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age in years
c. What is the median age of dogs at the dog park?
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d. Explain how you found the value of the median.
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Answer:

62

Step-by-step explanation:

Equation: x +28 =90

x = 59°

Measure of one angle = 59°

Measure of another angle = 31°

Equation to calculate the measurement: x + x - 28 = 90Given,

In geometry, an angle is formed when two rays are joined at their endpoints. These rays are called the sides or arms of the angle.

Given,

Sum of two angles = 90°

One angle is 28° larger than other

Let the measurement of one angle is x

then other angle = x - 28°

But,

x +  x - 28° = 90°

2x - 28° = 90°

2x = 90° + 28°

x = 118°/2

x = 59°

one angle = 59°

other angle = 59° - 28° = 31°

Hence, 59° is measure of one angle

and 31° is measure of other angle.

x + x - 28 = 90 is the Equation to calculate the measurement.

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Answer: (7,10)

Step-by-step explanation:

The second statement is the contrapositive of the first is the statement that relates the second statement and the first when the terms "XY = 7x" are used. The correct option is D. Contrapositive.

Contrapositive is a type of conditional statement that interchanges the hypothesis and conclusion while negating both. It is not a standard operation like converse, inverse, or hypothesis. The statement P-> Q is known as the original statement, where P is the hypothesis and Q is the conclusion, and this statement is also a conditional statement. Then the negation of P-> Q is the inverse, the converse is Q-> P, and the contrapositive is ~Q-> ~P.

The contrapositive of a conditional statement is a new statement obtained by reversing the hypothesis and conclusion of the original conditional statement and negating both parts. Example of Contrapositive

If an even integer is divided by 2, then the result is an integer. The contrapositive of the statement "If an even integer is divided by 2, then the result is an integer" is "If a number is not an integer, then it is not even."

This contrapositive statement is obtained by reversing the hypothesis and conclusion of the original conditional statement and negating both parts. Hence, D is the correct option.

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Answer:

a) Non car si le fils a 10 ans la mère a 30 ans et le père 33 or 10+30+33=73

b) Oui car si le fils a 12 ans la mère a 36 ans et le père 39 et 12+36+39=87

Step-by-step explanation:

The tens place is what we have to compare to determine the greater of the given numbers -7295 and 7259

To determine which number, 7259 or -7295, is greater, we can compare their place values starting with their leftmost digit.

7295 and 7259 have sevens in the thousands place; 7259 also has one; however, when we compare the next digit -7295 has twos while 7259 only has one in its hundreds place.

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Answer: 28

Step-by-step explanation:

28 is thhe missing number

The doubling time or half-life and understanding the properties of  functions, you can graphically represent the behavior of the quantity over time.

To graph an exponential function using the doubling time or half-life, follow these steps:

Understand the exponential function: An exponential function is of the form f(x) = a * bx, where 'a' is the initial value, 'b' is the base, and 'x' is the independent variable.

Doubling time: If you know the doubling time, which is the time it takes for the quantity to double, you can use it to determine the value of 'b'. The formula to calculate 'b' is b = 2(1/doubling time).

Half-life: If you know the half-life, which is the time it takes for the quantity to reduce to half its initial value, you can use it to determine the value of 'b'. The formula to calculate 'b' is b = 0.5^(1/half-life).

Determine the initial value 'a' based on the given information or observation.

Use the values of 'a' and 'b' to create ordered pairs (x, y), where 'x' represents time and 'y' represents the quantity. Choose several values of 'x' to calculate 'y' using the exponential function formula.

Plot the ordered pairs on a graph, with 'x' on the horizontal axis and 'y' on the vertical axis.

Connect the plotted points with a smooth curve to represent the exponential growth or decay. By using the doubling time or half-life and understanding the properties of exponential functions, you can graphically represent the behavior of the quantity over time.

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Answer:

She can expect 12 green shells.

There are 60 green shells out of a total of 1000; this makes the probability of drawing a green shell 60/1000.  If she repeats this process with replacement 200 times, the expected amount of green shells would be

60/1000(200) = 12000/1000 = 12

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

3/9 divide both sides by 3 for simplest form

1/3

Answer:

D. $9.50

Step-by-step explanation:

If you take the $155 and subtract the $15 per lawn mowed you get $95. If then you add up the total hours he spent mowing (10) and divide the $155 by the 10 you end up with $9.50 for each hour he spent mowing.

The equation for the forested area for t years after 1990 is  

y =  34400 \((0.983)^t\).

What is exponential decay?

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

Here the initial forest area a = 34400 square kilometer.

Average rate = 1.7% = 1.7/100 = 0.017.

Now using exponential decay formula then,

=> y = a\((1-b)^t\)

Where t = number of years.

=> y = 34400(\(1-0.017)^t\)

=> y =  34400 \((0.983)^t\)

Hence the equation for the forested area for t years after 1990 is  

y =  34400 \((0.983)^t\).

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Answer:

1/15

Step-by-step explanation:

Step 1 find probability of pulling 1 pink marble

Like stated previously probability = # of favorable outcomes / # of possible outcomes

The favorable outcomes is what we want to happen

We want to pull a pink marble and there are a total of 3 pink marbles

So # of favorable outcomes = 3

To find the # of possible outcomes we simply find the number of marbles. There are a total of ten marbles

So probability of pulling one pink marble = 3/10

Step 2 find the probability of pulling another pink marble ( IMPORTANT NOTE: It says to find the probability of pulling 2 pink marbles if the first one is NOT put back before the second pull. this meaning that we must subtract 1 from the total # of marbles and 1 from the total # of pink marbles )

3 - 1 = 2

10 - 1 = 9

So after the first pull there would be 2 pink marbles out of 9 total marbles

So the probability of pulling a pink marble on the second pull is 2/9

Finally we multiply the two probabilities together to find our answer

3/10 * 2/9 = 1/15

Answer: 125 ft.

Step-by-step explanation:

Assuming the perimeter of the park is 400 ft, the equation can be represented as

2l + 2w = 400

Since we know that the width is 50 ft shorter than the length, using algebra, you replace the variable w, with

2l + 2(l-50) = 400

Then, solve for variable l, or length

2l +2l - 100 = 400

4l = 500

l = 125

Now, plug in l and solve for w

2(125) + 2w = 400

250 + 2w = 400

2w = 150

w = 75

2(125) + 2(75) = 400

250+150 = 400

400=400

l = 125, w = 75

So the length is 125 ft

Answer:

125

Step-by-step explanation:

400 is perimeter!

50+w = Length

w = width

Solve:

50+ w + w +w + w + 50 = 400

100 + 4w = 400

4w = 300

w = 75

if w is 75, then length is = 75 +50

Length = 125

Answer:

angle c = 32.204°

The equation is x = 25 for 12 less than one-fifth of a number is -7. The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

The number will be x.

(1/5)x can be used to represent "one-fifth of a number."

Consequently, "12 less than one-fifth of a number" may be expressed as:

(1/5)x - 12

We may put up the equation because the problem statement states that this expression equals -7:

(1/5)x - 12 = -7

We may first add 12 to both sides of the equation to find x:

(1/5)x = 5

Next, multiply each side by 5:

x = 25

Consequently, the following equation represents the problem statement:

(1/5)x - 12 = -7

Moreover, x = 25 is the answer.

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A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

The denominator is the value written at the bottom of a fraction.

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Numerator:

It is the value written at the top.

Denominator:

It is the value written at the bottom when we write a fraction.

Example:

Fraction:

1/2, 3/4, and 5/6.

1, 3, and 5 are the numerator.

2, 4, and 6 are the denominator.

Thus,

The denominator is the value written at the bottom of a fraction.

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Answer:

3 pizzas

Step-by-step explanation:

34-4=30

30/10=3

Answer:

3 pizzas

Step-by-step explanation:

34-4=30 since we already know the delivery fee

30/10=3 since we have 30 dollars left without the delivery fee we are just left to divide 30 by 10 to get the total number of pizzas

Answer:

22

Step-by-step explanation:

multiply 5 and 8 , then multiply 2 and 9 . once you get your answer you subtract the 40-18

The value of the equation 5y - 2z = 22

What is an Equation?

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 expression be A = 5y - 2z

The value of y = 8

The value of z = 9

So , substituting the value of y and z in the equation , we get

A = 5y - 2z

A = 5 ( 8 ) - 2 ( 9 )

A = 40 - 18

A = 22

Therefore , the value of A = 22

Hence , the value of the equation 5y - 2z = 22

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The operation that Amjed should perform to determine the relative frequency of a person over 30 years old who prefers to ride a mountain bike is given as follows:

2) Divide 25 by 462.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of people is given as follows:

58 + 164 + 215 + 25 = 462.

Out of these people, 25 prefer mountain bike, hence the relative frequency is given as follows:

25/462.

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Answer:

tan(C) = √3/√2

Step-by-step explanation:

First, using Pythagorean Theorem, find AC.

=> AC = √(3√5)² - (3√3)²

=> AC = √45 - 27

=> AC = √18

=> AC = 3√2

tan C = 3√3/3√2

= √3/√2

Answer:

x = -32

Step-by-step explanation:

6(x + 15) = -102

Distribute the 6 inside the parenthesis.

6x + 90 = -102

Subtract 90 from both sides.

6x = -192

Divide both sides by 6.

x = -32.

Proof:

6(x + 15) = -102

Substitute variable.

6(-32 + 15) = -102

Add -32 and 15.

6(-17) = -102

Multiply 6 and -17.

-102 = -102.

Answer:

x = - 32

Step-by-step explanation:

6(x + 15) = - 102 ( divide both sides by 6 )

x + 15 = - 17 ( subtract 15 from both sides )

x = - 32

Answer:

a) factors of polynomial are: (x+1)(x-2)(x-5)

b) the required polynomial in standard form is: \(\mathbf{x^3-6x^2+3x+10}\)

Step-by-step explanation:

The polynomial has zeros at -1,2,5

Part A) Write the three factors of the polynomial

we have x=-1, x=2 and x=5 as zeros of polynomial

so factors will be:

(x+1)=0, (x-2)=0, (x-5)=0

So, factors of polynomial are: (x+1)(x-2)(x-5)

Part B) Write the polynomial in standard form

For finding polynomial, we will multiply all the factors i.e

(x+1)(x-2)(x-5)

\((x+1)(x-2)(x-5)\\=(x(x-2)+1(x-2))(x-5)\\=(x^2-2x+x-2)(x-5)\\=(x^2-x-2)(x-5)\\=x(x^2-x-2)-5(x^2-x-2)\\=x^3-x^2-2x-5x^2+5x+10\\=x^3-x^2-5x^2+5x-2x+10\\=x^3-6x^2+3x+10\)

So, the required polynomial in standard form is: \(x^3-6x^2+3x+10\)

Hence, Six ( 6 ) alarms are used to certain that a burglar is trying to enter and get detected by at least one alarm.

Given;

There are many automatic burglar alarms in a sizable bank vault.

The likelihood that a burglar will be discovered by a single alarm is 0.55.

We need to get;

How many of these alarms should be installed to be 99% confident that at least one alert will detect a thief attempting to enter

The probability of one alarm has a likelihood of failing to detect a burglar is

1 - 0.55 = 0.45

Let's say there are ' n ' alerts.

The likelihood that not one of the ' n ' alarms will sound is 0.45ⁿ.

The likelihood that at least one of the alarms catches the intruder is then just 1 - 0.45ⁿ.

This probability should be 99%, as desired.

In other words, if we solve for n and get

1 - 0.45ⁿ = 0.99

n = 5.76

n ≅ 6

Therefore, 6 alarms were utilized.

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Step-by-step explanation:

a. Belle as she only missed 50 questions where as Aurora missed 78. (500-450) and (650-572)

b. Belle scored 90% (450/500=0.9)

Answer:

a. Belle scored better, by scoring 2% more than Aurora.

b. She scored 90%

Step-by-step explanation:

Make your denominator out of a 100

So you will divide by 6,5

572÷6,5/650÷65

= 88/100

=88%

And divide the other by 5

450÷5/500÷5

=90/100

=90%

Answer:

her speed in still water = 11 km/hour

the speed of the current = 9 km/hour

Step-by-step explanation:

x = Ritu's speed of rowing.

y = the sites of the river water flowing

x + y = 20 km / 2 hours = 10 km / hour

x - y = 4 km / 2 hours = 2 km / hour

x = 2 + y

2 + y + y = 20

2y = 18

y = 9 km/hour

x = 2 + y = 2 + 9 = 11 km/hour

Speed of water while upstream is (x + y) km/hr,

downstream is (x – y) km/hr,

2(x + y) = 20 x + y = 10 ………… (i)

2(x – y) = 4 x – y = 2 …………… (ii)

x + y = 10

x - y = 2

_______________

x = 12

\(x = \frac{12}{2} = 6\)

(ii), Substituting the value,

(i), x + y = 10 6 + y = 10 y = 10 – 6

∴ y = 4

∴ Speed of Ritu in still water, x = 6 km/hr. in current water, y = 4 km/hr.

The mean for this binomial distribution is 12.

In probability theory, the mean of a binomial distribution is the product of the number of trials (n) and the probability of success in each trial (p).

Therefore, to find the mean of a binomial distribution with n = 20 and p = 3/5, we can simply multiply these two values together:

mean = n * p

= 20 * 3/5

= 12

So, the mean for this binomial distribution is 12. This means that on average, we can expect to see 12 successes in 20 independent trials with a probability of success of 3/5 in each trial

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