Using the factorization, the solution of given inequality is x>1/3 and x< -4.
In the given question we have to solve the given inequality.
The given inequality is 3x^2+11x>4.
Solving the given inequality
Subtract 4 on both side we get
3x^2+11x-4>0
Now factoring the binomial equation.
The multiplication of first and third term is 12 and middle term is 11.
So the possible factors are 1 and 12
3x^2+(12-1)x-4>0
3x^2+12x-x-4>0
3x(x+4)-1(x+4)>0
(3x-1)(x+4)>0
Equating equal to zero
3x-1>0 or x+4>0
Solving for x
x>1/3 or x< -4
Hence, the solution of given inequality is x>1/3 and x< -4.
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HELPPP I also have to round it yo the nearest tenth if possible
Which one of the following equations defines the line that contains the point (1,2) and is parallel to the line 4x+3y=7?
A radar gun measured the speed of a baseball at 103 miles per hour. If the baseball was actually going 102.8 miles per hour, what was the percent error in this measurement? Round to the nearest hundredth percent
Answer
Percent Error = 0.195%
Explanation
Percent error is given as
[tex]\text{Percent Error = }\frac{Error}{True\text{ value}}\times100\text{ percent}[/tex]Error = | (Incorrect value) - (True value) |
Incorrect value = 103 miles per hour
True value = 102.8 miles per hour
Error = | (Incorrect value) - (True value) |
Error = | 103 - 102.8 |
Error = 0.2 miles per hour
[tex]\begin{gathered} \text{Percent Error = }\frac{Error}{True\text{ value}}\times100\text{ percent} \\ \text{Percent Error = }\frac{0.2}{102.8}\times100\text{ percent} \\ \text{Percent Error = 0.195 percent} \end{gathered}[/tex]
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what is the volume of the can in cubic inches in terms of
Given data:
The height of the cylinder is h=9 in.
Th diameter of the cylinder is d=6 in.
The expression for the volume of the cylinder is,
V=(πd^2h)/4
Substitute the given values in the above expression.
[tex]\begin{gathered} V=\pi(6in)^2(9\text{ in)}\frac{1}{4} \\ =81\pi in^3 \end{gathered}[/tex]Thus, the volume of the given figure is 81 in^3. so C) option is correct.
Total blood cholesterol level was measured for each of 10 adults. Here are the 10 measurements (in mg/dL).176, 251, 247, 262, 150, 214, 192, 194, 154, 255Send data to calculator(a) What is the mean of this data set? If your answer is not aninteger, round your answer to one decimal place.00(b) What is the median of this data set? If your answer is notan integer, round your answer to one decimal place.(c) How many modes does the data set have, and what aretheir values? Indicate the number of modes by clicking in theappropriate circle, and then indicate the value(s) of themode(s), if applicable.zero modesone mode:two modes: andXS
a) 209.5mg/dL
b) 204mg/dL
c) zero modes
Explanations:Mean is also known as average of a dataset. Given the data expressed below;
[tex]Mean=\frac{sum\text{ of data}}{sample\text{ size}}[/tex]Given the following parameters
Sum of data = 176 + 251 + 247 + 262 + 150 + 214 + 192 + 194 + 154 + 255
Sum of data = 2095
Sample size = 10 (Total measurement)
Determine the mean of the data
[tex]\begin{gathered} Mean=\frac{2095}{10} \\ Mean=209.5 \end{gathered}[/tex]Therefore the mean of the data is 209.5mg/dL
b) The median of the dataset is the value in the middle after rearrangement. On rearranging in ascending order;
150, 154, 176,192, (194, 214), 247, 251, 255, 262
The two values at the middle are 194 and 214.
[tex]\begin{gathered} Median=\frac{194+214}{2} \\ Median=\frac{408}{2} \\ Median=204 \end{gathered}[/tex]c) The mode of the data is the value that occur the most in the dataset. SInce all the data only appear once in the dataset, hence there are ZERO MODES
Solve the triangle: Q=60", B = 60", y = 60". If it is not possible, say so.a= 1, b = 1,0 = 1a== 13,6 = 13,0 = 3a = 100,6 = 100,c = 100This triangle is not solvable.
Solution:
this triangle is not solvable because to solve this triangle we need one of the sides to find the missing sides.
Answer below due to inability to type out the following question.
ANSWER
[tex]11.04\text{ or }\frac{-2+\sqrt{580}}{2}[/tex]EXPLANATION
Given that:
In the figure provided, the triangle EFG is similar to the triangle is ECD
FE = 12
CD = 12
FG = CF + 2
To find the length CF, apply the similarity triangle theorem
[tex]\frac{\text{ FE}}{\text{ CF}}\text{ }=\frac{\text{ FG}}{CD}[/tex]Substitute the given data into the above equation
[tex]\begin{gathered} \text{ }\frac{12}{CF}=\frac{CF+2}{12} \\ \text{ cross multiply} \\ \text{ 12}\times12\text{ }=\text{ CF\lparen CF + 2\rparen} \\ \text{ 144 }=\text{ CF}^2\text{ }+\text{ 2CF} \\ CF^2\text{ }+\text{ 2CF -144 =0} \\ \text{ Find CF using the general formula} \\ x\text{ }=\text{ }\frac{-b\pm\sqrt{b^2-\text{ 4ac}}}{\placeholder{⬚}} \\ \text{ a }=1,\text{ b}=2,\text{ c}=-144 \\ \text{ x }=\frac{-2\text{ }\pm\sqrt{2^2-4\times1\times(-144)}}{2} \\ \text{ x}=\text{ }\frac{-2\pm\sqrt{4+576}}{2} \\ \text{ x }=\text{ }\frac{-2\pm\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+\sqrt{580}}{2} \\ \text{ x }=\text{ }\frac{-2+24.083}{2} \\ \text{ x }=\frac{22.083}{2} \\ \text{ x }=11.04 \\ \text{ Therefore, CF is 11.04 or }\frac{-2+\sqrt{580}}{2} \end{gathered}[/tex]10 Find x. 30° 5V3 10 5 73 1073
Do you have a pcture of this problem?
thanks
5
The Reyes family is going to the mall. When they leave home,
What is the problem about?
Average speed
What information is given?
Starting odometer reading, ending odometer reading, time taken
What do you need to find?
The average speed of the car
An odometer measures the distance traveled by a wheeled vehicle
The starting odometer reading was 54,362 miles
The ending odometer reading was 54,372 miles
It took 15 minutes to get to the mall
Step 1: Find how far Reyes traveled in 15 minutes
54372 - 54362 = 10 miles
At this speed, the car will travel 10 miles in 15 minutes
Step 2: How far the Reyes would travel in 60 minutes?
The Reyes would travel 40 miles in 60 minutes
Describe the transformations made on this function:(stretch/compression, reflect, left/right, up/down)
The function we have is:
[tex]f(x)=\frac{1}{2}(x-7)^3+6[/tex]Since this is a cubic function, we start with the parent cubic function (the simplest form of the cubic function):
[tex]f(x)=x^3[/tex]And compare it to the given function.
The first thing we can note is that there was a subtraction of 7 to the value of x:
[tex]x\longrightarrow x-7[/tex]When we add a number to the x value, the graph moves to the left, and when we subtract a number to the x value, the graph moves to the right.
So the first transformation is moving to the right 7 units.
Next, we have that there was +6 added to the expression --> When you add a number to the function, the graph moves up, and when you subtract a number to the function, the graph moves down.
In this case, since we added a constant value of 6, the graph is translated 6 units up.
The second transformation is moving up 6 units.
Finally, let's analyze the effect that the 1/2 has on the function.
We can compress or stretch the graph of a function by multiplying the x by a constant (a number). If the number of between 0 and 1, there is a stretch, and if the number is greater than 1 there is compression.
In this case, the number next to the x is:
[tex]\frac{1}{2}=0.5[/tex]Since the number is between 0 and 1 there is a stretch of the function.
In summary:
Answer:
Translation of 7 units to the right
Translation of 6 units up
Stretch of the function of 0.5
a cube has a volume of seven units. what is the edge length of a cube?
Given:
The volume of the cube = seven units.
Let a be the edge length of the cube.
Consider the formula for the volume of the cube.
[tex]V=a^3[/tex]Substitute V=7 in the formula, we get
[tex]7=a^3[/tex]Taking cubic root on both sides, we get
[tex]\sqrt[3]{7}=a[/tex][tex]T\text{he edge length of the given cube is }\sqrt[3]{7}\text{ units.}[/tex]or
[tex]T\text{he edge length of the given cube is }1.91\text{ units.}[/tex]The number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs0123stP(x)0.620.240.070.05.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?
Could you explain the following:Use s=rwt to find the value of the missing variable.S=pi/5m, r=7m, t=2sec
Answer:
[tex]0.0449[/tex]Explanation:
Here, we want to find the value of the missing variable w
We start by substituting the individually given values as follows:
[tex]\begin{gathered} \frac{\pi}{5}\text{ = 7}\times w\times2 \\ \\ w\text{ = }\frac{\pi}{5\times7\times2}\text{ = 0.0449} \end{gathered}[/tex]
I need help fast thanks it looks kinda hard and I can’t figure it out
Looking at the figure, we see that there are 6 identical squares of side 26 yd.
We know that the area of a square of side L can be calculated using the formula:
[tex]A=L^2[/tex]Now, if there are 6 squares, the total area is:
[tex]A_{\text{Total}}=6\cdot L^2[/tex]From the problem, L = 26 yd, then:
[tex]\begin{gathered} A_{\text{total}}=6\cdot26^2 \\ \therefore A_{Total}=4056yd^2 \end{gathered}[/tex]A Labrador retriever weighs 50kg. After a diet and exercise program the dog weighs 41kg. What is the percentage loss in weight.
inital weight = 50 kg
Final weight = 41 kg
loss = 50 - 41 = 9 kg
[tex]\begin{gathered} \text{percentage loss=}\frac{9}{50}\times100 \\ \text{percentage loss=}\frac{900}{50} \\ \text{percentage loss = }18\text{\%} \end{gathered}[/tex]I need help solving this problem. My answer isn’t coming out right. I have to find the missing length.
From the given diagram we get that the lines marked with the arrow are parallel, then the two triangles are similar.
To answer this question we will use the following diagram as a reference:
Therefore:
[tex]\frac{?}{18}=\frac{9-4}{9}.[/tex]Simplifying the above result we get:
[tex]\frac{?}{18}=\frac{5}{9}.[/tex]Multiplying the above result by 18 we get:
[tex]\frac{?}{18}\times18=\frac{5}{9}\times18.[/tex]Simplifying the above result we get:
[tex]\begin{gathered} ?=\frac{90}{9}, \\ ?=10. \end{gathered}[/tex]Answer:
[tex]?=10.[/tex]part A Jasmine ran 5 miles in 42 minutes at what rate did Jasmine run Jasmine ran at a rate of ? minutes per mile
We will find the rate as follows:
[tex]r=\frac{5}{42}[/tex]So the rate is the distance divided by the time it took to traverse.
Jennifer. Leigh Anne, and Karyn went out to eat. Jennifer bought an entrée for $12.95 and split a $4.95 dessert with Karyn, who bought a sandwich for $7.95. Leigh Anne bought soup for $3.95, a salad for $6.95, and coffee for $1.70. Determine the total amount each should pay if tax is 6% and each one tips 15% of her individual bill rounded up to the next quarter.
The total amount Leigh Anne spent is $3.95 plus $6.95 plus $1.7, that is $12.6. Since they pay a tax of 6% and a tip of 15%, she pays a total of 21% extra; this 21% can be obtained by the tule of three:
[tex]\begin{gathered} 12.6\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]then:
[tex]x=\frac{21\cdot12.6}{100}=2.65[/tex]Therefore, Leigh Anne spent a total of $15.25.
Assuming the dessert was split in half, then Jennifer spent a total of $15.43. To this amount we have to add the tax and tip. By the same logic as before we have:
[tex]\begin{gathered} 15.43\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]then:
[tex]x=\frac{21\cdot15.43}{100}=3.24[/tex]Therefore, Jennifer spent $18.75
Finally Karyn spent $10.43, obtaining the extra amount we have:
[tex]\begin{gathered} 10.43\rightarrow100 \\ x\rightarrow21 \end{gathered}[/tex]Then:
[tex]x=\frac{21\cdot10.43}{100}=2.19[/tex]Therefore, Karyn spent $12.75.
Based on the density graph below, what is the probability of a valuein the sample space being anywhere from 0 to 20?
Answer
Option A is correct.
Probability of a value in the sample space being anywhere from 0 to 20 = 80%
Explanation
The probability of an event is calculated as the number of elements in the event divided by the total number of elements in the sample space.
For this question,
Number of boxes from 0 to 20 = 20
Total number of boxes in the density graph = 25
Probability of a value in the sample space being anywhere from 0 to 20 = (20/25) = 0.8 = 80%
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If Lydia invests $3000 in a certificate of deposit and d dollars in a stock, write an expression for the total amount she invested.
ANSWER:
[tex]\text{ total amount }=3000+d[/tex]STEP-BY-STEP EXPLANATION:
The total invested is equal to 3000 investment and the previous money in stock, therefore, the expression would be:
[tex]\text{ total amount }=3000+d[/tex]What is the value of sin C? a) 15/17b) 15/8c) 8/15d) 8/17
Answer:
d) 8/17
Explanation:
From trigonometry, we know that in a right triangle:
[tex]\sin \theta=\frac{Opposite}{\text{Hypotenuse}}[/tex]From the diagram:
• The side, opposite C, is 8.
,• The ,hypotenuse, is 17.
Therefore:
[tex]\sin C=\frac{8}{17}[/tex]felicia owns 80 shares of electrify us power cooperative that pay dividends of $129. at this rate, what dividend would felicia recive after buying 600 shares.
The dividend that Felicia will receive after buying 600 shares is $967.50.
How to calculate the value?Dividends are regular profit-sharing payments made by a company to its shareholders. The board of directors of a company decides on the price per share as well as when and how often dividend payments are made. Dividend stocks can provide a steady stream of income, which is especially valuable during times of inflation.
From the information, Felicia owns 80 shares of electrifying us power cooperative that pay dividends of $129. It should be noted that the dividend rate will be:
= $129 / 80
= $1.6125
Therefore, the amount for 600 shares will be:
= 600 × $1.6125
= $967.50
The dividend is $967.50.
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what is 13 divided by 113.1
Give the name of the parent function and describe the transformation represented.
5 units to the left and 2 units downwards
Explanation:[tex]f(x)\text{ = |x + 5| - 2}[/tex]The parent function:
f(x) = |x|
Name of parent function is absolute value function
The transformtion from parent function to the new function:
[tex]\begin{gathered} \text{from f(x) = |x| to f(x) = |x + 5| - 2} \\ \text{For translation:} \\ f(x)\text{ = |x + a| (translation to the left)} \\ f(x)\text{ = |x - a| (translation to the right)} \\ \\ So\text{ f(x) = |x + 5| is a translation of 5 units to the left} \end{gathered}[/tex][tex]\begin{gathered} For\text{ translation: } \\ f(x)\text{ = |x| + a (translation upwards)} \\ f(x)\text{ = |x| }-\text{ a (translation downwards)} \\ \\ So\text{ f(x) = |x| - 2 is a translation downwards} \end{gathered}[/tex]Combining both transformation:
f(x) = |x + 5| - 2 is a translation of 5 units to the left and 2 units downwards
Find the equation of the line with the given properties. Sketch the graph of the line. Passes through (1, -6) and (8,3)
A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b the y-intercept.
If we evaluate our points on this form, we're going to have a linear system where the solutions are those coefficients.
[tex]\begin{cases}3=8m+b \\ -6=m+b\end{cases}[/tex]If we subtract the second equation from the first, we're going to have a new equation only for the slope.
[tex]\begin{gathered} 3-(-6)=8m+b-(m+b) \\ 3+6=8m+b-m-b \\ 9=7m \\ m=\frac{9}{7} \end{gathered}[/tex]Now that we have the slope, we can use any of the equations to find the b value.
[tex]\begin{gathered} -6=(\frac{9}{7})+b \\ -6-\frac{9}{7}=b \\ b=-\frac{51}{7} \end{gathered}[/tex]Then, our line equation is
[tex]y=\frac{9}{7}x-\frac{51}{7}[/tex]And this is the graph
Please help ASAP *image imported*
y=-2x + 4 3y + 6x = 12 O One Solution O No Solutions o Infinitely Many Solutions
To find the number of solutions of a system of linear equations you need to identify the slope (m) of each equation
[tex]y=mx+b[/tex]If the slope is the same in both lines the system has no solution.
If the slope is different in the lines the system has one solution.
If the equation are the same (incluided the value of b) the system has infinitely many solutions.
