Two cars drive from one end to the other, in opposite directions. Each goes at a constant speed. One car takes 30 seconds to get from one end to the other. The other takes 50 seconds. They both reach the end at the same time. Draw a graph and use it to find how far the cars are from each end of the track when they pass one another.

Answer:

A. [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,2) (3,3)

We see the y increase by 1 and the x increase by 3, so the slope is

m = 1/3

So, the answer is A. [tex]\frac{1}{3}[/tex]

The value of x in the circle is 3.

We have,

In geometry, a secant is a line that intersects a circle at two distinct points.

The formula for two secant segments on a circle states that the product of the lengths of one secant segment and its external segment is equal to the product of the lengths of the other secant segment and its external segment.

We will use the formula for two secants on a circle.

So,

There are two secant segments on the circle.

This means,

5 x (5 + 3x + 1) = 6 x (6 + 2x)

Now,

Solve for x.

5 x (5 + 3x + 1) = 6 x (6 + 2x)

Distributive property.

5 x (6 + 3x) = 6 x (6 + 2x)

Adding like terms

30 + 15x = 36 + 12x

15x - 12x = 36 - 30

2x = 6

Divide 2 on both sides.

x = 3

Thus,

The value of x in the circle is 3.

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The best estimate of the random sample in the survey that support the proposal is the option; 4.1

A random sample is a collection of data selected from a population such that each member of the population have the same chance of being selected.

The best estimate can be obtained from the mean value of the result from the poll, which can be obtained as follows;

The mean response = The sum of the response ÷ The count or the number of responses

The responses are; 7, 2, 6, 7, 3, 5, 5, 3, 2, 1

The sum of the response = 7 + 2 + 6 + 7 + 3 + 5 + 5  + 3 + 2 + 1 = 41

The number of response = 10

The mean of the response = (7 + 2 + 6 + 7 + 3 + 5 + 5  + 3 + 2 + 1)/10 = 4.1

The best estimate of the state citizens that support the proposal, therefore is; 4.1, which indicates that the citizens in the sample are slightly in support of the proposal.

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The missing values from the ratio table are underlined:

Peppermints: 14, 2, 2/7.

Chocolates: 21, 21, 189.

To fill in the missing values in the ratio table, we need to find the common ratio between the given values.

For the Peppermints row:

Common ratio = (2nd value) / (1st value) = 2 / 14 = 1/7

So, the missing value can be found by multiplying the 2nd value (2) by the common ratio:

Missing value = (2nd value) * (common ratio) = 2 * (1/7) = 2/7

Therefore, the missing value in the Peppermints row is 2/7.

For the Chocolates row:

Common ratio = (3rd value) / (2nd value) = 189 / 21 = 9

The missing value in the Chocolates row can be found by dividing the 3rd value (189) by the common ratio:

Missing value = (3rd value) / (common ratio) = 189 / 9 = 21

Therefore, the missing value in the Chocolates row is 21.

The completed ratio table is as follows:

Peppermints - 14, 2, 2/7

Chocolates - 21, 21, 189

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Answer: 0

Step-by-step explanation:

Range = Highest number - lowest number

range = 6 - 6

range = 0

Based on the information provided, the type of sample used in the research study would be a convenience sample.

A convenience sample is a non-probability sampling technique where participants are selected based on their availability and willingness to participate. In this case, the professor selected the first 55 students who arrived in class, which means the sample was not selected randomly or systematically. It is important to note that convenience samples may not represent the entire population accurately, and therefore, the results obtained from such samples may not be generalizable to the larger population. As such, caution should be taken when interpreting the findings of this research study.

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This means the Probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

To make the game fair, we need to ensure that the probability of drawing a card with a star is the same as the probability of drawing a card without a star.

Currently, there are 4 cards with stars and 6 cards without stars, which means the probability of drawing a star is 4/10 or 2/5, while the probability of drawing a card without a star is 6/10 or 3/5.

To make the game fair, we need to adjust the number of cards with stars and without stars so that the probabilities are equal.

Option A is not correct because the game is not currently fair.

Option B is not correct because adding 2 cards with stars will increase the probability of drawing a star to 6/12 or 1/2, which is not equal to the probability of drawing a card without a star.

Option C is also not correct because adding a star to 1 of the blank cards will still result in a probability of drawing a star that is not equal to the probability of drawing a card without a star.

Therefore, the correct answer is option D: take away 2 blank cards. If we remove 2 blank cards, we are left with 4 cards with stars and 4 cards without stars. This means the probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

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No, the Vaughns do not qualify for Chapter 7 bankruptcy.

Filing petition under chapter 7 stops most collection actions against the debtor or the debtor's property.

In the field of bankruptcy, the means test is used to determine whether an individual or family qualifies for Chapter 7 bankruptcy. This test compares the debtor's income to the median income in their state.

In this case, the Vaughns make $58,000 a year which is above Florida's median annual income of $47,778. Therefore, this stipulates they are not eligible for Chapter 7 bankruptcy.

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To find the test statistic for a test to show that the population mean height of the school district is lower than 59 inches, we can perform a one-sample t-test.

The test statistic is calculated using the sample mean, sample standard deviation, sample size, and the hypothesized population mean.

Given the sample heights of the 11 fifth-grade boy students: 59.0, 57.2, 57.1, 58.0, 57.0, 50.1, 52.3, 55.6, 57.8, 53.9, 57.8, we can calculate the sample mean () and sample standard deviation (s).

= (59.0 + 57.2 + 57.1 + 58.0 + 57.0 + 50.1 + 52.3 + 55.6 + 57.8 + 53.9 + 57.8) / 11

Next, calculate the sample standard deviation:

s = sqrt(((59.0 - )^2 + (57.2 - )^2 + ... + (57.8 - )^2) / (11 - 1))

Once you have the sample mean and sample standard deviation, you can calculate the test statistic (t):

t = ( - μ) / (s / sqrt(n))

where μ is the hypothesized population mean (in this case, 59 inches), and n is the sample size (11).

By substituting the values into the formula, you can calculate the test statistic rounded off to the first decimal place.

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The linear combination of u and v that gives us the vector ⟨−10,−6⟩ is (−22,−6)

To find a linear combination of the vectors u and v that results in the vector ⟨−10,−6⟩, solve the system of linear equations:

a u + b v = ⟨−10,−6⟩

where a and b are scalars.

Expanding the left-hand side using the given vectors:

a ⟨−2,−3⟩ + b ⟨−1,3⟩ = ⟨−10,−6⟩

Simplify:

⟨−2a − b, −3a + 3b⟩ = ⟨−10,−6⟩

The following system of equations is derived:

-2a - b = -10

-3a + 3b = -6

Solve for a and b by substitution. Rearrange the first equation to solve for b:

b = -10 + 2a

Substitute this expression for b into the second equation:

-3a + 3(-10 + 2a) = -6

Simplify:

-3a - 30 + 6a = -6

3a = 24

a = 8

Substitute the value for a into the expression for b:

b = -10 + 2a = -10 + 2(8) = 6

Therefore, the linear combination of u and v that gives us the vector ⟨−10,−6⟩ is:

8u + 6v = 8⟨−2,−3⟩ + 6⟨−1,3⟩ = ⟨−16,−24⟩ + ⟨−6,18⟩ = ⟨−22,−6⟩

So, 8u + 6v = ⟨−22,−6⟩ which is the desired linear combination of the vectors u and v.

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The complete question in ideal form is given as thus:

Given vector u = (-2,-3 and v (-1,3) , find a linear combination of the vectors U and v of the form au + bv that would result in the - vector (-10, -6).

The type of indeterminate form obtained by direct substitution in the given limit is 1^∞, where 1^∞ is not a determinate form and its value is not always predictable.

Applying L'Hôpital's Rule to the limit, we get:

lim_(xâ0^+) [cos(Ï/2 - x)]^x = lim_(xâ0^+) e^[x ln(cos(Ï/2 - x))]

Now, applying L'Hôpital's Rule to the exponent, we get:

= lim_(xâ0^+) e^[x (-tan(Ï/2 - x))]

= e^0 = 1

Therefore, the limit is equal to 1.

Using a graphing utility to graph the function, we can see that the limit approaches 1 as x approaches 0 from the right side. Therefore, the result obtained using L'Hôpital's Rule is verified by the graph.

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To use Lagrange multipliers, we first need to set up our objective function and constraint equation. Constructing a box with dimensions 12x12x6 feet will minimize the cost of construction.

Our objective is to minimize the cost of constructing the box, which is equal to:

C = 5xy + 2(3xy + 3xz + 3yz)

where x, y, and z are the dimensions of the box, and we have broken up the cost into the bottom and sides/top respectively. Our constraint is that the volume of the box must be 480 cubic feet, so:

xyz = 480

To use Lagrange multipliers, we set up the following equation:

∇C = λ∇(xyz)

where ∇C is the gradient of our objective function, ∇(xyz) is the gradient of our constraint equation, and λ is our Lagrange multiplier.

Taking the partial derivatives of our objective and constraint functions, we get:

∇C = (5y, 5x, 6x + 6y)
∇(xyz) = (yz, xz, xy)

Setting these equal and solving for λ, we get:

5y / yz = 5x / xz = (6x + 6y) / xy = λ

Simplifying, we get:

x = y = 2z

Substituting this into our constraint equation, we get:

4z^3 = 480

z = 6

Substituting this back into our dimensions, we get:

x = y = 12

So the minimum cost of constructing the box is:

C = 5(12)(12) + 2(3(12)(12) + 3(12)(6) + 3(12)(6)) = $1,296

Therefore, constructing a box with dimensions 12x12x6 feet will minimize the cost of construction.

To find the minimum cost for constructing a 480 cubic feet box with the bottom costing $5 per square foot and the top and sides costing $3 per square foot, we can use Lagrange multipliers. Let the dimensions of the box be length (x), width (y), and height (z).

First, we need to define the constraint function:
G(x, y, z) = xyz - 480 (the volume constraint)

Next, define the cost function:
C(x, y, z) = 5xy + 3(xz + yz + xy) (cost of bottom + cost of top and sides)

Now, we use the Lagrange multiplier λ and set the gradient of the cost function equal to the gradient of the constraint function multiplied by λ:
∇C(x, y, z) = λ∇G(x, y, z)

This results in a system of equations:

5y + 3z + 3y = λy
5x + 3z + 3x = λx
3x + 3y = λz

We also have the constraint equation:
xyz = 480

Solve this system of equations to find the optimal dimensions x, y, and z. Then, plug these dimensions into the cost function C(x, y, z) to find the minimum cost for constructing the 480 cubic feet box.

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Answer:

To solve the inequality 3 ≤ (x - 4)/2 + x/3 < 2, we can start by simplifying the expression on the right-hand side:

(x - 4)/2 + x/3 = (3(x - 4) + 2x)/6 = (5x - 12)/6

Substituting this back into the inequality, we have:

3 ≤ (5x - 12)/6 < 2

Multiplying both sides by 6, we get:

18 ≤ 5x - 12 < 12

Adding 12 to all sides, we get:

30 ≤ 5x < 24

Dividing all sides by 5, we get:

6 ≤ x < 4.8

Since x is an integer, the only integer that satisfies this inequality is x = 6. Therefore, the solution set for the inequality 3 ≤ (x - 4)/2 + x/3 < 2, where x belongs to an integer, is {6}.

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The expression (×) = 2× - 5ײ + 3 is a quadratic function. It represents a parabola that opens downward with a vertex at (0,3). The x-intercepts are (-1,0) and (3/5,0), and the y-intercept is (0,3).

The given expression (×) = 2× - 5ײ + 3 is a quadratic function in standard form, where the coefficient of the x² term is negative, indicating that the parabola opens downward. The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

To find the vertex of the parabola, we can use the formula x = -b/2a, which gives the x-coordinate of the vertex. In this case, a = -5 and b = 2, so x = -2/(2*(-5)) = 0. The y-coordinate of the vertex can be found by substituting x = 0 into the expression, which gives f(0) = 2(0) - 5(0)² + 3 = 3. Therefore, the vertex of the parabola is at (0,3).

To find the x-intercepts of the parabola, we can set the expression equal to zero and solve for x. This gives the quadratic equation 5x² - 2x - 3 = 0. Factoring this equation, we get (5x + 3)(x - 1) = 0, so the x-intercepts are -3/5 and 1. However, we can discard the negative value because it is not within the domain of the problem. Therefore, the x-intercept is (3/5,0).

To find the y-intercept of the parabola, we can set x = 0 in the expression, which gives f(0) = 3. Therefore, the y-intercept is (0,3).

In conclusion, the expression (×) = 2× - 5ײ + 3 represents a downward-opening parabola with a vertex at (0,3), x-intercept at (3/5,0), and y-intercept at (0,3).

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Answer:

a. The population distribution of the duration of your phone calls is likely to be bell shaped. This is because the mean, median, and mode are all equal to 2.4 minutes. This means that the data is evenly distributed around the mean.

b. The distribution of the 45 calls is likely to be bell shaped as well. This is because the sample size is large enough to be representative of the population. Additionally, the sample was randomly selected, so it is unlikely to be biased.

c. The sampling distribution of the sample mean is also likely to be bell shaped. This is because the central limit theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is large enough. In this case, the sample size is 45, which is large enough to satisfy the requirements of the central limit theorem.

It is important to note that the sampling distribution of the sample mean will only be exactly normal if the population distribution is normal. However, in most cases, the sampling distribution will be approximately normal, even if the population distribution is not.

Step-by-step explanation:

False. The number of steps involved in each type of hypothesis test depends on the specific details of the problem and the statistical method used.

what is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

False. The steps in a two-sample hypothesis test are not necessarily twice the number of steps in a one-sample hypothesis test.

Both one-sample and two-sample hypothesis tests involve similar basic steps such as stating the null and alternative hypotheses, selecting a significance level, calculating a test statistic, and making a decision to reject or fail to reject the null hypothesis based on the calculated p-value.

However, in a two-sample hypothesis test, there are additional steps required to compare the means or proportions of two different groups or samples. These additional steps involve checking the assumptions of equal variances and independence, calculating a pooled standard error or degrees of freedom, and performing a two-sample t-test or z-test depending on the sample size and distribution.

Therefore, False.  the number of steps involved in each type of hypothesis test depends on the specific details of the problem and the statistical method used.

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Answer:

The formula for the volume of a cone is V = (1/3)πr^2h,

r is the base radius

h is the height.

Substituting the given values, we get:

V = (1/3)π(4 yards)^2(9 yards)

V = (1/3)π(16 yards^2)(9 yards)

V = (1/3)π(144 yards^3)

V = 48π cubic yards

Therefore, the volume of the cone is 48π cubic yards.

Answer:

The slope is 0

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Using the slope-intercept form, the slope is 0.

m = 0

(See the attachment below)

Hope this helps :)

Pls brainliest...

Answer:

To tell if a polynomial is constant, linear, quadratic, cubic or quartic, you must first look at the highest power of the variable in the polynomial. If the highest power is 0, then the polynomial is a constant. If the highest power is 1, then it is a linear polynomial. If the highest power is 2, then it is a quadratic. If the highest power is 3, then it is a cubic and finally, if the highest power of the variable is 4, then the polynomial is a quartic.

Step-by-step explanation:

No, Jenna and Henry cannot both be correct. Jenna’s answer of 614 hours is incorrect, as it is much too long for a school day. Henry’s answer of 6.25 hours is also incorrect, as it is much too short for a school day.

The part of the length of the school day that is the same in all three ways the time is given is the hours. In the first way, the school day is given as 6 hours and 15 minutes.

In the second way, the school day is given as 6.25 hours. In the third way, the school day is given as 375 minutes. In each case, the number of hours in the school day is the same: 6 hours. However, the way that the minutes are expressed differs, leading to different numerical values.

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The volume of the cone is 57.44 cubic cm

The volume of the cone and sphere is 229.88 cubic cm

The height of the square pyramid will be 115.03 cm

The volume of a cone can be calculated using the formula:

V = (1/3)πr²h

where

V = volume of the cone

π = pi, approximately 3.14

r = radius of the base of the cone

h = height of the cone

2 x V = 2 * (1/3) * 3.14 * 2.8² * 3.5

The volume of the cone is 57.44 cubic cm

2.

Volume = volume of cone + volume of sphere

= (4/3)πr³ +  (1/3)πr²h

= (4/3) * 3.14 * 3.4³ +  (1/3) * 3.14 * 3.4² * 5.4

= 229.88 cubic cm

3. Volume of square pyramid

= base area * h/3

when base is 230

= 230² * 147/3 = 2592100

when base is 260

260² * h/3 = 2592100

h/3 = 2592100 / 260²

h = 115.03 cm

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Answer: 60

Step-by-step explanation:

Lowest common multiple is the smallest number that 5 10 and 12 can all multiply too

Multiples of 10 are easy, any number ending in 0

So you need to find a number that 5 and 12 go into that ends in 0

We can do this by doing 5*12 which gives us 60 which is divisible by 10

Step-by-step explanation:

a probability is airways the ratio

number of desired cases / number of totally possible cases

so, we have 7 nickels and 6 dimes. together that means we have 7+6 = 13 coins in total in the pocket.

since we return the coin from the first pull, we have the exact same probabilities for the second pull.

the 2 pulls are to be considered one combined event, so we need to combine the individual probabilities for the overall event probability.

the probabilty to pull a nickel in a pull is

7/13

7 desired possible outcomes over 13 total possible outcomes.

the combination of the probabilities of both pulls is simply their product.

so, the probability to pull 2 nickels is

7/13 × 7/13 = 49/169 = 0.289940828...

Answer:

8+17+5=30

Step-by-step explanation:

Kevin spends mixing, baking, and cooling the muffins. If you add 7 and 8 you get 15 and add another 5 you get 20+10 = 30

156.25cm

Step-by-step explanation:

The area of a square is L×L

12.5×12.5=156.25cm

The shape that has reflectional symmetry but not rotational symmetry is the water bottle and

bulb

A shape or object that exhibits reflectional symmetry but not rotational symmetry is one that can be reflected acros a line or axis to create a mirror image  but it cannot be rotated by any angle and still maintain the same appearance. In other words, it does not possess any rotational symmetry

Along the vertical axis, the water bottle has reflectional symmetry. Th bulb can possess reflectional symmetry when kept symmetrical to a particular axis.

Both lacks rotational symmetry

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Answer:

Kiera will use 15 yellow charms

Step-by-step explanation:

The pattern would look like this:

BBYYYBBYYYBBYYYBBYYYBBYYY

B = Blue Charms

Y = Yellow Charms

The domain of the function is all non-negative real numbers.

In this situation, the function F(n) is used to estimate the amount of adhesive needed to tile a floor with an area of n square feet. The expression F(n) = n√+1 represents the formula used for the estimation.

To determine the domain of the function, we need to consider the restrictions or limitations on the variable n. In this case, since we are dealing with the area of a floor, the area cannot be negative. Therefore, the domain of the function consists of all non-negative real numbers.

In other words, any non-negative value of n, including zero and all positive real numbers, can be used as input for the function. However, negative values are not applicable in this context since the area of a floor cannot be negative.

Hence, the domain of the function F(n) in this situation is all non-negative real numbers.

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The graph of the logaritmic function is on the image at the end.

So here we want to graph the function:

y = 3log₂(-x) - 9

To graph this, we can evaluate it in some values and then find some points. We can graph these points and then connect them.

if x = -1 then:

y = 3*log₂(1) - 9   = -9

So we have the point (-1, 9)

if x = -2 then:

y = 3*log₂(2) - 9   = -6

We have the point (-2, -6)

And so on, when you have enough points, you can graph them and connect them, you should get something like the graph in the image at the end.

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