Kaylee is working two summer jobs, making $6 per hour walking dogs and $13 per hour landscaping. Last week Kaylee worked a total of 8 hours and earned a total of $83. Determine the number of hours Kaylee worked walking dogs last week and the number of hours she worked landscaping last week.

Kaylee worked
hours walking dogs and
hours landscaping.

We can divide the given shape into a triangle and a rectangle.

We'll have to use Pythagoras Theorem.

\(\large\boxed{Formula:{a}^{2}={b}^{2}+{c}^{2}}\)

In this question we have to find the hypotenuse so we'll have to add.

Let's substitute the values according to the formula.

\(BC= {6}^{2}+{7}^{2}\)

\(BC= 85\)

\(BC = \sqrt{ 85} \)

\(\boxed{BC=9.22 \: cm}\)

Now, we can find the value of "x"

We can use any one from SOHCAHTOA.

Here I'm using tan.

\(\large\boxed{Formula: tan(a)= \frac{opp}{adj}}\)

Let's substitute the values according to the formula.

\(tan \: x= \frac{6}{7}\)

We'll have to use tan inverse.

\(x= {tan}^{-1}(\frac{6}{7})\)

\(\boxed{x=40.6°}\)

1)

=9.22 cm

2)

=40.6°

hope this helps

Answer:

ok so first they drove 55 for 3 hours so

55*3=165

and then they drove 45 for 2 hours

45*2=90

165+90=255

so in total they drove 255 miles

Hope This Helps!!!

The solution is : 255 miles total miles did the Ramos family drive.

Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

here, we have,

given that,

The Ramos family drove to their family reunion. Before lunch, they drove at a constant rate of 55 miles per hour for 3 hours. After lunch, they drove at a constant rate of 45 miles per hour for 2 hours.

we get,

Journey before lunch:

Speed = 55 mph

Time = 3 hrs

distance = 55*3 = 165 miles.

Journey after lunch:

Speed = 45 mph

Time = 2 hrs

distance = 45 * 2 = 90 miles

Total miles driven

= distance traveled before lunch + distance traveled after lunch

= 165 miles + 90 miles

= 255 miles

Therefore, the Ramos family drove 255 miles in total.

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Answer:

12 ft^2

Step-by-step explanation:

Base is the bottom..... area = 4 x 3 = 12 ft^2

Answer:

A-a fair cube

Step-by-step explanation:

She saved 324 number of 20p coins altogether.

And, Halley need 176 more 20p coins to saved £100.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Halley saves up twenty-pence coins.

And, At the last count she had saved £64.80.

Now,

We know that;

Number of 20p coins in £1 = 5

So, Number of 20p coins in £64.80 = 5 × 64.80

                                                       = 324

And, Number of 20p coins in £100 = 5 × 100

                                                      = 500

So, He need number of 20p coins = 500 - 324

                                                      = 176

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(a) the general solution of the nonhomogeneous ODE is y(x) = c1e^(-3x) + c2e^x + 2 + (3x + 4)e^x, where c1 and c2 are arbitrary constants.

(b) the weight of the original mass on the spring was 72 lb.

a) To find the general solution of the nonhomogeneous ODE y" + 2y' - 3y = 1 + xe^x, we first find the general solution of the associated homogeneous equation, which is y_h'' + 2y_h' - 3y_h = 0. The characteristic equation is r^2 + 2r - 3 = 0, which has roots r = -3 and r = 1. Therefore, the general solution of the homogeneous equation is y_h(x) = c1e^(-3x) + c2e^x, where c1 and c2 are arbitrary constants.

To find the particular solution, we assume a particular form for y_p(x) based on the nonhomogeneous terms. For the term 1, we assume a constant, and for the term xe^x, we assume a polynomial of degree 1 multiplied by e^x. Solving for the coefficients, we find y_p(x) = 2 + (3x + 4)e^x.

Thus, the general solution of the nonhomogeneous ODE is y(x) = c1e^(-3x) + c2e^x + 2 + (3x + 4)e^x, where c1 and c2 are arbitrary constants.

b) To find the weight of the original mass on the spring, we can use the formula for the period of an undamped spring/mass system, T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.

Initially, with the original weight on the spring, the period is 3 seconds. Let's denote the original mass as m1. Therefore, we have 3 = 2π√(m1/k).

When 8 lb is removed from the spring, the period becomes 2 seconds. Denoting the new mass as m2, we have 2 = 2π√((m1 - 8)/k).

Dividing the second equation by the first, we get (2/3)² = [(m1 - 8)/k] / (m1/k), which simplifies to 4/9 = (m1 - 8) / m1.

Solving for m1, we have m1 = 72 lb.

Therefore, the weight of the original mass on the spring was 72 lb.


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If repetitions are allowed, the largest possible result for the standard deviation would occur when we choose the same number four times. In other words, if we choose 4 four times, the standard deviation would be 0 because all of the numbers are the same and there is no deviation from the mean.

However, if we want to choose four different numbers, the largest possible standard deviation would occur if we choose one number twice and two other numbers once each. For example, if we choose 1, 2, 2, and 3, the standard deviation would be approximately 0.829. This is because the formula for standard deviation takes into account the differences between each number and the mean of all the numbers chosen.

In general, the larger the range of numbers to choose from, the larger the possible standard deviation. This is because there are more potential combinations of numbers that could have a high deviation from the mean. Additionally, allowing repetitions also increases the potential for deviation since the same number can be chosen multiple times.

Overall, the largest possible standard deviation when choosing four numbers from 1 to 5 with repetitions allowed would be 0 if we choose the same number four times, or approximately 0.829 if we choose two numbers twice and two other numbers once each.

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Answer:

1- Product of powers rule.

2- Quotient of powers rule.

3- Power of a power rule.

4- Power of a product rule.

5- Power of a quotient rule.

6- Zero power rule.

7- Negative exponent rule.

Step-by-step explanation:

Hope I helped! ^v^

The length of Stan's movie is 2 hours 25 minutes

The length of Talia's movie is 2 hours 55 minutes.

In order to determine the length of the movies, subtract the end time of the movie from the time the movie started.

Subtraction is the mathematical operation that is used to calculate the difference between two or more numbers. The sign that is used to represent subtraction is -.

Length of the movie = time the movie ended - time the movie started

Length of Stan's movie = 9:40 - 7:15 = 2 : 25 hours

Length of the Talia's movie = 10 : 10 - 7 : 15 = 2 : 55 hours

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Answer:

m∠ABD = 24°

m∠CBD = 24°

m∠ABC = 48°

Explanation:

m∠ABD: (3x + 6)°

m∠CBD: (7x - 18)°

(3x + 6)° = (7x - 18)°

x = 6

(3x + 6)° = 24

(7x - 18)° = 24

24 + 24 = 48

m∠ABC = 48°

To calculate the present value of $51,270 payments to be made at the end of each period for 17 periods at a 9% interest rate, we need to find the discounted value of each payment and sum them up.

The present value (PV) is calculated by discounting each future payment back to its current value using the interest rate. The formula to calculate the present value of a series of payments is:

PV = Payment × [1 - (1 + interest rate)^(-number of periods)] / interest rate.

In this case, the payment is $51,270, the interest rate is 9% (or 0.09 as a decimal), and the number of periods is 17.

Using the provided formula and rounding the factor values to 5 decimal places, we can calculate the present value as follows:

PV = $51,270 × [1 - (1 + 0.09)^(-17)] / 0.09.

Evaluating this expression will give us the present value of the payments. It's important to round the final answer to 0 decimal places, as stated in the question.

By substituting the values and calculating the expression, we can determine the present value of the $51,270 payments made over 17 periods at a 9% interest rate.

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Answer: I think Rick is 16 and jeff is 6

Step-by-step explanation:

\(24 \times 4 - 38 \times 3 - 23 \times 2 + 5x + 2 = 0\)

\(96 - 114 - 46 - 5x + 2 = 0\)

\(5x - 62 = 0\)

\(5x = 62\)

\(x = \frac{62}{5} \)

hope it's helpful for you...

Answer:

The slope is 13

The y intercept is -7

Step-by-step explanation:

The y intercept is found when x = 0

When x = 0, y = -7

The y intercept is -7

To find the slope, we can use the formula

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

Using any two points s(x) is equal to y

m = (32 - 6)/(3 - 1)

    = 26/2

   = 13

Answer:

To determine the concentration of the analyte in the unknown using the fit parameters and the linear model, you need to substitute the given signal value into the equation y = mx + b.

In this case, the linear model is represented by the equation y = mx + b, where:

y is the signal value (80.77 in this case),

m is the slope obtained from the regression analysis, and

b is the y-intercept obtained from the regression analysis.

You haven't provided the values of m and b, so I'll use placeholders for now.

Let's assume the slope (m) obtained from the LINEST formula is m = 2.5 and the y-intercept (b) is b = 10.

Substituting these values into the equation:

y = mx + b

80.77 = 2.5x + 10

To find the concentration (x), we can rearrange the equation:

2.5x = 80.77 - 10

2.5x = 70.77

x = 70.77 / 2.5

x ≈ 28.31

Therefore, based on the given fit parameters and the linear model, the concentration of the analyte in the unknown is approximately 28.31 ppm Co2+.

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The probability that three of out nine cars need new brakes is 0.294  

Combination:

The combination is the process of selecting items from a group of objects where the order of objects does not matter. In simple words, we can say that it is a combination of n things in r times without repetition.

The formula for the combination of 'a' things from the set of n things without replacement is given

Here from the given problem,

Number of automobiles = 25

Number of automobiles that need new tune-ups = 15  

Number of automobiles that need new brakes = 10

Number of automobiles chosen at time = 9  

From above formula

The number of ways of selecting 9 cars from 25 cars

²⁵C₉ = 25!/9!(25 - 9)!

= 25!/9!(16)!  

= 2,042,975

The number of ways that can be chosen as 3 out of 9 cars that need breaks

Choosing 3 cars that need breaks from 10 cars = ¹⁰C₃

= 10!/3!(10 - 3)!  

= 10!/3!(7)!

= 120

Choosing the remaining 6 cars from the 15 groups of cars that need new tune-ups =  ¹⁵C₆

=  15!/6!(15 - 6)!  

=  15!/6!(6)!    

= 5,005

From above calculations

The number of ways that can be chosen as 3 out of 9 cars that need new  breaks  = 120 × 5,005

= 600600

As we know that

Probability of event = No of favorable outcomes / total outcomes  

The probability that three of them need new brakes

= 600600/2042975

= 0.294  

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Answer:

23

Step-by-step explanation:

j = jeans

s = shirt

j + 3s = 114

jeans = 45

45+ 3s = 114

Subtract 45 from each side

45-45+3s = 114-45

3s =69

Divide each side by 3

3s/3 =69/3

s = 23

Each shirt is 23

Answer:

b.) 23

Step-by-step explanation:

114-45=69

69/3=23

The statements that are true when there exists a constant rate of change between x and y are:

1. The graph of the relationship between x and y is a straight line.
2. The slope of the line represents the constant rate of change between x and y.
3. The value of the slope is the same for any two points on the line.
4. The equation that represents the relationship between x and y can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
5. The value of the y-intercept is the y-coordinate of the point where the line crosses the y-axis.

Let's break down each statement:

1. The graph of the relationship between x and y is a straight line:
When there is a constant rate of change between x and y, the graph will be a straight line. This means that the points representing the relationship between x and y will lie on a straight line when plotted on a graph.

2. The slope of the line represents the constant rate of change between x and y:
The slope of a line is a measure of how steep or flat the line is. In this case, when there is a constant rate of change between x and y, the slope of the line will be the same for any two points on the line. It represents the rate at which y changes for every unit change in x.

3. The value of the slope is the same for any two points on the line:
As mentioned earlier, the slope represents the constant rate of change between x and y. Regardless of which two points we choose on the line, the ratio of the change in y to the change in x will always be the same.

4. The equation that represents the relationship between x and y can be written in the form y = mx + b, where m is the slope and b is the y-intercept:
When there is a constant rate of change between x and y, we can express their relationship using an equation in the form y = mx + b. The slope, represented by the variable m, will be the coefficient of x, and the y-intercept, represented by the variable b, will be the value of y when x is equal to 0.

5. The value of the y-intercept is the y-coordinate of the point where the line crosses the y-axis:
The y-intercept is the point where the line representing the relationship between x and y crosses the y-axis. It represents the value of y when x is equal to 0.

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The width of a rectangular piece is 28 and the length is 58.

let us consider

w=width

w+30=length

After cutting:

w-12 =width

w + 30-12=length, or w + 18

Now to calculate the length and width consider the area of a rectangle:

Area of a rectangle=w*l

substitute the values in the above formula:

(w-12)(w+18)(6) = 2400

(w-12 )(w+18) = 400

w²+6w-216 = 400

w²+6w-616 = 0

(w + 28)(w - 22) = 0

The roots of the equation are {-22, 28}.

to find the length just substitute in the length formula:

length=28+30

length=58.

The width is 28 and the length is 58.

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The unit rate in chapters per hour is 21/16 hours

Greg read 7/8 hours in 2/3 chapter

The unit rate can be calculated as follows

7/8= 2/3

1= x

cross multiply both sides

2/3x= 7/8

x= 7/8 ÷ 2/3

x= 7/8 × 3/2

x= 21/16

Hence 21/16 chapters is read in one hour

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The linear function is 8.50x + 5.50 and a $5.50 delivery fee would be included in the price of each hoodie purchased.

Part 1

The linear function rule is used in cases with only one shipping charge.

= 8.50x + 5.50, where x is the number of sweatshirts and y is the total cost in dollars.

Part 2

The linear function rule would be y = 8.50x + 5.50x = 14x, where y is the total cost in dollars and x is the number of sweatshirts if the shipping fee is applied to each sweatshirt. This implies that the $5.50 delivery fee would be included in the price of each hoodie purchased.

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Answer:

(2 x 3 x \(13x^6\)\(Y^{4\))

Step-by-step explanation:

The required value of the function at x=-2 is 10.

A function in mathematics from a set X to a set Y assigns precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two variable quantities.

We have

f(x) = -x + 3 for x≤-3

     = -3x - 4  for -3 ≤ 1

     = -(x- 2)² + 5  for x > 1

To find F(-2) we have to take

f(x) = -3x + 4

f(-2) = -3(-2) + 4

f(-2) = 6 + 4

f(-2) = 10.

Thus, required value of the function is 10.

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Answer: The median decreases to

Step-by-step explanation: The median without the added 60 degrees is 79.5, which I double checked using a calculator after using the MEAN formulas. All I had to do was then add 60 to the data set and run the calculator again, and it then changed to 77.

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

The expression which is equivalent to a given expression 24 + 18 is given by option a. 6 ( 4 + 3 ).

The expression is equal to,

24 + 18

verification of equivalent expression is as follow,

6 ( 4 + 3 )

Using the distributive law multiplication over addition is ,

A (B + C ) = AB + AC

Apply it on 6 ( 4 + 3 ) we have

= 6 × 4 + 6 × 3

= 24 + 18

It is correct option and equivalent to 24 + 18.

6 ( 4 + 4 )

Using the distributive law multiplication over addition is ,

A (B + C ) = AB + AC

Apply it on 6 ( 4 + 4 ) we have

= 6 × 4 + 6 × 4

= 24 + 24

It is not correct option and not equivalent to 24 + 18.

2 ( 22 + 9 )

Using the distributive law multiplication over addition is ,

A (B + C ) = AB + AC

Apply it on 2 ( 22 + 9 ) we have

= 2 × 22 + 2 × 9

= 44 + 18

It is not correct option and not equivalent to 24 + 18.

6 ( 4 + 12 )

Using the distributive law multiplication over addition is ,

A (B + C ) = AB + AC

Apply it on 6 ( 4 + 12 ) we have

= 6 × 4 + 6 × 12

= 24 + 72

It is not correct option and not equivalent to 24 + 18.

Therefore, the equivalent expression of 24 + 18 is equal to option a. 6 ( 4 + 3 ).

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Answer:

12 + 2x = y

Step-by-step explanation:

y would be the total cost

Answer:

$12 + $2 × x

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

Answer:

\(x < - 5\)

Step-by-step explanation:

\( - 2x - 6 > x + 9\)

\( - 2x - x > 9 + 6\)

\( - 3x > 15\)

\( \frac{ - 3x}{ - 3} > \frac{15}{ - 3} \)

\(x < - 5\)

Answer:

Volume of the prism: 120cm^3

Step-by-step explanation:

volume of a prism = area of cross-section x length

so

volume of triangular prism = 4 (h) x 6 (b) divided by 2 x 10 (length)

6 x 4 = 24

24 / 2 = 12

12 x 10 = 120

Hope this helped!

- profparis