Answer:
A (-1,-10) ; A (-1,14)
Step-by-step explanation:
[tex]\sqrt{(-1-4)^2 + (y-2)^2} = 13 \\ 25 + y^2 + 4 -4y = 169[/tex]
y^2 -4y - 140 = 0
Δ/4 = 4 + 140 = 144
y1 = 2 + 12 = 14
y2 = 2 -12= -10
is the sum of two rational numbers sometimes zero ture or false?
Answer:
True.
Step-by-step explana
-4/5 + 4/5 is 0
The volume of a rectangular prism is given by 24x3+78x2+49x+10. The height of the prism is given by 2x+5. Find an expression for the area of the base of the prism
Answer:
?
Step-by-step explanation:
i cant not explian that
at the present time, gerald is eight less than five times his nephews age. seven years ago gerald was 9 times his nephews age.
(A)if g represents geralds age now and n represents his nephews age today. use a system of equations that could be used to model this scenario?
(B)than use the equations to determine algebraically the ages of both Gerald and his nephew.
(C)than determine in how many years Gerald will be three times as old as his nephew?
What you know about rollin' down in the deep?
When your brain goes numb, you can call that mental freeze
When these people talk too much, put that sh*t in slow motion, yeah
I feel like an astronaut in the ocean, ayy
What you know about rollin' down in the deep?
When your brain goes numb, you can call that mental freeze
When these people talk too much, put that sh*t in slow motion, yeah
I feel like an astronaut in the ocean
Razon trigonometría que se requiere para calcular la altura de la torre si desde una distancia de 50 m se observa su punto mas alto con un ángulo de 48
Answer:
se supone que debes usar el SINE RATIO ya que se trata del lado opuesto y la hipotenusa.
course
Look at the following number line:
- 10
-5
0
5
10
What are two ways to write the inequality graphed?
x>-1 and -1
XS-1 and -12X
x < -1 and -1 > X
x2-1 and -1 5x
first and last one i think
Write the phrase as an algebraic expression and simplify if possible. Let x represent the unknown number
Three times a number, decreased by five
(Simplify your answer.)
To express the phrase "Three times a number, decreased by five" as an algebraic expression, we can use the variable x to represent the unknown number: 3x - 5
Now, let's simplify this expression: Given that the unknown number is represented by x, we can substitute it into the expression above. Substituting x into the expression, we have: [tex]3(x) - 5 3x - 5[/tex] Therefore, the algebraic expression representing "Three times a number, decreased by five" is [tex]3x - 5.[/tex] At this point, there is no further simplification possible since the expression is already in its simplest form.
For example, let's assume the unknown number x is 7. We can plug in this value to evaluate the expression: [tex]3(7) - 5 = 21 - 5 = 16[/tex] Similarly, if x is -2, the calculation would be: [tex]3(-2) - 5 = -6 - 5 = -11[/tex] In conclusion, the algebraic expression 3x - 5 represents the phrase "Three times a number, decreased by five."
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I need help please I dont understand
if a line with an angle of inclination 120⁰ and passes trough (√3,1),then what is the equation of a line
Answer:
The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation the equation of the straight line will be.
Step-by-step explanation:
Kyle buys a bag of cookies that contains 4 chocolate chip cookies, 9 peanut butter cookies, 9 sugar cookies and 7 oatmeal cookies. What is the probability that Kyle randomly selects a sugar cookie from the bag, eats it, then randomly selects a peanut butter cookie
Yam
190
Groundnuts
90
Vegetables
30. What is the ratio of the land used
for groundnuts to the land for
vegetables
Answer:
3:1
Step-by-step explanation:
90:30 simplified is 3:1
Q2 find the degree of the polynomial
x4(4x+1)
Step-by-step explanation:
x⁴(4x+1)
4x⁵+x⁴
degree is 5
When we expand (2x + 1/2)^6, what is the coefficient on the x^4 term?
Answer: The coefficient before x^4 is 60
Step-by-step explanation:
Hey! So I am not an expert at this, but you have to use the binomial theorem
I have attached of the Pascals Triangle (one shows the row numbering as well)
Basically in a pascal triangle, you add the two numbers above it to get the next number below
As you can see, the rows start from 0 instead of 1
The 6th row contains the numbers 1, 6, 15, 20, 15, 6, 1 which would be the coefficient terms
NOTE: the exponents always add to 6, the first term starts at 6 and decrease it's exponent by 1 each time (6, 5, 4, 3, 2, 1, 0) and the second term increases it's exponent by 1 each time (0, 1, 2, 3, 4, 5, 6)
Using this information the third term from the sixth row (15) would be where it is x^4 (I have circled it on the second image)
It would be 15 × 2^4 × (1/2)^2 = 60
The reason why it is 2^4 and (1/2)^2 is because the third term has the exponents 4 and 2 (bolded on the NOTE) which means that the first term must be put to the power of 4 and the second term must be put to the 2nd power
Sorry for the lousy explanation. I really hope this makes sense! Let me know if this helped :)
Which is the graph of f(x) = 2 (4)?
5
40.4)
404)
4
(4,4)
3
3
3 2
2
2
2
(2.1)
6,2)
1
5 -4 -3 -2 -14
1
3
4
-5 4 -3 -2 -14
234
-5 6 -3 -2 -14
2
3
4
5
X
-2
-2
نا دیا
-3
-3
4
W4
-5
5
Tu
5
4
(
24)
Answer:
The Third one
Step-by-step explanation:
Your Welcome :)
Graph of the function is attached below.
Correct option is D.
What is exponential function?As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:
Definition of exponential function
In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant called the base of the function, which must be greater than 0.
Given, exponential function
f(x) = (1/4)4ˣ
exponential function is defined for x∈R
Putting x = 0
f(0) = (1/4)4⁰
f(0) = 1/4
Point on curve is (0,1/4)
Putting x = 1
f(1) = (1/4)4¹
f(1) = (1/4)4
f(1) = 1
Point on curve is (1,1)
Putting x = 2
f(2) = (1/4)4²
f(2) = (1/4)16
f(2) = 4
Point on curve is (2,4)
Putting x = 3
f(3) = (1/4)4³
f(3) = (1/4)64
f(3) = 16
Point on curve is (3,16)
Point (0, 1/4), (1, 1), (2, 4), (3, 16) can be used to draw graph of the function.
Hence, graph of the function is drawn as follows.
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Can someone help me with this question please.
Answer:
40
Step-by-step explanation:
As the lawn size increases by 4 the weight increases by 8
A square-based tent covers an area of 64 square feet. What is the length of one side of the tent?
Answer:
8 feet
Step-by-step explanation:
A square's area can be expressed as l², with l representing one side of the tent. Therefore, as our area is 64, we can say that 64 = l². Taking the square root of both sides, we get that √64 = l, and l = 8 feet
which of the following statements is true
Answer: B ACE is similar to DCB
Step-by-step explanation:
Find the difference of (4.2x10^3)-(2.7x10^3)
Show work!
Step-by-step explanation:
Is it helpful ?
plz let me know
Find the value of y and show work
Answer:
75
Step-by-step explanation:
∠K and ∠ R are congruent (equal)
Triangle Sum Theory - angles of all triangles add to 180
180 - 79 - 26 = 75
Question 11 of 45
Which similarity postulate or theorem can be used to verify that the two
triangles shown below are similar?
12
6 R
X 2 z
O A. Similarity cannot be determined,
B. SSS theorem
O C. AA postulate
D. SAS theorem
Answer:
You are only given a Side, an Angle, and then a side. So that is what I would choose. It can't be AA because you weren't given two angles. It can't be SSS because you weren't given 3 sides.
Step-by-step explanation:
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Option B is the correct answer.
What is triangle congruency?There are ways to prove that two triangles are congruent.
- Side-Side-Side (SSS) Congruence.
The three sides of one triangle are equal to the corresponding three sides of another triangle.
- Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
- Angle-Side-Angle (ASA) Congruence.
The two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
- Angle-Angle-Side (AAS) Congruence.
We have,
Similar triangles are triangles that have the same shape but may have different sizes.
Two triangles are similar if their corresponding angles are equal, and their corresponding sides are proportional.
When two triangles are similar, they have the same shape, but one may be larger or smaller than the other.
Now,
ΔPQR and ΔXYZ
PQ/XY = 12/4 = 3
PR/XZ = 6/2 = 3
Since the two sides are proportional,
QR/YZ will be proportional.
Now,
PQ/XY = PR/XZ = QR/YZ
ΔPQR and ΔXYZ are similar due to the SSS theorem.
Thus,
ΔPQR and ΔXYZ are similar due to the SSS theorem.
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Please help please guys how are you doing
Answer:
the answer of the the triangle is 6
Answer:
6
Step-by-step explanation:
First row:
8 ÷ 2 = 4. → Square: 4
Second row:
14 - 4 = 10.
[two circles] = 10. So, 10÷2 = 5.
Circle = 5
Third Row:
[triangle] + 5 = 11
11 - 5 = 6
Triangle = 6
the probability that a customer of a network operator has a problem about you needing technical staff's help in a month is 0.01. This operator installs internet for 500 households in a residential area a, Calculate the average number of households in this residential area having internet problems in a certain month
b, Calculate the probability that in 6 consecutive months there is only one month that no customer in this area has a network problem that needs the help of technical staff
Answer:
(a) average calls = 5
(b) probability that there is exactly one call in 6 consecutive monts = 0.038
Step-by-step explanation:
Let event of a customer requiring help in a particular month = H
and event of a customer not requiring help in a particular month = ~H
Given
p= 0.01, therefore
Number of households, n = 500.
Binomial distribution:
x = number of households requiring help in a particular month
P(x,n,p) = C(x,n)*p^x*(1-p)^(n-x)
where
C(x,n) = n!/(x!(n-x)!) is the the number of combinations of x objects out of n
(a) Average number of households requiring help = np = 500*0.01 = 5
(b)
Probability that there are no calls requiring help in a particular month
P(0), q= C(0,n)*p^0(1-p)^(n-0)
= 1*1*0.99^500
= 0.006570483
Applying binomial probability over six months,
q = 0.006570483
n = 6
x = 1
P(x,n,q)
= C(x,n)*q^x*(1-q)^(n-x)
= 6!/(1!*5!) * 0.006570483^1 * (1-0.006570483)^5
= 0.038145
Therefore the probability that in 6 consecutive months there is exactly one month that no customer has called for help = 0.038
(08.07 MC)
A polynomial function is shown below:
f(x) = x3 − 3x2 − 4x + 12
Which graph best represents the function? (5 points)
Answer:
Graph A (first graph from top to bottom)
Step-by-step explanation:
Given [tex]f(x)=x^3-3x^2-4x+12[/tex], since the degree of the polynomial is 3, the function must be odd and will resemble the shown shape in the graphs. The degree of 3 indicates that there are 3 zeroes, whether distinct or non-distinct. Therefore, the graph must intersect the x-axis at these three points.
Factoring the polynomial:
[tex]f(x)=x^3-3x^2-4x+12,\\f(x)=(x+2)(x-2)(x-3),\\\begin{cases}x+2=0, x=-2\\x-2=0, x=2\\x-3=, x=3\end{cases}[/tex]
Thus, the three zeroes of this function are [tex]x=-2, x=2, x=3[/tex] and the graph must intersection the x-axis at these points. The y-intercept of any graph occurs when [tex]x=0[/tex]. Thus, the y-coordinate of the y-intercept is equal to [tex]y=0^3-3(0^2)-4(0)+12,\\y=12[/tex] and the y-intercept is (0, 12).
The graph that corresponds with this is graph A.
Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounces.
(a)What is the standard deviation of the average fill volume of 22 bags?
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
Answer:
a) 0.0171 fluid ounces.
b) 0% probability that the average fill volume of 22 bags is below 5.95 ounces
c) The mean should be of 6.153 fluid ounces.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard deviation of 0.08 fluid ounces.
This means that [tex]\sigma = 0.08[/tex]
(a)What is the standard deviation of the average fill volume of 22 bags?
This is s when n = 22. So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]s = \frac{0.08}{\sqrt{22}}[/tex]
[tex]s = 0.0171[/tex]
(b)The mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 22 bags is below 5.95 ounces?
We have that [tex]\mu = 6.16[/tex]. The probability is the p-value of Z when X = 5.95. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{5.95 - 6.16}{0.0171}[/tex]
[tex]Z = -12.3[/tex]
[tex]Z = -12.3[/tex] has a p-value of 0.
0% probability that the average fill volume of 22 bags is below 5.95 ounces.
(c)What should the mean fill volume equal in order that the probability that the average of 22 bags is below 6.1 ounces is 0.001?
[tex]X = 6.1[/tex] should mean that Z has a p-value of 0.001, so Z = -3.09. Thus
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-3.09 = \frac{6.1 - \mu}{0.0171}[/tex]
[tex]6.1 - \mu = -3.09*0.0171[/tex]
[tex]\mu = 6.153[/tex]
The mean should be of 6.153 fluid ounces.
Which expression is equivalent to -6(-⅔+2x)?
O-4-12x
O-4+ 2x
O 4-12x
O 4+ 12x
Answer:
4-12x
Step-by-step explanation:
opening the brackets;
(-6×-2/3)- 12x
-2×-2 -12x
4-12x
Answer:
4 - 12x
Step-by-step explanation:
We can find an equivalent expression by distributing
-6(-⅔+2x)
Distribute by multiplying -6 times what's inside of the parenthesis ( -2/3 and 2x )
-6 * -⅔ = 4
-6 * 2x = -12x
We would be left with 4 - 12x
I need help I’ll mark u as brainlest
Answer:
105 in³
Step-by-step explanation:
Volume of triangular prism = base area * height
here
base area = (10*7)/2 = 35
height = 3
Volume = 35* 3 = 105
Is 256.78 power by 10 100 or 1000
Answer:
I would say 100 since 256.78 is closer to 100 then 1000 or 10
Step-by-step explanation:
Alix is 10 years older than tamia. Alanna is twice as old as tamia. If the sum of their ages is 74, how old is alanna
Answer:
Alanna is 32 years old
Step-by-step explanation:
Hi there!
We're given that Alix is 10 years older than Tamia and Alanna is twice as old as Tamia.
Since Alix and Alanna's ages are in relation to Tamia's, let's make Tamia's age x
Alix is 10 years older than Tamia, so Alix must be x+10 years old
Alanna is twice as old as Tamia, so she must be 2x years old
We're also given that Alix+Alanna+Tamia=74
When we substitute it with the expressions we have, it becomes:
x+x+10+2x=74
now combine like terms
4x+10=74
subtract 10 from both sides
4x=64
divide both sides by 4
x=16
We found the value of x (Tamia's age)
However, the problem asks for Alanna's age, which we have set as 2x
So Alanna is 2*16, or 32 years old
Hope this helps! :)
Answer:
32 years
Step-by-step explanation:
that is the procedure above
The Rockwell hardness of a metal is determined by impressing a hardened point into the surface of the metal and then measuring the depth of penetration of the point. Suppose the Rockwell hardness of a particular alloy is normally distributed with mean 70 and standard deviation 3. (Rockwell hardness is measured on a continuous scale.)a. If a specimen is acceptable only if its hardness is between 67 and 75, what is the probability that a randomly chosen specimen has an acceptable hardness?b. If the acceptable range of hardness is (70-c, 70+c) , for what value of c would 95% of all specimens have acceptable hardness?c. If the acceptable range is as in part (a) and the hardness of each of ten randomly selected specimens is independently determined, what is the expected number of acceptable specimens among the ten?d. What is the probability that at most eight of ten independently selected specimens have a hardness of less than73.84? [Hint: Y = the number among the ten specimens with hardness less than 73.84 is a binomial variable; what is p?]
Answer:
a) The probability that a randomly chosen specimen has an acceptable hardness is 0.7938.
b) If the acceptable range of hardness is (70-c, 70+c), then the value of c would 95% of all specimens have an acceptable hardness of 5.88.
c) Expected number of acceptable specimens among the ten is 7.938.
d) Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Step-by-step explanation:
a )
[tex]P(67 < X< 75) = P( (67 - 70) / 3 < X < (75 - 70) / 3 )\\\\= P( - 1 < Z < 1.67) = 0.9525 - 0.1587 = 0.7938[/tex]
b )
[tex]c = 1.96 * 3 = 5.88[/tex] { Since Z = 1.96 for 95% CI refer table.}
c )
Expected number of acceptable specimens among the ten [tex]= 10 * P(67 < X< 75) \\\\= 10 * 0.7938 = 7.938[/tex]
d )
Binomial with n = 10 and p = P(X < 73.84)
[tex]p = P(Z <(73.84 - 70) / 3 ) = P(Z < 1.28) = 0.8997\\\\P(X <= 8) = 1 - P(X = 9) - P(X = 10)\\= 0.2650635[/tex]
Alla and Balla together drink 750 milliliters (ml) of water. If Alla drinks 50% more than
Balla, how much does Alla drink?
Answer:
Step-by-step explanation:
A + B = 750
A = 1.5 B
~~~~~~~~~~~~~~
750-B = 1.5 B
750 = 1.5 B + B
750 = B(1.5 +1)
750 = B (2.5)
B = 300
A = 450
When comparing two box-plots that show the same type of information, what determines agreement within the data?
A.the range of the quartiles in each data set
B.the median of each data set
C.the mean of each data set
D.the number of values in each data set
Answer:
c.the mean of each data set
Answer:
A
Step-by-step explanation:
