x = -4z - 19
y= 5x + z - 4
-5y - z = 25

The table shows the total cost to be a member of the gym for different numbers of months.



Number of months. total costs

3. $53.97

6. $77.94

12. $125.88



Create a function that gives the total cost C, in dollars to be a member of the gym given the number of months M of membership.

_____________________________________

Total cost = M* (factor per month ) + b

_____________________________________

The expression for a linear equation is

*The slope-intercept form.

y = mx + b

m= (y2-y1)/ (x2-x1) (I)

y-intercept is (0, b)

*and the point-slope form

y- y1 = m(x-x1) (II)

________________________

Point 1 (3, 53.97)

Point 2 (12, 125.88)

Replacing in (II)

The slope m = (y2- y1)/ (x2-x1) = (125.88- 53.97)/(12-3) = 7.99

y - 53.97 = 7.99* (x- 3)

y = 7.99 x - 7.99* 3 + 53.97

y = 7.99x + 30

____________________

Verifying

y = 7.99x + 30

x= 3

y = 7.99*3 + 30

y= 53.97

x= 6

y = 7.99*6 + 30

y= 77.94

x= 12

y = 7.99*12 + 30

y= 125.88

_________________________

Answer

The linear function is y = 7.99x + 30

An answer choice shows these weights in order from least to greatest is:

A numerical data can be defined as a data set that is primarily expressed in numbers only. This ultimately implies that, a numerical data refers to a data set consisting of numbers rather than words.

In order to arrange the given numerical data (weights) in order from least to greatest, we would convert the fractions into a decimal number as follows:

Now, we can arrange the numerical data in order from least to greatest based on the weight of each item:

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Considering the given triangle ABC that has vertices A(-4, 0), B(-4, 5) and C(1, 5). The option that has same slope with similar interval is B. D(-3, 0), E(-3, 1) F(-2, 1)

Slope refers to the gradient and is the ratio of the difference in the ordinate to the difference in the abscissa of in a given coordinate plane.

The given information from the question include

A(-4, 0), B(-4, 5) and C(1, 5)

The slope of the given triangle is calculated as follows

slope = ( 0 - 5 ) / ( -4 - 1 )

slope = -5 / -5

slope = 1

The domain of the line is -4 ≤ x ≤ 1

The range of the line is 0 ≤ y ≤ 5

options C and D values do not satisfy the domain and range conditions

Options B and A satisfies the the domain and range conditions however the slope of option B is what is equal to the slope of the sloping part of the given triangle and hence the correct option.

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The null and alternative hypothesis is H₀ : p = 0.30 and Hₐ : p ≠ 0.30 respectively.

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis.

Two alternatives being the same is the null hypothesis. The underlying assumption is that the observed difference is just the result of chance.

One of the ideas put out in the hypothesis test is the alternate hypothesis.

Mild depression affects about 30% of adults in the 50 to 60 age range.

500 people between the ages of 50 and 60 are chosen at random by the researcher, and they are instructed to take a vitamin D pill for six months.

The psychologist classifies 158 people as depressed.

The null hypothesis will be:

H₀ : p = 0.30 and;

The alternative hypothesis is,

Hₐ : p ≠ 0.30

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The angle subtended by an arc is twice the angle it subtends.

The angle is 90 degrees.

What is diameter of circle?

diameter is circle is twice the radius of circle.

The theorem to solve the given statement is :

The angle subtended by an arc is twice the angle it subtends.

let suppose, O be the center of circle,

The diameter AB forms on the circle and point P on the periphery of circle ,

so we have:

To prove : ∠APB=90°

We know that angle subtended by an arc at center is double the angle subtended at any point or circumference.

that is:

Angle subtended by arc AB at O = Double the angle subtended at P

⇒∠AOB=2∠APB

∵AOB is a straight line.

∠AOB=180°

2∠APB=180°

∠APB=90°

Angle formed by arc AB or semi circle is 90°

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The graph that matches the data on the table, representing the altitude and time of a hawk is the straight line graph in the second option.

A straight line graph is the graph of a linear function or relationship

From the he values in the given, we have;

The difference between the consecutive altitude values (the first difference) = 70 - 80 = 60 - 70 = 50 - 60 = -10 is constant

The difference between consecutive time values = 1

Therefore;

The relationship is a linear relationship and the graph is a straight line.

Slope of the graph = -10/1 = -10

The equation in point and slope form is therefore;

(y - 80) = (-10) × (x - 1) = -10•x + 10

(y - 80) = -10•x + 10

y = 80 + 10 - 10•x = 90 - 10•x

y = 90 - 10•x

The y–intercept = 90

The slope = -10

The correct option is therefore the second graph that has the altitude (ft) on the the vertical axis and the time (s) on the horizontal axis, with a straight line decreasing from left to right starting at the point (0, 90) on the left

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Answer:

(3×6)÷5

Step-by-step explanation:

We are given the following expression:

(3/5)*6

The 6 can also be written as a fraction(6/1).

So we have a multiplication of fractions, is which we multiply the numerators and denominators.

So

(3*6)/5

The fraction sign means division

So the answer is:

(3×6)÷5

6561m⁴ is the value of the expression (9m)⁴ without applying the exponent property.

What is an exponent?

The type of mathematical shorthand known as exponential notation enables us to write complex expressions more concisely. The base, which can be either a number or letter, is an exponent. It implies that the base is to be raised to a specific level of power. While n is the power, X is the base.

The expression is (9m)⁴.

The value of the expression (9m)⁴ without applying the property of the exponent will be

→ 9m × 9m × 9m × 9m

(we've simply expanded  (9m)⁴ )

which on further simplifying gives,

→ 6561m⁴

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The total surface area of the cylinder is equal to 117.8 in^2

The total surface area of a cylinder can be calculated using the formula

[tex]TSA = 2\pi rh + 2\pi r^2[/tex]

Let's substitute the values and proceed to solve.

[tex]TSA = 2\pi rh + 2\pi r^2\\TSA = 2\pi * 2.5 * 5 + 2\pi * 2.5^2\\TSA = 117.8in^2[/tex]

The total surface area of the cylinder is 117.8 squared inch.

The area of each circle is

[tex]A = \pi r^2 \\A = 19.6in^2[/tex]

And there are two identical circle in the diagram and this will have a total area of

[tex]A = 2 * 19.6\\A = 39.2in^2[/tex]

The area of the sum of the two circles is 39.2in^2 and the total surface area of the cylinder is 117.8in^2

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17.54% is the probability that 5 messages are received in 1 hour.

The chance that X reflects the number of successes of a random variable in a Poisson distribution is provided by the following formula:

P(X = x) = ([tex]e^{-u}[/tex] × [tex]u^{x}[/tex]) ÷ x!

In where x is the number of successes, e is the Euler number, and u is the mean in the specified time frame.

In this case, the average message rate is 5 messages per hour.

The probability of receiving 5 texts in one hour.

Determine the value of P for x = 5 and u = 6.

P(X = x) = ([tex]e^{-5}[/tex] × [tex](5)^{5}[/tex]) ÷ 5!

P(X = x) = 21.0560 ÷ 5!

P(X = x) = 0.1754

There is a 17.54% chance that 5 messages will be received in 1 hour.

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Answer:

1 , 7 , 7

Step-by-step explanation:

to evaluate f(- 2) means what is the value of y when x = - 2

locate x = - 2 on the x- axis , go vertically up to meet the graph at (- 2, 1)

f(- 2) = 1

similarly

f(0)

locate x = 0 , at the origin, go vertically up to meet the graph at (0, 7 )

f(0) = 7

f(3)

locate x = 3 on the x- axis , go vertically up to meet the graph at (3, 7 )

f(3) = 7

The volume of a pyramid is v = 1/3base area × height

height = 3volume/ base area

height = 3×168cm^3/ 36cm^2

height = 14cm

A pyramid is a three-dimensional shape. It has a flat polygon base. All the other faces are triangles which are called lateral faces. The number of lateral faces equals the number of sides on its base.

The volume of a pyramid is given by

v= 1/3base area × height

= 3×168 = 36h

therefore the height =3x168/36

= 14cm

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The domain of the given question is; 20 to 25.  

If she is paid $9 per hour, the range is; $180 to $225.

The independent quantity is defined as the quantity that causes a change in the dependent quantity.  

Now, In this question, the defined quantities are hours worked and weekly pay.  Applying the concept of independent and dependent quality, the number of hours she works causes her weekly pay to change. This means that hours worked is the independent quantity and weekly pay is the dependent quantity.

We are told that she plans to work between 20 and 25 hours. This means that;

The domain is 20 to 25.  

Now, as she is paid $9 per hour, this makes the range;

9(20) = $180 to 9(25) = $225.

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Answer:

[tex]2\sqrt{2}[/tex]

Step-by-step explanation:

x^2+x^2=16

x^2=8

x= 2sqrt2

:]

I l over here and I have no idea

The probability that the events (a) they both picked Limca = 0.04, (b) Ademola only picked Pepsi = 0.32, (c) They both picked the same brand = 0.33 (d) They picked different brand=0.67.

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

Total possible outcome of the event of picking drinks contained in the crate = 19

Hence, we can compute the following as follows;

(a) The probability they both picked Limca = (4/19)×(3/18)

Limca = 12/342

Limca = 0.04

(b) The probability Ademola only picked pepsi = 6/19

pepsi = 0.32

(c) The probability they both picked the same brand = (9/19)×(8/18)+(6/19)×(5/18)+(4/19)×(3/18)

=(72+29+12)/342

= 114/342

= 0.33

(d) The probability they picked different brand = (9/19)×(6/18)+(9/19)×(4/18)+(6/19)×(9/18)+(6/19)×(4/18)+(4/19)×(9/18)+(4/19)×(6/18)

The probability they picked different brand = (54+36+54+24+36+24)/342

The probability they picked different brand = 228/332

The probability they picked different brand = 0.67

Therefore, the probability for events (a) is 0.04, (b) is 0.32, (c) is 0.33 and (d) is 0.67.

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Samuel's average speed during his morning training is 0.41 miles/minute.

Here we have to find the average speed of Samuel. We can solve this problem by following a few steps.

According to the problem, Samuel was preparing for the triathlon. He did 3 activities every morning; ran for 30 minutes, covered 4.5 miles; swam for 20 minutes, covered 2.3 miles biked for 45 minutes, and covered 9 miles.

We have to recall the formula of average speed as,

average speed = total covered distance/ total time

The total distance which has been covered is,  

The total covered distance is, ( 4.5 + 2.3 + 9 ) = 36.5 miles.

The total time which has been spent is,

The total spent time is, (30+ 20+ 40) = 90 minutes.

Now, we can easily calculate the average speed. Which is (36.5/90) = .41 miles/minute.

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The value of x is 43.

As per the property of exterior angles, the exterior angle is equal to sum of opposite interior angles. Also, the rightmost interior angle of triangle will be 35°. This will be according to the property that opposite angles are equal. Now, forming the equation for sum of exterior angles.

109 = x + 31 + 35

Performing addition on Right Hand Side of the equation

109 = x + 66

Rearranging the equation

x = 109 - 66

Performing subtraction on Right Hand Side of the equation

x = 43

Therefore, as per the angles of triangle, the value of x is 43.

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Using the graph obtained value of k is 1/3. Option C is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that

f(x) and g(x) = f(k-x),

The standard equation of a line is,

y = mx + b

The slope of the line for the coordinate points are (1, 2) and (1.5, 5)

m = 5-2/1.5-1

m = 3/0.5

m = 6

The y-intercept of the line is,

2 = 6(1) + b

2 - 6 = b

b = -4

As a result the obtained  equation is g(x) = 6x - 4

For the other coordinate point (3, 2) and (2, 0), the slope is

m = 0-2/2-3

m = -2/-1

m = 2

The y-intercept of the line is,

2 = 2(3) + b

2 - 6 = b

b = -4

As a result the obtained equation will be f(x) = 2x - 4.

Substitute xk at the place of x in the function as

f(xk) = 2(xk)- 4

If g(x) to f(k⋅x)

6x + 4 = 2(xk)- 4

6x = 2xk

6 = 2k

k = 1/3

Thus, using the graph obtained value of k is 1/3. Option C is correct.

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The trapezoid's area can be understood as triangle a + triangle b. So, we write these triangles as an expression, and, since we cannot solve with no values, we simplify to prove the area of the trapezoid.

A triangle's area is 1/2bh. In their case, b is represented as b or a depending on the triangle.

t = 1/2ah + 1/2bh

Now, since both expressions use the terms 1/2 and h, distributed onto a second variable, it can be rewritten as a single expression where both are distributed onto both variables at the same time. This is because both terms being multiplied by something separately is the same as combining both terms and multiplying them both at the same time.

t = 1/2(a)h + 1/2(b)h
t = 1/2(a + b)h

Juniper spends $1300 out of the monthly income of $3250 on rent

Total income of Juniper = 3250 each month

Income is the money that an individual or organization receives in return for their services or goods. Depending on the context—such as taxation, financial accounting, or economic analysis—income may have a variety of definitions.

Percentage of expenditure on rent = 40%

Percentage of expenditure on food = 15%

Percentage of expenditure on utilities = 18%

The percentage for savings = 15%

Percentage of expenditure for personal items = 8%

Money Juniper spends on rent each month out of total income:

= Income per month*40%

3250*40%

= $1300

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Answer: k = 13

Step-by-step explanation:

The price of one candy box was $2.50 if the popcorn were of $3.20 and the total amount was $18.20.

The price of one candy box can be determined using an algebraic expression. An algebraic expression can be defined as one that consists of both numbers and letters.

As he ordered 6 boxes of candy and a bucket of popcorn and the popcorn was of $3.20 and the total was $18.20, an algebraic expression can be given as;

6(x) + 3.20 = 18.20

Here x is the price of one candy box

Solving for x;

6x = 18.20 - 3.20

6x = 15

x = 15 / 6

x = 2.50

Hence the price of one candy box is calculated to be $2.50.

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Answer:

There are two pairs:

1 and 3

2 and 4

Step-by-step explanation:

Verticle angles are angles opposite to each other when two lines intersect.

Answer:

5

Step-by-step explanation:

If Alex is 14 and he's 9 years older than his sister Kristen,then Kristen is 5

14-9=5

Answer:

14-9 = 5, so Kristen is 5 years old

The probability that the next chew Aaden removes from the bag will be a flavor other than apple is 24/31.

Probability is a branch of mathematics concerned with determining the likelihood of an event occurring. Probability assesses the likelihood of an event occurring and is equal to the number of favorable events divided by the total number of events.

Given:

Number of times Aaden performs the experiment = 31 times

A strawberry chew was selected 4 times.

An apple chew was selected 7 times.

A watermelon chew was selected 20 times.

So,

Probability of selecting a strawberry chew = 4/31

Probability of selecting an apple chew = 7/31

Probability of selecting a watermelon chew  = 20/31

So, the probability that the next chew Aaden removes from the bag will be a flavor other than apple i.e. it can be strawberry or watermelon chew.

Probability of selecting a strawberry chew + Probability of selecting a watermelon chew

= 4/31 + 20/31 = 24/31

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Answer:

24/31

Step-by-step explanation:

Based on these results, express the probability that the next chew Aaden removes from the bag will be a flavor other than apple as a fraction in simplest form.

The experiment occurred 31 times, a flavor other than apple was selected 4+20=24 times. Probability the next chew will be a flavor other than apple:

24/31

=

The probability as a fraction in simplest form is

24/31

Step-by-step explanation:

5 - (-7) = 5 + 7

because 2 negatives added together make positive.

Answer:

+ 7

Step-by-step explanation:

the rule of signs for addition/ subtraction

a + (- b ) = a - b

a + (+ b) = a + b

a - (+ b) = a - b

a - (- b) = a + b

Then

5 - (- 7 ) = 5 + 7

The area of the rectangle is  [tex]b^2[/tex] +9b square feet

The rectangle is the quadrilateral whose opposite sides are parallel and equal. The rectangle is a four sided shape that all the angles are 90 degrees

The area is defined as the total space occupied by the two dimensional shape like rectangle, triangle, circle etc..

The length of the rectangle = (5/3)b+15 feet

The width of the rectangle = (3/5)b feet

The area of the rectangle = The length of the rectangle × The width of the rectangle

Substitute the values in the equation

The area of the rectangle  = [(5/3)b+15] ×(3/5)b

Apply the distributive property in the equation

[(5/3)b+15] ×(3/5)b = [tex]b^2[/tex] +9b square feet

Hence, the area of the rectangle is  [tex]b^2[/tex] +9b square feet

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The area of half circle is 14.13 sq.unit

The total area of the figure is 86.13 sq.unit

Given,

The figure is combined by a triangle, rectangle and a half circle.

The area of triangle = 18 sq.units

The area of rectangle = 54 sq.units

We have to find the area of half circle to get the total area of the figure;

Here,

Area of circle = π r²

Then,

Area of half circle =  π r² / 2

Here,

r = 6/2 = 3 units

Now,

Area = π r² / 2 = π × 3² / 2 = 28.27/2 = 14.13 sq.units

That is,

The area of half circle is 14.13 sq.unit

Then,

The total area of figure = Area of [triangle + rectangle + half circle]

The total area of figure = 18 + 54 + 14.13 = 86.13 sq.units

Therefore,

The total area of the figure is 86.13 sq.unit

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Answer:

The original price was $864

Step-by-step explanation:

if the ring is now $840 $40 u do $40 - %40 = %24

$24 + $840 = $864

The area of a triangle is 1/2bh. We know the area, a, the base, b, and we are attempting to find the height, h. So, we simplify the area formula with the value of b and solve for h, given a.

1/2(6)h = 30
3h = 30

Isolate h.

3h/3 = 30/3
h = 10