In the given equations the slope is:
First equation:
[tex]y=-2x+4[/tex]Slope: m=-2Second equation:
[tex]3y+6x=12[/tex]Write the equation in slope-intercept form by solving for y:
[tex]\begin{gathered} 3y+6x-6x=-6x+12 \\ 3y=-6x+12 \\ \\ y=-\frac{6}{3}x+\frac{12}{3} \\ \\ y=-2x+4 \end{gathered}[/tex]Slope: m= -2In this case as the equatinos are the same the system has infinitely many solutions3 parts!!! Suppose that on January 1 you have a balance of $4500 on a credit card whose APR is 12%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1.a. Calculate your monthly payments.b. When the card is paid off, how much will you have paid since January 1?c. What percentage of your total payment from part(b) is interest?Part A: The monthly payment is ?(Do not round until the final answer. Then round to the nearest cont as needed.)
Given,
P=$4500
r=12%
For 1 month the rate is 12/12%=1%
So interest for one month is
[tex]I=\frac{4500\times1\times1}{100}=45[/tex]a. The monthly payment is:
[tex]\begin{gathered} A=\frac{4500\times0.01\times(1+0.01)^{12}}{(1+0.01)^{12}-1} \\ \Rightarrow A=\frac{50.70}{0.12} \\ \Rightarrow A=422.5 \end{gathered}[/tex]The monthly payment is $422.5
b. Total payment for a year is:
A=4500+(12x45)=$5040
Total amount paid since January is $5040
c. The percentage of interest is:
[tex]\frac{45\times12}{5040}\times100\%=10.71[/tex]The percentage interest is 10.71%
A basketball team has 13 Active players, in how many ways can 5 players be selected to start the game??
Answer:
1287
Explanation:
The number of distinct ways n objects can b selected from N total objects is given by
[tex]\frac{N!}{n!(N-n)!}[/tex]Now in our case, we have a total of 13 basketball players. N = 13 and 5 players to choose n = 5. Therefore, the above formula gives
[tex]\frac{13!}{5!(13-5)!}[/tex][tex]-\frac{13!}{5!8!}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5!\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10}{5!}[/tex][tex]=\frac{13\cdot12\cdot11\cdot10}{5\cdot4\cdot3\cdot2\cdot1}[/tex][tex]=1287[/tex]Hence, there are 1287 ways 5 different players can be selected from 13 players.
1.Find the quotient of 1/2and 3/4.2. Divide 4by2/33.If 5/9is divided by3, what is the quotient4. Mrs. Dolentebuys 5 1/2kilograms of rice. If she cooks 1/4kilogram for every meal, how many meals will it last?5.Marita needs 2/3meter of lace for each pillowcaseshe makes. How many pillowcasescan she make with 7 1 3meters of lace
1) We can find the quotient between two fractions by multiplying the first one by the reciprocal of the second one this way:
[tex]\frac{\frac{1}{2}}{\frac{3}{4}}=\frac{1}{2}\times\frac{4}{3}=\frac{4}{6}=\frac{2}{3}[/tex]2) Let's now divide 4 by 2/3 following the same principle:
[tex]\frac{4}{\frac{2}{3}}=4\times\frac{3}{2}=\frac{12}{2}=6[/tex]Notice that we have simplified as well as the previous item (1).
3) Proceeding with that we have:
[tex]\frac{\frac{5}{9}}{3}=\frac{5}{9}\times\frac{1}{3}=\frac{5}{27}[/tex]4) To find this out, we need to convert that Mixed Number to Improper Fraction:
[tex]\begin{gathered} 5\frac{1}{2}=\frac{2\times5+1}{2}=\frac{11}{2} \\ \frac{\frac{11}{2}}{\frac{1}{4}}=\frac{11}{2}\times4=\frac{44}{2}=22 \end{gathered}[/tex]We kept the denominator then multiplied it by the whole number and added it to 1. So it will last 22 meals.
5) To find it out we are going to divide 7 1/3 by 2/3 meter, after converting that Mixe Number into an Improper Fraction:
[tex]\begin{gathered} 7\frac{1}{3}=\frac{3\times7+1}{3}=\frac{22}{3} \\ \frac{\frac{22}{3}}{\frac{2}{3}}=\frac{22}{3}\times\frac{3}{2}=\frac{66}{6}=11 \end{gathered}[/tex]Notice, that we have used the same procedure to convert from Mixed Numbers to an Improper fraction. Marita can make 11 pillowcases.
And those are the answers.