At a concession stand, seven hot dog(s) and four hamburger(s) cost $21:25, four hot dog(s) and seven hamburger(s) cost $22.75 Find the cost of one hot dog and the cost of one hamburger

1= 136 degrees

2= 44 degrees

3= 136 degrees

Answer:

m<1=136

m<2=44

m<3=136

Step-by-step explanation:

hence m<4=44

m<2 is also likely to be 44

( vertically opposite angles)

44+ m<3 = 180 ( linear pair)

m<3=180-44

=136

m<1 = 136( vertically opposite angle of

<3)

Hope it helps

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Answer:

y = mx + b

m is the slope, and that is -2.

Step-by-step explanation:

Answer: 15

Step-by-step explanation: Use the formula: \(a^{2}+b^{2}=c^{2}\)

Remember \(c^{2}\) should always be the hypotenuse or the longest side.

\(112^{2}+b^{2}=113^{2}\) ---> evaluate the exponents

\(12544+b^{2}=12769\) ----> subtract 12544 to the other side

\(b^{2}=225\) ---> take the square root of both sides

\(b=15\)

Answer:

Step-by-step explanation:

Let the functions be

Their sum

Their product

A. When added, the sum of the y-intercepts must be 1.

B. When multiplied, the product of the y-intercepts must be –15.

C. Either f(x) or g(x) has a positive rate of change and the other has a negative rate of change.

D. f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2.

E. f(x) could have a rate of change equal to 2 and g(x) could have a rate of change of –6.

Answer:

25(m+3)

Step-by-step explanation:

25 is multiplied by (m+3)

'the sum of m and 3' is a quantity which must be indicated using parentheses

Hello!

The sum of means we add:

m+3

Multiply it times 25:

25(m+3)

The answer is Option C.

Now, the option you selected is wrong for the following reasons:

If you translate it into a verbal phrase, this is what it means:

25 plus the product of m and 3

Hence, Option C is correct.

Hope everything is clear.

Let me know if you have any questions!

Always remember: Knowledge is power! :-)

The cost of the wallpaper per square foot is $4.

To find the cost per square foot of the wallpaper, we first need to calculate the total surface area of the box. A rectangular prism has six faces, and each face is a rectangle.

The front and back faces have dimensions 6 feet by 3 feet, so their combined area is 6 ft * 3 ft * 2 = 36 square feet.

The top and bottom faces have dimensions 5 feet by 3 feet, so their combined area is 5 ft * 3 ft * 2 = 30 square feet.

The left and right faces have dimensions 6 feet by 5 feet, so their combined area is 6 ft * 5 ft * 2 = 60 square feet.

The total surface area of the box is 36 + 30 + 60 = 126 square feet.

Since the cost of the wallpaper is $504, we divide the total cost by the total surface area to find the cost per square foot: $504 / 126 sq ft = $4 per square foot.

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Answer:

268

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

12 x 12 = 144

144 + 144 = 288

Answer:

Step-by-step explanation:

Assuming that the given dimensions of 13, 13, 13 refer to the base of the rectangular pyramid, we can calculate the surface area of the pyramid as follows:

First, we need to calculate the area of the rectangular base, which is simply length x width:

Area of rectangular base = 13 x 13 = 169 square units

Next, we need to calculate the area of each triangular face of the pyramid. Since the rectangular base has two sets of parallel sides, there are two types of triangular faces: the isosceles triangles on the sides and the right triangles on the front and back.

To calculate the area of the isosceles triangles, we need to first find the length of the slant height, which can be found using the Pythagorean theorem:

a² + b² = c²

where a and b are the base and height of the triangle (both equal to 13 in this case), and c is the slant height.

13² + 13² = c²

338 = c²

c ≈ 18.38

Now that we have the slant height, we can calculate the area of each isosceles triangle using the formula:

Area of isosceles triangle = (1/2) x base x height

Area of isosceles triangle = (1/2) x 13 x 18.38

Area of isosceles triangle ≈ 119.14 square units

To calculate the area of each right triangle, we need to use the same slant height of 18.38, along with the height of the pyramid, which is also 13. Then we can use the formula:

Area of right triangle = (1/2) x base x height

Area of right triangle = (1/2) x 13 x 18.38

Area of right triangle ≈ 119.14 square units

Since there are two of each type of triangular face, the total surface area of the pyramid is:

Surface area = area of rectangular base + 2 x area of isosceles triangle + 2 x area of right triangle

Surface area = 169 + 2 x 119.14 + 2 x 119.14

Surface area = 546.28 square units

Therefore, the surface area of the rectangular pyramid with base dimensions of 13 x 13 and height of 13 is approximately 546.28 square units.

The length of the side P is 15 cm. And the right option is C.

Pythagoras theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides.

To calculate the length of side P we use Pythagoras theorem's formula

Pythagoras formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the right option is C 15 cm.

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Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

The scale factor is 4/5.

In mathematics, a fraction represents a part of a whole. A fraction consists of two numbers separated by a horizontal line called a fraction bar or a division sign. The number above the bar is called the numerator, and the number below the bar is called the denominator.

The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator. This fraction represents three parts out of a total of four equal parts.

Fractions can be written in different forms, such as proper fractions, improper fractions, and mixed numbers.

A proper fraction has a smaller numerator than the denominator, such as 2/3 or 5/8.

An improper fraction has a numerator that is equal to or greater than the denominator, such as 7/4 or 11/6.

A mixed number consists of a whole number and a proper fraction, such as 2 1/3 or 3 2/5.

Fractions are used in many real-life situations, such as cooking, measuring, and financial calculations. They are also an essential part of mathematics and are used in operations such as addition, subtraction, multiplication, and division.

To find the scale factor, we can compare the ratios of the corresponding side lengths of the congruent triangles.

Scale factor = (corresponding side length in triangle FQX) / (corresponding side length in triangle CVI)

Let's first identify the pairs of congruent angles:

Angle FQX = angle CVI (both are right angles)

Angle XQF = angle ICV (corresponding angles)

Angle FXQ = angle CVI (corresponding angles)

Now let's write the ratios of the corresponding side lengths in a proportion:

FQ / CV = QX / VI = XF / IC

Substituting the given values, we have:

28 / 35 = 36 / 45 = 24 / 30

Simplifying each fraction, we get:

4 / 5 = 4 / 5 = 4 / 5

Therefore, the scale factor is 4/5.

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On simplifying the given equation, the value of x = -7/2.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Variables, constants, and mathematical operations including addition, subtraction, multiplication, and division are frequently used in it. Equations can be solved to get the values of the variables that make the equation true. Equations are frequently symbolised with the equals sign (=).

Given,

\((1/4) ^{x+1} =32\)

1/4 can be simplified as\((1/2)^{2(x+1)\)

or it can be written as \(2^{-2x - 2}\)

32 can be expressed as 2⁵

⇒ \(2^{(-2x - 2)} = 2^5\)

As base is same, power will be same,

⇒ -2x - 2 = 5

⇒ 2x + 2 = -5

⇒ 2x = -7

⇒ x = -7/2

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Correct question -

What is the solution to this equation? \((1/4) ^{x+1} =32\)

a: 3/2b: 2c: -2d: -7/2

Answer: 18.78 cubic feet

Step-by-step explanation:

The detailed analysis is attached below.

Answer:

t = I/(Pr)

Step-by-step explanation:

We divide P*r on both sides to isolate t and we get t=I/(P*r)

Rounding to the nearest whole dollar, we get a predicted sales revenue of $290 for Saturday.

To calculate the 95% interval for the slope on "Cashiers", we need to use the t-distribution with n - k - 1 degrees of freedom, where n is the number of observations and k is the number of predictors (excluding the intercept).

In this case, n = 50 and k = 6, so the degrees of freedom is 43.

The standard error of the slope coefficient for "Cashiers" is given by SE = 4.049, and the t-statistic for a 95% confidence interval with 43 degrees of freedom is approximately 2.016.

Therefore, the margin of error for the slope coefficient is ME = 2.016 * 4.049 = 8.17.

To calculate the lower and upper bounds of the 95% confidence interval, we can use the formula:

lower bound = b1 - ME

upper bound = b1 + ME

where b1 is the coefficient for "Cashiers" from the regression output, which is 41.943.

Plugging in the values, we get:

lower bound = 41.943 - 8.17 = 33.77

upper bound = 41.943 + 8.17 = 50.11

Therefore, the 95% interval for the slope on "Cashiers" is (33.77, 50.11), rounded to two decimal places.

To predict sales for Saturday when the average temperature is 80 degrees, 8 cashiers are working, and $5250 worth of coupons are redeemed, we need to use the regression equation:

Y = b0 + b1 * X1 + b2 * X2 + b3 * X3 + b4 * X4 + b5 * X5 + b6 * X6 + e

where Y is the daily sales revenue, X1 is the average temperature,

X2 is the number of cashiers,

X3 is the total amount of coupons redeemed,

X4 is a binary variable for Sunday,

X5 is a binary variable for Tuesday,

X6 is a binary variable for Thursday, and e is the error term.

Plugging in the values, we get:

Y = -338.41 + 0.5487 * 80 + 41.943 * 8 + 0.07286 * 5250 + 0 + 0 - 139.15 + 0 + e

Y = 289.78 + e.

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Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

Given that there are 66.03 KM between the cliff and the island, the bearing will be 54.88°.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle. A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.

Here,

p=54 units

b=38 units

h=√(p²+b²)

=√54²+38²

h=66.03 units

sin θ=p/h

sin θ=54/66.03

sin θ=0.818

θ=54.88°

The bearing from the cliff to the island will be 54.88° as the distance is 66.03 Km.

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Answer: -7x+4y-z would be the answer

Step-by-step explanation:

Answer:

Coordinates of the starting point ( -50 ; 0 )

Coordinates 4 seconds later Q ( - 25*√3  ;  25 )

Coordinates 32 seconds later R ( 25  ;  - 25*√3 )

Step-by-step explanation:

a) If Jeremy takes 48 seconds fr a lap then

The length of the lap ( length of the circle ) is:

L =  2*π*r    ⇒   L = 100*π

If the time for one lap was 48 seconds at a constant speed, the speed was

v = 100*π / 48   [m/s]

v = 6,54 m/s

12 seconds  is  1/4 0f 48  in that time he (she) reach the northernmost point, then he(she) necessarily started on the negative side of the       x-axis the coordinates at this point are

( -50 ; 0 )

b) 4 seconds later, at v = 6,54 m/s by rule of three

In 12 seconds                         90⁰

In  4  seconds  (the third part )       x ??

x = 30⁰

sin 30⁰  = 1/2

cos 30⁰ = (√3)/2

And coordinates for the point are

sin 30⁰ =  1/2  = y/50     ⇒  y =  25

cos 30⁰ = (√3)/2  = x / 50   ⇒ x = 25*√3

coordinates of the point 4 seconds later

Q ( - 25*√3  ;  25 )    she (he) is in the negative part of x-axis

c) 32 seconds later

32  is    12   +   12    +    8

Then she (he) is 8 seconds below the positive side of x-axis

8 is 2/3 of 12   ( negative 60⁰ )

sin 60⁰ = (√3)/2   = y/50       y  =  25*√3    negative

cos  60⁰ = 1/2 * 50   =  X/50  x  = 25

Coordinates of the point R

R ( 25  ;  - 25*√3 )

The simplified expression when a polynomial is divided by a monomial is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)

A polynomial expression can be represented as a product of other, smaller polynomial expressions through the algebraic process of factoring. The process of factoring can be used to simplify expressions and solve problems. A polynomial equation's roots can be found by factoring, as can the common factors in an expression that can be eliminated. Factoring occasionally enables us to spot trends and connections between several expressions.

