Step-by-step explanation:
5w - 4 > 59 - 2w
add 4 to both sides:
5w - 4 + 4 > 59 - 2w + 4
5w > 63 - 2w
subtract 2w from both sides:
5w - 2w > 63 - 2w - 2w
3w > 63
divide both sides by 3:
3w/3 > 63/3
w > 21
in internal notation: (21, ∞)
let ???? represent the difference between the number of heads and the number of tails obtained when a coin is tossed ???? times. what are the possible values of ?????
The possible values of X are that if n is even X can takes even integers from [-n, n], and if n is odd, X can takes odd integers from [-n, n]
To solve this question, we can use X to represents the difference between the number of heads and the number of tails obtained when a coin is tossed X times, the possible values of X are now obtained below:
Let H be the no. of heads and T be the no. of tails, since the coin is tossed n times, we have:
H+T=n
now, X = H-T ,
X=H-(n-H)
X=2H-n
Now,
H takes values {0,1,2,3 ......,n-2, n-1,n}
2H takes values {0,2,4,6,.....,2n-4,2n-2,2n}
2H - n takes values {-n,-(n-2),-(n-4), -(n-6),.............,n-4, n-2,n}
X takes values {-n,-(n-2), -(n-4),-(n-6),.............,n-4, n-2, n}
therefore, if n is even X can takes even integers from [-n, n]
and, if n is odd, X can takes odd integers from [-n, n]
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The results of a survey about what 432 students would like as a career are shown below use the graph
We have in total 432 students.
8.
We know that 23% of the students want to be a teacher, this means that:
[tex]432\cdot0.23=99[/tex]99 students want to be a teacher.
9.
We know that 13% of the students want to be doctor or nurses, this means that 26% of them want to be one of those, then:
[tex]432\cdot0.26=112[/tex]112 students want to be doctor or nurses.
10.
Since 9% of the students want to be lawyers, this means that 91% of them did not want to be lawyers, then:
[tex]432\cdot0.91=393[/tex]393 students does not want to be lawyers.
Answer:
393 students do not want to be lawyers.
Step-by-step explanation:
Write a verbal expression of x+y
shirley earns £52 for an 8 hour shift at a call centre. In one week, shirley works fifty hours at the call centre. How much does shirley earn during this week
The amount she earned this week is £325
How to find the amount Shirley earn?Shirley earns £52 for an 8 hour shift at a call centre.
Therefore,
8 hours = £52
1 hour = ?
cross multiply
1 hour earning = 52 / 8
1 hour earning = £6.5
Therefore, In one week, Shirley works fifty hours at the call centre. The amount she earns during the week is as follows:
Hence,
amount she earns this week = 6.5 × 50
amount she earns this week = £325
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HELP
A toy rocket is launched from a 2.1 m high platform in such a way that its height, h (in meters), after t seconds is given by the
equation h = -4.9t² + 14.0t+2.1. How long will it take for the rocket to hit the ground?
Answer:
3 seconds
Step-by-step explanation:
The height of the rocket when it hits the ground will be zero meters.
Therefore, set the equation to zero and solve for t by using the quadratic formula.
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Given equation:
[tex]-4.9t^2+14t+2.1=0[/tex]
Therefore:
[tex]a=-4.9, \quad b=14, \quad c=2.1[/tex]
Substitute the values into the quadratic formula:
[tex]\implies t=\dfrac{-14 \pm \sqrt{14^2-4(-4.9)(2.1)}}{2(-4.9)}[/tex]
[tex]\implies t=\dfrac{-14 \pm \sqrt{196+41.16}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-14 \pm \sqrt{237.16}}{-9.8}[/tex]
[tex]\implies t=\dfrac{-14 \pm15.4}{-9.8}[/tex]
Therefore:
[tex]\implies t=\dfrac{-14 +15.4}{-9.8}=\dfrac{1.4}{-9.8}=-\dfrac{1}{7}[/tex]
[tex]\implies t=\dfrac{-14-15.4}{-9.8}=\dfrac{-29.4}{-9.8}=3[/tex]
As time is positive, t = 3 s only.
Therefore, it will take 3 seconds for the rocket to hit the ground.
The number of ounces of chocolate chips per batch of cookies can be represented with the equation y = 8x, where y represents ounces of chocolate chips and x represents batches of cookies.
Determine how many batches of cookies can be made using 28 ounces of chocolate chips.
3.5 batches
8 batches
36 batches
224 batches
Answer: 3.5 batches is correct.
Step-by-step explanation: Take 28 and divide that by 8 and that equals 3.5
Hope this helps!
The number of batches of cookies that can be made using 28 ounces of chocolate chips is 3.5 batches.
The correct answer option is option a
How to find number of batches of cookies can be made using 28 ounces of chocolate chips?Equation:
y = 8x
Where,
y = ounces of chocolate chips and x = batches of cookiesIf there are 28 ounces of chocolate chips:
y = 8x
28 = 8 × x
28 = 8x
divide both sides by 8x = 28/8
x = 3.5 batches
So therefore, the
So therefore, 3.5 batches of cookies can be made using 28 ounces of chocolate chips.
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team A and team B play in a competition
team A has twelve more points than team B
team A has five times as many points as team B
how many points does each team have
Answer:
A = 15
B = 3
Step-by-step explanation:
Since Team A has 12 more points than team B, then,
A - 12 = B
A = B + 12 ( equation 1 )
team A has 5 times as many points as team B, so,
5B = A. ( equation 2 )
Substitute equation 1 into equation 2
A = B + 12
5B = B + 12
5B - B = 12
4B = 12
B = 3
we'll substitute the answer into equation 2
5B = A
5(3) = A
A = 15
I hope this helps :D
have a nice day dear...
Which of the following is a correct way to solve 4 = 13 – 3x ?
A. 4 + 13 = 13 - 3x + 13. 17 = -3x. 17/-3 = -3x/-3. x = -17/3.
B. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/-3 = -3x/-3. x = 3.
C. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/-3 = -3x/-3. x = -3.
D. 4 - 13 = 13 - 13 - 3x. -9 = -3x. -9/3 = -3x/3. x = -3.
The solution of the equation 4 = 13 – 3x is x = 3 which is the correct answer would be an option (B).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given an equation as
4 = 13 – 3x
Rearrange the terms non-variables and variables,
3x = 13 - 4
Apply the subtraction operation,
3x = 9
x = 9/3
Apply the division operation, and we get
x = 3
Therefore, the correct answer would be an option (B).
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Using the Pythagorean theorem! Need to be in simplest radical form
The simplest radical form of the hypotenuse of the given right-angled triangle is therefore discovered to be [tex]6\sqrt{2}[/tex] units.
What is the theory of the Pythagorean Theorem?The Pythagorean Theorem states that the square on the hypotenuse of a right triangle is equal to the sum of the squares on the triangle's legs.
A simplest radical form is defined as what?If the number or algebraic expression under the radical has no factors that are perfect nth powers, then the radical is said to be in its simplest radical form.
The given right angled triangle has sides 6 units each.
We need to determine the hypotenuse using the Pythagorean theorem.
Hypotenuse = [tex]\sqrt{(side 1)^{2} + side 2)^{2} }[/tex]
[tex]=\sqrt{6^{2} + 6^{2} } \\\\= \sqrt{72}\\ \\= 6\sqrt{2}[/tex]
Therefore, the hypotenuse of the given right angled triangle is found to be [tex]6\sqrt{2}[/tex] units which is the simplest radical form.
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A stadium has 52,000 seats. Seats sell for $28 in Section A, $24 in Section B, and $20 in Section C. The number of seats in Section A equals the total number of seats in Sections B and C. Suppose the stadium
takes in $1,307,200 from each sold-out event. How many seats does each section hold?
Section A holds seats.
The number of seats in Section A is 26000 ,The number of seats in Section B is 14800 and, The number of seats in Section C is 11200.
What is a equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Let the number of seats in Section A is "a".
Let the number of seats in Section B is "b".
and, Let the number of seats in Section C is "c".
Now using the statement "stadium has 52,000 seats"
we can make equation: a + b + c = 52000
Now using the statement "Seats sell for $28 in Section A, $24 in Section B, and $20 in Section C" and "stadium takes in$1,307,200 from each sold out event".
we can make equation: 28a + 24b + 20c = $1,307,200
Now using the statement "he number of seats in Section A equals the total number of seats in Sections b and C"
we can make equation: a = b + c
Solving these three equations. We get,
a = 26000 , b = 14800 and c = 11200
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Which of the following whole numbers are perfect squares? (Please select ALL correct answers for full credit).
Answer: 9, 144, 225, 10,000
Step-by-step explanation:
9=3x3
144=12x12
225=15x15
10,000=100x100
Need help pls y’all will help me
The correct description regarding each table is given as follows:
1. Rate of change of 4, linear.
2. Rate of change of -2/3, linear.
3. Rate of change of 1/4, linear.
4. Rate of change of -1, linear.
5. Not linear.
6. Rate of change of 3, linear.
Linear functionsA linear function has the definition presented as follows:
y = mx + b.
In which:
m is the slope, which is the constant rate of change.b is the y-intercept.A data-set will only be classified as linear if the rate of change is constant.
Hence the tables in this problem are classified as follows:
Table 1: Linear, as for each two points, the change in the output y divided by the input x has a result of 4, which is the rate of change.Table 2: Linear, as for each increase of 3 in x, there is a decay of 2 in y, hence the rate of change is of -2/3.Table 3: Linear, as for each increase of 4 in x, there is a increase of 1 in x, hence the rate of change is of 1/4.Table 4: Linear, as for each increase of 1 in x, there is a decay of 1 in y, hence the rate of change is of -1.Table 5: Not Linear, as from x = 1 to x = 2 an increase of 1 in x resulted in a an increase of 2 in y, while from x = 2 to x = 3 an increase of 1 in x resulted in a an increase of 4 in y.Table 6: Linear, as an increase of 2 in x results in an increase of 6 in y, hence the rate of change is of 6/2 = 3.Learn more about linear functions at https://brainly.com/question/24808124
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Carlson Middle School has a total of 500 students in sixth, seventh, and eighth grades. The table below shows the number of students in each grade.
Grade Number of Students
Sixth 203
Seventh 126
Eighth 171
The principal randomly selects 25 students to receive a free school lunch today. What is the most likely number of sixth graders in the group of 25 selected by the principal?
There is also a picture down below
Answer: Around 10 sixth graders would get free lunch.
Step-by-step explanation: first, divide 500/25 to find the percentage of students receiving free lunches. You should get 0.05, or 5%. Then, multiply the number of sixth graders (203) by 5%. Your answer is 10.15, rounded down to 10. (Because it is impossible to have 0.15 of a student)
a set of license plates has three letters followed by 5 digits. (a) in how many ways can a license plate be made with three letters followed by 5 digits? (letters or digits may be repeated.)
The license plate can be made in 1,757,600,000 ways
For the license plate, we need 3 letters out of 26 letters of the English alphabet and 5 digits out of 0-9
For the alphabet:
So, the first letter can be chosen in 26 ways
The second letter can be chosen in 26 ways
The third letter can be chosen in 26 ways
For the digits:
The first number can be chosen in 10 ways
The second number can be chosen in 10 ways
Similarly, the remaining three numbers can be chosen in 10 ways each
So, total ways = 26*26*26*10*10*10*10*10 = 1,757,600,000
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What’s x??
Solve for x
5x+2=7x-4
Answer:
x = 3
Step-by-step explanation:
[tex]{ \rm{5x + 2 = 7x - 4}}[/tex]
- First, using equality order by collecting like terms of x together and constants together;
Using subtraction property of equality on constant 2 [subtracting 2 from both sides][tex]{ \rm{(5x + 2) { \green{- 2}} + = (7x- 4){ \green{ - 2}}}} \\ { \rm{5x = 7x - 6}}[/tex]
Using subtraction property of equality on term 7x [subtracting 7x from both sides][tex]{ \rm{5x - { \blue{7x}} = (7x - 6) - { \blue{7x}}}} \\ { \rm{ - 2x = - 6}}[/tex]
- Using division property of equality, by dividing -2 on both sides;
[tex]{ \rm{ \frac{ - 2x}{ \orange{ - 2}} } = \frac{ - 6}{ \orange{ - 2}} } \\ \\ { \rm{x = 3}}[/tex]
[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: \: creed}}}[/tex]
Answer:
x = 3Step-by-step explanation:
What’s x??
Solve for x
5x+2=7x-4
2 + 4 = 7x - 5x
6 = 2x
x = 6 : 2
x = 3
--------------
check
5 * 3 + 2 = 7 * 3 - 4
17 = 17
the answer is goodIt takes 200 coins to get a bag upgrade in Pokémon Go. The creators decided to throw a sale on bag upgrades. For one day only anybody can upgrade their bag for 125 coins. Find the percent of change
price change: 125 - 200 = -75 coins
percent of change = price change/original price *100 = -75/200*100 = -37.5%
that is, a discount of 37.5%
please help me find how many solutions there are
Answer:
A. No solutionStep-by-step explanation:
Use a distributive property.
Distributive property:
A(B+C)=AB+AC
A(B-C)=AB-AC
First, expand by distributive property from multiply the numbers from left to right.
-9j=-9(j-20)
-9(j-20)
-9*j=-9j
9*20=180
=-9j+180
-9j=-9j+180
Add by 9j from both sides.
-9j+9j=-9j+180+9j
Solve.
0=180
No solution.
Therefore, the correct answer is A. no solution.
I hope this helps, let me know if you have any questions.
help i need help with this question
x^5/x^2 can be simplified to what
Answer:
x^3
Step-by-step explanation:
Because they are the same base in a division question, you subtract the exponents.
5-2=3.
Answer = x^3
Hope this helps!
Btw, if this is right, please give me brainliest, thanks!
Answer:
x^3
Cancel the common factor of x^5 and x^2.
Hope you have a wonderful day :)
Lloyd is making a bouquets of flowers. He has 25c roses and 15v snapdragons.he divides flowers equally to make as many bouquets as possible . He uses all the flowers .what number snapdragons are in beach bouquet.
Answer:
A. 3
Step-by-step explanation:
45 + 15 + 25 = 85
There are 85 flowers.
There are 25 roses, 45 tulips, an 15 roses.
What are all 3 of these divisible by?
5!
That means that there will be 5 bouquets.
Let's divide each number by 5 to find out how many of each type of flower is in each bouquet.
25/5 = 5
5 roses in each bouquet
45/5 = 9
9 tulips in each bouquet
15/5 = 3
3 snapdragons in each bouquet
5 + 9 + 3 = 17
There are a total of 17 flowers in each bouquet.
Out of those 17 flowers, 3 are snapdragons.
A. 3
Please help!
Choose the mathematical sentence that most accurately expresses the
information in the problem, and would be most helpful in solving it.
After taking 4 pieces of fruit out of a bag, 12 pieces of fruit remained. How
many pieces of fruit were in the bag to start?
A. 12 + f = 4
B. 12 ÷ f = 4
C. 4+ f = 12
D. 12 - 4 = f
E. F ÷ 4 = 4
F. F - 4 = 12
Answer:
Option F
F - 4 = 12Step-by-step explanation:
According to given information
1) You had F fruits and took 4 pieces out of a bag, it is:
F - 42) Then you have 12 pieces of fruit remained:
F - 4 = 12This equation matches the answer choice F.
Which graph represents the system of inequalities? {y+3/4x<2 {y−1≥2x
The graph of the inequality is attached below to represent the solution.
Graph of InequalityTo solve this problem, we can simply plot the graph of the inequality using a graphing calculator. To do this, we can simply input the value of both inequalities and then plot the values.
In the graph below, the the red broken line represents the first equation which is "<" or less than and the second equation which is the straight blue line which represents the ">" or greater than sign.
Kindly find the attached image below.
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HELP PLS IM MARKING BRAINLEIST
The formula for the volume of a sphere is 4/3πr³. The formula for r is d/2. We know d, so we can substitute this for r.
4/3(3.14)(32/2)^3
4/3(3.14)(16)^3
4/3(3.14)4096
4.19(4096
17612.24 cm^3
[tex]\huge\boxed{\sf 17157.28} \\\\\\\displaystyle \sf Converting\ the\ diameter\ to\ radius\\\\r=\frac{d}{2} =\frac{32}{2} =16\\\\Finding\ the\ volume \\\\V=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 16^{3} \approx 17157.28 \\\\[/tex]
Given the domain (-5,-1,3,5) find the first number in the range of the function f(x)=-2x -3 .
The first number in the range of the function is 7
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?The function is given as
f(x) = -2x - 3
Also, we have the domain to be
(-5,-1,3,5)
The first value in this domain is
x = -5
So, we have
f(-5) = -2 x -5 - 3
Evaluate
f(-5) = 7
This represents the first number in the range
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8 is 20% of what number?
Answer: 40
Step-by-step explanation:
A cylindrical hollow metal pipe is 16 cm long.
It has an external diameter of 10 cm and an internal diameter of 8 cm.
The density of the metal from which the pipe is made is 8 grams per cm3
What is the mass of the pipe in grams?
Answer:
3617.28 grams
Step-by-step explanation:
Find the volume of the metal as following:
[tex]V_{metal}=V_{external}-V_{internal}[/tex][tex]V_{external} = \pi d_{external}^2h/4=\pi *10^2*16/4=1256[/tex] cm³[tex]V_{internal} = \pi d_{internal}^2h/4=\pi *8^2*16/4=803.84[/tex] cm³[tex]V_{metal}=1256-803.84 = 452.16[/tex] cm³Find the mass:
[tex]mass = volume*density[/tex][tex]mass = 452.16*8=3617.28[/tex] gramsAnswer:
3619.1 grams (nearest tenth)
Step-by-step explanation:
Volume of a cylinder
[tex]V=\pi r^2 h[/tex]
where:
r is the radius.h is the height.The radius of a circle is half its diameter.
Find the volumes of the external and internal cylinders by substituting the given values into the formula for volume of a cylinder:
[tex]\implies \textsf{Volume of the external cylinder}&=\pi \cdot 5^2 \cdot 16=400 \pi \; \sf cm^3[/tex]
[tex]\implies \textsf{Volume of the internal cylinder}&=\pi \cdot 4^2 \cdot 16=256 \pi \; \sf cm^3[/tex]
Find the volume of the cylindrical hollow metal pipe by subtracting the volume of the internal cylinder from the volume of the external cylinder:
[tex]\begin{aligned}\implies \textsf{Volume of the metal pipe}&=\sf Volume_{external}-Volume_{internal}\\&=400 \pi - 256 \pi\\& = 144 \pi \sf \; cm^3\end{aligned}[/tex]
Density formula
[tex]\rho=\dfrac{m}{V}[/tex]
where:
ρ = densitym = massV = volumeGiven:
ρ = 8 g/cm³V = 144π cm³Substitute the given values of density and the found volume into the density formula and solve for m:
[tex]\begin{aligned}\implies \rho&=\dfrac{m}{V}\\8&=\dfrac{m}{144 \pi}\\m&=8 \cdot 144\pi\\m&=1152 \pi \\m&=3619.11473...\\m&=3619.1\; \sf g \;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the mass of the pipe is 3619.1 grams (nearest tenth).
Note: I have used the exact value of π (not a rounded value).
-3p-4<6 help me please never done these before and teacher isn’t at school to ask!!!
Answer:
p>-1/3
Step-by-step explanation:
-3p-4<6
+4 +4
-------------
-3p<10
Divide -3 on both sides and you get something like p>-1/3 because you have to flip the sign.
Distance between (4,5) and (-1,3)
Answer:
[tex]D=\sqrt{29}[/tex]
Step-by-step explanation:
Solve and graph the solutions of the inequality - |x - 2| + 9 > 6.
i solved it
you graph it :)
A group of friends wants to go to the amusement park. They have no more than $150 to spend on parking and admission. Parking is $9.75, and tickets cost $13.75 per person, including tax. Write and solve an inequality which can be used to determine p, the number of people who can go to the amusement park.
group of friends have $150 to spend on the amusement park admission and parking.
150 - 13.50 = 136.50
136.50 / 22.75 = 6
x = 6
13.50 + 22.75x = 150
13.50 + 22.75(6) = 150
22.75 * 6 = 136.50
136.50 + 13.50 = 150