The solution to the equation is x = 9.71 (rounded to two decimal places). To solve the equation x + 4 + 3x = 72, we will combine like terms and then isolate the variable x.
To solve the linear equation x + 4 + 3x = 72, we'll combine like terms on the left side of the equation. The property that justifies this step is the distributive property. We distribute the coefficient 3 to both x terms, which results in 4x + 3x = 7x.
So, rewriting the equation with the combined like terms, we have 4x + 3x + 4 = 72.
The reason we chose to apply the distributive property is to simplify the equation by adding the coefficients of the x terms together. This allows us to work with a simpler equation and proceed with solving for x.
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Solve.
9. An engineer is designing a storage compartment in a spacecraft. The
compartment must be 2 meters longer than it is wide and its depth must
be 1 meter less than its width. The volume of the compartment must be
8 cubic meters.
a. Write an equation to model the volume of the compartment.
we get:(x + 2) × x × (x - 1) = 8x³ + x² - 2x - 8 = 0Thus, the equation to model the volume of the compartment is 8x³ + x² - 2x - 8 = 0.
Given that
the compartment must be 2 meters longer than it is wide and its depth must be 1 meter less than its width. Let's assume the width of the compartment to be x meters.
Then, the length of the compartment would be (x + 2) meters as it is 2 meters longer than its width. And the depth of the compartment would be (x - 1) meters as its depth must be 1 meter less than its width.
Now, the volume of the compartment would be given by; V = l × w × d V = (x + 2) × x × (x - 1)As given, the volume of the compartment must be 8 cubic meters.
Hence, we get:(x + 2) × x × (x - 1) = 8x³ + x² - 2x - 8 = 0Thus, the equation to model the volume of the compartment is 8x³ + x² - 2x - 8 = 0.
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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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For the functions f(x)=3x2+3x+2andg(x)=2x2−2x+3, find:
The sum of f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3 is 5x^2 + x + 5, while the difference is x^2 + 5x - 1. These results are obtained by adding and subtracting the corresponding terms of the two functions.
To find the sum and difference of the functions f(x) = 3x^2 + 3x + 2 and g(x) = 2x^2 - 2x + 3, we add and subtract the corresponding terms.
For the sum, we add the like terms: (3x^2 + 2x^2) + (3x - 2x) + (2 + 3) = 5x^2 + x + 5.
For the difference, we subtract the like terms: (3x^2 - 2x^2) + (3x + 2x) + (2 - 3) = x^2 + 5x - 1.
Therefore, the sum of the functions is given by f(x) + g(x) = 5x^2 + x + 5, and the difference of the functions is given by f(x) - g(x) = x^2 + 5x - 1.
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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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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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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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Suri makes $12 per hour and gets a weekly bonus of $20. Juan makes $12 per hour and gets a weekly bonus of $40. Is it possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week?
No, it is not possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week.
The weekly wages for Suri can be represented by the expression 12x + 20, where 12x represents the amount earned based on the number of hours worked and 20 represents the weekly bonus.
Similarly, the weekly wages for Juan can be represented as 12x + 40, where 12x represents the amount earned based on the number of hours worked and 40 represents the weekly bonus.
Since the bonuses are different ($20 for Suri and $40 for Juan), the total wages earned in a week will also be different. Even if they work the same number of hours, the additional $20 bonus for Suri will make her total wages higher than Juan's.
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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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Jema has a 45% coupon for a new curling iron. She buys the curling iron for a final price of $49. 95 after the discount is taken off. What is the original cost of the curling iron? Round to the nearest cent if necessary
The original cost of the curling iron was approximately $90.82.
Jema had a 45% coupon for a new curling iron, which means she was eligible for a discount of 45% on the original cost of the curling iron. The final price she paid after the discount was $49.95. To find out the original cost of the curling iron, we can use the formula:
Original cost = Final price / (1 - Discount rate)
In this case, since the discount rate is 45%, or 0.45 as a decimal, the formula becomes:
Original cost = $49.95 / (1 - 0.45)
Original cost = $49.95 / 0.55
Original cost ≈ $90.82
Therefore, the original cost of the curling iron was approximately $90.82.
This calculation shows that Jema took advantage of a significant discount on the original cost of the curling iron. By using the coupon, she was able to save around $41.87 on the purchase. This demonstrates the importance of looking for discounts and deals when shopping, as they can help save money and get more value for your purchases.
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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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The owner of an ice cream shop have determined that their daily revenue and cost in dollars are given by R = 4.15x C = 3.20x + 798 where x is the number of scoops served in a day
The daily revenue (R) is given by R = 4.15x, and the daily cost (C) is given by C = 3.20x + 798, where x is the number of scoops served in a day.
In more detail, the given equations represent a linear relationship between the number of scoops served (x) and both the revenue (R) and cost (C). The coefficient of x in the revenue equation, 4.15, represents the revenue generated per scoop served. Similarly, the coefficient of x in the cost equation, 3.20, represents the cost incurred per scoop served. The constant term 798 in the cost equation represents additional fixed costs.
To determine the daily profit, we can subtract the cost from the revenue: Profit = R - C = 4.15x - (3.20x + 798) = 0.95x - 798. This equation allows us to calculate the profit based on the number of scoops served.
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A man sets out to travel from A to C via B. From A he travels 8km on a bearing N30°E to B. From B, he travels a further 6km due East. Calculate how far C is (i) North of A (ii) east of A?
He travels: (i) C is 4 km north of A. (ii) C is 6 km east of A.
How to Calculate how far C is (i) North of A (ii) east of A(i) North of A:
The northward component from A to B is 8 km on a bearing of N30°E. To find the northward distance, we can use trigonometry. Since the bearing is N30°E, we can split it into two right-angled triangles: one facing north and one facing east.
In the northward triangle:
Opposite side = 8 km * sin(30°)
Opposite side = 8 km * 0.5
Opposite side = 4 km
Therefore, C is 4 km north of A.
(ii) East of A:
The eastward component from B to C is 6 km due East. Since this distance is directly east, it does not change the eastward position of C relative to A. Therefore, C is 6 km east of A.
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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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If a bookseller earns a profit of 25 percentage by selling a novel worth rs 300 calculate the selling price of the novel
The selling price of the novel would be Rs 375. The bookseller should sell the novel for Rs 375 to earn a profit of 25%. Profit percentage is a measure of the profit earned as a percentage of the cost price.
In this case, the bookseller earns a profit of 25%. To calculate the selling price, we need to determine the profit earned and add it to the cost price.
To find the profit earned, we multiply the cost price by the profit percentage. In this case, the cost price of the novel is given as Rs 300, and the profit percentage is 25%. To calculate the profit, we multiply Rs 300 by (25/100) or 0.25. The result is Rs 75, indicating that the bookseller earns a profit of Rs 75.
To obtain the selling price, we add the profit to the cost price. In this case, the cost price is Rs 300, and the profit is Rs 75. Adding them together, we get Rs 375 as the selling price of the novel.
To calculate the selling price, we need to determine the profit earned by the bookseller and add it to the cost price.
Given:
Profit percentage = 25%
Cost price of the novel = Rs 300
To calculate the profit, we multiply the cost price by the profit percentage:
Profit = 25% of Rs 300 = (25/100) * 300 = Rs 75
The selling price is obtained by adding the profit to the cost price:
Selling price = Cost price + Profit = Rs 300 + Rs 75 = Rs 375.
Therefore, the selling price of the novel is Rs 375.
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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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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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I'm trying to formulate an equation to solve for the total cost of each coffee that was bought. Im having trouble putting one together for this question. Any help would be greatly appreciated.
Neveah bought a cupcake for $5 and coffees for 5 coworkers. She spent $35. How much was each coffee
Let's denote the cost of each coffee as 'c'.Neveah bought a cupcake for $5, which we can represent as 5.
She also bought coffees for 5 coworkers, so the total cost of the coffees can be represented as 5c.
The total amount Neveah spent is $35.
Putting it all together, we can set up the equation:
5 + 5c = 35
To solve for 'c', we can isolate the variable by subtracting 5 from both sides:
5c = 30
Then, we divide both sides by 5 to solve for 'c':
c = 30/5
Simplifying the expression, we find that each coffee costs $6.
Therefore, each coffee was bought for $6.
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Kent put $8,500 into an 18 month CD. The interest rate is 3.25% How much money will Kent earn in interest?
Kent will earn $553.12 in interest from his 18-month CD with an interest rate of 3.25%.
To calculate the interest earned, we can use the formula: Interest = Principal × Rate × Time. In this case, the principal (amount invested) is $8,500, the interest rate is 3.25% (or 0.0325 as a decimal), and the time is 18 months (or 1.5 years). Plugging in these values into the formula, we get: Interest = $8,500 × 0.0325 × 1.5 = $553.12. Therefore, Kent will earn $553.12 in interest from his CD.
It's important to note that the interest rate is typically expressed as an annual rate. In this case, the interest rate is 3.25%, which means that for a full year, Kent would earn 3.25% of the principal amount. However, since the CD term is 18 months (or 1.5 years), we need to adjust the formula accordingly. By multiplying the principal by the interest rate and the time, we can determine the total interest earned over the given period. In this case, the interest earned is $553.12.
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Darren lives in Wrexham and works in Corwen.
a) Use the chart to find the road distance
between Wrexham and Corwen.
(a) The road distance between Wrexham and Oswestry is 15 miles.
(b) The number of miles Sarah travels to and from work each week is 330 miles.
Given a chart of the road distances between various towns and cities.
(a) From the chart,
Distance the corresponds to Wrexham and Oswestry = 15 miles
Road distance between Wrexham and Oswestry is 15 miles.
(b) Distance between Ruthin and Oswestry = 33 miles
Total distance travelled to and from work in a day = 33 × 2 = 66 miles
She works 5 days a week.
Total distance travelled for 5 days = 66 × 5 = 330 miles
Hence, the number of miles travelled by Sarah in a week is 330 miles.
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The chart is given below.
"Your question is incomplete, probably the complete question/missing part is:"
The chart shows the distances, in miles, between some towns and cities.
Toby lives in Wrexham and works in Oswestry.
Wrexham
18
Ruthin
a) Use the chart to find the road distance
between Wrexham and Oswestry.
15
21
12
Corwen
15
33
23
Oswestry
Sarah lives in Ruthin and works in Oswestry for
5 days a week. Each day she travels to and
from work using the route shown on the map.
MOLD
ROTHEN
WRESTHAM
b) How many miles, in total, does she travel to
and from work each week? 231 miles
CORNEN
OSWESTRY
Choose CI
B.
zoom in
Find the value of the variables for
which ABCD must be a parallelogram.
~ 3x
X
3
3y
3y
D
21
Required
X =
?/1
I
22
Required
y =
?/1
.
D
The value of the variables for which ABCD must be a parallelogram include the following:
x = 4.
y = 5.
How to determine value of the variables for ABCD?In order for any quadrilateral to be considered as a parallelogram, two pairs of its parallel sides must be equal (congruent). This ultimately implies that, the diagonals of a parallelogram would bisect one another only when their midpoints are the same:
Line segment AC = Line segment BD
Next, we would write an equation to model the length of the diagonals of this parallelogram as follows;
4x - 2 = 3y - 1 .........equation 1.
3y - 3 = 3x .........equation 2.
From equation 2, we have the following:
y - 1 = x .........equation 3.
By substituting equation 3 into equation 1, we have:
4(y - 1) - 2 = 3y - 1
4y - 4 - 2 = 3y - 1
4y - 3y = 6 - 1
y = 5.
For the value of x, we have:
x = y - 1
x = 5 - 1
x = 4
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Complete Question:
Find values of x and y for which ABCD must be a parallelogram.
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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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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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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Tommy walks 2 miles to school each morning. During his walk he sees billboards every 1/5 of a mile. How many billboards does he see each morning?
Tommy walks 2 miles to school each morning, and he sees a billboard every 1/5 of a mile.
To find out how many billboards he sees, we can divide the total distance he walks (2 miles) by the distance between each billboard (1/5 of a mile).
Number of billboards = Total distance / Distance between billboards
= 2 miles / (1/5 mile)
= 2 miles * (5/1)
= 10 billboards
Therefore, Tommy sees 10 billboards each morning.
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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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Julia writes 2 fractions with the same denominator that have numerators 8 and 2 . What could the denomination be if the sum is less than 1.?Equal to 1? Greater than 1?
If the sum of the fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.
To find a denominator that satisfies the given conditions, we can consider the fractions with numerators 8 and 2. If the sum of these fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.
To determine the possible denominators that satisfy the conditions, we need to consider the given numerators of 8 and 2. Since the fractions have the same denominator, let's denote it as 'd'. The fractions can be written as 8/d and 2/d.
If the sum of these fractions is less than 1, we have:
8/d + 2/d < 1
Combining the fractions, we get:
(8 + 2)/d < 1
Simplifying, we have:
10/d < 1
To satisfy this inequality, the denominator 'd' can be any number greater than 10. For example, if we choose d = 11, the fractions become 8/11 and 2/11, and their sum is 10/11, which is less than 1.
If the sum of the fractions is equal to 1, we have:
8/d + 2/d = 1
Combining the fractions, we get:
10/d = 1
Solving for 'd', we find that the denominator must be 10. For example, if we choose d = 10, the fractions become 8/10 and 2/10, and their sum is 10/10, which is equal to 1.
If the sum of the fractions is greater than 1, we have:
8/d + 2/d > 1
Combining the fractions, we get:
10/d > 1
To satisfy this inequality, the denominator 'd' must be less than 10. For example, if we choose d = 9, the fractions become 8/9 and 2/9, and their sum is 10/9, which is greater than 1.
In summary, if the sum of the fractions is less than 1, the denominator could be any number greater than 10. If the sum is equal to 1, the denominator must be 10. If the sum is greater than 1, the denominator must be less than 10.
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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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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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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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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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