The number of teachers that work in both schools is 97.
What is an addition?The addition is a way of combining things and counting them together as one large group.
We have,
Number of teachers in Alberts Elementary school = 76
Number of teachers in Bothel Elementary school = 24
Number of teachers that work in both schools = 3
The number of teachers that work in both schools:
= 76 + 24 - 3
We are subtracting 3 from the total because 3 teachers that work in both schools have been added twice.
= 100 - 3
= 97
Thus the number of teachers that work in both schools is 97.
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Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body bone mineral content (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased by a research lab and two operators were trained to take the measurements. TBBMC for eight subjects was measured by both operators. The units are grams (g). A comparison of the means for the two operators provides a check on the training they received and allows us to determine if one of the operators is producing measurements that are consistently higher than the other. Here are the data:
Subject
Operator 1 2 3 4 5 6 7 8
1 1.326 1.337 1.079 1.229 0.936 1.009 1.179 1.289
2 1.323 1.322 1.073 1.233 0.934 1.019 1.184 1.304
Take the difference between the TBBMC recorded for Operator 1 and the TBBMC for Operator 2. (Operator 1 minus Operator 2. Round your answers to four decimal places.)
X-bar=
S=
Describe the distribution of these differences using words. (which one is correct)
A. The distribution is left skewed.
B. The sample is too small to make judgments about skewness or symmetry.
C. The distribution is uniform.
D. The distribution is uniform.
E. The distribution is Normal.
Answer:
(a)
\(\bar x = 0.0075\)
\(s = 0.0049\)
(b)
B. The sample is too small to make judgments about skewness or symmetry.
Step-by-step explanation:
Given:
\(n = 8\)
\(\begin{array}{ccccccccc}{} & {S} & {u} & {b} &{j} & {e} & {c} & {t} & {s} &{Operator} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {1} & 1.326 & 1.337 & 1.079 & 1.229 & 0.936 & 1.009 & 1.179 & 1.289 & 2 & 1.323 & 1.322 & 1.073 & 1.233 & 0.934 & 1.019 & 1.184 & 1.304 \ \end{array}\)
Solving (a):
First, calculate the difference between the recorded TBBMC for both operators:
\(\begin{array}{ccccccccc}{} & {S} & {u} & {b} &{j} & {e} & {c} & {t} & {s} &{Operator} & {1} & {2} & {3} & {4} & {5} & {6} & {7} & {8} & {1} & 1.326 & 1.337 & 1.079 & 1.229 & 0.936 & 1.009 & 1.179 & 1.289 & 2 & 1.323 & 1.322 & 1.073 & 1.233 & 0.934 & 1.019 & 1.184 & 1.304 &{|1 - 2|} &0.003 & 0.015 & 0.006 & 0.004 & 0.002 & 0.010 & 0.005 & 0.015 \ \end{array}\)
The last row which represents the difference between 1 and 2 is calculated using absolute values. So, no negative entry is recorded.
The mean is then calculated as:
\(\bar x = \frac{\sum x}{n}\)
\(\bar x = \frac{0.003 + 0.015 + 0.006 + 0.004 + 0.002 + 0.010 + 0.005 + 0.015}{8}\)
\(\bar x = \frac{0.06}{8}\)
\(\bar x = 0.0075\)
Next, calculate the standard deviation (s).
This is calculated using:
\(s = \sqrt{\frac{\sum (x - \bar x)^2}{n}}\)
So, we have
\(s = \sqrt\frac{(0.003 - 0.0075)^2 + (0.015 - 0.0075)^2+ (0.006- 0.0075)^2+ ....... + (0.005- 0.0075)^2+ (0.015- 0.0075)^2 }{8}\)\(s = \sqrt\frac{0.00019}{8}\)
\(s = \sqrt{0.00002375\)
\(s = 0.0049\)
Solving (b):
Of the given options (A - E), option B is correct because the sample is actually too small
Find the missing length indicated.
65
25
O 100
O 144
O 121
O 136
helpppp!!!!!!
