Add Decimals-Instruction - Level E
June makes slime using 1.5 liters of white glue and 0.72 liter of a starch and water mixture.
Find the total volume of the slime.
Are there enough hundredths to make a tenth?
➡ There are ? hundredths. That is
enough to make a tenth.
✓is
is not

Distance of the house from the base of the cliff is 282.27 m.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

From the figure attached,

AB = Height of the cliff = 60 m

Let the distance between the base of the cliff and the house 'C' = x m

If the angle of depression = 12°

Then angle of elevation of the top of the cliff from the house = 12°

Now from right triangle ABC,

tan12=60/x

x=60/tan 12

x=60/0.21256

x = 282.27 m

Therefore, distance of the house from the base of the cliff is 282.27 m.

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The amount of natural oil needed to make 869 liters of Petrolyn oil is given as follows:

1520.75 liters.

The necessary amount of natural oil is obtained applying the proportions in the context of this problem.

Considering the ratio given in the problem, a rule of three is established, as follows:

7 liters of natural oil - 4 liters of Petrolyn oil.

n liters of natural oil - 869 liters of Petrolyn oil.

Applying cross multiplication, the desired amount is obtained as follows:

4n = 7 x 869

n = 7 x 869/4

n = 1520.75 liters.

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The measure of the angle m∠AEB, found using the angle of intersecting secant theorem, where the measure of the arcs intercepted by the secants are m[tex]\widehat{AB}[/tex] = 54°, and m[tex]\widehat{CD}[/tex] = 66° is; m∠AEB = 6°

The angle of intersecting secant theorem states that the measure of the angle formed by the intersection of two secant is half the positive difference of the arcs intercepted by the secants.

Please find attached the possible drawing in the question, obtained based on the specified parameters and on similar questions on the internet, created with MS Word.

The parameters indicates that we get;

m[tex]\widehat{AB}[/tex] = 54°

m[tex]\widehat{CD}[/tex] = 66°

The angle of intersecting secants theorem indicates that we get;

m∠AEB = (1/2) × (m[tex]\widehat{CD}[/tex] - m[tex]\widehat{AB}[/tex])

Therefore;

m∠AEB = (1/2) × (66° - 54°) = 6°

m∠AEB = 6°

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The positive coterminal angle less than 360° is, 55°

Angles with the same initial and terminal sides but a multiple of 360° degree difference are known as coterminal angles (or a full rotation). In other words, you can create an angle that is coterminal with the original angle by taking it and adding or subtracting 360 degrees (or any multiple of 360 degrees).

To find a positive angle that is coterminal with -1025°,

we can add or subtract any multiple of 360° until we get an angle between 0° and 360°.

Adding 1080° (which is 3 revolutions of 360°) to -1,025° gives us:

= -1,025° + 1080°

=   55°

Since this angle is less than 360°,

Therefore, a positive angle less than 360° that is coterminal with -1025° is 55°.

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The height of the plane to the nearest metres is 1023 metres. Therefore, the answer is A.

A pilot flying over the gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the plane to the island is 4812 metres .

Therefore, the height of the plane can be found as follows:

The situation forms a right angle triangle.

Using trigonometric ratios,

tan 12 = opposite / adjacent

tan 12° = x /  4812

cross multiply

x =  4812 tan 12°

x =  4812 × 0.21255656167

Therefore,

x = 1022.82217476

x = 1023 metres.

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Answer:

Step-by-step explanation:

You just need to remember to first convert percentages to decimal form by dividing the percent by 100. Then you can work out the calculations.

Also, remember that if the problem is asking you to find a percentage, you need to turn your decimal answer to a percentage by multiplying by 100.

I used x to represent what we are looking for:

6.5% of $400 = x

0.065 * 400 = $26

12.5% of 100 = x

0.125 * 100 = $12.5

x of 650 = 130

130/650 = 0.2 which equals 20%

x of $4.50 = $5.40

5.40/4.50 = 1.2 which equals 120%

x of $28 = $8.40

8.40/28 = 0.3 which equals 30%

56% of x = $21.84

21.84/0.56 = 39

55% of x = $495

495/0.55 = 900

x of 400 = 120

120/400 = 0.3 which equals 30%

4% of 975 = x

0.04 * 975 = 39

Answer:

See below

Step-by-step explanation:

a. 6.5% of $400:

[tex]= \frac{65}{100}[/tex]× ($400)

= $260

b. 12.5% of $100:

[tex]= \frac{12.5}{100}[/tex] × ($100)

= $12.5

c. 130 is what percent of 650:

[tex]=\frac{130}{650}[/tex]×100%
= 20%

d. $5.40 is what percent of $4.50:

[tex]= \frac{5.40}{4.50}[/tex]×100%
= 120%

e. $8.40 is what percent of $28:

[tex]= \frac{8.40}{28}[/tex]× 100%
= 30%

f. 56% of what number is $21.84:

=[tex]\frac{56}{100}[/tex]× number = $21.84

∴ Number = [tex]\frac{100}{56}[/tex]×$21.84

                 = $39

g. $495 is 55% of what number:

= $495 = [tex]\frac{55}{100}[/tex]× Number

∴Number = [tex]\frac{100}{55}[/tex]×($495)

                 = $900

h. 120 is what percent of 400:

= [tex]\frac{120}{400}[/tex]×100%
= 30%

i. 4% of 975 is what number:

= [tex]\frac{4}{100}[/tex]×975

= 39

The correct answer for given dilation will be A and D i.e. Point P is midpoint of AA' and XY⊥AA'.

What precisely is dilation?

Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit. This method is used in photography, arts and crafts, and logo design, among other things. In geometry, there are four basic types of transformations. These are their names:

Properties of Rotation, Translation, Reflection, and Resizing

Dilation properties

The following are some features of shapes that remain constant with dilation changes:

Now,

As The image of A is made on line XY and the image will be A'

then XY⊥AA' because line formed between images is always perpendicular to the plane it is formed on and

P is the midpoint of AA' because we know that AP and A'P are same in a image formation.

Hence,

           Point P is midpoint of AA' and XY⊥AA'.

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Answer:

x = 5/2

y = 1/2

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 6y = 7x + 2y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 4x - 7x = 2y + 6y[/tex]

[tex]\qquad \sf  \dashrightarrow \: 8y = - 3x[/tex]

[tex]\qquad \sf  \dashrightarrow \: y = - \dfrac{3}{8} x[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{y}{x} = - \dfrac{3}{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: {y}:{x} = - {3}:{8} [/tex]

That's our required ratio ~

The value equivalent to the expression is (2)√6 and option B is the correct answer.

Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.

the quantities that are multiplied to produce new quantities. For instance, the factors of 15 are 3 and 5, or 3 + 5 = 15.

The given expression is √24.

Find the prime factorization of 24:

2 | 24

2 | 12

2 | 6

3 | 3

  | 1

Thus, √24 can be written as:

√24 = √(2)²(2)3

√24 = (2)√6

Hence, the value equivalent to the expression is (2)√6 and option B is the correct answer.

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The two pieces relate to the number of minutes used, since there's the 400-minute limit.

Piece #1: When you use less than or equal to 400 minutes:

Cost calculation: $47.35 + $13.94 = $61.29

Piece #2: When you use more than 400 minutes:

Cost calculation: $47.35 + $13.94 + $0.60(x-400)

The x-400 piece is because you're only charged the $0.60/minute beyond the 400 minutes, so 401 minutes needs just 1 minute of extra charge

Cost calculation cleaned up: 61.29 + 0.60x - 240 = 0.6x - 178.71

Now it looks weird to have that -178.71, but keep in mind that this is only used if x > 400.

[tex]C(x) = \left \{ {{61.29 ~~~~~~~~~~~~~~ \text{ if } ~0 \leq x\leq 400} \atop {0.6x - 178.71~~~~ \text{ if } x > 400} \right.[/tex]

Your system might not require the "0≤x", but it technically should be there.

Answer: 8

Step-by-step explanation:  9 x 8 = 72

a) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05), which equals £630.

b) The expression showing the amount of money in the savings accounts compounded at 5% per annum after one year is 600 (1 + 0.05)^2, which equals £661.50.

A mathematical expression combines constants, numbers, variables, and values with mathematical operations without adding the equation symbol (=).

When the equation symbol is added to mathematical expressions, they become an equation.

In this situation, the compound interest final amount is depicted like an exponential growth function as follows:

f(x) = a(1+r)ˣ

f(x) = exponential growth function

a = initial amount

r = growth rate

x = number of time intervals

Initial amount = £600

Growth rate = 5% or 0.05

x = 1 or 2 years.

f(x) = 600 (1.05)^x

Thus, if $600 is compounded at 5% yearly for 1 or 2 years, the mathematical expressions showing the value of the account are 600 (1 + 0.05) and 600 (1 + 0.05)^2, respectively.

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The given triangles can be classified based on their sides and angles as:

1. Isosceles, acute triangle

2. Scalene, right triangle

3. Scalene, obtuse triangle

4 Equilateral

5. Isosceles, right triangle

6. Scalene, acute triangle

7. Equilateral, acute triangle

8. Isosceles, obtuse triangle

Triangles can be classified by both their sides and their angles.

Classification by sides:

Classification by angles:

Thus, using the sides or angles of the given triangles, they are classified as follows:

1. Isosceles, acute triangle

2. Scalene, right triangle

3. Scalene, obtuse triangle

4 Equilateral

5. Isosceles, right triangle

6. Scalene, acute triangle

7. Equilateral, acute triangle

8. Isosceles, obtuse triangle

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The circumference of the circle is 110 m.

Let us assume that the wire has been cut into two equal halves thus the radius of the circle would be 35 m/2 = 17.5 m

Then;

C = 2πr

C = circumference

r = radius

"pi" is a mathematical constant approximately equal to 3.14 and "r" is the radius of the circle. If the diameter of the circle is known, the radius can be calculated by dividing the diameter by 2.

C = 2 * 3.142 * 17.5

C = 110 m as we can see here

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1. The plane travelled a distance of 471.239 ft

2. The plane would travel further by 6283.185 ft

What is circumference?

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

If you move along a full circle of a radius 'r', the distance covered by you is equal to [tex]2\pi r[/tex]

Part 1:

Given that, Jack's aeroplane travels in a circle of a cord of length 15ft for 5 times

The total distance travelled by plane is [tex]15*2\pi *15[/tex]

[tex]=150\pi[/tex]

= 471.239 ft

Part 2:

Given that, Jack flew his aeroplane 100 times with a cord of 50 ft.

The total distance covered by the plane is 100 * (2*50*[tex]\pi[/tex])

If he increases the length by 10 ft, The cord will now be 60 ft.

The total distance it would cover then is 100 * (2*60*[tex]\pi[/tex])

Now,

100 * (2*60*[tex]\pi[/tex]) - 100 * (2*50*[tex]\pi[/tex])

= 100 * (2*(60-50))*[tex]\pi[/tex])

= 100 * 2 * 10 * [tex]\pi[/tex]

= 2000 * [tex]\pi[/tex]

= 6283.185 ft

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Answer:s

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the distance between a line and a point, we need to find the perpendicular distance from the point to the line. Here's the step-by-step process:

Find the equation of the line perpendicular to ℓ that passes through point F(-1, 7): Since the slope of line ℓ is -1, the slope of the perpendicular line will be the negative reciprocal of -1, which is 1. To find the equation of the line, we need a point and the slope. Point F(-1, 7) will be used, and the slope is 1.

Using the point-slope form of a line, we can write the equation of the perpendicular line passing through point F as: y - 7 = 1(x + 1). Simplifying, we get: y = x + 8.

To find the point of intersection between the two lines, we can substitute the equation of line ℓ into the equation of the perpendicular line:

-x + 4 = x + 8

Solving for x, we get x = 6. Substituting x = 6 into the equation of line ℓ, we get:

y = -6 + 4 = -2

So, the point of intersection between the two lines is (6, -2).

To find the distance between the point F and the line ℓ, we can use the distance formula:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the point F(-1, 7) and (x2, y2) is the point of intersection (6, -2).

So, substituting the values into the formula:

distance = √((6 - (-1))^2 + ((-2) - 7)^2) = √((7)^2 + (9)^2) = √(49 + 81) = √(130) = approximately 11.3

Therefore, the distance between the line ℓ and point F is approximately 11.3 units.

The required piecewise linear relations are f(x) = 4 if [0, 2), and f(x) = -2x + 8 if [2, 4).

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

The graph is given in the question, as shown

f(x) = 2x + 4 if [-2, 0]

This the sub-function define between the interval [-2, 0].

f(x) = 4 if [0, 2)

This the sub-function define between the interval [0, 2).

f(x) = -2x + 8 if [2, 4)

This the sub-function define between the interval [2, 4).

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The end behavior of the given fucntion is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].

End behavior of a equation is defined as behavior of graph of the function at the ends of the x-axis.

Given, [tex]4x^{5} +1[/tex].

We have to find the end behavior of the graph.

The corresponding graphical representation is given below:

From the graph it is clearly known that as,

Value of x increases ⇒Value of y decreases.

That is x approaches positive infinity and y approaches negative infinity.

i.e., [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex]

Hence, the end behavior of the given equation is [tex]x\rightarrow \infty , y\rightarrow-\infty\\x\rightarrow-\infty, y\rightarrow\infty[/tex].

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Example: Add 1/4 + 2/4

Solution: Let us add these fractions using the following steps.

Step 1: Check if the denominators are the same. (Here, the denominators are the same, so we move to the next step)

Step 2: Add the numerators and place the sum over the common denominator. This means (1 + 2)/4 = 3/4

Step 3: Simplify the fraction to its lowest form, if needed. Here, it is not needed. So, the sum of the given fractions is, 1/4 + 2/4 = 3/4

Answer: x=0.545455

Step-by-step explanation:

add 216 to both sides

divided both sides by 1331

take cube root

The sample standard deviation weight of the 50 candies is, 0.07 grams.

The amount of variation or dispersion in a set of data values is measured by standard deviation. A statistical calculation is used to determine how far the values vary from the mean (average) value. While a high standard deviation suggests that the data values are more dispersed, a low standard deviation suggests that the data values tend to be close to the mean.

To find the sample standard deviation weight,

we can use the formula:

[tex]s = \sqrt{((1/(n-1))} \sum((x - \bar x)^{2} ))[/tex]

where n is the sample size, x is the weight of each candy, [tex]\bar x[/tex] is the sample mean weight, and sum() means to add up the values.

We can first find the sample mean weight:

[tex]\bar x[/tex]= (0.98 + 0.85 + 0.92 + 0.98 + 0.71 + 0.88 + 0.86 + 0.75 + 0.85 + 0.85 + 0.86 + 0.78 + 0.75 + 0.75 + 0.74 + 0.82 + 0.85 + 0.91 + 0.78 + 0.72 + 0.81 + 0.81 + 0.81 + 0.84 + 0.87 + 0.85 + 0.89 + 0.77 + 0.85 + 0.97 + 0.74 + 0.89 + 0.82 + 0.86 + 0.82 + 0.84 + 0.91 + 0.87 + 0.94 + 0.85 + 0.71 + 0.83 + 0.87 + 0.94 + 0.81 + 0.81 + 0.78 + 0.77 + 0.85) / 50

[tex]\bar x[/tex] = 0.8456

Next, we can calculate the sample standard deviation:

s = √((1/(50-1)) x ((0.98-0.8456)² + (0.85-0.8456)² + ... + (0.77-0.8456)² + (0.85-0.8456)²))

s = sqrt(0.0045916)

s = 0.0678

Rounding to two decimal places, the sample standard deviation weight is 0.07 grams.

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Answer:

Step-by-step explanation:

The frequency of a cosine function is related to the number of cycles that the function completes in a unit interval (usually in 2π radians).

The frequency of a cosine function with the form f(x) = A * cos(Bx + C) is given by B/(2π), where A, B, and C are constants.

For the function f(x) = 9cos(4πx) + 10, the frequency is given by 4π / (2π) = 2 cycles per unit interval.

So, the frequency of the function f(x) = 9cos(4πx) + 10 is 2 cycles per unit interval.

On solving the provided question we can say that the net change will be 17 and average rate of change = 17/1 = 17.

The subject οf mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund.

The term "functiοn" refers to the relationship between a set of inputs, each of which has an associated output. A cοnnection between inputs and outputs in which each input leads to a single, distinct result is known as a functiοn.

Each function is given a dοmain and a codomain, or scope. Usually, f is used to denote functiοns (x). input is an x. There are fοur main types of functions accessible. based οn the following factors: οn functions, one-to-one functions, many-tο-one functions, inside functiοns, and on functions.

The functiοn will be

h(4)=2(4²)-4

=32-4

=28

h(5)=2(5²)-5

=50-5

=45

Net change is 45-28 = 17

average rate of change = 17/1 = 17

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Step-by-step explanation:

you have to be careful when typing questions and particularly formulae and expressions here. automatic text conversion has the habit of transforming e.g. fractions into one line divisions without any brackets.

what your wrote here :

575,000/1 + 4000e^-T = 575,000 + 4000e^-T

that cannot be the function.

I am sure it must be

F(T) = 575,000/(1 + 4000e^-T)

right ?

I am basing the rest of my answer on that assumption.

how many people became ill, when the outbreak began ? that means T = 0.

F(0) = 575,000/(1 + 4000e^-0) =

= 575,000/(1 + 4000×1) =

= 575,000/(4001) = 143.7140715... ≈ 144 people

6 weeks after the outbreak

F(6) = 575,000/(1 + 4000e^-6) =

= 575,000/(1 + 4000/(e^6)) =

= 575,000/(1 + 9.915008707...) =

= 575,000/10.915008707... =

= 52,679.75642... ≈ 52,680 people

limit t -> infinity

F(infinity) = 575,000/(1 + 4000e^-infinity) =

= 575,000/(1 + 4000/(e^infinity)) =

= 575,000/(1 + 0) = 575,000 people

Based on the rating information of 10.2, a total of 1,800,000 households watched the show that week is 18360000 household.

An evaluation of something's quality or appeal is given a rating. a 10 out of 10 value-for-money rating, as an illustration. The president's standing among the public is at its lowest point since assuming office.

Position is synonymous with ranking, evaluation, appraisal, and categorisation. Additional Ratings

Since 1 rating point is given = 1,800,000

Rating point = 1,800,000 household

Rating point = 10.2 × 1,800,000 household.

Rating point =18360000 household.

Therefore, correct to state that the number of households that watched the show that week are 18360000 household.

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The equation which correctly represents the sentence in discuss as required is; n + 328 = 13.

It follows from the task content that the equation which correctly represents the sentence given in the task content is to be determined.

The word phrase; n and 328 more can be represented as; n + 328.

Therefore, n and 328 more is the same as 13 can be represented as; n + 328 = 13.

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answer c)

cross x  at x = -2, x = 3, and x = 1

the square root tells us that it bounces off that location rather than intercepting

Answer:

D

Step-by-step explanation:

Front

5x4 = 20

Back

5x4 = 20

Top

5x8 = 40

Bottom

5x8 = 40

Right side

8x4 = 32

Left side

8x4 = 32

Add all the sides

20 + 20 + 40 + 40 + 32 +32 = 184