Answer:
P(green or purple) = 0.576
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
32 + 47 + 21 + 25 = 125 blocks.
Of those, 47 + 25 = 72 are green of purple
P(green or purple) = 72/125 = 0.576
PLEASE HELP !!!!!!
If the blueprint is drawn on the coordinate plane with vertices (1, 5) and (11, 15) for the corners labeled with red stars, would that be an accurate representation of the length of the diagonal of the square C? Show your work and explain your reasoning. (4 points—2 points for finding the length of the diagonal; 2 points for explanation)
Answer:
[tex]50\sqrt{2} feet[/tex]
Step-by-step explanation:
Given the vertices (1, 5) and (11, 15) for the corners labeled with red stars, the diagonal of the square C will be the length of the line joining the two vertices.
Using the Distance Formula:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex](x_1,y_1)=(1, 5) \:and\: (x_2,y_2)=(11, 15)[/tex]
[tex]Distance=\sqrt{(11-1)^2+(15-5)^2}\\=\sqrt{10^2+10^2}\\=\sqrt{200}\\=10\sqrt{2}[/tex]
Since 1 Square Unit = 25 Square Feet
1 Unit =5 feet
Therefore, the length of the diagonal
[tex]=5*10\sqrt{2} \\=50\sqrt{2} \:feet[/tex]
Answer:
50 with 2 squared
Step-by-step explanation:
A bet on "black" in Roulette has a probability of 18/38 of winning. If you win, you double your money. You can bet anywhere from $1 to $100 on each spin.
a. Suppose you have $10, and are going to play until you go broke or have $20. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value.
b. Suppose you have $10, and are going to play until you go broke or have $30. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value.
Answer:
Check the explanation
Step-by-step explanation:
let the money on bet is X.
probability of winning =18/38=9/19
probability of losing =(1-9/19)=10/19
expected outcome =[tex]\tiny \sum[/tex]probability *return =(
Expected value of return after one bet is =(9/19*x)-(10/19*x)=-1x/19
it is negative which is obvious cause casinos are there to earn money.
a) Our best strategy in this case as probability of winning is near by 50 %, we should place a bet of 1 $ each,and when we lose one bet consecutively we should bet twice the amount..
Cause two consecutive losses on black has less probability.
c) In case we have to reach 30 $ we have to use the same strategy as above.
Explaining the best gambling strategy using expected value in roulette scenarios.
Expected value is a key concept when determining the best strategy in gambling scenarios like this. In the given situation, if you want to play until you reach $20 starting with $10, the best strategy is to bet the maximum amount on each spin. This way, your expected value increases, giving you a higher chance of reaching $20.
On the other hand, if you aim to reach $30 starting with $10, it's better to bet smaller amounts on each spin to minimize the risk of going broke quickly. By betting conservatively, you increase your chances of eventually reaching $30.
A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, of which 900 support the candidate.
A 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is
A. 0.050 to 0.112.
B. 0.035 to 0.127.
C. 0.040 to 0.122.
D. 0.037 to 0.119.
Answer:
[tex](0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050[/tex]
[tex](0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112[/tex]
And the best option for this case would be:
A. 0.050 to 0.112.
Step-by-step explanation:
Data given
[tex]p_A[/tex] represent the real population proportion of who support the cnadite for the northern half state
[tex]\hat p_A =\frac{1062}{2000}=0.531[/tex] represent the estimated proportion of who support the candidate for the northern half state
[tex]n_A=2000[/tex] is the sample size required the northern half state
[tex]p_B[/tex] represent the real population proportion of who support the candidate for the southern half state
[tex]\hat p_B =\frac{900}{2000}=0.45[/tex] represent the estimated proportion of people who support the candidate for the southern half state
[tex]n_B=2000[/tex] is the sample size for the northern half state
[tex]z[/tex] represent the critical value
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}[/tex]
For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile in the normal standard distribution and we got.
[tex]z_{\alpha/2}=1.96[/tex]
Replacing into the formula we got:
[tex](0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050[/tex]
[tex](0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112[/tex]
And the best option for this case would be:
A. 0.050 to 0.112.
The x-intercept and y-intercept
Answer:
x intercept = (1.2 , 0)
y intercept = (0 , 0.75)
Step-by-step explanation:
You wan to get it into whatever formula makes it easiest for you to understand. I put it into standard slope formula ax + by = c
5x +8y = 6
6/5 = x
x= 1.2
6/8 = y
y = 0.75
5. Which of the following statements is true? (A) Histograms have gaps between each bar. (B) Dotplots do not provide enough information to determine if there are outliers in the data. (C) Bar graphs can display both quantitative and categorical data. (D) Stemplots are the best graphs for displaying data sets with two variables. (E) Boxplots clearly show the five-number summary of a data set.
Boxplots clearly show the five-number summary of a data set. Therefore, option D and E are the correct answer.
What is histogram?A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.
A) A histogram has an appearance similar to a vertical bar chart, but there are no gaps between the bars.
B) Both dot plots and stem plots can show symmetry, gaps, clusters, and outliers.
C) A bar chart or pie chart is often used to display categorical data. These types of displays, however, are not appropriate for quantitative data. Quantitative data is often displayed using either a histogram, dot plot, or a stem-and-leaf plot.
D) The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets.
E) A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.
Therefore, option D and E are the correct answer.
Learn more about the histogram here:
https://brainly.com/question/14421716.
#SPJ5
Among the listed statements, options C and E are true. Other statements about histograms, dotplots, and stemplots have inaccuracies.
Explanation:Let's go through each of the statements:
(A) Histograms have gaps between each bar: This statement is false as histograms present continuous data where the bars are adjacent to each other with no gaps. It's used for displaying large, continuous, quantitative datasets.
(B) Dotplots do not provide enough information to determine if there are outliers in the data: We can't completely conclude this as it would depend on the nature of the data and how it's presented. Dotplots can sometimes show outliers but they are not the most efficient graph for this purpose.
(C) Bar graphs can display both quantitative and categorical data: This is true. Bar graphs are very versatile and can represent both types of data. They compare categories of data with either horizontal or vertical bars.
(D) Stemplots are the best graphs for displaying data sets with two variables: This is false. Stemplots are good for displaying a single variable and summarizing the shape of the dataset.
(E) Boxplots clearly show the five-number summary of a data set: This is true. Boxplots are an excellent way to display the minimum, first quartile, median, third quartile and maximum values of a data set.
Learn more about Graphs in Statistics here:
https://brainly.com/question/31524512
#SPJ13
Parallelogram ABCD has vertices at A(-2,3), B(4,3), C(-1,1). What is the length of side AB? Answer choices ;
A) 2 units
B) 3 units
C) 4 units
D) 6 units
Answer:
D)6 units
Step-by-step explanation:
the answer is D because since side AB have the same y coordinate then you would have to either subtract or add the x. if one point on x is negative and the other is positive then you would add. but if they were both positive or both negative then you would subtract the x.
how many 2/3s are in 3/8
Final answer:
To determine how many 2/3s fit into 3/8, multiply 3/8 by the reciprocal of 2/3, resulting in 9/16, which is less than 1. Thus, there are around 0.5625 of 2/3 in 3/8.
Explanation:
To find how many 2/3s are in 3/8, we're essentially asking how to divide 3/8 by 2/3. This is done by multiplying 3/8 by the reciprocal of 2/3, which is 3/2:
Dividing fractions: (3/8) ÷ (2/3) = (3/8) × (3/2)
Multiplying fractions: (3 × 3) / (8 × 2) = 9/16
To simplify this and understand the proportion, we need to compare the fraction 9/16 to a whole number. Since 9/16 is definitely less than 1, there is less than one 'whole' 2/3 in 3/8. Therefore, there are somewhat around 0.5625 of 2/3 in 3/8 (since 9 divided by 16 equals 0.5625).
A player pays $2 to randomly draw a card from a standard deck of playing cards. He wins $10 if he draws a black 2, and $5 if a 10 or ace is picked. Determine the probability of each possible value of X (the amount won or lost) to complete the probability distribution for the game. Give each value as a fraction with a denominator of 52.
