Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.5 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less.

Write an inequality to determine the number of days Diego’s father can drive the car before the warning light comes on. Use t as your variable.

Answer:

total area = 18.28 in.^2

perimeter = 16.28 cm

Step-by-step explanation:

Area:

The total area of the figure is the sim of the area of the rectangle and the area of the semicircle.

total area = LW + (1/2)(pi)r^2

total area = (4 in.)(3 in.) + (1/2)(3.14)(2 in.)^2

total area = 12 in.^2 + 6.28 in.^2

total area = 18.28 in.^2

Perimeter:

The perimeter of the figure is the sum of the lengths of the left side, bottom side, and right side of the rectangle and the circumference of the half circle.

perimeter = 3 cm + 4 cm + 3 cm + (1/2)(pi)d

perimeter = 10 + (1/2)(3.14)(4 cm)

perimeter = 10 + 6.28 cm

perimeter = 16.28 cm

Answer:

Bob has 3 apples

.......

Answer:

40 apps in a minute!

The correct option is c: 46lb x (16 oz / 1lb). Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

The same attribute is expressed using a unit conversion, but in a different measurement unit. For example say, time can be mentioned in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Measurements are frequently offered in one set of measurements, like feet, but are required in another set, like chains. A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.

Given data:

ratio of ounces to pounds = 16:1

16 ounce / 1 pound

Let the weight of dog in ounce be 'x'.

weight of dog in pounds = 46 pounds.

ratio : x ounce /  46 pounds

Equating both ratios:

16 ounce / 1 pound = x ounce /  46 pounds

Cross multiplying:

x = 16*46  ounce

x = 736 ounce

The correct option is c: 46lb x (16 oz / 1lb)

Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

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Complete question is-

The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight

ounces. Which ratio shows the conversion to ounces?

The full question is attached.

The infinite sum of the given alternating series is equal to square root(3)/2 - 1/2 - (1/2) * square root(3)/2 = -1/2 - (1/2) * square root(3).

The given alternating series can be written as the sum of terms in the form \((-1)^n * (5pi)^(2n+1) / ((6^(2n+1)) * (2n+1)!)\). To find the infinite sum of this series, we substitute x = 5pi into the general formula of the alternating series.

Plugging x = 5pi into the formula, we have:

\((-1)^0 * (5pi)^(2(0)+1) / ((6^(2(0)+1)) * (2(0)+1)!) + (-1)^1 * (5pi)^(2(1)+1) / ((6^(2(1)+1)) * (2(1)+1)!) + (-1)^2 * (5pi)^(2(2)+1) / ((6^(2(2)+1)) * (2(2)+1)!) + ...\)

Simplifying the terms, we get:

\((5pi)/6! - (5^3pi^3)/(6^3 * 3!) + (5^5pi^5)/(6^5 * 5!) - ...\)

This pattern continues for each term.

The resulting infinite sum can be written as:

\((-1/2) * (1 - (5pi)^2/(6^2 * 2!) + (5pi)^4/(6^4 * 4!) - ...)\)

To evaluate this expression, we recognize that it represents the Taylor series expansion of cosine function evaluated at 5pi. Therefore, the infinite sum is equal to cos(5pi).

Using the trigonometric identity cos(5pi) = -1/2, we find that the infinite sum is equal to -1/2.

So, the infinite sum of the given alternating series is -1/2.

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Answer:

f(x) = x² - 6x

g(x) = (x³)² = x^6

( f o g) x

Wherever you see x in f(x) replace it by g(x)

That's

( f o g)(x) = (x^6)² - 6(x^6)

= x^12 - 6x^6

Hope this helps

Answer:

Probability=

(number if outcomes favourable)/(total number of outcomes)

Therefore P(no red/green)=1-(8/21+6/21)

=1-(8+6)/21=1-14/21=(21×1-14)/21=(21-14)/21

=7/21=1/3 ans

Step-by-step explanation:

Answer: its -11

Step-by-step explanation:

27-38 = -11

Answer:

I think the question is incomplete but i can say you something about it.

Step-by-step explanation:

To find the values of tanX, sinX, and cosX in a right triangle with side lengths a, b, and c, where c is the hypotenuse and X is the angle opposite to side a, we can use the following trigonometric ratios:

tanX = a/b

sinX = a/c

cosX = b/c

For example, if a = 3, b = 4, and c = 5, then the angle X opposite to side a is a right angle, and we can calculate:

tanX = a/b = 3/4 = 0.75

sinX = a/c = 3/5 = 0.6

cosX = b/c = 4/5 = 0.8

a). To maximize production within the budget, 600 units of labor and 100 units of capital should be purchased. b). The maximum production under the budgetary constraint is approximately 8,366 units.

a). To maximize production, we need to allocate the budget efficiently between labor and capital. We can calculate the number of units of labor and capital by dividing the budgeted amount by the cost per unit. The budget of $576,000 divided by the cost of labor per unit ($400) gives us 1,440 units of labor. Similarly, dividing the budget by the cost of capital per unit ($2,400) gives us 240 units of capital. However, this allocation does not maximize production within the budgetary constraint.

b). To find the optimal allocation, we can use the partial derivatives of the production function with respect to L and K. Taking the partial derivative of the production function with respect to L, we get 37.5L^(-0.25)K^0.25. Equating this to the budgeted amount of labor (600 units), we can solve for K, which comes out to be 100 units. Similarly, by taking the partial derivative of the production function with respect to K, we get 12.5L^0.75K^(-0.75). Equating this to the budgeted amount of capital (100 units), we can solve for L, which comes out to be 600 units.

By substituting these values into the production function, we can calculate the maximum number of units of production, which is approximately 8,366 units.

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Answer:

B)30°

hope it helps....

Answer:

9.8 gallons

Step-by-step explanation:

1900÷140=13.5714285714

round up to 14

0.7x14=9.8

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer:

YA isn't an angle bisector since it doesn't divide <XYZ into two perfectly half angles .<XYA doesn't equal to <AYZ .

<XYA & <AYZ . are approximately congruent within one degree .

The general equation of a line is y = mx+b, m being the slope and b the intercept on the y-axis.

We are given the line 7y-4x=-14, let's organize the equation like the general form:

In order to be parallel to your line, a line has to have the same slope as your line. So the slope has to be 4/7.

Thus any line parallel to the line y=4/7x-2 has an equation of the form y=4/7x+b, where b is any number.

By looking at the answer options, we can select the second option y= 4/7x-1

Answer:

A. and B. are true.

Step-by-step explanation:

For a, -4 + 3(-5) = -19, and 18 is obviously greater.

For b, -7 - 2(-5) = 3, and 3 is greater than 1.

Answer:

tru

Step-by-step explanation:

Answer:

k= 7

Step-by-step explanation:

First let's add like terms: a+b+a=c: a²+b=c

k+9+5=21

k+14=21

Subtract 14 from both sides of the equation

k+14-14=21-14

K=7

Hi!

\(\tt{9+k+5=21}\)

Step 1: Combine like terms.

\(\tt{9+5+k=21}\)

\(\tt{14+k=21}\)

Step 2: Subtract 14 from both sides.

\(\tt{k=7}\) \(\checkmark\)

Have a great day!

Hope that helps. :)

-Stargazing & daydreaming -

The probability of getting exactly 4 correct answers out of 10 multiple-choice questions, where each question has 4 possible choices and the probability of guessing correctly is 0.25, can be calculated using the binomial distribution formula.

The formula is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

In this case, n = 10, k = 4, and p = 0.25. Plugging these values into the formula, we get:

P(X = 4) = (10 choose 4) * 0.25^4 * (1-0.25)^(10-4)

P(X = 4) = (10 choose 4) * 0.25^4 * 0.75^6

Calculating this expression gives the probability that the student gets exactly 4 correct answers.

For the second question:

a. To find the probability that exactly 3 people out of a random sample of 5 Americans will agree with the statement that having a college education is not important to succeed in the business world, we can use the binomial distribution formula as well. In this case, p = 0.40 and n = 5, and we want to find P(X = 3).

b. To find the probability that at most two people out of the sample of 5 will agree with the statement, we need to find the cumulative probability from 0 to 2. So we calculate P(X = 0) + P(X = 1) + P(X = 2).

By plugging in the values and using the binomial distribution formula, we can find the probabilities for both parts (a) and (b) of the second question.

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Answer:

H (13, -16)

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}\)

Given:

Substitute the given endpoint G and midpoint M into the midpoint formula:

\(\implies M=\left(\dfrac{x_H+x_G}{2},\dfrac{y_H+y_G}{2}\right)\)

\(\implies (3, 4)=\left(\dfrac{x_H-7}{2},\dfrac{y_H+24}{2}\right)\)

x-value of endpoint H:

\(\implies 3=\dfrac{x_H-7}{2}\)

\(\implies 6=x_H-7\)

\(\implies x_H=13\)

y-value of endpoint H:

\(\implies 4=\dfrac{y_H+24}{2}\)

\(\implies8=y_H+24\)

\(\implies y_H=-16\)

Therefore, the coordinates of endpoint H are:

Answer: 13 -16

Step-by-step explanation: Edge 2023

The linear equation for their total combined age in 5 years is 2x + 17 = 31.

Let the age of Alex be x years old.

Let the age of June be 'y'.

June is exactly 7 years older than Alex.

y = x+7

In next 5 years, combined  total age will be of 31 years.

(x+5) + (y+5) = 31

Now, the linear equation that models total combined age in 5 years

Replace y with (x+7)

x + 5 + (x+7) + 5 = 31

2x + 17 = 31

Thus, linear equation for their total combined age in 5 years is 2x + 17 = 31.

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\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the concept of maths,

here, A.) is correct because.

2/3(27) - 6 ==> 18 - 6 = 12

hence, LHS = RHS,

so option A is correct

An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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Answer:

C. Consecutive Exterior Angles Theorem states that if the transversal passes through the two parallel lines then any two exterior angles are congruent

Answer:

B

Step-by-step explanation:

The width point highway is \(2x^{3} + 5x^{2} +118\)

To determine the width of the highway between the two buildings, we need to subtract the distances of the buildings from the highway from the total distance between the buildings.

Let's denote the distance between the buildings as "d," the distance of the first building from the highway as "a," and the distance of the second building from the highway as "b."

To find the width of the highway, we subtract the distances of the buildings from the total distance:

Width of the highway = (3x^3 - x^2 + 7x + 100) - (2x^2 + 7x) - (x^3 + 2x^2 - 18)

Simplifying the expression, we combine like terms:

Width of the highway = \(3x^3 - x^2 + 7x + 100 - 2x^2 - 7x - x^3 - 2x^2 + 18\)

Combining like terms further:

Width of the highway = (3x^3 - x^3) + (-x^2 - 2x^2 - 2x^2) + (7x - 7x) + (100 + 18)

Simplifying again:

Width of the highway = 2x^3 - 5x^2 + 100 + 18

Combining the constant terms:

Width of the highway = 2x^3 - 5x^2 + 118

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The following question may be like this:

Two buildings on opposites sides of a highway are 3x^3- x^2 + 7x +100 feet apart. One building is 2x^2 + 7x feet from the highway. The other building is x^3 + 2x^2 - 18 feet from the highway. What is the standard form of the polynomial representing the width of the highway between the two building

As per the U.S. population report, the black population is about 13.5% of the total U.S. population.

The black population in the United States refers to the total no people that identify themself as black or African American.

The exact percentage of the black population in the United States can vary based on the source and the methodology used to collect the data, but as of the population report from 2021, it was estimated to be about 13.5% of the total population.

This information can be used to understand the demographic composition of the United States and to help inform decisions about resource allocation, public policy, and other important issues that can affect different populations. it can be also noted that the demographics of a country can change over time, so it is crucial to regularly update this information to ensure that it remains accurate and relevant.

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Answer:

2.857m/s^2

Step-by-step explanation:

Acceleration (a) is the change in velocity (v) over the change in time (t), represented by the equation a = v/t.

Answer: y = 14.50x + 2.99

Step-by-step explanation:

The equation is y = mx + b

y is the total cost and x is the number of shirt

We know each shirt is $14.50, and she bought x shirts, so 14.50 is the slope

The 2.99 shipping fee is the y-intercept

So our equation is

y = 14.50x + 2.99