You pick a card at random. Without putting the first card back, you pick a second card at random. 6 7 8 9 What is the probability of picking a prime number and then picking a prime number? Simplify your answer and write it as a fraction or whole number.

Answer:

[tex]\huge\boxed{\sf x = 100\°}[/tex]

Step-by-step explanation:

So,

x = 61 + 39

[tex]\rule[225]{225}{2}[/tex]

The area of the sector is 36.6 ft².

We have,

To calculate the area of the sector, we need to find the fraction of the entire circle it represents and then multiply it by the area of the entire circle.

The central angle of 260° represents (260/360) or 13/18 of the entire circle.

The area of the entire circle with a radius of 4 ft can be calculated using the formula:

A = πr², where π is approximately 3.14.

Substituting the values,

The area of the entire circle is A = 3.14 x (4 ft)² = 3.14 x 16 ft² = 50.24 ft².

To find the area of the sector, we multiply the area of the entire circle by the fraction represented by the central angle:

Area of sector = (13/18) x 50.24 ft² = 36.64 ft².

Rounded to the nearest tenth

Thus,

The area of the sector is 36.6 ft².

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The lengths of the sides of triangle R'S'T'

R' = (-3.75, 2.25), S' = (2.25, 3) and T' = (2.25, -4.5).

We have the coordinates of triangle RST are given as

R (-5, 3), S(3, 4) and T(3, -6)

and, The scale factor is given as: 3/4

Now, The rule of dilation is

(x, y) = 3/4 (x, y)

Then, we can write

R' = (-5 x 3/4, 3 x 3/4)

R' = (-3.75, 2.25)

S' = (3 x 3/4, 4 x 3/4)

S' = (2.25, 3)

and, T' = (3x 3/4, -6x 3/4)

T' = (2.25, -4.5)

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Two sides are congruent to each other. The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle. The two angles opposite to the equal sides are congruent to each other.

In an isosceles triangle, two sides have the same length, making them congruent. These two sides are often referred to as the "legs" of the triangle.

The angles opposite the congruent sides in an isosceles triangle are also congruent. These angles are typically referred to as the "base angles."

The remaining side, called the "base," is not congruent to the legs of the triangle. The base is usually the side that connects the two base angles.

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Answer:

B

Step-by-step explanation:

Please say thank you

The transformation is described by option D.

It is the graph of f translated 3 units up and 7 units to the right.

The following transformation:

y = y=f(x-7)+3

Is a translation.

Remember that a vertical translation of N units is written as:

g(x) = f(x) + N

if N > 0, the translation is up.

if N < 0, the translation is down.

Remember that a horizontal translation of N units is written as:

g(x) = f(x + N)

if N > 0, the translation is to the left.

if N < 0, the translation is to the right.

Then:

y = f(x - 7) + 3

Is a translation of 7 units to the right and 3 units up.

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The probability of two heads when a biased coin is spun twice is 0.16.

The first time you flip the coin, the probability of seeing a heads is 2/5. The second time you flip the coin, the probability of seeing a heads is still 2/5 because the probability of a biased coin has not changed over the course of the two flips.

Since each flip is an independent event, you multiply the probabilities together.

The probability of two heads when a biased coin is flipped twice is (2/5) × (2/5) = 4/25 = 0.16.

Therefore, the probability of two heads when a biased coin is spun twice is 0.16.

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The graph of the system of equations on the image at the end, there we can see that the solution is (110, 95).

Here we want to solve the given system of equations:

2x + 3y = 505

5x + 3y = 835

Using a graphing tool.

To solve the system graphically we just need to graph both equations on the same coordinate axis and find the point where the graphs intercept.

On the image at the end, you can see the graph of the system of equations. On that image we can see that the solution of the system of equations is (110, 95).

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Answer:

no

Step-by-step explanation:

(I'll assume you're talking about a rectangle)

If the width is zero, the shape would be a line. Therefore, the width cannot be zero.

Feel free to tell me if I did anything wrong! :)

Answer: on the line y = x-3 and above the line y = -x + 2.

Step-by-step explanation:

The first inequality, y ≤ x-3, represents a shaded region below or on the line y = x-3. This line has a slope of 1 and y-intercept of -3. It is a straight line that slants upward from left to right.

The second inequality, y > -x + 2, represents a shaded region above the line y = -x + 2. This line has a slope of -1 and y-intercept of 2. It is a straight line that slants downward from left to right.

To determine which graph represents the system of linear inequalities, we need to look for a graph that shows the shaded region below or on the line y = x-3 and above the line y = -x + 2.

Answer:

simple interest=$97.50.

compound interest= $100.668

Step-by-step explanation:

Given:

Principal (P) = $750

Rate (R) = 6.5% (in decimal form, 0.065)

Time (T) = 2 years

Simple Interest = Principal*Rate*Time

Using the formula, the simple interest is calculated as follows:

Simple Interest = $750*0.065*2 = $97.50

Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.

Again:

Compound Interest = Principal*(1 + Rate)^(Time)-Principal

Using the same values as above, the compound interest can be calculated as follows:

Compound Interest = $750*(1+0.065)^(2)-$750

= $750*1.065^2 -$750

= $750 × 1.134225 - $750

= $850.66875-$750

= $100.668

Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668

The triangle that has been shown is a scalene obtuse triangle.

A triangle called a scalene triangle has three sides that are all different lengths. In other words, a scalene triangle has three different angles and no two of its sides have the same length.

A triangle with one obtuse angle is referred to as an obtuse triangle. Any angle that is greater than 90 degrees but less than 180 degrees is referred to as an obtuse angle.

Thus we have a scalene obtuse triangle.

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The exact value of the given expression of tan 15 ° can be found to be 1 / √3.

When given a tangent degree, you can find the exact value by relating it to the Sine and Cosine values as shown below :

tan ( x ) = sin ( x ) / cos ( x )

Given that x is 15 degrees, we have :

tan ( 15 ) = sin ( 15 ) / cos ( 15 )

The values of sine and cosine :

sin(30) = 1/2

cos(30) = √3/2

This means the relation is:

tan ( 15 ) = sin ( 15 ) / cos ( 15)

= ( 1 / 2 ) / (√3 / 2 )

= 1 / √3

=  0.2679

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Yes, because EFGH is a parallelogram and its diagonals are congruent.

To prove the statement, we have to know the properties of a rectangle.

The properties of a rectangle are listed thus;

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Using division operation, the nmber that is divided by 26 with a quotient of 5 and a remainder of 5 is 135.

The determination of the unknown in this scenario can be completed using the division operation.

The division operation involves the following parts:

Let the dividend = n

The divisor = 26

The quotient of the division operation = 5

The remainder after the division operation = 5

n = 26 x 5 + 5

n = 130 + 5

n = 135

Thus, the number or dividend in this division operation is 135.

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The quantity of the water in the water bottle is 648ml

Find the area,

Area of the bottle = 6 x 6

= 36cm²

To determine the quantity of the water in the bottle, multiply the area by the level of the water in the bottle:

area of the bottle x level of the water

= 36 x 18

= 648cm

When you convert it to ml, it becomes 648ml

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The complete question goes thus:

A water bottle has a square base of side 6 cm . If the bottle is filled up to a height of 18 cm .How much water is in the water bottle ?

The two equations that models the inverse proportion relationship are:

m³ = k/√n

m³√n = k

Inverse proportion is defined as a type of proportionality relationship. Thus, when two quantities are said to be inversely proportional, then it means that as one quantity increases, the other decreases.

We are told that the cube of m varies inversely as the square root of n. Thus:

m³ ∝ 1/√n

If k is the constant of proportionality , then we say that:

m³ = k/√n

We can also cross multiply to get:

m³√n = k

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The surface area for each rectangular prism is given as follows:

3) S = 195.5 mm².

4) S = 158.1 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

Hence, for item 3, the surface area is given as follows:

S = 2 x (8.2 x 5 + 8.2 x 4.3 + 5 x 4.3)

S = 195.5 mm².

For item 4, the surface area is given as follows:

S = 2 x (4.1 x 3 + 4.1 x 9.4 + 3 x 9.4)

S = 158.1 m².

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The 1st one/Top one.

X value is different each time. Function can have the same y-value (3, 1), (2, 1) but can't have the same x-value (3, 1) (3, 3)

The value of sin of θ given in the unit circle using the coordinates is -√13/7.

Given a unit circle.

We know that any point on the unit circle can be represented in terms of the angle that the point makes with the positive X axis as,

x = cos θ and y= sin θ

Here θ is the angle formed by the positive X axis with the point.

Here also given a unit circle.

So using the coordinates, we get

cos (θ) = -6/7

sin (θ) = -√13/7

Hence the value of sin of θ is -√13/7.

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Approximately 99.7% of scores lie in the shaded region.

We have,

The empirical rule, also known as the 68-95-99.7 rule, provides an estimate of the percentage of scores that lie within a certain number of standard deviations from the mean in a normal distribution.

According to this rule:

Approximately 68% of scores lie within 1 standard deviation of the mean.

Approximately 95% of scores lie within 2 standard deviations of the mean.

Approximately 99.7% of scores lie within 3 standard deviations of the mean.

Now,

In the given scenario, the shaded region represents the area between -2 and 3 standard deviations from the mean on the x-axis.

This encompasses the area within 3 standard deviations of the mean.

And,

Since 99.7% of scores lie within 3 standard deviations of the mean, we can estimate that approximately 99.7% of scores lie in the shaded region.

Therefore,

Approximately 99.7% of scores lie in the shaded region.

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Answer:

(x + 2)² + (y - 2)² = 3²

Step-by-step explanation:

Equation of a circle is (x - a)² + (y - b)² = r²,

where a is the x-coordinate of the centre of the circle, b is the y-coordinate of the centre of the circle, r is the circle's radius.

So, we have (x - -2)² + (y - 2)² = 3²

subtract a minus means we add.

(x + 2)² + (y - 2)² = 3²

The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted, where A is the total area.

Option C is the correct answer.

We have,

The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted.

The dimensions of the rectangular patio are given as (x + 15) for the length and (x + 10) for the width.

These values account for the extra length and width added to the original dimensions (x) to include the bench area.

To determine the total area of the patio that will be painted, we calculate the product of the length and width, which is (x + 15)(x + 10).

However, we need to subtract the area of the bench, which has a length of 5 and a width of 1.

Hence, we subtract 5 from the product to exclude the bench area.

Therefore,

The equation A = (x + 15)(x + 10) − 5 represents the area of the patio that will be painted, where A is the total area.

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Answer:

C

Step-by-step explanation:

i took the test :)

have a great day.!

The perimeter of the rectangle can be shown by Option C.

The perimeter of a rectangle is the total distance around its outer boundary. To calculate the perimeter of a rectangle, you need to know the lengths of its two adjacent sides, typically referred to as length (l) and width (w).

We know that the perimeter can be given by;

P = 2(l + b)

P = 2[(2.4x + 3.5) + (1.2x + 6.8)]

P = 2[2.4x + 3.5 + 1.2x + 6.8]

P = 2[2.4x +  1.2x + 3.5 + 6.8]

P = 2[3.6x + 10.3]

P = 7.2x + 20.6

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The solution to the given scatter plot is:

a)  Exponential

b) y = 587.52x

c) 894

Scatter plots are basically al type of data visualization that shows us the relationships that exists between variables.

a) The best model for the given scatter plot is definitely exponential because of the nature of the points and curve.

b) The regression equation for the model has the general formula:

Y = a + bx

Thus, from the given scatter plot, we can say that the equation is:

y = 587.52x

c) Using the equation that you found, in part B, using an online regression equation calculator, we can say that the prediction of the point total in the 10th level is: 894

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Answer: About two angles are congruent

Step-by-step explanation:

The slope of the points in this table is equal to -3.

In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided in the table, we can logically deduce the following data points on the line:

By substituting the given points into the slope formula, we have the following;

Slope, m = (4 - 7)/(1 - 0)

Slope, m = -3/1

Slope, m = -3.

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The bearing of B from A, given the locations of cities A and B can be found to be 30 degrees.

The bearing of A from B, can also be found to be 210 degrees.

First thing to do is to draw a vertical line from Point A and Point B, upwards. This line would signify the North direction which is needed to find the bearing.

Now, draw a line to B from A. From that line, draw an angle from the North Line of A to the line that joins Cities A and B.

Once this line is drawn, check the angle that forms and you will find that it is 30 degrees. This makes the bearing of B from A, to be 030 degrees.

The bearing from B of A would be 210 degrees by the same method.

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The full question is:

a) Measure the bearing of B from A.

b) Measure the bearing of A from B.

The graph first segment will represents the journey to her friend's place and would connect the points (0,0) and (2,192).

The graph second segment represents the journey back home and would connect the points (2,192) and (5,384).

We are given that:

We will calculate the time it takes for each leg of the journey which is:

= Distance/Speed

= 192 km / 96 km/h

= 2 hours

The time taken to drive back home:

= Distance/Speed

= 192 km / 64 km/h

= 3 hours.

To create the travel graph, we'll put time on the x-axis and distance on the y-axis. The journey would be a straight line from the origin (0,0) to the point (2,192) since she covers 192 km in 2 hours.

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