Depending on the kind of polynomial and the degree of the terms involved, there are several ways to factor. S

For the given expression \((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\) factor the common term.

\((12y^7u^2-32y^5u^6+15y^7u^6) / (-4y^2u^5)\\-4y^5u^2(3y^2 - 8u^4 - 3y^2u^4) / (-4y^2u^5)\)

Cancelling the -4:

\(= y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2)\)

Hence, the simplified expression is \(y^3 / u^3 (8u^4 - 3y^2u^4 - 3y^2).\)

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Answer:

Step-by-step explanation:

-2x +38 = 2(3 + 3x)

-2x + 38 = 2*3 + 2*3x

-2x + 38 = 6 + 6x

Add 2x to both sides

38 = 6 + 6x + 2x  

Combine like terms

38 = 6 + 8x

Subtract 8  from both sides

38 - 6 = 8x

8x = 32

Divide both sides by 8

x = 32/8

x = 4

Answer:

x = 4

Step-by-step explanation:

Use distributive property to multiply 2 by 3 and 3x

subtract 6x from both side

combine -2x and -6x to get -8x

subtract 38 from both side

subtract 38 from 6 to get -32

divide both side by -8

\( \small \sf \frac{-8x}{ -8} = \frac{-32}{-8} \\ \\ \small \sf x = \frac{- 32}{-8}\)

divide -32 by -8 to get 4

The area of regular hexagon in simplest radical form is \(600\sqrt{3}\) m².

There are many different types of hexagons. The most common type is a regular hexagon, which is a hexagon that has sides of equal length and angles of equal measure. The perimeter is the total length or distance around a two dimensional shape. In the figure below, the perimeter of each shape is the sum of the lengths of each side, shown in red. The perimeter of a circle or ellipse is called the circumference. For a polygon, the perimeter is the sum of its side lengths.

The given polygon is a regular hexagon with perimeter 120 m.

Thus, the length of each side,

s = 120/6 = 20 m.

The area, A, of a regular hexagon can be found given only its side length, s, with the formula:

\(A = \frac{3\sqrt{3} }{2} s^{2}\)

Substitute s = 120 m in above formula:

\(A = \frac{3\sqrt{3} }{2} (20)^{2} \\A = \frac{3\sqrt{3} }{2}(400)\\A = 600 \sqrt{3}\)

Thus, the area of regular hexagon in simplest radical form is \(600\sqrt{3}\) m².

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Answer: (2x - 1)(3x - 4)

(split -11x as -8x and -3x)

Step-by-step explanation:

I am assuming that it is actually 6x^2 - 11x + 4

To find out how to split the middle term: The two numbers should multiply to a*c (6*4 = 24) and add to b (-11)

-8, -3 works

(6x^2 - 8x) + (-3x + 4)

2x(3x - 4) + -1(3x - 4)

(2x - 1)(3x - 4)

Answer:

  all real numbers

Step-by-step explanation:

The domain of any polynomial function is "all real numbers." There is no value of x for which y is undefined.

Stella earn by babysitting is $5x and earn by working at an shop of icecream is $8y.

Part (A)

Stella earn at least $120 means sum of Stella's earning by babysitting and by working at an shop of ice cream is more than or equal to 120. So equation is,

Stella cannot work more than 20 hours. So equation is,

Part (B)

Substitute 7 for x in the equation

to obtain the value of y.

So value of y is greater than or equal to 10.62. So nearest whole number for y is 11.

Thus Stella work at least for 11 hours at the ice cream for eaning to be at least $120.

The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

here, we have,

Net operating profit = (22 million - 19 million)*(1 - 0.36)

                                = $1.92  million

EVA = net operating profit after taxes - invested capital*WACC

       = 1.92 million - 15 million*0.10

       = $0.42 million

Therefore, The firm’s economic value added (EVA), that is, how much value did management add to stockholders’ wealth during 2018 is $0.42 million.

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The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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