Answer:
1/52
2/52
4/52
Step-by-step explanation:
If you randomly draw a card from the standard deck the drawing an specific card will have a probability of 1/52
If you draw a black 2 it can be from Spades 2, or Clubs 2, therefore you have only two options, and the probability is 2/52
If you draw an ace it can be spades, clubs, hearts or diamonds, so the probability would be 4/52
12. Find the perimeter of the triangle below:
please help show steps thank you :)
Given:
The lengths of the three sides of the triangle are [tex]\frac{3}{x-4}[/tex], [tex]\frac{16-x}{x^{2}-2 x-8}[/tex] and [tex]\frac{x+5}{x+2}[/tex]
We need to determine the perimeter of the triangle.
Perimeter of the triangle:
The perimeter of the triangle can be determined by adding all the three sides.
Thus, we have;
[tex]Perimeter=\frac{3}{x-4}+\frac{16-x}{x^{2}-2 x-8}+\frac{x+5}{x+2}[/tex]
Factoring the term [tex]x^2-2x-8[/tex], we get, [tex](x-4)(x+2)[/tex]
Substituting, we get;
[tex]Perimeter=\frac{3}{x-4}+\frac{16-x}{(x-4)(x+2)}+\frac{x+5}{x+2}[/tex]
Taking LCM , we have;
[tex]Perimeter=\frac{3(x+2)+16-x+(x+5)(x-4)}{(x-4)(x+2)}[/tex]
Simplifying the numerator, we get;
[tex]Perimeter=\frac{3x+6+16-x+x^2-4x+5x-20}{(x-4)(x+2)}[/tex]
Adding the like terms in the numerator, we get;
[tex]Perimeter=\frac{x^2+3x+2}{(x-4)(x+2)}[/tex]
Factoring the numerator, we get;
[tex]Perimeter=\frac{(x+2)(x+1)}{(x-4)(x+2)}[/tex]
Cancelling the common terms, we have;
[tex]Perimeter=\frac{x+1}{x-4}[/tex]
Thus, the perimeter of the triangle is [tex]\frac{x+1}{x-4}[/tex]
Nielsen ratings are based on televisions in 50005000 households. Nielsen estimates that 12 comma 00012,000 people live in these households. Suppose Nielsen reports that American Idol had 6565% of the TV audience. Interpret this result with a 95% confidence interval, based on a sample size of 12 comma 00012,000 people.
Answer:
We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%
Step-by-step explanation:
-From the given information, [tex]\hat p=0.65[/tex].
-We calculate the confidence interval using this value at 95% confidence level:
[tex]CI=\hat p\pm z \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\=0.65\pm 1.96\times \sqrt{\frac{0.65\times 0.35}{12000}}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585][/tex]
So, the 95% confidence interval is (0.6515,0.6585).
Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.
Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. The pair of variables have a significant correlation. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent or a test and their scores on the test are shown below.Hours spend studying, x 1 2 3 3 4 6 (a) x = 2 hours (B) x = 3.5 hrsTest score, y 37 41 51 48 65 69 (c) x = 12 hours (d) x = 1.5 hrsFind the regression equation : Y (hat) = _____x +(_____) round to 3 decimal placesPlot the grapha. predict the value of y for x = 2b. predict the value of y for x = 3.5c. Predict the value of y for x = 12d. predict the value of y for x = 1.5
Answer:
(a)
x = 2
y = 42.019
(b)
x = 3.5
y = 51.833
(c)
x = 12
y = 107.447
(d)
x = 1.5
y = 38.747
Step-by-step explanation:
If you use a regressor calculator you will find that
y = 6.542x + 28.933
then for (a)
x = 2
y = 42.019
(b)
x = 3.5
y = 51.833
(c)
x = 12
y = 107.447
(d)
x = 1.5
y = 38.747
Regression equations are used to represent scatter plots
The regression equation is [tex]\^y = 6.54\^x + 28.94[/tex]The predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75The table is given as:
x | 1 2 3 3 4 6
y | 37 41 51 48 65 69
To determine the regression equation, we make use of an graphing calculator.
From the graphing calculator, we have:
Sum of X = 21 Sum of Y = 311 Mean X = 3.5 Mean Y = 51.8333 Sum of squares (SSX) = 17.5 Sum of products (SP) = 114.5The regression equation is represented as:
[tex]\^y =b\^x + a[/tex]
Where:
[tex]b = \frac{SP}{SS_x}[/tex] and [tex]a = M_y - bM_x[/tex]
So, we have:
[tex]b = \frac{SP}{SS_x}[/tex]
[tex]b = \frac{17.5}{114.5}[/tex]
[tex]b = 6.54[/tex]
[tex]a = M_y - bM_x[/tex]
[tex]a = 51.83 - (6.54*3.5)[/tex]
[tex]a = 28.94[/tex]
Substitute values for (a) and (b) in [tex]\^y =b\^x + a[/tex]
[tex]\^y = 6.54\^x + 28.94[/tex]
The predicted values when x = 2, 3.5, 12 and 1.5 are:
[tex]\^y = 6.54 \times 2 + 28.94 = 42.02[/tex]
[tex]\^y = 6.54 \times 3.5 + 28.94 = 51.83[/tex]
[tex]\^y = 6.54 \times 12 + 28.94 = 107.42[/tex]
[tex]\^y = 6.54 \times 1.5 + 28.94 = 38.75[/tex]
Hence, the predicted values when x = 2, 3.5, 12 and 1.5 are 42.02, 51.83, 107.42 and 38.75
Read more about regressions equations at:
https://brainly.com/question/5586207
For what value(s) of k is k-3/2k+5 undefined?
Answer:
The expression is undefined where the denominator equals
0 , the argument of an even indexed radical is less than
0 , or the argument of a logarithm is less than or equal to 0 . k = − 2 , k = 0 , k = 2 , k = 6
Step-by-step explanation:
I'm not rocket scientist but I hope this helps in anyway, if not i'm so sorry i tried. :)
The area of a rectangle is 45.5 square inches. The base of the rectangle is 7 inches. What is the height of the rectangle in inches?
The height of the rectangle in inches is 6.5 inches.
The area of a rectangle = lw
where
l = length
w = width
Therefore,
area = 45.5 in²
length = 7 inches
The height of the rectangle can be found below:
45.5 = 7h
divide both sides by 7
45.5 / 7 = h
h = 6.5 inches
learn more: https://brainly.com/question/22713030?referrer=searchResults
Based on the information given the height of the rectangle in inches is 6.5 inches.
Using this formula
Area of a rectangle = Length× Width
Where:
Area = 45.5 in²
Length = 7 inches
Hence,
Let solve for Length
45.5 = 7h
Divide both sides by 7
h=45.5 / 7
h = 6.5 inches
Inconclusion the height of the rectangle in inches is 6.5 inches.
Learn more about Area of a rectangle here:https://brainly.com/question/14383947
This cake was sliced parallel to the base. What shape will the cross-section make?
The shape of the cross-section of the cake is a square.
What is cross-section?In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher- dimensional spaces. Cutting an object into slices creates many parallel cross-sections.
Given that, a cake was sliced parallel to the base, we need to find the shape of the cross section,
we see that the shape of the cake is a square base pyramid,
That means if we cut it horizontally parallel to its base, we will always find a square,
Therefore, the cross-section is a square.
Hence, the shape of the cross-section of the cake is a square.
Learn more about cross-section, click;
https://brainly.com/question/15541891
#SPJ3
When slicing a cake parallel to its base, the resulting cross-section will be a circle, mirroring the shape of the base of the cake.
The question pertains to the shape of the cross-section resulting from slicing a cake parallel to its base. When you slice a three-dimensional object like a cake in this way, the cross-section will mirror the shape of the object's base. As the base of a cake is typically a circle, the cross-section in this case will be a circular shape. To understand this better, imagine a cylinder, which is similar to a circular cake. When you slice a cylinder parallel to its base, you always obtain a circular cross-section. This concept is consistent across different objects, given that the slice is parallel to the base, such as slicing a cylindrical polony or cutting a slice of brick-shaped bread.
put these numbers in order 55, 52, 46, 52, 46, 43, 49, 56, 42
Answer: 55
Step-by-step explanation:
Answer:
42,43,46,46,49,52,52,55,56
Step-by-step explanation:
free round trip tickets Hawaii were given to 0.4% of the people staying at a hotel. Larry says that tickets were given to 4/10 of the people at the hotel.
Answer: He is badly mistaken! It's 4/1000
Larry needs to learn how to read percentages!
Step-by-step explanation:
4/10 would be 40% For every 100 guests, 40 free tickets would be given away. A very popular offer, but the hotel will soon be out money, and out of business!
0.4% is less than 1% . As a decimal it is 0.004. That is Four thousandths!
Only 4 out of every 1000 people were given free round trip tickets to Hawaii.
Mar’s, In. claims that its M&M candies are distributed with the color percentages of 20% brown, 20% yellow, 30% red, 10% orange, 10 % green, and 10% blue. A classroom exercise involving a random sample of 460 M&M’s resulted in the observed frequencies were: 90 brown, 94 yellow, 99 red, 64 orange, 51 green, and 62 blue. Test the claim that the color distribution is as claimed by Mars, Inc (α= 0.05). What can you conclude if the test statistic is greater than the critical value?
Answer:
Null hypothesis is rejected. There is no or little evidence to support the claim made by Mars.In
Step-by-step explanation:
Solution:-
- A claim is made by Mars.In that the M&M candies in a packet are distributed by color percentage given below.
- A random sample of N = 460 M&M's was taken and the frequencies of different colors were observed as given below.
- We are to test a claim made by the Mars.In regarding the color distribution of M&Ms at significance level α = 0.05.
- Compute the expected frequency of distribution for color as per Mars.In claim. Use the following formula for expected outcome:
Expected = N*pi
Where, pi : The percentages for each color.
- The table for expected and observed frequencies for each color is tabulated below.
Colors Percentage Expected Observed
Brown 20% 460*0.2 = 92 90
Yellow 20% 460*0.2 = 92 94
Red 30% 460*0.3 = 138 99
Orange 10% 460*0.1 = 46 64
Green 10% 460*0.1 = 46 51
Blue 10% 460*0.1 = 46 62
- To test the claim for color distribution of M&Ms using X^2 - test. We will state the Null and Alternate hypothesis as follows:
Null Hypothesis: The distribution is colors is as its claimed by the company
Alternate Hypothesis: The distribution is colors is not its claimed by the company
- We will first determine the X^2 statistics value using the following relation:
[tex]X^2-test = Sum [ \frac{(Oi- Ei)^2}{Ei} ]\\\\X^2-test = \frac{(90- 92)^2}{92} + \frac{(94- 92)^2}{92} + \frac{(99- 138)^2}{138} + \frac{(64- 46)^2}{46} + \frac{(51- 46)^2}{46} + \frac{(62- 46)^2}{46} \\\\X^2-test = \frac{4}{92} + \frac{4}{92} + \frac{1521}{138} + \frac{324}{46} + \frac{25}{46} + \frac{256}{46} \\\\X^2-test = 0.04347 + 0.04347 + 11.0217 + 7.04348 + 0.54348 + 5.56522\\\\X^2-test = 24.2608[/tex]
- The rejection region is defined by the significance level ( α ) = 0.05 and degree of freedom. The bound ( critical value ), X^2-critical is determined using the look-up table:
degree of freedom = number of observation category - 1 = 6 - 1 = 5
P ( X < X^2 - critical ) = 0.025
X^2 - critical = 12.8
- All the test values of X^2 > X^2-critical lie in the rejection region.
24.2608 > 12.8
X^-test > X^2-critical
Hence, Null hypothesis is rejected.
Conclusion: As per Chi-square test the claim made by the Mars.In has little or no evidence to be true; hence, the color distribution of M&M is not what is claimed.
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
Answer:
The mean waiting time of all customers is significantly more than 3 minutes, at 0.05 significant level
Step-by-step explanation:
Step 1: State the hypothesis and identify the claim.
[tex]H_0:\mu=3\\H_1:\mu\:>\:3(claim)[/tex]
Step 2: We calculate the critical value. Since we were not given any significant level, we assume [tex]\alpha=0.05[/tex], and since this is a right tailed test, the critical value is z=1.65
Step 3: Calculate the test statistic.
[tex]Z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }=\frac{3.1-3}{\frac{0.5}{\sqrt{100} } }=2[/tex]
Step 4:Decide. Since the test statistic , 2 s greater than the critical value, 1.65, and it is in the critical region, the decision is to reject the null hypothesis.
Step 5: Conclusion, there is enough evidence to support the claim that the mean is greater than 3
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after 4 days? How long is it until there are 10,000 mosquitoes?
Answer: 3,917 days
Step-by-step explanation:
Over the interval [-3, 0], the local minimum is
Over the interval [0, 3], the local maximum is
Over the interval [0, 3] the local minimum is
Answer: 1. -16.18
2. 3.75
3. -3
Step-by-step explanation:
The value of the local minimum, maximum, and minimum will be -16, 4, and -1.5.
What is local minima and local maxima?The larger than the critical value of a set are really the highest and lowest items in the set, as described by mathematics.
From the graph, the conclusion are given below.
Over the interval [-3, 0], the local minimum is approximately -16.
Over the interval [0, 3], the local maximum is approximately 4.
Over the interval [0, 3] the local minimum is approximately -1.5.
The complete question is attached below.
More about the local minima and local maxima link is given below.
https://brainly.com/question/18687565
#SPJ2
Simplify the expression.
Answer:
(2x)(-2x+5)(x+2)
Step-by-step explanation:
what is the axis of symmetry for the graph of a quadratic function whose zeros or -2 and 4?
Answer:
x = 1
Step-by-step explanation:
As you might guess, the zeros are symmetrical about the axis of symmetry. That is, the axis of symmetry is midway between the zeros, so will be their average value:
x = (-2 +4)/2 = 1
The axis of symmetry is x = 1.
On the standard coordinate grid at initial moment, ship Tiger is at the position (0, 795), ship Lion is at the position (985, 0). Tiger sails along the straight line to the position (1229, 0). At the same time, Lion sails along the straight line to the position (0, 1039). Lion will reach her destination in one hour, Tiger – in two hours.
a) Find the point of intersection of the paths of the ships.
b) At what time from the moment of departure each of the ships will pass the point of intersection of the paths.
c) At what time (in minutes after departure) the distance between Lion and Tiger will be the shortest?
d) What is the shortest distance between Lion and Tiger?
e) What will be the positions of both ships at the moment when the distance between them is the shortest?
Answer:
A) (380, 640)
B) ship Tiger: Time = 0.96 hours
Ship Lion: Time = 0.62 hours
C) Ship Tiger = 57.6 minute
Ship Lion = 37.2 minutes
D) Distance = 533 metres
E) Ship Tiger (0, 795)
Ship Lion (1039,0)
Step-by-step explanation:
From the question, we can form the equation of the straight line from the initial and final position of the two ships. Using the general linear equation Y = mx + c. that is
Ship Tiger
Initial position (0, 795)
Final position (1229, 0)
M = (0 - 1229)/795
M = - 1.55
1229 = -1.55(0) + C
C = 1229
Hence the equation of the line for ship Tiger will be
Y = - 1.55x + 1229 ...... (1)
Ship Lion
Initial position (985, 0).
Final position (0, 1039).
M = 1039/ -985 = - 1.05
0 = -1.05(985) + C
0 = - 1039 + C
C = 1039
The equation of the line for ship Lion will be
Y = - 1.05(x) + 1039..... (2)
At the point of intersection of the paths of the ships, they will have common Y and X. Hence equation 1 is equal to equation 2
- 1.55x + 1229 = -1.05(x) + 1039
1.55(x) - 1.05(x) = 1229 - 1039
0.5x = 190
X = 190/0.5 = 380
Substitute x in equation 1
Y = -1.55(380) + 1229
Y = -589 + 1229
Y = 640
Therefore the point of intersection of the paths of the ships is (380, 640)
B) given that Lion will reach her destination in one hour, Tiger – in two hours.
Ship Tiger
distance = root(795^2 + 1229^2)
Distance = 1463.7
Speed = distance/time
Speed = 1463.7/2 = 731.9 m/s
Distance at the point of intersection will be
Distance = root(380^2 + (640-1229)^2)
Distance = root(144400 + 346921)
Distance = 700.9
Speed = distance/time
Time = distance /speed
Time = 700.9/731.9
Time = 0.96 hours
Ship Lion
distance = root(985^2 + 1039^2)
Distance = 1431.69
Speed = distance/time
Speed = 1431.69/1 = 1431.69
Distance at the point of intersection will be
Distance = root((380 - 985)^2 + (640)^2)
Distance = root(775625)
Distance = 880.7 meters
Speed = distance/time
Time = distance /speed
Time = 880.7/1431.69
Time = 0.615 hours
C) the time in minute the distance between Lion and Tiger will be the shortest will be
Ship Tiger: 0.96 × 60 = 57.6 minute
Ship Lion: 0.62 × 60 = 36.9 minutes
D) The shortest distance between Lion and Tiger will be achieved by using pythagorean theorem for the the distances at the point of intersection
Root (880.7^2 - 700.9^2)
Distance = 533 metres
E) the positions of both ships at the moment when the distance between them is the shortest will be the initial position of both ships
That is
Ship Tiger
Initial position (0, 795)
Ship Lion
Initial position (985, 0).
64= 4^3 in logarithmic form
Time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal distribution with mean value 9 min and standard deviation 4 min. If five individuals fill out a form on one day and six on another, what is the probability that the sample average amount of time taken on each day is at most 11 min? (Round your answer to four decimal places.)
Answer:
u know this carol
Step-by-step explanation:
The population of a community was 200 people 10 yrs ago. Today the population is 550 people. Using an exponential growth function when will the population be 1000?
Answer:
in 6 years
Step-by-step explanation:
Using t=10 to represent today, we can write the exponential growth function as ...
p(t) = 200(550/200)^(t/10)
Then we can set p(t) = 1000 and solve for t:
1000 = 200(11/4)^(t/10) . . . . simplifying the growth factor
1000/200 = (11/4)^(t/10) . . . . divide by 200
log(5) = (t/10)log(11/4) . . . . . . take logs
t = 10·log(5)/log(11/4) ≈ 15.91
That is, about 16 years from 10 years ago, the population will reach 1000.
The population will reach 1000 in about 6 years.
What does our base tell us about the exponent
Newberg is 5 miles due north of the airport, and Rockport is 12 miles due east of the airport. How far apart are Newberg and Rockport?
Step-by-step explanation:
No of miles Newberg is north of airport = 5
No of miles Rockport is east of the airport = 12
No of miles Newberg and Rockport are apart = 12+5 =17
Answer:
I did this now and was not 12 it was 13
Richie Rich started his day with 12 bucks. Richie Rich ended his day with a dozen bucks. A. How many bucks did Richie Rich share today? B. Explain your answer.
Answers and Step-by-step explanations:
A. He shared $0.
B. Richie Rich started out with $12. He ended his day with a dozen bucks. However, notice that a dozen is the same as 12, so he still has $12. In other words, he didn't share any money today, so he shared $0.
Hope this helps!
Answer:
A. 0
B. No difference in starting and ending amounts
Step-by-step explanation:
12 = 1 dozen
12 bucks is equal to 1 dozen bucks, which means he didn't spend/share any
what's the least common denominator of 4 and 16
Answer:16
Step-by-step explanation:
The lcm of 4 and 16 is 16.
16
the lcm of 4 and 16 is 16