The change in P in percentage terms is 51% decrease.
How to illustrate the information?Since the two variables are connected by the relation, this will be illustrated as:
P=k/Q^2
where k is the proportionality constant.
Now, If Q is increased by 40%, i.e. the update Q' = Q + 0.4Q.
Now, we have
P1 = k/Q^2 and P2 = k/(Q+0.4Q)^2
P2/P1 = {k/(Q+0.4Q)^2}/{k/Q^2}
P2/P1 = 1/(1.4)^2
P2=0.51*P1
P2 = 0.5P1
Hence P reduces by 51%.
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Ann's car can go 252 miles on 7 gallons of gas. During a drive last weekend, used 4 gallons of gas. How far did drive? Use pencil and paper. Explain how the problem changes if you were given the distance drove last weekend instead of how much gas used.
The distance that Ann drove last weekend is 144 miles.
What is the distance that Ann drove?The first step is to determine the rate of Ann's car. Rate is the distance traveled per gallon. It is determined by dividing the total miles traveled by the total gas used.
Rate = distance/gallons
= 252/ 7 = 36 miles per gallon
The next step is to multiply the rate by the gallons she used last weekend. Multiplication is the process of determining the product of two or more numbers. The sign that represents multiplication is x.
Distance Ann traveled = rate x gallons of gas used
= 36 x 4 = 144 miles
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The distance Ann's car travelled using 4 gallons is 144 miles.
What is the distance travelled?The first step is to determine how many miles Ann's car can go using one gallon. To do this, calculate the rate of Ann's car. Rate is the total distance divided by the total gallons.
Miles travelled on one gallon = 252 / 7 = 36 gallons per mile
Now, multiply the rate by the gallons she has. Multiplication is the process that is used to determine the product of two or more numbers.
Total distance travelled = 36 x 4 = 144 miles.
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2 x 10 to the power of 5 / 4 x 10 to the power of 2 in standard form
The result of 2 x 10 to the power of 5 ÷ 4 x 10 to the power of 2 in the standard form is 5×[tex]10^{2}[/tex]
The first number in standard form = 2×[tex]10^{5}[/tex]
The second number in standard form = 4×[tex]10^{2}[/tex]
Scientific notation of the number is a method to represent a very large number or very small number in a simple way. In scientific notation a very whole number from 1 to 10 is multiplied by the power of 10
The first number divided by the second number
2×[tex]10^{5}[/tex] ÷ 4×[tex]10^{2}[/tex] = (2/4)×[tex]10^{5-2}[/tex]
= 0.5×[tex]10^{3}[/tex]
= 5×[tex]10^{2}[/tex]
Hence, the result of 2 x 10 to the power of 5 ÷ 4 x 10 to the power of 2 in the standard form is 5×[tex]10^{2}[/tex]
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Trey rented a truck for one day. there was a base fee of $15.95, and there was an additional charge of 99 cents for each mile driven. trey had to pay $188.21 when he returned the truck. for how many miles did he drive the truck?
I need help please ASAP!!
Answer: x + 2y > 8
Step-by-step explanation:
2x + 4y + 5 + 35 > 56
Isolate variables
2x + 4y > 16
divide by lowest common denominator
x + 2y > 8
Two sisters like to compete on their bike rides. Ciara can go 4 mph faster than her sister, Colleen. If it takes Colleen one hour longer than Ciara to go 80 miles, how fast can Colleen ride her bike?
Question:
Two sisters like to compete on their bike rides. Ciara can go 4 mph faster than her sister, Colleen. If it takes Colleen one hour longer than Ciara to go 80 miles, how fast can Colleen ride her bike?
Explanation:
Note that Ciara can go 4mph faster than Collen.
Let's take the speed to ride a bike for Collen to be x mph.
The speed to ride a bike for Ciara will be (x + 4) mph
Now, to cover a distance of 80 miles, Collen takes 1 hour longer than Ciara. Applying the kinematics equation for motion at constant speed:
[tex]v=\frac{d}{t}[/tex]where v is velocity, d is distance and t is time, we can solve this equation for the time t:
[tex]t=\frac{d}{v}[/tex]Here time Collen takes to cover a distance of 80 miles in 1 hour is more than that taken by Ciara, hence:
Time taken by Collen:
[tex]t=\frac{80}{x}[/tex]Time taken by Ciara:
[tex]t=\frac{80}{x+4}[/tex]The equation for the difference in time:
[tex]\frac{80}{x}\text{ - }\frac{80}{x+4\text{ }}=1[/tex]Solve the equation for the difference in time to get the value of x which is Collen speed:
[tex]x^2+4x\text{ - 320=0}[/tex]Solving the quadratic equation by the quadratic formula where a=1,b=4, and c=-320, we get:
[tex]x=16[/tex]Answer: Colleen's speed is 16 mph.
The speedometer in Erin’s car is accurate within 2 miles per hour. It currently reads
56 mph. Write and solve an absolute value inequality to represent the situation. At what speeds could Erin be driving?
Answers:
The absolute value inequality is [tex]|\text{x}-56| \le 2[/tex] which solves to [tex]54 \le \text{x} \le 58\\\\[/tex] Her true speed could be anything between 54 mph and 58 mph, including both endpoints.===================================================
Explanation:
x = Erin's true speed
Her true speed x is within 2 mph of 56 mph.
This means the interval for x is [tex]56-2 \le \text{x} \le 56+2[/tex] which simplifies to [tex]54 \le \text{x} \le 58[/tex]
She could be going as slow as 54 mph, or as fast as 58 mph, or something in between.
The expression |x-56| measures the distance from x to 56 on the number line. Recall absolute value is used to ensure the distance isn't negative.
We want this distance to be within 2 units, i.e. we want the distance to be 2 or smaller.
[tex]\text{distance on number line} \le 2\\\\|\text{x}-56| \le 2[/tex]
----------------
Here's what the steps look like to solve that absolute value inequality
[tex]|\text{x}-56| \le 2\\\\-2 \le \text{x}-56 \le 2\\\\-2+56 \le \text{x}-56+56 \le 2+56\\\\54 \le \text{x} \le 58\\\\[/tex]
For the second step, we use the rule that |x| < k is the same as -k < x < k where k is some positive number.
In the third step, I added 56 to all three sides to isolate x fully.
Owen has 24 pens and 18 notebooks. He wants to divide the pens and notebooks into equal groups. What is the greatest number of groups he can make using all the pens and notebooks?
Answer:
6
Step-by-step explanation:
You have to think of the GCF (Greatest Common Factor)
List the numbers that multiply 24: 1,2,3,4,6,8,12,24
List the number that multiply 18: 1,2,3,6,9,18
You look at the greatest number that they both have in common.
I need help with this ASAP!!
The difference between the distances is 35 km.
Given, the car started at a distance 40 km.
The car finished the ride at 5 km.
The distance formula, d = st, or distance equals speed times time, can be used to calculate distance. Speed and rate are comparable because they both denote a certain amount of travel per unit of time, such as miles per hour or kilometers per hour. If speed s is equal to rate r
The difference between the distance is:
difference is:
40-5
= 35 km
Hence the difference between the distances are 35 km.
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Dawn bought 10 apples and 6 mangoes for $58.00. Each mango was $1.00 cheaper than an apple. Sita bought 4 apples and 4 mangoes from the same vendor. How much did Sita pay for the apples and mangoes if the prices were unchanged?
Please help me …………
Answer:
[tex] \frac{5}{8} = \frac{22}{x - 6} \\ x≠6 \\ 5(x - 6) = 176 \\ 5x -30 = 176[/tex]
plse answer the questions
Answer:
a. [tex]3^4[/tex]
b. [tex]7^5[/tex]
c. [tex]10^2[/tex]
d. [tex]5^7[/tex]
Step-by-step explanation:
When multiplying or dividing numbers with exponents, the rule is that you add the exponents together if multiplying, or subtract them if dividing. This is only possible with numbers of the same base (the number before the exponent).
[tex]3^2[/tex] multiplied by [tex]3^2[/tex] is [tex]3^4[/tex] because the exponents, 2 and 2, are added together. The bases remain unchanged.
[tex]7[/tex] times [tex]7^4[/tex] is [tex]7^5[/tex] because another way to write [tex]7[/tex] is [tex]7^1[/tex], and the exponents can be added together from there.
The same logic can be applied to the division questions, but with subtraction instead of addition.
Can somebody please explain what domain and range is on a graph and how to find them.
Answer:
Domain: x-values
Range: y-values
-
In the graph,
Domain: {-6, 4} or you could write {-6,-5,-4,-3,-2,-1,0,1,2,3,4}
Range: {-9,7} or you could write {-9,-8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}
-
(Please look at the picture attached, and read what's written above. You'll get a better understanding)
match each percent with the fraction or decimal equivalent.
Answer:
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Alexa is looking at T-Mobile for getting an Iphone. The promotion states that they will charge her $45 for activation fee and $64 per month. Write a linear equation for the amount T-Mobile will charge Alexa.
The linear equation for the situation mentioned can be written as T=a+mf, where "T" is the total cost of the the iPhone, "a" is then activation fee, "m" is the number of months of membership and "f" is the monthly membership fee. Hence T = 45 + 64m is our required equation.
As per the question statement, Alexa is looking at T-Mobile for getting an iPhone and the promotion states that they will charge her $45 for activation fee and $64 per month. We are supposed write a linear equation for the amount T-Mobile will charge Alexa.
Let the equation depicting the situation be T = a + mf, where
T = Total cost of the the iPhone
a = Activation fee
m= number of months of membership/installments
f = monthly fee amount for iPhone
If a = $45 and m=$64 then the equation becomes, T = 45 + 64m
So, if she pays for 10 months straight, m = 10, total price T will be:
T = 45 + 64(10) = 45 + 640 = $685.00.
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Thabo is conducting an experiment in which the temperature is measured
carefully. The temperature was 7°C at the end of the first minute, and then it
increased by 6°C every minute after that.
4.2.1 What will the temperature be after the third minute?
4.2.1
Determine a formula to calculate the temperature (7) after
m minutes.
Answer:
after 3 min the temp will be 19°
formula is (6•m)+1
A regulation-sized gymnasium is 80 feet wide and 100 feet long. If a scale model of the gymnasium is 12 inches long, how wide is the model?
The width of the scale model is 9.6 inches long
How to determine the width of the model?The dimensions of the regulation-sized gymnasium is given as
80 feet wide by 100 feet long
This means that
Width = 80 feet
Length = 100 feet
For the scale model, we have
Length = 12 inches
The scale can be represented as
Scale = Length : Width
This means that
12 inches : Width = 100 feet : 80 feet
Express as fraction
So, we have
Width/12 inches = 80 feet/100 feet
This gives
Width/12 inches = 0.80
Multiply both sides by 12 inches
Width = 9.6 inches
Hence, the width is 9.6 inches
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I need help I’ll give Brainliest
The perimeter of the triangle DEF is half the perimeter of triangle ABC.
We are given a triangle ABC with mid-points D,E, and F of AB, BC and CA respectively.
DEF forms a triangle.
We have to find the relationship between the perimeter of triangle ABC and triangle DEF.
Let us consider sides AB,BC, and CA as 2x, 2y and 2z.
We know that triangle ABC is divided into four equal triangles of sides which are half of the sides of triangle ABC.
Hence,
DE = x,
EF = y, and
DF = z
Hence,
Perimeter of triangle ABC = 2x + 2y + 2z = 2(x + y + z)
Perimeter of triangle DEF = x + y + z
Hence, we can say that the perimeter of triangle DEF is half the perimeter of triangle ABC.
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In 2014, Country x had 783 miles of paved roads. Starting in 2015, the country has been building 8 miles of new paved roads each year. After 2 years, how many miles of road will there be?
With children, there is an apparent strong correlation between low family income and poor performance in school. How did susan mayer’s research undermine the hypothesis that low income causes poor school performance?.
Greater access to school boards and greater time for homeschooling would be advantageous for higher-income families.
These two elements will aid in educating the kids and directing them toward academic excellence, which will ultimately benefit those kids in the long run.
Susan has a destitute family to support in addition to her plans to attend college.
She tells her parents she would live with them and support them financially, but in truth, she plans to attend college and pursue her education while leaving her family behind.
She is battling an internal conflict where she prioritizes her needs over those of her family.
The biggest issue today is one of health. The absence of illness does not imply good health. Illness is caused by a variety of circumstances, including a person's psychological, social, and physical health.
Poverty is correlated with low income, illiteracy, gender inequality, and environmental degradation. Poverty can also result from poor health. Wealthier individuals spend more on their health.
Additionally, the government invests in public health-related projects.
Therefore,
Greater access to school boards and greater time for homeschooling would be advantageous for higher-income families.
These two elements will aid in educating the kids and directing them toward academic excellence, which will ultimately benefit those kids in the long run.
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5^5=5x5x5x5x5=
i put 3125 but it wont work can someone help me with this
Answer: 4 i think
Step-by-step explanation:
A recipe for sparkling lemonade calls for 1/2 tablespoon of lemonade mix and 3/4
A recipe for sparkling lemonade calls for 1/2 tablespoon of lemonade mix and 3/4 cup of sparkling water. Find how many tablespoons of lemonade mix it takes per cup of sparkling water. pls, help me :(
The tablespoons of lemonade mix that it takes per cup of sparkling water is 0.67 tablespoon.
How to calculate the value?From the information, a recipe for sparkling lemonade calls for 1/2 tablespoon of lemonade mix and 3/4 cup of sparkling water.
Let the number of tablespoon be represented as x.
Based on the information given, the expression will be:
1/2 / 3/4 = x/1
0.5 / 0.75 = x/1
Cross multiply
0.75 × x = 0.5
0.75x = 0.5
Divide
x = 0.5 / 0.75
x = 0.67
0.67 tablespoon is needed.
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What is the equation of the line that passes through the point (-2, -4) and
has a slope of -1/2
15. Georgia works at the circus selling cotton
candy. The table shows the linear relationship
between the number of
cotton candy bags remaining Hours
in her stand as a function of
the hours she has been
selling. Write a linear
equation in slope-intercept/
form to model the situation.
3
5
12
16
Cotton
Candy
90
78
36
12
The linear equation in slope-intercept/ form to model the situation is 6x + y - 108 = 0
Given:
Georgia works at the circus selling cotton candy. The table shows the linear relationship between the number of cotton candy bags remaining Hours in her stand as a function of the hours she has been selling.
Table :
cotton candy
3 90
5 78
12 36
16 12
Let x,y be cotton,candy.
(x1,y1) = (3,90)
(x2,y2) = (5,78)
slope m = y2-y1/x2-x1
= 78 - 90/5 - 3
= -12/2
m= -6
Slope intercept form y=mx+c
y = -6x + c
substitue (3,90) in y = -6x + c
90 = -6(3) + c
c = 108
substitute c value in y = -6x + c
y = -6x + 108
6x + y - 108 = 0
Therefore the linear equation in slope-intercept/ form to model the situation is 6x + y - 108 = 0.
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Seven minus a number divided by eleven is greater than or equal to six.
Answer:
7 - x/11 ≥ 6
x ≤ 11
Step-by-step explanation:
7 - x/11 ≥ 6
(77- x)/11 ≥ 6
(77- x) ≥ 66
- x ≥ -11
11 ≥ x
x ≤ 11
a random sample of 1000 people from california (population over 35,000,000) and 1000 people from rhode island (population just over 1,000,000) was taken by the gallup poll. which is correct?
Option D is the right choice.
The Gallup poll randomly selected 1000 individuals from Rhode Island (population just over 1,000,000) and 1000 individuals from California (population over 35,000,000). Because both samples have the same sample sizes, it can be assumed that they will be roughly equally accurate.
Taking a poll in the US. The department of Gallup that routinely conducts public opinion polls is called The Gallup Poll. In the form of data-driven news, Gallup Poll findings, analysis, and videos are released every day.
A simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a method of choosing a sample at random. Random sampling makes sure that the findings you get from your sample should be close to what you would have gotten if you measured the complete population.
The Gallup survey randomly selected 1000 individuals from Rhode Island (population just over 1,000,000) and 1000 individuals from California (population over 35,000,000). Because both samples have the same sample sizes, it may be assumed that they will be roughly equally accurate.
Therefore, Option D is correct.
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COMPLETE QUESTION:
A random sample of 1000 people from California (population over 35,000,000) and 1000 people from Rhode Island (population just over 1,000,000) was taken by the Gallup Poll. Which is correct?
a) The sample from California will be more biased because the sampling fraction is smaller
b) The sample from Rhode Island will be substantially more accurate than that from California because a higher sampling fraction was chosen.
c) The sample from California will have a larger sampling error than from Rhode Island because less of the population is sampled.
d) Both samples will be approximately equally accurate because the sample sizes are the same
If 30 % of x =20 ,find value of x
Answer:
[tex]\sf 66\dfrac{2}{3}[/tex]
Step-by-step explanation:
Finding value of 'x':
[tex]\sf 30 \% \ of \ x = 20\\\\\\ \dfrac{30}{100}*x = 20\\\\[/tex]
To find the value of x, multiply both sides with the multiplicative inverse (Reciprocal) of 30/100.
[tex]\sf x = 20*\dfrac{100}{30}\\\\x = \dfrac{200}{3}\\\\x= 66\dfrac{2}{3}[/tex]
For each value of x, determine whether it is a solution to 30 > 5x.
X
6
12
2
4
Is it a solution?^
Yes
No
Answer: 6, No. 12, yes. 2 and 4 No.
Step-by-step explanation:
Simplify the inequality:
6 > x which means that any x that is less than 6 is not a solution.
a right square pyramid has an altitude of 10 and each side of the bass is 6. to the nearest tenth of a centimeter, what is the distance from the apex or top of the pyramid, to each vertex of the base?
The distance of the top of the square pyramid will be 10.5 unit.
How to calculate the distance?It should be noted that based on the information, the hypotenuse theorem will be illustrated. This will be:
AC² = AB² + BC²
AB = length of the segment
BC and AC are the other two sides
This will be illustrated as:
AC² = 10² + (6/2)²
AC² = 100 + 9
AC² = 109
AC = ✓109
AC = 10.5
Therefore, the distance is 10.5 units.
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Multiply (x + 1)3
(x + 1)3 = (x + 1)(x + 1)2
= (x + 1)(x2 + 2x + 1)
= x3 +
x2 +
x +
The solution of the expression (x + 1)³ will be;
(x + 1)³ = (x + 1) (x + 1)²
= (x + 1) (x² + 2x + 1)
= x³ + 3x² + 3x + 1
What is Mathematical expression?
The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.
Given that;
The expression is;
⇒ (x + 1)³
Now, Solve the expression as;
The expression is;
⇒ (x + 1)³
Expand it as,
⇒ (x + 1)³ = = (x + 1) (x + 1)²
= (x + 1) (x² + 2x + 1)
= x³ + 2x² + x + x² + 2x + 1
= x³ + 3x² + 3x + 1
Therefore,
The solution of the expression (x + 1)³ will be;
⇒ (x + 1)³ = (x + 1) (x + 1)²
= (x + 1) (x² + 2x + 1)
= x³ + 3x² + 3x + 1
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Answer:
3
3
1
Step-by-step explanation:
The perimeter of the rectangle is
A) 9.49
B) The p
C) 18.97
The area of the rectangle
A) 18.5
B) 20
C) 40
Please answer ASAP
The area of the rectangle = 13.12 square units.
Perimeter of the rectangle = 21.77 units.
What exactly is a rectangle?A rectangle is a quadrilateral with parallel sides that are equal to one another and four 90-degree vertices. degrees.As a result, it is sometimes referred to as an equiangular quadrilateral.A rectangle is also known as a parallelogram because its opposite sides are both equal and parallel.In response to the given question;
To determine the perimeter of the rectangle ABCD, first determine the length of each side.
Determine the lengths DA and DC using the distance formula.
(x2 - x1)2 + (y2 - y1)2 = DA
Enter the coordinates of points D and A.
DA = √(8 - 1)² + (2 - 0)²
= √49 + 4
= √53 units.
Now, we have to find length of DC
Here , DC = √(3 - 1)² + (3 - 0)²
= √4 + 9
= √13 units.
Here,
DA = CB = √53 units.
And,
DC = AB = √13 units.
So Perimeter of rectangle = DA + CB + DC + AB
= 2√53 + 2√13 units
= 2(√53 + √13) units.
= 21.77 units.
To find area,
Area = (1/2) base × height
Here area,
= (1/2) CB × CD
= (1/2) × √53 × √13
= 26.24/2
∴ Area = 13.12 sq. unit.
Thus, area = 13.12squnits
perimeter = 21.77 units .
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