Answer:
436g
Step-by-step explanation:
1kg=1000g
3kg=3000g
3000+52=3052
3052÷7=436
which of the contexts below could be modeled by a linear function? the amount of a certain medication in a person's bloodstream decreases by 1/3 every week. a town's population shrinks at a rate of 2.2% every year. a certain population of 4 aggressive zombies quintuples every hour. snow was falling at a rate of 2 inches per hour.
The context that could be modeled by a linear function is "snow was falling at a rate of 2 inches per hour."
What is function?In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. In other words, a function takes an input and produces a corresponding output. It is often represented as a mathematical equation or a graph. Functions are used to model real-world phenomena and are an important tool in many areas of mathematics, science, and engineering.
Here,
A linear function describes a constant rate of change, and in this context, the rate of snowfall is constant at 2 inches per hour. The other contexts involve exponential or percentage change, which cannot be modeled by a linear function.
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Jack owns a company which sells handmade greetings cards.
Last year, the company sold 2340 cards and made a total profit of £3510.
This means the average profit per card was £1.50.
This year, Jack is aiming for the company to make 18% more total profit
than last year.
If the average profit per card is 22% lower than last year, how many cards
will Jack's company need to sell this year in order to make their target
profit?
Answer:
Jack's company needs to sell 3540 cards this year in order to make their target profit.
Step-by-step explanation:
Given the average profit per card last year was £1.50, and the average profit per card is 22% lower this year, this year's average profit per card will be:
[tex]\begin{aligned}\implies \sf Average\;profit\;per\;card&= \£1.50 - (22\% \;\text{of}\; \£1.50)\\&=\£1.50-0.22 \times \£1.50\\&=\£1.50-\£0.33\\&=\£1.17\end{aligned}[/tex]
Given the total profit Jack is aiming for this year is 18% more than last year's profit of £3510, this year's target profit is:
[tex]\begin{aligned}\implies \sf Target\;profit&=\£3510 + (18\%\;\text{of}\;\£3510)\\&=\£3510 + 0.18 \times \£3510\\&=\£3510 + \£631.80\\&=\£4141.80\end{aligned}[/tex]
To calculate how many cards Jack's company needs to sell to make this target profit, divide the total target profit by the average profit per card:
[tex]\begin{aligned}\implies \sf Number\;of\;cards&=\dfrac{4141.80}{1.17}\\\\&=3540\end{aligned}[/tex]
Therefore, Jack's company needs to sell 3540 cards this year in order to make their target profit.
1. An Estate dealer sells houses and makes a commission of GHc3750 for the first house sold. He
receives GHc500 increase in commission for each additional house sold. How many houses must
she sell to reach a total commission of GHc6500?Arithmetic progression
The estate dealer must sell 13 houses to reach a total commission of GHc6500
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept that is used in many different contexts. Numbers can be used to represent a variety of different things, including quantities, values, and relationships. They are also used to represent abstract concepts such as time and money. In mathematics, numbers are used to represent sets, operations, and relationships between elements. Numbers play a crucial role in almost all areas of mathematics, from the simple counting to the study of complex equations.
Arithmetic progression is a mathematical process
which involves adding a constant number to a sequence of numbers. In this case, the constant
number is GHc500, and the sequence of numbers is the commission of GHc3750 for the first house
sold.
To find the total number of houses that must be sold to reach a commission of GHc6500, we
need to use arithmetic progression. To do this, we need to calculate the arithmetic mean of the
two numbers GHc3750 and GHc6500. This is done by adding the two numbers and dividing by two.
The arithmetic mean is GHc5125.
We then subtract the initial commission of GHc3750 from the arithmetic mean to find the
increment in the commission for each additional house sold. This gives us the amount of GHc500
for each additional house sold.
To find the total number of houses that must be sold to reach a commission of GHc6500, we
then need to divide the total commission of GHc6500 by the GHc500 increment. This gives us
13 houses. Therefore, the estate dealer must sell 13 houses to reach a total commission of GHc6500.
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* A chord PQ of a circle of radius 5 cm subtends an angle of 70° at the centre. Calculate the following: a) b) c) the length of the chord PQ the length of the arc PQ the perimeters of sector and segment.
Check the picture below.
so let's get the chord using the pythagorean theorem hmmm using sine
[tex]\sin(35^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{5}}\implies 5\sin(35^o )=x\implies 2.87\approx x~\hfill \underset{ PQ }{\stackrel{ 2.87+2.87 }{\approx \text{\LARGE 5.74}}}[/tex]
now let's get the arc
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =70\\ r=5 \end{cases}\implies s=\cfrac{(70)\pi (5)}{180}\implies s\approx \text{\LARGE 6.11}[/tex]
and the perimeters, keeping in mind that for the sector is just the arc plus the radii, and for the segment is simply the arc plus the chord.
[tex]\stackrel{ \textit{sector's perimeter} }{5+5+6.11 ~~ \approx ~~} \text{\LARGE 16.11}\hspace{5em}\stackrel{ \textit{segment's perimeter} }{5.74+6.11 ~~ \approx ~~} \text{\LARGE 11.85}[/tex]
The trip from Winston to Carver takes 8 min longer during rush hour, when the average speed is 75 km/h, than in off-peak hours, when the average speed is 90 km/h. Find the distance of between the two towns
The trip from Winston to Carver takes 8 min longer during rush hour, when the average speed is 75 km/h, than in off-peak hours when the average speed is 90 km/h. the distance between the two towns is 60 km.
Considering the distance between the Winston and carver be "d", since here we got that during off-peak hours, the average speed is 90 km/h. so by using the formula of distance which is distance =speed x time=> d = 90t.
Whereas in rush hour, the average speed is 75 km/h, we also know that the trip takes 8 minutes longer during rush hour. calling the time it takes to travel during rush hour "t+8/60"( since 8 minutes is 8/60 of an hour). Now using the same formula as before:
d = 75(t + 8/60), since here we have two equations for d we can equal them to each other then we get :
90t = 75(t + 8/60)
=>90t = 75t + 10
=>90t-75t=10
=>t = 2/3
Since during the off-peak hours, it takes 2/3 hours or 40 minutes to travel the distance between Winston and carver. now using either equation to find the distance we get
d = 90t = 90(2/3) = 60 km or d = 75(t + 8/60) = 75(2/3 + 8/60) = 60 km
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Sparx 4: Item C
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This data is going to be plotted on a scatter graph.
Distance (km)
37 6 71 28
Height (m) 61 32 94 48
The start of the Distance axis is shown below.
At least how many squares wide does the grid need to be so that the data fits on
the graph?
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In response to the stated question, we may state that To accommodate scatter plot the provided data on the scatter graph, the grid must be at least 65 squares wide and 62 squares height.
What exactly is a scatter plot?"Scatter plots are graphs that show the association of two variables in a data collection. It is a two-dimensional plane or a Cartesian system that represents data points. The X-axis represents the independent variable or characteristic, while the Y-axis represents the dependent variable. These plots are sometimes referred to as scatter graphs or scatter diagrams."
To plot the supplied data on a scatter graph, we must ensure that the distance and height values are both within the grid.
The given distances are 37, 6, 71, and 28. As a result, the distance axis's minimum and maximum values are 6 and 71, respectively.
Height values are as follows: 61, 32, 94, 48. As a result, the lowest and maximum height axis values are 32 and 94, respectively. To ensure that all of the height values fit on the graph, we need a grid at least 94-32 = 62 squares tall.
To accommodate the provided data on the scatter graph, the grid must be at least 65 squares wide and 62 squares height.
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if two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}? hint [see example 2.]
If two indistinguishable dice are rolled, what is the probability of the event {(3, 3), (2, 3), (1, 3)}The probability of the event {(3, 3), (2, 3), (1, 3)}
If two indistinguishable dice are rolled, it is 3/36 or 1/12.
Explanation: Indistinguishable dice are dice that appear identical to one another but do not have unique markings. As a result, indistinguishable dice will have the same number of faces, but the values on each face will be identical.
The total number of possible outcomes is 6 * 6 = 36 because there are six possible outcomes for each roll of a single die.
The probability of rolling the numbers (3, 3), (2, 3), or (1, 3) can be determined as follows: 3/36 or 1/12
For each die, there are six possible outcomes, so there are 6*6, or 36 possible outcomes for two dice.
Because (3, 3), (2, 3), and (1, 3) are the only possible ways to obtain a 3 on one of the dice and a 3, 2, or 1 on the other, the probability is 3/36 or 1/12.
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Values of 'x' satisfying: (x - 1)/(2 - x) >= 0
The values of x which satisfies the fractional inequality (x - 1) / (2 - x) ≥ 0 is x ≥ 1
What values of x satisfies the inequality?(x - 1) / (2 - x) ≥ 0
This is a fractional inequality whose numerator is (x - 1) and the denominator is (2 - x)
(x - 1) / (2 - x) ≥ 0
cross product
(x - 1) ≥ 0 × (2 - x)
(x - 1) ≥ 0
x - 1 ≥ 0
Add 1 to both sides
x ≥ 1
Therefore, x ≥ 1 satisfies the inequality.
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7 more than twice a number is 35.
Answer:
Let's call the number "x".
Then, we can write the equation:
7 + 2x = 35
To solve for x, we need to isolate x on one side of the equation.
Subtracting 7 from both sides:
2x = 28
Dividing both sides by 2:
x = 14
Therefore, the number is 14.
Step-by-step explanation:
Suppose E and F are two events, with the following probability table F F’
E 0.1 0.3 E' 0.2 0.4 a) Compute P(EF). b) Are E and F independent? Explain. c) Are E and F mutually exclusive? Explain.
a) With the following probability table F F, Let’s apply the formula for the intersection of events to solve the first part of the problem.
P(EF) = P(E) x P(F|E).We know that P(E) = 0.1 and that P(F|E) = 0.3. Therefore,P(EF) = P(E) x P(F|E) = 0.1 x 0.3 = 0.03.b) Two events E and F are independent if and only if their intersection is equal to the product of their individual probabilities.
P(EF) = P(E) x P(F) if and only if E and F are independent. We know that P(E) = 0.1 and that P(F) = 0.1 + 0.3 = 0.4. Therefore, P(EF) = 0.03, which is different from 0.1 x 0.4 = 0.04.
Since P(EF) is different from P(E) x P(F), it means that E and F are not independent.c) Two events E and F are mutually exclusive if and only if their intersection is the null set.P(EF) = ∅ if and only if E and F are mutually exclusive. We know that P(EF) = 0.03, which is not equal to the null set. Therefore, E and F are not mutually exclusive.
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A sample of automobiles traversing a certain stretch of highway is selected. Each automobile travels at a roughly constant rate of speed, though speed does vary from auto to auto. Let x = speed and y = time needed to traverse this segment of highway. Would the sample correlation coefficient be closest to 0.9,0.3,-3,or -0.9? Explain.
The right answer is -0.9, but I do not know the reason.
The sample correlation coefficient would be closest to -0.9.
Here's why:
Correlation Coefficient: The correlation coefficient is a statistical measure of the degree of correlation (linear relationship) between two variables. Pearson’s correlation coefficient is the most widely used correlation coefficient to assess the correlation between variables.
Pearson’s correlation coefficient (r) ranges from -1 to 1. A value of -1 denotes a perfect negative correlation, 1 denotes a perfect positive correlation, and 0 denotes no correlation. There is a negative correlation between speed and time. As the speed of the car increases, the time needed to traverse the segment decreases. So, the sample correlation coefficient would be negative.
Since the sample size is large enough, the sample correlation coefficient should be close to the population correlation coefficient. The population correlation coefficient between speed and time should be close to -1, which implies that the sample correlation coefficient should be close to -1.
Therefore, the sample correlation coefficient would be closest to -0.9.
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If a first sample has a sample variance of 12 and a second sample has a sample variance of 22 , which of the following could be the value of the pooled sample variance? 1 10 16 25
The value of the pooled sample variance is 25 when the first sample has a sample variance of 12 and a second sample has a sample variance of 22.
If a first sample has a sample variance of 12 and a second sample has a sample variance of 22, then the possible values of the pooled sample variance are given by the formula below:
Formula:
pooled sample variance = [(n₁ - 1) s₁² + (n₂ - 1) s₂²] / (n₁ + n₂ - 2)
Where s₁ and s₂ are the sample standard deviations of the first and second samples,
n₁ and n₂ are the sample sizes of the first and second samples, respectively.
Thus, substituting the given values into the formula above, we have pooled sample variance:
= [(n₁ - 1) s₁² + (n₂ - 1) s₂²] / (n₁ + n₂ - 2)
= [(n₁ - 1) 12 + (n₂ - 1) 22] / (n₁ + n₂ - 2)
Checking each of the answer options:
If pooled sample variance is 1, then:
(n₁ - 1) 12 + (n₂ - 1) 22
= (n₁ + n₂ - 2)(1)
= 12n₁ + 22n₂ - 34
= (12n₁ - 12) + (22n₂ - 22)
= 12(n₁ - 1) + 22(n₂ - 1)
The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.
Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 1.
Thus, 1 is not a possible value of the pooled sample variance.
If pooled sample variance is 10, then:
(n₁ - 1) 12 + (n₂ - 1) 22
= (n₁ + n₂ - 2)(10)
= 12n₁ + 22n₂ - 34
= (12n₁ - 12) + (22n₂ - 22)
= 12(n₁ - 1) + 22(n₂ - 1)
The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.
Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 10.
Thus, 10 is not a possible value of the pooled sample variance.
If pooled sample variance is 16, then:
(n₁ - 1) 12 + (n₂ - 1) 22
= (n₁ + n₂ - 2)(16)
= 12n₁ + 22n₂ - 34
= (12n₁ - 12) + (22n₂ - 22)
= 12(n₁ - 1) + 22(n₂ - 1)
The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.
Since 34 is not a multiple of 2, the equation cannot be true if the pooled sample variance is 16.
Thus, 16 is not a possible value of the pooled sample variance.
If pooled sample variance is 25, then:
(n₁ - 1) 12 + (n₂ - 1) 22
= (n₁ + n₂ - 2)(25)
= 12n₁ + 22n₂ - 34
= (12n₁ - 12) + (22n₂ - 22)
= 12(n₁ - 1) + 22(n₂ - 1)
The expression on the right-hand side of the equation is a sum of multiples of 12 and 22, and therefore, the expression itself will be a multiple of the greatest common divisor of 12 and 22, which is 2.
Since 46 is a multiple of 2, the equation can be true if the pooled sample variance is 25.
Thus, 25 is a possible value of the pooled sample variance.
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will the product of 2 numbers increase or decrease AND BY WHAT PERCENT if one of the numbers is increased by 50% and the other is decreased by 505
Answer: add and image
Step-by-step explanation:
not full question
Can some one help me? It’s three parts but the questions states use the interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant. The last question also says topics related to if its constant or not.
The function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)
What exactly are function and example?A function, which produces one output from a single input, is an illustration of a rule. The picture was obtained from Alex Federspiel. The equation y=x2 serves as an example of this.
a) We can see that the function is increasing from approximately x = -3 to x = -1 and from approximately x = 1 to x = 2.5. So, the increasing intervals are (-3,-1) and (1, 2.5)
(b) We can see that the function is decreasing from approximately x = -2 to x = -0.5 and from approximately x = 3 to x = 4. So, the decreasing intervals are (-2, -0.5) and (3, 4)
(c) We can see that the function is constant from approximately x = -4 to x = -3 and from approximately x = -1 to x = 1. So, the constant intervals are (-4, -3) and (-1, 1)
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The area of the composite figure is ? Round to two decimal places. (for example, 6.76)
Answer:
83219083219389238293829381293
Step-by-step explanation:
according to my calculations i am not smart
Calculate the area of this trapezium.
6 cm
4 cm
5 cm
8 cm
Answer: 28cm²
Step-by-step explanation: To calculate the area of the trapezium, we can use the formula:
Area = (1/2) x (sum of parallel sides) x (height)
In this case, the two parallel sides are 6 cm and 8 cm, and the height is 4 cm.
Plugging in the values, we get:
Area = (1/2) x (6 cm + 8 cm) x 4 cm
Area = (1/2) x 14 cm x 4 cm
Area = 28 cm²
Bonny has 3 cards and a standard rolling cube. She wants to pick a card and spin the rolling cube at random. How many outcomes are possible?
There are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.
How to calculate How many outcomes are possibleThere are a total of 6 outcomes for the rolling cube and 3 outcomes for picking a card. To find the total number of outcomes, we can use the multiplication rule of counting:
Total number of outcomes = number of outcomes for picking a card x number of outcomes for rolling a cube
Total number of outcomes = 3 x 6 = 18
Therefore, there are 18 possible outcomes for Bonny to pick a card and spin a rolling cube at random.
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What’s the area?
7 yd
4 yd
7 yd
3 yd
The area is 49 square yards.
A sphere is to be designed with a radius of 72 in. Use differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5 in. 4 (Hint: The formula for the volume of a sphere is V(r) = ²³.) O 452.39 in ³ O 16,286.02 in ³ O 65,144.07 in ³ O 32,572.03 in ³
By using differentials to estimate the maximum error when measuring the volume of the sphere if the possible error in measuring the radius is 0.5. It will be 32,572.03 in³. Which is option (d).
How to measure the maximum error while measuring the volume of a sphere?The possible error in measuring the radius of the sphere is 0.5 in
The formula for the volume of a sphere is given by V(r) = 4/3πr³
The volume of the sphere when r=72 in is given by V(72) = 4/3π(72)³
When r= 72 + 0.5 in= 72.5 in, the volume of the sphere can be calculated using the formula:
V(72.5) = 4/3π(72.5)³
The difference between these two volumes, V(72) and V(72.5), gives us the maximum error while measuring the volume of a sphere. It can be calculated as follows:
V(72.5) - V(72) = 4/3π(72.5)³ - 4/3π(72)³= 4/3π [ (72.5)³ - (72)³ ]= 4/3π [ (72 + 0.5)³ - 72³ ]= (4/3)π [ 3(72²)(0.5) + 3(72)(0.5²) + 0.5³ ]≈ (4/3)π [ 777.5 ]= 3.28 × 10⁴ in³
Therefore, the maximum error while measuring the volume of a sphere with a radius of 72 in, where the possible error in measuring the radius is 0.5 in, is approximately 3.28 × 10⁴ in³ or 32,572.03 in³. Therefore coorect option is (D).
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Suppose that 30 students take a quiz worth 30 points. The SD of the scores is 1 point. Which of the following gives the most reasonable description of the distribution of quiz scores?
A) All of the individual scores are one point apart.
B) The difference between the highest and lowest score is 1.
C) The difference between the 1st and 3rd quartile marks is 1.
D) A typical score is within 1 point of the mean.
The statement that gives the most reasonable description of the distribution of quiz scores is "A typical score is within 1 point of the mean." The correct answer is Option D.
What is Standard deviation?The standard deviation (SD) is a measure of the variability of data in a population. Standard deviation is a measure of how much each value differs from the mean (average) value of the data set.
What is the range?The difference between the highest and lowest values in a dataset is known as the range. It's a quick way to see the data's spread. If the range is big, it implies that the data is more diverse, while if it's small, it implies that the data is more consistent.
What is the first quartile?The first quartile (Q1) is the value that splits the lowest 25% of a data set from the rest of the data set. If we order the dataset from smallest to largest, the first quartile is the value at the 25th percentile.
What is the third quartile?The third quartile (Q3) is the value that splits the highest 25% of a data set from the rest of the data set. If we order the dataset from smallest to largest, the third quartile is the value at the 75th percentile.
What is the mean?The sum of all values in a dataset divided by the total number of values in the dataset is known as the mean. The mean, often known as the arithmetic mean, is one of the most basic measures of central tendency in statistics.
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The probability distribution of the amount of memory X (GB) in a purchased flash drive is given below. x 1 2 4 8 16 p(x) .05 .10 .35 .40.10 Compute the following: E(X), E(X2), V(X), E(3x + 2), E (3X² + 2), V (3x + 2), E(X +1), V(X + 1).
To solve the question asked, you can say: Therefore, the final answers expressions are: E(X) = 5.8; E(X²) = 59.8; V(X) = 21.16 and E(3X + 2) = 20.4
what is expression ?In mathematics, an expression is a set of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation that represent quantities or values. Expressions can be as simple as "3 + 4" or as complex as they can contain functions like "sin(x)" or "log(y)" . Expressions can be evaluated by substituting values for variables and performing mathematical operations in the order specified. For example, if x = 2, the expression "3x + 5" is 3(2) + 5 = 11. In mathematics, formulas are often used to describe real-world situations, create equations, and simplify complex math problems.
To calculate these values, we first need to compute the mean (expected value) and variance of X, which are given by:
E(X) = ∑[x * p(x)]
= 1 * 0.05 + 2 * 0.10 + 4 * 0.35 + 8 * 0.40 + 16 * 0.10
= 5.8
E(X²) = ∑[x² * p(x)]
= 1² * 0.05 + 2² * 0.10 + 4² * 0.35 + 8² * 0.40 + 16² * 0.10
= 59.8
V(X) = E(X²) - [E(X)]²
= 59.8 - 5.8²
= 21.16
E(3X + 2) = 3E(X) + 2
= 3(5.8) + 2
= 20.4
E(3X² + 2) = 3E(X²) + 2
= 3(59.8) + 2
= 179.4
V(3X + 2) = V(3X)
= 9V(X)
= 9(21.16)
= 190.44
E(X + 1) = E(X) + 1
= 5.8 + 1
= 6.8
V(X + 1) = V(X)
= 21.16
Therefore, the final answers are:
E(X) = 5.8
E(X²) = 59.8
V(X) = 21.16
E(3X + 2) = 20.4
E(3X² + 2) = 179.4
V(3X + 2) = 190.44
E(X + 1) = 6.8
V(X + 1) = 21.16
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help!! i really can't do this pls help me with this inquality question
Explanation:
2n is greater than 20, so 2n > 20. This solves to n > 10 after dividing both sides by 2. That inequality is the same as 10 < n.
5n is less than 60. It leads to 5n < 60. That solves to n < 12 after dividing both sides by 5.
To summarize:
"2n is greater than 20" leads to n > 10, aka 10 < n."5n is less than 60" leads to n < 12Combine 10 < n with n < 12 to write a compound inequality:
10 < n < 12
The value n is between 10 and 12. We exclude each endpoint.
The only possible whole number that works here is n = 11
1)
The burning times of scented candles, in minutes, are normally distributed with a mean of 249 and a standard deviation of 20. Find the number of minutes a scented candle burns if it burns for a shorter time than 80% of all scented candles.
Use Excel, and round your answer to two decimal places.
2) The number of square feet per house have an unknown distribution with mean 1670 and standard deviation 140 square feet. A sample, with size n=48, is randomly drawn from the population and the values are added together. Using the Central Limit Theorem for Sums, what is the mean for the sample sum distribution?
The Central Limit Theorem (CLT) states that as the sample size n increases, the sample mean approaches a normal distribution with a mean of μ and a standard deviation of σ/√n.
Therefore, when the number of houses in a population is unknown and a random sample of 48 houses is drawn from it, the mean for the sample sum distribution can be calculated using the CLT as follows:Mean for the sample sum distribution = nμ = 48 * 1670 = 80,160. The standard deviation for the sample sum distribution is given by:σ/√n = 140/√48 ≈ 20.20. Therefore, the sample sum distribution has a mean of 80,160 and a standard deviation of 20.20.To verify this, a histogram can be plotted in Excel using the following steps:Enter the data for the square footage of the 48 houses in column A of the Excel worksheet.Highlight column B and enter the formula =SUM(A1:A48) to sum the data in column A and store the result in column B.Highlight column C and enter the formula =B1/48 to calculate the mean for the sample sum distribution and store it in column C.Highlight column D and enter the formula =140/SQRT(48) to calculate the standard deviation for the sample sum distribution and store it in column D.Highlight columns B, C, and D, and select the Insert tab.Click on the Histogram icon under the Charts group.Select the Histogram chart type, and click OK to generate the histogram.The histogram should show a bell-shaped curve with a mean of 80,160 and a standard deviation of 20.20, indicating that the sample sum distribution is approximately normal.
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Please help!!!!!!!
What is the axis of symmetry of the quadratic function below?
Answer:
x = -1
Step-by-step explanation:
The axis of symmetry is a line that divides the two sides of a parabola through the vertex.
Work out the recipricol of 0.5
Answer:
the answer is 2
Step-by-step explanation:
this answer will be 200⁰0000000000⁰00000⁸⁰643367897⁶43677443⁵=5.0
The arrival time of an elevator in a 12 story dormitory is equally likely at any time range during the next 4.7 minutes. o. Calculate the expected arrival time. (Round your answer to 2 decimal place.) Expected arval time b. What is the probability that an elevator arrives in less than 1.8 minutes? (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) c. What is the probability that the wait for an elevator is more than 1.8 minutes? (Round intermediate c places and final answer to 3 decimal places.)
a. Calculate the expected arrival time:
Given: Time range for arrival of elevator during the next 4.7 minutes is equally likely. The expected value of a discrete random variable is calculated by multiplying each possible value by its probability and adding up the products. So, we can calculate the expected value of the elevator arrival time by integrating the value of the probability density function (which is a straight line in this case) over the given interval. The area under the curve of the probability density function over the entire interval of possible values is 1. The expected arrival time (E) of the elevator is given by: E = (1/4.7) ∫(0 to 4.7) tdt= (1/4.7) [t²/2] [from 0 to 4.7]= 2.3596 minutes or 2.36 minutes (rounded to 2 decimal places)Therefore, the expected arrival time is 2.36 minutes.
b. Probability that an elevator arrives in less than 1.8 minutes:
To calculate the probability of an event happening, we need to find the area under the probability density function (pdf) over the given interval (in this case, less than 1.8 minutes). The pdf is a straight line with a slope of 1/4.7, so the equation of the line is: f(t) = (1/4.7) t. The probability of the elevator arriving in less than 1.8 minutes is: P(T < 1.8) = ∫(0 to 1.8) f(t) dt= ∫(0 to 1.8) (1/4.7) t dt= (1/4.7) [t²/2] [from 0 to 1.8]= 0.56765 (rounded to 4 decimal places)Therefore, the probability that an elevator arrives in less than 1.8 minutes is 0.568 (rounded to 3 decimal places).
c. Probability that the wait for an elevator is more than 1.8 minutes: The probability that the wait for an elevator is more than 1.8 minutes is the complement of the probability that it arrives in less than 1.8 minutes. P(T > 1.8) = 1 - P(T < 1.8) = 1 - 0.56765= 0.43235 (rounded to 3 decimal places)Therefore, the probability that the wait for an elevator is more than 1.8 minutes is 0.432 (rounded to 3 decimal places).
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The value of 5^2000+5^1999/5^1999-5^1997
Answer:
Step-by-step explanation:
We can simplify the expression by factoring out a common factor of 5^1999 from the numerator:
5^2000 + 5^1999
= 5^1999(5 + 1)
= 5^1999(6)
And we can also factor out a common factor of 5^1997 from the denominator:
5^1999 - 5^1997
= 5^1997(5^2 - 1)
= 5^1997(24)
So the entire expression simplifies to:
(5^2000 + 5^1999) / (5^1999 - 5^1997)
= (5^1999 * 6) / (5^1997 * 24)
= (6/24) * 5^2
= 5/2
Therefore, the value of the expression is 5/2.
what is this pls help
Answer:
x = 45.
Step-by-step explanation:
We know the full angle of this is 180 degrees.
Given: (2x+45) + x = 180
First, collect like terms ( in this case 2x and x, 180 and 45 )
2x + x = 180 - 45
Then calculate:
3x = 135. ( Divide both sides by 3 )
x = 45
Describe the error in finding the distance between A(6, 2) and B(1,−4)
The error is the substitution of coordinates. Coordinates are ordered pairs of points that help us locate any point in a 2D plane or 3D space.
Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identifies a specific point's precise location on a grid. This grid is referred to as a coordinate plane.
The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by
[tex]AB = \sqrt{(x_{1} , x_{2})^{2} + (y_{1} - y_{2})^{2} }[/tex]
Observe that the x-coordinate of B is subtracted from the x-coordinate of A. This goes with the y-coordinates.
Therefore, the error is the substitution of coordinates.
The correct computation is
[tex]AB = \sqrt{(6-1)^{2} + [2 - (-4)]^{2} }[/tex]
[tex]= \sqrt{5^{2} + 6^{2} }[/tex]
[tex]= \sqrt{25 + 36} \\[/tex]
[tex]= \sqrt{61}[/tex]
≈ 7.81
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The complete question is as follows:
Describe and correct the error in finding the distance between A(6, 2) and B(1, -4). AB = √[(6 - 2)² + {2 - (-4)}²] = √(4² + 5²) = √(16 + 25) = √41 ≈ 6.4.
Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 2)
The angle of elevation of the sun is approximately 22.6 degrees.
What is trigonometry?The partnerships between the sides and angles of triangles are the subject of the mathematical discipline of trigonometry. It is used exhaustively in fields such as physics, engineering, and assessing.
In a right triangle, the side opposite the right angle is called the hypotenuse, while the other two sides are called the legs.
Given that, 7.6 m flagpole casts an 18.2 m shadow.
Using trigonometric ratio we have:
tan(θ) = h / s
Substituting the values:
tan(θ) = 7.6 / 18.2
tan(θ) ≈ 0.417
θ ≈ 22.6°
Hence, the angle of elevation of the sun is approximately 22.6 degrees.
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