assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
The mean of the sample proportion distribution is given by:
μp(hat) = p = 0.22
The standard deviation of the sample proportion distribution is given by:
σp(hat) = sqrt((p*(1-p))/n) = sqrt((0.22*0.78)/50) = 0.0802
To find the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night, we need to find the z-score corresponding to this value:
z = (0.20 - 0.22) / 0.0802 = -0.2494
Using a standard normal table or calculator, we find that the probability of obtaining a z-score of -0.2494 or less is 0.4019. Therefore, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night,
Hence assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.
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Answer pls my state test is cominggggg
(-3/4) x (3/4)
---When we multiply fractions, we multiply horizontally/across
(-3 x 3) / (4 x 4)
-9 / 16
Answer: -9/16
Hope this helps!
PLEASE HELP PLEASE!!
Complete the following statement to estimate the root of 75 to the nearest tenth. Use numbers that are closest to the root of 75
Answer:
√75 =8.66.
Step-by-step explanation:
The square root of 75 is an irrational number where the numbers after the decimal point go up to infinity. √75 = 8.660.√75 cannot be written in the form of p/q, hence it is an irrational number. irrational with never-ending digits.
How to Find the Square Root of 75?Let's see how to find the square root of 75 by the long division method.
Step 1: Express 75 as 75.000000. We take the number in pairs from the right. Take 75 as the dividend.
Step 2: Now find a quotient which is the same as the divisor. Multiply quotient and the divisor and subtract the result from 75.
Step 3: Now double the quotient obtained in step 2. Here is 2 × 8 = 16. 160 becomes the new divisor.
Step 4: Apply decimal after quotient '8' and bring down two zeros. We have 1100 as the dividend now.
Step 5: We need to choose a number that while adding to 160 and multiplying the sum with the same number we get a number less than 1100. 160+ 6 = 166 and 166 × 6 = 996. Subtract 996 from 1100. We get 104
Step 6: Bring down two zeros again and place it after 104, so that it becomes 10400 which is the new dividend. Now multiply the number in the quotient by 2. Here it is 86. We get 172. Have it as 1720. Now find a number at the unit's place of 1720 multiplied by itself gives 10400 or less. We find that 1726 × 6 = = 10356. Find the remainder.
Step 7 : Repeat the process until we get the remainder equal to zero. The square root of 75 up to two places is obtained by the long division method. Thus √75 = 8.66
PLEASE HELP SOLVE 30 PTS
Answer:
The polynomial has a unique zero in the interval [1,2] by using intermediate value theorem
Tyler is simplifying the expression: 6-2x+5+4x Here is his work
6-2x+5+4x
(6-2)x+(5+4)x
4x+x
13x
a. Explain the error he made
b. Simplify the expression: 6-2x+5+4x
Answer:
11-2x not 13x
Step-by-step explanation:
\(6-2)x + (5-4)x does = 13x
If there were parentheses as in the 2nd line, everything else is correct
the mistake is going from
6-2x + 5-4x to
(6-2x) + (5-4)x
PEMDAS is the order of operations. P for parentheses 1st, Multiplication 3rd, addition 4th, subtraction 5th
(there are no exponents or division or parentheses, so it's just M, A and S that apply)
combine like terms, 2x-4x =-2x
combine the constant terms 6+5 = 11
6-2x +5-4x = 11-2x
The mistake was assuming parentheses when they aren't there.
correct answer is 11-2x not 13x
What is 1 and 1/4
And 1 and 1/2
The mixed fraction 1 and 1/4 is equal to 5/4 and the mixed fraction 1 and 1/2 is equal to 3/2.
Given first number = 1 and 1/4.
1 and 1/4 is a mixed fraction so, we can write it in the form as [tex]1\frac{1}{4}[/tex] .
To find the value of [tex]1\frac{1}{4}[/tex] we have to multiply 4 with 1 and add the numerator part of the fraction which is 1 and then divide it by 4 which is the denominator. So,
[tex]1\frac{1}{4}[/tex] = ((4x1) + 1 )/4 = 5/4.
Similary, for 1 and 1/2,
[tex]1\frac{1}{2}[/tex] = ((2x1) + 1)/2 = 3/2.
