can someone tell me if why these triangles are similar

Answer:

a

Step-by-step explanation:

1. Reduce the index of the radical and exponent with 2

√(a^2) = a

Basically square root is also can be represent as power of 1/2. Which is (a^2)^1/2. Then you can multiply both power. So you will get a^(2/2). solve it hence the solution is a^1 which is a. Hopefully this will help

Answer:

(a)[tex]0.15731[/tex]

(b)0.02275

Step-by-step explanation:

We are given that

Mean=0

Standard deviation=0.5 g

True weight of a sample=166 g

Let X denote the normal random variable  with mean =166+0=166

(a)

P(166.5<X<167.5)

=[tex]P(\frac{166.5-166}{0.5}<\frac{X-\mu}{\sigma}<\frac{167.5-166}{0.5})[/tex]

=[tex]P(1<Z<3)[/tex]

=[tex]P(Z<3)-P(Z<1)[/tex]

[tex]=0.99865-0.84134[/tex]

[tex]=0.15731[/tex]

(b)

[tex]P(X>167)=P(Z>\frac{167-166}{0.5})[/tex]

[tex]=P(Z>2)[/tex]

[tex]=1-P(Z<2)[/tex]

[tex]=1-0.97725[/tex]

[tex]=0.02275[/tex]

Answer:

[tex]y = 125.00x + 591.00[/tex]

Step-by-step explanation:

Given

See attachment for table

Required

Equation for Paris

From the table, we have:

[tex]flight = 591.00[/tex]

[tex]hotel = 125.00[/tex]

Let the number of nights be x.

So, the equation for the total amount (y) is:

[tex]y = flight + hotel * x[/tex]

[tex]y = 591.00 + 125.00 * x[/tex]

[tex]y = 125.00x + 591.00[/tex]

Answer:

[tex]\frac{75}{100}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

secθ = 1/cosθ

cosθ = 0 for π/2, 3π/2

secθ is undefined for θ = π/2, 3π/2

Answer:

I think A

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{3x + 5}{2x + 7}[/tex] = 5

do cross multiplication

3x + 5 = 5(2x + 7)

3x + 5 = 10x + 35

5 - 35 = 10x - 3x

-30 = 7x

-30/7 = x

20 A

since there are 7 angles given it means that the polygon is heptagon as heptagon has 7 sides.

sum of interior angle of heptagon = (n-2)*180

(7-2)*180

5*180

900

Now ,

110 + 90 + 150 + 102 + 110 + 170 + x = 900

732 + x = 900

x = 900 - 732

x = 168 degree

20 B

since 5 angles are given it means that the polygon is pentagon as pentagon has 5 sides.

sum of interior angles of a pentagon = (n-2)*180

(5-2)*180

3*180

540 degree

Now ,

110 + 95 + 120 + 114 + x = 540

465 + x = 540

x = 540 - 465

x = 75 degree

21

let one rational number be x

according to the question,

1/7 * x = 2

x/7 = 2

do cross multiplication

x = 14

Answer:

G(x) = x+3

Step-by-step explanation:

The equation of the graph is G (x) = (x - 3)⁴

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A relation between a set of inputs having one output each is called a function.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The graph of function G (x) is shown in image.

Here, the graph is 3 units left to function F (x) = x⁴.

The equation of the graph is G (x) = (x - 3)⁴

Hence, the equation of the graph is G (x) = (x - 3)⁴

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Answer:

Ang pangit mo

Kamuka mo Yong clown

Answer:

0.5 liters of milk are available per child.

Step-by-step explanation:

Amount of milk available per children:

The amount of milk, in liters, available for x children is given by:

[tex]m(x) = \frac{25}{x}[/tex]

50 children are present on a day

This means that [tex]x = 50[/tex]

How much milk is available per child?

This is m(50). So

[tex]m(50) = \frac{25}{50} = 0.5[/tex]

0.5 liters of milk are available per child.

Answer:

Step-by-step explanation:

-6z²-10z-3=0

multiply by -1

6z²+10z+3=0

disc .=b²-4ac=10²-4×6×3=100-72=28≥0

also it is not a perfect square.

so roots are real,irrational and different.

[tex]z=\frac{-6 \pm\sqrt{28} }{2 \times 6} \\=\frac{-6 \pm 2 \sqrt{7}}{12} \\=\frac{-3 \pm\sqrt{7} }{6}[/tex]

Answer:

x = − 1

Step-by-step explanation:

Answer:

compound interest

Step-by-step explanation:

compound interest yields higher profit than simple interest

Answer:

the simple interest function will be greater in the beginning, but the

compound interest equation will overtake the simple after a while.

it appears that the 4% compound equation will overtake the simple at about 10 years

Step-by-step explanation:

[tex]1 + .05t = 1(1.04)^t[/tex]

Answer:

11x-8x+8y

3x+8y SEEESH IN DEEZ NU                           TS

Step-by-step explanation:

9514 1404 393

Answer:

  A, C, D, E, F

Step-by-step explanation:

The figure has 4 sides: 2 pairs of parallel sides, all of equal length. The angles are right angles.

The figure is a ...

Answer:

A, and F.

Step-by-step explanation: I hope this helps.

Four sides are called a quadrilateral.

Three sides are called a triangle.

Five sides are called a pentagon.

Six sides are called hexagons.

A rectangle is a quadrilateral with four right angles.

