Final answer:
Mei is 9 years old, her mother is 36 years old, and her grandmother is 72 years old, determined by defining variables for their ages and solving the equation based on their age relationships and the given total sum of their ages.
Explanation:
To solve the problem regarding the ages of Mei, her mother, and her grandmother, we can use a system of equations based on the information given. Let's define Mei's age as m, her mother's age as 4m (since her mother is 4 times Mei's age), and her grandmother's age as 8m (since the grandmother is twice as old as Mei's mother).
According to the problem, the sum of their ages is 117 years:
m + 4m + 8m = 117
Simplifying this equation gives us:
13m = 117
Next, we divide both sides by 13 to find m:
m = 117 / 13
m = 9
Now that we have Mei's age, we can easily calculate her mother's and grandmother's ages:
Mei's mother: 4m = 4(9) = 36 years oldMei's grandmother: 8m = 8(9) = 72 years oldTherefore, Mei is 9 years old, her mother is 36 years old, and her grandmother is 72 years old.
Assume Triangle EFG equals triangle JKL
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply.
Answer:
A,B,E
Step-by-step explanation:
HAVE A GOOD DAY
The required expressions that represent the given conditions are x = 1/2y - 3 or 2x - y = -6 and y = 10[x - 1]. Options A, B, and E are correct.
Given that,
A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number.
The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
According to the question,
A smaller number is 3 less than half a larger number.
x = 1/2y - 3
or
2x -y = -6
The larger number is 10 times 1 less than the smaller number.
y = 10[x - 1]
Thus, the required expressions that represent the given conditions are x = 1/2y - 3 or 2x - y = -6 and y = 10[x - 1]. Options A, B, and E are correct.
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Factor
12x^5+6x^2-18
A) 6x^2(2x^3+x−3)
B) 12(x^5+6x^2−18)
C) 6(2x^5+x^2−3)
D) 6(2x^5+6x^2−18)
Peyton has 2 pizzas. Each pizza is cut into 10 equal slices. She and her friends eat 14 slices. What part of the pizzas did they eat?
70% part of the pizzas they ate.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, Peyton has 2 pizzas. Each pizza is cut into 10 equal slices.
Thus, total slices of pizza = 10 *2
total slices of pizza = 20
Since, She and her friends eat 14 slices.
Thus,
Percentage of pizza they eat = 14/20*100
Percentage of pizza they eat = 14*5
Percentage of pizza they eat = 70%
Therefore, Alex and her friends Eat 70% of the pizza.
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Please help me with questions 14 and 15
The equation of a circle whose center is at (4, 0) and radius is length 2√(3) is (x - 4)² + y² = 2√3 (x - 4)² + y² = 12 (x + 4)² + y² = 12
Answer:
Equation of the circle is
[tex](x-4)^2+y^2=12[/tex]
Step-by-step explanation:
We have been given that
center of the circle = (4,0)
Radius of the circle = [tex]2\sqrt3[/tex]
The standard form of a circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here, (h,k) is the center and r is the radius. Thus, we have
h = 4, k = 0, r = 2√(3)
Substituting these values in the above equation, we get
[tex](x-4)^2+(y-0)^2=(2\sqrt3)^2[/tex]
Simplifying, we get
[tex](x-4)^2+y^2=12[/tex]
Therefore, equation of the circle is
[tex](x-4)^2+y^2=12[/tex]
Devin borrowed $1,058 at 13 percent for nine months.
What will he pay in interest?
How much is his total payment?
What will be his monthly payment?
Answer:
A. [tex]I\approx \$103.16[/tex]
B. [tex]\text{Total payment}=\$1161.16[/tex]
C. [tex]\text{The monthly payment}\approx \$129.02[/tex]
Step-by-step explanation:
We have been given that Devin borrowed $1,058 at 13 percent for nine months.
A. To find the amount of interest paid by Devin we will use formula: [tex]I=Prt[/tex], where,
[tex]I=\text{Amount of interest}[/tex],
[tex]P=\text{Principal amount}[/tex],
[tex]r=\text{Interest rate in decimal form}[/tex],
[tex]t=\text{Time in years}[/tex].
Let us convert our given interest rate in decimal form and time in years.
[tex]13\%=\frac{13}{100}=0.13\\\text{9 months}=\frac{9}{12}\text{ year}=\frac{3}{4}=0.75\text{ year}[/tex]
Upon substituting our given values in interest formula we will get,
[tex]I=\$1058*0.13*0.75[/tex]
[tex]I=\$103.155\approx \$103.16[/tex]
Therefore, the amount of interest paid by $103.16.
B. Since total payment will be equal to interest rate plus amount of interest.
[tex]\text{Total payment}=\$1058+\$103.16[/tex]
[tex]\text{Total payment}=\$1161.16[/tex]
Therefore, Devin's total payment will be $1161.16.
C. To find the monthly payment we will divide total amount by 9.
[tex]\text{The monthly payment}=\frac{\$1161.16}{9}[/tex]
[tex]\text{The monthly payment}=\$129.01722\approx \$129.02[/tex]
Therefore, the amount of Devin's monthly payment is $129.02.
A bag contains 15 red candies, 20 blue candies, and 10yellow candies. What is the probability of drawing a red candy? A blue candy? Something besides a yellow candy?
The probability of drawing a red, blue, and a candy that is not yellow from the bag is 1/3, 4/9, and 7/9 respectively.
Explanation:The question involves the concept of probability in mathematics, with a scenario of drawing candies from a bag. The total number of candies in the bag is 45 (15 red + 20 blue + 10 yellow).
The probability of drawing a red candy is the number of red candies divided by the total number of candies, which is 15/45 or 1/3.
The probability of drawing a blue candy is the number of blue candies divided by the total number of candies, which is 20/45 or 4/9.
If we want to find the probability of drawing something other than a yellow candy, this is essentially the sum of the probabilities of drawing a red or blue candy. This is 35 out of 45 (15 red candies + 20 blue candies), which reduces to 7/9.
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Describe the relationship that must exist between a, b, and c in the equation ax^2+bx+c=0 in order for the equation to have exactly one solution
You build and sell toy cars $36 each. So far you have built 24 toy cars how many more toys cars will you have to build and sell to earn 1,620?
A graduated cylinder is filled with 36π of liquid. The liquid is poured into a different cylinder that has a radius of 3 cm. What will the height of the liquid be in the new cylinder?
Answer:
The height of the liquid in the new cylinder = 4 cm
Step-by-step explanation:
∵ The volume of the liquid = 36π cm³
∵ It poured into a cylinder that has radius 3 cm
∵ The volume of any cylinder = πr²h
∴ The volume of the liquid in the cylinder = π(3)²h = 9πh
- Where h is the height of the liquid inside the cylinder
∴ 9πh = 36π ⇒ divide both sides by π
∴ 9h = 36 ⇒ h = 36/9
∴ h = 4 cm
∴ The height of the liquid in the new cylinder = 4 cm
The height of the liquid in the new cylinder will be 4 cm. The term height is frequently used to describe someone's or something's height.
What is the height?Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.
From the given conditions;
The volume of the liquid is, [tex]\rm V_L=36 \pi \ cm^3[/tex]
The radius of the cylinder is,[tex]\rm r=3 cm[/tex]
The volume of the cylinder is found as;
[tex]\rm V= \pi r^2 h \\\\ \rm V= \pi (3)^2 h \\\\ \rm V=9\pi h[/tex]
The height of the liquid is in the new cylinder is found as;
The volume of cylinder = Volume of liquid
[tex]\rm 9 \pi h= 36 \pi \\\\ \rm h=\frac{36}{9} \\\\ h= 4 \ cm[/tex]
Hence the height of the liquid in the new cylinder will be 4 cm.
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What is the median of this set of data? 1, 2, 5, 6, 9 1 5 8 9
A box of 24 chocolate truffles cost $28.50 and individual truffle cost $1.50 how much do you save by purchasing a box of 24
The necklace charm shown has two parts, each shaped like a trapezoid with identical dimensions.
What is the total area, in square millimeters, of the charm?
Answer:
855mm
Step-by-step explanation:
The area of the trapezoid can be calculated through the equation,
A = (b₁ + b₂)h / 2
where b₁ and b₂ are the bases and h is the height. Substituting the known values from the given,
A = (25mm + 32mm)(15 mm) / 2
A = 427.5 mm²
Since there are two trapezoids in the necklace, the area calculated is to be multiplied by two to get the total area.
total area = (427.5 mm²)(2)
total area = 855 mm²
is 4 yards bigger than 13 feet
what is the explicit rule for the following sequence -10 - 12 -14 -16
which answer is a reasonable estimate to the following problem? 94.689
evaluate r s + 14s when r= 6 and s= 1/4
Kevin rented a truck for obe day. There was a base fee of $15.99, and there was an additional charge of 83 cents for each mile driven. Kevin had to pay $177.01 when he returned the trunk. For how many miles did ge drive the trunk?
What is the ninth term in the binomial expansion of (x – 2y)13? 329,472x5y8 –329,472x5y8 –41,184x8y5 41,184x8y5
Graph the following inequality. Then click until the correct graph appears.
x - y < 2
the correct graph is the dotted diagonal one ( 3rd picture)
Solve for y
y >x-2
Answer:
Third picture
Step-by-step explanation:
If you simplify the inequality, it is y > x - 2. Because of this, we can graph it as such.
The common denominator of 3/4 and 9/10
(I NEED THIS ANSWERED IMMEDIATELY. IT'S WORTH 15 POINTS!!!!!
Write a ratio the situation in three ways comparing the first quantity to the second quantity. A zoo has 14 monkeys and 18 chimpanzees.
A zoo has 14 monkeys and 18 chimpanzees.
To write the ratio of numbers x and y we use three ways given below
1. x to y
2. x : y
3. [tex] \frac{x}{y} [/tex]
Now write the ratio in three ways comparing 14 monkeys and 18 chimpanzees.
Let x be the number of monkeys
y be the number of chimpanzees
So ratio becomes
14 to 18
14 : 18
[tex] \frac{14}{18} [/tex]
Randall is going to the grocery store. It is 3 3/5 miles from his house. He walks 2 2/5 miles before it starts to rain. How far will he have to walk in the rain?
Solve for W!
W - 2.76 = 6.7
Describe two different sequences of transformations that will map ABCD to EFGH.
Answer:
The orientation of the figure has been changed by 90°, but the points are not all rotated around the same center. Translation is involved.
Translation before rotation:
.. translate down 5 units
.. rotate counterclockwise 90° about the origin
Translation after rotation:
.. rotate counterclockwise 90° about the origin
.. translate right 5 units
This can also be accomplished by a double reflection.
.. reflect across the line y=x
.. reflect across the line x=2.5
Or,
.. reflect across the line y=2.5
.. reflect across the line y=x
Step-by-step explanation:
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Tony is baking cakes and loaves of bread for a family reunion. His cake recipe uses 5 cups of flour for each cake, and his bread recipe uses 6 cups of flour for each loaf. He has 90 cups of flour on hand.
Let c represent the number of cakes and b represent the number of loaves of bread that Tony bakes.
Create an inequality that symbolizes this situation, and then answer the question below.
Can Tony bake 8 cakes and 9 loaves of bread without buying more flour?
Solve and graph question 5 help with this problem
A hacker is trying to guess someone's password. the hacker knows (somehow) that the password is 6 digits long, and that each digit cound be a number between 0 and 8. assume that the hacker makes random guesses. what is the probability that the hacker guesses the password on his first try? round to four decimal places.
The probability that the hacker guesses the password on his first try is 0
How to determine the probability?The password is given as:
Password = 6 digit long
The usable numbers are:
Digits = 0 to 8 i.e. 9 digits
If the digits can be repeated, then the number of passwords is:
Password = 9^6
Evaluate the exponent
Password = 531441
The probability that the hacker guesses the password on his first try is
P = 1/531441
Evaluate
P = 0.00000188167
Approximate
P = 0.0000
Hence, the probability that the hacker guesses the password on his first try is 0
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The probability of guessing the password on the first try is 0.000001881.
Explanation:To calculate the probability of guessing the password on the first try, we need to determine the number of possible passwords and divide it by the total number of possible guesses. In this case, the password is 6 digits long and each digit can be a number between 0 and 8.
So, there are 9 possible digits for each of the 6 positions, giving us a total of 9^6 = 531441 possible passwords.
The hacker makes random guesses, so there are 9^6 = 531441 possible guesses they can make.
The probability of guessing the password on the first try is therefore 1/531441 = 0.000001881, rounded to four decimal places.
The sum of two numbers is 46 and the difference is 14. What are the numbers?