The sum of three numbers is -3. If the second number is subtracted from the sum of the first and third numbers, the result is -3. If the third number is subtracted from the sum of the first and second numbers, the result is -5. Find the three numbers.

[Hint: let x represent the first number, y the second number, and z the third number. Use the given conditions to write and solve a system of equations.]

Answer:

Step-by-step explanation:

4*2*6=48a

Step-by-step explanation:

3.3% = .033 in decimal

Use the compounding formula

a)  P(t) = 18000 (1 + .033)^t        

b)   for t =2 this computes to 19207.6  bacteria

The surface area of the cylinder in terms of pi is:

S = pi*301 cm²

We know that for a cylinder of radius R and height H the surface area is:

S = pi*( 2RH + R²)

Here the height is 18 cm and the diameter is 14cm, then the radius is.

R = 14cm/2 = 7cm

Then the surface area will be:

S = pi*(2*7cm*18cm + (7cm)*7cm)

S = pi*301 cm²

That is the surface area in terms of pi.

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The length of the intercepted arc is 4π unit.

We have,

Angle = 2π/3 = 2(180)/ 3 = 120 degree

r = 6 unit

So, length of Arc

= θ /360 x 2πr

= 120/360 2 π(6)

= 1/3 (12)π

= 4π unit

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The rate of change for the interval between 0 and 2 for the quadratic equation is 10.

A quadratic equation is a type of polynomial equation of the second degree, which means it has one or more terms that are raised to the power of two.

The general form is;

ax² + bx + c = 0

Where;

The rate of change for the interval between 0 and 2 for the quadratic equation is calculated as;

f(2) - f(0) = 7 - (-3)

             = 7 + 3

             = 10

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Answer: 5.5 months

Explanation:

To calculate the number of months it will take to pay off your credit card balance, we can use the formula for the time it takes to pay off a balance with fixed monthly payments:

n = -log(1 - (r * b) / p) / log(1 + r)

where:n is the number of months it will take to pay off the balancer is the monthly interest rate (which is the annual percentage rate divided by 12)b is the balance owedp is the fixed monthly paymentFirst, let's calculate the monthly interest rate r:

r = 0.147 / 12 = 0.01225

Next, we can substitute the values into the formula:

n = -log(1 - (0.01225 * 2264) / 500) / log(1 + 0.01225)

Using a calculator, we can simplify this to:

n = 5.5 months

The solution is :Total manufacturing cost per Lamp is $15.10 per lamp.

Explanation:

Cost per part of Material handling = $3000/6000 parts

Cost per part of Material handling = $0.50 per part

Assembling per hour = $7200/3000

Assembling per hour = $2.40 per hour

Packaging per lamp = $4000/2000

Packaging per lamp = $2 per lamp

Total manufacturing cost per Lamp = $8 + (9*$0.50) + ($2.40/4) + $2

Total manufacturing cost per Lamp = $8 + $4.5 + $0.6 + $2

Total manufacturing cost per Lamp = $15.10 per lamp

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complete question:

Traditions Home Accessories Company manufactures decorative lamps using an activity-based costing system to allocate all manufacturing conversion costs. The following information is provided for the month of June: Activity Estimated Indirect Activity Costs Allocation Base Estimated Quantity of Allocation Base Materials handling $3,000 Number of parts 6,000 parts Assembling $7,200 Number of hours 3,000 hours Packaging $4,000 Number of lamps 2,000 lamps Four lamps can be assembled in 1 hour. Each lamp consists of 9 parts. The total direct materials cost per lamp is $8.00. What is the total manufacturing cost per lamp

The slope of the line and its meaning in terms of the real-world scenario is; C. The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 24)/(6 - 0)

Slope (m) = -24/6

Slope (m) = -4.

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Answer:

4x² - 11xy - 3y²

Step-by-step explanation:

(4x + y)(x - 3y) =

Multiply each term of the first binomial by each term of the second binomial.

= 4x² - 12xy + xy - 3y²

Now combine like terms.

= 4x² - 11xy - 3y²

Answer:

DF = 15 cm

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{DF}{AC}[/tex] = [tex]\frac{EF}{BC}[/tex] ( substitute values )

[tex]\frac{DF}{9}[/tex] = [tex]\frac{25}{15}[/tex] ( cross- multiply )

15 DF = 9 × 25 = 225 ( divide both sides by 15 )

DF = 15

Answer:

12

Step-by-step explanation:

1. Use the Pythagorean theorem for triangle ABC

a squared (one side of the triangle) + b squared (another side) = c squared (hypotenuse)

so

c squared - b squared = a squared

225 - 81 = 144 ( Find the square root )

which is 12

since Triangle ABC is the same with Triangle DEF then

DF = 12

The volume of this rectangular prism include the following: 84.375 cubic meters.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;

Volume of rectangular prism = 5 × 4 1/2 ×  3 3/4

Volume of rectangular prism = 5 × 4.5 ×  3.75

Volume of rectangular prism = 84.375 cubic meters.

