What is the value of x in the triangle?

[tex]\dfrac{x^2 +7x +14 }{x+4} = x+3+ \dfrac{2}{x+4}[/tex]

Answer:

[tex]\{58198.2573,58239.7427\}[/tex]

Step-by-step explanation:

We assume that the following conditions are true before constructing the confidence interval:

Assumption #1: Random Sampling.

Assumption #2: Independence.

Assumption #3: Large Sample.

Assumption #4: The 10% Condition (sample size is no bigger than 10% of population

Assumption #5: The Success / Failure Condition.

Assumption #6: Homogeneity of Variances.

A 95% confidence level correlates to a critical value of [tex]z^*=1.96[/tex], hence:

[tex]\displaystyle CI=\bar{x}\pm z^*\biggr(\frac{s}{\sqrt{n}}\biggr)\\\\CI=58219\pm 1.96\biggr(\frac{56}{\sqrt{28}}\biggr)\\\\CI=58219\pm20.7427\\\\CI=\{58198.2573,58239.7427\}[/tex]

Therefore, we are 95% confident that the true mean of the average yearly income for a married couple living in city C is between $58,198.2573 and $58,239.7427

The 73 customers who spend money in this store if  margin of error of at most 0.075 with 80% confidence.

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

We have p = 0.50 MOE = 0.075

Z = 1.282 at 80% confidence from the Z table.

[tex]\rm 0.075 = (1.282)\sqrt{\dfrac{0.50(1-0.50)}{n}}[/tex]

After solving, we get:

n = (0.5)(0.5)/(0.0585)²

n = 73

Thus, the 73 customers who spend money in this store if  margin of error of at most 0.075 with 80% confidence.

Learn more about the Margin of error here:

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Não, não podemos fazer um triângulo com os comprimentos dos lados de 2 cm, 3 cm e 10 cm. Isso ocorre porque a soma de 2+3 < 10. (in english: No, we cannot make a triangle with the side lengths of measurement 2 cm, 3 cm, and 10 cm. This is because sum of 2+3 < 10).

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

[tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]

Now, for this case, the sides given are:

But we see that:

a+ b = 5 cm which is < c which is of 10 cm.

Thus, these lengths don't satisfy the triangle inequality theorem, and therefore, cannot be sides of any triangle.

Learn more about triangle inequality theorem here:

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Answer:

28 meters cubed

Step-by-step explanation:

V = 1/3 BH

V = 1/3 (4)(21)

V = 28

Hope this helped :))

have a great day :D <3

Answer: 4 = 80, 1 = 100, 5 = 80, 3 = 80

Step-by-step explanation:

Answer:

80°

Step-by-step explanation:

Vertically Opposing Angles are equal when they are cut by a transversal.

Answer:

The answer is A

Step-by-step explanation:

Because it's square all of the sides will be equal so 18*18=324. Hope this helps.

Answer:

200 miles

Explanation:

Here map to actual to scale: 1 inch = 50 miles

To find actual distance, simply multiply map distance by scale factor

Actual Distance : 4 × 50 = 200 miles

Answer:

Recheck your question

Step-by-step explanation:

I think your question should be what is the probability that the second card is a spade given that the first one was a club

Answer:

6 goats and 6 ducks

Step-by-step explanation:

The title of this graph shown in the image attached below is "Number of Kg. of rice donated for Typhoon Roly's victim."

Generally, the title of a graph is typically placed at the top. Based on the information provided in the graph (see attachment), the title of this graph is "Number of Kg. of rice donated for Typhoon Roly's victim."

In this scenario, the kind of graph shown is referred to as a bar graph.

A family with the most number of kilograms of rice donated is the "Carlage family" because their data has the tallest rectangular bar, which corresponds with 150 kg.

A family with the least number of kilograms of rice donated is the "Dioneda family" because their data has the shortest rectangular bar, which is equal to 75 kg.

The total number of kilograms of rice donated is given by:

Total number = 150 + 100 + 175 + 120 + 100

Total number = 645 kg.

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Rs. 5000

Step-by-step explanation:

To Find MP = ?

SP = rs 3000

Discount = 40%

=> MP-MP×40/100=3000

=> 100MP-40MP/100= 3000

=> 60MP/100 = 3000

MP = 3000 × 100 / 60

MP = 500 × 10

MP = Rs. 5000

Answer:

633.94 squared inches

Step-by-step explanation:

15.75 x 15.75 = 248.0625

12.25 x 15.75 x 1/2 = 96.46875

since there are 4 triangles and they are equivalent...

96.46875 x 4 = 385.875

Surface area is...

385.875 + 248.0625 = 633.9375

changing my answer hh

Answer:

528 cm²

Step-by-step explanation:

The surface area of this prism comprises:

Area of a triangle = 1/2 × base × height

                             = 1/2 × 16 × 6

                             = 48 cm²

Area of rectangle 1 / 2 = width × length

                                     = 10 × 12

                                     = 120 cm²

Area of rectangle 3 = width × length

                                = 16 × 12

                                = 192 cm²

Total Surface Area = 2 triangles + 2 rectangles + rectangle 3

                                = (2 × 48) + (2 × 120) + 192

                                = 96 + 240 + 192

                                = 528 cm²

Area of two triangles

Area of base rectangle

Area of rest two rectangles

Total area

Answer City's breaking down on a camel's back

Answer:

[tex]x = \frac{3}{2} [/tex]

Step-by-step explanation:

[tex] {2}^{2x} = {2}^{3 } \\ 2x = 3 \\ x = \frac{3}{2} [/tex]

Answer:

all x intercepts [-4, 0] [4, 0]

Step-by-step explanation:

x-intercept, i.e. y=0

f(x) = x^3 - 4x^2 - 16x + 64 = 0

(x^3 + 4^3) - 4x^2 - 16x = 0         [FYI, x^3 + y^3 = (x + y)(x^2 - xy + y^2)]

(x + 4)(x^2 - 4x + 16) - 4x^2 - 16x = 0

(x + 4)(x^2 - 4x + 16) - 4x(x + 4) = 0

(x + 4)(x^2 - 4x + 16 - 4x) = 0

(x + 4)(x^2 - 8x + 16) = 0

(x + 4)(x - 4)^2 = 0

x = -4 or 4

all x intercepts [-4, 0] [4, 0]

Step-by-step explanation:

one thing immediately catches the eye : the factors of the terms in the function follow the powers of 4 :

4⁰, 4¹, 4², 4³

and they are going against the powers of x :

x³ has the factor 4⁰

x² has the factor 4¹

x has the factor 4²

x⁰ has the factor 4³

with that we see that one 0 solution (an x- intercept) is x = 4.

f(4) = 4³ - 4×4² - 4²×4 + 4³ = 4³ - 4³ - 4³ + 4³ = 0

so, the functional expression is

(x-4)(x² + ...)

the other 2 zero solutions are covered by the quadratic term.

to get the quadratic term we divide f(x) by (x-4).

x³ - 4x² - 16x + 64 ÷ x - 4 = x² - 16

- x³ - 4x²

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

0 0 - 16x + 64

- - 16x + 64

----------------------‐--------

0 0

so,

f(x) = (x - 4)(x² - 16)

and as we know

(a² - b²) = (a + b)(a - b)

we get

f(x) = (x - 4)(x + 4)(x - 4) = (x - 4)²(x + 4)

so, x = 4 counts as 2 zero solutions, it is a point, where the curve makes a turn and only touches the x-axis, but does not fully intercept it (in the sense to continue on the other side of the x-axis).

and x = -4 is the third zero solution.

so, the x-intercepts are at x = -4, +4

Answer:

A) [tex]\frac{x}{11} < -21[/tex]

Step-by-step explanation:

Let "a number" be denoted by the variable, x. Set the equation:

"A number divided by 11": x/11

"is less than": <

"-21": -21

Put all the parts together:

"A number divided by 11 is less than -21": x/11 < -21

A) [tex]\frac{x}{11} < -21[/tex] is your answer.

~

Answer:

3. 261 ft³

Step-by-step explanation:

Volume of the figure = ½(volume of cylinder) + volume of triangular prism)

✔️Volume of cylinder = πr²h

r = 3 ft

h = 10 ft

Volume of cylinder = π*3²*10 = 282.74 ft³

✔️Volume of right triangular prism = ½*b*h*l

b = 3*2 = 6 ft

h = 4 ft

l = 10 ft

Volume of triangular prism = ½*6*4*10 = 120 ft³

✔️Plug in the values into the equation:

Volume of the figure = ½(282.74) + 120 = 261.37 ≈ 261 ft³

Answer:

1)  13,434

2)  During 2038 (by 2039)

Step-by-step explanation:

We can model this problem using an exponential equation.

General form of an exponential equation: [tex]y=ab^x[/tex]

where:

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

As the population increases by 3% each year, each year it will be 103% of the previous year.  Therefore, the growth factor in decimal form is 1.03

Given:

Substituting the given values into the equation:

[tex]y=8888(1.03)^x[/tex]

To find the population in 2025:

2025 - 2011 = 14

Therefore, set x = 14 and solve for y:

[tex]\begin{aligned}\implies y &=8888(1.03)^{14}\\& =13433.89747\\& = 13,434\end{aligned}[/tex]

To find the year in which the population will reach 20000, set y = 20000 and solve for x:

[tex]\implies 8888(1.03)^x=20000[/tex]

[tex]\implies (1.03)^x=\dfrac{20000}{8888}[/tex]

[tex]\implies \ln (1.03)^x=\ln \left(\dfrac{20000}{8888}\right)[/tex]

[tex]\implies x\ln (1.03)=\ln \left(\dfrac{20000}{8888}\right)[/tex]

[tex]\implies x=\dfrac{\ln \left(\frac{20000}{8888}\right)}{\ln (1.03)}[/tex]

[tex]\implies x=27.43785809[/tex]

2011 + 27.437... = 2038.437...

Therefore, the population will reach 20,000 some time during 2038.

Rewrite the fractions as decimals:

7/6 = 1.167

9/8 = 1.125

7/6 is greater then 9/8

the parts in 7/6 are greater than the parts in 9/8

so 7/6 is farther from 1 than 9/8 is

Answer:  123.3364311 degrees approximately

Round that value however your teacher instructs.

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Explanation:

Use the law of cosines to find side b

[tex]b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 43^2 + 19^2 - 2*43*19*\cos(35)\\\\b^2 \approx 871.5055596\\\\b \approx \sqrt{871.5055596}\\\\b \approx 29.521273\\\\[/tex]

Now use the law of sines to find angle A.

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\\\\frac{\sin(A)}{43} \approx \frac{\sin(35)}{29.521273}\\\\\sin(A)\approx 43*\frac{\sin(35)}{29.521273}\\\\\sin(A) \approx 0.8354581\\\\A \approx \sin^{-1}(0.8354581) \text{ or } A \approx 180-\sin^{-1}(0.8354581)\\\\A \approx 56.6635689^{\circ} \text{ or } A \approx 123.3364311^{\circ}\\\\[/tex]

Due to the side angle side (SAS) congruence theorem, we know that only one triangle is possible (notice angle B is between sides 'a' and c). This means only one of those values for angle A is possible.

The question is: Which one?

Well if you were to use the converse of the pythagorean theorem, then you'll find that the triangle is obtuse.

For any obtuse triangle, the longest side is always opposite the obtuse angle (aka the angle over 90 degrees). The side a = 43 is the longest side of this particular triangle.

This means angle A must be obtuse and the only possibility is that angle A = 123.3364311 degrees approximately.