Solve - the mean age of a family of seven is 23 years the median is 16 years the modes are 12 years and 45 years and the range is 35 years. Find the ages of the seven family members.

When applying the some rule, we only combine two equal ratios at once. Consequently, we deal with pairs of sides and angles that have equivalent ratios.

When two ratios are equal, a percentage is formed; alternatively, two equal ratios can be said to produce a proportion. When we understand that two ratios are equal, you can write a proportion. The ratios of these two numbers are equal.

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant. Two angles are said to be complimentary if their sum is 90 degrees. Alternatively put, two angles are said to be complimentary if they combine to make a right angle.

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Answer:

tanθ=-0.96

Step-by-step explanation:

see attachment below

Upon performing polynomial long division, we find that the width is (x - 7). So, the dimensions of the rectangle are length (x - 5) and width (x - 7).

Given that the area of a rectangle is equal to its length multiplied by its width, we can set up the equation as follows:

Area = Length × Width

In this case, the area is given as (x^2 - 12x + 35), and the length is (x - 5). We are asked to find the width.

So, we can rewrite the equation as:

(x^2 - 12x + 35) = (x - 5) × Width

To find the width, we need to divide the area by the length:

Width = (x^2 - 12x + 35) ÷ (x - 5)

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Answer:

Step-by-step explanation: To find a decimal approximation to, say √2, first make an initial guess, then square the guess, and depending how close you got, improve your guess. Since this method involves squaring the guess (multiplying the number times itself), it uses the actual definition of square root, and so can be very helpful in teaching the concept of square root.

Example: what is square root of 20?

You can start out by noting that since √16 = 4 and √25 = 5, then √20 must be between 4 and 5.

Then make a guess for √20; let's say for example that it is 4.5. Square that, see if the result is over or under 20, and improve your guess based on that. Repeat this process until you have the desired accuracy (amount of decimals). It's that simple and can be a nice experiment for students!

Answer:

The number’s square root is a number that, when multiplied by itself, equals the first number. Another way of saying this is: “What can we multiply by itself to get the number in question?”

Step-by-step explanation:

For example, the square root of 1 is 1 because 1 multiplied by 1 equals 1 (1X1=1). However, the square root of 4 is 2 because 2 multiplied by 2 equals 4 (2X2=4). Think of the square root concept by imagining a tree. A tree grows from an acorn. Thus, it’s bigger than but related to the acorn, which was at its root. In the above example, 4 is the tree, and 2 is the acorn.

Thus, the square root of 9 is 3 (3X3=9), of 16 is 4 (4X4=16), of 25 is 5 (5X5=25), of 36 is 6 (6X6=36), of 49 is 7 (7X7=49), or 64 is 8 (8X8=64), of 81 is 9 (9X9=81), and of 100 is 10 (10X10=100).[1]

Answer:

Class 8 has 27 and class 7 has 40

Step-by-step explanation:

8th (r) class has 13 fewer than 7th (x).
x -13 = r

Total for both classes = 67

r + x - 13 = 67
r + x = 80

80 divided by two = 40 (per class)

40 - 13 =  27

Answer:

A

Step-by-step explanation:

We need to find the correct options which represents the given equation . We can try it out by eliminating the given options , as

So , option A , and D are preferred choices .

Option A is the correct option . ✔️

Janie cannot do a fraction of a chore, the Number of chores that Janie would need to do to earn enough money to purchase the CD is at least 12.

Let us assume that "c" represents the number of chores that Janie could do. Let's now create an inequality to determine the number of chores, ccc, that Janie could do to have enough money to buy the CD.

Since Janie earns $1.20 for each chore she does, we can multiply that amount by the number of chores she completes to determine how much money she will earn.

Thus, we obtain the following inequality:1.20c >= 13.50To find the number of chores that Janie would need to do to earn enough money to purchase a CD, we can use algebra to solve for "c".

To do that, we must first divide each side of the inequality by 1.20:c >= 11.25After dividing each side by 1.20, we obtain the inequality c ≥ 11.25.

Since Janie cannot do a fraction of a chore, the number of chores that Janie would need to do to earn enough money to purchase the CD is at least 12.

Let's do a check: If Janie were to complete 12 chores, she would earn 1.20 × 12 = 14.40, which is greater than the cost of the CD.

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The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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Answer:

  k = 3/5

Step-by-step explanation:

You want the coefficient of π in the radian measure of 108°.

There are π radians in 180°, so a fraction of 180° will be that fraction of π radians.

  108° = (108°)×(π/180°) = (108/180)π = 3/5π

The value of k in 108° = kπ is 3/5.

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Answer:

x≓−0.505501270

A system has infinite solutions if the graphs of the equations intercept at infinite points.

The solutions of a system of equations are given by the intersection between the graphs of the two equations.

So, if the graphs intercept at infinite points, we will have infinite solutions.

That is the case of the systems where both equations represent actually the same function, for example:

y = 4x + 2

2y = 8x + 4

Notice that these two equations actually represent the same line, so the equations intercept at infinite points, then that system has infinite solutions.

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Answer:

ln 15 must be greater (larger than) if log 15 is common.

Step-by-step explanation:

log 15 [assumed to be a common logarithm]

‹–› 15 = 10 ^ log(15)

ln 15 [natural log which has a base of e] ‹–› 15 = e ^ ln(15).

10 > e

e ≈ 2.7218.

e is approximately 3 rounded to the nearest whole number.

Logically you would need to raise 3 to a greater power for 3ⁿ = 15. Than 10ⁿ = 15.

For example 3² < 10² → 3³ < 10³ → 3⁴ < 10⁴ → ... Thus 3ⁿ < 10ⁿ for n > 0.

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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Part (a)

Answers:  

-----------------------------------

Work Shown:

Refer to figure 1 in the screenshot attached below.

========================================================

Part (b)

Answers:  

-----------------------------------

Work Shown:

Refer to figure 2 in the screenshot attached below.

Correction:

The derivative for h should be

\(h(x) = f(x)*(x-1)^{-1}\\\\h'(x) = \frac{d}{dx}[f(x)*(x-1)^{-1}]\\\\h'(x) = \frac{d}{dx}[f(x)]*(x-1)^{-1}+f(x)*\frac{d}{dx}[(x-1)^{-1}]\\\\h'(x) = f'(x)*(x-1)^{-1}+f(x)*(-1(x-1)^{-2})\\\\\)

I had a -2 in there instead of -1 as the coefficient.

You should find that h ' (2) = -2

That would then lead to y = -2x+9

The steps shown in figure 2 are effectively the same, just with different numbers of course.

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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If an annuity pays 5.5% compounded monthly, then the "equal-monthly-deposit" to have $100000 in 10 years is $627.

In order to calculate the "monthly-deposit" needed to accumulate $100,000 in 10 years at 5.5% compounded monthly, we use the formula for the future value of an annuity:

Which is : FV = P × [(1 + r)ⁿ - 1]/r,

where:

FV is "future-value" = $100000,

P = monthly deposit

r = monthly interest rate (5.5%/12 = 0.00458)

n = number of months (10 years × 12 months per year = 120 months)

Substituting the values,

We get,

⇒ 100000 = P × [(1 + 0.00458)¹²⁰ - 1]/0.00458,

⇒ P = 100000 × 0.00458 / [(1 + 0.00458)¹²⁰ - 1],

⇒ P ≈ $627,

Therefore, an equal monthly deposit is approximately $627.

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The measure of the inscribed angle G in the circle is 85 degree.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationhip between an an inscribed angle and intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

Since the circle equals 360 degrees, we can determine the intercepted arc DF.

Hence:

Arc DF = 360 - ( 70 + 120 )

Arc DF = 360 - 190

Arc DF = 170°

Now, plug the value into the above formula:

Inscribed angle = 1/2 × intercepted arc.

Inscribed angle G = 1/2 × 170°

Inscribed angle G = 85°

Therefore, angle G has a measure of 85 degree.

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Answer

Step by step explantion:

bsf= 26

Eliana:98

SS teacher=203

David=55

Step-by-step explanation:

m= music

bsf: m

eliana:4m-6

David:2m+3

SS teacher: 2(4m-6)+7

m+4m-6+2m+3+8m-12+7

382=15m-7

7+ +7

389=15m

/15m /15m

m=26

multiply 26 to each one of them

200.60 interest does andy’s account earn.

Let x be the amount of interest earned by Andy's account.

According to the problem, Andy's account earns 0.3% more interest than Marty's account, which means that Andy's account earns the same amount plus an additional 0.3% of that amount. Mathematically, we can express this as:

x = 200 + 0.3% of 200

Simplifying the right-hand side of the equation, we get:

x = 200 + 0.003 × 200

x = 200.60

Therefore, the answer is option 1: 200.60.

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Answer:

mean = 24

Step-by-step explanation:

the mean is calculated as

mean = \(\frac{sum}{count}\)

the sum of the data set is

sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168

there is a count of 7 in the data set , then

mean = \(\frac{168}{7}\) = 24

Answer:172 cm²

Step-by-step explanation:

when we use the formula, and we can  solve out is like 172.05 and round to tenth and will have the answer

Formula is 1/2 × p × a  

The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units

If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0

Then the distance of a point from the line is given by the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

Given: the point (5,12) and the line y = 5x + 12. The line can be written as

5x-y+12 = 0. Thus:

x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:

d = (ax₁ + by₁ + c) / √(a² + b²)

d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)

d = 25/√26 = 4.90 units

Therefore, the distance between the point and the line is 4.90 units. Option D is the answer

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Proportion form of the given problem is (52/120)=(39/90). They both are equivalent to each other which gives the same value of 4.33 after solving the proportion.

Two ratios form a proportion if simplified form of both the ratios comes out as same ratio.

Using above method to find out whether the given ratios are forming proportion or not.

The question asks for an proportion.

So, 2 minutes = 120 seconds and set up the proportion

where it will be in the form of (words/seconds).

It is given that 52 words in 2minutes and 39 words in 90 seconds

Now, the proportion form will be;

(52/120) = (39/90).

They both are equivalent to each other which gives the same value of 4.33 after solving the proportion.

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Answer:

$82.50

Step-by-step explanation:

if 10% = $8.25

and we know 10 goes into 100, (Percentage is always 100) a total of ten times then We take the discounted price and times it by 10

Answer:

its C hope it helps

Step-by-step explanation:

Answer:

Sure if they are not too hard

Step-by-step explanation:

Based on Simple Interest, 8125 was invested at the rate 1.7%.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.

> The daily interest rate, the principle, and the number of days between payments are multiplied to determine simple interest.

> Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest.

> Simple interest loans are frequently used for auto loans and short-term personal loans.

Let the amount at 1.7% be x. Then:

\(0.017x+0.023(\frac{(25000-x)}{2}) +0.024(\frac{(25000-x)}{2})=535\)

\(0.023+0.024 = 0.047 \\\frac{0.047}{2} = 0.0235\)

Now we got rid of the two divisions. Rewrite the equation:

\(0.017x+0.0235(25000-x) = 535\)

\(0.017x+587.5-0.0235x = 535\)

\(-0.006x = -52.5\) Divide both sides by -0.006 and remember -/- = +

x = 8750

This is how much was invested at 1.7% The rest, the problem says, was invested in equal amounts:

\(25000-8750 = 16250\); \(\frac{16250}{2}=8125\) So, 8125 was invested each at 2.3% and 2.4%

Based on Simple Interest, 8125 was invested at the rate 1.7%.

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Answer:

a = -9

b = -3

c = 11

d = 19

Step-by-step explanation:

a. x = -2

y= x² + 3x + 1

y= -2²+ 3(-2)+1

y= -4-6+1

y = -9

b. x= -1

y= x² + 3x+ 1

y= -1² + 3(-1) +1

y= -1 -3 + 1

y = -3

c. x =2

y = x² + 3x +1

y= 2²+ 3(2) +1

y= 4 +6 +1

y = 11

d. x= 3

y = x² +3x +1

y = 3² +3(3) +1

y= 9 +9 +1

y = 19

9514 1404 393

Answer:

  35gh

Step-by-step explanation:

The standard form has one coefficient, and generally has the variables in lexicographical order.

  35gh