de║bc, ad=2cm and bd=3cm, then area(Δabc):area(Δade) is equal to
a) 4:25
b) 2:3
c) 9:4
d) 25:4

Answer:

h = 8 inches

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

given A = 24 and b = 6 , then

\(\frac{1}{2}\) × 6 × h = 24 , that is

3h = 24 ( divide both sides by 3 )

h = 8 inches

The Reimann sum with n rectangle will be given as \(\sum^{n-1}_{i = 0} f{(x_i)} \Delta x\)

Let us suppose that f is a non-negative function, defined over a closed interval represented by [a, b].

The integral of f with respect to x signifies the area between the graph of f and X-axis. This area would be called definite integral of a function f from a to b. Then Riemannian method of determining this area is:

“if the area is divided into n rectangles of very small breadth, then it would be simpler to calculate the area of such rectangles and then we can add them up

(i ) The width of each rectangle will be denoted as Δx

Δx = b-a/n,

where , a is lower bound

b is upper bound of the integral

(ii) The right-hand endpoints of each rectangle are refer as \(x_i\) and we can find the right endpoints by \(x_i\) = a + Δx.i

(iii) The height of each rectangle is the value of the function at the upper point of the interval.

a + (b-a)/n for the first rectangle , a + 2(b-a)/n for the second rectangle and so on

(iv) The area of the each rectangle will be

Area = Width × height

=> A = (b-a)/2 × a + i(b-a)/2

(v) The Riemann sum with n rectangles is

Area of rectangle = \(\sum^{n-1}_{i = 0} f{(x_i)} \Delta x\)

Which is also known as Reimann sum

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The probability that Sam chooses either the day or the night shift is 0.93.

Probability is a fine conception that measures the liability or chance of an event being. It's expressed as a number between 0 and 1, with 0 indicating that an event is insolvable, and 1 indicating that an event is certain.

Given to the question.

Since Sam can only choose moreover the day shift or the night shift, and the events" choosing the day shift" and" choosing the night shift" are mutually exclusive (i.e., they cannot do at the same time), we can use the addition rule of probability to find the probability that Sam chooses either the day or the night shift.

The addition rule states that the probability of the union of two events A and B, denoted as P (A or B), is given by.

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

where P (A and B) is the probability of the crossroad of events A and B.

Since Sam cannot choose both the day and night shift, P (A and B) = 0. thus, the probability that Sam chooses either the day or the night shift.

The addition rule states that the probability of the union of two events A and B, denoted as P (A or B), is given by:

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

where P (A and B) is the probability of the intersection of events A and B.

Since Sam cannot choose both the day and night shift, P (A and B) = 0. Therefore, the probability that Sam chooses either the day or the night shift is:

P (day or night) = P(day) + P(night) - P (day and night)

P (day or night) = 0.9 + 0.03 - 0

P (day or night) = 0.93

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Corbin's account will have a higher balance than Victoria's account at the end of 3 years" is true.

To calculate the balance at the end of 3 years, we can use the simple interest formula for Victoria's account and the compound interest formula for Corbin's account.

For Victoria's account:

Simple interest = P * r * t

= 2000 * 0.05 * 3

= $300

Balance after 3 years = P + Simple interest

= 2000 + 300

= $2300

For Corbin's account:

Balance after 3 years = \(P * (1 + r)^t\)

= 1800 * (1 + 0.09)³

= $2401.40

Therefore, the statement "Corbin's account will have a higher balance than Victoria's account at the end of 3 years" is true.

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Answer:

6.3 units (nearest tenth)

Step-by-step explanation:

\(\boxed{Distance \: between \: 2 \: points = \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } }\)

Using the formula above,

distance between (-8, 6) and (-6, 0)

\( = \sqrt{ {[ - 8 - ( - 6)]}^{2} + {(6 - 0)}^{2} } \)

\( = \sqrt{ {( - 8 + 6)}^{2} + {(6 - 0)}^{2} } \)

\( = \sqrt{ {( - 2)}^{2} + 6^{2} } \)

\( = \sqrt{4 + 36} \)

\( = \sqrt{40} \)

= 6.3 units (nearest tenth)

Answer:

a) $60

b) $132

Step-by-step explanation:

one ticket costs $48/4 = $12

a) 5 tickets will cost 5*12 = $60

b) 11 tickets will cost 11*12 = $132

Answer:

you answer is b 11 movie tickets

The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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To translate an entire triangle, find the coordinates of each of the triangle's vertices, add the horizontal translation then plot the three translated points.

Whenever an object is moved from one location to the next without changing its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Use P′(x+a,y+b) to translate the point P(x,y), a unit to the right, and b unit up. Use P′(x−a,y−b) to translate the point P(x,y), a unit to the left and b unit to the lower.

There are some steps of translating the triangle:

Step 1: Find the coordinates of each of the triangle's vertices in step one.

Step 2: Add the horizontal translation value to each vertex's x-coordinate and the vertical translation value to each point's y-coordinate to translate each point. If the horizontal translation is to the left or the vertical translation is downward for these translations, add a negative number.

Step 3: Plot the three translated points and draw the triangle by drawing a straight line between each pair of points.

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The true percentage of grocery shoppers that shop most frequently on Fridays from Monday to Friday, which is 20%, cannot be determined statistically. The value of p is 0.0130.

To solve this problem, we run a hypothesis test about the population proportion.

Proportion in the null hypothesis (p0) = 0.2

Sample size (n) = 75

Sample proportion (sp) = 24/75 = 0.32

Significance level = 0.01

\(H_{o}\) : p = 0.2

\(H_{a}\) : p ≠ 0.2

Test statistic percentage = ( \(sp\) - \(p_{o}\) ) / \(\sqrt{\frac{(p_{o})(1-p_{o} )}{n} }\)  

Left critical \(z_{0.01}\) = -2.5758

Right critical \(z_{0.01}\) = 2.5758

Calculated statistic = \(\frac{0.32-0.2}{\sqrt{\frac{(0.32)(1-0.32)}{75} } }\) = 2.2278

Since, -2.5758 < Test statistic < 2.5758, the null hypothesis cannot be rejected. There is not enough statistical evidence to state that the true proportion of grocery shoppers from Monday to Friday that goes most frequently on Fridays is different from 20%. The p - value is 0.0130.

Therefore,

The true percentage of grocery shoppers that shop most frequently on Fridays from Monday to Friday, which is 20%, cannot be determined statistically. The value of p is 0.0130.

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Answer:

$25.76

Step-by-step explanation:

$1.12×23ft=$25.76

Answer:

\((x^2+7)(x^4-7x^2+49)\)

Step-by-step explanation:

Factor x^6+343, and you will get the answer above. Hope this helps :)

Answer:

x = 10

missing angle = 83°

Step-by-step explanation:

These are supplementary angles meaning they have a sum of 180°.

8x + 3 + 97 = 180

8x + 100 = 180

8x + 100 - 100 = 180 - 100

8x = 80

x = 10

Substitute the value for the variable.

8(10) + 3

80 + 3

83

Answer:

x=10

Step-by-step explanation:

8*10=80

80+3=83

83+97=180

Answer:

x-degree is 150 degrees

Step-by-step explanation:

On a 180-degree plane the 150-degrees makes the unmarked angle 30-degrees. Since both unmarked angles are mirrors of each other (and unmarked) it can be assumed they are both 30-degrees (or that they have the same degree measurement). Therefore, it can be assumed from the image that the x-degree angle (mirroring the 150-degree angle) is 150-degrees.

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

False

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 1, 7 ) → (1, 7 )

Answer: True

Step-by-step explanation:

Because since it's getting reflected over the Y-axis it's gonna be all negatives.

Answer:

Hello,

Step-by-step explanation:

a)

\(y=a^x*b+c\\\\if\ x- > -\infty,\ y- > -1 \ \Longrightarrow\ c=-1\\if\ x=0\ y=1\ \Longrightarrow\ 1=b-1\ \Longrightarrow\ b=2\\if\ x=1\ y=5 \ \Longrightarrow\ a*2-1=5\ \Longrightarrow\ a=3\\\\\boxed{y=2*3^x-1}\\\)

b)

\(f(x,y)=(x-a)(y-b)-k=0\ since\ hyperbola\ "\' equilat\`ere\ in\ French"\\\\\dfrac{\partial{f}}{\partial{x}} =y-b=0\ \Longrightarrow\ y=b\\\\\dfrac{\partial{f}}{\partial{y}} =x-b=0\ \Longrightarrow\ x=a\\\\Here\ center\ is\ (0,2)\ so (x-0)(y-2)=k\\\\(-3,3)\ is \ a\ point\ of \ the\ hyperbola:\\-3*(3-2)=k\ \Longrightarrow\ k=-3\\\\\boxed{x(y-2)=-3}\\\)

c)

It is parabola

y=k*(x-3)(x+3)

(1,24) is a point of the parabola:

24=k*(1²-9) => k=-3

\(\boxed{y=-3(x^2-9)}\\\)

The area of the rectangular piece to be painted after cutting will be 1200 cm².

What is the definition of a rectangle?

Rectangles are four-sided polygons with 90-degree internal angles. Two sides meet at right angles at each corner or vertex. The rectangle is distinguished from the square by the fact that its opposite sides are of equal length.

If one side of a rectangle is 20 cm long, the opposite side is also 20 cm long.

A rectangle has two intersecting diagonals. The length of both diagonals is the same.

The perimeter is defined as P = 2 (Length + Width).

Area of a Rectangle=Length*Breadth

Now,

Length of cardboard=42cm

breadth=32 cm

Area of cardboard=42*32=1344cm²

Area of square to be cut=6*6=36cm²

and total 4 squares are cut

Then the area of the box that is made to be painted is =1344*4*36

=1200 cm²

hence,

          The area of the rectangular piece to be painted after cutting will be 1200 cm².

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Answer:

s = 4

Step-by-step explanation:

The equation for the line of best fit for the data is p=25s+40.

Where p is no. of points and s is no. fo strikes

We need to find the number of strikes made by a bowler with 140 points.

Put p = 140

p=25s+40

140 = 25s+40

Subtract 40 to both sides,

140-40 = 25s+40-40

100 = 25s

⇒ s = 4

So, there are 4 strikes made by a bowler with 140 points.

The total distance traveled by the taxi driver is 7 1/2 miles.

To find out how many miles the taxi driver travels for the two stops, we need to add up the distance to the first stop and the distance to the second stop.

The distance to the first stop is 4 5/8 miles.

To find the distance to the second stop, we need to subtract 1 3/4 miles from the distance to the first stop:

4 5/8 miles - 1 3/4 miles = 2 7/8 miles

Now we can add the distance to the first stop and the distance to the second stop to find the total distance traveled:

4 5/8 miles + 2 7/8 miles

= 7 1/2 miles

Therefore, the taxi driver will travel 7 3/2 miles for the two stops.

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Geometric sequence

an = a1 r ^(n-1)

____________________

f(n)=1/2*4^n, n≥0

in this case a1= 1/2

r = 4

n= 0 (you just replace n)

f( 0 )=1/2*4^0

f(0) = 1/2 =1/ 2

n f(n)

0 f(0) = 1/ 2 f( 0 )=1/2*4^0

1 f(1) = 2 f( 0 )=1/2*4^2 = 4/2

2 f(2) = 8 f( 0 )=1/2*4^2 = 16/2

3 f(3) = 32 f( 0 )=1/2*4^2 =64/2

4 f(4) = 128 f( 0 )=1/2*4^2 = 256/2

They will be able to spend $612.52 on their trip.

What is simple interest?

The interest on a loan or principal amount can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

Using the formula \(A = P(1 + r/n)^{(nt)\), where:

P = $500.00 (the principal)

r = 7% = 0.07 (the annual interest rate)

n = 1 (compounded annually)

t = 3 years

\(A = 500(1 + 0.07/1)^{(1*3)\)

\(A = 500(1.07)^3\)

A = 500(1.225043)

A = $612.52

Therefore, they will be able to spend $612.52 on their trip.

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Answer:

5

Step-by-step explanation:

5 |35 | (5 is the divisor and 35 is the dividend)

= 7|

For 25;

5 |25|

=5

35 = 5 * 7

25 = 5 * 5

Now, common factor =5

2.8, 4.6, 7, 17  

The first number is less than the second number by 1.8, second number is less than the third number by 2.4, third number is less than the forth number by 10.

Answer:

17/25

Step-by-step explanation:

You need to add the probability of choosing a blue marble to the probability of choosing a yellow one.

The probability of choosing a blue marble is 10/25, since there are 10 blue ones, and 25 total.

The probability of choosing a yellow marble is 7/25.

10 + 7 = 17

17/25

Answer:

15

Step-by-step explanation:

We are told in the question that:

Mr Smith's recipe calls for 2 1/2 cups of sugar for the cake and 1 1/4 cups of sugar for the vanilla glaze.

Step 1

We add up the total amount of sugar he would need

2 1/2 + 1 1/4

(2 + 1) + (1/2 + 1/4)

= 3 + (2 + 1/4)

= 3 3/4 cups of sugar.

Step 2

How many 1/4 cup scoops of sugar does he need?

This is calculated as:

3 3/4 cups of sugar ÷ 1/4

= 15/4 ÷ 1/4

= 15/4 × 4

= 15

Therefore, he would be needing 15 , 1/4 cup scoop of sugar

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

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Answer:

Irrational number

Step-by-step explanation:

A number which can be written in the form of a fraction \(\frac{p}{q}\), is a rational number.

Examples : \(\frac{1}{2}, \frac{3}{4}, 1.41414141....\)

In 1.41414141..... (41) is the repeating numbers after decimal. Therefore, it's a rational number.

Irrational numbers can't be written in the form of \(\frac{p}{q}\).

Examples : π, √3, 1.41456......

Given number in the question is 6.56556555....

In this number numbers after decimal are not repeating.

Therefore, given number is irrational.

The value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

Given that a researcher measures the relationship between two variables, X and Y.

If SS(XY) = 340 and SS(X)SS(Y) = 320,000, then we need to calculate the value of the correlation coefficient.

Correlation coefficient:

The correlation coefficient is a statistical measure that determines the degree of association between two variables.

It is denoted by the symbol ‘r’.

The value of the correlation coefficient lies between -1 and +1, where -1 indicates a negative correlation, +1 indicates a positive correlation, and 0 indicates no correlation.

How to calculate correlation coefficient?

The formula to calculate the correlation coefficient is as follows:

r = SS(XY)/√[SS(X)SS(Y)]

Now, substitute the given values, we get:

r = 340/√[320000]r = 0.34

Therefore, the value of the correlation coefficient is 0.34. Thus, the option (B) 0.34 is the correct answer.

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