the polygons in each pair are similar find the scale factor smaller figure to the larger

Answer:

B. √3 inches

Step-by-step explanation:

Apply trigonometry ratio to solve for AB

AB = DC (opposite sides of a rectangle are equal)

Given,

reference angle (θ) = 30°

Hypotenuse = BD = 2

Adjacent = DC = ?

Apply CAH, which is:

Cos θ = Adj/Hyp

Substitute

Cos 30° = DC/2

2*Cos 30° = DC

2*√3/2 = DC (Cos 30° = √3/2)

DC = √3 in.

AB = DC. Therefore,

AB = √3 inches

Answer:

3.31 cups

Step-by-step explanation:

1/× =16/53

16x = 53

x = 53/16

x = 3.3125

Answer:

Step-by-step explanation:

Use the change-of-base rule.

Answer:

180000 people

1 : 2

$40

80 stores

Step-by-step explanation:

1.)

Population in 2020 are equal : Let population =

City A increased by 20% From 120,000 in 2015

(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000

Hence, city A = 144,000.

Since, city A and B have equal population ; city B also has a population of 144000 in 2020.

Let population in 2015 = x

(1 - 0.2) * x = 144000

0.8x = 144000

x = 144000/0.8

x = 180,000

2.)

Let proportion of 20% butter = x and proportion of 50% butter = 1 - x

0.2x + 0.5(1 - x) = 0.4

0.2x + 0.5 - 0.5x = 0.4

-0.3x + 0.5 = 0.4

-0.3x = 0.4 - 0.5

-0.3x = - 0.1

x = 0.1/0.3

x = 0.3333

(1-x) = 1 - 0.33333 = 0.6666%

0.3333% of 20% butter

0.6666% of 50% butter

Hence ;

0.3333 : 0.6666

1 : 2

3.)

Let original price of book = x

Discount on sale = 30%

Sale price = $28

Sale price = original price * (1 - discount)

$28 = (1 - 0.3) * x

$28 = 0.7x

x = $28/0.7

x = $40

4.)

Let total number of stores = x

Store surveys needed = 32

40% of total stores = 32 stores

0.4x = 32

x = 32 / 0.4

x = 80

Answer:

1. 7:20hrs round to 7 hours (1 hour =60 minuite, and 20 is less than half of 60)

2. All numbers when divide by 1 is equal to itself (you can try with any number)

3. 9365<9635

the the second digit of 9635 is 6

the the second digit of 9365 is 3

Thus 9635 is greater

Brainliest please~

Answer:

x = -2

Step-by-step explanation:

Divide both sides by 3

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

Simplify

2x + 5 = 1

Subtract 5 from both sides

2x + 5 - 5 = 1 - 5

Simplify

2x = -4

Divide both sides by 2

2x/2 = -4/2

Simplify: 2x/2

Divide the numbers: 2/2 = 1

= x

Simplify: -4/2

Apply the fraction rule: -1/b = -a/b

= - 4/2

Divide the numbers: 4/2 = 2

= -2

x = -2

Answer:

(y, -x)

Step-by-step explanation:

Rotation of 90°

(Clockwise)

(x, y)  ---> (y, -x)

Rotation of 90°

(CounterClockwise)

(x, y) --> (-y, x)

Rotation of 180°

(Both Clockwise and Counterclockwise)

(x, y) ---> (-x, -y)

Rotation of 270°

(Clockwise)

(x, y) ---> (-y, x)

Rotation of 270°

(CounterClockwise)

(x, y) ---> (y, -x)

Answer:

Reject H0 and conclude that adults sway more than the mean forward sway for younger people.

Step-by-step explanation:

H0 : μ = 18.125

H0 : μ > 18.125

Sample data: 19 30 20 19 29 25 21 24 50

Sample size, n = 9

Sample mean, xbar = Σx / n = 237 / 9 = 26.333

Sample standard deviation, s = 9.772 (calculator)

The test statistic :

(xbar - μ) ÷ (s/√(n))

T = (26.333 - 18.125) ÷ (9.772/√(9))

T = 8.208 / 3.2573333

T = 2.519 = 2.520

Decison :

Reject H0 ; If Pvalue < α

The Pvalue :

Degree of freedom, df = n - 1 ; df = 9 - 1 = 8

Pvalue(2.520; 8) = 0.0179

Since 0.0179 < 0.05 ; WE reject H0 and conclude that adults sway more than the mean forward sway for younger people.

Answer:

what are the answers

Step-by-step explanation:

Answer:

(x, y) = (4,-3)

Step-by-step explanation:

...............

.

.

.

.

Answer:

Step-by-step explanation:

cotθ = cosθ/sinθ = 2/3

sinθ = 3/√(2²+3²) = 3/√13

cscθ = 1/sinθ = √13/3

Answer:

y=1/2(x-1)

Step-by-step explanation:

If x=t^2 and t>0, then t=sqrt(x).

If t=sqrt(x) or x^(1/2) and y =1-1/t, then y=1-x^(-1/2).

The x-intercept is when y=0.

So we need to solve 0=1-x^(-1/2) to find point P.

Add x^(-1/2) on both sides: x^(-1/2)=1.

Raise both sides to -2 power: x=1

So point P is (1,0).

Let's find tangent line at point (1,0).

We will need the slope so let's differentiate.

y'=0+1/2x^(-3/2)

y'=1/(2x^(3/2))

The slope at x=1 is y'=1/(2[1]^(3/2))=1/(2×1)=1/2.

Recall point-slope form is y-y1=m(x-x1).

So our line we are looking for is y-0=1/2(x-1)

Let's simplify left hand side y=1/2(x-1)

Answer:

The total sum of angles in a triangle is 180, thus the value of ∠ACB will be obtained as follows:

Given that the triangle is a right triangle, the sum of angles will be:

(4x)°+(7x-20)°+90=180

simplifying and solving for x we get:

4x+7x-20+90=180

11x=180+20-90

11x=110

dividing both sides by 11 we get:

(11x)/11=110/11

this gives us

x=10°

Thus substituting the value of x in:

∠ACB=(7x-20)°  

=(7*10-20)

=70-20

=50°

Answer: 50°

Answer:

50

Step-by-step explanation:

Answer:

I'm sorry but I don't know this one

Answer: [tex]Rs.3,69,000[/tex]

Step-by-step explanation:

Given

average monthly salary of a worker is [tex]Rs.8200[/tex]

If there are 45 workers in a factory

Total expenditure is calculated by taking the product of Average monthly salary and no of workers in the factory

[tex]\Rightarrow 8200\times 45\\\Rightarrow Rs.3,69,000[/tex]

Answer:

Step-by-step explanation:

2.5 = 5 * .5

1 = 1

70 = 2 * 5 *  7

LCM = 2 * 5 * 7

If you include the 1/2, you will reduce the LCM to 35, but 70 will be left out of the LCM.

Answer:

5.503484≤x≤9.116516

Step-by-step explanation:

The formula for calculating the CI is expressed as;

CI = x±z*s/√n

x is the mean= 7.31

z is the 99% z-score = 2.58

s is the standard deviation = 6.26

n is the sample size = 80

Substitute into the formula

CI = 7.31± 2.58*6.26/√80

CI = 7.31± 2.58*6.26/8.94

CI = 7.31± (2.58*0.7002)

CI = 7.31±1.806516

CI = (7.31-1.806516, 7.31+1.806516)

CI = (5.503484, 9.116516)

Hence the 99% confidence interval for the population mean is

5.503484≤x≤9.116516

Answer:

f(0) = 6

Step-by-step explanation:

Complete question:

The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y

From the pair of coordinates given, hence;

f(1) = 0

f(-10) = 2

f(0) = 6

f(3) = 17

f(-2) = -1

From the following options, this shows that f(0) = 6 is correct

Answer:

f(0) = 6

Step-by-step explanation:

EDGE

Answer:

Pick only one of these values. So if the first one doesn't work, then try the other one. Unfortunately, your teacher isn't clear on which value to go with.

===========================================================

Explanation:

Nice work on getting the mean so far.

To get the standard deviation, we'll use the value 236 in the table. This value is the sum of everything above it. So it's the sum of the [tex](x-\overline{x})^2[/tex] values. We call this the sum of the squared errors. The errors themselves being [tex]x-\overline{x}[/tex]

So we'll divide 236 over n = 4 to get 236/4 = 59

This will get us the population variance. Apply the square root to get [tex]\sqrt{59} \approx 7.68[/tex] which is the population standard deviation.

So if your teacher wants the population standard deviation, then the answer is 7.68

------------

If that answer doesn't work, then try this section.

Unfortunately, there are two flavors of standard deviation. The good news is that we don't have to do much work to find the sample standard deviation.

Instead of dividing by n = 4, we'll divide by n-1 = 4-1 = 3.

So 236/3 = 78.667

Since the value is approximate, I'll leave it as a fraction.

This represents the sample variance.

Apply the square root to get the sample standard deviation

[tex]\sqrt{\frac{236}{3}} \approx 8.87[/tex]

and that value is the sample standard deviation.

If the answer in the previous section doesn't work, then the answer must be 8.87

By taking the addition of the values in the table and overestimating a little bit, the correct option is B: $60.00

Here we have the following table of average costs:

Assuming you eat these 3 per day, the total cost in food per day is the sum of all the values in the table.

It gives:

Total cost: $12.98 + $18.95 + $26.58 = $48.51

Notice that these are average costs, so you should budget a little bit over that just in case, then the correct option is $60, which is the first option over the average total cost.

Learn more about additions:

https://brainly.com/question/25421984

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Answer:

45

Step-by-step explanation:

9514 1404 393

Answer:

  (d)   f(x) = 2x^2 - 16x + 35

Step-by-step explanation:

The x-coordinate of the extreme will be found at ...

  x = -b/(2a)

where the function is f(x) = ax²+bx+c.

The extreme will be a minimum when a > 0. (eliminates choices A and B)

The x-coordinates of the extremes are ...

  C: -(-4)/(2(4)) = 1/2

  D: -(-16)/(2(2)) = 4 . . . . . matches the requirement

The appropriate choice is ...

  f(x) = 2x^2 - 16x + 35

Answer:

21

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = x / 7 sqrt(3)

7 sqrt(3)  tan 60 = x

7 sqrt(3) sqrt(3) = x

7*3 = x

21 = x

Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \sqrt{(9 \times 2)} [/tex]

Take the square root of 9 out of the square root and leave the 2 in.

Answer:

3[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]

= [tex]\sqrt{3(6)}[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]\sqrt{9(2)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]

= 3[tex]\sqrt{2}[/tex]

Answer:

a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.

This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]

The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

Question b:

30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Answer:

11,232,000 license plates are possible.

Step-by-step explanation:

The order in which the symbols are chosen is important(ABC is a different plate than BAC), which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

3 letters from a set of 26.

3 digits from a set of 10. So

[tex]T = P_{26,3}P_{10,3} = \frac{26!}{23!} \times \frac{10!}{7!} = 11232000[/tex]

11,232,000 license plates are possible.

9514 1404 393

Answer:

  (b)  0 = -78

Step-by-step explanation:

Subtracting 6 times the first equation from the second will give ...

  (4x +15y) -6(2/3x +5/2y) = (12) -6(15)

  0 = -78

Answer:

the answer is b

Step-by-step explanation:

Answer:

280

Step-by-step explanation:

7 x 5 x 8

Answer:

  6.9%

Step-by-step explanation:

The amount of the discount was ...

  18.99 -17.68 = 1.31

As a percentage of the original price, that is ...

  1.31/18.99 × 100% ≈ 0.06898 × 100% ≈ 6.9%

The discount was about 6.9%.

Answer:

D

Step-by-step explanation:

The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The reflection does not change the shape and size of the geometry. But flipped the image.

Rectangle QRST with vertices Q(-3, 2), R(-1, 4), S(2, 1), and T(0, -1).

The coordinate of the new rectangle after the reflection across is given as,

Q' = (-3, -2)

R' = (-1, -4)

S' = (2, -1)

T' = (0, 1)

The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.

More about the transformation of a point link is given below.

https://brainly.com/question/27224339

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9514 1404 393

Answer:

Step-by-step explanation:

A suitable statistics calculator can tell you the coefficients of the linear regression equation. In the attached, we put the given x- and y-values into a table and asked for the best fit equation. Rounded to tenths, the equation is ...

  y = 32.1x +779.9

The year 2010 is 12 years after 1998, so we can find the desired projection using x=12.

  y = 32.1×12 +779.9 = 385.2 +779.9 = 1165.1

The number of cases is projected to be 1165 in 2010.

_____

We wonder if using the button "Open Statistics Calculator" will let you solve this question yourself.