Select the correct expressions.
A ladder that is 25 feet long is leaning against a pillar. The vertical height from the base of the pillar to the top of the ladder is 24 feet. Which
expressions represent the angle, 8, that the bottom of the ladder makes with the ground?
(answer options shown below)

There are 15 partitions for the number 7. Where the partitions are nothing but writing an integer in different ways as a sum of two or more integers.

A partition of a positive integer is the way of writing the integer as a sum of one or more positive integers. Where the order of the integers in the sum is not considered.

There are 15 partitions. They are as follows:

These are the 15 possible partitions of the number 7.

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The equivalent expressions of T=A^1.5 are: T= (A)^3/2 and T= ((A)^1/2)^3

According to the statement

we have to show that the 1.5 is same as 3/2 are equivalent to T.

So,

Equivalent expressions are expressions with the same value.

The Given expression is

T=A^1.5

we can write it as a

T= (A)^3/2

Because we know that the

1.5 = 3/2

So, it become T= (A)^3/2.

And From

T=A^1.5

we can write it as a

T= ((A)^1/2)^3

because we know that the

3/2 = (1/2)^3.

So, The equivalent expressions of T=A^1.5 are: T= (A)^3/2 and T= ((A)^1/2)^3.

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The expression which is equivalent to 4x²√5x⁴ × 3√5x^8 is; 60x^8.

The expression given in the task content is; 4x²√5x⁴ × 3√5x^8.

Hence, upon evaluation of the product; we have;

= 12x²√25x¹².

= 60x^8.

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Answer:

D

Step-by-step explanation:

Coefficient is the number next to the variable, and D is the only one where that number is 9. All the others are 6.

The probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen is 0.031 or 3.1%. So, this represents a dependent event.

It is given that there are 26 prize tickets in a bowl, labeled A to Z.

There are 5 vowels- A, E, I, O, U

So, the probability of choosing a ticket with a vowel will be - (5/26)

Another ticket with a vowel will be chosen without replacing the first ticket. Then, its probability is (4/25)

So, the required probability is,

(5/26) × (4/25) = 2/65 = 0.031

The event of choosing the first ticket with a vowel effect the event of choosing the second ticket with a vowel and vice-versa. So, this represents dependent events.

Therefore, the probability is 3.1 %.

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Answer:

  a₄₅ = 13

Step-by-step explanation:

The n-th term of an arithmetic sequence with first term a₁ and common difference d is given by the formula ...

  aₙ = a₁ +d(n -1)

You want the 45th term where a₁ = 2 and d = 1/4. Putting these values into the formula gives ...

  a₄₅ = a₁ +d(n -1) = 2 +(1/4)(45 -1)

Evaluating this expression, we have ...

  a₄₅ = 2 +44/4 = 2 +11

  a₄₅ = 13

The 45th term of the sequence is 13.

The forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]

How to find the nth term of the Arithmetic series?

The nth term of the arithmetic series is find by [tex]Tn = a+(n-1)d[/tex] where Tn is the nth term of the series a is called the initial number and is the common difference between two number. n is the number of term of that arithmetic series.

In the given series initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex]

We have the find the forty-fifth term of the given series.

= [tex]Tn=a+(n-1)d[/tex]

= [tex]Tn = 2+(45-1)\frac{1}{4}[/tex]

= [tex]Tn=2+44\cdot\frac{1}{4}[/tex]

= [tex]Tn = 2+11[/tex]

= [tex]Tn = 13[/tex]

So, the forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]

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Using a trigonometric identity, it is found that the secant and the cotangent of the angles are given as follows:

The following identity is used, considering an angle [tex]\theta[/tex].

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem we are given the sine, then the cosine can be found as follows:

[tex]\left(-frac{5}{8}\right)^2 + \cos^2{\theta} = 1[/tex]

[tex]\cos^2{\theta} = 1 - \frac{25}{64}[/tex]

[tex]\cos^2{\theta} = \frac{39}{64}[/tex]

[tex]\cos{\theta} = \pm \sqrt{\frac{39}{64}}[/tex]

In the fourth quadrant, the cosine is positive, hence:

[tex]\cos{\theta} = \frac{\sqrt{39}}{8}[/tex].

The secant of an angle [tex]\theta[/tex] is one divided by the cosine of the angle, hence:

[tex]\sec{\theta} = \frac{1}{\cos{\theta}} = \frac{1}{\frac{\sqrt{39}}{8}} = \frac{8}{\sqrt{39}} \times \frac{\sqrt{39}}{\sqrt{39}} = \frac{8\sqrt{39}}{39}[/tex]

The cotangent of an angle [tex]\theta[/tex] is the cosine divided by the sine of the angle, hence:

[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}} = \frac{\frac{\sqrt{39}}{8}}{-\frac{5}{8}} = -\frac{\sqrt{39}}{5}[/tex]

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Answer:

-2+i

Step-by-step explanation:

-7+4i represents (-7,4) and 3-2i represents (3,-2).

So, the midpoint is (-2,1), which represents -2+i.

The volume of the pyramid is 13 units³.

A pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces. The volume of a pyramid is one-third that of a prism.

Volume of a pyramid = 1/3 x prism

1/3 x 39 = 13

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Answer:

Step-by-step explanation:

We will assume that the first two columns are the numbers sold for Plain Wrapping and Decorative Wrapping.  The third colum does not equal the sum of the first two, so we'll assume it is the total paid for both options.  Let set the price of Plain Wrapping to x and the Decorative Wrapping to y.  The number of gift wrappings times the cost per warpping is the product of x or y timers the number wrapped as shown in columns 1 and 2.

Take the first row and set it as an equation:

10x+9y = 47   [10 Plain Wraps and 9 Decorative Wraps bring a total of $47]

Do the same for the second and third rows:

25x + 12y = 86, and

16x +12y =  68

===========

We can take any equation and rearrange it to isolate one of the 2 variables, x or y.  I'll pick 10x = 47-9y and isolate x:

10x = 47-9y

x = (47-9y)/10

-------------------

Now use this definition of x in another equation.  I'll use 25x + 12y = 86.

25x + 12y = 86

25(47-9y)/10 + 12y = 86     [since x = (47-9y)/10 from above]

117.5 - 22.5y + 12y = 86

-10.5y = -31.5

y = 3                                     [the price for decorative wrapping is $3]

If y = 3, then we can use this in any of the equations to find x:

x = (47-9y)/10

x = (47-9(3))/10     [Use y = 3]

x = (47-27)/10

x = 2                              [The price for plain wrapping is $3]

======================

Check to see if these values will expalin the total value of the three rows of numbers:

CHECK:

______UNITS____         $2 each          $3 each

PlainW DecG Total      PlainW ($)      DecG ($)      Total ($)

   x           y                          x                       y

   10         9        $47          $20                    $27              $ 47         OK

   25        12       $86          $50                    $36              $ 86         OK

   16        12       $68          $32                    $36              $ 68         OK

The values work.  Merry Christmas.

Answer:

The team charged $2 to wrap a gift with no bow and $3 to wrap a gift with a bow.

Step-by-step explanation:

just did it in edg

Answer:

660000

Step-by-step explanation:

Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.

According to the statement

We have given that the John and Peter, are running a 100-meter race.

In the first race that they run John beats Peter by 5 meters. and the next time they race John stands 5 meters behind the starting line.

Here the both participant's speed remain same in both races.

So, We have to find that the If they run at the constant speed as the first race, who will win the second race

So, for this purpose

According to the statement

in first race john beats the peter and wins the race and if they start the second race with the same speed then it is clear that the second time john won the race.

So, Second time john wins the race because he runs in the race with constant speed as same speed they run in 1st race.

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Answer: A. (4, 4) and (4, 5)

Step-by-step explanation:

The same x value maps onto more than one y value.

Answer:

$600

Step-by-step explanation:

For 8 hours she makes $120

For 1 hour she makes $120÷8 = $15

For 40 hours she makes $15 × 40 = $600

Our final answer is $600

Hope this helped and have a good day

Answer:

No.  They cannon be on the same straight line.

Step-by-step explanation:

As explained in the attached graphic, the slopes are slightly different between the three points.

Answer:

p = 7

Step-by-step explanation:

(x² + px - 3)(3x - 5)

each term in the second factor is multiplied by each term in the first factor, that is

x²(3x - 5) + px(3x - 5) - 3(3x - 5) ← distribute parenthesis

= 3x³ - 5x² + 3px² - 5px - 9x + 15 ← collect like terms

= 3x³ +x²(3p - 5) - x(5p + 9) + 15

given the coefficient of the x- term is - 44 , then

-(5p + 9) = - 44 ← - (5p + 9) is th coefficient of x in the expansion

- 5p - 9 = - 44 ( add 9 to both sides )

- 5p = - 35 ( divide both sides by - 5 )

p = 7

Hello,

52% of 230 = 52/100 × 230 = 0,52 × 230 = 119,6

Answer:

230 : 100 * 52 =

Step-by-step explanation:

Which expression can be used to find 52% of 230?

The expression is: 230 : 100 * 52 =

Answer:

1.857 pounds

Step-by-step explanation:

If the clay is divided into 4 equal parts, we divide 7.5lbs by 4: 7.5/4 = 1.857 lbs

The angle that the ramp makes with the ground is 16 degrees.

We can see that the ramp is and its support now constitutes a right angled triangle.

Thus, the hypotenuse of the triangle is 40feet while the opposite of the angle is 11 feet.

The angle made with the ground is;

sin x = 11/40

x = sin-1(11/40)

x = 16 degrees

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Answer:

x= 19/12, -41/12

Step-by-step explanation:

I'm guessing x is "t".

The quadratic formula is x=(-b+-sqrtb^2-4ac)/2a I know that this is hard to read sorry!

Plug in a, b, and c.

Oh yeah, first convert it to the form Ax^2+bx+c

so 6x^2-35=-11x

6x^2+11x-35=0

(-11+-sqrt11^2-(-4*6*35))/2*6

Simply: (-11+-sqrt 121+840)/12

(-11+-sqrt961)/12

(-11+-31)/12

-11+30=19

-11-30=-41

x= 19/12, -41/12

The point that is 5 units from W is (A) (-5, 2)

The point is given as:

W= (-5, -3)

A point 5 unit from W can be any of the following

W' = (-5 ± 5, -3)

W' = (-5, -3 ± 5)

When the above expressions are evaluated, we have:

W' = (0, -3), (-10, -3), (-5, 2) and (-5, -8)

Hence, the point that is 5 units from W is (A) (-5, 2)

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The transformed function is defined by:

g(x) = -f(x/5 - 2) - 6

Where f(x) is the given function.

Here we start with the function:

f(x) = (1/3)*x

(I don't know if this is the actual function, but that does not matter, I will solve it in a general way).

If first, we reflect it vertically, then the new function is:

g(x) = -f(x).

If now we compress it horizontally by a factor of 5, then we get:

g(x)  = - f(x/5)

Now we shift it 2 units to the right, then:

g(x) = -f(x/5 - 2)

Finally, we shift it down 6 units, then we get:

g(x) = -f(x/5 - 2) - 6

That is the general form of the function g(x).

Replacing f(x) by what is defined above, we get:

g(x) = -(1/3)*(x/5 - 2) - 6

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Answer:

1921.68 [tex]ft^{3}[/tex]

Step-by-step explanation:

V = pi*r*r*h

= 3.14*6*6*17

= 1921.68

Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.

Based on the test by result, Alex did better in the test by scoring 66.67%

Percentage scored by Alex = 40/60 × 100

= 0.66666666666666 × 100

= 66.6666666666666

= 66.67%

Therefore, Alex did better in the test

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B because it’s a linear graph.

Johnny created a Tally marks chart.

A frequency distribution table displays the frequency of each data set in an organized way. It helps us to find patterns in the data and also enables us to analyze the data using measures of central tendency and variance. The first step that a mathematician does with the collected data is to organize it in the form of a frequency distribution table. All the calculations and statistical tests and analyses come later.

Tally Marks are used to keep a track of numbers in the quickest possible way. Tally marks are used for counting and are represented as a set of five lines in which there are four vertical lines (one vertical line is made for each of the first four numbers) and the fifth number is represented by a diagonal line across the previous four numbers. It can be understood through the given figure

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The surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet is 996 ft².

A = Surface area

l = Length

w = Width

h = Height

A = 2 ( w l + h l + h w )

= 2 · ( 10 · 13 + 16 · 13 + 16 · 10 )

= 996 ft²

The gap occupied by using a dimensional flat surface is referred to as the region. it's far measured in rectangular gadgets. The location occupied by using a 3-dimensional object by means of its outer floor is referred to as the surface location.

The surface vicinity of a strong object is a degree of the total vicinity that the surface of the item occupies.

The floor location is the overall location included via all of the faces of a 3-d item. As an example, if we need to discover the amount of paint required to paint a cube, then the surface on which the paint will be implemented is its floor place. it is continually measured in square gadgets.

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The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.

Amount saved in 4 years = Amount Hartman family saves monthly × Number of months

= $400 × 48

= $19,200

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The statement which best explains whether the family will have enough money in 4 years is; The family will not have enough money. They will have saved only $19,200.

Amount saved in 4 years = Amount Hartman family saves monthly × Number of months

= $400 × 48

= $19,200

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