8. How many seconds are in 2 minutes? ​

The statement "The equation 2x + 7 = 2(x + 5) has one solution" is false because we would get 7 = 10 when we simplify the equation.

The equation 2x + 7 = 2(x + 5) can be simplified as shown below:

2x + 7 = 2(x + 5)

Distribute the 2 on the right side:

2x + 7 = 2x + 10

Isolate the variable x by subtracting 2x from both sides:

2x - 2x + 7 = 2x - 2x + 10 [subtraction property of equality]

Simplify:

7 = 10

Since we get 7 = 10, which is not true, it implies that the equation has no solution. Therefore, the statement is "The equation 2x + 7 = 2(x + 5) has one solution" is false.

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Complete Question:

(True or False). The equation 2x + 7 = 2(x + 5) has one solution.

We can write the probability density function:

f(x) = 1/10 for 2 ≤ x ≤ 12

f(x) = 0 otherwise

To find the value of k that makes the function a probability density function (PDF) over the interval [2, 12], we need to ensure that the integral of the PDF over the entire interval is equal to 1.

The probability density function is defined as:

f(x) = k for 2 ≤ x ≤ 12

f(x) = 0 otherwise

To find k, we integrate the PDF over the interval [2, 12] and set it equal to 1:

∫[2,12] f(x) dx = 1

Since f(x) is a constant k over the interval [2, 12], the integral becomes:

∫[2,12] k dx = 1

The integral of a constant is equal to the constant times the width of the interval:

kx ∣[2,12] = 1

Substituting the limits of integration:

k(12 - 2) = 1

k(10) = 1

10k = 1

k = 1/10

Therefore, the value of k that makes the function a probability density function over the interval [2, 12] is k = 1/10.

Now, we can write the probability density function:

f(x) = 1/10 for 2 ≤ x ≤ 12

f(x) = 0 otherwise

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Answer:

90 degrees, 125 degrees, 35 degrees, 70 degrees, 20 degrees

Step-by-step explanation:

Answer:

the middle of the shape

Step-by-step explanation:

Answer: The formula of a y-coordinate is y=mx+b.

Step-by-step explanation: A horizontal line has gradient 0. In a horizontal line all points have the same y-coordinate, but the x-coordinate can take any value.

Answer:

110

Step-by-step explanation:

10% of 100 is 10

100+10=110

Yes, providing additional information affect responses to a survey question. The difference in the proportion of shoppers who admitted to texting and driving in the two groups is 0.2.

To calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups, we need to first determine the number of shoppers in each group who admitted to texting and driving.

Let's assume that in Group A, 10 shoppers admitted to texting and driving, while in Group B, 5 shoppers admitted to texting and driving.

Then, we can calculate the proportion of shoppers who admitted to texting and driving in each group by dividing the number of shoppers who admitted to texting and driving by the total number of shoppers in each group:

Proportion in Group A = 10/25 = 0.4

Proportion in Group B = 5/25 = 0.2

The difference in proportions is then:

Difference = Proportion in Group A - Proportion in Group B

Difference = 0.4 - 0.2

Difference = 0.2

Therefore, the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B) is 0.2 or 20%.

This suggests that providing additional information about the potential consequences of texting and driving may reduce the proportion of people who admit to engaging in this behavior. However, it's important to note that this study has a small sample size and there may be other factors that influence people's responses to survey questions about texting and driving.

Correct Question :

Does providing additional information affect responses to a survey question? Two statistics students decided to investigate by asking different versions of a question about texting and driving. Fifty mall shoppers were divided into two groups of 25 at random. The first group was asked Version A and the other half were asked Version B. Version A: A lot of people text and drive. Are you one of them? Version B: About 6000 deaths occur per year due to texting and driving. Knowing the potential consequences, do you text and drive? Calculate the difference in the proportion of shoppers who admitted to texting and driving in the two groups (A-B).

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Card B is a better deal than Card A when the total annual purchases exceed $4,750. This is because the additional 0.5% cash back on Card B compensates for the $95 annual fee.

To determine when Card B becomes a better deal than Card A, we need to compare the cashback earnings of both cards and take into account the annual fee of Card B.Card A offers a flat 1.5% cash back on every purchase, while Card B offers a higher 2% cash back but also has a $95 annual fee.

To find the break-even point, we need to calculate the difference in cash-back earnings between the two cards and equate it to the annual fee:

2% - 1.5% = 0.5% cash back difference

To cover the $95 annual fee, the total annual purchases must generate an additional 0.5% cash back compared to Card A:

0.5% of x = $95

Solving for x, we find that the total annual purchases must exceed $4,750 for Card B to be a better deal than Card A. At this threshold, the additional 0.5% cash back on Card B compensates for the annual fee, making it a more advantageous option for the cardholder.

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Your answer will be 35

Answer:

slope = - \(\frac{1}{3}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ = X (1, 5 ) and (x₂, y₂ ) =  Z (7, 3 )

\(m_{XZ}\) =\(\frac{3-5}{7-1}\) = \(\frac{-2}{6}\) = - \(\frac{1}{3}\)

According to the Question, The interest earned in 4 years is $1,954.83.

What is compounded quarterly?

A quarterly compounded rate indicates that the principal amount is compounded four times over one year. According to the compounding process, if the compounding time is longer than a year, the investors would receive larger future values for their investment.

The principal is $10,000.

The annual interest rate is 4.5%, which is compounded quarterly.

Since there are four quarters in a year, the quarterly interest rate can be calculated by dividing the annual interest rate by four.

The formula for calculating the future value of a deposit with quarterly compounding is:

\(P = (1 + \frac{r}{n})^{nt}\)

Where P is the principal

The annual interest rate is the number of times the interest is compounded in a year (4 in this case)

t is the number of years

The interest earned equals the future value less the principle.

Therefore, the interest earned can be calculated as follows: I = FV - P

where I = the interest earned and FV is the future value.

Substituting the given values,

\(P = $10,000r = 4.5/4 = 1.125n = 4t = 4 years\)

The future value is:

\(FV = $10,000(1 + 1.125/100)^{4 *4} = $11,954.83\)

Therefore, the interest earned is:

\(I = $11,954.83 - $10,000= $1,954.83\)

Thus, the interest earned in 4 years is $1,954.83.

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The probability of a single randomly sampled observation having a value above the mean is approximately 0.1587, assuming a normal distribution.

if the mean of the data is μ and the standard deviation is σ, then the probability of a single observation being above the mean is given by:

P(X > μ) = 1 - P(X ≤ μ)

where X is the random variable representing the data. To calculate this probability, we need to standardize the data by subtracting the mean from each observation and dividing by the standard deviation. This gives us a standard normal variable Z, which has a mean of 0 and a standard deviation of 1.

Then, we can look up the probability in a standard normal table or use a calculator or software to find the area under the standard normal curve to the right of Z = 0.

For example, suppose we have a dataset with a mean of 10 and a standard deviation of 2. If we standardize the data, then a value of 12 would correspond to a Z-score of:

Z = (12 - 10) / 2 = 1

The probability of a value being above the mean is then:

P(X > 10) = 1 - P(X ≤ 10) = 1 - P(Z ≤ 1) = 1 - 0.8413 = 0.1587

Therefore, the probability of a single randomly sampled observation having a value above the mean is approximately 0.1587, assuming a normal distribution.

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Answer:

0.0065509804

Step-by-step explanation:

Answer:

If you follow the order of operations it would be 0.12103072956 or approximately

0.12

0.121

0.1210

0.12103

0.121031

The data appears to follow a quadratic curve, and a quadratic model would best describe the data. The quadratic function that models the data is y = 2x^2 - x - 1.

To graph the given data set, we can plot the points on a coordinate plane as follows:

  |

8 |  

7 |    ●

6 |        

5 |        

4 |        

3 |        

2 |  ●  

1 |    ●  

0 |  ●  

-1 |    ●

-2 |  ●  

  |_____________

    -2 -1  0  1  2

From the graph, we can see that the data appears to follow a quadratic curve. Therefore, a quadratic model would best describe the data.

To write a quadratic function that models the data, we can use the standard form of a quadratic equation:

y = ax^2 + bx + c

where a, b, and c are constants to be determined.

To find the values of a, b, and c, we can use the data points and solve the resulting system of equations

-1 = 4a - 2b + c

-2 = a - 2b + c

-1 = c

2 = 4a + 2b + c

7 = 4a + 8b + c

Solving the system of equations, we get:

a = 2

b = -1

c = -1

Therefore, the function that models the data is:

y = 2x^2 - x - 1

Answer:

Tommy is 14 years old.

Step-by-step explanation:

14+5=19

Jack is 19 years old.

14+19=33

Hope this helps!

\(\huge\mathcal {♨Answer♥}\)

\(\large\texttt{Let's get Jack's age as x}\)

\(\large\texttt{So Tommy's age is x-5}\)

( x - 5 ) + x = 33

2x - 5 = 33

2x = 33 + 5

2x ÷ 2 = 38 ÷ 2

x = 19

So Jack's age is 19

Then,

Tommy's age is = x - 5

= 19 - 5

= 14

☆...hope this helps...☆

_♡_mashi_♡_

Answer:

($5000 x 4% ) * 2 = $400

The ending balance : $5000 + $400 = $5400

Step-by-step explanation:

The cost of the water bottle per ounce is $0.077.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a 36-oz bottle of water costs $2.88. The cost of 1 ounce of the bottle is calculated as,

1 OZ = 1.04 ounces

36 OZ = 36 x 1.04 ounces

36 OZ = 37.44 ounces

37.44 ounces = $2.44

1 ounce = $2.44 / 37.44

1 ounces = $0.077

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The area of the trapezoid image attached is solved to be

Area of a trapezoid is solved using the formula given belos

= 1/2 (sum of parallel lines) * height

In the figure the parallel lines are

= 3 + 6 + 3 = 12 and 6, and the height is 8 in

Plugging in the values

= 1/2 (12 + 6) * 8

= 9 * 8

= 72 square in

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The area of the composite figure in this problem is given as follows:

A = 72 in².

The area of a composite figure is obtained as the sum of the areas of all the parts that compose the figure.

The figure in this problem is composed as follows:

Hence the area of the composite figure in this problem is given as follows:

A = 6 x 8 + 2 x 1/2 x 3 x 8

A = 72 in².

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The function g is defined by:

g(u) = - (1/lambda) * ln(1 - u) for 0 < u < 1.

The random variable X = g(U) has the exponential (lambda) distribution.

(i) To create a random variable X that has cdf F, and you have a number picked uniformly on (0,1), you should do the following:

Let U be a uniform (0,1) random variable. To construct a random variable X=F^(-1)(U) so that X has the cdf F, take the inverse of the cdf F, denoted as F^(-1), and apply it to the uniformly distributed random variable U.

(ii) To find the function g for an exponential distribution with parameter lambda, you should set F as the exponential cdf, which is given by:

F(x) = 1 - e^(-lambda * x)

Now, you can find the inverse function F^(-1)(u):

1. Set u = F(x): u = 1 - e^(-lambda * x)
2. Solve for x: x = - (1/lambda) * ln(1 - u)

So, the function g is defined by g(u) = - (1/lambda) * ln(1 - u) for 0 < u < 1. The random variable X = g(U) has the exponential (lambda) distribution.

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Answer:D

Step-by-step explanation:

The slope of a line will be 1/6. Then the correct option is D.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.

Slope = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

(-6,3) and (12,6)

(x₁, y₁) = (-6,3)

(x₂, y₂) = (12,6)

Then the slope of a line will be

Slope = (6 – 3) / (12 + 6)

Slope = 3 / 18

Slope = 1/6

Then the correct option is D.

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Based on the types of angle pairs we have:

1. Angles 1 and 5, 2 and 6, 3 and 7, 4 and 8

2. Angles 3 and 5, 4 and 6

3. Angles 3 and 6, 4 and 5

4. Angles 1 and 8, 2 and 7

5. Angles that are supplementary to 120°

6. Angles 3, 5, and 7

7. a. Angles 1 and 2; m<2 = 180 - 100 = 80°

b. Angles 1 and 2; m<2 = 75°

c. Angles 1 and 2; m<2 = 82°

d. Angles 1 and 2; m<2 = 77°

8. m<1 = 100°

9. a. m<1 = 127°; b. m<3 = 53°

Some types of pairs of angles include:

From the given figure, we have:

1. Angles 1 and 5, 2 and 6, 3 and 7, 4 and 8 are pairs of corresponding angles.

2. Angles 3 and 5, 4 and 6 are pairs of same side, interior angles.

3. Angles 3 and 6, 4 and 5 are alternate interior angles.

4. Angles 1 and 8, 2 and 7, are alternate exterior angles.

Using the figure given, we can determine the following:

5. Angles that are supplementary to 120 degrees are: angles 1, 2, 7, and 6.

6. Angles that are congruent to 120 degrees are: angles 3, 5, and 7

7. a. Angles 1 and 2 are Same side interior angles

m<2 = 180 - 100 = 80°

b. Angles 1 and 2 are alternate interior angles.

m<2 = 75°

c. Angles 1 and 2 are corresponding angles.

m<2 = 82°

d. Angles 1 and 2 are alternate exterior angles.

m<2 = 77°

8. The student made an error by thinking angle 1 is supplementary to the given angle.

Both angles are alternate interior angles, therefore:

m<1 = 100°

9. a. m<1 = 180 - 53 = 127°

b. m<3 = 53°

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Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:  £6.50

Step-by-step explanation:

Let the cost of one jumper be x, and since Kara buys 5 jumpers, she pays for 4 and gets 1 free.

Therefore, she effectively pays for 4 jumpers. Now we can form the equation to find the value of x: (4x / 5) = (5.20)

Now solving the equation, we get; x = £6.50

Hence, the regular cost of one jumper when not in this offer is £6.50.

To compute the average velocity over each time interval, we use the formula: average velocity = (h(t2) - h(t1))/(t2 - t1), where h(t) is the height function.

Using the given height function, h(t) = 34t - 4.9t^2, we calculate the average velocities:
1. [3, 3.01]:
Average Velocity = (h(3.01) - h(3))/(3.01 - 3) ≈ -17.147 m/s
2. [3, 3.001]:
Average Velocity = (h(3.001) - h(3))/(3.001 - 3) ≈ -17.194 m/s
3. [3, 3.0001]:
Average Velocity = (h(3.0001) - h(3))/(3.0001 - 3) ≈ -17.199 m/s
4. [2.99, 3]:
Average Velocity = (h(3) - h(2.99))/(3 - 2.99) ≈ -17.243 m/s
5. [2.999, 3]:
Average Velocity = (h(3) - h(2.999))/(3 - 2.999) ≈ -17.205 m/s
6. [2.9999, 3]:
Average Velocity = (h(3) - h(2.9999))/(3 - 2.9999) ≈ -17.200 m/s
To estimate the instantaneous velocity at t=3, observe the average velocities as the time intervals approach t=3:
As the intervals get closer to t=3, the average velocities appear to approach -17.2 m/s. Thus, the estimated instantaneous velocity at t=3 is:
V ≈ -17.2 m/s

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Steps to solve:

p(x) = 5x - 4x^2 + 3

~Substitute

p(0) = 5(0) - 4(0)^2 + 3

~Simplify

p(0) = 0 - 0 + 3

~Simplify

p(0) = 3

Best of Luck!

Statement Problem: Calculate the percentage of the income based on the amount used to start the business.

Solution:

The percentage income is;

Thus, we have;

The Taylor series of the function\(\(f(z) = e^z\) at \(z = 1\) is \(e \sum_{n=0}^{\infty} \frac{(z-1)^n}{n!}\) for \(|z - 1| < \infty\).\)

To show that the Taylor series of the function\(\(f(z) = e^z\) at \(z = 1\) is given by \(e \sum_{n=0}^{\infty} \frac{(z-1)^n}{n!}\) for \(|z - 1| < \infty\)\), we need to find the coefficients of the series expansion.

The Taylor series expansion of a function\(\(f(z)\) about \(z = a\)\) is given by:

\(\[f(z) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(z - a)^n\]\)

where\(\(f^{(n)}(a)\)\) represents the \(\(n\)th\) derivative of\(\(f(z)\)\) evaluated at\(\(z = a\).\)

Let's calculate the derivatives of \(\(f(z) = e^z\)\) and evaluate them at \(\(z = 1\)\) to find the coefficients of the Taylor series.

The derivatives of\(\(f(z) = e^z\)\) are:

\(\[f'(z) = e^z\]\[f''(z) = e^z\]\[f'''(z) = e^z\]\[\vdots\]\[f^{(n)}(z) = e^z\]\)

Now, let's evaluate these derivatives at\(\(z = 1\)\):

\(\[f'(1) = e^1 = e\]\[f''(1) = e^1 = e\]\[f'''(1) = e^1 = e\]\[\vdots\]\[f^{(n)}(1) = e^1 = e\]\)

So, all the derivatives of\(\(f(z) = e^z\)\)evaluated at \(\(z = 1\)\) are equal to \(\(e\).\)

Now, substituting these values into the Taylor series expansion formula, we get:

\(\[f(z) = f(1) + f'(1)(z - 1) + \frac{f''(1)}{2!}(z - 1)^2 + \frac{f'''(1)}{3!}(z - 1)^3 + \dots\]\[= e + e(z - 1) + \frac{e}{2!}(z - 1)^2 + \frac{e}{3!}(z - 1)^3 + \dots\]\)

Simplifying further, we have:

\(\[f(z) = e\left(1 + (z - 1) + \frac{(z - 1)^2}{2!} + \frac{(z - 1)^3}{3!} + \dots\right)\]\)

This matches the given form:

\(\[f(z) = e\sum_{n=0}^{\infty} \frac{(z-1)^n}{n!}\]\)

Thus, we have shown that the Taylor series of the function\(\(f(z) = e^z\) at \(z = 1\) is \(e \sum_{n=0}^{\infty} \frac{(z-1)^n}{n!}\) for \(|z - 1| < \infty\).\)

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they made a round trip, we need to divide this amount by the number of trips, which is 2.  Rs 21 per child for a single trip.

To calculate the bus fare for a single trip for one child, we need to divide the total amount spent by the number of children and the number of trips. In this case, we are given that 10 children spent Rs 420 to travel to and from Village A and Village B.

Since they made a round trip, we need to divide this amount by the number of trips, which is 2.

To calculate the fare for a single trip, we divide Rs 420 by 10 children and 2 trips: Rs 420 ÷ 10 children ÷ 2 trips = Rs 21 per child for a single trip.

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The bus fare for a single trip for one child is Rs 21

calculate the bus fare for a single trip for one child, we need to divide the total amount spent by the number of children and the number of trips.
In this case, 10 children spent Rs 420 to travel from village A to village B and back. Since they made a round trip, it means they made two trips.
the bus fare for a single trip for one child, we can divide the total amount spent by the number of children and the number of trips.
So, the calculation would be:
Bus fare for a single trip for one child = Total amount spent / (Number of children * Number of trips)
= Rs 420 / (10 * 2)
= Rs 420 / 20
= Rs 21
Therefore, the bus fare for a single trip for one child is Rs 21.

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Answer:

c

Step-by-step explanation:

The greatest possible whole-number length of the unknown side among the option is 9 inches.

Obtuse triangle is a triangle that has one of it internal angle greater than 90 degrees.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

If the sides of the triangles are x, y and z. Therefore,

x + y > z

x + z > y

y + z > x

Therefore, the greatest possible length among the option is 9.

Proof

12 + 14 > 9

12 + 9 > 14

14 + 9 > 12

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Answer:

g=24

Step-by-step explanation:

g/4 -5 = 1

g/4 = 6

g = 24

Answer:

\(g=24\)

Step-by-step explanation:

When given the following equation,

\(\frac{g}{4}-5 = 1\)

Solve for the variable (g) using inverse operations,

\(\frac{g}{4}-5=1\)

Add (5) to both sides

\(\frac{g}{4}=6\)

Multiply both sides by (4)

\(g=24\)