Suppose the number of glasses of water people drink
in a week is normally distributed with a mean of 50 and
a standard deviation of 5 glasses of water.
Find the probability a given person drank between 40 and 45
glasses of water.
2.35%
35
40
13.5%
45
34% 34% 13.5%
50
P = [?]%
55
60
2.35%
65
Enter

In conclusion √-36 can be simplified to 6i.

How to simplify and what does a square root mean?

The square root of a negative number is not a real number, as any real number squared gives a non-negative result. Therefore, the expression √-36 cannot be simplified in terms of real numbers.

However, in some mathematical contexts, we define the imaginary unit i as √-1. With this definition, we can write:

√-36 = √(36)√(-1) = 6i

Therefore, in this context, √-36 can be simplified to 6i.

In mathematics, the square root of a non-negative real number is a number that, when multiplied by itself, gives the original number. The square root is denoted by the symbol √.

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Answer: the right one is d

Step-by-step explanation:

Answer:

Table 4

Step-by-step explanation:

The first table is a linear function, with the points of (-240), (-72), (0), (2), and (6).

The second table is also a linear function, with the points of (-768), (-16), (0), (48), and (384)

The third table is a linear function, with the points of (-48), (-6), (0), (6), and (48)

The fourth table is the only one that is a linear function because the first four points are (0) and the last one is (-12)

Answer:

(x - 4)(x+8)

(Hopefully this helps, and if you can please give me brainliest)

By first method, he volume of the rectangular prism is (9/32) cubic feet.

By second method, the volume of the rectangular prism is (27/64) cubic feet, which agrees with the volume calculated using the first method.

Volume is a measurement of the amount of space that an object occupies. It is the three-dimensional space occupied by an object. Volume is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, and so on.

We can determine the volume of the rectangular prism in two different ways using the formula:

Volume = Length x Width x Height

First Method:

In the first method, we simply substitute the given dimensions of the rectangular prism into the formula and calculate the volume:

Volume = (3/4) ft x (3/8) ft x (3/4) ft

Volume = (9/32) ft³

Second Method:

In the second method, we can use the fact that the rectangular prism can be divided into 4 smaller rectangular prisms, each with dimensions (3/4) ft x (3/8) ft x (3/16) ft. We can calculate the volume of one of these smaller prisms and then multiply by 4 to get the total volume:

Volume of one smaller prism = (3/4) ft x (3/8) ft x (3/16) ft

Volume of one smaller prism = (27/256) ft³

Total volume = 4 x Volume of one smaller prism

Total volume = 4 x (27/256) ft³

Total volume = (27/64) ft³

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Step-by-step explanation:

8 ( 3 + 4 - 2)  =   8 x 3   + 8 x 4    -   8x 2       <  ===== distributive property

Step-by-step explanation:

the area of a rectangle is

length × width

the perimeter of a rectangle is

2×length + 2×width

so,

length×width = 48 cm²

2×length + 2×width = 28 cm

length + width = 14 cm

length = 14 - width

we use this in the first equation :

(14 - width) × width = 48

14×width - width² = 48

-width² + 14×width - 48 = 0

a quadratic equation

ax² + bx + c = 0

has the general solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = -1

b = 14

c = -48

width = (-14 ± sqrt(14² - 4×-1×-48))/(2×-1) =

= (-14 ± sqrt(196 - 192))/-2 =

= (-14 ± sqrt(4))/-2 =

= (-14 ± 2)/-2 =

= 7 ± 1

width1 = 7 + 1 = 8 cm

width2 = 7 - 1 = 6 cm

length1 = 14 - width1 = 14 - 8 = 6 cm

length2 = 14 - width2 = 14 - 6 = 8 cm

so, we see, one of them must be 8 cm, and the other 6 cm.

let's length be the longer side, so

length = 8 cm

width = 6 cm

Step-by-step explanation:

For a RIGHT triangle, you can use Pythagorean Theorem to calculate the length of the hypotenuse:

Hypotenuse^2 = leg1 ^2  + leg2 ^2

Hypotenuse^2  = 3^2 + 16 ^2

Hypotenuse ^2 = 265     sqrt both sides

hypotenuse = 16.3 m

Now the perimeter is just all three sides added together:

     3 + 16 + 16.3 = 35.3 m

Answer:

≈ 35,3 m

Step-by-step explanation:

First we need to find the third side of the right-angled triangle by the Pythagorean theorem:

[tex] {16}^{2} + {3}^{2} = 265[/tex]

[tex]265 > 0[/tex]

[tex]the \: third \: side \: is \: \sqrt{265} [/tex]

And now we can find the perimeter:

P = 16 + 3 + √265 ≈35,3 (m)

Answer:

y = (-3)2^x

Step-by-step explanation:

We can substitute the two points in the equation y = abˣ and we get two equations. By solving the two equations, we can find the values of a and b.

Substitute (0, -3)  in the equation y = abˣ            

-3 = a * b⁰            

-3 = a * 1              

[tex]\boxed{\bf a = -3}[/tex]

Substitute (4, -48) in the equation y =abˣ

-48 = (-3) * b⁴

[tex]\dfrac{-48}{-3}=b^4\\\\ b^4 = 16\\\\b^4 = 2^4\\\\ \boxed{\bf b = 2}[/tex]

Exponential function:

           [tex]y = (-3)2^x[/tex]

The dilation is an enlargement, then k > 1. If the dilation is a reduction, then 0 < k < 1.

The dilation constant, also known as the scale factor, represents the amount by which the original figure is enlarged or reduced in the dilation.

We can find the dilation constant by using the distance formula. Let the coordinates of point P be (x,y) and the coordinates of point A be (a,b). Let the coordinates of point B be (u,v), where u and v are unknown.

The distance from A to P is:

d(AP) = √[(x-a)² + (y-b)²]

The distance from A to B is:

d(AB) = √[(u-a)² + (v-b)²]

Since the dilation is centered at A and maps P onto B, we know that the ratio of the distances is the dilation constant:

d(AP)/d(AB) = k

Substituting the expressions for the distances and simplifying, we get:

√[(x-a)² + (y-b)²] / √[(u-a)² + (v-b)²] = k

Squaring both sides, we get:

[(x-a)² + (y-b)²] / [(u-a)² + (v-b)²] = k²

Since we know the coordinates of P and A, we can substitute these values into the equation and solve for k. Once we have k, we can use it to find the coordinates of B.

Note that if the dilation is an enlargement, then k > 1. If the dilation is a reduction, then 0 < k < 1.

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Answer:

Step-by-step explanation:

350x2x5=3500

Assumptions for above case:

1-Equal payments are made monthly.

2-Total amount deposited throughout the year are compounded by end of the year.

3-Annual interest is 6%

4-Total Amount invested plus interest at maturity are reinvested the following year.

Given above, if you create a table in excel for those calculations, you would get $296.330 /month which amounts to $12,000.00 in 3 years approximately.

Year 1 = $3,555.96 Pre-interest =>$3769.32 Post 6% interest

Year 2 = $7,325.28 Pre-interest =>$7,325.28 Post 6% interest

Year 3= $11,320.75 Pre-interest =>$12,000.00 Post 6% interest.

The way to calculate pre interest for each year is just $296.330*12=$3555.96

Afterwards just multiply by the annual interest rate to get the full amount invested + interest (6%) =>$3555.96*(1.06)= $3769.32

Then As per step 1, add another 3555.96 and multiply it all by 1.06, to get 305.06

x = $305.06

The relations that are functions are the ones in options 12 and 13

A relation is a function only if each one of the inputs is mapped to a single one output, so if you see a relation where the same input is mapped into different outputs, this is not a function.

Then the relations that are functions are options 12 and 13, in the other two we can see that there are multiple outputs for the same inputs.

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Answer:

the answer is 23 cm

Step-by-step explanation: just a guess

Answer:

118m

Step-by-step explanation:

102.25m+15.75m=118m

In this case, 3x plus 12 is 3x plus 12. in this situation, [tex]|3x + 12|[/tex] equals -(3x + 12) for expression.

For the expression:

Two vertical bars serve as the absolute value symbol in mathematics, which is used to represent a number's distance from zero regardless of its sign. In other words, a number's absolute value is never negative.

The number 3x + 12's absolute value is denoted by the expression |3x + 12|. We must take into account two scenarios in order to formulate this expression without the absolute value symbol: the non-negative case for 3x + 12 and the negative situation for 3x + 12.

Example 1: 3x + 12 ≥ 0

Because 3x + 12 is not negative, we may simply remove the absolute value symbols since they are not necessary. In this case, 3x plus 12 is 3x plus 12.

Example 2: 3x + 12 < 0

When 3x + 12 is a negative number, we can multiply it by -1 to get the absolute value. This is so because a negative number's absolute value is the same as its positive equivalent. As a result, in this situation, |3x + 12| equals -(3x + 12).

In light of the aforementioned examples, the phrase |3x + 12| can be expressed as follows:

[tex]|3x + 12| =\\{ 3x + 12 if 3x + 12 ≥ 0\\\\{ -(3x + 12) if 3x + 12 < 0[/tex]

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Here is a vector of observations representing the number of defects in 25 1-square-yard specimens of a particular type of woven fabric. This data is provided to facilitate its entry into R.

The data provided is the number of defects in 25 1-square-yard specimens of woven fabric of a particular type. This data can be used to analyze the quality of the fabric and identify any potential issues with the manufacturing process.

It is important to copy this data into R as a vector so that it can be easily analyzed using various statistical techniques. In R, vectors are used to store multiple values of the same type, and they can be used to perform mathematical operations and statistical analyses. Once the data is in R, various descriptive statistics, such as the mean, median, and standard deviation, can be calculated to gain insights into the quality of the fabric and identify any potential trends or patterns in the data.

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The appropriate choice is for all actual x values of x 1.5, the function is declining.

A linear polynomial is a polynomial of degree one, which means it is a polynomial that has only one variable raised to the power of one and no other variables or exponents.

A function f(x), which is made up of two linear polynomials, is given as follows:

f(x)=(x-4)(x+1)

We now know that when we multiply the two linear polynomials, a quadratic polynomial results.

As a result, the function f(x) will be shown as:

f(x)=x(x+1)-4(x+1)

f(x)=x²+x-4x-4

f(x)=x²-3x-4

In order to determine which claims about the function are accurate, we shall plot the function's graph.

1) The function increases for all real x values greater than zero.

Since we get from the graph that function f(x) is decreasing for x<0.

This statement is false.

2)The function is increasing for all real values of x where x < –1 and where x > 4.

This option is incorrect as the function is decreasing for x<-1

whereas it is increasing for x>4.

3)Where -1 <x<4, the function decrements for all real values of x.

This is the incorrect choice.

Because of the function's dual trend of growing and dropping in the interval (-1,4).

4)For all actual x values of x< 1.5, the function is declining.

This choice is the best one.

since, it is obvious from the graph that the function declines for x<1.5.

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The complete question is;

The graph of the function f(x) = (x – 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < –1 and where x > 4. The function is decreasing for all real values of x where –1 < x < 4. The function is decreasing for all real values of x where x < 1.5.

solution-

Actual measure= 6m wide ie.600cm wide

her model is =12cm wide

so scale factor =600/12= 50

so length will be =800/50 =16cm

hence gher model will be 16cm long

Answer:

A) 0.5%

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

0.5%

Step-by-step explanation:

7 out of 1400 walk

7/1400 = 1/ 200   divide by 2 equals   0.5/100=0.5%

Therefore, Jamie can make 8 bracelets with 1.04 meters of wire.

Perimeter is a measure of the distance around the edge of a two-dimensional object, such as a polygon, a circle, or a rectangle. It is the total length of all the sides or edges that make up the shape. In simple terms, perimeter is the length of the boundary of a flat object, such as the circumference of a circle, or the sum of the lengths of the sides of a polygon. It is usually measured in units such as meters (m), centimeters (cm), feet (ft), or inches (in).

Here,

Jamie has 1.04 meters of wire, which is equivalent to 104 cm (since 1 meter = 100 cm).

Each bracelet requires 13 cm of wire, so the number of bracelets she can make is:

Number of bracelets = Total length of wire ÷ Length of wire per bracelet

Number of bracelets = 104 cm ÷ 13 cm/bracelet

Number of bracelets = 8

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A possible value of a is a > 0 , b = 0 , c < 0

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

From this diagram we can observe the following:

The diagram opens upwards, which means that the coefficient 'a' is positive. The vertex of the parabola is on the y-axis, which means that the x-coordinate of the vertex is 0. This gives us evidence that the equation of the parabola is f(x) = a(x-0 )²c , which simplifies to f(x) = ax² c. It can also be observed that the y-intercept of the graph is c, which means that the constant term is c. Based on the above observations, we can derive the possible values ​​of a, b and c as follows:

A possible value of a is a > 0 because the graph opens up. A possible value of b is b = 0 because there is no horizontal displacement in the parabola. The possible value of C is c < 0; 0 because the y-intercept is negative. Note that c can be 0, but it cannot be positive because the graph does not intersect the x-axis.

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If the scooter travels 4.4km with the given radius, the wheel have number of revolutions about 1567 times.

In order to solve this issue, we must first determine the scooter wheel's circumference, which is given by the formula C = 2[tex]\pi[/tex]r, where r is radius of the wheel. Hence, the circumference of a wheel with a 14 cm radius would be:

C = 2[tex]\pi[/tex](14cm) = 28[tex]\pi[/tex] cm

We must translate the distance from kilometres to centimetres in order to determine how many revolutions the wheel completes if the scooter travels 4.4 kilometres. 1 km equals 100,000 cm, so 4.4 km is equal to 440,000 cm.

Now, we can calculate the number of rotations by dividing the distance travelled by the wheel's circumference:

Distance travelled divided by circumference equals the number of revolutions.

440,000 cm / 28 cm divided by the number of revolutions

1566.99 revolutions were made.

Therefore if the scooter travels 4.4km, the wheel will turn about 1567 times.

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For the given graph of the function: Period = π, Domain = [0,π], Range = (-∞, + ∞), Asymptotes at x = 0.

Period:

A function is referred to as periodic if it repeats a pattern, such as sine or cosine. The shortest interval with exactly one instance of the repeating pattern is said to have a period, which is its length.

Period = π

Domain:

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

Domain = [0,π]

Range:

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Range = (-∞, + ∞)

Asymptotes:

The graph of the a function approaches an asymptote as either x or y approach positive or negative infinity, respectively.

Asymptotes at x = 0.

As a result, whenever x = 0, the function possesses a vertical asymptote.

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Answer:

  40°

Step-by-step explanation:

You want the measure of ∠LNO, marked as y°, given the two vertical angle pairs {100°, (x -y)°} and {y°, 2/7x°}.

Vertical angles have the same measure, so we can write the equations ...

We want the value of y, so it makes sense to solve these equations using a method that eliminates x. Rewriting the second equation to solve for x, we have ...

  x° = 7/2y°

Substituting this into the first equation gives ...

  100° + (7/2y -y)°

  100° = 5/2y°

  2/5(100) = y° = 40°

The measure of ∠LNO is 40°.

The score that corresponds to the 85th percentile is 82, since it is greater than or equal to 85% of the scores in the data set.

The formula is: percentile = (number of scores below the percentile / total number of scores) x 100%

We want to find the score that corresponds to the 85th percentile, which means that 85% of the scores in the data set are below this score

percentile = 85%

total number of scores = 20

number of scores below the percentile = (85% / 100%) x 20 = 17

This means that we need to find the score that is greater than or equal to 17 of the 20 scores in the data set.

Next, we need to rank the scores in order from lowest to highest:

55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83

The score that corresponds to the 85th percentile is 82, since it is greater than or equal to 85% of the scores in the data set.

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cot θ = 7/4 and θ in degrees = 29.744881 degrees. In this case, the adjacent side is 7 and the opposite side is 4.

Cotangent (cot) is the ratio of the adjacent side to the opposite side of a right triangle.

In this right angle triangle, cot θ can be calculated using the formula

cot θ = adjacent/opposite.

In this case, the adjacent side is 7 and the opposite side is 4.

Therefore, cot θ = 7/4.

Now, to find theta in degrees, we can use the inverse cotangent function, arccot.

arccot (cot θ) = θ.

Therefore, θ = arccot (7/4).

Using a calculator, arccot (7/4) = 29.744881 degrees

Therefore, cot θ = 7/4 and θ in degrees = 29.744881 degrees.

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From the ogive, we can see that 10 people paid a rent of less than or equal to $1,000, and 19 people paid a rent of less than or equal to $1,700.The midpoint of class with highest frequency (900-1199) is $1,050.

In mathematics, data can be used to identify patterns, trends, and relationships, and to test hypotheses.

To draw an ogive for the given data, we first need to organize the data into classes and calculate their corresponding frequencies and cumulative frequencies. Based on the range of the data, we can choose the following seven classes:

Class 1: 300-599

Class 2: 600-899

Class 3: 900-1199

Class 4: 1200-1499

Class 5: 1500-1799

Class 6: 1800-2099

Class 7: 2100-2399

Using these classes, we can complete the following table:

Class Limit  Class Boundary   Midpoint        Frequency Cumulative Frequency

300-599                299.5-599.5     449.5               1                         1

600-899 599.5-899.5 749.5 4 5

900-1199 899.5-1199.5 1049.5 5 10

1200-1499 1199.5-1499.5 1349.5 4 14

1500-1799 1499.5-1799.5 1649.5 5 19

1800-2099 1799.5-2099.5 1949.5 1 20

2100-2399 2099.5-2399.5 2249.5 4 24

To draw the ogive, we plot the cumulative frequencies against the upper class boundaries. We start at the first lower class boundary and plot a point with a cumulative frequency of zero. Then we plot the cumulative frequency of each subsequent class at the upper class boundary of that class. We then connect the points with smooth curve.

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