Answer:
First figure:
Faces--5
Edges--8
Vertices--5
Type--pyramid
Second figure:
Faces--6
Edges--12
Vertices--8
Type--rectangular prism
Can anyone please help 10 points
The value of x using similar triangles theorem is = 13/3.
What are similar triangles?Triangles that resemble one another but may not be exactly the same size are said to be comparable triangles.
When two objects have the same shape but different sizes, they can be said to be comparable.
This indicates that comparable shapes superimpose one another when amplified or de-magnified.
The term "Similarity" refers to this characteristic of like shapes.
Now in the given figure,
the proportion of the triangles' side is same.
So, 12/4 = 13/x
x = 13/3
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suppose that 95% of adults with allergies report symptomatic relief with a specific medication. suppose the medication is given to 22 randomly selected new patients with allergies. round to the fourth for all answers.
The expected number of patients who will report symptomatic relief is 20.9. and the probability of exactly 20 patients reporting relief being 0.1977, and the probability of at least 20 patients reporting relief being 0.3832.
(a) The expected number of patients who will report symptomatic relief is 20.9.
The probability of a patient reporting symptomatic relief is 0.95, so the probability of a patient not reporting relief is 0.05. Using the binomial distribution formula, the expected value of the number of patients who will report relief is:
E(X) = n * p = 22 * 0.95 = 20.9
(b) The probability that exactly 20 patients will report symptomatic relief is 0.1977.
Using the binomial distribution formula, we can calculate the probability of exactly 20 patients reporting relief:
P(X = 20) = (22 choose 20) * 0.95^20 * 0.05^2 = 0.1977
(c) The probability that at least 20 patients will report symptomatic relief is 0.3832.
Using the binomial distribution formula, we can calculate the probability of 20 or more patients reporting relief:
P(X >= 20) = P(X = 20) + P(X = 21) + ... + P(X = 22)
P(X >= 20) = 1 - P(X < 20)
P(X >= 20) = 1 - (P(X = 0) + P(X = 1) + ... + P(X = 19))
P(X >= 20) = 1 - 0.6168
P(X >= 20) = 0.3832
Therefore, the probability that at least 20 patients will report symptomatic relief is 0.3832.
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I NEED HELP ASAP PLEASE use the number line to help solve the question
Between 4 and 4.5
sqrt(20)
Between 4.5 and 5
sqrt(22)
sqrt(23.1)
Between 5 and 5.5
sqrt(30)
sqrt(25.9)
sqrt(27.3)
Between 5.5 and 6
sqrt(31)
sqrt(34.9)
alison has five different hats, six different bracelets, and seven cats. she wants to take a selfie with a hat, a bracelet, and two cats. how many different selfies can she take?
Answer:
The answer is 60
Step-by-step explanation:
2x5x6
rearrange by the commutative property
(2x5)x6
Calculate
10x6
calculate the product or quotient to 60
hence the answer is 60
Hoped this helped:D
Alison has five different hats, six different bracelets, and seven cats. She wants to take a selfie with a hat, a bracelet, and two cats. So she can take 630 different selfies.
She wants to take selfies with what she has, and the question asks how many different selfies can she take.
Let's solve the question below:
The total number of selfies Alison can take is 5 × 6 × ( ₇C₂ )
As Alison wants to take a selfie with a hat, a bracelet, and two cats, there are 5 hats and 6 bracelets she can select from, and she needs to select 2 cats out of 7 available cats.
We can use the combination formula to calculate the total number of ways:
₇C₂ = [tex](7 * 6)/2[/tex]
= 21
Hence, Alison can take [tex]5 * 6 * 21[/tex] = 630 different selfies with a hat, a bracelet, and two cats.
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343^2x-5=49^x/2 solve for x
Answer:
Step-by-step explanation:
We can start by simplifying the expression using the laws of exponents:
343^(2x) * 49^(-x/2) = 49^(x/2)
We can then simplify further by expressing everything in terms of 7 (since 7 is the common factor of both 343 and 49):
(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)
Applying the laws of exponents again, we get:
7^(6x) * 7^(-x) = 7^x
7^(6x - x) = 7^x
7^(5x) = 7^x
Now we can solve for x by equating the exponents on both sides:
5x = x
4x = 0
x = 0
Therefore, the solution to the equation is x = 0.
Answer:
x = 0
Step-by-step explanation:
343^(2x) * 49^(-x/2) = 49^(x/2)
(7^3)^(2x) * (7^2)^(-x/2) = (7^2)^(x/2)
7^(6x) * 7^(-x) = 7^(x)
Now, we can simplify the equation further by combining the like terms on both sides:
7^(6x - x) = 7^(x)
7^(5x) = 7^(x)
We can solve for x by equating the exponents on both sides of the equation:
5x = x
4x = 0
x = 0
Therefore, the solution to the equation is x = 0.
2022-2023 Math_CoorAlgBenchmark2_ DCSD « Question 18. Two functions are represented in the chart. Function A Pause f(x) = 4x+1 Function B 1 10 2 g(x) 3 What is the rate of change over the interval [-1.2] for Function A? Explain how you found this value. What is the rate of change over the interval [-1,2] for Function B? Explain how you found this value. B IUEE X, X Q Zoom 24
Therefore, the rate of change over the interval [-1, 2] for Function B is 32/3.
What is function?In mathematics, a function is a rule that assigns to each input value (also known as the independent variable) a unique output value (also known as the dependent variable). In other words, a function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions can be represented in various forms such as algebraic expressions, tables, graphs, or even words. Functions play a crucial role in many areas of mathematics, science, and engineering, as they provide a way to model and describe real-world phenomena and relationships between quantities.
Here,
For Function A, the formula is f(x) = 4x + 1. To find the rate of change over the interval [-1, 2], we need to calculate the slope of the line that passes through the points (-1, f(-1)) and (2, f(2)). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the values for Function A, we get:
slope = (f(2) - f(-1)) / (2 - (-1))
slope = (4(2) + 1 - (4(-1) + 1)) / (2 - (-1))
slope = (9 + 5) / 3
slope = 14/3
Therefore, the rate of change over the interval [-1, 2] for Function A is 14/3.
For Function B, the formula is g(x) = 10x + 2. To find the rate of change over the interval [-1, 2], we need to calculate the slope of the line that passes through the points (-1, g(-1)) and (2, g(2)). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the values for Function B, we get:
slope = (g(2) - g(-1)) / (2 - (-1))
slope = (10(2) + 2 - (10(-1) + 2)) / (2 - (-1))
slope = (20 + 12) / 3
slope = 32/3
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Question 5
During gym class, Kathryn did 5 times as many pushups as Grace. Together, they did a total of 42 pushups. How
many push-ups did each person do during the gym class?
Part A
Write a system of equations that represents the situation.
y=
x + y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
The number of pushups done by Grace and Kathryn is 7 and 35 respectively
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 equation be represented as A
Now , the value of A is
Let the number of pushups by Grace be x
Let the number of pushups by Kathryn be y
Now, Kathryn did 5 times as many pushups as Grace
[tex]y = 5x[/tex] be equation (1)
And, they did a total of 42 pushups together
[tex]x + y = 42[/tex] be equation (2)
Substituting the value of y in the equation, we get
[tex]x + 5x = 42[/tex]
[tex]6x = 42[/tex]
Divide by 6 on both sides, we get
[tex]x = 7[/tex] pushups
And, [tex]y = 35[/tex] pushups
So, the number of pushups by Grace is 7 and by Kathryn is 35 respectively
4in 5in 6in 6in 8in 7in triangular prism surface area
the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
To calculate the surface area of a triangular prism, you need to find the area of each of the faces and add them up.
First, let's find the area of the two triangular faces. To do this, we need to find the base and height of each triangle. Since the prism is isosceles, the base of each triangle is 6 inches (the length of one of the sides of the equilateral triangle). The height of each triangle can be found using the Pythagorean theorem. We have two sides of the triangle: 4 inches and 5 inches. Using the Pythagorean theorem, we can find the height:
[tex]h^2 = 5^2 - 4^2\\h^2 = 25 - 16\\h^2 = 9\\h = 3[/tex]
So the height of each triangular face is 3 inches. Now we can find the area of each triangular face:
Area of one triangular face = (1/2) x base x height
= (1/2) x 6 x 3
= 9 square inches
Since there are two triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 2 x 9 = 18 square inches
Next, let's find the area of the three rectangular faces. We have two rectangles with sides of 6 inches by 8 inches, and one rectangle with sides of 4 inches by 8 inches. The area of each rectangular face is:
Area of rectangular face = length x width
So the area of the rectangular faces are:
Area of rectangular face 1 = 6 x 8 = 48 square inches
Area of rectangular face 2 = 6 x 8 = 48 square inches
Area of rectangular face 3 = 4 x 8 = 32 square inches
Therefore, the total surface area of the triangular prism is:
Total surface area = 18 + 48 + 48 + 32 = 146 square inches
So the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
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suppose there exists a hamming code of length 25 that corrects 2 errors. assuming that the probability of a correct transmission of an individual symbol is 0.75, find the probability that a message transmitted using this code will be correctly received.
The probability that a message transmitted using a Hamming code of length 25 and that corrects 2 errors will be correctly received is 0.6384.
Hamming codes use parity bits to detect and correct errors in the data. In this case, a code of length 25 with 2 error corrections can detect up to two errors and can correct up to one error.
Since the probability of a correct transmission of an individual symbol is 0.75, the probability of a correct transmission of the entire message is calculated by multiplying 0.75 by itself 25 times, giving a probability of 0.6384.
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What are the answers to a,b and c?
a) The linear function that gives the sales in x years after 2011 is of: S(x) = 18x + 191.
b) The slope of the graph of S(x) is of 18, meaning that the sales increase by 18 million a year.
c) The online sales were of 227 billion in the year of 2013.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.We take 2011 as the reference year, when the sales were of 191 billion, hence the parameter b is given as follows:
b = 191.
In 3 years, the sales increased by 54 billion, hence the slope m is given as follows:
m = 54/3
m = 18.
Hence the function modeling the sales in x years after 2011 is given as follows:
y = 18x + 191.
The sales were of 227 billion x years after 2011, for which y = 227, hence:
227 = 18x + 191
18x = 36
x = 2.
2 + 2011 = 2013.
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the distance from point p to point r
Total distance of 7m, which is the shortest distance between point P and point R.
What is distance?Distance is the physical separation between two objects or points. It is usually measured in units such as meters, kilometers, feet, miles, or light-years. Distance is a key concept in physics, mathematics, engineering, and other scientific disciplines. It plays an important role in our everyday life, such as when we measure the distance between two cities, two buildings, or two places.
To determine the shortest distance between point P and point R, we need to calculate the distances between each point and then find the shortest path.
First, we need to calculate the distances between each point. Starting with the points closest to point R, we can find the distance between point R and point Q to be 4m. The distance between point Q and point P is 3m, from the given information. To find the distance between point R and point U, we need to calculate the distance between point U and point V which is 10m, and then add 8m to account for the 8m between point R and point V. This gives us a distance of 18m. The distance between point R and point S is 8m, and the distance between point S and point T is 8m.
Next, we need to calculate the shortest path between point P and point R. From point P, the shortest route would be to travel 3m south to point Q, then 4m east to point R. This gives us a total distance of 7m, which is the shortest distance between point P and point R.
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Complete questions as follows-
Point U is 8m east of point R. Point P is 3m north of point Q. Point U is 10m north of point V. Point W is 8m west of point V. Point R is exactly between point S and point T. Point R is 4m east of point Q. Point T is in 8m south of point S.
What is the shortest distance between point P and point R?
Please help with these two questions if you are good at vertical angles! thank you!!
Step-by-step explanation:
Blank 1 = 82
Blank 2 = 82
Blank 3 = 98
A right pyramid has a square base with sides of length 14 units.
Each segment connecting the apex to a midpoint of a side of the base has length 25 units.
What is the volume of the pyramid?
cubic units
Answer:
Step-by-step explanation:
To find the volume of a pyramid, we can use the formula:
V = (1/3) * base area * height
First, we need to find the height of the pyramid. To do this, we can draw a diagram of the pyramid and create a right triangle using half a side of the base, the height of the pyramid, and one of the segments connecting the apex to a midpoint of a side of the base.
Using the Pythagorean theorem, we can solve for the height:
h^2 + (14/2)^2 = 25^2
h^2 + 49 = 625
h^2 = 576
h = 24
Now we can find the base area:
Base area = 14^2
Base area = 196
And finally, we can use the formula to find the volume:
V = (1/3) * 196 * 24
V = 1568 cubic units
Therefore, the volume of the pyramid is 1568 cubic units.
if we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect:
If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the interval to become wider.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. A 95% confidence interval means that if we were to repeat the sampling and estimation process many times, we can expect the true population parameter to fall within the interval about 95% of the time.
If we change the confidence level from 95% to 99%, we are increasing the degree of confidence. This means that if we were to repeat the sampling and estimation process many times, we can expect the true population parameter to fall within the interval about 99% of the time.
But, to achieve this higher degree of confidence, we need to widen the interval. This is because as the degree of confidence increases, the interval needs to become wider to capture more possible values of the population parameter.
Therefore, if we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the interval to become wider.
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Diana uses 30 grams of coffee beans to make a 48 fluid ounces coffee. When guests come,she makes 96 fluid ounces of coffee. How many grams of coffee beans does Diana use when she has visitors?
Diana needs 60 grams of coffee beans to make 96 fluid ounces of coffee for her guests.
What does a percentage formula mean?Determine whether two ratios or fractions are equivalent using the proportion formula. Dividing the provided values will reveal the value that is missing. As an example of the percentage formula: A and d are the extreme terms, while b and c are the mean terms. Hence, b::c: d = a/b = c/d.
We can resolve the issue by using proportions.
The ratio of coffee beans to liquid ounces in Diana's ordinary coffee must first be determined.
48 fluid ounces / 30 grammes
By reducing the numerator and denominator by 6, we may simplify the ratio:
Eight fluid ounces/5 grammes
We can now apply this proportion to determine how many grammes of coffee beans Diana needs to prepare 96 ounces of coffee:
5 grams/8 fluid ounces = 96 fluid ounces x grammes
After cross-multiplying and finding x, we obtain:
x = (96 ounces * 5 grammes) / 8 ounces
x=60 grammes.
In order to prepare 96 fluid ounces of coffee for her visitors, Diana needs 60 grammes of coffee beans.
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What is 2.5 as a fraction?
Answer: 5/2
fraction of 2.5 is 5/2
Answer:
2 1/2 or 5/2 as improper fraction
2 is a whole number and you have .5 left over
To convert to fraction .5 is the same as 1/2
So it gives you 2 1/2
By the way thanks for the Brainly points :)
Suppose that the random variable X represents the length of a punched part in
centimeters. Let Y be the length of the part in millimeters. If E(X) = 5 and V(X) = 0.25,
what are the mean and variance of Y?
Overall, finding the mean and variance of a random variable Y that is associated with another random variable X requires some knowledge of probability theory and calculus. However, by following the steps outlined above, we can arrive at an answer that is both accurate and concise.
When it comes to the question of finding the mean and variance of a random variable, Y, that is associated with another random variable X, it's important to take a few steps to calculate those values. Here's how to do it:
- Start with the formula for the expected value of Y: [tex]E(Y) = E(g(X))[/tex]. In this case, we want to find the expected value of Y, so we need to find the function g(X) that relates X to Y. The problem tells us that X represents the length of a punched part, and Y represents the number of parts that can be cut from a 12-foot rod. So we can say that Y = h(X), where h(X) = 12/X. This means that the expected value of Y is E(Y) = E(12/X).
- To find E(Y), we need to find E(12/X).
We can use the formula for the expected value of a function of a continuous random variable:[tex]E(g(X)) = ∫g(x)f(x)dx,[/tex]where f(x) is the probability density function of X. The problem doesn't give us a specific probability density function for X, but it does tell us that X is a random variable. So we can assume that X follows some distribution, such as a normal distribution or a uniform distribution. Depending on the distribution of X, we can use the appropriate formula to find E(12/X).
- Once we have found E(Y), we can use the formula for the variance of a random variable: Var(Y) = E(Y^2) - [E(Y)]^2. To find E(Y^2), we need to find E(h^2(X)). Since h(X) = 12/X, we can say that [tex]h^2(X) = 144/X^2. So E(h^2(X)) = E(144/X^2).[/tex]We can use the same method as before to find [tex]E(144/X^2)[/tex], and h^2(X) = 144/X^2. So E(h^2(X)) = E(144/X^2).then plug that into the formula for Var(Y).
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you can leave the basketball court if you make 3 free throws. the probability that you make a free throw is 0.4. what is the probability that you can leave the court in 10 or fewer attempts?
If the probability that a player makes a free throw is 0.4, the probability that they do not make a free throw is 1 – 0.4 = 0.6.
The probability that a player makes three consecutive free throws is 0.4 × 0.4 × 0.4 = 0.064. If a player attempts three free throws, there are three possible outcomes: make all three, miss one and make two, or miss two and make one.
The probability of making all three is 0.064, the probability of missing one and making two is 0.4 × 0.4 × 0.6 + 0.4 × 0.6 × 0.4 + 0.6 × 0.4 × 0.4 = 0.288, and the probability of missing two and making one is 0.6 × 0.6 × 0.4 + 0.6 × 0.4 × 0.6 + 0.4 × 0.6 × 0.6 = 0.432.
Therefore, the probability of leaving the court in three attempts is 0.064 + 0.288 + 0.432 = 0.784. If a player misses all three attempts, they will have to try three more times, and the probability of leaving the court in six attempts is 0.784 + 0.064 × 0.288 × 0.432 = 0.861.
If a player misses all six attempts, they will have to try three more times, and the probability of leaving the court in nine attempts is 0.861 + 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 = 0.926.
If a player misses all nine attempts, they will have to try three more times, and the probability of leaving the court in twelve attempts is 0.926 + 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 = 0.974.
Since the probability of leaving the court in twelve attempts is greater than 0.9, the probability of leaving the court in ten or fewer attempts is greater than 0.9. Therefore, the probability that a player can leave the court in 10 or fewer attempts is greater than 0.9.
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Sam works for his father for 2
; of the year and works for his mother = of the remainder year. What is the
ratio of the time Sam spends working for his mother to the time he spends working for his father per year?
6/1
1/2
2/1
1/6
1/9
The ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year is 1/6 οr 1:6. Thus, οptiοn D is cοrrect.
What is the ratiο?The relative size οf twο quantities expressed as the quοtient οf οne divided by the οther; the ratiο οf a tο b is written as a:b οr a/b.
If Sam wοrks fοr his father fοr 2/5 οf the year, then he wοrks fοr his mοther fοr the remaining time, which is 1 - 2/5 = 3/5 οf the year.
Tο find the ratiο οf the time Sam spends wοrking fοr his mοther tο the time he spends wοrking fοr his father per year, we can write:
Sam wοrked fοr his father = 2/3 οf year
Remaining time = 1/3
Sam wοrked fοr his mοther = 1/3(remainder year)=(1/3)*(1/3)
=1/9
Ratiο οf time spent fοr mοther and father is
= (1/9):(2/3)
=(1/3):2
= 1:6
Sο, οptiοn d) 1/6 is cοrrect answer
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Complete question:
Sam works for his father for 2/3; of the year and works for his mother = of the remainder year. What is the
ratio of the time Sam spends working for his mother to the time he spends working for his father per year?
6/11/22/11/61/9Question content area top
Part 1
Find the amount in the account for the given principal, interest rate, time, and compounding period.
P$, r%, t years; compounded quarterly
The amount in the account after compounded quarterly is found as: $1103.8.
Explain about the quarterly compounding?Compounding quarterly is the term used to describe the amount of interest that is earned on a quarterly basis on a savings account or investment at which interest is also reinvested.
Although most banks charge interest income here on deposits, which compounds quarterly, this information is useful in computing the fixed deposit income. It can also be used to figure out any revenue from money market instruments or other financial products that pay quarterly income.
The formula for quarterly compounding:
A = P * [tex](1+r/n)^{nt}[/tex]
P $1000, r = 10%, t = 2 years;
compounded quarterly : n = 4
A = 1000 * [tex](1+0.10/4)^{4*1}[/tex]
A = 1000 * 1.1038
A = 1103.8
Thus, the amount in the account after compounded quarterly is found as: $1103.8.
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Complete question:
Find the amount in the account for the given principal, interest rate, time, and compounding period.
P $1000, r = 10%, t = 2 years; compounded quarterly
a shopper buys 4 pounds apples for 4.60 what is the cost in dollars of 1 pound apples
Answer:
1.15 dollars
Step-by-step explanation:
To calculate the cost of 1 pound of apples, we can divide the total cost of 4 pounds of apples by 4.
The total cost of 4 pounds of apples is 4.60 dollars.
So, the cost of 1 pound of apples would be 4.60 / 4 = 1.15 dollars.
The cost in dollars of 1 pound apples is $1.15
What is division?Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.
The process of dividing a number up into equal parts, and finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"
Division is breaking a number up into an equal number of parts.
Given that, a shopper buys 4 pounds of apples for 4.60, we need to find the cost in dollars of 1 pound of apples,
To calculate the cost of 1 pound of apples, we can divide the total cost of 4 pounds of apples by 4.
The total cost of 4 pounds of apples is 4.60 dollars.
So, the cost of 1 pound of apples would be 4.60 / 4 = 1.15 dollars.
Hence, the cost in dollars of 1 pound apples is $1.15
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plssssssss help meeeeee
Answer:
slope = - [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 10 ) and (x₂, y₂ ) = (6, 8 )
m = [tex]\frac{8-10}{6-(-3)}[/tex] = [tex]\frac{-2}{6+3}[/tex] = [tex]\frac{-2}{9}[/tex] = - [tex]\frac{2}{9}[/tex]
What is the distance between
(
4
,
7
)
(4,7)left parenthesis, 4, comma, 7, right parenthesis and
(
2
,
2
)
(2,2)left parenthesis, 2, comma, 2, right parenthesis?
Answer:
d ≈ 5.4
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, 2 ) and (x₂, y₂ ) = (4, 7 )
d = [tex]\sqrt{(4-2)^2+(7-2)^2}[/tex]
= [tex]\sqrt{2^2+5^2}[/tex]
= [tex]\sqrt{4+25}[/tex]
= [tex]\sqrt{29}[/tex]
≈ 5.4 ( to the nearest tenth )
A cereal manufacturer distributes cases of cereal to grocery stores. Each case contains 11 identical boxes of cereal. The total weight of the
case consists of the weight of the 11 cereal boxes plus 33 ounces for the weight of the case's cardboard box. In order to pass a quality
assurance test, the case must weigh greater than 264 ounces and less than 286 ounces.
(a) Write a compound inequality to represent the weight of each box (in ounces), b, so that the case passes the quality assurance
test.
The weight of each box of cereal must be between 21 and 23 ounces for the case to pass the quality assurance test. We can write this as the compound inequality: 21 < b < 23.
What is quality assurance test?A quality assurance test is a process that is used to evaluate the quality of a product or service. It involves checking whether the product or service meets certain standards or specifications, and identifying any defects or issues that need to be addressed.
According to question:Let's start by finding the weight of a single box of cereal. We know that the weight of the entire case is the weight of 11 boxes plus the weight of the cardboard box, or:
Weight of case = 11b + 33
where b is the weight of a single box of cereal.
To pass the quality assurance test, the weight of the case must be greater than 264 ounces and less than 286 ounces. Therefore, we can write a compound inequality for b as follows:
264 < 11b + 33 < 286
Next, we can simplify this compound inequality by subtracting 33 from each term:
231 < 11b < 253
Finally, we can divide each term by 11 to solve for b:
21 < b < 23
Therefore, the weight of each box of cereal must be between 21 and 23 ounces for the case to pass the quality assurance test. We can write this as the compound inequality:
21 < b < 23 (in ounces)
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what is the dimension of the solution space if you have 3 linearly independent equations in 5 unknowns?
The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.
The dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2. This is because, when solving a system of equations, the number of equations must match the number of unknowns; otherwise, it is impossible to solve. In this case, the number of equations (3) is less than the number of unknowns (5), meaning that the system is underdetermined. This means that there are infinite solutions, and the dimension of the solution space is 2 (the number of free variables).
In other words, the solution space is a two-dimensional plane where each point represents a possible solution to the system of equations. As the equations are linear, the solution space forms a linear subspace, which means that it is a flat surface.
It is also important to note that the linear independence of the equations is crucial to this solution. If the equations are dependent, then the solution space can have a dimension of 1, 0, or even a negative number. So, the dimension of the solution space for 3 linearly independent equations in 5 unknowns is 2.
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What is the value of x in the right triangle below, rounded to the near-
est hundredth?
how do i solve this?
The height of the density curve for the given graph is 1/4.
What is density curve?A density curve is an idealised depiction of a distribution in which the area under the curve is defined to be 1. Although normality is not required, the normal density curve will be the most helpful to us. The "shape" of a distribution, including whether or not it includes one or more "peaks" of often occurring values and whether it is skewed to the left or right, may be determined using a density curve.
For a density curve the area under the curve must be equal to 1.
That is,
base (height) = 1
Here, the base = 4 units
Substituting the value we have:
(4) height = 1
height = 1/4
Hence, the height of the density curve is 1/4.
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6x6x6x6x6x6x6 devided by 6x6x6x6x6x6 in indext form
The result of 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 in index form is 6.
In index form, 6x6x6x6x6x6x6 divided by 6x6x6x6x6x6 can be written as:
(6⁷) / (6⁶).To divide two exponential expressions with the same base (in this case, 6), we can subtract the exponents:
6⁽⁷⁻⁶⁾ = 6¹ = 6.
Index form, also known as exponential form, is a way of writing numbers or expressions using exponents. In index form, a number is expressed as a base raised to a power or exponent.
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help
I need this asap
Answer: natural number=11
integer= -4
irrational= pi, 0.1010010001.....,root 5
rational= 0.1212...., -3/5,0.3,2 1/4
Step-by-step explanation:
(a) Place a right triangle with leg lengths of 7 units and 9 units in the coordinate plane. (b) Find the length of the hypotenuse. Round to the nearest tenth.
The hypotenuse is therefore around 11.4 units long.
DESCRIBE THE RIGHT ANGLE TRIANGLE?If one of a triangle's angles is 90 degrees or more, the triangle is said to be right-angled. The other two angles add up to 90 degrees. The sides that make up the right angle are perpendicular and the triangle's base.
where the hypotenuse length is c and the leg lengths are a and b, respectively.
The Pythagorean theorem can be used to determine the length of the hypotenuse of a right triangle with 7 and 9 unit legs:
a² + b² = c²
If we substitute 7 for letter a and 9 for letter b, we get:
7²+ 9² = c²
49 + 81 = c²
130 = c²
The result of squaring the two sides is: c = 130) 11.4
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