Equations will be AgNO3(aq)+HCl(aq)⟶AgCl(s)+HNO3(aq)
AgNO3+HCl⟶AgCl+HNO3 for acid
Ag:+1⟶+1
NO3:−1⟶−1
H:+1⟶+1
Cl:−1⟶−1
According to the solubility table, nitrates are always soluble, so the strong ionic bond between silver ions and nitrate ions are broken by water molecules because of ion-dipole attraction. Acids ionize in water to give mobile ions, so hydrogen chloride in aqueous solution gives out hydrogen ions (and form hydronium ions) and chloride ions.
There are five types of particles in the solution :
H2O molecules, Ag+ ions, NO3− ions, H+ ions, and Cl− ions. (Slight ionization of water is neglected in this case.) They freely bump into each other as they are mobile. However, this freely moving condition is inhibited by the interaction between Ag+ ions and Cl− ions.
According to the solubility table, AgCl is insoluble in water. When Ag+ ions and Cl− ions bump into each other, they strongly attract each other, in which the strong ionic force cannot be separated by the ion-dipole force between them and H2O molecules. As a result, AgCl evolves as a white solid.
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The list below gives the location of 3 friends who are scuba diving together. Mallory is exploring at an elevation of -25 feet. Jacob is standing on the boat, at an elevation of 15 feet. Eva just jumped in and is 5 feet below the surface of the water.
Which inequality correctly compares the distance of the scuba divers from the surface of the water?
Which one of these?
1- Eva > Mallory
2- Mallory < Jacob
3- Jacob < Eva
4- Mallory > Eva
Mallory is further from the surface than Eva. So, Mallory > Eva. Therefore, option D is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Mallory is exploring at an elevation of -25 feet.
So, distance between Mallory and the surface of water is 25 feet
Jacob is standing on the boat, at an elevation of 15 feet.
Distance between Jacob and the surface of water is 15 feet
Eva just jumped in and is 5 feet below the surface of the water.
Distance between Eva and the surface of water is 5 feet
In this case, the person closest to the surface is Eva, who is 5 feet from the surface.
So, the inequality is Mallory > Eva
Therefore, option D is the correct answer.
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Which of the following matrix multiplications are possible?
[a b] x [c d]
The matrix multiplication is possible for option (b) 1 × 3 by 3 × 3, and option (c) 2 × 1 by 1 × 2.
What is a matrix?
A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.
It is known that if the number of columns of a matrix A be equal to the number of rows of another matrix B then the product of matrix A and matrix B i.e. AB is defined.
a) In this option no of columns in first matrix is 1 and the no of rows in second matrix is 2.
That means no of columns in first matrix is not equal to no of rows in second matrix.
Hence, in this case matrix multiplication is not possible.
Therefore, option (a) is incorrect.
b) In this option no of columns in first matrix is 3 and the no of rows in second matrix is also 3.
That means no of columns in first matrix is equal to no of rows in second matrix.
Hence, in this case matrix multiplication is possible.
Therefore, option (b) is correct.
c) In this option no of columns in first matrix is 1 and the no of rows in second matrix is 1.
That means no of columns in first matrix is equal to no of rows in second matrix.
Hence, in this case matrix multiplication is possible.
Therefore, option (c) is correct.
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given the experimental data, what is the activation energy, ea, (in kj/mol) for this reaction? hint: r
The activation energy for the given reaction is166 KJ/mol. (Option B)
Activation energy refers to the minimum amount of extra energy that is required by a reacting molecule to be converted into product. It is the minimum amount of energy required to energize or activate atoms or molecules so that they can undergo a chemical reaction or transformation. In order to calculate the activation energy (Ea), the Arrhenius equation is used which is given by:
k=Ae^((-E)/RT)
where k is the rate of chemical reaction, A is a constant depending on the chemicals involved, E is the activation energy, R is the universal gas constant, and T is the temperature.
