What is 1 3/5 written as a division expression?

Answer:

1 The minimum number of fire extinguishers for Class A hazards for each floor of a building shall be determined by dividing the total floor area by the maximum area to be protected per extinguisher as determined by Table.

Step-by-step explanation:

The probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

Given that, at a wedding each guest asked the 80 guests whether they were a friend of the bride or of the groom.

What is the probability?

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

Total Number of Guests which forms the Sample Space, n(S)=80

Let the event (a friend of the bride) =A

Let the event (a friend of the groom) =B

n(A) =59

n(B)=50

Friends of both bride and groom,

So,

n(A∪B)=n(A)+n(B)-n(A∩B)

n(A∪B)=59+50-30

n(A∪B)=79

The number of Guests who was a friend of the bride OR of the groom = 79

Thus,

P(A∪B)=n(A∩B)/n(S)

= 79/80

= 0.9875

Hence, the probability that a randomly selected person from this sample was a friend of the bride OR of the groom is 0.9875.

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The equation of the straight line passing through (2, 3) and perpendicular to 3x + 2y = 1 is y = 2  /3 x + 5 / 3

The equation of a line can be represented in a slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line passes through (2, 3) and perpendicular to 3x + 2y = 1.

The product of the slopes of perpendicular lines is equals to negative 1. Therefore,

3x + 2y = 1

2y = - 3x + 1

y = - 3 / 2 x + 1 / 2

Hence, let's find the slope of the line.

m₁ m₂ = -1

- 3 / 2m₂ = -1

m₂ = 2 / 3

Therefore, let's find the y-intercept using (2, 3),

3 = 2 / 3 (2) + b

b = 3 - 4 / 3

b = 9 - 4/3

b = 5 / 3

Therefore, the equation is y = 2  /3 x + 5 / 3

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Answer:

804

Step-by-step explanation:

Just use a calculator.

Answer: cos4

Step-by-step explanation: 50 meters

B. 50-√3 meters

C. 100 meters

D. 100-√3 meters

40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.

The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."

A. sin 22

B. cos 22

C. tan 22

D. cot 22

Answer:

10.78% probability this student's score will be at least 2200

Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Conditional probability:

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

\(\mu = 1500, \sigma = 300\)

We pick a recognized student. What is the probability this student's score will be at least 2200

Event A: Recognized(scored at least 1900).

Event B: At least 1900.

Probability of scoring at least 1900.

1 subtracted by the pvalue of Z when X = 1900. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{1900 - 1500}{300}\)

\(Z = 1.33\)

\(Z = 1.33\) has a pvalue of 0.9082.

1 - 0.9082 = 0.0918.

So P(A) = 0.0918

Intersection:

The intersection between at least 1900 and at least 2200 is at least 2200.

Probability:

1 subtracted by the pvalue of Z when X = 2200. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{2200 - 1500}{300}\)

\(Z = 2.33\)

\(Z = 2.33\) has a pvalue of 0.9901.

So \(P(A \cap B) = 1 - 0.9901 = 0.0099\)

Then

\(P(B|A) = \frac{0.0099}{0.0918} = 0.1078\)

10.78% probability this student's score will be at least 2200

Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Answer:

24:60

60:24

Step-by-step explanation:

Answer:

24:60 = 24/3:60/3 = 8/20 = 8/4:20/4 = 2:5

Answer:

see below

Step-by-step explanation:

Answer:

7. -158

8.-87

9. 807

10.128

11.9

Answer:

Step-by-step explanation:

Answer:

The width of the new phone will be of 4.37 inches.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

In this question:

Length was of 2.2 inches, after the modification is of 2.09 inches.

Width was of 4.6 inches, after the modification is x. So

2.2 - 2.09

4.6 - x

Applying cross multiplication:

\(2.2x = 2.09*4.6\)

\(x = \frac{2.09*4.6}{2.2}\)

\(x = 4.37\)

The width of the new phone will be of 4.37 inches.

Using relations in a right triangle, the secant of angle θ is given by:

D. 5/4.

The relations in a right triangle are given as follows:

Using the Pythagorean Theorem, the hypotenuse of the triangle is given as follows:

h² = 9² + 12²

h = sqrt(9² + 12²)

h = 15.

The secant of an angle is 1 divided by the cosine, hence:

Which means that option D is correct.

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Pair of corresponding angles: angle ABD and angle CBD.

What is line?

In mathematics, a line is a geometric object that extends infinitely in both directions, without any curvature or thickness. It can be thought of as a straight path connecting two points in a two-dimensional (2D) or three-dimensional (3D) space. A line is often represented graphically as a straight line with arrows indicating its infinite extension in both directions.

A line can be defined using different mathematical representations, such as the slope-intercept form (y=mx+b), point-slope form (y-y1=m(x-x1)), or the general form (Ax+By+C=0). In addition, lines can be classified based on their relationship with other geometric objects, such as being parallel or perpendicular to another line, intersecting with a curve or another line, or lying in a particular plane or space.

Lines are fundamental objects in geometry and algebra, and they have many applications in different areas of science, engineering, and technology.

lines intersected by a transversal:

    |        |

    |        |

    |        |

-----A--------B-----

    |        |

    |        |

    |        |

Here are some angle pairs based on this diagram:

Pair of alternate exterior angles: angle ABD and angle EBC.

Pair of alternate interior angles: angle ABE and angle CBD.

Pair of corresponding angles: angle ABD and angle CBD. And

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Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answer:

c

Step-by-step explanation:

sheeesh 3 easy

The exact height of the triangle is 20.8ft

The area of the right tringle in radical form is 72√3 ft²

The area of the triangle in decimal form is 124.7 ft²

The side XY or height of the triangle can be found as follows:

Using trigonometric ratios,

tan 60° = XY / 12

XY = 12 tan 60°

XY = 12 × 1.73205080757

XY = 20.7846096908

height = 20.8ft

The area of XYZ = 1 / 2 bh

where

Therefore,

The area of XYZ = 1 / 2 × 12 × 20.8 = 124.707658145  = 124.7 ft²

The area in radical form = 1 / 2 × 12 × 12 tan 60°

The area in radical form =  1 / 2 × 12 × 12 × √3 = 144√3 / 2 = 72√3 ft²

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The correct answer is 4/5

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:so basicaly on this one bring the line down 3 units and 3 unit to the left it is really easy

Step-by-step explanation:

The image of triangle ABC under a translation by 3 units to the left and 3 units down is triangle A'B'C' with vertices A'(-7, 0), B'(-5, 1), and C'(3, -7).

To draw the image of triangle ABC under a translation by 3 units to the left and 3 units down, we need to apply the same translation to each of the three vertices of the triangle.

Original triangle ABC with vertices:

A(-4, 3)

B(-2, 4)

C(6, -4)

To translate each point 3 units to the left and 3 units down, we subtract 3 from the x-coordinate and subtract 3 from the y-coordinate of each vertex:

Translated triangle A'B'C' with vertices:

A'(-4 - 3, 3 - 3) => A'(-7, 0)

B'(-2 - 3, 4 - 3) => B'(-5, 1)

C'(6 - 3, -4 - 3) => C'(3, -7)

Now, let's plot the original and translated triangles on a coordinate plane:

Original Triangle ABC (in blue):

A(-4, 3)

B(-2, 4)

C(6, -4)

Translated Triangle A'B'C' (in red):

A'(-7, 0)

B'(-5, 1)

C'(3, -7)

In the above diagram, the original triangle ABC is shown in blue, and the translated triangle A'B'C' is shown in red. The red triangle is the image of the blue triangle after the translation by 3 units to the left and 3 units down.

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Answer:

170 points

Step-by-step explanation:

You multiply 200 and .85

a) Yes given statment concluded from the ANOVA test

b) No given statment cannot concluded from the ANOVA test

c) No given statment cannot concluded from the ANOVA test

d) Yes given statment concluded from the ANOVA test

a) On average, people in the middle class agree with the new government policies to a different extent than people in the upper class.

Can conclude: Yes, this can be concluded from the ANOVA test, as the null hypothesis was rejected in Test 2, indicating that there is a significant difference between at least two levels of socio-economic class.

b) All of the socio-economic classes are different in relation to the average extent of voter agreement with the new government policies.

Cannot conclude: No, this cannot be concluded from the ANOVA test, as Test 3 did not reject the null hypothesis, indicating that there is no significant interaction effect between age group and socio-economic class.

c) All of the socio-economic classes are the same in relation to the average extent of voter agreement with the new government policies.

Cannot conclude: No, this cannot be concluded from the ANOVA test, as Test 2 rejected the null hypothesis, indicating that there is a significant difference between at least two levels of socio-economic class.

d) At least one of the socio-economic classes is different to the rest in relation to the average extent of voter agreement with the new government policies.

Can conclude: Yes, this can be concluded from the ANOVA test, as Test 2 rejected the null hypothesis, indicating that there is a significant difference between at least two levels of socio-economic class.

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Answer:

Please see steps below

Step-by-step explanation:

Notice the following:

(a) Angles 5 and 1 are alternate angles between parallel lines, and then they must be congruent (equal in measure)  \(\angle 1 \,=\,\angle 5\)

(b) Angles 6 and 3 are also alternate angles  between parallel lines, so they must be congruent (equal measure)  \(\angle 3 \,=\,\angle 6\)

Therefore, instead of expressing the addition:

\(\angle 5\,\,+\,\,\angle 2\,\,+\,\,\angle 6\)

we can write:

\(\angle 1\,\,+\,\,\angle 2\,\,+\,\,\angle 3\)

which in fact clearly add to \(180^o\)

Using exponent rules we can simplify the expression to get:

√y³⁶ =  y¹⁸

Here we want to simplify the expression below:

√y³⁶

Remember that the square root is equivalent to an exponent of 1/2, then we can rewrite:

√y³⁶ = (y³⁶)¹´²

And that will be equal to:

(y³⁶)¹´² = y³⁶´² = y¹⁸

That is the expression simplified.

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Answer:

8x(7yz - 2y + 3z).

Step-by-step explanation:

Note that 8x is a factor common to all three terms.  Thus, we can factor as follows:

8x(7yz - 2y + 3z).

There is no other common factor, so the above expression is as far as we can go in factorizing the given expression.

The probability that the sum of the pips selected that is at least 11 would be = 1/12.

To determine the probability of the selected events, the formula for problem should be used which is given below;

Probability = possible outcome/sample space

Possible outcome = at least 11 = (5,6),(6,5),(6,6)

= 3

Sample space = 36

Probability = 3/36 = 1/12

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