the vat rate was reduced from 17.5% to 15% for one year. sally says that this reduced the VAT charged on her shopping by 2.5%. Tom says this is wrong. he thinks the VAT charged was reduced by over 14%. who is correct? explain your answer.​

Answer:

3x+1

Step-by-step explanation:

(2x+x+3+6x)/3

9x+3/3

3x+1

The final result is a simplified algebraic expression 3x + 1 that represents the average of 2x, x + 3, and 6x.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The average of 2x, x + 3, and 6x can be represented by the algebraic expression (2x + (x + 3) + 6x)/3.

This expression takes the sum of 2x, x + 3, and 6x, and then divides that sum by 3, which is the number of terms being averaged.

Alternatively, the average can be represented by (2x + x + 6x + 3) / 3 = (9x + 3) / 3 = 3x + 1.

In either case, the final result is a simplified algebraic expression that represents the average of 2x, x + 3, and 6x.

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9514 1404 393

Answer:

  ∠Z = 34°

  ∠T = 56°

Step-by-step explanation:

You can solve for x using the measure of the right angle:

  90 = 3x +6

  30 = x +2 . . . . . divide by 3

  28 = x . . . . . . . . subtract 2

Then the measure of T is ...

  ∠T = 2x° = 2(28)° = 56°

  ∠Z is its complement: 90° -56° = 34°

The angle measures are ...

  m∠Z = 34°

  m∠T = 56°

Answer:

1) The first term is $138

2) The difference is $55

3)  The iterative rule for the amount of money Mrs. Speas has after n weeks is 27.5·n² + 110.5·n

Step-by-step explanation:

The mount Mrs. Speas has in her bank account = $138

The amount of money she deposits each week = $55

The amount of money in Mrs. Speas account therefore, forms an Arithmetic Progression

1) The first term = a = The initial money Mrs. Speas has in her bank account = $138

2) The (common) difference = d =The amount she deposits at the end of each week = $55

The iterative rule for the amount of money Mrs. Speas has (in her bank account) after n weeks is given by the formula for the sum of an arthmetic progression (AP), Sₙ, as follows;

\(S_n = \dfrac{n}{2} \times \left [2 \times a + (n - 1)\times d \right ]\)

Substituting the values of a and d gives;

\(S_n = \dfrac{n}{2} \times \left [2 \times 138 + (n - 1)\times 55 \right ] = \dfrac{n}{2} \times \left [221 + n \times 55 \right ] = 110.5\cdot n + 27.5 \cdot n^2\)

∴ 3)  The amount of money she has after n weeks = Sₙ = 27.5·n² + 110.5·n.

Answer:

68 boys and 56 girls

Step-by-step explanation

your welcome

If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.

To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.

To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).

Plugging in the values, we have:

FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06

≈ $12,350

Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.

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Answer:

Step-by-step explanation:

Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.

Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)

On expansion

(3 - i)(3 + i)

=  9+3i-3i-i²

= 9-(-1)

= 9+1

(3 - i)(3 + i) = 10

For the expression (2 + i)(1 - i), we have;

(2 + i)(1 - i)

= 2-2i+i-i²

= 2-i+1

= 3-i

Multiplying 3-i with the last expression (1 + 2i)

(2 + i)(1 - i)(1 + 2i)

= (3-i)(1+2i)

= 3+6i-i-2i²

= 3+5i-2(-1)

= 3+5i+2

= 5+5i

Finally,  [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]

= 10(5+5i)

= 50+50i

Hence,  (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i

Proved that ∠1 and ∠2 are complementary

Two sides of two adjacent acute angles are perpendicular, then the angles are complementary

Given that the

Line BA and BC are perpendicular

If two lines are perpendicular, then the angles between the lines will be 90 degrees

The complementary angles is defined as the sum of the angles will be 90 degrees

Here Angle ABC = 90 degrees

Angle ABC = Angle 1 + Angle 2

Substitute the value of angle ABC

∠1 + ∠2 = 90 degrees

The sum of the angle 1 and angle 2 is 90 degrees

Hence, proved that ∠1 and ∠2 are complementary

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Answer: 9/25 or 36%

Step-by-step explanation:

The first time it is a probability of 3/5, and the second blue also has a prbability of 3/5. Multiply them together since it is an "and" situation, and you get 9/25. Or, in percentages, it is 60% * 60%, or 0.6 * 0.6, which is 36% or 0.36. Hope this helps!

Answer:

the correct answer is 36%

Step-by-step explanation:

I got it right on Edmentum

Hook me up with a 5 star and a thanks :)

Answer:

He would walk 20 miles in 5 hours.

Step-by-step explanation:

Mo walked 20 miles in 5 hours.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Mo walked 12 miles in 3 hours.

In 1 hour Mo walked= 12/3

                               = 4 miles

and, in 5 hours Mo walked

= 5 x 4

= 20 miles.

Hence, Mo walked 20 miles in 5 hours.

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The expression 2^7 times 19 can be simplified by first evaluating the exponential term, 2^7, which is equal to 128. Therefore:2^7 times 19 = 128 * 19We can then evaluate the product of 128 and 19 using multiplication. When we do that, we get:2^7 times 19 = 2432Therefore, the choice that is equivalent to the expression 2^7 times 19 is 2432

Answer:11

Just do 1/4*44cm2

Answer:

11 cm²

Step-by-step explanation:

the shaded portion covers one quarter of the circle , then

area of portion = \(\frac{1}{4}\) × 44 cm² = 11 cm²

While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. The three main types of linear equations are the slope-intercept form, standard form, and point-slope form. A straightforward equation shows the connection between two terms on either side of an equal sign. Additionally, simple equations incorporate one or more of the addition, subtraction, multiplication, and division arithmetic operations.

given

Let a = the cost in cents of a cheeseburger

Let b = the cost in cents of a shake

4a+2b=7 .90

2b=a+15

-a+2b=15

Subtract (2) from (1)

4a+2b=7 .90

a-2b=-15

5a=775

a=155

2b=a+15

b=170/2

b=85

While two milkshakes are cheaper by $0.15 than a cheeseburger, a cheeseburger costs $1.55 and costs $.85.

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The correct answer is D. The data are qualitative because they consist of counts or measurements.

Qualitative data refers to non-numerical information that is categorical or descriptive in nature. It describes qualities or characteristics of a subject.

In this case, the preferred hands of the experiment's participants would be categorical information, as it describes the quality or characteristic of which hand the participants prefer to use.

On the other hand, quantitative data refers to numerical information that can be measured or counted. It involves quantities or amounts.

Examples of quantitative data would include measurements such as height, weight, or number of participants.

Since the preferred hands in this scenario are categorical and not measured or counted, the data is qualitative. It focuses on the qualities or categories of left-handedness or right-handedness, rather than measuring or counting any specific quantities.

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The missing statement in Step 5 include the following: B. AC/DC = BC/EC.

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the angle, angle (AA) similarity theorem, we can logically deduce the following congruent triangles:

ΔABC ≅ ΔDEC  ⇒ Step 4

By the definition of similar triangles, we can logically deduce the following proportional and corresponding side lengths:

AC/DC = BC/EC ⇒ Step 5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

The total cost is $59.85

(rounded up from 59.846 since this problem is about money)

Hi there!

cost=59.846

1.Add both cost:

\(19.64+32.40= 52.04\)

2.Multiply 15% by 0.01:

\(15\)·\(0.01=0.15\)

3.Multiply cost by 0.15:

\(52.04\)·\(0.15= 7.806\)

4.Combine the two terms:

\(52.04+7.806= 59.846\)

Therefore, the total cost was 59.846$.

The equation connecting U,S and M is K = U√M/S

The value of M when U=110.5 and S=32 is 4.32

From the information given, we have that U partly varies directly as S and partly inversely as the square root of M.

This is represented mathematically as;

U ∝S/√M

To determine the constant of the variation, we have;

U = KS√M

Now, make 'K' the subject of formula;

K = U√M/S

Substitute the values

K = 124.6 √25/86.75

Find the square root

K = 7. 18

To determine the value of M, we have;

KS/U = √M

substitute the values

√M = 7.18(32)/110. 5

√M = 2. 08

find the square of both sides

M = 4. 32

Hence, the value is 4.32

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Hi there! You still remember the Pythagorean Theorem, right? It's useful when it comes to finding a missing leg or side of a right triangle. If you forget then here it is:

\( \large \boxed{ {a}^{2} + {b}^{2} = {c}^{2} }\)

Define c = hypotenuse while a and b can be both adjacent and opposite (because a²+b²=b²+a² via addition property)

Since we are missing the adjacent side. Thus,

We define a = 6 and c = 14.

\( \large{ {6}^{2} + {b}^{2} = {14}^{2} } \\ \large{36 + {b}^{2} = 196} \\ \large{ {b}^{2} = 196 - 36} \\ \large{ {b}^{2} = 160} \\ \large{ b = \sqrt{160} \longrightarrow \boxed{b = 4 \sqrt{10} }}\)

Put the value of b in a calculator then round to the nearest tenth and get 12.6

Thus, the value of b ≈ 12.6

Next we are going to find the angle in degree. We now know that b ≈ 12.6 or 4sqrt(10)

We can find the value of angle A by using tan or sin but I will use sin instead. Recall the sine ratio which is opposite to hypotenuse. Thus,

\( \large{sinA = \frac{6}{14} }\)

Use arcsin(6/14) and put it in calculator.

Then put the decimal value of arcsin in sin and convert in degree form which we should get 24. 555°. Round to the nearest whole number and we get 25°

Thus, the angle A is 25°

Next is we are finding the value of angle B. We aren't going to use any formula or equation. Recall that three angles add up to 180°.

Thus, 25° + 90° + x = 180°

90° comes from a right angle.

115+x = 180

x = 180-115

x = 65°

Thus, the angle B is 65°

Answer

Answer:

-17°C at sunset

15°C at sunrise

Answer:

D.) QIII

Step-by-step explanation:

Because 1.2 radians is in between 7π/6 and 5π/4

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

The total medical expenses = (22 * $P) + (12 * $S) + $1,375 + $E + $15,600

To solve this problem, we first need to calculate the total amount spent on each type of medical service.

For 22 physician visits at a cost of $P each, the total cost is: 22 * $P

For 12 specialist visits at a cost of $S each, the total cost is: 12 * $S

For 25 physical therapy appointments at $55 each, the total cost is: 25 * $55 = $1,375

For 1 ER visit at a cost of $E, the total cost is: $E

The hospital charge is $15,600.

With this, the total medical bills can be calculated:

Therefore, the total medical expenses = (22 * $P) + (12 * $S) + $1,375 + $E + $15,600

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Jacobi Duarte has a non-network family health insurance plan, which requires co-payments for various medical services. Over a certain period, Jacobi has made the following co-payments:

22 physician visits

12 specialist visits

25 physical therapy appointments at $55 each

1 ER visit

Hospital charge of $15,600

Find the total amount that Jacobi Duarte has spent on medical expenses?

Answer:

Go to the botom of the page

Step-by-step explanation:

Answer: The answer is C.

Step-by-step explanation:

Simplify the radical by breaking the radicals up into a product of known factors, assuming real numbers.

Answer: 1 real and 2 complex.

Step-by-step explanation:

A cubic polynomial is written as:

a*x^3 + b*x^2 + c*x + d

And the zeros are such that:

a*x^3 + b*x^2 + c*x + d  = 0

As the degree of the polynomial is 3, then we have 3 solutions (where some of them may be equal)

Now, an easy way to see the real and complex zeros of a polynomial is:

If after a change in curvature, the line touches the x-axis : that is a real zero

if it does not, then there we have a complex zero.

Here we can see two lines that do not touch the x-axis and one line that does touch the x-axis.

Then we have 2 complex zeros and one real zero.

a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. Frequently, the symbol "%" is used after the number to indicate percentages.

given,

The number of phone calls handled by the communications switch in a 10-second period is represented by the Poisson random variable n.

a)the chance that no call will be handled in 10 seconds is

for 10 sec= λ= 10*0.5 = 5 calls per sec

P(X=0) \(e^{-5}\)(5)° / 0!

P(X=0)= 0.0067

b) percent of classes will be processed in two seconds at least is

for 2 sec =λ = 0.5 *2 = 1

P(X≥2) = 1- P(X<2)

= 1-[P(X=2) + P(X=1)]

=0.2642

a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

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Answer:

x = .23

x = 1.43

Step-by-step explanation:

1. The root of a polynomial is when the y-value equals 0. So set the equation euqal to 0:

\(3x^{2} -5x+1=0\)

2. Solve with the quadratic formula and you get:

\(\frac{5+\sqrt{13} }{6}\) and \(\frac{5-\sqrt{13} }{6}\) which is x = .23 and x = 1.43.

Answer:

here is my answer

Step-by-step explanation:

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

We have,

To find the mean and variance of the return series, we can substitute the given model into the equation and calculate:

Mean of rt:

E(rt) = E(0.02 + 0.5rt-2 + et)

= 0.02 + 0.5E(rt-2) + E(et)

= 0.02 + 0.5 * 0 + 0

= 0.02

The variance of rt:

Var(rt) = Var(0.02 + 0.5rt-2 + et)

= Var(et) (since the term 0.5rt-2 does not contribute to the variance)

= 0.02

The mean of the return series rt is 0.02, and the variance is 0.02.

To compute the lag-1 and lag-2 autocorrelations of rt, we need to determine the correlation between rt and rt-1, and between rt and rt-2:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

Since we are given r100 = -0.01 and r99 = 0.02, we can substitute these values into the equations:

Lag-1 Autocorrelation:

ρ(1) = Cov(rt, rt-1) / (σ(rt) * σ(rt-1))

= Cov(r100, r99) / (σ(r100) * σ(r99))

= Cov(-0.01, 0.02) / (σ(r100) * σ(r99))

Lag-2 Autocorrelation:

ρ(2) = Cov(rt, rt-2) / (σ(rt) * σ(rt-2))

= Cov(r100, r98) / (σ(r100) * σ(r98))

To compute the 1- and 2-step-ahead forecasts of the return series at

t = 100, we use the given model:

1-step ahead forecast:

E(rt+1 | r100, r99) = E(0.02 + 0.5rt-1 + et+1 | r100, r99)

= 0.02 + 0.5r100

2-step ahead forecast:

E(rt+2 | r100, r99) = E(0.02 + 0.5rt | r100, r99)

= 0.02 + 0.5E(rt | r100, r99)

= 0.02 + 0.5(0.02 + 0.5r100)

The associated standard deviation of the forecast errors can be calculated as the square root of the variance of the return series, which is given as 0.02.

Thus,

Mean of rt = 0.02,

Variance of rt = 0.02,

Lag-1 Autocorrelation (ρ1) = -0.01,

Lag-2 Autocorrelation (ρ2) = Unknown,

1-step ahead forecast = -0.005,

2-step ahead forecast = 0.02,

The standard deviation of forecast errors = √0.02.

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Answer:

4: zero

Step-by-step explanation:

It's a zero slope because it's just a straight line. There is no x, so it's a zero slope. Take a look at my work! :)