A diagonal path divides a square park in half. If the park is 50 yards on each side, how long is the path? A. 10 yd. B. 250 C. 50 yd. D. 5000

The coordinate of each point is just the number it corresponds to.

a) 6

b) -5

c) 9

d) 0

Answer:

5.907 km

Step-by-step explanation:

2.783 km + 3.124 km = 5.907 km

Answer: [tex]160^{\circ}[/tex]

Step-by-step explanation:

By the exterior angle theorem,

[tex]4x-14+5x-182=5x-100\\\\9x-196=5x-100\\\\4x=96\\\\x=24\\\\\implies m\angle BCD=20^{\circ}\\\\\implies m\angle BCA=160^{\circ}[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

By Exterior angle property :

[tex]\qquad❖ \: \sf \:4x - 114 + 5x - 182 = 5x - 100[/tex]

[tex]\qquad❖ \: \sf \:9x -29 6 = 5x - 100[/tex]

[tex]\qquad❖ \: \sf \:9x - 5x = - 100 + 296[/tex]

[tex]\qquad❖ \: \sf \:4x = 96[/tex]

[tex]\qquad❖ \: \sf \:x = 24 \degree[/tex]

Next, Angle BCA = 180° - Angle BCD

( linear pair )

[ let angle BCA = y ]

[tex]\qquad❖ \: \sf \:y = 180 - (5x- 100)[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - (5(24) - 100)[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - (120 - 100)[/tex]

[tex]\qquad❖ \: \sf \:y = 180 - 20[/tex]

[tex]\qquad❖ \: \sf \:y = 160 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

The test statistic is 27.8484, the p-value is 0, and the final conclusion is that the null hypothesis H is rejected.

Given that 914 babies were born to parents who used the new method, and 877 of them were girls, the significance level to test the claim that the new method is effective in increasing the likelihood of a baby being a girl, is 0.01.

The following information is provided: the sample size is N = 914, the number of favorable cases is X = 877, and the sampling ratio is

pˉ = X / N

Pˉ = 877/914

pˉ = 0.9595 and the significance level is α = 0.01

(a) Hypothesis Zero and Alternative

The following null and alternative hypotheses should be tested:

null: p = 0.5

Alternative: p> 0.5

This is equivalent to a right-tailed test, which requires a z-test for a proportion of the population.

(b) Critical Value

Based on the information provided, the significance level is α = 0.01, so the critical value for this right-tailed test is Zc = 2.3263. This can be found using Excel or the Z distribution table. Region of rejection

The rejection area for this test on the right side is Z> 2.3263

Test statistics

The z-statistic is calculated as follows:

[tex]\begin{aligned}Z&=\frac{\bar{p}-p}{\sqrt{\frac{p(1-p)}{n}}}\\ &=\frac{0.9595-0.50}{\sqrt{\frac{0.5(1-0.5)}{914}}}\\ &=\frac{0.4595}{0.0165}\\ &=27.8484\end[/tex]

(c) The p-value

The p-value is the probability that the sample results are extreme or more extreme than the sample results obtained, assuming the null hypothesis is true. In this case,

the p-value is p = P (Z> 27.8484) = 0

(d) The decision on the null hypothesis

Using the traditional method

Since we observe that Z = 27.8484> Zc = 2.3263, we conclude that the null hypothesis is rejected.

Using the p-value method

Using the approximation of the P-value: the p-value is p = 0, and since p = 0≤0.01 we conclude that the null hypothesis is rejected.

(e) Conclusion

It is concluded that the null hypothesis H is rejected. Therefore, there is sufficient evidence to state that the population proportion p is greater than 0.5, at the significance level of 0.01.

Hence, for 914 babies born to parents using the new method, of which 877 were girls, the test statistic is 27.8484, the p-value is 0, and the final conclusion is that the null hypothesis is rejected.

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The period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

The function is given as:

y = 2∕3 cos(4∕7x) + 2.

The above function is a cosine function

A cosine function is represented as:

y = A cos(B(x + C)) + D

Where the period is

Period = 2π/B

By comparing the equations, we have

B = 4/7

Substitute B = 4/7 in Period = 2π/B

Period = 2π/(4/7)

Express as product

Period = 2π * 7/4

Divide 4 by 2

Period = π * 7/2

Evaluate the product

Period = 7/2π

Hence, the period of the function y = 2∕3 cos(4∕7x) + 2. is 7/2π

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The probability is P = 0.135

First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.

