Brianna makes a model of the Eiffel Tower for a school project. Her model is 25 centimeters wide at the bottom
If Brianna used a scale of 1 centimeter for every 5 meters, how vide is the actual Efe Towet?

The required volume of the given rectangular prism is given as 240 in ³.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
From the data we have,
Length of the rectangle prism = 12 in
Width of the rectangle prism = 2 in
Height of the rectangle prism = 10 in

The volume of the rectangular prism = length × width × height
                                                 = 12 × 2 × 10
                                                 = 240 in ³

Thus, the required volume of the given rectangular prism is given as 240 in ³.

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The question is incomplete.
Complete question is," Calculate the volume of the prism of dimensions length, width and height are 12, 2, and 10 respectively. "

Answer:

yes Cecilia make her first mistake in step 2

Answer:

See attached image

Step-by-step explanation:

With this type of reflection, one has to convert the points of the form (x, y) into (y, x).

So the vertices of the triangle will transform the following way:

(4, 4)   into image (4, 4)

(4, 1)   into image  (1, 4)

(2, 1)  into image  (1, 2)

Please see attached picture to find the new reflected triangle depicted in red.

The equation that shows the point-slope form of the line passing through (3, 2) with a slope of (1/2) is:

y - 2 = (1/2)(x - 3)

In the point-slope form of a linear equation, the formula is y - y1 = m(x - x1), where (x1, y1) represents a point on the line, and m represents the slope of the line. By substituting the given values into the formula, we can determine the correct equation.

In this case, the given point is (3, 2) and the slope is (1/2). Plugging these values into the formula, we get:

y - 2 = (1/2)(x - 3)

This equation represents the line passing through the point (3, 2) with a slope of (1/2). It is in the point-slope form, which allows us to easily determine the equation of a line based on a given point and slope.

Therefore, the correct equation is y - 2 = (1/2)(x - 3).

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Answer: B

Step-by-step explanation:

Answer:

  (-8, -6)

Step-by-step explanation:

When you graph the given equation on the given graph, you find the lines intersect at (-8, -6).

The solution to the system is (-8, -6).

__

The equation is given in slope-intercept form, so you can find the y-intercept (y=10) and draw a line with slope 2 from there. It will go through (-5, 0), so you know the solution lies in the 3rd quadrant and has an x-value less than -5. Only one answer choice matches.

Answer:

the first choice.

Step-by-step explanation:

Answer:

y=3

Step-by-step explanation:

12-3(3)<6

12-9<6

3<6

This makes the expression true so y=3

Answer:

y > 2

Step-by-step explanation:

isolate the y:

=> -3y < 6 -12

=> -3y < -6

=> y > 2

       ↑ have to change the inequality sign when divide/multiply by a negative number

Step-by-step explanation:

Given is the 30°x60°x90° right triangle.

The ratio of its sides is:

Find the missing sides using the ratio above:

Answer:

\(\sf x = 4\sqrt{6}\)   and   \(\sf y = 6\sqrt{2}\)

step-by-step explanation:

given:

using tan rule:

\(\sf tan(x)= \dfrac{opposite}{adjacent}\)

\(\sf tan(60)= \dfrac{y}{2\sqrt{6} }\)

\(\sf tan(60)*{2\sqrt{6}= y\)

\(\sf y = 6\sqrt{2}\)

using cosine rule:

\(\sf cos(x)= \dfrac{adjacent}{hypotensue}\)

\(\sf cos(60)= \dfrac{2\sqrt{6} }{x}\)

\(\sf x= \dfrac{2\sqrt{6} }{cos(60)}\)

\(\sf x = 4\sqrt{6}\)

the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.

therefore, for y =  5/16x² - 5x/4 -35/4

Quadratic coefficient = 5/16, linear coefficient = 5/4, constant term = -35/4

What are zeros ?

zeros denotes the factors of the given equation in other words the zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.

Polynomial roots are the same as polynomial zeros, so they can be found by factoring the quadratic equation into two linear factors, after which they can be equating to zero.

Its easiest to first start out with a vertex form equation because it can then be converted to a standard quadratic equation.

given a vertex at (2,-10) , and point of intersection at (6,-5), the equation can be set up like this in the form of :

y = a(x-h)²+ k

y = a(x-2)^2-10, as we know h and k from the vertex.

We also know y and x from the given point of intersection so a can be solved by substituting the values of x and y to get value of a.

y = a(x-2)²-10

-5 = a(6-2)² - 10

16a = 10-5

a = 5/16

a = 5/16 which is also known as the quadratic coefficient because it is part of a second degree quantity and a Trinomial as a whole(quadratic).

since all the variables are known, you can expand the equation and set it to standard form :

y = 5/16(x-2)²-10

y = 5/16(x-2)² - 10

y = 5/16(x²+4-4x) -10

y = 5/16x² + 5/4 - 5x/4 - 10

y =  5/16x² - 5x/4 -35/4

For reference, the standard form equation is y=ax²+bx+c where a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.

In this instance, 5/16x² - 5x/4 -35/4 = ax²+bx+c

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a)

In order to find Kyle's speed in miles per hour, we just need to divide the amount of miles he walked by the amount of time it took:

b)

In order to calculate the LCM of 2 and 4, let's factor them in their prime factors:

The LCM is the product of each prime factor the maximum number of times they appear in a single number, so we have LCM = 2 * 2 = 4.

Multiplying 1/2 and 1/4 by 4, we have:

So in one hour he walks 2 miles, so his speed is 2 miles per hour.

Answer:

Subjective

Conditional

Step-by-step explanation:

The 0% probability of accepting the offer is a subjective probability, since it is derived from candidate 4's individual personal judgment without calculations.

As for the 100%, it is a conditional probability, since it is linked to the probability of another event also happening. It is that probability of candidate 4 accepting the offer, given that candidate 5 is also hired.

Answer:

16

Step-by-step explanation:

Let the number be x.

\(\frac{3}{4}x = 12\)

∴ x = 12 ÷ \(\frac{3}{4}\)

     = 16

Answer:

x = 4

Step-by-step explanation:

You can solve for "x" by rearranging the equation and getting the "x" by itself on one side. Remember, whatever you do to one side of the equation, you must do to the other side.

-6 + x = -2                         <----- Original equation
+6         +6                        <----- Add 6 to both sides to isolate "x"

0 + x = 4                           <----- After the addition

x = 4                                 <----- Rewrite

Answer:

None of the above (x = 4) \( \sf {} \)

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ -6 + x = -2

Then the value of x will be,

→ -6 + x = -2

→ x = -2 + 6

→ [ x = 4 ]

Hence, the value of x is 4.

Answer:

$230

Step-by-step explanation:

Answer:

$230

Step-by-step explanation:

Divide 60 by 12 and get 5.

Then multiply 5 × 46 and get $230 dollars.

Answer:

3/16

Step-by-step explanation:

Prove that sin 20 ×sin40 × sin60 × sin80 = 3/16.

We have to prove sin 20 × sin40 × sin60 × sin80 = 3/16.

Consider LHS

sin 20 × sin 40 × sin60 × sin80

Sin Values

In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle. The sine function is used to find the unknown angle or sides of a right triangle.

We know the trigonometric values of sin function

Proof

Consider LHS

sin 20 × sin 40 × sin60 × sin80

= sin60 [sin20 × sin40 × sin80]

= √3/2[sin20 × sin(60 – 20) × sin(60 + 20)]

= √3/2[sin 3(20)/4]

= √3/2[sin 60/4]

= √3/2[√3/2 × 4]

= √3/2 × √3/8 =  3/16

∴ LHS = RHS

Hence proved

The solution to the inequality \(w - 0.9 >-2.1\) is \(w >-1.2\)

Inequalities are used to represent expressions of unequal values

The inequality is given as:

\(w - 0.9 >-2.1\)

Add 0.9 to both sides of the inequality

\(w - 0.9+ 0.9 >-2.1 + 0.9\)

Simplify the inequality

\(w >-1.2\)

The above inequality means that:

See attachment for the inequality that represents \(w >-1.2\)

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Answer:

6/24.

Step-by-step explanation:

24 = 4 * 6 so we:

multiply by 6/6:

1 * 6

------  =    6 / 24.

4 * 6

Answer:

a) 0.0465 = 4.65% probability that in one upperclassman House at MIT, enough students are vaccinated to achieve herd immunity.

b) \(1.02 \times 10^{-16}\) probability that herd immunity is achieved in all 12 Houses.

c) We needed that \(np \geq 10, n(1-p) \geq 10\), which was achieved.

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution, normal probability distribution and the central limit theorem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

For a proportion p in a sample of size n, as long as \(np \geq 10, n(1-p) \geq 10\) the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

a) Suppose that 94% of undergraduate students in the United States report having received two doses of the MMR vaccine. What is the probability that in one upperclassman House at MIT, enough students are vaccinated to achieve herd immunity? There are approximately 400 students in any house.

We have that \(p = 0.94, n = 400\). So

\(np = 400*0.94 = 376 \geq 10\)

\(n(1-p) = 400*0.06 = 24 \geq 10\)

The standard deviation is:

\(s = \sqrt{\frac{0.94*0.06}{400}} = 0.0119\)

The probability is 1 subtracted by the pvalue of Z when X = 0.96. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.96 - 0.94}{0.0119}\)

\(Z = 1.68\)

\(Z = 1.68\) has a pvalue of 0.9535

1 - 0.9535 = 0.0465 = 4.65% probability that in one upperclassman House at MIT, enough students are vaccinated to achieve herd immunity.

b) Calculate the probability that herd immunity is achieved in all 12 Houses.

Now, we use the binomial distribution. This is \(P(X = 12)\) when \(n = 12\) with \(p = 0.0465\). So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 12) = C_{12,12}.(0.0465)^{12}.(0.9535)^{0} = 1.02 \times 10^{-16}\)

\(1.02 \times 10^{-16}\) probability that herd immunity is achieved in all 12 Houses.

c) Discuss the validity of the assumptions required to make the calculation in part i.

We needed that \(np \geq 10, n(1-p) \geq 10\), which was achieved.

The bell-shaped curve, also known as a Gaussian curve or a symmetrical distribution , showcases a central peak with data symmetrically distributed around it .

Revered for its iconic shape, the bell curve enchants the discerning observer with its symmetrical countenance, reminiscent of a resonant chime.

This majestic distribution unveils its true essence through its discernible apex, a testament to central tendency , where the mean, median, and mode converge, bestowing upon it an air of distinction .

The rough sketch of the curve having the bell shape is shown attached to the question.

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Answer:

  f^-1(x) = (4x +3)/(1 -x)

Step-by-step explanation:

Solve for y:

  f(y) = x

  (y -3)/(y +4) = x

  y -3 = xy +4x . . . . . . multiply by y+4

  y -xy = 4x +3 . . . . . . add 3-xy

  y(1 -x) = 4x +3 . . . . . factor out y

  y = (4x +3)/(1 -x) . . . divide by the coefficient of y

The inverse function is ...

  f^-1(x) = (4x +3)/(1 -x)

Answer:

Step-by-step explanation:

Mean: Add all the values and divide by the # of values

Median: The center of the values

Mode: The value that appears the most in the data set

Mean for data set 1: 86

Mean for data set 2: (85+89+71+85+86+91+92+96+87)/2= approximately 86.89

Median for data set 1: 72,75,78,80,88,90,95,98,98

We've sorted it from least to greatest, and the center is 88 because there is 4 values to the left of it, and 4 values to the right. It's at the very center.

Median for data set 2: 71,85,85,86,87,89,91,92,96

The center for this is 87 because it is again, at the absolute center/middle between the data.

Mode for data set 1: 98 because it appears 2 times, which is more often than other values

Mode for data set 2: 85 because it appears most often (2 times) in the data set

Hope this helps! :)

Answer:

Step-by-step explanation:

You want the ratio of vowels to consonants in each of the words "pineapple" and "strawberry."

To form the reduced ratio vowels:consonants, we need to identify the type of letter each is. Here we use bold to identify the vowels.

  pineapple ⇒ 4:5

  strawberry ⇒ 3:7 . . . . counting "y" as a vowel

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

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Of(x) = 1,100(1.12) function represents the value of the painting each year.

This is a problem of exponential growth.

Quantity rises over time through a process called exponential growth. It happens when the derivative, or instantaneous rate of change, of a quantity with respect to time, is proportionate to the original quantity. In contrast to other types of growth, such as quadratic growth, a quantity undergoing exponential growth is described as an exponential function of time, meaning that the variable corresponding to time is the exponent.

Given that the original value of a painting is $1,100 and the value increases by 12% each year.

Let the original value of the painting be "x".

The increase percent given is 12% = 0.12

The Exponential Growth Function for this question can be written as,

y=x(1+0.12)^t  (t=no of years, x=original value)

For every year, t=1

Of(x)=y=x(1.12)^1

Of(x)=y=1,100(1.12)

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Answer:

............................

Answer:

Step-by-step explanation:

9514 1404 393

Answer:

  61.4

Step-by-step explanation:

The length of two semicircles of diameter 10 is the circumference of a circle of that diameter:

  C = πd = 10π ≈ 31.4

The perimeter includes that length plus the lengths of two straight sides that are 15 units each.

  P = 31.4 + 2×15

  P = 61.4 . . . . units

Answer:

3900

Step-by-step explanation:

let x= number of workers

we know that .15 (or 1-.85) of the people are not women

so

.15x=585

585/.15=x

3900=x

Answer: Should be 150mm

Step-by-step explanation:

Find the surface area of each figure. Round answers to the nearest tenth, if necessary

2 mm-

2/5 mm

10 mm

3 mm

O

75 mm2

150 mm2

92 mm2

86 mm2

Answer:

area of trapezium: 740 cm²

Step-by-step explanation:

\(\sf {Area \ of \ trapezium = \frac{1}{2}* (base \ 1 \ + base \ 2) \ * height }\)

Given here:

using the formula:

\(\sf {Area \ of \ trapezium = \frac{1}{2}* (base \ 1 \ + base \ 2) \ * height }\)

solve:

\(\sf {\frac{1}{2}* (34 \ + 40) \ * 20}\)

\(\sf {\frac{1}{2}* (74) \ * 20}\)

\(\sf 74 * 10\)

\(\sf 740\)