A streetlight hangs 5 meters above the ground. Regina, who is 1.5 meters tall, walks away from the point under the light at a rate of 2 meters per second. How fast is her shadow lengthening when she is 7 meters away from the point under the light

Answer:

The rate change between these points is 3.

Step-by-step explanation:

Answer:

Rate of Change is 3

Step-by-step explanation:

The rate of change between two points is called the 'slope'.

x1-x2         -6-8          -14

____  =      ____  =   ___  = Divide  = 3

y1-y2      -20 - 22      -42

Answer:

Sendiks.

Step-by-step explanation:

Sendiks- 6 ÷ 3.80= $1.58 per can

Sam's Club- 12÷6.90= $1.74 per can

Answer:

Step-by-step explanation:

Refer the attachment

Answer:

752.5 in³

Step-by-step explanation:

  Rectangular prism:

            l = 10 in ; w = 7 in ; h = 8 in

   \(\boxed{\text{Volume of rectangular prism=l*w*h}}\)

                                                = 10 * 7 * 8

                                                = 560 in³

Half cylinder:

Diameter of the cylinder will be equal to the width of the rectangular prism.

       r = 7/2 = 3.5 inches ; h = 10 in

\(\boxed{\text{Volume of half cylinder =$\dfrac{1}{2}\pi r^2h$}}\)

                                       \(\sf =\dfrac{1}{2}*3.14*3.5*3.510\\\\ = 192.5 \ in^3\)

Volume of composite figure = 560 - 192.5

                                               = 752.5 in³

We would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g by using properties of the normal distribution.

To find the range in which you would expect to find the middle 68% of amounts of nicotine in these cigarettes, we can use the properties of the normal distribution.

Given:
Mean (μ) = 0.946 g
Standard deviation (σ) = 0.289 g

For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, we can expect the middle 68% of amounts of nicotine to fall within the range:

μ ± σ

Substituting the given values:

0.946 ± 0.289

To calculate the range, we have:

Lower bound = 0.946 - 0.289 ≈ 0.657 g
Upper bound = 0.946 + 0.289 ≈ 1.235 g

Therefore, we can expect to find the middle 68% of amounts of nicotine in these cigarettes to be between approximately 0.657 g and 1.235 g.

Now, if we were to draw samples of size 41 from this population, the standard deviation of the sample mean (also known as the standard error) can be calculated as:

Standard error (SE) = σ / √n

where σ is the population standard deviation and n is the sample size.

Substituting the given values:

SE = 0.289 / √41 ≈ 0.045 g

To find the range in which we would expect to find the middle 68% of the sample means, we multiply the standard error by 1 to capture approximately 68% of the data, giving us:

Lower bound = μ - SE ≈ 0.946 - 0.045 ≈ 0.901 g
Upper bound = μ + SE ≈ 0.946 + 0.045 ≈ 0.991 g

Therefore, we would expect to find the middle 68% of the average amounts of nicotine in a sample of size 41 to be between approximately 0.901 g and 0.991 g.

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Answer:

Step-by-step explanation:

by inspection

angles 2 and 3 are equal, so they will be half angle ABC

angles 1 and 5 are equal  so they will be

      angle 1 + angle 5 + angleABC = 180°      kind of a rule for triangle

                                                                        the sum of all angles - 180°

      (angle 1) x 2 = 180° - 70°

       angle 1 = 90° - 35°

      angle 1 = 55°   which equals angle 5

angle 4 is clearly a right angle 90°

DO the same procedure for the bottom triangle

angle 8 and 9 are half of angle ADC

angle 8 and 9 are half of 46°

both are 23°

angle 6 equals angle 7

2 ×angle 6 = 180° - 46°

angle 6 = 90° - 23°

angle 6 = 67°    angle 7 = 67°

Did I find them all

We can write the solution set for the given system of equations as -

{x} = {EC/B - F}/{D - EA/B}

{y} = - { C + A [{ EC/B - F }/{ D - EA/B }] }/B

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is use the diagrams below, write and solve two simultaneous equations to work out the values of {x} and {y}.

Since the diagram is not given, we can learn how to solve the given set of simultaneous equations.

Assume that we have the simultaneous equations as -

Ax + By + C =0

Dx + Ey + F = 0

Now, we can write -

Ax + By + C =0

By = - C - Ax

By = - (C + Ax)

{y} = - (C + Ax)/B

Putting the value in the equation -

Dx + Ey + F = 0

Dx - E(C + Ax)/B + F = 0

Dx - EC/B - (EA/B)x + F = 0

x{D - EA/B} - EC/B + F  = 0

x{D - EA/B} = {EC/B - F}

{x} = {EC/B - F}/{D - EA/B}

We can write {y} as -

{y} = - { C + A [{ EC/B - F }/{ D - EA/B }] }/B

Therefore, we can write the solution set for the given system of equations as -

{x} = {EC/B - F}/{D - EA/B}

{y} = - { C + A [{ EC/B - F }/{ D - EA/B }] }/B

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Answer:

16-5=11

Step-by-step explanation:

Answer:

\(\text{(C) }300\pi\:\mathrm{cm^3}\)

Step-by-step explanation:

The volume of a cylinder with radius \(r\) and height \(h\) is given by \(V=r^2\pi \cdot h\).

What we're given:

Substituting given values, we get:

\(V=5^2\pi \cdot 12 =\boxed{300\pi\:\mathrm{cm^3}}\)

Answer:

c

Step-by-step explanation:

The formula for the volume of a cylinder is \(V=\pi r^2h\)

We know r is 5, and h is 12.

Then we can just plug the values into the formula.

\(V=\pi (5)^2(12)\\ V=\pi (25)(12)\\\V=\pi (300)\)

So the answer is c, 300pi

Answer:

$13,282.83

Step-by-step explanation:

The initial value of the investment is $1400, when t = 0.

The appropriate formula for this exponential growth is

A = Pe^(rt), where r is the exponential rate of change and t is the number of years.

Thus:

A = $1400e^(0.09t).  Note that when t = 0, A = $1400 as expected.

After 25 years:

A = $1400e^(0.09*25) = $13,282.83

the first is multiply, the second percent

the third is part and the next too

Answer:

A

Step-by-step explanation:

0<\(\frac{769000}{23}\)

ANSWER

1.23

EXPLANATION:

Given information:

Step 1: Convert the decimals into fraction

Hence, the answer is 2.3

The sets of transformations that result in the same image when performed in any order are:

Translation, dilation with center (0,0)

Two translations

In mathematics, a transformation refers to a process that changes the size, shape, position, or orientation of a geometric figure or an object in a coordinate plane or space. There are several types of transformations, such as translation, rotation, reflection, and dilation, which are used to alter the original figure to create a new one that is similar or congruent to the original. Transformations are used in geometry, algebra, and other branches of mathematics to study and understand various properties of geometric shapes and objects.

Here,

For the first set, if we perform a translation followed by a dilation with center (0,0), the result will be the same as if we perform the dilation first followed by the translation. This is because the dilation does not change the direction of the translation, and the center of dilation is at the origin, so the translation is unaffected.

For the second set, any two translations can be combined to form a single translation, so the order in which they are performed does not matter.

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A) If Sofi accidentally spills 5% of the container's maximum capacity on the counter, the container is now filled to 87.5% of its capacity.

B) If Sofi needs to add 16 ounces of water to her turtle tank, she needs to use 28.57% of the remaining water in the container.

Given that Sofi stores water for her turtle tank in a container with a maximum capacity of 64 ounces and the container is filled with 4.8 ounces less than its maximum capacity, to determine A) if Sofi accidentally spills 5% of the container's maximum capacity on the counter, to what percent of its capacity is the container now filled, and B) if Sofi needs to add 16 ounces of water to her turtle tank, what percentage of the remaining water in the container does she need to use, the following calculations must be made:

A)

Therefore, if Sofi accidentally spills 5% of the container's maximum capacity on the counter, the container is now filled to 87.5% of its capacity.

B)

Therefore, if Sofi needs to add 16 ounces of water to her turtle tank, she needs to use 28.57% of the remaining water in the container.

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Answer:

A=87.5%   b=28.57

Step-by-step explanation:

ADVICE PLEASE LOOK AT THIS VERY HELPFUL

PART                           percent

--------- over =          ----------------- over   Cross multiply and then divide by 100  

WHOLE                       100%

Answer:

thanks

Step-by-step explanation:

I have been patient trying to get a job

The slope is the steepness of a line on a graph and represents the ratio of the vertical change to the horizontal change, the rate of change refers to the amount of change in one variable corresponding to a unit change in another variable.

The slope of a line is a measure of its steepness or incline. It is calculated by dividing the vertical change (change in y-values) by the horizontal change (change in x-values) between two points on the line. The slope indicates how much the dependent variable (y) changes with respect to a unit change in the independent variable (x). In other words, it represents the ratio of the rise (vertical change) to the run (horizontal change) on the graph.

On the other hand, the rate of change is a broader concept that applies to any relationship between two variables, not just linear relationships. It measures how one variable changes in response to a unit change in another variable. The rate of change can be positive, indicating an increase in one variable for every unit increase in the other variable, or negative, indicating a decrease. It can also vary across different intervals of the relationship, indicating that the relationship is not constant.

In summary, the slope specifically refers to the steepness of a line on a graph and is calculated as the ratio of the vertical change to the horizontal change. The rate of change, on the other hand, is a more general concept that describes how one variable changes in response to a unit change in another variable and can be applied to any type of relationship between variables.

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115 pounds is equivalent to approximately 52.16 kilograms.

Converting pounds (lb) to kilograms (kg) is a common task, especially in the field of science and engineering, where measurements are often taken in metric units. A pound is a unit of weight commonly used in the United States, while a kilogram is the standard unit of mass in the metric system.

To convert pounds to kilograms, you need to use the following conversion formula: 1 lb = 0.45359237 kg. This means that for every pound, there are 0.45359237 kilograms. To convert 115 pounds to kilograms, simply multiply 115 by 0.45359237:

115 lb * 0.45359237 kg/lb = 52.16 kg

Therefore, 115 pounds is equivalent to approximately 52.16 kilograms.

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The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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The probability that a randomly selected student is taking a math class or an English class is 0.79.

Using the formula for the union of two events, P(A or B) = P(A) + P(B) - P(A and B), where A is the event "taking a math class" and B is the event "taking an English class", we can find the desired probability:

P(A or B) = 0.76 + 0.75 - 0.72 = 0.79

So,  "0.79" (which is given in upto two decimal places) is the probability that a randomly selected student is taking a math class or an English class.

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Answer:

4x + y = 1

Step-by-step explanation:

Start with the familiar format of y=mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).

With a slope of -4, we can write:

y = -4x + b

We need to find a value for b that forces the line through point (1,-3).  This is done by entering this point in the equation and solving for b:

y = -4x + b

-3 = -4*(1) + b

b = 1

The equation is y = -4x + 1,  This can be rewritten as:

4x + y = 1

Se attached graph.

With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

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The volume of the cone is approximately 37.7 cubic units

What is volume?

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

To find the volume of a cone, we use the formula:

V = (1/3) * π * r² * h

where π is the constant pi, r is the radius of the base of the cone, and h is the height of the cone.

Plugging in the given values, we get:

V = (1/3) * 3.14 * 3² * 4 ≈ 37.7

Therefore, the volume of the cone is approximately 37.7 cubic units (rounded to the nearest tenth).

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Consumption of resources at a 3.0 planet rate indicates that a country needs to reduce its resource consumption by 2/3 to be sustainable.

Humans will be benefited from two types of resources namely renewable and non-renewable resources. The former can be utilized for the long term but the latter needs to be handled carefully.

But, they are misused by humans which leads to a lack of resources for us. Common example of non-renewable resources includes natural gas, coal, oil, etc.

The consumption of resources at a given planet rate indicates the rate of utilization of resources. With the increased consumption of resources, pollution on the planet increases. It is accompanied by numerous health issues.

It additionally requires alternatives to the resources that we will consume completely.

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Here, we use the property of multiplication of exponential expression which states when we multiply two exponential expressions with the same base, we keep the base and add the exponents.

Therefore,

\(x^(3+5) = x^8\)

Now,

\(x^(3+5) = x^8\)

is of the form:

\(x^b = x^p\)

When we have two equal expressions on either side of the equation, the power of the base remains the same. Therefore,

p = 8

There we have it. The value of p is 8. The full solution is shown below:

\(x^3 × x^5 \\= x^px^8\\ = x^p\)

We can see that the base of the exponential expression on either side is equal.

Therefore, the power of the base must be equal as well. In other words

,p = 8.

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Answer:

no picture sorry but if either tanks line goes higher than the other than its filling faster

Step-by-step explanation:

Answer:

13 + \(\sqrt{89}\)

or

22.43398... (depends on how you round it)

Step-by-step explanation:

1. The question stated that the radius of the circle O is 5, so the length of AO and CO is 5.

2. Since line AB and line CB are both tangent to the circle, they have the same length. CB is 8, so AB will also be 8.

--> Both triangle AOB and COB share one side, and the other side (radius) has the same length, so the third side must be the same length

3. Tangent means having a 90-degree angle with the radius. We know that the triangle AOB is a right triangle since the angle OAB is 90 degrees.

We can use the Pythagorean theorem to find side OB. OB^2 = AO^2 + AB^2.

--> OB^2 = 25 + 64

--> OB^2 = 89

--> OB = \(\sqrt{89}\)

Now that we know the lengths of all three sides, we can add them up.

--> 5 + 8 + \(\sqrt{89}\)

--> 13 + \(\sqrt{89}\)

or

--> 22.43398113....

The formula to solve Euler's Formula for e, which relates the number of vertices v, the number of edges e, and the number of faces f, of a polyhedron is e = v + f - 2.

Euler's Formula, v − e + f = 2, is a relationship between the number of edges e, the number of vertices v, and the number of faces f in a polyhedron. The formula can be rearranged to solve for e which is e = v + f - 2. This formula can be used to find the number of edges in a polyhedron when the number of vertices and faces are known. Therefore, this formula is used to calculate the number of edges in a polyhedron. The formula states that the number of vertices, minus the number of edges, plus the number of faces is always equal to 2.

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Our required ratio will be 8: 2: 24: 5 as per the given problem.

In our question, it is given that 1 Pound is equal to 16 ounces.

We will use this criterion for the rest of our solution.

Let’s convert all pounds to ounces.

1 pound =16 ounce

3 pound = 48 ounce

Now as per the problem, we have to find the ratio of 1 pound, 4 ounces, 3 pounds, 10 ounces.

= 1 pound: 4 ounces: 3 pounds: 10 ounce

= 16 ounces: 4 ounces: 48 ounces: 10 ounce

= 8: 2 : 24: 5

So our required ratio is 8: 2 : 24: 5.

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