Write the equation of the function in slope-intercept form:

A line with a slope of 2 and passes through (-8, 3)

The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m   .

In the question ,

it is given that ,

the bottom of the box is =  square ,

let the side of the square bottom be = "s" ,

so , the base area [tex]=[/tex] s²

let the height of the box [tex]=[/tex] h ,

Volume of the box = height × (base area)

So , the Volume of the box [tex]=[/tex] s²h

given that the volume of the box is 252 m³ , that means

s²h = 252

h = 252/s²

given that the Cost of bottom = $40 per m²

and the Cost of sides = $30 per m²

So , the total cost = 40s² + 30×(4sh)

substituting the value of h= 252/s² , we get

C = 40s² + 120s×252/s²

C = 40s² + 30240/s

to minimize the cost we differentiate with respect to s , and equating it  to 0 ,

we get ,

80s - 30240/s² = 0

s³ = 30240/80

s³ = 378

s = 7.23
again differentiating C = 40s² + 30240/s with respect to s , and equating it  to 0 ,

we get ,

d²C/ds² = 80 + (30240*2)/s³

at s=7.23 , d²C/ds² > 0

So , the minimum is at s = 7.23 ,

we have h = 252/(7.23)²

h = 4.82 .

Therefore , The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m   .  

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Tension in each string in the 3 - box system is T1 =  m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.

In 3 - box system:

There are two tensions and two strings, let T1 and T2 be the tensions.

Let mass of boxes be m1,m2,m3

total mass m = m1+m2+m3

Acceleration a = force / m

a = f/m1+m2+m3

T1 = m2 * f/m

T2 = m3 * f/m.

Therefore Tension in each string in the 3 - box system is T1 =  m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.

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After factorizing we get the value as:

4sinαcosα

Given,

we have the expression as:

(sinα + cosα)² - (sinα - cosα)²

open the brackets using the identity of:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

now evaluate:

⇒ sin²α + cos²α + 2sinαcosα - (sin²α + cos²α - 2sinαcosα)

⇒ sin²α + cos²α + 2sinαcosα - sin²α - cos²α + 2sinαcosα

⇒ cancel the like terms

⇒ 2sinαcosα  + 2sinαcosα

= 4sinαcosα

hence after factorization we get the value as 4sinαcosα

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For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

As given in the question,

Height of the right circular cone = 2.5 units

And radius of right circular cone = 7.5 units

Let r be the radius of the cylinder and h be the height of the cylinder.

Volume of a cylinder 'V' = π r² h

Cylinder is inscribed in right circular cone

From origin edge cylinder is inscribed at x distance in right circular cone.

r = 7.5 - x

h = (2.5 /7.5) x

  = x/3

V  = π ( 7.5 - x )² ( x / 3)

⇒ V = π ( x² -15x + 56.25 ) (x/3)

⇒ V = (π /3)( x³ - 15x² + 56.25x)

For maximum volume ,

dV/dx = 0

dV/dx = (π/3)( 3x² -30x + 56.25)

(π/3) ≠ 0

⇒ 3x² -30x + 56.25 = 0

⇒ 3 ( x² -10x + 18.75) = 0

3 ≠ 0

⇒ x² -10x + 18.75 = 0

x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)

⇒ x = [ 10 ± √ 100 -75]/2

⇒ x=  ( 10 ± 5 ) / 2

⇒ x = 7.5 or 2.5

As r = 7.5 -x

Hence x ≠ 7.5

r = 7.5 -2.5

 = 5 units

h = x/3

  = 2.5/3

  = 0.8333 units

Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

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The length of the equator is 40192 km.

The radius of the earth is approximately 6400 km.  The equator is the circle around the earth dividing it into the northern and southern hemisphere.

Let's find the length of the equator as follows:

The length of the equator is the circumference.

Therefore,

L = 2πr

where

L = 2 × 3.14 × 6400

L = 6.28 × 6400

L = 40192 km

Therefore, the equator which is the circle around the earth has a length of 40192 km.

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Answer: x = 7

Step-by-step explanation: 6x = x^2 - 7

x^2 - 6x -7 =0

(x-7) (x+1) = 0

x = 7  

x = -1 ----> rejected

The positive solution of the required number is 7.

An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.

Let's start by translating the given sentence into an equation. Let "x" be the number we are trying to find. Then we can write:

6x = x² - 7

Now we need to solve for x. Let's rearrange the equation to get all the x terms on one side and all the constant terms on the other side:

x² - 6x - 7 = 0

We can solve this quadratic equation by factoring or using the quadratic formula, but let's use factoring for this problem. We need to find two numbers whose product is -7 and whose sum is -6. The two numbers are -7 and 1, so we can write:

(x - 7)(x + 1) = 0

This means that either x - 7 = 0 or x + 1 = 0. Solving for x, we get:

x = 7 or x = -1

Since we are looking for a positive solution, the answer is x = 7. Therefore, the positive solution is 7.

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As per the given system of linear equation, the number of solution is infinite.

Linear equations:

An algebraic equation of the form

y = mx + b

Involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept is known as linear equation.

Given,

A system of three linear equations in three variables is consistent and dependent.

Here we need to find the number of solution for this system.

Here we know that the given system of three linear equations in three variables which is consistent and dependent.

We know that, the system is said to be consistent if it has at least one solution. Which means that the system which has no solution is said to be inconsistent.

Similarly, the system is has consistent solution is said to be independent if it has only one solution whereas it is said to be dependent if it has an infinitely many solutions.

Therefore, here the given system of three linear equations in three variables which is consistent and dependent, the system has an infinitely many solutions.

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Answer:

D

Step-by-step explanation:

Unit rates always compare quantities with different units

Ex. 10 km per 1 hour (10kph)

At the ski shack, customers can rent,skis, snowboards, boots, and poles by the day Mrs.Alvarez is renting skis and poles she has a 18$ coupon off

which expression represents the total cost for Mrs.Alvarez to rent skis for s days and poles for p days

If the answer you asked is this:

48s+12p-18  the correct answer

The value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].

Given that

sinx = [tex]\frac{3}{5}[/tex]

sinx = [tex]\frac{opp}{hyp}[/tex]

Using the Pythagoras' theorem

[tex]hyp^{2} = opp^{2} + adj^{2} \\\\adj^{2} = 5^{2}- 3^{2} \\ \\= 25-9\\\\adj^{2} = 16\\ \\adj = \sqrt{16} \\[/tex]

adj = 4.

Now we have to find out tanx and cosx

[tex]tanx = \frac{opp}{adj}[/tex]

[tex]= \frac{3}{4}[/tex]

[tex]cosx = \frac{adj}{hyp}\\ \\= \frac{4}{5}[/tex]

Now we have to find out the given equation (tanx+2cox)

[tex]= \frac{3}{4} +2(\frac{4}{5})\\ \\= \frac{15+32}{20} \\\\= \frac{47}{20} \\\\or\\\\= 2\frac{7}{20}[/tex]

Hence the answer is the value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].

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The ratio which compares to be a whole is:

2/9

Given,

Kenny has 2 red marbles and 4 black marbles.

we are asked to determine the ratio which compares a part to whole.

Based on the given conditions, formulate:

2 ÷ (4+2+3)

Calculate the sum

2/6+3

calculate the sum:

2/9

hence ratio is:

2/9

Hence we get the ratio as 2/9.

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Answer:

XZ = 21 cm

Step-by-step explanation:

since the triangles are congruent then corresponding sides are congruent, so

LN = XZ , that is

5x - 19 = 2x + 5 ( subtract 2x from both sides )

3x - 19 = 5 ( add 19 to both sides )

3x = 24 ( divide both sides by 3 )\

x = 8

then

XZ = 2x + 5 = 2(8) + 5 = 16 + 5 = 21 cm

The ordered pair P within the line segment AB is (- 1, 1 / 2).

In this question we have a segment whose endpoints are known: A(x, y) = (- 3, 2), B(x, y) = (5, - 4), and in which we need to determine the location of point P such that the following relationship is known:

k = AP / PB

[tex]\overrightarrow {AP} = k \cdot \overrightarrow {PB}[/tex]

P(x, y) - A(x, y) = k · [B(x, y) - P(x, y)]

(k + 1) · P(x, y) = A(x, y) + k · B(x, y)

P(x, y) = [1 / (k + 1)] · A(x, y) + [k / (k + 1)] · B(x, y)

Where:

If we know that A(x, y) = (- 3, 2), B(x, y) = (5, - 4) and k = 1 / 3, then the location of the ordered pair is:

P(x, y) = [1 / (4 / 3)] · (- 3, 2) + [(1 / 3) / (4 / 3)] · (5, - 4)

P(x, y) = (3 / 4) · (- 3, 2) + (1 / 4) · (5, - 4)

P(x, y) = (- 9 / 4, 6 / 4) + (5 / 4, - 1)

P(x, y) = (- 9 / 4, 3 / 2) + (5 / 4, - 1)

P(x, y) = (- 1, 1 / 2)

The ordered pair P is (- 1, 1 / 2).

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The angles found by the given figure are:

m∠5 = 97°

m∠7 = 97°

From the graph given we can get that the two parallel lines are cut by a transversal and:

m ∠4 = m∠2

m∠2 = 83°

hence, m∠2 + m∠5 = 180°

so,:

m∠5 = 180° - m∠2

= 180 - 83

= 97°

hence m∠5 = 97°

now, m∠7 = m∠5

since the vertical angles of two increasing lines are equal

so, m∠7 = 97°

Hence we get the two angles respectively.

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Perimeter of the park = 10km

Part of the wall's construction completed =

[tex] \frac{4}{5}th \: of \: perimeter [/tex]

=

[tex] \frac{4}{5} \times 10[/tex]

(cancel 5 and 10)

=

[tex] \frac{4}{1} \times 2[/tex]

= 8km

•.• Part of the wall left (to be constructed) = 10km - 8km = 2km

HOPE THIS HELPS YOU

The length of each side of the square is 4x - 1 while the area for the dimensions of the rectangle is (9x + 2y) by (9x - 2y) using the factorization methods of grouping and difference in two squares respectively.

Factorization is the process of breaking down a number in which when multiplied together will arrive at the original number.

Part A: Given the area of square as 16x² - 8x + 1, applying factorization by grouping;

16x² - 8x + 1 = 16x² - 4x - 4x + 1 (group terms with common factors)

16x² - 8x + 1 = 4x(x - 1) - (4x - 1) (factor out the common factor in each group)

16x² - 8x + 1 = (4x - 1) × (4x - 1) (factor the common factor from the expression)

16x² - 8x + 1 = (4x - 1)²

Part B: For the area or rectangle given as 81x² - 4y², factorizing by the method of difference in two squares;

81x² - 4y² = 9²x² - 2²y² (express as squares)

81x² - 4y² = (9x)² - (2y)²

81x² - 4y² = (9x + 2y) × (9x - 2y)

Therefore, 4x - 1 is the length of one side of the square as all sides of a square are equal and (9x + 2y) by (9x - 2y) is the dimension of the rectangle using the factorization methods of grouping and difference in two squares.

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Step-by-step explanation:

d = number of dimes

n = number of nickels

one dime = $0.10

one nickel = $0.05

d = 3n

0.1×d + 0.05×n = 3.85

0.1×3n + 0.05×n = 3.85

0.3×n + 0.05×n = 3.85

0.35×n = 3.85

n = 3.85 / 0.35 = 11

d = 3n = 3×11 = 33

she has 33 dimes (and 11 nickels).

The amount of money that Richard will have when he turns 27 can be found to be $3, 474.26

Convert the interest rate to a periodic rate which will be in days as the interest is compounded daily:

= 7% / 365 days a year

= 0.019178%

The number of periods is:

= (27 - 15) years x 365 days a year

= 4, 380 days

The money that Richard will have when he turns 27 is:

= 1, 500 x ( 1 + 0.019178%) ⁴³⁸⁰

= $3, 474.26

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A retaurant cutomer left ​$1. 65 a tip. The tax was 6% and the tip was ​%15 of the cot including tax. Then the total bill is $13.31.

In the given question we have to find the total bill of the customer.

A retaurant cutomer left ​$1. 65 a a tip.

The tax was 6% and the tip was ​15% of the cost including tax.

The tip was 15%(0.15) of the cost including tax.

Thus 0.15*X= 1.65

Divide both sides of the equation by 0.15.

x = 11

Now 6%(0.06) tax on meal at 11 is

11* 0.06 = 0.66

So the total bill cost = 6% tax on meal + 15% tip on meal+cost of meal

The total bill cost = $1.65 + $11+0.66

The total bill cost = 13.31

A retaurant cutomer left ​$1. 65 a tip. The tax was 6% and the tip was ​%15 of the cot including tax. Then the total bill is $13.31.

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Answer:

cat = $30

dog = $45

Step-by-step explanation:

write the equation, assume cat = c, dog = d1

2c + 3d = 195 -> eq 1

4c + d = 165 -> eq 2

rewrite eq 2 so that dog is in term of cat

d = 165 - 4c -> eq 3

replace eq 3 into eq 1

2c + 3(165-4c) = 195

2c + 495 - 12c = 195

2c - 12c = 195 - 495

-10c = -300

c = -300/-10 = 30

replace c in eq 3

d = 165 - 4(30) = 165 - 120 = 45

There were total 276 guests in the wedding that Joy organised.

Given,

fraction of the guest that chose beef = 1/3

fraction of the guest that chose chicken = 5/12

fraction of the guest that chose vegetarian = 1  - 1/3 - 5/12 = 1/4

we are asked to find the total number of guests in the wedding:

guests that chose vegetarian = 1/4

guests that chose vegetarian = 69

1/4 of the guest = 69

4/4 of the guest = 69 x 4 = 276

Hence there are total 276 guests in the wedding.

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The probability that the sample proportion will be greater than 0.78 is:

78% of 400 is 0.78× 400 = 312.

So this probability is 1 subtracted by the p value of Z when x = 312

Z = (X - μ)/σ

We are going to approximate the binomial distribution to the normal.

Binomial probability distribution-

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

√V(X) = √np(1 - p)

Normal probability distribution-

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation o, the zscore of a measure X is given by:

Z = (X-μ)/σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z- score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that-

μ = E (X), σ = √V√(X).

In this problem, we have that:

n=400, p=0.8

So = E(X)=np=400-0.8=320

σ = √V(X) = √np(1-p)=√400×√0.8×√0.2=8

Hence, the probability that the sample proportion will be greater than 0.78 is:

78% of 400 is 0.78× 400 = 312.

So this probability is 1 subtracted by the p value of Z when x = 312

Z = (X - μ)/σ

Z = (312- 320)/8.

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The y-intercept of the equation means: D. It means the technician charges a fixed amount of $50 for the repair.

The y-intercept of an equation that models a situation is the initial or starting value. The y-intercept is represented in an equation that is expressed in slope-intercept form, y = mx + b, as "b". The value of "b" is the y-intercept.

Therefore, we are given that y = 20x + 50 represents the total amount the technician charges, in dollars, for a repair that takes specific hours. This implies that:

Therefore, y-intercept, b = 50, means: D. It means the technician charges a fixed amount of $50 for the repair.

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The Central Angle of the sector in radians is  0.3184 π  .

In the question ,

it is given that ,

the radius of the sector = 24 m

the area of the sector = 288 m²

we know that the Area of the sector of the circle is given by the formula

Area = πr²(θ/360)

Substituting the values , we get

288 = (3.14)*(24)²*(θ/360)

θ = (288*360)/((3.14)*(24)²)

θ = 1,03,680/1808.64

θ = 57.32°

converting the angle to radian ,

we get

θ = 57.32° ×  π/180 radian

= 0.3184 π

Therefore  , The Central Angle of the sector in radians is  0.3184 π  .

The given question is incomplete , the complete question is

A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .

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The area of the composed rectangle and the semicircle is 92.56 square units.

Area of rectangle and semicircle

The formula for the Area of a Rectangle.

A = l × w.

where l refers length and w refers width of the rectangle

The area of a semicircle refers the half of the area of the circle. Therefore, the area of a semicircle is 1/2(πr²), where r is the radius.

Given,

Here we have the figure below composed of a rectangle and a semicircle And we need to find the area of this figure then round to the nearest tenth place.

Here we know the following values,

Length of the rectangle = 10

Width of the rectangle = 8

Diameter of the circle = 8

Through the given diameter we have identified the radius as 4.

Now, the area of the rectangle is calculated as,

A = 10 x 8

A = 80 square units.

Similarly, the area of the semicircle is

A = 1/2 (π x 4²)

A = 1/2 x π x 8

A = π x 4

We know the value of π = 3.14, then the area of the semicircle is,

A = 3.14 x 4

A = 12.56 square units.

Therefore, the are of the figure is,

Total area = area of rectangle + area of semicircle

Total area = 80 + 12.56

Therefore, the total area of the figure is 92.56 square units.

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The value of z such that 0.05 of the area lies to the right of z is 1.64.

Given:

0.05 = 5%

The z score is calculated:

z = x - μ / σ

from the t table the value of z is:

= 1.64

More details is in the image uploaded.

Therefore the value of z such that 0.05 of the area lies to the right of z is 1.64.

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Answer:

Step-by-step explanation:

(2/3)20

Answer: 119 minutes

Step-by-step explanation:

Answer:

at least 17 sales

Step-by-step explanation:

On Wednesday she wants to earn 128.

Per day value = 60

128-60=68

She still needs to earn 68.

68 divided by 4=The number of sales needed to get 68 dollars=17

Thus she needs to make at least 17 sales, at most means maximum but she wants to earn AT LEAST 128 which means she wants more thus, answer is 4th option.