The table shows the number of patients who visited Dr. Louie's clinic each day during the first 15 days in April.
Number of Patients
23
14
28
15
24
18
21
16
27
18
29
21
26
17
33
The total number of patients who visited Dr. Louie's clinic during the first 15 days of April was
The number of days when more than 28 patients visited the clinic was

Answer: 7x + 4 y = 2

9x - 4y= 30

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

16x / = 32

x= 32:16

x=2

Step-by-step explanation: 7x+4y=2

7*2 + 4y=2

14 +4y=2

4y= 2-14

4y= -12

y= -12 : 4

y= - 3

answer: 85+85+85+25



Answer:

Step-by-step explanation:

Point: 10,-9

k=-2

y=-2x+b

So: 9, -7

8,-5

7,-3

6,-1

5,1

4,3

3,5

2,7

1,9

0,11

y=-2x+11

Answer:

y + 9 = - 2(x - 10)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - 2 and (a, b ) = (10, - 9 ) , then

y - (- 9) = - 2(x - 10) , that is

y + 9 = - 2(x - 10)

Answer:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

Step-by-step explanation:

Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

Step-by-step explanation:

Four less than twice a number is sixteen.

2x − 4 = 16

Add 4 to both sides.

2x = 20

Divide both sides by 2.

x = 10

Answer:

\(\boxed{the \: number \: is \: 10}.\)

Step-by-step explanation:

\(let \: this \: number \: be : n \\ then \\ Four \: less \: than \: twice \: the \: \\ number \: is \: sixteen. \to \: can \: be \: written \: as : \\ 2n - 4 = 16 \\ to \: find \: the \: number : we \: will \: have \: to \: solve \: for \: n \to \\ 2n - 4 = 16 \\ 2n = 16 + 4 \\ 2n = 20 \\ \boxed{n = 10}.\)

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Answer:

2(5) + 2√(3^2 + 7^2) = 10 + 2√58 = 25.2

B is the correct answer.

The sum of a number squared and three less than the number is 129.

Mathematical expression: x^2 + ( 2 x - 3 ) = 129

x^2 + 2 x -3 = 129

x ^2 + 2x - 3 - 129 =0

x ^2 + 2x - 132 = 0

Answer:

x= 10

Step-by-step explanation:

C(x) = 2,000x + 60,000

R(x) = 8,000x

Set the solution to zero.

R(x) - C(x) = 0

8,000x - (2,000x  + 60,000) = 0

6,000x - 60,000 = 0

x=10

Answer:

D: The interval becomes narrower if n = 28.

Step-by-step explanation:

D: The interval becomes narrower if n = 28.

The claim that is true regarding confidence interval would be:

D). The interval becomes narrower if n = 28.

Interval is described as the range in which the values fluctuate. This involves one initial or beginning value while the other is the end value and in between these two, the values range.

Given that,

Confidence interval = 95%(2.3, 3.7)

No. of data values = 24

In this case, the true statement about the effect of alteration in the size of the sample would be the interval becoming more concise/narrow in case n become 28 from 24.

Thus, option D is the correct answer.

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Answer:

.

Step-by-step explanation:

On solving the provided question, we got to know that  -Pythagoras' Theorem -  \(a^2 + b^2 = c^2 =\)\(5^2 + 8^2 = c^2\)

The square of the hypotenuse of a right triangle (90 degrees) is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC below. where BC is the hypotenuse, AB is the base, and AC is the height (height). Keep in mind that the hypotenuse of a right triangle is its longest side.

Pythagoras' Theorem -

\(a^2 + b^2 = c^2\)

where the other two sides' lengths are a and b, and c is the length of the hypotenuse.

so

\(5^2 + 8^2 = c^2\\c^2 = 25 + 64\\c^2 = 89\\c = \sqrt{89}\)

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Answer:

Here,

f(x)=2x+3(x-3)

if f(x)=11

we know that,

or,11=2x+3(x-3)

or,11=2x+3x-9

or,11+9=5x

or,20=5x

Therefore,x=4

Answer:

x = 4

Step-by-step explanation:

2x + 3x - 9 = 11

5x = 11+9

5x = 20

x = 4

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The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

Brian is constructing figures inscribed in circle C.

Equilateral triangle MNQ inscribed in circle C:

This option is possible since the points M, N, and Q are labeled and they lie on circle C.

Equilateral triangle ANP inscribed in circle C:

This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.

Regular hexagon AMNBPQ inscribed in circle C:

This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.

Square MNPQ inscribed in circle C:

This option is not possible based on the given information. The label points do not form a square.

Square ANBQ inscribed in circle C:

This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

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Answer:

\(\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66\)

Step-by-step explanation:

\(\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta\)

\(\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66\)

The exact value of tan(x) = -1, where 0 < x < 2π are; ​x = 135° and 315°

There are three primary trigonometric ratios based on a right angle triangle which are as follows;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Now, the location and their signs in a quadrant are;

All the three trigonometric functions are positive in the first quadrant which is 0° to 90°

Only Sine is positive in the second quadrant which is 270° to 360°.

Only tangent is positive in the third quadrant which is 180° to 270°.

Only cosine is positive in the fourth quadrant which is 90° to 180°.

We are given;

tan(x) = -1, where 0 < x < 2π ​

This means the domain of x is is 0 < x < 360

Thus, the only values of x that will result in a negative answer(-1) are;

x = 135° and 315°

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The Answer:

Width = 6

Step-by-step explanation:

Let width be w

(3w + 8) x w = 156

3 \(w^{2}\) x 8n - 156 = 0

(w + 8 x 6) (w-6) = 0

w = 6

The optimal production mix of the company is 56 chairs and 60 desks with a profit of $8800.

Linear programming problems are the problems involving the maximization or minimization of a linear function which is subjected to some linear constraints.

Given that,

Daily capacity of sawing department = 200 chairs or

                                                                80 desks

Daily capacity of chair assembling department = 120 chairs

Daily capacity of desk assembling department = 60 desks

Daily capacity of paint department = 150 chairs or

                                                             110 desks

These are the constraints.

Given,

Profit per chair = $50

Profit per desk = $100

Objective function is to maximize the profit.

Let x be the number of chairs and y be the number of desks.

Objective function is,

Maximize Z = 50x + 100y

Subject to

200x + 80y ≤ 16000 or 5x + 2y ≤ 400

150x + 110y ≤ 16500 or 15x + 11y ≤ 1650

x ≤ 120  

y ≤ 60  

The corner points are (120, -100), (56, 60), (120, 0) and (0, 60).

(120, -100) is not possible.

(56, 60) : z = (50 × 56) + (100 × 60) = 8800

(120, 0) : z = (50 × 120) + (100 × 0) = 6000

(0, 60) : z = (50 × 0) + (100 × 60) = 6000

Hence the optimal production mix is 56 chairs and 60 desks.

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Answer:

x=50

Step-by-step explanation:

x+37=3x-63

Subtract x from each side

x-x+37=3x-x-63

37 = 2x-63

Add 63 to each side

37+63 = 2x-63+63

100 =2x

Divide by 2

100/2 =2x/2

50=x

Answer:

Step-by-step explanation:

x - 37 = 3x - 63

x - x + 37 = 3x - x 63

37 = 2x - 63

2x = 63 + 37

2x = 100

x = 100 : 2

x = 50

Answer: 141.4

Step-by-step explanation:

(π)(1.5)(30)= 141.37

141.37 rounded to the nearest tenth is 141.4

a)  The students in the key club are 48students.

b)  The mean, median, mode, range, variance, and standard deviation for the distribution are 8.3, 8, 9, 9, 303.52, 17.4

The standard deviation is a statistic that measures the amount of variation or dispersion in a set of numbers. A low standard deviation implies that the values are close to the mean of the set, whereas a large standard deviation shows that the values are spread out over a greater range.

Given,

The number of echo beach trips are 5,6,8,9,12,14.

And also given that the frequencies are 8,7,11,15,3,4

a) The students in the key club are,

∑\(F_{i}\)=8+7+11+15+3+4

=48

∑\(F_{i}\)=48

Therefore, the students in the key club are 48students.

b) Mean= ∑\(X_{i}\)\(F_{i}\)/∑\(F_{i}\)

=397/48

=8.27≈8.3

Therefore, Mean=8.3

Total number of observations=48

Here, it is an even number

\((48/2)^{th}\)  \(24^{th}\)position and \(((48+2)/2)^{th}\) or \(25^{th}\) position

X                      5       6            8                 9                     12              14

F                       8        7           11                 15                    3                 4

position           8    8+7=15   15+11=26    26+15=41         41+3=44    44+4=48

The value of X at  \(24^{th}\) position is 8 and  \(25^{th}\) position is also 8

Then, Median=(8+8)/2

=8

Therefore, Median=8.3

Mode= Highest frequency corresponding to X value

=9

Therefore, Mode=9

Range=Highest value-Lowest value

=14-5

=9

Therefore, Range=9

Variance=∑\(F_{i}\)(\(X_{i}\)-\(\bar{X}\))/∑\(F_{i}\)

=8(5-8.3)²+7(6-8.3)²+11(8-8.3)²+15(9-8.3)²+3(12-8.3)²+4(14-8.3)²

=87.12+37.03+0.99+7.35+41.07+129.96

=303.52

Therefore, variance=303.52

Standard deviation=√variance

=√303.52

=17.4

Therefore, standard deviation=17.4

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The appropriate distribution to use is t distribution with df = 80.

Variance

Distribution

Given that:

n1 = 37

n2 = 45

The variances of the populations are not know so we can use t distribution

Degree of freedom = n1 + n2 - 2

                                = 37 + 45 - 2

                                = 80

Therefore, t distribution with df = 80

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Answer:

  f(x) = 10^x -4

Step-by-step explanation:

The horizontal asymptote of this exponential function is at y=-4, so there is a vertical translation of -4 added to the function. That is, the function is expected to be of the form ...

  y = a·b^x -4

The graph crosses 1 unit above the horizontal asymptote at x=0, so there is no horizontal translation. Effectively, a=1 in the above equation.

The graph crosses 10 units above the horizontal asymptote at x=1, so the base of the exponent is b = 10.

The function appears to be ...

  f(x) = 10^x -4

The equilibrium point for James T-shirt business is (P, Q) = (7, 24).

To find the equilibrium point (P, Q) for James T-shirt business

we need to set the demand function equal to the supply function and solve for the values of P and Q.

Demand function: P = -Q + 31

Supply function: P = Q - 17

Setting them equal:

-Q + 31 = Q - 17

Adding Q to both sides and subtracting 31 from both sides:

2Q = 48

Dividing both sides by 2:

Q = 24

Now, we can substitute this value of Q into either the demand or supply function to find the corresponding value of P.

P = Q - 17

P = 24 - 17

P = 7

Therefore, the equilibrium point for James T-shirt business is (P, Q) = (7, 24).

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10! can be expanded as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

A whole number's factorial is the result of multiplying the integer by each natural number below it. The sign "!" can be used to indicate a factorial symbolically. Therefore, "n factorial" is denoted by the number n and is the sum of the first n natural integers.

n! = 1 · 2 · 3 · ... · n

= Product of the first n positive integers

= n(n-1)(n-2)…………………….(3)(2)(1)

Given:

10!

We know that by the factorial property

n!= n (n-1)(n-2)(n-3)(n-4)..... 3.2.1.

So, 10!

= 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Hence, 10! can be expanded as 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

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Answer:

x > -4

Step-by-step explanation:

I just looked it up

But I know this is it

Answer:

Inequality Form:

x  >  − 4

Interval Notation:

(-4,∞)

Step-by-step explanation:

It will grow to $9991.15