Answers
The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.
What is a piecewise function?A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.
The intervals of the piecewise function are;
f(x) = √(x + 5) if x < -2
f(x) = |x + 1| -2 ≤ x ≤ 2
f(x) = (x - 2)² if x > 2
The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²
The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2
The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.
The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.
The correct option for the graph of the piecewise function is therefore the third option.
Please find the attached the graph of the piecewise function created with MS Excel
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Related Questions
Which expression represents the distance
between point G and point H?
|-12|16| |-12|+|-9|
1-9|-|-6|
|-12|+|6|
-15
H(-9,6)
G(-9,-12)
15+y
0
-15-
15
Answers
Answer:
Step-by-step explanation:
2
The rate at which a rumor spreads through a town of population N can be modeled by the equation dt/dx = kx(N−x) where k is a constant and x is the number of people who have heard the rumor. (a) If two people start a rumor at time t=0 in a town of 1000 people, find x as a function of t given k=1/250. (b) When will half the population have heard the rumor?
Answers
(a) The function x as a function of t is t = 250ln(499x/998)
(b) Half the population will have heard the rumor approximately 109.86 units of time after it was started.
(a) To solve the differential equation dt/dx = kx(N−x), we can separate the variables and integrate
dt/dx = kx(N−x)
dt/(N-x) = kx dx
Integrating both sides, we get
t = -1/k × ln(N-x) - 1/k × ln(x) + C
where C is the constant of integration.
To find C, we can use the initial condition that two people start the rumor at t=0, so x=2:
0 = -1/k * ln(N-2) - 1/k * ln(2) + C
C = 1/k * ln(N-2) + 1/k * ln(2)
Substituting C back into the equation, we get:
t = -1/k * ln(N-x) - 1/k * ln(x) + 1/k * ln(N-2) + 1/k * ln(2)
Simplifying, we get
t = 1/k * [ln((N-2)x/(2(N-x)))]
Substituting k=1/250 and N=1000, we get:
t = 250ln(499x/998)
(b) We want to find the time t when half the population has heard the rumor, so x = N/2 = 500. Substituting this into the equation we obtained in part (a), we get
t = 250ln(499(500)/998) = 250ln(249/499)
t ≈ 109.86
Therefore, half the population will have heard the rumor approximately 109.86 units of time after it was started.
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T/F. Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars.
Answers
The given statement "Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars." is True. The reason for this is that O and B stars are short-lived and burn through their fuel quickly.
The reason for this is that O and B stars burn through their fuel quickly, causing them to exhaust their nuclear fuel and end their lives in a relatively short period, typically within a few tens of millions of years.
On the other hand, stars of lower mass and cooler temperatures, like G and K type stars like our sun, have longer lifetimes and take billions of years to exhaust their nuclear fuel.
Therefore, clusters without any bright, blue stars are likely to have evolved for longer periods, allowing these short-lived stars to have already expired.
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Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long would you have to wait for 1/7 of it to disappear?
You would have to wait ___ years for 1/7 of the radium to disappear.
Answers
Accοrding tο the half-life fοrmula, we wοuld have tο wait apprοximately 4975 years fοr 1/7 οf the radium tο decay.
What is Expοnential Decay ?Expοnential decay is a mathematical prοcess in which a quantity decreases οver time in a manner prοpοrtiοnal tο its current value. This means that the rate οf decay is prοpοrtiοnal tο the amοunt οf the substance remaining, and as the amοunt οf the substance decreases, the rate οf decay alsο decreases. The fοrmula fοr expοnential decay is οften written as:
N(t) = N₀ *[tex]e^{(-kt)[/tex]
where N(t) is the amοunt οf substance remaining at time t, N₀ is the initial amοunt οf the substance, k is the decay cοnstant, and e is the base οf the natural lοgarithm.
The half-life οf radium is apprοximately 1590 years, which means that after 1590 years, half οf the οriginal radium will have decayed. Therefοre, we can use the half-life fοrmula tο find the amοunt οf time it wοuld take fοr 1/7 οf the radium tο decay:
N = N₀[tex]* (1/2)^{(t/t1/2)[/tex]
where N is the final amοunt (1/7 οf the οriginal amοunt), N0 is the initial amοunt, t is the time elapsed, and t1/2 is the half-life.
We can rearrange this fοrmula tο sοlve fοr t:
t = t1/2 * lοg2(N₀/N)
t = 1590 years * lοg2(7)
t ≈ 4975 years
Therefοre, we wοuld have tο wait apprοximately 4975 years fοr 1/7 οf the radium tο decay.
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Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between 0°C and 1.08°C. Round your answer to 4 decimal places
Answers
Answer: We are given that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C.
To find the probability of obtaining a reading between 0°C and 1.08°C, we need to calculate the z-scores for these values using the formula:
z = (x - mu) / sigma
where x is the value we are interested in, mu is the mean, and sigma is the standard deviation.
For x = 0°C, we have:
z1 = (0 - 0) / 1.00 = 0
For x = 1.08°C, we have:
z2 = (1.08 - 0) / 1.00 = 1.08
Using a standard normal table or a calculator, we can find the probability of obtaining a z-score between 0 and 1.08.
Using a standard normal table or a calculator, we find that the probability of obtaining a z-score between 0 and 1.08 is 0.3583.
Therefore, the probability of obtaining a reading between 0°C and 1.08°C is 0.3583, rounded to 4 decimal places.
Step-by-step explanation:
100 POINTS + BRAINLIEST PLS BE FAST!!
Answers
i) Find the mean, median, and mode of the frequency table as follows:
Mean = 6.6Median = 8Mode = 3.ii) The average that justifies the teacher's statement congratulating the class that 'over three quarters were above average' is the average mark of 10, which is 5.
What are the mean, median, and mode?The mean refers to the average or the quotient of the total values divided by the number of items.
The median is the middle value in the data, which occurs with marks 8 for the 13th and 14th students.
The mode is the value that occurs most frequently, which is 3 which occurs 6 times.
Frequency Table:
Mark Frequency Cumulative Frequency
3 6 18 (0 + 3 x 6)
4 3 30 (18 + 4 x 3)
5 1 35 (30 + 5 x 1)
6 2 47 (35 + 6 x 2)
7 0 47 (47 + 7 x 0)
8 5 87 (47 + 8 x 5)
9 5 132 (87 + 9 x 5)
10 4 172 (132 + 10 x 4)
Mean = 6.6 (172/26)
Median = 8
Mode = 3
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Can anyone help thanks!!!!
Answers
Answer:
B
Step-by-step explanation:
5^2 is the small square, 4(3x4x1/2) are the 4 triangles
Answer: The answer would be B.
Step-by-step explanation:
Hello.
First, we know that the smaller square is 5, and to find the area of the big square, we need to square 5 to get the area. We also know that C wouldn't be a viable option, so, our only remaining choices are A and B. We know that without the smaller square, there are 4 triangles, and the Area of a Triangle is: 1/2*b*h. So, this also takes A out as an option as well. After this, you will have your answer as B; 5^2 + 4(3 * 4 * 1/2)
(Or, you could have found the Area of the Triangles, and realize that neither A, nor C have those options, making B the answer by default.)
Hope this helps, (and maybe brainliest?)
which of the following code segments assigns bonus correctly for all possible integer values of score ?
Answers
The code segment that assigns bonus correctly for all possible integer values of score is D, which uses nested if statements to implement the game's rules for assigning a value to bonus based on the value of score.
The code segment that assigns bonus correctly for all possible integer values of score is D:
IF(score < 50)
{
bonus ← Ø
}
ELSE
{
IF (score > 100)
{
bonus ← score (10)
}
ELSE
{
bonus ← score
}
}
This code segment correctly implements the rules for assigning a value to bonus based on the value of score. It first checks if score is less than 50, and if so, it assigns 0 to bonus. If score is greater than or equal to 50, it checks if score is greater than 100, and if so, it assigns 10 times score to bonus. Otherwise, it assigns score to bonus. This covers all possible integer values of score and ensures that bonus is assigned correctly according to the game's rules.
