Ques 1)
Option: C is the correct answer.
c. 9 inches square.
Ques 2)
Option: c
c. By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.
Ques 3)
Option: b
b. 2 to the 7 over 3 power
Step-by-step explanation:Ques 1)
A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches.
i.e. let 'l' and 'b' denote the length and width of the rectangle.
i.e.[tex]l=\sqrt[3]{81}\\\\l=(3^4)^{\dfrac{1}{3}}\\\\l=3^{\dfrac{4}{3}[/tex]
since,
[tex](a^m)^n=a^{mn}[/tex]
and
[tex]w=3^{\dfrac{2}{3}}[/tex]
Hence, the area of rectangle is given by:
[tex]Area=l\times w\\\\\\Area=3^{\dfrac{1}{3}}\times3^{\dfrac{4}{3}}\\\\\\Area=3^({\dfrac{1}{3}+\dfrac{4}{3}})\\\\\\Area=3^{\dfrac{6}{3}}\\\\\\Area=3^2\\\\\\Area=9\ square\ inches[/tex]
As we know that:
[tex]a^m\times a^n=a^{m+n}[/tex]
Hence, Area=9 square inches.
Ques 2)
2 to the fifth power, over 8 = 2 to the 2nd power
i.e. we need to prove that:
[tex]\dfrac{2^5}{8}=2^2[/tex]
As we know that:
[tex]\dfrac{2^5}{8}=\dfrac{2^5}{2^3}=2^{5-3}=2^2[/tex]
( since
[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex] )
Hence, the correct answer is: Option: c
Ques 3)
The cube root of 2 to the seventh power.
i.e.
[tex]\sqrt[3]{2^7}\\\\=(2^7)^{\dfrac{1}{3}}\\\\=2^{\dfrac{7}{3}}[/tex]
Since,
[tex]\sqrt[n]{x}=x^{\dfrac{1}{n}}[/tex]
and
[tex](a^m)^n=a^{mn}[/tex]
Hence, the correct answer is: option: b
Julia surveyed her friends to find the number of hours they spend on homework during the week. The data from her survey is displayed in the first table. She then took a random sample of five responses from the population as shown in the second table. Compare the mean of the population with the mean of the given sample.
Population Data
4
5
3
1
3
2
2
3
5
7
3
6
3
0
1
5
0
4
3
6
Sample Data
5
4
6
2
1
What is the difference between the mean of the sample and the mean of the population?
0.2
0.3
0.4
0.5
Solution:
we are given with two kind of data set , one is Population data and the other is sample data.
we have been asked to Compare the mean of the population with the mean of the given sample.
Given Population Data
is
[tex] 4
, 5
, 3
,1
,3
,2,2
,3
,5
,7
,3
,6
,3
,0
,1
,5
,0
,4
,3
,6 [/tex]
Its mean can be calculated as below
[tex] Mean=\frac{4+5+3+1+3+2+2+3+5+7+3+6+3+0+1+5+0+4+3+6}{20} \\\\\Mean=\frac{66}{20}=3.3\\ [/tex]
Now the Sample data is
5,4,6,2,1
[tex] Mean=\frac{5+4+6+2+1}{5}\\\\Mean=\frac{18}{5}= 3.6\\ [/tex]
Hence the value of difference of the Mean is [tex] =3.6-3.3=0.3 [/tex]
Answer:
The answer is B. 0.3
Step-by-step explanation:
If you need any help, ask me! :)
I understand that the remainder is 0, I kinda guessed and it told me.
But we're using long division or synthetic division.
Can you explain to me what the quotient is?
Thanks!
True of False: If the measure of theta is A radians and B degrees, then A = 180B/pi. Please explain!
The number of mosquitoes in anchorage, alaska (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by: m(x)=-x^2+14xm(x)=−x 2 +14xm, left parenthesis, x, right parenthesis, equals, minus, x, start superscript, 2, end superscript, plus, 14, x how many centimeters of rain will produce the maximum number of mosquitoes?
Answer:
Step-by-step explanation:
49 million misquitos
Using the similar triangles which equation could be used to find the slope of line AB
The equation that could be used to find the slope of line AB is m = p/q.
What are similar triangles?Two triangles are said to be similar if they have congruent corresponding angles and their corresponding sides are in equal proportion.
Given that, is a graph showing two similar triangles, we need find the equation of the slope of the line AB.
So,
The slope = rise / run = Δy / Δx
Here, Δy / Δx = m/n
Since, the triangles are similar so, m/n = p/q
Therefore,
Δy / Δx = p/q
Hence, the equation that could be used to find the slope of line AB is m = p/q.
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Triangle DEF is circumscribed about circle R. Points S, T and U are points of tangency where SD = 4 m and UF = 7 m. What is the measure of DF
What is the equation of the line?
