Answer:
It meant that the results were more reliable and the average makes it more reliable.
Step-by-step explanation:
The researchers used data from ten trials and averaged them, rather than data from a single trial because the data from single trials are more likely to include errors.
What is the research?Research the issue utilizing data from a number of sources. It is critical to understand what one is attempting to achieve while designing an experiment.
The first method is to average identical successive trials, in which the researcher simply compares mean values across groups of patients or treatment effects. Averaging, to some extent, presume that the behavior is random. This premise is often ignored. If there is something systematic going on, such as a trial-by-trial change in response owing to adaptation/learning or weariness, this is potentially highly significant clinical information that is lost when the trials are averaged.
Thus, the data from single trials are more likely to include errors
Hence, the researchers used data from ten trials and averaged them, rather than data from a single trial.
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what should be subtracted from the sum of ( 5/6 + -2/3 ) to get 3/4?
-7/12 should be subtracted from the sum of ( 5/6 + -2/3 ) to get 3/4.
Linear equations in one variable
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For example, 2x+3=8 is a linear equation having a single variable in it.
Let x should be subtracted from the sum of ( 5/6 + -2/3 ) to get 3/4
Therefore
[ 5/6 + (-2/3 ] - x = 3/4
⇒ ( 5/6 - 2/3) - x = 3/4
⇒ ( 5/6 - 4/6) - x = 3/4
⇒ 1/6 - x = 3/4
⇒ x = 1/6 - 3/4
⇒ x = 4/24 - 18/24
⇒ x = -14/24
⇒ x = -7/12
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Use inverse trigonometric functions to solve the following equations. If there is more than one solution, enter all solutions as a comma-separated list (like "1, 3"). If an equation has no solutions, enter "DNE".Solve 7tan(θ)=−15 for θ (where 0≤θ<2π).θ=
ANSWER:
[tex]\theta=-1.13416,2.00743[/tex]STEP-BY-STEP EXPLANATION:
We have the following function
[tex]\begin{gathered} 7\cdot\tan (\theta)=-15 \\ 0\leq\theta<2\pi \end{gathered}[/tex]Solving for θ:
[tex]\begin{gathered} 7\cdot\tan (\theta)=-15 \\ \tan (\theta)=-\frac{15}{7} \\ \tan (\theta)=-\frac{15}{7} \\ \theta=\arctan (-\frac{15}{7}) \\ \theta_1=-1.13416 \\ \theta_2=2.00743 \end{gathered}[/tex]9) Simplify and name the resulting expressions according to the number of terms:
(Monomial, Binomial, Trinomial, Polynomial)
a) 2a-5a²-7a+ 9-3a²+ 10+8a³-13 + 7a
The given polynomial expression is Trinomial and the expression is 8a³-8a² +2a + 6.
What is polynomial expression?
In mathematics, the polynomial expression based on the degree of the equation. It is classified as monomial or binomial depending upon the highest power of the variable in the quadratic equation.
According to the question, the given polynomial expression for the simplification is as follows:
Expression: 2a-5a²-7a+ 9-3a²+ 10+8a³-13 + 7a
Rearranging the terms to check the polynomial degree of the equation:
Expression: 8a³-3a² -5a² +2a - 7a + 7a + 9 + 10 -13
Expression: 8a³-8a² +2a + 6
Hence, the given polynomial expression is Trinomial and the expression is 8a³-8a² +2a + 6.
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( will mark brainliest )
∠A and ∠B are vertical angles with m∠A = x and m∠B = 4x − 24.
m∠A = ____ degrees
Answer:
8
Step-by-step explanation:
Vertical angles are congruent. That means that they have the same measurement. Set them equal to each other and solve for x
x = 4x - 24 Subtract x from both sides of the equation
o = 3x - 24 Add 24 to both sides
24 = 3x Divide both sides by 3
8 = x
m<A is 8
(a) find a combination of step functions that is equal to 4 when 2 ≤t ≤3 and equal to 0 otherwise. (b) write the following function in one line (i.e. without cases) using step functions: f(t)
(a) Recall the definition of the step function,
[tex]\theta(t) = \begin{cases} 1 & \text{if } t \ge 0 \\ 0 & \text{if } t < 0 \end{cases}[/tex]
Then we have
• [tex]\theta(t-2) = 1[/tex] if [tex]t-2\ge0[/tex], or [tex]t\ge2[/tex]
• [tex]\theta(t-3) = 1[/tex] if [tex]t-3\ge0[/tex], or [tex]t\ge3[/tex]
and we can combine these to get
[tex]\theta(t-2) - \theta(t-3) = \begin{cases} 1 & \text{if }2\le t < 3 \\ 0 & \text{if }t<2 \text{ or } t\ge3 \end{cases}[/tex]
then scale up by 4 to get the value we want over [2, 3].
[tex]f(t) = \boxed{4\bigg(\theta(t-2) - \theta(t-3)\bigg)}[/tex]
At least that's what I get using the aforementioned definition of "step function". I don't see a way to have both [tex]f(2)=4[/tex] and [tex]f(3)=4[/tex] with this definition...
(b) No function was given...
Last month, Ronald sold 52 packages of home-made brownies, earning a total profit of $195.00. He plans to make 125 brownie packages for a bake sale. If he sells all 125 brownie packages, how much profit can Ronald expect to earn?
If he sells all 125 brownie packages, Ronald can expect to earn a profit of $468.75
Ronald sold 52 packages of home-made brownies.
He earns a total profit of $195.00
Profit from 52 packages = 195
Profit from 1 brownie package = 195/52 = 3.75
If he sells all 125 brownie packages
Total profit he can expect = profit from one brownie x 125 brownie packages
= 3.75 x 125
= 468.75
Therefore, If he sells all 125 brownie packages, Ronald can expect to earn a profit of $468.75
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2 A store sells sugar for $5 per bag. If a bag
contains 1.5 lbs., how many pound of sugar can
you buy with $8.
F 2.0 lbs.
G 26.7 lbs.
H 0.9 lbs.
J 2.4 lbs.
Jacob has golf scores of 120,112,130,128, and 124. he wants to have a mean, or average, golf score of 118. what score does he need in his next golf game to achieve this mean score?
Jacob needs a score of 94 in his next game to get the average or mean to be 118.
In the descriptive statistics, the mean may be confused with the median, mode, or midway since any of these might be referred to as a "average" (more formally, a measure of central tendency).
Although for skewed distributions, the mean may not be the same as the median or the value that is most likely to occur, the arithmetic mean of a collection of observations is the sum of the values (mode).Sometimes a batch of numbers will contain outliers. Outliers are frequently erroneous data that is caused by artefacts. In this case, a shorter mean can be used. After deleting specific amounts of data from either the top or bottom end, often an equal amount at either end, the process entails calculating the arithmetic average of the remaining data. The amount of values that were deleted is expressed as a percentage of the total number of values.Total score = 120 + 112 + 130 + 128 + 124 = 614
Let he scores x in his last game.
Therefore mean = (614 + x ) ÷ 6 = 118
Solving we get : x = 94.
Hence he will need top score 94 in his next game to get an average of 118 in the golf game.
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Cost price = £360: Selling price = £144 Percentage loss?
the student council to break even?
#. Justin and his sister Jayme are candying apples for their class parties. Justin has candied 15 apples
and is finishing them at a rate of 4 apples per hour Jayme has 10 apples candied and is finishing them
at a rate of 5 apples per hour. Once the siblings get to the point where they have candied the same
amount of apples they will stop for the day. How long will that take? How many candied apples will
they have altogether?
Answer:
Step-by-step explanation:
5 hours, 70 apples all together
A square piece of tin of side length 20 cm has four squares of side length x cm removed from each corner. the sides are folded up to form a tray. the centre square forms the tray base a write an expression for the side length of the base of the tray. b write an expression for the area of the base of the tray. expand your answer. c find the area of the tray base if x = 3. d find the volume of the tray if x = 3
Analyzing the square and finding expressions for length, area, and volume.
A. Expression for length = (20-2x)cm
B. Expression for area = [tex](20-2x)^{2}[/tex]
C. Expression for the area of tray base if x=3 : 196 cm^2
D. Volume of the tray if x=3: 2744 cm^3
A square piece of a tin of side length 20 cm has four squares of side length x cm removed from each corner. the sides are folded up to form a tray.
Since the side of x has been removed from each corner, that means, 2x length has been removed from 20 cm.[tex](20-2*3)^{2} =(20-6)^{2} = 14^{2} = 196[/tex]
So, the length of the tray base will be ( 20 - 2x ) cm.
The area of the square is given by [tex](side)^{2}[/tex]
So, the area of the base of the tray = [tex](20-2x)^{2}[/tex]
Expanding the expression, [tex](a+b)^{2} =a^{2} + b^{2} + 2ab[/tex]
Now, [tex](20-2x)^{2} = 400 + 4x^{2} -80x[/tex]
Area of the tray base if x=3, Area (x=3) =[tex]400 + 4(3)^{2} -80*3 = 400 +36- 240 = 196 cm^{2}[/tex]
Now, Volume = [tex](side)^{3}[/tex]
Volume = [tex](20-2x)^{3}[/tex]
Volume (when x = 3) = [tex](20-2x)^{3}= (20-2*3)^{3}=(20-6)^{3} = 14^{3} =2744 cm^{3}[/tex]
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REALLY SIMPLE 7TH GRADE MATH, WILL GIVE A THANKS AND VOTE BRAINLIEST
A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for
every 30 miles.
a. What is the actual area of the park?
___ square miles
b. The map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. At what scale should the map be reproduced so that it fits on the brochure?
1 inch for every ___ miles
Answer:
a) 21,600 square miles
b) the map will be reduced to 50% of its original size. 1 in = 60 miles
Step-by-step explanation:
You have a 4-in by 6-in map of a park with a scale of 1 in : 30 miles, and you want to know the actual area of the park, the reproduction factor to fit the map in 6 square inches, and the new scale of the map at that size.
a) Park sizeThe 4-inch dimension of the map corresponds to an actual length of ...
(4 in)(30 mi)/(1 in) = 120 mi
Similarly, the 6-inch dimension represents ...
(6 in)(30 mi)/(1 in) = 180 mi
The area of the park is the product of its dimensions:
(120 mi)(180 mi) = 21,600 mi²
The area of the park is 21,600 square miles.
b) ReductionThe area of the current map is (4 in)(6 in) = 24 in². The ratio of the reduced area to this original area is the square of the reduction scale factor:
k² = (6 in²)/(24 in²) = 1/4
k = √(1/4) = 1/2
The map must be reproduced at 1/2 its original size.
At this scale, the scale of the map is ...
(1/2 in) : (30 mi) = (1 in) : (60 mi)
It will be 1 inch for every 60 miles.
<95141404393>
At a school party there are 40 cookies. The ratio of chocolate cookies to oatmeal cookies is shown in the tape diagram. Chocolate: 5 Oatmeal: 3How many oatmeal cookies were at the party? Oatmeal cookies
Given:
Total number of cookies = 40 cookies
Ratio of chocolate to oatmeal = 5:3
To find the number of oatmeal cookies, first sum up the ratio.
Total sum of ratio = 5 + 3 = 8
Number of oatmeal cookies will be:
[tex]\frac{ratio\text{ of oatmeal}}{\text{total ratio}}\text{ }\ast\text{ total number of cookies}[/tex][tex]\frac{3}{8\text{ }}\text{ }\ast\text{ 40 = 15}[/tex]Therefore, total number of oatmeal cookies = 15
A debra is stuck in trac driving her kids to the park, 18km away from her home . She can only drive at a speed of 20km how long will it take debra to reach the park
It would take 54 minutes for Debra to reach park which is 18 km away from the house at speed of 20km/h.
What is speed?Speed is the rate at which an object moves along a path in time, whereas velocity is the rate and direction of an object's movement. In other words, speed is a scalar value, whereas velocity is a vector.
For example, 50 km/hr (31 mph) describes the speed at which a car travels along a road, whereas 50 km/hr west describes the velocity at which it travels.
We have given the speed 20km/h
the distance to cover is 18km
The formula for time is
t = D/S
where,
t is time
D is distance
S is speed
Substituting the values we get
t = 0.9 hours
t = 54 minutes
Thus, it would take 54 minutes for Debra to reach park which is 18 km away from the house at speed of 20km/h.
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Mike had $36 dollars. He spent 1/3 of his money for a moive and 2/9 for a sandwich and drink. How many dollars did Mike spend for the sandwich and drink?Does he have enough money left to buy a book for $18?
We are given that Mike has $36, if he spends 1/3 of this amount, the amount spent is the product of 36 and 1/3, that is:
[tex]\begin{gathered} A_1=36\times\frac{1}{3} \\ A_1=12 \end{gathered}[/tex]Therefore, he spends $12 on the movie.
Now we are told that he spends 2/9 of the money, therefore, he spent:
[tex]\begin{gathered} A_2=36\times\frac{2}{9} \\ A_2=8 \end{gathered}[/tex]In total, he spent $8 on the sandwich.
The money he has left is:
[tex]36-12-8=16[/tex]Therefore, he can't buy an $18 dollars book.
Mariana receives a $20 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $1.29. If m represents the number of songs downloaded, which inequality represents the given situation?
20 m greater-than-or-equal-to 1.29
20 m less-than-or-equal-to 1.29
1.29 m less-than-or-equal-to 20
1.29 m greater-than-or-equal-to 20
y = 1/2x + 8y = cx + 10In the system of equations above, c is a constant. Ifthe system has no solution, what is the value of c?
y = 1/2x + 8
y = cx + 10
In the system of equations above, c is a constant. If
the system has no solution, what is the value of c?
so, y=y
[tex]\begin{gathered} \frac{x}{2}+8=cx+10 \\ solve\text{ for x} \\ \\ \frac{x}{2}-cx=10-8 \\ x(\frac{1}{2}-c)=2 \\ x(\frac{1}{2}-c)=2 \\ \end{gathered}[/tex]this equation is indefinde when 1/2 - c= 0, there is not value for x that makes the equation true
[tex]\begin{gathered} \frac{1}{2}-c=0 \\ \frac{1}{2}=c \end{gathered}[/tex]so, the value of c =0.5
Mary’s credit card company charges 16% interest on her outstanding credit card balance each month. Her minimum payment is $20 each month. Mary’s credit card bill is $70 in January.
Mary only pays the minimum amount each month, and she does not spend any additional money on her credit card. How long, in months, will it take her to pay off her bill from January?
It will take Mary 3.6 months (The period will occur in April.) from January to pay off her bill of $70 if she continues to pay $20 per month.
How is the period determined?The period Mary will take to pay off her credit card balance is determined using an online finance calculator.
The input data required includes the interest rate, the present value of the bill, and the periodic payments.
I/Y (Interest per year) = 16%
PV (Present Value) = $70
PMT (Periodic Payment) = $-20
FV (Future Value) = $0
Results:
N = 3.608
Sum of all periodic payments = $-72.16
Total Interest = $2.16
Thus, Mary requires 3.6 months to pay off her credit card balance, which will occur in period 4 from January.
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An electrician charges $50 for a service call plus $25 an hour. The last service call cost $125. If n= hours worked, write an equation to describe this situation.
Answer:
125=50+25n
Step-by-step explanation:
to figure how many hours worked you want to subtract 50 from both sides [tex]\frac{125}{-50}=\frac{50+25n}{-50}[/tex]you get 75=25nthen you want to divide 25 from both sides[tex]\frac{75}{/25} =\frac{25n}{/25}[/tex]then you get3=nCompare the slopes and y-intercepts for the equations in this system of equations. How many solutions does this system of equations have? 2 x + 6 y Ž +6 y = 3 A) One solution B) No solution Infinitely many solutions
Infinitely many solutions
1) Given the equations, y =2/3x +6 and 2/3x +6
y=2/3x +6
y= 2/3x +6
2) As we have the same equation, then there will be infinitely many solutions since each and every point of line I belongs to line (II)
3) Hence, the answer is Infinitely many solutions
Write 4 1 /9 as an improper fraction.
Answer: 37/9
Step-by-step explanation:
1. Multiply the whole number by the denominator
4 × 9 = 36
2. Add the product from Step 1 to the numerator
36 + 1 = 37
3. Write answer from Step 2 over the denominator
37/9
Answer:
[tex]\frac{37}{9}[/tex]
Step-by-step explanation:
Improper fractions are fractions in which the numerator is greater than the denominator. To convert a mixed number to an improper fraction you multiply the whole number by the denominator.
So once you do that you will have [tex]\frac{36}{9}[/tex].
However, this isn't complete just yet. You now need to add the numerator you had before, this can be written as [tex]\frac{36}{9} + \frac{1}{9}[/tex].
Now you just solve and you'll end up with [tex]\frac{37}{9}[/tex].
calcular el valor de la constante razon
6/12 32/10 225/150
The value of the ratio (6/12) is 0.5, of (32/10) is 3.2 and that of (225/150) is 1.5.
As per the question statement, we are provided with three ratios, (6/12), (32/10) and (225/15).
We are required to calculate the values of the above mentioned ratios.
To solve this question, we need to simplify the ratios, and then divide their numerators by their denominators, to obtain our desired answers.
Therefore, (6/12) = [6/(6 * 2)] = (1/2) = 0.5
Similarly, (32/10) = [(16 * 2)/(5 * 2)] = (16/5) = 3.2
And finally, (225/150) = [(75 * 3)/(75 * 2)] = (3/2) = 1.5
Ratio: In Mathematics, Ratio is a term that is used to compare two or more numbers, typically to indicate how big or small a quantity is when compared to another, and is either expressed in the form of(a : b), or as a fraction of (a/b) both of which are equivalent.
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10+5x= 2+5x+1
What is the answer for x??
In this equation, x will be 0.
Define equation.In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities. Based on the degree, there are three different sorts of equations. Equations that are linear, quadratic, and cubic. In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance. Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations.
Given data
10+5x= 2+5x+1
Solving for x,
10+5x= 2+5x+1
5x - 5x = 1+2 - 10
x = 0
In this equation, x will be 0.
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State if the two triangles are congruent. If they are, state the congruence property. If they are not congruent, you do not need to write in the property. 10.Congruent? ___________ If so, what property? ________11.Congruent? ___________ If so, what property? ________
Answer:
The image for number 10 is shown below as
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Which function Best represents the graph shown?
Y=4x+2
Y=2x+4
Y=2x-4
Y=4x-2
In the picture, there is a graph. The equation of the line y=2x+4. Option-B is correct.
Given that,
In the picture, there is a graph.
We have to find the equation of the line.
From the graph we can see there are points.
The point are (1,6) and (-2,0)
So,
The formula for equation of the line is y-y₁=m(x-x₁)
We have to find the m value
The slope of the line m=[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=(0-6)/(-2-1)
m=-6/-3
m=2
Now,
Take a point (-2,0)
y-0=2(x+2)
y=2x+4
Therefore, the option-B is correct, the equation of the line is y=2x+4.
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The next stop as Washington,D.C., which was 1.38 inches feather from Boston. What was the total mileage from boston to washington,D.C.?
The total mileage from Boston to washington,D.C is d + 1.38.
How to calculate the distance?Based on the information given, let the distance from Boston be illustrated as d
In this case, the next stop as Washington,D.C., which was 1.38 inches feather from Boston.
It should be noted that the expression can be illustrated as the addition of the mileage given. This will be:
= d + 1.38
Note that d illustrate the initial distance.
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Dog weighs 80 pounds a year ago now he weighs 92 pounds what is the percentage increase in weight
A year ago: 80 pounds
This year: 92 pounds
Yearly increase: 92 - 80 = 12 pounds
The percentage increase in weight will be taken with respect to 80 pounds. Then:
[tex]\frac{12\text{ lbs}}{80\text{ lbs}}\cdot100\text{\% }=15\text{\%}[/tex]Oscar wants to both spend and save the money he earns.
For every $7 he puts in his wallet, he puts $3 in savings
2. If Oscar puts $70` in his wallet, how much will he put
in savings?
If Oscar earns $70 in total, how much will he put in
savin
Step-by-step explanation:
answer is explained in my working. hope it helps
The amount of savings Oscar will save is $30.00
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Oscar wants to spend and save money he earns
For every $ 7 , The amount of money Oscar saves = $ 3
So ,
For every $ 70 , the amount of money Oscar saves =
For every $ 7 , The amount of money Oscar saves x 10
And ,
For every $ 70 , the amount of money Oscar saves = $ 3 x 10
= $ 30
Hence , for every $ 70 Oscar puts in his wallet he saves $ 30
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can someone please please solve 13y>9 or 2y-6>2 for me? please show work too!
The inequalities are solved below
What is an inequality?
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. The notation a b indicates that an is less than b, while a > b indicates that an is more than b, among other distinct notations used to denote various types of inequalities. The notation a b indicates that a and b are not equal; this inequality is occasionally referred to as a type of stringent inequality. It doesn't even specify that a and b must be members of an ordered set, nor does it state that one is superior to the other.
The inequalities are
13y>9
or, y>9/13
and
2y-6>2
or, 2y>2+6
or, y>8/2
or, y>4
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Is 631,992 divisible by 6?
Answer:yes
Step-by-step explanation:
105332
but you can't anymore after that
Answer:
yes it is divisible by 6.
