Answers
Answer:
no
Step-by-step explanation:
using Pythagoreans theorem
a^2+b^2=c^2
3^2+5^2≈6^2
9+15=34
not 36 so no
Answer :
Here, It is stated that the triangle having sides 3, 5 and 6 respectively. So, we have to prove that whether the given triangle is right angled triangle or not.
For That :
We will be using the Pythagoras Theorem
Given Sides :- Side - A → 3 Side - B → 5Side - C → 6According to the Pythagoras Theorem , the sum of the square of Base side and perpendicular side is equal to the square of the longest side i.e, hypotenuse.
Pythagoras Theorem :
⠀⠀⠀⠀⠀⠀\({\bullet \: {\boxed{\sf {AC^{2} = AB^{2} + BC^{2}}}}} \\ \\ \)
So, here the longest side is Side A of measurement 6.
So, Now
Applying Pythagoras Theorem in it, we get :
The three sides , so let's plug the values in the formula :-
\(\dashrightarrow\:\:\sf AC^{2} = AB^{2} + BC^{2}\\ \\\)
\(\dashrightarrow\:\:\sf 6^{2} = 3^{2} + 5^{2}\\ \\\)
\(\dashrightarrow\:\:\sf 36 = 9 + 5^{2}\\ \\\)
\(\dashrightarrow\:\:\sf 36 = 9 + 25 \\ \\\)
\(\dashrightarrow\:\:\sf 36 \neq 34 \\ \\\)
\({\underline{\sf {L.H.S \neq R.H.S}}} \\ \)
If in a triangle, the square of the hypotenuse is not equal to the sum of the squares of the other two sides, then the given triangle and doesn't satisfy pythagoras theorem. Hence, Its not a right angled triangle.
Related Questions
A 14- ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?
Answers
The company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.
What is inequalities
In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).
To find the point at which the company starts to turn a profit, we need to find the value of x for which the revenue is greater than the cost of production.
The revenue function is R(x) = 7x, and the cost of production is C(x) = 13x + 132.
So, we need to solve the inequality:
R(x) > C(x)
7x > 13x + 132
Subtracting 13x from both sides, we get:
-6x > 132
Dividing both sides by -6 (and flipping the inequality because we're dividing by a negative number), we get:
x < -22
Therefore, the company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.
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A family has two cars. The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas. During one particular week, the two cars went a combined total of 1300 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
Answers
20 gallons of gas was consumed by the car that has efficiency of 20 miles per gallon and 30 gallons of gas was consumed by the car that has efficiency of 30 miles per gallon .
How to find the consumption of gallons using equation?The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas.
Therefore,
let
x = number of gallons for car that consume 20 miles per gallon of gas
y = number of gallons for car that consume 30 miles per gallon of gas
Hence,
x + y = 50
20x + 30y = 1300
20x + 20y = 1000
20x + 30y = 1300
10y = 300
y = 300 / 10
y = 30
Therefore,
x = 50 - 30
x = 20
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Find the center and radius of the circle with the glven equation. Then select the correct graph of the circle x2 + y2 = 16 The center is located at and the radius is
Answers
The general equation of a circle is
\(\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \text{ Where} \\ (h,k)\text{ are the coordinates of the center and} \\ r\text{ is the radius of the circle} \end{gathered}\)So, in this case, you have
\(\begin{gathered} x^2+y^2=16 \\ (x-0)^2+(y-0)^2=4^2 \\ \text{ Then} \\ h=0 \\ k=0 \\ r=4 \end{gathered}\)Therefore, the center is located at (0,0) and the radius is 4.
And the correct graph of the circle is the one shown in option C.
Work is apreciated! If you could at least include the formula also!
Answers
Answer:
184.5 ft³Step-by-step explanation:
Volume formula:
V = Bh/3, where B- area of the baseThe base is the pentagon, consisting of equal 5 triangles with the height of 4.1 ft and side of 6 ft.
Area of the base:
B = 5*1/2*6*4.1 = 61.5 ft²Volume:
V = 61.5*9/3 = 184.5 ft³lim h -> 0 [f(x_{0} + h) - f(x_{0})] / h
Answers
the limit expression gives the value of the derivative of a function at a specific point. where f'(x_0) denotes the derivative of f(x) at x = x_0.
what is derivative ?
The derivative of a function is a measure of how the function changes as its input variable changes. It gives the instantaneous rate of change or slope of the tangent line of the function at a specific point.
In the given question,
The expression you provided represents the limit definition of the derivative of a function f(x) at the point x = x_0. The limit evaluates the instantaneous rate of change or slope of the tangent line of the function f(x) at the point x = x_0.
To evaluate the limit, substitute x = x_0 + h in the expression of the function f(x) and simplify:
\(lim h - > 0 [f(x_{0} + h) - f(x_{0})] / h = f'(x_{0})\)
where f'(x_0) denotes the derivative of f(x) at x = x_0.
Therefore, the limit expression gives the value of the derivative of a function at a specific point.
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Suppose you take out a 45-year $150,000 mortgage with an APR of 6%. You make payments for 3 years (36 monthly payments) and then consider refinancing the original loan. The new loan would
have a term of 15 years, have an APR of 5.1%, and be in the amount of the unpaid balance on the original loan. (The amount you borrow on the new loan would be used to pay off the balance on the
original loan.) The administrative cost of taking out the second loan would be $1900. Use the information to complete parts (a) through (e) below.
a. What are the monthly payments on the original loan?
(Bound to the nearest cent as needed.)
Answers
The monthly payments on the original loan are $899.33.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To find the monthly payments on the original loan, we can use the formula for the monthly payment of an amortized loan:
M = P (r/12)(1 + r/12)ⁿ/ ((1 + r/12)ⁿ - 1)
where M is monthly payment, P is principal, r is monthly interest rate, n is total number of payments
For the original loan, P = $150,000, r = 0.06/12 = 0.005, and n = 45 years x 12 months/year = 540 months.
Substituting these values into the formula, we get:
M = 150,000(0.005)(1 + 0.005)⁵⁴⁰ / ((1 + 0.005)⁵⁴⁰- 1)
= 899.33
Therefore, the monthly payments on the original loan are $899.33.
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If x varies directly as y, find x when y = 8 a) x = 6 when y = 32 b) x = 14 when y = -2
Answers
a) The value of x is 42.6 when k =16/3 is directly proportional to y.
b) The value of x is -56 when k is -7 is directly proportional to y.
What kind of variation is one where x and y are directly proportional?
If x = ky for some constant k can be used to indicate the relationship between the variables y and x, then we may say that y varies directly with y or that x is directly proportional to y.x varies directly as y
x α y
x = ky
a) x=6 ; y = 32
x = ky
6 = k(32)
k = 16/3
if y = 8
then,
x = (16/3) * 8
= 128/3
x = 42.6
Hence, the value of x is 42.6 when k =16/3 is directly proportional to y.
b) x= 14 and y = -2
x = ky
14 = k(-2)
k = -7
if y = 8
then,
x = ky
x= (-7) 8
x = -56
Hence, the value of x is -56 when k is -7 is directly proportional to y.
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The demand equation for a popular brand of fruit drink is given by the equation:
Qx=10-5px+0.001M + 10Py
where:
Qx= monthly consumption per family in liters
Px= price perlite of the fruit drink =$2.00
M= median annual family income =$20,000
Py= price per liter of a competing brand of fruit drink = $2.50.
1. Interpret parameter estimates.
2. Calculate the monthly consumptioliterslitres) of the fruit.
3. Suppose that the median annual family income increased to ¢30,000. How does this change your answer to part (b)?
4. Determine the demand function and the inverse demand function.
Answers
Answer:
Parameter estimates
The coefficient for Px (-5) suggests that there is an inverse relationship between the price of the fruit drink and the quantity demanded. In other words, as the price of the drink increases, the quantity demanded decreases.
The coefficient for M (0.001) suggests that there is a positive relationship between the median annual family income and the quantity demanded. In other words, as the median income increases, the quantity demanded also increases.
The coefficient for Py (10) suggests that there is a positive relationship between the price of the competing brand of fruit drink and the quantity demanded for this brand. In other words, as the price of the competing brand increases, the quantity demanded for this brand also increases.
Step-by-step explanation:
To calculate the monthly consumption of the fruit drink, we plug in the given values into the demand equation,
Qx = 10 - 5(2) + 0.001(20,000) + 10(2.5)
Qx = 10 - 10 + 20 + 25
Qx = 45 liters per family per month.
Therefore, the monthly consumption of the fruit drink per family is 45 liters.
If the median annual family income increased to $30,000, then the new monthly consumption of the fruit drink per family can be calculated as follows,
Qx = 10 - 5(2) + 0.001(30,000) + 10(2.5)
Qx = 10 - 10 + 30 + 25
Qx = 55 liters per family per month.
Therefore, the monthly consumption of the fruit drink per family would increase from 45 liters to 55 liters per family per month.
To determine the demand function, we need to solve for Qx in terms of the other variables,
Qx = 10 - 5Px + 0.001M + 10Py
Qx - 10Py = 10 - 5Px + 0.001M
Qx = (10 - 5Px + 0.001M) / 10Py
Therefore, the demand function is:
Qx = (10 - 5Px + 0.001M) / 10Py
To find the inverse demand function, we need to solve for Px in terms of Qx.
Qx = 10 - 5Px + 0.001M + 10Py
5Px = 10 - Qx - 0.001M - 10Py
Px = (10 - Qx - 0.001M - 10Py) / 5
Therefore, the inverse demand function is,
Px = (10 - Qx - 0.001M - 10Py) / 5
3.37 a physicist estimated that the probability of a u.s. nickel landing on its edge is one in 6000. suppose a nickel is flipped 10,000 times. let x be the number of times it lands on its edge. find the probability that x is between one and three using (a) the exact distribution of x (b) an approximate distribution of x
Answers
(a) The probability that x is between one and three using the exact distribution is approximately 0.0000118.
(b) The probability that x is between one and three using the normal approximation is approximately 0.2120.
(a) To find the exact distribution of x, we can use the binomial distribution, which gives the probability of getting x successes in n independent trials, each with a probability p of success. In this case, n = 10,000 and p = 1/6000. Thus, the probability of getting exactly x edges in 10,000 flips is
P(x) = (10,000 choose x) × (1/6000)^x × (5999/6000)^(10,000 - x)
To find the probability that x is between one and three, we can add up the probabilities for x = 1, 2, and 3:
P(1 <= x <= 3) = P(1) + P(2) + P(3)
= (10,000 choose 1) × (1/6000)^1 × (5999/6000)^(9999)
+ (10,000 choose 2) × (1/6000)^2 × (5999/6000)^(9998)
+ (10,000 choose 3) × (1/6000)^3 × (5999/6000)^(9997)
≈ 0.0000118
(b) To find an approximate distribution of x, we can use the normal approximation to the binomial distribution. The normal approximation is valid when n is large and p is not too close to 0 or 1. In this case, np = 10,000/6000 = 5/3 > 10 and n(1 - p) = 10,000(5999/6000) ≈ 166.65 > 10, so the normal approximation is reasonable.
The mean of the binomial distribution is μ = np = 5/3, and the variance is σ^2 = np(1 - p) = 5/3 × 5999/6000 ≈ 0.998. Therefore, the standard deviation is σ ≈ 0.999.
To use the normal distribution to approximate P(1 <= x <= 3), we need to standardize the values of 1, 2, and 3
z1 = (1 - μ) / σ ≈ -0.332
z2 = (2 - μ) / σ ≈ 0.334
z3 = (3 - μ) / σ ≈ 1.000
Then we can use the standard normal distribution to find the probability
P(1 <= x <= 3) ≈ Φ(z3) - Φ(z1)
≈ Φ(1.000) - Φ(-0.332)
≈ 0.1587 - 0.3707
≈ 0.2120
where Φ is the standard normal cumulative distribution function. Therefore, the probability that x is between one and three, using the normal approximation, is approximately 0.2120.
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What is the domain of the function represented by this graph? the graph of a quadratic function y = x^2 – 4 with a minimum value at the point (0,-4) A. -2 ≤ x ≤ 2 B. x ≥ 4 C. x ≤ 0 D. all real numbers Reset
Answers
Domain of the function represented by the graph of a quadratic function y = \(x^2\) – 4 with a minimum value at the point (0,-4) is all real numbers.
The correct answer is option D.
To determine the domain of the quadratic function y = \(x^2\) - 4, we need to consider the x-values for which the function is defined. Since a quadratic function is defined for all real numbers, the domain of this function is "all real numbers."
Let's analyze the given function and its graph to understand why the domain is "all real numbers."
The function y = \(x^2\) - 4 represents a parabola that opens upward, which means it extends infinitely in both positive and negative x-directions. The vertex of the parabola is at the point (0, -4), indicating that the minimum value of the function occurs at x = 0.
Since there are no restrictions or limitations on the x-values for which the function is defined, the domain is unrestricted and encompasses all real numbers. In other words, the function can be evaluated and calculated for any real value of x, whether it is a negative number, zero, or a positive number.
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You send an email with a file size of 4 kilobytes. One kilobyte is 2^{10} bytes. What is the file size of your email in bytes? Write your answer as a power.
Answers
Answer:
2¹² Bytes
Step-by-step explanation:
One kilobyte is 2¹⁰ bytes.
File size of the email is 4 kilobytes. That is 4 times 1 kilobyte. Therefore multiply with 4.
4 KB = 4 × 2¹⁰ B
Now notice that you can rewrite 4 like 2².
4 KB = 2² × 2¹⁰ B
Use exponental rule (Product Rule):
\(a^x + a^y = a^{x+y}\)
4 KB = 2²⁺¹⁰ B = 2¹² B
−5/6h−2/3h=−24 for h
Answers
Answer: h = 16
Step-by-step explanation:
We will isolate the variable, h, with inverse operations and simplifying to solve for h.
Given:
\(\displaystyle -\frac{5}{6}h-\frac{2}{3}h=-24\)
Multiply both sides of the equation by 6:
➜ Why would we do this? This allows us to work without fractions.
-5h - 4h = -144
Combine like terms:
-9h = -144
Divide both sides of the equation by -9:
h = 16
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
Evaluate -7x + y5x
When x = -3, y = -9
Answers
Answer:
156
Step-by-step explanation:
-7(-3)+(-9)(5)(-3)
21+135
156
Answer:
156
Step-by-step explanation:
Substitute x and y values in the equation-7x+y5x
(-7)(-3)+(-9)*5*(-3)
21+135
156
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There are approximately 8,441 people per square mile in Phoenix. If Phoenix is 964 square miles,
approximately how many people live in Phoenix.
Answers
Answer: 8,137,124
Step-by-step explanation:
You can find the answer by multiplying the number of people by the number of sq miles.
8441 * 964
Marsha deposited 7,500 into a savings account 3 years ago. The simple interest rate is 5%. How much money did Marsha earn in interest
Answers
Answer:
$1,125 in interest.
Step-by-step explanation:
We need the formula of I = P * i * t where P is the total principle, i is the rate of interest per year, and t is the total time in years.
So we have
P = $7,500
i = 5%
t = 3 years
I = 7500 * 0.05 * 3
I = 1,125 (Interest)
Now we need to find the amount using A = P + I
A = 7,500 + 1,125
A = 8,625
Therefore $8,625 is our total. While our interest is $1,125.
Write the standard form of the equation of the circle with radius 8 and center (10,−7).
Answers
The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²
What is the standard form of the equation of a circle?The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.
We have given that circle having radius of 8 units. Thus, r = 8.
Since we know that circle having the center (10,−7).
Thus, the equation of the circle, with a radius of 8 units is;
(x - h)² + (y - k)² = r²
(x - 10)² + (y + 7)² = 8²
Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²
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Question 5 of 10
Which system of inequalities is graphed below?
5
O A. y
Answers
Answer:
you did not send the graph-_-
Step-by-step explanation:
Question 3: Mathematical proficiency and the construction of mathematics ideas. To answer this question, you need to understand paragraphs 2.12 and 2.13 in your study guide: Key to note the following concepts: constructivism and behaviourism. inductive and deductive thinking or reasoning. instrumental and relational understanding conceptual and procedural knowledge; and ● elements of mathematics proficiency. . e . (10 marks) ● 3.1 Create an activity where procedural and conceptual understanding co-exists. Revisit your content areas and choose a problem to solve and demonstrate how procedural and conceptual knowledge can be linked to the teaching and learning process. (6) 3.2 Provide an example to explain the difference between conceptual knowledge and procedural knowledge.
Answers
Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
3.1 Activity: Procedural and Conceptual Understanding in Action
Content Area: Fractions
Problem: Comparing Fractions
Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.
Activity Steps:
Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).
Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.
After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:
What does it mean for one fraction to be greater than or less than another?
Can you explain why we need a common denominator when comparing fractions?
How can you visually represent and compare fractions to better understand their relative sizes?
Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.
Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.
Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.
Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.
By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.
3.2 Example: Conceptual Knowledge vs. Procedural Knowledge
Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.
Example: Division of Fractions
Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.
Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.
In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
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PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
\(- 10(2) + y = 4\)
\( - 20 + y = 4\)
\(y = 24\)
For x=1\( - 10( 1) + y = 4\)
\( - 10 + y = 4\)
\(y = 14\)
For x=0\( - 10(0) + y = 4\)
\(0 + y = 4\)
\(y = 4\)
For x=-1\( - 10( - 1) + y = 4\)
\(10 + y = 4\)
\(y = - 6\)
For x=2\( - 10( - 2) + y = 4\)
\(20 + y = 4\)
\(y = - 16\)
Answer:
-2 = -16
-1 = -6
0 = 4
1 = 6
2 = 16
Step-by-step explanation:
The pharmacist has a 4.3 L bottle of cough syrup. If she fills a bottle that is 1,900 ml, how many ml of cough syrup does the pharmacist have left? (1 L = 1,000 ml)
240 ml
2,400 ml
3,100 ml
6,200 ml
Answers
Answer:Hi! The answer will be B I got a 100 on my test and i also did this before.
The total volume of cough syrup that the pharmacist will have left would be = 2,400ml. That is option B.
Who is a pharmacist?A pharmacist is an individual trained and licensed to dispense the correct amount of prescribed medication.
The volume of the cough syrup the pharmacist has = 4.3L
But 1 L = 1000 ml
4.3 L = 4.3 × 1000 = 4300ml
The volume of the available syrup bottle brought by the pharmacist = 1,900 ml
The quantity of syrup transferred to a bottle = 1,900 ml
Therefore the amount remaining = 4300 - 1900 = 2,400ml.
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Can somebody Answer this?
Answers
Garry needs 18.4 oz of glue and 9.2 oz of glitter to make 4 bottles.
What is direct proportion?In direct proportion between two or more than two quantities if one quantity is multiplied or divided by some constant k other quantities will also be multiplied or divided by the same constant k.
Given, Making 1 bottle of glitter glue Garyy requires 4.6 oz of glue and 2.3 oz of glitter.
∴ 4 bottles of glitter glue require (4.6×4) = 18.4 oz of glue and (2.3×4) = 9.2 oz of glitter.
As the no. of bottles is multiplied by 4 thus material requirements will also be multiplied by a factor of 4.
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Kent buys a pen that costs $1.21. How much will
4 pens cost?
Answers
Answer:
4 pens will cost $4.84
Step-by-step explanation:
1.21 times 4 = 4.84
Which of the following can be used to find the area of a circle?
A.
B.
C.
D.
Answers
Answer:
option B
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Answer:
\(\boxed{Option \ B}\)
Step-by-step explanation:
Area of a circle = \(\pi r^2\)
Finding the area of the circle, we need to know what the radius of the circle is. So, We would get the area of the circle.
A company is allowed to interview candidates until two qualified candidates are found. But budget constraints dictate that no more than 10 candidates can be interviewed. List the sample space.
Answers
Answer:
Kindly check attached picture for sample space design
45 ways
Step-by-step explanation:
Number of qualified candidates to be chosen = 2
Number of candidates to be interviewed = 10
Combination formula :
nCr = n! / (n-r)! r!
10C2 = 10! ÷ (10 - 2)!2!
10C2 = 10*9 / 2 * 1
10C2 = 90/2
10C2 = 45 different samples
Our sample space will contain 45 different samples
On Monday, he made 7 cakes. On Lionel makes cakes for the bake sale.
On Monday, he made 7 cakes. On Tuesday, he works an additional 2 hours and has a total of 13 cakes.
Determine how many cakes he makes in one hour. Tuesday, he works an additional 2 hours and has a total of 13 cakes.
Determine how many cakes he makes in one hour.
Answers
To determine how many cakes Lionel makes in one hour, we can use the following formula:
cakes per hour = total cakes / total hours worked
On Monday, Lionel made 7 cakes in some number of hours, so we don't know how many cakes he made per hour that day. However, on Tuesday, he made an additional 6 cakes (13 total cakes - 7 cakes made on Monday), and he worked for 2 hours longer than he did on Monday. Therefore:
cakes per hour on Tuesday = 6 cakes / 2 hours = 3 cakes per hour
So Lionel made 3 cakes per hour on Tuesday. We don't have enough information to determine how many cakes he made per hour on Monday.
100 Points!!! Algebra question, only looking for answer to last two. Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent. Photo attached. Thank you!
Answers
1) y = -3x and y = -3x + 2: inconsistent system of equations.
2) y = x - 5 and -2x + 2y = - 10: consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.
Explain about the consistent and inconsistent system of equations?If there is at least one solution, an equation system is considered consistent. If there is no solution, a system is inconsistent.If one equation is a multiple of the other in a pair of equations that have two variables, both equations are dependant. Every point in dependent systems is a potential solution, giving them an endless number of solutions.The given equation are:
The graph for each system of equations is plotted.
1) y = -3x and y = -3x + 2
From the graph 1 it is shown that the lines for the each equation form the parallel lines.
Thus, system of equations are inconsistent.
2) y = x - 5 and -2x + 2y = - 10
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
3) 2x - 5y = 10 and 3x + y = 15
From the graph 2 it is shown that the lines for the each equation form the coincident lines.
Thus, system of equations are consistent and independent.
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Suppose you have a litter of mice which consists of 5 males and 3 females. If you randomly grab two of them without replacement.
1. what is the probability that they are both male?
2. what is the probability that you get at least one female
3. what is the probability that one is male and one is female
Answers
Problem 1
Answer: 5/14-----------------------
Explanation:
We have 5 males and 3 females, so there are 5+3 = 8 mice total. The probability of selecting a male is 5/8. After that male is chosen, there are 5-1 = 4 of them left out of 8-1 = 7 total. This subtraction happens because the first mouse selected is not replaced. The probability of picking another male is 4/7.
Multiplying these fractions leads to the answer
(5/8)*(4/7) = (5*4)/(8*7) = 20/56 = 5/14
Note: to reduce 20/56 into 5/14, you divide both parts by the GCF 4.
====================================================
Problem 2
Answer: 9/14-----------------------
Explanation:
The events "selecting two males" and "selecting at least one female" are complementary events. One or the other, but not both, must happen.
If we let
A = event of selecting two malesB = event of selecting at least one female (ie one or more females)then we can say
P(A) + P(B) = 1
P(B) = 1 - P(A)
P(B) = 1 - (5/14)
P(B) = (14/14) - (5/14)
P(B) = (14-5)/14
P(B) = 9/14
Note how P(A) = 5/14 is the result from problem 1.
====================================================
Problem 3
Answer: 15/28-----------------------
Explanation:
The probability of selecting a male is 5/8. After the male is chosen, there are 8-1 = 7 mice left. The probability the second mouse is female is 3/7 since there are 3 female mice out of 7 left total.
We get this result after multiplying the values: (5/8)*(3/7) = 15/56
Now consider that the first mouse is female. The probability of this is 3/8. The probability that the second mouse is male is 5/7.
The fractions multiply to (3/8)*(5/7) = 15/56. We get the same result as before due to the numerators swapping places, but not much else happens. So we have a sort of symmetry going on here.
The last step is to add the two results we got:
(15/56)+(15/56) = (15+15)/56 = 30/56 = 15/28
Or you could compute it like this
2*(15/56) = (2*15)/56 = 30/56 = 15/28
The '2' is to signify there are two ways to select exactly one male and exactly one female, where the order doesn't matter.
--------------------------
Here's another way we can get the answer.
The probability we get both males is 5/14 found back in problem 1.
The probability we get both females will follow the same idea as problem 1, and we would compute (3/8)*(2/7) = 6/56 = 3/28
Add those fractions: (5/14) + (3/28) = (10/28) + (3/28) = 13/28
Now consider the events
C = event of selecting two mice of the same gender (both are male OR both are female; pick 1 scenario only)D = event of selecting two mice of different genders (the first is male, the other is female, or vice versa)Events C and D are complementary events.
We calculated that P(C) = 13/28, which means
P(D) = 1 - P(C)
P(D) = 1 - (13/28)
P(D) = (28/28) - (13/28)
P(D) = (28-13)/28
P(D) = 15/28
What is the slope of the line shown in the graph?
A) -1
B) -2
C) - 1/2
D) 2
Answers
Answer:
-2
Step-by-step explanation:
to find the slope from to points you can follow this equation
m=y2-y1 / x2-x1
so plug in the points
1-3/ 1-0
-2/1
-2
Does anyone know this answer??
Answers
Approximately 99.7% of scores lie in the shaded region.
We have,
The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.
According to this rule:
Approximately 68% of scores lie within 1 standard deviation of the mean.
Approximately 95% of scores lie within 2 standard deviations of the mean.
Approximately 99.7% of scores lie within 3 standard deviations of the mean.
Now,
In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.
This encompasses the area within 3 standard deviations of the mean.
And,
Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.
Therefore,
Approximately 99.7% of scores lie in the shaded region.
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