Monica deposits ​$200 into a savings account that pays a simple interest rate of 3.9​%. Paul deposits ​$300 into a savings account that pays a simple interest rate of 3.2​%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she​ correct? Justify your response.

Answer:

x < 11

Step-by-step explanation:

8 - 3x > -25

-8            -8    (subtract 8 from both sides)

-3x > -33

/-3      /-3        (divide each side by -3: because we divided we must flip the symbol)

x < 11

Answer:

5x⁴

Step-by-step explanation:

10x⁸÷2x⁴=

5x⁴

Answer:

3 different ways

Step-by-step explanation:

Answer:

3 different ways

Step-by-step explanation:

hope this helps

example of the diffrent way to write a ratio :

5 to 10

5 : 10

\(\frac{5}{10}\)

Answer:

KF = 35

Step-by-step explanation:

Since it's a line with K in the middle, we know that the distance SF is the same as SK + KF.

(Start at S, first go to K, then continue to F. You've traveled the same distance as from S to F.)

SF = SK + KF

Let's put in the values we got.

5x + 2 = 27 + (3x -1)

Opening the parenthesis.

5x + 2 = 27 + 3x - 1

5x + 2 = 26 + 3x

Now let's subtract 3x from both sides.

2x + 2 = 26

Now, subtract 2 from both sides.

2x = 24

If we divide by 2...

x = 12

We know that...

KF = 3x -1

Since x is 12, let's put that in.

KF = 3 * 12 - 1 = 36 - 1 = 35

Answer: KF is 35 !

Answer:

  a. f(n) = n(n+1)/2

  b. 351

  c. 19

  d. no; n would not be an integer for f(n) = 17.

Step-by-step explanation:

a. The terms are 1, 3, 6, 10, ...

Each term has the term number added to the previous term. That is, first differences are 3-1 = 2, 6-3 = 3, 10-6 = 4. These differences have a constant difference of 1.

When the 2nd differences are constant, a 2nd degree polynomial can describe the sequence. It is a little bit of trouble to find that polynomial.

For the polynomial ...

  \(f(n)=an^2+bn+c\)

We can substitute values for n and f(n) to get 3 equations in 3 unknowns:

  \(1=a\cdot1^2+b\cdot1+c\\\\3=a\cdot2^2+b\cdot2+c\\\\6=a\cdot3^2+b\cdot3+c\)

Solving these equations by your favorite method gives ...

  (a, b, c) = (1/2, 1/2, 0)

That is, the function representing the relationship is ...

  f(n) = n(n+1)/2 . . . . the function describing the relationship

__

b. f(26) = 26(27) = 13(27) = 351 . . . . the number of squares in term 26

__

c. The number of the term having 190 squares can be found by solving ...

  n(n +1)/2 = 190

  n(n +1) = 380 = 19(20)

The 19th term will have 190 squares.

__

d. Terms 5 and 6 are 15 and 21.

17 is not the value of one of the terms in this sequence.

Answer:

92

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

155+33=188-4=184 divided by 2 =92

we have that

Part A

s=3 1/2

Find A

A=s^2

s=3 1/2=7/2

substitute

A=(7/2)^2

A=49/4 unit2

convert to mixed number

49/4=48/4+1/4=12+1/4=12 1/4 unit2

Part b

S=8.257 units

A=(8.257)^2

A=72.71 unit2

Part c

A=361 unit2

Find s

A=s^2

substitute

361=s^2

square root both sides

s=19 units

Part d

A=562 unit2

A=s^2

562=s^2

s=23.71 units

The  trains are side by side after approximately 15 seconds.Option (b) is correct.

The position of the first train is given by the function:

\($$y_1 = 14t^2$$\)

The position of the second train is given by the function:

\($$y_2 = 130t + 1200$$\)

To find the time when the trains are side by side, we need to solve for the value of t that makes y1 = y2. Thus, we can set the two equations equal to each other:

\($$14t^2 = 130t + 1200$$\)

Rearranging the terms, we get:

\($$14t^2 - 130t - 1200 = 0$$\)

Dividing both sides by 2 to simplify the coefficients, we get:

\($7t^2 - 65t - 600 = 0$$\)

We can use the quadratic formula to solve for t:

\($t = \frac{-(-65) \pm \sqrt{(-65)^2 - 4(7)(-600)}}{2(7)} = \frac{65 \pm \sqrt{4225 + 16800}}{14}$$\)

Simplifying the expression under the square root, we get:

\($$\sqrt{21025} = 145$$\)

So the solutions are:

\($t_1 = \frac{65 + 145}{14}=15$$\)

\($t_2 = \frac{65 - 145}{14} \approx -5.71$$\)

Since time cannot be negative, we discard t2 as an extraneous solution. Thus, the viable time when the trains are side by side is:

\($t = t_1 =15$$\)

Therefore, the trains are side by side after approximately 15 seconds.

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the surface area of the cube is 150 square inches, and the volume of the cube is 125 cubic inches.

what is surface area ?

Surface area is the measure of the total area that the surface of an object occupies. It is the sum of the areas of all the faces, surfaces, and curved surfaces of the object. Surface area is expressed in square units such as square meters, square inches, square feet, and so on.

In the given question,

A cube is a three-dimensional shape with six identical square faces. To calculate the surface area and volume of a cube with length 5 inches, breadth 4 inches, and height 12 inches, we can use the following formulas:

Surface area of a cube = 6s²

where s is the length of one side of the cube.

Volume of a cube = s³

where s is the length of one side of the cube.

In this case, since all sides of the cube have the same length, s = 5 inches. Therefore:

Surface area of the cube = 6s² = 6(5 inches)² = 6(25 square inches) = 150 square inches.

Volume of the cube = s³ = (5 inches)³ = 125 cubic inches.

So, the surface area of the cube is 150 square inches, and the volume of the cube is 125 cubic inches.

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We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

Step one:

given

original price= $60

discount =20% of 60

discount = 20/100*60

discount = 0.2*60

discount = $12

selling price= 60-12= $48

Added price= 10% off $48

Added price= 10/100 *48

Added price= 0.1 *48

Added price= $4.8

new price= 4.8-48=$43.2

the new price of the jacket is $43.2

1. The jacket is now 40% off its original price

40/100*60=$24-----False

2. The jacket now costs $48.00-----False

3.  The jacket is now 72% of its original price= 72/100*60=$43.2----True

4. The jacket now costs $43.20------True

Answer:

Each exterior angle is 15°.

-------------------

We know sum of exterior angles is 360°.

There are 24 exterior angles and each has the measure of:

Answer:

  first step: sign error in application of the distributive property

Step-by-step explanation:

6x – 2(x – 5) = –2   . . .   given

6x – 2x – 10 = –2   . . .    X  -2(x -5) = -2x +10, not -10

Cameron made a sign error in application of the distributive property.

__

The next steps should have been ...

  \(4x+10-10=-2-10\\\\4x=-12\\\\\dfrac{4x}{4}=\dfrac{-12}{4}\\\\x=-3\)

Answer:

13.7

Step-by-step explanation:

15^2-6^2=189

The square root of 189 is 13.74 blah blah blah

Answer:

13.7

Step-by-step explanation:

a²+b²=c²

a²+6²=15²

a²+36=225

a²=189

a≈13.7

"R" is the distance from the origin to the point.

R = √(-3² + 7²)

R = √(9 + 49)

R =  √(58)

R = 7.62

tangent (Θ)  =  7 / -3

Θ  =  arctan (7 / -3)

Θ  =  113.2°  counterclockwise from the x-axis

Answer:

The original or the Bigger prism's volume would be 15 x 6 x 10= 900 cubic centimetres given that the smaller prism has not been cut out.

the volume of the cut-out cube would be 6 x 4 x 6= 144 cubic centimetres

so the original volume of the prism is 900 - 144= 756 cubic centimetres

Answer:

It will take them 7.89 days

Answer:

1

Step-by-step explanation:

Because the pre image and dilated image are congruent, the scale factor is 1.

Answer:

The answer is 3.18 miles/runner.

Step-by-step explanation:

To solve this problem, we need to find the distance that each member of the team runs. To do this, we have to divide the total distance of the race (12.72 miles) by the number of runners on the team (4 runners).

If we perform this operation, we get:

12.72 miles/4 runners

= 3.18 miles/runner

Therefore, the correct answer is that each team member runs 3.18 miles during the race.

Hope this helps!

The interval of convergence is (-∞,∞) and the radius of convergence is ∞.The power series for f(x) can be found using the formula:

f(x) = Σ(n=0 to ∞) [fⁿ(c)/n!]*(x-c)ⁿ

where fⁿ(c) represents the nth derivative of f evaluated at x=c.

In this case, we have:

f(x) = 5/2x-3

f'(x) = -5/2(x-3)⁻²

f''(x) = 5(x-3)⁻³

f'''(x) = -15(x-3)⁻⁴

and so on.

Evaluating these derivatives at c=-3, we get:

f(-3) = 5/2(-3)-3 = -15/2

f'(c) = -5/2(-3-3)⁻² = -5/36

f''(c) = 5(-3-3)⁻³ = 5/216

f'''(c) = -15(-3-3)⁻⁴ = -5/1296

and so on.

Substituting these values into the power series formula, we get:

f(x) = Σ(n=0 to ∞) [(-1)ⁿ*5/(2*3ⁿ)*(x+3)ⁿ]

This can be simplified to:

f(x) = Σ(n=0 to ∞) [(-1)ⁿ*5/(2*3ⁿ)*xⁿ] + Σ(n=0 to ∞) [(-1)ⁿ*5/(2*3ⁿ)*(-3)ⁿ]

The first sum represents the power series centered at 0, while the second sum is a constant term (-15/2) that is added to shift the series to be centered at -3.

To determine the interval and radius of convergence, we can use the ratio test:

|a(n+1)/a(n)| = |(-1)^(n+1)*5/(2*3^(n+1))/( (-1)^n*5/(2*3^n))|

= 3/2

Since this ratio is constant and less than 1, the power series converges for all values of x.

Therefore, the interval of convergence is (-∞,∞) and the radius of convergence is ∞.

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To solve this problem, we can use the Chinese Remainder Theorem. We need to find the remainder when 2202 202 is divided by both 2101 and 251.

First, note that 2101 and 251 are relatively prime. Therefore, by the Chinese Remainder Theorem, there exists a unique remainder between 0 and 2101 * 251 - 1 (inclusive) that satisfies the two conditions.

To find this remainder, we can use the remainders when 2202 202 is divided by 2101 and 251.

Note that 2202 is congruent to 101 (mod 2101) and 0 (mod 251). Therefore, we can use the Chinese Remainder Theorem to find that the remainder when 2202 202 is divided by 2101 * 251 is congruent to:

101 * (251^2) * (251^(-1)) + 0 * (2101^2) * (2101^(-1)) (mod 2101 * 251)

Using the fact that 251^(-1) is congruent to 201 (mod 2101) and 2101^(-1) is congruent to 1922 (mod 251), we can simplify this expression to:

101 * (251^2) * (201) + 0 * (2101^2) * (1922) (mod 2101 * 251)

Simplifying further, we get:

101 * 251 * 201 (mod 2101 * 251)

This is congruent to 101 * 201 (mod 251), which is congruent to 101 (mod 251).

Therefore, the remainder when 2202 202 is divided by 2101 251 1 is 101, which is option (b).

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Answer:

The 1 liter bottle is better value

Step-by-step explanation:

Cost of 750 ml = £1.90

Cost of 1 liter = £2.50

1000 ml = 1 liter

Cost per 250 ml

750 ml / 3 = £1.90 / 3

250 ml = £0.6333333333333

Approximately,

£ 0.633

Cost per 250 ml

1 liter / 4 = £2.50 / 4

250 ml = £0.625

The 750 ml bottle is not a better value

The 1 liter bottle is better value

Answer:

300

Step-by-step explanation:

375 divided by 5=75

Each “1”=75

4x75=300

There are 300 boys.

Hope this makes sense

Answer:

300 boys

Step-by-step explanation:

Let the number of boys = x

Girls: 375

boys : girls = 4 : 5

total in the ratio is 9

girls are 5/9 of total, and are 375

boys are 4/9 of total

5/9 x = 375

x = 375 × 9/5

x = 675

Boys are 4/9 of total.

4/9 × 675 = 300

It Will take approximately 1.99 minutes for the element to decay to 80 grams.

To solve this problem, you can use the formula for exponential decay: y = a * b^x

Where "y" is the final amount of the substance, "a" is the initial amount of the substance, "b" is the decay constant (in this case, b = 0.5 since the half-life of element x is 11 minutes), and "x" is the time in which the decay occurs.

In this case, we are trying to find the value of "x" (the time in which the decay occurs) given the values of "y" (80 grams) and "a" (300 grams).

Substituting these values into the formula, we get:

80 = 300 * 0.5^x

To solve for x, we can divide both sides by 300 and take the logarithm of both sides: log(80/300) = log(0.5^x)

-1.386 = x * log(0.5)

-1.386 = x * -0.693

x = 1.99

This tells us that it would take approximately 1.99 minutes for the element to decay to 80 grams. Rounding to the nearest tenth of a minute, this is approximately 2.0 minutes.

Therefore, it would take approximately 1.99 minutes for the element to decay to 80 grams.  

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Answer:

21 cm

Step-by-step explanation:

V = (4/3)(pi)r^3

(4/3)(3.14)(r^3) = 4851 cm^3

r^3 = 1158.1 cm^3

r = 10.5 cm

d = 2r = 2(10.5 cm) = 21 cm

Answer:

Step-by-step explanation:

You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).

Writing the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y -2 = 1/2(x -(-1)) . . . . . using given slope and point

  2y -4 = x +1 . . . . . . . . . . multiply by 2

  x -2y =  -5 . . . . . . . . . . . . add -1 -2y

Setting x=0 tells us the y-intercept is ...

  0 -2y = -5

  y = -5/-2 = 5/2

So, the y-intercept is (0, 5/2).

Setting y=0 tells us the x-intercept is ...

  x -2(0) = -5

  x = -5

So, the x-intercept is (-5, 0).

It will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...

  x -2y = -5

  x = -5 +2y = -5 +2(6) = 7

Another point on the line is (7, 6).

__

Additional comment

If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.

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Given equation g = x-1/k in terms of x would be x = 1 + gk

for given question,

we have been given an equation g = x-1/k

Dyani began solving the equation g = x-1/k for x by using the addition property of equality.

We solve given equation for x.

⇒ g = x-1/k                      ..........(Given)

⇒ gk = (x - 1/k)k               .........(Multiply both the sides by k)

⇒ gk = x - 1

⇒ gk + 1 = x - 1 + 1           .........(Add 1 to each side)

⇒ gk + 1 = x

⇒ x = 1 + gk

Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk

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The ratio of sin C in simplest form is 72/97

What is the trigonometric ratio?

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

Sin C = (Opposite side)/ (hypotenuse )

         =  AB/AC

         =  72/97

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Answer:

Will can buy 8 pounds of granola with $10.

Step-by-step explanation:

If it is $3.75 for 3 pounds of granola then it is $1.25 for 1 pound of granola.

1.25 * x = 10

this equation will allow us to find a number that will add up to 10.

Another way to write this equation is:

10/1.25 = x

10/1.25 = 8

Now check your work:

1.25 * x = 10

1.25 * 8 = 10

10 = 10

Final Answer:

Will can buy 8 pounds of granola with $10.

Using proportions, it is found that the amount that netball will receive is of:

B. $240,000

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Due to the ratios, the proportion of funding that is destined to netball is given by:

\(p = \frac{2}{5 + 3 + 2} = \frac{2}{10} = 0.2\)

Hence, out of $1.200,000, the amount destined to netball is:

A = 0.2 x $1.200,000 = $240,000.

Which means that option B is correct.

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