7.3 revised quiz part 1

Given DF bisects

In the quadrilateral ABCD, in which angle A = 60° and angle B = 50°. The measure of angles C and D are,

∠C = 200° and ∠D = 50°

In the quadrilateral ABCD, it is given that,

A = 60° and angle B = 50°

Now, since AC is the angle bisector of angles A and C, we have,

∠DAC = ∠BAC ......... (1)

And ∠ACD = ∠ACB ............ (2)

Also, AC divides the quadrilateral ABCD into two triangles, ΔABC and ΔACD.

In ΔABC, ∠BAC = 30° [from (2)] and ∠ABC = 50°

Using angle sum property of a triangle, we have,

∠BAC + ∠ABC + ∠ACB = 180°

⇒ 30° + 50° + ∠ACB = 180°

80° + ∠ACB = 180°

∠ACB = 180° - 80°

∠ACB = 100°

From (1), ∠ACD = ∠ACB = 100°

∠C = ∠ACD + ∠ACB

⇒ ∠C = 100° + 100°

∠C = 200°

Now, according to the angle sum property of a quadrilateral,

∠A + ∠B + ∠C + ∠D = 360°

Substituting the values of ∠A, ∠B, and ∠C, we get,

60° + 50° + 200° + ∠D = 360°

310° + ∠D = 360°

∠D = 360° - 310°

∠D = 50°

Hence, in quadrilateral ABCD, ∠C = 200° and ∠D = 50°

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Using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

According to the question,

The average household income for a recent year (x₁⁻) = $30,000

The average household income for a recent year (x₂⁻) = $24,500

sample sizes n₁ = n₂ = 34

standard deviation of both samples were $24,500. Thus, s₁ = s₂ = $5928.

Null hypothesis:  There is no evidence to believe that the average household income has increased.

H₀ : μ₁ ≤ μ₂

Alternative hypothesis:  There is evidence to believe that the average household income has increased.

H₁: μ₁ > μ₂  

To check hypothesis we have the formula

Standard error=  [tex]\sqrt{\frac{s_{1} ^{2} }{n_{1} } + \frac{s^{2} _{2} }{n_{2} } }[/tex]

= [tex]\sqrt{2067128.4706}[/tex]

= 1437.7512

Thus, standard error is $1437.7512.

Formula for test statistic = [(x₁⁻ -  x₂⁻) - (μ₁ - μ₂)]/standard error

= [(30000 -  24500) - 0]/1437.7512

= 3.8254

The critical value of z at 5% level of significance is 1.6449.

Here, the calculated value is greater than the critical value so we reject H₀.

Hence using hypothesis test, we conclude that there is evidence to believe that the average household income has increased.

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Answer:

x = 2 ;   x = -8

Step-by-step explanation:

 [tex]\sf \ log_4 \ x +log_4 \ (x +6) = 2\\\\ log_4 \ (x)*(x +6) = 2\\\\[/tex]

    log₄  ( x² + 6x) = 2

                        4² = x² + 6x

         x² + 6x - 16 = 0

   x² - 2x + 8x - 16 = 0  

   x(x - 2) + 8(x - 2) = 0

       (x - 2) (x + 8)   = 0

x - 2 = 0  or x + 8 = 0

    x  = 2  or      x  = - 8

Answer:171x+8

Step-by-step explanation:

3x^3+12x^2x+8

=27x+144x+8

=171x+8

Answer:

Step-by-step explanation:

Let the length be l and the width be y. We have the following:

l + w = 37

lw = 342

From here, we can find the factor pairs of 342, and see which pair has a sum of 37. Our desired pair is 18 & 19, so the dimensions of the field are 18 by 19 feet.

The remaining amount after 4 years is 1.25 kg

The half life of a function is represented as:

[tex]A = A_o * (1/2)^{t/h}[/tex]

Where

Ao represents the initial amount

So, we have:

[tex]A = 5 * (1/2)^{t/2}[/tex]

In 4 years, t = 4.

So, we have:

[tex]A = 5 * (1/2)^{4/2}[/tex]

This gives

[tex]A = 5 * (1/2)^2[/tex]

Evaluate the expression

A = 1.25

Hence, the remaining amount after 4 years is 1.25 kg

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Answer:

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

Any rational number can be written in the form of p/q as per definition of a rational number.

In case with zero, it can be:

So, we'll have:

Answer:

B

Step-by-step explanation:

solve equation.

The primary goal of a data scientist is to create new questions using data.

In the data ecosystem, a data scientist is one who creates new questions using data.

Unlike a data scientist, a data analyst uses existing data questions to find answers through insightful analysis of data.

Data designers design databases and database-specific constructs, and the procedures for storing, retrieving, and deleting persistent objects.

Data engineers build data systems to collect, manage, and convert data into information for both data scientists and analysts.

Thus, the primary goal of a data scientist is to create new questions using data.

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a) scientist

b) engineer

c) designer

d) analyst

Answer:

Step-by-step explanation:

−6m2 18m − 36

= -6(m2 - 3m + 6)

For birthday events 33/100 gifts were packed by the music boosters at the mall.

Total number of gift items = 100

For the wedding purpose,out of 100 gifts, 3/10 number of gifts were boxed = 3/10*100 = 30

For the baby shower, out of 100 gifts, 37/100 gifts were packed = 37

The rest amount of the gift = 100-( wedding + baby shower)

= 100-(30+37) = 33

So, according to the question, these 33 numbers gift was for a birthday.

When it is expressed as a fraction,

The fraction should be = 33/100

Therefore, it is concluded that 33/100 gifts were packed for birthday occasions.

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The volume of the cylinder having diameter 12 cm and height of 4 cm is 452 [tex]cm^{3}[/tex].

Given diameter of cylinder be 12 cm and height of cylinder be 4cm.

We are required to find the volume of cylinder.

Volume is the quantity of substance a container can hold in its capacity.

Diameter=12 cm

Radius=6 cm (Radius is always equal to half of diameter)

Volume of cylinder=π[tex]r^{2} h[/tex]

We have to just put the values of r, h and π in the formula to get the volume of the cylinder.

Volume=π[tex](6)^{2} 4[/tex]

=3.14*4*36

=452.57 [tex]cm^{3}[/tex]

After rounding off we will get 452 [tex]cm^{3}[/tex].

Hence the volume of cylinder is 452 [tex]cm^{3}[/tex].

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Question is incomplete as it should include height of cylinder be 4cm.

It looks like the limit you want to compute is

[tex]\displaystyle \lim_{x\to4} \frac{f(g(x)) - f(4)}{x-4}[/tex]

Since [tex]g(4)=4[/tex], this limit corresponds exactly to the derivative of [tex](f\circ g)(x) = f(g(x))[/tex] at [tex]x=4[/tex]. Recall that

[tex]f'(a) = \displaystyle \lim_{x\to a} \frac{f(x) - f(a)}{x - a}[/tex]

By the chain rule,

[tex](f\circ g)'(4) = f'(g(4)) \times g'(4) = f'(4) \times g'(4) = 3\times7 = \boxed{21}[/tex]

Since [tex]g'(4)[/tex] exists, [tex]g[/tex] is differentiable at [tex]x=4[/tex] so it must be continuous.

Answer:

n^3 + 1.

Step-by-step explanation:

Each term is 1 more than a perfect cube.

2 = 1^3 + 1

9 = 2^3 + 1

28 = 3^3 + 1

65 =  4^3 + 1

126 = 5^3 + 1

So the explicit formula is n^3 + 1.

The explicit formula that generates the given sequence is indeed aₙ = n³+1.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The nth term of the sequence can be obtained by substituting n = 1, 2, 3, ... into the expression n³+1:

a₁ = 1³+1 = 2

a₂ = 2³+1 = 9

a₃ = 3³+1 = 28

a₄ = 4³+1 = 65

a₅ = 5³+1 = 126

Hence, the explicit formula that generates the given sequence is indeed aₙ = n³+1.

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The characteristic of certificates of deposit (CDs) is that it last for a set period of time and is denoted as option B.

This is also referred to as time deposit and is characterized by a lump sum being saved at a fixed period of time and is stricter than the normal savings system.

This type of savings has a fixed interest rate and can't be withdrawn before the maturity date unlike savings account which can be accessed at any point in time which makes it unique and is therefore the most appropriate choice.

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Explanation:

You could use the AC method to factor this, but the quadratic formula is the most efficient route in my opinion. This will avoid any guess-and-check.

Compare the original equation to the form [tex]a\text{x}^2 + b\text{x} + c = 0[/tex]

We have a = 9, b = 6, and c = -8

Those values lead to...

[tex]\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(9)(-8)}}{2(9)}\\\\\text{x} = \frac{-6\pm\sqrt{324}}{18}\\\\\text{x} = \frac{-6\pm18}{18}\\\\\text{x} = \frac{-6+18}{18} \ \text{ or } \ \text{x} = \frac{-6-18}{18}\\\\\text{x} = \frac{12}{18} \ \text{ or } \ \text{x} = \frac{-24}{18}\\\\\boldsymbol{\text{x} = \frac{2}{3} \ \text{ or } \ \text{x} = -\frac{4}{3}}\\\\[/tex]

Side notes:

Answer:

Step-by-step explanation:

The volume of the prism is not equal to the volume of the cylinder.

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

Let x represent the cross sectional areas of a triangular prism and a right cylinder.

Volume of cylinder = cross sectional area * height = 3 * x = 3x

Volume of triangular prism = cross sectional area * height = 5 * x = 5x

The volume of the prism is not equal to the volume of the cylinder.

