The value of x and y in the geometric sequence are 1/r and 1
What is geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
If the first term of the sequence is a ,second term is ar , third term = ar²
r = ar²/ar
In the sequence 2y, 2xy, 2, xy/2, ...
r = 2y/2xy
therefore r = 1/x
r = 2/2xy
r = 1/xy
therefore 1/x = 1/xy
therefore y = 1
x = 1/r
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Kirk prepared 24 kilograms of dough after working 4 hours. How much dough did Kirk prepare if he worked for 7 hours? Solve using unit rates.
If Kirk had worked for 7 hours he would have made 42 kg of dough.
What is unit rate?A unit rate means a rate for one of something.
Given that, Kirk prepared 24 kilograms of dough after working 4 hours, we need to find the amount of dough if he worked for 7 hours.
Calculating the unit rates,
Since, he worked for 4 and made 24 kg,
So, in 1 hour = 24/4 = 6 kg
Therefore, in 1 hour he will make 6 kg
Therefore, in 7 hours he will make = 7x6 = 42 kg
Hence, If Kirk had worked for 7 hours he would have made 42 kg of dough.
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I really need help with this quetion, this would really help
The estimate for the mean book thickness is 3.2 mm.
What is mean?
In arithmetic, mean is the sum of all the added values of all the data in a set divided by the number of data in the set.
To find the mean book thickness, we can use the formula for the mean (also known as the average):
mean = (sum of all data points) / (number of data points)
Since we don't have the exact thickness of each book, but rather intervals of thickness and the number of books in each interval, we can use a weighted mean to estimate the mean thickness.
Here is the calculation:
First, we'll find the midpoint of each interval:
Interval 1: [0, 2] -> midpoint: x1 = 1
Interval 2: [2, 4] -> midpoint: x2 = 3
Interval 3: [4, 6] -> midpoint: x3 = 5
Next, we'll find the weight of each interval by multiplying the midpoint by the frequency:
Interval 1: x1 * f1 = 1 * 5 = 5
Interval 2: x2 * f2 = 3 * 8 = 24
Interval 3: x3 * f3 = 5 * 7 = 35
Finally, we'll sum up the weights and divide by the total frequency to find the weighted mean:
Weighted mean = (5 + 24 + 35) / (5 + 8 + 7) = 64 / 20 = 3.2
So, the estimate for the mean book thickness is 3.2 mm.
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61. Detecting a Speeder A policewoman has positioned herself
500 ft from the intersection of two roads. She has carefully
measured the angles of the lines of sight to points A and B as
shown in the drawing. If a car passes from A to B in 1.75 sec
and the speed limit is 55 mph, is the car speeding?
HINT Find the distance from B to A and use R = D/T.
The Distance between A, B based on the information will be 28.705 feet
How to calculate the distanceFrom the information, the policewoman has positioned herself 500 ft from the intersection of two roads and she has carefully measured the angles of the lines of sight to the points.
Distance between A, B will be:
= 500 tan(15.4) - 500 tan(12.3)
= 500 (tan 15.4 - tan 12.3)
= 500(0.0574)
= 28.705 feet
The speed will be:
= 28.705 / 1.75
= 16.403 ft/s
= 12.3 mph
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On 1 June Sipho opened a savings account at the Postbank that paid 4.5% interest. He deposited R600. Ten days later on 10 June he deposited R1 000.F days later on 15 June he deposited R500. No other deposits or withdrawals w made. Fifteen days later, at the end of the month, the bank calculated the nterest. a. How much simple interest (calculated to the nearest cent) did he earn? . What was the balance of the account at the end of the first 30 days?
Sipho earned R33.15 in simple interest.
The balance of the account at the end of the first 30 days was R2 133.15.
How to calculate thisa. To calculate the simple interest earned by Sipho, we need to calculate the total amount deposited and the interest earned on that amount.
Total amount deposited = R600 + R1 000 + R500 = R2 100
Interest earned = R2 100 x 4.5% x 30/365 = R33.15 (rounded to the nearest cent)
Therefore, Sipho earned R33.15 in simple interest.
b. The balance of the account at the end of the first 30 days can be calculated by adding the total amount deposited and the interest earned to the initial deposit:
Balance = R600 + R1 000 + R500 + R33.15 = R2 133.15
Therefore, the balance of the account at the end of the first 30 days was R2 133.15.
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The two triangles are congruent. Solve for x. Then find all missing angles.
(I found x but I don’t know how to figure out y)
Using the definition of congruent triangles, the missing values are:
x = 35
y = 30°
What are Congruent Triangles?Given that the two triangles in the image above are congruent, it implies that all its corresponding angles and corresponding side lengths have equal measure.
