The mass of two sacks of potatoes is 168 grams. One-eight of the mass of Sack A and three-quarter of the mass of Sack B is 76 grams. Write an equation to find the mass of Sack A. ​

Step-by-step explanation:

[tex]3\log x+\log2=\log3x-\log2\\\\\text{Domain:}\ x>0\\\\\text{Use}\\\\\log_ab^c=c\log_ab\\\\\log_ab+\log_ac=\log_a(bc)\\\\\log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\===================\\\log x^3+\log2=\log\left(\dfrac{3x}{2}\right)\\\\\log(2x^3)=\log\left(\dfrac{3}{2}x\right)\iff2x^3=\dfrac{3}{2}x\qquad\text{subtract}\ \dfrac{3}{2}x\ \text{from both sides}\\\\2x^3-\dfrac{3}{2}x=0\qquad\text{multiply both sides by 2}\\\\4x^3-3x=0\qquad\text{use distributive property}\\\\x(4x^2-3)=0\iff x=0\ \vee\ 4x^2-3=0[/tex]

[tex]x=0\notin\ \text{Domain}\\\\4x^2-3=0\qquad\text{add 3 to both sides}\\\\4x^2=3\qquad\text{divide both sides by 4}\\\\x^2=\dfrac{3}{4}\Rightarrow x=\pm\sqrt{\dfrac{3}{4}}\\\\x=\pm\dfrac{\sqrt3}{\sqrt4}\\\\x=-\dfrac{\sqrt3}{2}\notin \text{Domain}\\\\\boxed{x=\dfrac{\sqrt3}{2}}\in \text{Domain}[/tex]

The equivalent equation to 3logx + log2 = log3x - log2 is x² = 3/4, which is derived by applying properties of logarithms such as combining log terms and setting the resulting expressions equal to each other.

The equation 3logx + log2 = log3x - log2 can be simplified using the properties of logarithms. To find the equivalent equation, we use the property that log(a) + log(b) = log(ab) and log(a) - log(b) = log(a/b). Applying these properties:

The equivalent equation is x² = 3/4 or x = ±√(3/4), provided that x ≠ 0 since the logarithm of zero is undefined.

Answer:

Step-by-step explanation:

Letting "a" and "c" represent the costs of adult tickets and child tickets, the problem statement gives us two relations:

  3a +5c = 52

  2a +4c = 38

__

We can solve this system of equations using "elimination" as follows:

Dividing the first equation by 2 we get

  a +2c = 19

Multiplying this by 3 and subtracting the first equation eliminates the "a" variable and tells us the price of a child ticket:

  3(a +2c) -(3a +4c) = 3(19) -(52)

  c = 5 . . . . . . collect terms

  a +2·5 = 19 . . substitute for c in the 3rd equation above

  a = 9 . . . . . . subtract 10

One adult ticket costs $9; one child ticket costs $5.

Answer:

B)

Step-by-step explanation:

Do the zero property.

x-7=0, x+6=0

x=0+7=7,

x=0-6=-6

Answer:

b 100% true

Step-by-step explanation:

Answer:

The probability that 5 chosen bagels of which exactly 3 are Asiago cheese = 0.3087 or 30.87%

Step-by-step explanation:

Given:

Total  bagels brought to school = 10

Number of Asiago cheese bagels = 7

To find the probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese.

Solution:

Let probability of choosing an Asiago cheese bagel be the successful event.

Probability of choosing one Asiago cheese bagels = [tex]\frac{7}{10}=0.7[/tex]

Probability of success = 0.7

Probability of failure ( not choosing an Asiago cheese bagel) = 1 - Probability of success = [tex]1-0.7=0.3[/tex]

Using Bernoulli Trials

To calculate the binomial probability of obtaining  exactly [tex]r[/tex] events in [tex]n[/tex] trials the formula used is:

⇒ [tex]nCr.p^r.q^{(n-r)}[/tex]

where [tex]p\rightarrow[/tex] Probability of success

[tex]q\rightarrow[/tex] Probability of failure

Thus,  probability of randomly choosing 5 Asiago cheese bagels of which exactly 3 are Asiago cheese can be calculated as :

⇒ [tex]5C3(0.7)^3(0.3)^2[/tex]

⇒ [tex]\frac{5!}{(5-3)!3!}(0.343)(0.09)[/tex]

⇒ [tex]\frac{5!}{(2)!3!}(0.343)(0.09)[/tex]

⇒ [tex]10(0.343)(0.09)[/tex]

⇒ [tex]0.3087\ or\ 30.87\%[/tex] (Answer)

ln z + ln 7 = ln 63

When adding two logarithms of the same base, you can combine them into a single logarithm where the input is the product of both previous inputs

ln 7z = ln 63

Take the exponential of e to both sides

7z = 63

Divide both sides by 7

z = 9

Let me know if you need any clarifications, thanks!

Answer:

t=44°

Step-by-step explanation:

The sum of the interior angles of any pentagon is always 540 degrees.

Let's set up an equation with this information: (all figures are in degrees)

[tex]t+3t+t+32+149+139=540[/tex]

Now we combine all like terms.

[tex]5t+320=540[/tex]

Now begin to isolate t be subtracting 320 from both sides.

[tex]5t=220[/tex]

Finally divide both sides by 5 to isolate t.

t=44°

Answer:we multiply by the reciprocal of a fraction when completing a division problem because it is a rule in mathematics that when you divide two fraction, you change the division sign to multiplication and flip the fraction at the right of the multiplication sign.

Step-by-step explanation:

For example if you have 4÷ 1/2. It basically means how many 1/2 can one get in 4. And the answers is 8.

Therefore multiplying by the reciprocal of a fraction when completing a division problem is a short cut method that has been tested and proven to be correct.

Based on the calculations, the interquartile range of a data set is equal to 53.

In order to determine the statistical measures or the five-number summary, we would arrange the data set in an ascending order:

6,8,9, 30, 30, 36, 38, 54, 64, 70, 75, 81, 93

Based on the data set, the first quartile can be calculated as follows;

First quartile = [(n + 1)/4]th term

First quartile = (13 + 1)/4

First quartile = 3.5th term

First quartile = (30+9)/2

First quartile =  19.5.

For the third quartile, we have:

Third quartile = [3(n + 1)/4]th term

Third quartile = 3 × 3.5th term

Third quartile = 10.5th term

Third quartile = (75+70)/2

Third quartile = 72.5

Mathematically, the interquartile range of a data set is the difference between third quartile (Q₃) and the first quartile:

Interquartile range of data set = Third quartile - First quartile

Interquartile range of data set = 72.5 - 19.5

Interquartile range of data set = 53.

Answer:

3

Step-by-step explanation:

3+11t-9u=3+11(9)-9(11)=3+99-99=3

Answer:

5/3

Step-by-step explanation:

30/18=5/3

Answer:

22 4/5 yards

Step-by-step explanation:

(7 3/5) x 3 = 22 4/5

To convert 7 3/5 feet to yards, you use the conversion 1 yard = 3 feet. After converting the mixed number to an improper fraction, you divide by 3, yielding the answer 2 8/15 yards, which corresponds to option C.

To convert feet to yards, we can use the conversion factor that 1 yard is equal to 3 feet. Since the student needs to find out how many yards are in 7 3/5 feet, we can convert mixed numbers to improper fractions to simplify the calculation.

The mixed number 7 3/5 can be converted to an improper fraction by multiplying the whole number 7 by the denominator 5 and adding the numerator 3, then placing the result over the original denominator: (7 * 5) + 3 = 35 + 3 = 38, so 7 3/5 becomes 38/5.

To convert 38/5 feet to yards, divide by 3 because there are 3 feet in 1 yard:

38/5 feet * 1 yard/3 feet = (38/5)/3 = 38/5 * 1/3

This simplifies to 38/5 * 1/3 = 38/15 yards

Then divide 38 by 15 to get 2 with a remainder of 8, so we have 2 and 8/15 yards.

Therefore, the answer is C. 2 8/15 yards.

Answer:

5 1/4 or 5.25

Step-by-step explanation:

Multiplying fractions means that we can multiply the numerator by the numerator and the denominator by the denominator straight across without needing a common denominator.

3*7 = 21

4*1 = 4

We end up with the improper fraction 21/4. We can convert this into a mixed number.

Because 4 goes into 21 a total of 5 times with 1 left over, we end up with the mixed number of 5 1/4, or as a decimal, 5.25

Answer:

T1 =2 , Tn = 1 /tn-1 For The Geometricseries 6 + 3 + 3/2 + 3/4 + .

Step-by-step explanation:

Answer:

2, 5, 8, 11, 14

Step-by-step explanation:

Find the first 5 terms by substituting n = 2, 3, 4, 5 into the recursive formula

t₂ = t₁ + 3 = 2 + 3 = 5

t₃ = t₂ + 3 = 5 + 3 = 8

t₄ = t₃ + 3 = 8 + 3 = 11

t₅ = t₄ + 3 = 11 + 3 = 14

The first 5 terms are 2, 5, 8, 11, 14

Answer:

Multiples:

2: 2 4 6 8 10 12 14 16 18 20

3: 3 6 9 12 15 18 21 24 27 30

The LCM is 6 (underlined)

Answer:

520 eggs

Step-by-step explanation:

5%*2 is 10%.

10%*10 is 100%,that is the full carton of eggs.

26*2*10 is 520.

There were 520 eggs in the carton altogether.

Hope this helps :)

To find the total number of eggs in the carton, we use the information that 26 eggs (5% of the total) were broken. By solving the equation 0.05x = 26, we determine there were 520 eggs in the carton.

The question at hand is, "26 eggs in a carton were broken. This was 5% of the total number of eggs in the carton. How many eggs were in the carton altogether?"

To solve this problem, let us consider the total number of eggs in the carton as x. Given that 5% of x is equal to 26 eggs, we can write this relationship as an equation: 0.05x = 26. To find x, we divide both sides of the equation by 0.05, yielding x = 26 / 0.05. Calculating this result, we find that x = 520.

Therefore, there were 520 eggs in the carton altogether.

Answer:

[tex]3,462\ bacteria[/tex]

Step-by-step explanation:

In this problem we have a exponential function of the form

[tex]y=a(b^x)[/tex]

where

x is the time in hours

y is the numbers of bacteria

a is the initial value

b is the base

r is the rate of growth

b=(1+r)

we have that

[tex]a=3,000\ bacteria[/tex]

For x=8, y=3,300

substitute in the exponential function

[tex]3,300=3,000(b^8)[/tex]

solve for b

[tex]1.1=(b^8)[/tex]

[tex]b=\sqrt[8]{1.1}[/tex]

[tex]b=1.0120[/tex]

Find the value of r

[tex]r=b-1=1.0120-1=0.0120=1.20\%[/tex]

The equation is equal to

[tex]y=3,000(1.012^x)[/tex]

For x=12 hours

substitute the value of x in the equation

[tex]y=3,000(1.012^{12})[/tex]

[tex]y=3,462\ bacteria[/tex]

Answer:

Step-by-step explanation:

Here, the "whole number" is the portion of the number to the left of the decimal point: 593.

The "remainder" is the portion left after the whole number is subtracted: 0.5625.

the answer is 38

16+18+4

Answer:

46

Step-by-step explanation:

The picture are irrelevant and is used to trick you.

Let swirly hair = s

Let curly hair = c

Let flat hair = f

Ok, now we can rewrite the picture in math terms

s = 16

c = 2 + s = 2 + (16) = 18

s = 4 + f → f = s - 4 = (16) - 4 = 12

s + c + f = 16 + 18 + 12 = 46

The answer is 120 cubic inches.

There are 120 cubic inches contained inside the box.

The volume of space occupied by a substance or item, or the space enclosed within a container.

Volume = L * B * H (unit^3)

Given length of the cuboid = 12 inches

Given breadth of the cuboid = 5 inches

Given height of the cuboid = 2 inches

Volume of cuboid = 12 * 5 * 2 = 120 inch^3

Hence there are 120 cubic inches contained inside the box.

Learn more about volume on:

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For this case we can express the rates as:

[tex]\frac {2.40} {12} * \frac {dollars} {pen} = 0.2 \frac {dollars} {pen}[/tex]

Option A

[tex]\frac {12} {2.40} * \frac {pen} {dollars} = 5 \frac {pens} {dollar}[/tex]

Option C

If the pen package contains 12, then the cost of the package is $2.40.

Option B

Answer:

Option A, B, C

Answer: 1, 2, and 3

Step-by-step explanation: I did the question

Answer:

The line which is parallel to the given line [tex]y=-\frac{\bf 4}{\bf 3}x+{\bf 1}[/tex] is [tex]y=-\frac{\bf 4}{\bf 3}x+{\bf 2}[/tex]

Step-by-step explanation:

Given that the equation of the line is

[tex]y=-\frac{4}{3}x+1\hfill (1)[/tex]

To find the equation of the line is parallel to the given line equation.

We know that the given equation is in the slope intercept form

y=mx+c where m is the slope and c is the intercept.

Compare with given equation(1) we get

[tex]m=-\frac{4}{3}[/tex]  and c=1

Now change the y intercept c=1 to a intercept of c= 2

Therefore (1) becomes

[tex]y=-\frac{4}{3}x+2[/tex]

The above equation of the line is the parallel line to the given equation of the line

Answer:

3x - 4y = -28

Step-by-step explanation:

Answer:

The required points of the given line segment  are ( - 1, - 5 ).

Step-by-step explanation:

Given that the line segment AB whose midpoint M is ( 3, -2 ) and point A is ( 7, - 9), then we have to find point B of the line segment AB -

As we know that-

If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and  ( [tex]x_{2}, y_{2}[/tex] ) then the mid points M are-  

M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex]  , [tex]\frac{ y_{1} + y_{2} }{2}[/tex] )

Here,

Let A ( 7, - 9 ), B ( x, y ) with midpoint M ( 3, - 2 ) -

then by the midpoint formula M are-

( 3, - 2 )  = (  [tex]\frac{7 + x}{2}[/tex] , [tex]\frac{ - 9 + y}{2}[/tex] )

On comparing x coordinate and y coordinate -

We get,

( [tex]\frac{ 7 + x}{2}[/tex] = 3  , [tex]\frac{- 9 + y}{2}[/tex]  = - 2)

( 7 + x = 6, - 9 + y = - 4 )

( x = 6 - 7, y = - 4 + 9 )

( x = - 1, y = -5 )

Hence the required points  A are ( - 1, - 5 ).

We can also verify by putting these points into Midpoint formula.

The expression that gives the number of bacteria after 3 hours is

500 x  1.2³.

Given,

The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour.

There were initially 500 bacteria.

We need to find an expression that gives the number of bacteria after 3 hours.

Suppose we have a number 3 that gets multiplied by 2 every 1 minute.

So in 3 minutes, we have,

3 x 2 = 6

6 x 2 = 12

12 x 2 = 24

We see that we need to multiply the previous answer by the required factor till the required number of times.

We have,

The initial number of bacteria = 500

The number of bacteria in a petri dish is multiplied by a factor of 1.2 every hour.

This means the number of bacteria after one hour:

= 500 x 1.2

= 600 bacteria

After two hours,

= 600 x 1.2

= 720 bacteria

After 3 hours

= 720 x 1.2

= 864 bacteria

The expression that gives the number of bacteria is 500 x [tex]1.2^{h}[/tex] where h is the number of hours.

Learn more about how to write expressions where the amount gets multiplied per hour here:

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The number of bacteria after 3 hours, given an initial count of 500 and a growth factor of 1.2 per hour, can be calculated as 500 × 1.2^3, resulting in 864 bacteria.

The number of bacteria in a petri dish growing exponentially can be modeled mathematically. If the number of bacteria is multiplied by a factor of 1.2 every hour, and we began with 500 bacteria, the expression for the number of bacteria after 3 hours can be found using exponential growth formula.

To find the number of bacteria after 3 hours, we would start with the initial amount of 500 bacteria and multiply it by 1.2 for each hour that passes. Therefore, after 3 hours, the expression would be:

Number of bacteria after 3 hours = Initial number × (growth factor)number of hours = 500 × 1.23

Using a calculator, we can compute this to find:

500 × 1.23 = 500 × 1.728 = 864

Thus, there would be 864 bacteria in the petri dish after 3 hours.

0+6/10+2/100+4/100

Hope this helped! (plz mark me brainliest)

Answer:

86/1

Step-by-step explanation:

Step-by-step explanation:

A line that passes through the origin is proportional (y = mx).  But a line that doesn't pass through the origin isn't proportional (y = mx + b).  So all proportional relationships are linear, but not all linear relationships are proportional.

proportional relationship is just a linear relationship where the line passes through the origin (0, 0).

What is the solution to the following equation?

х+ (-21) = 8

О А. x= 27

B. х = 29

с.   х = 13

D. х = 17

Option B

The solution to given equation is x = 29

Given that we have to find the solution of given equation

Given equation is x + (- 21 ) = 8

The value of the variable is found by adding, subtracting, multiplying or dividing both sides of the equation to simplify the equation and isolate the variable.

The goal is to have the variable on one side of the equation and numbers on the other.

From given equation,

x + ( -21) = 8

Let us first remove the brackets around -21

We know when we multiply a positive sign number with negative sign number, we get a negative sign number

x + 1( - 21 ) = 8

x - 21 = 8

Move -21 from L.H.S to R.H.S

x = 21 + 8

x = 29

Thus solution to given equation is x = 29 Thus Option B is correct

Answer:

Step-by-step explanation:

Answer:

[tex]12x+3y\leq 60[/tex]

Step-by-step explanation:

Let

x ----> the numbers of trophies you can buy

y ----> the numbers of medals  you can buy

we know that

The term "at most" means "less than or equal to"

so

The number of trophies multiplied by $12 plus the number of medals multiplied by $3 must be less than or equal to $60

The inequality that represent this situation is

[tex]12x+3y\leq 60[/tex]

[tex]3x + 12y\leq 60[/tex]

Step-by-step explanation:

Answer: 31.43 cm

Step-by-step explanation:

The length of an arc  is calculated using the formula:

[tex]\frac{theta}{360}[/tex] X 2[tex]\pi[/tex]r

where : theta is the angle in degree

r = radius

If the angle is given in Radian , the length can be calculated using the formula:

L = r∅

Since , the angle is given in degree , we will use the first formula.

L = [tex]\frac{theta}{360}[/tex] X 2[tex]\pi[/tex]r

L = [tex]\frac{120}{360}[/tex] X 2 X π X 15

L = [tex]\frac{1}{3}[/tex] X 2 X [tex]\frac{22}{7}[/tex] X 15

L = [tex]\frac{660}{21}[/tex]

L = 31.42857143

L ≈ 31.43 cm