To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. So:
(0.4x10^-6)(0.7x10^-2) = (0.4)(0.7)x10^(-6-2) = 0.28x10^-8
Therefore, the answer is 0.28 x 10^−8 in scientific notation.
what is 59.58333333 rounded off to the nearest ten?
Given:
The number rounded to the nearest tenth is 59.6.
To find:
The approximate value of the given number to the nearest tenth.
Solution:
The required values shown in the below table:
Number Nearest tenth
59.58333333 59.6
What is the surface area of this right triangular prism?
Enter your answer in the box.
in²
Surface area of this right triangular prism=96in²
Define right triangular prismA right triangular prism is a three-dimensional geometric shape that has two parallel triangular bases and three rectangular faces that connect the bases. The triangular bases of a right triangular prism are always perpendicular to its rectangular faces. The prism is called "right" because the rectangular faces meet the bases at right angles, meaning the edges connecting the triangular and rectangular faces form right angles.
In the given right triangular prism
S₁=5in
S₂=5in
S₃=8in
l=4in
b=8in
h=3in
Total surface area of this right triangular prism = (S₁+S₂+S₃)l+(b×h)
=(5+5+8)×4+8×3
=96
Hence, surface area of this right triangular prism=96in².
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a cross-country course is in the shape of a parallelogram with a base of length 7 mi and a side of length 6 mi. what is the total length of the cross-country course?
The total length of the parallelogram-shaped cross-country course is equal to 26 miles.
We can calculate the total length of the cross-country course using the formula for the perimeter of a parallelogram, which is twice the sum of the lengths of its adjacent sides. In this case, the adjacent sides are the base of length 7 mi and the side of length 6 mi.
So, we can find the total length by first finding the sum of these two sides:
7 mi + 6 mi = 13 mi
Then, we can multiply this sum by 2 to get the total length:
2 x 13 mi = 26 mi
Therefore, the total length of the cross-country course is 26 miles.
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Anyone help on this problem will be much appreciated! The population of a culture of the bacterium Pseudomonas aeruginosa is given by p(t) = -1698t^2 + 85,000t + 10,000 where t is the time in hours since the culture was started.
a. The time at which the population is at a maximum is 25 hours. b. The maximum population is 1,182,500.
What is quadratic function?A polynomial function of degree 2 is a quadratic function, while one of degree 1 is a linear function. The formula for a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants and an is not equal to 0. A parabola, a U-shaped curve, is the graph of a quadratic function. Depending on the sign of the leading coefficient, the function's minimum or maximum value is located at the parabola's vertex.
a) The highest value of the population function, which is a quadratic function with a negative leading coefficient, occurs near the parabola's vertex.
Thus, t = -b/2a.
Substituting the values a = -1698, b = 85,000, and c = 10,000 we have:
t = -85000 / 2(-1698) = 25
Therefore, the time at which the population is at a maximum is 25 hours.
b) To determine the maximum population we substitute the value of t = 25.
p(25) = -1698(25)² + 85,000(25) + 10,000 = 1,182,500
Therefore, the maximum population is 1,182,500.
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The remainders obtained when px³ + qx² + 4x − 2 is divided by x-1 and x + 2 are
equal. Show that 3p - q = -4. If also the remainder is -18 when the polynomial is
divided by x-2, find the value of p and of q.
Our first equation yields p = 0. We obtain q = 3p = 0 by substituting this in the second equation. Hence, p = q = 0. As a result, the values of p and q are both zero.
what is polynomial ?A polynomial is a mathematical equation composed of variables and coefficients that is solved using mathematical operations like combination, deletion, multiplication, and quel integer exponents.
given
The result of dividing the same polynomial by x + 2 is
(p[tex]x^{2}[/tex] + (2p-q)x + (5q-2))(x+2) + (q[tex]x^{3}[/tex] + q[tex]x^{2}[/tex]+ 4[tex]x^{2}[/tex]) (12p-9q-2)
p+2q-2 = 12p-9q-2
When we simplify this equation, we obtain:
11p + 2q = 0
=> 3p - q = -4 (by adding 22p to both sides and multiplying both sides by 2)
Now, we also understand that the polynomial, when divided by x – 2, leaves a remainder of -18. Synthetic division or polynomial long division yields the following results:
= (p (x-2)³ + (7p-2q)(x-2) (x-2)² + (18q-8p)(x-2)) - 18
When we compare coefficients, we find:
p = 7p - 2q = 18q - 8p = 0
Our first equation yields p = 0. We obtain q = 3p = 0 by substituting this in the second equation. Hence, p = q = 0. As a result, the values of p and q are both zero.
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what is the equation of a rational function that has a x-intercept at (6,0), vertical asymptote at x=-3, and horizontal asymptote at y=-1
[tex]f(x) = (2/3)(x - 6)/(x + 3)[/tex]
m22 = 97°
m
3
2
4
10
9
11 12
m26 = 83°
5
7
n
13 14
15 16
8
9
→→S
Find measure of angle 14. (Just enter the number, no symbols)
A
Answer:
The measure of angle 14 is 83°.
Step-by-step explanation:
Angles 6 and 14 are congruent so if angle 6 is 83° so is angle 14.
how do you multiply 7(b-5)(b-4) step by step
To multiply 7(b-5)(b-4), you can follow these steps:
1.
Start by distributing the 7 to the terms inside the parentheses:
7(b-5)(b-4) = 7 * b * (b-4) - 7 * 5 * (b-4)
2.
Simplify each term using the distributive property:
= 7b^2 - 28b - 35b + 140
3.
Combine like terms:
= 7b^2 - 63b + 140
So, the final answer is 7b^2 - 63b + 140.
a box next to the register at tacos and stuff, where cooper works, is filled with different-flavored sauce packets. when a customer asks for some spicy sauce packets, cooper reaches into the box and pulls out a large handful of packets, looking for the spicy ones. here are the flavors he pulls out: mild, mild, spicy, medium, spicy, mild, spicy, super-hot, mild, spicy, super-hot, mild, mild based on the data, what is the probability that the next packet cooper pulls out of the box will be spicy?
Based on the given data, there are a total of 13 packets and 5 of them are spicy. Therefore, the probability that the next packet Cooper pulls out of the box will be spicy is 5/13 or approximately 0.385 (rounded to three decimal places).
To calculate the probability of the next packet being spicy, we need to know how many packets of each flavor are in the box. Assuming that Cooper doesn't put back the packets he has pulled out, we can count the number of spicy packets and divide it by the total number of packets he pulled out.
In this case, out of the 13 packets he pulled out, 5 were spicy. Therefore, the probability of the next packet being spicy is 5/13, or approximately 0.38, or 38%. However, if the box is refilled with packets of different flavors, this probability may not hold.
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Answer: 4/13
Step-by-step explanation: i did this IXL and this was the correct answer
what is the mean of 41,52,56,65,65,76,89
the mean of 41, 52, 56, 65, 65, 76, and 89 is 63.43.
Step-by-step explanation:
The mean of the value is 63.43i need help with this question?
Answer:
D. [tex]\sqrt{3}[/tex] ; 2
Hope this helps!
Step-by-step explanation:
Last night the temperature on a thermometer was −4°F. The temperature this morning was colder than last night. Which could represent the temperature on the thermometer this morning?
Select all the correct answers.
Answer:
-5, -12
Step-by-step explanation:
We just have to find somthing colder than -4f so it has to be less than -4 so it would be -5 and -12.
The correct answers to your question would be -5 and - 15.
4. Given the following: X(7, 0), Y(7, 5) and Z(0, 5), calculate the distance or
length of XY, YZ, and XZ. What is the perimeter of the triangle?
a. 6.8 units
b. 11.3 units
c. 15.8 units
d. 20.6 units
Answer:
To calculate the distance or length of XY, YZ, and XZ, we can use the distance formula: Distance = √[(x2 - x1)^2 + (y2 - y1)^2] For XY: Distance = √[(7 - 7)^2 + (5 - 0)^2] Distance = √[0 + 25] Distance = √25 Distance = 5 units For YZ: Distance = √[(0 - 7)^2 + (5 - 5)^2] Distance = √[49 + 0] Distance = √49 Distance = 7 units For XZ: Distance = √[(0 - 7)^2 + (5 - 0)^2] Distance = √[49 + 25] Distance = √74 Therefore, the length
ہے
A
Find the value of AB.
13
DE
E
12
AB= [?]
B
AB thus has a 12 unit length as the triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length.
what is triangle ?A closed triangle is a two-dimensional geometric shape having three straight edges and three angles. The shorter of a triangle's two sides is known as the hypotenuse, while its long sides are known as the triangle's legs. The longest side's opposing angle is referred to as the greatest or "opposite" angle in triangles. Angles are given names based on where they are in relation to the sides. An essential component of geometry is the study of triangles, and there are numerous varieties with distinctive characteristics. An equilateral triangle, on the other hand, has three equal edges and 3 equal angles that are each 60 degrees in length. A right triangle, for instance, has one angle that is 90 degrees in length.
given
The Pythagorean theorem can be used to determine the length of AB.
We can see from the diagram that triangle ADE is a right triangle with hypotenuse AE and legs measuring 12 and 5 (DE - AE = AD = 13 - 8 = 5). Well, here we are:
[tex]AD^2 + DE^2 = AE^2\\AE^2 = 5^2 + 12^2\\AE^2 = 169[/tex]
AE = 13
In a similar way, we can observe that triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length. Well, here we are:
AB2 = 169 - 25 when AE2 = AB2 + BE2 132 = AB2 + 5
AB^2 = 144
AB = 12
AB thus has a 12 unit length as the triangle ABE is a right triangle with hypotenuse AE and legs AB and 5 in length.
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PLEASE HELP ILL GIVE BRAINLIEST
Answer: 1 and 5
Step-by-step explanation:
Problems 13 & 14. Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar. If the triangles are similar, write a valid similarity statement.
The triangles ABE and CED are similar in figure 1 by SAS similarity criteria whereas in figure 2 the triangles PST and RPQ are not similar.
What is similar triangle?The triangles are similar if all angles in one triangle are congruent to corresponding angles in other triangle and sides are proportional. There are different criterias for similarity of triangles namely SSS, SAS, ASA/AAS and RHS. According to the criteria/rule
SSS(SIDE-SIDE-SIDE):triangles are similar, if all three sides of one triangle are proportional to the three sides of another triangle.
SAS(SIDE-ANGLE-SIDE):The b are similar if two sides are proportional and an angle included is congruent to two sides and included angle of another triangle.
ASA(ANGLE-SIDE-ANGLE):The triangles are similar if two angles are equal and an side between the angles is proportional to the two angles and side between the angles of another triangle.
Q13) Consider ΔABE and ΔCED ,
∠AEB = ∠CED = 90°
and,
AE=21 units ;BE= 26+16=42 units
CE=16 units ; ED=32 units
and
∴ Sides are proportional
Hence ΔABE is similar to ΔCDE by SAS criteria.
Q14)Consider triangles ΔPQR and ΔPST,
Given that ∠QPT=42°, and PR bisects ∠QPT
∴∠QPR=∠RPT=21°
Given that ∠PTS=102°,
In ΔPST, by angle sum property of triangle:
∠SPT+∠PTS+∠TSP=180°
21 + 102 + ∠TSP=180°
∠TSP=180° - 102 -21
∠TSP=57°
Given that ∠PRQ=58°
In ΔPRQ, by angle sum property of triangle:
∠RPQ+∠QRP+∠PQR=180°
21 + 58 + ∠PQR=180°
∠PQR=180°- 58 - 21
∠PQR=101°
In ΔPRQ the three angles are 21°,101° and 58° whereas in ΔPST the three angles are 21°,102° and 57°. As the angles are not congruent, the triangles are not similar.
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If we are given an acute ∠A, side a, and side b, and the height of the triangle is h = bsin A, state the criteria needed for the following to happen:
No triangles when...
One triangle when... (2 answers)
Two triangles when...
What is triangle?
A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.
The given information is an acute angle ∠A, and sides a and b, along with the height of the triangle h = b sin A. The criteria for the number of possible triangles that can be formed are as follows:
No triangles can be formed if the length of side a is less than or equal to the length of the height h. That is, if a ≤ h, then no triangle can be formed. This is because the height is the perpendicular distance from the vertex of the angle to the opposite side, and it is necessary for the opposite side to be longer than the height in order for a triangle to exist.One triangle can be formed if the length of side a is greater than the length of the height h. That is, if a > h, then one triangle can be formed. In this case, the triangle is unique, since the other two sides and the angle are fixed.Two triangles can be formed if the length of side a is greater than the length of the height h, and if sin A is less than or equal to a/b. That is, if a > h and sin A ≤ a/b, then two triangles can be formed. In this case, the angle and the two sides adjacent to the angle are fixed, but the length of the opposite side can vary, which leads to the possibility of two triangles with different lengths for the opposite side.Learn more about triangles on:
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Travis has the following books on his shelf: 6 myster, 5 science, 4 history, and 3 adventure. Travis will randomly choose 1 book to read. What is the probability (in fraction form) that he will choose a mystery book?
Answer: The probability that Travis will choose a mystery book is 1/3.
Step-by-step explanation: To find the probability that Travis will choose a mystery book, we need to determine the ratio of the number of mystery books to the total number of books on Travis's shelf.
Travis has 6 mystery books, and the total number of books on his shelf is 6 + 5 + 4 + 3 = 18.
Therefore, the probability (in fraction form) that Travis will choose a mystery book is 6/18.
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 6.
6 ÷ 6 = 1
18 ÷ 6 = 3
So, the simplified fraction is 1/3.
Write an equation tomorrow, the statement, the product of -8 and (y+3) is 32. How you can use the equation to reason about the value of Y?
The equation to model the statement is [tex]-8(y + 3) = 32[/tex] and the value of y is -7.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given statement is the product of – 8 and [tex](y + 3)[/tex] is 32.
Product means the operation is multiplication.
So the equation can be written as,
[tex]-8 (y + 3) = 32[/tex]
Dividing both sides by 8,
[tex]-(y + 3) = 4[/tex]
[tex]y + 3 = -4[/tex]
[tex]y = -4 - 3 = -7[/tex]
Hence the value of y is -7.
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what rationale is correct for the nusre to empty a hemovac woudn suction device when it is half full
A nurse should empty a Hemovac wound suction device when it is half full to ensure proper functioning and prevent discomfort or injury to the patient due to the device becoming too heavy.
The rationale for a nurse to empty a Hemovac wound suction device when it is half full is to ensure the device is functioning correctly and to prevent it from becoming too heavy and potentially causing discomfort or injury to the patient.
When a Hemovac wound suction device is half full, it may start to lose suction, which can result in less efficient drainage of fluid from the wound site. By emptying the device, the nurse can ensure that the device is functioning correctly and that the suction pressure is maintained.
Additionally, allowing the device to become too full can make it heavy and uncomfortable for the patient, potentially causing discomfort or injury to the wound site. Therefore, emptying the device when it is half full can help prevent these complications and ensure that the patient remains comfortable throughout the healing process.
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!!PLEASE HELPPP!! CHECK IF IM RIGHTTT
Answer:
You are correct
Step-by-step explanation:
PLEASE HELP will give brainliest
The value of f(11) for the recursive rule and an explicit rule is 149.
What is arithmetic sequence?An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a fixed amount (referred to as the common difference). The nth term is often indicated by an, while the first term of the series is typically marked by a1. The following formula is used to determine the nth term in an arithmetic sequence:
a = a1 + (n-1)d
where d is the common distinction. In mathematics and other disciplines, arithmetic sequences are frequently employed to represent circumstances in which the pace or degree of change remains constant.
The recursive and explicit rule for the arithmetic sequence is given as:
an = a1 + (n-1)d
From the given graph f(1) = 19 and common difference = 32 - 19 = 13
The recursive rule is:
f(n) = f(n-1) + 13
The explicit rule is:
f(n) = 19 + 13(n-1)
Now, f(11) is calculated as:
f(11) = 19 + 13(11-1) = 19 + 130 = 149
Hence, the value of f(11) for the recursive rule and an explicit rule is 149.
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(In a survey of 200 people, the ratio of people who were infected by covid-19 delta variant to omicron variant was 5: 3. The number of people who were infected by both variant was half of those who were infected by only omicron variant. If 60 people were infected by neither of the both variant then find the number of people who were infected by only one variant and show the result in a Venn-diagram.)
Step-by-step explanation:
The given attachments are the steps to getting the answer...
PLEASE HELP!!
Tone Sherburn bought a home with a 10.5% adjustable rate mortgage for 30 years. He paid $9.99 monthly per thousand on his original loan. At the end of 5 years he owes the bank $55,000. Now that interest rates have gone up to 12.5%, the bank will renew the mortgage at this rate or Tone can pay $55,000. Tone decides to renew and will now pay $10.68 monthly per thousand on his loan.
What is the amount of the old monthly payment? What is the percent of increase in his new monthly payment? You can ignore the small amount of principal that has been paid.
old monthly payment = $
new monthly payment = $
% increase
Tone's new monthly payment is 16.16% higher than his old monthly payment To solve the problem, we need to use the formula for the monthly payment of a mortgage loan:
monthly payment = (loan amount x monthly interest rate) / (1 - (1 + monthly interest rate)^(-n))
where:
loan amount = the amount of the loan
monthly interest rate = the annual interest rate divided by 12
n = the total number of payments (in months)
Let's first find the loan amount at the beginning of the mortgage. We know that Tone paid $9.99 per thousand, so we can set up a proportion:
$9.99 / 1000 = monthly payment / loan amount
Solving for the loan amount, we get:
loan amount = monthly payment / ($9.99 / 1000) = $1000 * (monthly payment / $9.99)
Substituting the given values, we get:
loan amount = $1000 * (monthly payment / $9.99) = $55,000
This means that Tone borrowed $55,000 at the beginning of the mortgage.
Now, let's find the old monthly payment. We know that Tone had a 10.5% adjustable rate mortgage for 30 years, which means he made 12 x 30 = 360 monthly payments. We can use the formula above to solve for the monthly payment:
monthly interest rate = 10.5% / 12 = 0.00875
n = 360
monthly payment = ($[tex]55,000 x 0.00875) / (1 - (1 + 0.00875)^(-360)[/tex]) = $512.47
Therefore, Tone's old monthly payment was $512.47.
Next, let's find the new monthly payment. We know that Tone will renew his mortgage at 12.5% interest rate, which means the new monthly interest rate is:
monthly interest rate = 12.5% / 12 = 0.01042
We also know that Tone will pay $10.68 per thousand, so we can set up a new proportion:
$10.68 / 1000 = new monthly payment / loan amount
Solving for the new monthly payment, we get:
new monthly payment = $10.68 / ($1000 / $55,000) = $595.40
Therefore, Tone's new monthly payment is $595.40.
Finally, let's find the percent increase in the new monthly payment compared to the old monthly payment. We can use the percent change formula:
percent increase = ((new value - old value) / old value) x 100%
Substituting the given values, we get:
percent increase = (($595.40 - $512.47) / $512.47) x 100% = 16.16%
Therefore, Tone's new monthly payment is 16.16% higher than his old monthly payment
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Find the volume of the solid generated when the semicircle below is rotated about its diameter RST. Round your answer to the nearest tenth if necessary.
The volume of the solid generated by the revolution is 33.5 cubic units.
It is given that, the diameter of the semi-circle is 4 and it is rotated to one full rotation around its diameter.
A solid generated when a semicircle is being rotated about its diameter is called a "SPHERE".
Therefore, the volume of the solid generated by the revolution is the volume of the sphere.
The formula for the volume of the sphere is given by,
Volume of sphere = (4/3)πr³
where r is the radius and π has the default value of 3.14
Here, the given diameter is 4.
To find the radius = diameter/2
radius = 4/2 = 2.
Now, to calculate the volume of the sphere substitute r=2 and π=3.14
volume of the sphere = (4/3)×3.14×2³
⇒ (4/3)×3.14×8
⇒ 100.48 / 3
⇒ 33.49 (approximately 33.5)
Therefore, the volume of the solid generated by the revolution is 33.5 cubic units.
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Question 3
A circular garden has
Round to the nearest
a circumference of 39.25 feet. Find the approximate diameter of the garden. Use 3.14 for T.
hundredth if necessary.
ft
Answer:
Sure! To find the diameter of the garden, we can use the formula: circumference = π x diameter Given that the circumference of the garden is 39.25 feet and π is approximately 3.14, we can plug in the values and solve for diameter: 39.25 = 3.14 x diameter diameter = 39.25 ÷ 3.14 diameter ≈ 12.5 feet (rounded to the nearest hundredth) Therefore, the approximate diameter of the garden is 12.5 feet.
eight people are sitting around a circular table, each holding a fair coin. all eight people flip their coins and those who flip heads stand while those who flip tails remain seated. what is the probability that no two adjacent people will stand? (2015amc10a problem 22 or 2015amc12a problem 17) (a) 47 256 (b) 3 16 (c) 49 256 (d) 25 128 (e) 51 256
The probability that no two adjacent people would stand is option C: 49/256, as there are 256 distinct counting rotations.
First, we assume that one person stands up. There are 8 possible ways to select which person does. We can, next, assume that no two adjacent people stand up. There are 4 ways to choose which of the remaining 7 people will stand up (since no two adjacent people can stand up).
Then, we can assume that no two adjacent people stand up again. There are 3 ways to choose which of the remaining 6 people will stand up (since no two adjacent people can stand up).
We continue this process until there is only one person left who can stand up.
The number of arrangements according to the number of people standing.
0 people standing = 1 arrangement.1 people standing = ₈C₁ = 8! / 1!7! = 8 arrangements.2 people standing = ₈C₂ = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements. 3 people standing = ₈C₃ = 56 arrangements. In this case, three people standing are next to each other = ₈C₁ = 8 arrangements. Two people standing are next to each other and the third person is not = ₈C₁ × ₄C₁ = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.4 people standing but no two adjacent people = 2 arrangements. Other than these, 5 people standing and 6 people standing would have one arrangement each.Therefore, the number of arrangements that no two adjacent people will stand.
n(S) = 1 + 8 + 20 + 16 + 2 + 2 = 49
The total number of possible outcomes is:
2⁸ = 256
So, the probability that no two adjacent people will stand would be:
= 49/256.
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Complete question is:
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?
(a) 47/256
(b) 3/16
(c) 49/256
(d) 25//128
(e) 51/256
find the value of g(7). g(x)=7/8x- 1/2
Answer:
Sure, I can help you with that! To find the value of g(7), we simply need to substitute x=7 into the expression for g(x): g(7) = (7/8)*7 - 1/2 g(7) = 49/8 - 1/2 g(7) = 95/8 Therefore, g(7) = 95/8.
0 / 350
Answer:
9. The weights, in pounds, of five pumpkins from a pumpkin patch are 17, 18, 17, 15, and 13.
What is the MAD of the weights?
Step-by-step explanation:
9. The weights, in pounds, of five pumpkins from a pumpkin patch are 17, 18, 17, 15, and 13.
What is the MAD of the weights?
what is the coefficent of x term
5xsquare plus 3x-2=
x/3=
Answer:
To solve this equation for the coefficient of the x term, we need to first simplify the equation by solving for x. 5x^2 + 3x - 2 = x/3 Multiplying both sides by 3 to eliminate the fraction, we get: 15x^2 + 9x - 6 = x Bringing all terms to one side: 15x^2 + 8x - 6 = 0 Now, we can use the quadratic formula to solve for x: x = [-b ± √(b^2 - 4ac)] / 2a where a = 15, b = 8, and c = -6 x = [-8 ± √(8^2 - 4(15)(-6))] / 2(15) x = [-8 ±
a semiconductor manufacturer recently found that 3% of the chips produced at its new plant are defective. assume that the chips are independently defective or non defective. use a normal approximation to determine the probability that a box of 500 chips contains: (a) at least 10 defective chips (b) between 15 and 20 (inclusive) defective chips.
(a) The probability of having at least 10 defective chips is approximately 0.9131. (b) The probability of having between 15 and 20 defective chips is approximately 0.4135.
First, we need to find the mean (μ) and standard deviation (σ) for the binomial distribution.
μ = np = 500 * 0.03 = 15
σ = sqrt(np(1-p)) = sqrt(15*0.97) ≈ 3.66
(a) To find the probability of at least 10 defective chips, we'll calculate the Z-score and use a Z-table:
Z = (X - μ) / σ = (10 - 15) / 3.66 ≈ -1.36
P(X ≥ 10) = 1 - P(X ≤ 10) = 1 - 0.0869 = 0.9131
So, the probability of having at least 10 defective chips is approximately 0.9131
(b) To find the probability of between 15 and 20 defective chips (inclusive), we'll calculate the Z-scores and use a Z-table:
Z1 = (15 - 15) / 3.66 ≈ 0
Z2 = (20 - 15) / 3.66 ≈ 1.36
P(15 ≤ X ≤ 20) = P(Z1 ≤ Z ≤ Z2) = P(0 ≤ Z ≤ 1.36) = 0.4135
So, the probability of having between 15 and 20 defective chips is approximately 0.4135.
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