which of these shapes is a right isosceles triangle?

Answer:

24 cans of soda for $8.89 is the better deal.

Step-by-step explanation:

Divide 24 cans of soda for $8.89 by 2. That way, with the same amount of cans, you can determine which one is more expensive.

1) 12 cans of soda: $4.75

2) 12 cans of soda: $4.445

The second one is cheaper.

The largest possible side length of the tiles that can be used is `12` inches as it can cover the entire bathroom without any gaps or cutting of tiles.

The largest tile that can be used is a square tile. To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4.

`48/4 = 12`

`60/4 = 15`

The largest possible side length of the tiles that can be used is `12` inches. Jayla's parents are replacing their bathroom floor with square tiles. The floor is a rectangle that is `48` inches by `60` inches. To cover the entire bathroom with no gaps, and without having to cut any of the tiles, they need to use a tile that is the same size as the largest possible tile that can cover the entire floor without any gaps.

To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4. This is because a tile needs to cover 4 sides of the floor without any gaps, so the side length of the tile needs to be equal to the length divided by 4, or the width divided by 4.

In this case, the side length of the largest possible tile is `12` inches. This is because `48/4 = 12`, and `60/4 = 15`. As `15` is larger than `12`, the side length of the largest possible tile is `12` inches. This means that the tiles need to be `12` inches by `12` inches in size to cover the entire bathroom without any gaps.

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The sequence is a geometric sequence with a common ratio of 4.

What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed non-zero number called the common ratio (r).

To determine whether the sequence is arithmetic or geometric, we can look at the differences between consecutive terms.

The difference between the second and first terms is 2 - 0.5 = 1.5.

The difference between the third and second terms is 8 - 2 = 6.

The difference between the fourth and third terms is 32 - 8 = 24.

The difference between the fifth and fourth terms is 148 - 32 = 116.

Since the differences are not constant, the sequence is not arithmetic.

To determine if it is a geometric sequence, we can look at the ratios of consecutive terms.

The ratio of the second and first terms is 2/0.5 = 4.

The ratio of the third and second terms is 8/2 = 4.

The ratio of the fourth and third terms is 32/8 = 4.

The ratio of the fifth and fourth terms is 148/32 = 4.

Since the ratios are constant, the sequence is geometric with a common ratio of 4.

Therefore, the sequence is a geometric sequence with a common ratio of 4.

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The value of MN is 3.05

Along with arithmetic, geometry is one of the earliest subfields of mathematics. It is concerned with spatial characteristics like the separation between objects, their shape and size, and their relative positions.

Since MN=NK,

draw an isosceles triangle (two sides are equal).

Mark the angle N as 110 degrees.

Now, draw a line from N to the opposite side at a right angle. This line will divide MK=5 in half since MN = NK.

It will also divide angle N into half. So, we will end up with a right triangle with one side 5/2 = 2.5 and the opposite angle 55 degrees.

sin(55) = opposite / hypotenuse = 2.5 / MN = 0.82

MN = 2.5 / 0.82 = 3.05

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Answer:

Subtracting integers can be represented using integer tiles. For example, if we want to subtract -3 from 4, we can lay out 4 tiles on the number line and then add -3 tiles, like this:

4 3 2 1 0 -1 -2 -3

The subtraction problem can be represented as 4 + (-3). Adding the opposite of the second number, as Paul suggests, means finding the sum of 4 and -3, which is 1. So, Paul is correct that subtracting integers is equivalent to adding the opposite of the second number.

If the circumference of a circular field is 308 m, then it's Area is (b) 7546 m²  .

The formula for the Circumference of circle is = 2πr  ; Where r is = radius ;

The circumference is 308m, so we substitute in the required value and solve for r  ;

⇒ 308 = 2πr

⇒ r = 308/(2π)

⇒ r = 49  ;

Now that we have the radius, Next , we use the formula for the area of a circle to find the area  ;

The area of circle is ⇒ Area = πr² ;

Substituting in the value of radius(r) , we get ;

⇒ Area = π(49)²  ;

⇒ Area = 7546 m²   ;

Therefore , area of the circular field is 7546 square meters.

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The given question is incomplete , the complete question is

The circumference of a circular field is 308m, Find its Area .

(a) 7050 m²

(b) 7546 m²

(c) 7946 m²

(d) 8129 m²

The probability of winning $2 without getting below $0 at any time is 1/4  or 0.25.

To calculate the probability of winning $2 without getting below $0 at any time, we can use a branching diagram to track the possible outcomes.

Starting from $0, there are two possible outcomes for the first flip: heads or tails. If the first flip heads, the outcome is $1 and there are two possible outcomes for the second flip: heads or tails. If the second flip heads, the outcome is $2 and we have won the game. If the second flip is tails, the outcome is back to $0 and we have to start over. If the first flip is tails, the outcome is $-1 and we also have two possible outcomes for the second flip: heads or tails. If the second flip heads, the outcome is back to $0 and we have to start over. If the second flip is tails, the outcome is $-2 and we have lost the game.

Putting all of the possible outcomes together, we get the following branching diagram:

              H                              T

         /          \                       /     \

       H             T                  H      T

     /     \          /                      \

    H      T     T                        H

   $2    $0   -$1                       -$2

The only way to win $2 without getting below $0 at any time is to get two heads in a row. This can only happen along the top branch of the diagram, which has a probability of (1/2) * (1/2) = 1/4.

Therefore, the probability of winning $2 without getting below $0 at any time is 1/4 or 0.25.

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The missing length of the triangle is the hypotenuse which is given by 12.08

Pythagorean theorem states that the sum of the square of the opposite and adjacent sides of a triangle is equal to the square of the hypotenuse.

a² + b² = c²

c = √a² + b²

a = 11

b = 5

c = √a² + b²

= √11² + 5²

= √121 + 25

= √146

c = 12.08304597359

Approximately,

c = 12.08

Consequently, the hypotenuse of the triangle is approximately 12.08

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When the outside temperature is 30°F, the sales is $414.13

When the sale is $1,993.33, the outside temperature is 78°F

Since the equation y = 32.9x - 572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, x, in degrees Fahrenheit (F).

Thus, when the outside temperature is 30°F, the sales can be estimated by substituting x = 30°F into the equation and solving for y. That is:

y = 32.9x - 572.87

y =  32.9(30) - 572.87

y = 987 - 572.87

y = $414.13

Thus, when the sale is $1,993.33, the outside temperature can be estimated by substituting y = $1,993.33 into the equation and solving for x. That is:

y = 32.9x - 572.87

1,993.33 = 32.9x - 572.87

32.9x = 1,993.33 + 572.87

32.9x = 2566.2

x = 2566.2/32.9

x = 78°F

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The probability of randomly drawing a candy that is not brown, replacing it, and then drawing a white candy is 0.08, or 8%.

There are 70 sweets in the jar, 14 of which are brown, hence the likelihood of getting a candy that is not brown on the first draw is:

(70 - 14) / 70 = 56 / 70 = 0.8 P(not brown)

The jar still has 70 candies after replacing the candy, and there are now 7 white candies. As a result, the likelihood of drawing a white candy on the second draw is:

P(white) = 0.1 / 70

Because the two drawings are independent (the first candy is replaced before the second), we can multiply the odds to get the likelihood of both events occurring:

P(not brown and white) = P(white) * P(not brown) = 0.8 * 0.1 = 0.08

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There is a 0.06% chance that a randomly selected individual from the population would have the same genotype as the evidence sample at the FGA locus.

As a forensic scientist, one of your important tasks is to determine the likelihood that a particular piece of evidence matches a specific individual.

To determine the random match probability for the evidence sample at the FGA locus, you will need to compare it to the reference sample. The reference sample is typically obtained from a suspect or a known individual who is not a suspect in the crime. The reference sample for the FGA locus has a genotype of 16,17.

The random match probability is the probability that a randomly selected individual from the population would have the same genotype at a specific locus as the evidence sample. To calculate this probability, you will need to use the allele frequency of the FGA locus in the population. This frequency is typically obtained from a large database of individuals.

Let's assume that the allele frequency for the FGA locus is 0.03 for the 16 allele and 0.02 for the 17 allele. To calculate the random match probability, you will need to multiply these two frequencies together since the evidence sample has both alleles present. This gives us a probability of 0.0006 or 0.06%.

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Complete Question:

You are a forensic scientist and you are able to obtain the following 3 CODIS STR genotypes from an evidence sample found at a crime scene:

Locus       Evidence Genotype

D55818    6,10

FGA         16,17

VWA        11,12

Based on the reference sample, what is the random match probability for the evidence sample at the FGA locus?

Answer:

C = 3.14

Step-by-step explanation:

Center of the circle is (h, k)

h = 4,  k = 1

Use the equation of a circle and the given point (4, -4) to find r:

r² = (x-h)² + (y-k)² = (4-4)² + (-4-1)² = 0 + (-5)² = 25

r = √25 = 5

Find circumference, C:

C = 2πr = 2π(5) = 31.4

Brainly doesn't provide drawing tools, but you can easily draw this circle.  Just plot the center point (4, 1), then draw a circle with a radius of 5 around it.  You'll see that this circle passes through the point (4, -4).

If a least square regression line fits the data well, the characteristic should the residual plot exhibit is random scatter

The least squares regression line fits the data well.

The least squares regression is defined as the method that used to find the regression line or best suitable line for the given pattern

So if the data shows a linear relationship between the two given variable so such line will be called least squares regression line

The residual plot is the measure that vertical line how much misses from the data point

Here the least square-square regression lines fits the data well so the characteristics will be random scatter

Therefore, the characteristic that the residual plot exhibit is random scatter

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Answer:

The statement "A = (1/2) (B)(B + 5)" represents the area of a triangle, where B is the base of the triangle and (B + 5) is the height. This formula is used by the carpenter to calculate the area of a triangle with a given base and height.

Step-by-step explanation:

Let L be the length of the rectangular garden.

The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

Substituting the given values, we get:

328 = 2L + 2(67)

Simplifying the equation, we get:

328 = 2L + 134

2L = 328 - 134

2L = 194

L = 194/2

L = 97

Therefore, the length of the rectangular garden is 97 meters.

Answer:

see explanation

Step-by-step explanation:

the cost C(x) is the total of the number of erasers made and the fixed cost

(a)

let x be the number of erasers

C(x) = 0.16x + 455

(b)

substitute x = 3000 into C(x) for total cost

C(3000) = 0.16(3000) + 455 = 480 + 455 = 935

total cost = $935

Answer:

a)  See the attachment for the completed Venn diagram.

b)  The number of people who liked to watch television only is 20.

c)  The total number of people who took part in the survey was 200.

Step-by-step explanation:

Draw a Venn diagram with two overlapping circles.

Label one circle "Radio" and the other circle "TV".

Given that 50 people like to listen to the radio but not like to watch television, place the number 50 in the part of the radio circle that does not overlap the TV circle.

Given that 120 people like to listen to the radio, and 50 people like to listen to the radio but not like to watch television, then the number of people who like to listen to the radio and watch tv is:

Therefore, place the number 70 in the part where the two circles overlap.

Given that 110 people don't like to watch television, and 50 people like to listen to the radio but not like to watch television, then the number of people who don't like to listen to the radio or watch television is:

Therefore, place the number 60 in the area outside the two circles.

Given that 80 people don't like to listen to the radio, and 60 people don't like to listen to the radio or watch television, then the number of people who like to watch the television only is:

Therefore, place the number 20 in the part of the TV circle that does not overlap the radio circle.

Now the Venn diagram has been completed, we can find the total number of people who took part in the survey by adding all the numbers in the Venn diagram:

Therefore, there was a total of 200 people who took part in the survey.

The proof that AE = EF is done from the congruency theorem of triangles and the Pythagorean identity.

In order to prove that AE = EF, note that angle CEF is a right angle since EF is perpendicular to the diameter CD and intersects it at E.

Since AE = EB, triangles AEB and CED are congruent (SAS theorem)

Therefore, angle EAF is congruent to angle ECF.

Also, angle EAF is a right angle, since it is inscribed in a semicircle with a diameter CD.

Therefore, triangles EAF and ECF are similar by the Angle-Angle (AA) theorem.

Since they are similar, the ratio of corresponding side lengths is the same.

Since AE = EB, we have that:

AE / EF = EC / CF

But we also know that EC = ED + DC = ED + 2EF, since CD is the diameter of the semicircle and EF meets it at E perpendicularly.

Similarly, we have CF = CD + DF

CF = 2EF + DF, where DF is the other leg of the right triangle CDF.

Substituting these expressions for EC and CF in the above equation, we get:

AE / EF = (ED + 2EF) / (2EF + DF)

Simplifying this equation, we get:

AE / EF = (ED/EF) + 2 / (2 + DF/EF)

But ED/EF = sin(DEF) and DF/EF = sin(EFD) by the definition of sine in right triangle DEF. Since the angles DEF and EFD add up to 90 degrees, their sines are complementary.

Therefore, we have that:

ED/EF = cos(EFD) and DF/EF = sin(DEF)

Substituting these expressions in the above equation, we get:

AE / EF = cos(EFD) + 2 / (2 + sin(DEF))

But cos(EFD) + 2 = sin(DEF) (Pythagorean identity).

Therefore, we have:

AE / EF = sin(DEF) / (2 + sin(DEF))

Multiplying both sides by (2 + sin(DEF)), we get:

AE = EF

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Answer: no answer

Step-by-step explanation:

All possible numbers that are co-primes with the following numbers are mentioned below in detail. The possible co-primes of 390 are 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.

Co-prime numbers are pairs of numbers that only share the factor 1 in common. They are additionally referred to as reasonably prime numbers.

In the given question,

(a) 390

The prime factors of 390 are 2, 3, 5, and 13. All of the numbers that are co-prime with 390 are those that do not share any of these prime factors. This includes the numbers 1, 7, 11, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, and 49.

(b) 210

The prime factors of 210 are 2, 3, 5, and 7. All of the numbers that are co-prime with 210 are those that do not share any of these prime factors. This includes the numbers 1, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, and 49.

(c) 49335

The prime factors of 49335 are 5, 7, 11, and 13. All of the numbers that are co-prime with 49335 are those that do not share any of these prime factors. This includes the numbers 1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, and 49.

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The experimental probability that the number rolled was odd is

23 over 60.

What is experimental probability?

Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A trial is a repeating of an experiment that is performed a certain number of times.

We are given a table showing he frequency of each number rolled.

We know that the odd number outcomes are 1, 3 and 5.

So,

P (x = 1) = 8/60

P (x = 3) = 6/60

P (x = 5) = 9/60

So, the experimental probability that the number rolled was odd is

⇒P ( x is odd) = P (x = 1) + P (x = 3) + P (x = 5)

⇒P ( x is odd) = 8/60 + 6/60 + 9/60

⇒P ( x is odd) = 23/60

Hence, the experimental probability that the number rolled was odd is 23 over 60.

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The slope of the line that passes through the points (0, - 4) and (30, -9) is -1/6.

In Mathematics, 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) = rise/run

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

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-9 + 4)/(30 - 0)

Slope, m = -5/30

Slope, m = -1/6.

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Answer:

Step-by-step explanation:

$3120 and $3888

width of the road=2m

outer Rectangle, I = 40m, b = 16m

Inner Rectangle, I = 36m, b = 12m

Area of Outer rectangle = 40x16= 640m2

Area of inner Rectangle = 36x12= 432m2

Area of the road=640-432 =208m2

cost of paving bricks  $15

=208x15 = $3120. Ans

Area of inner Rectangle 432m2

cost of covering with grass  $9

= 432x9= $3888.

Answer: brick cost= 3120 grass cost =3888

Step-by-step explanation:

Calculate area of the road by subtracting the area of the inner plot (36x12) from the area of the whole plot (40x16). Multiply the individual costs by the area of their respective places.

(40x16) - (36x12) = 208

208x16 = 3120

36x12 = 432

432x9 = 3888

Answer:

lower quartile = 75

Step-by-step explanation:

the lower quartile Q₁ is situated at the left side of the box.

lower quartile Q₁ = 75

Answer:

minimum is $14.40

maximum is $18

she can get 9 ice cream cups

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

On a graph that's up 1 over 4 and its rise over run or (rise/run)

The answers are a) standard deviation ≈  0.02 b) probability ≈ 0.95 c) standard deviation ≈  0.031 d) probability ≈ 0.8098 e) decrease in P = 0.1402

Given: p = 75% or 0.75

n = 450

a) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation is [tex]\sqrt \frac{p(1-p)}{n}[/tex]

= [tex]\sqrt{\frac{0.75(1-0.75)}{450} }[/tex] = 0.02

b) [tex]\^{p} - p[/tex] = 0.04

[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

z = ±1.96(approx.)

p(-0.04 <  [tex]\^{p} - p[/tex] < 0.04)

=P(-1.96 < z < 1.96) = 1 - 2P(z < -1.96)

= 1 - 2(0.0250) = 0.95

c) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation [tex]\sqrt \frac{p(1-p)}{n}[/tex]

= [tex]\sqrt{\frac{0.75(1-0.75)}{200} }[/tex] = 0.031

d) [tex]\^{p} - p[/tex] = 0.04

[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

z = ±1.31(approx.)

p(-0.04 <  [tex]\^{p} - p[/tex] < 0.04)

=P(-1.31 < z < 1.31) = 1 - 2P(z < -1.31)

= 1 - 2(0.0951) = 0.8098

e) Determine the difference in probabilities (of part b) and part d))

The loss in precision by decreasing the sample size 0.9500 - 0.8098 = 0.1402

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Complete question is:

In 2008 the Better Business Bureau settled 75% of complaints they received. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.75, the same as the overall proportion of complaints settled in 2008. a) Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex].b) Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? c) Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex] . d) Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? e) As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?