Juan spent 10 minutes on his history homework and 3 minutes per question on his math homework. Which graph shows the total homework time, t, related to the number of math questions, q?

Discrete graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 5 to 40, on the vertical axis. Solid circles appear at points (0, 10), (1, 13), (2, 15), (3, 19), (4, 22), (5, 25), (6, 29), (7, 32), (8, 34).

Continuous graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 5 to 40, on the vertical axis. Solid circles appear at points (0, 10), (1, 13), (2, 15), (3, 19), (4, 22), (5, 25), (6, 29), (7, 32), (8, 34).

Discrete graph on a coordinate plane shows number of math questions, numbered 1 to 8 along the horizontal axis, and total homework time, numbered 3 to 24, on the vertical axis. Solid circles appear at points (0, 0), (1, 3), (2, 6), (3, 9), (4, 12), (5, 15), (6, 18), (7, 21), (8, 24).

As per the combination concept, there are 735,471 ways to choose 16 shows from a set of 24.

To find the number of ways to choose 16 shows from a set of 24, we can use the formula for combinations, which is:

ⁿCₓ = n! / x!(n-x)!

Where n is the total number of objects in the set (in this case, 24), and x is the number of objects we want to choose (in this case, 16). The exclamation mark (!) denotes the factorial function, which means multiplying the number by all positive integers less than itself.

Plugging in the numbers, we get:

²⁴C₁₆ = 24! / 16!(24-16)! = 735471

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Answer:

Step-by-step explanation:

[tex]\frac{1}{5}[/tex] ∠ 7x

[tex]\frac{1/5}{7}[/tex] ∠ x

1/35 ∠x

x ≥ [tex]\frac{1}{35}[/tex]

The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.

A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]

The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.

The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.

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The earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.

Given, Power rating of charger = 12 W. Charge per kilowatt hour = 6 cents = 0.06/kWh.To calculate the earnings in 1 day, we need to calculate the power consumed by the charger in 1 day first.

P = Power rating of charger = 12 Wt = Time = 1 day = 24 hours. Energy consumed = Power x Time. E = P x t= 12 W x 24 hours= 288 Wh = 0.288 kWh. Therefore, energy consumed by the charger in 1 day = 0.288 kWh.

Now, we can calculate the earnings in 1 day as follows: Charge per unit = 0.06/kWh. Earnings = Energy consumed x Charge per unit. Earnings = 0.288 kWh x 0.06/kWh= 0.01728.

Therefore, the earnings made in 1 day when charging a device with a power rating of 12 W at a rate of 6 cents per kilowatt hour is 0.01728.

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Answer:

The answer should be 20,365.714 but I am not sure

Step-by-step explanation:

After solving the equation N x 4 = 28 for N, then the solution to the equation is N = 7.

An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables and may involve arithmetic operations such as addition, subtraction, multiplication, or division. Equations can be solved to determine the values of the variables that make the equation true. For example, the equation 2x + 5 = 11 is true when x = 3, since 2(3) + 5 = 11.

To solve the equation N x 4 = 28 for N, we need to isolate N on one side of the equation.

First, we can divide both sides of the equation by 4:

N x 4 ÷ 4 = 28 ÷ 4

Simplifying:

N = 7

Therefore, the solution to the equation is N = 7.

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The largest area a farmer can fence in is 612.5 m².

The given question is based on finding the largest area a farmer can fence in for building a rectangular enclosure.

The farmer is given with 70 meters of fencing for fencing 3 sides of a rectangular enclosure.

The enclosure's fourth side is the wall of the farmer's barn.

To find the largest area fenced in, the farmer must try to use all 70 meters of fencing to enclose as large an area as possible.

First, let's assume that the rectangular enclosure's width is x.

So, we can find the length by dividing the remaining length of fencing after subtracting the width of the fence from the total length of fencing.

The remaining length of fencing is 70 - 2x.

After calculating the length, the area of the rectangular enclosure can be calculated by multiplying length and width.

The formula for calculating the area of the rectangle is A = l x w.

A = (70 - 2x)x

  = 70x - 2x²

To find the maximum area fenced in, differentiate A with respect to x and equate it to zero.

dA/dx = 70 - 4x

          =0x = 17.5 meters.

After finding x, the length of the enclosure can be calculated by subtracting the width from the total length of fencing.

l = 70 - 2x = 70 - 2(17.5) = 35 meters.

Therefore, the largest area fenced in will be A = l x

w = 35 x 17.5 = 612.5 m².

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To solve this problem, we need to convert the hexadecimal numbers (20cba)16 and (a02)16 to decimal form, add them together, and then convert the result back to hexadecimal form.

(20cba)16 = 2x16^4 + 12x16^3 + 11x16^2 + 10x16^1 = 131402

(a02)16 = 10x16^2 + 0x16^1 + 2x16^0 = 256

Adding the two decimal numbers together gives us:

131402 + 256 = 131658

To convert this decimal number back to hexadecimal form, we can use the repeated division method.

131658 / 16 = 8228 remainder 10 (A)

8228 / 16 = 514 remainders 4 (4)

514 / 16 = 32 remainder 2 (2)

32 / 16 = 2 remainder 0

2 / 16 = 0 remainder 2

Therefore, (20cba)16 + (a02)16 = (131658)10 = (2002A)16.

To find their product, we can multiply the two decimal numbers together and then convert the result to hexadecimal form.

131402 x 256 = 33559552

Converting this decimal number to hexadecimal form gives us:

33559552 / 16 = 2097472 remainder 0

2097472 / 16 = 131092 remainder 0

131092 / 16 = 8193 remainder 4 (4)

8193 / 16 = 512 remainders 1 (1)

512 / 16 = 32 remainder 0

32 / 16 = 2 remainder 0

2 / 16 = 0 remainder 2

Therefore, the product of (20cba)16 and (a02)16 is (33559552)10 = (2011004)16.

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Answer:

N = N0 x 2^n

Step-by-step explanation:

The formula for calculating the number of bacteria cells after n generations is N = N0 x 2^n, where N is the total number of cells after n generations, N0 is the initial number of cells, and 2^n represents the number of times the population doubles after n generations. Assuming an initial population of 100 cells, there will be approximately 102,400 cells after 10 generations.

Answer:

The explicit formula for the number of bacteria cells after each generation can be written as:

N = N0 * r^n

Where:

N is the number of bacteria cells after n generations

N0 is the initial number of bacteria cells (at n=0)

r is the growth rate (how many new cells are produced per existing cell)

Assuming that each bacteria cell doubles in number with each generation (i.e. r=2), the formula can be simplified to:

N = N0 * 2^n

To find the number of cells after 10 generations, we can substitute n=10 into the formula:

N = N0 * 2^10

Since we don't have a specific value for N0, we can't find the exact number of cells after 10 generations. However, we can make some assumptions. For example, if we assume that there are initially 100 bacteria cells (N0=100), we can calculate:

N = 100 * 2^10 = 102,400

So, if each bacteria cell doubles in number with each generation and there were initially 100 cells, there will be 102,400 cells after 10 generations.

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The inverse function for the given function F(x)=1/x² -3x +1  is given by

f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.

Function f(x) is equals to,

F(x)=1/x² -3x +1

Inverse of a function, we need to swap the positions of the x and y variables and then solve for y.

Let's start with the original function

f(x) = 1/x^2 - 3x + 1

Now we will swap x and y,

⇒ x = 1/y^2 - 3y + 1

Next, Solve for y in terms of x

⇒ x = 1/y^2 - 3y + 1

⇒ x - 1 = 1/y^2 - 3y

⇒ 1/(x - 1) = y^2 - 3y

⇒ 1/(x - 1) = y(y - 3)

⇒ y(y - 3) = 1/(x - 1)

⇒ y^2 - 3y - 1/(x - 1) = 0

Using the quadratic formula, solve for y to get inverse function we have,

y = (3 ± √(9 + 4/(x - 1))) / 2

Therefore, the inverse function of f(x) is equal to f⁻¹(x) =(3 ± √(9 + 4/(x - 1))) /2.

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The above question is incomplete, the complete question is:

F(x)=1/x squared -3x +1 then Find the inverse

Bytaking the quotient between the probabilities we can see that Getting a 17 is three times more likely to get a 18.

