Answer:
The probability is 0.31084
Step-by-step explanation:
We can calculate this probability using the z-score route.
Mathematically;
z = (x-mean)/SD/√n
Where the mean = 16, SD = 3 and n = 36
For 15.8, we have;
z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4
For 16.2, we have
z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4
So the probability we want to calculate is;
P(-0.4<z<0.4)
We can get this using the standard normal distribution table;
So we have;
P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)
= 0.31084
How do I solve for y:
x²y² = 12/z²
Answer:
Y=Srt(12xs^2/z^2)
Step-by-step explanation:
Firstly
We multiply both sides with 1/x^2
We get
Y^2=12/z^2*1/x^2
Y^2=12x^2/z^2
Next: introduce a srt root
We have
Y=srt(12x^2/z^2)
A particular salad contains 4 units of vitamin A, 5 units of vitamin B complex, and 2 mg of fat per serving. A nutritious soup contains 6 units of vitamin A, 2 units of vitamin B complex, and 3 mg of fat per serving. If a lunch consisting of these two foods is to have at least 10 units of vitamin A and at least 10 units of vitamin B complex, how many servings of each should be used to minimize the total number of milligrams of fat
Answer:
2 servings of salad and 1 serving of soup
Step-by-step explanation:
In the given scenario the aim is to minimise the fat content of the food combination.
Fat content of soup is 3mg while fat content of salad is 2 mg.
Using Soup as 0 and Salad as 2 will not give the required vitamin content
The logical step will be to keep servings of soup to the minimum.
Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1
1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.
This will not work because amount of vitamin B complex is not up to 10 mg
2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat
This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.
Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving
A spring is hanging from a ceiling. The length L(t) (in cm) of the spring as a function of time t (in seconds) can be modeled by a sinusoidal expression of the form a*sin(b*t) +d. At t=0, when the spring is exactly in the middle of its oscillation, its length is 7 cm. After 0.5 seconds the spring reaches its maximum length, which is 12 cm. Find L(t).
Answer:
L(t) = 5·sin(πt) +7
Step-by-step explanation:
The middle of the oscillation of the given function occurs when t=0. At that point, ...
L(0) = d = 7
The next maximum of the oscillation occurs when the argument of the sine function is π/2.
b·t = π/2
b = π/(2t) = π/(2·0.5) = π
At that maximum, the length is 12, so we have ...
L(0.5) = a·sin(0.5π) +7 = 12
a = 5
The function L(t) is ...
L(t) = 5·sin(πt) +7
Help me please thank you
Answer:
x = 7
Step-by-step explanation:
The angles are alternate interior angles, so for the lines to be parallel, the angle measures must be equal.
7x - 7 = 4x + 14
3x = 21
x = 7
The manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2. The manufacturer also has fixed costs each month of $8,000.
Answer:
C(x)=1.2x+8,000.
Step-by-step explanation:
C(x)=cost per unit⋅x+fixed costs.
The manufacturer has fixed costs of $8000 no matter how many drinks it produces. In addition to the fixed costs, the manufacturer also spends $1.20 to produce each drink. If we substitute these values into the general cost function, we find that the cost function when x drinks are manufactured is given by
In order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.
What is a mathematical function, equation and expression? function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that the manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2.
Suppose that you have to sell [x] number of bars to make profits. So, we can write -
{2x} - {1.20x} > {8000}
0.8x > 8000
8x > 80000
x > 10000
Therefore, in order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
the fourth term of an AP is 5 while the sum of the first 6 terms is 10. Find the sum of the first 19 terms
Answer: S₁₉ = 855
Step-by-step explanation:
T₄ = a + ( n - 1 )d = 5 , from the statement above , but n = 4
a + 3d = 5 -------------------------1
S₆ = ⁿ/₂[(2a + ( n - 1 )d] = 10, where n = 6
= ⁶/₂( 2a + 5d ) = 10
= 3( 2a + 5d ) = 10
= 6a + 15d = 10 -----------------2
Now solve the two equation together simultaneously to get the values of a and d
a + 3d = 5
6a + 15d = 10
from 1,
a = 5 - 3d -------------------------------3
Now put (3) in equation 2 and open the brackets
6( 5 - 3d ) + 15d = 10
30 - 18d + 15d = 10
30 - 3d = 10
3d = 30 - 10
3d = 20
d = ²⁰/₃.
