The Census Bureau estimates that New York State has a population of
approximately 1,950,000 people. Write this number in scientific
notation.

Answer:

103 students tickets were sold

Step-by-step explanation:

103 times $5 = $515

212 times $8 = $1696

$515 + $1696 = $2211

Answer:

See below

Step-by-step explanation:

You pull-out what is common.

2\(x^{3} -16x^{2} -18x\)

\(2x(x^{2} -8x-9)\)

2x(x-9)(x+1)

To verify, set each answer = 0

2x = 0, x=0

x-9 = 0, x=9

x+1 = 0,  x=-1

Now, plug each value back into the equation and make sure each one equals 0.

Answer:

A. divide 168 by 28 and divide 108 by the answer

Step-by-step explanation:

you divide 168 by 28 to find the ratio

Answer:

It is joe mama

Step-by-step explanation:

Answer:

1/3^2 or 1/9

Step-by-step explanation:

Just think of the negative symbol in front of the exponent as a 1/ and then just add the exponent to the base.

Answer:

(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯     is true

Step-by-step explanation:

The positions of the letters in naming the triangles in the statement of congruent tells you which sides are congruent.

△ABC≅△EFG

Sides AB and EF are congruent

△ABC≅△EFG

Sides BC and FG are congruent

△ABC≅△EFG

Sides AC and EG are congruent

Look at the choices:

(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯     is true

First, since it's given the angle PRS=98 degrees we can find x.

(3x-8)+(2x+6)=98 we can solve for x

after solving this we find that

x=20

Now we can solve for angle QRS

2x+6 plug in our values and we get

40+6, which equals 46 degrees

a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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A. 0. 0063 is the correct answer.

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Answer:

\(y= 2x + 4\)

Step-by-step explanation:

We are given an equation of \(2x-y+3 =-1\) and we need to put into \(y = mx+b\) form.

First, we subtract 3 on both sides to get the variables all on one side.

\(2x-y+(3 - 3)=(-1 -3)\\\\\)

\(2x-y = -4\)

We need to now isolate y on its own so we subtract \(2x\) on both sides.

\((2x-2x)-y=(-4-2x)\)

\(-y=-2x-4\)

We almost done! We then need to divide the invisible negative on both sides which is a -1.

\(\frac{-y}{-1}=\frac{-2x-4}{-1}\)

\(y=2x+4\)

When we divide the the negatives together, we know that two negatives divided together is a positive. Therefore, we get our answer \(y=2x+4\)

Hoped this helped!

Answer: Point D

Step-by-step explanation:

Descriptive statistics is a branch of statistics that deals with the collection, analysis, interpretation, and presentation of data. It focuses on summarizing and describing the characteristics of a sample or population. The purpose of descriptive statistics is to provide a clear and concise summary of the data, including measures of central tendency, variability, and distribution.

True,This information can be used to make inferences about the population as a whole. Therefore, descriptive statistics helps statisticians to better understand and interpret the population data.

False, Descriptive statistics is a branch of statistics that focuses on summarizing and organizing data from a sample or population. It provides insights into the basic features of the data, such as the mean, median, and standard deviation, but does not make inferences about the population.

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The area of the region bounded by the curve y = f(x) = x³ - 4x + 1 and the tangent line to the curve at (-1, 4) = 8.25.

To calculate the area of the region bounded by the curve y = f(x) = x³ - 4x + 1 and the tangent line to the curve at (-1, 4), we need to obtain the points of intersection between the curve and the tangent line.

First, let's find the equation of the tangent line.

We know that the tangent line to a curve at a given point has the same slope as the curve at that point.

Taking the derivative of f(x), we get:

f'(x) = 3x^2 - 4

Evaluating the derivative at x = -1 to obtain the slope at that point:

f'(-1) = 3(-1)^2 - 4 = -1

So, the slope of the tangent line at (-1, 4) is -1.

Using the point-slope form of a linear equation, we have:

y - 4 = -1(x - (-1))

y - 4 = -1(x + 1)

y - 4 = -x - 1

y = -x + 3

Now, let's obtain the points of intersection between the curve and the tangent line.

We equate the two equations:

x^3 - 4x + 1 = -x + 3

Rearranging the equation:

x^3 - 3x + 4x - 2 = 0

x^3 + x - 2 = 0

x ≈ 1.328.

Now, we integrate the difference between the curve and the tangent line from x = -1 to x = 1.328 to obtain the area of the region:

Area = ∫[from -1 to 1.328] (f(x) - (-x + 3)) dx

Evaluating this integral, we get the area as approximately 8.25.

Therefore, the correct answer is O 8.25.

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Answer:

156 bundles

Step-by-step explanation:

Total area of the roof = 2(70 x 30) = 4200 sf  

(4200 sf) / (27sf/bundle) = 155.56 ≈ 156 bundles

Answer: The perimeter is about 20.26 units

Step-by-step explanation:

To calculate the distance between the points, we use the formula:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

where,

d = distance

\(x_2\text{ and }x_1\) are the coordinates of the points on x-axis

\(y_2\text{ and }y_1\) are the coordinates of the points on y-axis

For the given points:

B(0,3), C(4,-1), E(2,-3) and F(-2,1)

\(x_2=4\\x_1=0\\y_2=-1\\y_1=3\)

Putting values in above equation, we get:

\(BC=\sqrt{(4-(0))^2+(-1-3)^2}\\\\d=\sqrt{16+16}=5.66units\)

\(x_2=2\\x_1=4\\y_2=-3\\y_1=-1\)

Putting values in above equation, we get:

\(CE=\sqrt{(2-(4))^2+(-3-(-1))^2}\\\\d=\sqrt{36+4}=4.47units\)

To calculate the perimeter of a rectangle, we use the equation:

\(Perimeter=2(l+b)\) ....(1)

where,

l = length of the rectangle = BC = 5.66 units

b = breadth of the rectangle = CE = 4.47 units

Putting values in equation 1, we get:

\(Perimeter=2(5.66+4.47)\\\\Perimeter=20.26 units\)

Hence, the perimeter is about 20.26 units

Answer:

b

Step-by-step explanation:

used a calucator

Answer: 3x-5

Step-by-step explanation:

9x-5(-6x)

9x-5-6x

3x-5

Answer:

15x - 5

Step-by-step explanation:

We have the equation 9x - 5 - (-6x) and are asked to solve it.

We cannot combine 9x and 5 because they have a variable difference, with 9 having x as its variable and 5 having no variable. What we can do is distribute the minus sign to the right of 5 to (-6x), lets do as said :

9x - 5 - (-6x)

Two negatives make a positive, therefore :

9x - 5 + 6x

Since 9x and 6x have the same variable ending, we can combine them, do as followed :

9x - 5 + 6x

9x + 6x

15x - 5

Answer:

V = 80√3 cm³

Step-by-step explanation:

V = Ab×h/3

Ab = l²√3/4 = 64√3/4 = 16√3 cm²

V = 16√3cm²×15cm/3

= 16√3cm²×5cm

= 80√3 cm³

Answer:

138.56cm2

Step-by-step explanation:

B.a×hx1/3

B.a=1/2×8×8sin60=27.71cm2

1/3×27.71×15=138.56cm2

Surface Area of Larger Solid: S2 = k^2 * S1 and Volume of Larger Solid: V2 = k^3 * V1. Substitute in the given values for S1, V1, and k before solving for S2 and V2.

To solve this problem, we need to use the fact that similar solids have corresponding sides that are proportional in length.  

Let's call the scale factor between the two solids "k". This means that if the smaller solid has a side length of "s", then the corresponding side length in the larger solid is "ks".

Now let's use the given information to find the surface area and volume of the larger solid. Let's call the surface area and volume of the smaller solid "S1" and "V1", respectively.

Surface Area:
The surface area of a solid is proportional to the square of its linear dimensions. Since the scale factor between the two solids is "k", the surface area of the larger solid is k^2 times the surface area of the smaller solid. Therefore, the surface area of the larger solid (S2) can be found using the formula:

S2 = k^2 * S1

Volume:
The volume of a solid is proportional to the cube of its linear dimensions. Using the same logic as above, the volume of the larger solid (V2) can be found using the formula:

V2 = k^3 * V1

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x^2 + 4x - 32 = 0

To find the solutions we can factorice the expression as follows

(x + 8)(x - 4) = 0

if

x + 8 = 0

x = -8

or

x - 4 = 0

x = 4

The answers are x = -8 and x = 4

Answer:

B. 12x^2 + 31x + 20

Step-by-step explanation:

Use FOIL (First, Outer, Inner, Last)

(3x + 4)(4x + 5)

12x^2 + 15x +16x + 20

12x^2 + 31x + 20

Answer:

B

Step-by-step explanation:

You are going to want to use the FOIL method. First outer inner last. Multiply 3x*4x to get 12x^2 then multiply 3x*5 to get 15x then multiply 4*4x to get 16x and last multiply 4*5 to get 20. Since 15x and 16x are like terms we add them together to get 31x

According to the given function, we can throw it to the height of 6.6 m.  So, yes we can throw it high enough to reach the ledge.

The given equation is quadratic. A quadratic equation is defined as an equation of a single variable with the highest power of 2. In general, the quadratic equation can be expressed as h(x)= \(ax^2- bx + c\), where a, b and c are arbitrary constants. The solution for a quadratic equation is given by:

\(x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}\)

The maximum of a quadratic equation is given by:

= \(c-\frac{b^2}{4a}\)

The length to be covered by throwing=6 meters

It is given that the height of the grappling hook you throw is a function h(t) = -4.9t² + 10t + 1.5

Here a =4.9, b = 10 and c = 1.5

The maximum of a quadratic equation is given by:

\(c-\frac{b^2}{4a}\)

\(1.5-\frac{10^2}{4*(-4.9)}\)

6.6

A throw can be made to reach the wall since the height of wall is less than the maximum value that is 6.6 m.

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Answer: The answer is A.  30% of 88$ is 26.40.

Since we can't have a fraction of a year, we need to round up to the equation nearest whole number. Therefore, it will take at least 7 years for the value of the car to be less than $3,000.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

V(1) = 0.85 * 12,900 = $10,965

V(2) = 0.85 * 10,965 = $9,320.25

\(V(n) = 0.85^n * 12,900\\0.85^n * 12,900 < 3,000\\n > log(3,000/12,900) / log(0.85)\\n > 6.48\\\)

Since we can't have a fraction of a year, we need to round up to the nearest whole number. Therefore, it will take at least 7 years for the value of the car to be less than $3,000.

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Answer:

9 years

Step-by-step explanation:

As the car depreciates at a constant rate of 15% each year, we can use the exponential decay formula to find the value of the car after t years.

\(\boxed{f(t)=a(1-r)^t}\)

where:

Given the purchase price of the car is $12,900, a = 12900.

Given the car will depreciate at a rate of 15%, r = 0.15.

Substitute the values of a and r into the formula to create a function for the value of car after t years is:

\(f(t)=12900(1-0.15)^t\)

\(f(t)=12900(0.85)^t\)

To calculate after how many years the value of the car will be less than $3,000, substitute f(t) < 3000 and solve for t.

\(\implies 12900(0.85)^t < 3000\)

Divide both sides by 12900:

\(\implies (0.85)^t < \dfrac{3000}{12900}\)

\(\implies (0.85)^t < \dfrac{10}{43}\)

Take natural logarithms of both sides:

\(\implies \ln (0.85)^t < \ln\left(\dfrac{10}{43}\right)\)

Apply the log power law:

\(\implies t \ln (0.85) < \ln\left(\dfrac{10}{43}\right)\)

Divide both sides by ln(0.85), remembering to change the direction of the inequality sign since ln(0.85) is negative:

\(\implies t > \dfrac{\ln\left(\dfrac{10}{43}\right)}{\ln (0.85)}\)

\(\implies t > 8.9750695...\)

We need to round up to 9 years, since we can't have a fraction of a year.

Therefore, the value of the car will be less than $3,000 after 9 years.

Answer:

it will grow by 1.44 people

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

(a)

Given y is directly proportional to x then the equation relating them is

y = kx ← k is the constant of proportion

To find k use the condition when x = 3, y = 18 , then

18 = 3k ( divide both sides by 3 )

6 = k

y = 6x ← equation of proportion

(b)

(i)

when x = 12 , then

y = 6 × 12 = 72

(ii)

when y = 42

42 = 6x ( divide both sides by 6 )

7 = x

The probability that a randomly selected adult has an IQ greater than 130.0 is 2. 87 %.

Convert the IQ score of 130 to a z - score by the formula :

z = ( x - μ ) / σ

Where:

x is the IQ score

μ is the mean

σ is the standard deviation

The z - score is :

= ( 130.0 - 96.7 ) / 17.5

= 1.898

The probability that a randomly selected adult has an IQ greater than 130.0, using the standard normal distribution and z - score, would be :

= 1 - P( z ≤ 1. 898 )

= 1 - 0. 9713

= 0. 0287

= 2. 87 %

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Answer:

249 (249.23)

Step-by-step explanation:

Let the total number of employees be denoted by x

According to the question

65% of x = 162

(65/100) * x = 162

(65x)/100 = 162

65 x = 162 * 100

65 x = 16200

x = 16200/65

x = 249.23

therefore total number of employees = 249 (you can't count people in fraction so omit the digits after the decimal)

Answer:

True

Step-by-step explanation:

tan B = sin B / cos B = 3/4 Let sin B =3 and cos B = 4

Cot B = cos B / sin B = 4/3

This is true

Answer:

y = 4x - 2

Step-by-step explanation:

Formula: y = mx + b

Parallel means same slope as original and b is -2.