From the above analysis, we can conclude that the value of 1 and 1/4 is 5/4 and the value of 1 and 1/2 is 3/2.
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Enter your answer by filling in the boxes to correctly complete the statements. If necessary, round to the nearest hundredth.
The practical domain of the situation is [0, ∞].
The practical range of the situation is [0, 100].
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [0, ∞] or 0 ≤ x ≤ ∞.
Range = [0, 100] or 0 ≤ y ≤ 100.
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2.1/0.7=3 but how do you work it out (I cheated and used a calculator)
Answer: To work out 2.1/0.7 without a calculator, you can use long division as follows:
0.7 | 2.1
1.4 (3 times 0.7 is 2.1)
-----
0.7
0.0 (there is no remainder)
Therefore, 2.1/0.7 = 3, which means that 2.1 is equal to 3 times 0.7.
Answer:
see below
Step-by-step explanation:
2.1
-----
.7
Multiply the top and bottom by 10 to get rid of the decimals.
2.1 *10 = 21
.7 * 10 = 7
21/7 = 3
The distance from Hans house to Priyas house is 4/5 kilometer. Han has walked 3/4 of the way already. How many kilometers has he walked?
Han has walked 3/5 km.
What is distance?Distance is the length of space between two reference points. It is a scalar quantity, and it is measured in meters.
In the given question, we have that;
distance from Han's house to Priya's house = 4/5 km
Han has walked 3/4 of the way already.
Thus,
distance walked by Han = 3/4 of 4/5
= 3/4 x 4/5
= 12/ 20
= 3/ 5
distance walked by Han is 3/5 km.
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Trapezoid WXYZ is rotated 90 degrees clockwise around point A to create trapezoid WXYZ what must be true A angle W is half the measure of angle W B Wx is equal to WX
C WX is perpendicular to YZ D WZ is equal to WX
Answer:
B) Wx is equal to WX.
When a shape is rotated 90 degrees, the length of its sides and angles do not change. Therefore, the length of Wx in the original trapezoid will be the same as the length of WX in the rotated trapezoid.
Use the quadratic formula to solve -2x^2+2x+1
The solutions for -2x²+2x+1 are x = 1 + √(3)/2 and x = 1 - √(3)/2.
To use the quadratic formula to solve -2x²+2x+1, we first identify the coefficients a, b, and c of the quadratic equation in standard form: ax²+bx+c=0. In this case, a=-2, b=2, and c=1. We then plug these values into the quadratic formula
x = (-b ± √(b²-4ac)) / 2a
Substituting the values, we get
x = (-2 ± √(2²-4(-2)(1))) / 2(-2)
Simplifying the expression inside the square root
x = (-2 ± √(4+8)) / (-4)
x = (-2 ± √12) / (-4)
Simplifying the radical
x = (-2 ± 2√3) / (-4)
Reducing the fraction
x = (1 ± √3/2)
Therefore, the two solutions are x = (1 + √3/2) and x = (1 - √3/2).
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When doubling the dimensions of a rectangle, why does the area quadruple and the perimeter only doubles?
If you double the length and the width, you are quadrupling the area.
This is because 2 × 2 = 4.
Perimeter of new rectangle= 2 × perimeter of initial rectangle.
The perimeter will be double of if we double the length and breadth of rectangle
→ When doubling the dimensions of a rectangle, why the area is quadruple:
We know that :
Area of rectangle = l × b
where, l is length and b is breadth
A = L × W
This means area equals length times width.
if you double the length and you double the width, the formula becomes:
A = 2 × L × 2 × W
A = 2 × 2 × L × W
A = 4 × L × W
if you double the length and the width, you are quadrupling the area.
This is because 2 × 2 = 4.
→When doubling the dimensions of a rectangle, why the perimeter is doubles?
Let length be equal to ′l′
And breadth be equal to ′b′
Perimeter of rectangle = 2 (l + b) ____(equation i )
The perimeter if the length and breadth of the rectangle will increase by two, or will it double? So new parameters of rectangle when its length and breadth will get double on initial one.
