4. Sean bought 1.8 pounds of gummy bears and 0.6 pounds of jelly beans and paid $10.26. He went back to the store the following week and bought 1.2 pounds of gummy bears and 1.5 pounds of jelly beans and paid $15.09. What is the price per pound of each type of candy?Directions: For each problem - define your variables, set up a system of equations, and solve.

Answer:

x=27/10

Step-by-step explanation:

move all the terms not containing x to the right side of the equation

You have the following expression:

log(z) - log(18)

By the properties of logarithms, consider that the subtraction of two logarithms is equal to the logarithm of the quotient of the arguments:

log(z) - log(18) = log(z/18)

Hence, the answer is log(z/18)

Long Multiplication

1. Arrange the numbers one on top of the other and line up the place values in columns. The number with the most digits is usually placed on top as the multiplicand.

This will be written as follows:

467

x 48

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

2. Starting with the ones digit of the bottom number, the multiplier, multiply it by the last digit in the top number.

This product is 8*7 = 56

3. If that answer is greater than nine, write the ones place as the answer and carry the tens digit.

We should write 6 and carry 5:

467

x 48

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

6 (carry 5)

4. Proceed right to left. Multiply the ones digit of the bottom number to the next digit to the left in the top number. If you carried a digit, add it to the result and write the answer below the equals line. If you need to carry again, do so.

The next product is 8*6 = 48. Adding the carry: 48+5=53, Write 3, carry 5:

467

x 48

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

36 (carry 5)

Multiply 8*4 = 32. Add the carry 5: 32+5 = 37. Write the full number because it's the last of the products of this step:

467

x 48

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

3736

5. When you've multiplied the ones digit by every digit in the top number, move to the tens digit in the bottom number.

Multiply as above, but this time write your answers in a new row, shifted one digit place to the left.

Multiply 4*7 = 28. Write 8, carry 2.

467

x 48

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

3736

8 (carry 2)

Multiply 4*6=24. Add 2: 24+2=26. Write 6, carry 2:

467

x 48

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

3736

68 (carry 2)

Multiply 4*4=16. Add 2: 16+2=18. Write the full number:

467

x 48

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

3736

1868

6. When you finish multiplying, draw another answer line below your last row of answer numbers.

467

x 48

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

3736

1868

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

7. Use long addition to add your number columns from right to left, carrying as you normally do for long addition.

467

x 48

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

3736

1868

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

22416

Answer:

-54g or -9g(5+1)

Step-by-step explanation:

-45g - 9g

-9g(5+1)

I'm not sure which form you want it in lol. -9g(6)

:]

Answer:

-9g ( 5 + 1 )

Step-by-step explanation:

-45g - 9g

-(45g - 9g)

common factor or less number = 9

-9g (5 + 1)

The other point through which a line that describes a proportional relationship must pass is the point (0, 0)

A proportional relationship is one in which each the ratio of the x and y–values of each point on the line of the function is a constant.

The given relationship described by the line = A proportional relationship

The given point on the line = (6, 2)

Required; The other point through which the line must pass.

Given that the relationship described by the line, the ratio of all points on the line is a constant and each point (x, y) can be expressed in the form;

y = K•x

Which gives;

[tex] \displaystyle{ K = \frac{y}{x} }[/tex]

Where, K is a constant which is not equal to zero.

From the zero product property, which states that the product of all numbers and zero is also zero, we have;

When x = 0, k × 0 = 0 = y

A point through the line must pass is therefore; (0, 0)

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Let g represent gallons of water and let L represent loads.

Here, the gallons of water varies directly with the number of loads, thus we have:

g ∝ L

Now introduce a constant k:

g = kL

65 gallons is used to wash 5 loads, thus we have:

65 = k * 5

Let's solve for k:

65 = 5k

Divide both sides by 5:

To find the amount of water that will be used to wash 8 loads, we have:

g = kl

We are to find g, substitute 13 for k and 8 for l:

g = 13 x 8

g = 104

Therefore, to wash 8 loads, 104 gallons of water is needed.

ANSWER:

104

When going to the movies and we pay the ticket, most of the times (if we pay in cash) we will receive change for the bill we use.

For example, if the ticket costs $7 and we pay with $10, we will receive 10-7 = $3 as change.

We then have used math to know that the change we receive is correct.

Answer:

D: 9.75 * 10^6

Step-by-step explanation:

You can make it easy for yourself if you write both answers in the same form:

(9.4 * 10^6) = (9.4 *10 *  10^5 = 94*10^5) and (3.5 * 10^5) stays the same.

We can now add those numbers up easier:

(94*10^5) + (3.5*10^5) = ( 94 + 3.5 ) * 10^5 = ( 97.5 * 10^5 )

but this answer is not in the option list. We have to perform the same trick as in the beginning, but than the other way around:

(97.5 * 10^5) = (9.75 * 10) * 10^5 = 9.75 * 10^6,

which is exactly option D

5. Given

You know that:

a=-1

b=2

w=-10

Replace these values into the expression:

Following the order of operations, first, you have to solve the exponent and the multiplication:

Both minus signs form a "double negative" when this happens, the signs cancel each other and turn into a plus sign, so that:

Next, solve the addition

The result of this operation is 21.

We have

-2x + 6y = 8 ...(1)

x-3y=-3 ....(2)

we need to solve the system of equations

we will multiplicate the second equation by 2

then we sum the equation above with the first equation

we sum similar terms, and we obtain

that's an inconsistency

so we don't have a solution

the answer is no

Given;

There are given that the graph represents the number of siblings.

Explanation:

According to the given graph:

The frequency of the number of siblings is:

Now,

We need to find the value of the range:

So,

From the concept of range:

The value of the difference between the highest data and lowest data will be representing the value of the range:

So,

The highest number is 7 and the lowest data is 2:

So,

Final answer:

Hence, the value of the range is 5.

From the problem, the diameter of the sphere is 20 ft.

Note that radius is half of diameter, so the radius will be r = 20/2 = 10 ft

Using the volume formula of a sphere.

where π = 3

The answer is 4000 ft^3

A graph of what the proportional relationship would look like is: C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).

In Mathematics, a graph is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Generally speaking, the graph of a proportional relationship between two variables is always characterized by a straight line with its data points passing through the origin (0, 0).

In this context, the x-axis of this graph would be labeled Blueberries (in pints) while the y-axis would be labeled Cost (in dollars), with the data points starting from the origin (0, 0) and passes through (5, 17) as shown in the image attached below.

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Answer:

C. a coordinate plane with the x-axis labeled Blueberries (in pints) and the y-axis labeled Cost (in dollars) shows a line going through (0, 0) and (5, 17).

Step-by-step explanation:

Given that the meals in a hospital cafeteria are discounted 15% for all hospital employees,

The price an employee will pay for the grill chicken lunch worth of $8.00 will be,

Hence, the hospital employee will pay $6.8 for the grilled chicken lunch.

Answer:

14, 200 squared, 15

Step-by-step explanation:

Answer:

  3 ≤ x < ∞

Step-by-step explanation:

You want the domain of a square root function shifted right 3 units and up 1 unit. It goes through points (3, 1), (4, 2) and (7, 3).

The domain of a function is the set of values of the independent variable for which the function is defined. It is the horizontal extent of the graph.

The graph of the given square root function extends to the right from x=3.

The domain is 3 ≤ x < ∞. In interval notation, it is [3, ∞).

Given data:

The given length of the EC is CD=9.

The given length of the CD is CD=10.

The given length of TV is TV=27.

The given length of TU is TU=30.

The ratio of the corresponding sides is,

Susbtitute the given values in the above expression.

Thus, the ratio of the corresponding sides is equal so they are similar.

Congruent shapes are produced when the three transformations—rotations, reflections, and translations—are combined. Any pair of congruent shapes can actually be matched to one another by combining one or more of these three transformations.

An object's shape and/or location can vary in each of the four possible transformations of a point, line, or geometric figure. Pre-Image refers to the shape of the object before transformation, whereas Image refers to the location and shape of the object after transformation.

Data Presented

We now understand that stiff transformations preserve the size and shape of the figures (reflections, translations, and rotations). The pre-image and the actual image always concur.

The following transformational skills belong to Matt:

Reflection

A reflection maintains its initial form because the Comparable locations from the pre-image to the picture remain at the same distance from the line of reflection.

Rotations as a Congruence Transformation

A rotating figure twists. Despite being the same size and shape as before, the figure appears to have toppled over. A clock is an excellent example of how the globe actually rotates. Every hour or every day, a clock's connecting arms revolve around its axis. The degree of a rotation determines what kind of rotation it is; popular rotations include those of 90, 180, and 270 degrees. Before going back to its original position, the figure rotates a full 360 degrees. the clockwise or counterclockwise direction in which a revolution happens. This data can be used to determine the degree, amount, and a revolution's speed and direction.

Congruence translational transformation

When an object or shape is transferred from one location to another without altering its size, shape, or orientation, we refer to the transfer as a movement. A translation, often known as a slide, involves moving every point on an object or shape uniformly and in one direction.

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The point-slope form of the equation of a line is given by the following expression:

y - y1 = m(x - x1)

Where m is the slope of the line and (x1, y1) is a point where the line passes through.

The slope of the line can be determined with the following formula:

Where (x1, y1) and (x2, y2) are two points where the line passes through. In this case we are told that the line passes through the points (-2,-6) and (6,5). By replacing the x and y coordinates of these points into the formula of the slope, taking x1 as -2, x2 as 6, y1 as -6 and y2 as 5, we get:

Then, the slope of the line equals 11/8, by replacing 11/8 for m into the slope-point form, we get:

y - y1 = 11/8(x - x1)

By taking one of the points, for example (-2,-6), we replace the x and y-coordinates that appear in the equation of the line, to get:

y - (-6) = 11/8(x - (-2))

y + 6 = 11/8 (x + 2)

Then, the equation of the line in slope-point form is y + 6 = 11/8 (x + 2)

Given the sample mean of the distribution as 9 minutes.

Also, the sample deviation as 2 minutes;

Given the z-score formula;

Where;

Now, from the Z-table;

Thus, the percentage of the calls lasted less than 5 minutes is 2.3%

Using operations with mixed numbers and relations between hours and minutes, it is found that:

a) You will arrive in Seattle at 4:15 am.

b) You will arrive in Atlanta at 9:50 a.m.

c) You will arrive in Atlanta at 10:30 a.m.

A mixed number is represented as follows:

a b/c.

In which:

As a decimal, the number is given as follows:

a + (b/c).

For item a, it is found that the time it takes to arrive in Seattle from Atlanta is given by the addition of these following numbers:

Hence the time in hours is:

2.25 + 1.5 + 3.5 + 1.75 + 0.75 = 9.75 hours = 9 hours and 45 minutes.

Seattle is 3 hours behind Atlanta, hence the time you arrive there is:

6:30 pm + 9 hours and 45 minutes = 4:15 am, as:

For item b, we have that:

For item c, 2/3 of an hour is 40 minutes, 40 minutes after 9:50 am is 10:30 a.m., which is the time you would arrive.

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Answer:

a= 2 and b= 8

Step-by-step explanation:

a=5/9×18=10

b=4/9×18=8, then a-b=10-8=2

b=4/9×18=8

The account balance at the end of the month is $1051.

To estimate the balance in a bank account, one has to add the credit to the available balance of the account and subtract the debited amount from the same.

It is given that the account balance initially is $843.

The deposited balances are $92, $404, $39 and $51.

Add the credited amount to the account balance.

So, the current amount is = $843+ $92+ $404+ $39+ $51= $1429

The withdrawal amount is $70, $87 and $221

Subtract the debited amount to the account balance.

So, the current amount is = $1429 - $70 -$87 - $221 = $1051.

So, the account balance at the end of the month is $1051.

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Answer:

The ratio using the word "to" is;

Explanation:

Given on the table;

Number of O+ donors = 100

Number of B+ donors = 29

The ratio of the O+ donors to B+ Donors is:

Number of O+ to Number of B+

Which gives;

The ratio using the word "to" is;

Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

So we are told that the height of the innertube in meters is given by:

The minimum height is 2 meters, the maximum is 8 meters and the time between two consecutive maximums is 12 seconds. Here is important to note a few properties of the sine. First of all, the minimum value of sin(bx) is -1 and its maximum value is 1. Then the height of the innertube is minimum when sin(bx)=-1 and maximum when sin(bx)=1. With these two values we can build two equations for a:

So we have:

Substracting 5 from both sides of the second equation we get:

Using this in the first equation gives us:

Which confirms that a=3. Now we have to find b. For this purpose we can recal another property of the sine. Its period i.e. the distance (in this case the time) between two consecutive maximums is given by:

Since we know this time is 12 seconds we get:

If we multiply both sides by b and divide them by 12 we get:

So we have:

Which means that the answer is the second option.

The counterexample must satisfy the hypothesis of the conditional statement which is the correct answer would be option (B).

A counterexample is an example in which the hypothesis is correct but the conclusion is incorrect.

Since A counterexample is used to show that a conditional assertion is untrue.

So, just one counterexample is required to prove a statement untrue.

Also, when employing a counterexample to prove a conditional assertion untrue.

The counterexample must then meet the hypothesis of the conditional statement.

As a result, the correct statement concerning the counterexample is;

The conditional statement's hypothesis must be satisfied by the counterexample.

Hence, the correct answer would be option (B).

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Solution

- The inequality is:

- The graph of the inequality is graphed using a graphing calculator as follows: