Find the perimeter of the figure. If you need to use in your computation, approximate its value as 3.14.
Rectangle topped by a semicircle
10 m
a. 35.57 m
b.
65.40 m
C.
59.70 m.
d. 49.70 m

Answer:

Its the 3rd one

Step-by-step explanation:

The value of x is 80

The measure of angle FOW, m ∠FOW, is 80°

The measure of angle FLW, m ∠FLW, is 112°

The measure of angle OLW, m ∠OLW, is = 68°

From the question, we are to determine the measure of the missing angles

From the given diagram, we can write that

(2x - 48)° = x° + 32°

Solve for x

(2x - 48)° = x° + 32°

2x° - 48° = x° + 32°

Subtract x° from both sides of the equation

2x° - x° - 48° = x° - x° + 32°

x°  - 48° = 32°

Add 48° to both sides of the equation

x° - 48° + 48° = 32° + 48°

x° = 32° + 48°

x° = 80°

Therefore,

x = 80

Calculating the m ∠FOW

m ∠FOW = x°

m ∠FOW = 80°

Calculating the m ∠FLW

m ∠FLW = (2x - 48)°

m ∠FLW = (2(80) - 48)°

m ∠FLW = (160 - 48)°

m ∠FLW = 112°

Calculating the m ∠OLW

m ∠OLW + m ∠FOW + m ∠OWL = 180° (Sum of angles in a triangle)

m ∠OLW + 80° + 32° = 180°

m ∠OLW + 112° = 180°

m ∠OLW = 180° - 112°

m ∠OLW = 68°

Hence, the measure of m ∠OLW is 68°

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The area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8

over the interval [1, 5] is 164 square units.

Exactly one element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The domain and codomain of the function are, respectively, the sets X and Y as a whole.

The first presentation of the idea of function that is known about was developed by two Persian mathematicians, Al-Biruni and Sharaf al-Din al-Tusi. Originally, functions were used to depict the desired relationship between two varying values. For example, time affects the position of a planet. Up to the 19th century, the functions that were taken into consideration were differentiable.

Given,

f(x)=3x³-3x²-x+8

g(x) = 2x³- 10x² + 29x + 8

And the interval is  [1, 5].

By using area formula,

A=[tex]\int\limits^a_b {f(x)-g(x)} \, dx[/tex]

A=[tex]\int\limits^a_b[/tex](Upper function-Lower function)dx

A=[tex]\int\limits^3_1[/tex][g(x)-f(x)]dx+[tex]\int\limits^5_3[/tex][f(x)-g(x)]dx

A=[tex]\int\limits^3_1[/tex](-x³-7x²+30x)dx+[tex]\int\limits^5_3[/tex](x³+7x²-30x)dx

A= (118/3)+(374/3)

A=164 square units.

Therefore, the area bounded by f(x)=3x³-3x²-x+8, g(x) = 2x³- 10x² + 29x+8

over the interval [1, 5] is 164 square units.

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Answer:

2

Step-by-step explanation:

First, we must add 14 to both sides to put the variable and coefficient alone.

4s - 14 = -6

   +14     +14

4s = 8

s = 2

For each of the values of GPD, use the regression equation to predict the carbon dioxide emission amount is 1300.715.

What is carbon dioxide ?

Our atmosphere contains carbon dioxide, an odorless and colorless gas. According to its chemical composition, CO2, it is made up of one carbon atom joined to two oxygen atoms. It is a waste product created both by burning fossil fuels and by human bodies.

Given regression eq.

[tex]$$\hat{y}=166.92+115.725$$[/tex]

* Given [tex]$x=2.6$[/tex]

[tex]$$\begin{aligned}& \hat{y}=166.9(2.6)+115.725 \\& \hat{y}=549.665\end{aligned}$$[/tex]

* Given [tex]$x=4.0$[/tex]

[tex]$$\begin{aligned}& \hat{y}=166.9(4.0)+115.725 \\& \hat{y}=783.325\end{aligned}$$[/tex]

* Given [tex]$x=7.1$[/tex]

[tex]$$\hat{y}=166.9(7.1)+115.725$$[/tex]

[tex]\hat{y}=1300.715[/tex]

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the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.

Let f(x) = a0 + a1x + a2x2 + a3x3 be a polynomial function of odd degree 3.

We know that the degree of a polynomial is the highest power of the variable in the equation. Since the degree of f(x) is 3, then a3 ≠ 0.

Now, consider the Discriminant of the polynomial, which is defined as the expression below:

Discriminant = b2 - 4ac

In this case, b2 = a2^2, c = a0 and a = a3, thus the Discriminant is:

Discriminant = a2^2 - 4a0a3

Since a3 ≠ 0 (as mentioned before), the Discriminant will always be greater than or equal to zero. This means that the polynomial has at least one real root.

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Answer:

7 13/21 months

Step-by-step explanation:

10 2/3 ÷ 1 2/5 =

= 32/3 ÷ 7/5

= 32/3 × 5/7

= 160/21

= 7 13/21

Answer: 7 13/21 months

The correct expression to model the cost of manufacturing b basketballs in 1 day is:

O $5.25b-$1,400.00

The fixed costs of manufacturing the basketballs are $1,400.00 per day, and the variable costs are $5.25 per basketball. To find the total cost of manufacturing b basketballs in 1 day, you need to add the fixed costs and the variable costs for each basketball.

The variable costs for b basketballs would be $5.25 * b. To find the total cost, you need to subtract the fixed costs of $1,400.00 from this amount. This can be represented by the expression $5.25b - $1,400.00.

The other expressions do not correctly represent the cost of manufacturing b basketballs in 1 day because they do not correctly account for both the fixed costs and the variable costs.

The volume of the gas becomes 4L. Option B is correct.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

Here,

From the ideal gas equation, we know that,

Volume is directly proportional to the temperature,

So,

V₁ / V₂ = T₁ / T₂

Where,

V₁ and T₁ are the initial pressure and temperature,

V₂ and T₂ are the final pressure and temperature.

Substitute the values,

8 / V₂ = 400 / 200

V₂  = 4

Thus, the volume of the gas becomes 4L. Option B is correct.

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Answer:

92 apples remaining

Step-by-step explanation:

2 * 69 = 138 apples

138 * (3/9) =

138 * (1/3) =

138 * 1/3 =

138/3 = 46 apples

138 - 46 = 92 apples remaining

Answer:

you have 2 apples

then you got it 69 times= 2×69 = 138

then you give 3 ninths to a friend

138/9 = 15.33

you gave it 3 one-ninths = 3× 15.33 = 46

so must be left with 138-46 = 92

If the nail is measured with a ruler and its length is 5.46 cm , then the correct statements are :

(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ;

(b) The uncertainty is in the final digit of the measurement .

The Uncertainty of a number helps to estimates in comparison of experimental numbers .

it is given that , the reported length of the ruler is = 5.46 cm ;

we know that ,

the uncertainty In any number , is present in last digit only ,

the place value of the last digit in 5.46 is 0.01 .

So , uncertainty can be expressed by reporting measurement as 5.46 ± 0.1 cm

Therefore , the correct statements about the certainty and uncertainty are (a) and (b) .

The given question is incomplete , the complete question is

A nail is measured with a ruler and its length is reports as 5.46 cm.

Select ALL the statements that are correct about the certainty and uncertainty represented in this recorded measurement.

(a) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.1 cm ,

(b) The uncertainty is in the final digit of the measurement ,

(c) All three digits shown in the measurement are known with certainty ,

(d) The uncertainty can be expressed by reporting the measurement as 5.46 ± 0.01 cm  .

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(a) There are 10 units must be sold to maximize profit.

(b) The maximum profit is 480.

what is profit?

A profit is an income that is given to the owner in an efficient market production process in accounting. The owner's primary interest in the income-formation process of market production is profit, which is a measure of profitability. Different profit metrics are frequently employed.

Given:

A company sales x units of a product, its profits P can be determined

using the profit function P(x) = -2x² + 40x + 280       ..(1)

We have to find the maximum profit.

Differentiate equation (1) w.r.t x

     P'(x) = -4x +40            ..(2)

-4x + 40 = 0

        4x = 40

          x = 10

Again differentiate equation (2) w.r.t x

P''(x) = -4 which is negative.

Hence, there are 10 units must be sold to maximize profit.

Now, to find the maximum profit.

Plug x = 10 in equation (1)

P(10) = -2(10)^2 + 40(10) + 280

        = -200 + 400 + 280

P(10) = 480

Hence, the maximum profit is 480.

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Answer:

(7, 8)

Step-by-step explanation:

equation 1:  [tex]6x+6y=90[/tex]

equation 2: [tex]9x+2y=79[/tex]

This system of equations can be solved for using the elimination method.

First, multiply both sides of the first equation by 3/2 to match the number of x's in both equations so that when we subtract the first equation from the second, the x's cancel and we can solve for y.

[tex]\left(\dfrac{3}{2}\right)\left(6x+6y\right)=(90)\left(\dfrac{3}{2}\right)[/tex]

[tex]9x + 9y = 135[/tex]

Next, subtract this from the second equation.

    [tex]9x+2y=79[/tex]       ← eq. 2

[tex]\underline{- (9x+9y=135)}[/tex]    ← modified eq. 1

     [tex]0 - \, 7y \, = -56[/tex]

Then, solve for y by dividing by 7.

[tex]7y = 56\\\overline{\, 7 \ } \ \ \ \ \overline{\ 7 \: }[/tex]

[tex]y=8[/tex]

So, the y-coordinate of the solution pair is 8.

Now that we've solved for the y, all we have to do to get x is plug the solved y-value back into one of the equations. I'll use the first equation.

[tex]6x+6y=90[/tex]

[tex]6x + 6(8) = 90[/tex]

↓ multiplying out 6 and 8

[tex]6x + 48 = 90[/tex]

↓ subtracting 48 from both sides

[tex]6x = 90 - 48[/tex]

[tex]6x = 42\\\overline{\: 6 \: } \ \ \ \ \, \overline{\: 6 \: }[/tex]

[tex]x = 7[/tex]

So, the x-coordinate of the solution pair is 7.

Finally, put the x- and y-coordinates together into an ordered pair in the form [tex](x, y)[/tex].

(7, 8)

Answer:

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

First, simplify the first equation by dividing all terms by 6:

Then solve it for y:

Now, substitute this into the second equation:

Finally, find the value of y:

The pair of numbers is (7, 8).

T be the set of all points x in [0,1] by a Cantor set type construction is  x=∑∞n=1 qn/4n

for some sequence of qns with each qn∈{1,3}.

What is Cantor set type construction?

The Cantor set is a collection of points situated on a single line segment that possesses a variety of odd characteristics.

By deleting the center third of a line segment and then repeating the process with the remaining shorter segments, the Cantor ternary set, the most popular construction, is created. The ternary construction was only briefly described by Cantor as an illustration of a more basic concept—that of a perfect set that isn't dense anywhere.

According to the given question:

The proportion (i.e., measure) of the unit interval that is left can be determined by subtracting the entire length as the Cantor set is defined as the set of points that are not excluded.

T be the set of all points x in [0,1] by a Cantor set type construction is  x=∑∞n=1 qn/4n

for some sequence of qns with each qn∈{1,3}.

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Answer:

Step-by-step explanation:

Part 1: true

(-4, -1) and (0, 2)

m = 2+1/0+4

m = 3/4

(0, -3) and (4, 0)

m = 0+3/4+0

m = 3/4

Part 2: true

It intercepts at (0, -3)

Part 3:

I can't really see what slope it says but if it says -3/5, then its true, otherwise it's false.

(5, -1) and (0, 2)

m = 2+1/0-5

m = 3/-5

m = -3/5

Part 4: false

Graph A would have 2 and Graph C would have different intersecting points.

There are 1307674368000 possible methods to remove each ball from the box one at a time.

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.  examination of events subject to probability.

given,

the quantity of balls inside a box ,

four red balls

6 balls in blue

four green balls

The variety of ways the balls can be taken out of the box one at a time must be determined.

Here,

Combination is possible because order is imperceptible;

mixture formula; nCr is equal to n!/r1(n-r)!

Here, There are 15 balls in the box overall (5 + 4 + 6 balls).

Then.

¹⁵C₁₅ = 15! / 15! (15 - 15)! = 15! = 1307674368000

that is

There are 1307674368000 ways in which we can take the balls out of the box one at a time.

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Answer:

x = 7/3.

Step-by-step explanation:

DE is parallel to BC and AD= DB and AD = EC.

So, AD/DB = (x+1)/(4x-6)

(x + 1)/(4x - 6) = 1

x + 1 = 4x - 6

1 + 6 = 4x - x

3x = 7

x = 7/3.

The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.

How are the degrees of freedom determined?

Hence, the t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.

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Answer:

-7 - 4/4

= -7 - 1

= -8

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

-7 - 4/4= -7 - 1= -8

Answer:

25456

Step-by-step explanation:

592 over 43

592

x 43

multiply 3 by 2, 9 and 5. 3 by 2 is 6. 3 by 9 is 27. 3 by 5 is 15.

add a zero at the second row then,

multiply 4 by 2, 9, 5. 4 by 2 is 8. 4 by 9 is 36. 4 by 5 is 20.

if you aligned them properly, when you add them you should get 25456

I'll try to include a picture of my work, hopefully you can see it**

The number of sticks in pattern 6 is; 26

The nth term of the sequence formed is; aₙ = 4n + 2

From the attached image, we see that;

Number of sticks in pattern 1 is 6

Number of sticks in pattern 2 is 10

Number of sticks in pattern 3 is 14

Thus, the sequence will be;

6, 10, 14, ...

This is an AP because the difference is 4.

The formula for the nth term of an AP is;

aₙ = a + (n - 1)d

where;

a is first term

n is position of term

d is common difference

In our sequence, first term; a = 6

Common difference; d = 10 - 6 = 4

Thus, the equation for the nth term is;

aₙ = a + (n - 1)d

aₙ = 6 + (n - 1)4

aₙ = 6 + 4n - 4

aₙ = 4n + 2

Now, substitute n = 6 in the above equation to find the number of sticks in pattern 6. This gives;

a₆ = 4(6) + 2

a₆ = 26

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The equivalent expression for the given expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression ∛x⁵y.

expression is equivalent to ∛x⁵y is

[tex](x^5y)^{\frac{1}{3} }[/tex]

= [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]

The equivalent expression is [tex]x^{\frac{5}{3} }y^{\frac{1}{3} }[/tex]. Therefore, option B is the correct answer.

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Answer: 226.19

Step-by-step explanation:

Using the formula for a cyclinder{ V=πr2h} and inputing the values given in the diagram, (the radius and height given) you get 28.27.

Then adding the cone's volume (V=πr2h/3) and inputing that values in the diagram (the radius and height) you get 197.92.

Adding those values you got from the cyclinder and cone together, you get the volume of the composite solid.

(a) The standard deviation of the large wild cats is 25.5 (b)  The standard deviation of the birds in flight is 33 (c) The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate  more from the mean than the fastest recorded speeds of birds in flight . Option A

We should understand that standard deviation looks at the amount of deviation from the means of the set of data.

(a) (70+45+25+45+35+35+40+40+25)÷9 = 40

mean is = 40

(x-m) =30+5+-15+5+-5+-5+0+0+-15)

(x-m)²=(900+25+225+25+25+25+0+0+225)=1450/9

Standard deviation = √650

Standard deviation = 25.5

(b) x= (216+103+96+56+63+35+50+32+55+25+25+20)=776

Mean(m)=776/12=65

(x-m)=151+38+31+-9+-2+-30+-15+-33+-10+-40+-40+-45

Now the square of the deviations from the mean is

(x-m)²=(7396+1444+961+81+4+900+225+1089+100+1600+1600+2025)÷12

=1452

Standard deviation = √1452=33

(c) Therefore, from the calculations, the standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight

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The value of x in . (4x-101)° = (2x+3) is 52°.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

The value of x. (4x-101)° = (2x+3)

Collect the like terms

4x - 2x = 3 + 101

2x = 104

Divide

x = 104 / 2

x = 52°

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Complete question

Find the value of x. (4x-101)° = (2x+3)

When t = 3869, the rate of change of p is proportional to p.

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions.

Applications often involve functions that reflect physical quantities, derivatives that depict the rates at which those values change, and a differential equation that establishes a connection between the three. Due to the prevalence of these relationships, differential equations are widely used in many fields, including engineering, physics, economics, and biology.

The primary focus of studying differential equations is on the solutions—the collection of functions that satisfy each equation—as well as the characteristics of those solutions.

Only the most basic differential equations can be solved using explicit formulas, but many features of a particular differential equation's solutions can be deduced without doing an exact calculation.

When a closed-form expression is used, it is common for.

According to our question-

The revised equation is then

P=5000exp(-0.0513t)

Find P at t=5 now.

P=5000 exp(-0.0513×5)

P=5000 ×exp(-0.25647) (-0.25647)

P=5000 × 0.77378

P=3868.89.

P = 3869. Roughly

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Answer: b. radius of the cone = 5; height of the cone = 12

Step-by-step explanation:

The volume of the cylinder is [tex]\pi (5^2)(4)=100\pi[/tex].

The only option that makes the same volume is option b. In this case, the volume is [tex]\frac{\pi}{3}(5^2)(12)=100\pi[/tex].

Answer:  15,507.44.

Step-by-step explanation: To find the original price of the home before the down payment was made, you need to use the following formula:

Original price = Mortgage amount / (1 - Down payment percentage)

Plugging in the values given in the question, you get:

Original price = $170,000 / (1 - 8.6%)

The original price of the home before the down payment was made is $<<170000/(1-.086)=185507.44>>185,507.44.

This means that the down payment amount was $185,507.44 - $170,000 = 185507.44-170000=15,507.44.

Let f(t) be 51000+ (2100)t which represent Chelsea's salary at Company A and g(t) be 45000(1.041)t which Chelsea salary at Company B.

Chelsea's offer from company A includes a raise of $2100 annually and a starting salary of $45,000.

Since the increase is constant, the salary of Chelsea from Company A is a linear function, as can be seen here.

f(t) is salary of chelsea from company A after t years.

f(t) = 45000+ (2100)t

The offer made to Chelsea by company B includes a starting salary of $45,000 and an annual raise of 4.1%.

we can see here that raise is exponential, so raise is:

(1+4.1/100) = (1+0.041) = (1.041) per year.

Consequently, the salary of Chelsea from Company B is a function that is exponential.

g(t) is salary of chelsea from company B after t years.

g(t) = 45000(1.041)t

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