ABCD is a rhombus. If AC = 8 cm and BC = 6 cm, what is the area of the rhombus?

Answer:

The vertex of the function is at point (-4,-1).

Step-by-step explanation:

Given function:

[tex]f(x)=(x+4)^2-1[/tex]

Solution:

The vertex form of a function is given by:

[tex]f(x)=a(x-h)^2+k[/tex]

where [tex](h,k)[/tex] is the vertex of the function. At this point the function has the maximum or minimum value.

Writing the given function in the vertex form.

[tex]f(x)=(x-(-4))^2+(-1)[/tex]

On comparing the above function with the standard form we find that:

[tex]a=1\\h=-4\\k=-1[/tex]

Thus, the vertex of the function is at point (-4,-1)

The vertex of the function f(x)= (x + 4)² - 1 is at the point (-4,-1) by comparing it with the vertex form of a quadratic function f(x) = a(x - h)² + k.

The function given is in the vertex form of a quadratic function, which is f(x) = a(x - h)² + k. In this form, the vertex of the graph of the function is at the point (h, k). For f(x)=(x + 4)² - 1, you can see that h is -4 and k is -1. Therefore, the vertex of the graph of the function is at the point (-4,-1).

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Answer:

The maximum of the sinusoidal function is 5.

Step-by-step explanation:

The maximum of the sinusoidal function is 5.

The probability of selecting the 8 tallest players randomly from a list of 27 is found by dividing the single way to choose the tallest players by the number of ways to choose any 8 players from 27, calculated using the combination formula C(n, k).

To determine the probability that the 8 tallest players will be selected from a list of 27 players, we need to consider the combinatorial aspect of the selection process. Since the selection is random, any group of 8 players can be chosen. The total number of ways to select 8 players out of 27 is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of players (27), and k is the number of players to be selected (8).

Firstly, the number of ways to choose the 8 tallest players is 1, since there is only one group of the 8 tallest players. Secondly, we calculate the total number of ways to choose any 8 players from the 27, which is C(27, 8). We can then find the probability by dividing the number of ways to choose the tallest players by the total number of ways to choose any group of 8 players.

Using the combination formula, C(27, 8) is calculated as:

27! / (8! * (27-8)!)

= 27! / (8! * 19!)

Factor out the common terms from the numerator and denominator

The remaining terms give us the total number of combinations

The probability is therefore: 1 / C(27, 8).

Answer:

sin 80

Step-by-step explanation:

Answer:

Hence,

The measure of ∠A is 60.065°

[tex]\m\angle A= 60.065[/tex]

Step-by-step explanation:

Given:

ΔABC is a Right Angle Triangle at ∠ B = 90°

BC = Opposite side to ∠A = 13 unit

AC = Hypotenuse  = 15 unit  

To Find:

m∠A = ?  

Solution:

In Right Angle Triangle ABC ,Sine Identity,

[tex]\sin A= \dfrac{\textrm{side opposite to angle A}}{Hypotenuse}\\[/tex]

Substituting the values we get

[tex]\sin A= \dfrac{BC}{AC}=\dfrac{13}{15}=0.8666\\\angle A=\sin^{-1}(0.8666)\\m\angle A= 60.065\°[/tex]

Hence,

The measure of ∠A is 60.065°

[tex]\m\angle A= 60.065[/tex]

Answer:

Influencer

Step-by-step explanation:

An influencer is a person who has the power affect purchase decisions of others because of his ability such as knowledge, position with audience.

Final answer:

A person acting as a specifier in the buying center provides product specifications and may influence the purchase decision by setting requirements, interacting with both customer and seller but not making final purchasing decisions.

Explanation:

Depending on the product, there may be a person who acts as specifier in the buying center, often by providing specifications for the product being purchased or the vendor being considered.

A specifier plays a crucial role in the procurement process, ensuring that the product or service meets the organization's needs and standards. In a buying center, this individual might not have the authority to make final purchase decisions but is influential by setting the requirements that the potential products or suppliers must meet.

A specifier may interact closely with both the customer and seller to ensure that the right features, quality, and functionalities are captured in the procurement specifications.

This person may also assess the long-term reliability of supplier relationships, such as through exclusive dealer agreements, to safeguard the company's interests. The role of the specifier is analogous to that of a product consultant, providing insights without directly engaging in sales or price negotiations.

To figure this out, use the acronym SOHCAHTOA to determine which trigonometric function to use.

8 is opposite to <R and 3 is adjacent to <R so we use tangent.

Set up the following equation: tan(x)=8/3

Find the inverse (aka. tan^-1): x=69.44

So your answer is <R=69.4 degrees

Hope this helped!

Answer:

1. Yes, the lines are perpendicular.

2. [tex]y=\frac{5}{4}x+6[/tex]

Step-by-step explanation:

The first equation of Exercise 1 is incomplete. Let's assume that it is:

[tex]2x + 3y =n[/tex]

Where "n" is a number.

First, it is important to remember that the equation of a line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

By definition, the slopes of perpendicular lines are negative reciprocals.

1 . If you solve for "y" from the first equation, you get:

[tex]2x + 3y =n\\\\3y=-2x+n\\\\y=-\frac{2}{3}x+\frac{n}{3}[/tex]

You can identify that the slope is:

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

The second equation of the line is:

[tex]y=\frac{3}{2}x+4[/tex]

And its slope is:

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

Since the slopes are negative reciprocals, the lines are perpendicular.

2. Given the first equation of the line:

[tex]y= -\frac{4}{5}x+6[/tex]

You can identify that:

[tex]m=-\frac{4}{5}\\\\b=6[/tex]

Since the first line and the second one are perpendicular, you know that the slope of the other line is:

[tex]m=\frac{5}{4}[/tex]

According to the information given in the exercise, both lines have the same y-intercept; therefore, the equation of the second line is:

[tex]y=\frac{5}{4}x+6[/tex]

Answer:

the answer is c

Step-by-step explanation:

i took the test and got a 100

The range of the function is all real numbers less than or equal to 0.

A function is an expression that shows the relationship between two or more variables or numbers.

The domain of a function is the set of input values while the range is the set of output values.

From the graph, The range of the function is all real numbers less than or equal to 0.

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Answer:

x = 28.5 minutes

Step-by-step explanation:

Let x be the time taken for finishing the bike race.

Given:

Ella finished a bike race = 37.6 minutes

Miranda finished the race sooner than Ella = [tex]9\frac{1}{10} = \frac{91}{10} = 9.1\ minutes[/tex]

We need to find the minutes did it take Miranda to finish the race.

Solution:

From the statement, Miranda finished the race 9.1 minutes sooner than Ella finished it while Ella finished the same bike race in 37.6 minutes.

So, time taken by Miranda to finish the race:

[tex]Mirianda\ finshed\ a\ bike\ race = (Ella\ finshed\ a\ bike\ race) - 9.1[/tex]

[tex]x=37.6-9.1[/tex]

x = 28.5 minutes

Therefore, Miranda finished the bike race in 28.5 minutes.

Answer:

We have: b = 823 foot

h = 534 Ft ,

Substitute their values,

A = 823 * 534

A = 439482 Ft² briefly, Your Answer would be: 439482 Ft²

~

For a fraction;

49 and 10/12

 multiply 8 and 2/3 by 5 and 3/4!

Answer:

  a. Slant asymptote with a slope of 5

Step-by-step explanation:

Dividing out the polynomials, you get ...

  [tex]\dfrac{5x^2-x+13}{x+10}=5x-51+\dfrac{523}{x+10}[/tex]

As the magnitude of x gets large, the fraction goes to zero, and the behavior matches the line ...

  y = 5x -51

This is a slant asymptote with a slope of 5 and a non-zero y-intercept.

Answer:

Distance = 44 m

Change in position = 0 m

Step-by-step explanation:

Given:

Running around the house covering a total length of 44 m and reaching the same position where you started.

So, initial position is same as final position.

Change in position is given as:

Change = Final position - Initial position

Now, since, final position = Initial position.

So, Change in position = 0 m

Now, distance is the total length of the path covered. So, you started from your initial position and ran around the house covering a path length of 44 m before reaching the same starting position.

Therefore, the distance is equal to the path length and hence is equal to 44 meters

Answer:

X+y=237Litres

Step-by-step explanation:

Let a be mixture of milk and water.

Let x =milk

Let y= water

z = x+y

Final volume of mixture =63litres + z

5/12(3+z))+60=8/15(63-z)

z =x+y= 237litres

The value of [tex]x+y[/tex] is 237 liters.

Given information:

A 63 liter mixture contains milk and water in a ratio of 4:5.

Let the initial amount of water be a. So, the amount of milk will be [tex]63-a[/tex].

The initial mixture can be written as,

[tex]\dfrac{63-a}{a}=\dfrac{4}{5}[/tex]

The initial amount of water and milk will be,

[tex]\dfrac{63-a}{a}=\dfrac{4}{5}\\315-5a=4a\\9a=315\\a=35\\63-a=28[/tex]

x liters of milk and y liters of water are added to the mixture, resulting in a milk to water ratio of 7:5.

The mixture, now, can be written as,

[tex]\dfrac{28+x}{35+y}=\dfrac{7}{5}\\140+5x=245+7y[/tex]

60 liters of the mixture are drained and replaced with 60 liters of water, resulting in a milk to water ratio of 7:8.

Draining will release the amount of water and milk in the ratio 7:5 which is its concentration. So, 35 liters of milk and 25 liters of water will be drained.

The final mixture can be written as,

[tex]\dfrac{28+x-35}{35+y-25+60}=\dfrac{7}{8}\\\dfrac{x-7}{y+70}=\dfrac{7}{8}\\8x-56=7y+490[/tex]

Solve for x and y as,

[tex]140+5x=245+7y\\8x-56=7y+490\\3x-196=245\\x=147\\y=90[/tex]

So, the value of [tex]x+y[/tex] will be,

[tex]x+y=147+90\\=237[/tex]

Therefore, the value of [tex]x+y[/tex] is 237 liters.

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Answer:

The max altitude you can operate an sUAS on these given conditions is 1400ft AGL.

Step-by-step explanation:

Final answer:

The sUAS can fly at a maximum altitude of 1,100 feet AGL when inspecting a tower with a top at 1,000 feet AGL, assuming it stays within 100 feet of the tower as per 14 CFR Part 107.

Explanation:

In accordance with 14 CFR Part 107, specifically considering sUAS (small Unmanned Aircraft Systems) operations around structures, there are specific altitude regulations. When a drone operator is inspecting a tower, and the drone is within 100 feet laterally of the structure, the drone can operate above the standard 400 feet above ground level (AGL) limit. For a tower with a top at 1,000 feet AGL, the sUAS can fly at a maximum altitude of 1,100 feet AGL, assuming it stays within 100 feet of the structure. This is possible because the regulations allow the sUAS to fly 400 feet above the structure's uppermost limit when it is within a close radius of the structure.

Answer:

D. Isosceles trapezoid

Step-by-step explanation:

Answer: The answer is D. Isosceles trapezoid

Answer:

Step-by-step explanation:

It would take them 8 hours to complete the painting task if they worked together.

The addition operation in mathematics adds values on each side of the operator.

For example 4 + 2 = 6

If painter A can paint the area in 3 hours, and painter B can paint the same area in 5 hours, then it would take them a total of 3+5=8 hours to paint the area together.

It's worth noting that this assumes that both painters are able to work at their full capacity while working together and that they are able to divide the work between them in an efficient manner. If either of these conditions is not met, it could take them longer than 8 hours to complete the job.

Hence, working together, it would take them 8 hours to complete the painting job.

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Answer:

4(√2.5)x

Step-by-step explanation:

Let each side of the dragonal be P

Bringing out a Triangle out of the rhombus we have a right angle triangle with the base of x/2 and height of 3/2x.

And the hypothenus is P.

Applying Pythagoras theorem we have

p ^2= (1.5x)^2+(0.5X)^2

p ^2= 2.25X^2 +0.25X^2

P = (√2.5) X

Since the Rhombus consist of 4 triangles . The perimeter can best be expressed as 4 x the perimeter of the triangle.

P= 4(√2.5)x.

The longer diagonal of a rhombus is three times the length of the shorter diagonal. The expression that gives the perimeter of the rhombus cannot be determined with the information provided.

The perimeter of a rhombus can be found by adding the lengths of all four sides. In this case, the longer diagonal of the rhombus is three times the length of the shorter diagonal, which is represented by x. So, the shorter diagonal is x and the longer diagonal is 3x.

Since the longer diagonal of a rhombus creates two congruent right triangles, we can use the Pythagorean theorem to find the length of its sides. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, for one of the right triangles, the hypotenuse is 3x and the two sides are x. Using the Pythagorean theorem, we have:

x² + x² = (3x)²

2x² = 9x²

2 = 9

This equation is not true, which means that x cannot be the length of the shorter diagonal.

Therefore, since the given information is incorrect, we cannot find the expression that gives the perimeter of the rhombus.

If they were to win $30 they would expect to get $27 in profit.

If they were to win $10 they would expect $7.

If they were to win $0 they would expect $-3 in profit, so technically if they win nothing they lose money.

Hope I could help! :D

If player expect to get out of this game every time he/she plays then they would loose money.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

If a player rolls 2 dice and gets a sum of 2 or 12, he wins $30.

and, If they were to win $30, they would anticipate making a profit of $27.

Also, if they would anticipate $7 if they were to win $10.

So, if they were to win nothing, they would lose money because they would expect to make $-3 in profit.

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Answer:

The answer is x = -6.6

Step-by-step explanation:

Answer:

X= -6.6

Step-by-step explanation:

Just do 13.8 - 20.4. It will equal -6.6.

Answer:

x = 0.8 Mi

Step-by-step explanation:

for x = 4224 ft we can use the factor (1 Mi/5280 ft)

then

x = 4224 ft (1 Mi/5280 ft) = 0.8 Mi

Answer:

Weinstein, McDermott, and Roediger (2010) conducted an experiment to evaluate the effectiveness of different study strategies.

One part of the study asked students to prepare for a test by reading a passage.

In one condition, students generated and answered questions after reading the passage.

In a second condition, students simply read the passage a second time.

All students were then given a test on the passage material and the researchers recorded the number of correct answers.

a. Identify the dependent variable for this study:

   The dependent variable for this study is effectiveness.    

b. Is the dependent variable discrete or continuous?

   The dependent variable is discrete.

c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?

   The scale of measurement is ratio scale.

Step-by-step explanation:

a) To identify the dependent variable you need to find the item, circumstance, concept, sense, time frame, or any category in an specific scientific research, that is going to be measured. In this particular case, the dependent variable measured is the effectiveness of the different study strategies used based by the number of correct answers on a test. This variable could be influenced by independent variables also.

b) The method by which we obtain the resulting values make the difference between a discrete variable and a continuous variable. If measuring is the used method, then it is a continuous variable, but if counting is the utilized method to get the correct number of correct answers, as it is stated in this case, then it is a discrete, finite and countable.

c) The measurements´ accuracy are given by the different scales or levels and they are classified as:

- Nominal

- Ordinal

- Interval

- Ratio

Interval and ratio scales data are similiar is also known as called metric, sharing units, and represent quantiy., therefore the scale of measurement used in this study is ratio scale.

Answer:

Option A:    [tex]$ \frac{\textbf{2}}{\textbf{9}} $[/tex]

Step-by-step explanation:

Given there are 10 cards viz: 1, 2, 3, 4, . . . , 10

We find the probability of drawing two cards less than six, without replacing the first card.

Draw 1:

There are 5 cards with value less than 6. 1, 2, 3, 4, 5

The total number of cards is 10.

The probability of the number being less than 6 = [tex]$ \frac{number \hspace{1mm} of \hspace{1mm} cards \hspace{1mm} less \hspace{1mm} than \hspace{1mm} 6}{total \hspace{1mm} number \hspace{1mm} of \hspace{1mm} cards} $[/tex]

[tex]$ = \frac{5}{10} $[/tex]

Draw 2:

We are again drawing a card without replacing the card that was drawn earlier. This makes the total number of cards 9.

Also, the number of cards less than 6 will now be: 4.

Therefore, probability of drawing a number less than 6 without replacing

[tex]$ = \frac{4}{9} $[/tex]

Since, both draw 1 and draw 2 are happening we multiply the two probabilities. We get

[tex]$ \textbf{P} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{5}}{\textbf{10}} \hspace{1mm} \times \hspace{1mm} \frac{\textbf{4}}{\textbf{9}} $[/tex]

[tex]$ \therefore P = \frac{\textbf{2}}{\textbf{9}} $[/tex]

Hence, OPTION A is the required answer.

It's 1.25 seconds, I just took the test and got 100% Good Luck!!! :)

Answer: p=11

Step-by-step explanation:

12p+7)139

-7 -7

12p)132

÷12 ÷12

P)11

Answer:

p= 11

Step-by-step explanation:

1 2p + 7 > 1 39​

collection of like term

12p > 139 - 7

12p > 132

Divide both side by the coefficient of p

12p/12 > 132/12

p = 11

Answer:

All statements are correct for two congruent triangles

Step-by-step explanation:

If two triangles are congruent than the rules states that

Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.

As the fig shows two triangle

Δ PQR

Δ LMN

All three corresponding sides of triangle are congruent

all three corresponding  angles are congruent

Both triangle are of same size

Both are of same shape

hence all the statements are CORRECT

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Answer: B. 33%

Step-by-step explanation:

Given : Response  - Frequency

          Not satisfied - 20

              Satisfied - 40

         Highly satisfied - 60

Total customers = (Number of customers  Not satisfied) +  (Number of customers satisfied) + ( (Number of customers  Highly satisfied) )

= 20+40+60=120

Now , the percentage of the responses indicated that customers were satisfied = [tex]\dfrac{\text{Number of customers are satisfied}}{\text{Total customers}}\times100[/tex]

[tex]=\dfrac{40}{120}\times100=33.33\%\approx33\%[/tex]

Hence, the percentage of the responses indicated that customers were satisfied = 33%

Thus , the correct answer is B. 33%

To find the percentage of customers who were satisfied, add up all responses, calculate the fraction of satisfied responses, then convert that to a percentage. The answer is 33%.

To find out what percentage of the responses indicated that customers were satisfied, we first need to add up all the responses. This would include those who were Not satisfied, Satisfied, and Highly satisfied. The total number of responses will be 20 (Not satisfied) + 40 (Satisfied) + 60 (Highly satisfied) = 120 responses in total.

Next, we find the fraction of responses that were satisfied. For this, we divide the number of Satisfied responses (40) by the total number of responses (120). That gives us 40/120 = 0.333 or one-third.

To convert this fraction to a percentage, we simply multiply by 100. So, 0.333 x 100 = 33.3%, which rounds down to 33%. Thus, the answer to the question is 33%, option - B.

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Answer:

The solution to the differential equation

y' = 1 + y²

is

y = tan x

Step-by-step explanation:

Given the differential equation

y' = 1 + y²

This can be written as

dy/dx = 1 + y²

Separate the variables

dy/(1 + y²) = dx

Integrate both sides

tan^(-1)y = x + c

y = tan(x+c)

Using the initial condition

y(0) = 0

0 = tan(0 + c)

tan c = 0

c = tan^(-1) 0 = 0

y = tan x

In this exercise we have to use our knowledge of differential equations to calculate the value of the first solution, so we have to:

[tex]y = tan x[/tex]

Then say the differential equation as:

[tex]y' = 1 + y^2[/tex]

then rewriting as:

[tex]dy/dx = 1 + y^2\\dy/(1 + y^2) = dx[/tex]

Integrate both sides, we have that:

[tex]tan^{(-1)}y = x + c\\y = tan(x+c)[/tex]

So we already have a preview of the solution, so we will have to apply the initial conditions and this results in:

[tex]y(0) = 0\\0 = tan(0 + c)\\tan c = 0\\c = tan^{(-1)} 0 = 0\\y = tan x[/tex]

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Answer:

Answer is (A) One-half times 14 times 57

Step-by-step explanation:

Answer:

A

Step-by-step explanation: