Answer:
2/3
Step-by-step explanation:
ssions with Exponents Quiz - Level F
1) Trey's grandmother stores her picture frames in a box. Each side of the box is 20 inches long.
Trey wants to know the volume of the box.
What is the volume of a box with side
lengths that are 20 inches? Use the formula
V = 83, where s is the length of one side.
400 in.
800 in.
20 in.
2,400 in.
8,000 in.
20 in.
20 in.
Answer:
8000 inv^3
Step-by-step explanation:
6(3x+4)+2(2x+2)+2=22x+31 solve the equation for the given variable
The equation 6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31 has no solution for the variable x.
What is the solutuon to the given equation?Given the equation in the question:
6( 3x + 4 ) + 2( 2x + 2 ) + 2 = 22x + 31
To solve the equation 6(3x + 4) + 2(2x + 2) + 2 = 22x + 31 for the variable x, we will simplify and solve for x.
Apply distributive property:
6 × 3x + 6 × 4 + 2 × 2x + 2 × 2 + 2 = 22x + 31
18x + 24 + 4x + 4 + 2 = 22x + 31
Collect and combine like terms on both sides:
22x + 30 = 22x + 31
Next, we want to isolate the variable x on one side.
22x - 22x + 30 = 22x - 22x + 31
30 = 31
However, we notice that the x terms cancel out when subtracted:
30 ≠ 31
This means that there is no solution.
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Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
A has the larger standard devlation.
What is standard devlation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
We are given two plots of normal distributions A and B.
The mean of a normal distribution is located at the center of the plot.
Since the centers of both of the normal distributions A and B seems to be aligned, therefore, they both seems to have equal means.
The standard deviation basically determines the shape of the distribution.
As you can see, the normal distribution A is more spread out and thus has a larger standard deviation than normal distribution B.
Therefore, the two correct options are
• The means of A and B are equal.
• A has larger standard deviation.
Complete question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Select all that apply:
A has the larger mean.
B has the larger mean.
The means of A and. Q jual.
A has the larger standard devlation.
B has the larger standard deviation.
The standard deviations of A and B are equal.
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Alesha went to the movies. A popcorn is $3 more than a soda. She purchased 1 popcorn and 2 sodas. She spent $21. How much is a popcorn?
Answer: a popcorn is $9
Step-by-step explanation:
soda is $6
What is the difference?
47−55
Enter your answer in the box.
Answer:
-8
Step-by-step explanation:
47 - 55
= 47 + (-55)
= -8
Hope it helps ⚜
A right triangle and two of its side lengths are shown in the diagram. 39 cm 12 cm x cm Which measurement is closest to the value of x in centimeters?
A: 37.1 cm
B: 51 cm
C: 27 cm
D: 40.8 cm
Answer:
Hey Army! The correct answer would be A. 37.1cm
Step-by-step explanation:
I got this correct on my test :)
Find the length of the third side. If necessary, write in simplest radical form.
2√34, 6
The length of the third side is 2√34 + 6.
We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.
Let x be the length of the third side. Then we have:
2√34 + 6 > x
Subtracting 6 from both sides, we get:
2√34 > x - 6
Adding 6 to both sides, we get:
x < 2√34 + 6
Therefore, the length of the third side must be less than 2√34 + 6.
To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:
2√34 + 6 = x
If this is true, then the given sides can form a triangle.
Simplifying the equation, we get:
x = 2√34 + 6
The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.
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Ginny and her classmates formed a study group. The number of girls in the study group was 3 more than twice the number
of boys. There were 11 girls in the study group. How many boys were in the study group?
Answer:
I think the answer is 4 boys
Step-by-step explanation:
Let the no of boys be y.
No. of girls = 11
= 3 + 2y (equation)
3 + 2y = 11
3 - 3 + 2y = 11 - 3
2y = 8
2y/2 = 8/2
y = 4
Boys = 4
Sharon is baking cookies for her friend's birthday. She always uses 2 cups
how many cookies? for 2 cups
Step-by-step explanation:
2
The ratio of berries to oranges is 10:1. If there are 9 oranges, how many berries are there?
Answer:
90 berries
Step-by-step explanation:
Math of Finance: Chapter 2 Test
When we left James, he had decided to take a job at Jimmy John's as a sandwich artist with an expected salary of
$31,200 per year. James is really looking forward to the pay increase to help take care of his wife and two kids
After working four weeks, he gets his first check. It is much less than he expected. It turns out he will only get paid
for two weeks because Jimmy John's has a delayed paying process. Everyone gets paid two weeks after they work to
give Human Resources time to prepare the tax information. Since James gets paid every two weeks, a)what is his
gross income for his checks? His pay was much less. It tums out, other people get his money first. He had to pay
Federal Income Tax. b)Use the chart on the back of the test to determine his FIT. He also has to pay State
Income Tax. Oklahoma has a flat 5% tax. c)What is his SIT at 5% of his paycheck? Also, something called FICA
was on his paystub. His employer told him it was a required 6.2% tax for Social Security Retirement and a 1.45%
tax for Medicare when he gets older. d)Find James' Social Security Tax. e)Find his Medicare Tax. What is the
amount of FICA Tax listed as being withheld(add together)? Next came the big schock. Apparently, the
Republican Party still hasn't ended required healthcare. Because of this, James has to pay for group insurance with
Jimmy John's. It is $100 every paycheck, g)what percent of James' gross income is this each month? Finally,
James looks at the other category. It has two deductions listed. First, it has Sandwich Union Body Dues. Annual
dues are $130. h)How much was taken out for SUB dues just this paycheck? The second charged deduction for
other was IRA Retirement. He remembers signing up because Jimmy Johns' offers a matching 5%. If James' is
maximizing the match, i)how much is being taken out for retirement from his paycheck? After going over all the
numbers with his boss, it looks like James' check is correct. j)How much was his net income? If these numbers
remain consistent through the year, k)how much will James bring home for the year? DWhat percent of his
expected salary is this? James was really looking forward to his big paycheck. He thought he would have enough
money to get a loan on a new car. m)Do you think he should try to get the loan or not? n>Explain your opinion.
Answer:
6.2
Step-by-step explanation:
hope it helpes you in the long run
Help ASAP!!!!!!!!!!!!!!!! (25 POINTS + BRAINLIEST)
A rectangular prism has a square base with side length s units. It also has the curious property that the numerical value of the sum of its edge lengths (in units) is equal to the numerical value of its surface area (in square units).
If one edge of the prism has length 8 units and s 6= 8, then s can be written in the form a + √b, where a and b are integers. Find a + b.
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.
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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Compute the following using a calculator: sec(16π/9). Round your answer to two decimal places.
Answer:
sec(16π/9) ≈ -1.46
Step-by-step explanation:
We can use a calculator to compute the value of sec(16π/9).
On most calculators, we need to ensure that the calculator is set to radians mode. Then, we can enter the expression sec(16π/9) and evaluate it.
Using a calculator, we get:
sec(16π/9) ≈ -1.46
Rounding this to two decimal places, we get:
sec(16π/9) ≈ -1.46
16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
Find the 6terms of the series 247
The six terms of the series 247 are 2, 2, 2, 2, 2, and 2.
To find the six terms of a series, we need to first understand what a series is. A series is defined as the sum of the terms of a sequence. A sequence is a set of numbers in a specific order.
Therefore, a series is a sum of terms from a sequence. There are different types of series, and they have different formulas for calculating their terms.In this case, we are required to find the six terms of the series 247. Since this is a finite series, we can use a formula to calculate the nth term of a finite series.
The formula is given as follows:Tn = a + (n - 1) dWhere Tn is the nth term of the series, a is the first term of the series, n is the number of terms in the series, and d is the common difference between the terms of the series.To find the six terms of the series 247, we need to know the value of a and d. In this case, we can see that the first term of the series is 2. Therefore, a = 2.
Since this is a constant series, we can see that the common difference between the terms is 0. Therefore, d = 0.Substituting these values in the formula, we get:T1 = a + (1 - 1) dT1 = 2 + 0T1 = 2T2 = a + (2 - 1) dT2 = 2 + 0T2 = 2T3 = a + (3 - 1) dT3 = 2 + 0T3 = 2T4 = a + (4 - 1) dT4 = 2 + 0T4 = 2T5 = a + (5 - 1) dT5 = 2 + 0T5 = 2T6 = a + (6 - 1) dT6 = 2 + 0T6 = 2.
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5 (a) Write the ratio 15:35 in its simplest form.
Answer:
Step-by-step explanation:
5 is a factor of 15 and 35
15:35 = 3:7
Solve for x. -2(x + 1/4) +1=5 Enter your answer as a fraction in simplest fo X =
Answer:
exact form:negative 9/4
decimal form:- 2.25
Mixed number form:negative 2 \(\frac{1}{4}\)
Step-by-step explanation:
Write the following expression without negative exponents and without parentheses.
(9x)^-1
Answer:
1/9x
Step-by-step explanation:
The parenthesis around the 9x means that the -1 exponent goes to the whole thing (the 9x) To "fix" a negative exponent push the 9x across a fraction bar to make the exponent positive. When you push the 9x down across a fraction bar that leaves a 1 on top of the fraction, that has nothing to do with the 1 exponent. Its a 1 on top because when you push the 9x down there is nothing left on top so it is a 1.
(9x)^-1
= 1/9x
To be clear, this is a 1 one top and a 9x on the bottom of a fraction.
4. What is Probability?
(ii) State the axioms of probability
(iii)Two fair dice are thrown, what is the probability of getting
(a) the sum of 9
(b) two odd numbers
(c) two prime numbers
(d) two factors of 12
4c. What is Statistics?
(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.
(ii) The axioms of probability are:
the non-negativity (that the probability of an event is greater than or equal to zero), and
the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).
(iii) When two fair dice are thrown the probability of getting:
a) The sum of 9 = 1/9
b) Two odd numbers = 1/4
c) two prime numbers = 1/9
d) two factors of 12 = 1/9
(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.
How to find probability when two dice are thrown?To find probability when two dice are thrown, we have:
(a) The sum of 9:
We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways
A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.
(b) Two odd numbers:
We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).
possible outcomes = 9,
So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.
(c) Two prime numbers
We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)
possible outcomes = 4,
So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.
(d) Two factors of 12:
We count the number of ways and divide by the total possible outcomes.
The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways
possible outcomes = 6
Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12
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ALEKS Knowlege Check:
Evaluate the expressions.
Answer:
1, -1
Step-by-step explanation:
(-2/3)⁰
Anything that is raised to the power of 0 automatically becomes the value 1. Knowing this, apply the exponent.
(-2/3)⁰ = 1
-(7)⁰
Now using what we know, apply the exponent to the 7.
-(7)⁰ = -1
Notice that the negative is NOT inside the parenthesis and therefore does NOT get affected by the power.
I will mark your answer brainliest.
Answer:
$4
Step-by-step explanation:
12÷4=3
7÷7=1
3+1=4
therefore she spent 4 dollars
Determine the missing term to make these ratios equal:
5:11=25:
Answer:
5:11 = 25:55
Step-by-Step Explanation:
25/5=5
5*11=55
so 55 is the answer!
chau made $270 for 18 hours of work. At the same rate, how many hours would he have to work to make $105
Answer:
7 hours
Step-by-step explanation:
here,
270/18=105/x
x=(105*18)/270
x=7
Chau made $270 for 18 hours of work. At the same rate, Therefore Chau would have to work 7 hours at the same rate to make $105.
To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:
Let x be the number of hours Chau needs to work to make $105.
We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:
Rate = Total earnings / Number of hours
Rate = $270 / 18 hours
Rate = $15 per hour
Now, we can set up the proportion:
$15 per hour = $105 / x hours
To find x, we can cross-multiply:
$15 × x = $105
Now, solve for x:
x = $105 / $15
x = 7 hours
So, Chau would have to work 7 hours at the same rate to make $105.
