What is cos(30°)?
2
1
cos (30°)
30%
= =
√3
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The height of 70 inches, and location of the wristband as well as the period of 15 seconds gives the function for the height of the wristband as the equation;

The model for the height can be derived from the general form of the sine function as follows;

Maximum point = 70 - 4 = 66 at t = 0

Minimum point = 4

Amplitude, A = (66 - 4) ÷ 2 = 31

D = 4 + 31 = 35

At t = 0, we have;

66 = 31 × sin(B × 0 - C) + 35

31 = 31 × sin(- C)

sin(- C) = 1

C = -π/2

1 minute = 60 seconds

1 second= 1 minute/60

15 seconds = (15/60) minutes

Period = 15 seconds = 15/60 minutes

Period = 2•π/B

Therefore;

15/60 = 2•π/B

1/4 = 2•π/B

B = 2•π/(1/4) = 8•π

y = Height of the function

Let h represent the height of the wristband.

The equation for the height is therefore;

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Based on the figures above, the numbers of children that attended the park that day is 10,000.

Fist we have to use the determinant to solve for c and as such:

[tex]\frac{det.\frac{30000}{500000} \frac{1}{20} }{det. \frac{1}{10} \frac{1}{20} }[/tex]

=[tex]\frac{30000 x 20 - 500000 x 1}{1 x 20 - 1 x 10}[/tex]

= 100000/10

=10,000

Therefore, Based on the figures above, the numbers of children that attended the park that day is 10,000.

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Answer:

Ista is 11 years old. Her father is 46 years old.

Step-by-step explanation:

Let ista's age be x.

Fathers age=4x+2.

Fathers age + Ista's age = 57.

4x+2+x=57.

Combine like terms:

5x+2 -2 =57 -2

5x=55

x=11

Fathers age: 4(11)+2

= 46

If ista father has an age that is 2 years greater than four times her age. The sum of their ages is 57 years. Then ista age is 11 and her father age is 46.  

Two or more expressions with an equal sign is called as equation.

Given that,

ista father has an age that is 2 years greater than four times her age.The sum of their ages is 57 yeasrs

Let the age of ista be x.

ista father has an age that is 2 years greater than four times her age.

it means father age = 2+4x

The sum of ista age and her father age is 57.

So x+(2+4x)=57

Add the common terms

5x+2=57

Subtract 2 from both sides

5x=55

Divide both sides by 5

x=11

Hence ista age is 11 and her father age is 46.

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Answer:

22.25

Step-by-step explanation:

take the two values away

the sector is the full address , the triangle is in it. the segment is the bit left near the circumference

Answer:

A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school? and "how old are you?" are statistical questions.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

See below.  I assume that (x) = 8x2 - 7x + 3 is really (x) = 8x^2 - 7x + 3

Step-by-step explanation:

Substitute the value of x given in f(x) into the equation f(x) = 8x^2 - 7x + 3

For example, f(0) would be f(0) = 8(0)^2 - 7(0) + 3.  f(0) = 3

f(-2) would be f(-2) = 8(-2)^2 - 7(-2) + 3.  

                                =   8*4  + 14 +3

                                = 32 + 17        therefore      f(-2) = 49

x f(x)

-2 49

-1 18

0 3

1 4

2 21

Answer: $12.63

Step-by-step explanation:

$14.87 + $7.76 = $22.63

2pizzas x $5 = $10

$22.63 - $10 = $12.63

Answer:

7x-13y=-117

Step-by-step explanation:

I don't know how this question wants me to solve it, but I just used the slope intercept form. So first, start off with y = mx+b. Plug in the slope for m, so 7/13. Then plug in your points for x,y which is 0,9. You'll get 9 = b. So then you have y = 7/13x+9. So now you need to change into standard form. So, multiply by the denominator (13) and you'll get 13y = 7x+117. Then move the variable over and you'll get 13y - 7x = 117. But it doesn't fit any, so then just multiply by -1 and you'll get -13y + 7x = -117.  

Answer:

.5

Step-by-step explanation:

Point = P (1, 0, -2)

Origin= 0 (0, 0, 0)

The distance formula in 3D = √(n2 - n1)² + (y2 - y1)² + (Z2 - Z1)²

                                             = √(1 - 0)² + (0 - 0)² + (-2 - 0)²

                                             = √1 + 4

                                             = √5

As a special case of the distance formulation, think we need to recognize the distance of a point (x,y) to the beginning. in step with the gap formula, this is √(x−0)2+(y−0)2=√x2+y2. A point (x,y) is at a distance r from the starting place if and simplest if √x2+y2=r, or, if we square each aspect: x2+y2=r2.

Conclusion: The method to find the distance among the two factors is commonly given with the aid of d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the gap among any two factors on a coordinate aircraft or x-y plane.

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The procedure to rewrite the standard form in slope intercept form is as shown below.

The standard form of the equation of a line is;

ax + by + c  = 0

Slope intercept form is;

y = mx + c

Intercept form is;

x/p  + y/q = 1    

To Convert ax + by + c  = 0  into  y = mx + c

1) Move ax and c to the right hand side to get;

by = -ax  - c

Divide both sides by b to get;

y = - ax/b  - c/b

Comparing to slope intercept form, we can say that;

Slope = -a/b

y-intercept = -c/b

If we are using y = mx + b as slope intercept form, this will also be accurate because we will just switch c with b in the standard form to arrive at same answer.

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The equation of the circle is (x - 1)^2 +(y + 9)^2 = 144

The given parameters are:

Center, (a,b) = (1, -9)

Radius, r = 12

The circle equation is calculated as:

(x - a)^2 + (y- b)^2 = r^2

This gives

(x - 1)^2 +(y + 9)^2 = 12^2

Evaluate the exponent

(x - 1)^2 +(y + 9)^2 = 144

Hence, the equation of the circle is (x - 1)^2 +(y + 9)^2 = 144

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The compound periods and Interest rates for compound interest have been explained below.

1) Compound Periods (n); If we want to calculate the compound interest, the number of compounding periods makes a significant difference due to the fact that the higher the number of compounding periods, the greater the amount of compound interest.

2) Interest rate per compounding periods (I); This affects the interest rate compounded annually due to the fact that the interest rate will be compounded once a year.

Complete question is;

In your own words and using visuals, explain the following. Regarding compound interest, how does the number of times interest is compounded per year affect the:

a) number of compounding periods (n)

b) interest rate per compounding period (i)

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At least 832 teenagers must be interviewed.

It is given that the standard deviation is of 1.24 liters.

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2}[/tex] = 0.005

Now, we have to find z in the Ztable as such z has a p-value of [tex]1-\alpha[/tex].

So it is z with a p-value of [tex]1-0.005 = 0.995[/tex], so [tex]z= 2.575[/tex]

Now, find the margin of error M as such

[tex]M = Z * \frac{SD}{\sqrt{n} }[/tex]

In which SD is the standard deviation of the population and n is the size of the sample.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liters when constructing a 99% confidence interval?

At least n teenager must be interviewed.

n is found when M = 0.1.

We have that SD = 1.12

So

[tex]0.1 = 2.575*\frac{1.12}{\sqrt{N} }[/tex]

[tex]\sqrt{n} = \frac{2.575*1.12}{0.1}[/tex]

[tex]n = 831.7[/tex]

So rounding up to at least 832 teenagers must be interviewed.

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Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54

Transformation is the movement of a point from its initial point to a new location. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the increase or decrease in the size of a figure.

Figure A maps to figure B with a scale factor of 4/9, hence:

4/9 * x = 16

x = 54

Figure A maps to figure B with a scale factor of 4/9, hence the value of x is x = 54

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The computation of the decimals are illustrated below.

1. 7/4 + √5

= 1.75 + 2.24

= 3.99

2. -✓2 + 9

= -1.41 + 9

= 7.59

3. 2 - 5/4

= 2 - 1.25

= 0.75

4. 7.93 + 1/7

= 7.93 + 0.14

= 8.07

5. π + ✓5

= 3.14 + 2.24

= 5.38

6. ✓2 + 13/4 - 3

= 1.41 + 3.25 - 3

= 1.66

7. 8.5 - 12.65

= -4.15

8. 4 + ✓3 - 11/3

= 4 + 1.73 - 3.67

= 2.06

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Step-by-step explanation:

The radians is just the length of the arc, so if you had a unit circle where the radius was 1, the length of that entire circle would be [tex]2\pi[/tex] since the circumference of any circle is [tex]2\pi r[/tex] except r is 1 so the length is just [tex]2\pi[/tex]. So if you take 1/4 of this you get [tex]\frac{2\pi}{4}[/tex] which can be simplified to  [tex]\frac{\pi}{2}[/tex]

Answer:

Step-by-step explanation:

Comments

You need to get the radian measure of the circle.

The radian measure of the entire circle is 2 * pi

To get the radian measure of 1/4 of the circle, just divide by 4.

2 pi / 4 = pi/2

The central angle is = to 1/4 of the circumference of the circle.

So the central angle is also pi/2

Answer: pi/2

1) given

2) definition of an angle bisector

3) reflexive

4) [tex]\triangle ABD \cong \triangle CBD[/tex] (ASA)

5) [tex]\angle A \cong \angle C[/tex] (CPCTC)

Answer:

1. a+c is larger than b+d

2. No way to tell whether a+d or b+c is larger.

Step-by-step explanation:

1. Which is larger, a+c or b+d?

Let a, b, c, and d be any numbers such that [tex]a > b > c > d[/tex].

Specifically, note that [tex]a > b[/tex], and subtracting b from both sides of the inequality, observe that [tex]a-b > 0[/tex].

Similarly, [tex]c > d[/tex], and subtracting d from both sides of the inequality, observe that [tex]c-d > 0[/tex].

From this, add "a-b" (a positive number, as proven above) to both sides of the inequality.

[tex](a-b)+(c-d) > (a-b)+0[/tex]

Addition by zero (the additive identity) doesn't change anything, so the right side remains "a-b"...

[tex](a-b)+(c-d) > a-b[/tex]

... and "a-b" is positive...

[tex](a-b)+(c-d) > a-b > 0[/tex]

... so, by the transitive property of inequality...

[tex](a-b)+(c-d) > 0[/tex]

Recall that subtraction is addition by a negative number...
[tex]a+(-b)+c+(-d) > 0[/tex]

...and that addition is associative and commutative, so things can be added in any order, so the middle two terms on the left side can be rearranged...

[tex]a+c+(-b)+(-d) > 0[/tex]

Adding b + d to both sides of the inequality

[tex](a+c+(-b)+(-d))+(b+d) > 0+(b+d)[/tex]

... and simplifying

[tex]a+c > b+d[/tex]

So, a+c is larger than b+d.

2. Which is larger, a+d or b+c?

Consider the following two examples:

Example 1

Suppose a=10; b=3; c=2; d=1.

Note that [tex]a > b > c > d[/tex] ([tex]10 > 3 > 2 > 1[/tex]) and, also observe that [tex]a+d=(10)+(1)=11[/tex], and [tex]b+c=(3)+(2)=5[/tex], so a+d is larger than b+c.

Example 2

However, suppose a=10; b=9; c=8; d=1.

Note that [tex]a > b > c > d[/tex] ([tex]10 > 9 > 8 > 1[/tex]) but that [tex]a+d=(10)+(1)=11[/tex], and [tex]b+c=(9)+(8)=17[/tex], so a+d is smaller than b+c.

So, in one example, a+d is bigger, and in the other, a+d is smaller.  Therefore, there is no way to tell which of a+d or b+c is larger from only the given information.

Answer:

x<47

Step-by-step explanation:

Take -11 to the side which 36 is. Once it crosses it stops being negative and becomes positive so the equation becomes x<36+11 which is x<47

The conclusion is that there is sufficient evidence to support the claim that the percentage of vacant housing units in their district differs from the percentage of vacant housing units in the country.

Given that the total number of a housing units in her country is 550 and the number of vacant housing units in her country is 130.

The Null hypothesis is p₀=13%=0.13, n=550 and x=130

Significance level α=0.05

Claims given: percentage other than 13%

The claim is anyone of the null hypothesis or the alternative hypothesis. The null hypothesis shows that the proportion of the population is equal to the value stated in the claim. If the null hypothesis is a claim, then the alternative hypothesis states the opposite of the null hypothesis.

H₀:p=13%=0.13

Hₐ:p/0.13

I'm interested in testing population proportion claims, so I'll use z-text with proportions.

Conditions: Random sample, 10% condition, pass / fail condition

Sample: I'm happy because the housing units were randomly selected.  10% Condition: We are happy because the sample of 550 homes in your county is less than 10% of the population.

Pass/ fail condition: Satisfied because both np₀ and n(1-p₀) are both at least 10.

np₀=550(0.13)=71.5≥10

n(1-p₀)=550(1-0.13)=478.5≥10

Therefore, we conclude that all the conditions are met.

The sample percentage is the number of successes divided by the sample size.

[tex]\begin{aligned}\hat{p}&=\frac{x}{n}\\ &=\frac{130}{550}\\ &\approx 0.2364\end[/tex]

Determines the value of the test statistic:

[tex]\begin{aligned}z&=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \\ &=\frac{0.2364-0.13}{\sqrt{\frac{0.13(1-0.13)}{550}}}\\ &=\frac{0.1064}{0.0143}\\&\approx 7.41 \end[/tex]

The P-value is the probability of getting a test statistic value  or a  more extreme value if the null hypothesis is true. Use the normal probability table in the appendix to determine the P-value.

P=P(Z<−7.41 or Z>7.41)

P=2P(Z>7.41)

P=2(0)

P=0

If the P-value is less than the significance level α,  the null hypothesis is rejected.

P<0.05⇒ Reject H₀

Therefore, there is ample evidence to support the claim that the proportion of vacant homes in the area is different from the proportion of vacant homes in the country.

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Answer:

Step-by-step explanation:Rectangles have 4 sides--2 = lengths and 2 = widths, so perimeter = 2l + 2 w = 2(l + w).

l + w = (2x - 1) + (x + 3) = 3x + 2.  Then double with distributive property P = 2(3x + 2)

P = 6x + 4

You could also do distributive property twice:  2(2x - 1) + 2(x + 3) = 4x - 2 + 2x + 6 = 6x + 4.

50

---- ×700=350

100

700-350=350

Therefore 350 grams is left in a person's system after 5 hours

The simplified expression of [tex](4^3)(\frac{4^4^0x^4}{3^2x^2y^2})[/tex] is [tex]\frac{4^7x^2}{3^2y^2}[/tex]

The expression is given as:

[tex](4^3)(\frac{4^4^0x^4}{3^2x^2y^2})[/tex]

Expressions raise to power 0 is 1.

So, we have:

[tex](4^3)(\frac{4^4x^4}{3^2x^2y^2})[/tex]

Apply the law of indices to expression with common base

[tex](\frac{4^{4+3}x^{4-2}}{3^2y^2})[/tex]

Evaluate the sum and difference

[tex](\frac{4^7x^2}{3^2y^2})[/tex]

Remove the bracket

[tex]\frac{4^7x^2}{3^2y^2}[/tex]

Hence, the simplified expression of [tex](4^3)(\frac{4^4^0x^4}{3^2x^2y^2})[/tex] is [tex]\frac{4^7x^2}{3^2y^2}[/tex]

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Answer:

I think that the awnser to 59 is 24x⁴-15x²+27x

Answer:

x = 0

Step-by-step explanation:

if 2y + x = 4

we can assume that y = 2
if y - 3x = 2

it means 2 - 0 = 2

therefore x = 0

[tex]p(c) = 0.6 \\ p(ch) = 0.59 \\ p(any)= 0.77[/tex]

[tex]p(both) = p(c) + p(ch) - p(any) \\ p(both) = 0.6 + 0.59 - 0.77 \\ p(both) = 0.42[/tex]

Answer:

62 and 64

Step-by-step explanation:

Let x be the first number

Let y be the 2nd number

Given,

x + 2 = y (Consecutive even numbers)

x - y = -2 (rearranged) - Equation 1

x + y = 126 - Equation 2

Now we can solve for x and y to find the 2 numbers by using substitution method in solving simultaneous equations.

x = y-2 (rearranged equation 1)

Now we substitute equation 1 into equation 2.

y - 2 + y = 126

2y - 2 = 126

2y = 126 + 2

2y = 128

y = 128 / 2

= 64

Now we will substitute y into equation 1.

x - 64 = -2

x = -2 + 64

= 62

Therefore the 2 numbers are 62 and 64.

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Find two consecutive even numbers whose sum is 126.

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

For now, let the first number be x.

Let the second number be x+2. (consecutive even numbers are right next to each other, like 2 and 4)

These two integers add up to 126. This gives us an equation that we can solve in terms of x.

[tex]\bf{x+x+2=126}[/tex] | arrange the like terms

[tex]\bf{2x+2=126}[/tex] | subtract 2

[tex]\bf{2x=124}[/tex] | 2 was subtracted from BOTH sides

[tex]\bf{x=62}[/tex]

[tex]\cline{1-2}[/tex]

Now, the second integer is [tex]\bf{x+2}[/tex].

[tex]\bf{So\;let's\;put\;the\;first\;number\;into\;the\;formula\;x+2}[/tex].

[tex]\bf{62+2}[/tex] | add (mental arithmetic)

[tex]\bf{64}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                  [tex]\bf{=Number\;1=62}\\\\=Number\;2=64[/tex]

[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]