The length of a rectangle is five times its width.
If the perimeter of the rectangle is 108 cm, find its length and width.

Answer:

(A.)

Step-by-step explanation:

you just have to follow the order that there going in so when they say less than you use the less than sign

Answer:

Step-by-step explanation:

To find the margin of error for a 98% confidence level, we need to use the z-score that corresponds to this confidence level, which is 2.33 (found in a z-table or using a calculator).

The formula for the margin of error (E) is:

E = z*(sqrt(p*q/n))

Where:

z is the z-score for the desired confidence level (2.33 for 98% confidence)

p is the sample proportion (0.4, or 40%)

q is the complement of the sample proportion (1 - 0.4 = 0.6)

n is the sample size (800)

Substituting these values into the formula, we get:

E = 2.33*(sqrt(0.4*0.6/800)) = 0.045

So the margin of error for a 98% confidence level, with a sample size of 800 and a sample proportion of 40%, is 0.045 or approximately 4.5%. This means that we can be 98% confident that the true population proportion is within 4.5% of the sample proportion.

Answer: 2 hours 15 minutes

Step-by-step explanation:

To solve this problem, we need to use the formula:

distance = speed x time

First, let's calculate the distance Jaswat covered in the first 1 1/2 hours:

distance = speed x time

distance = 6 Km/h x 1.5 h

distance = 9 Km

So, Jaswat covered 9 Km in the first 1 1/2 hours. He still had to cover 12 Km - 9 Km = 3 Km.

Now, we need to calculate the time Jaswat took to cover the remaining 3 Km at a speed of 4 Km/h:

distance = speed x time

3 Km = 4 Km/h x time

time = 3 Km / 4 Km/h

time = 0.75 hours = 45 minutes

Therefore, Jaswat took 1 1/2 hours + 45 minutes = 2 hours 15 minutes to complete the journey.

The addition of the vectors [tex]\vec a + \vec b[/tex] is (3, -5) and it has been represented by using the head to tail method in the graph below.

In Mathematics and Science, a vector can be defined as an element of a vector space, which represents an object that is composed of both magnitude and direction.

In Mathematics and Science, a vector typically comprises two (2) points. First, is the starting point which is commonly referred to as the "tail" and the second (ending) point that is commonly referred to the "head."

Generally speaking, the head to tail method of adding two (2) vectors involve drawing the first vector ([tex]\vec a[/tex]) on a cartesian coordinate and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Lastly, the resultant vector is then drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

By solving the given vectors algebraically, we have the following:

[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)

[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))

[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]

[tex]\vec a + \vec b[/tex] = (3, -5).

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The shortest path from vertex A to vertex L is ACFIL. The total distance of the path is 27 units.

To find the shortest path from vertex A to vertex L, we can use Dijkstra's algorithm. We start by marking the distance of each vertex from A as infinite except for A, which is 0. Then, we choose the vertex with the smallest marked distance and update the distances of its neighbors. We repeat this process until we reach L.

In this case, we would start at A and update the distances of B and D to 2 and 19, respectively. We would then choose B and update the distances of C, F, and E to 11, 10, and 18, respectively.

Next, we would choose F and update the distances of I and L to 27 and 30, respectively. Finally, we would choose L and have found the shortest path from A to L: ACFIL with a total distance of 27.

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The measure of the angle is 36.9^o. Option B.

A right triangle is a form or type of triangle in which the measure of one of its internal angles is 90^o. As such, either the trigonometric functions or Pythagorean theorem can be applied to determine any of its properties as the case may be.

From the details given in the question, we can deduced that;

Sin θ = 3/5

       = 0.6

So that,

θ = Sin^-1 0.6

  = 36.87

θ = 36.9^o

The measure of the angle is 36.9^o. Option B.

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Answer:

0.1

Step-by-step explanation:

P(red shirt, black pants | 1 shirt, 1 pants)

= P(red shirt | 1 shirt) * P(black pants | 1 pants)

= (1)/(2+2+1) * (1)/(2)

= 1/10

=0.1

The cost of one T-shirt and one jacket is $12 and $13 respectively.

Let

cost of one t-shirt = x

cost of one jacket = y

8x + 3y = 135

7x + 5y = 149

Multiply (1) by 5 and (2) by 3

40x + 15y = 675

21x + 15y = 447

Subtract the equations to eliminate y

40x - 21x = 675 - 447

19x = 228

divide both sides by 19

x = 228/19

x = 12

Substitute x = 12 into (1)

8x + 3y = 135

8(12) + 3y = 135

96 + 3y = 135

3y = 135 - 96

3y = 39

y = 39/3

y = 13

Hence, a T-shirt and a Jacket cost $12 and $13 respectively.

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Assuming the interest is compounded continuously what interest rate to the nearest hundredths of a percent would be required in order for Jamar to end up with $4200 is 4.62%.

Using the formula r = ln(A/P) / t, the interest rate, r, can be determined using an online finance calculator as follows:

Total P+I (A) = $4,200.00

Principal (P) = $2,200.00

Compound (n) = Compounding Continuously

Time (t in years) = 14 years

R = 4.619% per year

The calculation steps are as follows:

Solving for rate r as a decimal

r = ln(A/P) / t

r = ln(4,200.00/2,200.00) / 14

r = 0.0461877

Then convert r to R as a percentage:

R = r * 100

R = 0.0461877 * 100

R = 4.62%/year

Thus, the interest rate required to get a total amount of $4,200.00 from compound interest on a principal of $2,200.00 compounded continuously over 14 years is 4.62% per year.

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Thee radius of the circle is 3. 696 feet

The formula that is used for calculating or determining the circumference of a circle is expressed as;

C = 2πr

Given that the parameters for the formula are expressed thus;

From the information given, we have that;

Radius = 23.21 feet

Substitute the values, we get;

23.21 = 2× 3.14r

Multiply the values

r = 23.21/6.28

Divide the values

r = 3. 696 feet

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About 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.

Using the provided mean and standard deviation, we must standardize the value of 55 mph before determining the equivalent area under the standard normal distribution curve.

The standardized value, or z-score, is calculated as:

z = (x - μ) / σ

Where

Plugging in the values, we get:

z = (55 - 62) / 5 = -1.4

The area under the usual normal distribution curve to the left of z = -1.4 must now be determined. Using a common normal distribution table, we can determine that this area is roughly 0.0808.

Therefore, about 8.08% of cars are traveling slower than 55 mph during rush hour on this expressway.

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The discussion for both cases is shown below.

Part a:

H0: there is no association between climate change and certainty.

H1: there is no association between climate change and certainty.

It seems that the null hypothesis (H0) and the alternative hypothesis (H1) are identical, which doesn't make sense. Typically, the null hypothesis states that there is no association or effect, while the alternative hypothesis states that there is an association or effect.

The statement also mentions that the p-value is a non-zero number, but it doesn't provide the actual value. The p-value is used to determine the statistical significance of the association and should be compared to a predetermined significance level (e.g., 0.05) to make a decision.

Part 2:

H0: there is no association between sleeping and the income class.

H1: there is a association between the income class and sleeping.

Similarly, the null hypothesis (H0) and the alternative hypothesis (H1) are stated incorrectly. The null hypothesis should state no association or effect, while the alternative hypothesis should state that there is an association or effect.

Again, the statement mentions a non-zero p-value but doesn't provide the actual value. The p-value needs to be compared to a significance level to determine the statistical significance of the association.

In both cases, it is important to provide the actual p-value and compare it to the significance level to make a proper conclusion about the association between the variables.

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x=15.4 units

First, some definitions before working the problem:

The three standard trigonometric functions, cosine, tangent, and sine, are defined as follows for right triangles:

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]cos(\theta)=\dfrac{adjacent}{hypotenuse}[/tex]

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

One memorization tactic is "Soh Cah Toa" where the first capital letter represents one of those three trigonometric functions, and the "o" "a" and "h" represent the "opposite" "adjacent" and "hypotenuse" respectively.

The triangle must be a right triangle, or there wouldn't be a "hypotenuse", because the hypotenuse is always across from the right angle.

Working the problem

For the given triangle, the right angle is at the bottom, so the side on top is the hypotenuse.  We know the angle in the upper right corner, so the side across from it with length 4.5, is the opposite side.

For this triangle, the "opposite" leg is known.  Additionally, the "hypotenuse" is unknown and is our "goal to find" side.

Therefore, the two sides of the triangle that are known or are a "goal to find" are the "opposite" & "hypotenuse".

Out of "Soh Cah Toa," the part that uses "o" & "h" is "Soh".  So, the desired function to use for this triangle is the Sine function.

[tex]sin(\theta)=\dfrac{opposite}{hypotenuse}[/tex]

[tex]sin(17^o)=\dfrac{4.5}{x}[/tex]

Multiply both sides by x, and divide both sides by sin(17°)...

[tex]x=\dfrac{4.5}{sin(17^o)}[/tex]

Make sure your calculator is set to degree mode, and calculate:

[tex]x=\dfrac{4.5}{0.2923717047227...}[/tex]

[tex]x=15.391366289249...[/tex] units

Rounded to the nearest tenth...

[tex]x=15.4[/tex] units