Write an equation of a circle with the given center and radius. Check your answers.
center (-4,-6) , radius 7

Answer:

7. ) 3 3/4   9.) 3 1/8  11.) 7/16  13.) 5 13/15  15.) 7 1/2

Step-by-step explanation:

Number 7, first make 4 1/6 into an improper fraction.

6x4+1= 25/6

25/6x9/10

225/60

Simplified- 3 3/4

Number 9, make 4 3/8 into an improper fraction.

4x8+3= 35/8

35/8x5/7

175/56

Simplified- 3 1/8

Number 11, make 2 5/8 into an improper fraction.

2x8+5= 21/8

21/8x1/6

21/48

Simplified- 7/16

Number 13, make 1 3/5 and 3 2/3 into an improper fraction.

1x5+3= 8/5,   3x3+2=11/3

8/5x11/3

88/15

Simplified- 5 13/15

Number 15, make 3 1/3 and 2 1/4 into an improper fraction.

3x3+1= 10/3,   2x4+1=9/4

10/3x9/4

90/12

Simplified- 7 1/2

Hope that helped! :D

In Tamika's equation  y = 45x + 67, 67 represents temperature in degree Fahrenheit.

An equation is a mathematical statement that compares two mathematical expressions by equating them  and on both sides the quantities are of same type . Like we cannot compare a length quantity with a temperature quantity.

Given that Tamika wants to predict the final temperature after some minutes of preheating her oven. She wrote the equation y = 45x + 67, where y represents the final temperature in degrees Fahrenheit.

y = 45x + 67

In this equation as y is temperature so the expression  45x + 67 is of  temperature in degrees Fahrenheit too and each term of this expression is also temperature in degrees Fahrenheit.

Therefore , 67 represents temperature in degree Fahrenheit.

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The least preferable and reliable method of selecting people to participate in a research study is convenience sampling.

Convenience sampling is a type of sampling in which you include people who are easy to reach. Convenience sampling is included in non-probability sampling because it doesn't include a random selection of the participants. Convenience sampling can be used when you need to conduct a study quickly or when you are on a shoestring budget as it is inexpensive compared to other methods of sampling.

It is the least preferable method because of the inability to generalize the result of the survey to the population as a whole. In addition to this, there is a possibility of under or over-representation of the population as a whole. The biggest problem with convenience sampling is dependence as the sample items are connected to each another in some way. This dependency interferes with statistical analysis.

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False , A permutation is an arrangement of objects in which order is NOT important.

In statistics, what does a probability mean?

This sentence is false.

A permutation is an arrangement of objects in which order is NOT important.

True sentence is -

State whether following sentence is true or false. If false, replace the underlined term to make a true sentence.

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Answer:

Minimum 1/4 Hour Maximum 1/2 Hour

Speed is the ratio of distance and time.

The maximum number of hours the boat will cruise is 1/2 hours.

The minimum number of hours the boat will cruise is 1/4 hour.

Speed is the ratio of distance and time.

It tells us how fast a body is moving.

We have,

Boat speed = 24 miles per hour.

Speed = distance / time

Distance = 9 miles

Time = distance / speed

Minimum number of hours:

Distance = 9 - 3 = 6 miles

Time = Distance / Speed = 6 / 24 = 1/4 hours

Maximum number of hours:

Distance = 9 + 3

Time = Distance / Speed = 12 / 24 = 1 / 2 hours

Thus,

The maximum number of hours the boat will cruise is 1/2 hours.

The minimum number of hours the boat will cruise is 1/4 hour.

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The probability that each of the balls will be; a) P( of the same color) = 0.08875. b) P ( of different color) = 0.247678

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

The Number of red balls = 5

The number of blue balls = 6

The number of green balls = 8

The Total number of balls = 5 + 6 + 8 = 19

Then with three balls selected at random, by using combination method ;

nCr = n!/(n-r)!r!

a) P( of the same color) = 5C3 + 6C3 + 8C3 / 19C3

=  86/969 = 0.08875

b) P ( of different color) = 5C1 X 6C1 X 8C1 /19C3

= 240/969 = 0.247678

Hence, The probability that each of the balls will be; a) P( of the same color) = 0.08875. b) P ( of different color) = 0.247678

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Explanation:

The number 1 is spelled as "one", which clearly has an "e" in it. This contradicts the original statement that we don't need this letter.

The other numbers of 6 (six), 2 (two), and 4 (four) don't involve "e"s at all. So they can be ruled out.

Answer:119 times

Step-by-step explanation:

833/7=119

After simplification, the value of the given expression (12x)⁰(6x⁻⁴) is 6/x⁴.

So, (12x)⁰(6x⁻⁴):

Therefore, after simplification, the value of the given expression is 6/x⁴.

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Answer: 3720087

Step-by-step explanation:

n=term number

an=term value

terms: 7, 21, 63...

term number: 1, 2, 3, ...

7 is 1st term. 21 is 2nd term. 63 is 3rd term.

21/7=3

63/21=3

Common change in each term is multiplication by 3

Hence, the formula can be expressed in exponents.

an=3^(n-1) * 7 where n is the term number, an is the term value, and 7 is the 1st term in the sequence.

an=3^(13-1) * 7

an=3^12 * 7

an=531441 * 7

an=3720087

The length of the garden will be - L = 3x - 8.

We have a rectangular garden.

We have to determine its length.

The area of rectangle is -

A = L x B

According to the question -

Area = [tex]24x^{2} -64x[/tex]

Width = [tex]8x[/tex]

Therefore -

Area = Length x Width

Length = Area / width

Length = [tex]$\frac{24x^{2} -64x}{8x} = 3x -8[/tex]

Hence, the length of the garden will be - L = 3x - 8.

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Answer:

Step-by-step explanation:

somewhat

Answer:

real x values is x < -1

Step-by-step explanation:

The fare for 47 miles is $32.9

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Total miles= 36  miles

Total fare = 25.20

fare for 1 miles

= 25.20/36

=0.7

Now, for 47 miles the fare will be

=0.7*47

=$32.9

Hence, the fare for 47 miles is $32.9

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Answer:

S' (- 3, 7 )

Step-by-step explanation:

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

S (3, 7 ) → (- 3, 7 )

Answer:

Step-by-step explanation:

The values of functions are as follows:

g(-6) = -6

g(0) = 5

g(7) = 8

h(-6) = 10

h(0) = -1

h(7) = -4

Given, that function g(x) = f(x)/3 and function h(x) = -g(x) + 4

Now to calculate the function values on different values of x.

g(x) = f(x)/3

h(x) = -g(x) + 4

1 )

When x = -6

f(-6) = -18

g(-6) = f(-6)/3

g(-6) = -18/3

g(-6) = -6

h(-6) = -g(-6) + 4

h(-6) = 6 + 4

h(-6) = 10

2)

When x = 0

f(0) = 15

g(0) = f(0)/3

g(0) = 15/3

g(0) = 5

h(0) = -g(0) + 4

h(0) = -5 + 4

h(0) = -1

3)

When x = 7

f(7) = 24

g(7) = f(7)/3

g(7) = 24/3

g(7) = 8

h(7) = -g(7) + 4

h(7) = -8 + 4

h(7) = -4

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Answer:

If the student is female then the probability that the student will participate is about 67%

If the student is male the probability that they participate is about 33%

Step-by-step explanation:

It is given that 48% of the students in the school are male. That means that the remaining students in this school are (for the sack of this problem) female out 100% of students. You would subtract 48% from 100% which is 52% which is the percentage of students in the school who are female.

From this point you need to find the percentage of students who would participated in the survey. To do that you would divide the number of the type of student who did the survey by the type of student in the school. For example for the male you would divide 16% from 48% or 16 ÷ 48 which would equal to the proposed of males who would participate which is about 33% of males. You would do the same math for finding the probability of females so it would be 35 ÷ 52 which is about 67% of females.

Even though the random student is more likely to be female the chances of the gender of the student is almost 50%/50% because if you round it to the nearest tenth it would be 50.

The expression for 36+48 is 12(3 + 4).

A number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.

Given:

36+48

Now, factorise 36 and 48

36=2*2*3*3

48=2*2*2*2*3

So, the common factor is 12.

Hence, the for the factor is 12(3 + 4)

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Answer:

relation

Step-by-step explanation:

To be a function each element from set x has only one unique element in y.

In our case x = 0 has two outcomes y = 1 and y = 3, so is a relation.

f(x) = y

f(-2) = 5

f(0) = 1  and f(0) = 3

f(5) = 8

f(7) = 5

Some memory aids:

Think about if we count how many likes we got on a social media post at the end of the day, then we can not have different numbers for same post yet we can have the same number of likes on different posts to be a function.

f(post 0) = 1  like  and f(post 0) = 3 likes ❌ not a function because same post has different numbers of likes at the end of the day -not possible

f(post -2) = 5 likes and f(post 7) = 5 likes ✅ could be a function because different posts can have the same number of likes at the end of the day

7 - 0 = 7/5(0 - (-5)) is the equation in slope intercept form for the line passes through points (-5,0) and (0,7).

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.

The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.  

Therefore,

m =  y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.

Be aware that tan ∅ = y/x

We also refer to this tan as the line's slope.

We have been asked  to write an equation of the line in point-slope form

of a  line which passes through (-5,0) and (0,7)

We know that  point-slope form = y₂ - y₁ = m(x₂ - x₁)

But first we will find slope(m)

We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

For the pairs of points (-5,0) and (0,7)

⇒ m = [tex]\frac{7- 0}{0 - (-5)}[/tex]

⇒ m = [tex]\frac{7}{5}[/tex]

⇒ m = 7/5

After we substitute the given information we get

7 - 0 = 7/5(0 - (-5))

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Answer:

1/4 or 25% or 0.25

Step-by-step explanation:

Since LM ⊥ JK, LM is an altitude by the definition of altitude. We don't know if it is a perpendicular bisector because it is not evident that M is the midpoint of JK.

An altitude of a triangle is a line segment through a vertex that is perpendicular to a line containing the base in geometry. The extended base of the altitude is the line that contains the opposite side. The intersection of the extended base and the altitude is known as the altitude's foot.

A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.

Since LM ⊥ JK, LM is an altitude by the definition of altitude. We don't know if it is a perpendicular bisector because it is not evident that M is the midpoint of JK.

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Answer:

a 50% chance of getting tails

but about the spinner It depends on what kind of spinner it is and how many sides/numbers/etc

does it have

The new price of the hockey stick based on the information is $109.25.

From the information, the hockey stick that Erik wants to purchase is $95.00. He knows the price will increase by 15% by the end of next month.

Therefore, the new price will be:

= $95 + (15% × $95)

= $95 + (0.15 × $95)

= $95 + $14.25

= $109.25

Therefore, the new price of the hockey stick is $109.25.

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The hockey stick that Erik wants to purchase is $95.00. He knows the price will increase by 15% by the end of next month. Erik needs to calculate the new price of the hockey stick. What will the new price be?

The statement that any two right triangles with the same hypotenuse have the same area is false.

Hypotenuse is defined as the longest side of a right-angled triangle.

let us take two triangles ΔXYZ & ΔDEF with same hypotenuse

for ΔXYZ let, XY(height)=7cm, YZ(base)=24cm, XZ(hypotenuse)=25cm.

for ΔDEF let, DE(height)=15cm, DF(base)=20cm, DF(hypotenuse)=25cm.

Area of a Right Angled Triangle is given by [tex]=\frac{1}{2} *base*height[/tex]

For ΔXYZ

Area=(1/2)*base*height

= (1/2)*24*7

=12*7

=84 ......(1)

For  ΔDEF

Area=(1/2)*base*height

= (1/2)*20*15

=10*15

=150 .......(2)

From equation (1) & (2) we can conclude that two triangles having same hypotenuse may not have same area.

Therefore , the statement that any two right triangles with the same hypotenuse have the same area is false.

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The length, in inches, of the perimeter of its base is 5in

A cube is a three dimensional object with 6 faces and 12 edges.

The formula for calculating the volume of a cube is expressed according to the equation;

V = l³

l = ∛V

where

l is the side length of the cube

Given the following parameters

V = 125in³

Substitute

125 = l³

l = ∛125

l = 5in

Hence the length, in inches, of the perimeter of its base is 5in

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Answer:

2.848 pound

Step-by-step explanation:

On 5 pizzas = 14.24 pound cheese

On 1 pizza = 14.24/5 pound

=2.848 pound

The solution fo the equation by completing the square is x = 12.544 or -4.544

Completing the square method is a method of solving quadratic equations in which the equation is converted into a perfect square binomial.

Given (x - 12)(x + 4) = 9

Expanding the brackets, we have

x² - 12x + 4x - 48 = 9

x² - 8x - 48 = 9

x² - 8x - 48 - 9 = 0

x² - 8x - 57 = 0

To complete the square, we add half the square of the coefficient of x to both sides. so,

x² - 8x - 57 = 0

x² - 8x - 57 + (-8/2)² = 0 + (-8/2)²

x² - 8x - 57 + (-4)² = 0 + (-4)²

x² - 8x + (-4)² - 57  = 0 + (-4)²

(x - 4)² - 57 = 16

(x - 4)² = 16 + 57

(x - 4)² = 73

Taking square roots, we have

x - 4 = ±√73

x - 4 = ±8.544

x = 4 ± 8.544

x = 4 + 8.544 or x = 4 - 8.544

x = 12.544 or -4.544

So, the solution fo the quadratic equation by completing the square is x = 12.544 or -4.544

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Answer:

Step-by-step explanation:

x=+/-square root 73