Starting at home, Ishaan travel uphill to the grocery store for 12 minutes at just 15 mph. He then traveled back home along the same path downhill at a speed of 30 mph. What is his average speed for the entire trip from home to the grocery store and back?

For the two lines to be parallel, the value of n must be 3

When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line. If the slopes are the same then the lines are parallel.

The slope of each line is calculated as (y2-y1)/x2-x1

for line AB, the slope = (6n-n)/10-4 = 5n/6

for line CD, the slope= 8n-(-6)/9-(-3)=( 8n+6)/12

for AB and CD to be parallel,

5n/6 = (8n+6)/12

multiply both sides by 12

10n= 8n+6

collect like terms

10n-8n= 6

2n= 6

n= 6/2= 3

therefore for the value of n= 3 line CD and AB are parallel.

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The rule of natural deduction that justifies the inference from ( P(0) ) to ( \exists x P(x) ) is the existential introduction ((\exists I)) rule.

The existential introduction rule states that if you have a statement ( P(t) ) where ( t ) is a term or object, then you can introduce an existential quantifier to assert the existence of an object such that ( P ) holds.

In this case, since you have ( P(0) ), which means that ( P ) holds for the value 0, you can introduce an existential quantifier to claim that there exists some ( x ) (in this case, ( x = 0 )) for which ( P(x) ) holds. Therefore, the justification is ( (\exists I) ).

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Answer:

5times largerof apolygon

Answer:

x>5

Step-by-step explanation:

hope this helps you!

Answer:

4%

Step-by-step explanation:

As, some rate of $320 will give u 12.80

Now to find the percentage u always use this procedure :

Sales tax value = 12.80 divided by the the total cost ( $320) multipled by hundred

So 12.80/320 x 100 = 4

So 4%

This method help me alot in my solving skills

And used it everytime a question like this is given

So I hope u use it for such questions and u will get right with all hope!

Hope this helps!!

The required, Mmusi borrowed R3000 from Aggie as per the given conditions.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on loan.

Amount = Principal [1 + rate×time]

Let's call the amount Mmusi borrowed from Aggie "P".

After two years, he has to pay back
= P + P * 18% * 2
= P + 0.18 * P * 2
= P + 0.36P
= 1.36P

So if he has to pay back R4080, we can set up an equation to solve for P:

1.36P = 4080

To find P, we can divide both sides by 1.36:

P = 4080 / 1.36 = 3000

So Mmusi borrowed R3000 from Aggie.

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Answer:

9x and -4x

This is the answer

The measure of each interior angle of a decagon is 144 degrees.

1. A decagon is a 10 sided polygon.

2. The sum of the interior angles of any polygon with n sides is (n - 2) * 180 degrees.

3. For a decagon, n = 10, therefore the sum of the interior angles is (10 - 2) * 180 degrees = 8 * 180 degrees = 1440 degrees.

4. Therefore, the measure of each interior angle of a decagon is 1440 degrees / 10 = 144 degrees.

The measure of each interior angle of a decagon is 144 degrees.

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Answer:

the answer is C

Step-by-step explanation:

Answer:

first: 27.5

second: 250%

Step-by-step explanation:

first: 17.16 ÷ 62.4% = 0.275, 27.5

second: 51 ÷ 127.5 = 0.4, 40%,

100% ÷ 40%, = 2.5, 250%

The angle in the fourth quadrant associated with trigonometric function is 314.415°. The exact values of the six trigonometric functions are listed below:

In this problem we find the exact form of a trigonometric function and the related quadrant on a Cartesian plane. By definition of the sine function and the features of the sine, the exact value has the following form and conditions:

y / √(x² + y²) = - 5 / 7, x > 0, y < 0

Then,

y = - 5, √(x² + y²) = 7

√[x² + (- 5)²] = 7

x² + 25 = 49

x² = 24

x = √24

x = 2√6

Then, the angle associated to the trigonometric function is:

θ = tan⁻¹ (y / x)

θ = tan⁻¹ (- 5 / 2√6)

θ ≈ 314.415°

And the five other trigonometric functions are:

cos θ = 2√6 / 7

tan θ = - 5 / 2√6

cot θ = - 2√6 / 5

sec θ = 7 / 2√6

csc θ = - 7 / 5

The angle associated with trigonometric function is 314.415°.

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The structure that is more than 1,000 meters (3,280.84 feet) off of the ocean floor and has a flat top is called a seamount.

The abyssal structure that is more than 1,000 meters.Seamounts are underwater mountains or volcanoes that rise from the seafloor but do not reach the ocean's surface. They have a distinct conical shape with a flat or gently sloping top, often referred to as a summit. Seamounts are common features in the abyssal plain, and they can vary in size and shape.Therefore,the abyssal structure that is more than 1,000 meters (3,280.84 feet) off of the ocean floor and has a flat top is called a seamount.

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Answer:

a) 40

b) 140

c) 70

d) 30

e) 80

Step-by-step explanation:

a:

a is an alternate interior angle of 40°. These angles are congruent.

b:

This is a same side interior angle to 40.  These are supplemental which means that they add to 180

180 - 40 = 140

c:

The sum of the interior angles of a triangle add to 180.  One angle is shown to be 30.  The unnamed angle is 80.  It is an alternate intermate interior angle with angle e that equals 80.

180 - 30 - 80 = 70

d:

This is an alternate interior angle of 30

e)

The sum of the interior angles of a triangle is 180

180 - 70 - 30 = 80

Helping in the name of Jesus.

Answer:

B'(5,-9)

Step-by-step explanation:

When reflecting across the x-axis, the "x" coordinate stays the same, and the "y" coordinate just becomes the opposite. So, the opposite of 9 is -9!

Therefore, B' is (5,-9), or "D"

Hope this helps!

Answer:equal and parallel opposite sides

Step-by-step explanation:

equal sides

parallel opposite sides

It is found that ABCD and ABEC are parallelograms because a parallelogram can be divided into congruent triangles of different orientations.

The pre-image of the rotations are given as: Triangle ABC

Triangle ABC

The image of the rotations are given as: Triangle CDA

Triangle ECB

Notice that the triangles ABC and CDA have a common line segment AC, while the triangles ABC and ECB have a common line segment CB because the triangle is rotated by 180 degrees through its own midpoint

ΔCAD = ΔABC but of different orientations, then ABCD is a parallelogram.

Also,

ΔABC = ΔECB, so that ABEC is a parallelogram.

So then:

ΔCAD = ΔABC = ΔECB

Therefore, ABCD and ABEC are parallelograms.

It is found that ABCD and ABEC are parallelograms because a parallelogram can be divided into congruent triangles of different orientations.

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first one is easy money

right angle = 90, and we also have 42 so:

90+42=132

180-132=48

2nd one is weird, why is there a 150 down there? triangles add up to 180 nso right angle already gets 90 degrees.--oh wait I just got it, so that is the angle of the outer. we know a line is 180 degrees, so 180-150=30 so we found that degree

So now 90+30=120, 180-120=60

Answer:

560

Step-by-step explanation:

check the attached file, I am a maths expert...kindly check the answer

The length and width of the triangular base of the prism are both √18 units, and the height is 10 units.

Given that:

Height, h = 10

Volume, v = 90

We can use the formula for the volume of a triangular prism to solve for x:

Volume = length x width x height

1/2 · x · x · 10 = 90

x² = 18

x = √18

Therefore, the length and width of the triangular base of the prism are both √18 units, and the height is 10 units.

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97.04 mg Initial mass = 48 mg, Mass after 7 weeks = 48 mg * (1/2)^(12.25) Half-life of the goo in minutes = 120 / (log(37/296) / log(1/2)) The artifact was made approximately 22920 years ago.

Question 26:

The half-life of Radium-226 is 1590 years. To determine how many milligrams will remain after 3000 years, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where:

N(t) is the remaining amount after time t,

N₀ is the initial amount,

t is the elapsed time, and

T is the half-life.

Given that the initial amount is 200 mg, the elapsed time is 3000 years, and the half-life is 1590 years, we can substitute these values into the formula:

N(3000) = 200 * (1/2)^(3000/1590).

Calculating this, we find:

N(3000) ≈ 200 * (1/2)^(1.8862) ≈ 200 * 0.4852 ≈ 97.04.

Therefore, approximately 97.04 mg of Radium-226 will remain after 3000 years.

Question 27:

The half-life of Palladium-100 is 4 days. We can use the half-life formula again to determine the initial mass and the mass after 7 weeks.

1. Initial mass:

After 12 days, the sample of Palladium-100 has been reduced to 6 mg. We need to determine how many half-lives have passed in 12 days to find the initial mass.

t = (12 days) / (4 days/half-life) = 3 half-lives.

Let's denote the initial mass as M₀. We can use the formula:

M(t) = M₀ * (1/2)^(t/T).

Substituting the values, we have:

6 mg = M₀ * (1/2)^(3).

Solving for M₀:

M₀ = 6 mg * 2^3 = 48 mg.

Therefore, the initial mass of the sample was 48 mg.

2. Mass after 7 weeks (49 days):

To find the mass after 7 weeks, we need to determine how many half-lives have passed in 49 days:

t = (49 days) / (4 days/half-life) = 12.25 half-lives.

Using the formula, we can calculate the mass after 7 weeks:

M(49 days) = M₀ * (1/2)^(12.25).

Substituting the initial mass we found earlier:

M(49 days) = 48 mg * (1/2)^(12.25).

Calculating this value will give us the mass after 7 weeks.

Question 28:

To find the half-life of the radioactive goo, we can use the formula:

N(t) = N₀ * (1/2)^(t/T),

where N(t) is the remaining amount at time t, N₀ is the initial amount, t is the elapsed time, and T is the half-life.

Given that the initial amount is 296 grams and the amount after 120 minutes is 37 grams, we can substitute these values into the formula:

37 g = 296 g * (1/2)^(120/T).

To find the half-life T, we can rearrange the equation:

(1/2)^(120/T) = 37/296.

Taking the logarithm of both sides, we have:

120/T * log(1/2) = log(37/296).

Solving for T:

T = 120 / (log(37/296) / log(1/2)).

Calculate the value of T using this equation to find the half-life of the radioactive goo in minutes.

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A) The equation of the linear model that relates pressure P (in pounds per square inch) to depth d (in feet) is: P = 0.45d + 14.7. B) Integral of the slope of the model = P = 0.45d + 14.7. C) The pressure at a depth of 80 feet is 50.7 pounds per square inch. D) The depth at which the pressure is 3 atm is 65.333 feet.

Given information:

At sea level, the weight of the atmosphere exerts a pressure of 14.7 pounds per square inch, commonly referred to as 1 atmosphere of pressure. as an object descends in water pressure P and depth d are Linearly relaind.

In h nit water, the preseute at a depth of 33 it is 2 - atms, ot 29.4 pounds per square inch.

(A) Linear model that relates pressure P (in pounds per square inch) to depth d (in feet):Pressure exerted by a fluid is given by the formula P = ρgh, where P is pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column above the point at which pressure is being calculated.

As per the given information, At a depth of 33 feet, pressure is 29.4 pounds per square inch.

When the depth is 0 feet, pressure is 14.7 pounds per square inch.

The difference between the depths = 33 - 0 = 33

The difference between the pressures = 29.4 - 14.7 = 14.7

Let us calculate the slope of the model; Slope = (y2 - y1)/(x2 - x1)

Slope = (29.4 - 14.7)/(33 - 0)Slope = 14.7/33

Slope = 0.45

The equation of the linear model that relates pressure P (in pounds per square inch) to depth d (in feet) is:

P = 0.45d + 14.7

(B) Integral of the slope of the model:

Integral of the slope of the model gives the pressure exerted by a fluid on a surface at a certain depth from the surface.

Integral of the slope of the model = P = 0.45d + 14.7

C) Pressure at a depth of 80 feet:

We know, the equation of the linear model is: P = 0.45d + 14.7

By substituting the value of d in the above equation, we get: P = 0.45(80) + 14.7P = 36 + 14.7P = 50.7

Therefore, the pressure at a depth of 80 feet is 50.7 pounds per square inch.

D) Depth at which the pressure is 3 atms:

The pressure at 3 atmospheres of pressure is: P = 3 × 14.7P = 44.1

Let d be the depth at which the pressure is 3 atm. We can use the equation of the linear model and substitute 44.1 for P.P = 0.45d + 14.744.1 = 0.45d + 14.7Now we can solve for d:44.1 - 14.7 = 0.45d29.4 = 0.45dd = 65.333 feet

Therefore, the depth at which the pressure is 3 atm is 65.333 feet.

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Answer: the real answer for this will be p=3/2 and s=5

Step-by-step explanation: here

2p=3

2p/2=3b/2 divide both sides by 2

P=3/2

3/2 for p in s=5

S=5

S=5

Answer P=3/2 and s= 5

Got it

Hey there!

“Evaluate 2ps for p=3 and s=5”

• Side note: If p = 3 then SUBSTITUTE where “p” is at in the equation; if s = 5 then SUBSTITUTE where “s” is at in the equation!

• New equation: 2(3)(5)

2(3)(5)

2(3) = 6

6(5) = 30

Answer: A. 30 ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

In the triangle, the values are p=10.3, \(\angle Q=19.5\textdegree\) and \(\angle R = 112.5\textdegree\).

The functiοns οf an angle in a triangle are knοwn as trigοnοmetric functiοns, cοmmοnly referred tο as circular functiοns. In οther wοrds, these trig functiοns prοvide the relatiοnship between a triangle's angles and sides. There are five fundamental trigοnοmetric functiοns: sine, cοsine, tangent, cοtangent, secant, and cοsecant.

Here in the given triangle PQR, \(\angle P = 48\textdegree\) , q=5 and r=13.

Now using law of cosine fοrmula,

=> \(p^2=q^2+r^2-2qr.cos\angle P\)

=> \(p^2=5^2+13^2-2.5.13.cos 48\textdegree\)

=> \(p^2=25+169-130cos48\textdegree\)

=> \(p^2=107\)

=> p = 10.3

Now using law of sine then,

=> \(\frac{p}{sinP}=\frac{q}{sinQ}\)

=> \(sinQ=\frac{q sinP}{p}\)

=> \(sin Q= \frac{5sin 48\textdegree}{10.3}\)

=> sin Q = 0.344

=>\(\angle Q = 19.5\textdegree\)

Now sum οf all angles in triangle is 180°. Then,

=>\(\angle P+\angle Q+\angle R = 180\textdegree\)

=> \(\angle R = 180-48-19.5=112.5\textdegree\)

Hence the answers are p=10.3, \(\angle Q=19.5\textdegree\) and \(\angle R = 112.5\textdegree\).

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The odds of obtaining a yellow marble from the second bag are $frac62245$. As a result, option D is right.

Bag A in this problem comprises $3 white marbles and $4 black marbles.

Bag B includes $6.00 worth of yellow marbles and $4.00 worth of blue marbles. Bag C includes $2 blue marbles and $5 yellow marbles.

A marble is picked at random from bag a, and if it is white, a marble is drawn from bag b.

If it is not black, a marble is selected from bag c. We must calculate the likelihood that the second stone drawn is yellow.

The Bayes theorem can be used to tackle this problem. First, we shall calculate the chance of pulling a white marble from bag a.

We are handed a bag containing $3 white marbles and $4 black marbles.

As a result, the likelihood of pulling a white marble from bag an is:$$P(text white from bag a) = frac33+4=frac377$$If we pull a white marble from bag a, the chance of obtaining a yellow marble from bag b is: $P(text yellow from bag b|white from bag a)=frac6+4=frac35$

Similarly, if we pull a black marble from the bag a, our chances of obtaining a yellow marble from bag c are as follows:$P(text yellow from bag c | black from bag a)=frac22+5=frac27$

As a result, the likelihood of drawing a yellow marble from the second bag is:$P(text yellow marbling)=P(text yellow from bag b|white from bag a)dot P(text white from bag a)dot P(text white from bag a) +P(text yellow from bag c|black from bag a)cdot P(text black from bag a)dot P(text yellow from bag a)cdot P(text yellow from bag a)cdo$$$$= frac35 cdot frac37 + frac27 cdot frac47 + frac247 cdot frac447$$$$=frac635 + frac8245 = frac62245$$

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Answer:

5.8 x 10 -4

Step-by-step explanation:

move decimal to 5.8 then find out how many times the decimal is moved from the final 5.8 to initial .00058

hope it helps you tell me in the comment box

(•‿•)

A "required parameter" requires an assigned value for the argument used to call the method, while "optional parameters" do not need to be included in the method call and have a default value assigned to them.

The type of parameter that requires that the argument used to call the method must have an assigned value is a "required parameter".

Required parameters are parameters that must be included in the method call, and the argument passed for the required parameter must have a value assigned to it. If a required parameter is not included in the method call, or if the argument passed for the required parameter does not have a value assigned to it, an error will be thrown.

In contrast, there are also optional parameters, which are parameters that do not need to be included in the method call. If an optional parameter is not included in the method call, the method will use a default value assigned to the parameter.

In many programming languages, the syntax for specifying required and optional parameters in a method or function call is specified using different symbols, such as parentheses or square brackets.

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The number that will be multiplied by -18 to give a product that is less than -18 would be =1.6. That is option D.

For option A : The product of -3.4 × -18 = 61.2. The answer is more than the given figure.

For option C : The product of 3/4 × -18 = -13.5. This product is bigger than the given figure.

For option D: The product of 1.6× -18 = −28.8. This is less than the given product and therefore the correct answer.

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