Answer:
A. $52,000
Step-by-step explanation:
The initial amount of the grant is $52,000. The correct option is a.
What is annuity?An annuity is a financial product that provides an individual with a series of regular payments in exchange for an initial investment or a series of payments.
Annuities are commonly used to generate income in retirement, but they can also be used for other purposes, such as covering the future expenses of a dependent or providing a guaranteed income stream for a set period of time.
We can use the formula for the present value of an annuity to find the initial amount of the grant:
PV = A * ([tex](1 - (1 + r)^{(-n)[/tex]) / r)
Where PV is the present value, A is the annual payment, r is the annual interest rate, and n is the number of periods.
Substituting the given values, we get:
PV = 12,177.17 x ((1 - [tex](1 + 0.055)^{(-5)[/tex]) / 0.055)
PV ≈ 51,765.57
Rounding to the nearest dollar, the initial amount of the grant is $52,000.
Therefore, the answer is option (a).
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A couple wishes to replace the carpeting in their master bedroom. Their master bedroom measures 24 ft by 16 ft. If carpeting is sold by the square yard, how many square yards of carpeting are needed
Answer:
128 yards^2
Step-by-step explanation:
So basically you just need to find the area of the room and then con vert it into yards.
24 ft x 16 ft = 384 ft^2
1 yard = 3 feet
384/3 = 128
128 yards^2
Hope this helps and have a good day!
42.7 yard² square yards of carpeting are needed to replace the carpeting in their master bedroom
3 feet = 1 yard
The length of bedroom = 24 ft. = 24 ft. * 1/3 yard per feet
Length of bedroom = 8 yards
Width of bedroom = 16 ft. = 16 ft. * 1/3 yard per feet
Width of bedroom = 16/3 yards
The area of the masters bedroom is:
Area = length * width
Area = 8 yards * 16/3 yards
Area = 42.7 yard²
Hence 42.7 yard² square yards of carpeting are needed to replace the carpeting in their master bedroom
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estimate each product 8 × 56.7
Answer:
465??
Step-by-step explanation:
20 PTS! Is the answer h=2.7?
Answer:
Yes your right
Step-by-step explanation:
2x + y = 9
5x + 3y = 26
Answer:
7X+4y=35
Step-by-step explanation:
If a couple has 3 children, what is the probability of all three children being girls? Justify.
Answer:
The probability of all three children being girls will Be: 1/8
Step-by-step explanation:
The couple has 3 children.
We have to determine the probability of all three children being girls.
As we know that for each child, the probability of being a girl is ' [tex]\frac{1}{2}[/tex] ' as is the probability of being a boy is ' [tex]\frac{1}{2}[/tex] '.
so for there to be all girls, the probability will be:
P ( all girls) = 1/2 × 1/2 × 1/2 = 1/8
Therefore, the probability of all three children being girls will Be: 1/8
what is 385divided by 24
Answer:
16.41 i think
Someone please help with this middle school math lol
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!
Answer:
the answer is c
Step-by-step explanation:
a person runs 1/ 4/5 miles i n 1/5 of and hour how many miles they are running per hour
Please help Find the missing area.
Answer:
turn the shape into three shapes two triangle and one square then you can do it easy
Step-by-step explanation:
What are the values of a and b?
a=
b=
Answer:
The values of a and b are:
a = 2[tex]b=4[/tex]Step-by-step explanation:
Given the exponential model
[tex]y=a\cdot \:b^x[/tex]
Given the points
(0, 2) and (3, 128)
We know that the y-intercept of [tex]y=a\cdot \:b^x[/tex] is (0, a).
so
a = 2
putting x = 3, y = 128 and a = 2
[tex]y=a\cdot \:b^x[/tex]
[tex]128=2\cdot \:b^3[/tex]
Switching sides
[tex]2b^3=128[/tex]
[tex]\frac{2b^3}{2}=\frac{128}{2}[/tex]
[tex]b^3=64[/tex]
Taking the real value such as:
[tex]\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)}[/tex]
so
[tex]b=\sqrt[3]{64}[/tex]
[tex]b=\sqrt[3]{4^3}[/tex]
[tex]b=4[/tex]
Therefore,
a = 2[tex]b=4[/tex]The following are prices of selected digital cameras. $158, $95 ,$175, $180 ,$95,$129, $228, $300 Find the standard deviation.
Answer: 69.23
Step-by-step explanation:
Given data:
N = 8.
μ = 170.
Solution:
First we calculate for the mean.
= 158 + 95 + 175 + 180 + 95 + 129 + 228 + 300/8
= 1360/8
= 170.
Next we calculate for (xi - μ)
(158 - 170) = (-20)^2 = 400
(95 - 170) = (-75)^2 = 5625.
(175 -170 ) = (5)^2 = 25.
(180 -170) = (10)^2 = 100
(95 - 170) = (-75)^2 = 5625.
(129-170) = (-41)^2 = 1681
(228 -170) = (58)^2 = 3364.
(300-170) = (130)^2 = 16900.
Summation of (xi - μ)
= 400 + 5625 +25 + 100 + 5625 + 1681 + 3364 + 16900
= 33720.
S = Σ√(xi - μ) /n-1
= √( 33720 - 170 ) / 8-1
= √ (33550/7)
= √4792.86
= 69.23
Standard deviation is 69.3
PLEASE HELP ME OR I WILL DIE...WHAT IS THE VALUE OF Y?!!!!!! I WILL BRAINLY, THANK FOR HELP AND FRENNNDDDDD
Answer:
Y = -128
Step-by-step explanation:
X is 36
5 divided by 10
(This is a random question I just thought of, whoever answers first I’ll give brainliest)
.5
Step-by-step explanation:
5 divided by 10 is 0.5
Compute $(\sqrt 3)^2\cdot (\sqrt 4)^3\cdot (\sqrt 5)^4$.
Answer:
\frac{x^{\frac{5}{2}}\cdot \:6y^2\sqrt[3]{y^4}}{12x^{\frac{1}{2}}\sqrt[4]{x^3}}=\frac{x^{\frac{5}{4}}y^{\frac{10}{3}}}{2}
I wrote it properly below :)
--------------------------------------------------------------------
[tex]\frac{x^{\frac{5}{2}}\cdot \:6y^2\sqrt[3]{y^4}}{12x^{\frac{1}{2}}\sqrt[4]{x^3}}=\frac{x^{\frac{5}{4}}y^{\frac{10}{3}}}{2}[/tex]
Answer:
600
Step-by-step explanation:
64, 57, 50, 43,... 50th term
Answer:
-279
Step-by-step explanation:
a=64
d=t2-t1=57-64=-7
t50=a+49d=64+49×(-7)
=64-343
=-279
estimate the unit rate to the nearest hundredth 2.35
Answer:
below
Step-by-step explanation:
The 5 represents the hundredth place so this means that its already rounded to the nearest hundredth.
Best of Luck!
If you started the problem by converting 1 pound to 16 ounces, would you get the same results?
Answer:
yes
Step-by-step explanation:
you would get results bc results are results
Flo and Carl each must read a 500-page book. Flo reads one page every minute. Carl reads one page every 50 seconds. Flo starts reading at 1:00, and Carl starts reading at 1:30. When will Carl catch up to Flo?
Answer:
Carl will catch up Flo at 4:00Step-by-step explanation:
Given
Flo reads one page every minuteCarl reads one page every 50 secondsCarl starts 30 minutes lateMax number of pages = 500Let x be the number of pages each reads when Carl catches up Flo
Then we have the time for Flo and Carl
Flo:
x pages after x minutesCarl:
x pages after 30 + x*50/60 minutesThe time is same:
x = 30 + 50/60xx = 30 + 5/6xx - 5/6x = 301/6x = 30x = 6*30x = 180180 minutes = 3 hours
1:00 + 3 hours = 4:00
✭Flo and carl must read a 500 page book.
✭Flo reads one page every 1 minute (60seconds).
✭Carl reads one page every 50 Seconds.
✭Flo starts reading at 1:00.
✭Carl starts reading at 1:30.
[tex]\large\bold{\underline{\underline{To \: Find:-}}}[/tex]When will carl catch up to flo?
[tex]\large\bold{\underline{\underline{Solution:-}}}[/tex]Let Flo read certain pages when carl catches up with him. Then carl also read the same amount pages at that time.
Let the time passed be "x" minutes.
If carl Reads 1 page every 50 seconds, then 50 seconds can be written as 5/6th of a minute.
Carl's rate will be:
[tex]Carl \: \: Rate \: = \frac{Page}{Minutes} = \frac{ \frac{1}{5} }{6} = \frac{6}{5} [/tex]Now, flo got a 30 minute head start. therefore, when carl catches up, he will read certain pages at x + 30 minutes.
And the number of pages that carl read after the time he had started, that is, "x" minutes will be:
[tex] ⇒\frac{6}{5} \times x[/tex]But, the number of pages carl and flo read will be the same at that time!
[tex] ⇒\frac{6x}{5} = x + 30[/tex][tex] ⇒\frac{6x}{5} - x = 30[/tex][tex] ⇒\frac{x}{5} = 30[/tex][tex]⇒x = (30 \times 5) \: \: minutes[/tex][tex]⇒x = (150) \: \: minutes[/tex]So carl catches up after 150 minutes.
Now, 1:30 + 150 minutes = 1.5 hours + 2.5 hours = 4:00.
Carl will catch up at 4:00.Work out the mean data for 9.7,4.5,1.9,8,6.6
Step-by-step explanation:
im not really sure about this but I think it's 6.1
Find the value of the expression: 1/3√.81-1
Answer:
1/6
Step-by-step explanation:
1/3÷by.81_81_1 and =1/6according to the calculator :^)
15 POINTS IF U ANSWER CORRECT
Max ran 5 miles on Thursday. One mile is equal to 5,280 feet. Which proportion can be used to determine how many feet, x, Max ran on Thursday?
Answer:
x/5 = 5280/1
Step-by-step explanation:
this is a proportion set up and then cross multiple. You will get your answer for x. Which is 26, 400 feet.
Find the indicated values, where g(t)=t^2-t and f(x)=1+x g(f(2)+3)
Answer:
[tex]g(f(2)+3)=30[/tex]
Step-by-step explanation:
We have the two functions:
[tex]g(t)=t^2-t\text{ and } f(x)=1+x[/tex]
And we wish to find:
[tex]g(f(2)+3)[/tex]
First, let’s find f(2) first. So, we will substitute 2 for x for f(x):
[tex]f(2)=1+(2)=3[/tex]
Hence, we can now substitute 3 for f(2):
[tex]g(f(2)+3)=g(3+3)=g(6)[/tex]
Now, we can find g(6). Substitute 6 for t for g(t):
[tex]g(6)=(6)^2-(6)=36-6=30[/tex]
Therefore:
[tex]g(f(2)+3)=30[/tex]
Understanding Prime Factorization
Which expressions show the prime factorization of 90?
Check all that apply.
2 3 x 15
22 x 3 x 5
0 2x 32 5
0 2 x 5 x 9
o 2 x 3 x 3 x 5
Intro
Done
Ans) The prime factorization of 90 is 2 × 3 × 3 × 5.
Answer 1 and 2 please and thank you
Answer:
C DONT REPORT ME
Step-by-step explanation:
Determine whether the planes are parallel, perpendicular, or neither.8x + 8y + 8z = 1, 8x − 8y + 8z = 1 parallel perpendicular neither Correct: Your answer is correct.If neither, find the angle between them. (Round your answer to one decimal place. If the planes are parallel or perpendicular, enter PARALLEL or PERPENDICULAR, respectively.)
Answer:
The answer is "[tex]\bold{\theta= 70.53^{\circ}}[/tex]"
Step-by-step explanation:
The given value:
[tex]8x+8y+8z = 1\ and \ 8x-8y+8z = 1[/tex]
When the normal vectors are in the plane:
[tex]n_1 = < 8,8,8 > \ and \ n_2 = < 8, -8, 8>:[/tex]
Because the two variables really aren't proportional to each other and the wings are not parallel.
Let us just find that two vectors' dot product.
[tex]n_1 \cdot n_2 =<8,8,8> < 8,—8,8>\\\\ = 64-64+ 64 \\\\ = 64 \neq 0[/tex]
Therefore, we won't find that angle between both the given planes as parallel.
[tex]\cos \theta = \frac{n_1 \cdot n_2}{|n_1||n_2|}\\\\\cos \theta =\frac{64}{\sqrt{192} \sqrt{192}}\\\\\cos \theta =\frac{64}{8\sqrt{3} 8\sqrt{3}}\\\\\cos \theta = \frac{1}{3}\\\\ \theta = 70.53^{\circ}[/tex]
It is required to know the orientation of one plane relative to the other.
The angle between the planes is 70.5°.
PlanesThe given planes are
8x + 8y + 8z = 1
8x − 8y + 8z = 1
Parallel
[tex]\dfrac{8}{8}=\dfrac{8}{-8}=\dfrac{8}{8}\\\Rightarrow 1\neq -1\neq 1[/tex]
The planes are not parallel.
Perpendicular
[tex]8\times 8+8\times -8+8\times8=64\neq 0[/tex]
The planes are not perpendicular as dot product is not 0.
Finding angle
[tex]\theta=\cos^{-1}\dfrac{8\times 8+8\times -8+8\times8}{\sqrt{8^2+8^2+8^2}\sqrt{8^2+(-8)^2+8^2}}\\\Rightarrow \theta=\cos^{-1}\dfrac{1}{3}\\\Rightarrow \theta=70.53^{\circ}[/tex]
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Find the product. Simplify before multiplying.
15/20 x 2/5
Answer:
simplification: 3/4 x 2/5 | answer: 3/10
Step-by-step explanation:
What is the area of the figure?
Answer: 17.5 square yards
================================================
Work Shown:
base = 5 yards
height = 7 yards
The base and height are always perpendicular to one another
area of triangle = 0.5*(base)*(height)
area of triangle = 0.5*(5)*(7)
area of triangle = 17.5 square yards
The other values aren't used. They're likely thrown in as a distraction.
In Megamind, how did Megamind trap Titan in the hologram without even fighting him?
Answer:
is tghis a joe?
Step-by-step explanation:
Answer:
with the mind on a mega
Step-by-step explanation:
Calificación mínima. Para obtener una A en un curso, Stephen Heasley debe
obtener una calificación promedio de 90 o mayor en cinco exámenes. Si en los
primeros cuatro exámenes de Stephen sus calificaciones son 92, 87, 96 y 77,
¿cuál es la minima calificación que Stephen puede recibir en el quinto examen
para obtener una A en el curso?
Answer:
La mínima calificación que Stephen puede recibir en el quinto examen para obtener una A en el curso es 98.
Step-by-step explanation:
La media (también llamada promedio o media aritmética) de un conjunto de datos es una medida de posición central. Es el valor obtenido al sumar todos los datos y dividir el resultado entre el número total de datos.
En este caso, el número total de datos es 5 y el valor de los datos de los cuales debes obtener el problema es 92, 87, 96, 77 y un valor desconocido de un quinto examen. Y sabes que este valor debe ser igual o mayor a 90.
Esto se expresa matemáticamente como:
[tex]\frac{92+87+96+77+nota}{5}[/tex]≥90
donde "nota" es la mínima calificación que Stephen puede recibir en el quinto examen para obtener una A en el curso.
Resolviendo:
[tex]\frac{352+nota}{5}[/tex]≥90
352+nota≥90*5
352+nota≥450
nota≥450 - 352
nota≥98
La mínima calificación que Stephen puede recibir en el quinto examen para obtener una A en el curso es 98.