Terrell brought 42 muffins to school for his birthday He gave one each to the 17students in his class and to the 19 student in the other third grade class

Answer:

50

Step-by-step explanation:

→ Evaluate n as 1, 2, 3 and 4 in 5n

5, 10, 15 and 20

→ Find the sum of these numbers

5 + 10 + 15 + 20 = 50

The percent of time the photographer spent negotiating with the bison greater than the time he spent taking pictures is 500%

Percentage of time negotiating greater than taking pictures = (difference in time) / time to take pictures × 100

= (30 - 5) / 5 × 100

= 25/5 × 100

= 5 × 100

= 500%

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To eliminate the biggest common factor, use the distributive property: Solution: 16 + 36 = 4 (4 + 9)

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Due to that,

To remove the most significant common factor, we must use the distributive property.

Given expression:16 + 36

1, 2, 4, 8, and 16 make up the number 16.

1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.

Then, 4 is the most prevalent component.

distributed property

The formula is ab + bc

subtracting 4 from the supplied expression.

Therefore, the distributive property is used.

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Answer: Draw a line through (0,5) and (1,2)

The graph is shown below.

=====================================================

Reason:

The equation y = -3x+5 is in the form y = mx+b

m = -3 = slope

b = 5 = y intercept

The y intercept is where the graph crosses the y axis. In this case, it's at (0,5). This is one point needed.

Another point can be found by going down 3 and to the right 1 to arrive at (1,2). The motion "down 3, right 1" is from the slope of -3/1.

Therefore, this line goes through (0,5) and (1,2)

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

Another approach:

Plug in x = 0 to get...

y = -3x+5

y = -3(0) + 5

y = 5

The input x = 0 leads to the output y = 5

This tells us the point (x,y) = (0,5) is on the line.

Repeat for x = 1

y = -3x+5

y = -3(1)+5

y = 2

So (1,2) is another point on the line.

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

Check out the graph below.

Step-by-step explanation:

[tex]y=-3x+5.\\[/tex]

x | 0 | 1 |

y | 5 | 2 |

Step-by-step explanation:

f(x) = y = -1/2 × sqrt(x + 3), x >= -3

-2y = sqrt(x + 3)

4y² = x + 3

x = 4y² - 3

and now we need to rename x to y and y to x to make it a "normal" function :

y = 4x² - 3

since in the original function x >= -3, this gave us y <=0.

and therefore (remember the x of the inverse function actually stands for the y of the original function) the limit for the inverse function is x <= 0.

so, again, the full answer is

f^-1(x) = 4x² - 3, x <= 0

The  trigonometry angle range -π ≤ α ≤ π in radians means angle α is

To answer the question, we need to know what a trigonometric angle range is

A trigonometric angle range is the range of values which the trigonometric angle can have

Since we need to find the meaning of the  trigonometry angle range -π ≤ α ≤π.

We know that

Since α is in the range -π ≤ α ≤ π = -180° ≤ α ≤ 180°, this implies that the angle α is

So, the  trigonometry angle range -π ≤ α ≤ π in radians means that angle α is

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Answer:

x ≥ 21.5/19

Step-by-step explanation:

-1.5(4x + 1) ≥ 45 - 25(x + 1)

-6x - 1.5 ≥ 45 - 25x - 25

-6x + 25x ≥ 45 - 25 + 1.5

19x ≥ 21.5

x ≥ 21.5/19

Answer:

no matter what he has to pay $52

Step-by-step explanation:

because it is annually.

Answer:

Using the slope-intercept form, the slope is 34 . All lines that are parallel to y=3x4+2 y = 3 x 4 + 2 have the same slope of 34 .

Step-by-step explanation:

3/4

The slope of a line describes the steepness of a line, as well as the direction.

Slope-Intercept Form

To answer the question, we first need to find the slope of the original line. This line is represented in the slope-intercept form, which is y=mx+b.

So, using this information we can say that the slope is 3/4.

Parallel Lines

Parallel lines are 2 lines that will never intersect. You can tell if 2 lines are parallel by their slopes. All parallel lines have equal slopes.

This means that the slope of a line parallel to y = 3/4x + 2 must be 3/4 as well.

Answer: 360

Step-by-step explanation:

The area of the bottom square is 100.

The area of each of the four triangular faces is 65.

Adding these together, we get 65(4) + 100 = 360.

Step-by-step explanation:

[tex]\sqrt[4]{81} -2\\=3-2 \\=1[/tex]

By the definition of a rectangle, JML and KLM are right angles.

From the information given, JKLM is a rectangle based on the definition as the opposite sides are equal.

Also, JML and KLM will be 90° since they're right angles. The opposite sides of a rectangle are congruent and equal.

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The percentage of cars that are black when 80 cars of 300 cars are black is 26.67 or 26 2/3 %.

The percentage is similar to the fractional representation of quantities, where the quantity is shown as a part of the whole, but here the whole is fixed to be 100.

To derive a percentage in fractional form, we divide it by 100.

To derive a fractional form in percentage, we multiply it by 100.

In the question, we are given that 80 cars of 300 cars are black.

We are asked the percentage of cars that are black.

The fraction representing black cars of whole cars can be shown as 80/300 = 4/15.

To convert this into a percentage, we multiply it by 100.

Thus, the percentage of cars that are black = 4/15 * 100% = 80/3% = 26 2/3% = 26.67%.

Thus, the percentage of cars that are black when 80 cars of 300 cars are black is 26.67 or 26 2/3 %.

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Answer:

108

Step-by-step explanation:

First evaluate both the squares separately, because combining the two within the sqrt symbol would result in a large number(harder to deal with).

sqrt81 = 9 (because 9*9=81)

sqrt144 = 12 (because 12*12=144)

Then multiply.

9*12 = 108

Answer:

6 quarts

Step-by-step explanation:

2 pints = 1 quart

4 cups = 1 quart

• 5 pints of orange juice

5 pints = 5/2 =>2.5 quarts

• 6 cups of grape juice

6 cups = 6/4 => 1.5 quarts

• 8 cups of apple juice

8 cups = 2 quarts

2.5 + 1.5 + 2 = 6 quarts

The probability that the randomly selected student is female or Physics major is 0.625.

Given Information

Total number of students = 40

Number of Physics major out of the total students, P = 15

Number of females in the class, F = 16

Number of females that are Physics major, (P∩F) = 6

We have to find the probability P(P∪F).

Calculating the Probability

Probability of Physics major students, P(P) = 15/40

= 0.375

Probability of female students, P(F) = 16/40

= 0.4

Probability of female students who are Physics major, P(P∩F) = 6/40

= 0.15

Since, we know that,

P(P∪F) = P(P) + P(F) - P(P∩F)

∴ P(P∪F) = 0.375 + 0.4 - 0.15

P(P∪F) = 0.625

Thus, the probability that the randomly selected student will be a Physics major or a female is 0.625

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The triangle ∆ABC inscribed in sphere P is given by the first graphic.

One figure is said to be inscribed in another figure when the vertices of the inscribed figure rests on the perimeter of the circumscribing figure.

The relationship between the figures in the given diagram are;

1st graphic : All points of the triangle ∆ABC are located on the surface of the sphere, P

Therefore;

2nd graphic: Point C of the triangle ∆ABC is located outside sphere P.

Therefore;

The 2nd graphic does not depicts ∆ABC inscribed in sphere P

3rd graphic: Point A of the triangle ∆ABC in the 3rd graphic is located outside sphere P.

Therefore;

The 3rd graphic does not depicts ∆ABC inscribed in sphere P

4th graphic: Point B of triangle ∆ABC in the 4th graphic is located outside sphere P.

Therefore;

The 4th graphic does not depicts ∆ABC inscribed in sphere P

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Answer:

357 mi²

Step-by-step explanation:

A = LW + 0.5πr²

A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²

A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²

A = 357 mi²

-0.22 as  a repeating fraction is -22/99

The decimal is given as:

-0.22

Express as fraction

-22/100

Subtract 1 from the denominator to rewrite it as a repeating number

-22/99

Hence, -0.22 as  a repeating fraction is -22/99

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1.9

Step-by-step explanation:

A = kB/C -----------(1)

A=12

B = 3

C= 2

substitute A, B and C into equation (1).

12 = K × 3/2

12 = 3k/2

12×2 = 3k

3K = 24

dividing bothsides by 3

3K/3 = 24/3

K = 8

substitute K = 8 into equation (1)

A = 8B /C --------------(2)

Equation (2) is the equation connecting

A,B and C.

Finding B when A = 10 and C = 1.5

10 = 8B / 1.5

10× 1.5 = 8B

15 = 8B

Dividing bothsides by 8 :

B = 15/8

B = 1.875

B = 1. 9 ( approximately)

Shape A was reflected over the y axis and translated 1 unit down to get shape B.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

Shape A was reflected over the y axis and translated 1 unit down to get shape B.

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Answer:

The given lines are perpendicular.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (0,5) and (3,3). Whereas, line 2 passes through (1,-5) and (3,-2).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.

Step 1 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{1}=\frac{3-5}{3-0} \\&m_{1}=\frac{-2}{3} \\&m_{1}=-\frac{2}{3}\end{aligned}$$[/tex]

Step 2 of 2

Find the slope of first line.

[tex]$$\begin{aligned}&m_{2}=\frac{-2-(-5)}{3-1} \\&m_{2}=\frac{3}{2} \\&m_{2}=\frac{3}{2}\end{aligned}$$[/tex]

And

[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{2}{3}\left(\frac{3}{2}\right) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]

Since, both slopes are reciprocals .

Therefore. the lines are perpendicular.

Using it's vertex, the maximum value of the quadratic function is -3.19.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

In this problem, the equation is:

y + 4 = -x² + 1.8x

In standard format:

y = -x² + 1.8x - 4.

The coefficients are a = -1 < 0, b = 1.8, c = -4, hence the maximum value is:

[tex]y_v = -\frac{1.8^2 - 4(-1)(-4)}{4(-1)} = -3.19[/tex]

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The probability that exactly 9 buyers would prefer green is 0.1408

We will use the Binomial probability formula to find the answer

The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ-ˣ

We have

n, the number of trial = 12

x, the sample we aim to try = 9

p, the probability of success = 0.6

Substitute these values into the formula

[tex]P(9)= ^{12}C_{9} (0.6)^{9} (1-0.6)^{12-9}[/tex]

P(9) = 0.1408 (rounded to four decimal places)

Hence, The probability that exactly 9 buyers would prefer green is 0.1408

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The linear equation is represented by the second table as  y= -2 .5 x-15 and the solution to the system of equations is  (-6, 0).

First, take two point from the table and as such it will be:

P (-4, -5) and Q(-2, -10)

So the two point is used to create a straight line and as such it will be:

y - y₁ = y₂ - y₁/ x₂ - x₁ (x₁-x )

y -(-5) = [tex]\frac{-10-(-5)}{-2-(-4)}[/tex]  (x -(-4))

y + 5 = [tex]\frac{-5}{2}[/tex]  x +4

y + 5 =  [tex]\frac{-5}{2}[/tex]  x - 10

y =  [tex]\frac{-5}{2}[/tex]  x - 15

y= -2 .5 x-15

The linear equation is represented by the second table as  y= -2 .5 x-15 and the solution to the system of equations is  (-6, 0)

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Answer:

1st one option A to lazy to right out location

2nd one -6,0

Step-by-step explanation:

The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

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Answer:

5

Step-by-step explanation:

→ Let x = √20 + √20 .....

x

→ Square both sides

x² = 20 + √20 +√20 + √20

→ Replace √20 +√20 + √20 with x

x² = 20 + x

→ Move everything to the left hand side

x² - 20 - x = 0

→ Factorise

( x + 4 ) ( x - 5 )

→ Solve

x = -4 , 5

→ Discard negative result

x = 5

Note that

[tex]\left(\sqrt{x+a} + b\right)^2 = \left(\sqrt{x+a}\right)^2 + 2b \sqrt{x+a} + b^2 = x + 2b \sqrt{x+a} + a+b^2[/tex]

Taking square roots on both sides, we have

[tex]\sqrt{x+a} + b = \sqrt{x + 2b \sqrt{x+a} + a+b^2}[/tex]

Now suppose [tex]a+b^2=0[/tex] and [tex]2b=1[/tex]. Then [tex]b=\frac12[/tex] and [tex]a=-\frac14[/tex], so we can simply write

[tex]\sqrt{x-\dfrac14} + \dfrac12 = \sqrt{x + \sqrt{x - \dfrac14}}[/tex]

This means

[tex]\sqrt{x-\dfrac14} = -\dfrac12 + \sqrt{x + \sqrt{x - \dfrac14}}[/tex]

and substituting this into the root expression on the right gives

[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x + \sqrt{x - \dfrac14}}}[/tex]

and again,

[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac14}}}[/tex]

and again,

[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac14}}}}[/tex]

and so on. After infinitely many iterations, the right side will converge to an infinitely nested root,

[tex]\sqrt{x - \dfrac14} + \dfrac12 = \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{x - \dfrac12 + \sqrt{\cdots}}}}}[/tex]

We get the target expression when [tex]x=\frac{41}2[/tex], since [tex]\frac{41}2-\frac12=\frac{40}2=20[/tex], which indicates the infinitely nested root converges to

[tex]\sqrt{20+\sqrt{20+\sqrt{20+\sqrt{\cdots}}}} = \sqrt{\dfrac{41}2 - \dfrac14} + \dfrac12 \\\\ ~~~~~~~~ = \sqrt{\dfrac{81}4} + \dfrac12 \\\\ ~~~~~~~~ = \dfrac92 + \dfrac12 = \dfrac{10}2 = \boxed{5}[/tex]

The statement that best describes a relationship between angles in the figure is option d: m SRU = m QPS  x 2.

In Geometry, an angle is known to be any figure is is created  by two rays or lines that  is said to have a common endpoint known as  an angle.

Note that:

From the diagram, angle QPS   is right angle and angle SRU is an angle on a straight line.

Therefore:

= QPS  x 2

= 90 x 2

= 180 degrees

Angle SRU = 180 degrees

Therefore, The statement that best describes a relationship between angles in the figure is option d: m SRU = m QPS  x 2.

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Answer:

Step-by-step explanation:

Answer:

the answer will be equal to x= 1962 over 7