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Answer:

14.7 (Because you asked for no units)

Step-by-step explanation:

The volume of this triangular prism is 1/2 BHL

0.5 * 3.5 * 2 * 4.2 = 14.7 ft^3

Answer:

Step-by-step explanation:

i think it is c

Answer:

A

Step-by-step explanation:

So let's look at each and determine whether they're true or not.

A. It's vertex is at the origin:

   This is true! The reason for this is because you can express a quadratic in vertex form as such: [tex]f(x)=a(x-h)+k[/tex] where (h, k) is the vertex. If you remember the parent function is simply: [tex]f(x)=x^2[/tex] which we can express as: [tex]f(x) = (x-0)+0[/tex] meaning the vertex is at (0, 0). This also intuitively makes sense, the x^2 will only output positive values for real numbers, so when x<0, f(x) is still going to be positive because it's squaring the negative, so that means when you go from -5 to -4, even though you increased x by 1, the f(x) decreases by 1, since it's squaring the value to get a positive value. The lowest value this can output is 0 because 0^2 = 0. This means you vertex is at the origin.

B. It is not a function:

   So the quadratic parent function only outputs 1 value for each input, although it isn't a one-to-one function, meaning that each output isn't unique, but each input still only outputs 1 output, which makes this a function

C. It is not a parabola:

   parabolas are expressed as quadratic equations, so this is false.

D. It is in quadrants ||| and IV:

   This is not true since the parent function opens upwards and has a vertex at (0, 0) so it will only be in quadrant I and II. I'll provide a diagram showing this.

The computed value must closely match the real value for a model to be considered valid. If the percentage of pleased or very satisfied students remains close to 75% after Mateo surveys additional students, Mateo's model is still viable. The model is faulty if the opposite is true.

In general, a valid model is one whose estimated value is close to the real value. This kind of model is considered to be accurate. It must be somewhat near to the real value if it doesn't resemble the real value.

If the findings of the survey are sufficiently similar to one another, then the model may be considered valid.

P1 equals 75%, which is the real assessment of the number of happy pupils

P2 is 70 percent; this represents the second assessment of happy pupils

In conclusion,  The estimated value of a model has to be somewhat close to the real value for the model to be considered valid. If the number of students who are either pleased or extremely satisfied remains close to 75 percent following Mateo's survey of more students, then Mateo's model is likely accurate. In any other scenario, the model cannot be trusted.

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Answer:

m = [tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

m = [tex]\frac{y2-y1}{x2-x1}[/tex]

m = [tex]\frac{1-7}{10-1}[/tex]

m = [tex]\frac{-6}{9}[/tex]

m = [tex]-\frac{2}{3}[/tex]

Answer:

-2/3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (1 - 7)/(10 - 1)

slope = -6/9

slope = -2/3

Using proportions, it is found that the seismic activity density for this state is of 0.0059 earthquakes per square mile.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the density is the proportion given by the number of earthquakes divided by the area, hence:

424/71,300 = 0.0059 earthquakes per square mile.

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Answer:  Using proportions, it is found that the seismic activity density for this state is of 0.0059 earthquakes per square mile.

Step-by-step explanation:

Using the sine ratio, the length of the missing side is: 11.8.

The sine ratio is, sin ∅ = opposite/hypotenuse.

Given the following:

∅ = 24°

Opposite = x

Hypotenuse = 29

sin 24 = x/29

x = (sin 24)(29)

x = 11.8

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The amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications

The functions are given as:

[tex]f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}[/tex]

[tex]g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)[/tex]

Next, we represent both functions on a graph.

From the attached graph, we can see that both functions intersect at (11.34, 3.04)

This means that the amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications

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Complete question

A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by [tex]f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}[/tex] where x is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is [tex]g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)[/tex]. Here are the graphs of

Answer:

It gives the initial amount + It gives the solution

Step-by-step explanation:

It gives the initial amount + It gives the solution

We know from the graph given and the data provided that the function can automatically be proven true.

It cannot describe the amount of time as the data says X is how much of the medicine is given, not the time.

It can't be the equal ratio because, for example, 1 milligram of medicine doesn't equal 1h of time in the body.

All you need to do for this is educational guessing, reasoning, and the process of elimination. Hope this helped! have a great day :7)

Answer:

Step-by-step explanation:

To solve this equation log both sides and apply log rules.

Substitute the values of logs:

Solve it as linear equation:

Let f(x) = x² + 6x²-x+ 5 then ,

number to be added be P

then,

f(x) = x² + 6x²-x+ 5 +P

According to the qn,

(x+3) is exactly divisible by zero then,

R=0

comparing .. we get a= -3

now by remainder theorm

R=f(a)

0=f(-3)

0=(-3)² + 6(-3)²-(-3)+ 5 + P

0= 9 + 54 + 3 + 5 + P

-71=P

therefore, -71 should be added.

Hope you understand

Answer:

the answer is 3/4 because 7/12 + 2/12 is 9/12 which simplified is 3/4

Step-by-step explanation: