Distance travelled by remote controlled car is 32 feet in 8 sec
What is speed ?Speed is the rate and direction of an object's movement, whereas speed is the scalar at which an object moves along a path in time. Velocity is a vector, whereas speed is a scalar integer.
Calculationspeed = 4 feet/sec
distance = d feet
time = t sec
4 = d / t
t = 8 sec
d = 4 *8
d = 32 feet
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The question is in the link pls help me, fast.
Answer:
The answer is B.
Step-by-step explanation:
The circle is filled in so we know the answer cannot be A. All the numbers after 4 are greater than or equal to 4. The arrowing is pointing toward the numbers after 4.
4x 3y2 Evaluate the expression for x = 3 and y = 4.
Explanation
[tex]-\frac{4x^3}{3y^2}[/tex]Step 1
to find the answer just replace the values for x and y
for x=3 and y =4
[tex]\begin{gathered} -\frac{4x^3}{3y^2} \\ -\frac{4(3)^3}{3(4)^2}=-\frac{4\cdot(3\cdot3\cdot3)}{3\cdot(4\cdot4)}=-\frac{4\cdot27}{3\cdot16}=-\frac{27}{12}=-\frac{9}{4} \end{gathered}[/tex]I hope this helps you
A square measures 8cm to the nearest
cm. What is the largest and smallest
possible area of the square?
Answer: smallest area- 56.25cm2 largest area- 70.56cm2
find the equation in point slope form of the line that lasses through the point (1,2) with the slope m=2/3
Input data
Point = (1, 2)
m = 2/3
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
[tex]\begin{gathered} b=y-mx \\ b=2-\frac{2}{3}1 \\ b=2-\frac{2}{3} \\ b=\frac{4}{3} \end{gathered}[/tex]The equation of the line that passes through the point (1,2) with a slope of 2/3
[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex][tex]y-2=\frac{2}{3}(x-1)[/tex]Mabel spends 4 hours to edit a 3-minute long video. She edits at a constant rate.
How long does Mabel spend to edit a 15 minute long video?
By the concept of unitary method, she will take 20 hours to complete a video as definition of unitary method says "The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value".
What is unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. A single or distinct unit is referred to by the word unitary. Therefore, the goal of this method is to establish values in relation to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel. The unitary method refers to the process of determining the value of a single unit from the values of several other units and using that value to determine the value of the necessary number of units.
Here,
As she takes 4 hours to edit a 3 minute video,
by unitary method,
so she take 4/3 hour to edit a 1 minute video.
To edit a 15 minute video,
she will take 15*4/3 hours.
=20 hours
As stated in the definition of the unitary method, "the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value," it will take her 20 hours to complete a video using this method.
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Help with number two please highlight the answer in bold
ANSWER
Options: II and IV
EXPLANATION
Mean: Is the sum of data values divided by the total number of data values
Deviation: Is the difference between an individual data item and the set's mean.
Absolute value: Is the distance (a positive quantity) between any two points on a number line.
Variability: This relates to how dispersed (or clustered) the values in a data set are. High variability indicates that the data is dispersed. Low variability indicates that the data is grouped together (close together).
MAD: Is the average distance between each data value and the mean is the Mean Absolute Deviation (MAD) of a set of data. The higher the MAD, the more data variability there is (the data is more spread out).
Hence, II and IV are most likely to have the greatest number of values in common because they both have higher MAD (8) meaning that they have more data variability (their data is more spread out) compared to I and III which have MADs equal 4 and 2 respectively.
A scuba diver descends below the surface of a lake at a rate of 12 feet per minute. What is the depth of the diver after 4 minutes?
The depth of the diver after 4 minutes when a scuba diver descends below the surface of a lake at a rate of 12 feet per minute is 48 feet.
What is a rate?The concept that is used in the solution is the concept of rate in mathematics. A rate can be described as a special ratio having two terms that are in different units.
The rate that is been given is 12 feet per minute which implies that 12 feet will operate at the time of 1 minute. Then we were now given the depth of the diver after 4 minutes, using the given rate, then ;
12feet = 1mins
X feet = 4mins
where X is the depth of the diver after 4 minutes then we can cross multiply,
X= (4mins *12feet) / 1mins
= 48feets.
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What is the slope of the line created by this equation?
Considering the linear equation in slope-intercept form:
[tex]y=11.2x-1[/tex]The y-intercept of the line is the constant of the equation, in this case, the y-intercept is -1.
The slope of the line corresponds to the coefficient of the x-term, i.e. the value that multiplies x. For this line, the slope is equal to 11.2
In a right triangle, the length of the hypotenuseis 14 cm and the length of one leg is 8 cm.What is the measure of the other leg?
Since it is a right triangle, we can use the Pythagorean Theorem. This one states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse. In algebraic notation:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{ Where a and b are the legs and c is the hypotenuse of the right triangle.} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} a=8\operatorname{cm} \\ b=? \\ c=14\operatorname{cm} \end{gathered}[/tex][tex]\begin{gathered} a^2+b^2=c^2 \\ (8cm)^2+b^2=(14cm)^2 \\ (8)^2cm^2+b^2=(14)^2cm^2 \\ 64cm^2+b^2=196cm^2 \\ \text{ Subtract }64cm^2\text{ from both sides of the equation} \\ 64cm^2+b^2-64cm^2=196cm^2-64cm^2 \\ b^2=132cm^2 \\ \text{ Apply square root to both sides of the equation} \\ \sqrt{b^2}=\sqrt{132cm^2} \\ \boldsymbol{b}\approx\boldsymbol{11.49\operatorname{cm}} \end{gathered}[/tex]Therefore, the measure of the other leg rounded to the nearest hundredth is 11.49 centimeters.
Select the correct answer.
Consider this equation.
cos(8) = -
If 8 is an angle in quadrant II, what is the value of tanê)?
ОА.
15
8
ов. 15
ос. -
✓15
8
OD. 15
Given that:
[tex]\cos \theta=\frac{adjacent}{hypothenus}[/tex]and we are given that:
[tex]\cos \theta=-\frac{7}{8}[/tex]we can say that:
adjacent = 7, hypothenus = 8
And we can apply the Pythagorean theorem which is:
[tex]\text{hypothenus}^2=opposite^2+adjacent^2[/tex]Thus, we have that:
[tex]undefined[/tex]i cant seem to be able to solve -6(8g+4)-5+6g
Answer: -42g-29
Step-by-step explanation:
-6(8g+4) -5+6g
-48g-24 -5+6g
-48g+6g=-42g
-24-5=-29
first test(x)=86,82,47,69,73,47,63,50,59,77,88,87second test (y)=81,71,51,75,69,44,48,48,58,68,83,77find a equation of the least squares regression line. Round the answer to three decimal places, if necessary.
To find the equation of the line, we will use the formula:
y=mx + b
The formula for calculating the slope is given as :
[tex]m=\frac{N\text{ }\Sigma(xy)-\Sigma x\Sigma y}{N\text{ }\Sigma(x^2)-(\Sigma x)^2}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
for each of the 7 you have to determine whether its alternative exterior angles, same side interior angles, vertical angles, alternate interior angles, definition of a parallelogram, SAS, Or Given
Statement Reason
WXYZ is a parallelogram Given
WX || ZY and WZ || XY Definition of a parallelogram
∠ZYW ≅ ∠XWY Alternate interior angles
WX ≅ YZ Definition of a parallelogram
WY ≅ WY Reflexive property of congruence
ΔWXY ≅ ΔZYW SAS
∠X ≅ ∠Z CPCTC
tsThe table below represents the concessions sold at the last three basketball games. Thegames were held on different days and times.Friday nightSaturday morningTuesday nightTotalCandy1489478320Hot Dogs10227150279Nachos Total1084297247358163325846What is the approximately probability of a person buying a hot dog and going to a Tuesdaynight game?
Given:
The total = 846.
The number of hot dogs sold at Tuesday night = 150.
Required:
We need to find the approximate probability of a person buying a hot dog and going to a Tuesday night game.
Explanation:
The total possible outcomes = 846.
[tex]n(S)=846[/tex]Let A be the given event.
The favourable outcomes = The number of hot dogs sold at Tuesday night = 150.
[tex]n(A)=150[/tex]The approximate probability of a person buying a hot dog and going to a Tuesday night game.
[tex]P=\frac{n(A)}{n(S)}\times100[/tex][tex]P=\frac{150}{846}\times100[/tex][tex]P=17.7[/tex][tex]P=18\text{ \%}[/tex]Final answer:
[tex]P=18\text{ \%}[/tex]What is the slope of the line that passes through the points (10, 6) and (6, 6)? Write
your answer in simplest form.
The slope of the line that passes through the points (10,6) and (6,6) is 0.
The Slope of a line can be described as a change in the y coordinate with respect to the x coordinate.
Formula to find the slope of the line that passes through the points [tex](x1,y1)[/tex] and [tex](x2,y2)[/tex] is
[tex]m= (y2-y1)/(x2-x1)[/tex]
where, m=slope
As per the given problem, let us consider
[tex](x1,y1)=(10,6)[/tex]
[tex](x2,y2)=(6,6)[/tex]
Substitute the given values such as [tex]x1=10,x2=6,y1=6,y2=6[/tex] in the formula,
[tex]m=(6-6)/(6-10)\\m=0/(-4)\\m=0[/tex]
Therefore, the slope of the line that passes through the points (10,6) and (6,6) is o.
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Andrea is 108 miles away from Destiny. They are traveling towards each other. If Destiny travels 9 mph faster than Andrea and they meet after 4 hours, how fast was each traveling?
The given information is:
Andrea is 108 miles away from Destiny.
Destiny travels 9 mph faster than Andrea.
They meet after 4 hours.
Let's convert that information into equations:
Let's call x the distance that Destiny travels to find Andrea and y the distance Andrea travels to find Destiny, then:
[tex]x+y=180\text{ Eq. (1)}[/tex]If they meet after 4 hours, the equation for the distance Destiny traveled is:
[tex]\text{velocity}\cdot\text{time}=\text{distance}[/tex]But the problem also says that Destiny travels 9 mph faster than Andrea, then let's call z the mph that Andrea is traveling, thus:
[tex](z+9)\cdot4=x\text{ Eq. (2)}[/tex]And the equation for the distance Andrea traveled is:
[tex]z\cdot4=y\text{ Eq.(3)}[/tex]Then you have a system of 3 equations and 3 variables.
Let's solve it to find how fast each was traveling.
From equation 3 you know that y=4z. You can replace the y-value into equation 1, you will obtain:
[tex]x+4z=180\text{ Eq. (4)}[/tex]Next, you can solve for x in terms of z, from equation 4:
[tex]x=180-4z\text{ Eq.(5)}[/tex]Replace the x-value into equation 2 and solve for z:
[tex]\begin{gathered} (z+9)\cdot4=180-4z \\ \text{Apply distributive property} \\ 4z+36=180-4z \\ \text{Add 4z to both sides} \\ 4z+36+4z=180-4z+4z \\ 8z+36=180 \\ \text{Subtract 36 from both sides} \\ 8z+36-36=180-36 \\ 8z=144 \\ \text{Divide both sides by 8} \\ \frac{8z}{8}=\frac{144}{8} \\ z=18 \end{gathered}[/tex]Then if z=18 mph, this is how fast Andrea is traveling.
And Destiny travels 9 mph faster than Andrea, then Destiny travels at (z+9)=18+9=27 mph
i am having trouble with a question on my geometry homework. on how to do it
a) Given the triangle ABC, you have to do a counterclockwise 90º rotation of the figure.
To make said rotation you have to invert the coordinates of each point of the figure and invert the sign of the x-coordinate of the image point.
In general:
Preimage point; Image point
P(x,y) → P'(-y,x)
The y-coordinate turns into the x-coordinate and the x-coordinate turns into the y-coordinate.
The x-coordinate of the image point must have the opposite sing as the original one.
So for triangle ABC:
A to A'
(3,-2) → (-(-2),3)= (2,3)
B to B'
(3,-6) → (-(-6),3)= (6,3)
C to C'
(9,-2) → (-(-2),9)= (2,9)
The coordinates for the 90º counterclockwise rotation are A'(2,3), B'(6,3) and C(2,9)
b) Triange A'B'C' was translated a certain number of units, its new position is given as triangle A''B''C'':
A''(-3,-4)
B''(1,-4)
C''(-3,2)
To determine what kind of translation was done, first step is to draw triangle A''B''C'' and compare it to triangle A'B'C':
As you can see in the graphic, triangle A'B'C' was translated horizontally to the left a k number of units and vertically downwards a m number of units.
Horizontal translation
These translations are made over the x-axis, the translation factor k is added (movement to the rigth) or subtracted (movement to the left) from the x-coordinate of each point:
In this case the translation was made to the left, so:
Preimage point; Image point
P(x,y) → P'(x-k,y)
Vertical translation
These translations are made over the y-axis, this means that the translation factor m will be added (↑up) or subtracted (↓down) from the y-coordinates of each point.
For the example, the movement was downwards so we can express it as:
Preimage point; Image point
P(x,y) → P'(x,y-m)
You can unite both movements in the same expression as:
Preimage point; Image point
P(x,y) → P'(x-k,y-m)
Going a little further you can determine the amount of units the figure was translated by comparing a set of points from the preimage and image:
Given A'(2,3) and A''(-3,-4)
For the horizontal movement compare the x-coordinates. We know that to determine the x-coordinate of A'', k units were subtacted from the x-coordinate of A', so:
2-k=-3
-k=-3-2
-k=-5
k=5
For the vertical movement, compare the y-coordinates of both point. We know that m units were subtracted from the y-coordinate of A' to determine the y-coordinate of A'', so:
3-m=-4
-m=-4-3
-m=-7
m=7
This means that the translation rule for A'B'C' → A''B''C'' is (x-5,y-7)
I need help with this practice I’m having trouble solving itNeed some help step by step If you can. Use Desmos to graph this
Given the function:
[tex]y=-4\cos \mleft(\frac{2}{3}x+\frac{\pi}{3}\mright)-3[/tex]The graph is attached below:
• The period of the function, T = π-(-2π)=3π.
Thus, the function has been graphed to show at least one full period, the x and y-axes are also clearly labeled above.
PLEASE HELP ASAP!!!!!
Answer the answer is 12 units:
Step-by-step explanation:
The population of a small city in 2010 was 36,000. In 2015, the population was 43,800. If the population growth is exponential and growth occurs at the same rate, what will be the population be in 2020? round your answer to the nearest whole number.
The population of the small city in the year 2020 using the given growth rate is; 51600 people
How to solve exponential growth rates?We are given that;
Population of the small city in the year 2010 = 36000
Population in the year 2015 = 43800
Now, we are told that the growth rate occurs at the same rate per year. Thus;
Population change from 2010 to 2015 = 43800 - 36000 = 7800
Thus, the population increases by 7800/5 = 1560 people each year.
General form of exponential function is; y = bˣ
where b is rate of growth while x is number of years
But here we will use sequence to get;
y(10) = 1560 * 10 = 15600
Thus;
Population in 2020 = 36000 + 15600 = 51600 people
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help meeeeeeeeeeeeeeeeeeee pleaseee rnnnn rn!!!!
Answer:
Shorter leg = 2.5 ft
Longer leg = 6.5 ft
Step-by-step explanation:
Pythagorean theorem:Let the shorter leg = x ft
Longer leg = (x + 4) ft
Hypotenuse = 7 ft
[tex]\sf x^2 + (x +4)^2 = 7^2[/tex]
x² + x² + 2*x*4 + 4² = 49
x² + x²+ 8x + 16 = 49
2x² + 8x + 16 - 49 = 0
2x² + 8x - 33 = 0
This is a quadratic equation. We can use the below mentioned formula to find the value of x.
a = 2 ; b = 8 ; c = -33
b² - 4ac = 8² - 4 * 2 * (-33)
= 64 + 264
=328
[tex]\sf x = \dfrac{-b \± \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\sf x = \dfrac{-8 \±\sqrt{328}}{2*2}\\\\\\x= \dfrac{-8 \±18.11}{4}\\\\\\x =\dfrac{-8+18.11}{4} ; \ x=\dfrac{-8-18.11}{4} > > \text{this is rejected because sides of } \\\\ \text{a triangle cannot be measured in negative value}[/tex]
[tex]\sf x = \dfrac{-8+18.11}{4}[/tex]
[tex]\sf x = \dfrac{10.11}{4}\\\\x =2.5275[/tex]
x+ 4 = 2.5275 + 4 = 6.5275
Shorter leg = 2.5 ft
Longer leg = 6.5 ft
Answer: the length of the shoter leg is 2,5 feet
the length of the longer leg is 6.5 feet
Step-by-step explanation:
Let the length of the shoter leg is x feet
Than the length of the longer leg is (x+4) feet
We use Pythagoras' theorem:
[tex]\displaystyle\\x^2+(x+4)^2=7^2\\\\x^2+x^2+2(x)(4)+4^2=7(7)\\\\2x^2+8x+4(4)=49\\\\2x^2+8x+16-49=49-49\\\\2x^2+8x-33=0\\\\D=b^2-4ac\\\\Hence,\\\\D=8^2-4(2)(-33)\\\\D=8(8)+8(33)\\\\D=64+264\\\\D=328\\\\\sqrt{D}=\sqrt{328} \\\\x=\frac{-bб\sqrt{D} }{2(a)} \\\\x=\frac{-8б\sqrt{328} }{2(2)} \\\\x=-6.5277\notin (x > 0)\\\\x=2.5277\ feet\\\\x+4=2.5277+4\\\\x+4=6.5277\ feet[/tex]
Write the number below in expanded notation. 14,422 A. 10,000 + 400 + 400 + 20 + 2 B. 10,000 + 4,000 + 400 + 20 + 2 C. 1,000 + 4,000 + 4 + 20 + 2 D. 1,000 + 400 + 40 + 2 + 2
Let's begin by listing out the information given to us:
[tex]14,422[/tex]Expanded notation is a form of writing in which the value of each digit; it arranges the digit in their values of tens, hundreds, tens etc.
[tex]\begin{gathered} 14,422\Rightarrow1\cdot10,000+4\cdot1,000+4\cdot100+2\cdot10+2\cdot1 \\ \Rightarrow10,000+4,000+400+20+2 \end{gathered}[/tex]Hence, option B is the correct answer
A worn, poorly set-up machine is observed to produce components whose length x follows a normal distribution with a mean equal to 14 centimeters and a variance equal to 9. Determine the probability that a component is at least 10 centimeters long. Round your answer to four decimal places.
80.64% probability that a component is at least 10 centimeters long.
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation , the z-score of a measure X is given by:
Z = x - μ / σ
Z-scores are used to measure how far a measure is from the mean. We find the p-value associated with this Z-score by looking at the z-score table after finding the Z-score. The p-value represents the probability that the measure is smaller than X, which is the percentile of X. The probability of the measure being greater than X is calculated by subtracting 1 from the pvalue.
μ = 14
Variance is 9.
The standard deviation is the square root of the variance.
So,
σ = √9 = 3
This is the pvalue of Z when X = 10
z = 10 - 14/3
z = -1.3
z = -1.3 has a p value of0.1936
1-0.1936 = 0.8064
80.64% probability that a component is at least 10 centimeters long.
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Answer:
0.7475
Step-by-step explanation:
The mean is μ=14, and the standard deviation is σ=9‾√=3.Open Excel. Click on an empty cell. Type =NORMDIST(12,14,3,1) and press ENTER.The probability, rounded to four decimal places, is P(X<12)≈0.2525.The desired probability is P(X≥12), so subtract from 1 to get P(X≥12)=1−0.2525=0.7475
Help! graph the systems of equations. {2x+y=8 −x+2y=6
A system of equations is simply a collection of equations that can be dependent, independent, consistent, or inconsistent.
2x + y = 8x - 2y = -6 is x,y = 2,4
How are equations graphed?To graph the equation, choose three x values and list them in a table. (Hint: choose values that are easy to calculate, such as 1, 0 and 1). Simplify the equation by substituting each value to find the associated y-coordinate. Draw a line between each point on a graph with the sorted pairings.A system of equations is simply a collection of equations that can be dependent, independent, consistent, or inconsistent.Given equation,
2x + y = 8x - 2y = -6
x,y = 2,4
[1] 2x + y = 8
[2] x - 2y = -6
Solve [2] for the variable x
[2] x = 2y - 6
Plug this in for variable x in [1]
[1] 2•(2y-6) + y = 8
[1] 5y = 20
Solve [1] for the variable y
[1] 5y = 20
[1] y = 4
By now we know this much
x = 2y-6
y = 4
Use the y value to solve for x
x = 2(4) -6 = 2
Hence, {x,y} = {2,4}
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Margaret''s parents gave her $40 to spend on video games. Used games are $8 and new games are $14.
Answer:
so? what is your question here?
Step-by-step explanation:
Jack earns $5250 per month. Jill earns $1143.50 a week. Who earns more per year, and by how much?
I have took a picture of the question and attached it here.
Given:
[tex](3-4i)(6i+7)-(2-3i)[/tex]1. Arrange the expression, with the variables are written first
[tex](-4i+3)(6i+7)-(-3i+2)[/tex]2. Distribute the "minus" operation
[tex](-4i+3)(6i+7)+3i-2[/tex]3. Expand by multiplying the first two expressions
[tex](-4i+3)(6i+7)[/tex]*multiply the first terms
[tex](-4i)(6i)=-24i^2[/tex]*multiply the outer terms
[tex](-4i)(7)=-28i[/tex]*multiply the inner terms
[tex](3)(6i)=18i[/tex]*multiply the last terms
[tex](3)(7)=21[/tex]This will give us:
[tex](-24i^2-28i+18i+21)[/tex]*combine like terms
[tex](-24i^2-10i+21)+3i-2[/tex]*Remove the parenthesis
[tex]-24i^2-10i+21+3i-2[/tex]4. Combine like terms
[tex]-24i^2-7i+19[/tex]The final answer would be:
[tex]-24i^2-7i+19[/tex]
A contractor bought 8.2 ft² of sheet metal. He has used 4.9 ft² so far and has $52.80 worth of sheet metal remaining. The
equation 8.2x -4.9x = 52.8 represents how much sheet metal is remaining and the cost of the remaining amount. How much
does sheet metal cost per square foot?
Sheet metal costs : per square foot.
1
The cost of the sheet metal per square foot is $30.
The first step is to determine the square feet that the contractor used. This can be determined by subtracting the square feet of sheet she bought from the sheet metal she has used so far.
Sheet metal used = 8.2 - 2.1 = 6.1 square feet.
This means that 6.1 square feet costs $183.
The second step is to determine the cost of one square feet of sheet metal. This can be determined by dividing $183 by 6.1
$183 / 6.1 = $30
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(ii) The lowest common multiple (LCM) of x and 60 is 240.
Find the smallest possible value of x.
(Please help + will mark as a brainliest!!)
The smallest value of x is 2 for which these three numbers 2, 60, and 240 have an LCM of 240.
What is LCM?LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.
Given, Are three numbers x, 60, and 240 of which x is unknown.
The lowest common multiple of these three numbers will be when x is the smallest.
Let x be 2 therefore the numbers are now, 2, 60, and 240.
And LCM of 2, 60, and 240 is 240 as it is the smallest number that is divisible by all these three numbers.
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