2) AABC and ADEF are shown below. The
m/A=51°and m/F =39°. Is AABC~ADEF?
Fill in the blanks with words from the
word bank then read it to see if it
sounds correct.
the triangles are
because all angles
and the sides are
Word bank: yes, no, maybe, parallel,
vertical angles, corresponding,
complimentary, congruent, right angles,
similar, proportional.

The probability that the student answers exactly 1 question correctly is

                            [tex]$\frac{135}{243}=\boxed{\frac{5}{9}}$[/tex]

What is the binomial coefficient?

In combinatorics, the binomial coefficient is used to denote the number of possible ways to choose a subset of objects of a given numerosity from a larger set.

There are a total of [tex]$3^5=243$[/tex] possible ways that the student can answer the quiz. To count the number of ways that the student can answer exactly 1 question correctly, we can use the binomial coefficient formula:

      [tex]\binom{5}{1}=5[/tex]

This counts the number of ways that the student can choose which 1 question to answer correctly.

For each of these 5 ways, there are 3 ways to choose the incorrect answer for each of the other 4 questions, so the total number of ways that the student can answer exactly 1 question correctly is

[tex]$5\cdot 3^4=135$[/tex].

Therefore, the probability that the student answers exactly 1 question correctly is

              [tex]$\frac{135}{243}=\boxed{\frac{5}{9}}$[/tex]

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Answer:

Yes, both men could drive at the rate of 112 miles in 2 hours. This is because you need to find the unit rate. For Theo's unit rate it is 57 miles per hour while Lex could drive at 62 miles per hour. Finally, the last statement ask if they could drive at a unit rate of 56 miles per hour and yes both men can.

Step-by-step explanation:

Answer: Theo's speed is 240 miles / 4 hours = <<240/4=60>>60 mph.

Lex's speed is 183 miles / 3 hours = <<183/3=61>>61 mph.

To determine whether Theo can drive 118 miles in 2 hours, we can calculate the time it would take him to travel 118 miles at his speed of 60 mph: 118 miles / 60 mph = <<118/60=1.97>>1.97 hours.

Since 1.97 hours is less than 2 hours, Theo could drive 118 miles in 2 hours.

To determine whether Lex can drive 118 miles in 2 hours, we can calculate the time it would take him to travel 118 miles at his speed of 61 mph: 118 miles / 61 mph = <<118/61=1.93>>1.93 hours.

Since 1.93 hours is less than 2 hours, Lex could also drive 118 miles in 2 hours.

Therefore, both Theo and Lex could drive 118 miles in 2 hours.

The new pay amount Helena will earn per month after the pay increase is equal to £3575.25

What is Percentage Increase?

In the question, it is given that Helena earns a monthly pay of £3150.

Now, we have to calculate the monthly pay earned by Helena when she receives a pay increase of 13.5%.

For calculating the new monthly pay amount, first, find 13.5% of the original pay.

[tex]\implies \frac{13.5}{100} \times 3150=425.25[/tex]  -------(1)

Next, adding the original monthly pay with the increased pay calculated in (1), we get the new monthly pay.

[tex]\implies 3150+425.25=3575.25[/tex]

Therefore, the new pay amount Helena will earn after the pay increase is equal to £3575.25

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Answer:

16 years old

Step-by-step explanation:

2x+3=35

  -3.  -3

2x=32

/2. /2

x=16

Leon is 16 years old

Hopes this helps please mark brainliest

The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0

A circle is a closed two-dimensional object in which every point in the plane is equally spaced from a certain point known as the "center" The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles. In the plane, the circle formula is as follows:

The coordinate coordinates (x,y) are equal to (x-h)2 + (y-k)2 = r2.

The centre of a circle is located at (h,k), and its radius is measured in units of r.

The equation of a circle having end points of the diameter as (x1​,y1​) and (x2​,y2​) is (x−x1​)(x−x2​)+(y−y1​)(y−y2​)=0.

we have (1,4) and (5,4) as (x1​,y1​) and (x2​,y2​)

(x−(1))(x−(5))+(y−(4))(y−(4))=0

⇒ ([tex]x^{2}[/tex] -5x -1x + 5 ) + ( [tex]y^{2}[/tex] -4y -4y + 16 ) = 0

[tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0

The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0.

