-2squreroot3+sequreoot75

Answer:

60°

Step-by-step explanation:

In similar triangles, the corresponding angles are congruent.

          ∠O = R

          O = 70°

In ΔOMN,

      ∠O + ∠M + ∠N = 180     {Angle sum property of triangle}

       70 + 50 + Ф    = 180

               120 + Ф  = 180

Subtract 120 from both sides,

                        Ф  = 180 - 120

                         Ф = 60°  

The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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A)

We will solve using:

The number of ways to choose 4 girls from 12 girls and 0 boys from 10 boys is:

So, the probability() of choosing 4 just 4 girls is:

So, that is the probability to get just 4 girls on the committee.

B)

For the committee to be just 4 boys is found as follows:

And the number of ways to choose 4 boys from 10 boys and 0 girls from 12 girls is:

So, the probability to get just 4 boys on the committee is:

C)

For the committee to have at least one girl is:

No. of ways to selecting at least 1 girl:

22C4 - 10C4 = 7315 - 210 = 7105

Now, we calculate the probability:

, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: The fraction 3/9

Now we can simplify the fraction further by dividing both the numerator and denominator by 3

let p=3/9

then p=3/3 / 9/3

       p= 1/3

Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

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Answer: i think the answer is 9

Step-by-step explanation:

Answer:

\(\\\)

Step-by-step explanation:

To find the total amount of berries that Mr. Alvarez bought, you need to add the amount of blueberries and raspberries.

\(\\\)

The fractions for the amount of blueberries and raspberries are:

\(\sf\qquad\dashrightarrow\rm{Blueberries = \blue{\dfrac{3}{4}}}\)

\(\sf\qquad\dashrightarrow\rm{Raspberries = \red{\dfrac{3}{8}}}\)

\(\\\)

To add these fractions, you need to find a common denominator. The smallest common denominator for 4 and 8 is 8.

\(\\\)

Converting the fractions to have a common denominator of 8:

\(\sf\qquad\dashrightarrow\rm{Blueberries = \blue{\dfrac{3}{4}} = \blue{\dfrac{6}{8}}}\)

\(\sf\qquad\dashrightarrow\rm{Raspberries = \red{\dfrac{3}{8}} = \red{\dfrac{3}{8}}}\)

\(\\\)

Now you can add the fractions:

\(\rm\implies{Total = \blue{\dfrac{6}{8}} + \red{\dfrac{3}{8}}}\)

\(\rm\implies{Total = \dfrac{\blue{6} + \red{3}}{\green{8}}}\)

\(\rm\implies\boxed{\boxed{\sf{\:\:\:Total = \green{\dfrac{9}{8}}\:\:\:}}}\)

\(\\\)

\(\\\)

\(\therefore\) Mr. Alvarez bought a total of 9/8 pounds of berries.

According to the solution we have come to find that, The equation of the line that is parallel to y = -7 and passes through the point (7,5) is y = 5.

what is mean by parallel lines?

Parallel lines are two or more lines that are always the same distance apart and never intersect. In other words, they have the same slope and they will never meet, no matter how far they are extended in both directions. Parallel lines always remain equidistant from each other and never touch or intersect, even if they are extended to infinity.

For example, in a Cartesian coordinate system, two lines are parallel if and only if they have the same slope. If the slope of one line is m1 and the slope of another line is m2, then the two lines are parallel if m1 = m2.

The given equation is y = -7, which is a horizontal line parallel to the x-axis. Since we need to find the equation of a line parallel to this line, the slope of the new line will also be zero.

To find the equation of the new line, we need to use the point-slope form of the equation, which is:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values of the given point and slope, we get:

y - 5 = 0(x - 7)

y - 5 = 0

y = 5

So, the equation of the line that is parallel to y = -7 and passes through the point (7,5) is y = 5.

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The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

Given that

f(x) = 2x^2 - 2

g(x) = 4x/(x - 1)

So, we have

f(10) = 2(10)^2 - 2 = 198

g(-6) = 4(-6)/(-6 - 1) = 24/7

Here, we have

h(x) = (7x - 4)/5x

Where

1 < x < 5

So, we have

h(1) = (7(1) - 4)/5(1) = 3/5

h(5) = (7(5) - 4)/5(5) = 31/25

So the range is 3/5 < h(x) < 31/25

Here, we have

P(x) = (5x - 1)/(3 - x)

So, we have

x = (5y - 1)/(3 - y)

This gives

3x - xy = 5y - 1

So, we have

y(5 + x) = -1 - 3x

This gives

y = -(1 + 3x)/(5 + x)

So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)

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For the given data, the range, variance, and standard deviation is 1.47, 0.1716, and 0.414, respectively.

To find the range, subtract the minimum value from the maximum value in the set of data. The minimum value is 0.48 and the maximum value is 1.95, so the range is: 1.95 - 0.48 = 1.47.

