Given:
The volume of water in a tank is modeled by the function
[tex]y=1.15x^3-0.1x^2+2[/tex]
where, x is the number of minutes after the faucet filling the tank is turned on.
To find:
The y-intercept and what does it represent in this context?
Solution:
We have,
[tex]y=1.15x^3-0.1x^2+2[/tex]
Substituting x=0, we get
[tex]y=1.15(0)^3-0.1(0)^2+2[/tex]
[tex]y=0-0+2[/tex]
[tex]y=2[/tex]
Therefore, the y-intercept is 2 and it represents the volume of water in a tank before the faucet filling the tank is turned on.
Answer:
The volume of water in a tank before the faucet filling the tank is turned on.
Step-by-step explanation:
#12 Eva took out a 5-year loan to buy a car at a 2% simple interest rate. If she has to pay $1,200 in interest, how much principal did she borrow? *
Answer:
$12,000
Step-by-step explanation:
2% for 5 years is 10% in total. if after the 5 years she gotta pay 1200, this mean 0.1p=1200
multiply 10 on both sides to find p, or principal.
p=12000
Answer:
$12,000
Step-by-step explanation:
P = 1200 / ( 0.02 × 5 ) = 12000
P = $ 12,000.00
Find the measure of each acute angle.
(19x - 1)
(13x - 5)
(193' - 1) =
and (132 – 5)° =
Answer:
(19x - 1)° = 56°
(13x - 5)° = 34°
Step-by-step explanation:
Property of the interior angles of a triangle:
Sum of interior angles of a triangle is 180°.
Therefore, sum of angles of the given right triangle will be,
(19x - 1)° + (13x - 5)° + 90° = 180°
32x - 6 + 90 = 180
32x = 96
x = 3
(19x - 1)° = 19×3 - 1 = 56°
(13x - 5)° = 13×3 - 5 = 34°
Jackie runs and dances for 75 minutes every day.
She dances 25 minutes more than she runs.
Part A: Write a pair of linear equations to show the relationship between the
number of minutes Jackie runs (x) and the number of minutes she dances (y)
every day.
Part B: How much time does Jackie spend running every day? Show your work.
Part C: Is it possible for Jackie to have spent 45 minutes dancing every day?
Explain your reasoning.
Answer: A. x + y = 75 B. She spends 25 minutes running and 50 minutes dancing every day. C. Yes it is.
Step-by-step explanation: B. She spends 25 minutes running and 50 minutes dancing every day, because if she dances for 25 more minutes then she runs then we can minus 25 from 75 which we get 50. Then we take the 50 a divide it by 2 because of the two categories dancing and running. So we know she spends 25 minutes running then 25 minutes dancing but we need to add the 25 minutes to dancing. So she spends 25 minutes running and 50 dancing. C. Yes it is because she already dances for 50 minutes a day so all she needs to do is workout for 10 minutes less so 65 minutes one day.
A system of linear equation consists of multiple linear equations
The system of linear equations is: [tex]\mathbf{x + y = 75}[/tex] and [tex]\mathbf{y = 25 + x}[/tex]She spends 25 minutes runningIt is possible to dance 45 minutes every day(a) A pair of linear equations
She dances and runs for 75 minutes.
So:
[tex]\mathbf{x + y = 75}[/tex]
She dances 25 minutes more than she runs.
So:
[tex]\mathbf{y = 25 + x}[/tex]
So, the system of linear equations is: [tex]\mathbf{x + y = 75}[/tex] and [tex]\mathbf{y = 25 + x}[/tex]
(b) The time she spends running every day
Substitute 25 + x for y in [tex]\mathbf{x + y = 75}[/tex]
[tex]\mathbf{x + 25 + x = 75}[/tex]
Subtract 25 from both sides
[tex]\mathbf{2x = 50}[/tex]
Divide both sides by 2
[tex]\mathbf{x = 25}[/tex]
Hence, she spends 25 minutes running
(c) Is it possible to dance 45 minutes each day
We have:
[tex]\mathbf{y = 25 + x}[/tex]
So:
[tex]\mathbf{y = 25 + 45}[/tex]
[tex]\mathbf{y = 70}[/tex]
This means that, she has to spend less minute running and dancing.
Read more about system of equations at:
https://brainly.com/question/12895249
Sophia can spend at most $50 on clothes. Which inequality represents this situation?
Answer:
x ≤ 50
I hope this was helpfull :)
5. List the vertices and find the eccentricity of the ellipse: (x + 1)2 + (y – 2)2 = 1
36 100
Answer:
x+y= 136099
&'&**!;;#$*$*$$-%-%=-$*$&2=28%%"
LCM of a2+b2 and a4-b4
Answer:
The LCM is:
[tex](a^2+b^2)(a+b)(a-b)[/tex]
Step-by-step explanation:
Given polynomials are:
[tex]a^2+b^2\\a^4 - b^4[/tex]
We can use factorization to find the LCM of the given polynomials.
Taking the second polynomial, using the identity
[tex]a^2 - b^2 = (a+b)(a-b)[/tex]
Applying on 2nd polynomial
[tex](a^2)^2-(b^2)^2\\=(a^2+b^2)(a^2-b^2)\\=(a^2+b^2)(a+b)(a-b)[/tex]
We can see that [tex]a^2+b^2[/tex] is common in both polynomials, it will be counted only one time. The LCM of given polynomials is:
[tex](a^2+b^2)(a+b)(a-b)[/tex]
if the side ratio is 9:12, then the volume ratio is
In one month Kimberly earned $500 at her part-time job, and $50 was withheld for federal income tax. Suppose she earns $750 next month. How much will be withheld for federal income
Answer:
It will be withheld $75 for federal income.
Step-by-step explanation:
Proportions
Assuming the federal income tax is proportional to the earnings, we can establish the following relationship between the income tax (T) and the earnings (E):
T = k.E
Kimberly earned E=$500 and paid T=$50 for federal income tax, With this information, we can calculate the value of k:
50 = k ( 500)
k = 50 / 500
k = 0.1
The model is now:
T = 0.1*E
If Kimberl earns $750 next month, the tax will be:
T = 0.1*($750)
T = $75
It will be withheld $75 for federal income.
I WILL MARK BRAINIEST
I got one correct there should be about one more that’s also right
So essentially an adjacent angle is when two angles have a common side and a common vertex.
So knowing that we can determine from the picture all the adjacent angles:
D) <2 and <3 are adjacent angles
E) <1 and <3 are adjacent angles
F) <1 and <5 are adjacent angles
I hope this helps.
when adding two rational numbers tell what the sign of the sum will be if one rational number is positive and one is negative
Answer:
True
When you add two negative numbers the sum is always negative ex.
When you add two numbers with different signs get the difference and get the sign by the larger absolute value ex.
Step-by-step explanation:
100 L 99 mL + 2,999 mL = __________________ mL
Evaluate the expression when t is 4.
Answer:
t=4
Step-by-step explanation:
there nothing more to do
Answer:
its 4 i think
Step-by-step explanation:
|x| = 4 This means: What value can we substitute for x to get an answer of 4?
**You might automatically say: x = 4 because |4| = 4
Yes, you are correct! However, this is not the only answer. You will have two answers for this equation because:
Isn't |-4| = 4 ?
So, this answer is x = 4 or -4.
please help me asap
Answer:
7/24 i think
Step-by-step explanation:
Answer:
5/12
Step-by-step explanation:
10/24 is equivalent to 5/12
how many groups of 2/3 go into 3/5
Answer:
2!
Step-by-step explanation:
(50 POINTS FOR THE FIRST ANSWER)
At the grocery store, Savvanah notices that it costs $2.48 for 40 ounces of jelly. What is the unit price?
Answer: 16.13
Step-by-step explanation: 40 divided by $2.48
which integer is greater.
l-5l or l3l
Answer:
|-5|
Step-by-step explanation:
When you see the absolute value signs and a number in between, that number is always going to be the positive version of that number (if the number is already positive, it stays positive)So, |-5| = 5, and 5 is greater than 3, therefore |-5| is greater than |3|I hope this helps!
Paul get 5$ week for doing his chores he is saving his money to buy a skateboard that cost 85$ he has already saved 5$
Answer:
16 weeks
Step-by-step explanation:
85 divided by 5 is 17. Take away one week for the $5 he already has. So you get 16 weeks.
Hope this helps you!
subtract the difference of d and c from 2
A number line going from negative 3 to 0 in increments of 1. There are 3 equal spaces between each number. Point A is 1 mark to the left of 0. Point B is 2 marks to the left of 0. Point C is 1 mark to the left of negative 1. Point D is 2 marks to the left of negative 2. Lukas plotted these points on the number line. Point A: −12 3 Point B: −2 3 Point C: −11 3 Point D: −22 3 Which point did he plot incorrectly? Point
HELP ME PLSSS
Answer:
Point A
Step-by-step explanation:
Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it uses different media to reach potential buyers. The mean annual family income for 15 people making inquiries at the first development is $150,000, with a standard deviation of $40,000. A corresponding sample of 25 people at the second development had a mean of $180,000, with a standard deviation of $30,000. Assume the population standard deviations are the same.
1. State the decision rule for 0.05 significance level: H0: μ1 = μ2; H1:μ1 ≠ μ2.2. Compute the value of the test statistic
Answer:
The decision rule is
Reject the null hypothesis
The test statistics is [tex]t = -2.699[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 15[/tex]
The mean at first deployment is [tex]\= x _1 = \$ 150 000[/tex]
The standard deviation is [tex]s_1 = \$ 40000[/tex]
The second sample size is [tex]n_2 = 25[/tex]
The mean at second deployment is [tex]\= x_2 = \$ 180000[/tex]
The standard deviation is [tex]s_2 = \$ 30 000[/tex]
The null hypothesis is [tex]H_o : \mu_1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 \ne \mu_2[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df =n_1 + n_2 -2[/tex]
=> [tex]df =40 -2[/tex]
=> [tex]df =38[/tex]
Generally the pooled variance is mathematically represented as
[tex]s_p^2 = \frac{x(n_1 -1) s_1^2 + (n_2 - 1)s_2^2}{df}[/tex]
=> [tex]s_p^2 = \frac{(15 -1) 40000^2 + (25 - 1)30000^2}{38}[/tex]
=> [tex]s_p^2 = 1.1579 * 10^{9}[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x_1 - \= x_2 }{\sqrt{s_p [\frac{1}{n_1} + \frac{1}{n_2} ]} }[/tex]
=> [tex]t = \frac{ 150000 - 180000 }{\sqrt{1.11579 *10^{9} [\frac{1}{15} + \frac{1}{25} ]} }[/tex]
=> [tex]t = -2.699[/tex]
Generally from the t distribution table the probability corresponding to the t statistics value to the left is
[tex]t_{-2.699 , 38} = 0.00516046[/tex]
Generally the p -value is mathematically represented as
[tex]p-value = 2* t_{-2.699, 38}[/tex]
=> [tex]p-value = 2* 0.00516046[/tex]
=> [tex]p-value = 0.01032[/tex]
From the obtained value we see that the [tex]p-value < \alpha[/tex] hence
The decision rule is
Reject the null hypothesis
What is the probability that the average of four babies' weights will be within 0.6 pounds of the mean; will be between 7.4 and 8.6 pounds
Answer:
.682
Step-by-step explanation:
Name 2 alternate exterior angles
Answer: Alternate exterior angles are formed by a transversal intersecting two parallel lines . They are located "outside" the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate exterior angles.
Step-by-step explanation:
Big Ben is a famous clock tower in London. The circumstance around the clock is 72.22. How long is the hour on the clock if it is the radius of the circle
The hour hand is 9 feet (2.7 m) long and the minute hand is 14 feet (4.3 m) long.
y > -x +2
y < 3x - 2
Answer:
make a better answer pls
Step-by-step explanation:
8.Convert the line into slope intercept form: 3x + 5y =-15
Answer:
Y= -3/5x - 3
Step-by-step explanation:
3x+5y=-15
-3x. -3x
5y=-3x-15 then you would divide 5 from all the numbers to get : y=-3/5x-3.
Please help me I’m giving brainliest and I need help
Answer:
c is the answer
Step-by-step explanation:
Answer:
A NUMBER
Step-by-step explanation:
Veronica bought 20 bags of candy for a school dance. The first 5 bags cost $1.79 each. The rest of the bags cost $1.19 each. How much did Veronica spend on candy?
Answer:
$26.80
Step-by-step explanation:
multiply 1.79 by 5 and you get 8.95
multiply 1.19 by 15 now because there are 15 uncounted bags left and you get 17.85
add together and you get 26.8. she spent 26.8 dollars on candy
Which of the following describes how to calculate net pay?
A)Subtract the total deductions from the net pay.
B)Add the total deductions to the gross pay.
C)Subtract the total deductions from the gross pay.
D) Subtract the total deductions from the take-home pay.
Answer: C
Step-by-step explanation: The answer is C because it is.
A recipe for banana bread requires 3 cups of bananas for every 1 1/2 cups of sugar used. At this rate, how many cups of sugar should be used if 8 cups of bananas are used?
Answer:
12
Step-by-step explanation:
3=1 1/2
3/8 = 1.5/x
So you cross multiply
3x + (8 x 1.5)
So 12 would be your answer.
8 xy + 1 =
PLEASE I CAN’T DO MATH
Answer:
send photo of question
