Answer:
Step-by-step explanation:
8=8a-4(a+8) => 8=8a-4a-32 =>4a=40 => a=10.
If you meant 8=(8a-4)(a+8), then it is 8a^2+60a-32=8 => 8a^2+60a-40=0.
Use the quadratic formula, to get your answer.
Use the given qualitative data to construct the relative frequency distribution. The 2545 people aboard a ship that sank include 406 male survivors, 1651 males who died, 362 female survivors, and 126 females who died.Complete the relative frequency distribution below. Relative Frequency Category Male survivors % Males who died % Female survivors % Females who died % (Round to one decimal place as needed.)
Answer:
The data that we have is:
total people: 2545
male survivors: 406
male who died: 1651
total males: 406 + 1651 = 2057
female survivors: 362
female who died: 126
total females: 362 + 126 = 488.
We want to know:
for the percentages, we must calculate the quotient between the total numbers of the set, and the number in the particular category we are looking for.
% male survivors = (number of male survivors/total number of males)*100%.
= (406/2057)*100% = 19.73%
% male who died = (1651/2057)*100% = 80.2%
% female survivors = (362/488)*100% = 74.18%
% female who died = (126/488)*100% = 25.82%
A quantity with an initial value of 830 grows exponentially at a rate such that the quantity doubles every 2 weeks. What is the value of the quantity after 21 day, to the nearest hundredth?
Answer:
The value of the quantity after 21 days is 2,347.59.
Step-by-step explanation:
The exponential growth function is
[tex]A=A_0(1+r)^t[/tex]
A= The number of quantity after t days
[tex]A_0[/tex]= initial number of quantity
r= rate of growth
t= time in days.
A quantity with an initial value of 830 grows at a rate such that the quantity doubles in 2 weeks = 14 days.
Now A= (2×830)= 1660
[tex]A_0[/tex] = 830
t = 14 days
r=?
Now plug all value in exponential growth function
[tex]1660=830(1+r)^{14}[/tex]
[tex]\Rightarrow \frac{1660}{830}= (1+r)^{14}[/tex]
[tex]\Rightarrow 2= (1+r)^{14}[/tex]
[tex]\Rightarrow (1+r) ^{14}=2[/tex]
[tex]\Rightarrow (1+r)=\sqrt[14]{2}[/tex]
[tex]\Rightarrow r=\sqrt[14]{2}-1[/tex]
Now, to find the quantity after 21 days, we plug [tex]A_0[/tex] = 830, t= 21 days in exponential function
[tex]A=830( 1+\sqrt[14]{2}-1)^{21}[/tex]
[tex]\Rightarrow A=830(\sqrt[14]2)^{21}[/tex]
[tex]\Rightarrow A=830(2)^\frac{21}{14}[/tex]
[tex]\Rightarrow A=830(2)^\frac{3}{2}[/tex]
[tex]\Rightarrow A=2,347.59[/tex]
The value of the quantity after 21 days is 2,347.59.
Final answer:
To calculate the value of a quantity after 21 days when it doubles every 2 weeks with an initial value of 830, use the exponential growth formula [tex]N(t) = N_0 \times 2^{t/T}[/tex]. Plugging in the values, the quantity after 21 days is 2347.14, to the nearest hundredth.
Explanation:
Calculating Exponential Growth
To find the value of a quantity after 21 days when it has an initial value of 830 and doubles every 2 weeks, we can use the formula for exponential growth:
N(t) = N_0 × 2^(t/T)
Where:
N(t) is the future value after time t,
N_0 is the initial value (830),
t is the time period in days (21 days),
T is the doubling period in days (2 weeks = 14 days).
First, we convert 21 days into weeks: 21 days / 7 days per week = 3 weeks.
Next, let's find the value after 3 weeks. We plug our values into the exponential growth formula:
[tex]N(3) = 830 \times 2^{3/2}[/tex]
To calculate 3/2 weeks in terms of doubling periods:
3 weeks / 2 weeks per doubling period = 1.5 doubling periods.
Now we can calculate the quantity:
N(21) = [tex]830 \times 2^{1.5}[/tex] = 830 × 2.828 = 2347.14
To the nearest hundredth, the value of the quantity after 21 days is 2347.14.
Suppose you wanted to change the state’s constitution to require public financing for all campaigns. If you were relying on professional signature gatherers (who charge at least $1.50 per signature), what is the minimum amount of money you could reasonably expect to spend in order to qualify this amendment for the ballot?
Answer: $1.5 millions
Step-by-step explanation:
Since the population is in millions and a million is like a fraction many millions.
Therefore, the minimum amount of money you could reasonably expect to spend in order to qualify for this amendment for the ballot is $1.5 millions
BRAINLIEST if right!
What is the equation of the line with a y-intercept of −10 and a slope of 3?
Answer:
y = 3x-10
Step-by-step explanation:
The slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
The slope is 3 and the y intercept is -10
y = 3x-10
The points A, B, C, and D are on a number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D ? (1) The distance between C and A is the same as the distance between C and B. (2) A is to the left of D on the number line.
Answer:
insufficient information
Step-by-step explanation:
If the order of the points is unknown, the distances AB and CD imply no particular distance for BD.
Scott is on his school's academic team. On average, it takes Scott 4 minutes, with a standard deviation of 0.25 minutes, to solve a problem at an academic bowl. How often will it take Scott more than 4.25 minutes to solve a problem at an academic bowl?
Answer:
15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 4 minutes
Standard Deviation, σ = 0.25 minutes
We standardize the given data.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(more than 4.25 minutes to solve a problem)
[tex]P( x > 4.25) = P( z > \displaystyle\frac{4.25 - 4}{0.25}) = P(z > 1)[/tex]
[tex]= 1 - P(z \leq 1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 4.25) = 1 - 0.8413 = 0.1587 = 15.87\%[/tex]
Thus,15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.
The correct answer is approximately 15.87%.
To solve this problem, we can use the properties of the normal distribution. Given that the average time Scott takes to solve a problem is 4 minutes with a standard deviation of 0.25 minutes, we can calculate the z-score for the time of 4.25 minutes to determine how many standard deviations away from the mean this time is.
The z-score formula is:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where[tex]\( X \)[/tex]is the value in question[tex](4.25 minutes), \( \mu \)[/tex] is the mean (4 minutes), and [tex]\( \sigma \)[/tex] is the standard deviation (0.25 minutes).
Plugging in the values, we get:
[tex]\[ z = \frac{4.25 - 4}{0.25} = \frac{0.25}{0.25} = 1 \][/tex]
Now, we look up the z-score of 1 in the standard normal distribution table or use a calculator to find the corresponding area to the left of this z-score. This area represents the probability that Scott will take 4.25 minutes or less to solve a problem.
The area to the left of a z-score of 1 is approximately 0.8413, or 84.13%. This is the cumulative probability up to 4.25 minutes.
To find the probability that it will take Scott more than 4.25 minutes, we subtract this value from 100% (since the total area under the normal distribution curve is 1, or 100%):
[tex]\[ P(X > 4.25) = 1 - 0.8413 = 0.1587 \][/tex]
Converting this to a percentage, we get:
[tex]\[ 0.1587 \times 100\% \approx 15.87\% \][/tex]
Therefore, it will take Scott more than 4.25 minutes to solve a problem approximately 15.87% of the time.
1. A dog is tied to a wooden stake in a backyard. His leash is 3 meters long and he runs around in circles pulling the leash as far as it can go. How much area does the dog have to run around in?
Answer:???
Step-by-step explanation:
Answer:
As the stake is 3 m long we will take it as the radius of the circle and find the area as per:
22/7*3*3=22/7*9=198/7m^2
198/7 metre square.
In 2002, a reproductive clinic reported 41 live births to 152 women under the age of 38, but only 4 live births for 86 clients aged 38 and older. Is there evidence of a difference in the effectiveness of the clinic's methods for older women? Complete parts a through c. Use alphaequals0.05.
Answer:
Difference is (0.181671, 0.263529)
We are more than 95% confident that the true percentage of life births for women under 38 years of age is between 18.17% and 26.35% higher than the true population of live births of women aged 38 or older.
Step-by-step explanation:
We are given;
x1 = 41
n1 = 152
x2 = 4
n2 = 86
Thus,
Sample proportion 1; p'1 = 41/152 = 0.2697
Sample proportion 2; p'2 = 4/85 = 0.0471
For confidence level, 1 - α = 1 - 0.05 = 0.95, using the z-table i attached under the column of z_α/2,we have
z_α/2 = 0.96
The end points of the confidence intervals for p1 - p2 are;
(p'1 - p'2) - z_α/2√[(p'1(1 - p'1)/n1) + (p'2(1 - p'2)/n2)
And
(p'1 - p'2) + z_α/2√[(p'1(1 - p'1)/n1) + (p'2(1 - p'2)/n2)
The first one is calculated as;
(0.2697 - 0.0471) - 0.96√[(0.2697(1 - 0.2697)/152) + (0.0471(1 - 0.0471)/86)
.= 0.2226 - 0.040929 = 0.181671
The second one is calculated as;
(0.2697 - 0.0471) + 0.96√[(0.2697(1 - 0.2697)/152) + (0.0471(1 - 0.0471)/86)
.= 0.2226 + 0.040929 = 0.263529
Thus, we are more than 95% confident that the true percentage of life births for women under 38 years of age is between 18.17% and 26.35% higher than the true population of live births of women aged 38 or older.
A bread recipe calls for 2 cups of wheat flour and 3 cups of white flour. How much flour does the recipe call for
altogether?
Answer:
5
Step-by-step explanation:
3+2=5
Answer:
5 cups
Step-by-step explanation:
2 cups plus 3 cups
Monique is an interior design student. As part of her internship, she is redesigning a small kitchen for a client. She would like to expand the kitchen and add a dining area. Before creating sketches for the client, she imagines the new layout in her mind, most likely using __________.A. tacit knowledge.
B. a proposition.
C. the method of loci.
D. a depictive representation.
Sophia factored 81y^6 as (9y^3)(9y^2) Ahmed factored 81y^6 as (3y^6)(27y) Which of them factored 81y^6 correctly?
To find if either of them are correct just multiply each of them:
(9y^3)(9y^2)= (9)(9)(y^3)(y^2)
=81y^5
Sophia is incorrect.
(3y^6)(27y)=(3)(27)(y^6)(y)
=81y^7
Ahmed isn't correct either!
Both the persons Sophia and Ahmed do not factor in the expression correctly.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that, Sophia factored 81y⁶ as (9y³)(9y²) and Ahmed factored 81y⁶ as (3y⁶)(27y).
We have to find the correct factored form,
= (9y³)(9y²)
The expression is to be arranged in order to find the understand the property of exponent as,
=(9×9)(y³.y²)
=(81)(y³⁺²)
=81y⁵
Thus, both the persons Sophia nor Ahmed do not factor in the expression correctly.
Learn more about the integer exponent here:
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6. 4ab + 13b
Can someone help me find the andwers
Answer:
You cannot simplify this. One has ab, and one has only b. So that is the most simplified it can get.
Answer: There are no like terms.
Step-by-step explanation:
need help on this math problem can someone help ax +by=cz
Answer:
a = (cx - by)/x
Step-by-step explanation:
ax + by = cz
ax = cz - by
a = (cx - by)/x
Can I get brainliest
Using the Zero Product Property, solve for the x-values given (x-2)(x+3)=0.
Answer:
x = 2 or -3
Step-by-step explanation:
The product will be zero when one of the factors is zero.
First factor:
x - 2 = 0
x = 2 . . . . . add 2 to both sides of the equation
Second factor:
x + 3 = 0
x = -3 . . . . .subtract 3 from both sides of the equation
The values of x that solve this equation are x = 2 and x = -3.
please hellllllllppppppppppppppppppppppppppp
Answer:
[tex]21^{10}[/tex]
Step-by-step explanation:
First, multiply the 3 and the 7 together, and then "multiply" the exponents -8 and 3. (However, when "multiplying exponents, you're really just adding them together: -8 + 5)
([tex]21^{-5}[/tex])^2
Then, multiply the -5 and -2 together, giving you:
[tex]21^{10}[/tex]
11: Jack is 10 years old.
Kylie is 17 years old.
Vanessa is 23 years old.
Kylie and Vanessa share £16 in the ratio of their ages.
Kylie gives 20% of her share to Jack.
Vanessa gives a quarter of her share to Jack.
How much money does Jack receive?
Answer:
£3.66
Step-by-step explanation:
17+23=40
40=16 what about 17
16×17=272÷40=£6.8
16-6.8=£9.2
20% of £6.8 = £1.36
1/4 of £9.2 = £2.3
1.36+2.3=£3.66
HELP MEE! 100 POINTS AND BRAINLY! GIVE ME THE STEPS, AND A GOOD ANSWER OR I WILL DELETE YOUR ANSWER AND GET MY POINTS BACK!
Example: solve √(2x−5) − √(x−1) = 1
Answer:
Solve the equation for
x by finding a , b , and c of the quadratic then applying the quadratic formula.
Exact Form:
x= 7 + 2 √ 5
Decimal Form:
x = 11.47213595 …
Step-by-step explanation:
Hi there! Hopefully this helps!
Answer: 11.47(to 2 decimal places).
Isolate one of the square roots: √(2x−5) = 1 + √(x−1)
Square both sides: 2x−5 = (1 + √(x−1))^2
We have removed one square root.
Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)
Simplify: 2x−5 = 2√(x−1) + x
Subtract x from both sides: x−5 = 2√(x−1)
Now do the "square root" thing again:
Isolate the square root: √(x−1) = (x−5)/2
Square both sides: x−1 = ((x−5)/2)^2
We have now successfully removed both square roots.
Let's continue with the solution.
Expand right hand side: x−1 = (x^2 − 10x + 25)/4
Since it is a Quadratic Equation! let's put it in standard form.
Multiply by 4 to remove division: 4x−4 = x^2 − 10x + 25
Bring all to left: 4x − 4 − x^2 + 10x − 25 = 0
Combine like terms: −x^2 + 14x − 29 = 0
Swap all signs: x^2 − 14x + 29 = 0
Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:
2.53 and 11.47 (to 2 decimal places)
2.53: √(2×2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1. So it is not the solution.
11.47: √(2×11.47−5) − √(11.47−1) ≈ 1 Yes that one works.
What is a tessalation
Answer:
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
Step-by-step explanation:
A principal gathered data about the distance, in miles, that his teachers and bus drivers live from school. The box plots below show these data.
Answer:
We choose C
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo
Basically, interquartile range represents the width or "dispersion" of the set. [1] The interquartile range is determined by the difference between the top quartile (25% highest) and lower quartile (25% lowest) point of the data set.
From the picture, we can find that:
The interquartile range of the bus drivers is: 20 -10 = 10 The interquartile range of the teachers is: 30 -15 = 15So the interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.
We choose C
Answer:
Step-by-step explanation:
Please help me with this
Step-by-step explanation:
Putting values of c and r
4 + 4(10) - 3(10 - 3)
4 + 40 - 3(7)
44 - 21
23
You went to the mall with $52.50. You bought three shirts that each cost x
dollars. Which expression represents the amount of money, in dollars,
that you had left after you bought the shirts? *
Carl bought 7 packs of pencils. He now has 42 pencils. He writes that 42 is 6 times as many as 7. Which comparison sentence below can he use to show the comparison?
Answer:
Option b
Step-by-step explanation:
Complete question is
Carl bought 7 packs of pencils. He now has 42 pencils. He writes that 42 is 6 times as many as 7. Which comparison sentence below can he use to
show the comparison?
A. 7 more than 6 is 42.
B. 7 is 6 times as many as 42.
C. 42 is 7 times as many as 6.
D. 6 is 7 times as many as 42
Solution -
It is given that Carl has 42 pencils.
It is not sure in which pack - the one with 6 pencils or the one with 7 pencils.
But when Carl wrote that "42 is 6 times as many as 7". By this he means that the present number of pencils i.e 42 is equal to 6 times the number of pencils in the pack of 7
Then, it becomes clear that Carl has 6 times the number of pencils in the pack of 7 pencils
Option B is correct
proving the converse of the parallelogram side theorem
Answer:
* LOOK AT THE PICTURE's*
I hope this helps and is the right one
The converse of the parallelogram side theorem states, If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
To prove this statement, we will assume that the opposite sides of a quadrilateral are congruent and demonstrate that it must be a parallelogram.
If both the opposite sides are parallel then we can easily prove that a parallelogram
Given: Quadrilateral PQRS, where PQ is congruent to RS and PR is congruent to QS.
To prove: PQRS is a parallelogram.
Proof:
Since PQ is congruent to RS (given), the segment PQ is parallel to the segment RS by the converse of the corresponding sides of congruent triangles are congruent (CPCTC). Since PR is congruent to QS (given), the segment PR is parallel to the segment QS by CPCTC.
Now we have both pairs of opposite sides of PQRS parallel, which satisfies the definition of a parallelogram.
Therefore, by proving that both pairs of opposite sides are PQRS parallel, we have shown that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
This completes the proof of the converse of the parallelogram side theorem.
Learn more about parallelograms here:
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Convert the angle 0 = 230° to radians.
Answer:
230° is equal to [tex]\displaystyle \frac{23 \pi}{18}[/tex] radians.
General Formulas and Concepts:
Trigonometry
Degrees to Radians Conversion: [tex]\displaystyle \frac{n\pi}{180}[/tex]
n is the degreesStep-by-step explanation:
Step 1: Define
Identify variables.
n = 230°
Step 2: Find Radians
Substitute in variable [Degrees of Radians Conversion]: [tex]\displaystyle \frac{230 \pi}{180}[/tex]Simplify: [tex]\displaystyle \frac{23 \pi}{18}[/tex]∴ 230° is equal to [tex]\displaystyle \frac{23 \pi}{18}[/tex] radians.
---
Topic: Pre-Calculus
Unit: Trigonometry
There are two peice pf gold and silver alloy. The ratio between the gold and silver in the first piece is 2:3, in the second peice 3:7. If we want to have 8 gram of gold and silver alloy with gold-silver ratio 5:11 how much of each peice of alloy is needed.
Answer:
1 grams of one of the alloy; and 7 grams of the other corresponding alloy.Step-by-step explanation:
The ratio between the gold and silver in the first piece = 2:3
The ratio between the gold and silver in the second piece =3:7
The ratio in the mixture = 5:11
We want to have 8 gram of the new mixture.
Let the gram of alloy taken from the first piece=x
Therefore: gram of alloy would be taken from the second piece=(8-x)
This gives:
[tex]\dfrac{2}{5}x+ \dfrac{3}{10}(8-x)=\dfrac{5}{16}*8[/tex]
We simplify the equation above for the value of x.
[tex]\dfrac{2x}{5}+ \dfrac{3(8-x)}{10}=\dfrac{5}{2} \\\dfrac{4x+24-3x}{10}=\dfrac{5}{2}\\\dfrac{x+24}{10}=\dfrac{5}{2}\\2x+48=50\\2x=50-48\\2x=2\\x=1[/tex]
Therefore to create 8 gram of gold and silver alloy with gold-silver ratio 5:11, we take 1 grams of one of the alloy and 7 grams of the other alloy.
A machine fills 75 bottles of water each minute. Write an equation to represent the number of bottles, B of water the machine can fill in m minutes.
Answer:
B x m
Step-by-step explanation:
Example: 75 x minutes
So no matter how much bottles you have, you just have to multiply the minutes.
Answer:I think it would be 75 divided by b = m
Step-by-step explanation:
Elinor determined that a triangle with side lengths 6, 10, and 8 does not form a right triangle.
62 + 102 = 82
36 + 100 = 64
136 ≠ 64
Is her answer correct?
Answer
No, she should have added 62 and 82 and compared that to 102.
Answer:
The correct answer is C) No, she should have added 62 and 82 and compared that to 102.
Step-by-step explanation:
Her answer is incorrect because she did not follow the steps correctly, she should have added the two numbers. Good luck!
Which of the following is the inverse of y = 6 Superscript x?
y = log Subscript 6 Baseline x
y = log Subscript x Baseline 6
y = log Subscript one-sixth Baseline x
y = log Subscript 6 Baseline 6 x
Answer:
Option A
Step-by-step explanation:
your welcome = )
The inverse of the function y = 6ˣ is y = log₆(x), which means option A is correct.
To find the inverse of the function y = 6ˣ, we need to swap the roles of x and y and then solve for y. The steps to find the inverse are as follows:
Start with the original function: y = 6ˣ
Swap x and y:
[tex]x = 6^{y}[/tex]
To solve for y, take the logarithm of both sides using the same base (in this case, base 6):
log₆x = log₆([tex]6^{y}[/tex])
Since [tex]log_{b} (b^{y} )[/tex] = y, we get: y = log₆x
Therefore, the inverse function is y = log₆x.
Kendra needs 2 3/4 cups of flour for cookies, 4 1/2 cups of flour for bread, and cup of flour 2/3 for biscuits , How much flour does she need in all?
Answer:
7 11/12
Step-by-step explanation:
amount of the flour
= 2 3/4 + 4 1/2 + 2/3
= 11/4 + 9/2 + 2/3
= 33/12 + 54/12 + 8/12
= 95/12
= 7 11/12
make as the brainliest
Answer:
Wofford College
Step-by-step explanation:
What are the factors of x2 + 3x - 4?
(x + 4) and (x - 4)
(x + 3) and (x-4)
(x + 4) and (x - 1)
(x + 3) and (x - 1)
Answer:
C. (x + 4) and (x - 1)
Step-by-step explanation:
The middle number is 3 and the last number is -4.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 3
Multiply together to get -4
Can you think of the two numbers?
Try -1 and 4:
-1+4 = 3
-1*4 = -4
Fill in the blanks in
(x+_)(x+_)
with -1 and 4 to get...
(x + 4) and (x - 1)