In the problems below, f(x) = log₂x and
g(x) = log₁₀x
Which point do the graphs of f and g have in common?

Answer:

h= 9

Step-by-step explanation:

you divide both sides by 32

and 288 divided by 32 is 9

The solution to system is x = 0 and y = -1

Solution:

Given system of equations are:

-8x + 2y = -2 ----------- eqn 1

4x + 4y = -4 ---------- eqn 2

We have to solve the system of equations

We can solve the equations by elimination method

Multiply eqn 2 by 2

8x + 8y = -8 ------ eqn 3

Add eqn 1 and eqn 3

-8x + 2y = -2

8x + 8y = -8

( + ) ---------------

0x + 2y + 8y = -2 - 8

10y = -10

Divide both sides by 10

y = -1

Substitute y = -1 in eqn 1

-8x + 2(-1) = -2

-8x - 2 = -2

-8x = -2 + 2

x = 0

Thus the solution to system is x = 0 and y = -1

The width of backyard is 45 feet.

Step-by-step explanation:

Given,

Length of backyard = 120 feet

Perimeter of backyard = 330 feet

Width of backyard = w

Perimeter = 2(Length + Width)

[tex]330=2(120+w)\\330=240+2w\\330-240=2w\\90=2w\\2w=90[/tex]

Dividing both sides by 2

[tex]\frac{2w}{2}=\frac{90}{2}\\w=45[/tex]

The width of backyard is 45 feet.

Keywords: perimeter, division

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The initial number is 7.

Step-by-step explanation:

Let the initial number be 'x'.

⇒ 7x-4 = 45

⇒ 7x = 49

⇒ x = 7

The initial number is 300. Multiply by 7.4 to get 2220, subtract 2220, then divide by 9 to get 247. Confirming: 7.4(300) - 2220 = 247(9) = 5.

Let's denote the initial number as ( x ). According to the given information:

1. Multiply by 7.4: ( 7.4x )

2. Take away from the product: ( 7.4x - (7.4x) )

3. Finally, divide by 9:[tex]\( \frac{{7.4x - 7.4x}}{9} \)[/tex]

We know that this resulting expression equals 5:

[tex]\[ \frac{{7.4x - 7.4x}}{9} = 5 \][/tex]

Now, let's solve for ( x ):

[tex]\[ \frac{{0}}{9} = 5 \][/tex]

As ( 7.4x ) cancels out, we are left with ( 0 = 5 ), which is not a valid equation.

Answer:

[tex]y=72.99+28.45(x-1)[/tex]

Step-by-step explanation:

Linear Modeling

Some situations in real life are bound to be modeled as mathematical functions. A model allows scientists and analysts to take decisions based on predicted values coming from those models.

To construct them we usually take or measure values of the variables of interest and find the general equation of the model. In this case, we'll find the relation between the service costs (y) of a cell phone provider and the number of months (x).

There are three points available: ( 1 , 72.99 ) , ( 2 , 101.44 ) , ( 3 , 129.89 ) and we only need two to find a function of the form

[tex]y=c+d(x-1)[/tex]

We'll use the first two points and use the third point to verify the validity of the model. Let's plug in the first point:

[tex]72.99=c+d(1-1)[/tex]

Operating

[tex]72.99=c\\c=72.99[/tex]

Now for the second point

[tex]101.44=72.99+d(2-1)[/tex]

Operating and rearranging

[tex]d=101.44-72.99=28.45[/tex]

Our model is complete:

[tex]\boxed{y=72.99+28.45(x-1)}[/tex]

Let's check the third point  ( 3 , 129.89 ) by plugging x=3

[tex]y=72.99+28.45(3-1)=72.99+56.9=129.89[/tex]

The point belongs to the function.

Final answer:

The cell phone provider's escalating monthly charges can be represented by a linear equation, demonstrating the initial cost plus the consistent monthly increase. The equation is y = 72.99 + 28.45(x - 1).

Explanation:

To find the equation representing the cell phone provider Talk of the Town, we observe the costs for the first three months: $72.99 for the first month, $101.44 for the second, and $129.89 for the third. The increase in cost from one month to the next is consistent, increasing by $28.45 each time. This situation can be expressed as a linear equation in the form y=c+d(x−1), where y is the total cost, c is the starting value, d is the difference per period, and x represents the month number.

To find c (the initial cost), we look at the first month's charge: $72.99. d, the monthly increase, is $28.45. Thus the equation for the total cost of service from Talk of the Town over x months is y = 72.99 + 28.45(x - 1). This equation accounts for the initial cost in the first month and the consistent monthly increase thereafter.

Answer:

A- 4h 18min

Step-by-step explanation:

First you look at the data provided that shows that this is this latest time, so when it is 10:15 in buffalo, it is 9:15 in Dallas. He arrives in Dallas at 1:33, so you can either think in central time which is 9:15-1:33, or in eastern time which is 10:15-2:33. From there you can subtract 15 from 33 getting 18, and from 10 o’clock to 2 o’clock (or 9 o’clock to 1 o’clock) is 4 hours.

Answer:

Yes 9 is larger than -10

Step-by-step explanation:

Any positive number is larger than a negative number

Answer: yes

Step-by-step explanation: this is so because on the number line 9 comes first while -10 is far behind from -1

To find the circumference of a circle, use the formula C = 2πr. To find the area, use the formula A = πr^2.

The question asks to match each circular flower bed on the left to its circumference and its area on the right. In order to find the circumference of a circle, we use the formula C = 2πr, where r is the radius of the circle.

To find the area of a circle, we use the formula A = πr^2. We can use these formulas to calculate the circumference and area of each circular flower bed and match them to the options on the right.

For example, if a circular flower bed has a radius of 3 meters, we can find its circumference by plugging the radius into the formula: C = 2π(3) = 6π meters. Similarly, we can find its area by plugging the radius into the formula: A = π(3^2) = 9π square meters.

The Option (1),(4) and (5) are correct.

Step-by-step explanation:

The  function given to us  is : y= f(x) =49(1/7)^x

The following  statements  are true regarding the above function is

Answer:

The correct options are 1, 4 and 5.  

Step-by-step explanation:

The general form of an exponential function is

[tex]f(x)=ab^x[/tex]

where, a is initial value and b is growth factor.

Domain of this function is all real numbers. If a>0, then range is all positive numbers.

The given function is

[tex]f(x)=49(\frac{1}{7})^x[/tex]

where, a =49 and b=1/7.

It is an exponential function. So, the domain is the set of all real numbers.

Since, a=49 which is a positive value, therefore the range is y>0.

The value of b is 1/7, it means as x increased by 1, each y-value is one seventh of the previous y-value.

Therefore, the correct options are 1, 4 and 5.  

Answer:

B =

Step-by-step explanation:B + C would be 8 because B=2 and C=5. 5 + 8 is 8

Answer:

Plane speed: 480mph

Wind speed: 80mph

Step-by-step explanation:

Miami to Seattle: time = 7hrs

Speed (s) = 2800mph

D = speed/time = 2800/7

= 400mph

Seattle to Miami:

Same speed = 2800mp

Time = 5hrs

Distance (D) = speed/time

= 2800/5 = 560mph

Let p be speed of plane and w wind speed.

Therefore, P+w = 560. . .1

P-w = 400. . .2

2p = 960

P = 960/2 = 480

Therefore, P + w = 560

480 + w = 560

W = 80mph

While P = 480mph

The possible dimensions of the sandbox are 5 and [tex](x+8)[/tex].

Important information:

We need to find the possible dimensions of the sandbox.

Formula for the area of a rectangle is:

[tex]\text{Area}=\text{Length}\times \text{Width}[/tex]

Factorize the given expression to find the possible dimensions of the sandbox.

[tex]5x+40=5x+5\times 8)[/tex]

[tex]5x+40=5(x+8)[/tex]

Thus, the possible dimensions of the sandbox are 5 and [tex](x+8)[/tex].

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Answer:

[tex](6W+6)\ in[/tex]

Step-by-step explanation:

we know that

The perimeter of a rectangle is equal to

[tex]P=2(L+W)[/tex] ----> equation A

where

L is the length

W is the width

we have

The length is 3 inches more than twice the width

so

[tex]L=2w+3[/tex] ----> equation B

substitute equation B in equation A

[tex]P=2(2W+3+W)[/tex]

Combine like terms

[tex]P=2(3W+3)\\P=(6W+6)\ in[/tex]

Answer:

Step-by-step explanation:

hello : the system is : y =-5x+8...(*)

                                  y =11/7x-4/7 ...(**)  

by (*) and (**) : 11/7x-4/7 = -5x+8

multiply by 7 : 11x-4 = -35x+56

11x+35x = 56+4

46x = 60

x = 60/46 = 30/23

continu.....put the value for x in (*) or (**)

Answer:

[tex]T_n=-1(-5)^n^-^1[/tex]

Step-by-step explanation:

We are given;

A geometric sequence;

-2,10,-50

Required to determine the nth term

The nth term in a geometric sequence is given by the formula;

[tex]T_n=a_1r^n^-^1[/tex]

where [tex]a_1[/tex] is the first term and r is the common ratio;

In this case;

[tex]a_1=-2[/tex]

r = 10 ÷ -2

  = -5

Therefore;

To get the nth term in the given geometric sequence we use;

[tex]T_n=-1(-5)^n^-^1[/tex]

Thus, the nth term is [tex]T_n=-1(-5)^n^-^1[/tex]

Multiply the number amount of cartridges by the number of books and add that tot he number of cartridges by the number of magazines.:

This needs to be either less than or equal tot he total cartridges she wants to use

40B + 30M ≤ 300

Do the same with pages:

200B + 80M ≤  1200

Answer:

0.5675

Step-by-step explanation:

We have that, the IQ of the ruling species is normally distributed with a mean of 118 and a standard deviation of 18.

We want to find the probability that a randomly selected person's IQ is over 115.

We need to find the z-score of 115

using

[tex]z = \frac{x - \mu}{ \sigma} [/tex]

We substitute x=115 to get:

[tex]z = \frac{115 - 118}{18} [/tex]

This implies that:

[tex]z = \frac{ - 3}{18} = - \frac{1}{6} = - 0.17[/tex]

We read from the normal distribution table to get;

P(X>115)=0.5675

By converting the IQ score of 115 into a Z score and finding the area to the right of this Z score in a standard normal distribution, we find that the probability of a randomly selected individual's IQ being over 115 is approximately 0.57 or 57%.

To answer this question, we need to understand how a normal distribution works. A random variable X, such as an individual's IQ, that is normally distributed can be converted into a standard normal variable Z, using the formula Z = (X - mean) / standard deviation.

In our case, the mean IQ is 118 and the standard deviation is 18. Therefore, to find the probability that a randomly selected individual's IQ is over 115, we convert 115 into a Z score using the aforementioned formula: Z = (115 - 118) / 18 = -0.167. This is the Z score for an IQ of 115.

To find the probability that a randomly selected individual's IQ is more than 115, we find the area to the right of Z = -0.167. From standard normal tables, we know that the area to the left of Z = -0.167 is approximately 0.4332. Therefore, the area to the right (which is the probability we want) is 1 - 0.4332 = 0.5668.

So, the probability that a randomly selected individual's IQ is over 115 is approximately 0.57 (or 57% when expressed as a percentage).

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answer is

o.7 liters 2000 milliliters and 4.1 liters  

Step-by-step explanation:

1 / 5

1 \text{ liter} ={1{,}000}\text{ milliliters}1 liter=1,000 milliliters1, start text, space, l, i, t, e, r, end text, equals, 1, comma, 000, start text, space, m, i, l, l, i, l, i, t, e, r, s, end text

So, 1 \text{ milliliter} = \dfrac1{1{,}000}\text{ liter}1 milliliter=  

1,000

1

​  

 liter1, start text, space, m, i, l, l, i, l, i, t, e, r, end text, equals, start fraction, 1, divided by, 1, comma, 000, end fraction, start text, space, l, i, t, e, r, end text

Hint #22 / 5

We know \maroonD{0.7}0.7start color #ca337c, 0, point, 7, end color #ca337c liters is less than \greenD{4.1}4.1start color #1fab54, 4, point, 1, end color #1fab54 liters. But where does \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters fit?

We need to convert \blueD{2{,}000}2,000start color #11accd, 2, comma, 000, end color #11accd milliliters to liters before we can compare.

Hint #33 / 5

\begin {aligned}{\blueD{2{,}000} \text{ mL}}&= {\blueD{2{,}000} \text{ mL}}\times \dfrac{1 \text{ L}}{{1{,}000 \text{ mL}}} \\\\ &= {\dfrac{\blueD{2{,}000} \cancel{\text{ mL}}}{1}}\times \dfrac{1 \text{ L}}{{1{,}000 \cancel{\text{ mL}}}} \\\\ &=\dfrac{\blueD{2{,}000}\text{ L} }{1{,}000}\\\\ &=\blueD{2{,}000}\text{ L}\div1{,}000\\\\ &=\blueD{2}\text{ L} \end{aligned}  

2,000 mL

​  

=2,000 mL×  

1,000 mL

1 L

​  

=  

1

2,000  

mL

​  

×  

1,000  

mL

1 L

​  

=  

1,000

2,000 L

​  

=2,000 L÷1,000

=2 L

​  

Answer:

12

Step-by-step explanation:

Answer:

The distributive property is used

Step-by-step explanation:

3(x - y) = 3x - 3y      Distribute the 3 to the (x - y)

a) To write the probability as a decimal, we divide the numerator (20) by the denominator (40). This gives us the decimal representation of the probability.

b) To change the fraction to a decimal, we divide the numerator by the denominator.

So, the correct answer is option B: Divide the numerator by the denominator.

Explanation:

To change the fraction [tex]\( \frac{20}{40} \)[/tex] to a decimal, we perform the division [tex]\( \frac{20}{40} \)[/tex].

[tex]\[ \frac{20}{40} = 0.5 \][/tex]

Therefore, the probability of choosing a green marble as a decimal is 0.5.

Step-by-step explanation:

In trapezoid ABCF, AB || CF.

Therefore, parallelograms ABEF & ABCD have same height and lie on the same base AB.

[tex] \therefore Ar(\parallel^{gm} ABEF) = Ar(\parallel^{gm}ABCD)\\... (1)\\\\

\because\: Ar(\parallel^{gm} ABEF) \\=Ar(\triangle AFD) + Ar(\square \: ABED)....(2) \\\\

\&\: Ar(\parallel^{gm}ABCD)\\= Ar(\triangle BCE) +Ar(\square ABED)....(3) [/tex]

From equations (1), (2) & (3), we find:

[tex] Ar(\triangle AFD) + Ar(\square \: ABED) \\ = Ar(\triangle BCE) +Ar(\square ABED)

\\ \\ \purple {\boxed {\therefore Ar(\triangle AFD) = Ar(\triangle BCE)}}

\\ [/tex]

Thus, the two triangular pieces of land are equal in area.

Hence proved.

Answer:

Option D

Step-by-step explanation:

step 1

Account 1

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=10\ years\\ P=\$6,000\\r=4.5\%=4.5/100=0.045[/tex]

substitute in the formula above

[tex]A=6,000(1+0.045*10)[/tex]

[tex]A=6,000(1.45)[/tex]

[tex]A=\$8,700[/tex]

step 2

Account 2

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=10\ years\\ P=\$6,000\\ r=4\%=4/100=0.04\\n=1[/tex]  

substitute in the formula above

[tex]A=6,000(1+\frac{0.04}{1})^{1*10}[/tex]  

[tex]A=6,000(1.04)^{10}[/tex]  

[tex]A=\$8,881.47[/tex]  

step 3

Find the difference

[tex]\$8,881.47-\$8,700=\$181.47[/tex]

therefore

Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years

Step-by-step explanation:

Given information is insufficient for finding the measures of angles B and D.

Answer:

110 and 70

Step-by-step explanation:

Answer:

There are a total of 495 people on the train

Step-by-step explanation:

Let's identify what we know:

1) The train has 3 passenger cars

2) Each passenger car has 4 columns, and each can accommodate 40 people.

3) All three passenger cars are full, but one of them has 15 additional people standing.

We can create a formula to model the problem:

x = ((3 x 4) x 40) + 15

x = the total number of passengers!

There are a total of 180 people sitting, and 15 additional people standing in one of the passengers cars, equaling a total of 495 passengers on the train.

The train has a total of 495 passengers.

To calculate the number of passengers on the train, we first need to determine the seating capacity of each car. Since each car has 4 columns of seats and each column holds 40 passengers, each car can seat a total of 4 x 40 = 160 passengers.

Next, we need to account for the 15 people standing in one of the cars. This means that one car has 160 + 15 = 175 passengers.

Finally, since the rest of the cars are full without anyone standing, we can assume that the other two cars also have 160 passengers each. Therefore, the total number of passengers on the train is 175 + 160 + 160 = 495.

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Answer:

To answer this you will use the formula V = pi x radius ^2 x height.  The substitution for this would be 3.14 x 4^2 x 8.  The approximate answer is 401.92 cubic units. 3.14 is an approximation of pi. 

Note:  It does not say that x is the height, but this is the only piece of information missing without an obvious label, so I am using it as the height.

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Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Given:

A bakery has 36 glazed donuts on display.

This is 80% of the total number of donuts.

Question asked:

what is the total number of donuts in the bakery ?

Solution:

Let total number of donuts in the bakery = [tex]x[/tex]

80% of total number of donuts = 36  (given)

[tex]80\% of x = 36[/tex]

[tex]\frac{80x}{100} = 36[/tex]

Multiplying both side by 100

[tex]80x = 3600[/tex]

Dividing both side by 80

[tex]x = 45\\[/tex]

Thus, the number of donuts in the bakery is 45

To find out how much Tina needs to run each day, divide the total miles she wants to run by the number of days. The result is that Tina needs to run 1.8 miles each day.

To find out how far Tina must run each day, we need to divide the total distance she plans to run by the number of days she plans to run. Tina wants to run 12 3/5 miles over 7 days. As a first step, convert her mixed number to an improper fraction. 12 3/5 is equivalent to 63/5.

Now, to find the distance she must run each day, simply divide 63/5 miles by 7 days. Carrying out this division gives us distance of 9/5 miles per day, or in decimal form, 1.8 miles per day.

So, Tina should run 1.8 miles each day to reach her goal.

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