1. Write down the first five multiples of:
a) 3
b) 9
c) 14

Answer:

Step-by-step explanation:

The statement "85% of 'a' is 'b'" can be represented mathematically as:

0.85a = b

This means that 'b' is 85% of 'a'.

To answer the question:

a = b/0.85

So, a is equal to 'b' divided by 0.85.

Therefore, the correct option is (a) a=b.

The solutions of the function as required to be determined is; x = 8 or x = -4.

As evident in the task content; the given equation are;

f(x)=9x² - 5x - 58 and

g(x) = 7x² + 3x + 6.

The solution of the equation can be determined as follows;

9x² - 5x - 58 = 7x² + 3x + 6.

2x² -8x - 64 = 0

x² - 4x - 32 = 0

(x - 8) (x + 4) = 0

x = 8 Or x = -4.

Ultimately, the solutions of the equation are; x = 8 or x = -4.

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The net that represents this solid figure is diagram D.

A solid figure is a three-dimensional geometric shape that has length, width, and height. It is also called a three-dimensional or 3D figure. Some examples of solid figures include cubes, spheres, cylinders, cones, and pyramids.

Solid figures are different from two-dimensional shapes, which only have length and width. In contrast, solid figures have depth or thickness, making them more complex and interesting.

Solid figures can be classified based on their properties, such as the number of faces, vertices, and edges they have. For example, a cube has six faces, eight vertices, and 12 edges, while a sphere has no faces, vertices, or edges.

In this case, it has 2 squares and 4 rectangles. The appropriate diagram is D

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Using geometry, we can find that the length of the line segment AC as per the distance between two points is= 18 ft.

What are line segments?

In geometry, a line segment's borders are determined by two distinct points on the line. Any portion of a line that connects two places is referred to as a line segment.

A segment has an endpoint, whereas a line doesn't.

What are some examples of line segments in the real world?

a scale, a ruler, a stick, and a boundary line.

Thus, the length of the line segment AC is = 18ft.

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Answer:

1483 pedro 1203 ricky

Step-by-step explanation:

1203+1483 = 2686

Answer:

4

Choice D

Step-by-step explanation:

[tex]\mathrm{Periodicity\:of\:}a\cdot \cos \left(bx\:+\:c\right)\:+\:d=\dfrac{\mathrm{periodicity\:of}\:\cos \left(x\right)}{|b|}[/tex]

[tex]\mathrm{Periodicity\:of\:}\cos \left(x\right)\:\mathrm{is}\:2\pi[/tex]

answer: 10

y = |2| + 8

y = 2 + 8

y = 10

The range of lengths Brett can use for the third piece of steel is 4 in. < x < 20 in.

The Triangle is a polygon with three line segments as its boundaries. That is the tiniest polygon imaginable. Three vertices, three internal angles, and three sides make up a triangle.

The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for every triangle, the sum of the lengths of the first two sides is always higher than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.

Using the triangle inequality theorem we have:

8 + 12 > x

x + 8 > 12

x + 12 > 8

20 > x

x > 4

x > -4

Therefore, the range of lengths Brett can use for the third piece of steel is 4 in. < x < 20 in.

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Answer:

146 and 1

Step-by-step explanation:

146+1=147

The answers to the questions are in the picture

Answer:

The principal square root of a non-negative real number is the positive square root. For example, the principal square root of 25 is 5, since 5^2 = 25.

When solving radical polynomials, the principal square root is used because it is the most commonly used square root. In many contexts, including mathematical and scientific calculations, the principal square root is the default choice unless otherwise specified. Additionally, when working with radical expressions, we often simplify expressions by taking the principal square root, as it can help us to simplify calculations and express answers more clearly.

[tex]101 - 99 = 2[/tex]

101 → 200

99 → 100

[tex]200 - 100 = 100[/tex]

⇒ the numbers could be: 99 and 101

other pairs of numbers: (199,201), (299,301) ...

The inequality x ≤ 3 indicates how many different bicycle outfits she can purchase.

She has $560 to spend at a bike shop on new accessories and clothing for riding.

For $425.05. she spends on a brand-new bicycle.

She spends $15.19 for each of four bicycle reflectors and $15.79 on a pair of cycling gloves.

She intends to use all or part of the remaining funds to purchase new bicycle clothing at $29.20 each.

The disparity that can be used to calculate how many garments she can purchase for her budget is as follows:

let

x = the number of garments

Therefore,

425.05 + 15.19(4) + 15.79 + 29.20x ≤ 560

425.05 + 60.76 + 15.79 + 29.20x ≤ 560

29.20x ≤ 560 - 425.05 - 60.76 - 15.79

29.20x ≤ 58.4

Divide the difference between the two sides by 29.20.

x ≤ 58.4 / 19.20

x ≤ 3.04166666667

x ≤ 3

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Answer:

D) PR and CK form right angles

Step-by-step explanation:

⟂ is the symbol for a perpendicular, so it is a perpendicular bisector.

- Perpendicular bisectors divide an angle into 2 90° angles.

Answer:

y = - 9x + 6

Step-by-step explanation:

the equation of a linear function in slope- intercept function is

y = mx + c ( m is the slope and c the y- intercept )

given slope = - 9 and f(0) = 6 , that is the point (0, 6 ) , then c = 6

y = - 9x + 6 ← linear function

a) The percentage of adults in the USA that have stage 2 high blood pressure is; 0.27%

b) The number of people that you will expect to have BP greater than 160 is; 54

a) if x is systolic blood pressure, then want to find probability that x ≥ 160.

The formula for z-score is;

z = (x - mean)/standard deviation

Thus;

z = (x - 119)/18

This is normally distributed with mean 0 and standard deviation 1

Transform x to z:

P(x > 160) = P(z > (160 - 119)/18)

= P(z > 2.78)

= P(z < -2.78)

= 0.0027 (from standard normal distribution table, which 0.27%.)

b)  Since probability of BP > 160 is 0.027.  

Then out of 2000 people, then 2000 * 0.027 = 54 people would have BP > 160.

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For the given function the intercepts are:

x-intercept: x = -4

y-intercept: y = 12.

Here we have a table that defines a function, and we want to find the intercepts of said function.

We can assume it is linear, then the slope of the function will be given by:

a = (9 - 3)/(-1 + 3) = 6/2 = 3

The linear function is like:

y = 3x + b

To find the value of b we can replace the values of the last point on the table, x = 2 and y = 18.

18 = 3*2 + b

18 = 6 + b

18 - 6 = b = 12

The linear function is:

y = 3x + 12

The x-intercept is the value of x when y = 0

0 = 3*x + 12

-12 = 3x

-12/3 = x = -4

And the y-intercept is the value of y when x = 0.

y = 3*0 + 12

y = 12

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Paul scοre 64 fοr the mοdel predict fοr 3 h οf hοmewοrk and test scοre tο be 40.

A functiοn is defined as a relatiοnship between a set οf inputs that each have οne οutput. A functiοn is a relatiοnship between inputs in which each input is related tο exactly οne οutput. Every functiοn has a dοmain and a cοdοmain, as well as a range. In general, a functiοn is denοted by f(x), where x is the input. A functiοn's general representatiοn is y = f. (x).

Scοre can be defined as tοtal number which any persοn achieve after dοing any wοrk οr target. Suppοse a Batsman make 100 run it means he scοre 100 fοr his team.

a.  Fοr three hοurs οf study we have that the nοte wοuld be apprοximately:

y = 8x + 4

b. The number 40 means that if yοu dο nοt devοte any study time, then yοu expect the test scοre tο be 40.

y = 8(3) + 40

y = 64

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Step-by-step explanation:

To simplify the expression x^-2y(x^3y^5)^3, we need to perform the operations inside the parentheses first, using the exponent rule that (a^m)^n = a^(mn):

x^-2y(x^3y^5)^3 = x^-2y(x^(33)y^(53)) = x^-2y(x^9y^15)

Next, we can simplify the expression by multiplying the coefficients (numbers) and adding the exponents of x and y, using the product rule that x^mx^n = x^(m+n) and (xy)^m = x^my^m:

x^-2y(x^9y^15) = (1y/x^2)(x^9*y^15) = y^(15+1)x^(9-2) = y^16x^7

Therefore, the simplified form of x^-2y(x^3y^5)^3 is y^16*x^7.

Note that this expression is defined for all values of x and y except for x=0.

The properties used to simplify the expression are given as follows:

In algebra, the combination of like terms refers to the process of simplifying expressions by adding or subtracting terms that have the same variable(s) raised to the same power(s).

In this problem, from step 1 to step 2, on the left side of the equality, all the terms with the variable n and exponent 1 were added, as were the constant terms, hence the like terms were combined.

In Step 4, the variable n was obtained applying the division operation, which is the inverse operation of the multiplication operation in Step 3.

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Answer:

54 square meters

Step-by-step explanation:

Given the scale is 1 centimeter represents 3 meters, to scale the dimensions of the drawing to the dimensions of the actual room, multiply the dimensions of the drawing by 3.

Therefore:

So the dimensions of the actual room are:

The area of a rectangle is the product of its width and length.

Therefore, the area of the actual room is:

The sums, differences, product, and quotient of the functions and their domains are;

f(x) = √(16 - x^2), g(x) = √(x + 3)

f + g = √(16 - x^2) + √(x + 3)

Domain; [-3, 4]

f - g = √(16 - x^2) - √(x + 3)

Domain: [-3, 4]

f × g = √(16 - x^2) × √(x + 3) = √(-x³ - 3·x² + 16·x + 48)

f × g = √(-x³ - 3·x² + 16·x + 48)

Domain; [-3, 4]

f/g = √(16 - x^2)/√(x + 3) = √(16 - x^2)/(x + 3))

f/g = √(16 - x^2)/(x + 3))

Domai; [-3, 4] ∪ [1, 4]

f(x) = √(81 - x^q2), g(x) = √(x² - 16)

f + g = √(81 - x^2) + √(x² - 16)

Domain [-9, -4] ∪ [4, 9]

f - g = √(81 - x^2) - √(x² - 16)

Domain: [-9, -4] ∪ [4, 9]

f × g = √(81 - x^2) × √(x² - 16) = √(-x⁴ + 97·x² - 1296)

f × g = √(-x⁴ + 97·x² - 1296)

Domain: [-9, -4] ∪ [4, 9]

f/g = √(81 - x^2)/√(x² - 16)

Domain: [-9, -4] ∪ [4, 9]

The sum of two functions is obtained by adding the values of the functions at each point.

The sum of two functions is obtained by adding the values of the functions at each point. The domain of the sum is the intersection of the domains of the two functions, In this case, the domain of f + g is [-3, 4]

The difference of two functions is obtained by subtracting the functions values at each point. The domain of the difference is the intersection of the domains of the two functions. In this case, the domain of f - g is [-3, 4]

The product of two functions is obtained by multiplying the values of the functions at each point. The domain of the product of the functions is the domain of the intersection of the domains of the two functions. The domain of f × g is  [-3, 4]

The quotient of two functions is obtained by dividing the values of the functions at each point. The domain of the quotient is the same as the domain of the intersection of two functions, excluding any points where the denominators is zero. The domain of f/g is [-3, -1] ∪ [1, 4].

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Answer:

1.65 pints

Step-by-step explanation:

If Tara used 6.6 pints of white and blue paint combined, and 3/4 of that amount is white paint, then we can find the amount of white paint she used by multiplying 6.6 by 3/4:

6.6 x 3/4 = 4.95

So Tara used 4.95 pints of white paint to paint her bedroom walls.

To find out how much blue paint she used, we can subtract the amount of white paint from the total amount of paint:

6.6 - 4.95 = 1.65

Therefore, Tara used 1.65 pints of blue paint to paint her bedroom walls.

A dice is tossed once,what is the probability that a prime number shows upwards

Volume, it is defined as the space occupied within the boundaries of any three-dimensional solid.

Volume is defined as a capacity occupied or captured by a 3-dimensional solid shape. It is difficult to visualise in any shape, yet it may be compared amongst shapes. For instance, a geometry box has a larger or bigger volume than an eraser placed inside of it. We split the area into equal square units to determine or get the area of any 2-dimensional form.

Cuboid, is a 6-sided solid known as a hexahedron in geometry. Quadrilaterals make up its faces. Cuboid is short for "like a cube".

[tex]Volume\ of \ Cuboid = Length * Breadth * Height[/tex]

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Since an actual mosquito is about 1.6 cm, the scale factor of the diagram is equal to 2.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (actual figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image (actual figure)

Conversion:

1 cm = 10 mm

1.6 cm = 1.6 × 10 = 16 mm.

Substituting the given parameters into the scale factor formula, we have the following;

Scale factor = 32/16

Scale factor = 2.

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Answer:

0.125

Step-by-step explanation:

Answer:

5% of 40 is 2

Step-by-step explanation:

number  = x

25% of x is = 10

25% = 25/100, or 1/4

[tex]\frac{1}{4}x = 10[/tex]

multiply each side by 4

[tex]x = 40[/tex]

5% is 5/100, or 1/20

[tex]\frac{1}{20}x = ?[/tex]

plug-in the known value

[tex]\frac{1}{20}*40 = ?\\\frac{40}{20} = ?\\\frac{4}{2} = ?\\\\? = 2[/tex]

Answer:

I think the answer is D.) 7/8 mile

Step-by-step explanation:

If you make the mixed numbers improper fractions. 2 and 1/8 is 17/8, 1 and 1/4 (2/8) is 10/8, then you subtract the numerators and keep the denomitators the same to get 7/8 mile (sorry if I spelt something wrong)

Answer:

Frequency distributions are visual displays that organize and present frequency counts so that the information can be interpreted more easily.

Step-by-step explanation:

The distribution of a variable is the pattern of frequencies, meaning the set of all possible values and the frequencies associated with these values.

The Venn diagram needed based on the question is given below:

             __________

            /          \

           /     A      \

          /____________\

          \            /

           \   E ∩ F  /

            \_________/

                 B

In the diagram, the set A represents the event of having an adequate supply of material A, and the set B represents the event of having an adequate supply of material B.

The overlap of A and B represents the event of having an adequate supply of both materials.

The set E represents the event of a shortage in material A, and the set F represents the event of a shortage in material B.

The intersection of E and F, denoted by E ∩ F, represents the event of a shortage in both materials.

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