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-15 ÷(-3)= help I'm stuck
Given:
-15 ÷ (-3)
Here, we are given a division problem.
We are to divide -15 by -3.
Let's evaluate the expression:
\(-15\div\mleft(-3\mright)=\frac{-15}{(-3)}=\frac{15}{3}=5\)ANSWER:
5
Write an algebraic expression for the verbal expression: "7 times the sum of a squared and b minus 4 times the sum of a squared and b".
3.1721 x 10⁻⁷
Write this in standard notion
Refer back to Example 1 in the Learning Activity titled “Minimum and Maximum Values.” A quadratic equation is provided, along with the coordinates of its vertex. In your own words, describe the logic that allows one to conclude that: 1) there must be a maximum or minimum value, and 2) the location for that maximum or minimum value must be at the vertex. Also, describe how you would be able to tell, from just the equation and the coordinates of the vertex, whether the quadratic had a maximum value or a minimum value. In formulating your response, consider both a geometric viewpoint (“From the perspective of the graph, what’s going on?”) and an algebraic one (“What do the numbers say, and why?”).
Example 1: Determine the maximum or minimum of the equation
Y=-4x^2+24 x-35
Solution: Because a = 4, we know that the parabola opens downward and there will be a maximum y-value. To find it, first find the x-value of the vertex.
X = -b x value of vertex
2a
= -24 substitute in a =4 and b=24
2(-4)
= 24 simplify
-8
= 3
Therefore, the x-value of the vertex is 3. Next, substitute this value into the original equation to find the corresponding y-value.
Y=-4x^2+24x-35 substitute x =3
=-4(3) ^2+24(3)-35 simplify
=-36+72-35
= 1
The vertex is (3, 1). Therefore, the maximum y-value is 1, which occurs where x = 3 as illustrated below:
Note: The graph is not required to answer this question.
Answer: The maximum is 1.
The logic behind concluding that there must be a maximum or minimum value for a quadratic equation is based on the geometric properties of a parabola and the algebraic understanding of the vertex.
The vertex represents the location of the maximum or minimum value, and the coefficient of the \(x^2\) term determines whether it is a maximum or a minimum.
To understand why there must be a maximum or minimum value for a quadratic equation and why the location of that maximum or minimum value must be at the vertex, we can consider both the geometric and algebraic perspectives.
Geometrically, a quadratic equation represents a parabola.
A parabola can either open upward (concave up) or downward (concave down) depending on the coefficient of the \(x^2\) term.
In Example 1, the coefficient of x^2 is -4, indicating that the parabola opens downward.
For a parabola that opens downward, there will always be a maximum value.
Similarly, for a parabola that opens upward, there will always be a minimum value.
This is because the shape of the parabola limits how high or how low it can go.
Algebraically, the maximum or minimum value of a quadratic equation occurs at the vertex, which is the point where the parabola reaches its highest or lowest point.
In Example 1, the x-coordinate of the vertex is found using the formula x = -b / (2a). By substituting the values of a = 4 and b = 24 into the formula, we find that x = 3.
To determine whether the quadratic equation has a maximum or minimum value, we can look at the coefficient of the x^2 term.
If the coefficient is positive, the parabola opens upward and has a minimum value at the vertex.
If the coefficient is negative, as in Example 1, the parabola opens downward and has a maximum value at the vertex.
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What’s the unit rate
Hi friend! Hope this helps!
When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. If you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.
Ed needed to extend the string on his kite. The current string was nine and three fourths feet. He cut a piece of string that measured 2.5 feet and added it to the existing string. What is the new length of the string?
twelve and one fourth feet
eleven and three fourths feet
seven and one half feet
seven and one fourth feet
Answer:
Twelve and one fourth feet
Step-by-step explanation:
9 and 3/4 feet =9.75
2 and 2/4 feet =2.50
9.75 + 2.50
= 12.25/12 and 1/4 feet