Double length of rectangle of initial one= 2 × l=2l
Double breadth of rectangle of initial one = 2×b=2b
So the perimeter of new rectangle whose length and breadth are double of initial one are:
As we know that:
Perimeter of rectangle = 2 (l + b)
So,
Perimeter of new rectangle= 2(2l+2b), (by taking 2 common)
Perimeter of new rectangle = 2×2(l + b) ____ equation (ii)
As from equation (i) perimeter of initial rectangle is = 2(l + b)
So from equation (i) and (ii)
Perimeter of new rectangle= 2 × 2(l + b)
Perimeter of new rectangle= 2 × perimeter of initial rectangle.
Hence, the perimeter will be double of if we double the length and breadth of rectangle.
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In tetrahedron $ABCO,$ $\angle AOB = \angle AOC = \angle BOC = 90^\circ.$ A cube is inscribed in the tetrahedron so that one of its vertices is at $O,$ and the opposite vertex lies on face $ABC.$ Let $a = OA,$ $b = OB,$ and $c = OC.$ Show that the side length of the cube is
\[\frac{abc}{ab + ac + bc}.\]
[asy]
import three;
size(180);
currentprojection = orthographic(6,3,2);
real a, b, c, s;
triple A, B, C, O;
a = 6;
b = 3;
c = 2;
s = a*b*c/(a*b + a*c + b*c);
A = (a,0,0);
B = (0,b,0);
C = (0,0,c);
O = (0,0,0);
draw(O--A,dashed);
draw(O--B,dashed);
draw(O--C,dashed);
draw(A--B--C--cycle);
draw((0,0,s)--(s,0,s)--(s,0,0)--(s,s,0)--(0,s,0)--(0,s,s)--cycle,dashed);
draw((s,s,0)--(s,s,s),dashed);
draw((s,0,s)--(s,s,s),dashed);
draw((0,s,s)--(s,s,s),dashed);
label("$A$", A, SW);
label("$B$", B, E);
label("$C$", C, N);
dot("$O$", O, NW);
dot((s,s,s));
[/asy]
pls help me
Answer:
Step-by-step explanation:To solve this problem, we can use similar triangles. Let the side length of the cube be s, and let the midpoints of AB, AC, and BC be P, Q, and R, respectively. Then OP, OQ, and OR are the diagonals of the faces of the cube, and so they are equal to .Consider triangle AOB. By the Pythagorean theorem, we have , so . Since angle AOB is 90 degrees, we can use similarity to see that triangle OAP is similar to triangle OAB, so . Solving, we find that .Using similar triangles, we can find that . Since the sum of the squares of the lengths of the diagonals of a cube is equal to three times the square of the side length, we have
$$(0P2 + 0Q? + OR?) = 35388 Substituting the values we found for $OP$, $OQ$, and $OR$, we haveSimplifying and solving for , we find that . Thus, the side length of the cube inscribed in the tetrahedron is .
The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
Group of answer choices
x = 0°, 30°, 150°, 180°
x = 0°, 180°, 210°, 330°
x = 30°, 90°, 150°, 270°
x = 90°, 210°, 270°, 330°
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
How to solveFor the frequencies to be the same, we need to find values of n and m such that:
n = m
Solving for n and m, we get:
n = m = 2
So both functions complete two cycles in the interval [0, 2π).
We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:
2sin2x = sin x
2sin2x - sin x = 0
sin x (2sin x - 1) = 0
sin x = 0 or 2sin x - 1 = 0
sin x = 0 when x is an integer multiple of π.
2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.
Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
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PLEASE IM BEGGING HELP PLEASE!!!!!
Answer:
C
Step-by-step explanation:
A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is odd.
Event B: The number rolled is greater than 3.
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
The possible outcomes for each of the given events are:
A --> {1, 3, 5}
B --> {4, 5, 6}
How to find the outcomes for each event?For a regular number cube, the sample space (possible outcomes) is:
S = {1, 2, 3, 4, 5, 6}
Now we have two events.
A = rolling an odd number
Here the outcomes can be any of the odd numbers in the sample space, so the possible outcomes are:
A --> {1, 3, 5}
The second event is:
B = the number rolled is greater than 3. Again, the outcomes are thevalues in the sample space that are larger than 3, these are:
B --> {4, 5, 6}
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math
imaginelearning.com/lesson player/essons/1129/
Two wading pools are being filled at the same time.
The orange pool contains 4 gallons when it starts willing at a rate of 4 galtons a minute.
The blue pool fills at a rate of 5 gallons a minute.
How should the axis be labeled?
The z-axis should be labeled
How should the y-axis be labeled?
The yaxis should be labeled
What does the slope of each line represent?
The slope of each line represents the
What should the x axis be labeled
What is the y axis labeled
What does the slope line of each represent
What does the y intercept of each line represent
What does the slope line of each represent?
The slope line represents the constant change in value.
What does the y intercept of each line represent
The y-intercept indicates the y-value when the x-value is 0.
In a certain survey, 511 people chose to respond to this question: "Should passwords be replaced with biometric security (fingerprints, etc)?"
Among the respondents, 51% said "yes." We want to test the claim that more than half of the population believes that passwords should be
replaced with biometric security. Complete parts (a) through (d) below.
a. Are any of the three requirements vicated? Can a test about a population proportion using the normal approximation method be used?
OA. All of the conditions for testing a claim about a population proportion using the normal approximation method are satisfied, so the method
can be used.
B. The conditions np 25 and nq 25 are not satisfied, so a test about a population proportion using the normal approximation method cannot
be used.
OC. One of the conditions for a binomial distribution are not satisfied, so a test about a population proportion using the normal approximating
method cannot be used.
D. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method
cannot be used.
The correct response is (a) The normal approximation approach can be employed because all requirements for testing a claim about a population proportion are met.
what is probability ?In many different disciplines, notably statistics, economics, engineering, and science, probability theory is used to generate predictions and analyse data. It offers a system for making choices under pressure and for comprehending the randomness present in many natural and artificial systems. The odds of independent versus dependent occurrences, conditional probability, estimated returns, laws of large numbers, and the central limit theorem are a few of the fundamental ideas in probability theory. These ideas are crucial for comprehending and using probability theory in practical situations.
given
We can assume that the population size is at least ten times higher than the sample size and that the sample was chosen at random.
We must compute np and nq in order to verify the second condition:
np = (511)(0.51) = 260.61nq = (511)(0.49) = 250.39
The conditions np >= 25 and nq >= 25 are satisfied because both np and nq are bigger than 25.
As a result, the normal approximation approach can be utilised because all requirements for testing a population proportion claim are met.
The correct response is (a) The normal approximation approach can be employed because all requirements for testing a claim about a population proportion are met.
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Answer:
D. The sample observations are not a random sample, so a test about a population proportion using the normal approximating method
cannot be used.
Step-by-step explanation:
The sample is not random.
Lara chooses a number less than 20
She divides it by 2 and then adds 6
She then divides this result by 3
Her answer is 4.5
What was the number she started with?
Working backward, the number that Lara started with in performing the mathematical operations was 15.
How the number is determined:We can use mathematical operations to determine the initial number that Lara started with.
Mathematical operations include addition, subtraction, division, multiplication, etc.
Let the number that Lara started with = x
x < 20
x ÷ 2 + 6 = y
y ÷ 3 = 4.5
y = 13.5 (4.5 x 3)
x ÷ 2 + 6 = 13.5
x ÷ 2 = 7.5
x = 15 (7.5 x 2)
Thus, Lara started performing the mathematical operations with 15 and got a final result of 4.5.
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3
Florence Griffith-Joyner was an Olympic runner who set the women's world records
for the 100- and 200-meter races in 1988. She completed the 100-meter race in
10.49 seconds and the 200-meter race in 21.34 seconds. How much faster did
Florence run in the 100-meter race than in the 200-meter race, in meters per second?