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Complete question is in the image attached below
How this app works? Why I can’t find any answers? I need pay for points when I ask questions? I subscribe this app and when I’m lucky to the answers almost the answers are wrong
Answers
Which of the following pairs of sample size n and population proportion p would produce the greatest standard deviation for the sampling distribution of a sample proportion p?
Answers
Therefore , the solution of the given problem of standard deviation comes out to be option C with n = 1,000 and p near to 1/2 is the right response.
What does standard deviation actually mean?Statistics uses variance as a way to quantify difference. The image of the result is used to compute the average deviation between the collected data and the mean. Contrary to many other valid measures of variability, it includes those pieces of data on their own by comparing each number to the mean. Variations may be caused by willful mistakes, irrational expectations, or shifting economic or business conditions.
Here,
The following algorithm determines the standard deviation of the sampling distribution of a sample proportion p:
=> √((p*(1-p))/n)
where n is the sample size, and p is the population percentage.
For the sampling distribution of a sample proportion p,
the pair of sample number n and population proportion p that would result in the highest standard deviation is:
=>n =1,000, and p is almost half.
Because p=1/2
yields the highest possible value of the expression (p*(1-p)), a bigger sample size will result in a smaller standard deviation.
The standard deviations will be lower for the other choices, which have smaller sample sizes or extreme values of p.
Therefore, (C) with n = 1,000 and p near to 1/2 is the right response.
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Linda deposits $50,000 into an account that pays 6% interest per year, compounded annually. Bob deposits $50,000 into an account that also pays 6% per year. But it is simple interest. Find the interest Linda and Bob earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits. Year First Second Third Interest Linda earns (Interest compounded annually) Interest Bob earns (Simple interest) Who earns more interest? Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount. Linda earns more. Bob earns more. They earn the same amount.
Answers
Answer:
Step-by-step explanation:
To calculate the interest earned by Linda for the first year, we can use the formula:
A = P(1 + r/n)^(nt)
Where A is the amount after t years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
For the first year, we have:
A = $50,000(1 + 0.06/1)^(1*1) = $53,000
So, the interest earned by Linda for the first year is:
Interest = $53,000 - $50,000 = $3,000
For the second year, we can use the same formula with t = 2:
A = $50,000(1 + 0.06/1)^(1*2) = $56,180
Interest = $56,180 - $53,000 = $3,180
For the third year, we can use the same formula with t = 3:
A = $50,000(1 + 0.06/1)^(1*3) = $59,468.80
Interest = $59,468.80 - $56,180 = $3,288.80
Now, to calculate the interest earned by Bob for each of the first three years, we can use the formula:
Interest = Prt
Where P is the principal amount, r is the annual interest rate, and t is the time in years.
For the first year, we have:
Interest = $50,0000.061 = $3,000
For the second year, we have:
Interest = $50,0000.061 = $3,000
For the third year, we have:
Interest = $50,0000.061 = $3,000
As we can see, Linda earns more interest than Bob for each year, as her interest is compounded annually, while Bob's interest is simple interest. Therefore, the answer is:
Linda earns more.
Answer:
Linda earns $9550.8 interest and bob earns $9000 interest
Step-by-step explanation:
Linda takes compound interest: C.I. = Principal (1 + Rate)Time − Principal
interest= 50,000(1+6/100)³
=59550.8 - 50000
Linda earns $9550.8 interest in 3 years.
bob takes simple interest: S.I = prt/100
interest = 50,000*6*3/100
Bob earns $9000 in 3 years.
thus, Linda earns more interest than bob.
mr.woodstock has a plot of land 36 meter long and 16 meters wide. he uses the land for mixed farming- rearing animals and growing crop? What length of wire does mr.woodstock need to fence his land?
