The cost of each lily is $3.50, and the cost of each rose is $2.25.
Dimensional analysis problemLet's use the variables L and R to represent the cost of each lily and each rose, respectively.
From the problem, we can write a system of two equations based on the information about the two arrangements:
5L + R = 19.75 (equation 1)
6L + 3R = 27.75 (equation 2)
To solve for L and R, we can use elimination. First, we can multiply equation 1 by 3:
15L + 3R = 59.25 (equation 3)
Then, we can subtract equation 2 from equation 3:
9L = 31.5
Solving for L, we get:
L = 3.50
Now we can substitute this value back into either equation 1 or equation 2 to solve for R. Let's use equation 1:
5L + R = 19.75
5(3.50) + R = 19.75
17.50 + R = 19.75
R = 2.25
Therefore, the cost of each lily is $3.50, and the cost of each rose is $2.25.
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If a + c = 4.98 and b + c = 6.48, what is the value of b^2+bc-ab-ca?
A) 7.47
B) 8.16
C) 9.08
D) 9.72
E) None of the preceding
Answer:
it is option no d at least
cuz it is what it is
Find the image matrix for quadrilateral ABCD
after the composite transformation.
A(−10, 0), B(−8, 6), C(−3, 7), and D(0, 3)
Rotation: 270º
Reflection: y = -x
The required transformed coordinates of the quadrilateral as:A'(-10, 0),B'(-8, -6),C'(-3, -7), D'(0, -3).
How to find the image matrix for quadrilateral ABCD?The image matrix for the composite transformation of a rotation of 270º and a reflection over the line y=-x can be found by multiplying the transformation matrices for each operation.
The rotation matrix for 270º counterclockwise can be represented as:
[tex]$R_{270} = \begin{bmatrix}0 & -1 \1 & 0\end{bmatrix}$[/tex]
The reflection over the line y=-x can be represented as:
[tex]$F_{y=-x} = \begin{bmatrix}0 & -1 \-1 & 0\end{bmatrix}$[/tex]
To find the composite transformation matrix, we multiply the two matrices:
[tex]$M = F_{y=-x} \cdot R_{270} = \begin{bmatrix}0 & -1 \-1 & 0\end{bmatrix} \cdot \begin{bmatrix}0 & -1 \1 & 0\end{bmatrix} = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix}$[/tex]
To apply this transformation to the coordinates of the quadrilateral ABCD, we write each point as a column vector:
[tex]$A = \begin{bmatrix}-10 \0\end{bmatrix}$[/tex],
[tex]$B = \begin{bmatrix}-8 \6\end{bmatrix}$[/tex],
[tex]$C = \begin{bmatrix}-3 \7\end{bmatrix}$[/tex],
and
[tex]$D = \begin{bmatrix}0 \3\end{bmatrix}$[/tex]
We can then apply the composite transformation matrix M to each of these vectors:
[tex]$A' = M \cdot A = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-10 \0\end{bmatrix} = \begin{bmatrix}-10 \0\end{bmatrix}$[/tex]
[tex]$B' = M \cdot B = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-8 \6\end{bmatrix} = \begin{bmatrix}-8 \-6\end{bmatrix}$[/tex]
[tex]$C' = M \cdot C = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}-3 \7\end{bmatrix} = \begin{bmatrix}-3 \-7\end{bmatrix}$[/tex]
[tex]$D' = M \cdot D = \begin{bmatrix}1 & 0 \0 & -1\end{bmatrix} \cdot \begin{bmatrix}0 \3\end{bmatrix} = \begin{bmatrix}0 \-3\end{bmatrix}$[/tex]
We can then write the transformed coordinates of the quadrilateral as:
A'(-10, 0),
B'(-8, -6),
C'(-3, -7),
D'(0, -3)
Therefore, the image matrix of quadrilateral ABCD after the composite transformation is:
[tex]$ \begin{bmatrix}-10 & -8 & -3 & 0 \0 & -6 & -7 & -3\end{bmatrix}$[/tex]
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These are the steps Brittany took to find the difference, but she made a mistake. Select the step at which Brittany made her first mistake. Then select the correct difference in simplest form. Select all the correct locations on the image.
