Math question 14 help

If Allister’s father measures 180 cm, then the height of Allister would be 150 cm

Let us assume that 'h' represents the height of Allister and 'm' represents the height of Allister’s father.

Here, Allister’s father is 120% of Allister’s height.

This means that m is 120 percent of 'h'

Using the formula of percentage,

m = 120% of h

m = 120/100 × h

m = 6h/5

But Allister’s father actually measures 180 cm

This means m = 180

so , 180 = 6h/5

We solve this equation to find the value of h.

⇒ h = 180 × 5/6

⇒ h = 150 cm

Therefore, Allister's height = 150 cm.

Learn more about percentage here:

https://brainly.com/question/16797504

#SPJ4

The complete question is:

Allister’s father is 120% of Allister’s height. If his father measures 180 cm, how tall is Allister?

5. 20% of students said that they enjoy Cookie Cake.

6. 25 students answered a survey regarding their favorite cake.

The percentage is defined as a ratio expressed as a fraction of 100.

The % formula is used to calculate a percentage of a whole in terms of 100.

Percentage = (Value/Total Value) × 100

Percentage of students said they like Cookie Cake:

5/(5 + 6 + 8 + 6) × 100%

5/25 × 100%

20%

The total number of students who answered this survey about their favorite Cake:

5 + 6 + 8 + 6

25

Thus, 25 students answered a survey regarding their favorite cake.

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ1

Answer:

You need to add 50 gallons of the 3% solution to the 50 gallons of the 7% solution and that will give 100 gallons of a 5% solution.

Answer:

  32 in

Step-by-step explanation:

You want the missing diameter of the smaller of two similar cylinders, where the larger is 12 ft in diameter and 3 ft high, while the smaller is 8 inches high.

The linear dimensions of similar figures have the same ratio.

The ratio of the diameter to the height of the larger figure is ...

  (12 ft)/(3 ft) = 4

The smaller figure will also have a diameter that is 4 times the height:

  d = 4 × 8 in = 32 in

The missing dimension is 32 inches.

Answer: 37.68 feet

Step-by-step explanation:

Circumference = 2 x π x r

Plug in values:

C = 2 x 3.14 x 6

C = 12 x 3.14

C = 37.68

The circumference is 37.68 feet

Hope this helps!

Using long division the quotient of  (2x^3-5x^2+3x-6) divided by (x+4)  is 2x^2 - 13x + 55.

Quotients are often used in algebra and other branches of mathematics to solve equations and expressions involving division. They are also commonly used in everyday life, such as when calculating the cost per unit of a product, or the average speed of a journey.

For example, if we divide 10 by 2, the quotient would be 5, since 10 divided by 2 equals 5. Similarly, if we divide 12 by 3, the quotient would be 4, since 12 divided by 3 equals 4.

Now let find the quotient using long division:

2x^2 - 13x + 55

_______________________

x + 4 | 2x^3 - 5x^2 + 3x - 6

- (2x^3 + 8x^2)

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

- 13x^2 + 3x

- (-13x^2 - 52x)

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

55x - 6

- (55x + 220)

-----------

-226

Therefore, the quotient is 2x^2 - 13x + 55 and the remainder is -226.

Learn more about quotient here:https://brainly.com/question/11995925

#SPJ1

The image of the figure under a dilation with scale factor 3/2 is attached

From the question, we have the following parameters that can be used in our computation:

Center = (0, 0).

Point = (6, 12), (8, 12) and (8, 8)

Scale factor = 3

A dilation with center (0, 0) and scale factor k multiplies the coordinates of a point by k.

So, to find the image of the point under the dilation with scale factor 3/2, we multiply each coordinate by 3/2:

Image = [(6, 12), (8, 12) and (8, 8)] * 3/2

Image = [(9, 18), (12, 18) and (12, 12)]

Hence, the image of the figure is attached

Read more about dilation at

brainly.com/question/3457976

#SPJ1

The value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).

To find the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid, we need to use the formula for the volume of a parallelopiped. The formula is:

V = l*w*h

Where V is the volume, l is the length, w is the width, and h is the height.

Since we are looking for the largest rectangular parallelopiped, we need to maximize the volume. This can be done by finding the maximum values of the length, width, and height.

The maximum values of the length, width, and height can be found by using the semi-axes of the ellipsoid. The semi-axes of the ellipsoid are given by:

a = √(x^2/a^2 + y^2/b^2 + z^2/c^2)

Where a, b, and c are the semi-axes of the ellipsoid, and x, y, and z are the coordinates of the point on the surface of the ellipsoid.

The maximum values of the length, width, and height can be found by setting the derivatives of the volume with respect to x, y, and z to zero:

∂V/∂x = 0

∂V/∂y = 0

∂V/∂z = 0

Solving these equations will give us the maximum values of the length, width, and height. Once we have these values, we can plug them into the formula for the volume of a parallelopiped to find the largest volume.

The largest volume of the rectangular parallelopiped that can be inscribed in the ellipsoid is given by:

V = (2a)*(2b)*(2c)

Where a, b, and c are the semi-axes of the ellipsoid.

Therefore, the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).

To know more about rectangular parallelopiped refer here:

https://brainly.com/question/14468924#

#SPJ11

If z varies jointly as x and y, then the value of z when x = 20 and y = 8 is 24.

When a variable varies jointly as two other variables, it means that the variable is directly proportional to the product of the two other variables.

In this case, we can use the formula:

z = kxy

where k is a constant of proportionality.

We can find the value of k by using the given values of z, x, and y:

6 = k(4)(10)

6 = 40k

k = 6/40

k = 3/20

Now that we know the value of k, we can use the formula to find z when x = 20 and y = 8:

z = (3/20)xy

z = (3/20)(20)(8)

z = (3)(8)

z = 24

Therefore, the value of z when x = 20 and y = 8 is 24.

Learn more about constant of proportionality here: https://brainly.com/question/28413384.

#SPJ11

\(\|v\|=\sqrt{50}\)

The norm of vector \(v\) is \( \|v\|=\sqrt{4^2 + \sqrt{3}^2 + \sqrt{6}^2}=\sqrt{50} \). Therefore, the answer is \(\|v\|=\sqrt{50}\).

  Learn more about vector

  brainly.com/question/29740341

  #SPJ11

Answer:

Your answer is x = 7.

Step-by-step explanation:

<HFG + <YFG = 180°

180° - <HFG = <YFG

<H + <G + <HFG = 180°

<H + <G  = 180° - <HFG

<H + <G  = <YFG

(6x + 8) + (65°)  = (3+16x)

6x + 8 + 65 = 16x + 3

Get x on one side and the other numbers on the other side.

8 + 65 - 3 = 16x - 6x

70 = 10x

x = 7

You can plug in x into the angle to solve for their angles.

Answer:

x = 7

Step-by-step explanation:

∠HFG must equal to 180° - ∠YFG. Because there are 180° in a triangle, we can subtract the known value, 65°, and be left with 115°.

From there, an equation can be formed.

115° = 6x + 8 + 180 - (3+16x)

115°= 6x + 188 - 3 - 16x

115°= 185 - 10x

-70° = -10x

x = 7

Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.

A probability calculated by a series of tests is known as experimental probability.

The given table is as follows:

              1    2    3    4

Jaylon:   6    8    9    7

Paula:    8     5     7   10

To determine the experimental probability of the pointer landing on 4 for Jaylon, we add up the number of times the pointer landed on 4 for Jaylon and divide by the total number of spins:

Experimental probability for Jaylon = (number of times the pointer landed on 4 for Jaylon) / (total number of spins)

= 7 / 30

Similarly,

Experimental probability for Paula:

= 10 / 30

Expected number of times the pointer will land on 4 = (experimental probability) x (total number of spins)

For Jaylon: (7 / 30) × 130 = 30.33

For Paula: (10 / 30) × 130 = 43.33

Therefore, Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.

Learn more about probability here:

brainly.com/question/11234923

#SPJ9

The missing table has been attached below.

Step-by-step explanation:

uuoflfjtnhgdhdurjsjueiei3io ghy

Answer:

u>36

Step-by-step explanation:

u>36

9×4=36

so u>36

The center of the ellipse is,

⇒ (3, 1)

An expression which is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division is called an mathematical expression.

We have to given that;

The equation of ellipse is,

⇒ (x - 3)²/4 + (y - 1)²/9 = 1

Now, We know that;

General form of the ellipse is,

⇒ (x - h)²/a + (y - k)²/b = 1

Where, (h, k) = the center of the ellipse.

Hence, We get;

The equation of ellipse is,

⇒ (x - 3)²/4 + (y - 1)²/9 = 1

By comparing;

The center of the ellipse is,

⇒ (h, k) = (3, 1)

Thus, The center of the ellipse is,

⇒ (3, 1)

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

Answer:

I found this

Step-by-step explanation:

To simplify 3x² * 4x⁵, we can multiply the coefficients (numbers in front of the variables) and add the exponents of x:

3x² * 4x⁵ = (3 * 4) x^(2+5) = 12x^7

Therefore, the simplified expression is 12x^7.

ds/dt = sec(t)

To find the length of the curve, we need to find the arc length. The arc length of the curve r(t) is given by:

LENGTH = $\int_{0}^{1} \sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)} dt$

To find ds/dt, we can take the derivative of the above equation with respect to t:

$\frac{ds}{dt} = \frac{d}{dt} \sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}$

$\frac{ds}{dt} = \frac{6^2\cos(t)\sin(t) + 10\sin(t)\cos(t)}{\sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}}$

$\frac{ds}{dt} = \frac{16\sin(t)\cos(t)}{\sqrt{6^{2}\cos^2(t) + 1 + 5^{2}\sin^2(t)}}$

$\frac{ds}{dt} = \frac{16\sin(t)\cos(t)}{\sqrt{1+tan^2(t)}}$

Thus, ds/dt = sec(t).

Learn more about derivative

brainly.com/question/30365299

#SPJ11

Answer:

x < 5

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x + 5

2x - 3 < x + 2 and x + 2 ≤ 5

x < 5 and x ≤ 3

Answer: x < 5

1 & -3 & 2
2 & 0 & -1

The cross product of two vectors can be calculated using the formula:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{ccc}
\vec{i} & \vec{j} & \vec{k}\\
u_{1} & u_{2} & u_{3} \\
v_{1} & v_{2} & v_{3}
\end{array} \right] \]

For your given vectors, we can calculate the cross product as follows:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{ccc}
\vec{i} & \vec{j} & \vec{k}\\
1 & -3 & 2 \\
2 & 0 & -1
\end{array} \right] \]

Which simplifies to:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{c} 6 \\ 2 \\ -1 \end{array} \right] \]

Learn more about cross product

brainly.com/question/29164170

#SPJ11

Three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°). These points are equivalent because they all have the same magnitude of 7, but their angles differ by multiples of 360°.

In polar form, these points are written as:
- (7,400°) = 7cis(400°)
- (7,-320°) = 7cis(-320°)
- (7,760°) = 7cis(760°)

These points are equivalent because the angle in polar coordinates is measured modulo 360°. This means that any angle that differs by a multiple of 360° will be equivalent. For example, 40° is equivalent to 400° because 400° - 40° = 360°. Similarly, -320° is equivalent to 40° because -320° + 360° = 40°, and 760° is equivalent to 40° because 760° - 720° = 40°.

In conclusion, the three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°), and they are written in polar form as 7cis(400°), 7cis(-320°), and 7cis(760°).

To learn more about polar form here:

https://brainly.com/question/29045307#

#SPJ11

Answer:

Step-by-step explanation:

d^2

When dividing subtract indices OR

dxdxdxdxd /dxdxd

d's cancel out leaving dxd=d^s

Answer:

One possible way to complete the array is:

    8  |  2 0 8

       |

    ------

       |

 2 |  2 6

 5 |  5 2

 1 |  1 7

 6 |  2 0

The answer is 26, so 208 ÷ 8 = 26.

To complete the array, we start by dividing the hundreds digit (2) by 8, which gives 0 with a remainder of 2. We write the remainder (2) in the ones place of the first row. Then we bring down the tens digit (0) and add it to the remainder to get 20. We divide 20 by 8, which gives 2 with a remainder of 4. We write the remainder (4) in the tens place of the second row, and bring down the ones digit (8) to the ones place of the second row. Finally, we add the digits in the second row to get 26, which is the quotient of the division

Step-by-step explanation:

The coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin is: OA (-8, 2) and B (-2, 6)

To find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin, we can use the following formula:

A' = k * (A - O) + O

B' = k * (B - O) + O

where k is the scale factor, O is the center point of dilation, and A and B are the original points.

In this case, k = 2 and O = (0, 0). So we have:

A' = 2 * (-4, 1 - (0, 0)) + (0, 0) = (-8, 2)

B' = 2 * (-1, 3 - (0, 0)) + (0, 0) = (-2, 6)

Therefore, the coordinates of A' and B' after the dilation are (-8, 2) and (-2, 6), respectively.

So, the answer is option (A) OA (-8, 2) and B (-2, 6).

Learn more about coordinates here:https://brainly.com/question/17206319

#SPJ1

Answer: -14.9 and 2.1

Step-by-step explanation:

If you take -6.4 - 8.5 in one direction you get -14.9 .

And if you add them together (-6.4 + 8.5) you get 2.1,

those are two possible values depending on if you add or subtract the 8.5 .

The answer is (r, θ) = (5, π).

To convert the rectangular coordinates (-5,0) to polar coordinates (r, θ) with r > 0 and 0 < θ < 2π, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

First, we need to find the value of r.

r = √((-5)² + (0)²)

r = √(25 + 0)

r = 5

Next, we need to find the value of θ.

θ = tan⁻¹(0/(-5))

θ = tan⁻¹(0)

θ = 0

However, since we need 0 < θ < 2π and the point (-5,0) is in the second quadrant, we need to add π to our θ value.

θ = 0 + π

θ = π

So, the polar coordinates of the point (-5,0) are (r, θ) = (5, π).

Therefore, the answer is (r, θ) = (5, π).

Learn more about rectangular coordinates

brainly.com/question/21432890

#SPJ11

Answer:

8183

Step-by-step explanation:

Plug in calculator

500(1+0.15)^20

The implied domain of the function y = (-6x^2 - 4x)/8 is found to be (-∞, ∞).

The first step in determining the implied domain of the function is to isolate the dependent variable, in this case y, on one side of the equation.

We can do this by adding 5y to both sides of the equation and subtracting 4x from both sides of the equation:

-6x^2 - 4x = 8y

Next, we can divide both sides of the equation by 8 to get y by itself:

(-6x^2 - 4x)/8 = y

Now we have the function in terms of y:

y = (-6x^2 - 4x)/8

The implied domain of the function is the set of all x-values for which the function is defined.

In this case, there are no restrictions on the values of x that can be used in the function, so the implied domain is all real numbers.

Therefore, the implied domain of the function y = (-6x^2 - 4x)/8 is (-∞, ∞).

To learn more about function:

https://brainly.com/question/12431044#

#SPJ11

a) The annual simple interest rate for this transaction is 16%.

b) Wolfgang paid $3,000 for the loan.

The annual simple interest rate is the percentage of the principal amount that is charged as interest for one year. It can be calculated using the formula I = P*R*T, where I is the interest, P is the principal amount, R is the annual interest rate, and T is the time in years.

(a) In this case, the principal amount is $2,500, the interest is $2,700 - $2,500 = $200, and the time is 180/360 = 0.5 years. We can plug these values into the formula and solve for R:

$200 = $2,500*R*0.5

$200 = $1,250*R

R = $200/$1,250

R = 0.16

The annual simple interest rate for this transaction is 16%.

(b) To find out how much Wolfgang paid for the loan, we can use the same formula and solve for P. The interest is $2,700 - $2,500 = $200, the annual interest rate is 20%, and the time is 120/360 = 0.3333 years:

$200 = P*0.20*0.3333

$200 = 0.06666*P

P = $200/0.06666

P = $3,000

Wolfgang paid $3,000 for the loan.

Learn about Annual simple interest rate

brainly.com/question/30937664

#SPJ11