You are working on a school newsletter and you need to resize some
pictures. You have a picture that is 6 inches by 9 inches but you need it
to fit into a space that is 4 inches by 6 inches. What scale factor would
change the size of the picture to make it fit the new space?
OA.2
OB. 3/2
QC.-2
OD. 2/3

The mean of the sampling distribution of p is 0.45, (b) the standard deviation of p is 0.02, (c) yes, the Normal approximation can be used, and (d) the probability that more than half of the sample is in favour is 2.2523.

A) The mean of the sampling distribution of p is equal to the population proportion who favour giving vouchers to parents, which is 0.45.

B) The standard deviation of p can be calculated using the formula:

σ = √(p(1-p) / n)

where p = 0.45 and n = 500.

The standard deviation of p is approximately 0.02. This value represents the variability of the proportion of adults in samples of size n = 500 who favour the idea.

C) In order to use the Normal approximation for the distribution of p, the sample size n must be large enough such that np ≥ 10 and n(1-p) ≥ 10. For this problem, n = 500, p = 0.45, np = 500 * 0.45 = 225, and n(1-p) = 500 * (1-0.45) = 275, which are both larger than 10, so the Normal approximation can be used.

D) The probability that more than half of the sample is in favour can be found by subtracting the area under the standard normal curve to the right of z = 0.5 from 1.

z = (p - 0.45)/0.02

= (0.5 - 0.45)/0.02

= 2.2523

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Answer:

x=–2

Step-by-step explanation:

x-8=-10

x=-10-8

x=–2

Answer:

-8= -10

, = -10+8

, = -2

additive identity is “0” as adding 0 to any number, gives the sum as the number itself. therefore, the answer is: Additive identity

Step-by-step explanation:

may it be

9.6

may it help u

one of them

when 45 is a degree use the first one

Answer:

20

Step-by-step explanation:

The number 3 will appear in the numbers 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93. In these numbers it appears 20 times.

Answer:

yes

Step-by-step explanation:

because if you multiply 6 and n it is 6n and 6 x 3 are 18 but subtract 4 and it is correct

Answer: b) $60.56 per year of age

Step-by-step explanation: If the scatterplot of two variables shows a line and the correlation between them is strong, we can calculate a regression line.

Regression line is a line graph that best fits the data. Like any other line, its formula is given by

y = mx + b

with

m being the slope

b the y-intercept

The slope of the line, correlation and standard deviations of the two variables have the following relationship:

\(m=r\frac{S_{y}}{S_{x}}\)

where

r is correlation

\(S_{y}\) is standard deviation for the y data

\(S_{x}\) is standard deviation for the x data

For our problem:

r = 0.34

\(S_{y}=\) 2850

\(S_{x}=\) 16

Calculating

\(m=0.34(\frac{2850}{16})\)

m = 60.56

Slope for the regression line of annual income per year of age is 60.56.

Answer:

There are 12 boys at the movie.

Step-by-step explanation:

Key skills needed in order to solve: Proportions, Ratios, and Multiplication

1) The ratio is 4 boys : 5 girls --> It can be written as a fraction --> 4/5

2) If there are 15 girls, we need to find the number of boys. let's say x is the number of boys when there are 15 girls. The ratio would then be x/15

3) Make a proportion --> \(\frac{4}{5}\) = \(\frac{x}{15}\)

You have to cross multiply here. You do the first fraction's numerator times the second fraction's denominator, and the first fraction's denominator times the second fraction's numerator.

4) This means you have to do: 4(15) = 5(x)

5) Multiply it out --> 60=5x

6) Divide by 5 and you will get x=12

Therefore there are 12 boys at the movie.

Hope you understand and have a nice day!! :D

Answer:

D. 24

Step-by-step explanation:

AM: 12 (radius)

AC: 24 (diameter)

Answer:

942 square millimeters.

Step-by-step explanation:

The formula for the surface area of a cylinder is:

S = 2πr^2 + 2πrh

where S is the surface area, r is the radius, and h is the height.

Substituting the given values, we get:

S = 2 x 3.14 x 10^2 + 2 x 3.14 x 10 x 5

S = 628 + 314

S = 942

Therefore, the surface area of the cylinder is 942 square millimeters.

Answer:

25

Step-by-step explanation:

5x5 = 25

Answer:

25

Step-by-step explanation:

Let's go through our times tables really quick!

5x1 = 5 (5 + 0)

5x2 = 10 (5 + 5)

5x3 = 15 (5 + 5 + 5 [10 + 5])

5x4 = 20 (5 + 5 + 5 + 5 [15 (5x3) + 5)

As we can see, if we know 5x4, we can easily find 5x5! It's just 5x4 + 5

So, 5x5 is 25

Hope this helped!

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

28.5 miles per gallon

Step-by-step explanation:

Take the number of miles and divide by the gallons

399/14

28.5

28.5 miles per gallon

Answer: 28. 5 miles per gallon

Step-by-step explanation:

To do this you must divide 399 by 14

399  ÷  14 = 28.5

To check:

28. 5 × 14 = 399

The probability of selecting a junior who takes the bus is P (Junior who takes the bus) = 12/200 = 0.06Hence, the probability that a randomly selected student is a junior who takes the bus is 0.06 or 6/100.

The given frequency table on how students get to school among the high school students is represented in the below table:Transportation Walk Bike BusDriveTotalGrade 9 11 10 14 15 50Grade 10 10 7 13 20 50Grade 11 8 6 12 24 50Grade 12 5 8 8 29 50 Total 34 31 47 88 200Given data from the above frequency table, we are interested in finding the probability of a randomly selected student being a junior who takes the bus.SolutionWe know that the total number of students is 200, and the total number of junior students is 50. Hence the probability of selecting a junior is P (Junior) = 50/200 = 0.25Similarly, the number of students who take the bus is 47 and the number of junior students who take the bus is 12.

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Answer: 6

Step-by-step explanation: Solution: Perimeter of the triangle is the sum of the lengths of its sides. Thus, perimeter = 10 cm. 6.

Answer:

-19x

Step-by-step explanation:

Answer:

− 19x

Step-by-step explanation:

Let's simplify step-by-step.

− 12x − 7x

= − 12x + − 7x

Combine Like Terms:

= − 12x + − 7x

=( − 12x + −7x )

= − 19x

Hope it helps,

Please mark me as the brainliest

Thank you

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

The relationship between logarithms and exponential functions is fundamental and provides a powerful tool for finding solutions in various mathematical and scientific contexts.

Logarithms are the inverse functions of exponential functions. They allow us to solve equations and manipulate exponential expressions in a more manageable way. By taking the logarithm of both sides of an exponential equation, we can convert it into a linear equation, which is often easier to solve.

One of the key properties of logarithms is the ability to condense multiplication and division operations into addition and subtraction operations. For example, the logarithm of a product is equal to the sum of the logarithms, and the logarithm of a quotient is equal to the difference of the logarithms.

Logarithms also help us solve equations involving exponential growth or decay. By taking the logarithm of both sides of an exponential growth or decay equation, we can isolate the exponent and solve for the unknown variable.

This is particularly useful in fields such as finance, population modeling, and radioactive decay, where exponential functions are commonly used.

Furthermore, logarithms provide a way to express very large or very small numbers in a more manageable form. The logarithmic scale allows us to compress a wide range of values into a smaller range, making it easier to analyze and compare data.

In summary, the relationship between logarithms and exponential functions enables us to simplify and solve equations involving exponential expressions, model exponential growth or decay, and manipulate large or small numbers more effectively.

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Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

Using area formula,

a. Area of the trapezium = 47.5m².

b. Area of parallelogram = 54inches².

The area of a thing is the amount of space it occupies in two dimensions. It is a way to count how many unit squares completely round the surface of a closed figure. The standard unit of area is the square unit, which is usually expressed as square inches, square feet, etc.

a. Sides of the trapezium are, a = 5m and b = 14m.

Height, h = 5m.

Area of the trapezium = (a+b)/2 × h

= (5 + 14)/2 × 5

= (19× 5)/2

= 95/2

= 47.5m².

b. Height of parallelogram = 6inches.

Base of parallelogram = 9inches.

Area = b × h

= 6 × 9

= 54inches².

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Answer:

1. = (-5 , -1)

2.= (4 , 0.5)

3 = infinite solutions

I dont know if 2 is right but I tried

it will take you approximately 31.4 seconds  to run around the baseball field at a rate of 9 feet per second.

The time it takes to run around the baseball field will depend on the distance around the field.

Assuming the field is a perfect circle and has a diameter of 90 feet (which is a common size for a baseball field).

The circumference of a circle with diameter 90 feet is:

C = πd = π(90) = 90π feet

To run around the perimeter of the baseball field, you will need to cover a distance of 90π feet.

Using the formula:

time = distance / rate

we can calculate the time it takes to run around the baseball field:

time = (90π feet) / (9 feet/second)

time = 10π seconds

time ≈ 31.4 seconds (rounded to the nearest tenth of a second)

Therefore, it will take you approximately 31.4 seconds (rounded to the nearest tenth of a second) to run around the baseball field at a rate of 9 feet per second.

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Answer:

2 is divisible by 1 and all even numbers are divisible by 2 so that means 4 but 2 is not divisible by 8 and 9 is not divisible by 2 but 1 is.

5 is not divisible by 4. 5 is divisible by 5, 5 is not divisible by 8, 9 is not divisible by 5, 1 is not divisible by 5.

10 is divisible by 1, 4 is not, 5 is not, 8 is not, 9 is not divisible by 10 but 1 is.

Answer:

Step-by-step explanation:

You need only take 45% of 200

Music = 45/100 * 200

Music = 9000/100

Music = 90

So of a grade of 200, there are 90 who take music.

The proportion equivalent with Two-thirds would be 6/9.

Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that the  proportion with Two-thirds

If you actually divide it’ll make since , so first  we want to divide the 2 , then you want to multiply the third of the two

2/3 x 3/3

6/9

thus, the answer will be 6/9.

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The 46th term of the sequence is 324.

We have,

To find the 46th term of the sequence, we need to determine the pattern or rule that generates the terms.

Since the difference between consecutive terms is a constant value of 7, we know that this is an arithmetic sequence with a common difference

of 7.

To find the 46th term, we can use the formula for the nth term of an arithmetic sequence:

a(n) = a(1) + (n - 1) d

where a(1) is the first term, d is the common difference, and n is the term number we want to find.

Using the given information, we have:

a(1) = 9

d = 7

n = 46

Plugging these values into the formula, we get:

a (46) = 9 + (46 - 1)7

a (46) = 9 + 45 (7)

a(46) = 9 + 315

a(46) = 324

Therefore,

The 46th term of the sequence is 324.

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