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Answer:

11 inches by 11 inches

Step-by-step explanation:

The dimensions of the original photo were 11 inches by 11 inches.

We are informed that the area of the reduced photo is 64 square inches and that In the equation (x – 3)^2 = 64, x represents the side measure of the original photo.

In order to solve for x, we shall first take square roots on both sides of the equation;

The square root of (x – 3)^2 is simply (x - 3).

The square root of 64 is ±8 but we ignore -8 since the dimensions of any figure must be positive.

Therefore, we have the following equation;

x - 3 = 8

x = 8 + 3

x = 11

Answer:

Option 1: 11 inches by 11 inches

Step-by-step explanation:

Answer: Third option

[tex]f(x) - 2[/tex]

Step-by-step explanation:

The function [tex]y=log_3 (x)[/tex] passes through the point (1,0) since the function [tex]y=log_a (x)[/tex] always cuts the x-axis at [tex]x = 1[/tex].

Then, if the transformed function passes through point (1,-2) then this means that the graph of [tex]y=log_3(x)[/tex] was moved vertically 2 units down.

The transformation that displaces the graphically of a function k units downwards is:

[tex]y = f (x) + k[/tex]

Where k is a negative number. In this case [tex]k = -2[/tex]

Then the transformation is:

[tex]f(x) -2[/tex]

and the transformed function is:

[tex]y = log_3 (x) -2[/tex]

Answer:

yes, x > 4

Step-by-step explanation:

Add 7 to your inequality to get ...

3x > 12

Then divide by 3, and you have ...

x > 4

_____

We're not understanding the meaning of your " = 4" in the problem statement. It appears to have no place, either in the problem or in the solution.

Answer: Last option

The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.

Step-by-step explanation:

Note that: [tex]-3\frac{1}{4} =-3-\frac{1}{4} =-3.25[/tex]

The inequality is:

[tex]k<-3 \frac{1}{4}[/tex]

The inequality is:

This means that the inequality includes all values of the number line that are less than -3.25 or that are to the left of -3.25

__-8.4_________-3.25_-3____0___0.9____________7.1__

Note that the number -8.4 is less than -3.25, because it is to its left on the number line.

Then the correct statement is:

The number -8.4 is a solution to the inequality because -8.4 is located to the left of [tex]-3\frac{1}{4}[/tex] on the number line.

Answer:

the last option!!!

Step-by-step explanation:

i took the unit test

Line integral: Parameterize [tex]C[/tex] by

[tex]\vec r(t)=\langle\sqrt{13}\cos t,\sqrt{13}\sin t,0\rangle[/tex]

with [tex]0\le t\le2\pi[/tex]. Then

[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle\sqrt{13}\cos t,\sqrt{13}\sin t,0\rangle\cdot\langle-\sqrt{13}\sin t,\sqrt{13}\cos t,0\rangle\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^{2\pi}0\,\mathrm dt=\boxed 0[/tex]

Surface integral: By Stokes' theorem, the line integral of [tex]\vec F[/tex] over [tex]C[/tex] is equivalent to the surface integral of the curl of [tex]\vec F[/tex] over [tex]S[/tex]:

[tex]\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S[/tex]

The curl of [tex]\langle x,y,z\rangle[/tex] is 0, so the value of the surface integral is 0, as expected.

The answer would b "C" 15/17 because Sin is Opposite over Hypotenuse

Step-by-step explanation:

The measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse option third is correct.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

We have a right angle triangle with dimensions shown in the picture:

From the sin ratio in the right angle triangle:

sin∠C = 15/17

Thus, the measure of the sin∠C is 15/17 because sin is the ratio of side opposite to the angle to hypotenuse.

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Rewrite [tex]f[/tex] as

[tex]f(x)=\dfrac{10}x=-\dfrac5{1-\frac{x+2}2}[/tex]

and recall that for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

so that for [tex]\left|\dfrac{x+2}2\right|<1[/tex], or [tex]|x+2|<2[/tex],

[tex]f(x)=-5\displaystyle\sum_{n=0}^\infty\left(\frac{x+2}2\right)^n[/tex]

Then the radius of convergence is 2.

The Taylor series for the function f(x) = 10/x, centered at a = -2, is given by the formula  ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence (R) for the series is ∞, which means the series converges for all real numbers x.

Given the function f(x) = 10/x, we're asked to find the Taylor series centered at a = -2. A Taylor series of a function is a series representation which can be found using the formula f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + .... For f(x) = 10/x, the Taylor series centered at a = -2 will be ∑(10(-1)^n*n!(x + 2)^n)/n! from n=0 to ∞. The radius of convergence R is determined by the limit as n approaches infinity of the absolute value of the ratio of the nth term and the (n+1)th term. This results in R = ∞, indicating the series converges for all real numbers x.

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Answer:

3/1

Step-by-step explanation:

Well there's 6 sides on a dice and only 2 winning numbers. 6/2=3/1. You have a good chance of losing lol. Is this what you're looking for?

~Keaura/Cendall.

Follow below steps:

To find the expected winnings for the game described, we need to calculate the expected value of one roll of the die based on the outcomes and their corresponding probabilities and payoffs. This is a classic example of a discrete probability distribution problem where the random variable X represents the winnings from one roll of the die.

There are two winning outcomes, rolling a four and rolling a five, each of which has a probability of 1/6 and a payoff of 8 dollars. There are four losing outcomes, rolling a one, two, three, or six, each with the same probability of 1/6 and a loss of 4 dollars.

Therefore, the expected value E(X) is calculated as follows:

E(X) = (2/6) * 8 + (4/6) * (-4) = (16/6) - (16/6) = 0

So the expected winnings for this game are 0 dollars, which means that, on average, a player neither wins nor loses money in the long term.

Answer:

The total is 8.

And the total of not green is 6

so the probability is 6/8 or you can write as

3/4

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Answer:

D. Confidence Level: 95%; Confidence Interval: 42 to 48

Step-by-step explanation:

48-42=6

6/2=3

3 is smallest

I tested A and got it incorrect so D is the awnser

Confidence Level: 95%; Confidence Interval: 42 to 48. Then the correct option is D.

Suppose the confidence interval at P% for some parameter's values is given by x ± y.

That means that the parameter's estimated value is P% probable to lie in the interval

[x - y, x + y]

Four research teams each used a different method to collect data on how fast a new iron skillet rusts.

Assume that they all agree on the sample size and the sample mean (in days).

Use the (confidence level; confidence interval) pairs below to select the team that has the smallest sample standard deviation.

Then we have

48 - 42 = 6

Then we have

6/2=3

3 is smallest

Then the correct option is D.

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Answer:

pizza: $4, coke: $3, chips: $2

Step-by-step explanation:

Lets make the price of a pizza=p a coke= k and a bag of chips=c

then we have the following equations

p+k+c=9

p+2k=10

2p+2c=12

Because p is common in all the equations we shall make it the subject of each equation.

p=9-(k+c)...........i

p=10-2k..............ii

p=6-c...................iii

We then equate i and iii

9-(k+c)=6-c

9-k-c=6-c

putting like terms together we get:

9-6=-c+c+k

1 coke, k=$3

replacing this value in equation ii

we get  p=10-2(3)

p=10-6= 4

1 pizza, p=$4

replacing this value in equation iii

4=6-c

c=6-4

=2

a bag of chips, c=$2

Thus, a pizza, a coke and a bag of chips= pizza: $4, coke: $3, chips: $2

For this case we have that variable "m" represents the cost of Jake's food. They tell us that he left an 18% tip. That is to say:

m -------------> 100%

tip ------------> 18%

Where "tip" is the cost of the tip based on the cost of the meal.

[tex]tip = \frac {18 * m} {100}\\tip = 0.18m[/tex]

The amount Jake pays is represented by:

[tex]m + 0.18m[/tex]

Where 0.18m is the tip

ANswer:

Tip

Answer:

the tip amount jake pays

Step-by-step explanation:

A. His solution is accurate

You can verify this by expanding his factored expression: 1/3x(4y+1), which gives you back the original expression 4/3xy+1/3x

Charles' solution is accurate because expression after factorization  is similar to Charles factor's of expression option (A) is correct.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

[tex]\rm = \dfrac{4}{3}xy+\dfrac{1}{3}x[/tex]

Taking common as (1/3)x

[tex]\rm = \dfrac{1}{3}x(4y+1)[/tex]

The above expression is similar to Charles factor's of expression.

Thus, Charles solution is accurate because expression after factorization  is similar to Charles factor's of expression option (A) is correct.

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Since [tex]X\sim\mathrm{Geom}(p)[/tex], [tex]X[/tex] has PMF

[tex]P(X=x)=\begin{cases}(1-p)^{x-1}p&\text{for }x\in\{1,2,3,\ldots\}\\0&\text{otherwise}\end{cases}[/tex]

By definition of conditional probability,

[tex]P(X=n+k\mid X>n)=\dfrac{P(X=n+k\text{ and }X>n)}{P(X>n)}[/tex]

[tex]X[/tex] has CDF

[tex]P(X\le x)=\begin{cases}0&\text{for }x<1\\1-(1-p)^x&\text{for }x\ge1\end{cases}[/tex]

which is useful for immediately computing the probability in the denominator:

[tex]P(X>n)=1-P(X\le n)=(1-p)^n[/tex]

Meanwhile, if [tex]X=n+k[/tex] and [tex]k\ge1[/tex], then it's always true that [tex]X>n[/tex], so

[tex]P(X=n+k\text{ and }X>n)=P(X=n+k)=(1-p)^{n+k-1}p[/tex]

Then

[tex]P(X=n+k\mid X>n)=\dfrac{(1-p)^{n+k-1}p}{(1-p)^n}=(1-p)^{k-1}p[/tex]

which is exactly [tex]P(X=k)[/tex] according to the PMF.

The memoryless property states that given there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k.

To show that if X ∼ Geom(p) then P(X = n + k|X > n) = P(X = k), for every n, k ≥ 1, we use the memoryless property of the geometric distribution. The memoryless property states that given that there are no successes in the first n trials, the probability that the first success comes at trial n + k is the same as the probability that a freshly started sequence of trials yields the first success at trial k. So, we have P(X = n + k|X > n) = P(X = k).

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Answer:

-8a(a+3b)

Step-by-step explanation:

(2a+6b)(6b−2a)−(2a+6b)^2

(2a+6b) {(6b−2a)−(2a+6b)(2a+6b)}

2(a+3b) (6b-2a-2a-6b)

2(a+3b) (-4a)

-2(a+3b) x 4a

-2 x 4a (a+3b)

-8a(a+3b)

The  simplified expression is -8a² - 24ab.

Given expression: (2a + 6b)(6b - 2a) - (2a + 6b)^2

First, let's expand the squared term (2a + 6b)^2:

(2a + 6b)(6b - 2a) - (2a + 6b)(2a + 6b)

Now, we have a common factor of (2a + 6b) in both terms, so let's factor it out:

(2a + 6b)[(6b - 2a) - (2a + 6b)]

Now, simplify the expression inside the brackets:

(2a + 6b)[6b - 2a - 2a - 6b]

Combining like terms within the brackets:

(2a + 6b)[-4a]

Now, multiply the remaining terms:

-4a(2a + 6b)

-8a² - 24ab

Therefore, the simplified expression is -8a² - 24ab.

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What's the question?

Answer:

80%

Step-by-step explanation:

"He will start with the Brachiosaurus which has an estimated height of 15 meters and make the model 3 meters on height. by what percent will Ruben decrease the size of the Brachiosaurus in order to fit it into the display"

The percent decrease is the difference in heights divided by the original height.

(15 - 3) / 15

12/15

0.8

So Ruben will decrease the size by 80%.

Answer:

6 is -3        

8 is -5

Step-by-step explanation:

Answer:

x=44

Step-by-step explanation:

33+103+x=180

136+x=180

x=44

The sum of all the angles of a triangle is 180 degrees.  

Add all the angles together and set it equal to 180, then solve for x

33 + 103 + x = 180

(136 - 136) + x = 180 - 136

x = 44

Hope this helped!

Evaluating a function in a specific point means to substitute all occurrences of x with the specific value.

In your case, we have to substitute "x" with "a+h":

[tex]f(x)= -5+4x^2 \implies f(a+h) = -5+4(a+h)^2\\ = -5+4(a^2+2ah+h^2)=-5+4a^2+8ah+h^2[/tex]

Step-by-step explanation:

A sequence is an ordered list of numbers.

lim n → ∞ an = 8 means that as n approaches infinity (becomes large), an approaches 8.

lim n → ∞ an = ∞ means that as n approaches infinity (becomes large), an approaches infinity (becomes large).

A sequence is an ordered list of numbers, and when lim n → ∞ an = 8, it means the sequence's terms approach 8 as n becomes large. Saying lim n → ∞ an = ∞ indicates that the sequence's terms grow without bound as n increases.

Answering your questions on sequences and limits:

(a) What is a sequence?

A sequence is an ordered list of numbers. Unlike a set where the order of elements does not matter, in a sequence, every number has a distinct place. For instance, the sequence of natural numbers is an ordered list starting from 1 and proceeding indefinitely in the order 1, 2, 3, 4, ... etc.

(b) What does it mean to say that lim n → ∞ an = 8?

This statement means that the terms an approach 8 as n becomes large. In other words, as you progress further along in the sequence, the values of the terms get closer and closer to 8, virtually reaching 8 as the sequence goes towards infinity. This is a fundamental concept in understanding sequences' behavior at their extremities.

(c) What does it mean to say that lim n → ∞ an = ∞?

This implies that the terms an become large as n becomes large. As the n value increases, the sequence's terms grow unlimitedly, indicating the sequence's divergence rather than converging to a definite number.

Answer:

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million

Answer:

370 million

Step-by-step explanation:

In the 10 years from 2000 to 2010, the population was multiplied by the factor ...

100% + 9.6% = 109.6% = 1.096

In the next 20 years from 2010 to 2030, the population will be multiplied by that factor twice, if it grows at the same rate:

2030 population = (308 million)·(1.096²) ≈ 370 million

Answer:

a=16

Step-by-step explanation:

Given

(y-4)(y^2+4y+16)

To find the value of a in the resulting polynomial we have to solve the given expression

=y(y^2+4y+16)-4(y^2+4y+16)

= y^3+4y^2+16y-4y^2-16y-64

To find the value of a, both the polynomials will be compared

y^3+4y^2+16y-4y^2-16y-64  

y^3+4y^2+ay-4y^2-ay-64

Comparing the coefficients of both polynomials gives us that

a=16

So, the value of a is 16 ..  

The formula for volume of a cone is V = PI x r^2 x h/3 where r is the radius and h is the height.

Volume of cone = 3.14 x 7^2 x 12/3

Volume of cone = 3.14 x 49 x 4

Volume of cone = 615.44 cubic inches.

The formula for volume of half a sphere is : 1/2 x (4/3 x PI x r^3)

Volume for half sphere = 1/2 x (4/3 x 3.14 x 7^3)

= 1/2 x 4/3 x 3.14 x 343

= 718.01 cubic inches.

Total volume = 615.44 + 718.01 = 1333.45 cubic inches.

Rounded to the nearest tenth = 1,333.5 cubic inches.

Answer:

Area of triangle = 6 in^2

Step-by-step explanation:

We need to find the area of triangle. The formula used is:

Area of triangle = 1/2 * b*h

where b=base and h= height

In the given question, b =2 and h= 6

Putting values in the formula:

Area of triangle = 1/2 *2*6

                          = 12/2

                          =  6 in^2

Answer:

The area is 6 in^2

Step-by-step explanation:

Part A is incorrect because for negative numbers, the greater the magnitude the smaller the number. -2 is smaller than -1, for example, and -20 is smaller than -15.

An elevation of -15ft means 15 ft below sea level, an elevation of -20ft means 20 ft below sea level, and an elevation of (+) 7ft means 7 ft above sea level.

If John started the trail at sea level (0ft elevation), then the greatest change in elevation would be between that and the second rest stop. Take the absolute value of all the numbers and see which one is the largest.

Answer:

  the length of the midsegment is 12 cm

Step-by-step explanation:

ΔMNK is a 30°-60°-90° triangle, so side MK is twice the length of side MN. That makes MN = (16 cm)/2 = 8 cm.

Dropping an altitude from N to intersect MK at X, we have ΔMXN is also a 30°-60°-90° triangle with side MN twice the length of side MX. That makes MX = (8 cm)/2 = 4 cm.

The length of the midsegment of this isosceles trapezoid is the same as the length XK, so is (16 -4) cm = 12 cm.

Answer:

12 cm.

Step-by-step explanation:

1. Consider right triangle MNK. In this triangle, angle N is right and m∠M=60°, then m∠K=30°. Thus, this triangle is a special 30°-60°-90° right triangle with legs MN and NK and hypotenuse MK=16 cm. The leg MN is opposite to the angle with a measure of 30°. This means that this leg is half of the hypotenuse, MN=8 cm.

2. Consider right triangle MNH, where NH is the height of trapezoid drawn from the point N. In this triangle m∠M=60°, angle H is right, then m∠N=30°. Similarly, the leg MH is half of the hypotenuse MN, MH=4 cm.

3. Trapezoid MNOK is isosceles because of MN=OK=8 cm. This means that NO=MK-2MH=16-8=8 cm.

4. The midsegment of the trapezoid is:

[tex]\frac{MK+NO}{2}=\frac{16+8}{2}=12cm[/tex]

Answer:

  1.92, 3.84, 4.8, 5.76

Step-by-step explanation:

In the given set, the sum of the last two numbers is 5+6 = 11; the sum of the first two numbers is 2+4 = 6. The difference between these sums is 11-6 = 5.

You want to scale all the numbers by a factor of 4.8/5 = 0.96 so that the difference computed the same way is 4.8 instead of 5.

Then the numbers are ...

  0.96{2, 4, 5, 6} = {1.92, 3.84, 4.8, 5.76}

Answer:

[tex]\boxed{\text{1.92, 3.84, 4.80, and 5.76}}[/tex]

Step-by-step explanation:

The numbers  must be in the ratio 2:4:5:6.

Let's call them 2x, 4x, 5x, and 6x. Then

5x + 6x =  11x = sum of last two numbers

2x + 4x =    6x = sum of first two numbers

According to the condition,

11x – 6x = 4.8

        5x = 4.8

          x = 0.96

2x = 1.92; 4x = 3.84; 5x = 4.80; 6x = 5.76

The numbers are [tex]\boxed{\textbf{1.92, 3.84, 4.80, and 5.76}}[/tex]

Check:

(4.80 + 5.76) – (1.92 + 3.84) = 4.8

     10.56       –       5.76       = 4.8

                              4.8         = 4.8

OK.

Answer:

27 ft

Step-by-step explanation:

I hope I helped

Answer:

C

Step-by-step explanation:

We need to write this in an algebraic form.

Therefore, the equation we would have is: [tex]x+3x+5x+2=47\\9x+2=47\\9x=45\\x=45/9\\x=5[/tex]

Thus, the longest piece is 27 feet long.

Answer:

[tex]f^{-1}(x)=\frac{1}{2}ln(x)+2[/tex]

Step-by-step explanation:

Start by changing the f(x) into a y.  Then switch the x and the y.  Then solve for the new y.  Like this:

[tex]y=e^{2x-4}[/tex] becomes

[tex]x=e^{2y-4}[/tex]

To solve for the new y, we need to get it out of its current exponential position which requires us to take the natural log of both sides.  Since a natural log has a base of e, natural logs and e's "undo" each other, just like taking the square root of a squared number.  

[tex]ln(x)=ln(e)^{2y-4}[/tex]

When the ln and the e cancel out we are left with

ln(x) = 2y - 4.  Add 4 to both sides to get

ln(x) + 4 = 2y.  Divide both sides by 2 to get

[tex]\frac{1}{2}ln(x) + 4 = y[/tex].

Since that is the inverse of y, we can change the y into inverse function notation:

[tex]f^{-1}(x)=\frac{1}{2}ln(x)+4[/tex]

Final answer:

To find the inverse function of f(x) = e²ˣ - 4, you switch x and y, solve for the new y, and arrive at the inverse function f^-1(x) = (1/2) * ln(x + 4).

Explanation:

To find the inverse function of f(x) = e²ˣ - 4, we first need to switch the roles of x and f(x), and then solve for the new x. Here are the steps:

So, the inverse function of f(x) = e²ˣ - 4 is f-1(x) = (1/2) * ln(x + 4).

Answer:

[tex]5x-40y=4[/tex]

Step-by-step explanation:

we know that

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers

In this problem we have

[tex]8y=x-0.8[/tex]

Multiply by 5 both sides

[tex]40y=5x-4[/tex]

Adds both sides 4

[tex]40y+4=5x[/tex]

Subtract 40y both sides    

[tex]4=5x-40y[/tex]

Rewrite

[tex]5x-40y=4[/tex] ----> equation of the line into standard form

A=5

B=-40

C=4