Part 4: By the theorem of inscribed angle in the circle: arc RP = 136°.
Part 5: From the central angle theorem: m∠LNM = 54°.
Explain about the inscribed angles:Part 4:
m∠QRP = 68°
By the theorem of inscribed angle in the circle:
Two chords with a shared termination point on the circle make up an inscribed angle in a circle. The vertex of a angle is this common terminal point.
arc RP = 2 * m∠QRP
arc RP = 2 * 68°
arc RP = 136°
Part 5:
From the central angle theorem:
An inscribed angle's measurement is equal to half of an intercepted arc's measurement.
As a result, any two inscribed angles in a circle with identical intercepted arcs remain congruent.
m∠LNM = 1/2 m∠LNP
m∠LNM = 1/2 * 108°
m∠LNM = 54°
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conditions for drawing triangles
side lengths of 6cm and 9 cm , 70° angle
Answer: 9cm
Step-by-step explanation: i hope this this helps!
A small nation of ten people idolizes the TV show “The Voice”. All they produce and consume are karaoke machines and CDs, in the following amounts:
Karaoke Machines
CDs
Quantity Produced
(in thousands)
Price of each Karaoke Machine
Quantity Produced
(in thousands)
Price of each CD
2017
10
$40
30
$10
2018
12
$60
50
$12
The population of the economy is 10000 in 2017 and it increased to 15000 in 2018.Using the CPI, compute the percentage change in the overall price level. Use 2017 as the base year and fix the basket at 1 karaoke machine and 3 CDs.
To compute the CPI, we first need to calculate the total cost of the basket in both years:
2017: (10 x $40) + (30 x $10) = $400 + $300 = $700
2018: (12 x $60) + (50 x $12) = $720 + $600 = $1320
Using 2017 as the base year, the CPI in 2017 is 100 (by definition). To calculate the CPI in 2018, we divide the cost of the basket in 2018 by the cost of the basket in 2017, and multiply by 100:
CPI in 2018 = (1320/700) x 100 = 188.57
Therefore, the percentage change in the overall price level is:
% change in price level = (CPI in 2018 - CPI in 2017) / CPI in 2017 x 100
% change in price level = (188.57 - 100) / 100 x 100
% change in price level = 88.57%
So, the overall price level increased by 88.57% from 2017 to 2018.
If trapezoid QRST is dilated about the origin by a scaled (k) of 2, what is the resulting coordinate of point T”?
Using dilation, we can find the coordinates of the new trapezoid and the coordinates of T" is (-6, -4).
Define dilation?Dilation is the process of increasing an object's size without altering its shape. Depending on the scale-factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation maths, but the square's shape doesn't change.
In geometry, dilation math is used to enlarge and reduce two- or three-dimensional figures.
Here in the question,
The coordinates of point T = (-3, -2)
Now, the trapezoid is dilated about the origin.
The scale factor here is. k = 2.
The new coordinates of the point T":
x coordinate = -3 × 2 = -6
y coordinate= -2 × 2 = -4
The coordinates of T" = (-6, -4).
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A shop gave different discounts to different customers. Libby paid $600 for a watch at a discount of 20%. However, Scott paid $630 for the same watch. How many percent discount was given to Scott?
Answer: Let x be the percentage discount given to Scott. Then we can write:
Discounted price for Libby = Original price - 20% of the original price
Discounted price for Scott = Original price - x% of the original price
We know that Libby paid $600 and Scott paid $630 for the same watch, so we can set up the following equation:
Original price - 20% of original price = $600
Original price - x% of original price = $630
Simplifying each equation, we get:
0.8 * Original price = $600
(1 - x/100) * Original price = $630
Dividing the second equation by the first, we get:
(1 - x/100) / 0.8 = 630/600
Simplifying the right-hand side, we get:
(1 - x/100) / 0.8 = 21/20
Multiplying both sides by 0.8, we get:
1 - x/100 = (21/20) * 0.8
Simplifying the right-hand side, we get:
1 - x/100 = 0.84
Subtracting 1 from both sides, we get:
-x/100 = -0.16
Multiplying both sides by -100, we get:
x = 16
Therefore, Scott was given a 16% discount on the original price of the watch.
Step-by-step explanation:
Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
x = 2;
y = √3
Step-by-step explanation:
Use trigonometry:
[tex] \tan(60°) = \frac{y}{1} [/tex]
Cross-multiply to find y:
[tex]y = 1 \times \tan(60°) = 1 \times \sqrt{3} = \sqrt{3} [/tex]
Use the Pythagorean theorem to find x:
[tex] {x}^{2} = {y}^{2} + {1}^{2} [/tex]
[tex] {x}^{2} = ( { \sqrt{3}) }^{2} + {1}^{2} = 3 + 1 = 4[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{4} = 2[/tex]
Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer:
y = 2;
x = 2√2
.
Step-by-step explanation:
Use trigonometry:
[tex] \tan(45°) = \frac{y}{2} [/tex]
Use the property of proportion to find x (cross-multiply):
[tex]y = 2 \times \tan(45°) = 2 \times 1 = 2[/tex]
Use the Pythagorean theorem to find x:
[tex] {x}^{2} = {y}^{2} + {2}^{2} [/tex]
[tex] {x}^{2} = {2}^{2} + {2}^{2} = 4 + 4 = 8[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{8} = \sqrt{4 \times 2} = 2 \sqrt{2} [/tex]
Whats the value of x?
Answer:
x = 25
Step-by-step explanation:
By the angle sum property,
2x + 2 + 5x + 3 = 180
7x + 5 = 180
7x = 175
x = 25
Pls like and mark as brainliest!
Answer:
x = 25
Step-by-step explanation:
2x + 2 + 5x + 3 = 180
7x + 5 = 180 and 7x=175
7x = 175
x = 25
so x is most likely the answer
x=25 Give her BRAINLEST for figuring it out first
Colton measured the high school and made a scale drawing. The scale he used was 1 centimeter : 2 meters. The parking lot is 88 meters long in real life. How long is the parking lot in the drawing?
centimeters
The length of the parking lot in the drawing is 44 centimeters.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.
Since the scale Colton used is 1 centimeter : 2 meters, this means that for every 2 meters in real life, he drew 1 centimeter in his scale drawing.
To find the length of the parking lot in the drawing, we can set up a proportion:
1 cm / 2 m = x cm / 88 m
where x is the length of the parking lot in the drawing in centimeters.
We can solve for x by cross-multiplying:
1 cm * 88 m = 2 m * x cm
88 cm = 2x
x = 44 cm
Therefore, the length of the parking lot in the drawing is 44 centimeters.
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please help thank you very much
Answer:5
Step-by-step explanation:
Use trigonometric ratios to find the indicated side lengths in the diagram shown. Round your answers to the nearest tenth.
x = _____ units
y = _____ units
(40 points)
The indicated side lengths are: x ≈ 13.2 units and y ≈ 11.9 units
What is angle of sin?the ratio between the side opposite the angle and the hypotenuse of the triangle.
given that a triangle with three sides x, y, 18 and angle opposite to side y is 42°.
then by sine formula, trigonometric ratio for the sine of an angle:
sin(42°) = perpendicular /hypotenuse = y/18
y = 18 sin(42°), we find that y ≈ 11.9 units (rounded to the nearest tenth).
To find x, the cosine of an angle:
cos(42°) =base /hypotenuse=x/18
x = 18 cos(42°)
we find that x ≈ 13.2 units (rounded to the nearest tenth).
Therefore, the indicated side lengths are:
x ≈ 13.2 units
y ≈ 11.9 units
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What is the value of x?
Enter your answer in the box.
x =
Answer:
x = 4
Step-by-step explanation:
In order to find x, we will either have to find the length QT or RT.