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The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15. When solved for C, the equation is K -  273.15. Therefore, the correct option is option C.

Temperature is a unit of warmth or coldness that can be defined in the context of any number of arbitrary scales. It indicates the direction through which the energy from heat will naturally flow, i.e., through a hotter (body) to a colder (body) body. Temperature cannot be the same as a thermodynamic system's energy; for instance, a blazing match is significantly hotter than an iceberg.

K = C + 273.15

K - 273.15 = C + 273.15 - 273.15

K -  273.15 = C

Therefore, the correct option is option C.

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Your question is incomplete but most probably your full question was,  

The temperature measured in Kelvin (K) is the temperature measured in Celsius (C) increased by 273.15. This can be modeled by the equation K = C + 273.15.

When solved for C, the equation is

C = K – 273.15

C = 273.15 – K

C = K + 273.15

C = 273.15K

Answer:

2 boxes

Step-by-step explanation:

8 cupcakes in 1 box = 16 cupcake in x box

We Take

16 ÷ 8 = 2 boxes

So, the answer is 2 boxes.

Answer:

z = 12.52 in.

Step-by-step explanation:

Because this is a right triangle, we can solve for z using on the trigonometric ratios.

If we allow 37° to be our reference angle, the 10 in. side is the adjacent side and z (directly across from the right angle) is the hypotenuse.

Thus, we can use the cosine ratio which is

[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]

Now, we can plug everything into the formula and solve for z, the hypotenuse:

[tex]cos(37)=10/z\\z*cos(37)=10\\z=10/cos(37)\\z=12.52135658\\z=12.52[/tex]

Answer:

32.13

Step-by-step explanation:

The value of c in the equation 15.3 = c/2.1 is 32.13. To solve for c, you can cross-multiply and simplify the equation to c = 15.3 x 2.1 = 32.13.

The solution to the equation "the quotient of a number and 8 is 16" is 128. To solve for the number, you can multiply both sides by 8 to get "the number is 16 x 8 = 128."

To translate the sentence "the quotient of a number and 8 is 16" into an equation, you can use "x" to represent the number and write x/8 = 16.

Answer:

c or a

Step-by-step explanation:

i thing a

Answer:

The height of the window ledge is the height of the box when t = 0. So, we need to find h(0).

```

h(0) = -16(0)^2 + 150

h(0) = 150

```

Therefore, the height of the window ledge is 150 feet.

Step-by-step explanation:

The formula for p(x) is p(x) = -0.1(x - 5)²(x + 3).

In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Also, the graph has a zero of multiplicity 2 at x = 5 and zero of multiplicity 1 at x = -3;

x = 5 ⇒ x - 5 = 0.

(x - 5)²

x = -3 ⇒ x + 3 = 0.

(x + 3)

In this context, an equation that represent the polynomial function is given by:

p(x) = a(x - 5)²(x + 3)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -7.5), we have;

-7.5 = a(0 - 5)²(0 + 3)

-7.5 = a75

a = -7.5/75

a = -0.1.

Therefore, the required polynomial function is given by:

p(x) = -0.1(x - 5)²(x + 3)

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a) Latonya is correct, as the scale factor of the dilation is of 12.8/4.8.

b) The scale factor was obtained dividing the side length on the dilated figure by the equivalent side length of the original figure.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The ratios for the scale factor are given as follows:

12.8/4.8 = 7.2/2.7 = 4.8/1.8 = 4/1.5 = 8/3.

8/3 as 4 x 2 = 8 and 1.5 x 2 = 3.

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The number of days it would take for the investment to be valued at £3,800 is 4.4 days

From the question, we have the following parameters that can be used in our computation:

A = 1200 × 1.3^n

For the investment to be valued at £3,800, the value of A would be

A = 3800

Substitute the known values in the above equation, so, we have the following representation

1200 × 1.3^n = 3800

Divide both sides by 1200

1.3^n = 3800/1200

So, we have

n = ln(3800/1200)/ln(1.3)

Evaluate the quotient

n = 4.4

Hence, it would take 4.4 days

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Answer:

check attachment

Step-by-step explanation:

First write in point-slope form:

y-y1=m(x-x1)

Now substitute:

y-(-1)=3/4(x-(-4))

And then just solve. You should get a y-intercept of 2.

a) The slope shows that the appropriate dose c for an older child increase by 6.225 mg if the child is one year older.

b) The dose for newborn baby is: 6.225 mg

The equation of a line in slope intercept form is:

y = mx + c

where: m is slope and c is y-intercept

(a) Let a be an age of an child in years. Then:

c = 0.0417Da + 0.0417D

Where D is a constant

Since D = 150 mg, then we have:

The slope of the graph = 0.0417(150)

= 6.225 mg/year

The slope shows that the appropriate dose c for an older child increase by 6.225 mg if the child is one year older.

(b) Newborn baby:  a=0

Thus:

c(0) = 0 + 6.225

= 6.225 mg

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Sample Response/ Explanation: The data sets could be the same, but not necessarily. It is possible for data sets to differ in their spread but still have the same measures of center. The measures of spread could be different.

The data sets could be the same, but not really. It is possible for the data sets to differ in their spread but still have the same measures of center. The measures of spread could be different though.

The Perimeter of the given figure rectangle will be 60m. The correct option is 1.

Perimeter refers to the total length of the boundary of a two-dimensional shape or object. It is the distance around the edge of a shape. To find the perimeter of a shape, you add up the lengths of all its sides.

The perimeter of a rectangle is given by the formula:

P = 2(l + w)

where P is the perimeter, l is the length, and w is the width.

Using the values you provided, we can substitute them into the formula:

P = 2(18 + 12) = 2(30) = 60 meters

Therefore, the perimeter of the rectangle with a length of 18 meters and a height of 12 meters is 60 meters.

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32% of the students surveyed preferred grilled cheese, so in a group of 3500 students, about 1120 students will prefer grilled cheese.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of people surveyed is given as follows:

80 + 40 + 50 + 20 + 60 = 250.

80 students preferred grilled cheese sandwich, hence the percentage is obtained as follows:

p = 80/250 x 100%

p = 32%.

Hence the expected amount of 3500 students is given as follows:

0.32 x 3500 = 1120 students.

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We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.

We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.

We can see here that it shows that a is an element of the subgroup of H.

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Answer:

Mean-27

Step-by-step explanation:

Add all of the numbers and it equals 162

Then divide 162 by the amount of numbers presented.

Since there are 6 numbers listed we divide by 6

162/6=27

The solution to the multiplication of both functions is:

2x³ - x² - 4x + 3

To multiply a function by another function, multiply their outputs. For example, if f (x) = 2x and g(x) = x + 1, then fg(3) = f (3) × g(3) = 6 × 4 = 24. fg(x) = 2x(x + 1) = 2x² + x.

We are told that the domain for f(x) and g(x) is the set of all real numbers.

The functions are given as:

f(x) = 2x² + x - 3

g(x) = x - 1

Thus:

f(x) · g(x) = (2x² + x - 3) * (x - 1)

= 2x³ + x² - 3x - 2x² - x + 3

= 2x³ - x² - 4x + 3

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Answer: All of them

Step-by-step explanation:

All of them can be divided into two equal halves.

The figures that show axis symmetry are 1, 2, and 3.

The axis of symmetry is a line, plane, or other axis that divides a geometric figure into two mirror-image halves that are congruent to each other.

A figure has axis symmetry if it looks the same after being rotated around an axis.

Out of the given figures, the ones that have axis symmetry are:

The figures that do not have axis symmetry are:

So, the figures that show axis symmetry are 1, 2, and 3.

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Based on the informtaion provided, the two-way table would be,

                                 Music        World Language         Totals

8th Grade                   20                    40                           60

7th Grade                    10                     50                           60

Total                          30                     90                           120

In this situation there were total 120 seventh and eighth grade CAVA students. And there were a total of 60 eighth grade students.

Total number of students = 120

This means that the number of students in 7th grade : 120- 60 = 60

Out of 120 seventh and eighth grade students, 30 students chose Music as their elechive course.

This means that remaining 120 - 30 = 90 students chose World Language as their elechive course.

Here, 40 eighth grade students chose World Language as their elective.

This means that out of total 90 students 90 - 40 = 50 students of 7th Grade  chose World Language as their elective.

Now consider the 8th grade students,

Out of 60 students 40 chose World Language.

So, 60 - 40 = 20 must chose Music as their elective.

Now consider the 7th grade students,

Out of 60 students 50 chose World Language.

So, 60 - 50 = 10 students must chose Music as their elective.

Hence the required two-way table would be,

                                 Music        World Language         Totals

8th Grade                   20                    40                           60

7th Grade                    10                     50                           60

Total                          30                     90                           120

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