at the zoo the length of each iguana is measured which statement is best supported by the information below

Answer:61.43

Step-by-step explanation:

yes

Answer:

Louis $61.43 now.

Step-by-step explanation:

Louis sells her bike and helmet for $88.50 and $8.75. Add these together and it gives you the total amount of money she has earned.

[tex]88.50+8.75= 97.25[/tex]

Louis now has $97.25. She then buys something for $35.82, so, subtract the amount of the basketball by the amount of money she earned to find out how much money she has left.

[tex]$97.25- 35.82=61.43[/tex]

Louis now has $61.43.  

let me know if you have any more questions on this problem. :)

To subtract two numbers in base 5, you perform the subtraction column by column, just like in base 10, but carrying and borrowing are done in base 5. Let's subtract 431 (base 5) - 144 (base 5):

431

- 144

42(1+5)

- 1 4

-------

2

42

- 1

-------

1

4

-

-------

4

431

- 144

-----

412

The approximate distance across the lake is 6.7 kilometers, which is closest to option D.

What is Pythagorean theorem?

The Pythagorean theorem is a fundamental concept in mathematics that relates to the lengths of the sides of a right triangle.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the distance across the lake is the hypotenuse of a right triangle, and the distances 6 km and 3 km are the lengths of the other two sides. Therefore, we can write:

distance across the lake = √(6 km)² + (3 km)²

distance across the lake = √(36 km² + 9 km²)

distance across the lake = √45 km²

distance across the lake ≈ 6.7 km

Therefore, the approximate distance across the lake is 6.7 kilometers, which is closest to option D.

To learn more about Pythagorean theorem from the given link:

https://brainly.com/question/14930619

#SPJ1

The values of the given trigonometric functions are 240° and 60° respectively.

What are trigonometric functions?

Trigonometric functions are mathematical functions that relate the angles and sides of a right triangle.

The three primary trigonometric functions are sine, cosine, and tangent.

The sine function (sin) relates the length of the opposite side of an angle to the length of the hypotenuse of a right triangle. It is defined as sin(θ) = opposite/hypotenuse.

The cosine function (cos) relates the length of the adjacent side of an angle to the length of the hypotenuse of a right triangle. It is defined as cos(θ) = adjacent/hypotenuse.

The tangent function (tan) relates the length of the opposite side of an angle to the length of the adjacent side of a right triangle.

Now To find

(a.)  sin⁻¹(-√3/2)

(b.)  cos⁻¹ (1/2)

For a

sin⁻¹(-√3/2)=sin⁻¹(-0.8660)=-⁻60° or 240°

and

For b

cos⁻¹ (1/2)=cos⁻¹ (0.5)=60°

Hence,

             the values of the given trigonometric functions are 240° and 60° respectively.

To know more about Trigonometric functions visit the link

brainly.com/question/9880303

#SPJ9

tower of height 105 feet and a shadow of length 117 feet. We want to find the angle of elevation of the sun, represented by the angle θ. the angle of elevation of the sun to the nearest degree is  [tex]43[/tex] degrees.

We can use the tangent function to find the angle of elevation of the sun:

tan(angle of elevation) = opposite / adjacent

In this case, the opposite side is the height of the tower (105 feet) and the adjacent side is the length of the shadow (117 feet).

tan(angle of elevation) [tex]= 105 / 117[/tex]

We can solve for the angle of elevation by taking the inverse tangent (tan^-1) of both sides:

angle of elevation [tex]= tan^-1(105 / 117)[/tex]

Using a calculator, we get:

angle of elevation  [tex]\approx 42.9[/tex] degrees

Therefore, the angle of elevation of the sun to the nearest degree is  [tex]43[/tex]degrees.

Learn more about elevation here:

https://brainly.com/question/14321045

#SPJ1

Answer:

20%

Step-by-step explanation:

Number of phone calls received second month = 4265 + 25% of 4265

                                                                               = 4265 + 0.25 * 4265

                                                                               = 4265 ( 1 + 0.25)

                                                                               = 4265 * 1.25

                                                                               = 5331.25

Number of calls in third month = 6396

Increased calls than second month = 6396 - 5331.25

                                                           = 1034.75

[tex]Increased \ percentage = \dfrac{Increased \ calls}{second \ month \ calls}*100[/tex]

                                   [tex]=\dfrac{1064.75}{5331.25}*100\\\\=19.97 \%\\\\= 20\%[/tex]

Answer: 19.5

Step-by-step explanation:

First order the numbers in ascending order: 105, 106, 107, 117, 118, 123, 125, 127, 136

Next find the median: 118

Then find the median of each quartile: First Quartile: 106.5, Second Quartile: 126

Then subtract 106.5 from 136 to find the range: 126-106.5=19.5

To find the IQR (Interquartile Range) of a set of data, we first need to find the median of the data set. The median is the middle value when the data set is arranged in order.

Arranging the given data set in order:

105 106 107 117 118 123 125 127 136

The median of this data set is the middle value, which is 123.

Next, we need to find the values of the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data set, and Q3 is the median of the upper half of the data set.

The lower half of the data set is: 105 106 107 117 118

The upper half of the data set is: 123 125 127 136

Q1 is the median of the lower half of the data set, which is:

Q1 = (107 + 117)/2 = 112

Q3 is the median of the upper half of the data set, which is:

Q3 = (125 + 127)/2 = 126

Finally, we can calculate the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 126 - 112 = 14

Therefore, the IQR of the given data set is 14.

The associative property of  (p+7) + 9 =  p+(7 + 9) so that both the sides equals p + 16.

The associative property is a property of binary operations, which are operations that involve two elements. It states that the way we group the elements in an operation does not affect the result of the operation.

For any three elements a, b, and c in a set, and a binary operation *, the associative property states that:

(a * b) * c = a * (b * c)

Addition and multiplication are associative operations.

(a + b) + c = a + (b + c) and (a * b) * c = a * (b * c)

The associative property of addition states that when adding three or more numbers, the way we group them does not affect the sum. More formally, for any three numbers a, b, and c, the associative property of addition can be written as:

(a + b) + c = a + (b + c)

In the case of (p+7) + 9, we can apply the associative property of addition as follows:

[(p+7) + 9] = p + (7 + 9)

p + 16 = p + 16

Here, we have grouped the numbers 7 and 9 together and added them first, and then added the result to p. This gives us the same sum as if we had added p and 7 first and then added 9 to the result.

Therefore, the associative property of addition tells us that we can add (p+7) and 9 in any order or group them differently, and still get the same result (p+16).

To know more about Associative property visit:

https://brainly.com/question/30111262

#SPJ1

the sunglasses will never hit the ground.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The height of the sunglasses at time t is given by the function h(t) = 16t^2 + 5776.

When the sunglasses hit the ground, their height will be 0. So we need to find the value of t that makes h(t) = 0.

16t^2 + 5776 = 0

Dividing both sides by 16, we get:

t^2 + 361 = 0.

This equation has no real solutions since t^2 is always non-negative and can never be equal to a negative number.

Therefore, the sunglasses will never hit the ground.

Learn more about function, by the following link.

https://brainly.com/question/25638609

#SPJ1

Answer:

3rd degree

3

-4

-(1/2)x³

-1/2

Step-by-step explanation:

1st blank: The largest exponent tells you the degree of the polynomial.

2nd blank: Count how many "parts" (terms) are separated by + or -

3rd: The term without variables is the constant term. Include the sign in front of it!!

4th: The term that includes the highest degree variable. Include the sign in front of it!!

5th: The number preceding the variable in the leading term. Again, include the sign...!!

Therefore, there are 36 possible values of n to satisfy the given equation.

In mathematics, an equation is a statement that asserts the equality of two expressions. Equations are formed using mathematical symbols and operations, such as addition, subtraction, multiplication, division, exponents, and roots. An equation typically consists of two sides, with an equal sign in between. The expression on the left-hand side is equal to the expression on the right-hand side. Equations can be used to model a wide range of real-world situations, from simple algebraic problems to complex scientific and engineering applications.

Here,

We can use the fact that sin(θ) + i cos(θ) = [tex]e^{(iθ)}[/tex], where e is the base of the natural logarithm.

So, the given equation becomes [tex]e^{(iθ)} ^= e^{(inθ)}[/tex]. Taking the natural logarithm of both sides, we get:

iθ = inθ + 2πik (where k is an integer)

Simplifying, we get:

nθ = (k - i)2π

Since b ≤ 2016, we know that n ≤ 2016. We can also see that k - i must be a multiple of n, so we have:

k - i = nm (where m is an integer)

Substituting this back into the equation, we get:

θ = m(2π/n)

So, the number of possible values of n is equal to the number of divisors of 2016. Prime factorizing 2016 as 2⁵ * 3² * 7, we get:

The number of divisors of 2016 = (5 + 1)(2 + 1)(1 + 1)

= 36

To know more about equation,

https://brainly.com/question/28243079

#SPJ1

The length of the third side in this right - angle triangle can be found to be 30 units.

To find the length of the hypotenuse (C) in a right-angled triangle with sides A and B given as 24 units and 18 units, respectively, you can use the Pythagorean theorem:

A² + B² = C²

In this case, A = 24 and B = 18. Plug the values into the formula:

(24)² + (18)² = C²

576 + 324 = C²

900 = C²

Now, take the square root of both sides to solve for C:

C = √900

C = 30

Find out more on length at https://brainly.com/question/30132893

#SPJ1

Answer:

about 403.1 miles

Step-by-step explanation:

262 miles is 65% of the distance to the grandmother's house. Let d be that distance.

[tex].65d = 262[/tex]

[tex]d = 403.1[/tex]

The distance from Ken's house to his grandmother's house is about 403.1 miles.

(a) An appropriate sample space S for this experiment is the set of all possible sequences of four children, where each child can be either a boy (b) or a girl (g). So, the sample space S is:

S = {bbbb, bbbg, bbgb, bgbb, gbbb, bggg, bgbg, gbgg, ggbb, gbgb, bggg, gbgg, gggg, gggb, gggg}

There are 2^4 = 16 possible outcomes in the sample space.

(b) The event E that there are three boys and a girl in the family can be represented by the set of all sequences in the sample space S that have three b's and one g. So, the event E is:

E = {bbbg, bbgb, bgbb, gbbb}

There are 4 possible outcomes in the event E.

Answer:

The average adult weighing 150 to 180 pounds should have about 1.2 to 1.5 gallons of blood in their body. 160 ounces.

Step-by-step explanation:

The minimum sample size required is 95, rounded up to the nearest integer.

We can use the formula to determine the minimum sample size required to construct the confidence interval with the specified characteristics:

[tex]n = (z^2 * s2) / E2,[/tex]

where n denotes the sample size.

z is the z-score that corresponds to the desired level of confidence (in this case, 85% corresponds to a z-score of 1.44) s2 is the population variance

E is the maximum estimate error we want to allow.

Using the given values, we obtain: [tex]n = (1.4412 * 1.96) / 0.062 n = 94.16[/tex]

The minimum sample size required is 95, rounded up to the nearest integer.

To know more about integer visit:-

https://brainly.com/question/15276410

#SPJ1

The graphical representations that would best display the data are:

A graph is a visual representation or diagram that organises facts or values. The points on the graph frequently reflect the relationship between two or more objects.

To display the weekly high temperatures in Bartow, Florida for the past six months, the following graphical representations could be used:

Therefore, the graphical representations that would best display the data are:

Learn more about graphs on:

https://brainly.com/question/11234618

#SPJ1

the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The given function is:

f(x) = -(x + 3) - 1

To find the interval over which the function is decreasing, we need to find the values of x where the function's derivative is negative.

The derivative of the function is:

f'(x) = -1

The derivative is a constant, which means the function has a constant slope of -1. Since the slope is negative, the function is decreasing over its entire domain.

Therefore, the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

Learn more about function, by the following link.

https://brainly.com/question/25638609

#SPJ1

The inequality c ≥ 20 represents the minimum number of candles that need to be sold to pay for a visit to Knotts costing $100 when each candle is sold for $5.

To write the inequality that represents c, we need to consider the cost of the visit to Knotts and the price of each candle that is being sold. Let's assume that the cost of the visit to Knotts is $100 and each candle is being sold for $5.

We know that the total amount of money she earns from selling c candles is given by 5c, and this amount must be greater than or equal to the cost of the visit, which is $100. Therefore, we can write:

5c ≥ 100

Dividing both sides of the inequality by 5, we get:

c ≥ 20

Therefore, the inequality that represents c is c ≥ 20. This means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

Learn more about inequality on:

https://brainly.com/question/24372553

#SPJ1

The largest possible value for f(4) applying the mean value theorem is 10

According to the Mean Value Theorem, there exists a value c between 0 and 4 such that:

f'(c) = (f(4) - f(0)) / (4 - 0)

Simplifying this equation, we get:

f(4) - f(0) = 4f'(c)

Since f'(x) ≤ 3 for all x, we can substitute 3 for f'(c) to obtain:

f(4) - (-2) ≤ 4(3)

f(4) + 2 ≤ 12

Therefore, we have:

f(4) ≤ 10

So the largest possible value for f(4) is 10.

Learn more on Mean Value Theorem here https://brainly.com/question/30371387

#SPJ1

Differentiating 8c to the fourth power gives 32c³, not 4 times 8c to the 4-1 power.

What is differentiation?

Differentiation is a mathematical operation that involves finding the derivative of a function with respect to one of its variables.

No, differentiating 8c to the fourth power is not equal to four times 8c to the 4-1 power.

To differentiate a term with a power, we use the power rule of differentiation, which states that:

d/dx [xⁿ] = n*x⁽ⁿ⁻¹⁾

where d/dx denotes differentiation with respect to x, n is the power of x, and x⁽ⁿ⁻¹⁾ is the derivative of xⁿ.

Applying this rule to 8c to the fourth power, we get:

d/dc [8c⁴] = 4*8c³

Notice that the power of c decreased by 1 after differentiation, not by 4 as suggested in the question.

Therefore, differentiating 8c to the fourth power gives 32c³, not 4 times 8c to the 4-1 power.

To know more about differentiation visit:

brainly.com/question/14295614

#SPJ1

The total area is 1570 square units.

Explain area

Area refers to the measurement of the size of a two-dimensional surface. It is typically expressed in square units, such as square meters or square feet. The area of a shape can be calculated by multiplying its length by its width, or by using specific formulas for more complex shapes. Area is an important concept in geometry and is used in many real-life applications, such as calculating the area of a room or a piece of land.

According to the given information

Here the base of the right triangle is 20 and the hypotenuse is 29, so we can set up the equation:

29² = 20² + h²

where h is the height of the triangle(length of dotted line) that we want to find.

Simplifying and solving for h, we get:

h² = 29² - 20²

h² = 841 - 400

h² = 441

h = √(441)

h = 21

Therefore, the length of the dotted line is 21 units

Now,

The area of a right triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. So, the area of the right triangle with base 20 and height 21 is:

A_triangle = (1/2)(20)(21) = 210

The area of a right trapezium is given by the formula A = (1/2)(a+b)h, where a and b are the parallel sides and h is the height. So, the area of the right trapezium with a longer side of 55, smaller side of 21, and height of 40 is:

A_trapezium = (1/2)(55+21)(40) = 1360

Therefore, the total area of the right triangle and right trapezium is:

A_total = A_triangle + A_trapezium = 210 + 1360 = 1570

To know more about area visit

brainly.com/question/27683633

#SPJ1

The area of the region enclosed by the curves can be found to be 1/6 square units.

To find the area enclosed by the curves y = x, y = 5x, and y = -x + 2, we first need to find the points where these curves intersect.

Intersection points of y = x and y = 5x: (0, 0)

Intersection points of y = x and y = -x + 2: Intersection point: (1, 1)

Intersection points of y = 5x and y = -x + 2: Intersection point: (1/3, 5/3)

Now we have the three intersection points: (0, 0), (1, 1), and (1/3, 5/3). The area enclosed by the curves is a triangle with vertices at these points.

To find the area of the triangle, we can use the Shoelace Formula:

Area = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Area = (1/2)|0(1 - 5/3) + 1(5/3 - 0) + (1/3)(0 - 1)|

Area = 1 / 6 square units

The area enclosed by the curves is 1/6 square units.