If you toss 3 dices with 6 sides each, then the total number of combinations is:

6*6*6 = 216

Now, the outcomes that add up to 18 are:

dice 1, dice 2, dice 3, sum:

6            6         6       , 18

The outcomes that add up to 17 are:

dice 1, dice 2, dice 3, sum:

5           6         6       , 17

6            5         6       , 17

6            6         5       , 17

So the probabilities are:

P(18) = 1/216

P(17) = 3/16

The quotient gives:

P(17)/P(18) = 3

Getting a 17 is 3 times more likely to get a 18.

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Alexis has 12 quarters and 8 dimes.

Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.

We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:

10d + 25q = 380

To make things easier, let's divide both sides of the equation by 5:

2d + 5q = 76

Now we can use the first equation to solve for d in terms of q:

d + q = 20

d = 20 - q

Substituting this into the second equation gives:

2(20 - q) + 5q = 76

Expanding the parentheses and simplifying, we get:

40 - 2q + 5q = 76

3q = 36

q = 12

Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:

d + q = 20

d + 12 = 20

d = 8

The total value of 12 quarters and 8 dimes is:

12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80


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Answer:

$10.98

Step-by-step explanation:

$10.98

0.06 x 183 = $10.98

The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.

If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.

The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)

It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.

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Answer:

In a right triangle, one angle is always 90 degrees (a right angle). The other two angles are acute angles, which means they are less than 90 degrees.

Let's call the acute angle we're interested in "a". We know that sin a = 3/5.

"Sin" is short for "sine", which is a ratio of two sides of the triangle. Specifically, it's the ratio of the length of the side opposite angle a to the length of the hypotenuse (the longest side of the triangle, which is always opposite the right angle).

So, in our triangle, if sin a = 3/5, that means the side opposite angle a is 3 units long and the hypotenuse is 5 units long.

Now, we can use the Pythagorean theorem to find the length of the third side of the triangle (the one adjacent to angle a). The Pythagorean theorem says that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. In other words:

a^2 + b^2 = c^2

where a and b are the lengths of the two shorter sides, and c is the length of the hypotenuse.

In our triangle, we know that b is the side adjacent to angle a, so we're trying to find its length. We also know that a = 3 and c = 5, so we can plug those values into the Pythagorean theorem and solve for b:

3^2 + b^2 = 5^2

9 + b^2 = 25

b^2 = 16

b = 4

So the length of the side adjacent to angle a is 4.

Now, we can use the ratios of the trigonometric functions (sine, cosine, and tangent) to find the values of cosine and tangent for angle a.

Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. So in our triangle:

cos a = adjacent/hypotenuse = 4/5

Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side. So in our triangle:

tan a = opposite/adjacent = 3/4

Therefore, if sin a = 3/5 in a right triangle, where a is an acute angle, then cos a = 4/5 and tan a = 3/4.

Answer:

area = 127[tex]units^{2}[/tex]

perimeter = 46 units

Step-by-step explanation:

count them

The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines.

An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.

For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.

Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.

To determine the double inequalities that define the shaded region, we need to find the equations of the two boundary lines that form the sides of the shaded region.

The two vertical lines are x=-4 and x=3. The two horizontal lines are y=1 and y=6.

The shaded region is enclosed by these four lines, so the double inequalities that define it are:

-4 ≤ x ≤ 3 and 1 ≤ y ≤ 6

The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines. Together, they define the rectangular shaded region with vertices (-4,1), (-4,6), (3,6), and (3,1).

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Answer:

Step-by-step explanation:

First, we need to make sure that we are comparing the units in the same system, either yards or feet. Let's convert 32 feet to yards:

32 feet * 1 yard/3 feet = 10.67 yards

Now we have:

Lighthouse height / Lighthouse shadow = Billboard height / Billboard shadow

Let x be the height of the lighthouse in yards.

x / 72 yards = 10.67 yards / 19 feet

We can simplify the equation by converting everything to yards:

x / 72 = 10.67 / 3.28

x / 72 = 3.25

To solve for x, we can cross-multiply:

x = 72 * 3.25

x = 234

Therefore, the height of the lighthouse is 234 yards.

Answer: A) 121.3 yd.

