Todd throws a ball from his tree house. The height in feet of the ball, h(t), above the ground after t seconds is modeled by the function h(t) = −3t2 + 9t + 12. Select the appropriate domain for the function.

Answer:

321489

Step-by-step explanation:

The surface area of the triangular prism is 162 square inches.

In geometry, a prism is a three-dimensional solid shape that has two identical, parallel faces (called bases) and rectangular or parallelogram-shaped sides. The sides connect the bases, and their shape determines the type of prism.

To find the surface area of the triangular prism, we need to find the areas of all five faces and add them together.

The area of each triangular base is:

A = (1/2)bh

where b is the length of the base (which is equal to 4 in) and h is the height (which is equal to 3 in).

A = (1/2)(4 in)(3 in) = 6 in²

So the total area of both triangular bases is:

2A = 2(6 in²) = 12 in²

The area of each rectangular side is:

A = lw

where l is the length (which is equal to 10 in) and w is the width (which is equal to 5 in).

A = (10 in)(5 in) = 50 in²

So the total area of all three rectangular sides is:

3A = 3(50 in²) = 150 in²

Therefore, the total surface area of the triangular prism is:

12 in² + 150 in² = 162 in²

Thus, the surface area of the triangular prism is 162 square inches.

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The greater angle has a 67.5° degree measurement. When two angles' measurements add up to 90°degrees, they are said to be complimentary.

Call that angle we're looking for "x" for convenience.

The degree that, if added to x, makes x equal 90° degrees is known as the compliment of x.

We now know that 3x, or 3 times x, is the compliment of x.

With this knowledge, we can construct the following equation:

x + 3x = 90°

combining comparable equations;

4x = 90°

x = 22.5°, when both sides are divided by 4.

As a result,

3x = 3(22.5°) = 67.5° degrees is the measurement of the greater angle, which is the complement of x.

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Answer:

(-8.89, -26.69)

Step-by-step explanation:

To find the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1), we can use the following steps:

[tex]\sqrt{(2 - (-|a|))^2 + (1 - (-3|a|))^2} = 5\\\sqrt{(2 + |a|)^2 + (1 + 3|a|)^2} = 5[/tex]

[tex]a^2 + 8a - 8 = 0[/tex]

[tex]a = \frac{-8 ±\sqrt{8^2 - 4(1)(-8)}} {(2(1))}\\a = \frac{-8 ± \sqrt{96}}{ 2}\\a = -4 ± 2\sqrt{6}[/tex]

[tex]a = -4 - 2\sqrt(6)[/tex]

(x, y) =[tex](-|-4 - 2\sqrt(6)|, -3|-4 - 2\sqrt(6)|)[/tex]

(x, y) ≈ (-8.89, -26.69)

Therefore, the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 from P(2,1) is approximately (-8.89, -26.69).

Answer:two lines are parallel if their slopes are equal and they have different y-intercepts

Step-by-step explanation:

Answer:

Vertically opposite angles are always same.

Straight angle=180°

Angle MQN=70°

Answer:

x = [tex]\frac{53}{40}[/tex]

Step-by-step explanation:

18 7/8 + __ = 20 1/5

18 7/8 = 151/8

20 1/5 = 101/5

[tex]\frac{151}{8}[/tex] + x = [tex]\frac{101}{5}[/tex]

x = [tex]\frac{101}{5}[/tex] - [tex]\frac{151}{8}[/tex]

x = [tex]\frac{53}{40}[/tex]

So, the answer is [tex]\frac{53}{40}[/tex]

Thus, the length of chord BD of the given circle is found to be 8.5 units.

A chord is indeed a straight line that connects two points on a circle's circumference. Because it connects to points on the circle's perimeter, the diameter is thought to be the chord with the longest length.

The lengthiest chord in a circle is called the diameter, and the chord's perpendicular distance to the circle's centre is zero.

Given that: From diagram.

Now, in right triangle, MAD, using the Pythagorean theorem:

(AD)² = (AM)² + (MD)²

(9.5)² = (4)² + (MD)²

(MD)² = 9.5² -  4²

(MD)² = 90.25  - 16

(MD)² = 74.25

MD = 8.5

Thus, the length of chord BD of the given circle is found to be 8.5 units.

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The mean of the data set is 25, the median is 25, the range is 20, the variance is 20, and the standard deviation is 4.47.

Given the dataset:

x = 30, 20, 35, 25, 15

N = 5

Mean of the data set is the average of the dataset. To find the average, we add up all the numbers and divide by the total number of values:

Mean (Xbar) = (30 + 20 + 35 + 25 + 15) / 5 = 25

Median is the number that fall at the middle of the dataset. To find the median of the data set, we need to arrange the numbers in order from smallest to largest:

15, 20, 25, 30, 35

The median is the middle number, which is 25 in this case.

Range of the data set can be calculated by subtract the smallest value from the largest value:

Range = 35 - 15 = 20

Standard Deviation and Variance

First find the deviations of each value from the mean:

(x - Xbar) = d

30 - 25 = 5

20 - 25 = -5

35 - 25 = 10

25 - 25 = 0

15 - 25 = -10

To find the variance, we square each deviation, add them up, and divide by the number of values:

Variance = d²/N

               = (5² + (-5)² + 10² + 0² + (-10)²) / 5

               = 100/5 = 20

To find the standard deviation, we take the square root of the variance:

Standard Deviation = sqrt(variance)

                                 = sqrt(20)

                                 = 4.47 (rounded to two decimal places)

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The best percentage bar graph that represents Camryn's data is:

C Winter | Spring | Summer | Fall

0% 20% 40% 60% 80% 100%

A bar graph's purpose is to visually convey relational information quickly. The bars show the value for a specific type of data.

This is because the graph correctly shows the percentage of students who prefer each season, with the bar for each season extending to the appropriate percentage mark on the graph. It also clearly labels each season under the corresponding bar.

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Therefore , the solution of the given problem of volume comes out to be the other leg of the right triangular pyramid's base is 3 yards long.

A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.

Here,

Let's use "x" yards to represent the other leg of the right triangle pyramid's base.

A pyramid's volume can be calculated using the following equation: => Volume = (1/3) * Base Area * Height

In this instance, we are informed that the pyramid has a volume of 168 cubic yards and a height of 14 yards.

=> 168 = (1/3) * 14 * base area

The base area can be estimated as (8 * x)/2 = 4x because we know that one leg of the base is 8 yards long and the other leg is designated as "x" yards.

=> 168 = (1/3) * 4x * 14

=> 168 = (4/3)x * 14

=>  168 = (4/3) * 14x

=> 168 = 56x

=> x = 168/56

=> x = 3

Therefore, the other leg of the right triangular pyramid's base is 3 yards long.

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Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

To represent a+b using the parallelogram method,

we must draw vectors representing a and b.

The initial point of vector a is (1, 3), and its terminal point is (-4, -2). The initial point of vector b is (-4, -2), and its terminal point is (1, 3).

Using the vector tool, we then  draw the vectors a and b. We start at the initial point of each vector and select the terminal point.

Vector a: start at (1, 3) and end at (-4, -2)

Vector b: start at (-4, -2) and end at (1, 3)

We the diagonal, we start at the initial point of vector a, (1, 3), and draw a line parallel to vector b that passes through the initial point of vector b, (-4, -2). This line intersects the line parallel to vector a that passes through the initial point of vector b at point (2, 7). This point is the terminal point of the diagonal vector, which is a+b.

We use the vector tool, we can draw vector a in blue, vector b in red, and vector a+b in green.

Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

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After answering the presented question, we may conclude that  As a percentage result, around 74.43 grammes of the drug will remain after 18 hours.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also used on occasion. However, it is commonly indicated using the percent symbol "%." The % amount has no dimensions. Percentages are just fractions with a denominator of 100. Place a percent sign (%) next to a number to indicate that it is a percentage. For example, if you answer 75 out of 100 questions properly on a test (75/100), you score a 75%. Divide the money by the total and multiply the result by 100 to calculate percentages. The percentage is derived by multiplying (value/total) by 100%.

A substance's radioactive decay rate is expressed as a percentage per unit time. This indicates that the amount of material left after each unit of time will be lowered by the set percentage.

We may use the exponential decay formula to this problem:

[tex]N(t) = N_0 * e^{(-kt)}[/tex]

where:

N₀  = starting drug quantity

N(t) = the amount of material that remains after time. t k = decay constant (related to decay rate)

t = the amount of time that has passed

To calculate the amount of material left after 18 hours, we must first determine the value of k. Using the rate of decay stated in the issue, we may accomplish the following:

[tex]3.75% = k * 1 hour\\k = 0.0375/hour\\N(18) = 150 * e^{(-0.0375*18)}\\N(18) = 74.43 grams \\[/tex]

As a result, around 74.43 grammes of the drug will remain after 18 hours.

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Answer:

no solution

Step-by-step explanation:

3r + 10 - 3r = 15 ← collect like terms on left side

10 = 15 ← false statement

this false statement indicates the equation has no solution

Answer: 1.75

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Since the garden bed looks like the shape of a trapezoid the equation to find the area of a trapezoid is A = 1/2h (base 1 + base 2)

The area is already given so you can just plug it in. Also you can plug in the bases.

21 = 1/2h (3 + 4)

21 = 1/2h (7)  rewrite

21 = 1/2(7)h

21 = 3.5h  Divide both sides by 3.5

6 = h

Answer:

Since there are only yellow and green balls in the tub, there is no possibility of picking a red ball. Therefore, the probability of picking a red ball is zero.

(i) The probability of picking a yellow ball can be calculated by dividing the number of yellow balls by the total number of balls. In this case, there are two yellow balls and three green balls, so the total number of balls is 2 + 3 = 5. The probability of picking a yellow ball is 2/5 or 0.4, which is 40%.

(ii) Similarly, the probability of picking a green ball can be calculated by dividing the number of green balls by the total number of balls. In this case, there are three green balls and five total balls. Therefore, the probability of picking a green ball is 3/5 or 0.6, which is 60%.

(iii) As mentioned earlier, there are no red balls in the tub. Hence, the probability of picking a red ball is 0.

Part a: Ratios of side = 1:3 ; Ratios of Area of base = 1: 9 ; Ratios of volume = 1: 27.

Part b: volume of medium box = 5832 cu. in .

A solid shape comprising six square faces is called a cube. Because every square face has the identical side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is called to as a vertex.

Given data:

Formula for the volume of cube :

V = side³

216 = x³

x = ∛216

x = 6 in.

Part A: length, with and height of cube is triples.

new side = 3*old side

new side = 3x

Ratios of side:

new side / old side = x / 3x  = 1/3

new side : old side = 1:3

Area of base = side²

Ratios of Area of base:

new area / old area = x² / (3x)²

new area / old are =  x² / 9x² = 1/9

new area : old are = 1: 9

Ratios of volume:

new vol / old vol = x³ / (3x³)

new vol / old vol = x³ / 27x³ = 1/27

new vol : old vol = 1:27

Part b: volume of medium box:

V = (3x)³

V = (3*6)³

V = (18)³

V = 5832 cu. in

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Answer:

[tex]\frac{sin(A)}{a}[/tex]

The percentage of Kira's free throws is 68%.

We have,

From the grid,

We can see that,

There are 25 boxes.

Now,

The number of shaded boxes = 17

Now,

The percentage of the shaded boxes.

= 17/25 x 100

= 17 x 4

= 68%

Thus,

The percentage of Kira's free throws is 68%.

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The complete question.

The shaded area on the grid represents the part of Kira's free throws that she made in the basketball practice today.

Find the percentage of Kira's free throws.

The statement that is false, given the table of Ms Stewart's class would be A. 15 % of her students are in biology.

The table shows that out of all he students, Ms. Stewart has 35 % that are doing Biology and not 15 %. But, she does have 15 % of Freshmen doing Biology and not of all her students.

30 % of the students are indeed engaged in doing physical science, and 35 % of her students are in chemistry from the table. 45 % of the total cohort that Ms. Stewart teaches are freshmen.

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The algebraic expression that represents the age of Ethan's dad is 4a - 5

Let's start by defining a variable to represent Ethan's age. We'll call this variable "a".

According to the problem, Ethan's dad is five years younger than four times Ethan's age. So, if we multiply Ethan's age by 4 and then subtract 5 years, we'll have the age of Ethan's dad.

Algebraically, we can represent this as:

4a - 5

Therefore, the algebraic expression that represents the age of Ethan's dad is 4a - 5.

Solve for x by simplifying both sides of the equation and isolating the variable.

[tex]3\frac{2}{3}x=2\frac{2}{5}[/tex]

Convert mixed numbers to improper fraction :

[tex]3\frac{2}{3} =\frac{11}{3}[/tex]

[tex]\frac{11}{3}x=2\frac{2}{5}[/tex]

Convert mixed numbers to improper fractions:

[tex]2\frac{2}{5} = \frac{12}{5}[/tex]

[tex]\frac{11}{3}x=\frac{12}{5}[/tex]

Multiply both sides by 3

[tex]11x=\frac{36}{5}[/tex]

Divide both sides by 11

[tex]x=\frac{36}{55}[/tex]

Therefore, [tex]3\frac{2}{3} x=2\frac{2}{5}[/tex] = [tex]x=\frac{36}{55}[/tex]

Steve sold 252 fruit baskets for the fundraiser. Therefore, we can find how many baskets Evie sold by using the ratio of her sales to Steve's sales, which is given as 25 baskets for each 100 baskets Steve sold.

We can set up a proportion to solve for the number of baskets Evie sold:

25/100 = x/252

Here, x represents the number of fruit baskets Evie sold.

To solve for x, we can cross-multiply and simplify:

25 * 252 = 100 * x

6300 = 100x

x = 63

Therefore, Evie sold 63 fruit baskets for the fundraiser.

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An equation that best models this set of data is: D. y = 9.74x - 0.06

In this scenario, the hours worked would be plotted on the x-axis (x-coordinate) of the scatter plot while the earnings would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a linear equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the hours worked and earnings, an equation for the line of best fit is given by:

y = 9.74x - 0.06

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I hope this helps you.

Answer: 285 mg is more than 34.4 mg

Step-by-step explanation:

To compare the two quantities, we can simply look at the whole numbers before the decimal point.

285 is a larger whole number than 34, so we can say that 285 mg is more than 34.4 mg.

The decimals after the whole numbers are used to represent the fractions of the numbers.

Recall the general equation for a line in slope-intercept form:

[tex]y=mx+b[/tex]

where:

[tex]\text{y = y-coordinate}[/tex]

[tex]\text{m}=\bold{slope}[/tex]

[tex]\text{x = x-coordinate}[/tex]

[tex]\text{b = y-intercept}[/tex]

In this equation, if you isolate for [tex]y[/tex], you end up with an equation that looks like this:

[tex]-4x+y=0[/tex]

[tex]-4x +4x+y=0+4x[/tex]

[tex]\implies y=4x+0[/tex]

Recall that in direct variation, the graph goes through the origin, (0,0). Since the y-intercept of this equation is 0, this means the graph intersects the origin. Thus, this graph represents direct variation.

If you were to graph the line, you would see the intersection at (0,0):

graph[tex]\{y=4x [-12.66, 12.65, -6.33, 6.33]\}[/tex]

The difference in volume between the two boxes would be = 156in³

To calculate the difference in volume between the boxes is the find the individual volume of the boxes using the formula ;

Volume = length×width×height.

For box 1 = length = 12in, width = 7¾in, height= 2in

Vol = 12×7¾×2 = 186in³

For box 2; length = 3⅔in, width = 3½in, height= 2⅓in

Volume = 3⅔×3½×2⅓ = 30

The difference = 186-30 = 156in³

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The inflection occurs at x = n*pi, while the absolute extreme points, while the critical points can be found with the expression 5 + 5cos(x) = 0.

To find local extreme points, absolute extreme points, and inflection points, we will first take the first and second derivatives of the function.

y = 5x + 5sin(x)

y' = 5 + 5cos(x)

y'' = -5sin(x)

To find critical points, we set the first derivative equal to zero.

5 + 5cos(x) = 0

cos(x) = -1

x = pi

This is the only critical point, so we only need to evaluate the function at x = pi to find any extreme points.

y(pi) = 5pi - 5

So the absolute minimum occurs at (pi, -5).

To find inflection points, we set the second derivative equal to zero.

-5sin(x) = 0

sin(x) = 0

x = k*pi, where k is an integer.

So the inflection points occur at x = n*pi, where n is an integer.

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Answer:

We need to convert both measurements to the same unit in order to compare them. Let's convert 6 1/3 feet to inches:

1 foot = 12 inches

6 feet = 6 x 12 = 72 inches

1/3 foot = (1/3) x 12 = 4 inches

6 1/3 feet = 72 + 4 + (1/3) x 12 = 76 inches

Therefore, the plumber has 76 inches of piping.

Since the plumber needs 75 inches of piping, we can see that she does have enough piping.

Step-by-step explanation:

Answer: The area of circle is 28.26 cm^2

Step-by-step explanation: As the diameter of the given circle is 6 cm, the radius of the same would be 3 cm.

Area of circle = pi r^2

And the value of pi is to be taken 3.14

The area of the given circle is 28.26cm^2.

There are 25  persons who actually voted, the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07 that is (0.13, 0.27).

In statistics, a confidence interval, means  the probability which a population parameter will fall between a set of values for a certain proportion of times. Confidence intervals measure the degree of uncertainty or certainty in a sampling method. There are various types of confidence interval such as 90%, 95%, 99% etc.

A certain randomly selected sample of 125 registered voters showed that 20% of them voted in the most recent school board election.

So in 125persons the persons who actually voted are

                (125×20)/100

              = 2500/100

              = 25

For 95% confidence interval the z value is 1.96.

If we take p as probability of success that is the persons who actually voted then 1-p denotes the probability of failure.

p= 25/125= 1/5 = 0.2          n= 125

1-p= 1-(1/5)

    = 1-0.2= 0.8

The formula for confidence interval is

p± z√{p(1-p)/n}

0.2 ±1.96√{(0.2×0.8)/125}

= 0.2 ± 1.96√(0.16/125)

= 0.2± 1.96 ×0.035777

= 0.2±0.07012

Hence , the 95% confidence interval for the population of registered voters who voted in the most recent school board election is 0.2±0.07

that is (0.13, 0.27).

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