Mrs.Galicia dropped a ball from the top of a tower. At the same time, her son, Antonio, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-4t+22.
The height of Antonio's rocket after t seconds can be represented by the linear function: p(t)=-2t+12.
What are the two solutions to this system? Show your work algebraically.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.

The equation that can use to find the weight w of the Golden Delicious apples w + 18 = 22.

The weight of the Golden Delicious apples is 4 pounds.

What is a linear equation?

The equation for a linear equation in one variable is written as ax+b = 0, where a and b are two integers, and x is a variable. This equation has only one solution. For instance, the linear equation 2x + 3 = 8 only has one variable.

Given that, Paul's family picks 22 pounds of apples.

They pick a bag of Honeycrisp apples weighs 18 pounds.

Assume that they take Golden Delicious apples with weight w.

Then the total weight of the bag is 18 + w.

The equation is

18 + w = 22

Subtract 18 from both sides:

18 + w - 18 = 22 - 18

w = 4

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Total cost , C become 30 + 10m

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

It is given that the registration fees is $30 and monthly fees be $10

Let the number of months be represented by m

Total cost, C = 30 + 10m

Therefore, Total cost , C become 30 + 10m

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Therefore , a)different orders can the spider put on its socks and shoes is  [tex]\frac{16!}{(2!)^{8} }[/tex]  and b)the total no of ways for people to discharge from lift is 14112 ways.

Selections are another name for combinations. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them. We write n C r to represent the number of distinct r-selections or combinations among a set of n objects. Compared to arrangements or permutations, combinations are different.

Here,

Each dressing sequence may be uniquely characterized by a series of two 1s, two 2s,..., and two 8s; the spider is said to put the sock on leg x in the first instance, and the shoe on leg x in the second instance.

The solution would be 16! if each number were unique.

However, because 8 words appear twice, the solution is

=>  [tex]\frac{16!}{(2!)^{8} }[/tex]

Thus different orders can the spider put on its socks and shoes is  [tex]\frac{16!}{(2!)^{8} }[/tex]

Thus,

Part A: When the elevator operator can't tell who is who.

Currently, there are 6 floors and 10 persons, and each floor loses one.

so 8+6-1=13

applying combination

=>[tex]C^{13} _{5}[/tex] =  1287 ways.

Part 2: When the elevator attendant separates males from ladies.

There are 3 females and 5 males.

The formula for choosing five men is (5 + 6)-1= (10).

Applying combination  

=> .[tex]C^{10} _{5}[/tex]= 252 ways

techniques to choose ladies = 3+6-1=8

Applying combination  

=> [tex]C^{8} _{5}[/tex] = 56 ways

Total no. of ways

=>  252*56 = 14112 ways.

Therefore , the total no of ways for people to discharge from lift is 14112 ways.

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The probability of the result is 11/21.

A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.

Ray has 4 even numbered cards and 5 odd numbered card.

Ray takes at random three of these cards.

Let, all the three cards are even numbered card.

So, the sum of even numbers is even.

Suppose, two cards are odd numbered and one card is even numbered.

And the combination of 2 odd numbered card and one even numbered card is even.

Now, the possible outcomes;

= {C³₄ + C¹₄C²₅} / C³₄

In order to solve the combination:

Simplify,

{C³₄ + C¹₄C²₅} / C³₄

= [ 3! / {4! x (4-3)!} + 1!/{4! x (4-1)!} x 2!/{5! x (5-2)!} ] / [3! / 4!x (4-3)!]

= 11/21

Therefore, the probability is 11/21.

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So, bottling process is in control thus .0124 portion is fall outside the limit.

In statistics, the standard deviation measures how widely distributed or how much a set of values might vary. While a high standard deviation denotes that values are scattered throughout a wider range, a low standard deviation suggests that values are normally close to the set's mean.

Here,

A sample consisting of a single bottle contain between 350 and 360 milliliters of product is taken

Since ,

bottles contain an average of 355 milliliters, has Standard deviation = 4 milliliters

using fomula

Sd= 4 milimeters

upper bound 360

an lower bound = 350

So, bottling process is in control thus .0124 portion is fall outside the limit.

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Answer:

To write and solve an inequality that can be used to determine the number of 50-kilogram crates that can be loaded into the shipping container, we need to first find the total weight of the crates that can be loaded into the container. The maximum weight that can be loaded into the container is 27500 kilograms, and other shipments weighing 9500 kilograms have already been loaded, so the total weight of the crates that can be loaded is 27500 kilograms - 9500 kilograms = 18000 kilograms.

Next, we need to divide the total weight of the crates that can be loaded by the weight of each crate to find the number of crates that can be loaded. Since each crate weighs 50 kilograms, the number of crates that can be loaded is 18000 kilograms / 50 kilograms = 360 crates.

To express this as an inequality, we can use the following equation:

x <= 360

This inequality states that the number of crates that can be loaded into the shipping container (x) must be less than or equal to 360. Therefore, the number of 50-kilogram crates that can be loaded into the shipping container is x <= 360.

Step-by-step explanation:

the 165 different committees are possible in combination.

What is combination?

If the order of the selections is unimportant, a combination is a mathematical choice made from a collection of various elements (unlike permutations). An apple and a pear are just one of three conceivable combinations if three fruits, such as an orange, an apple, and a pear, are provided. A k-combination of a set S is, technically speaking, a subset of the k distinctive elements of S. Alternatively said, two combinations are identical if and only if they have the same members. (How each set's members are ordered is not crucial.) the number of k-combinations given a set of n elements

That would be equal to the Combinations of 11 items taken 3 at a time.

C(n , k) = n!/[k!(n - k)!]

= 11!/[3!*(11 - 3)!]

= 11!/(3!*8!)

= 11*10*9/3*2

= 15*11

=165

Hence the 165 different committees are possible in combination.

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The information is provided below using a random sampling from a healthy population. a 90% confidence interval for . 114 is the lower bound of the confidence interval.

To find the lower bound of the 90% confidence interval, we need to calculate the 5th percentile of the data. To do this, use the formula that goes like this:

5th percentile = 114 + (0.90 * (512 - 114))

= 114 + (0.90 * 398)

= 114 + 358.2

= 472.2

Therefore, the lower bound of the 90% confidence interval is 472 (rounded to the nearest integer).

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The end behaviours of the functions are f(x) = x⁴ - x³ - 16x³ + 4x + 48

As x ⇒ +∝, f(x) ⇒ +∝ and as x ⇒ -∝, f(x) ⇒ -∝

The equation of the function is given as

f(x) = x⁴ - x³ - 16x³ + 4x + 48

Calculate f(∝) and f(-∝).

So, we have

f(∝ ) = ∝ ⁴ - ∝ ³ - 16∝ ³ + 4∝  + 48

So, we have;

f(∝) = ∝

Also, we have

f(-∝ ) = -∝ ⁴ - (-∝) ³ - 16(-∝) ³ - 4∝  + 48

Evaluate;

f(∝) = -∝

This means that the end behaviours of the functions are;

As x ⇒ +∝, f(x) ⇒ +∝

as x ⇒ -∝, f(x) ⇒ -∝

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The mass of an object on the moon will be same that is 20 Kg when it's mass on the Earth is 20 Kg .

In the question ,

it is given that ,

the mass of the object on the Earth is 20 Kg .

we have to find the mass of the same object on the moon ,

We know that Mass is defined as the numerical measure of its inertia ,

and weight is calculated as

weight = mass × gravity ,

and mass is a constant quantity ,

So , the mass remain unchanged that is 20Kg .

Therefore , the mass of the object on the moon will be same as of Earth that is 20 Kg .

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The rate of change of the linear function represented by the table is a = 4.

A general linear function is written as:

f(x) = a*x + b

Where a is called the slope and is also the rate of change of the function, and b is the y-intercept.

If we know two points on the line, (x₁, y₁) and (x₂, y₂), then the rate of change can be computed with the following formula:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we have a table with some points on that line, we can use any two we want.

For example, I will use the first two, these are:

(-4, -21) and (-3, -17)

Then the rate of change of the linear function is given by:

a = (-17 + 21)/(-3 + 4) = 4/1 = 4

The rate of change is a = 4.

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Answer:

84%

Step-by-step explanation:

To find the mean, you use a formula.

You add up all the numbers, then divide that by how many numbers you have:

80 + 92 + 80 + 84

336 / 4 = 84

thus 84 is the answer

Answer:

If a shirt is on sale for 25% off and the original price was $120, then the sale price is $90. This is because 25% of $120 is $30, and when we subtract this amount from the original price, we get $120 - $30 = $90.

In general, if an item is on sale for x% off and the original price was y dollars, then the sale price is y - (x/100) * y dollars. For example, if the discount is 25% and the original price is $120, then the sale price would be $120 - (25/100) * $120 = $90.

Step-by-step explanation:

Answer:

The sale price is $90

Step-by-step explanation:

Now,

(120 × 25) ÷ 100 = $30

Here, we get 25% of $120 is $30

So,

$120 - $30 = $90

Thus, The sale price is $90

Answer: 8 episodes it would have been 2 days

so 8 episodes will be watched for them to be caught up with each other

Answer: 40%

Step-by-step explanation:

Take 170 divided by 425, then times 100% = 40%

So 40% of the guests ordered food!

a. The solution to the system of equations is: (4, 12).

b. The graph is shown below.

c. (4, 12) is the point of intersection. It confirms the solution from part a.

The solution of a system of equations can be described as the value of x and y of a point, that makes both equations true. It is the point where the two lines of the equations of the system intersect.

If we are given two tables, the ordered pair that appears in both table is considered the solution of the system.

a. The ordered pair, (4, 12) appears in both tables. Therefore, the solution is: (4, 12).

b. The graph of the ordered pairs from each table are sketched in the image shown below, where the green line is for the first table, and the blue line is for the second table.

c. The point of intersection of the graph is (4, 12), this confirms the solution from part a.

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Answer:

ℎ(−5) is −14.

Step-by-step explanation:

To find the value of ℎ(−5), we plug −5 in for x in the expression for ℎ(x):

ℎ(−5) = −3|−5 − 1| + 4

To evaluate the absolute value, we need to find the distance between −5 and 1 on the number line. Since the absolute value function is always non-negative, the distance between −5 and 1 will be positive.

To find the distance between −5 and 1, we subtract the smaller number from the larger number:

|−5 − 1| = |−6| = 6

Now we can plug this value into the expression for ℎ(−5) to find its value:

ℎ(−5) = −3 * 6 + 4

ℎ(−5) = −18 + 4

ℎ(−5) = −14

Therefore, the value of ℎ(−5) is −14.

Yes a sound argument has true conclusion this statement is true.

1. A valid argument must have a true conclusion.

This statement(1) is false. A valid argument must have a true conclusion only if all of the premises are true.  So it is possible for a valid argument to have a false conclusion as long as at least one premise is false.

2.A sound argument must have a true conclusion.

This Statement(2) is true.

If an argument is sound, then it is valid and has all true premises.  Since it is valid, the argument is such that if all the premises are true, then the conclusion must be true.  A sound argument really does have all true premises so it does actually follow that its conclusion must be true.

3. If a valid argument has a false conclusion, then at least one premise must be false.

this statement(3) is true

A valid argument cannot have all true premises and a false conclusion.  So if a valid argument does have a false conclusion, it cannot have all true premises.  Thus at least one premise must be false.

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Answer:

Step-by-step explanation:

yall weird ok

The relationship between the points on the line and solutions to the linear equation is, the equation has a solution at each point along the line.

In the given question, we have to find the relationship between the points on the line and solutions to the linear equation.

The equation has a solution at each point along the line. This simply means that it is easy to tell whether an ordered pair is a solution to an equation. The ordered pair is a solution to the equation if it lies on the line drawn by the linear equation.

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4. Definition of midpoint

5. Definition of an equilateral triangle

6. SSS

The slope of the line that passes through the points (-5, 6) and (-9, -6) is 3

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Let the given points as shown:

(x1,y1)= (-5, 6) and (x2,y2)= (-9, -6)

Slope = m = (y2-y1) /( x2-x1)

                 = (-6-6) /(-9-(-5))

                 = -12/-4

                 = 3

So, the slope of the line that passes through the points (-5, 6) and (-9, -6) is 3

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The area of the surface = [tex]\pi \sqrt{14}[/tex] sq. units

As given in the question the part of,

plane ⇒ x + 2y = 3z = 1

cylinder = [tex]x^{2} + y^{2} = 3[/tex]

Let take P = projection on plane x + 2y + 3z = 1

The surface area of the equation is given by,

∫∫ₚ  √{1+(∂z/∂x)² + (∂z/∂y)²} dA

Using the coordinate of the cylinder,

x = n cos [tex]\alpha[/tex] , y = n sin [tex]\alpha[/tex]

= [tex]x^{2} + y^{2} = (n cos \alpha )^{2} + n sin \alpha ^{2}[/tex]

= [tex]n^{2} (cos^{2}\alpha + sin^{2}\alpha )[/tex]

= [tex]n^{2}[/tex] x 1 = [tex]n^{2}[/tex]

= [tex]n^{2}[/tex] = 2 ⇒ n =  [tex]\sqrt{2}[/tex]

Therefore, P =  {(r,θ)/ 0 ≤ r ≤ [tex]\sqrt{2}[/tex], 0 ≤ θ ≤ 2π}

x +2y + 3z =1

⇒ z = 1/3(1 - x - 2y)

∂z/∂x = -1/3 ; ∂z/∂y = -2/3

According to the formula of surface area,

= ∫∫ₚ √{1+ (-⅓) ² + (-⅔) ²} dA

= 14 /3 [tex]\int\limits_0^{2\pi } \int\limits_0^{\sqrt{3} }[/tex] dA is an area of region P

= [tex]\sqrt{14}[/tex] / 3 [tex]\int\limits_0^{2\pi } \int\limits_0^{\sqrt{3} }[/tex]r. dr. d[tex]\alpha[/tex]

= [tex]\sqrt{14}[/tex] / 3 [tex]\int\limits_0^{2\pi }[/tex] [tex][r^{2} / 2 ]^{\sqrt{3} }_0[/tex] .d[tex]\alpha[/tex]

= [tex]\sqrt{14}[/tex] /3 [tex]\int\limits_0^{2\pi }[/tex]3/2. d[tex]\alpha[/tex]

= [tex]\sqrt{14}[/tex] /2 [tex][\alpha ]^{2\pi }_ 0[/tex]

= [tex]\sqrt{14}[/tex] /2[[tex]2\pi[/tex] - 0]

= [tex]\pi \sqrt{14}[/tex]

Therefore, the area of the surface = [tex]\pi \sqrt{14}[/tex] sq. units

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The length of segment FG is 26 feet.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.

Given that line CE  bisects line FG.

DG= DE,

The length of segment CE is forty two feet.

CE=42 feet.

The length of segment CD is Twenty nine feet.

CD=29 feet.

We need to find the length of FG.

Firstly let us find the length of DE.

CE-CD=DE

42-29=13 feet.

As DG=DE then the length of DG is 13 feet.

DG=DF=13

FG=DG+DF

=13+13=26 feet.

Hence, if line CE bisects line FG, DG= DE, CE= 42 feet and CD= 29 feet then FG is 26 feet.

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Answer:

-11

Step-by-step explanation:

f(4)=-2(4)+1

f(4)= -8+1

f(4)= -7

g(x)= 3(-1)

g(x) = -4

f(4)+g(-1)= -7+(-4)

                -7-4

                -11

hopes this helps

Answer:

-11 just took the test and that was mine

Step-by-step explanation:

The number of buckets of fish that the sea otters fed each day is  7/6 buckets .

In the question ,

it is given that ,

the number of buckets of fish that the dolphin are fed at the Washington aquarium = 1/2 bucket

the sea otters are fed [tex]2\frac{1}{3}[/tex] times as many as fish .

So , the number of buckets that are fed to otters is = (7/3) × (number of buckets eaten by fish)

Substituting the values of number of buckets eaten by fish ,

we get

= (7/3) × (1/2)

Simplifying further ,

we get ,

= 7/6 buckets .

Therefore , the sea otters are fed 7/6 buckets of fish each day .

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The corresponding angle to angle 4 is angle 8.

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The integer numbers that will be repeating in the quotient is 36, the decimal representation of the fraction is 0.3636...

When 8 is divided by 22 we get the fraction 8/22 , when simplified this fraction gives 4/11 .

Now we will divide the numerator by the denominator we get:

4 ÷ 11 = 0.363636...

Thus, it is a repeating decimal .

Hence the numbers 36 will constantly repeat itself.

A quotient is the result of dividing two numbers. The quotient is a mathematical phrase that can also be used to refer to the integer component of a division, fraction, or ratio.

The term "quotient" has been used in many mathematical disciplines to depict structures generated by disassembling larger structures. Given a set with an equivalence relation specified on it, a "quotient set" having particular equivalence classes as items can be formed.

A quotient group is generated by dividing a group into numerous comparable co-sets, and a quotient space is formed by dividing a vector space into numerous comparable linear subspaces.

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Answer:

Step-by-step explanation:

IS =K