The temperatures, in degrees F, at 7:00 a.m. for five days during one week are shown.
-3, 4, -1, 6, 7
The mean temperature for all 7 days of the week was 0°F.
What was the mean of the temperatures for the two missing days?
a. -13
b. -10.5
c. -6.5
d. 0

The measure of the angle that turns through 3/10 of the circle is 108 degrees.

An angle is a geometric figure that is formed by two rays that share a common endpoint, which is called the vertex of the angle. The rays are referred to as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees.

Angles can be classified based on their degree of measurement: acute angles are less than 90 degrees, right angles are exactly 90 degrees, obtuse angles are greater than 90 degrees but less than 180 degrees, and straight angles are exactly 180 degrees.

Since a full circle has 360 degrees, 3/10 of the circle can be represented as:

(3/10) x 360 degrees = 108 degrees

Therefore, the measure of the angle that turns through 3/10 of the circle is 108 degrees.

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The complete question is :

The angle turns through 3/10 of the circle. What is the measure of the angle?

Based on the question, Xavier earned a commission of $270 on the last week.

Commissions is known to be a form of variable-pay remuneration that is said to be made for services given or products sold.

Note that from the question, Xavier earns a 15% commission on all washing machine he sells, so he sold four $450 machines last week.

So, the he total sale of the four machines is:

4 x $450 = $1,800

Since Xavier's commission is 15% of $1,800, it will be calculated as :

Commission = 15% x $1,800

                  = 0.15 x $1,800

                     = $270

Hence, Xavier earned a commission of $270 last week.

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The circumference of a circle whose area is 20π cm² in terms of pi is 8.94π centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

[tex]\text{A} = \pi \text{r}^2[/tex]

The circumference of a circle is expressed mathematically as;

[tex]\text{C} = 2\pi \text{r}[/tex]

Given that the area of the circle is 20π cm², we determine the radius of the circle.

[tex]\text{A} = \pi \text{r}^2[/tex]

[tex]20\pi \ \text{cm}^2 = \pi \times \text{r}^2[/tex]

[tex]\text{r}^2= \dfrac{ 20\pi \ \text{cm}^2}{\pi }[/tex]

[tex]\text{r}^2 = 20 \ \text{cm}^2[/tex]

[tex]\text{r} = \sqrt{20 \ \text{cm}^2}[/tex]

[tex]\text{r} = 4.47 \ \text{cm}[/tex]

Now, we determine the circumference of the circle.

[tex]\text{C} = 2\pi \text{r}[/tex]

[tex]\text{C} = 2 \times \pi \times 4.47 \ \text{cm}[/tex]

[tex]\text{C} = 8.94 \ \text{cm}\times\pi[/tex]

[tex]\text{C} = 8.94\pi[/tex]

Therefore, the circumference of the circle is 8.94π centimeters.

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The area of each triangle to the nearest square inch is approximately 95 square inches.

A triangle is a 2-dimensional geometric shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry, and it is widely used in various fields such as mathematics, engineering, architecture, and art.

To find the area of an equilateral triangle with a radius of 12.7 inches, we can use the formula:

Area = [tex](\sqrt{(3)/4})[/tex] x [tex](side)^2[/tex]

where side is the length of one of the sides of the equilateral triangle.

We know that the radius of the equilateral triangle is 12.7 inches, which means that the distance from the center of the triangle to one of the corners (i.e., the length of one of the sides) is also 12.7 inches. To find the length of the side, we can use the formula for the height of an equilateral triangle:

and solve for side:

side = Height / ([tex]\sqrt{(3)/2[/tex]) = (2 x Height) / [tex]\sqrt{(3)[/tex]

Plugging in the value of the radius, we have:

side = (2 x 12.7 inches) / [tex]\sqrt{(3)[/tex] ≈ 14.67 inches

Now we can use the formula for the area of an equilateral triangle:

Area = ([tex]\sqrt{(3)/4}[/tex]) x [tex](side)^2[/tex]

Plugging in the value of the side, we have:

Area = ([tex]\sqrt{(3)/4[/tex]) x [tex](14.67 inches)^2[/tex] ≈ 94.71 square inches

Therefore, the area of each triangle to the nearest square inch is approximately 95 square inches.

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If Joan has a square flower bed with a side length of 4 meters filled with tulips, the density of tulips in the bed is 22.1 tulips per square meter.

To find the density of tulips for the area of the bed, we need to divide the total number of tulips by the area of the bed. The area of the square flower bed is the side length squared, so in this case, it is 4 meters x 4 meters = 16 square meters.

So, the density of tulips in the bed is 354/16 ≈ 22.1 tulips per square meter. This means that there are approximately 22.1 tulips growing in every square meter of the flower bed.

The density is a measure of the amount of something per unit of space, so in this case, it is the number of tulips per square meter. It is a useful metric for understanding how many of something is present in a given area, which can be important for planning and management purposes.

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It can be found by graphing the points given and sketching the parabola. Another point on the graph is (-1, 9) that passes through them. You can move over and up from the vertex and do the same on the opposite side of the line x = -1.

In Mathematics and Geometry, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided, the vertex is located at point (2, 0), and this ultimately implies that the axis is represented by the vertical line x = 2 that passes through the vertex.

Additionally, the parabola would be bilaterally symmetric about the above axis, and the mirror image of the point (5, 9) would also be on this parabola.

Therefore, the mirror image would have the same y-coordinate of 9 while the x-coordinate is given by:

x = 2 - (5 -2)

x = -1.

In conclusion, the required point is (-1, 9).

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Complete Question:

The graph of a quadratic function has a vertex (2, 0). One point on the graph is (5, 9). Explain how to find another point on the graph. It can be found by graphing the points given and sketching the parabola. Another point on the graph is (-1, _) that passes through them. You can move over and up from the vertex and do the same on the opposite side of the line x=

After making six monthly payments on her car loan, Ms. Hughes's savings account balance will decrease by $1,470.

To find the change in Ms. Hughes's savings account balance each month due to her car payment, we can divide the total change in balance for the year ($-2,940) by the number of months in a year (12):

Change in savings account balance each month = $2,940 / 12 = -$245

So, Ms. Hughes's savings account balance decreases by $245 each month due to her car payment.

To find the total change in Ms. Hughes's savings account balance after making six monthly payments on her car loan, we can multiply the change in savings account balance each month by the number of months (6):

Total change in savings account balance after six monthly payments = -$245 * 6 = -$1,470

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Answer:

the area is 49m² this because for area you have to mutiple

Step-by-step explanation:

7×7=49

The graph of the piecewise function can be seen in the image attached below where (x+2)² terminates at x = -1,  |x - 1| between the interval of x = -1 to x = 1, and  [tex]-\sqrt[3]{x}[/tex] from +x-axis to infinity [tex]\infty[/tex]

A piecewise function is a type of function that has different expressions or formulas for different parts or intervals of its domain. This means that the formula that defines the function changes depending on which part of the domain we are looking at.

Now, to graph the piecewise function, we need to start by identifying the different intervals on which the function is defined and the corresponding expressions that define the function on each interval.

If we have a piecewise function f(x) defined as:

The graph of the piecewise function can be seen in the image attached below.

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Answer:

  2. 139π/90 radians ≈ 4.852

  3. -(9√5 +8√7)/77

  4. 2+√3

Step-by-step explanation:

You want exact answers involving various trig identities and angle sum formulas.

There are π radians in 180°, the number of radians in 278° is ...

  278°(π/180°) = (278/180)π

  278° = (139/90)π radians ≈ 4.852 radians

The cosine of the sum of angles is ...

  cos(x +y) = cos(x)cos(y) -sin(x)sin(y)

The relationship between sine and cosine is ...

  cos(x) = ±√(1 -sin(x)²)

  sin(x) = ±√(1 -cos(x)²)

The signs will depend on the quadrant of the angle.

To use the angle sum relation, we need the sine of the angle whose cosine is given, and vice versa.

  sin(arccos(-2/7)) = -√(1 -(-2/7)²) = -(√45)/7 = (-3/7)√5 . . . . in QIII

  cos(arcsin(-3/11)) = √(1 -(-3/11)²) = (√112)/11 = (4/11)√7 . . . . in QIV

The cosine of the sum of the angles is then ...

  cos(arccos(-2/7) +arcsin(-3/11)) = (-2/7)(4√7/11) -(-3√5)/7·(-3/11)

  = -8√7/77 -9√5/77

  cos(x +y) = -(9√5 +8√7)/77

The formula for the tangent of the sum of angles is ...

  tan(x +y) = (tan(x) +tan(y))/(1 -tan(x)tan(y))

We know that tan(π/4) = 1 and tan(π/6) = 1/√3, so the tangent of the sum of the angles is ...

  tan(π/4 +π/6) = (1 +1/√3)/(1 -(1·1/√3)) = (√3 +1)/(√3 -1) = (√3 +1)²/2

  tan(π/4 +π/6) = 2 +√3

__

Additional comment

A suitable calculator can be very handy computing and/or checking your results.

2) 278° to Radians = 4.85202

3) the exact value of cos (x+ y) is -0.0914

4) the exact value of the expression is 3.73

The formula ofr conversion from degree to radian is

2) 278° × π/180 = 4.852rad

3) in the above given expressions, Sin(x) is negative.

