if two times a positive number is added to one third of its square, the result is 9,find the number​

A triangle    can   be formed.

Value that goes in the box is [tex]31\frac{3}{4}[/tex]

It's the same as the first angle mentioned. The value doesn't change.

=====================================================

Explanation:

3/4 = 0.75

1/2 = 0.50

The three given angles in decimal form are:

If these angles add to 180 degrees, then a triangle can be formed.

31.75+53.50+94.75

85.25+94.75

180

So, 31.75+53.50+94.75 = 180 is definitely the case.

Therefore, a triangle can be formed.

You'll type the mixed number [tex]31\frac{3}{4}[/tex] into the box which was that first angle mentioned.

This means that Dr. Hart result may be not true for the entire population.

Heart disease is a condition when the heart is disturbed. Several types of heart disease, including:

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After finding the time period of particle, time elapsed between turning points is 1.57 seconds.

A particle is oscillating in one dimension, with a position by x=cos(2t).

The general equation of simple harmonic equation is

x = Acos(ωt)

At t = 0 the particle is at x =1.

On comparing ω = 2

Time period of the particle = 2π/ω

Now putting the value

Time period of the particle = 2π/2

Time period of the particle = π seconds

Thus, the particle takes half the time to get from one extreme to another, which is a turning point.

So, Time elapsed = π/2 seconds

Time elapsed = 3.14/2 seconds

Time elapsed = 1.57 seconds

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The complete question is:

A particle is oscillating in one dimension, with a position given by x=cos(2t). How many seconds elapse between turning points?

The domain and the range for the relation is {a, t, s, k, j, p} and {g, c, g, w, k, p} respectively.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it may take as input. The values in this set

Hence, once we input an x value, the function returns. The y values are those.

The domain is the input values or the x-coordinates. Hence the domain for the given relation is:

{a, t, s, k, j, p}

The range is the output value or the y-coordinate. Hence, the range of for the given relation is:

{g, c, g, w, k, p}

Hence, the domain and the range for the relation is {a, t, s, k, j, p} and {g, c, g, w, k, p} respectively.

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The growth of the population after .t. years would be [tex]y_t = 16000^{(1.06t)}[/tex].

The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0e^{(-kt)}.[/tex].

Given, The number of students enrolled at a college is 16,000 and grows ​6% each year.

Now, 6% in terms of decimals is 0.06 hence k = 1 + 0.06 = 1.06.

The initial amount is 16000.

So, After t number of years, the population would be, [tex]y_t = 16000^{(1.06t)}[/tex].

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From the given triangle JKL, measure angle K is 65 degrees.

The length of the sides distinguishes triangles of the scalene, isosceles, and equilateral kinds. If the lengths of the three sides are all different, the triangle is a scalene triangle. A triangle that has equal lengths on each of its three sides is said to be isosceles.

The measure of angle j in the triangle JKL is 30 degrees less than the measure of angle K, while the measure of angle L is 80 degrees. measure the angle K.

Suppose angle K = x, at which point angle J = x-30 degrees, and angle L = 80 degrees.

The total of a triangle's three angles is 180 degrees, or K+L+J = 180.

The angles of the triangle are

since x+80+x-30

= 180 + 2x

= 180-80+30

= 130 and

x= 130/2 = 65 degrees.

K = 65 degrees,

L = 80 degrees, and

J = 35 degrees

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Complete question -

In triangle JKL,the measure of angle j is 30 degrees less than the measure of angle K and measure angle L=80. find measure angle K.

Answer:

x = $20.40

Step-by-step explanation:

x = cost of 13 glue sticks

4 glue sticks cost $7.76, so to find the cost of 13 glue sticks, you would use the equation:

x = (13/4) * $7.76

or

x = $20.40

The slope of line is -3.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

A line intersects the points (7, 6) and (11, -6).

So, the slope is

= [tex](y_2 - y_1)/ (x_2 - x_1)[/tex]

= (-6 - 6) / (11 - 7)

= -12 / 4

= -3

Hence, the slope is -3.

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The probability that the proportion in a random sample is 0.99997.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given:

For this case we have a random sample of 2500 people, this value represent n.

We know that in the sample selected the number of people who say that prefer shop online rather than in a store are 1575.

For this case we can calculate the sample proportion with this formula:

h(p) = x/n

       = 1350/ 2500

       = 0.54

Now, [tex]\mu_p =[/tex] 0.54

and, [tex]\sigma_p[/tex] = √0.54 (1- 0.54)/2500

            = 0.00996

and, we want to calculate the following probability:

P(p>0.50)

= 1- P(p< 0.50)

= 1 - P(z < (0.5 - 0.54)/ 0.00996)

= 1 - P(z< -4.016)

= 1- 0.00003

= 0.99997

c) For this case since the probability is very high we can conclude that the manager is correct since is very improbable that the true proportion would be lower than 0.5.

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The actual perimeter of the triangular face will be B. 18 1/2 feet.

The perimeter of a shape is simply the total length of the boundary that the shape has. It should be noted that in this case, it's gotten by adding all the length that the shape has.

PQ + QR + PR

= 12 + 15 + 10

= 37 inches

Therefore, the actual perimeter of the triangular face will be:

= 37 / 2

= 18.5

The correct option is B.

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The perception of the Olympic logo as interlocking circles is due to the human brain's tendency to simplify and organize visual information.

This is known as "gestalt psychology," where our brain perceives objects as a whole rather than individual elements. The circles provide a clear and recognizable shape that is easy for our brain to process, whereas a series of complex shapes might be harder to understand and remember.

The circles are a consistent and repeated shape in the design, further emphasizing their perception as the main element. In conclusion, it's the brain's innate pattern recognition ability and our cultural familiarity with the design that lead us to see the Olympic logo as interlocking circles.

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In an isosceles triangle, if Angle DBC has a measure of 110 degrees and angle BDA has a measure of 22 degrees, then the measure of angle BAC is 48 degrees.

A triangle with two equivalent sides and angles with equal measures on opposing sides is said to be isosceles.

Triangle BAC's angles should be labelled as follows:

Angle BAC = x

Angle ABC = y

Angle BCA = z

Because a triangle's angles sum up to 180 degrees,

x + y + z = 180

As ACD and BCD are isosceles triangles,

angle DBC = angle DCB = 110 degrees

Because BDA and DBC are a pair of linear angles,

angle BDA + angle DBC = 180 degrees

Using values for angles DBC and BDA and substituting them,

22 + 110 = 180

By finding y,

y = 180 - 22 - 110

When the value of y is substituted in the equation x + y + z = 180,

x + (180 - 22 - 110) + z = 180

Solving for x,

x = 180 - (180 - 22 - 110) - z

Substituting the value of z = 180 - (22 + 110),

x = 180 - (180 - 22 - 110) - (180 - 22 - 110)

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The simplified expression is equal to 13/24 - 3/8b.

It represents a value that can change, depending on the values of the variables.

For example, "2x + 3" is an algebraic expression. The variable x can take on any value, and the expression represents a value that is the result of adding 2 times x to 3. When x is equal to 5, the expression equals 2 * 5 + 3 = 13.

Algebraic expressions can be combined using the operations of addition, subtraction, multiplication, and division to form more complex expressions. They can also be simplified by combining like terms or using the distributive property.

Algebraic expressions are an important tool in mathematics, and are used in many areas including science, engineering, and economics. They can be used to model and understand complex systems, and to make predictions and analyze data.

The expression -1/4 + 1/12 - 1/8b + 13/24 can be simplified by finding the common denominators and adding the numerators:

-1/4 + 1/12 - 1/8b + 13/24 = (3 * -1/12) + (3 * 1/12) - (3 * 1/8b) + (3 * 13/72) = 3 * (-1/12 + 1/12 - 1/8b + 13/72) = 3 * (13/72 - 1/8b) = 13/24 - 3/8b.

So, the simplified expression is equal to 13/24 - 3/8b.

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A bin of 50 parts contains 5 that are defective and a sample of 10 parts is selected without replacement, then total 40,753,713 samples contain at least 4 defective parts.

A bin of 50 parts contains 5 that are defective.

A sample of 10 parts is selected without replacement.

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = Samples with precisely 4 defectives + samples with precisely 5 defects

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = [tex]^{5}C_{4}\cdot ^{45}C_{6}+ ^{5}C_{5}\cdot^{45}C_{5}[/tex]

Using the formula [tex]^nC_{r} = \frac{n!}{r!(n-r)!}[/tex]

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = [tex]\frac{5!}{4!(5-4)!}\cdot\frac{45!}{6!(45-6)!}+\frac{5!}{5!(5-5)!}\cdot\frac{45!}{5!(45-5)!}[/tex]

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = [tex]\frac{5!}{4!1!}\cdot\frac{45!}{6!39!}+\frac{5!}{5!0!}\cdot\frac{45!}{5!40!}[/tex]

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = [tex]\frac{5\times4!}{4!\times1}\cdot\frac{45\times44\times43\times42\times41\times40\times39!}{6\times5\times4\times3\times2\times1\times39!}+1\cdot\frac{45\times44\times43\times42\times41\times40!}{5\times4\times3\times2\times1\times40!}[/tex]

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 5 × 15 × 44 × 43 × 7 × 41 + 1 × 9 × 11 × 7 × 41

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 40,753,713

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If the builder does not build houses with three-car or more garages, then the probability that the buyer will select no garage home is 0.1.

Probability is a measure of likelihood that a certain event occurs. The probability of an event A is defined as:

P(A) = n(A)/n(S)

Where:

n(A) = number of ways the event A can occur

n(S) = number of all possible outcomes.

Suppose there are 3 possible outcomes, A, B, C, then:

P(S) = P(A) + P(B) + P(C) = 1

In the problem, let's define the events:

A = buyer will select a one-car garage

B = buyer will select a two-car garage

C = buyer will select no car garage

We have:

P(A) = 0.2

P(B) = 0.7

Hence,

P(A) + P(B) + P(C) = 1

0.2 + 0.7 + P(C) = 1

P(C)  = 1 - 0.9 = 0.1

Therefore, the probability that the customer will choose no garage option is 0.1

Your question is incomplete, most likely it was:

In building new homes, a contractor finds that the probability of a home buyer selecting a two-car garage is 0.7 and of selecting a one-car garage is 0.2. Find the probability that the buyer will select no garage. the builder does not build houses with three-car or more garages

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The sample space of all the possible outcomes of rolling two six-faced dice is {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), . . ., (6,5), (6,6)}, and there are 36 possible outcomes in total.

Using the Fundamental Counting Principle, the possible outcomes can be determined.

(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

Rolling two six-sided dice: Each die has 6 equally likely outcomes, so the sample space is 6 • 6 or 36 equally likely outcomes.

A simple graphical representation of this set could be a shown in a table, where the top row is the possible outcomes of the first dice, the first column is the possible outcomes of the second dice, and the inner table is all the possible outcomes when these two dice are rolled at the same time.

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Each feature of the graph should be matched with the corresponding coordinate point as follows:

In Mathematics, the vertical intercept (y-intercept) of any graph such as a quadratic function or an exponential function, generally occur at the point where the value of "x" is equal to zero (x = 0).

By critically observing the graph which represents the function (see attachment), we can logically deduce that the vertical intercept (y-intercept) is equal to the ordered pair (0, 7).

Additionally, the maximum point of any graph is the point where the graph is at the highest point, which is equal to the ordered pair (4, 16) while the minimum point of any graph is the point where the graph is at the lowest point, which is equal to the ordered pair (1.5, 2).

In conclusion, there is no horizontal intercept (x-intercept) on this graph.

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The dimensions of cuboid C and cuboid D are 1,4,4 and 2,4,2 respectively.

What is a cuboid?

A closed three-dimensional geometric shape called a cuboid is surrounded by six rectangular plane sections.

Given that, the dimensions of the first two cuboids are 1,1,16 and 1,2,8.

Note that the volume of each cuboid is the same, therefore, the multiplication of the dimensions should be the same for each cuboid.

Therefore, the dimensions of cuboid C and Cuboid D are:

Cuboid C: 1,4,4 Since 1 ×4×4=16.

Cuboid D: 2,4,2 as 2×4×2 = 16

Hence, the dimensions of cuboid C and cuboid D are 1,4,4 and 2,4,2 respectively.

The given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.

Amount is a numerical quantity that is used to measure the size or magnitude of something. It is typically expressed in terms of a unit of measure such as a dollar, pound, or other currency.

The given k-value of 0.1459 corresponds to the rate of decay of the 9 gram sample of the substance over time. The equation for determining the amount of the sample left after a certain amount of time (t) is: N = -kt, where N is the amount of the sample left after the given amount of time, k is a positive constant that depends on the substance itself and on the units used to measure time, and t is the amount of time in days.

N = N0 e^(-kt)

for half life N/N0 = 1/2 and k = 0.1459

1/2 = e^(-0.1459t)

=> -0.1459 t = ln(0.5)

t = - ln(0.5) /0.1459

= 4.8 days       

Therefore, with the given k-value of 0.1459, we can calculate the amount of the sample left after any given amount of time.

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Complete question is:

A 9 gram sample of a substance that's used for drug research has a K value of 0.1459

Find the substances half-life in days, and round answer to the nearest ten. ( exponential decay )

This one shouldn't be too hard! :)

A diameter of a circle is just the total distance across the circle.

The two dots that stretch ALLLLL the way across the circle are dots R to S

Your answer is The third one RS

Hope this helps!

The speed of the person located at earth's equator traveling due to rotation is, 1670 km/hr.

The person at equator traveling due to it's rotation will cover one complete round of earth in 24 hours. Hence the distance travelled is the circumference of the earth.

The radius of the earth is, 6 378.1 kilometers.

The circumference can be calculated as, 2×π×R

Using R = 6 378.1 kilometers,

Circumference = 2×π×6 378.1 kilometers

Circumference = 40090.91 kilometers.

The distance traveled = 40090.91 kilometers.

Time taken is 24 hrs.

Hence speed = distance/time

Speed = 40090.91/24

Speed = 1670 km/hr

The speed of the person is 1670 km/hr.

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Answer:

4 miles: 3 hours has a unit rate of 4/3 = 1.33 miles/hour which is greater than 17

7 miles: 1 hour has a unit rate of 7 miles/hour which is greater than 17.

In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size. [Therefore proven] BD=BC.

A parallelogram is a straightforward (non-self-intersecting) quadrilateral in Euclidean geometry that has two sets of parallel sides.

In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

There are

As well as AB=AC, BC 2 = AC / CD.

B = C and BC = BC = AC

The notation AC BC equals BC CD, and B = C.

CA BC equals CB DC and B = C.

Thus, based on the similarity criterion of SAS, we have

△BCA∼△DCB

DC/ BC = CB /CA = DB/ BA

CB /CA = DB/ BA

CA/ BA = CB /DB

1 = CB / DB [BA=CA]

⇒ DB=CB

[Therefore proven] BD=BC.

The Complete Question.

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Answer:

see below

Step-by-step explanation:

-x+y=14 --> so x=y-14

2x+y=-7  put x in here

2(y-14)+y =-7

2y-28+y = -7

3y =21

y=7

x= y - 14 = -7

Answer:

See below

Step-by-step explanation:

Keisha walks faster than Ryan so she will lap Ryan as a way of catching up to him.