In triangle RST, the length RS is given so we can either length RT or ST. However, if we find the length RT, we can find the value of x.
sin Θ = [tex]\frac{opp}{hyp}[/tex]
sin 60° = [tex]\frac{2\sqrt{3} }{RT}[/tex]
RT = [tex]\frac{2\sqrt{3}}{sin 60}[/tex] = 4
tan Θ = [tex]\frac{opp}{adj}[/tex]
tan 45° = [tex]\frac{x}{4}[/tex]
x = tan 45° × 4 = 4
Suppose a random sample of 80 measurements is selected from a population with a mean of 25 and a variance of 200. Select the pair that is the mean and standard error of x. Rstudio
a) [25, 2.081]
b) [25, 1.981]
c) [25, 1.681]
d) [25, 1.581]
e) [80, 1.681]
[ 25 , 1.581 ] is the pair that is the mean and standard error of x.
What does standard error mean?
A statistical concept known as the standard error uses standard deviation to assess how well a sample distribution represents a population.
The standard error of the mean describes the statistical variation between a sample mean and the population's actual mean. Measures of variability include standard error and standard deviation: The standard deviation describes variation within a single sample.
n = 80
μ = 25
σ² = 200
mean of x = μ = 25
standard error = √ σ²/n
= √200/80
= 1.581
= [ 25 , 1.581 ]
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Change into passive voice a. They bring food for us.
Answer:
Food is brought for us by them.
Answer:
Food is brought for us by them.
Step-by-step explanation:
How much will you owe at the end of 10 years and a month, if you decide to pay your yearly bonus at the end of each year toward reducing your outstanding loan amount for a loan with the following details? Loan amount PV $320,000 Rate of interest APR 4.750% p. y. c. w. Loan term NPER 15 years Bonus payment at end of each year $4,500 Group of answer choices $21,619.43 $41,033.68 $58,527.87 $74,315.75
The correct option is $58,527.87
To solve this problemUsing the loan details and bonus payment provided, the remaining balance on the loan at the end of 10 years and a month can be calculated as follows:
Number of payments made = 10 years * 12 months/year + 1 month = 121
Monthly interest rate = 4.75% / 12 = 0.3958%
Yearly bonus payment = $4,500
Using the PMT function in Excel, the monthly payment on the loan can be calculated as:
PMT(0.003958, 15*12, 320000) = -$2,378.03
Since the bonus payment is made once a year, it can be applied as a lump sum to the remaining balance at the end of each year. Therefore, the remaining balance after 10 years and a month can be calculated as:
Remaining balance = PV(0.003958, 5*12, -2378.03, 0, 0) - 4500
where PV is the present value function.
Solving this equation yields:
Remaining balance = $58,527.87
Therefore, the answer is $58,527.87.
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The life of a Radio Shack record player is normally distributed with a mean of 3.3 years and a standard deviation of 0.8 years. Radio Shack guarantees its record players for 2 years.
Find the probability that a record player will break down during the guarantee period.
The probability that a record player will break down during the guarantee period is 26.4%.
What is cumulative distribution?Cumulative distribution shows the probability of a randomly-selected value falling below or equal to a certain value.
To find the probability that a record player will break down during the guarantee period, we need to calculate the probability of the record player breaking down within two years, which is given by the cumulative distribution function of the normal distribution.
This function uses the mean and standard deviation of the distribution, so for the Radio Shack record player, the probability of breaking down within two years is given by the cumulative distribution function
P(X ≤ 2) = CDF(X; 3.3, 0.8)
To find this probability, we can use a normal distribution calculator to find the cumulative probability of X ≤ 2.
The cumulative probability of X ≤ 2 for a normal distribution with a mean of 3.3 and standard deviation of 0.8 is 2.64.
Therefore, the probability that a Radio Shack record player will break down during the guarantee period is 2.64.
This indicates that there is a 26.4% chance that a Radio Shack record player will break down before the end of the two-year guarantee period.
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Find the slope of a line perpendicular to the line whose equation is 2x + 3y = 24.
Fully simplify your answer.
The slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2
What is Equation?An equation is a statement that two expressions are equal. It contains one or more variables and may also contain constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
To find the slope of a line perpendicular to the line whose equation is [tex]2x + 3y = 24[/tex], we need to first find the slope of the given line.
We can rearrange the equation into slope-intercept form (y = mx + b) by solving for y:
[tex]2x + 3y = 24[/tex]
[tex]3y = -2x + 24[/tex]
[tex]y = \huge \text(-\dfrac{2}{3}\huge \text )x + 8[/tex]
So the slope of the given line is -2/3.
A line perpendicular to this line will have a slope that is the negative reciprocal of -2/3.
The negative reciprocal of a number is the number flipped upside down and then negated. So the negative reciprocal of -2/3 is:
[tex]-1 \div \huge \text(-\dfrac{2}{3}\huge \text )=\dfrac{3}{2}[/tex]
Therefore, the slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2
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Simplify the function f(x)=1/2(27) 2x/3 then determine the key aspects of the function
The simplified form of the function f(x)=1/2(27) 2x/3 can be expressed as f(x) = (27/2) (2x/3).
What is function?Functions are one of the fundamental building blocks of mathematics and are used to describe and analyze relationships between different variables.
The function f(x)=1/2(27) 2x/3 can be simplified by factoring out the common factor of 1/2 and 27.
Thus, the simplified form of the function can be expressed as
f(x) = (27/2) (2x/3).
This function is a polynomial function with degree 1, which means that it is a linear function. The degree of a function is the highest power of the variable in the equation.
The key aspects of this function can be identified by looking at the constant values in the equation.
The constant value 27/2 is the y-intercept, which is the point at which the line crosses the y-axis.
This means that the y-value of the function at x = 0 is 27/2.
The constant value 2/3 is the gradient, which is the slope of the line. This means that for every increase in the x-value, the y-value will increase by 2/3.
This function can be represented graphically as a straight line with a y-intercept of 27/2 and a slope of 2/3.
The graph of this function will pass through the point (0, 27/2) and will have a positive slope of 2/3. This means that the graph will move up and to the right, with each increase in the x-value resulting in an increase of 2/3 in the y-value.
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Please help asap!!!
The exact values of trigonometric functions are, respectively:
sin (u + v) = - 13 /85
tan (u + v) = - 13 / 84
How to find the exact values of trigonometric functions
In this problem we need to determine the exact values of trigonometric functions, this can be done by using trigonometric formulas and relationships between trigonometric functions. We need to use the following expressions:
sin² x + cos² x = 1
sin (u + v) = sin u · cos v + cos u · sin v
tan x = sin x / cos x
tan (u + v) = (tan u + tan v) / (1 - tan u · tan v)
Where x, u, v are measured in radians.
Now we proceed to determine the exact values of each function:
cos u = √[1 - (- 3 / 5)²]
cos u = 4 / 5
sin v = √[1 - (15 / 17)²]
sin v = 8 / 17
sin (u + v) = (- 3 / 5) · (15 / 17) + (4 / 5) · (8 / 17)
sin (u + v) = - 13 /85
tan u = (- 3 / 5) / (4 / 5)
tan u = - 3 / 4
tan v = (8 / 17) / (15 / 17)
tan v = 8 / 15
tan (u + v) = (- 3 / 4 + 8 / 15) / [1 - (- 3 / 4) · (8 / 15)]
tan (u + v) = - 13 / 84
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The height above the ground in feet of a football thrown into the air from the balcony of a house is -12t + 20t + 30, where t is the time in seconds since the ball was thrown. How high above the ground is the balcony?
Answer: The height above the ground in feet of a football thrown into the air from the balcony of a house is given by the expression:
h(t) = -12t^2 + 20t + 30
where t is the time in seconds since the ball was thrown.
To find the height of the balcony above the ground, we need to determine the initial height of the football when it was thrown from the balcony. This initial height corresponds to the value of h(0), since the time elapsed since the throw was zero at that moment.
Therefore, we can substitute t = 0 into the expression for h(t):
h(0) = -12(0)^2 + 20(0) + 30 = 30
This means that the balcony is 30 feet above the ground.
Hence, the height of the balcony above the ground is 30 feet.
Step-by-step explanation:
Use the points (8, 12,800) and (14, 14,420) to enter and interpret the equation of the line of fit in slope-intercept form. y=
The cost of raising a child increases $ each year. The cost of raising a child from birth to age 1 is $ If the trend continues, what will be the approximate annual cost of raising a child born in 2013 at age 17? about $
the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues. we first need to calculate the slope (m) and the y-intercept (b)
what do you mean by approximate ?
Approximate means "close to but not exactly" or "an estimate". In other words, an approximate value is a value that is not exact but is close enough to the actual value to be useful or meaningful in a given context.
In the given question,
To find the equation of the line of fit in slope-intercept form, we first need to calculate the slope (m) and the y-intercept (b) using the two given points (8, 12,800) and (14, 14,420).
m = (y₂ - y₁) / (x₂ - x₁)
m = (14,420 - 12,800) / (14 - 8)
m = 1,620 / 6
m = 270
b = y - mx
b = 12,800 - 270(8)
b = 10,940
Therefore, the equation of the line of fit in slope-intercept form is:
y = mx + b
y = 270x + 10,940
To use this equation to estimate the cost of raising a child born in 2013 at age 17, we can plug in x = 17 and solve for y:
y = 270x + 10,940
y = 270(17) + 10,940
y = 15,050
Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues.
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Let f(x) = (x + 3)(x + 4) and g(x) = 1 3 (x + 3)(x − 4). The graphs of each are shown below.
Which graph represents which polynomial function? Explain how you can determine this without
using graphing software
Answer: We can determine which graph represents which polynomial function by analyzing the factors of each function.
First, let's consider f(x) = (x + 3)(x + 4). The factors are (x + 3) and (x + 4). When we multiply these factors together, we get a quadratic polynomial with a positive leading coefficient. This means that the graph of f(x) will be a parabola that opens upward.
Next, let's consider g(x) = 1/3(x + 3)(x − 4). The factors are (x + 3) and (x - 4). When we multiply these factors together and simplify, we get a quadratic polynomial with a leading coefficient of 1/3. This means that the graph of g(x) will also be a parabola that opens upward, but it will be narrower than the graph of f(x).
Based on this analysis, we can determine that the graph of f(x) corresponds to the wider parabola, and the graph of g(x) corresponds to the narrower parabola. We can also determine this without using graphing software by noting that f(x) has roots at x = -3 and x = -4, while g(x) has roots at x = -3 and x = 4. The graph of f(x) must therefore intersect the x-axis at -3 and -4, while the graph of g(x) must intersect the x-axis at -3 and 4. By examining the graphs, we can see that the wider parabola intersects the x-axis at -3 and -4, so it corresponds to f(x), while the narrower parabola intersects the x-axis at -3 and 4, so it corresponds to g(x).
Step-by-step explanation:
I NEED HELP
please help, this is late homework and im confused. (an explanation for the answer would be great)
Answer: then get help
Step-by-step explanation:
if x+2 is a factor of x^3-6x-11x+k, then k=
The value of k in the expression x³ – 6x² – 11x + k is –10.
What is polynomials?Polynomial is formed up of the terms Nominal, which means "terms," and Poly, which means "many." A polynomial is a mathematical expression made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.
From the question given above, the following data were obtained:
f(x) = x³ – 6x² – 11x + k
Factor => x + 2
Value of k =?
Next, we shall obtained the value of x from x + 2. This can be obtained as follow:
x + 2 = 0
Collect like terms
x = 0 – 2
x = –2
Finally, we shall determine the the value of k. This can be obtained as illustrated below:
f(x) = x³ – 6x² – 11x + k
x = –2
Value of k =?
f(–2) = 0 since x + 2 is a factor
x³ – 6x² – 11x + k = 0
(–2)³ – (–2)² – 11(–2) + k = 0
–8 – (4) + 22 + K = 0
–8 – 4 + 22 + K = 0
10 + k = 0
Collect like terms
k = 0 – 10
k = –10
Therefore, the value of k is –10
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Adele and her brother ran a race. Adele reached the finish line in 37.45 seconds and her brother reached the finish line 2.1 seconds later. How long did it take Adele's brother to run the race?
Answer:
It took Adele's brother 37.45 + 2.10 = 39.55 seconds to run the race.
To determine how far a boat is from shore, two radar stations 590
feet apart find the angles out to the boat, as shown in the figure below. Determine the distance of the boat from station A and the distance of the boat from shore. Round your answers to the nearest whole foot.
Distance to station A:
Distance to the shore:
A boat's distance from the coast is measured from station A, where the angle is [tex]50[/tex] degrees, and the shore lies [tex]868[/tex] feet away.
Class 6 distance: what is it?A scalar number known as distance measures "how so much ground an item has traversed" while moving. A vector quantity called displacement describes how far an item is out of place.
What does length vs. distance mean in physics?A segment's or a room's dimensions are examples of things that may be measured in terms of length. Distance is the separation between two things, like two major cities or 2 points. There will never be a zero sign for either length or distance.
Let Ø be the third angle in the triangle. Ø=180°-70°-60°=180°-130°=50°
Since we now have an angle and its opposite side, the Law of Sines can be used to find the lengths of other sides. Let [tex]X[/tex] be the distance from the boat to station A, then
590/sin(Ø)=X/sin(°70)
X=590[sin(70°)/sin(50°)]=868 ft
Distance boat to shore=868sin(70°)[tex]=868 ft[/tex]
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Find the perimeter and total area
Answer:
Perimeter: Add up all the sides (7.5, 6, 2.5, 3.5, 3.5) to get the answer for the perimeter as 23 ft.
Area: Split the shape into two rectangles either way and multiply the length and width. Then, add the two answers. This would leave us with the answer of the area as 35 square feet.
10. Substitute for A, P and T in the formula A = P(1 + r), given that A = 1 000 000, P = 10 000 and T = 2, and express as a quadratic equation.
Answer:
Step-by-step explanation:Let's first substitute the values of A, P, and T in the formula A = P(1 + r)^T.
Given: A = 1,000,000; P = 10,000; T = 2
1,000,000 = 10,000(1 + r)^2
Now let's express it as a quadratic equation. First, divide both sides by 10,000:
100 = (1 + r)^2
Next, expand the square:
100 = 1 + 2r + r^2
Finally, rearrange to form the quadratic equation:
r^2 + 2r - 99 = 0
To represent the formula A = P(1 + r) as a quadratic equation with the given values, we substitute A = 1,000,000, P = 10,000, and T = 2. The resulting equation is 10,000r - 9,000,000 = 0.
Explanation:To express the formula A = P(1 + r) as a quadratic equation, we substitute the given values for A, P, and T.
Given:
A = 1,000,000P = 10,000T = 2Substituting these values into the formula:
1,000,000 = 10,000(1 + r)
To express this equation as a quadratic form, we can expand the parentheses:
1,000,000 = 10,000 + 10,000r
Now, let's move all the terms to one side to form a quadratic equation:
10,000r - 9,000,000 = 0
Therefore, the quadratic equation that represents A = P(1 + r) with the given values is 10,000r - 9,000,000 = 0.
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6. The picture at the right shows the garden in Robert's
yard. He wants to cover the garden with plastic be-
cause of a sudden drop in temperature. How many
square yards of plastic does he need?
12 ft
15 ft
9 ft
Answer:
To determine the area of the garden that needs to be covered with plastic, we need to multiply the length by the width of the garden. However, we need to convert the measurements to the same unit of measurement. Let's convert the measurements into yards since we need to find the area in square yards. 12 ft = 4 yards 15 ft = 5 yards 9 ft = 3 yards Now, we can calculate the area: Area = Length x Width Area = 5 yards x 4 yards Area = 20 square yards Therefore, Robert needs 20 square yards of plastic to cover his garden.
single-cell of bacteria triples every 3 days. About how many days will it take one bacteria to produce a population of 2187?
Answer:
7 days
Step-by-step explanation:
what is a fraction between 6/7 and 1
Answer:
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What is a fraction between 6/7 and 1 whole?
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Expert-Verified Answer
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amitnrw
Genius
40.2K answers
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Given : 6/7 and 1 whole
To Find : a fraction between 6/7 and 1 whole
Solution:
There exist Infinitely many rational between two different rational numbers
There can be Different ways to find rational number in between two number
one way is to find mean of number
= (6/7 + 1)/2
= 13/14
13/14 is a fraction between 6/7 and 1 whole
6/7 = 18/21
1 = 21/21
19/21 , 20/21 are fraction between 6/7 andfraction