Answer:
15 miles per hour
Step-by-step explanation:
Average Speed is:
Average Speed = Total Distance/Total Time
Going uphill, she took 12 minuets, that is hours is 12/60 = 0.2 hours
We know D = RT, Distance = Rate(speed) * Time
Thus,
D = 10mph * 0.2 hr = 2 miles
So, total distance (uphill and downhill) = 2 + 2 = 4 miles
Downhill the time she took is
D = RT
2miles = 30mph * T
T = 2/30 = 1/15 hours = 1/15 * 60 = 4 minutes
Hence total time is 12 + 4 = 16 minutes
Note: 16 minutes = 16/60 = 4/15 hours
Now
Average Speed = Total Distance/Total Time
Average Speed = 4 miles/ 4/15 hours = 15 mph
Answer:
The Answer is 15.00000000000000000... miles per hour
Step-by-step explanation: You do tis by doing your work and not checking for answers
Is it proportional, inversely proportional or neither?? please explain
John and David are running around the same track at the same speed. When David started running, John had already run 3 laps. Consider the relationship between the number of laps that David run and the number of laps that John has run.
Answer:
neither
Step-by-step explanation:
The number of laps John has run is 3 + the number of laps David has run. That is, both numbers are not zero at the same time, so the relationship cannot be proportional.
The numbers have a constant difference, not a constant product, so they are not inversely proportional, either.
David's laps and John's laps are neither proportional nor inversely proportional.
The relationship between the number of laps David runs and the number of laps John has run is proportional because they increase at the same rate, with John always maintaining a 3-lap lead.
The question asks whether the relationship between the number of laps that David runs and the number of laps that John has run is proportional, inversely proportional, or neither. Since John and David are running at the same speed, but John started with a 3-lap lead, the relationship is linear. The more laps David runs, the more John runs as well, maintaining a constant gap of 3 laps. Thus, this scenario illustrates a proportional relationship where the number of laps run by each, ignoring the start difference, increases at the same rate. This relationship can be represented by a linear equation like y = x + 3, where x is the number of laps David runs, and y is the number of laps John runs.
What set of transformations are applied to parallelogram ABCD to create A'B'C'D'?
Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at negative 2, 1. Second parallelogram transformed formed by ordered pairs A prime at negative 4, negative 1, B prime at negative 3, negative 2, C prime at negative 1, negative 2, D prime at negative 2, negative 1.
Answer:
Reflection across the x-axis
Step-by-step explanation:
The only apparent transformation is negation of the y-coordinate, corresponding to reflection across the x-axis.
Answer:
Reflection across the x-axis
Step-by-step explanation:
The only apparent transformation is negation of the y-coordinate, corresponding to reflection across the x-axis.
Could I solve this inequality by completing the square? How would I do so?
Answer:
[tex]\large\boxed{x>-2+\sqrt{14}\ \vee\ x<-2-\sqrt{14}}\\\boxed{x\in(-\infty,\ -2-\sqrt{14})\ \cup\ (-2+\sqrt{14},\ \infty)}[/tex]
Step-by-step explanation:
[tex]x^2+4x>10\\\\x^2+2(x)(2)>10\qquad\text{add}\ 2^2=4\ \text{to both sides}\\\\x^2+2(x)(2)+2^2>10+4\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+2)^2>14\Rightarrow x+2>\sqrt{14}\ \vee\ x+2<-\sqrt{14}\qquad\text{subtract 2 from both sides}\\\\x>-2+\sqrt{14}\ \vee\ x<-2-\sqrt{14}[/tex]
What is the magnitude of the position vector whose terminal point is (6, -4)?
Answer:
2√13
Step-by-step explanation:
The distance formula is useful for this. One end of the vector is (0, 0), so the measure of its length is ...
d = √((x2 -x1)² +(y2 -y1)²) = √((6 -0)² +(-4-0)²)
= √(36 +16) = √52 = √(4·13)
d = 2√13 = |(6, -4)|
The Department of Natural Resources determined that the population of white-tailed deer in one of Indiana's state parks was 25 deer per square mile in 1991. By 1992, the population had increased to 30 deer per square mile. By what percentage does the deer population increase in this time frame?
Answer:
20%
Step-by-step explanation:
Population of white-tailed deer in 1991 = 25 deer per square mile
Population of white-tailed deer in 1992 = 30 deer per square mile
We have to find the percentage increase in the deer population. The formula for percentage change is:
[tex]\frac{\text{New Value - Original Value}}{\text{Original Value}} \times 100 \%[/tex]
Original value is the population in 1991 and the New value is the population in 1992.
Using the values, we get:
[tex]\frac{30-25}{25} \times 100 \%\\\\ = 20%[/tex]
Thus, the deer population increased by 20% from 1991 to 1992
Final answer:
The deer population in the state park in Indiana increased by 20% from 1991 to 1992.
Explanation:
The question asks by what percentage the deer population increased between 1991 and 1992 in a state park in Indiana. To calculate the percentage increase, we use the formula: Percentage Increase = ((New population - Original population) / Original population) × 100%. Applying this formula to the given numbers, we have:
Original population in 1991 = 25 deer per square mile
New population in 1992 = 30 deer per square mile
Percentage Increase = ((30 - 25) / 25) × 100% = (5 / 25) × 100% = 20%
Therefore, the deer population increased by 20% from 1991 to 1992.
HELP PLEASE!!
Select the correct answer.
What is the exact value of tan 75°?
Answer:
[tex]\tt B. \ \ \ \cfrac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}[/tex]
Step-by-step explanation:
[tex]\displaystyle\tt \tan75^o=\tan(45^o+30^o)=\frac{\tan45^o+\tan30^o}{1-\tan45^o\cdot\tan30^o} =\frac{1+\frac{\sqrt{3}}{3}}{1-\frac{\sqrt{3}}{3}}[/tex]
For this case we have to define that:
[tex]tg (x + y) = \frac {tg (x) + tg (y)} {1-tg (x) * tg (y)}[/tex]
So, according to the problem we have:
[tex]tg (45 + 30) = \frac {tg (45) + tg (30)} {1-tg (45) * tg (30)}[/tex]
By definition we have to:
[tex]tg (45) = 1\\tg (30) = \frac {\sqrt {3}} {3}[/tex]
Substituting we have:
[tex]tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1-1 * \frac {\sqrt {3}} {3}}\\tg (45 + 30) = \frac {1+ \frac {\sqrt {3}} {3}} {1- \frac {\sqrt {3}} {3}}[/tex]
Answer:
option B
Find all of the zeros of the function f(x) = x3 – 23x2 + 161x – 303.
Answer:
x = 3x = 10 ± iStep-by-step explanation:
A graph shows the only real zero to be at x = 3.
Factoring that out gives the quadratic whose vertex form is ...
y = (x -10)² +1
The roots of this quadratic are the complex numbers x = 10 ± i.
_____
For y = (x -10)² +1, the zeros are ...
(x -10)² +1 = 0
(x -10)² = -1 . . . . . . . . . . subtract 1
x -10 = ±√(-1) = ±i . . . . .take the square root
x = 10 ± i . . . . . . . . . . . . add 10
Answer:
3, 10±i
Step-by-step explanation:
Given is a function [tex]f(x) = x^3 - 23x^2 + 161x -303.[/tex]
By rational roots theorem, this can have zeroes as ±1, ±3,±101
By trial and error checking we find f(3) =0
Hence x-3 is a factor
f(x) = [tex](x-3)(x^2-20x+101)[/tex]
II being a quadratic equation we find zeroes using formula
[tex]x=\frac{20±\sqrt{400-404} }{2} =10+i, 10-i[/tex]
zeroes are 3, 10±i
What is the value of sin 0 given that (5, -12) is a point on the terminal side of 0 ?
Answer:
The first choice is the one you want.
Step-by-step explanation:
If we plot the point (5, -12) we will be in QIV. Connecting the point to the origin and then drawing in an altitude to the positive x axis creates a right triangle with side adjacent to the angle being 5 units long, and the altitude being |-12|. To find the sin of theta, we need the side opposite (got it) over the hypotenuse (don't have it). We solve for the length of the hypotenuse using Pythagorean's Theorem:
[tex]c^2=12^2+5^2[/tex] and
[tex]c^2=169[/tex] so
c = 13.
Now we can find the sin of the angle in the side opposite the angle over the hypotenuse:
[tex]sin\theta=-\frac{12}{13}[/tex]
The first choice in your answers is the one you want.
