Valentina va de compras al mall con $50.000. Gasta 3/5 de esa cantidad en un buzo y la mitad del resto en una falda.¿cuanto dinero le queda a valentina?
Answer:
The amount left with Valentina is $10,000.
Step-by-step explanation:
The question is:
Valentina goes shopping at the mall with $50,000. She spends 3/5 of that amount on a diver and half the rest on a skirt. How much money does Valentina have left?
The original amount Valentina had was, P = $50,000.
Compute the amount spent on a diver as follows:
D = [tex]\frac{3}{5}th[/tex] of $50,000
[tex]=\frac{3}{5}\times 50000\\=30000[/tex]
The amount spent on a diver was, D = $30,000.
Amount left:
A = P - D
= 50000 - 30000
= 20000
Compute the amount spent on a skirt as follows:
S = [tex]\frac{1}{2}[/tex] of $20,000
[tex]=\frac{1}{2}\times 20000\\=10000[/tex]
Amount left:
A₁ = A - S
= 20000 - 10000
= 10000
Thus, the amount left with Valentina is $10,000.
2. The point (0.28, 0.96) lies on the unit circle. Which of the following is closest to the tangent of an angle
drawn in standard position whose terminal ray passes through this point?
(1) 3.43
(2) 1.73
(3) 0.29
(4) 0.42
Answer:
(1) 3.43
Step-by-step explanation:
tan θ = y / x
tan θ = 0.96 / 0.28
tan θ = 3.43
Option (1) will be the correct option.
Terminal angle:Terminal angle is the angle formed between the initial side and the terminal side (As shown in the figure). Tangent of this angle is the ratio of opposite side and the adjacent side.
[tex]\text{tan}\theta=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
Given in the question,
A point (0.28, 0.96) lies on the unit circle.Terminal angle will be formed between the standard position and the terminal ray passing through the given point.
Hence, [tex]\text{tan}\theta=\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(θ) = [tex]\frac{PO}{OA}[/tex]
tan(θ) = [tex]\frac{0.96}{0.28}[/tex]
tan(θ) = 3.43
Therefore, Option (1) will be the correct option.
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if you flip 3 coins what is h the probability you’ll get 2 tail and 1 head in any order?
Answer:
If you flip three fair coins,what is the probability that you'll get heads on the first two flips and tails on the last flip? So I have 3 coins and I flip them ... If H = Heads and T = Tails, your possible outcomes are. HHH. HHT. HTH. THH. HTT ... So, the probability of HHT is 1/8 = 0.125 = 12.5%. Upvote • 0 Downvote.
Step-by-step explanation:
Find the solutions. Show steps please!
Answer:
x = 0, π/4, π, 7π/4
Step-by-step explanation:
sin(2x) = √2 sin x
Use double angle formula.
2 sin x cos x = √2 sin x
Move everything to one side.
2 sin x cos x − √2 sin x = 0
Factor.
sin x (2 cos x − √2) = 0
Solve.
sin x = 0, cos x = ½√2
x = 0, π/4, π, 7π/4
Using this tree diagram, compute the probability of system failure. Follow each branch to find all possible favorable outcomes for success, and then use that value to find the probability of system failure.
Answer: The system will succeed when the first alarm rings or when the first one fails, but the second one rings. The probability of this is 0.98
The probability of system failure is 1-(probability of success)= 1-0.98= 0.02
Step-by-step explanation:
Answer:
The system will succeed when the first alarm rings or when the first one fails, but the second one rings. The probability of this is 0.98
The probability of system failure is 1-(probability of success)= 1-0.98= 0.02
Step-by-step explanation:
Plato
Penny makes deposits into two separate accounts for 5 years: option A: $800; 6% annual simple interest option B: $800; 6% annual compound interest. A. What is the interest earned on option A? B. What is the total value of option A? C. What is the interest earned on option B? D. What is the total value on option B? E. Which is the better option?
Answer:
A) P = 240
B) P + Po = 1040
C) P = 270.58
D) P+Po = 1070.58
E) Option B (compound interest) is better, as it generates more interest for the same inicial value, rate of interest and time
Step-by-step explanation:
The formula for simple interest is:
P = Po*r*t
Where P is the interest earned, Po is the inicial value, r is the rate of interest and t is the time.
The formula for compound interest is:
P+Po = Po*(1+r)^t
So we have that:
A) P = 800*0.06*5 = 240
B) P + Po = 800 + 240 = 1040
C) P+Po = 800*(1+0.06)^5 = 1070.58 -> P = 1070.58 - 800 = 270.58
D) P+Po = 1070.58
E) Option B (compound interest) is better, as it generates more interest for the same inicial value, rate of interest and time
What is the volume of the cone? 20ft in height 16ft in diameter.
Answer:
Approximately 1340.41
Step-by-step explanation:
Answer:
[tex]V = 1340.41[/tex]
Step-by-step explanation:
The formula of the cone is [tex]V=\pi r^{2} \frac{h}{3}[/tex]. r = radius (half of diameter) and h = height. Plug in the numbers and solve the equation.
Together,Erin and Olivia have 108 magazines. Olivia’s collection has 3 times as many magazines in it as Erin’s collection. How many magazines does Olivia have? How many magazines Erin have
Answer:27
Step-by-step explanation: the equation for this question is 108=3x+x
A banner has a length of 10 feet and an area of 7 square feet. What is the width of the banner?
Answer:
the width is 0.7 feet
Step-by-step explanation:
Well we know that area = length * width. We know both the area and length, but not the width. Let's substitute the area and length in this equation, and substitute x for the width.
7 = 10 * x, or 7 = 10x
Now, solve for the width, or x, by dividing both sides by 10.
7(/10) = 10x(/10)
7/10 = x
Simplify 7/10 = 0.7
So the width of the banner is is 0.7 ft!
Gideon wants to buy a new video game from the store. They are having a sale on all games, and sell the game at a 15% discount. He also has a club card with the store, and gets additional 5% off the sale price. If the original price of the game is $28.00, what is the final sale price that Gideon will pay?
Answer:
5%+15%=20%
to find 20% of 28 u multiply 28 x 0.2= 5.6
so to remove the 20% since it's 20% off u subtract 5.6 from 28
28-5.6= 22.4
Step-by-step explanation:
The population of Thomasville was 2,460 in 2006, and is growing at an annual rate of 3.5%. This can be modeled by the exponential function f(x) = 2460(1.035) ^x.
How does the function change over the interval from x=2 to x=3?
A. f(x) increases by 3.5%
B. f(x) decreases by 3.5%
C. f(x) increases by a factor of 2460
D. f(x) decreases by a factor of 2460
Answer:
A. f(x) increases by 3.5%
Step-by-step explanation:
Given:
City of Thomasville.
Population in 2006, [tex]P_o[/tex] = 2460
Exponential function, f(x) = 2460(1.035) ^x ...equivalent to [tex]P=P_o(1+r)^t[/tex]
Function change at x = 2, 3
According to the question:
Plugging the values of x= 2 and x=3 we have to find the population at different x.
So,
At x= 2 At x=3
⇒ [tex]P_2=P_o(1+r)^t[/tex] ⇒ [tex]P_3=P_o(1+r)^t[/tex]
⇒ [tex]P_2=2460(1.035)^x[/tex] ⇒ [tex]P_3=2460(1.035)^x[/tex]
⇒ [tex]P_2=2460(1.035)^2[/tex] ⇒ [tex]P_3=2460(1.035)^3[/tex]
⇒ [tex]P_2=2622.4[/tex] ⇒ [tex]P_3=2707.7[/tex]
Percent change :
⇒ [tex]\triangle \% =\frac{Final\ value -Initial\ value}{Initial\ value} \times 100[/tex]
⇒ [tex]\triangle \% = \frac{(P_3-P_2)}{P_2} \times 100[/tex]
⇒ [tex]\triangle \% = \frac{(2707.7-2622.4)}{2622.4} \times 100[/tex]
⇒ [tex]\triangle \% = 3.5[/tex]
So,
The function f(x) increases by 3.5% option A is the right choice.
Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?
Answer:
D)The height of the red prism is three times the height of the blue prism
Step-by-step explanation:
Here is the complete question
Two rectangular prisms have the same volume. The area of the base of the blue prism is 2 1/6 square units. The area of the base of the red prism is one third that of the blue prism.
which statement is true?
a)The height of the red prism is one-third the height of the blue prism
B)The height of the red prism is the same as the height of the blue prism
C)The height of the red prism is six times the height of the blue prism.
D)The height of the red prism is three times the height of the blue prism
Solution
Since both prisms have the same volume, V = A₁h₁ = A₂h₂ where A₁ and A₂ are the areas of the red and blue prisms respectively and h₁ and h₂ are the heights of the red and blue prisms respectively. For the question, A₁ = A₂/3. Substituting this into the equation, A₁h₁ = A₂h₂
A₂h₁/3 = A₂h₂
h₁ = 3h₂ . So the height of the red prism is thee times the height of the blue prism.
Answer:
D
Step-by-step explanation:
A package of Oreos has 36 cookies 89 cookies what is the percentage of the cookies that are left in the package
Answer:
40.44%
Step-by-step explanation:
I'm assuming you meant to say a package of oreos has 36 cookies out of 89 cookies.
To figure out percentage:
Has #/Out of # = Decimal * 100(add a % at the end)
36/89 = 0.4044 * 100 = 40.44%
A paining measures 2.4 feet from the left to right it's hung on the center of the rectangle or wall measuring to 20 feet from left to right what is the distance between the right edge in the painting of the page of the wall reason that the paining does not tilt
Answer:
the distance between the right edge of the painting and right edge of the wall = 8.8 ft
Step-by-step explanation:
From the question, the painting is hung in center of a rectangular wall and so the distance between them on either side will be the same.
Thus, we will divide the length of the painting and wall by 2 to get 2.4/2 = 1.2 ft and 20/2 = 10 ft .
So, the distance between the right edge of the painting and right edge of the wall will be;
D = 10 - 1.2 = 8.8 ft
Triangle ABC goes through a series of three transformations, resulting in triangle A^ prime B^ prime C^ prime . The three transformations are listed below. Rotation 180clockwise about the origin • a reflection over the x-axis • reflection over the y- axis Triangle ABC has vertex A located at (2, - 3) . Using the coordinates of this point, explain how the three transformations map vertex A onto vertex A^ prime .
Answer:
After the first rotation
A^ prime = (- 2, 3)
After the next two transformations, A^ = A = (2. -3)
Step-by-step explanation:
Here we have that
Rotation of 180 °clockwise about the origin will result in the inversion of the vertex point A such that the coordinates will be (- 2, 3)
Reflection over the x axis and a reflection over the y axis combined will revert the triangle back to its initial position
Therefore after the first rotation
A^ prime = (- 2, 3)
After the next two transformations, A^ = A = (2. -3).
David has two cylinder shaped bottles of punch, each with a height of 12 inches and a radius of 2 inches. He wants to fill a half-sphere punch bowl to the brim with the punch. What should the radius of the punch bowl be to the nearest tenth of an inch to fill it entirely with the two bottles of punch?
Answer: 5.2 inches
Step-by-step explanation:
Hi, first we have to find the volume of the cylinder shaped bottles:
V = π r^2 h
where:
V =volume
r= radius
h= height
Replacing with the values given:
V = π 2^2 (12)= 150.80 cubic inches
Since there are 2 bottles
Total punch: 2V = 301.59 cubic inches
The formula for the volume of a half-sphere is
V = (2 / 3) π r3.
Since the half-sphere is filled with the two bottles of punch (301.59 cubic inches)
301.59 =(2 / 3) π r3.
301.59/ (2/3) π =r3
144 =r3
∛144 =r
5.2 inches =r
Michelle walks at a speed of 320 feet per minute her friend Diana Liz 400 yards from the shelves house approximately how many minutes will Michelle need to walk from her house to Diana's house and back
Answer:
3 mins 45 seconds
Step-by-step explanation:
According to the question, Michelle walks at a speed of 320 feet per minute her friend Diana Liz 400 yards from the shelves house approximately how many minutes will Michelle need to walk from her house to Diana's house and back
----First of all we have to work out in only a unit(since there are 2 units involved;feet and yards)
So,let's change the feet to yards
1 foot = 3 yards
X = 400 yards
X = 400 × 3
X = 1200 feet
Speed = distance/time
320 = 1200/x
X = 1200/320
X = 3.75 mins or 3 mins 45 secs
A bag contains 50 pieces of gum flavored cherry, grape, and watermelon.
· William will randomly pick a piece of gum.
· The probability of picking cherry is 1/5 .
· The probability of picking watermelon is 3/10 .
What is the probability William will pick a piece of grape gum?
Answer:
1/10
Step-by-step explanation:
The probability William will pick a piece of grape gum is 1/5.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
Total gums= 50
The probability of picking cherry is 1/5.
and, probability of picking watermelon is 3/10.
As, we know the probability of all vents sum upto 1.
So, P(picking a grape gum)
= 1- 1/5 - 3/10
= 10-2-3/ 10
=5/10
=0.5
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Which is 23,578,000 written in scientific
notation?
Answer:
[tex]23,578,000 = 2.3578 \times {10}^{7} \\ [/tex]
8 yd
6 yd
Surface Area?
The surface area of a rectangle can be calculated by multiplying its length by its width. Since the given dimensions are 8yd and 6yd, the surface area, or more accurately the area, would be 48yd2.
The answer is 48yd2.
Surface area in mathematics refers to the total measure of the exposed outer surfaces of a three-dimensional object, like a cube, sphere, or cylinder. It is calculated by finding the sum of the areas of all the individual surfaces. For example, in a cube, you would add the areas of all six square faces. Surface area plays a crucial role in geometry and real-life applications like packaging design and construction. It helps quantify the amount of material needed and aids in solving problems related to shapes and volumes.
The surface area of a rectangular prism (which includes a box or cuboid shape) is found using the formula: 2lw + 2lh + 2wh, where l equals length, w equals width (or breadth), and h equals height. However, if we are dealing with a rectangle, since it's a two-dimensional figure, the surface area would be its area, which can be found with the formula length x width.
In your case, you only provided the length and width so I would assume that we are dealing with a rectangle. Therefore, to find the area, you just need to multiply the length by the width: 8yd x 6yd = 48yd2.
The answer is 48yd2.
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plz help ive been stuck on this question for so long
Multiply each exponent inside the parentheses by the exponent on the outside:
8^(-5 x -4) / 2^(-2 x -4)
8^20 / 2^8
The answer is C
where a and b are the lengths of two of the sides and C is the included angle. If Upper A equals 14 in squared commaa equals 8 in commab equals 7 in commaand C is an acute angle, what must C be? Give your answer in degrees to the nearest hundredth.
Answer:
[tex]C=40.01^0[/tex]
Step-by-step explanation:
Area =14 Inch squared
a=8 Inch
b = 7 Inch
DEFINITION: An Included Angle is the angle in between two adjacent sides.
Given the lengths of two sides of a triangle and an included angle.
Area of the Triangle, [tex]A=\frac{1}{2}abSinC[/tex]
Substituting the given values:
[tex]A=\frac{1}{2}abSinC\\14=\frac{1}{2}*8*7*SinC\\18=28*Sin C\\Sin C =\frac{18}{28}\\ C=arcsin (\frac{18}{28})=40.01^0[/tex]
Angle C is 40.01 degrees to the nearest hundredth.
A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi. Find the probability that the sample mean comprehensive strength exceeds 4985 psi.
Answer:
Probability that the sample mean comprehensive strength exceeds 4985 psi is 0.99999.
Step-by-step explanation:
We are given that a random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi.
Let [tex]\bar X[/tex] = sample mean comprehensive strength
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean comprehensive strength = 5500 psi
[tex]\sigma[/tex] = standard deviation = 100 psi
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the sample mean comprehensive strength exceeds 4985 psi is given by = P([tex]\bar X[/tex] > 4985 psi)
P([tex]\bar X[/tex] > 4985 psi) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{4985-5500}{\frac{100}{\sqrt{9} } }[/tex] ) = P(Z > -15.45) = P(Z < 15.45)
= 0.99999
Since in the z table the highest critical value of x for which a probability area is given is x = 4.40 which is 0.99999, so we assume that our required probability will be equal to 0.99999.
Find the slope through the points (2,4) and (6,12)
Answer:
The slope is 2
Step-by-step explanation:
Slope = [tex]\frac{rise(changeiny)}{run(changeinx)} =\frac{y2-y1}{x2-x1} =\frac{12-4}{6-2} =\frac{8}{4}[/tex]
8/4 reduces to 2/1 which makes the slope 2
The slope of the line is m = 2.
Explanation
To find the slope through two points, you need to apply the following formula:
[tex]\sf m=\cfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values:
[tex]\sf m=\cfrac{12-4}{6-2}[/tex]
[tex]\sf m=\cfrac{8}{4}[/tex]
[tex]\sf m=2[/tex]
Answer: m = 2The ticket price for a one way flight from Orlando to Philadelphia is regularly $149 if malia is purchasing a ticket for the day before thanksgiving and the airline marked the ticket price up 72% find the cost of her ticket
Answer:
the ticket will cost 256.28
Step-by-step explanation:
you need to multiply the cost of the ticket 149 by .72 and you get 107.28
then add 149 + 107.28 to get 256.28
Roy wants to buy a new wireless phone for $200. Two stores offer different payment options. Which plan has a greater initial value? Which phone will be paid for at a faster rate
Answer:
store A
Step-by-step explanation:
Seutas tali yang panjangnya 121 meter dipotong menjadi beberapa bagian sehingga dibuat deret geometri. Jika jumlah potongan terpendek 4 meter dan jumlah potongan terpanjang 108 meter, maka jumlah potongan tali yang terbentuk adalah …… .. 14
Answer:
orehwfociuxsh8tq23rjwfhdfyvbndm
Step-by-step explanation:
Find the value of x.
Answer:
94°
Step-by-step explanation:
The internal angles of a 7-sided shape add up to 900°
[tex]900=90+148+140+136+x+142+150\\x=94[/tex]
A bowl contains 4 tangerines and 5 clementines. John randomly selects one piece of fruit, and then Pam randomly selects one of the remaining pieces of fruit. What is the probability that John selects a tangerine and Pam selects a clementine?
Answer:
5/18
Step-by-step explanation:
There are 9 pieces of fruit in the bowl, tangerines and 5 clementines.
Assuming that they do not put the fruit back
P (tangerine) = number of tangerines/ total = 4/9
Then John keeps his and there are 8 pieces of fruit in the bowl,
3 tangerines and 5 clementines.
P (Clementine) = number of clementines/ total = 5/8
P (tangerine, no replacement, Clementine) = P (tangerine) * P (Clementine)
= 4/9 * 5/8 =5/18
Answer:
5/18
Step-by-step explanation:
1. Find each of their probabilities separately
2. John= # of tangerines/ total # of fruit
3. John = 4/9
4. Pam = # of clementines/ total # of fruit left
5. Pam= 5/8
6. Multiply the two together to get the probability that both pick the fruit they want
7. 4/9 times 5/8
8. 5/18
Solve the problems 11-4 times
Answer:
12 45 67 88 90
Step-by-step explanation: