What is the length of one leg of the triangle?
9 cm
972 cm
18 cm
18/7 cm

Answer:

Prasant needs more than 4.5 bags of candy to hand out during Halloween.

Step-by-step explanation:

The correct method to write a statement that matches the inequality [tex]\( h > 4.5 \)[/tex] is to express that the value of [tex]\( h \)[/tex] is greater than 4.5. This can be done by stating that [tex]\( h \)[/tex] must be some quantity more than 4.5, without specifying the exact amount by which [tex]\( h \)[/tex]exceeds 4.5.

For example, one could write the statement as:

The value of [tex]\( h \)[/tex] is more than 4.5 units.

This statement correctly conveys that [tex]\( h \)[/tex] is not equal to 4.5 and is somewhere on the number line to the right of 4.5, with no upper limit specified. It is important to note that the inequality [tex]\( h > 4.5 \)[/tex] does not include the value 4.5 itself; [tex]\( h \)[/tex] must be strictly greater than 4.5.

In summary, the statement should indicate that \( h \) is any number that is greater than 4.5, and the value of [tex]\( h \)[/tex] can be infinitely close to 4.5 but never equal to or less than it.

Answer:

156.654

Step-by-step explanation:

162*.967=156.654

To multiply 162 by 0.967, use a calculator or perform the multiplication manually to get approximately 156.654.

The product of 162 and 0.967, you can multiply these two numbers together. When you multiply a whole number by a decimal, you're essentially combining that many groups of the decimal number. In this case, you are combining 162 groups of 0.967.

Here is the step-by-step calculation:

Write down the numbers: 162 and 0.967.

Multiply the whole number by the decimal: 162 * 0.967.

Use a calculator or long multiplication to find the product.

If you use a calculator, the answer you would get is approximately 156.654.

Answer:

No

Step-by-step explanation:

In a triangle, sum of any two sides is always grater than the third side.

Here,

[tex]3 + 2 = 5 \ngtr \: 5 \\ [/tex]

Hence, 3,2,5 can no tbe the lengths of a triangle

Using the formula for compound interest, you can calculate the future value of an investment for different compounding methods. These values turned out to be $66299.84 for annual compounding, $66933.56 for semi-annual compounding, $67183.56 for monthly compounding and $67239.46 for daily compounding.

To solve this problem, you need to understand the compound interest formula: A = P(1 + r/n)^(nt).

Where:

(a) For annual compounding (n=1): A = 47400*(1 + 0.07/1)^(1*5) = $66299.84

(b) For semi-annual compounding (n=2): A = 47400*(1 + 0.07/2)^(2*5) = $66933.56

(c) For monthly compounding (n=12): A = 47400*(1 + 0.07/12)^(12*5) = $67183.56

(d) For daily compounding (n=365): A = 47400*(1 + 0.07/365)^(365*5) = $67239.46

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Final answer:

Calculate the value of the investment after 5 years using different compounding methods.

Explanation:

The value of the investment at the end of 5 years:

Annual: $61,571.76

Semiannual: $62,041.46

Monthly: $62,263.11

Daily: $62,334.74

Answer:

x+5

Step-by-step explanation:

Given:

Dividend= x4 + 5x3 – 3x – 15

Quotient=(x3-3)

As per the rule of division of polynomial:

Dividend = Divisor × Quotient + Remainder

Divisor= required polynomial p(x)

remainder=0

x4 + 5x3 – 3x – 15= p(x) *(x3-3) + 0

p(x)=x4 + 5x3 – 3x – 15/x3-3

By long division we get

p(x)= x+5 !

Answer:

The polynomial is x+5.

Step-by-step explanation:

Here we need to recall the algorithm of the division for polynomials, which is very similar to the one for integers. Given polynomials P(x) and Q(x), there always exist polynomials S(x) and R(x) such that

P(x) = Q(x)S(x) + R(x)

where

In this particular case,  

Then, x⁴+5x³-3x-15 = (x³-3)Q(x). In order to find Q(x) we must complete the division x⁴+5x³-3x-15/x³-3. This gives us that Q(x)=x+5.

The expression 2a−4b+7c is a trinomial and a first-degree polynomial.

The expression 2a−4b+7c is a linear polynomial because each term has a variable (a, b, c) with an exponent of one.

It is also a first-degree polynomial since the highest power of any variable is 1.

For this case we must convert the given expression to degrees:

[tex]\frac {3 \pi} {8}[/tex]

By definition we have that [tex]\pi = 180[/tex] degrees, then:

[tex]\frac {3 \pi} {8} * \frac {180} {\pi} = \frac {180 * 3} {8} = \frac {540} {8} = 67.5[/tex]

Thus, we have [tex]\frac {3 \pi} {8}[/tex] is equal to 67.5 degrees.

Answer:

67.5 degrees

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which is more confusing.

Answer:

3.1x+2.8z

3.1 over 10x +14 over 15 z

1 over 10 x (3.1x + 2.8z)

4.3x - 1.2z =

43 over 10x - 6 over 5z

1 over 10 x (43x-12z)

Answer:−1.2x+4z

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

Sort the given data in ascending order:

47, 48, 50, 52, 53, 53, 55, 68

Possible outlier is number 68. Check whether this number is an outlier:

[tex]Q_1=49\\ \\Q_2=52.5 \\ \\Q_3=54[/tex]

The interquartile range is

[tex]Q_3-Q_1=54-49=5[/tex]

Multiply it by 1.5:

[tex]1.5\cdot 5=7.5[/tex]

and add to third quartile:

[tex]7.5+54=61.5[/tex]

Since [tex]68>61.5,[/tex] number 68 is an outlier.

The median of the sample with outlier is [tex]Q_2=\dfrac{52+53}{2}=52.5[/tex]

The median of the sample without outlier is 52

The difference between the median of the data, including the possible outlier and excluding the possible outlier is 52.5-52=0.5

Answer:

0.5

Step-by-step explanation:

i finished the assignment and it was right so yeah it’s 0.5

Answer:

Option C) 8 cups

Step-by-step explanation:

Let

x----> the number of cups

y ---> the number of plates

we know that

y=2x-4 -----> equation A

60%=60/100=0.60

y=0.60(x+y) ----> equation B

Substitute equation A in equation B and solve for x

2x-4=0.60(x+2x-4)

2x-4=0.6x+1.2x-2.4

2x-4=1.8x-2.4

2x-1.8x=4-2.4

0.2x=1.6

x=1.6/0.2

x= 8 cups

From looking at the question, the answer is C. 8

Answer:

1. so the total people including the teacher is 24. 12 and 8 are both factors of 24. 12x2 equals 24 and 8x3 equals 24 so if they get 2 packs of hot dogs and 3 pack of buns everyone can get 1 hot dog and 1 bun

Step-by-step explanation:

24 factors: 1, 2, 3,4 ,6,8,12 ,24

8×3=24

12×2=24

get 2 packs of sausages and 3 packs of buns

each person gets 1 hotdog and 1 bun

Answer:

1020000

Step-by-step explanation:

Step 1 : Use BODMAS (Bracket Open Divide Multiply Add Subtract)

Step 2 : Take the common term

7.8*10^5+2.4*10^5

10^5(7.8 + 2.4)

Step 3 : Solve

10^5(7.8 + 2.4)

100,000(10.2)

=1020000

!!

Answer:

1.02 × 106

Step-by-step explanation:

1.02 × 106

Answer:

754 inches

Step-by-step explanation:

you have to convert the 62 feet into inches which will be 62*12=744. You then add 10 to it to get 754 as your answer.

Answer:

Step-by-step explanation:

The image is blurred.

The given frequency is showing only 4 intervals, that means there should be only 4 bars in the right histogram, that lead us only to the first or second choice as right answers.

Now, according to the frequency table the first interval is larger than the second interval and the third interval is larger than the fourth interval. This means the first bar must be taller than the second bar, and the third bar must be taller than the fourth bar, and the second histogram is showing this.

Therefore, the right histogram is the second one.

Answer:

60(1/5)^(n-1).

Step-by-step explanation:

The common ratio  r   is 12/60 = 12/5 / 12  = 12/25 / 12/5 = 1/5.

The first term a1 = 60 so the explicit rule is

a1 * r^(n-1)

= 60(1/5)^(n-1).

aₙ=60(1/5)ⁿ⁻¹ is the explicit rule for the geometric sequence 60,12,12/5, 12/25,12/125,... .This can be obtained by using the formula of geometric sequence.

Sequence is s collection of objects in a particular order and repetitions are allowed.

Geometric Sequence:

In the given question, first term a=60

Common ratio r = a₂/a₁ = 12/60 = 1/5 ⇒ r = 1/5

By definition, arⁿ⁻¹ = (60)(1/5)ⁿ⁻¹ is the required explicit rule for the geometric sequence.

Hence aₙ=60(1/5)ⁿ⁻¹ is the explicit rule for the geometric sequence 60,12,12/5, 12/25,12/125,... .

Learn more about geometric sequence here:

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Answer: Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120

We know that David wants to increase the price per cup to increase his revenue. He found out that for every $0.25 grows( increase), x, in the price for each cup.

In the event of a price increase, 2 cups remain unsold, and doubling the cups is still not sold. Then the numbers are sold (60-2x). Depending on the choice:

Revenue= (60 -2x)(2 +0.25x)

60·2 +60·0.25x -2x·2 -2x·0.25x

= -0.5x² +11x +120

Answer:

Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120

Step-by-step explanation:

Here, x represents the times at which the price is increased,

Since, the original price of one cup = $ 2,

So, after increasing x times of $ 0.25, the new price of each cup = 2 + 0.25x,

Also, the original number of mochas = 60,

Given,

With increasing the price $ 0.25, x times, the number of cup is decreased by 2 times of x,

That is, the new number of mochas = 60 - 2x

Hence, the total revenue would be,

y = new price of each cup × new number of mochas

⇒ y = (2 + 0.25x)(60 - 2x)

⇒ y = 120 - 4x + 15x - 0.5x²

⇒ y = -0.5x² + 11x + 120

He can find find the equation which represents his daily revenue, by Multiplying (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x² + 11x + 120

Answer:

19

Step-by-step explanation:

Hey diddle diddle the medians in the middle you add then divide for the mean. the mode is the one that appears the most and the range is the difference in between.

Median: you have to organize the numbers from least to greatest then eliminate one by one.

12, 15, 15, 18, 20, 29, 33, 42

eliminate 12, and 42

15, 15, 18, 20, 29, 33

eliminate 15, and 33 ... so on

once you get to the median you end up with two numbers.

18, 20

because you can only have one median you find the number between, which in this case would be 19

Answer:

19

Step-by-step explanation:

The median is the middle value of the data in ascending order. If there is no exact middle then it is the average of the two values either side of the middle.

Arrange in ascending order

12, 15, 15, 18, 20, 29, 33, 42

The middle is between 18 and 20

median = [tex]\frac{18+20}{2}[/tex] = [tex]\frac{38}{2}[/tex] = 19

Answer:

Step-by-step explanation:

This is direct variation, and the pertinent equation is y = -2.5x, where -2.5 is the constant of variation.

Answer:

1/2

Step-by-step explanation:

The slope between two points is found by

m = (y2-y1)/(x2-x1)

   = (9-1)/(24-8)

   = 8/16

   = 1/2

Answer:

1/2.

Step-by-step explanation:

The slope = rise / run

= difference in y coordinates / corresponding differences in x coordinates

= (9 - 1) / (24 - 8)

= 8 / 16

= 1/2.

Answer:

0

Step-by-step explanation:

use the slope formula y^2-y^1

                                     x^2-x^1

Step-by-step explanation:

C. SAS the sides and angles are similar in both hence they are similar

F. SSS all sides equal

Answer:

SSS, SAS, LL, HL

Step-by-step explanation: because I got it incorrect by the last guy who tried to answer and I found out the hard way.. good luck everyone

Answer:

False

Step-by-step explanation:

XY is the diameter of the circle with the centre of this circle being O.

But O on it's own is just a coordinate, and not the circle.

Answer:

False, XY is not a diameter

Step-by-step explanation:

To be a diameter, it must go through the center of the circle, which is point O

The chord XY does not pass through the point O, so XY cannot be a diameter

Answer:

two real roots

Step-by-step explanation:

x^2 + 7x – 6 = 0

We can use the discriminant

This is in the form ax^2 +bx+c=0

b^2 -4ac

If  b^2 -4ac> 0 there are 2 real roots

If b^2 -4ac = 0 there is one real root

If b^2 -4ac <0 there are two complex roots

7^2 -4(1)*(-6)

49 +24

73

Since 73 > 0 there are two real roots

Answer:

The graph of the equation intersects the x-axis at two points. Therefore, it has two solutions.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex](g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=2x+1,\ g(x)=x+14\\\\\text{Exchange}\ x\ \text{in}\ g(x)\ \text{to}\ (2x+1):\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)=g(2x+1)=(2x+1)+14=2x+15[/tex]

I'm going to assume that you meant to write: The square of a number exceeds that number by 12. What are the two possible solutions.

In other words x² = x + 12

4² is 16.

4 + 12 = 16

(-3)² is 9

-3 + 12 = 9

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Shorter sides: 270 feet.

Larger side: 540 feet.

Greatest possible area: 145800 square feet.

Step-by-step explanation:

So we need fencing around the garden except along the river.

The opposite sides of a rectangular are congruent.

So the sides perpendicular to the river in the picture are both of the same length, let's call it x.  The length opposite the river is y.  

So the perimeter excluding the side along the river is

x+x+y or 2x+y or 1080 is how much fencing we want.

So we have the equation:

2x+y=1080

The area of rectangle can be found by multiplying it's dimensions:

xy=A

We want to find the dimensions that provide us with the maximum area.

This is our area function so for:

A=xy

We need the area to be in terms of one variable.

Let's use our condition that 2x+y=1080.

2x+y=1080

Subtract 2x on both sides:

y=1080-2x

or

y=-2x+1080

We are going to plug this into:

[tex]A=xy[/tex]

[tex]A=x(-2x+1080)[/tex]   :  I replaced y with -2x+1080 since y=-2x+1080.

[tex]A=-2x^2+1080x[/tex] :  I distribute.

Let's find the x-coordinate of the vertex.

To do this we need to determine [tex]a[/tex] and [tex]b[/tex] in the comparison of

[tex]A=ax^2+bx+c[/tex].

[tex]a=-2[/tex]

[tex]b=1080[/tex]

[tex]c=0[/tex]

The formula for the x-coordinate of the vertex is [tex]\frac{-b}{2a}[/tex].

[tex]\frac{-b}{2a}=\frac{-1080}{2(-2)}=\frac{1080}{4}=270[/tex]

We could plug this into our area Area function in terms of to find maximum area.

We could also wait til later.  I think I will do both for a later check.

[tex]A=-2x^2+1080x[/tex] with [tex]x=270[/tex]

[tex]A=-2(270)^2+1080(270)[/tex]

[tex]A=145800[/tex]

So we one dimension of the rectangle so for which is 270 feet.

We have the maximum area which is 145800 square feet.

Now recall y=-2x+1080.

y=-2x+1080 with x=270

y=-2(270)+1080

y=540

So we have one dimension of the rectangle is 270 feet.

Another dimension is 540 feet.

And the area of the rectangle is 145800 square feet.

Does 270(540) equal 145800? 270(540)=145800 so yes.

Let's check to see if we have 1080 feet of fencing.

So we have 2 small sides of 270 and 270 feet.

We have a larger side which is 540 feet.

270+270+540=10180 so everything checks out.