The joint probability is given by the product between the individual probabilities, so we get:

P = (1/2)*(3/6)*(28/52) = 0.135

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well, when it comes to fractions or rationals, they can never have a denominator that's 0, because if that ever happens, the fraction becomes undefined, so the values of "x" or namely the domain values, that we cannot have because they make the fraction undefined are those values that make the denominator 0, we can simply get them by setting the denominator to 0 and check what's "x".

[tex]x^2-9=0\implies x^2=9\implies x=\pm\sqrt{9}\implies x=\pm 3 \\\\[-0.35em] ~\dotfill\\\\ g(x)=\cfrac{x+6}{x^2-9}\hspace{5em} x\ne \begin{cases} 3\\ -3 \end{cases}[/tex]

[tex](g-f)(x)=g(x)-f(x)=2x-(-x)=3x[/tex]

The graph is shown in the attached image.

Answer:

y=5

Step-by-step explanation:

OK, let see, 2x+y=7, –3x+y=2:

[tex]2x + y = 7 \\ - 3x + y = 2 \\ we \: need \: to \: solve \: the \: equation \: so \\ - 2x - y = - 7 \\ - 3x + y = 2 \\ - 5x = - 5 = = > x = 1 \\ 2(1) + y = 7 = = = > y = 5[/tex]

There are 7 pounds in 112 ounces

There is 1 pound in 16 ounces

So, the number of pounds in 112 ounces is

Pounds = 116 ounces/16 ounces

Remove the unit

Pounds = 112/16

Evaluate the quotient

Pounds = 7

Hence, there are 7 pounds in 112 ounces

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The number of new cases be on Thursday after all of this growth and falling is 956.

An equation is an expression that shows the relationship between two or more variables and numbers.

There are initially 800 cases, hence:

Number of cases on Monday = 1.15 * 800 = 920

Number of cases on Tuesday = 1.05 * 920 = 966

Number of cases on Wednesday = 0.9 * 966 = 869.4

Number of cases on Thursday = 1.1 * 869.4 = 956.34

The number of new cases be on Thursday after all of this growth and falling is 956.

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The area of the triangle which is formed as described is; 60.

According to the task content, when Point A(5,6) is reflected over the y-axis, the point B formed is; (-5,6) and when reflected over both axis, the point C formed is; (-5,-6).

It therefore follows that the length of segments AB and BC which represents the base and height of the triangle formed are; 10 and 12 respectively.

Therefore, the area of the triangle is; (1/2) × 10 × 12 = 60.

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Let [tex]S(t)[/tex] denote the amount of salt (in lbs) in the tank at time [tex]t[/tex] min up to the 10th minute. The tank starts with 100 gal of fresh water, so [tex]S(0)=0[/tex].

Salt flows into the tank at a rate of

[tex]\left(0.5\dfrac{\rm lb}{\rm gal}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = 1\dfrac{\rm lb}{\rm min}[/tex]

and flows out with rate

[tex]\left(\dfrac{S(t)\,\rm lb}{100\,\mathrm{gal} + \left(2\frac{\rm gal}{\rm min} - 2\frac{\rm gal}{\rm min}\right)t}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = \dfrac{S(t)}{50} \dfrac{\rm lb}{\rm min}[/tex]

Then the net rate of change in the salt content of the mixture is governed by the linear differential equation

[tex]\dfrac{dS}{dt} = 1 - \dfrac S{50}[/tex]

Solving with an integrating factor, we have

[tex]\dfrac{dS}{dt} + \dfrac S{50} = 1[/tex]

[tex]\dfrac{dS}{dt} e^{t/50}+ \dfrac1{50}Se^{t/50} = e^{t/50}[/tex]

[tex]\dfrac{d}{dt} \left(S e^{t/50}\right) = e^{t/50}[/tex]

By the fundamental theorem of calculus, integrating both sides yields

[tex]\displaystyle S e^{t/50} = Se^{t/50}\bigg|_{t=0} + \int_0^t e^{u/50}\, du[/tex]

[tex]S e^{t/50} = S(0) + 50(e^{t/50} - 1)[/tex]

[tex]S = 50 - 50e^{-t/50}[/tex]

After 10 min, the tank contains

[tex]S(10) = 50 - 50e^{-10/50} = 50 \dfrac{e^{1/5}-1}{e^{1/5}} \approx 9.063 \,\rm lb[/tex]

of salt.

Now let [tex]\hat S(t)[/tex] denote the amount of salt in the tank at time [tex]t[/tex] min after the first 10 minutes have elapsed, with initial value [tex]\hat S(0)=S(10)[/tex].

Fresh water is poured into the tank, so there is no salt inflow. The salt that remains in the tank flows out at a rate of

[tex]\left(\dfrac{\hat S(t)\,\rm lb}{100\,\mathrm{gal}+\left(2\frac{\rm gal}{\rm min}-2\frac{\rm gal}{\rm min}\right)t}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = \dfrac{\hat S(t)}{50} \dfrac{\rm lb}{\rm min}[/tex]

so that [tex]\hat S[/tex] is given by the differential equation

[tex]\dfrac{d\hat S}{dt} = -\dfrac{\hat S}{50}[/tex]

We solve this equation in exactly the same way.

[tex]\dfrac{d\hat S}{dt} + \dfrac{\hat S}{50} = 0[/tex]

[tex]\dfrac{d\hat S}{dt} e^{t/50} + \dfrac1{50}\hat S e^{t/50} = 0[/tex]

[tex]\dfrac{d}{dt} \left(\hat S e^{t/50}\right) = 0[/tex]

[tex]\hat S e^{t/50} = \hat S(0)[/tex]

[tex]\hat S = 50 \dfrac{e^{1/5}-1}{e^{1/5}} e^{-t/50}[/tex]

After another 10 min, the tank has

[tex]\hat S(10) = 50 \dfrac{e^{1/5}-1}{e^{1/5}} e^{-1/5} = 50 \dfrac{e^{1/5}-1}{e^{2/5}} \approx \boxed{7.421}[/tex]

lb of salt.

The number of 150-pound gas cylinders are used each year  for the well is 22.

V = 500 gal/min x 1 year x 525600 min/year

V = 262,800,000 gallons =  994,806,216.835 liters

mass = density x volume

mass = 1.5 mg/L x 994,806,216.835 L

mass = 1,492,209,325 mg = 3289.75 lb

n = 3289.75 lb/150 lb

n = 21.9

n ≈ 22 gas cylinders

Thus, the number of 150-pound gas cylinders are used each year  for the well is 22.

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The net gain of the stock for these three days is 1 points

Net gain / net loss = Monday + Tuesday + Wednesday

= - 8 1/4 + (-2 3/4) + 12

= - 8 1/4 - 2 3/4 + 12

= -11 + 12

Net gain = 1 point

Therefore, the net gain of the stock for these three days is 1 points

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Answer:

D

Step-by-step explanation:

Yes a Linear Equation can be used and the slope and the y-intercept of the equation are respectively; B: slope = 10, y-intercept = 25

How to Write an equation in Slope Intercept Form?

We are given the coordinates;

(n, p) = (1, 35), (5, 75), (20, 225), (100, 1025)

Now, the way to find the slope is;

m = (y2 - y1)/(x2 - x1)

m = (75 - 35)/(5 - 1)

m = 10

The equation that models this is;

(y - 35)/(x - 1) = 10

y - 35 = 10x - 10

y = 10x + 25

Thus, y-intercept is at x = 0.

y = 10(0) + 25

y = 25

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The percentage discount from the base price result is 2.16%.

Discount percent will be:

= (Base price - New price)/Base price × 100

= (9.40 - 9.20)/9.40 × 100

= 0.20/9.40 × 100

= 2.16%

The new price will be:

= Base price - (2.16% of base price)

= 9.40 - (2.16% × 9.40)

= 9.20

Therefore, the percentage discount from the base price result is 2.16%.

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Complete question:

A rodent infestation has left a landlord with a major cleanup job; in fact, the cleanup will consist of ripping out all the walls and ceilings of an 1860-square-foot house to replace them. A trip to the local home improvement store reveals that 4'x8' sheets of drywall have three price points as indicated in the table. Another consideration for the landlord is that he is equipped with only a humble half-ton pickup truck, that can hold at most 20 sheets. His truck sips fuel, so he considers only wear and tear on his vehicle at $5 to haul all the sheets he will use for the job. The holding percentage is 20%. The landlord believes the entire job - all walls and ceiling - will require 10,080 square feet of drywall.

Consider the $9.40 per sheet figure as the base price and use the information in Scenario 11.4 to answer the following question. What percentage discount from the base price results in an optimal order quantity of 101 sheets?

1.42%

2.16%

2.03%

1.86%

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

Explanation:

These are the steps to focus on

step 3: -6x - 8 < -2

step 4: -6x < 6

The move from the third step to the fourth step has us adding 8 to both sides. Therefore, we use the addition property of inequality.

That property has four forms

It's similar to the idea of starting with a = b, then adding c to both sides to get a+c = b+c

We add the same thing to both sides to keep things balanced.

Based on the amounts that Janet Lopez has to invest in stocks and bonds, the linear programming model would be:

The return on stocks (x) is 18% and the return on bonds (y) is 6%, The objective function:

= 0.18x + 0.06y

There are constraints to watch out for:

Maximum to lose on stocks is 22% and on bonds is 5% but these are to be less than the total amount of $100,000.

0.22x + 0.05y ≤ 100,000

The total amount to invest is $72,000 which means that both bonds and stocks need to be less than this amount:

x + y ≤ 720,000

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The complete proof for part D is given in the attached text. Hence, by the nature of the converse corresponding angle,

OP is parallel to MN. (OP ║ MN).

A mathematical proof is an argument that is inferential with respect to a mathematical assertion that demonstrates that the provided assumptions logically ensure the conclusion.

The complete proof for part D is given as follow:

If a transversal line "t" divides through OP and MN as given in the attached image, and SE and "T.F" are the divider of ∠QSD and ∠STM, then:

∠QSE = 1/2 ∠QSO; and

∠"STF" = 1/2 ∠STM

If the corresponding angle is ∠QST = "STF", then

QSD = "STF"

Hence, by the nature of the converse corresponding angle,

OP is parallel to MN

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The point that is on the graph of the function [tex]F(x) = 5^x[/tex] is given by:

D. (1,5).

The function is defined by:

[tex]F(x) = 5^x[/tex]

When x = 0, [tex]F(x) = 5^0 = 1[/tex], hence point (0,1) is on the graph of the function.

When x = 1, [tex]F(x) = 5^1 = 5[/tex], hence point (1,5) is on the graph of the function, which means that option D is correct.

When x = 5, [tex]F(x) = 5^5 = 3125[/tex], hence point (5,3125) is on the graph of the function.

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The correct answer is Yes. The graph represents a function. The function given is: F(x) = y(-5). Note that the value of x is zero.

A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f might similarly be defined as the graph of the equation y = f. (x).

Thus, the correct answer or function represented in the graph is f(x) = y(-5)

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Using equivalent angles, we have that the measures are given as follows:

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

120º is in the second quadrant, hence the equivalent on the first quadrant is:

180º - 120º = 60º.

The sine on the second quadrant is positive, hence:

[tex]\sin{120^\circ} = \sin{60^{\circ}} = \frac{\sqrt{3}}{2}[/tex]

The cosine on the second quadrant is negative, hence:

[tex]\cos{120^\circ} = \cos{60^{\circ}} = -\frac{1}{2}[/tex]

The tangent is given by the sine divided by the cosine, hence:

[tex]\tan{120^\circ} = \frac{\sin{120^\circ}}{\cos{120^\circ}} = -\sqrt{3}[/tex]

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The probability that it will have an annual snowfall greater than 170 inches is 0.4.

The information is incomplete and the complete question wasn't found. An overview will be given. It should be noted that a probability means the likelihood of the occurence of an event.

Probability is calculated as:

= Number of ways of achieving success/Total number of possible outcomes

Let's assume that the total number of resort is 10 and those that have more than 170 inches are 4.

In this case, the probability will be:

= 4/10

= 0.4

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Answer:

I think the answer is 3.

Step-by-step explanation:

First make arrow diagram of function f and g.

Then show it as composite function of fog(x) in arrow diagram.

Then in range you find -8 whose domain as x is 3.

The large cone can hold more ice cream than the four smaller cones combined.

The large cone is a better deal.

A cone is a three-dimensional structure with a round base and a point at the top, known as the vertex.

A cone is a three-dimensional solid geometric object with a point at the top and a circular base. A cone has a vertex and one face. For a cone, there are no edges.

The radius, height, and slant height of the cone are its three constituent parts.

For the supersized cone,

Volume = π(5)(5)(12)/3 = 314.29 cubic inches

For a small cone,

Volume= π(2.5)(2.5)(6)/3 = 39.29 cubic inches

Combined volume of 4 such cones = 4*39.29 = 157.16 cubic inches

As the volume of the larger cone is more, thus it holds more ice cream. Also it is a better deal, as it costs less than 4 small cones.

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Using translation concepts, it is found that the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Considering the translations, the equivalent point is found as follows:

Hence the point (0, 0) on the graph of f(x) corresponds to point (4,-7) on g(x).

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Answer:

1000

Step-by-step explanation: