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Answer:

Step-by-step explanation:

-1/4 x 20z = -5z

24 x -1/4 = -6

So we have -5z-6. So the expression equivalent to 1/4(20z+24) is -5z-6.

Answer:

Length of Ladder(Hypotenuse)=18

Height of wall(Opposite) =14

How far from the base... This talks about the adjacent or distance between the wall and the base.

You can get your answer from Pythagoras theorem

Which states

The square of the hypotenuse is = to the squares of the adjacent and Opposite sides

H² = O² + A²

We're looking for the adjacent "A"

Making A the subject

A² = H² - O²

A= √H² - O²

A= √18² - 14²

A=√128

A= 8√2'

Answer:

  radius: 14.96 in

  length: 47 in

Step-by-step explanation:

The dimensions of the package with maximum volume can be found by differentiating the volume function, subject to the constraint on the dimensions.

__

The volume of the cylindrical package is ...

  V = πr²h

The constraint on the dimensions is ...

  circumference + length = 141 inches

  2πr +h = 141 . . . . . at maximum volume

Solving the second equation for h, we can write the volume function in terms of r alone:

  h = 141 -2πr

  V = πr²(141 -2πr) . . . . substitute for h

  V = 141πr² -2π²r³ . . . eliminate parentheses

__

Differentiating with respect to radius, we find the radius at maximum volume must satisfy ...

  V' = 282πr -6π²r² = 0

Dividing by 6πr, we can simplify this to ...

  47 -πr = 0

  r = 47/π ≈ 14.96 . . . . inches (radius)

  h = 141 -2πr = 47 . . . inches (length)

This is about optimization problems in mathematics.

Dimensions; Height = 48 inches; Radius =  48/π inches

We are told the combined length and girth is 144 inches.

Girth is same as perimeter which is circumference of the circular side.

Thus; Girth = 2πr

If length of cylinder is h, then we have;

2πr + h = 144

h = 144 - 2πr

Now, to find the dimensions at which the max volume can be sent;

Volume of cylinder; V = πr²h

Let us put 144 - 2πr for h to get;

V = πr²(144 - 2πr)

V = 144πr² - 2π²r³

Differentiating with respect to r gives;

dV/dr = 288πr - 6π²r²

Radius for max volume will be when dV/dr = 0

Thus; 288πr - 6π²r² = 0

Add 6π²r² to both sides to get;

288πr = 6π²r²

Rearranging gives;

288/6 = (π²r²)/πr

48 = πr

r = 48/π inches

Put 48/π for r in h = 144 - 2πr to get;

h = 144 - 2π(48/π)

h = 144 - 96

h = 48 inches

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

The best way to attempt this question is to solve it using a Venn diagram

From the given information, Let;

D = documentaries

I = interview shows

G = game show reruns

From the images attached below, we will see how the Venn diagrams are being drawn step by step and calculated.

i.e

= 300 - (90 + 60 + 24 + 6 + 12 + 18 + 24)

= 300 - 234

= 66

∴

No of those interested in exactly one kind of show = 66 + 60 + 18

= 144

∴\(\text{144 are interested in exactly one kind of show.}\)

Answer:

1 3

Step-by-step explanation:

divide 2 by 1 and u get 1

divide 6 by 2 and u get 1

Answer:

option 2

Step-by-step explanation:

Using trigonometric ratio:

\(Cos \ 60 = \frac{adjacent } {hypotenuse} \\\\\frac{1}{2} = \frac{4}{u}\\\\1 \times u = 2 \times 4 \\\\u = 8\)

Now using Pythagoras theorem we will find v

\(8^2 = 4^2 + v^2\\\\64 = 16 + v^2\\\\v^2 = 64 - 16 \\\\v = \sqrt{48} = \sqrt{16 \times 3} = \sqrt{4^2 \times 3 } = 4\sqrt{3}\)

By using trigonometric relations, we will see that v = 4*√3 and u = 8

Here we have a right triangle, we can use trigonometric relations to find the missing sides.

We can see that v is the opposite cathetus of the 60° angle, then we can use the relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing what we know, we get:

tan(60°) = v/4

4*tan(60°) = v = 4*√3

To get the value of u, we use:

cos(a) = (adjacent cathetus)/(hypotenuse).

cos(60°) = 4/u

u = 4/cos(60°) = 2*4 = 8

Then we have:

v = 4*√3

u = 8

If you want to learn more about triangles, you can read:

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Answer:

Step-by-step explanation: Use the Pythagorean Theorem to check this.

Remember that the squares of the lengths of the two smaller sides should be equal to the square of the bigger side.

10,11,15 = NO

5,12,13 = YES

12,15,20 = NO

16,30,34= YES

Hope this helps.

Answer:

A is the correct answer.

Step-by-step explanation:

It needs to intercept to be the same answer or else You are getting 2 different answers.

\(alternative \: interior \: angles\)

<4 and <6

\(alternative \: exterior \: angles\)

<1 and <7

\(corresponding \: angles\)

<1 and <5

0.0001 is a very small number, so we will use the scientific notation to help us answer this. When using the scientific notation with very small numbers, we will multiply this number by 10. When we multiply a decimal, we "move" the decimal place to the right. The scientific notation states we will multiply until we get a number greater or equal to one, but less then 10. Our process will look something like this.

0.0001 -> 0.001 -> 0.01 -> 0.1 -> 1

We now have a number greater or equal to 1 but less then 10- which is 1!

Now, we have to find our exponent. How many times did we multiply by 10?

We multiplied 4 times. So now we have 10^4. But we are not done. For very small numbers, the exponent is negative, so our exponent is negative, In which leaves us with the answer of 10^-4.

With best wishes- Asia Gil <3

Answer:

✔ 10/y – 4 + 8

.

Second,

✔ substitute

2 in for the variable, y.

Third,

✔ simplify

by using

✔ order of operations

.

The answer is

✔ 9

Step-by-step explanation:

i hope this helps-

Answer:

-27

Hope this helped in anyway

Answer:

the answer to this is -27.

Answer:

5

Step-by-step explanation:

You need to first add up all the berries: 2+2+5+7+9 which is 25.

There are 5 people so you need to divide 25 by 5: 25÷5 which is 5

So each person will have 5 berries each.

Answer:

A.) 67.78

B.) 76.48

C.) 87.34

Step-by-step explanation:

Given that:

Mean (m) = 80.6

Standard deviation (σ) = 10

A.) 10th percentile :

10th percentile corresponds to a Zscore of - 1.282

Zscore = (x - m) / σ

-1.282 = (x - 80.6) / 10

-12.82 = x - 80.6

x = -12.82 + 80.6

x = 67.78

B.)34th percentile of blood pressure ;

34th percentile corresponds to a Zscore of - 0.412

Zscore = (x - m) / σ

-0.412 = (x - 80.6) / 10

-4.12 = x - 80.6

x = - 4.12 + 80.6

x = 76.48

C.) third quartile = 75% = 0.75

75th percentile corresponds to a Zscore of 0.674

Zscore = (x - m) / σ

0.674 = (x - 80.6) / 10

6.74 = x - 80.6

x = 6.74 + 80.6

x = 87.34

a)The 10th percentile of blood pressure is 67.78.

b)The 34th percentile of blood pressure is 76.48.

c)The third quartile of the blood pressure is 87.34.

Mean blood pressure μ= 80.6

Standard deviation σ= 10

From the normal standard table, the z-score corresponding to the 10th percentile = - 1.282

A z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

z= (x-μ) /σ

-1.282 = (x - 80.6) /10

-12.82 = x - 80.6

x = -12.82 + 80.6

x = 67.78

So, the 10th percentile of blood pressure is 67.78.