Therefore, we have:
2x - 10 = x + 25
Solve for x:
2x - x = 10 + 25
x = 35
Plug in the value of x to find the missing angles:
y + 90 + (2x - 10) = 180 [triangle sum theorem]
y + 90 + (2(35) - 10) = 180
y + 90 + 60 = 180
y = 30°
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Katya sold
46 books at £1.40 each
32 bracelets at £1.50 each
some badges at 90p each
She got a total of £134
Work out how many badges Katya sold.
Answer:
This is a math problem. To solve it, you need to use algebra. Let me show you how.
Let x be the number of badges Katya sold. Then we can write an equation using the given information:
46 × 1.40 + 32 × 1.50 + 0.90 × x = 134
Simplifying the equation, we get:
64.4 + 48 + 0.9x = 134
Subtracting 64.4 and 48 from both sides, we get:
0.9x = 21.6
Dividing both sides by 0.9, we get:
x = 24
Therefore, Katya sold 24 badges.
Step-by-step explanation:
Leanne's Nursery buys crates of firewood to deliver to customers over the winter. Each crate
measures 4 feet long, 3.5 feet wide, and 4 feet high. How much storage space does the nursery
need for the wood if 60 crates are delivered in an order?
OA 675 cubic feet
OB 3,375 cubic feet
OC 3,937.5 cubic feet
OD 3,360 cubic feet
The volume of storage space that the nursery needs for the wood if 60 crates are delivered in an order is; D: 3360 cubic feet
How to find the total volume of a cuboid?The formula for volume of a cuboid is;
Volume = Length * width * height
We are given;
Length = 4 feet
Width = 3.5 ft
Height = 4 ft
Thus;
Volume of one crate = 4 * 3.5 * 4
= 56 cubic ft
We need a total of 60 crates. Thus;
Total Volume = 60 * 56
Total volume = 3,360 cubic feet
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trinomio cuadrado perfecto
[tex]\alpha^{3} -10\alpha ^{\frac{3}{2} } +25[/tex]
[tex]64x {}^{3} + y {}^{3} [/tex]
factorise fully
The function f(t)=12,000(1.075)t models the value of an investment t years from now. What is the meaning of the value of f(5)?
Answer:
The value of the investment in 5 years.
Step-by-step explanation:
The description of the function states that it tells us the value of an investment at some point in the future (t), measured in years. In other words, f(t). When the time is 5 years, it would be written as f(5), and the t term in the function will be set to 5 for the calculation, which will yield the value of the investment at that time.
at this point of contact, is the number of field lines per unit of balloon surface area equal to the number of field lines per unit of box surface area?
a) The electric field magnitude on the balloon surface will be different from the electric field magnitude on the box surface.
b) the electric field lines intersect with the planar surface of the box, the field lines will be compressed or spread out depending on the angle of incidence.
At the point of contact between the spherical balloon and the wall of the cubical box, the electric field magnitude will not be the same on both surfaces. This is because the surface of the balloon is spherical, while the surface of the box is planar. The electric field lines emanating from the charged ball will be spherically symmetric around the ball and perpendicular to the surface of the balloon. However, when the electric field lines intersect with the planar surface of the box, the field lines will be distorted due to the change in direction of the surface. As a result, the electric field magnitude on the balloon surface will be different from the electric field magnitude on the box surface.
At the point of contact, the number of field lines per unit area will also be different for the balloon surface and the box surface. The electric field lines from the charged ball will be distributed uniformly over the surface of the spherical balloon, so the number of field lines per unit area will be constant over the entire surface. However, when the electric field lines intersect with the planar surface of the box, the field lines will be compressed or spread out depending on the angle of incidence. Therefore, the number of field lines per unit area on the box surface will not be the same as the number of field lines per unit area on the balloon surface.
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Question:
A small charged ball is suspended at the center of a spherical balloon that is nestled snugly inside a cubical cardboard box. On one side, the balloon touches the wall of the box. (a) At this point of contact, is the electric field magnitude on the balloon surface equal to the electric field magnitude on the box surface? Assume neither object is polarized. (b) At this point of contact, is the number of field lines per unit of balloon surface area equal to the number of field lines per unit of box surface area?
Find the value of x =
Answer:
360-137+x+y
Step-by-step explanation:
Please help with this question!!
According to the information, we plan to have cruising speed on for a minimum of 3 hours and a maximum of 4.1 hours.
How to calculate how many hours we are going to have the cruising speed on?To calculate how many hours we are going to have the cruising speed on we must carry out the following process:
To calculate the minimum we must subtract 35 from 215 and then divide by the speed:
215 - 35 = 180180 / 60 = 3So the minimum hours would be 3 hours.
On the other hand, to calculate the maximum we must add 35 to 215 and divide it by the speed:
215 + 35 = 250250 / 60 = 4.1So the maximum time would be 4.1 hours.
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For which pair of functions f(x) and g(x) below will the limit as x goes to infinity of the quotient of f of x and g of x equals 0 ?
f(x) = ex; g(x) = x2
f(x) = ex; g(x) = ln(x)
f(x) = ln(x); g(x) = ex
f(x) = x; g(x) = ln(x)
The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex
How to explain the informationFor the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).
Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.
In conclusion, the correct option is C.
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Calculate the area of a triangle XYZ with
angle X = 90°, XZ = 15 cm and XY = 12 cm
The area of the right triangle with side lengths of 15cm and 12cm is 90 cm².
What is the area of the triangle ?The area of triangle can be determined using the equation;
Area = 1/2 × base × height.
The angle described forms a right-triangle.
Height of the triangle = XZ = 15cmBase of the triangle = XY = 12cmAngle X = 90°Area A = ?Area = 1/2 × base × height
Area = 1/2 × 12cm × 15cm
Area = 6cm × 15cm
Area = 90 cm²
Therefore, the area of the triangle is 90 cm².
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help me please help help
The equation that can be used to find the number of gardens that Kalisa welds is given as follows:
200 + 5.5w = 260.50.
How to construct the equation?Kalisa's earnings are divided as follows:
Mows 8 lawns for $25 each -> total of 25 x 8 = $200.Welds w gardens for $5.5 each -> total of 5.5w.Hence the equation for the total earnings is constructed follows:
T(w) = 200 + 5.5w.
Her total earnings are of $260.50, hence the number of gardens that Kalisa welds is given as follows:
200 + 5.5w = 260.50.
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PLEASE HELP!!!!!!!!!
1. y=-x^2+2 what is the
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
2. y=x^2-6x+3 What is the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
3: y=-2x^2-8x-5 What is the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
4. f(x)=-x^2+1 What’s the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
5. f(x)=-2x^2+8x-3 What’s the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
6. f(x)=2x^2+8x+1 what’s the:
Domain:
Range:
Vertex:
Axis of symmetry:
y intercepts:
A rectangle that has an area of 357 square inches is 17 inches wide. Using the formula for area ( A = lw), how long is the rectangle?
a. 21 inches
b. 340 inches
c. 20 inches
d. 15 inches
The length of the rectangle given the area and width is 21 inches
What is the length of the rectangle:Area of the rectangle = 357 square inches
Width of the rectangle = 17 inches
Length of the rectangle= l
Area of a rectangle = Length × width
357 = l × 17
357 = 17l
divide both sides by 17
l = 357 / 17
l = 21 inches
In conclusion, 21 inches is the length of the rectangle.
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I have 2 questions. 1.If the Percent of Discount is 80% and the Sale Price is $90 then what is the Original Price? 2. If the Percent of Discount is 15% and the Sale Price is $146.54 then what is the Original Price? HELP ME PLEASE!!???
The requried solutions are as follows,
(1) the original price is $450. (2) the original price is $172.40.
Sale price is defined as the price of a product marked including of various price cut such as discounts.
Here,
If the percent of discount is 80% and the sale price is $90, we can use the following formula to find the original price x (let)
Sale price = Original price - Discount
$90 = x - 0.8x
Simplifying the right-hand side:
$90 = 0.2x
x = $450
Therefore, the original price is $450.
If the percent of discount is 15% and the sale price is $146.54, we can use the same formula:
Sale price = Original price - Discount
$146.54 = x - 0.15x
Simplifying the right-hand side:
$146.54 = 0.85x
x = $172.40
Therefore, the original price is $172.40.
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yall know what the blanks are supposed to be??????
Answer: Region Z
Step-by-step explanation: Region X is smaller than Region Y, while Region Y is smaller than Region Z.
Two more than 3 times a number is 20. Find the number.
Answer: the number is 6
Step-by-step explanation: First, set up an equation. Two more means +2, 3 times a number means 3x. So your equation would be 3x+2=20. Then solve the equation for x.
Answer:
x = 6
Step-by-step explanation:
Let the number be 'x'
Then, the equation becomes,
2 + 3x = 20
3x = 20 - 2
3x = 18
x = 18/3
x = 6
Hope it helped :)
A basketball player plays for 30 out of 48 minutes in a game. She sits on the bench the rest of the game. What percentage of the game did the player sit on the bench?
Answer:5/8
Step-by-step explanation: you put the numbers in a fraction the smallest goes on top and the more enormous number at the bottom you simply by finding the most significant standard number between the 2 numbers which is in this case 6 divide it by that and that is how you get your answer
A study shows that at the end of a school day teenagers typically have 40% of their cell phone battery left when plugged in phone charge at a rate of 3% per minute when using the newest fast charger.
a: write an inequality to represent how many more minutes are needed to reach at least 80% battery life.
b. use the inequality to determine the how many more minutes it will take to have at least 80% battery life
The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Let 'x' be the number of minutes and 'y' be the total battery percentage. Then the equation is given as,
y = 3x + 40
The inequality that represents the more minutes are needed to reach 80 of battery is given as,
3x + 40 ≤ 80
Simplify the inequality, then we have
3x + 40 ≤ 80
3x ≤ 40
x ≤ 13.33 minutes
The inequality that represents the more minutes needed to reach 80% of the battery is 3x + 40 ≤ 80. And the number of minutes will be 13.33 minutes.
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Which equations are true for the values of x, y, and z? Select three options.
2 lines intersect to form 4 angles. Clockwise, from top, the angles are: 65 degrees, x, y, z.
The equations that are true of the values x, y, and z are :
x degrees + 65 degrees = 180 degreesx degrees = z degreesy degrees = 65 degreesHow to find the equations ?The line that x degrees and 65 degrees is on, is a straight line which means that they will both add up to 180 degrees :
x degrees + 65 degrees = 180 degrees
x and z are congruent angles which means they are both the same angle measure.
y would be equal to 65 degrees because, just like x and z, y and 65 degrees are congruent.
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Options include:
x degrees + 65 degrees = 180 degreesx degrees = z degreesy degrees = 65 degreesx degrees= 65 degreesx degrees + y degrees + z degrees = 115 degreesIn any set of positive integers the replacement of a set of three 2s with a set of two threes will not change the sum
The statement is incorrect. The replacement of three 2s with two threes will change the sum.
For example, consider the set {2, 2, 2}. The sum of this set is 6. However, if we replace three 2s with two threes, the new set becomes {3, 3}, and its sum is 6, which is different from the original sum. Hence, replacing a set of three 2s with a set of two threes does change the sum. An integer is a whole number that can be positive, negative, or zero. Integers are numbers that don't have any fractional or decimal component. Some examples of integers are: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, and so on. The set of integers is denoted by the symbol "Z", which stands for Zahlen, the German word for "numbers". Integers are an important mathematical concept used in many branches of mathematics and science, including algebra, number theory, and computer science.
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Complete Question
In any set of positive integers the replacement of a set of three 2s with a set of two threes will not change the sum" State whether the statement was correct or incorrect.
Pls help me fast fast fast
The value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.
What are similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "."
The two triangles are similar thus the measure of its angle are also equal.
Using the similar triangle we have:
Angle D = Angle A = 82 degrees.
Angle F = 67 degrees
Using the sum of interior angles of triangle we have:
∠D + ∠F + ∠E = 180
82 + 67 + ∠E = 180
∠E = 31
From the figure we observe that,
∠E + ∠G = 180 (straight line)
31 + ∠G = 180
∠G = 149
Hence, the value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.
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A quilter created the following shape to use in a block for a new quilt. What is the area of the shape for the quilt block?
The area of the shape for the quilt block is 166.5 in²
What is an area?The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape
Given that, a quilt has blocks of design on it, we need to find the area of the block,
To find the area of the block = sum of the areas of the right triangle and the rectangle,
Area of the block = 16 × 9 + 6 × 7.5 × 1/2 = 166.5 in²
Hence, the area of the shape for the quilt block is 166.5 in²
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The figure is unavailable is the question is solved for the figure attached
The expression 2.2x + 8 represents the number of miles Trent jogged during a race and 5x represents the number of miles that Ling jogged during the same race in x hours. Write and expression to show how many more miles did Ling Jog than Trent?
The number of miles Ling Jog than Trent can be written as the expression 2.8x - 8
How many more miles did Ling Jog than Trent?Trent's expression:
2.2x + 8
Ling's expression:
5x
Where,
Number of hours= x
Number of hours Ling Jog than Trent =Ling's expression - Trent's expression
= 5x - (2.2x + 8)
= 5x - 2.2x - 8
= 2.8x - 8
Therefore, Ling jog 2.8x - 8 miles than Trent.
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Is -y/4 = 2x -5 linear
A pole 6 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Ian measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
Answer:
here you go
Step-by-step explanation:
A guy wire runs from the top of a cell tower to a metal stake in the ground. Emily places a 10-foot tall pole to support the guy wire. After placing the pole, Emily measures the distance from the stake to the pole to be 11 ft: She then measures the distance from the pole to the tower to be 23 ft: Find the length of the guy wire, to the nearest foot.
