Answer:
5400
Step-by-step explanation:
8% of 5000 is 400. 5000 + 400 - 5400.
Answer:
$5400
Step-by-step explanation:
We need to find the amount of tax in $
So, if 100% = $5000
8% = ?
cross multiply to be : 8 × 5000
100
to get $400
Add it to the $5000 to get $5400
Mike is buying a car for $24,300. He wants to make a maximum down payment of $3.000. TWo. deals are available, both for 48-month loans. In the first deal, with a factory rebate his down payment will be $1,000. His monthly loan payments would be $573 21 at 8.4% interest. In the second deal, he gets no rebate and makes a $3,000 down payment but his interest rate is 0.9% resulting in a $451.95 loan payment. a) What total amount will Mike pay with the first deal? b) What total amount will Mike pay with the second deal?
Answer:
1,000
Step-by-step explanation:
A sample of bacteria is decaying according to a half-life model. If the sample begins with 500 bacteria,
and after 17 minutes there are 150 bacteria, after how many minutes will there be 10 bacteria
remaining?
When solving this problem, round the value of k to four decimal places and round your final answer to
the nearest whole number.
contact +2348021312463, he can help you
after approximately 137 minutes, there will be 10 bacteria remaining.
To find the time at which there will be 10 bacteria remaining, we can use the half-life model for exponential decay, which is given by:
N(t) = N₀ * [tex](1/2)^{(t / t_{half})[/tex]
where:
N(t) = the number of bacteria at time t
N₀ = the initial number of bacteria
t = time (in minutes)
t_half = the half-life of the bacteria
We are given that the initial number of bacteria (N₀) is 500 and after 17 minutes there are 150 bacteria (N(17) = 150).
Let's use this information to find the value of k (the decay constant):
150 = 500 * [tex](1/2)^{(17 / t_{half})[/tex]
Divide both sides by 500:
[tex](1/2)^{(17 / t_{half})[/tex] = 150 / 500
[tex](1/2)^{(17 / t_{half})[/tex] = 0.3
Now, we can write the equation as an exponent:
17 / t_half = log base (1/2) of 0.3
Using logarithms:
t_half = 17 / log base (1/2) of 0.3
Now, calculate t_half:
t_half = 17 / log base 2 of 0.3 ≈ 38.555
Now, we can find the time at which there will be 10 bacteria remaining (N(t) = 10):
10 = 500 * [tex](1/2)^{(t / 38.555)[/tex]
Divide both sides by 500:
[tex](1/2)^{(t / 38.555)[/tex] = 10 / 500
[tex](1/2)^{(t / 38.555)[/tex] = 0.02
Write the equation as an exponent:
t / 38.555 = log base (1/2) of 0.02
Using logarithms:
t = 38.555 * log base 2 of 0.02 ≈ 137.08
Rounding to the nearest whole number:
t ≈ 137
So, after approximately 137 minutes, there will be 10 bacteria remaining.
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A prize is divided in the ratio 5:1 if the larger share is £65 what is the total prize?
Answer:
£78
Step-by-step explanation:
65 divided by 5= £13
13+65=£78
Answer:
£78
Step-by-step explanation:
Let the total value be T.
£65/T = 5/(5 + 1)£65/T = 5/6T = 65 x 6 / 5T = 13 x 6T = £78135.99 rounded to two significant figures
Answer:
1.3×10^1
Step-by-step explanation:
For this, you need to use scientific notation
First, let's round up the decimal points
135.99 = ~ 136
1.3 ×.10^1
can someone please help with this problem please
Answer:
1360 seats sold
Step-by-step explanation:
total seats = 1600
total seats sold = 85% of 1600
= 85/100 × 1600
= 85 × 16
= 1,360 seats sold
4sin45 degrees cos 15degrees=1+square root 3
[tex]\text{R.H.S}\\\\=4\sin 45^{\circ} \cos 15^{\circ} \\\\=4\sin 45^{\circ} \cos (45^{\circ}-30^{\circ})\\ \\=4 \sin 45^{\circ} \left(\cos 45^{\circ} \cos 30^{\circ} +\sin 45^{\circ} \sin 30^{\circ} \right)\\\\=4 \left(\sin 45^{\circ} \cos 45^{\circ} \cos 30^{\circ} +\sin^2 45^{\circ} \sin 30^{\circ} \right)\\[/tex]
[tex]=4\left[\dfrac 1{\sqrt 2} \cdot \dfrac 1{\sqrt 2} \cdot \dfrac{\sqrt 3}2 +\left( \dfrac 1{\sqrt 2} \right)^2 \cdot \dfrac 12 \right]\\ \\=4\left(\dfrac{\sqrt 3}4 +\dfrac 14\right)\\\\=4\cdot \dfrac 14 \left(1+\sqrt 3\right)\\\\=1+\sqrt 3\\\\=\text{L.H.S}[/tex]
Complete the missing exponent 64=4_
Answer:
64=4^3
Step-by-step explanation:
4x4x4=64. 4x4x4=4^3 as there are three 4s. Hope it helps!
The graph shows the amount of caffeine left in the body after drinking a 20-ounce soft drink with 90 milligrams of caffeine. Which of the following exponential equations best fits the data?
y=90(2)^
y=2(90)^x
y=0.5(90)^x
y=90(0.5)^x
Answer:
y=90(0.5)^x
The y-intercept is (0,90), so when x=0, y should be 90.
By replacing x=0 in all equations you get;
1)
y=90(2)^0 =90 accepted
2)
y=2(90)^0 =2 rejected
3)
y=0.5(90)^0 =0.5 rejected
4)
y=90(0.5)^0 =90 accepted
Since this is an exponential decrease,
y=90(2)^x is rejected.
The following data points represent the number of children in each household in Cam's neighborhood.
0, 0,6,3,1,5, 0, 2,0
How many households in Cam's neighborhood have 0 children?
households
Answer:
4
Step-by-step explanation:
We can see that 9 households are represented in the data, 4 of them are zeros. This means 4 households in Cam's neighborhood have 0 children.
can someone please help me
Answer:
x = 49
Step-by-step explanation:
corner point b = 41
d = right angle ( 90 )
90 + 41 = 131
180- 131 = 49
x = 49
p.s
im not sure if d is a right angle if it is not please inform me.
What would you do if fear was not a factor and you could not fail?`
i know it's not a maths question but let's try
Answer:
Well, i would just say you just had to do your best in everything that you do. No pressure , no stress don't overwork yourself and simply take action. Then you will have a chance to get what you want because you tried your best to get to it. Although sometimes we don't get what we want, atleast we'll be closer. As they say, 'Aim for the sun to reach the moon"
Step-by-step explanation:
You're welcome
A picture frame measures 18 cm by 20 cm on the outside, and 168 cm?
of picture shows.
Find the width of the frame around the picture.
The width of the frame is
cm.
Answer:
hello
( 20 - 2 x ) ( 18 - 2 x )
= 360 - 40 x - 36 x + 4 x²
= 4 x² - 76 x + 360
Step-by-step explanation:
Rewrite the equation by completing the square. X^2-14x+40=0
Answer:
(x – 7)² – 9
Step-by-step explanation:
I hope this helps
find the 39th term for the aritmethic sequence, 10,15,20
The 39th term of the sequence is 200.
What is Arithmetic Sequence?Arithmetic sequence or arithmetic progression is the set of numbers for which the difference of any two consecutive numbers in that set will be a constant.
The constant term which is the difference of the two consecutive numbers is called the common difference and is usually denoted by 'd'.
Arithmetic sequence is usually represented as
a, a + d, a + 2d, ........, a + (n - 1)d
The nth term of an arithmetic sequence, aₙ is given by the formula,
aₙ = a + (n - 1) d
where, a is the first term and d is the common difference.
The given sequence is 10, 15, 20, ......
a = 10
d = 15 - 10 = 5
Here, we have to find the 39th term of the sequence.
a₃₉ = 10 + (39 - 1) 5
= 10 + (38 × 5)
= 10 + 190
= 200
Hence, the 39th term of the progression 10, 15, 20,..... is 200.
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In a certain year, 26% of people aged 65–69 worked. Suppose that a recent report claimed that the percentage of people aged 65–69 who work has increased since that year.
Considering the situation described, the appropriate hypotheses set is given by:
[tex]H_0: p = 0.26[/tex]
[tex]H_1: p > 0.26[/tex]
What are the hypotheses test?
At the null hypotheses, we test if there is not enough evidence that the percentage has increased, that is, it still is of 26%, hence:
[tex]H_0: p = 0.26[/tex]
At the alternative hypotheses, we test if there is evidence that it has increased, hence:
[tex]H_1: p > 0.26[/tex]
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How many gallons is equal to 48 cups?
Answer:
3 US galloons
write a function that transforms f(x)=2^3+4 in the following way: stretch vertically by a factor of 6 and shift 5 units left.
Answer:
f(x) = 2x3 + 4
Stretch vertically be a factor of 2:
f(x) = 2*2x3 + 4 = 4x3 + 4
Shift 5 units to the left:
f(x) = 4(x+5)3 + 4
In the figure below, triangle QRT, triangle RSQ, and triangle QST are scalene triangles.
If mQRS = 37° and mTQS = 34°, what is mTQR?
A.
87°
B.
90°
C.
93°
D.
109°
mTQR = 87°
HOPE IT HELPS...!!!
Answer:
[tex] \sf m \angle TQR = 87 \degree[/tex]
Step-by-step explanation:
Given:
∆QRT, ∆RSQ and ∆ QST are scalene traingle.
[tex]m \angle QRS = 37 \degree \\ m \angle TQS = 34 \degree \\ m \angle QST = 90 \degree[/tex]
To find:
[tex]m \angle TQR = ?[/tex]
Solution:
In ∆ QTS,
[tex] \sf \: m \angle TQS + m \angle QTS +m \angle QST = 180 \degree \: \\ \sf (properties \: of \: triangle)[/tex]
[tex] \sf \: 34 + m \angle QTS +90 = 180 \degree \: \\ \sf m \angle QTS = 180 - 90 - 34 \\ \sf \: m \angle QTS = 180 - 124 \\ \sf \: m \angle QTS = 56 \degree[/tex]
Now in ∆QTR,
[tex] \sf \: m \angle QTR + m \angle TQR + m \angle TRQ \: = 180 \degree \\ \sf (properties \: of \: triangle)[/tex]
[tex] \sf \: 56 + m \angle TQR + 37 \: = 180 \degree \\ \sf m \angle TQR = 180 - 56 - 37 \\ \sf m \angle TQR = 87 \degree[/tex]
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A company makes chocolate candies in the shape of a solid sphere. Each piece of candy has a diameter of 9 cm . If a box contains 10 pieces of candy, how much chocolate does the box contain?
Use 3.14 for π, and do not round your answer.
Step-by-step explanation:
The Volume of a Sphere ( One piece of candy ) = 4/3πr³
r = diameter/2 = 9/2 = 4.5 cm
Volume = 4/3(3.14)(4.5³)
V = 381.51 cm³
the box contains 10 pieces so the box contains :
381.51 x 10 = 3815.1 cm³ of chocolate
what is the area of the regular hexagon
Answer:
720
Step-by-step explanation:
n*180
n
the answer is 720
Ben is going on a 380-mile trip. If he drives for 2 hours at an average speed of 50 miles per hour, how many miles will he still have left to go on on his trip?
Answer:
19000
Step-by-step explanation:
1 hour = 50 miles
2 hour = 100 miles
50×380 = 19000
Figure ABCD is a parallelogram.
Parallelogram A B C D is shown. A diagonal is drawn from point A to point C.
Which sequence could be used to prove that AD = BC?
First prove TriangleABC is congruent to TriangleCDA, and then state AD and BC are corresponding sides of the triangles.
First prove TriangleABC is similar to TriangleCDA, and then state AD and BC are opposite sides of the parallelograms.
First prove ParallelogramABCD is congruent to ParallelogramCDAB, and then state AD and BC are corresponding sides of two parallelograms.
First prove ParallelogramABCD is similar to ParallelogramCDAB, and then state AD and BC are opposite sides of the parallelograms.
Answer:
A
First prove Triangle ABC is congruent to Triangle CDA, and then state AD and BC are corresponding sides of the triangles.
Hope this helps!
Please Mark Brainleast!!!
The sequence to prove that AD = BC is; First prove ABC is similar to CDA, and then state AD and BC are opposite sides of the parallelograms.
How to prove Quadrilateral Theorems?From the question, we see that the parallelogram ABCD has a diagonal AC. Thus; AB║ CD and AD║BC.
Now, the parallelogram is divided into two triangles ΔABC and ΔADC by its diagonal AC.
Thus;
∠ACB = ∠DAC and ∠CAB = ∠ACD because they are alternate interior angles.
Also, AC = AC (Reflexive property)
Thus; by ASA congruence postulate, we can say that; ΔABC ≅ ΔADC
Also, by corresponding sides of the congruent triangles are congruent we can say that AD = BC.
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Which of the numbers below is greater than 36.785 Select all that apply
A) 36.78
B) 36.79
C) 41.2
D) 36.789
candy that costs 31 cents per pound is mixed with candy that costs 46 cents per pound to obtain 50 pounds of candy that costs 40 cents per pound. How many pounds of each of the two types of candy are in the mix?
Answer:
20 lb of 31 cent candy, 30 lb of 46 cent candy
Step-by-step explanation:
sorry don't have one
here is a smiley face for you
:D
The amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we can assume the separate weights of each type of candies to be represented by variables.
Let we have:
x = weight (in pounds) of first type of candy whose cost is 31 cents per pound.y = weight (in pounds) of second type of candy whose cost is 46 cents per pound.x pounds of first type of candy is mixed with y pounds of second candy.
The weight of the mixture = x + y = 50 pounds
The cost of the mixture = 40 cents per pound = [tex]40 \times 50 = 2000[/tex] cents
Cost of the mixture = cost of x pounds of first candy+ cost of y pounds of second candy = [tex]31x + 46y[/tex]
Thus, we get [tex]31x + 46y =2000[/tex]
Therefore, we got a system of two linear equations as:
[tex]x +y = 50\\31x + 46y =2000[/tex]
From first equation, we get:
[tex]x = 50 -y[/tex]
Substituting this value in second equation, we get:
[tex]31(50-y) + 46y =2000\\1550 + 15y = 2000\\15y = 450\\\\y = 450/15 = 30[/tex]
Putting this value of y in equation for x, we get:
[tex]x = 50-y = 50-30 = 20[/tex]
Thus, the amount of each type of candy (in pounds) that are mixed for the considered condition is: 20 pounds of first type of candy and 30 pounds of second type of candy.
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how do you solve 7/8+(4/8-2/4)
evaluate the expression 4 3x when x is 2
You want to know the average height of your three closest friends.
Should you survey the population or a sample?
Answer:
population
Step-by-step explanation:
find measure of the missing angles and justify your answer with postulates and theorems.
Answer:
Step-by-step explanation:
I need step by step written answer for this
Answer:
-1/2
Step-by-step explanation:
2/5 * - 3/7 - 1/14 - 3/7 * 3/5
= - 6/35 - 1/14 - 9/35
= - (6*2)/(35*2) - (1*5)/(15*5) - (9*2)/(35*2)
= - 12/70 - 5/70 - 18/70
= (-12 - 5 - 18)/70
=- 35/70
= - 1/2
How much of a radioactive kind of promethium will be left after 20 days if you start with
9,056 grams and the half-life is 5 days?
in 20 days 4 half life will be completed
so n = 4
formula :-
[tex] \frac{ A\degree}{ {2}^{n} } = \frac{9056}{ {2}^{4} } = \frac{9056}{16} = 566grams[/tex]
The radioactive kind of promethium will have 566 grams left after 20 days.
What is half-life?Half-life is the time required for a quantity to reduce to half of its initial value.
Given, A radioactive kind of promethium with 9,056 grams and a half-life is 5 days.
∴ In the next 5 days, it'll have (9056/2) = 4528 grams.
Next 5 days it'll have (4528/2) = 2269 grams.
As it has a half-life in 5 days and 20 is multiple (4×5).
After 20 days the radioactive material will have (9056/2⁴) grams.
= 566 grams left.
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