John is 5 years 6 months. How old is John in months?

Step-by-step explanation:

f(x) = 3x² - 2x + 8 , x = 3

f(3) = 3.3² - 2.3 + 8

= 27 - 6 + 8

= 29

Answer:

x=-1/4

Step-by-step explanation:

-4/16=16x/16

-1/4=x

Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

The volume of water in this tank should be completed as follows:

Time (t min)            0         1              2                 3  

Volume (V cm³)      0     7,000     14,000       21,000

In this exercise, you are required to determine the volume of water in this tank and complete the table shown in the image. From the information provided, when the tank is initially empty, the volume of water it holds over a period of time is represented by this function:

V = 7t

where:

At time (t = 0), the volume of water in this tank would be calculated as follows:

V = 7t

V = 7(0)

V = 0 L.

In cm³; V = 0 cm³.

At time (t = 1), the volume of water in this tank would be calculated as follows:

V = 7t

V = 7(1)

V = 7 L.

In cm³; V = 7,000 cm³.

At time (t = 2), the volume of water in this tank would be calculated as follows:

V = 7t

V = 7(2)

V = 14 L.

In cm³; V = 14,000 cm³.

At time (t = 3), the volume of water in this tank would be calculated as follows:

V = 7t

V = 7(3)

V = 21 L.

In cm³; V = 21,000 cm³.

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Answer:

Yes by AA.

Step-by-step explanation:

Answer:

Step-by-step explanation:

-34 = (9/5)(-20) + b

b = -34 + 36 = 2

y = (9/5)x + 2

Answer:

He has to pay 14427.21 rupees.

Step-by-step explanation:

1. 13% of 16583 = 2155.79

2. 16583 - 2155.79= 14427.21

3. Has to pay 14,427.21 rupees

Answer:

Red ball=3/10

White ball=1/5

Step-by-step explanation:

Red balls=6. And all the balls are equal to 20. So probability of red ball=6/20=3/10.

White balls=4. So probability of white ball=4/20=1/5.

NB: Since the first ball was replaced, there's no need to deduct a ball from the original 20 balls.

Answer:

\(\displaystyle d = 2\sqrt{10}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Algebra II

Step-by-step explanation:

Step 1: Define

Point (-5, -2) → x₁ = -5, y₁ = -2

Point (-3, 4) → x₂ = -3, y₂ = 4

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Answer:

D.

Step-by-step explanation:

Statistics has a lot of usage in business.

Using statistics as well as statistical tools helps in the provision of data to be used for business analysis. With available data we can get patterns in a a large database. Statistics can be used for auditing, as in question option b. For option c, statistics can be used for making business forecasts after the careful observation of trends and patterns that are in the data.

Option d does not make use of statistics. It has nothing to do with statistics neither does it have a computational feature.

Therefore, d.) questioning the executive's strategic decision is the answer to this question

Answer:

1) 7/8     8/7

2) 4.4

3) 3.7

4) 2.8

Step-by-step explanation:

Length of bottom side of Figure A: 8 cm

Length of bottom side of Figure B: 7 cm

From Figure A to Figure B, the scale factor is 7/8.

7/8

8/7

5 × 7/8 = 35/8 = 4.375

4.4

3.2 × 8/7 = 3.657...

3.7

3.2 × 7/8 = 2.8

2.8

Answer:

2. A, the first option

3. A, first option

Step-by-step explanation:

A segment is the part of a line that connects two points. It is the shortest distance between the two points. It has a length.

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray. A ray is named using its endpoint first, and then any other point on the ray

I hope this helps!!! Have a wonderful day!!!

Answer: Constant.

The graph does not have an incline and therefore has a slope of 0. This means that the graph is constant.

No 4 can be factored from each term of the trinomial. Therefore, option C is the correct answer.

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given polynomial is x(4x²+8x+12).

Here, in the trinomial 4x²+8x+12, 4 is common factor in each term.

So, group and factor out the greatest common factor (GCF), then combine.

That is, 4(x²+2x+3)

Now, x(4x²+8x+12)= 4x(x²+2x+3)

Therefore, option C is the correct answer.

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Answer:

12

Step-by-step explanation:

4 x 3

Answer:

decimal: 0.23 Fraction 23/100

Step-by-step explanation:

If you need an explanation just say it in the box:)

Answer:

We conclude that the mean resting pulse rate for men is 72 beats per minute.

Step-by-step explanation:

We are given that he mean resting pulse rate for men is 72 beats per minute. Assume that the standard deviation of the resting pulse rates of all men who work out at Mitch's Gym is known to be 2.6 beats per minute.

A simple random sample of men who regularly work out at Mitch's Gym is obtained and their resting pulse rates (in beats per minute) are listed below;

87, 89, 69, 63, 70, 65, 88, 84, 58, 53, 66, 70.

Let \(\mu\) = mean resting pulse rate for men.

SO, Null Hypothesis, \(H_0\) : \(\mu\) = 72 beats/minute     {means that the mean resting pulse rate for men is 72 beats per minute}

Alternate Hypothesis, \(H_A\) : \(\mu\) < 72 beats/minute      {means that the mean resting pulse rate for men is less than 72 beats per minute}

The test statistics that would be used here One-sample z-test statistics as we know about population standard deviation;

                            T.S. =  \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\)  ~ N(0,1)

where, \(\bar X\) = sample mean mean resting pulse rate = \(\frac{\sum X}{n}\)

                =  \(\frac{87+ 89+ 69 +63 +70 +65+ 88+ 84+ 58+ 53+ 66+ 70}{12}\)  = 71.83 beats/minute

            \(\sigma\) = population standard deviation = 2.6 beats per minute

            n = sample of men = 12

So, the test statistics  =  \(\frac{71.83 - 72}{\frac{2.6}{\sqrt{12} } }\)    

                                     =  -0.23

The value of z test statistics is -0.23.

Also, P-value of the test statistics is given by;

            P(Z < -0.23) = 1 - P(Z \(\leq\) 0.23)

                                 = 1 - 0.59095 = 0.40905

Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.

Since our test statistic is more than the critical value of z as -0.23 > -1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean resting pulse rate for men is 72 beats per minute.

Approximately 0.0228 or 2.28% of your yard has more than 5 inches of snow.

Approximately 0.9759 or 97.59% of your yard has between 4 and 5.25 inches of snow.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

z-score = (X-ц )/σ

Standardize the value of 5 using the given mean and standard deviation:

Z = (5 - 4.5) / 0.25 = 2

Using a standard normal distribution table or a calculator, we can find the area to the right of Z = 2.

The area to the left of Z = 2 is 0.9772. Therefore, the area to the right of Z = 2 is:

1 - 0.9772 = 0.0228

This means that approximately 0.0228 or 2.28% of your yard has more than 5 inches of snow.

Standardized the values of 4 and 5.25 using the given mean and standard deviation:

Z_4 = (4 - 4.5) / 0.25 = -2

Z_5.25 = (5.25 - 4.5) / 0.25 = 3

Using a standard normal distribution table, we can find that the area to the left of Z = -2 is 0.0228 and the area to the left of Z = 3 is 0.9987. Therefore, the area between Z = -2 and Z = 3 is:

0.9987 - 0.0228 = 0.9759

This means that approximately 0.9759 or 97.59% of your yard has between 4 and 5.25 inches of snow.

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Step-by-step explanation:

-2(-3+2)2

(-2×-3)+(-2×2)2

(6-4)2

2(6-4)

(2×6)+(2×-4)

12-8=4

Step-by-step explanation:

Because straight lines (that are not the 'same line') can have at most, only one point of intersection...the unique solution.

Answer:

no it not have a unique solution.

The circumference of the given circle is approximately 47.3 inches.

Since the length of the arc KL and the measure of the central angle ∠KOL are known, we can use the formula for arc length to find the circumference of the circle:

arc length = (central angle / 360°) x circumference

Plugging in the known values, we have:

4.6 in = (35° / 360°) x circumference

Solving for the circumference, we get:

circumference = 4.6 in / (35° / 360°)

circumference = 4.6 in x (360° / 35°)

circumference ≈ 47.3 in (rounded to the nearest tenth)

Therefore, the circumference of the circle is approximately 47.3 inches.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

as ABC = 3* DEF

AB = 5

DE = 15 = 5*3

AC = 3

DF = 9 = 3*3

BC = 4

EF = 12 = 4 * 3

Answer:

\(y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}\)

Step-by-step explanation:

Hi there!

Slope-intercept form: \(y=mx+b\) where \(m\) is the slope and \(b\) is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

\(m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}\) where two given points are \((x_1,y_1)\) and \((x_2,y_2)\)

Plug in the given points (15,2.2) and (5,1.6):

\(m=\frac{\displaystyle 1.6-2.2}{\displaystyle 5-15}\\\\m=\frac{\displaystyle -0.6}{\displaystyle -10}\\\\m=\frac{\displaystyle 0.6}{\displaystyle 10}\\\\m=\frac{\displaystyle 0.3}{\displaystyle 5}\\\\m=\frac{\displaystyle 3}{\displaystyle 50}\)

Therefore, the slope of the line is \(\frac{\displaystyle 3}{\displaystyle 50}\). Plug this into \(y=mx+b\):

\(y=\frac{\displaystyle 3}{\displaystyle 50}x+b\)

2) Determine the y-intercept (b)

\(y=\frac{\displaystyle 3}{\displaystyle 50}x+b\)

Plug in a given point and solve for b:

\(1.6=\frac{\displaystyle 3}{\displaystyle 50}(5)+b\\\\1.6=\frac{\displaystyle 3}{\displaystyle 10}+b\\\\1.6-\frac{\displaystyle 3}{\displaystyle 10}=\frac{\displaystyle 3}{\displaystyle 10}+b-\frac{\displaystyle 3}{\displaystyle 10}\\\\\frac{\displaystyle 13}{\displaystyle 10}=b\)

Therefore, the y-intercept is \(\frac{\displaystyle 13}{\displaystyle 10}\). Plug this back into \(y=\frac{\displaystyle 3}{\displaystyle 50}x+b\):

\(y=\frac{\displaystyle 3}{\displaystyle 50}x+\frac{\displaystyle 13}{\displaystyle 10}\)

I hope this helps!

Answer:

x= 8

90+40=130

180-130=50

50-2=48

48/6=8

Answer:

2 acute, 1 obtuse, 1 right

The value of k is equal to -5.5

In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this equation:

\(a_n=a_1+(n-1)d\)

Where:

Based on the the common difference of an arithmetic sequence, we have:

k - 2 - 3k = k + 7 - (k - 2)

-2k - 2 = k + 7 - k + 2

-2k - 2 = 9

-2k = 11

k = -11/2

k = -5.5

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Remember that

For x=30 degrees

we know that

substitute

A. The following are sets A and B:

A = {2, 3, 5, 7, 11}

B = {1, 2, 3, 4, 6, 12}

C. Elements not in A or A' = ∅

B. The Venn diagram is attached

A universal set is a set which consists of all elements related to the given sets. It is denoted by U.

A. Set A:

A = {2, 3, 5, 7, 11}

Set B:

B = {1, 2, 3, 4, 6, 12}

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A' = {1, 4, 6, 8, 9, 10, 12}

C. Elements not in A or A' = ∅

Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.

Hence, the Venn diagram of sets A, B and U has been attached.

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