% chance that a repair claim will be between $40 and $1020.
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Lena make a fruit drink by mixing orange juice, pineapple juice and parkling water in the ratio orange : pineapple : water = 3 : 2 : 7. (a) What fraction of the mix i water? [
The fraction of water is 7/12, when the ratio orange:pineapple:water=3:2 :7
A fraction represented with its quotient and remainder is a mixed fraction, and also one having a fraction and a whole number.
For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given that the ratio of orange: pineapple: water = 3: 2: 7.
consider orange=3x
pineapple=2x
water=7x
Total mix fraction=12x
To know the fraction value of water just divide the water by and total fraction.
fraction of water=7x/12x
fraction of water=7/12
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Ms. Wu runs a house cleaning business. To save money, she bought a 1-gallon container of concentrated cleaner. She mixed the cleaner with 10 gallons of water. Then, she filled as many 1-pint spray bottles as she could. How many spray bottles did she fill?
She had filled 88 spray pint bottles.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Ms. Wu runs a house cleaning business. To save money, she bought a 1 gallon container of concentrated cleaner. She mixed the cleaner with 10 gallons of water. Then, she filled as many 1 - pint spray bottles as she could.
1 pint = 0.125 gallons
Total amount = 11 gallons.
The total number of bottles that can be filled are -
n = 11/0.125
n = 88
Therefore, she had filled 88 spray pint bottles.
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Madeline went to the store to buy some cherries. The price per pound of the cherries is $6.50 per pound and she has a coupon for $1 off the final amount. With the coupon, how much would Madeline have to pay to buy 2 pounds of cherries? Also, write an expression for the cost to buy
p
p pounds of cherries, assuming at least one pound is purchased
The cost of 2 pounds of cherries without the coupon would be $6.50 x 2 = $13.
With the coupon, Madeline would have to pay $13 - $1 = $12 for 2 pounds of cherries.
The expression for the cost of buying x pounds of cherries with the coupon is:
(6.5*x) - 1
Δ
A
B
C
is a right triangle. Choose the equation that represents the sum of the angles in the triangle. What is the value of x, the missing angle?
Therefore , the solution of the given problem of triangle comes out to be x value of right triangle is 65° .
What exactly does a triangle mean?Due to their four sides or more, triangles are considered polygons. It has a straightforward, geometric form. A triangle is a square angle formed by the letters ABC. A singular rectangle or square is produced by Euclidean geometry when the sides are still not collinear. Triangles are polygons because they have three sides and three corners. Where three sides of a triangle come together are its corners. A triangle's angles sum up to 180 degrees.
Here,
Given :
triangle has an right angle so its 90 degree.
The triangle sum of angle is 180 degree.
Thus,
=> x + 25° + 90° = 180°
=> x + 115° = 180°
=> x = 180° -115°
=> x = 65°
Thus , x value is 65° .
Therefore , the solution of the given problem of triangle comes out to be
x value of right triangle is 65° .
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what is the probability that x is within 1 standard deviation from its mean value? hint: find the p(x-x ≤ x ≤ x x) (round your answer to four decimal places.)
The probability that x is within 1 standard deviation from its mean value is 0.68.
Probability is the measure of the likelihood of an event occurring. In statistics, it is used to describe the chance of a particular value falling within a certain range.
A standard deviation is a measure of the spread of a set of data from its mean.
Typically, 68% of the data falls within 1 standard deviation from the mean, 95% falls within 2 standard deviations, and 99.7% falls within 3 standard deviations.
In order to find the probability that x is within 1 standard deviation from its mean value, we need to use a normal distribution.
In a normal distribution, 68% of the data falls within 1 standard deviation from the mean.
So, in this case, the probability that x is within 1 standard deviation from its mean value is 0.68 or 68%.
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The function f(x) = x^5 + (x + 3)^2 is used to create this table. Which value completes the table?
If the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.
What is meant by function?The graph is a function if any vertical line drawn through it can cross it at most one point. The graph is not a function if it has any locations where a vertical line can pass through the graph at two or more different places.
A mathematical function from a set X to a set Y assigns exactly one element of Y to each element of X. The function's domain and codomain, respectively, are the sets X and Y as a whole. Initially, functions represented the desired relationship between two fluctuating values.
A function is a relation that specifically links members of one set to those of another set. Formally speaking, a function from to is an object such that each is specifically connected with an object. Therefore, a function is a many-to-one (or occasionally, a one-to-one) relation.
Let the given function be f(x) = x⁵ + (x + 3)²
When x = -1 then f(-1) = (-1)⁵ + (-1+3)² = -1 + 4 = 3.
Therefore, the function f(x) = x⁵ + (x + 3)² will be 3 then x = -1.
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