For this item, all answers should be entered as whole numbers.

Gustavo made a fruit smoothie. He put 11 ounces of bananas, 5 ounces of blueberries, 3 ounces of strawberries, and 4 ounces of oranges in the smoothie.

Use whole numbers to complete the following statements.

The ratio of ounces of bananas to ounces of strawberries is 11:
3
.

So, there are nearly ______
ounces of bananas for each ounce of strawberries.

The exponential function showing the relationship between y and t is y = 41,000 x (1.07)^t

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

Initial value, a = 41,000

Rate = 7% increment

The exponential function for the college enrollment y of the college, in dollars, after t years can be expressed as:

y = a(1 + r)^t

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

y = 41,000 x (1 + 7%)^t

Evaluate

y = 41,000 x (1.07)^t

Where 1.07 is the factor by which the college enrolment increases

Hence, the function is y = 41,000 x (1.07)^t

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The given trinomial x^(2)+12x+35 is factorable. It's factors would be (x+7)(x+5).

To factor this trinomial, we need to find two numbers that multiply to 35 and add to 12. The two numbers that satisfy this condition are 7 and 5. Therefore, we can factor the trinomial as follows:

x^(2)+12x+35 = (x+7)(x+5)

So, the factored form of the given trinomial is (x+7)(x+5).

Therefore, the answer is (x+7)(x+5).

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V(t)=S ert-W/r

a. The rate at which the account changes (dt/dV) is equal to the interest rate (r) times the value of the account (V) minus the amount withdrawn (W). This can be written mathematically as dt/dV=rV-W. This is a separable differential equation, which can be solved by integrating both sides of the equation with respect to time. The solution is V(t)=S ert-W/r.

b. The value of the Jones' account at the end of 10 years can be found using the solution V(t) from part a: V(10)=500,000 e5%x10-50,000/5% = $387,468.51.

c. To keep their account unchanged at $500,000, the Jones' must withdraw an annual amount W such that V(t)=500,000. From the solution V(t)=S ert-W/r, we can solve for W: W = 500,000e5%x10 - 500,000/5% = $47,613.30.

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Answer:

0.33

Step-by-step explanation:

5.11-3.79= total for 4 postcards

then answer divided by 4 postcards

The value that represents the average residual for a student's GPA would be D. 0.691.

The average residual, denoted as S, is a measure of the variation or deviation of observed values from their predicted values in a statistical model. It is calculated as the mean of the differences between the observed values and their corresponding predicted values.

In other words, it is the average amount by which the predicted values differ from the actual values in a regression analysis.

In the relationship between a student’s number of absences and their GPA, the average residual is shown as S which is 0.691.

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The number is 63. The difference between the digits of a two-digit number is 1.

Number is a mathematical object used to count, measure, and label. Numbers can be represented in a variety of forms, such as numerals, symbols, or words. Numbers are fundamental to mathematics, and all other areas of science and technology. They are used to represent amounts of money, measurements, dates, and amounts of time. Numbers are also used to identify objects and people, and to create equations and formulas. Number is essential for understanding the world around us.

To solve this, the first thing to do is find the sum of the digits. Since the number is one more than five times the sum of its digits, the sum of the digits is (63/5)-1=12.5-1=11.5. This means that the tens digit is 11 and the unit digit is 11 + 1 = 12. Therefore, the two-digit number is 63.

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Answer:

$3,700

Step-by-step explanation:

12% of 9,250 is 1,110

so each year 1,110 is subtracted from the original price of the tractor.

So if you subtract 1,110 five times from 9,250 you get 3,700.

The estimate is that there were 30 million internet hosts in the year 1998.

Exponential growth is a function that shows an increase within a population that occurs at the same rate over time.

If the number of internet hosts increased by 100% per year, it means that it doubled every year. Therefore, we can use the formula for exponential growth to estimate the number of internet hosts in future years.

Let x be the number of years after 1993, and let H(x) be the number of internet hosts in year y. Then, we have:

H(x) = 1,313,000 * 2ˣ

To estimate the year when there were 30 million internet hosts, we need to solve the following equation for x:

H(x) = 30,000,000

Substituting the formula for H(y), we get:

1,313,000 * 2ˣ = 30,000,000

Dividing both sides by 1,313,000, we get:

2ˣ = 30,000,000 / 1,313,000

Taking the logarithm of both sides with base 2, we get:

x = log2(30,000,000 / 1,313,000)

Using a calculator, we get:

x ≈ 5.2

Therefore, the estimate for the year when there were 30 million internet hosts is: 1993 + 5.2 ≈ 1998.2

Hence, the estimate is that there were 30 million internet hosts in the year 1998.

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Answer:

2080cm^3

Step-by-step explanation:

Answer:

$9.84

Step-by-step explanation:

At the rates given and the quantities purchased,

Maya will pay
Green Beans:   3 lbs x $1.19/lb = $3.57

Zucchini:  2 lbs x $0.99/lb = $1.98

Lettuce: 1 pound x $1.29/lb = $1.29

Sweet Corn: 6 ears x $0.50 per ear = $3.00

Total paid
= $3.57 + $1.98 + $1.29 + $3.00

= $9.84

vector u can be written as a linear combination of the vectors in set S with the scalars a = 1 and b = 0.

To write vector u as a linear combination of the vectors in set S, we need to find scalars a and b such that:

u = a[1] + b[0]

Substituting the values of vector u and the vectors in set S into this equation, we get:

[1] = a[1] + b[0]

This equation can be simplified to:

[1] = [a] + [0]

Since the scalar b is being multiplied by the zero vector, it will always equal the zero vector, and can therefore be eliminated from the equation. This leaves us with:

[1] = [a]

We can see that the scalar a must equal 1 in order for this equation to be true. Therefore, vector u can be written as a linear combination of the vectors in set S as follows:

u = 1[1] + 0[0]

In conclusion, vector u can be written as a linear combination of the vectors in set S with the scalars a = 1 and b = 0.

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The expression can be explained as the trigonometric function of an angle as follows sin(15).

The given expression can be simplified using the trigonometric identity for the sine of the difference of two angles:

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Substituting the given values for a and b, we get:

sin(9 - (-6)) = sin(9)cos(-6) - cos(9)sin(-6)

Simplifying further, we get:

sin(15) = sin(9)cos(6) - cos(9)sin(-6)

Therefore, the given expression can be expressed as a trigonometric function of one angle as follows:

sin(15) = sin(9)cos(6) - cos(9)sin(-6)

-sin(15) = cos(9)sin(-6) - sin(9)cos(6)

So the final answer is -sin(15).

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Answer:

Step-by-step explanation:

Given: [tex]f(x)=x^{2} -3x - 8[/tex]

To find:

a) f(8)

To find f(8), replace x with 8 in f(x)

[tex]f(8) = 8^{2} -3(8) -8 = 32[/tex]

b)  f(x+9)

To find f(x+9), replace x with x +9 in f(x)

[tex]f(x+9) = (x +9)^{2} -3(x +9) -8 = x^{2} +18x+81-3x-27-8=x^{2} +15x+46[/tex]

c) f(-x)

To find f(-x), replace x with -x in f(x)

[tex]f(x)=(-x)^{2} -3(-x) - 8 =x^{2} +3x-8[/tex]

This is how we simplify these expressions.

Answer:

image is blur dear!!!

Step-by-step explanation:

12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex].

The weight of 12 blue whales will be the product of the weight of a single blue whale and the number of blue whales. To find the product, we simply multiply the weight of a single blue whale by the number of blue whales.

So, the weight of 12 blue whales will be:

[tex]\( 1.8 \times 10^{6} \mathrm{~kg} \) × 12 = \( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Therefore, 12 blue whales will weigh [tex]\( 2.16 \times 10^{7} \mathrm{~kg} \)[/tex]

Multiplication refers to binary operations in which different numerical sets are established. In mathematics the process of multiplication is elementary in several operations, it is also accompanied by addition, subtraction and division. Multiplication is the opposite of division.

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The notations x→∞⁻, x→∞⁺, x→-∞⁻, and x→-∞⁺ are not used in limits because they are ambiguous and can lead to confusion.

What are Limits?

In calculus, limits are used to describe the behavior of a function as the input values approach a certain value, usually infinity or a specific point. The concept of limits is essential in calculus and is used to define derivatives and integrals.

The notations x→∞⁻, x→∞⁺, x→-∞⁻, and x→-∞⁺ are not used in limits because they are ambiguous and can lead to confusion. In the limit notation lim x→a, the variable x is approaching the value a from both sides, meaning it can approach a from either the left or the right.

The notations x→∞⁻, x→∞⁺, x→-∞⁻, and x→-∞⁺ suggest that x is only approaching infinity or negative infinity from a specific direction, which is not the case in limit notation. Therefore, the notations x→∞⁻, x→∞⁺, x→-∞⁻, and x→-∞⁺ are not used in limits to avoid confusion and ensure clarity in mathematical expressions.

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The linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.

The linear speed of the circle can be found by calculating the length of the arc traveled in 25 seconds. The length of an arc is given by the formula L = rθ, where r is the radius of the circle and θ is the central angle in radians. Converting the given angle from degrees to radians, we have:

θ = 145 degrees * π/180 = 2.53 radians

Substituting the values into the formula, we get:

L = 21 cm * 2.53 = 53.13 cm

Therefore, the linear speed of the circle is:

v = L/t = 53.13 cm/25 s = 2.125 cm/s

The angular speed of the circle can be found by dividing the central angle by the time taken to travel that angle. Therefore, the angular speed of the circle is:

ω = θ/t = 2.53 radians/25 s = 0.1012 rad/s

Hence, the linear speed of the circle is 2.125 cm/s and the angular speed of the circle is 0.1012 rad/s.

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There are no values of x that satisfy the equation -6-(4x)/(x+2)=(8)/(x+2).

To find the values of x for the equation -6-(4x)/(x+2)=(8)/(x+2), we need to follow the following steps:

Multiply both sides of the equation by (x+2) to eliminate the fractions:
(x+2)(-6-(4x)/(x+2))=(x+2)(8)/(x+2)

Simplify the equation:
-6(x+2)-4x=8

Distribute the -6:
-6x-12-4x=8

Combine like terms:
-10x-12=8

Add 12 to both sides:
-10x=20

Divide both sides by -10:
x=-2

However, we need to check our answer to make sure it does not result in a zero denominator in the original equation. If we plug in x=-2 into the original equation, we get a zero denominator, which is not allowed. Therefore, there are no values of x that satisfy the equation.

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Answer:

Let's call the total number of people who will attend the movie "x". We know that 95% of these people have yet to arrive, which means that only 5% have already arrived.

We can set up an equation to represent this situation:

5% of x = 170

To solve for x, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 5% (or 0.05, which is the decimal equivalent of 5%):

5% of x / 5% = 170 / 5%

Simplifying the left side of the equation gives:

x = 170 / 0.05

Evaluating the right side of the equation gives:

x = 3400

Therefore, there were 3400 tickets sold for the movie.

(1) The length of AB in triangle ABC 24.58 units.

(2) The area of the triangles is 77.94 sq. units.

The length of AB in triangle ABC given is calculated by applying cosine rule as shown below.

Length AB is opposite angle C, so will denote the length as c.

c² = a² + b² - 2ab cos(C)

where;

c² = (18)² + (10)² - 2(18 x 10) cos(120)

c² = 604

c = √ 604

c = 24.58 units

The area of the triangles is calculated as follows;

A = ¹/₂ab sin C

A = ¹/₂ x 18 x 10 x sin (120)

A = 77.94 sq. units

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The relationship between ∠8 and ∠4 include the following: A. corresponding angles.

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines. This ultimately implies that, the corresponding angles will be always equal (congruent) when a transversal intersects two (2) parallel lines.

By applying corresponding angles theorem to lines l and m, we have the following:

8 ≅ ∠4

3 ≅ ∠7

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The required probability for the three dices to be rolled for the given condition is equal to ,

probability 0.579 when X=0,

probability 0.347 when X =1

probability 0.069 for X = 2

probability 0.005 when X = 3.

The random variable X represents the number of times the number '2' is rolled when three dices are rolled.

X represents the values from 0 (when no '2' is rolled) to 3 (when all three dices show '2'.

Probabilities for each case, use the binomial probability formula, we, have,

P(X = a) =ⁿCₐ × pᵃ × (1-p)ⁿ⁻ᵃ

n = Number of trials (in this case, n = 3)

a = Number of successes (here, 'a' ranges from 0 to 3).

p = Probability of success (rolling a '2' on a single die)

p = 1/6

Required probabilities for each possibility is,

P(X = 0) = (³C₀) × (1/6)^0 × (5/6)^3

             = 125/216

             ≈ 0.579

P(X = 1) = ((³C₁) × (1/6)¹ × (5/6)²  

            = 75/216

            ≈ 0.347

P(X = 2) = ³C₂× (1/6)²× (5/6)¹  

             = 15/216

             ≈ 0.069

P(X = 3) = (³C₃) × (1/6)³× (5/6)⁰

             = 1/216

             = 0.004629

             ≈ 0.005

Therefore, the random variable X for the number of times 2 is rolled for three dices are rolled represents probability distribution,

X = 0 with probability 0.579

X = 1 with probability 0.347

X = 2 with probability 0.069

X = 3 with probability 0.005

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The final response is:
−8x^3+6x^2−9x+4 / x−2 = -8x^2 - 10x - 29 + (62/(x-2))

The synthetic division of −8x^3+6x^2−9x+4 / x−2 can be performed as follows:

Step 1: Write the coefficients of the dividend in a row: -8, 6, -9, 4

Step 2: Write the divisor in the form x-a, in this case x-2, so a=2

Step 3: Bring down the first coefficient, -8, to the bottom row

Step 4: Multiply the first number in the bottom row, -8, by a, 2, and write the result, -16, in the next column

Step 5: Add the numbers in the second column, 6 and -16, to get -10, and write the result in the bottom row

Step 6: Repeat steps 4 and 5 with the new number in the bottom row, -10, until all columns have been completed

Step 7: The last number in the bottom row is the remainder, and the other numbers in the bottom row are the coefficients of the quotient

The synthetic division table looks like this:

| 2 |  |   |   |   |
|---|---|---|---|---|
|-8 | 6 | -9| 4 |   |
|   |-16|-20| 58|   |
|---|---|---|---|---|
|-8 |-10|-29| 62|   |

The quotient is -8x^2 - 10x - 29 with a remainder of 62.

So the final response is:
−8x^3+6x^2−9x+4 / x−2 = -8x^2 - 10x - 29 + (62/(x-2))

I hope this synthetic division explanation was helpful!

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Roman painted 36 faces in total

What is 3D Geometry?

Three-dimensional figures, also known as 3D figures, are shapes that have three dimensions: length, width, and height.

They can be represented using a variety of geometric shapes, including cubes, cylinders, spheres, cones, and pyramids.

3D figures are commonly used in geometry, architecture, and engineering to model and design real-world objects.

They are distinguished from two-dimensional figures, which only have length and width, by the addition of the third dimension of height.

Examples of 3D figures in everyday life include buildings, furniture, and toys.

The total faces painted are:

36 faces, this was calculated by counting the number faces left open from all the sides.

For these kind of questions one need to visualize the given figure in a 3D space

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The restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.

The restrictions on the variablex in the expression √6x-2 are determined by the fact that the square root of a negative number is not a real number. Therefore, the expression under the square root must be greater than or equal to zero. This gives us the following inequality:

6x-2 ≥ 0

Solving for x, we get:

6x ≥ 2

x ≥ 2/6

x ≥ 1/3

So the restriction on the variablex is that it must be greater than or equal to 1/3. If x is less than 1/3, the expression √6x-2 will not be a real number.

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The polynomial  3x³ - 4x² + 9x - 12 as a product of binomials is (3x - 4)(x² + 3).

To rewrite the polynomial 3x³ - 4x² + 9x - 12 as a product of binomials, we need to factor the polynomial. One method to do this is by grouping. Here are the steps:

1. Group the first two terms and the last two terms: (3x³ - 4x²) + (9x - 12)
2. Factor out the common factor from each group: x²(3x - 4) + 3(3x - 4)
3. Notice that (3x - 4) is a common factor in both groups, so we can factor it out: (3x - 4)(x² + 3)
4. Now we have the polynomial rewritten as a product of binomials: (3x - 4)(x² + 3)

Therefore, the polynomial 3x³ - 4x² + 9x - 12 can be rewritten as (3x - 4)(x² + 3).

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The equation of the parallel line is y = -4x - 23.

To find the equation of the perpendicular line that passes through (-7, 5), we need to first find the slope of the given line y = -4x + 6. The slope of this line is -4. The slope of a perpendicular line is the negative reciprocal of the original slope, so the slope of the perpendicular line is 1/4.

Next, we can use the point-slope form of an equation to find the equation of the perpendicular line:

y - y1 = m(x - x1)

y - 5 = (1/4)(x - (-7))

y - 5 = (1/4)(x + 7)

y = (1/4)x + 9/4 + 5

y = (1/4)x + 29/4

The equation of the perpendicular line is y = (1/4)x + 29/4.

To find the equation of the parallel line that passes through (-7, 5), we can use the same slope as the original line, -4, and the point-slope form of an equation:

y - y1 = m(x - x1)

y - 5 = -4(x - (-7))

y - 5 = -4(x + 7)

y = -4x - 28 + 5

y = -4x - 23

The equation of the parallel line is y = -4x - 23.

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The graph of the quadratic function is on the image at the end.

Here we have the quadratic function:

f(x) = (x + 1)*(x - 5)

To graph this, we need to find some points of the parabola and then connect them.

So let's evaluate the function.

if x = -1

f(-1) = (-1 + 1)*(-1 - 5) = 0

if x = 0

f(0) =  (0 + 1)*(0 - 5) = -5

if x = 1

f(1) =  (1 + 1)*(1 - 5) = 2*-4 = -8

if x = 5 then:

f(5) =   (5 + 1)*(5 - 5) = 0

So we have the points (-1, 0), (0, -5), (1, -8) and (5, 0).

With these we can graph the parabola (you can try to find more points to get a better graph).

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Emma would therefore receive $225 for a day in which she sold 7 laptops.

Mathematicians use a method called the unitary method to handle proportional problems. Finding the value of one unit must be done before using that value to determine the value of a specified quantity of units. When buying or cooking real-world products that are sold by weight or volume and whose prices are determined by those factors, this technique is frequently used. The unitary approach is also used to address issues involving time, space, and speed.

given

We must use the provided values in the table to determine the equation of the linear relationship between x and P in order to determine how much money Emma would be paid on a day when she sold 7 computers.

The first two data values can be used to determine the line's slope:

slope is equal to (145 - 105) / (3 - 1) / (P2 - P1) / (x2 - x1), or 20.

Next, we can determine the equation of the line using the point-slope form of the equation of a line:

P - P1 Equals m(x - x1) (x - x1)

P - 105 = 20(x - 1) (x - 1)

P = 20x + 85

To determine Emma's total pay, we can finally enter x = 7 into the equation:

P = 20(7) + 85\s= 225

Emma would therefore receive $225 for a day in which she sold 7 laptops.

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Answer:

Step-by-step explanation:

Assuming that the number of ingredients per pie is constant, we can write an expression for the total number of ingredients and pies baked in the two years as:

Total number of ingredients = (129 x ingredients per pie) + (b x ingredients per pie)

Total number of pies baked = 129 + b

So, if we let "i" represent the number of ingredients per pie, we can write the expression as:

Total number of ingredients = (129 x i) + (b x i)

Total number of pies baked = 129 + b

Note that without knowing the value of "i," we cannot simplify this expression any further.