What is the nth term rule of the linear sequence below?
-5, -2, 1, 4, 7, ...
Tn
-

For the given triangle ABC, Measures of given angles are m∠A=30 , m∠C=90 , m∠B=60 and side AC = 28 then the measure of side                   AB = 56√3/3 , BC =28√3/3.

As given in the question,

In the triangle ABC,

Measures of given angles are :

m∠A=30 , m∠C=90 , m∠B=60

And Measure of side AC = 28

As ABC is right angled triangle with m∠C=90,

If we take ∠A,

AC = Base

AB = Hypotenuse

BC = perpendicular side

Using trigonometric ratios,

tan A = BC/AC

⇒tan 30° = BC / 28

⇒1/√3 = BC /28

⇒ BC = 28/√3

⇒BC = 28√3/3

Now,

cos A = AC/AB

⇒ cos 30° = 28/AB

⇒ √3/2 = 28 /AB

⇒ AB = (28 × 2)/√3

⇒ AB = 56√3/3

Therefore, for the given triangle ABC, Measures of given angles are m∠A=30 , m∠C=90 , m∠B=60 and side AC = 28 then the measure of side AB = 56√3/3 , BC =28√3/3.

The complete question is:

What are AB and BC? AC=28 , m∠A=30 , m∠C=90 , m∠B=60.

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1133.98 grams of rice is required for the preparation of the recipe which calls for 40 ounces of rice.

Given that:

A recipe requires 40 ounces of rice for its preparation.

We know that,

1 ounce = 28.3495 grams

We also know that,

1 gram = .035274 ounces.

To find the value of 40 ounces multiplies both sides by 40.

40 ounce = 28.3495 grams x 40

40 ounce = 1133.98 grams

Hence, for the preparation of the recipe which calls for 40 ounces of rice, 1133.98 grams of rice is required.

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False Credentials: The "grant" was a fake certification rather than something that was given to Irvine.

False Experience: He was serving the president food. The fact that he was simply a line, however, was revealed

False chronology: Five Star Diamon Award for a couple of back-to-back years. However, it was found that it was not consecutive.

Embellished experience:  it was discovered that he had only chosen particular organic ingredients for the cake, didn't handle it

False References: The queen of England personally selected him for knighthood, which was inaccurate since it will never happen.

What is a resume?

A resume is a formal record that a candidate for a job makes to list their qualifications for the position. A personalized cover letter is typically included with a resume, in which the candidate expresses interest in a particular position or business and highlights the key information on the CV.

False Credentials: Robert Irvine misrepresented his education and experience by claiming on his résumé that he had completed a four-year program at the University of Leeds to earn a degree in food and nutrition. The college claimed they were unable to find any concrete connections between Irvine and the college in their records. Additionally, Irvine had to pay to participate in order to receive the "gift," making the American Academy of Hospitality Sciences anything but a licensed group. In this way, the "grant" was a fake certification rather than something that was given to Irvine.

False Experience: Irvine claimed to be a gourmet chef for the White House and implied that he was serving the president food. The fact that he was simply a line, however, was revealed

False chronology: According to Irvine, the American Academy of Hospitality Sciences gave him the Five Star Diamon Award for a couple of back-to-back years. However, it was found that it was not consecutive.

Embellished experience:He claimed on his resume that he had handled the wedding cake for Prince Charles and Princess Diana, although this was an inflated experience. Nevertheless, it was discovered that he had only chosen particular organic ingredients for the cake.

False References: Finally, he claimed that the Queen of England personally selected him for knighthood, which was inaccurate since it will never happen.

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The probability that exactly 3 automobiles fail the test is 0.01733.

The probability that fewer than 3 of the automobiles fail the test is

0.9803.

Complete question:

Car inspection of all the registered automobiles in Colorado, 5% fail the state emissions test. Twelve Automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places

(a) Find the probability that exactly three of them fail the test.

(b) Find the probability that fewer than three of them fail the test.

What is Binomial Distribution?

The probability of success is said to follow a binomial distribution when many similar and independent Bernoulli trials are conducted. The likelihood of success and the quantity of tries are its dimensions. For every trial, the chance of success is the same.

State emission test failure probability is 0.05.

12 vehicles total are present.

Let's look at failing the test as a victory. If success is represented by p, then p = 0.05.

Considering that n represents the number of cars, n equals 12.

Let X represent how many vehicles fail the test.

So, X ∼ Bin (8,0.05)

P(X=x)= [tex]^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]

         = [tex]^{12}C_{x}0.05^{x}(0.95)^{12-x}[/tex]

a) Probability that exactly 3 automobiles fail the test is given by,

  P(X=3)= [tex]^{12}C_{3}0.05^{3}(0.95)^{12-3}[/tex]

             =0.01733

So, the probability that exactly 3 automobiles fail the test is 0.01733.

b) Probability that fewer of them than 3 fail the test is given by,

P(X<3)= P(X≤2)

         = P(X=0)+P(X=1)+P(X=2)

         =  [tex]^{12}C_{0}(0.05)^{0}(0.95)^{12}[/tex] + [tex]^{12}C_{1}(0.05)^{1}(0.95)^{11}[/tex]+[tex]^{12}C_{2}(0.05)^{2}(0.95)^{10}[/tex]

         = 0.9803

Hence, the probability that fewer than 3 of the automobiles fail the test is

0.9803.

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me too. did you know that animals that lay eggs don't have belly buttons?

Answer:

y=-2x

Step-by-step explanation:

2=-2(-1)

2=2

Sorry for late response

Answer:

Take a look at the attachment...

Hope this helps! :)

If interest is paid at the rate of 2%, compounded semiannually, the amount of each deposit is $7,306.27.

Payment amount =x

Future value =80000

Periodic interest: 2% = .02

Number of periods: 5×2 = 10

Hence,

80,000=x [ (1+0.02)^10 -1 ) ÷ 0.02]

80,000=x [ (1.02)^10 -1) ÷ 0.02]

80,000=x [ (1.21899 -1) ÷ 0.02]

80,000=x (0.21899  ÷ 0.02)

80,000= x(10.9495)

x =80,000 /10.9495

x = $7,306.27

Therefore payment amount is $7,306.27.

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Answer:

Y= 20x + 35

Step-by-step explanation: I have the same test.

Answer:

y = (-1/2)x - 4

Step-by-step explanation:

y = 2x + 6

Perpendicular: y = (-1/2)x + 6

m = (-1/2); (2, -5)

                 (x₁, y₁)

y - y₁ = m(x - x₁)

y - (-5) = (-1/2)(x - 2)

y + 5 = (-1/2)x + 1

    -5               -5

----------------------------

y = (-1/2)x - 4

I hope this helps!

Step-by-step explanation:

the slope-intercept form is

y = ax + b

"a" being the slope, "b" being the y-intercept (the y- value when x = 0).

the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

a perpendicular slope simply turns the original slope upside-down with x and y, and it flips the sign.

the slope of the origins line is 2 = 2/1.

the perpendicular slope is -1/2.

so, the equation looks like

y = -1/2 x + b

to get b we use the point coordinates :

-5 = -1/2 × 2 + b = -1 + b

-4 = b

so, the full equation is

y = -1/2 x - 4

The answer of 11/3*7/3*5/3 after multiplication is 385/27.

According to the question,

We have the following expression:

11/3*7/3*5/3

We know that when we multiply two more than two fractions then numerator is multiplied into the numerator and the denominator is multiplied into the denominator of another fraction.

So, we have the following expression after multiplying first two fractions:

77/9*5/3

Now, again repeating the above step:

385/27

(This can not be further classified into the simplest form because the numerator and denominator of this fraction can not be divided by one number.)

Hence, the answer of 11/3*7/3*5/3 after multiplication is 385/27.

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Answer: honestly the only thing i know is that mean is another way of saying expected value

Step-by-step explanation:

The cost of each binder is $3.

Given,

In the question:

Angel spends $29 to order binders online.

They buy 8 binders and pay a flat fee of $5 for shipping.

To find the what is x, the cost of each binder?

Now, According to the question;

Based on the given conditions:

Formulate:

Angel spends = $29 to order binders online.

Buy the = 8 binders

Paying = $5 for shipping .

5 + 8 × x = 29

Solve the equation:

5 + 8x = 29

Rearrange the terms;

8x = 29 - 5

8x = 24

x = 24/8

x = 3

Hence, The cost of each binder is $3.

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The measures are:

The opposites sides of a parallelogram are parallel. Here, PQ ‖ RT and PR ‖ QT.

The opposite sides of a parallelogram are equal. Here, PQ = RT and PR = QT

The opposite angles of a parallelogram are equal. Here, ∠P = ∠T and ∠Q = ∠R

The diagonals of a parallelogram bisect each other. Here, RE = EQ and PE = ET

Same-side interior angles supplement each other. Here, ∠PRT + ∠RTQ = 180°, ∠RTQ + ∠TQP = 180°∘, ∠TQP + ∠QPR = 180°, ∠QPR + ∠PRT = 180°

The diagonals divide the parallelogram into two congruent triangles. Here, ΔRPQ is congruent to ΔQTR, and ΔRPT is congruent to ΔQTP

Therefore,

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The factored form of the given expression is (8x + 4)(2x - 3).

So, the expression is:

Now, evaluate to get the factors as follows:

Factors: (8x + 4)(2x - 3)

Therefore, the factored form of the given expression is (8x + 4)(2x - 3).

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The scale Alexander is using for his map is 1 inch : 300 feet

The height of Alexander's triangle in inches is 4 inches

The scale of the map is gotten by comparing the first dimensions Alexander drew

He made 10 inches to represent 3000 feet, this is equivalent to 1 inch to 300 feet hence the scale is 1 inch : 300 feet

Using the scale, a height of 1200 feet would be

1 inch = 300 feet

? inch = 1200 feet

cross multiplying

? * 300 = 1200 * 1

? = 1200 / 300

? = 4 inches

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Answer:

x = 27

Step-by-step explanation:

Cross-multiply. Wrap some parenthesis around the x+6 to keep it together. Use distributive property. See image.

Answer:

0.00075757575.

Step-by-step explanation:

I looked it up.

Answer:

  (a) 68.3%

  (b) 764 students

  (c) 49.87%

  (d) 1 student

Step-by-step explanation:

You want to know various percentages and numbers of students in different test score ranges when 800 students have scores normally distributed with a mean of 75 and a standard deviation of 7.

The range 68 to 82 is one standard deviation either side of the mean: 75±7. The "empirical rule" tells you about 68% of students will have a test score in this range. An appropriate calculator gives the fraction as 68.3%.

The range 61 to 89 is 2 standard deviations either side of the mean: 75±2·7. The "empirical rule" tells you about 95% of the 800 students will have a test score in this range. An appropriate calculator puts the number slightly higher than 760 students: 764 students.

The range 54 to 75 is 3 standard deviations below the mean. The empirical rule tells you about 99.7% of the group falls inside 3 standard deviations. Half this number is below the mean, about 49.85% An appropriate calculator puts the number slightly higher: 49.87%.

The scores at 96 and above are more than 3 standard deviations above the mean. As in part (c), the number in that tail are given by the empirical rule as about 0.15%, or 1.2 students. An appropriate calculator puts the number in the tail of the distribution at a slightly lower value. Hence, the estimated number of students with a score at least 96 is 1 student.

__

Additional comment

The numbers in this question seem to be chosen so you can use the empirical rule to find the answers. That rule will make the answers slightly different: 68%, 760 students, 49.85%, 1 student.

a) The percentage of a class has a test score between 68 and 82 is; 68.269%

b) The number of students that will score between 61 and 89 is; 764 students

c) The probability that a student chosen at random has a test score between 54 and 75 is; 0.49865

d) The number of students that have a test score greater than or equal to 96 is; 1

We are given;

Mean; μ = 75

Standard deviation; σ = 7 ;

a) We have to find percentage of a class has a test score between 68 and 82. This is expressed as; P(68 < X < 82)

P(68 < X < 82) = P(X < 82) - P(X < 68)

The formula for z-score is;

z = (x' - μ)/(σ)

Thus;

P(68 < X < 82) = P(Z < (82 - 75)/7) - P(Z < (68 - 75/7)

P(-1<x<1) = 0.68269 = 68.269%

b) The number of students that will score between 61 and 89 is;

P(61 < X < 89)

z -scores;

z = (61 - 75)/7

z = -2

z = (89 - 75)/7

z = 2

p-value between the two z-scores from online calculator is;

p = 0.9545

Number of students here = 0.9545 * 800 ≈ 764 students

c) The probability that a student chosen at random has a test score between 54 and 75;

P(54 < X < 75)

z -scores;

z = (54 - 75)/7

z = 3

z = (75 - 75)/7

z = 0

p-value between the two z-scores from online calculator is;

p = 0.49865

d) We want to find out how many students have a test score greater

than or equal to 96.

z = (96 - 75)/7

z = 3

p-value from z-score calculator gives;

p = 0.00135

Thus;

Number of students in this regards = 0.00135 * 800 ≈ 1

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(a) The information remembered by the person in starting is 100%.

(b) The information remembered by the person after 1 week is 66.67%.

(c) The information remembered by the person after 12 weeks is 12.46%.

(d) The information remembered by the person after 52 weeks is 10%

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given function is,

f(x) = [tex]90e^{-0.3x}+10[/tex]              (1)

(a)

Substitute x=0 in the equation (1)

f(0) = 90 e⁰ +10

Since, e⁰ = 1

f(0) = 90 +10

f(0) = 100

The information remembered by the person is 100.

(b)

Substitute x=1 in the equation (1)

f(1) = 90 [tex]e^{-0.3}[/tex]  +10

f(1) = 66.67 + 10

f(1) = 76.67

The information remembered by the person is 66.67%.

(c)

Substitute x=12 in the equation (1)

f(12) = 90[tex]e^{-3.6}[/tex] +10

f(12) = 2.46 + 10

f(12) = 12.46

The information remembered by the person is 12.46%.

(d)

Substitute x=52 in the equation (1)

f(52) = 90[tex]e^{-15.6}[/tex] +10

f(52) = 0.00015 + 10

f(52) = 10(approx)

The information remembered by the person is 10%.

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The graph of the  parent function Y = 2²⁻ ˣ +1 is presented below.

The parent function of a function is the simplest form of the function, which satisfies all the conditions of the given function.

The given function is,

Y= 4×2⁻ˣ+1

To find the parent function, simplify the given function,

Y = 2²ˣ2⁻ˣ+1

Y = 2²⁻ ˣ +1

Function Y = 2²⁻ ˣ +1  is the parent form of the given function Y= 4×2⁻ˣ+1.

The graph of the  Y = 2²⁻ ˣ +1 is presented below.

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Answer:

   (-10)  '  (-8)  '  |  '  |  '  |  '  (0)  '  |  '  |  '  |  '  |  '  (10)  

The minimum number of trophies that can be ordered so that the total charge at Company P is less than the total charge at Company R is 3

Company P charges $3.50 for each trophy and a one-time engraving fee of 25$

Let the number of trophies he buys be x

Total price at company P = 3.50x + 25

Company R charges $7.50 for each trophy and a one-time engraving fee of 17$.

Total price at company R = 7.50x + 17

minimum number of trophies that can be ordered so that the total charge at Company P is less than the total charge at Company R

3.50x + 25 < 7.50x + 17

- 4x < -8

4x > 8

x > 2

Therefore, minimum number of trophies that can be ordered so that the total charge at Company P is less than the total charge at Company R is 3

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Answer:

  (x, y) = (1, 2)

Step-by-step explanation:

You want to solve the system of equations x=2y-3, -4x+3y=2 using the substitution method.

The first equation gives you an expression for x that can be substituted into the second equation.

  -4(2y-3) +3y = 2 . . . . . . substitute (2y-3) for x

  -8y +12 +3y = 2 . . . . . simplify

  10 = 5y . . . . . . . . . . add 5y -2 to both sides

  2 = y . . . . . . . . . . divide by 5

Now, the value of x can be found from the first equation:

  x = 2(2)-3 = 1

The solution is (x, y) = (1, 2).

__

Additional comment

The advantage of the substitution method is that once you find the value of the remaining variable, you can use the substitution equation to find the value of the variable that was eliminated. That is, the equation for x made it easy to find x once we solved for y.

Substitution is easiest when there is already an equation for one of the variables. It can also be used fairly easily if one of the variables has a coefficient of 1 or -1.

Answer:

Step-by-step explanation:

In the following equation: 4x -3=8, x represents a variable

4x - 3  = 8

4x = 11

x = 11/4

-------------

check

4 x 11/4 - 3 = 8

11 - 3 = 8

8 = 8

the answer is good

The monthly deposit required to save up to $625,357.24 (future value) in 40 years at a 7.2% APR is $225.20.

The monthly deposits are the periodic savings that the investor must make to achieve future value.

The monthly deposit is compounded at the monthly annual percentage rate (APR).

We can compute the required monthly deposits using an online finance calculator as follows:

N (# of periods) = 480 months (40 years x 12)

I/Y (Interest per year) = 7.2%

PV (Present Value) = $0

FV (Future Value) = $625,357.24

Results:

Monthly Deposits (PMT) = $225.20

Sum of all periodic payments = $108,096 ($225.20 x 480)

Total Interest = $517,261.24

Thus, to save $625,357.24 in 40 years, you need to deposit $225.20 monthly.

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a. The two transformations we perform are

b. Find the graph in the attachment

Transformations are mathematical operation sthat are performed to change the shape or orientation of a function or object.

Since we require to transform the function f(x) = (x-3)² + 1 to g(x) = (x² -4), we perform the following transformation operations.

In f(x), first we shift the term (x - 3)² three units to the left. So,  (x - 3 + 3)²  = x²

So, f(x) = x² + 1

To transform f(x) = x² + 1 to g(x) = (x² - 4), we shift f(x) five units down.

So, the transformation is  f(x) = x² + 1

= x² + 1 - 5

= x² - 4

So, the two transformations we perform are

Find the graph in the attachment

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Answer:

4.5 i think

Step-by-step explanation:

The value of t from the given derivative is 7.38.... or −7.38....

The given second order derivative is r''(t)=2/t².

The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.

Here, r''(t)=2/t²

The anti-derivative is

Set the function up in integral form and evaluate to find the integral.

r'(t) = -2/t

Now, 3=-2/t

⇒ t=-2/3

Set the function up in integral form and evaluate to find the integral.

r(t)=-2ln(|t|)

So, -4=-2ln(|t|)

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form :t=e²,−e²

Decimal Form:

t=7.38905609…,−7.38905609…

Therefore, the value of t from the given derivative is 7.38.... or −7.38....

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