Answer:
120
Step-by-step explanation:
The angle below x is 40 degree cause alternate angle. Then you get,
20+x+40=180
60+x=180
x=180-60
x=120
Mrs. Oliver drew a box plot to represent her students’ scores on a mid-term test.
Answer:
About 1/4 scored higher and 3/4 scored lower
Step-by-step explanation:
84 is on the right side line
Each line represents 25 % of the score
It is 75 percent ( 3 lines) of the way
She scored higher than 75% of the students and lower than 25% of the students
About 1/4 scored higher and 3/4 scored lower
What is the equation of a line that goes through the point (0, -5) and
has a slope of -3?
O -5y = - 3x
O y = 3x - 5
O y=-3x - 5
O y = -5x - 3
Answer:
Equation of a line has a form as below:
y=ax+b
Given:
b ( the y intercept)= -5
a ( the slope)= -3
so, y= -3x -5 is the equation of the line.
Please give me Brainliest [:)
What is the standard form equation of the ellipse that has vertices (-15, 4) and (5, 4) and co-vertices (-5, -3) and
(-5, 11)?
Step-by-step explanation:
Notice that the main vertices (-15,4) and (5,4) both have the same y coordinate. This means that the focal axis is horizontal so we have a horizontal ellispe.
Equation of a horizontal ellipse is
[tex] \frac{(x - h) {}^{2} }{ {a}^{2} } + \frac{(y - k) {}^{2} }{ {b}^{2} } = 1[/tex]
I'll explain the variables.
Step 1: Find the center.
The center (h,k) is the midpoint of either the main or co vertices. It doesn't matter because of the definition of an ellipse.
So using the midpoint formula, let find the midpoint of the main vertices.
[tex]( \frac{ - 15 + 5}{2} ) = - 5[/tex]
[tex] \frac{4 + 4}{2} = 4[/tex]
So our center is (-5,4) so as of right now we have
[tex] \frac{(x + 5) {}^{2} }{ {a}^{2} } + \frac{(y - 4) {}^{2} }{ {b}^{2} } = 1[/tex]
Step 2: The variable a represents the semi major axis. This
basically means what is the distance from the center to either main vertex.
Here, let use (5,4). Using (5,4), our main vertex and (-5,4), our center.
Use the distance formula
[tex]a= \sqrt{(5 - ( - 5) {}^{2} + (4 - 4) {}^{2} } [/tex]
[tex]a = \sqrt{100} [/tex]
[tex]a= 10[/tex]
So our distance is 10, this means a=10
Step 3: The variable b represent the semi minor axis. This basically the distance from the center to either co vertex.
Using the distance formula,
[tex]b = \sqrt{ (- 5 - ( - 5) {}^{2} + (4 - 11) {}^{2} } [/tex]
[tex]b = \sqrt{49} [/tex]
[tex]b = 7[/tex]
So b=7, so finally we plug a=10, b=7
[tex] \frac{(x + 5) {}^{2} }{100} + \frac{(y - 4) {}^{2} }{49} = 1[/tex]
A recent food drive distributed 6,298 pounds of stoneground cornmeal to 1,007 people. Approximately how many pounds did each person receive? Round to the hundredths.
Answer: 6.25
Step-by-step explanation: Here, you want to find how much of 6,298 pounds of food each person got. You can do this by dividing. 6,298/1,007 should get you the answer because it shows how the 6,298 pounds were distributed amongst the 1,007 people.
7. A coin is tossed and a day of the week is selected. What is the probability that you get tails and a day that begins with "S"?
Answer:
1/7
Step-by-step explanation:
Lets start with the probability of flipping tails, 1/2.
Then the probability of the day starting with the letter s, 2/7.
Calculate the final probability by multiplying the two together.
[tex]\frac{1}{2}*\frac{2}{7}=\frac{2}{14}[/tex]
You can simplify 2/14 down to 1/7
How much is a one time investment of 250 be when invested at 6% for 40 years in compound annually
Hi
6% increase is multiply by 1,06
done 40 times
so : 250* 1,06^40 = 2571 ,
4. will give brainliest
The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
What is the equation of the ellipse associated with the coordinates of the foci?
By analytical geometry we know that foci are along the major axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the standard form of the equation of the ellipse is of the following form:
(x - h)² / a² + (y - k)² / b² = 1, where a > b (1)
Where:
a - Length of the major semiaxis.b - Length of the minor semiaxis.Now, we proceed to find the vertex and the lengths of the semiaxes:
a = 10 units.
b = 8 units.