By applying Pythagoras' Theorem, the missing length was found to be \(x = 144\).
What is the Pythagorean theorem's rule?The square directly on the hypotenuse is equal to the sum of the squares on the other two sides for all right-angled triangles, according to Pythagoras' theorem. The longest side, the hypotenuse, is always located on the other side of the right angle. This triangle has a right angle where a 2 Equals b 2 + c 2.
Is the Pythagorean theorem challenging?My year 9 pupils received instruction on Pythagoras' Theorem at my most recent placement. It was deceptively challenging for me. Why? The difficulty was twofold: First, the theory was somewhat familiar to the students because they had seen it in prior years.
Pythagoras' Theorem will be used to determine the elevation of the little rectangular prism on the RHS having angles of \(65\) and \(25\):
\(65^2 =25^2 + A^2\)
\(A =\)\(\sqrt{3600}\) \(=60\)
\(\sqrt{25}\) \(=60\)
\(5\sqrt{x} =60\) Divide both sides by \(5\)
\(x = 144\)
Another approach is to resolve:
\(Cos(25/65) = 65 /(x + 25)\)
Now you can solve for \(x\)
\(169 =x + 25\)
\(x =169 - 25 = 144\)
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you have the following test scores: 75, 82, 80, 70. if test carry a weight of 29% in the class, how many points will you have toward your overall grade? (round your final answer to the nearest hundredth)
You have the following test scores:
75, 82, 80, 70
The tests carry a weight of 29% in the class.
In order to determine how many point will you have toward your overall grade, based on tests points, you first calculate the average score of the obtained test scores, just as follow:
average test scores = (75 + 82 + 80 + 70)/4 = 307/4 = 76.75
Next, you calculate the 29% of the previous result:
0.29 x 76.75 = 22.257 ≈ 22.26
Hence, you will have 22.26 points due to test scores
Express the first quantity as percentage of the second of 45g and 75g
The first quantity (45g) as 60 percentage of second (75g).
What do you mean by Percentage?A part of whole expressed in Hundredth. Percentage is a fraction of a number out of 100%. It can be in fraction or in decimal.
To convert the given percentage value in decimal, divide the given value by 100.
For example:
1. 50% in decimal or fraction will be 50/100 = 0.5.
2. 20% in decimal or fraction will be 20/100 = 0.2.
How to calculate Percentage?1. Finding the total amount from which we need to find the percent.
2. Dividing the required amount to find the percentage by total amount.
3. Multiply it by 100.
For example:
1. It rained 10 of the 30 days in April.
Percentage will be 10/30 = (1/3) x 100
Percentage = 33.33%
Here, we have given that:
Total amount = 75g
Required amount for percent = 45g
Now, to find the percentage:
Percentage = 45/75
Percentage = 0.6 x 100
Percentage = 60%
Hence,
The first quantity (45g) as 60 percentage of second (75g).
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How long does it take for an investment of $6,400 to increase to $14,000 if
it is invested at 5% per year compounded continuously? Round to the
nearest tenth of a year.
An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈15.6
Define compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods.Given that :
P = $ 6,400
Q = $ 14,000
r = 5%
Let P be the initial investment
r be the rate of interest
t be the time
Q be the increase amount
Q = P \(e^{rt} }\)
14,000 = 6,400 (\(e^{0.05t}\))
\(e^{0.05t}\) = \(\frac{14000}{6400}\)
\(e^{0.05t}\) = 2.187
Taking log on both sides , we get
0.05t = ln (2.187)
0.05t = 0.78
t = \(\frac{0.78}{0.05}\)
t ≈ 15.6
An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈ 15.6
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A ball is thrown into the air. The function h(x) = -16x2 + 64x + 8 models the height, in feet above ground, of the ball after x seconds.
What was the height of the ball at the time it was thrown?
How many seconds after being thrown did the ball reach its maximum height?
Answer:
At the time the ball was thrown, it was 8 feet above the ground.
h'(x) = -32x + 64 = 0, so x = 2
The ball reaches its maximum height after 2 seconds.
Find the length of the rectangle whose area is 99 square inches and the width is 9 inches.
Answer:
the answer is 11
Step-by-step explanation:
??×9=99
9÷99=11
11×9=99
Answer: the answer is 11.
Step-by-step explanation:
because we know the width is 9, and the area is 99. but we don't know the length. so this is when you set up your equation: Lx9=99 (L= length) so the inverse operation of multiplication is division so divide 99 by 9 (99/9). and you get 11!
What’s the correct answer answer asap for brainlist
Answer: serbia
Step-by-step explanation:
How did you find the answer???
In a survey of 259 professional athletes, it was found that 110 of them owned a convertible, 91 of
them owned a giant screen TV, and 120 owned a sporting goods store. 15 owned a convertible and a
store, 43 owned a TV and a store, and 44 owned a covertible and a TV. 9 owned all three items.
1. How many athletes did not own any of the three items?
2. How many owned a covertible and a TV, but not a store?
3. How many athletes owned a convertible or a TV?
4. How many athletes owned exactly one type of item in the survey?
5. How many athletes owned at least one type of item in the survey?
6. How many owned a TV or a store, but not a convertible?
1. Number of athletes did not own any of the three items = 259 - 228
= 31.
2. Number of athletes own a convertible and a TV but not a store = 44 - 9
= 35.
3. Number of athletes own a convertible or a TV = 110 + 91 - 44
= 157.
4. Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
5. Number of athletes owned at least one type of item = 259 - 31
= 228
6. Number of athletes own a TV or a store, but not a convertible = 13 + 34 +71
= 118.
The number of athletes did not own any of the three items need to subtract the number of athletes who own at least one item from the total number of athletes surveyed.
Total number of athletes surveyed = 259
Number of athletes own at least one item = 110 + 91 + 120 - 15 - 43 - 44 + 9 = 228
Number of athletes who did not own any of the three items = 259 - 228 = 31.
The number of athletes who owned a convertible and a TV but not a store need to subtract the number of athletes who own all three items from the number of athletes who own a convertible and a TV.
Number of athletes who own a convertible and a TV = 44
Number of athletes who own all three items = 9
Number of athletes who own a convertible and a TV but not a store = 44 - 9 = 35
The number of athletes who owned a convertible, or a TV need to add the number of athletes who own a convertible to the number of athletes who own a TV and then subtract the number of athletes own both a convertible and a TV.
Number of athletes who own a convertible or a TV = 110 + 91 - 44
= 157.
The number of athletes owned exactly one type of item need to add up the number of athletes who own a convertible only the number of athletes own a TV only and the number of athletes who own a store only.
Number of athletes own a convertible only = 110 - 15 - 9 = 86
Number of athletes own a TV only = 91 - 44 - 9 = 38
Number of athletes own a store only = 120 - 15 - 43 - 9 = 53
Number of athletes owned exactly one type of item = 60 + 13 + 71 = 144.
The number of athletes who owned at least one type of item can use the result from part (1).
Number of athletes who owned at least one type of item = 259 - 31
= 228
The number of athletes who owned a TV or a store but not a convertible need to subtract the number of athletes who own all three items, and the number of athletes own a convertible and a TV from the number of athletes own a TV or a store.
Number of athletes own a TV or a store = 91 + 120 - 43 - 9 = 159
Number of athletes own a TV or a store not a convertible = 13 + 34 +71
= 118.
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Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
A 30-foot tree casts a 12-foot shadow as shown inthe picture.30 ftx12Find the angle of elevation to the nearest tenth.12.850°68.2°90°
Since the triangle has a right angle, we can conclude that the diagram is of a right triangle.
When dealing with right triangles, there are some useful formulas that are known as 'Trigonometric Identities'. There are a lot of them but we will need only one of those to solve the problem, that's the equation below:
\(\tan (\theta)=\frac{O}{A}\)Where θ is the angle, O is the length of the opposite side to the angle, and A the adjacent side to the angle.
Therefore, in the case of our problem,
\(\begin{gathered} \theta=x,O=30ft,A=12ft \\ \Rightarrow\tan (x)=\frac{30}{12}=2.5 \end{gathered}\)Solving for x, we get
\(x=\tan ^{-1}(2.5)=1.1902\text{rad}\)And we can transform radians into degrees,
\(\Rightarrow x\approx68.2\)Thus, the answer is the third option. 68.2°
what is the value of x?
Answer:
46
ayo how r u doin siahsvsgshsgsgsgsg
You leave your house and run 6 miles due west followed by 3.5 miles due north. At that time, what is your bearing from your house?
N 60° W
Explanation
Step 1
draw the situation
we have a right triangle, so we can use a trigonometric function to find the missing angle,
then
Let
\(\begin{gathered} \text{opposite side= 3.5 m} \\ \text{adjacent side=6 mi} \end{gathered}\)so, we need a function that relates those values
\(\tan \alpha=\frac{opposite\text{ side}}{\text{adjacent side}}\)replace
\(\begin{gathered} \tan x=\frac{3.5}{6} \\ \text{ Inverse tan in both sides} \\ \tan ^{-1}(\tan x)=\tan ^{-1}(\frac{3.5}{6}) \\ x=30.25 \\ \text{rounded } \\ x=30\text{ \degree} \end{gathered}\)so, the direction is
N 60° W
Classify the polynomial 5x3 + 4x − 2 by degree.
A. cubic
B. constant
C. quartic
D. linear
Classifying the polynomial 5x³ + 4x − 2 by degree gives a degree of
A. cubicHow to determine the degree of the polynomialAn equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.
Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.
The degree refers to the highest exponents which is a positive integer
examining the function the degree is 3 and referred to as cubic
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6. Evaluate f(-1).
7. What value of a will make the equation f(a) = 6 true?
someone please help lol I have a test <3
Answer:
6. -f 7. f= 6/8
Step-by-step explanation:
Hope dis helps!!
1.
(03.03 MC)
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent? (4 points)
Answer:
sept one
Step-by-step explanation:
Find the value of x that satisfy the equation
-3x + 4 = -17
Answer:
x=7
Step-by-step explanation:
-3x+4=-17
subtract 4 on both sides
-3x=-21
now u have to divide-3 on both sides
x=7
Can somebody please help me with this?
Найдите подходящее число, на которое можно разделить обе части уравнения и найти решение уравнения
3x = 12 | :
x =
5x = –10 | :
x =
–7x = 21 | :
x =
0,1x = 2 | :
x =
0,01x = –4 | :
x =
Answer:
Смотрите в объяснении.
Step-by-step explanation:
x=4
x=-2
x=-3
x=20
x=-400
Надеюсь, это помогло! :)
An angle whose measure is -102° is in standard position. Which quadrant does the terminal side of the angle fall?
Quadrant 1
Quadrant 2
Cuadrant 3
Cuadrant 4
Answer:3
Step-by-step explanation:
edg
emiah The length of a ruler is 12 inches. There are approximately 25.4 millimeters in 1 inch. Which measurement is closest to the length of the ruler in millimeters? A 3,048 mm B 30.48 mm C304.8 mm D 3.048 mm
Answer:
C 304.8
Step-by-step explanation:
Answer:
C 304.8 mm
Step-by-step explanation:
12*25.4 = 304.8
what is the solution to the equation:
5(n - 1/10) = 1/2
a. n= 13/5
b. n= 3/25
c. n= 0
d. n= 1/5
\( \sf \longrightarrow \: 5 \bigg( \: n - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{n}{1} - \frac{1}{10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10 \times n - 1 \times 1}{1 \times 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: 5 \bigg( \: \frac{10n - 1}{ 10} \bigg) = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: \frac{50n - 5}{ 10} = \frac{1}{2} \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =1(10) \\ \)
\( \sf \longrightarrow \: \: 2(50n - 5) =10 \\ \)
\( \sf \longrightarrow \: \: 100n - 10=10 \\ \)
\( \sf \longrightarrow \: \: 100n =10 + 10\\ \)
\( \sf \longrightarrow \: \: 100n =20\\ \)
\( \sf \longrightarrow \: \:n = \frac{2 \cancel{0}}{10 \cancel{0}} \\ \)
\( \sf \longrightarrow \: \:n = \frac{1}{5} \\ \)
Answer:-
Answer:- D) n = ⅕ ✅To solve the equation \(\sf 5(n - \frac{1}{10}) = \frac{1}{2} \\\) for \(\sf n \\\), we can follow these steps:
Step 1: Distribute the 5 on the left side:
\(\sf 5n - \frac{1}{2} = \frac{1}{2} \\\)
Step 2: Add \(\sf \frac{1}{2} \\\) to both sides of the equation:
\(\sf 5n = \frac{1}{2} + \frac{1}{2} \\\)
\(\sf 5n = 1 \\\)
Step 3: Divide both sides of the equation by 5 to isolate \(\sf n \\\):
\(\sf \frac{5n}{5} = \frac{1}{5} \\\)
\(\sf n = \frac{1}{5} \\\)
Therefore, the solution to the equation \(\sf 5(n - \frac{1}{10})\ = \frac{1}{2} \\\) is \(\sf n = \frac{1}{5} \\\), which corresponds to option (d).
\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)
♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)
The initial directions are in the pic below. I’m sending 2 pics now. And the other 2 soon. For a total of 4.
Recall that the rule of transformation of a point reflected over the y-axis is as follows:
\((x,y)\rightarrow(-x,y).\)Therefore, the transformed coordinates of the vertices of the triangle are:
\(\begin{gathered} N(4,6)\rightarrow N^{\prime}(-4,6), \\ P(1,6)\rightarrow P^{\prime}(-1,6), \\ Q(3,4)\rightarrow Q^{\prime}(-3,4)\text{.} \end{gathered}\)Therefore, the image of the triangle is the triangle with the above vertices.
Answer:
Based on the relative frequency histogram below , which of the following statements is supported by the plot? i. The IQR of the distribution is roughly 10
ii. There are no outliers in the distribution.
iii. It is not possible to estimate the median without knowing the sample size. iv. The distribution is multimodal v. The mean of the distribution is smaller than its median.
The statement supported by the plot is that the IQR of the distribution is roughly 10. It is possible to estimate the median from the plot, and the distribution appears to be unimodal, with the mean being smaller than the median. There are no outliers shown in the plot.
The relative frequency histogram provides a visual representation of the distribution of the data. From the plot, it is possible to estimate the median, which is the middle value of the distribution, as well as the interquartile range (IQR), which is the difference between the upper and lower quartiles. The IQR of the distribution is roughly 10, which can be seen by the distance between the upper and lower quartiles in the plot. Additionally, the distribution appears to be unimodal, which means that it has only one mode or peak. It is also apparent that the mean of the distribution is smaller than its median, as the peak is shifted to the left of the median. Finally, there are no outliers shown in the plot, as all of the values appear to be within the range of the distribution.
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Help please look at the picture
\(\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=8\\ r=12 \end{cases}\implies V=\cfrac{\pi (12)^2 (8)}{3} \\\\\\ V=384\pi \implies \stackrel{using~\pi =3.14 }{V=1206}~cm^3\)
Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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Using a calculator, find the decimal equivalent for the fraction 416888.
Answer:
0.46846846846
Step-by-step explanation:
if fraction was 416/888 thats the answer....
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Compare negative one and six tenths repeating and negative five thirds using symbols <, >, or =. negative one and six tenths repeating is less than negative five thirds negative one and six tenths repeating is greater than negative five thirds negative five thirds is equal to negative one and six tenths repeating negative five thirds is greater than negative one and six tenths repeating
Answer:
-1 6/10
is greater than
- 5/3
Step-by-step explanation:
Please help me solve these :)
I will give Brainlst:)
Answer:3 is nonlinear ,1 is function ,domain is the input and the range is the output, mx is the slope and the b is the y intercept
Step-by-step explanation: