Millie has a box of crayons. 30 of the crayons are red, 14 are green, and 16 are
blue. Millie randomly selects a crayon from the box, records the color and then
replaces the crayon in the box. If she selects a crayon 30 times, how many
times do you predict she will select a blue crayon?
6
07
0 10
08

Answer:

D

Step-by-step explanation:

5 + n is the sum of 5 and a number

amd then "less than or equal to -7" represents the no more than -7

Answer:

D

Step-by-step explanation:

To the moderator that deleted my answer, that was not necessary in the slightest. Go back to reporting bots, not removing correct answers that are put there to help people

Answer:

deductive reasoning

Step-by-step explanation:

it is based on what is true based on what happened before

Answer:

2 option, deductive reasoning

Step-by-step explanation:

based on true events

Answer: A. 7

Step-by-step explanation:

3y-2=19

3y-2+2=19+2 (add 2 to both sides)

3y=21

3y/3=21/3 (divide by 3 on each side)

y=7

Answer:

(5,0),(6,0)

Step-by-step explanation:

The x-intercept occurs when h(x) = 0

∴ let                  0 = (x – 5)(x – 6)                [using the knowledge that for the  

                                                                      produc to be 0, one of terms  

                                                                      must be zero]

⇒                 x - 5 = 0       ;      x - 6 = 0       [solve for x in each case]

⇒                      x = 5        ;           x = 6

Check:

If we graph the line we can see whether the intercepts are truly (5, 0) and (6,0). As seen below in the Desmos graph, it is.

Answer:

0.7

Step-by-step explanation:

Answer:

56.52km

Step-by-step explanation:

Circumference = π X D (D = diameter = 2 X radius)

= (3.14) X 18

= 56.52 km

Answer:

option A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

Terms: x, 4y, 32

variables: x, y

constant: 32

coefficients: 4, 1

Step-by-step explanation:

Hope this helps!

The largest possible rank of A is 5, which is the number of rows in the matrix. This occurs when all rows are linearly independent, meaning that no row can be written as a linear combination of the others. In this case, the columns of A would also be linearly independent, and the matrix would be said to have full rank.


The smallest possible rank of A is 0, which would occur if A is the zero matrix (i.e., all entries are zero). In this case, the columns of A would be linearly dependent, since any linear combination of them would also be zero.

The largest possible nullity of A is 8 - 5 = 3, which is the difference between the number of columns and the rank of A. This occurs when there are 3 linearly dependent columns in A, which means that there are 3 free variables in the equation Ax = 0.

The smallest possible nullity of A is 0, which would occur if A has full rank (i.e., all columns are linearly independent). In this case, the only solution to Ax = 0 is x = 0, and the nullspace is just the zero vector.
The matrix A is a 5x8 matrix, meaning it has 5 rows and 8 columns. The rank of a matrix refers to the number of linearly independent rows or columns in the matrix. The nullity of a matrix refers to the dimension of its null space.

1. The largest rank of A: Since there are 5 rows in matrix A, the largest rank it could have is 5.

2. The smallest rank of A: If all rows are linearly dependent, the smallest rank of A would be 0.

3. The largest nullity of A: According to the Rank-Nullity Theorem, rank(A) + nullity(A) = n (number of columns). If the rank is at its smallest (0), the largest nullity would be equal to the number of columns, which is 8.

4. The smallest nullity of A: If the rank is at its largest (5), the smallest nullity would be n - rank(A) = 8 - 5 = 3.

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The probability of a positive test, given breast cancer, is 223/303, while the probability of a negative test, given no breast cancer, is 684/697.

To find the probability of a positive test, given that the patient has breast cancer, we divide the number of true positive cases (223) by the total number of patients with breast cancer (303). This gives us a probability of 223/303.

The formal term used to describe this probability measure is conditional probability or the probability of an event A occurring given that event B has already occurred. In this case, the positive test is event A, and having breast cancer is event B.

Similarly, to find the probability of a negative test, given that the patient is breast cancer-free, we divide the number of true negative cases (684) by the total number of patients without breast cancer (697). This gives us a probability of 684/697.

The formal term used to describe this probability measure is also conditional probability, where the negative test is event A, and not having breast cancer is event B.

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Answer:

\(\mathrm{a=10,\ r=0.5}\)

Step-by-step explanation:

\(\mathrm{The\ nth\ term\ of\ any\ geometric\ sequence\ is\ given\ by:}\\\mathrm{t_n=ar^{n-1}}\\\mathrm{Given,}\\\mathrm{5th\ term(t_5)=6.25}\\\mathrm{or,\ ar^{5-1}=6.25}\\\mathrm{or,\ ar^4=6.25......(1)}\\\\\mathrm{And,\ 7th\ term(t_7)=1.5625}\\\mathrm{or,\ ar^{7-1}=1.5625}\\\mathrm{or,\ ar^6=1.5625.........(2)}\)

\(\mathrm{Dividing\ equation(2)\ by\ (1),}\\\mathrm{\frac{ar^6}{ar^4}=\frac{1.5625}{6.25}}\\\\\mathrm{or,\ r^2=\frac{1}{4}}\\\\\mathrm{or,\ r=\frac{1}{2}}\)

\(\mathrm{From\ equation(1)\ we\ have}\\\mathrm{ar^4=6.25}\\\mathrm{or,\ a(0.5)^4=6.25}\\\mathrm{or,\ a=100}\)

Alternative method:

\(\mathrm{Here,\ the\ sixth\ term\ of\ the\ sequence\ is\ geometric\ mean\ of\ the\ 5th\ and\ 7th}\\\mathrm{term.}\\\mathrm{So,\ we\ may\ say:}\\\mathrm{t_6=\sqrt{t_5\times t_7}}=\sqrt{6.25\times 1.5625}=3.125\\\mathrm{Now,\ common\ ratio(r)=\frac{t_6}{t_5}=\frac{3.125}{6.25}=\frac{1}{2}=0.5}\\\mathrm{We\ know,\ t_6=3.125}\\\mathrm{or,\ ar^5=3.125}\\\mathrm{or,\ a(0.5)^5=3.125}\\\mathrm{or,\ a=100}\)

The first term and common ratio of the geometric progression (GP) can be determined based on given information. First term (a₁) is 100, and the common ratio (r) is ±0.5, leading to correct answer c. a₁ = 100, r = ±0.5.

By analyzing the values of the 5th and 7th terms, we can find the relationship between them and solve for the unknowns. The correct answer is c. a₁ = 100, r = ±0.5. In a geometric progression, each term is obtained by multiplying the previous term by a constant ratio. Let's denote the first term as a₁ and the common ratio as r. Based on the given information, the 5th term is 6.25 and the 7th term is 1.5625.

Using the formula for the nth term of a geometric progression, we can express these terms in terms of a₁ and r:

a₅ = a₁ * r⁴ = 6.25

a₇ = a₁ * r⁶ = 1.5625

To solve for a₁ and r, we can divide the equations:

(a₇ / a₅) = (a₁ * r⁶) / (a₁ * r⁴)

1.5625 / 6.25 = r²

0.25 = r²

Taking the square root of both sides, we have:

r = ±0.5 Substituting the value of r back into one of the equations, we can solve for a₁:

6.25 = a₁ * (0.5)⁴

6.25 = a₁ * 0.0625

a₁ = 6.25 / 0.0625

a₁ = 100

Therefore, the first term (a₁) is 100, and the common ratio (r) is ±0.5, leading to the correct answer c. a₁ = 100, r = ±0.5.

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The correct option is a. Poisson.

The distribution used to describe the number of events that occur when a given average number of events is expected is the Poisson distribution.

The Poisson is a distribution of probabilities used in statistics to indicate number of times times an occurrence is likely to happen over a certain time period.

Some key features regarding the Poisson distribution are-

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Answer:

B) 24

D) 48

Step-by-step explanation:

Given:

Two fractions

\(\dfrac{1}6 \\and\\\dfrac{3}8\)

To find:

Number that can be chosen as Common denominator such that numerator is also a whole number ?

Solution:

Common denominator for two fractions \(\frac{p}{q}\) and \(\frac{r}{s}\) is chosen as LCM or multiple of LCM of (q, s).

OR

Common denominator for two fractions is chosen as the Least Common Multiple or multiple of LCM of denominators of the two fractions.

The denominators of the given fractions are 6 and 8.

Let us factorize and try to find the LCM of 6 and 8.

\(6 = \underline2 \times 3\\8 = \underline2 \times 2\times 2\)

Common part of the denominators (as underlined) will be taken only once.

So, \(LCM = 2 \times 3 \times 2 \times 2 =24\)

Multiples of LCM, 24 = 48

So, the correct answers are:

B) 24 and

D) 48

In a probability histogram, there is a correspondence between area and probability. So, the option(d) is right choice for answering this problem.

Probability histograms represent chance of occurrence an event. A probability histogram is a graphical representation that shows the probability of each outcome on the y -axis. It consists of a rectangle centered on for all values x, and the area of each rectangle is proportional to the probability of the corresponding value. The standard normal distribution is a normal probability distribution with μ = 0 and σ = 1. The area above a class interval denotes the chance of occurrence for that class interval. Because the total area under the curve is equal to one, therefore, is a correspondence between area and probability.

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Complete question:

In a probability histogram, there is a correspondence between _______.

a)volume and probability

b) area and volume

c)variation and area.

d) area and probability

The number of degrees of freedom is large, then the student's T distribution is close to the normal distribution.

