To answer this question we will use the following property:
[tex]|a|>b>0\text{ if and only if }a>b\text{ or }a<-b.[/tex]Subtracting 6 from the given inequality we get:
[tex]\begin{gathered} 2|4t-1|+6-6>20-6, \\ 2|4t-1|>14. \end{gathered}[/tex]Dividing the above inequality by 2 we get:
[tex]\begin{gathered} \frac{2|4t-1|}{2}>\frac{14}{2}, \\ |4t-1|>7. \end{gathered}[/tex]Then:
[tex]4t-1>7\text{ or }4t-1<-7.[/tex]Solving the above inequalities we get:
1)
[tex]4t-1>7.[/tex]Adding 1 to the above inequality we get:
[tex]\begin{gathered} 4t-1+1>7+1, \\ 4t>8. \end{gathered}[/tex]Dividing the above by 4 we get:
[tex]\begin{gathered} \frac{4t}{4}>\frac{8}{4}, \\ t>2. \end{gathered}[/tex]The above inequality in interval notation is:
[tex](2,\infty).[/tex]2)
[tex]4t-1<-7.[/tex]Adding 1 to the above inequality we get:
[tex]\begin{gathered} 4t-1+1<-7+1, \\ 4t<-6. \end{gathered}[/tex]Dividing the above result by 4 we get:
[tex]\begin{gathered} \frac{4t}{4}<-\frac{6}{4}, \\ t<-\frac{3}{2}. \end{gathered}[/tex]The above inequality in interval notation is:
[tex](-\infty,-\frac{3}{2}).[/tex]Answer:
[tex](-\infty,-\frac{3}{2})\cup(2,\infty).[/tex]9. A coin is tossed and a number cube is rolled. What is the probability of getting tails and rolling a two?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested probability, so we obtain the following:
Probability of getting tails and rolling a two=Probability of getting tails * Probability of getting a two
And basing ourselves on the fact that when tossing a coin there are two possible events and in this case a favorable one, and when tossing the die there are 6 possible events and one favorable for this case, we have:
Probability of getting tails and rolling a two=1/2*1/6
Probability of getting tails and rolling a two=1/12
Finally we obtain that the probability of getting tails and rolling a two is 1/12.
-20 increased by 4
translating words to algebraic expressions
The algebraic expression is -20 +4.
What is algebraic expression?
An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression.
Given, situation -20 increased by 4.
Translate the phrase -20 increased by 4 into an algebraic expression.
You probably already know that more than is associated with addition so the sign is not going to change. But what about the order of the terms?
Think about it this way: we have a number (some unknown value) and this phrase represents -20 increased by whatever that value is. So, in this case, you will start with the number -20 and add 4.
we get -20+4.
To know more about algebraic expression, visit:
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The graph of f(x) = 4+ is shown below in blue. This graph in red is a transformation of f(x). Write a function thatdescribes the
Solution
Step 1:
Write the parent function
[tex]f(x)\text{ = 4}^x[/tex]Step 2:
Transformation of f(x) to g(x)
First, f(x) was reflected across the x-axis
[tex]f(x)\text{ }\rightarrow\text{ -4}^x\text{ }\rightarrow\text{ g\lparen x\rparen}[/tex]Step 3:
Then the function is later shifted 3 units vertically down.
[tex]g(x)\text{ = -4}^x\text{ - 3}[/tex]Final answer
[tex]g(x)\text{ = -4}^x\text{ - 3}[/tex]Which is more 1163 millimeters or 1meters?
Given : 1163 millimeter and 1 meters
We need to compare between them
First make both numbers at the same units :
1163 millimeter
1 meters = 1000 millimeters
So, 1163 millimeters > 1000 millimeters
So, 1163 millimeters is more than 1 meters
pls help me here pls I need answers ty
2)
Answer: 87 liters
Explanation:
1 m^23 = 0.001 L
87000 cm^3 = 87000 * 0.001
= 87 liters
Determine whether the function Y = 7- (3)represents exponential growth orexponential decay.a) exponential decayb) exponential growth
Given any exponential function in the form
[tex]y=ar^x[/tex]• If ,r >1, ,the function represents ,growth
,• If ,1 > r > 0,, the function represents ,decay
Notice that for
[tex]y=7\cdot(\frac{2}{3})^x[/tex]The exponential factor (2/3) is between 0 and 1 (0.66)
Therefore, the function represents decay.
Answer: Option A
Find remaining zereos of f
the function is:
degree: 4
and we know that some zeros are:
[tex]x=7i,3,-3[/tex]because the function is degree 4 we know that it should have 4 zeros. we also know that the function is symetric because of the real solutions, so the las solution will be the negative of the imaginari root so the remaining zeros are:
[tex]x=-7i[/tex](-5,-11) and (17,-22)
Find the slope
Answer:
-1/2
Step-by-step explanation:
Estimate the mean of the data given in the following grouped frequency table.Value IntervalFrequency0−3124−7208−118Select the correct answer below:4.577.857.663.535.10
The mean (or average) of observations is the sum of the values of all the observations divided by the total number of observations.
The mean for grouped data is given by:
[tex]Mean=∑(f_i.x_i)/∑f_i[/tex]• So; first we calculate each class mark xi, as:
(0 + 3)/2 = 1.5
(4 + 7)/2 = 5.5
(8 + 11)/2 = 9.5
• Now; we calculate fixi, as:
1.5 x 12 = 18
5.5 x 20 = 110
9.5 x 8 = 76
• Hence, the mean is given by:
[tex]Mean=\frac{18+110+76}{12+20+8}=5.10[/tex]ANSWER
5.10
Cole's Ice Cream Shop sold 16 sundaes with nuts and 30 sundaes without nuts. What is the
ratio of the number of sundaes with nuts to the total number of sundaes?
Answer:
16:46
Step-by-step explanation:
A right triangle has the lengths of the legs are 60 centimeters and 80 centimeters. what is the length, in cm, of the hypotenuse?
The following image shows a diagram (not to scale) of the triangle with the indicated measurements:
We will label them as "a" and "b" for reference:
And we need to find the hypotenuse of the triangle, which is the side that is opposite to the 90° angle. We will label the hypotenuse as "c":
To solve the problem we have to us The Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]Substituting the values of the legs a and b:
[tex]c^2=60^2+80^2[/tex]Since 60^2=3,600 and 80^2=6,400:
[tex]\begin{gathered} c^2=3,600+6,400 \\ c^2=10,000 \end{gathered}[/tex]Finally, to find the hypotenuse "c", take the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{c^2}=\sqrt[]{10,000} \\ c=\sqrt[]{10,000} \\ c=100 \end{gathered}[/tex]The length of the hypotenuse is 100 cm.
Answer: 100cm
(4t^2-5u)^2What does this simplify to?What is the degree of the simplified answer?
Answer:
simplified expression = 16t⁴ - 40t²u + 25u²
degree = 4
Explanation:
The initial expression is:
[tex](4t^2-5u)^2[/tex]To simplify, we can solve the expression as:
[tex](4t^2-5u)(4t^2-5u)[/tex]Applying the distributive property, we get:
[tex]\begin{gathered} 4t^2(4t^2)+4t^2(-5u)-5u(4t^2)-5u(-5u) \\ 16t^4-20t^2u-20t^2u+25u^2 \end{gathered}[/tex]Adding the like terms, we get that the simplified expression is
[tex]16t^4-40t^2u+25u^2[/tex]Then, the degree of the simplified expression is 4 because it is the maximum exponent.
So, the answers are:
16t⁴ - 40t²u + 25u²
degree = 4
Each month Mark‘s phone company charges a flat fee of $12 plus $0.05 per minute his bill for last month was $18 how many minutes did Marty talk on the phone last Month
Given:
Flat fee = $12
Per minute charge = $0.05
Total bill for last month = $18
To find the number of minutes, we have the equation:
18 = 12 + 0.05M
Where M represents number of minutes
Let's solve for M:
Subtract 12 from both sides:
18 - 12 = 12 - 12 + 0.05M
6 = 0.05M
Divide both sides by 0.05:
[tex]\begin{gathered} \frac{6}{0.05}=\frac{0.05M}{0.05} \\ \\ 120\text{ = M} \end{gathered}[/tex]Therefore, Marty spent 120 minutes talking on the phone last month.
ANSWER:
120 minutes
which expression means the same as an increase of 20%
ANSWER:
[tex]x+0.2x[/tex]STEP-BY-STEP EXPLANATION:
We have that an increase in 20% is the original value added to 20% of that original value, just like this:
[tex]x+\frac{20}{100}x=x+0.2x[/tex]how do i find the type of relationship of a table? whether it is linear or quadradic and how do i find the formula for either relationship?
By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs. If the first difference is the same value, the model will be linear. If the second difference is the same value, the model will be quadratic.
Also you can solve it by plotting the dots. If the graph seems a straight line it is linear and quadratic if it is a parabola.
For the data set given it is a linear relation
Line of best fit: y=3.18x+54.92
For x=7;
y=3.18*7+54.92
y=77.18
I need help to find the indicated operation:g(n)= 2n-2h(n)= n^2+3nFind (g×h)(n)
Composition of functions:
You combine two functions bycomposition by using one of the functions to substitute the independient variable in the other one.
To find (g o h)(n) you substitute the n in the function g(n) for the function h(n):
[tex](g\circ h)(n)=2(n^2+3n)-2[/tex]Simplify:
[tex](g\circ h)(n)=2n^2+6n-2[/tex]The graphs of functions f(x) and g(x) = f(x) + k are shown below:g(x)65432f(x))3-3The value of k is.(1 point)
Solution
We know that :
g(x) = f(x) + k
For this case the answer is:
the value of k is: 4
If the distance from South Bend to Grand Rapids has been rounded to the nearestten and is listed as 120 miles, the actual distance is between what two mile numbers?
We need to have two numbers between 116 and 124. If we have these two numbers and average them, we can have:
[tex]\frac{116+124}{2}=120[/tex]If we rounded 116 to the nearest ten, it will be 120.
If we rounded 124 to the nearest ten, it will be also 120.
Then if we have these two numbers and average them, we finally have 120 miles.
The actual distance must be between 116 and 124.
Find the area of this irregular shape.
[Round off to the nearest whole number.]
sq. units
Answer:
Step-by-step explanation:
number of complete squares=14
number of half or more than half squares=4
whole squares=4/2=2
area≈14+2=16 sq. units
What are the solutions to the equation x- 8x = 10?1) 4 102) 4-263) 41104) 4+ 26
First, let's equal the expression to zero:
[tex]\begin{gathered} x^2-8x=10 \\ \rightarrow x^2-8x-10=0 \end{gathered}[/tex]Now, let's use the general formula for quadratic equations:
[tex]\begin{gathered} \text{For} \\ ax^2+bx+c=0 \\ \\ \rightarrow x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \end{gathered}[/tex]This way,
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(-10)}}{2(1)} \\ \\ \rightarrow x=\frac{8\pm\sqrt[]{64+40}}{2} \\ \\ \rightarrow x=\frac{8\pm\sqrt[]{104}}{2} \\ \\ \rightarrow x=\frac{8\pm2\text{ }\sqrt[]{26}}{2} \\ \\ \Rightarrow x=4\pm\sqrt[]{26} \end{gathered}[/tex]Answer: Option 2
Students were asked to prove the identity (cot x)(cos x) = csc x − sin x. Two students' work is given.Part A: Did either student verify the identity properly? Explain why or why not.Part B: Name two identities that were used in Student A's verification and the steps they appear in.
Part A
Looking at the work done by each student, both students verified the identity properly because the trigonometric identities were properly applied where necessary, the steps were clear, mathematical operations were applied correctly and at the end, both sides of the equation were the same.
Part B
Looking at student's A verification,
In step 3, the pythagorean identity was used
In step 5, the reciprocal identity was used
Could you please help me with this? I need to solve it.
Given: ( -100 ) + ( -4 ) + ( -2 + 6) ( 3 )
Required: Evaluation
Explanation:
We shall here use BODMAS rule.
First solve the brackets and the addition and subtraction
[tex]\begin{gathered} (-100)+(-4)+(-2+6)(3) \\ =-100-4+(4)(3) \end{gathered}[/tex]Further,
[tex]\begin{gathered} =-100-4+12 \\ =-104+12 \end{gathered}[/tex]Solving
[tex]-104+12=-92[/tex]Final Answer:
[tex]-92[/tex]If point B, shown on the coordinate plane below, is reflected over the y-axis to create B’, what will be the coordinates of B’?(-5, 2)(5, 2)(-5, -2)(5, -2)
Solution
- The transformation for reflection over the y-axis is given below:
[tex](x,y)\to(-x,y)[/tex]- We have been given the coordinate of B to be (-5, -2) as shown below:
- Thus, applying the transformation formula given above, we have:
[tex]\begin{gathered} (x,y)\to(-x,y) \\ (-5,-2)\to(-(-5),-2)=(5,-2) \end{gathered}[/tex]- Thus, the reflected point B' is
[tex](5,-2)[/tex]- This is shown below:
I will share a photo of the question it is to complicated to right
Answer : 6
We are given the above fraction to be
[tex]\frac{3}{4}\text{ divided by }\frac{1}{8}[/tex][tex]\begin{gathered} To\text{ proc}eed\text{ with this expression, we n}eed\text{ to find the reciprocal of }\frac{1}{8} \\ \text{Hence, the reciprocal of }\frac{1}{8}\text{ is 8} \\ \frac{3}{4}\text{ x }\frac{8}{1} \\ =\text{ }\frac{3\text{ x 8}}{4} \\ =\text{ }\frac{24}{4} \\ =\text{ 6} \end{gathered}[/tex]The answer is 6
Before you can change a division operator to a multiplication operator, we need to find the reciprocal of the left hand side fraction
The fraction at the left hand side is 1/8
The reciprocal of 1/8 is 8
Rita is applying for a job as an engineer. Her starting salary at Company A will be $80,000 with an $800 yearly raise. Her starting salary at company B will be $65,000 with a 5% increase each year. If Rita is working at a company for 5 years. Which company should she pick?
Given:
In company A, starting salary is $80,000.
The yearly increment is $800.
So,
80,000+800=80,800
80,800+800=81,600
81,600+800=82,400
82,400+800=83,200
83,200+800=84,000
So, at the 5 year, she will get $84,000
In company B,
The initial salary is $65000 with a 5% increase each year.
So,
[tex]\begin{gathered} 65000\times\frac{105}{100}=68250 \\ 68250\times\frac{105}{100}=71662.5 \\ 71662.5\times\frac{105}{100}=75245.625 \\ 75245.625\times\frac{105}{100}=79007.906 \\ 79007.906\times\times\frac{105}{100}=82958.30 \end{gathered}[/tex]In the 5th year, she will get $82,958.30.
If Rita is working at a company only for 5 years, then she would choose company A. Because she will get salary in company A more than company B.
But, if she works for more than 5 years, she will get a salary in company B more than company A.
QUESTION 16Find anequation of the circle that satisfies the given conditions.Radius 6 and center (3.-5)
A circle can be represented by the following equation:
[tex]\mleft(x-h\mright)^2+(y-k)^2=r^2[/tex]Where the radius is r and the center is (h, k).
Using the radius 6 and the center (3, -5), we have that:
[tex]\begin{gathered} (x-3)^2+(y-(-5))^2=6^2 \\ (x-3)^2+(y+5)^2=36 \end{gathered}[/tex]So the equation of the circle that satisfies radius = 6 and center = (3, -5) is:
(x-3)^2 + (y+5)^2 = 36
Thomas runs 34 of a mileevery day for 5 days. Howfar has he run total?
Guven:
Miles per day = 34 miles
Number of days = 5 days
To find the total distance(miles), we have:
Total distance = distance covered per day x Number per days
= 34 x 5 = 170 miles
Therefore, the total distance he has covered is 170 miles
ANSWER:
170 miles
accounts that earn 6% interest. If Emma’saccount earns simple interest and Paul’saccount earns compound interest, which is thevalue of each person’s account after 8 years?A. Emma – $2,960; Paul – $3,187.708. Emma – $960; Paul – $3,187.70C. Emma – $2,960; Paut- $ 1,187.70
So,
Remember that the simple interest of an initial amount after "t" years, can be found using the following formula:
[tex]A=P(1+rt)[/tex]Where A is the final amount, P is the initial amount, r is the rate and t are the years involved.
If we replace our values, Emma will has the following amount after 8 years:
[tex]\begin{gathered} A=2000(1+\frac{6}{100}(8)) \\ A=2960 \end{gathered}[/tex]So, Emma will has $2,960 after 8 years.
To find the amount that Paul will has, we should remember what the compound interest is.
Remember that the compound interest is given by the formula:
[tex]A=P(1+i)^n[/tex]Where A is the final amount, P is the initial amount, i is the rate and n are the years involved.
If we replace our values, Paul will has the following amount of money after 8 years:
[tex]\begin{gathered} A=2000(1+\frac{6}{100})^8 \\ A=3187.70 \end{gathered}[/tex]So, Paul will has $3187,70 after 8 years.
Therefore, the correct answer is A.
The graph shows the equation x=y^2 use the slider for a to move the vertical line on the graph. According to the vertical line test, is this equation a function why or why not?
Explanation
We are given the equation:
[tex]x=y^2[/tex]We are to use the vertical line test to determine if the equation is a function or not
The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections of the curve with vertical lines.
The typical example below helps give a better explanation
So for the function
[tex]x=y^2[/tex]We can observe that the equation is not a function because the vertical line cuts the graph in more than one point
This is shown below for values of x = and x =8
Acetone (fingernail polish remover ) has a density of 0.7857 g/cm^3.A) what is the mass in grams of 17.56 mL of acetone?B) what is the volume in milliliters of 7.22 g of acetone?
We can use density as a factor of conversion.
To find the mass in grams of the volume of acetone, multiply the volume by the density (always check the units, that in this case are consistent because 1cm^3=1mL):
[tex]17.56mL\cdot\frac{0.7857g}{mL}=13.79g[/tex]To find the volume of the mass of acetone, divide the mass by the density:
[tex]7.22g\cdot\frac{1mL}{0.7857g}=9.18mL[/tex]