∆ ABC is similar to ∆DEF and their areas are respectively 64cm² and 121cm². If EF = 15.4cm then find BC.​

Answer:

a) [-9,8)

b) [-5,5]

c) (-4,0), (1,6)

d) [-9,-4), (6,8)

e) [0,1]

f) just the y-value: 5;  as a point: (-8,5)

g) just the y-value: -5;  as a point: (-4,-5)

Step-by-step explanation:

a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).

b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.

For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.

c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?

d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?

e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?

f) Look for the highest non-infinity point on the graph

g) Look for the lowest non-infinity point on the graph

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

The slope represents the change/rise is the yearly imcome based on age. The y-intercept is the amount that they make when they first get a job.

Step-by-step explanation:

Step-by-step explanation: We may determine the range of potential further miles Charlie will run by deducting his present mileage from the maximum mileage if he has already run 17 miles and will only cover 35 miles this week.

Maximum mileage - current mileage = potential extra miles.

17 miles minus 35 miles equals 18 miles.

As a result, Charlie may run somewhere between 0 and 18 additional miles.

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Answer:

18 possible numbers

Step-by-step explanation:

If Charlie has already run 17 miles and he will run at most 35 miles this week.

We can calculate the possible numbers of additional miles he will run by subtracting the distance he has already run from the maximum distance he can run.

Maximum distance Charlie can run = 35 miles

Distance Charlie has already run = 17 miles

Possible additional miles he will run = Maximum distance - Distance already run

                              = 35 miles - 17 miles

                              = 18 miles

Therefore, there are 18 possible numbers of additional miles Charlie will run.

The probability that:

First, check if it is appropriate to use the normal approximation to the binomial distribution. The rule of thumb is that this approximation is reasonable if both np and n(1-p) are greater than 5. In this case, p = 0.83 (probability of failure), n = 70 (number of trials).

So,

np = 700.83 = 58.1,

n(1-p) = 700.17 = 11.9.

Both quantities are larger than 5, so use the normal approximation.

Convert this to a problem involving a normal distribution. The mean of this distribution is np = 58.1 and the standard deviation is √(np(1-p)) = √(700.830.17) = 6.35.

(a) within 2 years 47 or more fall:

This corresponds to a Z-score of (47.5 - 58.1) / 6.35 = -1.67. The probability that a standard normal variable is greater than -1.67 is 0.9525.

So the probability that 47 or more products fail is approximately 0.9525.

(b) within 2 years 58 or fewer fail:

This corresponds to a Z-score of (58.5 - 58.1) / 6.35 = 0.063. The probability that a standard normal variable is less than 0.063 is 0.5250.

So the probability that 58 or fewer products fail is approximately 0.5250.

(c) within 2 years 15 or more succeed:

Since the probability of success is 1-p, this is equivalent to fewer than (70 - 15 = 55) failing. This corresponds to a Z-score of (54.5 - 58.1) / 6.35 = -0.567.

The probability that a standard normal variable is greater than -0.567 is 0.7151.

So the probability that 15 or more products succeed is approximately 0.7151.

(d) within 2 years fewer than 10 succeed:

This is equivalent to more than (70 - 10 = 60) failing. This corresponds to a Z-score of (60.5 - 58.1) / 6.35 = 0.377.

The probability that a standard normal variable is less than 0.377 is 0.6478.

However, since we want more than 60 failing, the probability that the variable is greater than 0.377, which is 1 - 0.6478 = 0.3522.

So the probability that fewer than 10 products succeed is approximately 0.3522.

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Answer:

Step-by-step explanation:

Answer:

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Step-by-step explanation:

Answer:

I think it's c

Step-by-step explanation:

because  a*1=1

All of the other statements are incorrect because for one a+0=0 Only 0 can = 0

A*0=1? A number times 0 is always going to be zero

A+1=1? Only 0 is the only number that a number plus 0 is the same number

Answer:

It is option 2 "even degrees of 6 or greater

Step-by-step explanation:

The missing angles on the figure are as follows

The  missing angles ae solved as follows

v = y vertical angles theorem

Examining the figure shows that

v + 90 = 180 angle on a straight line

hence v = 180 - 90 = 90

so we can say that v = y = 90

Also, y + 38 + z = 180 angles in a triangle

90 + 38 + z = 180

z = 180 - 90 - 38

z = 52 degrees

furthermore, w = x base angle of isosceles triangle

w + x + v = 180

w + x + 90 = 180

w + x = 90

hence w = x = 45 degrees

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The corresponding sections of two triangles are equal when they are congruent, according to the CPCTC theorem. CPCTC is an abbreviation that stands for "corresponding parts of congruent triangles are congruent"

Congruent:

If two triangles are precisely the same size and shape, they are said to be congruent. Three of the sides and the angles in two congruent triangles are equal to one another. Corresponding Parts of Congruent Triangles are Congruent is abbreviated as CPCTC. According to the CPCTC theorem, every corresponding component of one triangle is congruent to the other when two triangles are congruent. This indicates that when two or more triangles are congruent, the accompanying sides and angles are likewise congruent or equivalent in size.

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Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Answer:

a) 34 students scored below an 81%

b) Interval 81-100

c) 34.6 rounded to 35% of students scored no higher than 60%

d) 38.4% of students scored at least 81%

Step-by-step explanation:

a) the frequency refers to the number of students and each of the bars shows how many students got into a certain range of scores. So you would count the frequency for 4 of the ranges except for the last one.

b) interval 81-100 contained the most scores as it has the highest frequency

c) 2+4+12= 18 students scored no higher than 60%, the total number of students is 52 students. So to get the answer you would divide

18/52= 0.346 x 100= 34.6= 35%

d) 20/52= 0.384 x 100= 38.4%

The situations that have a net result of zero are:

The first situation results in a debt of $3 and then payment of $3, which cancels out the debt.

The second situation involves combining three atoms with a total charge of zero (2 atoms with a charge of negative 2, and 1 atom with a charge of positive 4).

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Answer:

480

Step-by-step explanation:

Take 96 and divide it by 2 to get what ten percent would be: 48

Then just multiply 48 by ten for 100% (The number): 480.

To check, take a calculator and do 480-20% and it equals 96.

Answer:

d 6  

it is not A B or c its

Step-by-step explanation:

edge 2020

The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

In the given question,

We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.

Since we have to find the image after a dilation.

So we learn about it now,

Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.

So the given point is (-9,12).

Scale factor is 1/3.

So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as

=(-9×1/3,12×1/3)

Simplifying

=(-3,4)

Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

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If the nex day, the biologist retums to the lake and takes a sample of 7 fish. Of those fish, 2 of them have tags. The estimated number of fish in the lake is 35 fish.

Let x represent the estimated number of fish in the lake

Hence,

x /10 = 7/2

Cross multiply

2x = 10 × 7

2x = 70

Divide both side by 2x

x =70/2

x = 35 fish

Therefore 35 is the number of fish.

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Answer:

Refer to the step-by-step explanation.

Step-by-step explanation:

Come up with a monomial expression and solve it.

A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.

Here are a few examples of an monomial expression:

\(\hrulefill\)

Let's work with the monomial expression, 3x²y³z.

To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.

Plug these values into the expression:

3x²y³z

=> 3(3)²(2)³(1)

=> 3(9)(8)(1)

=> 27(8)(1)

=> 216(1)

=> 216

Thus, the expression is solved.

Answer: 1:55 PM

Step-by-step explanation:

Turn 4:15 to 24-hr clock system which is 1615hrs

16:15 - 02:20 = 1355hrs

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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Answer:

____  or x = 7/10

Step-by-step explanation:

Lets rewrite it

____ - 1/2 = 1/5

Lets say ____ = x

x - 1/2 = 1/5

x = 1/2 + 1/5

x = 5/10 + 2/10

x = 7/10

CHECK

7/10 - 1/2 =

7/10 - 5/10 = 2/10 = 1/5

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The length of c is c = 13.3, and the angle measures are A = 17.7 and B = 97.3

From the question, we have the given parameters to be:

b = 10 inches

a = 14 inches

<C = 65 degrees

To calculate the length of c, we use the following equation of law of cosine

c^2 = a^2 + b^2 - 2 * a * b * cos(C)

Substitute the known values in the above equation

c^2 = 14^2 + 10^2 - 2 * 10 * 14 * cos(65 degrees)

Evaluate cos(65 degrees)

c^2 = 14^2 + 10^2 - 2 * 10 * 14 * 0.4226

Evaluate the exponent

c^2 = 196 + 100 - 2 * 10 * 14 * 0.4226

Evaluate the product

c^2 = 196 + 100 - 118.328

Evaluate the sum and the difference

c^2 = 177.672

Take the square root of both sides

c = 13.3

To calculate the angle measure of A, we use the following equation of law of sine

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

This gives

14/sin(A) = 13.3/sin(65)

This gives

14/sin(A) = 14.7

Rewrite as:

sin(A)  = 14/14.7

Evaluate the quotient

sin(A)  = 0.9524

Take the arc sin of both sides

A = 17.7

Lastly, we have

B = 180 - A - C

This gives

B = 180 - 17.7 - 65

Evaluate

B = 97.3

Hence, the length of c is c = 13.3, and the angle measures are A = 17.7 and B = 97.3

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Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

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

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

a) Yes

b) No

c) Yes

d) No

e) No

Step-by-step explanation:

Right triangle:

The square of the larger side is equals to the sum of the squares of the smaller sides.

a. 6, 8, 10

\(6^2 + 8^2 = 36 + 64 = 100 = 10^2\)

The answer is yes.

b. 8, 15, 16

\(8^2 + 15^2 = 64 + 225 = 289 \neq 16^2 = 256\)

So no.

c. 10, 24, 26

\(10^2 + 24^2 = 100 + 576 = 676 = 26^2\)

So yes

d. 20, 21, 28

\(20^2 + 21^2 = 400 + 441 = 841 \neq 28^2 = 784\)

So no.

e. 9, 35, 41​

\(9^2 + 35^2 = 81 + 1225 = 1306 \neq 41^2 = 1681\)

Answer:

Step-by-step explanation:

From the given information:

The number of children that were randomly allocated to each vaccination group; n₁ = 200,000

No of polio cases X₁ = 57

Now, in the vaccine group:

the proportion of polio cases is:

\(\hat p_1 = \dfrac{57}{200000}\)

=  0.000285

The number of children that were randomly allocated to the placebo group, n₂ = 200,000

No of polio cases X₂ = 142

In the placebo group

the proportion of polio cases is:

\(\hat p_2 = \dfrac{142}{200000}\)

Null and alternative hypothesis is computed as follows:

H₀: There is no difference in the proportions of polio cases between both groups.  

H₁: There is a difference in the proportions of polio cases between both groups.

Let assume that the level of significance ∝ = 0.05

The test statistic  can be computed as:

\(Z = \dfrac{\hat p_1-\hat p_2}{\sqrt{\dfrac{\hat p_1 \hat q_1}{n_1}+ \dfrac{\hat p_2 \hat q_2}{n_2}}}\)

\(Z = \dfrac{0.000285-0.000710}{\sqrt{\dfrac{0.000285(1-0.000285)}{200000}+ \dfrac{0.000710(1-0.000710)}{200000}}}\)

\(Z = \dfrac{-4.25\times 10^{-4}}{\sqrt{\dfrac{0.000285(0.999715)}{200000}+ \dfrac{0.000710(0.99929)}{200000}}}\)

Z = - 6.03

P-value =  2P(Z < -6.03)

From the Z - tables

P-value =  2 × 0.0000

= 0.000

We reject the H₀ provided that P-value is very less.

Therefore, we may conclude that there is a difference in the proportions of polio cases between the vaccine group and placebo group not due to chance.

Answer: 4.5

Step-by-step explanation:

Since the two black chords are congruent, we know that since the bottom black chord is split into two congruent parts, x = 4.5.

Answer: 5/3

Step-by-step explanation:

Answer:

  C. Equation

Step-by-step explanation:

An equation generally provides the most specific information about a function. However, it cannot always be used for certain purposes—such as finding a specific inverse function value.

In the case of equations that are infinite series, even evaluating the function can become difficult when the series converges slowly.

Answer: B. 2(x - 3)(x - 4)

Step-by-step explanation: