In this question, you're solving for d.
Solve for d:
5(-6 - 3d) = 3(8+7d)
Use the distributive property:
-30 - 15d = 3(8+7d)
-30 - 15d = 24 + 21d
Add 30 to both sides:
-15d = 54 + 21d
Subtract 21d from both sides
-36d = 54
Divide both sides by -36
d = -3/2
Answer:
d = -3/2 or -1.5
Answer:
d = -1.5
Step-by-step explanation:
5 (- 6 - 3d) = 3 (8 + 7d)
- 30 - 15d = 24 + 21d
- 15d - 21d = 24 + 30
- 36d = 54
- d = 54/36
- d = 1.5
d = -1.5
if a negative number has to be added to another negative number, does it stay negative?
Yes because the number say on one side
yes because the numbers stay on one side of the number line
write a verbal phrase to describe f > -4
I would say it as "the letter F is greater than negative four."
Working alone at its constant rate, pump X pumped out \small \frac{1}{3} of the water in a pool in 4 hours. Then pump Y started working and the two pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 6 hours. How many hours would it have taken pump Y, working alone at its constant rate, to pump out all of the water that was pumped out of the pool?
Answer:
P(y) take 36 h to do the job alone
Step-by-step explanation:
P(x) quantity of water pump by Pump X and
P(y) quantity of water pump by Pump Y
Then if P(x) pumped 1/3 of the water in a pool in 4 hours
Then in 1 hour P(x) will pump
1/3 ⇒ 4 h
? x ⇒ 1 h x = 1/3/4 ⇒ x = 1/12
Then in 1 hour P(x) will pump 1/12 of the water of the pool
Now both pumps P(x) and P(y) finished 2/3 of the water in the pool (left after the P(x) worked alone ) in 6 hours. Then
P(x) + P(y) in 6 h ⇒ 2/3
in 1 h ⇒ x ?? x = (2/3)/6 x = 2/18 x = 1/9
Then P(x) + P(y) pump 1/9 of the water of the pool in 1 h. We find out how long will take the two pumps to empty the pool
water in a pool is 9/9 ( the unit) then
1 h ⇒ 1/9
x ?? ⇒ 9/9 x = ( 9/9)/( 1/9) ⇒ x = 9 h
The two pumps would take 9 hours working together from the beggining
And in 1 hour of work, both pump 1/9 of the water, and P(x) pump 1/12 in 1 hour
Then in 1 hour P(y)
P(y) = 1/9 - 1/12 ⇒ P(y) = 3/108 P(y) = 1/36
And to pump all the water (36/36) P(y) will take
1 h 1/36
x ?? 36/36 x = (36/36)/1/36
x = 36 h
P(y) take 36 h to do the job alone
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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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
An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air. This similar to the current problem as you have to consider the 25 mph tailwind and headwind. Plane on outbound trip of 4 hours with 25 mph tailwind and return trip of 5 hours with 25 mph headwind Let r = the rate or speed of the airplane in still air. Let d = the distance
a. Write a system of equations for the airplane. One equation will be for the outbound trip with tailwind of 25 mph. The second equation will be for the return trip with headwind of 25 mph.
b. Solve the system of equations for the speed of the airplane in still air.
Answer:
r = 225 Mil/h speed of the airplane in still air
Step-by-step explanation:
Then:
d is traveled distance and r the speed of the airplane in still air
so the first equation is for a 4 hours trip
as d = v*t
d = 4 * ( r + 25) (1) the speed of tail wind (25 mil/h)
Second equation the trip back in 5 hours
d = 5 * ( r - 25 ) (2)
So we got a system of two equation and two unknown variables d and
r
We solve it by subtitution
from equation (1) d = 4r + 100
plugging in equation 2
4r + 100 = 5r - 125 ⇒ -r = -225 ⇒ r = 225 Mil/h
And distance is :
d = 4*r + 100 ⇒ d = 4 * ( 225) + 100
d = 900 + 100
d = 1000 miles
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
A boat sails 20 miles wast of the port and then 15 miles south to an island how far is the boat from the port if you measure thr distance in a straight line ?
Answer:
25 miles
Step-by-step explanation:
Given: A boat sail 20 miles west of the port and then 15 miles south to an island.
Picture attached.
The distance from port to island could be measured in a straight line. It will form a hypotenous.
∴ we can use Pythogorean theorem to find the distance.
[tex]h^{2} = a^{2} +b^{2}[/tex]
Where, "a" is adjacent= 20 miles and "b" is opposite= 15 miles.
[tex]h^{2} = 20^{2} +15^{2}[/tex]
⇒ [tex]h^{2} = 400+225= 625[/tex]
⇒[tex]h^{2} = 625[/tex]
⇒[tex]h= \sqrt{625}= \sqrt{25^{2} }[/tex]
We know [tex]\sqrt{x^{2} } = x[/tex].
∴[tex]h= 25\ miles[/tex]
∴ Distance of Port from the Island is 25 miles.
Final answer:
Using the Pythagorean theorem, the straight-line distance from the port to the boat, after traveling 20 miles west and 15 miles south, is found to be 25 miles.
Explanation:
The problem presented involves calculating the straight-line distance, or 'hypotenuse', of a right-angled triangle formed by the boat's journey from the port, 20 miles west and then 15 miles south. We will use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c² = a² + b².
Let's apply this formula to find the distance:
The distance travelled west (a) is 20 miles.
The distance travelled south (b) is 15 miles.
We can calculate the straight-line distance using the formula:
c² = 20² + 15²
c² = 400 + 225
c² = 625
c = √625
c = 25 miles
Therefore, the boat is 25 miles away from the port if measured in a straight line.
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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Which association best describes the data in the table?
x y
3 2
3 3
4 4
5 5
5 6
6 7
8 8
A. no association
B. negative association
C. positive association
Answer:
'x' and 'y' have a positive association between them.
Step-by-step explanation:
We can see in the given data that as 'x' remains constant or increases by 1 unit, or two units in it's two consecutive values, in each of the cases 'y' increases by 1 unit.
Hence, 'x' and 'y' have a positive association between them.
Answer:
C. positive associationStep-by-step explanation:
Positive and negative association describe a relation between variables about a scatter plot.
A positive association happens when one variable increases while the other one also increases.
A negative association happens when one variable decreases while the other variable increases.
It's important to know that the variable that always increases is the independent variable, it increases no matter what.
In this case, we could say that we have a positive association, because while x increases, y also increases.
You could notice that there's some repetitive number. That's normal because a scatter plot doesn't describe a perfect linear relation at the beginning, actually, it's a bit messy, however, from such data we construct a linear relationship which is called "linear regression".
Therefore, the right answer is C.
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]
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.
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
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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Which inequality does the given graph represent?
A) y > 3x + 4
B) y > 1/3x − 4
C) y > 1/3x + 4
D) y ≥ 1/3x + 4
Answer:
The answer to your question is letter C
Step-by-step explanation:
Process
1.- Find two points of the dotted line
A (0, 4)
B (3, 5)
2.- Find the slope of the line
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Substitution
[tex]m = \frac{5 - 4}{3 - 0}[/tex]
[tex]m = \frac{1}{3}[/tex]
3.- Write the equation of the line
y - y1 = m(x - x1)
y - 4 = 1/3(x - 0)
y - 4 = 1/3x
y = 1/3x + 4
4.- Write the inequality
We are interested on the upper area so
y > 1/3x + 4
Answer: C) y > 1/3x + 4
Step-by-step explanation: The line is dashed hence >. The slope is 1/3 and the y- intercept is 4. This makes the inequality y > 1/3x + 4.
Hope this helps! :)
Find the perimeter of an equilateral triangle of which one side consists of point P(1, 5) and Q(3, 10). Reminder, perimeter means add all three sides.
Answer:
3√29 ≈ 16.155
Step-by-step explanation:
The distance formula can be used to find the length of the given side.
d = √((x2-x1)^2 +(y2-y1)^2)
PQ = √((3-1)^2 +(10-5)^2) = √(4 +25) = √29
The equilateral triangle has three same-length sides (the literal meaning of "equilateral"), so the perimeter is ...
Perimeter = 3×PQ = 3√29
£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.
A two week old puppy weighs 11 ounces. Two weeks later, it weighs 15 ounces. Right in equation to represent the weight y of the puppy X weeks after birth.
Answer:
y = 2x +7
Step-by-step explanation:
We are given two points on the growth curve: (weeks, ounces) = (2, 11) or (4, 15).
These can be used to write the equation of a line using the 2-point form:
y = (y2 -y1)/(x2 -1x)(x -x1) +y1
y = (15 -11)/(4 -2)(x -2) +11
y = 4/2(x -2) +11
y = 2x +7 . . . . . y = weight in ounces x weeks after birth
_____
Comment on the problem
There are an infinite number of equations that can be written to go through the two given points. A linear equation is only one of them.
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°
The ratio that relates how much debt a company has in proportion to its equity is?
Answer: The debt-to-equity ratio
Step-by-step explanation:
The debt-to-equity ratio is a company's debt as a percentage of its total market value. If your company has a debt-to-equity ratio of 50% or 70%, it means that you have $0.5 or $0.7 of debt for every $1 of equity
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.
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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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:
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.
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
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.
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
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.
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.
Lucia flips a coin three times. What is the probability she gets (Head, tail, Head) in that order?
Answer: [tex]\dfrac{1}{8}[/tex]
Step-by-step explanation:
The total outcomes of tossing a coin = 2
The total number of possible outcomes of flipping coin three times =2 x 2 x 2 = 8
Favorable outcome= (Head, tail, Head) in order
i.e. Number of Favorable outcomes = 1
We know that , Probability = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Therefore , The required probability [tex]=\dfrac{1}{8}[/tex]
Hence , the probability she gets (Head, tail, Head) in that order[tex]=\dfrac{1}{8}[/tex]