Stacy was a stay-at-home mom for most of her adult life. At age 46, she started working outside the home. Each year she earns the maximum number of Social Security credits. Until what age must she work to qualify to receive Social Security benefits when she retires?

Since the angles in DBC and BDA are equal, we have:

DBC ≅ BDA

What is the Angle-Angle Similarity Theorem?

The Angle-Angle Similarity Theorem, also known as the AA Similarity Theorem, states that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Given: AD // BC, AB // CD

To prove: DBC =~ BDA

From the given, we have AD // BC and AB // CD.

This means that AD is parallel to BC and AB is parallel to CD.

Since AB is parallel to CD, corresponding angles are equal.

Let the angle BCD = x.

Then, angle BAD = x.

Since AD // BC, corresponding angles are equal.

Let the angle DCB = y.

Then, angle DAC = y.

Now, we can see that angle BDA + angle DAC = y + x.

And angle DBC + angle DCB = y + x.

Since the sum of the angles in a triangle is 180 degrees,

angle BDA + angle DAC + angle DBC = 180.

So, y + x + y + x = 180.

Therefore, 2y + 2x = 180.

And, y + x = 90.

Since the angles in DBC and BDA are equal, we have:

DBC =~ BDA

To learn more about Angle-Angle Similarity Theorem, Visit

https://brainly.com/question/21247688

#SPJ1

The equation we need is[tex]P(3 < =x < =5) = (x^3 - 3x^2 + 5x - 3)/24[/tex]. We can solve this in R by using the dbinom() function. The code is: dbinom(3:5, size=4, prob=0.25) which yields an answer of 0.3125. This means that the probability of 3 to 5 bicycle accidents occurring in the next four months is 0.3125.

The equation for the probability of a certain number of bicycle accidents occurring in the next four months is [tex]P(x) = (x^3 - 3x^2 + 5x - 3)/24[/tex], where x is the number of accidents. To solve this equation with R, we can use the dbinom() function which is used to calculate the binomial cumulative distribution function. We set the size parameter to 4 (the number of months) and the probability parameter to 0.25 (the probability of a bicycle accident occurring at the intersection in a single month). The code is dbinom(3:5, size=4, prob=0.25). This yields an answer of 0.3125, meaning that the probability of 3 to 5 bicycle accidents occurring in the next four months is 0.3125. This calculation is useful for understanding the likelihood of certain numbers of bicycle accidents occurring in a given time period, and can be used to inform decisions about safety at intersections.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Answer:

The answer is 3.2 x 10-21.

Step-by-step explanation:

To solve this problem, we need to use the rules of exponents. The first step is to calculate the exponents for each number.

For 9 × 104, the exponent is 3 (9 × 104 = 90000).

For 3,000,000, the exponent is 2 (3,000,000 = 3000000).

For 0.00243, the exponent is -3 (0.00243 = 0.00000243).

Now, we can calculate the answer by multiplying the exponents:

3 × 2 × (-3) = -6

Then, we need to multiply the numbers together to get the final answer:

(9 × 104)² × (3,000,000)² × (0.00243) = 9 x 10-6 x 9 x 10-12 x 0.00243 = 3.2 x 10-21.

The coordinates of triangle ABC after dilation are; (-6, -3), (0, 9) and (3, 3)

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

Given that, a triangle ABC with coordinates, A (-2, -1) B (0, 3) C (1, 1)

This triangle is dilated by a scale factor of 3,

SInce, the scale factor is greater than 3, therefore, dilation shows an enlargement.

The rule of dilation is given by;

(x, y) → (kx, ky), where k is dilation factor.

Let triangle ABC is dilated to form triangle A'B'C'

Therefore, the coordinates of triangle A'B'C' are;

A' = 3(-2, -1) = (-6, -3)

B' = 3(0, 3) = (0, 9)

C' = 3(1, 1) = (3, 3)

The graph is attached.

Hence, the coordinates of triangle ABC after dilation are; (-6, -3), (0, 9) and (3, 3)

Learn more about dilation, click;

https://brainly.com/question/14976170

#SPJ1

This can be modeled as a Poisson distribution. The mean number of patients admitted per day is 2.5, so the Poisson parameter λ = 2.5. The probability that the hospital will not have enough beds on any given day is the probability that more than 1 patients will be admitted, which is given by:

P(X > 1) = 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - (e^-2.5 * 0 + e^-2.5 / 1!)

= 1 - e^-2.5 * (1 + 2.5)

This is the probability that the hospital will not have enough beds to accommodate its newly admitted patients on any given day.

To know more about Probability

https://brainly.com/question/13604758

#SPJ4

The written description of the given expression would be 14 less a number. That is option A.

Less than which is represented by the symbol such as < is used in arithmetics to show that a given value is less than the value of which it is being compared to.

The given expression = X - 14. Where X is the unknown number which is compared with 14.

Therefore, according to the expression, 14 less than a number is the same as X - 14.

Learn more about subtraction here:

https://brainly.com/question/28467694

#SPJ1

Answer: 4a = D; 4b = B

Step-by-step explanation:

Yes she is correct, because 810 km is approximately 500 miles

Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

The distance between Cale and Johannesburg is 810 km.

1 mile is converted as 1.609km

There 1km = 1/1.609 miles

810 km = 1/1.609 × 810

= 503.4 miles

If this value is approximated to the nearest hundred,then it will be

500 miles

learn more about distance from

https://brainly.com/question/26046491

#SPJ1

According to the information in the table, the histogram would be as shown in the attached image.

To graph the information in the table we must take into account the relationship of the data. On the one hand we have the frequency, which is the data that varies, and the different variations of time.

In accordance with the above, what we want to demonstrate with this table are the different frequencies of time that students take to do their math homework. Additionally, most students take between 10 and 25 minutes to do their math homework.

Learn more about histogram in: https://brainly.com/question/30354484

#SPJ1

The equation of line m passing through the points (0, 0) and (1, 6) is y = 6x

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Line M goes through the points (0, 0) and (1, 6). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-0=\frac{6-0}{1-0} (x-0)\\\\y=6x[/tex]

The equation of line m is y = 6x

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The code from solving the expressions is MGWMGWW

1. 7b

2. 6y - 1

3. -m + 0.5

4. 9x - 2y

5. 4j

6. -12x + 22

7. 6m - 8

Algebraic expressions are expressions that are composed of coefficients, variables, terms, factors and constants.

They also consist of mathematical operations, such as;

Given the expression;

b + b + b + b + 3b

collect the like terms

7b

2(4y-  3) - 2x + 5

collect like terms

6y - 1

Hence, the code is MGWMGWW

Learn about algebraic expressions on:

https://brainly.com/question/4344214

#SPJ1

The financial planner invested $4,737.50 in the mini-mall development plan and $1,012.50 in the savings account.

The amount invested in the savings account is equal to the total amount invested minus the amount invested in the mini-mall development plan. We can express this as an equation:

Total Investment - Investment in Mini-Mall Development Plan = Investment in Savings Account

Substituting the values given in the problem, we get:

$5,750 - Investment in Mini-Mall Development Plan = Investment in Savings Account

To solve for the Investment in Mini-Mall Development Plan, we need to use the combined interest earned for the first year. We can express this as an equation:

Interest Earned = (Investment in Savings Account x Interest Rate) + (Investment in Mini-Mall Development Plan x Interest Rate)

Substituting the values given in the problem, we get:

$475 = (Investment in Savings Account x 0.02) + (Investment in Mini-Mall Development Plan x 0.12)

Solving for Investment in Mini-Mall Development Plan, we get:

Investment in Mini-Mall Development Plan = ($475 - (Investment in Savings Account x 0.02))/0.12

Substituting the values given in the problem, we get:

Investment in Mini-Mall Development Plan = ($475 - ($5,750 - Investment in Mini-Mall Development Plan x 0.02))/0.12

Solving for Investment in Mini-Mall Development Plan, we get:

Investment in Mini-Mall Development Plan = $4,737.50

Therefore, the financial planner invested $4,737.50 in the mini-mall development plan and $1,012.50 in the savings account.

Learn more about savings account here:

https://brainly.com/question/9279115

#SPJ4

The value of p such that the matrix M does not have an inverse is given as follows:

p = -5.

The matrix M for this problem is given as follows:

M = [7 2

       p -1].

As it is a 2 x 2 matrix, the determinant is obtained with the multiplication of principal diagonal subtracted by the multiplication of the secondary diagonal, hence:

|M| = -7 - 2p.

The matrix does not have an inverse if the determinant assumes a value of zero, hence the value of p is obtained as follows:

-7 - 2p = 0

2p = -7

p = -7/2

p = -5.

More can be learned about matrices at https://brainly.com/question/2456804

#SPJ1

Yes, it would be unusual to get a score of 0 on a binomial distribution with a mean of 2.5 and a standard deviation of 1.4. This is because the expected value of such a distribution is much higher than 0.

Yes, it would be unusual to get a score of 0 on a binomial distribution with a mean of 2.5 and a standard deviation of 1.4. This is because the expected value of such a distribution is much higher than 0. The binomial distribution is a type of probability distribution which is used to describe the probability of a discrete event occurring a certain number of times in a given number of trials. The mean of the binomial distribution is the expected value of the events, while the standard deviation is a measure of how much the values of the events vary from the expected value. In this case, the expected value is 2.5, and the standard deviation is 1.4. This means that the probability of getting a score of 0 is quite low, since the expected value is so much higher than 0. Therefore, it would be considered unusual to get a score of 0 on this binomial distribution.

Learn more about standard deviation here

https://brainly.com/question/13905583

#SPJ4

The number of terms in the sequence is given as follows:

135 terms.

The general notation of a sequence is given as follows:

[tex]\sum_{m = a}^{k} f(m)[/tex]

The parameters are given as follows:

Hence the number of terms in the sequence is obtained as follows:

n = k - a + 1.

The parameter values for this problem are given as follows:

a = 1, k = 135.

Considering the parameter values above, the number of terms of the sequence is given as follows:

n = 135 - 1 + 1

n = 135.

More can be learned about sequences at https://brainly.com/question/27868858

#SPJ1

The length of ED is,  3√10

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

In a figure,

⇒ PB = BC = 6

Now, By the figure,

⇒ ΔFPD and ΔEMD are congruent.

Hence, We can formulate;

⇒ FP / EM = PD / MD

Let the length of MD = x

⇒ FP / EM = PD / MD

⇒ 6 / 3 = (9 + x) / x

⇒ 2x = 9 + x

⇒ 2x - x = 9

⇒ x = 9

Hence, The length of MD = 9

Now, In  ΔEMD;

⇒ ED² = EM² + MD²

⇒ ED² = 3² + 9²

⇒ ED² = 9 + 81

⇒ ED² = 90

⇒ ED = √90

⇒ ED = 3√10

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

The solution is, the retail price of the mattress, before the discount is $2,400. & the wholesale price, before the markup was $960

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

Part A:

Given that the mattress is sold for 50% off of the retail price, let the retail price of the mattress be x, then

50% of x = 1200

⇒ 0.5x = 1200

⇒ x = 1200 / 0.5 = 2400

Therefore, the retail price of the mattress, before the discount is $2,400.

Part B:

Given that the store marks up the retail price to 150% of the wholesale price. Let the whole sale price be p, then

(100% + 150%) of p = 2400

250% of p = 2400

2.5p = 2400

p = 2400 / 2.5 = 960.

Therefore, the wholesale price, before the markup was $960.

To learn more on percentage click:

brainly.com/question/13450942

#SPJ1

Answer:

The volume of the rectangular prism can be calculated by multiplying its length, width, and height: 8 x 4.12 x 3.12 = 128.064 cubic inches.

Answer:

V=342,784in

Step-by-step explanation:

V=1/3(L×W×H)

where v=volume of rectangular prism,L=length.W=width or breadth,H=height

V=1/3×8×412×312

V=342,784in

Answer:

C. 6/48

Step-by-step explanation:

mutliply both numerator and denominator

The required value of angle x for a given hexagon is 20°.

What is a hexagon?

In terms of geometry, a hexagon is a closed, six-sided polygon in two dimensions. Six vertices and six angles make up a hexagon. The words "hexa" and "gonio" both refer to six.

A hexagon's internal angles add up to 720°. All of the sides and interior angles of a regular hexagon are the same lengths.

Given, the interior angles of a hexagon are 7x°, 7x°, 4x°, 7x°, 7x°, and 4x° respectively.

So, the sum of interior angles = 720°

or, 7x° + 7x° + 4x° + 7x° + 7x° + 4x° = 720°

or, 36x° = 720°

or, x = 720/36

or, x =20°

Hence, the required value of x is 20°.

To learn more about the hexagon

https://brainly.com/question/15424654

#SPJ1

Answer:

Step-by-step explanation:

1.  ΔONG≅ΔLMI

2.  1:2

3. ON = 12

   NG = 30

4.  P-ONG = 6+7.5+12 = 25.5

    P-LIM = 12+15+24 = 51

5.  1:2

The second segment crosses the x-axis at (1.5, 0), and the slope of the segment is -1

The area under any probability density curve is always 1 and it is used for finding out the probabilities for any random variable X taking a certain range of values.

Let the second segment crosses at (a,0) on the X-axis:

The area under the density curve is 1.

the given fig can be divided into a rectangle and a triangle by dropping a line from the point (0.5, 1) in the x-axis.

The coordinate point of the second segment at the x-axis:

Now,

1*0.5+1/2*1*(a-0.5)=1

1+(a-0.5)=2

a-0.5=2-1

a=1+0.5

a=1.5

Thus the second segment crosses the x-axis at (1.5, 0)

The slope of that segment c:

The slope  of that segment=y₂-y₁/x₂-x₁

By considering the points (0.5, 1) and (1.5, 0)

We will have the slope as:

m=0-1/1.5-0.5

m=-1/1

m=-1

the equation of the line containing this segment:

The line passes from the point (0.5, 1)

y=mx+b is used to find the value of the intercept

so, substitute the values in the equation:

1=(-1)*0.5+b

1=-0.5+b

b=1.5

so, the equation for that line segment is

y=-x+1.5

x+y=1.5

To calculate the probability P(X > 1):

[tex]P(X > 1)=\int\limits\limits^1_1 {y} \, dx \\P(X > 1)=\int\limits^1_1 {(-x+1.5)} \, dx[/tex]

[tex]P(X > 1)=[\frac{-x^2}{2}+1.5x]_1^1^.^5\\\\P(X > 1)= (\frac{(-1.5)^2}{2} +1.5*1.5)-(\frac{-1^2}{2}+1.5*1)\\[/tex]

P(X>1)=-1.125+2.25+0.5-1.5

P(X>1)=0.125

To know more about the slope:

https://brainly.com/question/1884491

#SPJ4

Answer:

If x-y=9 is a true equation, we can substitute this equation into 5+x−y to find its value.

5 + x - y

= 5 + x - (x - 9) (since x - y = 9)

= 5 + x - x + 9

= 5 + 9

= 14

So, the value of 5 + x - y would be 14 if x-y=9 is a true equation.

Answer:

angle 1 = 26 degrees angle 2 is 154 degrees

DONT FORGET TO PUT THE DEGREES SIGN IN YOUR ANSWER

Step-by-step explanation:

Since the angles add up to a straight line, or 180 degrees, the equation is

(x+4)+7x=180 degrees

8x+4=180

8x=176

x=22

so, angle 1 is 26, angle 2 is 154 degrees

Note that 11 > S or S < 11 is given in the in the Line Graph attached. The above simply means that 11 as a quantity is greater that the factore represented by "s".

A line graph is a graphical depiction of changing information over time. It is a diagram created by connecting points with line segments.

Line graphs may be used to demonstrate how something evolves over time.

Line graphs are useful for displaying data that has peaks (ups) and troughs (downs) or was gathered in a short period of time. The pages that follow discuss the various components of a line graph.

Learn more about Line Graph:

https://brainly.com/question/23680294

#SPJ1

Answer:

cant see it clearly

Step-by-step explanation:

bc it's to far

Answer:

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Let x be the distance between 1st Street and 2nd Street along Pike Avenue.

As 1st Street and 2nd Street are parallel we can use the Side Splitter Theorem to calculate x:

[tex]\implies \sf x:300=40:40+160[/tex]

[tex]\implies \sf x:300=40:200[/tex]

[tex]\implies \sf \dfrac{x}{300}=\dfrac{40}{200}[/tex]

[tex]\implies \sf x=\dfrac{40}{200} \cdot 300[/tex]

[tex]\implies \sf x=60\; ft[/tex]

To calculate the distance between 2nd Street and the landmark along Pike Avenue, subtract the found distance between 1st Street and 2nd Street along Pike Avenue from the length of Pike Avenue:

[tex]\implies \sf 300-60=240\; ft[/tex]