The number -4 is a distance of 4 units away from 0 on the number line.

The answer should be
B, The price of each cup of lemonade is $0.25, less at Florence's Lemonade Stand.

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I'm just finishing the challenge answer 5 math questions.
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None of the given statements are true.

We are aware that a rectangle's area is equal to the product of its length and breadth, and that the perimeter of any 2D shape is equal to the sum of the lengths of its other sides, excluding the circle.

Given:

The rectangular shape has a width of 4 units and a length of 6 units.

So, The perimeter of the rectangle is,

= 2(6 + 4)

= 20 meters.

and, The area of the rectangle is,

= (6×4)

= 24 square meters.

From the given statements none of the statements are true.

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Based on the given square of ABCD, the length of BD is proven to be V3a. The Perimeter of the square is a (2 + 2√2 + √(√3)). The value of a is a = √(3/2 - 3/4√3) so that the area of the square equals to √3.

First, we can divide the square ABCD into 2 triangles, DAB and BCD. To find the length of BD, we will focus on triangle DAB.

On  triangle DAB, we have 2 angles and 1 side known. We will use the sinus formula to find the length of DB.

sin B = sin A = sin D

 DA      DB        AB

sin 120°  =   sin 30°

 DB                 a

We need to find the value of sin 120 using the sinus formula:

Sin 2a = 2 sin a. cos a

sin 2(60°) = 2 sin 60° cos 60°

sin 120° = 2 (1/2) (1/2√3)

sin 120° = 1/2 √3

sin 120° = sin 30°

DB            a

1/2 √3  = 1/2

 DB          a

DB = √3 a --> Proven!

To determine the perimeter of the square, we need to know the length of all sides of the square.

In the triangle DAB, we have not know the length of DA. We need to find the length of DA by finding the angle ABD. Since a triangle must have a sum of angles equals to 180, then:

180° = BDA + DAB + ABD

180° = 30° + 120° + ABD

180° = 150° + ABD

ABD = 30°

Since the angle ABD equals to BDA, the length of DA should be equal to AB which is a.

Next, we focus on the second triangle, BCD. We have 2 sides and 1 angle known. We need to find the length of CD. To solve this, we need to use the cosinus formula:

a² = b² + c² - 2bc. cos A

CD² = BC² + DB² - 2 BC DB cos DBC

CD² = (√3 a)² + (V2a)² - 2 (√3a)(√2a) cos 75°

CD² = 3a² + 2a² - 2√6a² cos 75°

CD² = 5a² - 2√6a² co 75°

To find the value of cos 75, we will use the cos formula:

cos (A+B) = cos A cos B - sin A sin B

cos 75° = cos (30° + 45°)

cos (30° + 45°) = cos 30° . cos 45° - sin 30° . sin 45°

cos 75° = (1/2 √3) (1/2 √2) - (1/2) (1/2 √2)

cos 75° = (1/4 √6) - (1/4 √2)

cos 75° = 1/4 (√6 - √2)

CD² = 5a² - 2√6a² cos 75°

CD² = 5a² - (2√6a²)(1/4(√6 - √2)

CD² = 5a² - 1/2(6)a² + 1/2√12a²

CD² = 5a² - 3a² +√3a²

CD² = 2a² + √3a²

We can find the perimeter of the square is:

P = AB + BC + CD + DA

P = a + √2a + a (√(2+√3)) + a

P = a (2 + 2√2 +√(√3))

To find the area of the square, we can try to find the area of each triangle first.

A triangle DAB is:

A₁ = 1/2 . a . a. sin 120°

A₁ = 1/2 a² (1/2 √3)

A ₁= 1/4 √3 a²

Area of triangle BCD is:

A₂ = 1/2 (a√2) (a√3) sin 75°

A₂ = 1/2 √6 a² sin 75

Sin 75° = sin (30° + 45°)

sin 75° = sin 30° cos 45° + cos 30° sin 45°

sin 75° = 1/2 (1/2 √2) + 1/2√3 (1/2√2)

sin 75° = 1/4√2 + 1/4 √6

sin 75° = 1/4 (√2+ √6)

A₂ = 1/2√6 a² (1/4 (√2 + √6))

A₂ = 1/8 √12 a² + 1/8 (6) a²

A₂ = 2/8 √3 a² + 6/8 a²

A₂ = (1/4 √3 + 3/4) a²

Total area of both triangle equals to √3, then:

A₁ + A₂ = √3

1/4 √3 a² + (1/4 √3 + 3/4) a² = √3

(1/2 √3 + 3/4) a² = √3

a² = √3 / (1/2√3 + 3/4)

a² =         √3                  x   1/2√3 - 3/4

         1/2√3 + 3/4                1/2√3 - 3/4

a² = 3/2 - 3/4√3

       3/4 - 9/16

a² = 3/2 - 3/4 √3

       3/4  - 3/4

a = √(3/2 - 3/4√3)

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The number of grasses is 17, the number of weeds is 3 × 17 - 7 = 42, and the number of trees is 3 × 17 + 3 = 56.

Pollen is a fine powdery substance consisting of microscopic grains that are produced by the male reproductive organs of seed plants.

Let's call the number of grasses "G".

The number of weeds is 3G - 7.

The number of trees is 3G + 3.

The total number of sources is G + (3G - 7) + (3G + 3) = 108.

Combining like terms, we get 7G = 118.

Dividing both sides by 7, we find G = 17.

Therefore, the number of grasses is 17, the number of weeds is 3 * 17 - 7 = 42, and the number of trees is 3 × 17 + 3 = 56.

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Answer:

494ft^2

Step-by-step explanation:

Area of trapezoid = [ (20 + 32) / 2 ] * 3 = 78 ft^2

Area of square = 32 * 13 = 416 ft^2

Total area: 78ft^2 + 416ft^2 = 494ft^2

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Answer:

Below

Step-by-step explanation:

5 = 1 / (1-r)

1-r = 1/5

r = 4/5

Step-by-step explanation:

and a line going from the point 0 comma 100 )

Which graph represents the equation

graph of a line passing through the points negative

A box that measures 2 meters × 2 meters × 6 meters. So the longest piece of rebar (inside diagonal) that could fit in this box is 2√11 cm.

These are the specified parameters:

Length of the box (l) = 2 m

Breadth of the box (b) = 2 m

Height of the box (h) = 6 m

The longest piece of rebar (inside diagonal)

For example, inside diagonal = x

x² = l² + b² + h²

   = 2² + 2² + 6²

   = 4 + 4 + 36

   = 44

x = √44

x = 2√11 cm

So the longest piece of rebar (inside diagonal) is 2√11 cm.

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Answer:

C

Step-by-step explanation:

you open up the brackets and multiply 2 to whatever is inside and you'll get C

The rate of the area with the circle is increased after each of the following.

a. after 1s 15,707.963cm^2/s b. after 4s 62,800.889cm^2/s c. after 7 s 109,955.74 cm^2/s

50cm/s is the radius of the ripple per second, that is, radius(r) of the ripple after t seconds = speed * time(t)

Speed = 50cm/s

r = 50t

Area of a circle(A) = πr^2

The rate of change of area with radius is measured by:

dA/dt = π2r . dr/dt

Speed of ripple 50cm/s.

This can be the rate at which the radius changes with time (dr/dt)

dr/dt = 50cm/s

The rate at which the area is increased with time:

dA/dt = π2r . dr/dt

dA/dt = π2(50t).50

dA/dt = 5000πt

After 1 second:

dA/dt = 5000π(1)

= 15,707.963cm^2/s

After 4 seconds:

dA/dt = 5000π(4)

= 62,800.889cm^2/s

After 7 seconds:

dA/dt = 5000π(7)

= 109,955.74cm^2/s

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Answer:

B. 79.

Step-by-step explanation:

1. to connect two points C and T with line;

2. m∠ACT=(63/2)° and m∠BTC=(95/2)°, then

3. in ΔCDT m∠CDT=180-(m∠ACT+m∠BTC)=101°;

4. finally, m∠BDC=180-101=79°.

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The required principal in accounts A and B are $150 and $500 respectively, while the interest earned by account B is greater than the interest earned by account A.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.

SI = Principal [rate×time]

Here,
For Account A,
SI = Principal [rate×time]
8.10 = P [0.036 × 18 / 12]
P = $150

Similarly

For Account B,

P = $500

Now,
for an account, A interest earned in the first month is given as,
SI = 150 × 0.036 × 1 / 12
SI = $0.45

Similarly,
for account B interest earned in the first month is given as,
SI = $0.92

Thus, the required principal in accounts A and B are $150 and $500 respectively, while the interest earned by account B is greater than the interest earned by account A.

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The probability that the grocery delivery time is more than 15 minutes on a given day is P ( x > 15 ) = 0.75

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the grocery delivery time is more than 15 minutes on a given day be P

Now , the equation will be

The density function is f ( x ) = 1 / ( b - a )

And , the uniform distribution is over 0 to 60 minutes

So , a = 0

b = 60

Substituting the values in the equation , we get

f ( x ) = 1 / ( 60 - 0 )

f ( x ) = 1/60

f ( x ) = 0.01667

Now , the probability P = P ( x > 15 ) , where the termination point is 60 minutes

So , P ( x > 15 ) = ( 60 - 15 ) f ( x )

P ( x > 15 ) = 45 x 0.01667

P ( x > 15 ) = 0.75

Hence , the probability is 0.75

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A vertical line can be written in the form x = a, where a is the x-coordinate of any point on the line.

In mathematics, an equation is a statement that asserts the equality of two expressions. It contains an equals sign (=) and one or more variables, which represent unknown values. Equations are often used to solve problems and find the values of the variables that make the equation true. There are many types of equations, including linear equations, quadratic equations, and systems of equations, among others.

Here,

1. To find the equation of a line in slope-intercept form, we need to use the formula y = mx + b, where m is the slope of the line and b is the y-intercept. We are given the x-intercept and y-intercept of the line, so we can use them to find the slope and y-intercept:

x-intercept = -2, y-intercept = -10

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1), where (x1, y1) = (-2, 0) and (x2, y2) = (0, -10)

m = (-10 - 0)/(0 - (-2)) = -10/2 = -5

So the slope of the line is -5.

Now we can use the slope-intercept form equation to find the equation of the line:

y = mx + b

Substituting the values of m and b, we get:

y = -5x - 10

Therefore, the equation of the line in slope-intercept form that passes through the x-intercept = -2 and y-intercept = -10 is y = -5x - 10.

2. We are given a point (0, -6) and the slope m = 8. We can use the slope-intercept form equation to find the equation of the line:

y = mx + b

Substituting the values of m and the point (0, -6), we get:

-6 = 8(0) + b

b = -6

Therefore, the equation of the line in slope-intercept form that passes through the point (0, -6) and has a slope of m = 8 is y = 8x - 6.

3. We are given that the line is parallel to y = 5 and passes through the point (4, 9). Since the line is parallel to y = 5, it has the same slope as y = 5, which is 0. We can use the point-slope form equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values of m, x1, and y1, we get:

y - 9 = 0(x - 4)

y - 9 = 0

y = 9

Therefore, the equation of the line in slope-intercept form that is parallel to y = 5 and passes through the point (4, 9) is y = 9.

4. We are given that the line is perpendicular to x = -4 and passes through the point (3, 7). Since the line is perpendicular to x = -4, it is a vertical line and its slope is undefined. We can use the equation x = 3 to represent the line.

5. To find the slope of a line, we can use the formula:

m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

6. If the slope of a line is undefined, it means that the line is vertical. This happens when the change in the x-coordinates between any two points on the line is zero, which makes the denominator in the slope formula zero. In this case, the line does not have a slope, since the slope is defined as the ratio of the change in y-coordinates to the change in x-coordinates.

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Answer:

Step-by-step explanation:nnbjnj

Answer:

Order the row {5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19} from the smallest number to the biggest number:

{1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27}.

The minimum is 1, the maximum is - 27.

The median is the middle number in this row - 9.

The median of left part {1, 2, 5, 6, 7} is 5 and the median of the right part {12, 15, 18, 19, 27} is 18.

From the option A-D only number 11 is absent (numbers 1, 5 and 9 are part of the five-number summary).

Answer: correct choice is D.

Step-by-step explanation:

Answer:

Step-by-step explanation:

8

The correct statement is about 95% of the shoppers have between a 23.6% and a 28.2% chance of purchasing cookies.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

95% confidence interval for the proportion of all shoppers at a large grocery store who purchase cookies here is given to be (0.236, 0.282).

As the minimum limit value here is 0.236 and max limit value is 0.282, therefore the inferences here are given as:

At least 23.6% of the shoppers purchase cookies.

At most 28.2% of the shoppers purchase cookies

Therefore, the correct answer is A.

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The largest marginal relative frequency and its interpretation is

0.80; Individuals with brown eyes.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given, 80% of the population of a city have brown eyes and 20% do not,

let B for brown eyes and B' for nonbrown eyes

p(B) = 0.80

p(B') = 0.20

The study also shows that 20% of the people who do not have brown eyes do not have brown hair, while 90% of the people who have brown eyes have brown hair,

here H for brown hair and H' for non-brown hairs

p(H given B) = 0.90

p(H given B') = 0.20

using bays theorem for calculation,

p(H ∩ B) = p(H given B) x p(B)

p(H ∩ B) =  0.90 x 0.80

p(H ∩ B) = 0.72

p(H' ∩ B)  = p(B) - p(H ∩ B)

p(H' ∩ B)  = 080 - 0.72

p(H' ∩ B)  = 0.08

p(H ∩ B') = p(H given B') x p(B')

p(H ∩ B') = 0.20 x 0.20

p(H ∩ B') = 0.04

p(H' ∩ B')  = p(B') - p(H ∩ B')

p(H' ∩ B')  = 0.20 - 0.40

p(H' ∩ B')  = 0.16

Hair/eyes      Brown    other       total

Brown              0.72      0.04         0.76

other                0.08      0.16          0.24

total                 0.80       0.20            1

so 0.80 is the highest which is for brown eyes.

Hence option C is correct.

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The mode of the data set of temperatures in various cities in San Diego County is 78°.

Mode is a measure of central tendency that represents the value that occurs most frequently in a data set. It gives an idea about which value is the most likely to appear in the data set. In a set of data, there can be one mode, more than one mode (referred to as bimodal or multimodal), or no mode at all (referred to as being non-modal).

In this case, the number 78 appears twice, while all the others appear only once.

Therefore, the mode is 78.

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Let the width be [tex]w[/tex] inches and the length be [tex]w+15[/tex] inches.

So, the dimensions of the box are [tex]w-6[/tex], [tex]w+9[/tex], and [tex]3[/tex] inches.

[tex]3(w-6)(w+9)=1350 \\ \\ (w-6)(w+9)=450 \\ \\ w^2+3w-54=450 \\ \\ w^2+3w-504=0 \\ \\ (w+24)(w-21)=0 \\ \\ w=-24,21[/tex]

Rejecting the negative case, [tex]w=21[/tex].

So, the dimensions are 21 by 36 inches.

The answers are proportional , ce, segment addition postulate if the Triangle XYZ is a right triangle with ZQ XY.

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

Given,

Triangle XYZ is a right triangle with ZQ XY.

proportional

ce

segment addition postulate

You want the words that finish the proof of the Pythagorean theorem.

Similar triangles

The proof makes use of the fact that the right triangles in the figure are all similar, and the fact that similar triangles have proportional sides.

The proportion b/c = e/b can be rearranged to b² = ce.

Then the segment addition theorem is invoked to let you use the fact that f+e = c.

Therefore, The answers are proportional , ce, segment addition postulate if the Triangle XYZ is a right triangle with ZQ XY.

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The graph of the function g(x) = f(2x) is given by the image presented at the end of the answer.

The asymptotes of f(x) are given as follows:

Hence the definition of the rational function f(x) is given as follows:

f(x) = 2/(x - 2) - 2.

The function g(x) is obtained replacing the lone instance of x on f(x) by 2x, hence:

g(x) = 2/(2x - 2) - 2

g(x) = 2/(2(x - 1)) - 2

g(x) = 1/(x - 1) - 2.

