Find the area of the trapezoid

The different sets of initials can be formed if every person has one surname (i.e., last name) and either one or two given names (i.e., a first name, or a first and middle name) is 15600.

There are 26 possible letters, each set of initials would have 3 letters in it, order doesn't matter, i.e. ABC does not equal ACB. using permutation   26P3 = 5600.

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters. Common mathematical problems involve choosing only several items from a set of items in a certain order.

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Rachel should perform better because of the spacing effect.

Given,

Rachel will study one hour each day for 5 days and Jennifer will study 5 hours the day before the exam.

What do you predict about their scores?  

Rachel should perform better because of the spacing effect.

The spacing effect demonstrates that learning is more effective when study sessions are spaced out. This effect shows that more information is encoded into long-term memory by spaced study sessions, also known as spaced repetition or spaced presentation, than by massed presentation.

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Answer:

I believe the answer should be -11/20

Step-by-step explanation:

Answer:

x = 14 1/2 or 14.5

Step-by-step explanation:

(4x-3)/5 - (2x-3)/2 = -2

make denominators match

2*(4x-3)/10 - 5*(2x-3)/10 = -2

(8x-6)/10 - (10x-15)/10 = -2

(8x-6-10x+15)/10 = -2

(-2x+9) = -2*10

-2x+9 = -20

-2x = -29

x = -29/-2

x = 14 1/2 or 14.5

gathmath

Answer: The three triangles shown are similar triangles. We can tell this by the Angle Angle theory. You can tell the angles are congruent by the matching marks in each corner of the triangles, the marks or “ticks” are the same in the same corners. The length of the sides can change but the angle measurements will still be the same.

Step-by-step explanation: explained in answer

Answer: Each of the corresponding angles of one triangle equal the corresponding angles of the other triangle.

The inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

The inverse of a matrix A is calculated by the formula:

A' = (1/|A|)(Adj A),

where A' represents the inverse of matrix A,

|A| represents the determinant value of matrix A, and

Adj A represents the Adjoin matrix of matrix A.

So, to calculate the inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] , we will first calculate its Adj.

Adj = [tex]\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}[/tex]= [tex]\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex].

Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.

Therefore A' = (1/|A|)(Adj A),

or, A' = [tex](1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right][/tex] ,

or, A' = [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

Therefore, the inverse of the matrix  [tex]\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right][/tex] is the matrix [tex]\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right][/tex] .

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By applying the quadratic formula and discriminant of the quadratic formula, we find that the maximum height of the ball is equal to 75.926 meters.

Herein we have a quadratic equation that models the height of a ball in time and the maximum height represents the vertex of the parabola, hence we must use the quadratic formula for the following expression:

- 4.8 · t² + 19.9 · t + (55.3 - h) = 0

The height of the ball is a maximum when the discriminant is equal to zero:

19.9² - 4 · (- 4.8) · (55.3 - h) = 0

396.01 + 19.2 · (55.3 - h) = 0

19.2 · (55.3 - h) = -396.01

55.3 - h = -20.626

h = 55.3 + 20.626

h = 75.926 m

By applying the quadratic formula and discriminant of the quadratic formula, we find that the maximum height of the ball is equal to 75.926 meters.

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Answer: 450 rest 100

Step-by-step explanation:

So, we need to calculate this division 100.000/222 and get the rest.

Well, 222 enters in 1000 by 4 times.

222 times 4 is 888

So, 100.000/222 = 4

       888-

We subtract 888 from 1000.

That will be 112

100.000/222 = 4

888

  112

Now, get the next 0 down next to 112

100.000/222 = 4

888

 1120

222 get in 1120 by 5 times.

5 times 222 = 1110

divide 1120 by 1110

100.000/222 = 45

888

 1120

 1110

That will be 10

100.000/222 = 45

888

 1120

 ==10

Get the next zero down

100.000/222 = 45

888

 1120

 ==100

222 gets in 100 by 0 times.

100.000/222 = 450

888

 1120

 ==100

         0

100 subtracted by 0 is 100

100.000/222 = 450

888

 1120

 ==100

         0

     100

The rest is 100 and the result is 450

Now, you can do the verification:

222 time 450 is 99,900.

If you add the rest to 99,900 it will be 100.000. So the result is good

The critical z value which should be used in determining the confidence interval is z=1.29 and the confidence interval is (38.43355,66.82645).

Given sample mean of $52.63 and standard deviation of $22.01.

We have to construct  the confidence interval of 80% for the mean repair cost for the washers.

μ=52.63

σ=22.01

n=4

First we have to find the value of z for the confidence level of 80% from z table and which is 1.29.

Margin of error is the difference between the calculated values and real values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where μ is mean

σ is standard deviation

n is sample size

z is z value for the confidence level

Margin of error=1.29*22.01/[tex]\sqrt{4}[/tex]

=14.19645

Confidence interval =mean ±margin of error

Upper level=mean +margin of error

=52.33+14.19645

=66.82645

Lower level=mean-margin of error

=52.33-14.19645

=38.43355

Hence the confidence interval is (38.43355,66.82645) and the critical value used is z=1.29.

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Answer:

OA=4x²-19

Step-by-step explanation:

4(x²-5)+1

4x²-19

Answer:

C. 92.16π mi²

Step-by-step explanation:

Use the formula: 4 · π · r²

r=4.8

4 · π · 4.8²=

=4 · π · 23.04=

=92.16π mi²

Hope this helps!

If not, I am sorry.

The probability that the sample proportion of Republicans will differ from the population proportion by greater than 5% is 100%

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

It is given that 58% of voters are Republican. The sample is 536 voters.

0.58×536 = 310.88 can be rounded off to 311.

536 - 311 = 225 are not republicans

311-225 = 86 is the difference

[tex]\frac{86}{536}[/tex]×100 = 16.044%

Hence, the probability is 100%.

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Hello,

[tex]( \frac{2}{3} ) {}^{n} = \frac{16}{81} [/tex]

[tex]nln( \frac{2}{3} ) = ln(\frac{16}{81})[/tex]

[tex]n = \frac{ln( \frac{16}{81} )}{ln( \frac{2}{3} )} = 4 [/tex]

Answer : 4

Answer:

^ is 4

Step-by-step explanation:

as you can see, [tex]\frac{16}{81}=\frac{2^4}{3^4}=(\frac{2}{3})^4[/tex]

Answer: $768

Step-by-step explanation:

Here, you'll just multiply:

16x8x6 = 768

three angles= 180

180/3

60

Answer:

  27 = 3³

Step-by-step explanation:

The prime factorization of 27 is ...

  27 = 3×3×3 = 3³

The exponent of 3 signifies the factor is repeated 3 times.

Answer:

9:12 10:24

Step-by-step explanation:

First find their least common divisor which is 36. which means every 36 minutes they will flashes together.

just add the 36 to the time where they flash at the same time which is 8:00am

8:36 9:12 9:48 10:24 11:00 11:36

Answer: 9:12 and 10:24

Step-by-step explanation:

if we start from 8 am and add 12 minutes for light A in intervals and do the same for Light B we can see where the times are the same

Light A: 8:00, 8:12, 8:24, 8:36, 8:48, 9:00, 9:12, 9:24, 9:36, 9:48, 10:00, 10:12, 10:24, 10:36, 10:48, 11:00, 11:12, 11:24

Light B: 8:00, 8:18, 8:36, 8:54, 9:12, 9:30, 9:48, 10:06, 10:24, 10:42, 11:00, 11:18

9:12 and 10:24 are the correct answers because this is when the two lights flash at the same time

Multiplying the binomials, we have (x - 7)(x - 2) = x² - 9x + 14.

Applying the distribution property of multiplication, the given binomials, (x - 7)(x - 2) can be multiplied as shown below:

(x - 7)(x - 2)

x(x - 2) -7(x - 2)

x² - 2x - 7x + 14

x² - 9x + 14

Therefore, (x - 7)(x - 2) = x² - 9x + 14.

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Answer:

Hence the expression [tex]$$(x-7)(x-2)=x^2-9x-14$$[/tex]

Step-by-step explanation:

The given expression is (x-7)(x-2).

We have to multiply the given expression.

Multiply the (x-7) by-2, multiply the (x-7) by x then add like terms.

[tex]$$\frac{\begin{matrix}{} & {} & x & - & 7 \\ \times & {} & x & - & 2 \\ \end{matrix}}[/tex]

____________

[tex]{\frac{\begin{matrix}{} & - & 2x & - & 14 \\ {{x}^2} & - & 7x & {} & {} \\ \end{matrix}}{\begin{matrix}{{x}^2} & - & 9x & - & 14 \\ \end{matrix}}}$$[/tex]

Answer:

1

Step-by-step explanation:

Start at any point on the line, for example (0, 1).

Each unit up correspond to a unit right. The next easy to read point going up to the right is (1, 2).

difference in y: 2 - 1 = 1

difference in x: 1 - 0 = 1

gradient = (difference in y)/(difference in x) = 1/1 = 1

Answer:

[tex]\huge\boxed{\sf Slope = 1 }[/tex]

Step-by-step explanation:

Take any two co-ordinates from the line.

I will take (0,1) and (-1,0)

So,

[tex](x_1,y_1)=(0,1)\\\\(x_2,y_2)=(-1,0)[/tex]

[tex]\displaystyle Slope = \frac{y_2-y_1}{x_2-x_1} \\\\Slope = \frac{0-1}{-1-0} \\\\Slope = \frac{-1}{-1} \\\\Slope = 1 \\\\\rule[225]{225}{2}[/tex]

The quotient of [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3} -3[/tex] is (x+5).

Given expression  [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3}-3[/tex] and we have to find the quotient of the first expression.

Quotient is any quantity produced by dividing two numbers. It can be of simple numbers or expressions also. Remainder is a number or expression that is left after division.

To find the quotient of [tex]x^{4}+5x^{3} -3x-15[/tex], we have to divide the expression by [tex]x^{3}-3[/tex].

We know that,

Divident=Divisor*quotient+remainder

[tex]x^{4}+5x^{3}-3x-15[/tex]=([tex]x^{3}-3[/tex])*(x+5)+0

By equating from the given formula we can find that the value of quotient is  (x+5).

Hence the quotient of [tex]x^{2} +5x^{3} -3x-15[/tex] by dividing it by [tex]x^{3} -3[/tex] is (x+5).

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Question is incomplete as the expressions are incomplete. They should be like [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3} -3[/tex]

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

Let's write in the point-slope form:

 [tex](y-y_0)=m(x-x_0)[/tex]

Let's find the slope:

 [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

        ⇒ [tex]Slope=\frac{8--1}{4-1}=\frac{9}{3}=3[/tex]

Let's gather what we know:

   Equation: [tex](y-y_0)=m(x-x_0)\\y+1=3(x-1)[/tex]

The equation could also be written in slope-intercept form:

 ⇒ simply isolate y on one side

  [tex]y+1=3(x-1)\\y=3x-3-1\\y=3x-4[/tex]

Answer:

  *Either answer works, just put the one that you are most familiar with

Hope that helps!

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Answer: y=3x-4

Step-by-step explanation:

Slope formula = ([tex]y_{1}[/tex] - [tex]y_2[/tex])/([tex]x_1 - x_2[/tex])

(-1-8)/(1-4) = (-9)/(-3) = 3

Slope = 3

Slope intercept formula = y=mx+b

m = slope = 3

y=3x+b

We can plug in x and y to find b

8=3(4)+b

8=12+b then subtract 12 from both sides

-4=b

Now we put it in

y=3x-4

Answer:

47 - 2n

Step-by-step explanation:

An algebraic expression is an idea of representing numbers using letters or alphabet.

From the question above,

The variable = n

twice the number = 2× n = 2n

Translating:

47 - 2n

Answer:

2700 - 2000 = 700 - 100 = 600 - 200 = 400 - 100 = 300

300 dollars

Recall the Pythagorean identity.

[tex]\sin^2(x) + \cos^2(x) = 1 \implies \left\langle \begin{matrix} \tan^2(x) + 1 = \sec^2(x) \\ 1 + \cot^2(x) = \csc^2(x) \end{matrix} \right.[/tex]

[tex]\implies \sec^2(\beta) - \csc^2(\beta) = (\tan^2(\beta) + 1) - (1 + \cot^2(\beta)) \\\\ ~~~~~~~~= \tan^2(\beta) - \cot^2(\beta)[/tex]

Recall the difference of squares identity.

[tex]a^2 - b^2 = (a - b) (a + b)[/tex]

[tex]\implies \sec^2(\beta) - \csc^2(\beta) = (\tan(\beta) - \cot(\beta)) (\tan(\beta) + \cot(\beta))[/tex]

[tex]sec^2\beta -csc^2\beta \\(1+tan^2\beta )-(1+cot^2\beta )\\1+tan^2\beta -1-cot^2\beta \\tan^2\beta -cot^2\beta \\(tan\beta -cot\beta )(tan\beta +cot\beta )[/tex]

The simplest form of  (–11.7y – 3.3x) + 1.2x + (5.2y + x) is -6.5y - 1.1x

(–11.7y – 3.3x) + 1.2x + (5.2y + x)

We have to open the brackets.

Therefore,

(–11.7y – 3.3x) + 1.2x + (5.2y + x)

-11.7y - 3.3x + 1.2x + 5.2y + x

combine like terms

Hence,

-11.7y + 5.2y - 3.3x + 1.2x + x

Therefore,

-6.5y - 1.1x

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Answer:   -6.5y - 1.1x

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

㏒₇1 = 0 and ㏒₅25 = 2, so the expression evaluates to 0.

The number of baskets that were sold for $2 is 299 baskets.

A word problem is a method we used in denoting mathematical expressions and variables and it can be solved with the use of fractions, ratios, algebra, and arithmetic operations as the case may be.

From the given information:

The number of baskets sold in the second week is obtained as follows

i.e.

x = (184 × 3.25)/2

x = 299 basket were sold for $2  

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Answer:

Starting a business can be a daunting task, but with a little algebra and some careful planning, it can be a successful endeavor. Algebra can help you determine how much start-up capital you will need, as well as how to price your products or services. It can also help you track your expenses and calculate your profits. Without these tools, it would be difficult to know if your business is viable or if you are making a profit.