Answer:
6
Step-by-step explanation:
because its the middle number
Using a number line place a point at 4 and the opposite of 4. Place a point at-2 and the opposite of -2. Place a point at 0.
Use a piece of paper showing your work
The graph of the number line showing the points 4,-4,2,-2, and 0 is attached with the answer.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
Given that the points are a point at 4 and the opposite of 4. Place a point at -2 and the opposite of -2.
The numbers are placed on the number line and the graph is attached with the answer below.
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4. In one semester, Doug and Laura spent a combined 230 hours in the tutoring lab. If Doug
spent 10 hours less than twice the hours Laura did, how many hours did Doug spend in
the lab?
Answer:
80 hours
Step-by-step explanation:
let d represent doug, let l represent laura
first, set up a system of equations representing the problem:
since doug spent 10 less than twice the hours laura did, and we know that the total amount of hours they spent together is 230:
l=2d+10
d+l=230
then solve:
*first i rearranged the equations so i can solve this system of equations using elimination method*
l-2d=10
l+d=230
*subtract*
3d=240
d=80
so, doug spent 80 hours in the lab
Find the length or area. I need help with 11 pls
Given the formula of a portion of the circle
\(A=\pi *r^2*\frac{\theta}{360}\)We are given that
\(A=20\pi ft^2\)\(\theta=72\)thus
\(20\pi=\pi *r^2*\frac{72}{360}\)Solving for r
\(20=r^2*\frac{1}{5}\)\(r^2=5*20\)\(r=\sqrt{100}\)\(r=10\)then the radius of the circle is 10ft
Find the missing angles.
with solution
Hello!
y = 88° (opposite are equal)
z = 180° - 128° = 52° (straight angle = 180°)
x = 180° - 140° = 40° (straight angle = 180°)
Answer:
x=40°
y=88°
z=52°
Step-by-step explanation:
Solution Given:
x+140°=180°
Since the sum of the angle of a linear pair or straight line is 180°.
solving for x.
x=180°-140°
x=40°
\(\hrulefill\)
y°=88°
Since the vertically opposite angle is equal.
therefore, y=88°
\(\hrulefill\)
z+128°=180°
Since the sum of the angle of a linear pair or straight line is 180°.
solving for z.
z=180°-128°
z=52°
G(x) = 3x 2 - 2x - 1
G(6) =
Find the course and ground speed for the following: Track 090°, airspeed 300km/h; wind 060°, 50km/h.
The course of the airplane relative to true north is 094°, and the ground speed is 344.2 km/h.
What is the ground speed of the plane?The horizontal and vertical component of the airspeed is calculated as follows;
Vx = 300 cos(30) = 259.8 km/h
Vy = 300 x sin(30) = 150 km/h
The horizontal and vertical component of the wind velocity is calculated as follows;
Vx = 50 cos(60) = 25 km/h
Vy = 50 sin(60) = 43.3 km/h
To find the resultant velocity, we can add the x and y components separately:
Vx = 259.8 km/h + 25 km/h = 284.8 km/h
Vy = 150 km/h + 43.3 km/h = 193.3 km/h
The magnitude of the resultant velocity is calculated as;
V = √(284.8² + 193.3²)
V = 344.2 km/h
The direction of the resultant velocity is calculated as;
θ = arc tan (193.3/284.8)
θ = 34.2⁰
The resultant direction to true north is calculated as;
track = 34.2 + 60 = 94.2°
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Solve the question below please
Answer:
b
Step-by-step explanation:
Kay loves to save coins. She has a piggy bank that she has been filling for a long time with only dimes and nickels. Recently, her piggy bank was filled to the brim so Kay counted her coins and she discovered that she had $10. She also noticed that she has 11 less dimes than nickels. How many coins were in Kay's bank?
The total number of coins that were in Kay's bank are 137 coins.
How to determine the number of coins?In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let d represent the number of dimes.Let n represent number of nickels.Since she has 11 less dimes than nickels, an equation which models this situation is given by;
n = d + 11 ....equation 1.
Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.
Additionally, the coins are worth 10 dollars;
0.1d + 0.05n = 10 ....equation 2.
By solving both equations simultaneously, we have:
0.1d + 0.05(d + 11) = 10
0.1d + 0.05d + 0.55 = 10
0.15d = 9.45
d = 63 dimes.
For nickels, we have:
n = d + 11
n = 63 + 11
n = 74
Now, we can determine the total number of coins;
Total number of coins = n + d
Total number of coins = 74 + 63
Total number of coins = 137 coins.
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When Alexander moved into a new house, he planted two trees in his backyard. At
the time of planting, Tree A was 36 inches tall and Tree B was 21 inches tall. Each
year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per
year. Let A represent the height of Tree At years after being planted and let B
represent the height of Tree Bt years after being planted. Write an equation for each
situation, in terms of t, and determine which tree is taller after 3 years.
Answer:
The equations for each situation are
A = 36 + 6t
B = 21 + 9t
After 3 years, Tree A is taller.
Step-by-step explanation:
From the question,
Tree A was 36 inches tall and Tree B was 21 inches tall at the time of planting; and
Tree A grew by 6 inches per year and Tree B grew by 9 inches per year after planting.
For Tree A,
Given a period of t years after planting, the height would have increased by 6t
∴ A = 36 + 6t
For Tree B,
Given a period of t years after planting, the height would have increased by 9t
∴ B = 21 + 9t
To determine, which tree is taller after 3 years,
t = 3
For Tree A
A = 36 + 6t
A = 36 + 6(3)
A = 36 + 18
A = 54 inches
For Tree B
B = 21 + 9t
B = 21 + 9(3)
B = 21 + 27
B = 48 inches
Hence, After 3 years, Tree A is taller.
according to government data, 22 percent of children in the united states under the age of 6 years live in households with incomes that are classified at a particular income level. a simple random sample of 300 children in the united states under the age of 6 years was selected for a study of learning in early childhood. if the government data are correct, which of the following best approximates the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level? (note: z represents a standard normal random variable.)
The probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level is approximately 0.04.
What is the binomial distribution?
In a binomial distribution, the probability of getting success must remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is ½ or 0.5 for every trial we conduct, since there are only two possible outcomes.
To approximate the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level, we can use a normal approximation to the binomial distribution.
The sample size is n = 300 and the proportion in the population is p = 0.22. The standard deviation of the sample proportion is:
\(\sigma_{p}\) = √(p(1-p)/n) = √(0.22(1-0.22)/300) = 0.0115
We can use the standard normal distribution to approximate the probability that the sample proportion is at least 0.27:
\(P(p_{hat} > = 0.27) \approx P( (p_{hat} - p) / \sigma_{p} > = (0.27 - 0.22) / 0.0115 )\)
P(z >= 1.74)
where z is the standard normal variable.
We can use a standard normal table or calculator to find the probability for z >= 1.74 is about 0.04.
Hence, the probability that at least 27 percent of the children in the sample live in households that are classified at the particular income level is approximately 0.04.
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Complete the table. Answer should be T or F.
P Q
T F P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
F T P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
P Q P V Q P ^ Q P -> Q -P -Q -P V -Q -P -> Q -P -> -Q P <-> Q
T T T T T F F F F F T T
F T T F F T T T T T F F
P F T F F T T T T T F F
-P T T F F T T T T T F F
-Q T T T T F T F F F T T
-P V -Q T T F F T T T T T F
-P -> Q T T F F T T T T T F
-P -> -Q T T F F T T T T T F
P <-> Q T T T T F T T T T F
Here is a more detailed explanation of how I filled out the table:
P | Q : This column is simply the truth value of P and Q. If P and Q are both true, then the entry in this column is T. If P is true and Q is false, then the entry in this column is F. If P is false and Q is true, then the entry in this column is F. And if P and Q are both false, then the entry in this column is T.
P V Q : This column is the truth value of P or Q. If P is true, then the entry in this column is T. If Q is true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.
