the diagram shows an artificial lake. When Amanda jogged twice around the lake she jogged a distance of 2,700 meters. Find the value of x
Answers
[tex]2 \div 2700[/tex]
Assuming that the attached file is the lake which you are mentioning in the question.
The perimeter is the distance around the lake, we need to set up an equation based on the statement "When Amanda jogged twice around the lake she jogged a distance of 2,700 meters" as below:
[tex] 2(Perimeter \; of\; the\; lake) =2700\\ \\ 2(x+140+x+x+250+x+x+3x)=2700\\ Group \; Like\; Terms\\ \\ 2(x+x+x+x+x+3x+140+250)=2700\\ Combine \; Like\; Terms\\ \\ 2(8x+390)=2700\\ Distribute\; 2\; in\; left\; side\; of\; the\; equation\\ \\ 16x+780=2700\\ Subtract \; 780\; on\; both\; sides\\ \\ 16x+780-780=2700-780\\ Combine \; like\; terms\\\\16x=1920 \\ Divide\; 16 \; on\; both\; sides\\ \\ \frac{16x}{16}=\frac{1920}{16}\\ Simplify\; fraction\; on\; both\; sides\\ \\ x=120 [/tex]
Conclusion:
The value of x is 120 meters
Related Questions
Convert 64°F to °C (to the nearest tenth) using one of the following formulas: Fahrenheit to Celsius Celsius to Fahrenheit °C = (°F - 32) × °F = × °C + 32.
HELP!
a. 17.8°
b. 54.2°
c. 72.0°
d. 161.6°
Answers
The answer is 17.8° C
Step-by-step explanation:In order to Convert Fahrenheit to centigrade scale we use the formula
°C = (°F - 32) × 5/9
So putting the values in the equation we get
(64°F − 32) × 5/9 = 17.778°C
Determine if the columns of the matrix form a linearly independent set. justify your answer. left bracket start 4 by 3 matrix 1st row 1st column negative 2 2nd column negative 1 3rd column 0 2nd row 1st column 0 2nd column negative 1 3rd column 3 3rd row 1st column 1 2nd column 1 3rd column negative 6 4st row 1st column 2 2nd column 1 3rd column negative 12 endmatrix right bracket −2 −1 0 0 −1 3 1 1 −6 2 1 −12
Answers
[tex] A= \left[\begin{array}{ccc}-2&-1&0\\0&1&3\\1&1&6\\2&1&-12\end{array}\right][/tex]
then here is an outline of how to determine whether the columns form a linearly independent set.
On a standardized exam for high school seniors in 2013, the mean scale for the mathematics portion of the exam was 514 and the standard deviation was 118. If the scores for this exam are approximately normally distributed, what percent of students taking the exam received a scale score between 396 and 632? Express your answer as a whole percent.
Answers
First we need to convert the scores 396 and 632 in z scores.
Mean scores = 514
Standard deviation = 118
396 converted to z score will be:
[tex]\frac{396-514}{118} =-1[/tex]
632 converted to z score will be:
[tex] \frac{632-514}{114} =1[/tex]
Using the z-table, we are to find the percentage of scores that is between -1 and 1. The value comes to be 0.68 or 68%
So, expressed to nearest whole percent, 68% of students received score between 396 and 632.
A patio has the shape of the quadrilateral drawn in the picture below.
1) Find the area of the patio.
2) What is the minimum number of square-tiles with sides of 30 cm that are needed to cover the patio if 10% more tiles will be needed to cover the non-rectangular shape of the patio?
Answers
To find the area of ΔACE, we must first find the length of segment AE. To do this, we will need to know both EC, which we are given, and AC, which we are not. We will use the Pythagorean theorem for ΔADC to find the length of AC.
6²+(4.5)²=(AC)²
36+20.25=(AC)²
56.25=(AC)²
√56.25=√(AC)²
7.5=AC
Now that we know the length of AC, we will use the Pythagorean theorem on ΔACE to find the length of AE:
7²+(AE)²=(7.5)²
49+(AE)²=56.25
49+(AE)²-49=56.25-49
(AE)²=7.25
√(AE)²=√7.25
AE≈2.69
Now we can find the area of ΔACE: A=1/2(7)(2.69)=9.415m²
To find the area of ΔBCE, we need to find the length of EB. We know that AB=9 and AE=2.69. Subtracting those two, we find the length of EB to be 6.31m. Therefore the area of ΔBCE=1/2(6.31)(7)=22.085m²
The total area is given by adding these three together:
13.5+9.415+22.985=45m².
It would take 15 rows of 20 tiles each to cover the rectangular portion of this patio (4.5m*100 =450cm; 450cm/30-cm tiles = 15 rows of tiles; 6m*100=600cm; 600cm/30-cm tiles = 20 tiles per row) which comes out to 300 tiles. However, adding an extra 10% to that:
300*0.1+300=30+300=330 tiles.
The line segments AC and CE break this quadrilateral into three triangles. The area of a triangle is given by A=1/2bh. The base of ΔADC is 6 and the height is 4.5; A=1/2(6)(4.5)=13.5m².
To find the area of ΔACE, we must first find the length of segment AE. To do this, we will need to know both EC, which we are given, and AC, which we are not. We will use the Pythagorean theorem for ΔADC to find the length of AC.
6²+(4.5)²=(AC)²
36+20.25=(AC)²
56.25=(AC)²
√56.25=√(AC)²
7.5=AC
Now that we know the length of AC, we will use the Pythagorean theorem on ΔACE to find the length of AE:
7²+(AE)²=(7.5)²
49+(AE)²=56.25
49+(AE)²-49=56.25-49
(AE)²=7.25
√(AE)²=√7.25
AE≈2.69
Now we can find the area of ΔACE: A=1/2(7)(2.69)=9.415m²
To find the area of ΔBCE, we need to find the length of EB. We know that AB=9 and AE=2.69. Subtracting those two, we find the length of EB to be 6.31m. Therefore the area of ΔBCE=1/2(6.31)(7)=22.085m²
The total area is given by adding these three together:
13.5+9.415+22.985=45m².
It would take 15 rows of 20 tiles each to cover the rectangular portion of this patio (4.5m*100 =450cm; 450cm/30-cm tiles = 15 rows of tiles; 6m*100=600cm; 600cm/30-cm tiles = 20 tiles per row) which comes out to 300 tiles. However, adding an extra 10% to that:
300*0.1+300=30+300=330 tiles.
If n = 10 and p = 0.70, then the standard deviation of the binomial distribution is
Answers
[tex]\sigma^2=npq=np(1-p)=10*0.7*0.3=2.1 [/tex]
[tex]\sigma=standard\,deviation=\sqrt{2.1}=1.449[/tex] (to 3 decimal places)
The standard deviation for the given binomial distribution is 1.449.
What is binomial distribution?A binomial random variable is the number of successes x in n repeated trials of a binomial experiment. The probability distribution of a binomial random variable is called a binomial distribution.
Formula for the calculation of standard deviationσ = [tex]\sqrt{nP(1 -P)}[/tex]
where,
σ is the standard deviation
n is the number of trials in the binomial experiment.
P is the probability of success on an individual.
According to the given question we have,
The number of trials in the binomial experiment, n = 10
The probability of success on an individual, p = 0.70
Therefore, the standard deviation is given by
σ = [tex]\sqrt{10(0.70)(1 -0.70)} = \sqrt{7(0.3)}=\sqrt{2.1} =1.449[/tex]
Hence, the standard deviation for the given binomial distribution is 1.449.
Learn more about the binomial distribution here:
https://brainly.com/question/14565246
#SPJ2
Find percentage of each quantity. 40% of an hour
Answers
Hope this help!
Answer:
2/5 of an hour and 24 min
Step-by-step explanation:
Minutes:
Turn the percent into a fraction to get 40/100Once you get 40/100 simplify to get 2/5After getting 2/5 multiply that with 60 (or make 60 into a fraction of 60/1) to get 120/5Again simplify the fraction 120/5 to get 24.Hours:
*Very easy*
Go back to step 3 for the minutes, and you will have your answer of 2/5 hours.I hoped I helped you :)
In triangle ABC, <A is a right angle, and m<B = 45°.
What is the length of BC? If your answer is not an integer, leave it in simplest radical form.
A. 14[tex] \sqrt{2} [/tex] ft
B. 28 ft
C. 14 [tex]\sqrt{3} [/tex] ft
D. 14 ft
Answers
Sin(α)=opposite leg/hypotenuse
The opposite leg is14 ft.
The hypotenuse is BC.
The Angle "α" is 45°.
2. Let's substitute in the formula:
Sin(α)=opposite leg/hypotenuse
Sin(45°)=14/BC
3. When we clear BC, we obtain:
BCxSin(45°)=14
BC=14/Sin(45°)
4. Then, the result is:
BC= 14√2 ft
5. What is the length of BC?
The answer is: The length of BC is 14√2 ft
Winners of the georgia lotto drawing are given the choice of receiving the winning amount divided equally over 2222 years or as a lump-sum cash option amount. the cash option amount is determined by discounting the annual winning payment at 44% over 2222 years. this week the lottery is worth $33 million to a single winner. what would the cash option payout be?
Answers
To calculate the cash option payout, we need to discount the annual payment at a rate of 44% over 2222 years using the present value formula. The cash option payout would be approximately $2,938,624.13.
Explanation:To determine the cash option payout, we need to calculate the present value of the annuity. The annual payment is the total amount of the lottery prize divided by the number of years, which is $33 million / 2222 = $14,808.81. To discount this amount at a rate of 44% over 2222 years, we can use the formula:
PV = Payment / ((1 + r)^n - 1) * (1 - (1 / (1 + r))^n)
where PV is the present value, Payment is the annual payment, r is the discount rate (0.44), and n is the number of years (2222). Plugging in the values, we get:
PV = $14,808.81 / ((1 + 0.44)^2222 - 1) * (1 - (1 / (1 + 0.44))^2222)
Solving this equation gives us the cash option payout, which is approximately $2,938,624.13.
A paperweight in the shape of a rectangular pyramid is shown:If a cross section of the paperweight is cut perpendicular to the base and passes through the top vertex,which shape describes the cross section
Answers
A triangle has 3 vertices. In this case one vertex will be located at the same position as is the vertex of the pyramid. The other two vertex will be located on the sides of the rectangular base of the pyramid.
None of the angle will be a Right Angle so the triangle will be an Oblique Triangle. To determine if the triangle is equilateral, isosceles or scalene we need to know the side lengths of the pyramid.
Answer:
The correct answer is a triangle will be formed.
Step-by-step explanation:
If a cross section of the paperweight is cut perpendicular to the base and passes through the top vertex, the resulting figure will have 3 sides or vertices. Hence, this shape will be a triangle. The triangle only forms if it does pass through the top vertex.
So, triangle is the answer.
its cost $75.00 dollars to rent the laser tag center ,plus 11.50 per person what will be the total cost to rent the laser tag center for 15 people
Answers
$75 + $11.5 * 15 =
$75 + $172.5 =
$247.5
Answer:
gjilohiklhjkl
Step-by-step explanation:
A young company expects to double their profits every year for the next ten years. If their profits were $5,000 this year, which expression represents their profits after ten years?
a) 5,000 × 2 × 10
b) 5,000 × 210
c) 5,0002 × 10
d) 5,00010
Answers
At a florist's shop two assistants made 13 flower arrangements in a certain amount of time. Assuming all assistants will work for the same amount of time and each assistant is trained to work at the same rate, how many assistants are needed to make: 195 arrangements
Answers
Number of assistants required to make 13 flower arrangements = 2
Let us use unitary method here.
Number of assistants required to make 1 flower arrangements = 2/13
Number of assistants required to make 195 flower arrangements = 2/13 *195 =30
Answer : So 30 assistants are required to make 195 flower arrangements.
Will give Brainliest Answer/ 5 stars for correct answer
Let u = <6, -9>, v = <1, -4>. Find u - v.
A) <5, -5>
B) <10, -10>
C) <15, 5>
D) <7, -13>
Answers
u - v = <6 - 1, -9 - (-4)> = <5, -5> . . . . . . . matches selection A)
_____
The sum or difference of vectors is simply the sum or difference of corresponding coordinates.
An asteroid has hit the Earth and created a huge crater. Engineers and scientists hove measured around the crater to be 79.5 miles. How much of the surfoce of the Earth hos been effected by the crater impact?
Answers
[tex]C= 2\pi r [/tex]
Plug in values
79.5=2*(3.14)r
Multiply 2 and 3.14
79.5 = 6.28r
Divide both sides by 6.28
r approximately 12.66 miles
Area of a circle
[tex]A= \pi r^2 [/tex]
Plug in values
A=(3.14)*12.66^2
Area = approximately 503.27 Sq Miles
To determine the affected area by an asteroid impact, calculate the radius from the circumference of the crater and then the area of the circle. The estimated crater area from a 79.5-mile circumference is approximately 506.7 square miles, indicating the surface area affected.
Explanation:To estimate how much of the Earth's surface has been affected by the asteroid impact that resulted in a crater with a measured circumference of 79.5 miles, we need to recognize that this measurement refers to the circumference of a circle (the crater). We use the circumference to find the radius of that circle, and then calculate the area of the circle to understand the extent of the impact.
First, we calculate the radius (r) of the crater using the circumference (C): C = 2πr. Plugging in the known circumference, r = C / (2π), so r = 79.5 miles / (2 × 3.14), which approximates to 12.7 miles. Moving forward, we can now find the area (A) of the crater using A = πr². Squaring the radius gives us [tex](12.7)^2[/tex] and then multiplying by π gives us approximately 506.7 square miles.
The actual crater area accounting for the circular shape is approximately 506.7 square miles, which roughly indicates the immediate surface area affected by the impact. It's noteworthy that the surrounding ecosystem and earth's surface may also experience indirect effects extending beyond this area.
In August cory begins school shopping for his triplet daughters. one day he bought 10 pairs of socks for $2.50 each and 3 pairs of socks for d dollars each. He spent a total of 135.97 write and solve an equation to find the cost of one pair of shoes
Answers
$25 + 3d = $135.97
-$25 -$25
_________________
3d = $110.97
___. _______
3. 3
_________________
d= $36.99
G find z such that 9.0% of the standard normal curve lies to the right of z. (round your answer to two decimal places.)
Answers
if 5ml=1 tsp, how many teaspoons are in 85ml
Answers
Fran made 8 cups of potato soup in a big pot, then served 4 bowls of soup to her family. each bowl holds 6 fluid ounces. how much soup was left in the pot
Answers
4 cups
According to the Bureau of Labor Statistics, in May 2014 the mean hourly wage of a social worker was $28.08 with a standard deviation of $1.97. Jeronica is a social worker with an hourly wage of $31.60. What is Jeronica’s z-score? (Round your answer to TWO decimal places.)
Answers
Explanation:
Let x = hourly wage for a social worker. Then, the z-score for x is given by
[tex]\text{z - score} = \frac{x - \mu}{\sigma} [/tex]
where
[tex]\mu = \text{ mean hourly wage of a social worker }= \$ 28.08 \\ \sigma = \text{ standard deviation of the wage of the social worker }= \$ 1.97[/tex]
Since Jeronica's salary is $31.60, the z-score of Jeronica's is given by
[tex]\text{z - score} = \frac{x - \mu}{\sigma} \\ \\ \text{z - score} = \frac{31.60 - 28.08}{1.97} \\ \\ \boxed{\text{z - score} = 1.79}[/tex]
1/2(18+14)-(18-14)power of 2
Answers
(18 + 14)/2 - (18 - 14)^2
| 1 | 8
- | 1 | 4
| 0 | 4:
(18 + 14)/2 - 4^2
| 1 |
| 1 | 8
+ | 1 | 4
| 3 | 2:
32/2 - 4^2
The gcd of 32 and 2 is 2, so 32/2 = (2×16)/(2×1) = 2/2×16 = 16:
16 - 4^2
4^2 = 16:
16 - 16
16 - 16 = 0:
Answer: 0
Final answer:
The given mathematical expression simplifies to 0, after performing the necessary arithmetic operations and applying the correct order of operations, including parentheses and exponents.
Explanation:
The question involves simplifying a mathematical expression with both arithmetic operations and exponentiation. To solve the expression [tex](1/2(18+14)-(18-14))^2[/tex] , you first perform the operations inside the parentheses, then multiply by 1/2 (which is the same as dividing by 2), and finally subtract the square of the difference between 18 and 14.
Calculate the sum inside the first set of parentheses: 18 + 14 = 32.Multiply this sum by 1/2: 1/2 × 32 = 16.Calculate the difference inside the second set of parentheses: 18 - 14 = 4.Square this difference: [tex]4^2[/tex] = 16.Subtract the squared difference from the first result: 16 - 16 = 0.Therefore, the solution to the expression is 0.
There is only one granola bar left out of a pan of 10 bars. if Will and Rachel decide to split the last granola bar what fraction of the entire pan of granola bars will each friend receive?
Answers
QUICKK EXPERTS/ACE/GENIUSES
Answers
x^2+1/2x+1/16=4/9 Factor the perfect-square trinomial on the left side of the equation. (x + )² = 4/9
Answers
Check:
(x+1/4)^2=x^2+2*(1/4)x+(1/4)^2=x^2+x/2+1/16. ok
Answer: x= 1/4
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
we have
[tex]x^{2} +\frac{1}{2}x+\frac{1}{16}=\frac{4}{9}[/tex]
we know that
[tex](x+a)^{2}=x^{2}+2ax+a^{2}[/tex]
in this problem
[tex]2ax=\frac{1}{2}x[/tex] ------> [tex]a=\frac{1}{4}[/tex]
[tex]a^{2}=\frac{1}{16}[/tex] -----> [tex]a=\frac{1}{4}[/tex]
so
[tex]x^{2} +\frac{1}{2}x+\frac{1}{16}=(x+\frac{1}{4})^{2}[/tex]
the missing number in the left side is [tex]\frac{1}{4}[/tex]
passes thru ( 7, -5) and has m=0
Answers
hope this helps
Pierre's parents ordered some pizzas for a party. 4.5 pizzas were eaten at the party. There were at least 5 1/2 whole pizzas left over. How many pizzas did pierre's parents order?
Answers
5 1/2= 5.5
Since 4.5 was eaten but there is 5.5 left, that shows what happen with the total amount of pizzas. So by just adding them, you can find how much pizzas are there in total.
5.5+4.5=
9+1=
10
There were 10 pizzas ordered by Pierre's parents.
How do you solve this problem
Answers
A radar gun used to determine the speed of passing cars must be within 7 mph of the actual speed of a selected car. If a highway patrol officer reads a speed of 59 mph for a car, does he have irrefutable evidence that the car was speeding in a 55 mph zone?
Answers
Then we have that:
59 mph - 7 mph = 52 mph approximately.
52mph <55mph
Answer:
He does not have irrefutable evidence that the car was speeding in a 55 mph zone
Which is the measure of AB? 10 feet 15 feet 20 feet 100 feet
Answers
The common stock of the downtowne should return 23 percent in a boom, 16 percent in a normal economy, and lose 32 percent in a recession. the probabilities of a boom, normal economy, and recession are 5 percent, 90 percent, and 5 percent, respectively. what is the variance of the returns on this stock?
a..012453
b..012914
c..011345
d..011663
e..012691
Answers
Jj sell tablets at a store. He earns $180 a week plus$15 for ever tablet he sells. Jj earns $315 last week. Write a equation that can be used to determine the number of computers Jj sold last week. how many was sold
Answers
so what we need to do is subtract his flat rate(180) from his total(315)
315
-180
____
135 So now we know how much money Jj has earned from selling tablets. But we still need to create an equation and find out how many he has sold.
So we know he get $15 per tablet so 135÷15=9
now we know he has sold 9 tablets
Bu what is our Equation?
well, what were the steps?
TP = total pay
FR= Flat rate
C= Computer profit
PPC= price per computer
#C = number of computers
#C = TP-FR=C C÷PPC=#C
can we simplify this further?
#C = C÷PPC
lets do this:
#C= x
C= y
PPC= z
So: (X = Y÷Z)
Answer:
so Jj earns a flat rate of 180 per week and an extra 15 per tablet he has sold
so what we need to do is subtract his flat rate(180) from his total(315)
315
-180
____
135 So now we know how much money Jj has earned from selling tablets. But we still need to create an equation and find out how many he has sold.
So we know he get $15 per tablet so 135÷15=9
now we know he has sold 9 tablets
Bu what is our Equation?
well, what were the steps?
TP = total pay
FR= Flat rate
C= Computer profit
PPC= price per computer
#C = number of computers
#C = TP-FR=C C÷PPC=#C
can we simplify this further?
#C = C÷PPC
lets do this:
#C= x
C= y
PPC= z
So: (X = Y÷Z)
Step-by-step explanation: