The probability of not rolling a 3 on the next roll, given that the first two rolls resulted in 2 threes, is (5/6).
Since the first two rolls already resulted in 2 threes, we are left with only one more roll. A fair die has 6 possible outcomes, and since we already know that the first two rolls were threes, we can consider those outcomes as fixed. Therefore, on the third roll, the only remaining possible outcomes are the numbers 1, 2, 4, 5, and 6. Out of these 5 remaining outcomes, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1 out of 5, which can be expressed as a fraction as 1/5. Simplifying this fraction further, we get 1/5 = 1/6. Therefore, the correct answer is (5/6).
Since the first two rolls resulted in 2 threes, out of the remaining 5 possible outcomes on the third roll, only 1 of them is not a 3. Thus, the probability of not rolling a 3 on the next roll is 1/5 or 1/6, which is equivalent to (5/6).
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3. An airplane is traveling at a speed of 450 miles per hour in the direction of N 54° W. While flying, the airplane hits wind traveling with a velocity of 55 miles per hour in the direction of S 70° W. Find the magnitude and direction (as a true bearing) of the resultant force.
The resultant force magnitude is approximately 448.6 miles per hour, with a true bearing of N 47° W.
To find the resultant force, we need to calculate the vector sum of the airplane's velocity and the wind velocity. We can break down both velocities into their horizontal and vertical components.
The airplane's velocity has a horizontal component of 450 * cos(54°) and a vertical component of 450 * sin(54°). Similarly, the wind velocity has a horizontal component of 55 * cos(70°) and a vertical component of 55 * sin(70°). Adding the horizontal and vertical components separately, we find the resultant horizontal and vertical velocities.
Finally, we use these components to calculate the magnitude of the resultant force using the Pythagorean theorem and the direction using the inverse tangent function.
The resultant force has a magnitude of approximately 448.6 miles per hour and a true bearing of N 47° W.
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From his eye, which stands 1. 62 meters above the ground, Amadou measures the angle of elevation to the top of a prominent skyscraper to be 44^{\circ}∘. If he is standing at a horizontal distance of 164 meters from the base of the skyscraper, what is the height of the skyscraper?
Based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.
Amadou measures the angle of elevation from his eye to the top of the skyscraper as 44 degrees. To determine the height of the skyscraper, we can use trigonometry. The tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
In this case, the opposite side represents the height of the skyscraper, and the adjacent side represents the horizontal distance from Amadou to the base of the skyscraper. We are given that the adjacent side is 164 meters and the angle of elevation is 44 degrees.
Using the tangent function, we can set up the following equation:
tan(44 degrees) = height of skyscraper / 164 meters
To solve for the height of the skyscraper, we rearrange the equation:
height of skyscraper = tan(44 degrees) * 164 meters
Using a scientific calculator or trigonometric table, we find that tan(44 degrees) is approximately 0.9659. Multiplying this value by 164 meters gives us the height of the skyscraper:
height of skyscraper ≈ 0.9659 * 164 meters ≈ 97.2 meters
Therefore, based on Amadou's measurements, the height of the skyscraper is approximately 97.2 meters.
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The Red Door Escape Room is a fully
immersive game where you are locked in
a room and have only 60 minutes to solve
cryptic games and puzzles to be able to
escape. They charge $28 per person.
Write a linear equation to model this
situation.
A linear equation that models the situation at the Red Door Escape Room, where participants are charged $28 per person for a fully immersive game, can be expressed as y = 28x, where y represents the total cost and x represents the number of participants.
To model the situation mathematically, we can use a linear equation, which represents a straight line on a graph. In this case, the equation y = 28x can be used, where y represents the total cost and x represents the number of participants.
In the equation, the coefficient 28 represents the cost per person. By multiplying the number of participants, x, by this coefficient, we can determine the total cost, y. This linear equation assumes a constant rate of $28 per person and does not take into account any additional fees or discounts.
For example, if there are 4 participants, we can substitute x with 4 in the equation: y = 28 * 4 = 112. This means that the total cost for 4 participants would be $112. Similarly, if there are 6 participants, the total cost would be $168 (28 * 6).
