Daniel created an intersection with his race track. One of the angles at the intersection is 55°. What are the three other angle measurements formed by the intersection?

Answer:

A) The solution set is (6,-8).

Step-by-step explanation:

3x - y = 26

-3x       - 3x        Subtract 3x from both sides

-y = -3x + 26     Divide both sides by -1

y = 3x - 26

Now plug this into 7x + 8y = -22 to solve for x

7x + 8(3x - 26) = -22        Distribute

7x + 24x - 208 = -22       Combine like terms

31x - 208 = -22

     + 208    + 208            Add 208 to both sides

31x = 186                           Divide both sides by 31

x  = 6

Plug this into y = 3x - 26 to solve for y

y = 3(6) - 26           Multiply

y = 18 - 26              Subtract

y = -8

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Final answer:

The system of equations is solved using the substitution method, resulting in x = 6 and y = -8. Hence, the correct choice is the ordered pair (6, -8).

Explanation:

To solve the system of equations by the substitution method, let's start by solving the second equation for y:

3x - y = 26
=> y = 3x - 26.

Now, substitute this expression for y into the first equation:

7x + 8(3x - 26) = -22
=> 7x + 24x - 208 = -22
=> 31x = 186
=> x = 6.

Now, substitute x back into the expression we found for y:

y = 3(6) - 26
=> y = 18 - 26
=> y = -8.

The solution to the system is the ordered pair (6, -8), which means the correct choice is:

O A. The solution set is { (6, -8) } (Type an ordered pair.)

Answer:

72 divided by 2 2/5 (or 2.4) = 30 in a row

Answer:

the answer is 30 in a row

Step-by-step explanation:

divide 72 by 2 2/5 and you get 30 in a row of the domino's

The extraneous solution of the logarithmic problem log₃( 18x³) -log(2x) = log₃144 is -4.

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c = b[/tex] can be written as,

log[tex]_a[/tex]b = c

where a is the base to which the power is to be raised,

b is the desired number that we want when power is to be raised,

c is the power that must be raised to a to get b.

Solving the function using the basic logarithmic value, we get,

log₃( 18x³) -log(2x) = log₃144

log₃ (18x³/2x) = log₃144

log(9x²) = log₃144

Take antilog.

9x² = 144

x = ±4

If we solve further we will get that the value of x can be either -4 or 4, if take the value of x as -4, in the beginning then you will get log₃(18(-4)³) as the log of negative value which is impossible.

Hence, x=-4 is an extraneous solution for the given expression log₃( 18x³) -log(2x) = log₃144.

Learn more about Logarithms:

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Answer:

5 miles

Step-by-step explanation:

In the diagram, the distance between the lighthouse is |AB|=c.

Using Cosine Rule,

c²=a²+b²-2abCos C

=7²+4²-2(4)(7)Cos 45°

=49+16-56cos45°

=25.40

c=√25.40=5.04 miles

The distance between the lighthouses is approximately 5 miles.

Answer:

The distance between the two lighthouse is 5miles

Step-by-step explanation:

Since the shape of the sketch is a right angled triangle we use SOHCAHTOA to solve. An image showing the step by step working is attached.

Step-by-step explanation:

The total number of students = 100

Let A represents calculus and B represents French

The no of students taking calculus = 32

The no of students taking French = 29

The no of students taking calculus and french = 13

the probability that the student is taking Calculus or French = ?

P (AUB) = P(A) + P(B) - P(A∩B)

= [tex]\frac{32}{100}[/tex] + [tex]\frac{29}{100}[/tex] - [tex]\frac{13}{100}[/tex]

= [tex]\frac{48}{100}[/tex]

Reducing to lowest fraction,  it becomes [tex]\frac{12}{25}[/tex]

The probability that the student is taking Calculus or French =  [tex]\frac{12}{25}[/tex]

The probability that a randomly selected student is taking Calculus or French is 12/25.

To find the probability that a randomly picked student is taking either Calculus or French, we use the principles of set theory, specifically the formula for the union of two sets:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Here,
A = Students taking Calculus = 32
B = Students taking French = 29
A ∩ B = Students taking both Calculus and French = 13
Total students = 100

The formulas for the probabilities are:
P(A) = 32/100
P(B) = 29/100
P(A ∩ B) = 13/100

Now substitute these values into the union formula:

P(Calculus or French) = 32/100 + 29/100 - 13/100 = 48/100 = 12/25

Therefore, the probability that a randomly picked student is taking either Calculus or French is 12/25.

Answer:

18%

Step-by-step explanation:

Say that the percent increase was x%. So, we can write this problem as:

70 + x% * 70 = 82.60

Remember that % means "out of 100", so x% is actually the same as x/100. We can then replace x% with x/100:

70 + (x/100) * 70 = 82.60

Both terms on the left side have 70, so we can factor that common number out:

70 * (1 + (x/100)) = 82.60

Divide both sides by 70:

1 + x/100 = 82.60/70 = 1.18

Subtract 1 from both sides:

x/100 = 0.18

Multiply by 100:

x = 18

Thus, the percent increase is 18%.

Hope this helps!

Answer:

18%

Step-by-step explanation:

Increase: 12.6

12.60/70 = 0.18

Your answer: 15.26%

Answer:

1 at (2.5, 2.5)

Step-by-step explanation:

you can try graphing it on desmo

Answer:

2300

Step-by-step explanation:

Answer:

2,300

Step-by-step explanation:

When we round to the hundreds place, we make sure the numbers behind the hundreds place are zero. Then we round. Here's the general rule for rounding: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. In this case we round the 2 in the hundreds place up to three because it is followed by a five.

Answer: ( C ) The perimeter of the rectangle is (10x+18) Units

Step-by-step explanation: This is the right answer because I just checked and I did the math

Answer:

it is c i had the same problem

Step-by-step explanation:

Answer:

x = 19cm

Step-by-step explanation:

use pythagorean theorem:

a² - c² = b²

10² - 22² = b²

100 - 484 = b²

384 = b²

√384 = b

19cm = b or x

Answer:

30.8cm

Step-by-step explanation:

i am from connexus 8th grd pre algrabra

unit 5 lesson 3

1. 1:2

2. C. yes they are similar they have porportional side lengths and = ange measures

3. x = 4.5m

4. x = 30.8cm

5. x = 6 m

i hope this helps! = ) <3

Answer: there would be 9 chipmunks after 5 years.

Step-by-step explanation:

An initial population of 7 chipmunks in Mary's yard increases by 6% each year. It means that the population is increasing in an exponential rate.

The function that models the situation is expressed as

f(x) = ab^x

Where

a represents the initial population of chipmunks

b represent the rate of growth

x represent the number of years

From the information given,

a = 7

b = 1 + 6% = 1 + 6/100 = 1.06

x = 5 years

After 5 years,

f(5) = 7 × 1.06^5

f(5) = 9

Answer:

Step-by-step explanation:

If a +  3b =  7, subtract 3b from both sides of the equation

       -3b  = -3b       then you get

   a = 7-3b        now plug this into the other equation: 3a-2b=8

3(7-3b) -  2b = 8

21 - 9b  - 2b = 8

21 - 11b = 8           add 11 b to both sides

   + 11b    +11b

21 = 8 + 11b          subtract 8 from both sides

-8    -8

13 = 11b

What is 4a+b?

4(7-3b) + b =

(28 - 12b) + b =

28-11b   (from above 13=11b)

28 - 13 = 15

Answer:

ok The circumference of a circle is 2πr or πD if diameter is given.

The answer is 25.13 cm

Step-by-step explanation:

Now method 1:

C=2πr

So finding for radius in this equation=diameter/2

8/2=4 cm

So now 2 × 22/7 × 4

176/7=25.13 cm

OR

C=πD

22/7 × 8

176/7=25.13 cm

Answer:

Step-by-step explanation:

8=8a-4(a+8) => 8=8a-4a-32 =>4a=40 => a=10.

If you meant 8=(8a-4)(a+8), then it is 8a^2+60a-32=8 => 8a^2+60a-40=0.

Use the quadratic formula, to get your answer.

Step-by-step explanation:

Cylinder volume = 703 [tex]cm^{3}[/tex], height = 18.5 cm

(i) Volume or area of the cylinder = [tex]\pi r^{2} h[/tex]

The formula for the volume of a cyclinder can be applied to find the area of the base.

Option (i) is correct

(ii) Volume or area of the cylinder = [tex]\pi r^{2} h[/tex]

The volume should be divivded by height to get the area

Option (ii) is wrong

(iv) Area of the base  = [tex]\frac{703\pi }{18}[/tex] = 38[tex]\pi cm^{2}[/tex]

Option (iv) is correct

(iii) The radius of the cyclinder is half the height.

[tex]\frac{38}{2}[/tex] = 19 cm not 18.5 cm

Option (iii) is wrong

(v)Area of the base  = [tex]\frac{703\pi }{18}[/tex] = 38[tex]\pi cm^{2}[/tex]

Option (v) is correct

Answer:

1 , 4 , & 5 ... which is also a , d, & e

Step-by-step explanation:

Answer:

Step-by-step explanation:

x+90°+33°+165°+20°=360° (complete angle)

x+ 308°=360°

x= 360°-308°

x= 52°

Answer:

x=52

Step-by-step explanation:

So what you would want to do is add up all of the angle measurements given. This give you 308. Now you take this number (308) and subtract it from 360, to give you the answer of 52.

Answer:

Step-by-step explanation:

number of samples, n = 10

Mean = (48 + 51 + 46 + 52 + 47 + 48 + 47 + 50 + 51 + 59)/10 = 49.9

Standard deviation = √(summation(x - mean)/n

Summation(x - mean) = (48 - 49.9)^2 + (51 - 49.9)^2 + (46 - 49.9)^2+ (52 - 49.9)^2 + (47 - 49.9)^2 + (48 - 49.9)^2 + (47 - 49.9)^2 + (50 - 49.9)^2 + (51 - 49.9)^2 + (59- 49.9)^2 = 128.9

Standard deviation = √128.9/10 = 3.59

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 10 - 1 = 9

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.262

Margin of error = 2.262 × 3.59/√10

= 2.57

the lower limit of this confidence interval is

49.9 - 2.57 = 47.33

the lower limit of this confidence interval is

49.9 + 2.57 = 52.47

So it is false

Answer:

Step-by-step explanation:

Solution:-

- The sample size = n

- The Error of estimation, E = 0.04

- The confidence level, CI = 99%

a)

What size sample should be obtained when she uses previous estimate of p = 0.52​?

- We are given the sample proportion p = 0.52, the required sample size is a function of confidence value and error of estimation (E):

                 [tex]n = p*( 1 - p ) * (\frac{Z-critical}{E})^2[/tex]

Where,

- The critical value of the confidence level = 99% would be:

           significance level ( α ) = 1 - CI = 1 - 0.99 = 0.01

           Z-critical = Z_α/2 = Z_0.005 = 2.575  

- The required sample size (n) can be calculated:

            [tex]n = 0.52*( 1 - 0.52 ) * (\frac{2.575}{0.04})^2\\\\n = 0.2304*(51.5)^2 = 611.0784[/tex]

- Hence, the minimum required sample size (n) should be = 612 adults.  

b)

- If the preliminary estimate of proportion is missing or not given, we are to assume the proportion p = 0.5.

- Similarly, repeat the calculations for sample size (n) when p = 0.5

               [tex]n = 0.5*( 1 - 0.5 ) * (\frac{2.575}{0.04})^2\\\\n = 0.25*(51.5)^2 = 663.0625[/tex]

- Hence, the minimum required sample size (n) should be = 664 adults.  

Answer:

algorithm

Step-by-step explanation:

It sounds like algorithm.

The mathematical terms that originated from the Arabic mathematician, al-Khwarizmi, are ""algorithm"" and ""algebra.""

Al-Khwarizmi was a Persian mathematician and astronomer who lived in the 8th and 9th centuries. His works were instrumental in the development of algebra and the use of Hindu-Arabic numerals. The term ""algorithm"" is derived from a Latinization of his name, Algoritmi, and originally referred to the numerical methods he described in his treatise on arithmetic.

The word ""algebra"" comes from the Arabic word ""al-jabr,"" which appears in the title of his book ""Kitab al-Jabr wa-l-Muqabala"" (The Compendious Book on Calculation by Completion and Balancing). This book laid the foundations for algebra as a branch of mathematics, and the terms he introduced are still in use today to describe mathematical procedures and the study of equations and algebraic structures.

Answer:

20.8%

Step-by-step explanation:

To find the final probability, two separate events must be done and the final propagation is the multiplication of these, like this:

First event:

Probability of black socks on Monday:

Total pair of socks: 1 + 3 + 5 = 9

Number of black socks on Monday: 3

Thus:

3/9 = 1/3

Second event:

Probability of white socks on Tuesday:

Total pair of socks: 8

Number of white socks on Tuesday: 5

Thus:

5/8

Final probability:

1/3 * 5/8 = 5/24

P = 0.208

So the probability would be 20.8%

The probability of black socks on Monday = 1/3

The probability of white socks on Tuesday = 5/8

To find the final probability, two separate events must be done and the final propagation is the multiplication of these, like this:

First event:

Probability of black socks on Monday:

Total pair of socks: 1 + 3 + 5 = 9

Number of black socks on Monday: 3

Thus:

Probability will be: 3/9 = 1/3

Second event:

Probability of white socks on Tuesday:

Total pair of socks: 8

Number of white socks on Tuesday: 5

Thus:

Probability will be: 5/8

Final probability:

1/3 * 5/8 = 5/24

P = 0.208

So, the probability would be 20.8%.

Find more information about Probability here:

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Answer:

-x^2(x-8)

Step-by-step explanation

The slopes are the only thing we care about when it comes to determining if the lines are parallel or perpendicular. The y intercepts do not affect the answer, so we can ignore them entirely.

The slopes of the two given equations are -4/5 and -5/4. Note how they are both negative. This means that we do not have perpendicular lines. One slope must be positive and the other negative, for perpendicular lines to form.

Another way to see it: the two slopes must multiply to -1 to have perpendicular lines form. We see that (-4/5)*(-5/4) = 1 instead.

Yet another way to see it: The term "opposite reciprocals" means we flip the fraction and we flip the sign (from positive to negative). The reciprocal part happens, but the sign change does not happen.

The lines are not parallel because the slopes would have to be equal for that to happen.

Answer:

you know 25% is one fourth of 100%, aka the whole number, so just multiply the 25% of the number times 4 to get the whole number

Answer:

r = 129.1 %

Step-by-step explanation:

Using the compounding formula:

A = P (1 + r/t)^nt

$12, 543 = $7178 (1 + r/12)^12(7)

-7178

$5365 = (1 + r/12)^84

[tex]\sqrt[84]{5365}[/tex] = [tex]\sqrt[84]{(1 +\frac{r}{12})^{84}}[/tex]

1.107642572 = 1 + r/12

(0.108 = r/12) (12)

r = 1.2917 = 129.1 %

............................

Answer:

-80 orchestra seats

-200 main seats

- 120 balcony seats

Step-by-step explanation:

Let x b number of orchestra seats

Let y be number of main seats

Let z be number of balcony seats.

Thus, we have the following equations;

For all seats sold;

70x + 45y + 35y = 18,800 - - - - eq1

For half of orchestra sold;

70•½•x + 45y + 35y = 16,000 - - eq2

For total seats;

x + y + z = 400 - - - - eq3

Solving eq1, eq2 and eq3 simultaneously, we have;

x = 80

y = 200

z = 120

Thus, we have;

-80 orchestra seats

-200 main seats

- 120 balcony seats

Answer:

It'll take 38.3 years to obtain the desired return of $25,000.

Step-by-step explanation:

In order to solve a continuosly coumponded interest question we need to apply the correct formula that is given bellow:

M = C*e^(r*t)

Where M is the final value, C is the initial value, r is the interest rate and t is the time at which the money was applied. Since he wants an return of $25,000 his final value must be the sum of the initial value with the desired return. So we have:

(25000 + 8000) = 8000*e^(0.037*t)

33000 = 8000*e^(0.037*t)

e^(0.037*t) = 33000/8000

e^(0.037*t) = 4.125

ln[e^(0.037*t)] = ln(4.125)

t = ln(4.125)/(0.037)

t = 1.4171/0.037 = 38.2991

t = 38.3 years

Answer:

The answer would be B) -2 1/8

Step-by-step explanation: i just took the test and i got that right

Answer:

B) -2⅛

Step-by-step explanation:

All other options are irrational

Answer:

The MAD of set 1 is 5 less than the MAD of set 2.

Step-by-step explanation: