Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. If the first 6 children born are girls, what is the probability the next born child is a boy?
Answers
For given Sample Space, the probability that the next born child is a boy, given that the first 6 children born were girls, is 0.5 i.e. A.
What exactly is a sample space?
A sample space is the collection of all potential results of an experiment or random process in probability theory. It is a key idea that allows us to define and assess event probability.
Consider the following experiment: rolling a six-sided die. This experiment's sample space is the set of all potential results of rolling the dice, which are 1, 2, 3, 4, 5, 6. Each member of the sample space indicates a possible experiment outcome.
Now,
The probability of a baby being a boy or a girl is 0.5 each, and each birth is an independent event, meaning that the outcome of one birth does not affect the outcome of the others. Therefore, the probability of having 6 girls in a row is (0.5)⁶ = 0.015625, or approximately 1.5625%.
Now, we want to find the probability that the next born child is a boy, given that the first 6 children born were girls.
Using the conditional probability formula:
P(boy | 6 girls) = P(boy and 6 girls) / P(6 girls)
The probability of having 6 girls and a boy is the same as the probability of having 7 children in a row, with the last one being a boy. The probability of having 7 children in a row, with any gender, is (0.5)⁷ = 0.0078125, or approximately 0.78125%.
Therefore,
P(boy | 6 girls) = (0.5)⁷ / (0.5)⁶ = 0.5
So the probability that the next born child is a boy, given that the first 6 children born were girls, is 0.5.
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Related Questions
if x+2 is a factor of x^3-6x-11x+k, then k=
Answers
The value of k in the expression x³ – 6x² – 11x + k is –10.
What is polynomials?Polynomial is formed up of the terms Nominal, which means "terms," and Poly, which means "many." A polynomial is a mathematical expression made up of variables, constants, and exponents that are mixed using addition, subtraction, multiplication, and division operations.
From the question given above, the following data were obtained:
f(x) = x³ – 6x² – 11x + k
Factor => x + 2
Value of k =?
Next, we shall obtained the value of x from x + 2. This can be obtained as follow:
x + 2 = 0
Collect like terms
x = 0 – 2
x = –2
Finally, we shall determine the the value of k. This can be obtained as illustrated below:
f(x) = x³ – 6x² – 11x + k
x = –2
Value of k =?
f(–2) = 0 since x + 2 is a factor
x³ – 6x² – 11x + k = 0
(–2)³ – (–2)² – 11(–2) + k = 0
–8 – (4) + 22 + K = 0
–8 – 4 + 22 + K = 0
10 + k = 0
Collect like terms
k = 0 – 10
k = –10
Therefore, the value of k is –10
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If trapezoid QRST is dilated about the origin by a scaled (k) of 2, what is the resulting coordinate of point T”?
Answers
Using dilation, we can find the coordinates of the new trapezoid and the coordinates of T" is (-6, -4).
Define dilation?Dilation is the process of increasing an object's size without altering its shape. Depending on the scale-factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation maths, but the square's shape doesn't change.
In geometry, dilation math is used to enlarge and reduce two- or three-dimensional figures.
Here in the question,
The coordinates of point T = (-3, -2)
Now, the trapezoid is dilated about the origin.
The scale factor here is. k = 2.
The new coordinates of the point T":
x coordinate = -3 × 2 = -6
y coordinate= -2 × 2 = -4
The coordinates of T" = (-6, -4).
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Suppose a random sample of 80 measurements is selected from a population with a mean of 25 and a variance of 200. Select the pair that is the mean and standard error of x. Rstudio
a) [25, 2.081]
b) [25, 1.981]
c) [25, 1.681]
d) [25, 1.581]
e) [80, 1.681]
Answers
[ 25 , 1.581 ] is the pair that is the mean and standard error of x.
What does standard error mean?
A statistical concept known as the standard error uses standard deviation to assess how well a sample distribution represents a population.
The standard error of the mean describes the statistical variation between a sample mean and the population's actual mean. Measures of variability include standard error and standard deviation: The standard deviation describes variation within a single sample.
n = 80
μ = 25
σ² = 200
mean of x = μ = 25
standard error = √ σ²/n
= √200/80
= 1.581
= [ 25 , 1.581 ]
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please help thank you very much
Answers
Answer:5
Step-by-step explanation:
Please help asap!!!
Answers
The exact values of trigonometric functions are, respectively:
sin (u + v) = - 13 /85
tan (u + v) = - 13 / 84
How to find the exact values of trigonometric functions
In this problem we need to determine the exact values of trigonometric functions, this can be done by using trigonometric formulas and relationships between trigonometric functions. We need to use the following expressions:
sin² x + cos² x = 1
sin (u + v) = sin u · cos v + cos u · sin v
tan x = sin x / cos x
tan (u + v) = (tan u + tan v) / (1 - tan u · tan v)
Where x, u, v are measured in radians.
Now we proceed to determine the exact values of each function:
cos u = √[1 - (- 3 / 5)²]
cos u = 4 / 5
sin v = √[1 - (15 / 17)²]
sin v = 8 / 17
sin (u + v) = (- 3 / 5) · (15 / 17) + (4 / 5) · (8 / 17)
sin (u + v) = - 13 /85
tan u = (- 3 / 5) / (4 / 5)
tan u = - 3 / 4
tan v = (8 / 17) / (15 / 17)
tan v = 8 / 15
tan (u + v) = (- 3 / 4 + 8 / 15) / [1 - (- 3 / 4) · (8 / 15)]
tan (u + v) = - 13 / 84
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Use the points (8, 12,800) and (14, 14,420) to enter and interpret the equation of the line of fit in slope-intercept form. y=
The cost of raising a child increases $ each year. The cost of raising a child from birth to age 1 is $ If the trend continues, what will be the approximate annual cost of raising a child born in 2013 at age 17? about $
Answers
the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues. we first need to calculate the slope (m) and the y-intercept (b)
what do you mean by approximate ?
Approximate means "close to but not exactly" or "an estimate". In other words, an approximate value is a value that is not exact but is close enough to the actual value to be useful or meaningful in a given context.
In the given question,
To find the equation of the line of fit in slope-intercept form, we first need to calculate the slope (m) and the y-intercept (b) using the two given points (8, 12,800) and (14, 14,420).
m = (y₂ - y₁) / (x₂ - x₁)
m = (14,420 - 12,800) / (14 - 8)
m = 1,620 / 6
m = 270
b = y - mx
b = 12,800 - 270(8)
b = 10,940
Therefore, the equation of the line of fit in slope-intercept form is:
y = mx + b
y = 270x + 10,940
To use this equation to estimate the cost of raising a child born in 2013 at age 17, we can plug in x = 17 and solve for y:
y = 270x + 10,940
y = 270(17) + 10,940
y = 15,050
Therefore, the approximate annual cost of raising a child born in 2013 at age 17 is about $15,050, assuming that the trend of increasing cost per year continues.
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Adele and her brother ran a race. Adele reached the finish line in 37.45 seconds and her brother reached the finish line 2.1 seconds later. How long did it take Adele's brother to run the race?
Answers
Answer:
It took Adele's brother 37.45 + 2.10 = 39.55 seconds to run the race.
Use trigonometric ratios to find the indicated side lengths in the diagram shown. Round your answers to the nearest tenth.
x = _____ units
y = _____ units
(40 points)
Answers
The indicated side lengths are: x ≈ 13.2 units and y ≈ 11.9 units
What is angle of sin?the ratio between the side opposite the angle and the hypotenuse of the triangle.
given that a triangle with three sides x, y, 18 and angle opposite to side y is 42°.
then by sine formula, trigonometric ratio for the sine of an angle:
sin(42°) = perpendicular /hypotenuse = y/18
y = 18 sin(42°), we find that y ≈ 11.9 units (rounded to the nearest tenth).
To find x, the cosine of an angle:
cos(42°) =base /hypotenuse=x/18
x = 18 cos(42°)
we find that x ≈ 13.2 units (rounded to the nearest tenth).
Therefore, the indicated side lengths are:
x ≈ 13.2 units
y ≈ 11.9 units
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Find the slope of a line perpendicular to the line whose equation is 2x + 3y = 24.
Fully simplify your answer.
Answers
The slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2
What is Equation?An equation is a statement that two expressions are equal. It contains one or more variables and may also contain constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.
To find the slope of a line perpendicular to the line whose equation is [tex]2x + 3y = 24[/tex], we need to first find the slope of the given line.
We can rearrange the equation into slope-intercept form (y = mx + b) by solving for y:
[tex]2x + 3y = 24[/tex]
[tex]3y = -2x + 24[/tex]
[tex]y = \huge \text(-\dfrac{2}{3}\huge \text )x + 8[/tex]
So the slope of the given line is -2/3.
A line perpendicular to this line will have a slope that is the negative reciprocal of -2/3.
The negative reciprocal of a number is the number flipped upside down and then negated. So the negative reciprocal of -2/3 is:
[tex]-1 \div \huge \text(-\dfrac{2}{3}\huge \text )=\dfrac{3}{2}[/tex]
Therefore, the slope of a line perpendicular to [tex]2x + 3y = 24[/tex] is 3/2
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Find the perimeter and total area
Answers
Answer:
Perimeter: Add up all the sides (7.5, 6, 2.5, 3.5, 3.5) to get the answer for the perimeter as 23 ft.
Area: Split the shape into two rectangles either way and multiply the length and width. Then, add the two answers. This would leave us with the answer of the area as 35 square feet.
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
x = 4
Step-by-step explanation:
In order to find x, we will either have to find the length QT or RT.
In triangle RST, the length RS is given so we can either length RT or ST. However, if we find the length RT, we can find the value of x.
sin Θ = [tex]\frac{opp}{hyp}[/tex]
sin 60° = [tex]\frac{2\sqrt{3} }{RT}[/tex]
RT = [tex]\frac{2\sqrt{3}}{sin 60}[/tex] = 4
tan Θ = [tex]\frac{opp}{adj}[/tex]
tan 45° = [tex]\frac{x}{4}[/tex]
x = tan 45° × 4 = 4
Simplify the function f(x)=1/2(27) 2x/3 then determine the key aspects of the function
Answers
The simplified form of the function f(x)=1/2(27) 2x/3 can be expressed as f(x) = (27/2) (2x/3).
What is function?Functions are one of the fundamental building blocks of mathematics and are used to describe and analyze relationships between different variables.
The function f(x)=1/2(27) 2x/3 can be simplified by factoring out the common factor of 1/2 and 27.
Thus, the simplified form of the function can be expressed as
f(x) = (27/2) (2x/3).
This function is a polynomial function with degree 1, which means that it is a linear function. The degree of a function is the highest power of the variable in the equation.
The key aspects of this function can be identified by looking at the constant values in the equation.
The constant value 27/2 is the y-intercept, which is the point at which the line crosses the y-axis.
This means that the y-value of the function at x = 0 is 27/2.
The constant value 2/3 is the gradient, which is the slope of the line. This means that for every increase in the x-value, the y-value will increase by 2/3.
This function can be represented graphically as a straight line with a y-intercept of 27/2 and a slope of 2/3.
The graph of this function will pass through the point (0, 27/2) and will have a positive slope of 2/3. This means that the graph will move up and to the right, with each increase in the x-value resulting in an increase of 2/3 in the y-value.
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Let f(x) = (x + 3)(x + 4) and g(x) = 1 3 (x + 3)(x − 4). The graphs of each are shown below.
Which graph represents which polynomial function? Explain how you can determine this without
using graphing software
Answers
Answer: We can determine which graph represents which polynomial function by analyzing the factors of each function.
First, let's consider f(x) = (x + 3)(x + 4). The factors are (x + 3) and (x + 4). When we multiply these factors together, we get a quadratic polynomial with a positive leading coefficient. This means that the graph of f(x) will be a parabola that opens upward.
Next, let's consider g(x) = 1/3(x + 3)(x − 4). The factors are (x + 3) and (x - 4). When we multiply these factors together and simplify, we get a quadratic polynomial with a leading coefficient of 1/3. This means that the graph of g(x) will also be a parabola that opens upward, but it will be narrower than the graph of f(x).
Based on this analysis, we can determine that the graph of f(x) corresponds to the wider parabola, and the graph of g(x) corresponds to the narrower parabola. We can also determine this without using graphing software by noting that f(x) has roots at x = -3 and x = -4, while g(x) has roots at x = -3 and x = 4. The graph of f(x) must therefore intersect the x-axis at -3 and -4, while the graph of g(x) must intersect the x-axis at -3 and 4. By examining the graphs, we can see that the wider parabola intersects the x-axis at -3 and -4, so it corresponds to f(x), while the narrower parabola intersects the x-axis at -3 and 4, so it corresponds to g(x).
Step-by-step explanation:
what is a fraction between 6/7 and 1
Answers
Answer:
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sandhyamahilane1116
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Math
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What is a fraction between 6/7 and 1 whole?
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Given : 6/7 and 1 whole
To Find : a fraction between 6/7 and 1 whole
Solution:
There exist Infinitely many rational between two different rational numbers
There can be Different ways to find rational number in between two number
one way is to find mean of number
= (6/7 + 1)/2
= 13/14
13/14 is a fraction between 6/7 and 1 whole
6/7 = 18/21
1 = 21/21
19/21 , 20/21 are fraction between 6/7 andfraction
Change into passive voice a. They bring food for us.
Answers
Answer:
Food is brought for us by them.
Answer:
Food is brought for us by them.
Step-by-step explanation:
Colton measured the high school and made a scale drawing. The scale he used was 1 centimeter : 2 meters. The parking lot is 88 meters long in real life. How long is the parking lot in the drawing?
centimeters
Answers
The length of the parking lot in the drawing is 44 centimeters.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.
Since the scale Colton used is 1 centimeter : 2 meters, this means that for every 2 meters in real life, he drew 1 centimeter in his scale drawing.
To find the length of the parking lot in the drawing, we can set up a proportion:
1 cm / 2 m = x cm / 88 m
where x is the length of the parking lot in the drawing in centimeters.
We can solve for x by cross-multiplying:
1 cm * 88 m = 2 m * x cm
88 cm = 2x
x = 44 cm
Therefore, the length of the parking lot in the drawing is 44 centimeters.
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A small nation of ten people idolizes the TV show “The Voice”. All they produce and consume are karaoke machines and CDs, in the following amounts:
Karaoke Machines
CDs
Quantity Produced
(in thousands)
Price of each Karaoke Machine
Quantity Produced
(in thousands)
Price of each CD
2017
10
$40
30
$10
2018
12
$60
50
$12
The population of the economy is 10000 in 2017 and it increased to 15000 in 2018.Using the CPI, compute the percentage change in the overall price level. Use 2017 as the base year and fix the basket at 1 karaoke machine and 3 CDs.
Answers
To compute the CPI, we first need to calculate the total cost of the basket in both years:
2017: (10 x $40) + (30 x $10) = $400 + $300 = $700
2018: (12 x $60) + (50 x $12) = $720 + $600 = $1320
Using 2017 as the base year, the CPI in 2017 is 100 (by definition). To calculate the CPI in 2018, we divide the cost of the basket in 2018 by the cost of the basket in 2017, and multiply by 100:
CPI in 2018 = (1320/700) x 100 = 188.57
Therefore, the percentage change in the overall price level is:
% change in price level = (CPI in 2018 - CPI in 2017) / CPI in 2017 x 100
% change in price level = (188.57 - 100) / 100 x 100
% change in price level = 88.57%
So, the overall price level increased by 88.57% from 2017 to 2018.
Find the missing side lengths. Leave your answers as radicals in simplest form
Answers
Answer:
x = 2;
y = √3
Step-by-step explanation:
Use trigonometry:
[tex] \tan(60°) = \frac{y}{1} [/tex]
Cross-multiply to find y:
[tex]y = 1 \times \tan(60°) = 1 \times \sqrt{3} = \sqrt{3} [/tex]
Use the Pythagorean theorem to find x:
[tex] {x}^{2} = {y}^{2} + {1}^{2} [/tex]
[tex] {x}^{2} = ( { \sqrt{3}) }^{2} + {1}^{2} = 3 + 1 = 4[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{4} = 2[/tex]
Light travels 1.8x10^7 kilometers in one minute. How far does it travel in 6 minutes?
Answers
1.8x10^7 km/minute * 6 minutes = 1.08x10^8 kilometers
So, light will travel 1.08x10^8 kilometers in 6 minutes.
1.08x10^8 kilometers is equal to 108,000,000 kilometers.
Given sinx=3/5 and is in quadrant 2, what is the value of tan x/2 ?
Answers
Answer:
[tex]\tan \left(\dfrac{x}{2}\right)=3[/tex]
Step-by-step explanation:
Trigonometric ratios are the ratios of the sides of a right triangle.
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
The sine trigonometric ratio is the ratio of the side opposite the angle to the hypotenuse.
Given sin(x) = 3/5, the side opposite angle x is 3, and the hypotenuse is 5.
As we have two sides of the right triangle, we can calculate the third side (the side adjacent the angle) using Pythagoras Theorem.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
Therefore:
[tex]\implies A^2+3^2=5^2[/tex]
[tex]\implies A^2+9=25[/tex]
[tex]\implies A^2+9-9=25-9[/tex]
[tex]\implies A^2=16[/tex]
[tex]\implies \sqrt{A^2}=\sqrt{16}[/tex]
[tex]\implies A=4[/tex]
Use the cosine trigonometric ratio to find the value of cos(x), remembering that cosine is negative in Quadrant II.
[tex]\implies \cos x=-\dfrac{4}{5}[/tex]
Now we have the values of sin(x) and cos(x) in Quadrant II, we can use the tangent half angle formula to find the value of tan(x/2).
[tex]\begin{aligned}\implies \tan \left(\dfrac{x}{2}\right)&=\dfrac{\sin x}{1+\cos x}\\\\&=\dfrac{\frac{3}{5}}{1-\frac{4}{5}}\\\\&=\dfrac{\frac{3}{5}}{\frac{1}{5}}\\\\&=\dfrac{3}{5} \cdot \frac{5}{1}\\\\&=3\end{aligned}[/tex]
Therefore, the value of tan(x/2) is 3.
How much will you owe at the end of 10 years and a month, if you decide to pay your yearly bonus at the end of each year toward reducing your outstanding loan amount for a loan with the following details? Loan amount PV $320,000 Rate of interest APR 4.750% p. y. c. w. Loan term NPER 15 years Bonus payment at end of each year $4,500 Group of answer choices $21,619.43 $41,033.68 $58,527.87 $74,315.75
Answers
The correct option is $58,527.87
To solve this problemUsing the loan details and bonus payment provided, the remaining balance on the loan at the end of 10 years and a month can be calculated as follows:
Number of payments made = 10 years * 12 months/year + 1 month = 121
Monthly interest rate = 4.75% / 12 = 0.3958%
Yearly bonus payment = $4,500
Using the PMT function in Excel, the monthly payment on the loan can be calculated as:
PMT(0.003958, 15*12, 320000) = -$2,378.03
Since the bonus payment is made once a year, it can be applied as a lump sum to the remaining balance at the end of each year. Therefore, the remaining balance after 10 years and a month can be calculated as:
Remaining balance = PV(0.003958, 5*12, -2378.03, 0, 0) - 4500
where PV is the present value function.
Solving this equation yields:
Remaining balance = $58,527.87
Therefore, the answer is $58,527.87.
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10. Substitute for A, P and T in the formula A = P(1 + r), given that A = 1 000 000, P = 10 000 and T = 2, and express as a quadratic equation.
Answers
Answer:
Step-by-step explanation:Let's first substitute the values of A, P, and T in the formula A = P(1 + r)^T.
Given: A = 1,000,000; P = 10,000; T = 2
1,000,000 = 10,000(1 + r)^2
Now let's express it as a quadratic equation. First, divide both sides by 10,000:
100 = (1 + r)^2
Next, expand the square:
100 = 1 + 2r + r^2
Finally, rearrange to form the quadratic equation:
r^2 + 2r - 99 = 0
To represent the formula A = P(1 + r) as a quadratic equation with the given values, we substitute A = 1,000,000, P = 10,000, and T = 2. The resulting equation is 10,000r - 9,000,000 = 0.
Explanation:To express the formula A = P(1 + r) as a quadratic equation, we substitute the given values for A, P, and T.
Given:
A = 1,000,000P = 10,000T = 2Substituting these values into the formula:
1,000,000 = 10,000(1 + r)
To express this equation as a quadratic form, we can expand the parentheses:
1,000,000 = 10,000 + 10,000r
Now, let's move all the terms to one side to form a quadratic equation:
10,000r - 9,000,000 = 0
Therefore, the quadratic equation that represents A = P(1 + r) with the given values is 10,000r - 9,000,000 = 0.
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Find the missing side lengths. Leave your answers as radicals in simplest form.
Answers
Answer:
y = 2;
x = 2√2
.
Step-by-step explanation:
Use trigonometry:
[tex] \tan(45°) = \frac{y}{2} [/tex]
Use the property of proportion to find x (cross-multiply):
[tex]y = 2 \times \tan(45°) = 2 \times 1 = 2[/tex]
Use the Pythagorean theorem to find x:
[tex] {x}^{2} = {y}^{2} + {2}^{2} [/tex]
[tex] {x}^{2} = {2}^{2} + {2}^{2} = 4 + 4 = 8[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{8} = \sqrt{4 \times 2} = 2 \sqrt{2} [/tex]
Four transformations of the function f (x ) = 2x are given below. For each transformation, drag the expression that shows the result of that transformation into the box under it.
Answers
For the four transformations based on f(x)= [tex]2^{x}[/tex],
1)6f(x)= 6 [tex]2^{x}[/tex]
2)f(6x)= [tex]2^{6x}[/tex]
3)f(x+6)=[tex]2^{x+6}[/tex]
4)f(x)+6 = [tex]2^{x}[/tex]+6
What are transformations?
Transformations in any given function is changing its original form to nre form by flipping, rotating, shifting, enlarging and compressing the function. We can move the given function up or down as per the given conditions by adding up or subtracting the constant in y axis. We can move the given function left or right as per the given conditions by adding up or subtracting the constant in x axis. We can stretch or compress the function about x or y axes. Also we can also flip,reverse the function, reflect about axes or enlarge the functions.
Here given that function f(x)= [tex]2^{x}[/tex]
From the given graph we can identify few points for the given function:
(-1,0.5); (0,1); (1,2); (2,4); (3,8); (4,16); (5,32); (6,64) and so on.
Now to identify the transformations, we can substitute the tranformed value of x in the function:
1)6 f(x) = 6 . [tex]2^{x}[/tex] {as we know that f(x)= [tex]2^{x}[/tex]}
∴6 f(x) will be equal to 6 . [tex]2^{x}[/tex]
2)f(6x) : for this we can replace 'x' by '6x'
f(6x) = [tex]2^{6x}[/tex]
3)f(x+6): for this function replace 'x' by 'x+6'
f(x+6)=[tex]2^{x+6}[/tex]
4)f(x)+6 : substitute f(x)= [tex]2^{x}[/tex], we get
f(x)+6 = [tex]2^{x}[/tex]+6
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6. The picture at the right shows the garden in Robert's
yard. He wants to cover the garden with plastic be-
cause of a sudden drop in temperature. How many
square yards of plastic does he need?
12 ft
15 ft
9 ft
Answers
Answer:
To determine the area of the garden that needs to be covered with plastic, we need to multiply the length by the width of the garden. However, we need to convert the measurements to the same unit of measurement. Let's convert the measurements into yards since we need to find the area in square yards. 12 ft = 4 yards 15 ft = 5 yards 9 ft = 3 yards Now, we can calculate the area: Area = Length x Width Area = 5 yards x 4 yards Area = 20 square yards Therefore, Robert needs 20 square yards of plastic to cover his garden.
Whats the value of x?
Answers
Answer:
x = 25
Step-by-step explanation:
By the angle sum property,
2x + 2 + 5x + 3 = 180
7x + 5 = 180
7x = 175
x = 25
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Answer:
x = 25
Step-by-step explanation:
2x + 2 + 5x + 3 = 180
7x + 5 = 180 and 7x=175
7x = 175
x = 25
so x is most likely the answer
x=25 Give her BRAINLEST for figuring it out first
The combined city/highway fuel economy of a 2016 Toyota 4runner 2wd 6-cylinder 4-L automatic 5-speed using regular gas is a normally distributed random variable with a range of 21mpg to 26mpg answer A and B URGENT
Answers
a)The range of 95% of the data is from 21 mpg to 26 mpg, which is a range of 5 mpg.
b)We need a sample size of 543 to estimate the mean with 98% confidence and an error of 0.25 mpg
What is Empirical Rule for a normal distribution?
If a dataset is normally distributed, we can expect that about 68% of the data points will fall within one standard deviation of the mean, about 95% of the data points will fall within two standard deviations of the mean, and about 99.7% of the data points will fall within three standard deviations of the mean. This rule is a useful guideline for understanding the spread of data in a normal distribution.
(a) Using Method 3 (the Empirical Rule for a normal distribution), we know that for a normally distributed random variable, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean.
Since the range of the combined city/highway fuel economy of a 2016 Toyota 4Runner 2WD 6-cylinder 4-L automatic 5-speed using regular gas is from 21 mpg to 26 mpg, the midpoint of the range is (21 + 26) / 2 = 23.5 mpg.
Using the Empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Therefore, the range of 95% of the data is from 21 mpg to 26 mpg, which is a range of 5 mpg.
We can set up the following equation to solve for the standard deviation, σ:
2σ = 5
σ = 5 / 2
σ = 2.5
Therefore, the estimated standard deviation is 2.5 mpg. Rounded to 4 decimal places, the estimated standard deviation is 2.5000 mpg.
(b) The formula for the margin of error is:
Margin of error = z-value×(standard deviation / √(sample size))
We want the margin of error to be 0.25 mpg and the confidence level to be 98%. Since we are using a z-value, we can look up the z-value for a 98% confidence level in a standard normal distribution table.
The z-value for a 98% confidence level is approximately 2.33 when rounded to 3 decimal places.
Plugging in the given values, we have:
0.25 = 2.33×(2.5 / √(sample size))
Solving for the sample size, we get:
√(sample size) = 2.33 × (2.5 / 0.25)
√(sample size) = 23.3
sample size = (23.3)²
sample size = 542.89
Rounded to the nearest whole number, we need a sample size of 543 to estimate the mean with 98% confidence and an error of 0.25 mpg.
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The height above the ground in feet of a football thrown into the air from the balcony of a house is -12t + 20t + 30, where t is the time in seconds since the ball was thrown. How high above the ground is the balcony?
Answers
Answer: The height above the ground in feet of a football thrown into the air from the balcony of a house is given by the expression:
h(t) = -12t^2 + 20t + 30
where t is the time in seconds since the ball was thrown.
To find the height of the balcony above the ground, we need to determine the initial height of the football when it was thrown from the balcony. This initial height corresponds to the value of h(0), since the time elapsed since the throw was zero at that moment.
Therefore, we can substitute t = 0 into the expression for h(t):
h(0) = -12(0)^2 + 20(0) + 30 = 30
This means that the balcony is 30 feet above the ground.
Hence, the height of the balcony above the ground is 30 feet.
Step-by-step explanation:
How will the product change if one number is increased by a factor of 12 and the other is decreased by a factor of 4
Answers
If one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will be multiplied by a factor of 3.
Let's suppose we have two numbers, A and B, and we want to know how their product will change if one number is increased by a factor of 12 and the other is decreased by a factor of 4.
The initial product of the two numbers is:
A x B
If we increase A by a factor of 12, the new value of A will be 12A. If we decrease B by a factor of 4, the new value of B will be B/4. Therefore, the new product of the two numbers will be:
(12A) x (B/4) = (12/4) x A x B = 3AB
So the new product of the two numbers will be three times the initial product. In other words, if one number is increased by a factor of 12 and the other is decreased by a factor of 4, the product of the two numbers will increase by a factor of 3.
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single-cell of bacteria triples every 3 days. About how many days will it take one bacteria to produce a population of 2187?
Answers
Answer:
7 days
Step-by-step explanation: