what is the difference between the longest and shortest distances the glider flew

Answer:

5+x+3 simplified is x+8

Step-by-step explanation:

when you simplify something, you combine terms and write it in the simplest way you can. So combine 5 and 3 to get 8, and then the final answer of x+8

Answer: x+8

Step-by-step explanation:

"5 + x + 3" can be simplified by combining the numerical terms, which are 5 and 3, to get 8.

Then, just rewrite the expression as "x + 8." Therefore, "5 + x + 3" simplified is just "x + 8".

-1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

A null hypothesis is a statistical hypothesis that presupposes that there is no link between two variables in a population or that there is no meaningful difference between two populations. It serves as the beginning point of a statistical hypothesis test and is typically marked as H0. A null hypothesis serves as a reference point against which the alternative hypothesis may be compared. The alternative hypothesis is accepted if there is sufficient evidence from the data to reject the null hypothesis. The null hypothesis is not rejected if there is insufficient evidence in the data to support it.

Using a significance threshold of 0.05, we may use a conventional normal distribution table or calculator to get the essential z value. The value that corresponds to the 0.025 percentile is the crucial z value (or the 0.975 percentile, depending on the direction of the alternative hypothesis).

The z value for the 0.025 percentile, as determined by a typical normal distribution table, is -1.96.

Hence, -1.96 and 1.96 are the essential z values for a two-tailed test with a significance level of 0.05.

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Answer:

A or 420

Step-by-step explanation:

Remember Length x Width x Height. 12 * 5 is 60, then 60 * 7 is 420.

The answer of the given question based on the compound interest is  the balance after 6 years is $14,162.62 (option a).

Amount refers to total value of something, usually in terms of a money. It can also be used in  context of a quantity of something, such as an amount of the  time or an amount of the material.

formula for the compound interest is :

A = P(1 + r/n)^(nt)

Where,

A = final amount

P = principal amount

r = annual interest rate

n = the number of times interest is to be compounded per year

t = time in years

In this case, we have:

P = $1,000

r = 3.75% = 0.0375 (annual interest rate as a decimal)

n = 12 (monthly compounding)

t = 6 years

Substituting the  values into  formula, we will get:

A = 1000(1 + 0.0375/12)⁽¹²*⁶⁾

A = $1,4162.62

Therefore, the balance after 6 years is $14,162.62 (option a).

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The jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.

An equation is a mathematical statement that shows that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems by finding the values of the variables that make the equation true.

Let x be the number of bracelets made, and y be the number of necklaces made.

Then, we can create the following system of equations:

Equation 1: 7x + 24y = 172 (the total amount of gold used is 172 grams)

Equation 2: y = x + 2 (the number of necklaces made is 2 more than the number of bracelets made)

So, the variables are x (the number of bracelets made) and y (the number of necklaces made).

We can solve this system of equations to find the values of x and y. We can use substitution or elimination to solve for one variable and then plug it into the other equation.

Substitution method:

From Equation 2, we have y = x + 2. Substituting this into Equation 1, we get:

7x + 24(x+2) = 172

7x + 24x + 48 = 172

31x = 124

x = 4

So, the jeweler made 4 bracelets.

Plugging this into Equation 2, we get:

y = x + 2 = 4 + 2 = 6

So, the jeweler made 6 necklaces.

Therefore, the jeweler made 4 bracelets and 6 necklaces using 172 grams of gold.

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The area of the figure is obtained to be approximately 74.1 units².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The rectangle has the length of 6 units.

The rectangle has the breadth of 10 units.

The semicircle has a diameter of 6 units.

The semicircle has the radius of 3 units.

The formula for area of rectangle is -

Area (r) = l × b

Substitute the values into the equation -

Area (r) = 6 × 10

Area (r) = 60 units²

The formula for area of semicircle is -

Area (r) = πr² / 2

Substitute the values into the equation -

Area (s) = [3.14 × (3)²] / 2

Area (s) = 28.26 / 2

Area (s) = 14.13 units²

The total area of the diagram is -

Total Area = Area (r) + Area (s)

Substitute the values into the equation -

Total Area = 60 + 14.13

Total Area = 74.13 units²

Therefore, the area of the figure is 74.1 units².

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The values of the variables and the side lengths are

From the question, we have the following parameters that can be used in our computation:

AB = AC

Perimeter = 27.3

Using the attached figure, we have

6x - 2y = x + 5

Evaluate

5x = 2y + 5

For the perimeter, we have

AC + AB + BC = 27.3

So, we have

6x - 2y + x + 5 + y + 6.3 = 27.3

Simplify

7x = y + 16

Multiply by 2

14x = 2y + 32

Subtract from 5x = 2y + 5

9x = 27

So, we have

x = 3

This means that

2y + 32 = 14 * 3

2y + 32 = 42

Evaluate

2y = 10

y = 5

For the side lengths, we have

AC + AB + BC = 27.3

So, we have

AC = 6(3) - 2(5) = 8

AB = 3 + 5 = 8

BC = 5 + 6.3 = 11.3

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Answer:

-12 and 2

Step-by-step explanation:

1. Notice that both numbers have to be negative. This means that one number has to be negative, and the number with the largest value has to be negative.

2. Think of numbers that multiply to -144

3. Check and see if they add to -10

4. The only numbers that satisfy this are -12 and 2

Step-by-step explanation:

that makes ORQ a right-angled triangle, and we can use Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

OQ is the radius of the circle = OM = LM/2 = 20/2 = 10 cm.

RQ = PQ/2 = 16/2 = 8 cm.

so, our Pythagoras equation looks like :

OQ² = RQ² + OR²

10² = 8² + OR²

100 = 64 + OR²

36 = OR²

OR = 6 cm

RM = OM - OR = 10 - 6 = 4 cm

Answer:

6 times

Step-by-step explanation:

24/4 = 6

The volume of the building is approximately 18,840 cubic feet.

So the answer is (B) 18,840 ft³

What is volume of cone ?

The volume of a cone is a measure of the amount of space that the cone occupies and can be calculated using the formula:

[tex]V = (1/3)\pi r^2h[/tex]

where V is the volume of the cone, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant approximately equal to 3.14.

According to the question:
The volume V of a cone can be calculated using the formula:

[tex]V = (1/3)\pi r^2h[/tex]

where r is the radius of the base of the cone, h is the height of the cone, and π is a constant approximately equal to 3.14.

In this case, the radius r is 30 feet and the height h is 20 feet. Substituting these values into the formula, we get:

[tex]V = (1/3)\pi (30)^2(20)[/tex]

[tex]V = (1/3)\pi (900)(20)[/tex]

[tex]V = (1/3)(56,520)[/tex]

[tex]V = 18,840[/tex]

Therefore, the volume of the building is approximately 18,840 cubic feet.

So the answer is (B) 18,840 ft³.

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5. The quadratic function for the height of the rock, h = -16·t² + 79·t + 50, indicates;

a. The height of the rock will be 125 feet above the beach at 1.28 seconds and 3.66 seconds after it is thrown

b. The maximum height reached is about 147.5 feet

The time it takes the rock to reach the maximum height is about 2.47 seconds

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where, a, b, and c are numbers, and a ≠ 0.

The initial velocity of the rock = 79 ft/s

Height of the cliff above the beach from which the rock is thrown = 50 feet

The function for the height of the rock above the beach is; h = -16·t² + 79·t + 50

Please find attached the graph of the height of the rock as a function of time, created with MS Excel.

Required; When the height of the rock will be 125 feet above the beach

When the height of the rock is 125 feet, we get;

h = 125 = -16·t² + 79·t + 50

-16·t² + 79·t + 50 - 125 = 0

-16·t² + 79·t - 75 = 0

The value of t obtained using an online tool are;

t = (79 + √(1441))/32 ≈ 3.66 and t = (79 - √(1441))/32 ≈ 1.28

The times at which the height of the rock will be 125 feet above the beach are; 1.28 seconds and 3.66 seconds after the rock is thrown

b. The maximum height of the rock can be obtained from the formula for finding the maximum height of a quadratic equation of the form; f(x) = a·x² + b·x + c, which is;

At the maximum point, x = -b/(2·a)

The function for the height; h = -16·t² + 79·t + 50, indicates that we get;

a = -16, b = 79, and c = 50

Therefore;

The time it takes the rock to reach the maximum height, t(max), is therefore;

t(max) = -79/(2 × (-16)) ≈ 2.47

It takes about 2.47 seconds for the rock to reach the maximum height

The maximum height, h(max) = -16 × 2.46875² + 79×2.46875 + 50 ≈ 147.5

The maximum height reached by the rock is about 147.5 feet

Possible part of the question, obtained from a similar online question, includes;

a. The time it takes the rock to reach a height of 125 feet above the beach
b. The maximum height reached by the rock and the duration it takes the rock to reach the maximum height.

Please find attached the possible graph in the question, created with MS Excel, using the function for the height of the rock.

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Answer:

  C.  m = 1440d

Step-by-step explanation:

You want to know the equation that represents the relationship between days (d) and minutes (m) given the table of values (d, m) = (4, 5760), (7, 10080), or (11, 15840).

On the off chance you don't already know that the number of days must be multiplied by minutes per day to find the number of minutes (m = 1440d), you can always try the table values in the response choices to see what works:

  A.  5760 = 4/1440 . . . . . . nope

  B.  5760 = 4 + 1440 . . . . . nope

  C.  5760 = 1440·4 . . . . . . . yep

  D.  4 = 1440·5760 . . . . . . . nope

The equation that works is m = 1440d.

__

Additional comment

Fractions work the same way with units that they do with numbers. Common factors in numerator and denominator cancel.

  [tex]\dfrac{2}{3}\times 3=2\\\\\dfrac{\text{minutes}}{\text{day}}\times \text{days}=\text{minutes}[/tex]

Using inequality, x < 63.33, Student take 62 and adult take 68.

By utilizing the "equal tο" symbοl in mathematics, equatiοns are nοt necessarily balanced οn bοth sides. Sοmetimes it can be abοut a "nοt equal tο" relatiοnship, which denοtes that οne thing is better than οr wοrse than anοther.

A relatiοnship between twο numbers οr οther mathematical expressiοns that yields an unfair cοmparisοn is referred tο as an inequality in mathematics. Certain algebraic mathematical expressiοns are referred tο as inequalities.

The student's ticket sells fοr $5,

adult ticket sells fοr $950,

Tοtal auditοrium = 130,

If x represents the number οf student, then adult = 130 - x,

∴ 5x + 9.5y > 950

insert y = 130 - x5x + 9.5(130 - x) > 950,

5x + 1235 - 9.5 x > 950

x < 63.33

∴ Student take 62 and adult take 68.

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Answer:

Step-by-step explanation:

4x + 6 + 24 - 2x =

2x + 30

The area of the region bounded by the curves y = x² + 6x + 9 and y = 4 is 16  ² / ₃ square units.

First, we need to find the points of intersection between the two curves. Set y = x² + 6x + 9 equal to y = 4:

x² + 6x + 9 = 4

Now, solve for x:

x² + 6x + 5 = 0

Factor the quadratic equation:

(x + 5)(x + 1) = 0

This gives us the solutions x = -5 and x = -1. These are the x-coordinates of the points of intersection.

Now, to find the area of the region bounded by the curves, we'll integrate the difference between the two functions with respect to x, from x = -5 to x = -1:

Area = ∫[4 - (x² + 6x + 9)]dx from -5 to -1

Area = ∫[5 - x² - 6x]dx from -5 to -1

Now, integrate:

Area = [5x - (x³/3) - 3x²] from -5 to -1

Plug in the limits:

Area = (5(-1) - (-1)³/3 - 3(-1)²) - (5(-5) - (-5)³/3 - 3(-5)²)

Area = (-5 - 1/3 - 3) - (-25 + 125/3 - 75)

Area = (-8 1/3) - (- 25/3)

Area = 16  ² / ₃ square units

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Answer:

0, -3.

Step-by-step explanation:

12x(x+3)=0

Either 12x = 0 or (x + 3) = 0

x = 0/12 or x = -3

So, x = 0 or x = -3

Answer:

11205 is correct answer

Answer:

69

Step-by-step explanation:

69

The probability of getting someone who tested positive, given that he or she had the disease, is 0.9.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

The probability of getting someone who tested positive, given that he or she had the disease, is equal to the probability that the individual has the disease and tests positive ( P(positive | disease) ).

This can be calculated using the formula P(A|B) = P(A∩B) / P(B)

P(positive | disease) = P(positive ∩ disease) / P(disease)

                    = 141 / (141+16)

                    = 0.898

Therefore, the probability of getting someone who tested positive, given that he or she had the disease, is 0.898, which is 0.9.

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Answer:

A

Step-by-step explanation:

simply divide each ter by -7x ..

Answer:

p = 6

Step-by-step explanation:

Answer:

Line DB and AC intersect at point E.

∠AEB = ∠DEC because they are vertical angles.

∠EAB and ∠ECD are alternate interior angles because AB and CD are parallel lines and line AC crosses through both parallel lines.

m∠EAB = m∠ECD because they are alternate interior angles.

ΔABE ≅ ΔCDE because there are two sets of congruent angles.

Answer: A. Nikko by 2 inches

Step-by-step explanation: Because 82 inches = 6ft 10in, which is 2 inches taller than Ricco.

The first five term of the sequence are -12, -24, -36, -48 and -60.

A sequence is an enumerated collection of objects that follows are particular pattern.

The explicit formula of the sequence is aₙ = -12n

where

Therefore, let's find the first five terms of the sequence as follows:

a₁ = -12(1) = -12

a₂ = -12(2) = - 24

a₃  = -12(3) = -36

a₄  = -12(4) = -48

a₅  = -12(5) = - 60

Therefore, the sequence are -12, -24, -36, -48 and -60.

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Answer:

CF =  12
DE  = 23
CD =  23
DF = 23.9

Step-by-step explanation:

We can see that there are 2 right-angled triangles: DEF and CDF with common side FD.

They are right angled triangles because the EF and CF are radii of the circle and these segments intersect the tangents at 90°

The common side DF is the hypotenuse for both triangles

The sides EF and CF are radii of the circle so EF = CF

We have two triangles which have two sides equal and one of the angles equal to the corresponding angle of the other

By the SSA theorem, the two triangles are similar

SSA Theorem

if two sides and an angle not included between them are respectively equal to two sides and an angle of the other then the two triangles are equal

Therefore by the law of similar triangles,

CD  = EF

Plugging in the expressions we get
13x - 16 = 4x + 11

Subtract 4x from both sides:
13x - 4x - 16 = 11
9x - 16 = 11

Add 16 to both sides:
9x - 16 + 16 = 11 + 16

9x = 27

x = 27/9 = 3

Therefore
ED = 4x + 11 = 4(3) + 11 = 12 + 11 = 23

and this is equal to CD

Using the Pythagorean theorem for right triangles,

For ΔDEF,

DF² = EF² + DE²

DF² = 12² + 23²

= 144 + 529

= 673

DF = √673

= 25.9422

= 25.9 rounded to the nearest tenth

So the measures of the segments are
CF = 12
DE = 23
CD = 23
DF = 23.9

Answer:

the value of (4m-n)/(n+2p) is 3/7.

Step-by-step explanation:

Let's substitute the given ratio in terms of a common multiplier, k:

m = 3k

n = 6k

p = 4k

Now we can substitute these values in the expression:

(4m-n)/(n+2p) = (4(3k) - 6k)/(6k + 2(4k)) = (12k - 6k)/(6k + 8k) = 6k/14k = 3/7

Therefore, the value of (4m-n)/(n+2p) is 3/7.

In exercise 1:

Situation: The account holder saves $30 each month

The first three terms of the sequence are: $120, $150, $180.

In exercise 2:

Situation: The account earns 25% interest each month.

The first three terms of the sequence are: $120, $150, $187.50.

A sequence in mathematics is described as an enumerated collection of objects in which repetitions are allowed and order matters.

Explaining  exercise 1:

In this exercise, the account balance for each month should form an arithmetic sequence with a common difference of $30

February 1 balance: $150

March 1 balance: $180

Hence, we have the first three terms of the sequence as:  $120, $150, $180.

Explaining exercise 2:

In this exercise, the account balance for each month should form a geometric sequence with a common ratio of 1.25.

The account earns 25% interest each month is the situation here.

February 1 balance: $150

March 1 balance: $187.50

The first three terms of the sequence are: $120, $150, $187.50.

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The total contribution to Sharon's account over the 25-year period is $64,800.

To find the total contribution to Sharon's account, we need to consider both her contribution and her employer's contribution.

Social Security taxes are generally split evenly between the employee and the employer, with each paying half of the tax.

Sharon paid $32,400 in Social Security taxes over the 25-year period, which represents her share (half) of the total Social Security taxes paid.

To find the total contribution to her account, we simply need to double her share to include the employer's contribution:

Total contribution = Sharon's contribution + Employer's contribution

Total contribution = $32,400 + $32,400

Total contribution = $64,800

The total contribution to Sharon's account over the 25-year period is $64,800.

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