The larger of two numbers is 1 more than 3 times the smaller. Their sum is 65. Find the numbers.

I WILL USE CROSS MULTIPLICATION

[tex] \frac{4}{7x} = 28 \\ 4 = 28(7x) \\ 196x = 4 \\ \frac{196x}{196} = \frac{4}{196} \\ x = \frac{1}{49} [/tex]

ATTACHED IS THE SOLUTION

Answer:

16

Step-by-step explanation:

7x=28x4

7x=112

x=112/7

x=16

27.80% is percentage of items .

What percentage means?

Mean = 7

standard deviation = 3 ounces

Required % = p (5.6<x < 7.1 ) × 100 = ?

z = x - μ/σ = 5.6 - 7/2

 z = 7.1 - 7/2 = 0.05

∴ P(5.6 < x < 7.1 ) = p ( - 0.7 < z < 0.05 )

   p( z < 0.05 ) - p (  z < - 0.7)

= 0.51994 - 0.24196 ≅ 0.2780

So, required % =  0.2780 × 100

                         = 27.80%

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The suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.

So, the flat rate is $7 and we're charged $0.65 per mile:

Then the suitable expression will be:

Cost if we traveled 15 miles:

So, 0.65x = y where x = 15.

It would cost $9.75 for 15 miles.

Therefore, the suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.

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Answer:

Step-by-step explanation:

30.25g=296.6511625 m/s^2

Answer:

If the same cup of 190∘F soup is instead placed into a freezer set at 30∘F, what is the time required for the soup to cool from 190∘Fto135∘F in this situation?

If she wants to meet her target distance 3/20 steps need to be taken.

Emily made the decision to walk 4/5 kilometers every day in order to keep healthy. She walked a distance of 2/5 miles to work and a distance of 1 mile for lunch.

The desired range is 4/5 miles.

walked for 2/5 miles and for 1/4 miles.

Total miles walked is [tex]\frac{2}{5} + \frac{1}{4}[/tex]

= [tex]\frac{13}{20}[/tex]

Mileage walked overall is +

LCD is 20

add the fractions after matching the denominators

The desired range is 4 to 5 miles.

Now deduct the distance you walked from the goal distance.

[tex]\frac{4}{5} - \frac{13}{20} \\\\\frac{16}{20} - \frac{13}{20} \\\\\frac{3}{20}[/tex]

the required walking distance is 3/20

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The elevation is 848 feet.

The word elevation is often used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying aeroplanes or orbiting satellites, and depth is used to describe locations below the surface.

A geographical feature's elevation is determined by how high it is above the mean sea level (MSL). Accordingly, elevation is the distance between the height that corresponds to the ocean's surface and the top of the feature.

Given:

Hilda hiked up 530 feet,

down 602 feet,

up 1003 feet,

and down 89 feet to get to the lake.

Taking all similar cases together

Hiked up

= 530 + 1003

= 1533 feet

and, hiked down

=602+83

= 685

Thus, the elevation is

= 1533 - 685

= 848

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The various values using mathematical operations are;

1) B: 70

2) C:  1300

3) A: 0.0063

4) B: 0.0037

5) B:  80

1) We want to multiply 0.7 times 100.

Now, 0.7 can be expressed as 0.7 = 7/10. Thus;

0.7 * 100 = 7/10 * 100 = 70

2) We want to multiply 0.13 by 10000.

0.13 can be expressed as;

0.13 = 13/100. Thus;

0.13 * 10000 = 13/100 * 10000 = 1300

3) We want to multiply 0.63 times 0.01.

They can be expressed as;

63/100 * 1/100 = 63/10000 = 0.0063

4) Divide 0.37 by 100.

0.37 can be expressed as 37/100. Thus;

0.37/100 = 37/100 ÷ 100

= 37/100 * 1/100 = 37/10000 = 0.0037

5) Divide 0.8 divided by 0.01.

They can be expressed as;

8/10  ÷ 1/100

= 8/10 * 100/1

= 80

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The most appropriate form for equation of circle will be given by-

Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units

What is equation of circle?

A round figure whose all points on the boundary maintains a fixed distance from a point known as the centre of the circle and the fixed distance is called the radius of the circle.

If radius of a circle is doubled, we will obtain the diameter of the circle.

Equation of circle

[tex](x-a)^2 + (y-b)^2 = r ^2[/tex]

where (a, b) is the centre of the circle and r is the radius of the circle.

Here,

[tex]x^2 + y^2 + 10x-6y + 15 = 0[/tex]

[tex]x^2 + 2\times x\times 5 + 5^2 -5^2 +y^2 -2\times y\times 3 + 3^2 - 3^2 + 15 = 0\\(x+5)^2 + (y-3)^2-25-9+15=0\\(x+5)^2 + (y-3)^2-19=0\\(x+5)^2 + (y-3)^2=19\\ (x+5)^2 + (y-3)^2=\sqrt{19}^2\\[/tex]

Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units

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The Solution:

Given the equation that modeled the population of fish after time (t) in years as below:

part 1:

We are to find the initial population of fish. This means we are to find the value of p when t = 0.

Part 2:

We are required to find the doubling time (t) for this population (Round the answer to the nearest tenth). This means we are to find t when P(t) = 500.

Note: double of 250 fish is 2x250 = 500 fish.

Dividing both sides by 3, we get

Taking the natural log of both sides, we get

The probability of getting heads is 1/2 which typically implies that the coin is fair. NO, procedure (b) does not give a fair coin flip outcome.

Given that, we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

The following procedure for accomplishing our task are:

1. Flip the coin.

2. Flip the coin again.

From here will know that the coin is first flipped twice

3. If both flips land on heads or both land on tails, it implies that we return to step 1 to start again. this makes the flip to be insignificant since both flips land on heads or both land on tails

But if the outcomes of the two flip are different i.e., they did not land on both heads or both did not land on tails , then we will consider such an outcome.

Let the probability of head = p

so P(head) = p

the probability of tail be = (1 - p)

This kind of probability follows a conditional distribution.

Therefore, the probability of getting heads is 1/2 which typically implies that the coin is fair. NO, procedure (b) does not give a fair coin flip outcome.

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"Your question is incomplete, probably the complete question/missing part is:"

Suppose that we want to generate the outcome of the flip of a fair coin, but that all we have at our disposal is a biased coin which lands on heads with some unknown probability p that need not be equal to1/2. Consider the following procedure for accomplishing our task:

1. Flip the coin.

2. Flip the coin again.

3. If both flips land on heads or both land on tails, return to step 1. 4. Let the result of the last flip be the result of the experiment.

(a) Show that the result is equally likely to be either heads or tails.

(b) Could we use a simpler procedure that continues to flip the coin until the last two flips are different and then lets the result be the outcome of the final flip?

If the front suspension system of a car has coiled springs of spring constant(k) of about 82,000N/m attached to the front wheels, then the force required to compress this spring by 1.2 cms will be  984N.

As per the question statement, the front suspension system of a passenger car has coiled springs attached to the front wheels and a typical spring has a spring constant "k" of about 82,000 k/m.

We are required to calculate the force required to compress this spring by 1.2 cms

To solve this question, we will need to apply the formula to calculate the force to compress a spring, which is known as the Hooke's Law. So, as per the Hooke's Law, the force (F) required to compress a spring of spring constant (k) by "x" units, can be represented as

[F = (k * x)]

Now comparing the RHS of the Hooke's Law equation with the data provided in the question statement, we get, (k = 82000 N/m) and

(x = 0.012 m), and using these values in the Hooke's law equation, we get, the force required to compress a spring of spring constant(k) of about 82,000N/m by 1.2 cms will be (82000 * 0.012)N = 984 N.

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To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w

We build the transformation, i.e, a new weight function, as follows: We want the elements with maximum weight to have minimum weight and. In other words, two weight functions need to be mutually opposite in this sense. Therefore, if we denote the maximum weight of all the elements with w ∗ : w ∗ = max w(x) x ∈ S we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly. Since we want the weight function to be strictly positive, we finish our construction with: w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)

Using equation (1) we can derive the following expression for the weight w ′

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To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w

We build the transformation,

or a new weight function, as follows:

We want the elements with maximum weight to have minimum weight a In other words, two weight functions need to be mutually opposite in this sense.

Therefore, if we denote the maximum weight of all the elements with

w ∗ : w ∗ = max w(x) x ∈ S

we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly.

Since we want the weight function to be strictly positive, we finish our construction with:

w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)

Using equation (1) we can derive the following expression for the weight w ′

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Answer:

Step-by-step explanation:

So, you have to isolate the variable. Think of it as finding how many plants she gave fertilizer to. 0.4n+8=25, when moving the 8 to the other side, it becomes negative. 0.4n=25-8. 0.4n=17. You then find the variable n. think of it as dividing 17 by 0.4 or multiplying n a certain number of times to find the number of plants.17/0.4 is 42.5. therefore, she gave 42 plants fertilizer, depending on what your teacher wanted to count. If she says round down, 42. If she wants to round up, 43. If she wants to be specific, 42.5. I would personally put the decimal.

It is to be noted that the graph of g(x) = (x+2)³ -6 compares to the parent function f(x) = x³ in that g(x) is shifted 2 units to the left and 6 units down. See the explanation below.

A parent function in mathematics is the simplest function in a family of functions that retains the concept of the whole family.

Here is how the transformation of a function can occur

Any change can occur during the transformation of a function.

Typically, they can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.

If the initial function is y = f(x), and the horizontal axis represents inputs and the vertical axis represents outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

A function sets the value of one set's elements to the value of another set's specified element.

Given that the parent function is f(x)=x³, while the transformed function is g(x)=(x+2)³ - 6. Therefore, the transformation of the parent function that results in the transformed function is that g(x) is shifted 2 units to the left and 6 units down.

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The transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.

The function is a type of relation, or rule, that maps one input to a specific single output.

A change can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.

If the initial function is y = f(x), and the horizontal axis shows the inputs and the vertical axis shows outputs, then:

Horizontal shift would be Left shift by c units; y=f(x+c) and Right shift by c units; y=f(x-c)

Vertical shift would be Up by d units; y = f(x) + d and Down by d units; y = f(x) - d

Stretching would be as Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given that the parent function is; f(x)=x³,

And the transformed function is; g(x)=(x+2)³ - 6.

Hence, the transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.

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Answer:

1422.5778

Step-by-step explanation:

8.89x8.89=79.0321. 79.0321x18=1422.5778

Answer:

a)

f(1/2) = 2

g(-1) = -3/2

Step-by-step explanation:

for f(x) = 2x + 1 substitute the x with 1/2

2(1/2) +  1 then solve

1+1

2

for g(x) = 3x - 1/2x + 1 substitute with -1

3(-1) - 1/2(-1) +1 then solve

-3 + 1/2 + 1

-3/2

Answer:

400

Step-by-step explanation:

=

1

We know that:

3 R=4% 1 = 48

T =3 R = 4% into formula 48 2 Substitute

1=Prt

48= Prt

Solve the equation:

3 × 0.04x= 48

3

X = 400

so Pablo invested 400$

Answer:

-1

Step-by-step explanation:

when you change g[×] to g[-2] , 3x+5 change to 3[-2] +5

Answer:

6.3 * 10^3

Step-by-step explanation:

6.3 * 10^3

:]

The annual percentage yield is 1.55% for any account if the interest is compounded daily.

Given that Island bank is advertising a special 1.55% APR for long-term CDs. Manny takes out a 1 year CD for $40,000. The interest is compounded daily.

Principal (P) = $40000

Interest rate(r) = 1.55% = 0.0155

Number of periods (n) = 365

The formula for Annual Percentage Yield (APY) for an account that is compounded continuously is given as

APY = [1 + (r/n)ⁿ - 1]

Substitute the values in the formula to get

= [1 + (0.0155/365)³⁶⁵ - 1]

= [1 + 0.000042)³⁶⁵ - 1]

= [1.000042]³⁶⁵- 1

= 1.015448 - 1

= 1.55%

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Answer:

Answer down below!

Step-by-step explanation:

(Part a):

So we have the information that after 20 minutes, the submarine descended 480 feet.

To find how many feet it descended per minute, all we need to do is divide 480 and 20 which will give us 24

Every 1 minute, the submarine descended 24 feet.

(Part b):

Now that we have how many feet it descended per minute, we have to make an expression that goes along with it.

Our unknown variable in this case will have to have to be the feet.

We can use the letter f to express that. We can also use the letter m to express our minutes in the end

So after 24(f) = m

(Part c):

After 5 Minutes: 120 ft

After 10 Minutes: 240 ft

After 15 Minutes: 360 ft

After 18 Minutes: 432 ft

y = f(2x)  ⇒ Shrink the graph of function f(X) by half horizontally .

What is function and example?

y = f((1/2)x)) ⇒ Stretch the graph of f(x) horizontally by factor 2 .

y=2f(2x)  ⇒ Shrink the graph of f(X) by half horizontally .

                     Shrink the graph twice ( vertically) .

y = f(2x)  ⇒ Shrink the graph of f(X) by half horizontally .

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8.32 Km is the distance of how much it would be covered

A unit rate means a quantity at a rate of one of something.

The distance traveled with 2 liters of petrol is 47.9 km.

A unit rate means a quantity at a rate of one of something.

It is written with a denominator of one. 

Example:

Man can walk 6km in 2 hours.

In one hour a man can walk 3 km.

We have,

A vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol.

This can be written as:

524/25 km = 7/8 liters

Multiply both sides by 8/7

8/7 x 524/25 km = 1 liter

23.95 km = 1 liter _____(1)

Now,

Multiply 2 on both sides of (1)

2 x 1 liter = 2 x 23.95 km

2 liter = 47.9 km

Thus,

The distance traveled with 2 liters of petrol is 47.9 km.

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The total number of students that are on the team is e. 210 if the ratio of  freshmen to sophomores to juniors to seniors is 1:3:4:6

As the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6, we can write the number of students as;

Freshmen = 1x

Sophomores = 3x

Juniors = 4x

Seniors = 6x

As the number of juniors on the team is 60, therefore;

4x = 60

To determine the value of x we divide both sides by 4;

4x/4 = 60/4

x = 15

Now the total number of students can be found by substituting the value of x;

1x + 3x + 4x + 6x

1(15) + 3(15) + 4(15) + 6(15) = 210

Hence, the total number of students on the team is 210.

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The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.

The given equation is 3x+3y²+6y+3=0.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Left

Vertex: (0, -1)

Focus: (-1/4, -1)

Axis of symmetry: y=-1

Directrix: x = 1/4

The coordinate points to plot (2, 0.41), (-2, -2.41), (-1, 0), (-1, -2) and (0, -1).

The parabola with vertex (-1, 0), focus (-1/4, -1) and directrix x = 1/4. Therefore, option C is the correct answer.

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Answer:

-3

Step-by-step explanation:

It was quite easy

Answer:

Step-by-step explanation: factor out x2

from the expression x2 (x+11) -3x-33

Factor out-3 from the expression x2 (x-+11) -3(x+11)

Factor out x+11 your solution is x2 (x+11) (x-3).