Find out more on area at https://brainly.com/question/9485980

#SPJ1

Answer:

It can be written in interval notation as [-5,5)

Answer:

0,95

Step-by-step explanation:

[tex] \frac{19}{20} [/tex]

Multiply the fraction by 5, so that the denominator would be equal to 100:

[tex] \frac{19 \times 5}{20 \times 5} = \frac{95}{100} = 0.95[/tex]

I don't know if I got it right, though...

Answer: The simplest form of 564/18 is 94/3.

Step-by-step explanation: Hope this helps

the probability that the student won an award for mathematics or for science is 0.6385 or approximately 64%.

How to solve probability?

To find the probability that the student won an award for mathematics or for science, we need to use the concept of set theory and the inclusion-exclusion principle.

Let A be the set of students who won awards for mathematics, and B be the set of students who won awards for science. We are interested in finding the probability of A union B, which represents the set of students who won awards for either mathematics or science or both.

From the given information, we know that |A| = 115, |B| = 42, and |A intersect B| = 21, where |X| denotes the cardinality of the set X, i.e., the number of elements in the set X.

Using the inclusion-exclusion principle, we can write:

|A union B| = |A| + |B| - |A intersect B|

Substituting the values, we get:

|A union B| = 115 + 42 - 21 = 136

Therefore, there are 136 students who won awards for either mathematics or science or both.

To find the probability of selecting a student who won an award for mathematics or for science, we divide the cardinality of A union B by the total number of students, which is given as 213:

P(A union B) = |A union B| / 213 = 136 / 213 = 0.6385 (rounded to four decimal places)

Therefore, the probability that the student won an award for mathematics or for science is 0.6385 or approximately 64%.

To know more about probability visit :-

https://brainly.com/question/13604758

#SPJ1

Total area = 63 cm² + 33 cm² + 4 cm² + 4 cm² = 104 cm²

The area of a trapezoid is given by the formula:

A = (a + b)h/2

where a and b are the lengths of the parallel sides of the trapezoid and h is the height (the perpendicular distance between the parallel sides).

To use this formula, simply plug in the values of a, b, and h and then solve for A. Note that all measurements must be in the same unit (such as centimeters or inches) for the formula to work correctly.

First, we can find the area of the rectangle with sides 7 cm and 9 cm:

Area of rectangle = length × width = 7 cm × 9 cm = 63 cm²

Next, we can find the area of the trapezoid with bases 2 cm and 5 cm and height 11 cm:

Area of trapezoid = (sum of bases × height) / 2 = ((2 cm + 5 cm) × 11 cm) / 2 = 33 cm²

Finally, we can find the area of the two squares with side lengths 2 cm and 2 cm:

Area of square 1 = side × side = 2 cm × 2 cm = 4 cm²

Area of square 2 = side × side = 2 cm × 2 cm = 4 cm²

Adding up the areas of all the shapes, we get:

Total area = 63 cm² + 33 cm² + 4 cm² + 4 cm² = 104 cm²

To know more about area visit:

https://brainly.com/question/27683633

#SPJ1

Answer: D

Step-by-step explanation:

Answer:to be honest i kinda dont know and i just can give you support so try your best or guess b

Step-by-step explanation:

Using the normal distribution, it is found that this type of fishing line have a breaking strength less than the advertised 6 pounds 27.76% of the time.

The z-score of a measure X of a normally distributed variable that has mean represented by  and standard deviation represented by  is given by the following rule:

Z = X - μ /σ

here, we have,

The z-score measures how many standard deviations the measure X is above or below the mean, depending if the z-score is positive or negative.

From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X.

The mean and the standard deviation for the breaking strengths are given as follows:

μ = 6.44 and, σ = 0.75

The proportion of times with breaking strength less than 6 inches is given by the p-value of Z when X = 6, hence:

Z = X - μ /σ

Z = (6 - 6.44)/0.75

Z = -0.59

Z = -0.59 has a p-value of 0.2776.

Hence the percentage is of 27.76%.

More can be learned about the normal distribution at brainly.com/question/4079902

#SPJ2

What is the missing information?

The question is:

How often will this type of fishing line have a breaking strength less than the advertised 6 pounds.