Answer:
Step-by-step explanation:
6 flights from New York to Denver
7 flights from Denver to San Francisco.
total number of combination
6*7= 42
Final answer:
For a trip from New York to San Francisco via Denver, with six airlines on the first segment and seven on the second segment, there are 42 different pairs of airlines that can be chosen.
Explanation:
The question asks how many different pairs of airlines can be chosen for a trip from New York to San Francisco via Denver, considering one airline for the leg from New York to Denver and another airline for the continuation from Denver to San Francisco. Since there are six different airlines that fly from New York to Denver and seven that fly from Denver to San Francisco, the total number of combinations of airlines for both segments of the journey is a simple multiplication of the two separate choices. Therefore, the number of unique airline pairs is 6 airlines from New York to Denver multiplied by 7 airlines from Denver to San Francisco.
To calculate this, we use the formula for the number of combinations for two independent choices, which is:
Total combinations = (Choices for first segment) × (Choices for second segment)
Total combinations = 6 × 7 = 42 different pairs of airlines.
Thus, a traveler could choose from 42 different combinations of airlines for their trip from New York to San Francisco via Denver.
Match the square root with its perfect square: 1 . √4 1 2 . √144 2 3 . √9 3 4 . √121 4 5 . √64 5 6 . √169 6 7 . √100 7 8 . √25 8 9 . √1 9 10 . √36 10 11 . √81 11 12 . √16 12 13 . √49 13
Answer:
√1 1
√4 2
√9 3
√16 4
√25 5
√36 6
√49 7
√64 8
√81 9
√100 10
√121 11
√144 12
√169 13
Step-by-step explanation:
1. = 49
2. = 169
3. = 81
4. = 100
5. = 441
6. = 36
I just finished the assignment, trust me.
Which expression gives the area of the RED rectangle.
A
(A + B)(C + D)
B
(A + B)(C - D)
C
(A + B)(C + D) - C(A + B) - BD
D
(A + B)(C + D) - D(A + B) - BD
The expression which gives the area of the RED rectangle is (A+B)(C+D)-C(A+B)-BD. option C is correct.
The area of rectangle is obtained by multiplying the length and width.
The length of the rectangle is C+D
The width of the rectangle is A+B.
Now the complete area of rectangle :
Area = (A+B)(C+D)
Now to find area of rectangle which is red we have to subtract the red rectangle which are in blue:
The area of left side rectangle which is blue:
Area =C(A+B)
The area of rectangle below red rectangle:
Area =BD
So the area of red rectangle : (A+B)(C+D)-C(A+B)-BD.
Hence, option C is correct, the expression which gives the area of the RED rectangle is (A+B)(C+D)-C(A+B)-BD.
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Sketch the graph of the given function. Then state the function’s domain and range. f(x)= 1/2(5)^x+3
Answer:
Graph of the following function is attached with the answer.
Domain : ( - ∞ , + ∞ )
Range : ( 3 , + ∞ )
Step-by-step explanation:
[tex]f(x)=\frac{1}{2}x^{2}+3[/tex]
Domain of any quadratic equation is from negative infinity to positive infinity under no restrictions.
So, Domain : ( - ∞ , + ∞ )
The Range of any function can be calculated easily if there is just one term with variable. The method to find Range by that method is explained with the example as follows:
Range of x : ( - ∞ , + ∞ )Range of [tex]\textrm{x}^{2}[/tex] : [ 0 , + ∞ ) as every square number is more than or equal to zero.Range of [tex]\frac{1}{2}\textrm{x}^{2}[/tex] : [ 0 , + ∞ ) as 0/2 = 0 and ∞/2 = ∞.Range of [tex]\frac{1}{2}\textrm{x}^{2}+3[/tex] : [ 3 , + ∞ ) as 0 + 3 = 3 and ∞ + 3 = ∞.Therefore the Range of [tex]\mathbf{f(x)\boldsymbol=\frac{1}{2}x^{2}\boldsymbol+3}[/tex] is [ 3 , + ∞ )
(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.
(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.
(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.
[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.
{a,b} means only 'a' and 'b'.
{a,b] or (a,b} doesn't mean anything. )
A 20 kg sphere is at the origin and a 10 kg sphere is at x = 20 cm. At what position on the x-axis could you place a small mass such that the net gravitational force on it due to the spheres is zero?
Step-by-step explanation:
Let the small mass be m and position on x axis be y.
A 20 kg sphere is at the origin.
Distance to 20 kg mass = y
A 10 kg sphere is at x = 20 cm
Distance to 10 kg sphere = 20 - y
We have forces between them are equal
We have gravitational force
[tex]F=\frac{GMm}{r^2}[/tex]
Where G = 6.67 x 10⁻¹¹ N m²/kg²
M = Mass of body 1
M = Mass of body 2
r = Distance between them
Here we have
[tex]\frac{G\times 20\times m}{y^2}=\frac{G\times 10\times m}{(20-y)^2}\\\\800-80y+2y^2=y^2\\\\y^2-80y+800=0\\\\y=68.28cm\texttt{ or }y=11.72cm[/tex]
So the small mass should be placed at x = 11.72 cm or x = 68.28 cm
The positions on the x-axis obtained using quadratic equation such that net gravitational force is zero are 68.28 and 11.72 cm respectively.
Recall the force of universal gravitational attraction :
[tex] \frac{Gm_{1}m_{2}}{r^{2}}[/tex]Sphere 1 :
Mass = 20 kg Distance of 20kg sphere = dSphere 2 :
Mass = 10kgDistance of 10kg sphere = 20 - dGravitational force ; sphere 1 :
[tex] \frac{G \times 20 \times m_{2}}{d^{2}}[/tex] --(1)Gravitational force ; sphere 2 :
[tex] \frac{G \times 10 \times m_{2}}{(20 - d)^{2}}[/tex] - - (2)Equate (1) and (2)
[tex] \frac{G \times 20 \times m_{2}}{d^{2}} = \frac{G \times 10 \times m_{2}}{(20 - d)^{2}} [/tex]
[tex] 20(20 - d)^{2} = 10 \times d^{2} [tex]
20(400 - 40d + d²) = 10d²
8000 - 800d + 20d² = 10d²
10d² - 800d + 8000 = 0
Divide through by 10
d² - 80d + 800 = 0
Using a quadratic equation solver :
d = 68.28 cm or d = 11.72 cm
The possible positions are 68.28 cm and 11.72 cm
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The measures of one acute angle in a right triangle is four times the measure of the other acute
angle. Write and solve a system of equations to find the measures of the acute angles.
Help with this exercise
[tex]A_2[/tex] = 18°
[tex]A_3[/tex] = 4(18°) = 72°
Step-by-step explanation:Given:
One angle in the triangle is 90°One angle that isn't 90° is 4 times larger than another angle that isn't 90°Angles:
[tex]A_1[/tex] = 90°
[tex]A_2[/tex] = x
[tex]A_3[/tex] = 4x
Solution Pathway:
Under the rules for any triangle, a triangle's interior angles must add up to 180°. Using this, we can set up the equation:
sum of the interior angles = 180°90° + x + 4x = 180°Now let's solve for x.
90 +x + 4x = 18090 + 5x = 1805x = 90x = 18°Now that we know x is 18°, lets plug this value into the two unknown acute angles.
[tex]A_2[/tex] = 18°[tex]A_3[/tex] = 4(18°) = 72°Answer:
72 degrees and 18 degrees.
Step-by-step explanation:
If the 2 angles are x and y, we have the system:
x + y = 90 (as it is a right triangle)
x = 4y (given).
Substitute x =- 4y in the first equation:
4y + y = 90
5y = 90
y = 18.
So x + 18 = 90
x = 90 - 18
x = 72.
The function f(x) = 6x + 8 represents the distance run by a cheetah in miles. The function g(x) = x − 2 represents the time the cheetah ran in hours. Solve (f/g)(3), and interpret the answer.
a. 26; the cheetah's rate in miles per hour
b. 26; the number of cheetahs
c. 1/26 ; the cheetah's rate in miles per hour
d. 1/26 ; the number of cheetahs
Option a. 26; the cheetah's rate in miles per hour is the correct answer.
Step-by-step explanation:
Given
[tex]f(x) = 6x+8\\g(x) = x-2[/tex]
As the function f is in miles and function g is is hours, and we are dividing the function f by function g so the new unit will be:
miles/hour = miles per hour
Now
[tex]\frac{f}{g}(x)= \frac{f(x)}{g(x)}\\\frac{f}{g}(x) = \frac{6x+8}{x-2}[/tex]
We have to find (f/g)(3) so putting 3 in place of x
[tex]\frac{f}{g}(x) = \frac{6(3)+8}{-2}\\= \frac{18+8}{1}\\= 26[/tex]
Hence,
Option a. 26; the cheetah's rate in miles per hour is the correct answer.
Keywords: Functions, function operations
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A couple needs $55,000 as a down payment for a home. If they invest the $40,000 they have at 4% compounded quarterly, how long will it take for the money to grow to $55,000? (Round your answer to the nearest whole number.)
Answer:
8 years
Step-by-step explanation:
Compound interest formula
[tex]A(t)= A_0(1+\frac{r}{n})^{nt}[/tex]
A(t) is the final amount 55000
A_0= 40000, r= 4% = 0.04, for quarterly n=4
[tex]55000=40000(1+\frac{0.04}{4})^{4t}[/tex]
divide both sides by 40000
[tex]1375=(1+\frac{0.04}{4})^{4t}[/tex]
[tex]1375=(1.01)^{4t}[/tex]
Take ln on both sides
[tex]ln(1375)=4tln(1.01)[/tex]
divide both sides by ln(1.01)
[tex]\frac{ln 1375}{ln 1.01}=4t[/tex]
Divide both sides by 4
t=8.00108
So it takes 8 years
The couple will need to invest their $40,000 at an interest rate of 4% compounded quarterly for about 7 years in order to reach their target of $55,000.
Explanation:The subject of this question is compound interest. Compound interest is the interest computed on the initial principal as well as the accumulated interest from previous periods. Since the couple's money is being compounded quarterly, we will need to use this information in our calculations.
First, we must understand the compound interest formula which is:
A = P (1 + r/n)^(nt)
where,
A is the final amount of money after n years. P is the principal amount (initial amount of money). r is the annual interest rate in decimal form (so 4% would be 0.04). n is the number of times the interest is compounded per year. t is the time the money is invested for in years. In this case, we are trying to find 't' when A = $55,000, P = $40,000, r = 0.04 and n = 4 (since the interest is compounded quarterly). Doing the math, we get the answer as approximately 7 years.
£980 is divided between Caroline, Sarah & Gavyn so that Caroline gets twice as much as Sarah, and Sarah gets three times as much as Gavyn. How much does Sarah get?
Sarah has received £ 294
Solution:
Given that £980 is divided between Caroline, Sarah & Gavyn
Let "c" be the amount received by caroline
Let "s" be the amount received by sarah
Let "g" be the amount received by gavyn
Caroline gets twice as much as Sarah
amount received by caroline = twice as much as Sarah
amount received by caroline = 2(amount received by sarah)
c = 2s ---- eqn 1
Sarah gets three times as much as Gavyn
amount received by sarah = three times as much as Gavyn
amount received by sarah = 3(amount received by gavyn)
s = 3g ------- eqn 2
Given that total amount is 980
c + s + g = 980 --- eqn 3
Let us solve eqn 1, 2, 3 to get values of "c" "s" "g"
From eqn 2,
[tex]g = \frac{s}{3}[/tex] --- eqn 4
Substitute eqn 1 and eqn 4 in eqn 3
[tex]2s + s + \frac{s}{3} = 980\\\\\frac{6s + 3s + s}{3} = 980\\\\6s + 3s + s = 980 \times 3\\\\10s = 2940\\\\s = 294[/tex]
Thus sarah has received £ 294
Final answer:
To solve for the amount Sarah receives, set up ratios based on the information provided and solve the resulting equation. The total amount divided among them is £980, which when divided by the total parts (10) gives Gavyn's share as £98. Sarah's share is three times Gavyn's share, resulting in £294.
Explanation:
The problem described is a classic division in ratio mathematics question where £980 is being divided among Caroline, Sarah, and Gavyn following certain rules.
According to the problem, Caroline receives twice the amount that Sarah receives and Sarah receives triple the amount that Gavyn receives.
We can set up the following ratios: C = 2S and S = 3G, where C stands for Caroline's amount, S for Sarah's, and G for Gavyn's. If we denote Gavyn's amount as G, then Sarah's amount is 3G and Caroline's is 2 × 3G which is 6G.
To find the value of G, we can write the equation G + 3G + 6G = £980 or 10G = £980. Solving for G gives us G = £98.
Therefore, Sarah, receiving three times as much as Gavyn, gets 3 × £98 = £294.
The Davis family traveled 35 miles in 1/2 of an hour. If it is currently 2;00 pm and the family destination is 245 miles away at what time will they arrive there explain how you solved the problem
Answer:
5.30 PM
Step-by-step explanation:
time taken=(1/2)×(1/35)×245=7/2 hrs=3hrs 30 min.
so time =2+3.30=5.30 PM
Answer: 5:30pm
Step-by-step explanation:
Distance of family destination from the starting point = 245miles
Average speed = 35miles/1/2hour
Therefore 245 miles = 245/35 x 30mins.
7 x 30 = 210minutes.
Converted to hour by dividing by 60
210/60 = 3hours 30minutes.
Current local time at the point of commencement
Therefore, the arrival time at their destination = 14hours + 3hours 30mins.
= 17hours 30minutes. Convert to local time
17hours 30minutes = 12hours
= 5:30 pm in the evening
They have succeeded in spending 3hours 30minutes on the road. The final answer = 5:30pm.
write a verbal phrase to describe f > -4
I would say it as "the letter F is greater than negative four."
What additional information will allow you to prove the triangles congruent by the HL Theorem?A. A = EB. bce= 90C. ac = dcD. ac=bd
Answer:
C) AC=DC
Step-by-step explanation:
In the figure of question attached below:
In Δ ACB and Δ DCE, AB and DE are hypotenuse respectively.
According to HL theorem:
"If hypotenuse and one leg of right angle triangle is congruent to Hypotenuse and one leg of other right angle triangle then triangles are congruent"
According to above statement if AB and DE are hypotenuse of Δ ACB and Δ DCE respectively then either
AC = DC (leg)
BC = EC (leg)
In order to prove congruence of triangles using HL theorem, AC must be equal to DC.
So option C is correct.
Answer:
C ) AC=DC
Step-by-step explanation:
edge 2021
Can someone please write the equation of hyperbola with vertices (0, -5) and (0, 5) and co-vertices (-2, 0) and (2, 0)?
Thank you so much!
Answer:
y^2/25 -x^2/4 = 1
Step-by-step explanation:
The equation can be written as ...
y^2/a^2 -x^2/b^2 = 1
where the vertices are at (0, ±a) and the co-vertices are at (±b, 0). Filling in the given values (a=5, b=2) gives the equation shown above.
Susan has 5 more pennies than dimes, three times more nickels than dimes and 4 less quarters than pennies. If Susan has 7 dimes, what is the total value of her money?
Ann increased the quantities of all the ingredients in a recipe by 60\%60%60, percent. She used 808080 grams (\text{g})(g)left parenthesis, start text, g, end text, right parenthesis of cheese. How much cheese did the recipe require?
Answer:
50 grams
Step-by-step explanation:
Let the amount of cheese required by the recipe be "x"
Ann increased 60% from original amount and then used up 80 grams. Thus:
Original, increased by 60%, became 80
This translated to algebraic equation would be:
x + 0.6x = 80
Note: 60% = 60/100 = 0.6
So we can solve the above equation for "x" and get our answer. Shown below:
[tex]x + 0.6x = 80\\1.6x=80\\x=\frac{80}{1.6}\\x=50[/tex]
Hence,
the recipe required 50 grams of cheese
Find the m∠p.
pls and thanks <3
Answer:
36°
Step-by-step explanation:
Like your other question, the angles of the triangle must add up to 180. The tangent line is perpendicular to the center, so the angle must be 90°.
90° + 54° + 36° = 180°
State if the triangles in each pair are similar. If so, State how you know they are similar and complete the similarity statement.
Answer:
Step-by-step explanation:
Looking at both triangles, angle P in triangle PQR = 38 degrees. Angle N in triangle LMN = 38 degrees. Both angles are equal.
Side PQ in triangle PQR = 16
Side MN in triangle LMN = 8
Therefore,
PQ/MN = 16/8 = 2
Side PR in triangle PQR = 14
Side LN in triangle LMN = 7
Therefore,
PR/LN = 14/7 = 2
Therefore, triangle PQR is similar to
triangle LMN because
1) the length of PQ is proportional to the length of MN.
2) the length of PR is proportional to the length of LN
3) angle P = angle N
4) Therefore, QR is also proportional to ML
Therefore,
PQ/MN = PR/LN = QR/ML = 2
21. What is the exact volume of a sphere whose diameter is 14 cm? Show your work.
Answer:
The exact volume of a sphere is [tex]V=1437cm^3[/tex]
Step-by-step explanation:
Given that the diameter of a sphere is 14cm.
That is d=14
First find the radius of the sphere with diameter
[tex]r=\frac{d}{2}[/tex]
[tex]r=\frac{14}{2}[/tex]
Therefore r=7cm
Now to find the volume of the sphere:
[tex]V=\frac{4}{3}\pi r^3cm^3[/tex]
[tex]V=\frac{4}{3}\frac{22}{7}(7)^3[/tex] (here[tex]\pi=\frac{22}{7}[/tex] and r=7)
[tex]V=\frac{4}{3}(22)(7)^2[/tex]
[tex]V=\frac{4}{3}(22)(49)[/tex]
[tex]V=\frac{4}{3}(1078)[/tex]
[tex]V=\frac{4312}{3}[/tex]
[tex]V=1437.33cm^3[/tex]
Therefore the volume of the given sphere is [tex]V=1437.33cm^3[/tex]
The exact volume of a sphere is [tex]V=1437cm^3[/tex]
A vegetable garden and its surrounding that are shaped like a square that together are 11 feet wide. The path is 2 feet wide. Find the total area of the vegetable garden and path.
Area of path and garden = 11 x 11 = 121 square feet.
Area of garden only = 7 x 7 = 49 square feet.
Area of just the path = 121 - 49 = 72 square feet.
Let A be a set with a partial order R. For each a∈A, let Sa= {x∈A: xRa}. Let F={Sa: a∈A}. Then F is a subset of P(A) and thus may be partially ordered by ⊆, inclusion.
a) Show that if aRb, then Sa ⊆ Sb.
b) Show that if Sa ⊆ Sa, then aRb.
c) Show that if B⊆A, and x is the least upper bound for B, then Sx is the least upper bound for {Sb:b∈B}
Answer:
See proofs below
Step-by-step explanation:
a) Suppose that aRb. Let y∈Sa , then y∈A and yRa. We have that yRa and aRb. Since R is a partial order, R is a transitive relation, therefore yRa and aRb imply that yRb. Now, y∈A and yRb, thus y∈Sb. This reasoning applies for all y∈Sa that is, for all y∈Sa, y∈Sb, threrefore Sa⊆Sb.
b) Suppose that Sa⊆Sb. Since R is a partial order, R is a reflexive relation then aRa. Thus, a∈Sa. The inclusion Sa⊆Sb implies that a∈Sb, then aRb.
c) Denote this set by S={Sb:b∈B}. We will prove that supS=Sx with x=supB.
