Answer:
Balance after one year will be $5830.
The perimeter of an equilateral triangle is 15 x + 30 units. Which expression can be used to show the side length of one side of the equilateral triangle? 15 (x + 2): Each side length is x + 2 units. 30 (one-half x + 1): Each side length is One-half x + 1 units. 5 (3 x + 6): Each side length is 3 x + 10 units. 3 (5 x + 10): Each side length is 5 x + 10 units.
Answer:
Each side length is 5x + 10 units.Step-by-step explanation:
An equilateral triangle is a triangle that has all of its sides equal. Let a, b and c be the sides of the equilateral triangle. Since all the sides are equal, then
a = b = c.
The perimeter of the triangle is the sum of all the sides of the triangle.
P = a + b+ c
GIVEN THE PERIMETER OF THE EQUILATERAL TRIANGLE AS P = 15 x + 30 units and a = b = c, then;
15 x + 30 = a + b + c
15 x + 30 = a + a + a (since all sides are equal)
15 x + 30 = 3a
3a = 15 x + 30
3a = 3(5x+10)
Dividing both sides by 3 will give;
3a/3 = 3(5x+10)/3
a = 5x+10
Hence, the length of one side of the equilateral triangle is 5x + 10 units.
Answer:
D.
Step-by-step explanation:
Edge 2020
Use the Chain Rule to find ∂z/∂s and ∂z/∂t. (Enter your answer only in terms of s and t. Please use * for multiplication between all factors.)
z = x8y9, x = s cos(t), y = s sin(t)
∂z/∂s =
∂z/∂t =
Answer:
Step-by-step explanation:
Using chain rule to find the partial deriviative of z with respect to s and t i.e ∂z/∂s and ∂z/∂t, we will use the following formula since it is composite in nature;
∂z/∂s = ∂z/∂x*∂x/∂s + ∂z/∂y*∂y/∂s
Given the following relationships z = x⁸y⁹, x = s cos(t), y = s sin(t)
∂z/∂x = 8x⁷y⁹, ∂x/∂s = cos(t), ∂z/∂y = 9x⁸y⁸ and ∂y/∂s = sin(t)
On substitution;
∂z/∂s = 8x⁷y⁹(cos(t)) + 9x⁸y⁸ sin(t)
∂z/∂s = 8(scost)⁷(s sint)⁹(cos(t)) + 9(s cost)⁸(s sint)⁸ sin(t)
∂z/∂s = (8s⁷cos⁸t)s⁹sin⁹t + (9s⁸cos⁸t)s⁸sin⁹t
∂z/∂s = 8s¹⁶cos⁸tsin⁹t + 9s¹⁶cos⁸tsin⁹t
∂z/∂s = 17s¹⁶cos⁸tsin⁹t
∂z/∂t = ∂z/∂x*∂x/∂t + ∂z/∂y*∂y/∂t
∂x/∂t = -s sin(t) and ∂y/∂t = s cos(t)
∂z/∂t = 8x⁷y⁹*(-s sint) + 9x⁸y⁸* (s cos(t))
∂z/∂t = 8(scost)⁷(s sint)⁹(-s sint) + 9(s cost)⁸(s sint)⁸(s cos(t))
∂z/∂t = -8s¹⁷cos⁷tsin¹⁰t + 9s¹⁷cos⁹tsin⁸t
∂z/∂t = -s¹⁷cos⁷tsin⁸t(8sin²t-9cos²t)
Solve of the following equations for x: 3 − x = 2
Answer:
Hello There!
~~~~~~~~~~~~~~~~~~~`
3 − x = 2 =
X = 1
Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helped you. Brainliest would be nice!
Answer: x = 1 / 1 = x.
Step-by-step explanation:
3 - x = 2
First, since you can't subtract x from 3, we find ways to subtract 2 from 3.
So, we write the 3 and attach (-) minus/negative sign to the 3 with 2. Because when a number crosses the equal sign and it is negative, it becomes positive and when it is positive, it becomes negative.
And 2 will cross the equal sign so,it will be (-) just like: -2. And -x will cross the equal sign so it will be x. Let's solve it with the steps above:
3 - x = 2
3 - 2 = x
1. = x
OR
3 - x = 2
-x = 2 - 3
-x/- = -1/-
So, negative will cancel negative.
x =1.
Please mark me as the brainliest!!
Thanks!!
A six sided number cube is rolled twice. What is the probability that the first roll is an even number and the second roll is a number grater than 4?
Answer:
1/6
Step-by-step explanation:
The probability of even number is 1/2. The probability of number greater than 4 is 1/3, because only 5 and 6 are greater than 4.
Multiply these two values
1/2*1/3= 1/6
The decline of salmon fisheries along the Columbia River in Oregon has caused great concern among commercial and recreational fishermen. The paper 'Feeding of Predaceous Fishes on Out-Migrating Juvenile Salmonids in John Day Reservoir, Columbia River' (Trans. Amer. Fisheries Soc. (1991: 405-420) gave the accompanying data on 10 values for the data sets where y = maximum size of salmonids consumed by a northern squaw fish (the most abundant salmonid predator) and x = squawfish length, both in mm. Here is the computer software printout of the summary: Coefficients: Estimate Std. Error t value Pr(> |t|) (Intercept) −90.020 16.702 −5.390 0.000 Length 0.701 0.044 15.798 0.000 Using this information, compute a 95% confidence interval for the slope.
Answer: { 0.5995, 0.8025 }
Step-by-step explanation:
Given that
Estimates Std. Error t value Pr(>/t/)
Intercept: -90.020 16.702 -5.390 0.000
length : 0.701 0.044 15.798 0.000
Now using the given information to compute a 95% confidence interval for the slope:
We use the formula
β₁ ± tₐ/₂, ₙ₋₂ × ∝β₁
So we know that number of values (n) = 10
therefore error of degree of freedom df = n -2 = (10-2) = 8
Level of significance α ( 1 - 0.95 ) = 0.05
so tₐ/₂, ₙ₋₂ = t ₍₀.₀₅/₂, ₁₀₋₂
t ₀.₀₂₅, ₈ = 2.306 (critical value)
From the given table ( regression analysis output)
slope regression β₁ = 0.701
The standard error of the slope is Sβ₁ = 0.044
Let “the maximum size of salmonids consumed by a northern squaw fish” be the response variable and “squawfish length” be the explanatory variable.
The 95% confidence interval for the slope of the regression is:
β₁ ± tₐ/₂, ₙ₋₂ × ∝β₁ = 0.701 ± 2.306 (0.044)
= 0.701 ± 0.101464
= { 0.701 - 0.101464, 0.701 + 0.101464 }
= { 0.599536, 0.802464 } ≈ {0.5995, 0.8025 }
The confidence interval of the slope is (0.599, 0.803)
The sample size is given as:
[tex]\mathbf{n = 10}[/tex]
The confidence interval is given as:
[tex]\mathbf{CI = 95\%}[/tex]
Start by calculating the degrees of freedom
[tex]\mathbf{df = n - 2}[/tex]
So, we have:
[tex]\mathbf{df = 10 - 2}[/tex]
[tex]\mathbf{df = 8}[/tex]
The level of significance is calculated as:
[tex]\mathbf{\alpha = 1 - CI}[/tex]
So, we have:
[tex]\mathbf{\alpha = 1 - 95\%}[/tex]
[tex]\mathbf{\alpha = 0.05}[/tex]
The critical value at 0.05 level of significance and 8 degrees of freedom is:
[tex]\mathbf{t_{\alpha} =2.306}[/tex]
The confidence interval of the slope is then calculated as:
[tex]\mathbf{CI = \beta_1 \pm t_\alpha \times S\beta_1}[/tex]
From the question, we have:
[tex]\mathbf{S\beta_1 = 0.044}[/tex] --- standard error of the slope
[tex]\mathbf{\beta_1 = 0.701}[/tex] -- the slope
So, the equation becomes
[tex]\mathbf{CI = \beta_1 \pm t_\alpha \times S\beta_1}[/tex]
[tex]\mathbf{CI = 0.701 \pm 2.306 \times 0.044}[/tex]
[tex]\mathbf{CI = 0.701 \pm 0.102}[/tex]
Split
[tex]\mathbf{CI = (0.701 - 0.102,0.701 + 0.102)}[/tex]
[tex]\mathbf{CI = (0.599,0.803)}[/tex]
Hence, the confidence interval of the slope is (0.599, 0.803)
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Write the equation of the function of a parabola with vertex at (–1,–2) and a point (1,–6) that lies on the curve.
Answer:
f(x) = -(x + 1)² - 2
Step-by-step explanation:
f(x) = a(x - h)² + k
-6 = a(1 - -1)² + -2
-6 = a(4) -2
-4 = 4a
a = -1
f(x) = -(x + 1)² - 2
Maria has $46 to buy fish for her aquarium. Each goldfish costs $6. How
many goldfish can she buy? Do not include units in your answer.
