kari is buying aa batters and d batteries. the store sells aa batteries in packs of 6 and d batteries in packs of 10. if kari wishes to buy the same number of aa and d batteries, what is the smallest number of each battery type that she can buy

We can solve the inequality |8x - 7| < 9 to get the compound inequality:

-1/4 < x < 2

Here we have an absolute value inequality:

|8x - 7| < 9

The absolute value part can be "broken" into two parts, these are:

(8x - 7) < 9

(8x - 7) > -9

Now we need to solve these two.

The first one gives:

8x - 7 < 9

8x < 9 + 7

8x < 16

x < 16/8

x < 2

The other gives:

(8x - 7) > -9

8x > -9 + 7

8x > -2

x > -2/8

x > -1/4

Then we have the compound inequality:

-1/4 < x < 2

Learn more about inequalties at:

https://brainly.com/question/24372553

#SPJ1

Therefore , the solution of the given problem of expression comes out to be  there is no value of x which can make equation true.

Mathematical operations like addition, multiplication, variables and proliferation, and division are necessary. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and operations like additions, subtraction, multiplication, and division are all included in a statement of fact. Different sentences and words can be contrasted and compared.

Here,

Given :

Expression  is :

=> (1/64)ˣ / 2 + 1 = (1/16)ˣ / 3  -3

=>  (1/64)ˣ / 2 + 4 = (1/16)ˣ / 3

=> ( (1/64)ˣ  + 8  ) / 2  = (1/16)ˣ / 3

=> (1/64)ˣ  + 8   = (1/16)ˣ 2 / 3

=> (1/4)³ˣ + 8 = (1/4)²ˣ * 2/3

=> 8 = (1/4)²ˣ ( 2/3 + (1/4)ˣ )

So,

We found that there is no value of x which can make equation true.

Therefore , the solution of the given problem of expression comes out to be  there is no value of x which can make equation true.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that  the tests are out of twenty points, and she has gotten the following scores. 17, 19, 20, 14, 16

The mode of a set of data is the value that occurs most frequently. In this case, Danielle's scores are: 17, 19, 20, 14, 16.

There is no mode value.

Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average.

Hence, Danielle would most likely use the mean as a central tendency to describe her test scores because the mean would be her average.

To learn more on Statistics click:

https://brainly.com/question/29093686

#SPJ1

The inequality equations of each an one described briefly with graphs.

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. The characters >, < , ≥ , or ≤ are used to denote an inequality, when the two expressions aren't always equal.

1.

y > 3x - 17

y ≤ - 4x + 11

The graph of the above inequality equations shown below:

2.

4x + 4y > - 40

-5x + 5y < 10

The graph of the above inequality equations shown below:

3.

x + 3y ≥ 31

4x - 2y > -2

The graph of the above inequality equations shown below:

4.

5x + y < 3

5x + y > 37

The graph of the above inequality equations shown below:

To know more about inequality equations refer to:

https://brainly.com/question/24372553

#SPJ1

The probability of getting at least one question wrong on a 7 question multiple-choice test with two answers for each question is 1 - (1/4)^7, which is approximately 99.2%.

The probability of getting one question wrong on a 7 question multiple-choice test with two answers for each question is 1/4. This is because there are two options for each question, and if you choose the wrong one, you get the question wrong. Therefore, the probability of getting all 7 questions wrong is (1/4)^7, or one in 16,384. The probability of getting at least one question wrong on the test is 1 - (1/4)^7, which is equal to 1 - 1/16,384, or approximately 99.2%. To calculate the probability of getting at least one question wrong, you subtract the probability of getting all 7 questions correct from 1. This is because if you do not get all 7 questions correct, then you must have gotten at least one question wrong.

The complete question: On a 7 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong? Give your answer as a fraction

Learn more about probability here

https://brainly.com/question/30034780

#SPJ4

The equation be x²(x + y)³ - 2xy²(x + y)² then the factorization be x(x + y)²(x - y)(x + 2y).

In mathematics, the term "factorization" or "factoring" refers to the splitting apart or "factoring" of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together yield the original number, matrix, etc.

Factoring is a useful skill in real life. Examples of typical uses include splitting something into equal portions, exchanging money, comparing costs, understanding time, and performing calculations while traveling.

Let the equation be x²(x + y)³ - 2xy²(x + y)²

Factor out common term [tex]$x(x+y)^2= x(x+y)^2\left(x(x+y)-2 y^2\right)$[/tex]

[tex]$=x(x+y)^2\left(x(x+y)-2 y^2\right)$$[/tex]

Expand [tex]$x(x+y)-2 y^2= x^2+x y-2 y^2$[/tex]

simplifying the above equation, we get

[tex]$=x(x+y)^2\left(x^2+x y-2 y^2\right)$$[/tex]

Factor [tex]$x^2+x y-2 y^2=(x-y)(x+2 y)$[/tex]

= x(x + y)²(x - y)(x + 2y)

Therefore, the factorization be x(x + y)²(x - y)(x + 2y).

To learn more about factorization refer to:

https://brainly.com/question/25829061

#SPJ1

Table A of conditional percentages answers the question of whether the region where one lives affects whether or not one has health insurance.

Table A is the appropriate table of conditional percentages to discover if one's region of residence influences if they have health insurance.

Table A provides the overall percentage of individuals who are insured and uninsured in each region of the country. It gives a clear picture of the proportion of people in each region who have health insurance coverage. The data in this table allows us to compare the percentage of uninsured individuals across different regions.

In contrast, Table B provides the percentage of uninsured individuals among the total number of insured and uninsured individuals in each region. This type of table does not give us a clear understanding of the overall proportion of insured and uninsured individuals in each region.

Table C provides the percentage of uninsured individuals among the total population in each region. However, it does not provide a clear picture of the proportion of insured individuals in each region, which is crucial information to determine if the region where one lives affects whether or not one has health insurance.

Learn more about conditional percentages here:

https://brainly.com/question/10902860

#SPJ4

Complete Question: Table image has been uploaded.

Answer: 5

Step-by-step explanation:

Using order of operations, you multiply 1 and 3 first to get 3. Then you add 1 to it to get 4. Then add 4 to get 8 and subtract 3 to get 5.

Answer: 5

To solve this equation we must do PEMDAS.

Parentheses, Exponents, Multiply, Divide, Addition, Subtract.

There is no Paratheses, or Expenonets so first we divide 1 by 3.

Our equation would now be

1+3+4-3.

Next we Divide, once again there is no division so we move on to addition. The firs thing we add is 1+3, which is 4. Then 4 plus 4 which 8.

Our eqatuion would now be

8-3

Lastly we subtract 8-3 is 5

This means our answer is 5.

I hope this helps & Good Luck <3!!!

According to the information, it can be inferred that the F bacterium had a greater growth over time. Additionally, the population of G si will exceed the population of F because it has an x exponent.

The functions express the relationship between the number of bacteria and time. In accordance with the above, the function of the bacterium A, expresses that the number of bacteria grows 36 individuals every hour.

On the other hand, the function of B expresses that the individuals grow exponentially in 3. According to the above, at some point the exponent of 3 will be so great that it will be able to exceed the number of individuals of A. (not in the first four hours).

Learn more about mathematical functions in: https://brainly.com/question/12195089

#SPJ1

The inverse function of g(x) is:

f(x) =  (x - 2)^(2/3) + 3

Two functions are inverses if their composition is equal to the identity, then if f(x) is the inverse of our function, we must have that:

g( f(x) ) = x

Here we know that:

g(x) = (x - 3)^(3/2) + 2

Evaluating this in f(x) we should get:

g( f(x) = (f(x) - 3)^(3/2) + 2  = x

Now we can solve that for f(x).

(f(x) - 3)^(3/2) + 2  = x

( (f(x) - 3)^(3/2) =  x - 2

f(x) - 3 = (x - 2)^(2/3)

f(x) =  (x - 2)^(2/3) + 3

That is the inverse function.

Learn more about inverse functions at:

https://brainly.com/question/14391067

#SPJ1

The value of x include the following: B. 52/3.

In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.

By applying the basic proportionality theorem to the given triangle, we have the following:

3x/4x = (3x + 7)/(5x - 8)

By cross-multiplying, we have the following:

3x(5x - 8) = 4x(3x + 7)

15x² - 24x = 12x² + 28x

3x² = 52x

3x = 52

x = 52/3.

Read more on basic proportionality theorem here: brainly.com/question/3213812

#SPJ1

Answer:

Step-by-step explanation:

[tex]5\frac{1}{2}=\frac{11}{2}\\\mathrm{So\:this\:becomes}\\2x-\frac{1}{2}=\frac{11}{2}\\\mathrm{Then,}\\(2x+\frac{-1}{2})+\frac{1}{2}=(\frac{11}{2})+\frac{1}{2}\\2x+\frac{(-1+1)}{2}=(\frac{11}{2})+\frac{1}{2}\\2x+\frac{0}{2}=(\frac{11}{2})+\frac{1}{2}\\\mathrm{Reduce}\\2x+0=(\frac{11}{2})+\frac{1}{2}\\2x=(\frac{11}{2})+\frac{1}{2}\\2x=\frac{(11+1)}{2}\\\mathrm{11+1=12,\:so}\\2x=\frac{12}{2}\\\mathrm{Prime-factorization}\\2x=\frac{(6\times 2)}{(1\times 2)}[/tex]

[tex]\mathrm{6\times2=12\:and\:1\times2=2\:so\:\frac{12}{2}\:equals\:6,}\\2x=6\\\mathrm{Now,\:divide\:by\:the\:leading\:term,\:2}\\\frac{(2x)}{2}=\frac{6}{2}\\\mathrm{Factorization}\\x=\frac{(3\times 2)}{(1\times 2)}\\\mathrm{3\times2=6\:and\:1\times2=2\:so\:\frac{6}{2}\:equals\:3,}\\x=3[/tex]

Hope this helps.

The solution to the equation 2x - 1/2 = 5 1/2 is x = 3.

Given Equation: 2x - 1/2 = 5 1/2

Step 1: Let's simplify the mixed number 5 1/2 to an improper fraction. 5 1/2 can be written as (11/2).

2x - 1/2 = 11/2

Step 2: To eliminate the fraction, multiply the entire equation by 2 to clear the denominators:

2  (2x - 1/2) = 2 (11/2)

This simplifies to:

4x - 1 = 11

Step 3: Add 1 to both sides of the equation to isolate the variable:

4x - 1 + 1 = 11 + 1

4x = 12

Step 4: Divide both sides of the equation by 4 to solve for x:

(4x)/4 = 12/4

x = 3

Therefore, the solution is x = 3.

Learn more about Equation here:

https://brainly.com/question/29538993

#SPJ6

The solution to the perimeter is 6.4 feet

From the question, we have the following parameters that can be used in our computation:

Side length = 1.6 ft

Shape = Square

Using the above as a guide, we have the following:

Perimeter = 4 * Side length

Substitute the known values in the above equation, so, we have the following representation

Perimeter = 4 * 1.6 ft

Evaluate

Perimeter = 6.4 ft

Hence, the perimeter is 6.4 ft

Read more about perimeter at

https://brainly.com/question/24571594

#SPJ1

Complete question

2) Determine the perimeter of a square with side length 1.6 ft

what is the answer​

The scatter plot is given in the attached image below.

The correct option is D.

The straight line on a scatter plot closest to the points is called a trend line. Two points on a trend line can create an equation in slope-intercept form.

Given:

The data are shown in the table.

From the table:

When the value of x = 1, then y = 11.

And when x = 3, then y = 30.

Similarly, all the values are placed as per the data.

The scatter plot is given in the attached image.

Therefore, the plot is given below.

To learn more about the trend line;

brainly.com/question/22722918

#SPJ1

Malik's mixed number is not correct and he needs to revise it to match the correct answer of 3 3/5.

A mixed number is a combination of a whole number and a fraction. It is written as a whole number followed by a fraction.

In Malik's case, the answer he found was 3 3/5, which means three and three fifths. However, he wrote the answer as 6 3/5, which means six and three fifths.

When adding a whole number and a fraction, the final result must still be a mixed number, with the whole number part representing the sum of the whole numbers and the fraction part representing the sum of the fractions.

In this case, adding 3 and 3/5 does not result in 6 and 3/5. To see this, we need to simplify the fractional part.

Dividing 5 by 5 gives us 1, so the fractional part of 3 3/5 is 1 3/5.

Adding 3 to the whole number part and 1 3/5 to the fractional part, we get 4 1/5, not 6 3/5.

Complete Question:

Malik solved a problem that had an answer of 3 3/5. He wrote his answer as the mixed number 6 3/5. Is his mixed number correct? Explain

To know more about mixed number here.

https://brainly.com/question/24137171

#SPJ4

Answer:

Graph of polynomial of 2nd degree,i.e,X^2

Step-by-step explanation:

The volume of cuboid with dimensions 9cm × 4cm × 5cm is 180 cm³

We know that the formula for the volume of the cuboid is:

V = l × w × h

where, V is the volume of the cuboid

l is the length of the cuboid

w is the  width of the cuboid

and h is the height of the cuboid

Here, the length of the cuboid is l = 9 cm,

the width of the cuboid is w = 4 cm

and the height of the cuboid is h = 5 cm

Using above formula,

V = l × w × h

V = 9 × 4 × 5

V = 180 cubic cm

Therefore, the required volume is 180 cubic centimeters

Learn more about the volume of cuboid here:

https://brainly.com/question/29568631

#SPJ4

Answer:

x = 48.6°

Step-by-step explanation:

see photo for explanation

The average amount of corn produced per acre represented in scientific notation is, 1.6 × 10² bushels per acre.

Scientific notation is a way of writing a very large or very small numbers. For example; 230,000,000 can be written in scientific notation as 2.3 x 10⁸.

Given that;

Nelly owns farm land that has an area of 4.2 × 10² acres. Each year, the farm produces 6.72 × 10⁴ bushels of corn.

Hence, The average amount of corn produced per acre is,

⇒ 6.72 × 10⁴ ÷ 4.2 × 10²

⇒ 6.72 × 10⁴ / 4.2 × 10²

⇒ 1.6 × 10²

Thus, The average amount of corn produced per acre represented in scientific notation is, 1.6 × 10² bushels per acre.

Learn more about the scientific notation visit:

brainly.com/question/1767229

#SPJ1

Consequently, when a1 is provided as 3 and the expression for the following term is a = 5an-1 + 1, the value of a5 is 2031.

An algebraic progression is when there is a continual difference between terms that follow each other in an series. For illustration, the decimal number 5, 7, 9, 11, 13, and 15 is an example of an algebraic expression with a tolerance of two. A advance with a set tolerance among any two consecutive numbers is referred to as a "arithmetic progression" (A.P.). Two types of algebraic progression are plausible: series in mathematics with a finite length A finite geometric evolution is a series with just a finite number of terms. The early, late, allowance, and frequency of terms may all be calculated using the terms in the series.

given

a1 = 3

a2 = 5 * 3 + 1 = 16

a3 = 5 * 16 + 1  = 81

a4 = 5* 81 + 1 = 406

a5 = 5* 406 + 1 = 2031

Consequently, when a1 is provided as 3 and the expression for the following term is a = 5an-1 + 1, the value of a5 is 2031.

To know more about arithmetic progression visit:

https://brainly.com/question/16947807

#SPJ1

The graph represents the function that maps the area of the original figure to the area of the dilated figure. If the original area is 9 square units and the dilated area is x square units, then the equation y = √√x represents the relationship between the two areas. Points (B), (F), (G), and (H) are on the graph because they satisfy the equation y = √√x. Points (A), (C), and (E) are not on the graph because they do not satisfy the equation.

The probability that this ball is red after the jar is then shaken and one ball is randomly selected is 11/18.

There are four red balls and two white balls in a jar

P(white removed and then red is chosen)'

P = 2/6 * 5/6

= 10/36

P= 5/18

Probability that the white removed and then red is chosen is 5/18.

P(red removed and then white is chosen)

P = 4/6 * 1/2

= 4/12

= 1/3

P = 6/18

Probability that the red removed and then white is chosen is 6/18.

The probability that this ball is red,

P(red is chosen) = 5/18 +6/18 = 11/18

Therefore, The probability that this ball is red is 11/18.

Learn more about Probability:

https://brainly.com/question/22499802

#SPJ4

Answer:

Let's call the two numbers x and 5x. We know that their difference is 1016:

5x - x = 1016

Expanding and solving for x:

4x = 1016

x = 254

So, the two numbers are 254 and 5 * 254 = 1270. These are the two numbers that have a difference of 1016 and satisfy the given condition.

Step-by-step explanation:

Answer:

1+5x=1016

Step-by-step explanation:

Answer:

B(1,-2)

Step-by-step explanation:

b is the answer from the above explanation

The top of the ladder slips down the wall at the rate of 5.6 ft/sec.

What is a rate?

The ratio of two related quantities expressed in several units is known as a rate. The numerator of the ratio indicates the rate of change in the other (dependent) variable if the denominator of the ratio is written as a single unit of one of these quantities, and if it is assumed that this quantity may be modified systematically (i.e., is an independent variable).

Here, we have

Given: A ladder 15ft in length leans against a vertical wall, with the bottom of the ladder 5ft from the wall on the horizontal floor. If at that time the bottom end of the ladder is being pulled away at the rate of 2ft/s .

Let: x = the distance from the base of the ladder to the base of the wall

y = the distance from the tip of the ladder to the base of the wall, we have:

x² + y² = 15²

y² = 15² - 5² = 225 - 25 = 200 => y = 14.14 ft

2x dx/dt + 2y dy/dt = 0

2 * 5 * dx/dt + 2 * 14.14 * (-2) = 0

10 dx/dt = 56.56

dx/dt = 5.6 ft/sec

Hence, the top of the ladder slips down the wall at the rate of 5.6 ft/sec.

To learn more about the rate from the given link

https://brainly.com/question/25793394

#SPJ1

The surface area and weight of the cylinder is 45.1805 in² and 11.107 lbs respectively.

A cylinder is a three-dimensional geometric shape that has two parallel circular bases and a curved lateral surface connecting the bases. The bases are located at opposite ends of the cylinder, and they have the same diameter. The lateral surface is a rectangle that has been bent around the circumference of the circular bases.

The height of a cylinder is the distance between the two bases, and the diameter of the bases is the distance across the circle through its center. The volume of a cylinder can be calculated by multiplying the area of one of its bases by its height. The formula for the volume of a cylinder is:

V = πr²h

where r is the radius of the circular base and h is the height of the cylinder.

Cylinders are commonly used in many real-world applications, such as in the design of pipes, cans, and other containers. They are also commonly used in mathematics and physics, where they can serve as models for objects with cylindrical symmetry, such as pipes and wires.

In summary, a cylinder is a three-dimensional shape with two parallel circular bases and a curved lateral surface connecting the bases. The height of the cylinder is the distance between the bases, and its volume can be calculated using the formula V = πr²h. Cylinders are commonly used in real-world applications and in mathematics and physics.

The following formula can be used to determine the cylinder's volume:

V = π × r² × h = π × (d/2)² × h = π × (1.35²) × 7.45 = 42.63374 in³

The following formula can be used to get the cylinder's surface area:

A = 2πr² + 2πrh = 2π × r² + 2π × r × h = 2π × (1.35²) + 2π × 1.35 × 7.45 = 45.1805 in²

The cylinder's weight can be determined using the formula below:

W = d × V = 0.259 lbs/in³ × 42.63374 in³ = 11.107 lbs.

To know more about area visit:

https://brainly.com/question/12187609?referrer=searchResults

#SPJ1

The probability of winning a prize worth more than the price of playing the game is 38%.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of samples

Given that the percentage of the winning price is:-

Toy = 25%

Soda = 25%

Candy = 37%

Mega win = 13%

The probability of winning a prize worth more than the price of playing the game is calculated as:-

P = ( 25 + 13 ) x 100 / 100

P = 0.38 x 100

P = 38%

Therefore, the probability will be 38%.

To know more about probability follow

https://brainly.com/question/24756209

#SPJ1

G(2, -6) is reflected in the line y=-2, the image is located at G' is (2, 2).

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given that, G(2, -6) is reflected in the line y=-2.

Since y=-2 is a horizontal line, the reflection will be vertical

So (2,-6) will reflect down 6 spaces vertically.

-6 + (4×2) = (-6 + 8) = 2  

Therefore, when we establish 4 below the line we just apply ×2 as a double as its across the line each side of the line to find that below the line = 4 = 4×2 and add it to -6

Therefore, G(2, -6) is reflected in the line y=-2, the image is located at G' is (2, 2).

To learn more about the reflection over y-axis visit:

https://brainly.com/question/15175017.

#SPJ1

The solution to the system of equations in this problem is given as follows:

x = 1.16, y = 3.71.

The system of equations for this problem is defined as follows:

Multiplying the first equation by 2, we have that:

x + 4y = 16

x = 16 - 4y.

Replacing into the second equation, the solution for y is obtained as follows:

3(16 - 4y) - 0.67y = 1

48 - 12y - 0.67y = 1

12.67y = 47

y = 47/12.67

y = 3.71.

Then the solution for x is of:

x = 16 - 4(3.71)

x = 1.16.

More can be learned about a system of equations at https://brainly.com/question/30584901

#SPJ1

Vito can not use same amount of water for 40 flower pots, as it would take 15 liters of water.

Vito uses 9 liters of water 24 flower pots.

To find: the amount of liters of water (w) it would take to water 40 flower pots.

This means, 9 liters is to 24 pots as w liters is to 40 pots

We write above statement as :

9:24::w:40

So, we get an a proportion,

9/24 = w/40

We solve above equation for w.

24w = 9(40)

24w = 360

w = 360/24

w = 15 liters

Therefore, 15  liters of water it would take to water 40 flower pots.

Learn more about the proportion here:

https://brainly.com/question/29774220

#SPJ4

The complete question is:

Vito uses 9 liters of water 24 flower pots. He is wondering how many liters of water (w) it would take to water 40 flower pots. He assumes he'll use the same amount of water on each pot. Which portion could Vito use to model this situation? Solve the proportion how many liters of water it takes to water 40 flower pads