Learning Task 2 : Find the area of each shaded region. Assume that all angles that appear to be right triangle (3 points each).
Step by step answer
PLS

The function f(x) = x² - x - 2 has x-intercepts at points x = 2 and x = - 1

To find the x-intercepts of the function, we set f(x) equal to zero and solve for x:

x² - x - 2 = 0

Factoring the left side, we get:

(x - 2)(x + 1) = 0

This gives us two solutions:

x - 2 = 0 or x + 1 = 0

Solving for x, we get:

x = 2 or x = -1

So the two x-intercepts of the function are x = 2 and x = -1.

To find the y-intercept of the function, we set x = 0 and evaluate f(x):

f(0) = 0² - 0 - 2 = -2

So the y-intercept of the function is y = -2.

To show that there is a point between the two x-intercepts where the function takes on a negative value (i.e., dips below the x-axis), we can use the fact that the function is a parabola that opens upward (since the coefficient of the x² term is positive). This means that the function is negative to the left of the left x-intercept (x = -1), and also negative to the right of the right x-intercept (x = 2). Since the function is continuous, it must pass through the x-axis at some point between these two x-intercepts. Therefore, there must be a point between x = -1 and x = 2 where the function takes on a negative value.

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Answer:

3/4 of a second

Step-by-step explanation:

step by step in picture

We knοw that the y-intercept is -1 here we get -25a = -1, which means that a = 1/25.

We can write the pοlynοmial P(x) as:

[tex]P(x) = a(x-1)^2(x+5)[/tex]

where "a" is a cοnstant cοefficient that we need tο determine.

We knοw that the y-intercept is -1, which means that P(0) = -1. Plugging in x=0, we get:

[tex]P(0) = a(0-1)^2(0+5) = -25a[/tex]

Therefοre, -25a = -1, which means that a = 1/25.

Sο, the pοlynοmial P(x) is:

[tex]P(x) = (1/25)(x-1)^2(x+5)[/tex]

We can see that this pοlynοmial has a multiplicity 2 rοοt at x=1 and a multiplicity 1 rοοt at x=-5, as required.

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The final cost of 4 pounds is $28.25 and the final cost of p pounds is $4.

Expression for the cost to buy is, Cost(x) = $7.50x - $1.75

The cost price is the price from which the seller buys the product. An expression simply consists of one or more numbers that are along the operation that is given.

In this case, the price per pound of the apples is $7.50 per pound and he has a coupon for $1.75 off the final amount.

The amount to amount that Khajida has to pay to buy 4 pounds of apples will be:

7.50p - 1.75 =

where P = number of pounds

p = 4

This will be:

5.50p - 2.5

7.5(4) - 1.75

27.5 - 1.75

28.25

The amount paid is $28.25.

Therefore, the final cost of 4 pounds: $28.25.

The final cost of p pounds: 4  dollars

To write an expression for the cost to buy x pounds of apples with the coupon, we can use the formula:

Cost = price per pound * number of pounds - coupon amount

Using this formula, we can write:

Cost(x) = $7.50x - $1.75

Where x represents the number of pounds of apples Khadija wants to buy. 

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Thus, the measure of angle  m∠SQP = 87° for given set of vertically opposite angles.

An adjacent pair of additional angles is known as a linear pair. Adjacent refers to being next to one another, and supplemental denotes that the sum of the two angles is 180 degrees.

Any two angles that sum up to 180 degrees are referred to as supplementary angles.

For the given question:

m∠PQT = m∠SQR (vertically opposite)

101 - 4b = 109 - 6b

on simplifying:

109 - 101 = 6b - 4b

2b = 8

b = 4

m∠PQT = 101 - 4(4) = 93

Now,

m∠PQT +  m∠SQP = 180 (linear pair)

93 +  m∠SQP = 180

m∠SQP = 180 - 93

m∠SQP = 87°

Thus, the measure of angle  m∠SQP = 87° for given set of vertically opposite angles.

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After the experiment begins, there will be 32 hours' worth of 23,233 bacteria.

Yet contagious microorganisms can give you a disease. Throughout your body, they multiply rapidly. Many emit toxins—a class of chemicals that may harm tissues and make you ill. The bacteria Streptococcus, Aureus, and E are just examples of those that cause infections.

Bacteria need to identify their preferred food source and be able to properly digest it in order to support growth and division. The simple sugar glucose is one of bacteria's preferred foods, much as people like eating candy.

To solve this problem, we can use the formula for exponential growth:

[tex]N = N_0 * 2^{(t/T)[/tex]

where:

N₀ = initial population

N = final population

t = time elapsed

T = doubling time (time it takes for the population to double)

T = t/log₂(N / N₀) = 14/log₂ (7000/100) = 1.89 hours

Now we can plug in all the values and solve for N:

[tex]N = N_o * 2^{(\frac{t}{T})} = 100*2^{(\frac{18}{1.89})} = 23,233[/tex]

Rounding to the nearest whole number, we get:

N = 23,233

Therefore, there will be approximately 23,233 bacteria in 32 hours from the start of the experiment.

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There are [tex]n=11[/tex] scores given.

[tex]\text{Median}=\dfrac{11+1}{2} =6^{\text{th}} \ \text{term}=78[/tex]

[tex]\text{Lower quartile range}=\dfrac{11+1}{4} =3^{\text{rd}} \ \text{term}=74[/tex]

[tex]\text{Upper quartile range}=\dfrac{3(11+1)}{4} =9^{\text{th}} \ \text{term}=88[/tex]

Interquartile range of team [tex]\text{A}=88-74=14[/tex]

By box and whisker plots,

Median of team [tex]\text{A}=78[/tex]

Median of team [tex]\text{B}=86[/tex]

Median of team [tex]\text{C}=82[/tex]

Team B has the highest median

[tex]\bold{Interquartile \ range = upper \ quartile - lower \ quartile}[/tex]

Interquartile range of team [tex]\text{A}=14[/tex]

Interquartile range of team [tex]\text{B}=90-78=12[/tex]

Interquartile range of team [tex]\text{C}=86-70=16[/tex]

Therefore, Team B has the lowest interquartile range and the highest median.

The value of x and y in the figure is solved to be

x = 6

y = 8

Similar triangles are two triangles that have the same shape, but not necessarily the same size. In other words, their corresponding angles are equal and their corresponding sides are proportional.

The proportion resulting from the similar triangles is used as follows

4 / 8 = 3 / x

4x = 8 * 3

x = (8 * 3) / 4 = 6

4 / 8 = (4 + 3) / (x + y)

4 / 8 = 7 / (6 + y)

cross multiplying

4 * (6 + y) = 8 * 7

(6 + y) = 8 * 7 / 4

(6 + y) = 14

y = 14 - 6

y = 8

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The union and intersection operations for the sets E and F are given as follows:

The union and intersection sets of multiple sets are defined as follows:

The sets are given as follows:

Hence the union and intersection sets are given as follows:

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Answer:

23.077%

Step-by-step explanation:

To find the percentage we have to create a similar equation

[tex]\frac{9}{39}=\frac{x}{100}\\[/tex]

Now we cross multiply

[tex]9 * 100 = 39 * x\\39x=900\\x= \frac{900}{39}= 23.077[/tex]

23.077/100 = 23.077%

Answer:

23.0769231% (23.08% rounded).

Step-by-step explanation:

To find a percent of a fraction or number, you have to multiply it by 100. But first, we have to divide 9 by 39 to get a fraction, which is 0.23076923076. (0.2308 rounded) Then, you multiply the number by 100 and you get 23.0769231% (23.08% rounded).

the baseball team needs 9 boxes for the order.

if the baseball team needs 100 new bats and can only put 12 bats in a box, we can find the number of boxes they need by dividing the total number of bats by the number of bats per box:

100 / 12 = 8.33

We must round to the nearest whole number because we cannot have a fraction of a box. Therefore, the baseball team must order 9 boxes.

If the team wants to make sure they get all the bats they ordered, the remaining 0.33, which represents the four bats that can't fit in a complete box, is important. They could either arrange an additional container to oblige the excess bats, or they could contact the provider to check whether they can buy simply 4 extra bats to finish their request.

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Step-by-step explanation:

3.

remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides. A, B, C are the corresponding opposite angles.

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

so, the angle opposite of W = 180 - 90 - 60 = 30°.

and we get

6×sqrt(3)/sin(60) = W/sin(30) = W / 1/2 = 2W

W = 6/2 × sqrt(3)/sin(60) = 3×sqrt(3)/sin(60) =

= 3×sqrt(3) / sqrt(3)/2 = 6

X we get via Pythagoras

X² = (6×sqrt(3))² + W² = 36×3 + 6² = 108+36 = 144

X = sqrt(144) = 12

in the lower triangle the angle opposite of X = 180 - 90 - 45 = 45°

so, it is an isoceles triangle (both legs are equal).

therefore,

Y = X = 12

Z² = 12² + 12² = 144 + 144 = 288

Z = sqrt(288) = sqrt(16×18) = sqrt(16×9×2) =

= 4×3×sqrt(2) = 12×sqrt(2)

4.

x² + 2x - 1 = 2

x² + 2x + 1 = 4

(x + 1)² = 4

x + 1 = ±2

x = ±2 - 1

x1 = 2 - 1 = 1

x2 = -2 - 1 = -3

5.

in a rhombus all 4 sides are equal, and the opposite sides are parallel.

a.

so, PQ = QR

3x + 7 = -x + 17

4x = 10

x = 10/4 = 2.5

b.

the diagonals are perpendicular to each other (90°), intersect each other at their midpoints and cut their corner angles in half.

the angle RSM = angle PSM = 40°.

c.

the sum of all angles in any quadrilateral is always 360°.

in a rhombus the opposing angles are equal.

so,

the angle SPQ = angle SRQ

360 = SPQ + SRQ + PSR + PQR = 2×SPQ + 2×40 + 2×40 =

= 2×SPQ + 160

2×SPQ = 360 - 160 = 200

the angle SPQ = 200/2 = 100°.

it is recommended that the hospital continue to monitor the length of stay for patients under each of the 15 new surgeons to ensure that there are no significant differences in the future

Dear [Name],

Thank you for your question regarding the evaluation of the performance of the new surgical specialty at ABC Hospital. As a member of the administrative team, you have decided to collect data in order to assess the length of stay for patients under each of the 15 new surgeons. This is an important measure that can help you determine if there is a statistically significant difference in the performance of the surgeons.

In order to conduct the analysis, you have decided to use a one-way ANOVA test. This is a statistical test that can help you determine if the different lengths of stay are due to chance or if there is a significant difference. Using SPSS, you can conduct this test on the data set provided, which includes the surgeon number and length of stay for five patients for each of the surgeons.

The null hypothesis for this test is that there is no significant difference in the length of stay for patients under each of the 15 new surgeons. The alternative hypothesis is that there is a significant difference.

After conducting the ANOVA test, the results table shows that the F-statistic is 1.75 and the p-value is 0.079. Based on these results, we cannot reject the null hypothesis, which means that there is no statistically significant difference in the length of stay for patients under each of the 15 new surgeons.

In terms of the graph, a boxplot is appropriate for this type of data as it can help us visualize the distribution of the data and identify any potential outliers. The boxplot shows that the median length of stay is similar for all surgeons, with some minor variations.

Based on these results, . Additionally, it may be helpful to collect more data in the future to increase the power of the analysis and identify any potential trends or patterns that may emerge.

Thank you for your question and please let me know if you have any further concerns.

Sincerely,
Ginny

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Step-by-step explanation:

tossing 2 coins at the same time, or one coin twice is the same scenario.

anyway, a probability is always the ratio

desired cases / all possible cases

when having 2 coin tosses, there are 2×2 = 4 total possible results (each toss has 2 possibilities, so 2 tosses have them 2×2 = 4 possibilities) :

head head

head tails

tail head

tail tails

how many of these 4 possible cases show at least one head ?

3 : head-head, head-tails, tails-head

so the probability to get at least one head is

3/4 = 0.75

formally calculated we would get this by saying either

this is NOT 2 times tail.

the probability of 2 times tails is

1/2 × 1/2 = 1/4 = 0.25

the probability for NOT 2 times tails is then

1 - 0.25 = 0.75

or by saying

this is either heads on the first coin and tails on the other, or tails on the first coin and heads on the other, or heads on both.

the probability of heads on the first and tails on the other coin is

1/2 × 1/2 = 1/4

the probability of tails on the first and heads on the other coin is

1/2 × 1/2 = 1/4

the probability of heads on both coins is

1/2 × 1/2 = 1/4

so, the total probability of all 3 cases is

1/4 + 1/4 + 1/4 = 3/4 = 0.75

you see : for an exclusive "or" condition we add the probabilities. for an exclusive "and" condition we multiply the probabilities.

Answer:

x-axis

Step-by-step explanation:

I'm 99.9% it's right

I'm really sorry if not!

hope this helps!

have a good day/night!

A graph of the coordinates of the vertices of the image after a dilation by the given scale factor and center of dilation is shown in the image below.

In Mathematics and Geometry, a dilation is a type of transformation which typically changes the size of a geometric object, but not its shape.

Next, we would apply a dilation to the coordinates of the pre-image by using a scale factor of 0.5 centered at the origin as follows:

Ordered pair J (-8, 0) → J' (-8 × 0.5, 0 × 0.5) = J' (-4, 0).

Ordered pair K (-4, 4) → K' (-4 × 0.5, 4 × 0.5) = K' (-2, 2).

Ordered pair L (-2, 0) → L' (-2 × 0.5, 0 × 0.5) = L' (-1, 0).

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 1/3 centered at the point B (3, 3) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A, B, and C, we have;

Coordinate A = (9, 9)  →  (1/3(9 - 3) + 3, 1/3(9 - 3) + 3) = (5, 5).

Coordinate B = (3, 3)  →  (1/3(3 - 3) + 3, 1/3(3 - 3) + 3) = (3, 3).

Coordinate C = (6, 0)  →  (1/3(6 - 3) + 3, 1/3(0 - 3) + 3) = (4, 2).

For coordinate D, E, and F, we have;

Coordinate D = (2, -2)  →  (1.5(2 - 4) + 3, 1.5(-2 + 2) + 3) = (0, 3).

Coordinate E = (4, -2)  →  (1.5(4 - 4) + 3, 1.5(-2 + 2) + 3) = (3, 3).

Coordinate F = (1, -4)  →  (1.5(1 - 4) + 3, 1.5(-4 + 2) + 3) = (-1.5, 0).

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Answer:

∠E = tan

∠D = tan

Step-by-step explanation:

Common sense, only perpendicular and base is present.

After answering the presented question, we can conclude that As a radius result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

In more modern parlance, the length of a circle or sphere is the same as its radius in classical geometry, which is one of the line segments from its centre to its circumference. The term was derived from the Latin word radius, which also refers to the spokes of a waggon wheel. The radius of a circle is the distance between its centre and any point on its periphery. It is usually denoted by "R" or "r." A radius is a line segment with one endpoint in the centre and one on the circle's circumference. The radius of a circle matches its diameter. The diameter of a circle is the segment that passes through its centre and has ends on the circle.

The formula for the volume of a sphere of radius "r" is:

V = (4/3)πr³

Substituting the specified radius value (r = 11 cm), we get:

V = (4/3)π(11)³ \sV = 5575.279 cm³

Now we must compute the weight of the titanium sphere, which can be found by multiplying its volume by its density:

Density = Volume Weight

Weight = 25121.811974 g Weight = 5575.279 cm3 4.506 g/cm3

When we divide 1000 by 1000 to convert grammes to kilogrammes, we get:

The weight is 25.121811974 kg.

As a result, a titanium sphere with a radius of 11 cm would weigh roughly 25.1 kg (rounded to 1 decimal place).

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Answer: Move 5 to the left of a.5a−day, 12.4 lb, day, 4 day, 8.39 lb, day, lb

Answer:

1) Elisa's puppy weighed 4 pounds when it was born. It gained 5 pounds per month until it was 9 months old. 5m + 4.

2) f(x) = -6.2x + 2.9

3) g(x) = 8.1x + 45.64

4) Michele has $125. She plans to spend $10 per week until she has a total of $75.

125 - 10n, or -10n + 125.

The estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To estimate the probability that it takes 10 or fewer shots to get his first successful shot, we need to add up the number of dots for the first 10 bars on the dot plot.

From the given dot plot, we can see that the number of dots for each value up to 10 shots are:

0 + 9 + 6 + 5 + 4 + 4 + 2 + 2 + 0 + 1 = 33

Therefore, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 33/40

This can also be written as a decimal:

P(10 or fewer shots) ≈ 0.825

Hence, the estimated probability that it takes 10 or fewer shots to get his first successful shot is:

P(10 or fewer shots) ≈ 0.825

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The equations that break the target are  x = 1, y = x + 5 and x = 4

There are 6 non collinear points

This means that there are at least three equations that can pass through the points

One of these equations is a vertical line that passes through x = 1

So, the equation is x = 1

The second equation passes through (-1, 4) and (0, 5)

The difference between the coordinates of these points is 5

So, the equation i

y - x = 5

y = x + 5

Lastly, we have a vertical line that passes through x = 4

So, the equation is x = 4

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Step-by-step explanation:

So we can start gathering all the variables. 2, 5, 7, and c. So starting from the beginning. Two more means 2+ something. Next, the quotient if a number (c) and 5. That would be c/5. Is 7 means =7. Now to combine it all. 2+ c/5 = 7

Answer:

The distance between the points (0, 4) and (0, 6) can be found using the distance formula: d = sqrt[(x2 - x1)^2 + (y2 - y1)^2] In this case, x1 = 0, y1 = 4, x2 = 0, and y2 = 6. Plugging in the values, we get: d = sqrt[(0 - 0)^2 + (6 - 4)^2] d = sqrt[0 + 4] d = sqrt(4) d = 2 Therefore, the distance between the points (0, 4) and (0, 6) is 2 units.

The formula you will need in order to solve this question is [tex]\sqrt(x_{2} -x_{1})^{2} +(y_{2}-y_{1})^{2}[/tex]

Please remember that you must substitute the order pairs into the question exactly as it is shown in the formula. By failing to do so, you may end up with the wrong answer.

(1) Consider the following:

[tex]x_{1} = 0[/tex] [tex]y_{1} = 4[/tex]

[tex]x_{2} = 0[/tex] [tex]y_{2} = 6[/tex]

(2) Substitute the ordered pairs into the formula accordingly

[tex]\sqrt (0 -0)^{2} +(6-4)^{2}[/tex]

(3) Solve

[tex]\sqrt (0 -0)^{2} +(6-4)^{2} = 2[/tex]

With that being said, the distance is 2.

To change a decimal to a percentage, we multiply it by 100 and add a percent sign (%).

Therefore, to change 8.28 to a percentage, we multiply it by 100 and get:

8.28 x 100 = 828%

So, 8.28 expressed as a percentage is 828%.

Step-by-step explanation:

The answer is 828%

The decimal 8.28 equals 828%

To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 8.28 × 100 = 828% ( Which is the answer ).

Which is the answer

Thus the answer to your problem is, 828%

Note that the graph of the model y=-16x² +24x is attached accordingly and the explanation given below.

The vertex is located at (0.75, 4.5). The vertex means that after 0.75 seconds, the egg reaches its highest point, 4.5 feet above the ground.

The y-intercept is located at (0,0), so the y-intercept is 0. This means that the initial height of the egg is 0 feet above the ground.

The zeros of the graph are 0 and 1.5. This means that the height of the egg is 0 feet after 0 seconds and after 1.5 seconds.

The egg is in the air for approximately 1.5 seconds.

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Therefore , the solution of the given problem of function comes out to be g(x) (-1)ⁿ (n+2)!/n! (9ⁿ⁻²) xⁿ.

On the midterm exam, there will be a variety of questions on each topic, including questions about both made-up and actual locations as well as numerical variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input.

Here,

With x = 0, we can use the formula for the geometric series to represent the function g(x) = 1/(9+x)3 as a power series:

=> 1 / (1 - t) =∑ (n = 0 to n) t

where |t|  1 and t is some integer.

In this instance, we have:

=>  g(x) = 1/(9+x)³ = [tex](1/9)^{3}[/tex] [tex](1+(-x/9))^{-3}[/tex]

So, using the above calculation and the value of t = -x/9, we can write:

=>  G(x) = (1/9)3 n(x/9) (n=0 to infinite)

If we condense this phrase, we get:

=>  (n=0 to infinite) = g(x) [tex](-1)^{n}[/tex] (n+2)!/n! ([tex]9^{n-2}[/tex]) [tex]x^{n}[/tex]

Thus, the power series expansion for g(x) with the origin at x = 0 is as follows:

=> (n=0 to infinite) = g(x) (-1)ⁿ (n+2)!/n! (9ⁿ⁻²) xⁿ

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The transformations to the parent function f(x) = x² to generate g(x) = 2x² - 4 are given as follows:

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The transformations to the parent function in this problem are given as follows:

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