for 1 and 2 draw front side and top views of each stack of unit blocks

The constant of proportionality in the equation y=1.5x is 1.5 .

The Constant Of Proportionality(k) in the equation can be defined as the constant value of the ratio between the two proportional quantities .

In Direct proportionality y=kx , where k is the constant of proportionality

means that if x increases then y also increases at the same rate ,

and if x decreases then y also decreases at the same rate .

For Example : constant of proportionality in y=6x , will be 6 .

In the question ,

it is given that

Kevin earns $6 for 4 polished rocks ,

the equation to represent the situation is y=1.5x

So 1.5 is the constant of proportionality .

Therefore , the constant of proportionality in the equation y=1.5x is 1.5 .

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The answer is given below

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STEP - BY - STEP EXPLANATION

What to find?

Determine how much greater the average rate of change over the interval [ 7, 9] than the interval [4, 6].

Given:

Step 1

Calculate the average rate of change over the interval [ 7, 9] using the formula below:

a= 7 f(a)=1852

b=9 f(b)=3878

Substitute the values into the formula and simplify.

Step 2

Calculate the average rate of change over the interval [4, 6] using the same formula in step 2.

a=4 f(a)=358

b=6 f(b)=1178

Step 3

Compare the average rate of change over the two intervals.

Clearly, the average rate of change over the the interval [7, 9] is greater than the average rate of change over the interval [4, 6].

ANSWER

T

Using the Rule of 70, it is found that after 40 years, the ratio of country B's GDP to country A's is of 2.

The rule of 70 is a rule that is used to determine how long it takes for an amount to double, dividing 70 by the variable's growth rate, as a percentage.

Country A grows at 3.5 percent per year, hence the time it takes to double is:

70/3.5 = 20 years.

Hence in 40 years, it's GDP will be of:

4n, in which n is the current GDP, and 4 because it will have doubled twice.

Country B grows at 7 percent per year, hence the time it takes to double is:

70/7 = 10 years.

Hence in 40 years, it's GDP will be of:

8n, in which n is the current GDP, and 8 because it will have doubled three times.

Then the ratio of country B's GDP to country A's will be of:

8n/4n = 2.

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Using it's concept, there is a 0.3913 = 39.13% probability of picking a non poisonous animal or a spider.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

In the context of this problem, we have that:

Applying it's concept, of desired outcomes divided by total outcomes, the probability of picking a non poisonous animal or a spider is given as follows:

p = 9/23 = 0.3913 = 39.13%.

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Answer:

Step-by-step explanation:

Answer

I hope this is not the tip!

Total Cost of the meal              15.96

Menu Cost                                 15.20               Subtract

Tax                                                  .76    

The tax on the meal is 76 cents or 0.76 dollars.

The probability that a person who is alive at age 10 will not be alive at age 70 if the following is true for males and Female is

This is further explained below.

Generally, A number that expresses the possibility or likelihood that a certain event will take place is referred to as its probability. Both proportions and percentages with values ranging from 0 to 1 may be used to indicate probabilities. Proportions can range from 0 to 1, while percentages can range from 0 to 100.

Probability is the area of mathematics that deals with providing numerical descriptions of the likelihood that an event will take place or the likelihood that a statement will be correct.

A number between 0 and 1 may be thought of as representing the chance of an event happening, with 0 indicating that the occurrence is impossible and 1 indicating that it will definitely happen.

The characteristic or condition of being probable; the degree to which something is likely to occur or be the case. the likelihood of anything happening or something is the case.

In conclusion,

P(not alive at age 70 | male)

=(99065-72066)/99065

=0.273

As fraction

=26999/99065​

P(not alive at age 70 | female)

=(99228-81944)/98983

0.17461

As fraction

17284/98983​

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The monthly payment when you want to buy a 28,000 car is $567.

It should be noted that when the 10% down payment is made, the amount left will be:

= $28000 - (10% × $28000)

= $28000 - $2800

= $25200

The interest will be:

= PRT / 100

P = $25200

R = 2%

T = 48 months = 4 years

Interest = (25200 × 2 × 4)/100

= $2016

Total amount to be paid:

= $25200 + $2016

= $27216

The monthly payment will be:

= Amount / 48 months

= $27216 / 48

= $567

The monthly payment is $567.

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Answer:

$546.72

Step-by-step explanation:

The slope of the line is 60 and speed of the bus is 60 miles per hour

The slope of the line is the measure of the steepness. In other words the slope of the line is the change in y coordinate with respect to the change in x coordinate.

Here the points are

(1,60) and (2,120)

The slope of the line m =[tex]\frac{y_{2}-y_{1} }{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the points

Substitute the values in the equation

The slope of the line m = [tex]\frac{120-60}{2-1}[/tex]

= 60

The speed = Distance / Time

Take one point (2,120)

The distance = 120 miles

Time = 2 hours

The speed = 120/2

= 60 miles per hour

Hence, the slope of the line is 60 and speed of the bus is 60 miles per hour.

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Answer:

234

Step-by-step explanation:

How do you answrt? I'm aknskwnwekene

Answer:

Step-by-step explanation:

$2143.5 = $62.75x - $888.5.

The resulting factors on factorizing the expression is (x+2)(x+3).

Quadratic equations are equation that has a leading degree of 2.

Writing a number or other mathematical object as the sum of several factors typically smaller or simpler things of the same kind—is known as factorization or factoring.

Given the quadratic equation below:

x^2 + 5x + 6

Factorize to have:

x^2 + 2x + 3x + 6

Group

(x^2+2x)+(3x+6)

Factor out the common variable or value

x(x + 2) + 3(x + 2)

Find the factors

(x+3)(x+2)

Hence the factored form of the expression in its simplest form is (x+2)(x+3)

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Complete question

Factorize x^2 + 5x + 6

Answer:

[tex]x = 3 - {e}^{12} [/tex]

Step-by-step explanation:

first let's isolate the logarythm:

[tex]ln(3 - x) = 12[/tex]

at this point we can apply the definition of logarythm to obtain

[tex]3 - x = {e}^{12} [/tex]

which, with some simple algebra returns

[tex]x = 3 - {e}^{12} [/tex]

Dallas, Texas, had a population of about 1 x 106 peoples in that specific year. There were above 3×10⁶ people in Los Angeles; The population of Pittsburgh was about 0.3 times of Dallas.

Given that,

Dallas, Texas, had a population of about 1 x 106 peoples in that specific year. If Los Angeles, California, had a population of

There were almost three times as many people there as in Dallas.

peoples who called Los Angeles home in that year.

In the same year, there were about 3 x 105 peoples living in Pittsburgh, Pennsylvania. one from Dallas.

In Dallas the population is P₁=1×10⁶

Then in Las Angeles the population is P₂=3P₁=3(1×10⁶)= 3×10⁶

In Pittsburgh the population is P₃=3×10⁵

P₃÷P₁=(3×10⁵)÷(1×10⁶)=0.3

Therefore, There were above 3×10⁶ people in Los Angeles; The population of Pittsburgh was about 0.3 times of Dallas.

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Factories produce a total of 21550 gallons in a calendar year.

The gallon is used as a unit of volume in both imperial and US customary measurements.

Eight pints make up a gallon, which is a unit of measurement for liquids. It is equivalent to roughly 4.546 litres in Britain. It is roughly equivalent to 3.785 litres in America.

Lemonade, it has been stated, equals 11,650 gallons.

Lemonade = 4,950 fewer than ice tea.

Ice tea: 3,500 fewer than Root beer.

Using the formula Ice tea = 11,650 - 4,950

6700 gallons of iced tea

Root beer = 6700 - 3,500

3200 gallons equals root beer.

Total manufacturing output for a year is equal to 11,650 + 6700 + 3200

Thus, 21550 gallons are produced in total by factories each year.

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If June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60  gallons

The bigger cooler is five times as large as the smaller cooler

Consider the capacity of smaller cooler as x

The capacity of bigger cooler=5x

June has 72 gallons of punch for a party

Then the linear equation will be

x+5x=72

6x=72

x=12

Then the capacity of bigger cooler=5x

=5×12

=60

Hence, if June has 72 gallons of punch for a party and June carries the punch in two different full coolers. The bigger cooler is five times as large as the smaller cooler, then the capacity of smaller cooler is 12 gallons and the capacity of bigger cooler is 60  gallons

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Answer:

h= 6

Step-by-step explanation:

To find out the value of h, start by forming an equation for the cost of renting a trampoline:

Cost of renting= $(75 +8t), where t is the rental duration.

When the cost is $125,

75 +8t= 125

Subtract 75 from both sides:

8t= 125 -75

8t= 50

Divide both sides by 8:

t= 50 ÷8

t= 6.25

Since she wants to spend less than $125, let's round the value down to the nearest hour.

∴ h= 6

Thus, she could rent it for 6 hours.

Let's check!

Total cost of renting for 6 hours

= 6(8) +75

= $123

Total cost of renting for 7 hours

= 7(8) +75

= $131

Hence, 6 hours is indeed the maximum number of hours she can rent the trampoline for, such that the total cost is less than $125.

Using unitary method we conclude that, 3.33 pounds of tomatoes will go into each tub.

In this question, we have been given a sub shop ordered 40 pounds of tomatoes.

The tomatoes are evenly distributed into 12 tubs.

We need to find the number of pounds of tomatoes will go into each tub.

Let x be the number of pounds of tomatoes will go into each tub.

By unitary method,

x = 40 / 12

x = 3.33 pounds

Therefore by using unitary method we conclude that, 3.33 pounds of tomatoes will go into each tub.

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The time it will take for a sample of this substance to decay to 20% of its original amount

t=16973.294years

This is further explained below.

The amount of time needed for a quantity to decrease to half of its original value is referred to as its half-life.

In nuclear physics, this word is often used to define the rate at which unstable atoms undergo radioactive decay or the amount of time stable atoms are able to persist.

Additionally, the phrase may be used in a broader sense to define any form of exponential decline.

Generally,

A = A0e^{-kt}

Therefore

A(t) = A0e^{[ln(0.5) / 7310 t}, t in years

0.20 = e^{ln(0.5) / 7310 ]t}

Solve for t.

ln(0.20) = [ln(0.5) / 7310 ]t

t = 7310 [ln(0.20) / ln(0.5)]

t=16973.294years

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Answer:

Step-by-step explanation:

Let n be the times that they knock on the door.

If five more than three times n and is equal to the difference between 21 and n;

Solve for n, using inverse operations to solve equations:

Hence the equation of the parabola is y = -x² + 4

In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical planar curve. The same curves can be defined by a number of seemingly unrelated mathematical definitions, which all correspond to it.

The general equation of a parabola is given by y = ax² + bx+ c

The parabola passes through (-3,-5) , (-1,3) , and (0,4).

Now substituting the values in the parabola we get :

-5 =  a(-3)² + b(-3)+ c

or , -5 = 9a -3b + c

again:

3 = a(-1)² + b(-1)+ c

or, 3 = a -b + c

again

4 = a(0)² + b(0)+ c

or, c =4

Solving the equation we get :

9a - 3b = -9 and a-b = -1

a= -1 and b = 0

Hence the equation of the parabola is

y = -x² + 4

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Step-by-step explanation:

it is just a matter of definition that can be easily looked up.

the domain is the interval or set of all valid x values.

while the range is the interval or set of all valid y (function result) values.

so, the domain here is every value of x used in this function.

e.g. does x = -6 have a functional (y) value in the curve ?

no, it does not.

x = - 4 ? no.

x = -2 ? no.

x = -1 ? ah, yes, this is just the left-most point of the curve.

and then all x values further to the right of -1 are covered. as the arrows indicate : into all eternity ("to infinity and beyond !")

so, the domain is [-1, +infinity).

and you need to use B.

please note, the round bracket indicates that that ends of the interval is not included or undefined (after all, infinity is not a number we can work with, it is basically undefined and only represents a principle).

for the range this is tricky, as the graph does not really show us the limit. it could be y = -1 or 0 down to y = -9 or -10.

The most appropriate choice for modulus of a number and ascending order will be given by-

|0.58|, 18, |-35| is in ascending order.

What is Modulus of a number and ascending order?

Modulus of a number returns the absolute value of the number.

Modulus of positive number is positive and modulus of negative number is also positive.

If the numbers in a series are arranged in increasing order of their value, then the series is arranged in ascending order

Here,

|-35| = 35

18 = 18

|0.58| = 0.58

As, 0.58, 18, 35 is in ascending order,

So, |0.58|, 18, |-35| is in ascending order

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Answer:Definition of Midpoint-A

Step-by-step explanation:

Step-by-step explanation:

[tex]i = prt \div 100[/tex]

p=539

r=17%

t=21

I=?

[tex]i = 539 \times 17 \times 21 \div 100[/tex]

Answer: Choice A

15C12

=============================================

Reason:

Imagine there are 15 students and we wish to form a committee of three people, where order doesn't matter. The answer to this problem is 15C3 using the nCr formula. Here n = 15 and r = 3.

The 15C3 represents the number of ways to pick the three people on the committee, while 15C12 is the number of ways to not pick a person for the committee. We can think of it like two separate committees if you want.

So 15C3 = 15C12

The numbers after the "C" add to the value of n

The identity is [tex]_nC_r = _nC_{n-r}[/tex]

The r and n-r add to n.