14. The number of bottles of water in a pantry after a delivery can be modeled by the
function f(x) = 24x + 35 where x is the number of cases of bottled water delivered.
Which statement is true?
A. Each case of water contains 24 bottles.
B. Each case of water contains 35 bottles.
С. There were 24 bottles of water in the pantry before the delivery.
D. There were 59 bottles of water in the pantry before the delivery.

Answer: Krysti's mistake was ordering only 12 small T-shirts when she should have ordered more. To figure out how many small T-shirts she should have ordered, we can start by finding out how many classmates wanted small T-shirts:

60% of 25 classmates = 0.60 x 25 = 15 classmates

So, 15 classmates wanted small T-shirts. If Krysti had ordered one small T-shirt for each of these classmates, she would have needed 15 small T-shirts. However, Krysti only ordered 12 small T-shirts, which means she is short by 3 shirts.

To avoid this mistake, Krysti should have double-checked her calculations and made sure that the number of small T-shirts she ordered matched the number of classmates who wanted small T-shirts.

Step-by-step explanation:

Your expected winnings from playing this game are 2 pounds.

A game is an activity or a form of play, often with a set of rules and goals, that is undertaken for enjoyment, competition, or skill development.

Let's analyze this game to see what your expected winnings are.

If the first roll is 1, 2, or 3, the game continues and you have a 3 in 6 chance (or 1/2 chance) of continuing to roll the die. Each subsequent roll has the same probabilities and outcomes as the first roll.

Let's start with the case where you win on the first roll with a probability of 1/2. In this case, your winnings are 1 pound.

If you don't win on the first roll, the game continues with a probability of 1/2, and your expected winnings from that point on are the same as your expected winnings from the beginning of the game (since the probabilities and outcomes are the same for all rolls).

Therefore, the expected winnings from the start of the game are:

E = 1/2 * 1 + 1/2 * E

Solving for E, we get:

E = 1 + E/2

E/2 = 1

E = 2

Therefore, your expected winnings from playing this game are 2 pounds.

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Answer:

y = 18 when x = 3

Step-by-step explanation:

y is directly proportional to x^2, meaning:

\(y=ax^2\)

where a is the proportion between them. We're given the values for both x and y, so plug those in and solve for a:

\(8=a(2)^2\\8=a4\\2=a\\a=2\)

Now you can use a to solve for y when x is 3:

\(y=ax^2\\y=(2)(3)^2\\y=2(9)\\y=18\)

The value of \(7^x = 77\) is C. x = 0.45 obtained by taking log of vase 7 on both sides.

The logarithm is exponentiation's opposite function in mathematics.

This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 100 = 10², the logarithm of 100 in base 10 is 2, or log10 = 2.

Given, an expression \(7^x = 77\).

Now, \(log_77^x = log_7(77)\).

We have taken log of base 7 on both sides to cancel out log base 7 of 7 to get x explicitly.

\(x = log_777\).

x = 0.4479 Or x = 0.45.

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Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

Given:

1 mile = 1,760 yards

Brody ran 6 miles to win the race.

Here, we are required to conver 6 miles to yards.

Where,

1 mile = 1760 yards

6 miles = x yards

We have:

Therefore, Brody ran 10,560 yards to win the race.

ANSWER:

10,560 yards

A perfect square refers to a number that is the result of multiplying an integer by itself. In this case, 6^1 is equal to 6.

However, 6 is not a perfect square because it cannot be obtained by multiplying an integer by itself. The perfect squares up to 6^1 would be 1^2 = 1 and 2^2 = 4.

Answer:

5419

Step-by-step explanation:

The probability that a randomly selected point within the circle would fall in the red- shaded area is 45. 833 %

The arc that is covered by the red - shaded area in the circle has a degree measure of 165 degrees. This is out of the total circle angle measure of 360 degrees.

This therefore means that the probability that a randomly selected point within the circle would fall in the red- shaded area can be found to be :

= Angle measure of red - shaped area / Total area x  100 %

= 165 / 360 x 100 %

=0. 45833 x 100 %

= 45. 833 %

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Answer:

x=0 and x=2

Step-by-step explanation:

We need to check at each  point where the function changes definition

At x= -2

On the left side  -4   on the right side = -( -2)^2 = -4  continuous

At  x=0

The point is not defined since neither side has an equals sign

discontinuous

x =2

on the left side 2^2 =4  on the right side 2

It is discontinuous

Answer:

x = 0

x = 2

Step-by-step explanation:

Edge 2020

~theLocoCoco

To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.

d = √((x - 5)² + (0 - (-8))²)

Simplifying:

d = √((x - 5)² + 64)

Now, we want the distance d to be equal to 16 units. So, we set up the equation:

16 = √((x - 5)² + 64)

Squaring both sides of the equation to eliminate the square root:

16² = (x - 5)² + 64

256 = (x - 5)² + 64

Subtracting 64 from both sides:

192 = (x - 5)²

Taking the square root of both sides

√192 = x - 5

±√192 = x - 5

x = 5 ± √192

Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:

Point 1: (5 + √192, 0)

Point 2: (5 - √192, 0)

In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).

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Answer:

123201

Step-by-step explanation:

This is an arithmetic sequence of common difference 2 and starting value 1,

So we can use the formula for an arithmetic sequence  if we know what is the order of the last term.

Then first use the formula for the nth term to find "n":

\(a_n=a_1+(n-1)d\)

where d = 2, first term = 1 and last term = 701

\(a_n=a_1+(n-1)d\\701=1+(n-1)*2\\700=(n-1)*2\\350=n-1\\n = 351\)

Knowing this, we can estimate the partial sum:

\(S=n\,\frac{a_1+a_n}{2} \\S=351\,\frac{1+701}{2} \\S=351\,*\,351\\S = 123201\)

2. The integration region,

\(\left\{(r,\theta)\mid\dfrac\pi6\le\theta\le\dfrac\pi2\land2\le r\le3\right\}\)

corresponds to what you might call an "annular sector" (i.e. the analog of circular sector for the annulus or ring). In other words, it's the region between the two circles of radii \(r=2\) and \(r=3\), taken between the rays \(\theta=\frac\pi6\) and \(\theta=\frac\pi2\). (The previous question of yours that I just posted an answer to has a similar region with slightly different parameters.)

You can separate the variables to compute the integral:

\(\displaystyle\int_{\pi/6}^{\pi/2}\int_2^3r^2\sin^2\theta\,\mathrm dr\,\mathrm d\theta=\left(\int_{\pi/6}^{\pi/2}\sin^2\theta\,\mathrm d\theta\right)\left(\int_2^3r^2\,\mathrm dr\right)\)

which should be doable for you. You would find it has a value of 19/72*(3√3 + 4π).

3. Without knowing the definition of the region D, the best we can do is convert what we can to polar coordinates. Namely,

\(r^2=x^2+y^2\)

so that

\(\displaystyle\iint_De^{x^2+y^2}\,\mathrm dA=\iint_Dre^{r^2}\,\mathrm dr\,\mathrm d\theta\)

In transversal lines, All angles are equal and parallel, so  TV ║ WY  are    parallel lines .                                      

What are transversal lines?

∠TUX  ≅  ∠UXY               ( Alternate angle)

∠SUV ≅  ∠TUX                 ( Vertically angle)

∠UXY ≅  ∠SUV                  ( Interior angle )

 TV ║ WY                          ( All angles are equal and parallel, so  TV ║ WY                                        

                                              are    parallel lines .

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Leroy would therefore need to put in 10 hours of effort to make the 40 kilos of dough.

In the World System of Units, a kilogramme serves as the default measure of mass. Since "kilo" is short for "thousand," a kilogramme is equal to 1000 pounds. "kg" is the sign for a kilogramme.

We can start by using a proportion to solve the problem:

kilograms of dough / hours worked = constant rate of dough prepared per hour

Let's call the constant rate of dough prepared per hour "r". We can set up two proportions for the two scenarios:

28 kg / 7 hours = r

40 kg / x hours = r

We want to solve for "x", the number of hours Leroy would need to prepare 40 kg of dough. We can rearrange the second proportion to solve for "x":

x = (40 kg) / (r)

To find "r", we can use the first proportion:

r = (28 kg) / (7 hours) = 4 kg/hour

Now we can substitute "r" into the second proportion and solve for "x":

x = (40 kg) / (4 kg/hour) = 10 hours

Therefore, Leroy would need to work for 10 hours to prepare 40 kilograms of dough.

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Step-by-step explanation:

50 110

190 240

425 485

was this your question?

Answer:

B

Step-by-step explanation:

using the equation 'y = 12x', if you plug in zero for 'x' you get zero for 'y'; the only graph that has the point (0, 0) is (b)

also, the x-axis represents time so, as time increases, so does the number of calories burned (which is measured on the y-axis) -- not staying flat or decreasing

Answer

-1.31 if its getting rounded to nearest number.

The fraction will be -21/16

Note that where Tom Harris is 24 years old and he wishes to purchase a $7,000 value 10-year term insurance, his annual premium will be:  $290.5.

Gross premiums written in the insurance sector are the sum of direct and assumed premiums written before subtracting ceded reinsurance. Direct premiums written are the premiums on all policies issued by the company's insurance subsidiaries throughout the fiscal year.

To compute Tom's insurance premium we must use the information given as well as the table above:

Given:

Tom's Age = 24 years

Value of Insurance Cover Requested = $7,000

Type of Insurance cover requested = 10-Year Term

The rate for the Type of Insurance Cover requested: Since he 24 and wants a 10-year term, the rate applicable from the table is; 4.15%

Thus, his annual premium  = 7000 * 4.15%
= 29050/ 100
= $290.5

Thus, Tom Harris' annual insurance premium is: $290.5

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Answer:

50 cards

Step-by-step explanation:

We can start by saying that his total card collection has x cards in it, meaning that 28% or 28/100 of his total cards, x, is equal to 14. Next, we can divide by 28/100 on both sides, and dividing is the same as multiplying by the reciprocal. The reciprocal of 28/100 is 100/28, so 14 * 100/28 is equal to 100/2, which is 50. We can say that 50 cards were in his card collection initially.

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Answer:

CAB is 37 degrees

Step-by-step explanation:

90 + 53 = 143

180 - 143 = 37

The value of x, given that when it divides a number, there is a quotient and a remainder, is 400

To find the value of divisor, we can use a variant of the division algorithm formula :

Divisor = ( Dividend - Remainder ) / Quotient

x is the divisor

Dividend = 19, 432

Remainder = 232

Quotient = 48

This means that the value of x is:

x = ( 19, 432 - 232 ) / 48

x = 19, 200 / 48

x = 400

In conclusion, x is 400.

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An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer:

Number 1 is 50 and Number 2 is 40

Step-by-step explanation:

25 X 2 = 50

2 X 20 = 40

Answer:

66

Step-by-step explanation:

dolars per hour