Answer:
Dimension = 6 feet × 3 feet
Step-by-step explanation:
From the question given above, the following data were obtained:
Length (L) = 6 feet
Distance around the fence (Perimeter) = 18 feet
Dimension of the fence =?
Next, we shall determine the breadth of the rectangular fence. This can be obtained as follow:
Length (L) = 6 feet
Perimeter (P) = 18 feet
Breadth (B) =?
Perimeter of rectangle is given by:
P = 2(L + B)
18 = 2 (6 + B)
Clear the bracket
18 = 12 + 2B
Collect like terms
18 – 12 = 2B
6 = 2B
Divide both side by 2
B = 6/2
B = 3
Thus, the breadth of the rectangular fence is 3 feet
Dimension of the rectangular fence is given by:
Dimension = length × Breadth
Length (L) = 6 feet
Breadth (B) = 3 feet
Dimension = 6 feet × 3 feet
How long does it take for an investment to quadruple in value if it is invested at 11% compounded
continuously? Type the exact answer as your answer (no decimal approximations).
Let's assume we have $100 and an interest rate of 7%. For the $100 to quadruple it means that the future value would be $400. Thus, because we are talking about compounding daily we will set us the equation as follows:
100 * (1+1.07)x = 400
Then we will take 400 and divide it by 100 getting:
1.07X = 4
Now we have encountered a problem where we do not know exponent, so we will use logarithm to calculate such and transform our equation to: Log1.07(4)=X
Using our calculator we will find that it takes about 20.4895 days to quadruple the money invested under 7% interest rate compounded daily.
2nd: Using the same $100 but with the rate of 5.5% compounded continuously we will be using A=PERT formula
where:
P (principal) is equal to hypothetical $100
E (e) is a mathematical constant, which is approximately 2.718
R (rate) is the interest rate, in our case it is 5.5%
T (time) is the time required for money to grow
A (amount) is the final amount desired, which is 4 times larger of $100, thus $400
We have the following:
400 = 100 * e0.055t
400/100 = e0.055t
4 = e0.055t
Then we will apply natural log to both sides of the equations and get the following:
ln(4) = ln(e0.055t)
Since e is the base of ln(x) the equation simplifies to:
ln(4) = 0.055t
Using the calculator to find ln(4) we are getting:
1.38629 = 0.055t
Lastly find t
t = 1.38629/0.055
t = 25.20535202
Plug the answers back to the original equation to verify the answers.
1st part of the question answer: t = 20.4895
2nd part of the question answer: t = 25.20535202
I just learned this kind of confused :(
Answer:
9.4247
Step-by-step explanation:
c= πd, c=(3.14)d , 3 is the diameter so we put it in the d spot. So c=(3.14)3 and you multiply those together to get the circumference.
You must be at least 42 inches tall to ride the bumper cars at an amusement park. Write an inequality that represents this situation. Let x represent the heights of people who are allowed to ride the bumper cars.
Answer:
x ≥ 42
Step-by-step explanation:
If you must be at least 42 inches tall to ride the bumper cars at an amusement park, this means that the minimum average height you can have is 42in i.e you can be more than 42inches tall.
The right inequality sign to represent this situations is a "greater than or equal to sign"(≥)
If x represent the heights of people who are allowed to ride the bumper cars, the required inequality expression will be x ≥ 42
Which statements are true? Select all that apply.
9514 1404 393
Answer:
A, B, D
Step-by-step explanation:
The figure is symmetrical about the horizontal centerline, so triangles, angles, and segments above that line are congruent with corresponding segments below that line. Choices A, B, D are true statements.
__
There is nothing in the figure to indicate that ΔFGK is isosceles, so statement C cannot be considered to be true.
A circle has a radius of 5 inches. What is the circumference of the circle? Use 3.14 for pi.
Answer:
C≈31.42in
Step-by-step explanation:
Answer:
The circumference of a circle is given by
C = 2 * pi *r
C = 2 * 3.14 * 5
C =31.4 inches
20x^2/12x+8 simplified
Rhion sat maths and English test
In the maths she scores 14 out of 17
In th english test she scored 31 out of 39
which one did she do better.
Answer:
Rhion did better in maths test.
Step-by-step explanation:
Given that:
Rhion scored 14 out of 17.
We will find percentage and then compare them.
