Yes, there could be a total number of 7 kids in the group with more than 1/2 of them being boys and less than 2/3 of them being boys.
Let's assume that the total number of kids in the group is x.
According to the problem, more than 1/2 of the group are boys. Mathematically, we can represent this as:
Number of boys > x/2
Also, the boys are less than 2/3 of the group. Mathematically, we can represent this as:
Number of boys < 2x/3
Now, let's substitute x=7 in the above two equations:
Number of boys > 7/2 = 3.5 --- (1)
Number of boys < 14/3 ≈ 4.67 --- (2)
From equation (1), we can conclude that there must be at least 4 boys in the group.
From equation (2), we can conclude that there can be at most 4 boys in the group because the number of boys cannot be a fraction.
Therefore, the possible number of boys in the group could be either 4 or 3. If there are 4 boys, then the number of girls in the group would be 3. If there are 3 boys, then the number of girls in the group would be 4.
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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 1 unit wide.
There are [tex]18[/tex] square units in the area of the shaded rectangle.
What makes it a rectangle?The Latin words "rect" (which means "right") and "angulus" (which means "angle") are the roots of the English word "rectangle." These two words together form the term "rectangle." A rectangle has 90° straight angles at each of its four corners. A rectangular also has two equal-length diagonals that meet in the centre.
What other name does rectangle go by?In addition to rectangles, we also refer to them as geometric figures, quadrilaterals, and polygons. This is so that it is clear that a rectangle fulfils the specifications of all of these other forms.
width [tex]= 7[/tex] units
length [tex]= 10[/tex] units
We remove the frame, each measure will lose[tex]2*2[/tex] units, or [tex]4[/tex] units
[tex]width = 7 units - 4 units = 3 units[/tex]
[tex]length = 10 units - 4 units = 6 units.[/tex]
[tex]A = (3 units)*(6 units) = 18[/tex] square units.
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The completed question is:
One rectangle is "framed" within another. Find the area of the shaded region if the
"frame" is 1 unit wide.
10
5
write the solution set of the given homogeneous system in parametric vector form. 2x1 + 2x2 + 4x3 = 0
-4x1 – 4x2 – 8x3 = 0
-3x2 – 9x3 = 0
[ x1 ]
Where the solution set is x = [ x2 ]
[ x3 ]
X = x3 _____
The solution set can be written in parametric vector form as: [tex]X = x3 [-1 0 1]^T + x2 [-2 1 0]^T[/tex]
How we get the solution of homogeneous system?We can rewrite the system of equations in matrix form as AX = 0, where [tex]A =[2 2 4]\\[-4 -4 -8]\\[0 -3 -9][/tex]
[tex]X = [x1 x2 x3]^T[/tex]
To solve for the solution set, we can row reduce the augmented matrix [tex][A|0].\\[2 2 4|0]\\[-4 -4 -8|0]\\[0 -3 -9|0][/tex]
[tex]R2 < - R2 + 2R1 and R3 < - R3 - 3R1[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 -3 -9|0][/tex]
[tex]R3 < - -1/3 R3[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
[tex]R1 < - R1 - R2[/tex] to obtain:[tex][2 2 4|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
[tex]R1 < - 1/2 R1 and R2 < - 1/2 R2[/tex] to obtain:[tex][1 1 2|0]\\[0 0 0|0]\\[0 1 3|0][/tex]
Therefore, the system has two free variables, x2 and x3, while x1 is a pivot variable. where x2 and x3 are arbitrary constants.
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Help meeeee pleaseee!
Using the given clues, we can fill out the table as follows:
Section Number Color
A 3 Green
B 5 Purple
C 9 Brown
D 8 Orange
E 1 Yellow
F 6 Blue
G 4 Pink
Completing the table of valuesUsing this information, we can deduce the values of each section:
The number 8 is in all shapes
So, D = 8
Number C is the largest
So, C = 9 because the numbers used are BETWEEN 0 and 10 i.e. 1 to 9Also, C = BrownFor the blue section, we have
F = Blue
For the triangle, we have
DEF = 48
D + E + F = 15
So, we have
EF = 6
E + F = 7
This means that
(E, F) = (1, 6) or (6, 1)
Number 1 is yellow
So, we have
E = 1 = YellowF = 6 = BlueSince F is not yellow, then
A = Green
A and G add up to 7, and A's number is smaller than G's.
So A and G must be (1, 6), (3, 4) because 2 and 7 are not used
Because of the values of E and F, we have
A = 3 and G = 4
Green and pink are in the rectangle only
So:
G = Pink
Purple and Orange are in the circle
So:
(B, D) = (Orange, Purple), (Purple, Orange)
The purple section is 5 and D = 8
So:
(B, D) = (Purple, Orange) = (5, 8)
The table has been completely filled
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The formula for the general term of 14,11,8,5,2
The formula for the general term of an arithmetic sequence is:
an = 14 - 3(n-1)
What do you mean by Arithmetic progression ?Arithmetic progression (AP) is a sequence of numbers in which each term after the first is obtained by adding a fixed constant value, called the common difference, to the preceding term. For example, 2, 4, 6, 8, 10, 12, 14... is an arithmetic progression with a common difference of 2. The formula for the nth term of an arithmetic progression is given by:
an = a1 + (n-1)d
The given sequence 14, 11, 8, 5, 2 is an arithmetic sequence with a common difference of -3.
The formula for the general term of an arithmetic sequence is:
an = a1 + (n-1)d
where:
an = the nth term of the sequence
a1 = the first term of the sequence
d = the common difference between consecutive terms
n = the position of the term we want to find
Using the values given in the sequence, we have:
a1 = 14
d = -3
To find the general term, we need to determine the value of n. Let's assume that the first term of the sequence corresponds to n = 1.
For the first term (n = 1):
a1 = 14
For the second term (n = 2):
a2 = a1 + d = 14 - 3 = 11
For the third term (n = 3):
a3 = a1 + 2d = 14 - 6 = 8
For the fourth term (n = 4):
a4 = a1 + 3d = 14 - 9 = 5
For the fifth term (n = 5):
a5 = a1 + 4d = 14 - 12 = 2
Therefore, the general term for the given sequence is:
an = 14 - 3(n-1)
or
an = 17 - 3n (Alternative form)
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sum1 help me please and asap put steps if possible
Answer:
8
Step-by-step explanation:
To find the length of the third side, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).
So, in this case, we have:
x^2 + 6^2 = 10^2
Simplifying this equation, we get:
x^2 + 36 = 100
Subtracting 36 from both sides, we get:
x^2 = 64
Taking the square root of both sides, we get:
x = 8 or x = -8
Since the length of a side of a triangle can't be negative, the length of the third side is x = 8 cm.
can you help me solve this e - 3.4 = 18.7
Answer:
evaluate: −0.68171817=18.7
Step-by-step explanation:
Gwen is making a circular garden that has a diamete of 10 feet. She is looking to buy fencing for the garden. How many feet if fencing will she need?
A spinner has five equal sections marked 1-5. What is the probability of not landing on four?
Answer: 4/5
Step-by-step explanation:
Five equal sides = 5
4 is just one side, so = 1
Not landing in 4 = 4/5
Answer: 4/5 or 80%
Step-by-step explanation:
Since the spinner has five equal sections, each numbered 1 through 5, the probability of landing on any particular number is 1/5.
To find the probability of not landing on 4, we need to add up the probabilities of landing on all the other numbers and subtract that sum from 1 (since the sum of all possible outcomes must equal 1).
The probability of landing on 4 is 1/5, so the probability of not landing on 4 is:
1 - 1/5 = 4/5
Therefore, the probability of not landing on 4 is 4/5 or 0.8, which is equivalent to an 80% chance.
Hope this helped!
this is a choose all that apply question
Answer: Option B
Step-by-step explanation:
A. The range of the ages are greater. This statement is false because in the box plot movies A, the range is 26 (subtract highest value from lowest value) which is not greater. Thus, this statement is false.
B. A smaller range normally means that there is a more consistent range. TRUE
C: The IQR, looking at the box plot, is much greater.
D: In Movie 2, the median ages of attendees are greater. False
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
What is inequality?Inequality refers to the state of being unequal, or not having equal access to resources, opportunities, or privileges. Inequality can manifest in many different ways, including but not limited to income inequality, wealth inequality, social inequality, gender inequality, racial inequality, and educational inequality.
Inequality can be caused by a variety of factors, including systemic discrimination, unequal distribution of resources, and societal structures that favor certain groups over others. It can have a significant impact on individuals and communities, leading to disparities in health, education, economic opportunities, and overall well-being. Addressing inequality requires a multifaceted approach that involves policies and initiatives aimed at promoting equal access to resources, opportunities, and rights for all individuals.
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
To solve the inequality3(8 – 4x) < 6(x – 5)[tex]3(8 - 4x) < 6(x – 5)[/tex], we first simplify both sides of the inequality:
[tex]3(8-4x) < 6(x -5)[/tex]
[tex]24 - 12x < 6x - 30[/tex]
[tex]54 < 18x[/tex]
[tex]3 < x[/tex]
So, the solution set for the inequality is x > 3. We represent this on a number line by placing an open circle at 3 and drawing a bold line pointing to the right to indicate all the values of x that satisfy the inequality. Therefore, the correct answer is:
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
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Answer:
it's 3
Step-by-step explanation:
How do -4.1 and -3 1/2 compare?
Step-by-step explanation:
you have to subtract them which would be -1.05
James returned home from a trip and opened the door if m<1 is 46 what is the measure of its complementary angle
A. 44
B. 54
C. 134
D. 224
A group of friends worked together at a lemonade stand. They earned $8.00 in all. Each friend was paid 20% of the total earnings. How much did each friend earn?
Answer: i would say $1.60 because 20% of $8.00 is $1.60
Each friend earned an amount of $1.6.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
Given that,
A group of friends worked together at a lemonade stand.
They earned $8.00 in all.
Each friend was paid 20% of the total earnings.
Total earnings = $8
Each friend earn = 20% × 8
= (20/100) × 8
= 0.2 × 8
= 1.6
Hence the amount each friend earned is $1.6.
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Michael solved this inequality as shown:
Step 1: -6(x + 3) + 10 < -2
Step 2: -6x − 18 + 10 < -2
Step 3: -6x − 8 < -2
Step 4: -6x < 6
Step 5: x > -1
What property justifies the work shown between step 3 and step 4?
A.
transitive property
B.
division property of inequality
C.
distribution property
D.
addition property of inequality
The property used between step 3 is the D)addition property of inequality and step 4 is the B) division property of inequality.
What is inequalities?In mathematics, an inequality is a mathematical statement that indicates that twο expressiοns are nοt equal. It is a statement that cοmpares twο values, usually using οne οf the fοllοwing symbοls: "<" (less than), ">" (greater than), "≤" (less than οr equal tο), οr "≥" (greater than οr equal tο).
The property used between step 3 is the addition property of inequality and step 4 is the division property of inequality. answer is D addition property of inequality.
In step 3, -6x - 8 < -2 is οbtained by adding 8 tο bοth sides οf the inequality -6x - 8 + 8 < -2 + 8.
Then, in step 4, -6x < 6 is οbtained by dividing bοth sides οf the inequality -6x - 8 < -2 by -6, which requires the use οf the division property of inequality.
Therefore, the property used between step 3 and step 4 is the addition property of inequality.
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please help me die today
Answer:
[tex]A = 212.1 \text{ cm}^2[/tex]
Step-by-step explanation:
We can identify the bases of the trapezoid as:
9cm and 21.3 cm
(notice how they are parallel)
We know the height is 14 cm.
Using these values, we can solve for the trapezoid's area.
[tex]A = \dfrac{1}{2}(b_1 + b_2) \cdot h[/tex]
↓ plugging in the values
[tex]A = \dfrac{1}{2}(9 + 21.3) \cdot 14[/tex]
↓ simplifying the parentheses
[tex]A = \dfrac{1}{2}(30.3) \cdot 14[/tex]
↓ multiplying 14 and (1/2)
[tex]A = 7 \cdot 30.3[/tex]
↓ multiplying
[tex]A = 212.1 \text{ cm}^2[/tex]
Number 12 please help
The two-column proofs that line segments AC ≅ EC are shown below
The complete proof that AC ≅ ECGiven that
AB || DE
BC ≅ DC
The proof is as follows
Statement Reason
AB || DE and BC ≅ DC Given
AB ≅ DE CPCTC
AC ≅ EC CPCTC (proved)
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Identify the transformation from the original to the image.
Original ABCD: A(-2, 5), B(1, 4), C(1, 1), D(-2, -1)
Image A'B'C'D': A'(5, 2), B'(4, -1), C'(1,-1), D'(-1,2)
A. Dilation B. Reflection C. Rotation D. Translation
PLEASE HELP!!!!!!!!!!!!!
What is the value of the expression 5x - 3y ?
3x - 4y= -24
3x +2y= -6
The value of the expression 5x - 3y, is -29 obtained by elimination method by eliminating the two equations.
The equations are :
3x - 4y= -24 ----------- A
3x +2y= -6 ----------- B
On multiplying minus sign in B equation, to eliminate the x- component in the equation.
3x +2y= -6 becomes (-3x - 2y = 6)
Then, the equation becomes,
3x - 4y= -24
-3x - 2y = 6 (+ 3x - 3x are equal and opposite becomes zero.)
------------------
-6y = -18
------------------
6y = 18 (both minus sign gets cancelled)
y = 18/6
= 3
The value of y=3.
Substitute the value of y=3 in A equation.
Equation A is, 3x - 4y= -24
3x - 4(3) = -24
3x = -24 + 12
3x = -12
x = -12 / 3
= -4
The value of x= -4.
Thus, the value of x= -4 and y = 3. By using this x and y values, the equation 5x - 3y, can be solved as,
= 5x - 3y
= 5(-4) - 3 (3)
= -20 -9
= -29
The value of the expressions 5x - 3y = -29.
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PLSS due by tomorrow I will give all my points
can you add the question?
Add a picture of the question.
a tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in length and a height of 12 meters. if water is being pumped into the pyramid at a rate of 23m3sec, at what rate is the height of the water increasing when the water is 2 meters deep? (the volume of a pyramid with height h and base area b is given by v
If a tank is shaped like an upside down square-pyramid, then the rate at which the height of water is increasing when the water is 2 m deep is 51.75 m/sec.
The tank is upside down square-pyramid, with sides as 4 meter,
Let the height of water at any time "t" be = "h",
The height of the tank is = 12 meter,
Let, the side of the base of pyramid shaped water at any time "t" be = "b",
So, b = (1/3)h ...because height of pyramid is 12 and each side is of 4, the ratio is 1/3,
The volume of water at nay time "t" is (V) = (1/3)b²h,
⇒ V = (1/3)(1/3h)²h,
⇒ V = h³/27,
Now, dv/dt = (d/dt)(h³/27),
On simplifying further,
we get,
⇒ dv/dt = (h²/9)(dh/dt),
⇒ dh/dt = (9/h²)(dv/dt),
We know that, when the water is 2 meter deep, and if water is pumped out at rate of 23 m³/sec, it means that h = 2, and dv/dt = 23,
So, dh/dt = (9/2²)(23) = 51.75 m/sec.
Therefore, the rate of change of height is 51.75 m/sec.
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onsider an economy with three industries: I1, I2, and I3. Consumer demand is currently
‚ 100 units from I1,
‚ 75 units from I2,
‚ 200 units from I3.
Also suppose that
‚ for every unit that I1 produces, it needs 0.5 units from I2 and 0.1 units from I3;
‚ for every unit that I2 produces, it needs 0.25 units from I1 and 0.2 units from I3;
‚ for every unit that I3 produces, it needs 0.3 units from I1 and 0.4 units from I2
Set up a system of equations
We have the following system of equations:
x₁ + 0.5x₂ + 0.1x₃ = 100
0.25x₁ + x₂ + 0.2x₃ = 75
0.3x₁ + 0.4x₂ + x₃ = 200
Define the term equation?Statement gives the equality of different mathematical expressions is called as an equation.
