A right triangle has legs with the lengths of 2 and 5, find the length of the hypotenuse

Answer Choices:
√21


√3


√7


√29

Mrs. Caldwell will travel 135 miles at an additional 20 mph to catch up to Mr. Caldwell. Therefore, it will take Mrs. Caldwell 6.75 hours to catch up to Mr. Caldwell.

This is a rate time distance problem in mathematics, typically learned in middle school. To calculate how long it will take Mrs. Caldwell to catch up with Mr. Caldwell, we need to compare the distance traveled by each person in the same time. Because rate equals distance over time (r=d/t), we know that the distance each person traveled is rate x time.

Mr. Caldwell left 3 hours before Mrs. Caldwell, so he traveled at 45 mph for 3 hours, or 135 miles. Once Mrs. Caldwell leaves, she needs to cover these 135 miles at a faster speed to catch up. Her speed is 20 mph greater than Mr. Caldwell’s. We divide the distance that Mr. Caldwell has covered (135 miles) by the difference in their speeds (20 mph) to find it will take Mrs. Caldwell 6.75 hours to catch up to him.

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Answer:

m+p-n

Step-by-step explanation:

given that Jerry manages a local car dealership. At the beginning of the month, his lot had m vehicles. During the month his salesman sold n vehicles, and he purchased p vehicles more

We are to find the number of vehicles did the dealership have at the end of the month

At the end of the month the dealer would have

no of vehicles at the start of the month- sales of the vehicle in that month+Purchase of vechicles during that month

No of vehicles at the start of the month = m

Purchase during month                           =p

Total vehicles including purchase         = m+p

LESS: Vehicles sold in the month         =   n

No of vehicles at the end                      = m+p-n

Answer:

y = -2x + 4

Step-by-step explanation:

Slope: -2

Intercept: +4

Answer:

i need more context

Step-by-step explanation:

Hence correct option is b with 4 colors.

Step by-step explanation:

We are given a graph in which we need to color every vertex or node such that no adjacent vertex or node should have the same color, ex:- If color of node B is blue than it's adjacent vertex A and D must not have the same blue color. Now, Let's start coloring of graph :

Color vertex A as red : Now, it's adjacent vertex as B,C,D,E must not have red color we know this!.

Color vertex B as blue: Now, it's adjacent vertex A and D must not have blue color!

Color vertex C as blue:  Now, it's adjacent vertex A,E and D must not have blue color!

Color vertex D as green:  Now, it's adjacent vertex A,B,C and E must not have green color!

Color vertex E as purple:  Now, it's adjacent vertex C and D must not have purple color!

Hence correct option is b with 4 colors.

Answer:

Tara bought a total of 160 treats.

Step-by-step explanation:

We are given the following in the question:

Number of boxes of dog treats = 3

Number of treats in each dog box = 40

Total number of treats in dog box =

[tex]40 \times 3 = 120[/tex]

Number of boxes of cat treats = 2

Number of treats in each cat box = 20

Total number of treats in cat box =

[tex]20\times 2 = 40[/tex]

Total number of treats Tara brought =

Total number of treats in dog box + Total number of treats in cat box

[tex](40\times 3)+(20\times 2)\\= 120 + 40\\=160[/tex]

Thus, Tara bought a total of 160 treats.

The interest expense for West Company in Year 1 is approximately $1,141, calculated using the principal of $38,000, the annual interest rate of 9%, and the time from the loan date to the end of Year 1, which is ⅓ of a year.

The student's question involves calculating the amount of interest expense to be reported on the income statement for West Company in Year 1, given that the company borrowed $38,000 on September 1, Year 1 at an annual interest rate of 9% with an 18-month term. To calculate the interest expense for Year 1, we need to consider the amount of time from the loan initiation date (September 1, Year 1) to the end of Year 1 (December 31, Year 1), which is 4 months or ⅓ of a year.

Interest Expense calculation:

Interest Expense = Principal Amount × Annual Interest Rate × Time in Years

Interest Expense for West's Year 1 = $38,000 × 9% × (⅓)

Interest Expense for West's Year 1 = $38,000 × 0.09 × 0.3333

Interest Expense for West's Year 1 = $1,141 (approximately)

Therefore, the interest expense appearing on West's Year 1 income statement would be approximately $1,141.

Answer:

666.667 feet

Step-by-step explanation:

Slope = -1

Intercept = 10

y = -t + 10

y is the acceleration

Integrate y fornv

v = -t²/2 + 10t + c

At t=0, v=0 so c = 0

v = -t²/2 + 10t

Turns when v = 0,

-t²/2 + 10t = 0

t = 0, 20

Integrate v for s

s = -t³/6 + 5t² + c

At t = 0, s = 10

10 = c

s = -t³/6 + 5t² + 10

s at t=30,

-(30³)/6 + 5(30)² + 10

= 10m

(Back to starting point)

At t = 20,

Displacement in

-(20³)/6 + 5(20)² + 10

= 343.333

Total distance = 2(343.333-10)

= 666.6667

The total distance the car travels in this 30 second interval is 1333.34 units

From the graph, we have the following points

(0, 10) and (10, 0).

Start by calculating the slope (m) of the graph

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{0 - 10}{10-0}[/tex]

[tex]m =- \frac{10}{10}[/tex]

[tex]m =- 1[/tex]

The equation is then calculated as:

[tex]y = m(x -x_1) + y_1[/tex]

This gives

[tex]y = -1(x -0) + 10[/tex]

[tex]y = -1x+ 10[/tex]

[tex]y = -x+ 10[/tex]

The above equation represents the acceleration (y) as a function of time (x).

Integrate to get the velocity (v)

[tex]v = -\frac{x\²}{2} + 10x + c[/tex]

From the question, we have:

The velocity (v) of the car is 0, when the time (x) is 0.

So, we have:

[tex]0 = -\frac{0\²}{2} + 10(0) + c[/tex]

This gives

[tex]c = 0[/tex]

So, the equation becomes

[tex]v = -\frac{x\²}{2} + 10x + 0[/tex]

[tex]v = -\frac{x\²}{2} + 10x[/tex]

Set v = 0.

So, we have:

[tex]-\frac{x\²}{2} + 10x = 0[/tex]

Multiply through by -2

[tex]x^2 -20x = 0[/tex]

Factorize

[tex]x(x -20) = 0[/tex]

Split

[tex]x = 0\ or\ x -20 = 0[/tex]

Solve for x

[tex]x = 0[/tex] or [tex]x = 20[/tex]  

Integrate velocity (v) to get the displacement (d)

[tex]v = -\frac{x\²}{2} + 10x[/tex]

[tex]d = -\frac{t\³}{6} + 5t\² + c[/tex]

From the question, we have:

The position (d) of the car is 10, when the time (x) is 0.

So, we have:

[tex]-\frac{(0)\³}{6} + 5(0)\² + c = 10[/tex]

[tex]c = 10[/tex]

So, the equation becomes

[tex]d = -\frac{t\³}{6} + 5t\² + 10[/tex]

The position at 30 seconds is:

[tex]d = -\frac{(30)\³}{6} + 5(30)\² + 10[/tex]

[tex]d = 10[/tex]

The position at 20 seconds is:

[tex]d = -\frac{(20)\³}{6} + 5(20)\² + 10[/tex]

[tex]d = 676.667[/tex]

The total distance is then calculated as:

[tex]Total = 2 \times (d_2 -d_1)[/tex]

This gives

[tex]Total = 2 \times (676.667 -10)[/tex]

[tex]Total = 2 \times 666.667[/tex]

[tex]Total = 1333.34[/tex]

Hence, the total distance is 1333.34 units

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Answer:

P ( 2 R , 4 O , 6 G ) = 0.0261

Step-by-step explanation:

Given:

- Red beans = 8

- Orange beans = 6

- Green beans = 9

Find:

What is the probability of reaching into the bag and randomly withdrawing 12 jellybeans such that the number of red ones is 2, the number of orange ones is 4, and the number of green ones is 6?

Solution:

- The question requires the number of selection of 12 jellybeans we can make from total available such that out of those 12 we choose 2 Red, 4 Orange and 6 Green.

- For selection we will use the combinations. So to choose 2 Red from 8; Choose 4 Orange from 6 and 6 green from 9 available. The number of possible outcomes with such condition is:

          Outcomes ( 2 R , 4 O , 6 G ) = 8C2 * 6C4 * 9C6

                                                         = 28*15*84

                                                         = 35280

- The total number of outcomes if we randomly select 12 beans irrespective how many of each color we select from available 23 we have:

          Outcomes ( Select 12 from 23 ) = 23C12

                                                               = 1352078

- Hence, the probability for the case is given by:

P ( 2 R , 4 O , 6 G ) = Outcomes ( 2 R , 4 O , 6 G ) / Outcomes ( Select 12 from 23 )

P ( 2 R , 4 O , 6 G ) = 35280 / 1352078 = 0.0261

Answer:

The first zero after decimal point and 4 only

Step-by-step explanation:

Despite having 5 decimal points, the rules of significant figures dictate that unless there is a digit other than zero after, the only significant numbers are those that come before zero. For this case, the significant digits are only 0.04 but if it was 0.0400005 then all the other zeros would have also be considered significant.

Answer:

2.8 units

You should get 2√(2) or √(8) which is less than 3 and greater than 2.

Answer: 2.8 units

Step-by-step explanation:

The formula for determining the distance between two points on a straight line is expressed as

Distance = √(x2 - x1)² + (y2 - y1)²

Where

x2 represents final value of x on the horizontal axis

x1 represents initial value of x on the horizontal axis.

y2 represents final value of y on the vertical axis.

y1 represents initial value of y on the vertical axis.

From the given points

x2 = 5

x1 = 3

y2 = 4

y1 = 2

Therefore,

Distance = √(5 - 3)² + (4 - 2)²

Distance = √2² + 2² = √4 + 4 = √8

Distance = 2.8 units

Answer:

B

Step-by-step explanation:

The slope is rise over run, meaning it is 3/4. The y-intercept is 2, making the equation y = (3/4)x + 2

The probability of picking a red marble 3 times in a row  = [tex](\frac{8}{125})[/tex]

Step-by-step explanation:

Here, the total number of red marbles  =  4

The total number of blue marbles  = 6

Now, as the Repetition is allowed.

Let E: The event of picking a red marble

[tex]P(E) = \frac{\textrm{The total number of red marbles}}{\textrm{Total marbles}}[/tex]

So, [tex]P(E) = \frac{4}{10} = \frac{2}{5}[/tex]

Now, as we know after first picking, the chosen red marble is REPLACED in the bowl.

So, again the bowl has 4 red marbles and 10 in total.

⇒P(picking a red marble again)  = 2/5

And similarly for the third time.

So, the probability of picking a red marble 3 times in a row  = [tex](\frac{2}{5}) \times (\frac{2}{5})\times (\frac{2}{5}) = \frac{8}{125}[/tex]

The probability of selecting a red marble on each of the three picks is 2/55.

To determine the probability of selecting a red marble on each of the three picks, we need to consider the number of red and blue marbles in the bowl and the fact that a marble is replaced after each pick.

First, there are 4 red marbles and 6 blue marbles in the bowl. For the first pick, the probability of selecting a red marble is 4/10. After the pick, the bowl will have 5 red marbles and 6 blue marbles.

For the second pick, the probability of selecting a red marble is 5/11. After the pick, the bowl will have 6 red marbles and 6 blue marbles. Finally, for the third pick, the probability of selecting a red marble is 6/12, which simplifies to 1/2.

To find the probability of all three picks being red, we multiply the probabilities of each pick: (4/10) * (5/11) * (1/2) = 2/55.

Therefore, the probability of selecting a red marble on each of the three picks is 2/55.

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For a given data set, the equation of the least squares regression line will always pass through the point [tex]\((\bar{x}, \bar{y})\),[/tex] where [tex]\(\bar{x}\)[/tex] is the mean of the x-values and[tex]\(\bar{y}\)[/tex] is the mean of the y-values.

The least squares regression line minimizes the sum of squared differences between the observed y-values and the values predicted by the line. The equation of the line is given byy = mx + b, where m is the slope and bis the y-intercept. The slopem and y-intercept b are determined by formulas involving the means[tex](\(\bar{x}\)[/tex] and [tex]\(\bar{y}\))[/tex]and other statistical measures from the data set.

The specific formulas for the least squares regression line are:

[tex]\[ m = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n} (x_i - \bar{x})^2} \]\[ b = \bar{y} - m\bar{x} \][/tex]

It can be observed from the formulas that when [tex]\(x = \bar{x}\)[/tex], the corresponding y value is[tex]\(\bar{y}\)[/tex]. Therefore, the least squares regression line passes through the point[tex]\((\bar{x}, \bar{y})\)[/tex]. This point represents the centroid of the data set and ensures that the line adequately represents the overall trend of the data.

Question:

It seems there might be some repetition or an incomplete question in your request. Could you please provide more details or clarify your question so that I can assist you accurately? If you have a specific question related to the least squares regression line or any other topic, feel free to provide more context, and I'll do my best to help you.

Answer: Option 'D' is true.

Step-by-step explanation:

Since we have given that

Number of points are 7,5,3, and 2 each.

Product of the point values of the removed beads = 147000

So, the possible way is given by

[tex]2^3\times 3\times 5^3\times 7^2=147000[/tex]

Since no other beads is a multiple of 7.

So, there must be two red beads removed.

Hence, Option 'D' is true.

Answer:

V = 11.3 ft^3

Step-by-step explanation:

The volume of a cone is given by one third of its base area multiplied by its height:

V = (1/3)*A*h

This cone have a circular base, so the base area is given by

A = pi*r^2, where r is the base radius

The length of a circumference is given by L = 2*pi*r

the base circumference is 5 ft, so we can calculate the base radius:

5 = 2*pi*r -> r = 5/(2*pi)

Using this value, we can calculate A:

A = pi*r^2 = pi * [5/(2*pi)]^2 = pi * 25/(4*pi^2) = 25/(4*pi) = 1.9894

Now, we use the formula to calculate the volume:

V = (1/3)*A*h = (1/3) * 1.9894 * 17 = 11.2735 ft^3

rounding it, we have V = 11.3 ft^3

Answer:

[tex]3\frac{3}{10} = \frac{33}{10}[/tex]

Step-by-step explanation:

Answer:

B) x=-3(y+3)^2+4

Step-by-step explanation:

Plug quadratic in for proof

Answer:

The answer to your question is Letter C

Step-by-step explanation:

Data

Vertex (4, -3)

Process

From the image, we notice that it is a horizontal parabola that opens to the left.

So, it formula must be          (y - k)² = 4p(x - h)

-Substitute the vertex

                                             (y + 3)² = 4p(x - 4)

Consider 4p = 1

                                             (y + 3)² = x - 4

Solve for x

                                             x = (y + 3)² + 4

Solution

Letter C

Answer:

a) 0.00019923%

b) 47.28%

Step-by-step explanation:

a) To find the probability of all sockets in the sample being defective, we can do the following:

The first socket will be in a group where 5 of the 38 sockets are defective, so the probability is 5/38

The second socket will be in a group where 4 of the 37 sockets are defective, as the first one picked is already defective, so the probability is 4/37

Expanding this, we have that the probability of having all 5 sockets defective is: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%

b) Following the same logic of (a), the first socket have a chance of 33/38 of not being defective, as we will pick it from a group where 33 of the 38 sockets are not defective. The second socket will have a chance of 32/37, and so on.

The probability will be (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%

Answer:

The probability of selecting a  person which is  self-employed but not married equals 1/8.

Step-by-step explanation:

Here, the given survey says:

Total number of people surveyed = 248

Number of people married = 156

The number of people are self employed = 70

Now, 25% of people who are married are SELF EMPLOYED.

Now, calculating 25% of 156 , we get:

[tex]\frac{25}{100} \times 156 = 39[/tex]

⇒ out of total 156 married people, 39 are self employed.

So, number of  self employed people but  not married

= Self employed people - Self employed people PLUS  married

=  70  -  39   =  31.

So, the probability that the person selected will be self-employed but not married = [tex]\frac{\textrm{The total number of people self-employed but not married}}{\textrm{Total Number of people}}[/tex] =  [tex]\frac{31}{248} = \frac{1}{8}[/tex]

Hence The probability of selecting a  person which is  self-employed but not married equals 1/8.

Answer:

The equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].

Step-by-step explanation:

Given:

Amount of food in the container = [tex]x \ cups[/tex]

Amount of food added in the container = [tex]2\frac12\ cups[/tex]

We will now convert the mixed fraction into Improper fraction by Multiplying the whole number part by the fraction's denominator and then add that to the numerator  and then write the result on top of the denominator.

[tex]2\frac12\ cups[/tex] can be rewritten as [tex]\frac{5}{4}\ cups[/tex]

Amount of food added in the container =  [tex]\frac{5}{4}\ cups[/tex]

Amount of food removed from container to feed dog  = [tex]\frac34 \ cups[/tex]

Amount of food remaining = [tex]5\frac{1}{4} \ cups[/tex]

[tex]5\frac{1}{4} \ cups[/tex] can be Rewritten as = [tex]\frac{21}{4}\ cups[/tex]

Amount of food remaining =  [tex]\frac{21}{4}\ cups[/tex]

We need to write the equation for above scenario.

Solution:

Now we can say that;

Amount of food remaining is equal to Amount of food in the container plus Amount of food added in the container minus Amount of food removed from container to feed dog.

framing in equation form we get;

[tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex]

Hence the equation representing the scenario is [tex]x+\frac{5}{4}-\frac{3}{4} = \frac{21}{4}[/tex].

Answer:

23, 22, 4, 3, -60

Step-by-step explanation:

f(x)=(x⁴ - 6x¹⁰)²³

f'(x)= 23(x⁴ - 6x¹⁰)²²(4x³ - 60x⁹)

Answer:

10%

Step-by-step explanation:

In this question, we are asked to calculate the percentage error in a measurement.

This can be obtained by first getting the error involved. That is calculated by Subtracting the value calculated from the actual value. That is 9.5 - 8.9 = 0.6

The percentage error is thus 0.6/9.5 * 100 = 6%

The value is actually 10% to the nearest tenth of a percent

Answer:

6.3%

Step-by-step explanation:

Answer: the Smaller number is 3

The larger number is 60

Step-by-step explanation:

Let x represent the smaller of the numbers.

Let y represent the larger number.

One number is 20 times another number. This means that

y = 20x

The product of the two numbers is 180. This means that

xy = 180- - - - - - - - - -1

Substituting y = 2x into equation 1, it becomes.

x × 20x = 180

20x² = 180

x² = 180/20 = 9

x = √9

x = 3

y = 20x = 20 × 3

y = 60

Answer:

There would be

13 x 8 x 4 x 3 = 3,276 different cheeseburger combinations

If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him

3276 x 10 = 32760 minutes

Eating round the clock, it would take him

32760 / 60 = 546 hours

546 / 24 = 22 days 18 hours

Now these are the numbers I'm seeing

1313 buns

88 cheese

44 lettuces

33 tomatoes

There would be

1313 x 88 x 44 x 33 = 167,769,888 different cheeseburger combinations

If the taste tester takes 10 minutes to eat a cheeseburger, then it would take him

167769888 x 10 = 1,677,698,880 minutes

1677698880 / 60 = 27,961,647 hours

27961647 / 24 = 1,165,068.62 days

1165068.62 / 365 = 3,191.97 years

Step-by-step explanation:

cos (a - b) is 56/65

Step-by-step explanation:

Given sin a = 5/13, find cos a.

sin a = opposite side/hypotenuse = 5/13

The adjacent side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Adjacent side² = Hypotenuse² - Opposite Side²

                             = 13² - 5² = 169 - 25 = 144

∴ Adjacent Side = 12

⇒ cos a = adjacent side/hypotenuse = 12/13

Given cos b = 3/5, find sin b.

cos b = adjacent side/hypotenuse = 3/5

The opposite side can be found using Pythagoras Theorem.

Hypotenuse² = Opposite Side² + Adjacent Side²

⇒ Opposite side² = Hypotenuse² - Adjacent Side²

                             = 5² - 3² = 25 - 9 = 16

∴ Opposite Side = 4

⇒ sin b = opposite side/hypotenuse = 4/5

Find cos(a - b).

cos(a - b) = cos a cos b + sin a sin b

               = 12/13 × 3/5 + 5/13 × 4/5

               = 36/65 + 20/65 = 56/65

Answer:

A. upside down

Explanation:

Pyramid population, sometimes called afe-gender population is an illustration showing showing various age group distribution. The illustration usually forms the shape of a pyramid, hence its name as the age group increases. It's assumed there are more younger people than older people in a region or country. In this case, the pyramid population is said to be Upside down, because in those regions listed, the number of elderly people is greater than those of the younger people. Population pyramid usually represents the distribution or breakdown of ages and gender of a region at a given point in time.

Answer:

Therefore the radius of curvature at A is 432.03 m.

Step-by-step explanation:

Radius of curvature : If an object moves in curvilinear motion, then any point of the motion, the radius of circular arc path which best approximates the curve at that point is called radius of curvature.

Radius of curvature =[tex]\rho = \frac{V^2_p}{a}[/tex]

[tex]V_p[/tex]= velocity

a = acceleration perpendicular to velocity.

Velocity at the point A = [tex]V_A= 100 \ km/h[/tex] [tex]=\frac{100 \ km}{1 \ h}= \frac{100\times 1000 \ m}{3600 \ s}=\frac{250}{9}[/tex] m/s

Velocity at the point C [tex]=V_C=50 \ km/ h=\frac{125}{9} \ m/s[/tex]

The distance between A and B is 120 m.

To find the declaration between the point A and C we use the following formula

[tex]V^2_C=V^2_A+2a_ts[/tex]

[tex]\Rightarrow( \frac{125}{9})^2=(\frac{250}9})^2+2a_t.120[/tex]

⇒[tex]a_t[/tex] = -2.41 m/s²

[tex]a_t[/tex]= tangential acceleration

Given the passengers experience a total acceleration of 3 m/s².

Total acceleration= 3 m/s².

[tex]a = \sqrt{a^2_t+a^2_n[/tex]

[tex]\Rightarrow a^2_n= a^2- a^2_t[/tex]

[tex]\Rightarrow a_n=\sqrt{3^2-(-2.41)^2}[/tex]

       = 1.786 m/s²

Radius of curvature  [tex]\rho_A=\frac{V^2_A}{a_n}[/tex]

                                   [tex]=\frac{(\frac{250}{9})^2}{1.786}[/tex]

                                  = 432.03 m

Therefore the radius of curvature at A is 432.03 m.

Answer:

a) [tex]\frac{x^{2}}{2352.25} + \frac{y^{2}}{529} = 1[/tex], b) [tex]c = 42.7 ft[/tex], c) [tex]A \approx 3504.447 ft^{2}[/tex]

Step-by-step explanation:

a) An Ellipse centered at origin is modelled by using this formula:

[tex]\frac{x^{2}}{a^2} +\frac{y^2}{b^2}=1[/tex]

Where [tex]a, b[/tex] represents the lengths of horizontal and vertical axis, respectively. Let consider that horizontal axis is parallel and coincident with width of Statuary Hall. So, the measures of each axis are, respectively:

[tex]a = 48.5 ft, b = 23 ft[/tex]  

By substituting known variables, the equation that models the hall is:

[tex]\frac{x^{2}}{2352.25} + \frac{y^{2}}{529} = 1[/tex]

b) The distance between origin and any of the foci is:

[tex]c = \sqrt{a^{2} - b^{2}} \\c = 42.7 ft[/tex]

c) The area of ellipse can determined by applying this formula:

[tex]A = \pi \cdot a \cdot b[/tex]

[tex]A \approx 3504.447 ft^{2}[/tex]