Donna bought 4 bags of dog treats for $10.72. What is the cost per bag of dog treats?

It take the car 7.33 seconds to travel a distance of 381 meters. Rounded to 2 decimal places.

QUESTION 1. A ball is dropped from the top of a 9371-meter-tall tower. How long will a take to hit the ground? Round your answer to 2 decimal places.

Using the formula;`d = 1/2gt^2`Where `g` is the acceleration due to gravity, `t` is the time it takes for the object to fall, and `d` is the distance fallen. We can solve for `t` using the given data.

First, solve for `g` by setting `d` equal to the height of the tower and solve for `g`:`d = 1/2gt^2`Therefore, `g = 2d/t^2``g = 2(9371)/t^2``g = 18742/t^2`Substitute `g` into the equation we get the formula;

`d = 1/2(18742/t^2)t^2``d = 9371`Solve for `t`:`9371 = 1/2(9.8)t^2`t = sqrt(2d/g)`t = sqrt(2(9371)/9.8)`t = sqrt(1909.183673469388)`t = 43.7`

Therefore, the time it takes for the ball to hit the ground is 43.7 seconds. Rounded to 2 decimal places.

QUESTION 2A car accelerates from rest to a speed of 248 m/s in 58 seconds.

How far does it travel during this time? Round your answer to 2 decimal places.

Use the formula to calculate displacement,`s = v_i t + 1/2at^2`Where `s` is displacement, `v_i` is initial velocity, `a` is acceleration, and `t` is time.

The initial velocity is zero, so:

`s = 1/2at^2`Substitute the values we get:`s = 1/2(0+ a)(58)^2`Given that the final velocity is 248 m/s, so the acceleration is:`a = (v_f - v_i)/t``a = (248 - 0)/58``a = 4.276 round to 2 decimal places

`Substitute `a` into the formula we get:`

s = 1/2(4.28)(58)^2`s = `23303.36`Therefore, the car travels 23303.36 m during the 58 seconds. Rounded to 2 decimal places.

QUESTION 3A ball is dropped from the top of a building and hits the ground 3.14 seconds later. How far did it fall? Round your answer to 2 decimal places.

Use the formula to calculate the distance fallen:

`d = 1/2gt^2`Where `g` is the acceleration due to gravity and `t` is the time it takes for the object to fall. Substituting the given data we get: `d = 1/2(9.8)(3.14)^2`So, `d = 48.5396`.

Therefore, the ball falls 48.54 meters. Rounded to 2 decimal places.

QUESTION 4. A car speeds up from 18.5 m/s to 37.8 m/s in 48 seconds. What is the average speed during this time? Round your answer to 2 decimal places. The formula for average speed is:`v_avg = Δx/Δt

`Where `Δx` is the change in position and `Δt` is the change in time.

`Δx` can be found by finding the average of the initial and final position, so:`Δx = 1/2(v_i + v_f)t``Δx = 1/2(18.5 + 37.8)48`Δx = 1296.6Therefore, `v_avg = Δx/Δt``v_avg = 1296.6/48`v_avg = 27.01`

Therefore, the average speed during this time is 27.01 m/s.

Rounded to 2 decimal places.

QUESTION 5. How long would it take a car traveling 52 m/s to go a distance of 381 meters? Round your answer to 2 decimal places. The formula to calculate time is:`t = Δx/v

`Where `Δx` is the distance traveled and `v` is the velocity of the car. Substituting the given values:

`t = 381/52`t = 7.33

Therefore, it would take the car 7.33 seconds to travel a distance of 381 meters. Rounded to 2 decimal places.

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Answer:

1, 2, 4, 8, 16

Step-by-step explanation:

Each gets higher everytime you multiply by 2

Answer:

C or 3

Step-by-step explanation:

It is the only one going in a pattern or arithmetic sequence

2 + 3 = 5

5 + 3 = 8

8 + 3 = 11

11 + 3 = 14

The relationship is 3

Given:

The length of a rectangle is 3 cm less than its width.

The area of the rectangle is 270 cm².

To find:

The dimensions of the rectangle.

Solution:

Let x be the width of the rectangle. Then,

\(\text{Length}=x-3\)

Area of a rectangle is:

\(\text{Area}=\text{Length}\times \text{width}\)

\(270=(x-3)(x)\)

\(270=x^2-3x\)

\(0=x^2-3x-270\)

Splitting the middle term, we get

\(x^2-18x+15x-270=0\)

\(x(x-18)+15(x-18)=0\)

\((x-18)(x+15)=0\)

\(x=18,-15\)

Width of the rectangle cannot be negative. So, the only value of x is 18.

\(Width=18\)

\(Length=18-3\)

\(Length=15\)

Therefore, the length of the rectangle is 15 cm and the width of the rectangle is 18 cm.

The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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To Sketch a graph of each of the four angles of 30°, 150°, 210°, 330°, one can follow the example that is given in the image.

In the mathematics, a sketch is known to be a given category  that tells what a thing is all about.

Note that in sketching, one need to take not of the key points and angles and as such, To Sketch a graph of each of the four angles of 30°, 150°, 210°, 330°, one can follow the example that is given in the image.

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Answer:

$75.3

Step-by-step explanation:

(7.80x7)+(6.90x3)

=54.6+20.7

=$75.3

The metric measurement will you use when telling your hairdresser how much to take off the ends is centimetres (cm).

The decimalized meter-based system of measurement that had been adopted in France in the 1790s was replaced by the metric system. The International System of Units (SI), which was invented/created in the middle of the 20th century with the help of an international standards body, was the historical culmination of the development of these systems.

The term "metrication" refers to the adoption of the metric system. The historical development of metric systems has led to the acceptance of a number of principles. A single base unit of measurement expresses all of nature's essential dimensions. More and more often now, natural principles rather than replicas of physical artifacts are used to define base units.

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The coefficients and constant in the quadratic function f(x) = x² - 5x + 6 are coefficients: 1, -5 and constant: 6.

A quadratic function is an algebraic function with one or more variables where the largest exponent of the variable is two. The equation for a quadratic function is of the form f(x) = ax² + bx + c, where 'a' is a non-zero integer and a, b, and c are real numbers. A quadratic function is a polynomial of degree 2, and its definition is as follows.

The "a", "b", and "c" from "ax2 + bx + c" are used in the quadratic formula; they are known as the "numerical coefficients" of the quadratic equation. Therefore,

f(x) = x²– 5x + 6

a = 1

b = -5

c = 6

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Question:

Identifying the Coefficients and Constanta

Consider the quadratic function f(x) = x2 – 5x + 6.

What are the values of the coefficients and constant in the function?

Answer:

19 = -37 + 8x

-8x= -37 -19

-8x = -56

x= 7

Answer:

$55.25

Step-by-step explanation:

35% × 85 = 29.75

85 - 29.75

= 55.25

Answer: 40%

Step-by-step explanation:

There are four red marbles and six blue marbles, so there is a total of 10 marbles. Since four of those marbles are red, there is a 4 in 10 chance to select a red marble, or 4/10. 4/10 equals 0.4 which in terms of percentage is 40% (multiply by 100).

The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

To determine the buckling load of the column shown in Figure P2.13, we need to determine the critical load at which the column will buckle under compression.

To calculate the buckling load, we can use the Euler's formula for the critical buckling load of a column:

P_critical = (π^2 * E * I) / (K * L)^2

Where:

- P_critical is the critical buckling load

- E is the modulus of elasticity of the material

- I is the moment of inertia of the column cross-section

- K is the effective length factor

- L is the length of the column

To obtain the buckling load, we need to know the values of E, I, K, and L for the specific column in Figure P2.13. Once these values are known, we can substitute them into the formula to calculate the buckling load.

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Answer:

$9,635.00

Step-by-step explanation:

41 bracelets×$235.00=$9,635.00

First can I just say, those are some expensive jewelry!

l

Step-by-step explanation:

The amount of bracelets that she sold last month, (Saturday + Sunday) is 41. So last month she sold 41 bracelets.  

Each bracelet cost $235 so we have to multiply to amount of money one bracelet cost, times how many she sold.

$235 x 41 = $9635

She made $9635 by selling bracelets last month.

The expected variance of red balls chosen is 2/3 from the urn.

Six red balls and four green balls are in an urn.

Till a urn is empty, we take balls out of it one at a time without replacing them and noting their order of the colors.

The, the variance is found as-

Variance(X,Y) = E(XY) - E(X).E(Y).E(XY)

E(XY)  = 25×(6/10)(4/9)

E(X) = 5×(6/10)

E(Y) = 5×(4/10)

Thus,

Variance(X,Y) = 25(6/10)(4/9) - 25(6/10)(4/10)

Variance(X,Y) = 2/3

Thus, the variance for choosing red balls is 2/3.

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The simplest form   \(\frac{2\sqrt{3} }{\sqrt{6} }\) is \(\sqrt{2}\)

Step-by-step solution:

\(=\frac{2\sqrt{3} }{\sqrt{6} }\)

\(=\frac{2\sqrt{3} }{\sqrt{2*3} }\)              (write factors of \(\sqrt{6}\) i.e. \(\sqrt{2*3}\))

\(=\frac{2\sqrt{3} }{\sqrt{2}\sqrt{3} }\)

\(=\frac{2\ }{\sqrt{2}\ }\)

\(=\frac{2\ }{\sqrt{2}\ } * \frac{\sqrt{2} }{\sqrt{2} }\)        (Rationalize it by \(\sqrt{2}\))

\(=\frac{2\sqrt{2} }{2}\)

\(=\sqrt{2}\)

Therefore, the correct solution to this question is \(\sqrt{2}\)

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Answer:

(1, -1)

Step-by-step explanation:

we isolate y in the first equation

2x+y=1

-2x.  -2x

y=1-2x

and now we fill y into second equation

4x-2(1-2x)=6

4x-2+4x=6

8x-2=6

   +2 +2

8x=8

/8 /8

x=1

and now to find y we insert x

2(1)+y=1

2+y=1

-2.   -2

y= -1

hopes this helps

There are various techniques to simplify algebraic expressions, including:

1. Combining like terms: In an algebraic expression, like terms are terms that have the same variable raised to the same power. To simplify the expression, we can combine these like terms. For example, in the expression 3x + 2y + 5x - 4y, we can combine the x terms and the y terms to get 8x - 2y.

2. Distributing: When a number or variable is outside a set of parentheses and is being multiplied by a sum or difference inside the parentheses, the number or variable can be distributed to each term inside the parentheses. For example, in the expression 3(x + 2), the 3 can be distributed to both x and 2, resulting in the simplified expression 3x + 6.

3. Simplifying exponents: When an expression contains exponents, rules of exponentiation can be used to simplify the expression. For example, in the expression x^2 * x^3, the exponents can be added to give x^(2+3) = x^5.

4. Factoring: When an expression contains common factors, those factors can be factored out. For example, in the expression 2x^2 + 4x, both terms have a factor of 2 and a factor of x, so these factors can be factored out to give 2x(x + 2).

Step-by-step explanation:

Use Pythagorean theorem to find the base of the right triangle

221^2 = 195^2 + b^2

b = 104 km

triangle area = 1/2 base * height =  1/2 * 104 * 195 = 10140 km^2

Now multiply by the height to find volume

10140 km^2  * 15 km  = 152100 km^3

Answer:5/6

Step-by-step explanation:

simplify

The domain of the function is{x | −4 < x < 6}.

A function's domain is the set of all potential inputs.

For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

What is range?

The statistical difference between the highest and lowest values for a given data collection is called the range.

For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. It is possible to think of the range as the distance between the highest and lowest observation as a result.

the domain of the function is{x | −4 < x < 6} because

there is no restriction on x domain and range both are the set of real numbers.

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Answer:

− 3 w 2 + 9 w + 1

There is a weak negative relationship between essential oils and hormone levels depicted in the scatter plot. So, a better headline for this information can be that "essential oils may disturb hormonal levels".

It is given to us that -

The current news headline claims that "essential Oils Cause Hormone Levels to Drop".

They show a scatter plot displaying a weak negative relationship (r = -0. 13) between essential oil use and hormone levels.

We have to determine a better headline for this information.

We know that a scatter plot is defined as a type of graph that depicts the pairs of data that are plotted as points in the plot.

We also know that, we can use a scatter plot to analyze trends in our data and to help us determine whether or not there is a relationship between two variables.

Again, a scatter plot can represent a positive relationship, a negative relationship, or no relationship.

It can be referred to as a negative relationship between the given variables if the points on the scatter plot form a line that spreads from left to right in the downward direction.

In case of a positive or negative relationship between the variables, we can draw a line that depicts the best fit.

This line depicted through a positive or negative relationship will not pass through each and every point on the scatter plot. However, it will represent the general trend of the available data.

So, it can be concluded that the weak negative relationship between essential oil and hormone levels displayed in the scatter plot suggests that the fact that "essential Oils Cause Hormone Levels to Drop" is not true.

This is because there is weaker relationship between essential oils and the hormone levels which is more of a lesser general trend that doesn't suggest any strong relationship or doesn't represent any stated fact.

Therefore, from the weak negative relationship between essential oils and hormone levels depicted in the scatter plot, a better headline for this information can be that "essential oils may disturb hormonal levels".

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60 to the negative 3 power

Answer:

-60

Step-by-step explanation:

Answer:

-∞ < x < 4

Step-by-step explanation:

→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x  ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.

Based on the formulas given for PR and QR, the length of PR is 19.8 units.

The shape that is given is an equilateral triangle. What this means is that all the sides of the triangle are equal.

This means that PR and QR are therefore equal:

PR = QR

This can help us to find the value of n by equating both formulas:

2n + 9 = 7n - 18

The value of n can then be found as:

7n - 2n = 18 + 9

5n = 27

n = 5.4

The length of PR can then be solved by substituting n into the formula:

= 2n + 9

= 2 (5.4) + 9

= 19.8 units

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83

Step-by-step explanation:

this consists of 5 sides

top and bottom (equal)

left

right

front

the total surface area is the sum of all 5 areas.

the area of a rectangle is

length × width

the area of a triangle is

baseline × height / 2

in our case we have

top and bottom : 10×4/2 × 2 = 10×4 = 40 cm²

left : 8×9 = 72 cm²

right : 5×9 = 45 cm²

front : 10×9 = 90 cm²

the total surface area is

40 + 72 + 45 + 90 = 247 cm²

Hey there!

This answer to your question is it is false.

This is because you could have a rectangle with a length of 6 and a width of 4, and the area would be the same as a rectangle with a length of 8 and a width of 3. They would both be 24.

Hope it helps and have an amazing day! Stay safe!