At a store sales tax is charged at a rate of 2% on the cost price of an item . the sales tax on a dress which cost $180 is
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Answer:

49 mph

Step-by-step explanation:

RT=D

T = D/R

[tex]\frac{1995}{(350 + x) } =\frac{1505}{350-x}[/tex]

1995(350-x) = 1505(350+x)

x=49

Answer:

C: parallelogram

Step-by-step explanation:

Answer:

D. It will increase by 1%.

Step-by-step explanation:

Given

[tex]u_1 = 5\%[/tex] --- initial rate

[tex]u_2 = 3\%[/tex] --- final rate

Required

The effect on the GDP

To calculate this, we make use of:

[tex]\frac{\triangle Y}{Y} = u_1 - 2\triangle u[/tex]

This gives:

[tex]\frac{\triangle Y}{Y} = 5\% - 2(5\% - 3\%)[/tex]

[tex]\frac{\triangle Y}{Y} = 5\% - 2(2\%)[/tex]

[tex]\frac{\triangle Y}{Y} = 5\% - 4\%[/tex]

[tex]\frac{\triangle Y}{Y} = 1\%[/tex]

This implies that the GDP will increase by 1%

Answer: A. It will increase by 7%.

Step-by-step explanation: I took this course!

Answer:

8^2+12x

Step-by-step explanation:

4x(2x+3)

=4x times 2x+4x times 3

=4 times 2xx+4 times 3x

Answer:

8x^2 +12x

Step-by-step explanation:

Step 1) Multiply each term in the parentheses by 4x

4xx2x+4xx3

Step 2) Calcuate the product

8x^2 +12x

Answer:

B. 7

Step-by-step explanation:

Recall: according to thee Mid-segment Theorem of a triangle, the Mid-segment of a triangle is half the length of the base of the triangle

Base length of the traingle, RQ = 14 (given)

Mid-segment = TS

Therefore,

TS = ½(RQ)

Plug in the value

TS = ½(14)

TS = 7

Answer:

[tex]{ \tt{g(x) = a {x}^{2} + bx + c = 0 }} \\ { \tt{f(x) = {a'x}^{2} + b 'x + c' = 0}} \\ { \boxed{ \bf{f(g(x)) = g(f(x))}}} : \\ { \tt{ =( \frac{a}{a'})x {}^{2} + ( \frac{b}{b'}) x} + \frac{c}{c'} } = 0[/tex]

Answer:

Part A

(1y^2+3y-6)+(4y-7+2y^2)+(3y^2-8+5y)

6y^2+12y-21

Answer:

58.80

Step-by-step explanation:

84 x .7(70%) =58.80

Answer:

78.81%

Step-by-step explanation:

We are given;

Population mean; μ = 149

Sample mean; x¯ = 147.8

Sample size; n = 88

standard deviation; σ = 14

Z-score is;

z = (x¯ - μ)/(σ/√n)

Plugging in the relevant values;

z = (147.8 - 149)/(14/√88)

z = -0.804

From z-distribution table attached, we have; p = 0.21186

P(X > 147.8) = 1 - 0.21186 = 0.78814

In percentage gives; p = 78.81%

Answer:

4 over 3

because is in side the bracket is part of inequalities

C. The two statements agree in point of truth or falsehood in virtue of their logical structure alone, i.e. the two statement are true or false in exactly the same conditions.

For two statements to be logically equivalent, their truth values (true or false) must be the same for every variation of their constituent variables. In other words, if the truth tables of both statements are the same for every possible value of their variables, then they are logically equivalent.

For example;

The two statements P ∩ (Q U R) and (P ∩ Q) ∪ (P ∩ R) are logically equivalent.

If P, Q and R are all true, then;

P ∩ (Q U R) = true

(P ∩ Q) ∪ (P ∩ R) = true

If P, Q and R are all true, then;

P ∩ (Q U R) = false

(P ∩ Q) ∪ (P ∩ R) = false

If P = false, Q = true and R = true, then;

P ∩ (Q U R) = false

(P ∩ Q) ∪ (P ∩ R) = false

Checking for all other possible combinations of truth values of P, Q and R will always give the same results for the two statements, therefore, they are logically equivalent.

Answer:

Slope = 2

Step-by-step explanation:

To find the slope of the line, you need to plot two points

My own two points will be: [tex](1,2)[/tex] and [tex](2,4)[/tex]

Now use the Slope-Formula to identify the slope of the line

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{4-2}{2-1}[/tex]

[tex]m=\frac{2}{1}[/tex]

[tex]m=2[/tex]

so the slope of the line in simplest form will be 2.

Answer:

m(x) is a dilation of scale factor K = 1/5 of f(x).

Step-by-step explanation:

The transformation is a horizontal dilation

The general transformation is defined as:

For a given function f(x), a dilation of scale factor K is written as:

g(x) = f(x/K)

If K > 1, then we have a dilation (the graph contracts)

if 0 < K < 1, then we have a contraction (the graph stretches)

Here we have m(x) = f(5*x)

Then we have a scale factor:

K = 1/5

So this is a contraction.

Then the transformation is:

m(x) is a dilation of scale factor K = 1/5 of f(x).

Answer:

Two lines that intersect and form right angles are called perpendicular lines.

Answer:

perpendicular lines

Step-by-step explanation:

Definition of perpendicular lines:

Two lines that intersect forming a right angle are perpendicular lines.

Answer: perpendicular lines

Answer:

5 + c > -22

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Sum of 5 and c is greater than -22

↓ Identify

Sum = addition

Is greater than = inequality

Add them all together:

5 + c > -22

The question is incomplete. The complete question is :

The breaking strengths of cables produced by a certain manufacturer have a mean of 1900 pounds, and a standard deviation of 65 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 150 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1902 pounds. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the mean breaking strength has increased?

Solution :

Given data :

Mean, μ = 1900

Standard deviation, σ = 65

Sample size, n = 150

Sample mean, [tex]$\overline x$[/tex] = 1902

Level of significance = 0.01

The hypothesis are :

[tex]$H_0 : \mu = 1900$[/tex]

[tex]$H_1 : \mu > 1900$[/tex]

Test statics :

We use the z test as the sample size is large and we know the population standard deviation.

[tex]$z=\frac{\overline x - \mu}{\sigma / \sqrt{n}}$[/tex]

[tex]$z=\frac{1902-1900}{65 / \sqrt{150}}$[/tex]

[tex]$z=\frac{2}{5.30723}$[/tex]

[tex]$z=0.38$[/tex]

Finding the p-value:

P-value = P(Z > z)

             = P(Z > 0.38)

             = 1 - P(Z < 0.38)

From the z table. we get

P(Z < 0.38) = 0.6480

Therefore,

P-value = 1 - P(Z < 0.38)

            = 1 - 0.6480

             = 0.3520

Decision :

If the p value is less than 0.01, then we reject the [tex]H_0[/tex], otherwise we fail to reject  [tex]H_0[/tex].

Since the value of p = 0.3520 > 0.01, the level of significance, then we fail to reject  [tex]H_0[/tex].

Conclusion :

At a significance level of 0.01, we have no sufficient evidence to support that the mean breaking strength has increased.

Answer:

129469.3194

342000

212530.6806

Step-by-step explanation:

Going to assume that the 8% is a nominal, montly rate

which means the effective monthly rate is .08/12= .006667

using the annuity immediate formula...

a.)

[tex]950(\frac{1-(1+.006667)^{-30*12}}{.006667})=129469.3194[/tex]

b.) we would pay 950*30*12= 342000

c.) the amount in interest would be 342000-129469.3194=212530.6806

a) The loan one can afford is $1,29,460.2

b) The total amount of money paid to the loan company over the life of the loan is $342,000.

c)  $212539.8 of the total amount paid is interest.

To determine the answers to these questions, we'll need to use the formula for calculating a fixed monthly mortgage payment:

[tex]M = \frac{P \times r \times (1 + r)^n}{((1 + r)^n - 1)}[/tex]

where:

M is the monthly payment,

P is the principal loan amount,

r is the monthly interest rate (annual interest rate divided by 12),

and n is the total number of payments (number of years multiplied by 12).

Given:

Monthly payment (M) = $950

Loan term = 30 years

Interest rate = 8% per year

a) How big of a loan can you afford?

Let's calculate the principal loan amount (P):

First, we need to convert the annual interest rate to a monthly interest rate:

r = 0.08 / 12

= 0.00667

n = 30 years × 12 months

n= 360

Using the formula and plugging in the values we have:

[tex]950 = \frac{P \times 0.00667 \times (1 + 0.00667)^{360}}{((1 + 0.00667)^{360} - 1)}[/tex]

[tex]950 = \frac{P \times 0.00667 \times 10.948}{10.948 - 1}[/tex]

[tex]950=\frac{P \times 0.07302316}{9.948}[/tex]

[tex]950\times9.948 = 0.0730P[/tex]

Divide by 0.073:

Now we can solve for P:

[tex]P=\frac{9450.6}{0.0730}[/tex]

[tex]P = 1,29,460.2[/tex]

Therefore, you can afford a loan amount of $1,29,460.2

b) The total amount paid to the loan company can be calculated by multiplying the monthly payment by the total number of payments:

Total amount = Monthly payment × Total number of payments

Total amount =[tex]$950 \times 360[/tex]

Total amount = [tex]342,000[/tex]

Therefore, the total amount of money paid to the loan company over the life of the loan is $342,000.

c) To find out how much of the total amount paid is interest, we can subtract the principal loan amount from the total amount:

Interest = Total amount - Principal loan amount

Interest = [tex]342,000 - 129460.2[/tex]

=$212539.8

Therefore, $212539.8 of the total amount paid is interest.

To learn more on Simple Interest click:

https://brainly.com/question/30964674

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Answer:

80b-11

Step-by-step explanation:

14b + 1 - 6(2 - 11b)

Distribute

14b+1-12+66b

Combine like terms

80b-11

Answer:

80b - 11

Step-by-step explanation:

what is the problem ?

just multiply it out and combine terms.

14b + 1 - 6(2 - 11b) = 14b + 1 - 12 + 66b = 80b - 11

Answer:

The probability that the mean of the sample would differ from the population mean by less than 36 points=0.9216

Step-by-step explanation:

We are given that

The variance of the scores on a skill evaluation test=143,641

Mean=1517 points

n=343

We have to find the probability that the mean of the sample would differ from the population mean by less than 36 points.

Standard deviation,[tex]\sigma=\sqrt{143641}[/tex]

[tex]P(|x-\mu|<36)=P(|\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}|<\frac{36}{\frac{\sqrt{143641}}{\sqrt{343}}})[/tex]

[tex]=P(|Z|<\frac{36}{\sqrt{\frac{143641}{343}}})[/tex]

[tex]=P(|Z|<1.76)[/tex]

[tex]=0.9216[/tex]

Hence,  the probability that the mean of the sample would differ from the population mean by less than 36 points=0.9216

Answer:

Step-by-step explanation:

Answer:

[tex]y=(x-7)^2-1[/tex]

Step-by-step explanation:

We want to convert the equation:

[tex]\displaystyle y=x^2-14x+48[/tex]

Into vertex form, given by:

[tex]\displaystyle y=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.

Method 1) Vertex Formulas

Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.

Recall that the vertex is given by:

[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:

[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]

To find the y-coordinate, substitute this value back into the equation. Hence:

[tex]y=(7)^2-14(7)+48=-1[/tex]

Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.

And since we already determined a = 1, our equation in vertex form is:

[tex]\displaystyle y=(x-7)^2-1[/tex]

Method 2) Completing the Square

We can also complete the square to acquire the vertex form. We have:

[tex]y=x^2-14x+48[/tex]

Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:

[tex]y=(x^2-14x)+48[/tex]

Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.

We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:

[tex]y=(x^2-14x+49)+48-49[/tex]

Factor using the perfect square trinomial and simplify:

[tex]y=(x-7)^2-1[/tex]

We acquire the same solution as before, with the vertex being (7, -1).

Answer:

10x-5

Step-by-step explanation:

f(x)=5x

g(x)=2x-1

To create a composite function, replace x in f(x) with g(x)

f(g(x)) = 5(g(x) = 5(2x-1) = 10x-5

Step-by-step explanation:

t8 = a1 + (n - 1)*d

t8 = 17

17 = a1 + 7*d

t12 = 25

25 = a1 + 11d

17 = a1 + 7d Subtract

8 = 4d Divide by 4

8/4 = 4d/4

2 = d

17 = a1 + 7d

17 = a1 + 7*2

17 = a1 + 14 Subtract 14

3 = a1

Sum 20 terms

The 20 term = a1 + 19*2

The 20 term = 3 + 38

= 41

Sum = (a1 + a20) * 20 / 2

Sum = (3 + 41)* 20/2

Sum = 44 * 10

Sum = 440

Answer:

(2k, k)

Step-by-step explanation:

x + y = 3k

x - y = k

Add the equations.

2x = 4k

x = 2k

2k + y = 3k

y = k

Answer: (2k, k)

Answer:

5 905 272

Step-by-step explanation:

you can refer to this lattice multiplication or u can search you tube for the examples of lattice multiplication

Answer:

You could save $20

Step-by-step explanation:

For buying them separately for $30 each for 5 people it would be $150 but if you buy the first option you would get 5 admission tickets for only $130

Answer:

20 dollars

Step-by-step explanation:

for the first deal is 5 for $130

and the second is for $30

$30 times 5 (the number of people) = $150

$150-$130= is 20

answer: $20

Answer:

(x+5)(x-3) / (x+5)(x+1)

Step-by-step explanation:

A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator.  It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x.  In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.

Answer:

200 test tubes will fill the container

Step-by-step explanation:

Hi there!

We need to find out how many 5 milliliter tubes will fill a 1 liter container

First, let's convert everything to the same unit, as the tubes and the container are in different units.

Let's do milliliters, as those are smaller than liters and we will avoid having decimals.

there are 1,000 milliliters in a liter (the unit prefix "milli-" means "thousand")

Let's say the number of test tubes needed to fill the container is x

As each tube has 5 milliliters of water, 5x milliliters will equal 1,000 milliliters (1 liter)

as an equation, that's

5x=1,000

divide both sides by 5

x=200

So that means 200 test tubes will fill the container

Hope this helps! :)

Answer:

Here is how to start

Step-by-step explanation:    7  2  13  42

1 milliliter is one one thousands of a liter      1 milliliter  = 0.001 liter

1000 milliliter is equal to 1 liter

How many 5 milliliter test tubes are in 1 liter?

1000 milliliter / 5 milliliter per test tube   =  ________  test tubes

Answer:

a) y=f(x)-2

b) y=f(-x)