Answer:
Area of triangle is 25.
Step-by-step explanation:
We have been given an isosceles right triangle
Isosceles triangle is the triangle having two sides equal.
Figure is shown in attachment
By Pythagoras theorem
[tex]BC^2=AC^2+AB^2[/tex]
AD is altitude which divides the triangle into two parts
DC=5 implies BC =10 since D equally divides BC
Let AC=a implies AB=a being Isosceles
On substituting the values in the Pythagoras theorem:
[tex]10^2=a^2+a^2[/tex]
[tex]100=2a^2[/tex]
[tex]\Rightarrow a^2=50[/tex]
[tex]\Rightarrow a=\pm5\sqrt{2}[/tex]
WE can find area of right triangle by considering height AB and AD
Area of triangle ABC is:
[tex]\frac{1}{2}\cdot BC\cdot AD[/tex] (1)
[tex]\Rightarrow \frac{1}{2}\cdot 10\cdot AD[/tex]
And other method of area of triangle is:
[tex]\frac{1}{2}\cdot AB\cdot BC[/tex] (2)
Equating (1) and (2) we get:
[tex]\frac{1}{2}\cdot 10\cdot AD=\frac{1}{2}\cdot a\cdot a[/tex]
[tex]\Rightarrow AD=\frac{a^2}{10}[/tex]
[tex]\Rightarrow AD=\frac{50}{10}=5[/tex]
Using area of triangle is: [tex]\frac{1}{2}\cdot BC\cdot AD[/tex]
Now, the area of triangle ABC=[tex]\frac{1}{2}\cdot 5\cdot 10[/tex]
[tex]\Rightarrow 25[/tex]
A parking garage has 6 levels.Each level has 15 rows.Each row has the same number as parking spaces.There are 2,250 parking spaces in all.How many parking spaces are in each row?
Answer:25 spaces in a row
Step-by-step explanation: Multiply 6 levels by 15 rows. Answer is 90.
Divide 90 into 2,250 parking spaces.
Answer is 25 spaces in each row.
How far is Town Center from Maple Station? (please look at attachment) 15 POINTS
4
2
5.83
5.57
Answer:
5.83 units
Step-by-step explanation:
We write the coordinate points of Maple Station (-3,5) and Town Center (0,0). We label the points left to right as [tex](x_{1}, y_{1}) and (x_{2}, y_{2})[/tex] and substitute the values.
[tex](x_{1}, y_{1}) = (-3, 5)\\(x_{2}, y_{2})=(0,0)[/tex]
[tex]d=\sqrt{(0-5)^{2} + (0-(-3) })^{2}}[/tex]
[tex]d=\sqrt{(0-5)^{2} + (0+3) })^{2}}[/tex]
[tex]d=\sqrt{(-5)^{2} + (3) }^{2}}[/tex]
[tex]d=\sqrt{25 +9}}[/tex]
[tex]d=\sqrt{34}}[/tex]
5.83 units
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
What is the remainder when you divide 4x^3 - 5x^2 + 3x - 1 by x - 2?
Answer: D
Step-by-step explanation:
x - 2 = 0 --> x = 2
Using synthetic division:
2 | 4 -5 3 -1
| ↓ 8 6 18
4 3 9 17 ← this is the remainder!
Using remainder theorem:
f(x) = 4x³ - 5x² + 3x - 1
f(2) = 4(2)³ - 5(2)² + 3(2) - 1
= 32 - 20 + 6 - 1
= 17
The table show the total distance d, in miles, a car traveled after t hours. Time in hours (h) Distance in miles (d) 0 0 1 50 2 100 3 150 Which equation shows the relationship between d and t? d=t+50 d=50t d=t+150 d=150t
answer is d=50t
am i right
Answer:
yes you are right
Step-by-step explanation:
d=50t
Answer:
Yes. It is :
D=50t
Step-by-step explanation:
If sin theta = -3/5 and q terminates in the fourth quadrant, find the exact value of tan2q.
A: -7/24
B:-24/7
C:-9/25
D:-25/9
[tex]\sin^2q+\cos^2q=1\to \cos^2q=1-\sin^2q\to\cos q=\pm\sqrt{1-\sin^2q}\\\\q\ \text{terminates in the fourth quadrant, therefore}\ \cos q > 0.\\\\\sin q=-\dfrac{3}{5}\to\cos q=\sqrt{1-\left(-\dfrac{3}{5}\right)^2}\\\\\cos q=\sqrt{1-\dfrac{9}{25}}\\\\\cos q=\sqrt{\dfrac{25}{25}-\dfrac{9}{25}}\\\\\cos q=\sqrt{\dfrac{16}{25}}\\\\\cos q=\dfrac{4}{5}[/tex]
[tex]\tan q=\dfrac{\sin q}{\cos q}\\\\\sin2q=2\sin q\cos q\\\\\cos2q=\cos^2q-\sin^2q\\\\\text{therefore}\\\\\tan2q=\dfrac{\sin2q}{\cos2q}=\dfrac{2\sin q\cos q}{\cos^2q-\sin^2q}\\\\\text{substitute}\\\\\tan2q=\dfrac{2\left(-\dfrac{3}{5}\right)\left(\dfrac{4}{5}\right)}{\left(\dfrac{4}{5}\right)^2-\left(-\dfrac{3}{5}\right)^2}=\dfrac{-\dfrac{24}{25}}{\dfrac{16}{25}-\dfrac{9}{25}}=\dfrac{-\dfrac{24}{25}}{\dfrac{7}{25}}=-\dfrac{24}{25}\cdot\dfrac{25}{7}=-\dfrac{24}{7}[/tex]
[tex]Answer:\ \boxed{B:\ -\dfrac{24}{7}}[/tex]
The exact value of tan 2θ will be –24/7. Then the correct option is B.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
If sin θ = -3/5.
Then the value of cos θ will be
cos² θ = 1 – sin² θ
cos² θ = 1 – (-3/5)²
cos² θ = 1 – 9/25
cos² θ = 16/25
cos θ = 4/5
Then the value of tan 2θ will be
[tex]\tan 2\theta = \dfrac{\sin 2\theta }{ \cos 2\theta}\\\\\\\tan 2\theta = \dfrac{2 \sin \theta \cos \theta }{ \cos^2 \theta - \sin ^2 \theta}\\\\\\\tan 2\theta = \dfrac{2 * \frac{-3}{5} * \frac{4}{5} }{( \frac{4}{5})^2 - ( \frac{-3}{5}) ^2 }[/tex]
Simplify the equation, we have
tan 2θ = (–24/25) / (7/25)
tan 2θ = –24/7
Then the correct option is B.
More about the trigonometry link is given below.
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Exponential functions exhibit exponential growth (or decay). What does this mean to the graphs of these functions?
Answer:
Option a is correct.
Exponential functions exhibit exponential growth (or decay) which mean the graph will rise or fall more dramatically than a polynomial graph
Step-by-step explanation:
An exponential function is in the form of [tex]y =ab^x[/tex] where a≠0 is a y-intercepts and b is a positive number other than 1, multiplier this base is constant , x is the independent variable and y is the dependent variable.
Exponential growth:
If b > 1 when x increases, y increases at a increasing rate .Exponential decay:
if b is between 0 and 1 i.e, 0 <b< 1 when x increases, y decreases at a increasing rate .therefore, the graph will rise or fall more dramatically than a polynomial graph
A ticket cost $4.80 the new ticket price will be 1.25 times the old price what will the new ticket be
Answer:
$6.
Step-by-step explanation:
Let x be the new price of ticket.
We have been given that a ticket cost $4.80. The new ticket price will be 1.25 times the old price.
We can represent this information as:
[tex]x=1.25\times 4.80[/tex]
[tex]x=6[/tex]
Therefore, the cost of new ticket will be $6.
Final answer:
The new ticket price will be $6.00
Explanation:
Increased Price: The problem states that the new ticket price will be 1.25 times the old price. This means the new price will be 25% higher than the old price.
Calculating the Increase: To calculate the new price, we need to find 1.25 times the old price. Mathematically, this is done by multiplying the old price by 1.25.
Old ticket price: $4.80
Calculation: New ticket price = Old ticket price × 1.25
Calculation: New ticket price = $4.80 × 1.25 = $6.00
Therefore, the new ticket price will be $6.00
Question 1 (5 points)
Correlation implies causation.
Question 1 options:
True
False
Question 2 (5 points)
A correlation between two variables means...
Question 2 options:
that both variables are always equal
that there is no relationship between the variables
that a change in one variable is matched by a change in the other variable
there is something wrong with the data
Question 3 (5 points)
A negative correlation between two variables means...
Question 3 options:
both variables are decreasing
both variables are increasing
there is no correlation
when one variable goes up, the other goes down
Question 4 (5 points)
A strong linear correlation means...
Question 4 options:
both variables are increasing
the graph of data points stay close to a line
there is a wide spread in the data
Question 5 (5 points)
Standard deviation is a measure of...
Question 5 options:
how linear data is.
the spread of data.
the difference between the greatest and the lowest values.
Question 6 (5 points)
The formula for standard deviation uses which average?
Question 6 options:
mean
median
mode
zero
Question 7 (5 points)
According the the fundamental counting principal for multiplication, if event A has m possible outcomes and event B has n possible, then even A followed by event B has...
Question 7 options:
m + n outcomes
m - n outcomes
m x n outcomes
m / n outcomes
Question 8 (5 points)
What is the value of 4! ("four factorial")
Question 8 options:
4
16
10
24
Question 9 (5 points)
If the probability of passing an exam is 80%, what is the probability of not passing it?
Question 9 options:
80%
50%
100%
20%
Question 10 (5 points)
Given that when flipping a coin, there is 1/2 chance of getting a heads:
What is the probability of flipping a coin and getting heads twice in a row?
Question 10 options:
1
1/2
1/4
1/2
Answer:
Question 1 (5 points)
Correlation implies causation.
False
Question 2 (5 points)
A correlation between two variables means...
that a change in one variable is matched by a change in the other variable
Question 3 (5 points)
A negative correlation between two variables means...
when one variable goes up, the other goes down
Question 4 (5 points)
A strong linear correlation means...
the graph of data points stay close to a line
Question 5 (5 points)
Standard deviation is a measure of...
the spread of data.
Question 6 (5 points)
The formula for standard deviation uses which average?
mean
Question 7 (5 points)
According the the fundamental counting principal for multiplication, if event A has m possible outcomes and event B has n possible, then even A followed by event B has....
m x n outcomes
Question 8 (5 points)
What is the value of 4! ("four factorial")
24
Question 9 (5 points)
If the probability of passing an exam is 80%, what is the probability of not passing it?
20%
Question 10 (5 points)
Given that when flipping a coin, there is 1/2 chance of getting a heads:
What is the probability of flipping a coin and getting heads twice in a row?
1/4
Step-by-step explanation:
These are just facts you should know.
A correlation between two variables means that a change in one variable is matched by a change in the other variable. Standard deviation is a measure of the spread of data. The probability of flipping a coin and getting heads twice in a row is 1/4 or 25%.
Explanation:A correlation between two variables means that a change in one variable is matched by a change in the other variable. For example, if there is a positive correlation between studying time and test scores, it means that as the studying time increases, the test scores also increase.
A negative correlation between two variables means that when one variable goes up, the other variable goes down. For instance, if there is a negative correlation between temperature and ice cream sales, it means that as the temperature increases, the ice cream sales decrease.
A strong linear correlation means that the data points on a graph stay close to a line. This indicates a strong relationship between the variables being measured.
Standard deviation is a measure of the spread of data. It tells us how much the individual data points differ from the mean (average) of the data set.
The formula for standard deviation uses the mean as the average.
According to the fundamental counting principal for multiplication, if event A has m possible outcomes and event B has n possible outcomes, then event A followed by event B has m x n outcomes.
The value of 4! (four factorial) is 24. Factorial represents the product of all positive integers from 1 to the given number.
If the probability of passing an exam is 80%, the probability of not passing it would be 20%.
The probability of flipping a coin and getting heads twice in a row is 1/4 or 25%.
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The area of the triangle is 1560 m2
True
False
Answer:
FALSE
Step-by-step explanation:
Area of triangle is given by formula :
[tex]Area\ =\ \frac{1}{2}\left(base\right)\left(Altitude\right)[/tex]
From picture we see that Altitude = 60 m
Base = 52 + 71 = 123 m
Now plug these values into above formula:
[tex]Area\ =\ \frac{1}{2}\left(123\right)\left(60\right)[/tex]
[tex]Area\ =\ \frac{1}{2}\left(15129\right)[/tex]
[tex]Area\ =\ \frac{15129}{2}[/tex]
[tex]Area\ =\ 7564.5[/tex]
Which is different than given area 1560 m^2.
Hence answer is FALSE.
What is the linear function equation that is represented in the graph?
Answer: y = (-1/2)*x + 1
Step-by-step explanation:
In the graph we can see a linear equation, the first thing we know is that a linear equation has the shape of:
y = ax + b
first, to find the slope we can use two pairs of the graphed ones, in the notation (x,y) we can select the pairs: (0, 1) and (2, 0)
we have that a = (y2 - y1)/(x2 - x1)
a = (0 - 1)/(2- 0 ) = -1/2
so the slope is -1/2
now, b is the y-intercept, this is the value of y when x = 0, and we can see that this value is 1 (the point where the graph intercepts the y-axis) so b = 1.
then the equation is y = (-1/2)*x + 1
Which of the following equations has a slope of -3 and a y-intercept of -4?
Answer:
An equation with a slope of -3 and an intercept of -4 is y = -3x - 4
Step-by-step explanation:
To find this we start with the base form of slope-intercept.
y = mx + b
Now we know that the slope goes in for m and the intercept goes in for b. Simply input those values.
y = -3x - 4
Solve.
{5x+y=2
{4x+y=4
Use the linear combination method.
(1, −8)
(0, 2)
(−2, 12)
(−3, 17)
Given these two equations:
1) 5x + y = 2
2) 4x + y = 4
Let's solve for x and y step by step.
Step 1: We start by subtracting equation (2) from equation (1) to eliminate y:
This gives us:
5x - 4x = 2 - 4
Which simplifies to:
x = -2
Step 2: Now, we substitute x = -2 into the equation (1) to find the value of y:
5*(-2) + y = 2
Which simplifies to:
-10 + y = 2
And therefore:
y = 12
So, the solution to the system of equations is x = -2 and y = 12.
Plz help on 36, with work if any
Answer:
A. (10,1)
Step-by-step explanation:
Janice bought juice packets for the 15 players on the soccer team The juice packets come in boxes of 6 How many boxes did Janice buy?
Answer:
3 boxes.
Step-by-step explanation:
We are told that Janice bought juice packets for the 15 players on the soccer team. The juice packets come in boxes of 6.
To find the number of boxes that Janice need to buy for 25 players, we will divide 15 by 6.
[tex]\text{Number of boxes that Janice needs to buy}=\frac{15}{6}[/tex]
[tex]\text{Number of boxes that Janice needs to buy}=2.5[/tex]
Since the juice packets come in boxes of 6, so we will round our answer to nearest whole number.
[tex]\text{Number of boxes that Janice needs to buy}=2.5\approx 3[/tex]
Therefore, Janice will buy 3 boxes of juice packets for 15 players.
The question entails a simple division operation of 15 players divided by 6 juice packets per box which gives 2.5. However, since Janice can't buy half a box, she ends up buying 3 boxes of juice packets.
Explanation:To answer your question, we need to perform a simple division arithmetic operation. This involves taking the total number of players which is 15 and dividing that by the number of juice packets in one box, which is 6 . The calculation is as follows: 15 ÷ 6 = 2.5. However, Janice cannot purchase half of a box so she would need to round up to the nearest whole number. Hence, Janice bought 3 boxes of juice packets for the soccer team.
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Caitlin went to the store to buy school clothes .She had a store credit from from a previous return in the amount of $39.58 if she bought 4 of the same style shirt in different colors and spent atotal of $52.22 after the store credit was taken off her total, what was the price of each shirt she bought?
Answer:
Each shirt costs $22.95
Step-by-step explanation:
39.58 + 52.22 = 91.80
91.80/4 = 22.95
Ludovica creates flash cards for her vocabulary words.She creates 3 more cards per noun.
Answer: what is the whole question angel?
Step-by-step explanation:
The area of a rectangle is length x width.Sasha is looking for rent the floor plan is rectangular.The length of the store is 21 and 2/3feet amd the area is 325 square feet.What is the width of the store?
Answer:
Width of the store = 15 feet.
Step-by-step explanation:
Area = length * width
Plugging in the given dimensions:-
325 = 21 2/3 * x
x = 325 / 21 2/3
= 325 / 65/3
= (325 * 3) / 65
= 15 feet (answer)
The population of a town increased by 15% in 2016, and decreased by 5% in 2017. If the population of the town was 60,000 in the beginning of 2016, then what was it at the end of 2017?
Answer:
The population at the end of 2017 is 65,550
Step-by-step explanation:
step 1; find the population at the end of 2016
if 60,000 increases by 15% therefore final % = 100 +15 =115%
Therefore 60,000 = 100%
? = 115%
by cross multiplication
={ (115 % x 60,000) /100} =69,000
Step 2: find the population at the end of 2017
if 69,000 decrease by 5% therefore the final% = 100 -5 =95%
Therefore 69000 = 100%
? = 95%
by cross multiplication
= 69000 x 95/100 = 65,550
At the newest animated movie, for every 99 9 children, there are 44 4 adults. There are a total of 3939 39 children and adults at the movie. How many children are at the movie?
Answer:
27 children.
Step-by-step explanation:
We are told that at the newest animated movie, for every 9 children, there are 4 adults. There are a total of 39 children and adults at the movie.
We can see that number of children is proportional to number of adults. So we will use proportions to solve for number of children at the movie.
[tex]\frac{\text{Number of children}}{\text{Number of children + Adults}}=\frac{9}{4+9}[/tex]
[tex]\frac{\text{Number of children}}{\text{Number of children + Adults}}=\frac{9}{13}[/tex]
Let us substitute number of children and adults in our proportion.
[tex]\frac{\text{Number of children}}{39}=\frac{9}{13}[/tex]
Multiply both side of equation by 39.
[tex]39*\frac{\text{Number of children}}{39}=39*\frac{9}{13}[/tex]
[tex]\text{Number of children}=39*\frac{9}{13}[/tex]
[tex]\text{Number of children}=3*9[/tex]
[tex]\text{Number of children}=27[/tex]
Therefore, 27 children are at the movie.
(02.03)A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles?
The number of orange fish is 1 1/4 times the number of blue fish. How many blue fish for every five orange fish
PUT IN POINT SLOPE FORM (-2,-3)m=8
Answer:
y+3= 8(x+2)
Step-by-step explanation:
original eq
y-y1=m(x-x1)
then you plug in given numbers
Answer:
[tex]y+3=8(x+2)[/tex]
Step-by-step explanation:
The point slope form:
[tex]y-y_1 = m(x-x_1)[/tex]
[tex]m=8\\(-2, -3)\\x_1=-2\\y_1=-3[/tex]
[tex]y-(-3)=8(x-(-2))[/tex]
[tex]y+3=8(x+2)[/tex]
Help me please!!Algebra Two!!
Answer:
a) -4 mult. 2
b) [tex](x+4)^2[/tex]
c) 2, quadratic
Step-by-Step Explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity.Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial.The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there is one real zero: -4
We can write them in intercept or factored form as (x+4) since x+4=0 gives x=-4.
Because the graph never crosses the x-axis it has an even multiplicity of at least 2.
The graph is facing up and is a U shape. This can only be a quadratic of degree 2. It is positive.
This means the function has a degree of 2.
Factor completely. 3x^2-3x-18 HINT: Factor out the greatest common factor first.
Answer:
3(x - 3)(x + 2)
Step-by-step explanation:
take out a common factor of 3 from each term
= 3(x² - x - 6)
to factor the quadratic consider the factors of - 6 which sum to - 1
These are - 3 and + 2, hence
3x² - 3x - 18 = 3(x - 3)(x + 2) ← in factored form
List the 6 congruency statements given ABC ~ DEF
Answer:
First choice is correct ∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF
Step-by-step explanation:
Given that triangles ABC and DEF are congruent. Now we need to choose correct congruency statements from the given choices.
We know that corresponding angles of congruent triangles are equal so we can write:
∠A ≅ ∠D
∠B ≅ ∠E
∠c ≅ ∠F
We know that corresponding sides of congruent triangles are equal so we can write:
AB = DE
BC = EF
AC = DF
comparing these with given choices we see that, First choice { ∠A ≅ ∠D, ∠B ≅ ∠E, ∠c ≅ ∠F, AB = DE, BC = EF, AC = DF} is correct.
630 baseball cards he sorts the cards into stacks of 30 how many stacks can he makes
Answer:21
Step-by-step explanation:
Answer:
21 stacks of 30
Step-by-step explanation:
630 divided into 30 stacks:
630/30= 21
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PLEASE HELP ME WITH THIS!!!
Answer:
E.
Step-by-step explanation:
Even though we have a sample of 40 units, we cannot determine that the units that are not in the sample will have the same or similar quality as the units that are in the sample. Thus none of the conclusions can be true.
Answer: Choice B) 100 pieces must be defective
Assuming the sample selected is representative of the population, we have two copies of "25" in that list (row 4; row 8) out of 40 total. So 2/40 = 1/20 = 0.05 = 5% of the items should be defective out of the entire population. Again this is assuming the sample is representative.
So we take 5% of 2000 and we end up with 0.05*2000 = 100 items we expect to be defective from a sample of 2000 items. Keep in mind that the true count will probably not be 100 items but some value close around it (eg: 98 or 101). This value is an estimate and not always perfect.
If choice B said "around 100" or "about 100" or "approximately 100" then I think it would be more technically correct. I think this is what your teacher is after.
In the 1918 baseball season Ty cobb had 421 at bats and 161 base hits. What was his batting average? Write your answer as a decimal rounded to the nearest thousandth
Answer:
Batting average = 0.382
Step-by-step explanation:
In the 1918 baseball season Ty cobb had 421 at bats and 161 base hits.
number of bat hits= 161
Number at bats = 421
Batting average = [tex]\frac{base \ hits}{at \ bats}[/tex]
Plug in the values in the formula
Batting average = [tex]\frac{161}{421}=0.382422802[/tex]
Now round the answer to three decimal places
Batting average = 0.382
Times spent studying by students in the week before final exams follow a normal distribution with standard deviation 8 hours. A random sample of 4 students was taken in order to estimate the mean study time for the population of all students a. Find the standard error of the mean b. What is the probability that the sample mean exceeds the population mean by more than 2 hours? c. What is the probability that the sample mean is more than 3 hours below the population mean? d. What is the probability that the sample mean differs from the population mean (on either side) by more than 4 hours? e. Suppose that a second (independent) random sample of ten students was taken. Without doing the calculations, state whether the probabilities in b, c, and d would be higher, lower, or the same for the second sample.
The sample mean X¯
X
¯
has normal distribution, mean the population mean μ
μ
, and standard deviation τ=84√
τ
=
8
4
. We want Pr(X¯−μ>2)
Pr
(
X
¯
−
μ
>
2
)
, which is Pr(Z>2τ)
Pr
(
Z
>
2
τ
)
, where Z
Z
is standard normal.
Th kc royals won 11 of 14 of their playoff games in 2014 what percent of their games did they win (round to the nearest ones)