3,725,000 in scientific notation

The swimming pool can hold a volume of 3.456 cubic meters of water.

The volume of water that the swimming pool can hold can be calculated by multiplying the base area of the pool by its depth. In this case, the base area is given as 192 m² and the depth is 1.8 cm.

However, it is important to note that the depth should be converted to meters before performing the calculation.

To convert 1.8 cm to meters, we divide it by 100 (since there are 100 centimeters in a meter):

Depth = 1.8 cm ÷ 100 = 0.018 m

Now we can calculate the volume of water using the formula:

Volume = Base Area × Depth

Substituting the given values, we get:

Volume = 192 m² × 0.018 m = 3.456 m³

Therefore, the swimming pool can hold a volume of 3.456 cubic meters of water.

In the explanation, we use the formula for calculating the volume of a rectangular prism, which is given by multiplying the base area by the depth. We convert the depth from centimeters to meters and then substitute the given values into the formula to find the volume of water that the swimming pool can hold, which is 3.456 cubic meters.

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1)1000

2) 4.4%

3) 4.4

4) 9%

5)4.4%

6) 0.6%

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The amount of money that Theresa has left is equal to £2,740.

In order to write a linear equation to describe this situation, we would assign variables to the cost of flights for each of them and the cost of accommodation for each of them respectively, and then translate the word problem into a linear equation as follows:

Let the variable a represent cost of flights for each of them.

Let the variable f represent cost of accommodation for each of them.

Since Theresa paid for herself and 11 friends to go on holiday with a flight cost of £339 and accommodation cost of £266, a linear equation to describe this situation is given by;

y = 12(a + b)

y = 12(266 + 339)

y = £7,260

For the amount of money left, we have:

Amount of money left = £10,000 - £7,260

Amount of money left = £2,740.

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The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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The equation to show the perimeter of the rectangle is P = 2(2w + 5)

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

Length = 5 more than the width

Also, we have

Perimeter = 58

This means that

P = 2(w + 5 + w)

P = 2(2w + 5)

In (a), we have

P = 2(2w + 5)

This gives

2(2w + 5) = 58

So, we have

2w + 5 = 29

2w = 24

w = 12

Next, we have

l = 12 + 5

l = 17

Lastly, we have

Area = 17 * 12

Area = 204

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Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

Answer:

5x+7 > 17 matches with 3.

1+3x > -5 matches with 2.

2x+1 < 3 matches with 1.

5-3x > 11 matches with 4.

Step-by-step explanation:

Answer:

A) 0.01

B) 0.07

Step-by-step explanation:

We are given;

P(accidents last year) = 0% = 0

P(accidents this year) = 6% = 0.06

P(accidents last year | accidents this year) = 10% = 0.1

A) We want to find the percentage of the employees will experience lost-time accidents in both years.

From multiplication rule in probability, we know that;

P(A & B) = P(A) × P(B|A) = P(B) × P(A|B)

Thus;

P(accident in both years) = P(accidents this year) × P(accidents last year | accidents this year)

P(accident in both years) = 0.06 × 0.1

P(accident in both years) = 0.006

To 2 decimal places gives; 0.01

B) from the addition rule, we know that;

P(A or B) = P(A) + P(B) - P(A & B)

Thus;

P(accident last year or this year) = P(accidents last year) + P(accidents this year) - P(accident in both years)

P(accident last year or this year) = 0 + 0.06 + 0.006 = 0.066

To 2 decimal places = 0.07

Answer:

5g

Step-by-step explanation:

14-9=5

Answer:

you... didn't put anything....

Step-by-step explanation:

try asking it again, but put an image

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

Answer:

First is option B)

Second is option B)

I hope my answer helps you.

Answer:

(b)    a = 50 * 2^(t/4)

(c)    951

Step-by-step explanation:

After t hours

a = 50 * 2^(t/4)

After 17 hours

a = 50 * 2^(17/4)

a = 50 * 2^(4.25)

Use calculator

a = 951.3656920022

Rounded

a = 951

Answer: −8  3 /4

Step-by-step explanation: (−3  1 /2 )(2  1 /2 )

(-7/2)(5/2)

−35 /4

−8  3 /4

Answer:

y=4.2x-3.7

Step-by-step explanation:

Slope-intercept form is y=mx+b, so just plug in the numbers to where they go in the formula.

Answer:

C: 52 degrees

Step-by-step explanation:

Answer:

solve simultaneously

start by labeling them equation 1 and 2 then choose whether you want to make x or y the subject from knew of the equations

Answer:

x = -1

Step-by-step explanation:

6+4 = 10

14-10 = 4

2x + 6 = 4

2x (-2) = -2

-2 + 6 = 4

Answer:

y= 11x

Step-by-step explanation:

find the slope: 22-11/2-1= 11/1 or 11

To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x

We need to simplify the following expression:

Answer:

Step-by-step explanation:

Given the order of operations A set of three scores to consists of the values 6, 3, and 2, we are to evaluate the following

1) Σ2X – 2

= 2(6)+2(3)+2(2) – 2

= 12+6+4–2

= 22–2

= 20

2) Σ(2X)² = (2×6)²+(2×3)²+(2×2)²

Σ(2X)² = 12²+6²+4²

Σ(2X)² = 144+36+16

Σ(2X)² = 144+52

Σ(2X)² = 196

The results of the order of operations are: \(\sum 2x -2 = 16\) and \(\sum (2x)^2 =196\)

The scores are given as:

x = 6, 3 and 2

This is represented as:

\(\sum 2x -2\)

So, we have:

\(\sum 2x -2 = 2 \times 6 - 2 + 2 \times 3 - 2 + 2 \times 2 - 2\)

Evaluate the products

\(\sum 2x -2 = 12 - 2 + 6 - 2 + 4- 2\)

\(\sum 2x -2 = 16\)

This is represented as:

\(\sum (2x)^2\)

So, we have:

\(\sum (2x)^2 =(2 \times 6)^2 + (2 \times 3)^2 + (2 \times 2)^2\)

Evaluate the products

\(\sum (2x)^2 =12^2 + 6^2 + 4^2\)

Evaluate the squares

\(\sum (2x)^2 =144 + 36 + 16\)

\(\sum (2x)^2 =196\)

Hence, the results of the order of operations are:

\(\sum 2x -2 = 16\) and \(\sum (2x)^2 =196\)

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Answer:

  96°

Step-by-step explanation:

You want the value of angle C in the diagram with two parallel lines and a triangle between them.

The sum of angles in a triangle is 180°, so the missing angle in the triangle is ...

  180° -60° -24° = 96°

Angle C and the one we just found are alternate interior angles with respect to the parallel lines and the transversal that forms those angles. As such, they are congruent:

  C = 96°

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Answer:

b. 5 meters

Step-by-step explanation:

1 meter = 1000 millimeters

5 meter = 5000 millimeters

Which is longer 5 meters or 400 millimeters?

5000 > 400

So, the answer is b. 5 meters.

The maximum height reached by the ball is 908.5 feet.

Using the given values, we can substitute v0 = 152 and h0 = 6 into the equation:

\(h(t) = -16t^2 + 152t + 6\)

This quadratic function models the height of the ball at any time t after it is thrown.

To find the maximum height of the ball, we need to find the vertex of the parabolic curve described by the quadratic function. The vertex can be found using the formula:

t = -b / 2a

where a = -16 and b = 152 are the coefficients of the quadratic function.

t = -152 / 2(-16) = 4.75

So the maximum height is reached after 4.75 seconds. To find the maximum height, we can substitute this value back into the equation:

\(h(4.75) = -16(4.75)^2 + 152(4.75) + 6 = 908.5\)feet

Therefore, the maximum height reached by the ball is 908.5 feet.

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Question

A ball is thrown vertically upward from a height of 6 feet with an initial velocity of 152 feet per second. Write a quadratic function to model the vertical motion of the ball, given that the height of the ball at time t is given by: h(t) = -16t^2 + v0t + h0

The exact value of sin(cos⁻¹ (2/5) ) is (√21)/5.

To determine the exact value, draw a triangle in the plane with the vertex:

( 2/5, √( 1² - (2/5)² ), (2/5,0) and the origin.

The cos⁻¹(2/5) is the angle between the positive x-axis and the ray beginning at the origin and passing through ( 2/5, √( 1² - (2/5)² ).

Hence;

sin(cos⁻¹ (2/5) ) is √( 21/25 )

Now, rewrite √( 21/25 ) as (√21)/(√25 )

We can simplify the denorminator

Rewrite 25 as 5²

(√21)/(√5² )

Take the square root of √5²

(√21)/5

Therefore, the simplified form of the expression is (√21)/5.

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Answer:

180 \(cm^2\)

Step-by-step explanation:

L x W x H

6 x 5 x 6

180

Answer:  180 cubic centimeters

Step-by-step explanation:

Each little blue cube measures 1 cm in each direction - width, height, and depth.

The volume of the whole figure is just the volume of all the little cubes, added up.

The block of cubes is 5 cubes wide and has a depth of 6 cubes. So each horizontal layer is 5 * 6 = 30 cubes, total.

The block of cubes is 6 layers deep, so we have 6 layers of 30 cubes each = 6 * (30 cubes) = 180 cubes in all.

Each cube is 1 cubic centimeter (abbreviated 1 cc), so 180 of them have a combined volume of 180 cc.

A shorter way to say all this is to say that V = width * depth * height =

    = 5 cm * 6 cm * 6 cm = (5)(6)(6) cm³ = 180 cubic centimeters

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

We have,

To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.

Now,

Prevalence of coronavirus in California: 3 out of 1000

False positive rate of the antigen test: 0.05 (5 out of 100)

Let's calculate the probability of a positive test result.

The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):

True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)

The probability of a positive test result can be calculated using Bayes' theorem:

P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)

P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)

P(Positive test) = 0.0024 + 0.04985

P(Positive test) = 0.05225

Therefore,

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

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The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960

We are told that  two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity

The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.

Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;

x + y ≤ 9

x ≥ 2

y ≥ 3

Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;

20x + 50y ≤ 360

Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;

Z = 80x + 120y  maximize

The solution from the graph attached is;

x = 3, y = 6

Thus, the maximum profit is;

Z = 80(3) + 120(6)

Z = 960

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You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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