The equivalent of the expression 2³/2⁷ using the law of indices is (a) 1/2⁴
How to determine the equivalent expression?From the question, we have the following parameters that can be used in our computation:
2³/2⁷
The above expression can be solved using the law of indices
When the law of indices is applied, we have the following representation
2³/2⁷ = 2(³ ⁻ ⁷)
Remove the bracket in the above expression
So, we have the following representation
2³/2⁷ = 2³ ⁻ ⁷
Evaluate the difference
This gives
2³/2⁷ = 2⁻⁴
Rewrite as
2³/2⁷ = 1/2⁴
Hence, the solution is (a) 1/2⁴
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find the value of 11 (a + b) when a = 7 and b = 3. (a) 110
(b)77
(c) 11,000
(d) 44
Answer:
(a) 110
Step-by-step explanation:
We can plug in 7 for a and 3 for b. Then we can simplify
11(a + b)
11(3 + 7)
11(10)
110
Thus, the value of 11(a + b) when a = 7 and b = 3 is 110, or answer a
a. it calculates the return values for the class b. it invokes all the class methods in order c. it is a method used when instantiating an object d. it is defined in the client code for the class e. it provides access to methods and instance variables
The right answer is C. It is a technique applied when creating an object.
When an object is generated from a class in object-oriented programming, a constructor, a particular method, is called. It is in charge of initializing the object and establishing its starting state. Typically, constructors are specified in the class specification and called when an object is created with the new keyword. They are used to create and initialize objects of that class and share the same name as the class.
In the event that a constructor's arguments include default values, it is possible to call it without any arguments. Additionally, a class may have many constructors with various amounts or kinds of parameters due to overloading, which allows for this.
Option A is erroneous since a constructor does not figure out the class's return values. Because a constructor does not call each of the class methods sequentially, option B is incorrect. Option D is erroneous since the class definition, not the client code, contains the definition of a constructor. Because a constructor gives access to methods and instance variables, Option E is valid, but it's not the only one.
The complete question is:-
Which statement is true about a constructor?
A. It calculates the return values for the class
B. It invokes all the class methods in order
C. It is a method used when instantiating an object
D. It is defined in the client code for the class
E. It provides access to methods and instance variables
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Haley bought a new truck for her landscaping business. She loves that it has space for all her equipment, but she wishes it got better gas mileage. She only gets 18.4 miles per gallon on the highway. If her gas tank holds 20.5 gallons, how far can she drive with a full tank?
Answer: 377.2 miles
Step-by-step explanation:
m x g. / 18.4 x 20.5
A rectangle has an area of 114cm squared and a perimeter of 50cm. What are the dimensions
If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.
Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².
So, we have:
lw = 114
Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.
So, we have:
2l + 2w = 50
We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:
l = 114/w
We can then substitute this expression for l in the second equation:
2(114/w) + 2w = 50
Multiplying both sides by w to eliminate the fraction, we get:
228 + 2w² = 50w
Rearranging and simplifying, we get a quadratic equation:
2w² - 50w + 228 = 0
We can solve for w using the quadratic formula:
w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5
Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:
l(5) = 114
l ≈ 22.8
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divide the polynomials x^2-10,000/x-100
Answer:
x+100
Step-by-step explanation:
x^2-10,000/x-100
x^2-10000 is a difference in squares and can be factored.
x^2-10000 = (x+100)(×-100).
(x+100)(x-100)/(x-100)
(x-100) cancel each other.
x+100 remains.
what is the property of 3x(5x7)=(3x5)7
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
Use factoring to solve the polynomial equation. Check by substitution or by using a graphing utility and identifying
x-intercepts.
8x4-32x² = 0
Rewrite the equation in factored form.
(Blank)=0
Then what is the solution pair?
The solution to the polynomial equation 8x⁴ - 32x² = 0 by factoring are x = 0 or x = -2 or x = 2
Using factoring to solve the polynomial equationTo solve the equation 8x⁴ - 32x² = 0 by factoring, we can factor out the greatest common factor of the terms:
8x²(x² - 4) = 0
Now we can use the difference of squares identity to factor the quadratic expression:
8x²(x + 2)(x - 2) = 0
Using the zero product property, we know that the product of two factors is zero if and only if at least one of the factors is zero.
