The diagram shows a right triangle and three squares. The area of the largest square is 55 units.
Which could be the areas of the smaller squares?
Choose all answers that apply:
A
12 and 43
B
14 and 40
16 and 37
​

Answer:

13

Step-by-step explanation:

We need to write our answer in exponential form. Ask yourself the question, "What times itself 3 times will give you 2197?" Your answer is [tex]13^{3}[/tex]. This will go inside of your cube root. You now have [tex]\sqrt[3]{13^{3} }[/tex]. Since there's a power of 3 and a cube root, those cancel each other out, and your answer is 13.

Answer:

[tex]\boxed{13}[/tex]

Step-by-step explanation:

=> [tex]\sqrt[3]{2197}[/tex]

Factorizing 2197 gives 13 * 13 * 13

=> [tex]\sqrt[3]{13*13*13}[/tex]

=> [tex]\sqrt[3]{13^3}[/tex]

We know that [tex]\sqrt[3]{} = ^{1/3}[/tex]

=> [tex]13^{3 * 1/3}[/tex]

=> [tex]13^1[/tex]

=> 13

Answer:

d) The t-distribution with 5 degrees of freedom must be used

Step-by-step explanation:

For cases of Normal Distribution where the variance is unknown and the sample size n is smaller than 30, we must use the t-student distribution.

The shape of the curve for t-student is bell-shape (flatter and with wider tails than the bell shape of normal distribution.

Actually, when we deal with t-student distribution we are dealing with a family of curves that will become closer and closer to the bell shape of the normal distribution as the degree of freedom increases. From values of n =30( and bigger),  we can assume that the curve of t-student is the same as for normal distribution

Answer:

a) y = 25495 - 2707x

b) y = 25495 - 2707(4) = 14,667

c) $2,707 per year

Step-by-step explanation:

Value now: $25,495

Value in 2 years: $20,081

Loss of value in 2 years: $25,495 - $20,081 = $5,414

Loss of value per year: $5,414/2 = $2,707

a) y = 25495 - 2707x

b) y = 25495 - 2707(4) = 14,667

c) $2,707 per year

Answer:

C. It is one-half the area of a square of side length 4 units.

Step-by-step explanation:

Hey there!

Well if a square has side lengths of 4 units,

the area would be 16 because of l*w.

Now the formula for the area of a triangle is,

b*h/2

b = 4

h = 4

4*4=16

16 ÷ 2 = 8

So the area of a square is 16 units^2 whereas the area of a triangle with the same dimensions is 8 units^2,

meaning the area of a triangle is one-half the area of a square.

Hope this helps :)

Answer:

x>3

Step-by-step explanation:

Answer:

  0.0228

Step-by-step explanation:

A suitable probability calculator (or spreadsheet) can tell you this.

It is about 0.0228.

Answer:

8 pounds

Step-by-step explanation:

2 x 3 = 6 tb of chili powder in pot 2

find pounds per tablespoon: 48 / 6 = 8 pounds

Answer:

1/2 pound per tablespoon

Step-by-step explanation:

Jaden sure does like his chili!

In the first and second pot, he uses 3 pounds worth of ground beef, which means, 12 ounces of something is a pound. And because Jaden had used 3 times the amount of chili powder in the second pot, he used 6 tablespoons worth of powder. 3 pounds divided by 6 equals 1/2.

Step-by-step explanation:

a. The point estimate is the mean, 47 days.

b. The margin of error is the critical value times the standard error.

At 31 degrees of freedom and 98% confidence, t = 2.453.

The margin of error is therefore:

MoE = 2.453 × 10.2 / √32

MoE = 4.42

c.  The confidence interval is:

CI = 47 ± 4.42

CI = (42.58, 51.42)

d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.

e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.

Answer:

5 years

Step-by-step explanation:

Principal Amount to be paid=$4500

Interest rate = 2%

Number if Times compounded= number of years

Number of years = x

Among total= $5010

A= p(1+r/n)^(nt)

But n= t =x

A= p(1+r/x)^(x²)

5010=4500(1+0.02/x)^(x²)

5010/4500 = (1+0.02/x)^(x²)

1.11333=( 1+0.02/x)^(x²)

Using trial and error method the number of years maximum to give approximately $5010 is 5 years

Answer:

The set of vectors A and C are linearly independent.

Step-by-step explanation:

A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:

[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)= t^{2}[/tex] and [tex]p_{3}(t) = 3 + 3\cdot t[/tex]:

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0[/tex]

[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1} + 3\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2} = 0[/tex]

[tex]\alpha_{3} = 0[/tex]

Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.

[tex]p_{1}(t) = t[/tex], [tex]p_{2}(t) = t^{2}[/tex] and [tex]p_{3}(t) = 2\cdot t + 3\cdot t^{2}[/tex]

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0[/tex]

[tex](\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1}+2\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2}+3\cdot \alpha_{3} = 0[/tex]

Since the number of variables is greater than the number of equations, let suppose that [tex]\alpha_{3} = k[/tex], where [tex]k\in\mathbb{R}[/tex]. Then, the following relationships are consequently found:

[tex]\alpha_{1} = -2\cdot \alpha_{3}[/tex]

[tex]\alpha_{1} = -2\cdot k[/tex]

[tex]\alpha_{2}= -2\cdot \alpha_{3}[/tex]

[tex]\alpha_{2} = -3\cdot k[/tex]

It is evident that [tex]\alpha_{1}[/tex] and [tex]\alpha_{2}[/tex] are multiples of [tex]\alpha_{3}[/tex], which means that the set of vector are linearly dependent.

[tex]p_{1}(t) = 1[/tex], [tex]p_{2}(t)=t^{2}[/tex] and [tex]p_{3}(t) = 3+3\cdot t +t^{2}[/tex]

[tex]\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0[/tex]

[tex]\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0[/tex]

[tex](\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0[/tex]

The following system of linear equations is obtained:

[tex]\alpha_{1}+3\cdot \alpha_{3} = 0[/tex]

[tex]\alpha_{2} + \alpha_{3} = 0[/tex]

[tex]3\cdot \alpha_{3} = 0[/tex]

Whose solution is [tex]\alpha_{1} = \alpha_{2} = \alpha_{3} = 0[/tex], which means that the set of vectors is linearly independent.

The set of vectors A and C are linearly independent.

Answer:

a. B1 is better than B2.

Step-by-step explanation:

Hyperplane is a geometric shape which has subspace whose dimension is one less than ambient space. Hyperplane that maximizes the margin it will have better generalization. Margin is calculated by [tex]\frac{2}{||W||}[/tex]. The correct option is a.

Answer:

A

Step-by-step explanation:

Answer:

a = 8.1

Step-by-step explanation:

Firstly, since we have a triangle, automatically, we have 3 interior angles

Mathematically the sum of these angles = 180

A + B + C = 180

27 + 25 + C = 180

52 + C = 180

C = 180-52

C = 128

We use the sine rule to find a

The sine rule posits that the ratio of a side to the sine of the angle facing that side is equal for all the sides of a triangle

Thus, mathematically according to the sine rule;

c/Sin C = a/Sin A

14/sin 128 = a/sin 27

a = 14sin27/sin 128 = 8.0657

which to the nearest tenth is 8.1

Answer:

A). 55

Step-by-step explanation:

Number of Variegated Fritillaries for each year is

2009 = 7

2010= 95

2011= 63

The sum total of the samples= 7+95+63

The sum total of the samples= 165

Number of years= 3

The average= total/number of years

The average= 165/3

The average= 55

Answer: A

Step-by-step explanation: I have a massive brain (•-*•)

The correct answer is 180 oranges

Explanation:

In mathematics, a ratio expresses two or more numbers that are related. In the case fo the ration 9: 40 this expresses 9 oranges are used to serve fruit salad for 40 people. Now, if you need to determine what is the number of oranges not for 40 people but for 800 people you can use cross multiplication. This process is explained below:

[tex]\frac{9}{40} = \frac{x}{800}[/tex]   - 1. Multiply  9 x 800 and 40 x x (cross multiplication)

[tex]7200 = 40x[/tex] - 2. Solve the equation by diving 7200 into 40

[tex]\frac{7200}{40} = x[/tex]

