Below are two similar triangles.
A base= 7 cm
B base= 14cm

The area of triangle A is 20cm^2
Work out the area of triangle B​

The equation of a circle having endpoints of diameter as (4,9) and (4,-3) is (x - 4)² + (y - 3)² = 36.

The "center" of circle is called as midpoint of diameter.

The "x-coordinate" of "mid-point" is = (4+4)/2 = 4, and

The "y-coordinate" of "mid-point" is = (9+(-3))/2 = 3.

So, center of circle is (4,3),

The radius of circle is half the length of the diameter, which is distance between two endpoints of diameter. We find distance using distance formula:

⇒ distance = √((x₂ - x₁)² + (y₂ - y₁)²), where (x₁,y₁) and (x₂,y₂) are "end-points" of diameter.

⇒ distance = √((4 - 4)² + (9 - (-3))²)

⇒ √(144) = 12.

So, radius is 6.

The equation of circle with center (h,k) and radius "r" is : ⇒ (x - h)² + (y - k)² = r²,

Substituting the values

We get,

⇒ (x - 4)² + (y - 3)² = 6²,

⇒ (x - 4)² + (y - 3)² = 36,

Therefore, the equation of the circle is (x - 4)² + (y - 3)² = 36.

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a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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Answer:

12 and 22

Step-by-step explanation:

let the smaller number be n then the larger number is n + 10 and their sum is

n + n + 10 = 34

2n + 10 = 34 ( subtract 10 from both sides )

2n = 24 ( divide both sides by 2 )

n = 12

smaller number is 12 and larger number is n + 10 = 12 + 10 = 22

Answer:3/28

Step-by-step explanation:

Answer:

An instructor at an army base wants to know if a new program that teaches gun safety is effective is described below in brief details.

Step-by-step explanation:

Although of your shooting practice, the handgun safety program illustrates the center fundamentals of handgun protection so that you can tour the range with courage and with safety in the brain. Study how to accurately control, transport, and deposit your handgun, as well as how to keep children secure around handguns.

The hire purchase price for the video recorder is 3,133.20.

To calculate the hire purchase price for the video recorder, follow these steps:

1. Calculate the initial deposit: 20% of the cash price (2,700) is (0.20 * 2,700) = 540.
2. Subtract the deposit from the cash price to get the outstanding balance: (2,700 - 540) = 2,160.
3. Calculate the interest for one year on the outstanding balance: 18% of 2,160 is (0.18 * 2,160) = 388.80.
4. Divide the interest by 12 to find the interest per month: (388.80 / 12) = 32.40.
5. Add the interest per month to the outstanding balance: (2,160 + 32.40 * 12) = 3,133.20.
6. The hire purchase price is 3,133.20, which is the total amount payable in 12 equal monthly instalments.

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Complete question:

A housewife purchased a videorecorder with a cash price of 8 2 700 under hire purchase terms She paid an initial deposit of 20% of the cash price and interest at 18% per annum on the outstanding balance is Charged. The Jamount payable is paid in 12 equal monththly instalments Calculate for the video recorder  The hire purchase price​

Answer:

Step-by-step explanation:

This problem bothers on probability

Given that two dice are expected to give an outcome of sum greater than 8

But in the problem statement the first die is already settled since it is showing 6 already.

Now for the second die, the possible outcomes that will add up with the first die to produce a figure greater than 8 are (3,4,5,6)  

The probability of obtaining either of these numbers is 4/6= 2/3

Having the first die settled, this means that the probability of obtaining a sum of 8 is 2/3

A variable that can only take on specific numeric values is called  A discrete random variable.

According to the statement

A variable which is used to select a specific numeric value and we have to find a those variable

A discrete random variable is one which may take on only a countable number of distinct values.

So, A variable that can only take on specific numeric values is called  A discrete random variable.

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The probability of observing a sample proportion (p) of 0.11 or less, given a population proportion (p) of 0.14 and a sample size (n) of 148, can be determined using the binomial distribution formula. The probability can be calculated using an Excel spreadsheet or other statistical software.

In this case, the probability is approximately 0.0003. This means that the chance of obtaining a sample proportion of 0.11 or less, given a population proportion of 0.14 and a sample size of 148, is very low. The probability value indicates that such an outcome is highly unlikely to occur by chance alone. It suggests that the observed sample proportion significantly deviates from the population proportion, indicating a potential difference between the sample and the population.

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The length PL is 17 centimeters

From the complete question, we have:

LM = 8 cm

PQ = 30 cm

The length PL is then calculated using the following Pythagoras theorem

PL^2 = LM^2 + (PQ/2)^2

The equation becomes

PL^2 = 8^2 + (30/2)^2

Evaluate the sum

PL^2 = 289

Take the square root of both sides

PL = 17

Hence, the length PL is 17 centimeters

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The volume of the right rectangular prism is the amount of cubes in it

The formula to determine the volume of the right rectangular prism is V(n) = n

The question is incomplete; as the figure is not given.

So, I will provide a general solution

The volume of a one inch cube is:

\(V = 1^3\)

\(V = 1\)

Assume the number of one inch cubes used to fill the right rectangular prism is n.

Then the volume of the right rectangular prism would be:

\(V(n) = n * 1\)

This gives

\(V(n) = n\)

Hence, the general formula to determine the volume of the right rectangular prism is V(n) = n

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The population mean of the data is 6.

The population has n = 16 scores.

The sum of all of the scores is equal to 96.

Therefore, the population mean can be found as follows:

The population mean is the mean or average of all values in the given population.

The population mean is represented mathematically as follows:

population mean = sum of terms / number of terms

Therefore,

sum of terms = 96

number of terms = 16

Hence,

population mean =  = 96 / 16

population mean =  6

Therefore, the population mean of the data is 6.

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Answer:

Equation of line is: \(\mathbf{y=4x+3}\)

Step-by-step explanation:

We are given:

A straight line has gradient 4 and passes through the point (5,23).

Work out the equation of the line.

The equation of line will be in slope-intercept form: \(y=mx+b\)

where m is slope and b is y-intercept

Finding slope

We have slope (gradient) m = 4

Finding y-intercept

Using slope m = 4 and point (5,23) we can find b i.e y-intercept

\(y=mx+b\\23=4(5)+b\\23=20+b\\b=23-20\\b=3\)

So, we get y-intercept b = 3

Finding Equation of Line

Now, writing equation of line having slope m = 4 and y-intercept b = 3 is:

\(y=mx+b\\y=4x+3\)

So, the Equation of line is: \(\mathbf{y=4x+3}\)

Answer:

The function y=x^2 or f(x)= x^2 is a quadratic function, and is the parent graph for all other quadratic functions. The shortcut to grapghing the function f(x) = x^2 is to start at the point (0,0) (the origin) and mark the point, called the vertex. Note that the point (0,0)is the vertex of the parent function only

Step-by-step explanation:

Answer:

1. \( \theta = 61.9^\circ \)

2. \( x = 23.7~cm \)

Step-by-step explanation:

Problem 1.

Use the Law of Sines.

This is SSA.

\(\dfrac{a}{\sin A} = \dfrac{c}{\sin C}\)

\( \dfrac{31.2~cm}{\sin 51^\circ} = \dfrac{35.4~cm}{\sin \theta} \)

\( \sin \theta = \dfrac{35.4~cm \times \sin 51^\circ}{31.2~cm} \)

\( \sin \theta = 0.88176 \)

\( \theta = \sin^{-1} 0.88176 \)

\( \theta = 61.9^\circ \)

Problem 2.

m<A + m<B + m<C = 180°

m<A + 67° + 58° = 180°

m<A = 55°

Use the Law of Sines.

\(\dfrac{a}{\sin A} = \dfrac{c}{\sin C}\)

\(\dfrac{x}{\sin 55^\circ} = \dfrac{24.5}{\sin 58^\circ}\)

\(x = \dfrac{\sin 55^\circ \times 24.5}{\sin 58^\circ}\)

\( x = 23.7~cm \)

The order of points is:

1. -33         5. -55         9. 2.4

2. -23        6. -2.6        10. 7.6

3. -11.5       7. -2.5        11. 9.3

4. -10         8. 2.33       12. 10.6

Given,

The equations:

1. y = (-2/3) × -16 = 10.66

2. y = (1/2) × -23 = -11.5

3. y = (3/2) × -22 = -33

4. y = (4/3) × -2 = -2.66

5. y = (1/3) × 23 = 7.66

6. y = (1/2) × -5 = -2.5

7. y = (-1/4) × 22 = -5.5

8. y = 1 × -23 = -23

9. y = (4/3) × 7 = 9.33

10. y = (1/3) × 7 = 2.33

11. y = -1 × 10 = -10

12. y = (-2/5) × -6 = 2.4

We have to order this from 1 to 12. That is ascending order:

Here is the equations:

1. y = (3/2) × -22 = -33

2. y = 1 × -23 = -23

3.  y = (1/2) × -23 = -11.5

4. y = -1 × 10 = -10

5. y = (-1/4) × 22 = -5.5

6. y = (4/3) × -2 = -2.66

7. y = (1/2) × -5 = -2.5

8. y = (1/3) × 7 = 2.33

9. y = (-2/5) × -6 = 2.4

10. y = (1/3) × 23 = 7.66

11.  y = (4/3) × 7 = 9.33

12. y = (-2/3) × -16 = 10.66

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The probability that out of 8 newly hired people is 3.2.

According to the statement

we have given that the some conditions and based on these conditions we have to find the probability that out of 8 newly hired people.

So, For this purpose,

we have given that the

new employee in a fast-food chain still being with the company at the end of the year is  0.5

Now, we See that is probability of remaining with the company.

There is only one is 0.5.

According to the probability law

P + Q = 1

and this become

Q = 1 - 0.60.

And the probability of one people hired is Q.

Then

Q = 0.4

And probability that out of 8 newly hired people is

8Q = 0.4 * 8

it become 3.2.

So, The probability that out of 8 newly hired people is 3.2.

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Answer:

y = 2x + 3

Step-by-step explanation:

to find the perpendicular line then you have to find the negative reciprocal which is 2 and to get that you flip the fraction and change the sign so

(-1/2) → 2/1 or 2

the y-intercept coordinate is (0, 3) so the y-intercept is 3

Slope of the Perpendicular line=2

Equation of line in point slope form

\(\\ \rm\Rrightarrow y-3=2x\)

\(\\ \rm\Rrightarrow y=2x+3\)

The possible dimensions of rectangular room A are 9 and 3x - 2.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

Given:

A fitness center has several rectangular rooms where exercise classes are held.

The area of Room A is 27x − 18 square units.

The area of the rectangle = length x width

27x − 18 = length x width

9 (3x - 2) = length x width.

Therefore, 9 and 3x - 2 are the dimensions.

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Answer:

for just the slope its 3/5 or in decimal its .6

Step-by-step explanation:

y's on top x's on bottom

1--2

1+2=3

2--3

2+3=5

so slope is 3/5 or .6

Answer:

22

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

\(\frac{3x+2}{5x-4}=\frac{15}{20}=\frac{3}{4} \\ \\ 12x+8=15x-12 \\ \\ 3x=20 \\ \\ \therefore SP=20+2=22\)

The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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Therefore , the solution of the given problem of variable comes out to be because a function's domain is all possible input values, not possible outcome values, b is not true.

A trait that can be measured and have different values is called a variable. A few instances of variables include height, age, salary, birthplace province,equation , academic standing, and type of residence.

Here,

A. Although all relations are functions, not all functions are relations.

c. Each input value will only have one output value if a connection is a function.

d. At least one input will have more than one exit value if a relation is not a function.

e. The input and result of a function are independent and dependent variables, respectively.

Because a function's domain is all possible input values, not possible outcome values, b is not true.

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The area of the field in square meters is approximately 679.2431 m².Given: Width (W) of rectangular field in a park = 66.5ftLength (L) of rectangular field in a park = 110ftArea

(A) of rectangular field in a park in square meters.We can solve this question using the following steps;Convert the measurements from feet to meters.Use the formula of the area of a rectangle to find out the answer.1. Converting from feet to meters1ft = 0.3048m

Now we can convert W and L to meters

W = 66.5ft × 0.3048 m/ft ≈ 20.27 m

L = 110ft × 0.3048 m/ft ≈ 33.53 m2. Find the area of the rectangle

The formula for the area of the rectangle is given as;A = L × W

Substituting the known values, we have;

A = 33.53 m × 20.27 mA = 679.2431 m²

Therefore, the area of the field in square meters is approximately 679.2431 m².

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Answer:

The answer is rectangle.

Answer:

circle a: 3.14x36= 113.04

circle b: 3.14 x 64 = 200.96

circle c: 3.14 x 121= 379.94

circle d : 3.14 x 81 = 254.34

Step-by-step explanation: circle a is 6cm, circle b is 8 cm, circle c is 11 cm and circle d is 9cm.

and (Area = π r²) example: circle a 6²=36 and π=3.14 so 3.14x36=113.04

Triangle KVM is similar to triangle BVG because angle M = angle G = 90° and angle V is common to both triangles.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio.

For two triangles to be similar, the corresponding angles must be congruent i.e equal.. Also the ratio of the corresponding sides of similar triangles are equal.

angle M and G are both 90° , this means they are equal.

angle KVM = BVG

therefore angle K = angle B

Since all the corresponding angles are equal, we can say triangle KVM is similar to triangle BVG

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Answer:

hi shaurya

Step-by-step explanation:

The positive measure is 220° and the negative measure is -140°.

First, we know that the reference angle is 40°, and it lies on the third quadrant.

So these 40° are measured from the negative x-axis (the axis where the quadrant starts).

This means that the angle measured in the standard way (from the positive x-axis) measures:

M = 40° + 90° + 90° = 220°.

To find the negative measure, we remember that any angle A is equivalent to:

B = A + n*360°.

Where n is an integer.

If we take n = -1 for our angle, we get:

M' = 220° + (-1)*360° = -140°.

So the positive measure is 220° and the negative measure is -140°.

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