The total of miles mark ran last week is 10.75 miles.
We have the dot plot.
So, the total number of miles Mark ran
= 1 1/4 x 1 + 2 x 2 + 2 2/4 x 1 + 3 x 1
= 5/4 x 1 + 4 + 10/4 x 1 + 3
= 5/4 + 4 + 10/4 + 3
= 15/4 + 7
= 15/4 + 28/4
= 43/4
= 10 3/4
= 10.75
Thus, the total number of miles Mark ran is 10.75 miles.
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Use the image to determine the line of reflection.
An image of polygon VWYZ with vertices V at negative 9, 1, W at negative 9, negative 1, Y at negative 3, negative 1, and Z at negative 3, 1. A second polygon V prime W prime Y prime Z prime with vertices V prime at 7, 1, W prime at 7, negative 1, Y prime at 1, negative 1, and Z prime at 1, 1.
Reflection across y = 1
Reflection across x = −1
Reflection across the x-axis
Reflection across the y-axis
The line of reflection is the line y = 0, which is the x-axis.
To see this, imagine folding the image of polygon VWYZ along the x-axis so that the top vertex, V, is reflected down to its corresponding point, V'. Similarly, W is reflected up to W', Y is reflected up to Y', and Z is reflected down to Z'. This produces the image of polygon V'W'Y'Z', which is the reflection of polygon VWYZ across the x-axis.
When reflecting a shape across a line, the line of reflection is the line that serves as the "mirror" for the shape. In this case, the given polygons VWYZ and V'W'Y'Z' are related by a reflection. By examining the vertices of the polygons, we can determine the line of reflection. The x-coordinates of the corresponding vertices are the same, which suggests that the line of reflection is vertical.
However, the y-coordinates are opposites, indicating that the line of reflection is actually the x-axis. Therefore, the reflection of polygon VWYZ onto polygon V'W'Y'Z' is achieved by folding the image along the x-axis so that each vertex is reflected across the x-axis to its corresponding point in the other polygon.
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Answer:
Reflection across x = −1
Step-by-step explanation:
Took test it's right!
QRST is a square inscribed is in O. The radius of O is 4.
30). Find the area of the circle.
31). Find the area of the square.
32). Find the area of the shaded region.
The area of the circle is 50.24.
The area of the square is 32.
The area of the shaded region is 18.24.
We have,
From the figure,
Area of the circle.
= πr²
Radius = 4
So,
= 3.14 x 4 x 4
= 50.24
In the triangle QST,
TS and TQ are congruent.
TS = TQ = x
QS = 8
This means,
From the Pythagorean theorem,
8² = x² + x²
64 = 2x²
x² = 32
x = √(16 x 2)
x = 4√2
Area of the square.
= Side²
Side = x = 4√2
= (4√2)²
= 16 x 2
= 32
Now,
Area of the shaded region.
= Area of the circle - Area of the square
= 50.24 - 32
= 18.24
Thus,
The area of the circle is 50.24.
The area of the square is 32.
The area of the shaded region is 18.24.
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Use the triangles below to find the missing length o segment TU.
Answer: 16
Step-by-step explanation:
I am not sure if this answer is 100% correct, but I believe this is a question involving proportions.
If you create a proportional equality equation that looks like this:
[tex]\frac{40}{30}=\frac{x}{12}[/tex]
It will give the x value as the answer to the problem. This is because the two triangles are proportional to one another.
what is the possibility of getting 9 heads out of 15 tries, flipping a coin?
The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.
We have,
The probability of getting a head or a tail when flipping a fair coin.
= 1/2 or 0.5
Assuming the coin is unbiased and each flip is independent of the previous flips.
To find the probability of getting 9 heads out of 15 tries, we need to use the binomial probability formula:
= P(9 heads out of 15 tries)
= [tex]^{15}C_9[/tex] x (0.5)^9 x (0.5)^6
Now,
P(9 heads out of 15 tries)
= 5005 x (0.5)^9 x (0.5)^6
= 0.19638 (rounded to five decimal places)
Thus,
The probability of getting exactly 9 heads out of 15 tries when flipping a fair coin is approximately 0.19638 or about 19.64%.
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. A corner shelf is in the shape of a triangle. One side measures while another side measures . What is the total of two sides? Show all work. If the perimeter measures , what is the length of the missing side? Show all work. If we know that then what are the lengths of the three sides of the triangle? Show all work. Is it possible to have these side lengths? Why or why not?
The three sides of the triangle are a, b, P - (a + b)
The length of the missing side, and the lengths of all three sides of a triangular corner shelf.
Given that one side of the triangular shelf measures "a" units and another side measures "b" units, we can find the total of two sides by adding them together:
a + b = total of two sides
If the perimeter of the triangle measures "P" units, we know that the perimeter is the sum of all three sides, so:
a + b + c = P
where "c" is the length of the missing side. We can rearrange this equation to solve for "c":
c = P - a - b
To find the lengths of all three sides of the triangle, we can substitute the value of "c" that we just found into the Triangle Inequality:
a + b > P - a - b
Simplifying this inequality, we get:
2a + 2b > P
Dividing both sides by 2, we get:
a + b > P/2
So, if "a + b > P/2", then the triangle can exist, and we can use the value of "c" that we found earlier to get the lengths of all three sides:
a + b + c = P
a + b + (P - a - b) = P
c = P - (a + b)
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An event lasts 3 hours and 15 minutes. How long did the event last in seconds? 2,700
The event lasted for 11,700 seconds.
Time is an essential concept that we use to measure the duration of events. In this context, let's consider an event that lasts for 3 hours and 15 minutes.
To convert time from hours and minutes to seconds, we need to know the number of seconds in an hour and a minute.
There are 60 minutes in an hour, and each minute has 60 seconds.
=> (3 x 60 x 60) = 10,800
=> 15 x 60 = 900
To find the total time of the event, we need to add the time in seconds for the hours and minutes, which is
=> 10,800 seconds + 900 seconds = 11,700 seconds.
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Could someone summarize the importance and purpose of the unit circle in Geometry i have a test coming up and im stressed bceause the unit circle feels simple but i dont get it
An important concept of unit circle in geometry and trigonometry is it helps us to understand and visualize the values of sine, cosine, and tangent functions for different angles.
The unit circle is a circle with a radius of 1 unit, centered at the origin of a coordinate plane.
The coordinates of points on the unit circle correspond to the values of sine and cosine of the corresponding angle.
For example, if we draw a line from the origin to a point on the unit circle that makes an angle of θ with the positive x-axis.
The x-coordinate of that point is cos(θ) and the y-coordinate is sin(θ).
The unit circle is also useful for understanding and visualizing the properties of periodic functions, such as sine and cosine.
Since sine and cosine are periodic with a period of 2π, the unit circle repeats itself every 2π radians or 360 degrees.
Which makes it easier to analyze and graph these functions.
In addition, the unit circle helps us understand the relationships between trigonometric functions.
Pythagorean identity (sin²(θ) + cos²(θ) = 1) is a fundamental relationship that is easy to see and prove using the unit circle.
Overall, the unit circle is an important concept that provides a visual and geometric representation of trigonometric functions and their properties.
It can be a useful tool for solving problems in geometry and trigonometry.
As well as for understanding more advanced concepts in calculus and other branches of mathematics.
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Are these two cylinders similar? The diagrams are not drawn to scale.
well the first cylinder is small the other is big and if this dosent help i'm so very sorry
It is now 2016. Mouse, Inc., a calendar year S corporation, is owned equally by four shareholders: Mickey, Minney, Topolino, and Topolina. The corporation owns investment land that was purchased for 345,000 four years ago. On September 6 of the current year, when the land is worth $510,000, it is distributed to Topolino.
Assuming that Topolino's basis in his S corporation stock is $470,000 immediately before the distribution. What is Topolino's basis in the corporation's stock immediately after the distribution?
Select one:
a.
$125,000
b.
($40,000)
c.
$1,250
d.
$0
As it was a non-liquidating distribution of investment land worth $510,000 to Topolino, it reduces his stock basis by the same amount, resulting in a negative basis of ($40,000) after the distribution. The answer is (b) ($40,000).
The distribution of the investment land with a fair market value of $510,000 to Topolino is a non-liquidating distribution, which means that it reduces Topolino's stock basis by the amount of the distribution ($510,000).
Topolino's basis in the stock immediately after the distribution will be the sum of his basis in the stock before the distribution ($470,000) minus the amount of the distribution ($510,000), which results in a negative basis of ($40,000). The correct answer is (b) ($40,000).
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a car dealer offers you a choice of 0% financing for 60 months or 2500 cash back on a new vehicle. You have a pre-approved 60 month loan you can use from your credit union at a 4% interest rate. f the monthly payments at 0% are 16.67 per 1000 financed, and the monthly payments at 4% are 18.41 per 1000 financed, what is the range of new car prices for which the cash back option will cost you less? For what range of car prices should you take the 0% financing?
Answer:
To determine the range of car prices for which the cash-back option will cost less, we need to find the total cost of each option over 60 months for different car prices and compare them. Let's assume the car price ranges from $20,000 to $30,000.
For the 0% financing option, the monthly payment is $16.67 per $1,000 financed, so the monthly payment for a car priced at $20,000 would be:
$20,000 / 1000 * $16.67 = $333.40 per month
Similarly, the monthly payment for a car priced at $30,000 would be:
$30,000 / 1000 * $16.67 = $500.10 per month
Over 60 months, the total cost for the 0% financing option for a car priced at $20,000 would be:
$333.40 * 60 = $20,004
And the total cost for a car priced at $30,000 would be:
$500.10 * 60 = $30,006
For the cash-back option, the cost of the car would be reduced by $2,500, so the total cost over 60 months for a car priced at $20,000 would be:
($20,000 - $2,500) + ($18.41 * $20) * 60 = $19,484
And the total cost for a car priced at $30,000 would be:
($30,000 - $2,500) + ($18.41 * $30) * 60 = $29,222
To find the range of car prices for which the cash back option will cost less, we need to compare the total cost of each option. Setting the two equations equal to each other and solving for x, we get:
($x - $2,500) + ($18.41 * $x) * 60 < $20,004
($x - $2,500) + ($18.41 * $x) * 60 > $30,006
Simplifying, we get:
$17.285x < $22,504
$17.285x > $34,256
Dividing by 17.285, we get:
$1,300.90 < x < $1,978.63
So, for car prices between $13,000.90 and $19,978.63, the cash-back option will cost less.
To find the range of car prices for which the 0% financing option is a better choice, we can simply look at the range of car prices for which the cash-back option is more expensive, which is anything outside of the range of $13,000.90 to $19,978.63. Therefore, for car prices outside of this range, the 0% financing option is the better choice.
Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
To solve the equation (x - 3)^2 = 49, we can take the square root of both sides to eliminate the exponent of 2. However, when taking the square root, we need to consider both the positive and negative square roots.
(x - 3)^2 = 49
Taking the square root of both sides, we get:
√((x - 3)^2) = ±√49
Simplifying, we get:
x - 3 = ±7
Adding 3 to both sides, we get:
x = 3 ± 7
So the possible values of x are:
x = 3 + 7 = 10
x = 3 - 7 = -4
Therefore, the correct values of x are -4 and 10. The options given are -46, -4, 10, and 52. So the correct values of x from the options are -4 and 10.
Answer:
-4 and 10.
Step-by-step explanation:
14. A 20 ft ladder leans against a wall. The ladder hits the wall at a height of 16 ft above the ground.
Find the angle of elevation. Include a sketch. Round to the nearest tenth.
The angle of elevation is 53.1( nearest tenth)
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. Trigonometric ratio is mainly used to solve problems in this case.
A 20ft ladder leans against the wall, the height of the wall will be the opposite to angle of elevation and the height of the ladder will be the hypotenuse.
Therefore using trigonometry ratio;
sin( tetha) = opp/hyp
sin(tetha) = 16/20
sin(tetha) = 0.8
tetha = sin^-1(0.8)
tetha = 53.1°( nearest tenth)
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In a Godiva shop, 40% of the cookies are plain truffles,
20% are black truffles, 10% are cherry cookies, and 30%
are a mix of all the others. Suppose you pick one at ran-
dom from a prepacked bag that reflects this composition.
a. What is the probability of picking a plain truffle?
b. What is the probability of picking truffle of any kind?
c. If you instead pick three cookies in a row, what is
the probability that all three are black truffles?
PLEASE HELP THANK YOU HURRY FAST
The zeros of a polynomial function are given as,
x= 1 , x= 2, x= 3 and x= -3
Let the polynomial in standard form be,
y = ( x- 1)(x - 2)(x - 3)(x +3)
⇒ y = (x² - 2x - x +2)( x² - 3x +3x - 9)
⇒ y = (x² - 3x +2)(x² - 9)
⇒ y = x⁴ - 9x² - 3x³ + 27x + 2x² - 18
⇒ y = x⁴ - 3x³ -7x² + 27x -18
Hence option c is the correct answer.
The given cubic equation is ,
x³ +6x² +11x +6 = 0
Calculating its roots we get,
x³ +6x² +11x +6 = 0
⇒ (x +1)( x+2 )(x+ 3) = 0
Thus the roots are -1, -2, and -3
Hence all the roots are real and are of different values.
Hence option d is the correct option.
The given radical expression can be simplified as,
[tex]\sqrt[4]{625 x^8 y^{12} }[/tex] = 5[tex]x^{2} y^3[/tex]
Hence option a is the correct option.
We can simplify the given expression as,
[tex]27^{1/3}[/tex] = ∛27 = ∛(3³) = 3
Hence option d is the correct option.
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Please answer this Calculus webwork question about differential equations:
Answer:
a)
[tex]4ydy = xdx[/tex]
[tex]2 {y}^{2} = \frac{1}{2} {x}^{2} + c[/tex]
[tex] {y}^{2} = \frac{1}{4} {x}^{2} + c [/tex]
[tex] {y}^{2} - \frac{1}{4} {x}^{2} = c [/tex]
b)
c = 4, so
[tex] {y}^{2} = \frac{1}{4} {x}^{2} + 4[/tex]
[tex]y = - \sqrt{ \frac{1}{4} {x}^{2} + 4} [/tex]
[tex]y = - \frac{ \sqrt{ {x}^{2} + 16} }{2} [/tex]
How many minutes are in 2/4 of an hour
There are 30 minutes in [tex]\frac{2}{4}[/tex] of an hour.
To find the no. of minutes in an hour we can multiply the no. of hours by 60. Suppose to find the no. of minutes in an hour we can simply multiply 1 by 60 so we can get 60 minutes in an hour.
Similarly to find the no. of minutes are in [tex]\frac{2}{4}[/tex] of an hour we can multiply the [tex]\frac{2}{4}[/tex] by 60 to get the required minutes.
[tex]\frac{2}{4}[/tex] × 60 = [tex]\frac{1}{2}[/tex] × 60 = [tex]\frac{60}{2}[/tex] = 30.
So, from the above explanation, we can conclude that there will be 30 minutes in the [tex]\frac{2}{4}[/tex] of an hour.
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5/3 divided by 7 (answer as a fraction)
Answer: 5/21
Step-by-step explanation: it just is
the answer is 5/21 (0.23)
FLOWER Delfina photographed a triangular flower for a photo contest. The flower was approximately regular and had
side lengths measuring about 4 centimeters. What is the area of the flower? Round your answer to the nearest
tenth.
Answer:
8 centimeters squared.
Step-by-step explanation
This is just me assuming flower was flat???
The triangle was regular, so it measured 4 by 4 by 4. Triangle formula is 1/2bh.
1/2bh
1/2*4*4
2*4
8
PLEASE HELP THANK YOU HURRY FAST
1) Polynomial of 4 terms.
2) The rational roots of the function are,
x = - 2, 1
3) The zeroes of the function are,
x = - 2, - 3, 2
4) The zeroes of the function are,
x = 1, - 1, 2i, - 2i
5) The correct function which shows the cubic equation is, option 1.
We have to given that;
1) Function is,
⇒ 3x⁵ + 5x⁴ - 7x³ + 15
Clearly, There are 4 terms in function.
Hence, Polynomial of 4 terms.
2) Function is,
⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0
The correct rational roots are satisfy the function,
Hence, We get;
Plug x = 1,
⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0
⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0
⇒ 0 = 0
Plug x = - 2;
⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0
⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0
⇒ 0 = 0
Thus, The zeroes of the function are,
x = - 2, 1
3) Function is,
⇒ y = (x + 3) (x + 2) (x - 2)
Hence, The zeroes of the function are,
x = - 3
x = - 2
x = 2
4) Function is,
⇒ 3x² - 4 = - x⁴
⇒ x⁴ + 3x² - 4 = 0
⇒ x⁴ + 4x² - x² - 4 = 0
⇒ x² (x² + 4) - 1 (x² + 4) = 0
⇒ (x² - 1) (x² + 4) = 0
⇒ x² - 1 = 0
⇒ x² = 1
⇒ x = ±1
⇒ x² + 4 = 0
⇒ x² = - 4
⇒ x = ±2i
Hence, The zeroes of the function are,
x = 1, - 1, 2i, - 2i
5) By given graph the correct function which shows the cubic equation is, Option 1.
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Evaluate the expression below when x = 1/2 and y = 4.
[tex] \frac{4x + 6}{8y} [/tex]
When x = 1/2 and y = 4, the value of the expression (4x + 6)/8y is 1/4.
We have,
The expression is (4x + 6)/8y.
Substituting x = 1/2 and y = 4 in the given expression.
= (4x + 6)/8y
= (4(1/2) + 6)/8(4)
= (2 + 6)/32
= 8/32
= 1/4
Therefore,
When x = 1/2 and y = 4, the value of the expression (4x + 6)/8y is 1/4.
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Ramon spent $1 more on peach snack packs than on apple snack packs. Is that True or False
Answer:
True
Step-by-step explanation:
Peach snack packs averagely cost more than apple snack packs so a reasonable solution can be P is greater than A
Select the correct answer from each drop-down menu.
sin 75°+ sin 15° =
sin 75°
sin 15° =
-
t
The values of the given problems are:
sin(75°) + sin(15°) ≈ 1.22sin(75°) - sin(15°) ≈ 0.71How to solveUsing angle sum and difference identities, we can calculate:
sin(75°) = sin(45°)cos(30°) + cos(45°)sin(30°)
sin(15°) = sin(45°)cos(30°) - cos(45°)sin(30°)
Then, we find:
sin(75°) + sin(15°) =
[sin(45°)cos(30°) + cos(45°)sin(30°)] + [sin(45°)cos(30°) - cos(45°)sin(30°)]
≈ 1.22
sin(75°) - sin(15°) =
[sin(45°)cos(30°) + cos(45°)sin(30°)] - [sin(45°)cos(30°) - cos(45°)sin(30°)]
≈ 0.71
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The Complete Question
Select the correct answer from each drop-down menu.
sin75° +sin15°=
sin75°-3in15º =
Each graph below was obtained by transformation(s) of the graph of the cubic function. Write the equation for the function each graph represents.
Correct answer gets brainliest !
Answer:
First graph:
y + 7 = C((x + 5)^3)
-3.8 + 7 = C(4^3)
3.2 = 64C, so C = .05
y = .05((x + 5)^3) - 7
Second graph:
y - 38.45 = C((x + 5)^3)
2 - 38.45 = C(4.5^3)
-36.45 = 91.125C
C = -.4
y = -.4((x + 5)^3) + 38.45
please help me answer this
Answer:
it's 0
Step-by-step explanation:
I don't know it's answer you have to ask it to the teacher
Examine the figure of two parallel lines cut by a transversal.
One interior angle has a measure of 2 x plus 10 degrees; its same-interior angle has a measure of 2 x minus 30 degrees.
What is the value of x?
The value of x is 50° from the given set of parallel lines.
Give that, two parallel lines cut by a transversal.
The interior angles are (2x+10)° and (2x-30)°.
Here, (2x+10)°+(2x-30)°=180° (Sum of co-interior angles is 180°)
4x-20=180
4x=200
x=200/4
x=50°
Therefore, the value of x is 50° from the given set of parallel lines.
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g(t)=−(t−1)
2
+5g, left parenthesis, t, right parenthesis, equals, minus, left parenthesis, t, minus, 1, right parenthesis, squared, plus, 5
What is the average rate of change of
�
gg over the interval
−
4
≤
�
≤
5
−4≤t≤5minus, 4, is less than or equal to, t, is less than or equal to, 5?
The average rate of change over is 1.
Given that;
the function is,
⇒ g (t) = - (t - 1)² + 5
Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.
The value of G(-4):
The value of G(-4) can be determined by substituting t = -4 in the function
⇒ g (t) = - (t - 1)² + 5
Thus, we have,
⇒ g (t) = - (-4 - 1)² + 5
⇒ g (t) = - 20
Thus, the value of G(-4) = -20
The value of G(5):
The value of G(5) can be determined by substituting t = 5 in the function , we get,
⇒ g (t) = - (t - 1)² + 5
⇒ g (t) = - (5 - 1)² + 5
⇒ g (t) = - 11
Thus, the value of G(5) is, -11
Now, Average rate of change:
The average rate of change can be determined using the formula,
⇒ G(b) - G (a) / (b - a)
where, a = - 4 and b = 5
Substituting the values, we get,
⇒ G(5) - G (-4) / (5 - (-4))
⇒ ( - 11 - (- 20)) / 9
⇒ 9/9
⇒ 1
Thus, the average rate of change over the interval is. 1.
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Given the point with Cartesian coordinates, (−7√3/2,7/2), find the polar coordinates of the point.
Select the correct answer below:
(7,4π/3)
(7,11π/6)
(3,4π/3)
(3,5π/6)
(3,11π/6)
(7,5π/6)
Answer: the last option is correct
Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
where x and y are the Cartesian coordinates, 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 to the point.
Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:
r = √((-7√3/2)^2 + (7/2)^2)
θ = atan2(7/2, -7√3/2)
Simplifying the expressions:
r = √(147/4 + 49/4) = √(196/4) = √49 = 7
θ = atan2(7/2, -7√3/2)
Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:
θ ≈ 5π/6
So the correct answer is: (7, 5π/6), which is option (6).
Please help
Francisca and Elizabeth are participating in a walk-a-thon fundraiser. Each girl walks for 3 hours. How much will the raise together
Francisca $ 25.50 every 1/2 hour
Elizabeth is $ 14.50 every 1/4 hour
Answer:
327
Step-by-step explanation:
To calculate how much Francisca and Elizabeth will raise together, we need to know how many laps or miles they walked. Unfortunately, the problem doesn't provide us with that information.
However, we can calculate how much each girl will raise individually.
Francisca will walk for 3 hours which is equal to 6 half-hours. She raises $25.50 every half-hour so she will raise:
$25.50 x 6 = $153
Elizabeth will walk for 3 hours which is equal to 12 quarter-hours. She raises $14.50 every quarter-hour so she will raise:
$14.50 x 12 = $174
Therefore, Francisca and Elizabeth will raise a total of:
$153 + $174 = $327
in how many ways can four boys and three girls be seated in a row containing seven seats if all three girls are together?
My last problem and i Can be done
Answer:
x = 21.1
y = 18.3
Step-by-step explanation:
left triangle right triangle large triangle
Short leg: 12 altitude y
Long legs: altitude 16 x
Hypotenuse: y x 28
The three triangles are similar, so the ratios of the lengths of corresponding sides are equal.
hypotenuse/short leg
28/y = y/12
y² = 12 × 28
y² = 336
y = 18.3
hypotenuse/long leg
28/x = x/16
x² = 28 × 16
x² = 448
x = 21.1