To find the sample variance, follow these steps.

1. Calculate the mean of the data set.

2. Subtract the mean from each value in the data set.

3. Take the summation of the squares of the result.

4. Divide the sample size minus 1.

Upon calculation, the sample variance is 0.1716.

Lastly, to find the sample standard deviation, take the square root of the sample variance: √0.1716. = 0.414.

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Answer:

y = -8x+19

Step-by-step explanation:

The slope intercept form of a line is

y = mx+b  where m is the slope and b is the y intercept

y = -8x+b

Substitute the point into the equation

3 = -8(2)+b

3 = -16+b

Add 16 to each side

3+16 = b

19 = b

y = -8x+19

Step-by-step explanation:

to find the equation of this line you use the equation of the slope intercept which is y-y1= m (x-x1)

y-3=-8(x-2)

y-3=-8x+16

y=-8x+16+3

y=-8x+19

I hope this helps

Using the Pythagorean theorem, the missing sides are:

1. 5

2. 13

3. √15

4. 3

The Pythagorean theorem is given as: c² = a² + b², where c is the longest side and a and b are the other two legs.

1. Missing side = √(3² + 4²) [Pythagorean theorem]

Missing side = 5

2. Missing side = √(12² + 5²) [Pythagorean theorem]

Missing side = 13

3. Missing side = √(4² - 1²) [Pythagorean theorem]

Missing side = √15

4. Missing side = √((√10)² - 1²) [Pythagorean theorem]

Missing side = √(10 - 1) = √9

Missing side = 3

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The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.

To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).

Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:

Confidence Interval = 70 ± (2.576 * 6.4 / √48).

Simplifying the expression, we get:

Confidence Interval ≈ 70 ± 1.855.

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The graph is a dashed line, the shade of the area below the boundary line.

The given inequality is \(y <\)\(\frac1}{3}x+1\).

We need to find the boundary line.

The slope-intercept form of the equation is y=mx+c.

We need to find the slope (m) and y-intercept (c) for the boundary line.

Now, simplify the right side

Combine \(\frac{1}{3}\) and x.

That is \(y < \frac{x}{3}+1\)

Use the slope-intercept form to find the slope and y-intercept.

Find the value of m and c using the form y=mx+c.

That is, m=\(\frac{1}{3}\) and c=1

The slope of the line is the value of m, and the y-intercept is the value of c.

Slope:1/3

y-intercept: (0, 1)

Graph a dashed line, the shade of the area below the boundary line.

Since, \(y < \frac{1}{3}x+1\).

Therefore, the graph is a dashed line, the shade of the area below the boundary line.

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Aiko incorrectly used the identity property by combining the real number and coefficient of imaginary part.

The numbers of the form a+ib, where a and b are real number an i=√(-1) is known as complex numbers. When we try to find the solution equation like x²+1=0, we need complex number . The symbol i is called iota.

Given expression is (4 + 5i) + (–3 + 7i). To simplify this expression we will add the real numbers with real part an the imaginary  numbers with imaginary part. We will add 4 and -3 together as these are real part and 5 and 7 together as these two numbers are part of imaginary number. Se below:

 (4 + 5i) + (–3 + 7i)

=(4-3)+(5+7)i

=1+12i

But Aiko wrote the expression (4 + 5i) + (–3 + 7i) as (–3 + 7)i + (4 + 5)i

And (–3 + 7)i + (4 + 5)i

=(-3+4)+(7+5)i

=1+12i

Clearly Aiko's answer will be same as correct answer of the given expression (4 + 5i) + (–3 + 7i). But Aiko made the mistake by adding real part and imaginary part together. Aiko incorrectly used the identity property by combining the real number and coefficient of imaginary part.

Hence, Aiko incorrectly used the identity property by combining the real number and coefficient of imaginary part.

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\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Let's solve ~

First we have to calculate g (-5) :

\(\qquad \tt \dashrightarrow \:x - 8\)

\(\qquad \tt \dashrightarrow \: - 5 - 8\)

\(\qquad \tt \dashrightarrow \: - 13\)

Now, let's find f (g (-5)) :

\(\qquad \tt \dashrightarrow \: {x}^{2} + 6x\)

\(\qquad \tt \dashrightarrow \:( - 13) {}^{2} + (6 \times - 13)\)

\(\qquad \tt \dashrightarrow \:169 + ( - 78)\)

\(\qquad \tt \dashrightarrow \:169 - 78\)

\(\qquad \tt \dashrightarrow \:91\)

Deepa makes use of the geometric property of similar triangles formed by

incident and reflected rays to determine the height of the goalpost.

Reasons:

When an object is reflected on a mirror, the angle of incidence, θ₁ is equal

to the angle of reflection, θ₂.

θ₁ = θ₂

Given that the angle, ∅₁, the incident ray of light and the angle, ∅₂, the

reflected light make with horizontal are both complementary angles, to the

angle of incident and reflection, respectively, we have;

θ₁ + ∅₁ = θ₂ + ∅₂

θ₁ = θ₂

Therefore, by subtraction property of equality, we have;

∅₁ = ∅₂

The vertical line from the top of the goalpost to the base of the goalpost

and the the vertical line from Deepa's eyes to the ground on which her feet

is standing are both perpendicular to the ground, therefore, the light from

the top of the goalpost to the mirror and to her eyes form similar triangles

by Angle Angle similarity postulate, which gives;

\(\displaystyle \frac{6.95}{9.35} = \frac{1.35}{The \ height \ of \ the \ goalpost}\)

6.95 × Height of the goalpost = 1.35 × 9.35

\(\displaystyle Height \ of \ the \ goalpost = \frac{1.35 \ m \times 9.35 \ m}{6.95 \ m} \approx 1.82 \ m\)

The height of the goalpost is approximately 1.82 meters.

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Answer:

(2) 6x^2+40x +50

Step-by-step explanation:

(4x+10)*(2x+5) = 8x^2 +40+50

minus 2x^2

=6x^2 +40 +50

Answer:

190.50 centimeters

Step-by-step explanation:

The range of the given equation is [-1, infinity).

We are given that;

Equation  y= underroot(x+5​)

Now,

The domain of this equation is the set of x values that make the expression under the square root non-negative.

That is, x+5 >= 0, or x >= -5. So the domain is [-5, infinity).

The range of this equation is the set of y values that are obtained by plugging in the domain values into the equation. Since the square root function is always non-negative, and we are subtracting 1 from it, the smallest possible value of y is -1, when x = -5. As x increases, y also increases, and there is no upper bound for y.

Therefore, by the range the answer will be [-1, infinity).

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Answer:

B. -7

Step-by-step explanation:

An integer is a whole number that is not a fraction.

Examples include: -4, -5, 8, 10, -7, 100, 50, etc.

Answer:

c

Step-by-step explanation:

integer must not be fraction and decimal

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer:

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

Given:

To find the arc measure (θ) in radians, we can use the formula:

Now, plug in the given values:

To solve for θ, divide both sides by 4:

Simplify the expression:

So, the arc measure (θ) is 2π/3 radians

Answer:

4.35 rounded to the nearest hundredth

4.3 rounded to the nearest tenth

4 rounded to the nearest whole number.

Step-by-step explanation:

\(8\frac{1}{6}\) ÷ \(1 \frac{7}{8}\) =

\(\frac{49}6}\) ÷ \(\frac{15}{8} =\)

\(\frac{49}{6} *\frac{8}{15} =\)

\(\frac{392}{90} =\)

\(4 \frac{32}{90} =\)

\(4\frac{16}{45}\) ≈ 4.35

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

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

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

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Complete Question:

41% of U.S. adults have very little confidence in newspapers. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who have very little confidence in newspapers is ​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four.

Answer:

a) P(exactly 5) = 0.209

b) P(at least six) = 0.183

c) P(less than four) = 0.358

Step-by-step explanation:

Sample size, n = 10

Proportion of adults that have very little confidence in newspapers, p = 41% p = 0.41

q = 1 - 0.41 = 0.59

This is a binomial distribution question:

\(P(X=r) = nCr p^{r} q^{n-r}\)

a) P(exactly 5)

\(P(X=5) = 10C5 * 0.41^{5} 0.59^{10-5}\\P(X=5) = 10C5 * 0.41^{5} 0.59^{10-5}\\P(X=5) = 252 * 0.01159 * 0.072\\P(X=5) = 0.209\)

b) P(at least six)

\(P(X \geq 6) = P(6) + P(7) + P(8) + P(9) + P(10)\)

\(P(X\geq6) = (10C6 * 0.41^6*0.59^4) + (10C7*0.41^7*0.59^3) + (10C8*0.41^8*0.59^2) + (10C9 *0.41^9*0.59^1) + (10C10 *0.41^{10})\\P(X\geq6) = 0.1209 + 0.0480 + 0.0125 + 0.0019 + 0.0001\\P(X\geq6) = 0.183\)

c) P(less than four)

\(P(X < 4) = 1 - [x \geq 4]\)

\(P(X<4)= 1 - [P(4) + P(5) + P(x \geq 6)]\)

\(P(X <4)= 1 - [(10C4*0.41^4*0.59^6) + 0.209 + 0.183]\\P(X <4)= 0.358\)

Answer:

36

Step-by-step explanation:

9x is equal to 9 multiplied by x.

x=4 so it is 9 x 4

9 x 4=36

Answer:

  -1

Step-by-step explanation:

The slope is the ratio of "rise" to "run" for the line.

Here, the line passes through points (-2, 0) and (0, -2). For a "run" of 2 units, the line decreases by 2 units, so the slope is ...

  m = rise/run = -2/2 = -1

The slope of the line is -1.