Answer:
C. √13
Step-by-step explanation:
The distance between two points is given by
d =sqrt( (x2-x1)^2 + (y2-y1)^2)
= sqrt( (3-0)^2 + (-3--1)^2)
= sqrt( 3^2 + (-3+1)^2)
= sqrt( 9+(-2)^2)
= sqrt( 9+4)
= sqrt(13)
To answer this, you basically use Pythagoras' Theroem, but instead of:
[tex]c = \sqrt{a^{2} + b^{2}}[/tex]
it will be :
[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2} }[/tex]
So you are finding the squareroot of the (difference in y coordinates)² plus (difference in x coordinates) ²:
x is the x-coordinate of (0, -1) (so x = 0)
y is the y-coordinte of (0, -1) ( so y = -1)
x1 is the x coordinate of (3, -3) ( so x1 = 3)
y1 is the y coordinate of (3, -3) (so y1 = -3)
--------------------------------------------------
Now, lets find the distance between the two points, by substituting all of this values into the equation at the top:
[tex]distance = \sqrt{(y - y1)^{2} + (x - x1)^{2} }[/tex] (substitute in values)
[tex]distance = \sqrt{( 0 -3)^{2} + (-1 - -3)^{2} }[/tex] (simplify: note -1 - - 3 = -1 + 3)
[tex]distance = \sqrt{( -3)^{2} + (-1 +3)^{2} }[/tex] (simplify)
[tex]distance = \sqrt{( -3)^{2} + (2)^{2} }[/tex] (now square the numbers)
[tex]distance = \sqrt{9 + 4 }[/tex] (simplify)
[tex]distance = \sqrt{13 }[/tex]
___________________________________________
Answer:C. [tex]\sqrt{13}[/tex]
Find \cos\left(\dfrac{19\pi}{12}\right)cos( 12 19π )cosine, left parenthesis, start fraction, 19, pi, divided by, 12, end fraction, right parenthesis exactly using an angle addition or subtraction formula.
Answer:
The value of given expression is [tex]-\frac{\sqrt{2}-\sqrt{6}}{4}[/tex].
Step-by-step explanation:
The given expression is
[tex]\cos\left(\dfrac{19\pi}{12}\right)[/tex]
The trigonometric ratios are not defined for [tex]\dfrac{19\pi}{12}[/tex].
[tex]\dfrac{19\pi}{12}[/tex] can be split into [tex]\frac{5\pi}{4}+\frac{\pi}{3}[/tex].
[tex]\cos\left(\dfrac{19\pi}{12}\right)=\cos (\frac{5\pi}{4}+\frac{\pi}{3})[/tex]
Using the addition formula
[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]
[tex]\cos (\frac{5\pi}{4}+\frac{\pi}{3})=\cos( \frac{\pi}{3})\cdot \cos (\frac{5\pi}{4})-\sin( \frac{\pi}{3})\cdot \sin (\frac{5\pi}{4})[/tex]
We know that, [tex]\cos(\frac{\pi}{3})=\frac{1}{2}[/tex] and [tex]\sin (\frac{\pi}{3})=\frac{\sqrt{3}}{2}[/tex]
[tex]\cos\left(\dfrac{19\pi}{12}\right)=\frac{1}{2}\cdot \cos (\frac{5\pi}{4})-\frac{\sqrt{3}}{2}\cdot \sin (\frac{5\pi}{4})[/tex]
[tex]\frac{5\pi}{4}[/tex] lies in third quadrant, by using reference angle properties,
[tex]\cos(\frac{5\pi}{4})=-\cos(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}[/tex]
[tex]\sin(\frac{5\pi}{4})=-\sin(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}[/tex]
[tex]\cos\left(\dfrac{19\pi}{12}\right)=\frac{1}{2}\cdot (-\frac{\sqrt{2}}{2})-\frac{\sqrt{3}}{2}\cdot (-\frac{\sqrt{2}}{2})[/tex]
[tex]\cos\left(\dfrac{19\pi}{12}\right)=-\frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{4}[/tex]
[tex]\cos\left(\dfrac{19\pi}{12}\right)=-\frac{(\sqrt{2}-\sqrt{6})}{4}[/tex]
Therefore the value of given expression is [tex]-\frac{\sqrt{2}-\sqrt{6}}{4}[/tex].
Final answer:
To find [tex]\(\cos(\frac{19\pi}{12})\),[/tex] we express the angle as the sum of [tex]\(\frac{4\pi}{3}\) and \(\frac{\pi}{4}\)[/tex] and then use the cosine addition formula. Calculating the values of cosine and sine for these angles gives us the exact value of [tex]\(\cos(\frac{19\pi}{12})\) as \(\frac{\sqrt{6} - \sqrt{2}}{4}\).[/tex]
Explanation:
To find [tex]\(\cos\left(\frac{19\pi}{12}\right)\)[/tex] using an angle addition or subtraction formula, let's break down the angle [tex]\(\frac{19\pi}{12}\)[/tex] into the sum or difference of angles whose cosine values we know. We can express[tex]\(\frac{19\pi}{12}\) as \(\frac{16\pi}{12} + \frac{3\pi}{12}\)[/tex] which simplifies to[tex]\(\frac{4\pi}{3} + \frac{\pi}{4}\).[/tex] Now we use the cosine addition formula [tex], \(\cos(a+b) = \cos a \cos b - \sin a \sin b\)[/tex], to find the answer:
[tex]\(\cos\left(\frac{19\pi}{12}\right) = \cos\left(\frac{4\pi}{3} + \frac{\pi}{4}\right) = \cos\left(\frac{4\pi}{3}\right)\cos\left(\frac{\pi}{4}\right) - \sin\left(\frac{4\pi}{3}\right)\sin\left(\frac{\pi}{4}\right)\)[/tex]
[tex]\(= (-\frac{1}{2})\cdot(\frac{\sqrt{2}}{2}) - (-\frac{\sqrt{3}}{2})\cdot(\frac{\sqrt{2}}{2})\)[/tex]
[tex]\(= -\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\)[/tex]
Combining these, we get:
[tex]\(\cos\left(\frac{19\pi}{12}\right) = \frac{\sqrt{6} - \sqrt{2}}{4}\)[/tex]
Ned some help with these questions
Answer:
14a. an = 149 -6(n -1)
14b. Evaluate the formula with n=8.
15. (no question content)
Step-by-step explanation:
14. Each week, sales decreases by 6, so the arithmetic sequence for sales has a first term of 149 and common difference of -6. The general formula for the n-th term is ...
an = a1 + d·(n -1) . . . . . . where a1 is the first term, d is the common difference
Putting the numbers for this sequence into the general formula, we get ...
an = 149 -6(n -1)
__
To predict the sales for the 8th week, put n=8 into the formula and do the arithmetic.
a8 = 149 -6(8-1) = 107 . . . . predicted sales for week 8
_____
15. The graph is shown attached. There is no question content.
In circle A below, if angle BAC measures 15 degrees, what is the measure of arc BC?
Answer:
15 degrees
Step-by-step explanation:
The arc measure of BC is equal to angle created by B, C and the central angle. The angle created by B,C, and the central angle is 15 degrees so the arc measure is 15 degrees.
Answer: 15°
Step-by-step explanation:
It is important to remember that, by definition:
[tex]Central\ angle = Intercepted\ arc[/tex]
Therefore, in this case, knowing that the angle BAC (which is the central angle) in the circle provided measures 15 degrees, you can conclude that the measure of arc BC (which is the intercepted arc) is 15 degrees.
Then you get that the answer is:
[tex]BAC=BC[/tex]
[tex]BC=15\°[/tex]
Marlow Company purchased a point of sale system on January 1 for $10,000. This system has a useful life of 10 years and a salvage value of $1,000. What would be the depreciation expense for the first year of its useful life using the double-declining-balance method?
Answer:
Given:
POS system = 3,400
useful life = 10 years
salvage value = 400
double declining method means that the depreciation expense is higher in the early years than the later years of the asset.
Straight line depreciation = (3,400 - 400) / 10 yrs = 300
300 / 3000 = 0.10 or 10%
10% x 2 = 20% double declining rate
Depreciation expense under the double declining method:
Year 1: 3,400 x 20% = 680 depreciation expense.
Year 1 book value = 3,400 - 680 = 2,720
Year 2 : 2,720 x 20% = 544 depreciation expense
Year 2 book value = 2,720 - 544 = 2,176
Use the standard normal distribution or the t-distribution to construct a 99% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 42 people, the mean body mass index (BMI) was 28.3 and the standard deviation was 6.09.
Answer:
(25.732,30.868)
Step-by-step explanation:
Given that in a random sample of 42 people, the mean body mass index (BMI) was 28.3 and the standard deviation was 6.09.
Since only sample std deviation is known we can use only t distribution
Std error = [tex]\frac{s}{\sqrt{n} } =\frac{6.09}{\sqrt{42} } \\=0.9397[/tex]
[tex]df = 42-1 =41[/tex]
t critical for 99% two tailed [tex]= 2.733[/tex]
Margin of error[tex]= 2.733*0.9397=2.568[/tex]
Confidence interval lower bound = [tex]28.3-2.568=25.732[/tex]
Upper bound = [tex]28.3+2.568=30.868[/tex]
Answer:
i think its uh
Step-by-step explanation: carrot
A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce: f(n) = 9(0.7)n What does the number 9 in the function represent?
Answer:
Initial height or what the ball was originally bounced from a height of 9 feet
Step-by-step explanation:
9 represents the height that the ball was originally bounced from.
If you plug in 0 for [tex]n[/tex] into [tex]f(n)=9(0.7)^n[/tex], you get:
[tex]f(0)=9(0.7)^0=9(1)=9[/tex].
9 feet is the initial height since that is what happens at time zero.
Answer:
Initial height or what the ball was originally bounced from a height of 9 feet
Step-by-step explanation:
9 represents the height that the ball was originally bounced from.
If you plug in 0 for into , you get:
.
9 feet is the initial height since that is what happens at time zero.
You just rode your bike for 45 minutes and burned 560 calories. How many calories did u burn per minute? plz hurry
Answer:
12.4 calories / minute to the nearest tenth.
Step-by-step explanation:
That would be 560 / 45
= 12.44... calories / minute.
Jayne stopped to get gas before going on a road trip. The tank already had 4 gallons of gas in it. Which best describes why the graph relating the total amount of gasoline in the tank, y, to the number of gallons that she added to it, x, will be continuous or discrete?
A: The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.
B: The graph will be continuous because we are not told a maximum value for the amount of gas.
C: The graph will be discrete because there are already exactly 4 gallons of gas in the tank, so to fill it up will take a whole number of gallons of gas.
D: The graph will be discrete because there is an end to the amount of gas she can use, as the tank will be completely full at some point.
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Answer:
The correct option is A. The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.
Step-by-step explanation:
Consider the given information.
If the value of a function is integer then the graph will be discrete, otherwise it will be a continuous graph.
The amount of gas that Jayne added does not need to be an integer. So, the graph will be continuous.
For example, 16.7 gallons of gas or 19.9 gallons of gas, etc. She can get amounts that are not integers.
This can be represent as:
y = x + 4
Where, y is total amount of gas in tank and x is number of gallons she added.
As it is a linear function which is continuous everywhere.
Thus, the correct option is A. The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.
Answer:
I want yo points
Step-by-step explanation:
Which expression is equal to f(x) + g(x)?
f(x)=x-16/x^2+6x-40x fo x /= -10 and x /= 4
g(x)=1/x+10x for x /= -10
(Answer choices given in photo)
Answer:
[tex]\frac{2x-20}{x^2+6x-40}[/tex]
Step-by-step explanation:
[tex]f(x)+g(x)[/tex]
[tex]\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}[/tex]
I'm going to factor that quadratic in the first fraction's denominator to figure out what I need to multiply top and bottom of the other fraction or this fraction so that I have a common denominator.
I want a common denominator so I can write as a single fraction.
So since the leading coefficient is 1, all we have to do is find two numbers that multiply to be c and at the same thing add up to be b.
c=-40
b=6
We need to find two numbers that multiply to be -40 and add to be 6.
These numbers are 10 and -4 since (10)(-4)=-40 and 10+-4=6.
So the factored form of [tex]x^2+6x-40[/tex] is [tex](x+10)(x-4)[/tex].
So the way the bottoms will be the same is if I multiply top and bottom of my second fraction by (x-4).
This will give me the following sum so far:
[tex]\frac{x-16}{x^2+6x-40}+\frac{x-4}{x^2+6x-40}[/tex]
Now that the bottoms are the same we just need to add the tops and then we are truly done:
[tex]\frac{(x-16)+(x-4)}{x^2+6x-40}[/tex]
[tex]\frac{x+x-16-4}{x^2+6x-40}[/tex]
[tex]\frac{2x-20}{x^2+6x-40}[/tex]
Jenny received a $70 gift card for a coffee store. She used it in buying some coffee that cost $8.01 per pound. After buying the coffee, she had $45.97 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds of coffee
Step-by-step explanation:
First you have to find how much Jenny spent on coffee.
To find this out subtract 70 by 45.97.
So, 70 - 45.97 = $24.03
Now you have to find how many pounds of coffee she bought, so to find this out you have to divide 24.03 by 8.01.
So, 24.03 divided by 8.01 = 3 pounds of coffee.
Heather has $45.71 in her savings account. She bought six packs of markers to donate to her school. If each pack of markers cost $3.99, how much money does she have in her bank account after the donation?
Answer:
21.77 After the donation
Step-by-step explanation:
3.99 Multiplied by 6 is 23.94
So 45.71 - 23.94 = 21.77
Which equation represents a line parallel to the line shown on the graph?
3x-7
-3x+3
1/3x+7/9
-1/3x + 12
Also please explain why it's the correct answer.
For me, I thought it was 3x-7 because the slope shows that it goes up 3 times and right 1 time. It could be other way around, but I'm not sure. Please answer this quickly!
Answer:
-3x+3
Step-by-step explanation:
The equation to the line shown is formed as follows.
It passes through the points (-6,0) and (-8,6)
The gradient of the line=Δy/Δx
=(y₂-y₁)/(x₂-x₁)
=(6-0)/(-8--6)
=6/-2
=-3
The line parallel to the line shown has the same gradient i.e -3
Therefore the line in question is
-3x+3.
Write an equation for the problem and then solve.
The perimeters of two rectangles are equal. The dimensions of one rectangle are 2x and x while the dimensions of the other rectangle are x + 12 and x - 3. What are the numerical dimensions of the rectangles? (Solve for x)
Answer: x =
Answer:
first rectangle: 18 by 9second rectangle 21 by 6x = 9Step-by-step explanation:
The perimeter in each case is double the sum of the side dimensions. Since the perimeters are equal, the sum of side dimensions will be equal:
2x +x = (x +12) +(x -3)
3x = 2x +9 . . . . . . . . collect terms
x = 9 . . . . . . . . . . . . . subtract 2x
Given this value of x, the dimensions of the first rectangle are ...
{2x, x} = {2·9, 9} = {18, 9}
And the dimensions of the second rectangle are ...
{x+12, x-3} = {9+12, 9-3} = {21, 6}
Which series of transformations will NOT map figure L onto itself?
A. (x + 1, y − 4), reflection over y = x − 4
B. (x − 4, y − 4), reflection over y = −x
C. (x + 3, y − 3), reflection over y = x − 4
D. (x + 4, y + 4), reflection over y = −x + 8
Answer:
A. (x + 1, y − 4), reflection over y = x − 4
Step-by-step explanation:
You must perform all the composed transformations to spot the one in which the coordinates of the preimage and the image are not the same.
The coordinates of the preimage are A(0,1), B(3,4), C(5,2) , and D(2,-1)
Option A is a translation (x + 1, y − 4), followed by a reflection over y = x − 4.
[tex]A(0,1)\to(1,-3)\to A'(1,-3)[/tex]
[tex]B(3,4)\to(4,0)\to B'(4,0)[/tex]
[tex]C(5,2)\to(6,-2)\to C'(2,2)[/tex]
[tex]D(2,-1)\to(3,-5)\to D'(-1,-1)[/tex]
Option B is a translation (x − 4, y − 4), followed by a reflection over y = −x
[tex]A(0,1)\to(-4,-3)\to A'(0,1)[/tex]
[tex]B(3,4)\to(-1,0)\to B'(3,4)[/tex]
[tex]C(5,2)\to(1,-2)\to C'(5,2)[/tex]
[tex]D(2,-1)\to(-2,-5)\to D'(2,-1)[/tex]
Option C is a translation (x +3, y − 3), followed by a reflection over y = x-4
[tex]A(0,1)\to(3,-2)\to A'(0,1)[/tex]
[tex]B(3,4)\to(6,1)\to B'(3,4)[/tex]
[tex]C(5,2)\to(8,-1)\to C'(5,2)[/tex]
[tex]D(2,-1)\to(5,-4)\to D'(2,-1)[/tex]
Option D is a translation (x +4, y + 4), followed by a reflection over y = −x+8
[tex]A(0,1)\to(4,5)\to A'(0,1)[/tex]
[tex]B(3,4)\to(7,8)\to B'(3,4)[/tex]
[tex]C(5,2)\to(9,6)\to C'(5,2)[/tex]
[tex]D(2,-1)\to(6,3)\to D'(2,-1)[/tex]
The correct choice is A.
Answer:
A. (x + 1, y − 4), reflection over y = x − 4
Step-by-step explanation:
The answer A. (x + 1, y − 4), reflection over y = x − 4 is right because I got it right on my test!! :)))
A motorboat takes 4 hours to travel 128 km going upstream. The return trip takes 2
hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Step-by-step explanation:
Rate × time = distance
If x is the rate of the boat and y is the rate of the water:
(x − y) × 4 = 128
(x + y) × 2 = 128
Simplifying:
x − y = 32
x + y = 64
Solve with elimination (add the equations together):
2x = 96
x = 48
y = 16
The speed of the boat is 48 km/hr and the speed of the water is 16 km/hr.
What translations occur when moving from
f(x) to g(x)?
f(x) = sin(x)
g(x) = 4 sin (3x – pi) +5
Step-by-step explanation:
The coefficient of the x is 3, so it is horizontally shrunk by factor of 3.
The coefficient of the sine is 4, so it is vertically stretched by factor of 4.
The constant inside the sine is -pi, so it is horizontally shifted pi units to the right.
The constant outside the sine is 5, so it is vertically shifted 5 units up.
he given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. C = 38°, a = 19, c = 10
Answer:
No, the triangle is not possible.
Step-by-step explanation:
Given,
A triangle ABC in which C = 38°, a = 19, c = 10,
Where, angles are A, B and C and the sides opposite to these angles are a, b and c respectively,
By the law Sines,
[tex]\frac{sin A}{a}=\frac{sin C}{c}[/tex]
[tex]\implies sin A = \frac{a sin C}{c}[/tex]
By substituting the values,
[tex]sin A = \frac{19\times sin 38^{\circ}}{10}[/tex]
[tex]=1.16975680312[/tex]
[tex]\implies A=sin^{-1}(1.16975680312)[/tex] = undefined
Hence, the triangle is not possible with the given measurement.
The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. Find the probability that house sales will increase but interest rates will not during the next 6 months.
Answer:
P(house)+P(interest)-P(both)=probability of P. Both subtracts the double counting.
0.25+0.74-P(Both)=0.89
P=0.10
P(neither) is the complement of P(either), which is OR. That is 1-0.89=0.11
If I can assume independence, which probably is not correct since the two are related, it is P(H)*P(not I)=0.25*0.26=0.065. Not I is 1-P(I)=0.26
Final answer:
The probability that house sales will increase but interest rates will not during the next 6 months is calculated using the addition rule for probabilities and is found to be 0.15 or 15%.
Explanation:
We are given three probabilities:
The probability that house sales will increase in the next 6 months (P(House Sales Increase)) = 0.25.The probability that the interest rates on housing loans will go up in the same period (P(Interest Rates Increase)) = 0.74.The probability that house sales or interest rates will go up during the next 6 months (P(House Sales Increase or Interest Rates Increase)) = 0.89.To find the probability that house sales will increase but interest rates will not during the next 6 months (P(House Sales Increase and Interest Rates Not Increase)), we can use the formula that relates the probability of the union of two events to the probability of each event and the probability of their intersection:
P(House Sales Increase or Interest Rates Increase) = P(House Sales Increase) + P(Interest Rates Increase) - P(House Sales Increase and Interest Rates Increase)
We rearrange the formula to solve for P(House Sales Increase and Interest Rates Not Increase):
P(House Sales Increase and Interest Rates Increase) = P(House Sales Increase) + P(Interest Rates Increase) - P(House Sales Increase or Interest Rates Increase)
Hence, the probability that interest rates will not increase when house sales increase is equal to 1 minus the probability that interest rates will increase. So:
P(House Sales Increase and Interest Rates Not Increase) = P(House Sales Increase) - P(House Sales Increase and Interest Rates Increase)
Plugging in the values we get:
P(House Sales Increase and Interest Rates Not Increase) = 0.25 - (0.25 + 0.74 - 0.89)
This simplifies to:
P(House Sales Increase and Interest Rates Not Increase) = 0.25 - 0.10 = 0.15
The probability that house sales will increase but interest rates will not during the next 6 months is 0.15 or 15%.
What is the area of a Reuleaux triangle that has a diameter of 4 in.? Round answer to the nearest hundredth.
Answer:
11.28 in²
Step-by-step explanation:
The area of a Reuleaux triange is given by ...
A = (1/2)(π -√3)d² . . . . . where d is the diameter of the triangle.
For a triangle of diameter 4 in, the area is ...
A = (1/2)(π -√3)(4 in)² = (π -√3)8 in² ≈ 11.28 in²
_____
A Reuleaux triangle is the shape of smallest area that has a constant diameter. The diameter of the shape is the radius of each of the arcs between the vertices of the inscribed equilateral triangle.
The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What is the probability that the volume of soda in a randomly selected bottle will be less than 32 oz? Round your answer to four decimal places. ti84
Answer: 0.4013
Step-by-step explanation:
Given : The volumes of soda in quart soda bottles are normally distributed with : [tex]\mu=32.3\text{ oz}[/tex]
[tex]\sigma=1.2\text{ oz}[/tex]
Let x be the volume of randomly selected quart soda bottle.
z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
[tex]z=\dfrac{32-32.3}{1.2}=-0.25[/tex]
The probability that the volume of soda in a randomly selected bottle will be less than 32 oz = [tex]P(x<32)=P(z<-0.25)[/tex]
[tex]=0.4012937\approx0.4013[/tex]
Hence, the probability that the volume of soda in a randomly selected bottle will be less than 32 oz is 0.4013
The probability that a randomly selected bottle of soda will be less than 32 oz is approximately 40.13%. This is calculated using the z-score and a standard normal distribution.
Explanation:To find the probability that the volume of soda in a randomly selected bottle will be less than 32 oz, we can use the concept of z-score in statistics. The z-score is a measurement of how many standard deviations a data point is from the mean.
First, we need to calculate the z-score associated with 32 oz. The formula for the z-score is (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation. Plugging our values in, we get (32 - 32.3) / 1.2 = -0.25.
Next, we consult a standard normal distribution table or use a calculator function to find the probability associated with this z-score. Using a TI-84 calculator, we perform the following steps: Go to the distribution menu ('2nd' then 'VARS'), choose '2: normalcdf(', input the following values: (-1E99, -0.25, 32.3, 1.2). Press 'ENTER' to get the result, which is approximately 0.4013. Thus, the probability that a randomly selected bottle of soda will be less than 32 oz is approximately 0.4013 or 40.13%.
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What is the circumference and area of a circle with a radius of 4 meters? Round your answer to the nearest tenth. Circumference: m Area: m2 (Use 3.14 for Pi.)
Answer:
Circumference = 25m
Area = 50 m2
Step-by-step explanation:
formula for circumference of a circle is π(d)
when radius is 4m, diameter is 8m
3.14(8)= 25.13
nearest tenth = 25m
formula for area of circle is 2πr or π(r)(r)
when radius is 4m
3.14(4)(4)=50.27 m2
nearest tenth =50m
Answer: circumference of the circle is 25.12 m and the area of the circle is 50.2 m²
Step-by-step explanation:
To find the circumference of the circle of radius 4 meters, we simply use the formula;
area of a circumference = 2πr
π is given to be 3.14 and radius r=4 meter, we will substitute this variable into the formula
area of a circumference = 2πr
= 2 × 3.14 × 4
=25.12
≈25.1 to the nearest tenth
Therefore, the circumference of the circle is is 25.1 meters
To find the area of the circle, we simply use the formula:
area of circle = π[tex]r^{2}[/tex]
= 3.14 × (4)²
=3.14 × 16
=50.24
≈50.2 to the nearest tenth
Therefore, the area of the circle is 50.2 m²
Can someone please help me with this math question PLEASE HELP THIS IS URGENT
Answer:
(- 1, 4 )
Step-by-step explanation:
x = 1 is a vertical line passing through all points with an x- coordinate of 1
The point P(3, 4) is to units to the right of x = 1.
Hence the refection will be 2 units to the left of x = 1
P' = (1 - 2, 4 ) = (- 1, 4 )
Alexa pays 7/20 of a dollar for each minute she uses her pay-as-you-go phone for a call, and 2/5 of a dollar for each minute of data she uses. This month, she used a total of 85 minutes and the bill was $31. Which statements are true? Check all that apply.
The system of equations is x + y = 31 and 7/20x+2/5y=85
The system of equations is x + y = 85 and 7/20x+2/5y=31
To eliminate the y-variable from the equations, you can multiply the equation with the fractions by 5 and leave the other equation as it is.
To eliminate the x-variable from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7.
A-She used 25 minutes for calling and 60 minutes for data.
B-She used 60 minutes for calling and 25 minutes for data.
C-She used 20 minutes for calling and 11 minutes for data.
D-She used 11 minutes for calling and 20 minutes for data.
Answer:
The system of equations is x + y = 85 and 7/20x+2/5y=31To eliminate the x-variable from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7.B-She used 60 minutes for calling and 25 minutes for data.Step-by-step explanation:
It is always a good idea to start by defining variables in such a problem. Here, we can let x represent the number of calling minutes, and y represent the number of data minutes. The the total number of minutes used is ...
x + y = 85
The total of charges is the sum of the products of charge per minute and minutes used:
7/20x + 2/5y = 31.00
We can eliminate the x-variable in these equations by multiplying the first by -7 and the second by 20, then adding the result.
-7(x +y) +20(7/20x +2/5y) = -7(85) +20(31)
-7x -7y +7x +8y = -595 +620 . . . . eliminate parentheses
y = 25 . . . . . . . . simplify
Then the value of x is
x = 85 -y = 85 -25
x = 60
Answer:
The second, fourth and B option are correct.
Step-by-step explanation:
In order to solve this problem, we are going to define the following variables :
[tex]X:[/tex] ''Minutes she used her pay-as-you-go phone for a call''
[tex]Y:[/tex] ''Minutes of data she used''
Then, we are going to make a linear system of equations to find the values of [tex]X[/tex] and [tex]Y[/tex].
''This month, she used a total of 85 minutes'' ⇒
[tex]X+Y=85[/tex] (I)
(I) is the first equation of the system.
''The bill was $31'' ⇒
[tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] (II)
(II) is the second equation of the system.
The system of equations will be :
[tex]\left \{ {{X+Y=85} \atop {(\frac{7}{20})X+(\frac{2}{5})Y=31}} \right.[/tex]
The second option ''The system of equations is [tex]X+Y=85[/tex] and [tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] .'' is correct
Now, to solve the system, we can eliminate the x-variable from the equations by multiplying the equation with the fractions by 20 and multiplying the other equation by -7. Then, we can sum them to obtain the value of [tex]Y[/tex] :
[tex]X+Y=85[/tex] (I)
[tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] (II) ⇒
[tex](-7)X+(-7)Y=-595[/tex] (I)'
[tex]7X+8Y=620[/tex] (II)'
If we sum (I)' and (II)' ⇒
[tex](-7)X+(-7)Y+7X+8Y=-595+620[/tex] ⇒ [tex]Y=25[/tex]
If we replace this value of [tex]Y[/tex] in (I) ⇒
[tex]X+Y=85\\X+25=85\\X=60[/tex]
The fourth option ''To eliminate the x-varible from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7'' is correct.
With the solution of the system :
[tex]\left \{ {{X=60} \atop {Y=25}} \right.[/tex]
We answer that the option ''B-She used 60 minutes for calling and 25 minutes for data'' is correct.
I need help with this question! I already have part c figured out but I'm having a hard time understanding a and b...
Becky is building a square rabbit cage. The length and width are both 3 feet less than the square dog pen she built for her dog. The area of the rabbit cage is 25 ft.
a. Using D to represent the side of the square dog pen, write an expression to represent the area of the rabbit cage.
b. Use the expression and the given area to find the length of a side of the square dog pen.
Since each side of the rabbit pen is 5ft (25 squared=5ft) add 3ft to each side because the dog pen is 3 ft bigger in length and width, equaling 8ft. The dog pen is 8ft by 8ft= 36ft
c. How many feet of fencing is needed to enclose the 4 sides of the rabbit cage? (SHOW WORK)
The rabbit cage is a square, and the area is 25ft, which has a square room of 5. Since there are 4 sides of the rabbit cage which will be fenced, multiply 5 (which is 25 squared) by 4 (the sides) equalling 20. There needs to be 20 ft of fencing to enclose all 4 sides of the rabbit cage. (thats my answer for part c )
[tex]\bf \boxed{A}\\\\ \stackrel{\textit{3 less than D}}{D-3}~\hspace{5em}A=(D-3)(D-3)\implies A=(D-3)^2 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\\\\ \stackrel{\textit{area of rabbits' pen}}{25=(D-3)^2}\implies \stackrel{\stackrel{\textit{same exponents}}{\textit{same base}}}{5^2=(D-3)^2}\implies 5=D-3\implies 8=D \\\\\\ \boxed{C}\\\\ 5+5+5+5=20[/tex]
Final answer:
To find the expression that represents the area of the rabbit cage, use (D - 3)². The side of the rabbit cage, given the area, is 25 square feet, is 5 feet, so the dog pen's side length is 8 feet. The rabbit cage requires 20 feet of fencing to be enclosed.
Explanation:
To solve for the expression that represents the area of the rabbit cage, we'll start by defining the side of the square dog pen as D. Since each side of the rabbit cage is 3 feet less than the dog pen, the side of the rabbit cage would be D - 3. Therefore, the area of the rabbit cage, which is a square, is given by the expression (D - 3)². This tells us that the area is the side length squared. Now, we know that the area of the rabbit cage is 25 square feet.
To find the side length of the rabbit cage, we would take the square root of the area, which gives us 5 feet. Hence, to find the side length of the dog pen, we would add the 3 feet back to the side length of the rabbit cage. This gives us D - 3 = 5, which means D = 5 + 3, so D = 8 feet.
For part c, to find out how many feet of fencing is needed to enclose the rabbit cage, we take the side length of the rabbit cage, which is 5 feet, and multiply it by 4, since a square has four equal sides. This means we would need 5 feet x 4 sides = 20 feet of fencing to enclose the rabbit cage.
A print shop purchases a new printer for $25,000. The equipment depreciates at a rate of 5% each year. The relationship between the value of the printer, y, and the year number, x, can be represented by the equation, y = 25,000 • 0.95 x . Complete the table below with the value of the printer, to the nearest cent, in years 1, 2, and 3. Include proper commas and decimals in your answer.
Answer:
Part 1) For x=1 year, [tex]y=\$23,750[/tex]
Part 2) For x=2 years, [tex]y=\$22,562.50[/tex]
Part 3) For x=3 years, [tex]y=\$21,434.38[/tex]
Step-by-step explanation:
we know that
The formula to calculate the depreciated value is equal to
[tex]y=P(1-r)^{x}[/tex]
where
y is the depreciated value
P is the original value
r is the rate of depreciation in decimal
x is the number of years
in this problem we have
[tex]P=\$25,000\\r=5\%=0.05[/tex]
substitute
[tex]y=25,000(1-0.05)^{x}[/tex]
[tex]y=25,000(0.95)^{x}[/tex]
Part 1) Find the value of the printer, to the nearest cent, in year 1
so
For x=1 year
substitute in the exponential equation
[tex]y=25,000(0.95)^{1}[/tex]
[tex]y=\$23,750[/tex]
Part 2) Find the value of the printer, to the nearest cent, in year 2
so
For x=2 years
substitute in the exponential equation
[tex]y=25,000(0.95)^{2}[/tex]
[tex]y=\$22,562.50[/tex]
Part 3) Find the value of the printer, to the nearest cent, in year 3
so
For x=3 years
substitute in the exponential equation
[tex]y=25,000(0.95)^{3}[/tex]
[tex]y=\$21,434.38[/tex]
According to a recent study, 9.3% of high school dropouts are 16- to 17-year-olds. In addition, 6.4% of high school dropouts are white 16- to 17-year-olds. What is the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old?
Answer:
0.688 or 68.8%
Step-by-step explanation:
Percentage of high school dropouts = P(D) = 9.3% = 0.093
Percentage of high school dropouts who are white = [tex]P(D \cap W)[/tex] = 6.4% = 0.064
We need to find the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old. This is conditional probability which can be expressed as: P(W | D)
Using the formula of conditional probability, we ca write:
[tex]P(W | D)=\frac{P(W \cap D)}{P(D)}[/tex]
Using the values, we get:
P( W | D) = [tex]\frac{0.064}{0.093} = 0.688[/tex]
Therefore, the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old is 0.688 or 68.8%
Find the mean, median, mode, and range of this data: 49, 49, 54, 55, 52, 49, 55. If necessary, round to the nearest tenth.
Answer:
Mean = 51.4.
Mode = 49.
Median = 52.
Range = 6.
Step-by-step explanation:
Mean = Sum of all observations / Number of observations.
Mean = (49+49+54+55+52+49+52)/7
Mean = 360/7
Mean = 51.4 (to the nearest tenth).
Mode = The most repeated values = 49 (repeated 3 times).
Range = Largest Value - Smallest Value = 55 - 49 = 6.
Median = The central value of the data.
First, arrange the data in the ascending order: 49, 49, 49, 52, 54, 55, 55.
It can be seen that the middle value is 52. Therefore, median = 52!!!
Each investment matures in 3 years. The interest compounds annually.
Calculate the interest and the final amount.
a) $600 invested at 5%
b) $750 invested at 4 3/4%
bearing in mind that 4¾ is simply 4.75.
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=600\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=600(1.05)^3\implies A=694.575 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=750\left(1+\frac{0.0475}{1}\right)^{1\cdot 3}\implies A=750(1.0475)^3\implies A\approx 862.032[/tex]
well, the interest for each is simply A - P
695.575 - 600 = 95.575.
862.032 - 750 = 112.032.
Write (2x - 5)2 as a trinomial.
Answer:
[tex]4x^2-20x+25[/tex]
Step-by-step explanation:
[tex](2x-5)^{2} \\(2x)^2+2(2x)(-5)+(-5)^2\\4x^2-20x+25[/tex]
Answer:
[tex]4x^2-20x+25[/tex]
Step-by-step explanation:
You can use the formula:
[tex](u+v)^2=u^2+2uv+v^2[/tex].
[tex](2x-5)^2=(2x)^2+2(2x)(-5)+(-5)^2[/tex]
[tex](2x-5)^2=4x^2-20x+25[/tex].
You could also use foil:
[tex](2x-5)^2=(2x-5)(2x-5)[/tex]
First: 2x(2x)=4x^2
Outer: 2x(-5)=-10x
Inner: -5(2x)=-10x
Last: -5(-5)=25
--------------------------Add.
[tex]4x^2-20x+25[/tex]
Proportions in Triangles (9)
Answer:
3.6
Step-by-step explanation:
Divide 6 by 4
You get 1.5
Multiply 1.5 by 2.4
You get 3.6