Answer:
75 square units
Step-by-step explanation:
(x+10)x=3x^2
x^2+10x=3x^2
10x=2x^2
5x=x^2
x=5
Plugging in 5 into either of the initial equations yields the answer.
If you deposit 4500 in an account paying 3.2% interest continually home much will the account balance be after 1.5 year
Answer:
We conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $4,500.00 at a rate of 3.2% per year compounded continuously over 1.5 years is $4,721.27.
Step-by-step explanation:
Given
Principle P = 4500 (Let say in $)Interest rate r = 3.2% = 0.032Time period t = 1.5 yearsTo determine
Accrue Amount A = ?
Using the formula
[tex]A\:=\:Pe^{rt}[/tex]
substitute r = 0.032, P = 4500, and t = 1.5
[tex]A\:=\:4,500.00\left(2.71828\right)^{\left(0.032\right)\left(1.5\right)}[/tex]
A = $ 4721.27
Therefore, we conclude that the total amount accrued, principal plus interest, from compound interest on an original principal of $4,500.00 at a rate of 3.2% per year compounded continuously over 1.5 years is $4,721.27.
.
Find the slope of the line y=-5/7x-1
Answer:
-5/7
Step-by-step explanation:
With the equation y = mx + b, m is the slope of the line.
Since the equation is y = -5/7x - 1, m is -5/7
So, the slope of the line is -5/7
Answer:
m = -5/7
slope = -5/7
Step-by-step explanation:
Use y = mx + b to find the slope m.
Let X represent the full height of a certain species of tree. Assume that X has a normal distribution with a mean of 191.8 ft and a standard deviation of 4 ft. A tree of this type grows in my backyard, and it stands 182.2 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.
Answer:
0.0082 = 0.82% probability that the height of a randomly selected tree is as tall as mine or shorter.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Assume that X has a normal distribution with a mean of 191.8 ft and a standard deviation of 4 ft.
This means that [tex]\mu = 191.8, \sigma = 4[/tex]
A tree of this type grows in my backyard, and it stands 182.2 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.
This is the pvalue of Z when X = 182.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{182.2 - 191.8}{4}[/tex]
[tex]Z = -2.4[/tex]
[tex]Z = -2.4[/tex] has a pvalue of 0.0082
0.0082 = 0.82% probability that the height of a randomly selected tree is as tall as mine or shorter.
at school there are 8 students who only play violin, 10 students who only play guitar, 3 students who play both, and 12 students who don't play any instrument at all. if a student is randomly selected from this school, what is the probability that they play violin or guitar
Answer:
[tex]\frac{7}{11}[/tex]Step-by-step explanation:
[tex]\frac{21}{33}[/tex] simplified would be [tex]\frac{7}{11}[/tex]
The probability that they play violin or guitar is 7/11 .
What is Probability ?Probability is the likeliness of an event to occur.
It is given that
The number of students who only play violin is 8
The number of students who only play guitar is 10
The number of Students who play both is 3
The number of students who don't play either is 12
Total Students = 8+10+3+12 = 33
Total favorable outcomes (violin or guitar) = 8 + 10 +3
Probability = Total favorable outcomes / Total outcomes
Probability = 21 / 33
Probability = 7/11
Therefore the probability that they play violin or guitar is 7/11 .
To know more about Probability
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Josh's sink leaks 12 of a gallon of water in 14 of an hour. How many
gallons of water does Jacob's sink leak in 2 days?
write the equation of the line in fully simplified slope-intercept form. (6, 10) (4,5) (-2,-10)
Answer: the equation will be y = 5/2x -5
Step-by-step explanation:
First find the slope of the line by finding the change in the y coordinates and diving it by the change in the x coordinates.