Let x₁, x₂, and x₃ be the outputs of I₁, I₂, and I₃, respectively. Then the total production must satisfy the following system of equations:
For I₁:
I₁ itself produces x₁ unitsIt requires 0.5 units of I₂ for every unit, so it requires 0.5x₂ unitsIt requires 0.1 units of I₃ for every unit, so it requires 0.1x₃ unitsTherefore, total demand from I₁ is x₁ + 0.5x₂ + 0.1x₃ = 100For I₂:
I₂ itself produces x₂ unitsIt requires 0.25 units of I₁ for every unit, so it requires 0.25x₁ unitsIt requires 0.2 units of I₃ for every unit , so it requires 0.2x₃ unitsTherefore, total demand from I₂ is x₂ + 0.25x₁ + 0.2x₃ = 75For I3:
I₃ itself produces x₃ unitsIt requires 0.3 units of I₁ for every unit, so it requires 0.3x₁ unitsIt requires 0.4 units of I₂ for every unit, so it requires 0.4x₂ unitsTherefore, total demand from I₃ is x₃ + 0.3x₁ + 0.4x₂ = 200Therefore, the system equations are:
x₁ + 0.5x₂ + 0.1x₃ = 100
0.25x₁ + x₂ + 0.2x₃ = 75
0.3x₁ + 0.4x₂ + x₃ = 200
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Find the vector and parametric equations for the line through the point P(-2, 2, 5) and orthogonal to the plane 5x-3y-3z=-3. Vector Form: < , , 5> + t < , , -3> Parametric form (parameter t, and passing through P when t = 0):
x=x(t)=
y=y(t)=
z=z(t)=
The parametric equation of the line is given by; x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t
Find the parametric equation of the line?To find the vector and parametric equations for the line through the point P(-2, 2, 5) and orthogonal to the plane 5x - 3y - 3z = -3, the following
Write the equation of the plane.5x - 3y - 3z = -3 is the given equation
Find a vector that is orthogonal to the planeThis can be done by finding the normal vector of the plane. Using the coefficients of x, y, and z in the equation of the plane. A normal vector of the plane is obtained and simplified:<5,-3,-3>.
Find the vector equation of the line.
Let L be the line through P(-2, 2, 5) and orthogonal to the plane. A direction vector of the line, v is the normal vector of the plane (which is <5,-3,-3>), a point P(-2, 2, 5) on the line can be used to obtain the vector equation of the line:
Parametric form (parameter t, and passing through P when t = 0):x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t
The vector form:<-2, 2, 5> + t<5,-3,-3> The parametric equation of the line is given by; x(t)=-2 + 5ty(t)=2 - 3tz(t)=5 - 3t
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(703. When asked to find the equation of the parabola pictured
at right, Ryan looked at the z-intercepts and knew that the
answer had to look like y a(x+ 1)(x-4), for some coefficient
a. Justify Ryan's reasoning, then finish the solution by finding
the correct value of a.
AND
704 (Continuation) Find an equation for the parabola, in fac-
tored form, y a(z-p)(z-g), whose symmetry axis is parallel
to the y-axis, whose a-intercepts are -2 and 3, and whose y
intercept is 4. Why is factored form sometimes referred to as
intercept form?
The equation of the parabola in factored form is: y = 16(z - 1/2)(z - 8)
What is parabola?
A parabola is a symmetrical plane curve that is shaped like an arch. It is a quadratic function and is defined by the equation y = ax² + bx + c, where a, b, and c are constants.
Ryan's reasoning is justified because the z-intercepts of a parabola are the points where the parabola intersects the z-axis, which are the points where x = 0. Therefore, if the parabola can be expressed in the form y = a(x + 1)(x - 4), then its z-intercepts are at x = -1 and x = 4. This is because when x = -1, (x + 1) = 0 and when x = 4, (x - 4) = 0, which makes y = 0, indicating that the parabola intersects the z-axis at these two points.
To find the value of a, we need to use the given information that the y-intercept of the parabola is at (0, 2). Substituting x = 0 and y = 2 into the equation y = a(x + 1)(x - 4), we get:
2 = a(0 + 1)(0 - 4)
2 = -4a
Therefore, a = -1/2. So the equation of the parabola is y = (-1/2)(x + 1)(x - 4), in factored form.
To find the equation of the parabola in factored form y = a(z-p)(z-g), we can use the given information about its intercepts and symmetry axis. Since the symmetry axis is parallel to the y-axis, the parabola is of the form y = a(z - h)² + k, where (h, k) is the vertex. We know that the a-intercepts are -2 and 3, which means that the points (-2, 0) and (3, 0) lie on the parabola. Substituting these points into the equation, we get:
0 = a(-2 - h)² + k
0 = a(3 - h)² + k
Solving for h and k, we get:
h = 1/2
k = 4
Therefore, the vertex is at (1/2, 4), and the equation of the parabola is:
y = a(z - 1/2)² + 4
We can find the value of a by using the fact that the y-intercept is 4. Substituting z = 0 and y = 4, we get:
4 = a(0 - 1/2)² + 4
4 = a(1/4)
a = 16
Therefore, the equation of the parabola in factored form is:
y = 16(z - 1/2)(z - 8), which is sometimes referred to as intercept form because it explicitly shows the intercepts of the parabola on the z-axis.
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TIMED PLS HELP - GIVING MOST PTS I CAN
Rounding to the nearest tenth, the measure of UV is 7.1.
What is angle?An angle is a measure of space between two lines or planes. It is measured in degrees, using a protractor, and can range from 0 to 360. Angles can be either acute, obtuse, right, straight, reflex, or full. Acute angles are angles that measure less than 90 degrees, obtuse angles measure more than 90 degrees, right angles measure exactly 90 degrees, straight angles measure 180 degrees, reflex angles measure more than 180 degrees, and full angles measure 360 degrees.
To find the measure of UV in ∆ UVW, we will use the law of cosines. The law of cosines states that [tex]c^{2} =a^{2} +b^{2} -2ab cos C[/tex], where c is the length of the side opposite angle C, a and b are the lengths of the other two sides, and C is the angle opposite side c. In this case, side c is UV, a is UW, b is VW, and C is ∠ W.
Plugging in the given values, we get:
[tex]U^{2}V^{2}[/tex] = [tex]9^{2} + 12^{2} - 2 *9* 12 cos *35[/tex]
[tex]U^{2} V^{2}[/tex] = 81 + 83.44 – 162.08 cos 35°
[tex]U^{2} V^{2}[/tex] = 164.44 – 114.45
[tex]U^{2} V^{2}[/tex] = 49.99
Taking the square root of both sides, we get:
UV = 7.086
Rounding to the nearest tenth, the measure of UV is 7.1.
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The vertex of f(x)=-4.9x^(2)+26.1+65
Is the vertex a maximum/minimum?
The y-intercept and x-intercept of f(x)=-4.9x^(2)+26.1+65
gregs backyard is 42 feet wide how many yards and feet is that?
pls show your work. thx
Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.
To convert 42 feet to yards and feet, we need to know that there are 3 feet in 1 yard. We can divide the total number of feet (42) by 3 to get the number of yards, and then take the remainder to get the remaining feet.
So, 42 feet divided by 3 feet/yard equals 14 yards. This means that Greg's backyard is 14 yards wide.
To find the remaining feet, we can multiply the decimal part of the result by 3. So, 0.333 x 3 = 0.999. Since we cannot have a fraction of a foot, we round up to the nearest whole foot, which gives us 1 foot.
Therefore, Greg's backyard is 14 yards and 1 foot wide. To summarize, we can say that 42 feet is equivalent to 14 yards and 1 foot.
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NEED HELP DUE TODAY WELL WRITTEN ANSWERS ONLY!!!!
Here is a graph of f given by f(Θ) = tan(Θ). What are the Θ-intercepts of the graph of f? Explain how you know.
The straight lines that pass through the points Θ = π, Θ = 2π, Θ = 3π, and so on are known as the f-intercepts. At the multiples of, these lines cross the x-axis (or -axis).
What do you mean by x and y intercepts?The points where a line intersects an axis are known as the x-intercept and the y-intercept, respectively.
A periodic function, f(Θ) = tan(Θ), oscillates between positive and negative infinity at certain points that correlate to the function's zeros. These zeros are referred to as the function's x-intercepts or roots.
The x-intercepts are not clearly specified, though, because the function has a periodic nature with a period of. Or, to put it another way, the function has an unlimited number of x-intercepts at each integer multiple of π (i.e., π, 2π, 3π, -π, -2π, -3π, and so on).
The values are represented by the x-axis in the setting of the function's graph. As a result, the values of for which the function equals zero correlate to the x-intercepts or roots of the function.
We can see that the function equals zero when sin() = 0, which happens when is an integer multiple of, by using the equation tan() = sin() / cos().
As a result, the vertical lines going through Θ = π, Θ = 2π, Θ = 3π, and so on are the -intercepts of the graph of f. These lines cross the x-axis (also known as the -axis) at multiples of.
In conclusion, the straight lines at = n, where n is an integer, are the -intercepts of the graph of f(Θ) = tan(Θ).
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Find the surface area of each triangular prism.
Also don't mind my writing on the paper
The surface area of the given triangular prism is approximately 58.26 square units.
what is triangular prism?
A triangular prism is a three-dimensional geometric shape that consists of two congruent parallel triangles as its bases and three rectangular faces that connect the corresponding sides of the two triangles.
In the given question,
To find the surface area of a triangular prism, we need to add the area of all the faces of the prism. A triangular prism has two congruent triangular bases and three rectangular lateral faces.
First, let's calculate the area of the triangular bases. We can use the formula for the area of a triangle:
Area of a triangle = (1/2) * base * height
In this case, the base of the triangle is 5 and the height is 6. To find the height, we need to use the Pythagorean theorem because we are given the slant height of the triangular prism, which is the hypotenuse of the right triangle formed by the base, the height, and the slant height. The Pythagorean theorem is:
slant height² = base² + height²
Substituting the given values, we get:
6.5² = 5² + height²
42.25 = 25 + height²
height² = 17.25
height = √17.25 ≈ 4.15
Now we can calculate the area of each triangular base:
Area of a triangular base = (1/2) * base * height
Area of each triangular base = (1/2) * 5 * 4.15
Area of each triangular base ≈ 10.38
Next, we need to calculate the area of each rectangular lateral face. The length of each lateral face is the same as the base of the triangle, which is 5, and the width is the same as the width of the prism, which is 2.5. The height of each lateral face is the same as the height of the prism, which is 6. Therefore, the area of each rectangular lateral face is:
Area of a rectangular lateral face = length * width
Area of each rectangular lateral face = 5 * 2.5
Area of each rectangular lateral face = 12.5
Finally, we can find the total surface area of the prism by adding up the areas of the two triangular bases and the three rectangular lateral faces:
Total surface area = 2 * area of a triangular base + 3 * area of a rectangular lateral face
Total surface area ≈ 20.76 + 37.5
Total surface area ≈ 58.26
Therefore, the surface area of the given triangular prism is approximately 58.26 square units.
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1)If 24 kids Sharded and 1789 kids went to a taco bell in 24 hours how many kid sharded in total?
2.a)1638 men cheated on their wife in one week how many men cheated on their wife’s in 7 weeks?
2.b) 47 percent of the men that cheated on their wife’s in 7 weeks have cheated many times before, how many men have cheated before?
1) Given that 1789 children visited a Taco Bell in 24 hours. We can calculate the number of students who went every hour by dividing this number by the number of hours:
[tex]1789 / 24 = 74.54\\\frac{1789}{24} = 74.54[/tex]
We get 75 students each hour, rounded up to the nearest whole number.
If 24 children shared, we can calculate the total number of children who shared by multiplying the number of hours by the number of children shared every hour:
24 x 75 = 1800
As a result, 1800 children shared.
How many men cheated on their wives in 7 weeks?2)If 1638 men cheated on their wives in one week, multiplying by 7 gives us the number of men who cheated on their wives in seven weeks:
1638 x 7 = 11,466
As a result, 11,466 men cheated on their wives in just 7 weeks.
How many men have cheated before?c) If 47% of the men who cheated on their spouses in 7 weeks cheated numerous times before, we can calculate the number of men who cheated previously by multiplying the total number of men who cheated by the proportion of men who cheated previously:
11,466 x 0.47 = 5,390.02
Rounding to the nearest whole number, we get 5,390 men who have cheated in the past.
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Find ratio in which line joining of points A(–7, –1) and B(8, 2) is divided by x + y = 2 ?
After answering the presented question, we can conclude that As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.
what is ratio?In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit dish, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of numbers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.
[tex]m = (y2 - y1)/(x2 - x1) = (2 - (-1))/(8 - (-7)) = 3/15 = 1/5\\y - y1 = m(x - x1)\\y - (-1) = (1/5)(x - (-7))\\y + 1 = (1/5)(x + 7)\\y = (1/5)x + 6/5 - 1\\y = (1/5)x + 1/5\\x + (1/5)x + 1/5 = 2\\(6/5)x = 9/5\\x = 3\\[/tex]
[tex]y = (1/5)(3) + 1/5\\y = 4/5\\AP = \sqrt[(3 - (-7))^2 + (4/5 - (-1))^2] = \sqrt[10^2 + 9/5^2] = \sqrt[100 + 81/25] = \Sqrt[4301]/5\\PB = \Sqrt[(8 - 3)^2 + (2 - 4/5)^2] = \sqrt[25 + 81/25] = \sqrt[3206]/5\\[/tex]
The ratio in which AB is divided by x + y = 2 is:
[tex]AP:PB = \sqrt[4301]:\sqrt[3206] = 65.63:56.63 \\[/tex]
As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.
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