similarity statements between triangles

Answer:

n = 6

Step-by-step explanation:

See attachment for diagram

Triangle PQR is similar to triangle FGH.

Similar triangles are similar in shape but different in size.

The ratio of their corresponding sides are equal.

QP=10.5

QR=9

RP=6

GF=7

HF=4

GH=n

(Hypotenuse in ∆PQR)/ (hypothenuse in ∆FGH)

=(Adjacent in ∆PQR)/(adjacent in ∆FGH)

= 6/4 = 9/n

Cross multiply

6×n = 9×4

6n = 36

n = 36/6

n = 6

Therefore ratio of their corresponding sides = 3/2

Answer:

g(x) = 4x - 1

Step-by-step explanation:

Linear function in the format: g(x) = ax + b

g(2t) is a*(2t)+b

g(2t) = 8t - 1 means that:

when x = 2t, g = 8t - 1.

So

Equaling both sides

8t - 1 = a*2t + b

So

b = -1,

and

2a = 8, a = 8/2, a = 4

So

g(x) = 4x - 1

The original translation < 3, -3 > moves the figure 3 units to the right and 3 units down.

We undo this by moving 3 units left and 3 units up, which is what < -3, 3 > describes.

The translation <-3, 3> will move the image back to the preimage original position.

The displacement of a image from one place to another is called translation of image.

If a figure is on the origin, i.e. (0, 0), then if turns 3 cells right.

We can see that, It translated as (3,0)

Again if it go down 3 cells, then the translated one is (3, -3)

So, moving it back, we should translate it 3 cells left & 3 cells up.

So after translation, it should be (-3, 3).

Learn more about Translation here :

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Answer: 24

Step-by-step explanation:

7+12+5=24

Answer:

24

Step-by-step explanation:

Answer:

Y = 2X + 19

Step-by-step explanation:

the relationship is linear

gradient equals 2

Answer:

7/20

Step-by-step explanation:

35/100 is simplified to 7/20. Here is another example with a different percentage. Change 25% to a fraction. 25/100 is simplified to 1/4

Answer:

Diameter = 22.9 ft

Step-by-step explanation:

We are told that volume of the sphere is 6329 ft³

Now formula for volume of sphere is given as;

V = (4/3)πr³

Thus,

(4/3)πr³ = 6329

Multiply both sides by 3/4 to get;

πr³ = (6329) * 3/4

πr³ = 4746.75

Divide both sides by π to obtain;

r³ = 4746.75/π

r = ∛(4746.75/π)

r = 11.4749 ft

Now, diameter = 2 x radius

Diameter = 2 × 11.4749

Diameter = 22.9498 ft

Approximating to a tenth of a feet gives;

Diameter = 22.9 ft

Answer:

14 bags

Step-by-step explanation:

Dimension of lawn : 230 feet by 180 feet

area of rectangle is given by length * width

Since lawn is rectangular area of lawn = 230 feet * 180 feet = 41,400 sq. feet

Given that one bag of fertilizer covers 3000 square feet of lawn.

Thus , to find no. of bags required to cover whole lawn will be

total area of lawn/area which one bag of  fertilizer covers

no. of bags required to cover whole lawn = 41,400 sq. feet/3000 sq. feet

    = 13.8 bags.

As no. of bags cannot be fractional , hence rounding bag to nearest unit place is 14 bags.

Answer:

12*sqrt(3)

Step-by-step explanation:

since it is isosceles its angles are 45, 45, 90, therefore the hypotenuse is 12*sqrt(3).

Answer:

Number of permutations for a 4 digit number using the digits 0 – 9 (10 available digits in total), supposing numbers cannot be repeated, is calculated by:

10P4 = 10!/(10-4)! = 5040

Hope this helps!

:)

Answer:

A is correct.

Step-by-step explanation:

Left figure's area = base x height = L x h x 6 = 6Lh

Right figure's area = L x h + L x h + L x h + L x h + L x h + L x h = 6Lh

Hope this helps!

:)

Answer:

-3 !!!!!

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

just did the test on edg

Answer:

[tex]\sqrt[4]{10x2}[/tex]

Answer:

⁴√10√x

Step-by-step explanation:

⁴√5x*⁴√2x

⁴√5x = ⁴√5⁴√x

=⁴√5 ⁴√x⁴√2x

⁴√2x = ⁴√2⁴√x

=⁴√5⁴√2⁴√x⁴√x

⁴√x⁴√x = x1/4x1/4 = x1/4+1/4

=⁴√5⁴√2⁴x1/4+1/4

1/4+1/4 = 1/2

=⁴√5⁴√2⁴√x

⁴√5⁴√2⁴ = ⁴√5*2

=⁴√5*2√x

5*2 = 10

= ⁴√10√x

Answer:

$275

Step-by-step explanation:

Day                                   Price                     Unit price

Monday                            $245                        $2.45

Tuesday                           $315                          $3.15

Wednesday                     $275                         $2.75

Thursday                         $200                         $2.00

Friday                              $225                         $2.25

the first in, first out (FIFO) method uses the price of the oldest units to determine the cost of goods sold:

the ending inventory should = 100 units purchased Friday + 25 units purchased Thursday = (100 x $2.25) + ($25 x $2) = $225 + $50 = $275

Answer: $375

Step-by-step explanation:

Answer:

I think you are correct. bc you have 4 different caps, and four different sections of a spinner that are equal same with the cap. So I believe so.

Step-by-step explanation:

I hope this helps! Im in algebra 2 so its been awhile since i have done this. Good Luck!!:)

Answer:

A

Step-by-step explanation:

I agree with your answer. The question is basically just saying the beverage company randomly chooses one of those letters to put under the bottle caps. For example, one bottle cap might have a T on it, and another might have an A on it. If you try to get all 4 letters, then you will have to keep buying those drinks until you manage to collect all 4 letters. Therefore, there are only 4 possible options for which letter you can get.

If you spin a spinner that has 4 equal sections, then this is similar. You have 4 possible options you can get.

Hope this helps! :)

Answer:

c) 21.4

Step-by-step explanation:

9.5 times 1.5 times 1.5 is 21.375 or 21.4 rounded

Answer:

Step-by-step explanation:

[tex]s=y, t = y- x^2[/tex]

[tex]x^2=y-t[/tex]

[tex]x=\sqrt{s-t}[/tex]

[tex]y=0, y=16, y=x^2, and\\ y=x^2-5.[/tex]

[tex]y-x^2=0,y-x^2=-5[/tex]

therefore,

[tex]s=[(s,t)10\leq s\leq 16,-3\leq t \leq 0][/tex]

Taking partial derivatives

[tex]\frac{dx}{ds} =\frac{1}{2\sqrt{s-t} } \\\\\frac{dx}{dt} =\frac{1}{2\sqrt{s-t} } \\\\\frac{dy}{ds} =1\\\\\frac{dy}{dt} =0[/tex]

[tex]\frac{\delta (x,y)}{\delta (s,t)} =\left|\begin{array}{ccc}\frac{1}{2\sqrt{s-t} } &-\frac{1}{2\sqrt{s-t} } \\1&0\end{array}\right|[/tex]

[tex]=\frac{1}{2\sqrt{s-t} }[/tex]

[tex]\int\limits \int\limits_R {x} \, dx \, dy=\int\limits\int\limits_s {x} \sqrt{s-t} |\frac{\delta(x,y)}{\delta (s,t)} |dsdt[/tex]

[tex]=\int\limits^{16}_0\int\limits^0_{-5} \sqrt{s-t} \frac{1}{2\sqrt{s-t} } dt ds[/tex]

[tex]=\frac{1}{2} \int\limits^{16}_0 ds\int\limits^0_{-5} \, dt \\\\=\frac{1}{2} [s]^{16}_0[t]^0_{-5}\\\\=\frac{1}{2} (16)(5)\\\\=40[/tex]

Answer:

  C.  795.45 in^2

Step-by-step explanation:

The formula for the surface area of a cylinder is ...

  SA = 2πr^2 +2πrh = 2πr(r +h)

For r=6 and h=15.1, the surface area is ...

  SA = 2π(6)(6 +15.1) = π(12)(21.1) = 253.2π

  SA ≈ 795.45 . . . . square inches

Answer:

did it

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

you have to multiply by 9.

2times9=18,5times 9=45,4times 9=36,

3times9=27.

Answer:

8 = -1 (x - 2)

:)

Answer:

8 = -1 (x - 2)

Step-by-step explanation:

Answer:

a) The mean is 0.15 and the standard error is 0.056.

b)  1. Yes

Step-by-step explanation:

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.

For proportions p, in samples of size n, the mean is [tex]\mu = p[/tex] and the standard error is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]. The Central Limit Theorem applies is np > 5 and np(1-p)>5.

In this question:

[tex]n = 40, p = 0.15[/tex]

So

(a) Find the mean and the standard error of the distribution of sample proportions.

[tex]\mu = 0.15, s = \sqrt{\frac{0.15*0.85}{40}} = 0.056[/tex]

So the mean is 0.15 and the standard error is 0.056.

(b) Is the sample size large enough for the Central Limit Theorem to apply?

np = 40*0.15 = 6 > 5

np(1-p) = 40*0.15*0.85 = 5.1>5

So yes

The standard error of the distribution of sample proportions is 0.056 and mean is 0.15.

Yes, the sample size is enough for the Central Limit Theorem to apply.

(a). Given that, size of sample, [tex]n=40[/tex]

        Proportion, [tex]p=0.15[/tex]

In the distribution of sample proportions, mean [tex]\mu=p[/tex]  

and, standard error = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

So, mean [tex]\mu=0.15[/tex]

Standard error =[tex]\sqrt{\frac{0.15(1-0.15)}{40} }=0.056[/tex]

(b). The Central Limit Theorem applies if np > 5 .

 [tex]np=40*0.15=6>5[/tex]

Thus, the Central Limit Theorem is applied.

Learn more:

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Answer:

a) This is a continuous random variable because the set of possible values is an interval.

b) Height = 0.5

Graph attached.

c) P(Y≤1) = 0.5

Step-by-step explanation:

a) If the density curve of the outcomes has a constant height, we have a uniform distribution for values between 0 and 2 (outside this range, the density function has a value of 0).

This function is continous and has a value for each real number. The set of possible values has a is an interval between 0 and 2, all with equal probability (the ones that are otuside this interval have 0 probability, so they are not possible values).

b) The height is calculated so that the total area under the density curve has to be equal to 1.

Then, we have to calculate the integral between 0 and 2 of the density function:

[tex]\int\limits^2_0 {U(x)} \, dx =\int\limits^2_0 {H} \, dx =H\int\limits^2_0 dx=H(x_2-x_1)=H(2-0)=1\\\\2H=1\\\\H=0.5[/tex]

The height is H=0.5

(Graph attached)

c) The probability can be calculated by integrating the density function (which is equal to the area under the curve) between 0 and 1, or using the graph.

With the graph, we see that the area is equal to the height (0.5) by the width of the interval (1), so the total area is 0.5 x 1 = 0.5.

The probability P(Y≤1) is equal to 0.5.

Using the uniform distribution, it is found that:

a)

This is a continuous random variable because the set of possible values is an interval.

b)

The height is [tex]\frac{1}{2}[/tex], and the sketch is given at the end of this answer.

c)

P(Y ≤ 1) = 0.5

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

In this problem, uniformly distributed between 0 and 2, thus [tex]a = 0, b = 2[/tex].

Item a:

Values in an interval, thus continuous. Discrete are for sample spaces, which is not the case here.

Item b:

The height is:

[tex]h = \frac{1}{b - a} = \frac{1}{2}[/tex]

The graph is sketched at the end of this answer.

Item c:

[tex]P(Y \leq 1) = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5[/tex]

Thus, P(Y ≤ 1) = 0.5.

A similar problem is given at https://brainly.com/question/13547683

Answer:

976

Step-by-step explanation:

would you stop it already

Answer: 976m^2

Step-by-step explanation:

An easy way to find the surface area of a prism is to find the area of each side and add them all together.

Area of rectangle:

14mx10m=140m^2

Area of rectangle:

25mx10=250m^2

Since there are 2 of the long rectangles, you multiply by 2:

250m^2x2=500m^2

Area of triangle:

(24mx14m)/2=168m^2

Since there are 2 triangles, you multiply by 2:

168m^2x2=336m^2

Surface Area:

140+500+336=976m^2