Answers
Mr. Woodstock will need to purchase 144 meters of wire to fully encircle his land. He will need to measure the length of the four sides of the land and add them together. The four sides measure 36 meters + 36 meters + 16 meters + 16 meters, which equals a total of 104 meters. He should buy enough wire to cover an additional 40 meters to account for any extra material he may need. Therefore, he needs to purchase 144 meters of wire for his fencing.
I will mark you brainiest!
In a triangle, the interior angles add up to 180º.
True
False
Answers
Answer:
it should be true because sum of 3 interior angle of a triangle is 180 degree
Answer:
True.
Step-by-step explanation:
A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.
35% of households say they would feel secure if they had 50000 in savings he randomly selected 8 households and ask them if they would feel secure if they had 50000 in savings find the probability that the number that say that they would feel secure a exactly 5B more than 5 &c at most 5
Answers
Probability that precisely 5 people will respond that they would feel comfortable is 0.0808
Probability that more than 5 people will respond that they would feel comfortable is0.1061
Probability that at most 5 people will respond that they would feel comfortable is 0.9747
Probability Definition in MathProbability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence.
Solving the problem:35 percent of households claim that having $50,000 in savings would make them feel comfortable. Ask 8 homes that were chosen at random if they would feel comfortable if they had $50,000 in savings.
Binomial conundrum with p(secure) = 0.35 and n = 8.
the likelihood that the number of people who claim they would feel comfortable is
(a) The number exactly five is equal to ⁸C₅ (0.35)5×(0.65)×3=binompdf(8,0.35,5) = 0.0808.
(b) more than five = 1 - binomcdf(8,0.35,4) = 0.1061
(c) at most five = binomcdf(8,0.35,5) = 0.9747.
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Use the graphs shown in the figure below. All have the form f(x) = abª. Which graph has the smallest value for b?
Answers
Graph D of the given function has the smallest value for b.
Exponential Function: What Is It?As per name signifies, exponents are used in exponential functions. But take note that an exponential function does not have a constant as its base and a variable as its exponent. One of the following forms can be used for an exponential function.
f (x) = aˣ
According to the graph,y=f(x) >0
f(x)=abˣ , where a>0
So, f(x)=abˣ
When, b<1 f(x) decreases
When, b>1 f(x) increases and the larger the b the steeper the graph
So, graph of D is increasing and is steepest
So, graph D has the smallest value for b.
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1.The volume of a toaster is 100 in . If the toaster is 2.5 inches wide and 4 inches high, how long is the toaster, in inches?
2. Find the volume of a cylinder with a diameter of 9 ft and a height of 1 ft.
Use 3.14 or the calculator value for pi and provide an answer accurate to the nearest tenth.
Answers
Answer:
10 in.
Step-by-step explanation:
V = LWH
100 = L × 2.5 × 4
L = 10
Karina is making a quilt and she has determined she needs 420 square inches of green fabric and 688 square
inches of burgundy. How many square yards of each material will she need? Round your answers up to the
nearest quarter yard.
The green fabric:
square yards
The burgundy fabric:
How many total yards of fabric will she have to buy?
square yards
square yards
Answers
1. The total yards of each fabric that Karina will buy to make a quilt is as follows:
a) Green Fabric = 12 square yards
b) Burgundy Fabric = 19 square yards
2. The total yards of fabric she will buy is 31 square yards.
How are the total determined?The total yards of fabric can be determined by unit conversion using division operation.
Given that 36 inches = 1 yard, the square inches of fabric are converted to square yards by dividing the total by 36.
The total number of green fabric Karina requires = 420 square inches
= 12 square yards (420/36)
The total number of burgundy fabric Karina requires = 688 square inches
= 19 square yards (688/36)
The total number of fabric (green and burgundy) = 1,108 square inches (420 + 688)
36 inches = 1 yard
1,108 inches = 30.78 square yards (1,108/36)
= 31 square yards or (12 + 19)
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Mr. Roy captures 15 snapping turtles near some wetland by his house. He marks them with a “math is cool” label and releases them back into the wild. 6 months later, he captures another 15 snapping turtles – 4 of which were marked. Estimate the population of snapping turtles in the area to the nearest whole number. Show your work.
Answers
Answer: 56
Step-by-step explanation:
One possible method to estimate the population of snapping turtles in the area is by using the mark and recapture method, also known as the Lincoln-Petersen index.
According to this method, the population size can be estimated by dividing the number of marked individuals in the second sample by the proportion of marked individuals in the combined sample. In other words:
Estimated population size = (Number of individuals in sample 1 × Number of individuals in sample 2) / Number of marked individuals in sample 2
Using the information provided in the problem, we can fill in the formula as follows:
Estimated population size = (15 × 15) / 4
Estimated population size = 56.25
Rounding to the nearest whole number, we get an estimated population size of 56 snapping turtles in the area.
I need help with this
Answers
Answer:
(x -14)² +(y -7)² = 1²
Step-by-step explanation:
You want the equation of the circle that represents the border of a logo centered 14 m right and 7 m up from the lower left corner of a soccer field. The logo is 2 m in diameter.
Equation of a circleThe equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Since the origin of the coordinate system is the lower left corner of the field, the center is located at (h, k) = (14, 7). The diameter of 2 m means the radius is 1 m. Using these values in the equation, it becomes ...
(x -14)² +(y -7)² = 1²
ONQ is a sector of a circle with centre O and radius 13 cm. A is the point on ON and B is the point on OQ such that AOB is an equilateral triangle of side 9 cm. Calculate the area of the shaded region as a percentage of the area of the sector ONQ. Give your answer correct to 1 decimal place.
Answers
The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%
What is an equilateral triangle?The shape of an equilateral triangle is an equilateral triangle.
The word "Equilateral" is formed by combining two words. H. "Equi" means equal, "lateral" means side.
Equilateral triangles are also called regular polygons or equilateral triangles because all sides are equal.
In geometry, an equilateral triangle is a triangle with all sides of equal length.
Three sides are equal, so three angles on the same side are equal. Therefore, it is also called an equilateral triangle with each angle of 60 degrees.
Like other types of triangles, equilateral triangles have formulas for area, perimeter, and height.
According to our question-
AB=OA=BO= 9CM
ONQ-AOB/ONQ*100
PUTTING VALUES
60.3%
Hence, The area of the shaded region as a percentage of the area of the sector ONQ= 60.3%
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find the value of the derivative (if it exists) at
each indicated extremum
Answers
Answer:
The value of the derivative at (-2/3, 2√3/3) is zero.
Step-by-step explanation:
Given function:
[tex]f(x)=-3x\sqrt{x+1}[/tex]
To differentiate the given function, use the product rule and the chain rule of differentiation.
[tex]\boxed{\begin{minipage}{5.4 cm}\underline{Product Rule of Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{7 cm}\underline{Differentiating $[f(x)]^n$}\\\\If $y=[f(x)]^n$, then $\dfrac{\text{d}y}{\text{d}x}=n[f(x)]^{n-1} f'(x)$\\\end{minipage}}[/tex]
[tex]\begin{aligned}\textsf{Let}\;u &= -3x& \implies \dfrac{\text{d}u}{\text{d}{x}} &= -3\\\\\textsf{Let}\;v &= \sqrt{x+1}& \implies \dfrac{\text{d}v}{\text{d}{x}} &=\dfrac{1}{2} \cdot (x+1)^{-\frac{1}{2}}\cdot 1=\dfrac{1}{2\sqrt{x+1}}\end{aligned}[/tex]
Apply the product rule:
[tex]\implies f'(x) =u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}[/tex]
[tex]\implies f'(x)=-3x \cdot \dfrac{1}{2\sqrt{x+1}}+\sqrt{x+1}\cdot -3[/tex]
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-3\sqrt{x+1}[/tex]
Simplify:
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-\dfrac{3\sqrt{x+1} \cdot 2\sqrt{x+1}}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{3x}{2\sqrt{x+1}}-\dfrac{6(x+1)}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{3x+6(x+1)}{2\sqrt{x+1}}[/tex]
[tex]\implies f'(x)=- \dfrac{9x+6}{2\sqrt{x+1}}[/tex]
An extremum is a point where a function has a maximum or minimum value.
From inspection of the given graph, the maximum point of the function is (-2/3, 2√3/3).
To determine the value of the derivative at the maximum point, substitute x = -2/3 into the differentiated function.
[tex]\begin{aligned}\implies f'\left(-\dfrac{2}{3}\right)&=- \dfrac{9\left(-\dfrac{2}{3}\right)+6}{2\sqrt{\left(-\dfrac{2}{3}\right)+1}}\\\\&=-\dfrac{0}{2\sqrt{\dfrac{1}{3}}}\\\\&=0 \end{aligned}[/tex]
Therefore, the value of the derivative at (-2/3, 2√3/3) is zero.
I need your help to buy a door for my house. I have a scale drawing for the door I want but I am not sure of the true size. In the scale drawing the length is 4 in and the width as 7in. The scale for the door is 1 in = 1.5 ft. What are the actual measurements of the door?
Answers
Answer:
According to the scale, 1 inch on the drawing represents 1.5 feet in real life. So, to find the actual length of the door, we need to multiply the length on the drawing by the scale factor:
4 inches x 1.5 feet/inch = 6 feet
Similarly, to find the actual width of the door, we need to multiply the width on the drawing by the scale factor:
7 inches x 1.5 feet/inch = 10.5 feet
Therefore, the actual measurements of the door are 6 feet by 10.5 feet.
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than 0.35°C.
Round your answer to 4 decimal places
Answers
The probability of obtaining a reading less than 0.35° C is approximately 35%.
What exactly is probability, and what is its formula?Accοrding tο the prοbability fοrmula, the likelihοοd οf an event οccurring is equal tο the ratiο οf the number οf favοurable οutcοmes tο the tοtal number οf οutcοmes. Prοbability οf an event οccurring P(E) = The number οf favοurable οutcοmes divided by the tοtal number οf οutcοmes.
The readings at freezing οn a set οf thermοmeters are nοrmally distributed, with a mean (x) οf 0°C and a standard deviatiοn (μ) οf 1.00°C. We want tο knοw hοw likely it is that we will get a reading that is less than 0.35°C.
To solve this problem, we must use the z-score formula to standardise the value:
[tex]$Z = \frac{x - \mu}{\sigma}[/tex]
Z = standard score
x = observed value
[tex]\mu[/tex] = mean of the sample
[tex]\sigma[/tex] = standard deviation of the sample
Here
x = 0.35° C
[tex]\mu[/tex] = 0° C
[tex]\sigma[/tex] = 1.00°C
Using the values on the formula:
[tex]$Z = \frac{0.35 - 0}{1}[/tex]
Z = 0.35
The probability of obtaining a reading less than 0.35° C is approximately 35%.
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Use the equation f=d–5 to find the value of f when d=7.
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Therefore answer is 2
Answer:
2
Step-by-step explanation:
since d=7 and the equation is d-5 in the place of d we'll put 7 therefore 7-5=2
The roots of a quadratic equation a x +b x +c =0 are (2+i √2)/3 and (2−i √2)/3 . Find the values of b and c if a = −1.
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[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]
A mountain is 13,318 ft above sea level and the valley is 390 ft below sea level What is the difference in elevation between the mountain and the valley
Answers
Answer: 13,708 ft
Step-by-step explanation:
To find the difference in elevation between the mountain and the valley, we need to subtract the elevation of the valley from the elevation of the mountain:
13,318 ft (mountain) - (-390 ft) (valley) = 13,318 ft + 390 ft = 13,708 ft
Therefore, the difference in elevation between the mountain and the valley is 13,708 ft.
Answer: The difference is 13,708 ft.
Given that a mountain is 13,318 feet above sea level. So the elevation of the mountain is [tex]= +13,318 \ \text{ft}[/tex].
Given that a valley is 390 feet below sea level.
So the elevation of the valley is [tex]= -390 \ \text{ft}[/tex].
So the difference between them is [tex]= 13,318 - (-390) = 13,318 + 390 = 13,708 \ \text{ft}.[/tex]
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Jonathan says that the function represented by the graph is always decreasing. Is he correct? fI not, where is the function decreasing?
Explain your reasoning.
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If the slope of the graph is increasing from positive x-axis to negative x-axis, then the function is not that decreasing. Therefore, Jonathan's statement is incorrect.
What is the graph function about?The function is decreasing on intervals where the slope is negative. In this case, since the slope is increasing from positive x-axis to negative x-axis, the function is decreasing on the interval where x is negative.
To determine this interval more precisely, we would need to find the x-value(s) where the slope changes sign from positive to negative. These x-values correspond to critical points, such as local maximums or minimums. The function is decreasing before a local maximum and after a local minimum.
Therefore, Jonathan's statement is not correct, and the function represented by the graph is decreasing on the interval where x is negative.
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Find the standard normal area for each of the following Round your answers to the 4 decimal places
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The standard normal areas are given as follows:
P(1.22 < Z < 2.15) = 0.0954. P(2 < Z < 3) = 0.0215.P(-2 < Z < 2) = 0.9544.P(Z > 0.5) = 0.3085.How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.Considering the second bullet point, the areas are given as follows:
P(1.22 < Z < 2.15) = p-value of Z = 2.15 - p-value of Z = 1.22 = 0.9842 - 0.8888 = 0.0954.P(2 < Z < 3) = 0.0215 = p-value of Z = 3 - p-value of Z = 1 = 0.9987 - 0.9772 = 0.0215.P(-2 < Z < 2) = p-value of Z = 2 - p-value of Z = -2 = 0.9772 - 0.0228 = 0.9544P(Z > 0.5) = 1 - p-value of Z = 0.5 = 1 - 0.6915 = 0.3085.More can be learned about the normal distribution at https://brainly.com/question/25800303
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Find the missing length indicated
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The calculated value of the indicated missing length x in the right triangle is 12
How to determine the value of the indicated missing lengthGiven the right triangle
We can start by calculating the value of x using the following equivalent ratio
x : 9 = 25 - 9 : x
Evaluate the difference
This gives
x : 9 = 16 : x
Next, we express the equivalent ratio as a fraction
So, the ratio becomes
x/9 = 16/x
Cross multiply the equation to calculate x
So, we have the following
x * x = 9 * 16
Evaluate the product
x² = 144
Take the square root of both sides
So, we have the solution to be
y = 12
Hence, the value of x is 12
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Really need help asap !
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The value of h(x) using exponents are as follows:
For -1, the value of h(x)=1/10
For 0, the value of h(x) = 1
For 1, the value of h(x) = 10
For 2, the value of h(x) = 100
For 3, the value of h(x) = 1000
What are exponents?The exponent of a number tells us how many times the original value has been multiplied by itself. For instance, 2×2×2×2 can be expressed as [tex]2^{4}[/tex] the result of 4 times multiplying 2 by itself. Thus, 4 is referred to as the "exponent" or "power," while 2 is referred to as the "base."
Generally speaking, [tex]x^{n}[/tex] denotes that x has been multiplied by itself n times. Here x is the base and n is the power.
Now here, as we put the value of x in the equation, h(x) we can get the value of h(x) for each value of x.
So,
For -1, the value of h(x)=1/10
For 0, the value of h(x) = 1
For 1, the value of h(x) = 10
For 2, the value of h(x) = 100
For 3, the value of h(x) = 1000
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