A 10.85
B 0.1085
C 0.0016
D 0.16
Florence was 0.16 m/s faster in the 100-meter race than in the 200-meter race
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
Speed is the ratio of distance travelled to time taken. It is given by:
Speed = distance / time
She completed the 100-meter race in 10.49 seconds and the 200-meter race in 21.34 seconds. Hence:
For 100 meters:
Speed = 100 m / 10.49 s = 9.53 m/s
For 200 meters:
Speed = 200 m / 21.34 s = 9.37 m/s
The speed difference = 9.53 m/s - 9.37 m/s = 0.16 m/s
Florence was 0.16 m/s faster
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Write an Equation for the ellipse. The center is (1, -3).
The standard form of the equation of the ellipse is (x - 1)² / 16 + (y + 3) / 9 = 1.
How to define the standard form of the equation of an ellipse
In this problem we find the representation of an ellipse on Cartesian plane, whose center is at (h, k) = (1, - 3), whose major semiaxis length is 4 units and whose minor semiaxis length is 3 units. The standard form of the equation of the ellipse is described below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
(h, k) - Coordinates of the center.a - Length of the major semiaxis.b - Length of the minor semiaxis.If we know that (h, k) = (1, - 3), a = 4 and b = 3, then the standard form of the equation of the ellipse is:
(x - 1)² / 16 + (y + 3) / 9 = 1
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What is the perimeter of the regular pentagon?
Answer:
To find the perimeter of a regular pentagon, you need to know the length of one side and the number of sides. In a regular pentagon, all sides have the same length and the shape has 5 sides.
Let's say the length of one side of the regular pentagon is 's'.
The formula for the perimeter of a regular pentagon is:
Perimeter = 5s
This is because a regular pentagon has 5 sides of equal length, so you can simply add the length of each side together 5 times.
Therefore, the perimeter of a regular pentagon with a side length 's' is 5s.
Step-by-step explanation:
Find the distance between the zeros of the (2x-8)^2-4=12
The distance between the zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12 is 4 units.
First, we can simplify the equation [tex](2x-8)^{2}[/tex] - 4 = 12 by adding 4 to both sides:
[tex](2x-8)^{2}[/tex] = 16
Next, we can take the square root of both sides:
2x-8 = ±4
Solving for x in each case, we get:
2x-8 = 4: 2x = 12 → x = 6
2x-8 = -4: 2x = 4 → x = 2
So the zeros of the equation are x=6 and x=2. The distance between them is:
distance = |6 - 2| = 4
As a result, there are 4 units between zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12.
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What is Mine-craft Incorrect Responses Only
Mine-craft Incorrect Responses is known to be a sort of game or challenge where members are inquired to reply to Mine-craft-related questions or explanations with intentioned inaccurate answers.
What is Mine-craft?
The thought is to utilize humor and creativity to come up with reactions that are totally off-base but still somehow related to Mine-craft.
Mine-craft Incorrect Responses is an amusing way of reacting to questions or statements related to the prevalent sandbox video diversion Mine-craft with intentioned off base answers. The objective is to be as imaginative and amusing as conceivable whereas intentionally giving off-base answers to Mine-craft-related questions or comments.
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A company gives a 12% discount to his customers on retail price. If the total is over $10,000 after the discount, they give an additional 3% discount on the remaining balance. A customer’s total came to $13,500 (discounted price). How much did he save?
Answer:
Therefore, the customer saved $2,448.45.
Step-by-step explanation:
To answer this question, we need to use the percentage discount formula to find the original price and the amount saved.
Let x be the original price of the product. Then, after applying the 12% discount, the price becomes 0.88x. If the total is over $10,000 after this discount, then an additional 3% discount is applied on the remaining balance, which means the final price becomes 0.97 * 0.88x.
We are given that the final price is $13,500, so we can set up an equation and solve for x:
0.97 * 0.88x = 13,500 x = 13,500 / (0.97 * 0.88) x = 15,948.45
Therefore, the original price was $15,948.45.
The amount saved is the difference between the original price and the final price:
15,948.45 - 13,500 = 2,448.45
Can someone help me with this please
The matrix after the row operation is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
How to do the row operation?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{ccc}7&-4&8\\-12&7&-13\end{array}\right][/tex]
We want to have element 1 into row 1 and column 1, that is, the element of 7 must assume a value of -1.
A valid row operation is the multiplication of the row by a constant, and as the element has a value of 7, the constant to obtain a value of 1 is:
7/k = 1
k = 7.
Dividing every element of the first row by 7, the matrix is given as follows:
[tex]\left[\begin{array}{ccc}1&-\frac{4}{7}&\frac{8}{7}\\-12&7&-13\end{array}\right][/tex]
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A gas can hold 10 L of gas how many cans could we filled filled with 7 L of
Answer:
2 cans
Step-by-step explanation:
which expresion shows 7+21 written as a product of two factors
As we used the distributive property of multiplication to rewrite 7+21 as a product of 7 x (1+3) or 7 x 4.
However, you are asked to express this sum as a product of two factors. A factor is a number that is multiplied by another number to produce a product. Therefore, to express 7+21 as a product of two factors, we need to find two numbers that, when multiplied together, give us the sum of 7+21.
One way to approach this problem is to use the distributive property of multiplication, which states that a(b+c) = ab + ac. We can apply this property by rewriting 7+21 as 7+3*7, since 21 is equal to 3 times 7. Then, we can factor out the common factor of 7 from the expression to get:
7+37 = 7(1+3)
Now, we have expressed 7+21 as a product of two factors: 7 and (1+3), or simply 7 and 4. Therefore, the expression that shows 7+21 written as a product of two factors is:
7 x (1+3) or 7 x 4
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16
Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?
О А.
m. All rights reserved.
2 Fr
Arc
Length
Q Search
I:
3=
IA
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0
A graph that correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r is: C. graph C.
How to calculate the length of the arc?In Mathematics and Geometry, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.
Mathematically, the length of an arc formed by a circle can be calculated by using the following equation (formula):
Arc length = 2πr × θ/360
In this context, we can reasonably infer and logically deduce that the arc length is directly proportional to the radian measure of the central angle.
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Frank spends $90 on his $1800 monthly income what percent of monthly check does not go toward food
If Frank spends $90 on his $1800 monthly income, then 95 percent of monthly check does not go toward food.
Let's say Frank spends $90 on food and has a monthly income of $1800. We can calculate the percentage of his monthly check that does not go towards food as follows:
Percentage = (Total Income - Food Expenses) / Total Income
Percentage = (1800 - 90) / 1800
Percentage = 0.95 = 95%
Therefore, 95% of Frank's monthly check does not go towards food.
Here are the steps in detail:
Subtract the food expenses from the total income to get the amount of money that is not spent on food.
Divide the amount of money that is not spent on food by the total income to get the percentage.
In this case, the amount of money that is not spent on food is $1800 - $90 = $1710. The percentage of the monthly check that is not spent on food is $1710 / $1800 = 0.95 = 95%.
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In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC
In triangle ACE, with BD parallel to CE, using similar triangles and ratios, we get a quadratic equation with two possible solutions. Only the positive one is chosen, so AC is approximately 30.96 units long.
Since BD is parallel to CE, we can use the property of similar triangles to find the length of AC.
Triangles ABD and ACE are similar because they have the same corresponding angles. This means that the ratios of their corresponding side lengths are equal.
We know that AB = 10, AD = 16, and DE = 22.
Let x be the length of AC. Then, we have
AB/AD = CE/EA (by similarity of triangles ABD and ACE)
10/16 = CE/(x-16+22) (substituting CE = EA - DE and simplifying)
5/8 = CE/(x-6)
CE = (5/8)(x-6)
We also know that
BD/DE = AB/AE (by similarity of triangles ABD and ADE)
BD/22 = 10/(x-22) (substituting BD = CE and AE = AC - CE - DE, and simplifying)
CE = (220 - 10x)/(x-22)
Since CE is equal in both expressions, we can equate them and solve for x
(5/8)(x-6) = (220 - 10x)/(x-22)
5x² - 196x + 1320 = 0
x² - 39.2x + 264 = 0
Using the quadratic formula, we get
x = 30.96 or x = 8.54
The length of AC must be positive, so we choose x = 30.96.
Therefore, the length of AC is approximately 30.96 units.
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--The given question is incomplete, the complete question is given
" In the diagram shown, points B and D lie on sides AC and AE such that BD is parallel to CE. If AB=10, AD=16, and De=22 then find the length of AC "--