If
m ≤ f(x) ≤ M
for
a ≤ x ≤ b,
where m is the absolute minimum and M is the absolute maximum of f on the interval [a, b], then
m(b − a) ≤
b
a
f(x) dx ≤ M(b − a).
Use this property to estimate the value of the integral.
⁄12 7 tan(4x) dx

Answer:

98 degrees

Step-by-step explanation:

In a quadrilateral, we have 4 angles whose sum is 360 degrees which can be derived using the Exterior Angle Sum Theorem which essentially states that any convex polynomial will have a sum of 360 degrees for it's exterior angles.

Since we know that two of the angles are equal, we can just represent angle A and D as "x", and since they're congruent, and there is two of them, the sum can be represented as "2x"

So using all the known values we can set up the following equation:

[tex]2x+64+100=360[/tex]

Simplify on the left side

[tex]2x+164=360[/tex]

Subtract 164 from both sides

[tex]2x=196[/tex]

Divide both sides by 2

[tex]x=98[/tex]

Since we know that "x" represents both angle A and B, then the angle A is 98 degrees.

The solutions to the exponential growth problem are:

A. [tex]P(t) = 260e^0.3662t[/tex]

B.[tex]P(3) = 260e^0.3662(3) = 779[/tex]

C.3.367 hours

The  exponential growth problem obeys the equation:

P(t) = P0ekt

P0=population

time t

We can find the value of k At t=3 hours as,

780 = 260e^k(3)

k = (1/3) ln(780/260) hours-1 ≅ 0.3662 hours-1

A. [tex]P(t) = 260e^0.3662t[/tex]

B. [tex]P(3) = 260e^0.3662(3) = 779[/tex]

C.  1870 = 260e^0.3662t

To Solve for t, w2e make t the subject of the formula

t = ln(1870/260) / 0.3662 hours = 3.367 hours

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Answer: $3.2a

Step-by-step explanation: We need to decrease $8a by 60 percent because $8a is the price after a 60% increase. 8 x 6/10 is 48/10 which as a mixed number is 4 8/10 or 4.8. Now, we subtract 4.8 from 8 which yields our answer of 3.2.

Answer:

x = 52

Step-by-step explanation:

Since the inscribed angle measures 64 degrees, the minor arc is 64*2 = 128 degrees. Therefore the major arc is 180-128 = 232 degrees. Angle X is the difference of major and minor arc divided by 2, so X = (232-128)/2 = 52 degrees.

X=1.33

Y=4.9875;approx. 5.0

Answer:

(2/120=X/80)=Y/300

2×80=120×X

X=160/120

X=1.33

X/80=Y/300

But X=1.33

By substituting

X=1.33, We have that

1.33/80=Y/300

80×Y=1.33×300

80Y=399

Y=399/80

Y=399/80

Y=5.0 approx.

Answer:

1/5 of it

Step-by-step explanation:

5/5 represents all of her homework

5/5-4/5= 1/5

4/5 represents the homework she did before dinner

1/5 represents the homework left to do

The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.

Let x represent the distance travelled, hence:

x² = 14² + 30²

x = 33 miles

tanФ = 14/33

Ф = 23°

The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.

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The percentage that each transaction contributed to the total transactions in the same account (Cash Account and Service Revenue) is computed as follows:

1. Service Revenue $900   = 8%

2. Owner's Equity, Barbara Hanson $2,200 = 19.8%

3. Accounts Receivable $750 = 6.8%

5. Note Payable $6,000 = 54.1%

6. Unearned Revenue $1,250 = 11.3%

Total cash receipts = $11,100

1. Cash $900 = 70.6%

4. Accounts Receivable $375 = 29.4%

Total $1,275

The percentage that each transaction contributed to the total transactions in the same account can be computed by taking the dollar value of the transaction over the total value of transactions in the same account and then multiplying by 100.

Percentage values show the degrees of relationship among variables.

The formula for computing percentage in this scenario is transaction value/total transactions value × 100%.

1. Cash $900 Service Revenue $900

2. Cash $2,200 Owner's Equity, Barbara Hanson $2,200

3. Cash $750 Accounts Receivable $750

4. Accounts Receivable $375 Service Revenue $375

5. Cash $6,000 Note Payable $6,000

6. Cash $1,250 Unearned Revenue $1,250

The following transactions occurred during July:

1. Received $900 cash for services provided to a customer during July.

2. Received $2,200 cash investment from Barbara Hanson, the owner of the business.

3. Received $750 from a customer in partial payment of his account receivable, which arose from sales in June.

4. Provided services to a customer on credit, $375.

5. Borrowed $6,000 from the bank by signing a promissory note.

6. Received $1,250 cash from a customer for services to be rendered next year.

Use the transactions to compute the percentage of each transaction relative to the total transactions in the same account.

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The monthly payment is $796.40.

The total amount she would deposit is $286,705.51

The total interest earned is $513,294.49

The payments made by Jessica are known as deferred annuities. Deferred annuities are when a series of payments are made in exchange for an amount of money in the future.

The formula that can be used to determine the amount of monthly deposit is: future value / annuity factor

Annuity factor = {[(1+r)^n] - 1} / r

Where:

r = interest rate = 6%/12 = 0.5%

n = number of years = 30 x 12 = 360

Annuity factor = ](1.005^360) - 1] / 0.005 = 1004.515

Monthly payments = 800,000 / 1004.515 = $796.40

Total amount she would deposit = monthly payment x number of years x number of months in a year

$796.40 x 30 x 12 = 286,705.51

Total interest earned = value of the retirement account - total amount deposited

800,000 - 286,705.51 = 513,294.49

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Answer:

D

Step-by-step explanation:

Widrawal is - 30

Deposit is +30

-30+30 = 0

The expression which can be used to determine the algebraic sum of the given polynomials as in the task content is; -11x² +4x +14.

It follows from the task content that the polynomials whose sum are to be determined are; (9 - 3x2) + (-8x2 + 4x + 5).

Hence, the sum can be evaluated as follows;

= 9 - 3x² + -8x² + 4x + 5

= -11x² +4x +14.

Consequently, the required expression is; -11x² +4x +14.

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Answer:

Step-by-step explanation:

is 100 for the points

Answer:

angle B = 78.46°

Step-by-step explanation:

Use the cosine ratio

[tex]cosB=\frac{2}{10} =0.2[/tex]

[tex]B=cos^{-1} (0.2)=78.46^{0}[/tex]

Hope this helps

Considering the given function, we have that:

The function is:

f(x) = 4 - 2x + 6x².

When x = a, we have that:

f(a) = 4 - 2a + 6a².

When x = a + h, we have that:

f(a + h) = 4 - 2(a + h) + 6(a + h)² = 6a² + 12ah + 6h² - 2a - 2h + 4.

For the fraction, we have that:

[f(a + h) - f(a)]/h = [6a² + 12ah + 6h² - 2a - 2h + 4 - 4 + 2a - 6a²]/h = [12ah + 6h² - 2h]/h = h(12a + 6h - 2)/h

Hence:

[f(a + h) - f(a)]/h = 12a + 6h - 2.

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Answer:

f(y-2)+f(4-y)=4

Step-by-step explanation:

Assume (let) x=y-2

So: y=x+2

f(y-2)+f(4-y)=f(x)+f(-x+2)=f(x)+f(2-x)

The value of that expression is 4 from the given.

Answer:

No.

Step-by-step explanation:

Negative decimal numbers are rational numbers since rational numbers include all the integers both positive and negative integers, decimal as well as a fraction because decimals can be written as fractions.

Using it's concept, the probability that the first coin is a nickel and the second coin is a quarter is: 2/39.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Hence:

Then the probability for both coins is:

p = 4/13 x 1/6 = 4/78 = 2/39

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Answer:

transitive property

Step-by-step explanation:

This is the answer by definition.

The substitution property is demonstrated in the case of m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so, m∠AZF=m∠SZW+m∠LZF.

In order to find the value of the unknown, the substitution property is a concept in algebra that is used to substitute the value of a given variable or quantity into an expression.

According to the substitution property of equality, "If two variables x and y are equal, then x can be substituted for y in any equation or expression, and y can be substituted for x in any equation or expression."

According to the question, m∠AZF=m∠AZL+m∠LZF and m∠AZL+m∠LZF=m∠SZW+m∠LZF, so by the substitution property, on substituting the value of  m∠AZL+m∠LZF in the first expression, we get, m∠AZF=m∠SZW+m∠LZF.

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Answer:

2x + 8

Step-by-step explanation:

(4x + 5) - (2x - 3)

4x + 5 - 2x + 3

2x + 8

Answer: 2x+8

Step-by-step explanation:

4x+5-2x+3

=2x+8

Answer:

$824.56

Step-by-step explanation:

Use the compound interest formula which is A = P(1+r/n)^nt

1st using the given information we are going to find out values:
P is our initial amount of $500
r is the annual rate of interest (expressed as a decimal) 8% becomes 0.08.
n is how many times interest is compounded per year, in this case since its not stated we are going to assume its annually, so n is 1
t is how long the money is deposited (in years) so t is 6.5
A is our final amount

2nd plug in our values into the equation

Plugging all these values we get A = 500 (1 +0.08/1)^(0.08)(6.5)

A = $824.56

Answer:

No classification is guaranteed.

Answer:

subtraction

Step-by-step explanation:

If she had 7 sqft and used up 4 sqft, she no longer has that 4 sqft. It's used up, gone, taken away. We remove it from her total. That is "take away" this means subtraction.

7 - 4

= 3 she has 3sqft of construction paper left.

Answer:

2/3rds of liad's run

Step-by-step explanation:

3 min 45s = 3 3/4 min = 15/4 min; 10/(15/4) = 8/3 laps

2min 30s = 2 1/2 min = 5/2 min; 10/(5/2) = 4 laps

(8/3)/4 = 2/3

Could you try reposting the question clearly

If the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1) then the area of the rhombus is 16 square units.

Given the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1).

We are required to find the area of the rhombus when the fourth point Z is plotted.

We have to plot the points of the rhombus in the graph. We know that all the sides of the rhombus should be equal to each other. So by adjusting the blocks in the graph we will be able to plot Z as (-2,3).

In this way the diagonals are ZX and WY.

ZX=[tex]\sqrt{(3-3)^{2} +(6+2)^{2} }[/tex]

=[tex]\sqrt{64}[/tex]

=8 units

WY=[tex]\sqrt{(1-5)^{2} +(2-2)^{2} }[/tex]

=[tex]\sqrt{16}[/tex]

=4 units

Area of rhombus=1/2 *([tex]d_{1} *d_{2}[/tex])

=1/2* (8*4)

=8*2

=16 Square units.

Hence if the three vertices of the rhombus are W(2,5),x(6,3),Y(2,1) then the area of the rhombus is 16 square units.

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The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Given the polynomial:

-2x³ - 7x² + 3x - 4

Simplifying:

= -(2x² - x + 1)(x + 4)

Hence:

-2x³ - 7x² + 3x - 4 = (-2x² + x - 1)(x + 4)

(x + 4)(ax² + bx + c) = −2x³ − 7x² + 3x − 4

The values of the coefficients a, b and c in the equation is -2, 1 and -1 respectively.

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The area is:

A = (θ/2)*R^2

The circumference is:

C = θ*R

And the area of the circle when the angle is π/4 is: 39.25 cm^2

For a circle of radius R, the area is:

A = pi*R^2

where pi = 3.14

And the circumference is:

C = 2*pi*R

Now, remember that a circle has an angle of 2pi radians, then if we only define an arc in the circle, defined by an angle θ, the area of said arc will be:

A = (θ/2pi)*pi*R^2 = (θ/2)*R^2

And the circumference is:

C = (θ/2pi)*2pi*R = θ*R

Now, we want to find the area when the circle has a radius R = 10cm and θ = pi/4

Replacing that in the area equation, we get:

A = (pi/4/2)*(10cm)^2 = (3.14/8)*(10cm)^2 = 39.25 cm^2

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Answer:

7.61577310586

Step-by-step explanation:

Pythagoras Theorem 7 squared + 3 squared= 49+9=58

[tex]\sqrt{58}[/tex]

Answer:

x = -9

Step-by-step explanation:

12 + 2x + 24 = 27 + x

(12 + 24) + 2x = 27 + x

36 + 2x = 27 + x

subtract 27 from both sides

36-27 + 2x = 27-27 + x

9 + 2x = x

subtract x from both sides

9 + x = 0

subtract 9 from both sides

x = -9

(the steps could've been faster but that shows the most work)

check:

12 + 2(-9) + 24 = 27 + (-9)

36 - 18 = 18

18 = 18

True!

so -9 is correct

Answer:

Step-by-step explanation:

To solve for x, bring the variable to one side, and bring all the remaining values to the other side by applying arithmetic operations on both sides of the equation. Simplify the values to find the result.