P(a number greater than 5 and an even number) = 1/6 or 0.167

Part 1 of 3 (a) To find the probability of getting an even number, divide the number of favorable outcomes (rolling a 2, 4, or 6) by the total possible outcomes (rolling any number between 1 and 6). There are 3 even numbers and 6 total possible outcomes.

P(an even number) = [tex]3/6 = 1/2 or 0.500[/tex]

Part 2 of 3 (b) To find the probability of getting a number less than or equal to 4, count the favorable outcomes (rolling a 1, 2, 3, or 4) and divide by the total possible outcomes (6). There are 4 favorable outcomes and 6 total possible outcomes.

P(a number less than or equal to 4) =[tex] 4/6 = 2/3 or 0.667[/tex]

Part 3 of 3 (c) To find the probability of getting a number greater than 5 and an even number, count the favorable outcomes (rolling a 6) and divide by the total possible outcomes (6). There is 1 favorable outcome and 6 total possible outcomes.

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the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.

To calculate the surface area of a triangular prism, you need to find the area of each of the faces and add them up.

First, let's find the area of the two triangular faces. To do this, we need to find the base and height of each triangle. Since the prism is isosceles, the base of each triangle is 6 inches (the length of one of the sides of the equilateral triangle). The height of each triangle can be found using the Pythagorean theorem. We have two sides of the triangle: 4 inches and 5 inches. Using the Pythagorean theorem, we can find the height:

[tex]h^2 = 5^2 - 4^2\\h^2 = 25 - 16\\h^2 = 9\\h = 3[/tex]

So the height of each triangular face is 3 inches. Now we can find the area of each triangular face:

Area of one triangular face = (1/2) x base x height

= (1/2) x 6 x 3

= 9 square inches

Since there are two triangular faces, the total area of the triangular faces is:

Total area of triangular faces = 2 x 9 = 18 square inches

Next, let's find the area of the three rectangular faces. We have two rectangles with sides of 6 inches by 8 inches, and one rectangle with sides of 4 inches by 8 inches. The area of each rectangular face is:

Area of rectangular face = length x width

So the area of the rectangular faces are:

Area of rectangular face 1 = 6 x 8 = 48 square inches

Area of rectangular face 2 = 6 x 8 = 48 square inches

Area of rectangular face 3 = 4 x 8 = 32 square inches

Therefore, the total surface area of the triangular prism is:

Total surface area = 18 + 48 + 48 + 32 = 146 square inches

So the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.

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Answer:

(15/4)4^x

Step-by-step explanation:

Substituting the x and y values of the first point, we get:

y = ab

60 = ab^(2)

Substituting the x and y values of the second point, we get:

y = ab

960 = ab^(4)

Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:

960/60 = (ab^(4))/(ab^(2))

16 = b^(2)

Taking the square root of both sides, we get:

b = ±4

Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:

60 = a(4^(2))

60 = 16a

a = 60/16

a = 15/4

Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.

Under the null hypothesis, this test statistic follows a t-distribution with (n nap + n coffee - 2) degrees of freedom and the p-value is less than the significance level of 0.05,

To determine if there is sufficient evidence that taking a nap promotes faster reaction time than drinking coffee, we can perform a two-sample t-test assuming equal variances. The null hypothesis is that there is no difference in the mean reaction times between the nap and coffee groups, while the alternative hypothesis is that the mean reaction time for the nap group is less than the mean reaction time for the coffee group.

Let's assume that we have collected data on reaction times for both the nap and coffee groups, and have calculated their sample means ( X nap and X coffee) and sample standard deviations (snap and  s coffee). We can then calculate the pooled standard deviation using the formula:

[tex]Sp = sqrt(((nnap - 1) * snap^2 + (ncoffee - 1) * scoffe^2) / (nnap + ncoffee - 2))[/tex]

where n nap and n coffee are the sample sizes for the nap and coffee groups, respectively. We can then calculate the test statistic using the formula:

t = (X nap - X coffee) / (Sp * sqrt(1/nnap + 1/ncoffee))

Under the null hypothesis, this test statistic follows a t-distribution with (n nap + n coffee - 2) degrees of freedom. We can calculate the p-value for this test statistic using a t-distribution table or a calculator. Alternatively, we can use Python or R to perform the test and calculate the p-value.

If the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence that taking a nap promotes faster reaction time than drinking coffee. Otherwise, we fail to reject the null hypothesis.

After calculating the appropriate test statistic, we would save it into variable p2.C.Stat, rounding the value to two decimal places. We would then calculate the p-value for this test statistic and save it into variable p2.C.P, rounding the value to three decimal places.

It's important to note that the assumptions of the two-sample t-test, such as normality and equal variances, should be checked before performing the test. If these assumptions are not met, alternative tests such as the Wilcoxon rank-sum test may be more appropriate.

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Answer:

16/5

Step-by-step explanation:

We can see that the new triangle is larger than the original triangle so we know the scale factor is greater than 1.

The scale factor can be found by calculating the ratio of the length of any two corresponding sides. The length of the bottom side of the original triangle is 5. The length of the bottom side of the new triangle is 16. We can calculate the ratio which is 16:5 or 16/5.

Answer:

m = 50 + 6

m= 56

lol easy ques

This one is easy. All you have to do is add 6 to both sides to get the value of m

m-6=50

m=50+6

m=56

Diameter = 16 mm

Radius = Diameter/2

= 16/2

= 8 mm

Total height of figure = 32 mm

Height of cylinder = 19 mm

Height of cone = 32 - 19

= 13 mm

Volume of cylinder = πr²h

Substituting the values of r and h in above formula,,

[tex] \longrightarrow \sf \pi \times {(8)}^{2} \times 19 \\ \\ \longrightarrow \sf \pi \times 64 \times 19 \\ \\ \longrightarrow \sf 1216 \pi \\ \\ \longrightarrow \sf 3820.17 \: mm^{3}\\ \\ [/tex]

Hence, Volume of cylinder is 3820.17 mm³

Now,

Volume of cone = 1/3 πr²h

[tex] \longrightarrow \sf \dfrac{1}{3} \times \pi \times {(8)}^{2}\times 13 \\ \\ \longrightarrow \sf \dfrac{1}{3} \times \pi \times 64 \times 13 \\ \\ \longrightarrow \sf 871.26~ mm^3 \\ \\ [/tex]

Hence, Volume of the cone is 871.26 mm³

Volume of composite figure = Volume of cylinder + Volume of cone.

= 3820.17 + 871.26

= 4691.43 mm³

Therefore, Volume of the composite figure is 4691.43 mm³.

Answer:

the area of the photograph when it is put into the frame is 80 square inches, and the area of the frame is 88 square inches.

Step-by-step explanation:

Answer: 36 inches(2)

Step-by-step explanation:

The measure of angle ACD is approximately 109.5 degrees.

What are parallel lines ?

Parallel lines can be defined in which the lines which are equidistant to each other and they never intersect.

To solve for m<ACD, we can use the fact that the sum of the angles in a triangle is 180 degrees.

We can start by finding the measure of angle ACD, which is opposite to the known side length of 10 units. Using the Law of Cosines, we have:

cos(ACD) = (AD * AD + CD * CD - 100) / (2 * AD * CD)

We know that AD = 8 units and CD = 6 units, so plugging in these values, we get:

cos(ACD) = (64 + 36 - 100) / (2 * 8 * 6) = -1/3

Since -1/3 is negative, we know that angle ACD is obtuse, meaning it measures between 90 and 180 degrees. Therefore, we can take the inverse cosine of -1/3 to find its measure:

cos(ACD) = (-1/3) ≈ 109.5 degrees

Therefore, the measure of angle ACD is approximately 109.5 degrees.

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the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%

Probability refers to the measure of the likelihood or chance of a particular event occurring. It is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.

The formula for the binomial distribution can be used to resolve this issue:

P(X=k) = (n choose k) × pᵇ×(1-p)ⁿ⁻ˣ

where:

The number of trials, n, is five in this instance.

bis the number of successes we want (in this case, b = 2)

p is the probability of success on each trial (in this case, p = 0.20)

So, plugging in the values:

P(X=2) = (5 choose 2) ×0.20² × (1-0.20)⁵⁻²

= 10 × 0.04×0.512

= 0.2048

Therefore, the probability of winning exactly 2 of the 5 times is 0.2048, or approximately 20.48%.

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