LCM of 7 and 5 is 35 which is the time taken to meet up again at the starting line

Thus she will have walked 7 laps and he will have walked 5

The value of y when x = -12 is given as follows:

y = 32.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

For which the parameters are given as follows:

From the table, when x increases by 2, y decays by 4, hence the slope m is obtained as follows:

m = -4/2

m = -2.

Hence:

y = -2x + b.

When x = -3, y = 14, hence the intercept b is obtained as follows:

14 = -2(-3) + b

b = 8.

Hence the function is:

y = -2x + 8.

When x = -12, the value of y is given as follows:

y = -2(-12) + 8

y = 24 + 8

y = 32.

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The constant of proportionality in the equation 3y = 2x is 2/3.

Two or more expressions with an Equal sign is called as Equation.

if y is directly proportional to x, this is expressed as:

y ∝ x

y = kx .................... 1

k = y/x

Given the expression 3y = 2x

Divide both sides by 3

3y/3 = 2x/3

y = 2/3 x ................ 2

Compare equation 1 and 2 to find "k"

kx = 2/3 x

k = 2/3

Hence,  the constant of proportionality in the equation 3y = 2x is 2/3.

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If Kim has health insurance with a deductible of $500 and 80/20 coinsurance then amount she pay if she incurs a loss of $1500 is (c)$700 .

In an 80/20 coinsurance, the insurance company pays 80% of covered expenses after the deductible has been met, and the policyholder is responsible for paying the remaining 20%.

So , if Kim incurs a loss of $1500, she first needs to pay the $500 deductible before her insurance kicks in. After that, she will pay for 20% of the remaining $1000 in covered expenses:

⇒ 20% of $1,000 = $200

So, in total, Kim will pay $500 for the deductible plus $200 in coinsurance, for a total of:

⇒ $500 + $200 = $700

Therefore, If Kim will pay (c) $700.

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The statements that complete the proofs are; One half the measure of their intercepted arcs; mARC CDE = 2·m∠CFE and mARC CFE = 2·m∠CDE

The two column proof that ∠CFE and ∠CDE are supplementary is presented as follows;

Statement                                                              Reason

Quadrilateral CDEF is inscribed is circle A         Given

m<CDE + m<CFE = 360°                           Measure of angle round a circle

∠CFE and ∠CDE are inscribed angles                Given

∠CFE  + ∠CDE = 1/2 × ( m<CDE + m<CFE )     Inscribed angles are (i) one half the measure of their intercepted arcs

2 × (∠CFE  + ∠CDE) = (m<CDE + m<CFE )

So, (ii)  = 2 × m∠CFE and  = 2 × m∠CDE From the inscribed angle theorem above (See attached drawing)

2·m∠CFE + 2·m∠CDE = 360°      Using substitution property of equality

(2·m∠CFE + 2·m∠CDE)/2 = 360°/2 → m∠CFE + m∠CDE) = 180°                 Dividing both sides by 2

m∠CFE and m∠CDE) are supplementary   Angles that sum up to 180°

The statements that complete the proofs are;

(i) One half the measure of their intercepted arcs

(ii) mARC CDE = 2·m∠CFE and mARC CFE = 2·m∠CDE

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Complete question:

Quadrilateral CDEF is inscribed in circle A. Which statements complete the proof to show that ∠CFE and ∠CDE are supplementary?

Quadrilateral CDEF is inscribed in circle A, so mARC CDE + mARC CFE= 360°. ∠CFE and ∠CDE are inscribed angles, which means that their measures are _________________. So, _________________. Using the substitution property of equality, 2 ⋅ m∠CFE + 2 ⋅ m∠CDE = 360°. Using the division property of equality, divide both sides of the equation by 2, resulting in m∠CFE + m∠CDE = 180°. Therefore, ∠CFE and ∠CDE are supplementary.