A resort rents surfboards for $15 plus $3 for each hour the surfboard is rented. An expression for the total cost of renting a surfboard for h hours is 15 + 3h. if teresa wants to rent a surfboard for 4 hours, how much money will she have left over if she paids with $40?

Answer:

Step-by-step explanation:

Answer:

$20.52

Step-by-step explanation:

19x0.08 (that's 8% or 8/100) = $1.52

$19+$1.52= $20.52 :)

Answer:

504

Step-by-step explanation:

6 x 10 = 60 x 2 =120

6 x 12 = 72 x 2 = 144

10 x 12 = 120 × 2 = 240

120 + 144 + 240 = 504

this should be correct

Answer:  4  inches

Step-by-step explanation:

1. We gonna find the the length of the right triangle legs using Phitagor theorem.

c²=a²+b²  (1)   , where c is triangle's  hypotenuse

a and b are the triangle's  legs.

Let the leg a =x,    so leg b=x+1 inches

Now we can write the equation using (1)

25=x²+(x+1)²

25=x²+x²+2*x+1

2*x²+2*x-24=0     ( divide by 2 both sides of the equation)

x²+x-12=0

Find the discriminant D=1+12*4=49

√D=7

x1= (-1+7)/2=3     x2=(-1-7)/2=-4 - x2=-4 not possible so length of the leg can not be negative.

So the shorter leg a=x= 3 inches

The longer leg b=x+1=4 inches

Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

Answer:

156 + k = 102

Step-by-step explanation:

Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

Learn more about the total Surface Area of the Cone :

https://brainly.com/question/15153049

Answer:

The expectation of the policy until the person reaches 61 is of -$4.

Step-by-step explanation:

We have these following probabilities:

0.954 probability of a loss of $50.

1 - 0.954 = 0.046 probability of "earning" 1000 - 50 = $950.

Find the expectation of the policy until the person reaches 61.

Each outcome multiplied by it's probability, so:

\(E = -0.954*50 + 0.046*950 = -4\)

The expectation of the policy until the person reaches 61 is of -$4.

Answer:

42

Step-by-step explanation:

[ ( 7 - 3 ) * 2 + 6 ] * 3

= [ 4 * 2 + 6 ] * 3

= [ 8 + 6 ] * 3

= 14 * 3

= 42

Answer:

Step-by-step explanation:

(0,0)

i hope this helps

The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ1

Answer:

y = x + 60

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 = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line

The slope which shows  the cost per guest is $35 per guest

The given cost for 50 guests is $2150.

The cost for 75 guests is $3025.

It can also be represented as:

(Guest, Cost) =(50, $2150) & (75, $3025)

The slope can now be calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (50, $2150) & (75, $3025)

Substituting the given values in the equation as follows:

Slope = (3025 - 2150)/(75 - 50)

Slope = 35

Hence, the slope is $35 per guest.

To know more on Slope click:

https://brainly.com/question/29481191

#SPJ1

The probability that a mouse leaves first and then a bat is given as follows:

14/55.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

As the animal is not replaced, the probabilities for this problem are given as follows:

Hence the probability is given as follows:

4/11 x 7/10 = 2/11 x 7/5 = 14/55.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer:

Umbrella insurance is a type of personal liability coverage the goes above and beyond the amount the a regular home or vehicle insurance offers.

Step-by-step explanation:   I just looked it up hope that answers your question.

Step-by-step explanation:

Height of tower - 80m

Distance between foot of tower and boat 1 = x

Distance between boat 1 and boat 2 =y

Tan 45 = 1 = 80/x

x = 80

Tan 30 = 1 / root 3 = 80 / 80 + y

y = 80 root 3 + 80

Answer:

3ft

Step-by-step explanation:

it takes a while to explain and I dont have much time, but the answer is 3

Answer: -6.25, -2, 3/4, 3, 5, 6, 67/10 would be the soliton

The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

Learn more about length here:

https://brainly.com/question/29882625

#SPJ1

Answer:

The y-coordinate of point A is \(\sqrt{3}\).  

Step-by-step explanation:

The equation of the circle is represented by the following expression:

\((x-h)^{2}+(y-k)^{2} = r^{2}\) (1)

Where:

\(x\) - Independent variable.

\(y\) - Dependent variable.

\(h\), \(k\) - Coordinates of the center of the circle.

\(r\) - Radius of the circle.

If we know that \(h = 0\), \(k = 0\) and \(r = 2\), then the equation of the circle is:

\(x^{2} + y^{2} = 4\) (1b)

Then, we clear \(y\) within (1b):

\(y^{2} = 4 - x^{2}\)

\(y = \pm \sqrt{4-x^{2}}\) (2)

If we know that \(x = 1\), then the y-coordinate of point A is:

\(y = \sqrt{4-1^{2}}\)

\(y = \sqrt{3}\)

The y-coordinate of point A is \(\sqrt{3}\).  

The entire area is under the standard normal distribution curve, which is 1 by definition.

In other words, a typical normal random variable has a 100% chance of landing anywhere within its range of potential values (-∞ to +∞).

This makes sense since the area under the standard normal distribution curve, which is a continuous probability distribution, shows the likelihood that the random variable will take on any value within its range. Since the entire area under the curve is 1, the likelihood that any potential value for the random variable will occur is 1, or 100%.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

#SPJ1

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Therefore, the correct answer is "The data is skewed, with a range of 4.5. This might be because Sergio has a hard time riding further than 6 miles."

A line plot is a type of graphical display that shows the frequency of data along a number line. In a line plot, each data point is represented by a dot or mark above the number line, and the number of dots or marks above each value on the number line indicates the frequency of that value in the data set. Line plots are often used to display small to moderate-sized data sets and are particularly useful for showing how the data are distributed and identifying any outliers.

Here,

The data is spread out with a range of 4.5, and appears to be slightly skewed to the right with a majority of the data falling between 6 and 7 miles. This might suggest that Sergio has a preferred route that is around 6-7 miles long, but is capable of biking longer distances on occasion.

To know more about line plot,

https://brainly.com/question/23902686

#SPJ1

Answer: its b

Step-by-step explanation:

I got it right on flvs

Answer:

4 degrees Celsius

Step-by-step explanation:

It is asking for the change in temperature, or the difference. In word problems like this it is asking for subtraction.

So you just need to subtract the temperature at noon from the temperature at 8 am.

18 - 14 = 4 degrees

Answer:

4 degrees Celcius

Step-by-step explanation:

From 8 am to 12 pm is 4 hours. However, it is asking for the change in degrees from 18 degrees Celcius to 14 degrees Celcius.

It is asking for the change in temperature. In order to figure this out, you need to subtract. 18 - 14 = 4

Therefore, the change in degrees is 4 degrees Celcius.

Answer: An equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:

y = -4x + 20

Step-by-step explanation:

The given equation is in slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line is 2, which means the line has a slope of 2 and is inclined at an angle of tan^-1(2).

To find an equation of a line that is perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1/2. This means the slope of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is -1/2.

Now we can use the point-slope form of a linear equation to find the equation of the line passing through point P(-6, 4) and having a slope of -1/2. The point-slope form of a linear equation is:

y - y1 = m(x - x1)

Where (x1, y1) is the given point, and m is the slope of the line. So by substituting the values we get:

y - 4 = -1/2(x + 6)

Which can be written as:

y = -1/2x + 4

So the equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:

y = -1/2x + 4

Graphing the equations can confirm that the lines are perpendicular as the slope of the first line is 2 and the slope of the second line is -1/2, the product of these slopes is -1 which means they are perpendicular to each other.

The mean and the standard deviation, from the frequency table, are given as follows:

The frequency table gives the number of times that each observation appears.

The mean of a data-set is given by the sum of all observations divided by the number of observations, hence it is given as follows:

Mean = (1 x 13 + 2 x 12 + 3 x 5)/(13 + 12 + 5) = 1.73.

The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of observations, hence it is given as follows:

Standard deviation = sqrt((13 x (1 - 1.73)² + 12 x (2 - 1.73)² + 5 x (3 - 1.72)²)/30) = 0.73.

More can be learned about the mean and the standard deviation of frequency tables at https://brainly.com/question/20914474

#SPJ1

We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

Learn more about trigonometric identity :

https://brainly.com/question/3785172

#SPJ1