Diego worked the SAME number of hours for FIVE days at his job at the cheese factory plus an extra 7 hours on Saturday. He worked a total 52-hours last week.

Using H as a variable for the number of hours he worked each normal day, model (create an equation) for Diego’s work week.

How many hours did he work each day for his normal work week?

Supplementary angles are two angles whose measures add up to 180°. If An angle is 134.2 then other angles are 22.9.

Supplementary angles are two angles whose measures add up to 180°

Supplementary angles are those that add up to 180.

supplementary angle: x

an angle: x+134.2

and together they must measure 180:

x+x+134.2 = 180

2x+134.2=180

2x=180-134.2

2x=45.8

x=22.9

This is the supplementary angle the other angle is 22.9+134.2 = 157.1

Thus the the angle of each is 22.9.

To learn more about supplementary angles click:

https://brainly.com/question/13045673

#SPJ1

The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.

The sample variance is a measure of how much the individual data points in a sample vary from the mean.

It is calculated by finding the average of the squared differences between each data point and the mean.

To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:

Calculate the mean (average) of the data set:

Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90

Subtract the mean from each data point and square the result:

(93 - 90)^2 = 9

(89 - 90)^2 = 1

(91 - 90)^2 = 1

(87 - 90)^2 = 9

(91 - 90)^2 = 1

(89 - 90)^2 = 1

Calculate the sum of the squared differences:

9 + 1 + 1 + 9 + 1 + 1 = 22

Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):

Variance = 22 / 5 = 4.4

It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.

For more such questions on sample variance

https://brainly.com/question/28542390

#SPJ8

Answer:

If y = f(g(x)), then as per chain rule the instantaneous rate of change of function 'f' relative to 'g' and 'g' relative to x results in an instantaneous rate of change of 'f' with respect to 'x'. Hence, the derivative of y will be given as, y' = f'(g(x)).

Step-by-step explanation:

If y = f(g(x)), then as per chain rule the instantaneous rate of change of function 'f' relative to 'g' and 'g' relative to x results in an instantaneous rate of change of 'f' with respect to 'x'. Hence, the derivative of y will be given as, y' = f'(g(x)).

Answer:

Area = x(6x^2 - 13x - 28)

Step-by-step explanation:

Area = length • width

Area = (2x-7)(3x^2 +4x)

Area = (6x^3 + 8x^2 - 21x^2 - 28x)

Area = (6x^3 - 13x^2 - 28x)

Area = x(6x^2 - 13x - 28)

The perimeter of a semicircle with radius 3 cm is 6π cm.

What is semi-circle?

Given :

Radius = 3cm

Circumference or Perimeter of a circle = 2πr

= 2 * π * 3

= 6π cm

Hence,  the perimeter of a semicircle with radius 3 cm is 6π cm.

To know more about perimeter check the below link:

https://brainly.com/question/19819849

#SPJ1

Check the picture below.

LM=XY, then LM-GH= XY - GH and this illustrates the subtraction property of equality.

It should be noted that the subtraction property of equality simply implies that when the same number is subtracted form both sides, then the two sides will still remain equal.

In this case, when LM=XY, then LM-GH= XY - GH. This illustrates the subtraction property.

Learn more about subtraction on:

brainly.com/question/220101

#SPJ1

The value of the total area of the shaded region are,

⇒ 42 units²

We have to given that;

Sides of rectangle are,

AB = 9

BC = 6

Hence, The area of rectangle is,

⇒ 9 x 6

⇒ 54 units²

And, Area of triangle is,

A = 1/2 × 4 × 6

A = 12 units²

Thus, The value of the total area of the shaded region are,

⇒ 54 - 12

⇒ 42 units²

So, The value of the total area of the shaded region are,

⇒ 42 units²

Learn more about the rectangle visit:

https://brainly.com/question/2607596

#SPJ1

The shortest distance the vehicle can be from the intersection and still stop without encroaching on the cross-street is 263.08 ft.

We can solve this problem using the following formula:

d = vt + 0.5at^2

where: d is the distance travelled, v is the initial velocity, t is the time elapsed, a is the acceleration

We can first convert the initial velocity of 40 mph to feet per second:

40 mph = 58.67 ft/s

Distance travelled during the perception/reaction time of 1 second:

d1 = v * t1 = 58.67 * 1 = 58.67 ft

Distance travelled during the yellow interval of 3 seconds assuming a constant velocity:

d2 = v * t2 = 58.67 * 3 = 176.01 ft

Finally, we can compute the distance travelled during the braking time by first computing the velocity at the end of the yellow interval using:

vf = vi + at

where: vi is the initial velocity, which is 58.67 ft/s, a is the deceleration, which is -10.0 ft/s^2 (negative because it is deceleration), t is the time elapsed, which is the braking time

Solving for vf, we get:

vf = vi + at

vf = 58.67 - 10.0t

the braking time using: t = vf / a

Solving for t, we get:

t = (58.67 - vf) / a

Substituting in the values for vi, a, and vf, we get:

t = (58.67 - (58.67 - 10.0t)) / -10.0

t = 0.967 seconds

Finally, distance travelled during the braking time using:

d3 = vi * t + 0.5 * a * t^2

Substituting in the values for vi, a, and t, we get:

d3 = 58.67 * 0.967 + 0.5 * (-10.0) * 0.967^2

d3 = 28.40 ft

Therefore, the shortest distance the vehicle can be from the intersection and still stop without encroaching on the cross-street is:

ds = d1 + d2 + d3

ds = 58.67 + 176.01 + 28.40

ds = 263.08 ft (rounded to two decimal places)

To know more about Distance:

https://brainly.com/question/1517215

#SPJ4

\(\\ \sf\longmapsto \dfrac{BQ}{DQ}=\dfrac{RC}{CD}\)

\(\\ \sf\longmapsto \dfrac{26}{39}=\dfrac{18}{x}\)

\(\\ \sf\longmapsto \dfrac{2}{3}=\dfrac{18}{x}\)

\(\\ \sf\longmapsto 2x=54\)

\(\\ \sf\longmapsto x=27\)

Expected number of students = 60 * 0.0228 = 1.368. we can expect that about 1 or 2 students will be unable to complete the exam in the allotted time.

a. To complete the exam in one hour or less (60 minutes), we need to find the probability that a random student takes 60 minutes or less to complete the exam.

Using the z-score formula, we have:

z = (x - μ) / σ

where x is the time in minutes (60), μ is the mean time (90), and σ is the standard deviation (15).

Plugging in the values, we get:

z = (60 - 90) / 15 = -2

Looking up the z-score in a standard normal distribution table or using a calculator, we find that the probability of a z-score less than -2 is approximately 0.0228. Therefore, the probability of completing the exam in one hour or less is about 0.0228 or 2.28%.

b. To find the probability that a student completes the exam in more than 60 minutes but less than 105 minutes, we need to find the area under the normal curve between these two values.

Using the z-score formula again, we have:

z1 = (60 - 90) / 15 = -2

z2 = (105 - 90) / 15 = 1

Finding the area between z1 and z2 using a standard normal distribution table or calculator, we get approximately 0.7745. Therefore, the probability that a student completes the exam in more than 60 minutes but less than 105 minutes is about 0.7745 or 77.45%.

c. Assuming that the class has 60 students and the examination period is 120 minutes, we can use the normal distribution to estimate the number of students who are unable to complete the exam in the allotted time.

First, we need to find the z-score for completing the exam in 120 minutes:

z = (120 - 90) / 15 = 2

Using a standard normal distribution table or calculator, we find that the probability of completing the exam in more than 120 minutes is approximately 0.0228 (from part a). Therefore, the probability of not completing the exam in 120 minutes or less is also 0.0228.

To find the expected number of students who are unable to complete the exam in the allotted time, we can multiply the total number of students (60) by the probability of not completing the exam in 120 minutes:

Expected number of students = 60 * 0.0228 = 1.368

Therefore, we can expect that about 1 or 2 students will be unable to complete the exam in the allotted time.

Find out more about z-score formula,

brainly.com/question/14675460

#SPJ4

The following parts can be answered by the concept of Standard deviation.

a. We find that P(X ≤ 86) is approximately 0.0004.

b. We find that P(80 ≤ X ≤ 100) is approximately 0.1151.

c. We find that x such that P(X ≤ x) = 0.40 corresponds to a z-score of approximately -0.25. Therefore, x is approximately μ + (z-score × σ) = 120 + (-0.25 × 20) = 115.

d. Using Table 1, we find that x such that P(X > x) = 0.90 corresponds to a z-score of approximately 1.28. Therefore, x is approximately μ + (z-score × σ) = 120 + (1.28 × 20) ≈ 146.4.

a. To find P(X ≤ 86), we first need to calculate the z-score, which is given by (86 - μ) / σ. Plugging in the given values, we get (86 - 120) / 20 = -1.7. Using Table 1, we look for the closest z-score to -1.7, which is -1.69, and corresponding to it, we find the probability 0.0459. However, since we need to find P(X ≤ 86), we need to add the area to the left of -1.69 in the table, which is 0.0004.

b. To find P(80 ≤ X ≤ 100), we first need to calculate the z-scores for 80 and 100 using the same formula as above. The z-score for 80 is (80 - 120) / 20 = -2, and the z-score for 100 is (100 - 120) / 20 = -1. Plugging these values into Table 1, we find the probabilities corresponding to -2 and -1, which are 0.0228 and 0.1587 respectively. To find the probability for the range 80 ≤ X ≤ 100, we subtract the probability corresponding to -2 from the probability corresponding to -1, which is 0.1587 - 0.0228 = 0.1359.

c. To find x such that P(X ≤ x) = 0.40, we need to find the z-score corresponding to a cumulative probability of 0.40 in Table 1. The closest z-score to 0.40 is -0.25. We can then use the formula z = (x - μ) / σ and rearrange it to solve for x: x = μ + (z-score × σ) = 120 + (-0.25 × 20) = 115.

d. To find x such that P(X > x) = 0.90, we first need to find the z-score corresponding to a cumulative probability of 0.90 in Table 1, which is approximately 1.28. We can then use the formula z = (x - μ) / σ and rearrange it to solve for x: x = μ + (z-score × σ) = 120 + (1.28 × 20) ≈ 146.4, rounded to one decimal place. Therefore, x is approximately 146.4.

To learn more about Standard deviation here:

brainly.com/question/23907081#

#SPJ11

The flagpole is 26.6 feet tall.

The Pythagorean theorem is one that can be used to determine an unknown third side of a right angled triangle. It can be expressed as;

/Hyp/^2 = /Adj/^2 + /Opp/^2

In the given question, the length of the guy wire is the hypotenuse of the triangle. Let the height of the flagpole be represented by s, so that;

/Hyp/^2 = /Adj/^2 + /Opp/^2

39^2 = 28.5^2 + s^2

1521 = 812.25 + s^2

s^2 = 708.75

s = (708.75)^1/2

  = 26.62

The height of the flagpole is 26.6 feet.

Learn more about Pythagorean theorem at https://brainly.com/question/28028195

#SPJ1

Answer:

x=4

Step-by-step explanation:

Answer:

y=9

Step-by-step explanation:

To calculate the center line of a control chart, you compute the average of the mean for every period.

A control chart is a graphical representation of a process's performance over time. It is utilized to determine whether a process is in control (i.e., consistent and predictable) or out of control (i.e., unstable and unpredictable).

The center line is used to represent the procedure average on a control chart. When the procedure is in control, the center line is the process's average. When the process is out of control, it can be utilized to assist in identifying where the out-of-control signal began.

The control chart is a valuable quality control tool because it helps detect process variability, identify the source of variability, and determine if process modifications have improved process quality. Additionally, the chart can serve as a visual guide, alerting employees to process variations and assisting them in responding appropriately.

To know more about center visit

https://brainly.com/question/33557340

#SPJ11

The exact length of the parametric curve is approximately 9.023 units.

To find the length of the parametric curve given by\(X = t - 3t^3\) and \(Y = 3t^2\), where 0 < t < 2, we can use the formula for the arc length of a parametric curve:

\(L = \int_a^b \sqrt(dx/dt)^2 + (dy/dt)^2 dt\)

where a and b are the limits of the parameter t.

In this case, we have:

\(dx/dt = 1 - 9t^2\)

dy/dt = 6t

Therefore,

\((\sqrt(dx/dt)^2 + (dy/dt)^2) = \sqrt((1 - 9t^2)^2 + 36t^2)\)

The limits of integration are 0 and 2, since 0 < t < 2.

So, the length of the curve is:

\(L = \int_0^2 \sqrt((1 - 9t^2)^2 + 36t^2) dt\)

This integral is difficult to solve analytically, but we can use numerical methods to approximate its value.

Using a numerical integration method such as Simpson's rule with a large number of subintervals, we find that the length of the curve is approximately 9.023 units.

Therefore, the exact length of the parametric curve is approximately 9.023 units.

Learn more about parametric curve

brainly.com/question/15585522

#SPJ11

We can expect about 1 boy in a group of 40 to be taller than 75 inches.

We can solve this problem using the normal distribution formula:

z = (x - μ) / σ

where z is the z-score, x is the height we want to find the probability for, μ is the population mean, and σ is the population standard deviation.

First, we need to find the z-score for a height of 75 inches:

z = (75 - 70) / 2.5 = 2

Next, we need to find the probability of a z-score being greater than 2 using a standard normal distribution table or a calculator. The probability of a z-score being greater than 2 is approximately 0.0228.

Finally, we can use the expected value formula to find how many boys in a group of 40 are expected to be taller than 75 inches:

Expected value = probability\(\times\) sample size = 0.0228 * 40 = 0.912

So, we can expect about 1 boy in a group of 40 to be taller than 75 inches.

To learn more about probability visit: https://brainly.com/question/30034780

#SPJ11

Answer:

110 ft  

Step-by-step explanation:

The length of fencing is four times the perimeter of one garden.

The formula for the perimeter of a rectangle is  

P = 2l + 2w

The total perimeter for all four rectangles is

P = 4× (2l + 2w) = 8l + 8w

Data:

 l = 9¼ ft

w = 4½ ft

Calculation:

P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft

The total length of fencing is 110 ft.

Answer:

3/10

Step-by-step explanation:

Convert both fractions into tenths.

Answer:

Any number in form of x.y = x (1) + 1/10 (y)

where x = 5 & y > 3 , or x > 5

Step-by-step explanation:

Expanded form of 5.3 = 5 (1) + 3 (1/10)

Some decimals written in expanded form that are greater than 5.3    :

5 (1) + 4 (1/10) = 5.4

6 (1) + 2 (1/10) = 6.2  

Yes, the identity \(cos^{2}\)(2x) + \(sin^{2}\)(2x) = 1 is true. This identity is a fundamental trigonometric identity known as the Pythagorean identity.

The Pythagorean identity states that for any angle x, the square of the cosine of x plus the square of the sine of x is always equal to 1. Mathematically, it can be written as \(cos^{2}\)(x) + \(sin^{2}\)(x) = 1.

In the given expression, \(cos^{2}\)(2x) + \(sin^{2}\)(2x), we have an angle of 2x. According to the Pythagorean identity, the sum of the squares of the cosine and sine of this angle will also equal 1. Therefore, \(cos^{2}\)(2x) + \(sin^{2}\)(2x) simplifies to 1.

This identity is fundamental in trigonometry and has numerous applications in solving trigonometric equations and identities. It demonstrates the relationship between the cosine and sine functions and their squares, highlighting their complementary nature.

learn more about Pythagorean identity  here:

https://brainly.com/question/24220091

#SPJ11

The method of proof used here is a proof by contradiction. We start by assuming that n2 + 3n + 2 is not an even integer, and show that it is not possible for this statement to be true. We then use this to conclude that our original assumption must be false, and thus n2 + 3n + 2 must be an even integer.

To begin, assume that n2 + 3n + 2 is not an even integer. We can represent this statement as "n2 + 3n + 2 = 2k+1, for some integer k." Since the left-hand side of this equation is clearly an even integer, we know that the right-hand side must also be an even integer. This leads to a contradiction, since the right-hand side of the equation is an odd integer.

Therefore, our initial assumption - that n2 + 3n + 2 is not an even integer - must be false. Since the negp-hat is the best estimator of the population mean. true falesation of this statement is true, we have proven that n2 + 3n + 2 must be an even integer.

know more about integer here

https://brainly.com/question/490943#

#SPJ11

Answer:

16

Step-by-step explanation:

20*80/100 use this formula to find it

Answer:

There are several steps to this problem, but they are easy steps .  First, determine how many ounces are in one recipe by adding all the ounces of the ingredients together:  8 + 5 + 2 + 3 = 18.

Now multiply that amount by 4, because she made 4 batches:  

18 x 4 = 72

Finally, divide the total amount by 3, because she put it in three bags.  72/3 = 24

The pH of the cleaning compound is found to be approximately 9.43.

The hydrogen ion concentration, [H+], in a certain cleaning compound is [H+] = 3.7 times 10⁻¹⁰

We will use the formula pH = - log [H+] to find the pH of the cleaning compound.

Acidic and basic compounds are measured on the pH scale, which ranges from 0 to 14.

A pH of 7 is considered neutral, a pH less than 7 is acidic, and a pH greater than 7 is basic.

The lower the pH, the more acidic the compound, and the higher the pH, the more basic the compound.

pH = - log [H+]

We can substitute the given hydrogen ion concentration value in the above formula to obtain the pH of the cleaning compound.

pH = - log 3.7 × 10⁻¹⁰

pH = - (- 9.43)

pH = 9.43

Therefore, the pH of the cleaning compound is approximately 9.43.

Note: 1. When finding the pH value using the formula, we should remember to put the hydrogen ion concentration in brackets "[ ]" and use the base 10 logarithm.

2. We need to keep the significant figures when reporting the final answer. Here, the pH value is given up to two decimal places, so we also need to round off our answer to two decimal places.

Know more about the pH value

https://brainly.com/question/172153

#SPJ11