Enlarge shape A by scale factor 2 with centre of enlargement (1, 5)

The volume of Joe chocolate box is 48in³

1. Volume of Joe chocolate box

Given the following dimensions:

length = 6in

height = 2in

width = 4in

Recall that,

Volume = length x width x height

Volume = 6 in x 4 in x 2 in

Volume = 48in³

2. Gift paper to wrap rectangular gift box

To calculate the amount of gift paper required to wrap the rectangular box, we need to find the surface area of the box.

Recall that,

Surface Area = 2(length x width) + 2(length x height) + 2(width x height)

Surface Area = 2(15 in x 10 in) + 2(15 in x 8 in) + 2(10 in x 8 in)

Surface Area = 300 in² + 240 in² + 160 in²

Surface Area = 700in²

3. Quantity of pasta served to Olivia

To find the quantity of pasta served to Olivia, we need to calculate the volume of the rectangular prism lunch box.

The volume of a rectangular prism can be calculated by multiplying its length, width, and height.

Given the dimensions of the lunch box, we have:

Volume = Length x Width x Height

Volume = 5 in x 4 in x 3 in

Volume = 60in³

Therefore, the quantity of pasta served to Olivia is 60in³

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Answer: \(y=26^{\circ}\)

Step-by-step explanation:

Using linear pairs, we can determine the two angles in the picture attached.

Thus, as angles in a triangle add to \(180^{\circ}\), \(y=26^{\circ}\)

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

6-16y

Step-by-step explanation:

Distribute, 2 x 3 and 2 x 8

6-16y

Answer:

0.6

Step-by-step explanation:

3 divided by 5

Answer:

\(7\frac{1}{2}\)

Step-by-step explanation:

15/2=7.5

7.5 as a fraction is \(7\frac{1}{2}\)

Step-by-step explanation:

7whole number 1/2

that's your answer

If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Answer:

c = 10.6

Step-by-step explanation:

c² = a² + b²

c² = 7² + 8²

c² = 49 + 64

c² = 113

Take the square root of both sides

c = 10.6301458127

Rounded

c = 10.6

The total length of the nylon rope that Jamie will use would be 15.3 feet of nylon rope.

Within this scenario specifically, one side of the right-angled triangle comprises the height of the tent (standing at 6.5-feet), and the other forms as the measure from the center of the tent to where Jaime stakes the ropes stretching outwards in another direction (with a calculated measure of 4-feet). Subsequently, we will refer to the extent of the nylon rope as R.

The Pythagorean theorem formula is:

R ² = 6.5 ² + 4 ²

R ² = 42. ²25 + 16

R ² = 58.25

R = 7. 63 ft

There are two ropes so the length would be :

= 7. 63 + 7. 63

= 15. 3 ft

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Based on the information, the confidence interval doesn't contradict the claim.

Based on the information, the following vs be deduced:

Mean = 2.87

Sample size = 35

Population standard deviation = 1.36

Critical value = 2.576

Standard error = Standard deviation / ✓Sample size

= 1.36 / ✓35

= 0.2299

The margin of error will be:

= 2.576 × 0.2299

= 0.5922

The 99% confidence interval will be 2.5678 < U < 3.7522

In conclusion, the confidence interval doesn't contradict the claim. Hence, the publication claim of 2.87kg is inside the 99% confidence interval.

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Answer: 1.7004 × 10^2

Step-by-step explanation:

Answer: Multiple Choice $15 understated. $135 overstated. $135 understated. $150 understated. $150 overstated. 2.The numbering system used in a company's chart of accounts: Typically begins with income statement accounts.

Step-by-step explanation:

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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The requried, local minimum and maxium for the given function is √2 and -√2.

We need to find the local maximum and local minimum of the function \(f(x) = 2x + 4x^{(-1)}.\)

First, we find the derivative of f(x):

\(f'(x) = 2 - 4x^{(-2)} = 2 - 4/x^2\)

Setting f'(x) = 0 to find the critical points:

\(2 - 4/x^2 = 0\)

Solving for x, we get:

x = ±√2

To determine whether these critical points are local maxima or minima, we need to examine the sign of the second derivative:

\(f''(x) = 8x^{(-3)}\)

When x = √2, f''(√2) = 8/(√2)³ = 8√2 > 0, so x = √2 is a local minimum.

When x = -√2, f''(-√2) = 8/(-√2)³ = -8√2 < 0, so x = -√2 is a local maximum.

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The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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The triangles 1, 2, 4, 7 and 8 are right triangles by Pythagorean relationship.

Triangles are closed figures formed by three line segments, a right triangle is a triangle with one right angle. Right triangles have a long side known as hypotenuse (r) and two shorter sides known as legs (x, y), whose Pythagorean relationship is shown below:

r = √(x² + y²)

Now we proceed to check whether each triangle is a right triangle or not:

Case 1:

D = √(8² + 6²)

D = 10 (YES)

Case 2:

D = √(5² + 12²)

D = 13 (YES)

Case 3:

D = √(12² + 9²)

D = 15 (NO)

Case 4:

D = √(8² + 15²)

D = 17 (YES)

Case 5:

D = √(4² + 9²)

D ≈ 9.849 (NO)

Case 6:

D = √(14² + 5²)

D ≈ 14.866 (NO)

Case 7:

D = √(20² + 15²)

D = 25 (YES)

Case 8:

D = √(24² + 10²)

D = 26 (YES)

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

0.1733 = 17.33% probability the first stack was selected.

Step-by-step explanation:

To solve this question, it is needed to understand conditional probability, and the hypergeometric distribution.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Conditional probability:

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

Probability of all red cards for the first stack:

For this, we use the hypergeometric distribution, as the cards all chosen without replacement.

7 + 4 = 11 cards, which means that \(N = 11\).

7 red, which means that \(k = 7\)

3 are chosen, which means that \(n = 3\)

We want all red, so we find P(X = 3).

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 3) = h(3,11,3,7) = \frac{C_{7,3}*C_{4,0}}{C_{11,3}} = 0.2121\)

Conditional probability:

Event A: All red

Event B: From the first stack.

Probability of all red cards:

0.2121 of 50%(first stack)

1 of 50%(second stack). So

\(P(A) = 0.2121*0.5 + 1*0.5 = 0.60605\)

Probability of all red cards and from the first stack:

0.21 of 0.5. So

\(P(A \cap B) = 0.21*0.5 = 0.105\)

What is the probability the first stack was selected?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.105}{0.60605} = 0.1733\)

0.1733 = 17.33% probability the first stack was selected.

Answer:

12

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Find the greatest common factor of 50,60:

Answer:

7pi/9

Step-by-step explanation:

subtract 360 from 500 as many times as you can

number left should be converted to radians

500 - 360 = 140

140 * (pi/180) =

140Pi/180 =

simplify by dividing by 20 top & bottom

7Pi/9

varsitytutors

Step-by-step explanation:

The body reverses direction whenever we go from Positve velocity to negative velocity or vice versa.

So here it is (2,7) exclusive then (7,10) exclusive.

A constant speed means a slope of 0. Here it is (3,6).

c. Since speed is non negative, we would reflect any part of the velocity function that is below the time.axis about the time axis

So we would get

Above is the function, don't worry bout the math part.

D. Knowing that acceleration is the derivative of velocity with respect to time, the derivative of any linear function is the slope of that linear function. So if we find the slope of different paths, we will get a constant and then we can graph it

We must use the original graph because acceleration is a vector meaning it can be negative.

We would get

the second graph is acceleration vs time

Answer:

r = 0.7

Step-by-step explanation:

Then the 3 integer even numbers are:

-24, -22, -20

We know that the sum of 3 consecutive even numbers is -78, that can be written as:

x + (x + 2) + (x + 4) = -78

Now we can solve that equation for x:

3x + 6 = -78

3x = -78 - 6 = -72

x = -72/3 = -24

The next even integer is:

-24 + 2 = -22

-24 + 4 = -20

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The three consecutive integer even numbers are -24, -22, -20

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

The sum of three consecutive even integers is -78

Represent the smallest integer with x

So, we haee the following equation:

x + (x + 2) + (x + 4) = -78

Evaluate the like terms

3x + 6 = -78

So, we have

3x = -72

Divide both sides by 3

x = -72/3 = -24

This means that the next integers are

-24 + 2 = -22

-24 + 4 = -20

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Answer:

C

Step-by-step explanation:

trust me c is the correct answer

35 16 oz jars and 47 28 oz jars of peanut butter were donated to the food bank by solving equation

Let x be the number of 16 oz jars of peanut butter collected, and y be the number of 28 oz jars of peanut butter collected.

The system of equations that represents the constraints in this situation is:

x + y = 82 (total number of jars collected)

16x + 28y = 1876 (total amount of peanut butter collected in ounces)

b. To solve for the number of 16 oz jars and 28 oz jars of peanut butter donated to the food bank

we need to solve the system of equations from part (a). One way to do this is to use elimination:

Multiplying the first equation by 16, we get:

16x + 16y = 1312

Subtracting this equation from the second equation, we get:

12y = 564

Dividing both sides by 12, we get:

y = 47

Substituting this value of y into the first equation, we get:

x + 47 = 82

Subtracting 47 from both sides, we get:

x = 35

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Answer:

22 degree

Step-by-step explanation:

We know

∠1 and ∠2 combined must be 90 degrees. We know angle 2 is 68 degrees.

What is the measure of angle 1?

90 - 68 = 22 degrees

So, angle 1 is 22 degrees.