Arthur is 7 years older than his brother. In 8 years, Arthur will be twice his brother's current age. How old is Arthur now?

The probability of selecting two socks of same color is 0.96.

According to the given question.

Total number of green socks = 4

Total number of yellow socks = 6

So, the total number of socks in a drawer = 4 + 6 = 10

Since as we know that, the probability of an event is computed as: P(E) = Number of favourable outcome /Total number of outcomes. Hence, the probability is the possibility of the occurrence of a random event.

So, the probability of selecting a green scoks = 4/10 = 2/5

And the probability of selecting a yellow socks = 6/10 = 3/5

Therefore, the probability of selecting two socks of same color

= probability of selecting both the green socks or probability of selecting both the yellow socks

= [( 2/5) + (2/5)] × [(3/5)+(3/5)]

= (4/5) × (6/5)

= 24/25

= 0.96

Hence, the probability of selecting two socks of same color is 0.96.

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Answer: a. y=0.03x+29.99

b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.

y-int: (0, 29.99). Total cost per month when phone isn't being used.

c. $34.07

Step-by-step explanation:

a. p=Cell phone plan. m=minutes used for phone.

3¢=$0.03

p=29.99+0.03m

y=0.03x+29.99

b. Slope: 0.03. $0.03 charged every minute Clear-Bell Cell phone is used.

y=0.03(0)+29.99

p=29.99 ==> y-int: (0, 29.99). Total cost per month when phone isn't being used.

c. y=0.03(136)+29.99

y=4.08+29.99

y=$34.07

The pharmacist should mix 9 g of a power to make a larger amount of the medicine

To solve this problem, we have to state the equation using the information of the problem

Information about the problem:

Calculating the rate of the medicine with the 1st mixed:

rate = mass(1)/ volume(1)

rate = 5g / 45cm3

rate = 0.11 g/cm3

Calculating how much power the pharmacist needs for the volume(2):

mass(2) = rate * volume(2)

mass(2) = 0.11 g/cm3 * 81 cm3

mass(2) = 9 g

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Answer:

x = 3

Step-by-step explanation:

AB is the line segment and is 20 cm

Since M is the midpoint, AM = MB = 20/2 = 10

3x + 1 = 10

==> 3x = 10- 1 = 9

==> x = 9/3 = 3

Answer:

AB=20 then AM =10

now,

[tex]3x + 1 = 10 \\ 3x = 10 - 1 \\ 3x = 9 \\ x = 3 [/tex]

Answer:

Step-by-step explanation:

The combination of hours that Keitaro can walk and run in a month to reach his goal will be A. 2 hours walking; 12 hours running

From the information, Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles.

The equation is

3w + 6r ≥ 36

3w + 6r ≤ 90

The combination of hours that Keitaro can walk and run in a month to reach his goal will be 2 hours walking; and 12 hours running.

This will be:

3w + 6r ≤ 90

3(2) + 6(12)

6 + 72 = 78

Therefore, 78 is less than 90.

The correct option is A.

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The surface area of a cube with side length of 6 1/2 inches is 253.5 square in

The formula for calculating the surface area of cube is expressed as:

Surface area = 6L^2

where

L is the side length of the cube

Substitute

SA = 6(13/2)^2

SA = 6 * 169/4

SA = 3 * 169/2

SA = 253.5 square in

Hence the surface area of a cube with side length of 6 1/2 inches is 253.5 square in

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Answer:if it is division it is:

Divide

233.91

by

3.45

=

67.8

Step-by-step explanation:

Answer:

x > 2 or x < −4

Step-by-step explanation:

Let's solve your inequality step-by-step.

|3x + 3| −5 > 4

Step 1: Add 5 to both sides.

|3x + 3| −5 + 5 > 4 + 5

|3x + 3| > 9

Step 2: Solve Absolute Value.

|3x + 3| > 9

We know either3x + 3 > 9 or 3x + 3 < −9

3x + 3 > 9(Possibility 1)

3x + 3 −3 > 9 −3(Subtract 3 from both sides)

3x > 6

3x > 6    (Divide both sides by 3)

3      3

x > 2

3x + 3 < −9(Possibility 2)

3x + 3 −3 < −9 −3(Subtract 3 from both sides)

3x < −12

3x < -12  (Divide both sides by 3)

3       3

x < −4

Answer:

{-9, 3, 10}

Step-by-step explanation:

Place the elements (the numbers marked by red) within curly brackets.

Step-by-step explanation:

THE POINT WHERE

[tex]f( - 4) = ( { - 4})^{2} + 1 \\ f( - 4) = 16 + 1 \\ f( - 4) = 17[/tex]

Now we have point (-4,17)

the gradient of the tangent line at that point of f(x) is the first derivative f'(x)=2x at that point

f'(x) =m

f'(-4)=2(-4)

f'(-4)=-8

The gradient therefore is -8

the general equation of a straight line is given by

[tex]y = mx + c \\ 17 = ( - 8)( - 4) + c \\ 17 = 32 + c \\ c = 17 - 32 \\ c = - 15 \\ \\ y = - 8x - 15[/tex]

HOPE THIS HELPS!!

The perimeter of the polygon will be 20 units and the area will be 21 square units.

From the given vertices a rectangle will be formed. A rectangle is a closed figure in which each interior angle is a right angle. The Perimeter of the rectangle can be given by formula 2(l + b) and the area is given by l×b where l is the length and b is breadth of rectangle. Now from the given points the dimensions of rectangle will follow the order W (5, -1), X (5, 6), Z (2, 6) and Y (2, -1).

The length of the rectangle is given by l = √ (6 + 1) ² + (5 - 5) ²

l = √49

l = 7 units

The breadth of the rectangle is given by b = √ (6 - 6) ² + (2 - 5) ²

b = √9

b = 3 units

Now, the perimeter of rectangle = 2 (l + b)

P = 2(7 + 3)

P = 20 units

Area of the rectangle = l×b

A = 7×3

A = 21 square units.

Thus, the perimeter and area are 20 units and 21 square units respectively.

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Answer:

659

Step-by-step explanation: Divishion of practice

Answer:

Area : 63.6 square inches.

Cost: Cost per square inch = 18.60 / 63.6 = $0.29 (rounded to the nearest cent)

Step-by-step explanation:

Natalie will choose 7 and 8 as the yellow-shaded region corresponds to Natalie's possible choices.

Even though it appears complex, 3-dimensional trilateration is a straightforward mathematical process that underlies GPS. It's critical to have a fundamental understanding of 2-D Trilateration, which is necessary to completely comprehend 3-D Trilateration. Similar principles apply to three-dimensional trilateration, however, spheres rather than circles are used. Here is how the Global Positioning System uses 3-D trilateration to pinpoint an object's precise location. When the first satellite sends a signal, the GPS receiver measures the distance between the two. Say the distance between the receiver and the satellite is 20 000 miles. This implies that the receiver might be located anywhere on the 20 000 km diameter green sphere's surface and in any direction.

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Answer:

Step-by-step explanation:

The variable here is u, and the highest power of u is u^8.  The first term is thus -u^8, and the coefficient of this is -1.  Thus, the leading coefficient of the polynomial is -1.  The degree is 8.

Answer:

$750

Step-by-step explanation:

I = interest

p = principle

r = rate

t = time

I = prt  Plug in what you know and solve for p

360 = p (.06)(8)

360 =p.48  Divide both sides by .48

750 = p

The principal is deposited in the account is $750.

Given that, rate of interest =6%, time period = 8 years and simple interest = $360.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Now, 360 = (P×6×8)/100

⇒ 360 = 48P/100

⇒ 48P = 36000

⇒ P = 36000/48

⇒ P = $750

Therefore, the principal is deposited in the account is $750.

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The average time of Lynden's first two, 100-meter-dash is 12.813 seconds.

We are given the 100-meter-dash times of Lynden in first two races. So, the average time for first two races will be calculated using the formula -

Average = sum of all observations ÷ total number of observations

Sum of all observations here will be the sum of time of race.

Sum of observations = 13.075 + 12.55

Performing addition

Sum of observations = 25.625 seconds

Number of observations is the number of races whose time is taken in calculation.

Number of observations = 2

Keep the values in formula to find the average time.

Average time = 25.625 ÷ 2

Average time = 12.8125 seconds.

Rounding to nearest thousands place : 12.813 seconds

Hence, the average time of Lynden's first two, 100-meter-dash is 12.813 seconds.

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Answer:   To find the average rate of change, divide the change in y-values by the change in x-values

Step-by-step explanation:

Answer: B

Step-by-step explanation: the square root of 2 cannot really be expressed as a fraction where both the numerator and the denominator are integers.

Answer:

B

Step-by-step explanation:

Answer: n=24

Step-by-step explanation:

n=number

2/3 * n - 5=11

2n/3=16

2n=48

n=24

Answer:

c) -66%, -0.45, -1/3, 1.8

Step-by-step explanation:

Numbers provided:

Rewrite them in decimals:

In ascending order (from least to greatest):

Solution: -66%, -0.45, -1/3, 1.8

Answer:

When multiplying the tens, the student didn't use the 0 place holder for the ones place.

Step-by-step explanation:

When using or doing long multiplication the answer was correct (2871) BUT before multiplying the tens, a zero should be placed in the ones place of the results. So, the tens should be 19140

2871+19140=22011

Answer: 1) When multiplying the ones, the student did not carry over a ten to the next place in the first multiplication.

2) When multiplying the ones, the student should have calculated 3 times 2 plus 5 as 11 and placed a 1 in the tens place.

3) When multiplying the tens, the student did not use the 0 place holder for the ones place.

4) When multiplying the tens, the student should have calculated 2 times 1 plus 9 as 11 and used a 1 should in the hundreds place.

Answer:

The correct option is;

4) When multiplying the tens, the student did not use the 0 place holder for the ones place

Step-by-step explanation:

Here we have when doing long multiplication, the student correctly multiplies the ones as 2871, however, before commencing multiplication of the tens, a 0 should be placed in the ones place of the result as a place holder such that the outcome of the multiplication of the tens should be;

19140

Hence, the correct result should be 2871 + 19140 = 22011

The correct option is therefore, that "When multiplying the tens, the student did not use the 0 place holder for the ones place."

Step-by-step explanation:

Answer: c. P=43

d. P=3x^2+5x+8

Step-by-step explanation:

c. P=12x+19 ==> See how I got this formula in my previous answer to parts a and b

P=12(2)+19

P=24+19

P=43

d. P=a+b+c+d

P=x^2 +4x+8+2x^2 +x

P=x^2 +2x^2 +4x+x+8

P=3x^2+5x+8

The rule(s) of algebra illustrated by the statement is the identity property of algebra

The statement is given as:

1 · (1 + x) = 1 + x

The identity property of algebra states that:

1 * a = a or a * 1 = a

In the above (given) statement, we can see that the expression 1 + x is multiplied by 1 to given 1 + x

This can be illustrated as

1 * a = a

The rule(s) of algebra that illustrates the above equation is the identity property of algebra

Hence, the rule(s) of algebra illustrated by the statement is the identity property of algebra

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The measures of angles q, r and s are 100°, 135° and 125° and the sum of the three angles equals 360°.

In this problem we find a geometric system generated by three lines no collinear to each other, which generate the triangle DEF. In accordance with the Euclidean geometry, the sum of the measures of internal angles in a triangle equals 180°:

m ∠ FDE + m ∠ DEF + m ∠ DFE = 180°            (1)

If m ∠ FDE = 80° and m ∠ DEF = 45°, then the measure of the angle DFE is:

m ∠ DFE = 55°

Finally, we find the values of the angles q, r and s by definition of supplementary angles:

q = 180° - 80°

q = 100°

r = 180° - 45°

r = 135°

s = 180° - 55°

s = 125°

The sum of the measures of angles q, r and s is:

q + r + s = 360°

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In words, the ratio of the number of jeans bought to the cost is four to thirty two.

We are told that you just bought 4 pairs of jeans for $32.

Now, since you bought 4 pairs for a cost of $32, then we can say that the ratio to represent the number jeans per dollars is;

4 :32

Thus, writing this in words we can say that the ratio of the number of jeans bought to the cost is four to thirty two.

Alternatively, we can also express it as a fraction with numerator and denominator as 4/32.

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Complete question is;

You just bought 4 pairs of jeans for $32. write a ratio and sentence comparing the number of jeans bought to the cost

The length of u by using sine rule is 7.4 to the nearest 10th of an inch.

In mathematics, sine rule is a trigonometric method which relates the angle and side of a triangle. We can say that by using the sine rule we can find the side of any triangle if we knows the angle and vice versa. This rule is also known as law of sines.

Formulas for sine rule:

If we have three sides a, b, c and angle say A, B and C respectively .Then sine rule is :

[tex]\frac{Sin A}{a} = \frac{Sin B}{ b} = \frac{Sin C}{c}[/tex]

In the given question,

Sine rule will be used to get the unknown side of the triangle.

According to the rule;

[tex]\frac{Sin U}{u} = \frac{Sin V}{ v} = \frac{Sin W}{w}[/tex]

Given w = 3 in, ∠W=23° and ∠U=73°,  substitute into the equation above to get u we have;

we can write the eq. as

[tex]\frac{Sin U}{u} = \frac{Sin W}{w}[/tex]

[tex]= > u = \frac{w \ sinu}{sinw} \\\\= > u = \frac{3 sin73}{sin 23} \\\\= > u = \frac{2.87}{0.39}\\ \\= > u = 7.398 = 7.4[/tex]

Hence,  length of u is 7.4 inches to the  nearest 10th of an inch.

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The value of [m + √n] is 183.

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