First, Sx is an upper bound of S: let Sb∈S. Then b∈B and since x=supB, x is an upper bound of B, then bRx. Then b∈Sx. Now, for all y∈Sb, yRb and bRx, then by transitivity yRx, thus y∈Sx. Therefore Sb⊆Sx for all Sb∈S, which means that Sx is an upper bound of S (remember that the order between sets is inclusion).
Now, let's prove that Sx is the least upper bound of S. Let Sc⊆A be another upper bound of S (in the set F). We will prove that Sx⊆T.
Because Sc is an upper bound, Sb⊆Sc for all b∈B. Thus, if y∈Sb for some b, then y∈Sc. That is, if yRb then yRc. In particular, bRb then bRc for all b∈B. Thus c is a upper bound of B. Byt x=supB, then xRc. Now, for all z∈Sx, zRx and xRc, which again, by transitivity, implies that z∈Sc. Therefore Sx⊆Sc and Sx=sup S.
In a partial order set, if aRb, then Sa ⊆ Sb. If Sa ⊆ Sb, then aRb. If B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}.
Explanation:a) To show that if aRb, then Sa ⊆ Sb, we need to prove that if x ∈ Sa, then x ∈ Sb. Since x ∈ Sa, that means xRa holds. And since aRb, we can conclude that xRb holds as well. Therefore, x ∈ Sb, which implies that Sa ⊆ Sb.
b) To show that if Sa ⊆ Sb, then aRb, we need to prove that if aRb does not hold, then Sa ⊆ Sb does not hold. If aRb does not hold, it means that b is not in Sa. However, if Sa ⊆ Sb, it implies that every element in Sa is also in Sb. Hence, we arrive at a contradiction, which proves that if Sa ⊆ Sb, then aRb.
c) To show that if B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}, we need to prove that Sx is an upper bound for {Sb : b ∈ B} and that it is the least upper bound. Since x is the least upper bound for B, this means that every element of B is contained in Sx. Therefore, Sx is an upper bound for {Sb : b ∈ B}. Additionally, if there exists an upper bound U for {Sb : b ∈ B}, then every element of {Sb : b ∈ B} must be contained in U. Since Sb is a subset of Sa for every b ∈ B, it follows that every element of Sa is contained in U. Therefore, Sa ⊆ U for every a ∈ A. In particular, Sx ⊆ U, which proves that Sx is the least upper bound for {Sb : b ∈ B}.
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Flip a coin 5 times. What is the probability that heads never occurs twice in a row?
Answer:
[tex]\frac{15}{32}[/tex]
Step-by-step explanation:
Given that a coin is flipped 5 times. Let us assume it is a fair coin with probability for head or tail equally likely and hence 0.50
Sample space would have [tex]2^5 = 32[/tex] possibilities
For two heads never occurring in a row favourable outcomes are
HTTTT,HTTHT,HTTTH, HTHTH, HTHTT, THTHT, THTTT, THTTH, TTHTH, TTHTT, TTTHT, TTTTH, TTTTT, TTTTH
Hence probability =
Favorable outcomes/Total outcomes=
[tex]\frac{15}{32}[/tex]
Here are the records of two different sequences (A,B ) of a coin tossed eight times. A: T H H H H H H H B: H T T H T H H T If you know for sure that the coin is fair, are these two sequences equally probable outcomes or, if they are not, which sequences is more probable than the other?"
Answer: Sequence B is more probable than A.
Step-by-step explanation:
This two sequences are not equally probable. Sequence B is more probable than A due to the equal chances of getting head (H) and a tail (T). The probability of getting a head is equal to the probability of getting a tail which is 4/8 i.e 0.5
The sequence A is less probable because the head(H) occur more than tail (T). The probability of head occurring is almost a sure event i.e 1 which is not feasible.
Three pounds of dried cherries cost $15.90, 5 pounds of dried cherries cost $26.50, and 9 pounds of dried cherries cost $47.70. Which equation gives the total cost y of x pounds of dried cherries?
Final answer:
The equation that gives the total cost of x pounds of dried cherries is y = (10.60/2)x.
Explanation:
Let's create a table to represent the given information:
Pounds of Dried Cherries (x)Total Cost (y)315.90526.50947.70
To find an equation that gives the total cost of x pounds of dried cherries, we need to find a pattern in the data. From the table, we can see that as the pounds of dried cherries increase, the total cost also increases. This suggests a linear relationship between pounds and cost.
Now, let's analyze the changes in cost for each additional pound of dried cherries:
From 3 to 5 pounds: The cost increased by $26.50 - $15.90 = $10.60.From 5 to 9 pounds: The cost increased by $47.70 - $26.50 = $21.20.Based on these changes, the cost increased by $10.60 for every 2 additional pounds of dried cherries. Therefore, the equation that gives the total cost y of x pounds of dried cherries is:
y = (10.60/2)x
Jasmine weigh 150ib he is loading a freight elevator with identical 72-pound boxes. The elevator can carry no more than 2000ib. If Jasmine rides with the boxes,how many boxes can be loaded on the elevator?
Answer:
Jasmine can load maximum of 25 boxes with herself on the elevator.
Step-by-step explanation:
Given:
Weight of Jasmine = 150 lb
Weight of each boxes = 72 lb
Load elevator can carry = 2000 lb
we need to find the number of boxes that can be loaded
Let number of boxes be 'x'
Now we know that Maximum load the elevator can carry is 2000 lb.
So We can say Weight of jasmine plus Number of boxes multiplied by Weight of each boxes should be less than or equal to Load elevator can carry.
Framing in equation form we get;
[tex]150+72x\leq 2000[/tex]
Solving the equation we get:
We will first Subtract 150 on both side;
[tex]150+72x-150\leq 2000-150\\\\72x\leq 1850[/tex]
Now Dividing both side by 72 by using Division property we get;
[tex]\frac{72x}{72}\leq \frac{1850}{72}\\\\x\leq 25.69[/tex]
Hence Jasmine can load maximum of 25 boxes with herself on the elevator.
A chain letter works as follows: One person sends a copy of the letter to five friends, each of whom sends a copy to five friends, each of whom sends a copy to five friends, and so forth. How many people will have received copies of the let- ter after the twentieth repetition of this process, assuming no person receives more than one copy?
Answer:
The number of people that received copies of the letter at the twentieth stage is 9.537 × 10¹³ .
Step-by-step explanation:
Using the discrete model,
a_k = r a_(k-1) for all integers k ≥ 1 and a₀ = a
then,
aₙ = a rⁿ for all integers n ≥ 0
Let a_k be equal to the number of people who receive a copy of the chain letter at a stage k.
Initially, one person has the chain letter (which the person will send to five other people at stage 1). Thus,
a = a₀ = 1
The people who received he chain letter at stage (k - 1), will send a letter to five people at stage k and thus per person at stage (k - 1), five people will receive the letter. Therefore,
a_k = 5 a_(k - 1)
Thus,
aₙ = a rⁿ = 1 · 5ⁿ = 5ⁿ
The number of people that received copies of the letter at the twentieth stage is
a₂₀ = (5)²⁰ = 9.537 × 10¹³ copies
On July 31, Oscar checked out of the Sandy Beach hotel after spending four nights. The cost of the room was $76.90 per night. He wrote a check to pay for his four-night stay. What was the total amount of his check?
Answer:
$307.60
Step-by-step explanation:
multiple $76.90 by the 4 nights he stayed. $76.90×4
Answer:
76.00
Step-by-step explanation:
Nancy performs a full backup of her server every Sunday at 1 A.M. and differential backups on Mondays through Fridays at 1 A.M. Her server fails at 9 A.M. Wednesday. How many backups does Nancy need to restore?
Answer:
4
Step-by-step explanation:
To restore her server after a failure on Wednesday morning, Nancy would need to restore the full backup from Sunday, and then restore the differential backup from Tuesday.
Explanation:In Nancy's case, she would need two backups to fully restore her server. These would be the full backup from Sunday and the differential backup from Tuesday. Here's why:
A full backup involves copying all of the data in a system. It's the most comprehensive type of backup but also requires the most storage space and time. A differential backup, on the other hand, only backs up the data that has changed or been added since the last full backup.
Because Nancy performs full backups every Sunday, the full backup will have all the data up until Sunday at 1 A.M. The differential backup from Tuesday will contain all the changes that occurred on Monday and Tuesday until 1 A.M.
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If you have a lowest score of 21 and a range of 47, your highest score will be:________
Answer: 68
Step-by-step explanation:
range=47 lowest score = 21 let highest score =x
Range=highest score - lowest score
47 = x - 21
x = 47 + 21
x = 68
Therefore the highest score is 68
The highest score is 68.
Range = Highest Score - Lowest Score
In this case,
the lowest score is 21 and
the range is 47.
So, we can rearrange the formula to solve for the highest score:
Highest Score = Range + Lowest Score
Substituting in the given values:
Highest Score = 47 + 21
Thus, the highest score will be 68.
The scale model of a rectangular garden is 1.5 ft by 4 ft. The scale model is enlarged by a scale factor of 7 to create the actual garden. What is the area of the actual garden
Answer:
The Area of the actual garden is 294 square feet.
Step-by-step explanation:
The scale model of a rectangular garden is 1.5 ft by 4 ft.
Length of scale model=1.5 ft
Breath of scale model=4 ft
The scale model is enlarged by a scale factor of 7 to create the actual garden.
It means that the dimension of the garden are multiplied with the scale factor to find the actual dimension.
Hence,
Length of actual garden=[tex]1.5\times 7= 10.5\ ft[/tex]
Breath of actual garden=[tex]4\times 7 = 28\ ft[/tex]
Now Area of garden can be calculated by multiplying length and breadth.
Framing the equation we get;
Area of actual garden=[tex]10.5\ ft \times 28\ ft = 294\ ft^2[/tex]
Hence, area of the actual garden is 294 square feet.
Answer:294 took test
What is the measure of a°?
Answer:
The correct answer is C. 129.
Step-by-step explanation:
Let's recall that the Inscribed Quadrilateral Theorem states that a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary.
In the case of the inscribed quadrilateral ABCD in the graph attached, we have that:
m∠C= 51°, therefore its supplementary angle, ∠A, should be the difference between 180° and m∠C.
m∠C= 180° - m∠A
Replacing with the real values:
51 = 180 - m∠A
m∠A = 129°
The correct answer is C. 129.
Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.
To calculate the interest that Rich will accrue during the 4.5-year nonpayment period on his federal unsubsidized student loan, we can use the formula for simple interest:
Interest = Principal (loan amount) x Rate x Time
Where:
Principal (loan amount) = $7,900
Rate = 4.29% (0.0429 as a decimal)
Time = 4.5 years
Now, plug these values into the formula:
Interest = $7,900 x 0.0429 x 4.5
Interest = $7,900 x 0.19205
Interest ≈ $1,518.45
So, Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.
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Rich has been approved for a federal unsubsidized student loan and wants to know the interest that will accrue during his 4.5 years as a freshman in college. Calculating the interest using the formula, the total accrued interest is $1,146.75.
Explanation:Rich is attending a 4-year college and has been approved for a 10-year federal unsubsidized student loan of $7,900 at an interest rate of 4.29%. During his 4 years as a freshman, he has the option to start repaying the loan after 4.5 years. However, interest will continue to accrue at a rate of 4.29% during this non-payment period.
To calculate the interest that will accrue during the 4.5 years, we can use the formula:
Interest Accrued = Principal x Interest Rate x Time
Substituting the values, we get:
Interest Accrued = $7,900 x 0.0429 x 4.5 = $1,146.75
Therefore, the interest that will accrue during the non-payment time is $1,146.75.
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