By using this linear equation, the Red Door Escape Room can calculate the total cost based on the number of participants, allowing them to effectively manage their pricing structure and revenue.
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Gena and her friends each estimated the quotient of –137. 56 divided by –6. 12 using compatible numbers. Which shows the best estimate using compatible numbers?.
The best estimate using compatible numbers is approximately 23.33.
To find the best estimate using compatible numbers for the quotient of -137.56 divided by -6.12, we need to identify compatible numbers that are close to the given values.
Compatible numbers are numbers that are easy to work with mentally and provide a close approximation of the actual values.
Let's consider compatible numbers for -137.56 and -6.12:
For -137.56, we can use -140, which is close to -137.56.
For -6.12, we can use -6, which is close to -6.12.
Now, let's calculate the estimate:
-137.56 ÷ -6.12 ≈ -140 ÷ -6
Dividing -140 by -6, we get:
-137.56 ÷ -6.12 ≈ 23.33
Therefore, the best estimate using compatible numbers is approximately 23.33. By selecting compatible numbers close to the given values and performing the division using those numbers, we can obtain a reasonable estimate of the quotient.
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On Monday, 238 students and 10 teachers went on a trip to the zoo. If a bus can hold 58 people each, how many busses are needed? (Hint: remember you cannot have part of a bus and you must have enough to fit all people
we would need a total of 5 buses to accommodate all the students and teachers on the trip.To determine the number of buses needed, we divide the total number of students and teachers by the capacity of each bus, which is 58 people.
238 students + 10 teachers = 248 people
To calculate the number of buses needed, we divide 248 people by 58 people per bus:
248 people ÷ 58 people/bus ≈ 4.276 buses
Since we cannot have a fraction of a bus, we round up to the nearest whole number. Therefore, we would need a total of 5 buses to accommodate all the students and teachers on the trip.
It's important to note that rounding up ensures that there are enough buses to accommodate all the individuals, even if there are some empty seats on each bus.
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asap please and thank you
The correct statement is given as follows:
The can of pringles has a z-score close to zero, which means it's more likely to happen.
How to interpret z-scores?The z-score formula is given as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
In which:
X is the measure.[tex]\mu[/tex] is the population mean.[tex]\sigma[/tex] is the population standard deviation.The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).
The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.
The z-score for pretzels is given as follows:
Z = (25 - 23)/1.2
Z = 1.67.
The z-score for pringles is given as follows:
Z = (40 - 34)/4
Z = 1.5. -> closer to zero -> more likely to happen.
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A rally car race course covers 515. 97 miles. The winning car completed the course in 6. 5 hours. What was the average speed of the winning car
The average speed gives us an indication of how fast the winning car was able to cover the race course on average. The average speed of the winning car in the rally car race was approximately 79.38 miles per hour.
To calculate the average speed of the winning car, we divide the total distance covered (515.97 miles) by the time taken to complete the course (6.5 hours).
Average speed = Total distance / Time taken
Average speed = 515.97 miles / 6.5 hours
Calculating the division, we find that the average speed is approximately 79.38 miles per hour.
The average speed gives us an indication of how fast the winning car was able to cover the race course on average. It is a measure of the car's performance and efficiency over the given time period.
In this case, the winning car had an average speed of 79.38 miles per hour, indicating a relatively fast and efficient performance throughout the race.
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It is 185 miles to Fort Worth if vangs drives 2 hours at 65 miles per hour how far will he be from Fort Worth
If Vangs drives for 2 hours at a speed of 65 miles per hour, we can calculate how far he will be from Fort Worth. Vangs will be 125 miles away from Fort Worth.
Given that Vangs drives at a speed of 65 miles per hour for 2 hours, we can calculate the distance traveled using the formula Distance = Speed × Time.
Distance = 65 miles/hour × 2 hours = 130 miles.
Since Vangs started 185 miles away from Fort Worth and traveled a distance of 130 miles, we subtract the distance traveled from the initial distance to find how far he will be from Fort Worth.
Distance from Fort Worth = Initial distance - Distance traveled = 185 miles - 130 miles = 55 miles.
Therefore, Vangs will be 55 miles away from Fort Worth after driving for 2 hours at a speed of 65 miles per hour.
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Solve the problem using a system of equations. Use substitution or Elimination.1. 14x+17y=99
This simplifies to: 42x + 51y = 297. We now have a new equation in terms of y. To solve for y, we need another equation. If you have another equation, please provide it, and we can continue solving the system of equations.
To solve the system of equations represented by 14x + 17y = 99, we can use either substitution or elimination methods. In this case, let's use the elimination method.
To use the elimination method, we need to manipulate the equations to eliminate one variable. In this case, we can eliminate the variable x by multiplying the first equation by 17 and the second equation by 14, resulting in:
(17)(14x + 17y) = (17)(99)
(14)(14x + 17y) = (14)(99)
Simplifying these equations gives us:
238x + 289y = 1683
196x + 238y = 1386
Now, we can subtract the second equation from the first equation to eliminate x:
(238x + 289y) - (196x + 238y) = 1683 - 1386
This simplifies to: 42x + 51y = 297
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The circumstances of the region watered by the sprinklers is equal toA. None of the aboveB 87.92 ftC 8.792 ftD 6.28 ft
To provide a comprehensive explanation about the circumstances of the region watered by sprinklers, let's discuss some relevant factors that can influence the extent and coverage of water distribution.
Sprinkler Type and Design: Different types of sprinklers have varying spray patterns and distribution capabilities. Factors such as nozzle size, rotation speed, and spray angle can affect the distance and coverage area of water dispersion. Sprinklers can be designed for specific applications, including fixed, rotating, or oscillating patterns. Water Pressure: The water pressure supplied to the sprinkler system plays a crucial role in determining the coverage area. Higher water pressure can result in increased spray distance and wider coverage, while lower pressure may restrict the reach of the sprinklers. Sprinkler Spacing and Layout: The arrangement of sprinklers within the irrigated area affects the overall coverage. Proper spacing ensures adequate overlap between adjacent sprinklers, minimizing dry spots and achieving uniform water distribution. Wind Conditions: Wind speed and direction can impact the efficiency of sprinkler systems. Strong winds can cause water drift and uneven distribution, leading to areas with insufficient water coverage.
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A cake shop bakes a variety of brownies. The top-selling brownies are ones with toppings of chocolate chip, walnuts, or both. A customer enters the store. The probability that the customer will pick both toppings is 0. 4. What is the probability that they will pick neither the chocolate chip nor the walnut toppings? A. 0. 5 B. 0. 3 C. 0. 45 D. 0. 8 E. 0. 2.
The probability that they will pick neither the chocolate chip nor the walnut topping is, 0.7
Since, the total of all probabilities is 1.00, or 100%.
Now, In the Venn diagram, we have the probabilities 0.2, 0.4 and 0.1;
these sum to,
0.2+0.4+0.1
= 0.6+0.1
= 0.7.
Therefore, the probability that they will pick neither the chocolate chip nor the walnut topping is,
⇒ 1.00-0.7 = 0.3
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Sansa was explaining the meaning and usefulness of the statement tan 40° ≈ 0. 84. Which
true statements below could be part of that explanation? Select all that apply.
o All right triangles with an acute angle of 40° are similar to each other.
o The sum of the squares of the legs of right triangles with a 40° angle equal 40".
o Knowing that tan 40° ≈ 0. 84 is enough information to calculate the sides of any 40°-
50°-90° triangle.
o If you know tan 40° ≈ 0. 84 and the length of the leg opposite to the 40° angle, then
you can calculate the length of the other leg.
o The ratio of the opposite side to the hypotenuse in any right triangle with an angle of
40° is always approximately 0. 84
The true statements that could be part of the explanation of the statement "tan 40° ≈ 0.84" are: All right triangles with an acute angle of 40° are similar to each other. If you know tan 40° ≈ 0.84 and the length of the leg opposite to the 40° angle, then you can calculate the length of the other leg. The ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84
In a right triangle, the tangent of an acute angle is defined as the ratio of the opposite side and the adjacent side of that angle. Mathematically, for an acute angle A, tan(A) = opposite/adjacent. In the current case, we are discussing tan 40°. So, if the angle A in a right triangle is 40°, and if the opposite side to that angle is x and the adjacent side is y, then tan 40° = x/y .If we know the value of tan 40°, then we can calculate the value of x/y or y/x .In the following true statements, we will discuss how we can use tan 40° to make some conclusions: The ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84This statement is true. This is based on the definition of tangent. tan 40° = opposite/adjacent. In a right triangle with an angle of 40°, the hypotenuse is neither the opposite side nor the adjacent side. But, we can write the above equation as opposite/hypotenuse = tan 40°/1. So, the ratio of the opposite side to the hypotenuse in any right triangle with an angle of 40° is always approximately 0.84.
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Willie Crash was out Sunday flying in his spaceship. As he approached Mars, he changed his mind, and decided that he did not wish to visit that planet and fired his retro-rocket. The spaceship slowed down, and if all went well (or did it?), stopped for an instant then started pulling away. While the rocket motor was firing, Willie's distance, d, from the surface of Mars depended by a quadratic function on the number of minutes, t, since he started firing the retro-rocket. Willie finds that at time t= 1, 2, and 3 minutes, his distances were d= 425, 356, and 293 kilometers, respectfully.
what is the INDEPENDENT variable? (t or d)
what is the DEPENDENT variable? (t or d)
what does the INDEPENDENT variable represent? 1. the distance D from the surface of Mars OR 2.The number of minutes Titi since he started firing the retro-rocket
"t" is the independent variable representing the number of minutes since Willie started firing the retro-rocket, while "d" is the dependent variable representing the distance from the surface of Mars
The independent variable "t" represents the number of minutes since Willie started firing the retro-rocket. It is the variable that Willie has control over and chooses to manipulate. By changing the value of "t," Willie can observe how it affects the dependent variable "d," which is the distance from the surface of Mars. The independent variable is typically the input or the cause in a relationship or function.
On the other hand, the dependent variable "d" represents the distance from the surface of Mars. It depends on the value of "t" and is influenced by the independent variable. As Willie changes the number of minutes, the distance "d" changes accordingly. The dependent variable is usually the output or the effect in a relationship or function.
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Select the correct answer.
Solve the exponential equation for X.
216 6(41 +11)
OA.
I = 2
OB.
I = -2
OC.
I = 3
OD.
= -3
The given equation is I = -2OD where I is the intensity of light, O is the aperture of the lens and D is the distance between the lens and the object. This equation is known as the Inverse Square Law of Light.
The equation states that the intensity of light decreases as the square of the distance between the object and the ens increases. This means that if we double the distance between the object and the lens, the intensity of light becomes 1/4th of its original value.Similarly, if we triple the distance between the object and the lens, the intensity of light becomes 1/9th of its original value. This law is applicable to all types of light sources, including natural light sources like the sun and artificial light sources like bulbs.One practical application of this law is in photography. If a photographer wants to capture an image of a subject that is far away, they need to use a lens with a larger aperture to let in more light. This will ensure that the image is bright and clear even when the distance between the subject and the camera is large.Similarly, if a photographer wants to capture an image of a subject that is close to the camera, they need to use a lens with a smaller aperture to reduce the amount of light that enters the camera. This will prevent the image from being overexposed and washed out.Overall, the Inverse Square Law of Light is an important principle that governs the behavior of light in various applications, including photography, cinematography, and physics.For such more question on Square Law
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What is the sum of a geometric series of 12 terms that begins with 10 and has a common ratio of 2?
A) 240
B) 252
С) 20,480
D) 40,950
The sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.
To find the sum of a geometric series, we can use the formula:
S = a * (1 - r^n) / (1 - r)
Where:
S is the sum of the series,
a is the first term of the series,
r is the common ratio,
n is the number of terms in the series.
In this case, the first term (a) is 10, the common ratio (r) is 2, and the number of terms (n) is 12.
Plugging in the values into the formula, we have:
S = 10 * (1 - 2^12) / (1 - 2)
Simplifying further:
S = 10 * (1 - 4096) / (1 - 2)
S = 10 * (-4095) / (-1)
S = 10 * 4095
S = 40,950
Therefore, the sum of the geometric series with 12 terms, starting from 10 and with a common ratio of 2, is 40,950.
The correct answer is D) 40,950.
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An item originally costs $175. 0. The item is now on sale for $99. 75. What percent
is the sale price of the original price? Is this an example of percent increase or
decrease? Explain how you know. *
It is percentage decrease by 43 percent.
Given that, the original cost of item = $175.00 and the sale price of item = $99.75.
Percentage increase or decrease = (Original Price - Sale Price)/Original Price ×100
= (175.00-99.75)/175.00 ×100
= 75.25/175.00 ×100
= 0.43×100
= 43%
Therefore, it is percentage decrease by 43 percent.
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The function p = 0. 0089t^2+1. 1149t+78. 4491 models the united states population in millions since 1900. Use the function P to predict the year in which the population exceeds 1 billion.
a. 2165
b. 2156
c. 2457
d. 2378
Using the function p = 0.0089t^2 + 1.1149t + 78.4491, the United States population in millions, we can predict that the population will exceed 1 billion around the year 2156.
To predict the year in which the United States population exceeds 1 billion, we can set up the equation p = 0.0089t^2 + 1.1149t + 78.4491 and solve for t, representing the year. We need to find the value of t (time) when p (population) surpasses 1,000 (1 billion in millions).
0.0089t^2 + 1.1149t + 78.4491 > 1000
By rearranging the equation and solving for t, we can find the approximate year when the population exceeds 1 billion.
After performing the calculations, it is determined that the population is predicted to exceed 1 billion around the year 2156.
Therefore, the correct answer is option b) 2156.
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There are
128
128128 ounces in a gallon. There are
4
44 quarts in a gallon.
How many ounces are in a quart?
There are 32 ounces are in a quart
How to determine how many ounces are in a quart?From the question, we have the following parameters that can be used in our computation:
128 ounces in a gallon
Also, we have
4 quart in a gallon
using the above as a guide, we have the following:
128 ounces = 4 quart
Divide both sides by 4
So, we have
32 ounces = 1 quart
Hence, there are 32 ounces are in a quart
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WILL MARK BRAINLIEST :
How can standard deviations and means help you to describe the results of a simulation? What are the important things to consider when calculating these measures? What does it mean if a data set has a very small standard deviation? What does it mean if the set has a very large standard deviation?
Standard deviations and means are important in describing the results of a simulation. The mean represents the average value of the data, while the standard deviation measures the spread or variability around the mean.
Key considerations when calculating these measures include:
1. Sample size: Larger sample sizes provide more reliable estimates.
2. Data quality: Ensure accurate and unbiased data.
3. Distribution assumptions: Assess if the data follows a normal distribution.
4. Outliers: Identify and handle extreme values appropriately.
A small standard deviation indicates less variability and greater precision in the simulation results. A large standard deviation suggests more variability and potential uncertainty.
In summary, standard deviations and means help describe the spread and average of simulation results. Consider sample size, data quality, distribution assumptions, and outliers. A small standard deviation signifies less variability, while a large standard deviation implies greater variability.
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A beverage company sells juice in all the major restaurants. It costs the beverage company $0.75 to make each bottle of juice. The company uses a 35% markup. What is the selling price of the juice?
The selling price of juice that costs a beverage company $0.75 to make with a 35% markup is $1.01.
What is markup?
Markup is the difference between the cost of a product or service and its selling price.
The cost of a product is the amount spent on making or buying the product.
The selling price is the amount for which the product is sold.
Therefore, when a company wants to make a profit, it applies a markup to the cost of the product to determine the selling price.
The markup represents the amount of money a company adds to the cost of a product to make a profit.
Here's how to solve the problem:
A beverage company sells juice in all the major restaurants. It costs the beverage company $0.75 to make each bottle of juice. The company uses a 35% markup. What is the selling price of the juice?
Markup = 35% of the cost
Price = cost + markup
Step 1: Find the markup
Markup = 35% of 0.75
Markup = 0.35 x 0.75
Markup = 0.26
Step 2: Find the selling price
Price = cost + markup
Price = 0.75 + 0.26
Price = 1.01
The selling price of juice that costs a beverage company $0.75 to make with a 35% markup is 1.01.
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Noah needs to peel a lot of potatoes before a dinner party. He has already peeled some potatoes. If he keeps peeling at the same rate, will he finish all the potatoes in time?
If the remaining time is greater than or equal to N/P minutes, he will finish in time. Otherwise, he won't be able to finish before the dinner party.
To determine if Noah will finish peeling all the potatoes in time for the dinner party, we need to consider the amount of time he has left and his peeling rate.
Let's assume Noah has N potatoes left to peel and he can peel P potatoes per minute. If he keeps peeling at the same rate, the time required to peel all the remaining potatoes is given by N/P minutes.
If Noah has enough time before the dinner party, meaning the remaining time is greater than or equal to N/P minutes, he will be able to finish peeling all the potatoes.
However, if the remaining time is less than N/P minutes, it means there isn't enough time for Noah to finish peeling all the potatoes before the dinner party.
Therefore, to determine if Noah will finish peeling all the potatoes in time, compare the remaining time with N/P minutes. If the remaining time is greater than or equal to N/P minutes, he will finish in time. Otherwise, he won't be able to finish before the dinner party.
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Each morning Eric makes 50 cinnamon bagels for his customers at barneys bagels because of a recent increase in popularity of cinnamon bagels he has increase the number he backs each morning 58% how many cinnamon bagels does Eric bake each day?
Eric bakes 79 cinnamon bagels each day at Barney's Bagels, resulting from a 58% increase in the number he previously made.
Originally, Eric made 50 cinnamon bagels each morning. However, due to the increased demand and popularity of cinnamon bagels, he decided to increase his production. The increase is given as 58%, which means he is now baking 58% more bagels than before.
To calculate the new number of cinnamon bagels, we need to find 58% of 50 and add it to the original quantity.
58% of 50 can be calculated by multiplying 50 by 0.58:
58% × 50 = (58/100) × 50 = 0.58 × 50 = 29.
Now, adding the increase to the original quantity:
50 + 29 = 79.
Therefore, Eric now bakes 79 cinnamon bagels each day at Barney's Bagels, reflecting a 58% increase from his previous production.
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janine spends 1 tenths hour making the bed 1 fiths hour getting dressed and 1 half hour eating breakfast what fraction of an hour does she spend doing these activitys
Therefore, Janine spends 4/5 of an hour doing these activities.
To determine the fraction of an hour that Janine spends doing the given activities, we need to convert the given times to fractions of an hour. We know that 1 hour is equivalent to 1 whole, which means that half an hour would be equivalent to half of a whole.
Similarly, one-fifth of an hour would be equivalent to 1 ÷ 5, which is 0.2, and one-tenth of an hour would be equivalent to 1 ÷ 10, which is 0.1.
Now, let's add the three times together to find the total time:
1/10 hour making the bed + 1/5 hour getting dressed + 1/2 hour eating breakfast = 1/10 + 2/10 + 5/10= 8/10 (which can be simplified to 4/5).
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Alli has $382. 45 in her checking account and $450 in her savings account. She writes a check for $400. Alli’s bank automatically takes money from her savings to cover the amount of a check if the money in the checking account is not sufficient. Unfortunately for Alli, the bank also withdraws $25 from her savings account for this service. Once the check has cleared, how much money does Alli have in her savings account?
$17. 55
$17. 55
$42. 55
$42. 55
$407. 45
$407. 45
$442. 55
$442. 55
Once the check has cleared, Alli has $17.55 in her savings account. Finally, the amount of money Alli has in her savings account after the check has cleared is $25, so the answer is option A: $17.55.
Initial amount in Alli's checking account = $382.45
Initial amount in Alli's savings account = $450
Amount Alli withdrew from checking account = $400
Amount the bank withdrew from Alli's savings account = $25
Total cost of the check = 400+25
=425
Since the initial amount in her checking account was insufficient, the bank automatically withdrew $25 from her savings account to cover the cost of the check. This means that Alli has a total of $425 - $400 = $25 left in her savings account.After the withdrawal from her savings account, Alli's remaining savings balance is $450 - $25 = $425. However, she spent $400 to cover the check, so her final savings balance is $425 - $400 = $25.
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Which mixed number is equal to 4 7/5?9 2/54 7/55 2/97 4/5
The mixed-number that is equal to 4 7/5 is 4 7/5 itself. The correct option is B) 4 7/5, using conversion into improper-fraction & vice-versa.
To convert the mixed number 4 7/5 into an improper fraction,
we will multiply the denominator by the whole number and add the numerator. 4 × 5 + 7 = 27.
Thus, 4 7/5 as an improper fraction is 27/5.
Now, we have to convert the given mixed numbers into improper fractions one by one, and then
compare it to 27/5 , is the fraction equivalent to 4 7/5.
Let's do it:
Option A:9 2/5 = 47/5
Divide 47 by 5 and we get 9 with a remainder of 2.
Thus, 9 2/5 = 47/5 which is not equal to 27/5.
Option B:4 7/5 = 27/5
As we know 4 7/5 as an improper fraction is 27/5, and it matches our answer with the given mixed number.
Option C:5 2/9 = 47/9
Divide 47 by 9 and we get 5 with a remainder of 2.
Thus, 5 2/9 = 47/9 which is not equal to 27/5.
Option D:4/5 = 0.8
Clearly, 0.8 is not equal to 27/5.
So, the mixed number that is equal to 4 7/5 is 4 7/5 itself. The correct option is B) 4 7/5.
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Asha by 60 fruit baskets. 25% of the fruit baskets have 12 pieces of fruit in each basket. The remaining 75% of the baskets have 15 pieces of fruit in each basket
Asha has a total of 180 + 675 = 855 pieces of fruit in the 60 fruit baskets she bought.Asha bought 60 fruit baskets. Let's calculate the number of fruit baskets in each category:
25% of 60 = (25/100) * 60 = 15 fruit baskets
These 15 fruit baskets have 12 pieces of fruit in each basket.
75% of 60 = (75/100) * 60 = 45 fruit baskets
These 45 fruit baskets have 15 pieces of fruit in each basket.
To find the total number of fruit in each category, we multiply the number of fruit baskets by the number of fruit in each basket:
For the 15 baskets with 12 pieces of fruit: 15 * 12 = 180 fruits.
For the 45 baskets with 15 pieces of fruit: 45 * 15 = 675 fruits.
Therefore, Asha has a total of 180 + 675 = 855 pieces of fruit in the 60 fruit baskets she bought.
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Rob spends 1/2 of his earnings this weeks on bills and then buys a video game for $25. 75. How many much of his earnings from this week does rob have left?
Rob has (1/2) * x - $25.75 of his earnings left from this week. This is obtained by subtracting the amount spent on bills and the cost of the video game from his total earnings.
To find out how much of his earnings Rob has left, we need to calculate the portion he spent and subtract it from his total earnings.
Given that Rob spends 1/2 of his earnings on bills, he has 1 - 1/2 = 1/2 of his earnings remaining.
If Rob buys a video game for $25.75, we can subtract this amount from his remaining earnings.
Let's say Rob's total earnings for the week were x dollars.
Amount spent on bills: (1/2) * x
Amount spent on the video game: $25.75
Remaining earnings: x - [(1/2) * x + $25.75]
Simplifying the expression, we have:
Remaining earnings: x - (1/2) * x - $25.75
Remaining earnings: (1/2) * x - $25.75
So, Rob has (1/2) * x - $25.75 of his earnings left from this week.
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Which polynomial is the correct product? 15y3 17y2 22y 15 6y3 17y2 22y 15 6y3 20y2 22y 15 6y3 17y2 22y 25.
The correct polynomial product is indeed Option B: 6y^3 + 17y^2 + 22y + 15.
Let's break down the options to see why Option B is correct:
Option A: 15y^3 + 17y^2 + 22y + 15
This option does not match the given product as it includes an additional term, 15y^3, that is not present in the correct polynomial product.
Option B: 6y^3 + 17y^2 + 22y + 15
This option matches the given polynomial product exactly. It includes all the terms and coefficients mentioned: 6y^3, 17y^2, 22y, and 15.
Option C: 6y^3 + 20y^2 + 22y + 15
This option differs from the correct product in the coefficient of the second term. It includes 20y^2 instead of 17y^2.
Option D: 6y^3 + 17y^2 + 22y + 25
This option differs from the correct product in the coefficient of the last term. It includes 25 instead of 15.
Therefore, Option B, 6y^3 + 17y^2 + 22y + 15, is the correct polynomial product based on the given information.
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Lalasa and Yasmin are designing a triangular banner to hang in the school gymnasium. They first draw the design on paper. The triangle has a base of 5 inches and a height of 7 inches. If 1 inch on the drawing is equivalent to 1. 5 feet on the actual banner, what will the area of the actual banner be?.
The area is then calculated as (1/2) * base * height, resulting in approximately 39.375 square feet.
To find the area of the actual banner, we need to scale up the dimensions from the drawing to real-world measurements. We are given that 1 inch on the drawing is equivalent to 1.5 feet on the actual banner.
The base of the triangle on the drawing is 5 inches, so the base of the actual triangle will be:
5 inches * 1.5 feet/inch = 7.5 feet
Similarly, the height of the actual triangle will be:
7 inches * 1.5 feet/inch = 10.5 feet
Now that we have the base and height of the actual triangle, we can calculate its area using the formula for the area of a triangle:
Area = (1/2) * base * height
Area = (1/2) * 7.5 feet * 10.5 feet
Area ≈ 39.375 square feet
Therefore, the area of the actual banner will be approximately 39.375 square feet.
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Garrett found the slope of the values in the table: A 2-column table with 3 rows. Column 1 is labeled Years: x with entries 4, 8, 12. Column 2 is labeled Hourly rate: y with entries 12. 00, 13. 00, 14. 0. 1. Slope = StartFraction 12 minus 8 Over 14. 00 minus 13. 00 EndFraction. 2. Slope = StartFraction 4 Over 1. 00 EndFraction. 3. Slope = 4. Is Garrett’s slope correct? If not, identify his error? Yes. Garrett found the slope correctly. No. He should have put the x values in the denominator and the y values in the numerator. No. He should have gotten a negative answer for slope because the values are decreasing. No. He should have gotten the answer StartFraction 1 Over 25 EndFraction.
No, Garrett's slope is not correct. He should have put the x values in the denominator and the y values in the numerator.
Garrett made an error in calculating the slope. The slope represents the change in the dependent variable (y) per unit change in the independent variable (x). In this case, the independent variable is "Years" (x) and the dependent variable is "Hourly rate" (y).
To calculate the slope correctly, we need to divide the change in y by the change in x. Garrett incorrectly subtracted the x values from each other and the y values from each other, resulting in an incorrect calculation.
The correct calculation would be:
Slope = (13.00 - 12.00) / (8 - 4)
= 1.00 / 4
= 0.25
Therefore, the correct slope is 0.25 or StartFraction 1 Over 4 EndFraction.
Garrett's error was that he should have put the x values (4, 8, 12) in the denominator and the y values (12.00, 13.00, 14.00) in the numerator to calculate the slope correctly.
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