write the expressions as the power of 2 (4*2^5)/(2^3*1/16)

The measure of the Largest angle using the angle sum property of a triangle is: 80°

What is the Angle sum property of a triangle?

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.

In the given figure, we have:

Measure of 1st angle = 64°

Measure of 2nd angle = (2x + 14)°

Measure of 3rd angle = (6x + 14)°

and we know the angle of the property,

using the  angle of property,

64° + (2x + 14)° + (6x + 14)° = 180°

⇒64° + 8x + 14° + 14° = 180°

⇒92°  + 8x = 180°

⇒ 8x = 180° - 92°

⇒8x = 88°

⇒ x = 11°

So,

Measure of 2nd angle = (2x11 + 14)°

Measure of 2nd angle = (36)°

Measure of 3rdangle = (6x11 + 14)°

Measure of 2nd angle = (80)°

Hence,

The measure of the Largest angle using the angle sum property of a triangle is: 80°

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The number of months after which she will be able to vault 11 feet is 30 months.

For a pole-vaulter in training, the height the athlete will be able to pole-vault after t months of training is given by a mathematical formula. The formula is given below.

H(t) = 17 - 11e^(-0.02t)

We need to find the number of months after which she will be able to vault a height equal to 11 feet. We will substitute the value of height in the given equation.

11 = 17 - 11e^(-0.02t)

11e^(-0.02t) = 17 - 11

11e^(-0.02t) = 6

e^(-0.02t) = 6/11

Now, we will take the natural logarithm on both sides of the equation.

-0.02t = -0.606

t = 0.606/0.02

t = 30.3

Thus, she will be able to vault 11 feet in approximately 30 months.

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Answer:  2(x+4) >3(x+7)-4

Step-by-step explanation:

Hope this helps

Answer:

2(n+4)≤3(n+7)-4

Step-by-step explanation:

The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4

What is a solution set to an inequality or an equation?

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solutions to that equation or inequality.

We need to find the inequality of the statement given;

"Two times the sum of a number and four is no more; than three times the sum of the number and seven decreased by four"

Let n be the unknown number

Then it would be;

2(n+4) ≤ 3(n+ 7) - 4

Hence, The statement "Two times the sum of a number and four is no more than three times the sum of the number and seven decreased by four" is 2(n+4)≤3(n+7)-4

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The solution of the composite function (f/g)(x) is [tex]\frac{-4x+3}{6+7x}[/tex]

Composite functions are when the output of one function is used as the input of another.

In other words, a composite function is generally a function that is written inside another function.

Composite function involves the composition of functions is combining two or more functions as a single function.

Therefore, let's solve the function below:

f(x) = -4x + 3

g(x) = 6 + 7x

Hence,

(f/g)(x) = f(x) / g(x)

Therefore,

f(x) / g(x) = [tex]\frac{-4x+3}{6+7x}[/tex]

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The solutions of the equations are x = 1 and y = 2

The system of equations are

4x + 3y = 10

-4x + 5y = 6

Here we have to use the elimination method. Eliminate the x term and find the value of y term

Add both equation

3y + 5y = 10 +6

Add the like terms

8y = 16

y = 16 / 8

Divide  the terms

y = 2

Substitute the value of x in the first equation

4x + 3y = 10

4x + 3×2 =  10

Multiply the terms

4x + 6  = 10

4x = 10 - 6

4x = 4

x = 4 / 4

Divide the terms

x = 1

Hence, the solutions of the equations are x = 1 and y = 2

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1. It will take 5 hours for the five-gallon tank full of water to become empty at the drainage rate of 1/(1 + t) gallons per hour.

2. A correct setup of the equation problem above in terms of function is D. None of these will give the correct solution.

An equation is a mathematical statement that shows that two or more mathematical expressions share equality or are equivalent.

Functions, which are mathematical expressions involving one or more variables known as domain (or the independent variable) and range (or the dependent variable), using the equation symbol to show that two expressions are equal.

Drainage rate per hour = 1/(1 + t) gallons

t = 0

The capacity of the tank = 5 gallons

1/(1 + t) gallons

= 1/(1 + 0) gallons

= 1/1 gallons

= 1 gallon per hour

Since the tank is 5 gallons, it will take = 5 hours (5/1)

Thus, based on the drainage equation rate, the five-gallon tank will empty in 5 hours.

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After solving the linear programming problem, we get the answer as 250.

What is linear programming?

When a linear function is exposed to multiple restrictions, linear programming maximizes or minimizes the function. This method determines the best way to use the resources that are currently available and aids managers in using the process to make decisions about the most efficient use of scarce resources, such as money, time, materials, and machinery. Linear programming has been useful for guiding quantitative decisions in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences.

Solution explained:

[tex]\left \{ {{2x + y = 12} \atop {x + y = 7}} \right.[/tex]            x=3, y=4    P(3,4)       Coordinates of the solution point

[tex]\left \{ {{x + y = 7} \atop {x + 2y = 10}} \right.[/tex]            x=4, y=3    Q(4,3)      

                                                           Coordinates of the simultaneous eqs.

[tex]\left \{ {{2x + y = 12} \atop {x + 2y = 10}} \right.[/tex]            x=14/3, y=8/3

Putting the values of x and y in the equation P = 30x + 40y and calculating we get

P(P) = 250, P(Q) = 240, P(R) = 246.67

So, the answer is 250

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Answer:

x=9 (9,25)

Step-by-step explanation:

9*7=27

27-2=25

Answer:

-8

Step-by-step explanation:

f(-3) = 2(-3)-2

f(-3) = -6 -2

f(-3) = -8

Answer:

[tex] \huge{f( - 3) = - 8}[/tex]

Step-by-step explanation:

[tex]f(x) = 2x - 2[/tex]

In order to find f(-3) we substitute the value of x that's -3 into f(x) that's wherever we find x in f(x) we substitute it with -3 and solve for f(-3).

We have

[tex]f( - 3) = 2( - 3) - 2 \\ = - 6 - 2 \\ = - 8[/tex]

We have the final answer as

[tex] \bold{f( - 3) = - 8}[/tex]

Hope this helps you

The lengths of the base of the triangle are 31cm while the height of the triangle is 39cm

A triangle is a polygon that has 3 sides, three angles and three vertices whose sum of angles equal to 180 degrees.

How to find the lengths and height of a triangle?

from the statement,

A=1/2bh

A=1/2 xbx(8+b)

cross multiplying,

713 = 8b+b²

rearrange the function

b²+8b-713=0

Simplyfying the equation,

(b²+23b)-(31b-713)=0

b(b+23)-31(b+23)=0

b-31=0 or b+23 =0

b=31 or b=-23

length cannot be negative. therefore base = 31cm

Recall the h= b+8

this implies that h=8+31

h=39cm

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Answer:140

Step-by-step explanation:

14 x 10=

The number of eraser Stefanie bought is 10.

Stefanie bought a package of pencils for $1.75 and some erasers that cost $0.25 each. She paid a total of $4.25 for these items, before tax.

Therefore, the number of eraser Stefanie bought can be calculated as follows;

let

x = number of eraser bought

Therefore,

4.25 = 1.75 + 0.25x

subtract 1,75 from both sides of the equation

4.25 - 1.75 = 1.75 - 1.75 + 0.25x

2.5 = 0.25x

divide both sides by 0.25

x = 2.5 / 0.25

x = 10

Therefore,

number of eraser = 10

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Answer:

[tex]y=-\frac{5}{7}+5[/tex]

Step-by-step explanation:

the goal is to isolate y on one side

5x+7y=35

-5x.     -5x

7y=35-5x

/7. /7.  /7

y=-5/7x+5

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The value of x in  the following equation: 3|x+3|−12=0 is -7 and 1

The equation is 3|x+3|−12=0

We need to rewite the equation above in standard form

The modulus function can be positive and negative

Considering it to be negative,

the equation is

3((-1)(x + 3) - 12

3(-x - 3) - 12

-3x - 9 - 12 = 0

3x + 21 = 0

3x = -21

x = -7

3(x + 3) - 12

3x + 9 - 12

3x - 3 = 0

3x = 3

x = 1

Therefore, the value of x in  the following equation: 3|x+3|−12=0 is -7 and 1

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The probability that the next number pointing north is between 2 and 7 is 13/18 .

1) The circle is divided into 9 parts.

Now the parts are uneven.

So the data about the spins is required to calculate the probability .

The total number of items in the box = 18

favorable outcomes (between 2 and 7) = 13 possible outcome.

Required probability

= favorable outcome / total outcome

= 13 / 18

2) Using the Venn diagram we can calculate the various parts of the problem:

Shoppers at big-box store or online or local store = sum of all the shoppers = 109+57+107+18+17+38+34 = 380 shoppers

3) Shoppers made purchase online or locally owned shop but not at a big box store = 107 + 38 + 34 = 179 shoppers.

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The formula of the parabola is y = 2/35(x + 7)(x - 5)

The parameters in the question are given as

These parameters can be represented as

x₁ = -7 and x₂ = 5

(x, y) = (0, -2)

The quadratic function can be represented as

y = a(x - x₁)(x - x₂)

Substitute the known values in the above equation So, we have the following equation

y = a(x + 7)(x - 5)

At (x, y) = (0, -2), we have

-2 = a(0 + 7)(0 - 5)

Evaluate

a = -2/-35

Divide

a = 2/35

So, we have

y = 2/35(x + 7)(x - 5)

Hence, the equation is y = 2/35(x + 7)(x - 5)

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Answer:

Step-by-step explanation:

-21 = -7x

-21 divided by -7 = -7 divided by -7

3=x

500

Step-by-step explanation:

research

Answer:

Step-by-step explanation:

they are asking for probability

so they want to know,  what's the probability of getting a "heads"  on a coin toss.   What do you think it is?  You probably know this intuitively.

P(H) = ?

P(T) = ?  

They are asking for fractions,    so just say what  you already know to be how often you'll get a "heads"   in words, then just make that a fraction.  :)

Answer:

11

Step-by-step explanation:

Find the difference using subtraction:

18 - 7 = 11

So, the numbers are 11 units apart.

[tex]-\frac{5}{2} (8a - 2b) = ...[/tex] the answer for this question is zero (0)

How can the answer is zero?

The first thing that we should do is simplify questions.

[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (- 2b)\\= - 20a + 5b[/tex]

After that, we will search for "a" and "b" to solve the question. For me, i will search for "b" first.

[tex]- 20a + 5b \\5b = 20a\\b = \frac{20}{5} a\\b = 4a[/tex]

Next step is find the "a" by enter the "b" into the same question.

[tex]- 20a + 5b =\\20a = 5b\\20a = 5 (4a)\\20a = 20a\\a = 1[/tex]

After we find the "a" and "b", the next step is to enter it into the main question to find the right answer.

[tex]-\frac{5}{2} (8a - 2b) \\= -\frac{5}{2} (8a - 2[4a]) \\= -\frac{5}{2} (8a) + -\frac{5}{2} (-8a)\\= - 4a + 4a\\= -4 (1) + 4 (1)\\= -4 + 4\\= 0[/tex]

So, the answer is zero (0).

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Answer:

[tex] - 20a + 5b[/tex]

Step-by-step explanation:

[tex] - \frac{5}{2} (8a - 2b)[/tex]

[tex] - \frac{5}{2} (8a) - \frac{5}{2} ( - 2b)[/tex]

[tex] - 20a + 5b[/tex]

The F Test statistic is 1.58.

Given data is

Source       SS           df          MS

between   21,000.00       2        6,000.00

within  442,500.00  117        3,782.00

The SStotal is sometimes easier to calculate than SSbetween Since ......

SSwithin +SSbetween = SStotal you can use SStotal to calculate SSbetween.

= 442,500+21,000 =  463,500

In ANOVA, the F test statistic is the  ratio of the between - treatments variance and the within-treatments variance. The value of the F test statistic is 1.58 when the null hypothesis is true , the F test statistics is closer to 1, when the null hypothesis is false, the F test statistic is most likely large in general, you should reject null hypothesis for larger values of the F test statistic.

Hence the answer is the F Test statistic is 1.58.

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Answer:

x<1

Step-by-step explanation:

since the circle is not filled it will not be equal to one but either grater or equal to it

Since the arrow is pointing left than x is less than 1

x<1
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The volume V of the water in the cone as a function of the height h of the water is,

V = (1/48)πh³

Given, water is poured into a container in the shape of a right circular cone with a radius 4 inches and height 16 inches.

We have to express the volume V of the water in the cone as a function of the height h of the water.

Now, at any instant let the height of the water in the cone be h and radius of the water in the cone be r,

So, using the concept of similarity in triangles

we get, r/4 = h/16

r = h/4

Now, the volume of the water in the cone be,

V = (1/3)πr²h

V = (1/3)π(h/4)²h

V = (1/48)πh³

So, the function expressing the volume of the water in the cone be,

V = (1/48)πh³

Hence, the volume V of the water in the cone as a function of the height h of the water is,

V = (1/48)πh³

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The eastbound airplane traveled 44 miles far.

Given:

Two airplanes leave the same airport. One heads north, and the other heads east. After some time, the northbound airplane has traveled 33 miles. If the two airplanes are 55 miles apart.

Let x be the eastbound airplane traveled.

we know that,

north and east direction are perpendicular and with hypotenuse 55 miles it forms a right angle triangle with side = 33 miles.

According to pythagorean theorem:

[tex]33^2+x^2=55^2[/tex]

[tex]x^{2} =55^2-33^2[/tex]

= 3025 - 1089

x = [tex]\sqrt{1936}[/tex]

= 44 miles.

Therefore The eastbound airplane traveled 44 miles far.

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The solution is Option D.

Line plot , because a small number of scores are reported individually

What is a line plot?

A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.

If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions

Given data ,

Total number of athletes = 15

The score points of athletes = { 1 , 2 , 3 , 4 , 5 }

The number of athletes = { 1 , 2 , 3 , 4 , 5 }

The best option to plot the line plot because of the data set

The line plot , a data visualization chart that more accurately represents the small data set, is chosen.

And , to begin, unlike a line plot , a histogram involves data ranges or intervals. A line plot uses a dot to represent each observation, whereas a histogram divides the data into intervals, masking the identity of each observation

Furthermore, because line plots are one of the simplest statistical plots, they are better suited to small to moderate-sized data sets. They are more effective than histograms at highlighting clusters and gaps

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Answer:D

Step-by-step explanation:

Answer:

0.32

Step-by-step explanation:

[tex]\frac{780-532}{780}[/tex] = [tex]\frac{248}{780}[/tex] = 0.32 Rounded.

The approximate of √59 is 7.7 when rounded off to the nearest tenth place.

Given,  √59

we are asked to determine the approximation without using a square root button.

√59 is a decimal number since it is not a perfect square. Therefore, rather than finding a precise value, we will need to obtain a near approximation of 59 in decimal form.

the square root of the number 59 is:

7.6811

You rounded to the nearest tenths place. The 6 in the tenths place rounds up to 7 because the digit to the right in the hundredths place is 8.

= 7.7

When the digit to the right is 5 or greater we round away from 0.

7.6811 was rounded up and away from zero to 7.7

Hence we get the required approximation.

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