The mean and standard deviation of the sample data collected on continuous variable Y are −0.5 and 0.5, respectively. The following table shows the relative frequencies of the data in the given intervals. Based on the table, is it appropriate to use the normal model to approximate the population distribution?

Step-by-step explanation:

it'll be undefined and 2 for the surface area

Answer:

The investments were made as follows:

$10,000 at 7% interest
$13,000 at 6% interest

Step-by-step explanation:

First remember that percentages are to be divided by 100 before any calculations can be made

So 7% = 0.07

8% = 0.08

Let x be the amount invested at 7% and y be the amount invested at 8%

We have:

x + y = 23000    (total amount is $23000)

Return on x = 0.07x

Return on y = 0.06y

Total return is

0.07x + 0.06y = 1480

The two equations are

x + y = 23000    [1]
0.07x + 0.06y = 1480  [2]

To solve for x and y,

multiply [1] x 0.07

=> 0.07x + 0.07y = 0.07(23000)

=> 0.07x + 0.07y =  1610  [3]

Since the coefficients of x are the same we can subtract [2] from [3] to eliminate the x term and solve for y

[3] - [2]:

(0.07x + 0.07y ) - (0.07x + 0.06y) = 1610   - 1480  

0.07x + 0.07y - 0.07x - 0.06y = 130

Collecting like terms

0.07x-0.07x +0.07y - 0.06y = 130

0.01y = 130

y = 130/0.01 = 13000

x = 23000 - 13000 = 10000

Therefore the investments were made as follows:

$10,000 at 7% interest
$13,000 at 6% interest

In golf, players use the concept of angles to evaluate their club head position and the angle of attack on the ball. By understanding the principles of geometric angles, golfers can adjust their swing and improve the accuracy and distance of their shots.

In basketball, players use the concept of spatial awareness to evaluate their positioning on the court. By understanding geometric concepts such as lines, angles and planes, they can improve their ability to move without the ball and find open spaces on the court.

In soccer, players use the concept of geometric shapes to evaluate their positioning on the field. By understanding the principles of triangles and circles, soccer players can improve their ability to move and pass the ball effectively, as well as to anticipate the movements of the opposing team.

Overall, the concepts of geometry, such as angles, spatial awareness, and geometric shapes, are essential for athletes in many sports to evaluate their positions and postures and improve their performance.

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Based on the table which shows the pricing for four different types of gasoline, a type that cost the least per gallon is: C. type C.

In order to determine the gasoline that costs least per gallon, we would determine the unit rate for the cost per gallon by using the following mathematical expression;

Unit rate = Cost of gasoline/number of gallons

Substituting the given parameters into the unit rate formula, we have the following;

Unit rate = $20.20/10

Unit rate = $2.02 per gallon.

For type B, we have the following unit rate:

Unit rate = $26.04/12

Unit rate = $2.17 per gallon.

For type C, we have the following unit rate:

Unit rate = $28.24 / 24

Unit rate = $2.01 per gallon.

For type D, we have the following unit rate:

Unit rate = $30.45 / 25

Unit rate = $2.03 per gallon.

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An expression that narrates this sentence using function notation and mathematical symbol: C(B) ≥ A

According to the question,

The cost of the large pizza is at least A dollars B days into the promotion.

The statement that a pizza is at least A dollars B days into the promotion means that the cost of a large pizza B days into the promotion and denoted C(B) and it is greater than or equal to A dollars. Thus, an expression that reports this sentence using function notation and mathematical symbols is simply :

                 C(B) ≥ A

So, the expression is C(B) ≥ A .

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Answer: The formula you provided is the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (h) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula can be written as:

h = √(a^2 + b^2)

To make a the subject of the formula, we can start by squaring both sides of the equation:

h^2 = a^2 + b^2

We can then subtract b^2 from both sides:

h^2 - b^2 = a^2

Now we can take the square root of both sides:

√(h^2 - b^2) = √a^2

a = √(h^2 - b^2)

So, a is the square root of the difference between the square of the hypotenuse and the square of the other side.

Step-by-step explanation:

The correct statement from the given options is Line: Solid, Shade: above.

Graphing inequalities is quite similar to graphing linear equations but we need to focus on the inequalities symbol that is used in the given expression.

Step 1, we need to decide if we need to use a solid boundary line or a dotted boundary line. For this, we need to check the inequality symbol that is given in the expression.  

If there is a greater than (>) or less than (<) symbol we will use a dotted boundary line.

If there is a greater than or equal to or less than or equal to symbol we will use a solid boundary line.

Step 2, In this we need to decide which half-plane should be shaded. For this, we need to determine which side of the line does the solutions will lie on.

Here we have

y ≥ -2x + 3    

Here the symbol used is greater than or equal to hence, the boundary line should be a solid boundary line.  

Now substitute (0, 0) in the given expression

0 ≥ -2(0) + 3    

0 ≥  3  

Since '0' is less than 3, we need to shade the right side of the graph

Therefore,

The correct statement from the given options is Line: Solid, Shade: above.  

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Answer:

D)  Line: solid,  Shade: above

Step-by-step explanation:

Given inequality:

[tex]y \geq-2x + 3[/tex]

When graphing inequalities:

Therefore, for the given inequality:

Answer:

[tex]\huge\boxed{\sf 25x\² + 30x + 9}[/tex]

Step-by-step explanation:

= (5x + 3)²

= (5x + 3)(5x + 3)

= 5x(5x + 3) + 3(5x + 3)

= 25x² + 15x + 15x + 9

[tex]\rule[225]{225}{2}[/tex]

x² - 81 = 0 can be factored as (x-9)(x+9)=0. Therefore, the solutions are x=9 and x=-9.

The sum of all the integers from -√14 to √84 is 39.

To find the sum of the integers that are between √14 to √84, you first need to find √14 and √84.

The value is √14 is :

= √14

= 3. 74

The value of  √84 is :

=  √84

= 9.17

Integers are whole numbers and the whole numbers between these figures are:

4, 5, 6, 7, 8, 9

The sum of these integers is:

= 4 + 5 + 6 + 7+ 8 + 9

= 39

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The inverse demand function is P = 2400 + 5Q

Given that

Q = 480 - 0.2P

We simply make P the subject of the formula

So, we have

0.2P = 480 - Q

Divide by 0.2

P = 2400 + 5Q

To find the marginal revenue function, we can use the inverse demand function P = 2400 + 5Q, and take the derivative of this function with respect to Q.

The derivative of P with respect to Q is dP/dQ = 5. This represents the change in price for a one unit change in the quantity of operations performed.

So the Marginal Revenue function is MR = dP/dQ * Q = 5Q

To maximize profit, the doctor should equate marginal revenue to marginal cost, which is

MC = dAVC/dQ

So, we have

MC = d(2Q² - 15Q + 400)/dQ

Evaluate

MC = 4Q - 15.

So, we have

5Q = 4Q - 15

Q = -15

Take the absolute value

Q = 15

So, the number of operations is 15

We have

P = 2400 + 5Q

This gives

P = 2400 + 5 * 15

Evaluate

P = 2475

To find the profit, we need to subtract the total cost from the total revenue.

The total revenue is found by multiplying the price by the quantity of operations performed: TR = P * Q = 2475 * 15 = 37125

The total variable cost is found by multiplying the average variable cost by the quantity of operations performed: TVC = AVC * Q = (2Q^2 - 15Q + 400) * Q = 2Q^3 - 15Q^2 + 400Q

The total fixed cost is the fixed cost that doesn't change regardless of the level of output : TFC = $8000

The total cost is the sum of the total variable cost and total fixed cost: TC = TVC + TFC = 2Q^3 - 15Q^2 + 400Q + $8000

The profit is the difference between total revenue and total cost:

π = TR - TC = 37125 - (2Q^3 - 15Q^2 + 400Q + $8000)

When Q = 15,

profit is π = 37125 - (2(15)^3 - 15(15)^2 + 400(15) + $8000)

= 19750

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The required decimal value of fraction 2/5 is 0.4, and a fraction of decimal value is 0.55 is 11/20.

Fraction is defined as the number of compositions that constitutes the Whole.

Here,
Given expression,
Fraction = 2 / 5
decimal value = 0.4

Given expression,
decimal value = 0.55
fraction value = 0.55 = 55/100
fraction = 11/20

Thus, the required decimal value of fraction 2/5 is 0.4, and a fraction of decimal value is 0.55 is 11/20.

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The equation for the cross section exists x = z , -z.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. The equation's solution, or root, is the value of the variable for which the equation holds true. Even if the RHS and LHS are switched, an equation still holds true.

In the question it is given that

Equation of curve => x² = 49y² + z²

(a) Write an equation for the cross section at z = -7

Putting z = -7 in the equation,

⇒ x² = 49y² + (-7)²

⇒ x² - 49y² = 49

(b) Write an equation for the cross section at z = 0

Putting z=0

⇒ x² - 49y² = 0

(c) Write an equation for the cross section at z = 7

Putting z = 7 ,

⇒  x² - 49y² = 49

(d) Write an equation for the cross section at y = -7

Putting y = -7 in equation this time,

⇒  x² = 49( -7)² + z²

⇒ x² - z² = 2401

(e) Write an equation for the cross section at y = 0

Putting y = 0,

⇒ x² = z²

⇒ x = z , -z

Therefore, the equation for the cross section exists x = z , -z.

The compete question is:

Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) x2 = 49y2 + z2 = (Write an equation for the cross section at z = -7 using x and y.) (Write an equation for the cross section at z = 0 using x and y.) (Write an equation for the cross section at z = 7 using x and y.) (Write an equation for the cross section at y = -7 using x and z.) IIIIIIII (Write an equation for the cross section at y = 0 using x and z.) (Write an equation for the cross section at y = 7 using x and z.) (Write an equation for the cross section at x = -7 using y and z.) (Write an equation for the cross section at x = 7 using y and z.)

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Answer:

2x-3=3x+3

Step-by-step explanation:

I think this is right if not sorry

The slope of the line perpendicular to the line whose equation is 15x - 12y = 216 is m{p} =  -0.8.

What is the general equation of a straight line?

straight line equation: The general equation of a straight line is -

y = mx + c.

where,

{m}: slope of the line.

{c} : y-intercept

To find the slope of a line perpendicular to the line whose equation is 15x - 12y = 216, we need to find the negative reciprocal of the original line's slope.

To find the original line's slope, we can use the equation of the line in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To convert the equation of the line from standard form to slope-intercept form, we can add 12y to both sides to get 12y = -15x + 216.

Then divide both sides by 12 to get y = -(15/12)x + 18.

So the slope of the original line is -(15/12).

The slope of a line perpendicular to the original line is the negative reciprocal of the original line's slope.

So the slope of the line perpendicular to 15x - 12y = 216 is -12/15 or -0.8

The slope of the line perpendicular to the given line is -

m =  -12/15 =  -0.8

Therefore, the slope of the line perpendicular to the line whose equation is 15x - 12y = 216 is m{p} =  -0.8.

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Penalty time = 2 months of interest = 2 x (7/100 x 18,000) = $2520.00

This serves as a deterrent to encourage individuals to leave their money in the CD until the maturity date.

Penalty = 2 months of interest = 2 x (Interest rate/100 x Value of CD)

= 2 x (7/100 x 18,000)

= $2520.00

A certificate of deposit (CD) is a financial product offered by banks and credit unions that allows an individual to deposit a certain amount of money for a fixed period of time, usually a few months to a few years. Most CDs will pay a higher rate of interest than a traditional savings account, but they come with certain restrictions. One of these restrictions is that if you withdraw funds from the CD before it reaches maturity, you will be charged a penalty time. This penalty usually involves two months of interest. Therefore, the amount of the penalty for early withdrawal on a CD with a value of $18,000 and paying 7 percent interest would be 2 x (7/100 x 18,000) = $2520.00. This serves as a deterrent to encourage individuals to leave their money in the CD until the maturity date.

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Answer:

C or 9,9

Step-by-step explanation:

M=(xM,yM)

M=(x1+x22,y1+y22)

M=(4+142,5+132)

M=(182,182)

M=(9,9)

a) V = x^3 b) Domain of V = [0, ∞) c) See attached graph d) Maximum = 8 in., V = 512 in^3

a) V = x^3

b) Domain of V = [0, ∞)

c) See attached graph

d) Maximum = x = 8 in., V = x^3 = 512 in^3

The volume V of a cardboard box with a square base is a function of the length x of each edge of the base. To calculate the volume of the box, we can use the formula V = x^3. This means that for any given base length, we can find the volume by cubing the length. The domain of V is the set of all possible values of x, which must be positive. This means that the domain of V is [0, ∞). We can also graph the function V = x^3. The graph looks like a parabola that opens up, with the vertex at the origin. We can then find the maximum of the function, which will be when x = 8 in. At this value, the volume of the box will be V = 512 in^3

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The greatest common factor (GCF) of two different whole numbers will be one of the numbers when they are relatively prime.

The GCF also known as highest common factor can be defined as the highest or greatest factor that is common or present in between given two or more numbers.

The greatest common factor (GCF) of two different whole numbers will be one of the numbers when the two numbers are relatively prime, meaning they have no common factors other than one.

In conclusion, when their GCF is one, the only possible common factor is one, which means the numbers are relatively prime.

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The volume of water which the tank holds when it is full is 136830 cm³.

The amount of space a three-dimensional solid shape takes up is referred to as its volume. Though difficult to visualise in any shape, it can be compared to others. In comparison to an eraser placed inside of it, a compass box has a larger volume. The area of any two-dimensional shape can be calculated by splitting it into equal squares. When calculating the volume of solid shapes, equal cubical units will also be divided.

If the both have diameter of 46 cm then the height of hemisphere is

46/2 = 23 cm = radius

Height of the cylinder = 90 - 23

                                     = 67

Volume of hemisphere + Volume of cylinder =  volume of water

volume of water = (2/3)πr³ + πr²h

volume of water = (2/3)π(23)³ + π(23)²×67

                            = 136830 cm³

                            = 136.83 l

Thus, the volume of water which the tank holds when it is full is 136830 cm³.

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Answer:

8,00000

Step-by-step explanation:

;_!($($+#(#(#)!#;;;;vhejdnsndbsndns sjnd snsjs s ska. snsjss

Therefore, the explicit formula for f(n) is: f(n) = 10 * [tex]3^{(n - 1)}[/tex]

f(1)=10

An explicit formula for f(n), the number of members the creators have a goal of getting n weeks after the website is made available, can be determined by using the information provided that the number of members is tripled every week.

So, we can start with the initial number of members (10) and multiply it by 3 for each week.

Therefore, the explicit formula for f(n) is:

f(n) = 10 * [tex]3^{(n - 1)}[/tex]

A recursive formula for f(n) can be determined by using the information that the number of members is tripled every week, and the initial number of members is 10.

So, we can start with the initial number of members (f(1)=10) and use the previous value of f(n-1) to calculate the current value of f(n).

Therefore, the recursive formula for f(n) is:

f(n) = 3f(n-1) + 10

for n>1

f(1)=10

In this way, we can calculate the number of members for any week using the explicit formula or the recursive formula.

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(a) The sample mean of the 49 fly balls is 250 feet.

(b) The standard error of the 49 fly balls is 50/sqrt(49) = 7.14 feet

(c) P(x bar < 240) = P(Z < (240-250)/7.14) = P(Z < -1.40) = 0.0822

(ii) The sketch of the distribution of the average of the 49 fly balls is a normal curve with a mean of 250 feet and a standard deviation of 7.14 feet. The probability of getting a sample mean of less than 240 feet is 0.0822.

(iii) This is usual, as the probability of getting a sample mean of less than 240 feet is 0.0822, which is within the range of expected probabilities for a normal distribution.

(d) P(X< 240) = P(Z < (240-250)/50) = P(Z < -2) = 0.0228

(e) The 80th percentile of the distribution of the average of the 49 fly balls is equal to the mean plus (1.28 * standard deviation), which is equal to 250 + (1.28 * 7.14) = 266.6 feet.

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Answer:

see below

Step-by-step explanation:

116+16=132 =120% * x

x=110

profit =132-110 =22

He made $12 by selling the bicycle helmet to Jin!

Let x be the original cost of the bicycle.

The cost of the helmet is $16, so the original cost of the bicycle and helmet is x + $16 algebraically.

Jin pays a total of $116 + $16 = $132 for the bicycle and helmet, which is 120% of what Stefan spent originally, so x + $16 = 1.2 * (x + $16)

Expanding the right-hand side gives x + $16 = 1.2x + 1.2 * $16.

Solving for x, we find that x = $104.

So, Stefan originally spent $104 for the bicycle and $16 for the helmet, for a total of $104 + $16 = $120.

Stefan sells the bicycle and helmet to Jin for $116 + $16 = $132, so he makes a profit of $132 - $120 = $12.

Answer:

91 - 60i

Step-by-step explanation:

(-10 + 3i)² = (-10)² + (2 * -10 * 3i) + (3i)²

= 100 - 60i + 9i²

= 100 - 60i - 9

= 91 - 60i

In the form of a + bi, the answer is 91 - 60i.

Answer:

Please see the answer in the picture:

The function y = 1/4(x - 4)² + 2, after a translation right 3 units and down 4 units, is given as follows:

y = 1/4(x - 7)² - 2.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function for this problem is given as follows:

y = 1/4(x - 4)² + 2

The changes with each translation are given as follows:

Hence the function is defined as follows:

y = 1/4(x - 3 - 4)² + 2 - 4

y = 1/4(x - 7)² - 2.

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Answer:

A gain of $5,000.

Step-by-step explanation:

The area of the trapezoid is 278.63 square units.

An open, flat object with four straight sides and one set of parallel sides is referred to as a trapezoid or trapezium. A trapezium's non-parallel sides are referred to as the legs, while its parallel sides are referred to as the bases.

Given:

KFLM is a trapezoid.

Side KF = 10 units

KL = 26 units

The angle measure of KFM = 48°.

So, in ΔFPK,

Sin48° = FP / KF

Sin48° = FP / 10

FP= Sin48° x 10

FP = 0.7431 x 10

FP  = 7.431

Now, the area of the trapezoid,

= 1/2 x sum of the parallel sides x distance between parallel sides,

= 1/2 (26 + 49) (7.431)

= 278.63 square units

Therefore, the area is 278.63 square units.

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