5. The number of bananas consumed each day by the chimpanzees at a zoo can be calculated using the equation 2x+5=y-9 where x is the number of chimpanzees and y is the number of bananas consumed. If there are five chimpanzees in one particular enclosure, how many bananas will they eat in a day? ​

Answers

Answer 1

Answer:

24 bananas

Step-by-step explanation:

To solve the equation 2x+5=y-9, we need to substitute x with the number of chimpanzees in the enclosure, which is 5. Therefore:

2(5) + 5 = y - 9

Simplifying the equation, we get:

10 + 5 + 9 = y

y = 24

Hence, the chimpanzees in the enclosure will eat 24 bananas in a day.


Related Questions

The average value of f(x)= 1 + x2 in the interral (1,-2) is: al1 blo () 2 d) 1/3

Answers

The average value of f(x) = 1 + x^2 in the interval (-2, 1) is 2/9.

To find the average value of f(x) = 1 + x^2 in the interval (-2, 1), you need to use the Average Value of a Function formula:

Average Value = (1/(b - a)) * ∫[a, b] f(x) dx

Here, a = -2 and b = 1.

Step 1: Compute the integral of f(x) from -2 to 1.
∫[-2, 1] (1 + x^2) dx

Step 2: Apply the integral rules for polynomials.
∫(1) dx + ∫(x^2) dx = [x] + [1/3x^3]

Step 3: Evaluate the integral from -2 to 1.
([x] + [1/3x^3])| from -2 to 1 = [(1) + (1/3(1)^3)] - [(-2) + (1/3(-2)^3)] = (1 + 1/3) - (-2 + 8/3) = (4/3) - (2/3)

Step 4: Calculate the average value using the formula.
Average Value = (1/(1 - (-2))) * (4/3 - 2/3) = (1/3) * (2/3) = 2/9

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Here is a scatter plot that shows the number of assists and points for a group of hockey players. The model, represented by y=1.5x+1.2, is graphed with the scatter plot. What does the slope mean in this situation? Based on the model, how many points will a player have if he has 30 assists?

Answers

Based on the model, 46.2 points a player will have if he has 30 assists. The graphs that show the association among two variables within a data set are called scatter plots.

The graphs that show the association among two variables within a data set are called scatter plots. It displays data points either on a Cartesian system or a two-dimensional plane. The X-axis is used to represent the independent variable and attribute, while the Y-axis is used to plot the dependent variable. These diagrams or graphs are frequently used to describe these plots.

number of points for a player with 30 assists

x = 30

y = 1.5x + 1.2

= 1.5(30) + 1.2

= 45 + 1.2

= 46.2

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Need an answer please.

Answers

Answer:

(B). 1255.7 yd³

Step-by-step explanation:

16^x = 64x + 4

a x = −12
b x = −2
c x = 2
d x = 12

Answers

The value of x in the given equation by using the graphical method to the nearest whole number is 2.

What is a quadratic equation?

Quadratic equations are algebraic equations that have their highest power raised to the power of two. There are different methods by which we can solve quadratic equations.

Some of the methods for solving quadratic equations include:

Factoring methodQuadratic formulaCompleting the square method, Graphical method

Here, we have 16^x = 64x + 4, to solve this type of equation, we will need to graph both sides of the equation on the graph, by doing so; we have the value of x at the point of intersection of both axis as:

x = −0.0489, 1.7055

Since x cannot be negative, the value of x to the nearest whole number is 2.

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pleaseee help me with this

Answers

Answer:

the eight answer is E hope it helped can you help me with my question

Write the equation of the line in fully simplified slope-intercept form.

Answers

The equation of the line in fully simplified slope-intercept form is y = -7/8x - 7

Writing the equation of the line in fully simplified slope-intercept form.

from the question, we have the following parameters that can be used in our computation:

The linear graph

Where we have the points

(0, -7) and (-8, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx - 7

Next, we have

0 = -8m - 7

Evaluate

m = -7/8

So, we have

y = -7/8x - 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -7/8x - 7

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create a model for one bounce of type b bouncy ball

Answers

To create a model for one bounce of a type B bouncy ball, you would need to consider factors such as the ball's material, initial height, and the surface it's bouncing on.

You can model this bounce using a simplified equation that accounts for energy conservation and the coefficient of restitution. 1. Determine the initial height (h1) from which the ball is dropped. 2. Measure the coefficient of restitution (COR) for the type B bouncy ball.

This value represents how much energy is conserved during a bounce (typically between 0 and 1). 3. Calculate the height (h2) the ball reaches after one bounce using the formula: h2 = COR^2 * h1. 4.

The bounce can be modeled by tracking the ball's vertical position as it falls, rebounds, and reaches the height h2.

This simplified model assumes that air resistance and friction are negligible, and provides an estimation of the bouncy ball's behavior during a single bounce.

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module 52: using shannon’s expansion theorem, factor out 1. x 2. y 3. z from the equation: f = xy !xyz !x!y!z x!yz

Answers

To factor out 1. x 2. y 3. z from the equation f = xy !xyz !x!y!z x!yz using Shannon's Expansion Theorem, we can first write the equation in sum-of-products form:

f = xy !xyz !x!y!z x!yz
 = xy(!xyz)(!x!y!z)(x!yz)

Then, we can apply Shannon's Expansion Theorem to the first variable x, which states that:

x = x(1) + x(!1)

where x(1) represents the case where x is true (1) and x(!1) represents the case where x is false (!1). Applying this theorem to the first term xy, we get:

xy = xy(1) + xy(!1)

where xy(1) represents the case where both x and y are true (1) and xy(!1) represents the case where either x or y (or both) is false (!1).

Using similar expansions for the remaining variables y and z, we can rewrite the equation as:

f = (xy(1) + xy(!1))(yz(1) + yz(!1))(xz(1) + xz(!1))

Expanding this out, we get:

f = xy(1)yz(1)xz(1) + xy(!1)yz(1)xz(1) + xy(1)yz(!1)xz(1) + xy(!1)yz(!1)xz(1) + xy(1)yz(1)xz(!1) + xy(!1)yz(1)xz(!1) + xy(1)yz(!1)xz(!1) + xy(!1)yz(!1)xz(!1)

Now, we can see that the terms that include either x, y, or z (but not all three) are common to each of the eight terms. So, we can factor them out to get:

f = (x+y+z)(xy(1)z(1) + xy(!1)z(1) + xy(1)!z(1) + xy(!1)!z(1))

Finally, we can factor out 1. x 2. y 3. z from this expression to get:

f = xyz(xy(1)z(1) + xy(!1)z(1) + xy(1)!z(1) + xy(!1)!z(1))

Therefore, the factored form of the equation using Shannon's Expansion Theorem is:

f = xyz(xy(1)z(1) + xy(!1)z(1) + xy(1)!z(1) + xy(!1)!z(1))
Factor out variables from the given equation using Shannon's Expansion Theorem. First, let's rewrite the given equation more clearly:

f = xy + !xyz + !x!y!z + x!yz

Now, let's apply Shannon's Expansion Theorem to factor out the variables one by one.

1. Factor out x:

f(x) = x(y + !yz) + !x(!y!z + yz)

2. Factor out y:

f(x, y) = x[y(1 + !z) + !y(z)] + !x[y(!z) + !y(z)]

3. Factor out z:

f(x, y, z) = x[y(z + !z) + !y(z)] + !x[y(!z) + !y(z)]

So, the factored equation is:

f(x, y, z) = x[y(1) + !y(z)] + !x[y(!z) + !y(z)]

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A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students that are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. The student plans to test the hypotheses, H0: μ = 1 versus Ha: μ < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. Are the conditions for inference met?

No, the random condition is not met.
No, the 10% condition is not met.
No, the Normal/large sample condition is not met.
Yes, all conditions for inference are met.


last option is correct

Answers

The correct answer is that No, the Normal/large sample condition is not met.

In order to conduct a hypothesis test about the population mean, we need to check whether the sample data meets the necessary conditions for inference.

There are three main conditions that need to be met:

Random sample: The sample should be selected randomly from the population of interest.

Normality of population or large sample size: If the population distribution is normal, then the sample distribution will also be normal regardless of the sample size.

Independence: Each observation in the sample must be independent of the others.

In this case, we have a sample size of n = 6,

Sample size is smaller than the recommended sample size for the central limit theorem to apply.

So, the correct answer is that No, the Normal/large sample condition is not met.

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Part of a bus table is shown.
The average speed of the bus between Emmanuel Street and Cloeridge Road is 23 km/h.

Work out how many kilometers the bus travels between these two stops. (If answer is a decimal, give to 1 d.p)

Answers

The kilometers the bus travels between these two stops is 5.8 km

Working out the kilometers the bus travels between these two stops.

From the question, we have the following parameters that can be used in our computation:

Speed = 23 km/h

Time = 13 : 40 - 13 : 25 = 15 minutes = 1/4 hr

The kilometers the bus travels between these two stops is calculated as

Distance = Speed * Time

Substitute the known values in the above equation, so, we have the following representation

Distance = 23 * 1/4

Evaluate

Distance = 5.8 km

Hence, the distance is 5.8 km

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Find all possible values of x. The triangles are not drawn to scale
10000
1000
10x

Answers

The possible value of x is any value less than 1100, under the condition that the triangles are not drawn to scale.

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side. Using this theorem, we can find possible values of x in the triangle with sides 10000, 1000 and 10x.

So we have:

10000 + 1000 > 10x
11000 > 10x
1100 > x

Therefore, x can be any value less than 1100.
The triangle inequality theorem states the relationship regarding the three sides of a triangle. According to this theorem, for any particular triangle, the summation of lengths of two sides is always greater than the third side. In short , this theorem aids to  specify that the shortest distance between two distinct points is always a straight line.


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a particular employee arrives at work sometime between 8:00 a.m. and 8:40 a.m. based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:40 a.m. find the probability that the employee will arrive between 8:10 a.m. and 8:15 a.m. round your answer to four decimal places, if necessary.

Answers

The probability that the employee will arrive between 8:10 a.m. and 8:15

a.m. is 0.125 or 12.5% when rounded to two decimal places.

The employee can arrive at any time between 8:00 a.m. and 8:40 a.m, and

we are given that each of these times is equally likely.

The total time interval is 40 minutes (from 8:00 a.m. to 8:40 a.m.), and the

interval between 8:10 a.m. and 8:15 a.m. is 5 minutes.

Therefore, the probability that the employee arrives between 8:10 a.m. and

8:15 a.m. is equal to the ratio of the time interval between 8:10 a.m. and

8:15 a.m. to the total time interval between 8:00 a.m. and 8:40 a.m.:

P(arrival between 8:10 a.m. and 8:15 a.m.) = (5 minutes) / (40 minutes) = 1/8

So the probability that the employee will arrive between 8:10 a.m. and 8:15

a.m. is 0.125 or 12.5% when rounded to two decimal places.

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The sum of two rational number is always a ____________ number

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The sum of two rational numbers is always a rational number.

Any two rational numbers added together will always be a rational number. A rational number is one that can be generally written as the ratio or quotient of two integers with a non-zero denominator. In other words, if p and q are integers and q is not equal to zero, then a rational number may be written as a fraction of the form p/q.

Adding or subtracting two rational numbers is equivalent to adding or subtracting two fractions. Finding a common denominator also an integer and adding or subtracting the numerators while holding the common denominator constant are required steps in the rules for adding and subtracting fractions.

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do blood pressure levels change after listening to soothing music? a random sample of 15 people was selected to determine the change in blood pressure after listening to 5 minutes of soothing, instrumental music. there was an outlier in the data.

Answers

It is possible that blood pressure levels could change after listening to soothing music, but it is unclear from the data given whether this is the case or not.

A sample of 15 people is a relatively small sample size, so it may not be representative of the population as a whole. In addition, it is not clear what method was used to select the sample, so there may be issues with sampling bias.

Furthermore, the presence of an outlier in the data could indicate that there are other factors influencing the change in blood pressure, such as an underlying medical condition or a reaction to a specific type of music. This outlier could also significantly affect the overall results of the study, making it difficult to draw reliable conclusions.

Therefore, it is not possible to determine from the information given whether or not blood pressure levels change after listening to soothing music. A larger and more carefully selected sample would be needed to provide more reliable results.

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(1 point) let f(x,y,z)=(4xz2,−5xyz,−7xy3z) be a vector field and f(x,y,z)=x3y2z. ∇f=( , , ). ∇×f=( , , ). f×∇f=( , , ). f⋅∇f=

Answers

Using vector calculus:

∇f = [tex](4z^2, -5xz, -7xy^3)[/tex]

∇×f = [tex](-35xy^2, 0, 4z)[/tex]

f × ∇f = [tex](-5x^2y^2z^2, 28x^3y^5z^2, 16x^4y^4z)[/tex]

f ⋅ ∇f = [tex]16x z^4 - 25x^2y^2z^2 + 49x^2y^6z[/tex]

To find the gradient, curl, cross product, and dot product of the given vector field and scalar field, we can use the standard formulas for vector calculus:

For the vector field f(x,y,z) = ([tex]4xz^2, -5xyz, -7xy^3z[/tex]), we have:

∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)

= ([tex]4z^2, -5xz, -7xy^3[/tex])

To find the curl of f, we compute the determinant of the following matrix:

| i j k |

| ∂/∂x ∂/∂y ∂/∂z |

| [tex]4xz^2 -5xyz -7xy^3z[/tex] |

This gives:

∇×f = (∂([tex]-7xy^3z[/tex])/∂y − ∂(−5xyz)/∂z, ∂([tex]4xz^2[/tex])/∂z − ∂([tex]-7xy^3z[/tex])/∂x, ∂(−5xyz)/∂x − ∂([tex]4xz^2[/tex])/∂y)

= ([tex]-35xy^2, 0, 4z[/tex])

To find the cross product of f and ∇f, we have:

f × ∇f = det | i j k |

| [tex]4xz^2 -5xyz -7xy^3z[/tex] |

| [tex]x^3y^2z x^2y^2 x^3y^2[/tex] |

= ([tex]-5x^2y^2z^2, 28x^3y^5z^2, 20x^4y^4z - 4x^4y^4z[/tex])

= ([tex]-5x^2y^2z^2, 28x^3y^5z^2, 16x^4y^4z[/tex])

Finally, to find the dot product of f and ∇f, we have:

f ⋅ ∇f = [tex]4xz^2 * 4z^2 - 5xyz * 5xz - 7xy^3z * (-7xy^3)[/tex]

= [tex]16x z^4 - 25x^2y^2z^2 + 49x^2y^6z[/tex]

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a national survey asked 1,501 randomly selected employed adults how many hours they work per week. based on the collected data, a 95 percent confidence interval for the mean number of hours worked per week for all employed adults was given as (41.18,42.63) . which of the following statements is a correct interpretation of the interval?
A. Ninety-five percenr of all employed adults work between 41.18 hours and 42.63 hours per week.
B. The pribability is 0.95 that a sample of size 1501 will produce a mean between 41.18 hours and 42.63 hours
C. Of all samples od size 1501 taken from the population, 95% of the samples will have a mean between 41.18 hours and 42.63 hours
D. We are 95% confident that the mean number of hours worked per week for employed adults in the sample is 41.18 hours and 42.63 hours
E. We are 95% confident that the mean number of hours worked per week for all employed adults is 41.18 hours and 42.63 hour

Answers

We are 95% confident that the mean number of hours worked per week for employed adults in the sample is between 41.18 hours and 42.63 hours.

Option D is correct because it accurately interprets the meaning of a 95% confidence interval.

Option A is incorrect because we cannot make a statement about all employed adults, only about the sample of 1,501 employed adults that was surveyed.

Option B is incorrect because the probability of obtaining a mean between 41.18 hours and 42.63 hours applies only to the specific sample of 1,501 employed adults that was surveyed, not to all possible samples.

Option C is incorrect because the statement refers to 95% of all possible samples, which is not the same as the 95% confidence interval calculated for the specific sample of 1,501 employed adults that was surveyed.

Option D is the correct interpretation of the confidence interval. It means that if we were to take many samples of 1,501 employed adults from the population and calculate a 95% confidence interval for each sample, about 95% of those intervals would contain the true population mean. In other words, we can be 95% confident that the true population mean falls between 41.18 hours and 42.63 hours.

Option E is incorrect because we cannot make a statement with confidence about the true population mean, only about the sample mean.

Hence option D is correct.

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In this assignment we will use the mtcars dataset from RStudio to build a multiple regression model. To build this model, consider the response variable as mpg and the explanatory or independent variables as: cyl, disp, hp, drat, wt, gear, carb. After forming the null hypothesis and the alternative hypothesis, estimate the coefficients and discuss your findings (with the p-value). Are any of the independent variables significant in the model? Build the regression model a second time with the same response variable but this time for the predictive variables only include: drat, gear, and carb. Build the null and alternative hypothesis and discuss the findings from R. Are any of the predictive variables significant? What is the difference between the coefficients considering the two models?

Answers

Answer: who would know thos brp

Step-by-step explanation: ong

a polar curve =() has parametric equations =()cos() and =()sin(). t

Answers

The given polar curve can be represented by the parametric equations x = rcos(t) and y = rsin(t), where r is the distance from the origin to a point on the curve and t is the angle between the positive x-axis and the line segment connecting the origin to that point.

To express the polar curve in terms of the polar coordinate system, we can use the equation r = f(theta), where r is the distance from the origin to a point on the curve and theta is the angle between the positive x-axis and the line segment connecting the origin to that point.

Using the parametric equations x = rcos(t) and y = rsin(t), we can see that:

r = sqrt(x^2 + y^2)

tan(t) = y/x

Therefore, we can express the polar curve as r = f(theta) by eliminating t from the equations:

r = sqrt(x^2 + y^2)

tan(t) = y/x

tan(t) = sqrt(y^2/x^2)

tan(t)^2 = y^2/x^2

1 + tan(t)^2 = (x^2 + y^2)/x^2

(x^2 + y^2)/x^2 = 1/sec(t)^2

(x^2 + y^2)/x^2 = sec(t)^2

(x^2 + y^2)/r^2cos(t)^2 = sec(t)^2

(x^2 + y^2)/r^2 = 1/cos(t)^2

r^2 = x^2 + y^2 = f(theta)^2cos(theta)^2

r = f(theta) = sqrt(x^2 + y^2)/cos(t)

Therefore, the polar curve can also be expressed as r = f(theta) = sqrt(x^2 + y^2)/cos(t) or r = f(theta) = sqrt(x^2 + y^2)/cos(theta).

We can then eliminate t from the equations to express the polar curve in terms of r and theta.

The resulting equation is r = f(theta), where f(theta) is some function of theta that describes the shape of the curve.

Finally, we can rewrite the equation in terms of x and y to get a better understanding of the shape of the curve.

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sally's sweet shoppe has cylindrical cups that have a diameter of 8 centimeters and a height of 5 centimeters which cup has the larger volume in cubic centimeters the cone or the cylinder and by how many cubic centimeters.

HELP IS GREATLY APPRECIATED (ASAP) THANK YOU!
have a good day/night/or morning :)
~Madi

Answers

The cylinder has a larger volume than the cone by 167.55 cubic centimeters.

The cups at Sally's Sweet Shoppe have a diameter of 8 centimeters, so the radius of the cups is 4 centimeters.

The height of the cups is 5 centimeters.

For the cylinder, we have:

Volume of cylinder = π × 4² × 5

= 80π cubic centimeters

For the cone, we have:

Volume of cone = (1/3)× π × 4² × 5

= 80/3π cubic centimeters

Comparing the two volumes, we can see that the cylinder has the larger volume.

The difference in volume between the cylinder and the cone is:

Volume of cylinder- Volume of cone = 80π - (80/3)π

= (240/3)π - (80/3)π

= (160/3)π

= 167.55 cubic centimeters

Therefore, the cylinder has a larger volume than the cone by approximately 167.55 cubic centimeters.

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mr. bray prepares a list of 43 4343 us presidents, 8 88 of whom died in office. then 18 1818 of his students each select a president at random (there can be repeats) for their creative writing assignments. what is the probability that at least one of the students select a president who died in office? round your answer to the nearest hundredth.

Answers

The probability is approximately 0.97.

To find the probability that at least one student selects a president who died in office, we can use the complementary probability method. We'll first find the probability that none of the 18 students select a president who died in office, and then subtract that from 1.

There are 43 presidents, and 8 of them died in office, so there are 35 presidents who did not die in office. The probability that a single student selects a president who did not die in office is 35/43. Since there can be repeats and the selections are independent, the probability that all 18 students select a president who did not die in office is (35/43)^18.

Now, to find the probability that at least one student selects a president who died in office, we subtract the above probability from 1:

Probability = 1 - (35/43)^18 ≈ 0.9743

Rounded to the nearest hundredth, the probability is approximately 0.97.

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there are two charges q1= -5c and q2 = -8c placed 20 cm apart

Answers

The two charges q1=-5c and q2=-8c are placed 20 cm apart from each other. Given two charges, q1 = -5C and q2 = -8C, placed 20 cm apart, you might be interested in finding the electrostatic force between them.

Given two charges, q1 = -5C and q2 = -8C, placed 20 cm apart, you might be interested in finding the electrostatic force between them. To do this, we can use Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
- F is the electrostatic force
- k is the electrostatic constant (8.9875517923 × 10^9 N m²/C²)
- q1 and q2 are the charges (-5C and -8C)
- r is the distance between the charges (20 cm or 0.2 m)
Now, plug the values into the formula and calculate the force:
F = (8.9875517923 × 10^9 N m²/C² * |-5C * -8C|) / (0.2 m)^2
F = (8.9875517923 × 10^9 N m²/C² * 40 C²) / 0.04 m²
F = 8,987,551,792.3 N (approx.)
The electrostatic force between the two charges, 20 cm apart, is approximately 8,987,551,792.3 Newtons.

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For whThe area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room.

Which equations can be used to solve for y, the length of the room? Select three options.

y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0

Answers

Equations that can be used to solve for y, the length of the room is [tex]y^{2}[/tex] - 5y = 750, y(y - 5) = 750 and 750 - y(y - 5) = 0.

Let's assume that the length of the room is y, then the width of the room will be y - 5 (as per the given information).

The area of the rectangular room can be calculated as the product of its length and width, i.e., y(y - 5) = 750.

Now we can simplify this equation to a quadratic equation by bringing all the terms to one side:

[tex]y^{2}[/tex] - 5y - 750 = 0

So, the equations that can be used to solve for y, the length of the room are:

y^2 - 5y - 750 = 0 (This is the simplified quadratic equation)

y(y - 5) = 750 (This is the original equation obtained from the area formula)

750 - y(y - 5) = 0 (This is the same as the equation in option 2, but with terms rearranged)

Therefore, the correct options are:

[tex]y^{2}[/tex] - 5y = 750

y(y - 5) = 750

750 - y(y - 5) = 0

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Write 720,080 in expanded form in two different ways

Answers

720,080 in expanded form in two different ways is

700,000 + 20,000 + 80

7 x 100,000 + 2 x 10,000 + 8 x 10

The given number is seven lakh twenty thousand and eighty

It has 7 lakhs, 2o thousands and 8 tens

720,080 can be written in expanded form in two different ways:

700,000 + 20,000 + 80

This can be expanded as below

7 x 100,000 + 2 x 10,000 + 8 x 10

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After testing H0: p = 0.33; versus HA: p < 0.33; at α = 0.05, with = 0.20 and n = 100, we do not reject H0.Group of answer choicesTrueFalse

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True. After testing H0: p = 0.33 versus HA: p < 0.33 at α = 0.05, with a sample proportion of 0.20 and a sample size of n = 100, we do not reject H0.

True. After conducting a hypothesis test with the given parameters, if the p-value is greater than the significance level (α = 0.05), we do not reject the null hypothesis (H0: p = 0.33). This means that there is not enough evidence to support the alternative hypothesis (HA: p < 0.33) and we conclude that the proportion is not significantly less than 0.33 based on the sample data.

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work out the size of angle x

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The size of angle x is 75° as the ∠BFE and ∠ABC are corresponding angles.

From the attached figure we can observe that line DA and line HE are parallel lines intersected by a transversal CG at points B and F.

We can observe that ∠BFE and ∠EFG are linear angles.

⇒ m∠BFE + m∠EFG = 180°

⇒ m∠BFE + m∠EFG = 180°

⇒  m∠BFE + 105° = 180°

⇒  m∠BFE = 180° - 105°

⇒  m∠BFE = 75°

Also, ∠BFE and ∠ABC are corresponding angles.

We know that corresponding angles are congruent.

so,  m∠BFE = m∠ABC

x =  m∠BFE

x = 75°

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Need answer for number 6 please:)

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Answer:

see below

Step-by-step explanation:

The product will be product because when you multiply 2 negative numbers together, it will always equal a positive number because the negative signs cancel each other out.

Hope this helps :)

at a race track, the average speed of the race cars is measured every lap. the box-and-whisker plot represents the average speed of a certain car for several laps. what is the median?

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The median of the box-and-whisker plot is the value that lies exactly in the middle of the data set. the median is a useful measure of central tendency for the data set, as it provides a representative value that summarizes the central location of the data.

In this case, the box-and-whisker plot represents the average speed of a certain car for several laps at a race track. To find the median, we need to locate the middle value of the data set, which is the point where half of the data is below it and half is above it. The median is represented by the line in the middle of the box on the plot. It indicates that half of the laps recorded had an average speed below this value and half had an average speed above it. Therefore, the median is a useful measure of central tendency for the data set, as it provides a representative value that summarizes the central location of the data.

In the context of a race track and a box-and-whisker plot, the median represents the middle value of the average speeds recorded for a certain car during several laps. The plot organizes the data into four quartiles, with the median being the boundary between the second and third quartiles. To find the median, you would look at the box-and-whisker plot and identify the line within the box that separates the lower and upper halves of the data. This value indicates the median average speed for the car over the measured laps.

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please please help me

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a) The coordinates of Q' are given as follows: Q'(-1, 4).

b) The coordinates of S' are given as follows: S'(-3,2).

What are the translation rules?

The four translation rules are defined as follows:

Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.

The coordinates of Q and S are given as follows:

Q(4, 1), S(2, -1).

Considering the vector, the translation rule is given as follows:

(x, y) -> (x - 5, y + 3).

Hence the coordinates of Q' and S' are obtained as follows:

Q': (4 - 5, 1 + 3) = (-1,4).S': (2 - 5, -1 + 3) = (-3, 2).

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If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet after tt seconds is given by y=40t−16t2y=40t−16t2.

(a) Find the average velocity for the time period beginning with t=2t=2 and

(1) lasting 0.5 seconds:

(2) lasting 0.1 seconds:

(3) lasting 0.05 seconds:

(4) lasting 0.01 seconds:

b) Find the instantaneous velocity when t=2t=2:

Answers

(a) The average velocity for the time period beginning with t=2t=2 and

(1) lasting 0.5 seconds: -40 ft/s

(2) lasting 0.1 seconds: -88.4 ft/s

(3) lasting 0.05 seconds: -67.2 ft/s

(4) lasting 0.01 seconds: -64.36 ft/s

(b) The instantaneous velocity when t=2 is -24 ft/s.

(a) To find the average velocity for a given time period, we need to find the displacement during that time period and divide it by the duration of the time period.

(1) For the time period lasting 0.5 seconds, the initial time is t=2 and the final time is t=2.5. The displacement during this time period is:

[tex]y(2.5) - y(2) = (402.5 - 162.5^2) - (402 - 162^2) = -20 ft[/tex]

The duration of the time period is 0.5 seconds. Therefore, the average velocity is:

average velocity = displacement / duration = -20 / 0.5 = -40 ft/s

(2) For the time period lasting 0.1 seconds, the initial time is t=2 and the final time is t=2.1. The displacement during this time period is:

[tex]y(2.1) - y(2) = (402.1 - 162.1^2) - (402 - 162^2) = -8.84 ft[/tex]

The duration of the time period is 0.1 seconds. Therefore, the average velocity is:

average velocity = displacement / duration = -8.84 / 0.1 = -88.4 ft/s

(3) For the time period lasting 0.05 seconds, the initial time is t=2 and the final time is t=2.05. The displacement during this time period is:

[tex]y(2.05) - y(2) = (402.05 - 162.05^2) - (402 - 162^2) = -3.36 ft[/tex]

The duration of the time period is 0.05 seconds. Therefore, the average velocity is:

average velocity = displacement / duration = -3.36 / 0.05 = -67.2 ft/s

(4) For the time period lasting 0.01 seconds, the initial time is t=2 and the final time is t=2.01. The displacement during this time period is:

[tex]y(2.01) - y(2) = (402.01 - 162.01^2) - (402 - 162^2) = -0.6436 ft[/tex]

The duration of the time period is 0.01 seconds. Therefore, the average velocity is:

average velocity = displacement / duration = -0.6436 / 0.01 = -64.36 ft/s

(b) To find the instantaneous velocity when t=2, we need to find the derivative of the position function y(t) and evaluate it at t=2:

[tex]y(t) = 40t - 16t^2[/tex]

y'(t) = 40 - 32t

y'(2) = 40 - 32(2) = -24 ft/s

Therefore, the instantaneous velocity when t=2 is -24 ft/s.

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express the triple integral tripleintegral_e f(x, y, z) dv as an iterated integral in the two orders dz dy dx and dx dy dz

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Let's consider the triple integral of a function f(x, y, z):
∭f(x, y, z) dV
∫(∫(∫f(x, y, z) dx) dy) dz
These are the two orders for the given triple integral of the function f(x, y, z).

The triple integral_ e f(x, y, z) dv can be expressed as an iterated integral in the two orders dz dy dx and dx dy dz as follows:

First, let's express the integral in the order dz dy dx:

tripleintegral_e f(x, y, z) dv = ∫∫∫ f(x, y, z) dz dy dx

To evaluate this integral, we need to integrate with respect to z first, then y, and finally x. So, we have:

tripleintegral_e f(x, y, z) dv = ∫∫ [∫ f(x, y, z) dz] dy dx

= ∫∫ F(x, y) dy dx

where F(x, y) = ∫ f(x, y, z) dz.

Now, let's express the integral in the order dx dy dz:

tripleintegral_e f(x, y, z) dv = ∫∫∫ f(x, y, z) dx dy dz

To evaluate this integral, we need to integrate with respect to x first, then y, and finally z. So, we have:

tripleintegral_e f(x, y, z) dv = ∫ [∫∫ f(x, y, z) dx dy] dz

= ∫ G(z) dz

where G(z) = ∫∫ f(x, y, z) dx dy.

So, we have expressed the triple integral tripleintegral_e f(x, y, z) dv as an iterated integral in the two orders dz dy dx and dx dy dz. The first order is suitable when the function depends on z and is easier to integrate with respect to z. The second order is suitable when the function depends on x and y and is easier to integrate with respect to x and y.


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