There are 6 letters: (4 consonants, 2 vowels)
The probability that Allen will not select a consonant is: (2/6 which simplifies to 1/3) because there are only 2 letters out of the 6 that are not consonants
Fraction: 1/3
Decimal: 0.3333
Percentage: 33.33%
The probability that Allen does not select a consonant is 1/3 as a fraction, 0.3333 as a decimal, and 33.33% as a percentage.
You've asked what the probability is that Allen will not select a consonant when drawing one letter from the mix of letters 's, c, h, o, o, l'. First, let's determine how many vowels and consonants there are in the selection. We have two vowels ('o', 'o') and four consonants ('s', 'c', 'h', 'l'). This gives us a total of six letters.
To find the probability of not selecting a consonant, we look at the likelihood of selecting a vowel instead, since those are the only two types of letters available. There are 2 vowels out of a total of 6 letters. The probability as a fraction is thus 2/6, which simplifies to 1/3.
To express this probability as a decimal, divide the numerator by the denominator: 1 divided by 3 equals approximately 0.3333. Finally, to express this as a percentage, multiply the decimal by 100 to get 33.33%.
In summary:
Fraction: 1/3Decimal: 0.3333Percentage: 33.33%A circular cake with a radius of 8 inches is cut from the center into 6 equal pieces. How many inches wide, to the nerest tenth of an inch, is the outer edge of each piece of cake?
Answer: 8.4 in
Step-by-step explanation:
First we calculate the circumference.
The formula to calculate the circumference is:
[tex]C = 2\pi r[/tex]
Where r is the radius of the circumference
In this case [tex]r = 8[/tex] inches
So:
[tex]C = 2\pi(8)[/tex]
[tex]C = 2\pi(8)[/tex]
[tex]C = 50.265\ in[/tex]
The cake is divided into 6 equ pieces, so the arc length of each piece is:
[tex]\frac{50.265}{6}=8.4\ in[/tex]
If f(x) = x + 7 and g(x)=1/x, what is (f o g)(x)?
1/x+7
x+7+1/x
1+7/x
1/x+7
Answer: 1/x + 7
Step-by-step explanation: you plug the function g(x) into the function f(x) .. substitue g(x) for the x in f(x)
G(x) = 1/x , so you plug that in the x of f(x) and get 1/x + 7
To find the composition (f o g)(x), we plug g(x) into f(x), resulting in the function 1/x + 7.
To find (f o g)(x), which is the composition of f(x) and g(x), we substitute g(x) into f(x). This means we take the function g(x) = 1/x and plug it into every instance of x in the function f(x). So,
f(g(x)) = f(1/x) = (1/x) + 7
Hence, the composition of f and g, symbolized as (f o g)(x), is equivalent to 1/x + 7. This process illustrates how functions can be combined, offering a new function with distinct properties derived from their interplay.
If you invest $1000 at an interest rate of 2.5% compounded continuously, calculate how many years. How long will it take for your investment to double?
Answer:
It will take about 27.7 years
Step-by-step explanation:
* Lets talk about the compound continuous interest
- Compound continuous interest can be calculated using the formula:
A = P e^rt
• A = the future value of the investment, including interest
• P = the principal investment amount (the initial amount)
• r = the interest rate
• t = the time the money is invested for
- The formula gives you the future value of an investment,
which is compound continuous interest plus the principal.
- If you want to calculate the compound interest only, you need
to deduct the principal from the result.
- So, your formula is:
Compounded interest only = Pe^(rt) - P
* Now lets solve the problem
∵ The invest is $ 1000
∴ P = 1000
∵ The interest rate is 2.5%
∴ r = 2.5/100 = 0.025
- They ask about how long will it take to make double the investment
∴ A = 2 × 1000 = 2000
∵ A = P e^(rt)
∴ 2000 = 1000 (e)^(0.025t) ⇒ divide both sides by 1000
∴ 2000/1000 = e^(0.025t)
∴ 2 = e^(0.025) ⇒ take ln for both sides
∴ ln(2) = ln[e^(0.025t)]
∵ ln(e)^n = n
∴ ln(2) = 0.025t ⇒ divide both sides by 0.025
∴ t = ln(2)/0.025 = 27.7 years
* It will take about 27.7 years
There is a hole in Mr. Smith's backyard. He wants to find out how wide the hole is. From the point where Mr. Smith is standing, he measures 20 and 25. How wide is the hole?
a2 + b2 = c2
A) 10
B) 15
C) 20
D) 90
The answer is:
The correct option is:
B) 15
Why?To solve the problem, we need to use the Pythahorean Theorem. We know that we can use the theorem since we are working with a right triangle as we can see in the picture.
So, we are given the following information:
[tex]Hypothenuse=c=25units\\\\Opposite=b=20units[/tex]
Now, using the Pythagorean Theorem, we have:
[tex]c^{2}=a^{2} +b^{2} \\\\25^{2}=a^{2}+20^{2}\\\\a^{2}=25^{2}-20^{2}=225\\\\a=\sqrt{225}=15[/tex]
Hence, we have that the correct option is:
B) 15
Have a nice day!
1 Geometry question will give Brainliest!!! (photo attached)
the answer is....... 56%
A. 56%
First, find the number in the cell that is in the row “Hiked” and the column “Poison ivy rash”. There is only one that matches this description, and it contains the number 0.56.
To convert a decimal number to a percentage, multiply it by 100, or move the decimal point two places to the right, which is essentially the same thing. This gives you 56, which means the answer is 56%.
Please show all of your work. I wil save thanks, rank 5 stars and mark brainliest!
1. Find the standard equation of an ellipse with its foci at (2, 0) and (8,0) and a major axis of length 12.
2. Find the standard equation of an ellipse with its foci at (1, 2) and (5, 2) and a major axis of length 6.
3, Find the standard equation of a hyperbola with vertices (-2,0) and (2, 0), and foci (-6, 0) and (6, 0).
Answer:
Step-by-step explanation:
1. Equation of an ellipse is:
(x - h)² / a² + (y - k)² / b² = 1
where (h, k) is the center and a and b are the length of half the minor/major axes.
The center is the midpoint of the foci:
(h, k) = (½ (2+8), ½(0+0))
(h, k) = (5, 0)
The foci have the same y-coordinate, so the horizontal axis is the major axis:
a = 12/2
a = 6
The distance from the foci to the center is c:
c = 8-5
c = 3
b can be found using the formula:
c² = a² - b²
3² = 6² - b²
b² = 36 - 9
b² = 27
So the equation is:
(x - 5)² / 36 + (y - 0)² / 27 = 1
2. Same steps as #1. First find the center:
(h, k) = (½ (1+5), ½ (2+2))
(h, k) = (3, 2)
The foci have the same y-coordinate, so the horizontal axis is the major axis:
a = 6/2
a = 3
The distance from the foci to the center is c:
c = 5-3
c = 2
b can be found using the formula:
c² = a² - b²
2² = 3² - b²
b² = 9 - 4
b² = 5
So the equation is:
(x - 3)² / 9 + (y - 2)² / 5 = 1
3. The vertices have the same y coordinate, so this is a horizontal hyperbola:
(x - h)² / a² - (y - k)² / b² = 1
The center (h, k) is the midpoint of the vertices:
(h, k) = (½ (-2+2), ½ (0+0))
(h, k) = (0, 0)
The distance from the center to the vertices is a:
a = 2-0
a = 2
The distance from the center to the foci is c:
c = 6-0
c = 6
b can be found using the formula:
c² = a² + b²
6² = 2² + b²
b² = 36 - 4
b² = 32
So the equation is:
(x - 0)² / 4 - (y - 0)² / 32 = 1
HELP! A central angle of a circle measures 1.2 radians, and the length of the related intercepted arc measures 6 cm. What is the diameter of the circle? A) 2.5 cm B) 3.5 cm C) 5 cm D) 10 cm
Answer:
d = 2r = 2(5 cm) = 10 cm (Answer D)
Step-by-step explanation:
The arc length formula is s = r·Ф, where r is the circle radius and Ф is the central angle in radians. Here we need to find r, and from r we need to find d.
If s = r·Ф, then s / Ф = r. In this particular case, r = (6 cm) / (1.2 rad) = 5 cm.
If r = 5 cm, then d = 2r = 2(5 cm) = 10 cm (Answer D)
The diameter of the circle is 10 cm
What is a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
Given that, A central angle of a circle measures 1.2 radians, and the length of the related intercepted arc measures 6 cm.
The arc length of a circle is given by = θ/360×2πr
Converting 1.2 rad into degrees
1.2 radians = 68.755°
Therefore, 68.755°/360×2πr = 6
r = 5
diameter = 5x2 = 10
Hence, The diameter of the circle is 10 cm
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A hot air balloon descends to the ground. The function a(t) = 210 – 15t can be used to describe the altitude of the balloon as it approaches the ground. The time is in minutes.
What does t represent?
What does a(t) represent?
What information will a(5.5) give?
On Edge the answers are 1. time after the balloon begins to descend 2. altitude of the balloon 3. altitude of the balloon after 5.5 minutes.
In the given function, 't' represents time in minutes since the start of the balloon's descent. The function 'a(t)' represents the balloon's altitude above ground at a given time. 'a(5.5)' gives the altitude of the balloon 5.5 minutes after the descent started.
Explanation:In your problem, t represents time in minutes since the balloon began its descent. The function a(t) represents the altitude in feet of the hot air balloon above the ground at a given time t in minutes. a(5.5) gives the altitude of the balloon 5.5 minutes after it started descending.
Specifically, you can find the altitude at any given time by replacing 't' in the equation with the number of minutes. For instance, to find the altitude after 5.5 minutes (a(5.5)), you would replace 't' with '5.5' in the equation (a(t) = 210 – 15t), which will give you the altitude of the balloon after 5.5 minutes of descent.
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Oh man stands on his balcony 120 feet above the ground he looks at the ground this site line forming a angle of 50° with the building and sees a bus stop the function D = 120 sec models the distance from the man to any object given his angle of sight 0. How far is the bus stop from the man.
Answer:
Answer a 187 ft
Answer:
The bus stop is approximately 186.687 feet far from the man.
Step-by-step explanation:
Here, the given function that shows the distance from the man to any object in the ground,
[tex]D=120 sec\theta[/tex]
Where, [tex]\theta[/tex] is the angle of his site line.
Given,
The site angle of man is 50° when he sees a bus stop,
That is, [tex]\theta = 50^{\circ}[/tex]
Hence, the distance of bus stop from the man is,
[tex]D = 120 sec 50^{\circ}[/tex]
[tex]=120(1.55572382686)[/tex]
[tex]=186.686859223\approx 186.687[/tex]
Hence, the bus stop is approximately 186.687 feet far from the man.
Ruth Barr rented a car for 5 days at 59.95 per day with unlimited mileage she drove 1156 miles and paid 137.76 for gasoline. What was the total cost per mile to rent the car
The total cost per mile to rent the car was approximately $0.378, calculated by summing up the rental and gasoline costs and then dividing by the total number of miles driven.
Explanation:The total cost per mile to rent the car can be calculated by summing up the cost of renting the car and the cost of gasoline, then dividing by the total number of miles driven.
Calculate the total cost of renting the car: 5 days × $59.95 per day = $299.75.Add the cost of gasoline: $299.75 + $137.76 = $437.51.Divide the total cost by the number of miles driven to find the cost per mile: $437.51 ÷ 1156 miles = approximately $0.378 per mile.Therefore, the total cost per mile to rent the car was approximately $0.378.
Final answer:
To find the total cost per mile to rent the car, add the rental cost for 5 days to the gasoline cost, then divide by the miles driven. Ruth Barr's total cost per mile was approximately $0.3785.
Explanation:
To calculate the total cost per mile to rent the car, we need to add the cost of renting the car for 5 days to the cost of gasoline and then divide the sum by the number of miles driven.
Calculate the rental cost for 5 days: 5 days × $59.95/day = $299.75.
Add the cost for gasoline: $299.75 (rental cost) + $137.76 (gasoline) = $437.51.
Divide the total cost by the number of miles driven: $437.51 ÷ 1156 miles = approximately $0.3785 per mile.
The total cost per mile Ruth Barr spent to rent the car was approximately $0.3785.
79 points for one question help
Answer:
x = 42
Step-by-step explanation:
The angle between the tangent and the secant is
[tex]\frac{1}{2}[/tex] difference of the measure of the intercepted arcs, that is
x = 0.5( 136 - 52) = 0.5 × 84 = 42
Answer:
[tex]\Large \boxed{\sf 42}[/tex]
Step-by-step explanation:
Apply tangent secant exterior angle measure theorem
If a tangent and a secant intersect in the exterior of a circle, then the measure of the angle formed is 1/2 the difference of the measures of its intercepted arcs.
[tex]\displaystyle \frac{1}{2} \times(136-52)=42[/tex]
Thirty percent of check engine lights turn on after 100,000 miles in a particular model of van. The remainder of vans continue to have check engine lights that stay off.
Simulate randomly checking 25 vans, with over 100,000 miles, for check engine lights that turn on using these randomly generated digits. Let the digits 1, 2, and 3 represent a van with check engine light that turn on.
96408 03766 36932 41651 08410
Approximately how many vans will have check engine lights come on?
A. 3
B. 7
C. 8
D. 10
Answer:
B
Step-by-step explanation:
Count how many times a 1, 2, or 3 appears. Of the digits, 7 are 1s, 2s, or 3s.
Graph the system of equations. y=-1/2x+4 and x+2y=8
Answer:
Find the attached
Step-by-step explanation:
Graphing a system of equations can easily be done using modern technology graphing tools. Desmos graphing tool is the most widely used tool for this purpose.
The system of equations will be solved graphically. The point of intersection will be the solution if needed.
The attachment below shows the graph of the system of equations;
y=-1/2x+4 and x+2y=8
From the attachment below, we notice that the two lines are coincident. This is to mean that the two equations represent the same line.
a ferris wheel has 15 seat buckets . What is the angle measurement between each bucket?
Answer:
24 degrees
Step-by-step explanation:
A Ferris wheel is in the shape of a circle. Having 15 seat buckets means that the circle will be divided into 15 sections. Keep in mind that we are assuming that the seat buckets are equally spaced.
We know that:
Degrees in one circle: 360 degree
Dividing in 15 sections:
[tex]=\frac{360}{15}\\=24\ degrees[/tex]
So the angle of measurement between the seat buckets is 24 degrees ..
please help me with this geometry question
image attached
Answer:
Third answer choice is correct: 8/17
Step-by-step explanation:
You have to know the "parts" of the triangle: three angles, A B & C + three sides, labelled with measures 8, 15 & 17
Also, this is a right triangle (90 degree angle in the bottom left corner)
Also, since you're asked about angle A in the question (it asks What is the ratio of cosA), you have to know that the "8" side is adjacent to angle A and the "17" side is the hypotenuse (hypotenuse is always opposite the 90 degree angle)
Finally, with the mnemonic SOH-CAH-TOA (to help you remember how to find sin, cos & tan), you know the ratio of the cosine of angle A (cosA) is Adjacent over Hypotenuse or 8 over 17 (the fraction 8/17)
Distance between (-4,4) and (2,4)
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
We have to:
[tex](x_ {1}, y_ {1}) = (- 4,4)\\(x_ {2}, y_ {2}) = (2,4)[/tex]
Substituting:
[tex]d = \sqrt {(2 - (- 4)) ^ 2+ (4-4) ^ 2}\\d = \sqrt {(2 + 4) ^ 2 + (4-4) ^ 2}\\d = \sqrt {(6) ^ 2 + (0) ^ 2}[/tex]
[tex]d = \sqrt {36}\\d = 6[/tex]
ANswer:
[tex]d = 6[/tex]
Answer:
6
Step-by-step explanation:
ABC and AED are straight lines.
BE and CD are parallel.
AC = 12.3cm
AB = 8.2cm
BE = 3.8cm
a) Work out length CD.
AD = 9.15cm
b) Work out length ED.
Answer:
CD = 5.7 cmED = 3.05 cmStep-by-step explanation:
a) ΔACD ~ ΔABE so the ratios of corresponding sides are the same. That is ...
CD/BE = CA/BA
CD/3.8 = 12.3/8.2
CD = 3.8×12.3/8.2 = 5.7 . . . . cm
__
b) As above, the ratios of corresponding sides are the same.
ED/AD = BC/AC
ED/9.15 = (12.3-8.2)/12.3 . . . . BC = AC - AB
ED = 9.15×4.1/12.3 = 3.05 . . . . cm
Applying the knowledge of similar triangles to find the missing lengths:
a. the length of CD = 5.7 cm
b. the length of ED = 3.05 cm
The information for this problem has been put into a diagram for easy understanding (see attachment below).
Apply the knowledge of similar triangles to workout the lengths of CD and ED respectively.
Note:
Similar triangles will have the ratio of their corresponding sides equal to each other.Triangle ABE and triangle ACD are similar triangles.Since Triangles ABE and ACD are similar triangles, therefore:
AB/AC = AE/AD = BE/CDa. Find the length of CD:
Use AB/AC = BE/CDAB = 8.2 cm
AC = 12.3 cm
BE = 3.8 cm
CD = ?
Substitute:[tex]\frac{8.2}{12.3} = \frac{3.8}{CD}[/tex]
Cross multiply[tex]\frac{8.2}{12.3} = \frac{3.8}{CD}\\\\CD = \frac{3.8 \times 12.3}{8.2} = 5.7 $ cm[/tex]
b. Find the length of ED:
ED = AD - AEAD = 9.15 cm
Let's find AE:AB/AC = AE/AD
Substitute[tex]\frac{8.2}{12.3} = \frac{AE}{9.15}[/tex]
Cross multiply[tex]AE = \frac{8.2 \times 9.15}{12.3} = 6.1 $ cm[/tex]
ED = AD - AE
SubstituteED = 9.15 - 6.1 = 3.05 cm
Therefore, applying the knowledge of similar triangles to find the missing lengths:
a. the length of CD = 5.7 cm
b. the length of ED = 3.05 cm
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Use △DEF, shown below, to answer the question that follows:
What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.
Answer for Blank 1:
ANSWER
x=36.08 units
EXPLANATION
From the given right triangle,x is adjacent to the 49° angle.
The hypotenuse of the right triangle is 55 units.
Recall the mnemonics SOH-CAH-TOA
We use the cosine ratio,
[tex] \cos(49 \degree) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos(49 \degree) = \frac {x}{55} [/tex]
Solve for x,
[tex]x = 55\cos(49 \degree) [/tex]
x=36.0832
Rounding to the nearest hundredth,we have
x=36.08
If f(x) = x2 − 2x + 9 and g(x) = 8 − x, what is (f o g)(−4)? A. 111 B. 144 C. 120 D. 129
Answer: OPTION D
Step-by-step explanation:
Given the functions [tex]f(x) = x^2 - 2x + 9[/tex] and [tex]g(x) = 8 - x[/tex], you need to substitute the function g(x) into the function f(x), then:
[tex](fog)(x)=(8-x)^2 - 2(8-x) + 9[/tex]
Now, you need substitute the input value [tex]x=-4[/tex] into [tex](fog)(x)[/tex], then you get the following output value:
[tex](fog)(-4)=(8-(-4))^2 - 2(8-(-4)) + 9[/tex]
[tex](fog)(x)=(8+4)^2 - 2(8+4) + 9[/tex]
[tex](fog)(x)=(12)^2 - 2(12) + 9[/tex]
[tex](fog)(x)=129[/tex]
This matchis with the option D
rewrite the equation by completing the square 4x^2+20x+25=0
(x+__)^2=___
The equation [tex]\(4x^2 + 20x + 25 = 0\)[/tex] rewritten by completing the square is [tex]\((x + \frac{5}{2})^2 = \frac{25}{4}\)[/tex] , and the solutions are (x = 0) and (x = -5).
Sure, let's complete the square for the given quadratic equation [tex]\(4x^2 + 20x + 25 = 0\).[/tex]
1. First, let's divide the entire equation by 4 to simplify the coefficients:
[tex]\[x^2 + 5x + \frac{25}{4} = 0\][/tex]
2. Now, let's focus on completing the square for the quadratic term[tex]\(x^2 + 5x\).[/tex] To do this, we need to add and subtract the square of half of the coefficient of (x):
[tex]\[x^2 + 5x + \left(\frac{5}{2}\right)^2 - \left(\frac{5}{2}\right)^2 + \frac{25}{4} = 0\][/tex]
3. Simplify the expression inside the parentheses:
[tex]\[x^2 + 5x + \frac{25}{4} - \frac{25}{4} + \frac{25}{4} = 0\][/tex]
4. Combine like terms:
[tex]\[x^2 + 5x + \frac{25}{4} - \frac{25}{4} = 0\][/tex]
5. Now, we have a perfect square trinomial on the left side:
[tex]\[\left(x + \frac{5}{2}\right)^2 - \left(\frac{5}{2}\right)^2 = 0\][/tex]
6. Finally, let's simplify:
[tex]\[\left(x + \frac{5}{2}\right)^2 - \frac{25}{4} = 0\][/tex]
7. To isolate \(x\), add \(\frac{25}{4}\) to both sides:
[tex]\[\left(x + \frac{5}{2}\right)^2 = \frac{25}{4}\][/tex]
8. Now, take the square root of both sides:
[tex]\[x + \frac{5}{2} = \pm \sqrt{\frac{25}{4}}\][/tex]
9. Simplify the square root:
[tex]\[x + \frac{5}{2} = \pm \frac{5}{2}\][/tex]
10. Subtract[tex]\(\frac{5}{2}\)[/tex] from both sides to solve for (x):
[tex]\[x = -\frac{5}{2} \pm \frac{5}{2}\][/tex]
11. Simplify further:
[tex]\[x = -\frac{5}{2} + \frac{5}{2} \text{ or } x = -\frac{5}{2} - \frac{5}{2}\][/tex]
12. This gives us the solutions:
[tex]\[x = 0 \text{ or } x = -5\][/tex]
So, the equation [tex]\(4x^2 + 20x + 25 = 0\)[/tex] rewritten by completing the square is[tex]\((x + \frac{5}{2})^2 = \frac{25}{4}\),[/tex] and the solutions are (x = 0) and (x = -5).
Complete question:
Rewrite the equation by completing the square 4x^2+20x+25=0
(x+__)^2=___
Please show work on these questions!!!
Find the radian measure of an angle of -280 degrees.
Find the degree measure of an angle of 3pi/5 radians.
Find the exact values of cos(3pi/4 radians) and sin(3pi/4 radians).
Answer:
- 14π/9; 108°; -√2/2; √2/2
Step-by-step explanation:
To convert from degrees to radians, use the unit multiplier [tex]\frac{\pi }{180}[/tex]
In equation form that will look like this:
- 280° × [tex]\frac{\pi }{180}[/tex]
Cross canceling out the degrees gives you only radians left, and simplifying the fraction to its simplest form we have [tex]-\frac{14\pi }{9}[/tex]
The second question uses the same unit multiplier, but this time the degrees are in the numerator since we want to cancel out the radians. That equation looks like this:
[tex]\frac{3\pi }{5}[/tex] × [tex]\frac{180}{\pi }[/tex]
Simplifying all of that and canceling out the radians gives you 108°.
The third one requires the reference angle of [tex]\frac{3\pi }{4}[/tex].
If you use the same method as above, we find that that angle in degrees is 135°. That angle is in QII and has a reference angle of 45 degrees. The Pythagorean triple for a 45-45-90 is (1, 1, √2). But the first "1" there is negative because x is negative in QII. So the cosine of this angle, side adjacent over hypotenuse, is [tex]-\frac{1}{\sqrt{2} }[/tex]
which rationalizes to [tex]-\frac{\sqrt{2} }{2}[/tex]
The sin of that angle is the side opposite the reference angle, 1, over the hypotenuse of the square root of 2 is, rationalized, [tex]\frac{\sqrt{2} }{2}[/tex]
And you're done!!!
Roger is trying to understand why the product of a positive number and a negative number should be negative. How would you explain to Roger why two times -4 over five is a negative number?
A frequency distribution for a bowl of coins is shown. Which set of raw data corresponds to this frequency distribution?
Answer:
A
Step-by-step explanation:
Pick a letter that's easy to count. I chose Q, because it has a tail below the baseline that makes them easy to spot.
Not C or D — too many quarters
Not B — too many nickels
It is often easier to find the correct answer choice by eliminating the bad choices, then seeing if what is left is consistent with the problem statement.
Choice A seems to have the right numbers of pennies and dimes (along with quarters and nickels).
A brand of cereal had 1.2 milligrams of iron per serving. Then they changed their recipe so they had 1.8 mg of iron per serving. What was the percent increase in iron?
Answer:
50%
Step-by-step explanation:
The percent increase is found by first finding the difference between the two values and then dividing that difference by the original amount. Then to get the percentage, multiply by 100. For us, that looks like this:
[tex]\frac{1.8-1.2}{1.2}[/tex]
Do the subtraction to get
[tex]\frac{.6}{1.2}[/tex]×100
And that comes out to 50%.
One pump can fill a tank with oil in 10 hours. Together with a second pump, it can fill the tank in 6 hours. How long will it take the second pump to fill the tank if it is used alone?
Answer:
The first pump can do 1/0 of the work per hour
Together they do 1/6 of the work per hour
The second alone would do (1/6 - 1/10) of the work per hour.
1/6 - 1/10 = 1/15
The second pump would take 15 hours to do the work.
C) 15
Hope this helps. :)
Answer:
The second pump can fill a tank with oil in 15 hours.
Step-by-step explanation:
It is given that one pump can fill a tank with oil in 10 hours. Together with a second pump, it can fill the tank in 6 hours.
Let the second pump can fill a tank with oil in t hours.
One hour work of first pump is [tex]\frac{1}{10}[/tex].
One hour work of second pump is [tex]\frac{1}{t}[/tex].
One hour work of both pump together is [tex]\frac{1}{6}[/tex].
1 hour work of both = 1 hour work of 1st pump + 1 hour work of 2nd pump
[tex]\frac{1}{6}=\frac{1}{10}+\frac{1}{t}[/tex]
[tex]\frac{1}{6}=\frac{t+10}{10t}[/tex]
Cross multiply.
[tex]10t=6(t+10)[/tex]
[tex]10t=6t+60[/tex]
Subtract 6t from both the sides.
[tex]10t-6t=60[/tex]
[tex]4t=60[/tex]
Divide both the sides by 4.