P ^ Q : This column is the truth value of P and Q. If P and Q are both true, then the entry in this column is T. And if P and Q are both false, then the entry in this column is F.
P -> Q : This column is the truth value of P implies Q. If P is true and Q is false, then the entry in this column is F. And if P is false or Q is true, then the entry in this column is T.
-P : This column is the negation of P. If P is true, then the entry in this column is F. And if P is false, then the entry in this column is T.
-Q : This column is the negation of Q. If Q is true, then the entry in this column is F. And if Q is false, then the entry in this column is T.
-P V -Q : This column is the truth value of not P or not Q. If P and Q are both true, then the entry in this column is F. If P and Q are both false, then the entry in this column is T. And if P or Q is true, then the entry in this column is T.
-P -> Q : This column is the truth value of not P implies Q. If P is true and Q is false, then the entry in this column is T. And if P is false or Q is true, then the entry in this column is F.
-P -> -Q : This column is the truth value of not P implies not Q. If P and Q are both true, then the entry in this column is T. If P is false or Q is false, then the entry in this column is T. And if P is true and Q is true, then the entry in this column is F.
P <-> Q : This column is the truth value of P if and only if Q. If P and Q are both true or P and Q are both false, then the entry in this column is T. And if P and Q have different truth values, then the entry in this column is F.
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Which of the following matches the graph of f (x) = 2(x – 1)2(x + 1)(x + 2)?
Answer: C. The third graph.
Step-by-step explanation:
A function assigns the values. The graph of the function f(x) = 2(x – 1)2(x + 1)(x + 2) can be drawn as shown below.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
A function assigns the values. The graph of the function f(x) = 2(x – 1)2(x + 1)(x + 2) can be drawn as shown below.
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What is the area of the rectangle, in square centimeters?
5 cm
12 cm
O 17
O 34
O 30
O 60
Answer: D
Step-by-step explanation:
The store clerk created a display of R rows of cereal boxes. Each row contained 16 boxes. Choose the expression that shows the total number of cereal boxes on display.
Answer:
16R = T or T = 16R
Step-by-step explanation:
R represents the unknown amount of rows and we know there are 16 boxes in each row.
This means to find the total number of boxes on display, you will have to times the number of rows by 16 as the clerk puts 16 boxes of cereal in each row
e.g, if there are 3 rows, then to find the total amount of cereal boxes, you would do 3 × 16 = 48
Since it's an expression, you need something to represent the total number so that can be represented by any letter ( I chose T ) — in most cases you can probably represent the total as x
Hence the expression should be 16R = T or T = 16R
...at least I think so
What is the mean of the data set below?12, 11, 14, 14, 14, 12, 7
Circle A has been transformed to Circle B.
What is the scale factor of Circle A to Circle B?
Scale Factor
=
Image Radius
Pre- Image Radius
Answer: 21
Step-by-step explanation: im not guessing im a certified expert at calculus and have a masters degree in mathmatics so yeah
Answer:
21
Step-by-step explanation:
I did the test
Hope this helps :)
The area of a rectangle is 3x2 - 12x square yards. If the width is 3x yards, what is the length of the rectangle?
Answer:
x - 4 yards.
Step-by-step explanation:
Given:
Area of rectangle = 3x^2 - 12x square yards
Width = 3x yards
To find:
Length of rectangle
Solution:
The area of a rectangle is equal to the product of its length and width.
Area of rectangle = Length * Width
Substituting the given values, we get:
3x^2 - 12x = Length * 3x
Length =( 3x^2 - 12x )3x
Length = x-4
Therefore, the length of the rectangle is x - 4 yards.
Answer: The length of the rectangle is x - 4 yards.
Step-by-step explanation:
We can create an equation to solve this word problem, where the variable L = length.
3x × L = \(3x^2 - 12x\)
We need to solve for the variable L, to find the length of the rectangle.
First lets factor the right side of the equation to make it easier to divide with.
3x × L = \(3x^2 - 12x\)
We can factor out 3x from the right side of the equation.
