The given expression is
[tex]54\frac{.}{.}2\times3-x^2[/tex]where x=3
the dot in the expression means multiplication
substitute into the expression above we have
[tex]\begin{gathered} 54\frac{.}{.}2\times3-3^2 \\ \end{gathered}[/tex]Applying BODMAS
[tex]27\times3-3^2[/tex][tex]\begin{gathered} 81-3^2 \\ 81-9 \\ 72 \end{gathered}[/tex]Therefore the value of the expression is 72
Mean player age Mean Absolute Team Three golf teams wanted to compare the ages of their players. Each team calculated their players' mean age in years and the mean absolute deviation of their ages. They displayed the results in this table. 9.5 45 Appleton Coalvale 31 15.9 Which statements are true? Summerton 43 16.1 Select each correct answer. Team Coalvale's players ages and Team Summerton's players ages vary about the same amount Team Summerton's players ages and Team Appleton's players ages vary about the same amount Team Appleton's players ages vary less than do Team Summerton's players ages. Team Appleton's players ages vary more than do Team Coalvale's players ages. a ? 7+ O i JOTE to search
Given:
• Appleton: Mean = 45; Mean Absolute deviation = 9.5
,• Coalvale: Mean = 31; Mean Absolute deviation = 15.9
,• Summerton: Mean = 43; Mean Absolute deviation = 16.1
Using the given data, let's select the correct statements.
From the data we can see the difference between the Mean Absolute Deviations of team Coalvale and Summerton is (16.1 - 15.9) = 0.2
This means the ages of team Coalvale and Summerton vary about the same about.
The Mean Absolute deviation of Appleton is far from other mean absolute deviation. This means the players ages for team Appleton vary less than others.
Therefore, the correct statements are:
• Team Coalvale's players ages and Team Summerton's players ages vary about the same amount.
• Team Appleton's players ages vary less than do Team Summerton's players ages.
ANSWER:
• Team Coalvale's players ages and Team Summerton's players ages vary about the same amount.
• Team Appleton's players ages vary less than do Team Summerton's players ages.
log (2x+ 9) = 1+ log(x- 8)
x = 11.125
STEP - BY - STEP EXPLANATION
What to do?
Solve the given equation.
Given:
log (2x+ 9) = 1+ log(x- 8)
To solve, we will follow the steps below:
Step 1
Re-arrange by subtracting log(x-8) from both-side of the equation.
[tex]log(2x+9)-log(x-8)=1[/tex]Step 2
Apply the law of logarithm that is applicable to the given problem.
[tex]log\frac{(2x+9)}{(x-8)}=1[/tex]Step 3
Replace 1 by log10
Step 4
[tex]log\frac{(2x+9)}{(x-8)}=log10[/tex]Step 5
Cancel-out the log from both-side of the equation.
[tex]\frac{2x+9}{x-8}=10[/tex]Step 6
Cross - multiply
[tex]2x+9=10(x-8)[/tex]Step 7
Open the parenthesis.
[tex]2x+9=10x-80[/tex]Step 8
Collect like term.
[tex]10x-2x=80+9[/tex][tex]8x=89[/tex]Step 9
Divide both-side of the equation by 8
[tex]\frac{8x}{8}=\frac{89}{8}[/tex][tex]x=11.125[/tex]Therefore, the value of x is 11.125
3 1/2 ÷ 47/815/88/73/4
the given expression is,
[tex]\begin{gathered} 3\frac{1}{2}\div4=\frac{7}{2}\div4 \\ =\frac{\frac{7}{2}}{4}=\frac{7}{8} \end{gathered}[/tex]so the answer is option A
POSSIBLE POINTS: 1One-half of a number increased by 16 is 4 less than two-thirds of the number. What is the number?
Let the number be x.
[tex]\begin{gathered} \frac{1}{2}x+16=\frac{2}{3}x-4 \\ \\ \frac{2}{3}x-\frac{1}{2}x=20 \\ \frac{4-3}{6}x=20 \\ \frac{1}{6}x=20 \\ x=120 \end{gathered}[/tex]The number is 120
What is the explicit rule for the nth term of the geometric sequence? Thanks
Solution.
