Johnny has 121 apples, Johnny buys 3 apples from David 61 times. How many apples does Johnny have now?

The probability that a man who developed diabetes is very active is 0.0625.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

You want P(a/d) where a means active, d means diabetic. Then Bayer's rule gives

P(a/d)=P(d/a)p(a)/P(d)

We know P(d)=202/5990.

P(a)=1/4 and P(d/a) we need to figure out.

But

P(d)=1/4P(d/a)+3/4p(d/s)=1/4P(d/a)+3/4∗5P(d/a)

P(D&A)/P(A) = 1/5*P(D&A')/P(A')

I am given P(A) = 1/4, so this can be reduced to

P(D&A)/(1/4) = 1/5*P(D&A')/(3/4) 15*P(D&A) = P(D&A')

The probability I am interested in is P(A|D) = P(D&A)/P(D) = P(D&A)/(P(D&A) + P(D&A')) = P(D&A)/(P(D&A) + 15*P(D&A)) = 1/16

Hence ,The probability that a man who developed diabetes is very active is 0.0625.

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The solution set of the quadratic inequality x² - 5 < 0 is - √5 < x < √5

From the question, we have the following parameters that can be used in our computation:

The quadratic inequality is:

x^2-5<0

Express properly

x² - 5 < 0

Add 5 to both sides of the inequality

x² < 5

Take the square root of both sides

x < ±√5

Expand the inequality expression

- √5 < x < √5

Hence, the solution is - √5 < x < √5

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The value of the variable x in the circle is 18 units

From the question, we have the following parameters that can be used in our computation:

Diameter = (2x - 4) units

Radius = 16 units

These parameters can be expressed as

d = 2x - 4

r = 16

Start by calculating the radius of the circle

So, we have the following representation

Radius = Diameter/2

Substitute the known values in the above equation, so, we have the following representation

16 = (2x - 4)/2

Evaluate the quotients in the above equation

16= x - 2

Add 2 to both sides of the equation

x = 16 + 2

Evaluate the like terms

x = 18

Hence, the variable x is 18 units

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Answer:

  x = (π/2 +2nπ) ± π/3

Step-by-step explanation:

You want the solutions to the radical equation involving sin(x).

  [tex]\sqrt{\sin^2{x}-4\sin{x}+4}+\sqrt{\sin^2{x}+4\sin{x}+4}=\sqrt{\sin^2{x}+7\sin{x}+12.25}\\\\\sqrt{(\sin{x}-2)^2}+\sqrt{(\sin{x}+2)^2}=\sqrt{(\sin{x}+3.5)^2}\\\\|\sin{x}-2|+|\sin{x}+2|=|\sin{x}+3.5|\\\\(2-\sin{x})+(\sin{x}+2)=\sin{x}+3.5\\\\0.5=\sin{x}[/tex]

The values of x that make this true are ...

  x = {π/6, 5π/6} +2πn . . . . . for any integer n

__

Additional comments

  √(x²) = |x|

  sin(x) -2 is always less than zero, so its absolute value is 2-sin(x).

The attachment shows the equation written so the x-intercepts give the desired solutions.

The real number solution set for the trigonometric equation is x = 2πn + π/6 or 2πn + 5π/6 where n = is an integer

A trigonometric equation is an equation that contains the trigonometric ratios.

Given the trigonometric equation

√(sin²x - 4sinx + 4) + √(sin²x + 4sinx + 4) = √(sin²x + 7sinx + 12.25)

We know that sin²x - 4sinx + 4 = (sinx - 2)².

Also, sin²x + 4sinx + 4 = (sinx + 2)².

Also, sin²x + 7sinx + 12.25 = (sinx + 3.5)².

So, substituting these into the equation, we have that

√(sin²x - 4sinx + 4) + √(sin²x + 4sinx + 4) = √(sin²x + 7sinx + 12.25)

√(sinx - 2)² + √(sinx + 2)² = √(sinx + 3.5)²

|sinx - 2| + |sinx + 2| = |sinx + 3.5|

(2 - sinx) + (sinx + 2) = (sinx + 3.5)

2 - sinx + sinx + 2 = sinx + 3.5

Colecting like terms, we have that

-sinx + sinx + 2 + 2 = sinx + 3.5

0 + 4 = sinx + 3.5

4 = sinx + 3.5

Subtracting 3.5 from both sides, we have that

sinx = 4 - 3.5

sinx = 0.5

Taking inverse sin, we have that

x = sin⁻¹(0.5)

x = π/6 or 5π/6

So, the real number solution set is x = 2πn + π/6 or 2πn + 5π/6 where n = is an integer

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The length of the hypotenuse of the triangle is √181 cm

Pythagoras theorem states that in the right -angled triangle , the square of the hypotenuse side is equal to the sum of the square of other two sides.

Hypotenuse it the longest side , as it is opposite to the angle 90°

Pythagoras theorem formula :

Let a be the base

b be the perpendicular and c is hypotenuse

So, according to the Pythagoras

c² = a² + b²

According to the question,

We have to find the length of hypotenuse

Given that base = 10

Perpendicular = 9

Let Hypotenuse = x

Using above theorem

=> x² = (10)² + (9)²

=> 100 + 81 = x²

=> c = √181

The length of hypotenuse is √181

I've answered the question in general as the question is incomplete

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Standard Deviation is a measure of the spread of a data set. The smaller the standard deviation, the closer the values are to the mean.

In the box and whisker plots, the box represents the middle portion of the dataset (the middle 50%), the whiskers represent the outer 25% of the data, and the line inside the box is the median.In this case, the box and whisker plot with the smallest standard deviation is the plot on the right, which shows a box that is wider than the other plot but with less variation in the whiskers. This indicates that the values in the plot on the right are closer to the median than in the plot on the left, which suggests that the standard deviation of the plot on the right is smaller than the standard deviation of the plot on the left.

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Answer:

200 cupcakes

Step-by-step explanation:

Let "x" be the total number of cupcakes sold at the bakery.

We know that 26 cupcakes represents 13% of the total number of cupcakes sold, so:

26 cupcakes = 13/100 * x

Solving for x, we get:

x = 26 / (13/100)

Simplifying the fraction, we get:

x = 2600 / 13

Dividing 2600 by 13 gives us 200, so:

x = 200

Therefore, the bakery sold a total of 200 cupcakes on that day.

Answer:

the slope is 1

Step-by-step explanation:

where: m is the slope and b is the y-intercept. Therefore, for the equation y=x+5 , the slope is 1 , and the y-intercept is 5

The statement is AB=CD,BC=AD due to definition of parallelogram. The statement is AC=AC due to Reflexive property of equality.

A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size. A quadrilateral with the opposing sides parallel is called a parallelogram. A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus.

Here,

1. Statement: AB=CD,BC=AD

Reason: By definition of parallelogram.

2. Statement: AC=AC

Reason: Reflexive property of equality.

The definition of a parallelogram causes the sentence to be AB=CD,BC=AD. Due to the reflexive feature of equality, the assertion is AC=AC.

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The chi-square test for independence compares the two variables within a sample set to one another, instead of comparing the single observed variable into the theoretical population.

The chi-square takes a statistical look in order to compare the found consequences of the with that of the familiar outcomes. The main goal of this test is to take a statistical view in order to make a distinction between the observed records and the expected facts, is due to the risk present, or if it's miles because of courting the variables that you are studying.

A chi-square test is used to measure the degree of variation between the frequencies which are determined and the expected frequencies according to the hard and fast rules of variables and occasions. Chi-rectangular is used to measure the differences of the nominal variables.

The term, 'independence' refers to the individual's own freedom of doing things, without being affected by other's opinions. As and when, a small child grows up to an adult, he/she tends to make their own decisions and selections. This is one of the example of independence. Realizing the importance of independence is crucial as the people of the nation are its most important assets. The way in which the founders of India has reunited the country into a single state, the same, if followed in USA, this would relieve the country from the chains of caste, sex, religion and exploitation.

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Answer:

Step-by-step explanation:

its all explained in picture

2.5% of values will lie above 29.

What is normal distribution?

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

The 68-95-99.7 rule is an illustration of how those many percentage of values lie in between  mean +/- 1, 2, and 3 standard deviations respectively.

For values to lie above 29, their z value comes out to be

(29-19) / 5 = 10/5 = 2

(Note: z value means how many standard deviations above the mean)

Thus for a z value = 2 (which 29 is in this problem) the percentage of values that lie between mean +/- 2*(standard deviation) is 95 (as stated by the 68-95-99.7 rule).

Thus only 5% values wont lie between mean +/-2 standard deviations.

So 5% values wont lie between 29 (z value=2) and 9 (z value=-2).

Since normal curve is symmetric, half of the values of the 5% will lie above 29 and the rest half will lie below 9.

So 50% of 5 % which is 2.5% of values will lie above 29.

Hence, 2.5% of values will lie above 29.

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The value of x after simplification is 6/5.

What is an equation?

A mathematical equation is a formula that uses the equals sign to express the equality of two expressions. The meanings of the word equation as well as its cognates in those other languages can vary slightly. For instance, in French, an equation is defined as having one or even more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. Finding the values for the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables that the equation must be solved, and the unknown variable values that satisfy this same equality are known as the equation's solutions.

Main Body:

according to the given equation,

5x = 6

to solve it , divide by 5 on both sides,

5x *1/5  = 6*1/5

x = 6/5

Hence the value of x after simplification is 6/5.

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Answer:

B which I assume to be a typo where you had meant 3/4

Answer:

B. [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

We need to find the HCF of 18 and 24 to simplify it into its lowest terms.

The HCF of 18 and 24 is 6, therefore we need to divide 6 on both sides to simplify it into its lowest terms.

Hence, [tex]\frac{18}{24}=\frac{3}{4}[/tex]

I would appreciate it if you mark my answer as brainliest.

The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  

w + l ≥ 17.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

w + l ≥ 17

Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  w + l ≥ 17.

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The area of the rectangle, in square meters, is 7.56 meters².

Rectangles are quadrilaterals having four equal vertices and parallel sides that are equal to one another.

Given;

a rectangle has a length of 42 centimeters,

and a width of 18 centimeters.

To find the area of the rectangle:

We multiply the length of the rectangle by the width of the rectangle.

Use formula,

The area of the rectangle = length x width

Substitute the value of length and width

The area of the rectangle = 42 x 18

The area of the rectangle = 756 cm².

To change centimeter to meter:

We have the rate of change,

1 centimeter = 0.01 meter

756 centimeters = 0.01 x 756 meters

756 centimeters = 7.56 meters

Therefore, the area of the rectangle = 7.56 meters².

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Answer:

3.35

Step-by-step explanation:

38.86=11.6x

x=3.35

Answer:

The answer is option (C). Four Rivers Bank

Explanation:

a). The total amount Jane will receive after 5 years after investing $40,000 in the Mystic Bank can be expressed as follows;

A = P (1 + r/n) (nt)

where;

A = the future value of the initial investment

P = initial investment amount/principal amount

r = the annual interest rate

n = the number of times that interest is compounded per unit t

t = the time the money is invested for

In our case;

P=$40,000

r=12/100=0.12

n=interest is compounded quarterly which is four times a year=4

t=5 years

Replacing values in the formula;

A=40,000(1+0.12/4)^(4×5)

A=40,000(1+0.03)^20

A=40,000×1.806

A=72,244.45

The total amount Jane will receive after 5 years if she chooses to invest with the Mystic Bank is $72,244.45

b). The total amount Jane will receive after 5 years after investing $40,000 in the Four Rivers Bank can be expressed as follows;

A = P (1 + r/n) (nt)

where;

P=$40,000

r=14/100=0.14

n=interest is compounded semiannually which is two times a year=2

t=5 years

Replacing values in the formula;

A=40,000(1+0.14/2)^(2×5)

A=40,000(1+0.07)^10

A=40,000×1.967

A=78,686.05

The total amount Jane will receive after 5 years if she chooses to invest with the Four Rivers Bank is $78,686.05

c). The best deal would be to invest with Four Rivers Bank for 5 years since the total amount Jane will receive after 5 years will be $78,686.05 which is greater than $72,244.45, which is the total amount she will receive if she chooses to invest with Mystic Bank

Step-by-step explanation:

you marked the important pieces of information correctly.

a parallel line must have the same slope. otherwise it is tilted differently, and it is therefore not parallel.

the slope in a y = ... equation is always the factor of x.

in our case therefore 1/5.

so, the parallel line starts with

y = (1/5)x + b

and to get b we use the x and y coordinates of the given point :

3 = (1/5)×5 + b = 5/5 + b = 1 + b

b = 2

and our equation is

y = (1/5)x + 2

The balance will be $34,677.45 in Jarad's account, at the end of 10 years.

The balance in the account is computed as illustrated follow as:

Future value = Present value (1 + r)n

Because the amount is compounded semi-annually, the interest rate is split by two and the number of time periods is multiplied by two.

So, the balance in the account is computed as follows:

= $10,000 x (1 + 0.10 / 2)10 x 2 + $5,000 x (1 + 0.10 / 2)5 x 2

= $26,532.97705 + $8,144.473134

= $34,677.45 Approximately

Thus, the balance will be $34,677.45 in Jarad's account, at the end of 10 years.

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The perimeter of smaller circle is 78.5 ft

What is area?

Area is that the amount that expresses the extent of a vicinity on the plane or on a semicircular surface. space|the world|the realm} of a plane region or plane area refers to the world of a form or planate plate, whereas area refers to the world of associate degree open surface or the boundary of a three-dimensional object.

Main Body:

A new arboretum was designed to contain two circular gardens. Garden A has a diameter of 25 ft and Garden B has a diameter of 45 ft.

outline the smaller garden means circumference of the circle.

Perimeter of circle is 2πr.

diameter = 25 ft

radius = 25/2 = 12.5 ft

Radius = 2π *12.5

            = 25 π

            = 25*3.14

            = 78.5 ft

Hence the perimeter of circle is 78.5 ft

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The equation y(x,t)=0.8[(4x+5t)2+5] , represents a moving pulse where x and y are in meter and t is in second.

i) Direction of wave propagation is negative x-axis.

ii) The wave speed is 1.25m/s.

iii)The maximum displacement from the mean position (i.e., the amplitude of the wave) is 0.16 m.

iv)The wave pulse is symmetric.

We compare the given wave equation from the standard wave equation. On comparing, direction and wave speed is found out. The Remaining two parts are found by maxima concept and changing x by −x at t=0 to get a wave is symmetric.

Moving pulse is given by

⇒y(x,t)=0.8[(4x+5t)2+5]

Comparing (4x+5t) with (ax+bt) then we get,

⇒a=4 and b=5 ⋯⋯⋯(1)

(i) When coefficients of x and t are positive then the wave pulse is moving negative x-direction. So, given an equation with coefficients a = 4 and b= 5 are positive. Therefore, the direction of the given equation will be negative x axis.

(ii) After getting the coefficient a and b, we can calculate the speed by determining the value of b/a. And we have value of a =4 and b =5 from the equation (1) .Then speed of the wave will be

=> b/a=5/4

=> speed of the wave =1.25m/s

(iii) To get the maximum displacement from the mean position we put (4x+5t)=0. As the denominator is minimum, the fraction will be maximum. Therefore displacement will be

=> y=0.85, putting the (4x+5t) is equal to zero.

After simplify we get,

=> y=0.16 m

Hence maximum displacement is 0.16m from the mean position,

(iv) We replace x by −x and also put t= 0 in the given equation. If the equation does not change, replacing the x by −x, it will be symmetric otherwise not.

Putting t=0 in the given equation y(x,t) we get,

=> y=0.8(4x)2+5

Now replace x by −x on the above equation we get, y=0.8(4x)2+5

there will not be any change. Therefore, the given equation is symmetric.

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Complete question:

If y(x,t)=0.8[(4x+5t)2+5] , represents a moving pulse where x and y are in meter and t is in second. Find

(i) Direction of wave propagation.

(ii) The wave speed.

(iii) The maximum displacement from the mean position (i.e., the amplitude of the wave)

(iv) Whether the wave pulse is symmetric or not.

Answer:

Below

Step-by-step explanation:

(x-10)^2 = 90     sqrt both sides

x-10  =  ± sqrt (90)

x  =   10 ± sqrt (90)

The nth term of the given sequence is 8(3)ⁿ⁻¹. The given sequence is a geometric series and its common ratio is r = 3.

The nth term of a geometric series is calculated by the formula

tₙ = arⁿ⁻¹

Here a is the first term of the sequence and r is the common ratio of the sequence.

The common ratio is calculated by r = aⁿ⁺¹/aⁿ

The given sequence is 8, 24, 72, 216

Here, the first term in the given sequence is a = 8;

The ratios of the terms of the sequence are:

24/8 = 3

72/24 = 3

216/72 = 3

Since the ratios are the same, then the given sequence is geometric.

Thus, the common ratio is r = 3.

And the nth term of the given geometric sequence is

tₙ = arⁿ⁻¹ = (8)(3)ⁿ⁻¹

Therefore, the nth term of the given geometric sequence is 8(3)ⁿ⁻¹.

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The given point estimators are unbiased and estimator b₁  is more efficient than b₂.

A statistic used to precisely estimate a population parameter is called an "unbiased estimator." An estimator's expected value must match the population parameter's value to be considered unbiased. The discrepancy between an estimator's expected value and the parameter value is known as bias. The estimator tends if this difference is not zero.

a) To show whether the given point estimators are unbiased, first, find whether the expected value of the given estimators is equal to the population parameter μ.

[tex]\begin{aligned}E(b_1) &= E(0.10X_1 + 0.20X_2 + 0.40X_3 + 0.30X_4)\\&=0.10E(X_1) + 0.20E(X_2) + 0.40E(X_3) +0.30E(X_4)\\&=0.10\mu+0.20\mu+0.40\mu+0.30\mu\\&=\mu\\E(b_2) &= E(0.25X_1 + 0.25X_2 + 0.30X_3 + 0.20X_4)\\&=0.25E(X_1) + 0.25E(X_2) + 0.30E(X_3) +0.20E(X_4)\\& = 0.25\mu + 0.25\mu + 0.30\mu + 0.20\mu\\&=\mu \end{aligned}[/tex]

Therefore, both estimators are found to be unbiased.

b) To show which estimator is more efficient, first, find the two-point estimators' variance.

[tex]\begin{aligned}V ar(b_1)&= Var(0.10X_1+0.20X_2+0.40X_3+0.30X_4)\\&= 0.10^2V ar(X_1)+0.20^2Var(X_2)+0.40^2Var(X_3)+0.30^2Var(X_4)\\&= 0.10^2\sigma^2+ 0.20^2\sigma^2+ 0.40^2\sigma^2 + 0.30^2\sigma^2\\&=0.3\sigma^2\\Var(b_2)&= Var(0.25X_1+0.25X_2+0.30X_3+0.20X_4)\\&= 0.25^2Var(X_1)+0.25^2Var(X_2)+0.30^2Var(X_3)+0.20^2Var(X_4)\\&= 0.25^2\sigma^2 + 0.25^2\sigma^2 + 0.30^2\sigma^2 + 0.20^2\sigma^2\\&= 0.255\sigma^2\end{aligned}[/tex]

From this, we can say that Var(b₁) > Var(b₂). Therefore, b₁ is more efficient.

The complete question is -

Let X₁, X₂, X₃, and X₄ be a random sample of observations from a population with mean μ and variance σ². Consider the following two-point estimators:

b₁ = 0.10X₁ + 0.20X₂ + 0.40X₃ + 0.30X₄, and

b₂ = 0.25X₁ + 0.25X₂ + 0.30X₃ + 0.20X₄

(a) Show that both estimators are unbiased.

(b) Which estimator is more efficient, b₁ or b₂? Explain in detail.

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1) The equation that solves for Katherine age, x is 5(x - 4) = 400.

2) Katherine is 84 years old.

3) Mabel is 80 years old.

An algebraic equation represents the mathematical form of two expressions that are related by an equal in between them.

From the given information, we can write,

Katherine's age is represented by 'x'

Mabel is 4 years younger than Katherine ie., x - 4

Five times Mabel's age is equal to 400 i.e., 5(x - 4) = 400

Thus, the equation that solves Katherine's age is 5(x - 4) = 400.

On simplifying the obtained equation, we get

5(x - 4) = 400

⇒ 5x - 20 = 400

⇒ 5x = 400 + 20

⇒ 5x = 420

∴ x = 420/5 = 84

Thus, the age of Katherine is 84 years.

Then, Mabel's age = x - 4 = 84 - 4 = 80 years.

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The value which is round off to the nearest thousand for 231469.335329 is 232000.

What is rounding off?

When a number is rounded off, its value is maintained but is brought closer to the next number, simplifying the number. For entire numbers as well as decimals at different places of hundreds, tens, tenths, etc., it is done. The important figures are preserved when numbers are rounded off.

The given value in the question is 231469.335329

The rules for rounding off says,

If the last digit of the given number is above 5 or equal to 5 then 1 is added to pre digit of last number and last digit is replaced by 0.

So, the given value,

231469.335329 the digit after the point is less than 5 so we eliminate the value without adding 1.

It becomes, 231469.00

In above value, if 231469 we add one to the before the last digit, it becomes 231470

As a next step, add the number in the 2 digit by adding 1 to before the 2nd digit, it becomes 231500.

Now Finally, the process of adding one to the 4 digit depends on the values of 3rd digit takes place and it becomes 232000.  

Hence, the number is 232000.

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The new interval for mu becomes narrower, If the number of observations stays the same, but the confidence is reduced to 90%.

The population mean 95% confidence interval is calculated to be between 65.32 and 73.54. The confidence interval for mu will get narrower if the range is trimmed to 90%. This is because the margin of error has decreased. The mean's potential values would be reduced as a result.

The probability that the confidence interval contains the actual population mean is known as the confidence level. You would anticipate that the true value would fall within these ranges 95% of the time if the study were to be repeated and the range computed each time. The more confident you may be that the interval contains the true mean, the greater the confidence level.

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Internal validity refers to the accuracy of the evaluation in attributing the changes identified to the program and not to other factors, such as demographic differences between the participants and the control group.

To ensure internal validity, one must compare the participants and the control groups on demographic characteristics in order to show that the differences found in the evaluation are due to program differences and not to demographic differences. This is done by conducting a statistical comparison of the two groups and calculating the probability that any differences found between them are due to the program and not to some other factor. This is done by computing the probability that the two groups are the same, given the observed mean differences, and then evaluating the results to determine if the differences are statistically significant. For example, if the two groups have different means, the probability of them being the same is calculated, and if this probability is low, then the difference is likely to be due to the program and not to some other factor. This type of statistical analysis speaks to the internal validity of the evaluation.  

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Answer:

$29,000

Step-by-step explanation:

To calculate the cost of merchandise sold, you can use the following formula:

Cost of Merchandise Sold = Sales - (Beginning Inventory + Purchases - Purchase Discounts - Ending Inventory)

Plugging in the values from the data provided, the cost of merchandise sold would be:

Cost of Merchandise Sold = $50,000 - ($6,000 + $20,000 - $1,000 - $4,000)

Cost of Merchandise Sold = $50,000 - $21,000

Cost of Merchandise Sold = $29,000

So, the cost of merchandise sold would be $29,000.