To find the sine of an angle, we use the point given on its terminal side to represent a right triangle. The sine is calculated as the ratio of the opposite side to the hypotenuse. Using the point (5, -12), our calculation gives sin(θ) as -12/13.
Explanation:The question asks about the value of sin 0 where the point on the terminal side is (5, -12). However, in trigonometry, we more commonly write it as sin(θ) such that θ is the angle being referenced. Specifically, we are being asked to find the value of sin(θ) when a point on the terminal side of the angle is (5, -12).
To figure out what sin(θ) is, we use the mathematical definition of sine which states that sin(θ) = opposite/hypotenuse. In this context, we can treat the point (5,-12) as a representation of a right triangle. The x-coordinate is adjacent to the angle and the y-coordinate is opposite the angle. Accordingly, we can say that sin(θ) = -12/13.
This is because the hypotenuse can be calculated using Pythagoras' theorem, where hypotenuse = √[(x-coordinate)^2 + (y-coordinate)^2] which equals √[(5)^2 + (-12)^2] = √169 = 13. Hence, sin(θ) = (-12)/13.
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The ratio of the side lengths of a quadrilateral is 3:3:5:8, and the perimeter is 380cm. What is the measure of the longest side?
20 cm
160 cm
60 cm
Answer:
160
Step-by-step explanation:
Add the ratios together to get the sum of them is 19. Since the perimeter is 380, divide 380 by 19 to get 20.
The shortest side is 3(20) = 60,
the next side is 5(20) = 100, and
the longest side is 8(20) = 160
Which is equivalent of 278.24 written in DMS form
Answer: [tex]278\°14'24''[/tex]
Step-by-step explanation:
You know that:
[tex]1\ hour=60\ minutes\\\\1\ minute=60\ seconds[/tex]
Then, in order to convert the given decimal degree to Degrees Minutes Seconds (DMS), you need to follow these steps:
1) The whole number 278 gives you the degrees.
2) Multiply 0.24 by 60:
[tex]0.24*60=14.4[/tex]
The whole number 14 gives you the minutes.
3) Multiply 0.4 by 60:
[tex]0.4*60=24[/tex]
This gives you the seconds.
Therefore, 278.24 written in DMS form is:
[tex]278\°14'24''[/tex]
Answer:
The answer is 278°14'24''
Step-by-step explanation:
Given : 278.24
To find : written in DMS form.
Solution : We have given that 278.24
Multiply 24 by 60 to convert it into minute
We can write it as 278 + .24(60).
278°14.4'
Rewrite 278°14+.4'
4' = 4 ( 60) to convert minute in to second.
278°14+.4(60)
278°14'24''
The answer is 278°14'24'' ....
According to the chart, from 1986-1996, unintentional drug overdose deaths per 100,000 population began to rise. The numbers for each year are, roughly, 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3. What is the mean of these statistics? hope
Answer:
The mean of these statistic is 2.18.
Step-by-step explanation:
According to the chart, from 1986-1996, unintentional drug overdose deaths per 100,000 population began to rise.
The given data set is
2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3
Formula for mean:
[tex]Mean=\frac{\sum x}{n}[/tex]
Using this formula, the mean of the data is
[tex]Mean=\frac{2+1+2+2+1+2+2+3+3+3+3}{11}[/tex]
[tex]Mean=\frac{24}{11}[/tex]
[tex]Mean=2.181818[/tex]
[tex]Mean\approx 2.18[/tex]
Therefore the mean of these statistic is 2.18.
The mean of these statistics is [tex]\large{\boxed{\bold{2.18}}[/tex]
Further explanationStatistics is a study of a collection, preparation, analysis,presentation/conclusions from some data
Data is a collection of information presented in the form of numbers
Data collection can be done through a sample that represents all data (can be called a population) that is used as research
Data information can be stated in tables, diagrams or graphs
Tables are usually in the form of frequency tables that show the frequency distribution of dataDiagrams can be in the form of bar charts, pie charts, line charts or pictogramsThe average value or mean is a measure to provide an overview of a set of data
Mean is the average of a number of data
To determine the mean: the sum of all data divided by the amount of data
General formula
[tex]\large{\boxed{\bold{mean=\frac{\sum_{xi}}{n} }}}[/tex]
xi = data
n = amount of data
The numbers for each year for unintentional drug overdose deaths per 100,000 population are: 2, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3
Total amount of data:
[tex]\displaystyle 2+1+2+2+1+2+2+3+3+3+3=\large{\boxed{24}[/tex]
Amount of data: [tex]\large{\boxed{11}}[/tex]
So the mean value:
[tex]\displaystyle mean=\frac{\sum_{xi}}{n}=\frac{24}{11}=\large{\boxed{\bold{2.18}}}[/tex]
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A squirrel family collected 727272 nuts to store for the winter. They spread the nuts out evenly between their 666 favorite locations. Sadly, a crow stole half the nuts from one of the locations. How many nuts did the crow steal?
Answer:
546 nuts
Step-by-step explanation:
727272 / 666 = 1092 nuts in each location
crow stole half nuts in 1 location
1092 / 2 = 546 nuts stolen
Answer:
6 nuts.
Step-by-step explanation:
The number of nuts in each location is 72 / 6 = 12 nuts.
So the crow stole 1/2 * 12 = 6 nuts.
(Will get brainliest) Simplify the expression: left square bracket left parenthesis 18 − 6 right parenthesis ⋅ 3 plus 1 right square bracket ⋅ 7
A.
43
B.
259
C.
7
D.
336
Answer:
B. 259
Step-by-step explanation:
This is an exercise in PEMDAS, the order of mathematical operations:
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
Parentheses: [(18 − 6)⋅3 + 1]⋅7
Subtraction: = [(12)·3 +1]·7
Multiplication: = [36 + 1]·7
Addition: = [37]·7
Parentheses: = 37·7
Multiplication: = 259
Answer:
259
Step-by-step explanation:
The polynomial below is a perfect square trinomial of the form A2 - 2AB + B2.
Answer: Option B.
Step-by-step explanation:
Given the polynomial:
[tex]16x^2-36x+9[/tex]
Observe that [tex]16x^2[/tex] and [tex]9[/tex] are perfect squares. Then, you can rewrite the polynomial in this form:
[tex](4x)^2-36x+(3)^2[/tex]
You can identify that:
[tex]A=4\\B=3[/tex]
Then, we can check if [tex]2AB=36[/tex]
[tex]2(4x)(3)=36x\\\\24x\neq 36x\\\\2AB\neq36x[/tex]
Since [tex]2AB\neq36x[/tex], the polynomial [tex]16x^2-36x+9[/tex] IS NOT a perfect square trinomial of the form [tex]A^2 - 2AB + B^2[/tex]
Answer: B
Step-by-step explanation:
What is the area of a parallelogram with a base of 38 meters and a height of 12 meters?
For this case we have by definition that the area of a parallelogram is given by:
[tex]A = b * h[/tex]
Where:
b: It's the base
h: It's the height
According to the data we have:
[tex]b = 38\ m\\h = 12 \ m[/tex]
Substituting in the formula:
[tex]A = 38 * 12\\A = 456[/tex]
The area of the parallelogram is [tex]A = 456 \ m ^ 2[/tex]
Answer:
[tex]A = 456 \ m ^ 2[/tex]
Answer:
A=456m²
Step-by-step explanation:
Vector E is 0.111 m long in a 90.0 direction.Vector F is 0.234 m long in a 300 direction. What is the magnitude and direction of their vector sum?
Answer:
0.148623∠321.93°
Step-by-step explanation:
You can work these without too much brain work by converting the coordinates to rectangular coordinates, adding those, then converting back to a vector length and angle as may be required.
0.111∠90° + 0.234∠300° = 0.111(cos(90°), sin(90°)) +0.234(cos(300°), sin(300°))
= (0, 0.111) + (0.117, -0.2026499) = (0.117, -0.0916499)
The magnitude of this is found using the Pythagorean theorem:
|E+F| = √(0.117² +(-0.0916499)²) ≈ 0.148623
The angle can be found using the arctangent function, paying attention to the quadrant. This sum vector has a positive x-coordinate and a negative y-coordinate, so is in the 4th quadrant.
∠(E+F) = arctan(y/x) = arctan(-0.0916499/0.117) ≈ -38.07° = 321.93°
The vector sum is E+F = 0.148623∠321.93°.
__
You can also draw the triangle that has these vectors nose-to-tail and find the magnitude of the sum using the Law of Cosines. The two sides of the triangle are the lengths of the given vectors and the angle between those can be seen to be 30°. Then the length of the 3rd side of the triangle is ...
|E+F|² = |E|² +|F|² -2·|E|·|F|·cos(30°) = .012321 +.054756 -.044988 = 0.0220887
|E+F| = √0.0220887 ≈ 0.148623
The direction of the vector sum can be figured from the direction of vector E and the internal angle of the triangle between vector E and the sum vector. That angle can be found from the law of sines to be ...
(angle of interest) = arcsin(sin(30°)·|F|/|E+F|) = 128.07°
Then the angle of the vector sum is 450° -128.07° = 321.93°.
A diagram is very helpful for keeping all of the angles straight.
|E+F| = 0.148623∠321.93°
A football team had 4 big mistakes in a game. Because of these mistakes, the team lost a total of 60 yards. On average, how much did the team's yardage change per mistake?
Answer: 15 yards per mistake.
Step-by-step explanation:
Given : A football team had 4 big mistakes in a game.
i.e. the number of big mistakes done by the football team = 4
The total lost of yards because of the big mistakes done by football team = 60 yards
Now, the portion of team's yardage change per mistake is given by :-
[tex]\dfrac{\text{Total lost of yards}}{\text{Number of big mistakes}}\\\\=\dfrac{60}{4}=15\text{ yards}[/tex]
Hence, the team's yardage changes by 15 yards per mistake.
Answer:
-15 yardage per mistake
Step-by-step explanation:
From 1960 to 1970, the consumer price index (CPI) increased from 29.6 to 48.2. If a dozen donuts cost $0.89 in 1960 and the price of donuts increased at the same rate as the CPI from 1960 to 1970, approximately how much did a dozen donuts cost in 1970?
Answer:
$1.45
Step-by-step explanation:
The cost of a dozen doughnuts in 1970 is $1.44.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
To calculate the cost of a dozen doughnuts in 1970 we have to know the percentage increase in the price index from 1960 to 1970 and this will be:
Rate = [(48.2 – 29.6) / 29.6] × 100%
Rate = (18.6 / 29.6) × 100%
Rate = 62.83 %
Let's represent the price of a dozen doughnuts in 1970 by X and solve. This will be:
62.83 = (X - 0.89) × 100 / 0.89
(62.83 × 0.89 ) = 100X - 89
55.9 = 100X - 89
100X = 144.9
X = 144.9 / 100
X = $1.44
X = $1.44
Therefore, the cost of a dozen doughnuts in 1970 is $1.44.
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There's a linear relationship between the number of credits a community college student is enrolled for and the total registration cost. A student taking 9 credits pays $ 983 to register. A student taking 13 credits pays $ 1411 to register. Let x represent the number of credits a student enrolls for and let y represent the total cost, in dollars. Write an equation, in slope-intercept form, that correctly models this situation.
Answer:
y = 107x + 20
Step-by-step explanation:
The points that represent the number of credits and the cost of those credits in coordinate form are (9, 983) and (13, 1411).
We can use the slope formula to first find the slope of the line containing those 2 points:
[tex]m=\frac{1411-983}{13-9}=\frac{428}{4}=107[/tex]
The slope is 107. Now we can pick one of the 2 points and use it in the point-slope form of a line to get the equation we are looking for:
[tex]y-983=107(x-9)[/tex] simplifies to
[tex]y-983=107x-963[/tex] so in slope-intercept form:
y = 107x + 20
The population of a city is modeled by P(t)=0.5t2 - 9.65t + 100,where P(t) is the population in thousands and t=0 corresponds to the year 2000. a)In what year did the population reach its minimum value? How low was the population at this time?b)When will the population reach 200 000?
Answer:
Step-by-step explanation:
This equation is a positive parabola, opening upwards. Parabolas of this type have a vertex that is a minimum value. In order to find the year where the population was the lowest, we have to complete the square to find the vertex. The rule for completing the square is to first set the parabola equal to 0, then next move the constant over to the other side of the equals sign. The leading coefficient on the x-squared term HAS to be a positive 1. Ours is a .5, so will factor it out. Doing those few steps looks like this:
[tex].5(t^2-19.3t)=-100[/tex]
Next we take half the linear term, square it, and add it to both sides. Don't forget the .5 sitting out front there as a multiplier. Our linear term is 19.3. Taking half of that gives us 9.65, and 9.65 squared is 93.1225
[tex].5(t^2-19.3t+93.1225)=-100+46.56125[/tex]
In this process, we have created a perfect square binomial on the left. Stating that binomial and doing the addition on the right looks like this:
[tex].5(t-9.65)^2=-106.8775[/tex]
Now finally we will divide both sides by .5 then move over the constant again to get the final vertex form of this quadratic:
[tex](t-9.65)^2+106.8775=y[/tex]
From this we can see that the vertex is (9.65, 106.8775) which translates to the year 2009 and 107,000 approximately.
In our situation, that means that the population was at its lowest, 107,000 in the year 2009.
For part b. we will replace the y in the original quadratic with a 200,000 and then factor to find the t values. Setting the quadratic equal to 0 allows us to factor to find t:
[tex]0=.5t^2-9.65t-199900[/tex]
If you plug this into the quadratic formula you will get t values of
642.02 and -622.72
The two things in math that will never EVER be negative are distances/measurements and time, so we can safely disregard the negative value of t. Since the year 2000 is our t = 0 value, then we will add 642 years to the year 2000 to get that
In the year 2642, the population in this town will reach 200,000 (as long as it grows according to the model).
Please help me with this problem
Answer:
C [tex]P(v)=2(v+7)[/tex]
Step-by-step explanation:
Lets say that [tex]P(v)=y[/tex] for simplicity.
In order to find the inverse of a function, we must switch the location of the variable, v, and y. Then we have to solve for y.
As we are already given the inverse, doing the same process again will give us the original function.
First we can set up the equation
[tex]y=\frac{1}{2} v-7[/tex]
Next we can switch the location of the variables
[tex]v=\frac{1}{2} y-7[/tex]
Now we can solve for y
[tex]v=\frac{1}{2} y-7\\\\v+7=\frac{1}{2} y\\\\y=2(v+7)\\\\P(v)=2(v+7)[/tex]
This gives us the function
[tex]P(v)=2(v+7)[/tex]
Answer:
C P(v) = 2(v+7)
Step-by-step explanation:
To find P(v), we need to take the inverse of P^-1 (v)
y = 1/2 v-7
Exchange y and v
v = 1/2 y-7
Solve for y
Add 7 to each side
v+7 = 1/2 y -7+7
v+7 = 1/2y
Multiply each side by 2
2(v+7) = 1/2 y*2
2(v+7) = y
P(v) = 2(v+7)
You have recorded your car mileage and gasoline use for 5 weeks Estimate the
number of miles you can drive on a full 15-gallon tank of gasoline,
Number of miles 198 115 154 160 132
| Number of gallons
9 5 7 8 6
Answer:
I'm not quite sure but I think it's either 21.6 miles or 22 (Mostly 21.6 though, is what i think at least).
Which situation requires the addition counting principle to determine the number of possible outcomes?
Answer:
Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available
Step-by-step explanation:
Creating a stuffed animal when there are 6 animals, 3 fur colors, and 12 clothing themes available
This condition requires multiplication or factorials to determine outcomes
Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available
This situation requires the addition counting principle to determine the number of possible outcomes as there is only one car to be picked so all the numbers 10+5+3 = 18 will be added to get the possible outcomes ..
HELP MEEE!!
Select the correct answer.
Which of the following is not an identity for ?
Answer:
only C
Step-by-step explanation:
Pleasee help me!!!
Type the correct answer in the box.
The value of is .
The value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1
What is the Law of Base change in Logarithm ?According to the law of base change
[tex]\rm \log _b a = \dfrac{ log _d b}{log_d a}[/tex]
The given expression is
[tex]\rm { log _3 5}\times{log_{25} 9}[/tex]
This can be written as
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 9 }{log_{10} 3*log _{10}25}[/tex]
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 3^2 }{log_{10} 3*log _{10}5^2}[/tex]
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *2log _{10} 3 }{log_{10} 3* 2 log _{10}5}[/tex]
On solving this the value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1
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Answer:
Step-by-step explanation:
A formula for finding the area of a rectangle is A=l?w. If you know the area (A) and length (l) of a rectangle, which formula can you use to find the width (w)?
Answer:
[tex]w=\frac{A}{l}[/tex]
Step-by-step explanation:
The formula to find the area of a rectangle is: [tex]A=w \times l[/tex], where [tex]w[/tex] is width and [tex]l[/tex] is length.
So, if we knoe the area [tex]A[/tex] and the length [tex]l[/tex], we can find the width with the formula
[tex]w=\frac{A}{l}[/tex]
You can get this answer by using the defintion of area, which is the first equation, and isolating [tex]w[/tex].
Remember, when we want to move a factor to the other side of the equalty, we must pass it with the opposite operation. So, in this case, width was multiplying, and it passed to the other side dividing.
Therefore, the answer here is [tex]w=\frac{A}{l}[/tex]
A mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt. The chance that the dart thrower hits the bullseye at least once in 6 attempts is:
Answer:
The probability of hitting the bullseye at least once in 6 attempts is 0.469.
Step-by-step explanation:
It is given that a mechanical dart thrower throws darts independently each time, with probability 10% of hitting the bullseye in each attempt.
The probability of hitting bullseye in each attempt, p = 0.10
The probability of not hitting bullseye in each attempt, q = 1-p = 1-0.10 = 0.90
Let x be the event of hitting the bullseye.
We need to find the probability of hitting the bullseye at least once in 6 attempts.
[tex]P(x\geq 1)=1-P(x=0)[/tex] .... (1)
According to binomial expression
[tex]P(x=r)=^nC_rp^rq^{n-r}[/tex]
where, n is total attempts, r is number of outcomes, p is probability of success and q is probability of failure.
The probability that the dart thrower not hits the bullseye in 6 attempts is
[tex]P(x=0)=^6C_0(0.10)^0(0.90)^{6-0}[/tex]
[tex]P(x=0)=0.531441[/tex]
Substitute the value of P(x=0) in (1).
[tex]P(x\geq 1)=1-0.531441[/tex]
[tex]P(x\geq 1)=0.468559[/tex]
[tex]P(x\geq 1)\approx 0.469[/tex]
Therefore the probability of hitting the bullseye at least once in 6 attempts is 0.469.
NEED HELP WITH A MATH QUESTION
Answer:
(- 6, 6 )
Step-by-step explanation:
Assuming the centre of dilatation is the origin, then
The coordinates of the image points are 3 times the original points
B = (- 2, 2 ), then
B' = ( 3 × - 2, 3 × 2 ) = (- 6, 6 )
Rectangle ABCD was dilated to create rectangle A'B'C'D.
What is AB?
6 units
7.6 units
9.5 units
12 units
Answer:
6
Step-by-step explanation:
Let's setup a proportion to find AB.
AB corresponds to A'B'.
BC corresponds to B'C'.
So setting up proportion this would look like:
[\tex]\frac{AB}{A'B'}=\frac{BC}{B'C'}[/tex]
[\tex]\frac{AB}{15}=\frac{3.8}{9.5}[/tex]
Cross multiply:
[tex]AB(9.5)=15(3.8)[/tex]
Divide both sides by 9.5:
[tex]AB=\frac{15(3.8)}{9.5)}[/tex]
Put into calculator:
[tex]AB=6[/tex]
Answer: AB=6 so A is correct, hope this help! Branliest would be awesome :)
Step-by-step explanation:
Since the larger rectangle and the smaller rectangle are essentially the same just bigger, they will be proportionate.
Therefore..
9.5/3.8=15/AB
You can cross multiply to find AB...
9.5AB=57
Divide 57 by 9.5 to separate AB, which you can think of like x...
AB=57/9.5
AB=6
Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no". The point estimate of the proportion in the population who will respond "yes" is:
Answer:
0.75
Step-by-step explanation:
Total number of people = 400
Number of people who say yes to gun laws being more stringent = 300
Number of people who say no to gun laws being more stringent = 100
The proportion of people who will say yes = Number of people who say yes to gun laws being more stringent / Total number of people
[tex]\text{The proportion of people who will say yes}=\frac{300}{400}\\\Rightarrow \text{The proportion of people who will say yes}=\frac{3}{4}=0.75[/tex]
∴ Proportion in the population who will respond "yes" is 0.75