-1) cm 23 The diagram shows triangle POR P 4.2 cm 1.6 cm PQ = 1.6 cm Given that angle PQR is obtuse, work out the area of triangle PQR Give your answer correct to 3 significant figures. PR= = 4.2 cm Q 18° R Angle PRO = 18° Diagram NOT accurately drawn​

The area of the circle is 78.5m² And when the radius is doubled, the area will be 314m².

The ratio of the larger circle to the smaller circle is 4 : 1

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area is measured in squared units.

The area of a circle is expressed as :

A = πr²

A = 3.14 × 5²

A = 3.14 × 25

A = 78.5m²

When the radius is doubled, i.e

r = 5×2 = 10m

A = πr²

A = 3.14 × 100

A = 314m²

Therefore the area of the new circle is 314m²

The ratio of the area of the larger circle to the area of the smaller circle is ;

314/78.5 = 4/1 = 4 : 1

therefore the ratio of the larger circle to the smaller circle is 4 : 1

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Assuming the trend continues, the next 12 animals will include 4 sheep.

Number is a mathematical concept that represents a quantity or amount. It is usually used to identify a specific value or set of values that can be used for calculation and measurement. Numbers are used in many different fields, including mathematics, science, engineering, and economics. They help us to keep track of quantity and count objects, measure distances and time, and even help to solve problems. Numbers are an essential part of our everyday lives and are essential for understanding the world around us.

This is calculated by taking 2 sheep from the initial group of 8 animals and then multiplying that number by the additional 12 animals for a total of 4 sheep.

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Therefore, the z-score of a data value x = 21 is 0.

Answer: 0.

Data are pieces of information that have undergone modifications to make them transferable or computer-processable. For usage with modern computers and communication networks, data is information that has been converted into binary digital form. The topic of the data is admissible in both its singular and plural variants.

To find the z-score of a data value x, we use the formula:

z = (x - μ) / σ

where:

x is the data value

μ is the mean

σ is the standard deviation

In this case, we are given the mean μ = 21 and the standard deviation σ = 1.2. The data value x is also equal to 21.

Substituting the values into the formula, we get:

z = (21 - 21) / 1.2 = 0 / 1.2 = 0

Therefore, the z-score of a data value x = 21 is 0.

Answer: 0.

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Therefore , the solution of the given problem of area comes out to be

option B 864 sq. centimetres is the correct response.

The amount of area it takes to cover the outside is a good indicator of its overall size. When calculating a trapezoidal shape surface, the immediate environs are taken into account. The surface area of something determines its overall measurements. The internal water capacity of a cuboid is the sum of the limits for each of its six rectangular edges. Utilize the following technique to determine the box's dimensions: The area is the same in 2lh, 2lw, but also 2hw (SA). The area is represented by the adaptable shape's face.

Here,

The following algorithm determines a cube's surface area:

=> SA = 6s²

where s represents the cube's edge lengths.

=> S =12 cm in this instance.

The result of substituting into the algorithm is:

=> SA = 6 (12)²

=> 6 (144 )²

=> 864 square centimetres.

The cube's surface size is 864 sq. cm as a result.

B) 864 sq. centimetres is the correct response.

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Answer: I believe the answer would be 53.85%

Step-by-step explanation:

6+8=14

14+7+5=26

14/26=.53846

Move decimal and round up.

The eighth term of the sequence is 256.

To find the eighth term in the sequence 4, 16, 36, 64, 100, ...., we need to first determine the pattern that generates the sequence.

Looking at the sequence, we notice that;

Therefore, we can see that the nth term of the sequence is equal to n^2 * 2^0, 2^2, 2^2, 2^2, 2^2, 2^2, ...

So, the eighth term of the sequence would be:

8^2 * 2^2 = 64 * 4 = 256

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Answer:

12723.5(cm^2)

Step-by-step explanation:

the area of the circle

S=Tur^2

The sems-circle is s.=1/2 s =1/2Tur^2

The length of the line of sight from the ship to Nicole is approximately 2046.1 feet, rounded to the nearest tenth.

Trigonometry is a branch of mathematics that studies the relationships between triangle sides and angles.

The term trigonometry is derived from the Latin derivative of the Greek words for triangle (trigonon) and measurement (measur) (metron).

Trigonometry is a branch of mathematics concerned with angle relationships and length ratios.

Let's assume that the distance between Nicole's window and Nick's position is "x" feet. Then, we can use trigonometry to set up the following equation:

tan(5) = (175 + 10) / x

Simplifying and solving for "x", we get:

x = (185) / tan(5)

x ≈ 2046.1 feet

Therefore, the length of the line of sight from the ship to Nicole is approximately 2046.1 feet, rounded to the nearest tenth.

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Answer:  28/9  (choice D)

Explanation:

You don't need a calculator for this.

Each fraction involves 9 in the denominator. The numerators are the only thing that change. Let x be the numerator.

x/9 = 3.1 can be estimated to x/9 = 3 and that solves to x = 27

The numerator is around 27.

Choices A,B,C are ruled out since the numerators are smaller than 28. The only thing left is choice D.

You can use a calculator or long division to confirm that 28/9 = 3.1111... where the '1's go on forever.

The simplified forms are;

1) 2x[tex]y^2[/tex]

2) [tex]x^2y^3[/tex]

3) [tex]2xy^3z^5[/tex]

4)[tex]5p^2q[/tex]

5) [tex]5a^3b^5c^3/2[/tex]

6)[tex]4x^4y^5/3z^3[/tex]

7)[tex]7a^3b^3/2[/tex]

8) [tex]x^2y^3z^6[/tex]

9)-4a

10) [tex]3xy^5z^13/2[/tex]

To simplify a surd, you need to find the largest perfect square factor that divides the number under the square root symbol.

We can see that the surds here can be reduced to the simplest forms when we apply the basics of the rules of exponent which have been used to show the simplified forms as shown here.

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The roots of the function y = 2x^3+ 8x^2 - 32x - 128, considering it's graph, are given as follows:

The roots of a function can be obtained from the graph of the function, as they also represent the x-intercepts of the function.

The x-intercepts of a function are given by the values of x at which the graph of the function crosses the x-axis, which is the horizontal axis.

The multiplicities of each root are given as follows:

From the graph given by the image presented at the end of the answer, the roots of the function are given as follows:

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the answer is 42 will be 42 because i answer that before

The factoring of the polynomial expression is presented as follows;

Part A; The greatest common factor is; 5

Part B; 15·x² + 25·x - 10 = 5·(3·x - 1)·(x + 2)

Part C; 5 × (3·x - 1) × (x + 2) = 15·x² + 25·x - 10

A polynomial is an expression containing algebraic terms that consists of variables and coefficients, joined together by operators.

The expression is 15·x² + 25·x - 10

Part A; The greatest common factor of the polynomial is the value that divides each of the terms of the polynomial, therefore;

The greatest common factor of 15·x² + 25·x - 10 is obtained as follows;

The largest number that divides each term of he polynomial expression is 5

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2)

Part B; The expression, 15·x² + 25·x - 10, can be factored as follows;

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2)

3·x² + 5·x - 2 = 3·x² + 6·x - x - 2

3·x² + 6·x - x - 2 = 3·x·(x + 2) - 1·(x + 2) = (3·x - 1)·(x + 2)

3·x² + 5·x - 2  = (3·x - 1)·(x + 2)

15·x² + 25·x - 10 = 5·(3·x² + 5·x - 2) = 5·(3·x - 1)·(x + 2)

Factoring the expression completely, we get;

15·x² + 25·x - 10 = 5·(3·x - 1)·(x + 2)

Part C: The factoring of the expression, 15·x² + 25·x - 10, can be checked as follows;

The factored expression is; 5·(3·x - 1)·(x + 2)

5 × (3·x - 1) × (x + 2) = 5 × (3·x² + 6·x - x - 2) = 5 × (3·x² + 5·x - 2)

5 × (3·x² + 5·x - 2) = 15·x² + 25·x - 10, which is the original expression

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The product of any two terms in the sequence is also a term in the sequence has been proved.

What is a sequence?

A series is an ordered collection of numbers (or other things like geometric objects), and it typically has a particular structure or function. Sequences can be A series is an ordered collection of numbers (or other things like geometric objects), and it typically has a particular structure or function. Sequences can be either infinite or illimitable in length.either infinite or illimitable in length.

Suppose there is a sequence 3, 9, 27, 81.

Taking product of first two numbers, we get

3 × 9 = 27

We can see that the term 27 is present in the sequence.

This represents that in a sequence, the product of two numbers will be the term in the sequence.

Hence, the product of any two terms in the sequence is also a term in the sequence.

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The requried it cannot conclude whether the variable is normally distributed or skewed based on the given data. None of the options are correct.

The statistic is the study of mathematics that deals with relations between comprehensive data.

It is not possible to determine if the variable "footprint" is normally distributed or skewed based on the given data.

The data represents the measurements of shoe prints for 5 males, but it is not enough to determine the distribution of the variable without additional information such as a larger sample size, the mean and standard deviation of the variable, or a histogram or frequency plot of the data.

Therefore, we cannot conclude whether the variable is normally distributed or skewed based on the given data.

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Answer:

If Input is 150, then Output is 25.

Step-by-step explanation:

The rule is to divide 6.

IF: You input 72 & the output is 12:

72/6 = 12

IF: You input 54 & the output is 9:

54/6 = 9

IF: You input 120 & the output is 20:

120/6 = 20

etc.

Therefore, you are dividing 6 each time. The given input is 150. Divide 150 with 6 to find your output:

150/6 = 25

25 would be your output.

~

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Answer:

h'(1) = 19

Step-by-step explanation:

if h(x) = f(x) + g(x), and f(x) = x³ and g(x) = 4x⁴,

then h(x) = (x³) + (4x⁴)

h(x) = x³ + 4x⁴

h'(x) is the derivative of h(x), which = 3x² + 16x³. Thus, h'(1) = 3(1)² + 16(1)³ = 19

The point after 30, 000 km will they first have to change the oil, rotate the tires and replace the wiper blades all at once.

Arithmetic Progression (AP) is a numerical series in which the difference between any two consecutive numbers is a constant value. Arithmetic Sequence is another name for it.

The First term is an "oil change" with a step d = 3000 km;

and, the second term is tire rotation = 10, 000 Km

and, the third term is replacement of wiper blades = 15, 000 Km

Now, we know from the formula of Arithmetic Progression is

= + d(n-1)

So, 15,000 = 10,000 + 10,000 (n-1)

15, 000 = 10,000 + 10, 000n- 10,000

150000 = 10000n

n = 1.5

This means that at the point 15 000 km and all three progressions will not intersect.

Now, We take the second term of the progression as  = 30,000 km

So, 30,000 = 10,000 + 10,000 (n-1)

20,000 = 10,000n - 10,000

30, 000 = 10,000n

n= 3

Similarly, check this intersection point for the first progression with a step of d = 3 000 km we get n =9.

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The complete question is :-

Peter's parents follow a regular schedule for taking care of the car. They change the plugs every 30 000km, rotate the tyres every 10 000km and replace the brake pads blades every 15 000km. After how many kilometers will they have to change the plugs, rotate the tyres and replace the brake pads all at once for the first time?

As a result, the variable x is 9 which is the correct answer.

By combining two expressions, the equation generates a mathematical expression, similar to an expression. A typical equation would have been 3x - 5 = 16. The solution to this equation reveals that the value assigned to the variable x is 7.

We'll refer to the number we're looking for as "x" for the time being.

The problem states that the result of "x" and -6.5 is -58.5:

-6.5x = -58.5

We can divide all of the equation's components by -6.5 to find the answer to "x":

x = -58.5 ÷ -6.5

x = 9

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Answer:

6

Step-by-step explanation:

radius is 1/2 the diamiter

Answer:

Step-by-step explanation:

Answer: 6 inches.

Explanation:

Since the radius is 3 inches, the diameter will be twice the size of the radius. The radius is half the width of a circular object. The diameter is the full width. Therefore Omar's lollipop has a diameter of 6 inches.

The vοlume οf the pyramid is 64 cubic centimeters (cm^3).

The vοlume οf a pyramid is given by the fοrmula V = (1/3) Bh, where B is the area οf the base and h is the height.

In this case, the base οf the pyramid is a square with side length s = 8 cm, sο its area is [tex]B = s^2 = 8^2 = 64 cm^2[/tex].

The height οf the pyramid is h = 3 cm.

Therefοre, the vοlume οf the pyramid is:

[tex]V = (1/3) Bh = (1/3) (64 cm^2) (3 cm) = 64 cm^3[/tex]

Hence, the vοlume οf the pyramid is 64 cubic centimetres (cm^3).

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The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Temperature is a unit of hotness and coldness that can be described in terms of any number of arbitrary scales. It also represents the direction wherein heat energy will naturally flow, from either a hotter (i.e., higher temperature) body to a colder body.

Temperature is not the same as the energy of such a thermodynamic system; for instance, an iceberg has a significantly larger total heat energy than a match, despite the fact that a match is burning at a significantly higher temperature. The linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

Therefore, the linear model would be a reasonable way to predict the temperature as temperature determines the number of ice cream that would be sold.

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The first term in this sequence is 7 and the common ratio is -3, so the formula for the 7th term, a7, can be written as a7 = 7(-3)6.7 multiplied by -18 is equal to -126, so the 7th term in this geometric sequence is -126.

Geometric sequences are used to represent growth and decay. The common ratio determines whether the sequence is increasing (if r > 1) or decreasing (if 0 < r < 1). When the common ratio is a whole number, such as 2 or 3, the terms in the sequence are whole numbers as well.

Geometric sequences are sequences where each term is found by multiplying the previous term by a fixed number, called the common ratio. In this case, the first term is 7 and the common ratio is -3, so each term is found by multiplying the previous term by -3. This means that the second term is 7(-3) = -21, the third term is -21(-3) = 63, the fourth term is -63(-3) = -189, and so on. By using the formula a7 = ar6 and substituting in the first term and common ratio, the 7th term can be calculated as -126.

The 7th term of a geometric sequence is calculated by using the formula a7 = ar6, where a is the first term and r is the common ratio. The first term in this sequence is 7 and the common ratio is -3, so the formula for the 7th term, a7, can be written as a7 = 7(-3)6. To calculate this, the exponent 6 must be multiplied by -3, giving -18. 7 multiplied by -18 is equal to -126, so the 7th term in this geometric sequence is -126.

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Answer:

Step-by-step explanation:

A standard deck of cards has 52 cards, including 4 queens. If you are certain to get a queen when selecting 49 cards from a shuffled deck, it means that one of those 49 cards must be a queen, and the remaining 48 cards can be any of the remaining 48 cards in the deck.

So, the probability of selecting a queen from a shuffled deck of cards is:

probability = number of favorable outcomes / total number of possible outcomes

Since we are certain to get a queen, the number of favorable outcomes is 4 (the number of queens in the deck), and the total number of possible outcomes is 49 (the number of cards selected from the deck).

Therefore, the probability of selecting a queen is:

probability = 4/49

This fraction cannot be simplified any further. Since the probability value is between 0 and 1 inclusive, we can express the indicated degree of likelihood as a probability value of approximately 0.0816.

Answer:

Step-by-step explanation:

The statement "65% of 150 students" could represent the estimate that 100 students attended the school's play.

To see this, we can calculate 65% of 150:

0.65 x 150 = 97.5

Since 97.5 is close to 100, it is possible that the estimate was based on 65% of 150 students.

The other statements do not come close to 100, so they are not likely to represent the estimate that 100 students attended the school's play.

Answer:

12 lbs of food per bag

Step-by-step explanation:

To distribute cat food equally into a certain number of bags, we can divide the amount of cat food by the number of bags to get how much food should go in each bag.

60 lbs of food ÷ 5 bags = 12 lbs of food per bag

Answer:

Rounding 395,621 to the nearest ten thousand is 400,000.

Step-by-step explanation:

Answer:

the nearest 10 thousand is 400,000.

Step-by-step explanation:

hope this helps!

If a water sample shows 0.37 grams of some trace element for every cubic centimeter of water.  Terrence has collected 841.51 grams of the trace element.

First, we need to find the volume of the cylinder container:

Volume of cylinder = π(radius)² height)

= π(7.9cm)²(11.6cm)

= 2,274.37 cm³

Amount of trace element = concentration x volume

= 0.37 grams/cm³ x  2,274.37 cm²

= 841. 51 grams

Therefore, Terrence has collected  841.51 grams of the trace element.

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(I) Break even sales: S = 40,000

(ii) Sales needed to earn a profit  Rs 6000 per period: S = Rs. 45,000.

The formula for the Break even sales is:

(S‐v) /S= F + P  

s x P/V Ratio = Contribution

First calculate P/V Ratio:

P/V Ratio = Contribution/sales x 100

P/V Ratio = (40‐24)/40 x 100

P/V Ratio= 16/40 x 100

P/V Ratio = 40%

(I) Break even sales  

S x P/V Ratio = Fixed Cost

For break even sales, deposition equals fixed cost.

Thus,

Put the values:

S x 40/100 = 16,000

S = 16,000 x 100 / 40

S = 40,000

S = 1000 units

(II) Sales to gain a profit of Rs. 6,000

S x P/V Ratio = F + P

Put the values:

S x 40/100 = 16000 + 2000

S = 18,000 x 100/40  

S = Rs. 45,000

S =  1125 units

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