Answer:
0.46 repeating 6
Step-by-step explanation:
plug it into a calculator
Divide 13 by v. Then, subtract 7.
Which of the following expressions matches the statement above?
A. 13 ÷ (v - 7)
B. 13 ÷ (7 - v)
C. 13 ÷ v - 7
D. v ÷ 13 - 7
Solve for x. Round your answer to the nearest hundredth.
13.48x − 200 < 256.12
Answer:
x<33.84
Step-by-step explanation:
13.48x - 200 < 256.12
13.48x - 200 + 200 < 256.12 + 200
13.48x < 456.12
13.48x / 13.48 < 456.12 / 13.48
x < 33.84
Answer:
b
Step-by-step explanation:
Hello there. May somebody help me simplify this problem? It would be very kind.
It is about radicals etc.
Answer:
27 / (4x⁶y⁸)
Step-by-step explanation:
[tex]\frac{4(3x^{2}y^{4})^{3}}{(2x^{3}y^{5})^{4}}[/tex]
When raised to a power, multiply the exponents.
[tex]\frac{4(3^{3}x^{6}y^{12})}{2^{4}x^{12}y^{20}} \\\\\frac{2^{2}3^{3}x^{6}y^{12}}{2^{4}x^{12}y^{20}}[/tex]
When dividing, subtract the exponents.
[tex]2^{2-4}3^{3}x^{6-12}y^{12-20}\\2^{-2}3^{3}x^{-6}y^{-8}[/tex]
Move negative exponents to the denominator.
[tex]\frac{3^{3}}{2^{2}x^{6}y^{8}}\\\frac{27}{4x^{6}y^{8}}[/tex]
Which statements are true about the graph of
y< 2x + 1? Check all that apply.
Graph: y < }x+1
The slope of the line is 1.
The line is solid.
The area below the line is shaded.
A solution to the inequality is (2.3).
The x-intercept of the boundary line is (-3.0).
Draw
Click or tap the graph to plot a point
Answer:
The area below the line is shaded.
Step-by-step explanation:
Using the zero-interval test [test point (0, 0)], we plug in 0 for both y and x to determine whether we shade below the line [the portion that DOES contain the origin] or above the line [the portion that does not contain the origin]. This is where me must verify the inequality as false or true:
[tex]\displaystyle 0 < 2[0] + 1 → 0 < 1[/tex]
This is a genuine statement, therefore we shade below the line.
I am joyous to assist you anytime.
kathryn bought an aquarium to replace her fishbowl.The directions for the aquarium say that it should be filled with 9 cubic feet of water. If the aquarium is 2 feet wide and 3 feet long, how high should the water fill the aquarium
The water should fill the aquarium to 1.5 feet
Solution:
Given that the directions for the aquarium say that it should be filled with 9 cubic feet of water.
This means volume of aquarium is 9 cubic feet
Given that aquarium is 2 feet wide and 3 feet long
To find: Height of aquarium
Since a aquarium is in shape of cuboid, we can use the volume of cuboid formula
The volume of cuboid is given as:
volume of cuboid = [tex]l \times w \times h[/tex]
Where "l" is the length
w is the width
"h" is the height
Substituting the values, we get,
[tex]9 = 3 \times 2 \times h\\\\9 = 6 \times h\\\\h = \frac{9}{6} = 1.5[/tex]
Thus the height of aquarium is 1.5 feet
Definition: This is the process of cell reproduction where cell splits into two daughter cells. Example: Mitosis
Answer:
Cell division
Step-by-step explanation:
During the process where the cell splits, it’s going through a process of cell division where the cell divides into two
Which expression is equivalent to the given expression? 2(3a+2b−7)
A 5a+4b−5
B 6a+2b−7
C 6a+4b−7
D 6a+4b−14
The expression which is equivalent to the given expression; 2(3a+2b−7) is; 6a +4b -14
Equivalent expressionsThe given expression is;
2(3a+2b−7)Upon expansion by multiplying all elements in the parenthesis by 2; we have;
2(3a+2b−7) = 6a +4b -14Read more on equivalent expressions;
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Final answer:
By distributing the 2 across each term in the expression 2(3a+2b-7), the equivalent expression is 6a + 4b - 14, which corresponds to answer choice D.
Explanation:
To determine which expression is equivalent to 2(3a+2b-7), we need to distribute the 2 across each term in the parentheses. This means we'll multiply 2 by 3a, 2b, and -7 separately. Here's the step-by-step distribution:
2 × 3a = 6a2 × 2b = 4b2 × -7 = -14Combining these results, we get the equivalent expression: 6a + 4b - 14, which matches answer choice D.
Plz help, It’s kinda easy I’m just kinda dumb ig :( 25+ points
Answer:
Let x = (the height of the fourth plant)
Then the average of the four heights will be:
(70+71+72+x)/4
Simplify it to (213+x)/4
This average has to be at least 73 inches. Meaning, it has to be greater than or equal to 73.
(I don't have the sign for greater/equal so I'll type >=)
(213+x)/4 >= 73
This is the inequality. Just solve for x, and you have the answer.
(213+x) >= 292
x >= 79
Another way: (I think it's easier to do it like this in my head)
You need average 73.
Look at the heights of the plants you have now: how far are they from 73?
The first is 3 less, the second is 2 less, and the third is 1 less.
The 'total deficit'' is 6.
So to make the average be 73, you need to cancel out the deficit by making an equal overage (by 6).
If you can only add one more plant... that plant has to be 6 inches higher than the average you want. So 73+6=79.
Step-by-step explanation:
Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below.
Male Female
16,051 24,017
26,378 12,962
1440 17,644
7875 17,399
18,237 12,486
15,728 16,581
14,306 16,533
26,823 18,967
a. Use a 0.05 significance level to test the claim that among couples, males speak fewer words in a day than females.
In this example, mu Subscript d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesis test?
The test statistic is -0.35
The P-value is 0.369
What is the conclusion based on the hypothesis test?
We are testing the claim that males speak fewer words than females. With a p-value of 0.369, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, no significant evidence supports the claim that males speak fewer words than females.
Explanation:The objective here is to test the claim that on average, males speak fewer words in a day than females. To do this, we compare two means using a hypothesis test for paired data.
The null hypothesis (H0) is that there is no difference between the mean number of words spoken by males and females. The alternative hypothesis (Ha) is that the mean number of words spoken by males is less than that spoken by females.
Since the p-value (0.369) is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means we do not have significant evidence to support the claim that males speak fewer words than females.
A key takeaway from this is that the test statistic and p-value are critical elements in hypothesis testing. They determine whether or not you have significant evidence to reject the null hypothesis.
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need help solving this
Answer:
p( <18 years old) =[tex]\frac{72162}{330623}=0.2183=21.83\%[/tex]. Here you evaluate the probability of finding people who are less than 18 years old, by comparing the amount of people who are less than 18 years old (72162), with to the total amount of people in the sample (330623).p( <18 years old /no health insurance)= [tex]\frac{7663}{46340} =0.1654=16.54\%[/tex]. This means that assuming that people does not have insurance (this happens in 46340 cases), in 7663 of this cases, besides not having insurances, the persons are lessthan 18 years old.This events are not independent, because the condition that should hold to obtain independece is that P(<18 years old/ no health insurance)= P(<18 years old), which would mean that, knowing that a person has not health insurance should not add any information to the main fact: that the person's age is below 18. If the equality does not hold, then, knowing that the person has not health insurance helps knowing about the age of the person.Abigail bought 15 chicken wings for $18. What was the cost of the wings in wings per dollar?
Answer:
$1.20 per chicken wing
Step-by-step explanation:
15 chicken wings = $18
1 chicken wing = $18/15 = $6/5 = $1.20
A cylindrical well has a radius of 10 feet and a height of 15 feet. What volume of water will it take to fill in the well?
Answer:
4712.39(2 decimal place)
Step-by-step explanation:
Volume of cylinder is πr^2(h)
π10^2(15):
is 4712.39(2dp)
Answer:
1500π
Step-by-step explanation:
The volume of water is just the normal volume so,
the volume of a cylinder is πr²h
where π is pi, as in 3.14 ..., r is the radius, and h is the height.
Using what was given to us, we can plug this into the formula
so, π ×10² ×15 = 100π×15 = 1500π
Given the equation f(x) = 2x² + 4x - 1, what is axis of symmetry? a. 1 c. -1 b. 2 d. 0
Answer: x=-1
Step-by-step explanation:
the x value of the vertex = -b/2a if the equation is in "ax^2+bx+c" for
you are in luck
x value of the vertex = -4/4 = -1
the line of symmetry is a vertical line, and since it must pass through the vertex
line of symmetry: x=-1
8 lb 1 oz − 3 lb 6 oz
Answer:
4.6875 is the answer
Step-by-step explanation:
First, lets put both into just ounces. (1lb = 16oz.)
8lb. 1oz. = 129oz.
3lb. 6oz. = 54oz.
Second, subtract.
129 - 54 = 75
Third, put into pounds and ounces.
75oz. = 4lb. 11oz.
_______
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a 13 ounce package of pistachios costs $5.99 find the unit rate
Answer:
about 0.46 cents per ounce
Step-by-step explanation:
5.99 divided by 13 gives you a long decimal and you round to 0.46
NFL quarterback Patrick mahomes threw a pass that clocked 62mph. How fast is this in yards per second?
Answer:
The speed of the pass that clocked is 30.31 yards per seconds
Step-by-step explanation:
Given as :
The speed of the pass = 62 miles per hour
Let The speed in yards per second = x yps
So, ∵ The speed = 62 miles per hour
Or, The speed = [tex]\dfrac{\textrm 62 miles}{\textrm 1 hour}[/tex]
or, The speed = [tex]\dfrac{\textrm 62 miles}{\textrm 3600 secons}[/tex]
∵ In 1 hour = 3600 seconds
So, The speed = 0.0172 miles per second
Now, Again
Since 1 mile = 1760 yards
So, 62 miles = 1760 × 62 = 109,120 yards
∴ The speed in yard per second = [tex]\dfrac{\textrm 109,120 yard}{\textrm 3600 seconds}[/tex]
I.e The speed in yards per second = 30.31 yards per seconds
Hence The speed of the pass that clocked is 30.31 yards per seconds Answer
Jackie has 6 skirts and 2 dresses. she has brown shoes and black shoes. if each choice is equally likely how much greater is the probability of her choosing a skirt and brown shoes than the probability of her choosing a dress and black shoes?
Answer:
1/2
Step-by-step explanation:
both have equal chances
The required probabilities are 3/8 and 1/8 respectively.
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: Jackie has 6 skirts and 2 dresses.
Total number of dresses=8
Thus the probability of picking a skirt is = 6/8
=3/4
And the probability of picking a dress is =2/8
=1/4
Also, the probability of choosing either shoe is 1/2
Therefore the conditional probability that she chooses a skirt and brown shoes is = 3/4×1/2
=3/8
Similarly Probability( dress+black shoes)=1/4×1/2
=1/8
Hence, The required probabilities are 3/8 and 1/8 respectively.
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What is the length of segment A.B.
Answer:
The distance between A and B is l(AB) = 13 units
Step-by-step explanation:
Given:
let,
A ≡ ( x1, y1 ) ≡ ( 0, 12 )
B ≡ ( x2, y2 ) ≡ ( 5, 0 )
To Find:
Length AB = ?
Solution:
Distance Formula for the distance between the two points ( x1, y1 ) and ( x2, y2 ) we have,
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
On substituting the above values we will get,
[tex]l(AB) = \sqrt{((5-0)^{2}+(0-12)^{2} )}\\l(AB)=\sqrt{(5^{2} +(-12)^{2} } \\l(AB)=\sqrt{(25+144)}\\ l(AB)=\sqrt{169} \\l(AB)=13\ unit[/tex]
Therefore the distance between A and B is l(AB) = 13 units
9. Alicia Martin's savings account has a principle of $1,200. It earns 6% interest compounded quartly
for two quarters
10. Aubrey Daniel's savings account has a principle of $5,725. It earns 4% interest compounded
quarterly for 3 years.
11. The principle of Angelo Carrera's savings account is $9,855. It earns 6% interest compounded
quarterly for 2 quarters.
12. Milo Simpson deposited $860 in a new regular savings account that's earns 5.5% interest
compounded semiannually for 1 year,
13. Jana Lacey deposits $4,860in a new credit union savings account on the first day of the quarter.
The principle earns 4% interest compounded quarterly for 6 months.
Answer:
[tex]9) \$1236.27\,10)\,\$6451.07\, 11)\,\$10,152.87 \,12)\,\$907.95 \,13)\,\$4957.69[/tex]
Step-by-step explanation:
9) Since Alicia Martin's savings earns 6% quarterly for two quarters then:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] ⇒ Amount (A), Principle (P), rate (r) in decimal form, number of compoundings (n) a year and t, in year or its fractions.
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=1200(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A=\$1236.27[/tex]
10) Aubrey Daniel's case:
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=5725(1+\frac{0.04}{4})^{4*3}\Rightarrow A\approx \$6451.07[/tex]
11) As for Angelo, similarly to Alicia.
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=9855(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$10,152.87[/tex]
12) Simpson's. For semiannual n=2
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=860(1+\frac{0.055}{2})^{2*1}\Rightarrow A\approx \$907.95[/tex]
13) Jana Lacey amount:
[tex]A=P(1+\frac{r}{n})^{nt}\Rightarrow A=4860(1+\frac{0.04}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$4957.69[/tex]
Which of the following is something that will not affect your homeowners insurance premium?
a. the age of the home
b. the size of the home
c. the color of the home
d. the location of the home
Please select the best answer from the choices provided
Answer:
c. the color of the homeStep-by-step explanation:
Option C is the most reasonable answer, because there's no way that the color of the house affects the homeowners insurance premium.
A homeowners insurance premium refers to a monthly or annual payment to an insurance company which maintain the house and stuff insured. This amount can be variate depending on the size, location and age of the home, but not depends on the color of it.
The forestry service personnel at a national forest are estimating the average height of the trees in the forest. They measure the heights of 31 trees and prepare the histogram above. What percentage of the trees are less than 75 feet tall?
A. 45.2
B. 80.6
C. 19.4
D. 77.4
Answer:
The correct answer is A. 45.2
Step-by-step explanation:
1. Let's review all the information provided for solving this question:
Number of trees of the sample = 31
Number of trees of the sample with a height between 60 and 65 feet tall height = 3
Number of trees of the sample with a height between 65 and 70 feet tall height = 3
Number of trees of the sample with a height between 70 and 75 feet tall height = 8
Number of trees of the sample with a height between 75 and 80 feet tall height = 10
Number of trees of the sample with a height between 80 and 85 feet tall height = 5
Number of trees of the sample with a height between 85 and 90 feet tall height = 2
2. Let's calculate the percentage of the trees that are less than 75 feet tall:
Percentage of the trees less than 75 feet tall = [(Number of trees of the sample with a height between 60 and 65 feet tall + Number of trees of the sample with a height between 65 and 70 feet tall + Number of trees of the sample with a height between 70 and 75 feet tall)/Number of the trees of the sample] * 100
Replacing with the real values, we have:
Percentage of the trees less than 75 feet tall = [(3 + 3 + 8)/31] * 100
Percentage of the trees less than 75 feet tall = [(14)/31] * 100
Percentage of the trees less than 75 feet tall = 0.451613 * 100
Percentage of the trees less than 75 feet tall = 45.1613% = 45.2% (Rounding to one decimal place)
The correct answer is A. 45.2
A business has two loans totaling $85,000. One loan has a rate of 4.5% and the other has a rate of 6%. This year, the business expects to pay $4,650 in interest on the two loans. How much is each loan?
Answer:
$30,000 and $55,000
Step-by-step explanation:
If 4.5% loan is x, and the 6% loan is y, then:
x + y = 85000
0.045x + 0.06y = 4650
Solve the system of equations with substitution or elimination. Using substitution:
0.045x + 0.06(85000 − x) = 4650
0.045x + 5100 − 0.06x = 4650
450 = 0.015x
x = 30000
y = 55000
Loan I = $ 30,000
Loan II = $ 55,000
Further Explanation
Total loan of $ 85,000
Loan I rate at 4.5%
Loan II rate at 6%
This year's loan repayments are $ 4,650
0.045 + 0.06 = 4,650
Loan II = $ 85,000 - Loan I
0.045 ($85,000-b)+0.06 b= 4,650
Loan II = $55,000
Loan I = $ 85,000 - Loan II
Loan I = $85,000 - $55,000
Loan I = $30,000
Loan I rate = $ 1,350
Loan II rate = $ 3,300
Total Loans rate (I + II) - Payments = ($ 1,350 + $ 3,300) - $ 4,650 = $ 0 (Remaining balance)
Loans are a type of debt that can involve all types of tangible objects, although usually more often are identified with monetary loans. Like other debt instruments, a loan requires a redistribution of financial assets over time between the borrower (indebted) and the debtor (the creditor).
The borrower initially receives an amount of money from the lender to be paid back, often in the form of periodic installments, to the lender. This service is usually provided with certain costs which are referred to as interest on the debt. Borrowers can also get restrictions in the form of loan conditions.
Before applying for a loan you should know how to calculate the percent interest on a loan to check the correctness of the interest calculation specified on your credit.
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Grade: High School
Subject: Mathematics
Keyword: loan, payment, borrowers
five friends will pay $9 per ticket, $3 per drink, and $6 per popcorn at the movies. write an expression that could be used to determine the cost for them to go to the movies
Final answer:
To calculate the total movie-going cost for five friends, multiply the cost of each item by five and sum them up. The total cost is represented by the expression [tex](5 \times\$9) + (5 \times\$3) + (5 \times\$6)[/tex], which simplifies to $90.
Explanation:
The question involves writing an expression to determine the cost for five friends to attend a movie considering the cost of tickets, drinks, and popcorn. To calculate the total cost for the group, we need to know the price per individual item and the quantity consumed. We know that each ticket costs $9, each drink costs $3, and each popcorn costs $6. Since there are five friends, we will multiply each of these costs by five to get the total cost per item for the group.
The expression for the total cost for the movie tickets is [tex]5\ tickets \ \times \$9/ticket[/tex], for drinks it's [tex]5\ drinks\ \times\$3/drink[/tex], and for popcorn, it's [tex]5\ popcorns \times\$6/popcorn[/tex]. To find the overall total, we add these expressions together:
Total Cost = [tex](5 \times\$9) + (5 \times\$3) + (5 \times\$6)[/tex]
The expression simplifies to:
Total Cost = ($45) + ($15) + ($30)
Therefore, the simplified expression for the total cost is:
Total Cost = $90
Need help plz very difficult
Answer:
D - 9x^(2)+2x-5
Step-by-step explanation:
In rhombus MOTH, angle HTM=(5x+6) degrees. If angle HMO=(12x-6)degrees, what is angle HMO?
Answer:
m∠HMO=102°
Step-by-step explanation:
we know that
In a Rhombus the diagonals bisect the angles and opposite angles are equal
In this problem
Angles HMO and HTO are opposite angles
m∠HMO=m∠HTO
m∠HTM=(1/2)m∠HMO ----> because the diagonals bisect the angles and opposite angles are congruent
substitute the values
[tex](5x+6)\°=(1/2)(12x-6)\°[/tex]
solve for x
[tex]10x+12=12x-6\\12x-10x=12+6\\2x=18\\x=9[/tex]
Find the measure of angle HMO
m∠HMO=(12x-6)°
substitute the value of x
m∠HMO=(12(9)-6)=102°
see the attached figure to better understand the problem
what is the solution to this equation 8x-5(x-3)=18
Answer:
x=1
Step-by-step explanation:
use distributive property for the negative 5, then simplify, then bring the 15 to the other side, then divide by 3. picture included.
Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an angle.
Answer:
[tex]\sin \theta=-\frac{4}{5}[/tex]
Step-by-step explanation:
Given:
Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).
So, the 'x' value is 3 and 'y' value id -4.
Using Pythagoras Theorem, we find the hypotenuse.
Hypotenuse = [tex]\sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]
Now, using the sine ratio for the angle, we have
[tex]\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}[/tex]
Therefore, the value of [tex]\sin \theta[/tex] is [tex]-\frac{4}{5}[/tex].
The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,
find the values of x and y that satisfy the equation.
-10x+12i=20+3yi
Answer:
x = -2
y = 4
Step-by-step explanation:
Given
[tex]-10x+12i=20+3yi[/tex]
Two complex numbers are equal when they have equal real and imaginary parts.
Equate real parts:
[tex]-10x=20\\ \\x=-\dfrac{20}{10}=-2[/tex]
Equate imaginary parts:
[tex]12=3y\\ \\y=\dfrac{12}{3}=4[/tex]
Final answer:
The values of x and y that satisfy the given complex equation are x = -2 and y = 4, found by equating the real and imaginary parts respectively.
Explanation:
To find the values of x and y that satisfy the equation -10x + 12i = 20 + 3yi, we need to equate the real parts and the imaginary parts of the complex numbers on both sides of the equation.
For the real parts, we have:
-10x = 20
=> x = -2
For the imaginary parts, we have:
12 = 3y
=> y = 4
So the solution for the equation is x = -2 and y = 4.
Which of the following expressions represents the statement below?
two times the sum of a number and 9
A. 9n + 2
B. 9(n + 2)
C. 2n + 9
D. 2(n + 9)
Option D. 2(n + 9) is the right answer
Step-by-step explanation:
The word problems are converted into mathematical problems to solve simply.
for the given problem
"two times the sum of a number and 9"
Let n be a number then
when there is and between two things they are performed first then next operation is performed so
the sum of a number and 9
[tex]n+9[/tex]
Then
two times the sum of a number and 9
[tex]2(n+9)[/tex]
Hence,
Option D. 2(n + 9) is the right answer
Keywords: Mathematical notation
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Final answer:
The correct expression is '2(n + 9),' which corresponds to choice D and represents two times the sum of a number and 9.
Explanation:
The expression that represents the statement 'two times the sum of a number and 9' is D. 2(n + 9). This is because you first need to find the sum of the number (let's call it n) and 9, which is represented as (n + 9). Then, the statement says 'two times' which means you need to multiply that sum by 2, resulting in 2 × (n + 9).
Biff is 25 years older than Hannah today. Four years from now,Biff will be 6 times as old as Hannah will be. How old is Hannah today? Use algebra to solve.
Hannah is 1 year old, and Biff is 26 years old today.
Let's denote Hannah's current age as H and Biff's current age as B.
According to the given information, we can set up two equations based on the provided conditions.
Biff is 25 years older than Hannah today:
B=H+25
Four years from now, Biff will be 6 times as old as Hannah will be:
B+4=6(H+4)
Now, we have a system of two equations with two variables.
We can substitute the expression for B from the first equation into the second equation:
(H+25)+4=6(H+4)
Combine like terms:
H+29=6H+24
Subtract H from both sides:
29=5H+24
Subtract 24 from both sides:
5H=5
Divide by 5:
H=1
So, Hannah is currently 1 year old. To find Biff's age, we can use the first equation:
B=H+25
B=1+25
B=26
Therefore, Hannah is 1 year old, and Biff is 26 years old today.