Answer:
Option D
Step-by-step explanation:
step 1
Account 1
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10\ years\\ P=\$6,000\\r=4.5\%=4.5/100=0.045[/tex]
substitute in the formula above
[tex]A=6,000(1+0.045*10)[/tex]
[tex]A=6,000(1.45)[/tex]
[tex]A=\$8,700[/tex]
step 2
Account 2
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$6,000\\ r=4\%=4/100=0.04\\n=1[/tex]
substitute in the formula above
[tex]A=6,000(1+\frac{0.04}{1})^{1*10}[/tex]
[tex]A=6,000(1.04)^{10}[/tex]
[tex]A=\$8,881.47[/tex]
step 3
Find the difference
[tex]\$8,881.47-\$8,700=\$181.47[/tex]
therefore
Susie should invest her money in Account 2 because the account will earn $181.47 more interest than Account 1 after 10 years
In a class, 8/9 of the students have blue eyes.
If 32 students have blue eyes, how many students are in the class in total?
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
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)
if a car is 200 inches long, and the truck is 75% longer, how long is the truck
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.
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
Oh the other side of the balance is 4 oz and another 4 oz and on the other side is 8 oz. <— To help you find out the answer. Please I’d like some help?
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.
Learn more about Factors and Multiples here:https://brainly.com/question/14410356
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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
What would be 49.38 rounded to tenthes
Answer:
49.4
Step-by-step explanation:
Round up, since the 8 [tex]\geq[/tex] 5
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.
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:
(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:
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
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.
Tickets to the garden show cost $6.75 for adults and $3.75 for children. By rounding to the nearest whole dollar, find an estimate of the cost for a family with 2 adults and 3 children to visit the garden show. A. $21 B. $23 C. $24 D. $26
Answer:
$26
Step-by-step explanation:
$6.75 - $7
$3.75 - $4
2 adults = 7x2= $14
3 children = 4x3= $12
$14 + $12 = $26
The answer is D. $26.
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.
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:
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 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
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
Learn more:
You can learn more about the reflection in brainly.com/question/4057490
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Answer:
C
Step-by-step explanation:
edge 2020
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).
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]
X3-8y3+27+18xy factorise
Answer:
this expression is not factorable
Step-by-step explanation:
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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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.
I NEED THE ANSWER ASAP PLEASE
the altimeter in a plane
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)