Hence the graph of the function g(x) = 1/(x - 1) is given by the image presented at the end of the answer.

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One possible solution from the graph(attached at the end of the solution) is selling 9 bags of popcorn and 5 bags of candies.

As per the given data:

The number of popcorn bags is x

The number of candies is y

The cost of each popcorn bag is $7

The cost of each candy is $4

She has $80 to spend on them

Inequality is the nonequal comparison of two or more variables and numbers.

So the first inequality is

7 x + 4 y ≤ 80

Since she must buy no less than 16 bags of popcorn and candies

The second inequality is

x + y ≥ 16

The red area represents the 1st inequality

The blue area represents the 2nd inequality

The solutions lie in the common part of red and blue colors

One possible solution is ordered pair (9,5)

(Graph attached at the end of solution)

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If  Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, the distance he can  explore and still make it back by sunset is : 1.24 miles.

In order to find how far  Derrick can explore, we need to know how much time he has before sunset.

If the sun sets at 4:45 pm, and he leaves at 12 pm, we can find the amount of time he has by subtracting 12 pm from 4:45 pm.

4:45pm - 12:00pm

= 4:45pm

We can convert the hours and minutes to minutes only.

4 hours × 60 minutes/hour + 45 minutes

= 260 minutes

Since Derrick's walking speed is 3.5 mph, let convert this to minutes per mile by using the conversion factor 1 hour = 60 minutes.

Now let find the  distance Derrick can travel

Distance = 260 minutes / 3.5 mph × 60 minutes/hour

Distance = 260 minutes / 210 minutes/mile

Distance  = 1.24 miles

Therefore Derrick can explore 1.24 miles before sunset.

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These connections are best represented using equations. M-3T-10 as well as M + T = 50 are in Option B.

a time frame in a person's life, defined in years from birth, that is frequently characterized by a distinct stage or stage of physical and mental development and involves the development of legal ability and responsibility: the legal age of majority; the legal age of consent; The legal drinking age was increased by the state from 18 to 21.

As of 1971, a minor in the U.s. is typically considered to be someone who is underneath the age age 18. However, those below the age of twenty-one may also occasionally be referred to that as minors in the framework of drinking or gambling legislation.

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Answer:

$58.50

Step-by-step explanation:

5616/96

The value of X is 22.

Value is regard that something is held to deserve,  the important worth or usefulness of something.

The calculation is as follows:

In the case of an isosceles trapezoid if there is any lower base angle is supplementary to any upper base angle.

So,  

6x + 2x + 4 = 180

8x + 4 = 180

8x = 176

x = 22

Therefore we can conclude that The value of X is 22.

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If a  colony of bacteria has an initial population of 5,000. After applying a test serum to the bacteria, the population decreases 7% each day. The equation that represent  change in bacteria population is: P(t) = 5000(1-0.07)^t.

The equation for the change in bacteria population over time can be represented as:

P(t) = P0(1-r)^t

Where:

P(t) =  population at time t (in days)

P0 =  initial population = 5,000

r = rate of change = -0.07 for a 7% decrease per day

t = number of days

So,  the equation is:

P(t) = 5000(1-0.07)^t

Therefore the equation that represent  change in bacteria population is: P(t) = 5000(1-0.07)^t.

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The best interpretation is A) We are 95% confident that the proportion who intend to vote for Candidate R from the random sample is between 42% and 52%.

The confidence interval is constructed based on the sample data, not the population. The interval represents the range in which the true proportion of people who intend to vote for Candidate R in the population is likely to fall, given the sample data. The margin of error of 5% indicates that the estimate may be off by up to 5%. So, there is a 95% chance that the true proportion is between 42% (47% - 5%) and 52% (47% + 5%).

Option D) We are 95% confident that the proportion who intend to vote for Candidate R from the population is 47% is not correct because there is always some degree of uncertainty in sample estimates. The confidence interval takes into account this uncertainty by providing a range of possible values.

Option E) We are confident that 95% of the population intended to vote for Candidate R is not correct because the confidence level refers to the level of confidence in the estimate, not the proportion of people who actually intend to vote for the candidate.

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