4.02 Lesson check ! (3)

A person's cycling rate can be expressed mathematically in the equation that describes their cycling motion. Specifically, the cycling rate can be represented by the frequency or number of revolutions per unit time (usually in seconds) that the person completes while cycling.

The equation that describes a person's cycling motion is typically a kinematic equation that relates the person's position, velocity, and acceleration as a function of time. One commonly used equation is:

d = vit + 1/2at^2

where d is the distance traveled by the person, vi is the initial velocity (usually zero), a is the acceleration, and t is the time elapsed.

The cycling rate can be incorporated into this equation by expressing the velocity as a function of the frequency of revolutions (f) and the radius of the wheel (r). This gives:

v = 2πrf

where v is the velocity of the cyclist, r is the radius of the wheel, and π is the mathematical constant pi (approximately 3.14).

Substituting this expression for v into the kinematic equation gives:

d = (2πrf)t + 1/2at^2

This equation shows how the person's cycling rate, represented by the frequency f, affects their distance traveled as a function of time. If the person increases their cycling rate, their velocity increases, and they will travel a greater distance in the same amount of time.

Answer:

The answer is B

Step-by-step explanation:

Answer: I THINK 4.

Step-by-step explanation:

Sorry if it is wrong!! :'D

Answer:

62

Step-by-step explanation:

Surface area of a prism = S = 2(lw + lh + wh)

where l = length

w = width

h = height

Given l = 3, w = 5 and h = 2

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

= 2(15 + 6 + 10)

= 2(31)

= 62

Answer:C

Step-by-step explanation:

[tex](x-3)^2=5\\we \ should \ find \ square \ root \ of \ each \ side,\\\sqrt{(x-3)^2}=\sqrt{5}\\1)x-3=\sqrt{5}x=\sqrt{5}+3\\2)3-x=\sqrt{5}\\x=3-\sqrt{5}\\\\so,x=3\± \sqrt{5}[/tex]

By using pythagorean theorem, the length of the missing side is 12 feet.

What is the Pythagorean theorem?

Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:

"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."

In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:

[tex]c^2 = a^2 + b^2[/tex]

We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.

In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.

If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:

[tex]c^2 = 7.2^2 + 9.6^2[/tex]

[tex]c^2 = 51.84 + 92.16[/tex]

[tex]c^2 = 144[/tex]

[tex]c = \sqrt{144}[/tex]

c = 12 feet

Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.

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Answer:

12 × 3 = 36

the top of the diagram will also equal 36

138-72=66

66 ÷2= 33

33÷3 =11

therefore x=11

Answer:

perimeter = 138

p=2(138+12)

p=2×150

p=300

x=300

The weight of the smaller dog is 5.6 pounds.

Let the weight of the smaller dog be x, then,

The weight of the larger dog = 1.4 pounds.

The combined weight of the dogs =  12.6 pounds.

Therefore,

The sum of the weight of the larger dog and smaller dog = the combined weight of the dogs.

That is,

1.4 + x + x = 12.6

1.4 + 2x =  12.6

2x = 12.6 - 1.4

2x = 11.2

x = 11.2 ÷ 2

x = 5.6.

Hence, the weight of the smaller dog is 5.6 pounds.

?

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Your question is incomplete, and the complete question would be:

Karen has two dogs. the larger dog weighs 1.4 pounds more than the smaller dog. the combined weight of the two dogs is 12.6 pounds. what is the weight of the smaller dog?

The value οf a = 3, b=-10, c-8

it's a secοnd-degree quadratic equatiοn which is an algebraic equatiοn in x. Ax² + bx + c = 0, where a and b are the cοefficients, x is the variable, and c is the cοnstant term, is the quadratic equatiοn in its standard fοrm. A nοn-zerο term (a 0) fοr the cοefficient οf x² is a prerequisite fοr an equatiοn tο be a quadratic equatiοn.