Therefore, we can set each factor equal to zero and solve for x:
8x² = 0 or x + 2 = 0 or x - 2 = 0
Solving for x, we get:
x = 0 or x = -2 or x = 2
So the solution set for the equation is {0, -2, 2}.
To check the solution, we can substitute each value into the original equation and verify that it equals zero.
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i need help
can you look over this picture and see what the answer is
Answer:
AC = 12
Step-by-step explanation:
If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore
ΔABC is similar to ΔADE.
The sides of smaller triangle are in proportion with sides of bigger triangle.
Therefore we have the equation:
AC/AE = AB/AD
Substitute the given numbers:
x/x+15 =8/18
18x= 8(x+15)
18x = 8x+120
10x = 120
x = 12
AC=12
I don't know how to do.
Solve for the missing side length. Round to the nearest tenth.
5.8
5.2
5.4
5.6
Answer:
C) 5.4-------------------------
Given two legs of a right triangle and we need to find the hypotenuse.
Use Pythagorean theorem:
\(PQ = \sqrt{QR^2+PR^2}\)\(PQ = \sqrt{2^2+5^2} =\sqrt{29} =5.385 = 5.4\ (rounded)\)The matching choice is C.
25/22 as a decimal rounded to the nearest hundredths
Answer:
Hi there!
Step-by-step explanation:
First thing we have to do is make 25/22 a proper fraction. That is 1 3/22. This converted to a decimal is 1.1(36) or, rounded to the nearest hundredth, that is 1.1 :)
Hope you enjoy!
What is the effect on the graph of f(x) = x2 when it is transformed to h(x) = 2 x2 + 15?
Answer:
B
Step-by-step explanation:
The effect on the graph of f(x)=x² when it is transformed to h(x)=2x²+15 is the graph of f(x) is vertically streched by 2 and moved up by 15 unit.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)
Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given two functions, f(x) and h(x). Also, the function f(x) = x² is transformed to form h(x) = 2x² + 15. Therefore, we can write the transformation as,
f(x) vertically streched by a factor of2 first, Therefore,
g(x) = 2f(x)
= 2x²
Now, the function g(x) is moved up by 15 units, therefore,
h(x) = g(x) + 15
= 2x² + 15
Hence, the effect on the graph of f(x)=x² when it is transformed to h(x)=2x²+15 is the graph of f(x) is vertically streched by 2 and moved up by 15 unit.
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What is the rate of change from x = 0 to x = pi over 2 ? (6 points) trig graph with points at: (0, negative 4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, negative 4)
Answer:
Rate of Change : 8 / π
Step-by-step explanation:
To determine this rate of change, we have to first consider the points at x = 0 and x = π / 2.
When x = 0, f( x ) = - 4,
When x = π / 2, f( x ) = 0
Remember that rate of change is represented by a change in y / change in x. Therefore,
( 0 - ( - 4 ) ) / ( π / 2 - 0 ),
( 0 + 4 ) / ( π / 2 ),
4 / π / 2 = 8 / π
Therefore the rate of change from x = 0 ➡ x = π / 2 will be 8 / π.
A researcher wishes to determine what percentage of college freshmen also work full time. To do this, the researcher obtains a list of all enrolled freshunen, manipulates the list so that females appear twice is often as males, and then selects from this list
a. Probability Sampling
b. Convenience Sampling
c. Voluntary Sampling
d. Stratified Sampling
e. None of the above
Answer:
d. Stratified Sampling
Step-by-step explanation:
Stratified Sampling is a form of sampling in which the researcher selects a population sample based on a demographic factor or strata such as race or gender. From the different strata, a random sample is then made such that each group or subpopulation is represented in the final sample.
It should be noted that retaining the percentages while selecting a randomized sample is essential to stratified sampling.
Hence, in this case, when the researcher obtains a list of all enrolled freshmen, manipulates the list so that females appear twice as often as males, and then selects from this list, this is an example of stratified sampling
The container that holds the water for the football team is 1/5 full. After pouring in gallons of water, it is 7/10 full. How many gallons can the container hold?
The required container can hold (10/3) times the amount of water poured into it.
What is the equation model?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let's assume the container can hold "x" gallons of water.
According to the problem, the container is 1/5 full initially, which means it contains (1/5)x gallons of water.
After pouring in some water, it is 7/10 full, which means it contains (7/10)x gallons of water.
The difference between the initial and final amounts of water is the amount of water poured into the container. Therefore, we can set up an equation:
(7/10)x - (1/5)x = the amount of water poured into the container
(7/10 - 1/5)x = (3/10)x = the amount of water poured into the container
We know that this amount of water is in gallons, so we have:
(3/10)x = the amount of water poured into the container in gallons
We can solve for "x" by dividing both sides by 3/10:
x = (the amount of water poured into the container in gallons) / (3/10)
x = (10/3) x (the amount of water poured into the container in gallons)
Therefore, the container can hold (10/3) times the amount of water poured into it.
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Question Below.
Answers: 250|253|254|255|307|433|434|435|507|.
First to answer this question the quickest is rewarded branliest + 100 points
Answer:
Minimum--> 250
Q1--> 255
Q2--> (Median): 307
Q3--> 433
Maximum-->507
Step-by-step explanation:
To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.
First, we need to sort the data set in ascending order:
{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }
Minimum: 250
Maximum: 507
To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.
Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.
Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.
Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.
How would you graph the solutions to the inequality on a number line? k > 5
To graph the inequality k > 5 on a number line, mark an open circle at 5 and shade the region to the right.
To graph the solutions to the inequality k > 5 on a number line, follow these steps:
Draw a horizontal line and mark a point for the number 5 on the line.
-------------------|---|---|---|---|---|---|---|---|---|---|
0 1 2 3 4 5 6 7 8 9 10
Since the inequality is k > 5, the solution includes all values greater than 5. Therefore, draw an open circle (○) at the number 5 to represent that 5 itself is not included in the solution.
-------------------|---|---|---|---○---|---|---|---|---|---|
0 1 2 3 4 5 6 7 8 9 10
Shade the region to the right of the open circle. This shading represents all values that are greater than 5 and satisfy the inequality k > 5.
-------------------|---|---|---|---○===================>
0 1 2 3 4 5 6 7 8 9 10
The resulting number line graph illustrates that any value to the right of the open circle (excluding 5 itself) satisfies the inequality k > 5.
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find the missing coordinate of p, using the fact that p lies on the unit circle in the given quadrant. ( , -7/25) is in the 4th quadrants
The missing x coordinate is (24/25).
What is a Circle ?
A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle.
As per the given data:
p lies on the unit circle
radius of circle = 1 unit
p is in 4th quadrant:
Let's assume p as (x, (-7/25))
equation of the circle:
x² + y² = 1
x² + (-7/25)² = 1
x² = 1 - (49/625)
x² = (576/625)
x = ± 24/25
But as point is in 4th quadrant, x will be positive.
x = (24/25)
The coordinate of point p is ((24/25), (-7/25))
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Forty percent of all undergraduates at a university are chemistry majors. In a random sample of six students, find the probability that exactly two are chemistry majors. 12. The probability that exactly two are chemistry majors is Type an integer or a decimal. Round to four decimal places as needed.)
Answer:
0.3110
Step-by-step explanation:
This is a binomial distribution with probability of success (being a chemistry major) p = 0.40.
The general formula for a binomial distribution is:
\(P(x=k)=\frac{n!}{(n-k)!k!}*p^k*(1-p)^{n-k}\)
Where n is the sample size and k is the desired number of successes.
The probability of k=2 in a sample of n =6 is:
\(P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2} \\P(x=2)=\frac{6!}{(6-2)!2!}*0.4^2*(1-0.4)^{6-2}\\P(x=2)=3*5*0.4^2*0.6^4\\P(x=2)=0.3110\)
The probability is 0.3110
Probability which can be classified as an event
The probability of an event is the number of favorable outcomes divided by the total number of outcomes possible. Converting the fraction 35 to a decimal, we would say there is a 0.6 probability of choosing a banana. This basic definition of probability assumes that all the outcomes are equally likely to occur.
hope it helps...!!!
XYZ company is situated in Ghana. They have been commissioned your organisation to design a database for them. The database is expected to keep data on employees, customers, suppliers, and products. Important records on employees such as employee's ID, date of birth, and dependants are expected to be captured in the database. Products information such as product's ID, name of product, manufacturing and expiring data, and name of supplier are expected to be captured. The company receives suppliers from different organisations, hence, it would like the database to capture relevant details of these suppliers. Each supplier supplies only one type of product for the company. Every customer is assigned one sales representative, yet sales representatives maybe assigned up to ten customers. Customers can order an unlimited number of good. Properly represent all entities, relationships, constraints, and appropriate keys in an E-R diagram that can readily be used in a database.
By answering the presented question, we may conclude that Sales Rep: expression This entity maintains information about sales reps such as SalesRepID and SalesRepName.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
The ER diagram above depicts the database entities and their connections. Here's a quick rundown of each entity and its characteristics:
Employee: This object contains information on employees such as EmployeeID, Name, DateOfBirth, and Dependents.
ProductID, ProductName, ManufacturingDate, ExpiryDate, and SupplierID are all stored in this object.
Supplier: This entity holds supplier-specific information such as SupplierID, SupplierName, ContactPerson, and ContactNumber.
CustomerID, CustomerName, ContactPerson, and ContactNumber are all stored in the Customer entity.
Sales Rep: This entity maintains information about sales reps such as SalesRepID and SalesRepName.
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g During winter, red foxes hunt small rodents by jumping into thick snow cover, without any visual clue. Researchers examined the compass direction of hundreds of such jumps. They found that 73% of jumps in the northeast direction were successful, compared with 60% of jumps in the southwest direction and only 18% of jumps in all other directions. True or False: Jumping direction and jump outcome are independent.
Answer: False
Step-by-step explanation:
Events can be classed as being dependent or independent depending on whether the outcome of a certain event affects the outcome of another. In the scenario above, the success rate of jumps in the Northeast direction is higher than in the southwest direction and even much than in other directions. With these uneven rate of success, the probability that a fox will have a successful jump will depend on the direction in which the fox is jumping. With an high expected success probability in the Northeast and southwest than in other directions
What is the result when you combine only the constants in the following expression?
3 a minus 6 b + 3 minus 7 a + 10
Answer:
6b-4a+13
Step-by-step explanation:
3a-6b+3-7a+10
3+10=13
3a-7a=-4a
6b-4a+13
Answer:
13
Step-by-step explanation:
Which is true about the solution to the system of inequalities shown? y > 3x + 1 y < 3x – 3 On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded. Only values that satisfy y > 3x + 1 are solutions. Only values that satisfy y < 3x – 3 are solutions. Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions. There are no solutions.
There are no solutions to the system of inequalities Option (d)
Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.
A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is
y > 3x + 1
y < 3x - 3
The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.
The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.
Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.
To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.
When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.
There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.
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Complete Question :
Which is true about the solution to the system of inequalities shown?
y > 3x + 1
y < 3x – 3
On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.
Options:
a)Only values that satisfy y > 3x + 1 are solutions.
b)Only values that satisfy y < 3x – 3 are solutions.
c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.
d)There are no solutions.
Answer:
D
Step-by-step explanation:
There are 20 Nickels in one dollar, How
many dollars do you have in 1940
Nickels?
$ 114
$ 54
$ 19
S 97
Answer:
97
Step-by-step explanation:
it is 97 because you divide 1940 by 20
Answer:
388 nickles "i hope this helps"
Step-by-step explanation:
Find the volume of the cylinder to the nearest cubic foot. Use a calculator. A. 236 ft3 B. 942 ft3 C. 251 ft3 D. 75 ft3
\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3\)
Answer:
236 ft^3
Step-by-step explanation:
Base radius = 5 ft
Height = 3 ft
Volume = πr^2h
= π × 5^2 × 3
= 75π
= 235.61944901923 feet^3
Nearest Cubic Foot = 236 ft^3
Nearest Cubic Foot:
Hence Answer is:
236 ft^3
Hope this helps!
10 POINTS
MIDDLE SCHOOL 8TH GRADE MATH
Need some help with this question can anyone please give me the answer?
How do I find percent change, so confused, please help.
HELP THIS IS DUE TODAY
Answer:
cars per minute
Step-by-step explanation:
time is in minutes at the bottom so it cant be cars per hour
Vanessa and Zack are playing a game where the player with the lower score wins. At the end of the game, Vanessa has a score of Negative 3 and StartFraction 5 over 8 EndFraction and Zack has a score of Negative 3 and two-thirds. Which statement explains who won?
Answer:
-3 2/3 < -3 5/8 so -3 2/3 is lesser
Step-by-step explanation: