Which rectangular prism will have the largest volume

Answer:

The area of the quadrilateral ABCD is 114 square units

Step-by-step explanation:

We must calculate the area of each triangle and then add these areas so we calculate the area of the quadrilateral ABCD

First for the BAD right triangle:

AD = sqrt [BD ^ 2 - AB ^ 2]

AD = sqrt [15 ^ 2 - 12 ^ 2]

AD = sqrt [225-144]

AD = sqrt [81]

AD = 9

The area of a triangle is half the product of the base times the height, that is:

A1 = AB * AD / 2 = 12 * 9/2 = 54

Then for the second triangle in the right triangle BDC:

DC = sqrt [BC ^ 2 - BD ^ 2]

DC = sqrt [17 ^ 2 - 15 ^ 2]

DC = sqrt [289 - 225]

DC = sqrt [64] = 8

We calculate the area

A2 = DC * BD / 2 = 8 * 15/2 = 60

The total area then is:

AT = A1 + A2

AT = 54 + 60 = 114

Which means that the area of the quadrilateral ABCD is 114 square units

Answer:

x = -3

y = -3

Step-by-step explanation:

To solve this system of equations, you can use the elimination method, which is to have one of the variables match, but be the opposite sign of the other:

- x + y = 0

4x - 3y = -3

The easier one to match is the 1st equation, and to make it match oppositely, you multiply the whole equation by 4:

4(-x + y = 0)

-4x + 4y = 0

4x - 3y = -3

-4x and 4x cancel each other out:

4y = 0

-3y = -3

_______

y = -3

Then plug in -3 for y, into one of the equations:

- x + y = 0

- x - 3 = 0

Add 3 to both sides:

- x = 3

Divide both sides by -1:

x = -3

Step-by-step explanation:

-2a + 2a + 7 = 8

Solving like terms

7 = 8

= 8 - 7 = 1

Has one solution

Answer:

3

Step-by-step explanation:

Well, first off I'm assuming that by "scar factor" you mean scale factor. So if the two squares are similar then that means the sides are also similar, that means that they are equivalent. So all you have to do is 12/4 to get 3. So then to check it, you do 4 times 3 which gets you to 12.

So the final answer is 3

Answer:

The theoretical probability of drawing a red marble is 1/3.

Step-by-step explanation:

1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.

2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.

3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.

Answer:

2x³ - 17x² + 13x + 11

Step-by-step explanation:

(2x + 1)(x² - 9x + 11)      Distribute the 2x then the 1

2x³ - 18x² + 22x + x² - 9x + 11       Combine like terms

2x³ - 17x² + 13x + 11

If this answer is correct, please make me Brainliest!

Answer:

We conclude that the true average estimated calorie content in the population sampled exceeds the actual content.

Step-by-step explanation:

We are given that an article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories.

The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88.

Let [tex]\mu[/tex] = true average estimated calorie content in the population sampled.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 153 calories     {means that the true average estimated calorie content in the population sampled does not exceeds the actual content}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 153 calories     {means that the true average estimated calorie content in the population sampled exceeds the actual content}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                             T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean estimated calorie level = 193 calories

            s = sample standard deviation = 88

            n = sample of individuals = 58

So, the test statistics  =  [tex]\frac{193-153}{\frac{88}{\sqrt{58} } }[/tex]  ~ [tex]t_5_7[/tex]

                                       =  3.462

The value of t test statistics is 3.462.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical value of 1.6725 at 57 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 3.462 > 1.6725, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true average estimated calorie content in the population sampled exceeds the actual content.

Answer:

radius-8 inches cause math

circumference-50.27

Step-by-step explanation:

Answer:

I also belive for Part A the second one is the answer because it equals 120 Part B is 120 pints! Good Luck! And I hope this Helps!

Answer:

B

Step-by-step explanation:

Answer:

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And the confidence interval is given by:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar X_1 = 186[/tex] the sample mean for the first sample

[tex] \bar X_2 = 171[/tex] the sample mean for the second sample

[tex]s_1 =33[/tex] the sample deviation for the first sample

[tex]s_2 =23[/tex] the sample deviation for the second sample

[tex]n_1 = 8[/tex] the sample size for the first group

[tex]n_2 = 7[/tex] the sample size for the second group

The confidence interval for the true difference is given by:

[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]

We can find the degrees of freedom are given:

[tex] df = n_1 +n_2 -2 =8+7-2= 13[/tex]

The confidence level is given by 90% so then the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex] we can find the critical value with the degrees of freedom given and we got:

[tex] t_{\alpha/2}= \pm 1.77[/tex]

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And replacing into the formula for the confidence interval we got:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

Answer:

x + (x+1) + (x+2) = 114

3x = 111

x = 37

the numbers are 37, 38 and 39

the smallest number is 37

Step-by-step explanation:

Answer:

level of water in a reservoir each....

Step-by-step explanation:

The scatter plot

A scatter plot is like a scatter chart or graph that uses the dots for representing the values of two different numeric variables. The horizontal value indicates the individual point data. Thus is used for observing the realtisohips between the variables.

This the answer is level of the water in a dam each day and date during 1 month.

Learn more about the which type of data.

brainly.com/question/22485501.

Answer:3

Step-by-step explanation:

edg

Answer:

1/1 x 7/1 x 1/12

Is there any options?

Step-by-step explanation:

Answer:6/8 adding 1/4

Step-by-step explanation: Because im right probably

Answer:

50b ≥ 560.

Step-by-step explanation:

Number of bikers on a team is b so the total number of miles ridden  if each rides 50 miles is  50b. The team must complete at least 560 miles so the inequality is

50b ≥ 560.

Explanation:

We assume your question is "why is that name given to these three numbers?"

There are many names in mathematics that are given to sequences or sets of numbers having a particular characteristic. The term "Pythagorean triple" is usually reserved for three positive integers that satisfy the relation "the sum of the squares of the smaller two is equal to the square of the largest."

This relationship exists between the side lengths of a right triangle, which is the point of the Pythagorean theorem. So, integer side lengths of a right triangle constitute a "Pythagorean triple."

_____

If your question is "why do right triangle side lengths have the relationship specified by the Pythagorean theorem?", that demands a different answer. In general, the sides and angles of a triangle obey the Law of Sines and the Law of Cosines.

One of the expressions of the Law of Cosines is ...

  c² = a² +b² -2ab·cos(C)

where C is the angle opposite side c in the triangle. You may recall that the cosine of 90° is zero, so the cosine term in this equation vanishes when angle C is a right angle. The remaining equation is ...

  c² = a² +b²

This is an expression of the Pythagorean theorem, and it is true only for right triangles.

Answer:

A'B'= 3 cm and B'D' = 1.6 cm

Step-by-step explanation:

First of all, we are told that the scale factor = 1/5

Now,we know that If the scale factor is less than 1, then the dilation is a reduction.

Thus, in this question the dilation is a reduction.

For us to calculate the dimensions of the dilated rectangle, we'll multiply the original dimensions by the scale factor

Thus;

A'B' = AB(1/5)

A'B' = 15(1/5) = 3 cm

B'D' = BD(1/5) = 8(1/5) = 1.6 cm

Thus, The length of each side of the dilated rectangle are;

A'B'= 3 cm and B'D' = 1.6 cm

Answer:

  6

Step-by-step explanation:

The greatest common factor of 36, 42, and 54 is 6:

  36 = 6·6

  42 = 6·7

  54 = 6·9

Jacqueline's bouquets will have 6 tulips, 7 carnations, and 9 daffodils in each one. There will be 6 bouquets.

Answer:  b commutative property

Step-by-step explanation: idid the test and i got it right

The property of algebra that allowed jakob simplify the given expression as stated is called; B: The commutative Property

She wants to simplify the expression -3a + 4b + 5a + (-7b)

Now, there are different properties of algebra but the one that jakob used here is called commutative property of algebra.

Commutative property is expressed as an example like;

a + b = b + a

Thus, using commutative property, he arrived at –3a + 4b + 5a + (–7b) = –3a + 5a + 4b + (–7b).

Read more about commutative property at; https://brainly.com/question/2475734

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer: [tex]1\frac{1}{2} *9=\frac{3}{2}*9=\frac{27}{2}=13\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:             27

                        -------  

                           2

Step-by-step explanation:

Answer:

I think its A

Step-by-step explanation:

Answer:

The solutions to the system of equations are [tex]y=4,\:x=5[/tex].

Step-by-step explanation:

To solve the system [tex]\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}[/tex]

First,

[tex]\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84[/tex]

[tex]\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}[/tex]

Subtract the first equation from the second equation

[tex]12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36[/tex]

Solve [tex]-9y=-36[/tex] for y:

[tex]\frac{-9y}{-9}=\frac{-36}{-9}\\y=4[/tex]

For [tex]12x+15y=12[/tex] plug in [tex]y=4[/tex] and solve for x

[tex]12x+15\cdot \:4=120\\12x=60\\x=5[/tex]

The solutions to the system of equations are:

[tex]y=4,\:x=5[/tex]

The meaning of each parameter is given as follows:

Then the yearly percent increase is of:

4%.

C(3) represents the cost in 2015, which was of $33,746.

a) The expression to represent the cost in 2007 is of: C(-5).

b) The cost was of: $24,658.

An exponential function is defined as follows:

y = ab^x.

In which:

For this problem, the function is defined as follows:

y = 30000(1.04)^x.

In which:

C(3) represents the cost in 2015 and is obtained as follows:

C(3) = 30000(1.04)^3 = $33,746.

C(-5) represents the cost in 2007 and is obtained as follows:

C(-5) = 30000(1.04)^(-5) = $24,658.

(as 2007 was five years before 2012).

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Answer:

Step-by-step explanation:

A general equation of a hyperbola is

 x^2     y^2

-------- - ------- = 1   (This applies only when the center of the hyperbola

 a^2     b^2                               is at (0, 0)  ).

You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.

The equation represents the hyperbola shown in the graph is  (y - 1)² / 9 - (x + 4)² / 4  = 1

A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

Given that, a graph, showing hyperbola, we need to find the equation,

We have the general equation for up - down facing hyperbola as

(y - k)² / b²- (x - h)² / a²  = 1.

Let's start listing the properties of this graph -

Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).

Therefore, (h, k) = (- 4,1).

This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.

Therefore, a = 3.

That gives asymptotes. Now remember that it will be in the form

y = ± b / a.

We already know a = 3, so we have to find b.

Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).

Calculating the slope of the dotted line would be as follows,

Given: (- 4,1) and (- 2, - 2)

Slope = - 2 + 4 / - 2 - 1 = 2 / 3

We have the equation y = 2 / 3x.

Therefore, b = 2.

Let's substitute to equation...

h = - 4, k = 1, b = 2, a = 3

(y - 1)² / (3)²- (x + 4)² / (2)²  = 1

(y - 1)² / 9 - (x + 4)² / 4  = 1

Hence, the equation represents the hyperbola shown in the graph is  (y - 1)² / 9 - (x + 4)² / 4  = 1

Learn more about hyperbolas, click;

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The complete question is attached

Answer:

18.333

Step-by-step explanation:

Answer:

hes

56 inches

hope it helps

Answer:

Black Line     y = 3 + 2x ,     y = 2x +3

Red Line       y = -2 - .5x.     y = -.5x -2

vice versa

Step-by-step explanation:

For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x

For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.

Answer:

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Step-by-step explanation:

x < 7