Answer:
$625
Step-by-step explanation:
You start with $500
The interest per year is 5% or 500 x 0.05 = $25
If it matures 5 years and each year has an increase of $25 then
Year 1 - $525
Year 2 - $550
Year 3 - $575
Year 4 - $600
Year 5 - $625
Answer:
Step-by-step explanation:
We express the interest rate r in decimal form, so we have r=5%=5100=0.05. The principal is P=500 and the time in years is t=5. So, the interest is I=Prt=(500)(0.05)(5)=$125. The interest earned is $125.
If a, b and c are positive integers for which (a,b,c) is the only
ordered triple such that 6a +9b + 20c = 61, then what is
a+b+c?
If a, b, and c are all positive integers and 6a + 9b + 20c = 61, then right away you know c < 3, because if c = 3, then 20c = 60, and there are no solutions for a and b.
So consider two cases:
• If c = 2, then we're left with 6a + 9b = 21.
• If c = 1, then 6a + 9b = 41.
We have gcd(6, 9) = 3, but 41 is prime and 3 does not divide 41. So we throw out the second case.
This leaves us with 6a + 9b = 21. Notice that if a = b = 1, then 6a + 9b = 15. Add 6 to both sides to get 21. So a = 2, b = 1, and c = 2, and hence a + b + c = 5.
How much mixed spice will she need for 6 spice
Answer:
who
Step-by-step explanation:
what is the equation of the line perpendicular to the line y = -x + 2 through the point (3, 5)?
Answer:
First, solve 3x+2y=4 for y.
*Subtract 3x from both sides*
2y=-3x+4
*Divide both sides by 2*
y=-3/2x+2
Parallel lines have the same slope so the answer is y=-3/2x+7/2
Hope this helps!!
Write a positive or negative integer that represents the situation.
An elevator goes down 8 floors.
solve the quadratic equation 3x^2-5x-7=0
Step-by-step explanation:
[tex]3x^{2} -5x -7 = 0 \\ 3x^{2} -5x = 7 \\ x^{2} -\frac{5}{3}x = \frac{7}{3} \\ x^{2} -\frac{5}{3}x +\frac{25}{36} = \frac{7}{3} +\frac{25}{36} \\ (x -\frac{5}{6})^{2} = \frac{84 +25}{36} \\ (x -\frac{5}{6})^{2} = \frac{109}{36} \\ x -\frac{5}{6} = ±\sqrt{\frac{109}{36}} \\ x -\frac{5}{6} = ±\frac{\sqrt{109}}{6} \\ x = ±\frac{\sqrt{109}}{6} +\frac{5}{6}[/tex]
Equation from the positive root:
[tex]x = \frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{\sqrt{109} +5}{6}[/tex]
Equation from the negative root:
[tex]x = -\frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{-\sqrt{109} +5}{6}[/tex]
Answer:[tex]x = \frac{\sqrt{109} +5}{6}\\[/tex] and [tex]x = \frac{-\sqrt{109} +5}{6}\\[/tex] satisfy your quadratic equation.
Given : A quadratic equation is given to us . The equation is 3x² - 5x - 7 = 0 .
To Find : The roots of the equation .
Solution : Given quadratic equation is 3x²-5x-7=0. So , let's factorise it to get the zeroes of the equation .
⇒ 3x² -5x - 7 = 0.
Here now , use Quadratic formula , of the quadratic equation in standard form of ax² + bx + c = 0.
[tex]\boxed{\red{\bf x\:\:=\:\:\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}[/tex]
On substituting respective values ,
⇒ x = -(-5) ± √ (-5)² - 4×3×(-7) / 2 × 3.
⇒x = 5 ± √ [ 25 + 84 ]/ 6 .
⇒ x = 5 ± √ 109 / 6 .
⇒ x = 5 + √109 / 6 , 5 - √109 / 6.
[tex]\purple{\underbrace{\underline{\boxed{\red{\tt \purple{\longmapsto} x = \dfrac{5+\sqrt{109}}{6}, \dfrac{5-\sqrt{109}}{6}}}}}}[/tex]
if m<2 = 115 degrees what is m<1 ? (There you go)
Answer:
65
Step-by-step explanation:
180 - 115 = 65
This is the easiest way to think about and do it but your teacher might want you to do it a different way.
Answer:
65
Step-by-step explanation:
The slope of a line is 2. The y-intercept of the line is 6. Which statements accurately describe how to graph the
function?
O Locate the ordered pair (0, -6). From that point on the graph, move up 2, right 1 to locate the next ordered pair
on the line. Draw a line through the two points.
Locate the ordered pair (0, -6). From that point on the graph, move up 2. left 1 to locate the next ordered pair
on the line. Draw a line through the two points.
O Locate the ordered pair (-6, 0). From that point on the graph, move up 2, right 1 to locate the next ordered pair
on the line. Draw a line through the two points.
Locate the ordered pair (-6, 0). From that point on the graph, move up 2, left 1 to locate the next ordered pair
on the line. Draw a line through the two points.
Answer:
A
Step-by-step explanation:
Solve the equation. Then check your solution.
