the weight of the crackers originally in the box was 120/23 pounds.
Let the weight of the entire box be x pounds. Now, Roger served 5/8 pound of crackers, which was 2/3 of the entire box.
Therefore, the weight of the crackers left in the box = (1 - 2/3) x = 1/3 xSince the crackers served by Roger was 5/8 pound, the weight of the crackers left in the box = x/3, then we can set up the following equation to find the value of x:5/8x + 1/3x = x
Multiplying the equation by 24 (the least common multiple of 8 and 3) on both sides gives us:
15x + 8x = 24x
Therefore, 23/24 x = 5/8 pound of crackers served by Roger.So, x = (5/8) x (24/23) pounds = 15/23 pounds
To solve the given question, let us suppose that the weight of the entire box of crackers is x pounds. Now, the given information is that Roger served 5/8 pound of crackers which was 2/3 of the entire box.
Therefore, the weight of the crackers left in the box = (1 - 2/3) x = 1/3 x.Now, we need to find out the original weight of the crackers in the box, which is the value of x.
To do that, we can set up an equation as follows:5/8x + 1/3x = xMultiplying both sides by the least common multiple of 8 and 3, which is 24, we get:15x + 8x = 24x
Simplifying further, we get:23x = 120x = 120/23 poundsThis is the weight of the entire box of crackers.
Therefore, the weight of the crackers originally in the box was 120/23 pounds.
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If f(x)=x-1/3 and g(x)=3x+1 what is (f times g)(x)?
3x+1
x-3
3x
x
The expression (f times g)(x) represents the product of the functions f(x) and g(x). In this case, f(x) = x - 1/3 and g(x) = 3x + 1. To find the product, we substitute g(x) into f(x) and simplify the expression.
When we substitute g(x) into f(x), we get:
(f times g)(x) = f(g(x)) = f(3x + 1)
Now, substituting the expression for f(x) into f(g(x)), we have:
f(g(x)) = (3x + 1) - 1/3
Simplifying further, we combine like terms:
= 3x + 1 - 1/3
Thus, the product of f(x) and g(x), (f times g)(x), simplifies to:
(f times g)(x) = 3x + 1 - 1/3
(f times g)(x) equals 3x + 1 - 1/3.
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The cost c of supplies for school depends on other factors lost at least 2 independent variables that could effect the cost of school supplies
Here are two independent variables that could affect the cost of school supplies:1. Inflation Rate: The inflation rate is a measure of the overall increase in prices over time.
It can impact the cost of various goods and services, including school supplies. If the inflation rate is high, the prices of school supplies may increase, leading to higher costs for purchasing these items.
2. Demand for School Supplies: The demand for school supplies can also influence their cost. Probability of Higher demand typically leads to increased prices, as suppliers may adjust their prices to match the demand. Factors such as back-to-school seasons, educational policies, and population growth can affect the demand for school supplies.
By considering the inflation rate and the demand for school supplies as independent variables, we can better understand how these factors can impact the cost of school supplies.
However, it's important to note that there could be other variables that can also affect the cost, such as production costs, supply chain disruptions, and changes in government policies related to education or trade.
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The cost c of supplies for school depends on other factors lost at least 2 independent variables that could effect the cost of school supplies?
Find the distance of this point from the center of the earth. The masses of the earth and the moon are 5. 98 * 10*24.
The distance of this point from the center of the earth is 5280248.56 m.
Newton's law of gravitation is used to calculate the distance of an object from the center of the earth. The distance of this point from the center of the earth and the masses of the earth and the moon are both determined using Newton's law of gravitation.
The distance of a point from the center of the earth can be calculated using Newton's law of gravitation, which states that
[tex]F = \frac{G(m1\times m2)}{d^2}[/tex],
where F is the force between the two masses, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.
Given that the masses of the earth and the moon are 5.98 * 10²⁴ kg each, we can substitute these values into the formula and solve for d. We know that the force of gravity between the earth and the moon is the centripetal force acting on the moon that keeps it in orbit.
Thus, we can equate the gravitational force to the centripetal force. So,
[tex]F_{gravity} = F_{centripetal}[/tex]
[tex]G(m_1m_2)/r^2 = m\omega^2r[/tex]
Here, ω is the angular velocity of the moon.
So, [tex]d = [(Gm)/(\omega^2)]^{1/3}[/tex]
Where G = 6.674×10^-11 Nm²/kg², m is Mass of earth, ω is angular speed of the moon which is 2.7*10-6/s.
From the above formulas, we can calculate the distance of this point from the center of the earth as follows:
[tex]d = [(6.674\times10^{-11} Nm^2/kg^2 \times 5.98 \times 10^{24} kg)/(2.7\times10^{-6}/s^2)]^{1/3}[/tex]
d = 5280248.56 m
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Janis needs 3 gallons of lemonade for a party she has 4/4 six prints and 4 cups of lemonade or ready-made how many more cups of lemonade does Janice need
Janis needs 3 gallons of lemonade for the party. She already has 4/4 six-packs and 4 cups of ready-made lemonade. The task is to determine how many more cups of lemonade Janis needs to meet the required amount.
To find the answer, we need to convert the gallons of lemonade into cups. Since 1 gallon is equal to 16 cups, 3 gallons would be equal to 3 * 16 = 48 cups.
Janis already has 4 six-packs, which means she has 4 * 6 = 24 cups of lemonade from the six-packs. Adding the 4 cups of ready-made lemonade, Janis has a total of 24 + 4 = 28 cups of lemonade.
To determine how many more cups of lemonade Janis needs, we subtract the cups she already has from the required amount. Thus, 48 - 28 = 20 more cups of lemonade are needed for the party.
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A car dealership buys a used car for $18,790. They mark-up the car by 20%. How much are you as the buyer going to pay?
Therefore, as the buyer, you will pay $22,548 for the used car after the dealership marks it up by 20%.
To calculate the price you, as the buyer, will pay after the car dealership marks up the car by 20%, you need to add the markup amount to the original price.
Markup amount = 20% of $18,790
Markup amount = 0.20 * $18,790
Markup amount = $3,758
The markup amount is $3,758.
To determine the final price you will pay, you need to add the markup amount to the original price:
Final price = Original price + Markup amount
Final price = $18,790 + $3,758
Final price = $22,548
Therefore, as the buyer, you will pay $22,548 for the used car after the dealership marks it up by 20%.
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Select at least two digital communication strategies you can control to protect yourself. Explain why you chose them and how they can safeguard you if you feel like someone is trying to cause you harm.
Two digital communication strategies you can control to protect yourself are:
1. **Strong Passwords**: One of the most effective ways to safeguard your digital communication is by using strong, unique passwords for your online accounts. A strong password should be a combination of upper and lowercase letters, numbers, and special characters. By using strong passwords and regularly updating them, you can prevent unauthorized access to your accounts. This can safeguard you if someone is trying to cause harm by attempting to gain unauthorized access to your personal information or accounts.
2. **Two-Factor Authentication (2FA)**: Enabling two-factor authentication adds an extra layer of security to your digital communication. With 2FA, you need to provide a second form of verification, such as a unique code sent to your mobile device, in addition to your password, to access your accounts. This can protect you if someone manages to obtain your password, as they would still need the second factor to gain access. 2FA makes it significantly harder for malicious individuals to compromise your accounts, providing an added safeguard against potential harm.
By implementing strong passwords and enabling two-factor authentication, you enhance the security of your digital communication and reduce the risk of unauthorized access and potential harm. These strategies provide an additional barrier against malicious activities and help ensure the confidentiality and integrity of your personal information and online accounts.
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An X-15 flew at a top speed of 4520 mph with a max altitude of 354,200 ft. a) What would the stagnation temperature on the nose of the airplane be under those conditions
Under the given conditions and assuming an ambient temperature of 20°C, the stagnation temperature on the nose of the X-15 airplane would be approximately 2337.8 Kelvin.
We have,
Let's proceed by assuming a general value for the ambient temperature. We'll use 20°C as an approximation.
Given:
V = 7274.69 km/h
T = 20°C = 20 + 273.15 K = 293.15 K (conversion to Kelvin)
c_p = 1005 J/kg°C
Now we can substitute these values into the total temperature equation:
T(0) = T + (V² / (2 x c(p)))
T(0) = 293.15 K + ((7274.69 km/h)² / (2 x 1005 J/kg°C))
First, we need to convert the velocity from km/h to m/s:
V = 7274.69 km/h x (1000 m/km) / (3600 s/h) ≈ 2026.86 m/s
Now we can calculate the stagnation temperature:
T(0) = 293.15 K + ((2026.86 m/s)² / (2 x 1005 J/kg°C))
T(0) = 293.15 K + (4111017.56 m²/s² / 2010 J/kg°C)
T(0) ≈ 293.15 K + 2044.65 K
T(0) ≈ 2337.8 K
Therefore,
Under the given conditions and assuming an ambient temperature of 20°C, the stagnation temperature on the nose of the X-15 airplane would be approximately 2337.8 Kelvin.
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Hello would really appreciate it
Answer:
1. Reflect f(x) about the x-axis, obtaining -f(x).
2. Shift -f(x) 5 units left, obtaining -f(x + 5).
3. Shift -f(x + 5) 2 units up, obtaining
-f(x + 5) + 2.
Complete the division problem by determining the number that should be placed in the box.Division bracket with 13 on the left, 4498 inside, and 346 above it. Underneath the 4498, there is a minus 3900. Then there is a solid line with 598 under the line. There is a minus sign and an empty box followed by a solid line. Beneath the line, there is a 78 minus 78 underneath. There is a solid line and a 0 to end the problem.
The number that should be placed in the empty box is 13.
In the given division problem, we start by dividing 4498 by 346. The quotient obtained is written above the solid line as 13. Then, we subtract 13 times 346 (which is 4498) from 4498 itself and write the result, -3900, below the line. Next, we bring down the 598 and subtract 598 from -3900, resulting in -3498.
We continue the process, bringing down the minus sign and subtracting 78 from -3498, which gives us -3576. Finally, we bring down the 0 and subtract 0 from -3576, resulting in 0. Since there is no remainder, the division is complete. Therefore, the number that should be placed in the empty box is 13.
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What is the greatest common factor of 24s3, 12s4, and 18s?
3
6
3s
6s
Mark this and return
The greatest common factor (GCF) of the given expressions 24s^3, 12s^4, and 18s is 6s.
To find the GCF, we need to identify the highest power of each variable (s) that appears in all the expressions. In this case, the highest power of s that appears in all the expressions is s^3.Next, we consider the numerical coefficients. The GCF of the numerical coefficients 24, 12, and 18 is 6.
Finally, we combine the GCF of the numerical coefficients (6) with the highest power of the variable (s^3) to obtain the GCF of the entire expressions, which is 6s^3.Therefore, the greatest common factor of 24s^3, 12s^4, and 18s is 6s^3.
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Tom and zara have a dog walking business. They walk their costomor dogs together and share all th money they make equally
This arrangement ensures that both partners share the workload and the profits equally.
In their dog walking business, Tom and Zara have decided to work together as partners. Whenever they walk a customer's dog, they do it together, combining their efforts to provide a quality service. This partnership allows them to share the workload, ensuring that the responsibilities are divided equally between them. By working together, they can efficiently handle multiple dogs and ensure the safety and well-being of the animals under their care.
In terms of the financial aspect, Tom and Zara have agreed to split the money they make equally. Regardless of who physically handles the payment or interacts with the customers, both partners receive an equal share of the earnings. This fair distribution of profits ensures that neither Tom nor Zara feels disadvantaged or unfairly compensated. By sharing the money equally, they maintain a cooperative and balanced business relationship, fostering trust and harmony in their partnership.
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The area of a rectangle is 400 square inches and its length is 4 times its width how many inches wide is the rectangle
The width of the rectangle is 10 inches, as it is calculated by finding the square root of the ratio of the area to the length.
Let's denote the width of the rectangle as "w" inches. According to the given information, the length of the rectangle is 4 times its width, so the length can be expressed as "4w" inches.
The formula for the area of a rectangle is length multiplied by width. In this case, the area is 400 square inches, so we have the equation:
Area = Length × Width
400 = (4w) × w
400 = 4w^2
To find the width, we can rearrange the equation and solve for "w":
4w^2 = 400
w^2 = 100
w = √100
w = 10
Therefore, the width of the rectangle is 10 inches. This means that the length of the rectangle is 4 times the width, which is 40 inches.
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Plot these coordinates:(1,2),(1,7),(9,7),(9,3),(6,5). What is the area
To find the area of the region formed by the given coordinates, we can use the method of Shoelace Formula or Gauss's Area formula. The area of the polygon formed by the given coordinates is 25 square units
1. Plot the given coordinates: (1,2), (1,7), (9,7), (9,3), (6,5). These points represent the vertices of the polygon.
2. Connect the plotted points in order to form the polygon.
3. Use the Shoelace Formula or Gauss's Area formula to calculate the area of the polygon. The Shoelace Formula involves multiplying the differences of the x-coordinates with the corresponding y-coordinates and summing them up.
4. Apply the Shoelace Formula:
Area = 1/2 * |(1*7 + 1*7 + 9*3 + 9*2 + 6*7) - (2*1 + 7*9 + 7*9 + 3*6 + 5*1)|
= 1/2 * |(7 + 7 + 27 + 18 + 42) - (2 + 63 + 63 + 18 + 5)|
= 1/2 * |101 - 151|
= 1/2 * |-50|
= 25
Therefore, the area of the polygon formed by the given coordinates is 25 square units.
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Points X(4, 1), Y(7, 1) and Z(4, 6) are in standard (x,y) coordinate plane. If XYZW is a rectangle, what is the length, in coordinate units, of XW
The length of XW in coordinate units is [tex]\sqrt{34}[/tex] units.
Given that X (4,1), Y(7,1) and Z(4,6) are the coordinates of a rectangle XYZW in the standard (x,y) coordinate plane.
We need to find the length, in coordinate units, of XW.
Since XZ is perpendicular to XY and XZ and XY are sides of rectangle XYZW, lets use the Pythagorean Theorem to find the length of XW. The length of XZ can be calculated by finding the distance between the coordinates of X and Z.
Using the distance formula, we have;
[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex] = [tex]\sqrt{(4 - 4)^2 + (6 - 1)^2}[/tex][tex]\sqrt{(0)^2 + (5)^2}[/tex][tex]\sqrt{25}[/tex] = 5 units
The length of XY is calculated by finding the distance between the coordinates of X and Y.
Using the distance formula, we have;
[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex] = [tex]\sqrt{(7 - 4)^2 + (1 - 1)^2}[/tex][tex]\sqrt{(3)^2 + (0)^2}[/tex][tex]\sqrt{9}[/tex] = 3 units
Therefore, the length of XW can be calculated as follows:
XW = [tex]\sqrt{(XZ)^2 + (XY)^2}[/tex]XW = [tex]\sqrt{(5)^2 + (3)^2}[/tex]XW = [tex]\sqrt{34}[/tex] units
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Profit, P(-2), is the difference between revenue, R(x), and cost, C(x), so P(x) = R(x) - C(x). Which
expression represents P(x), if R(x) = 2x4 -- 30% + 22-1 and C(x) = 24 x² + 2x + 3?
help
The expression for the profit function P(x) is P(x) = 2x^4 - 24x^2 - 2x - 1.3.
To find the expression for the profit function P(x) when given the revenue function R(x) and cost function C(x), we can substitute the given functions into the equation P(x) = R(x) - C(x).
Given:
R(x) = 2x^4 - 30% + 2^(2-1)
C(x) = 24x^2 + 2x + 3
We substitute the functions into the expression for P(x):
P(x) = R(x) - C(x)
= (2x^4 - 30% + 2^(2-1)) - (24x^2 + 2x + 3)
Simplifying the expression:
P(x) = 2x^4 - 0.3 + 2 - 24x^2 - 2x - 3
= 2x^4 - 24x^2 - 2x - 0.3 - 3 + 2
= 2x^4 - 24x^2 - 2x - 1.3
Therefore, the expression for the profit function P(x) is P(x) = 2x^4 - 24x^2 - 2x - 1.3.
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The weights of 3 year old boys are normally distributed with a mean 21 lbs and standard deviation 0. 7 lbs.
Find the z-score that corresponds with a little boys weight of 33
When the weights of 3-year-old boys are normally distributed with a mean of 21 lbs and a standard deviation of 0.7 lbs then the z-score that corresponds to a little boy's weight of 33 lbs is approximately 17.14.
The weights of 3-year-old boys are normally distributed with a mean of 21 lbs and a standard deviation of 0.7 lbs.
We need to find the z-score corresponding to a little boy's weight of 33 lbs.
The z-score measures the number of standard deviations an observation is from the mean of a distribution.
It helps in determining the relative position of a value within a distribution.
To calculate the z-score, we use the formula:
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation.
In this case, the observed weight is 33 lbs, the mean is 21 lbs, and the standard deviation is 0.7 lbs.
Substituting these values into the formula, we get:
z = (33 - 21) / 0.7
Calculating the numerator, we have:
z = 12 / 0.7
Simplifying further, we get:
z ≈ 17.14
Therefore, the z-score that corresponds to a little boy's weight of 33 lbs is approximately 17.14.
This indicates that the weight of the little boy is about 17.14 standard deviations above the mean weight of 3-year-old boys.
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_ questions can only be answered in your head
A- random
B- on-the-page
C-out-of-left-field
D- From-my-brain
Random questions can be solved in your head. option A
What is random questions?In common usage, randomness is the apparent or actual lack of pattern or predictability in information.
A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable
A random question has no particular pattern therefore it can be asked any how.
Therefore, we can conclude that random questions can only be answered in your heard with any research.
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Write a simplified equivalent expression for the SUM. (5x – 2) + (2x + 9)
The simplified equivalent expression for the sum (5x – 2) + (2x + 9) is 7x + 7.
This can be obtained by combining like terms, which involves adding the coefficients of x and the constant terms separately.
In the given expression, we have (5x – 2) and (2x + 9). To simplify, we can add the coefficients of x together: 5x + 2x = 7x. Similarly, we can add the constant terms: -2 + 9 = 7. Therefore, the simplified expression becomes 7x + 7, where 7x represents the combined coefficient of x and 7 represents the combined constant term.
Overall, by combining like terms, we obtain the simplified equivalent expression of the sum (5x – 2) + (2x + 9) as 7x + 7.
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The volume of a spherical balloon is 950 cm. Find the radius of the
4
balloon. (Volume of a sphere
ZAR).
the radius of the spherical balloon is 8.53 cm.
The volume of a sphere of radius r is given by the formula (4/3)πr³ cm³.
Given that the volume of the spherical balloon is 950 cm³, we have:(4/3)πr³ = 950 cm³
Dividing both sides of the equation by (4/3)π, we get:r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5
Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)
Given that the volume of the spherical balloon is 950 cm³, we need to find the radius of the balloon.
To do this, we will use the formula for the volume of a sphere, which is given by (4/3)πr³ cm³, where r is the radius of the sphere. Using this formula, we can write:
4/3)πr³ = 950 cm³
Dividing both sides of the equation by (4/3)π, we get:
r³ = (950 × 3)/(4 × π) cm³= (2850/4) π/π= 712.5Therefore, r = ∛(712.5) cm= 8.53 cm (approx.)
Hence, the radius of the spherical balloon is 8.53 cm.
The radius of a spherical balloon was to be calculated based on the given volume of the balloon. The formula for the volume of a sphere was used which is (4/3)πr³.
On substituting the given volume and simplifying the obtained equation, we get the value of the radius of the spherical balloon. The final answer for the radius of the balloon was calculated to be 8.53 cm.
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A sphere has a radius of 1. 5 inches. What is the volume of the sphere rounded to the nearest tenth? Use 3. 14 for pi.
A sphere has a radius of 1. 5 inches. What is the volume of the sphere rounded to the nearest tenth, The volume of the sphere with a radius of 1.5 inches is approximately 14.1 cubic inches.
To calculate the volume of a sphere, we use the formula: V = (4/3) * π * r^3
Given that the radius (r) is 1.5 inches and π is 3.14, we substitute these values into the formula:
V = (4/3) * 3.14 * (1.5)^3
V = (4/3) * 3.14 * 3.375
V ≈ 14.1375
Rounding to the nearest tenth, the volume of the sphere is approximately 14.1 cubic inches.
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Calculate the average change in the inflation rate the past five years including 2021 rounded to two decimal places
We calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).= 0.25%. ( fictional )
To calculate the average change in the inflation rate, we require the inflation rates for each of the five years, including 2021. Let's assume the inflation rates for the five years are: 2.5%, 3.2%, 2.8%, 4.1%, and 3.9%.
To find the change in inflation rate for each consecutive year, we subtract the inflation rate of the previous year from the inflation rate of the current year. For example, the change in inflation rate from 2020 to 2021 would be 3.2% - 2.5% = 0.7%.
Next, we calculate the sum of these changes: 0.7% + (current year's change) + (current year's change) + (current year's change).
Finally, we divide the sum by the number of years (five in this case) to find the average change in the inflation rate over the five-year period. After rounding the result to two decimal places, we will have the desired average change in the inflation rate.
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A group of students collected distance versus time data for a model car
Which describes how the speed of the car is changing over time?
A The speed is increasing because the distance traveled during each time increment is increasing.
B The speed is increasing because the distance traveled during each time increment is decreasing.
C The speed is decreasing because the distance traveled during each time increment is increasing.
D The speed is decreasing because the distance traveled during each time increment is decreasing.
Pls help! No trolls
The correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.
The answer to the question is option C) The speed is decreasing because the distance traveled during each time increment is increasing.
Explanation:A group of students collected distance versus time data for a model car. There could be many types of data that can be collected with respect to distance and time.
For instance, distance could be in miles or kilometers, whereas time could be in seconds, minutes, or hours.In this case, the relation between the distance and time of a model car is given, and we have to describe how the speed of the car is changing over time. If the distance traveled during each time increment is increasing, then the speed is decreasing.
Thus, the correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.
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On a map, the scale is 2 inches = 7 miles. What is the actual distance between the two cities if the map distance is 3 inches?
Please help
The actual distance between the two cities is 10.5 miles
How to calculate the actual distance between the two citiesFrom the question, we have the following parameters that can be used in our computation:
Scale: 2 inches = 7 miles
Given that
Map distance = 3 inches
using the above as a guide, we have the following:
1.5 * 2 inches = 7 miles * 1.5
Evaluate the products
3 inches = 10.5 miles
Hence, the actual distance between the two cities is 10.5 miles
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If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to x from the first equation is substituted into the second equation. X 4y = −9 2x 5y = −6 2x 5(4y − 9) = −6 2x 5(−4y − 9) = −6 2(4y − 9) 5y = −6 2(−4y − 9) 5y = −6.
The new equation obtained after substituting the expression equivalent to x from the first equation into the second equation is -18 - 13y = -6.
To solve the given system of equations using the substitution method, we need to substitute the expression equivalent to x from the first equation into the second equation.
To find the new equation, we can follow these steps:
Start with the first equation: x + 4y = -9.
Solve the first equation for x: x = -9 - 4y.
Substitute the expression (-9 - 4y) for x in the second equation: 2x - 5y = -6 becomes 2(-9 - 4y) - 5y = -6.
Simplify the equation by performing the multiplication: -18 - 8y - 5y = -6.
Combine like terms: -18 - 13y = -6.
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A ship’s sonar detects a submarine 880 feet below a point on the ocean’s surface 1450 ft dead ahead of the ship. To the nearest degree, find the angle x. A right triangle. Angle x is opposite to side with length 880 feet. Another side is 1450 feet. The hypotenuse is not labeled. A. 59º b. 37º c. 31º d. 53º.
The measure of the angle x is 59 degrees. Option A
How to determine the valuesThe different trigonometric identities are listed as;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
The measure of the adjacent is 880 feet
The opposite side is the ocean's surface = 1450 feet
The angle is x
Using the tangent identity, we have;
tan θ = opposite/adjacent
Now, we have to substitute the values, we get;
tan x = 1450/880
Divide the values, we get;
tan x = 1. 6477
Take the tangent inverse, we get;
x = 59 degrees
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In 1990, Jerry´s gross pay was $78,000.
A. What was his gross monthly pay?
B. In What month did Jerry hit the maximum taxable Social Security Income?
C. How much Social Security tax did Jerry pay in January of 1990?
D. How much Social Security tax did Jerry pay in December of 1990?
Show Work
A. Jerry paid $403 in Social Security tax both in January and December.
What was Jerry's gross monthly pay? To calculate Jerry's gross monthly pay, you will need to divide his gross pay of $78,000 by the number of months in a year, which is 12.Gross Monthly Pay= Gross Pay/12= $78,000/12= $6,500B. In what month did Jerry hit the maximum taxable Social Security Income?
The maximum taxable Social Security income is $51,300. This implies that Social Security tax is applied only on the first $51,300 of Jerry's income. Jerry's gross pay was $78,000; thus, the maximum taxable Social Security Income for Jerry is $51,300.
Social Security tax is calculated on gross pay, not net income. Jerry will hit the maximum taxable Social Security Income as soon as he earns $51,300 for the year.
The social security tax will no longer be deducted from his paychecks for the remainder of the year. This will occur at the point when Jerry's gross pay equals the maximum taxable Social Security income.
This occurs in August. Gross monthly pay is $6,500. Thus, by August, Jerry will have earned $51,300 (8*$6,500).C. How much Social Security tax did Jerry pay in January of 1990?
Social Security tax rate for 1990 was 6.2 percent of gross pay. This implies that Jerry paid 6.2 percent of his gross pay as Social Security tax. Social Security Tax paid in January= Gross Monthly Pay * Social Security Tax Rate= $6,500 * 6.2%= $403D. How much Social Security tax did Jerry pay in December of 1990?
Social Security tax rate for 1990 was 6.2 percent of gross pay.
This implies that Jerry paid 6.2 percent of his gross pay as Social Security tax. Social Security Tax paid in December= Gross Monthly Pay * Social Security Tax Rate= $6,500 * 6.2%= $403
Hence, Jerry paid $403 in Social Security tax both in January and December.
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Select a value to tell how each pair of angles is related.
The value to determine the relationship between each pair of angles is their sum. we can determine whether they are complementary (90 degrees), supplementary (180 degrees), or explementary (360 degrees), which helps us understand their relationship and properties.
To determine the relationship between two angles, we can consider their sum. If the sum of two angles is equal to 90 degrees, they are complementary angles. Complementary angles are pairs of angles that, when added together, result in a right angle. For example, if Angle A measures 40 degrees and Angle B measures 50 degrees, their sum is 90 degrees, so they are complementary angles.
If the sum of two angles is equal to 180 degrees, they are supplementary angles. Supplementary angles are pairs of angles that, when added together, result in a straight angle. For instance, if Angle C measures 120 degrees and Angle D measures 60 degrees, their sum is 180 degrees, so they are supplementary angles.
On the other hand, if the sum of two angles is equal to 360 degrees, they are explementary angles. Explementary angles are pairs of angles that, when added together, result in a complete revolution or a full circle. For example, if Angle E measures 120 degrees and Angle F measures 240 degrees, their sum is 360 degrees, so they are explementary angles.
By considering the sum of the angles, we can determine whether they are complementary (90 degrees), supplementary (180 degrees), or explementary (360 degrees), which helps us understand their relationship and properties.
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Time
(seconds)
Height
(feet)
12
1
2
24
36
4
48
a. Determine the average rate of change for the problem situation. Be sure to include units
of measure
The average rate of change for the given problem situation is 2 feet per second.
To find the average rate of change between any two points, we divide the change in the output variable by the change in the input variable. The output variable is height in feet and the input variable is time in seconds. The average rate of change between the first and second points is:Change in height: 2 - 1 = 1 foot
Change in time: 12 - 2 = 10 seconds
Average rate of change: 1/10 = 0.1 feet per second
The average rate of change between the second and third points is:Change in height: 4 - 2 = 2 feet
Change in time: 24 - 12 = 12 seconds
Average rate of change: 2/12 = 0.1667 feet per second
The average rate of change between the third and fourth points is:Change in height: 36 - 4 = 32 feet
Change in time: 48 - 24 = 24 seconds
Average rate of change: 32/24 = 1.3333 feet per second
The average rate of change between the first and fourth points is:Change in height: 48 - 1 = 47 feet
Change in time: 48 - 12 = 36 seconds
Average rate of change: 47/36 = 1.3056 feet per second
Thus, we can see that the average rate of change for the problem situation is 2 feet per second.
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Which models represent the sum? 1.2 + 0.3 Select each correct answer. Number line from 0 to 4 by tenths. An arrow shows a jump starting at 0 and ending 2 marks past 1. Another arrow shows a jump starting at 2 marks past 1 and ending at 5 marks past 1. One column, divided into 10 small squares. Two small squares. Plus sign. Three columns, each divided into 10 small squares. Two 10 by 10 grids of 100 squares. All 10 columns of first square and 2 columns of the second square shaded one color. Three columns of the second square shaded a different color. Large square divided into a 10 by 10 grid of 100 small squares. Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares. Ten by 10 grid of 100 squares. The first column and 2 squares of the second column are shaded one color. The next three columns are shaded another color.
Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares. These models provide visual representations of the sum 1.2 + 0.3, helping to understand the addition of these numbers.
To identify the models that represent the sum 1.2 + 0.3, let's analyze the given options:
Number line from 0 to 4 by tenths - This model represents the sum as it includes the values 1.2 and 0.3 on the number line, allowing for visualizing the addition of these numbers.
An arrow shows a jump starting at 0 and ending 2 marks past 1 - This model does not directly represent the sum of 1.2 + 0.3. It only illustrates a jump on the number line, which may not correspond to the sum in question.
Another arrow shows a jump starting at 2 marks past 1 and ending at 5 marks past 1 - Similar to the previous option, this model does not directly represent the sum of 1.2 + 0.3. It demonstrates another jump on the number line, unrelated to the given sum.
One column, divided into 10 small squares - This model does not directly represent the sum 1.2 + 0.3 as it only presents a column without any values or operations.
Two small squares. Plus sign. Three columns, each divided into 10 small squares - This model represents the sum 1.2 + 0.3. The two small squares likely represent 1.2 and 0.3, and the plus sign indicates the operation of addition. The three columns divided into 10 small squares may provide a visual representation of the place value concept.
Two 10 by 10 grids of 100 squares - This model does not directly represent the sum of 1.2 + 0.3. It shows two grids of squares but does not include the given numbers or an addition operation.
All 10 columns of the first square and 2 columns of the second square shaded one color - This model does not directly represent the sum 1.2 + 0.3. It describes shading specific columns in squares, which is unrelated to the given sum.
Three columns of the second square shaded a different color - Similar to the previous option, this model does not directly represent the sum of 1.2 + 0.3. It focuses on shading specific columns in squares without providing a representation of the sum.
Large square divided into a 10 by 10 grid of 100 small squares - This model does not directly represent the sum 1.2 + 0.3. It describes a large square divided into smaller squares but does not include the given numbers or an addition operation.
Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares - This model represents the sum 1.2 + 0.3. The two columns divided into 10 small squares likely represent 1.2 and 0.3, and the plus sign indicates the operation of addition. The three columns divided into 10 small squares may provide a visual representation of the place value concept.
Ten by 10 grid of 100 squares. The first column and 2 squares of the second column are shaded one color. The next three columns are shaded another color - This model does not directly represent the sum 1.2 + 0.3. It focuses on shading specific columns in a grid of squares, which is unrelated to the given sum.
Based on the analysis, the models that represent the sum 1.2 + 0.3 are:
Number line from 0 to 4 by tenths
Two small squares. Plus sign. Three columns, each divided into 10 small squares
Two columns, each divided into 10 small squares. Plus sign. Three columns, each divided into 10 small squares
These models provide visual representations of the sum 1.2 + 0.3, helping to understand the addition of these numbers.
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Terrence is recording what kind of shoes people are wearing at the mall. Out of the 20 people he has seen, 2 are wearing sneakers. What is the experimental probability that the next person Terrence sees will be wearing sneakers?
Terrence saw, and out of those, only two people were wearing sneakers. Therefore, the probability of the next person Terrence sees wearing sneakers is 2/20 or 0.1 or 10%.
The experimental probability of an event happening is the ratio of the number of times the event occurs to the number of trials, i.e., the number of opportunities for the event to happen.Here, Terrence recorded what kind of shoes people are wearing at the mall.
He found out that 2 out of the 20 people he has seen are wearing sneakers. We can determine the experimental probability of the next person Terrence sees wearing sneakers with this information.The experimental probability that the next person Terrence sees will be wearing sneakers can be calculated as follows:Probability of seeing the next person wearing sneakers = Number of people wearing sneakers / Total number of people seen= 2/20
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