Triangle A B C is cut by line segment S T. Line segment S T goes from side A B to side C B. Lines S T and A C are parallel. The length of S B is 10 feet, the length of B T is 9 feet, and the length of C T is 2.7 feet. What is the length of Line segment S A? a) 1.89 ft b) 2.43 ft c) 3 ft d) 7 ft.

Answer:

72 yrs old.

Step-by-step explanation:

The combined age

D+O=96

The owner is 3 times older than dog

O=3D

D+3D=96

4D = 96

D= 24

Now substitute the value of D in O=3D

O=3.24= 72

The owner is 72 years old.

To solve this problem, we can use algebra. Let's define the dog's age as 'd' and the owner's age as 'o'. By solving the two equations (o + d = 96 and o = 3d), we can determine that the dog is 24 years old and the owner is 72 years old.

The question asks us to find the age of a dog's owner, given that the combined ages of the owner and the dog are 96 years, and the owner's age is three times the age of the dog. We can use algebra to solve this problem.

Let's define the dog's age as 'd' and the owner's age as 'o'. We know that o = 3d (the owner's age is three times the dog's age) and o + d = 96 (the combined ages of the owner and the dog are 96).

To find the owner's age, substitute '3d' for 'o' in the second equation: 3d + d = 96. This simplifies to 4d = 96. Dividing both sides of the equation by 4 gives us d = 24, meaning the dog is 24 years old. Now we substitute d = 24 into the equation o = 3d, resulting in o = 72. Therefore, the owner is 72 years old.

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Answer:

[tex]x=\frac{83}{50}[/tex]

Step-by-step explanation:

we know that

If the three points are collinear

then

[tex]m_A_B=m_A_C[/tex]

we have

A (1, 2/3), B (x, -4/5), and C (-1/2, 4)

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

step 1

Find the slope AB

we have

[tex]A(1,\frac{2}{3}),B(x,-\frac{4}{5})[/tex]

substitute in the formula

[tex]m_A_B=\frac{-\frac{4}{5}-\frac{2}{3}}{x-1}[/tex]

[tex]m_A_B=\frac{\frac{-12-10}{15}}{x-1}[/tex]

[tex]m_A_B=-\frac{22}{15(x-1)}[/tex]

step 2

Find the slope AC

we have

[tex]A(1,\frac{2}{3}),C(-\frac{1}{2},4)[/tex]

substitute in the formula

[tex]m_A_C=\frac{4-\frac{2}{3}}{-\frac{1}{2}-1}[/tex]

[tex]m_A_C=\frac{\frac{10}{3}}{-\frac{3}{2}}[/tex]

[tex]m_A_C=-\frac{20}{9}[/tex]

step 3

Equate the slopes

[tex]m_A_B=m_A_C[/tex]

[tex]-\frac{22}{15(x-1)}=-\frac{20}{9}[/tex]

solve for x

[tex]15(x-1)20=22(9)[/tex]

[tex]300x-300=198[/tex]

[tex]300x=198+300[/tex]

[tex]300x=498[/tex]

[tex]x=\frac{498}{300}[/tex]

simplify

[tex]x=\frac{83}{50}[/tex]

Answer:0.277

Step-by-step explanation:

Given there are three boxes i.e. A , B and C

Probability of selecting any box is [tex]P_1=\frac{1}{3}[/tex]

Box A contains 2 keys out of which is 1 is correct so Probability of selecting the right key is [tex]P_2=\frac{1}{2}[/tex]

Box B contains 3 keys out of which is 1 is correct so Probability of selecting the right key is [tex]P_3=\frac{1}{3}[/tex]

Box C contains 2 keys out of which is 1 is correct but we cannot use it so Probability of selecting the right key is [tex]P_4=0[/tex]

Probability of selecting the right key is [tex]P=P_1\times P_2+P_1\times P_2+P_1\times P_3[/tex]

[tex]P=\frac{1}{3}\times \frac{1}{2}+\frac{1}{3}\times \frac{1}{3}+\frac{1}{3}\times 0[/tex]

[tex]P=\frac{5}{18}[/tex]

[tex]P=0.277[/tex]

Step-by-step explanation:

the answer is

Y=2.5

X=3.75

Answer:

6 brownies and 2 cupcakes.

Step-by-step explanation:

Let the number of brownies be b and the number of cupckes be c.

We have the following system:

b = 3c

1.5b + 3c = 15

Substituting for  b in the second equation:

4.5c  + 3c = 15

7.5c = 15

c =  2.

Thus b = 3c = 6.

Answer:

[tex]8\times10^5m^2[/tex]

Step-by-step explanation:

To find the cross-section area at a point below the faucet

we can use following equations

[tex]v_1^2=v_2^2+2ay[/tex]

and equation of continuity

[tex]A_1v_1=A_2v_2[/tex]

v_1= velocity at the out let

v_2=  velocity at the inlet (faucet)= 0.75 m/s

y = distance below the faucet = 0.10 m

A_1= cross-sectional area of the water stream at a point 0.10 m below the faucet.

A_2= area of faucet= 1.9 × 10-4m2

from above two equation we can write

[tex]A_1= \frac{A_2v_2}{\sqrt{v_2^2+2ay} }[/tex]

now putting the values we get

[tex]A_1= \frac{1.9\times10^{-4}\times0.75}{\sqrt{0.75^2+2\times9.80\times0.10} }[/tex]

A_1= 0.00008= [tex]8\times10^5[/tex]

Answer:

The fractional reserve banking system depends upon the confidence and trust of the public.

Step-by-step explanation:

The fractional reserve banking means that bank uses the deposits of customers to lend money to the borrowers.

Answer:

  x 2 −2 3 −3

  y 4 4 9 −9

Step-by-step explanation:

A table does not represent a function if any x-value is repeated. The table shown above is the only one with unique x-values.

Answer:

[tex] x= 5*400 ft = 2000 ft[/tex]

Step-by-step explanation:

For this case we can use the figure attached and we are interested in order to find the value of x.

We have two similar triangles (DEC and ABC) and we can find the scale factor like this:

[tex]Factor= \frac{EC}{BC}=\frac{500ft}{100ft}=5[/tex]

And now we can apply proportions in order to find the value of x using the two sides DE and BA, since we have the ratio between the triangle DEC and ABC we have this:

[tex]Factor=5=\frac{x ft}{400 ft}[/tex]

And solving for x we got:

[tex] x= 5*400 ft = 2000 ft[/tex]

And then the distance across the lake would be 2000 ft

Answer:

ewq

Step-by-step explanation:

Answer:

  $295

Step-by-step explanation:

Let d represent the amount Danny contributed. Then Beth contributed (d+80) and Katie contributed ((d+80)-20) = (d+60). The total from the three friends is ...

  d + (d+80) +(d+60) = $1025

  3d = 885 . . . . . . . . . . . . . . . . . . . subtract 140

  d = 295 . . . . . . . . . . . . . . . . . . . . divide by 3; Danny's contribution

Danny contributed $295.

Answer:

Solution

(x, y) = (2, 3)

Step-by-step explanation:

Answer:

View Image

Step-by-step explanation:

Solve for y.

You have a ≥ so it's a solid line and you shade above that line.

Answer:

108 degrees

Step-by-step explanation:

To solve this adequately, we simply make a substitution. We can say let sin2.5x = x

Hence we can thus have the quadratic equation form which we can solve.

x ^2 − 4x − 5 = 0.

Solving this yields the following:

x^2 +x - 5x -5 = 0

x( x + 1) -5(x + 1) = 0

(x - 5) (x + 1) = 0

x = 5 or -1

Recall the substitution:

sin2.5x = x

We cannot use the value -5 as the value of the sine function cannot be in this range. We thus ignore it and pick the -1 answer only.

Sin2.5x = -1

2.5x = arcsin(-1) = 270

2.5x = 270

x = 270/2.5 = 108 degrees

Answer: the number of the parking space covered by the car is 87

Step-by-step explanation:

Numbers are assigned to each parking spot. Looking closely at the numbers assigned to each spot, the numbers are inverted and the number on each successive spot differ by one. The numbers are 86, 87, 88, 89, 90, 91

Therefore, the number assigned to the spot where the car would be 87

Answer:

$18.40

Step-by-step explanation:

64*1.15=73.60

73.60/4=18.40

Answer:

Statements (1) and (2) TOGETHER are NOT sufficient.

Explanation:

As in the equation (327)(510)(z) = (58)(914)(xy) there are THREE variables in total i.e. "x", "y" and "z" hence minimum three equations are required to find out values of all variables. Hence,

If the given number of equations is equal to total variable used in any of the equation, values of all the variables can be find out otherwise there can be unlimited number of solutions.

So, value of "x" cannot be determined with the given data.

A linear function can be used to represent the total retail cost of renting a vacuum cleaner: F(x) = 31.50 + 32x.

A linear function can be used to represent the total retail cost of renting a vacuum cleaner. Let's denote the fixed fee as $31.50 and the hourly rate as $32. The linear function F for the total retail cost of a vacuum cleaner can be written as:

F(x) = 31.50 + 32x

Where x represents the number of hours the vacuum cleaner is rented for and F(x) gives the total retail cost.

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The flat fee that the store charges is $14 and the cost for 7 hours is $56

A linear equation is on the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

let f for the total rental cost of a vacuum cleaner for x hours

Using the points (1, 20) and (3, 32) from the table:

f-f1=(f2-f1)/(x2-x1) (x-x1)

f-20=(32-20)/(3-1) (x-1)

f(x)=6x+14

The flat fee that the store charges is $14

The reasonable domain is 1 ≤ x ≤ 12

The cost for 7 hours is:

f(7) = 6(7) + 14 = 46

here is the complete question-

A hardware store rents vacuum cleaners that customers may use for part or all of a day before returning. The store charges a flat fee plus an hourly rate. Part A Write a linear function f for the totall rental cost of the vacuum cleaner. A. f(x)=6x+14 B. f(x)=3x+14 C, f(x)=3x+22 D. f(x)=6x+24 Part B What is a reasonable domain for the function? A. 14 B. 1 C. 0 D. 20

Given the width and length of the rectangle in terms of x, the formula for the perimeter is substituted with these expressions. After simplifying, the perimeter of the rectangle is found to be represented by the equation 8.5x + 3.

The subject represents a problem in mathematics, specifically geometry. The perimeter of a rectangle is calculated by the formula 2(width + length). Given that the width is meant to be represented by (3x - 1.5) and the length is represented by (1.25x + 3), we substitute these expressions into our formula to find the perimeter of the rectangle.

Perimeter = 2[(3x - 1.5) + (1.25x + 3)].

To simplify, the above equation becomes:

Perimeter = 2[4.25x + 1.5],

which then further simplifies to:

Perimeter = 8.5x + 3.

The perimeter of the rectangle is therefore represented by the expression 8.5x + 3.

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Answer:

The saving amount on selling of three books together after discount of 20% is $2.69

Step-by-step explanation:

Given as :

The original price of first book = $2.50

The original price of second book = $4.95

The original price of third book = $6.00

The total percentage discount on the book = d = 20%

Let The saving money after purchased of book = $x

And Let the selling price of the book = s.p = $y

Now, According to question

The total market price of three books = m.p = $2.50 + $4.95 + $6.00

I.e m.p = $13.45

Now, from discount formula

Discount % = [tex]\dfrac{market price - selling price}{market price}[/tex]

Or, d% = [tex]\dfrac{m.p - s.p}{m.p}[/tex]

Or, 20% = [tex]\dfrac{13.45 - y}{13.45}[/tex]

Or, [tex]\dfrac{20}{100}[/tex] = [tex]\dfrac{13.45 - y}{13.45}[/tex]

Or, 20 × 13.45 = (13.45 - y) × 100

Or, 269 = 1345 - 100 y

Or, 100 y = 1345 - 269

Or, 100 y = 1076

∴  y = [tex]\dfrac{1076}{100}[/tex]

i.e y = $10.76

So, The selling price of three books = y = $10.76

∴ The saving amount on selling of three books together after discount of 20% = x = Total market price - Selling price

i.e x = m.p - y

or, x = $13.45 - $10.76

or, x = $2.69

Hence ,The saving amount on selling of three books together after discount of 20% is $2.69  Answer

On 12th day Rosita will walk all three dogs

Solution:

Given that Rosita earns money by walking dogs after school and on weekends

She walks Madeline every other day,buddy every fourth day,and ernie every third day

Today she walked all three dogs

To find: the day when she walked all three dogs

From given question,

Madeline is walked every other day means every two days:  2

Buddy is walked every fourth day:  4

Ernie is walked every third day:  3

To find the day when she walked all three dogs, we have to find the least common multiple (LCM) of 2, 4, 3

L.C.M of 2, 4, 3:

List all prime factors for each number

Prime Factorization of 2 shows:

2 is prime  => [tex]2^1[/tex]

Prime Factorization of 3 shows:

3 is prime  => [tex]3^1[/tex]

Prime Factorization of 4 is:

[tex]2 \times 2 = 2^2[/tex]

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

2, 2, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 = 12

Thus on 12th day Rosita will walk all three dogs

Answer: the second option is the correct answer

Step-by-step explanation:

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

From the information on the graph y2 = - 1

y1 = - 2

x2 = 4

x1 = 0

Slope = ( - 2 - - 1)/(4 - 0) = - 1/4

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

To find the slope of a line we need two points through which it is passing.

From the figure, we can see that the line passes through (0,-2) and (4,-1).

Slope of a line passing through two points [tex](x_{1},y_{1})\ and\ (x_{2},y_{2})[/tex] is given by the formula:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Here x1=0 y1=-2 x2=4 y2=-1

Slope = [tex]\frac{-1-(-2)}{4-0}=\frac{1}{4}[/tex]

Hence the slope of the line is [tex]\frac{1}{4}[/tex]

Answer:

130000m^2

Step-by-step explanation:

a = 800m

b = 800m

c= 650m

α = 30°

4th he triangular trench is an isosceles triangle.

Area of a triangle = 1/2(bcsinA)

= 1/2(800*650*sin30°)

= 130,000m^2

Answer:

The area enclosed by the trenches is 130 000[tex]m^{2}[/tex]

Step-by-step explanation:

The two given sides of the trenches are 800m and 650m. Since the included angle of the two sides are given, then the area covered by the trenches can be calculated using the formula;

     Area of a triangle = [tex]\frac{1}{2}[/tex] × abSin C

where: a is the length of one side and b the length of the second side and C represents the value of the included angle.

Thus,

    a = 800m, b = 650m and C = 30°

So that,

Area enclosed by the trenches  = [tex]\frac{1}{2}[/tex] × abSin C

                                                          =  [tex]\frac{1}{2}[/tex] × 800 × 650 × Sin30°

                                                          = [tex]\frac{1}{2}[/tex] × 800 × 650 × 0.5

                                                          = 130 000

The area enclosed by the trenches  is 130 000[tex]m^{2}[/tex].

Answer:

$796

Step-by-step explanation:

We have been given that Marge bought a computer for $699 on the installment plan. The terms of the plan were a down payment of $100, then payments of $58 a month for 12 months.

First of all, we will find the amount paid in 12 months by multiplying $58 by 12 as:

[tex]\text{Amount paid in 12 months}=\$58\times 12[/tex]

[tex]\text{Amount paid in 12 months}=\$696[/tex]

Since Marge paid $100 as down payment, so her total cost would be down payment plus amount paid in 12 months.

[tex]\text{Marge's total cost}=\$100+\$696[/tex]

[tex]\text{Marge's total cost}=\$796[/tex]

Therefore, Marge's total cost was $796.

Answer:

the nth term of the sequence is [tex]a_n=6n+7[/tex]

Step-by-step explanation:

Given : An arithmetic sequence begins as follows: [tex]a_1=13, a_2=19[/tex]

To find : Which of the following gives the definition of its nth term?

Solution :

The nth term of the A.P is [tex]a_n=a+(n-1)d[/tex]

The first term is [tex]a=a_1=13[/tex]

The common difference is [tex]d=a_2-a_1[/tex]

[tex]d=19-13=6[/tex]

Substitute in the formula,

[tex]a_n=13+(n-1)6[/tex]

[tex]a_n=13+6n-6[/tex]

[tex]a_n=6n+7[/tex]

Therefore, the nth term of the sequence is [tex]a_n=6n+7[/tex]

The nth term of the given arithmetic sequence is defined by the formula an = 13 + (n-1)*6. This is derived from the general formula for an arithmetic sequence and using the given first two terms.

In this given problem, we have an arithmetic sequence. An arithmetic sequence is a list of numbers in which each term is obtained by adding a constant difference to the preceding term. For this particular sequence, the first term (a1) is 13, and the second term (a2) is 19. Hence, the common difference (d) between the terms is 19 - 13 = 6.

The general formula for the nth term (an) of an arithmetic sequence is given by an = a1 + (n-1)*d. In this situation, to represent any term in the series, the formula would be an = 13 + (n-1)*6. This formula can generate any term in the sequence, given the term number.

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Answer:

[tex]p_v = P(\chi^2_{4,0.05} >3.81)=0.43233[/tex]

Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed. So we can say that the 3 remedies ar approximately equally effective.

Step-by-step explanation:

A chi-square goodness of fit test "determines if a sample data matches a population".

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".

Assume the following dataset:

                               NyQuil          Robitussin       Triaminic     Total

No relief                    11                     13                      9               33

Some relief               32                   28                     27              87

Total relief                7                       9                      14               30

Total                         50                    50                    50              150

We need to conduct a chi square test in order to check the following hypothesis:

H0: There is no difference in the three remedies

H1: There is a difference in the three remedies

The level os significance assumed for this case is [tex]\alpha=0.05[/tex]

The statistic to check the hypothesis is given by:

[tex]\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]

The table given represent the observed values, we just need to calculate the expected values with the following formula [tex]E_i = \frac{total col * total row}{grand total}[/tex]

And the calculations are given by:

[tex]E_{1} =\frac{50*33}{150}=11[/tex]

[tex]E_{2} =\frac{50*33}{150}=11[/tex]

[tex]E_{3} =\frac{50*33}{150}=11[/tex]

[tex]E_{4} =\frac{50*87}{150}=29[/tex]

[tex]E_{5} =\frac{50*87}{150}=29[/tex]

[tex]E_{6} =\frac{50*87}{150}=29[/tex]

[tex]E_{7} =\frac{50*30}{150}=10[/tex]

[tex]E_{8} =\frac{50*30}{150}=10[/tex]

[tex]E_{9} =\frac{50*30}{150}=10[/tex]

And the expected values are given by:

                               NyQuil          Robitussin       Triaminic     Total

No relief                    11                     11                       11               33

Some relief               29                   29                     29              87

Total relief                10                     10                     10               30

Total                         50                    50                    50              150

And now we can calculate the statistic:

[tex]\chi^2 = \frac{(11-11)^2}{11}+\frac{(13-11)^2}{11}+\frac{(9-11)^2}{11}+\frac{(32-29)^2}{29}+\frac{(28-29)^2}{29}+\frac{(27-29)^2}{29}+\frac{(7-10)^2}{10}+\frac{(9-10)^2}{10}+\frac{(14-10)^2}{10} =3.81[/tex]

Now we can calculate the degrees of freedom for the statistic given by:

[tex]df=(rows-1)(cols-1)=(3-1)(3-1)=4[/tex]

And we can calculate the p value given by:

[tex]p_v = P(\chi^2_{4,0.05} >3.81)=0.43233[/tex]

And we can find the p value using the following excel code:

"=1-CHISQ.DIST(3.81,4,TRUE)"

Since the p values is higher than the significance level we FAIL to reject the null hypothesis at 5% of significance, and we can conclude that we don't have significant differences between the 3 remedies analyzed.

To test the hypothesis that three cough remedies are equally effective, conduct an Analysis of Variance (ANOVA) test and use the p-value, compared to the pre-set level of 0.05, to decide if the null hypothesis should be rejected or failed to reject.

The subject matter pertains to hypothesis testing, a method used in statistics to test the validity of a claim (hypothesis) about a population. In this case, the null hypothesis in your question is that the three cough remedies are equally effective. The alternative hypothesis (Ha) is that at least one of the remedies is different. The P-value, when set at 0.05, helps to decide on the rejection or non-rejection of the null hypothesis, depending on whether it’s greater or smaller than the P-value.

First, we need to perform an Analysis of Variance (ANOVA) test since we have more than two samples to compare. After conducting the test, we compare the P-value with our pre-set alpha (0.05). If the p-value obtained is less than 0.05, we can reject the null hypothesis, letting us conclude that not all cough remedies are equally effective. If, however, the p-value is more than 0.05, we fail to reject the null hypothesis, and hence, we can't confidently say that one cough remedy is more effective than the others.

Remember that failing to reject the null hypothesis does not prove it true, it only suggests that there's not enough evidence against it given our data and chosen significance level.

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Answer:

Aleatory

Step-by-step explanation:

This is an example of Aleatory type of insurance contact.

Definition:

A contract preoccupied with an unclear occurrence that delivers for imbalanced transfer of worth between the parties. Insurance plans are discretionary investments and, after sustaining a reported loss, a person must pay premiums for many years. Most insurance policies are aleatory contacts.

Answer:

??????????????????? what

The function's derivative, f'(x) = x²(x + 1)³3(x - 4)³, has 2 relative maximum and minimum points.

So, the correct answer is C) 2.

The function's derivative, f'(x) =  x²(x + 1)³3(x - 4)³, gives us information about the critical points of the function. Relative maximum and minimum points occur where the derivative is zero or undefined. To find these points, we set the derivative equal to zero and solve for x:  x²(x + 1)³3(x - 4)³ = 0. By analyzing the signs of the factors, we can determine the number of relative maximum and minimum points:

Therefore, the total number of relative maximum and minimum points is 2.

So, the correct answer is C) 2.

Answer:Lucas is faster

Step-by-step explanation:

Distance = speed × time

Time = distance × speed

the path from the bottom to the top of the mountain was 2 miles.

James climbed at an average rate of 3 mph. This means that the time it took James to climb to the top of the mountain would be

2/3 hours

James ran back at 4 mph. This means that the time it took James run back to the bottom of the mountain would be

2/4 = 1/2 hours

Total time that James spent would be

2/3 + 1/2 = 7/6 = 1.7 hours.

Lucas climbed at an average rate of 2 mph. This means that the time it took Lucas to climb to the top of the mountain would be

2/2 = 1 hour

Lucas ran back at 5 mph. This means that the time it took Lucas to run back to the bottom of the mountain would be

2/5 hours

Total time that James spent would be

1 + 2/5 = 1.4hours.

Answer:

James is faster

Step-by-step explanation:

It took 70 minutes for James to finish and 84 minutes for Lucas to finish and James was faster.

Step-by-step explanation:

Keep in mind that Distance = Speed * Time

First lets starts off with James,

Climbing rate of James = 3 mph

Running back rate of James = 4 mph

Total time taken by James =  3/4 x 2/4 = 14/12 = 7/6

Lets convert that into min to make it easier,

7/6 x 60 = 70 min

Now, lets look at lucas,

Climbing rate of Lucas = 2/2 = 1 hour(s) or 60 minutes

Climbing back rate of Lucas = 2/5 of an hour

Now lets convert this one into minutes,

2/5 x 60 = 24 minutes

Total time taken by Lucas = 24 + 60 = 84 minutes

so that means

James = 70 minutes

Lucas = 84 minutes

Therefore James was faster

Hope this helped and please correct me if I got something wrong :)

Answer:

$150

Step-by-step explanation:

Dad gives the girl 50 and she save 20 so 50-20 = 30. Then u multiply that by the number of months given...so 30*5= 150

Answer: 150

Step-by-step explanation:

50-20=30

30x5=150