Question 3 (1 point)
Which story represents the equation 9+
1
= 182
2
Оа Luke has 9 granola bars and wants to divide them equally to share with his friends. He wants to give each friend 1/2 of a granola
bar. How many of Luke's friends will get granola?
Oь Mario ordered 9 pizzas and wants to divide the pieces equally on plates. He wants to put 2 pieces of pizza on each plate. How
many plates will Mario need in all?
O Lucky has 1/2 of a box of brownies and wants to divide it equally among 9 family members. What fraction of the brownies will
each family member receive?

The number of subs in the order is 8 or 9

Let's call the number of subs in the order "x".

Since the cost of 3 subs is $20, the cost per sub is $20 / 3 = $6.67.

And since the cost of 4 subs is $26, the cost per sub is $26 / 4 = $6.50.

So the cost per sub is between $6.50 and $6.67.

If the total cost is $56, then the cost per sub must be $56 / x.

So:

x = 56/6.5 or x = 56/6.67

Evalutate

x = 8.6 or x = 8.4

Approximate

x = 9 or 8

Hence, the subs is 8 to 9

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Answer:

14boxes

Step-by-step explanation:

Given the following

Length of truck: 3 1/2 yds

Width of truck: 5 yds

Height of truck: 2 1/2 yds

Volume of truck = Length * Width * Height

Volume of truck = 3 1/2 * 5 * 2 1/2

Volume of truck = 7/2 * 5 * 5/2

Volume of truck  = 7/4 cubic yards

For each box

Length L = 1/2 yd

Volume of each box = 1/2 * 1/2 * 1/2

Volume of each box = 1/8 cubic yds

Since 1 box = 1/8 cubic yds

x box = 7/4 cubic yds

Cross multiply

1/8x = 7/4

Cross multiply

4 * x =   7 * 8

4x = 56

x = 56/4

x = 14

Hence the total boxes that can fit in the trunk is 14boxes

Answer:

See below for proof of identity.

Step-by-step explanation:

Since both terms of \(\sin^3\theta+\cos^3\theta\) are perfect cubes, we can use the formula \(a^3+b^3=(a+b)(a^2-ab+b^2)\) where \(a=\sin\theta\) and \(b=\cos\theta\):

\(\displaystyle \frac{\sin^3\theta+\cos^3\theta}{\sin\theta+\cos\theta}\\\\\frac{(\sin\theta+\cos\theta)(\sin^2\theta-\sin\theta\cos\theta+\cos^2\theta)}{\sin\theta+\cos\theta}\\ \\\frac{(\sin\theta+\cos\theta)(1-\sin\theta\cos\theta)}{\sin\theta+\cos\theta}\\\\1-\sin\theta\cos\theta\)

Thus, the identity is proven.

Answer:

Concept: Rectangular Figures

Answer:

x=3

Step-by-step explanation:

3(2x−4)−5(x−2)=1

Step 1: Simplify both sides of the equation.

3(2x−4)−5(x−2)=1

(3)(2x)+(3)(−4)+(−5)(x)+(−5)(−2)=1(Distribute)

6x+−12+−5x+10=1

(6x+−5x)+(−12+10)=1(Combine Like Terms)

x+−2=1

x−2=1

Step 2: Add 2 to both sides.

x−2+2=1+2

x=3

Answer:

lol i would listen to music or do/stay somewhere comfortable it helps me  

Step-by-step explanation:

The volume of the solid generated by rotating function f(x) = 64 − x² about the x-axis on [2, 8] is approximately 858.31 cubic units.

The volume of the solid generated by rotating function f(x) = 64 − x² about the x-axis on [2, 8] can be determined using the disk method. The formula for the volume of the solid of revolution using the disk method is: V = π ∫(R(x))² dx where R(x) is the radius of the disk and dx is the thickness of the disk. Since the function f(x) is rotated about the x-axis, the radius R(x) is simply the function f(x). Therefore, we can substitute f(x) into the formula and evaluate the integral to find the volume of the solid. V = π ∫(f(x))² dx  = π ∫(64 − x²)² dx  = π ∫(4096 − 128x² + x⁴) dx  = π [4096x − (128/3)x³ + (1/5)x⁵] evaluated from x = 2 to x = 8  = π [(4096(8) − (128/3)(8³) + (1/5)(8⁵)) − (4096(2) − (128/3)(2³) + (1/5)(2⁵))]  = π [(2048/15) + (2048/15)]  = π (4096/15)  ≈ 858.31Therefore, the main answer is: The volume of the solid generated by rotating function f(x) = 64 − x² about the x-axis on [2, 8] is approximately 858.31 cubic units. The answer more than 100 words is explained above through the disk method. The disk method was used to evaluate the definite integral over the region [2, 8]. Finally, we determined the volume of the solid of revolution by subtracting the volume of the inner disk from the volume of the outer disk.

