Simplify.

3/2(x+3/4)−(x+1)

When Jerry puts 1500 pounds in the bank for 5 years then the rate of interest which makes the amount equal for Jerry and Neil is 1.85%.

Given Neil puts 1550 pounds in the bank, at a rate of 3% compound interest.

we need to calculate the total amount and interest at the end of 5 years.

P=1500 pounds

r = 3%

n = 5 years.

A = P(1+r/100)ⁿ

A = 1500(1+3/100)⁵

A = 1500(103/100)⁵

A = 1500 × 103/100 × 103/100 × 103/100

A = 3278181/2000

A = 1639.09

C.I = A-P

= 1639.09 - 1500

= 139.09

From the question, After 5 years they have the same amount.

Therefore we use the amount to calculate rate of interest as :

A = 1639.09

Simple interest = 1639.09 - 1500

= 139.09

Therefore, P = 1500

I = 139.09

t = 5 yrs

R = (100×I)/(P×t)

R = (100×139.09)/(1500×5)

R = 1.85%

Hence the rate of interest is 1.85%.

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The smallest possible range of the chosen integers is; 2015

First of all, the range of a set of numbers is the difference between the largest and smallest numbers in the set.

The smallest range of a set of four different positive integers is 3. This occurs when the integers are consecutive, and only in this case. We first show that we cannot have four consecutive integers

with a mean of 2017.

Assume, to the contrary, that n is a positive integer such that the consecutive integers n, n + 1, n + 2 and n + 3 have 2017 as their mean.

Thus;

[n + n + 1 + n + 2 + n + 3]/4 = 2017

4n + 6 = 2017 * 4

n = 2015.5

Since n is an integer, then this can't be true. However, with a little tweaking of this, we can tell that we can use 2015 as our least integer.

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The equation that can be used to determine the number of onion rings and the number of chicken wings are x + y = 19 and 40x + 75y = 970.

To verify a proportionality, that is, whether the quantities are proportional or not, we must make an equality of ratios. If these ratios are equal, the values ​​will be proportional.

Let x represent the number of onion ring and y represent the number of chicken wings.A combination meal with onion rings and chicken wings has a total of 19, hence:

x + y = 19      (1)

Also, they altogether contained 970 calories:

40x + 75y = 970     (2)

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If a football team gained [tex]2\frac{3}{4}[/tex] yards and then lost [tex]4\frac{3}{5}[/tex] yards on the next play, then their total loss is  [tex]1\frac{17}{20}[/tex] yards

The total yards they gained in first match =  [tex]2\frac{3}{4}[/tex] yards

Convert the mixed fraction to the simple fraction

[tex]2\frac{3}{4}[/tex] yards = 11/4 yards

The total yards they loss in second match = [tex]4\frac{3}{5}[/tex] yards

Convert the mixed fraction to the simple fraction

[tex]4\frac{3}{5}[/tex] yards = 23/5 yards

Total loss = The total yards they loss in second match- The total yards they gained in first match

Substitute the values in the equation

Total loss = 23/5 - 11/4

= 37/20 yards

Convert the simple fraction to the mixed fraction

37/20 yards = [tex]1\frac{17}{20}[/tex] yards

Hence, If a football team gained [tex]2\frac{3}{4}[/tex] yards and then lost [tex]4\frac{3}{5}[/tex] yards on the next play, then their total loss is  [tex]1\frac{17}{20}[/tex] yards

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Answer:

350%

Step-by-step explanation:

1) To convert a decimal to a percentage multiply the given decimal by 100. So,

3.5 x 100 = 350

2) 350% is the final answer

Answer:

  8 cups

Step-by-step explanation:

Given a recipe for trail mix that calls for 1 cup of nuts for each 2 cups of granola, you want to know the number of cups of granola required for 12 cups of trail mix.

The fraction of the total volume of trail mix that is granola is ...

  granola / (trail mix) = granola / (nuts + granola)

  (2 cups)/(1 cup +2 cups) = 2/3

Applied to the quantity 12 cups of trail mix, we find the volume of granola to be ...

  granola = (2/3)×(12 cups) = 8 cups

You need 8 cups of granola for 12 cups of trail mix.

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The number of randomly selected Americans that must be surveyed is equal to 38 if the confidence interval is 97.5% with a 0.16 margin of error.

First, we calculate the critical value as follows;

a = (1 - 0.975) = 0.025 = 0.025 / 2 = 0.0125 = (1 - 0.0125) = 0.9875

Z - Critical value = NORM.S.INV (0.9875) = 1.96

As margin of error(ME) = 0.16

Therefore;

n = pq(Z²) / ME²

n = 0.5 × 0.5 (1.96)² / (0.16)²

n = 0.25 × 3.8416 / 0.0256

n = 0.9604 / 0.0256

n = 37.515

Rounding it to the nearest whole number;

n = 37.515 = 38

Hence 38 randomly selected Americans must be surveyed if the estimated confidence interval is 97.5% and the margin of error is 0.16.

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Differences with in number of volunteers can explain  60.01% of the variation in the amount of trash bags collected.

The coefficient of correlation (r) between both the number of volunteers x and also the number of trash bags collected y is 0.775.

To calculate the percentage of variation for one derivative contract by the other, simply square the correlation coefficient.

Here, r = 0.775

Squaring both side.

r² = 0.775²

r² = 0.600625

Simply multiply with 100 to get the percent.

r² = 60.0625

r² = 60.01

Thus, differences in the number of volunteers can explain 60.01% of the variation in the number of trash bags collected.

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Answer:

48484

Step-by-step explanation:

47rururiuddjdjdjdjdjdjfifiififififfififiduududdidikddkkfdkdkdkdkdkdiriiritifififjfjfjfjfjrjrjrjfififirififjfjfifififififififififififififififififififififirirjjrririi

The problem formed can be:

And the answer to the formed problem will be 26 miles.

So, using the above-given information about Angela, the problem that can be formed is:

To solve the problem, we will make a mathematical expression and then solve by mathematical operations as follows:

Therefore, the problem formed can be:

And the answer to the formed problem will be 26 miles.

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Answer:x+y=36

xy=256

x=256/y

256/y + y = 36

256/y + y²/y = 36y/y

y² - 36y +256 = 0

use the quadratic formula to get 18+2√17 and 18-2√17.

Step-by-step explanation:

Answer:

Car C  with a gas mileage of 18.18 mpg

Step-by-step explanation:

Compute mileages by the formula: Miles Driven/Gas Consumed and choose the highest value

Car A:  500 /  33.4 = 14.97 mpg

Car B : 43 / 2.5  = 17.2 mpg

Car C: 100 / 5.5 = 18.18 mpg

The most appropriate choice for Green's Theorem, Cauchy Riemann Equation and Cauchy Goursat Theorem will be given by-

Cauchy Goursat Theorem has been proved using Green's Theorem-

What is Green's Theorem, Cauchy Riemann Equation and Cauchy Goursat Theorem?

Green's Theorem

Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. Then

Green's Theorem states that

[tex]\int_c (Mdx + Ndy)=\int_D(M_x - N_y)dxdy[/tex]

M and N are functions of x and y

Cauchy Goursat Theorem

If a function f is analytic at all points interior to and on a simple closed contour C, then

[tex]\int_c f(z) dz = 0[/tex]

Cauchy Riemann Equation

If [tex]f(z)=u(x,y) + i v(x,y)[/tex] is analytic at z = x + iy then Cauchy Riemann Equation states that

[tex]u_x = v_y, u_y = -v_x[/tex]

Here,

Let [tex]f(z) = U(x,y) + iV(x,y)[/tex]

[tex]U, V, x, y[/tex] are continuous

[tex]f(z)dz = (U + i V)(dx + i dy)[/tex]

[tex]f(z) dz = (U dx - Vdy)+i(Vdx + Udy)[/tex]

[tex]\int_c f(z) dz = \int_c(U dx - Vdy)+i\int_c(Vdx + Udy)[/tex], C is the curve

By Green's Theorem,

[tex]\int_c f(z)dz = \int_D(U_ydydx - V_xdxdy)+i\int_D(U_xdxdy + V_ydydx)[/tex], D is the surface

[tex]\int_c f(z)dz = \int_D(-U_y - V_x)dxdy+i\int_D(U_x - V_y)dxdy[/tex][tex]\int_c f(z)dz = \int_D(V_x - V_x)dxdy+i\int_D(U_x - U_x)dxdy[/tex]

Since [tex]f'[/tex] is continuous, [tex]f[/tex] is analytic

So [tex]f[/tex] satisfies Cauchy Riemann equation

[tex]U_x = V_y, U_y = -V_x[/tex]

So,

[tex]\int_c f(z)dz = \int_D(V_x - V_x)dxdy+i\int_D(U_x - U_x)dxdy[/tex]

[tex]\int_c f(z)dz = 0[/tex]

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Complete Question

Suppose f is continuously complex differentiable on Ω , and T⊂Ω is a triangle whose interior is also contained in Ω . Apply Green's theorem to show that

[tex]\int_T[/tex] f(z)dz=0

This provides a proof of goursat’s theorem under the additional assumption that f′ is continuous.

.

Answer:

n = 5

Step-by-step explanation:

Any 3-digit number to the base n will have its rightmost digit have a place value of n⁰, its next rightmost digit a place value of n¹ and the leftmost digit will have a place value of n²

This means 133can be represented as follows
n²     n¹     n⁰

1       3      3

The actual value in terms of a base of 10

= 3 x n⁰ + 3  x n¹   + 1 x n²

= 3 x 1 + 3 x n + 1 x n²      (n⁰ = 1 and n¹ = n)

= 3 + 3n + 1n²

Since we are given the information that 133ₙ = 43₁₀
3 + 3n + 1n²  = 43

subtract 3 from both sides
3n + 1n² = 40

Rewrite as

n² + 3n = 40

Factoring n on the left side=>
n(n + 3) = 40

If we look at the factors of 40:
1 x 40

2 x 20

4 x 10

5 x  8

5 and 8 satisfy the condition n(n + 3) = 40

So n = 5

Answer:

2/5--1/4=3

Step-by-step explanation:

lcm is 20 =8-5=3/20=3 =20

Answer:

Q14 = 45

Q15 = 1.98

Step-by-step explanation:

Q14.

2t = 90 degrees (right angle)

(1) t = 45 (90 ÷ 2)

45 + 8 = 53

45 - 12 = 33

Q15.

43s = 85 degrees

s = 1.98 (85 ÷ 43)

A: To make it more pumpkin-y, Pumpkin Puree or Pumpkin Spice. To make it less pumpkin-y, Banana, milk, or yogurt.

Answer:

hello!

your answer would be 258, because the y-intercept goes upwards.

:D have a good day <3

The definition based on the given biconditional is B. A polygon is a hexagon with six sides.

A conditional statement combined with its opposite is known as a biconditional statement. As a result, one conditional is only true if and when the other is also true. It frequently employs the phrase "if and only if" or the abbreviation "if." It serves as a reminder that the conditional must be true in both directions by using the double arrow.

The biconditional statement is that the polygon is a hexagon if and only if it has six sides.

Therefore, the correct option that illustrates this is B.

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The probability that at least one electrical components does not function properly is 83.3%

To make the calculation easier, use the following property:

P(at the very least one) = 1 - P (None)

The total number of electrical components is 6.

Number that which not work well: 1

Number that works well: 5

We have options for selecting 4 good components from a set of 5 by;

⁵C₄  = 5

We have 4 options from a total of 6 components by;

⁶C₄ = 6

We have a way to do this if everything works properly; ¹C₀ = 1

P(at the very least one) = ⁵C₄× ¹C₀ /⁶C₄

P(at the very least one) = 5 / 6

P(at least one) = 0.833 = 83.3%

Thus, the probability that at least one of the electrical component will not function is 83.3%.

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Considering the numeric values of the function, we have that:

a) S(0) represents the remaining number of socks after 0 pairs are sold, and S(6) represents the remaining number of socks after 6 pairs are sold.

b) S(0) = 14, S(6) = 12.

c) The domain is not all real numbers, as the remaining number of socks cannot be negative, hence the domain is of 0 ≤ p ≤ 7.

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.

For this problem, the function is given as follows:

S(p) = 14 - 2p.

In which S(p) is the remaining number of socks after p socks are sold.

Then the numeric values are:

The domain of a function is the set that contains all possible input values of the function. The remaining number of socks cannot be negative, hence the domain is of 0 ≤ p ≤ 7, and the graph is given at the end of the answer.

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Answer:

Step-by-step explanation:

The Graph of the Equation |x-1| +5 = 2 is attached below

This is further explained below.

Generally, An equation is a mathematical statement that demonstrates that two mathematical expressions have the same value.

This is the most basic version of the definition of an equation in algebra. For example, the phrase "3x + 5" = 14 is an equation, in which the two expressions "3x + 5" and "14" are separated by the symbol for "equal."

In conclusion, Please find attached the graph representing the equation "x-1 + 5 = 2."

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Answer: 11.78

Step-by-step explanation: So 11 would be your number before the decimal ( and stands for the decimal point ) then 78 would go after the decimal point.

Hope this helped!!!

Answer: no idea

Step-by-step explanation:

Answer:

25 mph

Hope this helps! :)