[tex]x = 180[/tex] - 3. 180 represents the number of oranges to serve 800 people, which   can be expressed as 180: 800

Answer: E(X) = 4

              V(X) = [tex]\frac{16}{3}[/tex]

Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:

f(x) = [tex]\left \{ {{\frac{1}{b-a} } \atop {0}} \right.[/tex]  

The mean or expectation of an unifrom distribution is:

E(X) = [tex]\int\limits^b_a {x.f(x)} \, dx[/tex]

For the density function in interval [0,8], expectation value is:

E(X) = [tex]\int\limits^8_0 {x.(\frac{1}{8-0} )} \, dx[/tex]

E(X) = [tex]\int\limits^8_0 {\frac{x}{8} } \, dx[/tex]

E(X) = [tex]\frac{1}{8}. \int\limits^8_0 {x} \, dx[/tex]

E(X) = [tex]\frac{1}{8}.(\frac{x^{2}}{2} )[/tex]

E(X) = [tex]\frac{1}{8} (\frac{8^{2}}{2} )[/tex]

E(X) = 4

Variance of a probability distribution can be written as:

V(X) = [tex]E(X^{2}) - [E(X)]^{2}[/tex]

For uniform distribution in interval [0,8]:

V(X) = [tex]\int\limits^b_a {x^{2}.\frac{1}{8-0} } \, dx - (\frac{8+0}{2})^{2}[/tex]

V(X) = [tex]\frac{1}{8} \int\limits^8_0 {x^{2}} \, dx - 4^{2}[/tex]

V(X) = [tex]\frac{1}{8} (\frac{x^{3}}{3} ) - 16[/tex]

V(X) = [tex]\frac{1}{8} (\frac{8^{3}}{3} ) - 16[/tex]

V(X) = [tex]\frac{64}{3}[/tex] - 16

V(X) = [tex]\frac{16}{3}[/tex]

The mean and variance are 4 and 16/3, respectively

Answer:

  10%

Step-by-step explanation:

Using the given formula with the given data, we have ...

  efficiency = output work / input work

  = (10 J)/(100 J) = 0.10 = 10%

Answer:

A) 10%

Step-by-step explanation:

10/100=10

Answer:

YTM = 5.45%

Step-by-step explanation:

Here, we are interested in calculating the yield to maturity.

Mathematically;

Annual coupon=1000*4.3%=43

YTM=[Annual coupon+(Face value-Present value)/time to maturity]/(Face value+Present value)/2

=[43+(1000-870)/18]/(1000+870)2

=5.45%

Answer:

Step-by-step explanation:

Hello!

You have to estimate the mean length of 4000 b.c. human skulls trough a 95% confidence interval.

You know that

n= 6 human skulls

[tex]\frac{}{X}[/tex]= 94.2mm

S= 4.9

Assuming that the variable X: length of a 4000b.c. human skull (mm) has a normal distribution, to construct the interval you have to use the t statistic:

[[tex]\frac{}{X}[/tex] ± [tex]t_{n_1;1-\alpha /2} * \frac{S}{\sqrt{n} }[/tex]]

[tex]t_{n-1;1-\alpha /2}= t_{5; 0.975}= 2.571[/tex]

[94.2 ± 2.571 * [tex]\frac{4.9}{\sqrt{6} }[/tex]]

[89.06; 99.34]mm

With a 95% confidence level you'd expect the interval [89.06; 99.34]mm to contain the value for the average skull length for humans 4000 b.c.

I hope this helps!

Answer:

6n=48

Step-by-step explanation:

product means multiplication

6×n=48

6n=48

An equation that shows this relationship is: A. 6n = 48.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The product of 6 and a number is 48," we can logically deduce the following algebraic equation;

6 × n = 48

6n = 48

n = 48/6

n = 8.

Read more on equation here: brainly.com/question/18912929

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Answer:

32.5%

Step-by-step explanation:

0.325 x 100%=32.5%

Answer:

45

Step-by-step explanation:

The n th term of a GP is

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Given a₂ = 6 and a₅ = 48, then

ar = 6 → (1)

a[tex]r^{4}[/tex] = 48 → (2)

Divide (2) by (1)

[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is

r³ = 8 ( take the cube root of both sides )

r = [tex]\sqrt[3]{8}[/tex] = 2

Substitute r = 2 into (1)

2a = 6 ( divide both sides by 2 )

a = 3

Thus

3, 6, 12, 24 ← are the first 4 terms

3 + 6 + 12 + 24 = 45 ← sum of first 4 terms

Answer:

45

Step-by-step explanation:

Let's call the missing side x

This is a right triangle and in right triangles the square length of hypotenuse is equal to sum of square length of base and side lengths

53^2 = 28^2 + x^2

x = 45

Answer:

Z (The one on the bottom right)

Step-by-step explanation:

You said that the y intercept goes down by 1 unit which makes only W and Z possible.

The slope is 1/2 and if you multiply that by -4 the new slope is -2 which means the change in y is -2 every time the change in x is 1. Which perfectly fits Z and if you have any questions please ask me with the comments!

Answer:

The point of interception of the graph and x axis are -2.366 and -0.634.

The only graph that satisfy this conditions is Graph A

Step-by-step explanation:

Given the equation;

[tex]y = 2x^2 + 6x + 3\\[/tex]

at y = 0

[tex]2x^2 + 6x + 3=0\\[/tex]

the roots of the quadratic equation (at y =0) can be calculated using the quadratic formula;

[tex]x = \frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]

Using the quadratic equation to solve for the roots;

[tex]x = \frac{-6\pm \sqrt{6^2 -4*2*3}}{2*2}\\x = \frac{-6\pm \sqrt{36 - 24}}{4}\\x = \frac{-6\pm \sqrt{12}}{4}\\so, we have \\x = -2.366\\or\\x = -0.634\\[/tex]

Therefore, the point of interception of the graph and x axis are -2.366 and -0.634.

The only graph that satisfy this conditions is Graph A

Answer:

Step-by-step explanation:

Confidence interval for the population mean is expressed by the formula;

CI = xbar ± Z(S/√n) where;

xbar is the sample mean = 12.5

Z is the z score at 99% confidence = 2.576

S is the standard deviation = √variance

S = √2.4 = 1.5492

n is the sample size = 25

Substituting the given values into the formula given above,

CI = 12.5 ± 2.576(1.5492/√25)

CI = 12.5 ± 2.576(0.30984)

CI = 12.5 ± 0.7981

CI = (12.5-0.7981, 12.5+0.7981)

CI = (11.2019, 12.7981)

Hence the 99% confidence interval for the population mean is 11.2≤[tex]\mu[/tex]12.8 (to 1 decimal place)

A 99% confidence interval for the population mean will be "11.2 [tex]\leq[/tex] 12.8".

According to the question,

Sample mean, [tex]\bar x[/tex] = 12.5

Z score at 99%, Z = 2.576

Standard deviation, S = √Variance

                                    = √2.4

                                    = 1.5492

Sample size, n = 25

We know the formula,

Confidence interval, CI = [tex]\bar x \ \pm[/tex] Z ([tex]\frac{S}{\sqrt{n} }[/tex])

By substituting the given values, we get

                                        = 12.5 [tex]\pm[/tex] 2.576 ([tex]\frac{1.5492}{\sqrt{25} }[/tex])

                                        = 12.5 [tex]\pm[/tex] 2.576 (0.30984)

                                        = 12.5 [tex]\pm[/tex] 0.7981

Now,

                                   Cl = (12.5 - 0.7981, 12.5 + 0.7981)

                                        = (11.2019, 12.7981) or,

                                        = (11.2, 12.8)

Thus the above answer is appropriate.        

Find out more information about mean here:

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Answer:

40091.

Step-by-step explanation:

Multiply 40.091 by 10 three times to get the answer.

40.091 * 10 = 400.91

400.91 * 10 = 4009.1

4009.1 * 10 = 40091.

The expression 40.091 x 10³ can be represented as 40091.

The term xⁿ, read as x to the power n, shows an exponent n, which implies x is multiplied by itself n times.

In the question, we are asked to arrange the cards showing '.', '0', '0', '1', '4', and '9', to show the solution to the expression 40.091 x 10³.

Now, 10³ is 10 to the power 3, where 3 is the exponent, so 10 is multiplied by itself 3 times = 10*10*10 = 1000.

Now, the expression 40.091 x 10³ = 40.091 * 1000 = 40091.

∴ The expression 40.091 x 10³ can be represented as 40091.

Learn more about exponents at

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Answer:

Step-by-step explanation:

In algebra, we always need to follow a set of steps that involve undoing the operations that led to the equation to reveal the value of x.

e < -12

(Since we divided by a negative number, we must reverse the inequality sign.)

(-1/6)(-12) > 2

2 > 2 ✅

Now we check a number less than -12, such as -14.

(-1/6)(-14) > 2

2 1/3 > 2 ✅

Answer:

B. (1,7)

Step-by-step explanation:

We can substitute the x and y values of each coordinate into the inequality and test if they work.

Let's start with A, 5 being y and 0 being x .

[tex]5 > |0|+5\\5> 0+5\\5 > 5[/tex]

5 IS NOT greater than 5, they are the exact same, so A is out.

Let's try B, 1 being x and 7 being y.

[tex]7 > |1| + 5\\7 > 1 + 5\\7 > 6[/tex]

7 IS greater than 6, so B. (1,7) does work for this inequality!

Let's do C for fun, when 7 is x and 1 is y.

[tex]1 > |7| + 5\\1>7+5\\1>12[/tex]

1 IS NOT greater than 12, it is quite less than 12, so C doesn't work.

Therefore B. (1,7) works for the inequality of [tex]y > |x|+5[/tex].

Hope this helped!

Answer:

The graph at the bottom left in your group of possible answers.

Step-by-step explanation:

Notice that the original given graph corresponds to the equation:

[tex]y=2x+1[/tex]

since the line's slope is 2/1 = 2 and the y-intercept is at the point (0, 1).

So if one modifies the equation multiplying the current slope by 1/2, and the y intercept increased by 3 units, Then the new function would be:

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

A line of slope 1 and y-intercept at (0, 4)

Notice that the graph at the bottom left in your possible answers is representing such function.

Answer:

Answer Y: or Bottom Left of Given Answers

Step-by-step explanation:

Answer:

y = -0.85 + 0.09x; $49.82

Step-by-step explanation:

1. Calculate Σx, Σy, Σxy, and Σx²  

The calculation is tedious but not difficult.

[tex]\begin{array}{rrrr}\mathbf{x} & \mathbf{y} & \mathbf{xy} & \mathbf{x^{2}}\\526 & 52.08 & 27394.08 & 276676\\625& 59.00 & 36875.00 &390625\\589 & 56.12 & 33054.68 & 346921\\409 & 25.72 & 10519.48 & 167281\\489 & 34.12& 16684.68 & 293121\\500 & 53.00 & 26500.00 &250000\\906 & 76.48 & 71102.88 & 820836\\251 &26.08 & 6546.08 & 63001\\595 & 50.60 & 30107.00 & 354025\\719 & 68.52 & 49265.88 & 516961\\\mathbf{5609} & \mathbf{503.72} &\mathbf{308049.76} & \mathbf{3425447}\\\end{array}[/tex]

2. Calculate the coefficients in the regression equation

[tex]a = \dfrac{\sum y \sum x^{2} - \sum x \sum xy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{503.7 \times 3425447 - 5609 \times 308049.76}{10 \times 3425447- 5609^{2}}\\\\= \dfrac{1725466163 - 1727851103.84}{34254470 - 31460881} = -\dfrac{2384941}{2793589}= \mathbf{-0.8537}[/tex]

[tex]b = \dfrac{n\sumx y - \sum x \sumxy}{n\sum x^{2}- \left (\sum x\right )^{2}} = \dfrac{3080498 - 2825365.48}{2793589} = \dfrac{255132}{2793589} = \mathbf{0.09133}[/tex]

To two decimal places, the regression equation is

y = -0.85 + 0.09x

3. Prediction

If x = 563,

y = -0.85 + 0.09x = -0.85 + 0.09 × 563 = -0.85  + 50.67 = $49.82

(If we don't  round the regression equation to two decimal places, the predicted value is $50.56.)