Just curious to know

The red car is actually traveling at a speed of 45 feet per second.

What is the concept of related rates and how does it apply to this problem?

Related rates is a calculus topic that deals with finding the rate of change of one variable with respect to another variable. In this problem, the distance between the police car and the red car is decreasing at a constant rate, and we need to find the speed of the red car. The key is to set up an equation that relates the variables involved and differentiate it with respect to time, using the chain rule. This allows us to find the rate of change of the variables with respect to time, and then solve for the desired rate of change.

Calculating the actual speed of the red car :

Let's call the distance between the police car and the red car "d" and the speed of the red car "v". We want to find [tex]dv/dt[/tex], the rate of change of v with respect to time.

From the problem statement, we know that [tex]dd/dt = -75[/tex] feet per second, since the distance between the cars is decreasing at a rate of 75 feet per second.

To find [tex]dv/dt[/tex], we need to use the Pythagorean theorem to relate d and v. We have a right triangle with legs of length 30 and 160, and hypotenuse d. Using the Pythagorean theorem, we get:

[tex]d^2 = 30^2 + 160^2[/tex]

[tex]d= \sqrt{(30^2 + 160^2)} =161.24[/tex] feet

Now we take the derivative of both sides of this equation with respect to time:

[tex]2\times\d(dd/dt) = 0.5\times(2d)\times(dv/dt)[/tex]

[tex]dd/dt = -75[/tex]

[tex]d = 161.24[/tex]

Substituting these values, we get:

[tex]2(161.24)(-75) = 0.5(2(161.24))(dv/dt)[/tex]

Simplifying and solving for [tex]dv/dt,[/tex] we get:

[tex]dv/dt = (-2)(161.24)(-75)/(2(161.24))[/tex]

[tex]dv/dt = 45[/tex] feet per second

Therefore, the red car is actually traveling at a speed of 45 feet per second.

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Answer:

Step-by-step explanation:

Simplify the expressionApply the logarithm power identityApply the logarithm product identitySimplify the expression2Exponentiate both sides

log10(4x8)=2log10(48)=2

48=102

x=258=258√

Answer:

Second option [tex]y=\text{log}(2\text{x})+3[/tex]

Solution:

Based on the family of graphs shown in the attached file, the equation could represent the graph is [tex]y=\text{log}(2\text{x})+3[/tex]

This graph is the graph of the function [tex]y=\text{log}(\text{x})[/tex] stretched horizontally by a factor of 2 and translated 3 units upward.

Answer:

B

Step-by-step explanation:

Edge 2023

Turner had predicted he would run for 30 yards in the game.

In terms of a number out of 100, a % is a means to express a proportion or a fraction. It is represented by the symbol "%". For example, if 25 out of 100 students in a class are girls, we can say that the percentage of girls in the class is 25%.

To find out how many yards Turner predicted he would run for, we can use the following steps:

Therefore, Turner had predicted he would run for 30 yards in the game.

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So, when 14 pounds of blue goo as well as 16 pounds of red goo are present, there are 2688 pounds of green goo.

Let the green goo be G.

Let the blue goo be B.

Let the red goo be R.

G ∝ B*R

G = k*B*R (k is the constant of proportionality)

Put the values:

G = 288 = k*B*R

288 = k*8*3

288 = k*24,  

k = 288/24 = 12

Now, for the second case:

G = k*B*R

Put the value of k.

G = 12*14*16 = 2688.

So, when 14 pounds of blue goo as well as 16 pounds of red goo are present, there are 2688 pounds of green goo.

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Answer:

Step-by-step explanation:

ut it A

As a result, the rectangular prism has a volume of 1 cubic centimeter.

The volume of an object is the area enclosed inside its three-dimensional boundaries. It is referred to as an object's capability on occasion.

We must multiply the rectangular prism's length, width, and height to determine its volume. Although we don't directly know these values, we can use the regions of the faces to locate them.

Let's use the letters l, w, and h to denote the prism's length, breadth, and height, respectively. The area of a top and bottom sides is thus determined to be lw = 10 cm², the front and rear faces are lh = 15 cm², and the left and right sides are wh = 6 cm².

These equations can be used to solve for every variable using the following descriptions of the other variables:

l = 10/w

h = 15/l

w = 6/h

When we add these expressions to the volume formula, we obtain:

V = lwh = (10/w)(6/h)(15/l) = 900/whl = 900/(6×10×15) = 1 cm³

As a result, the rectangular prism has a volume of 1 cubic centimeter.

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Answer:

linear

Step-by-step explanation:

this is a linear function!

linear functions follow y = mx+b, where m is the slope and b is the y-intercept

let's write our y = mx+b equation

for each value that x increases, y increases by DOUBLE that amount. slope is y/x, so since y increases by 2 and x increases by 1, the slope is 2/1 which is 2.

the y-intercept is where the line passes the x axis, or when x is 0. in this table, it gives you your y-intercept, which is -6

your equation is y=2x+(-6); which simplified to y=2x-6

if you plug in the y and x values, you'll get the same thing. i hope this helped!

Answer:

To calculate the speed of the athlete in meters per second (m/s), we can use the formula:

Speed = Distance / Time

Here, the distance is 200 meters and the time is 25 seconds. Substituting these values into the formula, we get:

Speed = 200 meters / 25 seconds

Simplifying, we get:

Speed = 8 meters/second

Therefore, the athlete ran at a speed of 8 meters per second.

Answer:

Step-by-step explanation:

Let x be the cost per pound of the cinnamon tea and y be the cost per pound of the spice tea.

From the first mixture, we have:

12x + 3y = 39

From the second mixture, we have:

16x + 6y = 58

We can solve this system of equations by elimination. Multiplying the first equation by 2 and subtracting it from the second equation gives:

16x + 6y = 58

(24x + 6y = 78)

-8x = -20

Dividing both sides by -8 gives:

x = 2.5

Substituting this value of x into the first equation, we get:

12(2.5) + 3y = 39

Simplifying, we get:

30 + 3y = 39

Subtracting 30 from both sides gives:

3y = 9

Dividing both sides by 3 gives:

y = 3

Therefore, the cost per pound of the cinnamon tea is $2.50 and the cost per pound of the spice tea is $3.

The total balance that Sue will have in the two accounts after 5 years can be calculated as follows:

Balance of the first account with simple interest:

FV = P(1 + rt)

FV = $600(1 + 0.075 x 5)

FV = $825

Balance of the second account with compounded interest:

FV = P(1 + r)^n

FV = $900(1 + 0.06)^5

FV = $1,286.87

Total balance = $825 + $1,286.87

Total balance = $2,111.87

The closest answer choice to this amount is F) $2,029.40, which is only off by a small margin. Therefore, the answer is F) $2,029.40.

Answer:

Step-by-step explanation:

1. u would do 315/15 bc y/x=k

2. u would do 81/9

3. u would do 56/2

so basically for the next ones just do the money divided by oz to find the unit rate. Note always do y/x y is the dependent variable and x is the independent variable

To draw the image of ABC under a dilation whose center is C and scale factor is 2, there are several steps by which we can draw the triangle.

Draw the original ABC triangle. A, B, and C are the vertices.

Make a point C' that is twice as far away from C as any other point on the triangle ABC. Draw a ray from C through any vertex of the triangle to accomplish this. (say, B). Then, double the length of the ray to find point C'.

Connect point C' to each vertex of the triangle with lines. A' and B' are the points where these lines intersect the original triangle.

Your new triangle A'B'C' is the dilation of ABC with centre C and scale factor 2.

The sides of the new triangle A'B'C' are twice as long as the sides of the original triangle ABC, and the angle between any two corresponding sides in both triangles is the same.

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Answer:

17.6

Step-by-step explanation:

2.7÷6= 0.45

0.45×8= 3.6

17+3.6 - 3=17.6

The normal hourly rate is   16.28  units

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Let r be your rate you get paid per hour normally.

Total = 33 hours

Extra hour = 33 -32 = 1 hour

We have

32r + 1.5r =  545.38

=> 33.5r = 545.38

=> r = 545.38 /33.5 = 16.28

The normal hourly rate is   16.28  units

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Answer:

c

Step-by-step explanation:

because I did it in my book ‍️

Answer:

1/128

Step-by-step explanation:

The probability of tossing a head is 1/2.

Each toss is an independent event.

We toss 7 times and get a head each time.

1/2 * 1/2* 1/2* 1/2* 1/2* 1/2* 1/2

1/128

Answer:

1039.23 square inches

Step-by-step explanation:

                      a = 20 inches

    [tex]\sf \boxed{\text{\bf Area of regular hexagon = $\dfrac{3\sqrt{3}}{2}a^2$}}[/tex]

                                                   [tex]= \dfrac{3\sqrt{3}}{2}*20*20\\\\= 3\sqrt{3}*200\\\\= 1039.23 \ inches^2[/tex]

Assuming that the 75 feet measurement is the distance from where Justin is at the ground level to the fish (and not the diagonal distance from his location to the fish), the angle is given by arctan(28/75) = 28.472 degrees. This is probably the right answer.

If the 75 feet measurement is the diagonal distance, the angle is arcsin(28/75) = 21.921 degrees.

We know this from a relation of right triangle trigonometry. Tell me if you need more clarification.

A. the derivative of y = log_a(x) is: y' = log_a(x) / (x ln(a))

B. the derivative of y = log_8(x) is: y' = 1 / (x ln(8 ln(10)))

a) Using the chain rule and the given identity, we have:

y = log_a(x)

ln(y) = ln(log_a(x))

ln(y) = ln(x) / ln(a)

y' / y = 1 / (x ln(a))

Multiplying both sides by y and simplifying, we get:

y' = y / (x ln(a))

y' = log_a(x) / (x ln(a))

Therefore, the derivative of y = log_a(x) is: y' = log_a(x) / (x ln(a))

b) Using the change of base formula for logarithms, we have:

y = log_8(x)

y = log(x) / log(8)

Using the chain rule, we have:

y' = (1 / (x ln(10))) * (1 / ln(8)) * d/dx [log(x)]

Using the chain rule for the natural logarithm, we have:

y' = (1 / (x ln(10))) * (1 / ln(8)) * (1/x)

Simplifying, we get:

y' = 1 / (x ln(8 ln(10)))

Therefore, the derivative of y = log_8(x) is:

y' = 1 / (x ln(8 ln(10)))

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I'm sorry, but your question is not clear. Did you mean "What is the angle measurement of a unit circle when radius equals 1?" If so, the answer is that the angle measurement is 360 degrees or 2π radians.

the fraction of the class that are boys is 4/9. And the fraction of the class that are girls is 5/9.

What is ratio?

A ratio is a comparison of two or more quantities that are related in some way. It expresses the relationship between these quantities in terms of the number of times one quantity contains another. Ratios are usually expressed as a fraction, where the numerator represents the first quantity and the denominator represents the second quantity. For example, the ratio of boys to girls in a class of 40 students may be expressed as 2:3 or 2/3, meaning there are 2 boys for every 3 girls. Ratios can also be expressed in other forms, such as percentages or decimals. Ratios are commonly used in mathematics, science, engineering, and everyday life to compare quantities and make predictions or decisions.

A fraction is a number that represents a part of a whole or a ratio of two quantities. It consists of two numbers, a numerator and a denominator, separated by a line. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole or in the comparison. Fractions are used in many areas, such as mathematics, science, engineering, cooking, and everyday life. They can be added, subtracted, multiplied, and divided, and can be converted to decimals or percentages.

a) The total ratio of boys to girls in the class is 4+5 = 9. Therefore, the fraction of the class that are boys is 4/9.

b) The question is unclear as it seems to be asking for the same answer as in part (a). If you meant to ask for the fraction of the class that are girls, you can use the same approach: the fraction of the class that are girls is 5/9.

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The equation of the line is slope intercept form is y = 3x + 45.

What is a graph?

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, Danny is opening a savings account with an initial deposit of $45 and he saves $3 per day.

Let y be the total amount he saves and x is the no. of days.

As he starts with $45 deposit it'll be added as a constant.

∴ The equation of the required line is y = 3x + 45.

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Therefore, if we are using 27 cups of sugar, we also need 18 cups of wheat.

An ordered combination of integers a and b, rendered as a / b, is a ratio if b is not equal to 0. A percentage is an expression that sets two numbers at the same value. For instance, you could put the percentage as follows: 1: 3 if it's 1 male and 3 girls. (for every one boy there are 3 girls)

If 8 cups of flour are mixed with 12 cups of sugar, then the ratio of flour to sugar is:

8 : 12

Simplifying this ratio by dividing both numbers by 4, we get:

2 : 3

This means that for every 2 cups of flour, we need 3 cups of sugar.

If we are using 27 cups of sugar, we can set up a proportion to find out how much flour we need:

2/3 = x/27

Multiplying both sides by 27:

2 × 27 / 3 = x

Simplifying:

x = 18

Therefore, we need 18 cups of flour if we are using 27 cups of sugar.

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Answer:

9 is answer you fool......

answer: Click THANKS if you like my answer. have a good day sir/maam #keep safe

First, we need to find the maximum height that the rocket will reach. To do that, we need to find the vertex of the parabolic function h(t) = -16t^2 + 144t + 9. We can use the formula for the vertex of a parabola, which is given by the formula t = -b/2a, where a = -16 and b = 144.

t = -b/2a = -144/(2*(-16)) = 4.5

So the rocket will reach its maximum height after 4.5 seconds.

To find the maximum height, we need to substitute t = 4.5 into the function h(t):

h(4.5) = -16(4.5)^2 + 144(4.5) + 9 = 324

So the maximum height that the rocket will reach is 324 feet.

Therefore, the rocket will reach its maximum height of 324 feet after 4.5 seconds.

Step-by-step explanation:

hope its help<:

Answer:

Taking radius of a semicircle to be 3cm calculate the area using (1/2πr²) and add the area of rectangle calculated by use of formula L×w

Therefore Area=π(1/2×3²)+(12×6)

=76.5π

Answer:

82.27

Step-by-step explanation:

Please see the diagram attached to this solution for measurements

Area of the figure = Area of semi circle + area of rectangle

As per the figure

[tex]l_{rectangle} = 9\\w_{rectangle} = 6\\r_{semi-circle} = 3[/tex]

therefore,

[tex]Area = \dfrac{\pi r^{2}}{2} + l\cdot w[/tex]

substitute values of l, w and r, we get

[tex]Area = 82.27 cm^2[/tex]

Hopefully this answer helped you!!!

To find the surface area of a triangular prism with side lengths 3, 4, 4, and 5, we can use the formula:

Surface Area = 2(Area of the base) + (Perimeter of the base) x (Height of the prism)

First, let's find the area of the base. Since the base is a triangle, we can use the formula for the area of a triangle:

Area of base = (1/2) x base x height

The base of the triangle is the side with length 5, and the height can be found using the Pythagorean theorem:

height^2 = 4^2 - (3/2)^2

height^2 = 16 - 2.25

height^2 = 13.75

height = sqrt(13.75)

So the area of the base is:

Area of base = (1/2) x 5 x sqrt(13.75)

Area of base = 10.825

Next, let's find the perimeter of the base. Since the base is a triangle with side lengths 3, 4, and 5, the perimeter is:

Perimeter of base = 3 + 4 + 5

Perimeter of base = 12

Finally, let's find the height of the prism. We can use the Pythagorean theorem again:

height^2 = 4^2 - (3/2)^2

height^2 = 16 - 2.25

height^2 = 13.75

height = sqrt(13.75)

So the height of the prism is also sqrt(13.75).

Now we can plug these values into the formula for the surface area:

Surface Area = 2(Area of the base) + (Perimeter of the base) x (Height of the prism)

Surface Area = 2(10.825) + 12 x sqrt(13.75)

Surface Area = 21.65 + 41.4

Surface Area = 63.05

Therefore, the surface area of the triangular prism with side lengths 3, 4, 4, and 5 is 63.05 square units.

Answer:

Step-by-step explanation:

The theoretical probability of an event is the number of favorable outcomes over the total number of possible outcomes. In this case, the total number of possible outcomes is 2, since each camper can either swim or hike. The number of favorable outcomes for swimming is also 2 (heads on a coin flip). Therefore, the theoretical probability of swimming is 2/2 or 1/2.

The experimental probability of an event is the number of times the event occurred in the experiment divided by the total number of trials. In this case, there were 12 students who chose to swim out of 40 total students. Therefore, the experimental probability of swimming is 12/40 or 3/10.

Comparing the two probabilities, we see that the theoretical probability of swimming is 1/2 while the experimental probability of swimming is 3/10. Therefore, the statement "The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40" is true.

The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.

The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40. (option b)

The theoretical probability of an event is calculated based on the assumption of equal likelihood for all possible outcomes. In this case, since each student flips a fair coin, there are two equally likely outcomes: heads (swimming) and tails (hiking). Therefore, the theoretical probability of swimming (P(swimming)) is 1/2, and the theoretical probability of hiking is also 1/2.

However, the experimental probability is determined by the actual outcomes observed in the experiment. According to the data provided, out of the 40 students, 12 students got heads (swimming) and 28 students got tails (hiking). To find the experimental probability of swimming, we divide the number of students who swam by the total number of students:

12/40 = 0.3.

The theoretical probability of swimming, P(swimming), is one half (0.5), but the experimental probability is 28 over 40 (0.7).

The theoretical probability of swimming, P(swimming), is one half (0.5), but the experimental probability is 12 over 40 (0.3).

The theoretical probability of swimming, P(swimming), is 12 over 28 (~0.4286), but the experimental probability is one half (0.5).

The theoretical probability of swimming, P(swimming), is 28 over 40 (0.7), but the experimental probability is one half (0.5).

Out of these options, the correct one is the theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40. (option b).

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Answer:

We have the equation:

√2 - √36 - 2x = 6

Simplifying the radicals we get:

√2 - 6 - 2x = 6

Adding 6 to both sides we get:

√2 - 2x = 12

Subtracting √2 from both sides we get:

-2x = 12 - √2

Dividing by -2 we get:

x = (6 - (1/√2))

Therefore, the real solution is:

x = (6 - (1/√2))

To check for extraneous solutions, we need to substitute this value of x back into the original equation and check if it satisfies the equation.

√2 - √36 - 2(6 - (1/√2)) = 6

Simplifying this we get:

-6 = 6

This is not true, so the solution x = (6 - (1/√2)) is extraneous.

Therefore, there is no real solution to the equation.