Two angles in a triangle have measures of 42 and 82. (Degrees)

What is the measure of the third angle?

Answer:

[tex]x[/tex] = 67°

Step-by-step explanation:

As we can see in the diagram, ∠[tex]x[/tex] and the 78° angle together make up the 145° angle.

∴ [tex]x[/tex] + 78° = 145°

⇒ [tex]x[/tex] = 145° - 78°

⇒ [tex]x[/tex] = 67°

Answer:

all real values of x where x < -1

Step-by-step explanation:

See attached graph.

Answer:

1000

Step-by-step explanation:

Answer: Answer C is correct, 50.9.

The probability that at least 8 patients show improvement is; 0.94

The formula for Binomial Probability Distribution is;

P(X = r) = nCr * p^(r) * (1 - p)^(n - r)

where;

n = number of trials

r = number of specific events you wish to obtain

p is  probability of success

From the question, we have;

n = 12

r = 8

p = 81% = 0.81

The probability that at least 8 patients show improvement is expressed as;

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

Using online binomial probability calculator gives us;

P(X ≥ 8) = 0.11954 + 0.22649 + 0.28967 + 0.22453 + 0.07977

P(X ≥ 8) = 0.94

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Answer:

x = 3, -5

Step-by-step explanation:

I just know

Answer:

x= -5

x=3

Step-by-step explanation:

You are factoring here. The standard form of an equation is Ax² + Bx + C.

The 2 factors must multiple together to be C, but add together to be B. The easiest way to do this is to factor C.

C is -15. Factoring this, we find the only factors of 15 that will add together to be 2 are 5 & -3.

Therefore, the factors are (x+5) and (x-3). If you set each of these factor pairs to 0 and solve, the answers are:

x+5=0

x = -5

x-3 = 0

x=3

Answer:

  A.  Function f has exactly two complex solutions.

Step-by-step explanation:

The function will have real solutions where the graph crosses the x-axis. It will always have a total number of solutions equal to its degree. The ones that are not real are complex.

The graph has its vertex above the x-axis and extends upward from there. It never crosses the x-axis, so there are no real solutions. That means both solutions are complex.

Applying the law of sines, when the first lighting was made, the distance from the ship to the lighthouse was: 3.2 miles.

The law of sines is expressed by the equation, sin A/a = sin B/b = sin C/c.

Using the information we are provided with, the diagram that shows the ship and other information is drawn and shown in the image attached below, where:

m∠CAB = 65 + 30 = 95°

m∠BCA = 50 - 30 = 20°

m∠B = 180 - 95 - 20 = 65°

c =  the distance from the ship to the lighthouse

Considering triangle ABC, use the Law of Sines to find c:

sin B/b = sin C/c

B = 65°

b = 8.5 miles

C = 20°

Plug in the values

sin 65/8.5 = sin 20/c

Cross multiply

c(sin 65) = (8.5 × sin 200)

Divide both sides by sin 65

c(sin 65)/sin 65 = (8.5 × sin 200)/sin 65

c = (8.5 × sin 200)/sin 65

c ≈ 3.2 miles

Thus, when the first lighting was made, the distance from the ship to the lighthouse was: 3.2 miles.

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The amount of money Craig paid more than Tim if the shop has an offer of reduction if a particular amount is spent is £88.

The shop discount:

£5 reduction if you spend more than £100

or

£10 reduction if you spend more than £140

or

£20 reduction if you spend more than £180

Cost of a shirt = £49

Tim buys 3 shirts

Total cost of Tim's shirt = £49 × 3

= £147

Amount Tim paid = £147 - £10

= £137

Craig buys 5 shirts

Total cost of Craig's shirt = £49 × 5

= £245

Amount Craig paid = £245 - £20

= £225

Difference between Tim and Craig's pay = £225 - £137

= £88

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Considering the given rectangle, the coordinates of p are (6,7).

For x, there are two vertices at x = 3 and one at x = 6, hence the x-coordinate of p is x = 6.

For y, there are two vertices at y = 9 and one at y = 7, hence the y-coordinate of p is y = 7.

Then, the coordinates of p are (6,7).

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The equation that shows a pair of equivalent ratios that can be used to find the unknown is [tex]\frac{22}{1} =\frac{x}{3}[/tex]

From the question, we are to determine which equation shows a pair of equivalent ratios that can be used to find the unknown

In the given table, the unknown is x

Consider the given values in the table,

The equation that shows a pair of equivalent ratios that can be used to find the unknown is

[tex]\frac{22}{1} =\frac{x}{3}[/tex]

Hence, the equation that shows a pair of equivalent ratios that can be used to find the unknown is [tex]\frac{22}{1} =\frac{x}{3}[/tex]

Here is the complete question:

A car travels 22 miles for every gallon of gasoline used. The table below represents this relationship. Gas Mileage Distance Traveled (miles) Gasoline Used (gallons) 22 1 44 2 x 3 88 4. Which equation correctly shows a pair of equivalent ratios that can be used to find the unknown.

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Let A, B, and W denote the sets of students apply to Addis Ababa Uni (A), Bahir Dar Uni (B), or Wachemo Uni (W). Let U denote the universal set of all students in the class.

We're given the cardinalities of several sets:

• total number of students: [tex]n(U) = 60[/tex]

• A applicants: [tex]n(A) = 30[/tex]

• B applicants: [tex]n(B) = 25[/tex]

• W applicants: [tex]n(W) = 24[/tex]

• A and B applicants: [tex]n(A\cap B) = 11[/tex]

• A and W applicants: [tex]n(A \cap W) = 6[/tex]

• B and W applicants: [tex]n(B\cap W) = 9[/tex]

• non-applicants: [tex]n(U \setminus (A\cup B\cup W)) = 4[/tex]

The last cardinality tells us [tex]n(A\cup B\cup W) = 60-4 = 56[/tex] students applied anywhere at all.

We want to find [tex]n(A\cap B\cap W)[/tex], the number of students that applied to each of the three universities.

By the inclusion/exclusion principle,

[tex]n(A\cup B\cup W) = n(A) + n(B) + n(W) \\\\~~~~~~~~~~~~~~~~~~~~~~~~ - n(A\cap B) - n(A\cap W) - n(B\cap W)\\ \\~~~~~~~~~~~~~~~~~~~~~~~~ + n(A\cap B\cap W)[/tex]

That is, we count up all the students in the sets A, B, and W, then subtract the number of students in each pairwise intersection to not double-count, then add back the number of students in the intersection of all three sets since it was removed in the previous step.

Now solve.

[tex]56 = 30 + 25 + 24 - 11 - 6 - 9 + n(A\cap B\cap W)[/tex]

[tex]\implies n(A\cap B\cap W) = \boxed{3}[/tex]

The way to convert counts into relative frequencies in a Two Way Relative Frequency Table is to divide the count by the total number of items

This refers to the depiction of the number of times in which an event occurs in the form of a table.

Hence, when a two-way frequency table is used, it shows the visual representation of the possible relationship between different sets of data.

Please note that your question is incomplete as you did not provide the frequency table needed and also the trends and generalizations to find, so a general overview was given.

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Answer:

The relative frequency table shows a trend that a majority of people prefer coffee over tea: the ratio in the total row for coffee is 0.65 and just 0.35 for tea. Similarly, more people are night owls than early birds: the total column for night owl is 0.6, but the early bird column is only 0.4.

Answer:

[tex]f(x) = \frac{1}{2}x + 5[/tex]

Step-by-step explanation:

So you can generally express a linear function use the slope-intercept form as such: [tex]y=mx+b[/tex] where m=slope, and b=y-intercept.

The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule: [tex]f(x) = mx+5[/tex]

The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and this can be found using any two points, since the slope is constant.

We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run

[tex]\frac{6-5}{2-0} = \frac{1}{2}[/tex]

So plugging this into the slope-intercept form you get the function

[tex]f(x) = \frac{1}{2}x + 5[/tex]

The quadratic equation has the following results: (p, q) = (8, 15), minimum point: (h, k) = (1, 4), range of values: - 4 < x < - 3

In this question we have a quadratic equation of the form y = x² + p · x + q , whose missing coefficients can be found by solving on the following system of linear equations:

- 5 · p + q = - 25

- 3 · p + q = - 9

(p, q) = (8, 15)

The vertex represents the minimum point, which is found by changing the form of the equation from standard form into vertex form:

y = x² + 8 · x + 15

y + 1 = x² + 8 · x + 16

y + 1 = (x + 4)²

(h, k) = (1, 4)

And lastly we must solve for x in the following inequality:

x² + 8 · x + 15 < x + 3

x² + 7 · x + 12 < 0

(x + 3) · (x + 4) < 0

- 4 < x < - 3

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Answer:

IM  and  YM

Step-by-step explanation:

not sure about the symbol part, but it's a ray !!

Answer: IM and YM

Step-by-step explanation:

It can be broken down into to different rays

The list of data points used to generate the histogram is

   x            Frequency

15-20              0

20-25             4

25-30              6

30-35              3

35-40              4

40-45              0

45-50              3

From the question, we are to write the list of data points used to generate the given histogram

The list of data points used to generate the histogram is

   x            Frequency

15-20              0

20-25             4

25-30              6

30-35              3

35-40              4

40-45              0

45-50              3

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cancel by 3

Answer:

[tex]\sf \dfrac{8}{21}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x}[/tex]

When multiplying fractions, simply multiply the numerators and multiply the denominators:

[tex]\implies \sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x} = \dfrac{6x \cdot 4}{-7 \cdot -9x} =\dfrac{24x}{63x}[/tex]

Cancel the common factor x:

[tex]\implies \sf \dfrac{24 \diagup\!\!\!\!x}{63 \diagup\!\!\!\!x}=\dfrac{24}{63}[/tex]

Rewrite 24 as 3 · 8 and rewrite 63 as 3 · 21:

[tex]\implies \sf \dfrac{24}{63}=\dfrac{3 \cdot 8}{3 \cdot 21}[/tex]

Cancel the common factor 3:

[tex]\implies \sf \dfrac{\diagup\!\!\!\!\!3 \cdot 8}{\diagup\!\!\!\!\!3 \cdot 21}=\dfrac{8}{21}[/tex]

Answer:

  (c)  y = 3^x

Step-by-step explanation:

A function is described as exponential if the independent variable is found in the exponent.

  y = x^(1/2) . . . a square root function, not exponential

  y = 2x^3 . . . . a cubic (polynomial) function, not exponential

  y = 3^x . . . . . an exponential function

The inequalities that match the given expressions are

x ≤ 95

x > 100

5x ≤ 100

20 ≤ x ≤100

respectively

From the question, we are to match the statements with the corresponding inequalities

x ≤ 100 -5

x ≤ 95

x > 100

5x ≤ 100

x ≤ 100

and

x ≥ 1/5 × 100

x ≥ 20 ≡ 20 ≤ x

∴ 20 ≤ x ≤100

Hence, the inequalities that match the given expressions are

x ≤ 95

x > 100

5x ≤ 100

20 ≤ x ≤100

respectively

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Assume that the entries have not been made. The effect that these errors have on the reported net income is: Net income will be overstated by $17,000.

Using this formula

Net income=Expired rent+Depreciation+Supplies

Let plug in the formula

Net income=$6400+$7600+$3000

Net income=$17,000 (Overstated)

Therefore the net income will be overstated by $17,000.

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Answer:

here ya go :)

the black line is y=-2x-3

the lavender line is y=-x+6

Answer:Joey is 18 hope that helped you

The appropriate  journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.

Sheffield corporation entries

Debit Cash $18,870

[$21500-($480+ ($21500×10%))]

Debit Advertising expense $480

Debit Commission expense $2,150

(21,500×10%)

Credit Revenue from consignment sales $21,500

Debit Cost of goods sold $13,888

[($20400+$2000)×62%]

Credit Inventory on consignment $13,888

Therefore  journal entry when the cash is received is: Debit Cash $18,870, Debit Advertising expense $480, Debit Commission expense $2,150, Credit Revenue from consignment sales $21,500.

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The blank space to form a linear pair with m∠BPD is m∠APD.

Linear pair of angles are formed when two lines intersect each other at a single point.

Linear pair angles are adjacent to each other.

Therefore, the sum of a linear pair angles is equals to 180 degrees.

This means linear pair angles are supplementary.

Hence,

m∠APD + m∠BPD = 180°

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Vertex of the equation is (-2, 5)

Focus of the equation is (-2, 8)

Directrix of the equation is 2

What is a Quadratic curve?

A quadratic curve is a parabolic curve is a graph of the points which define a quadratic function. It shows how a function behaves in the cartesian plane.

Quadratic curve may bend upwards, or downwards depending on the gradient of the curve.

Analysis:

setting the equation in the form, [tex]x^{2}[/tex] +4x -12y = -64 in the form [tex](x-h)^{2}[/tex] = 4p(y-k)

Firstly we take -12y to the right hand side

[tex]x^{2}[/tex] +4x = 12y - 64

Making the left hand side a perfect square expression, we square both sides with -2

[tex]x^{2}[/tex] +4x + [tex](2)^{2}[/tex] = 12y -64 + [tex](2)^{2}[/tex]

[tex](x+2)^{2}[/tex] = 12y -60

[tex](x+2)^{2}[/tex]  = 12(y - 5)

comparing with the other equation

-h = , h = -2, -k = - 5 k = 5, 4p = 12, p = 3

Vertex is (h, k) = (-2, 5)

Focus is (h, k+p) = (-2, 5+3) = (-2, 8)

Directrix is y = k-p = 5 - 3 = 2

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Answer:

Vertex (2 , -25)

Axis of symmetry: x = 2

Step-by-step explanation:

 The vertex is the highest point if the parabola open downwards and the lowest point if the parabola opens upward.

 f(x) = (x - 2)² - 25

The given quadratic function  is in vertex form.

 f(x)  = a(x - h)² + k

Here,  (h , k) is the vertex of the parabola.

 h = 2  ; k = -25

[tex]\sf \boxed{\bf Vertex (2 , -25)}[/tex]

 The axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

Axis of symmetry: x = h

  [tex]\sf \boxed{\bf x = 2}[/tex]

The relative minimum point in the graph is (-6, 2)

To do this, we simply locate a point that at a lower level, when compared to its neighboring points

Using the above highlight, there is only one relative minimum point in the graph

And the point is located at (-6,2)

Hence, the relative minimum point in the graph is (-6, 2)

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Answer: A

Step-by-step explanation:

[tex]-\frac{4}{x}+1=0\\\\1=\frac{4}{x}\\\\x=4[/tex]