Given that
y
= 12 cm and
θ
= 40°, work out
x
rounded to 1 DP.
Answer:
Step-by-step explanation:
Need diagram of what you are looking for....
x^2-2x−4=0 please leave ans in surd form and simplify
Step-by-step explanation:
using the quadratic formula......
Hi there!
How are you?
Answer:
\(\boxed{x = + \sqrt{5} |Or| x = 1 - \sqrt{5} }\)
Step-by-step explanation:
First you have to use quadratic formula with \(a=1, b=-2, c=-4.\)
\(x = \frac{-b \± \sqrt{b^2 -4ac} }{2a}\)
\(x = \frac{-(-2) \± \sqrt{(-2)^2 - 4(1)(-4)} }{2(1)}\)
\(x = \frac{\sqrt{^2\± \sqrt{20} } }{2}\)
\(x = + \sqrt{5}\) or \(x = 1 - \sqrt{5}\)
Hvae a good day/night!
A basketball player has a 0.689 probability of making a free throw. If the player shoots 18 free throws, what is the probability that she makes no more than 11 of them
It is determined while using the binomial distribution that there is still a 1.145=114.5% chance that she produces no more than 11 of them.
Calculating the probabilityThere are just two possible results for each throw. Either she succeeds or she fails. The binomial probability distribution is employed to answer this issue since the probability of completing a shot is regardless of all other throws.
Binomial probability distribution-
\(P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}\)
\(C_{n,x} = n!/x! (n-x)!\)
where,
the no. of success= x
the no. of trials = n
the probability of a success on one trial = p
The probability of throwing not more than 11 will be:
P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)
Where,
\(P(X=x) = C_{n,x} .p^{x}(1-p)^{n-x}\)
\(P(X=0) = C_{18,0} .(0.689)^{0}(0.311)^{18}\)≈0
\(P(X=1) = C_{18,1} .(0.689)^{1}(0.311)^{17}\)≈0
\(P(X=2) = C_{18,2} .(0.689)^{2}(0.311)^{16}\)≈0
\(P(X=3) = C_{18,3} .(0.689)^{3}(0.311)^{15}\)≈0
\(P(X=4) = C_{18,4} .(0.689)^{4}(0.311)^{14}\)≈0
\(P(X=5) = C_{18,5} .(0.689)^{5}(0.311)^{13}\)= 0.0003
\(P(X=6) = C_{18,4} .(0.689)^{6}(0.311)^{12}\)=0.0016
\(P(X=7) = C_{18,7} .(0.689)^{7}(0.311)^{11}\)=0.0062
\(P(X=8) = C_{18,8} .(0.689)^{8}(0.311)^{10}\)=0.0188
\(P(X=9) = C_{18,9} .(0.689)^{9}(0.311)^{9}\)=0.0463
\(P(X=10) = C_{18,10} .(0.689)^{10}(0.311)^{8}\)=0.9232
\(P(X=11) = C_{18,11} .(0.689)^{11}(0.311)^{7}\)=0.1488
So,
P(X<11) = P(X=0) + P(X=1) +P(X=2) + P(X=3) +P(X=4) +P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)
=0+0+0+0+0+0.0003+0.0016+0.0062+0.0188+0.0463+0.9232+0.1488 =1.145
Therefore, she makes 1.145=114.5% probability, no more than 11 of them.
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round to the nearest ten 426,889
68. What is the value of x?
If there is NO relationship between primary time spent at work and energy level for the population of all full-time employees, what is the mean of the test statistic?
a) 20.573
b) 0
c) 0.0003847
d) 4
The mean of the test statistic is 0.
Why will be mean of the test statistic is 0?
If there is NO relationship between primary time spent at work and energy level for the population of all full-time employees, the mean of the test statistic is b) 0.
A test statistic is a statistical data point that is used to evaluate whether or not a hypothesis is likely to be valid.
A hypothesis is typically an assertion about the characteristics of a population or the connection between two populations.
The test statistic aids in the decision-making process of whether or not to approve or reject the null hypothesis.
A test statistic is used to calculate the significance level of a hypothesis test. It assesses how well the evidence supports the null hypothesis.
We can determine the p-value by comparing the test statistic to a probability distribution's critical value.
If the p-value is lower than the significance level, the null hypothesis is rejected. If the p-value is greater than the significance level, the null hypothesis is not rejected.
0 because if there is NO relationship between primary time spent at work and energy level for the population of all full-time employees, the mean of the test statistic is 0.
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Y=2x
6x+3y=-12
What is the answer and how did you get the answer? Write the answer and show the process of how you got that answer.
Step-by-step explanation:
By substitution method
6x+3(2x)=12
6x+6x =12
12x=12
x=1
y=2x
y=2*1
y=2
CAN SOMEONE HELP ME PLEASE ASAP!?
Answer:
false
Step-by-step explanation:
the sides of the new shape are not parallel to the sides of the original shape.
and there is no center of the dilation.
for example, the lines with AA' and CC' cross somewhere else than BB' and DD'.
Elsa sells knitted hats for $5 each. Her goal is to make $300 in sales, so she wants to calculate how many hats she needs to knit (x). choose ALL equations in which x correctly represents the number of hats she needs to sell to meet her goal.
A) x/5 = $300
B) 5x = $300
C) $300x = 5
D) 300/5 = x
E) 5/300 = x
Answer:
B
Step-by-step explanation:
Answer:d and e
Step-by-step explanation:
YESIRRRRRRRRRRRRRRRRRRRRRRRRRRRR
In 1974 a mother was 6 times as old as her daughter. If the mother turned 50 in the year 2000, in what year was the mother double her daughter’s age?
This is in the topic of linear equations and please provide an explanation. (The working out)
Answer:
1990
Step-by-step explanation:
Since the mother was 50 years old in 2000, she was 50 - (2000-1974) = 50 - 26 = 24 years old in 1974.
Hence, the daughter was 24/6 = 4 years old in 1974.
In "x" years after 1974, the daughter will be 4+x years old, while the mother will be 24+x years old.
We need to find "x" from the equation
2(4 + x) = 24+x.
8 + 2x = 24 + x,
x = 24 - 8 = 16.
1974 + 16 = 1990.
Answer In 1990 the mother doubles her daughter's age
Check In 1990 mother's age is/was 24 + 16 = 40 years.
In 1990 the daughter's age is/was 4 + 16 = 20 years.
Francis surveyed a random sample of 70 7070 students at Franklin High School about their favorite season. Of the students surveyed, 18 1818 chose fall as their favorite season. There are 1816 18161816 students at Franklin High School. Based on the data, what is the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall? Choose 1 answer: Choose 1 answer:
Answer:
467
Step-by-step explanation:
Determine the percentage of those sampled whose favourite season is fall
(18/70) x 100 = 25.7%
the sample is representative of the population of students. So, 25.7% of the students would like fall
number of students at Franklin High School whose favourite season is fall = 25.7% x 1816 = 466.7 students
rounding off to the nearest whole number gives 467
Answer:
467
Step-by-step explanation:
Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options.
A) 2.3p – 10.1 = 6.4p – 4
B) 2.3p – 10.1 = 6.49p – 4
C) 230p – 1010 = 650p – 400 – p
D) 23p – 101 = 65p – 40 – p
E) 2.3p – 14.1 = 6.4p – 4
Answer: Multiplying both sides of the original equation by 100 gives the same
the solution as follows;
100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)
230·p - 1010 = 650·p - 400 - p
Step-by-step explanation:
We've known each other for so long Your heart's been aching but you're too shy to say it
In this exercise, find the area of the shaded part.
How is field data aggregated? Number of failed parts Number of failures Hours of operation Maintenance time Mark for follow up Question 3 of \( 7 . \) Data collection extends over a large number of it
Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,
such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.
Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,
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What is the volume of the cylinder? Express the answer in term of x.
On top of the picture says d=8cm
Step-by-step explanation:
d = 8 cm
r = 8 : 2
r = 4 cm
V = πr²h= π × 4 × 4 × 18
= 288π cm³
#CMIIWFind the value of F (5)
Using the slope of graph, we can find the value of F(5) to be = 12.
Define slope of graph?The slope of a line is determined by taking the tangent of the angle it forms with the x-axis. The slope of a straight line remains constant over time.
Y = mx + b can be used to calculate a straight line's slope-intercept form. The slope is denoted by the letter m and can be calculated as follows:
m = tanθ = (y2 - y1)/ (x2 - x1)
y = f(x)
y = (x-2) ² + 3
Now when x = 5,
y = (5-2) ² + 3
= 3² + 3
= 9 + 3
= 12
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Help me pleaseeeeeeee
Answer:
The surface area is:
276cm^2
Step-by-step explanation:
10x5=50x2=100
4x5=20x2=40
10x4=40x2=80
100+40+80=220
6x2=12x4=48
2x2=4x2=8
48+8=56
220+56=276
The volume of a right rectangular prism can be found by finding the product 3(6)(12) Which expression could also be used to determine the volume of this prism? 36(6) 2(3 + 12 + 6) 4(3)(12) 12 + 6 +3
Answer:
D
Step-by-step explanation:
Use a two-dimensional model and the dimensions provided to calculate perimeter or circumference and area of each object. Round to the nearest tenth if necessary.
The perimeter and the area of the flower are 7.9 inches and 19.6 square inches, respectively.
How to determine the perimeter of a real life object in a picture
The picture of a flower is seen in the image attached aside, whose perimeter must be estimated. To do this we must use an approximation by using the most similar geometric figure, look for all required dimensions and calculate the value.
We see that a circle offers the best approximation to the perimeter of the flower. The equation of the circumference is:
s = 2π · r
Where:
s - Perimeter of the flower, in inches.r - Radius of the flower, in inches.If we know that r = 2.5 in, then the perimeter of the flower is:
s = 2π · (2.5 in)
s ≈ 7.854 in
And the area of the flower (A), in square inches, is:
A = π · r²
A = π · (2.5 in)²
A ≈ 19.635 in²
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Answer:C=15.7in A=19.6in^2
Step-by-step explanation:
C(3.14)d
C=(3.14)(5)
C=15.7in
A=(3.14)r^2
A=(3.14)(2.5in)^2
A=19.6in^2
the 3.14 is pi but just the actual number
I will give brainiest
Richard and Teo have a combined age of 25. Richard is 7 years older than twice Teo's age. How old are Richard and Teo?
Answer:
Teo is 7 and Richard is 18
Step-by-step explanation:
7 + x = 25
x = 18
Please mark me brainliest!!
Richard is 19 years old and Teo is 6 years old.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Let Richard's and Teo's age be R and T years old respectively.
R +T= 25 -----(1)
R= 2T +7 -----(2)
Substitute (2) into (1):
(2T +7) +T= 25
3T +7= 25
3T= 25 -7
3T= 18
T=18 ÷3
T= 6
Substitute T= 6 into (2):
R= 2(6) +7
R= 12 +7
R= 19
Thus, Richard is 19 years old and Teo is 6 years old.
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You go to the State Fair, and have fun. Your Cost Equation can be represented by the
equation
C(r) = 6r + 10 where Crepresents the total cost, and r represents the number of
rides you went on
Find rif C (r) = 28
Answer:
r = 3
Step-by-step explanation:
C(r) = 6r + 10
C(r) = 28
Substitute 28 for C(r)
28 = 6r + 10
Subtract 10
18 = 6r
Divide by 6
3 = r
r = 3
Help i need to finish it today And can you explain the steps so i wont need help next time or if you don’t want to its okay :)
Answer:
264 sq. in.
Step-by-step explanation:
The easiest way to find the lateral surface area is to multiply the perimeter of the base times the height.
In your case the perimeter of the base is 2(8) + 2(3) = 16 + 6 = 22
The height is 12, so multiply 12 times 22 = 264 sq. in.
What equation should i write?
Answer:
6t = 9
Step-by-step explanation:
The two pieces of tape are the same length and one tape represents 9 while the other represents 6 pieces of t. Thus, the equation should be:
6t has the same length as 9.
6t = 9
F(x)=4x-11, what is the value of f(5)
Answer:
f(15) = 49
Step-by-step explanation:
f(x) = 4x - 11
f(15) = 4(15) - 11 (substitute 15 instead of x)
f(15) = 60 -11
f(15) = 49
Answer:
f(5)=9
Step-by-step explanation:
f(x)=4x-11
f(5)=4(5)-11
= 20-11
=9
what is the probability of obtaining a sample mean greater than m 5 60 for a random sample of n 5 16 scores selected from a normal population with a mean of m 5 65 and a standard deviation of s 5 20?what is the probability of obtaining a sample mean greater than m 5 60 for a random sample of n 5 16 scores selected from a normal population with a mean of m 5 65 and a standard deviation of s 5 20?
The probability of obtaining a sample mean greater than 60 from a random sample of 16 scores selected from a normal population with a mean of 65 and a standard deviation of 20 is approximately 0.8413 or 84.13%.
To calculate the probability of obtaining a sample mean greater than 60 from a random sample of 16 scores taken from a normal population with a mean of 65 and a standard deviation of 20, we can use the Central Limit Theorem.
The Central Limit Theorem states that the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a population mean (μ) of 65, a population standard deviation (σ) of 20, and a sample size (n) of 16.
First, we need to calculate the standard deviation of the sample mean (σm):
σm = σ / √n
= 20 / √16
= 20 / 4
= 5
Now, we can calculate the z-score, which measures how many standard deviations the sample mean is away from the population mean:
z = (x - μ) / σm
= (60 - 65) / 5
= -1
Using a standard normal distribution table or a calculator, we can find the probability associated with a z-score of -1. The probability of obtaining a sample mean greater than 60 can be calculated as the complement of the probability associated with a z-score of -1.
P(sample mean > 60) = 1 - P(z < -1)
Looking up the z-score in a standard normal distribution table, we find that the probability associated with a z-score of -1 is approximately 0.1587.
P(sample mean > 60) = 1 - 0.1587
= 0.8413
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Determine if the triangles shown below are similar. If they are similar, state which postulate is true and complete the similarity statement.
Triangle LMN has sides MN=42 and NL=52.5. Triangle GHN has sides HN=32 and NG=40.
Both triangles are similar.
Given that;
Triangle LMN has sides MN=42 and NL=52.5.
And, Triangle GHN has sides HN=32 and NG=40.
Hence, Ratio of MN and NL is,
MN / NL = 42 / 52.5 = 0.8
And, Ratio of HN and NG is,
HN / NG = 32 / 40 = 0.8
So, Both triangles are similar.
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according to the 1990 census, those states with an above-average number of people, x, who fail to complete high school tend to have an above average number of infant deaths, y. in other words, there is a positive association between x and y. the most plausible explanation for this is
There are certainly hidden variables, which is the most likely explanation for this correlation. (C) States with large populations, for instance, will also have a larger percentage of infant death and high school dropouts.
What is a positive association?When the values of one variable tend to rise as the values of the other rise, two variables are said to be positively correlated.
When the values of one variable tend to fall as the values of the other rise, two variables are said to be negatively correlated.
A favorable connection occurs when the graph's line is advancing, as in Problem 1.
In this illustration, we make the assumption that the number of years of schooling and the expected pay are positively correlated.
So, in the given situation the most likely explanation for this correlation is that there are likely lurking variables.
For instance, states with big populations will also have a higher proportion of neonatal mortality as well as high school dropouts.
Therefore, there are certainly hidden variables, which is the most likely explanation for this correlation. (C) States with large populations, for instance, will also have a larger percentage of infant death and high school dropouts.
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Complete question:
According to the 1990 census, those states with an above average number X of people who fail to complete high school tend to have an above average number Y of infant deaths. In other words, there is a positive association between X and Y. The most plausible explanation for this association is
a. X causes Y. Thus, programs to keep teens in school will help reduce the number of infant deaths.
b. Y causes X. Thus, programs that reduce infant deaths will ultimately reduce the number of high school dropouts.
c. lurking variables are probably present. For example, states with large populations will have both a larger number of people who fail to complete high school and a larger number of infant deaths.
d. the association between X and Y is purely coincidental. It is implausible to believe the observed association could be anything other than accidental.
Find two numbers having a difference of 16 such that the result of adding their sum and their product is a minimum
Answer:
-8.5 and 7.5
Step-by-step explanation:
Let's call the two numbers x and y. We know that their difference is 16, so we can write:
x - y = 16 or x = y + 16
We want to find the values of x and y that minimize the expression:
x + y + xy
Substituting x = y + 16, we get:
(y + 16) + y + (y + 16)y
Simplifying and expanding, we get:
y^2 + 17y + 16
To minimize this expression, we can take its derivative with respect to y and set it equal to 0:
d/dy (y^2 + 17y + 16) = 2y + 17 = 0
Solving for y, we get:
y = -8.5
Substituting y = -8.5 into x = y + 16, we get:
x = 7.5
Therefore, the two numbers with a difference of 16 such that the result of adding their sum and their product is a minimum are -8.5 and 7.5.
2 - 14. What is the equation of the line perpendicular to y - 4 = (x - 6) and passes through the point - (-3,2)? 5 5 - 2 5 = O -2= O A. y-2=-(x + 3) x OB. y + 3 = -(x - 2) (- 2 O c. y - 2 = = (x + 3) OD. y + 3 = (x - 2) 2 2 2 5
Solution:
The equation of a line that passes through a point is expressed as
\(\begin{gathered} y-y_1=m(x-x_1)\text{ ---- equation 1} \\ where \\ m\Rightarrow slope\text{ of the line} \\ y\Rightarrow y-intercept\text{ of the line} \\ (x_1,y_1)\Rightarrow coordinate\text{ of the point through which the line passes} \end{gathered}\)Two lines A and B are said to be perpendicular if the slope of line A is equal to the negative reciprocal of the slope of line B.
Thus, lines A and B are perpendicular if
\(m_A=-\frac{1}{m_B}\text{ ---- equation 2}\)Let the line equation
\(y-4=\frac{2}{5}(x-6)\)represent the line A.
step 1: Evaluate the slope of line A.
Comparing the equation of line A with equation 1, we can conclude that the slope of the line A is
\(m_A=\frac{2}{5}\)step 2: Evaluate the slope of line B.
Since lines A and B are perpendicular, we have
\(\begin{gathered} From\text{ equation 2,} \\ \begin{equation*} m_A=-\frac{1}{m_B} \end{equation*} \\ where \\ m_A=\frac{2}{5} \\ thus, \\ \frac{2}{5}=-\frac{1}{m_B} \\ cross-multiply \\ -2m_B=5 \\ divide\text{ both sides by -2} \\ \frac{-2m_B}{-2}=\frac{5}{-2} \\ \Rightarrow m_B=-\frac{5}{2} \end{gathered}\)step 3: Evaluate the line B.
Since the line B passes through the points (-3,2), recall from equation 1
\(\begin{equation*} y-y_1=m(x-x_1)\text{ } \end{equation*}\)where
\(\begin{gathered} x_1=-3 \\ y_1=2 \\ m=m_B=-\frac{5}{2} \end{gathered}\)Substitute these values into equation 1.
Thus,
\(\begin{gathered} y-2=-\frac{5}{2}(x-(-3)) \\ \Rightarrow y-2=-\frac{5}{2}(x+3) \end{gathered}\)Hence, the equation of the line is
\(y-2=-\frac{5}{2}(x+3)\)The correct option is A