A children's wading pool is in the shape of a right circular cylinder, and has a diameter of 6 feet. The pool is filled to a uniform depth of 1.5 feet.
Which of the following values is closest to the volume of
water in the pool, in cubic feet?
A. 28
B. 42
C. 57
D. 67
E. 133

Answer:

Step-by-step explanation:

Y/1 = 2x + 5

Y = 2x + 5

Y = 2x + 5

When x = 1

Y = 2 ×1 +5

Y = 2 + 5

Y = 7

When x =0

Y = 2 × 0 + 5

Y = 5

When x = -2

X = 2 × -2 + 5

X = 1

( Make a table in the side of the page)

X | 1 0 -2

_ _______

Y 7 5 1

The graph for the coordinate points (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7) is plotted below.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation of a line is y=1/2x+5.

Substitute x=0, 1, 2, 3, 4, 5,....in a equation y=1/2x+5, we get

When x=0, y=5

When x=1, y=5.5

When x=2, y=6

When x=3, y=6.5

When x=4, y=7

So, the coordinate points are (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7)

Therefore, the graph for the coordinate points (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7) is plotted below.

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Answer:

Is an acute triangle

Step-by-step explanation:

we have

[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]

so

The polygon is a triangle

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Remember that

If applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex] -----> is a right triangle

[tex]c^{2}>a^{2}+b^{2}[/tex] -----> is an obtuse triangle

[tex]c^{2}<a^{2}+b^{2}[/tex] -----> is an acute triangle

where

c is the greater side

step 1

Find the distance GH

[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]

substitute

[tex]d=\sqrt{(0-3)^{2}+(9-7)^{2}}[/tex]

[tex]d=\sqrt{(-3)^{2}+(2)^{2}}[/tex]

[tex]GH=\sqrt{13}\ units[/tex]

step 2

Find the distance HI

[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]

substitute

[tex]d=\sqrt{(-1-0)^{2}+(5-9)^{2}}[/tex]

[tex]d=\sqrt{(-1)^{2}+(-4)^{2}}[/tex]

[tex]HI=\sqrt{17}\ units[/tex]

step 3

Find the distance GI

[tex]G(7, 3),H(9, 0),I(5, -1)[/tex]

substitute

[tex]d=\sqrt{(-1-3)^{2}+(5-7)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(-2)^{2}}[/tex]

[tex]GI=\sqrt{20}\ units[/tex]

step 4

Let

[tex]c=GI=\sqrt{20}\ units[/tex]

[tex]a=HI=\sqrt{17}\ units[/tex]

[tex]b=GH=\sqrt{13}\ units[/tex]

Find [tex]c^{2}[/tex] ------> [tex]c^{2}=(\sqrt{20})^{2}=20[/tex]

Find [tex]a^{2}+b^{2}[/tex] ----> [tex](\sqrt{17})^{2}+(\sqrt{13})^{2}=30[/tex]

Compare

[tex]20 < 30[/tex]

therefore

Is an acute triangle

Answer: Yes it is.

Step-by-step explanation: So we are already told that segment AC is congruent to segment DC. They both have a right angle, as indicated by the angle symbol, and they share side-length BC.

According to the Hypotenuse-Leg Theorem, two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles. AC and DC are hypotenuses and they are congruent. And BC, the shared side, is a corresponding congruent leg. And since they are both right triangles, we then know that the HL Theorem applies.

The symmetric property of equality justifies the statement 'If m₁ = m₂, then m₂ = m₁'.

Property of Equality: The property that justifies the statement 'If m₁ = m₂, then m₂ = m₁' is the symmetric property of equality. This property states that if a = b, then b = a. It is a fundamental property of equality in mathematics.

Answer:

x ≈ 20.42, y ≈ 11.71

Step-by-step explanation:

Using the cosine ratio on the right triangle on the right, that is

cos20° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{11}{y}[/tex]

Multiply both sides by y

y × cos20° = 11 ( divide both sides by cos20° )

y = [tex]\frac{11}{cos20}[/tex] ≈ 11.71

Using the sine ratio on the right triangle on the left, that is

sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{x}[/tex] = [tex]\frac{11.71}{x}[/tex]

Multiply both sides by x

x × sin35° = 11.71 ( divide both sides by sin35° )

x = [tex]\frac{11.71}{sin35}[/tex] ≈ 20.42

Answer:

x = 20.41 units, y = 11.71 units to the nearest hundredth.

Step-by-step explanation:

Consider the small triangle:

cos 20 = 11/y

y = 11 / cos 20

= 11.706 units.

Now the larger triangle:

sin 35 = 11.706 / x

x = 11.706 / sin 35

x = 20.409 units.

[tex]\tan a-1=0\\\tan a =1\\\\a=\dfrac{\pi}{4}+k\pi, k\in\mathbb{Z}[/tex]

Answer:

The chord is bisected.

Step-by-step explanation:

see the attached figure to better understand the problem

In the circle of the figure

The diameter is the segment DE

The chord is the segment AB

PA=PB=r ----> radius of the circle

Triangles PAC and PBC  are congruent right triangles by SSS

Because

PA=PB

PC is a common side

AC=BC ----> Applying Pythagoras Theorem

therefore

The chord AB is bisected

Answer:

The chord is bisected

Step-by-step explanation:

Answer:

The graph of g(x) is equal to the graph of f(x) shifted 3 units to the right and 4 units above.

Step-by-step explanation:

we know that

[tex]f(x)=x^{3}[/tex] ----> the turning point is the point (0,0)

[tex]g(x)=(x-3)^{3}+4[/tex] ----> the turning point is the point (3,4)

The rule of the translation of f(x) to g(x) is equal to

(x,y) ------> (x+3,y+4)

That means-----> The translation is 3 units at right and 4 units up

therefore

The graph of g(x) is equal to the graph of f(x) shifted 3 units to the right and 4 units above.

Answer:

side GH is proportional to segment CD

Step-by-step explanation:

Corresponding sides are those sides that are in the same spot in two different  shapes.

Since parallelogram EFGH is dilated form of Parallelogram ABCD and Side BC is proportional to side FG.

So, side GH is proportional to segment CD

Answer:

See below in bold.

Step-by-step explanation:

Convert the equation into slope-intercept form:

7x - 6y = -5

6y = 7x + 5

y = (7/6) x + 5/6

- so the slope is 7/6.

The slope of a line parallel to this has the same slope 7/6.

The slope of a line perpendicular to this has a slope of - 1 / 7/6

= -6/7.

Answer:

Step-by-step explanation:

calculate the slope of given line :

7X-6Y=-5

6y = 7x+5

y=7/6 x +5/6

the slope is : 7/6

the slope of a line parallel to this lineis 7/6 ( same slope )

the slope of a line perpendicular to this line is : a    when : a× 7/6= - 1

so : a = -6/7

Answer:

[tex]y = \frac{1}{2}x+3[/tex]

Step-by-step explanation:

The standard form of a line with slope and point is:

y= mx+b

We know the slope is 1/2

So,

[tex]y=\frac{1}{2} x+b[/tex]

Putting the point to find the value of b

[tex]4=\frac{1}{2}(2) +b\\ 4=1+b\\4-1 =b\\b=3[/tex]

So the equation of line is:

[tex]y = \frac{1}{2}x+3[/tex]

..

Answer:

The boy has 28 blue pencils

Step-by-step explanation:

Given

Total pencils = 40

The ratio of red to blue= 0.15:0.35

We have to find the number of blue pencils

For that we need the sum of ratio = 0.15+0.35 = 0.5

So, the number of blue pencils = (ratio of blue/sum of ratio) * total pencils

=0.35/0.5 * 40

=0.7*40

=28 pencils

Therefore, the boy has 28 blue pencils ..

Final answer:

The ratio of red to blue pencils is 0.15 to 0.35. By converting the ratio into parts and calculating the pencils per part, we conclude that the boy has 28 blue pencils in his pencil case.

Explanation:

Calculating the Number of Blue Pencils

To find out how many blue pencils the boy has, we start by understanding the ratio of red to blue pencils, which is given as 0.15 to 0.35. This ratio can also be represented as a fraction, so for every 0.15 red pencils, there are 0.35 blue pencils. To find out the total parts the ratio represents, we add them up: 0.15 (red) + 0.35 (blue) = 0.5 parts. We then divide the total number of pencils (40) by the total parts (0.5) to find out how many pencils each part represents: 40 pencils / 0.5 parts = 80 pencils per part. Since we are looking for the number of blue pencils, we multiply the blue part (0.35) by the number of pencils per part (80): 0.35 * 80 pencils per part = 28 blue pencils.

Answer: B. 36

Step-by-step explanation: Round each number.

11.72 -> 12

3.01 -> 3

Multiply the rounded numbers.

12 x 3 = 36

The answer would be 36.

Answer:

M<A is less than or equal to 90°

Step-by-step explanation:

If it is less than or equal to, then the first statement has to be false, that it is greater. This means the statement is negated because they can't work together.

Answer: 0.999548

Step-by-step explanation:

If the probability that a person will die next year is 425/1,000,000

The the probability of them not dying is:

(1,000,000-425)/1,000,000=999548/1,000,000

Next let’s move the decimal 6 spots to the left.

The answer would be 0.999548

[tex]\bf (\stackrel{x_1}{10}~,~\stackrel{y_1}{8})~\hspace{10em} slope = m\implies \cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-8=\cfrac{2}{5}(x-10) \\\\\\ y-8=\cfrac{2}{5}x-4\implies y=\cfrac{2}{5}x+4[/tex]

f(x-5) because when it's with the x, + indicates a translation to the left and - indicates a translation to the right.

Answer:

f(x−3)+1, f(x−5)

Step-by-step explanation:

I took the checkpoint and got it right.

Answer:

4

Step-by-step explanation:

−36−9+14−31−(−66)

=−45+14−31−(−66)

=−31−31−(−66)

=−62−(−66)

=4

Answer:

Left 4 units

Step-by-step explanation:

h(x) is a line with slope 2.  Let's say it has y-intercept b.  So:

h(x) = 2x + b

d(x) is h(x) shifted up 8 units.  So:

d(x) = h(x) + 8

d(x) = 2x + b + 8

We want to shift h(x) left or right to get d(x).  If we say that shift is a units to the right, then:

h(x−a) = d(x)

2(x−a) + b = 2x + b + 8

2x − 2a + b = 2x + b + 8

-2a = 8

a = -4

a is negative, so the shift is to the left.

h(x) should be shifted to the left 4 units.

The h(x) should be Left 4 units

Since

h(x) represent a line with slope 2.  

Let's assume it has y-intercept b.  

Therefore,

h(x) = 2x + b

d(x) represent h(x) shifted up 8 units.  

So,

d(x) = h(x) + 8

d(x) = 2x + b + 8

Now

h(x−a) = d(x)

2(x−a) + b = 2x + b + 8

2x − 2a + b = 2x + b + 8

-2a = 8

a = -4

Since a is negative, so the shift is to the left.

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Answer: The black hole is [tex]3.302\times10^{6}[/tex] times more masive than the sun.

Step-by-step explanation:

Given : The mass of black hole =  [tex]6.57\times10^{36}\ kg[/tex]

The mass of Sum is approximately [tex]1.99\times10^{30}\ kg[/tex]

Now, the number of times the mass of black hole more massive than the mass of sun is given by :-

[tex]n=\dfrac{6.57\times10^{36}}{1.9\times10^{30}}[/tex]

i.e.[tex]n=\dfrac{6.57}{1.9}\times\dfrac{10^{36}}{10^{30}}[/tex]

Using the division law of exponent :-

[tex]\dfrac{a^m}{a^n}=a^{m-n}[/tex]

[tex]=\approx3.302\times10^{36-30}}\\\\=3.302\times10^{6}[/tex]

Hence, the black hole is [tex]3.302\times10^{6}[/tex] times more masive than the sun.

Area of the given polygon is required.

The area of the polygon is A. [tex]147\ \text{square units}[/tex]

The polygon is a rectangle with one corner of the rectangle removed.

The removed area is a square.

The area of the complete rectangle is

[tex]13\times 12=156\ \text{square units}[/tex]

Area of the removed square

[tex]3\times 3=9\ \text{square units}[/tex]

The area of the polygon is

[tex]156-9=147\ \text{square units}[/tex]

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Answer:

5 sqrt2.

Step-by-step explanation:

sqrt8 = sqrt4 * sqrt2 = 2 sqrt2

sqrt18 = sqrt9 * sqrt2 = 3 sqrt2

So simplifying:

5sqrt 8 - sqrt18 - 2 sqrt2

= 5*2sqrt2 - 3 sqrt 2 - 2 sqrt2

= 10 sqrt2 - 5 sqrt2

= 5 sqrt2 (answer).

For this case we must simplify the following expression:

[tex]5 \sqrt {8} - \sqrt {18} -2 \sqrt {2}[/tex]

Rewriting we have:

[tex]8 = 2 * 2 * 2 = 2 ^ 2 * 2\\18 = 9 * 2 = 3 ^ 2 * 2\\5 \sqrt {2 ^ 2 * 2} - \sqrt {3 ^ 2 * 2} -2 \sqrt {2} =[/tex]

We have that by definition of properties of roots and powers it is fulfilled:

[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]

So:

[tex]5 * 2 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -5 \sqrt {2} =\\5 \sqrt {2}[/tex]

Answer:

[tex]5 \sqrt {2}[/tex]

[tex]\huge{\boxed{\text{No.}}}[/tex]

Unless the points are both the same point, there is only one straight line to connect them both. Any other line would either only touch one point or touch neither of the points.

Answer:

Step-by-step explanation:

[tex]A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] \\\\\det A=\left|\begin{array}{ccc}a&b\\c&d\end{array}\right|=ad-bc[/tex]

[tex]\left\{\begin{array}{ccc}x+2y=5\\x-3y=7\end{array}\right\\\\A=\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] \\\\\det A=A=\left|\begin{array}{ccc}1&2\\1&-3\end{array}\right|=(1)(-3)-(1)(2)=-3-2=-5[/tex]

Answer:

-5

Step-by-step explanation:

Answer:

Front section tickets: $40

Back section tickets: $25

Step-by-step explanation:

If x is the price of back section tickets, and x + 15 is the price of front section tickets, then:

275 (x + 15) + 325 x = 19125

275 x + 4125 + 325 x = 19125

600 x = 15000

x = 25

So back section tickets are $25, meaning front section tickets are $40.

Answer:

Overlapping events

Step-by-step explanation:

Note that in the question, it specifically specifies that there is only a number cube (or 1 number cube). Note that the two events asked for us to solve is does not conflict at all.

Event A is asking for the probability of you rolling a prime number (1 , 3 , 5), while Event B is asking for the probability of you rolling a number larger than 4 (5 , 6). These two can occur at the same time, and both events can be confirmed by rolling the number 5.

~

Answer:

overlapping events

Step-by-step explanation:

Event A: Rolling a prime

The following are the prime numbers from 1 to 6 (inclusive):

2,3,5

Event B: Rolling a number larger than 4

The following are larger than 4 from 1 to 6 (inclusive):

5,6

Do you see any overlap?

The overlap is 5.

These are overlapping events.

2.375 is 0.95% of 250

Equation: Y = P% multiplied by X

Y = 0.95% multiplied by 250

Converting percent to a decimal:

P = 0.95%÷100 = 0.0095

Y = 0.0095 × 250

Y = 2.375

Therefore, 2.375 is 0.95% of 250

Final answer:

To find the new interest rate compounded quarterly, divide the annual interest rate by the number of compounding periods per year.

Explanation:

To rewrite the equation to find the new interest rate, we need to consider the compounding frequency. Currently, the interest is compounded annually. To find the new interest rate compounded quarterly, we need to divide the annual interest rate by the number of compounding periods per year.

So, for an interest rate of 10%, the quarterly interest rate would be 10% divided by 4, which is 2.5%.

Therefore, the approximate new interest rate, compounded quarterly, would be 2.5%.

The new interest rate when compounded quarterly that would keep the future value (A) and the present value (P) the same is approximately 9.38%.

To find the new interest rate when the interest is compounded quarterly instead of annually, we need to use the compound interest formula and equate the two expressions for A.

Given:

[tex]A = 250(1.1)^_t[/tex] (interest compounded annually)

[tex]A = P(1 + r/m)^_(mt)[/tex] (compound interest formula)

Where:

A = Future value

P = Present value (250)

r = Annual interest rate

m = Number of times interest is compounded per year

t = Time in years

Step 1: Equate the two expressions for A.

[tex]250(1.1)^t = 250(1 + r/m)^_{(mt)}[/tex]

Step 2: Substitute m = 4 (interest compounded quarterly).

[tex](1.1)^t = (1 + r/4)^_{(4t)}[/tex]

Step 3: Solve for r.

[tex](1 + r/4)^4 = 1.1[/tex]

[tex]1 + r/4 = (1.1)^_{(1/4)}[/tex]

[tex]r/4 = (1.1)^_(1/4)} -1[/tex]

[tex]r= 4((1.1)^_(1/4)} -1)[/tex]

r ≈ 0.0938 or 9.38%

Answer:

x+2

5x-2

Step-by-step explanation:

There is only 2 binomials that will multiply together that will give the given trinomial.

ax^2+bx+c

5x^2+8x-4

Goal: Find two numbers that multiply to be a*c and add up to be b.

We will use this goal to factor our trinomial.

a=5

b=8

c=-4

--------

a*c=-20

b=8

Can you think of two numbers that multiply to be -20 and add up to be 8? I hope you said 10 and -2.

So we are going to replace 8x with -2x+10x.

5x^2+8x-4

5x^2-2x+10x-4

We are going to pair the first terms together and the second two terms together like so:

(5x^2-2x)+(10x-4)

Now we are going to factor each pair.

x(5x-2)+2(5x-2)

(5x-2)(x+2)

So (x+2) is a factor of the given trinomial and (5x-2) is a factor of the given trinomial.

Answer

x+2 and 5x-2

Step-by-step explanation: