If Peggy does it in 12 minutes, she does 1/12 of the work in 1 min
If Butch does it in 27 minutes, he does 1/27 of the work in 1 min
So:
\(\begin{gathered} \frac{1}{12}+\frac{1}{27}=\frac{1}{x} \\ \\ \frac{1(27)+1(12)}{27(12)}=\frac{1}{x} \\ \\ \frac{27+12}{324}=\frac{1}{x} \\ \\ \frac{39}{324}=\frac{1}{x} \\ x=\frac{324}{39}=\frac{108}{13} \end{gathered}\)They can do it in 108/13 or 8.3 minutes working together.
Natalie is selling fruit at the Saturday market. She has a
otal of 48 pears that she wants to sell. She makes bags of
pears and sells them for $5 per bag. In which equation
oes b represent the number of bags of pears?
If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:
b = total_number_of_pears / pears_per_bag
In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.
Given that Natalie has a total of 48 pears, we can substitute the value into the equation:
b = 48 / pears_per_bag
Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.
Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:
b = 48 / 4
Simplifying the equation gives:
b = 12
So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.
It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.
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find the square root of 14+6√5
Answer:
3 + √5
Step-by-step explanation:
Find the square root of 14+6√5
Change to √ ( 14 + 6√5 ) = √x + √y
1️⃣ Square.
14 + 6√5 = x + y + 2√xy
14 + 2√45 = ( x + y) + 2√xy
2️⃣ Compare.
(x + y) = 14
xy = 45
3️⃣ Solve.
(x - y)² = (x+y)² - 4xy
( x - y)² = 14² - 180
( x - y)² = 196 - 180
( x - y)² = 16
( x - y) = 4
x + y = 14
x - y = 4
2x = 18
x = 9 .
y = 5 .
14 + 6√5 = √9 + √5 = 3 + √5 .
Answer: 3 + √5 .
Done ✔
You have ten box's of ten muffins each, and each muffin has been blueberry. Use an exponent to write an expression for the total number of blueberries
Answer:
I'm pretty sure it's 10 to the power of 3.
Step-by-step explanation:
A couple decides that sophia will drive the first 3/5 of a trip and toby the last 2/5. the entire trip is 500 miles long. how far will sophia drive?
The miles Sophia drove is 60 miles
The distance Sophia drove is represented in fractions.
What is a Fraction?A number is expressed as a quotient where a numerator is divided by a denominator. In a simple fraction, both are integers.
A fraction consists of a numerator and a denominator. An example of a fraction is 1/2 where 1 is the numerator and 2 is the denominator.
In order to determine the miles Sophia drove, the total distance of the trip would be multiplied by the fraction of the time Sophia drove.
Miles Sophia drove = 3/5 x 100
= 60 miles
So sophia drove 60 miles in 500 miles.
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Find an equation of a line with slope -4 and y-intercept 9. y =
Answer:
Y= -4X+9
Step-by-step explanation:
solve the equation by the help of the standard equation Y = MX + C
where M is the slope and C is the Y intercept
A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
Many consumer groups feel that the U.S. Food and Drug Administration (FDA) drug approval process is too easy and, as a result, too many drugs are approved that are later found to be unsafe. On the other hand, a number of industry lobbyists have pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. Consider a null hypothesis that a new, unapproved drug is unsafe and an alternative hypothesis that a new, unapproved drug is safe.
a. Explain the risks of committing a Type I or Type II error.
b. Which type of error are the consumer groups trying to avoid? Explain.
c. Which type of error are the industry lobbyists trying to avoid? Explain.
d. How would it be possible to lower the chances of both Type I and Type II errors?
Answer:
A) The risk of committing Type I error would imply that an unsafe drug is approved. However, the risk of committing a Type II error would imply that a drug is safe but not approved.
B) They are trying to avoid type I error because they don't want drugs that are unsafe to be approved.
C) They are trying to avoid type II errors because the companies would have to continue testing even when the drugs are safe.
D) To lower the chances of type I error, the significance level has to be reduced and they need to make sure that the tests are run for longer periods so that a good representation of the sample size would have been tested which means we are increasing the credibility of the test results.
To lower the chances s of type II error, we have to ensure we increase the sample size and decrease the variants of the drugs.
Step-by-step explanation:
In errors in statistics, we can define type I error as when the null hypothesis is rejected even when it is true while a type II error is when we fail to reject the null hypothesis even when it is false.
A) The null hypothesis in this question is that a drug is unsafe. Thus, the risk of committing Type I error would imply that an unsafe drug is approved. However, the risk of committing a Type II error would imply that a drug is safe but not approved.
B) The consumer groups feel that too many approved drugs are found out later to be unsafe. Thus, they don't want drugs that are unsafe to be approved and it means they are trying to avoid type I error.
C) The error that the Industry lobbyists are trying to avoid is the Type II error. This is because the companies would have to continue testing even when the drugs are safe.
D) To lower the chances of type I error, the significance level has to be reduced and they need to make sure that the tests are run for longer periods so that a good representation of the sample size would have been tested which means we are increasing the credibility of the test results.
To lower the chances s of type II error, we have to ensure we increase the sample size and decrease the variants of the drugs.
For a floral arrangement class, Jayvon has to create an arrangement of twigs and flowers that has a total of 9 objects. Jayvon has to pay for the twigs and flowers that he uses in his arrangement. Each twig costs $1, and each flower costs $3. He spends a total of $15 on the twigs and flowers. Write and solve a linear system to find the number of twigs and the number of flowers he used. Use the method of substitution.
Answer:
3 flowers 6 twigs
Step-by-step explanation:
set flowers to x and twigs to y
15 = 3x + y subtract 3x both sides to get y
9 = x+y sub 15-3x in for y 9= x + 15-3x simplify to 2x =6 so x =3 put that in for x in 9=x+y 9= 3+ y so y =6
graph h(x)=(x-1)^2-9
The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.
The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.
The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.
The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).
Based on this information, we can draw the following conclusions:
The graph will be a U-shaped curve with the vertex at (1, -9).
The vertex represents the minimum point of the parabola since it opens upward.
The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.
The graph will extend indefinitely in both directions.
To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.
Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.
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Which expression shows another way to write 36+16?
4(9)+4
4(9+4)
6(6+8)
(6+4)(6+4)
Answer:
36+16= 52
4(9)+4= 40, which does not equal 52.
4(9+4) = 52.
6(6+8) = 84, which does not equal 52.
(6+4)(6+4) = 100, which does not equal 52.
So, 4(9+4) is correct.
Let me know if this helps!
What can be concluded about line that passes through the points (1,-2) and (4,-2)? Check all that apply.
The slope is 0.
The y-intercept is -2.
The line is vertical.
O The line is horizontal.
The line has no y-intercept.
The equation of the line is Y--2
All that apply are:
The slope is 0.
The y-intercept is -2
The line is horizontal.
The equation of the line is Y = -2.
Given points:
(1,-2) and (4,-2)
slope m = -2-(-2) / 4 - 1
= -2+2/3
= 0
so slope is 0
y = mx + c
(1,-2) passes
-2 = 0*1 + c
c = -2
y = 0*x + -2
y = -2
so the line is horizontal and equation of the line is y = -2.
The y-intercept is -2.
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Which is longer 5 meters or 400 millimeters?
a. 400 millimeters
b. 5 meters
c. both a and b are correct.
d. both a and b are incorrect
Answer:
b. 5 meters
Step-by-step explanation:
1 meter = 1000 millimeters
5 meter = 5000 millimeters
Which is longer 5 meters or 400 millimeters?
5000 > 400
So, the answer is b. 5 meters.
7.8 x 10 3
--------------
1.2 x 10 4
Step-by-step explanation:
7.8 ×1000=7800.
1.2×10000=12000.
7800÷12000=0.65.
Which expression represents a cube root of 1 + i?
OVE (cos()+ i sin (24))
OVE (cos (37) + i sin (3))
/
O & (cos (4) + i sin (24))
V2 (cos (37) + 1 sin (37))
Answer:c
Step-by-step explanation is va cuz when your multiply:
Answer:
\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)
Step-by-step explanation:
The analysis is as attached below.
CAN SOMEONE HELP ME UNDERSTAND THIS PLEASE
YEAH OFC SHAWTY!
so for A its -4^11 because if the powers have the same base and they are being multiplied you add the powersFor B its the same idea, they have the same base, and are being multiplied so you add the powers- 13^9For C its similar, you have the same base, but since its Dividing, you subtract the powers. So, 9^5for D you pretend like the denominator has a power of 1 and subtract. So its -24^5-24^1 which hopefully puts it into perspective of being -24^4 becuase we subtracted the powersI cant do 2 right now, but i will in a minute
And for 3 his mistake is that they arent the same bases so he cant add the powers, he should have converted them to the same base first.
PLEASE HELP Find the product. (a²b³)⁴
Answer:
\(a^8b^{12}\)
Step-by-step explanation:
when you raise an exponent to a power you multiply
Also since the terms inside the parenthesis are multiplied and not added, you don't have to worry about expanding it
\((a^2b^3)^4 = a^{2*4}b^{3*4}=a^8b^{12}\)
Answer is there in a chart
Marbles, and 4 green marbles. The second bag contains 3 red marbles,2 blue marbles, and 4 green marbles. Aakesh will randomly select one marble from each bag. What is the probability that Aakesh will select a blue marble from each bag ?
The probability that Aakesh will select a blue marble from each bag is 4/45.
To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.
Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:
P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag
P(Blue from first bag) = 2 / 5
Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:
P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag
P(Blue from second bag) = 2 / 9
To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:
P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)
P(Blue from both bags) = (2 / 5) * (2 / 9)
P(Blue from both bags) = 4 / 45.
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Simplify these thing below please. I am stuck again... Thank you
\(9\sqrt{56 x^7 y^{12}}\qquad \begin{cases} 56=7\cdot 2\cdot 2\cdot 2\\ \qquad 7\cdot 2^2 \cdot 2\\ \qquad 2^2\cdot 14\\ x^7=x^{(3)(2)+1}\\ \qquad (x^3)^2\cdot x^1\\ y^{12}=y^{(6)(2)}\\ \qquad (y^6)^2 \end{cases}\hspace{5em} \begin{array}{llll} 9\sqrt{2^2(14)(x^3)^2 x (y^6)^2} \\\\\\ 9(2)(x^3)(y^6)\sqrt{14x} \\\\\\ {\Large \begin{array}{llll} 18x^3y^6\sqrt{14x} \end{array}} \end{array}\)
Answer:
\(\textsf{1.} \quad 18\;x^3\;y^{6}\sqrt{14x}\)
\(\textsf{2.} \quad -8\sqrt{2}\)
Step-by-step explanation:
Question 1Given expression:
\(9\sqrt{56x^7y^{12}}\)
\(\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:\)
\(\implies 9\sqrt{56}\sqrt{x^7}\sqrt{y^{12}}\)
Rewrite 56 as 4·14:
\(\implies 9\sqrt{4 \cdot 14}\sqrt{x^7}\sqrt{y^{12}}\)
\(\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:\)
\(\implies 9\sqrt{4}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}\)
Rewrite 4 as 2²:
\(\implies 9\sqrt{2^2}\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}\)
Simplify:
\(\implies 9\cdot 2\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}\)
\(\implies 18\sqrt{14}\sqrt{x^7}\sqrt{y^{12}}\)
\(\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:\)
\(\implies 18\sqrt{14}\;(x^7)^{\frac{1}{2}}\;(y^{12})^{\frac{1}{2}}\)
\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)
\(\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^{\frac{12}{2}}\)
\(\implies 18\sqrt{14}\;x^{\frac{7}{2}}\;y^6\)
Rewrite ⁷/₂ as 3 + ¹/₂
\(\implies 18\sqrt{14}\;x^{(3+\frac{1}{2})}\;y^{6}\)
\(\textsf{Apply exponent rule} \quad a^{b+c}= a^b \cdot a^c:\)
\(\implies 18\sqrt{14}\;x^3 \; x^{\frac{1}{2}}\;y^{6}\)
\(\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:\)
\(\implies 18\sqrt{14}\;x^3 \; \sqrt{x}\;y^{6}\)
Rearrange:
\(\implies 18\;x^3\;y^{6}\sqrt{14x}\)
Question 2Given expression:
\(7\sqrt{32}-6\sqrt{72}\)
Rewrite 32 as 16·2 and 72 as 36·2:
\(\implies 7\sqrt{16 \cdot 2}-6\sqrt{36 \cdot 2}\)
\(\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:\)
\(\implies 7\sqrt{16}\sqrt{2}-6\sqrt{36}\sqrt{2}\)
Rewrite 16 as 4² and 36 as 6²:
\(\implies 7\sqrt{4^2}\sqrt{2}-6\sqrt{6^2}\sqrt{2}\)
\(\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:\)
\(\implies 7 \cdot 4\sqrt{2}-6\cdot 6\sqrt{2}\)
Simplify:
\(\implies 28\sqrt{2}-36\sqrt{2}\)
\(\implies -8\sqrt{2}\)
answer this please pretty please
Answer:
Wassup Obito
Step-by-step explanation:
I would have done it if you had asked for only 1 question but you have asked someone to do more than 10 q
You must be mad to think someone will do the entire thing
Mark me brainliest
Write an inequality for the graph below.
You are saving money to buy a new video game. You already have $12, and each week you save another $5. Which expression can you use to represent the money you have after 'w' weeks?
Answer:yes 12 +5
Step-by-step explanation:Idrk
Answer:
12 + 5
Step-by-step explanation:
Which equation represents a line that passes through (5, 1) and has a slope of StartFraction one-half EndFraction?
y – 5 = y minus 5 equals StartFraction one-half EndFraction left-parenthesis x minus 1 right-parenthesis.(x –1)
y – y minus StartFraction one-half EndFraction equals 5 left-parenthesis x minus 1 right-parenthesis. = 5(x –1)
y – 1 = y minus 1 equals StartFraction one-half EndFraction left-parenthesis x minus 5 right-parenthesis.(x –5)
y – 1 = 5y minus 1 equals 5 left-parenthesis x minus StartFraction one-half EndFraction right-parenthesis.
Step-by-step explanation:
Slope 1/2 point 5,1
in point slope form would be
(y-1) = 1/2 (x-5)
there's 240 candy bars 1/4 of candy bars are snickers 1/3 of the candy bars are twix 1/8 of the candy bars are hershey. how many candy bars are Mars? explain not with a lot of words but in numbers please.
Answer:
you have to add all the fractions of the candy1/4+1/3+1/8
=17/24
subtract from 1Step-by-step explanation:
1-17/24
=7/24
multiply with the total number of candy7/24×240
=70
Please help with this math question!
Answer:
\(2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25\)
HELP PLS !% POINTS!!
Answer:
149 sq. ft
Step-by-step explanation:
For the triangle:
Base = 16-9 = 7 ft
Area of Triangle = 1/2 of b.h
= 1/2 of 7 * 6
= 21 sq. ft
Area of Rectangle = l.b
= 5 * 16
= 128 sq. ft
Total Area = 149 sq. ft
Graph the line. pllzzzzzzzz
Answer:
Step-by-step explanation:
X: -2, -1, 0, 1, 2,...
Y: -2, -1, 0, 1, 2,...
(y=x)
Solve the following inequality:
4x^2-25<0
I will give the person who answers this correctly brainiest.
Answer:
−2.5<x<2.5
Step-by-step explanation:
Let's find the critical points of the inequality.
4x2−25=0
4x2−25+25=0+25(Add 25 to both sides)
4x2=25
4x24=25/4(Divide both sides by 4)
x2=25/4
x=±√254(Take square root)
x=2.5,−2.5
Check intervals in between critical points. (Test values in the intervals to see if they work.)
x<−2.5(Doesn't work in original inequality)
−2.5<x<2.5(Works in original inequality)
x>2.5(Doesn't work in original inequality)
Which function below results in f(2) = 13? *
f(x) = x² + 8
f(x) = 3x² + 1
f(x) = 2x³ + 5
f(x) = x² + x
Answer:
f(x) = 3x² + 1
Step-by-step explanation:
In this question, we need to find what equations equals to 13 when we plug in 2 to x.
Solve the equations to find which one is true:
f(2) = 2² + 8
= 4 + 8
= 12
---------------
f(2) = 3(2)² + 1
= 3(4) + 1
= 12 + 1
= 13
---------------
f(2) = 2(2)³ + 5
= 2(8) + 5
= 16 + 5
= 21
---------------
f(2) = 2² + 2
= 4 + 2
= 6
You will see that the 2nd equation, f(x) = 3x² + 1, is the only one that equals to 13, which makes it correct.
Please helppppppppppppppppppppppppppppppp
Imagine a motion graph with distance on the Y-axis and time on the X-axis. The graph shows the motion of two objects using two separate lines. Explain how you could use the lines to compare the speed of the two objects. Then, tell how you could determine whether the speed of either object changed during the time shown on the graph.
You could use the lines by comparing the steepness of the lines. The one that has more slope is the one that woul have the greater speed.
How to get the speedTo compare the speed of the two objects, we can look at the steepness of their respective lines. The steeper the line, the faster the object is moving. If the lines have the same slope, then the objects are moving at the same speed.
To determine whether the speed of either object changed during the time shown on the graph, we need to look for changes in the slope of the lines. If the slope of a line becomes steeper, then the object is accelerating and its speed is increasing. If the slope becomes less steep, then the object is decelerating, and its speed is decreasing. If the slope remains constant, then the object is moving at a constant speed.
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-2x^2+4x=5
using the Quadratic formula, the equation needs to be in standard form first. Then label a, b and c and plug it into the quadratic formula and simplify using the order of operations. I
The solution by using the quadratic formula is,
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
What is Quadratic formula?
To solve a quadratic equation ax²+ bx + c = 0 , we use the quadratic formula,
x = - b ± √b² - 4ac / 2a
The given expression is;
- 2x² + 4x = 5
Now, The given equation is solve by using Quadratic formula as;
- 2x² + 4x = 5
Move terms to the left side
- 2x² + 4x - 5 = 0
- ( 2x² - 4x + 5 ) = 0
2x² - 4x + 5 = 0
Compare with quadratic equation ax²+ bx + c = 0 we get;
a = 2, b = -4, c = 5
Since, Quadratic formula is,
x = - b ± √b² - 4ac / 2a
Hence, Substituting all the values of a, b and c in quadratic formula we get;
x = - (-4) ± √(-4)² - 4*2*5 / 2*2
x = 4 ± √16 - 40 / 4
x = 4 ± √-24 / 4
x = 4 ± 2√-6 / 4 ( Since, i = √-1 )
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
So, The solution by using the quadratic formula is,
x = 4 + 2√6 i / 4 and x = 4 - 2√6 i / 4
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