Now substitute for d to get a in equation 3
a = 5 - 3( ²⁰/₃)
a = 5 - 3 ₓ ²⁰/₃
= 5 - 20
a = -15.
Now to find the sum of the first 19 terms,
we use the formula
S₁₉ = ⁿ/₂( 2a + ( n - 1 )d )
= ¹⁹/₂( 2 x -15 + 18 x ²⁰/₃ )
= ¹⁹/₂( -30 + 6 x 20 )
= ¹⁹/₂( -30 + 120 )
= ¹⁹/₂( 90 )
= ¹⁹/₂ x 90
= 19 x 45
= 855
Therefore,
S₁₉ = 855
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan?
Answer:
federal loans = $29,000
private loans = $14,000
Step-by-step explanation:
x + y = 43000
.045x + .02y = 1585
x = 29,000
y = 14,000
Answer:
Amount of loan from federal : $ 29,000
Amount of loan from private bank : $ 14,000
Step-by-step explanation:
We know that Linda owes $43,000 in student loans. It is also given that the interest rate on the federal loans is 4.5%, while the interest rate on private loans is 2%, the total interest for a year being $1,585.
If Linda were to say own x dollars in federal loans, and y dollars in private loans, we know that she owns a total of $43,000, so -
x + y = 43,000
At the same time the loan interest amount is $1,585, while the interest rate on the federal loans is 4.5%, and the interest rate on private loans is 2%. The loans from each account will add to $1,585 -
0.045x + 0.02y = 1585
Let's solve the following system for x and y, the amount of each loan,
[tex]\begin{bmatrix}x+y=43000\\ 0.045x+0.02y=1585\end{bmatrix}[/tex] ( Substitute x = 43000 - y )
[tex]0.045\left(43000-y\right)+0.02y=1585[/tex] ( Simplify )
[tex]1935-0.025y=1585[/tex],
[tex]1935000-25y=1585000[/tex],
[tex]-25y=-350000[/tex],
[tex]y=14000[/tex],
[tex]x=29000[/tex]
Thus, the amount of loan from federal is $ 29,000 and the amount of loan from private bank is $ 14,000.
brainliest to correct
Answer:
27
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
-9 × -3
= 27
Note: When you multiply two integers with same sign, then their product is positive.
is y=-2/5x+1 inverse or direct variation
A segment with endpoints at $A(2, -2)$ and $B(14, 4)$ is extended through $B$ to point $C$. If $BC = \frac{1}{3} \cdot AB$, what are the coordinates for point $C$? Express your answer as an ordered pair.
Answer:
C = (18, 6)
Step-by-step explanation:
You have ...
AB : BC = 1 : 1/3 = 3 : 1
(B -A) / (C -B) = 3/1 . . . . . another way to write the distance relation
B -A = 3(C -B) . . . . . . . . . multiply by (C-B)
4B -A = 3C . . . . . . . . . . . add 3B
C = (4B -A)/3 . . . . . . . . . divide by 3 to get an expression for C
C = (4(14, 4) -(2, -2))/3 = (54, 18)/3
C = (18, 6)
Karim has two investments, one in Company A, and another in Company B. Karim purchased 3,000 shares in company A at $2.65 per share. Since purchasing the shares, the price per share increased to $2.95 per share, after which point Karim decided to sell, realizing a profit. At the same time, Karim purchased 2,000 shares in Company B at $1.55 per share. Since purchasing the shares, the share price fell to $1.30 per share, after which Karim decided to sell the shares, suffering a loss. Karim is required to pay tax at a rate of 28% on the combined profit from both investments. Calculate how much tax Karim must pay.
Answer:
A:$2478
B:$728
Total:$3206
Step-by-step explanation:
2.95x3000=8850
1.30x2000=2600
8850x0.28=2478
2600x0.28=728
2478+728=3206
please solve asap thanks
Answer:
A' (-2,3)
B' (-1,1)
C' (-4,0)
Step-by-step explanation:
Given coordinates:
A (3,0)
B (4,-2)
C (1,-3)
We want to find the location of the coordinates after a translation of <-5,3>
Explanation of translation
<-5,3>
Subtract 5 from the x value and add 3 to the y value
Applying translation
A (3,0) ---------> (3-5,0+3) ---------> (-2,3)
B (4,-2) ---------> (4-5,-2+3) ---------> (-1,1)
C (1,-3) ---------> (1-5,-3+3) ---------> (-4,0)
So the new coordinates would be
A' (-2,3)
B' (-1,1)
C' (-4,0)
11. What is the midpoint of CD?
12. a. What are the exact lengths of
segments AB and CD?
b. How do the lengths of AB and CD
compare?
c. Is the following statement true or
false?
AB=CD
9514 1404 393
Answer:
11. (-1.5, 3)
12. √29, identical lengths, true they are congruent
Step-by-step explanation:
11. The midpoint is halfway between the end points. On a graph, you can count the grid squares between the ends of the segment and locate the point that is half that number from either end.
Points C and D differ by 2 in the y-direction, so the midpoint will be 1 unit vertically different from either C or D. That is, it will lie on the line y = 3. The segment CD intersects y=3 at x = -1.5, so the midpoint of CD is (-1.5, 3).
If you like, you can calculate the midpoint as the average of the end points:
midpoint CD = (C +D)/2 = ((-4, 4) +(1, 2))/2 = (-3, 6)/2 = (-1.5, 3)
__
12. The exact length can be found using the Pythagorean theorem. The segment is the hypotenuse of a right triangle whose legs are the differences in x- and y-coordinates.
In the previous problem, we observed that the y-coordinates of C and D differed by 2. The x-coordinates differ by 5. Looking at segment AB, we see the same differences: x-coordinates differ by 5 and y-coordinates differ by 2. Then the lengths of each of these segments is ...
AB = CD = √(2² +5²) = √29
a) The exact lengths of segments AB and CD are √29 units.
b) The lengths of the segments are identical
c) It is TRUE that the segments are congruent.
Based on the measures provided in the diagram, determine the measure of AEG
Answer:
277°
Step-by-step explanation:
The measure of arc AEG = AB + BE + EF + FG
The central angle is congruent to the arc that subtends it
∠ ECB = 180° - 44° = 136° ( adjacent angles )
∠ECF = ∠ ACB = 44° ( vertical angles ), thus
AEG = 44° + 136° + 44° + 53° = 277°
en un taller de futbol se inscribieron en total 240 personas . de ese total 80% son mujeres . ¿Cuántos hombres se inscribieron en el taller ?
a) 192 hombres
b) 160 hombres
c) 48 hombres
d) 18 hombres
Simplify: n- 10 + 3 + 4n
Answer:
5n-7
simply like terms
Answer:
5n - 7
Step-by-step explanation:
n- 10 + 3 + 4n
n + 4n = 5n
-10 + 3 = -7
5n- 7
What is 2x-40y=73 and 7x+65y=332?
[tex]\large\mathfrak{{\pmb{\underline{\orange{Given }}{\orange{:}}}}}[/tex]
[tex]2x - 40y = 73...(i)[/tex]
[tex]7x + 65y = 332...(ii)[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\pink{To\:find }}{\pink{:}}}}}[/tex]
The values of [tex]x[/tex] and [tex]y[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\green{Solution }}{\green{:}}}}}[/tex]
[tex]x=43.96 [/tex] and [tex]y = 0.373 [/tex].
[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]
Let us solve this by substitution method.
From [tex]eqn.\:(i),\:we\:have [/tex]
↬[tex]2x - 40y = 73[/tex]
↬[tex]2x = 73 + 40y[/tex]
↬[tex]x = \frac{73 + 40y}{2}...(iii) \\ [/tex]
Substituting the value of [tex]x[/tex] in [tex]eqn.\:(ii)[/tex] gives us
↬[tex]7( \frac{73 + 40y}{2} ) + 65y = 332 \\ [/tex]
↬[tex] \frac{511 + 280y}{2} + \frac{65y \times 2}{1 \times 2} = 332 \\ [/tex]
↬[tex] \frac{511 + 280y + 130y}{2} = 332 \\ [/tex]
↬[tex]410y + 511 = 332 \times 2[/tex]
↬[tex]410y = 664 - 511[/tex]
↬[tex]y = \frac{153}{410} \\ [/tex]
↬[tex]y = 0.373[/tex]
Now, plug the value of [tex]y[/tex] in [tex]eqn.\:(i)[/tex]
↬[tex]2x - 40 \times 0.373 = 73 \\ [/tex]
↬[tex]2x - 14.92= 73 [/tex]
↬[tex]2x = 73 +14.92[/tex]
↬[tex]x = \frac{87.92}{2} \\ [/tex]
↬[tex]x = 43 .96[/tex]
Therefore, the values of [tex]x[/tex] and [tex]y[/tex] are [tex]\boxed{ 43.96 }[/tex] and [tex]\boxed{ 0.373 }[/tex] respectively.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35}}}}}[/tex]
Given the function, Calculate the following values:
Answer:
[tex]f(-2)=33\\f(-1)=12\\f(0)=1\\f(1)=0\\f(2)=9[/tex]
Step-by-step explanation:
[tex]f(x)=5x^{2} -6x+1\\f(-2)=5(-2)^{2} -6(-2)+1\\f(-2)=5(4)+12+1\\f(-2)=20+13\\f(-2)=33[/tex]
[tex]f(x)=5x^{2}-6x+1\\f(-1)=5(-1)^{2} -6(-1)+1\\f(-1)=5(1)+6+1\\f(-1)=5+7\\f(-1)=12[/tex]
[tex]f(x)=5x^{2}-6x+1\\f(0)=5(0)^{2}-6(0)+1\\f(0)=5(0)-0+1\\f(0)=0+1\\f(0)=1[/tex]
[tex]f(x)=5x^{2}-6x+1\\f(1)=5(1)^{2}-6(1)+1\\f(1)=5(1)-6+1\\f(1)=5-5\\f(1)=0[/tex]
[tex]f(x)=5x^{2}-6x+1\\f(2)=5(2)^{2}-6(2)+1\\f(2)=5(4)-12+1\\f(2)=20-11\\f(2)=9[/tex]
Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)
9514 1404 393
Answer:
10·2^-8 grams
Step-by-step explanation:
The each day, the initial amount for that day is multiplied by 1/2. After 8 days, the initial amount has been multiplied by (1/2)^8, where the exponent of 8 signifies that (1/2) is a factor 8 times in the product.
After n days, the quantity remaining is ...
q(n) = 10·(1/2)^n = 10·2^(-n)
after 8 days the remaining amount is ...
q(8) = 10·2^-8 . . . grams
(SAT Prep) Find the value of x.
Answer:
The value of x is 30°
Step-by-step explanation:
We are given that the outer angle of the parallelogram is 60 degrees. Therefore it's respective inner angle will be 180 - 60 = 120 degrees. And, by properties of a parallelogram, the angle opposite to this angle will be 120 degrees as well.
If we draw extend the line creating angle 2x, then we will make ( 1 ) a vertical angle to 2x, ( 2 ) a 90 degree angle, and ( 3 ) and angle that we can let be y. Therefore, 2x + y = 90, and 3x + y = 120.
[tex]\begin{bmatrix}2x+y=90\\ 3x+y=120\end{bmatrix}[/tex] ,
[tex]\begin{bmatrix}6x+3y=270\\ 6x+2y=240\end{bmatrix}[/tex] ,
[tex]6x+2y=240\\-\\\underline{6x+3y=270}\\y=30[/tex],
[tex]2x + (30) = 90,\\2x = 60,\\x = 30[/tex]
Solution : x = 30°
Answer:
x = 30
Step-by-step explanation:
a+ 60 = 180
a = 120
3x+b = 120 because opposite angles in a parallelogram are equal
2x+90+b = 180 since it forms a line
2x+b = 90
We have 2 equations and 2 unknowns
3x+b = 120
2x+b = 90
Subtracting
3x+b = 120
-2x-b = -90
---------------------
x = 30
2m-t=sm+5 you would have to find m
Answer:
m=5+t/2-s
Step-by-step explanation:
arrange like terms
2m-sm=5+t
factotise m in the first side of the equation
m(2-s)=5+t
divide both sides by (2-s)
therefore m=5+t/2-s
Soan made a $400 down payment on a washer and dryer cost a total of $1200. What is the ratio of the amount soan has paid to the amount he still owes?
Answer:
800:1200 or 2:3
Step-by-step explanation:
400 payed
1200 in total
1200-400=800
800:1200 or 2:3
Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
15x - y = - 126
Step-by-step explanation:
will make it simple and short
first we need to find the slope (m) first in order to get the equation
given: (-8,6) (-9,-9)
y2 - y1 -9 - 6
Slope = m = ----------- = ------------------ = 15
-x2 - x1 -9 - (-8)
so the equation of the line using point (-8,6) and slope 15 is y - 6 = 15( x + 8)
y - 6 = 15x + 120
using the form equation Ax + By = C, 15x - y = -120-6
therefore... 15x - y = - 126 is the answer
Explain the sum of geometric progression
YOU THE REAL OG
IF YOU CAN DO THIS FOR ME
YES IT IS HAIKU
How much would you need to deposit in an account each month in order to have $50,000 in the account in 8 years? Assume the account earns 4% annual interest compounded monthly.
THANK YOU TO ANY OG WHO CAN SOLVE THIS , BRAINLIEST GUARANTEE TO ANYONE WHO REALLY TRIES
9514 1404 393
Answer:
$442.80
Step-by-step explanation:
The formula for the amount of an ordinary annuity is ...
A = P(12/r)((1 +r/12)^(12t) -1)
where payment P is made n times per year and interest is accrued at annual rate r.
Filling in the given values, we want ...
50,000 = P(12/0.04)(1 +0.04/12)^(12·8) -1) = 112.91854P
P = 50,000/112.91854 ≈ 442.80
You would need to deposit $442.80 each month for 8 years.
According to the U.S. Energy Information Administration the average number of televisions per household in the United States was 2.3. A college student claims the average number of TV’s per household in the United States is different. He obtains a random sample of 73 households and finds the mean number of TV’s to be 2.1 with a standard deviation of 0.84. Test the student’s claim at the 0.01 significance level.
Let [tex]\mu[/tex] be the average number of televisions per household in the United States .
As per given ,
[tex]H_0:\mu =2.3\\\\ H_a:\mu\neq2.3[/tex]
Since [tex]H_a[/tex] is two-tailed and population standard deviation is unknown, so the test is two-tailed t-test.
For sample : Sample size : n= 73, sample mean: [tex]\overline{x}[/tex] = 2.1, sample standard deviation : s= 0.84.
[tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
[tex]t=\dfrac{2.1-2.3}{\dfrac{0.84}{\sqrt{73}}}\\\\ t=-2.034[/tex]
T-critical value for degree of freedom n-1 = 73-1=72 and 0.01 significance level is 2.646 . [By students' t-distribution table]
Since, [tex]|2.034|<2.646[/tex] i.e. [tex]|T_{cal}|<|T_{crit}|[/tex]
This means we cannot reject null hypothesis.
We conclude that the average number of televisions per household in the United States is 2.3 at the 0.01 significance level.
Write an equation in slope-intercept form for the line with slope 4/3 and y-intercept -6.
Answer:
y=mx+b
Step-by-step explanation:
m=4/3×-6
I think this is the answer
What are the roots of the quadratic equation below?
x2 + 2x= -5
Answer:
No real root.
Complex roots:
[tex] x = -1 \pm 2i [/tex]
Step-by-step explanation:
[tex] x^2 + 2x = -5 [/tex]
[tex] x^2 + 2x + 5 = 0 [/tex]
There are no two integers whose product is 5 and whose sum is 2, so this trinomial is not factorable. We can use the quadratic formula.
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-2 \pm \sqrt{2^2 - 4(1)(5)}}{2(1)} [/tex]
[tex] x = \dfrac{-2 \pm \sqrt{4 - 20}}{2} [/tex]
[tex] x = \dfrac{-2 \pm \sqrt{-16}}{2} [/tex]
Since we have a square root of a negative number, there are no real roots. If you have learned complex numbers, then we can continue.
[tex] x = \dfrac{-2 \pm 4i}{2} [/tex]
[tex] x = -1 \pm 2i [/tex]
8th class maths reader answer
Answer:
plz complete question
so I can help you.
for the following questions, determine how many solutions each equation has. if one solution, state the value of x. x+6+8=2x-x+14? and is it a No solution, or a many solution or is it a one solution?
Answer:
infinite solutions
Step-by-step explanation:
x+6+8=2x-x+14
x+6+8=x+14
x+14=x+14
14=14
or
x=x
plug in any number
2+6+8=2(2)-2+14
16=16
another example
8+6+8=2(8)-8=14
22=22