1. An airplane flies a distance of 3000 miles in 6 hours. How tast is it going? Hint: Uses=d/t. Show our work.

2. A skydiver opens her parachute and is dropping toward the ground at a constant speed of 0.3 m/s. If she is currently 200 meters above the ground, how long will it be before she lands on the ground? Hint: Use t = d/s. Show your work.

3. A snail crawls over the ground at 1 meter per hour. How far will the slug move in 6 minutes. Hint: Use d = s x t after you convert 6 minutes into hours. Show your work.

4. A race car accelerates from 0 to 30 mi/he (44 ft / sec) in 4 seconds. What is it's acceleration in ft /sec²? Hint: Use a = v / t.

5. A fighter jet is flying along and the pilot wants to go faster. He pushes the throttle so the jet engine is producing full power. The jet accelerates at a rate of 20 m/s² for 10 seconds. How much does the jet increase it's velocity? Hint: Use v = a x t. Show your work.

6. If the jet in question 5 above was traveling at 1000 m/s before it accelerated, how fast was it going after it accelerated for 10 seconds? Show your work.

7. A boy drops a ball. The ball accelerates at 9.8 m/s². How long does it take for the ball to reach a velocu if 1 m/s? Hint: Use t = v / a. Show your work including units.

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Answer:

The first term is -3 and the common difference is 6

Step-by-step explanation:

Recall that the nth term of an arithmetic progression AP is given as

Tn = a + (n - 1)d

where

Tn is the nth term

a is the first term and

d is the common difference while n is the number of terms

Given that the 18th term of Arithmetic progression is 99 and 29th term is 165 then

substituting the given values into the formula

a + 17d = 99

a + 28d = 165

solve both equations simultaneously

11d = 165 - 99

11d = 66

d = 66/11

= 6

recall that a + 17d = 99

a + 17(6) = 99

a + 102 = 99

a = 99 - 102

= -3

hence the first term is -3 and the common difference is 6

Answer:

4

Step-by-step explanation:

4*3=12

12*3=36

36*3=108

Answer:

\(\boxed{\mathrm{4}}\)

Step-by-step explanation:

Hi student, let me help you out!

......................................................................

First, let's take a look at the common ratio, which is 3.

Common ratio ===> the amount we multiply or divide by to obtain the next term in a geometric sequence.

Now that we know the common ratio, let's divide 12 by the common ratio, 3. This gives us 4, which is the missing term

Hope this helped you out, ask in comments if any queries arise.

Best Wishes!

\(\star\bigstar\underline{\overline{\underline{\overline{\text{Reach far. Aim high. Dream big.}}}}}\bigstar\star\)

\(\underline{\rule{300}{4}}\)

Answer: x=5

Step-by-step explanation:

Combine like terms:

2x+7=3x+2

Make zeros:

x=5

Answer:

x is greater than 7, so x can be 8 or more.

Answer:

if x is greater than seven it would be 8 or more can't be 7 because its not >

Step-by-step explanation:

Estimate π as 3.14

Do the maths : 6 x 3.14 x 3 = 56.52

1 d.p : 56.5
Nearest whole number : 57

Step-by-step explanation:

k = √(49 - 12√5)

= √(45 + 4 - 2 √180)

= √45 - √4

= 3 √5 - 2.

So, k + 2 = 3 √5 - 2 + 2 = 3 √5.

Answer:

k + 2 = 3√5

Explanation:

\(\sf Given: k = \sqrt{49 - 12\sqrt{5} }\)

\(\sf \rightarrow k = \sqrt{49 - 12\sqrt{5} }\)

step 1: breakdown

\(\sf \rightarrow k = \sqrt{4 + 45- 2 \times 2 \times 3 \sqrt{5} }\)

step 2: rewrite 45 = (3√5)²

\(\sf \rightarrow k = \sqrt{4 + (3\sqrt{5})^2 - 2 \times 2 \times 3 \sqrt{5} }\)

step 3: rearrange as per a² -2ab + b² = (a - b)²

\(\sf \rightarrow k = \sqrt{ (3\sqrt{5})^2 - 2 \times 3 \sqrt{5} \times 2 +2^2}\)

step 4: comparing, here: a = 3√5, b = 2

\(\sf \rightarrow k = \sqrt{ (3\sqrt{5} -2)^2}\)

step 5: simplify √a² = a

\(\sf \rightarrow k = 3\sqrt{5} -2\)

Then find k + 2

\(\rightarrow \sf k = 3\sqrt{5} -2 + 2\)

\(\rightarrow \sf k = 3\sqrt{5}\)

The general indefinite integral of 4 sin(2x) sin(x) dx is -2 cos(2x) - (1/2) cos(4x) + c, where c represents the constant of integration.

To find the indefinite integral, we can use the product-to-sum formula for sine:

sin(A) sin(B) = (1/2) [cos(A - B) - cos(A + B)]

In this case, A = 2x and B = x. Substituting the values into the formula, we have:

sin(2x) sin(x) = (1/2) [cos(2x - x) - cos(2x + x)]

                = (1/2) [cos(x) - cos(3x)]

Now, we can integrate each term separately:

∫ (1/2) [cos(x) - cos(3x)] dx

= (1/2) ∫ cos(x) dx - (1/2) ∫ cos(3x) dx

= (1/2) sin(x) - (1/6) sin(3x) + c

Simplifying further, we get:

= -2 cos(2x) - (1/2) cos(4x) + c

Therefore, the general indefinite integral of 4 sin(2x) sin(x) dx is -2 cos(2x) - (1/2) cos(4x) + c, where c represents the constant of integration. This represents the antiderivative or primitive function of the given expression.

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The value of expression is,

⇒ x ÷ 12

We have to given that;

The algebraic expression is,

⇒ x divided by 12

Hence, We can formulate;

The value of correct expression is,

⇒ x ÷ 12

⇒ x / 12

Thus, The value of expression is,

⇒ x ÷ 12

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Answer:

X=11

Step-by-step explanation:

Vertical angles equal each other.

5x+10 = 7x -12

Then solve for x by placing all the X values on one side and the number values on the other side.

5x+10=7x-12

5x-7x=-12-10

-2x=-22

x=11

The given double integral is ∫ ∫ (x² + y²)dx dy, and we need to evaluate it over the region in the positive quadrant where x+y≤1.

To evaluate this double integral, we can first determine the limits of integration for both x and y based on the given region. In the positive quadrant, x and y both range from 0 to 1.

Now, integrating the inner integral with respect to x, we get:

∫ (x² + y²)dx = (1/3)x³ + y²x + C1,

where C1 is the constant of integration.

Next, we integrate the resulting expression with respect to y:

∫ [(1/3)x³ + y²x + C1] dy = (1/3)x³y + (1/3)y³x + C1y + C2,

where C2 is another constant of integration.

Finally, we evaluate this double integral over the given region by substituting the limits of integration:

∫∫ (x² + y²)dx dy = ∫[0 to 1] ∫[0 to 1-x] (x² + y²)dy dx.

Performing the integration, we can find the numerical value of the double integral within the given region.

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A unit of measurement which is equal to one thousands meters is known as one kilometers.

Therefore, the given units of measurement equal to one thousand meters is called one - kilometers.

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The number of students that enrolled = 3,500 students.

This is defined as the intake of individuals into an organism or students into an institution through adherence to specific orders given by the administrative department of the organisation.

The number of students that apply= 20,000 students

The percentage of students that are accepted= 70% of 20,000

That is, 70/100× 20,000

= 1400000/100

= 14,000 students.

The quantity of students that actually enroll = 25% of 14,000

That is, 25/100× 14000

= 350000/100

= 3,500 students.

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If WX is If WX is parallel to YZ, then we have opposite sides that are parallel, and we can conclude that WXYZ is a parallelogram. Therefore, the correct answer is (c).

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram have the same length, and the opposite angles are congruent.

Here,

In order to conclude that WXYZ is a parallelogram, we need to show that both pairs of opposite sides are parallel.

Option (a) only provides information about the lengths of two sides, but does not give any information about the parallelism of the sides.

Option (b) provides information about the lengths of two sides, but again does not give any information about parallelism.

Option (d) provides information about two angles, but does not give any information about the sides.

Option (c) provides the information we need.

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Answer:

Step-by-step explanation: So first, you're gonna distribute the 4/5 to the b and the -5, by doing that u will get 3.2=4/5b - 4. Then you're gonna cancel out the -4 by adding it on both sides - 3.2+4=4/5b, you get 7.2=4/5b.  Multiply by the reciprocal of 4/5 which is 5/4 on both sides. 7.2 x 5/4 = b. you get 9 = b

The lowest term of the given expression after simplifying the fractions are 3(x - 2/3)(x - 3)/(x - 5)(x + 3) - 2x(x - 1)/(2x + 1)

1. To reduce the expression x^2 - 9x/28x + 15 to lowest terms, we first factor the numerator and denominator:

x^2 - 9x + 15 = (x - 3)(x - 5)
28x + 15 = 7(4x + 3)

So the expression becomes (x - 3)(x - 5)/7(4x + 3). We cannot simplify this any further, so the answer is (a) x - 3/x + 5.

2. To simplify a^2 - 25/a^2 - 3a - 15, we first factor the numerator and denominator:

a^2 - 25 = (a + 5)(a - 5)
a^2 - 3a - 15 = (a - 5)(a + 3)

So the expression becomes (a + 5)(a - 5)/(a - 5)(a + 3). We can cancel out the (a - 5) term, so the answer is (c) a(a - 5)/3.

3. To simplify 3x^2 - 4x + 6/x^2 - 2x - 15 - 2x^2/2x + 1, we first combine the numerator of the first fraction:

3x^2 - 4x + 6 = 3(x^2 - (4/3)x + 2)

Then we factor the denominator of the first fraction:

x^2 - 2x - 15 = (x - 5)(x + 3)

We can also factor the numerator of the second fraction:

-2x^2 = -2x(x - 1)

And finally, we factor the denominator of the second fraction:

2x + 1 = (2x + 1)

Putting it all together, we have:

3(x - 2/3)(x - 3)/(x - 5)(x + 3) - 2x(x - 1)/(2x + 1)

We cannot simplify this any further, so this is the answer.

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In the book "Sarah, Plain and Tall" by Patricia MacLachlan, Anna, one of the main characters, describes what she thinks the prairie looks like after the hail storm.

After the hail storm, the prairie is likely to have undergone some visible changes. Hail storms can cause damage to crops, vegetation, and the overall landscape. It's possible that Anna perceives the prairie as altered or damaged due to the hail storm.

Given Anna's deep connection to the prairie and her love for the natural world, it is likely that she feels concerned and saddened by the effects of the storm. The prairie holds great significance to Anna and her family, representing their home and way of life. Therefore, she may have mixed emotions of worry and sadness, hoping for the prairie to recover and return to its previous beauty.

Anna's observations and thoughts about the prairie after the hail storm may also reflect her resilient and optimistic nature. Despite the temporary changes caused by the storm, Anna may find solace in the knowledge that the prairie has the ability to heal and rejuvenate over time. She may view it as a natural cycle, understanding that the prairie will eventually flourish once again.

In summary, while the exact thoughts of Anna about the prairie after the hail storm are not explicitly stated in the book, we can infer that she experiences a mixture of concern, sadness, and hope for the prairie's recovery. The book portrays Anna as a character deeply connected to the land, making her emotional response to the storm's impact on the prairie significant and meaningful.

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To maximize the profit 29.6 units must be produced.

What is the maxima or minima?

The maxima and minima of a function collectively referred to as extrema in mathematical analysis, are the highest and lowest values of the function, either on the whole domain or within a specific range.

We have given,

The revenue function is,

R(x)=3x

Cost function,

C(x)=0.05x^2+0.04x+10,

Where

x = number of units produced.

Thus, profit = revenue - cost

P(x) = 3x - (0.05x^2+0.04x+10)

= -0.05x^2 + 2.96x - 10

Differentiating with respect to x,

P'(x) = -0.1x + 2.96

Again differentiating with respect to x,

P''(x) = -0.1

For maxima or minima,

P'(x) = 0,

0 = -0.1x + 2.96

-0.1x = -2.96

x = 2.96/0.1

For x = 29.6,

P''(x) = negative,

Hence, to maximize the profit 29.6 units must be produced.

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The mean weight of certain sheets of wrapping paper is 10 g each.

The mean weight of the sheets of wrapping paper is given as 10 g each. This means that on average, each sheet weighs 10 grams. The standard deviation of the weight of the sheets is given as 0.05 g.

This indicates the degree of variability or spread in the weight of the sheets around the mean weight of 10 g. A standard deviation of 0.05 g suggests that most of the sheets will have a weight that is very close to 10 g, with only a few sheets having a weight that deviates significantly from the mean.

The mean weight of the sheets of wrapping paper can be used as a reference point for determining the weight of a particular sheet or for calculating the weight of a bundle of sheets.

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Answer:

45 mph

Step-by-step explanation:

180 / 4= 45

Answer:

24

Step-by-step explanation:

3*8=24 Inches^2

Answer: 24 sq. In.

Step-by-step explanation: area of a rectangle is l x w, or ab

Answer:

(0,3)

Step-by-step explanation:

The parent function's vertex is at (0,0) and this function is being translated 3 units up, so the vertex is at (0,3)

Answer: Unclear

Step-by-step explanation: I can't see your image/sentence, so I can't help u

Answer:

The variable represents BOOKS. I decided to represent BOOKS by using b.

Jennifer will be able to buy 3 books with the rest of her money

The equation is 12 - 8b = 36

Step-by-step explanation:

Jaleel and Angela purchased a bag of sugar and used it evenly so the amount of flour that they each need, based on their brownie recipes are:

Jaleel and Angela purchased a 20-cup bag of sugar and divided it evenly which means that they each get 10 cups of sugar.

The number of cups of sugar needed per cup of flour is:

= Change in sugar / Change in flour

= (3 - 1.5) / (2 - 1)

= 1.5 cups of sugar

The amount of flour needed would be:

= Number of cups of sugar / Cups of sugar per cup of flour

= 10 / 1.5

= 6 ²/₃ cups of flour

Angela's recipe shows that the cups of sugar needed per cup of flour is:

= (2 - 0) / (1 - 0)

= 2 cups of sugar

This means that with 10 cups of sugar, the amount of flour needed is:

= 10 x 1/2

= 5 cups of flour

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Answer:

.2 Cm

Step-by-step explanation:

There are 70 different committees possible combinations from the 8 students in the class, where no member has any specific responsibilities.

To find the number of different committees possible, we will use the concept of combinations. In this case, we have 8 students and need to choose 4 of them to form a committee. A combination is a selection of items from a larger set, such that the order of the items does not matter.

Step 1: Identify the number of items in the set (n) and the number of items to be chosen (r). Here, n = 8 and r = 4.

Step 2: Use the formula for combinations, which is C(n, r) = n! / (r!(n-r)!), where C(n, r) represents the number of combinations, n! denotes the factorial of n, and r! denotes the factorial of r.

Step 3: Calculate the factorials involved in the formula. Factorial of a number is the product of all positive integers less than or equal to that number.
- 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320
- 4! = 4 × 3 × 2 × 1 = 24
- (8-4)! = 4! = 24

Step 4: Substitute the values into the formula and calculate the number of combinations.
C(8, 4) = 40,320 / (24 × 24) = 40,320 / 576 = 70

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Answer:

Step-by-step explanation:

-23=-3X-8

Answer:

given below

Step-by-step explanation:

Valid:

Invalid: