Answer:
B. Multiply 6 by 3
Step-by-step explanation:
Do the opposite order of what Hannah did. The last step that she did was divide by 3, so you would multiply the result (6) with 3:
B. Multiply 6 by 3
Your step by step for getting the number Hannah started with:
First, multiply 6 with 3:
6 x 3 = 18
Next, subtract 4:
18 - 4 = 14
Next, divide by 2:
14/2 = 7
Hannah started with the number 7.
~
Answer: Hannah started with 7.
B. Multiply 6 by 3
Explanation:
Let the number be y
2 × y = 2y
(2y + 4)/3 = 6
2y + 4 = 6×3 = 18
2y + 4 = 18
2y = 18 - 4 = 14
y = 14/2 = 7
To solve the problem backward, the first step is to multiply 6 by 3.
Ava's bacteria population is modeled by an equation. Chase models his bacteria
population with a graph. Ava says that on day 14, she will have more bacteria than Chase
Is she right? Why or why not?
Answer:
P(Chase) > P(Ava)
700 > 587
Therefore, Ava's claim is wrong!
On day 14, Chase's bacteria population will be greater than Ava's bacteria population.
Step-by-step explanation:
Please refer to the attached image.
Ava's bacteria population is modeled by the following equation.
[tex]$ b(t) = 200(1+0.08)^t $[/tex]
Where t is time in days and b(t) is the population of the bacteria after t days.
The graph represents the population of Chase's bacteria.
Ava claims that on day 14, she will have more bacteria than Chase.
Let us compare the population of both bacteria.
Chase bacteria population when t = 14 days:
From the graph, the population is approximately 700 at t = 14 days
P(Chase) ≈ 700
Ava bacteria population when t = 14 days:
at t = 14 days
[tex]b(t) = 200(1+0.08)^t \\\\ b(14) = 200(1.08)^{14} \\\\ b(14) = 200 (2.93719)\\\\ b(14) = 587.44[/tex]
So, the population is approximately 587 at t = 14 days
P(Ava) ≈ 587
P(Chase) > P(Ava)
700 > 587
Therefore, Ava's claim is wrong!
On day 14, Chase's bacteria population will be greater than Ava's bacteria population.
Answer:
D
Step-by-step explanation:
Trust
PLEASE I NEED HELP!!! FIRST ANSWER IS BRANLIEST!!!
Apply the distributive property to create an equivalent expression. 6(5x-3)
Answer:
30x - 18
Step-by-step explanation:
6(5x - 3)
Apply the distributive property.
6(5x) + 6(-3)
30x + - 18
Answer:
30x - 18 is your final answer
When we carry out a chi-square goodness-of-fit test for a normal distribution, the null hypothesis states that the population:________
a. Does not have a normal distribution
b. Has a normal distribution
c. Has a chi-square distribution
d. Does not have a chi-square distribution
e. Has k-3 degrees of freedom
Answer:
Option B
Step-by-step explanation:
The null hypothesis for a chi-square goodness of fit test states that the data are consistent with a specified distribution.
While the alternative hypothesis states that the data are not consistent with a specified distribution.
In this case study, the test is for a nose distribution. Thus the null hypothesis would be that the population has a normal distribution.
find the value of the geometric series
1000 + 1000(1.03) + 1000(1.03)2 + . . . + 1000(1.03)9
Answer:
[tex]\boxed{\sf \ \ \ 11,464 \ \ \ }[/tex]
Step-by-step explanation:
hello
we need to compute the following
[tex]\sum\limits^9_{i=0} {1000(1.03)^i}=1000\dfrac{1.03^{10}-1}{1.03-1}=11463.879...[/tex]
hope this helps
There are (7^13)^3 x 7^0 strawberries in a field . What is the total number of strawberries in the field
Answer:
Step-by-step explanation:
[tex]7^{0}=1[/tex]
[tex](7^{13})^{3}*7^{0}=7^{13*3}*1\\\\=7^{39}[/tex]
Find the hypotenuse of a right triangle (in cm) if one leg measures 7 cm and the other leg measures 11 cm. Round to the nearest thousandth. ____________ cm
Using the Pythagorean theorem
Hypotenuse = sqrt( 11^2 + 7^2)
= sqrt( 121 + 39)
= sqrt( 160)
= 12.694
Two ships leave a port at the same time.
Ship A sails 12 knots on a bearing of 035°
Ship B sails 16 knots on a bearing of 270°
Calculate the distance between the ships after 2 hours
(1 knot = 1 nautical mile per hour)
Answer:
49.8 nautical miles
Step-by-step explanation:
Recall that speed = distance/time
Time = 2hours
Speed = 12knots and 16 knots respectively
D = speed×time
D1 = 12×2 = 24
D2 = 16×2 = 32
Using the 'cosine rule' we have:
a^2 = b^2+c^2-2bc cos Θ
Where a =?
b =24
c = 32
Θ = 125°
a² = 24² + 32² - 2(24)(32)cos125°
a^2 = 576+1024 - 1536cos125°
a² = 1600 - 1536(-0.57357)
a² = 1600+881.0134
a² = 2481.0134
Then, a² = 2481.013406
a =√2481.013406
Hence, a = 49.8 nautical miles
In this exercise we must use the knowledge about triangles to calculate the distance that a ship will travel, in this way we find that:
49.8 nautical miles
First, remember the formula for distance, which is:
[tex]Speed = distance/time[/tex]
And knowing that the data reported in the exercise are:
Time = 2hours Speed = 12 knots and 16 knots respectively
So putting the values informed in the distance formula, we have:
[tex]D = speed*time\\D_1 = 12*2 = 24\\D_2 = 16*2 = 32[/tex]
Using the 'cosine rule' we have:
[tex]a^2 = b^2+c^2-2bc cos \theta[/tex]
Find the a, will have:
[tex]b =24 \ \ \ c = 32 \ \ \ \theta = 125\\a^2 = 24^2 + 32^2 - 2(24)(32)cos125\\a^2 = 576+1024 - 1536cos125\\a^2 = 1600 - 1536(-0.57357)\\a^2 = 1600+881.0134\\a^2 = 2481.0134\\a=49.8[/tex]
See more about triangles at brainly.com/question/25813512
Help with one integral problem?
Answer: [tex]2\sqrt{1+tant}+C[/tex]
Step-by-step explanation:
To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.
[tex]\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } } \[/tex]
Let's first use our identities to rewrite the function. Since [tex]\frac{1}{cosx} =secx[/tex], we can use this identity.
[tex]\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,[/tex]
[tex]u=\sqrt{1+tant}[/tex]
[tex]du=\frac{sec^2t}{2\sqrt{1+tant} } dt[/tex]
Now that we have u and du, we can plug them back in.
[tex]\int\limits {2} \, du[/tex]
[tex]\int\limits{2} \, du=2u[/tex]
Since we know u, we can plug that in.
[tex]2\sqrt{1+tant}[/tex]
This may seem like the correct answer, but we forgot to add the constant.
[tex]2\sqrt{1+tant}+C[/tex]
There are 3 times as many novels as comic books in a bookstore.If there are 2480 books altogether, how many comic books are there in the bookstore.
Answer:
620 comic books
2480 / 4 is 620.
620 x 3 is 1860.
1860 + 620 is 2480.
Done!
Write the equation of a line that goes through point (0, -8) and has a slope of 0
Answer:
Step-by-step explanation:
y + 8 = 0(x - 0)
y + 8 = 0
y = -8
When would you need to arrange polynomials
Question
Shelly has 50 shortsin her closet. Shawnie her
Sister borrowed Some of
her shorts. Now shelly has
44 Shosts. How many
Shorts did Shawnie borrow.
A. 50-n = 44
B. 50 t n = 44
c. 50 n = 44
D.44 n =50
Answer:
A.50-n=44, 6 shorts borrowed
Step-by-step explanation:
If her sister borrowed n shorts, that means Shelly now has n less shorts. Since her amount of shorts is 50, then 50-n must equal how many shorts she has now, meaning 50-n=44. Solving the equation we get n=6. This means that her sister borrowed 6 shorts.
Answer:
A
Step-by-step explanation:
50 minus the shorts Shawnie borrowed (n) equal to 44
If Q(x) = x2 – X – 2, find Q(-3).
Answer:
10
Step-by-step explanation:
for this you need to sub the value of -3 for x
Q(-3)=(-3)^2-(-3)-2
=9+3-2
=10
Answer:
Q= x - X/x - 2/x
Step-by-step explanation:
hope this helps !
What is the value of 500$ invested at 4% interest compounded annually for 7 years
Answer:
657.96
Step-by-step explanation:
use formula A=P(1+r/n)^nt
A=500(1+.04/1)^1*7
A=500(1.04)^7
A=500(1.3159~)
A= 657.96~
Lisa drew three circles to form a figure. The areas of the circles were in the
ratio 1:4:16. She then shaded some parts of the figure as shown.
What fraction of the figure was shaded?
Answer:
Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]
Step-by-step explanation:
Ratio of the areas of the given circles are 1 : 4 : 16
Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]
= 1 : 2 : 4
If the radius of the smallest circle = x units
Then the radius of the middle circle = 2x units
and the radius of the largest circle = 4x units
Area of the smallest circle = πx²
Area of the middle circle = π(2x)² = 4πx²
Area of the largest circle = π(4x)²= 16πx²
Area of the region which is not shaded in the middle circle = πx²(4 - 1)
= 3πx²
Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded
= 16πx² - 3πx²
= 13πx²
Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]
= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]
= [tex]\frac{13}{16}[/tex]
16. Find m<2.
a. 86°
b. 43°
C. 94°
d. 133
What is 200 percent of (0.020(5/4) + 3 ((1/5) - (1/4)))
Answer:
0.1/4-3/20=1/40-6/40=-1/8 200% of this is -1/4
Step-by-step explanation:
This shows that 200 percent of (0.020(5/4) + 3 ((1/5) - (1/4))) is -2.75
Given the expression as shown in the question:
[tex]200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{1}{5}- \frac{1}{4} )][/tex]
Expand the expression in the square bracket using the distribution law as shown:
[tex]=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{4-5}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )+3(\frac{-1}{20} )]\\=200\% \ of \ [0.020(\frac{5}{4} )-(\frac{3}{20} )]\\=200\% \ of \ [0.020(1.25 )-\frac{3}{20}]\\=\frac{200}{100} \times [0.025-0.15]\\=2 \times [-0.125]\\=-2.75[/tex]
Hence the correct answer to the expression is -2.75.
Learn more here: https://brainly.com/question/19383460.
is this right one more i think lol
Answer:
Yup P is the right one having 62.26%
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
We can set it up as
P = 33/53
Q = 20/48
R = 54/90
S = 44/83
This is because we are calculating the percent of yellow birds in the total amt. of birds in a specified park.
Now we calculate =>
P = 33/53 = around 0.62
Q = 20/48 = around 0.416
R = 54/90 = 0.6
S = 44/83 = around 0.53
We find that Park P has the greatest percentage and -->
Thus, Park P is our answer and yes, you are correct.
I need help with this exercise please. What I need to know is the measure of one side of the square. Sorry for the language of the exercise
Answer:
[tex]\boxed{\sf \ \ x=6 \ \ }[/tex]
Step-by-step explanation:
Hello,
BMN and NPC are two similar triangles so
[tex]\dfrac{BM}{MN}=\dfrac{NP}{PC}\\\\ \dfrac{10-x}{x}=\dfrac{x}{15-x}\\\\<=>(15-x)(10-x)=x^2\\\\<=>150-25x+x^2=x^2\\\\<=>25x=150\\\\<=>x=6[/tex]
espero que esto ayude
what is the slope of the line given by the equation?
Answer:
the slope is 8
Step-by-step explanation:
The coefficient of x, "m" is the slope in the slope-intercept form:
y = mx + b
How do you write 89,700,000,000 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]89.7 \times {10}^{9} [/tex]
Or
[tex]8.97 \times {10}^{10} [/tex]
Hope this helps you
Answer:
8.97 * 10 ^10
Step-by-step explanation:
We want one nonzero digit to the left of the decimal
8.97
We moved the decimal 10 places to the left
The exponent is positive 10 since we moved 10 places to the left
8.97 * 10 ^10
8÷2 2/9 −2 11/15 I need help and this is a whole equation I need this ASAP
Answer: (1 and 22/45)
Step-by-step explanation:
I guess that we are working with mixed numbers here, and we have the equation:
(8÷2 2/9) − (2 11/15)
first we solve: 8÷2 = 4.
Now, we can write this as:
(4 + 2/9) - (2 + 11/15)
(4 - 2) + (2/9 - 11/15)
now, 9*5 = 45
15*3 = 45
then we can write the right side as: 2/9 - 11/5 = 10/45 - 33/45 = -23/45
2 - 23/45
But in mixed numbers we also need to work with a positive rational, then we have:
2 - 23/45 = 1 + 1 -23/45 = 1 + 45/45 - 23/45 = 1 + 22/45
then the solution is:
(1 and 22/45)
Is the answer correct in this question
Answer:
Yeah, you got the answer right.
Step-by-step explanation:
Una persona se dirige a un edificio y observa lo alto del mismo con un ángulo de elevación “x”, después de caminar 10m observa al mismo punto anterior con ángulo de elevación “y”, si la altura del edificio es de 30m. Calcule: "3Tgx.Ctgy + Tgx"
Answer:
3
Step-by-step explanation:
To begin with notice that
[tex]\displaymode{ \tan(x) = \frac{30}{10 + 30\cot(y)} }[/tex]
From that equation you get that
10 tan(x) + 30tan(x) cot(x) = 30
therefore
tan(x) + 3 tan(x) cot(x) = 3
what is -34/15 in decimal form
Answer:
2.26 repeating
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
hope this helpes
be sure to give brainliest
A square has a perimeter of 12x+52 units. Which expression represents the side leagth of the square in units
Answer:
12x/2 or 52/2
Step-by-step explanation:
Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.
write 26 as repeated multiplication
Answer:
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
2¹³
13 x 13
Step-by-step explanation:
We simply find numbers that can multiply to 26 and write out the multiplication to get our answer.
As a young professional in the future, it is good to start saving money to have a
security for the future and have something to use when emergency cases happen
related to the need of cash. The Philippine Average Family income last 2015 was
around P276,000 per year. Lets say every year you earn the same amount and save
P76,000 yearly in your frusted bank giving 4% compounded interest annually. How much
will the account worth in the future after 40 years?
a. Solve for the future value of the account:
FV=PMT
( \frac{(1 + i) ^{n} - 1 }{i} )(i(1+i)n−1)
Answer:
Step-by-step explanation:
We would apply the future value which is expressed as
FV = C × [{(1 + r)^n - 1}/r]
Where
C represents the yearly payments of the young professional.
FV represents the amount of money
in your account at the end of 40 years.
r represents the annual rate.
n represents number of years or period.
From the information given,
r = 4% = 4/100 = 0.04
C = $76000
n = 40 years
Therefore,
FV = 76000 × [{(1 + 0.04)^40 - 1}/0.04]
FV = 76000 × [{4.8 - 1}/0.04]
FV = 76000 × 95
FV = P7220000
Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor air pollution. The article "Domestic Fuels, Indoor Air Pollution, and Children's Health" (Annals of the N.Y. Academy of Sciences, 2008: 209-217) pm-tented information on various pulmonary characteristics in samples of children whose households in India used either biomass fuel or liquefied petroleum gas (LPG). For the 755 children in biomass households, the sample mean peak expiratory flow (a person's maximum speed of expiration) was 3.30 Us, and the sample standard deviation was 1.20. For the 750 children whose households used liquefied petroleum gas, the sample mean PEF was 4.25 and the sample standard deviation was 1.75.
a. Calculate a confidence interval at the 95% confidence level for the population mean PEF for children in biomass households and then do likewise for children in LPG households. What is the simultaneous confidence level for the two intervals?
b. Carry out a test of hypotheses at significance level .01 to decide whether true average PEF is lower for children in biomass households than it is for children in LPG households (the cited article included a P-value for this test).
c. FEV1, the forced expiratory volume in 1 second, is another measure of pulmonary function. The cited article reported that for the biomass households the sample mean FEY, was 2.3 L/s and the sample standard deviation was .5 L/s. If this information is used to compute a 95% CI for population mean FEV1, would the simultaneous confidence level for this interval and the first interval calculated in (a) be the same as the simultaneous confidence level deter-mined there? Explain.
Answer:
A) 95% confidence interval for the population mean PEF for children in biomass households = (3.214, 3.386)
95% confidence interval for the population mean PEF for children in LPG households
= (4.125, 4.375)
Simultaneous confidence interval for both = (3.214, 4.375)
B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.
C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.375)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Step-by-step explanation:
A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.
Finding the critical value from the z-tables,
Significance level for 95% confidence interval
= (100% - 95%)/2 = 2.5% = 0.025
z (0.025) = 1.960 (from the z-tables)
For the children in the biomass households
Sample mean = 3.30
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.20
N = sample size = 755
σₓ = (1.20/√755) = 0.0436724715 = 0.04367
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 3.30 ± (1.960 × 0.04367)
CI = 3.30 ± 0.085598
95% CI = (3.214402, 3.385598)
95% Confidence interval = (3.214, 3.386)
For the children in the LPG households
Sample mean = 4.25
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.75
N = sample size = 750
σₓ = (1.75/√750) = 0.063900965 = 0.063901
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 4.25 ± (1.960 × 0.063901)
CI = 4.25 ± 0.125246
95% CI = (4.12475404, 4.37524596)
95% Confidence interval = (4.125, 4.375)
Simultaneous confidence interval for both = (3.214, 4.375)
B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.
The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.
Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂
The null hypothesis is
H₀: μ ≥ 0 or μ₁ ≥ μ₂
The alternative hypothesis is
Hₐ: μ < 0 or μ₁ < μ₂
Test statistic for 2 sample mean data is given as
Test statistic = (μ₂ - μ₁)/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = 3.30
n₁ = 755
s₁ = 1.20
μ₂ = 4.25
n₂ = 750
s₂ = 1.75
σ = √[(1.20²/755) + (1.75²/750)] = 0.07740
z = (3.30 - 4.25) ÷ 0.07740 = -12.27
checking the tables for the p-value of this z-statistic
Significance level = 0.01
The hypothesis test uses a one-tailed condition because we're testing in only one direction.
p-value (for z = -12.27, at 0.01 significance level, with a one tailed condition) = < 0.000000001
The interpretation of p-values is that
When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.
Significance level = 0.01
p-value = 0.000000001
0.000000001 < 0.01
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.
C) For FEY for biomass households,
Sample mean = 2.3 L/s
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation = 0.5
N = sample size = 755
σₓ = (0.5/√755) = 0.0182
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 2.30 ± (1.960 × 0.0182)
CI = 2.30 ± 0.03567
95% CI = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.375)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Hope this Helps!!!
Bill and Ben each have three cards numbered 4,5,6 they each take one of their own cards then they add the two numbers on the cards what is the probability that their answer is an odd number. What is the probability that their answer is a number less than 11.
Answer:
P(odd) = 4/9P(<11) = 2/3Step-by-step explanation:
There are 9 possible outcomes for (Bill, Ben)'s cards:
(4, 4) total 8; (4, 5) total 9; (4, 6) total 10;
(5, 4) total 9; (5, 5) total 10; (5, 6) total 11;
(6, 4) total 10; (6, 5) total 11; (6, 6) total 12.
Of these 9 outcomes, 4 have an odd total; 6 are less than 11.
P(odd) = 4/9
P(sum < 11) = 2/3