Answer:
7
Step-by-step explanation:
Take the amount of money and divide by the cost per fish
46/6 =7 with 4 dollars remaining
She can buy 7 goldfish
Answer:
7
Step-by-step explanation:
7 x 6 = 42
g Suppose that twenty different hypothesis tests for whether jellybeans cause acne are conducted. In order that the probability of one or more type I error between these should be at most 0.05, at most what significance level should be used for each of them?
Answer:
The level of significance to be used is α = 0.0025
Step-by-step explanation:
Here, we are interested in calculating the the level of significance which at most must be used for each of the hypothesis test
We proceed as follows;
P(type 1 error) = α
From the question, n = number of hypotheses = 20
P( of one or more type one error) ≤ 0.05
1- P(no type one error) ≤ 0.05
Hence;
1- (1-α)^20 ≤ 0.05
(1-α)^20 ≥ 0.95
1- α ≥ 0.997438621223
α ≤ 0.00256
Thus α = 0.0025
Write the Verbal phrases as an equation or an inequality? Use "x" as the variable?
Step-by-step explanation:
8.x×8-12=50
8x-12=50
9.1/2x>or=100
10.2 whole number5/9-x=31
Can someone solve this for me
Answer:
[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]
Step-by-step explanation:
divide each term by 2y^3
Multiply through by the least common denominator.
What is the value of x
Answer:
x=7
Step-by-step explanation:
Which value is a solution to the inequality 9-y >12
I believe the value is negative 4. If not, well, try any negative below that, such as -5,6,7,8, etc.
Answer:
y is less than -3
Step-by-step explanation:
To do this you would just subtract 9 from both sides so you get -y is greater than 3. Since you cannot have y as a negative number you will divide -1 from both sides but when you do that you will have to flip the sign so you get y is less than -3.
Solve for w in terms of t
3w-8=t
Please explain steps
Answer:
[tex]w=\frac{t+8}{3}[/tex]
Step-by-step explanation:
[tex]3w - 8 = t[/tex]
Add 8 on both sides.
[tex]3w - 8 + 8 = t + 8[/tex]
[tex]3w = t + 8[/tex]
Divide both sides by 3.
[tex]\frac{3w}{3} =\frac{t+8}{3}[/tex]
[tex]w=\frac{t+8}{3}[/tex]
The value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an equation:
3w - 8 = t
To solve for w in terms of t
Make the subject as w
In the equation:
3w - 8 = t
Add 8 on both sides:
3w - 8 + 8 = t + 8
3w = t + 8
Divide by 3 on both sides:
3w/3 = (t + 8)/3
w = (t + 8)/3
The equation represents a function of w in terms of t
As we know, the function can be defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
Thus, the value of w is w = (t + 8)/3 in terms of t after solving and making the subject w the answer is w = (t + 8)/3.
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En una fábrica de refrescos se envasan 1100 litros en 400 envases, unos de 2 litros y otros de 3 litros. ¿Cuantos envases de 2 y 3 litros se utilizan?
Greetings from Brasil...
X = 2 liter container
Y = 3 liter container
the total of containers are:
X + Y = 400
the capacity of the containers is
2X + 3Y = 1100
Assembling the equation system
2X + 3Y = 1100
X + Y = 400 x(-2)
2X + 3Y = 1100
-2X -2Y = - 800
Y = 300X + Y = 400 so
X + 300 = 400
X = 400 - 300
X = 100----------------------------------------------------------
BR:
Observe que:
1 vasilha de 2L = 1 × 2 = 2L
2 vasilhas de 2L = 2 × 2 = 4L
3 vasilhas de 2L = 3 × 2 = 6L
X vasilhas de 2L = X × 2 = 2X litros
.....
1 vasilha de 3L = 1 × 3 = 2L
2 vasilhas de 3L = 2 × 3 = 4L
3 vasilhas de 3L = 3 × 3 = 6L
X vasilhas de 3L = X × 3 = 3X litros
Logo 2X + 3Y = 1100
Existem X e Y vasilhas que num total sao 400, logo
X + Y = 400
Find the slope and y-intercept of the equation. y= 2/3x + 1
A. 2/3; 1
B. 1; 2/3
C. 2/3; -1
Answer:
The answer is A.
Step-by-step explanation:
In a linear equation, y = mx + b, m is represented as gradient (slope) and b is the y-intercept.
So for this question, m is 2/3 and b is 1.
What is the solution to the quadratic equation x2 + x - 30 = 0?
Answer:
try 3x=30 or 10
Step-by-step explanation:
The length and width of a rectangle are measured as 27 cm and 50 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
7.7cm
Step-by-step explanation:
Area of a rectangle is expressed as
A = Length × Width
A = LW
Let dL and dW be the errors in the measurements.
If there is an error of at most 0.1cm each in the measurement, then dL = dW = 0.1cm.
The area of the rectangle with error will be expressed as A = LdW + WdL
Given L = 27cm and W = 50cm
A = 27(0.1)+50(0.1)
A = 2.7+5.0
A = 7.7cm
Hence, the maximum error in the calculated area of the rectangle is 7.7cm
I bought a tv for 532.50 including the 6%sales tax. What was the original price of the tv without the sales tax?
Step-by-step explanation:
Hey, there !!!
According to your question,
total c.p = 532.50
tax rate =6%
let original price be x.
now,
total c.p = x + tax rate of x.
or, 532.50= x+ (6/100) × x
or, 532.50 = 106x/100
or, 53200 = 106x
or, x= 53200/106
Therefore, the original price was 501.88.
Hope it helps...
Raul and his friends each way 1/20 of a ton are standing on a truck scale . The total weight shown by the scale is 3/4 of a ton . How can I find the total number of people on the scale when Raul and his friends are weighed?
Answer:
15 people
Step-by-step explanation:
since Raul and his friends each weigh 1/20 ton,
and the total weight reads 3/4 ton
The total number pf people on the scale will be:
The total weight of Raul and his friends divided by their individual weight
==> (3/4 ton) ÷ (1/20 ton)
= 3/4 X 20/1 = 15 people
Answer:
I can find the total number of people by dividing the total weight by the weight of one person.
This is the plato answer, I hope this is the answer youre looking for! :))
Franklin the fly starts at the point $(0,0)$ in the coordinate plane. At each point, Franklin takes a step to the right, left, up, or down. After $10$ steps, how many different points could Franklin end up at?
Answer: Franklin could end at 4 different points.
Step-by-step explanation:
Given: Franklin the fly starts at the point (0,0) in the coordinate plane.
At each point, Franklin takes a step to the right, left, up, or down.
i.e. there are 4 choices of directions [A coordinate plan has 4 quadrants]
If he moves 10 steps, then the number of different points Franklin could end up at = choices of directions
= 4
Hence, Franklin could end at 4 different points.
Trey is choosing a 2-letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are
possible?
Answer:
10
Step-by-step ex1planation:
Solve equation :
A=Bt+c for t
Answer:
( A -c) /B =t
Step-by-step explanation:
A=Bt+c
Subtract c from each side
A-c=Bt+c-c
A -c = Bt
Divide each side by B
( A -c) /B = Bt/B
( A -c) /B =t
Answer:
Hey there!
A=Bt+c
A-c=Bt
t=(a-c)/B
Hope this helps :)
a total of 309 tickets were sold for the school play. they were either adult tickets or student tickets. the number of student tickets sold was two times the number of adult tickets sold. how many adult tickets were sold
Answer: 103 adult tickets
Step-by-step explanation:
Adult tickets (a) = a
Student tickets (s) = 2a
Total = 309
a + 2a = 309
3a = 309
a = 103
Answer:
103Step-by-step explanation:
Total tickets sold = 309
Let the number of adult tickets sold be x
Let the number of student tickets sold be 2x
Adult tickets + student tickets = 309
[tex]x + 2x = 309[/tex]
Collect like terms
[tex] 3x = 309[/tex]
Divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{309}{3} [/tex]
Calculate
[tex]x = 103[/tex]
Hence, 103 adult tickets were sold.
Hope this helps..
Good luck on your assignment...
Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs
of which 2 are defective, Box 2 has 1 defective and 3 functional bulbs and Box 3
contains 3 defective and 4 functional bulbs. A box is selected at random and a bulb
drawn from it at random is found to be defective. Find the probability that the box
selected was Box 2.
Answer:
1/6
Step-by-step explanation:
As we already know that selected bulb is defective the required probability doesn't depend on functional bulbs at all.
The probability, that selected defective bulb is from Box2 is number of defective bulbs in Box 2 divided by total number of defective bulbs.
P(defective in box 2)= N(defective in box 2)/N(defective total)
As we know there is only 1 defective lamp in box 2.
So N(defective in box 2)=1
Total number of defective bulbs is Box1- 2 defective bulbs, box2- 1 defective bulbs, box3 - 3 defective bulbs. Total are 6 defective bulbs.
So N(defective total)=6
So P(defective in box 2)=1/6
How many solutions does the system have? You can use the interactive graph below to find the answer. 4x-2y=8 2x+y=2 4x−2y=8 2x+y=2 A.One solution B.two solutions. C.Many solutions
Answer:
one solution
Step-by-step explanation:
The given system of equations has one solution.
Hence option A is correct.
The given system is
4x-2y=8
2x+y=2
Since we know that,
For system
a₁x + b₁ y = c₁
a₂x + b₂y = c₂
If
a₁/a₂ = b₁/b₂ = c₁/c₂ then it has an infinite solution
a₁/a₂ ≠ b₁/b₂ then unique solution
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ then no solution
Here we have
a₁ = 4, b₁ = -2 and c₁ = 8
a₂ = 2, b₂ = 1 and c₂ = 2
Now since
a₁/a₂ ≠ b₁/b₂ ⇒ 4/2 ≠ -2/1
⇒ 2 ≠ -2
Hence, the given system has a unique solution.
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please help me pleaseeeeeeee
Answer:
the first blank is 2, the second one is 1
Answer:
Yellow box #1=2
Yellow box #2=1
Step-by-step explanation:
#1) 8-6=2
#2)8-7=1
Use Green's Theorem to evaluate F · dr. C (Check the orientation of the curve before applying the theorem.)F(x, y) = y cos(x) − xy sin(x), xy + x cos(x) , C is the triangle from (0, 0) to (0, 8) to (2, 0) to (0, 0)
Notice that C has a clockwise orientation. By Green's theorem, we have
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\iint_D\left(\frac{\partial(xy+x\cos x)}{\partial x}-\frac{\partial(y\cos x-xy)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]
where D is the triangule region with C as its boundary, given by the set
[tex]D=\{(x,y)\mid0\le x\le2\land0\le y\le8-4x\}[/tex]
So we have
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}((y+\cos x-x\sin x)-(\cos x-x\sin x))\,\mathrm dy\,\mathrm dx[/tex]
[tex]\displaystyle\int_C\mathbf F(x,y)\cdot\mathrm d\mathbf r=-\int_0^2\int_0^{8-4x}y\,\mathrm dy\,\mathrm dx=\boxed{-\dfrac{64}3}[/tex]
Draw the straight line y = x + 2
Answer:
Graph is attached below
Step-by-step explanation:
You first need to plot any two points on the coordinate plane(you can also do more than two points to make it more accurate). Then, using a ruler connect the points and extend the line outwards.
The plotted straight line is as shown in below graph.
Given straight line equation is y = x + 2
To plot a straight line, take two different values of x which output different values of y. Then plot those points in the graph.
After plotting those two points, you connect both dots with straight line and extend that line infinitely from both endpoints.
Example, take x = 1 and x = 2 for straight line y = x + 2
Then we get:
For x = 1, y = 1 + 2 = 3
For x = 2, y = 2 + 2 = 4
The plot of points (1,3) and (2,4) and the straight line y = x + 2 is shown below.
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A researcher measures job satisfaction among married, single, and divorced employees to determine whether marital status can influence job satisfaction. Based on the following description in APA format, state the value for k, N, and n. A one-way analysis of variance showed that job satisfaction did not vary by marital status, F(2, 24) = 1.93, p > 0.05.
a. k = _____
b. N = _____
c. n = _____
Answer:
a. k = 3
b. N = 27
c. n = 9
Step-by-step explanation:
Given that,
Source : sS dF mS F
Between: k -1 sSB/k-1 mSB
within N-K sSw/N-K mSw
total N-1
Therefore F ( 2, 24 ) = F ( K - 1, N - K )
so K - 1 = 2
K = 2 + 1
K = 3
N - K = 24
N - 3 = 24
N = 24 + 3
N = 27
married, single and divorced are equal sizes
so n = N/3
n = 27 / 3
n = 9
a. k = 3
b. N = 27
c. n = 9
The equations x + 5 y = 10, 3 x minus y = 1, x minus 5 y = 10, and 3 x + y = 1 are shown on the graph below. On a coordinate plane, there are 4 lines. Green line goes through (0, negative 1) and (1, 2). Blue line goes through (0, 1) and (1, negative 2). Pink line goes through (0, 2), and (2, 1.5). Orange line goes through (negative 2, negative 2.5) and (2, negative 1.5). Which is the approximate solution for the system of equations x + 5 y = 10 and 3 x + y = 1? (–0.3, 2.1) (–0.3, –2.1) (0.9, –1.8) (0.9, 1.8)
Answer:
A: (–0.3, 2.1)
Answer:a
Step-by-step explanation: