Factorise -75ab² - 15ac
5a(3b - c)

-15b²(3a + c)

-15a(5b² + c)

15a(5b² - c)

A triangle has a base of length 6 cm and an area of less than 12 cm². Which of the following gives the height h of the triangle

h < 4 cm

h < 6cm

h < 12 cm

h < 24 cm

Expand (2x-3)(2x +3)

4x² + 12x + 9

4x² - 12x – 9

4x² - 9

4x² + 9

A woman buys 8 tubers of yam at #200 each and sells them at a profit of 12%. Calculate the selling price.

#192

#1600

#1792

#2000

What is the size of each angle of a regular 15-sided polygon?

78⁰

156⁰

185⁰

200⁰

The height of a boy is t cm. His father is two times his height. Express the height of the father in terms of t.

5t cm

2t cm

t cm

t² cm

Factorise 4am² - 6am

2am(2m – 3)

m²(2a - 3m)

am²(4 - 6a)

2a²m²(2m - 3)

What is the slant height of a cone of height 8cm and base diameter of 12cm?

5 cm

6 cm

8 cm

10 cm

Express 51 x 10⁻⁵ as a decimal number.

0•000051

0•00051

0•0051

0•51

A television costs #54 000. A 12¹/₂% discount is given for cash. What is the cash price ?

# 54 000

# 47 000

# 47 250

# 6 750

Find y-intercept in the graph below



(0, 1)

(0, 5)

(5, 0)

(0, 2)

Simplify - 40pq ÷ (-2)²

-10p

-10q

-10pq

10pq

Express the product of 0•003 and 0•045 in standard form.

3•45 x 10⁵

1•35 x 10⁵

1•35 x 10⁻⁵

1•35 x 10⁻⁴

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Which of these is the three figure bearing of the acute-angle bearing N40⁰W ?

320⁰

310⁰

270⁰

040⁰

The volume of a cylinder is 700π cm³. What is the base diameter of the cylinder if its height is 7 cm ?

6•5 cm

7cm

10 cm

20 cm

What is the LCM of 2x²y, 3xy² and 4x²y ?

16x²y²

12x²y²

12x²y

7xy

Express 636 000 in standard form.

6.36 x 10⁻⁵

6.36 x 10⁻⁴

6.36 x 10⁴

6.36 x 10⁵

A cone and a cylinder have equal volumes and radii. The height of the cone is 12 cm. What is the height of the cylinder?

4 cm

12 cm

36 cm

50 cm

Find the angle measured clockwise between the directions: N and SW

45°

135°

180°

225°

What is the total surface area of a cylinder opened at one end if its height is 20cm and it's diameter is 14cm (π = 3¹/₇)

880 cm²

1034 cm²

1188 cm²

1250 cm²

I think of a number. I then double it. The result is 58. What number did I think of ?

29

20

16

10

RSTU is a quadrilateral as seen below. What is the value of X?



5

10

11

15

​

Answer:

100 square inches

Step-by-step explanation:

20*4=100

Answer:

Step-by-step explanation:

The answer is C because t = 2 so 75x2=150 and 150 + 10= 160.

9514 1404 393

Answer:

  D.  1 : 1

Step-by-step explanation:

The ratio of the two legs in any isosceles triangle is 1 : 1. That is also true of this isosceles right triangle. (You can tell it is isosceles because the acute angles are identical in size.)

The pricing and flowers from both businesses will be the same at 5 flowers and 160 dollars.

Let x be the number of flowers ordered from both shops at the same cost.

For R'U shop,

Total cost = Per flower cost + delivery charges

Total cost = 2*x+150

For Flowers Lobby,

Total cost = Per flower cost + delivery charges

Total cost = 4*x+140

Thus, for the same cost, the value of x will be,

4x+140= 2x+150

2x = 10

x=5

Therefore, for 5 flowers and 160$, the price and the flowers will be equal from both shops.

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Step-by-step explanation:

Since we have given that

Total no. if students= 34

no. of girls = 19

so, percentage of the class are girls is given by

\( \frac{number \: of \: girls}{total \: number \: of \: students} = \frac{19}{34} \times 100 \\ = 55.88 \: percentage\)

The probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is, 0.9192

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 90 inches, and a standard deviation of 14 inches.

z score is given by,

z = (x - μ)/(σ/√n) = (92.8 - 90)/(14/√49) = 2.8/2 = 1.4

The  required probability is,

p(z < 1.4) = 0.9192, by standard normal table.

Hence, the  probability that the mean annual precipitation of a sample of 49 randomly picked years will be less than 92.8 inches is,  0.9192.

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Answer:

\(P(A\ and\ B) = 44\%\)

Step-by-step explanation:

Given

Represents the event as follows:

A = \(Elon\ Musk\) will offer you a \(free\ trip\) into space in the next month\

B = Scientists from \(Area\ 51\) will \(start\ selling\) pet aliens next month

So, we have:

\(P(A) = 41\%\)

\(P(B) = 27\%\)

\(P(A\ or\ B) = 24\%\)

Required

Determine \(P(A\ and\ B)\)

This is calculated as:

\(P(A\ and\ B) = P(A) + P(B) - P(A\ or\ B)\)

So, we have:

\(P(A\ and\ B) = 41\% + 27\% - 24\%\)

\(P(A\ and\ B) = 44\%\)

Answer:

A

Step-by-step explanation:

By adding both the x and y coordinates individually and dividing them by two u get the mid point

Answer:

1/2

Step-by-step explanation:

Let H = the possible outcomes that include flipping heads

Let T = the possible outcomes that include flipping tails

In order to have an outcome of two coins having tails, that means for each outcome, you must have at least two T's.

Therefore, the possible outcomes are:

(H, T, T)

(T, H, T)

(T, T, H)

(T, T, T)

This is 4 possible outcomes, and since we want to find the probability we find the total number of outcomes and make a fraction.

\(4/8 = 1/2\)

There are 8 outcomes, and since 4 work for this scenario, the answer is 1/2.

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The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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there are 11 such valid strings.

To find the recurrence relation, let's consider the possibilities for the last digit of a valid bit string. It can either be 1 or 0. If it's 1, the remaining n-1 digits can be any valid bit string of length n-1. If it's 0, the second-to-last digit must be 1 to avoid having two consecutive 0s. In this case, the remaining n-2 digits can be any valid bit string of length n-2.

Therefore, the total number of valid bit strings of length n can be obtained by summing the number of valid strings of length n-1 (when the last digit is 1) and the number of valid strings of length n-2 (when the last digit is 0). This gives us the recurrence relation F(n) = F(n-1) + F(n-2).

For the initial conditions, we observe that F(1) = 2 because there are two valid bit strings of length 1: 0 and 1. Similarly, F(2) = 3 because there are three valid bit strings of length 2: 01, 10, and 11.

To find the number of valid bit strings of length five, we apply the recurrence relation iteratively. Starting with F(1) = 2 and F(2) = 3, we can compute F(3) = 5, F(4) = 8, and finally F(5) = 13. Therefore, there are 13 valid bit strings of length five.

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Based on the given information "all other things being equal," we can estimate that the traffic will be higher for a dealership in a suburban location compared to a rural location. Therefore, we would estimate a positive number, indicating that the traffic in the suburban location is expected to be higher than in the rural location.

In general, a dealership in a suburban location tends to experience higher traffic compared to a rural location. This estimation is based on several factors. Suburban areas are typically more densely populated and have a higher concentration of residential and commercial activities, leading to increased overall traffic volume.

Additionally, suburban locations often have better transportation infrastructure, including highways, main roads, and public transportation options, which attract more commuters and potential customers to the area.

On the other hand, rural areas are characterized by lower population densities and fewer amenities, resulting in lower levels of traffic. Therefore, the estimate of a positive difference in traffic between a suburban and rural dealership is reasonable.

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The missing length of the given triangle is 28/3 which is equal to 9.3.

The Side-Splitters Theorem:

If BC is drawn parallel to DE and ADE is any triangle, then AB/BD = AC/CE

The parallelogram formed by the line BF and AE demonstrates that this is the case. BCEF

Triangles ABC and BDF are comparable because they have the same angles.

Side AB and Side AC are corresponding to Side BD and Side BF, respectively.

Thus, AB/BD = AC/BF while BF = CE

Hence, AB/BD = AC/CE.

Example:

Then,

28/18 = x / 6

(14/9) * 6 = x

x = 28/3

x = 9.3

Hence, the missing length of the given triangle is 28/3 which is equal to 9.3.

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Answer:

The length of x in the simplest radical form with a rational denominator will be:      

Step-by-step explanation:

Given

hypotenuse = 5

angle Ф = 60°

To determine

x = ?

Using the trigonometric ratio

cos Ф = adjacent / hypotenuse

here

Ф = 60°

adjacent of 60° = x

hypotenuse = 5

so substituting Ф = 60°, adjacent = x and hypotenuse = 5 in the equation

cos Ф = adjacent / hypotenuse

so

\(cos\:60^{\circ }\:=\:\frac{x}{5}\)

       \(\frac{\sqrt{3}}{2}=\frac{x}{5}\)

switch sides

         \(\frac{x}{5}=\frac{\sqrt{3}}{2}\)

Multiply both sides by 5

         \(\frac{5x}{5}=\frac{5\sqrt{3}}{2}\)

Simplify

         \(x=\frac{5\sqrt{3}}{2}\)

Therefore, the length of x in the simplest radical form with a rational denominator will be:      

Answer:

0.95=95%

Step-by-step explanation:

25,000*0.95=23750

Answer:

181..

Step-by-step explanation:

        1 8  1   <     answer

      -----------

        32761

  1     1    

        227

 28   224      

              361

 361        361

T A can be seen as a linear transformation from R^2 to R^3.

To find the range and codomain of the matrix transformation T A, we need to first determine the matrix T A . The matrix T A is obtained by multiplying the input vector x by A:

T A (x) = A x

Therefore, T A can be seen as a linear transformation from R^2 to R^3.

To determine the range of T A , we need to find all possible outputs of T A (x) for all possible inputs x. Since T A is a linear transformation, its range is simply the span of the columns of A. Therefore, we can find the range by computing the reduced row echelon form of A and finding the pivot columns:

A =  (\left[\begin{array}{cc}1 & 2 \ 1 & -2 \ 0 & 1\end{array}\right]) ~ (\left[\begin{array}{cc}1 & 0 \ 0 & 1 \ 0 & 0\end{array}\right])

The pivot columns are the first two columns of the identity matrix, so the range of T A is spanned by the first two columns of A. Therefore, the range of T A is the plane in R^3 spanned by the vectors [1, 1, 0] and [2, -2, 1].

To find the codomain of T A , we need to determine the dimension of the space that T A maps to. Since T A is a linear transformation from R^2 to R^3, its codomain is R^3.

If the functions were not linear, it would not make sense to talk about their range or codomain in this way. The concepts of range and codomain are meaningful only for linear transformations.

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To find the 60th percentile for the given set of data (0, 2, 3, 5, 5, 6, 8, 10, 10, 11, 12, 14, 16), the answer is 8.4.

To determine the 60th percentile, we need to arrange the data in ascending order. The ordered set of data is: 0, 2, 3, 5, 5, 6, 8, 10, 10, 11, 12, 14, 16.

To find the 60th percentile, we need to calculate the position of the value within the data set. Since the percentile represents the percentage of values below a certain point, we can calculate the position using the formula: (p/100) * (n + 1), where p is the percentile and n is the total number of data points.

For the 60th percentile, the calculation would be: (60/100) * (13 + 1) = 7.2. Since the position is not an integer, we can interpolate between the values. The value at the 7th position is 8, and the value at the 8th position is 10. By interpolating, we find that the 60th percentile is 8 + 0.2 * (10 - 8) = 8.4.

Therefore, the 60th percentile for the given set of data is 8.4.

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ATQ

\(\\ \tt\hookrightarrow 12+2.5r=95.75\)

\(\\ \tt\hookrightarrow 2.5r=95.75-12=83.75\)

\(\\ \tt\hookrightarrow r=83.75/2.5\)

\(\\ \tt\hookrightarrow r=33.5\)

Answer:

1

Step-by-step explanation:

Using the rules of exponents

\((a^m)^{n}\) = \(a^{mn}\)

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

Given

\((\frac{1}{x^{(a-b)}) } ^{a+b}\) × \((\frac{1}{x^{b+a}) } ^{b-a}\)

= \(\frac{1}{x^{(a-b)(a+b)} }\) × \(\frac{1}{x^{(b+a)(b-a)} }\)

= \(\frac{1}{x^{(a^2-b^2)} }\) × \(\frac{1}{x^{(b^2-a^2)} }\)

= \(\frac{1}{x^{(a^2-b^2+b^2-a^2)} }\)

= \(\frac{1}{x^{0} }\)

= \(\frac{1}{1}\)

= 1

well you already got an answer so can i have free 25

Answer:

m<CAB = 59

m<ACB = 59

Step-by-step explanation:

4x - 41 = 2x + 9

2x - 41 = 9

2x = 50

x = 25

m<CAB: 4x - 41

4(25) - 41

59

m<ACB: 2x + 9

2(25) + 9

59

First way to solve the problem: To find the increase in the surface area of the box, we need to calculate the difference in surface areas before and after the increase in height.

Let's denote the original height of the box as h1 = 31 cm and the increased height as h2 = 31 cm + 0.8 cm = 31.8 cm.

The surface area of a rectangular prism can be calculated using the formula: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the box, respectively.

Before the increase, the surface area (SA1) of the box is SA1 = 2lw + 2lh1 + 2wh1.

After the increase, the surface area (SA2) of the box is SA2 = 2lw + 2lh2 + 2wh2.

By subtracting SA1 from SA2, we can find the increase in surface area: SA2 - SA1 = 2lw + 2lh2 + 2wh2 - 2lw - 2lh1 - 2wh1 = 2l(h2 - h1).

So, the increase in surface area of the box is 2l(h2 - h1), where l represents the length of the box.

Second way to solve the problem:

Alternatively, we can calculate the increase in surface area by focusing on the change in the height only.

The two faces of the box that are affected by the increase in height are the top and bottom faces, each with an area equal to lw, and the two side faces, each with an area equal to lh1 and lh2.

Therefore, the increase in surface area of the box is equal to 2lw + 2lh2 - (2lw + 2lh1) = 2l(h2 - h1).

I prefer the second way of solving the problem because it directly focuses on the change in the height and eliminates the need to calculate the entire surface area of the box in both cases. It simplifies the calculation and reduces the chances of making errors. By isolating the change in the height, we can directly compute the increase in surface area, which is the desired result.

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According to the given data we have the following expression to solve:

- 1/2 + 3 1/2

To solve this expression we would have to make the following calculations:

First we would multiply 3 times 1/2

So, we would get:

So, Finally we would get the fraction 2/2 that would be equal to 1.

Therefore, - 1/2 + 3 1/2=1

330 m/s also means \(\dfrac{330 \text{ m}}{1 \text{ s}}\), which is the same as \(\dfrac{1 \text{ s}}{330 \text{ m}}\).

If you take that last version and multiply it by 80 m:

\(80 \text{ m} \cdot \dfrac{{1 \text{ s}}}{330 \text{ m}} = \dfrac{80}{330} \text{ s}\)

80/330 ≈ 0.2424...

Answer: 8.4

Step-by-step explanation: 5.25 divided by 5 is 1.05. So 1.05 x 8 is 8.4

The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.

To find the maximum value of f(x), we can take the limit as x approaches infinity:

6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.

What does circumference mean?

The boundary length of any circular shape is known as the

circumference.

What is scale factor?

A scale factor is a quantity multiplier (also known as a scale). The scaling factor for x, for instance, is represented by the letter "C" in the equation y = Cx. The factor would be 5 if y = 5x were the equation.

According to the given data:

After scale factor 2 is applied, 6.4 cm must be the gasket's needed circumference.

It includes a rubber gasket with a 3.2 cm circumference. The circumference of the gasket has must be calculated after scaling up by factor 2.

Here,

3.2 cm is the gasket's circumference.

The circumference changed upon scale factor 2 dilatation.

Dilated gasket circumference: 2 * 3.2 = 6.4 cm

As a result, 6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.

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Answer:

C. 6.4 cm

Hope this helps!

Step-by-step explanation:

Answer:

E= 52 degrees and F=21 degrees

(sorry)

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

seen it before