Christine is 4 years younger than Mark. 3 years from now, she will be two-thirds as old as Mark find their present ages.Complete solution​

The distance from Point B (-1, 11) to line y = (-1 ÷ 3x) - 6 is 15.811.

The distance from the point B(-1 , 11) to the line y= (-1 ÷ 3x) - 6 is given by the distance formula d = (|Ax1 + By1 + C|) ÷ (√(A² + B²)).

Comparing the equation  y= (-1 ÷ 3x) - 6 with the standard forms Ax + By+ C = 0.

It is clear that the coefficient of x, A = -1 ÷ 3.

The coefficient of y, B = -1. The constant C = -6 and the points x1 = -1 and y1 = 11.

Substituting these data in the equation the distance d = (|(-1÷3)×(-1)+ (-1)×11 + (-6)|) ÷ √((-1 ÷ 3)² + (-1)² ) solving the equation the distance d becomes,

d = 15.811.

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Answer:

d=-6.5

Step-by-step explanation:

2d+13=0

2d=-13

d= -13/2

d=-6.5

Answer:

\((x + 8)^2 = 55\)

Step-by-step explanation:

Given

\(x^2 + 16x + 17 = 8\)

Required

Get an equivalent equation

\(x^2 + 16x + 17 = 8\)

Subtract 17 from both sides

\(x^2 + 16x + 17-17 = 8-17\)

\(x^2 + 16x = -9\)

Add 64 to both sides

\(x^2 + 16x + 64 = -9+64\)

\(x^2 + 16x + 64 = 55\)

Expand the expression on the left-hand side

\(x^2 + 8x + 8x + 64 = 55\)

Factorize:

\(x(x + 8) + 8(x + 8)= 55\)

\((x + 8)(x + 8)= 55\)

\((x + 8)^2 = 55\)

Answer:

y = -5/2x + 27/2

Step-by-step explanation:

line formula is y = mx + b

perpendicular means number next to the x (slope or m) becomes a negative reciprocal

2/5x -> -5/2x

then use point slope formula

y - y1 = m (x - x1)

y - 6 = -5/2 (x - 3)

y - 6 = -5/2x + 15/2

y = -5/2x + 15/2 + 6

y = -5/2x + 15/2 + 12/2

y = -5/2x + 27/2

Step-by-step explanation:

the inside expression of an absolute value expression can be positive or negative, but the result is only the positive one.

therefore, for our example here the negative case would be

2.5x - 6.8 = -12.9

which gives us

2.5x = -6.1

x = -6.1/2.5 = -2.44

and the positive case would be

2.5x - 6.8 = 12.9

and that gives us

2.5x = 19.7

x = 19.7/2.5 = 7.88

Answer

x = 3

Explanation

The equation is given as

If k = 3, then we are asked to solve for x.

Hope this Helps!!!

The given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.

What is Euclid's algorithm?

The Euclidean algorithm, also known as Euclid's algorithm, is an effective way to determine the greatest common divisor of two integers, or the biggest number that divides them both evenly without leaving a remainder. It is named after the Greek mathematician Euclid, who first discussed it in his Elements and gave it that name.

A common fraction can be reduced to its simplest terms using the Euclidean algorithm. For instance, the algorithm will demonstrate that the GCD of 765 and 714 is 51, and that 765/714 = 15/14 as a result. Additionally, it has several applications in more complex mathematics.

Hence, the given statement to reduce a rational number to its lowest terms, you first compute the greatest common divisor (gcd) of the numerator and the denominator, using Euclid's algorithm is correct.

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Answer:

x = w/(4a -9)

Step-by-step explanation:

w = x(4a - 9)

x = w/(4a -9)

Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.

We need to compare their volumes.

We can use the formula:

Density = mass / volume

To solve for volume, we rearrange the formula:

Volume = mass / density

For nickel:

Volume = 130g / 8.90 g/cm³ = 14.61 cm³

For magnesium:

Volume = 60g / 1.78 g/cm³ = 33.71 cm³

Therefore, Since magnesium has a larger volume than nickel, it will displace more water from an overflow can.

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Answer:

2 students play both

Step-by-step explanation:n(u)=28

n(b)=7,n(b)=5,n(who play neither sport)=18

HERE,

n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)

28=7+5-n(BnB)+18

28=30-n(BnB)

n(BnB)=30-28

 =2 answer

Answer:

Edie sold 9 fruit baskets

Step-by-step explanation:

The solution to the system of equations is (x, y) = (-261/47, 44/47) as an ordered pair.

To solve the given system of equations:

Equation 1: 8x + 9y = -36

Equation 2: x + 7y = 1

We can use the method of substitution or elimination to find the values of x and y. Let's use the method of substitution:

From Equation 2, we can solve for x:

x = 1 - 7y

Substituting this value of x into Equation 1:

8(1 - 7y) + 9y = -36

8 - 56y + 9y = -36

-47y = -44

y = 44/47

Substituting the value of y back into Equation 2 to find x:

x + 7(44/47) = 1

x + 308/47 = 1

x = 1 - 308/47

x = (47 - 308)/47

x = -261/47

Therefore, as an ordered pair, the solution to the system of equations is (x, y) = (-261/47, 44/47).

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Step-by-step explanation:

what r the answer choses??

Answer:

\(x<-6\text{ or } x>2\)

Step-by-step explanation:

We have the inequality:

\(\frac{2}{5}|5x+10|-14>-6\)

First, we can factor out a 5 from our absolute value. This yields:

\(\frac{2}{5}(5|x+2|)-14>-6\)

Simplify:

\(2|x+2|-14>-6\)

Add 14 to both sides:

\(2|x+2|>8\)

Divide both sides by 2:

\(|x+2|>4\)

Definition of Absolute Value:

\(x+2>4\text{ or } -(x+2)>4\)

Solve each case individually:

Case 1:

\(x+2>4\)

Subtract 2 from both sides:

\(x>2\)

Case 2:

\(-(x+2)>4\)

Divide both sides by -1. Flip the sign:

\(x+2<-4\)

Subtract 2 from both sides:

\(x<-6\)

So, our answers are:

\(x<-6, x>2\)

Since our inequality is a greater than, we will have an "or" inequality.

So, our answer is all values left to the first solution and all values to the right of the second solution:

\(x<-6\text{ or } x>2\)

And we're done!

Answer:

Step-by-step explanation:

Formula: Area=(a+b)/2 * h

72=(16+8)/2*h

72=24/2*h

72=12*h

h=72/12

h=6

It will be nice if you give me brainlies.Good luck!

Answer:

51

Step-by-step explanation:

Hope this helps

Answer:

51

Step-by-step explanation:

Answer:

d. 90 cm, 1.2 cm

Step-by-step explanation:

Given that:

The sample size n = 36

For the  length of the link:

The mean \(\overline x\) = 2.5

The standard deviation s = 0.2 cm

In a chosen 36 links, The mean and standard deviation for the length chain is as follows:

Mean = n\(\overline x\)

Mean = 36×2.5

Mean = 90 cm

The Standard deviation = s×√n

The Standard deviation = 0.2×√36

The Standard deviation = 0.2×6

The Standard deviation = 1.2 cm

Answer:

Please give brainliest

Step-by-step explanation:

c

E'

F and O

Because the special is fish and the number is odd, the selection is an example of F and O. Since the selection is not odd, it is an element of E′ (remember that E′ is the complement of E). Therefore, it is also an example of C AND O, and E′.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, the probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

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Therefore ,the radius of the given cylinder is 10 inches

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

Here,

The volume of the cylinder is 1570 cubic inches

Volume of the cylinder = 1570 cubic inches

Volume of cylinder = π\(r^{2}\)h

Where r is the radius of cylinder

h is the height of cylinder

So,

Volume of the cylinder = 1570 cubic inches

=> 1570 = π\(r^{2}\)h

=> 1570 = 3.14*\(r^{2}\)*5

=> 1570/3.14 = \(r^{2}\)*5

=> 500=\(r^{2}\)  *5

=> 500/5 =\(r^{2}\)

=>100 =\(r^{2}\)

=>r=10 inches

Therefore the radius of the given cylinder is 10 inches.

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Answer:

origin-the place at which the horizontal and vertical number lines cross

y-axis- the horizontal number line

x-axis- the vertical number line

quadrant- each of the four quarters of a plane, as it is divided by the number lines

Step-by-step explanation:

they all match up

The radius of the cylinder is 7. 9 in

First, we need to know the formula for volume of a cylinder

The formula for calculating the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters of the formula are expressed as;

From the information given, we have that;

Substitute the values

196 = 3.14 × 1 × r²

Divide both sides by the values

r² = 62. 42

Find the square root of both sides

r = 7. 9 in

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Answer and Step-by-step explanation:

Let f(x) = x4 + x3 + x2 +x + 1 Є Z2[x]. Prove that f(x) is irreducible over Z2[x] or not?

Proof:-  

Let f(x) = x4 + x3 + x2+ x+1 Є Z2[X].  

Then f (0) = 1 = f(1), so f(x) has no roots,  By Factor theorem, which states that polynomial f(x) has a factor(x-a) if and only if f(a)=0.                                                                                                                                      Hence, f(x) has no linear factor.                                                                                                                                                 If f(x) is reducible, it must have factors of degree 2 and degree 3. But f(x) has no degree 2 factors.

We know that only irreducible quadratic in Z2[X] is x2  + x +1. When we divide f(x) by x2  + x +1 we get a remainder of 1, so x2  + x +1 is not a factor of f(x) therefore f(x) is irreducible.

Answer:

Step-by-step explanation:

Each family experiences stages over time that follow a fairly predictable pattern

Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.

According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.

Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.

Interest = Principal * Rate

= $13,250.00 * 0.10358

≈ $1,370.56

Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.

Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.

Calculating the interest with a credit score of 680:

Interest = Principal * Rate

= $13,250.00 * 0.09132

≈ $1,210.57

Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.

Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.

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The probability of an adult having hypertension is  0.344 and an adult having hypertension and being classified as a low level of obesity is 0.102, having hypertension given he/she is classified as a high level of obesity is 0.540. If an adult has hypertension, the probability that he/she also has a high level of obesity is  0.444.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of the likelihood of an event occurring divided by the number of possible outcomes. Probability is used to determine the chances of a particular outcome occurring and can range from 0 to 1.

a)The probability of an adult having hypertension is (34 + 30 + 51) / (34 + 30 + 51 + 119 + 99 + 82) = 115 / 334 = 0.344.

b) The probability of an adult having hypertension and being classified as a low level of obesity is 34 / (34 + 30 + 51 + 119 + 99 + 82) = 34 / 334 = 0.102.

c) The probability of an adult having hypertension given he/she is classified as a high level of obesity is 51 / (30 + 51 + 82) = 51 / 163 = 0.312.

d) The probability of an adult being classified as a high or average level of obesity is (30 + 51 + 99) / (34 + 30 + 51 + 119 + 99 + 82) = 180 / 334 = 0.540.

e) If an adult has hypertension, the probability that he/she also has a high level of obesity is 51 / (34 + 30 + 51) = 51 / 115 = 0.444.

f) No, an adult's hypertension status and obesity categorization are not independent. This is because the probability of an adult having hypertension given he/she is classified as a high level of obesity (0.312) is not the same as the probability of an adult having hypertension (0.344).

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Answer:

A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The required image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

To find the image T of triangle ABC under the transformation (x,y) → (x-4, y+1), apply this transformation to each of the vertices of triangle ABC and then connect the new vertices to form the image T.

Let's assume that the coordinates of the vertices of triangle ABC are A(a,b), B(c,d), and C(e,f).

To find the image of vertex A under the transformation, we substitute x = a and y = b into the transformation equation:

(x,y) → (x-4, y+1)

(a,b) → (a-4, b+1)

Therefore, the image of vertex A is A'(a-4, b+1).

Similarly, we can find the images of vertices B and C:

B'(c-4, d+1)

C'(e-4, f+1)

Therefore, the image T of triangle ABC under the transformation (x,y) → (x-4, y+1) is formed by connecting the vertices A'(a-4, b+1), B'(c-4, d+1), and C'(e-4, f+1)

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Based on the given data, the probability that exactly 2 insects will survive is 0.1402 rounded to four decimal places.

The probability mass function for the binomial distribution is given by:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (surviving insects), k is the specific number of successes we're interested in (k=2 in this case), n is the total number of trials (n=11), p is the probability of success (p=0.3), and (n choose k) is the binomial coefficient, which is the number of ways to choose k objects from a set of n objects.

Plugging in the values, we get:

P(X=2) = (11 choose 2) * 0.3² * 0.7²

= (55) * 0.09 * 0.02825

= 0.1402

Therefore, the probability that exactly 2 insects will survive is 0.1402 (rounded to four decimal places).

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