Vertex
V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)
V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)
V(x, y) = (1.5, 1) + (- 4.5, 1)
V(x, y) = (- 3, 2)
The equation of the ellipse in standard form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
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Show all work to write the expression in simplified radical form:
[tex]\sqrt[4]{3^{7}}[/tex]
(Fourth root of three to the seventh power)
Answer:
1.873
Step-by-step explanation:
Use the exponent rule for roots
[tex]\sqrt[4]{3^{7} } = 3^{\frac{4}{7} }=3^{0.5714} = 1.873[/tex]
Good luck!
Part A: In complete sentences, explain the relationships between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e.
The relationship between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e include:
Angle 4 and 3 would be considered equal because they are alternative interior angles.Angle 1 and 2 are supplementary to each other i.e sum of their angle is 180 degrees.Angles 1 and 3 are vertical angles thereby making them equal.What is an Angle?These are usually formed when two straight lines meet at a common endpoint or vertex.
Angles 3 and 4 are equal due to them being alternative interior angles and other relationships are mentioned above.
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Which of the following is the solution to the inequality below? 9 - 3x >= 2(x - 3) A . x <= 15 B. x >= 15 C. x >= 3 D. x <= 3
Answer: [tex]x \leq 3[/tex]
Step-by-step explanation:
[tex]9-3x \geq 2(x-3)\\\\9-3x \geq 2x-6\\\\15-3x \geq 2x\\\\15 \geq 5x\\\\3 \geq x\\\\x \leq 3[/tex]
Find x(will give brainlest)
Can someone help me with Algebra 2?
1. Solving linear equations:
(a) x = 4.
(b) r = 2/3.
2. Proportion:
(a) When x = 40, y = 100.
(b) When x = 40, y = 4.
3. System of equations:
(a) r = 8, s = 3.
(b) p = 5, q = -2.
4. Graphing lines:
(a) The slope of the line through (3, 4) and (-1, 3) is 1/4.
(b) The slope of the line 3x - 4y = 7 is 3/4.
(c) The slope-intercept form of the line through (5, -2) and (-1, 6) is y = (-4/3)x + 14/3.
5. Introductory quadratics:
(a) The solutions to the equation 4x² = 81 are -9/2, and 9/2.
(b) The solutions to the equation x² + 8x + 12 are -6, and -2.
(c) The solutions to the equation x² - 3x - 88 are -8, and 11.
6. The weight of an orange is 1 unit, the weight of an apple is 5 units, and the weight of a banana is 2 units.
7. x = 3.
1. Solving linear equations:
(a) 3x - 7 = 9 - x,
or, 3x + x = 9 + 7,
or, 4x = 16,
or, x = 16/4 = 4.
Thus, x = 4.
(b) (7 - 2r)/3 = 4r,
or, 7 - 2r = 3*4r = 12r,
or, -2r - 12r = -7,
or, -14r = -7,
or, r = -7/-14 = 1/2.
Thus, r = 1/2.
2. Proportion:
(a) x and y directly proportion, means x/y = constant.
When x = 8, y = 20.
Thus, x/y = constant, or, 8/20 = constant, or, constant = 0.4.
When x = 40,
x/y = 0.4,
or, y = x/0.4 = 40/0.4 = 100.
Thus, when x = 40, y = 100.
(b) x and y indirectly proportion, means xy = constant.
When x = 8, y = 20.
Thus, xy = constant, or, 8*20 = constant, or, constant = 160.
When x = 40,
xy = 160,
or, 40y = 160,
or, y = 160/40 = 4.
Thus, when x = 40, y = 4.
3. System of equations:
(a) r - s = 5 ...(i)
3r - 5s = 9 ... (ii)
3*(i) - (ii) gives:
3r - 3s = 15
3r - 5s = 9
(-) (+) (-)
_________
2s = 6,
or, s = 3.
Substituting in (i), we get
r - s = 5,
or, r - 3 = 5,
or, r = 8.
Thus, r = 8, s = 3.
(b) 3p + 7q = 1 ...(i).
5p = 14q + 53,
or, 5p - 14q = 53 ...(ii).
2*(i) + (ii) gives:
6p + 14q = 2
5p - 14q = 53
____________
11p = 55,
or, p = 5.
Substituting in (i), we get:
3p + 7q = 1,
or, 3*5 + 7q = 1,
or, 7q = 1 - 15 = -14,
or, q = -14/7 = -2.
Thus, p = 5, q = -2.
4. Graphing lines:
(a) Slope of the line through (3, 4) and (-1, 3) is,
m = (4 - 3)/(3 - (-1)),
or, m = 1/4.
Thus, the slope of the line through (3, 4) and (-1, 3) is 1/4.
(b) The graph given: 3x - 4y = 7.
Representing in the slope-intercept form, y = mx + b, gives:
3x - 4y = 7,
or, 4y = 3x - 7,
or, y = (3/4)x + (-7/4).
Thus, the slope of the line 3x - 4y = 7 is 3/4.
(c) Slope of the line through (5, -2) and (-1, 6) is,
m = (6 - (-2))/(-1 - 5),
or, m = 8/(-6) = -4/3.
Substituting m = -4/3 in the slope-intercept form, y = mx + b, gives:
y = (-4/3)x + b.
Substituting y = 6, and x = -1 gives:
6 = (-4/3)(-1) + b,
or, b = 6 - 4/3 = 14/3.
Thus, the slope-intercept form of the line through (5, -2) and (-1, 6) is y = (-4/3)x + 14/3.
5. Introductory quadratics:
(a) 4x² = 81,
or, 4x² - 81 = 0,
or (2x)² - 9² = 0,
or, (2x + 9)(2x - 9) = 0.
Either, 2x + 9 = 0 ⇒ x = -9/2,
or, 2x - 9 = 0 ⇒ x = 9/2.
Thus, the solutions to the equation 4x² = 81 are -9/2, and 9/2.
(b) x² + 8x + 12 = 0,
or, x² + 2x + 6x + 12 = 0,
or, x(x + 2) + 6(x + 2) = 0,
or, (x + 6)(x + 2) = 0.
Either, x + 6 = 0 ⇒ x = -6,
or, x + 2 = 0 ⇒ x = -2.
Thus, the solutions to the equation x² + 8x + 12 are -6, and -2.
(c) x² - 3x - 88 = 0,
or, x² - 11x + 8x - 88 = 0,
or, x(x - 11) + 8(x - 11) = 0,
or, (x + 8)(x - 11) = 0.
Either, x + 8 = 0 ⇒ x = -8,
or, x - 11 = 0 ⇒ x = 11.
Thus, the solutions to the equation x² - 3x - 88 are -8, and 11.
6. We assume the weight of one orange, one apple, and one banana to be x, y, and z units respectively.
Thus, we have:
3x + 2y + z = 15 ... (i)
5x + 7y + 2z = 44 ... (ii)
x + 3y + 5z = 26 ... (iii)
2(i) - (ii) gives:
6x + 4y + 2z = 30
5x + 7y + 2z = 44
(-) (-) (-) (-)
______________
x - 3y = -14 ... (iv)
5(i) - (iii) gives:
15x + 10y + 5z = 75
x + 3y + 5z = 26
(-) (-) (-) (-)
________________
14x + 7y = 49 ... (v)
14(iv) - (v) gives:
14x - 42y = -196
14x + 7y = 49
(-) (-) (-)
_____________
-49y = -245,
or, y = 5.
Substituting in (v), we get:
14x + 7y = 49,
or, 14x + 35 = 49,
or, x = 14/14 = 1.
Substituting x = 1 and y = 5 in (i), we get:
3x + 2y + z = 15,
or, 3 + 10 + z = 15,
or, z = 2.
Thus, the weight of an orange is 1 unit, the weight of an apple is 5 units, and the weight of a banana is 2 units.
7. 3/(1 - (2/x)) = 3x,
or, 3/((x - 2)/x) = 3x,
or, 3x/(x - 2) = 3x,
or, 3x = 3x(x - 2),
or, 3x = 3x² - 6x,
or, 3x² - 9x = 0,
or, 3x(x - 3) = 0.
Either, 3x = 0 ⇒ x = 0,
or, x - 3 = 0 ⇒ x = 3.
Since we had a term 2/x, x cannot be 0.
Thus, x = 3.
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I need help asap. everythings in the image
Answer:
I believe it should be d
Step-by-step explanation:
Write all possible values of y if y is a multiple of 9: 248
The possible values of y are 9n where n is an integer greater than 0 equal to 0
How to determine the possible values of y?The statement is given as;
y is a multiple of 9
The above means that
The number y can be divided by 9 without remainder
The numbers in this category are:
Numbers = 9, 18, 27, 36, 45......
This can be rewritten as:
Numbers = 9n where n is an integer greater than 0 equal to 0
Hence, the possible values of y are 9n where n is an integer greater than 0 equal to 0
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Work with your teacher/tutor. Match each inequality with its graph. Use the online tool to complete this
activity. The first one Is done for you.
The inequalities are matched with the respective graphs as shown in the attached image.
What is an inequality?In mathematics, inequality is the relationship between two non-equal expressions, denoted by a sign such as 'not equal to,' > 'greater than,' or 'less than.'
Roads feature speed limits, some movies have age limitations, and the time it takes to go to the park are all instances of inequalities in the real world.
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HELPPPPPP PLSSSSSSSSSS
Answer:
wait ewiai twia it i ti i got this soon
(1+3) x (2 x 3)
Trucks in a delivery fleet travel a mean of 120 miles per day with a standard deviation of 18 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 150 and 156 miles in a day. Round your answer to four decimal places.
The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.
How to calculate the probability distribution?The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,
Z = (X - μ)/σ
Where X - random variable; μ - mean; σ - standard deviation;
Then the probability is calculated by P(Z < x), using the values from the distribution table.
Calculation:The given data has the mean μ = 120 and the standard deviation σ = 18
Z- score for X =150:
Z = (150 - 120)/18
= 1.67
Z - score for X = 156:
Z = (156 - 120)/18
= 2
So, the probability distribution over these scores is
P(150 < X < 156) = P(1.67 < Z < 2)
⇒ P(Z < 2) - P(Z < 1.67)
From the standard distribution table,
P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254
On substituting,
P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471
Rounding off to four decimal places,
P(150 < X < 156) = 0.0247
Thus, the required probability is 0.0247.
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La dodecahedral die (one with 12 sides numbered from 1 to 12) is tossed once. Find the following probability. The number on the upward face is not 7
Answer:
11/12
Step-by-step explanation:
no of sample space=12
number of 7 to occur is 1/12
number of not 7:
since the total probability is 1
so 1-1/12=11/12
please help with question
Applying precedence of operations, the result of the expression is of 161.
What is the precedence of operations?Power operations are done before multiplication/division, which are also done before addition/subtraction.
Operations inside brackets or parenthesis also take precedence.
In this problem, the operation is:
[3 x 2^5 + 13 x (-2)] + 7[8 - (4 - 9)]
First the power:
[3 x 32 + 13 x (-2)] + 7[8 - (4 - 9)]
Now the multiplications on the first bracket, and the subtraction on the second:
[96 - 26] + 7[8 - (-5)]
Then, applying the parenthesis to the negative number, we have that:
[96 - 26] + 7[8 - (-5)] = 70 + 7 x 13 = 161.
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[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3 \times 2^5 + 13(-2)] + 7[8 - (4 - 9)]}[/tex]
[tex]\mathsf{= 3\times32 + 13\times -2 + 7[8 - (4 - 9)] }[/tex]
[tex]\mathsf{= 96 + 13\times -2 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 96 - 26 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 70 + 7(8 - (4 - 9))}[/tex]
[tex]\mathsf{= 70 + 7(8 - (-5))}[/tex]
[tex]\mathsf{= 70 + 7\times13}[/tex]
[tex]\mathsf{= 70 + 91}[/tex]
[tex]\mathsf{= 161}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{161}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Use five different colors to paint the four rectangles A, B, C and D shown in the figure. No two rectangles sharing an edge can be the same color. How many ways are there to color the rectangles?
There are 120 ways to color the 4 rectangles
How to determine the number of ways?The given parameters are:
Paints, n = 5
Rectangles, = 4
The number of ways to color the rectangles is
[tex]Ways = ^nP_r[/tex]
This gives
[tex]Ways = ^5P_4[/tex]
Apply the permutation formula
[tex]Ways = \frac{5!}{1!}[/tex]
Evaluate the expression
Ways = 120
Hence, there are 120 ways to color the 4 rectangles
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Una página de plástico diseñada para guardar cromos puede contener hasta 9 cartas. ¿Cuántas páginas se necesitarán para almacenar 517 tarjetas? Dé una respuesta numérica adecuada a la pregunta. (Encuentre el número contable mínimo que funcionará).
Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.´
¿Cuántas páginas se necesitarán para almacenar 517 tarjetas?Sabemos que cada página puede almacenar hasta 9 cartas.
Entonces queremos ver cuantos grupos de 9 cartas hay en el conjunto de 517, para ver esto tomamos el cociente entre 517 y 9.
N = 517/9 = 57.44
Y no podemos tener un numero racional, así que debemos redondear al proximo número entero, que es 58.
Esto significa que debemos tener 58 páginas de plástico para contener las 517 tarjetas.
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? km
2.6 km
Area = 20.8 km²
What is the height of Thai rectangle?
How many grams of the isotope remains after 90 days?
Answer:
84,08964 [gr.].
Step-by-step explanation:
for more details see in the attachment.
Suppose the length and width of the box double. Does the surface area S double? Complete the explanation.
Help!
Find the rational roots f(x) =3x3+ 2x2 + 3x + 6
The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
How to determine the rational root of the function f(x)?The function is given as:
f(x) = 3x^3 + 2x^2 + 3x + 6
For a function P(x) such that
P(x) = ax^n +...... + b
The rational roots of the function p(x) are
Rational roots = ± Possible factors of b/Possible factors of a
In the function f(x), we have:
a = 3
b = 6
The factors of 3 and 6 are
a = 1 and 3
b = 1, 2, 3 and 6
So, we have:
Rational roots = ±(1, 2, 3, 6)/(1, 3)
Split the expression
Rational roots = ±(1, 2, 3, 6)/1 and ±(1, 2, 3, 6)/3
Evaluate the quotient
Rational roots = ±(1, 2, 3, 6, 1/3, 2/3, 1, 2)
Remove the repetition
Rational roots = ±(1, 2, 3, 6, 1/3, 2/3)
Hence, the rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
The complete parameters are:
The function is given as:
f(x) = 3x^3 + 2x^2 + 3x + 6
The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
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There are 48 people coming to a family reunion. One fourth of them live out of state. How many live in-state?
Step-by-step explanation:
1/4×48
=12
So if 12people are out of state
48-12=36,is the number of people living in the state
Find the mean for the amounts: $17,484, $14,978, $13,521, $14,500, $18,540, $14,978
Answer:
$15666.83 (2dp)
Step-by-step explanation:
Mean = Total of all values / Number of Values
= [tex]\frac{17484+14978+13521+14500+18540+14978}{6}[/tex]
=[tex]\frac{94001}{6}[/tex]
= $15666.83 (2dp)
Which equation has no solution?
4(x + 3) + 2x = 6(x + 2)
5 + 2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 6(2 + x) = 2(3x + 8)
Answer:
equation 1 has no solution
Step-by-step explanation:
when you compare each of the equations, all the equations gives a correct answer with the exception of equation 1
When it is Noon (12 pm) in London, it is 10pm in Sydney, Australia. Dan in London rings his friend Boski in Sydney at 15:30pm on Christmas Day. What time is it in Sydney?
A. 1am
B. 1:30am
C. 2am
S. 2:30am
The time at Sydney when Dan rings his friend is 1 : 30 am (option B).
What is the time at Sydney?The first step is determine the time difference between London and Sydney.
Time difference = time at Sydney - time at London
( 12 + 10pm) - 12pm
22pm - 12pm = 10 hours
The second step is to add the time difference to the time it was when Dan rang.
15 : 30 pm + 10pm = 25 : 30
We know that there are only 24 hours in day, so subtract 24 hours from 25 : 30
25 : 30 - 24 = 1 : 30 am
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Determine the five-number summary for this data set, taking into account any outliers. 10 13 15 12 12 4 12 17 12 13 15 18 10 11 20 19 Tiles 11.5 13 16 20 10 12.5 17
The value of the median, lower and upper quartile
Median = 21.5lower quartile = 12upper quartile = 29What is the five-number summary for this data set?
The minimum value = 10
The maximum value = 38
The median is the value that is found in the center of the data when it is ordered from lowest to highest. In the event that there is no value that precisely corresponds to the center, the value will be determined by taking the average of the values that are located on each side of the middle.
10 11 12 15 19 24 27 29 33 38
Median = 21.5
The intermediate value of the data that is located to the left of the median is known as the lower quartile.
10 11 12 15 19
lower quartile = 12
The intermediate value of the data that is located to the right of the median is known as the upper quartile.
24 27 29 33 38
upper quartile = 29
In conclusion, the 5 number summary is 10, 12, 21.5, 29, 38 → A
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Answer: minimum 10 first quartile 11.5 median 12.5 third quartile 16 maximum 20
Step-by-step explanation: