Final answer:
The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. The formula represents the rise over run between these points.
Explanation:
We can use a specific formula to calculate the slope of a line using two points on that line. The slope is found by taking the difference in the y-value (also known as the rise) and dividing it by the difference in x-value (also known as the run). In mathematical terms, if we have two points (x1,y1) and (x2,y2), the formula for slope (m) is as follows:
m = (y2 - y1) / (x2 - x1)
Therefore, between two given points, you subtract the y-value of the starting point from the y-value of the end point to find the rise, and then remove the x-value of the starting point from the x-value of the end point to determine the run. The slope is then the quotient of these two differences.
The quality control manager of a peanut butter manufacturing plant want to ensure the quality of the peanut butter in the jars coming down the assembly line.describe a representative sampling method she could use?
Final answer:
The quality control manager can use a representative sampling method to test jars of peanut butter for quality, with tests such as total plate count and adherence to quality control protocols and good measurement practices for reliable results.
Explanation:
A quality control manager at a peanut butter manufacturing plant can ensure the quality of peanut butter jars using a representative sampling method. This involves selecting jars at regular intervals from the assembly line, and then conducting tests such as total plate count to measure potential bacterial contamination. For accurate quality control, the process should follow good measurement practices and a standardized quality control protocol that includes recording and analyzing the data and evaluating any deviations from set specifications.
The personnel responsible can reject any sample or batch that does not meet the required standards. For continuous quality assurance, statistical process control methods like mean, standard deviation, and coefficient of variation can be utilized to monitor ongoing production. Furthermore, post-production specifications will determine whether to release or reject the final product. Appropriate documentation and adherence to standard operations procedures (SOPs) are crucial throughout the process, maintaining a systematic approach to product quality.
Jonathan bought a new computer for $1,716, using the electronics store's finance plan. He will pay $143 a month for 12 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?
Answer:
y = 1716 -143x
Step-by-step explanation:
You want an equation for the amount owed after x months on a purchase of $1716 paid at the rate of $143 per month.
PaidAfter x months, the amount paid will be 143·x. The amount owed is the difference between the original purchase price and the amount paid:
owed = $1716 - paid
y = 1716 -143x . . . . . . . . . the amount Jonathan still owes after x months
The Hamden board of education wants to know how the community feels about building a new media center for the middle school. They called every tenth person on the registration list of 7,300 voters until they had called a total of 40 voters. Which of the following are true of the sample of 40 voters? Check all that apply.
The sample is not randomly chosen.
The sample should be larger to give more reliable information.
The sample size is too large to make inferences.
The sample size is too small to represent the population.
The sample size is too small and will show larger variation.
The sample is invalid because it randomly chooses voters.
The sample size is too small and can lead to false inferences.
The sampling method used by the Hamden board of education was systematic, not random, and the sample size of 40 voters out of a population of 7,300 is too small to produce reliable conclusions regarding the community's opinion about building a new media center.
Explanation:The quality of conclusions drawn from opinion polls largely depends on the methods used to choose a sample and the sample size. When the Hamden board of education sampled every tenth person from the registration list of 7,300 voters to reach 40 voters, they applied a systematic sampling method, as opposed to a truly random sample. While systematic sampling can be used as an approximation of random sampling, this method still poses a risk of introducing bias if there are hidden patterns in the voter registration list.
The sample size is indeed critical for the reliability of the poll. In this case, surveying only 40 voters out of 7,300 is too small to capture the diverse opinions of the entire voter population, which may lead to false inferences and less confidence in the results. For public opinion polls, especially on matters like building a new media center, a larger sample would provide more reliable information and reduce the potential variation that can arise from a smaller sample. Industry standards suggest varying sizes that can balance the accuracy and cost-effectiveness, often ranging from 500 to 2,500 respondents or more depending on the desired level of accuracy.
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Consider isosceles ΔXYZ.
What is the value of n?
What is the measure of leg XY?
ft
What is the measure of leg XZ?
ft
1) An Isosceles triangle has three sides, in which two sides are of the same length and the third has a different length. It has two angles of the same value and a third angle with a different value, as well.
In the figure is shown that angles Y and Z are the same, then the sides of this angles must be of the same length. This means that:
XY=XZ
(9n+12)ft=(15n-6)ft
From this equation we have to find n:
9n-15n=-6-12
-6n=-18
[tex]n=\frac{-18}{-6}[/tex]
n=3
2) The measure of the leg XY in ft
XY=(9n+12)ft
Substitute the value of n calculated in the first question:
XY=(9(3)+12)ft
XY=39 ft
3) The measure of the leg XZ in ft
XZ=(15n-6)ft
Substitute the value of n calculated in the first question:
XZ=(15(3)-6)ft
XZ=39ft
A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.
a) the value of n is 3 units.b) the measure of leg XY is 39 feet.c)the measure of leg XZ is 39 feet.What is isosceles triangle?A triangle is isosceles triangle when the two sides and two angle of the triangle in equal in measure.
Given information-
The length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).
The length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).
The measure of angle,
[tex]m\angle Y=m\angle Z[/tex]
a) the value of n-For the isosceles triangle, the two sides and two angle of the equal in measure.
As the measure of angle,
[tex]m\angle Y=m\angle Z[/tex]
Thus the opposite side of this angles must be equal. Thus,
[tex]XY=XZ[/tex]
Put the values as,
[tex]9n+12=15n-6\\15n-9n=12+6\\6n=18\\n=3[/tex]
Hence the value of n is 3 units.
b) the measure of leg XYThe length of the side [tex]XY[/tex] is ([tex]9n+12[/tex]).
Put the value of n,
[tex]XY=9n+12\\XY=9\times3+12\\XY=27+12\\XY=39 \rm ft[/tex]
Hence the measure of leg XY is 39 feet.
c) the measure of leg XZThe length of the side [tex]XZ[/tex] is ([tex]15n-6[/tex]).
Put the value of n,
[tex]XZ=15n-6\\XZ=15\times3-6\\XZ=39\rm ft[/tex]
Hence the measure of leg XZ is 39 feet.
a) the value of n is 3 units.b) the measure of leg XY is 39 feet.c)the measure of leg XZ is 39 feet.Learn more about the isosceles triangle here;
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Algebra 2 help?
5. A construction explosion has an intensity I of 1.25 x 10–4 W/m2. Find the loudness of the sound in decibels if W/m2. Round to the nearest tenth. (1 point)
81 decibels
161 decibels
82.2 decibels
12.5 decibels
The example question in the textbook is totally different so I'm not sure how to do this. I tried to make the equation and then got confused. An explanation would be great! Thanks
Answer:
1. B) logb(q^2t^8)
2. D) None of these (it is actually log (x^4/(x+2)^6) :D)
3. B) log5(7)+5log5(a)
4. C) 6.209
5. A) 81 decibels
Step-by-step explanation:
trust me bro
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Find the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
Answer:
The length of the hypotenuse of the isosceles right triangle with leg of length unit is:
√2 units.
Step-by-step explanation:
Let a and b denote the leg of a right triangle and c denote the hypotenuse of the right triangle.
Now we apply the Pythagorean Theorem as:
[tex]c^2=a^2+b^2[/tex]
Now as triangle is isosceles.
Hence, a=b=1 unit
[tex]c^2=1^2+1^2\\\\c^2=2\\\\c=\sqrt{2}[/tex]
Hence, the length of the hypotenuse is:
√2 units.
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25 POINTS to answer question!
The Thrill amusement park charges an entry fee of $40 and an additional $5 per ride, x. The Splash water park charges an entry fee of $60 and an additional $3 per ride, x. Based on this information, which system of equations could be used to determine the solution where the cost per ride of the two amusement parks, y, is the same?
The costs per ride for Thrill and Splash amusement parks can be represented by the equations y = 40 + 5x and y = 60 + 3x respectively. Equating these will give us the number of rides where the costs at both parks will be the same.
Explanation:The cost of visiting each park can be represented as a linear equation. For Thrill amusement park it can be written as y = 40 + 5x, where y is the total cost, 40 is the entry fee and 5x represents the cumulative cost of the rides, with x being the number of rides. For Splash Water Park, the equation is y = 60 + 3x, where 60 is the entry fee and 3x is the cost of the individual rides. To find out when the costs per ride at the two parks will be the same, we solve the system of equations by setting the two equations equal to each other: 40 + 5x = 60 + 3x.
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The length of a rectangle is 7mm longer than its width. It’s perimeter is more than 62mm. Let W equal the width of the rectangle, write an inequality and solve it
Factor the polynomial completely. 4x3 – 12x2 + 7x – 21 4x2(x – 3) + 7(x – 3) Which is the completely factored polynomial? 4x2(x + 4) 3x2(x – 3) (4x2 – 7)(x + 3) (4x2 + 7)(x – 3)
The correct answer for this problem would be D. (4x^2 + 7)(x – 3) .
Hope this helps and clears up any confusion!
The hypotenuse of a 45°-45°-90° triangle measures 7√2 units.
What is the length of one leg of the triangle?
A. 7 units
B. 7√2 units
C. 14 units
D. 14√2 units
Answer:
Option A is correct.
Step-by-step explanation:
Given:
Angle of the right angles triangle are 45° , 45°, 90°
Length of the Hypotenuse = 7√2 units.
To find: Length of the one leg of the triangle.
Since two angles of the triangles are equal.
⇒ Opposite sides to equal angles are also equal.
We have Isosceles right angled triangle.
⇒ both legs are equal.
Let x be the length of the leg
using Pythagoras theorem,
(7√2)² = x² + x²
2x² = 49 × 2
x² = 49
x = ±7
Length cannot be negative so, x = 7
Therefore, Option A is correct.
A regression line was calculated as ŷ = 1.7x + 2.1. What is the slope of the regression line. is _____. Type a numerical answer in the space provided.
How many rays intersect at point O
1. 5
2. 4
3. 6
4. 3
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2 QUESTIONS!
What’s the value of x in 46+(7x+9)
HOW would I go about figuring this out? I need explanation not just answer
You have a bag of bubble gum containing six grape, nine sour apple and five regular flavored pieces. You randomly pick one piece , give it to your friend, and then randomly pick another piece for yourself. What is the probability that both pieces are grape?
The probability that both pieces of bubble gum picked are grape flavored is 3/38, calculated by multiplying the probability of picking a grape piece first (6/20) and then another after the first is given away (5/19).
Explanation:The question asks us to calculate the probability that both pieces of bubble gum picked from the bag are grape flavored. The bag contains six grape, nine sour apple, and five regular flavored pieces. To find the probability that both pieces are grape, we calculate the probability of picking one grape piece and then another grape piece after the first has been given away.
The total number of pieces initially is 6 (grape) + 9 (sour apple) + 5 (regular) = 20 pieces. The probability of picking a grape piece first is 6/20. After giving it away, there are 5 grape pieces left and the total number of pieces in the bag is now 19. The probability of then picking another grape piece is 5/19. To find the overall probability of both events occurring, we multiply the individual probabilities: (6/20) * (5/19) = 30/380 = 3/38.
Therefore, the probability that both pieces are grape is 3/38.
Find an ordered pair (x,y) that is a solution to the equation.
3x-y=3
Answer: The required ordered pair is (1, 0).
Step-by-step explanation: We are given to find an ordered pair (x, y) that is a solution to the following equation:
[tex]3x-y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find an ordered pair, we should either take a value of x and find the corresponding value of y,
or,
we should take a value of y and find the corresponding value of x.
Let us consider that
x = 1.
Then, from equation (i), we get
[tex]3\times 1-y=3\\\\\Rightarrow 3-y=3\\\\\Rightarrow y=3-3\\\\\Rightarrow y=0.[/tex]
Thus, the required ordered pair is (1, 0).
What is the area of the polygon given below?
Which of the following choices represents the expanded form of the number 38,072?
30,000+800+70+2
30,000+8,000+70+2
30,000+8,000+700+2
3,000+800+70+2
Final answer:
The expanded form of 38,072 is 30,000 + 8,000 + 70 + 2, where each term represents the digit's value as a product of its place value.
Explanation:
The expanded form of the number 38,072 is written by separating each digit according to its place value and expressing it as the digit multiplied by the power of ten that represents its position. Therefore, the correct expanded form is:
30,000 + 8,000 + 70 + 2
To understand this, we can consider the place value of each digit in the number 38,072. The '3' is in the ten-thousands place, so it is 3 times 10,000, which is 30,000. The '8' is in the thousands place, so it is 8 times 1,000, which is 8,000. The '0' stands for no hundreds, so we skip it. The '7' is in the tens place, so it is 7 times 10, which is 70. Finally, the '2' is in the ones place, which is just 2.
When triangle ABC is rotated about side AB, what figure is formed?
cylinder
prism
pyramid
cone
Answer:
Cone
Step-by-step explanation:
We are given that a triangle ABC .
We have to find that what shape is formed when a triangle ABC is rotated about side AB.
A given triangle ABC is a right triangle.
When we rotate the figure about side AB then the figure will be cone .The side AB will be height of cone and side AC will be radius of cone.
Hence, when a triangle ABC is rotated about side AB, the cone is formed.
Answer: Cone
Given Sin x= 0.5, what is cos x?
Enter your answer as a decimal, round only your final answer to the nearest hundredth.
If sin x = 0.5, cos x is approximately 0.87.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = Perpendicular / Hypotenuse
Cosec = Hypotenuse / Perpendicular
Cos x = Base / Hypotenuse
Sec x = Hypotenuse / Base
Tan x = Perpendicular / Base
Cot x = Base / Perpendicular
We have,
To find cos x, we can use the identity: cos² x + sin² x = 1
We are given that sin x = 0.5.
We can substitute this into the identity to solve for cos x:
cos² x + sin² x = 1
cos² x + (0.5)² = 1
cos² x + 0.25 = 1
cos² x = 0.75
cos x = ±√0.75
We take the positive square root since cosine is positive in the first and fourth quadrants.
Evaluating the square root gives:
cos x ≈ 0.87 (rounded to two decimal places)
Therefore,
cos x is approximately 0.87.
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what is the value of x to the nearest tenth?
Find the zeros of the polynomial function.
f(x) = x^2 - 12x + 20
I THINK THE ANSWER IS A 2,10
a. 2, 10
b. - 4, -5
c. -2, -10
d. 4, 5
which scale factor would produce a contraction?
A.) 5/2
B.) 1.2
C.) 2.3
D.) 3/4
which descriptions from the list below accurately describe the relationship between QRS and TUV
Answer:
A. Similar
Step-by-step explanation:
We are given the measurements of ΔQRS and ΔTUV as,
QR = RS = 4, QS = 2 with ∠Q = ∠S = 76°, ∠R = 28°
TU = UV = 12, TV = 6 with ∠T = ∠V = 76°, ∠U = 28°
Now, we see that,
These triangles have different side lengths. So, option C i.e. same sides is not correct.
Also, they are different in size. So, option D i.e. same size is not correct.
Since, they do not have same size, they cannot overlap each other. Thus, are not congruent. So, option B is also not correct.
Thus, we see that from SAS Similarity and the measurements,
QR = RS = 4 and ∠R = 28°
TU = UV = 12 and ∠U = 28°
Both the triangles are similar to each other.
Hence, option A is correct.
what is the answer to 2+2*8
Which rectangle if translated 12 units down and 7 units right will result in rectangle E?
A) Rectangle A
B) Rectangle B
C) Rectangle C
D) Rectangle D
Answer:
option D
Step-by-step explanation:
translated 12 units down and 7 units right
(x,y)-> (x+7, y-12)
Lets pick a point on Rectangle A and apply the translation
(-11,4) -> (-11+7, 4-12) ->(-4, -8) That is not in our Rectangle E
Lets pick a point on Rectangle B and apply the translation
(-7,1) -> (-7+7, 1-12) ->(0, -11) That is not in our Rectangle E
Lets pick a point on Rectangle C and apply the translation
(-5,5) -> (-5+7, 5-12) ->(2, -7) That is not in our Rectangle E
Lets pick a point on Rectangle D and apply the translation
(-3,1) -> (-3+7, 1-12) ->(4, -11) That is in our Rectangle E
So option D is correct
You made 1/2 quart of lemonade. How many 1/4 quart-sized glasses will you be able to fill with lemonade?
The solution is 2 glasses
The number of 1/4 quart-sized glasses to fill the lemonade is given by the equation A = 2 glasses
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of 1/4 quart-sized glasses to fill the lemonade be A
Now , the equation will be
The amount of lemonades = 1/2 quart of lemonade
The size of the glasses = 1/4 quart-sized glasses
So , the equation will be
A x 1/4 quart-sized glasses = 1/2 quart of lemonade
On simplifying the equation , we get
A / 4 = 1/2
Multiply by 4 on both sides of the equation , we get
A = ( 1/2 ) x 4
A = 2 glasses
Therefore , the value of A is 2 glasses
Hence , the number of glasses is 2
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