A square is a quadrilateral with four right angles.

A rhombus is a quadrilateral with four equal sides.

A parallelogram is a quadrilateral with two pairs of parallel sides.

A trapezoid is a quadrilateral with one pair of parallel sides.

Acute angles are less than 90°

Right angles are exactly 90°

Obtuse angles are more than 90°

Acute triangle has three acute angles.

Right triangle has one right angle.

An obtuse triangle has one obtuse angle.

Isosceles triangle has the minimum of two sides that are equal length.

Equilateral triangle has three sides that are at an equal length.

Scalene triangles have three sides of different lengths,

Acute triangles with three equal sides are called an equiangular triangle.

Answer:

-3

Step-by-step explanation:

Answer:

The probability that the company will receive 7 property damage claims on a randomly selected day is 0.137

Step-by-step explanation:

Given,

[tex]\lambda=6[/tex],

The probability mass function of Poisson distribution is used for evaluating the probability of the company will receive 7 property damages claims on any selected day is,

[tex]\begin{aligned}P(X=K)&=e^{-6} \times \dfrac{6^7}{7!}\\&=0.002478\times\dfrac{279936}{5040}\\&=\dfrac{693.89136}{5040}\\P(X=7)&=0.1365927874\\P(X=7)&=0.137\; (\rm{rounded \;off})\end{aligned}[/tex]

To learn more about this, please refer to the below link:

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Answer:

Please find the complete question and its solution in the attached file.

Step-by-step explanation:

Shortest had survived after 6741 hours [tex]2.5\%[/tex] of the lights burnt.

[tex]\to 0.15\% + 2.35\% = 2.50\%[/tex]

Answer:

Solution given:

f(x)=x²

g(x)=x+5

h(x)=4x-6

now

23:

(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25

24:

(gof)(x)=g(f(x))=g(x²)=x²+5

25:

(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36

26:

(hof)(x)=h(f(x))=h(x²)=4x²-6

27;

(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1

28:

(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14

Answer:

30 additional teachers will have to be hired to reduce the ratio to 1:20.

Step-by-step explanation:

Given that Jefferson School has 1800 students, and the teacher-pupil ratio is 1:30, to determine how many additional teachers will have to be hired to reduce the ratio to 1:20, the following calculation must be performed:

30 = 1800

1 = X

1800/30 = X

60 = X

20 = 1800

1 = X

1800/20 = X

90 = X

90 - 60 = 30

Therefore, 30 additional teachers will have to be hired to reduce the ratio to 1:20.

Answer:

$49.5

Step-by-step explanation:

* means multiply

at $1.98 per loaf

25 * 1.98 =

49.5

Answer:

48.75

Step-by-step explanation:

It would be the cheapest option

Answer:

[tex]\frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt3 \ + \ \sqrt2 }{5 \ + \ \sqrt2 } \\\\=\frac{\sqrt3 \ + \ \sqrt2 }{5 \ + \ \sqrt2 } \times \frac{5 \ - \ \sqrt2 }{5 \ - \ \sqrt2 } \\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2)}{(5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 )}\\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2)}{(5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 )}\\\\=\frac{5 \sqrt3 \ + \ 5\sqrt 2 \ - \ \sqrt{ 3\times 2 } \ - \ \sqrt{2 \times 2}}{(5)^2 \ - \ (\sqrt2)^2}\\\\= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{25 - 2}\\\\[/tex]

[tex]= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}[/tex]

Answer:

Not sure if this is right, but I hope it helps. Please see attached pic

Step-by-step explanation:

Answer:

0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.

This means that [tex]p = 0.07[/tex]

Sample of 459 phone calls:

This means that [tex]n = 459[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.07[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\sqrt{\frac{0.07*0.93}{459}}} = 0.0119[/tex]

What is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%?

Proportion below 0.07 - 0.03 = 0.04 or above 0.07 + 0.03 = 0.1. Since the normal distribution is symmetric, these probabilities are the same, which means that we find one of them and multiply by 2.

Probability the proportion is below 0.04.

p-value of Z when X = 0.04. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.04 - 0.07}{0.0119}[/tex]

[tex]Z = -2.52[/tex]

[tex]Z = -2.52[/tex] has a p-value of 0.0059

2*0.0059 = 0.0118

0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%

Answer:

The answer is 209 pi cm^2

L.A.(Lateral Area) = π19×11 = 209 π

The lateral area of the given cone with a raidus of 19 cm and a slant height of 11 cm is: D. 209π cm²

Lateral area of a cone = πrL, where r is the radius and L is the slant height of the cone.

Given the following:

Lateral area of a cone = π(19)(11)

Lateral area of a cone = 209π cm²

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Answer:

Step-by-step explanation:

Take the first real number and keep a decimal point to the right of it. Write the number after it.

Put a multiplication symbol and then 10.

Now count the number places to the right of the first real number and the number of place will be the power of 10.

If , number of place are before the first real number, then the power of 10 will be negative.

0.0009 = 9 * 10⁻⁴

12 = 1.2 *10

1000 = 1* 10³

0.03 = 3 *10⁻²

120  = 1.2 * 10²

1.12 = 1.12 *10⁰

Answer:

One larger, more stable nucleus

Answer:

 $10,000

Step-by-step explanation:

.05 x = 500

x = 500/.05

x = $10,000