Please I need your help!
Select each equation that the number 10 to the 3rd power makes true.
6.01 × ⬜ = 601
0.305 × ⬜ = 305
0.54 × ⬜ = 540
0.097 × ⬜ = 970
0.97 × ⬜ = 97
Answers
Related Questions
ayuda porfa nose como se hace :'((((((((((((
esta es la fórmula: y=a(x-h)²+k
Answers
The quadratic function in vertex form is y = (8/9)(x - 5)^2 + 7
Calculating the quadratic function in vertex formThe vertex form of a quadratic function is given by:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola.
In this case, we are given that the vertex is (5, 7), so we can write:
y = a(x - 5)^2 + 7
To find the value of a, we can use one of the points on the parabola.
Let's use the point (2, 15):
15 = a(2 - 5)^2 + 7
8 = 9a
a = 8/9
Substituting this value of a into the equation above, we get:
y = (8/9)(x - 5)^2 + 7
Therefore, the quadratic function in vertex form is y = (8/9)(x - 5)^2 + 7
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An artist buys 2 liters of paint for a project. When he is done with the project, he has 350 milliliters of the paint left over. The paint costs 2¢ per milliliter. How many dollars’ worth of paint does the artist use for the project?
Answers
The artist used a total of $0.33 worth of paint for the project.
The artist purchased 2 liters of paint, which is equivalent to 2,000 milliliters of paint. This amount of paint was used to complete a project, and after the project was finished, there were 350 milliliters of paint left over.
To determine how much paint was used for the project, we subtract the amount of leftover paint from the total amount of paint purchased, which gives us 2,000 - 350 = 1,650 milliliters of paint used for the project.
The cost of the paint is 2 cents per milliliter, which is equivalent to $0.02/100 milliliters or $0.0002 per milliliter. To determine the cost of the paint used for the project, we multiply the amount of paint used by the cost per milliliter.
Therefore, the cost of 1,650 milliliters of paint used for the project can be calculated by multiplying 1,650 milliliters by $0.0002 per milliliter, which gives us $0.33.
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Louise stops at the gift store to buy a souvenir of the statue of liberty. the original height of the statue is 151 ft. if a scale factor of 1in = 20 ft is used to design the souvenir, what is the height of the replica?
Answers
The height of the replica souvenir is approximately 7.55 inches.
To find the height of the replica souvenir of the Statue of Liberty, we'll use the given scale factor of 1 inch = 20 feet. The original height of the statue is 151 feet. Divide the original height by the scale factor:
151 ft / 20 ft/in = 7.55 inches
The height of the replica souvenir is approximately 7.55 inches.
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Charity can make 36 cupcake in 45 minutes. If she continues at this rate, how many cupcakes can she make in 8 hours?
a. 280 cupcakes b. 384 cupcakes c. 360 cupcakes d. 300 cupcakes
Answers
The total number of cupcakes charity can make in 8 hours is 384
The total number of cupcakes she can make in 45 minutes is 36
Cupcakes she can make in 1 minute = 36/45
Cupcakes she can make in 1 minute = 0.8
Cupcakes she can make in 8 hours
We will convert hours into minutes
1 hour = 60 min
8 hour = 8 × 60 min
8 hour = 480 min
Cupcakes she can make in 8 hours that is 480 min = 480 × 0.8
Cupcakes she can make in 8 hours = 384
Total number of cupcakes she can make is 384
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PLEASE ANSWER!!! FOR BRAINLY!!! ASAP!!
A system of linear equations is shown on the graph.
The graph shows a line that passes through negative 10 comma 10, negative 5 comma 9, and 0 comma 8. The graph also shows another line that passes through negative 8 comma 12, negative 5 comma 9, and 0 comma 4.
What is the solution to the system of equations?
A There are infinitely many solutions.
B There is no solution.
C There is one unique solution (−5, 9).
D There is one unique solution (0, 8).
Answers
Answer:
(-1/5)x + 8 = -x + 4
(4/5)x + 8 = 4
(4/5)x = -4
x = -5, so y = 9
C. There is one unique solution (-5, 9).
Refer to the data in exercise 2. should sarah use the mean or the median to show that she exercises for large amounts of time each day? explain
for exercise 2 this is what it says;
last week, sarah spent 34,30,45,30,40,38, and 28 minutes exercising. find the mean, median, and mode. round to the nearest whole number
Answers
The mean is 35 minutes and the median is 34 minutes.
let's first calculate the mean, median, and mode for Sarah's exercise times: 34, 30, 45, 30, 40, 38, and 28 minutes.
Step 1: Calculate the mean
Add up all the values and divide by the total number of values:
(34 + 30 + 45 + 30 + 40 + 38 + 28) / 7 = 245 / 7 = 35 minutes (rounded)
Step 2: Calculate the median
Arrange the values in ascending order: 28, 30, 30, 34, 38, 40, 45
There are 7 values, so the median is the middle value: 34 minutes
Step 3: Calculate the mode
Determine the value(s) that occur most often: 30 minutes (occurs twice)
Now, should Sarah use the mean or the median to show she exercises for large amounts of time each day? The mean is 35 minutes and the median is 34 minutes. Both values are close and represent the central tendency of the data. However, since the mean is slightly higher than the median, Sarah should use the mean (35 minutes) to show she exercises for a larger amount of time each day.
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What is the area of a 125 degree sector for a circle with a radius of 12 m, rounded to the nearest whole number
Answers
The area of the 125 degree sector for a circle with a radius of 12 m is approximately 158 square meters.
To find the area of a 125 degree sector of a circle with a radius of 12 m, we need to use the formula for the area of a sector:
Area of sector = (θ/360) x πr², where θ is the central angle of the sector, r is the radius of the circle, and π is a constant equal to approximately 3.14.
Substituting the given values, we get: Area of sector = (125/360) x π x 12² = (0.3472) x π x 144 = 158.03
Rounding to the nearest whole number, we get the area of the sector as 158 square meters. Therefore, the area of the 125 degree sector for a circle with a radius of 12 m is approximately 158 square meters.
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A store has two large vats of juice
containing a total of 28 gallons of juice.
One-eighth of container A is orange juice.
Three-fourths of container B is orange
juice. Together the two containers hold 11
gallons of orange juice. Which system of
equations can be used to determine a and
b, the total amounts of juice, in gallons, in
containers A and B?
F
H
+
b = 11
a
a + b 28
a + b = 28
320
b = 28
J
+ b = 28
4
a + b = 11
a + b = 11
Answers
The system of equations can be used to determine the gallons of juice in container A and the gallon of juice in container B is A + B = 28 and A + 6B = 88
Total amount of juice in both the vats is 28
Let the first container = A
second container = B
A + B = 28
Orange juice in A = 1/8 of A
Orange juice in B = 3/4 of B
Total orange juice in container A and B = 11
(1/8)A + (3/4)B = 11
A + 6B = 88
Hence the two equations will be A + B = 28 and A + 6B = 88
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coordinate grid by equation y=4 what line would represent a row parallel to it ?
Answers
A row parallel to the line y = 4 on a coordinate grid would be represented by a line with an equation of the form y = c.
How to find a row parallel to y=4 on a coordinate grid?A coordinate grid is a two-dimensional plane consisting of a horizontal x-axis and a vertical y-axis. The point where the x and y-axes intersect is called the origin, and it has coordinates (0, 0).
An equation in the form y = c, where c is a constant, represents a horizontal line parallel to the x-axis. In this case, the equation y = 4 represents a horizontal line that intersects the y-axis at 4, as all points on the line have a y-coordinate of 4.
To find a row parallel to this line, we need to look for another line that also has a constant y-coordinate of 4. One way to represent this line is by the equation y = 4 again, since all points on this line have a y-coordinate of 4.
Alternatively, we can look for an equation in the form y = mx + b, where m is the slope of the line (which is zero for a horizontal line), and b is the y-intercept (which is 4 in this case). Thus, the equation for the row parallel to y = 4 would also be y = 4, since its slope is zero and it intersects the y-axis at y = 4, just like the line y = 4.
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Jamie mixes 2 parts of red paint with 3 parts of blue paint to make purple paint.
He uses 12 cans of blue paint.
How many cans of red paint does he use?
Answers
2(4)=8
answer is 8
The table shows the amount of time, in minutes, it takes to walk a given distance, in miles, along each path. complete the table to show the average walking rate, in miles per hour, for each path. path distance (mi) time (min) walking rate (mph) a 0.5 12 b 1.5 45 с 0.75 15
Answers
The average walking rate for Path A is 2.5 mph, path B's is 2 mph and path C's is 3 mph.
Average walking rate = distance/time
for path A = 0.5/12 = 0.0416 mpm
To convert miles per meter into miles per hour it we will multiply the equation by 60 because 1 hour has 60 min
so, for path A = 0.0416 × 60 = 2.5 mph
Similarly , for path B = (1.5/45) × 60 = 2 mph
For path C = (0.75/15)×60 = 3 mph
Table to show the average walking rate
Path Distance(mi) Time(min) Walking rate (mph)
A 0.5 12 2.5
B 1.5 45 2
C 0.75 15 3
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1. A company is testing a new energy drink. Volunteers are asked to rate their energy one hour
after consuming a beverage. Unknown to them, some volunteers are given the real energy
drink and some are given a placebo-a drink that looks and tastes the same, but does not have
the energy-producing ingredients. Show your work using the following list of random digits to
assign each participant listed either the real drink or the placebo.
69429 86140 11625 87049 23167
Volunteer
Abby
Barry
87524 24575 87254 97801 82231
Callie
Dion
Ernie
Falco
Garrett
Hallie
Indigo
Jaylene
Real or Placebo
2. The local water authority has received complaints of high levels of iron in the drinking water.
They decide to randomly select 20 houses from each subdivision of 100 houses to visit and test
their water. Describe how to use random numbers to select the 20 houses in each division.
3. A couple is willing to have as many children as necessary to have two girls.
a) Describe a simulation that can be performed to estimate the average number of children
required to have two girls.
Answers
- Assign the first five volunteers (Abby, Barry, Callie, Dion, and Ernie) to the first five digits in the list (6, 9, 4, 2, 9).
- If the digit is even, assign the volunteer the real drink; if it is odd, assign the volunteer the placebo.
- Repeat this process for the remaining volunteers (Falco, Garrett, Hallie, Indigo, and Jaylene) using the next five digits in the list (8, 6, 1, 4, 0).
Here is the assignment:
Volunteer | Real or Placebo
----------|----------------
Abby | Real
Barry | Real
Callie | Placebo
Dion | Real
Ernie | Placebo
Falco | Real
Garrett | Real
Hallie | Real
Indigo | Placebo
Jaylene | Placebo
2. To select the 20 houses in each division, we can use the following method:
- Assign each house in the subdivision a number from 01 to 100.
- Use a random number generator to generate 20 random numbers between 01 and 100.
- Visit the houses corresponding to the 20 numbers generated.
Repeat this process for each subdivision.
3. One way to simulate the average number of children required to have two girls is to use the following method:
- Assign a value of 0 to a counter variable.
- Repeat the following steps until two girls are born:
- Use a random number generator to generate a number between 0 and 1.
- If the number is less than 0.5, add 1 to the counter variable (representing a boy); otherwise, add 2 to the counter variable (representing a girl).
- Record the value of the counter variable.
- Repeat this process a large number of times (e.g., 10,000).
- Calculate the average value of the counter variable across all simulations. This will give an estimate of the average number of children required to have two girls.
If two fair dice are rolled, what is the probability that the total showing is either even or less than five? 5.
these are the choices:
a. 5/9
b. 17/36
c. 19/36
d. 11/18
Answers
If two fair dice are rolled, the probability that the total showing is either even or less than five is 17/36. The correct answer is B.
There are 36 possible outcomes when rolling two dice, since each die has 6 possible outcomes.
To find the probability that the total showing is either even or less than five, we can first find the probability that the total showing is even, and then add to that the probability that the total showing is less than five, excluding the outcomes where the total showing is even.
To find the probability that the total showing is even, we can consider the following possibilities:
both dice show even numbers (probability 1/4)
both dice show odd numbers (probability 1/4)
So the probability of rolling an even total is 1/4 + 1/4 = 1/2.
To find the probability that the total showing is less than five, excluding the outcomes where the total showing is even, we can consider the following possibilities:
the two dice show 1 and 1 (probability 1/36)the two dice show 1 and 2 (probability 1/18)the two dice show 2 and 1 (probability 1/18)the two dice show 1 and 3 (probability 1/12)the two dice show 3 and 1 (probability 1/12)the two dice show 2 and 2 (probability 1/9)the two dice show 1 and 4 (probability 1/9)the two dice show 4 and 1 (probability 1/9)the two dice show 3 and 2 (probability 1/6)the two dice show 2 and 3 (probability 1/6)the two dice show 1 and 5 (probability 1/6)the two dice show 5 and 1 (probability 1/6)the two dice show 4 and 2 (probability 1/6)the two dice show 2 and 4 (probability 1/6)So the probability of rolling a total less than five, excluding the outcomes where the total showing is even, is 1/36 + 1/18 + 1/18 + 1/12 + 1/12 + 1/9 + 1/9 + 1/9 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 11/36.
Therefore, the probability that the total showing is either even or less than five is 1/2 + 11/36 = 17/36.
So the correct answer is (b) 17/36.
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What is the volume of the following rectangular prism?
2 units and 7 1/3 units
Answers
The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, we are given the length and width, but not the height. So, we cannot calculate the exact volume without knowing the height.
To find the volume of a rectangular prism, we need to multiply its length, width, and height.
Given:
Length = 2 units
Width = 7 1/3 units
To calculate the volume, we first need to convert the mixed fraction to an improper fraction.
7 1/3 = (7 * 3 + 1) / 3 = 22/3 units.
Now, we can calculate the volume:
Volume = Length * Width * Height
= 2 units * (22/3 units) * Height.
Since the height is not provided, we cannot calculate the exact volume without that information. However, if you provide the height of the rectangular prism, I can help you find the volume by substituting the value into the formula.
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Please answer the question with the image provided.
Answers
Based on the information on the number line, the numbers that represent the percentages are: 42 (100%), 21 (50%), 63 (150%).
How to calculate the number that equals each percentage?To calculate the number that is equivalent to each percentage we must carry out the following procedure: Rule of three. In this case we must take into account that 42 represents 100% of the people.
100% = 42 people100% = ? people100 * 42 / 100 = 42 people100% = 42 people50% = ? people50 * 42 / 100 = 21 people100% = 42 people150% = ? people150 * 42 / 100 = 63 peopleLearn more about rule of three at: https://brainly.com/question/9264846
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Calcula el trabajo realizado al elevar 75cm sobre el piso unas
pesas de 90 kg
Answers
The work done to lift a 90 kg weight by 75 cm is approximately 661.5 joules.
How to calculate work?Para calcular el trabajo realizado al elevar una pesa de 90 kg a una altura de 75 cm sobre el piso, necesitamos conocer la fuerza necesaria para levantar la pesa y la distancia que recorre la pesa para llegar a su altura máxima.
El trabajo se define como la energía necesaria para mover un objeto a través de una distancia determinada, y se calcula como el producto de la fuerza aplicada y la distancia recorrida.
En este caso, la fuerza necesaria para levantar la pesa es igual a su peso, que se calcula como su masa multiplicada por la aceleración debido a la gravedad (9.8 m/s²):
peso = masa x gravedad
= 90 kg x 9.8 m/s²
= 882 N
La distancia que recorre la pesa para elevarse 75 cm (o 0.75 m) es:
distancia = 0.75 m
Por lo tanto, el trabajo realizado al elevar la pesa es:
trabajo = fuerza x distancia
= 882 N x 0.75 m
= 661.5 J
Por lo tanto, se requiere un trabajo de 661.5 J para elevar una pesa de 90 kg a una altura de 75 cm sobre el piso.
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Your answer should be in the form p(x) +k/x+2 where p is a polynomial and k is an integer of x^2 +7x+12/x+2
Answers
p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:
x + 5 + 2 / (x + 2)
To express the given expression x^2 + 7x + 12 / (x + 2) in the form p(x) + k / (x + 2), we will perform polynomial division.
1. Divide the numerator (x^2 + 7x + 12) by the denominator (x + 2):
(x^2 + 7x + 12) ÷ (x + 2)
2. Perform long division:
x + 5
________________
x + 2 | x^2 + 7x + 12
- (x^2 + 2x)
________________
5x + 12
- (5x + 10)
________________
2
3. Write the result:
p(x) + k / (x + 2) = x + 5 + 2 / (x + 2)
So, p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:
x + 5 + 2 / (x + 2)
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➡) Which ratios have a unit rate of 3? Choose ALL that apply. 2 cups : 2 3 cup 3³14 3- cups: 2 cups 4 2 3 cup: 1 cup 1 1 cup: cup 15 K 1 2 cups cup 2 15 2 5 6 1 cups: 22 2 cups
Answers
The ratios that have a unit rate of 3 include the following:
A. 15/2 cups: 2 1/2 cups
C. 2 cups: 2/3 cups
F. 2 1/2 cups: 5/6 cups
What is the unit rate?In Mathematics, the unit rate is sometimes referred to as unit ratio and it can be defined as the quantity of material that is equivalent to a single unit of product or quantity.
15/2 cups : 5/2 cups
15/2 ÷ 5/2 : 5/2 ÷ 5/2
15/2 × 2/5 : 1
3 : 1 (True)
1 cup: 1/4 cups
1 × 4 : 1/4 × 1
4 : 1 (False)
2/3 cups: 1 cup
2/3 × 3/2 : 1 × 3/2
1 : 3/2 (False)
3 3/4 cups: 2 cups
(4 × 3 + 3)/4 : 2
15/4 : 2
15/8 : 2/2
15/8 : 1 (False).
2 cups: 2/3 cups
2 × 3/2 : 2/3 × 3/2
3 : 1 (True).
2 1/2 cups: 5/6 cups
(2 × 2 + 1)/2 : 5/6
5/2 : 5/6
5/2 × 6/5 : 5/6 × 6/5
3 : 1 (True).
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Complete Question:
Which ratios have a unit rate of 3? Choose all that apply.
15/2 cups: 2 1/2 cups
1 cup: 1/4 cups
2/3 cups: 1 cup
3 3/4 cups: 2 cups
2 cups: 2/3 cups
2 1/2 cups: 5/6 cups
Urgenttttt what is true about the series given: 25+5+1+...
the series converges to 31.25 the series diverges .
the series converges to 125
the series does not converge or diverge .
Answers
The statement "the series converges to 31.25" is true about the given series.
Given series is 25 + 5 + 1 + ....
We can clearly see that given series is infinite geometric series.
First term is a=25
common ratio is r = 5/25
= 1/5
We know that the formula of sum of an infinite geometric series is
S = a / (1 - r)
S = 25 / (1 - 1/5)
S = 25/(4/5)
S = (25*5)/4
S = 125/4
S = 31.5
Therefore, the sum of the infinite geometric series is 31.25.
Since, the sum of the series is a finite number, we can say that the series converges.
Therefore, the statement "the series converges to 31.25" is true about the given series.
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Find the values of U and d for an arithmetic sequence with U20 = 100 and U25 = 115.
Answers
The values of U and d for an arithmetic sequence with U20 = 100 and U25 = 115 is U = 43 and d = 3.
The formula for the nth term of an arithmetic sequence: Un = U1 + (n-1)d
We know that U20 = 100 and U25 = 115, so we can set up two equations using the formula above:
U20 = U1 + 19d = 100
U25 = U1 + 24d = 115
We now have two equations with two variables (U1 and d) that we can solve for.
First, we'll isolate U1 in the first equation:
U1 = 100 - 19d
Then we'll substitute this expression for U1 into the second equation and solve for d:
100 - 19d + 24d = 115
5d = 15
d = 3
Substitute d = 3 in the equation, U1 = 100 - 19d
So, U1 = 100 - 19(3) = 43.
Therefore, the values of U and d for the arithmetic sequence are U= 43 and d = 3.
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What is the mean absolute deviation of 10 10 9 8 10 5 6 4 8 4
Answers
The mean absolute deviation of the given data set is approximately 2.16.
To find the mean absolute deviation (MAD), we first need to calculate the mean of the data set:
Mean = (10 + 10 + 9 + 8 + 10 + 5 + 6 + 4 + 8 + 4) / 10 = 7.4
Next, we calculate the absolute deviation of each data point from the mean:
|10 - 7.4| = 2.6
|10 - 7.4| = 2.6
|9 - 7.4| = 1.6
|8 - 7.4| = 0.6
|10 - 7.4| = 2.6
|5 - 7.4| = 2.4
|6 - 7.4| = 1.4
|4 - 7.4| = 3.4
|8 - 7.4| = 0.6
|4 - 7.4| = 3.4
Then, we find the average of these absolute deviations:
MAD = (2.6 + 2.6 + 1.6 + 0.6 + 2.6 + 2.4 + 1.4 + 3.4 + 0.6 + 3.4) / 10 ≈ 2.16
Therefore, the mean absolute deviation of the given data set is approximately 2.16.
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Question
The figure is made up of a rectangle, 2 right triangles and a 3rd triangle.
What is the area of the figure?
Responses
46 in2
136 in2
34 in, 2
52 in2
Answers
The area of the polygon composed of rectangles and triangle is 52 in²
What is area?Area is the amount of space occupied by a two dimensional shape or object.
For the first right triangle:
base = 2 in, height = 6 in
Area of first right triangle = 1/2 * base * height = 0.5 * 2 in * 6 in = 6 in²
For the second right triangle:
base = 2 in, height = 6 in
Area of second right triangle = 1/2 * base * height = 0.5 * 2 in * 6 in = 6 in²
For the triangle:
base = (2 + 4 + 2) = 8 in, height = 4 in
Area of triangle = 1/2 * base * height = 0.5 * 8 in * 4 in = 16 in²
For the rectangle:
length = 4 in, width = 6 in
Area of rectangle = length * width = 4 in * 6 in = 24 in²
Area of polygon = 6 + 6 + 16 + 24 = 52 in²
The area of the polygon is 52 in²
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Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a
20
%
20%20, percent chance of winning each game and that Cam has a
50
%
50%50, percent chance of winning each game.
Answers
Based on the information provided, the probability that Ben wins the board game is 30%.
What is the probability for Ben to win the board game?To calculate the probability of Ben winning the board game, let's start by checking the information provided:
Probability for Justin to win: 20% or 0.2
Probability for Cam to win: 50% or 0.5
Now, the total probability is always equivalent to 100% or 0.1. Based on this, let's calculate now the probability that Ben wins the game.
1 - (0.2 + 0.5)
1 - 0.7 = 0.3
Note: Here is the complete question:
Justin, Cam, and Ben are playing a board game where exactly one player will win. Ben estimates that Justin has a %20 percent chance of winning each game and that Cam has a %50 percent chance of winning each game. What is the probability that Ben will win the board game?
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Buy-Rite Pharmacy has purchased a small auto for delivering prescriptions. The auto was purchased for $26,000 and will have a 6-year useful life and a $5,500 salvage value. Delivering prescriptions (which the pharmacy has never done before) should increase gross revenues by at least $33,500 per year. The cost of these prescriptions to the pharmacy will be about $28,000 per year. The pharmacy depreciates all assets using the straight-line method. The payback period for the auto is closest to (Ignore income taxes. ): (Round your answer to 1 decimal place. )
Answers
The payback period for the auto is approximately 8 years.
Buy-Rite Pharmacy has purchased an auto for delivering prescriptions. The auto was purchased for $26,000, and it has a useful life of 6 years with a $5,500 salvage value. By delivering prescriptions, the pharmacy aims to increase gross revenues by at least $33,500 per year. The pharmacy will incur a cost of $28,000 per year for these prescriptions.
Using the straight-line method, the annual depreciation of the auto is ($26,000 - $5,500) / 6 = $3,917. This means that the total cost of the auto over 6 years will be $26,000 - $5,500 + ($3,917 x 6) = $43,502.
To calculate the payback period, we need to determine how long it will take for the increased gross revenues to cover the cost of the auto.
The net increase in revenues will be $33,500 - $28,000 = $5,500 per year. Therefore, the payback period is $43,502 / $5,500 = 7.9 years, which is rounded to 8 years.
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Adam is purchasing a new television that costs $2,187. 96 after tax. He borrowed the money from his parents and must pay back the full amount plus simple interest at the rate of 3. 5%. What is the interest he will pay if he takes 2 years to pay his parents back? (Include Decimal with the cents; No Commas)
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Adam is purchasing a new television that costs $2,187. 96 after tax. He borrowed the money from his parents and must pay back the full amount plus simple interest at the rate of 3. 5%. What is the total amount he will pay if he takes 2 years to pay his parents back? (Include Decimal with the cents; No Commas)
please
Answers
he interest he will pay if he takes 2 years to pay his parents back is $153.16. The total amount he will pay if he takes 2 years to pay his parents back is $2,341.12.
To calculate the interest Adam will pay, we need to use the simple interest formula:
Interest = Principal x Rate x Time
The principal is the amount borrowed, which is $2,187.96. The rate is 3.5% per year, or 0.035 in decimal form. The time is 2 years.
Interest = $2,187.96 x 0.035 x 2 = $153.16
Therefore, Adam will pay $153.16 in interest if he takes 2 years to pay his parents back.
To calculate the total amount he will pay, we need to add the interest to the principal:
Total amount = Principal + Interest
Total amount = $2,187.96 + $153.16 = $2,341.12
Therefore, Adam will pay a total of $2,341.12 if he takes 2 years to pay his parents back.
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Dig deeper! a police dog spends of his workday in a police car, of his workday in public, and the rest of his workday
at the police station. what fraction of the dog's day is spent at the police station?
fraction of workday
Answers
The police dog spends 1/6 of its workday at the police station.
To find the fraction of the police dog's workday spent at the police station, we need to add up the fractions of time spent in each location and subtract them from 1, since the dog spends the rest of the day at the police station.
Fraction of time spent in police car = [tex]1/3[/tex]
Fraction of time spent in public = [tex]1/2[/tex]
To add these fractions, we need to find a common denominator:
[tex]1/3 = 2/6\\1/2 = 3/6[/tex]
So, the fraction of the dog's day spent at the police station is:
[tex]1 - (2/6 + 3/6) = 1 - 5/6[/tex]
= [tex]1/6[/tex]
Therefore, the police dog spends 1/6 of its workday at the police station.
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Find the volume and surface area of the composite figure. Give your answer in terms of π.
The figure shows a compound solid that consists of a hemisphere with a right cone on top of it. The radii of both the hemisphere and the right cone are equal to 6 centimeters. The slant of the right cone is equal to 8 centimeters.
I WILL GIVE BRAINLIST,
Answers
To find the volume and surface area of the composite figure, we need to first find the individual volumes and surface and the right cone, and then add them together.
The volume of a hemisphere with radius r is (2/3)πr^3, and the surface area is 2πr^2.
The volume of a right cone with radius r, height h, and slant s is (1/3)πr^2h, and the surface area is πr^2 + πrs.
In this case, the radius r and slant s are both 6 cm, and the height h of the cone can be found using the Pythagorean theorem: h = √(s^2 - r^2) = √(8^2 - 6^2) = √28 ≈ 5.29 cm.
So, the volume of the hemisphere is (2/3)π(6 cm)^3 = 72π/3 = 24π cubic cm, and the surface area is 2π(6 cm)^2 = 72π square cm.
The volume of the right cone is (1/3)π(6 cm)^2(5.29 cm) = 62.83π/3 ≈ 20.94π cubic cm, and the surface area is π(6 cm)^2 + π(6 cm)(8 cm) = 36π + 48π = 84π square cm.
Therefore, the total volume of the composite figure is 24π + 20.94π = 44.94π cubic cm, and the total surface area is 72π + 84π = 156π square cm.
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A forester is 50 m from the base of a tree and measures the angle between the ground and the top of the tree. If the angle is 768, fi nd the height of the tree. Round your answer to the nearest meter
Answers
The height of the tree is approximately equal to the tangent of 768 radians multiplied by 50 meters, rounded to the nearest meter.
How to determine the height of a tree using trigonometry and angle measurement?To find the height of the tree, we can use trigonometry. Let's assume that the height of the tree is represented by the variable "h."
In a right triangle formed by the forester, the base of the tree, and the top of the tree, the tangent of the angle is equal to the opposite side (height of the tree, h) divided by the adjacent side (distance from the base of the tree, 50 m).
Using the tangent function, we can write:
tan(angle) = [tex]\frac{h }{ 50}[/tex]
We can rearrange this equation to solve for h:
h = tan(angle) * 50
Now we can substitute the given angle into the equation and calculate the height:
h = tan(768) * 50
Calculating this in degrees might result in an error because the tangent function expects the angle to be in radians.
Therefore, we need to convert the angle to radians before evaluating the tangent.
There are 180 degrees in pi radians, so we can convert the angle as follows:
angle_radians = [tex]\frac{768 \* \pi }{ 180}[/tex]
Substituting this value into the equation:
h = tan(angle_radians) * 50
Now we can calculate the height using a calculator:
h ≈ [tex]tan(\frac{768 \pi }{ 180}) 50[/tex]
After evaluating this expression, we get the height of the tree. Rounding the answer to the nearest meter will give us the final result.
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The town of Madison has a population of
25
,
000
25,00025, comma, 000. The population is increasing by a factor of
1.12
1.121, point, 12 each year.
Write a function that gives the population
P
(
t
)
P(t)P, left parenthesis, t, right parenthesis in Madison
t
tt years from now.
Do not use commas in your answer.
Answers
The function for the population of Madison t years from now is:[tex]p(t) = 25000 (1.12)^{t}[/tex]
To write a function that gives the population P(t) in Madison t years from now, considering the town has an initial population of 25,000 and an annual increase factor of 1.12, you can use the formula:
[tex]p(t) = P_{0} (1 + r)^{t}[/tex]
Where:
- P(t) is the population at time t
- P_0 is the initial population (25,000)
- r is the annual increase factor (1.12 - 1 = 0.12)
- t is the number of years
So, the function for the population of Madison t years from now is:
[tex]p(t) = 25000 (1.12)^{t}[/tex]
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Which equation has a focus at (–6, 12) and directrix of x = –12?
1. ) ( y - 12)^2 = 1/12 ( x + 9 )
2. ) ( y - 12 )^2 = -1/12 ( x + 9 )
3. ) ( y - 12)^2 = 12 ( x+9 )
4. ) ( y - 12)62 = -12 (x + 9 )
Answer: C
Answers
None of the given options have a focus at (-6, 12) and directrix of x = -12,so none of the option is correct.
To find the equation with a focus at (-6, 12) and directrix of x = -12, we can use the general equation for a parabola with a vertical axis of symmetry:
(y - k)^2 = 4p(x - h)
where (h, k) is the focus and x = h - p is the directrix.
Given the focus (-6, 12) and directrix x = -12, we can determine the value of p:
p = h - (-12) = -6 - (-12) = 6
Now, we can plug in the values of h, k, and p into the equation:
(y - 12)^2 = 4(6)(x + 6)
Simplify the equation:
(y - 12)^2 = 24(x + 6)
Now, let's compare this equation to the given options:
1. (y - 12)^2 = 1/12 (x + 9)
2. (y - 12)^2 = -1/12 (x + 9)
3. (y - 12)^2 = 12 (x + 9)
4. (y - 12)^2 = -12 (x + 9)
None of the given options match the equation we found. Therefore, none of the given options have a focus at (-6, 12) and directrix of x = -12
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