Garret bought 7 bags of apples. The red Apple came in bags of 5 and green came in bags of 2. Garret bought a total of 17 apples. How many of each type of apple did he buy.

The measure of angle MTU m∠MTU is 114 degree.

From the figure in the diagram:

Measure of angle STU is 145 degrees and measure of angle STM is 31 degree.

Since, angle STU composes or is the sum of angle STM and angle MTU.

To find angle MTU, simply subract angle STM from angle STU.

m∠STU = m∠STM + m∠MTU

Hence:

m∠MTU = m∠STU - m∠STM

Plug in the given values and simplify

m∠MTU = 145° - 31°

Subtract 31 from 145

m∠MTU = 114°

Therefore, angle MTU measure 114°.

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Answer:

9:34 pm

Step-by-step explanation:

First:

8:17 am

Go back 12 hours

8:17 pm

Round to 8:20

(keep the 3) Minus 43-17=26(3 is in this)

Therefore, 9:34 pm

Sorry if this doesn't make sense, it's hard to explain haha

Answer:

I hope this helps!

The population density of Rio de Janeiro in people per square meter is 5. 377 x 10 ⁻³ people per m²

To find the population density in meters squared when given the population density in kilometers squared, you first need to find the conversion factor between kilometer squared and meters squared.

1 kilometer squared is equal to 1, 000, 000 meters squared.

The population density of Rio de Janeiro in meters squared is therefore:

= Population density in kilometers squared / Conversion factor

= 5, 377 / 1, 000, 000

= 0. 005377

= 5. 377 x 10 ⁻³ people per m²

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The full question is:

In 2016, the city of Rio de Janeiro had a population density of 5377 people/km2.

What was the population density of Rio in people per square meter?

Answer:

Step-by-step explanation:

You need to put parentheses around the radicands.

√z · √(30z²) · √(35z³) = √(z·30z²·35z³)

= √(1050z⁶)

= √(5²·42z⁶)

= √5²√z⁶√42

= 25z³√42

The obtained expression would be 25z³√42 which is determined by the multiplication of the terms of expression.

A perfect Square is defined as an integer multiplied by itself to generate a perfect square, which is a positive integer. Perfect squares are just numbers that are the products of integers multiplied by themselves.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

We have been the expression as:

⇒ √z · √(30z²) · √(35z³)

Multiply and remove all perfect squares from inside the square roots

⇒ √(z·30z²·35z³)

⇒ √(1050z⁶)

⇒ √(5²·42z⁶)

Assume z is positive.

⇒ √5²√z⁶√42

⇒ 25z³√42

Therefore, the obtained expression would be 25z³√42.

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The value for expression 2/3xy² when x = -1/3 and y = 1/2 is 8.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is 2/3xy².

The value of x is given as x = -1/3.

The value of y is given as y = 1/2.

To find the value of the expression, substitute the value of x and y in the expression -

= 2/3xy²

Expand using the power rule -

= [2/(3 × (-1/3) × (1/2)²)]

Use the arithmetic operation of multiplication -

= [2/(3 × (-1/3) × (1/4)]

= [-2/(-3/12)]

= -2/(-1/4)

The denominator will reciprocate -

= -2 × -4

= 8

Therefore, the final value is obtained as 8.

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There are 280 students attending the play.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given  student tickets cost $6 each and adult tickets cost $11 each,

let a number of students be x and the number of tickets be y

total tickets sold = 400

x + y = 400

and total amount made = $3000

so 6x + 11y = 3000

from equation 1,

y = 400 - x

substitute in the equation,

6x + 11y = 3000

6x + 11(400 - x) = 3000

6x + 4400 - 11x = 3000

-5x = 3000 - 4400

-5x = -1400

x = 1400/5

x = 280

and y = 400 - 280

y = 120

Hence 280 students attended the play.

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To find the height of the cylinder when the volume is given as 1500 in³ and the radius is 7 inches, we can use the formula for the volume of a cylinder:

Volume = π * r² * h

Substituting the given values, we have:

\(1500 = 3.14 * 7^2 * h1500 = 3.14 * 49 * h1500 = 153.86 * h\)

To solve for h, we divide both sides of the equation by 153.86:

h = 1500 / 153.86

h ≈ 9.75

Rounding the answer to the nearest hundredth, the height of the cylinder is approximately 9.75 inches.

Therefore, the height of the cylinder is 9.75 inches.

Note: It is important to use the accurate value of π, which is approximately 3.14159, for precise calculations. However, in this case, since you specified to use 3.14 for π, I have used that approximation to calculate the height.

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True

A statistic is a characteristic of a sample, a portion of the target population. A parameter is a fixed, unknown numerical value, while the statistic is a known number and a variable which depends on the portion of the population.

Parameter Definition: a quantity or statistical measure that, for a given population, is fixed and that is used as the value of a variable in some general distribution or frequency function to make it descriptive of that.

Population: The mean and variance of a population are population parameters.

Statistic Definiton: A statistic or sample statistic is any quantity computed from values in a sample that is used for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average of sample values is a statistic.

The set of prime numbers greater than 11 with the cardinality of 5 is {13, 17, 19, 23, 29}

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

Set = prime numbers

Cardinality = 5

The cardinality implies that the number of elements in the set is 5

5 prime numbers greater than 11 are 13, 17, 19, 23, 29

Hence, the set is {13, 17, 19, 23, 29}

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TRUE. Combinations and permutations are used in probability calculations to determine the number of possible outcomes in a sample space.

When order is important, permutations are utilized, and when order is not important, combinations are used. The formula P(n,r) = n!/(n-r)!, where n! signifies the factorial of n, and the expression C(n,r) = n!/r!(n-r)!, give the number of permutations of n items taken r at a time and the number of combinations of n objects taken r at a time, respectively.

It is possible to count the number of ways that a subset of items can be chosen from a larger set using both permutations and combinations. These ideas are crucial for estimating probabilities because they let us know how many different outcomes could satisfy a certain condition.

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4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.

The relationship between two things is called Ratio. It is written in p:q form.

It is given that

For 10 pounds of soil , farmer mixes 8 ounces of fertilizer.

=8/16 = 0.5 pounds of fertiliser

The ratio is 10 : 0.5

Suppose he mixes x pounds of fertilizer for 80 pounds of soil

to determine x

The ratio is 80 : x

As they are in Proportion

10 / 0.5 = 80 /x

x = 80 * 0.5 /10

x = 4 pounds

Therefore 4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.

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Answer:

[cos(10x) - cos(8x)]/2

Step-by-step explanation:

sin(-x) sin(9x) = {cos[9x - (-x)] - cos(9x + (-x)]}/2

= [cos(10x) - cos(8x)]/2

Answer:

f(x)g(x) = 2x² - 6x

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

f(x) = 2x

g(x) = x - 3

Step 2: Find f(x)g(x)

We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Answer:

y = (-1/6)x represents a proportional relationship.

Answer:

There is 1 solution

Step-by-step explanation:

y = -3 (x+1) ^2

Using the zero product property

0 =  -3 (x+1) ^2

Divide by -3

0 =   (x+1) ^2

Take the square root of each side

sqrt(0) =  sqrt( (x+1) ^2)

0 = x+1

Subtract 1 from each side

-1 =x

There is 1 solution

The smallest possible value of the entire expression is 7.5, which occurs when A = 5, B = 2, and C = 4.

We are given the three different numbers 4, and C represent three different numbers from 2 through 5 and we have to find out the smallest possible value of the entire expression 10 - A B/C.

To find the smallest possible value, we need to take the greatest value of A, the smallest value of B, and the smallest value of C.

The given number 4 is in between 2 and 5, so it cannot be the greatest value.

Therefore, A must be 5. Now, the other two numbers must be chosen from the remaining three numbers 2, 3, and 4.

We need to choose the smallest possible value of B and C to make the entire expression the smallest. The smallest value of B is 2.

Now, we need to choose the smallest possible value of C. If C is 4, then the entire expression becomes:10 - 5(2/4) = 10 - 2.5 = 7.5If C is 5, then the entire expression becomes:10 - 5(2/5) = 10 - 2 = 8

Thus, the smallest possible value of the entire expression is 7.5.

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Answer:

A.

Step-by-step explanation:

The angles are not always congruent as the only way for them to all be congruent is if it were to be a square, and not all parallelograms are squares.

Approximately 75% of the students in the class listen to rap music.

Percentage is a way of expressing a proportion or a fraction of a whole quantity in terms of 100. It is denoted by the symbol "%". The term "percent" comes from the Latin word "per centum," which means "per hundred."

To calculate the percentage of students who listen to rap music, you can use the following formula:

Percentage = (Number of students who listen to rap music / Total number of students) * 100

In this case:

Number of students who listen to rap music = 27

Total number of students = 36

Percentage = (27 / 36) * 100 ≈ 75%

So, approximately 75% of the students in the class listen to rap music.

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The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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Answer:

Add 3 to both sides

Property: Addition property of equality

Step-by-step explanation:

Action: Add 3 to both sides.

⇒ x - 3 =               12

(cancel out)+ 3     + 3

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

     x    =        15  

The property used:

→ equation is true and the same #is added to each side the resulting equation is true. for any #s a,b,c,if a=b then a+c=b+c.

Answer:

6666

Step-by-step explanation:

On solving the inequalities a ≥ 10, y ≥ 55, 7a + 10y ≥ 690, the solution is obtained as (20,55).

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

Use the variables a and y to represent the number of student and adult tickets sold, respectively.

Then write the following system of inequalities -

a ≥ 10 (they must sell a minimum of 10 student tickets)

y ≥ 55 (they must sell at least 55 adult tickets)

7a + 10y ≥ 690 (they must make no less than $690 from ticket sales)

The first two inequalities are constraints on the number of tickets sold, and the third inequality represents the revenue constraint.

To find a possible solution, graph these inequalities on a coordinate plane and look for the feasible region that satisfies all three inequalities.

Alternatively, solve the system of inequalities using algebra.

First, simplify the third inequality by subtracting 7a from both sides -

10y ≥ 690 - 7a

Then, divide both sides by 10 -

y ≥ (690 - 7a)/10

This inequality represents the revenue constraint in terms of the number of student tickets sold.

Now combine the revenue constraint with the other two constraints -

a ≥ 10

y ≥ 55

y ≥ (690 - 7a)/10

Use substitution to solve for a in terms of y -

y ≥ (690 - 7a)/10

10y ≥ 690 - 7a

7a ≥ 690 - 10y

a ≥ (690 - 10y)/7

To find a possible solution, substitute a = (690 - 10y)/7 into the other two constraints -

(690 - 10y)/7 ≥ 10

y ≥ 55

These inequalities can be simplified -

690 - 10y ≥ 70

y ≥ 55

The first inequality can be solved for y -

-10y ≥ -620

y ≤ 62

Since it is known y ≥ 55, the feasible values for y are between 55 and 62, inclusive -

55 ≤ y ≤ 62

Now use the expression for a in terms of y to find the corresponding values of a -

a = (690 - 10y)/7

For each value of y between 55 and 62, inclusive, we can calculate a and check whether it satisfies the constraints -

a ≥ 10

y ≥ 55

7a + 10y ≥ 690

For example, when y = 55 -

a = (690 - 10(55))/7 = 20

7a + 10y = 7(20) + 10(55) = 690

Therefore, these values satisfy all three constraints, so one possible solution is a = 20 and y = 55.

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Answer: B

Step-by-step explanation:

Answer:

j= 15k−27/2

Step-by-step explanation:

9514 1404 393

Answer:

  (a) (-∞, -8), (-5, -2), (2, 5)

  (b) -8, -2, 5

  (c) negative

  (d) 6

Step-by-step explanation:

(a) The function is increasing on intervals where the graph slopes upward left-to-right. Those are (-∞, -8), (-5, -2), and (2, 5).

__

(b) The local maxima are at the right end of each interval on which the function is increasing: -8, -2, 5.

__

(c) The function opens downward (∩), so has a negative leading coefficient.

__

(d) There are three local maxima and two local minima (left end of an increasing interval), so a total o 5 turning points. The degree of the polynomial is at least one more than this: 6.