Given the sequence
[tex]3,18,108,648,3888[/tex]Test which kind of sequence it is
[tex]\begin{gathered} \frac{18}{3}=6 \\ \frac{108}{18}=6 \\ The\text{ sequence has a common ratio which is 6. } \\ Thus,\text{ it is a geometric sequence} \\ \end{gathered}[/tex][tex]\begin{gathered} The\text{ nth term of a geometric sequence can be determined by the formula} \\ a_n=ar^{n-1} \\ where\text{ a = 1st term} \\ r=common\text{ ratio} \end{gathered}[/tex][tex]a_n=3(6^{n-1})[/tex][tex]The\text{ answer is a}_n=3(6^{n-1})[/tex]As cashier, you need to record all over times you worked in hours. If you worked 330 mnts of over time how many hours will you record ?
First, we need the next equivalence
1 hour = 60 min
we have 330 min in order to know the number of hours we need to divide the 330 min between 60
[tex]\frac{330}{60}=5.5[/tex]He will record 5.5 hours
f(x)=x^6+10x^4 - 11x^2
You can notice that the given function is symmetric respect to the y-axis.
It means that the value of the function for both x and -x is the same:
[tex]f(-x)=f(x)[/tex]This is the characteristic of a even function.
Hence, the answer is B
i need some help list the integers in the set
Solution
The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero. {...,−5,−4,−3,−2,−1,0,1,2,3,4,5,...} The set of integers is sometimes written J or Z for short. The sum, product, and difference of any two integers is also an integer.
The whole numbers are set of real numbers that includes zero and all positive counting numbers. Whereas, excludes fractions, negative integers, fractions, and decimals. All the whole numbers are also integers, because integers include all the positive and negative numbers
The integers are real numbers
Therefore the numbers are list of integers
[tex]-8,9,\frac{0}{7},\frac{12}{4}[/tex]2. The product of two consecutive odd numbers is 143. Find the numbers. (Hint: If the first odd number is x, what is the next odd number?)
Step-by-step explanation:
we have the 2 numbers x and (x+2).
x × (x + 2) = 143
x² + 2x = 143
x² + 2x - 143 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case this is
x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =
= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =
= (-2 ± 24)/2 = (-1 ± 12)
x1 = -1 + 12 = 11
x2 = -1 - 12 = -13
so, we have 2 solutions : 11 and 13, -13 and -11
11× 13 = 143
-11×-13 = 143
Solve for the missing side of the triangle. Round to the hundredths place if needed.
The Pythagoras theorem gives the relation for the right-angle triangle between the perpendicular, base, and hypotenuse thus the perpendicular x will be 14.70.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with in our daily life.
In a triangle, the sum of all three angles is 180°
As per the given right-angle triangle,
Pythagoras' theorem states that in a right-angle triangle →
Hyp² = Perp² + Base²
In the given triangle Hyp = 21 , Base = 15 and Perp = x
So,
21² = x² + 15²
x² = 21² - 15²
x = √216 = 14.6993 ≈ 14.70
Hence "The value of x for the given right-angle triangle is 14.70 units".
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a. During a basketball practice, Mai attempted 40 free throws and was successful on
25% of them. How many successful free throws did she make?
410
0
free throws
25%
Unit 3, Lesson 11
50%
75% 100% 125% 150%
Answer: 10
1/4 (25%) of 40 is 10, meaning Mai made 10 successful free throws.
Which value of w makes 6W + 7 = 12 true
6W + 7 = 12
to solve this, just isolate W
[tex]\begin{gathered} 6W+7=12 \\ \text{substract 7 in both sides} \\ 6W+7-7=12-7 \\ 6W=5 \\ divide\text{ each side by 6} \\ \frac{6W}{6}=\frac{5}{6} \\ W=\frac{5}{6} \end{gathered}[/tex]so, the answer is w=5/6
Solve the direct variation problemsJohn is working at a bank and receives 25 dollars an hour. a. Write an equation that relates x and y.b. what is the constant of proportionality?
Let "x" represent the number of hours that John works and "y" represent John's earnings after working x hours.
b) John receives $25/hour → this value represents the change in John's earnings for every unit increase of x, which is, the constant proportionality (k) of the relationship.
a) If x and y have a direct relationship, you can express it as follows:
[tex]y=25x[/tex]Find the volume of this triangular prism.Be sure to include the correct unit in your answer.8 cm7 cm→5 cm
The formula to find the volume of a triangular prism is the following:
[tex]V=\frac{1}{2}h\cdot b\cdot w[/tex]where:
h - height
b - base length
w - width
for this problem:
h = 8 cm
b = 5 cm
w = 7 cm
then
[tex]V=\frac{1}{2}8\cdot5\cdot7[/tex]solving this, we obtain that the volume of the triangular prism is 140 cm^3 or cubic centimeters
Write vector h= 8i – 11j in vector component form.
Solution:
Given the vector h;
[tex]h=8i-11j[/tex]The vector in component form is;
[tex]h=<(8,-11)>[/tex]according to recent study 7 out of every 500 Americans aged 13-17, years are vegetarian.in a group of 350 13 to 17- years old about how many would you expect to he vegetarian
7 out of every 500 Americans aged 13 -17 years are vegetarians
This implies that in a group of 500 Americans , 7 Americans that are within the age range of 13 - 17 years are vegetarians
7 ======== 500
x ======== 350
Introduce cross multiplication
7 x 350 = x * 500
2450 = 500x
Divide both sides by 500
2450/500 = 500x/ 500
x = 4.9
Approximately, 5
5 vegetarians aged 13 - 17 years will be present is in a group of 350 Americans
The answer is 5
pls help i Dont get it
Answer:
what do you need
Step-by-step explanation:
I already wrote the answer I just need you to work it out for me please and thank you
Answer:
[tex]A=470\frac{1}{4}ft^2[/tex]Detailed Explanation: The area of the figure provided is the sum of two areas, a rectangle, and a triangle:
The total area is calculated next, and the necessary steps are shown as follows
[tex]\begin{gathered} A=A_1+A_2 \\ A_1=\frac{1}{2}(b\cdot h)=\frac{1}{2}\cdot\lbrack(25ft-22.5ft)\times19.8ft\rbrack \\ A_1=\frac{1}{2}\cdot\lbrack2.5ft\times19.8ft\rbrack=\frac{49.5ft^2}{2}=24.75ft^2 \\ A_1=24.75ft^2 \\ A_2=w\cdot h=22.5ft\cdot19.8ft=445.5ft^2 \\ A_2=445.5ft^2 \\ \therefore\Rightarrow \\ A=A_1+A_2=24.75ft^2+445.5ft^2 \\ A=470.25ft^2 \\ A=470\frac{1}{4}ft^2 \end{gathered}[/tex]Jan plans to tell two people each day and will ask that person to tell two other people each day through the day of the opening, and so on. Assume that each new person who hears about the soft opening is also asked to tell two other people each day through the day of the opening and that each one starts the process of telling their friends on the day after he or she first hears. When should Jan begin telling others about the soft opening in order to have at least 700 people know about it by the day it occurs?
Explanation:
From the given question, we can sketch the pattern observed
The figure above helps show how the number of people increases
Initially, Jan tells 2 more people, then the two people tell two more people, then they also tell two more people
Thus
we can see that the model is given by
[tex]\begin{gathered} (2)^n \\ where\text{ n is the number of days} \end{gathered}[/tex]In order to have at least 700 (it also means a minimum of 700), we will have the equation
[tex]2^n\ge700[/tex]We then solve for n
Taking the log of both sides
[tex]n\text{ }log2\ge log700[/tex][tex]n\ge\frac{log700}{log2}[/tex]So that
[tex]\begin{gathered} n\ge\frac{2.845}{0.301} \\ \\ n\ge9.451 \end{gathered}[/tex]So, the number of days will be at least 10 days (Rounded to the nearest whole day )
Below, the two-way table is given for a classof students.FreshmenSophomoreJuniorsSeniorsTotalMale4622Female 3463TotalIf a female student is selected at random, find theprobability that the student is a senior.
Conditional Probability
First, we must complete the totals in the table as follows:
The formula for the conditional probability is:
[tex]P(B|A)=\frac{P(B\cap A)}{P(A)}[/tex]Where A is an event we know has already occurred, B is an event we want to calculate its probability of occurrence, and P∩A is the probability of both occurring.
We know a female student has been selected, so that is our known event and:
[tex]P(A)=\frac{16}{30}=\frac{8}{15}[/tex]The probability that a female student is also a senior is:
[tex]P(A\cap B)=\frac{3}{30}=\frac{1}{10}[/tex]Substituting:
[tex]\begin{gathered} P(B|A)=\frac{\frac{1}{10}}{\frac{8}{15}} \\ \\ P(B\lvert\rvert A)=\frac{1}{10}\frac{15}{8}=\frac{3}{16} \end{gathered}[/tex]The required probability is 3/16
Instructions:Prepare a written response to the prompt below using a word processor. Please save your file in .doc or .docx format. Yourresponse should be in complete sentences.*To view the grading rubric for this assignment, click on the name of the assignment and click "View Rubric"Assignment Prompt:1. Explain, using the numeric expression below, how to use Order of Operations to compute a numeric value of anexpression.70-2052 - 22)3 +5.(-2)2. Why is it important to have an agreed upon set of rules to determine the order of how we add, subtract, multiply.divide, etc.?3. Please submit your document by clicking on the name of this assignment (above) and attaching your file on the nextscreen.4. If you have any questions, please ask your professor.
We need to solve the following expression:
[tex]70-2(5^2-22)^3+5(-2)[/tex]The order of operations is a rule that tells the correct sequence of steps for evaluationf a math expression. We can remember the order using PEMDAS: Parenthesis, Exponents, Multiplication and Division (from left to right).
Then, in our expression, we must solve parenthesis first. It yields
[tex]\begin{gathered} 70-2(25-22)^3-10 \\ 70-2\times3^3-10 \end{gathered}[/tex]The next step is to raise exponents,
[tex]70-2\times27-10[/tex]and now, the multiplication step
[tex]70-54-10[/tex]then, we get 70-64 and the solution is 6.
What is the smallest fraction?5/1210/15 1/32/4
Answer:
1/3
Explanation:
In order to get the smallest fraction, we will need to express each of the fractions as a percentage as shown below:
For 5/12;
[tex]\begin{gathered} =\frac{5}{12}\times100 \\ =\frac{500}{12} \\ =41.7\% \end{gathered}[/tex]For 10/15;
[tex]\begin{gathered} =\frac{10}{15}\times100 \\ =\frac{1000}{15} \\ =66.7\% \end{gathered}[/tex]For the fraction 1/3
[tex]\begin{gathered} =\frac{1}{3}\times100 \\ =\frac{100}{3} \\ =33.3\% \end{gathered}[/tex]For the fraction:
[tex]\begin{gathered} =\frac{2}{4}\times100 \\ =\frac{200}{4} \\ =50\% \end{gathered}[/tex]From the resulting percentage, we can see that the smallest among the fraction is 1/3.
What is the axis of symmetry for the following quadratic?(x-3)(x+7)
The symmetry of a quadratic equation is given by the line that passes through its vertex, so in order to find the axis of symmetry we need to find the coordinate of the vertex, which is done below.
[tex]x_{\text{vertex}}=\frac{-b}{2a}[/tex]Where "a" is the number multiplying the square factor and "b" is the number multiplying the factor that isn't squared. To find these two constants we need to expand the equation given.
[tex]\begin{gathered} (x-3)\cdot(x+7) \\ x^2+7x-3x-21 \\ x^2+4x-21 \end{gathered}[/tex]We have that a = 1 and b = 4, therefore:
[tex]x_{\text{vertex}}=\frac{-4}{2\cdot1}=-2[/tex]The axis of symmetry for this quadratic equation is x=-2.
Identify whether the following real world examples should be modeled by a linear quadratic or exponential function
Solution
- Linear:
The general form of a linear function is
[tex]\begin{gathered} y=ax+b \\ where, \\ a,\text{ and b are constants} \end{gathered}[/tex]- Quadratic:
The general form of a quadratic function is:
[tex]\begin{gathered} y=ax^2+bx+c \\ where, \\ a,b,c\text{ are constants} \end{gathered}[/tex]- Exponential:
The general form of an exponential function is:
[tex]\begin{gathered} y=ab^x \\ where, \\ a,b\text{ are constants} \end{gathered}[/tex]- Now that we know the general forms of these functions, we can proceed to solve the question.
- The amount a person is paid per hour in wages is the amount that the person collects for every hour that he works
- Let us imagine that a person receives $a for every hour worked.
- This means that:
After 1 hour, the person makes $a
After 2 hours, the person makes $a + $a = $2a
After 3 hours, the person makes $a + $a +$a = $3a
- We can therefore generalize as follows:
Thus, after x hours, the person makes:
[tex]x\times a=\$ax[/tex]- Thus, the function representing the amount a person makes per hour of work is given by:
[tex]y=ax[/tex]- Comparing this result with the 3 function definitions above, we can see that this corresponds to a Linear function
Final Answer
The answer is Linear
ok so the question is Write an expression to rubbers in the area of the figure the figure is a right triangle with 2X -2 and 4X plus 2 in the answer to that is 4X to the power of 2 - 2X -2 and that's part a and amp RP is what would the area be if X equals negative 2
ANSWERS
a) A = 4x² - 2x - 2
b) if x = -2, A = 18 units²
EXPLANATION
The area of a triangle is the length of the base, multiplied by its height and divided by 2:
[tex]A=\frac{b\cdot h}{2}[/tex]In this triangle, b = 4x + 2 and h = 2x - 2. The area is:
[tex]A=\frac{(4x+2)(2x-2)}{2}[/tex]We can simplify this expression. First we have to multiply the binomials in the numerator:
[tex]\begin{gathered} A=\frac{4x\cdot2x-4x\cdot2+2\cdot2x-2\cdot2}{2} \\ A=\frac{8x^2-8x+4x-4}{2} \\ A=\frac{8x^2-4x-4}{2} \end{gathered}[/tex]Now, using the distributive property for the division:
[tex]\begin{gathered} A=\frac{8x^2}{2}-\frac{4x}{2}-\frac{4}{2} \\ A=4x^2-2x-2 \end{gathered}[/tex]For part b, we just have to replace x with -2 in the expression above and solve:
[tex]\begin{gathered} A=4(-2)^2-2(-2)-2 \\ A=4\cdot4+4-2 \\ A=16+2 \\ A=18 \end{gathered}[/tex]Describe the situation and why you think analytical or Euclidean geometry is more applicable need helps with this homework question
EXPLANATION
Since the Euclidean Geometry is the Geometry of the Flat Space, we can affirm that it's in two dimensions, where rotation and similarity make sense.
Although it may be expanded to three-dimensional space and beyond, it is still referred to as flat space. The concept is that all dimensions are equal and that they are equal everywhere in space.
The area of a square created on the diagonal of a rectangle, rectangular parallelepiped, or higher dimensional hyperrectangle is equal to the sum of the areas of the squares built on the mutually perpendicular sides of the rectangle, according to the Pythagorean Theorem.
This is known as Euclidean Geometry. Non-Euclidean Geometry, such as spherical, elliptic, hyperbolic, or relativistic geometry, is distinguished by the fact that the same Pythagorean theorem does not apply (though variations do).
So the true dilemma is when to utilize synthetic geometry instead of analytic geometry. Whenever possible, we could say. The challenge with synthetic geometry is that proofs and constructions frequently need some ingenuity on the prover's side.
Find the length of the arc. Use 3.14 for it.270°8 cm
The radius of circle is r = 8 cm.
The arc is of angle 270 degree.
The formula for the arc length is,
[tex]l=2\pi r\cdot\frac{\theta}{360}[/tex]Determine the length of the arc.
[tex]\begin{gathered} l=2\cdot3.14\cdot8\cdot\frac{270}{360} \\ =37.68 \end{gathered}[/tex]So lenth of the arc is 37.68.
In a film, a character is criticized for marrying a woman when he is three times her age. He wittily replies, "Ah, but in 21 years time I shall only be twice her age." How old are the man and the
woman?
Write a linear function that models the total monthly costs for each option for x hours of court rental time.
The age of man is 63 years and the age of women is 21 years.
Given that, a character is criticized for marrying a woman when he is three times her age.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let age of man be x and the age of women be y.
Now, x=3y ---------(1)
In 21 years time man will be twice her age.
x+21=2(y+21)
⇒ x+21=2y+42
⇒ x-2y=21 ---------(2)
Substitute equation (1) in (2), we get
3y-2y=21
⇒ y = 21
So, x=3y=63
Therefore, the age of man is 63 years and the age of women is 21 years.
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I would like to know if I have this question correct thank you
Remember that
For a 95% confidence interval --------> the value of z=1.960
Find out the value of
[tex]Z\frac{s}{\sqrt{n}}=1.960(\frac{12}{\sqrt{36}})=3.92[/tex]therefore
[tex]\begin{gathered} 230\pm3.92 \\ 230+3.92=233.92 \\ 230-3.92=226.08 \\ therefore \\ The\text{ answer is} \\ (226.08,233.92) \end{gathered}[/tex]P(A) = 1/4 P(A n B) = 1/12 P(AUB) = 13/24 Find P(B) c 21/24 5/24 O O O 3/8 11/24
Okay, here we have this:
Considering that P(AUB)=P(A)+P(B)-P(AintersectionB), we obtain that:
P(B)=P(AUB)-P(A)+P(AnB)
P(B)=(13/24)-(1/4)+(1/12)
P(B)=3/8
Finally we obtain that P(B) is equal to 3/8.
