Complete the table.
I
Y=x+9
-2
-1
0
1
2

The constant rate of change of the altitude of the Hawk is -10 ft/s. The meaning of the -10 ft/s rate of change in altitude is the hawk is diving vertically down towards the prey with a speed of 10 feet per second

The average rate of change of a function is the rate at which the output values of the function changes with regards to the change in the argument of the function.

A function that has a constant rate of change is a linear function.

The rate of change of a linear function or equation that gives a straight-line graph is found from the slope, m, of the function.

The formula for the slope of a function, using the points (x₁, y₁), and (x₂, y₂), is presented as follows;

[tex]Slope, \, m = \dfrac{y_2-y_1}{x_2- x_1}[/tex]

The points on the graph are; (x₁, y₁) = (3, 60) and (x₂, y₂) = (6, 30)

Which gives;

[tex]Slope, \, m = \dfrac{30\, ft-60 \, ft}{6\, s- 3\, s} = -10 \, ft/s[/tex]

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The difference between the sum of the first 50 counting numbers and the sum of the first 100 counting numbers is 3775.

Here we have to find the difference between the first 50 counting numbers and first 100 counting numbers.

Formula to find the sum of the number n is:

[tex]S_{n}[/tex] = n/2( 2a + (n-1)d)

a = first number of the series

d = common difference

n = number of series

Sum of first 50 counting numbers:

[tex]S_{50}[/tex] = 50/2( 2× 1 + (50-1) 1)

    = 25 × 51

    = 1275

Sum of first 100 counting numbers:

[tex]S_{100}[/tex] = 100/2 ( 2×1 + (100- 1) 1)

      = 50 × 101

      = 5050

Now the difference between them:

[tex]S_{100}[/tex] - [tex]S_{50}[/tex] = 5050 - 1275

              = 3775

Therefore the difference is 3775.

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A circular arc has measure and is intercepted by a central angle of radians.

The radius (r) of circle is 1.91 m

Here given data :

• circular arc (s)  = 5 cm

• Angel  (A)  = 5π/6

We know that the following formula is,

        Length arc  = radius  × angel  

      =>   Radius (r) =  Length / angel

      =>   Radius (r) =  5 m / (5π /6)

        =>   Radius (r) = ( 5 × 6 / 5π ) m

        =>  Radius  (r) =   6/π m

        =>  Radius  (r) =   1.91 m

Therefore, radius of the circle is 1.91 m.

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There are total 18 markers in the box.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -  

P(A) = n(A)/n(S)

where -

n(A) = Number of outcomes favorable to event A.

n(S) = Total number of outcomes

Given is that there are 3 black markers in a bin. The probability that a marker selected at random is black is -

P(black marker) = 1/6

Assume that there are [x] markers in the box. Then, we can write -

P(black marker) = 3/x

1/6 = 3/x

x = 18

Therefore, there are total 18 markers in the box.

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The value of the expression are as follows

An algebraic expression consists of unknown variables, numbers and arithmetic operators.  It does not contain any equality or inequality symbols.

Let's solve the expression by substituting the actual values of the variables.

a.

5x when x = 6

5x = 5(6) = 30

b.

3y when y = -7

3y = 3(-7) = -21

c.

10z when z = 0.8

10z = 10(0.8) = 8

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Ax^2 +Bx + C

x^2 +11x +24

Using the number in place of C gives us what values could be inside the brackets.

For 24 the multiples are

1 and 24

2 and 12

3 and 8

4 and 6

We want the one that can add or subtract to give the number in place of B, which is 11.

The only multiples that add to 11 are 3 and 8

Therefore we know that 8 and 3 need to be in the brackets.

Giving us (x+8)(x+3)

Answer:

if i have 19

Step-by-step explanation:

The distance between the complex plane's origin (0, 0) and the point (a, b) is what is known as the absolute value of a complex number, a+bi (also known as the modulus).

Without taking into account direction, absolute value defines how far a number is from zero on the number line. A number's absolute value can never be negative. Look at some illustrations. 5 is the sum of its absolute values. There are 5 units between 5 and 0. A number's absolute value is determined by how far it is from zero on the number line. For instance, the absolute value of -7 would be 7, as it is 7 units away from zero. Additionally, since 0 is 7 units distant, the value of 7 would likewise be 7.

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Answer:

(0, -2)

Step-by-step explanation:

What is the y-intercept of the line 6x – 9y = 18?

(0, -2)

(0, 3)

(3, 0)

(-2, 0)

You need to solve for y:

6x – 9y = 18

6x – 9y  - 6x = 18 - 6x

– 9y = 18 - 6x

– 9y/-9 = 18/-9 - 6x/-9

y = - 2 + 2/3x

or:

y = 2/3x - 2

y-intercept is: (0 , -2)

Answer:

(0, - 2 )

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

6x - 9y = 18 ( subtract 6 from both sides )

- 9y = - 6x + 18 ( divide through by - 9 )

y = [tex]\frac{2}{3}[/tex] x - 2 ← in slope- intercept form

with y- intercept c = - 2 , that is (0, - 2 ) in coordinate form

Answer:  The correct answer is A) Mrs. Reynolds y = 1/2x + 1/2

Step-by-step explanation:

In the slope-intercept form of y=mx+b, m=the slope of the line

Therefore, y=1/2x + 1/2 has a slope of 1/2

As noted in the graph below, it is the only option listed that also intersects the point (5,3).

Answer:

Step-by-step explanation:

We will find the 41st term of the given arithmetic sequence is equal to 88.

The function in the values menu would you use to summarize the data is SUM

Because

I would use the SUM function to figure out how much box office revenue each genre earned. In the pivot table, the SUM function would add the total revenue separately for each genre.

This function, as clear from the name, is used to add all the values provided as arguments and to display the result in the cell-containing function. Argument Type All Numbers Return Type Number. Syntax = SUM(number 1 , number2, ).

The SUM function will sum hardcoded values and numbers that result from formulas. If you need to sum a range and ignore existing subtotals, see the SUBTOTAL function.

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By using the concept of slope, it is obtained that

Slope of the required trend line is [tex]\frac{22}{9}[/tex]

What is slope of a line?

Slope of the line is the tangent of the angle that the line makes with the positive direction of x axis

If the angle is [tex]\theta[/tex], the slope of the line is given by

[tex]m = tan\theta[/tex]

If the line passes through ([tex]x_1, y_1[/tex]) and ([tex]x_2, y_2[/tex]), then the slope of the line is given by

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

The line passes through (1, 3) and (10, 25)

[tex]x_1 = 1, y_1 = 3, x_2 = 10, y_2 = 25[/tex]

Slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}\\[/tex]

         =  [tex]\frac{25 - 3}{10 - 1}[/tex]

         = [tex]\frac{22}{9}[/tex]

Slope of the required trend line is [tex]\frac{22}{9}[/tex]

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Answer:

[tex]5x {}^{2} - 5y { = }0 [/tex]

The probability that she has to pick 5 batteries in order to find one that works is 5/12.

What is probability?

Probability shows the likelihood of an event happening.  it can be calculated by dividing the number of outcomes of an event by the total number of possible outcomes or sample space. Probability is equal to '1' when the event is certain to occur. i.e P =1. It is less than '1' when it is not likely to occur. i.e P< 1

Probability P=no. outcomes/total no. of the possible outcomes

From the question;

No of out comes=5

No. of total possible outcome=12

Therefore probability P= 5/12

                                   P=5/12

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The equation of the parabola is x = -1/16([tex]y^{2}[/tex]+6y-7).

According to the question,

We have the following information:

A parabola can be drawn given a focus of (−3,−3) and a directrix of x=5.

Now, let's take (x,y) to be the points of parabola.

So, we have the following expression:

Distance between (-3,-3) and (x,y) = Distance between (x,y) and x = 5

Distance between (x,y) and x = 5 will be Ix-5I

Now, we will use distance formula to solve this expression further.

[tex]\sqrt{(y+3)^{2}+ (x+3)^{2} }= (x-5)} }[/tex]

Squaring on both sides of the equation:

[tex]{(y+3)^{2}+ (x+3)^{2} }= (x-5)^2} }[/tex]

[tex]y^{2}[/tex]+9+6y+[tex]x^{2}[/tex]+9+6x = [tex]x^{2}[/tex]+25-10x

[tex]y^{2}[/tex]+6y+6x+18-25+10x = 0

[tex]y^{2}[/tex]+6y+16x-7 = 0

16x = [tex]-(y^{2}[/tex]+6y-7)

x = -1/16([tex]y^{2}[/tex]+6y-7)

Hence, the equation of the parabola is x = -1/16([tex]y^{2}[/tex]+6y-7).

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Rewriting the expression with bracket and parentheses in numerical expression is: [(3^2 + 7) * 4] + 5.

In numerical expression, the brackets and parentheses are mathematical symbols that are used in pairing the group things together or specify the order of operations. These are used in creating or solving equations, helping in grouping numbers and defining the order of operations.  Parentheses are curved ( ), brackets are square [ ], and braces are curly { }. In indicating the order of operations, the innermost parentheses are calculated first, followed by the brackets (which form the next layer), followed by braces (which form a third layer outwards).

The given expression written with parentheses and brackets to be equivalent to 69 is:

[(3^2 + 7) * 4] + 5

[(9 + 7) * 4] + 5

[16 * 4] + 5

64 + 5

69

Note: The question is incomplete: The complete question is A printing error in a math book removed the brackets and parentheses from a numerical expression. Rewrite the expression 32 + 7 x 4 + 5 with parentheses so that it is equivalent to 69.

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Answer:

the answer is 3,6 6,0 2,3 4,2 that is the answer :)

Step-by-step explanation:

becuase that is the answer

A department needs to choose six members consists of 3 women and 3 men from 10 men and 15 women. The number of ways it can be selected is 54,600.

If r persons need to be selected from total n members and the order does not matter, the number of ways it can be selected is calculated using the combination formula:

  ⁿCr = n! / [(n-r)! r!]

Data from the problem:

Total man = 10

Man to be chosen = 3

Total woman = 15

Woman to be chosen = 3

Hence,

The number of ways men can be selected =   ¹⁰C₃ = 10! /(3! 7!)

                                                                       = 120

The number of ways women can be selected =   ¹⁵C₃ = 15! /(3! 12!)

                                                                       = 455

The number of ways men and women selected:

= ¹⁰C₃ x  ¹⁵C₃

= 120 x 455 = 54,600 ways

Hence, the  number of ways the members can be selected =  54,600 ways.

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Step-by-step explanation:

perimeter:

74 + 74 + 48 = 196 yd

area:

48/2=24

√74^2+√24^2 = 77.79 (2dp)

77.79 x 48 = 3734.14

3734.14/2=1867.07yd^2

The cost of each bottle of orange juice is 0.78 dollars.

Xavier buys 18 bottles of orange juice at the corner store for a total cost of $14.04. Each bottle costs the same amount.

Therefore, the cost of each bottle of orange juice can be found as follows:

cost of each bottle of orange juice = total cost of the whole orange juice / number of orange juice bought

cost of each bottle of orange juice = 14.04 / 18

Therefore,

cost of each bottle of orange juice = $ 0.78

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Answer:

$1,480.24

Step-by-step explanation:

An investment of $1,000 made today will be worth $1,480.24 in five years at interest rate of 8% compounded semi-annually.

60 percent of the players scored more than 10 points if three of the five basketball players scored more than 10 points.

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

Three of the five basketball players scored more than 10 points.

Total number of basketball players = 5

The number of players who scored more than 10 points = 3

In fraction:

= 3/5

= 0.6

To convert the above fraction into the percentage multiply it by 100:

= 0.6x100

The percent of the players scored more than 10 points = 60%

Thus, 60 percent of the players scored more than 10 points if three of the five basketball players scored more than 10 points.

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The 90% confidence interval is  (5.09% , 5.41%)  and the 99% confidence interval is (52.24% , 52.76%)  .

In the question ,

it is given that ,

number of sample of loans taken = 28

the average of the sample is = 5.25%

the standard deviation of the normally distributed population is 0.5 %

The formula to find the Confidence Interval (CI) for the population mean is written as

[tex]\bar{x}[/tex] ±[tex]t_{n-1} , _{\alpha /2} \frac{\sigma}{\sqrt{n} }[/tex]

it is given that the 30 year fixed mortgage rates are normally distributed .

the sample size (n) = 28

Since sample size is less than 30 , the t - test is applied .

Sample mean ( [tex]\bar{x}[/tex] ) = 0.0525

the standard deviation (σ) = 0.005

the significance level : α = 1 - 0.90 = 0.1

critical value = [tex]t_{n-1} , _{\alpha}[/tex] = [tex]t_{27} , _{0.05}[/tex] = 1.703

So , 90% confidence interval will be :

= 0.525 ± (1.703)×(0.005/√28)

≈ 0.0525 ± 0.0016

= (0.0525 - 0.0016 , 0.0525 + 0.0016)

= (0.0509 , 0.0541)

= (5.09% , 5.41%)

For the 99% confidence interval ,

the significance level : α = 1 - 0.99 = 0.01

critical value = [tex]t_{n-1} , _{\alpha}[/tex] = [tex]t_{27} , _{0.005}[/tex] = 0.2771

So , 99% confidence interval will be :

= 0.525 ± (0.2771)×(0.005/√28)

≈ 0.0525 ± 0.00026

= (0.0525 - 0.00026 , 0.0525 + 0.00026)

= (0.05224 , 0.05276)

≈ (52.24% , 52.76%)

Therefore , The 90% confidence interval is  (5.09% , 5.41%)  and the 99% confidence interval is (52.24% , 52.76%)  .

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Tom saved 14.55% money in this sale.

Given that the sale price of 3 T shirts is $14.50.

And Tom saved in this sale $2.47.

So original selling price of that 3 T shirts is = 14.50+2.47 = 16.97

So the percentage of savings = (2.47/16.97)*100% = 14.55% (approximately)

Hence he saved approximately 14.55% in this sale.

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For the value of L = 144.48, the probability of having L greater than the mean glucose level of Shelia is 0.02.

Here it is given that Sheila's glucose level follows a normal distribution with a mean of 128 mg/dl and a standard deviation of 8 mg/dl

L is the patient's blood test level.

It is given that the probability that the mean glucose level i.e 128 mg/dl is above L is 0.02.

We need to find L

We know

P(128>L) = 0.02

or, 1 - P(128 ≤ L) = 0.02

or, P(128 ≤ L) = 0.98

We know that for any Normal distribution we find the probability by converting it to standard form and then checking the p-value.

P(X < x) = Φ[(x - μ)/σ]

where,

μ = mean

σ = standard deviation

Therefore,

Φ[(L - 128)/8] = 0.98

we see that for a Z score of 2.06,

Therefore we get

(L - 128)/8 = 2.06

or, L - 128 = 16.48

or, L = 128 + 16.48

= 144.48

Therefore, the value of L would be 144.48

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Complete Question

Shelia's doctor is concerned that she may suffer from gestational diabetes (high blood glucose levels during pregnancy). There is variation both in the actual glucose level and in the blood test that measures the level. A patient is classified as having gestational diabetes if the glucose level is above 140 milligrams per deciliter one hour after a sugary drink is ingested. Shelia's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with a mean of 128 mg/dl and a standard deviation of 8 mg/dl. Let L denote a patient's glucose level.

If measurements are made on four different days, find level L such that there is a probability of only 0.02 that the mean glucose level of four test results falls above L for Shelia's glucose level distribution. What is the value of L?

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Answer:

125

Step-by-step explanation:

150/30=5

25x5=25

The ounces of milk chocolate that the shop sells is 1/27 ounces.

A fraction is a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the chocolate shop sold 1/6 ounces of white chocolate and it sold 2/9 times as much milk chocolate as white chocolate.

The milk chocolate sold will be:

= 1/6 × 2/9

= 2/54.

= 1/27

The ounces is 1/27 ounces.

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Equation of the line 'm' is 5x - 6y - 30 = 0.

According to graph,

A(6,0) and B(0,-5) lies on the line m.

Slope-intercept form -> y = mx + c

Putting B(0,-5) in slope-intercept form,

-5 = m(0) + c

 c = -5

Putting A(6,0) in slope-intercept form,

  0 = m(6) - 5

6m = 5

 m = 5/6

Putting the values of m and c in slope-intercept form,

 y = (5/6)x - 5

6y = 5x - 30

5x - 6y - 30 = 0

Hence, equation of the line is 5x - 6y - 30 = 0.

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x⁴⁸ = x/2

Multiply to remove the fraction, then set equal to

0

and solve.

Exact Form:

x

=

0

,

1

47

√

2

Decimal Form:

0,0.98536040