Solve the word problems. The price of a bed was $2600. MDM Yap bought the bed and had to pay an additional 7% GST. (a) What was the amount of GST she had to pay? (b) What was the price of the bed including GST?​

9514 1404 393

Answer:

  x = 7

  y = 5

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

__

For a=-j and b=7,

  (-j)^-7 = 1/(-j)^7   ⇒   x = 7

For a=k and b=-5,

  k^-5 = 1/k^5   ⇒   y = 5

Answer:

1/4

Step-by-step explanation:

White = w

Black = B

Blue = b1

Tan = t

Wb1

Wt

Bbi

Bt

The answer will be 1/4, because there are 4 ways it can work and only 1 way it can be white shirt and tan pants.

Answer:

1/4

Step-by-step explanation:

it would be 1/4 because there are 4 different clothing pieces in total and there is only one way it would work the way the problem says.

Answer:

Amount gained = $900

Step-by-step explanation:

Let the cost price be = x

Given selling price = 8400

And profit% = 12%

Profit = selling price - cost price

        = 8400 - x

[tex]Profit \ \% = \frac{profit}{cost \ price} \times 100\\\\12\% = \frac{8400 - x}{x} \times 100\\\\\ 12 \times \frac{1}{100} = \frac{8400 - x}{x}\\\\\frac{12 \ x}{100} = 8400 - x \\\\\frac{12x}{100} + x = 8400\\\\12x + 100x = 8400 \times 100\\\\112x = 8400 \times 100\\\\x = \frac{8400 \times 100}{112} = 7500[/tex]

Therefore , cost price of the radio $7500

The amount she gained = 8400 - 7500 = $ 900

If 6ˣ = 5, then

(6ˣ)³ = 6³ˣ = 5³ = 125,

and

6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500

Answer:

8

Step-by-step explanation:

As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8

9514 1404 393

Answer:

  a) Lahulspiti: -8; Srinigar: -2; Shimla: 5; Ooty: 14; Bengahuru: 22

  b) 30

  c) 6

  d) yes; no

Step-by-step explanation:

a) The values are read from the graph.

__

b) 22 -(-8) = 22 +8 = 30 . . . . difference between highest and lowest

__

c) -2 -(-8) = -2 +8 = 6 . . . positive difference

(Technically, the difference between L and S is L - S = (-8) -(-2) = -6.)

__

d) -2 + 5 < 5 . . . . true

  -2 + 5 < -2 . . . . false

Answer:

Step-by-step explanation:

2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3

Answer:

X(-12,-7)

Step-by-step explanation:

This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.

Answer:

False

Step-by-step explanation:

well i think that the answer from my calculations

Answer:

AB is correct as It is the shorter parallel line

as the line measures 6 units.

Step-by-step explanation:

The polygon is a trapezoid / (trapezium Eng/Europe)

We see the given coordinates  (2, 6) - (-4, 6) = x-6 y 0 = x = 6units

as x always is shown as x - 6  as  x= 6

We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6

y = 0  x = 6 = 6 units as its horizontal line.

when y is 6-6 = 0 then we know the line is horizontal for y = 0.

The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.

When looking at diagonal lines we still group the x's and y's and make the fraction whole.

When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.

Answer: A (x+1)(x+2)(x+5)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

substitute the values in the eq. Ot is also arithmetic progression.

Step-by-step explanation:

Since the ratio of monthly income to savings of the family is 7:2, we assume that the income be 7t and savings be 2t

Now, we are given that the savings is =Rs 500

So, According to our assumption, 2t=500

⇒t=250

Hence, the income of the family is =7×250=Rs 1750

And the expenditure is =Income−Savings

=Rs 1750−Rs 500

=Rs 1250

Answer:

Angle A = Angle D = 69° 30'

Angle B = Angle C = 110° 30'

Step-by-step explanation:

     B ___ C

    /              \

  /                  \

A ________ D

AB and CD are 10

BC is 6

AD is 14

If we divide the trapezoid, we can imagine a line.

     B_ F_C

    /      |      \

  /        |         \

A ___E____ D

AE = ED = 7 (14/2)

BF = FC = 3

So now, we draw another line from B or C to AE or ED

     B_ F_ C

    /      |     | \

  /        |     |    \

A ___E_ G_ D

EG = GD = 3.5 (7/2)

There is a right triangle now, GCD

GD is 3.5 and CD is 10. To determine angle D, we can apply trigonometric function:

CD is H, and GD is A

cos D = A/H

cos D = 3.5/10 → 0.35

angle D = 69° 30'

By theory, we know that angle D and angle A, are the same so:

Angle D = Angle A = 69° 30'

Angle B = Angle C

We also make a cuadrilateral, which is EFCD.

Angle D is 69° 30', Angle E is 90°, Angle F is also 90°

Sum of angles in cuadrilateral is 360°

360° - 69° 30' - 90° - 90° = Angle C = Angle B

Angle C = Angle B = 110° 30'

Let's confirm the angles in the trapezoid:

69° 30' + 110° 30' + 69° 30' + 110° 30' = 360°

A + B + C + D

Answer:

101 cm

Step-by-step explanation:

Add all the side lengths up to get 101 cm.

Answer:

b. The actual count of bike riders is too small.

d. n*p is not greater than 10.

Step-by-step explanation:

Confidence interval for a proportion:

To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]

Of the 123 students surveyed 5 ride a bike to campus.

Less than 10 successes, that is:

The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.

Answer:

5 ≤ x ≤ 10             5 ≤ y ≥ -1

Step-by-step explanation:

Answer:

x > 21

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

x + 34 > 55

Step 2: Solve for x

The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.

You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].

So let us take a look at the possible options.

Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.

Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.

So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].

Hope this helps :)

Answer:

cos theta  = adj / hyp is positive (+/+)

Step-by-step explanation:

In this open interval, the hypotenuse (radius) is always positive, whereas the adjacent side is positive and the opposite side negative.

in this interval:

sin theta = opp / hyp is neg (-/+)

cos theta  = adj / hyp is positive (+/+)

tan theta = opp / adj = (-/+) :  negative

Answer:

No

Step-by-step explanation:

If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.

[tex]6^{2}+8^{2}=c^2[/tex]

If the triangle is a right triangle, c would equal 11

Solve.

[tex]36+64=100[/tex]

Then find the square root of 100.

The square root of 100 is 10, not 11.

So this is not a right triangle.

I hope this helps!

Step-by-step explanation:

[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]

[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]

[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]

Question :

Required solution :

Here we would be considering L.H.S. and solving.

Identities as we know that,

By using the identities we gets,

[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]

[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]

Now, here we would be using the identity of square relations.

By using the identity we gets,

[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]

[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]

[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]

"RS tangent to circle a..." is first statement          Reason: Given

Second Reason: "Radius perpendicular to tangent"

Second Statement: "AR is parrallel to BS"      Reason: "2 lines perpendicular..."

Answer:

khai niem hinh cat don gian?

Answer:

The answer is "".

Step-by-step explanation:

Please find the complete question in the attached file.

We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval

[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]

Using formula:

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

The probability that perhaps the mean shells length of the sample is over 4.03 pounds is

[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]

Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution

[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]

the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]