Graph the equation -2y+12=-3x​

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Kirk must earn an annual rate of return of approximately 6.07% on his investment to accumulate enough money to pay for the ring.

To calculate the annual rate of return Kirk must earn on his investment, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = final amount (the cost of the ring, which is $13,000 in 9 years)
P = initial amount (the amount Kirk currently has, which is $4,532)
r = annual interest rate (what we need to solve for)
n = number of times interest is compounded per year (assuming it's compounded annually, n = 1)
t = number of years (9 years)

Plugging in the given values:
$13,000 = $4,532(1 + r/1)^(1*9)
Next, simplify the equation:
(1 + r)^(9) = 13000/4532
Take the ninth root of both sides:
1 + r = (13000/4532)^(1/9)
Solve for r:
r = (13000/4532)^(1/9) - 1
Now, plug the value into a calculator to find r:
r = 0.0607

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Answer:

the answer is 29.61

Step-by-step explanation:

cross multiply or set up a basic multiplication box removing the decimals and adding it back

Answer:

I believe the answer would be -20 percent

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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The approximation for 8.4 using the linear approximation is approximately 2.9712 + √2.

To approximate 8.4 using linear approximation (the tangent line) to the function f(x) = √x at x = 8, we first need to find the equation of the tangent line.

We start by finding the derivative of f(x). The derivative of √x is (1/2√x). Evaluating the derivative at x = 8, we have:

f'(8) = (1/2√8) = (1/2√4*2) = (1/4√2) = √2/8.

Now we have the slope of the tangent line, which is √2/8.

Next, we find the y-coordinate of the point of tangency, which is f(8). Substituting x = 8 into the function, we have:

f(8) = √8 = 2√2.

Therefore, the equation of the tangent line can be written as:

y = (√2/8)x + b.

To find the value of b, we substitute the coordinates (x, y) = (8, 2√2) into the equation:

2√2 = (√2/8)(8) + b.

Simplifying, we have:

2√2 = √2 + b.

Subtracting √2 from both sides, we get:

2√2 - √2 = b,

b = √2.

Thus, the equation of the tangent line is:

y = (√2/8)x + √2.

Using this tangent line, we can approximate 8.4 by substituting x = 8.4 into the equation:

y ≈ (√2/8)(8.4) + √2.

Calculating the expression, we have:

y ≈ (0.3536)(8.4) + √2,

y ≈ 2.9712 + √2.

Therefore, the approximation for 8.4 using the linear approximation is approximately 2.9712 + √2.

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If probability of winning a teddy bear at a carnival is 0.89 and 40 turns are taken, then he should have won about 35 teddy bears.

The probability of winning a teddy bear at a carnival is = 0.89, then

The probability of not winning a teddy bear is = 1 - 0.89 = 0.11,

We use binomial-distribution to calculate the probability of winning "k" teddy bears in "n" turns,

Where probability of winning (p) = 0.89,

The formula for the binomial distribution is,

⇒ P(k) = C(n,k) × p^k × (1-p)^(n-k),

The probability of winning "k" teddy bears in 40 turns is :

⇒ P(k) = C(40,k) × 0.89^k × 0.11^(40-k),

To find "expected-number" of teddy bears won, we multiply the probability of winning k teddy bears by k, and sum over all possible values of k,

⇒ E(number of teddy bears won) = \(\[ \sum_{k=0}^{40} \]\) k × P(k),

⇒ \(\[ \sum_{k=1}^{40} \]\) k × C(40,k) × 0.89^k × 0.11^(40-k),

On further solving ,

We get,

⇒ E(number of teddy bears won) ≈ 35.6,

Therefore, we expect to win about 35 teddy bears if we take 40 turns .

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The sampling technique used in each study is as follows: (a) convenience sampling, (b) systematic sampling, and (c) stratified random sampling.

(a) In the first study, where a journalist goes to a campground to ask people about their feelings regarding air pollution, the sampling technique used is convenience sampling. This is evident because the journalist approaches individuals who are readily available and easily accessible at the campground. However, convenience sampling may introduce bias as it does not ensure a representative sample of the population.

(b) In the second study, where every tenth machine part is selected from an assembly line for measurement, the sampling technique used is systematic sampling. Systematic sampling involves selecting every nth element from a population after establishing a sampling interval. In this case, every tenth machine part is selected to ensure a systematic and unbiased approach to quality assurance.

(c) In the third study, where attitudes about smoking are studied at a college and students are divided by class and then randomly sampled from each class for interviews, the sampling technique used is stratified random sampling. Stratified random sampling involves dividing the population into homogeneous subgroups (strata) and then randomly selecting samples from each subgroup. By dividing the students into different class strata and randomly selecting samples from each class, this study aims to ensure representation from each class in the final sample.

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Answer:  5.6 N/cm^2

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

Work Shown:

Pressure = (Force)/(Area)

P = F/A

P = (84 N)/(15 cm^2)

P = (84/15) (N/cm^2)

P = 5.6 N/cm^2

For every square cm, 5.6 newtons of force is applied.

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

Extra info:

If you wanted to convert this to pascals, then you would need to convert 15 cm^2 to 0.0015 square meters. Then apply the formula above to get 56,000 pascals. 1 pascal is equivalent to 1 N/m^2.

Answer:

5/16=s/32

Step-by-step explanation:

What we know:

- a school team has 80 swimmers

The ratio of 7th grade swimmers to every swimmer in their school (counting all the grades) is 5:16. Write a proportion of this for a value of s.

a ratio can also be expressed in a fraction by simply putting it from x:y to x/y

so, the ratio 5:16 can also be expressed as 5/16.

note: let sgs represent seventh grade swimmers.

also, let x represent the value of the equivalent amount of swimmers (in the denominator that serves as a value for the proportion of 5/16.

we need to find:

5 sgs/16 swimmers = s amount of sgs/x

5/16=s/x

equivalent fractions could literally be anything, just multiply that ratio by a value equal to one; ex 4/4, or 16/16, or 2/2.

the simplest proportion is to multiply 5/16 by 2/2.

5/16*(2/2)=s/x

10/32=s/x

so s=10 and x=32 but we only need to know x cuz your problem doesn't have a box to answer the s=10.

so... 5/16=s/32.

Answer:

D. 25

Step-by-step explanation:

16 divided by 64% is 25

Answer:

25

Step-by-step explanation:

Hope I helped you.

Answer:

line 1, the slope is positive. line 2,the slope is undefined. line 3, the slope is negative. line 4, the slope is zeeo

Answer:

1. Negative

2. Zero

3. Positive

4. Undefined

Step-by-step explanation:

1. The slope is going down, therefore negative

2. A slope that is horizontal is zero

3. The slope is going up, therefore positive

4. The slope is vertical, therefore undefined

I hope this helps!

Answer:

Acceleration and velocity

Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force.

Answer: B and D

Step-by-step explanation:

The diameter of the circle is 12.5 inches

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: 157 breaks required to make a circular garden and cover the boundary.

Now each brick is 4 inches long

Thus total length of the circumference of the circular garden we get

157/4=39.25 inches long

Thus the circumference of the circle is given by

2πr=39.25

2r=39.25/3.14

d=12.5 inches

Thus the diameter is 12.5 inches.

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Answer:

Girls: 11

Boys: 18

Step-by-step explanation:

x: number of girls

x+x+7=29

2x=22

x=11

number of guys:

x+7=11+7=18

The given quadratic equation x² - 3y² = 2 cannot be solved using congruences modulo 3, 4, or 11.

Modulo 3

We can observe that for any integer x, x² ≡ 0 or 1 (mod3) since the only possible residues for a square modulo 3 are 0 or 1. However, for 3y² the residues are 0, 3, and 2. Since 2 is not a quadratic residue modulo 3, there is no solution to the equation modulo 3.

Modulo 4

When taking squares modulo 4, we have 0² ≡ 0 (mod 4), 1² ≡ 1 (mod 4), 2² ≡ 0 (mod 4), and 3² ≡ 1 (mod 4). So, for x², the residues are 0 or 1, and for 3y², the residues are 0 or 3. Since 2 is not congruent to any quadratic residue modulo 4, there is no solution to the equation modulo 4.

Modulo 11:

To check if the equation has a solution modulo 11, we need to consider the quadratic residues modulo 11. The residues are: 0, 1, 4, 9, 5, 3. We can see that 2 is not congruent to any of these residues. Therefore, there is no solution to the equation modulo 11.

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Answer:

51 m^2

Step-by-step explanation:

Area = 11(3) + 6(3) = 51 m^2

Answer:

51 m^2

Step-by-step explanation:

Divide the shape into 2 shapes that are easily identified

Calculate each area and add them up.

You have two different dimensions:

6x3

And

11x3

You’d get 51 if you add them all up.

Answer:

11 and 6

Step-by-step explanation:

11-6=5 <--- difference

11+6=17 <--- sum

so, since we know that the derivative is simply the equation we use to get the slope at any point on the curve, thus df/dx will be that.

now, we know that g(x) is already in slope-intercept form, so it has a slope of "4", hmmm what's "x" at that instance?

\(f(x)=-x^2+8x+20\implies \cfrac{df}{dx}=-2x+8 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\stackrel{\stackrel{m}{\downarrow }}{4}x+k\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\\\ 4~~ = ~~-2x+8\implies 2=x\)

well, now we know that x = 2, hmmm what's "y" at that instance? well, our "y" will be simply f(2) = g(x), because g(x) is touching f(x) at that point on the curve.

\(f(2)=-(2)^2+8(2)+20\implies f(2)=32 \\\\[-0.35em] ~\dotfill\\\\ g(x)=4x+k\implies 32=4(2)+k\implies 32=8+k\implies \boxed{24=k}\)

Check the picture below.

Answer:

R(-4,-8) and T(-8,8)

Step-by-step explanation:

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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The value of x is 7.82

Following these procedures will help us use proportions to solve challenges in the real world:

1. Set up two ratios comparing the identical quantities using the information from the problem.

2. Create a proportion by setting the ratios equal.

3. To find the proportional unknown, use cross multiplication.

\(AB/ AD = TS/ UT\)

\(7/ 14.8= 3.7/ x\)

On cross multiplying we get

7x= 54.76

x= 7.822

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The solutions are all the points inside the shaded region:

(1, 0.5) , (2,-1) and (2.5, -2)

Answer:

x = -12

Step-by-step explanation:

Let x be the number.

The product of 5 and x increased by 9 is equal to 15 less than 3 times x.

5x + 9 = 3x - 15.

We can isolate x, getting (5-3)x = -15-9

Then we can solve:

2x = -24

x = -12.

The required number is -12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, The product of five and a number, increased by 9 is equal to fifteen less than three times then number.

Let x be the number.

Establishing the equation,

5x + 9 = 3x - 15.

(5-3)x = -15-9

Then we can solve:

2x = -24

x = -12.

Hence, the number is -12

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The given expression is 4(8x + 5). This is a product of a coefficient and a binomial expression. In mathematics, a binomial is a polynomial with two terms.

They are represented as ax + b or a + bx or (a + b) etc. Given expression is 4(8x + 5). We can simplify this by applying the distributive property. It is given as follows; The distributive property of multiplication states that a(b + c) = ab + ac To simplify the given expression, we need to multiply the coefficient 4 with each term in the parentheses.

It can be done as follows; 4(8x + 5) = 4*8x + 4*5 We multiply 4 with 8x and 4 with 5 to obtain; 32x + 20 This is the main answer. Therefore, the simplified form of 4(8x + 5) is 32x + 20. To simplify the given expression 4(8x + 5), we can use the distributive property. According to this property, the product of a number with the sum of two or more terms is equal to the sum of the products of that number with each term of the sum. In other words, a(b + c + …) = ab + ac + … In the given expression, 4 is multiplied with the binomial (8x + 5). Hence,

4(8x + 5) = 4*8x + 4*5

= 32x + 20

Hence, the simplified form of 4(8x + 5) is 32x + 20.

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Step-by-step explanation:

$1.00 - $0.75 = $0.25

She needs $0.25