Percentage = [tex]\frac{Score}{Total\ marks}*100[/tex]
Percentage = [tex]\frac{14}{17}*100[/tex]
Percentage = 82.35%
Rhion scored 31 out of 39.
Percentage = [tex]\frac{31}{39}*100[/tex]
Percentage = 79.48
On comparing,
82.35 > 79.48
Hence,
Rhion did better in maths test.
Sara went shopping. She bought six oranges at $0.25 each, two apples at $0.40 each, three plums at $0.18 each. She gave the cashier $5.00. How much change will Sara receive from the $5.00?
Answer:
$2.16
Step-by-step explanation:
Amount of change received
= $[5.00-0.25(6)-0.40(2)-0.18(3)]
= $(5.00-1.50-0.80-0.54)
= $2.16
PLEASE ANSWER I REALLY NEED HELP
Determine which of following points lie in the solution set of the inequality y >= 2x-4 and which do not. Justify each choice.
a) (5,4)
b) (0,1)
c) (10,16)
d) (2,-1)
The points lie on the given inequality y ≥ 2x-4 are (0,1) and (10,16)
What is inequality?A relationship between two expressions or values that are not equal to each other is called inequality.
Given that an inequality y ≥ 2x-4
We need to check whether the given points lie on the solution of the inequality or not,
1) (5, 4)
Put x = 5
2×5-4 = 10-4 = 6
4 ≥ 6, this is a contradiction which means (5, 4) do not lie on the solution,
2) (0, 1)
Put x = 0
2×0 - 4 = 0-4 = -4
1 ≥ -4, satisfying the condition hence lies on the solution.
3) (10, 16)
Put x = 10
2×10-4 = 20-4 = 16
16 = 16. satisfying the condition hence lies on the solution.
4) (2, -1)
Put x = 2,
2×2-4 = 4-4 = 0
-1 ≥ 0, this is a contradiction which means (5, 4) do not lie on the solution,
Hence, points lie in the solution set of the inequality are (0,1) and (10,16)
For more references on inequality, click;
https://brainly.com/question/28823603
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Which statements about the diagram are correct? Check all that apply.
BD = 9 in.
AB = 36 in.
DC = 6 StartRoot 3 EndRoot in.
AC = 12 StartRoot 3 EndRoot in.
BC = 18 StartRoot 3 EndRoot in.
Answer:
(C)DC = 6 StartRoot 3 EndRoot in.
(D)AC = 12 StartRoot 3 EndRoot in.
Step-by-step explanation:
What is the circumference of a circle with radius 2.1 cm? Use > (inserts wavey = sign) 3.14.
Step-by-step explanation:
The formula for the circumference of a circle is 2*pi*radius
Circumference = 2(3.14)(2.1)
= 13.188cm
the difference of a number t and 9
t-9 or 9-t
Need help on this asap please
Answer:
the second one
so B
Step-by-step explanation:
Answer:
3.15=315% is true
Step-by-step explanation:
The last one D is true
I hope this helps. Best of luck
HELP!! Mr. Posey is buying a baseball bat that normally cost $160. It is now on sale for 24% off. If sales tax is 10%, how much will he pay for the baseball bat?
Answer:
he will pay $133.10
Step-by-step explanation:
what is thirty five percent
Answer:
i dont know what you need 35% as but..
Step-by-step explanation:
Decimal : 0.35
Fraction: 7/20
6. Create an equation and solve for n.
5n - 11
Answer:
11-n=5
Step-by-step explanation:
A coin has heads on one side and tails on the other. The coin is tossed 50 times and lands
heads up 19 times. How does this frequency compare to the expected frequency based on
the probability of the coin landing with heads up?
Answer: A “The Frequency is 31 lower than expected.”
Step-by-step explanation:
The frequency is 12 fewer than expected.
What is relative frequency?Relative frequency or experimental probability is calculated from the number of times an event happens, divided by the total number of trials in an actual experiment.
The experimental relative frequency at which the coin lands heads up is [tex]\frac{19}{50}[/tex] or 0.38.
If the coin were a fair one, we would expect that it had heads up 25 out of 50 times, which would be a relative frequency of 0.50.
Since this is not happening, we conclude that the coin is NOT a fair one.
Expected frequency = 0.50
Experimental relative frequency = 0.38
= 0.50 - 0.38
= 0.12 or 12 %
Hence, the frequency is 12 fewer than expected.
Find out more information about relative frequency in probability here
https://brainly.com/question/16722133
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Which expression is NOT equivalent to 2.89 × 0.6?
(289 × 6) × (110 × 110)
(0.289 × 6) × (10 × 110)
(289 × 6) × (1100 × 110)
(289 × 60) × (1100 × 1100)
Answer:
(289x6)x(110x110)
Step-by-step explanation:
A computer software company models its profit with the function P(x) = -x2 + 15x – 34 where x is the number of games, in hundreds, that the company sells and P(x) is the profit, in thousands of dollars. How many games must the company sell to get $16,000 in profit?
Step-by-step explanation:
A computer software company models its profit with the function :
[tex]P(x) = x^2 + 15x -34[/tex] ....(1)
Where
x is the number of games, in hundreds, that the company sells and P(x) is the profit, in thousands of dollars.
We need to find the number of games the company sell to get $16,000 in profit.
Put P(x) = 16,000 in equation (1).
[tex]x^2 + 15x -34=16000\\\\x^2+15x-34-16000=0\\\\x^2+15x-34-16000=0\\\\x^2+15x-16034=0[/tex]
Using quadratic formula with a=1, b=15, c=-16034.
[tex]x=\frac{-15+\sqrt{15^{2}-4\left(1\right)\left(-16034\right)}}{2\left(-1\right)}, \frac{-15-\sqrt{15^{2}-4\left(1\right)\left(-16034\right)}}{2\left(-1\right)}\\\\=-119.34, 134.34[/tex]
Neglecting negative value,
No of games = 134 (approx)
The midtown middle school cheerleaders earned $175 at a car wash. If this amount is 25% of the cost of a new set of uniforms, what is the total cost for a set of uniforms?
Answer:
700
Step-by-step explanation:
multiple 175 × 4 to get to 100%
A 2-D shape has a length of 8cm and a width of 3cm. Find the perimeter and the area.
With steps please.
Answer:
Area formula: l x w
= 8 x 3
24 cm^2
Perimeter formula: Sum of all sides
= 8+8+3+3
= 25 cm
Answer: 24cm
Step-by-step explanation:
8 multiplied by 3
BlacIf w = -2 and v = -8, which of the following expressions shows the values correctly substituted in for the variables in the expression w2 - v + 1?
(-2) 2 - (-8) + 1
(-2) 2 - (8) + 1
-2 2 - (-8) + 1
-2 2 - 8 + 1
Answer:
-2² - (-8) + 1
Step-by-step explanation:
The values given are:
w = -2 and v = -8
Expression given:
w² - v + 1
When we substitute, we put a certain value in place of another. In an equation, variables are used as placeholders.
For this problem:
w = -2
v = -8
So;
-2² - (-8) + 1
Answer:
Given that w=-2 and v=-8
The expression is w²-v+1
Now putting the value of w=-2 and v=+8 in the given expression, we get
(-2)²-(-8)+1
Hence, (-2)²-(-8)+1 is the right answer.
what is 4.8 × d = 1.2
Answer:
0.25
Step-by-step explanation:
1.2 divide by 4.8=0.25
0.25*4.8=1.2
5 = .25
4.8 x .25 = 1.2
ASAP pls pls pls pls pls pls
Answer:
D is the answer.
[tex]16x {}^{2} - 81 = 0 \\ (4x - 9) \times (4x + 9) = 0 \\ [/tex]
[tex]4x - 9 = 0 \\ 4x = 9 \\ x = \frac{9}{4} \\ or \\ 4x + 9 = 0 \\ 4x = - 9 \\ x = - \frac{9}{4} [/tex]
Cydni is working with some algebra tiles at her desk. She makes groups of tiles like the ones below. Which expressions represent the sum of the tiles that Cydni has arranged on her desk? help
Answer:
3x+9
Step-by-step explanation:
If it’s multiple choice the other one is
x +1+1+1+x +1+1+1+ x +1+1+1
I hope this helps!
Select the correct answer.
You're given three angle measurements of 30°, 70°, and 80°.
How many triangles can you construct using these measurements?
A. 0
B. 1
C. 2
D. Infinitely many
Answer:
The answer is not 1 or 0
I think its D. infinitely many
Step-by-step explanation:
Solve for x.
And solve for Z
From Tales theorem: [tex]\dfrac{8x-2}{2x+1}=\dfrac{3z+z+22}{3z}[/tex]
Solving for x:[tex]\dfrac{8x-2}{2x+1}=\dfrac{4z+22}{3z}\\\\(8x-2)(3z)=(2x+1)(4z+22)\qquad\qquad\{divide\ both\ sides\ by\ 2\}\\\\(4x-1)(3z)=(2x+1)(2z+11)\\\\12xz-3z=2x(2z+11)+1(2z+11)\\\\12xz-2x(2z+11)=3z+2z+11\\\\x(12z-4z-22)=5z+11\\\\x(8z-22)=5z+11\qquad\qquad\{divide\ both\ sides\ by\ (8z-22)\}\\\\x=\dfrac{5z+11}{8z-22}[/tex]
Solving for z:[tex]\dfrac{8x-2}{2x+1}=\dfrac{4z+22}{3z}\\\\(8x-2)(3z)=(2x+1)(4z+22)\qquad\qquad\{divide\ both\ sides\ by\ 2\}\\\\(4x-1)(3z)=(2x+1)(2z+11)\\\\(12x-3)(z)=(2x+1)(2z)+(2x+1)(1)\\\\(12x-3)(z)-(4x+2)(z)=(2x+1)\\\\\ [(12x-3)-(4x+2)](z)=(2x+1)\\\\(12x-3-4x-2)(z)=(2x+1)\\\\(8x-5)(z)=(2x+1)\qquad\qquad\{divide\ both\ sides\ by\ (8x-5)\}\\\\z=\dfrac{2x+1}{8x-5}[/tex]
Giving 40 points
Solve each system by substitution
Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}} : [/tex]
-4x - y = 19 -------- Equation ( i ) x - 2y = -7 ----------- Equation ( ii )[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
Value of x & y[tex] \underline {\underline{ \text{ Solution}}} : [/tex]
From equation ( i ) :
-4x - y = 19
-y = 19 + 4x
-y = - ( -19 - 4x )
y = -4x - 19 ------ Equation ( iii )
Substituting the value of y from equation ( iii ) in equation ( ii ) , we get :
[tex] \tt{x - 2y = - 7 }[/tex]
⇾ [tex] \tt{x - 2( - 4x - 19) = - 7}[/tex]
⇾ [tex] \tt{x + 8x + 38 = - 7}[/tex]
⇾ [tex] \tt{9x = - 7 - 38}[/tex]
⇾ [tex] \tt{9x = - 45}[/tex]
⇾ [tex] \tt{x = \frac{ - 45}{9}} [/tex]
⇾ [tex] \boxed{ \tt{x = - 5}}[/tex]
Substituting the value of x in equation ( i ) , we get :
⇾ [tex] \tt{ - 5 - 2y = - 7}[/tex]
⇾ [tex] \tt{ - 2y = - 7 + 5}[/tex]
⇾ [tex] \tt{ - 2y = - 2}[/tex]
⇾ [tex] \tt{y = \frac{ - 2}{ - 2}} [/tex]
⇾ [tex] \boxed{ \tt{y = 1}}[/tex]
The possible solution of the system is ordered pair ( x , y ) = ( -5 , 1 ) .
[tex] \red{ \boxed{ \boxed { \tt{Our \: final \: answer : \boxed{ \tt{( - 5 \:, 1 \: )}}}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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MARKING BRAINLIST!!! In a couplet one statement is _____ and one is ______
A. Agreeing and rejecting
B. Deciding and Acting
C. Informing and Agreeing
A cat chased after a dog for l mile, and then stop to rest. As soon as the cat sotped,the dog chased after the cat for 1500 yard back towards their starting point. How many yards were the ainmals for her starting point?
Answer:
0.14768 mile
Step-by-step explanation:
Given that:
Distance at which cat chased dog = 1 mile ; hence they've moved 1 mile from their starting position
Distance for. Which dog chased cat =. 1500 yards towards starting position
Converting miles to yards
1 mile = 1760 yards
1 yard = 0.000568 mile
Number of miles the animals are from Their starting position :
1760 yards - 1500 yards = 260 yards
260 * 0.000568 = 0.14768 mile