In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
9/16 + 1/16 * (2/3)^(-1)
Step 02:
we must apply the algebraic rules to find the solution
[tex]\frac{9}{16}+\frac{1}{16}\cdot(\frac{2}{3})^{-1}=\frac{9}{16}+\frac{1}{16}\cdot\frac{3}{2}=\frac{9}{16}+\frac{3}{32}[/tex][tex]\frac{9\cdot2+3\cdot1}{32}=\frac{21}{32}[/tex]The answer is:
21 / 32
Which fraction is equivalent to 80%? (in simplest fraction form)
Answer:
4/5 or four fifths
Step-by-step explanation:
First you make 80% the fraction 80/100
Next you find the greatest common factor (GCF) which in each of them is 20
Finally you divide 80 and 100 by 20 and you get 4 and five now make them a fraction and you get 4/5
jaylens snow cone stand went thourgh 10 bags of ice in the first hour it was open and 8 1/6 simplify your answer and write it as a fraction or as a whole or mixed number
The fraction form of 8 1/6 is 49/8 as the definition of fraction says, "An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided".
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction merely informs us of the number of parts that make up the whole. The slash that is written between the two numbers identifies a fraction. The numerator is the highest number, and the denominator is the lowest number. 1/2, for instance, is a fraction.
Here,
8 1/6=(6*8+1)/8
=49/8
According to the definition of a fraction, which states that it is "a number represented mathematically as a quotient, where the numerator and denominator are divided," the fraction form of 8 1/6 is 49/8.
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Attendance at october fest was 15% more than last year. this year's attendance was 1785 people. find the number of people who attended the festival last year. rounded to the nearest person
Using the concept of equations, 1552 people attended the festival last year.
What are algebraic equations?Two algebraic expressions are combined to create an algebraic equation using the equals (=) sign. Algebraic equations are also known as polynomial equations since they contain polynomials on both sides of the equal sign. An algebraic equation consists of variables, coefficients, constants, and algebraic operations including addition, subtraction, multiplication, division, and exponentiation.
An integer or set of integers that satisfy the condition in the equation are the roots or solutions of an algebraic equation.
Let the number of people who attended the festival last year =x
Then, we can write an equation as
1785=1.15 × x
x = 1785/1.15
=1552 people
So, last year's attendance = 1552
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Convert the following fraction to a decimal 3/10
Answer:
Step-by-step explanation: 0.3
Answer:
Step-by-step explanation:
1. The answer is 0.3.
Expand. Your answer should be a polynomial in standard form.
(x - 2)(x - 6) =
(x-2) (x-6)
x(x-6)-2(x-6)
x²-6x-2x-12
X²-4x-12
Which lines are parallel if x=y?
Answer:
the horizontal lines for #9 and those slanted ones for #10
Step-by-step explanation:
parallel lines are lines that never intercept. if these following lines continue infinetly they will never touch
Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-interceptform.x1520253035HHHу160200240280320An equation of the line in point-slope form is
Point slope form: y - 160 = 8(x-15)
Slope intercept form: y = 8x + 40
Explanation:
To write an equation of the line in point-slope form that passes through the given points in the table, we need to pick any two of the points in the table for x and y axis and find the changes of x and y
Points chosen: (20, 200) and (15, 160)
m = slope = (change in y)/ (change in x)
[tex]\begin{gathered} m\text{ = }\frac{200-160}{20-15}\text{ = }\frac{40}{5} \\ m\text{ = 8} \end{gathered}[/tex]Point-slope form:
[tex]\begin{gathered} y-y_1=m(x-x_1)\text{ then we would pick any of the points used earlier} \\ U\sin g\text{ (15, 160)} \\ y\text{ - 160 = 8( x - 15)} \\ y\text{ - 160 = 8x -120} \\ y\text{ =}8x\text{ + 40} \end{gathered}[/tex]The equation in the slope intercept form:
[tex]\begin{gathered} y\text{ = mx + b} \\ y\text{ = 8x + 40} \\ \text{where m = 8 b = intercept = 40} \end{gathered}[/tex]Hence, Point slope form: y - 160 = 8(x-15)
Slope intercept form: y = 8x + 40
Mia is deciding between two truck rental companies. Company A charges an initial fee of $30 for the rental plus $3 per mile driven. Company B charges an initial fee of $85 for the rental plus $2 per mile driven. Let AA represent the amount Company A would charge if Mia drives xx miles, and let BB represent the amount Company B would charge if Mia drives xx miles. Write an equation for each situation, in terms of x,x, and determine which company would be cheaper if Mia needs to drive 80 miles with the rented truck.
Answer:
(a.): Company A: 3x + 30; Company B: 2x+85
(b.) Company B is cheaper as it would cost $245 for Mia to drive 80 miles
Step-by-step explanation:
The equations we need are linear and we can think of them as such. x represents the slope (cost per mile) and the initial fee represents our y-intercept or constant (amount paid before Mia ever drives)
(a.): Thus, for company A, we have y = 3x + 30 and for company B we have y = 2x + 85.
(b.) Since we know that Mia needs to drive 80 miles, we plug this into x for both companies and find which one is lower
Company A: 3(80) + 30 = $270
Company B: 2(80) + 85 = $245
Company B's price would be lower for Mia's needs.
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: Width = 4.7 meters, Length = 6.7 meters
Step-by-step explanation:
Let the width be [tex]w[/tex]. It follows that the length is [tex]w+2[/tex].
[tex]w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7[/tex]
What are the missing parts that correctly complete the proof? given: point m is on the bisector of angle j k l. prove: point m is equidistant from the sides of angle j k l. art: three rays k j, k m, and k l point in rightward direction sharing a common endpoint at k. ray k m is horizontal and bisects angle j k l equally. the perpendicular from point m to ray k j is made by a dotted line. the perpendicular cuts ray k j at x. angle k x m is labeled a right angle. the perpendicular from point m to ray k l is made by another dotted line. the perpendicular cuts ray k l at y. angle k y m is labeled a right angle. drag the answers into the boxes to correctly complete the proof.
The missing parts of proof are:
∠JKM≅∠LKMMK≅MKAAS Congruence PostulateCorresponding parts of congruent triangle are equalDefinition of equidistantExplain property of anglesIn geometry, a line that divides an angle into two equal angles is referred to as an angle bisector. By definition, a bisector is something that divides an object or a shape into two equal parts. A ray is said to be an angle bisector if it divides an angle into two equal portions of the same measure.
Angle Bisector's Qualities:
All of the angle bisector's points are equally spaced from both of the angle's arms.Any angle, including acute, obtuse, and right angles, can have an angle bisector drawn to it.The ratio by which the angle bisector splits the opposite side of a triangle is the same as the ratio by which the other two sides are divided.Given,
KM is the bisector of ∠JKL
1. As per the definition of bisector, ∠JKM≅∠LKM
Given,
∠KXM and ∠KYM are right angles
∠KXM≅∠KYM because all right angles are congruent
2. Because of Reflexive Property of congruence, MK≅MK
3. Given △KXM≅△KYM, AAS congruence postulate
4. Given MX≅MY, this is according to CPCTE property
5. Given, Point M is equidistant from the sides of ∠JKL, as per the definition of equidistant
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Simplify the equation 10x - 8x +2 + 10
Suppose your math teacher was running for Governor. In a pre-election poll of 750 people, the estimate (called a point estimate) was 40%, meaning that 40% of the people would vote for your math teacher. Suppose there was a 4% margin of error. How many people (out of 750) said they would vote for your math teacher? Show your work. Write the answer as a complete sentence.
Solution
- 40% of peole would vote for the mMath teacher out f the 750 people. This implies that the number of people tahat would vote for him is
[tex]\begin{gathered} 40\%\times750 \\ \frac{40}{100}\times750=300\text{ people} \end{gathered}[/tex]- We are also told that there is a margin of error of 4%. This implies that the number of people that vote for the math teacher is either 4% more or 4% less than the 300 people
- 4% margin of error can be gotten as follows:
[tex]\frac{4}{100}\times750=30[/tex]- Thus, the number of people that vote for him is 300 give or take 30 people
what is evaluate 5-(6/3)
Solve for x: 6x + 3 = 5x - 8
О -11
О 11
о
О -5
0
О 5
F
Answer:
6x+3=5x-8
6x-5x= -8-3(match the like terms)
x= -11
Construct a Venn diagram to determine the validity of the argument (Use Euler's diagram)Some animals are dangerousA car is not an animalTherefore a car is not dangerous
We will have the following:
Here it is the Venn diagram for both; the statement is not valid, since they fall in different categories.
24. Find fl-1).For questions 24-27, use the graph below.25. Find f(4).26. Find f(-3).27. If f(x) = 9, find x.
Let's start by calculating the value for f(-1).
For this we go to the graph and count the number of squares to the left of the axis to be at -1. In this case f(-1) would be 5.
Now let's calculate f(4)
For this case the value of f(4) would be 0.
Similarly we calculate f(-3). As you can see in the graph it would be 6.
The last scenario would be for when f(x) = 9, we look for that value on the curve and realize that it corresponds to x = 1.
PLEASE I NEED HELP ASAP WITH THIS MATH STUFF!!
-download them and draw over them or write over them
The system of equations are y = 50 + 100x and y = 300 + 75x which is linear equations in two variables.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The linear equation can be written in form of:
y = mx + c
From the question:
The equation for Little Learners Pre-School:
y = 50 + 100x
The equation for Growing Place Pre-School:
y = 300 + 75x
Thus, the system of equations are y = 50 + 100x and y = 300 + 75x which is linear equations in two variables.
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HELO EMEMENEJEJJEJEH
Answer:
E
Step-by-step explanation:
[tex]3 \leq x-2 \\ \\ x-2 \geq 3 \\ \\ x \geq 5[/tex]
Answer:
E
Step-by-step explanation:
if it is supposed to be more or equal to then it has to add 5 or more. It has to add 5 or more because the 2 is negative and 5-2 is 3 so it has to be at least 5
3 times x increased by 20 as a algebraic expression
Answer:
3x+20
Step-by-step explanation:
One third times the difference of thirty and a variable is three fourths. one third times the quantity 30 minus y equals three fourths one third times the quantity y minus 30 equals three fourths one third times 30 minus y equals three fourths one third times y minus 30 equals three fourths
The original statement is same as third statment and value of y is 27.
Writing the equation form for each statement -
Let the variable be represented as y.
One third times the difference of thirty and a variable is three fourths1/3(30 - y) = 3/4
one third times the quantity 30 minus y equals three fourths1/3×30 - y = 3/4
one third times the quantity y minus 30 equals three fourths1/3×y - 30 = 3/4
one third times 30 minus y equals three fourths1/3(30 - y) = 3/4
one third times y minus 30 equals three fourths1/3(y - 30) = 3/4
Based on the interpretation of all the sentences in equation form, we find the statement 3 to be same as original statement. Solving the equation to get the value of y.
1/3(30 - y) = 3/4
10 - y/3 = 3/4
10 = 3/4 + y/3
10 = (3×4 + y×4)/12
10×12 = 12 + 4y
4y + 12 = 120
4y = 120 - 12
4y = 108
y = 27
Hence, the value of y is 27.
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Answer:
the answer is A.
1 over 3 (30 - y) = 3 over 4
Write 2^40 as a power with the following base: 2^10
The equivalent expression as a base of 2¹⁰ is (2¹⁰)⁴
How to rewrite the expression?The mathematical statement in the question implies that
We rewrite 2^40 as a power in the base 2^10
Start by expressing the given number properly
So, we have
2⁴⁰
Express 40 as the product of 10 and 4
So, we have
2⁴⁰ = 2¹⁰ ˣ ⁴
Express as exponents
So, we have the following representation
2⁴⁰ = (2¹⁰)⁴
Hence, the new expression is (2¹⁰)⁴
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How do you decide how well data represent
a population?
Use examples to explain.
The data that represent a population is helpful when we have to find the information only about one field.
In the given question we have decide how well data represent a population.
The total group you want to make judgments about is referred to as a population. Data is a set of quantitive data which refers the population only in numbers. So the data is only helpful when we have to find the only in small amount and only one field.
Data collection from a large population is typically only simple when the population is small, approachable, and cooperative.
Example: Gathering information from a population
A high school administrator is looking for trends in the final exam results of all graduating seniors. They use the entire population dataset since they are only interested in applying their findings to the graduating seniors in this high school. So the data is useful.
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A lawnmower designer wants to build a lawnmower that measures
8 feet in height, 3 feet width, and 7 feet in length. She needs to construct a three dimensional model of the lawnmower. First, determine
the width for the scale model given a height of 10 inches?
The width of the scale model given a height of 10 inches as in the task content is; 3.75 inches.
What is width of the scale model given a height of 10 inches?It follows from the task content that the width of the scale model is to be determined given a height of 10 inches.
According to the design, the lawnmower measures; 8 feet in height, 3 feet width, and 7 feet in length.
Hence, since 8 feet in height corresponds to 10 inches on the scale, the width on the scale can be determined by proportion as;
8/10 = 3/x
x = ( 10 × 3 ) / 8
x = 30/8
x = 3.75 inches.
Therefore, the width on the scale as required is; 3.75 inches.
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I need help evaluating/answering this!
The value of the expression is equal to 6.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is [3(6-14)]/(-4). The value of the expression will be calculated below,
E = [3(6-14)]/(-4).
Simply the expression by using mathematical operations,
E = [3( -8)]/(-4).
E = 3 x 2
E = 6
Therefore, the value of the expression is equal to 6.
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there is a step missing from the solution. Which equation is the missing step?
To determine the next step, we need to slove the expression.
divide both sides by -1:
[tex]\begin{gathered} \frac{8}{-1}=\frac{-\sqrt[]{0.025x+7}}{-1} \\ -8=\sqrt{0.025x +7} \end{gathered}[/tex]Square both sides of the equation:
[tex]\begin{gathered} 8^2=(\sqrt{0.025x +7})^2 \\ 64\text{ = 0.025x + 7 } \\ 64\text{ - 7 = 0.025x } \\ 57\text{ = 0.025x } \\ Hence,\text{the missing step: }64\text{ = 0.025x + 7 (option B)} \end{gathered}[/tex]What is the reciprocal of 1 1/8 ?
Answer:
0.8 repeated
Step-by-step explanation:
Because it is
help meeeeeeeeee pleasee
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
Torren deposits $4500 in an account earning 2% interest, compounded annually. The equation that represents this situation is:A(n) = 4500(1 + 0.02) - 1How much will he have in the account at the beginning of year 8? Round youranswer to the nearest dollar.A. $5169B. $32,130C. $16,124D. $5272
Torren will have $5169 in the account at the beginning of year 8. Option A is correct.
The following formula can be used to calculate the compound interest.
[tex]A(n) = P(1 + r)^{(t- 1)}[/tex]
where,
A(n) denotes the final sum.
P stands for the initial deposit.
r denotes the interest rate (in decimal).
t denotes the time (in year).
The compound interest will be C.I = A - P in this case.
We are given in the question;
The account's initial deposit is $4500, and the term is 8 years.
As a result,
A = 4500 and
t = 8
As we all know, interest is compounded once a year.
We shall divide the interest rate in percentage form by 100 to convert it to decimal form.
r = 2% = 2/100
⇒r = 0.02
The given equation is
[tex]A(n) = 4500(1 + 0.02)^{(n- 1)}[/tex]
Substituting the given values in the above equation, we will get,
[tex]A(n) = 4500(1 + 0.02)^{(8- 1)}[/tex]
[tex]A(n) = 4500(1 + 0.02)^{7}[/tex]
[tex]A(n) = 4500 \times 1.14868[/tex]
[tex]A(n) = 5169.06[/tex]
[tex]A(n) = 5169[/tex]
Thus, Torren will have $5169 in the account at the beginning of year 8. Option A is correct.
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write and equation in slope-intercept form to represent each table x-3,6,9,12 y-5, -1, -7, -13
The equation that represents the table, in slope-intercept form, is: y = -2x + 11.
How to Write the Equation of a Line in Slope-intercept Form?The slope-intercept form of an equation that represents a line is expressed as y = mx + b, where:
m = slope = change in y / change in x.b = y-interceptUsing two pairs of values from the table, (6, -1) and (9, -7):
Slope (m) = (-7 -(-1)) / (9 - 6)
Slope (m) = -6/3
Slope (m) = -2.
Find the y-intercept, b, by substituting m = -2 and (x, y) = (6, -1) into y = mx + b:
-1 = -2(6) + b
-1 = -12 + b
-1 + 12 = b
b = 11
To write the equation, substitute m = -2 and b = 11 into y = mx + b:
y = -2x + 11
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Vivian has $535 in her stavings account and she has to pay $5.00 each month for her cell phone Reza has $145 and he saves $25 each month for his job walking the dogs at this rate when will they had the same amount of money and how much will they have
Answer: $456
Step-by-step explanation: They will both have the same amount of money at 7 months