1. Harold and his pet chicken, Simone, leave their home traveling by bicycle at a constant-
speed that allows them to cover 500 feet in 2 minutes.
a) Express the rate of speed of Harold and Simone traveling on their bicycle in feet per
minute.
In miles per hour.

Answer:-1/6

Step-by-step explanation:

Draw a line out in the 2nd quadrant.

Your y=[tex]\sqrt{35}[/tex]    hypotenuse=6  use pythagorean theorem to solve for x

6² = 35 + x²

x=1

so

cosΘ = -1/6

The complete algebraic expression would be

Gross wages = 4.15 × hours worked + 0.21 × total food sales.

What is an algebraic expression?

The idea of expressing numbers using letters or alphabets without specifying their actual values is called Algebraic expressions . The basics of algebra taught us to express an unknown value with letters like x, y, z, etc. These letters are called variables here. It can be a combination of both constants and variables. Any value placed in front of a variable and multiplied by it is a coefficient.

Examples,

3x + 4a – 7, 4x – 10, etc.

These expressions are represented using unknown variables, constants, and coefficients. A combination of these three (as terms) is considered an expression. It should be remember that unlike an algebraic equation, an algebraic expression has no sides or an equal sign. Some examples of this include,

An algebraic expression that could be used to represent Enrique's gross salary would be:

Gross salary = hourly rate x hours worked + tip

Where Hourly rate = $4.15 per hour

Hours Worked = Number of hours worked by Enrique

Tipping = 21% of total food sales

So the complete algebraic expression would be:

Gross wages = 4.15 × hours worked + 0.21 × total food sales.

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The solution to the equation ln {A} = .552 is A = e[tex]^{0.552}[/tex] = 2.7. In order to calculate eˣ for both sides of the equation ln {A}=.552, one must first understand what the equation signifies.

A logarithmic equation is an equation involving logarithms of different variables. Logarithmic equations are used to solve various types of problems. It uses the logarithmic properties of multiplication and division to simplify the equation.

This equation is a logarithmic equation, in which ln (natural logarithm) is used to represent a number's exponential value.

This means that the equation is actually stating that A is equal to e raised to the power of 0.552 (e[tex]^{0.552}[/tex] ).

In order to solve for A, one must use the basic rule of logarithms: for any logarithmic equation of the form ln {A} = B, A = e^B.

Therefore, the solution to the equation ln {A} = .552 is

A = e[tex]^{0.552}[/tex] .

This equation can be solved using basic algebra, as e[tex]^{0.552}[/tex]  can be replaced with an equivalent expression.

The equation can be rewritten as A = (e[tex]^{0.5}[/tex])(e[tex]^{0.052}[/tex]).

The value of e[tex]^{0.5}[/tex] can be calculated using a calculator, and can be rounded to the nearest tenth.

The value of e[tex]^{0.052}[/tex] can then be calculated, which can also be rounded to the nearest tenth.

Adding the two values together will give the solution to the equation, which is A = 2.7.

Therefore, the solution to the equation ln {A} = .552 is

A = e[tex]^{0.552}[/tex]

= 2.7.

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Answer:

$2.4675

Step-by-step explanation:

you could have just used a calculator for this one tbh

Answer:

71%

Step-by-step explanation:

To calculate the percent decrease in the stock, we can use the following formula:

Percent decrease = ((Original value - New value) / Original value) * 100

Given:

Original value (purchase price) = $2.99 per share

New value (selling price) = $0.88 per share

Plugging in the values into the formula:

Percent decrease = ((2.99 - 0.88) / 2.99) * 100

Percent decrease = (2.11 / 2.99) * 100

Percent decrease = 70.57%

Rounding to the nearest whole percent, the correct answer is 71%.

The price for an adult ticket is $3 and the price for a student ticket is $14

Given that

So, we have

10x + 7y = 128

7x + 14y = 217

Where

x = adults and y = students

When solved graphically, we have

x = 3 and y = 14

Hence, the price of the student ticket is $14

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The probability that the point land in square S will be 5/6.

What is probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

The probability that the point does not land in triangle T is equal to subtract the area of triangle T from the area of rectangle and divided the result by the  the area of rectangle

so, Find out the area of rectangle

A = (6)(4)

= 24 unit²

Find out the area of triangle T

A = 1/2(2)(4)

= 4 unit²

The probability is equal to

P = (24-4) / 24

= 20/24

= 5/6

Hence, the probability that the point land in square S will be 5/6.

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The amount in the account after 5 years would be $9555.42.

What is the formula for compound interest?

[tex]A = P(1 + \frac{r}{n} )^{(nt)}[/tex]

Where:

A = the amount of money in the account after t years

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $6500, r = 8% = 0.08, n = 1 (compounded annually), and t is the number of years.

If no withdrawals are made from the account, then the amount of money in the account after t years will be

[tex]A = 6500(1 + \frac{0.08}{1})^{(1t)} \\ A = 6500(1.08)^t[/tex]

Now the amount of money in the account after a specific number of years,

A = 6500(1.08)⁵

A = 6500(1.469328)

A = $9555.42

So after 5 years, the amount in the account would be $9555.42

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Correct question is "Suppose Juan places $6500 in an account that pays 8% interest compounded each year. Assume that no withdrawals are made from the account.Then find What would be the amount in the account after 5 years?"

Sequence 1: 13, 16, 19, 22, 25, Sequence 2: 15, 13, 11, 9, 7 and Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7).

what is sequence?

An ordered list of numbers is a sequence. The three dots indicate that the established pattern should move forward.

A. Sequence 1: 13, 16, 19, 22, 25

Sequence 2: 15, 13, 11, 9, 7

Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)

B. Sequence 1: 1, 5, 17, 53, 161

Sequence 2: 6, 15, 33, 69, 141

Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (161, 141)

C. Input (x) | Output

1 | 17,  2 | 19, 3 | 21, 4 | 23

D. Input (x) | Output

1 | 30, 2 | 15, 3 | 7.5

To find the outputs, we use the formula: output = 60 ÷ 2x.

For x = 1, output = 60 ÷ 2(1) = 30

For x = 2, output = 60 ÷ 2(2) = 15

For x = 3, output = 60 ÷ 2(3) = 7.5

E. Input (x) | Output

1 | 23, 2 | 30, 3 | 37, 14 | 102, 15 | 109, 16 | 116, 27 | 205, 70 | 498

To find the outputs, we use the formula: output = 16 + 7x.

For x = 1, output = 16 + 7(1) = 23

For x = 2, output = 16 + 7(2) = 30

For x = 3, output = 16 + 7(3) = 37

For x = 14, output = 16 + 7(14) = 102

For x = 15, output = 16 + 7(15) = 109

For x = 16, output = 16 + 7(16) = 116

For x = 27, output = 16 + 7(27) = 205

For x = 70, output = 16 + 7(70) = 498

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Answer:

Step-by-step explanation:

Draw a line out in the 3rd quadrant.  Hyponuse would be 3; y=-2 find x using pythagorean theorem

so 3²=2²+x²

x=[tex]\sqrt{5}[/tex]

so cos Θ = [tex]\frac{\sqrt{5} }{3}[/tex]

The correct answer is: B. They have the same y-intercept, but the graph of g(x) gets faster over time.

Exponents and powers are ways of representing very large  or very small numbers in a simplified way. For example, if we need to represent 3 x 3 x 3 x 3 in a simple way,  we can write it as 34, where 4 is the exponent and 3 is the base. The whole expression 34 is said to be a force.

The  functions provided are:

[tex]f(x) = 500(1.015)^x[/tex]

[tex]g(x) = 500(1.021)^x[/tex]

Both functions have an initial value of $500 (when x = 0). Therefore, they share the same y-intercept, which is (0, 500).  

To compare the graphs of f(x) and g(x), we can look at their growth rates. Note that the exponent of f(x) has a base of  1.015, while the exponent of g(x) has a base of  1.021. Since both bases are greater than 1, both functions grow exponentially with time.  

However, since 1.021 is greater than 1.015, the function g(x) increases with time faster than f(x). This means that the graph of g(x) is steeper than the graph of f(x).  

Therefore, the correct answer is:

B. They have the same y-intercept, but the graph of g(x) gets faster over time.

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The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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Answer:

15 = m

Step-by-step explanation:

10 − 3(m − 5) = 2(5 − m)

10 - 3m + 15 = 10 - 2m

25 - 3m = 10 - 2m

25 - 10 = - 2m + 3m

15 = m

__________

hope it helps!

Answer:

m=15

Step-by-step explanation:

10 − 3(m − 5) = 2(5 − m)

-3m+25=10-2m

-3m= -2m -15

-m=-15

m=15

The solutions to the equation [tex]x^{2} + x[/tex]  = 11/4 are x = -1/2 + [tex]\sqrt{3}[/tex] and x = -1/2 - [tex]\sqrt{3}[/tex]

What is the equation?

An equation is a mathematical statement that indicates that two expressions are equivalent. It has two sides, one on each side, divided by an equals sign (=). An equation's left and right sides can contain numbers, variables, and mathematical operations, including addition, subtraction, multiplication, and division.

The left side of the equation should be rewritten in the form (x + a)2, where an is a constant, in order to complete the square and find the solution to the equation [tex]x^{2}+x[/tex] = 11/4.

To accomplish this, add and remove [tex](1/2)^{2}[/tex](which is equivalent to 1/4) inside of the brackets, as seen in the example below:

[tex]x^{2} +x[/tex]= 11/4

[tex]x^{2} +x[/tex]+ 1/4 - 1/4 = 11/4

[tex](x+1/2)^{2}[/tex] - 1/4 = 11/4

[tex](x+1/2)^{2}[/tex] = 3

Next, we take the square root of both sides:

x + 1/2 = ±[tex]\sqrt{3}[/tex]

Finally, we solve for x by subtracting 1/2 from both sides:

x = -1/2 ± [tex]\sqrt{3}[/tex]

So the solutions to the equation [tex]x^{2} +x[/tex]  = 11/4 are x = -1/2 + [tex]\sqrt{3}[/tex] and x = -1/2 - [tex]\sqrt{3}[/tex].

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Answer:

First account: $6380.

Second account: $4251.

Step-by-step explanation:

let the first account have $x at the start of the first year

So at the end of 1 year it had x + 0.1x = $1.1x

In the same we we calculate the amount in the second account

= $1.09(9700 - x)

So we have the following equation

1.1x + 1.09(9700 - x) = 9700 + 931

1.1x + 10573 - 1.09x = 10631

0.01x = 10631 - 10573 = 58

x = 58/0.01

   =$5800

So at the end of the year there was

5800 * 1.1 = $6380 in first account

and

the second account had

1.09 (9700 - 5800) = $4251.

The graph will bounce like a polynomial of degree equal to the multiplicity minus 1.

What is polynomial?

A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.

The power of the factor that causes the graph to bounce at the corresponding zero depends on the multiplicity of the zero.

If the zero has odd multiplicity, the graph will cross the x-axis at the zero, meaning there will be no bounce.

If the zero has even multiplicity, the graph will bounce at the zero. Specifically, if the multiplicity is 2, the graph will bounce like a parabola; if the multiplicity is 4, the graph will bounce like a quartic; and so on. In general, the graph will bounce like a polynomial of degree equal to the multiplicity minus 1.

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For the given normal distribution a. We expect approximately 954 chicks to hatch between 25 and 33 days. b. We expect approximately 683 chicks to hatch between 27 and 31 days.

A probability distribution that is frequently used in statistics is the normal distribution, usually referred to as the Gaussian distribution. The majority of the data are within one standard deviation of the mean, resulting in a bell-shaped curve that is symmetrical around the mean.

In a normal distribution, the mean, median, and mode are all equal, and the mean and standard deviation serve as the two parameters that define the curve. While the standard deviation reflects the distribution's spread, the mean represents the distribution's centre.

The z-score is given by the formula:

z = (x - mu) / sigma

a. For 25 to 33 days:

z = (25 - 29) / 2

z = -2

and

z = (33 - 29) / 2

z = 2

Thus, P(z < 2) = 0.9772.

Now, we have:

P(25 < x < 33) = P(z < 2) - P(z < -2)

P(25 < x < 33) = 0.9772 - 0.0228

P(25 < x < 33) = 0.9544

Expected number of chicks = 0.9544 x 1000 = 954.4

Hence, we expect approximately 954 chicks to hatch between 25 and 33 days.

b. For 27 to 31 days:

P(27 < x < 31) = P(z < 1) - P(z < -1)

P(27 < x < 31) = 0.8413 - 0.1587

P(27 < x < 31) = 0.6826

Expected number of chicks = 0.6826 x 1000 = 682.6

Therefore, we expect approximately 683 chicks to hatch between 27 and 31 days.

c. For 29 days or fewer:

P(x <= 29) = P(z <= 0) = 0.5

Expected number of chicks = 0.5 x 1000 = 500

d. In 23 to 35 days:

P(23 < x < 35) = P(z < 3) - P(z < -3)

P(23 < x < 35) = 0.9987 - 0.0013

P(23 < x < 35) = 0.9974

Expected number of chicks = 0.9974 x 1000 = 997.4

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Answer:

x = 7

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

9x - 3 + 30 + 90 = 180

9x + 117 = 180 ( subtract 117 from both sides )

9x = 63 ( divide both sides by 9 )

x = 7

Answer:

1499.06 cm³

Step-by-step explanation:

volume = length × width × height

length = 22.5 cm

width = 10.25 cm

height = 6.5 cm

volume = 22.5 cm × 10.25 cm × 6.5 cm

volume = 1499.0625 cm³

Answer: 1499.06 cm³

Answer:

normal distribution curve

Step-by-step explanation:

It is given that the bars decrease evenly from the middle to the left and from the middle to the right.

Answer: 12

                                                      ........................................

Based on the calculations given below, the value of the marginal product is option A: $37.50.

The value of marginal product (VMP) is one that can be calculated as the additional revenue generated by hiring an additional worker.

So to o calculate the VMP of the first worker, it will be:

Hence:

VMP of the first worker = (output with one worker - output with zero workers) x price per unit

VMP of the first worker = (25 - 0) x $2

                                            = $50

Note that the ingredients needed to make each cup of coffee cost 50 cents, so the total cost of making 25 cups of coffee with one worker will be:

Total cost = ingredients cost x output

                = $0.50 x 25

                   = $12.50

So, the value of the marginal product of the first worker can be obtained by:

VMP of the first worker = additional revenue - additional cost

                                  = $50 - $12.50

                                    = $37.50

So the value of the marginal product is: $37.50.

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The median, mean, range and mode will be 6, 5.4, 9 and 7.

What is median?

The median is the middle number in the data set when the data set is written from least to greatest.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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We can see that for one who doesn't fall ill frequently, the PPO Plan will be the best. This is as a result of its lower premium and broader network of healthcare providers.

A PPO (Preferred Provider Organization) plan is known to be a type of health insurance plan which allows individuals to actually choose their healthcare providers. It allows them to choose from a network of preferred providers who have agreed to provide services at a discounted rate.

We can see here that in the PPO Plan, the PPO (Preferred Provider Organization) plan actually has a lower premium, but the coverage is only 80%, and you need to pay 20% of the cost-sharing or co-insurance.

Also, the PPO plan has a higher deductible of $1,000, which means that the insurance coverage starts later.

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The inequality with the given solution set is given as follows:

D. -2 ≤ x + 5 < 6.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

The solution to the compound inequality in this problem is given as follows:

-7 ≤ x < 1.

Hence the inequality can be obtained adding 5 to each term, as follows:

-7 + 5 ≤ x + 5 < 1 + 5 = -2 ≤ x + 5 < 6.

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Answer:

the solution is d = -10.75.

Step-by-step explanation:

To solve for d in this equation, we need to first simplify it by distributing the 3 on the right side:

-115 = 20 + 12d - 6

Next, we combine like terms on the right side:

-115 = 14 + 12d

Then, we isolate the variable term by subtracting 14 from both sides:

-129 = 12d

Finally, we solve for d by dividing both sides by 12:

d = -10.75

Therefore, the solution is d = -10.75.

Answer:

[tex]d=-\frac{43}{4}[/tex]

Step-by-step explanation:

First, let's apply the distributive property and multiply 4d and -2 by 3.

We have:

[tex]-115=20+3(4d-2)=\\-115=20+3(4d)+3(-2)=\\-115=20+12d-6[/tex]

Now, let's combine like terms.

[tex]-115=20+12d-6=\\-135=12d-6=\\-129=12d=\\-\frac{129}{12} =d[/tex]

Both 129 and 12 are divisible by 3, so let's simplify the fraction:

[tex]d=-\frac{129}{12} =\\d=-\frac{43}{4}[/tex]

Answer:

We are given that 50% of the ELTs are made by Company A, 45% are made by Company B, and 5% are made by Company C. We also know the rate of defects for each company's ELTs: 4% for Company A, 6% for Company B, and 9% for Company C.

Let D be the event that an ELT is defective, and let Bi be the event that an ELT was made by Company i, where i = A, B, or C. We want to find the probability that an ELT is made by Company B given that it is defective, i.e., we want to find P(B|D).

Using Bayes' theorem, we can write:

P(B|D) = P(D|B) * P(B) / P(D)

where P(D|B) is the probability that an ELT made by Company B is defective, P(B) is the prior probability that an ELT is made by Company B, and P(D) is the overall probability of an ELT being defective.

We can calculate each of these probabilities as follows:

P(D|B) = 0.06 (given)

P(B) = 0.45 (given)

P(D) = P(D|A) * P(A) + P(D|B) * P(B) + P(D|C) * P(C)

= 0.04 * 0.5 + 0.06 * 0.45 + 0.09 * 0.05

= 0.0355

Substituting these values into Bayes' theorem, we get:

P(B|D) = P(D|B) * P(B) / P(D)

= 0.06 * 0.45 / 0.0355

≈ 0.762

Therefore, the probability that an ELT made by Company B is defective given that it is found to be defective is approximately 0.762, or 76.2%.