A cylinder with height 10 inches and radius 4 inches is filled with water. The water is poured into a bowl
(hemisphere) with radius 5 inches. Sketch a cylinder and a hemisphere with dimensions labeled. If all the water
will fit, tell how much empty space remains in the bowl. If all the water will not fit, tell how much water is left in
the cylinder. (leave your answer in terms of pi)

Complete Question:

Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the area of the image to be one eight of the original photograph. Write an equation to represent the area of the reduced image. Find the dimensions of the reduced image.

Correct Answer:

A) [tex](10-x)(12-x)=15[/tex]

B) Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

Step-by-step explanation:

a. Write an equation to represent the area of the reduced image.

Let the reduced dimensions is by x , So the new dimensions are

[tex]length=10-x\\breadth=12-x[/tex]

According to question , Area of new image is :

⇒ [tex]Area = \frac{1}{8}Length(breadth)[/tex]

⇒ [tex]Area = \frac{1}{8}(10)(12)[/tex]

⇒ [tex]Area = 15[/tex]

So the equation will be :

⇒ [tex](10-x)(12-x)=15[/tex]

b. Find the dimensions of the reduced image

Let's solve :  [tex](10-x)(12-x)=15[/tex]

⇒ [tex]120-10x-12x+x^2=15[/tex]

⇒ [tex]120-22x+x^2=15[/tex]

⇒ [tex]x^2-22x+105=0[/tex]

By Quadratic formula :

⇒ [tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

⇒ [tex]x = \frac{22 \pm8 }{2}[/tex]

⇒ [tex]x = \frac{22 +8 }{2} , x = \frac{22 -8 }{2}[/tex]

⇒ [tex]x = 15 , x =7[/tex]

x = 15 is rejected ! as 15 > 10 ! Side can't be negative

⇒ [tex]x =7[/tex]

Therefore, Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch

Answer:

A.5

Step-by-step explanation:

11x+7x+90=180

11x and the unlabeled angle in the triangle are alt. interior and are equal

18x=90

divide both sides by 18

x=5

Answer:

x=2

Step-by-step explanation:

shdhvejsjheuhchsjcyhejc7738

Answer:

11

Step-by-step explanation:

divide 5 and 15.25

then multiply by 33.55

Answer:

31.48 square feet

Step-by-step explanation:

We can find the area of half the figure first.

Half the figure can be split up into the triangle and the semicircle.

Area of triangle:

1/2bh

Plug values in.

1/2(4)(3)

1/2(12)

6

Area of semicircle:

πr^2/2

Radius is half of Diameter.

Radius is 2.5. (5/2)

Plug values in.

π2.5^2/2

6.25π/2

9.7389372262

Round.

9.74

Add the area of triangle to area of semicircle to find area of half the figure.

6+9.74=15.74

Multiply by 2 to find area of whole figure.

15.74*2=31.48

Answer:

1/12 of a jug is what is left

Answer:

The temperature that represents a smaller value would be the one with negative eighty (or -80) degrees Fahrenheit. Although it is negative, the value of 80 does not mean it has a smaller value as to 134 degrees. It is just that the difference between the absolute values of the two show that 134 degrees Fahrenheit has a bigger value.

Step-by-step explanation:

Answer:

|X-134| < 7

           _

Step-by-step explanation:

Answer: C. 2^63

second part: greater than

Step-by-step explanation:

The number of pennies on square 64 is 2^63

A square is a quadrilateral, that have its four sides to be equal, and all its angles to be right-angles

From the question, the number of pennies on a square is:

[tex]T_n = 2^{n-1[/tex]

So, we have:

[tex]T_{64} = 2^{64 - 1}[/tex]

Evaluate the difference

[tex]T_{64} = 2^{63[/tex]

Hence, the number of pennies on square 64 is 2^63

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The requried expression of the given expression which is a product of two binomials is (x - 3)(x - 7).

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.

Here,
Given expression,
x² - 10x + 21 = 0

In order to factor the above expression in two binomial expressions, split the 10x in two where the multiplication of two numbers produces 21 and their difference produces -10x,
So,
y = x² -7x -3x + 21
y= x(x - 7) - 3 (x - 7)
y = (x - 3)(x - 7)

Thus, the requried expression of the given expression which is a product of two binomials is (x - 3)(x - 7).

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Answer:

-4

B

The second one.

Step-by-step explanation:

As per quadratic equation, the value of 'y' for [tex]x = 3[/tex] is 0.

"A quadratic equation is an algebraic equation of the second degree in 'x'. The quadratic equation in its standard form is [tex]ax^{2} + bx + c = 0[/tex], where 'a' and 'b' are the coefficients, 'x; is the variable, and 'c' is the constant term."

Given quadratic equation is:

[tex]y = x^{2} -2x - 3[/tex]

When  [tex]x = 3[/tex], the value of 'y' is:

[tex]= 3^{2} -2(3) - 3\\= 9 - 6 - 3\\= 0[/tex]

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When [tex]\( x = 3 \)[/tex] is substituted into [tex]\( y = x^2 - 2x - 3 \)[/tex], it yields y = 0 after simplification.

To find the value of y when x = 3 in the equation [tex]\( y = x^2 - 2x - 3 \),[/tex]substitute [tex]\( x = 3 \)[/tex] into the equation and solve for (y):

[tex]\[ y = (3)^2 - 2(3) - 3 \]\[ y = 9 - 6 - 3 \]\[ y = 0 \][/tex]

So, when [tex]\( x = 3 \), \( y = 0 \).[/tex]

Answer:

[5 2.6 8 2]

Step-by-step explanation:

For this we simply add the digits

A+ B

[3+2 2+.6 0+8 -1+3]

[ 5 2.6 8 2]

Given:

Given that the coordinates are (3.9, 5.9), (–1.1, 5.9), (–4.1, 3.9), (–4.1, –2.1)

We need to determine domain and range and also find whether the relation is a function.

Domain:

The domain is the set of all independent x - values.

Thus, we have;

[tex]Domain=\{3.9,-1.1,-4.1\}[/tex]

Thus, the domain is {3.9,-1.1,-4.1}

Range:

The range is the set of all dependent y - values.

Thus, we have;

[tex]Range=\{5.9,3.9,-2.1\}[/tex]

Thus, the range is {5.9,3.9,-2.1}

Function:

We need to determine whether the given relation is a function.

For a relation is said to be a function, if every value of x has only one image in the y - coordinate.

After plotting the graph, it is obvious that the x - value -4.1 has two images 3.9 and 2.1

Hence, the given relation is not a function.

Answer:

A.

Subtract 37 – 13. Then divide the difference by 4.

Step-by-step explanation:

After the box:

37 - 13 left

No. of bags:

(37 - 13)/4

Answer:

1.2%

Step-by-step explanation:

Since only 82 were chosen by supreme Court,

The total is 6954

To calculate the percentage of the case decided by the court

82/6954 ×100

8200/6954

1.179~1.2

So the final answer is 1.2%

Final answer:

The percentage of cases decided by the Supreme Court compared to those filed is approximately 1.18%.

Explanation:

To calculate the percentage of cases decided by the Supreme Court out of the total number of cases filed, we use the formula for finding a percentage: (Number of cases decided / Total cases filed) × 100. In this scenario, the Supreme Court decided 82 cases out of 6,954 cases filed.

So, the calculation would look like this:

(82 / 6,954) × 100 = (0.01179) × 100 ≈ 1.18%

Therefore, approximately 1.18% of the cases filed with the Supreme Court were decided by the court.

Answer:

jl = 19cos24 = 17.4.   jk = 19sin24 = 7.7.

Step-by-step explanation:

We have a rt. triangle; the hyp is kl

and the hor side is jl. The angle between the hor side and hyp = 24 deg.

The value of JL rounding up to the nearest tenth will be 17.36.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

Angle is the measurement of rotation motion for example if you want to measure the length in rotation geometry then it is helpful.

Given that the KL = 19 units, the angle LJK = 24°

Now by a trigonometric function

cos24° = Jl/19

JL = 19 × cos24°

JL = 17.36 hence, the correct answer or the length of the JL is 17.36 units.

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Answer:

a=43

Step-by-step explanation:

w+w+w= 45 which means 15+15+15=45

b+b+b=21 which means 7+7+7=21

s+s+s=12 which means 4+4+4=12

w+b×s= a which means 15+7×4= 43

(hope this helps)

Answer:

The answer to the question is 43

Step-by-step explanation:

Let us recall the values from the following question stated:

Three witches each holds a broom and a spoon, saying plus witch plus witch = 45

Three brooms say broom plus broom plus a broom at = 21

Three spoons say spoon plus spoon plus = 21

Now, let us find when a plain witch plus broom x spoon

Then,

Three witches = 45, resulting to  15+15+15=45

Three brooms (b+b+b) which is =21 or  7+7+7=21

Three spoons (s+s+s) is =12  or 4+4+4=12

we make use of multiplication for the witches, the brooms, and the spoons

Therefore

w+b×s= a,  which is 15+7×4= 43

Answer:

5:9 | 5/9 | 5 to 9

Step-by-step explanation:

you can choose any form

Answer:

25:45 or simplified 5:9

Step-by-step explanation:

to simplify find a common factor and divide both by that number to simplify.

Answer:

To find the square root of a fraction you first have to find the square root of the numerator and the denominator if your denominator has a square root that is irrational then you multiply the numerator and the denominator by that irrational number.

To find the square root of a decimal you have would have to divide two numbers like 64 and 8

Step-by-step explanation:

Final answer:

To find the square root of a decimal, use a calculator. Convert the fraction to a decimal first and then use the same process.

Explanation:

To find the square root of a decimal, you can use a calculator. Simply enter the decimal number and press the square root button. The calculator will give you the square root as a decimal or a simplified fraction, depending on the value.

For example, to find the square root of 4.45, enter it into the calculator and press the square root button. The calculator will give you the result as approximately 2.107.

To find the square root of a fraction, you can use the same process. Convert the fraction to a decimal by dividing the numerator by the denominator. Then, follow the steps for finding the square root of a decimal using a calculator.

Answer:

He will miss 2 shots.

Step-by-step explanation:

40 Total Shots

He missed [tex]\frac{10}{40}[/tex]

[tex]\frac{10}{40} = \frac{x}{8} \\40x = 80\\x=2[/tex]

Answer:

no clue

Step-by-step explanation:

Answer:

The three answers are B,C,F

The correct statements of the triangle are; AC = 5 cm; BA = 4 cm; The perimeter of triangle ABC is 12 cm.

As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.

Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.

Using Pythagoras theorem in ΔACF :

AC² = FA² + CF²

Thus;

AC² = 3² + 4²

AC = √25

AC = 5

Using Pythagoras theorem in ΔDAB, we have;

BA = √(5² - 3²)

BA = 4 cm

Using Pythagoras Theorem, we have;

CB = √(5² - 4²)

CB = 3 cm

Perimeter of ΔABC = Side AB + Side CB+ Side AC

Perimeter of ΔABC = 4 + 3 + 5

Perimeter of ΔABC = 12 cm

Area of ΔABC = (1/2) * 4 * 3 = 6 cm²

Area of ΔDEF = (1/2) * 8 * 6 = 24 cm²

Area of ΔABC =  (6/24) * Area of ΔDEF

Area of ΔABC = (1/4) * Area of ΔDEF

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Given the information provided, we can determine the lengths of the sides of triangle ABC and its perimeter and area.

Given that points A, B, and C are midpoints of the sides of right triangle DEF, we can determine the lengths of the sides using the information provided.

To find the perimeter of triangle ABC, we sum the lengths of all three sides: AB + BC + CA. Substituting the given lengths, AB = BA = 4 cm, BC = 6 cm, and CA = AC = 5 cm, the perimeter is 4 cm + 6 cm + 5 cm = 15 cm.

The area of triangle ABC can be determined using the formula A = bh, where b is the base and h is the height. Triangle ABC and triangle DEF are similar triangles, so their areas are proportional. Since point A is the midpoint of DE, half the base of triangle DEF is equal to the base of triangle ABC. Substituting the given length of DE = 10 cm, the base of triangle ABC is 10 cm / 2 = 5 cm. The height of triangle ABC is equal to the length of AC = 5 cm. Therefore, the area of triangle ABC is A = 5 cm * 5 cm = 25 cm².

9514 1404 393

Answer:

  3

Step-by-step explanation:

There are 3 grid nodes suitable for vertex D that lie the same distance from the center of the rectangle as points A and C.

3 rectangles have vertices ABCD that lie on grid nodes.

Answer:

y = x - 3

Step-by-step explanation:

Basically, if the lines are parallel, they have the same slope, right? So that part is already complete

And to get the rest of the equation, plug in the points -2 and 1 into the equation for the x values. Then set the equation to solve for b

After you do that you should get b = -3

The slope is 1 and the y-int is -3

Thank me later ;)

Answer:

5 cups and 4 tbsp

Step-by-step explanation:

4 cups and 20 tbsp of flour

There are 16 tablespoons in 1 cup

5 cups and 4 tbsp

- The measure of arc [tex]\( BD \)[/tex] is 260°.

- The measure of arc [tex]\( ADB \)[/tex] should be 320° (corrected).

- The measure of arc [tex]\( ABC \)[/tex] is 80°.

To find the measure of each arc in the circle, we need to remember that the total degrees in any circle is 360°. The diagram shows a circle with specific arcs and angles labeled.

Here are the steps to find each arc's measure:

1. Measure of arc [tex]\( BD \)[/tex]:

  - Arc [tex]\( BD \)[/tex] is opposite the central angle [tex]\( \angle BRD \)[/tex], which is not directly given.

  - Since [tex]\( \angle BRC \)[/tex] is 40° and [tex]\( \angle CRD \)[/tex] is 60°, then [tex]\( \angle BRD = 360° - (\angle BRC + \angle CRD) \)[/tex].

  - Calculating [tex]\( \angle BRD \)[/tex] gives [tex]\( 360° - (40° + 60°) = 260° \)[/tex].

  - Therefore, the measure of arc \( BD \) is 260°.

2. Measure of arc [tex]\( ADB \)[/tex]:

  - Arc [tex]\( ADB \)[/tex] includes arcs [tex]\( AD \)[/tex] and [tex]\( DB \)[/tex].

  - We already know [tex]\( DB \)[/tex] is 260°.

  - [tex]\( AD \)[/tex] is opposite the central angle [tex]\( \angle ARD \)[/tex], which is given as 120°.

  - Adding them together, the measure of arc [tex]\( ADB = \angle ARD + \angle BRD = 120° + 260° = 380° \).[/tex]

  - This exceeds 360°, which suggests an error. Since [tex]\( AD \)[/tex] and [tex]\( BD \)[/tex] are parts of the circle that add up to its whole circumference, they should add up to 360°, not more. Hence, [tex]\( ADB \)[/tex] should be [tex]\( 360° - \angle BCD \)[/tex] which is 360° - 40° = 320°.

3. Measure of arc [tex]\( ABC \)[/tex]:

  - Arc [tex]\( ABC \)[/tex] includes arcs [tex]\( AB \)[/tex] and [tex]\( BC \).[/tex]

  - [tex]\( BC \)[/tex] is opposite the central angle [tex]\( \angle BRC \)[/tex], which is given as 40°.

  - [tex]\( AB \)[/tex] is the rest of the circle not included in \( ADB \), so [tex]\( AB = 360° - \angle ADB \)[/tex].

  - Since we've found an inconsistency with [tex]\( ADB \)[/tex], we should instead calculate [tex]\( AB \)[/tex] as [tex]\( 360° - (BD + CD) = 360° - (260° + 60°) = 40° \).[/tex]

  - Adding \( AB \) and \( BC \), the measure of arc [tex]\( ABC = AB + BC = 40° + 40° = 80° \).[/tex]

There seems to be an error with the measure of arc [tex]\( ADB \)[/tex] as calculated before. Arcs [tex]\( AD \)[/tex] and [tex]\( DB \)[/tex] should add up to 360° because they complete the circle together. It's also worth noting that in a properly drawn circle, the sum of the measures of arcs [tex]\( BC \)[/tex], [tex]\( CD \)[/tex], and [tex]\( DA \)[/tex]should add up to 360°. If [tex]\( BC \)[/tex] is 40° and [tex]\( CD \)[/tex] is 60°, then [tex]\( DA \)[/tex] should be 360° - (40° + 60°) = 260°, not 120°. This discrepancy suggests there may be a mistake in the given information or a misinterpretation of the diagram.

To summarize, given the information provided:

- The measure of arc [tex]\( BD \)[/tex] is 260°.

- The measure of arc [tex]\( ADB \)[/tex] should be 320° (corrected).

- The measure of arc [tex]\( ABC \)[/tex] is 80°.

Answer:

1. Skateboard: 2,743.2. Scooter: 2,590.8. Bike: 4,800. Go-cart: 3,000.

After converting all distances to centimeters, it's clear that Diego's bike traveled the furthest (4800 cm) in 5 seconds, making it the fastest.

Understanding the speed of Diego's vehicles requires us to convert the distances all to the same unit, centimeters. First, we know that 1 foot equals 30.48 cm. Therefore, the skateboard traveled 90 feet * 30.48 cm/foot = 2743.2 cm. The scooter traveled 1020 feet, which means it traveled 1020 feet * 30.48 cm/foot = 31,089.6 cm. The bike traveled 4800 cm, so no conversion is needed for this vehicle. Lastly, 1 kilometer equals 100,000 cm, meaning the go-kart traveled 0.03 kilometers * 100,000 cm/kilometer = 3,000 cm. Now that we have all the distances in the same unit, we can compare and state that the bike traveled the furthest in 5 seconds, making it the fastest.

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Answer:

I think it's C

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

A graph can only be curved when it has an exponential. B and C are slopes so it cannot be that.

Answer:

a. 0.69x + 0.14

b. 5.67 - 30.48a

c. 1.1x - 3.01y

Step-by-step explanation:

a) 2.56x + 0.14 − 1.87x

To simplify this algebraic expression, you start by collecting like terms;

2.56x − 1.87x  + 0.14

Then perform arithmetic operation

0.69x + 0.14

b) 7.32a + 2.1 (2.7 − 18a)

Here; first, the bracket must be opened

To open the bracket; each expression in the bracket is multiplied by 2.1. This leaves us with

7.32a + 2.1 * 2.7 − 2.1 * 18a

7.32a + 5.67 - 37.8a

Then, you collect like terms

7.32a - 37.8a + 5.67

Then perform arithmetic operation

-30.48a + 5.67

Rearrange

5.67 - 30.48a

c) 0.12x + 0.34y + 0.98x − 3.35y

Here, you start by collecting like terms

0.12x + 0.98x + 0.34y − 3.35y

Then perform arithmetic operation

1.1x - 3.01y