Similarly, the 34th percentile of blood pressure =76.48

The third quartile of the blood pressure =87.34

Therefore a) the 10th percentile of blood pressure is 67.78.

b)the 34th percentile of blood pressure is 76.48.

c)The third quartile of the blood pressure is 87.34.

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The three quadratic equation with different maximum and/or minimum values are y = (x-4)² – 1, y = -(x-4)² + 1, and y = -3(x-4)² + 3.

Quadratic equation:

In math, quadratic equation is the algebraic equation of the second degree in x.

The general form of quadratic equation is

ax² + bx + c = 0,

where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0).

Given,

Here we need to find the three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.

As per the definition of quadratic equation, here we have to write the quadratic equation, that have the roots of 3 and 5,

Here the problem was going to call for two equations but then we have realized that it could be as simply as multiplying the a and c values by -1. Therefore, the equation are,

=> y = (x-4)² – 1,

=> y = -(x-4)² + 1,

=> y = -3(x-4)² + 3.

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The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.

The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).

Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.

Here,

\(\bar x\) =1.267, s=1.23, n=30

The standard error is Se= 1.23/√30

= 0.2246

Item a:

The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.

Item b:

Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.

\(\bar x\pm tS_c\)

\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479

\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861

Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.

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Answer:

24  =  6084

Step-by-step explanation:

24 is already simpflied. So 78 times 78 is left.

Which is easy and equals to 6084.

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Answer:

1.40

Step-by-step explanation:

The checkboxes are denoted by brackets ([]) for checked and 'x' for unchecked states, respectively.

The fertilizing techniques that would be most effective for each example are as follows:

1. Farm with numerous workers and sensitive crops:

a. UDP (Unchecked )

b. Precision management (Checked)

2. A gardener raising produce for a family:

a. UDP (Checked).

b. Precision management (Unchecked )

3. Company that delivers corn to 10 states:

a. UDP (Unchecked)

b. Precision management (Checked)

Please note that the checkboxes are denoted by brackets ([]) for checked and 'x' for unchecked states, respectively.

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The inequality that represents the value of x is (b)  x > 80

from the question, we have the following parameters that can be used in our computation:

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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100+2y = 180

2y=180-100

2y=80

y=40

Answer:

790

Step-by-step explanation:

7098uuilu4645

Answer:

3 ( 3y - 1 )

Step-by-step explanation:

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Answer: Shorter side = 10 feet

Longer side = 24 feet

Hypotenuse = 26 feet

The side lengths of the triangle are 10ft, 24ft and 26ft.

Step-by-step explanation:

Let the length of the shorter leg be x.

The length of the longer leg of a right triangle is 4ft more than twice the length of the shorter leg. This will be: = 2x + 4

The length of the hypotenuse is 6ft more than twice the length of the shorter leg. This will be: = 2x + 6

Note that the square of the hypothenuse will be equal to the square of the other two sides. This will be:

x² + (2x + 4)² = (2x + 6)²

x² + (2x + 4)(2x + 4) = (2x + 6)(2x + 6)

x² + 4x² + 8x + 8x + 16 = 4x² + 12x + 12x + 36

x² + 4x² + 16x + 16 = 4x² + 24x + 36

5x² + 16x + 16 = 4x² + 24x + 36

Collect like terms

5x² - 4x² + 16x - 24x + 16 - 36 = 0

x² - 8x - 20 = 0

x² - 10x + 2x - 20 = 0

x(x - 10) + 2(x - 10) = 0

Therefore, x - 10 = 0

x = 10

a. length of the shorter side = 10ft

b. Length of the longer side = 2x + 4 = 2(10) + 4 = 20 + 4 = 24ft

c. length of the hypotenuse = 2x + 6 = 2(10) + 6 = 20 + 6 = 26ft

d. The side lengths of the triangle are 10ft, 24ft and 26ft.

Answer:

egg

Step-by-step explanation:

yes