The measures of the angles of a triangle are shown in the figure below. Solve for x.

83 ⁰
to
59°

The equation to model the above scenario is [tex]x^{2}[/tex] +22x - 23 = 0

The perimeter of the expanded rectangle is 48 units

A rectangle is a quadrilateral with its 4 angles 90°

Analysis:

First rectangle:

length = 10 + x

width = x

Second rectangle:

length = x + 14

width = x + 8

Area of expanded rectangle = 135 square unit

(x+8)(x+14) = 135

[tex]x^{2}[/tex] + 8x + 14x + 112 = 135

[tex]x^{2}[/tex] + 8x + 14x -23 = 0

[tex]x^{2}[/tex] + 22x -23 = 0

[tex]x^{2}[/tex] + 23x - x - 23 = 0

(x-1)(x+23) = 0

Therefore x = 1

Expanded length = 1+14 = 15

Expanded width = 1+8 = 9

Perimeter = 2(9+15) = 48 units

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Answer:

-16, 16, 16

Step-by-step explanation:

1) -16

2) 16

3) 16

The simplified expressions are

1.  990√2

2.  80 √3

3. 30- √35 / √42

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

(11 √40) (9 √5)

= 11*9* √40*√5

= 99*√200

= 99* 10√2

= 990√2

(2 √6) (10 √8)

= 2*10 *  √6 * √8

=20*  √48

= 20* 4 √3

= 80 √3

5 √6 ÷ √7 - √5 ÷ √6

=30- √35 / √42

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Answer:

C=55m + 30

Step-by-step explanation:

You would multiply 55 by the number of months so you'd get 55m, and since 30 is a one time fee you would just add 30 to your monthly payment.

Answer:

the answer for the 2nd question is 1/4

Step-by-step explanation:

i took the test

If [tex]m=-4[/tex]

and a point is [tex](2,3)[/tex]

[tex]y=mx+b[/tex]

[tex]3=(-4)(2)+b[/tex] using the point and the slope

[tex]3=-8+b[/tex]

[tex]b=8+3[/tex]

[tex]b=11[/tex]

Therefore, the equation of the line will be [tex]y=-4x+11[/tex]

The length of the side c, to the nearest integer is 12.

Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.

u² = s² + t² - 2(s)(t)·cos U

In ΔABC, m < C = 50* , a = 14 and b = 15.

We can solve for the length of side a to the nearest whole number using the Laws of Cosines

c² = b² + a²- 2ba CosC

Solving for the value of a, we have:

c² = 15² + 14²- 2(15)(14)cos50°

c² = 225 + 196 - 269.97

c² = 151.029

c = 12.28

Hence, The length of the side c, to the nearest integer is 12.

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distance = speed * time

the first bus speed = x

second bus = x - 12

the sum of distance = 765 miles

first distance = 6x

second distance = 6 (x -12)

6x + 6(x-12) = 765

x + x -12 = 127.5

2x = 139.5

x = 69.75 mi/h which is the faster bus

the second bus speed = 57.75 mi/h

Answer:

[tex]\text{A}) \text{ } -\infty < x < 3\\\\\text{C}) \text{ } -1 < x < 2\\\\[/tex]

Step-by-step explanation:

The graph lies above the x-axis for these intervals.

The hypothesis test shows that we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%

The claim that the return rate is less than 20% is p < 0.2. From the given information, we can compute our null hypothesis and alternative hypothesis as:

[tex]\mathbf{H_o :p =0.2}[/tex]

[tex]\mathbf{H_i:p < 0.2}[/tex]

Given that:
Sample size (n) = 6965

Sample proportion [tex]\mathbf{\hat p = \dfrac{x}{n} = \dfrac{1302}{6965} \sim0.1869}[/tex]

The test statistics for this data can be computed as:

[tex]\mathbf{z = \dfrac{\hat p - p}{\sqrt{\dfrac{p(1-p)}{n}}}}[/tex]

[tex]\mathbf{z = \dfrac{0.1869 -0.2}{\sqrt{\dfrac{0.2(1-0.2)}{6965}}}}[/tex]

[tex]\mathbf{z = \dfrac{-0.0131}{0.0047929}}[/tex]

z = -2.73

From the hypothesis testing, since the p < alternative hypothesis, then our test is a left-tailed test(one-tailed.

Hence, the p-value for the test statistics can be computed as:

P-value = P(Z ≤ z)

P-value = P(Z ≤ - 2.73)

By using the Excel function =NORMDIST (-2.73)

P-value = 0.00317

P-value ≅ 0.003

Therefore, we can conclude that since P-value is less than the significance level at ∝ = 0.01, we reject the null hypothesis and there is sufficient evidence to support the claim that the return rate is less than 20%

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Answer:

See below

Step-by-step explanation:

Answer:

34.562

Step-by-step explanation:

To find the perimeter of a circle, it's 2 * the radius * pi. In this case, we have a semicircle, so it would be the circle's perimeter divided by 2, or just the radius * pi.

The radius, 11, times pi (3.142), is 34.562.

Brainliest, please :)

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.6625, 0.7388).

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

Given sample, n= 782

As, 548 were not captured.

x= 548

So, p= 548/ 782

     p = 0.7007

q= 1- 0.7007 = 0.2993

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

Now,

α = 1 - 0.98 = 0.02

α/2 = 0.02/2 = 0.01

For confidence level of 98% , z is 2.33

Now,

(0.70007 - 2.33√ (0.7007(0.2993))/782 , 0.70007 + 2.33 √(0.7007(0.2993))/782

= (0.6625, 0.7388)

Hence, 98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.6625, 0.7388).

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It's the sum of a geometric sequence.

Let's rewrite it a bit:

[tex]\displaystyle\\\sum_{n=1}^{10}8\left(\dfrac{1}{4}\right)^{n-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot \left(\dfrac{1}{4}\right)^{-1}=8\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n\cdot 4=32\sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]

And now let's calculate this sum [tex]\displaystyle \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n[/tex]:

[tex]S_n=\dfrac{a(1-r^n)}{1-r}\\\\a=\dfrac{1}{4}\\n=10\\r=\dfrac{1}{4}\\\\S_{10}=\dfrac{\dfrac{1}{4}\cdot\left(1-\left(\dfrac{1}{4}\right)^{10}\right)}{1-\dfrac{1}{4}}=\dfrac{\dfrac{1}{4}\cdot\left(1-\dfrac{1}{1048576}\right)}{\dfrac{3}{4}}=\dfrac{\dfrac{1048575}{1048576}}{3}=\dfrac{1048575}{3145728}=\\=\dfrac{349525}{1048576}[/tex]

Now let's calculate the initial sum:

[tex]\displaystyle 32\cdot \sum_{n=1}^{10}\left(\dfrac{1}{4}\right)^n=32\cdot \dfrac{349525}{1048576}=\dfrac{349525}{32768}\approx10.67[/tex]

The minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.

Mean is the ratio of the sum of all the data points to the number of data points.

It is given that

mean of $220,000 with a standard deviation of $7450.

The range is given , let the range is represented by x - --y

It is given that x = 197650 and y = 242350

Let the number of homes sold is k

To determine the value of k

upper level = (y-mean)/standard deviation = (242350-220000)/7450 = 3

lower level = (mean-x)/standard deviation = (220000-197650)/7450 = 3

probability = 1-(1/k²)

k= 3

= 1 - (1/3^2)

= 1 - 1/9

= 0.889 or 88.9%

So, the minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.

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The truth set for each predicate are:

a) d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}

b) d ∈ {  1, 2, 3, 6}

c) x ∈ { [-2, -1] U [1, 2]}

d) x ∈ {-2, -1, 1, 2}

We only need to find the sets of values such that the statements are true.

a)

We want to find vales of d, such that d is an integer, and 6/d is an integer.

Here the possible values of d will be:

d ∈ { -6, -3, -2, -1, 1, 2, 3, 6}

Which are all the factors of 6, so all these integers divide 6.

b) Same as before, but this time the domain is a positive integer, so now the truth set will be:

d ∈ {  1, 2, 3, 6}

c) We want to find real values of x such that:

1 ≤ x² ≤ 4

If we apply the square root to the 3 sides, we get two inequalities:

-√1 ≥ x ≥ -√4

√1 ≤ x ≤ √4

Simplifying:

-1  ≥ x ≥ -2

1  ≤ x ≤ 2

So the truth set is:

x ∈ { [-2, -1] U [1, 2]}

c) Same as before, but now we only have integer solutions, so the truth set is:

x ∈ {-2, -1, 1, 2}

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Step-by-step explanation:

[tex]h(x) = \frac{3}{x}\\h(h(x)) = \frac{3}{\frac{3}{x}}\\\\h(h(x)) = \frac{3}{1} * \frac{x}{3}\\h(h(x)) = \frac{3x}{3}\\h(h(x)) = x\\\\\\f(f(x)) = (x^2-3)^2-3\\f(f(x)) = x^4+2(x^2)(-3)+(-3)^2-3\\f(f(x)) =x^4-6x^2+9-3\\f(f(x)) = x^4-6x^2+6\\[/tex]

Answer:

Decimal: 1.75

Percentage: 175%

Hey there!

1 3/4

= 1 * 4 + 3 / 4

= 4 + 3 / 4

= 7 / 4

= 7 ÷ 4

= 1.75

= 1.75 * 100

= 175%

Therefore, your answer should be:

• 1.75 (as your decimal form)
• 175% (as your percentage form)

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Line q has slope 3, as you've found.

Any line perpendicular to q will then have slope -1/3, as you've found.

Line p thus has slope -1/3 and we know it passes through (6, -5), so from the point-slope formula we get the equation

[tex]y - (-5) = -\dfrac13 (x - 6) \implies \boxed{y + 5 = -\dfrac13 (x - 6)}[/tex]

Using the permutation formula, it is found that there are 57,120 ways to fill the 4 positions.

There are different roles, hence the order is important, which means that the permutation formula is used.

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

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

In this problem, 4 roles are chosen from a set of 17, hence the number of ways is given by:

[tex]P_{17,4} = \frac{17!}{13!} = 57120[/tex].

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Answer:

1/2*b*h

1/2*18*14

1*9*14

126

Answer:

X + 35° = 70° ( this is one of the property of triangle in which the sum of two interior angles of a triangle is equal to its other angle)

X = 70 - 35

X = 35°

The book does nick shelve in 2 hours is 60.

Given coordinates:

(0, 0), (2, 60) and (4, 120).

If we look at the coordinates (2, 60)

The value corresponds to 2 hours is 60.

Hence, the book nick shelves in 2 hours is 60.

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Answer: [tex]-\frac{3}{2} \leq x < 5[/tex]

Step-by-step explanation:

We can split this into two inequalities, namely [tex]2x-3 < x+2[/tex] and [tex]x+2 \leq 3x+5[/tex].

Solving the first inequality,

[tex]2x-3 < x+2\\\\x-3 < 2\\\\x < 5[/tex]

Solving the second inequality,

[tex]x+2 \leq 3x+5\\\\2 \leq 2x+5\\\\-3 \leq 2x\\\\-\frac{3}{2} \leq x[/tex]

So, the solution is [tex]-\frac{3}{2} \leq x < 5[/tex]

Answer:

Yes.

Step-by-step explanation:

In mathematics, a number line ends in arrows on both sides, signifying it going infinite in the positive and negative directions.

Answer:

Yes.

Step-by-step explanation:

A number line is infinite in both directions it faces. This means left or right there is a infinite amount of numbers.

Answer:

[tex]g(x) = x^3+1\\f(x) = x^2[/tex]

Step-by-step explanation:

Answer:

f(x)=x^2 and g(x)=x^3+1

Step-by-step explanation:

to find y=f(g(x))

substitute g(x) into f(x)

y= (x^3+1)^2.

Answer:

slant length (l) = 7.5 m

perimeter of base P = 40 m

area of base B = 100 m^2

Surface Area = 250 m^2

Step-by-step explanation:

Surface area of a pyramid formula

1/2Pl + B

1/2 (40)(7.5) + 100

150 + 100 = 250 square meters