Answer:
Step-by-step explanation:
Here is Annie's method to find angle ABC. Explain the mistake that Annie has made. Let angle ABC = 0 8 sin == 10 8= sin-1 8 10 0 = 53.13 (2 dp) Is there more than one possible mistake? Find angle ABC. A 6 cm C 10 cm 8 cm -B
Annie made mistake in her trigonometric ratios. The opposite side of the right triangle should be 6 cm not 8 cm.
How to find the angles of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Annie tries to solve the angle ABC of the right triangle. The angle ABC can be found using trigonometric ratios as follows:
where
∅ = angle ABC
Therefore,
sin ∅ = opposite / hypotenuse
sin ∅ = 6 / 10
sin ∅ = 3 / 5
∅ = sin⁻¹ 0.6
∅ = 36.8698976458
∅ = 36.87 degrees
Therefore, she made mistake in her trigonometric ratios.
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What is the value of this expression when x=-4 and y=64
Therefore , the solution of the given problem of expressions comes out to be the expression's value at x = -4 and y = 64 is 0.
What is an expression?Instead of using approximations produced at random, it is better to use shifting integers that may prove increasing, reducing, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, components, or mathematical remarks for techniques like additional disapproval, production, and mixture may be included in a statement of truth equation.
Here,
The phrase is entrusted to us:
=> -4∛y + x²
Additionally, we are told that x = -4 and y = 64. When these numbers are inserted into the expression, we obtain:
=> -4∛y + x² = -4∛(64) + (-4)²
=> -4∛4³ + 16
=> -4(4) + 16
=> 0
Consequently, the expression's value at x = -4 and y = 64 is 0.
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Please explain on how to solve this Question
Answer:
i) ABCDEF has an area of 98m
ii) Flower bed has an area of 6m
iii) The area of the grass is 92m
Hope this helps!
Step-by-step explanation:
The area of a triangle is [tex]\frac{1}{2}[/tex] × L × H
The area for the triangle flower bed will be [tex]\frac{1}{2}[/tex] × 6m × 2m or 6m.
In order to find the entire area of ABCDEF, draw a segment FC to create a trapezoid and a rectangle. The rectangle has an area of 77m ( 7 × 11 ). The trapezoid has a formula of [tex]\frac{1}{2}[/tex] × ( b + b ) × h, this would be [tex]\frac{1}{2}[/tex] × ( 10 + 11 ) × 2.
The trapezoid has an area of 21, this added to the rectangle's area of 77 equals 98m as the total area of the garden.
Subtract the area of the flower bed ( 6 ) from the area of the garden, and you get an area of 92m. This is the area of grass.
a client shows you the greek vanilla yogurt he eats for breakfast most mornings. determine the calories from protein if the client eats 3/4 cup. 54 calories 72 calories 122 calories 162 calories
The number of calories from protein if the client eats 3/4 cup is 54 calories. So, the correct option is 54 calories.
Calories are a unit of energy. The energy needed to raise the temperature of 1 gram of water through 1 °C is equal to one calorie. Calories are the energy that food supplies to the body.
Calories from protein: Protein supplies 4 calories per gram. To calculate the total number of calories from protein, you must first know the amount of protein that the food item contains.
To calculate the calories from protein in Greek vanilla yogurt: Greek vanilla yogurt contains about 10 grams of protein per cup.
Therefore, Calories from protein = Protein x 4 = 10 x 4 = 40 Calories per 1 cup Greek vanilla yogurt
If the client eats 3/4 of a cup of Greek vanilla yogurt, the number of calories from protein would be:
Calories from protein = 40 Calories x 3/4 cup = 30 Calories
Hence, the correct answer is 54 calories.
