What is 8 11/12 + 9 5/18

The point estimate here is 0.

Calculating the Mean of Each Set

The sample set of production rates exhibited by workers before workshop, S1 = {20, 25, 27, 23, , 22, 20, 17}

The sample set of production rates exhibited by workers after workshop, S2 = {22, 23, 27, 20, 25, 19, 18}

The mean of set S1 = (20+25+27+23+22+20+17)/7

= 154/7

= 22

The mean of set S2 = (22+23+37+20+25+19+18)/7

= 154/7

=22

Calculating the Point Estimate

The formula for point estimate is given as,

Point Estimate  = The mean of set S1 - The mean of set S2

Point Estimate = 22-22

Point Estimate = 0

Therefore, the point estimate for the difference between the means of the two populations or sets is 0

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The length of the shortest side is DC

As a general rule in triangle;

The smallest angle in a triangle is opposite the shortest side.

Similarly, the largest angle in a triangle is opposite the largest side.

From the given figure of triangles, the smallest angle is angle CBD with a measure of 47 degrees.

The side opposite this angle is side length DC

Hence, the length of the shortest side is DC

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The inequality passing through (1, 4), (-2, -2), intersecting the y-axis at 2 units and intersects the x-axis at (-1, 0) to form shaded portions on the left side is y > 2x+2

An equation is an expression that shows the relationship between two or more variables and numbers.

An inequality shows the non equal comparison of two or more numbers and variables.

The inequality passing through (1, 4), (-2, -2), intersecting the y-axis at 2 units and intersects the x-axis at (-1, 0) to form shaded portions on the left side is y > 2x+2

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The Ratio would be 43:100.

Lets simplify the problem,

Expected increase of nurses = 711900

Expected increase of physicians = 168300

Ratio = Expected increase of nurses / Expected increase of physicians

Ratio = 711900 / 168300

= 43/100

Ratio = 43:100

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Answer:

The longest side of room is 24m

The researchers could utilize a probability sample.

Meaning of a Probability Sample

Every member of a population must have an equal chance of being chosen for a study in order for a sample to be considered a probability sample, and the researcher must be aware of this likelihood. The most typical type of sampling used in public opinion research, election polling, and other studies whose findings will be generalized to a larger population is probability sampling in which probability samples are made use of.

Probability Sample as the Representative of Population Sample

Here, a sample that qualifies for a representative of the population the researchers are studying, must consist of members having equal chances to be chosen for the study. Thus, a probability sample is the best representative of their study population.

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Angle M corresponds to angle M' and

Side N'O' is the image of side NO

The vertices of each triangle must have a one-to-one correspondence. This phrase means that the measure of each side and angle of each triangle is equal to the side or angle of the other triangle.

Here it is given that Triangle MNO maps to triangle M'N'O'

We need to find that Angle M corresponds to which angle and the image of side NO

By one to one correspondence we get that

Angle M corresponds to angle M' and

Side N'O' is the image of side NO

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Answer:

Step-by-step explanation:

$1,248.92

Answer: G=4

Step-by-step explanation:

The relationship that represents the law of cosines if the measure of the included angle between the sides a and b is D. area of square c² = area of square a² area of squareb² area of defect1 area of defect2

It should be noted that the cosine law is simply used to solving triangles.

The law simply states that c² = a² + b² - 2abcosC.

The correct option that illustrates this is D.

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Answer:

c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2

Step-by-step explanation:

Answer:

[tex]x = \frac{b}{6a} - c[/tex]

Step-by-step explanation:

Steps are as below:

(I will refer A as 'a' and B as 'b')

[tex]a = \frac{b}{c + x} - 5a \\ a + 5a = \frac{b}{c + x} \\ 6a = \frac{b}{c + x} \\ 6a(c + x) = b \\ 6ac + 6ax = b \\ 6ac = b - 6ax \\ b - 6ax = 6ac \\ - 6ax = 6ac - b \\ 6ax = - (6ac - b) \\ 6ax = b - 6ac \\ x = \frac{b - 6ac}{6a} \\ x = \frac{b}{6a} - \frac{6ac}{6a} \\ x = \frac{b}{6a} - c[/tex]

Hi! ❄

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The rule for this sequence is 'multiply by -6'.

Verification ↓

-3*(-6)[tex]\stackrel\checkmark{=}[/tex]18

18*(-6)[tex]\stackrel\checkmark{=}[/tex]-108

So the rule for the sequence is 'multiply by -6'

And the Common ratio is -6.

Hope that made sense !!

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[tex]\star\tiny\pmb{calligraphy}\star[/tex]

[tex]\textbf{Heya !}[/tex]

✏✏[tex]\large\textsf{Given:-}[/tex]

✏✏ [tex]\large\textsf{To Find:-}}[/tex]

✏✏ [tex]\large\textsf{Solution Steps:-}[/tex]

What do we multiply each term of the sequence by to arrive at the next one ? we can find that by dividing the last term of the sequence, -108, by the middle term, 18:-

[tex]\large{\sf{\longmapsto{-108\div18=-6}[/tex]

Now divide 18 by the first term (-3) :-

[tex]\longmapsto\sf{18\div-3=-6}[/tex]

we arrived at -6 twice, So the rule for this sequence is:- "Multiply by -6, And you'll arrive at the next term"

`hope it helped ~ :D

The wide-area search method employs the use of markers such as knots at regular intervals along the search line.

Given the method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line.

In order to locate, relieve distress, and preserve the life of a person who has been reported missing or is believed to be lost, stranded, or is considered a high-risk missing person, wide area search and rescue refers to activities occurring within large geographic areas. It also refers to the removal of any survivors to a safe location.

Hence, the wide-area search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line

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It is likely is it to snow tomorrow in the mountains is 1/4

A chance is the occurrence of events without apparent purpose or cause. It is simply the possibility that something will happen. When chance is defined in mathematics, it is called probability. Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to the total number of possible cases. Mathematically, the probability that an event occurs is equal to the ratio of the number of cases favorable to a particular event to the number of all possible cases. The theoretical probability of an event is referred to as P(E). P(E) = number of outcomes more favorable to E/Nnumber of all possible outcomes of the experiment

We need to find that what is the chance that it will snow tomorrow in the mountains

According to the weather report, there is a 25% chance of snow in the mountains tomorrow.

Therefore the possible chance that it will snow tomorrow is 25/100 = 1/4

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Answer:

? = 38°

Step-by-step explanation:

We can use the property of sine to find the missing angle value.

sin (angle) = opposite / hypotenuse

sin (?) = 16 / 26                                  <----- Insert values

? = sin⁻¹(16 / 26)                                 <----- Rearrange

? = 37.97...                                         <----- Solve

? = 38°                                               <----- Round

There can be 18, 12, 9, 6, 4 , 3 or 2 students on each team depending on the number of teams selected.

Considering there are at least 2 teams but no more than 19 teams, let's calculate the number of students in each case:

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Answer:

Step-by-step explanation:

70 = x/4

x = 4 cos 70 = 1.37m

x = 4 cos  80 = 0.69m  

The range is ( 0.69m, 1.37m)

The range of distances from the wall (x) that the foot of the ladder  placed to fall within the safety guidelines is between 0.7052 meters and 1.456 meters.

To determine the range of distances from the wall that the foot of the ladder may be placed to fall within the safety guidelines,  use trigonometry.

Let's assume the distance from the wall to the foot of the ladder is x meters the ladder is 4 meters long.

The angle between the ladder and the ground is given to be between 70° and 80°. Let's consider the extreme cases for each angle:

When the ladder makes an angle of 70° with the ground:

In this case, the angle between the wall and the ladder (θ) will be 90° - 70° = 20°.

When the ladder makes an angle of 80° with the ground:

In this case, the angle between the wall and the ladder (θ) will be 90° - 80° = 10°.

Now, use trigonometry to calculate the range of distances (x) from the wall:

For the first case (θ = 20°):

tan(20°) = Opposite / Adjacent

tan(20°) = x / 4

x = 4 × tan(20°)

For the second case (θ = 10°):

tan(10°) = Opposite / Adjacent

tan(10°) = x / 4

x = 4 × tan(10°)

Now, let's calculate the values:

x ≈ 4 × 0.3640 ≈ 1.456 meters (rounded to three decimal places) - for the first case.

x ≈ 4 × 0.1763 ≈ 0.7052 meters (rounded to four decimal places) - for the second case.

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The number of degrees that the direction of the boat change when it made its first turn is 39°.

From the information given, we would use the cosine function to solve the information.

This will be:

18² = 28² + 25² - 2(28)(25)(cos x)

324 = 784 + 625 - 1400cosx

x = 39.19

Therefore, the value is 39°.

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Answer:

I and II only

(C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.

To find what fraction of the marbles now in the bag is blue:

Therefore, (C) [tex]\frac{1}{3}[/tex] fraction of the marbles now in the bag is blue.

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Complete question:

A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only 1 / 3 of the marbles in the bag are blue. Then yellow marbles are added to the bag until only 1 / 5 of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?

(A) 1/5

(B) 1/4

(C) 1/3

(D) 2/5

(E) 1/2

Answer:

y=

[tex] - \frac{x {}^{2} + 8x + 16 }{2} - 7[/tex]

Step-by-step explanation:

calculate the product, use (a+b)^2=a^2+2ab+b^2

The perimeter of the polygon that circumscribes the circle is 78 cm

An equation is an expression that shows the relationship between two or more variables and numbers.

The circle tangent theorem states that tangents which meet at the same point are equal in length. Hence:

The missing lengths are 8, 6, 9 and 16.

Perimeter of the polygon = 2(8) + 2(6) + 2(9) + 2(16) = 78 cm

The perimeter of the polygon that circumscribes the circle is 78 cm

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Q1

Nominal - D

Ordinal-  B, G

Ratio - A, C, E, F

Q2

Quantitative- A, C, D, G

Qualitative -B, E, F, G

Q3

Simple Random - A, C

Systematic Sample - B

Nominal measures are the most accurate and meaningless, as they only show the "characteristics" or "identities" that we are interested in. In other words, in a nominal variable, a number just gives the attribute a unique "name". In this case, the number is just a label.

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The blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.

The theoretical probability of any event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.

If we have an event A, the number of favorable outcomes to event A as n, and the total number of possible outcomes in the experiment as S, then the theoretical probability of event A is given as:

P(A) = n/S.

In the question, we are given that Ellen has a bag with 3 red marbles and 2 blue marbles in it. She is going to randomly draw a marble from the bag 300 times, putting the marble back in the bag after each draw.

We are asked the predict the number of times that the marble picked will be blue using the theoretical probability.

Let the event of picking a blue marble be A.

The number of favorable outcomes to event A (n) = 2 {The total number of blue marbles in the bag}.

The total number of possible outcomes in the experiment of picking a ball (S) = 5 {The total number of marbles in the bag}.

Thus, the theoretical probability of event A is,

P(A) = n/S = 2/5 = 0.4.

To predict the number of times marble picked was blue, we multiply the time's the experiment was performed by the theoretical probability of picking a blue ball.

Thus, the predicted number of times = 300 * 0.4 = 120.

Thus, the blue marble is predicted to be picked 120 times, in the experiment of picking a marble from a bag containing 3 red and 2 blue marbles and performing this experiment 300 times, using the theoretical probability.

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When two or more given triangles are congruent, this implies that the measures of their corresponding angles and sides are equal. So that the additional information required in the question is FG ≅ IJ.

When two or more given triangles are congruent, this implies that the measures of their corresponding angles and sides are equal. Thus the congruent relations of the triangles can be with respect to their angles or/ and sides.

The two given triangles in the question would be congruent with respect to the Side-Angle-Side (SAS) postulate if the condition below is true:

i.e FG ≅ IJ

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Based on the angle of the seesaw and the height off the ground, the maximum length of the seesaw is 2 meters.

This can be found as:

Sin 30° = 1 / Maximum length

Solving gives:

Sin 30° = 1 / Maximum length

Ml = 1 / Sin 30°

= 1 / 0.5

= 2 meters

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