Given
4
18
Procedure
The mean proportional, or geometric mean, of two positive The mean proportional, or geometric mean, of two positive
[tex]\frac{a}{x}=\frac{x}{b}[/tex]When solving
[tex]\begin{gathered} x=\sqrt[]{a\cdot b} \\ x=\sqrt[]{4\cdot81} \\ x=\sqrt[]{324} \\ x=18 \end{gathered}[/tex]The answer would be 18
Several students use stopwatches to measure how quickly a sensitive plantreacts to stimuli. They record the times in milliseconds. Which kind of dataare the students recording?OA. Qualitative dataOB. Audio dataC. Quantitative dataOD. Categorical data
Given: Several students use stopwatches to measure how quickly a sensitive plant reacts to stimuli. They record the times in milliseconds.
Required: To determine which kind of data the students are recording.
Explanation: The given kinds of data can be summarized as follows-
→Qualitative data determines the quality of a single data. Example: The colour of cars in a parking lot.
→Audio data have the data in the form of audio. Example: The sound of different dogs barking.
→Quantitative data represents the quantity of some data. Example: Recording the number of the height of students in a class.
→Categorical Data represents the data of various categories. Example- Recording some person's age, sex, hair colour, etc.
Hence, measuring how quickly a sensitive plant reacts to stimuli is an example of Qualitative Data.
Final Answer: Option A (Qualitative Data) is correct.
radius = 3 ¼ydlearning something about area of circle
Given that the radius of a circle is;
[tex]r=3\frac{1}{4}yd[/tex]Recall that the area of a circle can be calculated using the formula;
[tex]A=\pi r^2[/tex]substituting the value of r;
[tex]\begin{gathered} A=\pi(3\frac{1}{4})^2 \\ A=\pi(\frac{13}{4})^2 \\ A=\pi(\frac{169}{16}) \\ A=33.18yd^2 \end{gathered}[/tex]Therefore
Lucy bought a plant and planted it in a pot near a window in her house. The initial height of the plant was 12 inches and it grew at a rate of 2 inches per month. Make a table of values and then write an equation for H, in terms of t, representing the height, in inches, of the plant tt months after Lucy bought the plant.
I need the equations
The equation for H, in terns of t, representing the height , in inches, of the plant tt months after Lucy bought the plant is :
H=12+2t
Given, A plant that Lucy had purchased was placed in a pot next to a window in her home. The plant initially stood 12 inches tall and grew at a rate of 2 inches per month.
from the given information, the equation can be framed as:
H = 12 +2t
where the initial height of the plant is increased at a rate of two inches every month.
from the table substitute the value of months in t, to find the height of the plant in that particular month.
t = 0
H=12+2(0)
H=12
hence when t=0 then H=12
t=1
H=12+2(1)
H=12+2
H=14
after a month the height of the plant changes to 14 inches.
t=2
H=12+2(2)
H=12+4
H=16
after two months the height changes to 16 inches.
t=3
H=12+2(3)
H=12+6
H=18
after three months the height changes to 18 months.
t=4
H=12+2(4)
H=12+8
H=20
finally after four months the height of the plant changes to 20 months.
hence we get the required equation as H=12+2t
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Find the minimum value of the parabola y = x2 − 6.
The minimum value of the parabola is y = -6
An equation of a parabola is given as
y = x²-6
We will find its minimum value using the differentiation method.
For this first we will find the derivative with respect to x and find the value of x at which the derivative becomes zero. The derivative becomes zero only when the parabola has either a maximum or minimum value. We further check whether the parabola has a minimum or maximum at that x by finding the second derivative of the parabola at that x.
So first derivative of y with respect to x is 2x.
So 2x = 0
⇒ x =0
Now take the second derivative of y with respect to x at x = 0,
Second derivative = 2 > 0 at x = 0
Here the second derivative is greater than zero at x = 0. So y has a minimum value at x = 0
The minimum value of the parabola is,
y = 0² - 6
⇒ y = -6
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Add 5/6+ 3/4 + 2/3 Simplify the answer and write it as a mixed number, if possible.2122O12
In order to add those fractions, we need to write them using a commom denominator. We can do so by finding a common multiple for the original denominators:
6, 4 and 3
Since 12 is a multiple of those three numbers, we can use 12 as a new denominator for each of the fractions:
5/6 = (5 * 2)/(6 * 2) = 10/12
3/4 = (3 * 3)/(4 * 3) = 9/12
2/3 = (2 * 4)/(3 * 4) = 8/12
Notice that 10/12 is equivalent to the the original fraction 5/6, because we obtained 10/12 by multiplying both the numerator and the denominator by the same factor. The same applies to the other pairs of fractions.
Now, we can add:
5/6 + 3/4 + 2/3 = 10/12 + 9/12 + 8/12
= (10 + 9 + 8)/12
= 27/12
Now, we can simplify the result by dividing both the numerator and the denominator by the same factor. Since both 27 and 12 are multiples of 3, we can write:
27/12 = (27 : 3)/(12 : 3)
= 9/4
Now, since 9 is greater than 4, we can write the fraction 9/4 as a mixed number:
9 = 8 + 1
= 2*4 + 1
9/4 = (2*4 + 1)/4
= 2*4/4 + 1/4
= 2 + 1/4
= 2 1/4 (using the notation of mixed number)
Could someone please help me with this?
Answer:
1. f(4) = 4
2. g(2) = -4
3. f(-5) = -14
4. g(-3) = 21
5. f(0) = -4
6. g(0) = 0
7. f(3) - 1 = 1
8. f(1/4) = -3.5 or -7/2
9. g(1/4) = -0.9375 or -15/16
10. f(a^2) = 2a^2 - 4
11. f(k+1) = 2k - 2
12. g(2n) = 2n^2 - 8n
13. f(3x) = 6x - 4
14. f(2) + 3 = 3
15. g(-4) = 32
Step-by-step explanation:
here’s a pic of my work:
Triangle ABC is similar to triangle DEFwhich proportion can be used to find the length of DE in centimeters?A. 4/3 = DE/9B. 5/15 = DE/4C. 4/DE = 9/3D. 9/DE = 3/5
In the given figure, Triangle ABC is similar to triangle DEF.
Applying the Similar Triangle Formula, the proportion to be used to find the length of DE is:
[tex]\frac{4\text{ cm}}{3\text{ cm}}\text{ = }\frac{DE}{9\text{ cm}}[/tex]Therefore, the answer is A.
Help me please this is due tn
Fifty-two percent of realtors have a college degree. If a continuing education course enrolls a random selection of 1,600 realtors every year, what is the average number of realtors attending the course with a degree each year?
SOLUTION:
The average is given by the formula;
[tex]\begin{gathered} Mean=xP(x) \\ =0.53\times1600 \\ =848 \end{gathered}[/tex]Thus, the average number of realtors who have a degree attending the course is 848
a rotation of 180 degrees maps figure A onto itself. It has
Letter A doesn't show rotational symmetry of 180 degrees.
The letter 'A' has just one vertical line of symmetry.A vertical line of symmetry is that line which runs down a picture thus dividing it into two identical halves. In other words, it's a straight standing line that divides an image or shape into two identical halves.
The rotational symmetry of a shape explains that when an object is rotated on its own axis, the form of the object looks the same. Many geometrical shapes appear to be symmetrical once they are rotated 180 degrees or with some angles, clockwise or anticlockwise. A number of the examples are square, circle, hexagon, etc.
Complete Question- A rotation of 180 degrees maps figure A onto itself. It has transformation or not?
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Please help with math ! These are due tomorrow.
3) Alex had 20 video games at the beginning.
2) The strategy to solve the problem backward is:
The number of games Alex has now is 16 games.
The number of games he gave to his brother is 2, so add 2 to the current number of video games, 16 + 2 = 18
Now add the games he sold, which are given as 3
18 + 3 = 21
Subtract the games he traded with Hector,i.e. 6 video games
21 - 6 = 15
This obtained number is 3/4 of his games,
3/4 of the total video games = 15
Therefore, the total video games were = (15×4)/3 = 20
4) Yes the answer makes sense.
Operations in reverse order are:
The number of video games given by Alex to hector is = 1/4 of 20 = 5
Remaining video games = 20 - 5 = 15
Number of games after adding exchanged 6 video games = 15+6 = 21
Number of games after Alex sold 3 video games = 21 -3 = 18
Number of games after Alex gave 2 to his brother = 18 - 2 = 16 video games
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What the are of this parallelogram?
find a formula for the nth term of the arithmetic sequence the first term is 7 and the common difference is -3
The formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is - a[n] = 10 - 3n
What is an Arithmetic progression?An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -
a₁ , a₂, a₃ , a₄ ...... aₙ
will be an arithmetic progression if -
a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.
Given is the the first term equal to 7 and the common difference equal to
- 3.
We can calculate the nth term of an A.P. using the formula -
a[n] = a + (n - 1)d
a[n] = 7 + (n - 1)(- 3)
a[n] = 7 - 3n + 3
a[n] = 10 - 3n
Therefore, the formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is -
a[n] = 10 - 3n
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7- At the school car wash, Kelly washes a car in 13 minutes, and Libby washes a car in 17 minutes, How many more minutes does it take Kelly to wash a car alone than it takes Kelly and Libby to wash a car when working together? Express your answer as a decimal to the nearest tenth.
Kelly will take 5.64 minutes more to wash the car as compared to Kelly and Libby when they are working together
Time taken by Kelly to wash the car = 13 minutes
Time taken by Libby to wash the car = 17 minutes
Time taken by Kelly and Libby to wash the car together:
LCM of 13 and 17 is 221. So, the total work required to be done is 221 units
Hence, Kelly does 17 units of work each minute and Libby does 13 units of work each minute
If both work together, they will finish the work in = Total work required to be done/ Work done in a minute by Kelly + Work done in a minute by Libby
= 221/(17+13)
= 221/30 = 7.36 minutes
The extra time taken by Kelly working alone = 13-7.36 = 5.64 minutes
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Walnuts make up half of the nuts in this nut bread:
It has exactly 2 pecans
The number of walnuts is double the number of pecans.
Write an equation to show how many of each nut this nut bread contain.
An equation showing how many of each nut this nut bread contains is Y = 2p + 4w + 2t.
What is an equation?An equation is a mathematical expression of equality between two variables or expressions.
Equations are shown using the equation mark, symbol, or sign (=).
The number of walnuts in the nut bread = 1/2
The number of pecan nuts = 2
The number of walnuts which is double of pecan nuts = 4 (2 x 2)
The number of other nuts = 2 since walnuts equal 1/2 of the nuts
The total number of nuts = 8 (2 pecan, 4 walnuts, and 2 others)
Let the number of nuts in the bread = Y
Let the number of walnuts, w = 4
Let the number of pecan nuts, p = 2
Let the number of other nuts, t = 2 (8 - 4 - 2)
Thus, the equation of each nut contained in the nut bread is Y = 2p + 4w + 2t.
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Mr.Kermshner has 168 bandages march through June. How much is it if each bandage is 3 cents
504 bandages if it is each bandage is 3 cents.
Given,
Mr. Kermshner has 168 bandages march through June.
To find the how much is it if each bandage is 3 cents ?
Now, According to the question,
Based on the given conditions,
Formulate:
Total bandage is 168
and, each bandage is 3 cents
= 168 x 3
= 504
Alternative form = 5.04 x 10^2
Hence, 504 bandages if it is each bandage is 3 cents.
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Write the correct equation for the following statement.
You decide to rent a limo for prom. The rate is $250 plus $6 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
250+6m
If you travel 45 miles what will be your total bill at the end
of the evening?
Answer:
Easy;
Substitute m (miles) for 45.
250+6(45)
(6 dollars per mile, times 45 miles, plus the 250 flat rate)
250+270
520
So you would be charged 520 dollars total at the end of the evening.
Hope this helped!
Solve the following using substitutionY = -2X + 10.5x - y = 4
We are to solve the equations
[tex]\begin{gathered} y=-2x+1 \\ 0.5x-y=4 \end{gathered}[/tex]The equation can be rewritten as
[tex]\begin{gathered} y+2x=1------------\text{equation 1} \\ -y+0.5x=4-----------\text{equation 2} \end{gathered}[/tex]Using substitution method
From equation 1
[tex]y=1-2x--------\text{equation 3}[/tex]Substitute 1 - 2x for y into equation 2
This gives
[tex]\begin{gathered} -(1-2x)+0.5x=4 \\ -1+2x+0.5x=4 \\ -1+2.5x=4 \\ 2.5x=4+1 \\ 2.5x=5 \\ x=\frac{5}{2.5} \\ x=2 \end{gathered}[/tex]Therefore, x = 2
Substitute 2 for x into equation 3
This gives
[tex]\begin{gathered} y=1-2(2) \\ y=1-4 \\ y=-3 \end{gathered}[/tex]Therefore the solution to the equations is
x = 2, y = -3
Which inequality is true?O A. 31 - 1<8B. + 6 < 9O c. <3D. 477 > 12
The answer is D
To solve this, we can use similar values of the ones in the problems and compare it:
With a just add one to each side:
[tex]undefined[/tex]Alex buys 32oz of yogurt for $2.56. John buys a Goz yogurt for $0.48. Are the unit prices equal? Write an equation using the unit price to represent this relationship if they are equal. options: Yes, y=5.33x . Yes, y=12.5x, No, the ratios are not equivalent . Yes, y=0.08x
Answer:
Yes, y=0.08x
Explanation:
The unit price can be calculated as the price divided by the number of ozs, so the unit prices are:
[tex]\frac{\text{Price}}{\text{Ounces}}=\frac{\text{ \$2.56}}{32\text{ oz}}=\text{ \$0.08 per ounce}[/tex][tex]\frac{Price}{Ounces}=\frac{\text{ \$0.48}}{6\text{ oz}}=\text{ \$0.08 per ounce}[/tex]Therefore, the unit prices are equal, so the equation that represents the relationship is:
y = kx
Where k is the unit price, so replacing k by 0.08, we get:
y = 0.08x
So, the answer is:
Yes, y=0.08x
The velocity of a body as a function of time is given as Vt=5e-2t+4 where t is in seconds, and V is in ms. The acceleration in ms2 at t=0.6s is .....
The velocity of a body as a function of time is given as Vt=5e-2t+4 where t is in seconds, and V is in ms acceleration at t = 0.6s is -10x 0.30119m/[tex]s^{2}[/tex].
The velocity of a body is given by
Vt=5e-2t+4
acceleration a(t)= [tex]v'(t)[/tex]
= d/dt [tex]v'(t)[/tex]
= d/dt 5e-2t+4
= -10[tex]e^{-2t}[/tex]
put t = 0.6
acceleration at t= 0.6= a(0.6)
= [tex]-10e^{-2\times0.6}[/tex]
= -10x [tex]e^{-12}[/tex]
= -10x 0.30119m/[tex]s^{2}[/tex]
What is acceleration?acceleration is the rate of change of the speed of an object with respect to time. Accelerations are vector quantities. The direction of the target's acceleration is obtained from the direction of the net force on the target.
Three types of accelerated motion
Uniform acceleration non-uniform acceleration intermediate acceleration.The term uniform acceleration refers to motion in which an object moves in a straight line with increasing speed at equal intervals of time.
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Finding the Slope of a LineVy10What is the slope of a line that contains the points (1,9) and (4, 3)?The slope of the line is<88642N2x624.8
Given the points: (1, 9) and (4, 3)
To find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{3-9}{4-1}[/tex]m = -2
Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
v
Consequently, y = x + 2 is the equation for the line CD.
Points C(0, 2) and D are given (4, 6).
We must identify the equation of the line CD.
Given is the equation for the line through two points
[tex]\frac{y-y_{1} }{y_{1} - y_{2} } = \frac{x-x_{1} }{x_{1} -x_{2} }[/tex]
[tex]\frac{y-2}{6-2} = \frac{x-0}{4-0}[/tex]
y - 2 = x
x - y + 2 = 0
Consequently, y = x + 2 is the equation for the line CD.
What is the equation of the line?
The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine if a given point lies on a line using the equation of any line.
The line's equation is a linear equation of degree one. Let's learn more about the various ways a line's equation may be expressed and how to calculate it.
The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
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The graph below represents the number of miles, y, that Jacob can drive his car for every x gallons of gas. Find the rate of change.
The slope (rate of change) of the graph shown is 31.3 miles per gallon.
What is an equation?An equation is an expression that shows the relationship between two variables and expressions.
Slope is the ratio of vertical rise to horizontal run. It is given by:
Slope = rise / run
The point passes through (10, 313) and (20, 626), hence:
Slope = rise/run
Slope = (626 - 313) / (20 - 10) = 31.3
The graph's slope is 31.3 miles per gallon.
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The diameter of a cylindrical pipe is 7 ft. If the pipe is 42 ft long, what is it’s volume? Use the value 3.14 for n, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
ANSWER:
1616 ft³
STEP-BY-STEP EXPLANATION:
We have that the formula to determine the volume of the cylinder is as follows:
[tex]V=\pi r^2\cdot h[/tex]The radius is equivalent to half the diameter, therefore the radius is equal to 3.5 ft (7/2) while the height, in this case, is equivalent to the length, so it is equal to 42 ft. Therefore, we replace each value and calculate the volume, like this:
[tex]\begin{gathered} V=\left(3.14\right)\left(3.5^2\right)\left(42\right) \\ \\ V=1615.53\cong1616\text{ }ft^3 \end{gathered}[/tex]The volume of the cylindrical pipe is 1616 ft³.
Solve the inequality and graph the solution.
−2p + 4.5 < −2.9
number line with open circle plotted at 3.7 and arrow pointing right
number line with closed circle plotted at 3.7 and arrow pointing left
number line with open circle plotted at 3.7 and arrow pointing left
number line with closed circle plotted at 3.7 and arrow pointing right
The solution of the inequality −2p + 4.5 < −2.9 is number line with open circle plotted at 3.7 and arrow pointing right, the graph of the inequality has been plotted.
The inequality is −2p + 4.5 < −2.9
Subtract 4.5 from both side
-2p + 4.5 - 4.5 <-2.9 - 4.5
-2p < -7.4
Divide both sides by -2
-2p/-2 < -7.4/-2
p > 3.7
Draw the graph using the result of the inequality
Hence, the solution of the inequality −2p + 4.5 < −2.9 is number line with open circle plotted at 3.7 and arrow pointing right, the graph of the inequality graph has been plotted.
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Answer:
number line with open circle plotted at 3.7 and arrow pointing right
Step-by-step explanation:
hope this helps :)
4 strings 5 strings 6 strings 25% off 4 4 8 50% off 6 8 3 Vhat is the probability that a randomly selected Simplify any fractions.
number of banjos that have 5 or 6 strings: 4 + 8 + 8 + 3 = 23
total number of banjos: 6 + 4 + 4 + 8 + 8 + 3
Solve this system of equations byusing the elimination method.x - 5y = 164x – 2y = -8([?],
Given:
There are given two equations:
[tex]\begin{gathered} x-5y=16...(1) \\ 4x-2y=-8...(2) \end{gathered}[/tex]Explanation:
To find the value by using the elimination method, we need to multiply by 4 into the equation (1) and 1 into the multiply by (2):
Then,
From the equation (1):
[tex]\begin{gathered} 4(x-5y=16) \\ 4x-20y=64...(3) \end{gathered}[/tex]And,
From the equation (2):
[tex]\begin{gathered} 1(4x-2y=-8) \\ 4x-2y=-8...(4) \end{gathered}[/tex]Now,
From the equation (3) and equation (4):
[tex]4x-20y-64=4x-2y+8[/tex]Then,
[tex]\begin{gathered} 4x-20y-64-4x+2y-8=0 \\ -20y-64+2y-8=0 \\ -18y-72=0 \\ -18y=72 \\ y=-4 \end{gathered}[/tex]Now,
Put the value of y into the equation (3):
[tex]\begin{gathered} \begin{equation*} 4x-20y=64 \end{equation*} \\ 4x-20(-4)=64 \\ 4x+80=64 \\ 4x=64-80 \\ 4x=-16 \\ x=-4 \end{gathered}[/tex]Final answer:
Hence, the value of x and y is shown below:
[tex](-4,-4)[/tex]Distribute property of 41×8
Using distribute property on 41×8 is 328.
What is the Distributive Property?
The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.
We know that,
Distributive property is A × (B + C) = AB + AC.
So, 41 × 8 is 41 × (5 + 3 ) = 41×5 + 41×3
41 × (5 + 3 ) = 205 + 123
41 × (5 + 3 ) = 328
Hence, using distribute property on 41×8 is 328.
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For y = 10*0.5^x (that is read y equals ten times one half to the power of x), doesthis model exponential growth or decay? Explain how you know.
f(1)=1/2 f(2)=(1/2)^2=(1/2)*(1/2)=1/4
1/2>1/4 => f(1)>f(2) => it is decreasing, because with the grow of x the value(y) is decreasing what we have shown