Using Pythagorean rule, we can state:

sin(x ) = √(1 - cos^2(x)) =

√(1 - (-2/7)²)

= -3√(3)/7

Also,

given that cos( y) is positive, we c  n also use the Pythagorean idetity

cos  (y) = √(1 - sin ²(y) )

= √(1 - (-3/1 1)²)

= 8√(2)/11

substituting into cos (x + y)


cos(x+y) = cos(  x)cos (y ) - sin (x) sin(y)

= (-2/7)( 8 √(2)/11) - (-3√(3)/7) ( -3/11)

= -1 6 √(2) /77 + 9√( 3)/ 77

= -0.09141506142

The exact value is approximately -0.0914

3)

Using the formula for tangent of sum of angles we say

tan( ( π/4) + (π/6) )   = (tan ( π / 4) + tan (π/6))/(1 - tan ( π/4) tan( π/6))

Sutstituting ....

tan ((  π/4) + ( π/6) )  = (1 + √ 3/3)/( 1 - √ 3 /3 )

tan( (π/ 4) + (π /6 )) =   (1 + √3/   3) (1 + √3/3 )]/ [(1 - √3/ 3)(1 + √3/3)]

Simplifying

  tan ( (π /4) + ( π/6) ) = ( 2 + √3 )/  ( 2 - √ 3)

This is the exact value of tan((π/4) + (π/6)) or 3.73

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The three numbers are 10, 20, and 40.'

Let's assign variables to each number:

According to the problem, the sum of these three numbers is 70:

x + y + z = 70

Now, we can substitute the expressions for y and z in terms of x:

x + 2x + 2(2x) = 70

Combine the terms:

x + 2x + 4x = 70

7x = 70

Now, divide by 7 to find the value of x:

x = 70 / 7

x = 10

Now that we have the value of x, we can find the values of y and z:

y = 2x = 2(10) = 20

z = 2y = 2(20) = 40

So, the three numbers are 10, 20, and 40.

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The question in English is

The sum of 3 numbers is 70, the second number is twice the first and the third is twice the second.

The polar coordinates of the point (17,0) are (r,θ) = (17,0). This means that the point is located on the positive x-axis, at a distance of 17 units from the origin.

To find the polar coordinates of a point given in rectangular coordinates, we need to use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin and the point.

In this case, the point is (17,0), so x = 17 and y = 0. Using the formulas above, we get:

r = √(17² + 0²) = 17θ = tan⁻¹(0/17) = 0

In polar coordinates, a point is represented by an ordered pair (r,θ), where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin and the point, measured in radians.

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The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

We have,

Assuming that the probability of a child being born with the disease is independent of whether or not their siblings are born with the disease, we can use the multiplication rule of probability:

P(all 3 children have the disease)

= P(first child has the disease) x P(second child has the disease) x P(third child has the disease)

Since each child has a 57% chance of being born with the disease:

P(all 3 children have the disease)

= 0.57 x 0.57 x 0.57

Now,

P(all 3 children have the disease)

= 0.195

Therefore,

The probability that all 3 children will be born with the disease is approximately 0.195 or 19.5%.

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Answer:

y=(x+8)^2/6 - 5/2

Step-by-step explanation:

Khan Academy

Answer: The first number is the X-axis and the second is the Y-axis.

Step-by-step explanation:

5, 1, 4, and 2 belong in X. 35, 7, 28, and 14 belong in Y.

The rule is that X always goes first the Y goes after.

a. 4. b > 0

If b is positive, then we know it will be greater than 0.

b. 1. s ≤ 0

If s is nonpositive, this means it is negative or 0. We will use a less than or equal to symbol.

c.  3. w ≥ -8

If w is greater than or equal to -8, we will use a greater than or equal to symbol.

The equation x = 1/16y² - 1/8y + 17/16 in conic form is (y - 1)² = 16(x - 1)

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

x = 1/16y² - 1/8y + 17/16

Multply through the equation by 16

S, we have

16x = y² - 2y + 17

Rewrite as

16x - 17 = y² - 2y

Add the square of half the coefficient of y to both sides

So, we have

16x - 17 + 1 = y² - 2y + 1

Evaluate and express as perfect squares

16x - 16 = (y - 1)²

Factor out 16

16(x - 1) = (y - 1)²

Rewrite as

(y - 1)² = 16(x - 1)

The above equation is an equation of a parabola whose inverse has been calculated

Hence, the conic equation is (y - 1)² = 16(x - 1)

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The calculated measure of the arc XYZ is 83 degrees

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

The circle

The angles created by secants and tangents that intersect outside a circle, which states that

The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.

So, we have

XYY = 1/2 * (166 - 0)

Evaluate

XYY = 83

Hence, the measure of the angle is 83 degrees

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Answer:0.125

Step-by-step explanation:

Answer: b, c, d,

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