Solve the equation. Show your work. Express your answer as both a simplified mixed number and as a decimal.

-2.25 + 0.4x = -2.8

Khalil can make a amount of 6 portions of trail mix, with each containing 2 bags of nuts and 3 bags of dried fruit.

Khalil has 12 bags of nuts and 18 bags of dried fruit. To ensure that each new portion of trail mix has the same combination of ingredients, he must divide the bags into equal portions. Since 12 divided by 2 is 6 and 18 divided by 3 is 6, Khalil can make a maximum of 6 portions of trail mix, with each containing 2 bags of nuts and 3 bags of dried fruit. If he were to use different amounts of bags per portion, he would have some bags left over. For example, if he used 1 bag of nuts and 4 bags of dried fruit, he would have 6 bags of nuts and 14 bags of dried fruit left over. Therefore, the greatest number of portions of trail mix Khalil can make is 6.

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9514 1404 393

Answer:

  3x -y = -5

Step-by-step explanation:

The parallel line will differ only in the constant. The new constant can be found by filling in the x- and y-values for the given point.

  3x -y = 3(-4) -(-7) = -12 +7

  3x -y = -5

Answer:

Rate of gas in gallons per mile

= 0.045454545 gallon/mile

Or

Rate of gas in gallons per mile

= 1/22 gallon/mile

Step-by-step explanation:

Ava's car uses 6 gallons of gas to drive through a distance of 132 miles.

Thanks rate of gallon to distance will be given by the formula below

Rate of gas in gallons per mile

=Number of gallons/ distance covered in miles

Rate of gas in gallons per mile= 6/132

Rate of gas in gallons per mile= 1/22

Rate of gas in gallons per mile

= 0.045454545 gallon/mile

Answer:4^6

Step-by-step explanation:

The number of times a term is multiplied is the exponent you use.

In this problem

4 is multiplied 6 times.

Therefore: 4*4*4*4*4*4=4^6

The given expression is `(A + BC) (A . BC)`. This is a Boolean algebraic expression that we can simplify using the distributive property and De Morgan's laws.

To write the truth table of this expression, we must consider all possible combinations of A, B, and C. There are 2 x 2 x 2 = 8 possible combinations of A, B, and C. Here is the truth table for the given expression: Truth Table: Before simplification

A B C AB BC A + BC A . BC (A + BC) (A . BC)0 0 0 0 0 0 0 00 0 1 0 0 1 0 00 1 0 0 0 1 0 00 1 1 0 1 1 0 00 1 0 0 0 1 0 00 1 1 0 1 1 0 00 0 0 0 0 0 0 00 0 1 0 0 1 1 00 1 0 0 0 1 1 00 1 1 1 1 1 1 1After simplification, we get `(A . B . C)`.

Here is the truth table for the simplified expression: Truth Table: After simplification A B C A . B . C0 0 0 00 0 1 00 1 0 01 0 0 01 0 1 01 1 0 01 1 1 1

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Answer:

B. Point A is the center of the circle that passes through points X, Y, and Z.

C. ZA=YA

E. AX=AY

Step-by-step explanation:

Took the test got it right...

Answer:

2, 3, 5

Step-by-step explanation:

edge2020

the C-CAPM with power utility and lognormal consumption growth predicts that the representative agent in country A will consume more in the current period and that the price of an identical financial asset will be lower compared to country B.

The C-CAPM is a financial model that relates the consumption patterns and asset prices in an economy. In this scenario, the difference in subjective discount factors implies that the representative agent in country A values future consumption relatively less compared to country B. As a result, the representative agent in country A tends to consume more in the current period, prioritizing immediate consumption over saving for the future.

Furthermore, the C-CAPM suggests that the price of an identical financial asset, such as a stock or bond, will be lower in country A. This is because the higher subjective discount factor in country A implies a higher expected return requirement for investors. As a result, investors in country A will demand a higher risk premium, leading to a lower price for the financial asset.

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Answer:

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

4) 180-47=133

5) 115+5x-10=180

125+5x=180

5x=55

x=11

My brainly isn't working. Please refer to the picture below. Hope this helps :)

The height of the cylinder is \(3 inch\)

Based on the attached figure,

Volume of the cylinder = 282.7 square inches

Radius of the cylinder =5 inches.

The height of the cylinder = ?

The volume of the cylinder  can be found with the formula as :

\(V=pi r^{2} h\)

\(h=\frac{V}{pi r^{2} } \\\\h = \frac{282.7}{3.142 * 5^{2} } \\\\=3 inch\)

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The price of the pant after the discount is $16.

The question relates to a percentage. A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, Adam went shopping for a new pair of pants because of a sale and the store was offering a 50% discount while the price on the tag was $32.

The new price will be:

= Old price - Discount

= $32 - (50% × $32)

= $32 - $16

= $16

The new price is $16.

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We are given the values of a and b and an equation involving exponents. We need to solve for the value of x.

The given equation is \((a)^2\) =\((b)^2\) * \((x)^2\).

We can solve for x by isolating it on one side of the equation. Let's rewrite the equation: \((a)^2\) = \((b)^2\) * \((x)^2\)

Taking the square root of both sides, we have: \(\sqrt{a^2}\)= \(\sqrt{b^2}\) * \((x)^2\)

Simplifying further, we get: a = b * x

Now we can solve for x by dividing both sides of the equation by b: x = a / b.

Substituting the given values of a and b into the equation, we have: x = 0.697 / 0.6

Evaluating this expression, we find: x ≈ 1.162

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Answer:

67

Step-by-step explanation:

Answer:

The volume of the gas under these circumstances is 30 cm³.

Step-by-step explanation:

To determine the variation equation for this situation, we start with the formula V = Tk/P

where k is the constant of variation.

To solve for k, we use the initial values of V, T, and P

V = 42 cm³, T = 84 °C, P = 50 mmHg

Substituting these values into the formula, we get

42 = 84k/50

Solving for k, we have

k = (42 x 50)/84 = 25

Therefore, the variation equation for this situation is

V = 25T/P

To find the volume of gas when T = 48 °C and P = 40 mmHg, we substitute these values into the variation equation

V = 25 x 48/40 = 30 cm³

Therefore, the volume of the gas under these circumstances is 30 cm³.

The value of x in the circle shown with the given diameter is calculated as: x = -3.

The diameter of a circle is the line segment that divides a circle into two halves or semicircle. The measure round the circumference of a semicircle is equal to 180 degrees. One full circle is equal to 360 degrees.

-44x + 3 = 50 + 85

-44x + 3 = 135

-44x = 135 - 3 [subtraction property of equality]

-44x = 132

x = 132/-44 [division property]

x = -3

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Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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A 15-ounce bottle of the same medicine contains 90 doses.

The unitary method is a method used to solve problems related to proportionality. It involves finding the value of a single unit or the value of a given quantity when the value of one or more units is known.

In the given problem, we will find the number of doses in 1 unit from that will find the number of doses in a 15-ounce bottle.

Here we have

A 6-ounce bottle of medicine contains 36 doses.

Number of doses in a 1-ounce bottle

= 36/6 = 6 doses  

Then the number of doses in a 15-ounce bottle of medicine  

= 15 × Number of doses in 1 ounce

= 15 × 6

= 90

Therefore,

A 15-ounce bottle of the same medicine contains 90 doses.

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The graph of the inequality y > 3/5x - 2 includes the origin also and the shaded region is above the line for the graph that is attached below.

Inequality:

Inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.

While we plot the inequality on the graph instead of make a line it will make the shaded region on it.

Given,

Here we have the inequality. y > 3/5x - 2

Now, we need to determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the inequality.

In order to solve this, first we have to plot the graph for this inequality.

To plot the graph for the inequality here, we have to use the graphing calculator.

Then we get the graph like the following.

While we looking in the graph we have identified that the origin (0,0) is included in the shaded region.

And the shaded region will be placed above the line for the inequality.

Which means the resulting values of he inequality are placed upwards.

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Answer:

x=-6

Step-by-step explanation:

Answer:

x=-6

Step-by-step explanation:

8(2x-2)=7(3x+2)

simplify both sides

(8)(2x)+(8)(-2)=(7)(3x)+(7)(2)

distribute

16x+-16=21x+14

16x-16=21x+14

subtract 21x from both sides

-5x-16=14

add 16 to both sides

-5x=30

divide both sides by -5

x=-6

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Answer:

x3

Step-by-step explanation:

Answer:

452.389

Step-by-step explanation:

The required dimensions of a rectangular rancher with perimeter for fencing, 3000 feet are equal the 500 feet and 375 feet at maximum area of 3,75,000 ft².

We have a rancher which to construct adjacent, equally sized rectangular pens with the fencing of 3000 feet. Suppose that the rancher need to be fenced in the way shown in the attached figure. Then, the perimeter is 4x + 3y = 3000

=> x \( =\frac{3000 - 3y}{4} \).

The area of rectangle is represented by A=L × W --(1) , where L and W are dimensions of rectangles. The total area will be A = 2× x × y --(2)

=> A = 2× (\(\frac{3000 - 3y}{4}\))× y

= ( \( 1500 - \frac{3y}{2} \))y

= \( 1500y - \frac{3y²}{2} \)

Now, differentiate above area function, with respect to y, and equate to 0, for determining the critical points on the graph, \(\frac{dA}{dy} \) = A'(y) =\( 1500 - \frac{6y}{2} \) = 0

=> y = \(\frac{1500}{3} = 500 \)

Also, x \( =\frac{3000 - 3× 500}{4} \).

\( =\frac{1500}{4} = 375 \).

Maximum area = 375 × 500 × 2 = 375000 ft². Hence, the dimensions that will give the maximum area are 500 feet and 375 feet.

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Complete question : attached figure complete the question.

The equations represents that 5 less than 10 times a number is 15 is option A) 10n - 5 = 15

Equation with polynomials on both sides is known as an algebraic equation or polynomial equation (see also system of polynomial equations). They are further divided into levels: linear formula for level one.

The statement "5 less than 10 times a number is 15" is one that can be translated into an equation.

For example, Let's use the variable 'n' to stand for the unknown number.

The phrase "10 times a number" can be shown as 10n.

The statement "5 less than 10 times a number" implies subtracting 5 from 10n, and that gives us 10n - 5.

So, one have the equation 10n - 5 = 15.

This equation implies that "10 times a number, reduced by 5, is equal to 15." It stands for the relationship shown in the original statement.

Therefore, option A) 10n - 5 = 15 is the correct equation that stand for the given scenario.

To simplify it:

10n - 5 = 15

10n= 15 +5

10n =20

n = 20/10

n = 2

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First simplify the equation.

3x+3y= -x+5y

4x=2y

2x=y

y=2x

Means that the y value is 2 times the x value.

answer: (1,2) and (2,4) but there are more solutions

Answer:

Composition and vertical translation must be done in the parent function.

Step-by-step explanation:

Let be \(j(x)\) the parent function, if \(g(x) = j(4\cdot x) -27\), then two transformation must be done in the following order:

Composition

\(j \circ h (x) \rightarrow j(h(x))\), where \(h(x) = 4\cdot x\)

Vertical translation

\(g(x) = j(4\cdot x) -27\)

Composition and vertical translation must be done in the parent function.

Answer: Option D

Horizontal compression by a factor of 1/4, and a translation 27 units down

Answer:

  (a)  15 -18i

Step-by-step explanation:

You want the simplified form of the expression -2i(5- i) + (17- 8i).

For many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.

  -2i(5- i) + (17- 8i) = -10i +2i² +17 -8i

  = -2 +17 +(-10 -8)i

  = 15 -18i

__

Additional comment

Your scientific or graphing calculator can probably help you evaluate such expressions.

For the given sample space we have the probabilities as follows: 1. P(sum=11) = 6/64 = 3/32 2. P (sum < 6) = 10/64 3. P ( sum is greater than or equal to 7) = 49/64 4.  P(sum is a multiple of 3 or a multiple of 4) = 33/64.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

For the sample space of rolling two 8 sided die we have:

1. P (sum = 11):

The samples that give the sum equal to 11 are:

(3, 8), (4, 7), (5, 6), (6, 5), (7, 4), and (8, 3)

Thus,

P(sum=11) = 6/64 = 3/32

2. P (sum < 6):

(1, 1), (1, 2), (1, 3), (1, 4)

(2, 1), (2, 2), (2, 3)

(3, 1), (3, 2)

(4, 1)

Thus, P (sum < 6) = 10/64

3. P ( sum is greater than or equal to 7):

(1, 6), (1, 7), (1, 8) = 3

(2, 5), (2, 6) (2, 7), (2, 8) = 4

(3, 4), (3, 5) (3, 6) (3, 7) (3, 8) = 5  

(4, 3) (4, 4) (4, 5) (4, 6), (4, 7) (4, 8) = 6

(5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (5, 7) (5, 8) = 7

(6, 1) upto (6, 8) = 8

(7, 1) upto (7, 8) = 8

(8, 1) upto (8, 8) = 8

Total = 3 + 4 + 5 + 6 + 7 + 8 + 8 + 8 = 49

Thus, P ( sum is greater than or equal to 7) = 49/64

4. P (sum is a multiple of 3 or a multiple of 4):

Multiple of 3: 3, 6, 9, 12, ........

(1, 2) (1, 5) (1, 8) (2, 1) (2, 4) (2, 7) (3, 1) (3, 3) (3, 6) (4, 2) (4, 5) (4, 8) (5, 1) (5, 4) (5, 7), (6, 3), (6, 6) (7, 2) (7, 5) (7, 8) (8, 1) (8, 4), (8, 7) = 23

Multiple of 4: 4, 8, 12, 16, .........

(1, 3) (1, 7) (2, 2) (2, 6) (3, 1) (3, 5) (4, 4) (4, 8), (5, 3), (5, 7), (6, 2), (6, 6) (7, 1) (7, 5) (8, 4) (8, 8) = 16

Common terms = 6

Thus, P(sum is a multiple of 3 or a multiple of 4) = 23 + 16 - 6 / 64 = 33/64

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a. The encrypted message "AN APPLE A DAY" using the Caesar cipher is "DR DSSOH D GDB".

b. The decrypted message "NHHSV WKH GRFWRU DZDB" using the Caesar cipher is "MEET THE ENGINEER BILL".

The Caesar cipher is a substitution cipher where each letter in the plaintext is shifted a certain number of positions down or up the alphabet. In the case of encryption, the letters are shifted forward, while in decryption, the letters are shifted backward. The number of positions to shift is known as the key.

For the encryption in (a), each letter in the message "AN APPLE A DAY" is shifted three positions forward in the alphabet, resulting in "DR DSSOH D GDB".

For the decryption in (b), each letter in the message "NHHSV WKH GRFWRU DZDB" is shifted one position backward in the alphabet, resulting in "MEET THE ENGINEER BILL".

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The answer is b because an intersection looks like this:

Hope this helps! <3