We know that the total is 40 students, and 24 of them are girls, then the fraction that represents it is
[tex]\frac{24}{40}[/tex]But we must simplify the fraction, let's divide the denominator and numerator by 4
[tex]\frac{24}{40}=\frac{6}{10}[/tex]Now we can do it again by 2
[tex]\frac{24}{40}=\frac{6}{10}=\frac{3}{5}[/tex]Therefore the correct answer is the letter B.
[tex]\frac{3}{5}[/tex]Answer: 12 1/4
Step-by-step explanation: 16 =4 is 12, and 3/4 - 2/4 is 1/4
hope this helps :)
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
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%
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]
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.
To learn more about negatively skewed distribution, use the link given
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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
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
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
Find S3 of the sum of the geometric series. az = 4, a3 = 1, r= 1
Given:
a1 = 4
a3 = 1
r = ½
Let's find the S3 of the sum of the geometric series.
Apply the sum of geometric series formula below:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]Let's solve for S3.
Substitute the values into the equation.
Where: n = 3
Thus, we have:
[tex]S_3=\frac{4(1-(\frac{1}{2})^3)^{}^{}}{1-\frac{1}{2}}[/tex]Solving further:
[tex]\begin{gathered} S_3=\frac{4(1-(\frac{1}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}))}{\frac{1}{2}} \\ \\ S_3=\frac{4(1-\frac{1}{8})}{\frac{1}{2}} \\ \\ S_3=\frac{4(\frac{7}{8})}{\frac{1}{2}} \\ \\ S_3=\frac{4\ast\frac{7}{8}}{\frac{1}{2}} \\ \\ S_3=\frac{\frac{7}{2}}{\frac{1}{2}} \\ \\ S_3=\frac{7}{2}\ast\frac{2}{1} \\ \\ S_3=7 \end{gathered}[/tex]Therefore, the S3 of the sum of the given geometric series is 7
ANSWER:
7
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.
-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
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:
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:
the figures in each pair are similar. Find the unknown measures.
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%
in a stable there are H horses 6 of them are taken into the the yard to exercise ⁰how many are left in the stable
Explanation:
If there are H horses and 6 are taken into the yard, then we have 6 horses less in the stable.
Answer:
There are (H - 6) horses left in the stable
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]f(x) is a linear function. f(0) = 7 and f(3) = 5. Find the equation for f(x).
Let us calculate the slope of the line. We get two points (0,7) and (3,5)
[tex]m=\frac{7-5}{0-3}=-\frac{2}{3}[/tex]given the slope we have that
[tex]f(x)=-\frac{2}{3}x+7[/tex]so the function is:
[tex]f(x)=-\frac{2}{3}x+7[/tex]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
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.
1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x. The figure is not drawn to scale
1 and ∠2 are complementary angles. The measure of ∠1 is 14°. The measure of ∠2 is 4x°. Find the value of x.
Remember that
the sum of complementary angles is 90 degrees
so
<1+<2=90
substitute given values
14+4x=90
solve for x
4x=90-14
4x=76
x=19Calculate the area of the square JKLM if KM = 42 mm.
Calculate the area of the square JKLM if KM = 42 mm.
given that KM=42 mm
KM is also the diagonal of the square.
Also, the diagonal KM is the hypotenuse of a right triangle with sides JK and JM the Pythagoras theorem.
Now , let's remember that the angle formed by two sides of a square is equal to 90 degrees, this means, that the angle formed by the diagonal and any side must be the half, it is 45 degrees
so, if we solve the right triangle MLK we will find the length of the s
[tex]\begin{gathered} \text{cos}\emptyset=\frac{x}{\text{Hypotenuse}} \\ x=\text{Hypotenuse }\cdot\text{ cos}\emptyset \\ x=42\cdot\cos 45 \\ x=29.69 \end{gathered}[/tex]Now, is it a square, so the sides are equal, and the area is given by
[tex]\begin{gathered} \text{Area}=x^2 \\ A\text{rea}=(29.698)^2 \\ \text{Area}=882\text{ square milimeteres} \end{gathered}[/tex]so, the answer is 882 square millimeters
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}
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.
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.
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
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.
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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
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]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.
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!!!