A skyrocket is launched from a 30–foot-high platform, with initial speed 300 ft/s. If the polynomial −16t2 + 300t + 30 gives the height that the rocket will rise in t seconds, how high will a rocket with a 2–second fuse rise? The rocket will rise feet.

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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Answer:

$30.18

divide 241.45 by 8

Answer:

price per day to rent this car is $ 30.18

Step-by-step explanation:

For 8 days it costs 241.45 dollar.

8/8 = 1 and you want to know the price per 1 day...

8 = 241.45

multiply left and right of the = sign by 1/8

1/8 * 8 = 1/8 * 241.45

8/8 = 30.18125

Rounded to the nearest cent = $ 30.18

The height of plant B growing at a rate of 3.33 centimeters per week should have a height of 19.98 cms.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

First we need two points (x, y) to obtain the slope.

Assuming height to be 'y' and weeks to be 'x'.

Therefore, (0, 0) and (3, 10) are the two points.

Slope(m) = (10 0)/(3 - 0).

Slope(m) = 10/3.

Slope(m) = 3.33

Now, To obtain the y-intercept.

10 = 3(3.33) + b

b = 0.01 Or neglegible.

Therefore y = 3.3x.

Now, In the 6th week, the height of plant B will be,

y = 3.33(6).

y = 19.98 or 20 cm.

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Answer:

$13

Step-by-step explanation:

$65 x 0.20 = 13

Answer: 20% off 65 is $52.00 so it was $13 saved

Answer:

$17

Step-by-step explanation:

$30/6- 5

$132/6-22

22-5

17

The width of the walkaway be 4 feet.

The discriminant formula is used to determine the nature of the roots of a quadratic equation. The discriminant of a quadratic equation\(ax^{2} +bx+c=0\) is D =\(b^{2} -4ac\)

If D > 0, then the equation has two real distinct roots.

If D = 0, then the equation has only one real root.

Given that: \(Area\; of \;walkway,\; a(w)\;= 4w^{2} + 100 w\)

also, area of walkaway = 464 square feet.

So, \(4w^{2} + 100 w =464\)

     \(4w^{2} + 100 w -464=0\)

Using Discriminant method,

a=4, b=100, c=-464

\(w= \frac{-b\pm\sqrt{b^{2}-4ac} }{2a}\)

w= \(\frac{-100\pm\sqrt{(100)^{2}-4*4*(-464)} }{2*4}\)

w= \(\frac{-100\pm\sqrt{17424} }{8}\)

So, \(w_1= \frac{-100+\sqrt{17424} }{8} \;\;\;\; w_2= \frac{-100-\sqrt{17424} }{8}\)

\(w_1= \frac{-100+132 }{8} \;\;\;\; w_2= \frac{-100-132}{8}\)

\(w_1 = 4 \;\;\;\; and \;\;\; w_2= -29\)

Hence the width of the walkaway be 4 feet.

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x=-3

-6x + 8 + 3x = 17

-3x + 8 = 17

-3x = 17 - 8

-3x=9

x=-9/3

x=-3

The apparent weight of the rock when submerged in water is 70 N.

When an object is submerged in a fluid, it experiences an upward buoyant force due to the displacement of the fluid. This buoyant force reduces the apparent weight of the object.

To calculate the apparent weight of the rock when submerged in water, we need to determine the buoyant force acting on it. The buoyant force is equal to the weight of the fluid displaced by the rock.

The volume of the rock is given as 0.00312 m^3. This volume represents the volume of water displaced by the rock when submerged.

The weight of the fluid displaced is equal to the weight of the water with the same volume. The density of water is approximately 1000 kg/m^3, so the weight of the displaced water is:

Weight of displaced water = density × volume × acceleration due to gravity

                        = 1000 kg/m^3 × 0.00312 m^3 × 9.8 m/s^2

                        ≈ 30.816 N

Since the buoyant force is equal to the weight of the displaced water, the apparent weight of the rock when submerged in water is:

Apparent weight = Weight in air - Weight of displaced water

              = 100 N - 30.816 N

              = 69.184 N

Rounding to the nearest Newton, the apparent weight of the rock when submerged in water is 70 N.

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The given trigonometric identity, sinθ tanθ = secθ - cosθ, is not true.

To verify the given identity, we will simplify the left-hand side (LHS) and the right-hand side (RHS) of the equation and check if they are equal.

LHS: sinθ tanθ

Using the definition of tanθ as sinθ/cosθ, we can rewrite the LHS as sinθ * (sinθ/cosθ). Simplifying further, we get sin²θ/cosθ.

RHS: secθ - cosθ

Using the definition of secθ as 1/cosθ, we can rewrite the RHS as 1/cosθ - cosθ. To combine the fractions, we need a common denominator, which is cosθ. So the RHS becomes (1 - cos²θ)/cosθ.

Now, let's compare the LHS and RHS:

sin²θ/cosθ vs (1 - cos²θ)/cosθ

To check if they are equal, we can simplify both sides separately and see if they yield the same result. However, after simplification, we find that the LHS and RHS are not equal.

Therefore, we can conclude that the given trigonometric identity sinθ tanθ = secθ - cosθ is not true.

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Answer:

B ?

Step-by-step explanation:

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

\(V=1000\ cm^3\)

Step-by-step explanation:

The edge of the cube, a = 0.1 m

We need to find the volume of the cube. The formula for the volume of the cube is given by :

\(V=a^3\)

Put the respected values,

\(V=(0.1)^3\\\\V=0.001\ m^3\\\\or\\\\V=1000\ cm^3\)

So, the volume of the cube is equal to \(1000\ cm^3\).

1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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Answer:

y=14.62

Step-by-step explanation:

The height of the screen will be;

⇒ h = 28 inches

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

A flat screen television is a rectangle with a 53-invh diagonal and a width of 45 inches.

Here,

The diagonal of the screen television = 53 inches

And, The width of the screen television = 45 inches

Let the height of the television = h

So, By the Pythagoras theorem, we get;

⇒ AC² = AD² + DC²

Where, AC = Diagonal of television.

AD = Height of the television

DC = Width of the television.

Substitute all the values, we get;

⇒ 53² = h² + 45²

⇒ 2809 = h² + 2025

⇒ 2809 -2025 = h²

⇒ h² = 784

⇒ h = √784

⇒ h = 28 inches

Thus, The height of the screen = 28 inches

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Answer:

its B

Step-by-step explanation:

the second graph

Answer: B

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

The maximal margin of error associated with a 99% confidence interval for the true population mean dog weight is ±4.78 ounces.

We have the sample size n = 35, sample mean X = 40, population standard deviation σ = 11, and confidence level = 99%.We can use the formula for the margin of error (E) for a 99% confidence interval:E = z(α/2) * σ/√nwhere z(α/2) is the z-score for the given level of confidence α/2, σ is the population standard deviation, and n is the sample size. We can find z(α/2) using a z-table or calculator.For a 99% confidence interval, α/2 = 0.005 and z(α/2) = 2.576 (using a calculator or z-table).Therefore, the margin of error (E) for a 99% confidence interval is:E = 2.576 * 11/√35 ≈ 4.78 ounces (rounded to two decimal places).

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The secοnd beach ball has a vοlume abοut 57,791.69 cubic cm less than the first beach ball.

Each thing in three dimensiοns takes up sοme space. The vοlume οf this area is what is being measured. The space οccupied within an οbject's bοrders in three dimensiοns is referred tο as its vοlume. It is sοmetimes referred tο as the οbject's capacity.

The vοlume οf a sphere with radius r is given by the fοrmula V = (4/3)πr³.

Fοr the first beach ball, with radius 24 cm, the vοlume is represented by the equatiοn-

V1 = (4/3)π(24 cm)³

V1 ≈ 57,904.79 cubic cm

Fοr the secοnd beach ball, with radius 3 cm, the vοlume is represented by the equatiοn -

V2 = (4/3)π(3 cm)³

V2≈ 113.10 cubic cm

The difference in vοlume between the twο beach balls is -

V1 - V2 ≈ 57,904.79 - 113.10

V1 - V2 ≈ 57,791.69 cubic cm

Therefοre, tο the nearest cubic centimeter, the vοlume is 57,792 cubic cm difference in bοth the beach balls.

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Answer:

2+x=5

X+1=4

0-5+X= -2

These are the answers

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Answer:

the second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

E 2021

Answer: angle 7 is equal

Step-by-step explanation: I help ;)

Step-by-step explanation:

triangle BCD ~ triangle EFD so

angle BCD= angle EFD

9x+2=15x-52

6x=54

x=9

angle CBF =9x+2=83°

In the triangle ΔCBD, the angle measure of ∠CBF is 83°.

When the triangles have equal shape, but different sizes. It is called as similar triangles. The corresponding angles are congruent. And the sizes have the same proportionality rate.

Given:

The angle measures,

∠CBD = (9x + 2)°

∠EFD = (15x -52)°

From the diagram,

ΔCBD is similar to ΔEFD.

So, the corresponding angles are equal.

∠CBD = ∠EFD

(9x + 2)° = (15x -52)°

15x - 9x = 52 + 2

6x = 54

x = 9°

And ∠CBF = ∠CBD

So, ∠CBF = (9x + 2)°

Substituting the value of x,

∠CBF = (9(9) + 2)°

∠CBF = 83°

Therefore, the angle measure of ∠CBF is 83°.

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Answer:

36% of 90 = 32.4

Step-by-step explanation:

36% of 90 = 0.36 × 90 = 32.4.

Trisha needs to invest $ 26,666.66 to save $ 8,000 in 5 years.

Given that Trisha needs to save $ 8000 in order to afford to buy a car in five years, and she is going to invest in a savings account that promises an APY (Annual Percentage Yield) of 6% rounded to the nearest penny, to determine how much does she need to invest, the following calculation must be performed:

You must consider an unknown number, and multiply that number by the interest generated and the amount of time of said interest.

Therefore, Trisha needs to invest $ 26,666.66 to save $ 8,000 in 5 years.

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Within data classification schemes, it is important that all categories used be unique and mutually exclusive, it is true.

Within data classification schemes, it is important that all categories used to be classified and mutually exclusive. A data classification scheme is a formal access control methodology used to assign a level of availability to an information asset and thus restrict the number of people who can access it.

The MSC is a hierarchical scheme, with three levels of structure. A classification can be two, three, or five digits long, depending on how many levels of the classification scheme are used. The first level is represented by a two-digit number, the second by a letter, and the third by another two-digit number.

There are two main types of classification schemes: universal and specialized. Universal classification schemes cover all subject areas. They include Universal Decimal Classification (UDC), Dewey, and the Library of Congress. Specialized classification schemes include the National Library of Medicine (NLM).

Within data classification schemes, it is important that all categories used be unique and mutually exclusive, it is true.

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The first movie was ⅔ hours longer than the second one.

The difference in length between the two movies, we need to subtract the length of the second movie from the first.

we need to convert the mixed numbers to improper fractions to make the subtraction easier.

2 ⅓ hours can be written as 7/3 hours.

1 ⅘ hours can be written as 8/5 hours.

Now, we can subtract them

7/3 - 8/5

we need a common denominator. The least common multiple of 3 and 5 is 15.

(7/3) * (5/5) - (8/5) * (3/3) = 35/15 - 24/15 = 11/15

Therefore, the first movie was 11/15 hours (or approximately 44 minutes) longer than the second one

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(a) To find y in terms of x, we can separate the variables and integrate both sides with respect to their respective variables:

dxdy​ =x^2y^−3

dxdy​ =x^2(1/y^3)

y^3 dy = dx / x^2

Integrating both sides gives:

(1/4)y^4 = (-1/x) + C

where C is an arbitrary constant of integration.

Substituting the initial condition y(0) = 4 into this equation gives:

(1/4)(4)^4 = (-1/0) + C

C = 64

Therefore, the solution to the differential equation is given by:

(1/4)y^4 = (-1/x) + 64

Multiplying both sides by 4 and taking the fourth root gives:

y(x) = [(256/x) + 1]^(-1/4)

(b) The expression for y(x) is only defined if the argument of the fourth root is positive, i.e., if:

256/x + 1 > 0

Solving for x gives:

x < -256 or x > 0

Since the initial condition is at x = 0 and the derivative is continuous, the solution is defined on the interval (-256, 0) U (0, +infinity), or equivalently, (-256, +infinity). Therefore, the solution is defined on the interval x ∈ (-256, +infinity).

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