The average speed is 50 meters per second
How to determine the average speed?The given parameters are:
Laps = 4
Time = 2 minutes
1 lap = 25 meters
Start by calculating the total distance
Distance = Laps * Meters
Distance = 4 * 25 meters
Distance = 100 meters
The average speed is then calculated as:
Speed = Distance/Time
This gives
Speed = 100 meters/2 minutes
Evaluate
Speed = 50 meters per second
Hence, the average speed is 50 meters per second
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Which expressions are equivalent to 2(4f+2g)-
choose three answers
A. 8f+2g
B. 2f(4 + 2g)
C. 8f+4g
D. 4(2f+g)
E. 4f+4f+4g
8. What do you know about triangles PDX and triangle CRX? Justify your answer.
Answer:
The triangles are Congruent for the same reason as the answer above
Step-by-step explanation:
Decrease 100kg by 30%
Answer:
70
Step-by-step explanation:
the 30/100 of 100 is 30
So 100-30=70
Answer:
70kg
Step-by-step explanation:
30% of 100kg is
--> 100 x 30/100 which is 30kg.
If you want to decrease 100kg by 30%, you can take away 30kg from 100kg.
--> 100 - 30 = 70
So 70kg is the remainder.
What is piaget's term for cognitive development between the ages of about 2 and 6?
On a number line, point D is at -3, and point E Is at 6. The point F lies on DE. The ratio of Df to FE ls 2:3. Where does point F lie on the
number line?
Point F is at
. All rights reserved.
on the number line.
Helppp me please
The point F as described in the task content is at point; 0.6 on the number line.
Where does point F lie on the number line?Since it follows from.tge task content that; point D is at -3, and point E Is at 6, it follows that the length of segment, DE is; |-3-6| = 9.
Consequently, since the ratio of Df to FE ls 2:3
It follows that point F is at -3 + (2/5) × 9.
Point F is therefore at 0.6 on the number line.
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Express tan D as a fraction in simplest terms. 40 B 24 32 C
Answer:
[tex]\sf Tan \ D = \dfrac{4}{3}[/tex]
Step-by-step explanation:
Trigonometry ratios:
[tex]\sf \boxed{\bf \tan \ D =\dfrac{opposite \ side \ of \ \angle \ D}{adjacent \ side \ of \ \angle D}}[/tex]
[tex]\sf =\dfrac{BC}{DC}\\\\ =\dfrac{32}{24}\\\\=\dfrac{4}{3}[/tex]
URGENT WILL GIVE BRAINLIEST
Answer:
626.7 [tex]cm^{2}[/tex]
Step-by-step explanation:
Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.
CIRCLE
A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7
RECTANGLE
A = l*w = 15*30 = 450
176.7 + 450 = 626.7 [tex]cm^{2}[/tex]
Answer: 626.7cm^2
Step-by-step explanation:
30 * 15 = 450
area of circle = πr^2
r = 15/2 = 7.5
[tex]7.5^2=56.25*pi=176.7[/tex]
450+176.7 = 626.7
1. Find the pattern in this sequence. Then write
the next three terms in the sequence.
5,2,1,...
Answer:
-1,-3,-4 it is just subtracting the same amount.
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. A shaded polygon A B C D is graphed in an x y plane, where x axis ranges from 0 to 7 in increments of 1 and y axis ranges from 0 to 6 in increments of 1. The vertices are as follows: A (1, 1), B (2, 3), C (5, 4), and D (4, 2). Polygon ABCD, shown in the figure, is dilated by a scale factor of 8 with the origin as the center of dilation, resulting in the image A′B′C′D′. The slope of C'D' is___ .
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
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The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Rigid transformation is a transformation that preserves the shape and size of a figure such as translation, reflection and rotation. Dilation preserves only the shape.
Polygon ABCD has vertex at A(1, 1), B(2, 3), C(5, 4), and D(4, 2).
Slope of CD = (2 - 4) / (4 - 5) = 2
Polygon ABCD is dilated by a scale factor of 8 with the origin resulting in the image A′B′C′D′.
Slope of C'D' = slope of CD (because preserves shape) = 2
The slope of C'D' is equal to the slope of CD because dilation preserves shape which is 2
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A cylinder with a base diameter of x units has a volume of πx3 cubic units. a cylinder with a base diameter of x units has a volume of pi x cubed cubic units. which statements about the cylinder are true? select two options.
The height of the cylinder is 4 x units.
The area of the cylinder’s base is One-fourthπx2 square units .
What is the volume of cylinder?
We know the volume of a cylinder is given by the formula π r2 h, where r is the radius of the cylinder and h is the height.
Formula for volume of the cylinder
V = r² π h
Volume of the cylinder= πx³
Diameter=x
Radius (r)=diameter/2
r = x/2
V = r² π h
πx³=(x/2)² πh
πx³= (x²/4)πh
Divide both sides by π
x³ =(x²/4)h
Make h the subject of the formula
h = x³ ÷ x²/4
=x³ ×4 / x²
=4x³ / x²
=4 * x * x * x / x * x
h=4x
Area of the base:
B = r² π
r=x/2
B=(x/2)² * π
=(x²/4)π
=πx²/4
=1/4(πx²)
Therefore, The area of the cylinder’s base is One-fourthπx2 square units.
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The complete question is -
A cylinder with a base diameter of x units has a volume of πx3 cubic units. A cylinder with a base diameter of x units has a volume of pi x cubed cubic units. Which statements about the cylinder are true? Select two options. The radius of the cylinder is 2x units. The area of the cylinder’s base is One-fourthπx2 square units. The area of the cylinder’s base is One-halfπx2 square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.
PLEASE HELP AND SHOW ALL STEPS
Combining the like terms, the simplified polynomials are given as follows:
a) 4x² - 14x + 17
b) -5x² - 20x + 8
How are polynomials simplified?Polynomials are simplified combining the like terms, that is, adding these numbers with the same variable.
Item a:
4(x - 2)(x + 1) - 5(2x - 5)
Applying the distributive property:
4(x² - x - 2) - 10x + 25
4x² - 4x - 8 - 10x + 25
Combining the like terms:
4x² - 4x - 10x - 8 + 25
4x² - 14x + 17
Item b:
-5(x + 2)² + 28
-5(x² + 4x + 4) + 28
-5x² - 20x - 20 + 28
-5x² - 20x + 8
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David invested $230 in a savings account that offers a 3% return on the investment. the value of david's investment will be at least $415 after a
period of years.
hint: use the formula a = a1 + ', where a is the amount after tyears, pis the amount invested, r is the rate of interest, and is the time period.
use a calculator to compute the answer, and round it off to the nearest year.
20 years is the answer.
A= R(1+r)^ t
A-415
R=230
r=3%
415=230 (1+3%)^ t
t=log1.03 315/230
t=19.89 (use calculator)
David will invest at least 20 years.
An investment is a dedication of an asset to achieve an increase in value over a period of time. Investing requires the sacrifice of current assets such as time, money and effort. In finance, the purpose of an investment is to generate a profit on the invested asset
The most common example of an investment type. Investment is generally what you want to use in the future with the aim of generating regular cash flow or increasing the value of something over time so that you can sell it at a higher price than you purchased.
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Solve the triangle. A = 46°, a = 31, b = 27
A. B = 38.8°, C = 115.2°, c ≈ 34.3
B. B = 38.8°, C = 95.2°, c ≈ 25.7
C. B = 38.8°, C = 95.2°, c ≈ 42.9
D. Cannot be solved
Answer:
C. B=38.8, C=95.2, c=42.9
Step-by-step explanation:
Find B by using sine rule
sin 46/31=sin B/27
sin B= 27 sin 46/31
B=sin‐¹(0.627)
B=38.8
Find C
C= 180-(A+B)
C=180-(38.8+46)
C=95.2
Using sine rule, Find c
31/sin 46=c/sin 95.2
c=31 sin 95.2/sin 46
c=42.9
Compare the theoretical probability to the experimental probability of landing on H.
The correct statement comparing the theoretical and experimental probabilities is given as follows:
[tex]\frac{1}{4} < \frac{7}{25}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
The theoretical probability is taken before any experiment. Since the four sections are equal, the theoretical probability is:
T(H) = 1/4.
The experimental probability is taken considering previous experiments. Out of 100 tosses, 28 landed on H, hence:
E(H) = 28/100 = 7/25.
Hence the correct statement is:
[tex]\frac{1}{4} < \frac{7}{25}[/tex].
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Which of the following ordered pairs is a solution of the system?
x + 3y = 12
y-x=12
Answer:
Step-by-step explanation:
1.an examination in three subjects algebra,biology ,chemistry was taken by 41 students. the following table shows how many students failed in each single subject and their various combinations: subject a b c ab ac bc abc failed 12 5 8 2 6 3 1 how many students failed at least in one subject?
find the domain and range of f^-1 where f(x)=x+1/6x+7
Answer:
Step-by-step explanation:
hello here is an solution
The domain and range are (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=(x+1)/6x+7
Let f(x)=y
(x+1)/6x+7=y
x+1=y(6x+7)
x+1=6xy+7y
6xy-x=7y-1
x(6y-1)=7y-1
Divide both sides by 6y-1
x=7y-1/6y-1
So f⁻¹(x)=1-7x/6x-1
The domain is (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6}
The range is (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6}
Hence, the domain and range are (-∞,1/6)∪ (1/6, -∞), {x/x≠1/6} and (-∞,-7/6)∪ (-7/6, ∞), {y/y≠-7/6} respectively.
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A taxi company charges a $2.00 base fare plus an additional fare based on a per-mile rate and a per-minute rate. Ryan's first taxi ride was 3.0 miles, took 7 minutes, and cost $8.50. His second taxi ride was 7.0 miles, took 14 minutes, and cost $16.00. If his third taxi ride took 10 minutes and cost $13.50, approximately how many miles was the third taxi ride
A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles
How can the length of the third ride be calculated?The base fare = $2.00
Let x represent the per-mile rate, and let y represent the per-minute rate, we have;
The cost of Ryan's first taxi ride = $8.50
Distance traveled in the first ride = 3.0 miles
Time taken during the first ride = 7 minutes
Therefore;
2 + 3•x + 7•y = 8.5
Which gives;
3•x + 7•y = 8.5 - 2 = 6.5
3•x + 7•y = 6.5...(1)Distance traveled in the second ride = 7.0 miles
Duration of the second ride = 14 minutes
The second ride cost = $16.00
Therefore;
2 + 7•x + 14•y = 16
Which gives;
7•x + 14•y = 16 - 2 = 14
7•x + 14•y = 14...(2)Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;
(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1
x = 1
The per-mile rate, x = $13•x + 7•y = 6.5
7•y = 6.5 - 3•x
7•y = 6.5 - 3×1 = 3.5
y = 3.5/7 = 1/2 = 0.5
The per-minute rate, y = $0.5Duration of the third taxi ride = 10 minutes
Cost of the third ride = $13.50
Therefore;
2 + 1×a + 10×y = $13.50
Where a is the distance traveled during the third ride, we have;
2 + 1×a + 10×0.5 = $13.50
2 + a + 5 = 13.5
a = 13.5 - 2 - 7 = 4.5
The third ride was, a = 4.5 milesLearn more about simultaneous linear equations here:
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Which of the following could be appropriate values for an equation to be in Standard Form (Ax + By = C)?
A=-6, B = 8 and C = 3
A=4, B = 0 and C = 9
A=1/6, B = 2/9 and C=0
A=4, B = 1/4 and C=0
Answer:
(2) A=4, B=0, C=9 . . . (4x = 9)
Step-by-step explanation:
A linear equation in standard form has mutually prime integer coefficients with a positive leading coefficient.
Choices:The leading coefficient is negative. Not appropriateCoefficients meet the criteria. Appropriate valuesCoefficients are not integers. Not appropriateCoefficients are not integers. Not appropriateThe values that would be the appropriate values for an equation to be in standard form (Ax + By = C) is A = 4, B = 0 and C = 9.
Linear equation in standard form:The linear equation is the equation which has the coefficient as the mutual prime numbers and the coefficient must be the positive leading coefficient.
From the choices,
A = -6, B = 8 and C = 3. In this case, the coefficient of x (A = -6) is negative, which doesn't leads to positive leading coefficient.A = 4, B = 0 and C = 9. In this case, the coefficient also leads to positive leading coefficient and also lead to mutual prime.A = 1/6, B = 2/9 and C = 0. In this case, the coefficient of x and y which are A = 1/6 and B = 2/9 are integers, which doesn't leads to mutual prime.A = 4, B = 1/4 and C = 0. In this case, the coefficient of y which is B = 1/4 is integers, which doesn't leads to mutual prime.Therefore, the values that would be the appropriate values for an equation to be in standard form as it lead to positive leading coefficient and mutual prime is A = 4, B = 0 and C = 9.
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If point E is the midpoint of and point D is the midpoint of , which expression represents the value of s
The length of ED is half the length of AB.
What is the length?Distance is measured by length. Length is a quantity with the dimension distance in the International System of Quantities. Most measurement systems use a base unit for length from which all other units are derived. The meter is the foundation unit of length in the International System of Units.Reasons:
The given parameters are;
In ΔABC, point E is the midpoint of AC
The midpoint of BC is the point D
Segment ED = s
Segment CE = p
Segment EA = r
Segment CD = q
Segment DB = t
Segment ED = s
Segment AB = u
Required:
The expression that represents the value of [tex]s[/tex].
Solution:
CE = 0.5 × AC Definition of midpoint
CD = 0.5 × CB Definition of midpoint
Therefore, we have;
[tex]\frac{CE}{AC} =\frac{CD}{CB} =0.5[/tex]
Therefore, given that ∠C ≅ ∠C, by the reflexive property, we have;
ΔABC is similar to ΔCDE by Side-Angle-Side similarity
Which gives;
[tex]\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} =0.5=\frac{1}{2}[/tex]
ED = s and AB = u which gives;
[tex]\frac{ED}{AB}=\frac{s}{u} =0.5=\frac{1}{2}[/tex]
[tex]\frac{s}{u} =\frac{1}{2}[/tex]
Which gives:
[tex]s=\frac{1}{2} *u[/tex]
The expression that represents the value of s is; s = one-half u
Therefore, the length of ED is half the length of AB.
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The question you are looking for is here:
If point E is the midpoint of segment AC and point D is the midpoint of segment BC, which expression represents the value of s? triangle CAB, point E is on segment AC between points A and C and point D is on segment BC between points B and C, creating segment ED, CE equals p, EA equals r, CD equals q, DB equals t, ED equals s, and AB equals u s equals p over q s = one half s equals q over p s = 2u
Which factorization could represent the number of water bottles and weight of each water bottle?
The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2). Option B
What is factorization?The term factorization has to do with the process of obtaining common factors in an expression. It involves dividing each term in the expression with a factor that is common to all the terms in the expression.
The factorization that could represent the number of water bottles and weight of each water bottle is 12(5x^2 + 4x + 2).
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Missing parts;
Mara carried water bottles to the field to share with her team at halftime. The water bottles weighed a total of 60x2 + 48x + 24 ounces. Which factorization could represent the number of water bottles and weight of each water bottle? 6(10x2 + 8x + 2) 12(5x2 + 4x + 2) 6x(10x2 + 8x + 2) 12x(5x2 + 4x + 2)
If BE−→− bisects ∠ABD and m∠ABD = 66°, find m∠ABE.
Answer:
∠ABE = 33°
Step-by-step explanation:
Angle bisector:Angle bisector is a straight line that divides the angle into two congruent (equal) angles.
So, BE bisects the ∠ABD into two equal angles.
⇒∠ABE will be half of ∠ABD
∠ABD = ∠ABE + ∠BED
66° = ∠ABE + ∠ABE
66 = 2∠ABE
∠ABE = 66/2
∠ABE = 33°
so confused pls help>>>> there’s a pic
Answer:
(c) 25/4
Step-by-step explanation:
A perfect square trinomial is obtained by "completing the square." The constant in a perfect square trinomial is the square of half the x-coefficient.
Square of a binomialA "perfect square trinomial" is the square of a binomial.
(x +a)² = x² +2ax +a²
Of note here is that the constant (a²) is the square of half of the x-term coefficient:
((2a)/2)² = a²
Completing the squareThe given expression (x² +5x) has an x-term coefficient of 5. The square of half that is ...
(5/2)² = 25/4
The constant that must be added to make x² +5x into a perfect square trinomial is 25/4.
(x² +5x) +25/4 = x² +5x +25/4 = (x +5/2)²
The function a(b) relates the area of a trapezoid with a given height of 12 and
one base length of 9 with the length of its other base.
It takes as input the other base value, and returns as output the area of the
trapezoid.
2.b19
a(b)-12..
Which equation below represents the inverse function b(a), which takes the
trapezoid's area as input and returns as output the length of the other base?
A. b(a)-2-9
B. b(a)-+9
OC. b(a)- +6
OD. b(a)-9-6
The inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9
How to determine the inverse function?The function is given as:
[tex]A(b) = 12 \cdot \frac{b + 9}2[/tex]
Divide 12 by 2
[tex]A(b) = 6 \cdot (b + 9)[/tex]
Rewrite the function as
[tex]a = 6 \cdot (b + 9)[/tex]
Divide both sides by 6
a/6 = b + 9
Subtract 9 from both sides
b = a/6 - 9
Express as a function
b(a) = a/6 - 9
Hence, the inverse function of [tex]A(b) = 12 \cdot \frac{b + 9}2[/tex] is b(a) = a/6 - 9
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(d) Percentage of viewers given they are 18 to 34 who prefer videos on a mobile or laptop device. (Round your answer to 2 decimal places.)\
52.94% of the viewers prefer videos on a mobile or laptop device
How to determine the percentage?The given parameters are
Viewers that prefer videos on a mobile or laptop device = 18
Total number of viewers = 34
The percentage of voters in this category is then calculated as
Percentage = 18/34 * 100%
Evaluate the expression
Percentage = 52.94%
Hence, 52.94% of the viewers prefer videos on a mobile or laptop device
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A sector has a radius of 12 centimeters and an angle 65 degrees. find its arc length
If the radius of sector is 12 centimeters and angle of 65 degrees then the arc's length is 13.6 cm.
Given a sector has a radius of 12 cm and an angle 65 degrees.
We have to calculate arc's length.
We know that arc's length is equal to Θr where Θ is in radians.
We have been given angle in degrees ,so we have to convert degrees in radians.
Angle=65*π/180=13π/36
length of arc =Θr
Putting the values in the formula above :
length =13π/36*12
=13*3.14/3
=40.82/3
=13.6
Hence if the radius of sphere is 12 cm and angle 65 degrees then the length of arc of sphere is 13.6 cm.
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The circle below is centered at (3, 1) and has a radius of 2. What is its
equation?
Answer:
( x-3) ^2 + ( y-1) ^2 = 4
Step-by-step explanation:
The equation for a circle is given by
( x-h)^2 + ( y-k) ^2 = r^2 where (h,k) is the center and r is the radius
( x-3) ^2 + ( y-1) ^2 = 2^2
( x-3) ^2 + ( y-1) ^2 = 4
hi please help 10 Points
Percentage for lakeside is 38%
Percentage for Jungle is 26%
Percentage for Desert is 18%
Percentage for Coast is 12%
Percentage for Prairie is 6%
How to determine the percentageTo determine the percentage, divide the given value by the total number and multiply by 100
Total = 24000
Percentage for lakeside = [tex]\frac{9120}{24000}[/tex] × 100
% of lakeside = [tex]0. 38[/tex] × 100 = 38%
Percentage for Jungle = [tex]\frac{6240}{24000}[/tex] × 100
% of Jungle = [tex]0. 26[/tex] × 100 = 26%
Percentage for Desert = [tex]\frac{4320}{24000}[/tex] × 100
% of Desert = [tex]0. 18[/tex] × 100 = 18%
Percentage for Coast = [tex]\frac{2880}{24000}[/tex] × 100
% of coast = [tex]0. 12[/tex] × 100 = 12%
Percentage for Prairie = [tex]\frac{1440}{24000}[/tex] × 100
% of Prairie = [tex]0. 06[/tex] × 100 = 6%
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The standard deviation of win percentage for the 32 teams in the NBA in 2005 - 2006 was 0.134. The NBA plays an 82 game season. The standard deviation of win percentage for the 20 teams in the English Premier League in 2005 - 2006 was 0.158. The EPL plays a 38 game season., which league exhibits more competitive balance
The NBA league exhibits more competitive balance.
The chance that each team in a league has of winning the title is referred to as competitive balance. The championship would be won by each team on a regular basis in an ideal competitive environment. In contrast, if there was no balance between the two types of competition, the same team would consistently prevail.
Competitive balance is often regarded as a desirable trait because too much predictability makes fans of the lesser franchises angry and fans of the defending champions complacent, which lowers interest in the sport as a whole.
The "Noll-Scully" measure is the competitive balancing metric that is most frequently used in sports. The winning percentage of each league team's standard deviation (SD) is used to compute it. The SD is then divided by what it would be if all teams had equal talent and the outcomes were entirely random.
For NBA team, competitive balance = 0.134/32*82 = 0.343
For EPL team, competitive balance = 0.158/20*38 = 0.30
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Chandra invests $75 every month at 4.8%/a compounded monthly for 8 years. What is the total amount of Chandra's investments after 8 years? Show your work.
The total amount of Chandra's investments after 8 years is $110.03
Compound interestThe formula for calculating the compound interest is expressed as;
A = P(1+r/n)^nt
where
P is the amount invested = $75
r is the rate. = 0.048
t is the time =8years
n = 12 (monthly)
Substitute
A = 75(1+0.048/12)^96
A = 75(1.467)
A = 110.03
Hence the total amount of Chandra's investments after 8 years is $110.03
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