We need to simplify the following expression
[tex]\frac{3}{4}m^3+8-\frac{1}{2}m^3[/tex]We first group the similar terms, they are the first and the third one
[tex](\frac{3}{4}m^3-\frac{1}{2}m^3)+8[/tex]then we use common factor to take out the m^3 of the parenthesis
[tex]m^3(\frac{3}{4}-\frac{1}{2})+8=\frac{1}{4}m^3+8=4(m^3+2)^{}[/tex]What is the difference between a rectangle and a rhombus?
A rhombus is a two-dimensional shape and is also characterized as a special parallelogram. It has four equal sides, with the opposite angles being equal to each other, whereas its adjacent angles are supplementary.
A rectangle is a also two-dimensional shape. It has four equal angles and four vertices. All the four angles of a rectangle measure 90°.
Rhombuses and Rectangles have the following differences:
1) A rhombus has four equal sides while in a rectangle, the opposite sides are equal.
2) The diagonals of a rhombus bisect each other at 90° while the diagonals of a rectangle bisect each other at different angles.
If x+4 is a factor of this polynomial, what is the value of a ?
Answer: -86
Given:
[tex]P(x)=2x^3-11x^2+ax-40[/tex]If we consider x+4 as a factor of the given polynomial, this would mean that x=-4. For an x- value to be a factor of a polynomial, P(x) must be equal to 0. With that, we will have:
[tex]\begin{gathered} P(-4)=0 \\ P(-4)=2x^3-11x^2+ax-40 \\ 0=2(-4)^3-11(-4)^2+a(-4)-40 \\ 0=-128-176-4a-40 \\ 4a=-128-176-40 \\ 4a=-344 \\ a=-86 \end{gathered}[/tex]Therefore, the answer is -86
Which symbol is used to represent Integer Numbers?1. Z2. W3. Q4. N
Answer: Letter Z.
The notation Z for the set of integers comes from the German word Zahlen, which means "numbers". Integers strictly larger than zero are positive integers and integers strictly less than zero are negative integers.
Y S 18. Graph triangle DEF with vertices D(-5,2), E(1.3), and F(-4,-3). Then graph the image of the triangle after it is translated 4 units right and 3 units down. What are the vertices of triangle D'E'F? 4 3 2 1 o 1 2 J 4 SX YTY
Graphing the triangle DEF, we have:
Now, translating the triangle 4 units right and 3 units down, we have the new vertices:
[tex]\begin{gathered} D(-5,2)\to D^{\prime}(-5+4,2-3)=D^{\prime}(-1,-1) \\ E(1,3)\to E^{\prime}(1+4,3-3)=E^{\prime}(5,0) \\ F(-4,-3)\to F^{\prime}(-4+4,-3-3)=F^{\prime}(0,-6) \end{gathered}[/tex]Graphing the triangle D'E'F', we have:
pol: Practice & Problem Solving 2.PS-22 Question Help Three sisters are saving for a special trip. The ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4. Together all 3 sisters have saved $60. How much has each girl saved? Answer questions 3–4. IS 4 squares long. Then, use the diagrams to show $60. (Type whole numbers.) 4. Complete the table. Helga's savings Maurice's savings Nora's savings $8 $ $24 $32 $ $6 $ $ 12 $4 $ $ $16 + Vi 1 1,0 More Enter your answer in the edit fields and then click Check Answer. 1 pant Clear All Check Answer remaining
Answer:
Explanation:
We know that the ratio of Helga's savings to Maurice's savings is 8:3 and the ratio of Maurice's savings to Nora's savings is 3:4.
It means that if Helga has $8, Maurice has $3 and Nora has $4
In the same way, we can multiply one quantity by 2, and all the quantities will be multiplied by 2, so if Helga has $16, Maurice has $6 and Nora has $8
Because:
$8 x 2 = $16
$3 x 2 = $6
$4 x 2 = $8
So, following the same logic, we can complete the table as:
Therefore, the complete table is:
Please give me the correct answer.True or false.If a =b, then a +c = b+c.
Answer
a = b
a + c = b + c (Addition Property of Equality)
This operation is True.
Explanation
If we are told that
a = b
Adding the same number to both sides of an equation is called the Addition Property of Equality.
And it produces the same number on both sides after this operation.
a = b
Add c to both sides
a = b
a + c = b + c (Addition Property of Equality)
This operation is True.
Hope this Helps!!!
Use the point-slope formula to write an equation of the line that passes through 4, 2 and 6,5.Write the answer in slope-intercept form (if possible).
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
point 01 (4 , 2)
point 02 (6 , 5)
Step 02:
equation of the line:
slope:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{5-2}{6-4}=\frac{3}{2}[/tex]Point-slope form of the line
(y - y1) = m (x - x1)
[tex]\begin{gathered} (y-2)=\frac{3}{2}(x-4) \\ \\ (y-2)=\frac{3}{2}x\text{ -}\frac{12}{2} \\ \\ y-2=\frac{3}{2}x-6 \\ \\ y=\frac{3}{2}x-6+2 \\ \\ y=\frac{3}{2}x-4 \end{gathered}[/tex]The answer is:
y = 3/2 x - 4
Cassius is purchasing flower baskets to be placed on each table at a volunteer appreciation lunch. Store Acharges $19.25 per flower basket plus a $15.00 delivery fee. Store B charges $17.50 per flower basket plusa $30.00 delivery fee. Which inequality can determine x, the maximum number of flower baskets that canbe ordered for the total cost at Store A to be cheaper the total cost from Store B?O 19.25 + 15x > 17.5 + 30xO 19.25 + 15x < 17.5 + 30x19.25x + 15 < 17.5x + 30O 19.25x + 15 > 17.5x + 30
We will have the following expressions for store A and B respectively:
[tex]19.25x+15[/tex][tex]17.50x+30[/tex]From this, we can see that after certain ammount of flowers the price will be better if we arrage it as follows:
[tex]19.25x+15>17.50x+30[/tex]Study the data given,Below are the weights of 6 randomly selectedblack bears and 6 randomly selected grizzly bearsliving on a wildlife refuge.Which type of bear had morevariation in weight?Black Bear Weights (lbs): 102, 151, 248, 342,453, 498A. Black BearsMean: 299MAD: 132B. Grizzly BearsC. Both showed the same amount ofvariation in weightHaven't learned this yet.Grizzly Bear Weights (lbs): 294, 302, 347, 422,553, 596Mean: 419MAD: 104 2/3
The mean absolute deviation (MAD) is a statistical measure of how much the different data points "move away" from the mean of the data set. In this case the weights of the bears have been given, the mean has been calculated and the MAD is derived by deducting each data point from the mean. The MAD has been given already by the way. Some data points fall below the mean while some are above it. but whatever the difference is, you'll have to take the "absolute value" that is positive value only. For example, the mean weight of the black bears is 299, and the weight of the first black bear is 102, that gives you adifference of 197. note that the result should be negative 197 (-197) but we are interested in the absolute values only.
Same way you find the absolute deviation for the other data points and you have, 197, 148, 51, 43, 154, and 199. Sum up these numbers and divide by the number of observed data (number of black bears) and you have 792 divided by 6 which gives you 132. This means the mean absolute deviation of the observed data is 132 as compared to the mean which is 299.
If you compare the MAD of the black bears with that of the grizzly bears, you would see that the MAD of the grizzly bears is more varied, because 104 2/3 moves further away from 419 than the MAD of the black bears which is 132 moving away from 299.
please help due in 5 minutes would mean a lot
Answer:
150 degrees
Explanation:
Given: m∠8=150 degrees
Angles 8 and 5 are vertically opposite angles.
Vertical angles are equal, therefore:
[tex]\begin{gathered} m\angle5=m\angle8 \\ m\angle5=150\degree \end{gathered}[/tex]Next, angles 1 and 5 are corresponding angles.
Corresponding angles are equal, therefore:
[tex]\begin{gathered} m\angle1=m\angle5 \\ m\angle1=150\degree \end{gathered}[/tex]The measure of angle 1 is 150 degrees.
A cosmetics company makes small, cylindrical bars of soap, and wraps them in plastic prior to packing them in boxes for shipping. Each bar of soap has a diameter of 5 cm and is 2 cm in height.a. How much soap material is used to make each bar of soap?b. How much plastic is required to wrap each bar of soap, assuming it is shrink-wrapped tightly around each bar?C.The company wants to be able to ship a minimum of 60 bars per box to save on shipping costs. What will be the dimensions of the box if the soap must be stacked no more than 5 bars high?d. Find the capacity of the box in litres.
a. In order to determine how much soap material is used for each bar of soap, consider that the shape of the bar is a cylinder, then, use the folowing formula for the volume of a cylinder:
V = π r² h
where r is the radius of the base and h is the height.
The diameter is 5 cm, then, the radius is r = d/2 = 5 cm/2 = 2.5 cm
The height is h = 2 cm
replace the previous values into the formula for V:
V = (3.14)(2.5 cm)²(2 cm)
V = 39.25 cm³
Hence, 39.25 cm³ of soap material is used to make each bar.
b. In this case it is necessary to calculate the suface area of the plastic used. As before, take into account that the bar has a cylindrical shape. Then, use the following formula for the surface area of a cylinder:
S = 2πr² + 2πrh
replace the values of the parameters to find S:
S = 2π(2.5 cm)² + 2π(2.5cm)(2cm)
S = 70.68 cm²
Hence, 70.68 cm² of plastic is required to wrap each bar
c. Take into account that the soap must be stacked no more than 5 bars high, and that the company wants to ship a minimum of 60 bars.
If there are 5 bars high x 3 bars length, in one face of the box you have 15 bars. Moreover, if there are 4 bars width, then, you have a total of 15x4 = 60 bars in one box, which is what the company wants.
The height of the box is given by 5 times the height of one bar (because there are 5 bars high). The length is given by 3 times the diameter of one bar and the width of the box is given by 4 times the diameter of one bar:
height of the box = 5(2 cm) = 10 cm
length of the box = 3(5 cm) = 15 cm
width of the box = 4(5 cm) = 20 cm
d. First, calculate the volume of the box, as follow:
V = h x l x w = (10 cm)(15 cm)(20 cm) = 3,000 cm³
take into account the conversion 1,000 cm³ = 1 L, then, the capacity of the box is:
V = 3,000 cm³ = 3L
Complex numbers are used to describe current. I voltage, E, and impedance, Z. These three quantities are related by the equation E = IZ. Given two ofthese quantities, solve the equation E = IZ for the missing variable.I = 4 + 4i, Z= 7+3iE=(Simplify your answer. Type your answer in the form a+b/. Use integers or fractions for any numbers in the expression.)
We have the following equation to solve
[tex]E=I\cdot Z[/tex]Where E, I, and Z are complex numbers, therefore let's put it in numbers
[tex]E=(4+4i)(7+3i)[/tex]We can solve it directly into the rectangular form by doing the distrutive
Then
[tex](4+4i)(7+3i)=28+12i+28i+12i^2[/tex]Remember that
[tex]i^2=-1[/tex]Then
[tex]\begin{gathered} (4+4\imaginaryI)(7+3\imaginaryI)=28+12i+28i-12 \\ \\ (4+4\imaginaryI)(7+3\imaginaryI)=16+40i \end{gathered}[/tex]Now we have completely solved the problem!
[tex]E=16+40i[/tex]______________________
The second solution (usual)
When we have real engineering problems, we like to do multiplication and division with the polar form, then let's convert Z and I to the polar form
[tex]\begin{gathered} I=4+4i=4\sqrt{2}\angle45° \\ \\ Z=7+3i=\sqrt{58}\angle23.2° \end{gathered}[/tex]Now to do the multiplication we multiple the magnitude and sum the phases (angles)
[tex]\begin{gathered} ZI=4\sqrt{2}\cdot\sqrt{58}\angle45°+23.2° \\ \\ ZI=4\sqrt{116}\operatorname{\angle}68.2° \end{gathered}[/tex]We already have the result, now just put it in the rectangular form
[tex]\begin{gathered} ZI=4\sqrt{116}\cdot\cos(68.2)+i4\sqrt{116}\sin(68.2) \\ \\ E=16+40i \end{gathered}[/tex]Find each percent decrease. Rounf to thr nearest percent. The first one is done for you.From $60 to $40?
So the 100% percent is equal to $60 and is decreasing $40 so is:
[tex]60-40=20[/tex]So is decreasing $20. now we can made a rule of 3 to finde the percentage so:
[tex]\begin{gathered} 60\to100 \\ 20\to x \end{gathered}[/tex]and the ecuation will be:
[tex]\begin{gathered} x=\frac{100\cdot20}{60} \\ x=33.33\approx33 \end{gathered}[/tex]So in total the decrese a 33%
Question 5 of 9Translate the phrase into a variable expression. Use the letter m to name thevariable. If necessary, use the asterisk (*) for multiplication and the slash(/) for division.... the total number of minutes billed on the phone bill split between 3phones...Answer here
SOLUTION
From the question, let the total number of minutes billed on the phone bill be m
Splitting this into 3 phones, we have
[tex]\frac{m}{3}[/tex]Hence the answer is m/3
Which single transformation below would have the same effect as rotating the point (-3,4) by 180 degrees around the origin and then reflecting it in the y-axis?
First i will draw the original point in red
the rotation of 180° will give us the point (3,-4) the blue point
next, we reflect this point in the y-axis, the green point
if we see only the red point and the green point the transformation is equivalent to a reflection in the x-axis
the correct answer is 1
2.A group of students in MATH 105 start a walking program. The chart below shows eachmember's self-reported walking time in minutes during May 2022.X-300A-325B-550C-400D - 900E-150F-60G-600H - 250By what percent did X exceed or fall below the mean? it’s number 2
Given: 300, 400, 60, 325, 900, 600, 550, 150, 250
1st we find the mean or avaerage of all the numbers.
Mean:
[tex]\frac{300+400+60+325+900+600+550+150+250}{9}=\frac{3525}{9}\approx392.778[/tex]From here we can see that X=300 falls below the mean.
So we can use this formula:
[tex]\frac{mean-actual\text{ }value}{mean}*100\%\Rightarrow\frac{392.778-300}{392.778}*100\%\approx23.688\%[/tex]Answer: X falls below the mean by 23.688%
solving compound qualities
S = {x ∈ R : 3≤x≤12}
1) To solve a compound inequality, we must do it one by one.
Let's start with
1.1) 0≤1/3x -1
1≤1/3x-1+1
1≤1/3x Multiplying both sides by 3
3≤x Flipping it
x≥3
1.2) 1/3x -1≤3
1/3x -1+1≤3+1
1/3x≤4
x≤12
2) Let's find out the solution, by graphing on three lines. The first one for the first solution, the second for the second inequality's solution, and the third for the intersection of the above:
So the Solution set is S = {x ∈ R : 3≤x≤12}
Question 3X1127INXRewrite in simplest rational exponent form VxVx. Show each step of your process.
Given
[tex]\sqrt[]{x}\cdot\sqrt[4]{x}[/tex]So, we have that
[tex]\begin{gathered} \sqrt[]{x}=x^{\frac{1}{2}} \\ \sqrt[4]{x}=x^{\frac{1}{4}} \end{gathered}[/tex]Therefore, the expression given is
[tex]x^{\frac{1}{2}}\cdot x^{\frac{1}{4}}[/tex]Apply the laws of exponents
[tex]x^{\frac{1}{2}+\frac{1}{4}}=x^{\frac{3}{4}}[/tex]Answer:
[tex]x^{\frac{3}{4}}[/tex]what is the time it took to reach maximum height? round the answer to the nearest whole second.
3 seconds
Explanation
we have a graph where
x-axis: indicates the time
y-axis:indicates the height
to solve this we need to find the time, where the maximum heigth is reached
Step 1
check the coordinate where the maximum heigth is reached
and go down vertically to intersect the x-axis:
so, we have , it took around 3 seconds to reach the maximum heigth
I hope this helps you
It takes Jenny 8.4 minutes to sweep a porch.Mofor can sweep the same porch in 13.3minutes. If they worked together how longwould it take them?
Rate of Jenny = 1/ 8.4 minutes
Rate of Mofor = 1/13.3 minutes
We know time and rate are inverses of each other.
So, if they work together, their rates would be:
[tex]\frac{1}{8.4}+\frac{1}{13.3}[/tex]The time they will take will be the inverse of this, thus:
[tex](\frac{1}{8.4}+\frac{1}{13.3})^{-1}[/tex]So, let's calculate it:
[tex]\begin{gathered} (\frac{1}{8.4}+\frac{1}{13.3})^{-1} \\ =5.1484 \end{gathered}[/tex]That is around 5.15 minutes.
Construct a truth table of the following statement. Jack will not play or Chris is hurtUse the symbolic representationp: Jack will playr: Chris is hurt
ANSWER and EXPLANATION
We want to construct a truth table for the following statement:
Jack will not play or Chris is hurt
where p: Jack will play; r: Chris is hurt
"Jack will not play" will be represented by -p.
This implies that "Jack will not play or Chris is hurt" will be represented by - p v r.
Let us now construct the truth table:
That is the truth table for the statement.
how to find the center and scale factor of #5?
SOLUTION:
Case: Enlargement
Method:
Scale factor: The scale factor is the 3, because the image is three times the size of the object.
From the tracing, the center of dilation is at C(-2, -2).
Final answer:
Center = (-2, 2)
Scale factor = 3
Vector performed an experiment at a local farm to determine if the addition of bananas to his biomass cow menure recipe helps produce more or less energy. Me collected random samples of menure and benenes from the farm, prepared 15 bottles each of both matures, and placed oballeen on top of each bottle. Alter two weeks, he measured the circumference of each balloon in centimeters: the bigger the balloon grew, the more energy that was produced. The results of the experiment are displayed in the box plots below. Which description most accurately summarizes the sample results? 10. 11. 13. 13. 14. 15. 15. 15. 18. 18. 19 20. 22. 25. 26 22.22.26 29 30 31 36. 36 38. 39. 43 46. 46. 49. 50 MORE CONSISTENT LESS S OUT THE Autor behind ONE CON nece MORE
Notice the smaller range and values of the experiment with cow manure (smaller box diagram and also located at smaller values of total energy.
The banana mixture clearly generates a wider box diagram (so less consistent) and also located at higher values (to the right).
Therefore, the answer we choose is the last one (bottom right) that says that the cow manure data is more consistent than the other one, and also, since the mashed banana data is so much higher, combined with the previous will clearly give larger amounts of biogas.
Please select the bottom right option.
Solve for xx and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.45≥4x+5 and 53>4x+5
Expression given:
[tex]45\ge4x+5[/tex][tex]53>4x+5[/tex]Procedure:
• Solving for ,x ,in first inequality
[tex]-4x\ge-45+5[/tex][tex]-4x\ge-40[/tex][tex]x\le\frac{-40}{-4}[/tex][tex]x\le10[/tex]• Solving for ,x ,in second inequality
[tex]-4x>-53+5[/tex][tex]x<\frac{-48}{-4}[/tex][tex]x<12[/tex]Thus, the graph would be:
If the solution is for both inequalities, then the answer is in which both are included:
[tex]x\le10[/tex]Find the percent of change and classify as a percent increase or decrease. Round to the nearest tenth of a percent when necessary. A $39 watch is now on clearance for $17.50.
The percent of increase or decrease = change/original x 100%
Since the original price of the watch is $39
Since its price now is $17.50, then
The change of the price = 39 - 17.50 = 21.50 dollars
The percentage of decrease = 21.50/39 x 100%
The percentage of decrease = 55.1282
Round it to the nearest tenth
The percentage of decrease is 55.1%
50 POINTS!!!!!!
1. Angles A and B are supplementary. Determine the measure of angle A if the measure of angle B is 109.6°.
A) 250.4°
B) 63.2°
C) 70.4°
D) 19.6°
Answer:
C) 70.4°Step-by-step explanation:
We know supplementary angles add up to 180°:
A + B = 180°Find the missing one:
A + 109.6° = 180°A = 180° - 109.6°A = 70.4°Correct choice is C.
-14x > -3 all I have to do is simplify it
The first step in simplifying the inequality is to divide both sides by -14:
[tex]\frac{1}{-14}\times-14x>-3\times\frac{1}{-14}[/tex]Since we are dividing both sides by a negative number, the inequality reverses direction, and hence it becomes
[tex]\textcolor{#FF7968}{x<\frac{3}{14}}\text{\textcolor{#FF7968}{.}}[/tex]This is the farthest we can go in simplifying the inequality; therefore, the above inequality is our answer
Prove that these 3 equations are the same. There is more than one way to do this. Show in multipleways for a higher score.y = (x + 5)(x + 1)y = (x + 3)^2 - 4y = x^2 + 6x + 5
For the first equation:
y = (x + 5)(x + 1)
apply distribution property:
y = (x + 5)(x) + (x + 5)(1)
y = x·x + 5·x + x·1 + 5·1
y = x² + 5x + x + 5
y = x² + 6x + 5
For the second equation:
y = (x + 3)² - 4
use the fact that (a + b)² = a² + 2ab + b², for the term (x + 3)², then, you have:
y = x² + 2·x·3 + 3² - 4
y = x² + 6x + 9 - 4
y = x² + 6x + 5
The third equation is already in the convenient form.
Then, you can notice that all three equations are the same equations.
1. Describe the shape of
distribution A:
Answer choices:
Symmetric
Negatively skewed
Positively skewed
Uniform
The shape of the distribution A is Negatively skewed.
What is a negatively skewed distribution?\
A negatively skewed distribution sometimes referred to as a left-skewed distribution, is a type of distribution where more values are concentrated on the right side (tail) of the distribution graph and the left tail of the distribution graph is longer.
The idea of skewness is used in finance to analyze the distribution of investment returns. An investor may anticipate frequent tiny wins and a few significant losses, according to the distribution's negative skewness. In fact, traders frequently use trading methods that are based on distributions that are negatively skewed.
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find f^-1(f(x)) for f(x)=(x-3)/2
After solving the given equation for f(x) the resultant answer is f(x)=1.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, find f(x):
When f^-1(f(x)) in f(x)=(x-3)/2.Now, calculate as follows:
f(x)=(x-3)/2f(x)=(f⁻¹-3)/2f(x)=(1/f - 3)/2f(x)=(1 -3f/f)/2f(x)=(1-3)/2f(x)=2/2f(x) = 1Therefore, after solving the given equation for f(x) the resultant answer is f(x)=1.
Know more about equations here:
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