3x × L = 3x(x - 4)
Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.
3x × L = 3x(x - 4)
/3x /3x
L = x - 4
The length of the rectangle is x - 4 yards.
Which graph represents the following piecewise defined function?
The graph that represents the given piecewise function has a range of
R: (-∞, 0) ∪ (0,2] ∪ (4, ∞).
What is a piecewise function?A piecewise function is a combination of subfunctions that are defined with different intervals in the domain.
The range of the piecewise function is the union of all the ranges of the subfunctions.
Calculation:The given piecewise function is
g(x) = x², x < 0
= 1/2 x, 0 < x ≤ 4
= x, x > 4
The domain and range for the subfunctions in the given piecewise function are:
for g(x) = x²; Domain is {x < 0} and Range is (-∞, 0)
for g(x) = 1/2 x; Domain is {0 < x ≤ 4} and Range is (0, 2]
for g(x) = x; Domain is {x > 4} and Range is (4, ∞)
Then, the range of the given piecewise function is
Range: (-∞, 0) ∪ (0, 2] ∪ (4, ∞)
Thus, the graph shown in the question is the correct one.
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Answer: c, its da 3rd graph
Step-by-step explanation:
10. Two cards are drawn from a deck with replacement. What is the probability of drawing
a spade and then drawing an ace?
Answer:
The question is with replacement, so the probability of drawing an ace would be 4/52 and the probability of drawing a spade would be 13/52. What am I missing? You found the probability that the first card is an ace and the second card is a spade, but there are other ways to draw an ace and a spade.
Step-by-step explanation:
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
The equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p
How to determine the equations that have the same solution?Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.
Using this given property, let's write the equation
We can subtract like terms (6.5p– 0.01p = 6.49p) to get:
2.3p – 10.1 = 6.5p – 0.01p – 4
2.3p – 10.1 = 6.49p – 4
Also, we can multiply both sides of the algebraic equation by 100:
(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100
230p – 1010 = 650p – 400 – p
Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers
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On the planet of Mercury, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.4 hours and the amount of time spent alone is normally distributed. We randomly survey one Mercurian 4-year-old living in a rural area. We are interested in the amount of time X the child spends alone per day. (Source: San Jose Mercury News) Round all answers to 4 decimal places where possible.
Required:
a. What is the distribution of X?
b. Find the probability that the child spends less than 1.4 hours per day unsupervised.
c. What percent of the children spend over 3.5 hours per day unsupervised.
Answer:
a
The distribution of X is normal
b
\(P(X < 1.4) = 0.12654\)
c
\(P(X > 3.5) = 0.36051\)
Step-by-step explanation:
From the question we are told that
The population mean is \(\mu = 3 \ hours\)
The standard deviation is \(\sigma = 1.4 \ hours\)
Generally given from the question that the amount of time spent alone by the population size is normally distributed then then the distribution of X (i.e the amount of time spent by the sample size (the one Mercurian)) will be normally distributed
Generally the probability that the child spend less than one hour in a day is mathematically represented as
\(P(X < 1.4) = P(\frac{X - \mu}{\sigma} < \frac{1.4 - \mu}{\sigma} )\)
Here \(\frac{X - \mu}{\sigma } = Z (The\ standardized\ value\ of\ X)\)
So
\(P(X < 1.4) = P(Z < \frac{1.4 - 3.0}{1.4} )\)
\(P(X < 1.4) = P(Z < -1.1429 )\)
From the z-table the value of
\(P(Z < -1.1429 )=0.12654\)
So \(P(X < 1.4) = 0.12654\)
Generally the percentage of children that spends over 3.5 hours unsupervised is mathematically represented as
\(P(X > 3.5) = P(\frac{X - \mu}{\sigma} > \frac{3.5 - \mu}{\sigma} )\)
\(P(X > 3.5) = P(Z > \frac{3.5 - 3.0}{1.4} )\)
\(P(X > 3.5) = P(Z > 0.3571 )\)
From the z-table the value of
\(P(Z >0.3571 )=0.36051\)
So \(P(X > 3.5) = 0.36051\)
Find the solution to the system. Write your solution as an ordered pair (x,y)
with no spaces, no solution, or infinitely many. x-3y=7 and 3x-9y=21*
Answer:
Infinitely many
Step-by-step explanation:
If we multiply the equation x-3y=7 by 3, we get 3x-9y=21, which is also the second equation. That means the two lines are on top of each other, meaning infinite many solutions.
A survey of 400 students yielded the following information: 262 were seniors, 215 were commuters, and 150 of the seniors were commuters. How many of the 400 surveyed students were seniors or were commuters?
Out of the 400 surveyed students, 327 were either seniors or commuters.
To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.
According to the information given:
There were 262 seniors.
There were 215 commuters.
150 of the seniors were also commuters.
To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.
Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters
= 262 + 215 - 150
= 327
Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.
It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.
This ensures an accurate count of the students who fall into either category.
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Please help! Will give brainliest
\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)
we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.
Raj was friends with his waitress so he left her a 90 percent tip.
Percents
90%
10% 10%
Total
100%
10%
10%
10%
10%
10%
10%
10%
10%
10%
х
If his tip was $27.54, what is the value of x in the table above?
$24.48
$24.79
$27.54
$30.60
Mark this and retum
Save and Exit
Next
Submit
Answer:
The bill was 30.60 before tip
Step-by-step explanation:
x * 90 % = 27.54
Change to decimal form
x * .90 = 27.54
Divide each side by .90
x = 27.54 /.90
x =30.60
Answer:
the answer is 30.60
Step-by-step explanation:
lmk if dat right!
Sally made a profit of $2500 after selling stocks for $19000 after 2.5 years. What was her average annual percentage gain?
13.25%
6.06%
3.78%
Sally's average annual percentage gain is approximately 5.26%.
To calculate Sally's average annual percentage gain, we can use the formula:
Average Annual Percentage Gain = (Profit / Initial Investment) * (1 / Time) * 100
Profit = $2500
Initial Investment = $19000
Time = 2.5 years
Substituting the values into the formula:
Average Annual Percentage Gain = (2500 / 19000) * (1 / 2.5) * 100
= (0.1316) * (0.4) * 100
= 5.26
Therefore, Sally's average annual percentage gain is approximately 5.26%.
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simplify :
10b + a+ 6b + 10
Step-by-step explanation:
i think 16b+a+10 is the answer
The scatter plot shows the relationship between the number of coffee drinks sold and the total expenses of a coffee shop.
The slope of the line is....
The intercept of the line is.....
The regression equation is
For the linear function built from the scatter plot, it is found that:
The slope of the line is of: 5.The intercept of the line is of: b = 500.The equation is of: y = 5x + 500.What is a linear function?The slope-intercept representation of a linear function is the rule presented as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the numeric value of the output variable y when the input variable x increases by one.b is the y-intercept of the function, which is the numeric value of the output variable y when the input variable x has a value of 0.From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:
b = 500.
When the input increases by 200, the output increases by 1000, hence the slope is:
m = 1000/2 = 5.
Thus the equation is:
y = 5x + 500.
Missing InformationThe graph is given by the image at the end of the answer.
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Solve. 12. - (-4) =
9
16
17
8
Answer:
16
Step-by-step explanation:
12-(-4)=12+4=16
Answer:
16
Step-by-step explanation:
12 - (-4)
when you subtract a negative, you add.
12 + 4 = 16
Can anyone help me with this question
The relative maximum from the given graph is (2, 0). Therefore, options B, C, D and E are the correct answers
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
From the given graph,
The zeros of function are x=-3, x=2 and x=5.
So, the number of zeros are 3 and the degree of the polynomial is 3.
The relative maximum from the given graph is (2, 0).
The leading coefficient test tells us that the graph rises or falls depending on whether the leading terms are positive or negative.
Here, the leading coefficient is negative.
The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as the graph multiplicity.
Here, the multiplicity is 2.
Therefore, options B, C, D and E are the correct answers
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