A) x + 3y = 9
B) 3x - y = 9
C) x - y = 9
D) 3x + y = 9
Simplify 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n
Final answer:
The simplified expression of 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n is -2 + 5.5n - 0.5p after combining like terms.
Explanation:
To simplify the algebraic expression 1 + 4.25n + 3/2p - 3 + (-2p) +5/4n, we need to combine like terms. The constants 1 and -3 can be combined, and the terms with 'n' and 'p' can each be combined respectively. Let's do this step by step:
Combine the constants: 1 - 3 = -2.Combine the 'n' terms: 4.25n + 5/4n = (17/4)n + (5/4)n = (22/4)n = 5.5n.Combine the 'p' terms: (3/2)p + (-2p) = (1.5 - 2)p = -0.5p.The simplified expression is -2 + 5.5n - 0.5p.
There were some pencils in a pencil box. Zoe added 7 more pencils to the pencil box. Now there are 24 pencils in the box. How many pencils were in the box to start with?
Find the product of (x + 7)2. (1 point)
x2 − 14x + 49
x2 + 14x + 49
x2 − 49
x2 + 49
A map of a public park shows a circular pond. there is a bridge along a diameter of the pond that is 0.85 mi long. you walk across the bridge, while your friend walks halfway around the pond to meet you at the other side of the bridge. how much farther does your friend walk? round your answer to the nearest hundredth. use 3.14 for π.
Answer:
Your friend walks about 0.48 miles farther than you.
Step-by-step explanation:
Find the circumference of the park.
C = πd Use the circumference formula.
C ≈ 3.14(0.85) Substitute for the diameter and π.
C ≈ 2.669 Multiply.
The circumference of the park is about 2.669 centimeters.
Find how far your friend walks when he or she walks halfway around the pond to meet you on the other side of the bridge. Divide the circumference by two.
0.785 ÷ 2 = 1.33
Your friend walks 1.33 miles.
Find how much farther your friend walks. Subtract the miles you walk from the miles your friend walks. Round your answer to the nearest hundredth.
1.33 − 0.85 ≈ 0.48
A rental company charges $9.50 per hour for a scooter plus a $15 fee. Write an equation in slope- intercept form for the total rental cost C of renting a scooter for h hours
In which quadrant of the coordinate graph does point F lie?
The sign notations for four Quadrants is as follows:
Quadrant I : both x and y positive.
Quadrant II : x negative and y positive
Quadrant III: x and y both negative.
Quadrant IV: x positive and y negative.
Point F has coordinates (1,-5)
x is positive and y is negative.
So point F is in quadrant IV.
PUTTING MAX POINTS
Find all polar coordinates of point P where P = (6, -π/5)
Answer choices:
(6, -π/5 + 2nπ) or (-6, -π/5 + 2nπ)
(6, -π/5 + 2nπ) or (-6, -π/5 + (2n + 1)π)
(6, -π/5 + (2n + 1)π) or (-6, -π/5 + 2nπ)
(6, -π/5 + 2nπ) or (6, π/5 + (2n + 1)π)
Your answer should be d
What is the inverse of the following statement? If you live in Toronto, then you live in Canada
The inverse of the statement "If you live in Toronto, then you live in Canada" is:
"If you do not live in Toronto, then you do not live in Canada."
What is a conditional statement?A conditional statement is a type of logical statement that consists of two parts: a hypothesis (or antecedent) and a conclusion (or consequent).
The hypothesis is a statement that serves as a condition, while the conclusion is a statement that follows from the condition.
A conditional statement is usually written in the form "If p, then q", where p is the hypothesis and q is the conclusion.
The symbol "→" is often used to represent the phrase "if...then".
We have,
To make the inverse of a conditional statement "if p, then q", you simply negate both the hypothesis and the conclusion, and then switch their positions.
The inverse of "if p, then q" is "if not p, then not q".
This can be symbolically represented as:
Original Statement: If p, then q
Inverse Statement: If not p, then not q
So,
The inverse of a conditional statement:
If p, then q is If not p, then not q".
Therefore,
The inverse of the statement "If you live in Toronto, then you live in Canada" is:
"If you do not live in Toronto, then you do not live in Canada."
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PLEASE HELP!!! 100 POINTS!!! WILL GIVE BRAINLIEST!!!!
Graph the two lines:
2x + 3y = 18
3x -4y > 16.
Give the Domain and Range, Slope, and Y-intercept for each line.
Graph each equation above on the graph below and show all work.( Or tell me how to graph it)
Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer.
2x + 3y = 18 3x -4y > 16
Slope-Intercept Form: Slope-Intercept Form:
Domain: Domain:
Range: Range:
Slope: Slope:
Y-intercept: Y-intercept:
1. Simplify (4xy^2)^3(xy)^5
2. Simplify (2t^–3)^3(0.4r)^2
Thank you whoever answers so much!,
Note main rules:
[tex]1.\quad (a\cdot b)^n=a^n\cdot b^n,\\ \\2.\quad a^m\cdot a^n=a^{m+n},\\ \\3.\quad (a^m)^n=a^{mn}.[/tex]
1. Consider expression [tex](4xy^2)^3(xy)^5.[/tex] Using previous rules:
1 step: [tex](4xy^2)^3=4^3\cdot x^3\cdot (y^2)^3=64x^3y^{2\cdot 3}=64x^3y^6;[/tex]2 step: [tex](xy)^5=x^5\cdot y^5;[/tex]3 step: [tex](4xy^2)^3(xy)^5=64x^3y^6x^5y^5=64x^{3+5}y^{6+5}=64x^8y^{11}.[/tex]2. Consider expression [tex](2t^{-3})^3(0.4r)^2.[/tex] Using previous rules:
1 step: [tex](2t^{-3})^3=2^3\cdot (t^{-3})^3=8t^{-3\cdot 3}=8t^{-9};[/tex]2 step: [tex](0.4r)^2=0.4^2\cdot r^2=0.16r^2;[/tex]3 step: [tex](2t^{-3})^3(0.4r)^2=8t^{-9}\cdot 0.16r^2=8\cdot 0.16t^{-9}r^2=1.28t^{-9}r^2.[/tex]Answer:
[tex]64x^8y^{11};[/tex][tex]1.28t^{-9}r^2.[/tex]Find all the zeroes of the equation. -3x4+27x2+1200=0 I need to learn how to do it! Just not the answer please
Read the word problem. George has 2 times the amount of points that is 4 less than his sister’s. His sister has 16 points. How many points does George have? What operations are needed to solve this word problem, and in what order should they be used?
addition and subtraction, in that order
addition and multiplication, in that order
subtraction and division, in that order
subtraction and multiplication, in that order
D- subtraction and multiplication, in that order.
Step-by-step explanation:
EDG 2022
△ABC has interior angles with measures x°, 100°, and 70°, and △DEF has interior angles with measures y°, 70°, and 20°. Using the given information, which statement is true? The triangles are similar because they each have an interior angle with a measure 70°. The two triangles are not similar because x≠y . The two triangles are not similar because y=90 so it is impossible to have three congruent angles. The two triangles are not similar because the interior angles are congruent but the side lengths are different.
△ABC has interior angles with measures x°, 100°, and 70°.
By using angle sum property, which states that the sum of measures of all three angles is 180 degrees.
[tex] x^{\circ}+100^{\circ}+70^{\circ}=180^{\circ} [/tex]
[tex] x^{\circ}=10^{\circ} [/tex]
Now, △DEF has interior angles with measures y°, 70°, and 20°.
By using angle sum property,
[tex] y^{\circ}+70^{\circ}+20^{\circ}=180^{\circ} [/tex]
[tex] y^{\circ}=90^{\circ} [/tex]
Now, we can say that,
"The two triangles are not similar because x≠y"
As one angle of measure 70 degree is common in both the triangles.
If 'x' would be equal to 'y' , then we could say that the triangles are similar by AA criteria.
Therefore, the two triangles are not similar because x is not equal to y.
The perimeter of the rectangle is 64 cm. Find the value of x.
A. 7
B. [tex] \frac{64}{33} [/tex]
C. 32
D. 50
The value of x is 7 and the right option is A. 7.
What is perimeter?Perimeter is the total distance around an object.
To find the value of x, we use the formula of the perimeter of a rectangle.
Formula:
P = 2(L+W)............... Equation 1Where:
P = Perimeter of the rectangleL = Length of the rectangleW = Width of the rectangleFrom the question,
Given:
L = 3xW = 11 cmP = 64 cmSubstitute these values into equation 1 and solve for x
64 = 2(11+3x)64 = 22+6x6x = 64-226x = 42x = 42/6x = 7Hence, the value of x is 7 and the right option is A. 7.
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A collection of quarters and dimes is worth $6.75. The number of dimes is 4 less than three times the number of quarters. How many quarters and dimes are in the collection?
which sampling method would most likely be used in a poll of voters regarding a referendum calling for a national gun control standardization?
(A) Use satisfied random sampling
(B) Use simple random sampling
(c) Use convenience sampling
(D) Use cluster sampling
(E) Use systematic random sampling
Answer:
(A) Use stratified random sampling
Step-by-step explanation:
Since, the population include all the citizens of that country so it is quite large data and working on this population is quite time taken and costly. Thus, Sample must be taken and it must be taken by appropriate sampling method.
Here Stratified Sampling is used because by this sampling method peoples of every state, every cities, every village can be taken without much expense and in less time.
Further,
If the samples from the population are chosen randomly, where each and every unit has an equal chance of selection in a sample. This type of sampling is called Simple Random Sampling.
If the observers collect the sample as his\her convenience, then this type of sampling method is called Convenience Sampling.
In Cluster Sampling the population is distributed into a distinct group (clusters) and one or more groups (clusters) are chosen as a sample.
In Systematic Sampling the selection of sample is taken by some criteria . Like he\she is taken every 7th unit as a sample from the population.
Anybody have any answers?
15. A restaurant has one type of milk that has 2% fat and another that has 7% fat. how many quarts of each type does the restaurant need to make 40 quarts of a milk mixture that is 5% fat?
a. 24 quarts of the 2% milk and 16 quarts of the 7% milk
b. 16 quarts of the 2% milk and 24 quarts of the 7% milk
c. 16 quarts of the 2% milk and 16 quarts of the 7 milk
d. 24 quarts of the 2% milk and 24 quarts of the 7% milk,
From an airplane at an altitude of 1200m the angle of depression to a rock on the ground measures 28. Find the distance from the plane to the rock
The distance from the plane to the rock can be calculated using trigonometry. Here, the tangent of the given angle is used, with the formula: Distance = 1200m / tan(28°).
Explanation:The subject matter in the question relates to trigonometry. We can use the tangent of the given angle to find the distance to the rock. We are given an altitude of 1200m (which is equivalent to the opposite side in a right angle triangle) and an angle of depression of 28°. We know from trigonometry that the tangent of an angle is equal to the opposite side divided by the adjacent side (tan(θ) = opposite / adjacent).
Since we want to know the distance from the plane to the rock, we're trying to find the length of the hypotenuse. This forms a right-angled triangle with the height of the plane as the opposite side, and the line of sight to the rock as the hypotenuse.
We can use the following formula which is derived from the principles of trigonometry:
Distance to the rock (hypotenuse) = Opposite side / tan(θ)
Plugging the given values into this formula gives:
Distance to the rock = 1200m / tan(28°) This calculation will give the answer.
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Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1 f(n) = 35n Which one of these formulas show the sequence written rercursively and which shows it written explicity? Justify your explanantions. Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Use the explicit formula to demonstrate the most direct method to find f(40). Explain why you chose that method and what your answer means. Show your calculations. Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function.
The value of f(40) is 1400 .The sequence can be considered a function because each position has a unique value.
Let's analyze the given formulas for Bill's savings:
The recursive formula is: f(1) = 35, f(n) = f(1) + f(n-1) for n > 1
The explicit formula is: f(n) = 35n
A recursive formula defines each term based on the previous terms, which we see in f(n) = f(1) + f(n-1). An explicit formula provides a direct calculation, shown in f(n) = 35n.
Recursive Formula Table for 1 ≤ n ≤ 5n = 1: f(1) = 35n = 2: f(2) = 35 + f(1) = 35 + 35 = 70n = 3: f(3) = 35 + f(2) = 35 + 70 = 105n = 4: f(4) = 35 + f(3) = 35 + 105 = 140n = 5: f(5) = 35 + f(4) = 35 + 140 = 175Using the Explicit Formula to Find f(40)The explicit formula f(n) = 35n allows us to directly calculate:
f(40) = 35 * 40 = 1400
This method is chosen because it provides a straightforward calculation without needing to compute all the preceding values.
Analyzing the Sequence 5, 6, 8, 11, 15, 20, 26, 33, 41, ...This sequence can be considered a function because each input (position in the sequence) has a unique output (value in the sequence).
At the end of a factory assembly line, completed widgets are deposited into a box until it is filled. if after 10 minutes the box contains 25 widgets and it takes 2 hours total to fill up a box, how many widgets must each box hold?
Final answer:
Each box must hold a total of 300 widgets.
Explanation:
To determine how many widgets must each box hold, we need to calculate the rate of production and then use it to find the total number of widgets produced in 2 hours (the total time it takes to fill the box).
First, we'll find out how many widgets are produced per minute. Since 25 widgets are deposited in 10 minutes, we divide the number of widgets by the time (in minutes) to get the rate:
Rate of production = 25 widgets / 10 minutes = 2.5 widgets per minute.
Now, we need to find out how many minutes are in 2 hours:
2 hours = 2 hours * 60 minutes/hour = 120 minutes.
Finally, we multiply the rate of production by the total production time (in minutes) to find out the total number of widgets per box:
Total widgets per box = 2.5 widgets/minute * 120 minutes = 300 widgets.
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates. slope: −2, ordered pair: (−5,1)
The equation of line is, y= -2x-9.
what is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given:
slope= -2
points= (-5, 1)
Now, using slope intercept form
y= mx+ b
1 = (-2)((-5) + b
1= 10 + b
b= -9
Thus, the equation of line
y= mx + b
y= -2x- 9
Hence, the equation of line is, y= -2x-9.
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PLEASE HELP ASAAAPPPPP