A Ferris wheel 50ft in diameter makes one revolution every 40sec. If the center of the wheel is 30ft above the ground, how long after reaching the low point is a rider 50ft above the ground?
Answers
Answer:
The rider is 15.91 seconds 50 ft above the ground after reaching the low point
Step-by-step explanation:
We can evaluate the angle α
using trigonometry applied to the orange small triangle with height 50-30 = 20 ft and hypotenuse equal to the radius r = 25ft
Now
[tex]20 = \frac{25}{sin(\alpha)}[/tex]
[tex]\alpha = arcsin{\frac{20}{25}[/tex]
[tex]\alpha = 53.13^{\circ}[/tex]
So 50 ft of height corresponds to the total angle:
[tex]90^{\circ} =53.13^{\circ} = 143.13 6^{\circ}[/tex] = 2.498 radians
Now the angular velocity
[tex]\omega = \frac{2\pi}{T}[/tex]
[tex]\omega = \frac{2 \pi}{40}[/tex]
[tex]\omega =0.157rad/s[/tex]
To describe 2.498 rad it will take:
[tex]t = \frac{2.498}{0.157}[/tex]
t = 15.91 s
The rider reaches 50 feet above the ground approximately 4.09 seconds after reaching the lowest point.
To solve the problem of determining how long after reaching the low point a rider on the Ferris wheel is 50 feet above the ground, we can follow these steps:
Step 1: Define the parameters
Diameter of the Ferris wheel: 50 feet.
Radius of the Ferris wheel: [tex]\( r = \frac{50}{2} = 25 \)[/tex] feet.
Center of the wheel height: 30 feet above the ground.
Rotation period: 40 seconds per revolution.
Step 2: Establish the equation for the height of a rider
The vertical position ( h(t) ) of a rider at time ( t ) seconds can be modeled using the cosine function (assuming the lowest point at ( t = 0 ):
[tex]\[ h(t) = 30 + 25 \cos\left(\frac{2\pi t}{40}\right) \][/tex]
Step 3: Set the height equation to 50 feet
Since we want the height h(t) to be 50 feet:
[tex]\[ 50 = 30 + 25 \cos\left(\frac{2\pi t}{40}\right) \][/tex]
Step 4: Solve for the cosine term
[tex]\[ 50 = 30 + 25 \cos\left(\frac{2\pi t}{40}\right) \][/tex]
[tex]\[ 20 = 25 \cos\left(\frac{2\pi t}{40}\right) \][/tex]
[tex]\[ \cos\left(\frac{2\pi t}{40}\right) = \frac{20}{25} \][/tex]
[tex]\[ \cos\left(\frac{2\pi t}{40}\right) = 0.8 \][/tex]
Step 5: Determine the angle
[tex]\[ \frac{2\pi t}{40} = \cos^{-1}(0.8) \][/tex]
[tex]\[ \frac{2\pi t}{40} = 0.6435 \][/tex]
[tex]\[ t = \frac{0.6435 \times 40}{2\pi} \][/tex]
[tex]\[ t \approx 4.09 \text{ seconds} \][/tex]
Thus, the rider reaches 50 feet above the ground approximately 4.09 seconds after reaching the lowest point.
Related Questions
A 25-foot ladder rests against a building. The base of the ladder is 15 feet away from the base
of the building. At what height does the ladder rest on the building?
Answers
Answer: the top of the ladder is 20ft below the ground.
Step-by-step explanation:
The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.
The length of the ladder represents the hypotenuse of the right angle triangle.
The ground distance between the base of the house and the base of the ladder represents the adjacent side of the right angle triangle.
Therefore, to determine the height at which the ladder rest on the building, x, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
25² = x² + 15²
625 = x² + 225
x² = 625 - 225 = 400
x = √400 = 20 ft
A cell phone company charges a monthly fee plus $.25 for each text message. The monthly fee is $30 and you owe $59.50. How many text messages do you have?
Answers
Answer: you have 118 text messages.
Step-by-step explanation:
Let x represent the number of text messages that you have or sent.
A cell phone company charges a monthly fee plus $.25 for each text message. The monthly fee is $30. This means that the total cost of x sending x messages in a month would be
0.25x + 30
If you owe $59.50, then your total cost is $59.50
Therefore,
59.50 = 0.25x + 30
0.25x = 59.50 - 30
0.25x = 29.5
x = 29.5/0.25
x = 118
x2 - 2x - 24 = 0
Solve for X
Answers
Answer:
x = 6 or x = -4
Step-by-step explanation:
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x - 6 =0 or x + 4 = 0
x = 6 or x = -4
if 12, 15, 18 and 16, 20, and x are the lengths of the corresponding sides of two similar triangles, what is the value of x?
Answers
To find the value of x for the corresponding sides of two similar triangles, we set up a proportion using the given sides.
Upon simplifying the ratio, x is calculated to be 24, which is the side length in the second triangle.
Explanation:To find the value of x in two similar triangles with side lengths 12, 15, 18 and 16, 20, x, we use the concept that corresponding sides in similar triangles have proportional lengths.
We start by setting up a proportion using the corresponding sides:
[tex]\(\frac{12}{16} = \frac{15}{20} = \frac{18}{x}\)[/tex]
We can simplify the first two ratios to find a single scale factor:
[tex]\(\frac{12}{16} = \frac{15}{20} \rightarrow \frac{3}{4} = \frac{3}{4}\)[/tex]
This confirms the triangles are indeed similar since the ratios are equal. We then use the third ratio to solve for x:
[tex]\(\frac{18}{x} = \frac{3}{4} \rightarrow x = \frac{4}{3} \cdot 18 = 24\)[/tex]
Therefore, the value of x is 24, which is the length of the corresponding side in the second triangle.
Levi wants to order the fractions 1/3, 2/5, and 11/30 in descending order? How can you help him by using a common denominator? Explain and order the fractions in descending order.
Answers
Answer:
The correct order of fractions in descending order will be:
[tex]\frac{2}{5}, \frac{11}{30}, \frac{1}{3}[/tex]
Step-by-step explanation:
Given fraction:
[tex]\frac{1}{3}, \frac{2}{5}, \frac{11}{30}[/tex]
To arrange them in descending order.
Solution:
In order to arrange the fractions in descending order, we will have to find the least common denominators.
To find the least common denominator, we will find the least common multiple of the denominators 3,5, and 30.
Since 30 is a common multiple of all 3 numbers, so it will be the least common denominator.
So, we multiply the numerators and denominators with same numbers in order to make the denominators = 30.
So, we have:
[tex]\frac{1}{3}, \frac{2}{5}, \frac{11}{30}[/tex]
⇒ [tex]\frac{1\times 10}{3\times 10}, \frac{2\times 6}{5\times 6}, \frac{11\times 1}{30\times 1}[/tex]
⇒ [tex]\frac{10}{30}, \frac{12}{30}, \frac{11}{30}[/tex]
Now, we compare the numerators and arrange them accordingly.
[tex]\frac{12}{30} > \frac{11}{30} > \frac{10}{30}[/tex]
So, the correct order of fractions in descending order will be:
[tex]\frac{2}{5}, \frac{11}{30}, \frac{1}{3}[/tex]
The combined height of one oak tree and one pine tree is 21 meters. The height of 4 oak trees stacked on top of each other is 24 meters taller than one pine tree. How tall is the oak tree and the pine tree
Answers
Answer:
Height of an oak tree= 9 meters
Height of a pine tree = 12 meters
Step-by-step explanation:
Given:
The combined height of 1 oak tree and 1 pine tree = 21 meters
Height of 4 oak trees = 24 meters more than 1 pine tree
To find the height of 1 pine tree and height of one oak tree.
Solution:
Let the height of one oak tree be = [tex]x[/tex] meters.
Let height of one pine tree = [tex]y[/tex] meters.
Combined height can be given as :
[tex]x+y=21[/tex]-------------[1]
Height of 4 oak trees = 24 meters more than 1 pine tree
The above statement can be given as :
[tex]4x=24+y[/tex]------------[2]
Rearranging equation [2] by subtracting both sides by [tex]y[/tex].
[tex]4x-y=24+y-y[/tex]
[tex]4x-y=24[/tex]-------------[2]
Adding rearranged equation [2] to [1].
[tex]x+y=21[/tex]
[tex]4x-y=24[/tex]
+--------------------
[tex]5x\ = 45[/tex]
Dividing both sides by 5.
[tex]\frac{5x}{5}=\frac{45}{5}[/tex]
∴ [tex]x=9[/tex]
Plugging in [tex]x=9[/tex] in equation [1]
[tex]9+y=21[/tex]
Subtracting both sides by 9.
[tex]9-9+y=21-9\\\therefore y=12[/tex]
Height of an oak tree= 9 meters
Height of a pine tree = 12 meters
Select the perfect square trinomial for each polynomial. (There are 2 correct answers)
Question 1 options:
x^2−10x−25
x^2−18x+81
x^2+2x+1
x^2+7x+49
Answers
Answer:
x^2−18x+81
x^2+2x+1
Step-by-step explanation:
we know that
A trinomial is a perfect square trinomial if it can be factored into a binomial multiplied to itself
so
[tex]a^2\pm2ab+b^2=(a\pm b)(a\pm b)=(a\pm b)^2[/tex]
Verify each case
case a) x^2−10x−25
we know that
[tex](x-5)^2=x^2-10x+25[/tex]
therefore
Is not a perfect square trinomial
case b) x^2−18x+81
we know that
[tex](x-9)^2=x^2-18x+81[/tex]
therefore
Is a perfect square trinomial
case c) x^2+2x+1
we know that
[tex](x+1)^2=x^2+2x+1[/tex]
therefore
Is a perfect square trinomial
case d) x^2+7x+49
we know that
[tex](x+3.5)^2=x^2+7x+12.25[/tex]
therefore
Is not a perfect square trinomial
The recommended angle for a wheel chair ramp is 5 degrees. If the rise of the ramp to go up the steps is 2 feet, find the horizantal run length that the ramp must start. (Round to one decimal place)
wheel chair ramp
Answers
Answer:
22.9 feet
Step-by-step explanation:
You are using Tangent because you have the opposite and adjacent sides
Tan 5 = 2/x
x Tan 5= 2
x= 2/Tan5
= 22.860
To find the horizontal run length of a wheelchair ramp with a 5-degree angle and a 2-foot rise, use the tangent function of trigonometry. Plug the given values into the tangent formula, rearrange to solve for 'Run', and calculate to get a run length of approximately 22.8 feet.
Explanation:The question is referring to the use of trigonometry to solve real-life problems. Here, we are going to use the tangent of the angle, which is defined as the ratio of the opposite side (the rise) to the adjacent side (the run). In this case, we know that the angle is 5 degrees and the rise is 2 feet.
In mathematical terms, this can be written as:
Tan(ρ) = Rise/Run
Substituting the values into the equation, we get:
Tan(5°) = 2/Run
Solving for Run, we get:
Run = 2/Tan(5°)
You can find this value using a calculator, rounding to the nearest tenth, to get the run as approximately 22.8 feet.
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Susan and Jim each on a lawn care business the amount Susan charges for lawn care by the hour is shown in the table 2 hours $48.03 hours $72.07 hours $168.11 hours
Answers
Question is Incomplete;Complete question is given below;
Susan and Jim each own a lawn care business. The amount Susan charges for lawn care is shown in the table. The amount him charges for lawn care is shown in the table.
What is the DIFFERENCE between Susan's and Jim's lawn care business in the amounts they charge for 10 hours at work ?
Susan
2 hrs $48
3 hrs $72
7 hrs $ 168
11 hrs $264
Jim
1 hr $20
2 hrs $40
3 hrs $60
4 hrs $80
5 hrs $100
6 hrs $120
A) $16
B) $20
C) $28
D) $40
Answer:
D) $40
Step-by-step explanation:
We need to find the DIFFERENCE between Susan's and Jim's lawn care business in the amounts they charge for 10 hours at work.
Solution:
First we will find the hourly charges of lawn care for both.
Given:
From the table of Jim we can see that
Charges of Jim for 1 hour = $20
So for 10 hour = Charges of Jim for 10 hour.
By using Unitary method we get;
Charges of Jim for 10 hour = [tex]10\times 20 =\$200[/tex]
Now From table of Susan we can see that;
for 2 hours = $48
So for 1 hour = Charges of Susan for 1 hour.
By Using Unitary method we get;
Charges of Susan for 1 hour = [tex]\frac{48}{2}= \$24[/tex]
Now we know that;
Charges of Susan for 1 hour = $24
So for 10 hour = Charges of Susan for 10 hour
again by using Unitary method we get;
Charges of Susan for 10 hour = [tex]24\times10 =\$240[/tex]
Now we need to find the difference between their charges.
Difference can be calculated by subtracting Charges of Jim for 10 hour from Charges of Susan for 10 hour.
framing in equation form we get;
Difference = [tex]\$240-\$200=\$40[/tex]
Hence The difference in the charges for 10 hour of work is $40.
Match the following. 1 . congruent circles the set of all points in a plane that are at a given distance from a given point in the plane 2 . circle two or more circles that lie in the same plane and have the same center 3 . concentric circles circles that have equal radii 4 . diameter a chord of a circle that contains the center of the circle 5 . radius a segment joining the center of a circle to a point of the circle
Answers
Answer:
1 is concentric circles
2 is concentric circles, they have same center
3 is congruent circles, they have equal radii
4 is correct
5 is correct
Step-by-step explanation:
Congruent circles are circles of the same size while concentric circles are circles that have same center but different radii. Diameter is the line passing through the center of a circle joining two points on the circumference while radius is the joining the center of the circle to any point on the circumference.
For a project on Egypt, Nick is building a paper model of a square based pyramid. The square base measures 8 inches by 8 inches. The slant height is 10 inches. Which measurement BEST describes the amount of construction paper needed to make this pyramid? (round to nearest whole number)
Answers
Answer:
Step-by-step explanation:
The square base measures 8 inches by 8 inches. The slant height is 10 inches.
The formula for determining the area of the square base of the pyramid is l^2. Therefore,
Area of the base = 8^2 = 64 inches^2
The formula for determining the perimeter of the square base is
4l. It becomes
4 × 8 = 32 inches
The amount of construction paper needed to make this pyramid is the total surface area of the pyramid. Therefore,
Total surface area = (1/2 × 32 × 10) + 64
= 160 + 64 = 224 inches^2
Nick will need approximately 224 square inches of construction paper for his square based pyramid project with a base measuring 8 inches by 8 inches and a slant height of 10 inches.
Explanation:To find the amount of construction paper needed for Nick's square based pyramid project, we need to calculate the surface area of the pyramid. The surface area of a pyramid includes the area of the base plus the area of the four triangular sides.
The area of the base (Abase) is the side length squared:
Abase = side × side = 8 inches × 8 inches = 64 square inches.
The area of one triangular side (Atriangular side) is given by the formula:
Atriangular side = 1/2 × base × slant height.
For Nick's project, the base of a triangular side is equal to the side of the square, so:
Atriangular side = 1/2 × 8 inches × 10 inches = 40 square inches.
Since there are four identical triangular sides:
Total area of triangular sides = 4 × 40 square inches = 160 square inches.
Adding the base and triangular sides areas together gives us the total construction paper needed:
Total construction paper needed = Abase + Total area of triangular sides = 64 square inches + 160 square inches = 224 square inches.
Therefore, Nick will need approximately 224 square inches of construction paper for his project. To get the nearest whole number, we round 224 to 224.
You are asked to draw a triangle with side lengths of 8 inches and 10 inches. What is the longest whole number length that your third side can be? Group of answer choices 18 20 16 21
Answers
Answer:
Correct number : c = 16
Step-by-step explanation:
The triangle theorem states that each side of the triangle is smaller than the sum of the other two and larger than their difference. We denote the three sides of a triangle as a, b, and c.
Suppose that a = 8 and b = 10 and as we see b is greater than a , b > a
b - a < c < b + a => 10 - 8 < c < 10 + 8 => 2 < c < 18
from the offered answers we choose number 16
c = 16
God is with you!!!
Answer:
Step-by-step explanation:
if a,b,c are three sides of a triangle,then a<b+c,b<c+a,c<a+b
or in general we can say any side < sum of other two sides.
third side<8+10
or third side <18
Here third side=16
if you are asked smallest side then any side >difference of other two sides.
third side >10-8 or>2
Choose which statement is true.
Question 3 options:
The product of (2x−5)(x^2+3x−1)is 2x^3+11x^2+13x+5 because the following are like term pairs: 6x^2+5x^2 and −2x+15x
The product of (2x−5)(x^2+3x−1)is 2x^3−11x^2−17x+5 because the following are like term pairs: −6x^2−5x^2 and −2x−15x
The product of (2x−5)(x^2+3x−1)is 2x^3+11x^2−13x+5 because the following are like term pairs: 6x^2+5x^2 and 2x−15x
The product of (2x−5)(x^2+3x−1)is 2x^3+x^2−17x+5 because the following are like term pairs: 6x^2−5x^2 and −2x−15x
Answers
The correct statement is,
⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
To find the correct statement about the expression.
Now, We have;
The expression is,
⇒ (2x - 5) (x² + 3x - 1)
Hence, We can simplify as;
⇒ (2x - 5) (x² + 3x - 1)
⇒ (2x³ + 6x² - 2x - 5x² - 15x + 5
⇒ 2x³ + x² - 17x + 5
Thus., The correct statement is,
⇒ The product of (2x−5)(x²+3x−1) is 2x³+x²−17x+5 because the following are like term pairs: 6x²−5x² and −2x−15x.
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Zacarías and paz together have $756.80 if Zacarías has $489.50, how much does Paz have? Write and solve an addition equation to find how much money belongs to Paz.
Answers
ANSWER: Paz have $267.30
STEP BY STEP EXPLANATION
Let be Z for Zacarías and P for Pax
Z+P= 756.80
Z= 489.50
P=756.8 - Z
P=756.80 - 489.50
P= 267.30
Plan A is a flat rate of $50 per month unlimited data. Plan B is zero dollars per month but you pay five dollars per gigabyte of data used. If you average about 6 GB of data used per month, which option will be least expensive?
Answers
Answer:
B
Step-by-step explanation:
For Plan A ---> you pay $50 per month flat
For Plan B,
average usage = 6 GB
cost per GB = $5 per GB
average cost per month = $5 per GB x 6 GB = $30
comparing the cost per month between the 2, we can clearly see that for plan B, $30 a month is the least expensive option
Plan B would be the least expensive option for someone who uses about 6 GB of data per month, costing $30, compared to Plan A's flat rate of $50 per month. It is important to also consider other costs and usage patterns when selecting a phone data plan.
When finding the least expensive phone data plan between a flat rate plan and a pay-per-gigabyte plan, you need to calculate the total costs based on the average data usage. In this case, Plan A offers unlimited data for a flat rate of $50 per month, while Plan B charges $5 per gigabyte of data used, with no monthly base cost.
For an average use of 6 GB of data per month:
Plan A would cost $50 every month, regardless of how much data you use.
Plan B would be 6 GB x $5/GB = $30 per month.
Comparing the two plans, Plan B is the least expensive option for someone who uses about 6 GB of data each month, as it would cost $30 as opposed to the $50 charged by Plan A.
However, it's important to consider your personal usage patterns and other potential costs, such as monthly charges for other services, occasional charges for peripherals or repairs, and any relevant annual costs or major costs when choosing a plan that fits your budget effectively.
Four out of 12 pieces of fruit in the basket are apples.Select all the fractions below that are equivalent to the fraction of fruit that is apples. 3/6 1/3 2/6 1/4 1/6
Answers
Four out of twelve converts to the fraction
4/12
if both sides are divided by four, you can simplify this fraction to
1/3
therefore, a is correct
1/3 times two makes
2/6
therefore, c is correct
1/3 has no more multiples in this selection
The equivalent fraction are 1/3 and 2/6.
What is Fraction?The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.
How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned in the fraction's upper portion.
Given:
Four out of twelve converts to the fraction
= 4/12
Now, simplifying the fraction we get
= 4/12
= 1/3
Now, 3/6 = 1/2
2/6 = 1/3
Hence, the equivalent fraction are 1/3 and 2/6.
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Tiva earns $48 of 6 hours of babysitting. Complete each statement if Tiva keeps earning her babysitting money at this rate. For 8.5 hours of babysitting Tiva will earn? If Tiva babysits for Hours, she will earn $35.
Answers
Answer:
67
Step-by-step explanation:
48=6
35=8.5
67
Answer:
A.)$68
B.)$32
Step-by-step explanation:
For 8.5 hours of babysitting, Tiva will earn $ 68
If Tiva babysits for 4 hours, she will earn $32.
Find the distance between the pair of points given on the graph
Answers
Answer: distance = 5
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = 1
x1 = - 2
y2 = 0
y1 = - 4
Therefore,
Distance = √(1 - - 2)² + (0 - - 4)²
Distance = √3² + 4² = √9 + 16 = √25
Distance = 5
The length of Martin's driveway, rounded to the nearest foot, is 121 ft. What is the minimum possible length of the driveway? A 121.0 ft B 120.5 ft C 120.9 ft D 120.3 ft
Answers
Answer:
B. 120.5 ft
Step-by-step explanation:
Given:
Length of Martins drive way = 121 ft
We need to find the minimum possible length of the driveway
Solution:
Now we know that ;
When a number is rounded to nearest whole number.
We can say that the number is in decimal format.
Also rounding techniques applies when the decimal number has digit 5 or more in ten's place after decimal then the number in increase by 1 as a whole number.
Here the number is rounded to nearest foot which is 121 ft.
So we an say that;
Number ranging from 120.50 to 120.99 can be made to 121 as nearest foot.
Hence the minimum possible length of the drive way could be 120.5 ft
A truck can be ready for company a 420 dayPlus $.30 per mile can we be charges $50 a day plus $.50 per mile to rent the same truck find the number of miles in a day at which the rental costs for a company a and Company B same
Answers
Answer:it will take 1850 miles
Step-by-step explanation:
Let x represent the number of miles in a day at which the rental costs for a company A and Company B same.
Let y represent the total cost of renting the truck for x miles with company A.
Let z represent the total cost of renting the truck for x miles with company A.
Company A charges $420 a day Plus $.30 per mile. This means that
y = 420 + 0.3x
Company B charges $50 a day plus $.50 per mile to rent the same truck. This means that
z = 50 + 0.5x
To determine the number of miles in a day at which the rental costs for a company A and Company B same, we will equate y to z. It becomes
420 + 0.3x = 50 + 0.5x
0.5x - 0.3x = 420 - 50
0.2x = 370
x = 370/0.2 = 1850 miles
Alison bought jelly beans to share with her friends she bought 1 1/4 pounds of blueberry jelly beans and 2 1/3 pounds of Lemon Jelly Beans if she gave 1 and 2/3 pounds of jelly beans away to a friend how many pounds of jelly beans does she have left
Answers
After giving away 1 and 2/3 pounds of jelly beans, Alison has 4/3 pounds left.
Explanation:To find out how many pounds of jelly beans Alison has left after giving away 1 and 2/3 pounds, we need to subtract that amount from the total.
1 1/4 pounds + 2 1/3 pounds - 1 2/3 pounds = 2/4 + 7/3 - 5/3 = 8/12 + 28/12 - 20/12 = 16/12 = 4/3 pounds
Therefore, Alison has 4/3 pounds of jelly beans left.
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Perform the indicated operation. 5/8-[1/2-(-1/4)]
Answers
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]
Solution:
Given that, we have to perform the indicated operation
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})][/tex]
We can use BODMAS rule to perform the operation
According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right
So, in the given expression, we have to solve for brackets first
Solve the innermost bracket
[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}][/tex]
Now solve the bracket again
[tex]\frac{5}{8}-[\frac{1}{2}+\frac{1}{4}] = \frac{5}{8}-[\frac{4+2}{8}] = \frac{5}{8}-[\frac{6}{8}][/tex]
Now remove the parenthesis
[tex]\rightarrow \frac{5}{8} - \frac{6}{8}[/tex]
Now perform subtraction operation
[tex]\rightarrow \frac{5}{8} - \frac{6}{8} = \frac{5-6}{8} = \frac{-1}{8}[/tex]
Thus we got,
[tex]\frac{5}{8}-[\frac{1}{2}-(-\frac{1}{4})] = \frac{-1}{8}[/tex]
Thus the indicated operation is performed
how to solve (-2/5x)(2/6y)=
Answers
Answer:
-2yx/15?
Step-by-step explanation:
A basketball hoop in your backyard casts a shadow 109 inches long. You are 5‘8" tall in cast a shadow 62 inches long. Find the height of the basketball hoop in inches round your answer to the nearest whole number
Answers
Step-by-step explanation:
Height of shadow of basketball hoop = 109 inches
Height of person = 5 foot 8 inches = 68 inches
Height of shadow of person = 62 inches
[tex]\frac{\texttt{Height of person}}{\texttt{Height shadow of person}}=\frac{68}{62}=\frac{34}{31}[/tex]
[tex]\frac{\texttt{Height of basketball hoop}}{\texttt{Height of shadow of basketball hoop}}=\frac{34}{31}\\\\\frac{\texttt{Height of basketball hoop}}{109}=\frac{34}{31}\\\\\texttt{Height of basketball hoop}=119.55inches=120inches[/tex]
Height of the basketball hoop = 120 inches
The popcorn stand sells only soft drinks and popcorn, and only one size of each. In fact, the same cup is used for both products this is part of the stand's "sales pitch. "A soft drink cost $2.00 and a popcorn cost $4.00. On a certain day, 120 cups were used and $330.00 was collected. How many soft drinks and how many popcorns were sold on that day? Use a system of equations approach to find your answer. Show all work.
Answers
Answer:
On that day 75 soft drinks and 45 popcorn were sold.
Step-by-step explanation:
Given:
Let the number of soft drinks be 'x'.
Let the number of popcorn be 'y'.
Number of cups sold = 120
Now we know that;
Number of cups sold is equal to sum of the number of soft drinks and the the number of popcorn.
framing in equation form we get;
[tex]x+y=120 \ \ \ \ equation \ 1[/tex]
Also Given:
Cost of Soft drink = $2 .00
Cost of popcorn = $4.00
Total amount collected = $330.00
Now we know that;
Total amount collected is equal to sum of the number of soft drinks multiplied by Cost of Soft drink and the number of popcorn multiplied Cost of popcorn.
framing in equation form we get;
[tex]2x+4y = 330 \ \ \ \ eqaution \ 2[/tex]
Hence The System of equation to determine the number of softdrinks and cups sold is [tex]\left \{ {{x+y=120} \atop {2x+4y=330}} \right.[/tex].
Now to find the number of each type of cups sold we will solve the above equations.
First we will multiply equation 1 with 2 we get;
[tex]2(x+y)=120\times2\\\\2x+2y =240 \ \ \ \ equation \ 3[/tex]
Now we will subtract equation 3 from equation 2 we get;
[tex]2x+4y-(2x+2y)=330-240\\\\2x+4y-2x-2y=90\\\\2y = 90[/tex]
Now Dividing both side by 2 we get;
[tex]\frac{2y}{2}= \frac{90}{2}\\\\y=45[/tex]
Now we will substitute the value of 'y' in equation 1 we get;
[tex]x+y=120\\\\x+45 =120\\\\x=120-45 = 75[/tex]
Hence On that day 75 soft drinks and 45 popcorn were sold.
Tito receives a weekly salary of $350 at an appliance store. He also receives a 5% commission on a total dollar amount of all sales he makes. What must his total sales be in a week if he is to make a total of $675
Answers
Answer:his total sales be $6500 in a week if he is to make a total of $675
Step-by-step explanation:
The total amount of money that Tito receives as weekly salary at an appliance store is $350.
He also receives a 5% commission on a total dollar amount of all sales he makes.
Let x represent his total sales in a week.
The amount of commission that he receives would be
5/100 × x = 0.05x
if he is to make a total of $675 in a week, it means that
0.05x + 350 = 675
0.05x = 675 - 350 = 325
x = 325/0.05 = $6500
By setting up an equation to represent Tito's total earnings and solving for total sales, we find that Tito must make $6500 worth of sales to earn a total of $675 in a week.
Explanation:The subject of this question is Mathematics, specifically dealing with algebraic calculations to find the value of the variable. The variable in this case is the total sales Tito must make to earn a total of $675 in a week.
We know that Tito earns a fixed weekly salary of $350 and he also receives a 5% commission on his total sales. He wants to know how much he needs to sell to reach a total earning of $675.
To solve this, we set up an equation to represent the total earnings that Tito wishes to make: $350 (salary) + 0.05x (sales commissions) = $675.
Now we solve the equation for x (total sales). First, subtract $350 from both sides to get 0.05x = $675 - $350, which simplifies to 0.05x = $325.
Next, divide both sides of the equation by 0.05 to find x, so x = $325 / 0.05.
Therefore, Tito's total sales in a week must be $6500 for him to make a total of $675.
Learn more about Sales Commission Calculation here:https://brainly.com/question/32023975
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In May, the school store sells 80 erasers. In June, the store sells only 16 erasers. What is the percent of change in erasers sold from May to June?A) 80% B) 20% C) 64% D) 80%
Answers
Answer: 80%
Step-by-step explanation:
Since we have given that
Number of erasers sold in May = 80
Number of erasers sold in June = 16
Decrement in 1 month gap is given by
16-80=-64
So, Percentage of change in erasers sold from May to June is given by
[tex]\frac{-64}{80}[/tex] × 100
= -80% (Decreased 80%)
Answer:
80%
Step-by-step explanation:
I took a test with this question on it
Two hunters started to walk towards each other simultaneously from two different locations in the forest. The distance between them was 21 miles. The first hunter walked at a rate of 4 mph, while the second one walked at a rate of 3 mph. The first hunter took a dog with him, who ran at an average rate of 5 mph. The dog started to run towards the second hunter, met him and ran back to the first hunter. The dog repeated this until the two hunters met each other. How many miles did the dog run?
Answers
Answer:
The dog ran 15 miles
Step-by-step explanation:
The combined speed of the 2 hunters is 7mph, therefore, they will met in 21/7 = 3 hours, becuse they are walking in opposite directions. In this 3 hours the dog kept running and thus it ran 3*5 = 15 miles. Note that the position of the dog is always between the position of both hunters, therefore when both hunters met each other, the dog will be alredy there.
Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice.
Answers
Answer:
22 yards
Step-by-step explanation:
Use a (+) sign for yards gained and a (-) sign for yards lost.
Geno gained 4 yards 3 times: (+4) × 3.
Geno lost 1 yard twice: (-1) × 2.
Geno gained 6 yards twice: (+6) × 2.
Net change
in field position
=
(4 × 3) + (-1 × 2) + (6 × 2)
=
12 − 2 + 12
=
10 + 12
=
22.
Geno gained 22 yards.
The net change in the position of Geno if In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice, is 22 yards.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice,
Calculate the net change in position as shown below,
The net change = Total gained - Total lost,
Total gained = 4 × 3 + 6 × 2
Total gained = 12 + 12
Total gained = 24
Total lost = 1 × 2
Total lost = 2
The net change = 24 - 2
The net change = 22
Thus, the net change in the Geno position is 22 yards.
To know more about addition:
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The complete question is:
Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice. Find the net change in the position of Geno.
To receive a grade of A on 80 question test 90% of the questions must be answered correctly what is the maximum number of questions that can't be missed to still receive an A
Answers
Answer:
Step-by-step explanation:
Total number of questions in the test is 80.
To receive a grade of A on the 80 question test, 90% of the questions must be answered correctly. It means that the number if questions that must be answered correctly would be
90/100 × 80 = 0.9 × 80 = 72.
Therefore, the maximum number of questions that can't be missed to still receive an A is 72