A woman drives an SUV that gets 15 mi/gal (mpg). Her husband drives a hybrid that gets 65 mg. Every week, they travel the same number of miles. They want to improve their combined mpg. They
have two options on how they can improve it.
Option 1: They can tune the SUV and increase its mileage by 1 mpg and keep the hybrid as it is.
Option 2: They can buy a new hybrid that gets 80 mpg and keep the SUV as it is.
Which option will give them a better combined mpa?

The inequality is a < 10

Given that a number a is no more than 10, we need to find the inequality, showing the inequality,

Inequalities are the mathematical expressions in which both sides are not equal.

In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

For example = Olivia is selected in the 12U Softball. How old is Olivia? You don't know the age of Olivia, because it doesn't say "equals". But you do know her age should be less than or equal to 12, so it can be written as Olivia's Age ≤ 12.

This is a practical scenario related to inequalities.

So, the inequality will be =

a < 10

Plotting the inequality,

(check the file attached)

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The value of the interquartile range (IQR) of their scores is,

Interquartile range = 25

Since, WE know that;

A box plot is the 5 -number summary of the set of data.

And, 5 -number summary is name as, the first quartile, median, third quartile, minimum, and maximum.

We have to given that;

The box pot shows the points for the Houston Rockets scored last season.

Now, From given box plot,

First Interquartile = 65

Third Interquartile = 90

Hence, The interquartile range (IQR) of their scores is, difference between Third Interquartile and first Interquartile.

So, We can formulate;

Interquartile range = Third Interquartile - First Interquartile

Substitute the given values, we get;

Interquartile range = 90 - 65

Interquartile range= 25

Therefore, We get;

The interquartile range (IQR) of their scores is,

Interquartile range= 25

Which is difference between Third Interquartile and first Interquartile.

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The quadratic function is defined as follows:

p(x) = 2(x - 3)² - 1.

The quadratic function of vertex(h,k) is given by the rule presented as follows:

y = a(x - h)² + k

In which:

The vertex is the turning point of the quadratic function, where it changes from decreasing to increasing or vice-versa, hence it's coordinates are given as follows:

(3,-1).

Then:

p(x) = a(x - 3)² - 1.

When x = 0, p(x) = 17, hence the leading coefficient a is obtained as follows:

17 = 9a - 1

9a = 18

a = 2.

Hence the equation is:

p(x) = 2(x - 3)² - 1.

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Answer:

The additive inverse of A is -A. So, the additive inverse of A = [p q] is -A = [-p -q].

Here's how we can find the additive inverse of a matrix:

Find the additive inverse of each element in the matrix.

Replace each element in the matrix with its additive inverse.

For example, the additive inverse of p is -p. So, the additive inverse of the first element in A is -p.

The additive inverse of q is -q. So, the additive inverse of the second element in A is -q.

Plugging in these values, we get the following:

Additive inverse of A = [-p -q]

Step-by-step explanation:

Answer: £102.60

Step-by-step explanation:

79165-78937=228

228x45=10260

10260/100=102.60

The expression that shows the correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top would be = V = (3.14)(3.75)2(5). That is option B.

To calculate the volume of the cake mold needed, the formula for the volume of a cylinder should be used and it is given below;

Volume of cylinder = πr²h

radius = diameter/2 = 7.5/2 = 3.75

Height = 5cm

π = 3.14

Volume = 3.14×(3.75)²×5

Therefore the correct expression that will determine the volume of cake batter needed to fill the mold would be = Volume = 3.14×(3.75)²×5

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The best approximation of the volume of a sphere with a diameter of 12 units is approximately 904.78 cubic units.

The formula for the volume of a sphere is V = (4/3)πr^3, where V represents the volume and r represents the radius.

Given the diameter of 12 units, we can find the radius by dividing the diameter by 2: r = 12 / 2 = 6 units.

Now, we can substitute the radius into the volume formula:

V = (4/3)π(6^3)

 = (4/3)π(216)

 ≈ 904.78 cubic units

Using the approximation of π as 3.14, we can calculate the volume as follows:

V ≈ (4/3) * 3.14 * 216

 ≈ 904.78 cubic units

Therefore, the best approximation of the volume of the sphere with a diameter of 12 units is approximately 904.78 cubic units.

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[tex]D:\dfrac{4000}{x} > 0 \wedge x\not =0\\D:x > 0\\\\\\\log\left(\dfrac{4000}{x}\right)=3\\\e^3=\dfrac{4000}{x}\\\\x=\dfrac{4000}{e^3}[/tex]

Answer:

1111 in binary is 10001010111. Unlike the decimal number system where we use the digits 0 to 9 to represent a number, in a binary system, we use only 2 digits that are 0 and 1 (bits).

when k = 4, the function x + k/x will have a relative maximum at x = -2.

To find the value of k that will make x+k/x have a relative maximum at x=-2, we can use the first derivative test.

First, we find the derivative of x+k/x with respect to x:

f'(x) = 1 - k/x^2

Next, we set x = -2 and solve for k to make f'(-2) = 0:

f'(-2) = 1 - k/(-2)^2 = 1 - k/4

1 - k/4 = 0

k = 4

what is derivative?

A derivative is a mathematical concept that represents the rate at which a function changes over time or space. It is the slope of a tangent line to a curve at a particular point.

In other words, the derivative of a function f(x) at a point x=a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim[h→0] [f(a+h) - f(a)]/h

The derivative gives us information about how quickly the function is changing at a specific point.

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Answer:

 can be written as  without exponent.Given:To find:Write the given expression without exponent.Solution:Formula to be used:Step 1:Write the expanded form of given expression.Step 2:simplifyorThus, can be written as 125×y×y×y without exponent.Learn more:1) Let us simplify some more questions using the exponent rules. (i) (ii) ... brainly.in/question/196047402) find ( 46656)power of -1/6 brainly.in/question/4383230

Answer: 5y³ can be written without using exponents as 5y multiplied by itself three times:

5y × 5y × 5y

Alternatively, we can also write it as:

5 × y × y × y

The statement to be proved is that if (an)[infinity]n=1 is a bounded sequence and (bn)[infinity]n=1 converges to 0, then (anbn)[infinity]n=1 converges to 0 as well.

To prove this statement, we can use the squeeze theorem. Let M be a bound for the sequence (an)[infinity]n=1, i.e., |an| <= M for all n. Since (bn)[infinity]n=1 converges to 0, for any ε > 0, there exists an integer N such that |bn| < ε/M for all n ≥ N.

Now, for any n ≥ N, we have

|anbn| = |an||bn| ≤ M|bn| < ε,

where we used the fact that |an| ≤ M. This shows that (anbn)[infinity]n=1 converges to 0 as well, since the absolute value of each term is bounded by ε for n ≥ N.

In other words, we have shown that for any ε > 0, there exists an integer N such that |anbn - 0| < ε for all n ≥ N. This is the definition of convergence to 0, and so we have proven that (anbn)[infinity]n=1 converges to 0.

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To find the median of salaries of 5 doctors at a private practice, we need to arrange the salaries in order from smallest to largest. The median of these values, since there are 5 values, is the 3rd value which is $175,000.

The subject of your question is Mathematics, specifically the concept of the median in statistics.

The median of a set of numbers is found by arranging the numbers in order from least to greatest, and the median is the middle number in this arrangement.

Hence, in order to find the median of the given salaries, we first arrange them in ascending order: $110,000, $145,000, $175,000, $190,000, $190,000.

Since there are 5 doctors, which is an odd number of observations, the median is the 3rd number ($175,000) considering they are arranged in order from smallest to largest.

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Approximately 32.14% of the renters do not keep a pet.

We know that there are 28 units in the apartment complex. Out of these, 19 renters keep a pet. To calculate the number of renters who do not keep a pet, we subtract the number of renters with pets (19) from the total number of renters (28):

Number of renters without pets = Total number of renters - Number of renters with pets

Number of renters without pets = 28 - 19

Number of renters without pets = 9

Now that we have the number of renters without pets (9), we can calculate the percentage of renters who do not keep a pet. To do this, we divide the number of renters without pets by the total number of renters and multiply by 100:

Percentage of renters without pets = (Number of renters without pets / Total number of renters) × 100

Percentage of renters without pets = (9 / 28) × 100

Percentage of renters without pets ≈ 32.14%

Therefore, approximately 32.14% of the renters in the apartment complex do not keep a pet.

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Answer:

D. 42

Step-by-step explanation:

y=4x+10

substitute x=8

y=4(8)+10

y=32+10=42

Answer:

The answer is 42 cyclists

Step-by-step explanation:

y=4x+10

where,x=Temperature

y=cyclists

y=4x+10;when x=10

Y=4×8+10

y=32+10

y=42

this equation is only valid at the point (a, b) where we found the slope of the normal line. To find the equation of the normal line at a different point, we would need to repeat this process with new values of a and b.

To find the equation of the line normal (perpendicular) to the graph of y = x^3 + 3x^2 + 7x - 1 at a point (a, b), we need to determine the slope of the normal line at that point.

The slope of the tangent line to the curve at (a, b) is given by the derivative:

f'(x) = 3x^2 + 6x + 7

So the slope of the tangent line at x = a is:

m = f'(a) = 3a^2 + 6a + 7

The slope of the normal line is the negative reciprocal of the slope of the tangent line, so:

m_n = -1/m = -1/(3a^2 + 6a + 7)

Now we have the slope of the normal line at (a, b), and we just need to find the equation of the line in point-slope form, using the point (a, b):

y - b = m_n(x - a)

Substituting the expression for m_n, we get:

y - b = (-1)/(3a^2 + 6a + 7)(x - a)

Multiplying both sides by 3a^2 + 6a + 7 to eliminate the fraction, we get:

(3a^2 + 6a + 7)(y - b) = -(x - a)

Expanding and rearranging, we get the equation of the line normal to the graph of y = x^3 + 3x^2 + 7x - 1 at (a, b):

(3a^2 + 6a + 7)y = -x + (3a^2 + 6a + 7)b + a

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The radius of the cone to the nearest inch is equal to 8.0 inches.

In Mathematics and Geometry, the surface area (SA) of a cone can be calculated by using this mathematical expression:

Surface area (SA) of a cone = πr(l + r)

Where:

By substituting the given parameters into the formula for the surface area (SA) of a cone, we have the following;

364 = 3.14 × r(6.5 + r)

115.92 = 6.5r + r²

r² + 6.5r + 115.92 = 0

By solving the quadratic function, we have:

Radius, r = (-20.41 + √4988.4081)/6.28

Radius, r = 7.9966 ≈ 8.0 inches.

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The coordinates of the point on the graph are (0, -7).

We have,

The concept being used here is the Cartesian coordinate system, which is a system for representing points in a two-dimensional space.

In this system, each point is described by an ordered pair (x, y), where x represents the position along the horizontal x-axis, and y represents the position along the vertical y-axis.

The coordinates are always in an ordered pair.

i.e

(x, y)

Where x is the value of the x-axis and y is the value of the y-axis.

We see that,

The point lies in (0, -7)

Thus,

The coordinates of the point on the graph are (0, -7).

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One possible transformation is a reflection in the x-axis followed by a dilation centered at the origin with a scale factor of 3.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

Before the dilation, the figure was reflected from the first quadrant to the second quadrant, which is a lateral reflection, hence the figure was reflected over the x-axis.

The height of the blue triangle is of 1 unit, while the height of the larger triangle is of 3 units, hence the scale factor is given as follows:

k = 3/1

k = 3.

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The solution is, in the drop down activity, you should listen to each sentence and determine whether the verb is a form of "ser" or "ir" based on the context and conjugation of the verb.

The verb "ser" means "to be" and is used to describe characteristics, professions, and origins. The verb "ir" means "to go" and is used to indicate movement or direction. To determine whether a verb in a sentence is a form of "ser" or "ir", you should look at the context of the sentence and the conjugation of the verb. If the verb is conjugated in a way that indicates it is a form of "ser", then it is likely a form of "ser". If the verb is conjugated in a way that indicates it is a form of "ir", then it is likely a form of "ir".

For example, in the sentence "Ella es bonita" (She is pretty), the verb "es" is a form of "ser" because it is used to describe a characteristic. In the sentence "Voy a la playa" (I'm going to the beach), the verb "voy" is a form of "ir" because it is used to indicate movement or direction.

In conclusion, to answer the questions in the drop down activity, you should listen to each sentence and determine whether the verb is a form of "ser" or "ir" based on the context and conjugation of the verb.

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complete question:

1 - escogerdrop down activity 1 attempt left listen to each sentence and indicate whether the verb is a form of ser or ir. questions

To find the point of intersection between the two lines represented by the given equations, we can solve the system of equations simultaneously.

The given equations are:

1) X + Y = 2

2) Y = (1/2)X + 5

We can solve this system by substituting the value of Y from the second equation into the first equation. Let's proceed with the substitution method:

Substitute Y = (1/2)X + 5 into the first equation:

X + (1/2)X + 5 = 2

Combine like terms:

(3/2)X + 5 = 2

Subtract 5 from both sides:

(3/2)X = -3

Multiply both sides by 2/3 to isolate X:

X = -2

Now, substitute the value of X back into the second equation to find Y:

Y = (1/2)(-2) + 5

Y = -1 + 5

Y = 4

Therefore, the lines represented by the given equations intersect at the point (-2, 4).

The matching based on the information given will be:

A composite number is a positive integer greater than 1 that has at least one factor other than 1 and itself. In other words, it is a number that can be divided by more than just 1 and itself, such as 4.

The least common denominator (LCD) is the smallest number that two or more denominators can be multiplied by to obtain a common denominator.

Categorical data is data that can be sorted into categories or groups based on non-numerical criteria. For example, the colors of cars on a parking lot or the types of pets in a household are both categorical data.

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Answer:

Step-by-step explanation:

Your welcome

Answer:

8 meters

Step-by-step explanation:

4(16)=64

They have the same area so the area of the square is also 64.

x^2=64

x=8

The dimension of the new picture frame is around 51.49 cm by 61.49 cm in size.

Given that,

The measure of rectangular  picture = 20 cm x 30 cm

And the resulting enclosed area = 1064 cm²

Let the length of each side = x

Therefore,

The new rectangular frame will have dimensions = 20 cm + x, 30 cm + x

The new rectangular frame's surface area is:

= (20 + x) x (30 + x).

Since area is given,

So that we can create an equation:  1064 = (20 cm + x) x (30 cm + x)

Increasing the brackets results in: 600 + 50x + x² = 1064

Organizing and making it simpler: x² + 50x - 464 = 0.

By using quadratic formula,

x = (-50 ± 174.96) / 2

Neglecting the undesirable outcome,

x = 62.98 / 2 x = 31.49

Consequently, each side length has increased by around 31.49 cm.

Use this value to determine the new rectangular frame's dimensions:

Length is equal to 20 + 31.49 = 51.49 cm.

Width is equal to 30 + 31.49 = 61.49 cm.

Consequently, the new picture frame is around 51.49 cm by 61.49 cm in size.

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Answer:

8.4

Step-by-step explanation:

C^2-B^2=A^2

12.3^2=151.29

9^2=81

151.29-81=70.29

square root of 70.29

is 8.38

Rounded to the nearest tenth is

8.4 or B

The cost equation is used to estimate total costs associated with a given level of activity or output, where f is the fixed cost and v is the variable cost per unit of activity. The variable cost component (vx) changes in proportion to the level of activity or output (x), whereas the fixed cost component (f) remains constant regardless of the level of activity.

In the cost equation tc = f + vx, x is best described as the level of activity or the quantity of the input variable. The cost equation is a mathematical representation of the relationship between the total cost of production and the level of activity or the quantity of the input variable. The variable x represents the number of units produced or the amount of resources used in the production process, which can be measured in terms of labor hours, machine hours, or any other relevant unit of measure. The variable v represents the variable cost per unit of activity, and f represents the fixed cost of production.

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The answer to the question is 32/52 = 8/13.

There are 52 cards in a deck in total.

Of those 52 cards, there are four different suits (diamonds, hearts, clubs, spades).

There are 13 cards in each of the different suits. Also, there are 3 face cards in each of the different suits (therefore, there are 12 face cards in total).

Diamonds and Hearts are red cards (there are 26 total red cards) and

Clubs and Spades are black cards (there are 26 total black cards).

There are 26 black cards and 12 face cards in total.

However, of those 26 black cards, there are 6 face cards. That means there are

26+12-6 = 32 cards in total that are either a black card or a face card, but not both.

That means the answer to the question is 32/52 = 8/13.

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