The proportion that could be used to solve for the variable is:
[tex]\frac{7}{1.68}=\frac{p}{2.88}[/tex] ; p = 12 ⇒ b
Step-by-step explanation:
Direct proportion means that two (or more) quantities increase or decrease in the same ratio
y = k x is the equation of direct proportion, where k is the constant of proportionality[tex]\frac{y_{1}}{x_{1}}=\frac{y_{2}}{x_{2}}=k[/tex] is the another way to write a proportionThe number of pencils and the cost of them is increased together or decreased together
∴ The number of the pencils and their costs are in direct proportion
- By using the 2nd rule above
∵ The cost of the 7 pencils is $1.68
∵ The cost of p pencils is $2.88
∴ [tex]\frac{7}{1.68}=\frac{p}{2.88}[/tex]
The proportion that could be used to solve for the variable is: [tex]\frac{7}{1.68}=\frac{p}{2.88}[/tex]
∵ [tex]\frac{7}{1.68}=\frac{p}{2.88}[/tex]
- By using cross multiplication
∴ p × 1.68 = 7 × 2.88
∴ 1.68 p = 20.16
- Divide both sides by 1.68
∴ p = 12
The value of variable p is 12
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The ingredients for making chocolate cookies are 3/4 cup of brown sugar, 1/4 cup of white sugar, 3/2 cup of butter, 11/8 cup of flour, and 5/2 cup of chocolate chips. What is the total number of cups of ingredients needed in making chocolate cookies?
Answer:
[tex]\frac{51}{8}[/tex] cups.
Step-by-step explanation:
It is given that the ingredients for making chocolate cookies are [tex]\frac{3}{4}[/tex] cup of brown sugar, [tex]\frac{1}{4}[/tex] cup of white sugar, [tex]\frac{3}{2}[/tex] cup of butter, [tex]\frac{11}{8}[/tex] cup of flour, and [tex]\frac{5}{2}[/tex] cup of chocolate chips.
Now, we have to calculate the total number of cups of ingredients needed in making chocolate cookies.
So, it will be given by
[tex](\frac{3}{4} + \frac{1}{4} + \frac{3}{2} + \frac{11}{8} + \frac{5}{2})[/tex] cups
= [tex]\frac{3 \times 2 + 1 \times 2 + 3 \times 4 + 11 + 5 \times 4}{8}[/tex] cups
= [tex]\frac{51}{8}[/tex] cups. (Answer)
Gina and Rhonda work for different real estate agencies. Gina earns a monthly salary of $5,000 plus a 6% commission on her sales. Rhonda earns a monthly salary of $6,500 plus a 4% commission on her sales. How much must each sell to earn the same amount in a month?
A $750,000
B $75,000
C $15,000
D $1,500
which has gradient -1/2 and cuts the y-axis at 4
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] and c = 4, thus
y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
A circle has a diameter of 7.6feet. Which measurement is the closest to the circumference of the circle in feet.
Answer:
23.9
Step-by-step explanation:
A circle has a diameter of 7.6 feet. Which measurement is closest to the circumference of the circle in feet?
TRUST ME
(4,0) reflected across x axis and y axis
Answer:
The x axis is horizontal (sideways) while the y axis is vertical (up and down)
Step-by-step explanation:
Jeff has ten packages that he wants to mail. Nun identical packages weigh 2 7/8 pounds each. A tenth package weighs two times as much of one the nine packages. How many ponds do all packages weigh?
Answer:31.625
2 7/8 8 times 9 =25.875 +(2.875 times 2) =31.625
A bag holds 11 beads. 7 are red, the rest are white. Two beads are taken at random from the bag. What is the probability that one bead of each colour is taken? You must show your working
Final answer:
To determine the probability of drawing one red bead and one white bead from a bag, calculate the probability of each sequence (red then white, white then red) occurring and add them together. The result is that the probability that one bead of each color is taken is 4/11.
Explanation:
To find the probability that one red bead and one white bead are taken from a bag containing 7 red beads and 4 white beads (11 beads in total), we follow these steps:
Calculate the probability of drawing one red bead first and then one white bead.
Calculate the probability of drawing one white bead first and then one red bead.
Add the probabilities from step 1 and 2 together to find the total probability of drawing one bead of each color.
The probability of drawing one red bead first is 7/11 since there are 7 red beads out of 11 total beads.
After drawing a red bead, there are now 10 beads left in the bag, with 4 being white. So, the probability of drawing one white bead next is 4/10.
Multiplying these two probabilities gives us the probability of this particular sequence occurring: (7/11) * (4/10) = 28/110, which reduces to 2/11 when simplified.
We do a similar calculation for the reverse sequence, where a white bead is drawn first followed by a red bead. The probability for the first white bead is 4/11, and for the red bead after that, it's 7/10 since one white bead is already taken.
Multiplying these probabilities gives us: (4/11) * (7/10) = 28/110, which also simplifies to 2/11.
Finally, to find the total probability we add the probabilities of both sequences together: 2/11 + 2/11 = 4/11.
So, the probability that one bead of each color is taken is 4/11.
Which expression is equivalent to -2(3a + 6b) + (4a - 2b)?
A) -2(a + 7b)
B) -2(a - 7b)
C) 2(a + 7b)
D) 2(a - 7b)
Answer:
Option A) -2(a+7b) is correct
Therefore -2(3a+6b)+(4a-2b)=-2(a+7b)
The equivalent expression to the given expression is -2(a+7b)
Step-by-step explanation:
Given expression is -2(3a+6b)+(4a-2b)
To find the equivalent expression to the given expression :
-2(3a+6b)+(4a-2b)
=-2(3a)-2(6b)+4a-2b ( apply the distributive property a(x+y)=ax+ay )
=-6a-12b+4a-2b
=-2a-14b ( adding the like terms )
=-2(a+7b) ( taking common term -2 outside )
Therefore -2(3a+6b)+(4a-2b)=-2(a+7b)
The equivalent expression to the given expression is -2(a+7b)
Therefore option A) -2(a+7b) is correct
so the right option is A.
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9. Martika says factors and multiples are
related. Use the equation 6 X 7 = 42
to describe the relationship between
factors and multiples.
BBOUD SOTTO
Answer:
So the factors and multiples of 42 are 1, 2, 3, 6, 7, 14, 21, 42
Step-by-step explanation:
Factors are what you can multiply to get a number and a multiples are what you get after multiplication. We can determine the factors of 42. The multiples of 42 are:
[tex]1 x 42= 42[/tex]
[tex]2 x 21= 42[/tex]
[tex]3x 14 = 42[/tex]
[tex]6 x 7 = 42[/tex]
So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The multiples of 42 are 1,2,3,4,5,6 etc
So common multiples and factors are 1, 2, 3, 6, 7, 14, 21, 42
In the equation 6 X 7 = 42, 6 and 7 are factors and 42 is the multiple. Factors are numbers that can be exactly multiplied to get another number, while a multiple is a number that can be divided evenly by another number. Hence, the relationship between factors and multiples is inherently interconnected.
Explanation:In the equation 6 X 7 = 42, 6 and 7 are the factors, and 42 is the multiple. Factors are numbers you can exactly multiply together to get a another number, in this case 6 and 7 are factors of 42 because when multiplied together, they equal 42. On the other hand, a multiple is a number that can be divided by another number without leaving a remainder, so 42 can be evenly divided by 6 or 7, making it a multiple of those numbers. The relationship between factors and multiples can be seen as two sides of the same coin - factors are what you multiply together to get a multiple.
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if a car is 200 inches long, and the truck is 75% longer, how long is the truck
A turboprop plane flying with the wind flew 400 mi in 4 h. Flying against the wind, the plane required 5 h to travel the same distance. Find the rate of the plane in calm air and the rate of the wind.
Answer:
Rate of the plane in calm air is 90 miles/hr and rate of the wind of wind is 10 miles/hr
Step-by-step explanation:
Average speed of plane in with wind = 400 /4 = 100 miles/hr
Average speed of plane against wind = 400/5 = 80 miles/hr
Consider the speed of plane in wind be x miles/hr and speed of plane against wind be y miles/hr
As such speed of plane in wind would be x + y miles/hr and speed of plane against wind would be x - y miles/hr . i.e
x+y = 100
x-y = 80
by solving these two equation, we get
2x=180
x= 90 miles/hr
y=100-90
y= 10 miles/hr
hence, Rate of the plane in calm air is 90 miles/hr and rate of the wind of wind is 10 miles/hr
What would be 49.38 rounded to tenthes
Answer:
49.4
Step-by-step explanation:
Round up, since the 8 [tex]\geq[/tex] 5
A math teacher graded 45 problems in 3/5 of an hour. At that rate, how many problems can she grade in one hour
Answer:
75
Step-by-step explanation:
45*1/3=15
15*5=75
Answer: 75 problems
Step-by-step explanation:
3/5 of an hour is the same as 3/5 x one hour.
one hour is the same as 60 minutes , this means that 3/5 of an hour is the same as :
3/5 x 60 = 36 minutes
This means that , the teacher graded 45 problems in 36 minutes. then in 1 minutes ;
The teacher will grade 45/36 problems
so in 60 minutes ;
the teacher will grade 45/36 x 60 = 75 problems
Consider the function f(x)=√2x−6. If f−1(x) is the inverse function of f(x), find f−1(−4).
To find the inverse function f−1(x) for f(x)=√(2x−6), we first express f(x) as y, swap x and y, remove the square root by squaring both sides, solve for y, and substitute -4 into the new expression. This calculation reveals that f−1(-4) is 11.
Explanation:To find the value of f−1(-4) for the function f(x)=√(2x−6), we need to find the value of x such that f(x) equals -4. Here is how to find the inverse function:
First, replace f(x) with y: y = √(2x−6).Next, swap x and y to begin finding the inverse: x = √(2y−6).Square both sides to eliminate the square root: x² = 2y − 6.Rearrange the equation to solve for y: 2y = x² + 6.Divide both sides by 2: y = (x² + 6)/2.This new y is actually f−1(x), the inverse function.To find f−1(-4), substitute -4 into the inverse function:
y = ((-4)² + 6)/2
y = (16 + 6)/2
y = 22/2
y = 11
Therefore, f−1(-4) = 11.
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To find f−1(−4) for the function f(x) = √(2x − 6), solve for x in terms of y, square both sides, solve for x, and then substitute the value to find that f−1(−4) equals 11.
To find the value of f−1(−4) for the function f(x) = √(2x − 6), follow these steps:
Solve for x in terms of y by setting y = f(x):
y = √(2x − 6)
Square both sides to eliminate the square root:
y2 = 2x − 6
Solve for x:
x = (y2 + 6) / 2
Replace y with x to get f−1(x):
f−1(x) = (x2 + 6) / 2
Now, find f−1(−4):
f−1(−4) = (−42 + 6) / 2 = (16 + 6) / 2 = 22 / 2 = 11
Thus, the value of f−1(−4) is 11.
I NEED THE ANSWER ASAP PLEASE
Is a 24 square centimeter rectangle larger than a 24 square inch rectangle?
Answer:
No, a 24 square centimeter rectangle is smaller than a 24 square inch rectangle
Step-by-step explanation:
we know that
[tex]1\ in=2.54\ cm[/tex]
so
Convert in^2 to cm^2
[tex]24\ in^2=24(2.54)^2=154.8\ cm^2[/tex]
so
[tex]24\ cm^2 < 154.8\ cm^2[/tex]
therefore
[tex]24\ cm^2 < 24\ in^2[/tex]
A 24 square inch rectangle is larger than a 24 square centimeter rectangle due to unit conversion.
No, a 24 square inch rectangle is larger than a 24 square centimeter rectangle.
To compare rectangles of different units, we need to convert the units to the same measurement. Since 1 inch is equal to 2.54 centimeters, a square inch is larger than a square centimeter.
Therefore, a 24 square inch rectangle has a greater area than a 24 square centimeter rectangle.
3(-3a-1) what is the answer if you answer it correct you get 10 points
Answer: the best answer is 3(-3a-1)
Step-by-step explanation:
If side A is twice as long as B and C is 25 using the Pythagorean Theorem,What are the lengths of side A and B? Round to the nearest tenth if necessary
Answer:
The lengths of side A is 22.4 and B is 11.9.
Step-by-step explanation:
Given:
If side A is twice as long as B and C is 25 using the Pythagorean Theorem.
Now, to find the lengths of side A and B.
Let the side B be [tex]x.[/tex]
So, the side A be [tex]2x.[/tex]
Side C = 25.
Now, to solve by using Pythagorean Theorem:
A² + B² = C²
[tex](2x)^2+(x)^2=(25)^2[/tex]
[tex]4x^2+x^2=625[/tex]
[tex]5x^2=625[/tex]
Dividing both sides by 5 we get:
[tex]x^2=125[/tex]
Using square root on both sides we get:
[tex]x=11.18.[/tex]
B rounding to the nearest tenth = 11.9.
Now, to get A by substituting the value of [tex]x[/tex]:
[tex]2x\\=2\times 11.18\\=22.36.[/tex]
A rounding to the nearest tenth = 22.4.
Therefore, the lengths of side A is 22.4 and B is 11.9.
the equivalent fraction of 2/4
Answer:
1/2
Step-by-step explanation:
u could simplify it to 1/2 pls give brainliest answer
Answer: 1/2 and if you mean multiplying 4/8 because 2 ÷ 2 = 1 and 4 ÷ 2 = 2, and if you mean multiplying 2 • 2 = 4 and 4 • 2 = 8 so those are two answers.
Four research teams each used a different method to collect data on how
fast a new brand of paint dries. Assume that they all agree on the sample size
and the sample mean (in minutes). Use the confidence level; confidence
interval) pairs below to select the team that has the smallest sample
standard deviation.
O
A. Confidence Level: 99.7%; Confidence Interval: 42 to 48
B. Confidence Level: 95%; Confidence Interval: 40 to 50
O
C. Confidence Level: 95%; Confidence Interval: 35 to 55
D. Confidence Level: 68%; Confidence Interval: 44.5 to 45.5
Answer:
Option D.
Step-by-step explanation:
Recall that the wider the confidence interval, the greater the variability.
In other words, wider confidence interval will have bigger sample standard deviation.
For option A, the width is |48-42|=6
For option B, the width is |50-40|=10
For option C, the width is |55-35|=20
For option D, the width is |45.5-44.5|=1
Therefore the team in option D has the smallest sample standard deviation.
As for the confidence level, it is just telling us the extent to which we confidence that, the parameter is within the interval
Answer: D
Step-by-step explanation:
Where would you put 2 1/8th on a number line?
Answer:
See diagram and explanation
Step-by-step explanation:
A number on the right is greater than a number on the left on the number line.
Mark numbers 2 and 3 on number line (number 3 is to the right from number 2, because 3 > 2).
Divide the unit segment between numbers 2 and 3 into 8 equal parts (this segment is the unit segment because the distance between 3 and 2 is 1).
Each such part represents [tex]\frac{1}{8}[/tex] of the segment.
Mark the number [tex]2\dfrac{1}{8}[/tex] next to the right from 2 (you have to take 2 and 1/8).
Select the correct answer.
The temperature on Saturday was 2°C. On Sunday, it became 4°C colder. What was the temperature on Sunday?
7O
Answer:
6C
Step-by-step explanation:
Final answer:
By subtracting the 4°C decrease from the initial temperature of 2°C, it is determined that the temperature on Sunday was -2°C.
Explanation:
The question involves a basic mathematics operation related to temperature changes. The temperature on Saturday was 2°C, and on Sunday, it became 4°C colder. To find the temperature on Sunday, you simply need to subtract 4°C from Saturday's temperature:
Saturday's temperature: 2°C
Temperature decrease: 4°C
Sunday's temperature: 2°C - 4°C = -2°C
Thus, the temperature on Sunday was -2°C.
28v^3+16v^2-21v-12 factor by group please
Step-by-step explanation:
The given equation:
[tex]28v^3+16v^2-21v-12[/tex]
To find, the factors of [tex]28v^3+16v^2-21v-12[/tex] = ?