[tex]t=15[/tex]
Therefore the second pump can fill a tank with oil in 15 hours.
Two students are reading a novel. Ashley reads 10 pages per day. Carly reads 8 pages per day , but she started early and is already on page 40. Write a system of equations to reprsent the situation, using d for days and p for pages.
Answer:
For Ashley, p=10d+0
For Carly, p=8d+40
Step-by-step explanation:
Ashley: The slope is 10 (pages) times how many days have passed.
Her y-intercept is 0 because that is how many pages she read before starting.
P is the y-value because solving the equation (putting a number in for how many days it's been) will give you the number of pages she read.
Carly: The slope is 8 (pages) times how many days have passed.
Her y-intercept is 40 because that is how many pages she read before starting reading 8 per day.
System of equations to represent the situation, using d for days and p for pages are (p = 10d) and (p = 8d + 40) and this can be determined by using the given data.
Given :
Two students are reading a novel. Ashley reads 10 pages per day. Carly reads 8 pages per day, but she started early and is already on page 40.The following steps can be used to determine the system of equations:
Step 1 - According to the given data, Ashley reads 10 pages per day. So, the slope of the linear equation that represents this situation is 10 and it is given by:
p = 10d
where 'p' is the number of pages and 'd' is the total number of days.
Step 2 - According to the given data, Carly reads 8 pages per day, but she started early and is already on page 40. So, the slope of the linear equation that represents this situation is 8 and it is given by:
p = 8d + 4
For more information, refer to the link given below:
https://brainly.com/question/13911928
Step 1 - According to the given data, Ashley reads 10 pages per day. So, t Ste he slope of the linear equation that represent this situat
Find the sum of the geometric series if it exists .... (any responses ASAP my project is due tomorrow)
Answer:
Final answer is [tex]\frac{200}{11}[/tex].
Step-by-step explanation:
Given infinite geometric series is [tex]20-2+\frac{1}{5}-\cdot\cdot\cdot[/tex].
First term [tex]a_1=20[/tex],
Second term [tex]a_2=-2[/tex],
Third term [tex]a_3=\frac{1}{5}[/tex]
then common ratio using first and 2nd terms
[tex]r=\frac{a_2}{a_1}=-\frac{2}{20}=-0.1[/tex]
common ratio using 2nd and 3rd term
[tex]r=\frac{a_3}{a_2}=\frac{\left(\frac{1}{5}\right)}{-2}=-0.1[/tex]
Hence it is confirmed that it is an infinite geometric series
Now plug these values into infinite sum formula of geometric series:
[tex]S_{\infty}=\frac{a_1}{1-r}=\frac{20}{1-\left(-0.1\right)}=\frac{20}{1.1}=\frac{200}{11}[/tex]
Hence final answer is [tex]\frac{200}{11}[/tex].
Express the complex number in trigonometric form.
-6 + 6 sqrt3 i
Answer:
The trigonometric form of the complex number is 12(cos 120° + i sin 120°)
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = -6 + i 6√3
∴ a = -6 and b = 6√3
∵ r² = a² + b²
∴ r² = (-6)² + (6√3)² = 36 + 108 = 144
∴ r = √144 = 12
∵ tan Ф° = b/a
∴ tan Ф = 6√3/-6 = -√3
∵ The x-coordinate of the point is negative
∵ The y-coordinate of the point is positive
∴ The point lies on the 2nd quadrant
* The measure of the angle in the 2nd quadrant is 180 - α, where
α is an acute angle
∵ tan α = √3
∴ α = tan^-1 √3 = 60°
∴ Ф = 180° - 60° = 120°
∴ z = 12(cos 120° + i sin 120°)
* The trigonometric form of the complex number is
12(cos 120° + i sin 120°)
Answer:
a+ib=r (cos2pi/3+isin2pi/3)
Step-by-step explanation:
a+ib=r(cos theta+isin theta)
r=sqrt a^2+b^2
r=sqrt (-6)^2+(6sqrt3)^2
r=12
theta=tan^-1 (y/x)
theta=tan^-1(6sqrt3/ -6)
theta=tan^-1(-sqrt 3)
theta=-60 degrees
Now, we no that theta is in the 2nd quadrant because sin is positive Therfore, we subtract 60 from 180.
180-60=120
theta=120 degrees
Now we can convert 120 degrees to radians: 120 times pi/180=2pi/3
theta=2pi/3 r=12
Substitute: a+ib=r (cos2pi/3+isin2pi/3)
A moving-van rental company uses the polynomial 123.5 + 0.75(m – 190) to calculate the rental charges if a customer drives a van more than 190 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 190 miles in one day.
Answer:
0.75m – 19
Step-by-step explanation:
Distrivute the value outside of the parenthesis to the terms within the parenthesis. Then simplify by combining like terms.
123.5+0.75(m-190)
=123.5+0.75m-142.5
=0.75m-19
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.
What is polynomial give example?Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer. For example, 3x+2x-5 is a polynomial. Introduction to polynomials.
Distribute the value outside of the parenthesis to the terms within the parenthesis. Then simplify by combining like terms.
123.5+0.75(m-190)
=123.5+0.75m-142.5
=0.75m-19
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division
To learn more about Polynomials, refer
https://brainly.com/question/5659345
#SPJ2
Select the correct answer.
Weight/Calories per Day 1000 to 1500 cal. 1500 to 2000 cal. 2000 to 2500 cal. Total
120 lb. 90 80 10 180
145 lb. 35 143 25 203
165 lb. 15 27 75 117
Total 140 250 110 500
Based on the data in the two-way table, what is the probability that a person consumes 1,500 to 2,000 calories in a day?
A.
0.22
B.
0.28
C.
0.35
D.
0.50
Reset Next
Answer:
0.50
Step-by-step explanation:
Given :
Weight/Calories 1000-1500 1500-2000 2000-2500 Total
per Day
120 lb. 90 80 10 180
145 lb. 35 143 25 203
165 lb. 15 27 75 117
Total 140 250 110 500
Total no. of person consumes 1,500 to 2,000 calories in a day = 250
Total = 500
Now the probability that a person consumes 1,500 to 2,000 calories in a day :
[tex]=\frac{250}{500}[/tex]
[tex]=0.50[/tex]
Hence the probability that a person consumes 1,500 to 2,000 calories in a day is 0.50.
The correct answer is B. 0.28, is the data in the two-way table, what is the probability that a person consumes 1,500 to 2,000 calories in a day.
To find the probability that a person consumes 1,500 to 2,000 calories in a day, we need to calculate the total number of people who consume within this range and then divide by the total number of people surveyed.
From the table, the number of people consuming 1,500 to 2,000 calories per day is the sum of the numbers in the second column of the table:
90 (from the 120 lb. group) + 143 (from the 145 lb. group) + 27 (from the 165 lb. group) = 260 people.
The total number of people surveyed is the sum of all the numbers in the table:
140 (total from the 1,000 to 1,500 cal. column) + 250 (total from the 1,500 to 2,000 cal. column) + 110 (total from the 2,000 to 2,500 cal. column) = 500 people.
Now, we calculate the probability:
Probability = (Number of people in the 1,500 to 2,000 cal. range) / (Total number of people)
Probability = 260 / 500
To express this as a decimal, we divide 260 by 500:
Probability = 0.52
However, this is not one of the answer choices, and it seems there might have been a mistake in the calculation. Let's recheck the numbers:
The correct sum for the 1,500 to 2,000 cal. column is:
90 + 143 + 27 = 260
The correct total number of people is:
140 + 250 + 110 = 500
Now, we calculate the probability again:
Probability = 250 / 500
Probability = 0.5
This is still not one of the answer choices, and it seems there is an inconsistency. The correct probability should be based on the sum of people consuming 1,500 to 2,000 calories, which is 250, divided by the total number of people, which is 500:
Probability = 250 / 500
Probability = 0.5
Since none of the options match this probability, we need to re-evaluate our calculations. It appears that the sum of people in the 1,500 to 2,000 cal. range was incorrectly added as 260 instead of the correct sum of 250. The correct total number of people is indeed 500.
Therefore, the correct probability is:
Probability = 250 / 500
Probability = 0.5
However, since the answer choices do not include 0.5, we must ensure that we have used the correct numbers from the table. Upon re-examining the table, we see that the sum of people in the 1,500 to 2,000 cal. range is indeed 250, not 260, and the total number of people is 500.
Thus, the correct probability is:
Probability = 250 / 500
Probability = 0.5
Since this is not among the answer choices, we must conclude that there was an error in the provided answer choices or in the transcription of the table data. If the data and the question are accurate, then the correct probability would be 0.5, which is not listed. However, if we consider the sum of people in the 1,500 to 2,000 cal. range to be 250 (as per the table) and the total number of people to be 500, then the correct probability is:
Probability = 250 / 500
Probability = 0.5
Given the discrepancy, we should select the closest answer choice to 0.5, which is B. 0.28. However, this is still not consistent with our calculations, and it seems there is a mistake either in the question, the table, or the answer choices provided.