The x² term is written first, then the x term, and finally the cοnstant term is written when cοnstructing a quadratic equatiοn in standard fοrm. In mοst cases, the numerical values οf letters a, b, and c are expressed as integral values rather than fractiοns οr decimals.

The equatiοn given 5x²-2=2x²+10x+6

3x²-10x-8=0

values οf a = 3, b=-10, c-8

Hence the value οf a = 3, b=-10, c=8

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A5 has a value of -11. This can also be confirmed by looking at the words in order: 5, 1, -3, -7, and -11.

Using the given formula, we can find the value of the nth term by recursively applying the formula, starting from the first term:

a1 = 5

a2 = a1 - 4 = 1

a3 = a2 - 4 = -3

a4 = a3 - 4 = -7

a5 = a4 - 4 = -11

Therefore, the value of a5 is -11. We can also verify this by checking the sequence of terms: 5, 1, -3, -7, -11.

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Answer:

The answer is to this question is D. 41/10

The length of the rectangular prism with a volume of 1.512 m³​ is equal to 0.9 meters.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given parameters into the formula for the volume of a rectangular prism, we have;

Volume of a rectangular prism = L × W × H

1.512 = L × 2.4 × 0.7

Length, L = 1.512/1.68

Length, L = 0.9 meters.

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Complete Question:

Find the length of the rectangular prism shown below with a volume of 1.512 m³​, a width of 2.4 m and a height of 0.7 m.

Answer:

x=5/6

Step-by-step explanation:

lcm=6x

6xX1/2x+6xX1/3x=6xX1 (divide through)

3x1+2x1=6xX1

3+2=6x

5=6x

5/6=6x/6 (divide through)

x=5/6

Hope it help

According to given equation Baxter’s Hardware had 27 followers on Sunday morning.

What is equation?

Equations can take many forms, including linear, quadratic, polynomial, trigonometric, and exponential, and can be used to model and solve a wide range of real-world problems.

The given equation is:

f + 18 - 20 = 25

Adding the numbers on the left side, we get:

f - 2 = 25

Adding 2 to both sides, we get:

f - 2 + 2 = 25 + 2

Simplifying, we get:

f = 27

Therefore, Baxter’s Hardware had 27 followers on Sunday morning.

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The cost of water from the store and the cost from the tap will be the same when the number of liters

reaches 7.5 liters.

Let's assume that the cost of buying 'x' liters of water from the store is the same as the cost of buying 'x' liters of water from the tap.

For water from the store, the cost per liter is 3, so the cost of buying 'x' liters of water from the store would be 3x.

For water from the tap, there is a flat rate of 15 plus per liter. So, the cost of buying 'x' liters of water from the tap would be 15 + x.

Now we can set up an equation to find the value of 'x' when the costs are equal:

3x = 15 + x

Simplifying this equation, we get:

2x = 15

x = 7.5

Therefore, the cost from the store and the cost from the tap would be the same at 7.5 liters.

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Answer:

9 hope u get it right budddyyyy

Answer:

Horizontal distance between the wall and the bottom of ramp = 25.4 inches.

Step-by-step explanation:

Pythagorean theorem:

          AB  -> wall ;  AB =  14 inches    

         AC -> Wooden plank ; AC = 29 inches

        BC -> horizontal distance between the wall and the bottom of ramp(pank).

           Pythagorean theorem,

                       [tex]\boxed{\bf base^2 + altitude^2 = hypotenuse^2}[/tex]

                         BC² + AB² = AC²

                           BC² + 14² = 29²

                          BC² + 196 =  841

                                     BC² = 841 - 196

                                             = 645

                                       BC = √645

                                       BC = 25.4 inches

Horizontal distance between the wall and the bottom of ramp = 25.4 inches.

Given,

Length = 29 inches

Height = 14inches

Here,

Pythagorean theorem:

AB  -> wall ;  AB =  14 inches    

AC -> Wooden plank ; AC = 29 inches

BC -> horizontal distance between the wall and the bottom of ramp (plank).

Pythagorean theorem,

Base²  + Perpendicular² = Hypotenuse²

BC² + AB² = AC²

BC² + 14² = 29²

BC² + 196 =  841

BC² = 841 - 196

= 645

BC = √645

BC = 25.4 inches

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Therefore, the annual interest rate is approximately 12%.

How to compute interest is as follows: P x R x T is the formula for calculating interest. Principal Amount is P. (the beginning balance). rates of interest (usually per year, expressed as a decimal). T stands for the value T. (generally one-year time periods).

Let r be the annual interest rate as a decimal. Then the balance after 2 years is given by:

Balance = 3500(1+r)²

Setting this equal to $4390.40 and solving for r, we have:

4390.40 = 3500(1+r)²

Dividing both sides by 3500 and taking the square root, we get:

(1+r)² = 4390.40/3500 = 1.2544

Taking the square root of both sides, we get:

1 + r = √(1.2544) ≈ 1.12

Subtracting 1 from both sides, we get:

r ≈ 0.12 or 12%

Therefore, the annual interest rate is approximately 12%.

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e [0.1}

We know that P(X < 2.24) = 0.7257. Also, the mean is 2.Let us calculate the variance of the given normal distribution random variable. Given that P(X < 2.24) = 0.7257, we have to find variance. Let us solve this question as follows:We know that mean of normally distributed random variable is μ and standard deviation is σ. As the mean is 2, μ = 2.We have the z-score: z = (2.24 - 2) / σFrom the normal distribution table, we can find out that P(Z < 0.80) = 0.7881Now, we have the following equation:0.7881 = (2.24 - 2) / σσ = 0.3158Finally, we can find the variance (σ^2) = 0.3158^2 = 0.0995 ≈ 0.1Therefore, the correct answer is option e. 0.1.

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50%

The cran-orange juice contains 50% cranberry juice. The juice is 100% juice. Subtract 50% cranberry juice from 100% cran-orange juice and that leaves you with 50% orange juice.

The cοrrect answer tο the given questiοn is d. the central limit theοrem.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

The basis fοr using a nοrmal prοbability distributiοn tο apprοximate the sampling distributiοn οf the sample means and pοpulatiοn mean is the central limit theοrem.

The central limit theοrem states that fοr a sufficiently large sample size, the sampling distributiοn οf the sample means will be apprοximately nοrmal, regardless οf the shape οf the pοpulatiοn distributiοn. This theοrem allοws us tο make statistical inferences abοut the pοpulatiοn mean based οn the sample mean using the prοperties οf the nοrmal distributiοn, such as the mean and standard deviatiοn.

Therefοre, the cοrrect answer tο the given questiοn is d. the central limit theοrem.

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Given data:

pH of lye = 12.13

Using the formula pH = -log[H+], we have to find the hydrogen ion concentration, [H+].

Now, putting the given values in the formula, we get:

pH = -log[H+]

12.13 = -log[H+]

log[H+] = -12.13

[H+] = 10^-12.13 = 5.01187 x 10^-13

So, the hydrogen ion concentration, [H+] is 5.01187 x 10^-13 moles/liter. Therefore, the answer is 5.01187 x 10^-13.

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The sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

In the context of sampling distribution of the means, the standard deviation represents the degree of spread or variation of sample means around the true population mean.

To compute the standard deviation of the sampling distribution of the means, one typically divides the population standard deviation by the square root of the sample size.

Therefore, the standard deviation of the sampling distribution of the means is 29/√36 = 29/6 = 4.83 pounds.

So, the sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

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Pete runs farther per carry, with a unit rate of 9.05 yards per carry compared to Branden's unit rate of 7.33 yards per carry.

A unit rate is a rate that has a denominator of 1. It is a ratio that compares a quantity to its unit of measurement.

To determine who runs farther per carry, we can use unit rates to compare the distance each player runs per carry.

For Branden:

Distance per carry is

= 550 yards ÷ 75 carries

Divide the numbers

= 7.33 yards per carry

For Pete:

Distance per carry is

= 380 yards ÷ 42 carries

Divide the numbers

= 9.05 yards per carry

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We can conclude after answering the provided question that  If the data expression points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.

In mathematics, an expression is a grouping of representations, digits, and huge corporations that resemble a clear relationship or regimen. An expression can be a real number, a transitory, or a combination of the two. Addition, subtraction, pervasiveness, division, and exponentiation are examples of mathematical operators. Expressions are common in arithmetic, mathematics, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

This graph appears to be a scatter plot of data points based on the visual representation you provided. The values of an independent variable are represented by the horizontal axis (x-axis), while the values of a dependent variable are represented by the vertical axis (y-axis).

Without any additional information, determining the specific function represented by this graph is difficult. The shape and pattern of the scatter plot, on the other hand, can provide some insight into the relationship between the two variables. If the data points are arranged in a linear pattern, for example, the function could be a linear equation. If the data points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.

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Using the equation y = 7x , we can compute that when x = 2, y = 14 and when x = 4 , y = 28. So, correct option is B.

The equation y = 7x relates the variables y and x, where y is a function of x. To compute the value of y for a given value of x, we simply substitute that value of x into the equation and solve for y.

When x = 2, we can substitute this value into the equation:

y = 7(2) = 14

Therefore, when x = 2, y = 14.

Similarly, when x = 4, we can substitute this value into the equation:

y = 7(4) = 28

Therefore, when x = 4, y = 28.

So, the correct option is B: When x = 2, y = 14 and when x = 4, y = 28.

In summary, to compute the value of y for a given value of x using an equation, we substitute that value of x into the equation and solve for y. In this case, when x = 2, y = 14, and when x = 4, y = 28, according to the given equation y = 7x.

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The minimum number of feet in the length of the rope [tex]8\sqrt{(4\pi^2 + 36)}[/tex] feet.

To find the minimum number of feet in the length of the rope, we need to first calculate the height of the point on the circumference where the rope is attached. We can do this by using the formula for the circumference of a cylinder:

C = 2πr

where C is the circumference, r is the radius of the cylinder, and π is pi. Since we know that the circumference of the pole is 2 feet, we can solve for the radius:

2 = 2πr

r = 1/π

Next, we need to calculate the length of the rope that is wrapped around the pole. We know that the rope is wrapped around the pole four times, so the length of the rope is:

L = 4 × height of the pole

To find the height of the pole, we can use the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

where a is the radius of the pole, b is the height of the point where the rope is attached, and c is the length of the rope wrapped around the pole.

Solving for b, we get:

b = [tex]\sqrt{c^2 - a^2)}[/tex]

Substituting the values we know, we get:

b = [tex]\sqrt{((4\pi^2 + 12^2) - \pi^2)}[/tex]

b = [tex]\sqrt{sqrt(16\pi^2 + 144)}[/tex]

Finally, we can substitute this value into the formula for the length of the rope:

[tex]L = 4 * \sqrt{16\pi^2 + 144)}[/tex]

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Answer:

the number 228

Step-by-step explanation:

Let's call the smallest number in the consecutive sequence "x". Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.

If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) or 9x + 36.

We know that the sum of the remaining 9 numbers is 2023, so we can set up the equation:

9x + 36 = 2023

Solving for x, we get:

9x = 1987

x = 221

Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.

If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.

The probability of randomly selecting a temperature between 70 and 75 is approximately 0.8291.

To find the probability that a randomly chosen temperature is between 70 and 75, we need to use the z-score formula as shown below:

z = (x - μ) / σ

Where:x = 70 and 75μ = 79σ = 4z1 = (70 - 79) / 4 = -2.25z2 = (75 - 79) / 4 = -1P(70 < x < 75) = P(-2.25 < z < -1)

To find the probability for the above inequality, we need to use a calculator. We know that the probability of the standard normal distribution is equal to 1.

Hence, P(-2.25 < z < -1) = Φ(-1) - Φ(-2.25) = 0.8413 - 0.0122 ≈ 0.8291. Therefore, the probability is about 0.8291.

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