The volume of the solid generated by rotating function f(x) = 64 − x² about the x-axis on [2, 8] is approximately 858.31 cubic units.

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A possible confounding variable that that would help explain the relationship between hair length and height of college age students is their gender.

Confounding variable is an extraneous variable that is related to both the dependent and independent variable, and it affects the result of the study. Therefore, it causes the effect of the independent variable on the dependent variable to be distorted. A possible confounding variable that would help explain the relationship between hair length and height of college age students is their gender. If the study didn't control for gender, then it would be difficult to determine if the relationship between hair length and height of college age students was a direct relationship or if it was due to the confounding variable (gender).For example, if the study found that female college age students tend to have shorter hair and are shorter than male college age students. Therefore, this would make the relationship between hair length and height spurious. Hence, a possible confounding variable that would help explain the relationship between hair length and height of college age students is their gender.

A possible confounding variable that would help explain the relationship between hair length and height of college age students is their gender. The gender of college age students could play a role in determining their height and hair length. If the study didn't control for gender, then it would be difficult to determine if the relationship between hair length and height of college age students was a direct relationship or if it was due to the confounding variable (gender). For example, if the study found that female college age students tend to have shorter hair and are shorter than male college age students. Therefore, this would make the relationship between hair length and height spurious. This means that the relationship between the two variables was not a direct one, but was rather due to the confounding variable (gender). Therefore, in order to determine if there is a direct relationship between hair length and height of college age students, the study needs to control for gender.

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The combined cost of 1 pound of salmon and 1 pound of trout is $16.60

Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign.

The expression on the left and the expression on the right are shown to be equal in reference to one another.

Let x be the cost per pound of salmon and y be the cost per pound of trout.

Melissa buys 212 pounds of salmon and 114 pounds of trout. She pays a total of $31.25

2.5 × x + 1.25× y = $31.25

2.5x + 1.25y = 31.25

The trout costs $0.20 per pound less than the salmon.

y = x - 0.20

hence

2.5x + 1.25y = 31.25

2.5y + 1.25(x - 0.20) = 31.25

2.5y + 1.25x - 0.25 = 31.25

2.5x + 1.25x = 31.25 + 0.2

x = 31.5/3.75

x = $8.4

The cost per pound of salmon be represented by x = $8.4

y = x - 0.20

y = 8.4 - 0.20

y = $8.2

The cost per pound of trout be represented by y = $8.2

The cost of a pound of salmon and trout is:

= $8.4 + $8.2

= $16.60

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The linear equation that represents the given situation is :

y = 4x + 1 and the elephant's tusk at 6-years old will be 25 inches.

represents the situation.

Given is that Elephants are born with tusks, and their tusks grow 4 inches a year. A 1 - year old elephant's tusk measured 5 inches.

Since the tusks grow 4 inches a year, we can write -

y = 4x + c

{y} - length of tusk
{x} - number of years

Now, at (1, 5) -

5 = 4 x 1 + c

c = 5 - 4

c = 1

So, the linear equation that represents the given situation is -

y = 4x + 1

For {x} = 6, we can write -

y = 4 x 6 + 1

y = 25 inches

Therefore, the linear equation that represents the given situation is :

y = 4x + 1 and the elephant's tusk at 6-years old will be 25 inches.

represents the situation.

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Answer:

The radius of the clock is 7.72 meters

Step-by-step explanation:

Here, we want to calculate the radius of a clock which has a circumference of 48.5 m

Mathematically;

Circumference C = 2 * pi * r

48.5 = 2 * 22/7 * r

7 * 48.5 = 44r

r = (7 * 48.5)/44

r = 7.72 meters

Hello!

[ 50; 41; 30 ] = ?

50 | 2 × 5

5 | 5 => 50 = 2 × 5²

1 |

41 | 41 => 41 = 41

1 |

30 | 2 × 5

3 | 3 => 30 = 2 × 3 × 5

1 |

[ 50; 41; 30 ] = 2 × 3 × 5² × 41 = 2 × 3 × 25 × 41 = 6 × 25 × 41 = 150 × 41 = 6150

Good luck! :)

Step-by-step explanation:

Lola's pet turtle walked 10 feet, and then half that length again. This means that Lola's pet turtle walked:

= 10 + (1/2 × 10) = 10 + 5 = 15 feet

Lola's baby brother walked 3 feet, and then half that length again. Total length walked will be:

= 3 + (1/2 × 3) = 3 + 1.5 = 4.5 feet

Lola's hamster walked 6.5 feet, and then half that length again. Total length walked will be:

= 6.5 + (1/2 × 6.5) = 6.5 + 3.25 = 9.75

Lola's mom walked x feet, and then half that length again. Total length walked will be:

= x + (1/2 × x) = x + 0.5x = 1.5x

Total feet walked by the whole member of the family will be:

= 15 + 4.5 + 9.75 + 1.5x

= 29.25 + 1.5x

Answer:

turtle: 10 + 5 = 15

brother:  3 + 1 1/2 = 4 1/2

hamster: 6 1/2 + 3 1/4 = 9 3/4

Mom: x + 1/2x = 1 \(\frac{1}{2}\)x

Step-by-step explanation:

Answer:  3/4

Step-by-step explanation:

1. square root the denominator and nominator, 36= 6 and 64= 8

2. put them together (6/8)

3. simplify 6/8

4. 6/8 divided by 2

5. 3/4 is your answer

Answer:

A concave meniscus, which is what you normally will see, occurs when the molecules of the liquid are attracted to those of the container. This occurs with water and a glass tube. A convex meniscus occurs when the molecules have a stronger attraction to each other than to the container, as with mercury and glass.

Equation V + Iwh , I = 32, w = 14, and h = 7, V = -3,136. The correct answer is B.

To solve for V in the equation V + Iwh, we can plug in the given values of I, w, and h, and then isolate V on one side of the equation. Here are the steps:

1. V + Iwh = V + (32)(14)(7)
2. V + 3,136 = V + 3,136
3. Subtract 3,136 from both sides of the equation: V = -3,136

The correct answer is option B: 3,136. Here is the solution in HTML format:

To solve for V in the equation V + Iwh, we can plug in the given values of I, w, and h, and then isolate V on one side of the equation. Here are the steps:

V + Iwh = V + (32)(14)(7)
V + 3,136 = V + 3,136
Subtract 3,136 from both sides of the equation: V = -3,136

The correct answer is option B: 3,136.

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Answer:

Plot the points on the graphing calculator, and then generate a linear regression model.

y = 8.4833x - 14.5278

r^2 = .9518, so r = .9756

The data has a strong positive correlation.

Answer:

D.

Each line has the 3 dashes meaning equivalent

Answer:

The answer is 175 grams

Step-by-step explanation:

100 than 150, its close to 175 if u estimate

Using the concept of Equation of a line, equation of the line that satisfies given conditions is y = 2x - 4.

A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value where the line intersects the y-axis. On the y-axis, this number c is known as the intercept. A straight line on the y-axis with gradient m and intercept c has the equation y = mx + c.

Given that,

Line passes through (-1,-6),

And is perpendicular to the line passing though (2,6) and (6,4),

So let us find the slope, m of line through (2,6) and (6,4),

m = \(\frac{Rise}{run}\) = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

Here,

(\(x_{1}, y_{1}\))  = (2,6) and

(\(x_{2},y_{2}\)) = (6,4) so,

m = \(\frac{4-6}{6-2}\) = \(\frac{-1}{2}\)

Remember for two perpendicular lines with slopes \(m_{1}\) and \(m_{2}\),

\(m_{1}\) × \(m_{2}\) = -1

So the perpendicular line will have slope 2.

A line with slope m passing through a point (a,b) has the equation,

y-b = m(x-a) so,

putting values of a, b and m together we get,

y - (-6) = 2( x- (-1) )

y + 6 = 2x + 2

y = 2x - 4

Hence the required equation is y = 2x - 4.

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Answer: 0.15, 3/20

0.8, 4/5

0.02, 1/50

Those are answers unless you didn’t include the actual question in your picture

Step-by-step explanation:

The possible lengths of the rectangular parking lot are any value less than or equal to 80 feet or any value greater than or equal to 110 feet, as long as the width is calculated accordingly to satisfy the given conditions of the perimeter and area.

The possible lengths of the rectangular parking lot can vary, but they must adhere to the conditions of having a perimeter of 380 feet and an area of at least 8800 square feet.

Let's assume the length of the parking lot is L and the width is W. The perimeter of a rectangle is given by the formula P = 2L + 2W. In this case, we are given that the perimeter is 380 feet, so we can write the equation as 2L + 2W = 380.

Additionally, the area of a rectangle is given by the formula A = L × W. We are given that the area must be at least 8800 square feet, so we can write the inequality as L × W ≥ 8800.

To determine the possible lengths of the parking lot, we can use these equations. First, let's solve the perimeter equation for W: W = (380 - 2L)/2 = 190 - L. Next, substitute this value of W into the area inequality equation: L × (190 - L) ≥ 8800.

Simplifying this inequality, we get L² - 190L + 8800 ≥ 0. To find the possible values of L, we can solve this quadratic inequality. By factoring or using the quadratic formula, we can determine that the possible lengths are L ≤ 80 or L ≥ 110.

Therefore, the possible lengths of the rectangular parking lot are any value less than or equal to 80 feet or any value greater than or equal to 110 feet, as long as the width is calculated accordingly to satisfy the given conditions of the perimeter and area.

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Answer:

a) = -8

b) 1 - (-7) = 8

b) -7 - 1 = -8

c) for both they are still the same answer so  

[1- (-7)] = 8

[-7 - 1] = -8

I'm pretty sure these are the answers hope this helped

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

The sum of the interior angles of a quadrilateral = 360°

Sum the angles and equate to 360

9x + 15 + 85 + 90 + 80 = 360, that is

9x + 270 = 360 ( subtract 270 from both sides )

9x = 90 ( divide both sides by 9 )

x = 10

a. The position of the particle at t = 1 is (1, 4, 0).

   The velocity of the particle at t = 1 is (2, 4, 4).

   The acceleration of the particle at t = 1 is (2, 0, -4).

b. The total distance traveled by the particle from t = 1 to t = e is approximately 8.277 units.

c. The curvature of the path when t = 1 is √5 / 12 units⁻¹.

The speed at which velocity varies with respect to time.

(a) To find the position, velocity, and acceleration of the particle when t = 1, we need to evaluate the position function, r(t), and its derivatives at t = 1.

Position:

r(1) = (12, 4(1), 4 ln(1)) = (1, 4, 0)

Therefore, the position of the particle at t = 1 is (1, 4, 0).

Velocity:

v(t) = r'(t) = (2t, 4, 4t⁻¹)

v(1) = (2(1), 4, 4(1)⁻¹) = (2, 4, 4)

Therefore, the velocity of the particle at t = 1 is (2, 4, 4).

Acceleration:

a(t) = v'(t) = (2, 0, -4t⁻²)

a(1) = (2, 0, -4(1)⁻²) = (2, 0, -4)

Therefore, the acceleration of the particle at t = 1 is (2, 0, -4).

(b) To find the total distance traveled by the particle from t = 1 to t = e, we need to integrate the magnitude of the velocity function, |v(t)|, over the interval [1, e].

|v(t)| = √(2t² + 16 + 16t⁻²)

∫|v(t)| dt = ∫√(2t² + 16 + 16t⁻²) dt from t = 1 to t = e

This integral is difficult to evaluate analytically, so we can approximate the value using numerical methods, such as Simpson's rule or the trapezoidal rule. Using Simpson's rule with n = 4 intervals, we get:

∫|v(t)| dt ≈ 8.277

Therefore, the total distance traveled by the particle from t = 1 to t = e is approximately 8.277 units.

(c) To find the curvature of the path when t = 1, we need to evaluate the curvature function, κ(t), at t = 1.

Curvature:

κ(t) = |a(t)| / |v(t)|³

κ(1) = |(2, 0, -4)| / |(2, 4, 4)|³

κ(1) = √20 / (2³ * √84)

κ(1) = √5 / 12

Therefore, the curvature of the path when t = 1 is √5 / 12 units⁻¹.

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Answer:

y>15/4

Step-by-step explanation:

y/3-3/4>1/2

y/3>1/2+3/4

y/3>2/4+3/4

y/3>5/4

y>5/4*3

y>15/4

The correct value of p(x<8) is 1.875.

To determine how probable something is gonna occur, use probability. It is a number between 0 and 1, where 0 denotes the absence of a possibility and 1 denotes the existence of one. By dividing the number of favorable outcomes by the entire number of potential possibilities, the probability of an occurrence is determined.

To find the probability that is greater than 8, we need to integrate this probability density function from 5.5 to 20.5:

P(X < 8) = ∫[5.5,20.5] f(x) dx

= ∫[5.5,20.5] (1/8) dx

= [x/8] from 5.5 to 20.5

= (20.5/8) - (5.5/8)

= 15/8

= 1.875.

Therefore, the correct probability is 1.875.

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