Based on experience, Farmer Fern knows that 15% of her eggs will be damaged in
route to the stores. In a sample of 100 eggs, what is the probability that less than
13% will be damaged?

Answer:

increasing, constant, decreasing, constant

Step-by-step explanation:

the first line is going up so it's increasing

the line then goes horizontal which is constant

then the line goes down which is decreasing

then the line again goes horizontal which is constant

Answer:

The area of this triangle is about 21.2132 square units.

Step-by-step explanation:

First, find the lengths of the legs AB and BC.

Length of AB ===

Find the difference in position vertically:

\(-2-4=-6\)

The points are 6 units apart vertically.

Find the difference in position horizontally:

\(3-0=3\)

The points are 3 units apart horizontally.

These lengths form a right triangle with the distance between the points as the hypotenuse, so you can use the pythagorean theorem to solve:

\(a^2+b^2=c^2\\3^2+6^2=c^2\\9+36=c^2\\45=c^2\\c\approx6.7082\)

AB is about 6.7082 units long.

Length of BC ===

Same process as above.

Find the vertical distance:

\(-4--2=-2\)

2 units apart vertically.

Find the horizontal distance:

\(-3-3=-6\)

6 units apart horizontally.

Use the pythagorean theorem:

\(2^2+6^2=c^2\\4+36=c^2\\40=c^2\\c=6.3246\)

BC is about 6.3246 units long.

Area ===

Finally, you can use these to find the area of the triangle. The area of a right triangle is just half the area of a rectangle with the same base and height:

\(A=\frac{b\times h}{2}\\\\A=\frac{6.7082\times6.3246}{2}\\\\A=\frac{42.4264}{2}\\\\A=21.2132\)

The area of this triangle is about 21.2132 square units.

Answer:

Step-by-step explanation:

You want the number of text messages sent by each of Yolanda, Ryan, and Henry if they sent a total of 127, and Ryan sent 7 more than Yolanda, while Henry sent 4 times as many as Yolanda.

The relationships expressed in the problem statement can be written as equations:

Using the last two equations to substitute into the first, we have ...

  y +(y +7) +(4y) = 127

  6y = 120 . . . . . . . . . . . . subtract 7

  y = 20 . . . . . . . . . . . divide by 6

  r = 20 +7 = 27

  h = 4·20 = 80

Yolanda sent 20 text messages, Ryan sent 27, and Henry sent 80.

MMCMLVII in Hindu-Arabic is 2957

The Hindu-Arabic system uses the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 to count.

Analysis:

MM = 2000

+

CM = 900

+

L = 50

+

VII = 7

MMCMLVII = 2957

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Answer:

 1/6

Step-by-step explanation:

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

# of successful outcome = 24

a) a multiple of 5

(multiple of 5) = no of possible outcome/ no of successful outcome

= 4/24

= 1/6

Answer:

Below in bold.

Step-by-step explanation:

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48.

There are 24 even numbers  less than 50.

Of these 10 20 30 and 40 are multiples of 5 - a total of 4.

So the required probability is  4/24 = 1/6.

Answer:

1:3

Step-by-step explanation:

7:21

1:3

so , 7:21 is 1:3.

Formula-

If a set has “n” elements, then the number of subset of the given set is 2n and the number of proper subsets of the given subset is given by 2n-1. Consider an example, If set A has the elements, A = {a, b}, then the proper subset of the given subset are { }, {a}, and {b}

Symbol that can be used-

The symbol "⊆" means "is a subset of". The symbol "⊂" means "is a proper subset of".

Hope it helps you... pls mark brainliest if it helped you.

Note- this answer was taken a little from "Byjus, shaala and remaining I typed myself.

Answer:

12 1/2

Step-by-step explanation:

2 x 5 = 10

1/2 x 5 = 2 1/2

10 + 2 1/2 = 12 1/2

Answer:

Step-by-step explanation:

183,883,72

Answer:

18388372

Step-by-step explanation:

1 )Use the algorithm method.

      3 2 1 7

×              5      7      1      6

        1      1       1      4                      

        1      9      3      0     2            

        3 2  1  7 0

  2 1  1     4  

  2 2 5    1       9      0     0

1  1     3

1  6 0 8   5       0      0     0

      1  1    1

1  8 3 8   8       3       7     2

2 )Therefore, 3217 × 5716 = 18388372.

18388372

Answer:

When two like-poles point together.

Step-by-step explanation:

When two like-poles point together, the arrows from the two magnets point in OPPOSITE directions and the field lines cannot join up. So the magnets will push apart (repel). ... It's only when you hold unlike-poles together (a north pointing to a south) that magnets stick together (they are attracted).

Answer:

When two like-poles point together, the arrows from the two magnets point in opposite directions and the field lines cannot join up. So the magnets will push apart. It's only when you hold unlike-poles together that magnets stick together.

Step-by-step explanation:

The solution to the equation 3 / 5x-2 = 2 / 3x-1 is x = 1.

Given the equation in the question;

3 / 5x-2 = 2 / 3x-1

To solve for x, cross multiply the equation

3 / 5x-2 = 2 / 3x-1

3( 3x - 1 ) = 2( 5x - 2 )

Apply distributive property

3( 3x - 1 ) = 2( 5x - 2 )

3×3x + 3×-1 = 2×5x + 2×-2

9x - 3 = 10x - 4

Subtract 10x from both sides

9x - 10x - 3 = 10x - 10x - 4

9x - 10x - 3 = - 4

Add 3 to both sides

9x - 10x - 3 + 3 = - 4 + 3

9x - 10x  = - 4 + 3

-x = -1

Divide both sides by -1

-x/-1 = -1/-1

x = 1

Therefore, the value of x is 1.

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If Leila makes a dot plot of the heights of the girls in her class to the nearest ¹/₂ inch, the number of different heights that will include on the number line is 5.

A dot plot is a data visualization tool that consists of data points plotted as dots on a graph with an x- and y-axis.

The number of dots plotted on each number line shows the frequency of the data group.

Height    Frequency   Cumulative Frequency

56¹/₂             2                               2

57                 2                               4

57¹/₂             2                               6

58                2                               8

58¹/₂             1                               9

Thus, arranging the heights according to groups, the different heights on the number line can be classified into 5.

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The linear function for the total cost C is:

A function is an expression, rule, or law that defines a relationship between one variable.

Example:

\(f(\text{x}) = 2\text{x} + 1\)

\(f(1) = 2 + 1 = 3\)

\(f(2) = 2 \times 2 + 1 = 4 + 1 = 5\)

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The total cost for x cubic yards.

\(\bold{C = 28 + 48x}\)

Thus, the function is C = 28 + 48x.

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The shorter distance he can take if directly from cabin to firepit that is 1.41x.

Trigonometry is a branch of mathematics that focuses on the study of the relationships between the sides and angles of triangles. It is based on the fact that the ratios of the lengths of the sides of a right-angled triangle are always constant, regardless of the size of the triangle. Trigonometry involves the use of several mathematical functions such as sine, cosine, and tangent, which are defined based on the ratios of the sides of a right triangle. For instance, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse, while the cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.

Here,

Let x be he distance from firepit to dock, y be the distance from dock to cabin and z be the distance from firepit to cabin.

tan 45=1

x/y=1

x=y

sin 45=1/√2

x/z=1/√2

z=x√2

Total distance:

Path 1: Patrick walks directly from his cabin to the firepit, so the distance he walks is z.

z=x√2

z=1.41x

Path 2: Patrick walks from his cabin to the dock, and then from the dock to the firepit. The distance he walks is y + z.

=x+y

=2x

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Answer:

There are 40 apples in the basket.

This is because 5 apples to 3 pears have a difference of 1.66666667 when dividing 5 by 3 to show the ratio difference. Then, all you do is multiply this number by the number of total pears which would look like 24 x 1.66666667 = 40.

I hope this helped you, have an amazing day! :)

The dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.

A box plot, sometimes called a box whisker plot, shows the distribution of a dataset graphically. The minimum value, the first quartile (25th percentile), the median (50th percentile), the third quartile (75th percentile), and the maximum value are the five main values used to standardise this method of displaying the distribution of data.

Two whiskers that extend from a rectangular box make up a box plot. The range of values between the first and third quartiles is represented by the box, which is known as the interquartile range (IQR).

From the given box plot we observe that the minimum value is 12 and the maximum value is 24.

Here, the median is 19.

From the information the two data set that have the corresponding values are:

12, 15, 15, 17, 19, 19, 20, 22, 24

12, 15, 17, 17, 19, 19, 22, 22, 24

The lower quartile is 15.

The upper quartile is 21.

Calculating the lower quartile for the data sets:

12, 15, 15, 17, 19, 19, 20, 22, 24

Lower quartile = 15

Hence, the dataset represented by the given box plot is 12, 15, 15, 17, 19, 19, 20, 22, 24 option B.

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The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$20000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &18 \end{cases} \\\\\\ 20000=P[1+(0.08)(18)]\implies \cfrac{20000}{1+(0.08)(18)}=P \\\\\\ \cfrac{20000}{2.44}=P\implies 8196.72\approx P\)

Answer:

366

Step-by-step explanation:

2×3+4×100-50+10​

PEMDAS says multiply and divide from left to right

6 + 400 - 50 +10

Then add and subtract

406-50+10

356+10

366

Answer:

\(\boxed{366}\)

Step-by-step explanation:

\(2 \times 3+4 \times 100-50+10\)

Multiplication is first.

\(6+400-50+10\)

Add or subtract the numbers.

\(350+10+6\)

\(366\)

Answer:

$0.12

Step-by-step explanation:

cost of one bag of puppy treats after using the coupon: 10.24-2.80=$7.44

cost per puppy treat= 7.44/62=$0.12

Answer:

-14

Step-by-step explanation:

-14 - x  =   -1 x (x + 14)

-x-14 = 0

Add  14  to both sides of the equation : -x = 14

Multiply both sides of the equation by (-1) :  x = -14

Answer:

2^4   * 9^4

Step-by-step explanation:

(2*9)^4

We can take the power to each term inside the parentheses

2^4   * 9^4

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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The solutions are: x = ln(2) for 2eˣ = 4,  x = ln(25)/4 for e⁴ˣ = 25, x = ln(72) for eˣ = 72 and x = ln(124)/3 for e³ˣ = 124.

To solve these equations using natural logarithm, we can use the following rules:

Using these rules, we can solve the given equations as follows:

2eˣ = 4

Divide both sides by 2 to get

eˣ = 2.

Take the natural logarithm of both sides to get

ln(eˣ) = ln(2).

Using rule 1 above, we can simplify ln(eˣ) to x, and we get

x = ln(2).

e⁴ˣ = 25

4x = ln(25).

Divide both sides by 4 to get

x = ln(25)/4.

eˣ = 72

Take the natural logarithm of both sides to get

x = ln(72).

e³ˣ = 124

Take the natural logarithm of both sides to get

3x = ln(124).

Divide both sides by 3 to get

x = ln(124)/3.

For the second set of equations, we use the same rule as above

So, we have

ln(x - 3) = 2

x - 3 = e²

x = e² + 3.

x ≈ 10.389.

Therefore, the solution is x ≈ 10.389.

ln(2t) = 4

2t = e⁴

t = 0.5 * e⁴

t ≈ 27.299.

Therefore, the solution is t ≈ 27.299.

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Answer:

2nd option: 2y=6x+8 and y=3x+4

Step-by-step explanation:

If you divide the first by 2, you get the second equation.

This means that both equations plot an identical line (they lie on top of each other /also known as "coincide"). This means, that there are infinitely many solutions.

In 2D (x-y plane for example), straight lines can have no solutions if they have the same gradient/slope/ they are parallel and different y-intercepts, because they will never cross.

Here, they have same gradient and y-intercept so all points on the line are valid solutions to the equation

Answer:

Step-by-step explanation:

y + 2 = 5(x - 0)

y + 2 = 5x - 0

y = 5x - 2

Answer:

y = 5x - 2

Step-by-step explanation:

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

The y-intercept is where x = 0, or where the graph crosses the y-axis. Given in the problem, we have that the y-intercept is (0, -2), so b = -2.

We also know the slope is 5.

So, our slope-intercept form is:

y = 5x - 2

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