A carpenter needs to cut 24-inch pieces of wood from a board that is 17 feet in length. What is the greatest number of 24-inch pieces the carpenter can cut from 6 of these boards of wood?

Therefore, the solution to the system of equations is: x = 1/5 and y = 8.

An equation is a mathematical statement that asserts the equality of two expressions. Equations contain variables, which are symbols that represent unknown or varying quantities, and constants, which are known values. The variables and constants are connected by mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation, and the resulting expression on both sides of the equation must have the same value. Equations are used to solve problems, find unknowns, and express relationships between quantities. Some common types of equations include linear equations, quadratic equations, polynomial equations, exponential equations, and trigonometric equations.

Here,

We have the following system of equations:

y = 10x + 6

2y + 5x = 17

Using substitution method, we can substitute the expression for y in the second equation with the expression for y in the first equation:

2(10x + 6) + 5x = 17

Simplifying:

20x + 12 + 5x = 17

25x = 5

x = 5/25 = 1/5

Now we can substitute this value of x into either of the two original equations to find the corresponding value of y. Using the first equation:

y = 10(1/5) + 6

y = 2 + 6

y = 8

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To triple the area of a square, the new side lengths must be the length of the old sides multiplied by the square root of three (√3).

A square is a two-dimensional (2D) geometric shape that has four equal sides, and its angles are right angles, i.e., they measure 90°. The perimeter of a square is the sum of the length of all its sides, and its area is the product of its length and width. The diagonals of a square are equal in length and intersect at right angles.

To triple the area of a square, you need to increase the length of the square's sides by a certain factor. That factor is the square root of three, which is approximately 1.732. This implies that if the old side length of the square is "x," then the new side length of the square will be 1.732x.

This ratio of new side length to old side length of the square will triple the square's area (since (1.732x)² = 3x²). Therefore, to triple the area of a square, the new side lengths must be the length of the old sides multiplied by the square root of three (√3).

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[tex]\bold{Solution:}[/tex]

[tex]\text{Total number of Bags} = 4[/tex]

[tex]\text{Total mass in 4 bags } = 6 \ \text{kg}[/tex]

[tex]\text{Total mass in 1 bag}}=\dfrac{6}{4} \ \text{kg}[/tex]

[tex]\bold{We \ know \ that}[/tex]

[tex]\text{1 kg = 1000 gram}[/tex]

[tex]\text{1 gm}= \dfrac{1}{1000} \ \text{kg}[/tex]

[tex]\text{we have to convert} \ \dfrac{6}{4} \ \text{kg to grams}[/tex]

​

[tex]\dfrac{6}{4} \ \text{kg} = \dfrac{6}{4} \times 1000 \ \text{gm}[/tex]

[tex]=1750 \ \text{gm}[/tex]

[tex]\bold{So, \ the \ total \ mass \ of \ the \ box \ in \ grams \ is \ 1,500 \ gm}[/tex]

The soda can has an estimated volume of 1,026.72 cubic centimeters and an estimated surface area of 452.39 square centimeters.

To find the volume and surface area of a soda can with radius 6 cm and height 11 cm, we can use the formulas:

Volume of cylinder = πr²h

Surface area of cylinder = 2πrh + 2πr²

Substituting the given values, we get:

Volume = π × 6² × 11

Volume = 1,026.72 cubic centimeters (rounded to two decimal places)

Surface area = 2π × 6 × 11 + 2π × 6²

Surface area = 452.39 square centimeters (rounded to two decimal places)

Therefore, the volume of the soda can is approximately 1,026.72 cubic centimeters, and the surface area is approximately 452.39 square centimeters.

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A school stadium contains 2,000 seats. for a certain game, student tickets cost $3 each and nonstudent tickets cost $6 each. it is proved that at least 1,200 non-student tickets must be sold so that the total ticket sales will be at least $8,400.

Let x be the number of student tickets sold, and y be the number of non-student tickets sold. Then the total ticket sales can be given as follows:Total ticket sales = 3x + 6y As per the given statement, the total ticket sales must be at least $8,400, that is,3x + 6y ≥ 8,400Dividing the above equation by 3, we get, [tex]x + 2y \geq  2,800[/tex]The school stadium contains 2,000 seats, hence the total number of tickets that can be sold is[tex]x + y = 2,000[/tex].Rearranging the above equation, we get, [tex]x = 2,000 - y[/tex]

Substituting this value in the equation [tex]x + 2y \geq  2,800[/tex], we get[tex](2,000 - y) + 2y \geq  2,800[/tex] ⇒ [tex]2,000 + y \geq  2,800[/tex] ⇒[tex]y \geq 800[/tex] Thus, the minimum number of non-student tickets that must be sold so that the total ticket sales will be at least $8,400 is 800. But it has to be more than 800 since only selling 800 non-student tickets is not enough to get at least $8,400. Let's assume that 1,200 non-student tickets are sold.

Now, if 1,200 non-student tickets are sold, then the number of student tickets sold is, [tex]x = 2,000 - y = 2,000 - 1,200 = 800[/tex] Therefore, the total ticket sales can be calculated as follows:Total ticket sales = [tex]3x + 6y= 3(800) + 6(1,200) = 2,400 + 7,200 = 9,600[/tex] Since $9,600 is greater than $8,400, it is proved that at least 1,200 non-student tickets must be sold so that the total ticket sales will be at least $8,400.

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Pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

We can write quadradic equation as [tex]y=1+x^2[/tex]

Where y is number οf dοts and x is step number.

Then if x=0 and y=1

If x = 1 and y = 2

If x = 2 and y = 5

If x = 3 and y = 10

Hence Patten B fοllοws the quadratic realatiοnship.

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The hourly cost of electricity in your home is $0.20

So, if we divide your $145.68 electric bill by the number of kilowatt-hours used in that month, we can determine the cost per kilowatt-hour.

If you used 500 kWh in the month of August, your cost per kWh would be $0.29136 ($145.68 / 500 kWh).

If you used 500 kWh in August, your average power usage would be approximately 0.69 kW (500 kWh / 720 hours).

To calculate the hourly cost of electricity, simply multiply the average power usage in kW by the cost per kWh.

Then, the hourly cost of electricity would be approximately $0.20 ($0.29136 * 0.69 kW).

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The trapezoid has a surface area of 480 square units.

So, a trapezoid measured in feet offers an area in square feet; one measured in millimetres gives an area in square centimetres; and so on. If it's simpler for you, you can add the lengths of the bases and then divide the total by two. Keep in mind that multiplication by 12 is equivalent to dividing by 2.

We must apply the formula for a trapezoid's area to this issue in order to find a solution:

[tex]A = (1/2) * (a + b) * h[/tex]

where h is the trapezoid's height (or altitude) and a and b are the lengths of its parallel sides.

The values for a, b, and h are provided to us, allowing us to change them in the formula:

A = (1/2) * (20 + 60) * 12

A = (1/2) * 80 * 12

A = 480 square units

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The equation you would use to properly calculate the dollar cost of entering the park and enjoying rides is Total Cost = Entrance Fee + (Number of Rides x Ride Fee).

In this case, Total Cost is the cost of entering the park and enjoying rides, Entrance Fee is the fee for entering the park, Number of Rides is the number of rides you will be taking, and Ride Fee is the fee charged for each ride.

Thus, plugging in the given values, the equation becomes  Total Cost = Entrance Fee + (Number of Rides x Ride Fee).

Therefore, if the Entrance Fee is $ and each ride costs an additional $ , the Total Cost of entering the park and enjoying rides is $ .

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Answer:

C is your answer

Step-by-step explanation:

in my opinion, i think it would be the mode.

a. To approximate the change in alcohol level from 3 to 3.2 hours and the correct expression is OC: A'(3).

For this we need to calculate the difference between the values of A(t) at t = 3.2 and t = 3. The expression that correctly approximates this change is given by: A'(3) * 0.2, where A'(t) is the derivative of A(t) with respect to t. Therefore, the correct expression is OC: A'(3).

b. Similarly, to approximate the change in alcohol level from 4 to 4.2 hours, we need to calculate the difference between the values of A(t) at t = 4.2 and t = 4. The expression that correctly approximates this change is again given by: A'(4) * 0.2. Therefore, the correct expression is also OC: A'(4).

To calculate the approximate changes in alcohol level, we need to find the derivative of A(t) with respect to t:

A'(t) = 0.03746 + 0.20242t

a. The approximate change in alcohol level from 3 to 3.2 hours is:

A'(3) * 0.2 = (0.03746 + 0.20242(3)) * 0.2 ≈ 0.118

Therefore, the approximate change in alcohol level from 3 to 3.2 hours is 0.118.

b. The approximate change in alcohol level from 4 to 4.2 hours is:

A'(4) * 0.2 = (0.03746 + 0.20242(4)) * 0.2 ≈ 0.149

Therefore, the approximate change in alcohol level from 4 to 4.2 hours is 0.149.

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The length and width of the rectangle are 12.5 cm and 22 cm, respectively.

Let L be the length of the rectangle, and W be the width of the rectangle, then we have that:

L x W = 297 sq cm 1.

If the length is increased by 3 cm and width decreased by 1 cm, then we have that:

(L + 3) x (W - 1) = 297 + 3 sq cm -......(2).

Expand equation 2, we have:

LW + 2L - W = 300 sq cm-.......(3)

We have two equations from 1 and 3:

LW = 297 sq cm         LW + 2L - W = 300 sq cm 3.

Substitute equation 1 into equation 3.

297 + 2L - W = 300 sq cm

2L - W = 3 sq cm  

2L - W = 3 sq cm

2L = W + 3 sq cm

L = (W + 3)/2 sq cm

W x (W + 3)/2 = 297 sq cm

W² + 3W - 594 = 0 (W + 27) (W - 22) = 0

Therefore, the width of the rectangle is either 22 cm or -27 cm. Since the width cannot be negative, we discard the value of -27 cm. Therefore, the width of the rectangle is 22 cm. Finally, let's calculate the length of the rectangle:

L = (W + 3)/2 sq cm L = (22 + 3)/2 sq cm L = 25/2 sq cm L = 12.5 sq cm

Therefore, the length and width of the rectangle are 12.5 cm and 22 cm, respectively.

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Answer:

cot(-x) cos(-x) + sin(-x)= f(x) = (1 point) Simplify and write the trigonometric expression in terms of sine and cosine: 1 tan u +cot u = f(u) f(u) (1 point) Simplify and write the trigonometric expression in terms of sine and cosine: |(1-cos y)(1 +cos y) (f(y) f(y)= (1 point) tings sin f If sin 1+cos t tan r then A+tan t A = 1 then (1 point) If sec t - tan t = f()+tan f)= (2 points) If tan2 t - sin2 t = sind r then cos t the positive power a = the positive power b = sec r-1 A-COS 1 (1 point) If then A+cos sec 1+1 gs A = A+sin x = B-sin x then (2 points) If (tanx + sec x)2 A = В Vx- 1 (1 point) If 0 u< r/2 and x = f(u), where sec u, then f(u) = (1 point) Simplify the expression as much as possible. cos (t)-1 help (formulas) sin(t) IS (1 point) Simplify and write the trigonometric expression in terms of sine and cosine: 2+tan2 x sec x -1 (f (x) f(x)= (1 point) Simplify completely into an expression with sin(A) or cos(A) only: sin(A) tan(A) + cos(A) = (1 point) Simplify the expression as much as possible. 1 1 + 1 + sin(t) help (formulas) 1-sin(t)

sin x + cot x cos x =

f(x)

f(x)=

(1 point) Simplify and write the trigonometric expression in terms of sine and cosine:

2 + tan2 x

- 1 (f(x)

sec x

f(x) =

Answer:

Step-by-step explanation:

The area of given circle is 28.27 sq.m. The circumference of given circle is 18.85 m (rounded to the nearest hundredth).

The circumference of a circle is the distance around the edge or boundary of the circle. It is also the perimeter of the circle. The circumference is calculated using the formula:

C = 2πr

where "C" is the circumference, "π" is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle.

The circumference of a circle is proportional to its diameter, which is the distance across the circle passing through its center. Specifically, the circumference is equal to the diameter multiplied by π, or:

C = πd

where "d" is the diameter of the circle.

Given that the diameter of the circle is 6m.

We know that the radius (r) of the circle is half of the diameter (d), so:

r = d/2 = 6/2 = 3m

The area (A) of the circle is given by the formula:

A = πr²

Substituting the value of r, we get:

A = π(3)² = 9π ≈ 28.27 sq.m (rounded to the nearest hundredth)

The circumference (C) of the circle is given by the formula:

C = 2πr

Substituting the value of r, we get:

C = 2π(3) = 6π ≈ 18.85 m (rounded to the nearest hundredth)

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The complete question is:

The predicted fuel efficiency for a speed of 30 miles per hour is given as follows:

26.50 mpg.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is defined as follows:

In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).

The speed is of 30 miles per hour, hence the predicted fuel efficiency is given as follows:

In(Fuel Efficiency) = 1.437 + 0.541 x In(30).

In(Fuel Efficiency) = 3.277.

The exponential is the inverse of the ln, hence:

Fuel Efficiency = e^3.277

Fuel Efficiency = 26.50 mpg.

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The answer is: C. 1.5%

If sin(2x) = cos(x), where 0° ≤ x < 180°, then,  The possible angle values of x are 90°, 30° and 150°.

The sine and the cosine are trigonometric functions of the angles. The sine and cosine of an acute angle are defined in the context of a right triangle: for a given angle, its sine is the ratio of the length of the side opposite the angle to the length of the longest side of the angle. triangle (the hypotenuse ), and the cosine is the adjacent side The ratio of the length to the hypotenuse.

According to the Question:

Given that,

sin(2x) = cos(x) where 0° ≤ x < 180°

We know that:

sin(2x) = 2 sin(x) cos(x)

⇒ 2 sin(x) cos(x) = cos(x)

Subtract cos(x) on both sides

2 sin(x) cos(x) - cos(x) = 0

cos(x) (2sinx-1)=0

It means, cos(x) = 0 and (2sin x -1 ) = 0

cos x = cos0           and        sinx(x) = 1/2

x = 90°                     and        x = 30°, 150°

Hence, the possible values of x are 90°, 30° and 150°.

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Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.

A rectangle is a geometric shape with four edges and four angles that exists in two dimensions. Because it is a sort of quadrilateral, it has four sides that are parallel to one another. Rectangles are a form of parallelogram because they have opposite sides that are the same length and opposite angles that are the same size. A rectangle's two adjacent sides make right angles, so all four of the angles, which each measure 90 degrees, are right angles.

given

The tray has a breadth of 17 inches and a length of 12.5, according to the measurements given. The package is 13 inches by 11 inches by 11 inches in size.

The platter can fit inside the box because its length is less than the box's length, which is 13 inches. But we also need to think about the box's breadth and height.

The tray cannot fit inside the box in that dimension because its width, which is 17 inches, is larger than the box's, which is 11 inches. The tray cannot fit inside the box because the height of the box is also 11 inches, which is shorter than the length of the tray neither in that realm.

Therefore, the correct response is OB: No, the box is a rectangle, and the tray's 12.5-inch length is greater than the box's 11-inch breadth.

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Answer:

h = 15 cm

Step-by-step explanation:

Area of triangle equals the area of rectangle. As the dimensions of the rectangle is given, we can first find the area of the rectangle.

      [tex]\boxed{\bf Area \ of \ the \ rectangle = length * width}[/tex]

                                               = 10 * 9

                                               = 90 cm²

Area of triangle = area of rectangle

                          = 90 cm²

base of the triangle = b = 12 cm

 [tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}bh}[/tex]  where h is the altitude and b is the base.

         [tex]\bf \dfrac{1}{2} b* h = 90 \\\\\dfrac{1}{2}*12* h = 90[/tex]

                      [tex]\bf h = \dfrac{90*2}{12}\\\\\boxed{\bf h = 15 \ cm}[/tex]

The correct option is A. The amount of variation in the data that is explained by the regression model is shown by the Coefficient of determination.

Regression is a statistical technique used to estimate the relationship between a dependent variable and one or more independent variables. The dependent variable is the variable we are interested in understanding or predicting, while independent variables are the predictors. The goal of regression analysis is to create a mathematical equation that describes the relationship between these variables.

Regression models can be used for prediction or understanding the relationship between variables. The simplest form of regression is linear regression, which assumes a linear relationship between the dependent and independent variables. However, there are many types of regression models that can accommodate more complex relationships, including polynomial regression, logistic regression, and ridge regression.

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The number of hamsters owned according to the circle graph is 28.

A pie chart is a visual representation of data that looks like a pie with the slices representing the size of the data. To show data as a pie chart, a list of numerical variables and category variables are required. Each slice in a pie chart has an arc that is proportionate to the quantity it depicts, and as a result, the area and center angle it generates are also proportional.

Let us suppose the total number of animals = x.

Given that, a total of 35 rabbits are owned.

Thus,

5% of x = 35

5/100 (x) = 35

x = 35(100)/5

x = 700

Now, there are 4% hamsters, thus:

4% of 700 = number of hamsters.

H = 4/100 (700)

H = 28

Hence, the number of hamsters owned according to the circle graph is 28.

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Answer:

B. The sum of two negative integers

Cage different of a positive integer that is greater than it

Step-by-step explanation:

I don't get it, if it means this -(-7) then is not negative

if it this -9-7 then it's correct

hope it helps

Mabel will have to read for a total of 28 hours to have read a total of 476 pages.

To solve this problem using unit rates, we can start by finding the rate at which Mabel reads in pages per hour. This can be calculated by dividing the total number of pages she read by the total number of hours she spent reading:

Rate = Total pages / Total hours

Rate = 340 / 20

Rate = 17 pages per hour

This means that Mabel reads at a rate of 17 pages per hour. To find out how many hours of reading she will have to do to reach a total of 476 pages, we can use the unit rate to set up a proportion:

17 pages / 1 hour = 476 pages / x hours

Simplifying the proportion by cross-multiplying:

17x = 476

Dividing both sides by 17:

x = 28

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Answer:

The number x that is midway between x and 27, and has a midpoint of -3, is -33

midpoint = (x + 27) / 2

We also know that the midpoint is equal to -3, so we can set these two expressions equal to each other and solve for x:

-3 = (x + 27) / 2

Multiplying both sides by 2 gives:

-6 = x + 27

Subtracting 27 from both sides gives:

x = -33

The distance between L1 and L2 is $\frac{1}{\sqrt{3}}$ units.

Given two lines, L1 and L2, as follows:L1: x = 1 + t, y = t, z = 2 + tL2: x - 3 = y - 1 = z - 3a. Verification of parallel lines L1 and L2L1 can be written as the vector equation, (x, y, z) = (1, 0, 2) + t(1, 1, 1)Similarly, L2 can be written as the vector equation, (x, y, z) = (3, 1, 3) + t(1, 1, 1)We can see that both the vector equation of L1 and L2 has the same direction ratios (1, 1, 1).Therefore, both lines are parallel.b. Calculation of the distance between L1 and L2To find the distance between L1 and L2, we can find a point on L1 and its perpendicular distance from L2. As L2 passes through the point (3, 1, 3), we can take this point as a point on L1 as well. The perpendicular distance of (3, 1, 3) from L1 can be calculated as follows:We can write the general equation of a plane, P, containing the line L1 as follows: x - y + z - 3 = 0The normal vector of P is (1, -1, 1). Therefore, the perpendicular distance between P and the point (3, 1, 3) is given byd = $\frac{|(1, -1, 1)\cdot (3, 1, 3) - 3|}{\sqrt{1^2 + (-1)^2 + 1^2}}$d = $\frac{|-1|}{\sqrt{3}}$d = $\frac{1}{\sqrt{3}}$Therefore, the distance between L1 and L2 is $\frac{1}{\sqrt{3}}$ units.

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The null hypothesis and alternative hypothesis in the notation for the individual t-test for testing the slope coefficient associated with a simple linear regression are given below:

Null hypothesis: H₀: β₁ = 0

Alternative hypothesis: Hₐ : β₁ ≠ 0

The hypothesis test is used to determine whether or not there is sufficient evidence to support the alternative hypothesis that the slope of the regression line is not equal to zero. The null hypothesis is that the slope of the regression line is equal to zero.

Therefore, we will use the individual t-test for the slope coefficient to test the hypothesis regarding the slope of the regression line. The formula for the t-test for the slope coefficient is given below:

t = (b₁– β₁) / SEb₁

Where b₁ is the sample slope coefficient β₁ is the hypothesized value of the slope coefficient (i.e., 0) SEb₁ is the standard error of the slope coefficient.

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The value of the given expression 1 5/6 + 1/2 = 14/6.

A fraction with a numerator higher than or equal to the denominator is said to be inappropriate. A mixed number is transformed into an improper fraction by multiplying the whole number by the fraction's denominator, which is followed by the addition of the numerator. The denominator of the improper fraction changes to reflect the outcome, while the numerator remains the same.

The given expression is 1 5/6 + 1/2.

Convert the mixed fraction into improper fraction:

1 5/6 = (1 x 6 + 5)/6 = 11/6

Thus,

11/6 + 1/2

Take the LCM:

11/6 + 3/6 = 14/6

Hence, the value of the given expression 1 5/6 + 1/2 = 14/6.

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