(6,10)
(4,5)
5 - 10 = -5
4 - 6 = -2
Slope: 5/2
(4,5)
(-2,-10)
-10 - 5 = - 15
-2-4= - 6
-15/-6 = 5/2
Now we know the slope is 2, so use the formula y=mx + b to solve for the y intercept which is b by using one of the given points.
y = mx + b
5 = 5/2(4) + b
5 = 10 + b
b = -5
Find the exact value of tan e.
A. 15
3
B. 3/14
14
C. 35
5
D. 2/14
a=bc
Work out the value of c when
a=4 b=2
Answer:
c=2
Step-by-step explanation:
Divide the equation with b
a/b=c
4/2=c
c is equal to 2
Jules wants to put a fence around his backyard. What is the perimeter of his backyard?
PLEASE HELP QUICK!!! GIVING BRAINLEST OUT
Answer:
44
Step-by-step explanation:
Answer:
use the pythagorean theorem to solve for the sides and the degree for both triangles so your using cos sin or tan im not sure which one
Step-by-step explanation:
i really hope this helps the question is really vague im sorry if this wasnt a help
sin(θ) = Opposite / Hypotenuse
cos(θ) = Adjacent / Hypotenuse
tan(θ) = Opposite / Adjacent
Hopper Middle School wants to buy 40 t-shirts for the soccer team. They look at two stores to see which will give them the better deal. Store A charges $6.96 per shirt. Store B said the total cost for all 40 shirts would be $325, but they will give the school a 20% discount. Which store has the better deal?
How much will the shirts cost from store A?
How much will the shirts cost from store B?
How much does one shirt cost from store B?
Answer:
store A is 278.4 and store B is 260 and the cost for one shirt from store b is 8.125
Step-by-step explanation
6.96 x 40 gives you 278.4
325 - 20% gives you 260
325 divided by 40 gives you 8.125
then to check your answer you multiply 40 and 8.125 and it gives you 325
Diane sells candles online and ships them to her customers. Each candle weighs 1.5 pounds. When a customer orders more than one candle, Diane ships all of the customer's candles in one box. She weighs the box to determine shipping cost. This table shows the weight per shipment. Choose ALL amounts that could be added to this table. A) 4.5 B) 5 C) 6 D) 6.5 E) 7
Answer:4.5 and 6 should be on there
Step-by-step explanation: multiply 1.5 by the number of candles to get the answer
The average hotel price in Moscow is $216 per night with a standard deviation of $32. The average hotel price in Cancun is $161 per night with a standard deviation of $22. The average hotel price in Bangkok is $100 per night with a standard deviation of $17. A room at the Emerald Hotel in Moscow costs $200 per night, a room at the Ocean View Hotel in Cancun costs $183 per night, and a room at the Emperor Hotel in Bangkok costs $120 per night.
Required:
Which hotel is more expensive compared to other hotels in its city?
Answer:
The Emperor Hotel in Bangkok has the higher z-score, so it is more expensive compared to other hotels in its city.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
The most expensive hotel has the higher z-score. So
Emerald Hotel in Moscow:
Costs $200, which means that [tex]X = 200[/tex]
The average hotel price in Moscow is $216 per night with a standard deviation of $32, which means that [tex]\mu = 216, \sigma = 32[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{200 - 216}{32}[/tex]
[tex]Z = -0.5[/tex]
Ocean View Hotel in Cancun
Costs $183, which means that [tex]X = 183[/tex].
The average hotel price in Cancun is $161 per night with a standard deviation of $22, which means that [tex]\mu = 161, \sigma = 22[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{183 - 161}{22}[/tex]
[tex]Z = 1[/tex]
Emperor Hotel in Bangkok
Costs $120, which means that [tex]X = 120[/tex].
The average hotel price in Bangkok is $100 per night with a standard deviation of $17, which means that [tex]\mu = 100, \sigma = 17[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 100}{17}[/tex]
[tex]Z = 1.18[/tex]
The Emperor Hotel in Bangkok has the higher z-score, so it is more expensive compared to other hotels in its city.
Help? I cannot get my head around it.
