The radius of a cylindrical construction pipe is 2ft. If the pipe is 19ft long, what is its volume?

Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.

Answer:

An expression y = 10+ 2x

Step-by-step explanation:

As per the statement: To play bingo,there is a $10 cover charge plus $2 per bingo card.

Let x represents the number of bingo card and y represents cost .

"$2 per bingo card" means 2x

"$10 cover charge plus $2 per bingo card" means 10 + 2x

then,

an expression to represents this statement;

y = 10 + 2x

Answer:

30

Step-by-step explanation:

4.50=15%

30=100%

check;

30*0.85=25.5

30-25.5=4.50

Answer:

(A)The systolic pressure of a person of age 44 is 135.1 mm Hg

(B) If a person's systolic pressure is 133.36 mm Hg, their age is 41 years.

Step-by-step explanation:

Given : P = 0.007 y² - 0.01 y +122

where P is systolic pressure and y is age of a person

(A) Here age of the person, y =44

So, P =0.007 (44²) -0.01 (44) +122 = 13.552 -0.44 +122 = 135.112 =135.1 mm

∴ The systolic pressure of a person of age 44 is 135.1 mm Hg

(B) Here P = 133.36 mm Hg

So,

133.36 = 0.007 y² - 0.01 y +122

=>0.007 y² -0.01 y -11.36 =0

=> 7 y² -10 y -11360 =0

Solving the above quadratic equation using quadratic formula, we have

[tex]y = \frac{5+\sqrt{79545} }{7}[/tex]

or [tex]y = \frac{5-\sqrt{79545} }{7}[/tex]

y = 41 or y = -39.57

Since age cannot be negative, y= 41

∴ If a person's systolic pressure is 133.36 mm Hg, their age is 41 years.

The systolic pressure of a 44-year-old person is approximately 132.8 mm Hg, and a person with a systolic pressure of 133.36 mm Hg is roughly 46 years old.

To answer this question, we will be using the given equation P = 0.007y^2 - 0.01y + 122, where P represents a person's systolic blood pressure and y represents their age.

A) To find the systolic pressure for a person aged 44 years, we substitute y=44 into the equation. This gives us P = 0.007 * (44)^2 - 0.01 * 44 + 122 = 132.8 mm Hg.

B) To find the age of a person with a systolic pressure of 133.36 mm Hg, we set P=133.36 and solve the equation for y. This can be done using methods such as factoring, completing the square, or using the quadratic formula. Upon solving, we find y roughly equals 46, so the person is approximately 46 years old when rounded to the nearest whole year.

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Answer:

A. 34 millimeters.

B. 118 millimeters.  

Step-by-step explanation:

We have been given that after m months the height of a plant is [tex]10+3m[/tex] millimeters.

To find the height of plant after 8 months we will substitute m=8 in our given expression.

[tex]\text{The height of plant after 8 months}=10+3\times 8[/tex]

[tex]\text{The height of plant after 8 months}=10+24[/tex]

[tex]\text{The height of plant after 8 months}=34[/tex]

Therefore, the height of plant after 8 months will be 34 millimeters.

B. Now let us find height of plant after 3 years.

First of all we will convert 3 years into months by multiplying 3 by 12 as 1 year equals to 12 months.

[tex]\text{3 years}=3*12\text{ months}=36\text{ months}[/tex]

Now let us substitute m=36 in our given expression.

[tex]\text{The height of plant after 36 months}=10+3\times 36[/tex]

[tex]\text{The height of plant after 36 months}=10+108[/tex]

[tex]\text{The height of plant after 36 months}=118[/tex]

Therefore, the height of plant after 3 years (36 months) will be 118 millimeters.

Question:

Approximate log base b of x, log_b(x).

Of course x can't be negative, and b > 1.

Answer:

f(x) = (-1/x + 1) / (-1/b + 1)

Step-by-step explanation:

log(1) is zero for any base.

log is strictly increasing.

log_b(b) = 1

As x descends to zero, log(x) diverges to -infinity

Graph of f(x) = (-1/x + 1)/a is reminiscent of log(x), with f(1) = 0.

Find a such that f(b) = 1

1 = f(b) = (-1/b + 1)/a

a = (-1/b + 1)

Substitute for a:

f(x) = (-1/x + 1) / (-1/b + 1)

f(1) = 0

f(b) = (-1/b + 1) / (-1/b + 1) = 1

Answer:

11

Step-by-step explanation:

I guess

Answer:

The equation would be y = 1/23x - 251/23

Step-by-step explanation:

To start, you need to locate the slope of the first equation. Since the slope is the coefficient of x, we know it to be -23. Now, the perpendicular slope is the opposite and reciprocal of that, which makes the new slope 1/23.

Now that we have this, we can use the point and the slope in point-slope form to get the equation.

y - y1 = m(x - x1)

y - 11 = 1/23(x - 2)

y - 11 = 1/23x - 2/23

y = 1/23x - 251/23

Answer:

Step-by-step explanation:

Answer:

(-4,-1)

Step-by-step explanation:

The solution to the system of equations is where the two lines cross.

The x coordinate is -4

The y coordinate is -1

Answer:

[tex]y=(x+3)^{2} -1[/tex]

Step-by-step explanation:

General equation of a parabola that opens up is [tex]y=a(x-h)^{2} +k[/tex] , a>0

So equation becomes [tex]y=(x-h)^{2} +k[/tex] which implies option A and option B can never be true for this parabola.

Also this parabola's vertex lies in 3rd quadrant where coordinates of both x and y will be negative.

So, the equation of parabola will be of the form [tex]y=(x+h)^{2} - k[/tex]

Hence, option 4 that is [tex]y=(x+3)^{2} -1[/tex] is correct.

The correct equation of the graph is: x² + 6x - 35y + 8 = 0.

The equation of the graph shown, which is a parabola that opens upwards and crosses the x-axis at -2 and -4, can be determined by examining its key features.

The fact that the parabola opens upward indicates that the coefficient of the squared term (x²) in the equation must be positive.

The parabola crosses the x-axis at -2 and -4. This means that the two x-intercepts are -2 and -4.

Putting this information together, we can form the equation:

y = a * (x - r1) * (x - r2)

where 'a' is a positive constant (coefficient of x²), and r1 and r2 are the x-intercepts.

Since the x-intercepts are -2 and -4, the equation becomes:

y = a * (x - (-2)) * (x - (-4))

y = a * (x + 2) * (x + 4)

Now, let's find the value of 'a.' We are given that the parabola passes through the point (3, 1). We can substitute these coordinates into the equation to find 'a':

1 = a * (3 + 2) * (3 + 4)

1 = a * 5 * 7

a = 1 / (5 * 7)

a = 1 / 35

Now that we have the value of 'a,' we can finalize the equation:

y = (1/35) * (x + 2) * (x + 4)

Expanding the equation:

y = (1/35) * (x² + 6x + 8)

To put the equation in standard form, we can multiply both sides by 35 to eliminate the fraction:

35y = x^2 + 6x + 8

Finally, rearrange to get the equation in standard form:

x² + 6x - 35y + 8 = 0

So, the correct equation of the graph is: x² + 6x - 35y + 8 = 0.

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To find a rectangular field with the same perimeter but a larger area than the original field (115m x 70m), we should search for dimensions that sum up to half of the perimeter (185m) and form a shape closer to a square. An example would be a field measuring 92.5m by 92.5m, which has the same 370m perimeter but a larger area.

You have asked about the length and width of another rectangular field that has the same perimeter but a larger area than a field measuring 115 meters in length and 70 meters in width. To find the dimensions of such a field, we must first calculate the perimeter of the original field.

The formula for the perimeter (P) of a rectangle is P = 2(length + width). Plugging in the given dimensions, we get P = 2(115m + 70m) = 2(185m) = 370 meters. Now we need to find dimensions that add up to half this perimeter, since length + width = P/2, which is 185 meters, but form a rectangle with a larger area.

Area (A) is calculated by the formula A = length x width. To maximize the area for a given perimeter, the rectangle should be closer to a square because a square has the largest area for a given perimeter. Hence, the dimensions we are looking for should be closer to each other compared to the original dimensions of 115m x 70m.

An example of dimensions that meet these criteria would be 92.5 meters by 92.5 meters. Although this results in a square, it fulfills the condition of having the same perimeter (since 2(92.5m + 92.5m) = 370m) but a larger area (92.5m x 92.5m = 8556.25 square meters) than the original rectangular field (115m x 70m = 8050 square meters).

Solution:

[tex]\frac{3}{5}=\frac{6}{10}=\frac{9}{15}[/tex]

Two or more fractions are said to be equivalent , if reduced in lowest terms that is numerator and denominator are co-prime, they are equal.

[tex]\frac{3}{5}[/tex] Three out of five is shaded.

Equivalent fraction of

[tex]\frac{3\times 6}{5\times 6}=\frac{18}{30} \\\\  \frac{3\times 8}{5\times 8}=\frac{24}{40}[/tex]

Answer:

Step-by-step explanation:

Final answer:

By defining variables for the prices and setting up a system of equations, we determine that each shirt costs $12 and each pair of jeans costs $40 after solving the system using the elimination method.

Explanation:

The subject of this question is a problem involving systems of equations, which falls under the category of Mathematics. We are given a scenario where Lucy and Ethel are buying clothing at the same prices, but in different quantities and we need to determine the cost of each item. First, let's define variables: let s be the price of a shirt and j be the price of a pair of jeans. We then have two equations based on the purchases:

To solve these equations using the elimination method, we will multiply the first equation by 5 and the second by 4 to eliminate the jeans variable:

Subtract the second equation from the first:

Now divide by 2 to find the price of one shirt:

We can substitute s = $12 into the first original equation to find the price of a pair of jeans:

m<1 is 90 degrees

m<2 is 121 degrees

m<3 is 42 degrees

m<4 is 42 degrees

m<5 is 35 degrees

m<6 is 90 degrees

m<7 is 48 degrees

m<8 is 35 degrees

m<9 is 35 degrees

Olivia drinks 0.375 gallons of water.

Problem-solving is defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. For example, a trainer may need to figure out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Calculation:-

Quantity of water Olivia took = half a gallon i.e 0.5 gallons.

Quantity of water Olivia drank =0.75 of 0.5

      ∴  75% of 0.5 gallons

          = 75/100 × 0.5

           = 0.375 gallons.

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ANSWER

g(x) > h(x) for x = -1 is TRUE

For positive values of x, g(x) > h(x) is TRUE

For negative values of x, g(x) > h(x) is also TRUE

EXPLANATION

The given functions are

[tex]g(x)={x}^{2}[/tex]

and

[tex]h(x)=-{x}^{2} [/tex]

If

[tex]x=0[/tex]

[tex]g(0)={0}^{2}=0[/tex]

[tex]h(0)=-({0})^{2}=0[/tex]

Based on this options A and B are FALSE.

When

[tex]x=-1[/tex]

[tex]g(-1)={( - 1)}^{2}=1[/tex]

[tex]h(-1)=-{(-1)}^{2}=-1[/tex]

[tex]g( - 1)>\:h(-1)[/tex]

for x=-1 is True.

When x=3,

[tex]g(3)={3}^{2}=9[/tex]

and

[tex]h(3)=-{3}^{2}=-9[/tex]

[tex]g(3)>\: h( 3)[/tex]

g(x) < h(x) for x = 3 is a FALSE statement.

For positive values of x, g(x) > h(x) is TRUE

See graph.

For negative values of x, g(x) > h(x) is also TRUE

See graph

The statements that are true for the functions g(x) = x^2 and h(x) = -x^2 are: h(x) will always be greater than g(x), g(x) < h(x) for x = 3, and for positive values of x, g(x) > h(x).

The statements that are true for the functions g(x) = x^2 and h(x) = -x^2 are:

These statements can be verified by plugging in values for x and comparing the outputs of the functions.

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Answer:

78*50/100= 78/2 ( half of 78) = 39

Step-by-step explanation:

Answer:

Rational

Step-by-step explanation:

A rational number would be a number or a fraction that has a repeating decimal, or as ones say it ... "terminating decimal".

Answer:

[tex]\frac{13}{20}[/tex]

Step-by-step explanation:

First, we need to add the two fractions together. To do this we need to make the denominator a factor of both 8 and 5. Easy way to do this is to multiply each fraction by the denominator of the other fraction:

[tex]\frac{3}{5} * 8 = \frac{24}{40}[/tex]

[tex]\frac{6}{8} * 5 = \frac{30}{40}[/tex]

[tex]\frac{24}{40} + \frac{30}{40} = \frac{54}{40}[/tex]

We can also show 2 brownies as [tex]\frac{2}{1}[/tex] or [tex]\frac{80}{40}[/tex]

Now we can subtract the two:

[tex]\frac{80}{40} -  \frac{54}{40} = \frac{26}{40}[/tex]

Simplify the fraction down by dividing by two:

[tex]\frac{13}{20}[/tex]

Which is the fraction of brownie left!

Answer:

C) 68 in

Step-by-step explanation:

We use sine ratio

= 68 inches

Thank you.

Answer: (D) P=24√6,  A=96√3

Step-by-step explanation:

Consider ΔABC where D is the midpoint of BC. Since ABC is an equilateral triangle, then segment AD is a perpendicular bisector with length of 12√2.   This creates ΔADC which is a 30°-60°-90° triangle.

Now you can use the rules for this special triangle to find the length of the hypotenuse.

30° ⇄ side length "a"        base - DC on ΔADC

60° ⇄ side length "a√3"   height - AD on ΔADC

90° ⇄ side length "2a"      hypotenuse - AC on ΔADC

Step 1: solve for "a"

[tex]AD: a\sqrt3=12\sqrt{12}[/tex]

       [tex]\dfrac{a\sqrt3}{\sqrt3}=\dfrac{12\sqrt2}{\sqrt3}[/tex]

       [tex]a=\dfrac{12\sqrt2}{\sqrt3}\bigg(\dfrac{\sqrt{3}}{\sqrt{3}}\bigg)[/tex]

            [tex]= \dfrac{12\sqrt6}{3}[/tex]

            [tex]=4\sqrt6[/tex]

Step 2: solve for "2a"

[tex]AC: 2a =2(4\sqrt{6})[/tex]

       [tex]=8\sqrt{6}[/tex]

Step 3: find the perimeter

The side length is equivalent for all 3 sides so

P = 3(AC)

  [tex]=3(8\sqrt{6})[/tex]

  [tex]=24\sqrt{6}[/tex]

Step 4: find the area

[tex]A=\dfrac{1}{2}b \cdot h[/tex]

    [tex]=\dfrac{1}{2}(8\sqrt6)(12\sqrt2)[/tex]

    [tex]=(48\sqrt{12})[/tex]  

    [tex]=(96\sqrt3)[/tex]  

Answer:

y = 3500(3/7 ) ^ 1/3

y = 239.23

Step-by-step explanation:

For exponential decay

y =a b^x

a = 3500

b<1

We can use the point (3, 1500)

1500 = 3500 * b^3

Divide each by 3500

1500/3500 = 3500/3500 b^3

15/35 = b^3

3/7 = b^3

Take the cube root of each side

(3/7) ^ 1/3 = b^3 ^ 1/3

b = (3/7 ) ^ 1/3

The function is

y = 3500 (3/7) ^ 1/3 x

We want to find y when x=9.5

y = 3500 (3/7) ^ (9.5 /3)

y = 3500 ( 3/7) ^ 3. 166666666

y = 3500 (.06835)

y = 239.23

Lets check a point and see if we a close

(7,500)

y = 3500 (3/7)^ (1/3*7)

y = 3500 (3/7) ^ (7/3)

y = 484.68

That is pretty close.  We do not know the exact value since we are reading from a graph.

Answer:

The percentage of left-handed 6th graders is 20%.

Step-by-step explanation:

To find this, start by finding the total number of lefties.

19 girls + 11 boys = 30 students.

Next find the total number of students

90 girls + 60 boys = 150 students

Now divide the lefties by the total number.

30/150 = 20%

Answer:

<C =120

Step-by-step explanation:

Since the figure in inscribed in the circle, <A = <C  and <B = <D

<B= <D

2x-1=3x-59

Subtract 2x from each side

2x-2x-1=3x-2x-59

-1= x-59

Add 59 to each side

-1+59 = x-59+59

58 =x

<A = 2x+4

<A= 2(58) +4

    = 116+4

<A =120

<C = <A

<C =120

B) 6 hours

Let h represent the total trip time. Then h/2 is the time spent traveling at each speed. The distance covered is ...

... distance = speed · time

The sum of the distances in each mode is the total distance.

... 1020 = 55·h/2 +285·h/2

... 2040 = h·(55+285) . . . . multiply by 2

... 2040/340 = h = 6 . . . . . . . divide by the coefficient of h

The trip took a total of 6 hours.

Answer:

B

Step-by-step explanation:

Rotation 180° is accomplished by negating both the x- and y-coordinates. That is, you multiply each of them by -1. You want the opposite of the identity matrix, so matrix B.

We have that the Rotation of matrix [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] will be rotated 180 degree if [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] is multiplied by [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]  

Option D is correct

From the Question we are given

[tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex]

it is important to note that the rotation of the identity matrix  [tex]\begin{pmatrix}1 & 0\\0 & 1\end{pmatrix}[/tex] rotating across the Cartesian co-ordinate is a [tex]180 \textdegree[/tex] is going to give a matrix   [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]  

Therefore

The Rotation of matrix [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] will be rotated 180 degree if [tex]Matrix =\begin{pmatrix}1 \\3\end{pmatrix}[/tex] is multiplied by [tex]\begin{pmatrix}-1 & 0\\0 & -1\end{pmatrix}[/tex]  

Option D is correct

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Answer:

The range is  { -1,3,7,11,15}

Step-by-step explanation:

The range is just the output values

f(-2) = 4(-2) +7 = -8+7 =-1

f(-1) = 4(-1) +7 = -4+7 = 3

f(0)= 4(0) +7 = 7

f(1) = 4(1) + 7 = 11

f(2) = 4(2) +7 = 8+7 = 15

Answer:

The answer is B

Step-by-step explanation:

First you should make a table to explain it better to yourself. Make 2 columns named Domain(Input) and Range(Output). Now put your ordered pair in the range area. Now calculated the function by replacing X with the range. Calculate.

Answer:

The equation of this line would be y + 8 = 4(x - 3)

Step-by-step explanation:

In order to get this we can start with the base form of point-slope.

y - y1 = m(x - x1)

Now that we've got this, we can plug in the slope for m. We can also plug in the point for (x1, y1).

y + 8 = 4(x - 3)