∴ [tex]28v^3+16v^2-21v-12[/tex]
[tex]=(4\times 7)v^3+(4\times 4)v^2-(3\times 7)v-(3\times 4)[/tex]
= [tex]4v^2(7v+4)-3(7v+4)[/tex]
= [tex](7v+4)(4v^2-3)[/tex]
= [tex](7v+4)[(2v)^2-\sqrt{3}^2][/tex]
Using the algebraic identity,
[tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]
= [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex]
∴ The factor of [tex]28v^3+16v^2-21v-12[/tex] = [tex](7v+4)(2v+\sqrt{3})(2v+\sqrt{3})[/tex] or [tex](7v+4)(4v^2-3)[/tex]
Factor the expression. 36y2 – 84y – 147
(2y + 7)(6y – 7)
3(2y + 7)(6y + 7)
3(2y – 7)(6y + 7)
(2y – 7)(18y + 21)
Answer:
1) 3 (6y+7) (2y−7)
2) 12y2+28y−49
3) 36y2+168y+147
4) 36y2−84y−147
5) 3(6y+7)(2y−7)
Solve the following system of equations graphically.
x = -5
y = -6
What is the solution set?
Ø
{(-5, -6)}
{(-6, -5)}
Answer: The right answer is [{-5,-6]}
Explanation: I got it right on my test
Answer:
[{-5,-6]}
Step-by-step explanation:
A cone has a height of 7 ft and a radius of 4 ft. Which equation can find the volume of the cone?
V = one-third pi (7 squared) (4) feet cubed
V = one-third pi (4 squared) (7) feet cubed
V = 3 pi (7 squared) (4) feet cubed
V = 3 pi (4 squared) (7) feet cubed
Answer:
V = one-third pi (4 squared) (7) feet cubed
Step-by-step explanation:
Volume of cone v = 1/3×π(r²h)
r = 4 and h = 7
V = 1/3 × π(4²×7)
Answer:
B
Step-by-step explanation:
the altimeter in a plane
Anna departs from the city A with coordinates (1, 1) towards city B with coordinates (9, 11). At the same time, Mary departs from city B towards city A. Find the coordinates of point C, where Anna and Mary meet, if the ratio of Anna to Mary's rates is 3:5 respsectivley
Answer:
C = (4, 4.75)
Step-by-step explanation:
Point C will divide segment AB into the ratio 3:5, matching the respective rates of travel. Then the location of point C can be found from ...
C = (5A +3B)/(3+5)
C = (5(1, 1) +3(9, 11))/8 = (5 +27, 5 +33)/8 = (4, 4.75)
The point where Anna and Mary meet is (4, 4.75).
Answer:
4, 4.75
Step-by-step explanation:
find the greatest common factor of 3y^2 -4y
Answer:
y.
Step-by-step explanation:
y is common to both terms so the GCF is y.
Factoring we get:
y(3y - 4).
Answer:
Step-by-step explanation:
3y^2 = 3 * y *y
4 y = 4 * y
GCF = y
3y^2 -4y = y*(3y - 4)
Which best describes the range of the function f(x) = 2(one-fourth) Superscript x after it has been reflected over the y-axis?
all real numbers
all real numbers less than 0
all real numbers greater than 0
all real numbers less than or equal to 0
"All real numbers greater than 0" best describes the range of the function after it has been reflected over the y-axis ⇒ 3rd answer
Step-by-step explanation:
The form of the exponential function is [tex]f(x)=a(b)^{x}[/tex], where
a is the initial value (value f(x) at x = 0)b is the growth/decay factorThe domain of the function is {x : x ∈ R} (all real numbers)The range of the function is {y : y > 0} (all positive real numbers)∵ [tex]f(x)=2(\frac{1}{4})^{x}[/tex]
- Compare it with the form above
∴ a = 2 ⇒ initial value
∴ b = [tex]\frac{1}{4}[/tex] ⇒ decay factor because its between 0 and 1
∵ The domain of the function is the values of x
∴ The domain of the function is {x : x ∈ R} ⇒ all real numbers
∵ The range of the function is values of y
∴ The range of the function is {y : y > 0}
∵ Reflection over the y-axis change the sign of x
∴ The image of f(x) is [tex]y=2(\frac{1}{4})^{-x}[/tex]
- That means, all x-coordinates of the points on the graph
opposite in signs, but that does not effect the domain
because the domain is all real numbers
∵ There is no change of the sign of y
- That means reflection over y-axis does not effect the range
∴ The range of the function after reflection is the same as the
range of f(x)
∴ The range of the image of f(x) is {y : y > 0}
"All real numbers greater than 0" best describes the range of the function after it has been reflected over the y-axis
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Answer:
C
Step-by-step explanation:
edge 2020