Is 7 a solution of 5x - 3 = 12 ? Justify your answer
Answer:
Step-by-step explanation:
NO x=3
At what rate of interest would a sum of money becomes one and half in 10 year ?
Let the Principle be 100.
P = 100, then A = 200 and SI will be 200 - 100 = 100
YES = 100 in 10 years
Rate = 100/10 = 10%.
∴ The interest rate is 10%.
The traditional method is:Given:
Time period = 10 years
Formula used:
SI = (P × R × T)/100
A = P + SI
Where P = main amount, R = rate, T = time, SI = primary interest
Calculations:
Monetary amount 2P
YES = 2P - P
⇒ P = (P × R × 10)/100
⇒ 1 = R/10
⇒ R = 10%
∴ The interest rate is 10%
9. The average amount of soda consumed per person in the US from 1990 to 2010 can be modeled by the following equation, where x is the number of years since 1990. f(x) 5.852x^4-0.002x³ + 0.006x² + 0.029x + 47.855 Find the average rate of change for each time interval. a. 1990 to 1996 b. 1990 to 2000 c. 2005-2010
Using it's concept, the average rates of change are given as follows:
a. 1264.03 soda per person per year.
b. 5851.89 soda per person per year.
c. 128010.89 soda per person per year.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For this problem, the function is given as follows:
f(x) = 5.852x^4 - 0.002x³ + 0.006x² + 0.029x + 47.855.
From 1990 to 1996, we have t = 0 to t = 6, hence:
f(0) = 47.855.f(6) = 5.852(6)^4 - 0.002(6)³ + 0.006(6)² + 0.029(6) + 47.855 = 7632.01.Hence the rate is:
(7632.01- 47.855)/6 = 1264.03.
1264.03 soda per person per year.
From 1990 to 2000, we have t = 0 to t = 10, hence:
f(0) = 47.855.f(10) = 5.852(10)^4 - 0.002(10)³ + 0.006(10)² + 0.029(10) + 47.855 = 58566.75.Hence the rate is:
(58566.75 - 47.855)/10 = 5851.89.
5851.89 soda per person per year.
From 2005 to 2010, we have t = 15 to t = 20, hence:
f(15) = 5.852(15)^4 - 0.002(15)³ + 0.006(15)² + 0.029(15) + 47.855 = 296300.39.f(20) = 5.852(20)^4 - 0.002(20)³ + 0.006(20)² + 0.029(20) + 47.855 = 936354.84.Hence the rate is:
(936354.84 - 296300.39)/5 = 128010.89.
128010.89 soda per person per year.
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2) Segundo o censo do IBGE, em 2010, o Brasil tinha 147,4 milhões de pessoas com 10 anos ou mais que eram alfabetizadas, o que correspondia a 91% da população nessa faixa etária. Determine o número de brasileiros com 10 anos ou mais em 2010
*
162 milhões
161,9 milhões
160,9 milhões
160 milhões
Answer: 162 million
Step-by-step explanation:
147.4 million= 147,400,00
Make a proportion:
147,400,000 - 91%
x - 100%
Hence,
[tex]\displaystyle\\x=\frac{147,400,000*100}{91} \\\\x=\frac{14,740,000,000}{91} \\\\x\approx162,000,000\\\\x=162 \ million[/tex]
A ball is dropped from a state of rest at time t=0.
The distance traveled after t seconds is s(t)=16t2 ft.
(a) How far does the ball travel during the time interval [6,6.5]?
Δs= ___ft
(b) Compute the average velocity over [6,6.5].
ΔsΔt= ___ ft/sec
(c) Compute the average velocity over time intervals [6, 6.01] , [6, 6.001] , [6, 6.0001] , [5.9999, 6] , [5.999, 6] , [5.99, 6] .
Use this to estimate the object's instantaneous velocity at t=6.
V(6)=____ ft/sec
The distance traveled by the ball as a function of time, s(t) = 16•t² ft., and the rate of change, based on calculus, gives;
(a) During the time interval [6, 6.5], the distance traveled is 100 feet
(b) In the interval, [6, 6.5], the average velocity is 200 ft/s
(c) The calculated average velocities in ft/s, for the respective time intervals are;
[6, 6.01]. 192.16
[6, 6.001]. 192.016
[6, 6.0001]. 192.0016
[5.9999, 6]. 191.9984
[5.999, 6]. 191.984
[5.99, 6]. 191.84
The instantaneous velocity at t = 6 is v(6) = 192 ft/s
What are the average and instantaneous velocities of the ball?The distance traveled as a function of time is s(t) = 16•t² ft.
(a) The distance traveled during the time interval [6, 6.5] is found as follows;
s(6) = 16 × 6² = 576
s(6.5) = 16 × 6.5² = 676
The distance traveled in the interval, [6, 6.5], ∆s(t) = 676 - 576 = 100
The distance traveled during the time interval [6, 6.5] = 100 feet
(b) Average velocity = ∆s(t)/∆t
∆t = 6.5 - 6 = 0.5
Therefore;
∆s(t)/∆t = 100/0.5 = 200
The average velocity = 200 ft./s
(c) The average velocities over the given time intervals, obtained using a graphing calculator, are;
Interval. Average velocity
[6, 6.01]. 192.16
[6, 6.001]. 192.016
[6, 6.0001]. 192.0016
[5.9999, 6]. 191.9984
[5.999, 6]. 191.984
[5.99, 6]. 191.84
Given that at t = 6, as the time interval approaches zero from the right and from the left, the average velocity approaches 192 ft./s, the instantaneous velocity at t = 6, v(6) is 192 ft./s
v(6) = 192 ft./s
Using calculus, differentiation, we have;
v(t) = ds/dt = 2×16 × t = 32•t
v(6) = 32 × 6 = 192
Therefore;
v(6) = 192 ft./s
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SOME HELP ME PLS, I ONLY NEED CORRECT ANSWERS SO DON’T PUT A RANDOM ANSWER
Answer:
≈67.81
Step-by-step explanation:
1. Rhonda is competing on a game show. First she randomly decides on a target of 1 or 2 and chooses card A or B. Then she spins the spinner on the other side
of the card.
a) What is P(1) if Rhonda chooses spinner A? P(1|A) = __
b) What is P(1) if Rhonda chooses spinner A? P(1|B) = __
c) Choose the correct symbol to make the statement true
Using probability we get (a) P(1|A) = 1/2 and (b)P(1|B) =3/4 , hence P(1|A) ≠ P(1|B).
Probability is the study of chance . The part of mathematics known as probability deals with fractional representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, 0 denotes the event's impossibility and 1 denotes certainty.
Probability is calculated by the fraction possible outcomes ÷ total outcomes
a) The first spinner has the total 4 sections. so there are 4 total outcomes.
Favorable outcome = 1
Total number of favorable outcome=2
Probability P(1|A) = favorable outcome ÷ total outcome
∴ P(1|A) =2/4 or P(1|A) =1/2
b) The first spinner has the total 4 sections. so there are 4 total outcomes.
Favorable outcome = 1
Total number of favorable outcome=3
Probability P(1|B) = favorable outcome ÷ total outcome
∴ P(1|B) =3/4 or P(1|B) =3/4
c)Therefore P(1|A)≠P(1|B) so the events A and B are dependent.
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I’ll give points + brainalist
The line which is perpendicular to the given line y = -x/8 + 3 is y - 8x =-2, there slopes are negative reciprocals of each other
How to fine the line that is perpendicular to the given lineGiven data
line y = -x/8 + 3
The equation of a line is represented as y = mx + c where m represents the slope. The unique feature of perpendicular line is that the slopes are negative reciprocals of each other.
Hence we find the line that has same value of m which is the slope
using the second option: y - 8x = -2
y - 8x = 2
y = 8x - 2
y = 8x - 2
the slope here is m = 8 which is equal to the negative reciprocals of the slope in the given equation and hence the correct option
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Tom got 72 marks in 8 tests. How much did he get in each test on average?
Given
Tom got 72 marks in 8 tests.
Answer
[tex] \frac{72}{8} = 9[/tex]
he get 9 mark on average
In 2011 the marathon had 29967 men and 16,928 Women how many Men T Shirts and how many women t shirts were given
The number of men T Shirts and how many women t shirts that were given to the nearest thousand will be 30000 and 17000 respectively.
How to illustrate the information?It should be noted that based on the information illustrated, the marathon had 29967 men and 16,928 Women.
Therefore, the number of men T Shirts and how many women t shirts that were given to the nearest thousand will be:
29867 = 30000
16982 = 17000
Therefore, the number of men T Shirts and how many women t shirts that were given to the nearest thousand will be 30000 and 17000 respectively.
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In 2011 the marathon had 29967 men and 16,928 Women how many Men T Shirts and how many women t shirts were given to the nearest thousand.
A helicopter takes off from the roof of a building that is 225 feet above the ground. The altitude of the helicopter increases by 125
Answer: i think you want y=125x+225
Step-by-step explanation:
the linear equation is created by sticking these two numbers into y=mx+b
so we start at 225 feet, which means that goes where b is, and the helicopter goes up 125 per whatever, which means we put 125 where m is
Triangle CDE, with vertices C(-4,2), D(-3,7), and E(-7,6), is drawn inside a rectangle,
as shown below.what is the area in square units of triangle CDE?
Area of triangle ΔCDE with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ) is 9.5 square units.
We have a triangle ΔCDE with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ). To calculate the area of triangle when its vertices are given we have the formula as shown below,
Area of triangle ΔCDE = [tex](1/2)(x_{1} (y_{2} - y_{3} ) + x_{2} (y_{3} -y_{1} ) + x_{3} (y_{1} -y_{2} ))[/tex]
Here, [tex]x_{1}[/tex] = -4 , [tex]x_{2}[/tex] = -3 ,[tex]x_{3}[/tex] = -7 , [tex]y_{1}[/tex] = 2 , [tex]y_{2}[/tex] = 7 and [tex]y_{3}[/tex] = 6
On substituting the above values in the formula of area of triangle , we will get
Area of triangle ΔCDE = (1/2)( -4 ( 7 - 6 ) + ( -3 ) ( 6 - 2) + (-7 ) ( 2 - 7 ))
Area of triangle ΔCDE = (1/2) ( - 4 - 12 + 35 )
Area of triangle ΔCDE = 19/2
Area of triangle ΔCDE = 9.5 square units
Area of triangle ΔCDE with the vertices C( -4 , 2 ), D( -3 , 7 ), and E( -7 , 6 ) is 9.5 square units.
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A shirt normally costs $22.50 and is on sale for 12% off. What is the sale price?
Answer:
$19.8($2.7 subtracted off)
Step-by-step explanation:
[tex]P = 22.5(1 - 12\%)\\P = 22.5(1 - 0.12)\\P = 22.5(0.88)\\P = 19.8[/tex]
Draw the Venn diagram showing the inclusion relation among the different Sets of numbers.
Answewhats the number mason
Step-by-step explanation:
Question
Shonda jogs 5 miles per hour.
Graph the relationship between the number of hours Shonda jogs and the total number of miles jogged.
here hope this helps u
What is the value of −5 + |−18|?
13
23
−13
−23
Answer:
your answr would be a 13
Step-by-step explanation:
Answer:
A) 13
Step-by-step explanation:
[tex]-5 + |-18|\\where\:|-a|=|a|\:\:\mathrm{if}\:a\neq 0\\|-18| = |18|\\= -5 + 18\\Inverse\:\:the\:\:expression\\= 18 - 5\\= 13[/tex]
What is the image of (-4,-2) after a reflection over the x-axis?
According to the image the x-axis, there is a reflection (- 4, 2 ).
How can a coordinate be found to mirror itself?An image that has been flipped has no points that are closer to the mirror line than the original shape. The point's coordinate must be multiplied by -1 in order to reflect it over the axis. Simply add -1 to the coordinate of the point to reflect it over the axis.
What does the term coordinate geometry refer to?Analytic geometry, often known as coordinate geometry, is the study of geometry using coordinate points. It is possible to determine distances between points using coordinate geometry, as well as divide lines into m:n segments, locate a line's midpoint, determine the area of a triangle in the Cartesian plane, and perform other operations.
According to the given data:Under the x-axis reflection.
A point (x, y) → (x, -y), so
(- 4, - 2 ) → (- 4, 2 )
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Find the average rate of change of f (x)=x-2√x on the interval [1, 9].
The average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
We have,
f(x) = x - 2√x
On the interval [1,9].
[1, 9] = [a, b]
The average rate of change:
= f(b) - f(a) / b - a
= f(9) - f(1) / 9 - 1
= [(9 - 2√9) - (1 - 2√1)] / 8
= [ (9 - 6) - (1 - 2) ] / 8
= (3 + 1) / 8
= 4 / 8
= 1/2
Thus the average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
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does anyone know how to do this
Answer:
Step-by-step explanation:
add 99 and 36 together to get 135 degrees
Answer:
135°
Step-by-step explanation:
You add the two angles together.
The current plans describe a fountain 9 feet in diameter. Around the sides of the fountain, the contractors will install a chain barrier to prevent children from falling into the fountain. How much area in the park will the designers need to set aside for the fountain? How much chain will the contractors need to install? Round your answers to the nearest hundredth of a square foot or foot. Type the correct answer in the box. Use numerals instead of words.
hundred people bearajsbsj
Answer:
I don't know about this question
wats the answer help mee
Answer:
6
Step-by-step explanation:
The diameter is half of the given radius, therefore, split the radius in half.
[tex]\frac{12\:in^2}{2} = 6\:in^2[/tex]
Arithmetic Mean of 128,144,146,143,136,142,138,120,140,152,144,140,150,142,154
Answer: 141.26666666667
Step-by-step explanation:
Is 7x+y+3=y a linear equation
Answer:
7x+y=3 is not a linear equation.
Explain how to use place-value blocks to find the difference between the monthly cost of using the DVD player, $0.40, and the dishwasher, $0.85. Then find the difference.
Place-value blocks can be used to find the difference between the monthly cost of using the DVD player, $0.40, and the dishwasher, $0.85 by converting them to the nearest ten. The difference will be $0.50.
What are place value blocks?It should be noted that base ten blocks are used to represent numbers as a base ten model. It should be noted that they are useful because they show the value of each digit in a number and make it easier to visualize the size of a number.
In this case place value blocks mimic the base ten number system by representing the ones, tens, hundreds, and thousands places
Therefore, place-value blocks can be used to find the difference between the monthly cost of using the DVD player, $0.40, and the dishwasher, $0.85 by converting them to the nearest ten. The difference will be $0.50.
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PLEASE HELP! DUE IN LESS THAN 2 HOURS! IM STUCK! PLEASE HELP ME! THANKS QUESTION DOWN BELOW!!! PLEASE SHOW THE WORK! DETERMINE THE NUMBER OF LINE SEGMENTS IN THE 100TH PATTERN!
Answer:
Step-by-step explanation:
So we are not counting each line segment forming a cube. We are actually counting the four sides of the overall shape, and the number of segments inside it.
It will increase by 2 each time.
So if we start at 4(the four outside lines), go to 6(adding 2 on the inside), then to 8(adding 2 more on the inside), we continue this 100 times, correct?
So our equation would be
(x times 2) +4 (if we start at the SECOND term and count that as the first )
so, to figure out the answer to out problem, we insert 100 for x
(100 x 2)+4 = 204
This would leave us with one big square (4 outside line segments) With 100 segments going horizontal, and 100 vertical)
Hope this helps! ^^
Debra bought 4 hammers and 6 tape measures for $94. Heather bought 5 hammers and 3 tape measures for $77 . Letting x represent the price of each hammer and y represent the price of each tape measurewrite a cost equation for both Debra and Heather
The cost equation for Debra is given by 4x + 6y = 94 and for Heather is 5x + 3y = 77.
What are Linear equations in two variables?Linear equations in two variable have one, none, or infinitely many solutions, with the highest exponent order of 1 in each of the two variables. The standard form of a two-variable linear equation is ax + by + c = 0, where x and y are variables. Solutions can also be written in pairs, for example (x, y). A two-variable linear equation system is represented graphically by two straight lines that can intersect, parallelize, or coincide.
According to the given condition, we have 2 equations:
4x + 6y = 94
5x + 3y = 77
Now, multiply by 2 on both sides of the equation 5x + 3y = 77 to obtain:
10x + 6y = 154
Now, subtracting the equation 10x + 6y = 154 and 4x + 6y = 94.
[10x + 6y = 154] - [ 4x + 6y = 94]
6x + 0y = 60
x = 10
Putting the value of x = 10 in equation 4x + 6y = 94, we get
y = 9
So, the cost of 1 hammer is 10$ and tape is 9$.
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The zookeeper mentioned that the scale used to weigh some of the larger animals can be off by 12 pounds. The scale read 438.2 lbs. for one of the larger animals. If the animal’s actual weight is x pounds, write an expression to represent the number of pounds the weight on the scale is from the actual weight of the animal. Then explain the range of values in which the actual weight might be.
The actual weight of the animal is between 450.2 and 426.2 pounds
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequality can be used to show that two variables or numbers are not equal to each other.
The weight of the larger animals can be off by 12 pounds. Let x represent the actual weight of the animal. If the scale reads 438.2 lbs, hence:
|x - 438.2| = 12
x - 438.2 = 12; or -(x - 438.2) = 12
x = 450.2; or x = 426.2
The actual weight of the animal is between 450.2 and 426.2 pounds
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Solve the equation 5k^2−20k=15 . Present exact values of the solutions. If there are more than one solutions, separate them by a comma.
The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.
What are the roots of the equation?Let the equation be ax² + bx + c = 0.
Then the roots of the equation will be
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\\[/tex]
The quadratic equation is given below.
5k² - 20k = 15
Simplify the equation, then we have
k² - 4k = 3
k² - 4k - 3 = 0
Then the roots of the equation will be
[tex]\rm k = \dfrac{ -(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times (-3) }}{2 \times 1}\\\\k = \dfrac{4 \pm \sqrt {28}}{2}[/tex]
Simplify the equation, then we have
k = (4 ± 5.30) / 2
k = (4 + 5.30) / 2, (4 - 5.30) / 2
k = 4.65, -0.65
The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.
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During a game of one-on-one, Rodney and Justin scored 39 points altogether. If Justin lost the game by 1 point, how many points did each player score? Use a system of linear equations in two variables to solve the problem
The points scored by Rodney is 20 points.
The points scored by Justin is 19 points.
How many points did each player score?x + y = 39 equation 1
x - y = 1 equation 2
Where:
x = points scored by Rodney
y = points scored by Justin
In order to determine the points scored by Justin, take the following steps:
Subtract equation 2 from equation 1 :
2y = 38
Divide both sides of the equation by 2
y = 38/2
y = 19 points
To determine the value of x, substitute for y in equation 2
x - 19 = 1
Combine similar terms: x = 19 + 1
Add similar terms together: x = 20
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2x + 5 < -3 or 6x - 5 > 7
Answer: 2x-5/3=7
Tiger shows you, step by step, how to Isolate x (Or y or z) in a formula