1. Compare two spheres. The first has a diameter of 4 inches.
The second sphere has a diameter of 428 inches.
Determine the ratio of the volume of the large sphere to the volume
of the small sphere.
Ratio =
The ratio of the volume of the large sphere to the volume
of the small sphere is 1226 .
How to find the volume of 3d objects?V = 4/3 r³ is the equation to calculate a sphere's volume. The volume of a sphere is calculated using the following formula: 4/3rds of Pi and the cube of the sphere's radius. A sphere is a geometrical object that is a three-dimensional equivalent of a two-dimensional circle . A sphere is a collection of points in three-dimensional space that are all located at the same r distance from a particular point. The radius of the sphere is equal to r, and the provided point is its center. In the works of the ancient Greek mathematicians, spheres are first mentioned.
In several branches of mathematics, the sphere serves as a basic building block. Also found in nature and industry are spheres and nearly-spherical shapes.
Volume sphere = 4/3πr³
Volume of sphere 1
D = 4 inches
r = 2 inches
So,
Volume = 4/3π(2)³
= 33.51 inches³
Volume of sphere 2
D = 428 inches
r = 214 inches
So,
Volume = 4/3π(214)³
= 4.11 ×[tex]10^{7}[/tex] inches³
Ratio
= sphere 2: sphere 1
= 4.11 ×[tex]10^{7}[/tex] : 33.51
= 1226
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Jim wants to plan a meal with 150 grams of carbohydrates and 1400 calories. If green beans have 7 grams of carbohydrates and 30 calories per half cup serving and if french fried shrimp have 9 grams of carbohydrates and 190 calories per three-ounce serving, how many servings of green beans and shrimp should he use?
There are 16 half-cup servings of beans and 4, three-ounce servings of shrimp.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represents number of half-cup servings of beans
Let y represents number of 3 ounce servings of shrimp
We have a system of equations, one for carbs and one for calories;
7x + 9y = 150
30x + 190y = 1400
Now,
30(7x + 9y) = 30(150)
-7(30x + 190y) = -7(1400 )
210x + 270y = 4440
-210x - 1330y = -8680
-1060y = -4240
y = 4
Then substitute we get;
7x + 9y = 150
7x + 9(4) = 150
7x + 36 = 150
7x = 112
x = 16
Hence; X = 16 and Y= 4
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This table shows the ratio of the number of adults to the number of students on a class field trip. A 2-column table has 4 rows. Column 1 is labeled Number of adults with entries 1, 2, 4, 6. Column 2 is labeled Number of students with entries 7, x, 28, y. Which values are missing from this table? x = y =
Answer:
x = 14 and y = 42
Step-by-step explanation:
From the two entries that have both the numbers od adults*A) and students(S) we find a ratio of S/A to be 7 for both cases. We'll make the assumption that is the same ratio in the two cases involving x and y.
To find x and y, multiply the number of adults by 7 to find the number of students,
x = 14 and y = 42
A S Ratio S/A = 7
1 7 7
2 x 14
4 28 28
6 y 42
ear Equations Question 1 of 5 Find the solution to the following system using substitution or elimination: y = 3x + 2 y = -2x - 8 O A. (-3, -8 OB. (1,-6) C. (-2,-4) OD. (-3. - 31
suppose you have a sample of 29 women over 35 who have not previously given birth who exercise daily, and who have an average duration of labor of 17.3 hours and a sample variance of 37.2 hours. you want to test the hypothesis that women over 35 who have not previously given birth and who exercise daily have a different duration of labor than all women over 35 who have not previously given birth.
There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women.
Standard error sm = 1.634
Test statistic t = 1.102
P-value = 0.28
This is a hypothesis test for the population mean.
The claim is that women who exercise daily have a significantly different duration of labor than all women.
Then, the null and alternative hypothesis are
[tex]H_{0}[/tex] : μ=16
[tex]H_{0}[/tex] : μ≠ 16
The significance level is 0.05.
The sample has a size n=29.
The sample mean is M=17.8.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=√77.4=8.8.
The estimated standard error of the mean is computed using the formula:
[tex]s_{M}[/tex] = [tex]\frac{s}{\sqrt{n} }[/tex] = [tex]\frac{8.8}{\sqrt{29} }[/tex]= 1.634
Then, we can calculate the t-statistic as
t=(M-μ)/(s/[tex]\sqrt{n}[/tex])=(17.8-16)/1.634)=1.102
The degrees of freedom for this sample size are:
df=n-1=29-1=28
This test is a two-tailed test, with 28 degrees of freedom and t=1.102, so the P-value for this test is calculated as (using a t-table):
[tex]P_{value}[/tex]=2.P(t≥1.102)=0.28
As the P-value (0.28) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that women who exercise daily have a significantly different duration of labor than all women
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f(x) = -4x² + 3x − 11
Find f(-4)
Answer:
f(-4) = - 87
Step-by-step explanation:
f(-4) = - 4·(-4)^2 + 3·(-4) - 11
f(-4) = - 4·16 - 12 - 11
f(-4) = - 64 - 12 - 11
f(-4) = - 87
Step-by-step explanation:
1.
[tex]f( - 4) = - 4( - 4) ^{2} + 3( - 4) - 11[/tex]
2.
[tex] f( - 4) = - 4(16) - 12 - 11[/tex]
3.
[tex]f( - 4) = - 64 - 23[/tex]
4.
[tex]f( - 4) = - 87[/tex]
Susie started a rock collection.
She started with 26 rocks. Each month she adds 5 to the collection.
Which equation can be used to find y, the total number of rocks in Susie's collection after x months?
A. y = 26x - 5
B. y = 5x + 26
C. y = 26x + 5
D. y = 5x - 26
Answer:
B) y= 5x + 26
Step-by-step explanation:
if susie starts with 26 rocks and adds 5 rocks each month and x=months then the correct option is Option B
Answer: y = 5x+26 (choice B)
==========================================
Explanation:
The equation y = mx+b is in slope intercept form
m = slope
b = y intercept
The y intercept is the starting amount. In this case, she starts with b = 26 rocks. The m = 5 refers to the fact she adds 5 rocks per month. Each time x goes up by 1, y goes up by 5. Think of slope = rise/run = 5/1
rise = 5 = go up by 5 rocks
run = 1 = each time you go up by 1 month
Please help me please I’m begging I WILL GIVE YOU BRAINLEST
Answer:
I haven't done much of this off the internet but from what I found you would just write the same number so 1 would be 1 however if it's super serious you might want to wait for someone else to answer this.
Step-by-step explanation:
If the water level rises 12 centimeters every 7 minutes and you record the data point of (21,y), what is the value of y? Use slope to justify your answer.
The rate of change of the given relation is 1.7142 the value of y is 36 centimeters.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
As per the given question,
The water level rises 12 centimeters every 7 minutes.
0 minutes → 0 cm
7 minutes → 12 cm
14 minutes → 24 cm
21 minutes → 36 cm.
Since, (21,y) best match with the above condition.
So, 21 minutes is the time taken while 36 cm is the level of water.
Slope or rate of change = 12/7 cm/minutes.
And, 36/21 = 12/7 (proved)
Hence "The rate of change of the given relation is 1.7142 the value of y is 36 centimeters".
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Find all real numbers r for which there exists exactly one real number a such that when (x+a)(x2 +rx+1)
is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero.
All real numbers r for which there exists exactly one real number a such that when (x+a)(x² +rx+1) is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero are given as r = -1
A real number is a quantity of a continuous number that can express a distance along a line in mathematics.
Hence the workings for the above result are indicated as follows:
Expanding the brackets, we see that we want the following three inequalities to be true.
a ≥ 0 (constant term) (1)
ar + 1 ≥ 0 (coefficient of x) (2)
a + r ≥ 0 (coefficient of x²) (3)
If r ≥ 0, then any a ≥ 0 meets the requirement of (1), (2), and (3).
It remains to address r < 0. In this case, note that (3) immediately suggests (1)
Hence, we only need to look at (2) and (3). Given that r < 0, inequalities (2) and (3) are equivalent to the following.
a ≤ − 1/r (4)
a ≥ − r (5)
Therefore, we seek all values of r < 0 such that there is exactly one real number satisfying the expression −r ≤ a ≤ −1/r (6)
Thus −r = −1/r ,
This implies r = ±1.
Given that r < 0 we have r = −1.
This implies that the only corresponding value of a is a = 1.
It only remains to follow that (x + 1)(x² − x + 1) = x³ + 1, which has no negative coefficients.
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Full Question:
Find all real numbers r for which there exists exactly one real number a such that when (x+a)(x² +rx+1) is expanded to yield a cubic polynomial, all of its coefficients are greater than or equal to zero.
Members of our lacrosse team raised 1672.50 to go to a tournament they rented a bus for 1068.50 and budgeted $37.75 per player for meals write and solve an equation which can be used to determine x
The equation is 1068.50 + 37.75 x = 1672.50 and the value of x is 16.
Members of our lacrosse team raised 1672.50 to go to a tournament.
Amount raised by lacrosse team = 1672.50
Let the number of players in lacrosse team = x
They rented a bus for 1068.50 and budgeted $37.75 per player for meals. So, mathematically this can be represented as
1068.50 + 37.75 x
Total amount paid by lacrosse team = 1068.50 + 37.75 x
As amount raised by lacrosse team and the amount paid by lacrosse team are equal so we can write
1068.50 + 37.75 x = 1672.50
37.75 x = 1672.50 - 1068.50
37.75 x = 604
x = 16
Thus, we can conclude that the value of x is 16 and the equation is 1068.50 + 37.75 x = 1672.50.
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Handmade socks, knitted using pure cashmere wool, are very expensive to buy. Rowena buys cashmere wool in 20g balls. Each ball of cashmere wool costs her £1.42 . She pays her sister £8 to knit each pair of socks. 135g of cashmere wool is used to knit each pair of socks. Rowena sells 40 pairs of cashmere socks at £18.95 per pair. What is her percentage profit? Give your answer correct to 2 significant figures.
The percentage profit for the so is that were made is 40.32%.
How to calculate the profit?From the information, Rowena buys cashmere wool in 20g balls. Each ball of cashmere wool costs her £1.42 and she pays her sister £8 to knit each pair of socks. The cost will be:
= (£1.42 × (20 + 135) + (40 × £8)
= £220.1 + £320
= £540.1
The selling price will be:
= £18.95 × 40
= £758
Therefore, the percentage profit will be:
= Profit / Cost price × 100
= (758 - 540.1) / 540.1 × 100
= 217.9 / 540.1 × 100
= 40.32%
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Convert to a decimal. 13 --- 4
if you have a 6.83 m solution of naoh, what is the ph of the solution? assume the solution is at 25 ° c. provide your response to one digit after the decimal.
A solution of NaOH is a really strong base, so, when it's dissolved in water to form a solution, it dissociates completely in it's ions: and its
pH = 14.8344 and rounded it will be 14.8
it dissociates completely in it's ions:
NaOH -------> Na⁺ + OH⁻
So, to calculate the pH, we first need to calculate the OH concentration. As it was stated before, a strong base like this, it will dissociate completely so the concentration of OH will be the same concentration of NaOH:
[OH⁻] = 6.83 M
The pH is calculated with the following expression:
14 = pH + pOH
So, with the OH we can calculate the pOH, and then, the pH:
pOH = -log[OH⁻]
pOH = -log(6.83) = -0.8344
So the pH:
pH = 14 - pOH
pH = 14 - (-0.8344)
pH = 14.8344 and rounded it will be 14.8
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11. Which of the following equations best represents
the graph below?
A. -2x + 3y = 6
C. 3x - 2y = 6
B. 2x + 3y = 6
D. -3x-2y = 6
Answer: A
Step-by-step explanation:
At its peak, an online shopping site was selling 420 items per second. How many items would it sell in 30 minutes
The online shopping site would sell 756000 items in 30 minutes
Given
The online site would sell 420 items in a second
To find number of items it would sell in 30 minutes first of all convert minutes into seconds and continue to solve the problem.
To convert minutes into seconds just multiply minutes with 60.
because one minute is equal to 60 seconds.
Therefore 30 minutes = 30 x 60 seconds
30 minutes = 1800 seconds
Say the number of items sold by sire in 30 minutes be x.
now according to the condition in equation
420 x 1800 = x
x= 756000
Hence the site will sell 756000 items in 30 minutes.
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Do number 3 please thank you.
Answer:
Answer down below!
Step-by-step explanation:
Let's rewrite the sentence and then pinpoint the exact points!
Your conclusion will be bolded!
"If you are living in California, then you live in the state that has the tallest mountain in the lower 48 states."
The conclusion is the last part of the statement that clearly states the decision based on the components of the test (or hypothesis)
12 | 13
1
3/4
5/6
7/8
1₁
2
Angles 1 & 4 are an example of:
1₂
· 13. PLEASE HURRY
Answer: c. Vertical angles
Step-by-step explanation:
joey and chloe and their daughter zoe all have the same birthday. joey is 11 year older than chloe, and zoe is exactly 11 year old today. today is the first of the 99 birthdays on which chloe's age will be an integral multiple of zoe's age. what will be the sum of the two digits of joey's age the next time his age is a multiple of zoe's age?
The sum of the two digits of Joey's age the next time his age is a multiple of Zoe's age is of 11, and this measure was found using a system of equations.
What is the system of equations?The variables for the system of equations in this problem are given as follows:
Variable x: Joey's age.Variable y: Chloe's age.Variable z: Zoe's age.Joey is one year older than Chloe, hence:
x = y + 1.
Zoe is exactly one year old, hence:
z = 1.
The difference between the ages of Chloe's and Zoe's have 9 factors. Numbers with nine factors have the following format:
x² x y² , with different x and y.
These numbers have to be different of 1, due to Zoe's age, hence the smallest number is given as follows:
2² x 3² = 4 x 9 = 36.
Since the difference is of 36 years old, so the ages are as follows:
Zoe: 1 year old. Chloe: 37 years old.Joey: 38 years old.The next time this will happen is in 36 years, hence Joey's age will be of:
36 + 38 = 74 years old.
The sum of the digits will be of:
7 + 4 = 11.
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WILL GIVE BRAINLY Given f(x)=3x-1 and (f∘g)(x)=x^2, find g(x)
[tex]\begin{cases} f(x)=3x-1\\\\ (f\circ g)(x) = x^2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (f\circ g)(x)\implies f( ~~ g(x) ~~ )~~ = ~~3( ~~ g(x) ~~ ) - 1\implies \stackrel{(f\circ g)(x)}{x^2}~~ = ~~3g(x)-1 \\\\\\ x^2+1=3g(x)\implies \cfrac{x^2+1}{3}=g(x)[/tex]
HW Score: 83.33%, 15 of 18 points
Points: 0 of 1
An automobile purchased for $34,000 is worth $2200 after 6 years. Assuming that the car's value depreciated steadily from year to year, what was it worth at the end of the third year?
The value 3 years after it was purchased is $
Carmin Wimberley
< Question 13, 1.3.29
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The car' s worth after the end of third year will be $18100.
What is depreciation?An asset loses value over time as a result of use, damage, or obsolescence. Depreciation is the measurement for this decline. Depreciation, or a decline in asset value, can be brought on by a variety of other variables, such as bad market conditions, etc. Depreciation is the estimated decrease in value of fixed assets over the course of a fiscal year. Large lump sum purchases are made for tangible things like real estate, machinery, vehicles, and so forth.
Given Data
An automobile purchased for $34,000 is worth $2200 after 6 years.
Annual depreciation = [tex]\frac{34000-2200}{6}[/tex]
Annual depreciation = [tex]\frac{31800}{6}[/tex]
Annual depreciation = 5300
In 3 years depreciation would be
= 5300(3)
= 15900
Thus the value after the end of third year will be:
34000 - 15900
18100
The car' s worth after the end of third year will be $18100.
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The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H . A wall of uniform height that is 16 feet long is constructed using 280 bricks. What is the height, in feet, of the wall?
The height of the wall in feet is 2.5 feet.
According to the question,
We have the following information:
The number of bricks, B , needed to build a wall of length L feet and uniform height H feet can be found by the equation B = 7 L H .
A wall of uniform height that is 16 feet long is constructed using 280 bricks.
So, we have:
B = 280 and H = 16
Putting these values in the given expression:
B = 7LH
280 = 7*L*16
L = 280/(7*16)
L = 280/112
L = 2.5 feet
Hence, the height of the wall in feet is 2.5 feet.
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round the number 2,745 to the nearest 1,000
Answer: 3,000
Step-by-step explanation: the 7 in the hundreds place is greater than 5 so you increase the 2 in the thousands place by 1
1. The number of miles a car can travel on a gallon of gasoline is related to its fuel
efficiency. Fuel efficiency depends on many factors including the speed of the car.
Driving at very slow or very fast speeds uses more gas than driving at a moderate
speed, which means fuel efficiency can often be modeled by a quadratic function.
For a certain model of car the fuel efficiency is maximized at 32 miles per gallon
with a speed of 55 mph. At 65 mph the car can get 31 miles per gallon.
The quadratic equation that models the fuel efficiency of the car is given by:
y = -0.01(x - 55)² + 32.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which the parameters of the equation are described as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficientFor a certain model of car the fuel efficiency is maximized at 32 miles per gallon with a speed of 55 mph, hence the vertex is given by:
(h,k) = (55,32).
Hence the rule is:
y = a(x - 55)² + 32
When x = 65, y = 31, hence we can find the leading coefficient a as follows:
31 = a(65 - 55)² + 32
100a = -1
a = -0.01.
Hence the equation is given by:
y = -0.01(x - 55)² + 32.
What is the missing information?The problem is incomplete, hence we suppose that it asks for the quadratic model of the car's fuel efficiency.
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v/8 - 3.1 = -15.9 solve for v
[tex]\frac{v}{8} -3.1=-15.9[/tex]
Simplify equation:
[tex]\frac{1}{8}v+-3.1=-15.9[/tex]
[tex]\frac{1}{8} v-3.1=-15.9[/tex]
Add 3.1 to both sides:
[tex]\frac{1}{8} v-3.1+3.1=-15.9+3.1\\[/tex]
[tex]\frac{1}{8} v=-12.8[/tex]
Multiply both sides by 8:
[tex]8\times(\frac{1}{8} v)=(8)\times(-12.8)\\-102.4[/tex]
[tex]\fbox{v=-102.4}[/tex]
Lance the alien is 5 feet tall. His shadow is 8 feet long. At the same time of day, a tre shadow is 24 feet long. What is the height of the tree?
Answer:
15 ft
Step-by-step explanation:
5:8
?:24
8x3=24 SO 5x3=15
Ill give points to whoever can answer this question
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The given system of equations has no solution.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example: 2x + 3 = 4 is an equation.
We have,
-3x + 3y = 4 ____(1)
2x = 2y + 6 _____(2)
From (2) we get,
x = (2y + 6) / 2
x = y + 3 ____(3)
Substituting (3) on (1).
-3 (y + 3) + 3y = 4
-3y - 9 + 3y = 4
-9 = 4
We see that there are no solutions to the given equation.
Thus,
The given system of equations has no solution.
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Pleaseee help will give brainliest to best and most detailed answer!
f(x) = x3 + 5x2 –32x – 7 is divided by x – 4
I really need help on this, and please show me every step!
Answer:
[tex]f(x)=x^2+9x+4+\dfrac{9}{x-4}[/tex]
Step-by-step explanation:
Long Division Method of dividing polynomials
Divide the first term of the dividend by the first term of the divisor and put that in the answer.Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.Repeat until no more division is possible.Write the solution as the quotient plus the remainder divided by the divisor.Given:
[tex]\textsf{Dividend: \quad $x^3+5x^2-32x-7$}[/tex]
[tex]\textsf{Divisor: \quad $x-4$}[/tex]
[tex]\large \begin{array}{r}x^2+9x+4\phantom{)}\\x-4{\overline{\smash{\big)}\,x^3+5x^2-32x-7\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-4x^2)\phantom{-b))))))..)}}\\9x^2-32x-7\phantom{)}\\-~\phantom{(}\underline{(9x^2-36x)\phantom{)))..}}\\4x-7\phantom{)}\\-~\phantom{()}\underline{(4x-16)\phantom{}}\\9\phantom{)}\\\end{array}[/tex]
Therefore:
[tex]f(x)=x^2+9x+4+\dfrac{9}{x-4}[/tex]
Definitions
Dividend: The polynomial which has to be divided.
Divisor: The expression by which the divisor is divided.
Quotient: The result of the division.
Remainder: The part left over.
for a between-subjects experiment, any factor that increases the variance within treatments also increases the likelihood of finding a significant difference between treatments.
The answer is FALSE. The likelihood of discovering a substantial difference between treatments does not increase with any factor that makes treatments more variable.
In experiments, you create situations where several treatments (such a are used in order to investigate the impact of an independent variation.
Every participant in a between-subjects or between-groups design only experiences one condition, and group differences between participants in various conditions are compared. In contrast, no participant in a within-subjects design is exposed to every condition.
As a result, the likelihood of discovering a substantial difference between treatments is not increased by factors that enhance variation within treatments.
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The point (-2, K) lies on the circle x^2 +y^2= 20. Find the values of k. Show all the steps
I will plug in the POINTS including k in the equation each point in its place either x or y.
[tex]( - 2)^{2} +( {k})^{2} = 20 \\ 4 + {k}^{2} = 20 \\ k^{2} + 4 - 20 = 0 \\ {k}^{2} - 16 = 0 \\ (k + 4)(k - 4) = 0 \\ \\ k + 4 = 0 \\ \\ or \\ \\ k - 4 = 0 \\ \\ k = 4 \\ or \\ k = - 4[/tex]
ATTACHED IS THE SOLUTION