Determine whether the statement is true or false. If false, give a counterexample.

Being an equilateral rectangle is both a necessary and sufficient condition for being a square.

Using binomial probability, the probability of having exactly 4 dice on 4, 5 or 6 is 5/32.

Using binomial probability, we can calculate the probability that out of the 5 dice thrown, the probability of having exactly 4 dice on 4, 5 or 6 can be calculated as;

\(P(X=k) = C(n, k) * p^k * (1-p)^(^n^-^k^)\)

In the given data;

n = 5

k = 4

p = 3/6 = 1/2

Using the binomial probability formula, we can calculate:

P(X=4) = C(5, 4) * (1/2)⁴ * (1 - 1/2)⁵⁻⁴

P(X=4) = 5 * (1/2)⁴ * (1/2)¹

P(X=4) = 5 * (1/16) * (1/2)

P(X=4) = 5/32

Therefore, the probability that exactly 4 dice land on a 4, 5, or 6 when rolling five fair dice is 5/32.

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Answer:

$30.00

Step-by-step explanation:

The total walking area available to pedestrians visiting the park is approximately 15,310.7 square meters.

The total walking area available to a pedestrian visiting the park is the area of the park minus the area of the fountain. We can calculate these areas as follows:

Area of park = π(70)^2 = 4,900π

Area of fountain = π(5)^2 = 25π

Therefore, the total walking area available to pedestrians visiting the park is:

4,900π - 25π = 4,875π

This can be simplified as:

≈ 15,310.7 square meters

Therefore, the total walking area available to pedestrians visiting the park is approximately 15,310.7 square meters.

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Answer:

-1

Step-by-step explanation:

since the negative sign is directly next to the parentheses it will switch all the values in between the parentheses.

-1(-x+5) = (x-5)

Answer:

B

Step-by-step explanation:

-3^2 =+8999999999999999999999(9())))))))(-"""&+(()))))(&&%422222222222223

Answer:

a

Step-by-step explanation:

Answer:

3240°

Step-by-step explanation:

The sum of the interior angles of a polygon is found by (n-2)(180) where n is the number of sides so (20-2)(180) = (18)(180) = 3240°

Answer: The correct answer is b

Step-by-step explanation:

25% off $30 is 22.50 and then when you add 7%ax it turns out to be 24.08

Answer:

100

Step-by-step explanation:

y = % · x

y = 40% · 250

y = 0.40 · 250

y = 100

The windshield sector area is 706.86 cm².

To calculate the sector area of the windshield wiper, we need to use the formula for the area of a sector of a circle. The formula is:

A = (θ/360°) x πr²

where A is the area of the sector, θ is the central angle of the sector in degrees, and r is the radius of the circle.

In this problem, we are given that the windshield wiper has a length of 45 cm, which means that the radius of the circle traced by the wiper is 45 cm/2 = 22.5 cm.

We are also given that the wiper creates a central angle of 120° in one wipe. Substituting these values into the formula, we get:

A = (120°/360°) x π(22.5 cm)²

A = (1/3) x π x (22.5 cm)²

A ≈ 706.86 cm²

Therefore, the sector area of the windshield wiper is approximately 706.86 square centimeters.

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So first of all we need to list the three points A, B and C so we can properly calculate the transformation:

The first transformation we have to perform is a 90° clockwise rotation about the origin. If we perform this rotation on a point (x,y) we get:

Then we apply this to A, B and C:

Then we must perform a reflection over the x-axis on the points of triangle A'B'C'. A reflection over the x-axis is achieved by applying this transformation:

If we transform points A', B' and C' with this we get:

Then if we graph all the three triangles in the same grid we get the following picture:

As you can see this image is the same as the one in option D. This means that the answer to this question is graph D.

The concentration of salt in the incoming brine is 0.185 g/L.

The rate of change in the amount of salt, dx/dt, is determined by the difference between the rate of incoming salt and the rate of outgoing salt. The rate of incoming salt is the product of the concentration of the incoming brine, c, and the flow rate of 3 liters per minute.

The rate of outgoing salt is the product of the concentration of the solution in the tank, x/40, and the flow rate of 3 liters per minute. Therefore, the formula for the rate of change in the amount of salt is:

dx/dt = 3c - 3(x/40)

To find the formula for the amount of salt, x(t), after t minutes have elapsed, we can integrate the rate of change formula with respect to time:

x(t) = ∫(3c - 3(x/40))dt

Using the initial condition that x(0) = 0, we can solve for the constant of integration and obtain the formula:

x(t) = 120c - 3ct - (3/40)x(t)

Rearranging the terms and solving for x(t), we get:

x(t) = (120c - 3ct)/(1 + 3/40)

Finally, to find the concentration of salt in the incoming brine, c, given that x(15) = 20, we can plug in the values of t and x(t) into the formula and solve for c:

20 = (120c - 3c(15))/(1 + 3/40)

Simplifying and solving for c, we get:

c = (20 + 900/40)/(120 - 45)

c = 0.185 g/L

Therefore, the concentration of salt in the incoming brine is 0.185 g/L.

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Answer:

The Answer is (2x+3)(x+2)

The distance far up the wall that the top of the ladder​ touches is 24 cm.

Given that a the ladder is 25 cm long and the foot of the ladder is 7 m away from the base of the wall.

This forms a right triangle.

From Pythagoras theorem;

Hypotenuse² = A leg² + B leg²

Plug the given values in and solve for B leg

Hypotenuse² - A leg² = B leg²

B leg = √( Hypotenuse² - A leg² )

B leg = √( 25² - 7² )

B leg = √( 625 - 49 )

B leg = √576

B leg = 24 cm

Therefore, the height at which the top of the ladder sits on the wall is 24cm.

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Therefore, The explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

To find an explicit formula for the sequence, we first need to solve the recurrence relation. We can do this by finding the roots of the characteristic equation r^2 - 4r + 3 = 0, which are r = 1 and r = 3. Therefore, the general solution to the recurrence relation is ak = A(1)^k + B(3)^k, where A and B are constants determined by the initial conditions. Plugging in a0 = 1 and a1 = 2, we get the system of equations A + B = 1 and A + 3B = 2. Solving for A and B, we get A = 1/2 and B = 1/2. Therefore, the explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

Therefore, The explicit formula for the sequence is ak = (1/2)(1)^k + (1/2)(3)^k.

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The dimensions of the room will be 12m x 6m.

So, now calculate the dimensions of the room as follows:

Solve as shown:

Therefore, 12m x 6m will be the dimensions of the room.

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Answer:

n = 3200

Step-by-step explanation:

200 = 1000 - \(\frac{n}{4}\) ( subtract 1000 from both sides )

- 800 = - \(\frac{n}{4}\) ( multiply both sides by 4 to clear the fraction )

- 3200 = - n ( multiply both sides by - 1 )

n = 3200

Answer:

black

black

Step-by-step explanation:

y = (-6/5)x + 14/5 is the equation of line parallel to 6x+5y=1 and passing through (4,-2)

y = (-2/3)x - 19/3 is the equation of perpendicular to 3x-2y=3 and passing through (3,-7)

To find the equation of a line parallel to the given line, we need to use the same slope.

The given line has the equation 6x + 5y = 1.

5y = -6x + 1

y = (-6/5)x + 1/5

The slope of this line is -6/5.

The parallel line must have the same slope, the equation of the line parallel to 6x + 5y = 1 and passing through (4, -2) is:

y - (-2) = (-6/5)(x - 4)

y = (-6/5)x + 14/5

To find the equation of a line perpendicular to the given line, we need to use the negative reciprocal slope.

-2y = -3x + 3

y = (3/2)x - 3/2

The slope of this line is 3/2.

The negative reciprocal of 3/2 is -2/3.

So, the equation of the line perpendicular to 3x - 2y = 3 and passing through (3, -7) is:

y - (-7) = (-2/3)(x - 3)

y = (-2/3)x - 19/3

The line is at an angle of 60° from the x-axis, the slope can be determined using the tangent of 60°, which is √3. So, the slope (m) is √3.

To find the y-intercept (c), we can use the point-slope form of a line. Since the perpendicular distance is 3 units

Let's choose (0, 3) as a point on the line.

Using the point-slope form, we have:

y - 3 = √3(x - 0)

y - 3 = √3x

y = √3x + 3

Therefore, the equation of the line is y = √3x + 3.

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The transition matrix is [0.6 0.4; 0.2 0.8]. The probability of a blue male having a blue male after two and three generations is 0.52 and 0.448, respectively.

Let's denote the probability of a blue male having a blue male as P(BB) and the probability of a blue male having a green male as P(BG). According to the given information, P(BB) = 0.6 and P(BG) = 0.4 (since 100% - 60% = 40%).

