Plot the point given by the following polar coordinates on the graph below. Each circular grid line is 0.5 units apart.(-15. **)

On a dilation, all angles remain the same, and the side lengths are proportional by the same factor of the dilation.

The LCM of 3, 16, and 24 = 48

The LCM of 3, 16, and 24 is found below

The LCM = 3 x 2 x 2 x 2 x 2

The LCM = 48

Therefore, the LCM of 3, 16, and 24 = 48

The mathematical expression is 20÷n and the value of the expression at n=5 is 4.

We are given a phrase and we have to convert it into a mathematical expression. The phrase is given below :

P = "the quotient of twenty and a number"

An expression or mathematical expression is a finite collection of symbols that are well-formed according to context-dependent norms. In mathematics, an expression is a statement that involves at least two distinct numbers (known or unknown) and at least one operation. The mathematical expression equivalent to the above phrase is 20/n.

We now need to evaluate the mathematical expression for n = 5.

20/5 = 4

The value is 4.

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We have that the empirical rule to construct a 68% confidence interval can be expressed with the following general rule:

in this case, we have the following information:

then, the confidence interval with 68% of confidence is:

therefore, the confidence interval with 68% of confidence is (282,342)

Answer: (307,317)

Step-by-step explanation:

The population standard deviation is known (and is assumed to be normally distributed). Using the Empirical Rule, we know that approximately 68% of the data lies within one standard deviation of the mean. So, the confidence coefficient is zα2=1, approximately.The point estimate for the population mean, μ, is the sample mean, x¯=312.  The standard error for the sampling distribution is σx¯=σn√, where σ is the population standard deviation and n is the sample size. So, the standard error is σx¯=30n√. We did not list a decimal approximation because the instructions stated that only the final answer should be rounded. The error bound for the mean (EBM) is given by the formula EBM=zα2(σn√)=1(3030√). Again, we did not list a decimal approximation because the instructions stated that only the final answer should be rounded. Finally, we can calculate the confidence interval at the desired level of significance using the formula (point estimate−EBM , point estimate+EBM)(312−1(3030‾‾‾√),312+1(3030‾‾‾√))(307,317)

The fewest number of miles he can drive each day is option a which is 343.

The mathematical technique used to divide big numbers into more manageable groups or portions in mathematics is called long division. Making a difficulty into manageable, straightforward steps is beneficial. There are remainders, quotients, dividends, and divisors in long divisions. The dividend, which is the big number divided by the divisor in a long division problem, is the problem's large number. The excess amount that cannot be divided is referred to as the residue, and the quotient is the outcome of the division. Compared to multiplication, division is the opposite. When you divide 12 into three equal groups, you get four in each group if three groups of four add up to 12, which they do when you multiply. Determine how many equal groups are created by splitting the population.

Total miles = 1375

Number days = 4

1 day = 1375/4

= 343.75

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The function h is defined, for all real numbers , answer is as follows -

h(1) = - 2

h(2) = 3

h(4) = 3.

function, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable

We have been given that

h(x) = 1/4(x) - 1       if x < -2

h(x) = -(x + 1)² + 2  if -2 ≤ x < 2

h(x) = 3                  if x ≥ 2

Find h (1), h (2), and h (4)

For h (1) -

Value of h(1) for h(x) = -(x + 1)² + 2 as if -2 ≤ x < 2

So put x = 1

h(x) = -(x + 1)² + 2

h(1) = -(1 + 1)² + 2

h(1) = -4 + 2

h(1) = - 2

For h (2) -

Value of h(2) for h(x) = 3 as  if x ≥ 2

h(x) = 3

h(2) = 3

For h (4) -

Value of h(4) for h(x) = 3 as  if x ≥ 2

h(x) = 3

h(4) = 3

Hence , the value for given functions - h(1) = - 2 , h(2) = 3 and h(4) = 3.

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Vertical angles are always congruent - they always have the same angle measure. If one angle is 40 degrees, the vertical angle across from it will also be 40 degrees.

The angles that occupy the same relative location when a transversal cuts two or more lines are known as corresponding angles.

The figure's matching angle pairings are:

∠1 and ∠5 and ∠2 and ∠6 and ∠7 and ∠8

The matching angles are equivalent when the lines are parallel.

The pairs of angles on one side of the transversal and inside the two lines that make up a transversal that cuts two lines are known as the successive internal angles.

The further internal angles in the illustration above are:

∠3, ∠6, ∠4, and ∠5.

When a transversal cuts two parallel lines, supplemental pairs of subsequent interior angles result.

Pairs of angles on one line are generated when two parallel lines are sliced by a transversal, and these alternate internal angles are congruent.

The pairs of angles outside the two lines and on either side of a transversal that cuts two lines are referred to as the alternate external angles

∠1 and ∠7; ∠2 and ∠8;

When a transversal divides two parallel lines, the resulting alternate exterior angles are congruent.

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ANSWER:

19.72

STEP-BY-STEP EXPLANATION:

To calculate the magnitude of the vector, we must apply the norm to its coordinates.

That is, its magnitude is equal to the square root of the sum between the squares of its value at x and its value at y.

Therefore:

We replacing:

The magnitude of the vector is 19.72

Distance Between Two Points

The length of a segment that connects two points can be calculated as the distance between those points (x1,y1) (x2,y2) with the formula:

The endpoints of segment AB are A(-5, 2) and B(4, -3). Calculating the distance:

Calculate:

Calculating and rounding to one decimal place:

d = 10.3

The length of segment AB is 10.3 units

Answer:

40 years old

Step-by-step explanation:

Define the variables:

Given Ryan is 93 years younger than Stacy:

⇒ r = s - 93

Given 9 years ago, Stacy's age was 4 times Ryan's age:

⇒ 4(r - 9) = (s - 9)

Substitute the first equation into the second equation and solve for s:

⇒ 4(s - 93 - 9) = (s - 9)

⇒ 4(s - 102) = s - 9

⇒ 4s - 408 = s - 9

⇒ 3s = 399

⇒ s = 133

Substitute the found value of s into the second equation and solve for r:

⇒ r = 133 - 93

⇒ r = 40

Therefore, Ryan is 40 years old now.

Regular pay = 40*19.80 = $792

overtime pay = 11*19.8*1.5 = $326.7

gross pay​ = Regular pay + overtime pay = $792 + $326.7 = $1118.7

Answer: 43 texts

Step-by-step explanation: first you see your total amount used on texts, so you would do 37-29.99 to give you 7.01. then using that 7.01 you divide it by 0.16, to give you 43.8125, and because you can't go over the 37$ you would round down to 43 texts.

The length of the hypotenuse x is 36 units.

So, let us assume that side x is the hypotenuse of the triangle:

Now, substitute values in the formula as follows:

Rounding off: 36

Therefore, the length of the hypotenuse x is 36 units.

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Answer:

36 units  

Step-by-step explanation:

The True statements are,

The False statements are,

Any number that can be written as a ratio (or fraction) of two integers is a rational number.

A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0. Example: √2, √3, √5, √11, √21, π(Pi) are all irrational.

Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.

Real numbers ⇒ Rational , Irrational numbers

Rational numbers ⇒ Integer, Fraction

Based on the given statement,

(1) . If a number is in integer. then the number is else rational.  [ TRUE ]

The rational numbers are include integers.

So, this statement is True.

(2) . If a number is real. then it is else rational. [ False ]

The real numbers are include rational and irrational numbers.

So, this statement is False.

(3) . 3.456 is an irrational number. [ FALSE ]

= 3.456

= 3456/1000

So, it is rational number.

Then, it is not irrational number. So, this statement is False.

(4) . √11 is a real number. [ TRUE ]

This statement is True, because √11  is real number.

(5) . zero is an natural number. [ TRUE ]

This statement is True, because zero is natural number.

(6) . 9 is an integer. [ TRUE ]

We can write,

= 9

= 3*3

So, this statement is true, because 9 is an integer.

(7) .  If a number is natural. then it else whole​. [ TRUE ]

This statement is true, because natural means the whole larger than zero, like 0 , 1 , 2 , ........

So, this statement is True.

Therefore,

The True statements are,

The False statements are,

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Given: The equation below

To Determine: The value of x

Solution

Let us apply the exponent rule

Hence, the approximate value of x is 2.77, OPTION A

Equation of line passing through two points (-2,11) and (1,-4) is f(x)=

y=mx+b is the equation of line where m is the slope and b is the y intercept.

Since slope of line passing through two points (x₁, y₁) and (x₂, y₂)

m=y₂-y₁/x₂-x₁

slope of line passing through two points (-2,11) and (1,-4)

y₂=-4,y₁=11, x₂=1, and x₁=-2

m=-4-11/1-(-2)

m=-15/1+2

m=-15/3

m=-5

Therefore, the slope of the line is -3.

Now use the slope and either of the two points to find the y-intercept.

y=mx+b for (-2, 11)

11=-3(-2)+b

11=6+b

11-6=b

5=b

Hence equation of line will be

y=-3x+5

f(x)=-3x+5

Therefore equation of line passing through two points (-2,11) and (1,-4) is f(x)=-3x+5

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The missing measurement for z would be 6 yds.

The volume of the rectangular prism is the product of the base area and the height.

Given the volume of a rectangular prism is 24 yds cubed

Length of prism = z

Width of prism = 1 yds

Height of prism = 4 yds

The volume of the rectangular prism would be :

volume of the rectangular prism = Base Area × Height

volume of the rectangular prism = Length × Width × Height

Substitute the values in the above formula,

24 yds cubed = z × 1 × 4

Apply the multiplication operation, and we get

24 = 4 z

z = 24/4

z = 6 yds

Therefore, the missing measurement for z would be 6 yds.

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The image of the function after the translation is g(x) = |x - 2| + 10

From the question, the given parameters are:

f(x) = |x|

The transformation is given as

Translate the function to the right 2 units and up by 10 units

Mathematically, this transformation can be represented as

(x, y) = (x, - 2 y + 10)

When represented as a function, we have

g(x) = f(x - 2) + 10

So, we have

g(x) = |x - 2| + 10

So, we have the following equation

f'(x) = |x - 2| + 10

Hence, the equation of g(x) is g(x) = |x - 2| + 10

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Given:

We are given this figure.

To find:

The area of the given figure.

Step-by-step solution:

As per the question, It is a trapezoid:

Area of trapezoid = 1/2 × (a + b) × h

Here a and b are lengths of parallel sides.

Area = 1/2 × (a + b) × h

Area = 1/2 × (8 + 27) × 6

Area = 1/2 × 35 × 6

Area = 35 × 3

Area = 105 cm²

Final answer:

The final area of the trapezoid = 105 cm²

Answer:

C.

Explanation:

We were given the following information:

We will proceed to derive the sinusoidal equation for this as shown below:

Hence, the correct option is C

The plot that represents

Is the one in Option A.

Now, in comparison to the graph of

The graph of

Is horizontally compressed by a factor of 4/7

After solving for x, we get the value of n as an improper fraction:

(-3).(-1)/2

Given, the expression is:

1/8÷√2=2ⁿ

convert the expression to exponential form.

1/8 ÷ 2¹/² = 2ⁿ

1/2³ ÷ 2¹/² = 2ⁿ

convert both sides of the equation into terms with same base.

2⁻³ ÷ 2¹/² = 2ⁿ

Simplify using exponent rule with same base.

aⁿ.aˣ=aⁿ⁺ˣ

2⁻³⁻¹/²=2ⁿ

Based on the given conditions, corresponding exponents are equal.

n=-3-1/2

Rewrite the fraction using the least common denominator.

n = -6-1/2

calculate the difference.

n = -7/2

improper fraction is : (-3).(-1)/2

Hence we get the value for n as (-3).(-1)/2

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We are given the following expression:

To solve the expression we will add the numbers inside the parenthesis:

Now we solve the squares:

Now we solve the product:

Now we solve the operation:

Therefore, the expression is equivalent to 184.

Answer: First one is 12

Second is 6:8

Third is 3:5

Fourth is 240

Last one is 3:5

Step-by-step explanation:

If you get 2 loaves of bread for 3 cups of raisins and you need 8 loaves then you do 3x4 to get 12

Do 3x2=6 then 4x2=8 so 6:8

Do 3x4=12 and 5x4=20 so 3:5

12/4 is 3 so we know that we divide by 3 720/3 is 240

Same question as #3

Solution

Step 1:

Write the expression

Step 2

Answer

6.8 ( 2 significant figure)

given the system of equations:

We will solve the system by substitution as follows:

From equation (2)

substitute with (y) from equation (4) into equation (1)

From the equation (4) and (5) substitute with (x) and (y) into equation (3):

solve the equation to find the value of (z):

substitute into the equations (4) and (5) to find the values of (x, y)

So, the answer will be:

The system has only one solution

x = 5

y = 1

z = 1

In the graph y will always be smaller than 1/5(x) - 4 in the inequality x−5y<20.

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Olivia is chosen for the 12U softball team. What age is Olivia? Because it doesn't say "equals," you are unaware of Olivia's age. But since you already know Olivia's age should be below or equal to 12, you can write it as Olivia's Age 12. This scenario relates to inequalities in the real world.

First we will write the equation in the y-intercept form

y = mx + b

So,

⇒ x−5y<20    

⇒ x -5y - 20 < 20 - 20

⇒  x -5y - 20 < 0

⇒ x -5y - 20 - x +20 < - x +20

⇒ -5y < - x +20

⇒ 5y < x - 20

⇒ y < 1/5(x) - 4

Here slope is 1/5

So the graph is give below ↓↓↓

Thus, In the graph y will always be smaller than 1/5(x) - 4 in the inequality x−5y<20.

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step 1

Find the slope

we need two points

so

we take (0,3) and (2,2)

m=(2-3)/(2-0)

m=-1/2

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-1/2

b=3

substitute

y=-(1/2)x+3

therefore

the rule is

We can use the exponential growth function as follows:

Where:

a = Initial amount = 28300

r = Growth rate = 7% = 0.07

t = time ( in years)

so:

Evaluate the function for 17 years:

Answer:

Approximately 89394