Estimate [tex] \sqrt[3]{20} [/tex] between two integers.

Answer:

4 and 1/2.

Step-by-step explanation:

There are 9 oranges, so there are not enough for both to get a whole amount.

They will split the last one into half, so they has 4 and 1/2 oranges each.

Answer: 4 and 1/2

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Answer:

5/10

15/30

Step-by-step explanation:

The triangles are similar, so the lengths of corresponding sides are in the same ratio.

One pair of corresponding sides is 5 and 10.

10 is twice 5.

5/10

The other pair of corresponding sides is 15 and ?.

? must be twice 15, so ? is 30.

15/30

The diameter of Keisha's favorite marble is 2.5cm

The radius of the sphere is the half of the diameter : Radius = Diameter/2

Given diameter of marble = 2.5 cm

So, radius = diameter/2

Radius of the marble = 2.5/2

Radius of the marble = 1.25 cm

The general expression for the volume of sphere with radius 'r' is :

So, the volume of one sphere is :

Substitute the value of r = 1.25 cm

As, Keisha take 6 marbles

So, the volume of 6 marbles = 8.18 x 6

Volume of 6 marbles = 49.08 cm³

It is given that : 1 cubic centimeter has the massof 2.6 grams

1 cm³ = 2.6 gm

As the volume of 6 marbles is 49.08cm³

So, The mass of 49.08cm³ = 49.08 x 2.6

The mass of 6 marbles = 127.608 gm

127.608 to the nearest whole number is 128

Mass of the 6 marbles is 128 gm

Answer : 128 gm

Given:

There are given that the parent function:

Explanation:

According to the concept:

The function reflected over the x-axis means, we need to multiply with a negative sign.

That means:

And,

Vertically shrinking by a factor of 1/2 means, multiply by 1/2 in the entire function:

So,

Then,

Translating 2 units up means, adding 2 in the entire function:

So,

Final answer:

Hence, the correct option is C.

Given: A system of linear equations in three variables x, y, and z as follows-

Required: To solve the system using elimination.

Explanation: Let the given system as-

We can solve the system by reducing the system to a system of 2 variables. Suppose we would like to remove the variable z.

Multiplying equation (1) by 2, adding to equation (2) as follows-

Now, add equations (1) and (3) as follows-

Now, equations (4) and (5) represent a system of linear equations in two variables. Subtracting the equations as follows-

Substituting x=3 in equation (4)-

Substituting x=3 and y=-1 in equation (1) as follows-

Final Answer: The solution to the system is-

Answer:

2 quarts

Explanation:

Let the number of quarts to be drained and replaced = x

From the given problem:

60% of (12-x)=50% of 12

2 quarts of the solution needs to be drained and replaced with pure water to reach the ideal mixture.

Answer

The exact value of the lateral surface area = 395 cm²

The exact value of the total surface area = 572 cm²

Explanation

The solid shape is a cone with a height of 15 cm and the diameter of the base of the solid shape is 15 cm.

The Lateral Surface Area of the Solid Shape:

The formula to calculate the lateral surface area (LSA) of a cone is given by:

The radius will be = diameter/2 = 15cm/2 = 7.5 cm

To find legth, we use Pythagoras rule:

Put π = 3.14, r = 7.5 cm, and l = 16.77 cm into the lateral surface area formula:

Therefore, The exact value of the lateral surface area = 395 cm²

Total Surface Area of the Solid Shape:

To find the exact value for the total surface area of the solid shape, we use the total surface area (TSA) formula of a cone which is:

put π = 3.14, r = 7.5 cm, and l = 16.77 cm

The exact value of the total surface area = 572 cm²

Solution

We want to solve

The zero product property states that if a⋅b=0 then either a or b equal zero. This basic property helps us solve equations like (x+2)(x-5)=0.

For the question,

The answer is x = 0 and x = 1/3

The graph of the function is

The domain of the function is determined as the x -value of the function that satisfy the given function.

a) The inverse of a statement : If If two angles are not supplementary then the angles are not a linear pair. FALSE

b) The converse of a statement : If the angles are a linear pair, then the two angles are supplementary. TRUE

c) The contrapositive of a statement : If the angles aren't supplementary, then they aren't linear pair . FALSE

The given statement is : If two angles are supplementary then the angles are a linear pair .

(a) The inverse of a statement : If If two angles are not supplementary then the angles are not a linear pair.

This statement is FALSE because supplementary angles do not have to be adjacent, whereas a linear pair must be adjacent and create a straight line. So, no, supplementary angles are not always linear pairs. However, linear pairs are always supplementary.

(b) The converse of a statement : If the angles are a linear pair, then the two angles are supplementary.

This statement is TRUE because in a linear pair, if the two angles have a common vertex and a common arm, then the non-common side makes a straight line and the sum of the measure of angles is 180°. Linear pairs are always supplementary.

(c) The contrapositive of a statement : If the angles aren't supplementary, then they aren't linear pair .

This statement is FALSE because if they are adjacent and share a vertex and one side. See the first picture below. They might not form a linear pair, like in a parallelogram.

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The y-intercept is found replacing x = 0 into the equation as follows:

5*0 + y = 5

y = 5

Then, the line intercepts the y-axis at (0, 5)

The x-intercept is found replacing y = 0 into the equation as follows:

5x + 0 = 5

5x = 5

x = 5/5

x = 1

Then, the line intercepts the x-axis at (1, 0)

The line is graphed connecting these two points

the area of the windshield, cleaned by the windshield wiper is mathematically given as 0.096inche^2

This is further explained below.

The term "acute area of the windshield glazing" refers to the section of the windshield that measures eight and one-half inches by eleven inches and is located immediately in front of the driver's line of sight, as seen in the image.

Then, let's call the part of the windshield labeled "ABC" A.

[tex]A=\frac{1}{2} r^2 \theta[/tex]

Now, substituting the given values we get,

[tex]\begin{aligned}&A=\frac{1}{2} r^2 \theta \\&A=\frac{1}{2} \times(7)^2 \times \frac{\pi}{180} \\\end{aligned}$$[/tex]

A=0.4276

Then let the area of the windshield, ADE, be denoted by the letter A',

[tex]A^{\prime}=\frac{1}{2} r^2 \theta[/tex]

Now, after replacing those values with the ones we were provided,

[tex]\begin{aligned}&A^{\prime}=\frac{1}{2} r^2 \theta \\&A^{\prime}=\frac{1}{2} \times(1)^2 \times 60 \times \frac{\pi}{180} \\&A^{\prime}=0.5236\end{aligned}[/tex]

In conclusion, In order to calculate the area of the windshield, you need to take the difference between A and A'.

0.5236-0.4276=0.096

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For a sequence to be an arithmetic sequence the terms have to have a constant difference between them

2) We have the sequence: -12, 4, 0, 2...

The difference between the terms is not constant, so this is not a arithmetic sequence.

For example, from 4 to 0, there is -4 and from 0 to 2, is 2.

3) The sequence -6,0, 6, 12,... is an arithmetic sequence, because it has a constant difference between the terms (it always add 6 in each step).

Answer:

2. -12,4,0, 2....... No

3. -6,0, 6, 12 ..... Yes​

SOLUTION :

Step 1 :

In this question, we have that the recipe for trail mix requires

5/6 cup of raisins for 1 batch.

Then, Alaina uses

Step 2 :

To get the number of batches of trial mix Alaina makes, we have that :

CONCLUSION :

There would be 2 batches .

Answer:

(3000/(5-3))(3+5)

= (3000/2) 8

= 12000

Step-by-step explanation:

Given

a) The car has its original (initial) value when no time has passed since it was bought; in other words t=0. Then,

The initial value is 19900.

b) After 11 years, t=11; then,

Rounded to the nearest tenth, the second answer is 2924

Answer:

n=0

Step-by-step explanation:

Given:

ANSWER

B. 25

EXPLANATION

We want to identify the number of students that live between 1 and 1.9 miles from school.

To do this, we have check the frequency corresponding to the bar for 1 - 1.9 miles on the frequency axis.

From the histogram, we see that the number of students that live between 1 and 1.9 miles from the school is 25.

The correct answer is option B.

In this relation  table value of x = ( 2,5,7,-4) are following same pattern .

but x = 5 is not input and output of a function.

What is input and output of a function in math?

x = 2 * 1 = 2                     , y = 2

x = 5 * 1 = 5                      , y = 5

x = 7 * 1 = 7                       , y = 7

x = -4 * 1 = -4                     , y = -4

x = 5 * 2 + 1 = 11                , y = 11

In this relation  table value of x = ( 2,5,7,-4) are following same pattern .

but x = 5 is not .

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By using commutative property the result after solving expression (1/4 + 1/3 + 3/4) will be 7/4.

The commutative property of addition for three numbers is given by -

a + (b + c) = (a + b) + c

Given is the following expression -

1/4 + 1/3 + 3/4

We have the following expression -

1/4 + 1/3 + 3/4

Now, lets solve the expression by adding first two terms first and than add the third term to result of the addition of first two terms. Mathematically -

(1/4 + 1/3) + 3/4

Let (1/4 + 3/4) = K

Than the expression becomes -

K + 3/4

Now, first solve K, we will get -

K = 1/4 + 3/4

K = 4/4 = 1

Now, adding the resultant [K] to third term -

1 + 3/4

1/1 + 3/4

(4 + 3)/4

7/4

So, using commutative property, we have solved the expression (1/4 + 1/3 + 3/4) and the final value will be 7/4.

Therefore, by using commutative property the result after solving expression (1/4 + 1/3 + 3/4) will be 7/4.

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Question:

Find the length of AC.

Solution:

Applying the Pythagorean Theorem, we get:

this is equivalent to:

then, we can conclude that the length of AC side is:

We have the following equation

Now we solve for "x", we must use the logarithmic properties

If two variables x and y are proportional (direct variation), one can be written in terms of the another using a constant of proportionality, which is often represented using a letter k:

Isolate y from the given relationship:

As we can see, the variable y can be written in terms of x through a constant of proportionality equal to 15/4. Then, the relationship is a direct variation. The answer to Question 2 is: yes.

To find the playing time, replace the value of x. Since 1 foot is equal to 12 inches and the equation y=15/4 x works when x is in inches and y is in seconds, replace x=12 to find the playing time in seconds:

Then, the playing time for a tape 1 foot long is 45 seconds. The answer to Question 3 is: 45.

To find the percentage that Tracey paid, we can use the rule of three:

Now, the original price $560 represent the 100%.

If $560 ----------- 100%

then $180----------- x

where x =($180*100)/$560

x = 32.14

Therefore, the percent that Tracey paid was 32.14%

The answer is rounded to the nearest hundredth.

We have the equation:

And we want to find the value n, correspondign to the number of years necessary in order to the substance to decay in half.

Let's say that we have 1 Kg of the substance, this is Wo, the initial weight. Since we want to find the the decay of half the substance we use W = 1/2

And write:

Now we can use a property of logarithms:

Thus applying natural log on both sides:

By the property:

We can divide on both sides by ln(1/2):

The number of years for the radioactive substance to decay to half its initial weigh are 100 years.

The step to get rid of the ln(1/2) is:

Answer: x=107​=0.7

Step-by-step explanation:

1001​=70x​Multiply both sides by 70.1001​×70=xMultiply 1001​ and 70 to get 10070​.10070​=xReduce the fraction 10070​ to lowest terms by extracting and canceling out 10.107​=xSwap sides so that all variable terms are on the left hand side.x=107​

He spent $6.75 on art supplies and made the cards .

she sold the made cards on monday and tuesday.

Monday sales = $3.50

Tuesday sales = $5.25

Total sales = 3.50 + 5.25 = $8.75

profit = sales - cost

profit = 8.75 - 6.75 = $2.00

To find the number of term, we will use the formula;

when n= 1

for the second term

n = 2

= 3 + 5

=8

For n= 3

=3 + 2(5)

=3 + 10

=13

For n=4

=3+3(5)

= 3 + 15

= 18

For n= 5

= 3 + 4(5)

= 3 + 20

= 23

Therefore, the terms; 3, 8, 13, 18 and 23

Because angle 5 and 6 are supplementary, the only true statement is:

m∠5 + m∠6 =180°

By using the diagram we can see that:

Where two angles are supplementary if their measures add up to 180°, then:

Then the statements that are true are:

m∠5 + m∠6 =180°

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