The coordinates of X are (5, 11).
Solution:
Given points of the line segment are P(2, 2) and T(7, 17)
Let X be the point that partitions the directed line segment PT in the ratio 3 : 2
Using section formula, we can find the coordinate of the point that partitions the line segment.
Section formula:
[tex]$X(x, y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+n y_{1}}{m+n}\right)[/tex]
Here, [tex]x_{1}=2, y_{1}=2, x_{2}=7, y_{2}=17[/tex] and m = 3, n =2
Substitute these in the section formula,
[tex]$X(x, y)=\left(\frac{3 \times 7+2 \times 2}{3+2}, \frac{3 \times 17+2 \times 2}{3+2}\right)[/tex]
[tex]$=\left(\frac{21+4}{5}, \frac{51+4}{5}\right)[/tex]
[tex]$=\left(\frac{25}{5}, \frac{55}{5}\right)[/tex]
[tex]=(5, 11)[/tex]
X(x, y) = (5, 11)
The coordinates of X are (5, 11).
Use a sample n=1400 , p=0.20 and a 99% confidence level to construct a confidence interval estimate of the population proportion, p
Answer:
[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]
[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]
The 99% confidence interval would be given by (0.172;0.228)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values given we got:
[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]
[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]
The 99% confidence interval would be given by (0.172;0.228)
The confidence interval for the proportion is CI = 0.20 ± 0.0275.
Confidence intervalThe formula for calculating the confidence interval for proportion is expressed as:
[tex]CI=p \pm z \cdot \sqrt{\frac{p(1-p)}{n} }[/tex]
where:
p is the proportion = 0.20n is the sample space = 1400z is the z-score at 99% interval = 2.98Substitute into the formula;
[tex]CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(1-0.2)}{1400} }\\CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(0.8)}{1400} }\\CI = 0.20 \pm 0.0275\\[/tex]
Hence the confidence interval for the proportion is CI = 0.20 ± 0.0275.
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A stack of nested paper cups is 8 inches tall . The 1st cup is 4 inches tall and each of the rest of the cups in the stack adds 1/4 of an inch to the height of the stack. How many cups are in the stack?
Answer:
17
Step-by-step explanation:
For n cups, the height of the stack is ...
4 + (1/4)(n -1)
For a height of 8 inches, we can find n from ...
8 = 4 +(1/4)(n -1)
4 = (1/4)(n -1) . . . . . . subtract 4
16 = n -1 . . . . . . . . . .multiply by 4
17 = n . . . . . . . . . . . .add 1
There are 17 cups in the stack.
30 determine the coefficient on x 12 y 24 x12y24 in ( x 3 + 2 x y 2 + y + 3 ) 18 . (x3+2xy2+y+3)18. (be careful, as x x and y y now appear in multiple terms!)
Answer: Coefficient of x²y² =5184
Step-by-step explanation:
18(3x + 4xy + y +3)*18(3x + 4xy + y + 3)
324( 9x² +12x²y + 3xy + 9x + 12x²y + 16x²y² + 4xy² +12xy + 3xy + 4xy² + y² + + 3y + 9x +12xy + 3y +9)
Already, x12y24x12y24 = 82944x²y²
From the expansion above, we have that: 324*16x²y²= 5184x²y²
Since, 82944x²y²/5184x²y² = 16
∴ Coefficient = 5184
A movie studio took a poll after showings of a new movie. The studio found that 5 out of every 24 people did not like the movie. About what percent of the people did not like the movie?
Answer:
= 20.83%
Step-by-step explanation:
5/24 * 100
= 20.83%
To find what percent of people did not like the movie when 5 out of every 24 people did not, we calculate 5/24 as a percentage which is approximately 20.83%, rounded to about 21% of the people.
To calculate the percentage of people who did not like the movie, we need to set up a proportion where the number of people who did not like the movie is to the total number of people. Given that 5 out of every 24 people did not like the movie, we can express this as a fraction: 5/24. To find the equivalent percentage, we set up a fraction with 100 as the denominator and cross-multiply:
5/24 = x/100
Now we cross-multiply and solve for x:
24x = 5imes 100
x = (5 imes 100) / 24
x = 500 / 24
x = 20.833...
This equates to approximately 20.83%, which can be rounded to about 21%. Therefore, about 21% of the people did not like the movie.
A consumer takes out a loan for $500 that charges 10% annual interest. What is the total cost of the loan if the consumer pays it back one year from the date of origination?
Answer:the answer is life
Step-by-step explanation:
well life is life that you need
Answer:
$550 i think
Step-by-step explanation:
Simplify.
−4(3−1)+2 please
Answer: -6
Step-by-step explanation:
-4(3-1)+2
-12+4+2
-12+6
=-6
Hey there!
Just do PEMDAS
• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction
–4(3 – 1) + 2
= –4(2) + 2
= -–8 + 2
= –6
Therefore, your answer is: -6
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A power plant is located on a river that is 600 feet wide. To lay a new cable from the plant to a location in a city 1 mile downstream on the opposite side costs $175 per foot across the river and $100 per foot along the land. Suppose that the cable goes from the plant to a point Q on the opposite side that is x feet from the point P directly opposite the plant. Write a function C(x) that gives the cost of laying the cable in terms of the distance x. 1 mi city Cl 600 ft power plant
Answer:
C(x) = 175√(x² + 360000) + 528000 - 100x
Step-by-step explanation:
See the attachment below (Line PR = 1mile)
C(x) = Cost of Distance across the river + Cost of Distance along the land
Calculating Distance Across the river:
In triangle OPQ,The distance across the river is represented by line y
Line y is the hypothenus of the triangle
Pythagoras theorem states that:
if one angle of a triangle is 90 degrees, then the square of the length of the hypotenuse - the side opposite the right angle - is equal to the sum of the squares of the lengths of the other two sides.
So,
y² = x² + 600²
y² = x² + 360000
y = √(x² + 360000)
If it costs $175 per foot across the river then It'll cost
175 * √(x² + 360000) to lay cables across the river.
Calculating Distance along the land
Distance along the land is represented by line QR
Line QR = Line PR - PQ.
Where PR = 1 Miles (1 mile = 5280 feet)
So, PR = 5280
Line PQ = x
So, QR = 5280 - x
If it costs $100 per foot along the land,then it'll cost
100 * (5280 - x) to lay cables along the land
= 528000 - 100x
C(x) = 175√(x² + 360000) + 528000 - 100x
Sonya is renting a car. She pays a fee of $50 for the rental plus $20 each day she had the car. Suppose she pays a total for $130. For how many days did she rent the car?
Answer: she rented the car for 4 days.
Step-by-step explanation:
Let x represent the number of days for which Sonya rented the car.
She pays a fee of $50 for the rental plus $20 each day she had the car. This means that if she rents the car of x days, the total amount that she would pay is
20x + 50
Suppose she pays a total for $130, it means that the number of days for which she rented the car would be
20x + 50 = 130
Subtracting 50 from the left hand side and the right hand side of the equation, it becomes
20x + 50 - 50 = 130 - 50
20x = 80
x = 80/20 = 4
The ratio pv to nrt is plotted against pressure for ch4 at 0°c and 200°c. why does the curve for 0°c drop below the horizontal line for an ideal gas whereas the curve for 200°c does not?
Answer:
See answer below
Step-by-step explanation:
the ratio of pv against nrt is called compressibility Z and measures the deviation from an ideal gas behaviour . When Z is plotted against pressure for CH₄ for 0°C and 200°C the curves will differ because there are
- negative deviations ( Z decreases) due to intermolecular forces
- positive deviations (Z increases ) due to molecular size of gas particles
then
- at 0°C the negative deviations prevail respect to positive deviations at lower pressures ( so Z drops below the horizontal line first ) and then Z increases when pressure increases since the effect of positive deviation is higher ( then Z increases)
- Nevertheless, at 200°C the effect of intermolecular forces is lower and thus the positive deviations always prevail ( thus you observe only Z increasing(
Sam is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 9 feet more than 6 times the width. He needs 74 feet of fencing to do the job. How many feet is the length of the garden?
Answer:
The length of the garden is 33 feet and the width of the garden is 4 feet.
Step-by-step explanation:
We are given the following in he question:
Perimeter of rectangular garden = 74 feet
Let l be the length of the garden and w be the width.
The length of the garden is 9 feet more than 6 times the width.
Thus, we can write
[tex]l = 9 + 6w\\\Rightarrow l-6w = 9[/tex]
Perimeter of rectangular garden =
[tex]2(l + w) = 74\\\Rightarrow l+w = 37[/tex]
Solving the two equation by elimination method, we get,
[tex]l-6w-(l+w) = 9 -37\\-7w = -28\\w = 4\\l = 9 + 6(4) = 33[/tex]
Thus, the length of the garden is 33 feet and the width of the garden is 4 feet.
He drank 2 small bottles and 2 large bottles, for a total of 76 ounces. The day before, he drank 4 small bottles and 1 large bottle, for a total of 83 ounces. How much does each bottle hold?
Answer: the small bottle holds 15 ounces while the large bottle holds 23 ounces.
Step-by-step explanation:
Let x represent the number of ounces that a small bottle holds.
Let y represent the number of ounces that a large bottle holds.
He drank 2 small bottles and 2 large bottles, for a total of 76 ounces. It means that
2x + 2y = 76 - - - - - - - - - - - - 1
The day before, he drank 4 small bottles and 1 large bottle, for a total of 83 ounces. This means that
4x + y = 83 - - - - - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 1, it becomes
4x + 4y = 152
4x + y = 83
Subtracting, it becomes
3y = 69
y = 69/3 = 23 ounces
Substituting y = 23 into equation 1, it becomes
2x + 2 × 23 = 76
2x + 46 = 76
2x = 76 - 46 = 30
x = 30/2 = 15 ounces
Answer:
its 15 and 19 ounces on IXL
Step-by-step explanation:
2. Mama Bear ate 80% as much porridge as Papa Bear did. Baby Bear ate as much as Mama Bear did. Papa Bear ate 1.2 liters more porridge than Mama Bear did. How much porridge did the three bears eat, in all?
Answer:
15.6 liters
Step-by-step explanation:
Let the porridge eaten by Papa bear be 'x' liters.
Given:
Mama Bear ate 80% as much porridge as Papa Bear did.
Baby Bear ate as much as Mama Bear did.
Papa Bear ate 1.2 liters more porridge than Mama Bear did
So, porridge eaten by Mama Bear = 80% of 'x' = [tex]0.80x[/tex]
Now, Baby Bear eats same amount as Mama Bear. So,
Porridge eaten by Baby Bear = [tex]0.80x[/tex]
Papa Bear ate 1.2 liters more than Mama Bear.
Framing in equation form, we get:
[tex]x = 1.2 + 0.80x[/tex]
[tex]x-0.80x=1.2[/tex]
[tex]0.20x=1.2[/tex]
[tex]x=\frac{1.2}{0.20}=6\ liters[/tex]
So, Papa Bear ate 6 liters of porridge.
Mama Bear ate = 0.80 × 6 = 4.8 liters
Baby Bear ate = 4.8 liters.
So, total porridge = Papa Bear + Mama Bear + Baby Bear
Total porridge eaten = 6 + 4.8 + 4.8 = 15.6 liters
Answer:
Step-by-step explanation:answer is 20%
Which best describes the three-dimensional figure obtained from rotating the figure around the y-axis?
a cylinder with a radius of 1 unit
a cone with a radius of 1 unit
a cylinder with a radius of 2 units
a cone with a radius of 2 units
Yo sup??
This question can be solved by just imagining the object formed or practically trying it out.
Therefore the correct answer to this question is option 2 ie
a cylinder with a radius of 1 unit.
Hope this helps.
The figure created is a cone with a height of 2 units and a radius of 1 unit.
Which figure will be created?
Notice that we have a triangle, so if we rotate it around the y-axis, we will get a cone.
Because the rotation is around the y-axis, the height of the cone will be equal to the side AB of the triangle, so the height of the cone is 2 units.
And the radius of the cone is equal to BC, then we can see that the radius measures 1 unit.
Then the figure created is a cone with a height of 2 units and a radius of 1 unit.
If you want to learn more about figures
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Lisa and Daisy work at a hair salon. The salon charges $21 for a hair styling session with Lisa and $17 for a session with Daisy.
Their income on a certain day is projected to be $357. This situation can be represented by the equation 21x + 17y = 357, where x is the number of Lisa's customers and y is the number of Daisy's customers.
(Technical details: x ≥ 0, y ≥ 0, and x and y take only integer values.)
How many customers would Lisa need to serve to attain the projected income if Daisy calls in sick that day?
Answer:
jursssursztsdigsdigssit
Step-by-step explanation:
hjnf
Answer: Lisa would need to serve 17 customers to attain the projected income.
Step-by-step explanation:
Their income on a certain day is projected to be $357.
This situation can be represented by the equation 21x + 17y = 357, where x is the number of Lisa's customers and y is the number of Daisy's customers.
On a day that Daisy is sick, the income from Daisy would be zero. For Lisa to attain the projected income of $357, the equation becomes
21x + 0 = 357
21x = 357
x = 357/21
x = 17
The mean value of land and building per acre from a sample of farms if 1400 with a standard deviation of 100. the data set has a bell shaped distribution. Assume thenumber of farms in the sample 80.
A. Use the empirical rule to estimate the number of farms whose land and buildings values per acre between 1200 and 1600
B. If 24 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between 1200 per acre and 1600 per acre?
Answer:A)54 farms
B) 16 farms
Step-by-step explanation:
Y(1200) = (1200-1400)/100 = -200/100
Y(1200) = -2
Y(1600) = 1600-1400)/100
Y(1600) = 200/100 = 2
P(1200-1600) = (2y<-2)
2 standard deviation from the range = 68%=0.68
80 farms × 0.68 = 54 .4 approximately 54
B) 24× 0.68= 16.32 approximately 16
By using the empirical rule, it is expected that around 54 farms among the sample of 80 farms, as well as approximately 71 of 104 farms (after addition of 24 farms) will have land and building values per acre between 1300 and 1500.
Explanation:The question deals with the concept of mean, standard deviation, and the empirical rule, specifically in the context of data relating to the values of land and buildings per acre on various farms.
A. Using the empirical rule, we know that approximately 68% of the population of a bell-curve distribution lies within one standard deviation from the mean. In this case, the mean is 1400 and the standard deviation is 100. So, one standard deviation above and below the mean is between 1300 and 1500. Therefore, approximately 68% of the 80 farms, or roughly 54 farms, have land and building values per acre between 1300 and 1500.
B. If we add 24 more farms to the sample, the total number of farms will be 104. Applying the same empirical rule, we'd expect approximately 68% of these, roughly 71 farms, to have land and building values per acre between 1300 and 1500.
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A corner store bakery sells cake and pies. The cakes are $5 and the pies are $7. In one day the store sells 15 goods and makes a total of $91. How many cakes did they sell?
Answer:
The answer to your question is it sold 7 cakes.
Step-by-step explanation:
Data
cakes = c = $5
pies = p = $7
total pieces = 15
total sell = $91
Process
1.- Write equations to solve this problem
c + p = 15 ------------ l
5c + 7p = 91 ----------- ll
2.- Solve the system of equations by elimination
Multiply equation I by -5
-5c - 5p = -75
5c + 7p = 91
0 + 2p = 16
Solve for p
p = 16/2
p = 8
3.- Substitute p in equation l to find c
c + 8 = 15
solve for c
c = 15 - 8
c = 7
4.- Conclusion
It sold 7 cakes and 8 pies.
Answer: 7 cakes were sold.
Step-by-step explanation:
Let x represent the number of cakes that were sold.
Let y represent the number of cakes that were sold.
The cakes are $5 and the pies are $7. The store makes a total of $91. This means that
5x + 7y = 91- - - - - - -- -1
The store sold a total number of 15 goods. This means that
x + y = 15
Substituting x = 15 - y into equation 1, it becomes
5(15 - y) + 7y = 91
75 - 5y + 7y = 91
- 5y + 7y = 91 - 75
2y = 16
x = 16/2 = 8
x = 15 - y = 15 - 8
x = 7
An architect wants to do a rectangle with the diagonal of 25 inches the length of the rectangle is to be 3 inches more than triple the width. What is the dimensions she should make the rectangle
Answer: The length is 24 inches. The width is 7 inches.
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The length of the rectangle is to be 3 inches more than triple the width. This means that
L = 3W + 3
The diagonal of the rectangle divides it into two right angle triangles and the diagonal represents the hypotenuse. The length and width represents the opposite and adjacent side. Applying Pythagoras theorem,
Hypotenuse² = opposite side² + adjacent side²
Therefore,
25² = L² + W²
625 = L² + W² - - - - - - - - - -1
Substituting L = 3W into equation 1, it becomes
625 = (3W + 3)² + W²
625 = 9W² + 9W + 9W + 9 + W²
10W² + 18W - 625 + 9 = 0
10W² + 18W - 616 = 0
Dividing through by 2, it becomes
5W² + 9W - 308= 0
5W² + 44W - 35W - 308 = 0
W(5W + 44) - 7(5W + 44) = 0
W - 7 = 0 or 5W + 44 = 0
W = 7 or W = - 44/5
Since the width cannot be negative, then W = 7
L = 3W + 3 = 7 × 3 + 3
L = 24
Please help asap for the answer
Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle
AC represents the hypotenuse of the right angle triangle.
With ∠A as the reference angle,
AB represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine the ratio of Tan A , we would apply the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side. Therefore,
Tan A = 28/45
A seven-year medical research study reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug.a. This study involved the comparison of two populations. What were the populations?b. Do you suppose the data were obtained in a survey or an experiment?c. For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic that could be used to estimate the number of women out of 1000 in this population who have tissue abnormalities.d. For the population of women whose mothers did not take the drug DES during pregnancy, what is the estimate of the number of women out of 1000 who would be expected to have tissue abnormalities?e. Medical studies often use a relatively large sample (in this case, 3980). Why?
Answer:
16 women per 1 000
Step-by-step explanation:
The data was likely to be obtained from a survey. The question states how the information was gathered - most probably from questionnaires.
c. A simple model will be 16 women per 1 000 women. Proportion has been taken into account here.
Let 63 correspond with those that are going to get cancer out of 3980. The women have 63/3980 chance of getting cancer.
For 1 000 women that will be 1000/3980 × (63) = 16
Therefore the probability of a person getting cancer is 16 per 1 000 Ans
e. Large samples are essential to ensure that the results are representative of the actual population. In addition, large samples reduce inherent errors from deviations. Furthermore, useless data can be discarded and the remaining data still represent the actual population size. Lastly, large amounts of data are easy to scale up and use to develop models.
The two populations compared in the study were women whose mothers took the drug DES during pregnancy and those whose mothers did not. The data in the study were obtained through an observational study. A descriptive statistic can be used to estimate the number of women with tissue abnormalities out of 1000 in the population of women whose mothers took the drug DES during pregnancy.
Explanation:a. The two populations in the study were: 1) women whose mothers took the drug DES during pregnancy and 2) women whose mothers did not take the drug.
b. The data in this study were obtained through an observational study, specifically a cohort study. This means that the researchers observed and compared the outcomes between the two groups of women without directly manipulating any variables.
c. A descriptive statistic that could be used to estimate the number of women out of 1000 in the population of women whose mothers took the drug DES during pregnancy and developed tissue abnormalities is:
Number of women with tissue abnormalities in the sample: 63
Descriptive statistic: (63 / 3980) * 1000 = 15.83
Therefore, an estimate is that 15.83 out of 1000 women in this population have tissue abnormalities that might lead to cancer.
d. Since the study only reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities, without providing an exact percentage, it is not possible to estimate the number of women without more specific information.
e. Medical studies often use a relatively large sample size, like 3980, to increase the reliability and representativeness of the findings. A larger sample size helps to reduce the chance of biased or random results and increases the generalizability of the findings to the larger population.
Harper picked 3.5 baskets of apples. Cooper picked 4 1/4 baskets of apples did Harper and cooper pick together? Express your answer as a decimal number and as a mixed number
Answer:
The number of basket of apples picked by Harper and Cooper together is [tex]5\frac{1}{4} \ \ Or \ \ 5.25[/tex].
Step-by-step explanation:
Given:
Number of basket picked by Harper = 3.5
Number of basket picked by cooper = [tex]4\frac{1}{4}[/tex]
We need to find the number of basket of apples picked by Harper and Cooper together.
Solution:
Now we can see that one number is in decimal form and other number is in mixed fraction form so we will convert both the number in simplest fraction form and then solve the same.
Number of basket picked by Harper = 3.5
Now if we divide 7 from from 2 we get the answer as 3.5 so we can say that;
3.5 can be rewritten as [tex]\frac{7}{2}[/tex]
Number of basket picked by Harper = [tex]\frac{7}{2}[/tex]
Number of basket picked by cooper = [tex]4\frac{1}{4}[/tex]
[tex]4\frac{1}{4}[/tex] can be rewritten as [tex]\frac{17}{4}[/tex]
Number of basket picked by cooper = [tex]\frac{17}{4}[/tex]
Now we can say that;
to find the number of basket of apples picked by Harper and Cooper together we will add Number of basket picked by Harper and Number of basket picked by cooper.
framing in equation form we get;
number of basket of apples picked by Harper and Cooper together = [tex]\frac{7}{2}+\frac{17}{4}[/tex]
now we will use LCM to make the denominator common we get;
number of basket of apples picked by Harper and Cooper together = [tex]\frac{7\times2}{2\times2}+\frac{17\times1}{4\times1}=\frac{14}{4}+\frac{17}{4}[/tex]
Now denominators are common so we will solve the numerators we get;
number of basket of apples picked by Harper and Cooper together = [tex]\frac{14+7}{4} = \frac{21}{4} \ \ Or\ \ 5\frac{1}{4} \ \ Or \ \ 5.25[/tex]
Hence the number of basket of apples picked by Harper and Cooper together is [tex]5\frac{1}{4} \ \ Or \ \ 5.25[/tex].
Please help!!!
Find the area of the following figure: (Use π = 3.14 and do NOT include units in your answer.)
The composite shape's area is 61.12.
Step-by-step explanation:
Step 1; To calculate the value of the composite shapes area we first divide it into shapes whose areas we know. In this case, the composite shape consists of only a circle's half and a triangle attached below it. If we can sum the individual areas of the two shapes we should be able to determine the area of the unknown shape.
Step 2; The triangle has a base length of 8 as it is from (6, 10) to (14, 10) so 14 - 6 = 8 and the height is from (10,10) and (10,1) so the height is 10 -1 = 9. So the area of any given triangle is 0.5 times the product of its base length and height. So area of this triangle = 0.5 × 8 × 9 = 36. The circle is not an entire one but only half so we calculate the entire circle's area and then half it to find its area. The diameter is 8 as the circle's ends are at (6, 10) and (14, 10) and radius = 14 - 6 / 2 = 4. The area of any circle is π times the square of its radius. So area of this circle = π × r²/2= 3.14 × 4²/ 2 = 25.12.
Step 3; Now we calculate the given composite shapes area by summing the two areas i.e areas of the half-circle and the rectangle.
Area of the composite shape = 36 + 25.12 = 61.12.
1 Suppose you choose at random a real number X from the interval [2, 10]. (a) Find the density function f(x) and the probability of an event E for this experiment, where E is a subinterval [a, b] of [2, 10]. (b) From (a), find the probability that X > 5, that 5 < X < 7, and that X2 − 12X + 35 > 0.
Answer:
Step-by-step explanation:
Given that you choose at random a real number X from the interval [2, 10].
a) Since this is a contnuous interval with all number in between equally likely
E = probability for choosing a real number is U(2,10)
pdf of E is [tex]\frac{1}{8}[/tex]
b) P(X>5) = [tex]\int\limits^10_5 {1/8} \, dx = \frac{5}{8}[/tex]
[tex]P(5<x<7) = \frac{2}{8} =\frac{1}{4}[/tex]
For
[tex]x^2-12x+35 >0\\(x-5)(x-7)>0\\x<5 or x >7[/tex]
P(X<5 or x>7) = 1-P(5<x<7)
= [tex]\frac{3}{4}[/tex]
The density function of a real number selected randomly within the range [2,10] is 1/8, with the probability of an event being the difference between the two values divided by 8. The probabilities that X is greater than 5, lies between 5 and 7 and that the inequality X^2 - 12X + 35 > 0 always holds are 5/8, 1/4 and 1 respectively.
Explanation:The subject of this question is probability, particularly continuous uniform distribution. (a) A real number X selected from a certain interval [2, 10] has a continuous uniform distribution. Hence, the density function f(x) = 1/(b-a) = 1/8 for 2 ≤ x ≤ 10 and0otherwise. The probability of an event E, where E is [a,b], is the integral of f(x) from a to b, which is (b-a)/(10-2).
(b) Probability that X > 5 is the integral of f(x) from 5 to 10, which is (10-5)/8 = 5/8. Probability that 5 < X < 7 is the integral from 5 to 7, which is (7-5)/8 = 1/4. Lastly, the inequality X^2 - 12X + 35 > 0 factors out to (X-5)^2 + 10 > 0 which is always true as square number is always non-negative, thus the probability is 1.
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A Television nanufacture sells 21 of TV model at$299 each, 13 of TV Model B at $549 each and 8 of TV Model C at $619 each. Find tge average price per TV Sold.
Answer:
Step-by-step explanation:
The formula for determining average is expressed as
Average = the total cost of the televisions/ the sum of the televisions
Total number of model A television that was sold is 21
Total cost of 21 televisions = 299 × 21 = $8671
Total number of model B television that was sold is 13
Total cost of 13 televisions = 549 × 13 = $7137
Total number of model C television that was sold is 6
Total cost of 6 televisions = 619 × 6 = $3714
Total number televisions sold is 21 + 13 + 6 = 40
Total cost of the televisions is 8671 + 7137 + 3714 = 19522
Therefore, the average price per TV Sold is
19522/40 = $488.05 per television
The price of an mp3 player is $149.99. The mp3 player was on sale for 20% off. Matt bought the mp3 player at the sale price and also had a rebate of $50. How much did Matt pay for the mp3 player?
Matt paid $70 for mp3 player.
Step-by-step explanation:
Given,
Cost of mp3 player = $149.99
Discount = 20%
Amount of discount = 20% of 149.99
Amount of discount = [tex]\frac{20}{100}*149.99[/tex]
Amount of discount = 0.2*149.99
Amount of discount = $29.99
Sale price = Cost of mp3 - Amount of discount
Sale price = [tex]149.99 - 29.99 = \$120[/tex]
Rebate = $50
Amount paid by Matt = sale price - rebate
Amount paid by Matt = 120-50 =$70
Matt paid $70 for mp3 player.
Keywords: subtraction, percentage
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x squared equals 9 what is the answer
Answer: x = 3
Step-by-step explanation:
x^2 = 9
x = [tex]\sqrt{9}[/tex]
x = 3
Another way to think about it:
We think what number can be multiplied by itself to get 9.
since 3*3=9, our answer is 3
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
Answer:
[tex]m\angle R=69.4^o[/tex]
Step-by-step explanation:
we know that
In the right triangle PQR
[tex]tan(R)=\frac{PQ}{QR}[/tex] ----> by TOA (opposite side divided by adjacent side)
substitute the given values
[tex]tan(R)=\frac{8}{3}[/tex]
using a calculator
[tex]m\angle R=tan^{-1}(\frac{8}{3})=69.4^o[/tex]
Figure the standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 10
Answer:
standard deviation of the distribution = 6.325.
Step-by-step explanation:
i) standard deviation of the population σ = 20
ii) size of sample n = 10.
iii) standard deviation of the distribution = [tex]\frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{10}} = \frac{20}{3.162} = 6.325[/tex]
Final answer:
To find the standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 10, use the formula: Standard Deviation of the Distribution of Means = Population Standard Deviation / Square Root of Sample Size. By substituting the values, you get the standard deviation of 6.32.
Explanation:
The standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 10 is calculated using the formula:
Standard Deviation of the Distribution of Means = Population Standard Deviation / Square Root of Sample Size
Substitute the values: 20 / √10 = 6.32. Therefore, the standard deviation of the distribution of means is 6.32 for this scenario.
A license plate consists of seven symbols on each plate, where the first two symbols are letters of the alphabet and the following five symbols are the digits selected from the set StartSet 0 comma 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 EndSet? How many license plates can be produced if any digit or letter can be repeated on any given license plate?
Final answer:
To find the total number of possible license plates with two letters followed by five digits (with repetition allowed), multiply the number of options for each position: 26 letters and 10 digits result in 67,600,000 different license plates.
Explanation:
The question asks for the total number of license plates that can be produced when the first two symbols are letters from the alphabet and the following five symbols are digits from 0 to 9, with repetition allowed for both letters and digits. To find the number of possible license plates, we use the principle of counting, multiplying the number of choices for each position.
There are 26 possible letters for each of the first two positions (since there are 26 letters in the English alphabet) and 10 possible digits (0-9) for each of the last five positions.
Therefore, the total number of license plates that can be created is calculated as:26 * 26 * 10 * 10 * 10 * 10 * 10. This equals 67,600,000 possible license plates.
This calculation assumes that each symbol (letter or digit) can be repeated, meaning the same letter or digit can be used more than once in the license plate.
Using the piling method, which of the following can be constructed from polygons alone?
Check all that apply.
Answer:
B and C.
Step-by-step explanation:
A prism can be constructed from 4 sided polygons like a rectangle.
A pyramid (not including the vertex) can be constructed from squares of diminishing size.
The piling method allows for the construction of various three-dimensional shapes using polygons alone. Some of the shapes that can be constructed include prisms, pyramids, and cones.
Explanation:The piling method, also known as the additive method or stacking method, allows for the construction of various three-dimensional shapes using polygons alone. Some of the shapes that can be constructed include prisms, pyramids, and cones.
Prisms:
A prism is a three-dimensional shape with two congruent polygonal bases and rectangular lateral faces connecting the corresponding vertices of the bases. Examples of prisms include rectangular prisms (cuboids), triangular prisms, and hexagonal prisms.
Pyramids:
A pyramid is a three-dimensional shape with a polygonal base and triangular faces connecting the vertices of the base to a single point called the apex or vertex. Examples of pyramids include square pyramids, triangular pyramids, and pentagonal pyramids.
Cones:
A cone is a three-dimensional shape with a circular base and a curved surface that connects the base to a single point called the vertex. Cones can be constructed using polygons by approximating the curved surface with a series of smaller polygons.
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Needing help with getting the slope
Answer:
The answer is 2/5
Step-by-step explanation:
I found 2 points and did y2-y1/ x2-x1 and got 2/5. And then I tested it and it worked.
Answer: the slope is 2/5
Step-by-step explanation:
The formula for determining slope is expressed as
Slope = change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
Looking at the graph given,
y2 = 0
y1 = - 2
x2 = 5
x1 = 0
Slope = (0 - -2)/(0 - 0) = 2/5