Answer:
60cm³
Step-by-step explanation:
jenna works for the city transportation department. she made a table to show the number of people that can be transported on a different number of buses. complete the equation to show the relationship between the number of buses, x, and the number of people that can be transported, y.
Answer: y=52x
at this rate, how many people will be transported on 30 buses? answer: 1560 you have to multiply 52x30=1560
Step-by-step explanation:
i’m doin this i-ready and got it right
daniela uses 1/5 cups of choclate chip for every 1/7 batch of cookies he makes. How many cups of choclate chips does he use in 1 batch of cookies?
Answer:
1 2/5 cups
Step-by-step explanation:
1/5 ÷1/7
1/5×7
7/5
1 2/5 cups
2/6 + 1/3 simplified
Find the equation (in terms of x) of the line through the points ( − 1 , − 1 ) and( 4 , − 4 )
Answer:
[tex]y = -\frac{3}{5}x -\frac{8}{5}[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1) = (-1,-1)[/tex]
[tex](x_2,y_2) = (4,-4)[/tex]
Required
Determine the line equation
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-4 - (-1)}{4 - (-1)}[/tex]
[tex]m = \frac{-4 +1}{4 +1}[/tex]
[tex]m = \frac{-3}{5}[/tex]
[tex]m = -\frac{3}{5}[/tex]
The equation is then calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
This gives:
[tex]y - (-1) = -\frac{3}{5}(x - (-1))[/tex]
[tex]y + 1 = -\frac{3}{5}(x +1))[/tex]
Open bracket
[tex]y + 1 = -\frac{3}{5}x -\frac{3}{5}[/tex]
Make y the subject
[tex]y = -\frac{3}{5}x -\frac{3}{5}-1[/tex]
[tex]y = -\frac{3}{5}x +\frac{-3-5}{5}[/tex]
[tex]y = -\frac{3}{5}x +\frac{-8}{5}[/tex]
[tex]y = -\frac{3}{5}x -\frac{8}{5}[/tex]
2) In 2 ½ hours, Joaquin can bake 4 ¼ dozen cookies.
a. What is his unit rate in dozen cookies per hour?
Answer:
1.7
Step-by-step explanation:
4.25 : 2.5 = 1.7 per hour
answer me for brainlyest
its quite eazy tdh⊄≈∴∵ФωФ∵∴≈⊅
Answer: 1. The right side of the real object is 4 units long.
2. The top side of the scale drawing is 6 units long.
Step-by-step explanation:
2:1
Scale drawing: 6x8
Object: 3x4
Divide the length in the scale drawing by 2--- The right side of the real object is 4 units long.
8/2= 4
Multiply the top side in the real object by 2--- The top side of the scale drawing is 6 units long.
3x2=6
Which fraction has a terminating decimal?
- 11/19
- 4/7
- 1/3
- 3/150
==========================================================
Explanation:
With the use of a calculator, we see that,
11/19 = 0.57894736842106...., the decimals eventually repeat; but unfortunately my calculator ran out of room to show the repeating portion4/7 = 0.5714285714285714..., the block "571428" repeats forever1/3 = 0.333333.... the 3s go on forever3/150 = 0.02So 3/150 converts to the terminating decimal 0.02
The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.
----------------------
A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.
If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.
What is -11/4 plus -11/8
Answer:
-4.125
Step-by-step explanation:
4) Bethany bought s yards of satin fabric priced at $7.06 per yard, and c
yards of cotton fabric priced at $2.89 per yard. She wrote the expression
7.06s + 2.89c. If she bought 4 yards of satin fabric and 11 yards of cotton
fabric, how much did Bethany spend in all? * I will give brainlest
Answer:
$60.03
Step-by-step explanation:
7.06 x 4= 28.24
2.89 x 11 =31.79
28.24+31.79=60.03
On August 20, 1989, in Cologne, West Germany, Said Aouita of Morocco also established a world record when he ran the 3000. m run in 7 minutes, 29.45 seconds. What was his average speed (in m/s) for the race? Remember to include your data, equation, and work when solving problem
PLS HURRY I HAVE TO TURN THUS IN!!!!!
Answer:
Average speed of Aouita = 6.68 meter per second.
Step-by-step explanation:
To create a world record Aouita ran a distance = 3000 m
He took the time to cover this distance = 7 minutes 29.45 seconds
= (7×60) + 29.45 seconds
= 449.45 seconds
Since, formula for the average speed is given by,
Average speed = [tex]\frac{\text{Total distance covered}}{\text{Total time taken}}[/tex]
Therefor, average speed of Aouita = [tex]\frac{3000}{449.45}[/tex]
= 6.675
≈ 6.68 meter per second
Average speed of Aouita was 6.68 meter per second.
Answer:
6.67 m/s
Step-by-step explanation:
7 * 60 = 420
420 + 29.45 = 449.45
V = 3000. / 449.45= 6.67 m/s
Which arithmetic sequence has a common difference of -21?
{1,245; 1,224; 1,203; 1,182; …}
{32, 20, 8, -4, …}
{873, 894, 915, 936, …}
{1,563; 1,587; 1,611; 1,635; …}
WILL GIVE BRAINLIEST!!!!
Answer:
first one
just subtract 21 from each number
Answer:
C - {873, 894, 915, 936, …}
Step-by-step explanation:
Difference means subtraction. So, subtract -21 from the number to get your next value.
1245 - (-21) = 1266 So, A is not the answer
32 - (-21) = 53 So, B is not the answer.
873 - (-21) = 894 So, C is the answer.
1563 - (-21) = 1584 So, D is not the answer.
To double check, subtract -21 from the other numbers too.
873 - (-21) = 894
894 - (-21) = 915
915 - (-21) = 936
and so on...
This matches up with the list of numbers on option C so it it correct.
I hope this helps you Cheers!
Find the slope of the line passing through the points (5, -6) and (1, -1).
Answer: -5/4
Step-by-step explanation:
The equation for solving for slope is y2-y1/x2-x1
substitute
-1-(-6) / 1-5
5/-4
slope= -5/4
Help due soon plz helpp
Answer: 7) -12;
8) 0 или 1.
Step-by-step explanation:
7.
x ≤ - 12
x ∈ ( - ∞; - 12]
Наибольшее целое значение, при котором верно неравенство равно -12.
8.
-9,6*8 > - 9,627
Варианты возможных чисел: -9,618 и -9,608.
Значит вместо звездочки можно подставить цифры 0 или 1.
Factor this expression
15y - 30
Answer:
2
Step-by-step explanation:
15y-30. Factor by finding the larger common factor.
15*y-15*2
15(y-2)
You can't solve this unless it is written as an equation:
15(y-2)=0
%2815%2F15%29%28y-2%29=0%2F15
y-2=0
y-2%2B2=0%2B2
y=2
Happy Calculating!!!
An inspector working for a manufacturing company hasa 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifyinga good item as defective. The company has evidence that 0.9% of the items its line produce isnonconforming.(a) What is the probability that an item selected for inspection is classified as defective
Answer:
Step-by-step explanation:
From the given information:
Let A be the event where an item is identified as defective;
B₁ to be the event where an item is actually defective
B₂ to be the event that the item is good
So;
P(B₁) = 0.009
P(B₂) = 0.991
Probability that an item is classified as defective when it is actually defective is P(A|B₁) = 0.99
Probability that an item is classified as defective when it is actually good is P(A|B₂) = 0.005
∴
Probability of classifying a product as defective = P(A)
P(A) = P(A|B₁) × P(B₁) + P(A|B₂) × P(B₂)
P(A) = 0.99 × 0.009 + 0.005 × 0.991
P(A) = 0.0139
P(A) = 1.39%
Write the phrase as an expression.
3 times a number x
Answer:
It would have to be 3x or 3(x)