The equation can be expressed as
ln〖k=ln〖A-(E/RT)lne〗 〗
2.303 log〖k=2.303 log〖A-E/RT〗 〗
log〖k=log〖A-E/2.303RT〗 〗
As there are two temperatures and two rate constants given, the Arrhenius equation is rearranged:
log〖k2/k1=E/2.303(1/T1〗-1/T2)
According to the data,
k1 = 2.7 x 10^-4
T1 = 600 K
k2 = 3.5 x 10^-3
T2 = 650 K
R = 8.314
log〖(3.5 x10^(-3))/(2.7 x 10^(-4) )=E/(2.303*8.314)(1/600〗-1/650)
E = 166208 J/mol or 166 KJ
Note: The question is incomplete. The complete question probably is: Calculate the activation energy (Ea) in kJ/mol for a reaction if the rate constant (k) is 2.7 × 10^-4 (M^−1sec^−1) at 600 K and 3.5 × 10^−3 (M−^1sec^−1) at 650 K. a. −166 kJ/mol b. 166 kJ/mol c. 1.64 kJ/mol d. 1.66 × 10^5 kJ/mol. (R
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Use the distributive property to solve 12x9
The value of given expression 12*9 is 108
What is Algebraic expression ?
Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The basics of algebra taught us how to express an unknown fee using letters which includes x, y, z, and so forth. these letters are known as here as variables. An algebraic expression can be a aggregate of both variables and constants. Any price that is placed before and accelerated through a variable is a coefficient.
Given expression ,
12*9 = (3*4) * (3*3)
= 9*(3*4)
= 9* 12
= 108
Hence, The value of given expression 12*9 is 108
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Sample Spaces and Probabilities (18 points) For each of the following scenarios first describe the sample space and indicate how big it is (i.e., what its cardinality is) and then answer the question. (a) [3 Points] You flip a fair coin 50 times. What is the probability of exactly 20 heads? (b) [3 Points] You roll 2 fair 6-sided dice, one red and one blue. What is the probability that the sum of the two values showing is 4? (c) [3 Points] You are given a random 5 card poker hand (selected from a single deck). What is the probability you have a full-house (3 cards of one rank and 2 cards of another rank)? (d) [3 Points] 20 labeled balls are placed into 10 labeled bins (with each placement equally likely). What is the probability that bin 1 contains exactly 3 balls? (e) [3 Points] There are 30 psychiatrists and 24 psychologists attending a certain conference. Three of these 54 people are randomly chosen to take part in a panel discussion. What is the probability that at least one psychologist is chosen? What is the probability that exactly three psychologists are chosen? (f) [3 Points] You buy ten cupcakes choosing from 3 different types (chocolate, vanilla and caramel). Cupcakes of the same type are indistinguishable. What is the probability that you have at least one of each type?
(a) Sample space: 2^50 (1,024,000). Probability of exactly 20 heads: 0.000244140625.
(b) 6^2 (36). Probability of a sum of 4: 1/9.
(c) C(52,5) (2,598,960). Probability of a full house: 0.001441.
(d) 10^20 (10^19). Probability of bin 1 containing exactly 3 balls: 1/10^19.
(e) C(54,3) (19,323). Probability of at least one psychologist: C(24,1)/C(54,3) (0.841). Probability of exactly three psychologists: C(24,3)/C(54,3) (0.037).
(f) 3^10 (590,490). Probability of at least one of each type: 0.001690.
(a) The sample space consists of all the possible outcomes of flipping a fair coin 50 times, which is 2^50 (1,024,000). There are only two possible outcomes for each flip, heads or tails. The probability of getting exactly 20 heads is 0.000244140625.
(b) The sample space consists of all the possible outcomes of rolling a red and a blue 6-sided die, which is 6^2 (36). The probability of getting a sum of 4 is 1/9.
(c) The sample space consists of all the possible 5 card poker hands (selected from a single deck), which is C(52,5) (2,598,960). The probability of getting a full house (3 cards of one rank and 2 cards of another rank) is 0.001441.
(d) The sample space consists of all the possible ways of placing 20 labeled balls into 10 labeled bins, which is 10^20 (10^19). The probability of bin 1 containing exactly 3 balls is 1/10^19.
(e) The sample space consists of all the possible ways of selecting 3 of the 54 people attending the conference, which is C(54,3) (19,323). The probability of at least one psychologist being chosen is C(24,1)/C(54,3) (0.841). The probability of exactly three psychologists being chosen is C(24,3)/C(54,3) (0.037).
(f) The sample space consists of all the possible ways of buying ten cupcakes from the 3 different types, which is 3^10 (590,490). The probability that you have at least one of each type is 0.001690.
