Gary's backpack weighs 1.2 pounds. His math textbook weighs 3.75 pounds, and his science textbook weighs 2.85 pounds. How much will his backpack weigh with the math and science textbooks in it?

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 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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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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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:

[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]

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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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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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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The amount of owing that Hollie in 13 years will be £3739.68.

We know that the compound interest is given as

A = P(1 + r)ⁿ

A = £800[tex](1 + 0.26)^{13}[/tex]

Simplify the equation, then we have

A = £800 x [tex](1 + 0.26)^{13}[/tex]

A = £800 x [tex]1.26^{13}[/tex]

A = 800 × 4.6746

A = 3739.68

Compound interest refers to the interest earned not only on the principal amount of a loan or investment but also on any accumulated interest that has been added to it over time. In other words, the interest is calculated on both the initial amount of money borrowed or invested, as well as on the interest that has accrued on that amount.

This means that as time goes on, the interest earned on an investment or loan can grow exponentially, as the interest earned in previous periods is included in the calculation for future periods. This compounding effect can result in significant growth over long periods of time. compound interest is an essential concept in finance and can have a significant impact on the growth of investments over time.

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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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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

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:

ames have 18 litres of water. He poured unequally into 3 tank

I. Poured three quarter of water from tank one into tank 2

II. Poured half of the water that is now in tank 2 into tank 3

III. Poured one third of water that is now in tank 3 into tank 1

Find how much water is in each tanks

Step-by-step explanation:

Let's start with the amount of water in tank 1 as x liters.

I. Poured three quarter of water from tank one into tank 2, so tank 1 now has 1/4 of x liters and tank 2 has 3/4 of x liters.

II. Poured half of the water that is now in tank 2 into tank 3, so tank 2 now has 3/8 of x liters and tank 3 has 3/8 of x liters.

III. Poured one third of water that is now in tank 3 into tank 1, so tank 3 now has 1/3 * 3/8 * x = 1/8 * x liters and tank 1 has 1/4 * x + 1/8 * x = 3/8 * x liters.

We know that James poured 18 liters of water into the three tanks, so the sum of the water in the three tanks must be 18 liters.

3/8 * x + 3/8 * x + 1/8 * x = 18

Simplifying the equation, we get:

7/8 * x = 18

x = 18 * 8 / 7 = 20.57 (rounded to two decimal places)

Therefore, the amount of water in each tank is:

Tank 1: 3/8 * x = 7.71 liters

Tank 2: 3/8 * x = 7.71 liters

Tank 3: 1/8 * x = 2.57 liters

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 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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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 viewing angle a of a person sitting a distance x from the front wall of a classroom with a blackboard that is 12 ft long and starts 3 ft from the wall they are sitting next to can be calculated as: a = cot-1(x/15) - cot-1(x/3)

To understand this calculation, let's consider a diagram of the classroom.

We can see from the diagram that the blackboard has length 12 ft, starting 3 ft from the wall the student is sitting next to. The student is sitting a distance x from the front wall.

The viewing angle a is the angle between the wall the student is sitting next to and the line from the student to the front wall. This angle can be calculated using the tangent of the opposite side (front wall) and adjacent side (wall the student is sitting next to).

We can therefore write: a = tan-1(12/3) - tan-1(x/3)

Simplifying this equation, we can rewrite it as: a = cot-1(x/15) - cot-1(x/3).

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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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The graph of f(x) = one half to the power of x  is:

graph begins in the second quadrant and decreases quickly while crossing the ordered pair (0, 1). The graph then begins to decrease slowly as it approaches the x axis.

The graph of f(x) = one half to the power of x is an exponential function with a base of one half.

This is written in equation form as

f(x) = (1/2)^x

As x increases, the value of the function decreases exponentially, but the rate of decrease slows down as x approaches positive infinity.

When x is zero, the value of the function is 1, and as x increases, the value of the function decreases slowly.

The graph is attached

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The answer is: C. 1.5%

Answer:

235.65

Step-by-step explanation:

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:

C is your answer

Step-by-step explanation:

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

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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Vertex: The vertex of the function is at the point (-2, 3).

The domain of a function is the set of all possible input values (often represented as x) for which the function is defined. In other words, it is the set of all values that can be plugged into a function to get a valid output. The domain can be limited by various factors such as the type of function, restrictions on the input values, or limitations of the real-world scenario being modeled.

The range of a function refers to the set of all possible output values (also known as the dependent variable) that the function can produce for each input value (also known as the independent variable) in its domain. In other words, the range is the set of all values that the function can "reach" or "map to" in its output.

In the given question,

Domain: The domain of the function is all real numbers greater than or equal to -2, since the square root of a negative number is not defined in the real number system.

Range: The range of the function is all real numbers less than or equal to 3, since the maximum value of the function occurs at x=-2, where f(x)=3.

Vertex: The vertex of the function is at the point (-2, 3).

Four additional points:When x=-1, f(x)=-(√(-1)+2)+3 = -1, so (-1,-1) is a point on the graph.

When x=0, f(x)=-(√0+2)+3 = 1, so (0,1) is a point on the graph.

When x=1, f(x)=-(√1+2)+3 = 2, so (1,2) is a point on the graph.

When x=4, f(x)=-(√4+2)+3 = -1, so (4,-1) is a point on the graph

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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 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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