-4/5 w+ 1/4= 1/5 + 1/3w. A.-27/68.
B.3/68.
C.3/28.
D-3/68
Answer:
CORRECT ANSWER IS B
Step-by-step explanation:
edge 2023 ;D
Determine how many solutions the following equation has using quadratic formula x^2+5x=-8
Answer:
I will be using differentiation method
Step-by-step explanation:
x^2+5x =-8
2×x ×x^2-1 +5x = -8
2x +5x = -8
7x = -8
divide both sides by the co-efficient of x
7x÷7=-8÷7
x =-1.5
Cualquiera de las dos rectas puede ser la de pendiente 1 o pendiente 2, sólo hay que
conservarla hasta el final de la operación.
BLO
Fórmula que vamos a aplicar:
m-m
1+m-m
tan 0=
Pendiente de la recta 3x - 4y + 8 = 0
Pendiente de la recta 2x + 3y - 23 = 0
Sustitución de datos
tan 0 =
Al realizar la operación de la fórmula se obtiene la tangente del ángulo, por lo que hay
que buscar el inverso de la tangente, que es el valor del ángulo de intersección entre
las rectas dadas.
tan 8 =
El valor del ángulo e es
There is a box with an area of 112 sq inches and a height of 3.5 inches. What is the width of the box?
Answer:
32 inches
Step-by-step explanation:
Because height times width equals area,
we can divide 112 by 3.5 to get the width
So it is 32 inches
I mark as brainliest
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
:)
the function is graphed below. On which interval of X is the average rate of change of the function the greatest?
Answer:
Between x = 48 and x = 45.
Step-by-step explanation:
Average rate of change of a function in the given interval is represented by,
Average rate of change = [tex]\frac{\triangle y}{\triangle x}[/tex]
From the table attached,
Average rate of change of the function between x = 3 and x = 9
= [tex]\frac{16-7}{9-3}[/tex]
= 3
Average rate of change in the interval x = 9 and x = 22
= [tex]\frac{32-16}{22-9}[/tex]
= [tex]\frac{16}{13}[/tex]
= 1.23
Average rate of change in the interval x = 9 and x = 22,
= [tex]\frac{45-32}{45-22}[/tex]
= [tex]\frac{13}{23}[/tex]
= 0.57
Average rate of change in the interval x = 45 and x = 48,
= [tex]\frac{63-45}{48-45}[/tex]
= 6
Therefore, average rate of change is maximum between x = 45 and 48.
Option given in bottom right will be the answer.
What is 5 8/100
as a decimal?
O
A. 5.008
0
B. 5.08
O
C. 5.8
0 D. 58
Answer:
5.08
Step-by-step explanation:
5 8/100
Since there are 2 zero's in 100, we need two numbers in the top
Replace 8 with 08 which is the same number
5 08/100
Now write as a decimal
5.08
Answer:
B. 5.08
Step-by-step explanation:
[tex]5\frac{8}{100} = \frac{508}{100}[/tex] 508 ÷ 100 = 5.08I hope this helps!
Find the surface area of a right cone with a diameter of 6 inches and a slant height of 5 inches.
Answer:
about 172.82
Step-by-step explanation:
Answer:
83.23
Step-by-step explanation:
to work out surface area of a right cone u
A=πr(r+h2+r2)
hope this helps
im not sure if its right tho
Helpppppp!!! PLEASE
:((
Answer:
Using the vertical line test, the functions are b, c, d, and f
Step-by-step explanation:
a and e both fail the vertical line test, therefore, it's not a functions.
find the value of x.
The answer is 13, but I need to show my work
Thank you guys
Answer:
Know the properties of vertical angles.
Step-by-step explanation:
Vertical angles are equal to each other, so we must make them equal to each other in an equation:
6x+2=80
6x=78
x=13
f(x) = x^3- 9x
What is the average rate of change of f over the interval [1, 6]
Answer:
Step-by-step explanation:
[tex]\frac{f(b)-f(a)}{b-a}[/tex] This is the formula for the average rate of change
over the interval (a, b)
a and b are x values
f(a) ad f(b) think of them as y values
Start calculating f(a) and f(b) a=1 b=6
replace all x's in formula with a, (1)
f(1)=1³-9(1) = 1-9= -8 f(1) = -8
Now do : b (6)
f(6) = 6³ - 9 (6) = 216-54=162 f(6) = 162
now plug everything into your equation
[tex]\frac{f(6)-f(1)}{6-1} =\frac{162- (-8)}{5} =\frac{170}{5} =34[/tex] average rate of change.
notice the 162 - (-8) In math there is no subtraction, and you would change it to + and when you do that you much change the sign of the next value making -8 a +8.
Hope this helps. Good luck!
A juice box has a length of 2 inches, a width of 1 inch, and a height of 4 inches. What is the volume of the juice box?
Answer:
8 in
Step-by-step explanation:
L × W × H = V2 × 1 × 4 = 8 inI hope this helps!
Rectangle ABCD has a perimeter represented by the expression 9x + 3. Rectangle PQRS has a
perimeter represented by the expression 6x + 2. Write the expression that represents the
difference in the perimeters of Rectangle ABCD and Rectangle PQRS. Write the steps and
solution.
Answer:
D. [tex] 3x + 1 [/tex]
Step-by-step explanation:
Perimeter of Rectangle ABCD = [tex] 9x + 3 [/tex]
Perimeter of Rectangle PQRS = [tex] 6x + 2 [/tex]
Difference between perimeter of Rectangle ABCD and Perimeter of Rectangle PQRS:
[tex] (9x + 3) - (6x + 2) [/tex]
Open Parentheses
[tex] 9x + 3 - 6x - 2 [/tex]
Collect like terms
[tex] 9x - 6x + 3 - 2 [/tex]
[tex] 3x + 1 [/tex]
please help explain if you can
Answer:
A
Step-by-step explanation:
58-90 bc its a right triangle
hope this helps
Hi Guys
Please answer this question. I will choose Brainliest.
Also please do a step by step method.
Worth 10 points and it is a Maths question.
Cheers,
Jake
Answer:
In simplifying this is simple.
2-4 x + 3x-12.2x+9x2-x-12A regular hexagon is rotated about its center. By which angle could the hexagon be rotated so that it is mapped onto itself?
30°
45°
600
90°
Previous
Answer: 60
Step-by-step explanation:
8x - 9 = - 2x + 11
Answer:
10/3
3.333333
3 1/3
Step-by-step explanation:
hope this helps
Aging workers of the Neotropical termite, Neocapritermes taracua, develop blue crystal containing glands ("backpacks") on their backs, When they fight intruding termites and are hampered, these "blue" termites explode, and the glands spew a sticky liquid (Sobotnik et al. 2012). The following data are from an experiment that measured the toxicity of the blue substance. A single drop of the liquid extracted from blue termites was placed on individuals of a second termite species, Labiotermes labralis, and the number that were immobilized (dead or paralyzed) within 60 minutes was recorded. The frequency of this outcome was compared with a control treatment in which liquid from glands of "white" termites lacking the blue crystals was dropped instead.
Is the blue liquid toxic compared to liquid from white termites?
Liquid source Unharmed Immobilized
Blue workers 3 37
White workers 31 9
Answer:
The blue liquid is toxic
Step-by-step explanation:
From the calculations I have done and attached to this problem
Null hypothesis:
H0 : p1 <= p2
Alternate hypothesis:
H1 : p1 > p2
^p1 = 0.925
^p2 = 0.2250
^P = (x1 + x2)/(n1+n2)
= 0.575
After calculating, I got test statistics = 6.33 ( check attachment)
P(z > 6.33) = 0.0000
In conclusion, our pvalue has been found to be less than the level of significance 0.05 so we reject null hypothesis and accept that we have enough sample evidence that the blue liquid is more toxic in comparison to white one.
Please check attachment for calculated test statistics.
Find the slope of the line passing through the points (8,-4) and (-6,-3).
Anybody know this ?
Answer:
= -1/14
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -3 - -4)/( -6 -8)
= ( -3+4)/( -6-8)
1/-14
= -1/14
30% of what equals 600
Answer: it equals 180 hope it helps
Answer:
180
Step-by-step explanation:
30% × 600 =
(30 ÷ 100) × 600 =
(30 × 600) ÷ 100 =
18,000 ÷ 100 =
180
Hope this helps!! Good luck on your assignment!
Top Brass Trophy Company, makes large championship trophies for youth athletic teams. At the moment they are planning production for fall sports: football and soccer. Each football trophy has a wood base, an engraved plaque, a large brass football on top, and returns $12 in profit. Soccer trophies are similar except that a brass soccer ball is on top, and the unit profit is only $9. Since the football has an asymmetric shape, its base requires 4 board feet of wood; the soccer base requires only 2 board feet. At the moment there are 1000 brass footballs in stock, 1500 soccer balls, 1750 plaques, and 4800 board feet of wood.
Required:
a. Define your decision variables and variable restrictions.
b. Build and present your linear programming model.
c. If you can, solve your linear programming model by graphical method. Otherwise, state your reason. Note that you can derive an optimal solution exactly by solving related equations.
d. If the number of available plaques is 200, modify your model and solve it again.
Answer:
a) maximize 12F + 9S
where:
F = football trophies
S = soccer trophies
b) constraints:
wood ⇒ 4F + 2S ≤ 4800
plaques ⇒ F + S ≤ 1750
brass footballs ⇒ F ≤ 1000
brass soccer balls ⇒ S ≤ 1500
c) using solver, the optimal solution is 650F + 1100S = $17,700
d) plaques ⇒ F + S ≤ 200, then
optimal solution is 200F = $2,400
324 soldiers queued up such that the number of queues is equal to the number of soldiers in each queue. find the number of queues
1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?
Answer:
Step-by-step explanation:
Since the Tootsie Roll lollipop is a sphere
volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]
the negative sign indicates that the volume is decreasing
upon differentiating
as the diameter given is =0.75 so radius will be = 0.375
[tex]dV/dt = 4piR^2*dR/dt[/tex]
so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]
So the radius is decreasing at the rate of dR/dt= 0.142in/min