A landscaper has 6 pounds of seed available. He uses of a pound of grass seed for each acre he plants. Determine how many whole acres can be planted with the available seed.​

Answer:

Let x be the larger angle and y be the smaller angle

Larger angle is 2 less than 3 times the smaller angle that is x = 3y - 2

As the angles are complementary, their sum equals 90°

or, x + y = 90°

or, 3y - 2 + y = 90°

or, 4y = 92°

or, y = 23°

So, x = 3 * 23 - 2 = 67°

Larger angle = x = 67°

Smaller angle = y = 23°

The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

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A problem that could be solved by multiplying 4.63 x 9 is "the product of 4.63 and 9"

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

4.63 x 9

In the above expression, we can see that

4.63 and 9 are multiplied

This means that the problem is a product expression

And a problem that can represent 4.63 x 9 is "the product of 4.63 and 9"

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option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.

First, let us study the definition of Atomic Mass,

Atomic mass -

So we can also conclude that the 1 atomic mass unit is equal to 1/12 of the mass of the C-12 atom

Therefore, option c) = [tex]\frac{1}{12}[/tex]th of the mass of C - 12 atom is correct.

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Answer:

D. 142 degree

Step-by-step explanation:

A triangle has 180 degree

77 + 65 = 142 degree

180 - 142 = 38 degree

38 degrees is the missing angle of the triangle. This angle must add with angle 1 outside equal to 180

180 - 38 = 142 degree

So, the answer is D

The required linear inequality is [tex]-\frac{2}{3} \geq -\frac{7}{8}x[/tex]

What is linear inequation?

A linear inequation is an equation that contains one or more variables, such as x, and involves linear functions. Unlike a linear equation, its solution set is not a single point, but a range of values. Linear inequations are used to represent situations where the exact value of a variable is not known, but a range of values can be determined based on certain conditions. For example, if x represents the amount of money a person makes in a year and we know that it must be greater than $50,000, then we can write the linear inequation x > 50,000.

Let the number be x

[tex]-\frac{2}{3}[/tex] is a minimum of the product of a number and  [tex]-\frac{7}{8}[/tex]

[tex]-\frac{2}{3} \geq -\frac{7}{8}x[/tex]

This is the required linear inequality

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The product of linear factors of the given polynomial are;

(x + 3 )*(x² + 2x + 50 + (−100/(x + 3)))

We are given the polynomial expression as;

g(x)= x³ + 5x² + 56x + 150

Now, we are told that  -3 is a zero. Thus, if -3 is a zero that means x = -1

and x + 3 is a factor.

Using online polynomial division calculator, the the polynomial is divided by (x + 3) to get;

(x³ + 5x² + 56x + 150)/(x + 3) = x² + 2x + 50 + (−100/(x + 3))

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The equation with x about the number thought by Natasha is (x + 2.5) × 2 = 61

Let the number thought by Natasha be x. To formulate the equation, we will perform the same operations as done by Natasha. Forming the equation now -

(x + 2.5) × 2 = 61

Performing multiplication on Left Hand Side of the equation

2x + 5 = 61

Rewriting the equation

2x = 61 - 5

Performing subtraction on Right Hand Side of the equation

2x = 56

Rewriting the equation

x = 56/2

Performing division on Right Hand Side of the equation

x = 28

Thus, the equation is (x + 2.5) × 2 = 61 and the number thought by Natasha is 28.

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The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The equation is given below.

x² + 14x − 24 = 4x

Simplify the equation, then we have

x² + 14x − 24 = 4x

x² + 10x − 24 = 0

Factorize the equation, then we have

x² + 10x − 24 = 0

x² + 12x − 2x − 24 = 0

x(x − 12) − 2(x − 12) = 0

(x − 2)(x − 12) = 0

x = 2, 12

The solutions of the quadratic equation x² + 14x − 24 = 4x will be 2 and 12.

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Answer:

m = -5/2 or -2.5

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The equation becomes z + 5 = 1 and the value of the z in the given equation by completing the square is z = -4.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given equation,

z - 5 = z² - 25

z - 5 = z² - 5²

By property that A² - B² = (A + B)(A - B)

z - 5 = (z - 5)(z + 5)

z + 5 = 1    

z = - 1 / 5 = - 4

Hence "By completing the square, the equation is changed to z + 5 = 1, and the value of z in the given equation is changed to z = -4".

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Answer:

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

Given equation:

Solve it as follows:

The value of x = 25

The measure of the angle ∠R = 101°

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be TPRS

Now , the measure of ∠T = ( 4x + 1 )°

The measure of ∠S = ( 3x + 4 )°

Now , from the properties of a parallelogram ,

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

So ,

The value of ∠T = ∠R

And , value of ∠T + ∠S = 180°

Substituting the values in the equation , we get

∠T + ∠S = 180°

( 4x + 1 ) + ( 3x + 4 ) = 180

On simplifying the equation , we get

7x + 5 = 180

Subtracting 5 on both sides of the equation , we get

7x = 175

Divide by 7 on both sides , we get

x = 25

So , the value of x = 25

Now , the measure of ∠T = ( 4x + 1 )° = ∠R

So , the measure of ∠R = ( 4 x 25 + 1 )°

The measure of ∠R = 101°

Hence , The value of x = 25

The measure of the angle ∠R = 101°

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In studies intended to measure the distance a golf ball is struck with weapons made of various materials, the material of the golf ball and the direction of the wind at the moment the experiment was done become standardized variables.

In tests intended to assess the distance a golf ball is struck with clubs made of various materials, the kind of material the club is composed of is an independent variable.

Independent variables are those that a researcher tries to manipulate or control to observe how they impact the dependent variable. In this experiment, the effect of different club construction materials on golf ball distance is investigated.

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The number of coins which Craig collected as calculated from the given data is 49.

Given ,

percentage of foreign coin = 72%

Therefore the percentage of normal coins will be 28%.

Hence , the number of normal coins which he collected can be found out as ,

 28% of 175

= 28% × 175

= 28/100 × 175

= 0.28 × 175

= 49

When we divide a given number by 100 as a fraction , the result we get is known as percentage .

It is represented by the percentage sign which is "%".

The percentage is denoted by the letters "pct" or "pc," respectively. In other words, the percent or % is calculated at a value of around 100 and represents the proportion of one quantity made up of another.

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Based on the values you've listed, it appears that the expression P(7, 5) represents a combination calculation. In combinatorics, the notation P(n, k) represents the number of ways to choose a subset of k items from a set of n items, without regard to the order in which the items are chosen. This is also known as the number of k-permutations of n items.

In this case, the expression P(7, 5) would represent the number of ways to choose a subset of 5 items from a set of 7 items. Using the formula for combinations, this would be calculated as follows:

P(7, 5) = 7! / (5! * (7 - 5)!)

= 7! / (5! * 2!)

= 7 * 6 * 5 * 4 * 3 / (5 * 4 * 3 * 2 * 1 * 2 * 1)

= 7 * 6 / 2

= 21

Therefore, the correct answer for the expression P(7, 5) is 21.

Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.

a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.

Here,

One piece of bacon has 42 calories in it.

There are 60 calories in 1 slice of turkey.

2 slices of bacon are 2 calories each (42)

So 84 calories in 2 slice of bacon

3 slices of roasted turkey have 3 calories each slice (60)

Three slices of roasted turkey have 180 calories each.

180-84 is the difference in the amount of calories.

96 calories are added due to the calorie difference.

Two slices of bacon had 96 less calories than three slices of roasted turkey.

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Although part of your question is missing, you might be referring to this full question: The radius of a spherical ball is increasing at a rate of 2 cm/min. At what rate is the surface area of the ball increasing when the radius is 8 cm? The surface area of a sphere with radius r is given by 4πr².

The rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.

Given A = 4πr²

So, we have:

dA/dt = d/dt (4πr²)

= 4π * d/dt * (r²)

= 4π * 2r * dr/dt

= 8πr * dr/dt

Now, we have that dr/dt = 2 cm/min. So, when the radius of the ball is 8 cm, we have that:

dA/dt = 8πr * dr/dt

= 8π * 8 * 2

= 128π

Since we are measuring area, our unit is cm²/min, not cm/min.

Thus, the rate at which the surface area of the ball increasing when the radius is 8 cm is 128 cm²/min.

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The end behavior of the function is that;

D. As x decreases in value, f(x) decreases in value.

As x increases in value, f(x) increases in value.

The end behavior of a function f(x) describes the behavior of the graph of the function at the "ends" of the x-axis.

Now, in the graph attached, at the end point of the curve on the left of the x-axis, we see that the coordinate is (-3, 0) and to the right which is when x has increased to 9 and now has a coordinate point of (9, 6).

Thus, we conclude that we see that as the value of x increased from left to right, f(x) also increased and as the value of x decreased from right to left, f(x) also decreased.

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Labels on a line graph can make the visualization more accessible in a few ways:

Overall, labels can help make a line graph more accessible by providing additional context, improving readability, and helping the viewer quickly find the data they are interested in.

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Answer:

below

Step-by-step explanation:

Area of rectangle ( 3 x 4 )  minus the area of the circle (pi * 1^2) =

= shaded area = 8.86 cm^2

Answer:

$0.39

Step-by-step explanation:

First find the unit rate for store B ( $8.84/13)

At store B Artuto spends $0.68 for one bottle of apple juice

At store A they spent $0.29

0.68-0.29= 0.39

The estimate made by Warner is 95% reasonable.

Given is that Warner received 7 letters and each letter weighed between 3.92 ounces and 4.1 ounces.

If the we take the maximum possible weight of each letter, which is 4 ounces, then the total weight of 7 letters will be equal to (4 x 7) = 28. But since the weights are weighted between 3.92 ounces and 4.1 ounces, let us assume that the weight of each letter is equivalent to -

w(a) = (3.92 + 4.10)/2 = 8.02/2 = 4.01

So, the weight of 7 letters would be -

W{7} = w(a) x 7 = 7 x 4.01 = 28.7

28.7 = 29 (round off) ≈ 30

So, yes the estimate of the Warner is reasonable.

Therefore, the estimate made by Warner is 95% reasonable.

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Answer:

  y = -3x

Step-by-step explanation:

You want the slope-intercept equation of the line with slope -3 through the point (-1,3).

The equation of the line with slope m through point (h, k) can be written ...

  y -k = m(x -h)

For slope -3 and point (-1, 3), the equation is ...

  y -3 = -3(x +1)

Eliminating parentheses gives ...

  y -3 = -3x -3

Adding 3 gives the equation ...

  y = -3x

__

Additional comment

As you can see, the y-intercept is 0.

Answer: -4 < n [tex]\leq[/tex] 5

Step-by-step explanation:

When a buh wa firt planted in a garden,it wa 12 inche tall. After two week, it wa 120% a tall a when it wa firt planted. Tall wa the buh after the two week is   [tex]\\26 \frac{2}{5}[/tex].

What is improper fractions?

An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 3/4, 2/11, and 7/19 are proper fractions, while 5/2, 8/5, and 12/11 are improper fractions.

12 times 120% + 12

12*120%+12

[tex]$$\begin{aligned}& 120 \% \text { in fractions: } \frac{6}{5} \\& =12 \times \frac{6}{5}+12\end{aligned}$$[/tex]

Follow the PEMDAS order of operations

Multiply and divide (left to right) [tex]$12 \times \frac{6}{5}: \frac{72}{5}$[/tex]

[tex]=\frac{72}{5}+12$$[/tex]

Add and subtract (left to right) [tex]$\frac{72}{5}+12: \frac{132}{5}$[/tex]

[tex]=\frac{132}{5}$$[/tex]

Convert improper fractions to mixed numbers: [tex]$\frac{132}{5}=26 \frac{2}{5}$[/tex]

[tex]=26 \frac{2}{5}$$[/tex]

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Answer:

C

Step-by-step explanation:

S = .6T + 331.4    

When S = 331.4:

331.4 = .6T + 331.4    <=====you should be able to see this is true when T= 0

Answer:

x = 302/999

HERE THE ANSWER

Step-by-step explanation: