Answer:
Step-by-step explanation:
The formula for determining the length of an arc is expressed as
Length of arc = θ/360 × 2πr
Where
θ represents the central angle.
r represents the radius of the circle.
π is a constant whose value is 3.14
From the information given,
Radius, r = 3
θ = π/6
2π = 360 degrees
π = 360/2 = 180
Therefore,
θ = 180/6 = 30 degrees
Therefore,
Length of arc = 30/360 × 2 × 3.14 × 3
Length of arc = 1.6 to the nearest tenth
Final answer:
To find the length of the intercepted arc on a circle with radius 3 and a central angle of π/6, calculate using the formula s = rθ. The result is approximately 1.6 units after rounding to the nearest tenth.
Explanation:
The question asks to find the length of the intercepted arc given a central angle of measure θ=π/6 on a circle with radius r = 3 and to round the answer to the nearest tenth. To calculate the arc length (θ), we use the formula s = rθ, where θ is measured in radians. Given θ=π/6 and r=3, the arc length s is therefore 3*(π/6)= π/2. To get a numerical answer, substitute π with approximately 3.14159, resulting in s = (3*3.14159)/6 which simplifies to s ≈ 1.57. Rounding to the nearest tenth gives us an arc length of 1.6 units.
A recipe for a apple cider calls for 4 cups of apple and 3 cups of water. Witch equation can be used to find x, the percent of a apple juice in the recipe?
A.4/3=x/100
B.3/4=x/100
C.7/3=100/x
D.7/4=100/x
Idk can ya help me I think is b but am not sure what do you think?
The percent of apple juice in the recipe is D.7/4=100/x
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Ratio of apple juice to water is 4 : 3 = Y i.e 4+ 3 = 7
To find the exact percent of apple juice used in the recipe, we will use the ratio of juice to water provided, given Y as any amount of apple cider.
The equation 4/7 × Y = amount of apple juice.
for percentage, 4/7 × Y × 100 = amount of apple juice.
In 200ml apple cider, the amount of apple juice presented as;
= 4/7 × 200 = 114.2ml of juice
To make up to 00ml cider, add (200-114.2) ml of water.
Hence, the percent of apple juice in the recipe is D.7/4=100/x
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Solve for x in the triangle round your answer to the nearest tenth
Answer:
8,55
Step-by-step explanation:
use trigonometric functions
If MATH is an isosceles trapezoid and the m∠A = 60°, what is the m∠H?
Answer: C, 120°
Step-by-step explanation:
If MATH is an isosceles Trapezoid, and the measurement of Angle A is 60°, then the Measurement of Angle M would be equivalent to the Measurement of Angle A. Then, using the Same Side Interior Theorem, the Measurement of Angle H would be equal to 180°- 60° (The Measurement of Angle M), which is equal to 120°, C.
Answer:
C 120°
Step-by-step explanation:
In an isosceles trapezoid, base angles are congruent.
[tex]\therefore m \angle A = m\angle M= 60°..(1)\\
\&\: m \angle T = m\angle H..(2)\\
m\angle M +m\angle A + m\angle T +m\angle H= 360°\\
\therefore 60° + 60° +m\angle H +m\angle H= 360°\\
[From\: equations\: (1)\: \& \:(2)] \\
\therefore 120° +2m \angle H = 360°\\
\therefore 2m \angle H = 360°-120°\\
\therefore 2m \angle H = 240°\\
\therefore m \angle H = \frac{240°} {2} \\
\huge\purple {\boxed {\therefore m \angle H = 120°}} [/tex]
The polygons in each pair are similar. Find the missing side length.
Answer:
12
Step-by-step explanation:
If you flip the polygon on the right so it looks like the polygon on the left, the scale factor for the small polygon to the big polygon is 32/40 or 4/5.
Now use that scale factor, 4/5, to find the missing length
4/5 = ?/15
5*3 = 15 so 4*3 = ?
? = 12
The missing side of the given polygon is 12 units.
What is Polygon?
In geometry, a polygon is any closed curve made up of a collection of continuous line segments (sides) without any intersections. Triangles (three sides), quadrilaterals (four sides), and pentagons are the three simplest polygons (five sides).
If you flip the polygon on the right so it looks like the polygon on the left, the scale factor for the small polygon to the big polygon is 32/40 or 4/5.
Let x be the missing side of the polygon.
Now use that scale factor, 4/5, to find the missing length.
4/5 = x/15
5*3 = 15 so 4*3 = x
x = 12
therefore, 12 is the missing side of the given polygon.
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Which describes the effect of the transformations on the graph of ƒ(x) = x2 when changed to ƒ(x) =1/2(x − 5)2 + 7?
A) stretched vertically, shifted left 5 units, and shifted down 7 units
B) stretched vertically, shifted right 5 units, and shifted up 7 units
C) compressed vertically, shifted left 5 units, and shifted down 7 units
D) compressed vertically, shifted right 5 units, and shifted up 7 units
The graph is stretched vertically, shifted left 5 units, shifted up 7 units.
We have to determine the effect of the transformations on the graph of ƒ(x) = x^2 when changed to ƒ(x) =1/2(x − 5)^2 + 7
What is the vertex form of the quadratic equation?The vertex form of the quadratic equation is f(x) = a(x-h)^2 + k.
ƒ(x) =1/2(x − 5)^2 + 7 compare with vertex form therefore we have
a=1/2,h=5 k=7.
a=1/2 means the closer to zero the a value, the wider, so this will stretch vertically.
h=5 and this means that the graph is shifted left 5 units.
k=7 this means that the graph is shifted up 7 units.
The answer is stretched vertically, shifted left 5 units, shifted up 7 units.
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Final answer:
The graph of f(x) = x^2 undergoes a vertical compression, horizontal shift to the right by 5 units, and a vertical shift up by 7 units to become f(x) = 1/2(x - 5)^2 + 7, corresponding to option B.
Explanation:
When comparing the original function f(x) = x^2 with the transformed function f(x) = 1/2(x − 5)^2 + 7, we can analyze the effects of transformation as follows:
Vertical Compression: The coefficient 1/2 in front of (x − 5)^2 causes a vertical compression by a factor of 1/2 compared to the original function.
Horizontal Shift: The term (x − 5) inside the function indicates a horizontal shift to the right by 5 units.
Vertical Shift: The constant +7 added outside the square indicates the graph is shifted up by 7 units.
Therefore, the correct description of the transformations applied to f(x) = x^2 to obtain f(x) = 1/2(x − 5)^2 + 7 is option B: compressed vertically, shifted right 5 units, and shifted up 7 units.
amanda enjoys cycling. The graph shows the relationship between the number of hours she rides her bike, x, and the number of miles she covers. The equation that represents the relationship between the number of hours she rides, x, and the distance she covers, y, is a 14y = x
b y=14x c y+14=x d y= 14+x. Using the equation, the distance she would cover if she rode for 1.5 hours would be a 12.5 b 15.5 c 21 d 28 miles.
Answer:
y is 14x
Step-by-step explanation:
every time she travels 14 miles, she is on her bike for one hour
Answer:
y=14x and 21 miles
Please solve this worksheet.Please
Know that quadrilaterals’ with 4 sides the degrees should all add up to 360
a. 110
(110+62+78= 250
360 - 250 = 110)
b. 66
(84+78+2b+b = 360
162+3b = 360
3b = 198
b = 66)
c. 83
For 5 sides the degrees should add up to 540)
(101+152+38+2c+c = 540
291+3c=540
3c = 249
c = 83)
d. 30
For 6 sides the degrees should add up to 720
(108+102+4d+4d+4d+5d = 720
210+17d= 720
17d = 510
d = 30)
As for the others I’ll label them 1, 2, and 3...
1. 60
(105+75+2b+b = 360
180+3b= 360
3b = 180
b = 60)
2. 78
(125+65+92+a = 360
282+a = 360
a = 78)
3. 80
(130+65+120+[2c-15]+c = 540
315+[2c-15]+c = 540
3c-15 = 225
3c = 240
c = 80
Place a number in each box so that each equation is true and each equation has at least one negative number. Choose a number single-digit number starting with the positive number, negative number - not ZERO 2^_x2^_=2^0
Answer:
x=1, y=-1
Step-by-step explanation:
Given the equation: [tex]2^{x}X2^{y}=2^0[/tex]
where x and y are the blank boxes.
We want to find
A positive value of xA negative value of yThat makes the equation true.
If x=1, y=-1
[tex]2^{1}X2^{-1}=2^0[/tex]
This can be confirmed using addition law of indices([tex]a^x+a^y=a^{x+y}[/tex])
[tex]2^{1}X2^{-1}=2^{1+(-1)}=2^{1-1}=2^0[/tex]
In general, any pair of a number and its negative value will satisfy the equality.a. -5
b. -2
c. -3
Let's fill in the blanks for each equation:
a.[tex]\( 2^5 \times 2^{(-5)} = 2^0 \)[/tex]
b. [tex]\( 2^3 / 2^5 = 2^{(-2)} \)[/tex]
c. [tex]\( 2^{(-3)} \times 5^{(-3)} = 10^{(-3)} \)[/tex]
For each equation:
- In (a), [tex]\( 2^{(-5)} = \frac{1}{32} \)[/tex], which is a negative exponent.
- In (b),[tex]\( 2^{(-2)} = \frac{1}{4} \)[/tex], another negative exponent.
- In (c), [tex]\( 10^{(-3)} = \frac{1}{1000} \)[/tex], a negative exponent.
So, the numbers to fill in the blanks are:
a. -5
b. -2
c. -3
Complete question
Place a number in each box so that each equation is true and each equation has at least one negative number.
a. 2^5* 2^(□)=2^0
b. 2^3/2^5 =2^(□)
C. 2^(-3)* 5^(-3)=10^(□)
On hot, sunny, summer days, Jane rents inner tubes by the river that runs through her town. Based on her past experience, she has assigned the following probability distribution to the number of tubes she will rent on a randomly selected day.
(a) Find P(X = 75).
(b) Find P(X ≤ 75).
(c) Find P(X > 50).
(d) Find P(X < 100).
(e) Which of the probability expressions in parts (a)–(d) is a value of the CDF?
X 25 50 75 100 Total
P(X) .20 .40 .30 .10 1.00
Answer:
a) P(X = 75) = 0.30
(b) P(X ≤ 75)
= 0.2 + 0.4 + 0.3 = 0.90
(c) P(X > 50).
= 0.3 + 0.1 = 0.40
(d) P(X < 100)
= 0.2 + 0.4 + 0.3 = 0.90
(e) parts b, c & d are CDF
Answer:
the answer is C,D,B enjoy your day
Step-by-step explanation:
Write a single algebraic expression for the following sequence of operations. Begin with a number represented by n. Multiply by -2 add 5 to the previous expression divide the previous expression by 3 subtract 6 from the previous expression multiply the previous expression by 4 add 7 to the previous expression
Answer:
-2n-15 1/3
Step-by-step explanation:
-2n+5/3-6(4)+7
-2n+5/3-24+7
-2n+1 2/3-17
-2n-15 1/3
What is the volume of the triangular prism?
A) 12 cm3
B) 18 cm3
C) 24 cm3
D) 48 cm3
Find the area of the triangle side, then multiply by the length of the prism.
Area of triangle = 1/2 x height x base
Area = 1/2 x 2 x 3 = 3 square cm
Volume = 3 x 4 = 12 cubic cm.
Answer is A) 12 cm^3
5 - (-7) = 5+ ___ write as addition
Subtracting a negative is the same as adding its positive counterpart. Therefore, (5 - (-7)) can be written as (5 + 7), resulting in the answer of 12. So, 5 - (-7) = 5 + 7.
To write the subtraction problem (5 - (-7)) as an addition problem, we can use the rule that subtracting a negative is equivalent to adding its positive counterpart. Therefore: 5 - (-7) = 5 + 7.
In this case, subtracting a negative 7 is the same as adding 7. The result of this addition is 12. So, 5 - (-7) is equal to (5 + 7) and both expressions evaluate to 12.
This concept is fundamental in understanding the operations of addition and subtraction and their relationship to positive and negative numbers.
To rewrite subtraction as addition, change the sign of the number being subtracted and then add it to the other number. In the equation 5 - (-7), this becomes 5 + 7 because we flip the negative sign to a positive.
Explanation:The equation 5 - (-7) can be rewritten as addition by changing the subtraction of a negative number to the addition of a positive one. So, replacing the minus sign with an addition sign, and flipping the sign of the second number from negative to positive yields 5 + 7.
The general rule for subtracting integers is to change the sign of the number being subtracted (the subtrahend) and then proceed with addition. For example, 5 - (+3) = 5 - 3 becomes 5 + (-3) = 2. Another example: subtracting -6 from 2 can be rewritten as 2 - (-6) = 2 + 6 = 8. When handling subtraction, this is how we can always rewrite it as an addition problem.
The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 log StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 12 and is the least intense sound a human ear can hear. Brandon is trying to take a nap, and he can barely hear his neighbor mowing the lawn. The sound intensity level that Brandon can hear is 10-10. Ahmad, Brandon’s neighbor that lives across the street, is mowing the lawn, and the sound intensity level of the mower is 10-4. How does Brandon’s sound intensity level compare to Ahmad’s mower?
Answer: A Brandon’s sound intensity is 1/4 the level of ahmads mower
Step-by-step explanation:
Brandon's audible sound level is 60 decibels less than the sound intensity level of Ahmad's mower. This is because the sound intensity from the mower is one million times (or 10^6 times) greater than the sound intensity level that Brandon can hear.
Explanation:The sound intensity, I, is given in terms of decibels, Db, as defined in the formula L = 10 log (I/I0). Here, I0 = 10-12 watts per square meter is the least intense sound a human ear can hear. Now, to compare the sound intensity levels for Brandon and Ahmad's mower, we need to look at their respective sound intensities.
Brandon hears a sound level of 10-10 watts per square meter, and Ahmad's mower generates a sound intensity of 10-4 watts per square meter.
The logarithmic scale used in calculating decibels means that for every increase in 10 times the sound intensity, the loudness increases by 10 decibels.
So, since Ahmad's mower generates a sound that is 106 (=10-4/10-10) times more intense than Brandon's audible level, it means that the mower is 60 decibels louder (since 10*6 = 60) than the sound Brandon can hear.
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The probability that a student takes a history class and a sociology class is 0.051. The probability that a student takes a history class is 0.32. What is the probability that a student takes a sociology class, given that the student is taking a history class?
0.051
0.159
0.269
0.32
Answer: 0.159
other answer is wrong i did the quiz
A shirt that normally costs $35.00 is on sale for 28.00. What is the percent discount?
Answer:
$25.20
Step-by-step explanation:
$35 x 0.28
= $9.80
35-9.80
= $25.20
Answer:
20%
Step-by-step explanation:
35 x .2 = 7
35 - 7 = 28
Hope this helps & best of luck!
Feel free to message me if you need more help! :)
Help❤️
Thank you❤️❤️
Answer:
Step-by-step explanation:
B
Answer:
the answer is B
Step-by-step explanation:
Find the area of the circle. Round your answer to the nearest tenth. PLEASE HELP QUICK!!!
Papa Fred's Pizza has found that the menu time to deliver a pizza is 21.2 minutes with a
standard deviation of 6.1 minutes. They want to have a guaranteed delivery time. In order to
deliver 99% within the guaranteed time you need to find the time represented by the 99
percentile. What is this value?
Answer:
That time is 35.4 minutes.
Step-by-step explanation:
The mean time of delivery follows a Normal Distribution pattern.
So we need to apply Z-scores to find out.
99% confidence in delivery time means P(z > value) = 0.01 = 1%
So z > 2.325
so. Pr [ (x - 21.2) / 6.1 > 2.325 ] = 1%
so x > 2.325*6.1 + 21.2
x > 35.3825 minutes would be out of the 99th percentile
Final answer:
To calculate the 99th percentile of pizza delivery times, use the z-score corresponding to a 0.99 probability and apply the formula X = μ + (z * σ), where X represents the delivery time, μ is the mean, and σ is the standard deviation.
Explanation:
The student is asking for the 99th percentile of the pizza delivery time, given that the times are normally distributed with a mean of 21.2 minutes and a standard deviation of 6.1 minutes. To find the 99th percentile, one would typically use a z-score table or a statistical software to find the z-value that corresponds to the 0.99 probability. Once the z-score is found, the formula X = μ + (z * σ) is used to calculate the specific time that corresponds to the 99th percentile, where X is the delivery time, μ is the mean delivery time, σ is the standard deviation, and z is the z-score. Since the student is asking for a guaranteed delivery time that covers 99% of the deliveries, this time will be longer than the average to account for the variability represented by the standard deviation.
What is 3× 1/10 in decimal notation?
Answer:
.3
Step-by-step explanation:
3* 1/10 = .3
.3 is decimal notation
Answer:
0.3
Step-by-step explanation:
1/10 in decimal notation is 0.1 so multiplying it by 3 = 0.3
Eiko is wearing a magic ring that increases the power of her healing spell by 30% without the ring her healing spell restores H health points which expressions could represent how many health points the spell restores when eiko is wearing the magic ring
When wearing the magic ring, health points increase by 30% more.
Some expressions that could represent how many health points the spell restores are:
1.3(H)
H + 0.3(H)
Hope this helps!! :)
The healing spell with the magic ring restores 130% of the health points, represented as 1.30 imes H.
If Eiko's healing spell restores H health points without the magic ring, then with the ring, the spell's power increases by 30%. Thus, the total healing power with the ring can be expressed as H + 0.30 x H, which can also be simplified to 1.30 x H. This means, with the ring, Eiko would restore 130% of the health points that the spell would normally heal without the ring.
How long does it take to double a $1,000 investment that pays 6.5% annual interest, compounded monthly?
Which equation can you use to solve this problem?
To the nearest year, it will take about ___
years to double the original investment.
Answer: edgen
B 2=(1+0.065/12)^12t
Step-by-step explanation:
To the nearest year, it will take about 10.7 years to double the original investment.
How to solbve for the period it would takeIn this case, the principal P is $1,000, the interest rate r is 6.5% or 0.065 (in decimal form), the number of times compounded per year n is 12 (compounded monthly), and we want to find the time t when the investment doubles, so A is $2,000.
[tex]2000 = 1000(1 + 0.065/12)^{12t}[/tex]
[tex]2 = (1 + 0.065/12)^{12t}[/tex]
ln(2) = 12t * ln(1 + 0.065/12)
t = ln(2) / (12 * ln(1 + 0.065/12))
t ≈ 10.7
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A point $(x, y)$ with integer coordinates is randomly selected such that $0 \le x \le 8$ and $0 \le y \le 4$. what is the probability that $x + y \le 4$? express your answer as a common fraction.
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
A point (x, y) with integer coordinates is randomly selected such that [tex]0 \le x \le 8 \:and\: $0 \le y \le 4$.[/tex]
The possible pairs of (x,y) are:
(0,0),(0,1),(0,2),(0,3),(0,4)
(1,0),(1,1),(1,2),(1,3),(1,4)
(2,0),(2,1),(2,2),(2,3),(2,4)
(3,0),(3,1),(3,2),(3,3),(3,4)
(4,0),(4,1),(4,2),(4,3),(4,4)
(5,0),(5,1),(5,2),(5,3),(5,4)
(6,0),(6,1),(6,2),(6,3),(6,4)
(7,0),(7,1),(7,2),(7,3),(7,4)
(8,0),(8,1),(8,2),(8,3),(8,4)
The Total Possible Outcomes n(S)= 45
The pair (x, y) that satisfies the given condition (say event A: [tex]x + y \le 4[/tex]) are:
[tex](0,0),(0,1),(0,2),(0,3),(0,4)\\(1,0),(1,1),(1,2),(1,3)\\(2,0),(2,1),(2,2)\\(3,0),(3,1)\\(4,0)[/tex]
n(A)=15
Therefore:
[tex]P(A)=\frac{n(A)}{n(S)} =\frac{15}{45} =\frac{1}{3}[/tex]
Final answer:
To find the probability that a randomly selected point with integer coordinates satisfies "x + y ≤ 4", we counted the number of qualifying points and divided by the total number of possible points. With 15 points meeting the condition out of 45 possible points, the probability is 1/3.
Explanation:
The probability question asks for the likelihood that a point (x, y) with integer coordinates will satisfy the condition "x + y ≤ 4" when 0 ≤ x ≤ 8 and 0 ≤ y ≤ 4. To solve this, we first count the total number of possible points with integer coordinates within the given ranges for x and y. Since x can take 9 values (0 through 8) and y can take 5 values (0 through 4), there are 45 possible points (9 times 5).
Next, we identify the points that satisfy the condition "x + y ≤ 4". These points are (0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (3,0), (3,1), and (4,0), which results in a total of 15 points satisfying the condition.
The probability is therefore the number of satisfying points divided by the total number of possible points, which is 15/45 or simplified to 1/3. Thus, the probability that a randomly selected point with integer coordinates will have "x + y ≤ 4" is 1/3.
A large container has a maximum capacity of 64 ounces. The container is filled with 8 ounces less than its maximum capacity. Answer parts a and b.
a. To what percent of its capacity is the large container filled?
b. (I have to finish part a first)
Answer:
I believe A. is 82.352941176471%
Step-by-step explanation:
Let v⃗ 1=⎡⎣⎢⎢⎢0.50.50.50.5⎤⎦⎥⎥⎥, v⃗ 2=⎡⎣⎢⎢⎢0.50.5−0.5−0.5⎤⎦⎥⎥⎥, v⃗ 3=⎡⎣⎢⎢⎢0.5−0.5−0.50.5⎤⎦⎥⎥⎥. v→1=[0.50.50.50.5], v→2=[0.50.5−0.5−0.5], v→3=[0.5−0.5−0.50.5]. find a vector v⃗ 4v→4 in r4r4 such that the vectors v⃗ 1v→1, v⃗ 2v→2, v⃗ 3v→3, and v⃗ 4v→4 are orthonormal.
To find a fourth vector v₄ that is orthonormal with vectors v₁, v₂, and v₃, you must find the values of v₄ such that the dot product of v₄ and each other vector is zero and v₄'s magnitude is one. This results in a system of linear equations. Solving this system will give you the components of vector v₄.
Explanation:Given that the vectors v₁=[0.50.50.50.5], v₂=[0.50.5−0.5−0.5], and v₃=[0.5−0.5−0.50.5] are orthonormal, we need to find a fourth vector v₄ in R⁴ such that the set of these four vectors are also orthonormal. In an orthonormal set of vectors, each vector has a length (or magnitude) of one, and the dot product of each pair of different vectors is zero, indicating they are orthogonal or perpendicular to each other.
By inspection, we can see that the given vectors v₁, v₂, and v₃ already satisfy these conditions. So, the challenge is to find v₄ such that its dot product with each of the other three vectors is zero and its magnitude is one. Let's denote v₄ as [a, b, c, d].
Setting the dot product of v₄ and the other three vectors to zero gives the set of equations: 0.5a + 0.5b + 0.5c + 0.5d = 0, 0.5a + 0.5b - 0.5c - 0.5d = 0, and 0.5a - 0.5b - 0.5c + 0.5d = 0. Furthermore, to satisfy the condition that the magnitude of v₄ is one, we have the equation a² + b² + c² + d² = 1.
Solving these simultaneous equations will give the components of the vector v₄ that is orthogonal to v₁, v₂, and v₃ and has a magnitude of one, thus completing the orthonormal set.
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If a rectangle is 4 inches wide and 7 inches long. When the length and width are increased by the same amount, the area is increased by 26 square inches. What are the new dimensions.
Answer:
New length = [tex]2+7=9[/tex] inches
New width = [tex]2+4=6[/tex] inches
Step-by-step explanation:
Given:
Length of rectangle is 7 inches
Width of a rectangle is 4 inches
The area is increased by 26 square inches when the length and width are increased by the same amount.
To find: new length and width
Solution:
With length of rectangle is 7 inches and width of a rectangle is 4 inches,
area = 7×4 = 28 inches
Let length and width be increased by x inches
New length = x + 7 inches
New Width = x + 4 inches
New area = [tex](x+7)(x+4)=x^2 +11x+28[/tex]
Also, new area = 28 + 26 = 54 square inches.
So,
[tex]28+11x+x^2 =54\\x^2+11x-26=0\\x^2 +13x-2x-26=0\\x(x+13)-2(x+13)=0\\(x-2)(x+13)=0\\x= 2, -13[/tex]
As dimension can not be negative, [tex]x=-13[/tex] is rejected.
So, [tex]x=2[/tex]
New length = [tex]2+7=9[/tex] inches
New width = [tex]2+4=6[/tex] inches
Final answer:
The new dimensions of the rectangle are 6 inches by 9 inches, after increasing both the original width and length by 2 inches to achieve the new area of 54 square inches.
Explanation:
Solution to the Rectangle Problem
The original rectangle is 4 inches wide and 7 inches long, with an area of 28 square inches (since area = width imes length). When both the length and width are increased by the same amount, the area is 28 inches + 26 inches = 54 square inches. Let's denote the increase in dimension by 'x', thus the new dimensions are (4 + x) inches and (7 + x) inches. The new area is then (4 + x)(7 + x) = 54. Expanding this, we get 28 + 11x + x2 = 54. Simplifying, x2 + 11x - 26 = 0.
To find 'x', we can solve the quadratic equation. Factoring the quadratic, we get (x + 13)(x - 2) = 0, giving us two potential solutions for 'x': -13 and 2. However, since a negative increase in dimension is not possible, we only consider x = 2. Hence, the new dimensions of the rectangle are 6 inches by 9 inches.
Of 58 cities, 3 have a lake and 23 have a river running through them. What fraction of these 58 cities have a lake or a river running through them?
Out of 58 cities, 26 have either a lake or a river, which simplifies to a fraction of 13/29 of the cities having one of these features.
Explanation:To find the fraction of 58 cities that have either a lake or a river running through them, we need to determine how many cities have at least one of these features. It is important to check if any city has both a lake and a river, but since the question does not provide this information, we will assume that there are no cities that have both. The question tells us that 3 cities have a lake and 23 have a river. We simply add these counts together to find the total number of cities with at least one water feature.
The calculation would be:
3 (cities with a lake) + 23 (cities with a river) = 26 (cities with a lake or a river)
To find the fraction of the 58 cities that have a lake or a river, we divide the number of cities with a water feature by the total number of cities:
26 (cities with a lake or a river) / 58 (total cities) = 13/29 (simplified fraction).
Final answer:
Of the 58 cities, 26 have either a lake or a river, which means the fraction of cities with a lake or a river is 26/58.
Explanation:
To determine what fraction of the 58 cities have a lake or a river running through them, we must consider that the question does not specify whether some cities might have both a lake and a river. Assuming that the cities with lakes and the cities with rivers do not overlap, we simply add the number of cities with each feature.
There are 3 cities with a lake and 23 with a river. To find the total number of cities with either a lake or a river, we add these two numbers together:
3 (cities with a lake) + 23 (cities with a river) = 26 (cities with a lake or a river).
Now, to find the fraction of the 58 cities that have a lake or a river, we divide the number of cities with water features by the total number of cities:
26 / 58 = fraction of cities with a lake or a river running through them.
Todd plans to swim 18 laps in the pool.Each Lap is 50 yards.So far Todd has swam 738 yards. What percentage of the total has Todd completed? A.18% B.82% c.62% D77%
Answer:
Step-by-step explanation: 18 * 50 = 900
738/900 = .82
Move two decimal to right .82 = 82%
As an estimation we are told £3 is €4.
Convert €65.90 to pounds.
Give your answer rounded to 2 DP.
Answer:
49.43£
Step-by-step explanation:
Given that £3 is equal to €4
There fore one euro is equal to
£3 = €4
1 € = 3/4 £ = 0.75 £(pound)
to find value of €65.90 in terms of pound we multiply both side of above equation with 65.90
=> 65.90 € = 0.75 * 65.90 £
=> 65.90 € = 49.425£ (Answer)
65.90 € is equal to 49.43 rounded to two decimal points.
Mrs. Ting cut each pizza into 8 slices. Together the children ate 12 3 4 pizzas. If each child ate two slices of pizza, how many children were at the party?
Answer:
Hence there were total of 19 pizza and were ate among the 76 children in party.
Step-by-step explanation:
Given:
8 slices for each pizza
No of pizza ate are =12+3+4=19
To Find:
How many children were are party
Solution:
Given that each children ate 2 slices per head so
Total pizza=19
and each pizza is sliced in 8 parts so
19 pizza will give =19 *8=152 slices
Hence there are 152 total number of slices
So 2 slices/child and 152 slices
152 slices/ 2 slices/child
=(152/2)children
=76 children.
Can someone please help me
Answer:
5.83 or E
Step-by-step explanation:
Use Pythagorean theorem. 5^2+3^2=c^2 because the diameter is perpendicular it cuts the chord in half.
25+9=c^2
34=c^2
5.83
Answer:
x = 5.83.
Step-by-step explanation:
The diameter bisects the vertical chord so the right triangle has legs 3 and 5.
So x^2 = 3^2 + 5^2
x^2 = 34
x = 5.83.
That is odd - if we work it out another way we get a different answer. I guess that must be because the numbers given in the diagram are not possible.
If we use the intersecting chords theorem, we get (3+6)*3 = 27
= 5 * y where y is the other leg of the right triangle giving y = 5.4
and then this will give x = 6.18.