Answer:
the dimensions of rectangle are length = 15 m and width = 6 m
Step-by-step explanation:
Given; The width of a rectangle is [tex]\frac{2}{5}[/tex] its length i.e, [tex]w=\frac{2}{5}l[/tex]
and perimeter of rectangle is 42 meters.
Perimeter(P)of a rectangle in meters is given by:
[tex]P = 2(l+w)[/tex] ; where [tex]l[/tex] is the length of the rectangle and w is the width of the rectangle.
then, substitute the value of P =42 m and [tex]w=\frac{2}{5}l[/tex] in above formula we get;
[tex]42 = 2(l+\frac{2}{5}l) =2 \cdot (\frac{7}{5}l)[/tex]
divide both side by 2 we get;
[tex]21=\frac{7}{5}l[/tex]
On Simplify:
[tex]l = \frac{21 \cdot 5}{7} =3 \cdot 5 =15[/tex] m
Now, substitute the value of [tex]l = 15[/tex] m in [tex]w=\frac{2}{5}l[/tex] to solve for w;
[tex]w= \frac{2}{5} \cdot 15 =2 \cdot 3 =6[/tex] m
Therefore, the dimensions length = 15 m and width = 6 m
A-Town wants to know the number of cell phones in each household the town divides the population up by neighborhood and surveys a random number of households and eat what type of survey is this
A-Town is conducting a survey using a random sample method by dividing the population into neighborhoods and surveying random households in each, which ensures each household has an equal chance of being selected and provides a representative sample.
Explanation:A-Town's approach to determining the number of cell phones in each household through a survey is an example of a random sample. The method involves dividing the population into neighborhoods and surveying a random selection of households within each area. This technique helps to ensure that every household has an equal chance of being selected, which should provide a representative sample of the town's population. Such methods are necessary to obtain reliable data that reflects the true distribution and characteristics of the target population without regional bias.
Using a representative sample is crucial in research and polling to measure accurately public opinion or collect data on phenomena. As in the given example where the market research firm surveys 500 randomly selected residents to estimate the percentage of adults with cell phones, the firm employs statistical measures like confidence intervals to infer about the entire population's cell phone ownership based on the sample data. Moreover, the concept of probability sampling is also important for achieving a sample that can be generalized to the whole population with reasonable accuracy.
Which line of symmetry for the parabola (x-1)^2= 4(y-1)^?
The line of symmetry for the parabola is x = 1.
The line of symmetry for the parabola is x = 1. In the given equation (x-1)^2 = 4(y-1)^2, the x-coordinate of the vertex is 1, which means the line of symmetry is a vertical line passing through x = 1.
Use the graph below to answer the question that follows:
What is the rate of change between the interval x = π and x = three pi over two?
pi over 16
negative 16 over pi
pi over 4
negative 4 over pi
I need Help with this TRIG question
Sandy releases a javelin 1.6 m above the ground with an initial vertical velocity of 25 m/s. How long will it take the javelin to hit the ground?
Using a quadratic function, it is found that it will take 5.17 seconds for the javelin to hit the ground.
What is the quadratic function for a projectile's height?Considering meters as the measure of height, it is given by:
h(t) = -4.9t² + v(0)t + h(0).
In which:
v(0) is the initial velocity.h(0) is the initial height.In this problem, we have that v(0) = 25, h(0) = 1.6, hence:
h(t) = -4.9t² + 25t + 1.6
It hits the ground when h(t) = 0, hence:
-4.9t² + 25t + 1.6 = 0
4.9t² - 25t - 1.6 = 0.
Which is a quadratic function with coefficients a = 4.9, b = -25, c = -1.6. Hence:
[tex]\Delta = (-25)^2 - 4(4.9)(-1.6) = 656.36[/tex]
[tex]x_1 = \frac{25 + \sqrt{656.36}}{9.8} = 5.17[/tex]
[tex]x_2 = \frac{25 - \sqrt{656.36}}{9.8} = -0.06[/tex]
For time we want the positive value, hence, it will take 5.17 seconds for the javelin to hit the ground.
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An isoceles triangle has congruent side of 20 cm. The base is 10 cm. Find the height of the triangle
the mean mark for the class was 70%. There are 30 students in the class, 20 of whom are boys. The mean mark for the boys is 62%. What is the mean mark for the girls?
Nikolai has a jar filled with 120 marbles. he has 72 red marbles, 17 blue marbles, 13 green marbles, and 18 purple marbles. what is the probability that he will randomly select a blue marble, without replacement, and then a purple marble from the jar
The probability of selecting a blue marble followed by a purple marble from a jar containing 120 marbles with different colors is approximately 2.2%.
The probability of grabbing a blue marble and then a purple marble is determined by multiplying the probability of grabbing a blue marble first and the probability of grabbing a purple marble second. Here's the calculation:
Probability of selecting a blue marble first: 17/120
Probability of selecting a purple marble second (after one blue marble is already taken out): 18/119
Multiplying the probabilities: (17/120) * (18/119) ≈ 0.022, or 2.2%
Someone please help me?
Farmer toby's chickens and pigs have a total of 30 heads and 84 legs. a chicken has 2 legs, a pig has 4 legs, and each animal has 1 head. how many of each type of animal does toby have
What is the value of the rational expression 2x+1/x2 when x = 5?
The solution is A = 11/25
The value of the equation A = ( 2x + 1 ) / x² is 11/25
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = ( 2x + 1 ) / x²
when x = 5 , substitute the value of x as 5 in the equation , we get
A = ( 2 ( 5 ) + 1 ) / 5²
The value of A = ( 10 + 1 ) / 25
The value of A = 11/25
Therefore , the value of A = 11/25
Hence , The value of the equation A = ( 2x + 1 ) / x² is 11/25
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(2n + 3)(n – 4) = 0
need help asap!!!
A tractor was purchased for $30,000 six years ago. what is the value of the tractor today if the depreciation rate was 2.5%?
In sakura’s garden, for every 5 red flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden. How many ref flowers are in Sakura’s garden?
Convert 7.2*10^-3 to standard form please help thanks
The slope of a line in a blueprint must be . A line is drawn that contains the points 5/6 < | m | <7/4. Determine if the line meets the required specifications.
A.No, the rooftop does not meet the specifications, because the absolute value of the roof’s slope is greater than the parameters.
B.No, the rooftop does not meet the specifications, because the absolute value of the roof’s slope is less than the parameters.
C.Yes, the rooftop does meet the specifications, because the absolute value of the roof’s slope is within the parameters.
D.Yes, the rooftop does meet the specifications, because the absolute value of the roof’s slope is less than the parameters.
plz help me!!!!
A cross country coach records the number of miles his athletes on the Junior Varsity and Varsity teams ran today and displays the data in the provided dot plots. Given the shape of each distribution, determine which measures of center and spread are appropriate for him to use to summarize the data from each team.
Answer:
Step-by-step explanation:
The function h=−16t2+26t models the height h (in feet) of the dolphin after t seconds. after how many seconds is the dolphin at a height of 5 feet? round your answers to the nearest tenth.
Answer:
The dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.
Step-by-step explanation:
Given : The function [tex]h=-16t^2+26t[/tex]models the height h (in feet) of the dolphin after t seconds.
To Find: After how many seconds is the dolphin at a height of 5 feet?
Solution:
Function: [tex]h=-16t^2+26t[/tex]
h is the height
t is the time
Now we are supposed to find After how many seconds is the dolphin at a height of 5 feet
Substitute h = 5
So, [tex]5=-16t^2+26t[/tex]
[tex]16t^2-26t+5=0[/tex]
[tex]16t^2-26t+5=0[/tex] ---1
Using quadratic formula : [tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
General quadratic equation: [tex]ax^2+bx+c=0[/tex] ---A
On Comparing equation 1 with A
a = 16
b = -26
c=5
Substitute the values in the quadratic formula.
[tex]x = \frac{-(-26)\pm\sqrt{(-26)^2-4(16)(5)}}{2(16)}[/tex]
[tex]x = \frac{26\pm 18.86796}{32}[/tex]
[tex]x = \frac{26+18.86796}{32},\frac{26-18.86796}{32}[/tex]
[tex]x = 1.4021,0.2228[/tex]
Thus the dolphin is at height 5 feet after 1.40 seconds or 0.228 seconds.
The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.
Polynomial
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Let h represent the height of dolphin at t seconds.
Given the function:
h = −16t² + 26tFor a height of 5 ft.:
5 = −16t² + 26t
16t² - 26t + 5 = 0
t = 0.2 or t = 1.4
The dolphin is at a height of 5 feet at 0.2 second and 1.4 seconds.
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Please help me idk this
The quarters, buckled, and dimes totaled 20 and their value was $2.05. How many kind were there if there were 3 times as many dimes as quarters
How many arrangements are possible using the letters in the word fuzzy if each letter "z" is distinctly different than the other? how many arrangements are possible if the letter "z" is interchangeable with the other? explain your reasoning?
Case 1: If the letter z is distinctly different
If we have the letter z which is distinctly different than the other "z", then we have five letters in the word F U Z Z Y and the number of arrangements would be = 5*4*3*2*1 =5! = 120 different arrangements
Case 2: If the letter Z is interchangeable
If the letter "Z" is interchangeable with the other "z" then we have 2 letters which cancel out each other that would be represented by 2*1 = 2! = 2
So, the number of arrangements in this case would be 5!/2! = 5*4*3*2*1/2*1 = 60 arrangements
Evaluate at the given value
4x^2+6x-5 when x=-3
Solve for c in the equation 3x^2-18x+5=47
A travel website reports that in a particular city, the probability of rain on any day in April is 40%. What is the expected number of rainy days in this city during the month of April?
Which of the following sequences of numbers are arithmetic sequences? Check all that apply.
A.99, 100, 101, 102, 103, ...
B.-3, -5, -7, -9, -11, ...
C.2, -2, 2, -2, 2, ...
D.1, 6, 11, 16, 21, ...
E.-4, 7, -10, 13, -16, ...
Jake is younger than Sophie. Sophie is 14 years old. Write an inequality that compares Jake's age in years, (j), to Sophie's age.
To express that Jake is younger than Sophie who is 14, we use the inequality j < 14, where j symbolizes Jake's age in years.
Explanation:The question is asking for an inequality that represents Jake's age compared to Sophie's age. Since we are told that Jake is younger than Sophie and Sophie is 14 years old, we can use an inequality symbol to express this relationship. The appropriate inequality is j < 14, where j represents Jake's age in years. The symbol < means 'less than,' which correctly compares Jake's age to Sophie's, indicating that Jake's age is less than 14 years.
The equation of a parabola is 1/32 (y−2)2=x−1 .
What are the coordinates of the focus?
(1, 10)
(1, −6)
(−7, 2)
(9, 2)
The given equation of parabola is
[tex] \frac{1}{32} (y-2)^2 = x-1 [/tex]
Which can also be written as
[tex] x = \frac{1}{32} (y-2)^2 +1 [/tex]
Here vertex (h,k) is (1,2)
And value of a is
[tex] a = \frac{1}{32} [/tex]
Formula of focus is
[tex] (h+ \frac{1}{4a} , k) [/tex]
Substituting the values of h,k and a, we will get
[tex] (1+ \frac{1}{4*(1/32) } , 2} = (1+ 8,2) = (9,2) [/tex]
Therefore the correct option is the last option .
Answer: The correct option is (D) (9, 2).
Step-by-step explanation: We are given to find the co-ordinates of the focus for the following parabola:
[tex]\dfrac{1}{32}(y-2)^2=x-1~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that the standard form equation of a parabola is
[tex](y-k)^2=4p(x-h),[/tex]
where the co-ordinates of the focus are (h+p, k).
From equation (i), we have
[tex]\dfrac{1}{32}(y-2)^2=x-1\\\\\\\Rightarrow (y-2)^2=32(x-1)\\\\\Rightarrow (y-2)^2=4\times 8(x-1).[/tex]
Comparing the above equation with the standard form equation of the parabola, we get
h = 1, k = 2, and p = 8.
Therefore, the co-ordinates of the focus are
[tex](h+p,k)=(1+8,2)=(9,2).[/tex]
Thus, option (D) is CORRECT.
Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16
pppppppllllllleeeeaaaassssseeeee ANSWER FASRT
According to the discriminant:
[tex]y = -3x^2 + x + 12[/tex] has two real solutions.[tex]y = 2x^2 - 6x + 5[/tex] has zero real solutions.[tex]y = x^2 + 7x - 11[/tex] has two real solutions.[tex]y = -x^2 - 8x - 16[/tex] has one real solution.The number of real solutions of quadratic equation [tex]y = ax^2 + bx + c[/tex] depends on the discriminant [tex]\Delta = b^2 - 4ac[/tex].
If [tex]\Delta > 0[/tex], the equation has two real solutions.If [tex]\Delta = 0[/tex], the equation has one real solution.If [tex]\Delta < 0[/tex], the equation has zero real solutions.Equation [tex]y = -3x^2 + x + 12[/tex]
The coefficients are: [tex]a = -3, b = 1, c = 12[/tex]The discriminant is: [tex]\Delta = 1^2 - 4(-3)(12) = 145[/tex].Positive, thus two real solutions.Equation [tex]y = 2x^2 - 6x + 5[/tex]
The coefficients are: [tex]a = -2, b = -6, c = 5[/tex]The discriminant is: [tex]\Delta = (-6)^2 - 4(2)(5) = -4[/tex].Positive, thus zero real solutions.Equation [tex]y = x^2 + 7x - 11[/tex]
The coefficients are: [tex]a = 1, b = 7, c = -11[/tex]The discriminant is: [tex]\Delta = (7)^2 - 4(1)(-11) = 93[/tex].Positive, thus two real solutions.Equation [tex]y = -x^2 - 8x - 16[/tex]
The coefficients are: [tex]a = -1, b = -8, c = -16[/tex]The discriminant is: [tex]\Delta = (-8)^2 - 4(-1)(-16) = 0[/tex].Positive, thus one real solutions.A similar problem is given at https://brainly.com/question/19776811
Another geometry question! Please help!
The total cost (c) in dollars of renting a sailboat for n days is given by the inequality c≥120+60n. what is the maximum number of days for which a sailboat could be rented if the total cost was $360?
Answer:
4 days
Step-by-step explanation: