Sue has 200 m&m's. She plans on eating half of what she has each day. How many
candies will she have on the fourth day?

It is observed that the ice in Leah's glass of juice will melt first that the ice in Philip's glass of juice which sits on the table.

___________________________________

It is given that Leah and Philip both have a glass of juice with ice cubes. Leah stirs her juice with her spoon. Philip let's his sit on the table.

Now, we need to answer whose ice cubes will melt first and why;

Firstly, let us assume that the ice is at a temperature of 0°C and the surroundings of the ice are at a temperature of 20°C.

Now, for the ice to melt, it should gain some energy from it's surroundings which can be transferred to the ice from it's surroundings by conduction through metal piece or a plastic piece.

We know that, metal is a best conductor as compared to plastic which means that the above-mentioned energy will be transferred more quickly through the metal as compared to plastic.

Furthermore, in the given condition, Leah stirs her juice with her spoon which we assume is of metal, proving the above-mentioned statements true.

Therefore, it is observed that the ice in Leah's glass of juice will melt first that the ice in Philip's glass of juice which sits on the table.

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The given statement "A right solid has an axis that is also an altitude" is False. The Correct statement is "A right Cone has an axis that is also an altitude".

The altitude of the cone is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is also the height of the cone. So we can say that A right Cone has an axis that is also an altitude.

A right solid have an axis that is also an altitude is the incorrect statement. So, the correct statement is that a right cone has an axis that is also an altitude.

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Answer:

144 ft

Step-by-step explanation:

Put in '3' where 't' is and compute

Height = -16(3^2) + 83(3) + 39 = 144 ft

Answer:   6 1/6 hours after 9 am, or 3 1/6 hours after noon

Step-by-step explanation:

If we count time (x) in hours after 9 am, the stock prices will be ...

 A = 16.15 +0.06x

 B = 16.90 -0.12(x -3)

The value of x when A = B can be found from ...

 A = B

 16.15 +0.06x = 16.90 -0.12(x -3)

 0.18x = 1.11 . . . . . . . . add 0.12x-16.15

 x = 6.16666...(repeating) = 6 1/6

6 1/6 hours after 9 am, the prices will be the same. That is 3 1/6 hours after noon.

_____

The attached graph shows the time as military time: 15.167. That's 3:10 pm, or 6 1/6 hours after 9 am.

Answer:

£3250

Step-by-step explanation:

ann : ben : cheryll

  3  :    7   :     10

The difference between ben and ann in the ratio is 7 - 3 = 4

The real difference between ben and ann is £650.

The real numbers are in the ratio 3:7:10, but they are many times greater than 3, 7, and 10.

Introduce a variable in the ratio.

3x : 7x : 10x

The difference between ben and ann is 7x - 3x = 4x.

The real difference between ben and ann is £650.

Therefore,

4x = £650

x = 162.5

The total money in the ratio is 3x + 7x + 10x = 20x

20x = 20(162.5) = 3250

Answer: £3250

The false statement regarding the t-distribution is the t-distribution is completely defined by its degrees of freedom (df). The t-distribution is a family of distributions,

and the shape of the distribution depends on the degrees of freedom. As the degrees of freedom increase, the t-distribution gets closer to the standard normal distribution. However, the t-distribution is never completely defined by its degrees of freedom.

The other statements about the t-distribution are true. The t-distribution is centered at zero, has fatter tails than the standard normal distribution, and is completely defined by its degrees of freedom.

Here is a more detailed explanation of the false statement:

The t-distribution is a family of distributions, and the shape of the distribution depends on the degrees of freedom. The degrees of freedom are a measure of the sample size, and they determine how spread out the t-distribution is.

When the degrees of freedom are large, the t-distribution is very similar to the standard normal distribution. However, when the degrees of freedom are small, the t-distribution has fatter tails than the standard normal distribution. This means that the t-distribution is more likely to produce extreme values.

The t-distribution is never completely defined by its degrees of freedom because the shape of the distribution also depends on the sample mean. However, the degrees of freedom are the most important factor that determines the shape of the t-distribution.

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Without complete and accurate information for each question. Please provide the full and correct expressions.

When you asked for answers to questions 4, 5, 6, and 7, the given expressions or questions were incomplete or contained errors.

As a result, I couldn't provide accurate answers without complete and accurate information.

To ensure I can assist you effectively, please provide the complete and accurate expressions or questions you would like help with.

Once I have that information, I'll be able to explain the concepts and provide you with the appropriate solutions.

