[tex]~~~~~~\text{Arc length} = r \theta \\\\\implies 4\pi = r\left( 45 \times \dfrac{\pi}{180} \right)~~~~~~~~;[\theta ~ \text{is in radians.}]\\\\\implies 4 = \dfrac{45r}{180}\\\\\implies 45r = 180 \times 4 = 720\\\\\implies r = \dfrac{720}{45}\\\\\implies r = 16~ \text{units.}\\\\\text{Now,}\\\\\text{Area} = \pi r^2\\\\~~~~~~~=\pi \cdot 16^2\\\\~~~~~~~=256\pi~ \text{units}^2[/tex]
Solve for [x]. The pair of polygons are similar.
5x+2
B
16
The scale factor from A to B is 2:9
I need help with this problem
The box plots below represent the scores for games played by two high school basketball teams over the last 5 seasons.
Based on these plots, which statement regarding the means of the two data sets is is most likely true?
A The mean score per game is higher for South County High School because the distribution of South County High School's scores is not as skewed as the distribution of Central High School's scores.
B The mean score per game is about the same for both schools because their median scores are about the same.
C The mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.
D No conclusion can be drawn regarding the means because the box plots only show medians and quartiles.
The mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.
What is mean?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
From the data given in the box plot, we can conclude that the mean score per game is higher for Central High School than for South County High School because the distribution of Central High School's scores is skewed right and contains large outliers.
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Solve the question within the screenshot please
Answer:
See below in bold.
Step-by-step explanation:
Let t be the number of tulips you buy and r be the number of rose bushes.
a.
The system is:
t + r = 13
4t + 10r = 100
b.
Solving:
4t + 10r = 100
t + r = 13 Multiply this by 4:
4t + 4r = 52 Subtract this from the first equation:
0 + 6r = 48
r = 8.
Now substitute for r in t + r = 13:
t + 8 = 13
t = 5.
c.
To buy 13 plants and spend $100 you need to buy 5 tulips and 6 rose bushes.
Is c = 11 a solution to this equation? 3 c = 17
Answer:
a=17/33
Step-by-step explanation:
c=11a ----(1)
3c=17 ---- (2)
Substitute equation (1) into equation (2)
3(11a)=17
33a=17
Divide both side by 33
a=17/33
Which of the following could be calculated using the Pythagorean theorem? Select all that apply.
area of a circle
length of an arch
height of a building
distance to an airport
size of a window pane
Answer: height of a building
Step-by-step explanation:
a^2 + b^2 = c^2
used for finding missing side angle of a triangle
What is the volume of this sphere?
Use a 3.14 and round your answer to the nearest hundredth.
4 m
cubic meters
radius= 4 m
to find:the volume of the given sphere.
solution:[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]
[tex]v = \frac{4}{3} \times 3.14 \times {4}^{3} [/tex]
[tex]v = 267.9466667 \: {m}^{3} [/tex]
[tex]v = 267.95 \: {m}^{3} [/tex]
therefore, the volume of the given sphere is 267.95 cubic meters.
[tex]\large\boxed{\bold{Formula: V= \frac{4}{3}\pi{r}^{3}}}[/tex]
[tex]\large\boxed{\bold{\red\pi\red=\red3\red.\red1\red4}}[/tex]
In this question the radius is given so we'll simply have to substitute and solve.
Let's solve!
Substitute the values according to the formula.
Instead of π we are asked to use 3.14
[tex]V= \frac{4}{3}\times\ 3.14\times{4}^{3}[/tex]
Calculator answer:
[tex]\bold{V= 267.9466667 \:{m}^{3}}[/tex]
Now, we can round off to the nearest hundredth.
The value in thousandths place is greater than 5 so, we will have to round up by adding 1 to the hundredths place.
Final answer:
[tex]\large\boxed{\bold{V= 267.95 \: {m}^{3}}}[/tex]
Hence, the volume of the given sphere is 267.95 cubic meters.
The ratio of number of student wearing sneakers in a class to the number of students wearing sandals in the class is 3:4 How many were are waring sneakers if there are 28 student in the class
12 students are wearing sneakers.
Answer:
12
Step-by-step explanation:
So, the ratio is 3:4. That means this is for every 7 students. We have 28 students, so we need to know how many times 7 was multiplied to get to 28. 28 divided by 7 gives you 4. Now, we have to multiply both numbers in the ratio by 4. 3 times 4 is 12, and 4 times 4 is 16. The new ratio is 12:16. The students wearing sneakers were originally the 3 that got multiplied into 12, so the answer is 12.
Hope this helps!
Evaluate the following expressions for x=2, y=3 and z=-2
a). 2(x-y)
b). 4x+3y-z
C). -2(3z+y)
[tex]\text{Given that}~ x = 2,~ y = 3 ~ \text{and}~ z = -2\\\\\textbf{a)}\\\\2(x-y)=2(2-3) = 2(-1) = \boxed{-2}\\\\\textbf{b)}\\\\4x+3y-z = 4(2) +3(3) -(-2) = 8+9+2=\boxed{19}\\\\\textbf{c)}\\\\-2(3z+y) = -2[3(-2) +3] = -2(-6+3) = -2(-3) = \boxed{6}[/tex]
What is the length of the diagonal of the rectangle?
a) 2.5 units
b) 4.5 units
c) 5 units
d) 7 units
Answer:
I do believe its 5 units, if I am incorrect I apologize
Step-by-step explanation:
You are in charge of snacks for a youth event. You send your cousin Norm who is a complete nerd to
the store to price some items for you. For some inexplicable reason instead of telling you the price
for each item, he gives you this information:
If you buy 3 bags of Reese's Peanut Butter Cups and 6 bags of York Peppermint Patties, it costs $48.
If you buy 4 bags of Reese's Peanut Butter Cups and 3 bags of York Peppermint Patties, it costs $51.
Figure out how much each single bag costs. (Do not enter a $, just the number)
Reese's Peanut Butter Cups:
York Peppermint Patties:
Answer:
Reese's Peanut Butter Cups: 10.8
York Peppermint Patties: 2.6
Step-by-step explanation:
Let Reese's Peanut Butter Cups be r and York Peppermint Patties y.
Step 1: Make equations.
1) If you buy 3 bags of Reese's Peanut Butter Cups and 6 bags of York Peppermint Patties, it costs $48.
[tex]3r + 6y = 48[/tex]
2) If you buy 4 bags of Reese's Peanut Butter Cups and 3 bags of York Peppermint Patties, it costs $51.
[tex]4r + 3y = 51[/tex]
Step 2: Solve the system of equations.
We have system of equations. I'll solve them by elimination.
[tex](1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 4r + 3y = 51[/tex]
Multiply the second equation with 2 so we'll get 6y.
[tex](1.) \text{ } 3r + 6y = 48\\(2.) \text{ } 8r + 6y = 102[/tex]
Now let's subtract second equation from first and solve for r.
[tex]3r - 8r + 6y - 6y = 48 - 102\\-5r = -54\\r = \frac{-54}{-5}\\r = \$10.8[/tex]
To get y let's substitute the value of r in first equation.
[tex]3r + 6y = 48\\3 \cdot 10.8 + 6y = 48\\32.4 + 6y = 48\\6y = 15.6\\y = \$2.6[/tex]
Solve the following linear equation: 6(x-3)=18
Answer:
x=6
Step-by-step explanation:
6(x-3)=18
Then divide both sides by 6
x-3=3
Add 3 to both sides
x=6
Answer:
x = 6
Explanation:
6(x-3) = 18use distributive property: a(b + c) = ab + ac
6x - 18 = 18change sides
6x = 18 + 18add integers
6x = 36divide both sides by 6
x = 6Problema 2 (Reto) Considera que Nueva York y Londres están ubicadas a la misma latitud. Utilizando la información del radio de la tierra y lo aprendido hasta ahora, calcula distancia aproximada que separa las dos ciudades, especificando cada uno de los razonamientos seguidos en tu estrategia de solución.
Bajo la suposición de que las ciudades se hallan en la misma latitud, la distancia estimada entre las dos ciudades es de aproximadamente 6814 kilómetros.
Cómo se estima la distancia entre dos ciudades
En esta pregunta asumimos que la Tierra tiene una geometría esférica, de modo que los cálculos de arcos circulares se pueden obtener de manera simple y ágil. Por otra parte, también asumimos que las que la ciudad de Londres se encuentra a la misma latitud que la ciudad de Nueva York.
Es posible determinar la distancia estimada mediante la siguiente ecuación de arco circular:
s = [(θ' - θ) · π/180] · R · cos α (1)
Where:
θ' - Longitud de la ciudad de Londres, grados.θ - Longitud de la ciudad de Nueva York, en grados.α - Latitud de la ciudad de Nueva York, en grados.R - Radio ecuatorial de la Tierra, en kilómetros.Si sabemos que θ' = 7°, θ = - 73°, α = 40° y R = 6371 km, entonces la distancia estimada entre la ciudades de Nueva York y Londres es:
s = [(7+73)/180] · π · (6371 · cos 40°)
s ≈ 6814.420 km
Bajo la suposición de que las ciudades se hallan en la misma latitud, la distancia estimada entre las dos ciudades es de aproximadamente 6814 kilómetros.
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how do you do 7.8 plus 917.62
The value of the addition of the numbers 7.8+917.62 will be 925.42.
What is addition?The method of increasing the number is called the addition. or the sum of the two numbers is termed as the addition.
The addition of the numbers will be done as:-
917.62
+7.80
925.42
First, arrange the number one to another then add from the unit places you will get your answer.
So the addition of the numbers will be 925.42
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The points (−8,−2) and (7,4) are the endpoints of the diameter of a circle. Find the length of the radius of the circle.
Answer
8.08
Use the distance formula:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf d =\sqrt{(7-(-8))^2 + (4-(-2))^2}[/tex]
[tex]\rightarrow \sf d =\sqrt{(15)^2 + (6)^2}[/tex]
[tex]\rightarrow \sf d =3\sqrt{29}[/tex]
This is the length of diameter.
Then radius:
· diameter/2
[tex]\sf \cdot \dfrac{3\sqrt{29} }{2}[/tex]
[tex]\sf \cdot 8.0777[/tex]
[tex]\sf \cdot 8.08 \ \ (rounded \ to \ nearest \ hundreth)[/tex]
pls answer asap!!! much appreciated
Answer:
e. 0.308.
Step-by-step explanation:
I can't draw the tree diagram but the answer is
P(red first) = 7/14 = 1/2
P( then black) = 4/13
P(red then black) = 1/2 * 4/13 = 2/13
P(black first) = 4/14 = 2/7
P( then red) = 7/13
P(black then red) =2/7 * 7/13 = 2/13
So Probability of red and black in any order
= 2/13 + 2/13 = 4/13
= 0.308.
Michael has a room in his house that is shaped like a parallelogram the length of the room measures 16 feet and the width measures 26 what is the perimeter of the
Answer:
84 ft
Step-by-step explanation:
16 + 16 + 26 +26 = 84
Does the graph show a linear function?
DOES THE GRAPH SHOW A LINEAR FUNCTION?
[tex] \sf \large \color{grey}{YES IT SHOWS A GRAPHIC LINEAR}[/tex]
Answer:
yeah, cuz it's a line that's straight
Mike wants to be elected president of the 7th-grade student council. he wants to determine his chance of winning the election. which would be the best way for mike to determine if he will win the election?
Answer:
B. survey a random sample of 7th-grade students
Step-by-step explanation:
this answer would make the most sense because it is a example of a random statistical question.
Draw and label a point, a line, a line segment, a ray, and an angle in a triangle
Answer:
a point
a line
a line segment
a ray
and an angle in a triangle
Step-by-step explanation:
multiply 7 by the fourth power of the square root of forty-nine.
Answer:
16807
Step-by-step explanation:
7 * ((sqrt49)^4 = 7 * 7^4 = 7^5 = 16807
You have a standard deck of 52 cards. Find the probability of drawing one card, then drawing another without replacement.
A) You draw an even-numbered card and then a face card.
B) Both cards you drew are "4" or higher (if aces are considered low cards and face cards are nonnumerical)
C) You drew a black face card and then a black "5".
Assuming that the all the cards have the same probability of being drawn we get:
A) P = 0.07B) P = 0.21C) P = 0.001How to find the probabilities?
We have a deck of 52 cards.
A) The probability of drawing an even-numbered card is given by the quotient between the number of even-numbered cards and the total number of cards.
On the 52 card deck, there are 16 even cards (2, 4, 6, 8 for each type), so the probability is:
p = 16/52
Then the probability of drawing a face card is given in the same way, notice that now there are 51 cards in the deck and 12 face cards, so we get:
q = 12/51
The joint probability is the product of these two:
P = (16/52)*(12/51) = 0.07
b) Both cards are 4 or larger.
There are 6 cards equal or larger than 4 for each type, so the probability for the first card is:
p = 24/52
For the second card, there is one card less in the deck (and one card less that is equal or larger than 4) so the probability is:
q = 23/51
The joint probability is:
P = (24/52)*(23/51) = 0.21
C) There are 6 black face cards, so the probability first is:
p = 6/52
Then there are 2 black cards with the number 5, so the probability is:
q = 2/51
The joint probability is:
P = (6/52)*(2/51) = 0.001
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the graph of y=x^3+x^2-6x is shown estimate the x coordinates of the turning point of the graph,
(a). From the graph the x estimates of the turning points are
-1.8 and 1.1.
(b). The solutions are where the graph crosses the x axis .. They are:
x = -3, 0 and 2.
What is polynomial?A polynomial is defined as the sum of the same variables having different powers.
Here we have the two third-degree polynomials
x³+x²-6x=0
For this the value of the variable at the turning point of the graph will be
at x=-1.8 and 1.1.
The another equation is :-
x³+x²-6x=0
The solution of the equation will be x = -3, 0 and 2. where the graph crosses the x-axis.
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Please Evaluate this equation
Answer:
Step-by-step explanation:
1.169
Answer:
8^2−38+85+3√8 =111+6√2
(Decimal: 119.485281)
Identify the amount (a) and the growth factor (b) in each exponential function. Break B into (1+r) where the rate of growth. Give r as a percentage.
y=1.07 (1.96)x
a
b=
r(as a percentage)
Answer:
a = 1.07
b = 1.96
r = 96%
Step-by-step explanation:
In an exponential function, modeled by f(x) = a(b)ˣ, a is the initial value and b is the growth factor. If we apply this formula to the given function y = 1.07(1.96)ˣ, we can see that the initial value, a, is 1.07, and the growth factor, b, is 1.96.
Now, to break down b, 1.96, into a rate, you simply set it equal to the problem’s given (1 + r) equation to find the rate.
1.96 = 1 + r
So r = .96
Now, we just have to convert .96 into a percentage to get a growth rate of 96%.
A grandsons age in years is equal to his grandfather's age in years. The difference of the grandsons age in years and the grandfather's age in years is 77. Find the grandsons age in years.
The age of the grandson is 7 years and the grandfather is 84 years if the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let's suppose the age of the grandsons is x years and
age of the grandfather's age is y years
Here some data are misprinted, so we are assuming the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.
Then according to the problem:
12x = y (as in 1 year, there are 12 months)
y -x = 77 (as difference in age is 77)
After solving both equations, we get:
x = 7 years and y = 84 years
Thus, the age of the grandson is 7 years and the grandfather is 84 years if the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.
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Lines m and n are parallel on a coordinate plane. Lines m and n are transformed by the same rotation, resulting in image lines s and t. Which statement describes the relationship between lines s and t? A. Lines s and t are intersecting but not perpendicular. B. The relationship between lines s and t cannot be determined without knowing the angle of the rotation. C. Lines s and t are parallel. D. Lines s and t are perpendicular.
The best statement that describes the relationship between lines s and t : (C). Lines s and t are parallel.
Meaning of Parallel linesA line can be defined as a figure that is one dimensional. It is a trace that is made by the movement of points in opposite direction.
Parallel lines can be defined as a group of lines that are of the same orientation. They face the same direction and are on the same axis.
In conclusion, The best statement that describes the relationship between lines s and t : Lines s and t are parallel.
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what is the absolute vale of |-18|
Answer:
18
Step-by-step explanation:
the absolute value is 18
Help me please! so jarring
Answer:
y = -5x + 4.
Step-by-step explanation:
y = mx + c is the general form
- where m = the slope of the line and c is the y-value where the graph cuts the y-axis.
The graph passes through the points (0, 4) and (1, -1) so the slope
= (Y2 - y1) / (x2 - x1)
= (-1-4) / (1-0)
= -5 = m.
and c = 4.
A class has 45 students. Each student has either 5 dollars or 2 dollars. Which Which situation results in the class having an average of 3 dollars per student
Step-by-step explanation:
an average of $3 per student would mean
sum(all students $) / 45 = 3
sum(all students $) = 3×45 = 135
x students have $5.
therefore (45-x) students have $2.
5x + 2(45-x) = 135
5x + 90 - 2x = 135
3x = 45
x = 15
so, 15 students have $5, and 45-15 = 30 students have $2.