Which is the area of the rectangle?

Given:

The base of the given triangle has two part:

Left( left side of the hypotenuse) = 25

Right ( right side of the hypotenuse) = x

The altitude (h) = 60

To find the value of x.

Formula:

By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,

[tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]

Now,

Putting,

left = 25, altitude = 60 and right = x we get,

[tex]\frac{25}{60} = \frac{60}{x}[/tex]

or,  [tex](25)(x)=(60)(60)[/tex] [ by cross multiplication]

or, [tex]x= \frac{3600}{25}[/tex]

or, [tex]x=144[/tex]

Hence,

The value of x is 144.

Answer:

x = 144

Step-by-step explanation:

Height Theorem

60² = 25·x

3600 = 25x

x = 3600 : 25

x = 144

Answer:

linear and lateral

Step-by-step explanation:

thsts it

Final answer:

A coordinate grid, also known as a Cartesian coordinate system, is a mechanism used in mathematics to define every point in a plane with a pair of numerical values indicating horizontal and vertical positions from an origin. Systems like UTM and SPC are derived from this concept, using a grid to simplify plotting and calculations on a plane surface.

Explanation:

A coordinate grid, or a Cartesian coordinate system, is a tool used in mathematics to specify each point uniquely in a plane by a pair of numerical coordinates. These are typically written as an ordered pair (x, y) where 'x' represents the horizontal displacement and 'y' represents the vertical displacement, both measured from a specific origin point. This system of geometry was developed by René Descartes, hence the name Cartesian.

For example, the origin of a coordinate system is the starting point where both x and y are zero, designated as (0,0). If we move to the right, x increases, and if we move up, y increases. Conversely, moving to the left decreases x and moving down decreases y. So, for instance, the point (3,4) is located 3 units to the right of the origin and 4 units above it.

Plane coordinate systems, like the Universal Transverse Mercator (UTM) and the State Plane Coordinate (SPC) systems, simplify calculations by using a grid pattern superimposed on a flattened representation of the Earth's surface, facilitating easier and more precise location plotting than spherical coordinate systems like latitude and longitude.

Answer:

There will be 1134.6 infected people on April 25 if on March 22 there were 69 case.

Step-by-step explanation:

Given : Equation [tex]15.4x+72[/tex]

To find : Calculate how many infected people there will be on April 25 if on March 22 there were 69 case ?

Solution :

Equation [tex]y=15.4x+72[/tex]

Plug the x value in the equation,

[tex]y=15.4(69)+72[/tex]

[tex]y=1062.6+72[/tex]

[tex]y=1134.6[/tex]

Therefore, there will be 1134.6 infected people on April 25 if on March 22 there were 69 case.

The midpoint is just the average of the coordinates,

M = (1/2) ( (0,2) + (2,8) ) = ((0+2)/2, (2+8)/2) = (1, 5)

Answer: (1,5)

Answer:

(1,5)

Step-by-step explanation:

(0,2) and (2,8)

Midpoint: (0+2)/2, (2+8)/2

2/2, 10/2

(1,5)

Answer:

a) sample size ≥ 30

b) 0.0017

Step-by-step explanation:

a) The central limit theorem states that for population with mean μ and standard deviation σ and take sufficiently large random samples from the population. This will hold provided the sample size is sufficiently large (usually n > 30) for a normal population.

Therefore the sample size should be greater or equal to 30 i.e n ≥ 30.

b) Given that n = 45, μ = 11.4 minutes and σ = 3.2 minutes, the z score (z) is given by the equation:

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

Substituting values to get:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }= \frac{10-11.4}{\frac{3.2}{\sqrt{45} } }=-2.93[/tex]

Using the z table:

P(x < 10) = P(z < -2.93) = 0.0017

the probability that a random sample of n=45 oil changes results in a sample mean time of less than 10 minutes is 0.0017

For part (a), a sample size larger than 30 would be sufficient for using the normal model. For part (b), we'd use the standard error and z-score to find the corresponding probability for the sample mean time being under 10 minutes with a sample size of 45.

The questions revolve around the normal distribution model, which is a concept in Statistics, and the sample size needed to use the normal model to make inferences about a population (in this case, the duration of oil changes). For part (a), we must note that the Central Limit Theorem allows us to assume the distribution of sample means will approximate a normal distribution if the sample size is large enough (mostly, n > 30 is sufficient).

Thus, for this particular scenario, a sample size greater than 30 would be adequate. For part (b), using the standard error (standard deviation / sqrt(n)) with n = 45, we can find the z score = (X - μ) / standard error, where X is 10. We consult a normal distribution table or use software to find the probability associated with this z-score, which would be the answer.

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Answer:

ST = 12 units

Step-by-step explanation:

Δ RAS and Δ TES are similar triangles, thus the ratios of corresponding sides are equal, that is, noting that SR = 21 - ST, thus

[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{AR}[/tex] substitute values

[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )

6ST = 8(21 - ST)

6ST = 168 - 8ST ( add 8ST to both sides )

14ST = 168 ( divide both sides by 14 )

ST = 12

Answer:

Time taken to reach maximum height=0.875 seconds

Maximum height = 78.25 ft

Step-by-step explanation:

The function which models the height of the ball is given as:[tex]s(t)=-16t^2+28t+66[/tex]

The function s(t) reaches its maximum height at the axis of symmetry. For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex], the axis of symmetry occurs at [tex]x=-\frac{b}{2a}[/tex].

In s(t), a=-16, b=28

[tex]t=-\frac{28}{2(-16)}=0.875 seconds[/tex]

The ball reaches its maximum height after 0.875 seconds

(b)Maximum Height

Given [tex]s(t)=-16t^2+28t+66[/tex]

At t=0.875

[tex]s(0.875)=-16(0.875)^2+28(0.875)+66=78.25 ft[/tex]

Maximum height = 78.25 ft

Answer:

time: 0.875 seconds

maximum height: 18.25 feet

Step-by-step explanation:

The function that gives the height of the ball in feet after t seconds is:

s(t) = −16t^2 + 28t + 6

The inicial velocity is 28 ft/sec, and the inicial position is 6 feet.

So, to find the time when the ball reaches the maximum heigth, we need to find the vertix of the equation −16t^2 + 28t + 6.

We can use the following formula to find it:

t_vertix = -b/2a

where a and b are coefficients of the quadratic equation (in our case, a = -16 and b = 28).

So, we have that:

t_vertix = -28/(-32) = 0.875 seconds

To calculate the maximum height we just need to use this time in the equation of position:

s(0.875) = −16*(0.875)^2 + 28*0.875 + 6 =  18.25 feet

Answer:

65%

Step-by-step explanation:

Divide 13 by 20:

0.65

Times 100:

65

So 65%

The height of the pole is 20ft.

Step-by-step explanation:

Let the height of the pole be '(h+6)'

Distance between the pole and Sven = 48ft.

Height of Sven = 6 ft.

Distance between the bird and his eyes = 50 ft.

We can find the value of 'h' using pythogoras theorem,

h = √(2500-2304)

h = √(196)

h = 14 ft.

The height of the pole = h + 6

= 14 + 6

= 20ft.

The height of the pole is 20ft.

Answer:

1) 14

2) 8

3) 5

4) 11

5) 10

6) 6

7) 10

8) 17

9) 26

10) 18

Step-by-step explanation:

Merry Early Christmas :)

Answer:

a radius

x-h

y-k

x-h, y-k

Step-by-step explanation:

The standard form of the circle is given by ( x - h )² + ( y - k )² = r²

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the equation of circle be C

Let the center of the circle be represented as A ( h , k )

Now , the radius of the circle is = r units

And , standard form of a circle is

( x - h )² + ( y - k )² = r²

when it is a unit circle , the center is at ( 0 , 0 )

S0 , the equation of circle is x² + y² = r²

Hence , the standard form of circle is ( x - h )² + ( y - k )² = r²

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Answer:

85263

Step-by-step explanation:

In Penelope's account $ 85262.6 would be there after 14 years.

The compound Interest is the interest you earn on Interest .

The formula for calculating the amount when the interest is compounded continuously

P = P₀[tex]\rm e^{rt}[/tex]

Penelope invested $32,000 in an account

interest rate of 7% compounded continuously.

After 14 years the amount will be

P = 32000 * [tex]\rm e^{0.07*14}[/tex]

P = $ 85262.6

Therefore $ 85262.6 would be in the account after 14 years.

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Answer:

48 feet

Step-by-step explanation:

Since 1 yard = 3 feet

Therefore, 48 yards = 3* 48 = 144 feet

[tex]P = 2(l + w) \\ 144 = 2(l + 24) \\ \frac{144}{2} = l + 24 \\ 72 = l + 24 \\ 72 - 24 = l \\ l = 48 \: feet[/tex]

Hence, length of the field is 48 feet.

Answer:

48 ft im pretty sure

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

log2(16)

log2(2^4)

4 log2(2)

4 × 1

4

It should be 4

Answer:

1 stack of 60

2 stacks of 30

3 stacks of 20

4 stacks of 15

5 stacks of 12

6 stacks of 10

60 stacks of 1

30 stacks of 2

20 stacks of 3

15 stacks of 4

12 stacks of 5

Prime Factorisation

[tex]60=2^{2}*3*5[/tex]

Step-by-step explanation:

To find the number of stacks you can make just divide the total by the size of the stacks. This also works in reverse.

To find the prime factorisation you just find the factors of the number by dividing it by the largest prime possible.

The monkey can arrange the 60 coconuts into different numbers of stacks, from 1 stack of 60 coconuts to 60 stacks of 1 coconut. The prime factorization of 60 is 2^2 x 3 x 5.

The monkey, who has collected 60 coconuts, can distribute them in various different ways. The distribution depends on the number of coconuts in each stack as well as the total number of stacks. Here are the various possibilities:

Now, for the prime factorization of 60. This involves breaking down 60 into its smallest prime factors, which are 2, 3, and 5. Thus, the prime factorization of 60 is: 22 x 3 x 5

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Answer:

Step-by-step expla0000000000000000000000000nation:

9514 1404 393

Answer:

  216 J

Step-by-step explanation:

The kinetic energy is given by ...

  KE = 1/2mv^2

  KE = (1/2)(3 kg)(12 m/s)^2 = 216 kg·m²/s² = 216 J

The kinetic energy of the toy is 216 joules.

__

Its potential energy depends on its height.

Answer:216 J Is the answer I just checked

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The probability simply refers to the chance of an event occurring. What this means is that when a coin is tossed once, the chance that we can get a head is 50%. This is simply just referring to the likelihood of the event happening.

Now for the first toss, there is a likelihood of 50%, for the second toss too there will be a likelihood of 50%.

This is different from the fact that for every 2 throws there must be a head showing up

Answer:

You should carry 2 other batteries.

Step-by-step explanation:

If the average life of each battery tends to last 6.9 months, and what you need is a year of battery supply, you probably need to carry two batteries.

The battery inside the flashlight has probably already spent much of its half-life.

We are told that the flashlight already has a battery inside, the batteries are discharged inside the flashlight even if the flashlight is not being used.

Which means that the average life of that battery is wearing out.

It would take 2 more batteries in addition to the one already inside the flashlight to supply the need for these for a year.

Answer:

558.036 lb

Step-by-step explanation:

Let x is the amount of the sea water to collect 125 lb of sea salt

As given: 64 lb/ft³ has 0.0035 dissolved salt by weight

So the formula to find out the amount of the sea water is:

64 lb/ft³ * 0.0035 *x ft³  = 125 lb

<=> x = [tex]\frac{125}{64*0.035}[/tex] = 558.036 lb

Hope it will find you well.

Answer:

61 miles per hour

Step-by-step explanation:

because you need to divide 274.5 by 4.5 to get the average speed per hour.

Answer:

61 miles per hour

Step-by-step explanation:

To find the average speed, divide the miles by the hours

miles/hours

274.5/4.5

61

So, the average speed is 61 miles per hour

Answer:

y = -6x + 30

Step-by-step explanation:

The inicial value you have is $30, so this will be the value of y after 0 weeks, that is, x = 0

After one week, you spend $6, so you will have y = 30 - 6 = 24 when x = 1.

With these pair of values, we can find the linear equation:

y = ax + b

for x = 0, y = 30:

30 = a*0 + b

b = 30

for x = 1, y = 24:

24 = a*1 + 30

a = 24 - 30 = -6

So, our equation is:

y = -6x + 30

Answer:

AB = 24 cm, BC = 6 cm

Step-by-step explanation:

The perimeter of PQRS = 2(8) + 2(2) = 16 + 4 = 20 cm

Given the perimeter of ABCD is 60 cm, then

scale factor = [tex]\frac{60}{20}[/tex] = 3

That is the dimensions of ABCD are 3 times those of PQRS, so

AB = 3 × 8 cm = 24 cm

BC = 3 × 2 cm = 6 cm

Answer:

AB = 24 cm.

BC =  6 cm.

Step-by-step explanation:

The outer rectangle is a dilation of the inner rectangle centered at the origin. Therefore:

The inner and outer rectangles are similar so the ratio of length to width of the outer rectangle is the same as the ratio of length to width of the inner one.

so AB / BC = 8/2 = 4

AB  = 4BC   -------------(1)

Also as the perimeter  = 60

2AB + 2BC = 60.............(2)

Substituting AB = 4BC in equation (2):

2(4BC) + 2BC = 60

10BC = 60

BC = 6 cm.

and AB = 4*6 = 24 cm.

Answer:

Correct option:

Fail to reject H₀. There is enough evidence at the 5% level of significance to support the claim.

Step-by-step explanation:

The claim to be tested is:

Claim: μ ≠ 0.

The information provided is:

α = 0.05

σ = 2.62

Sample statistics: = -0.69

n = 60

As the population standard deviation is provided, it can be determined that a z-test for single is used to performed the test.

Decision rule:

If the p-value of the test is less than the significance level, α then the null hypothesis will be rejected and vice-versa.

Compute the p-value as follows:

[tex]p-value=2P(Z<-0.69)\\=2\times [1-P(Z<0.69)]\\=2\times [1-0.7549]\\=0.4902[/tex]

*Use a z-table for the probability.

The p-value = 0.4902 > α = 0.05.

The null hypothesis was failed to rejected at 5% level of significance.Thus, it can be concluded that there is enough evidence at the 5% level of significance to support the claim.

Answer:

c = 30 inch

Step-by-step explanation:

perpendicular (p) = 18 inch

base(b) = 24 inch

hypotenuse (h) = ?

we know by using Pythagoras theorem

h² = p² + b²

h² = 18² + 24²

h² = 324 + 576

h² = 900

h= √900

therefore h = 30 inch

Hope it will help you. :)

Answer:

f(x) = -15x² + 50x

Step-by-step explanation:

You're given the rocket start at ground level, so we can assume,

f(0) = 0

after 1 second the rocket is 35 feet up.

f(1) = 35

and after 2 second the rocket is 40 ft up.

f(2) = 40

Now you have 2 values to  plug in your formula to solve.

Plug in f(x) = ax² + bx + c and solve:

f(0) = a(0)² + b(0) + c = 0

f(1) = a(1)² + b(1) + c = 35

f(2) = a(2)² + b(2) + c = 40

a(0)² + b(0) + c = 0

a(1)² + b(1) + c = 35

a(2)² + b(2) + c = 40

0 + 0 + c = 0   ,   we got c=0, so substitute it

a + b + c = 35

4a + 2b + c = 40

Solve for a and b

c = 0

a + b + 0 = 35

4a + 2b + 0 = 40   , solve it using elimination

-2a - 2b + 0 = -70

4a + 2b + 0 = 40  

2a + 0 = -30

a = -15   , we got a, solve for b now

a + b + 0 = 35

(-15) + b + 0 = 35

b = 50

Now we got c=0, a=-15, and b=50, plug it back in your equation

f(x) = -15x² + 50x + 0

Answer:

7 boys.

Step-by-step explanation:

Given:

Total number of students in the school = 60

Total number of girls in the school = 33

Total number of students currently studying chemistry = 24

Total number of girls not currently studying chemistry = 16

Question asked:

How many boys are currently studying chemistry ?

Solution:

Total number of girls in the school = 33

Total number of girls not currently studying chemistry = 16

Total number of girls currently studying chemistry = Total number of girls in the school - Total number of girls not currently studying chemistry

Total number of girls currently studying chemistry =  33 - 16 = 17                                                  

Now:-

Total number of boys and girls currently studying chemistry = 24

Total number girls currently studying chemistry = 17

Total number of boys currently studying chemistry = Total number of boys and girls currently studying chemistry - Total number girls currently studying chemistry

Total number of boys currently studying chemistry = 24 - 17 = 7

Therefore, 7 boys are currently studying chemistry.

Answer:

side c = 10.2

A = 52.6°

B = 37.4°

Step-by-step explanation:

c² = 8.1² + 6.2²

c² = 104.05

c = 10.20049018

Using cosine law:

8.1² = 10.2² + 6.2² - 2(10.2)(6.2)cos

cosA = 7687/11648

A = 52.57199409

A = 52.6°

B = 180 - 90 - 52.6 = 37.4°

Answer:

The price of chair in furniture house is $137.16

Step-by-step explanation:

We are given the following in the question:

Wholesale price of chair = $108

Marked percentage = 27%

We have to find the price of the chair in the furniture store.

Increased price =

[tex]=27\%\times 108\\\\=\dfrac{27}{100}\times 108\\\\=29.16\$[/tex]

Price of chair in furniture house =

= Wholesale price + Increased price

[tex]=108 + 29.16\\=137.16\$[/tex]

Thus, the price of chair in furniture house is $137.16