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How do I check what answers I got correct on Edmentum?
Below are few steps given to check what answer you got correct on edmentum.
What is edmentum?
Edmentum is an online learning platform that offers educational software and digital curriculum for K-12 students.
What is use of edmentum?
Edmentum is designed to support student learning and achievement, provide teachers with the tools and resources they need to be successful, and help schools and districts meet their academic goals.
According to given information:To check your answers on Edmentum, you can navigate to the assignment or quiz that you completed and click on the "View Results" button. This will show you a breakdown of your score and which questions you answered correctly or incorrectly.
If you want to review specific questions and their answers, you can click on the individual question numbers to see the question prompt and your response. Depending on how your instructor has set up the assignment or quiz, you may also be able to see the correct answer and an explanation for why it is correct.
If you have trouble finding your results or accessing specific information, you can reach out to your instructor or the Edmentum support team for assistance.
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If my friend went to bed at 1:00am on Friday. Then she woke up at 1:00pm on Friday how many hours of sleep did she get?
If your friend went to bed at 1:00am on Friday and woke up at 1:00pm on Friday, she slept for 12 hours.
To see why, you can count the number of hours between 1:00am and 1:00pm:
1:00am to 2:00am = 1 hour
2:00am to 3:00am = 1 hour
...
11:00am to 12:00pm = 1 hour
12:00pm to 1:00pm = 1 hour
The total number of hours between 1:00am and 1:00pm is 12 hours.
⚠️URGENT !!! ⚠️Bonjour, pouvez-vous m'aider a resoudre ce problème ?
Énoncé :
Paul roule avec son vélo à la vitesse constante de 8,3m/s (30km/h) pendant une durée égale à 120 secondes.
Question :
Quelle durée mettra-t-il à cette vitesse pour parcourir 3km ?
Merci d'avance,
Bonne journée.
PS : est-il possible de mettre me calcul pour que je comprenne mieux?
bonjour,
a) on pourrait faire un produit en croix
8,3 m ----> 1s
combien de m en ----> 120s
120*8,3= 996m en 120s
soit 0,996 km (on décale de 3 rangs vers la gauche)
il parcoure donc 996m en 120secondes
b) pour parcourir 3km, de même faisons un produit en croix
(3 km = 3000m)
8,3 m ---> 1s
3000m ----> combien de secondes ?
3000*1/8,3= environ 361,45 secondes
transformons les en heures, minutes
361,45/60 = 6,02 minutes
0,02*60= 1,2
donc pour parcourir 3km, à cette vitesse, il mettra environ 6 minutes et 1 seconde.
c) posons un produit en croix :
vitesse en km/h
15km ----> 25 min
? -----> 60 min (1h)
60*15/25= 36
donc il a une vitesse de 36km/h
vitesse en km/mn
15km ----> 25 min
?km ------> 1 min
1*15/25 =0,6 km/mn
voilà j'espère t'avoir aidé
si t'as des questions n'hésite pas
a new car is purchased for 18500 dollars. the value of the car depreciates at 8% per year. to the nearest tenth of a year, how long will it be until the value of the car is 9100 dollars?
Answer:
8.5 years
Step-by-step explanation:
You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.
ValueThe depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...
value = (initial value) × (1 - (depreciation rate))^t
where the rate is "per year" and t is in years.
Applicationvalue = 18500·(1 -0.08)^t
9100 = 18500·0.92^t . . . . fill in the value of interest
9100/18500 = 0.92^t . . . . divide by 18500
log(91/185) = t·log(0.92) . . . . take logarithms
t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509
It will be about 8.5 years until the value is $9100.
__
Additional comment
The graph shows the solution to ...
18500·0.92^t -9100 = 0
We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.
Write the equation of a line perpendicular to y = -4x and passing through the point (12,6).
1. y = -1/4 x + 9
2. y = -1/4 x + 3
3. y = 1/4 x + 9
4. y = 1/4 x + 3
The equation of line perpendicular to y = -4x and passing through the point (12, 6) is y = 1/4 x + 3.
How to determine a line's equation from two points?Using the slope method, determine the slope.
To find the y-intercept (b), use the slope and one of the locations.
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).
The given equation is y = -4x and we need to find the equation of the line which is passing through the point (12,6).
As y=-4x, therefore compared to the standard equation y = mx, hence the slope of the line is m = -4.
Therefore any line which is perpendicular and has a slope that is the negative reciprocal of the -4 is 1/4.
The modified equation becomes for the line that passes through (12, 6).
y-6 = 1/4 (x-12)
solving this equation we get,
y-6 = 1/4 x - 1/4 * 12
y-6 = 1/4 x - 3
y = 1/4 x -3 + 6
y = 1/4 x + 3
Therefore option 4 is correct, y = 1/4 x + 3
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Gizmo
Helpp pleaseee
25 points!!
Model reef can sustain 20% net fishing because the species didn’t increase as much as it did with the other net fishing method.
Explanation:
What is reef fishing ?
Reef fishing is commonly called “Bottom Bouncing” where anglers using heavy 60-100lb handline and rod techniques to target such prized eating fish as Coral Trout, Red Emperor and Nannygai.
What is net fishing ?
A fishing net is a net used for fishing. Nets are devices made from fibers woven in a grid-like structure. Some fishing nets are also called fish traps, for example fyke nets.
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Naomi went shopping for a new pair of sneakers because of a sale. The store was offering a 10% discount. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
She should multiply the prices on the tags by 0.9 to find the price she would have to pay, before tax, after the 10% discount.
To find the price Naomi would have to pay for her new sneakers after the 10% discount, she needs to multiply the original price on the tag by a factor that reflects the discount.
Since the discount is 10%, the factor by which she should multiply the original price is 1 minus 10% or 0.9. This is because the final price is equal to the original price minus the discount, which is 10% of the original price, or 0.1 times the original price.
So, if the price on the tag is $100, the price Naomi would have to pay, before tax, after the 10% discount would be:
$100 * 0.9 = $90
This means that she would save $10, which is 10% of the original price.
In general, if the original price on the tag is P, the price Naomi would have to pay, before tax, after the 10% discount would be:
P * 0.9 = 0.9P
Therefore, she should multiply the prices on the tags by 0.9 to find the price she would have to pay, before tax, after the 10% discount.
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Here are some of my clues to a mystery number the GCF of 18, 36, and me is 2, i am a multiple of 5, i am greater than 18 and less than 30. what am I? PLEASE HELP!
Answer:
I am 20.
Step-by-step explanation:
The GCF is 2 so the mystery number x must be even.
And as I am between 18 and 30 I could be
20, 22, 24, 26 or 28
But I am a multiple of 5 so i must be 20.
Ines's younger brother will be home in a half hour. If her garden hose flows at a rate 24 gal/min, does she have enough time to fill the pool before he gets home? Explain.
No, she have not enough time to fill the pool before he gets home. The garden hose with flow rate 24 gal/min will take 40 minutes to complete fill up the tank that is t ~ 40 minutes. So, she cannot complete fill up the pool before he come.
We have, the time in which Ines's younger brother will be home = an half hour = 1/2 hour
water flow rate of garden's hose = 24 gal/min
She want to fill up the pool. From the figure, depth of pool = 3 ft
Width of pool = 10 in.
1 inch = 0.0833 feet
So, 10 inches = 0.833 feet
outer diameter of pool = 9 ft
so, outer radius of pool = 4.5 ft
Now, inner diameter of pool/tank = outer diameter - 2(width)
= 9 - 2×0.833
= 9 - 1.666 = 7.334
Inner radius of pool = 7.334/2 = 3.667 ft
Water flow rate, Q = 24 gal/min
= 24/7.48 gal ( since 1 ft³ = 7.48 gal)
= 3.20 ft³
Using formula, Q = volume/ time
where t --> time to fill up the pool through hose
Volume of tank/pool = surface area × height (depth)
= π r² × h , where r is inner radius
= π (3.667)² × 3 ft³
= 126.71 ft³
So, Q = 126.71 ft³/t
=> t = 126.71 ft³/3.20 ft³
=> t = 39.59 min
Hence, required time is 39.59 ~ 40 minutes and she cannot complete before he come.
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Complete question:
Ines's younger brother will be home in a half hour. If her garden hose flows at a rate 24 gal/min, does she have enough time to fill the pool before he gets home? See the above figure
Explain. (Hint: 1 ft³ = 7.48 gal)
I am needing some help
28.26 is the volume of the fig.
What is volume?Each thing in three dimensions takes up some space.
The volume of this area is what is being measured.
The space occupied within an object's borders in three dimensions is referred to as its volume.
It is sometimes referred to as the object's capacity.
Knowing an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.
Hence, 28.26 is the volume of the fig.
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the library is having a used book sale books cost $3 each or 10 for 25 if you buy 10 how much do you save on each book?
6+4
7777777777777777777777777777777777
Answer:
10,
7777777777777777777777777777777777
Step-by-step explanation:
select all the lines that intersect y=3
v
To identify which lines intersect the line y = 3, you would need to provide a list of lines to choose from. In general, any line that is not parallel to y = 3 will intersect it. Lines parallel to y = 3 will have equations of the form y = c, where c is a constant value different from 3.
4. The tree is 15 feet away from the edge of the lake. What is the distance across the lake (water's edge to opposite side)? Justify your decision.
The distance across the lake, given the distance of the tree and Cade would be 14.36 ft.
How to find the distance ?We can use the concept of similar triangles to solve this problem:
(Length of the tree's shadow) / (Distance from the tree to the edge of the lake) = (Length of Cade's shadow) / (Cade's height)
36.2 / 15 = 2.5 / 6.2
Now we can set up another proportion using the length of the tree's shadow and the length of the lake:
(Length of the tree's shadow) / (Length of the lake) = (Distance from the tree to Cade) / (Length of Cade's shadow)
Plugging in the values we know, we get:
36.2 / 15.6 = 15 / 2.5
6.2 * 2.32051282 = 14.36 ft
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The full question is:
The trees shadow is 36.2 feet long. The tree is 15 feet away from the edge of the lake. Cade is 6.2 feet tall and his shadow is 2.5 feet long, his shadow is measured at the exact time the trees shadow reaches the other side of the lake which is 15.6 feet long. What is the distance across the lake (water's edge to opposite side)
An isosceles triangle has an angle that measures 90°. What measures are possible for the other two angles? Choose all that apply.
90 45 75 20
Step-by-step explanation:
All three angels of a triangle have to sum to 180 degrees ....so there is only 90 degrees left for the other two equal-sized angles (isosceles).....they must be 45° each
The point P(-1, 6) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, P'?
The coordinates of the resulting point, P' as required to be determined in the task content is; (1, -6).
What are the coordinates of the image point?It follows from the task content that the coordinates of the image point P' formed when point P(-1, 6) is rotated 180° counterclockwise around the origin is to be determined.
On this note, since a rotation of 180° is such that we have;
(x , y) ======> (-x, -y).
Hence, when point P(-1, 6) is rotated 180° counterclockwise around the origin, the resulting image point, P' has coordinates; (1, -6).
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The arithmetic mean of 25, 29, and x is 29. Find x.
you have been asked to design a can shaped like right circular cylinder that can hold a volume of 432⇡-cm3. what dimensions of the can (radius and height) will use the least amount of material?
The dimensions of the can that use the least amount of material are a radius of approximately 4.38 cm and a height of approximately 3.11 cm.
To design a can that uses the least amount of material, we want to minimize its surface area. Since the can is shaped like a right circular cylinder, its surface area is given by:
A = 2πr² + 2πrh
where r is the radius of the base of the cylinder and h is its height.
We also know that the volume of the can is given by:
V = πr²h
We can use these equations to express h in terms of r, and then substitute this expression for h into the equation for surface area. Then we can differentiate the resulting equation with respect to r, set it equal to zero, and solve for r to find the value of r that minimizes surface area.
First, we solve for h in terms of r by rearranging the equation for volume:
h = V/(πr²)
Substituting this expression for h into the equation for surface area, we get:
A = 2πr² + 2πr(V/(πr²))
A = 2πr² + 2V/r
To minimize A, we differentiate with respect to r:
dA/dr = 4πr - 2V/r²
Setting this expression equal to zero and solving for r, we get:
4πr = 2V/r²
r³ = V/(2π)
Substituting the given value for V, we get:
r³ = 432/2π
r ≈ 4.38 cm
Now we can use the expression for h in terms of r to find the corresponding height:
h = V/(πr²) ≈ 3.11 cm
Therefore, the dimensions of the can that use the least amount of material are a radius of approximately 4.38 cm and a height of approximately 3.11 cm.
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A scientist has three small jars of chemicals to use for an experiment jar one has a mass of 0.62 g jar to has a mass of 1.431 g jar three has a mass of 0.5 g what is the total mass of jars in grams complete the chart Each box
According to the question we can conclude that the total mass of the jars is 2.561 g.
Explain law of mass conversion?The mass is the amount of matter in an object. It is measured in grams, kg, ect. According to the law of conservation, mass in such an isolated system may only be changed through one form to another and cannot be created or destroyed.
To find the total mass of the jars, we simply need to add up the masses of jar one, jar two, and jar three:
Total mass of jars = mass of jar one + mass of jar two + mass of jar three
Total mass of jars = 0.62 g + 1.431 g + 0.5 g
Total mass of jars = 2.561 g
So the total mass of the jars is 2.561 g.
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Circumference=14.4
Area =?
Answer:
[tex]a = \frac{1296}{5\pi} [/tex]
Step-by-step explanation:
Given:
C = 14,4 (circumference)
Find: A - ? (area)
Let's start by writing down both circumference and area formulas:
[tex]c = 2\pi \times r[/tex]
[tex]a = \pi \times {r}^{2} [/tex]
We can find the radius (r) from the 1st formula:
[tex]r = \frac{c}{2\pi} = \frac{14.4}{2\pi} =14 \frac{4}{10} \times \frac{1}{2\pi} = \frac{144}{10} \times \frac{1}{2\pi} = \frac{144}{20\pi} = \frac{36}{5\pi} [/tex]
Now, that we know the length of the radius, we can find the area:
[tex]a = \pi \times( { \frac{36}{5\pi} })^{2} = \frac{1296}{25 {\pi}^{2} } \times \frac{\pi}{1} = \frac{1296}{25\pi} [/tex]
In analyzing hits by certain bombs in a war, an area was partitioned into 561 regions, each with an area of 0.75 km2. A total of 525 bombs hit the combined area of 561 regions. Assume that we want to find the probability that a randomly selected region had exactly four hits. In applying the Poisson probability distribution formula, P(x)=
μx•e−μ
x!, identify the values of μ, x, and e. Also, briefly describe what each of those symbols represents.
Answer:
x is the number of successes
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
There is a 17.18% probability that a randomly selected region had exactly two hits.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]
In which
x is the number of successes
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
In this problem we have that:
A total of 525 bombs hit the combined area of 561 regions. So the mean hits per region is:
[tex]P=\dfrac{525}{561}=0.9358[/tex]
Assume that we want to find the probability that a randomly selected region had exactly two hits.
This is P(X = 2).
[tex]P(X=x)=\dfrac{e^{-\mu}\times\mu^x}{(x)!}[/tex]
[tex]P(X=2)=\dfrac{e^{-0.9358}\times(0.9358)^2}{(2)!}=0.1718[/tex]
There is a 17.18% probability that a randomly selected region had exactly two hits.
a card is drawn at random from an ordinary deck of 52 playing cards. find the probability that it is (a) an ace, (b) a jack of hearts, (c) a three of clubs or a six of diamonds, (d) a heart, (e) any suit except hearts, (f) a ten or a spade, (a) neither a four nor a club.
The probability that a card drawn at random from an ordinary deck of 52 playing cards is: (a) An ace is 1/13. (b) A jack of hearts is 1/52. (c) A three of clubs or a six of diamonds is 1/26. (d) A heart is 1/4. (e) Any suit except hearts is 3/4. (f) A ten or a spade is 4/13. (g) Neither a four nor a club is 10/13.
We will find the probability of the given situations.
a) An aceThere are 4 aces in the deck.
Therefore, the probability of drawing an ace is given by
P(Ace) = 4/52 = 1/13
b) A jack of hearts
There is only one jack of hearts in the deck.
Therefore, the probability of drawing a jack of hearts is given by
P(Jack of hearts) = 1/52
c) A three of clubs or a six of diamonds
There is one three of clubs and one six of diamonds in the deck.
Therefore, the probability of drawing a three of clubs or a six of diamonds is given by
P(Three of clubs or six of diamonds) = 2/52 = 1/26
d) A heart
There are 13 hearts in the deck.
Therefore, the probability of drawing a heart is given by
P(Heart) = 13/52 = 1/4
e) Any suit except hearts
There are 39 cards that are not hearts in the deck.
Therefore, the probability of drawing any suit except hearts is given by
P(Any suit except hearts) = 39/52 = 3/4
f) A ten or a spade
There are 16 cards that are either tens or spades.
Therefore, the probability of drawing a ten or a spade is given by
P(Ten or spade) = 16/52 = 4/13
g) Neither a four nor a club
There are 12 cards that are either fours or clubs.
Therefore, the probability of drawing neither a four nor a club is given by
P(Neither four nor club) = 40/52 = 10/13
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The tables represent the points earned in each game for a season by two football teams. Saints
21 12 3
3 10 10
14 3 12
28 40 10
17 20 7
Cowboys
10 3 8
6 24 12
21 3 10
28 28 7
7 13 3
Which team had the best overall record for the season? Determine the best measure of center to compare and explain your answer. Cowboys; they have a larger median value of 10 points
Saints; they have a larger median value of 12 points
Cowboys; they have a larger mean value of about 12. 2 points
Saints; they have a larger mean value of about 14 points
The Saints had the best overall record for the season because they had a larger mean value of about 200 points, whereas the Saints had a larger median value of 12 points.
To determine which team had the best overall record for the season, we need to consider the total number of points earned by each team across all games. We can calculate the total points for each team by adding up the points earned in each game.
For the Saints:
Total points = 21+12+3+3+10+10+14+3+12+28+40+10+17+20+7 = 200
For the Cowboys:
Total points = 10+3+8+6+24+12+21+3+10+28+28+7+7+13+3 = 183
Therefore, the Saints earned a total of 200 points, while the Cowboys earned a total of 183 points. Therefore, the Saints had the better overall record for the season.
To compare the central tendency of the points earned by each team, we can use either the mean or the median. However, in this case, the median is a better measure of center because it is less sensitive to extreme values than the mean.
Calculating the median for each team:
For the Saints:
Arrange the points earned in ascending order: 3 3 7 10 10 12 12 14 17 20 21 28 40
The median value is the middle value, which is 12.
For the Cowboys:
Arrange the points earned in ascending order: 3 3 6 7 8 10 10 12 13 21 24 28
The median value is the middle value, which is 10.
Therefore, the Cowboys have a median value of 10 points, while the Saints have a median value of 12 points. However, as we already determined, the Saints had a better overall record for the season based on the total points earned.
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