The degrees of freedom is the number of observation in a sample that are free to vary when we estimate the statistical data. Degree of freedom will also indicate the independent piece of information in the data.

Basically, the T distribution or student's distribution is a family's of distribution that look identical to the normal distribution.

So, the number of degrees of the freedom is large then it will closely related to normal distribution.

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To determine the number of ways Samantha can arrange her mathematics books and computer science books on the shelf, we can use the concept of permutations.

1. First, we'll arrange the 3 mathematics books in the first 3 positions. Since Samantha has 7 mathematics books to choose from, she can arrange them in 7P3 ways:
7P3 = 7! / (7-3)! = 7! / 4! = 7 x 6 x 5 = 210 ways

2. Next, we'll arrange the 2 computer science books in the last 2 positions. Since Samantha has 5 computer science books to choose from, she can arrange them in 5P2 ways:
5P2 = 5! / (5-2)! = 5! / 3! = 5 x 4 = 20 ways

3. Now, we need to multiply the number of ways to arrange the mathematics books by the number of ways to arrange the computer science books since these are independent events:
Total ways = 210 (mathematics books) x 20 (computer science books) = 4200 ways

So, Samantha can arrange her 7 mathematics books and 5 computer science books in 4200 different ways, with the first 3 positions occupied by math books and the last 2 by computer science books.

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Answer:

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Step-by-step explanation:

The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The given figure can be decomposed into the following figure.

- Semicircle

- Trapezoid

- Two rectangles

Thus,

A semicircle, a trapezoid, and two rectangles.

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Exponents laws are

\(a^n . a^m = a^{n + m}\)

\(a^n / a^m\) = \(a^{n - m}\)

Exponent laws are important to use because they will help us to simplify complex expressions easier.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Exponents are written in the form \(a^n\)

Where n can be any real numbers.

Now,

a = 2

For n = 0, 1, 2, 3, -1, -2, -3

We get,

\(2^0\) = 1

2² =  2 x 2 = 4

2³ = 2 x 2 x 2 = 8

\(2^{-1}\) = 1/2

\(2^{-2}\)  = 1/(2 x 2) = 1/4

\(2^{-3}\) = 1/(2 x 2 x 2) = 1/8

Exponents laws are:

\(a^n . a^m = a^{n + m}\)

\(a^n / a^m\) = \(a^{n - m}\)

Thus,

Exponent laws are important to use because they will help us to simplify complex expressions easier.

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Answer:

Step-by-step explanation:

false true true false

Answer:

false true true and false

Step-by-step explanation:

Answer:

$120

Step-by-step explanation:

40% off means that the post reduction price is 60% of the original.

Therefore, if $45 is 60% of the original,

100% of the original price = 45 / 60 x 100 = $75

Therefore, the total cost of both = 45 + 75 = 120

Answer:

Step-by-step explanation:

The distance formula or the Pythagorean theorem will tell you the length of DF:

  DF = √((m -0)² +(0 -n)²)

  DF = √(m² +n²)

The slope can be found from the slope formula or by looking at rise/run.

  slope = rise/run

  slope = -n/m

The midpoint is the average of the end points:

  midpoint = ((0, n) +(m, 0))/2

  midpoint = (m/2, n/2)

Answer

1296

Step-by-step explanation:

The explanation is 2x is written as 2*2 = 4

then 3x is written as 3*3 = 9  so

so you do 4*9 = 36 * 2 = 1296

Answer:

The answer to your problem is: 6x³

Answer:

5. c = 13

6. b = 6

Step-by-step explanation:

Our equation is a^2 + b^2 = c^2

5. 144 + 25 = 169

Then square root 169

c = 13

6. 64 + b^2 = 100

b^2 = 36

b = 6

Answer:

542.1

Step-by-step explanation:

you round up since 7 is above 5

Answer:

542.1

Step-by-step explanation:

Find the number in the tenth place  0  and look one place to the right for the rounding digit  7 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

Slope Intercept Form Calculator is a free online tool that uses the slope-intercept form to show a line's equation.

A line's slope, also known as its gradient, is a number that indicates the line's steepness and direction.

The slope-intercept form is one way to express a line's equation in mathematics. The equation of a line can be defined in one of three ways: standard form, point-slope form, or slope-intercept form. The equation of the line can be easily determined once the slope and y-intercept value is known. The slope-intercept form can be expressed as y = mx + b, where b denotes the y-intercept and m denotes the slope.

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Answer:

Do cross multiplication

Answer:

a) 3

b) 9

Step-by-step explanation:

I used a calculator, pls let me know if im incorrect

The mean number of hours studied in one month is 115.50.

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number. Mean is a measure of central tendency. Measures of central tendency attempts to describe a data set by determining its central value. Other measures of central tendency are mode and median.

Mean = sum of the numbers / total number

(46 + 88 + 52 + 85 + 97 + 94) / 6

462 / 4 = 115.50

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