The dog wash washes 30 dogs for charity. they had different prices for the dogs. big dogs cost $36.00, small dogs cost $12.50, and average size dogs cost $14.00. they made $559.00. there were 3 more small dogs than big dogs

a) The vertical component of the velocity v upwards will be v0sinθ, where the angle is formed with respect to the y axis.

b)  The final velocity of the rock approaches the free-fall velocity √(2gh) and Vav-y approaches this same value.

Here, the initial velocity is given V0. It is the product of acceleration g and time t. thus, u = gt.

The height travelled within the time t and acceleration g, is written as:

h = 1/2 gt²

The two components of velocity in the two axis are,

vertical component = v sinθ

Horizontal component = v cosθ.

Here, the vertical component along the y -axis with an angle θ being,

⇒ V0 sinθ.

b) . If the height of the building H is zero, then the rock is not thrown up in the first place, and instead, it is simply dropped from the roof.

In this case, the initial velocity V0 is zero, and the rock falls straight down to the ground.

Since the rock is only moving in the downward direction, the vertical component of the average velocity Vav-y is simply the final velocity of the rock just before it hits the ground.

The final velocity is given by,

⇒ v= √(2gh),

where g is the acceleration due to gravity and h is the height of the building.

Therefore, as H approaches zero, the final velocity of the rock approaches the free-fall velocity √(2gh) and Vav-y approaches this same value.

c) Equation (2.10) states that the displacement y of an object in free fall near the surface of the Earth is given by:

y = v0t + 1/2gt²

where v0 is the initial velocity, g is the acceleration due to gravity, t is the time, and y is measured in the vertical direction.

Apply this equation to the motion of the rock from the roof to the ground, we can set the initial velocity v0 to the upward velocity with which the rock is thrown from the roof.

Since the direction of motion changes from up to down, the final displacement y should be negative, representing the distance traveled in the downward direction.

Therefore, we have:

y = -H

v0 = V0

g = -9.8 m/s²

t = the time it takes for the rock to fall from the roof to the ground

Using this information, we can rearrange the equation to solve for the time t:

t = √(2H/g)

Now, we can use this expression to calculate the vertical component Vav-y of the average velocity of the rock:

Vav-y = (y - v0t) / t

Plugging in the values for y, v0, and t, we get:

Vav-y = (-H - V0 * sqrt(2H/g)) / √(2H/g)

Simplifying this expression, we get:

Vav-y = -√(2gH)

This result agrees with the value of the average velocity of the object in free fall near the surface of the Earth, which is given by Eq. (2.10), since the vertical component of the velocity is simply the derivative of the displacement with respect to time:

Vav-y = dy/dt = v0 + gt

For an object in free fall near the surface of the Earth with an initial velocity of V0 = 0, this reduces to:

Vav-y = gt

Using the acceleration due to gravity g = -9.8 m/s² and the time t = √(2H/g), we get:

Vav-y = -√(2gH)

which is the same as our previous result.

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Answer:

Between 12.8 and 12.9

Step-by-step explanation:

Firstly, we would need to get the value of the surd

So we have this as;

2 √41 = 12.81

Now, looking at the options, we can see that it lies between 12.8 and 12.9; this is our answer

Answer:

72

Step-by-step explanation:

Given:

There were 120 people in total.

60% were parents.

To find:

Number of parents attended.

Solution:

1. 60% of 120

It can also be written as:

\(\frac{60}{100}\times \frac{120}{1}\)

Simplify

\(\frac{60}{100}\\\\=\frac{6}{10}\)

\(\frac{6\div2}{10\div2}=\frac{3}{5}\)

2. \(\bold{\frac{3}{5}\times \frac{120}{1}}\)

Multiply

\(\frac{3\times120}{5\times1} = \frac{360}{5}\)

Divide

\(\frac{360}{5}= 360\div5=72\)

Therefore, 72 parents attended the game.

Answer:

Amount earned in 1 hour = $9

In one week Micheal works = 28 hours

So, in one week she gets $9 * 28

=> $252

Hence, she would earn $252 in one week, in Six weeks she will get,

=> $252 * 6 = $1512

If my answer helped, kindly mark me as the brainliest!

Thank You!!

After 37 bounces, the ball's height will be less than 1 foot.

The initial height of the ball is 50 feet.

After first bounce, the ball will reach a height of:

= 50 feet * (1 - 10%)

= 45 feet.

After second bounce, it will reach a height of:

= 45 feet * (1 - 10%)

= 40.5 feet.

Height decreases by 10% after each bounce.

We have to set up an equation:

50 feet * (0.9)^n < 1 foot

Simplifying:

0.9^n < 1/50

Taking the logarithm:

n * log(0.9) < log(1/50)

n > log(1/50) / log(0.9)

n > 37.1298771746

n > 37.13.

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The domains from the two functions are different according to the change in quantity.

The domain is a term in math to define the set of values that we can plug into a function.

The natural numbers domain is when we use a natural number such as 1, 2, 3, etc. The natural number domain will use if the function only allows the change in quantity in natural number. Market A uses this.

The real number domain is when we use a real number such as 1, 2, 2.4, etc. The natural number domain will use if the function only allows the change in quantity in real numbers. Since market B is selling rice in bulk based, it will be easier to use the real number domain.

Thus, the two functions have the same value with different domain because market A use natural number and don't allow fraction, but market B since it sells rice in bulk so it allows fraction and uses a real number.

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\(\qquad\qquad\huge\underline{{\sf Answer}}☂\)

Let's find the Area of sector ~

\(\qquad \sf  \dashrightarrow \: \dfrac{ \theta}{360} \times \pi{r}^{2} \)

\(\qquad \sf  \dashrightarrow \: \dfrac{ 270}{360} \times \pi{6}^{2} \)

\(\qquad \sf  \dashrightarrow \: \dfrac{ 3}{4} \times {36}^{} \pi\)

\(\qquad \sf  \dashrightarrow \:3 \times 9 \pi\)

\(\qquad \sf  \dashrightarrow \:27\pi \: \: ft {}^{2} \)

Answer:b=227

Step-by-step explanation:

Answer:

yes the person above me is correct it is 227

Step-by-step explanation:

The system of linear inequalities to model the situation is 10x + 20y ≤ 100 and y > 2x

From the question, we have the following parameters that can be used in our computation:

Using the following representations:

We have the following system of inequalities from the given statements

10x + 20y ≤ 100

y > 2x

Hence, the system of inequalities is 10x + 20y ≤ 100 and y > 2x

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Answer:

11.6 is your answer. brainliest pls

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I think its C

X + Y = Z

and Y can't be negative so I think its C

There is no triangle ABC with the dimensions AB=3 cm, BC=3.5 cm, and CA=6.5 cm.

What is triangle inequality rule?

The triangle inequality theorem states that for any given triangle, the sum of the two sides is always greater than the  third side. The Triangle is a polygon with three line segments as its boundaries.

Suppose A, B and C are three sides of a triangle, then by using triangle inequality rule, A + B > C then A, B and C make a triangle.

Here,

AB = 3 cm

BC = 3.5 cm

AC = 6.5 cm

Let AB + BC = 3 + 3.5 = 6.5

AB + BC = AC

However, in this case, the length of the third side is equal to the sum of the lengths of the other two sides, which renders the triangle's condition false.

Hence, there is no triangle ABC with the dimensions AB=3 cm, BC=3.5 cm, and CA=6.5 cm.

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To solve the initial value problem y'' - 2y' - 3y = 0, with y(0) = 1 and y'(0) = 2, we can use the method of Laplace transforms.

First, we take the Laplace transform of the given differential equation to obtain an algebraic equation in terms of the Laplace transform of the unknown function y(t). Then, we solve the algebraic equation for the Laplace transform of y(t) using standard algebraic techniques. Finally, we take the inverse Laplace transform to obtain the solution y(t) in the time domain.

Applying the Laplace transform to the given differential equation, we have s²Y(s) - sy(0) - y'(0) - 2(sY(s) - y(0)) - 3Y(s) = 0, where Y(s) represents the Laplace transform of y(t). Simplifying this equation, we get (s² - 2s - 3)Y(s) - (s - 2) = s²Y(s) - 3s - 4. Rearranging the equation, we have Y(s) = (s - 2) / (s² - 2s - 3).

To solve this equation for Y(s), we can decompose the expression into partial fractions, which yields Y(s) = 1 / (s - 3) - 1 / (s + 1). Taking the inverse Laplace transform of Y(s), we obtain y(t) = e^(3t) - e^(-t), which is the solution to the initial value problem.

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Answer:

Step-by-step explanation:

You want to know the number of nickels, dimes, and quarters that comprise $8.00, when the number of nickels is 3 times the number of quarters, and 4 more than the number of dimes.

Let n, d, q represent the numbers of nickels, dimes, and quarters, respectively. The given relations can be written as equations:

  5n +10d +25q = 800 . . . . . value of the coins in cents

  n = 3q . . . . . . . . 3 times as many nickels as quarters

  n -d = 4 . . . . . . . 4 fewer dimes than nickels

Writing the numbers of dimes and quarters in terms of the number of nickels, we have ...

  q = n/3

  d = n -4

Substituting these into the last equation gives ...

  5n +10(n -4) +25(n/3) = 800

  5n +10n -40 +(8 1/3)n = 800 . . . . expand parentheses

  (23 1/3)n = 840 . . . . . . . . . . . . . add 40, collect terms

  n = 840/(23 1/3) = 36 . . . . . . . divide by the coefficient of n

  q = 36/3 = 12

  d = 36 -4 = 32

There are 36 nickels, 32 dimes, and 12 quarters.

__

Additional comment

The solution shown is "ad hoc", meaning it is chosen based on the fact that substitutions are made relatively easy by the given relations.

Writing the equations in the form of an augmented matrix allows use of standard tools and procedures, independent of the given coefficients. The attachment shows a calculator solution of the system of equations.

The correct R code to build a linear regression model with response variable y and explanatory variable x is (d) lm(x ~ y).

Step 1: Load data into R

Perform the following four steps for each dataset:

Step 2: Make Sure Your Data Meets Assumption

Simple regression

1. Independence of observations (no autocorrelation)

Since we only have one independent variable and one dependent variable, we don't need to test for hidden relationships between the variables.

2. Normality

To check whether the dependent variable follows a normal distribution, use the hist() function. In this case, the observations are roughly bell-shaped (more observations in the middle of the distribution and less in the tails), so we can do a linear regression.

3. Linear

The relationship between the independent variable and the dependent variable must be linear. We can test this visually with a scatterplot to see if the distribution of data points can be described by a straight line.

4. Homoscedasticity :

This means that the forecast errors do not vary significantly over the forecast range of the model.

Multiple regression

1. Independence of observations (aka no autocorrelation)

Use the cor() function to test the relationship between independent variables and ensure that they are not strongly correlated. When we run this code, the output is 0.015. The correlation between cycling and smoking was weak (0.015 with a correlation of only 1.5%), so we can include both parameters in the model.

2. Normality

Use the hist() function to test whether your dependent variable follows a normal distribution. The distribution of observations is roughly bell-shaped, so we can do a linear regression.

3. Linear

We can check this using two scatterplots: one for cycling and heart disease, and one for smoking and heart disease.

Step 3: Perform Linear Regression Analysis

Now that you have determined that your data matches your assumptions, you can perform linear regression analysis to assess the relationship between the independent and dependent variables.

Simple Regression:

The Coefficients section displays:

The standard error of the estimated value (Std. Error). The test statistic (t-value, in this case the t-statistic).

The last three lines are model diagnostics - the most important thing to note is the p-value (here 2. 2e-16, or close to zero), which will indicate how well the model fits the data.

Based on these results, it can be said that there is a significant positive relationship (p-value < 0.001) between income and happiness, with each unit increase in income being associated with an increase in happiness of 0.713 units (+ /- 0.01).

From these results, we can say that there is a significant positive relationship between income and happiness (p-value < 0.001), with each unit increase in income being associated with an increase in happiness of 0.713 units (+/- 0.01).

Multiple regression:

To test this relationship, we first fitted a linear model with heart disease as the dependent variable and cycling and smoking as the independent variables. The estimated effect of cycling on heart disease is -0.2, while the estimated effect of smoking is 0.178.

At the same time, for every 1% increase in smoking prevalence, the incidence of heart disease increased by 0.178%.

These regression coefficients have very small standard errors and very large t-statistics (-147 and 50.4, respectively). The p-values ​​reflect these small errors and large t-statistics. For these two parameters, the probability that this effect is chance is almost nil.

Result:

Include a short statement explaining the results of the regression model in addition to the graph.

Results of a simple linear regression

We found a significant relationship between income and happiness (p < 0.001, R2 = 0.73 ± 0.0193), 0.

Reported happiness increased by 73 units for every $10,000 increase in income.

Results of multiple linear regression

In our survey of 500 municipalities, we found significant relationships between the frequency of cycling to work and the frequency of heart disease and the frequency of smoking and heart disease ( p < 0 and p ) < 0.001, respectively).

We specifically found a decrease of 0.2% (± 0.0014) Each 1% increase in cycling and smoking was associated with a 0.178% (± 0.0035) increase in heart attack frequency.

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According to the question, the average score for the variable x1 is 1.88.

To find the average score for the variable x1, we need to assign numerical values to the categories S, M, and L. Let's assign S = 1, M = 2, and L = 3, as instructed.

Suppose we have a dataset with n observations of x1. Let's denote the values of x1 as \(x1_1, x1_2, ..., x1_n\). To find the average score, we need to calculate the sum of all the scores and divide it by the total number of observations.

The average score for x1 can be calculated as:

\(\[ \text{Average score} = \frac{\text{Score of } x1_1 + \text{Score of } x1_2 + \ldots + \text{Score of } x1_n}{n} \]\)

Let's assume we have the following values for x1: S, L, M, S, M, M, L, S. The corresponding scores are 1, 3, 2, 1, 2, 2, 3, 1.

Now we can calculate the average score:

\(\[ \text{Average score} = \frac{1 + 3 + 2 + 1 + 2 + 2 + 3 + 1}{8} \]\)

            = \(\frac{15}{8}\)

            = 1.875

Rounding the answer to two decimal places, the average score for the variable x1 is 1.88.

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The solution to the provided differential equation with the initial condition y(0) = 5 and u as a step change of unity is y = -2

The provided differential equation is: \(\[\frac{{dy}}{{dt}} = y + 2u\]\) with the initial condition: y(0) = 5 where u is a step change of unity.

To solve this differential equation, we can use the method of integrating factors.

First, let's rearrange the equation in the standard form:

\(\[\frac{{dy}}{{dt}} - y = 2u\]\)

Now, we can multiply both sides of the equation by the integrating factor, which is defined as the exponential of the integral of the coefficient of y with respect to t.

In this case, the coefficient of y is -1:

Integrating factor \(} = e^{\int -1 \, dt} = e^{-t}\)

Multiplying both sides of the equation by the integrating factor gives:

\(\[e^{-t}\frac{{dy}}{{dt}} - e^{-t}y = 2e^{-t}u\]\)

The left side of the equation can be rewritten using the product rule of differentiation:

\(\[\frac{{d}}{{dt}}(e^{-t}y) = 2e^{-t}u\]\)

Integrating both sides with respect to t gives:

\(\[e^{-t}y = 2\int e^{-t}u \, dt\]\)

Since u is a step change of unity, we can split the integral into two parts based on the step change:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 2\int_{t}^{{\infty}} 0 \, dt\]\)

Simplifying the integrals gives:

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt + 0\]\)

\(\[e^{-t}y = 2\int_{{-\infty}}^{t} e^{-t} \, dt\]\)

Evaluating the integral on the right side gives:

\(\[e^{-t}y = 2[-e^{-t}]_{{-\infty}}^{t}\]\)

\(\[e^{-t}y = 2(-e^{-t} - (-e^{-\infty}))\]\)

Since \(\(e^{-\infty}\)\) approaches zero, the second term on the right side becomes zero:

\(\[e^{-t}y = 2(-e^{-t})\]\)

Dividing both sides by \(\(e^{-t}\)\) gives the solution: y = -2

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The area of the region enclosed by one loop of the curve r = 3cos(7θ) can be found by calculating the definite integral of the function r with respect to θ over the appropriate interval. The result of this integral will give us the area of the region enclosed by one loop of the curve.

To find the area of the region enclosed by one loop of the curve, we need to evaluate the definite integral of the function r = 3cos(7θ) with respect to θ. Since the curve completes one loop for every interval of θ from 0 to π/7, we can set up the integral as follows:

A = ∫[0, π/7] (1/2) r^2 dθ

Using the given function r = 3cos(7θ), we substitute it into the integral and simplify:

A = ∫[0, π/7] (1/2) (3cos(7θ))^2 dθ

  = (9/2) ∫[0, π/7] cos^2(7θ) dθ

To evaluate this integral, we can use trigonometric identities or integration techniques such as u-substitution. After integrating, we obtain the value of A, which represents the area of the region enclosed by one loop of the curve.

It's important to note that the given curve r = 3cos(7θ) forms multiple loops, and to find the area of one loop specifically, we need to consider the appropriate interval for θ that corresponds to one complete loop.

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Answer:

3/2

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

6      x

-   =   -

8      12

the relationship from 8 to 12 is divided by.666666666666

So, we do the same for 6

We get 9.

Answer:

b=sqrt7

Step-by-step explanation:

16=9+b^2

Answer:

angle x = 30 degrees

Step-by-step explanation:

180-117-33= x

180 - 117- 33= 30

117+33+x=180

117+33=150

180-150=30

x=30

117+33+30=180

180=180

honestly i dont know what you wanted me to do so i did what i know

Answer:

Step-by-step explanation:

Substitute for r.

1/5(1/4) + 9/20  ->  1/20 + 9/20 = 10/20.

Simplify the final answer.

10/20 = 1/2

Answer:

69

Step-by-step explanation:

lol

Answer:

132 cm²

Step-by-step explanation:

To find the area of the figure, start by dividing the figure into smaller rectangles.

Area of figure

= area of shaded rectangle +area of unshaded rectangle

\(\textcolor{steelblue}{\text{Area of rectangle= length ×breadth}}\)

Shaded rectangle

Length= 4 cm

Breadth= 6 cm

Area

= 4(6)

= 24 cm²

Unshaded rectangle

Length= 9 cm

Breadth= 12 cm

Area

= 9(12)

= 108 cm²

After finding the area of each rectangle, we can add the two areas together to obtain the total area of the figure.

Area of figure

= 108 +24

= 132 cm²

The value of 6x is 102.

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. LHS = RHS is a common mathematical formula.

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:

x=51/3

For 6x put x= 51/3 we get

6x = 6 x 51/3

6x = 2 x 51

6x = 102

Or, \(x^6\) = \((51/3)^6\)

\(x^6\) = 17,596,287,801 / 531,441

Hence, the value of 6x = 102.

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Given:

The area of the blue rug is:

And the area of the red rug is :

So, the area of both of them is the sum of the given areas:

So, the total area =

so, the area of the new rug in factored form = 2 ( 9x + 4 )