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Answer:

OP/PQ

Step-by-step explanation:

You need corresponding sides in triangle OPQ.

The ratio equivalent to the given ratio is OP/PQ

Two shapes are said to be similar if their corresponding sides are in the same proportion and the corresponding angles are congruent.

Given are two triangles having two pairs of the corresponding angles equal,

So, according to the definition of the similar figures, we can say that the triangles are similar,

Also,

Their corresponding sides will be in the same proportion.

Therefore,

RS / OP = ST / QP = RT / QO

Hence, the ratio equivalent to the given ratio is OP/PQ

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The given statement " All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant. " is true.

The term t statistics refers the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error.

Here we have the statement All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.

And we need to identify whether the statement is true or not.

As per the definition of t statistics, we have identified that the t statistic falls from 0. which states that is goes on the negative direction.

Therefore, the more likely it is that the difference between two population averages is statistically significant.

So, the statement is correct.

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Answer:

Step-by-step explanation:

Sophie was offered a job after college earning a salary of $30,000. She will get a raise of $2,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company.

Step-by-step explanation:

it is an isoceles triangle (both legs are equally long).

that means also both base angles are equal :

angle J = angle L = 40°

the sum of all angles in a triangle is always 180°.

so,

180 = angle J + angle L + angle K = 40 + 40 + angle K

angle K = 180 - 40 - 40 = 100°

The coordinates of the vertices with the base b and the height h is  O(0, 0), W(b, 0), T(b, h) and S(0,h).

What is rectangle?

An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.

The rectangle with  base b and height h.

We know that:

The point O is shown in the graph is at Origin.

So, its coordinates are O(0, 0)

Since, the height of the rectangle is h,

as S and T are h units away from the x-axis.

and the base of the rectangle is b, T and W are b units away from the y-axis.

thus the coordinates of the other vertices are:

S(0, h), T(b, h) and W(b, 0)

Therefore, the coordinates of the vertices of the following rectangle with base b and height h are:

O(0, 0), W(b, 0), T(b, h) and S(0,h)

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The sample size of 502 should be the required size to perform the experiment.

The confidence interval (1 - alpha )% for population percentage p is as follows,

CI =p +- z √pq/n

The following formula is used to determine the margin of error,

MOE = z * √pq/n

The information provided is, with a margin of error of 0.03 and = 0.32.

The z-value for an 85% degree of confidence is,

For the z-value, use a z-table.

The sample size n is then determined by,

MOE = z * √pq/n

= 1.44 √ 0.32( 1 - 0.32 ) ²/ 0.03

= ( 22.392 )²

= 502

Therefore, a sample of size 502 would be needed to assess the percentage of subjects that experience blackouts at 6 or more Gs.

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The number of bacteria after 4 hours is 800

The complete question is added at the end of this solution

Given that,

This means that the rate of production is by doubling

So, we have the following parameters

a = 50

r = 2

An exponential function is represented as

A(n) = arⁿ

Substitute the known values in the above equation, so, we have the following representation

A(n) = 50(2)ⁿ

We have to find,

Find the number of bacteria after 4 hours.

This means that n = 4

So, we have

A(4) = 50(2)⁴

Evaluate

A(4) = 800

Hence, the population is 800

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Complete question

in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.

Find the number of bacteria after 4 hours.

Answer:

d) y = -3x-3

e) y = -3x - 1

f) y = -3x + 2

Step-by-step explanation:

Knowledge Needed:

Slope-Intercept Form: y = mx + b

y and x stay as variables so you can solve for the intercepts and graph.

m is the slope, or the constant amount that the y-value on a line changes when the x-value increases by 1.

b is the y-intercept, or when t he line has an x-value of 0.

When lines are parallel, they have the same slope.

Question

d)

Examine the line: At what y-value does the line have a x-value of 0?

y-value: -3

Alternatively, you could also solve be getting a set of points on the line and plugging in.

(1,0)

Our equation for line d:

y = -3x - b

0 = -3(1)  - b

0 = -3 - b

0 + 3 = -3 + 3 - b

3 = -b

b = -3

d) y = -3x-3

e)

Repeat the same steps.

y-intercept: -1

Because they are parallel, they have the same slope.

e) y = -3x - 1

f)

Repeat the same steps.

y-intercept: 2

Because they are parallel, they have the same slope.

f) y = -3x + 2

Answer: 17

Step-by-step explanation:

11x - 39 = 10x - 22

11x = 10x + 17

x = 17

Answer:

y+6=(1)/(3) (x+2)

Step-by-step explanation:

substitute (-2,-6) until equality is found

y+6=(1)/(3) (x+2)

(-6)+6=(1)/(3) ((-2)+2)

0 = 1/3 (-2+2)

0 = 0

confirm it with a graph

The monthly periodic interest rate on a credit card with a 24.99% APR is 0.0685% .

Hence, the monthly periodic interest rate on a credit card with a 24.99% APR is 0.0685% .

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The two  statements that are logically true as per the given data is q=>p and  p ∧ q .

p = raining

q = Robert is laughing

q=>p   this is because the entire proposition is logically true when the conclusion of the condition is true.

and

p ∧ q   means that it is raining and Robert is laughing which is again logically true.

If two logical statements have the same truth value in all circumstances, they are said to be comparable. This fact can occasionally be used to demonstrate a mathematical result by switching out one expression for an equivalent one while maintaining the original compound proposition's truth value.

Propositional types based on Truth values

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Answer:

28

Step-by-step explanation:

Determine which integer in the solution set will make the equation true. t − 42 = −14 {−56, −28, 3, 28}

replace 28 for t:

t − 42 = −14

28 − 42 = −14

−14 = −14

Answer:

  28

Step-by-step explanation:

You want the value of t that satisfies t − 42 = −14.

The solution to this 1-step linear equation is to add the opposite of the unwanted constant (-42).

Adding 42 to both sides of the equation gives ...

  t -42 +42 = -14 +42

  t = 28

The integer that makes the equation true is 28.

13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.

Height, length, and width are the three dimensions that all of the places we dwell and things we utilize on a daily basis have.

Height, depth, and other dimensions are examples of dimensions.

The dimensions of a line, a square, and a cube are each one, two, and three, respectively.

However, we consider the Universe to have one temporal dimension and three spatial dimensions (north-south, east-west, and up-down).

So, we have the area (A):

A = (54 – 2x)x

A = 54x - 2x²

Differentiate to obtain: dA/dX = 54 - 4x

We shall differentiate and equate to zero for a maximum Area, so dA/dx = 0.

54 – 4x = 0

x = 54/4

x = 13.5 m

It covers 280 m². Consequently, the other potential dimension:

w = 280/13.5

w = 20.74 m

Therefore, 13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.

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Reflection across the y-axis on a coordinate plane.

What is the short definition of a coordinate plane?

Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is a single horizontal number line. The y-axis is a vertical number line, which is the other number line. A place known as the origin is where the two axes collide. The coordinate plane allows us to graph points, lines, and more.

What is reflaction of coordinate plane?

Transformation is the process of making each point in a shape appear at the same distance on the other side of a specified line.

                           The term "line of reflection" refers to introspection with relation to that line. A line is crossed to flip the image.

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Answer: S

Step-by-step explanation:

The width of a confidence interval for a population mean depends on group of answer choices the sample proportion is population size and sample mean .

Given :

What is population size ?

population is the entire set of items from which you draw data for a statistical study. It can be a group of individuals, a set of items, etc.

What is sample mean ?

The sample mean from a group of observations is an estimate of the population mean .

so the width of a confidence interval is dependent on population size and sample mean .

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Answer:

g(x) will be the line y=x, reflected across the y-axis and shifted down 2 units.

Step-by-step explanation:

The -x negates every x-value, which has the effect of reflecting the graph across the y-axis. The -2 moves the graph down 2 units.

Answer:

3x + 5y = 5

Multiply by 2 on both sides.

-2x - 8y = -6

Multiply by 3 on both sides.

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases} \;\;\:3x + 5y = 5\\-2x-8y = 6\end{cases}[/tex]

To eliminate the x-terms in the given system of equations:

3x + 5y = 5 → Multiply  by 2 on both sides:

[tex]\implies 2(3x+5y)=2(5)[/tex]

[tex]\implies 6x+10y=10[/tex]

-2x - 8y = 6 → Multiply by 3 on both sides:

[tex]\implies 3(-2x - 8y) = 3(6)[/tex]

[tex]\implies -6x - 24y = 18[/tex]

Add them together to eliminate x:

[tex]\begin{array}{crcccc}&6x&+&10y&=&10\\+&(-6x&-&24y&=&18\\\cline{2-6} &&-&14y&=&28\end{array}[/tex]

a) The amount of money that he earned with the stock was of: $382.05.

b) The return on the investment was of: 96.40%.

The amount of money earned is obtained by the subtraction of the price that the stock was sold by the price the stock was bought. If this amount is negative, it means that money was lost, otherwise money was earned.

Considering the values on the problem, the amount that he earned with the stock is given as follows:

778.38 - 396.33 = $382.05.

The return on the investment is given by the amount earned/lost divided by the initial value, and multiplied by 100% to obtain the value as a percentage, hence it is of:

382.05/396.33 x 100% = 96.40%.

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The required value of "a" would be 3.

Perpendicular lines are two lines that cross one other and create a 90-degree angle.

As per the question, we have

Line m has the equation y = −13x − 2

Here slope of line m = -13

The slope of the given line m will be -13,

Line k passes through the points (0,4) and (9, a).

The slope of line k = (a - 4)/(9-0)

The slope of line k = (a - 4)/9

Given line m and line k are both perpendicular to each other,

We know that two lines are perpendicular if the product of their slopes is -1.

So,  -13 × (a - 4)/9 = -1

⇒ -13a + 52 = 13

⇒ 13a = 52 - 13

⇒ 13a = 39

⇒ a = 39/13

⇒ a = 3

Therefore, the required value of "a" would be 3.

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[tex]-\dfrac{3}{8} x\leq 24[/tex]

Multiply both sides by [tex]-\dfrac{8}{3}[/tex]:

[tex](-\dfrac{8}{3} )\times(-\dfrac{3}{8} x)\leq (-\dfrac{8}{3} )\times24[/tex]

When multiplying or dividing by negative numbers, the sign will flip.

[tex]\fbox{x}\geq \fbox{-64}[/tex]

The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.

Hypothesis;-

A put forward explanation for a phenomenon is called a hypothesis (plural: hypotheses).

A hypothesis cannot be called a scientific hypothesis unless it can be tested using the scientific process. Observations from the past that cannot be fully explained by the body of knowledge at this time often serve as the foundation for scientific ideas.

A scientific hypothesis is distinct from a scientific theory, despite the fact that the phrases "hypothesis" and "theory" are sometimes used interchangeably.

A working hypothesis is a theory that has been accepted provisionally and is put forth for further investigation[1], beginning with an educated guess or way of thinking.

As a result, the alternative hypothesis of a test indicates the effect or relationship that your research predicts, whereas the null hypothesis of a test always predicts that there will be no effect or no association between variables.

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The length of RB of the given triangle is; RB = 54 cm

We are given that in △QRS;

Point A is between points Q and R

Point B is between points R and S

AB∥QS

QA = 23 cm

QR = 41 cm

RS = 123 cm

Let us first find the ratio between RS and QR.

Ratio = RS ÷ QR

Ratio = 123 ÷ 41 = 3

QA × 3

23 × 3 = 69

Thus;

BS = 69

Thus;

RB = RS - BS

RB = 123 - 69

RB= 54 cm

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