interior and exterior of angles of triangles
please help !!

A labor plan was created for truck unloading and box storage during an 8-hour shift, with the productivity measured in boxes processed per worker per hour.

To fully answer the question, it is necessary to provide the details of the labor plan, including the specific productivity rates for each task and the number of workers assigned to each task. Without this information, it is not possible to provide a comprehensive explanation. However, the labor plan aims to optimize the efficiency of truck unloading and box storage within the given 8-hour shift. It likely involves assigning workers to different tasks based on their productivity levels and the estimated time required for each task.

To know more about labor planning here: brainly.com/question/32563890 #SPJ11

we should reject H0 if the standardized test statistic is greater than 1.645

Given a sample size of n = 48 and a level of significance of α = 0.1, we can use the z-test to test the claim μ ≤ 25.6.

Since the level of significance is α = 0.1, we need to find the critical value corresponding to a 90% confidence level (1 - α).

The critical value for a 90% confidence level is 1.645.

what is statistic?

A statistic is a numerical value or measure that summarizes a specific characteristic or property of a sample or population. It is commonly used in statistics and research to provide information about a data set or to make inferences about a larger population based on the observed sample.

To know more about statistic visit:

brainly.com/question/31577270

#SPJ11

The x-coordinates of the points (x, y) on the curve where the tangent line is horizontal are x = 7 and x = 3.

To find the x-coordinates of the points where the tangent line to the curve is horizontal, we need to find the values of x that make the derivative of the function equal to zero.

Given the curve equation \(y=\frac{(x - 7)^6}{(x - 3)^7}\), let's differentiate it with respect to x: \(y=\frac{(x - 7)^6}{(x - 3)^7}\)

Taking the derivative of both sides: \(\frac{dy}{dx} = [\frac{(x - 7)^6}{(x - 3)^7}]''\)

To simplify the expression, we can rewrite it as: \(\frac{dy}{dx} = (x - 7)^6 (x-3)^{-7}\)

Now, let's set the derivative equal to zero: \(0=\frac{dy}{dx} = (x - 7)^6 (x-3)^{-7}\)

Since we're looking for the x-coordinates, we need to solve the equation for x. This equation suggests that either the numerator \((x - 7)^6\) should be zero or the denominator \((x - 3)^7\) should be zero.

Setting the numerator equal to zero:

\((x - 7)^6 = 0\)

Solving this equation yields:

x - 7 = 0

x = 7

Now, setting the denominator equal to zero:\((x - 3)^7 = 0\)

Solving this equation yields:

x - 3 = 0

x = 3

Therefore, the x-coordinates of the points (x, y) on the curve where the tangent line is horizontal are x = 7 and x = 3.

To know more about "Functions" refer here:

https://brainly.com/question/10500042

#SPJ11

Answer:

9/13

Step-by-step explanation:

rise = y₂ - y₁ = -1 - (-10) = -1 + 10 =   9

run = x₂ - x₁ =   9 - (-4)   =   9 +   4 = 13

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.

We have been given parametric equations x = t^2 − 3t, y = √t

We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

NWe know that the formula to find the area under the curve.

A = ∫[a to b] g(t)f'(t) dt

here, a = 0 and b = 3

so, A = ∫[0 to 3] √t (2t - 3) dt

A = ∫[0 to 3] (2t√t - 3√t) dt

A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt

A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]

A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0

A = 4/5 3^(5/2) - 2 3^(3/2)

A = 6√3 /5

A = 2.08

Therefore,  the area of the curve is 2.08 square units.

Learn more about parametric equations here:

brainly.com/question/28537985

#SPJ4

The distance between the point (-3,3) and (a, b) is;

⇒ d = √(a + 3)² + (b - 3)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two points are,

(-3,3) and (a, b)

Now,

The distance between the point (-3,3) and (a, b) is;

d = √(a - (-3))² + (b - 3)²

d = √(a + 3)² + (b - 3)²

Thus, The distance between the point (-3,3) and (a, b) is;

⇒ d = √(a + 3)² + (b - 3)²

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer: Factoring is essentially the reverse of the distributive property. You are basically trying to simplify the polynomial by taking out common factors. You also may try reducing the power (or the highest exponent) of the polynomial with factoring. I would say that factoring is the breaking down of a bigger polynomial into a product of two expressions that are usually multiplied by each other. One specific use of factoring we see a lot is the quadratic formula.

1. Quadratic Factoring --> \(x^2+2x-15\) --> we have an \(x^2\) but we want there to only be "\(x\)"s. Here we need to constant numbers (integers), that multiply together to get \(-15\), and add up to \(+2\). (5 and -3)

    - \(x^2+2x-15\) ==> \(x^2+5x-3x-15\) ==> \(x(x+5)-3(x+5)\) ==> \((x-3)(x+5)\)

Above: We can see that we factor out \(x\) from \(x^2+5x\) (This shows that we are aiming to break it down to make it easier to evaluate).

Remember: Factoring does not always mean that the polynomial is in a simpler form. There are many situations where factoring is totally unnecessary and complicates the polynomial even more.

--------------------------------------------------------------------------------------------------------------On a separate note: Distributive Property, if you are unsure or not fully sure on what that means, is when you multiply two expressions together to create one expression. Multiple expressions are combining into one.

Answer:

235.3$ for part a

The amount in the account on April first of the following year is $3799.358 and the compound interest is $179.358.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

(a) The amount in a compound interest can be found as,

A = P(1 + \(\frac{r}{n}\)) ^(nt)

where A is the final amount, P is the initial or principal amount, r is the interest rate, n is the number of times compounding occurs in a year and t is the number of years.

Given P = $3,620, r = 6.5% = 0.065, t = 9 months = 0.75 year

n = 4 (since compounded quarterly)

A = 3620 (1 + \(\frac{0.065}{4}\)) ^(4 × 0.75)

  = 3620 (1.01625)³

  = 3799.358

(b) Compound Interest = Final amount - Initial amount

                                      = 3799.358 - 3,620

                                      = $179.358

Hence the compound interest is $179.358.

Learn more about Compound Interest here :

https://brainly.com/question/14295570

#SPJ2

Answer:

c.) x = -3

Step-by-step explanation:

Solve for x:

-10 x = 2 (9 - 2 x)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

-10 x = 18 - 4 x

Hint: | Move terms with x to the left hand side.

Add 4 x to both sides:

4 x - 10 x = (4 x - 4 x) + 18

Hint: | Look for the difference of two identical terms.

4 x - 4 x = 0:

4 x - 10 x = 18

Hint: | Combine like terms in 4 x - 10 x.

4 x - 10 x = -6 x:

-6 x = 18

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -6 x = 18 by -6:

(-6 x)/(-6) = 18/(-6)

Hint: | Any nonzero number divided by itself is one.

(-6)/(-6) = 1:

x = 18/(-6)

Hint: | Reduce 18/(-6) to lowest terms. Start by finding the GCD of 18 and -6.

The gcd of 18 and -6 is 6, so 18/(-6) = (6×3)/(6 (-1)) = 6/6×3/(-1) = 3/(-1):

x = 3/(-1)

Hint: | Simplify the sign of 3/(-1).

Multiply numerator and denominator of 3/(-1) by -1:

Answer: x = -3

this is not the write answer im just it bec whevener but i think it is 13=845-684x3 i think it is the answer

Step-by-step explanation:

The required function is P(t)=50000 + 5000t.

In this problem we need to form the function of the population in a town.

Here it is given that the initial population of the town is 50000.

the rate at which the population increases is 5000 per year.

So, the increase for the first year will be 5000. And the population will be 55000.

Then again for the next year the growth will be 5000 and the population will be 50000 + (5000×2)

        = 60000

So we can see clearly that the population is varying with time and we can write the function as P(t)=50000 + 5000t where t is the time in years.

To learn more about the function visit the link:

https://brainly.com/question/12431044

#SPJ4

Answer:

7/16

Step-by-step explanation:

\(\dfrac78 \times \dfrac24=\dfrac{7 \times 2}{8 \times 4}=\dfrac{14}{32}=\dfrac{7}{16}\)

Answer:

see explanation

Step-by-step explanation:

(a)

x² + 2x + 1 = 2x² - 2 ( subtract x² + 2x + 1 from both sides

0 = x² - 2x - 3 ← in standard form

0 = (x - 3)(x + 1) ← in factored form

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

x - 3 = 0 ⇒ x = 3

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

(b)

\(\frac{x+2}{3}\) - \(\frac{2}{15}\) = \(\frac{x-2}{5}\) ( multiply through by 15 to clear the fractions )

5(x + 2) - 2 = 3(x - 2) ← distribute parenthesis on both sides

5x + 10 - 2 = 3x - 6

5x + 8 = 3x - 6 ( subtract 3x from both sides )

2x + 8 = - 6 ( subtract 8 from both sides )

2x = - 14 ( divide both sides by 2 )

x = - 7

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

(c) Assuming lg means log then using the rules of logarithms

log \(x^{n}\) ⇔ nlogx

log x = log y ⇒ x = y

Given

log(2x + 3) = 2logx

log(2x + 3) = log x² , so

x² = 2x + 3 ( subtract 2x + 3 from both sides )

x² - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = 3 , x = - 1

x > 0 then x = 3

The limit of (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity is 0.

To find the limit of the function (2x-1)(3-x)/(x-1)(x+3) as x approaches infinity, we will divide both the numerator and denominator through the highest power of x. In this case, the highest power of x is x², so we can divide both the numerator & the denominator through x²:

\([(2x-1)/(x^2)] * [(3-x)/((x-1)/(x^2)(x+3))]\)

Now, as x approaches infinity, every of the fractions within the expression procedures zero except for (2x-1)/(x²). This fraction techniques 0 as x procedures infinity because the denominator grows quicker than the numerator. therefore, the limit of the expression as x strategies infinity is:

0 * 0 = 0

Consequently, When x gets closer to infinity, the limit of (2x-1)(3-x)/(x-1)(x+3) is 0.

Learn more about numerator and denominator:-https://brainly.com/question/20712359

#SPJ4

Answer:

domain: x<2 or x>2

x-intercepts: (3/2, 0), (-3/2, 0)

The integral ∫[-2, 4] |t^2 - 2t - 3| dt evaluates to -35/2. The roots of the integrand are t = 3 and t = -1, and the evaluation is done using the Fundamental Theorem of Calculus.

To evaluate the integral ∫[-2, 4] |t^2 - 2t - 3| dt using the Fundamental Theorem of Calculus, we need to identify the roots of the integrand to remove the absolute values.

Step 1: Find the roots of the integrand:

We have |t^2 - 2t - 3|. To find the roots, we set the expression inside the absolute value bars equal to zero and solve for t:

t^2 - 2t - 3 = 0

To factorize the quadratic equation, we look for two numbers that multiply to -3 and add up to -2. The factors are -3 and +1:

(t - 3)(t + 1) = 0

Setting each factor equal to zero gives us:

t - 3 = 0 --> t = 3

t + 1 = 0 --> t = -1

So, the roots of the integrand are t = 3 and t = -1.

Step 2: Evaluate the integral using the Fundamental Theorem of Calculus, Part 2:

We divide the interval [-2, 4] into three subintervals:

[-2, -1], [-1, 3], and [3, 4].

Within each subinterval, we have different expressions for the integrand:

For the subinterval [-2, -1]:

|t^2 - 2t - 3| = -(t^2 - 2t - 3) = -t^2 + 2t + 3

For the subinterval [-1, 3]:

|t^2 - 2t - 3| = t^2 - 2t - 3

For the subinterval [3, 4]:

|t^2 - 2t - 3| = -(t^2 - 2t - 3) = -t^2 + 2t + 3

Now, we can evaluate each part of the integral using the Fundamental Theorem of Calculus:

∫[-2, -1] -t^2 + 2t + 3 dt:

= [-t^3/3 + t^2 + 3t] from -2 to -1

= [(-(-1)^3/3 + (-1)^2 + 3(-1))] - [(-(-2)^3/3 + (-2)^2 + 3(-2))]

= [1/3 + 1 - 3] - [-8/3 + 4 - 6]

= [-5/3] - [-2/3]

= -5/3 + 2/3

= -3/3

= -1

∫[-1, 3] t^2 - 2t - 3 dt:

= [t^3/3 - t^2/2 - 3t] from -1 to 3

= [(3^3/3 - 3^2/2 - 3(3))] - [(-1^3/3 - (-1)^2/2 - 3(-1))]

= [27/3 - 9/2 - 9] - [-1/3 - 1/2 + 3]

= [9 - 9/2 - 9] - [-1/3 - 1/2 + 3]

= [9 - 18/2 - 18] - [-2/6 - 3/6 + 18/6]

= [9 - 9 - 18] - [13/6]

= -18 - 13/6

= -36/2 - 13/6

= -72/6 - 13/6

= -85/6

∫[3, 4] -t^2 + 2t + 3 dt:

= [-t^3/3 + t^2 + 3t] from 3 to 4

= [-(4^3/3) + 4^2 + 3(4)] - [-(3^3/3) + 3^2 + 3(3)]

= [-64/3 + 16 + 12] - [-27/3 + 9 + 9]

= [-64/3 + 28] - [-9 + 18]

= [-64/3 + 84/3] - [9]

= [20/3] - [9]

= 20/3 - 27/3

= -7/3

Finally, we sum up the results for each subinterval to get the overall integral:

∫[-2, 4] |t^2 - 2t - 3| dt = ∫[-2, -1] -t^2 + 2t + 3 dt + ∫[-1, 3] t^2 - 2t - 3 dt + ∫[3, 4] -t^2 + 2t + 3 dt

= -1 + (-85/6) + (-7/3)

= -1 - (85/6) - (7/3)

= -6/6 - (85/6) - (14/6)

= -(6 + 85 + 14)/6

= -105/6

= -35/2

Therefore, the value of the integral ∫[-2, 4] |t^2 - 2t - 3| dt is -35/2.

Learn more about Fundamental Theorem of Calculus here: brainly.com/question/30761130

#SPJ11

Answer:

No

Step-by-step explanation:

Hope this helps :)

Answer:

90

Step-by-step explanation:

1/5x+4=1/3x-8

add 8 to both sides and subtract 1/5x from both sides

4+8=1/3x-1/5x

12=5/15x-3/15x

12=2/15x

divide both sides by 2/15

12÷2/15=x

when dividing by a fraction, invert and multiply

12*15/2=x

90=x

CHECK:

1/5(90)+4=1/3(90)-8

18+4=30-8

22=22

\([Hello,BrainlyUser]\)

Answer:

20 Plots

Step-by-step explanation:

Given:

Plants 30 roses in 5 plots

Plants 120 roses in [?] Plots

Question:

How many plots he needs ?

Solve:

\(\frac{roses}{plots}=Solution\)

Divide 30 roses by 5 plots  = 6

Hence, 120 roses divide by 6

\(\frac{120}{6}=20\)

Therefore, Mohamed need 20 Plots.

\([CloudBreeze]\)

Answer:

12x-94

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

Hope this helps!

Have a great day and God bless! :)

Answer:

32

Step-by-step explanation:

A : B : C: total

2   3    4   2+3+4 = 9

Take the number of rolls received 72 and divide by 9

72/9 = 8

Multiply each number by 8

A     :  B    :   C   : total

2*8   3*8    4*8   9*8

 16     24      32    72

C received 32 rolls

Answer:

The area of the shaded region is 7π square centimeters.

Step-by-step explanation:

Note that Circle B has a radius of 3 cm, and the two smaller circles, Circles O and C, both have a radius of 1 cm.

The area of a circle is given by:

\(\displaystyle A = \pi r^2\)

Therefore, the area of Circle B, the entire circle, is:

\(\displaystyle \begin{aligned} A_B &= \pi (3)^2 \\ &= 9\pi \end{aligned}\)

The area of Circle O is:

\(\displaystyle \begin{aligned} A_O &= \pi (1)^2 \\ &= \pi \end{aligned}\)

And likewise, the area of Circle C is:

\(\displaystyle \begin{aligned} A_C &= \pi (1)^2 \\ &= \pi \end{aligned}\)

The area of the shaded area is the area of the Circle B subtracted by the area of Circles O and C. Hence:

\(\displaystyle A_\text{shaded} =A_B - \left(A_ O + A_ C\right)\)

Substitute and evaluate:

\(\displaystyle \begin{aligned} A_\text{shaded} &= (9\pi ) - (\pi + \pi) \\ &= 9\pi - 2\pi \\\ &= 7\pi \end{aligned}\)

The area of the shaded region is 7π square centimeters.

Answer:

Perpendicular bisector

Step-by-step explanation:

The construction is of a perpendicular bisector, because the line in bisected and the angle formed by the bisector is a right angle.