Match each pair of equivalent values.
1.
square root of 16
2. square of 8
3. 42
4. 12
5. √4
6. √144
k
16
1
4
2
64
12

Answer:

42 mi²

Step-by-step explanation:

Break it up into 2 shapes, top and bottom, then add the areas together.

Area 1 (top rectangle) = 12 x 3 = 36

Area 2 (bottom rectangle) = 2 x 3 = 6

Total area = 36 + 6 = 42 mi²

The slope-intercept equation of this linear function is y = -3x + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

At point (0, 5), a linear equation of this line can be calculated in slope-intercept form as follows:

y - 5 = (2 - 5)/(1 - 0)(x - 0)

y - 5 = -3(x - 0)

y = -3x + 5

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The length x of the right triangle is 8.66 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using trigonometric ratios as follows:

Hence,

tan 60° = opposite / adjacent

where

opposite side = x

adjacent side = 5

Therefore,

tan 60° =  x  / 5

cross multiply

x = 5 tan 60°

x = 5 × 1.73205080757

x = 8.66025403784

x = 8.66 units

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In the simplest terms, the expression for the difference between (-9x-7) and (-4x+4) is -5x - 11.

To find the difference between (-9x-7) and (-4x+4), we can subtract the second expression from the first expression and get: (-9x - 7) - (-4x + 4)

Simplifying the double negative, we get: (-9x - 7) + (4x - 4)

Next, we can combine like terms: -9x + 4x - 7 - 4

Simplifying this expression further down, we get: -5x - 11

Therefore, the expression that represents the difference between (-9x-7) and (-4x+4) in simplest terms is -5x - 11.

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Hence, it is proven that PQRS is a parallelogram

Quadrilateral PQRS formed by joining the midpoints of quadrilateral ABCD is a parallelogram. (see attached image)

Let A (x1, y1), B(x2, y2), C (x3, y3) & D (x4,y4) be the coordinates of A, B, C & D respectively. Draw the line BD. (see attached image)

Since the midpoint divides a side into equal parts, AP=PB and the same will apply to all sides.

According to the midpoint theorem, SR = BD/2

Same as in triangle ABD, SP is parallel to BD, and SP =BD/2

From the above two equations SR is parallel to SP and SR=SP.

As one pair of opposite sides are equal in length and parallel to each other, the resultant figure by joining the midpoints of a quadrilateral become a parallelogram.

Draw diagonal BD.

BD is the diagonal of the quadrilateral which forms two triangles ABD and BCD. Consider the triangle BCD. BD is parallel to QR.

Hence PQRS is a parallelogram

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Solve the following problem below.

1. Midpoints in a Quadrilateral

Draw a quadrilateral ABCD. Try to draw your quadrilateral so that no two sides are congruent, no two angles are congruent, and no two sides are parallel.

Let P, Q, R, and S be the midpoints of sides AB, BC, CD, and DA, respectively. Use a ruler to locate these points as precisely as you can, and join them to form a new quadrilateral PQRS. What do you notice about the quadrilateral PQRS?

Suppose your quadrilateral ABCD lies in the coordinate plane. Let (x1,y1) be the coordinates of vertex A, (x2,y2) the coordinates of B, (x3,y3) the coordinates of C, and (x4,y4) the coordinates of D. Use coordinates to prove the observation you made in part (a).

The set representing the ordered numbers is given as follows:

0.45, 52%, 10/11, 31.

The numbers for this problem are given as follows:

For the three numbers with an integer part of zero, we order them according to the decimal part, hence:

0.45, 52%, 10/11.

31 has an integer part of 31 and is greater than the other numbers, hence the ordered data-set is given as follows:

0.45, 52%, 10/11, 31.

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a) The prior probability that the selected person is a male is 0.51

b) The probability that the selected subject is a male is 92.9%.

We start by using the given information that 51% of adults in Orange County are males. We can interpret this as the prior probability of selecting a male adult randomly, which we denote by P(M). Since we know that there are only two genders, the probability of selecting a female adult is simply 1 - P(M), which is 49%.

a) To find the prior probability that the selected person is a male, we simply use the information given to us. Thus, P(M) = 0.51 and P(F) = 0.49, where F denotes the event of selecting a female adult.

b) We are given new information that the selected survey subject was smoking a cigar. We denote the event of selecting a smoker by S. We are also given the conditional probabilities of cigar smoking given the gender of the adult. Specifically, P(S|M) = 0.095 and P(S|F) = 0.017, where the vertical bar denotes the conditional probability.

We want to find the probability that the selected subject is a male given that they were smoking a cigar, denoted by P(M|S). We can use Bayes' theorem to update our prior probability based on this new information:

P(M|S) = P(S|M) x P(M) / P(S)

To find P(S), we can use the law of total probability, which states that the probability of an event can be obtained by summing over all possible ways it can occur. Thus,

P(S) = P(S|M) x P(M) + P(S|F) x P(F)

We can substitute the values given to us to find that:

P(S) = 0.095 x 0.51 + 0.017 x 0.49

P(S) = 0.05212

Using this value, we can now calculate the probability that the selected subject is a male given that they were smoking a cigar:

P(M|S) = P(S|M) * P(M) / P(S)

P(M|S) = 0.095 * 0.51 / 0.05212

P(M|S) = 0.929

This means that given the new information that the selected subject was smoking a cigar, the probability that they are a male is 92.9%.

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Complete question:

In Orange County, 51% of the adults are males. (It doesn't take too much advanced mathematics to deduce that the other 49% are females.) One adult is randomly selected for a survey involving credit card usage.

a) Find the prior probability that the selected person is a male.

b) It is later learned that the selected survey subject was smoking a cigar. Also, 9.5% of males smoke cigars, whereas 1.7% of females smoke cigars (based on data from the Substance Abuse and Mental Health Services Administration).

Use this additional information to find the probability that the selected subject is a male.

Answer: 7/10

Step-by-step explanation:

multiply 4/5 by 7/8=28/40 or 7/10

Answer:

In Bag A, the ratio of red counters to yellow counters is 1 : 4. (ii) The number of counters in the two bags is the same.

Step-by-step explanation:

Two events that are disjoint are not independent. This is because that disjoint events do not overlap, which means that if one event occurs, the other cannot. So, the occurrence of one event provides information about the absence of the other, which violates the definition of independence.

Two events A and B are considered independent if the occurrence of A has no effect on the likelihood of B occurring, and vice versa.

In other words, the probability of both events happening at the same time is equal to the product of their individual probabilities:

[tex]P(A and B) = P(A) * P(B) (B).[/tex]

This formula cannot be satisfied when two events are disjoint because if one event occurs, the other cannot occur. As a result, two disjoint events are not independent.

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The equation y < - 4 · x - 1 represents the inequality seen in the figure.

According to analytic geometry, we can derive the equation of a line from the knowledge of two points along the line. In this problem we must determine an inequality of the form:

y < m · x - b

m = Δx / Δb

Where:

We know that points (x, y) = (- 1, 3) and (x, y) = (0, - 1) are points of the line. Now we proceed to determine the equation of the line:

m = (- 1 - 3) / [0 - (- 1)]

m = - 4

b = - 1

y < - 4 · x - 1

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The unknown number's variable w is equal to -10.

In mathematics, a variable is an alphabet or phrase that represents an unknown quantity, unknown value, or unknown number. The variables are used, particularly when dealing with algebraic expressions or algebra. As an example, the variables x and 9 are constants in the linear equation x+9=4.

The following information can be written as an equation to express it:

4 + w/5 = 2

By deducting 4 from both sides of the equation, we may isolate the variable on one side and solve for w:

w/5 = -2

Then, to find w, we can multiply both sides by 5.

w = -10

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The missing number in the sequence is 64

From the question, we have the following parameters that can be used in our computation:

1, 4, 16, ____, 256, 1024, ...​

Using the above as a guide, we have the following:

To obtain the next term, we can multiply the previous term by 4:

So, we have

Next term = 16 * 4

Next term = 64

Therefore, the next term in the sequence is 64.

The completed sequence is: 1, 4, 16, 64, 256, 1024, ...

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Answer:

The radical approximations of 7.07, 7.21, and 7.93 to the nearest whole number are:

2.65

2.68

2.82

Step-by-step explanation:

Sure, here's a step-by-step explanation of finding the approximate square root of 7.07, 7.21, and 7.93 to the nearest whole number:

Start by finding an approximate square root by making an educated guess or by using a calculator.

Use the initial guess to determine if the number is closer to the actual square root or to a smaller or larger value.

Refine the estimate by averaging the guess and the number divided by the guess.

Repeat the process of refining the estimate until a satisfactory level of accuracy is reached.

Here's an example for 7.07:

An educated guess for the square root of 7.07 could be 2.7

Dividing 7.07 by 2.7 gives an estimated value of 2.61, which is closer to the actual value.

To get a more accurate estimate, the average of 2.7 and 2.61 (2.655) is taken as the new estimate.

Repeat steps 2 and 3 until the desired level of accuracy is achieved.

After several iterations, the square root of 7.07 is approximately equal to 2.65.

Similarly, you can find the approximate square roots of 7.21 and 7.93.

She travel  31.25 miles we calculate it by multiply by speed and time

Speed indicates how quickly something or someone is moving. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example because the distance is measured in metres (m) and the time is measured in seconds (s).The formula can be rearranged in three ways:

speed = distance ÷ time

distance = speed × time

time = distance ÷ speed

To calculate one of the variables (speed, distance or time) we need the other two.

As given in Question she cycled at speed 12 1/2 miles per hours

12 1/2  can be written as 12.5 miles per hours

and she cycled for 2 1/2 hours which can be written as 2.5 hours

and to find the distance how much she total travel we have to multiply the speed and time

distance = 12.5x2.5 = 31.25 miles

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Answer:

∠ B = 121°

Step-by-step explanation:

ABCD is a cyclic quadrilateral

• opposite angles sum to 180°

∠ B and ∠ D are opposite angles , then

∠ B + 59° = 180° ( subtract 59° from both sides )

∠ B = 121°

The sequence is a geometric sequence with a common ratio of 4.

What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed non-zero number called the common ratio (r).

To determine whether the sequence is arithmetic or geometric, we can look at the differences between consecutive terms.

The difference between the second and first terms is 2 - 0.5 = 1.5.

The difference between the third and second terms is 8 - 2 = 6.

The difference between the fourth and third terms is 32 - 8 = 24.

The difference between the fifth and fourth terms is 148 - 32 = 116.

Since the differences are not constant, the sequence is not arithmetic.

To determine if it is a geometric sequence, we can look at the ratios of consecutive terms.

The ratio of the second and first terms is 2/0.5 = 4.

The ratio of the third and second terms is 8/2 = 4.

The ratio of the fourth and third terms is 32/8 = 4.

The ratio of the fifth and fourth terms is 148/32 = 4.

Since the ratios are constant, the sequence is geometric with a common ratio of 4.

Therefore, the sequence is a geometric sequence with a common ratio of 4.

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The value of the equation is A = 6ab - 2bc + 12ac - b²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = 2b ( 3a - c ) + 12ac - b²   be equation (1)

On simplifying the equation , we get

A = 2b ( 3a ) - 2b ( c ) + 12ac - b²

On further simplification , we get

A = 6ab - 2bc + 12ac - b²

Hence , the equation is A = 6ab - 2bc + 12ac - b²

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The pair of functions f(x) and g(x) below that equals 0 as the limit as x goes to infinity of the quotient of f of x and g of x will be C. f(x) = ln(x); g(x) = ex

For the limit of the quotient of f(x) and g(x) to equal 0 as x approaches infinity, it is necessary for f(x) to grow more slowly than g(x).

Out of the options given, the only pair of functions where this is true is f(x) = ln(x) and g(x) = ex. As x approaches infinity, ex grows much faster than ln(x), so the limit of the quotient of these two functions as x approaches infinity is 0.

In conclusion, the correct option is C.

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Answer: To determine the amount in Heidi's 401(k) account after 15 years, we need to calculate her total contribution each month and the interest earned on that contribution over the 15-year period.

First, let's calculate Heidi's contribution each month:

11% of $3,250 = $357.50

Next, let's calculate her employer's contribution each month:

6% of $3,250 = $195

Since Heidi's contribution is $357.50, and her employer matches her contribution up to 6% of her salary, her employer will contribute $195 each month.

So, Heidi's total contribution each month is $357.50 + $195 = $552.50

Next, we can use the formula for compound interest to calculate the balance in her 401(k) account after 15 years:

A = P * (1 + r/n)^(nt)

where:

A is the balance in the account after t years

P is the principal (initial deposit)

r is the interest rate

n is the number of times the interest is compounded in a year

t is the number of years

In this case, n = 12 (because interest is compounded monthly) and t = 15 (because the calculation is for 15 years). The principal P is $552.50 (Heidi's total contribution each month). The interest rate r is 6.25%.

Plugging in the values, we get:

A = $552.50 * (1 + 0.0625/12)^(12 * 15) = $552.50 * (1.00520833)^180

Using a calculator or spreadsheet software, we can calculate this value to be approximately $27,973.81.

So, the amount in Heidi's 401(k) account after 15 years, rounded to the nearest cent, is $27,973.81.

Step-by-step explanation:

Answer:

Cos A: [tex]\frac{15}{17}[/tex]

Tan A: [tex]\frac{8}{15}[/tex]

Sin C: [tex]\frac{8}{17}[/tex]

How I did it:

Cos A: [tex]\frac{Base}{Hypotenuse}[/tex] This is the basic " fraction "

Or in similar terms: = [tex]\frac{ab}{bc}[/tex]

Cos A = [tex]\frac{15}{17}[/tex]

Tan A = [tex]\frac{Perpendicular}{Base}[/tex]

Similar terms once again = [tex]\frac{ac}{ab}[/tex]

Tan A = [tex]\frac{8}{15}[/tex]

Sin A = [tex]\frac{Perpendicular}{Hypotnuse}[/tex]

Similar terms = [tex]\frac{ac}{bc}[/tex]

Since A = [tex]\frac{8}{17}[/tex]

Thus your answers are:

Cos A = [tex]\frac{15}{17}[/tex]

Tan A = [tex]\frac{8}{15}[/tex]

Sin A = [tex]\frac{8}{17}[/tex]

To convert 640 L to cL, you would move the decimal point 4 places to the right. So the answer is 640 L = 64,000 cL.

Converting units is a common task in science, engineering, and everyday life. The conversion factor between liters (L) and centiliters (cL) is 1 L = 100 cL. To convert a quantity from liters to centiliters, you can multiply the number of liters by 100 or move the decimal point two places to the right. In this case, we have 640 L. To convert this to centiliters, we need to multiply 640 by 100, or move the decimal point two places to the right. Since there are two digits after the decimal point in 640, we can simply move the decimal point four places to the right to get 64,000 cL. Therefore, 640 L is equal to 64,000 cL.

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Answer:

4 more laps to reach the goal of 14.4 km.

Step-by-step explanation:

First, let's find the total distance covered so far: 720 m x 16 laps = 11,520 m.

Next, let's convert the goal distance to meters: 14.4 km x 1000 m/km = 14,400 m.

Finally, let's subtract the total distance covered from the goal distance to find the remaining distance: 14,400 m - 11,520 m = 2,880 m.

Since a lap is 720 m long, the remaining distance can be divided by 720 m to find the number of laps left: 2,880 m ÷ 720 m = 4 laps.

Therefore, the runner needs to run 4 more laps to reach the goal of 14.4 km.

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

The solution is, x= StartFraction t Over 4 + 2 EndFraction, is equivalent to 4 x = t + 2.

An equation can be stated  a  mathematical statement that is made up of two expressions connected by an equal sign.  In its normal form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

given that,

4 x = t + 2

or, x = (t + 2) /4

or, x = t/4 + 2/4

or, x = t/4 + 2

Hence, The solution is, x= StartFraction t Over 4 + 2 EndFraction, is equivalent to 4 x = t + 2.

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The area of the right triangular puppy pen found using the formula 1/2(b.h²) is 4900.90 feet².

What is a triangle?

A polygon with three edges and three vertices is called a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A right triangle is a specific kind of triangle that has one angle that is exactly 90 degrees.

Given,

 The length of OY = 12 feet

The length of DY = 31 feet

m∠OYD = 65°

Since SDOG is a rectangle, m∠DOY = 90°.

So the ΔDOY is a right triangle.

Area of right triangle = 1/2 * b * h²

where b = base length

          h = height

From the given figure,

b = OY = 12

h = OD

h can be found using Pythagoras' theorem.

DY² = OD² + OY²

OD² = DY² - OY² = 31² - 12²  = 817

OD = √817 = 28.58 feet = h

Therefore the area of the right triangle ΔDOY is

area =  1/2 * b * h² = 0.5 * 12 *28.58² = 4900.90 feet².  

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If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.

However, the frog slips back 1 foot while resting for an hour, so the frog would only have covered 5 feet of the well after each hour of climbing. The frog would need to climb for a total of

40/5 = 8 hours

to reach the top of the well. Additionally, the frog would need to take 8 hours of rest to make up for the slipping back.

So the total time it would take the frog to get out of the well would be 8 hours + 8 hours = 16 hours.

If the well was 40 feet deep and the frog climbs 6 feet per hour, it would take the frog 40/6 = 6.67 hours to reach the top of the well.

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The value of x and y in the quadratic and linear equation are (0.37, -137) and (-3.26 , -6.74) respectively

In the problem given;

2x² + 4x - y = -3 ..eq(i)

-2x + y = -4 ..eq(ii)

From equ(ii)

Using the linear equation;

y = 2x - 4 ...eq(iii)

Put eq(iii) into eq(i)

2x² + 4x - (2x - 4) = -3

2x² + 4x - 2x - 4 = -3

2x² + 2x - 4 = -3

Rearrange the equation;

2x² + 2x - 4 + 3 = 0

2x² + 2x - 1 = 0

Solving the quadratic equation;

x = 0.37 or -1.37

Put the value of x into eq(ii)

-2(0.37) + y = -4

y  = -3.26

or

-2(-1.37) + y = -4

y = -6.74

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The algebraic expression is h - 21 = 62

If we let "h" be Holly's original height,

The phrase "Holly's height decreased by 21 is 62" can be translated into an algebraic expression as:

h - 21 = 62

This equation represents the relationship between Holly's original height and her current height, after a decrease of 21 units.

We can solve for h by adding 21 to both sides of the equation:

h - 21 + 21 = 62 + 21

h = 83

Hence, Holly's original height was 83 units.

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Answer:

just 150x2 = 300 minutes or just 150 minutes to cook

Step-by-step explanation:

The cooking time of a turkey depends on its weight, so a 16-pound turkey will take longer to cook than an 8-pound turkey. However, without additional information such as the cooking method, temperature, and the shape and size of the turkeys, it's not possible to determine the exact cooking time for the 16-pound turkey.

The Original Price of helmet is $20.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The helmet Clare plans to buy is on sale for 20% less than the original price.

let the sale price be x.

So, the Original price is (x+5).

Also, Sales price = Original price - 20% of Original price

x= x+ 5 - 0.20(x+5)

x = x+ 5 - 0.20x - 1

0.20x = 4

x= 4/ 0.20

x= $20

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