the shape of the density curve for a dataset is like a triangle. that is, as we move to the left of the horizontal axis, it starts from zero height, then rises linearly until some peak, then declines linearly until reaches zero, then stays zero from there onward. if we standardize this dataset by calculating the standard scores, what is the geometrical shape of the density curve for the standardized dataset?

A) The ingredient she needed = Fruit juice  = 21 litres

                                                      Lemonade = 14 litres

B) The extra punch she can make = 20litres

C) The ratio of fruit juice and lemonade for second batch = 7:6

What is Ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

A)

Let 3x be fruit juice and 2x be the lemonade

3x + 2x = 35litres

5x = 35

x = 35/5

x = 7

Then, required ingredient she needed

Fruit juice = 3x7 = 21 litres

Lemonade = 2x7 = 14 litres

B)

According to question

The amount of fruit juice she had = 12litre

Let x be 12litre

as we know that the ratio of fruit juice to the lemonade is 3 : 2

Thus,

Fruit juice = 3(x) = 12 litres

                    x = 12/3

                    x = 4

Fruit juice = 3 x 4 = 12litres

putting the value in lemonade

Lemonade = 2(4) = 8 litres

So, The extra punch she can make :

12 + 8 = 20litres

C)

The ratio for new second batch she added 4litres in lemonade

Then it become :

Fruit juice = 21 litres

Lemonade = 14 litres + 4litres = 18

The ratio will be

21:18

7:6

Thus, the ratio of fruit juice to lemonade in second batch will be 7:6

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Given: The angle

To Determine: The supplement of the given angle

Solution

Please note that two angle are supplement if they are add up to 180⁰

So if the supplement is x. Therefore

Hence, the supplement of 123⁰ is 57⁰, OPTION C

Answer:

w = 35

Step-by-step explanation:

29 + 17w = 624

subtract 29 from both side

17 w = 595

divide both sides by 17

w = 35

6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)

A triangle is a three-sided polygon that consists of three edges and three vertices.

The given three vertices are D(1, 1), E(3, −1), and F(4, 4)

we need to find the area of triangle

Area of triangle=1/2|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|

x₁=1, x₂=3, x₃=4, y₁=1, y₂=-1, y₃=4

put in the formula

Area of triangle=1/2|1(-1-4)+3(4-1)+4(1-(-1))|

=1/2|-5+9+8)|

=1/2 |12|

=6 square units.

Hence 6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)

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The possible coordinates of the other points are (3 + √7, -1) and (3 - √7, -1)

From the question, we have

Where (x, -1) represents the other points

The distance between the points is the number of units between them

It is calculated using the following distance formula

d = √[(x₁ - x₂)²+ (y₁ - y₂)²]

Where x and y represent the coordinates of the given points

Substitute the known values in d = √[(x₁ - x₂)²+ (y₁ - y₂)²]

So, we have

d = √[(3 - x)²+ (2 + 1)²]

Evaluate the expression

d = √[(3 - x)²+ 9]

Recall that d = 4

So, we have

√[(3 - x)²+ 9] = 4

Square both sides

(3 - x)²+ 9 = 16

This gives

(3 - x)² = 7

So, we have

3 - x = ±√7

Solve for x

x = 3 ± √7

Hence, the coordinates are (3 + √7, -1) and (3 - √7, -1)

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7 cows will eat all the grass on the farm in 28 days

17 cows eat all the grass on the farm in 10 days

15 cows eat all the grass in the farm in 12 days

We can see a relationship between the number of cows and the number of days. A reduction of 2 cows leads to an increase in 2 days for the cows to eat the grass.

As a result, when we reduce the cows by 4 the increase in the number of days will be 8.

Hence, to reduce the cows from 15 to 7 we will reduce the number of cows by 8 resulting in an increase in 16 days for the grass on the farm to be eaten up

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Answer:

They are congruent by SAS:

Side: AB = CB

Angle: ∠ABD = ∠CBD

Side: BD = BD

Explanation:

Two triangles are congruent if they have the same interior angles and the same length of their corresponding sides.

If two of the angles are equal, we can say that all the interior angles are equal.

So, based on the given information we get:

1. AC ⊥ BD means that AC is perpendicular to BD, therefore,

∠ADB = ∠CDB = 90°

2. It is given that ∠A = ∠C

3. Since both of their interior angles are equal, we can say that all the interior angles are equal and:

∠ABD = ∠CBD

4. The triangle ABC is isosceles because two of their interior angles are equal, therefore AB = CB

5. BD = BD because it is the same segment.

6. By SAS (Side-angle-Side) we can say that ΔABD = ΔCBD

Because the side AB is equal to side CB, the angle ABD is equal to angle CBD, and the side BD is equal to itself.

Step 1

Given; A graph

Required; To find f(-4)

Step 2

The graph at x=-4 has a removable discontinuity. Therefore we can then conclude that f(-4) is undefined.

Hence, f(-4) is undefined

A removable discontinuity is a point on the graph that is undefined or does not fit into the rest of the graph.

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This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by

1

3

gives the next term. In other words,

a

n

=

a

1

r

n

−

1

.

Geometric Sequence:

r

=

1

3

This is the form of a geometric sequence.

a

n

=

a

1

r

n

−

1

Substitute in the values of

a

1

=

486

and

r

=

1

3

.

a

n

=

486

(

1

3

)

n

−

1

Apply the product rule to

1

3

.

a

n

=

486

1

n

−

1

3

n

−

1

One to any power is one.

a

n

=

486

1

3

n

−

1

Combine

486

and

1

3

n

−

1

.

a

n

=

486

3

n

−

1

Substitute in the value of

n

to find the

n

th term.

a

5

=

486

3

(

5

)

−

1

Simplify the denominator.

Tap for more steps...

a

5

=

486

81

Divide

486

by

81

.

a

5

=

6

Answer:

False

Step-by-step explanation:

Check using Pythagorean theorem (proof for right triangles)

[tex]10^2+24^2=25^2[/tex]

[tex]100+576=625[/tex]

[tex]676\neq 625[/tex]

False

Answer: The image and the preimage have the same orientation.

Answer:

The image and the preimage have the different orientation.

Step-by-step explanation:

i

took

the

test

The above relation is not a function

What is a function?

A function from either a set X to just a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. The Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi are credited with the first known attempt to the concept of function. Originally, functions were the idealization of how a variable quantity depended on another quantity. A planet's location, for example, is a function of time. Historically, the notion was developed with the infinitesimal calculus at the end of the 17th century, and the functions investigated were differentiable until the 19th century.

The above relation is not a function

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The balcony can hold 25 people of 160-pound weight.

According to the question,

We have the following information:

The maximum weight balcony can hold = 1816 kg

Weight of 1 person = 160 pound

Now, we will convert this weight into kilogram so that both the measurements have same units.

1 pound = 0.454 kg

160 pound = 160*0.454 kg

160 pound = 72.64 kg

Now, let's take the number of people balcony can hold to be x.

So, we have:

72.64x = 1816

x = 1816/72.64

x = 25

Hence, the number of people the given balcony can hold is 25.

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It is enough for him to use a simple random sample of 172 cars.

It is required that there are at least 10 successes and 10 failures to test a hypothesis that involves a proportion p in a sample of size n.

Following conditions are required for it:

1) np ≥ 10

2) n (1-p) ≥ 10

p = 6% = 0.06

n = 172

So, there are at least 10 successes and 10 failures in the 172 cars sample, it is enough for him to use a simple random sample of 172 cars.

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The equation of a function that results in a graph that shows exponential decay is f(x) = 3(0.7)ˣ

An exponential function is represented as

f(x) = abˣ

Where

A function that represents an exponential decay would have a rate less than 1

This is represented as b <1

From the list of options, we have

f(x) = 3(0.7)ˣ

By comparing f(x) = 3(0.7)ˣ and f(x) = abˣ, we have

b = 0.7

0.7 is less than 1

Hence, the exponential decay function is f(x) = 3(0.7)ˣ

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Answer:

   See below, where we have used the definitions of vertical angles and complementary angles, and used the substitution property of equality.

Step-by-step explanation:

You want a proof that angles complementary to congruent angles are congruent. That is, ∠1 ≅ ∠4.

1. ∠1 and ∠3 are complementary . . . . given

2. ∠2 and ∠4 are complementary . . . . given

3. ∠2 ≅ ∠3 . . . . vertical angles are congruent

4. ∠1 +∠3 = 90° . . . . definition of complementary

5. ∠2 +∠4 = 90° . . . . definition of complementary

6. ∠1 +∠3 = ∠2 +∠4 . . . . substitution property of equality

7. ∠1 +∠2 = ∠2 +∠4 . . . . substitution property of equality

8. ∠1 = ∠4 . . . . subtraction property of equality

9. ∠1 ≅ ∠4 . . . . definition of angle congruence

__

Additional comment

The idea of congruence applies to the shape of the geometry. The idea of equality applies to the measures of the angles. Angles are congruent when they have the same measure.

Using Pythagoras's theorem, the set of measurement that can be used to form a right triangle is √2, √7 and 9.

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The sides of a right angle triangle can be found using Pythagoras's theorem.

Therefore, Pythagoras's theorem is described as follows;

c² = a² + b²

where

Therefore, the sides of the triangle that can be used to form a right triangle will have to obey the Pythagoras's theorem,

(√2)² + (√7)² = 9

2 + 7 = 9

Therefore, the last option can form a right triangle.

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Answer:

(a)  19.6 ms⁻¹

(b)  2 s

(c)  9.8 ms⁻¹

(d)  4 s

Step-by-step explanation:

Constant Acceleration Equations (SUVAT)

[tex]\boxed{\begin{array}{c}\begin{aligned}v&=u+at\\\\s&=ut+\dfrac{1}{2}at^2\\\\ s&=\left(\dfrac{u+v}{2}\right)t\\\\v^2&=u^2+2as\\\\s&=vt-\dfrac{1}{2}at^2\end{aligned}\end{array}} \quad \boxed{\begin{minipage}{4.6 cm}$s$ = displacement in m\\\\$u$ = initial velocity in ms$^{-1}$\\\\$v$ = final velocity in ms$^{-1}$\\\\$a$ = acceleration in ms$^{-2}$\\\\$t$ = time in s (seconds)\end{minipage}}[/tex]

When using SUVAT, assume the object is modeled as a particle and that acceleration is constant.

Acceleration due to gravity = 9.8 ms⁻².

When the ball reaches its maximum height, its velocity will momentarily be zero.

Given values (taking up as positive):

[tex]s=19.6 \quad v=0 \quad a=-9.8[/tex]

[tex]\begin{aligned}\textsf{Using} \quad v^2&=u^2+2as\\\\\textsf{Substitute the given values:}\\0^2&=u^2+2(-9.8)(19.6)\\0&=u^2-384.16\\u^2&=384.16\\u&=\sqrt{384.16}\\\implies u&=19.6\; \sf ms^{-1}\end{aligned}[/tex]

Therefore, the initial speed is 19.6 ms⁻¹.

Using the same values as for part (a):

[tex]\begin{aligned}\textsf{Using} \quad s&=vt-\dfrac{1}{2}at^2\\\\\textsf{Substitute the given values:}\\19.6&=0(t)-\dfrac{1}{2}(-9.8)t^2\\19.6&=4.9t^2\\t^2&=\dfrac{19.6}{4.9}\\t^2&=4\\t&=\sqrt{4}\\\implies t&=2\; \sf s\end{aligned}[/tex]

Therefore, the time taken to reach the highest point is 2 seconds.

As the ball reaches its maximum height at 2 seconds, one second before this time is 1 s.

Given values (taking up as positive):

[tex]u=19.6 \quad a=-9.8 \quad t=1[/tex]

[tex]\begin{aligned}\textsf{Using} \quad v&=u+at\\\\\textsf{Substitute the given values:}\\v&=19.6+(-9.8)(1)\\v&=19.6-9.8\\\implies v&=9.8\; \sf ms^{-1}\end{aligned}[/tex]

The velocity of the ball one second before it reaches its maximum height is the same as the velocity one second after.

Proof

When the ball reaches its maximum height, its velocity is zero.

Therefore, the values for the downwards journey (from when it reaches its maximum height):

[tex]u=0 \quad a=9.8 \quad t=1[/tex]

(acceleration is now positive as we are taking ↓ as positive).

[tex]\begin{aligned}\textsf{Using} \quad v&=u+at\\\\\textsf{Substitute the given values:}\\v&=0+9.8(1)\\\implies v&=9.8\; \sf ms^{-1}\end{aligned}[/tex]

Therefore, the velocity of the ball one second before and one second after it reaches the maximum height is 9.8 ms⁻¹.

From part (a) we know that the time taken to reach the highest point is 2 seconds.  Therefore, the time taken by the ball to travel from the highest point to its original position will also be 2 seconds.

Therefore, the total time taken by the ball to return to its original position after it is thrown upwards is 4 seconds.

Answer: y = 1

Step-by-step explanation:

Given

7 + y = 5(2y - 1) + 3y ← distribute and simplify right side

7 + y = 10y - 5 + 3y

7 + y = 13y - 5 ( subtract y from both sides )

7 = 12y - 5 ( add 5 to both sides )

12 = 12y ( divide both sides by 12 )

1 = y

Answer:

Step-by-step explanation:

The simplified form of the expression as a fraction is -43/390.

Fractions are expression written as a ratio of two integers. For instance, a/b are known as fractions.

Given the expression below:

[2-|-2/3-2(-1/5)|]÷(-13)

In order to solve the expression, we will use the PEMDAS rule to have:

[2-|-2/3-2(-1/5)|]÷(-13)

[2-|-2/3+1/10)|]÷(-13)

Find the LCM

[2-|-20+3/30|]÷(-13)

[2-|-17/30|]÷(-13)

[2-(17/30)]÷(-13)

[60-17/30]÷(-13)

43/30÷(-13)

Change the division sign to multiplication

43/30÷(-13)

43/30 * -1/13

-43/390

This gives the simplified form of the expression.

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Proportion = 0.2119

P (X is less than or equal to 0.18) = P [(X-μ)/ sigma is less than or equal to (0.18-0.22)/ 0.05] = P(Z is less than or equal to -0.80). Using z-table proportion = 0.2119

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The length and width of the rectangle are 5.5 inches and 10.5 inches.

So, the dimensions of the rectangle:

Substitute the values in the formula as follows:

Therefore, the length and width of the rectangle are 5.5 inches and 10.5 inches.

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Answer:

8.2 units (nearest tenth)

Step-by-step explanation:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where (x₁, y₁) and (x₂, y₂) are the two points.

Given points:

Substitute the given points into the distance formula and solve for d:

[tex]\implies d=\sqrt{(4-6)^2+(-1-7)^2}[/tex]

[tex]\implies d=\sqrt{(-2)^2+(-8)^2}[/tex]

[tex]\implies d=\sqrt{4+64}[/tex]

[tex]\implies d=\sqrt{68}[/tex]

[tex]\implies d=8.2 \; \sf (nearest\;tenth)[/tex]

Therefore, the distance between the two given points is 8.2 units to the nearest tenth.

Answer: Yes

Step-by-step explanation: 250-250

An outlier is when some of the data is spread farther away from the rest of the data. It is far off from other data

Multistage cluster sampling with stratification, systematic sampling, simple random sampling and disproportionate stratified sampling are examples of probability sampling.Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection.

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If Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.

The total amount he earned = $893

The amount of retainer he earned = $125

The percentage he earned = 30%

30% of the sales = The total amount he earned - The amount of retainer he earned

Substitute the values in the equation

= 893-125

= $768

Consider the total sales as x

Then,

x × (30/100) = 768

0.3x = 768

x = 768/0.3

x = $2560

Hence, if Andrew earns 30% on all sales plus a retainer of $125 per week and If he earns $893 in one week, then the value of the his sales for that week is $2560.

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The arithmetic mean is 59.

What is arithmetic mean?

It is the sum of collection of numbers divided by the count of the numbers.

Conider AB is the nuber satisfying the condition. Hence,

[tex]10A+B=A+B+A\times B\\9A=A\times B\\[/tex]

Since AB is a two digit number hence, [tex]A\neq 0\\[/tex]. Hence, divide both sides by [tex]A[/tex].

[tex]9=B[/tex]

Hence, B is 9 and A can take any value from 1 to 9.

Hence, numbers are 19, 29, 39, 49, 59, 69, 79, 89,99.

Now, calculate arithmetic mean as follows:

[tex]AM=\frac{Sum \ of \ numbes}{Count \ of \ numbers}\\=\frac{19+29+39+49+59+69+79+89+99}{9}\\=59[/tex]

Hence, arithmetic mean of numbers is 59.

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