To construct the transition matrix, we arrange the probabilities in the following format:

[ P(BB) P(BG) ]
[ P(GB) P(GG) ]

Since we only have information about the male parrots, the probabilities for females are not provided. Assuming independence between generations, the transition matrix for the male parrots is:

[ 0.6 0.4 ]
[ 0.2 0.8 ]

To calculate the probability of a blue male having a blue male after two generations, we multiply the transition matrix by itself:

[ 0.6 0.4 ] [ 0.6 0.4 ] = [ 0.52 0.48 ]
[ 0.2 0.8 ] [ 0.2 0.8 ] [ 0.28 0.72 ]

Therefore, the probability of a blue male having a blue male after two generations is 0.52.

To calculate the probability after three generations, we multiply the transition matrix by itself twice:

[ 0.6 0.4 ] [ 0.52 0.48 ] = [ 0.448 0.552 ]
[ 0.2 0.8 ] [ 0.28 0.72 ] [ 0.352 0.648 ]

Thus, the probability of a blue male having a blue male after three generations is 0.448.

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Given data:

The cost of the car is C=$20,000.

(a)

The final prize after sales tax in Los angeles is,

The final prize after sales tax in California is,

(b)

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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Answer: vertical angles

Step-by-step explanation:

The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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T satisfies property 1, and is thus a linear transformation.

T also satisfies property 2, and is a linear transformation.

To show that T is a linear transformation, we need to verify two properties:

1. T(a*u + b*v) = a*T(u) + b*T(v) for any vectors u, v in R3 and any scalars a, b.

2. T(c*u) = c*T(u) for any vector u in R3 and any scalar c.

Let's start with property 1. Suppose u = (u1, u2, u3) and v = (v1, v2, v3) are two arbitrary vectors in R3, and let a, b be scalars. Then, we have:

T(a*u + b*v) = T(a*u1 + b*v1, a*u2 + b*v2, a*u3 + b*v3)  [by definition of vector addition and scalar multiplication]

= (a*u1 + b*v1, a*u2 + b*v2, -(a*u3 + b*v3))  [by definition of T]

= (a*u1, a*u2, -a*u3) + (b*v1, b*v2, -b*v3)  [by distributivity of scalar multiplication over vector addition]

= a*(u1, u2, -u3) + b*(v1, v2, -v3)  [by definition of T]

= a*T(u) + b*T(v)  [by definition of T]

Therefore, T satisfies property 1, and is thus a linear transformation.

Now, let's check property 2. Suppose u = (u1, u2, u3) is an arbitrary vector in R3, and let c be a scalar. Then, we have:

T(c*u) = T(c*u1, c*u2, c*u3)  [by definition of scalar multiplication]

= (c*u1, c*u2, -c*u3)  [by definition of T]

= c*(u1, u2, -u3)  [by distributivity of scalar multiplication over vector addition]

= c*T(u)  [by definition of T]

Therefore, T also satisfies property 2, and is a linear transformation.

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Answer:

A concept in geology that describes transitions and relationships among the three main rock types

please mark as brainliest.

Answer:

b. A concept in geology that describes transitions and relationships among the three main rock types. and

c. A series of processes that create and transform the types of rocks in Earth's crust

Step-by-step explanation:

ive studied and this is correct because i took the test and i  got it correct

please give me 5 stars

The area of the sector is  305. 2 cm²

The area of the shaded part is equivalent to the area of the sector.

The formula for determining the area of a sector is expressed with the equation;

A = θ/360 × πr²

Given that the parameters of the equation are;

From the diagram shown, we have;

Area = 120/360 × 3.14 × 18²

find the square values

Area = 0. 3 × 3. 14 × 324

multiply the values

Area = 305. 2 cm²

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The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.

The critical value can be determined using a statistical table.

The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).

The critical value for a 5% level of significance is 10.76.

This value can be found in the statistical table given in the textbook.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.

The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).

The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).

In this case,

The F statistic is 3738/1048.93 = 3.56.

The critical value for a 5% level of significance can be found using a statistical table.

According to the table,

The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76

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Answer:

90 cm

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, then

50 ÷ 20 = 2.5

The legs of the similar triangle are 2.5 times the original legs, that is

legs of similar triangle = 2.5 × 36 cm = 90 cm

Answer:

522 miles

Step-by-step explanation:

Answer:

522 miles

Step-by-step explanation:

Ryan drove 754 miles in 13 hours.

754/13 = 58

That would be 58 miles per hour.

58 * 9 = 522

Ryan should drive 522 miles in 9 hours at the same rate.

Hope this helps.