Answer:
38
Step-by-step explanation:
add 189+115 = 304
then 304÷8 =38
Use z scores to compare the given values.
Based on sample data, newborn males have weights with a mean of 3217.9g and a standard deviation of 780.1g. Newborn females have weights with a mean of 3086.5g and a standard deviation of 523.8g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700g or a female who weighs 1700g?
Using z-scores, it is found that a female who weighs 1700g has the more extreme value relative to the group from which they came.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For the newborn male, we have that [tex]X = 1700, \mu = 3217.9, \sigma = 780.1[/tex], hence the z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1700 - 3217.9}{780.1}[/tex]
Z = -1.946.
For the newborn female, we have that [tex]X = 1700, \mu = 3086.5, \sigma = 523.8[/tex], hence the z-score is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1700 - 3086.5}{523.8}[/tex]
Z = -2.645.
Due to the higher absolute value of the z-score, a female who weighs 1700g has the more extreme value relative to the group from which they ca,e.
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y=5x-3 input and output
Answer:
y out put x input and 3 is input and as 5 . tell me if you get it right
Sarah plays softball where a single is one base, a double is two bases, a triple is three bases, and a home run is four bases. In her last game, she only hit singles and triples, for a total of 14 bases. She had two more triples than singles. Choose the graph that best depicts this problem. graph the solution
The graph of y+21 > 6 is
Answer:
Image attached below.
Step-by-step explanation:
Hello!
First let's isolate y:
y + 21 > 6y > -15This means that we are looking at all the values on the coordinate plane that are above the line y = -15.
The red shaded region is the solution region. Note that -15 is not a solution of y > -15 (the dotted line indicates that).
# The size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles. If the greater of the opposite interior angles exceeds smaller by 30°, find the measure of the interior angles of the triangle.
please help me
Answer:
30° and 60°
Step-by-step explanation:
Let the interior angles be ∠x₁ (smaller) and ∠x₂ (larger), and the exterior angle ∠X.
Making the statements into equations :
Size of an exterior angle of a triangle is the supplement of smaller of two opposite interior angles ⇒ ∠X + ∠x₁ + ∠x₂ = 180° [Equation 1]
Greater of the opposite interior angles exceeds smaller by 30° :
⇒ ∠x₂ = ∠x₁ + 30° [Equation 2]
By exterior angle property :
⇒ ∠x₁ + ∠x₂ = ∠X [Equation 3]
Substituting Equation 3 in Equation 1 :
⇒ ∠x₁ + ∠x₂ + ∠x₁ + ∠x₂ = 180°
⇒ 2 (∠x₁ + ∠x₂) = 180°
⇒ ∠x₁ + ∠x₂ = 90°
⇒ ∠x₂ = 90° - ∠x₁ [Equation 4]
Substituting Equation 4 in Equation 2 :
⇒ 90° - ∠x₁ = ∠x₁ + 30°
⇒ 2∠x₁ = 60°
⇒ ∠x₁ = 30°
Substituting the value of ∠x₁ in Equation 2 :
⇒ ∠x₂ = 30° + 30°
⇒ ∠x₂ = 60°
The measures of the interior angles are 30° and 60°
Hello, help me please)
Answer:
Given equation:
[tex]10^{5x-2}=2^{8x-3}[/tex]
Take natural logs of both sides:
[tex]\implies \ln 10^{5x-2}= \ln 2^{8x-3}[/tex]
[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]
[tex]\implies (5x-2)\ln 10=(8x-3) \ln 2[/tex]
Expand brackets:
[tex]\implies 5x\ln 10 - 2\ln 10=8x \ln 2 -3 \ln 2[/tex]
Collect like terms:
[tex]\implies 5x\ln 10 - 8x \ln 2 =2\ln 10-3 \ln 2[/tex]
Factor left sides:
[tex]\implies x(5\ln 10 - 8 \ln 2) =2\ln 10-3 \ln 2[/tex]
[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]
[tex]\implies x(\ln 10^5 - \ln 2^8) =\ln 10^2- \ln 2^3[/tex]
[tex]\textsf{Apply log Quotient law}: \quad \ln_a\frac{x}{y}=\ln_ax - \ln_ay[/tex]
[tex]\implies x\left(\ln\left(\dfrac{10^5}{2^8}\right)\right) =\ln\left(\dfrac{10^2}{2^3}\right)[/tex]
Simplify:
[tex]\implies x\left(\ln\left(\dfrac{3125}{8}\right)\right) =\ln\left(\dfrac{25}{2}\right)[/tex]
[tex]\implies x=\dfrac{\ln\left(\dfrac{25}{2}\right)}{\ln\left(\dfrac{3125}{8}\right)}[/tex]
[tex]\implies x=0.4232297737...[/tex]
If five quarts of paint are needed for 250 square-feet of room, 13 quarts of paint will cover how many square feet of room?
Do not put units or commas, only put the number value to the nearest whole number.
Answer:
650
Step-by-step explanation:
let the unknown feet of room = X
5 paints = 250 square feet of room
13 paints = X
cross multiply
5*X = 250*13
X =3250÷5
X = 650 square feet of room
please help me do this mathematics question..experts .
The partial differential expression is equal to the expression 30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²) and the total differential formula is Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³).
How to apply partial derivatives and total differentials
In the first part of this question we must apply the concept of partial derivatives to find the form of the entire expression, whose variables are two. Partial differentiation is a generalization of the ordinary differentiation:
[tex]\frac{\partial f}{\partial x} = 6\cdot x^{5}+12\cdot x^{3}\cdot y^{4}+y^{6}[/tex] (1)
[tex]\frac{\partial^{2} f}{\partial x^{2}} = 30\cdot x^{4}+36\cdot x^{2}\cdot y^{4}[/tex] (2)
[tex]\frac{\partial^{2} f}{\partial x \,\partial y} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex] (3)
[tex]\frac{\partial f}{\partial y} = 12\cdot x^{4}\cdot y^{3} +6\cdot x \cdot y^{5}[/tex] (4)
[tex]\frac{\partial^{2} f}{\partial y^{2}} = 36\cdot x^{4}\cdot y^{2} + 30\cdot x\cdot y^{4}[/tex] (5)
[tex]\frac{\partial f}{\partial y \,\partial x} = 48\cdot x^{3}\cdot y^{3}+6\cdot y^{5}[/tex] (6)
Then, the entire expression is:
30 · x⁴ + 36 · x² · y⁴ + 36 · x⁴ · y² + 30 · x · y⁴
30 · (x⁴ + x · y⁴) + 36 · (x² · y⁴ + x⁴ · y²)
30 · x · (x³ + y⁴) + 36 · x² · y² · (y² + x²)
In the second part we must determine the total differential of z with respect to two variables:
[tex]\Delta z = \frac{\partial f}{\partial x}\cdot \Delta x + \frac{\partial f}{\partial y}\cdot \Delta y[/tex] (7)
If we know that z = sin (x³ + y³), Δx = 0.3 and Δy = 0.2, then the total differential of the function is:
Δz = 3 · cos (x³ + y³) · x² · (0.3) + 3 · cos (x³ + y³) · y² · (0.2)
Δz = (0.9 · x² + 0.6 · y²) · cos (x³ + y³)
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Transformation of quadratic functions
Answer:
g(x) = a(x − h)2 + k, where a ≠ 0.
Step-by-step explanation:
The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.
In Autobiography by Abraham Lincoln Lincoln avoids embellishing on his own life and keeps his portrayal of his life very______.
A.neutral
B. negative
C. humorous
Holly scored an 88, 91, 89, 84, and a 98 on the last five math tests. What is her mean test score?
Answer:the mean is 90
Step-by-step
you find the sum of the values then divide them by the amount of numbers in the set
what is the sign of a times -b/b when a = 0 and b < 0?
The sign of a times -b/b when a = 0 and b < 0 is neutral neither negative nor positive .
What is a integers ?An integer is a whole number (not a fractional number) that can be positive, negative, or zero
As b<0 which means b would be negative.
So, -b/b gives a negative value.
Because if any of the either numerator or denominator is negative then the resulting value also be negative.
and if zero '0' is multiplied and number whether it is positive or negative the resulting value will be zero.
So, a* (-b/b)= 0* negative= negative zero, but zero is neither negative nor positive .
hence, the sign of a times -b/b is neutral neither negative nor positive .
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Find an equation of the plane passing through the points (1, 5, -3), (2, 5, -3) and (3, 5,2)
Answer:
[tex]y = 5[/tex].
Or, equivalently:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Step-by-step explanation:
Every plane in [tex]\mathbb{R}^{3}[/tex] could be represented with a vector equation of the form [tex]\vec{n}\, (\vec{r} - \vec{r}_{0}) = 0[/tex], where:
[tex]\vec{n}[/tex] is a vector normal to the plane (a normal vector), and [tex]\vec{r}_{0}[/tex] is the position vector of a point in the plane.Notice that in this question, the coordinates (and hence the position vectors) of the points in this plane are already given. For example, the position vector of the point [tex](1,\, 5,\, -3)[/tex] is the vector:
[tex]\begin{aligned}\vec{r}_{0} = \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\end{aligned}[/tex].
Specifically in [tex]\mathbb{R}^{3}[/tex], normal vectors of a plane could be found by:
finding two distinct directions parallel to that plane, and taking the cross product between the two directions.Subtracting position vectors of points in this plane from each other would give directions that are parallel to this plane:
[tex]\begin{aligned}\begin{bmatrix}2 \\ 5 \\ -3\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix}\end{aligned}[/tex].
[tex]\begin{aligned}\begin{bmatrix}3 \\ 5 \\ 2\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix} = \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix}\end{aligned}[/tex].
The cross product between these two vectors in [tex]\mathbb{R}^{3}[/tex] would be:
[tex]\begin{aligned} \vec{n} = \begin{bmatrix}1 \\ 0 \\ 0\end{bmatrix} \times \begin{bmatrix}2 \\ 0 \\ 5\end{bmatrix} = & \begin{bmatrix}0 \times 5 - 0 \times 0 \\ 0 \times 2 - 1 \times 5\\ 1 \times 0 - 0 \times 2\end{bmatrix} = \begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix}\end{aligned}[/tex].
(Note that the cross product between other directions parallel to the plane might give other normal vectors that are parallel to the one in this example.)
Using the position vector of the point [tex](1,\, 5,\, -3)[/tex] as [tex]\vec{r}_{0}[/tex], one possible vector equation for this plane would be:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \left(\begin{bmatrix}x \\ y \\ z\end{bmatrix} - \begin{bmatrix}1 \\ 5 \\ -3\end{bmatrix}\right) = 0\end{aligned}[/tex].
Expand the dot product and simplify to obtain a scalar equation for this plane:
[tex]\begin{aligned}\begin{bmatrix}0 \\ -3 \\ 0\end{bmatrix} \begin{bmatrix}x - 1 \\ y - 5 \\ z - (-3)\end{bmatrix} = 0\end{aligned}[/tex].
[tex]0\, (x - 1) + (-3)\, (y - 5) + 0\, (z - (-3)) = 0[/tex].
[tex](-3)\, (y - 5) = 0[/tex].
[tex]y = 5[/tex].
A board 120inches long is divide into 2 sections. If the ratio of the 2 sections. 3:5 Wht are the lengths of the section
Answer:
45, 75
Step-by-step explanation:
3+5 = 8
120 / 8 = 15
15 x 3 = 45
15 x 5 = 75
Answer:
45,75
3+5 = 8
120 / 8 = 15
15 x 3 = 45
15 x 5 = 75
Step-by-step explanation:
have a great day!
This rectangular prism has a length of 14 inches, a height of 8 inches, and a width of 3 inches. What is the volume
height= 8 in
length= 14 in
width= 3 in
to find:the volume of the given rectangular prism.
solution:[tex]v = whl[/tex]
[tex]v = 8 \times 14 \times 3[/tex]
[tex]v = 336 \: {in}^{3} [/tex]
hence, the volume of the given rectangular prism is 336 cubic inches.
answer= option D
[tex]\large\boxed{Formula: V= lbh}[/tex]
All the values are given so we'll simply have to solve.
Let's solve!
Substitute the values according to the formula.
We'll have to multiply the length, breadth and the height.
[tex]V= 14 \times 3 \times 8[/tex]
[tex]\large\boxed{V= 336 \: {in}^{3}}[/tex]
We get a whole number to the final answer so we won't have to round off.
Therefore, the volume of the given rectangular prism is 336 cubic inches.
Correct option: Option D
PLEASE HELP ASAP *URGENT* 20 POINTS!!!!
Answer:
a5 = 122
Explanation:
Given:
a1 = 2an = -3aₙ₋₁ + 2Solve:
a1 = 2
a2 = -3a1+2 = -3(2)+2 = -4
a3 = -3a2 + 2 = -3(-4)+2 = 14
a4 = -3a3 + 2 = -3(14) + 2 = -40
a5 = -3a4 + 2 = -3(-40) + 2 = 122
Answer:
a₅ = 122
Step-by-step explanation:
What is a₅ for the sequence defined by:
[tex]\left\{\begin{array}{ccc}a_1=2\\a_n=-3a_{n-1}+2\\\end{array}\right\\\\\\\hrule[/tex]
Letting n=2:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{2-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{1}+2\\\\\\\\\Longrightarrow a_2=-3(2)+2\\\\\\\\\therefore a_2=-4[/tex]
Letting n=3:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{3-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{2}+2\\\\\\\\\Longrightarrow a_3=-3(-4)+2\\\\\\\\\therefore a_3=14[/tex]
Letting n=4:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{4-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{3}+2\\\\\\\\\Longrightarrow a_4=-3(14)+2\\\\\\\\\therefore a_4=-40[/tex]
Letting n=5:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{5-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{4}+2\\\\\\\\\Longrightarrow a_5=-3(-40)+2\\\\\\\\\therefore \boxed{\boxed{a_5=122}}[/tex]
what is the different between replacing the first card and not replacing the first card
Replacing the first card illustrates an independent event, while not replacing the card illustrates a dependent event
How to determine the difference?In probability, when a selected card or item is replaced before another item is selected, then the event is an independent event.
This is so because, the selected card do not have effect on the probability of selecting the next card
However, if the card is not replaced, then the event is dependent
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What is the length of side a rounded to the nearest 12.9 cm tenth of a centimeter? a a 15.3 cm
Answer:
8.227 then rounded to tenth is 8.2
Step-by-step explanation:
just smart.
please rate good. have a good day.
Find mKNL.
A. 264
B. 196
C. 184
D. 247
Applying the angle of intersecting secants and tangents theorem, m(KNL) is: A. 264°.
What is the Angle of Intersecting Secants and Tangents Theorem?The angle of intersecting secants and tangents theorem states that the angle formed outside a circle has a measure that equals 1/2 the positive difference of the measures of the intercepted arcs.
60 = 1/2(18x - 6 - 5x - 17) [angle of intersecting secants and tangents theorem]
Solve for x
2(60) = 13x - 23
120 = 13x - 23
120 + 23 = 13x
143 = 13x
x = 143/13
x = 11
m(KNL) = (18x - 6 + 5x + 17)
m(KNL) = 23x + 11
Plug in the value of x
m(KNL) = 23(11) + 11
m(KNL) = 264° (option A)
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Bob walks dogs after school. He charges $43. 50 for 6 hours and $65.25.75 for 9 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Bob works
and y represent the amount he charges.
The equation of the amount charged by Bob will be y = 7.25x.
What is an equation?
The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given that:-
Bob walks dogs after school. He charges $43. 50 for 6 hours and $65.25.75 for 9 hours.The equation will be generated as follow:-
6 hours = $ 43.50
1 hours = $ 7.25
9 hours = $ 65.2575
1 hours = $ 7.25
Let x represent the number of hours Bob works and y represent the amount he charges. The equation will be:-
y = 7.25x dollars.
Therefore the equation of the amount charged by Bob will be y = 7.25x.
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HELPPPPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!
Angle t= 37 degrees angle u=? Angle v= 63
Answer:
[tex]m <U = 80°[/tex]
Step-by-step explanation:
Before we start calculating we have to first note that the angles in a triangle always add up to 180°. Therefore in order to find the missing angle U we have to add both the angles we know, 37° and 63°, then subtract the sum from 180°
[tex]m < U = 180- (37 + 63) \\ \\ m < U = 180 - 100 \\ \\ m< U = 80[/tex]
if x-y=5 and xy=4,find the value of x3-y3
[tex]\text{Given that,} ~ x-y = 5~ \text{amd}~ xy = 4\\\\\text{Now,}\\\\x^3 -y^3\\\\=(x-y)(x^2 +xy+y^2)\\\\=(x-y)[(x-y)^2 +2xy +xy]\\\\=(x-y)[(x-y)^2 +3xy]\\\\=5(5^2+3\cdot 4)\\\\=5(25+12)\\\\=5(37)\\\\=185[/tex]
URGENT!!!! What is the number of solutions in this system?
A None
B one
C Infinite
Answer:
C? Not 100% sure
Step-by-step explanation:
Can someone answer theese questions do all of them and I will give you brainily
1 .
What does each line on the protractor stand for?
five degrees
one-half of a degree
ten degrees
one degree
2 What part of the protractor do you line up with the vertex?
zero line
degree line
center mark
top of the protractor
3.
What is the first step in constructing an angle?
Make a mark at the number of degrees you want the angle to be.
Connect the endpoint and the mark at the angle measure
Draw a horizontal ray.
Place the center of the protractor on the endpoint of the ray, and line up the ray with the zero line of the protractor.
Answer: i think is b
Step-by-step explanation: because I do read lesson so I guess I think is b that why.
What is the value of x in | - 6| = x? O 6 and -6 00 06 -6 HOURME
Answer:
I believe, 6.
Step-by-step explanation:
Not sure if the rest of the question is the answer choices but the absolute of any number, is it's exact opposite. The reason for this is that an absolute number, or |?| is equal to whatever distance it is from 0. Since adding 1, and subtracting 1, both do such but in opposite directions, the absolute value of both would be 1.
−11 ≤ −5; Add 16 to both sides
The resulting inequality is:
Answer:
True, (-∞, ∞) 5 ≤ 11
Step-by-step explanation:
−11 ≤ −5 Add 16 to both sides
−11 + 16 ≤ −5 + 16
5 ≤ 11
Which relation is a function?
Answer:
A function means that we get one input and one output. In this example that means for every x-value that we have, we only have one y-value.
Looking at the first option, we can see that there is no x-value that has more than one y-value which means that it is a function.
The rest of the options are seen with at least two values for one x-value in one of the points. Therefore, they wouldn't be considered a function leaving us with only option A as the solution.
A ladder that is 5 meters long is leaning against a wall. The vertical height from the base of the wall to the top of the ladder is 3 meters. If ∠θ is the angle that the ladder makes with the ground, what is the approximate measure of ∠θ?
The approximate angle that the ladder makes with the ground is 37 degrees
Angle of elevationThe given question will be solved using the SOH CAH TOA identity.
The given statement will form a right triangle with the following parameters
Hypotenuse = 5m
Height(opposite) .= 3m
Determine the approximate measure of ∠θ
sin ∠θ = opp/hyp
sin ∠θ = 3/5
sin ∠θ = 0.6
∠θ = arcsin(0.6)
∠θ = 37degrees
Hence the approximate angle that the ladder makes with the ground is 37 degrees
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I really need help on this math problem, pls anyone that can help?!
Answer:
y = 3/2x + 6
Step-by-step explanation:
Equation of the given line
slope = rise/run = -2/3y-intercept = (0, -2)Equation is y = -2/3x - 2Perpendicular
Slope is the negative reciprocalm ⇒ -(1/[-2/3]) = 3/2Intersection point is (-2, 3)Using Point-slope equation
y - 3 = 3/2 (x + 2)y - 3 = 3/2x + 3y = 3/2x + 6