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The town of Simpsonville has two tow truck companies. Company A charges an initial fee of $30 plus $2 per mile. Company B charges an initial fee of $20 plus $4 per mile. Use the graph to determine when it's cheaper to use Company B instead of Company A.
Using the graph, it's cheaper to use Company B instead of Company A; when the number of miles is less than 5 miles.
How to interpret Linear equation graphs?For us to solve this question, we need to first create an equation;
If A company initially supplies $30 and then $2 per mile, then the equation here is:
y = 2x + 30
If B company initially supplies $20 and then $4 per mile, then the equation is expressed as:
y = 4x + 20
Due to the fact that the two wages are asked to be equalized, we equate these two equations with each other and find the result.
2x + 30 = 4x + 20
2x = 10
x = 10/2
x = 5
This is the number of miles that both companies will charge a customer the same amount.
Then the time for which it is cheaper to use company B is when number of miles is less than 5.
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6. Write a polynomial function of the least degree that has the root x = (5+ i).
Factors:
Polynomial Function:
To much to right but have it in pic: \/ \/
3x+12y=-8 show ur work
Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.
Draw two rectangles that have the same area but are not congruent.
Violet creates a rectangle with an area of 12 square feet. Bertie makes a rectangle with an area of 12 squares meters. Do the two rectangles have the same area?
Same-sized rectangles are possible. However, because their sides might differ in length, they are not congruent.
What does it mean when two rectangles are congruent?Congruent refers to two rectangles having the same dimensions and shape. So, two rectangles are said to be congruent if their length and width are equivalent in size. The length and width of two rectangles must match for them to be congruent.
Also having the same area are congruent shapes, such as rectangles. However, congruent rectangles with the same area are not always the case. There are differences among rectangles. Figures that have the exact same shape but differ in size are referred to as similar figures.
These two polygons are incongruent because while their matching sides are equal, their corresponding angles are not. Despite the sides being the same size, they have different forms.
The complete question is:
Draw two rectangles that have the same area but are not congruent.
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Dorothy bought 4 boxes of chocolates for $12. Find the unit price.
Answer:
3
Step-by-step explanation:
12/4=3
-8.8/x = 1.5/10
Pls help
Answer:
x = 58.67
Step-by-step explanation:
[tex]\frac{-8.8}{x}[/tex] = [tex]\frac{1.5}{10}[/tex]
Cross multiply
1.5x = (-8.8)(10)
1.5x = -88
Divide, solve for x
x = -88/1.5 = -58.6666667 = around -58.67
Write True if the statement is correct and Faise if the statement is incorrect
1. Every composite number can be expressed as a product of primes
, 2. Some quadratic equation has infinite solution
3. For any two real numbers x andythenix-yl=ly=xl
4. 2(3+√7)-2√7 = 6√7
5. 25,471,287 is not divisible by 3 and 9,
6. √6 is not rational number,
7. Between every two real numbers there is another real number,
8. For any natural numbers a and b GCF (a, b) * LCM(a,b) = a*b.
9. Integer is not closed under division,
10. The product of non zero rational number and irrational number is rational⁹
1. Every composite number can be expressed as a product of primes - True
2. Some quadratic equation has infinite solution - True
3. False (ix-yl = |x-y|, which may not equal ly = |y|)
What is Rational Number?A rational number is a number that can be expressed as the ratio of two integers.A rational number can be written in the form p/q, where p and q are integers and q ≠ 0.Examples of rational numbers include -3/4, 0, 1/2, and 5.Every integer is a rational number, since it can be expressed as the ratio of the integer and 1.Every fraction can be represented as a rational number, since it is the ratio of two integers.The decimal representation of a rational number will either terminate (e.g. 1/4 = 0.25) or repeat (e.g. 1/3 = 0.3333...).The set of rational numbers is dense, meaning that between any two rational numbers, there is another rational number.4. 2(3+√7)-2√7 = 6√7 - False
5. False (25,471,287 is divisible by 3)
6. √6 is not rational number - True
7. Between every two real numbers there is another real number -True
8. For any natural numbers a and b GCF (a, b) * LCM (a, b) = a*b. -True
9. Integer is not closed under division -True
10. False (The product of a non-zero rational number and an irrational number is not necessarily rational)
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5. Jenna is making
bracelets.
She needs 7
inches of string for each
bracelet. She has a spool
with 16 feet of string. How
many bracelets can Jenna
make?
Answer:
Step-by-step explanation:
Each bracelet need 7 inches of string. Jenna has a total of 16 feet of string.
Divide the total amount of string by the number of inches needed for each bracelet.
Step 1: Convert 16 feet into inches. 12 inches = 1 foot
16 feet x (12 inches/1 foot) = 192 inches
This is the total inches of string.
Note that feet and foot units cancel and you are left with inches.
Step 2: Find the number of bracelets that can be made. Use the answer from step 1. Each bracelet needs 7 inches of string.
Total inches of string / 7 inches of string for each bracelet
192 inches / 7 inches = 27.4
Round the answer to 27.
the manager of a large company that sells pet supplies online wants to increase sales by encouraging repeat purchases. the manager believes that if past customers are offered $10 off their next purchase, more than 40 percent of them will place an order. to investigate the belief, 90 customers who placed an order in the past year are selected at random. each of the selected customers is sent an e-mail with a coupon for $10 off the next purchase if the order is placed within 30 days. of those who receive the coupon, 38 place an order.
At the significance level of a = 0.05, there is no strong statistical support for the manager's assertion.
Accepting it would be a type II error because the null hypothesis might not be true.
The 'null' and 'alternative' hypotheses should be
p 0.4 for H0 and p > 0.4 for Ha
q= 1-p= 1-0.4= 0.6
The alpha level for significance is 0.05.
For one-tailed tests, the crucial area is Z> ± 1.645
The sample proportion is p^= x/n= 38/90=0.42222
Using the z statistic
z= p^- p/ √pq
z= 0.422-0.4/ √0.4*0.6
z= 0.04536
We are unable to reject the null hypothesis since the calculated value of z=0.04536 does not fall within the crucial zone Z> 1.645.
The manager's assertion is not sufficiently supported by the available data.
When we reject the actual null hypothesis, we commit a type I mistake.
When we accept the incorrect null hypothesis, we make type II errors.
Accepting it would be a type II error because the null hypothesis might not be true.
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Mr. Smith owns a car that is currently worth $8,000. The value of the car depreciates at the rate of 25% each year. Which of the following graphs represents the value of the car, y, in dollars, after x years? V
Answer:
Car Value Depreciation Graph
The graph that represents the value of the car, y, in dollars, after x years is the graph that starts at $8,000 on the y-axis and decreases at a steady rate of 25% each year on the x-axis. It would be the graph V.
Derek tried to solve an equation step by step. 8d=72 8d/8 = 72/8 d=8 Find Derek's mistake
The mistake of Derek is that 72 divided by 8 is 9, not 8.
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 is an equation that Derek is trying to solve.
The equation is 8d = 72.
8d = 72
In the first step, Derek divided both sides of the equation by 8, which is a correct way to solve the problem.
We have to divide both sides of the equation by 8.
8d / 8 = 72 / 8
This step is correct.
After dividing, in the left hand side, there will be only 'd' remaining and in the right hand side, 27/8 = 9.
d = 9
But Derek got 8 instead of 9 in the right hand side.
Hence the value of d is 9 and not 8, which is the mistake of Derek.
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You go to the grocery store and purchase the items listed in the table. What is your total if
the sales tax is 7%?
The total price is obtained following these two steps:
Adding the price of all the products in the table.Multiplying the total by 1.07, due to the sales tax of 7%.How to obtain the total price?The first step is obtain the price without taxes, which is done adding the price of all the items in the data-set.
Then the proportion is applied, relative to the sales tax of 7%.
The percentage of a sales tax of 7% is given as follows:
107%.
Hence the multiplier relative to this sales tax is given as follows:
1.07.
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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4. Explain how to use division to find an
equivalent fraction for 20/16
Answer:
5/4
Step-by-step explanation:
divide 20 and 16 by 4
20/4=5
16/4=4
Qasim is deciding between two truck rental companies. Company A charges an initial fee of $15 for the rental plus $1 per mile driven. Company B charges an initial fee of $45 for the rental plus $0.50 per mile driven. Graph each function and determine which company would be cheaper if Qasim needs to drive 80 miles with the rented truck.
Equation for the cost of company A: f(x) = 15 + x
Equation for the cost of company B: g(x) = 45 + x/2
For 80 miles, company B is cheaper than company A.
What is linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
Given,
Company A charges an initial fee of $15 for the rental plus $1 per mile driven
f(x) = 15 + x
Company B charges an initial fee of $45 for the rental plus $0.50 per mile driven
g(x) = 45 + 0.5x
g(x) = 45 + x/2
x is number of miles
For 80 miles company A charges
f(80) = 15 + 80
= 95
For 80 miles company B charges
g(80) = 45 + 80/2
= 85
By the above calculation, Company B is cheaper than Company A for 80 miles drive.
Hence,
f(x) = 15 + x is Equation for the cost of company A
g(x) = 45 + x/2 is Equation for the cost of company B
Company B is cheaper than company A for drive of 80 miles.
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Housing prices in a small town are normally distributed with a mean of
$147,000 and a standard deviation of $7,000. Use the empirical rule to
complete the following statement.
Approximately 95% of housing prices are between a low price of
$Ex: and a high price of $
Approximately 95% of housing prices are between a low price of $133,000 and a high price of $161,000.
What is defined by the Empirical Rule?These approximate percentages are defined by the Empirical Rule, for a normally distributed variable.
68% of the measures within one standard deviation of the mean.95% of the measures within two standard deviation of the mean.99.7% of the measures within three standard deviation of the mean.Hence the prices within two standard deviations of the mean are given as follows:
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The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
The likelihood of randomly selecting a chocolate chip cookie from the batch is unlikely. Therefore, option C is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
Given that, the baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies.
P(chocolate chip) = 0.25
In probability, larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 0.5 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
Here, 0.25<0.5
Therefore, option C is the correct answer.
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Answer:unlikely
Step-by-step explanation:
William and his children went into a restaurant that sells hamburgers for $8 each and drinks for $2.50 each. William has $95 to spend and must buy no less than 18 hamburgers and drinks altogether. If xx represents the number of hamburgers purchased and yy represents the number of drinks purchased, write and solve a system of inequalities graphically and determine one possible solution.
Answer: We can set up the following system of inequalities to represent the situation:
8x + 2.5y <= 95 (the total cost of the hamburgers and drinks must be less than or equal to $95)
x >= 18-y (William must buy no less than 18 hamburgers and drinks altogether)
x >= 0, y >= 0 (non-negative values for the number of hamburgers and drinks purchased)
To graph the system of inequalities, we can start by graphing the inequality 8x + 2.5y <= 95, which represents a boundary line in the xy-plane. Since it's a less or equal sign, we will shade the area that is below the line.
The second inequality represents a boundary line which is the line x = 18-y. Since x must be greater than or equal to 18-y, we will shade the area that is on or above the line.
The third inequality is a non-negative constraint for both x and y, so we will graph the x and y axis and shade the area that is above them.
After combining all the shaded areas, we'll get a feasible solution region that represents possible values of x and y that satisfies the system of inequalities.
One possible solution to the system of inequalities is x=24 and y=6, which is a point in the feasible region that satisfies all the inequalities.
It's worth noting that there could be other solutions as well, depending on the number of hamburgers and drinks William wants to buy.
Step-by-step explanation:
When adding two vectors, I should do the following: O Pick an angle and just go with it. O Write each vector in component form and add the components separately. O Combine all the vector components into one number and add them. O Calculate the magnitude of each vector and add them.
Write each vector in component form and add the components separately. This new vector will represent the sum of the two original vectors. This is the most straightforward way to add two vectors.
1. Write each vector in component form. This means breaking down each vector into its x- and y-components.
2. Add the x-components of each vector together and the y-components of each vector together.
3. The result will be a single vector with both x- and y-components.
To add two vectors, I should write each vector in component form, breaking them down into their x and y components. Then, I should add the components together, resulting in a new vector with components that are the sum of the two original vectors' components. This new vector will represent the sum of the two original vectors. This is the most way to add two vectors.
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Please help me out. I Need it today
Answer:
greetings!!!
Look at the attachment above
and If you have any questions or unclear ideas tag on the comments.
Hope it helps!!!
what is 5 3/5 divided by 2 2/3
Answer:
Exact Form:
21/10
Decimal Form:
2.1
Mixed Number Form:
2 1/10
Step-by-step explanation:
75,232 = ___ in
expanded form
Answer:
seventy-five thousand two hundred thirty-two
Step-by-step explanation:
One Step Equations Exit Ticket help i ned answers fast
The value of the equations are
n = 6
x = 20
b = -4
k = 176
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
a)
-15 + n = -9 be equation (1)
On simplifying the equation , we get
Adding 15 on both sides of the equation , we get
n = -9 + 15
n = 6
Therefore , the value of n is 6
b)
x - 7 = 13 be equation (2)
On simplifying the equation , we get
Adding 7 on both sides of the equation , we get
x = 13 + 7
x = 20
Therefore , the value of x is 20
c)
14b = -56 be equation (3)
On simplifying the equation , we get
Dividing 14 on both sides of the equation , we get
b = - ( -56/14 )
b = -4
Therefore , the value of b is -4
d)
16 = k/11 be equation (4)
On simplifying the equation , we get
Multiply by 11 on both sides of the equation , we get
k = 16 x 11
k = 176
Therefore , the value of k is 176
Hence , the equations are solved
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Compute the probability of x successes in the n independent trials of the experiment. n=9, p=0.5, x≤3
The probability of x successes in the n independent trials of the experiment is 0.1640625
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, n=9, p=0.5, x≤3 we need to find probability of x successes in the n independent trials of the experiment.
We know that,
P(X=x) = ⁿCₓpˣq⁽ⁿ⁻ˣ⁾
q = 1-p = 1-0.5
q = 0.5
P(X=x) = ⁹C₃(0.5)³(0.5)⁹⁻³
P(X=3) = ⁹C₃ (0.5)³(0.5)⁶
⁹C₃ = 9! / 3!(9-3)! = 9!/3! × 6!
⁹C₃ = 84
P(X=3) = 84×0.125×0.015625
= 0.1640625
Hence, the probability of x successes in the n independent trials of the experiment is 0.1640625
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The rule for the glide reflection that maps △ABC with vertices A(–4, –2), B(–2, 6), and C(4, 4) to △A′B′C′ with vertices A′(–2, –2), B′(0, –10), and C′(6, –8) is T⟨a, b⟩ ∘ Rx-axis where
The ΔABC reflects across x-axis with point a=2 and scale factor of x+2 to form the ΔA'B'C'.
What is reflection?
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The vertices of ΔABC is given as -
A(–4, –2), B(–2, 6), and C(4, 4)
The vertices of ΔA'B'C' is given as -
A′(–2, –2), B′(0, –10), and C′(6, –8)
To find the scale factor of the reflection use the formula -
x + a = x' and y + b = y'
Substitute the values in the equation.
For vertex A and A' -
x1 + a = x1'
-4 + a = -2
a = -2 + 4
a = 2
y1 + b = y1'
-2 + b = -2
b = -2 + 2
b = 0
For vertex B and B' -
x2 + a = x2'
-2 + a = 0
a = 0 + 2
a = 2
y2 + b = y2'
6 + b = -10
b = -10 - 6
b = -16
For vertex C and C' -
x3 + a = x3'
4 + a = 6
a = 6 - 4
a = 2
y3 + b = y3'
4 + b = -8
b = -8 - 4
b = -12
It can be seen that the values of a is constant whereas the values of y varies. This happens due to reflection of coordinates across the x-axis.
Therefore, the reflection happens across the x axis.
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Mr. Casey needs to drive 278 miles in 7 hours. He estimates that he should drive at a speed of 50 miles per hour. Is his estimate greater than or less than the actual speed at which he should travel? Explain.
The actual speed of Mr Casey is 39.71 miles per hour and his estimation is greater than the actual speed at which he should travel.
What is estimation?Estimation is a roughly calculated answer of something for which we get an approximate result of it.
Given that, Mr. Casey needs to drive 278 miles in 7 hours. He estimates that he should drive at a speed of 50 miles per hour. We need to find whether his estimation correct or not,
We know that,
Speed = distance / time
Therefore, Mr. Casey's actual speed =
Speed = 278 / 7
= 39.71 miles per hour
As, he estimated his speed being 5o miles per hour, and actual speed is 39.71 miles per hour, therefore, his estimation is greater than the actual speed at which he should travel.
Hence, the actual speed of Mr Casey is 39.71 miles per hour and his estimation is greater than the actual speed at which he should travel.
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