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The equation for the plane through P0(8,1,−4) perpendicular to the following line is x + 4y + 5z - 8 = 0

The slope of the perpendicular line should be a/b, and if one line is perpendicular to this line, the product of slopes should be -1. The equation of a line perpendicular to a given line ax + by + c = 0 is bx - ay + = 0, where is a constant.

The given parameters are

x=8−t​, y=1−2t​, z=3t​,

P0(- 9, 6, - 5).

Direction vector of line is < -1, 4, 5>,

This vector is normal vector for unknown plane.

So, equation of plane: -1(x - (-9)) + 4(y - 6) + 5(z - (-5)) = 0; - x - 9 + 4y - 24 + 5z + 25 = 0;

In conclusion the equation is given as  -x + 4y + 5z - 8 = 0

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Answer:

y=40°

Z + Y = 70°

z. = 70°-40°

z. = 30°

POH=X

=180-70

=110°

Answer: 4/7

Step-by-step explanation: If you graph out the equation sand do rise/run to get your slope, the rise will be 4 and the run will be 7.

Hope this helps! Please mark me brainliest!

Answer:

Step-by-step explanation:

We know that:

Step-1: Change the equation into its original form.

Now, let's compare the equation with its formula.

We can clearly see that the slope is 4/7.

Answer:

x + 15 = 3 (x - 5)

William’s current age: 15. Years old

Step-by-step explanation:

x + 15 = 3(x-5)

x + 15 = 3x - 15

15 + 15 = 3x - x

30 = 2x

x = 15

The intervals where the graph is decreasing are given as follows:

The behavior of the function regarding increase or decrease depends on the orientation of the graph, as follows:

Hence the intervals describing the behavior of the function are given as follows:

The decreasing interval can be divided into two intervals, as follows:

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Answer:

x= 6.02953586.......

Step-by-step explanation:

Answer: 198 dogs

Step-by-step explanation: Assuming you meant to say that the ratio of dogs to cats is 9:7, then you can quickly figure out the amount of dogs by looking at the ratio as a fraction. Instead of seeing it as 9:7, look at the ratio as \(\frac{9}{7}\) and then use that fraction to find the dog amount. You just multiply the amount of cats by the ratio, which we found is \(\frac{9}{7}\) and you should get the final answer of 198 dogs

Answer:

Answer: 198 dogs

Step-by-step explanation: Assuming you meant to say that the ratio of dogs to cats is 9:7, then you can quickly figure out the amount of dogs by looking at the ratio as a fraction. Instead of seeing it as 9:7, look at the ratio as  and then use that fraction to find the dog amount. You just multiply the amount of cats by the ratio, which we found is  and you should get the final answer of 198 dogs

Step-by-step explanation:

The function y(t) = (a/k) * e^(kt) is the solution to the given differential equation dy/dt = k(a*y - 1).

The given differential equation is dy/dt = k(a*y - 1). To find which of the given functions is a solution, we need to substitute each function into the differential equation and check if the equation holds true.

Let's consider the given functions:

a) y(t) = a^2 * e^(kt) - This function is not a solution to the differential equation because when we substitute it into the equation, we don't get a valid equality. The left side becomes dy/dt = a^2 * k * e^(kt), while the right side becomes k(a * (a^2 * e^(kt)) - 1). These two expressions are not equal, so this function is not a solution.

b) y(t) = (a/k) * e^(kt) - This function is a solution to the differential equation. When we substitute it into the equation, the left side becomes dy/dt = k * (a/k) * e^(kt) = a * e^(kt), and the right side becomes
k * (a * ((a/k) * e^(kt)) - 1) = a * e^(kt). Since the left side and the right side are equal, this function satisfies the differential equation and is a solution.

Therefore, the function y(t) = (a/k) * e^(kt) is the solution to the given differential equation dy/dt = k(a*y - 1).

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We have to find the measure of angle at vertex B.

We can use the Law of sines, that let us write proportions between the sine of an angle of the triangle and the sides.

This law tells us that the quotient between the sine of an angle of the triangle and the length of the opposite side is equal for each of the three angles of the triangle.

So in this case we can write:

We can replace the values we already know and calculate the measure of B as:

Answer: B = 37.75°

Maximum and Minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9.

The maximum value is 3

The minimum value is -3

To find the maximum and minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9, follow these steps:

1. Use the constraint equation (ellipse equation) to solve for one of the variables, either x or y.

Here, let's solve for y:
y² = 9 - 3x²
y = ±√(9 - 3x²)

2. Substitute y in the function f(x, y) with the expressions found in step 1:
f(x, y) = x(±√(9 - 3x²))

3. Differentiate f(x, y) with respect to x to find critical points (maximum or minimum):
f'(x, y) = ±(√(9 - 3x²) - (3x² / √(9 - 3x²)))

4. Set f'(x, y) = 0 and solve for x:
√(9 - 3x²) - (3x² / √(9 - 3x²)) = 0

5. Find the corresponding y values for the x values found in step 4 by substituting x back into the expressions found in step 1.

6. Evaluate f(x, y) at each critical point (x, y) found in steps 4 and 5 to determine the maximum and minimum values.

The maximum value of f(x, y) = xy on the ellipse 3x² + y² = 9 is 3, and the minimum value is -3.

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Substitute 80 for C in the formula F = 9/5C +32 to obtain the temperature in fahrenheit.

Thus temperature in

They support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. the correct answer is (d) 0.40.

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data

set.  The mean, median and mode are the three commonly used measures of central tendency.

To calculate the mean, we need to add the total values given in a datasheet and divide the sum by the total number of

values.

The mean, μ, of the sampling distribution of p can be found using the formula

μ = p,

where p is the proportion of adults in the entire population who support the increase.

In this case, 40% of all adults in Ohio support the increase, so p = 0.40.

Therefore, the mean of the sampling distribution of p is:

μ = 0.40

So the correct answer is (d) 0.40.

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The interaction plot consistent with the combination of main effects and interactions described is Plot D, which shows an interaction between squirrels and location.

An interaction occurs when the effect of one independent variable (in this case, squirrels) on the dependent variable (cone sizes) depends on the level of another independent variable (location).

Based on the given information, we have the following main effects and interactions:

1. Main effect of location: This means that the location (island vs. mainland) has an independent effect on cone sizes. It suggests that there is a difference in cone sizes between the two locations.

2. Main effect of squirrels: This means that the presence or absence of squirrels has an independent effect on cone sizes. It suggests that the presence of squirrels may influence cone sizes.

3. Interaction between squirrels and location: This means that the effect of squirrels on cone sizes depends on the location. In other words, the presence or absence of squirrels may have a different impact on cone sizes depending on whether the trees are on an island or the mainland.

Among the given interaction plots, Plot D is consistent with these main effects and interactions. It shows that the effect of squirrels on cone sizes differs between the island and mainland locations, indicating an interaction between squirrels and location.

Therefore, Plot D is the interaction plot that aligns with the combination of main effects and interactions described in the question.

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Answer:

A. 312 cm²

Step-by-step explanation:

The figure compromises of a rectangle and 2 equal triangles.

Area of the figure = area of the rectangle + area of the two triangles

Area = L*W + 2(½*b*h)

Where,

L = 16 cm

W = 12 cm

b = 12 cm

h = 10 cm

Plug in the values

Area = 16*12 + 2(½*12*10)

= 192 + 120

= 312 cm²

The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.

To find the rate of change of an edge of the cube, given that the volume decreases at a rate of 4 cubic meters per minute when the volume is exactly 27 cubic meters, follow the solution below:Let the length of the edge of the original cube be L.Let the volume of the original cube be V, such that V = L³.The rate of change of volume is given as -4 m³/min; the negative sign is used to indicate a decrease in volume, and this is obtained when the derivative of the volume with respect to time is multiplied by the negative sign.Let V₀ be the original volume of the cube, and V₁ be the volume after t minutes. Thus, V₁ = V₀ - 4t m³. We are told that V₁ = 27 m³, hence:V₀ - 4t = 27 ⇒ V₀ = 27 + 4t m³Substituting V₀ in terms of t into the expression V = L³, we have:L³ = 27 + 4tTaking the derivative of both sides with respect to t, we have:3L²(dL/dt) = 4 ⇒ dL/dt = 4/(3L²)Substituting L from the expression L³ = 27 + 4t, we have:L = (27 + 4t)^(1/3)Therefore, the rate of change of an edge of the cube is given by the derivative of L with respect to t:dL/dt = 4/(3L²) = 4/(3(27 + 4t)^2/3) ≈ 0.048 m/min (to 3 decimal places)Answer: The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.

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In order to find the equation of the line, you take into account the following formula:

y = mx + b

which is the equation of the line

Now, you calculate m, named the slope, by using the following formula:

m = (y2-y1)/(x2-x1)

where x1, x2, y1 and y2 are the coordinates of the given points (0, -6) and (4,10).

Thus, you have x1 = 0, x2 = 4, y1 = -6 amd y2 = 10. You replace these values into the formula for m:

m = (10 - (-6))/()

The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution

From the graph, we have:

f(x) = x² - 3

g(x) = -x² + 2

Next, we change the equations to inequalities as follows:

y ≤ x² - 3

y > -x² + 2

To modify the graph, we then perform the following transformations:

After the modifications in (a), we have:

y ≤ x² - 3 and y > -x² + 2

Substitute y > -x² + 2 in y ≤ x² - 3

-x² - 2 ≤ x² - 3

This gives

2x² ≤ - 1

Divide by 2

x² ≤ - 0.5

The square root of numbers less than 0 is a complex number

Hence, the set of inequalities do not have a solution

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In a chi-square test, the expected values should be greater than or equal to 5 for each cell in the contingency table. If any expected value is less than 5, then the validity of the chi-square test is in question and a different test or a modification of the chi-square test may be necessary. Therefore, the correct answer to your question is "greater than or equal to 5".

The chi-square test is a statistical test used to determine if there is a significant association between two categorical variables. The test involves comparing the observed frequencies of the categories with the expected frequencies that would be observed if there were no association between the variables.

The expected frequencies are calculated based on the assumption that there is no association between the variables, and are obtained by multiplying the marginal totals for each row and column, and dividing by the total sample size.

In order for the chi-square test to be valid, the expected frequencies for each cell should be greater than or equal to 5. This is because the chi-square test relies on the assumption that the expected frequencies follow a normal distribution, and if the expected frequencies are too small, the distribution may not be normal and the test may not be accurate.

If any of the expected frequencies are less than 5, there is a risk of a type I error (rejecting the null hypothesis when it is actually true), and a different test or a modification of the chi-square test may be necessary.

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Answer:

7 1/2

Step-by-step explanation:

To find the quotient, convert the mixed number to an improper fraction first

Find the quotient now

Simplify

Divide by  both numerator and denominator

Convert to a mixed number

Answer:

\( (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656{x}^{} + 46656 \)

Step-by-step explanation:

we want to solve the following binomial:

\((x + 6 {)}^{6} \)

There is a handy way to expand powers of binomials which is known as binomial theorem . and it describes the algebraic expansion of powers of a binomial. binomial theorem is given by

\( \displaystyle (a + b {)}^{n} = \sum _{k = 0 }^{n} \binom{n}{k} {a}^{n - k} {b}^{k} \)

comparing (x+6)⁶ to (a+b)ⁿ , we get

now substitute them on the formula which yields:

\( \displaystyle (x + 6 {)}^{6} = \sum _{k = 0 }^{n} \binom{6}{k} {x}^{6 - k} \cdot {6}^{k} \)

converting the summation notation into sum yields:

\( \displaystyle (x + 6 {)}^{6} = \binom{6}{0} {x}^{6 - 0} \cdot {6}^{0} + \binom{6}{1} {x}^{6 - 1} \cdot {6}^{1} + \binom{6}{2} {x}^{6 - 2} \cdot {6}^{2} + \binom{6}{3} {x}^{6 - 3} \cdot {6}^{3} + \binom{6}{4} {x}^{6 - 4} \cdot {6}^{4} + \binom{6}{5} {x}^{6 - 5} \cdot {6}^{5} + \binom{6}{6} {x}^{6 - 6} \cdot {6}^{6} \\ \implies(x + 6 {)}^{6} = \binom{6}{0} {x}^{6 } \cdot 1 + \binom{6}{1} {x}^{5} \cdot {6} + \binom{6}{2} {x}^{4} \cdot 36+ \binom{6}{3} {x}^{3} \cdot 216 + \binom{6}{4} {x}^{2} \cdot 1296+ \binom{6}{5} {x}^{} \cdot 7776+ \binom{6}{6} {x}^{0} \cdot 46656 \\ \implies(x + 6 {)}^{6} = 1 \cdot {x}^{6 } \cdot 1 + 6 \cdot{x}^{5} \cdot {6} + 15 \cdot {x}^{4} \cdot 36+ 20 \cdot {x}^{3} \cdot 216 + 15 \cdot{x}^{2} \cdot 1296+ 6 \cdot {x}^{} \cdot 7776+ 1 \cdot {x}^{0} \cdot 46656 \\ \implies \boxed{ (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656 {x}^{} + 46656 }\)

and we're done!

Answer:

750 gallons per hour

Step-by-step explanation:

divide 18000 by 24 and you get 750

Answer:

30000

Step-by-step explanation: