A water balloon is catapulted into the air so that its height h, in meters, after t seconds is given by the equation h(t) = –4.9t² + 27t + 2.5.

Answer:

12.41

Step-by-step explanation:

[tex]29 \times 0.40 = 11.6[/tex]

[tex]11.6 \times 0.07 = 0.812[/tex]

[tex]0.812 + 11.6 = 12.412[/tex]

Answer:

100 dimes.

Step-by-step explanation:

Two equations.

First modeling the total money with x as nickels and y as dimes.

0.05x + 0.1y = 12.50

Second, modeling the amount of coins.

x + y = 150

Which you can alter to substitute for in the first equation.

x = 150 - y

Subsitute.

0.05(150 - y) + 0.1y = 12.50

7.5 - 0.05y + 0.1y = 12.50

0.05y = 5

y = 100

Paul has 100 dimes and 50 nickels.

The probability of choosing a fisher from Clearwater who had a license is 54/(54+36) = 0.6, and the probability of choosing a fisher from Mountain View who did not have a license is 10/(10+90) = 0.1.

Assuming that the choices are independent, the probability of both events happening together is the product of their probabilities:

P(Clearwater had a license and Mountain View did not have a license) = P(Clearwater had a license) x P(Mountain View did not have a license)

= 0.6 x 0.1

= 0.06

Therefore, the probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license is 0.06.

Answer:

The probability that the fisher chosen from Clearwater had a license and the fisher chosen from Mountain View did not have a license is 0.06

Step-by-step explanation:

To solve this problem, we can use the multiplication rule of probability, which states that the probability of two independent events both occurring is equal to the product of their individual probabilities.Let event A be the event that a fisher chosen from Clearwater Park had a license, and let event B be the event that a fisher chosen from Mountain View Park did not have a license. Then, we need to find the probability of A and B occurring together, which we can write as P(A and B).

Using the given information, we can calculate the probabilities of events A and B as follows:

P(A) = 54/(54+36) = 0.6 (the proportion of fishers at Clearwater Park with a license)

P(B) = 10/(90+10) = 0.1 (the proportion of fishers at Mountain View Park without a license)

Since the events are independent (since no one fished at both parks), we can use the multiplication rule to find the probability of A and B occurring together:

P(A and B) = P(A) * P(B) = 0.6 * 0.1 = 0.06

Answer: Unclear

Step-by-step explanation: I can't see your image/sentence, so I can't help u

The image below (see attachment) illustrates how the rectangle with a vertex of C and a side on line CD is built.

A rectangle can be thought of as a four-sided polygon with two opposite pairs of equal sides and four interior angles that are each 90 degrees. At each corner or vertex, the two sides come together at an angle. Rectangles differ from squares in that their opposite sides are of equal length. Additionally, it is known as an equiangular quadrilateral. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. As a result, the rectangle with the stated lengths and a vertex of C is built as shown in the image attached below (see attachment).

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For f(1) = 0 the statement is true that (x - 1) is the factor of the function.

Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given a function,

f(x) = x⁶ - x⁴ + 2x² - 2

and f(1) = 0

substitute the values,

f(x) = x⁶ - x⁴ + 2x² - 2

f(1) = 1⁶ - 1⁴ + 2(1)² - 2

f(1) = 0

so when x = 1 function is zero,

so x - 1 = 0 and (x - 1) is one of the factor of function f(x).

Hence the statement is true.

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There are no such pairs. The sum of the reciprocals of any two positive integers is always greater than[tex]$\frac14$[/tex].

The sum of the reciprocals of any two positive integers is [tex]$\frac{1}{m} + \frac{1}{n}$[/tex], which is always greater than [tex]$\frac14$[/tex]. Therefore, there are no distinct ordered pairs of positive integers [tex]$(m,n)$[/tex] so that the sum of the reciprocals of m and n is [tex]$\frac14$[/tex]

For any two positive integers m and n, the sum of their reciprocals is [tex]$\frac{1}{m} + \frac{1}{n}$[/tex] which is always greater than [tex]$\frac14$[/tex] This is because [tex]\frac{1}{m}$ ,$\frac{1}{n}[/tex] are both positive numbers, and so their sum must be greater than [tex]$\frac14$[/tex]Therefore, there are no distinct ordered pairs of positive integers [tex]$(m,n)$[/tex] so that the sum of the reciprocals of m and n is [tex]$\frac14$[/tex].

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Answer:

f(x) = x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-0}{0-(-5)}[/tex] = [tex]\frac{5}{0+5}[/tex] = [tex]\frac{5}{5}[/tex] = 1

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = x + 5 , or

f(x) = x + 5

Answer:

x+5

Step-by-step explanation:

Because I said so

The volume of the ball is 267.95cm³ and the density of the ball is  0.335gcm⁻³

Density is a measure of the mass of an object per unit of volume. It is usually expressed in units of grams per cubic centimeter (g/cm3).

In this problem, the density of the ball is calculated as;

density = mass / volume

volume = volume of sphere

volume = 4/3πr³

volume = 4/3 * 3.14 * 4³

volume = 267.95cm³

The volume is 267.95cm³

The density of the ball = mass / volume

density = 90 / 267.95 = 0.335gcm⁻³

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Answer: Let's denote the length of the candle on day 1 as L.

On day 2, the length of the candle is L/2, on day 3 it is L/2^2, on day 4 it is L/2^3 and on day 5 it is L/2^4.

So, on day 5, the length of the candle is L/2^4 = L/(222*2) = L/16.

Given that the length of the candle on day 1 is 18 inches, we have:

L = 18

And the length of the candle on day 5 is:

L/16 = 18/16 = 9/8

So, the length of the candle on day 5 is 9/8 inches.

Step-by-step explanation:

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

in our experiment the totally possible cases for pulling not a heart is 40.

7 + 11 + 9 + 13 = 40

in that experiment we see that out of these 40 pulls we got 9 hearts. and therefore 40 - 9 = 31 non-hearts.

so, the experimental probability for not pulling a heart is

31/40 = 0.775 = 77.5%

Answer:

yes 77.5%

Step-by-step explanation:

A local restaurant charges $15 for a jumbo cheese pizza and $1.35 for each additional topping.

the total cost, y, for x toppings on a jumbo pizza is represented  in slope-intercept form, by the equation y = $1.35x + $15

The slope-intercept equation for the total cost, y, for x toppings on a large cheese pizza is y = mx + b, where m is the slope and b is the y-intercept.

First, we must determine the slope (m). The slope shows the $1.35 cost of each subsequent topping. So, m = $1.35.

The y-intercept must then be determined (b). The y-intercept shows the large cheese pizza's starting cost of $15. So, b = $15.

When we plug these values into the equation, we get:

y = $1.35x + $15

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Based on the fractional value, the amount of the shells that Terrence sorted is A. twelve twenty-fourths.

A fractional value is a value that represents a portion or part of the total value.

Fractional values can be depicted as proper, improper, or complex fractions.  They can also be depicted as decimals or percentages.

The remaining quantity of the shell pile = ³/₄

The quantity sorted by Terrence = ⁴/₆

The fractional value sorted by Terrence = (⁴/₆ x ³/₄) = ¹²/₂₄ = 0.5 or 50%

Thus, we can conclude that Terrence sorted 50% or ¹²/₂₄ of the shell pile.

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The work needed to build the pyramid is calculated by multiplying the area of the base by the height and the density of the stone.

The work needed to build the pyramid can be calculated by using the formula Work = Area x Height x Density. The area of the base of the pyramid can be calculated by using the formula Area = Side^2, where Side is the length of the side of the square base. In this case, the side of the square base is 7740 ft. So, the area of the base is 7740^2 ft^2. The height of the pyramid is 860 ft (due to erosion, its current height is slightly less). The density of the stone is estimated at 168 lb/ft. So, the work needed to build the pyramid is calculated by multiplying the area of the base by the height and the density of the stone, like this: Work = 7740^2 ft^2 x 860 ft x 168 lb/ft = 9.76 x 10^9 lb-ft.

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Answer:

11

Step-by-step explanation:

Let e represent the number of students with blue eyes. Then the number of students with blond hair is 2e. The total number of students is ...

 3 + e + 2e -6 = 30

We subtracted 6 because the expressions e and 2e cause the 6 students with both blond hair and blue eyes to be counted twice.

 3e = 33 . . . . add 3 and simplify

 e = 11

11 students have blue eyes.

Answer:

11

Step-by-step explanation:

11

venn daigram

The value of x is 10.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

Given;

Base=6

Perpendicular=8

Now

x^2=6^2+8^2

X^2=36+64

X^2=100

x=10

Therefore, by pythagoras theorem the answer will be 10.

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The equation of line is y = -10x + 1500 , where the slope is m = -10

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = -10x + 1500   be equation (1)

where x is the number of minutes

and y is the altitude in feet

when x = 0

Substituting the value of x = 0 in the equation , we get

y = 1500 feet

when x = 5

Substituting the value of x = 5 in the equation , we get

y = -10 ( 5 ) + 1500

y = -50 + 1500

y = 1450 feet

when x = 8

Substituting the value of x = 8 in the equation , we get

y = -10 ( 8 ) + 1500

y = -80 + 1500

y = 1420 feet

when x = 10

Substituting the value of x = 10 in the equation , we get

y = -10 ( 10 ) + 1500

y = -100 + 1500

y = 1400 feet

when x = 30

Substituting the value of x = 30 in the equation , we get

y = -10 ( 30 ) + 1500

y = 300 + 1500

y = 1200 feet

So , the plane's altitude after 5 minutes would be 1450 feet and after 30 minutes, the plane's altitude would be 1200 feet

Now , the plane will reach the ground when y = 0

0 = -10x + 1500

10x = 1500

x = 150 minutes

Hence , the equation of line is y = -10x + 1500

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The two amount of numbers are 11 and 135. 11 is a multiple of 11 and 135 is a multiple of 17. The sum of the two numbers is 146.

Step 1: One of the numbers is a multiple of 11

Let the number be 11x, where x is an integer

Step 2: The total of the two numbers is 146

Therefore, 11x + 17y = 146, where y is an integer

Step 3: Solve the equation

11x + 17y = 146

11x = 146 - 17y

x = (146 - 17y) / 11

Step 4: Find the two numbers

x = (146 - 17y) / 11

For y = 1, x = 11

Therefore, the two numbers are 11 and 17.

The two numbers that add up to 146 are 11 and 135. 11 is a multiple of 11, which means it is divisible by 11 without any remainder. 135 is a multiple of 17, which means it is divisible by 17 without any remainder. When these two numbers are added together, the sum is 146. This means that 11 and 135 are the two numbers that add up to 146. 11 is a multiple of 11 and 135 is a multiple of 17, which explains why the sum of the two numbers is 146. The two numbers together can be used to represent a variety of different mathematical equations, such as the addition of two integers or the multiplication of two fractions. Knowing the two numbers that add up to 146 can be useful in a variety of different scenarios, such as solving math problems or accounting for the total of two items.

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After 15 years, the area of the forest will be approximately 1523.4 km

A percentage is a unit used to express a portion of a whole number as a fraction of 100.

In this scenario, we are know that the area of a forest decreases by 6.25% each year. This means that each year, the area of the forest will decrease by

=> 6.25/100 times its original size.

To find the area of the forest after 15 years, we need to calculate the total decrease in area over 15 years. We can do this by multiplying the original area of the forest by the percentage decrease each year, and then repeating this calculation 15 times.

Starting with the original area of 2500km, we can calculate the first year's decrease by multiplying

=> 2500  x 100/6.25 = 157.5 km.

To find the area after the first year, we subtract

=> 2500 km - 157.5 = 2342.5 km.

We can repeat this calculation for the next 14 years to find the total decrease in area over 15 years. We can also use the calculator provided to simplify the calculation.

To do this, we enter 2500, then press the multiply button, enter 0.0625, then press the equal button, then press the subtract button, and finally enter the result from the previous calculation until we reach the final answer.

This means that the total decrease in area over 15 years was approximately

=> 1523.4 km,

which is equal to 61% of the original area of the forest

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Let assume the probability of the three events as P(A), P(B), and P(C), respectively. Then:

(a) The probability that at least one of the three events occurs is given by:

P (A or B or C) = 1 - P (not A and not B and not C) = 1 - P (not A) * P (not B) * P (not C)

where P (not A) is the complement of P (A), and similarly for P (not B) and P (not C).

(b) The probability that exactly one of the three events occurs can be calculated by adding the probabilities of each event occurring individually and then subtracting the probability that two events occur simultaneously.

P (exactly one) = P(A) + P(B) + P(C) - 2 * P (A and B) - 2 * P (A and C) - 2 * P(B and C) + 3 * P (A and B and C)

Note that the above formulas assume that the events are mutually exclusive and exhaustive, meaning that one and only one of the events must occur and the sum of the probabilities of the individual events is equal to 1.

If this is not the case, the probabilities need to be adjusted accordingly.

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Kim was solving a problem using the six steps first she read the problem then she wrote down the facts and figures next she knew she had to find a relation between what’s given and what's asked for.

After that, she formulated a plan or strategy to solve the problem. Then, she carried out the plan and solved the problem. Finally, she checked her answer to see if it made sense and if it was reasonable.

These six steps are often used in problem-solving and are a useful way to approach a problem systematically. By following these steps, one can ensure that all the relevant information is taken into consideration, a plan is developed to solve the problem, and the solution is verified before presenting it as the final answer.

The six steps are:

1. Determining the problem statement.

2. Identifying the main causes of the problem.

3. Developing viable solutions relevant to the problem.

4. Selecting one solution among the options.

5. Applying the solution on the problem at hand.

6. Evaluating the effect of the solution on the problem.

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The degree of effect refers to the extent to which any differences in the outcome variables are related to the experimental treatment. It can be quantified using various statistical measures and is an important consideration in experimental design and analysis. However, it is not the only factor to consider, and other factors such as the magnitude of effect and potential confounding variables should also be taken into account.

In experimental design and analysis, the degree to which any differences in the outcome variables are related to the experimental treatment is an important consideration. This is typically referred to as the "degree of effect" or "degree of difference."

The degree of effect refers to the extent to which the experimental treatment produces differences in the outcome variables being measured. This can be quantified using various statistical techniques, such as the analysis of variance (ANOVA) or regression analysis, which compare the variation in the outcome variable between groups or over time. It is typically expressed as a statistical measure, such as a p-value or a confidence interval, which indicates the level of confidence that can be placed in the observed differences. A low p-value or a narrow confidence interval indicates a high degree of effect, indicating that any observed differences are likely to be related to the experimental treatment rather than chance or other factors.

In addition to the degree of effect, it is also important to consider the magnitude or size of the effect. This refers to the extent or strength of the differences between the treatment groups, and can be expressed using various effect size measures, such as Cohen's d or eta-squared. A larger effect size indicates a stronger or more meaningful difference between the groups, and is generally considered to be more important than a smaller effect size.

However, it is important to note that the degree of effect and magnitude of effect are not the only factors to consider when evaluating the results of an experiment. Other factors, such as the study design, sample size, and potential confounding variables, can also affect the interpretation of the results and the conclusions that can be drawn.

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The domain of the function here is {0 ≤ x ≤ 600}. The first option is the right answer.

The domain of a function is the set of all input values (or independent variables) for which the function is defined and produces a valid output (or dependent variable). It is the set of values that can be plugged into a function and yield a valid result.

The domain of this function in this context is {0 ≤ x ≤ 600}.

This is because x represents the number of t-shirts Henry sells and he has ordered 600 shirts. So, he can only sell a non-negative number of shirts (x ≥ 0) and a maximum of 600 shirts (x ≤ 600). Any values outside this range are not meaningful in this context, hence they are not part of the domain.

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Answer:

30/100

Step-by-step explanation:

25%= 25/100

50%= 50/100

3/100 is in the middle of the two fractions. So one of the possible answer can be 30/100 or 30%

Answer:

[tex]\sf \dfrac{2}{5}[/tex]

Step-by-step explanation:

"per cent" means "per hundred".  Therefore, to change a percent to a fraction, remove the % sign and place the number as the numerator of a fraction with 100 as the denominator.

[tex]\sf 25\%=\dfrac{25}{100}[/tex]

[tex]\sf 50\%=\dfrac{50}{100}[/tex]

Any percent between 25% and 50% can be written as a fraction in the same way.  

Choose a number between 25 and 50, place it as the numerator of a fraction with 100 as the denominator:

[tex]\sf \dfrac{40}{100}[/tex]

Now reduce the fraction to its simplest term by dividing the numerator and denominator by the greatest common factor (GCF):

[tex]\sf \dfrac{40 \div 20}{100\div 20}=\dfrac{2}{5}[/tex]

Therefore, the fraction ²/₅ is between 25% and 50% as it is equivalent to 40%.

The diameter of circle A is equal to line segment TB.

In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Based on the information provided about circle A, we can reasonably infer and logically deduce that its diameter is represented by line segment TB. Furthermore, the radius of circle A can be calculated as follows;

Diameter = radius + radius

Diameter = TA + AB

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The confidence interval for the proportion of adults who approve of the candidate is given as follows:

(0.45, 0.51).

A confidence interval is obtained as the proportion estimate plus/minus the margin of error.

The parameters for this problem are given as follows:

Hence the bounds of the confidence interval are given as follows:

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Work Shown:

c^5 x c

c^5 x c^1

c^(5+1)

c^6

The rule is to add the exponents when multiplying exponential expressions. The bases must be the same. The rule in symbolic form is a^b*a^c = a^(b+c)

x equals 1 ± the square root of 5 end root