Brian invests £6300 into his bank account.

He receives 4.9% per year compound interest.

How much will Brian have after 2 years?

Give your answer to the nearest penny where appropriate.

Answer:

  2 + h = 14 and k - 25 = 2

Step-by-step explanation:

An equation has an equal sign.

Apparently, your answer choices are of the form ...

  (math expression) and (math expression)

In order for this to be "only equations", each "math expression" must contain an equal sign. That is, you must have ...

  ( ... = ... ) and ( ... = ... )

Something like ...

  c -14  and  d +134

contains no equal signs, so has no equations.

It looks like your appropriate choice is ...

  2 + h = 14 and k - 25 = 2

Answer:

the answer is a

Step-by-step explanation:

i took the test

:)

note: have a wonderful day!

Answer:

118 cm

Step-by-step explanation:

1 m = 100 cm

1 m = 1000 mm

1.18 m = 118 cm = 1180 mm

11.8 mm   ----> too small

118 cm   ----> just right

1.8 m    ----> too big

11.18 mm    ----> too small

Where the above dimensions are given, the suitable guitar case for Liam would be the one that is 1.8 m long.

Since Liam's guitar case needs to be 1.18 m long, we need to select the option that is closest in length without exceeding it.

Among the given options, 11.8 mm and 11.18 mm are too small, and 118 cm is equal to 1.18 m, which exceeds the required length.

Hence , the only suitable option is 1.8 m, which matches Liam's requirement of a guitar case with a length of 1.18 m.

Learn more about dimension at:

https://brainly.com/question/26740257

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Answer:

A.0.059 , B.0.063

Step-by-step explanation:

1. There are 13 clubs in a pack of 52 cards;

Hence the probability of picking the first club is 13/52;

The probability of picking the second is 12/ 51( remember one card has been removed already so the total number of cards decreases).

Probability of picking two clubs in succession is ;

13/52 × 12/51 = 0.0588 = 0.059( to the nearest thousandth).

2. The probability of drawing a club followed by a club with replacement is;

13/52 × 13 /52 = 0.0625 = 0.063( to the nearest thousandth)

Answer:

The resultant polynomial is: [tex]6x^2-6x+5[/tex]

Step-by-step explanation:

We need to subtract [tex](x+1)^{2}[/tex] from [tex]7x^2-4x+6[/tex]

so, we start by performing the multiplication involved in the perfect square of the binomial [tex](x+1)[/tex], and obtain its expression in separate terms that can be combined:

[tex](x+1)^{2}=(x+1)\,(x+1)=x^2+x+x+1=x^2+2x+1[/tex]

Now we can subtract this trinomial from  [tex]7x^2-4x+6[/tex], and  combining like terms to get the resultant polynomial expression:

[tex]7x^2-4x+6-(x^2+2x+1)=7x^2-4x+6-x^2-2x-1=7x^2-x^2-4x-2x+6-1=6x^2-6x+5[/tex]

Then the resultant polynomial is: [tex]6x^2-6x+5[/tex]

Answer:

Height = 12 inches

Step-by-step explanation:

Volume = Area × Height

1080 = 90 × H

H = 1080/90

H = 12 inches

Answer:

(a)Area

(b)Andre is Right

Step-by-step explanation:

(a)Frost is spread on the surface of a cookie, therefore the question is talking about the area of the circular cookie.

(b)

Andre says, "The diameter of the cookie is about 3 inches, so the space for frosting is about 2.25 sq. in

Area of a Circle[tex]=\pi r^2[/tex]

Radius =Diameter/2 =3/2=1.5 Inches

Therefore, Space for frosting on the cookie

[tex]=\pi *1.5^2\\=2.25\pi$ in^2[/tex]

Andre is right.

Answer:

The correct answer will be Option B (multinomial population).

Step-by-step explanation:

Other given options are not connected to the given situation. So that Option B seems to be the perfect solution.

Answer:

The experimental group in this case are the group of bees that are put in the small cage.

Step-by-step explanation:

The experimental group is the group of subjects that participate in the test. They are usually assigned to the treatments in study. In some cases there is a control group, with no assigned treatment.

In this case, the bees that she put in the cage, and they are not assigned to a particular treatment. It can be considered a control group.

Answer:

[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]

And if we solve this equation for x we got:

[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]

We can cancel [tex]x^2[/tex] in both sides and we have this:

[tex] 22x -6x= 256+9-121 =144[/tex]

And then we got:

[tex] 16 x= 144[/tex]

[tex] x =\frac{144}{16}= 9[/tex]

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

Step-by-step explanation:

For this case we have a right triangle and we can use the Pythagoras Theorem and using the info given by the triangle we can set up the following equation:

[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]

And if we solve this equation for x we got:

[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]

We can cancel [tex]x^2[/tex] in both sides and we have this:

[tex] 22x -6x= 256+9-121 =144[/tex]

And then we got:

[tex] 16 x= 144[/tex]

[tex] x =\frac{144}{16}= 9[/tex]

And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side side.

Lenght of the smaller unknown side: 12m

Lenght of the larger unknown side: 20m

The answer is graph A 7/9/20 edge

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

  ∠F ≈ 43.9°

Step-by-step explanation:

The Law of Cosines is used to find an angle when all triangle sides are known.

  f² = d² +e² -2de·cos(F)

  cos(F) = (d² +e² -f²)/(2de) = (25² +28² -20²)/(2·25·28) = 1009/1400

  F = arccos(1009/1400)

  F ≈ 43.9°

Answer:

Step-by-step explanation:

A. The front elevation of the pyramid in the direction of the arrow is herewith attached to this answer.

B. Base of the pyramid is a square of side 12 cm.

   The height of the pyramid is 8 cm.

   Slant height, XT, is 10 cm.

The total surface area of the pyramid can be determined by adding the surface areas that make up the shape.

Area of the triangular face = [tex]\frac{1}{2}[/tex] × base × slant height

                                            =  [tex]\frac{1}{2}[/tex] × 12 × 10

                                            = 60 [tex]cm^{2}[/tex]

Area of the square base = length × length

                                         = 12 × 12

                                         = 144  [tex]cm^{2}[/tex]

Total surface area of the pyramid = area of the base + 4 (area of the triangular face)

                              = 144 + 4(60)

                              = 144 + 240

                              = 384 [tex]cm^{2}[/tex]

Therefore, total surface area of the pyramid is 384 [tex]cm^{2}[/tex].

Answer:

[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]

And we can find the probability using the normal standard distribution table and with the complement rule we got:

[tex]P(z<-1.11)= 0.1335[/tex]

Step-by-step explanation:

For this problem we have the following parameters:

[tex] \mu = 520, \sigma = 90[/tex]

We select a sample size of n =100 and we want to find this probability:

[tex] P(\bar X <510) [/tex]

The distribution for the sample mean using the central limit theorem would be given by:

[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]

And we can solve this problem with the z score formula given by:

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

And if we find the z score formula we got:

[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]

And we can find the probability using the normal standard distribution table and with the complement rule we got:

[tex]P(z<-1.11)= 0.1335[/tex]

Answer:

Relative frequency:

[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]

The most serious threat to aviation safety is, according to this data, "mechanical failures". It can be improved by more rigorous inspection and better maintenance policies and execution.

Step-by-step explanation:

We have the data for fatal plane crashes. The sum of plane crashes is

We can calculate the relative frequency as:

[tex]\text{Pilot error}=415/1370=0.30\\\\\text{Other human error}=96/1370=0.07\\\\\text{Weather}=169/1370=0.12\\\\\text{Mechanical problems}=622/1370=0.45\\\\\text{Sabotage}=68/1370=0.05\\\\[/tex]

We can see that the most frequent cause is "mechanical problems", with a relative frequency of 0.45.

Answer:

see explanation

Step-by-step explanation:

Given

y = x² - 2x - 8

To find the x- intercepts let y = 0 , that is

x² - 2x - 8 = 0 ← in standard form

(x - 4)(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 2 = 0 ⇒ x = - 2

x- intercepts : x = - 2, x = 4

The x- coordinate of the vertex is mid way between the x- intercepts, that is

[tex]x_{vertex}[/tex] = [tex]\frac{-2+4}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1

Substitute x = 1 into the equation for corresponding y- coordinate

y = 1² - 2(1) - 8 = 1 - 2 - 8 = - 9

vertex = (1, - 9 )

Answer:

AOB = 73

BOC = 107

Step-by-step explanation:

So make an equation.

9x + 27 = 180

9x = 153

x = 17

AOB = 73

BOC = 107

Answer:

Savannah

Step-by-step explanation:

Emery has solved it incorrectly;

x = 100

Answer:

  (x, y) = (-3, -6)

Step-by-step explanation:

The (x, y) distance from R to T is ...

  (Δx, Δy) = T - R = (3, -3) -(-5, -7) = (3 -(-5), -3 -(-7)) = (8, 4)

Then 1/4 of the distance is ...

  (Δx, Δy)/4 = (8, 4)/4 = (2, 1)

This is added to the R coordinates to find the desired point:

  point = R +(2, 1) = (-5, -7) +(2, 1) = (-5+2, -7+1) = (-3, -6)

The coordinates are ...

  x-coordinate: -3

  y-coordinate: -6

Answer:

a) 48.80% probability that his travel time to work is less than 30 minutes

b) The mean is 30.7 minutes and the standard deviation is of 3.83 minutes.

c) 13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 30.7, \sigma = 23[/tex]

a. If a worker is selected at random, what is the probability that his travel time to work is less than 30 minutes?

This is the pvlaue of Z when X = 30. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 30.7}{23}[/tex]

[tex]Z = -0.03[/tex]

[tex]Z = -0.03[/tex] has a pvalue of 0.4880.

48.80% probability that his travel time to work is less than 30 minutes

b. Specify the mean and the standard deviation of the sampling distribution of the sample means, for samples of size 36.

[tex]n = 36[/tex]

Applying the Central Limit Theorem, the mean is 30.7 minutes and the standard deviation is [tex]s = \frac{23}{\sqrt{36}} = 3.83[/tex]

c. What is the probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes?

This is 1 subtracted by the pvalue of Z when X = 35. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{35 - 30.7}{3.83}[/tex]

[tex]Z = 1.12[/tex]

[tex]Z = 1.12[/tex] has a pvalue of 0.8687

1 - 0.8687 = 0.1313

13.13% probability that in a random sample of 36 NJ workers commuting to work, the mean travel time to work is above 35 minutes

Answer:

hope this helps :)

Step-by-step explanation:

1/4 because 2/1 is 2 and 2 to the power of -2 is 1/4

Answer:

Step-by-step explanation:

[tex]\int\limits^{\infty}_0 {A^2_1} (e^{-r/a})r^2dr= {A^2_1}\int\limits^{\infty}_0r^2(e^{-r/a})^2\, dr)[/tex]

[tex]=A_1^2\int\limits^{\infty}_0 r^2e^{-2r/a}\ dr[/tex]

[tex]=A_1^2[\frac{r^2e^{2r/a}}{-2/a} |_0^{\infty}-\int\limits^{\infty}_0 2r\frac{e^{-2r/a}}{-2/a} \ dr][/tex]

[tex]=A^2_1[0+\int\limits^{\infty}_0 a\ r\ e^{-2r/a}\ dr][/tex]

[tex]=A^2_1[\frac{a \ r \ e^{-2r/a}}{-2/a} |^{\infty}_0-\int\limits^{\infty}_0 \frac{a \ e^{-2r/a}}{-2/a} \ dr][/tex]

[tex]=A_0^2[0-0+\int\limits^{\infty}_0 \frac{a^2}{2} e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} \int\limits^{\infty}_0 e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} [\frac{e^{-2r/a}}{-2/a} ]^{\infty}_0[/tex]

[tex]=\frac{A_1^2a^2}{2} -\frac{a}{2} [ \lim_{r \to \infty} [e^{-2r/a} -e^0]\\\\=\frac{A_1^2a^2}{2} -(\frac{a}{2}) (0-1)[/tex]

[tex]=\frac{A_1^2a^3}{4}[/tex]

[tex]\therefore A_1^2\int\limits^{\infty}_0 r^2(e^{-r/a}) \ dr =\frac{A_1^2a^3}{4}[/tex]

Find the unique positive value of A1

[tex]=4\pi (\frac{A_1^2a^3}{4} )\\\\=A_1^2a^3\pi\\\\A_1^2=\frac{1}{a^3\pi} \\\\A_1=\sqrt{\frac{1}{a^3\pi} }[/tex]

Answer:

Option (2).

Step-by-step explanation:

In the figure attached,

A, C and B are the points lying on a straight line.

2 lines EC and DC have been drawn by extending the lines from C to E and D respectively.

Ray CE is the angle bisector of ∠ACD.

That means CE divides ∠ACD in two equal parts.

m∠ACE = m∠DCE

Since m∠ACD = m∠ACE + m∠DCE

                        = 2(m∠ACE)

          m∠ACE = [tex]\frac{1}{2}(\angle ACD)[/tex]

Therefore, option (2) will be the answer.

Answer:

b

Step-by-step explanation:

took test

Answer:

So if 17/25 of the students like math, science, and art and 3/20 of the students like art only. We first need to find common demoninator. 68/100 and for the second one 15/100. Subtract them both

68-15 = 53/100 of the students factor math, and science or 53%

Answer:

x=-2

Step-by-step explanation:

3 + -4x = 5+ -3x

-4x = 2 - 3x

-x = 2

x = -2

Answer:

(a) P(CBM) = 0.07

(b) P(not CBW) = 0.996

(c ) P(neither is color-blind) = 0.926

(d) P=(at least one is color-blind) = 0.074

Step-by-step explanation:

The correct data is  that Approximately 7% of American men and 0.4% of American women are red-green color-blind.

(a) Probability that he is red-green color-blind:

[tex]P(CBM) = 0.07[/tex]

(b) Probability that she is NOT red-green color-blind:

[tex]P(not\ CBW) =1- P(CBW)\\P(not\ CBW) = 1 -0.004\\P(not\ CBW) =0.996[/tex]

(c) Probability that neither are red-green color-blind

[tex]P(neither) = P(not\ CBW)*P(not\ CBM) \\P(neither) = 0.996 *(1-0.07)\\P(neither)=0.926[/tex]

(d) Probability that at least one of them is red-green color-blind

[tex]P(at\ least\ one) = 1- P(neither) \\P(at\ least\ one) = 1-0.926\\P(at\ least\ one) = 0.074[/tex]

Answer:

The Probability that will pick a red tile from the bag

[tex]P(E) = \frac{6}{11}[/tex] = 0.545

Step-by-step explanation:

Explanation:-

Given data 4 blue tiles, 12 red tiles, and 6 green tiles in a bag

Total = 4 B + 12 R + 6 G = 22 tiles

Total number of exhaustive cases

         n (S) = [tex]22 C_{1} = 22 ways[/tex]

The Probability that will pick a red tile from the bag

[tex]P(E) = \frac{n(E)}{n(S)} = \frac{12 C_{1} }{22 C_{1} } = \frac{12}{22}[/tex]

[tex]P(E) = \frac{6}{11}[/tex]

P(E) = 0.545

Final answer:-

The Probability that will pick a red tile from the bag = 0.545

Answer:

D. (250, 80)

Step-by-step explanation:

a) Outliers are values that "lie outside" the other values in a dataset, because their values are "far away" from the main group of data.

b) In this case, the values of A, B, and C have ratios of their coordinates of about 2.5, but the coordinate ratio of D is more than 3.  This makes it to lie far away from the group of data, and therefore an outliner.

c) The Ratios of the Coordinate Values are calculated as follows: A = 2.5 (150/60), B = 2.5 (50/20), C = 2 (200/100), while D = 3.125 (250/80).

Answer:

17.3 Inches

Step-by-step explanation:

Given that the diagonal of a cube = 30 inches

For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]

Therefore:

[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]

Side Length of the cube is 17.3 Inches.

Answer:

17.3

Step-by-step explanation:

Edge 2020

Answer:

  closest choice: (-2, 0.2)

Step-by-step explanation:

The attached image from a graphing calculator shows the solutions (to the nearest tenth) to be ...

  (-1.9, 0.2)

  (1.0, 6.0)

The closest of the offered choices is (-2, 0.2). None are actually correct.

Answer:

3x-5=2x+6

x-5=6

x=11