Solve for x: 7x = 63 A. x = 70 B. x = 56 C. x = 7 D. x = 9

The mean is 14.7, the median is 16, and the mode is 16.

To find the mean, we need to calculate the sum of all the data values and divide it by the total number of observations.

The sum of the data values is:

14 x 14 + 15 x 11 + 16 x 23 + 17 x 10 + 18 x 13 = 196 + 165 + 368 + 170 + 234 = 1043

The number of observations is:

14 + 11 + 23 + 10 + 13 = 71

The mean is calculated as follows,

1043 / 71 = 14.7 (rounded to one decimal place)

The median is the central value in the data collection. To find the median, we need to arrange the data values in ascending order and find the middle value. In this case, we have an odd number of observations, so the median is simply the middle value.

14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18

The median is 16.

The mode is the value that appears most repeatedly in the data set. In this case, the mode is 16 since it occurs the most (23 times).

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Answer:

B. 3188.5 cubic inches.

Step-by-step explanation:

The volume of a cone is calculated using the following formula:

Volume = (1/3) * π * r² * h

Where:

In this problem, we are given that r = 17 inches and S.h = 20 inches.

First we need to find height h.

py using Pythagorous theorem,we get

c²=a²+b²

here c= slight height and a is radius

20²=17²+b²

20²-17²=b²

111=b²

b=√(111)

Plugging these values into the formula, we get:

Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches

Therefore, the volume of the cone is 3188.5 cubic inches.

Answer:

B.

H0 : PA - PB = 0

Ha : PA - PB > = 0

Step-by-step explanation:

The Null hypothesis refers to the initial truth in which of there is no significant evidence provided by statistical analysis will remain ; else, the alternative hypothesis which is the opposite of the Null will be favored in place of the Null.

In the scenario above, the claim by the researcher, that "the proportion of the population of polydactyl cats in region A is greater than the proportion in region B." is the Alternative hypothesis ; Ha : PA - PB > = 0 while the Null will be of the notion that the proportion of polydactyl cats in region A and region B are the same.

Answer:

6root2

Step-by-step explanation:

3-1,5-1. (2,4)

R=root(4+16). =6root 2

Answer: The answer is A.

Step-by-step explanation:

Seems the most appropriate, but I’m not sure.

Take the risk.

The amount it cost for Yvonne to go to college is = $40,000

The number of years to complete college= 5 years

Yvonne salary per year = $45,000

For 5 years her salary = 45,000

4.5 years = X

Make X the subject of formula,

X = 45,000 × 4.5/5

X = 202,500/5

X =$ 40,000

Therefore, the amount it cost for Yvonne to go to college is = $40,000.

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Answer:

D.

Step-by-step explanation:

3x + 4 is another way of writing 2 + 3x + 2, if you add the 2's together you get a four (3x + 4).

Answer:

1/2=10

Step-by-step explanation:

it depends upon the area of the triwngle

Answer:

The third one

Step-by-step explanation:

600-225 (the weight of Terrell and his equipment)

=375

375/25(weight of each box)

=15

the circle is close because it can be exactly 15 or or less.

Answer:

actually is 2

Step-by-step explanation:

its not 1 or 3, its 2 I did clicked 3 got it wrong then I clicked one and got it wrong, its 2

The linear function which represents a slope of -3 as required in the task content is; A two column table with five rows. The first column, x, has the entries, negative 5, negative 1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8.

It follows that the task requires that a linear function whose slope, i.e rate of change is -2 is to be determined.

Since slope is the rate of change in y with respect to x;

The required linear function is; A two column table with five rows. The first column, x, has the entries, -5, -1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8 so that we have;

Slope = (24 - 32) / (-1 -(-5)) = -8 / 4 = -2.

Remarks: The complete question is such that the required slope is -2.

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Answer: the second option

Step-by-step explanation:

i took the assignment

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

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PLATO

i got it correct :)

Answer:

X=3

Step-by-step explanation:

3 is in the middle of the figure.

I hope this helps!

The total surface area of the given regular triangular pyramid is 64.2 cm².

The objective of every surface area formula for a geometric shape is to calculate the total area occupied by all of the objects' faces. In this section, various formulas for calculating an object's surface area will be covered.

The total surface area accounts for all faces of the 3D shape, including the flat and curved surfaces, whereas the lateral surface area is calculated to determine the area occupied by the shape's curved surface. The base area is not included. A sphere is a 3D shape with only one round surface and no flat base.

As the opposite sides will have same features, the formula for Total surface area of the regular triangular pyramid will be:

As its a regular triangular pyramid all lateral surface is same,

Substituting the given values we have:

A = 3(1/2 × 6 × 5.4) + (1/2 × 6 × 5.2)

A = 3(16.2) + 15.6

A = 64.2 cm²

Thus, The total surface area of the given regular triangular pyramid is 64.2 cm².

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Answer:

1/2 Kg

Step-by-step explanation:

To find the quantity of flour used multiply the (2/3) by (3/4)

     \(\sf Quantity \ of \ flour \ used = \dfrac{2}{3} \ of \ the \ whole\)

                                       \(= \dfrac{2}{3} \ of \ \dfrac{3}{4} \ Kg\)

                                       \(= \dfrac{2}{3}*\dfrac{3}{4}\\\\=\dfrac{1}{2}\ Kg\)

Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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Answer:

6 cookies

Step-by-step explanation:

Roger wants to place 84 sugar cookies and 66 chocolate chip cookies into plastic bags. Each bag must have the same number of cookies and only one type of cookie must be in each bag.

For the 84 sugar cookies:

number of cookies : 1    2     3      4      6     7      12      14      21     28    42    84

number of bags    : 84   42   28    21    14    12     7        6       4       3      2        1

For the 66 chocolate cookies:

number of cookies : 1       2      3       6      11       22     33      66

number of bags      : 66   33    22     11       6       3        2       1

The maximum common factor between 84 and 66 is 6.

Therefore 6 cookies should be placed in each bag. For sugar cookies, 6 cookies would be placed in each of the 14 bags while for the chocolate cookies, 6 cookies would be placed in each of the 11 bags.

Let's denote the three numbers A, B, and C.

Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.

Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.

Let's list the possible combinations:

These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).

Answer:

30 minutes.

Step-by-step explanation:

You can make a proportion, which would be 10 selfies : 12 minutes. The second one will be 25 selfies : x minutes.

They have to be equal, since it is given that the rate stays the same. So 10:12=25:x

A proportion can be written as a fraction, so 10/12=25/x.

Cross multiply, and you get 10*x=12*25, or 10x=300.

Now divide both sides by 10 to get x=30.

Answer:

R= R-(P+Q)

Step-by-step explanation:

Total amount=

Total amount - (amount given to brother + amount given to sister)

The perimeter of triangle ABC = 60 + 20√3  cm

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

In triangle ADB,

sin (30°) = AD/AB

1/2 = ( 10 √3 ) /AB

AB  = 20√3

In triangle ABC,

cos (30°) = AB/BC

√3 /2 =  20√3 / BC

BC = 40

tan (30°) = AC/AB

1/√3 =  AC/ 20√3

AC = 20

Perimeter of triangle ABC =  AB +BC  + AC

                                           = 20√3  +  40  + 20

                                           = 60 + 20√3

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2.5% of values will lie above 29.

What is normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

The 68-95-99.7 rule is an illustration of how those many percentage of values lie in between  mean +/- 1, 2, and 3 standard deviations respectively.

For values to lie above 29, their z value comes out to be

(29-19) / 5 = 10/5 = 2

(Note: z value means how many standard deviations above the mean)

Thus for a z value = 2 (which 29 is in this problem) the percentage of values that lie between mean +/- 2*(standard deviation) is 95 (as stated by the 68-95-99.7 rule).

Thus only 5% values wont lie between mean +/-2 standard deviations.

So 5% values wont lie between 29 (z value=2) and 9 (z value=-2).

Since normal curve is symmetric, half of the values of the 5% will lie above 29 and the rest half will lie below 9.

So 50% of 5 % which is 2.5% of values will lie above 29.

Hence, 2.5% of values will lie above 29.

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Answer:

  Always true

Step-by-step explanation:

If you can't express the number as a ratio of integers, multiplying or dividing it by integers will not make it so you can.

If π is irrational, 2π is also irrational.

It is always true that the product of a rational and an irrational number is irrational.

Answer:

all ways true

Step-by-step explanation:

Step-by-step explanation:

Flip f(x) about the x-axis by multiplying it by -1

  - f(x)

  the squish it skinnier by multiplying it by 4

g(x) = - 4 f(x)   = -4 x^2

#The 75% of 3/4?

#Just times it.

75/100 × 3/4 = 225/400 =9/16

#so, the 75% of 3/4 is 9/16

The equivalent value of the percentage is A = 9/16 = 0.5625 = 56.25 %

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be represented as p

Let the percentage be represented as q

Now , A = pq

when the value of p = 3/4

And , when the value of q =75 %

On simplifying the equation , we get

A = ( 75 % ) ( 3/4 )

So , the left hand side of the equation is equated to the right hand side by the value of ( 75 % ) ( 3/4 )

Now , the value of 75 percentage = 3/4

A = ( 3/4 ) ( 3/4 )

A = 9/16

On simplifying , we get

Multiply by 3 on the fraction , we get

A = 0.5625

Therefore , the value of A = 9/16

Hence , the fraction is A = 9/16

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Answer: 36.56

Step-by-step explanation:

Answer:

3x - 5 + 2x² + 9x = 3x + 2x² + 9x - 5​ = TRUE = 2 x^2 + 12 x - 5

Step-by-step explanation:

left: Simplify the following:

2 x^2 + 9 x + 3 x - 5

Grouping like terms, 2 x^2 + 9 x + 3 x - 5 = 2 x^2 + (3 x + 9 x) - 5:

2 x^2 + (3 x + 9 x) - 5

3 x + 9 x = 12 x:

Answer: 2 x^2 + 12 x - 5

_______________________

Simplify the following:

2 x^2 + 9 x + 3 x - 5

Grouping like terms, 2 x^2 + 9 x + 3 x - 5 = 2 x^2 + (3 x + 9 x) - 5:

2 x^2 + (3 x + 9 x) - 5

3 x + 9 x = 12 x:

Answer: 2 x^2 + 12 x - 5

Answer:  11

Step-by-step explanation:

XY + YZ = XZ

  XY + 3 = 14

         XY = 11

Answer:

52 m²

Step-by-step explanation:

A(trap) = 1/2h · (sum of bases)

A = 1/2(8)·(3 + 10)

A = 4(13)

A = 52

Answer:

a. cosθ = ¹/₂[e^jθ + e^(-jθ)] b. sinθ = ¹/₂[e^jθ - e^(-jθ)]

Step-by-step explanation:

a.We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Adding both equations, we have

e^jθ = cosθ + jsinθ

+

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ + cosθ + jsinθ - jsinθ

Simplifying, we have

e^jθ + e^(-jθ) = 2cosθ

dividing through by 2 we have

cosθ = ¹/₂[e^jθ + e^(-jθ)]

b. We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Subtracting both equations, we have

e^jθ = cosθ + jsinθ

-

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ - cosθ + jsinθ - (-jsinθ)

Simplifying, we have

e^jθ - e^(-jθ) = 2jsinθ

dividing through by 2 we have

sinθ = ¹/₂[e^jθ - e^(-jθ)]