You are building a ramp for your grandparent’s house. The ramp will replace the steps that go to their front door which is 3 feet off the ground. You want the ramp to start 10 ft from the front door. How long will the ramp need to be?

Answer:

2 : 12

Step-by-step explanation:

There are 2 blue triangles, so 2 will come first. It's then followed by the sum of blue and yellow, which is 2 + 10, which is 12. So, the ratio is 2 : 12.

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The expected value for the person buying the insurance is -25.

The expected value is the average gain or loss of an event if the event is repeated a number of times.

Expected value = ∑xP(x)

It is given that,

The probability of a 47-year-old woman passing away during the coming year is 0.179% = 0.00179

The death benefit = $100,000 - $204 = $99,796

The loss from living = -204

Then the expected value = 99796(0.00179) + (-204)(0.99821) = -25

Therefore, the expected value for the person buying the insurance is -25.

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Answer:

6a. 13.5m

6b. 12.4m

Step-by-step explanation:

We can use trig identities to solve these problems because each triangle is a right triangle.

6a. Find the measure of the hypotenuse.

Using the angle in the top corner, which is defined as 66 degrees and its adjacent side, we can find the hypotenuse. Remember that the hypotenuse is the longest side, which in this case would be AB. The adjacent side is the side next to the angle that is not the hypotenuse, in this case it would be AC, which is shown to be 5.5m.

The trig identity cos(x) is defined as adjacent/hypotenuse, or the value of the adjacent side divided by the value of the hypotenuse, where x is the degrees of the angle.

So we can set up the equation:

cos(x)=adj/hyp

If we know that x=66 (the degree of the angle) and adj=5.5m, we can substitute this into the equation. Let c represent the hypotenuse.

cos(66)=5.5/c

Then we can multiply by c:

c*cos(66)=5.5

Then divide by cos(66):

c=5.5/cos(66)

Use a calculator to estimate that c approximately equals 13.5m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).

6b. Find the measure of side a.

Side a is the side opposite to angle A. This can also be known as side CB or the bottom of the triangle.

Method 1: Use trig identity tan(x)tan(x)=opp/adj

Remember x=66 and adj=5.5m. Let a represent the opposite side. Plug in these values into the equation:

tan(66)=a/5.5

Multiply both sides by 5.5:

a=tan(66)*5.5

Use a calculator to estimate that a approximately equals 12.4m when rounded to the nearest tenth (remember to use degree mode because our angle is measured in degrees).

Method 2 (I would recommend method 1, however because you are basing this answer off of the first answer, and in a test or a quiz, you might not be sure if your first answer was correct):

Use Pythagorean Theorem:

a^2+b^2=c^2

c, or the hypotenuse is 13.5m as found in out last problem, and b, the adjacent side is 5.5m which was a given. Substitute these values into the equation:

a^2+5.5^2=13.5^2

a^2+30.25=182.25

a^2=152a=sqrt(152) which rounds to 12.3m, which is almost the same as Method 1, however our answers are different because we used a rounded value of b, rather than the approximate.

The largest size of a team according to the task content is; 20 kids.

It follows from the task content that the population is; 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class.

However, since, the team forming condition states that students be placed on teams of equal size with students from only their own class.

It therefore follows that the largest size of a team is 20 as only 20 students are in Mrs. Tanya's class hence leaving 4 kids in Mrs. Olga's class without a team.

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The percentage of vehicle mileage expectancies that are more than 188,600 miles is 93%

The given parameters are:

Mean = 169200

Standard deviation = 19400

x = 188600

Calculate the z value using:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

So, we have:

[tex]z = \frac{188600 - 169200}{19400}[/tex]

Evaluate

z = 1

Using the Empirical Rule, we have:

P(x > 188600) = P(z > 1.5)

From z table of probability, we have:

P(x > 188600) = 0.93319

Express as percentage

P(x > 188600) = 93.319%

Approximate

P(x > 188600) = 93%

Hence, the percentage of vehicle mileage expectancies that are more than 188,600 miles is 93%

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Answer:

D.{15,23,25,38,53}

Step-by-step explanation:

Replace f(x) with any other variables of your choice.

Substitute the value of the variable for the given set of hits

that is {4,12,14,27,42}

Solve for x for each value of the variable from the above set

Put all the solution for x in a set that is inside {,} brackets.

The correct option should be D

The two figures are similar because each side length of the image is times the corresponding side length of the preimage and all the pairs of corresponding angles are congruent.

The transformations are given as:

Rotation and translation would preserve the lengths and the angles of the triangles. Because they are rigid transformations.

Dilation would only preserve the angle of the triangles. Because it is a nonrigid transformation.

The above means that the angles of triangle PQR and triangle P'Q'R' are congruent

Hence, the true statement is (d)

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The equation of the axis of the curve is determined by (c) c

The equation is given as:

y= a sin[k(x - d)] + c

In the above equation, the midline is

y = c

This represents the equation of the curve axis

Hence, the equation of the axis of the curve is determined by (c) c

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The customer will to pay $2,970 in 12 days.

What does 3/10 mean?

3/10 is cash discount term which means that a discount of 3% would be given to the customer if payment for the goods purchased is made within 10 days of purchase.

In this  case, 3% is not applicable since the payment was made after 12 days.

What does 1/20 mean?

1/20 is cash discount term which means that a discount of 1% would be given to the customer if payment for the goods purchased is made within 20 days of purchase, the payment is within this range, hence, a 1% discount would be applied to invoice price so as to determine the cash payable

cash payable=$3,000*(1-1%)

cash payable=$3,000*0.99

cash payable=$2,970

What does n/30 mean?

It means a payment is expected latest after 30 days which does not entitle the customer no discount.

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Answer: 175 ft squared

Step-by-step explanation: A= a + b / 2h= 20 + 152 · 10 = 175

250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.

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

Let x represent the amount of alloy #11 and y represent the amount of alloy #15, hence:

(0.36x) + (y * 0.36) = 1(0.36)   (1)

Also:

0.28x + 0.64y = 1(0.55)    (2)

From both equations:

x = 0.25, y = 0.75

250 grams of dragon alloy #11 and 750 grams of dragon alloy #35 is needed to make 1000 grams (1 kg) of Dragon alloy #17.

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Debido a restricciones de longitud invitamos cordialmente a leer la explicación de esta pregunta para aprender sobre las cuestiones de las ecuaciones cónicas.

Según la geometría analítica, existen cinco tipos de secciones cónicas: recta, circunferencia, elipse, parábola e hipérbola. Aquí se presentan problemas que emplean este tipo de ecuaciones.

1) La trayectoria de la rana describe la forma de una parábola. Asumimos que el punto máximo de la trayectoria de la rana es de la forma (h, k) = (0, k), entonces tenemos que la ecuación de la parábola es:

y - k = C · x²       (1)

Donde C es la constante del vértice.

Si sabemos que (h, k) = (0, 3) y (x, y) = (9, 0), entonces la ecuación de la parábola es:

C = (0 - 3) / 9²

C = - 1 / 27

La ecuación de la parábola es y - 3 = (- 1 / 27) · x².

2) Se determina el tipo de categoría de cada ecuación:

a) 3 · x - 2 · y + 4 = 0: Recta (a · x + b · y + c = 0)

b) 4 · x + y² - 7 = 0: Parábola ((y² - k) = 4 · p · (x - h))

c) x² + y² = 16: Circunferencia ((x - h)² + (y - k)² = r²)

d) y = x³ - 3 · x + 1: Ecuación cúbica

e) x² + 4 · y² = 4: Elipse (b² · (x - h)² + a² · (y - k)² = a² · b²)

3) Se debe hallar el valor C de la función lineal tal que S = 0.35 por medios algebraicos:

0.35 = 0.03 + 1.805 · C

0.32 = 1.805 · C

C = 0.32 / 1.805

C = 0.177

4) El arco semielíptico tiene una longitud de semieje mayor de 25 pies (paralelo al eje x) y una longitud de semieje menor de 15 pies (paralelo al eje y). Si consideramos que el centro de la elipse está en el origen, entonces tenemos que la ecuación es:

x² / 25² + y² / 15² = 1

y = 15 · √(1 - x² / 25²)

y = 15 · √(1 - 12² / 25²)

y = 13.159 pies

5) a) y b) Ahora graficamos la hipérbola y presentamos las ubicaciones de los focos y las asíntotas correspondientes. a) Las ecuaciones de las asíntotas son y = ± (3 / 2) · x, b) Las ecuaciones de las asíntotas son y = ± (√ 2 / 2) · x.

c) Se puede determinar la naturaleza de cada ecuación por métodos algebraicos:

9 · x² - 4 · y² - 54 · x - 16 · y + 29 = 0

[9 · x² - 2 · 9 · (3 · x) + 81] - [4 · y² - 2 · 8 · (2 · y) + 64] = 116

(3 · x - 9)² - (2 · y - 8)² = 116

9 · (x - 9)² - 4 · (y - 4)² = 116

(x - 9)² /12.889 - (y - 4)² / 29 = 1  - Hipérbola

4 · x² + 2 · y² - 7 · x + y - 5 = 0

[4 · x² - 2 · (7 / 4) · (2 · x) + 49 / 16] + [2 · y² + 2 · (√2 / 2) · (√2 · y) + 1 / 2] = 5

(2 · x - 7 / 4)² + (√2 · y + √2 / 2)² = 5

4 · (x - 7 / 8)² + 2 · (y + 1 / 2)² = 5

(x - 7 / 8)² / 1.25 + (y + 1 / 2)² / 2.5 = 1  - Elipse  

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Answer:

Let's go through the following example to show how to solve a system of equations by graphing. I won't solve this system, I will just show how to.

[tex]8x-3y = 17\\4x+y=21[/tex]

If you have an online grapher (like Desmos) at your disposal, then you can put each equation in it as it is.

1. Get both equations in the form [tex]y=mx+b[/tex] by solving for y.

[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex]               [tex]4x+y=21\\y=-4x+21[/tex]

2. Put both equations in the graphing calculator

1. Get both equations into the form [tex]y=mx+b[/tex] by solving for y.

[tex]8x-3y=17\\-3y=-8x+17\\y=\frac{8}{3}x-\frac{17}{3}[/tex]                    [tex]4x+y=21\\y=-4x+21[/tex]

2. Plug in a few different points for x and calculate their y-values.

3. Plot those points on the graph paper

The information that can be collected to make an insurance policy will be information regarding the drivers.

It should be noted that the probability simply means the likelihood of the occurence of an event.

In this case, when choosing a car insurance policy, we can use the probability to determine the likelihood for the need to file a claim.

The course of action is to survey a number of drivers to get information from them.

Also, the benefit of this approach is that the food drivers can pay less premium while the disadvantage can be the cost that's involved.

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1. A situation that can use probability to make an informed decision is when deciding on an insurance policy to take.

2. The information that you would collect for an insurance policy decision includes insurance:

3. An understanding of probability helps the policyholder to:

Using probability, the insurance policyholder enjoys these benefits:

However, the limitations of probability in measuring insurance risks become prominent under the following situations:

Thus, probability analyzes insurance policies to determine the best plans and their deductible amounts.

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The measure of Angle EDH = 50°.

The angle EDH exists given as 5x° and the angle HDG exists given as 4x°. The angles EDG and FGD exist at right angles. That signifies both angles exist equivalent to 90°.

Angle EDH = 5x°

Angle HDG = 4x°

Angle EDG = 90°

5x + 4x = 90

9x = 90

Divide both sides by 9

x = 90/9

x = 10°

Angle EDH = 5x = 5 × 10 = 50°

The measure of Angle EDH = 50°.

Therefore, the correct answer is option c) 50°.

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The interval notation of the possible values of x according to.the given inequalities is; -3 > x and x>= 2.

The interval notation of the given inequalities which describes the possible value of x according to the task content are as follows;

For − 2 x − 2 > 4; we have;

− 2 x > 4 +2

-2x > 6

x < -3.

For − 8 x − 7 ≤ − 23; we have;

− 8 x ≤ − 23 +7

-8x ≤ -16

x >= 2.

Consequently, the interval notation of the given inequalities is; -3 > x and x >= 2.

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The true options regarding the triangle diagram are;

m∠5 + m∠6 = 180°

m∠2+ m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

We see the attached image showing ΔABC with Exterior angles as;

∠ 1 , ∠ 4 ,and ∠ 6

Now, the exterior angle property of triangles states that; An exterior angle of a triangle is equal to the sum of the opposite interior angles.

For Exterior ∠1 we have;

∠1 = ∠5 + ∠3 (Exterior angle Property of Triangle)

Similarly,

For Exterior ∠ 4 we have;

∠4 = ∠5 + ∠2   (Exterior angle Property of Triangle)

For Exterior ∠6 we have;

∠6 = ∠2 + ∠3   (Exterior angle Property of Triangle)

From Triangle Sum Property, we know that the sum of the measures of angles in a triangle is equal to 180°. Thus;

m∠2 + m∠3 + m∠5 = 180° (Triangle Sum Property)

Linear Pair of angles states that the measure of a straight angle is 180° and as such a linear pair of angles must add up to 180°. Thus;

m∠5 + m∠6 = 180°  (Linear Pair)

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The expression [tex]\sqrt{\frac{5}{x-1} }[/tex] is equivalent to the given quotient.

Option A is correct.

When we divide one number by another, the result is a quotient. Although a quotient can be greater than the divisor, it will never be greater than the dividend.

In mathematics, the outcome of dividing a number by any divisor is known as the quotient. It refers to how many times the dividend contains the divisor.

After the division has been done, the quotient is obtained. This signifies that the quotient is the result of dividing a dividend by a divisor.

According to the question,

[tex]\sqrt{25(x-1)}[/tex] ÷ [tex]\sqrt{5(x-1)^{2} }[/tex] =  5[tex]\sqrt{x-1}[/tex] ÷ (x-1)[tex]\sqrt{5}[/tex]

                                     =  [tex]\sqrt{\frac{5}{x-1} }[/tex]

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Using it's concept, the probability that the teenager picked at random is male and their favorite hobby is playing video games is:

[tex]\frac{1}{16}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, it is found that out of 32 teenagers, 2 are males who prefer playing videogames, hence the probability is:

[tex]p = \frac{2}{32} = \frac{1}{16}[/tex]

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Answer:

$42,600

Step-by-step explanation:

284000 x .15

The point-slope equation of the line is: y - 2 = 8(x - 2).

The point-slope equation is: y - b = m(x - a), where:

Using the coordinates of the point shown in the graph, substitute (a, b) = (2, 2) and m = 8 into y - b = m(x - a):

y - 2 = 8(x - 2)

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Using the Poisson distribution, there is a 0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

A bank gets an average of 12 customers per hour, hence the mean is [tex]\mu = 12[/tex].

The probability that there will be 4 or more customers at this bank in one hour is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-12}12^{0}}{(0)!} \approx 0[/tex]

[tex]P(X = 1) = \frac{e^{-12}12^{1}}{(1)!} \approx 0[/tex]

[tex]P(X = 2) = \frac{e^{-12}12^{2}}{(2)!} = 0.0004[/tex]

[tex]P(X = 3) = \frac{e^{-12}12^{3}}{(3)!} = 0.0018[/tex]

Then:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0 + 0 + 0.0004 + 0.0018 = 0.0022.

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.0022 = 0.9978[/tex]

0.9978 = 99.78% probability that there will be 4 or more customers at this bank in one hour.

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Answer:

A = 30 ft²

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the height and b₁, b₂ the parallel bases , then

A = [tex]\frac{1}{2}[/tex] × 4 × (5 + 10) = 2 × 15 = 30 ft²

The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.

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

A non linear function is a function whose graph is not linear or can be represented by a straight line.

The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.

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Answer:

An equilateral triangle with a length of 2

Step-by-step explanation:

A 2-by-2 square implies that the square has a length and width of 2. Since equilateral triangles have the same length for all sides, it tells you that if one side is a certain length, all the other sides must have the same length. The largest length we can fit into this square would be 2 because any larger, the sides of the triangles would not fit into the square. Under the assumption that the length needs to be a whole number, the answer would be 2.

Answer:

a) 10/21 b) 5/21 c)1/21

Step-by-step explanation:

a) your have 7 choice and 5 or them or red, 5/7.  You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3.  We multiple these two numbers together:

5/7(2/3) = 10/21

b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7.  The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified).  We multiply these together.

5/7(1/3) =5/21

c)  I am assuming that you are still selecting 2 marbles.  The first draw would be 2/7.  This time I am selecting yellow and there are only 2 choices for yellow.  My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6.  We multiply these together

2/7(1/6) = 2/42 or 1/21

Answer:

both two

Step-by-step explanation:

because it is in alphabetical order

keeping in mind that the range is vertical values covered by the function, Check the picture below.